%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU252+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:58:43 AM UTC 2026
% Result : Theorem 165.16s 165.46s
% Output : Proof 165.31s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(antisymmetry_r2_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
=> ~ proper_subset(B,A) ),
file('theBenchmark.p',antisymmetry_r2_xboole_0) ).
fof(cc1_funct_1,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('theBenchmark.p',cc1_funct_1) ).
fof(cc1_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc1_ordinal1) ).
fof(cc1_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('theBenchmark.p',cc1_relat_1) ).
fof(cc2_funct_1,axiom,
! [A] :
( ( function(A)
& empty(A)
& relation(A) )
=> ( one_to_one(A)
& function(A)
& relation(A) ) ),
file('theBenchmark.p',cc2_funct_1) ).
fof(cc2_ordinal1,axiom,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
=> ordinal(A) ),
file('theBenchmark.p',cc2_ordinal1) ).
fof(cc3_ordinal1,axiom,
! [A] :
( empty(A)
=> ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc3_ordinal1) ).
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(connectedness_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(B,A)
| ordinal_subset(A,B) ) ),
file('theBenchmark.p',connectedness_r1_ordinal1) ).
fof(d10_relat_1,axiom,
! [A,B] :
( relation(B)
=> ( B = identity_relation(A)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> ( C = D
& in(C,A) ) ) ) ),
file('theBenchmark.p',d10_relat_1) ).
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
fof(d11_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( relation(C)
=> ( C = relation_dom_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),A)
& in(D,B) ) ) ) ) ),
file('theBenchmark.p',d11_relat_1) ).
fof(d12_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( C = relation_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( D = apply(A,E)
& in(E,B)
& in(E,relation_dom(A)) ) ) ) ),
file('theBenchmark.p',d12_funct_1) ).
fof(d12_relat_1,axiom,
! [A,B] :
( relation(B)
=> ! [C] :
( relation(C)
=> ( C = relation_rng_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),B)
& in(E,A) ) ) ) ) ),
file('theBenchmark.p',d12_relat_1) ).
fof(d12_relat_2,axiom,
! [A] :
( relation(A)
=> ( antisymmetric(A)
<=> is_antisymmetric_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d12_relat_2) ).
fof(d13_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(apply(A,D),B)
& in(D,relation_dom(A)) ) ) ) ),
file('theBenchmark.p',d13_funct_1) ).
fof(d13_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = relation_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) ) ) ) ),
file('theBenchmark.p',d13_relat_1) ).
fof(d14_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) ) ) ) ),
file('theBenchmark.p',d14_relat_1) ).
fof(d14_relat_2,axiom,
! [A] :
( relation(A)
=> ( connected(A)
<=> is_connected_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d14_relat_2) ).
fof(d16_relat_2,axiom,
! [A] :
( relation(A)
=> ( transitive(A)
<=> is_transitive_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d16_relat_2) ).
fof(d1_enumset1,axiom,
! [A,B,C,D] :
( D = unordered_triple(A,B,C)
<=> ! [E] :
( in(E,D)
<=> ~ ( E != C
& E != B
& E != A ) ) ),
file('theBenchmark.p',d1_enumset1) ).
fof(d1_ordinal1,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('theBenchmark.p',d1_ordinal1) ).
fof(d1_relat_1,axiom,
! [A] :
( relation(A)
<=> ! [B] :
~ ( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) ) ),
file('theBenchmark.p',d1_relat_1) ).
fof(d1_relat_2,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_reflexive_in(A,B)
<=> ! [C] :
( in(C,B)
=> in(ordered_pair(C,C),A) ) ) ),
file('theBenchmark.p',d1_relat_2) ).
fof(d1_setfam_1,axiom,
! [A,B] :
( ( A = empty_set
=> ( B = set_meet(A)
<=> B = empty_set ) )
& ( A != empty_set
=> ( B = set_meet(A)
<=> ! [C] :
( in(C,B)
<=> ! [D] :
( in(D,A)
=> in(C,D) ) ) ) ) ),
file('theBenchmark.p',d1_setfam_1) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d1_wellord1,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = fiber(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(ordered_pair(D,B),A)
& D != B ) ) ) ),
file('theBenchmark.p',d1_wellord1) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
fof(d1_zfmisc_1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('theBenchmark.p',d1_zfmisc_1) ).
fof(d2_ordinal1,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('theBenchmark.p',d2_ordinal1) ).
fof(d2_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( A = B
<=> ! [C,D] :
( in(ordered_pair(C,D),A)
<=> in(ordered_pair(C,D),B) ) ) ) ),
file('theBenchmark.p',d2_relat_1) ).
fof(d2_subset_1,axiom,
! [A,B] :
( ( empty(A)
=> ( element(B,A)
<=> empty(B) ) )
& ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) ) ),
file('theBenchmark.p',d2_subset_1) ).
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('theBenchmark.p',d2_tarski) ).
fof(d2_wellord1,axiom,
! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> ! [B] :
~ ( ! [C] :
~ ( disjoint(fiber(A,C),B)
& in(C,B) )
& B != empty_set
& subset(B,relation_field(A)) ) ) ),
file('theBenchmark.p',d2_wellord1) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('theBenchmark.p',d2_xboole_0) ).
fof(d2_zfmisc_1,axiom,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) ) ) ),
file('theBenchmark.p',d2_zfmisc_1) ).
fof(d3_ordinal1,axiom,
! [A] :
( epsilon_connected(A)
<=> ! [B,C] :
~ ( ~ in(C,B)
& B != C
& ~ in(B,C)
& in(C,A)
& in(B,A) ) ),
file('theBenchmark.p',d3_ordinal1) ).
fof(d3_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(A,B)
<=> ! [C,D] :
( in(ordered_pair(C,D),A)
=> in(ordered_pair(C,D),B) ) ) ) ),
file('theBenchmark.p',d3_relat_1) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(d3_wellord1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_well_founded_in(A,B)
<=> ! [C] :
~ ( ! [D] :
~ ( disjoint(fiber(A,D),C)
& in(D,C) )
& C != empty_set
& subset(C,B) ) ) ),
file('theBenchmark.p',d3_wellord1) ).
fof(d3_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d3_xboole_0) ).
fof(d4_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( ( ~ in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> C = empty_set ) )
& ( in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) ) ) ) ),
file('theBenchmark.p',d4_funct_1) ).
fof(d4_ordinal1,axiom,
! [A] :
( ordinal(A)
<=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',d4_ordinal1) ).
fof(d4_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('theBenchmark.p',d4_relat_1) ).
fof(d4_relat_2,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_antisymmetric_in(A,B)
<=> ! [C,D] :
( ( in(ordered_pair(D,C),A)
& in(ordered_pair(C,D),A)
& in(D,B)
& in(C,B) )
=> C = D ) ) ),
file('theBenchmark.p',d4_relat_2) ).
fof(d4_subset_1,axiom,
! [A] : cast_to_subset(A) = A,
file('theBenchmark.p',d4_subset_1) ).
fof(d4_tarski,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(D,A)
& in(C,D) ) ) ),
file('theBenchmark.p',d4_tarski) ).
fof(d4_wellord1,axiom,
! [A] :
( relation(A)
=> ( well_ordering(A)
<=> ( well_founded_relation(A)
& connected(A)
& antisymmetric(A)
& transitive(A)
& reflexive(A) ) ) ),
file('theBenchmark.p',d4_wellord1) ).
fof(d4_xboole_0,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d4_xboole_0) ).
fof(d5_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) ) ) ),
file('theBenchmark.p',d5_funct_1) ).
fof(d5_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('theBenchmark.p',d5_relat_1) ).
fof(d5_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,B) = set_difference(A,B) ),
file('theBenchmark.p',d5_subset_1) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(d5_wellord1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( well_orders(A,B)
<=> ( is_well_founded_in(A,B)
& is_connected_in(A,B)
& is_antisymmetric_in(A,B)
& is_transitive_in(A,B)
& is_reflexive_in(A,B) ) ) ),
file('theBenchmark.p',d5_wellord1) ).
fof(d6_ordinal1,axiom,
! [A] :
( being_limit_ordinal(A)
<=> A = union(A) ),
file('theBenchmark.p',d6_ordinal1) ).
fof(d6_relat_1,axiom,
! [A] :
( relation(A)
=> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
file('theBenchmark.p',d6_relat_1) ).
fof(d6_relat_2,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_connected_in(A,B)
<=> ! [C,D] :
~ ( ~ in(ordered_pair(D,C),A)
& ~ in(ordered_pair(C,D),A)
& C != D
& in(D,B)
& in(C,B) ) ) ),
file('theBenchmark.p',d6_relat_2) ).
fof(d6_wellord1,axiom,
! [A] :
( relation(A)
=> ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B)) ),
file('theBenchmark.p',d6_wellord1) ).
fof(d7_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( B = relation_inverse(A)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> in(ordered_pair(D,C),A) ) ) ) ),
file('theBenchmark.p',d7_relat_1) ).
fof(d7_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('theBenchmark.p',d7_xboole_0) ).
fof(d8_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
<=> ! [B,C] :
( ( apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
=> B = C ) ) ),
file('theBenchmark.p',d8_funct_1) ).
fof(d8_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( relation(C)
=> ( C = relation_composition(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) ) ) ) ) ) ),
file('theBenchmark.p',d8_relat_1) ).
fof(d8_relat_2,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_transitive_in(A,B)
<=> ! [C,D,E] :
( ( in(ordered_pair(D,E),A)
& in(ordered_pair(C,D),A)
& in(E,B)
& in(D,B)
& in(C,B) )
=> in(ordered_pair(C,E),A) ) ) ),
file('theBenchmark.p',d8_relat_2) ).
fof(d8_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ! [C] :
( element(C,powerset(powerset(A)))
=> ( C = complements_of_subsets(A,B)
<=> ! [D] :
( element(D,powerset(A))
=> ( in(D,C)
<=> in(subset_complement(A,D),B) ) ) ) ) ),
file('theBenchmark.p',d8_setfam_1) ).
fof(d8_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('theBenchmark.p',d8_xboole_0) ).
fof(d9_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> function_inverse(A) = relation_inverse(A) ) ),
file('theBenchmark.p',d9_funct_1) ).
fof(d9_relat_2,axiom,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> is_reflexive_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d9_relat_2) ).
fof(dt_k10_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k10_relat_1) ).
fof(dt_k1_enumset1,axiom,
$true,
file('theBenchmark.p',dt_k1_enumset1) ).
fof(dt_k1_funct_1,axiom,
$true,
file('theBenchmark.p',dt_k1_funct_1) ).
fof(dt_k1_ordinal1,axiom,
$true,
file('theBenchmark.p',dt_k1_ordinal1) ).
fof(dt_k1_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k1_relat_1) ).
fof(dt_k1_setfam_1,axiom,
$true,
file('theBenchmark.p',dt_k1_setfam_1) ).
fof(dt_k1_tarski,axiom,
$true,
file('theBenchmark.p',dt_k1_tarski) ).
fof(dt_k1_wellord1,axiom,
$true,
file('theBenchmark.p',dt_k1_wellord1) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(dt_k2_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( function(function_inverse(A))
& relation(function_inverse(A)) ) ),
file('theBenchmark.p',dt_k2_funct_1) ).
fof(dt_k2_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k2_relat_1) ).
fof(dt_k2_subset_1,axiom,
! [A] : element(cast_to_subset(A),powerset(A)),
file('theBenchmark.p',dt_k2_subset_1) ).
fof(dt_k2_tarski,axiom,
$true,
file('theBenchmark.p',dt_k2_tarski) ).
fof(dt_k2_wellord1,axiom,
! [A,B] :
( relation(A)
=> relation(relation_restriction(A,B)) ),
file('theBenchmark.p',dt_k2_wellord1) ).
fof(dt_k2_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k2_xboole_0) ).
fof(dt_k2_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k2_zfmisc_1) ).
fof(dt_k3_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k3_relat_1) ).
fof(dt_k3_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> element(subset_complement(A,B),powerset(A)) ),
file('theBenchmark.p',dt_k3_subset_1) ).
fof(dt_k3_tarski,axiom,
$true,
file('theBenchmark.p',dt_k3_tarski) ).
fof(dt_k3_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k3_xboole_0) ).
fof(dt_k4_relat_1,axiom,
! [A] :
( relation(A)
=> relation(relation_inverse(A)) ),
file('theBenchmark.p',dt_k4_relat_1) ).
fof(dt_k4_tarski,axiom,
$true,
file('theBenchmark.p',dt_k4_tarski) ).
fof(dt_k4_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k4_xboole_0) ).
fof(dt_k5_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(relation_composition(A,B)) ),
file('theBenchmark.p',dt_k5_relat_1) ).
fof(dt_k5_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(union_of_subsets(A,B),powerset(A)) ),
file('theBenchmark.p',dt_k5_setfam_1) ).
fof(dt_k6_relat_1,axiom,
! [A] : relation(identity_relation(A)),
file('theBenchmark.p',dt_k6_relat_1) ).
fof(dt_k6_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(meet_of_subsets(A,B),powerset(A)) ),
file('theBenchmark.p',dt_k6_setfam_1) ).
fof(dt_k6_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> element(subset_difference(A,B,C),powerset(A)) ),
file('theBenchmark.p',dt_k6_subset_1) ).
fof(dt_k7_relat_1,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('theBenchmark.p',dt_k7_relat_1) ).
fof(dt_k7_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(complements_of_subsets(A,B),powerset(powerset(A))) ),
file('theBenchmark.p',dt_k7_setfam_1) ).
fof(dt_k8_relat_1,axiom,
! [A,B] :
( relation(B)
=> relation(relation_rng_restriction(A,B)) ),
file('theBenchmark.p',dt_k8_relat_1) ).
fof(dt_k9_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k9_relat_1) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc10_relat_1,axiom,
! [A,B] :
( ( relation(B)
& empty(A) )
=> ( relation(relation_composition(B,A))
& empty(relation_composition(B,A)) ) ),
file('theBenchmark.p',fc10_relat_1) ).
fof(fc11_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_inverse(A))
& empty(relation_inverse(A)) ) ),
file('theBenchmark.p',fc11_relat_1) ).
fof(fc12_relat_1,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc12_relat_1) ).
fof(fc13_relat_1,axiom,
! [A,B] :
( ( relation_empty_yielding(A)
& relation(A) )
=> ( relation_empty_yielding(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) ) ),
file('theBenchmark.p',fc13_relat_1) ).
fof(fc1_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B)
& function(A)
& relation(A) )
=> ( function(relation_composition(A,B))
& relation(relation_composition(A,B)) ) ),
file('theBenchmark.p',fc1_funct_1) ).
fof(fc1_ordinal1,axiom,
! [A] : ~ empty(succ(A)),
file('theBenchmark.p',fc1_ordinal1) ).
fof(fc1_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(set_intersection2(A,B)) ),
file('theBenchmark.p',fc1_relat_1) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc1_zfmisc_1,axiom,
! [A,B] : ~ empty(ordered_pair(A,B)),
file('theBenchmark.p',fc1_zfmisc_1) ).
fof(fc2_funct_1,axiom,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
file('theBenchmark.p',fc2_funct_1) ).
fof(fc2_ordinal1,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('theBenchmark.p',fc2_ordinal1) ).
fof(fc2_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(set_union2(A,B)) ),
file('theBenchmark.p',fc2_relat_1) ).
fof(fc2_subset_1,axiom,
! [A] : ~ empty(singleton(A)),
file('theBenchmark.p',fc2_subset_1) ).
fof(fc2_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(A,B)) ),
file('theBenchmark.p',fc2_xboole_0) ).
fof(fc3_funct_1,axiom,
! [A] :
( ( one_to_one(A)
& function(A)
& relation(A) )
=> ( function(relation_inverse(A))
& relation(relation_inverse(A)) ) ),
file('theBenchmark.p',fc3_funct_1) ).
fof(fc3_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) ) ),
file('theBenchmark.p',fc3_ordinal1) ).
fof(fc3_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(set_difference(A,B)) ),
file('theBenchmark.p',fc3_relat_1) ).
fof(fc3_subset_1,axiom,
! [A,B] : ~ empty(unordered_pair(A,B)),
file('theBenchmark.p',fc3_subset_1) ).
fof(fc3_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(B,A)) ),
file('theBenchmark.p',fc3_xboole_0) ).
fof(fc4_funct_1,axiom,
! [A,B] :
( ( function(A)
& relation(A) )
=> ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) ) ),
file('theBenchmark.p',fc4_funct_1) ).
fof(fc4_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( ordinal(union(A))
& epsilon_connected(union(A))
& epsilon_transitive(union(A)) ) ),
file('theBenchmark.p',fc4_ordinal1) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(fc4_subset_1,axiom,
! [A,B] :
( ( ~ empty(B)
& ~ empty(A) )
=> ~ empty(cartesian_product2(A,B)) ),
file('theBenchmark.p',fc4_subset_1) ).
fof(fc5_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( function(relation_rng_restriction(A,B))
& relation(relation_rng_restriction(A,B)) ) ),
file('theBenchmark.p',fc5_funct_1) ).
fof(fc5_relat_1,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_dom(A)) ),
file('theBenchmark.p',fc5_relat_1) ).
fof(fc6_relat_1,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_rng(A)) ),
file('theBenchmark.p',fc6_relat_1) ).
fof(fc7_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_dom(A))
& empty(relation_dom(A)) ) ),
file('theBenchmark.p',fc7_relat_1) ).
fof(fc8_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_rng(A))
& empty(relation_rng(A)) ) ),
file('theBenchmark.p',fc8_relat_1) ).
fof(fc9_relat_1,axiom,
! [A,B] :
( ( relation(B)
& empty(A) )
=> ( relation(relation_composition(A,B))
& empty(relation_composition(A,B)) ) ),
file('theBenchmark.p',fc9_relat_1) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('theBenchmark.p',idempotence_k3_xboole_0) ).
fof(involutiveness_k3_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,subset_complement(A,B)) = B ),
file('theBenchmark.p',involutiveness_k3_subset_1) ).
fof(involutiveness_k4_relat_1,axiom,
! [A] :
( relation(A)
=> relation_inverse(relation_inverse(A)) = A ),
file('theBenchmark.p',involutiveness_k4_relat_1) ).
fof(involutiveness_k7_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> complements_of_subsets(A,complements_of_subsets(A,B)) = B ),
file('theBenchmark.p',involutiveness_k7_setfam_1) ).
fof(irreflexivity_r2_xboole_0,axiom,
! [A,B] : ~ proper_subset(A,A),
file('theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(l1_wellord1,lemma,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> ! [B] :
( in(B,relation_field(A))
=> in(ordered_pair(B,B),A) ) ) ),
file('theBenchmark.p',l1_wellord1) ).
fof(l1_zfmisc_1,lemma,
! [A] : singleton(A) != empty_set,
file('theBenchmark.p',l1_zfmisc_1) ).
fof(l23_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('theBenchmark.p',l23_zfmisc_1) ).
fof(l25_zfmisc_1,lemma,
! [A,B] :
~ ( in(A,B)
& disjoint(singleton(A),B) ),
file('theBenchmark.p',l25_zfmisc_1) ).
fof(l28_zfmisc_1,lemma,
! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
file('theBenchmark.p',l28_zfmisc_1) ).
fof(l29_wellord1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B)) ),
file('theBenchmark.p',l29_wellord1) ).
fof(l2_wellord1,lemma,
! [A] :
( relation(A)
=> ( transitive(A)
<=> ! [B,C,D] :
( ( in(ordered_pair(C,D),A)
& in(ordered_pair(B,C),A) )
=> in(ordered_pair(B,D),A) ) ) ),
file('theBenchmark.p',l2_wellord1) ).
fof(l2_zfmisc_1,lemma,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('theBenchmark.p',l2_zfmisc_1) ).
fof(l32_xboole_1,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',l32_xboole_1) ).
fof(l3_subset_1,lemma,
! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( in(C,B)
=> in(C,A) ) ),
file('theBenchmark.p',l3_subset_1) ).
fof(l3_wellord1,lemma,
! [A] :
( relation(A)
=> ( antisymmetric(A)
<=> ! [B,C] :
( ( in(ordered_pair(C,B),A)
& in(ordered_pair(B,C),A) )
=> B = C ) ) ),
file('theBenchmark.p',l3_wellord1) ).
fof(l3_zfmisc_1,lemma,
! [A,B,C] :
( subset(A,B)
=> ( subset(A,set_difference(B,singleton(C)))
| in(C,A) ) ),
file('theBenchmark.p',l3_zfmisc_1) ).
fof(l4_wellord1,lemma,
! [A] :
( relation(A)
=> ( connected(A)
<=> ! [B,C] :
~ ( ~ in(ordered_pair(C,B),A)
& ~ in(ordered_pair(B,C),A)
& B != C
& in(C,relation_field(A))
& in(B,relation_field(A)) ) ) ),
file('theBenchmark.p',l4_wellord1) ).
fof(l4_zfmisc_1,lemma,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',l4_zfmisc_1) ).
fof(l50_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
file('theBenchmark.p',l50_zfmisc_1) ).
fof(l55_zfmisc_1,lemma,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('theBenchmark.p',l55_zfmisc_1) ).
fof(l71_subset_1,lemma,
! [A,B] :
( ! [C] :
( in(C,A)
=> in(C,B) )
=> element(A,powerset(B)) ),
file('theBenchmark.p',l71_subset_1) ).
fof(l82_funct_1,lemma,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
<=> ( in(B,A)
& in(B,relation_dom(C)) ) ) ),
file('theBenchmark.p',l82_funct_1) ).
fof(rc1_funct_1,axiom,
? [A] :
( function(A)
& relation(A) ),
file('theBenchmark.p',rc1_funct_1) ).
fof(rc1_ordinal1,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
file('theBenchmark.p',rc1_ordinal1) ).
fof(rc1_relat_1,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('theBenchmark.p',rc1_relat_1) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc1_subset_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_funct_1,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('theBenchmark.p',rc2_funct_1) ).
fof(rc2_ordinal1,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc2_ordinal1) ).
fof(rc2_relat_1,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('theBenchmark.p',rc2_relat_1) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(rc3_funct_1,axiom,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc3_funct_1) ).
fof(rc3_ordinal1,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('theBenchmark.p',rc3_ordinal1) ).
fof(rc3_relat_1,axiom,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc3_relat_1) ).
fof(rc4_funct_1,axiom,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc4_funct_1) ).
fof(redefinition_k5_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> union_of_subsets(A,B) = union(B) ),
file('theBenchmark.p',redefinition_k5_setfam_1) ).
fof(redefinition_k6_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> meet_of_subsets(A,B) = set_meet(B) ),
file('theBenchmark.p',redefinition_k6_setfam_1) ).
fof(redefinition_k6_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> subset_difference(A,B,C) = set_difference(B,C) ),
file('theBenchmark.p',redefinition_k6_subset_1) ).
fof(redefinition_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('theBenchmark.p',redefinition_r1_ordinal1) ).
fof(reflexivity_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ordinal_subset(A,A) ),
file('theBenchmark.p',reflexivity_r1_ordinal1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t106_zfmisc_1,lemma,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('theBenchmark.p',t106_zfmisc_1) ).
fof(t10_ordinal1,lemma,
! [A] : in(A,succ(A)),
file('theBenchmark.p',t10_ordinal1) ).
fof(t10_zfmisc_1,lemma,
! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
file('theBenchmark.p',t10_zfmisc_1) ).
fof(t115_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_rng(relation_rng_restriction(B,C)))
<=> ( in(A,relation_rng(C))
& in(A,B) ) ) ),
file('theBenchmark.p',t115_relat_1) ).
fof(t116_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),A) ),
file('theBenchmark.p',t116_relat_1) ).
fof(t117_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng_restriction(A,B),B) ),
file('theBenchmark.p',t117_relat_1) ).
fof(t118_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ),
file('theBenchmark.p',t118_relat_1) ).
fof(t118_zfmisc_1,lemma,
! [A,B,C] :
( subset(A,B)
=> ( subset(cartesian_product2(C,A),cartesian_product2(C,B))
& subset(cartesian_product2(A,C),cartesian_product2(B,C)) ) ),
file('theBenchmark.p',t118_zfmisc_1) ).
fof(t119_relat_1,lemma,
! [A,B] :
( relation(B)
=> relation_rng(relation_rng_restriction(A,B)) = set_intersection2(relation_rng(B),A) ),
file('theBenchmark.p',t119_relat_1) ).
fof(t119_zfmisc_1,lemma,
! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('theBenchmark.p',t119_zfmisc_1) ).
fof(t12_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
file('theBenchmark.p',t12_xboole_1) ).
fof(t136_zfmisc_1,lemma,
! [A] :
? [B] :
( ! [C] :
~ ( ~ in(C,B)
& ~ are_equipotent(C,B)
& subset(C,B) )
& ! [C] :
( in(C,B)
=> in(powerset(C),B) )
& ! [C,D] :
( ( subset(D,C)
& in(C,B) )
=> in(D,B) )
& in(A,B) ),
file('theBenchmark.p',t136_zfmisc_1) ).
fof(t140_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> relation_dom_restriction(relation_rng_restriction(A,C),B) = relation_rng_restriction(A,relation_dom_restriction(C,B)) ),
file('theBenchmark.p',t140_relat_1) ).
fof(t143_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_image(C,B))
<=> ? [D] :
( in(D,B)
& in(ordered_pair(D,A),C)
& in(D,relation_dom(C)) ) ) ),
file('theBenchmark.p',t143_relat_1) ).
fof(t144_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_image(B,A),relation_rng(B)) ),
file('theBenchmark.p',t144_relat_1) ).
fof(t145_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> subset(relation_image(B,relation_inverse_image(B,A)),A) ),
file('theBenchmark.p',t145_funct_1) ).
fof(t145_relat_1,lemma,
! [A,B] :
( relation(B)
=> relation_image(B,A) = relation_image(B,set_intersection2(relation_dom(B),A)) ),
file('theBenchmark.p',t145_relat_1) ).
fof(t146_funct_1,lemma,
! [A,B] :
( relation(B)
=> ( subset(A,relation_dom(B))
=> subset(A,relation_inverse_image(B,relation_image(B,A))) ) ),
file('theBenchmark.p',t146_funct_1) ).
fof(t146_relat_1,lemma,
! [A] :
( relation(A)
=> relation_image(A,relation_dom(A)) = relation_rng(A) ),
file('theBenchmark.p',t146_relat_1) ).
fof(t147_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( subset(A,relation_rng(B))
=> relation_image(B,relation_inverse_image(B,A)) = A ) ),
file('theBenchmark.p',t147_funct_1) ).
fof(t160_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> relation_rng(relation_composition(A,B)) = relation_image(B,relation_rng(A)) ) ),
file('theBenchmark.p',t160_relat_1) ).
fof(t166_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_inverse_image(C,B))
<=> ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) ) ) ),
file('theBenchmark.p',t166_relat_1) ).
fof(t167_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_inverse_image(B,A),relation_dom(B)) ),
file('theBenchmark.p',t167_relat_1) ).
fof(t16_wellord1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_restriction(C,B))
<=> ( in(A,cartesian_product2(B,B))
& in(A,C) ) ) ),
file('theBenchmark.p',t16_wellord1) ).
fof(t174_relat_1,lemma,
! [A,B] :
( relation(B)
=> ~ ( relation_inverse_image(B,A) = empty_set
& subset(A,relation_rng(B))
& A != empty_set ) ),
file('theBenchmark.p',t174_relat_1) ).
fof(t178_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( subset(A,B)
=> subset(relation_inverse_image(C,A),relation_inverse_image(C,B)) ) ),
file('theBenchmark.p',t178_relat_1) ).
fof(t17_wellord1,lemma,
! [A,B] :
( relation(B)
=> relation_restriction(B,A) = relation_dom_restriction(relation_rng_restriction(A,B),A) ),
file('theBenchmark.p',t17_wellord1) ).
fof(t17_xboole_1,lemma,
! [A,B] : subset(set_intersection2(A,B),A),
file('theBenchmark.p',t17_xboole_1) ).
fof(t18_wellord1,lemma,
! [A,B] :
( relation(B)
=> relation_restriction(B,A) = relation_rng_restriction(A,relation_dom_restriction(B,A)) ),
file('theBenchmark.p',t18_wellord1) ).
fof(t19_wellord1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_field(relation_restriction(C,B)))
=> ( in(A,B)
& in(A,relation_field(C)) ) ) ),
file('theBenchmark.p',t19_wellord1) ).
fof(t19_xboole_1,lemma,
! [A,B,C] :
( ( subset(A,C)
& subset(A,B) )
=> subset(A,set_intersection2(B,C)) ),
file('theBenchmark.p',t19_xboole_1) ).
fof(t1_boole,axiom,
! [A] : set_union2(A,empty_set) = A,
file('theBenchmark.p',t1_boole) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t1_xboole_1,lemma,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('theBenchmark.p',t1_xboole_1) ).
fof(t1_zfmisc_1,lemma,
powerset(empty_set) = singleton(empty_set),
file('theBenchmark.p',t1_zfmisc_1) ).
fof(t20_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_rng(C))
& in(A,relation_dom(C)) ) ) ),
file('theBenchmark.p',t20_relat_1) ).
fof(t20_wellord1,lemma,
! [A,B] :
( relation(B)
=> ( subset(relation_field(relation_restriction(B,A)),A)
& subset(relation_field(relation_restriction(B,A)),relation_field(B)) ) ),
file('theBenchmark.p',t20_wellord1) ).
fof(t21_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(relation_composition(C,B)))
<=> ( in(apply(C,A),relation_dom(B))
& in(A,relation_dom(C)) ) ) ) ),
file('theBenchmark.p',t21_funct_1) ).
fof(t21_ordinal1,lemma,
! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ( proper_subset(A,B)
=> in(A,B) ) ) ),
file('theBenchmark.p',t21_ordinal1) ).
fof(t21_relat_1,lemma,
! [A] :
( relation(A)
=> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))) ),
file('theBenchmark.p',t21_relat_1) ).
fof(t21_wellord1,lemma,
! [A,B,C] :
( relation(C)
=> subset(fiber(relation_restriction(C,A),B),fiber(C,B)) ),
file('theBenchmark.p',t21_wellord1) ).
fof(t22_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(relation_composition(C,B)))
=> apply(relation_composition(C,B),A) = apply(B,apply(C,A)) ) ) ),
file('theBenchmark.p',t22_funct_1) ).
fof(t22_wellord1,conjecture,
! [A,B] :
( relation(B)
=> ( reflexive(B)
=> reflexive(relation_restriction(B,A)) ) ),
file('theBenchmark.p',t22_wellord1) ).
fof(t23_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(B))
=> apply(relation_composition(B,C),A) = apply(C,apply(B,A)) ) ) ),
file('theBenchmark.p',t23_funct_1) ).
fof(t23_ordinal1,lemma,
! [A,B] :
( ordinal(B)
=> ( in(A,B)
=> ordinal(A) ) ),
file('theBenchmark.p',t23_ordinal1) ).
fof(t24_ordinal1,lemma,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ in(B,A)
& A != B
& ~ in(A,B) ) ) ),
file('theBenchmark.p',t24_ordinal1) ).
fof(t25_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(A,B)
=> ( subset(relation_rng(A),relation_rng(B))
& subset(relation_dom(A),relation_dom(B)) ) ) ) ),
file('theBenchmark.p',t25_relat_1) ).
fof(t26_xboole_1,lemma,
! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ),
file('theBenchmark.p',t26_xboole_1) ).
fof(t28_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('theBenchmark.p',t28_xboole_1) ).
fof(t2_boole,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
file('theBenchmark.p',t2_boole) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('theBenchmark.p',t2_tarski) ).
fof(t2_xboole_1,lemma,
! [A] : subset(empty_set,A),
file('theBenchmark.p',t2_xboole_1) ).
fof(t30_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_field(C))
& in(A,relation_field(C)) ) ) ),
file('theBenchmark.p',t30_relat_1) ).
fof(t31_ordinal1,lemma,
! [A] :
( ! [B] :
( in(B,A)
=> ( subset(B,A)
& ordinal(B) ) )
=> ordinal(A) ),
file('theBenchmark.p',t31_ordinal1) ).
fof(t32_ordinal1,lemma,
! [A,B] :
( ordinal(B)
=> ~ ( ! [C] :
( ordinal(C)
=> ~ ( ! [D] :
( ordinal(D)
=> ( in(D,A)
=> ordinal_subset(C,D) ) )
& in(C,A) ) )
& A != empty_set
& subset(A,B) ) ),
file('theBenchmark.p',t32_ordinal1) ).
fof(t33_ordinal1,lemma,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(A,B)
<=> ordinal_subset(succ(A),B) ) ) ),
file('theBenchmark.p',t33_ordinal1) ).
fof(t33_xboole_1,lemma,
! [A,B,C] :
( subset(A,B)
=> subset(set_difference(A,C),set_difference(B,C)) ),
file('theBenchmark.p',t33_xboole_1) ).
fof(t33_zfmisc_1,lemma,
! [A,B,C,D] :
( ordered_pair(A,B) = ordered_pair(C,D)
=> ( B = D
& A = C ) ),
file('theBenchmark.p',t33_zfmisc_1) ).
fof(t34_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( B = identity_relation(A)
<=> ( ! [C] :
( in(C,A)
=> apply(B,C) = C )
& relation_dom(B) = A ) ) ),
file('theBenchmark.p',t34_funct_1) ).
fof(t35_funct_1,lemma,
! [A,B] :
( in(B,A)
=> apply(identity_relation(A),B) = B ),
file('theBenchmark.p',t35_funct_1) ).
fof(t36_xboole_1,lemma,
! [A,B] : subset(set_difference(A,B),A),
file('theBenchmark.p',t36_xboole_1) ).
fof(t37_relat_1,lemma,
! [A] :
( relation(A)
=> ( relation_dom(A) = relation_rng(relation_inverse(A))
& relation_rng(A) = relation_dom(relation_inverse(A)) ) ),
file('theBenchmark.p',t37_relat_1) ).
fof(t37_xboole_1,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',t37_xboole_1) ).
fof(t37_zfmisc_1,lemma,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('theBenchmark.p',t37_zfmisc_1) ).
fof(t38_zfmisc_1,lemma,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(B,C)
& in(A,C) ) ),
file('theBenchmark.p',t38_zfmisc_1) ).
fof(t39_xboole_1,lemma,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
file('theBenchmark.p',t39_xboole_1) ).
fof(t39_zfmisc_1,lemma,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',t39_zfmisc_1) ).
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
file('theBenchmark.p',t3_boole) ).
fof(t3_ordinal1,lemma,
! [A,B,C] :
~ ( in(C,A)
& in(B,C)
& in(A,B) ),
file('theBenchmark.p',t3_ordinal1) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t3_xboole_0,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t3_xboole_0) ).
fof(t3_xboole_1,lemma,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('theBenchmark.p',t3_xboole_1) ).
fof(t40_xboole_1,lemma,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
file('theBenchmark.p',t40_xboole_1) ).
fof(t41_ordinal1,lemma,
! [A] :
( ordinal(A)
=> ( being_limit_ordinal(A)
<=> ! [B] :
( ordinal(B)
=> ( in(B,A)
=> in(succ(B),A) ) ) ) ),
file('theBenchmark.p',t41_ordinal1) ).
fof(t42_ordinal1,lemma,
! [A] :
( ordinal(A)
=> ( ~ ( being_limit_ordinal(A)
& ? [B] :
( A = succ(B)
& ordinal(B) ) )
& ~ ( ! [B] :
( ordinal(B)
=> A != succ(B) )
& ~ being_limit_ordinal(A) ) ) ),
file('theBenchmark.p',t42_ordinal1) ).
fof(t43_subset_1,lemma,
! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,powerset(A))
=> ( disjoint(B,C)
<=> subset(B,subset_complement(A,C)) ) ) ),
file('theBenchmark.p',t43_subset_1) ).
fof(t44_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> subset(relation_dom(relation_composition(A,B)),relation_dom(A)) ) ),
file('theBenchmark.p',t44_relat_1) ).
fof(t45_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> subset(relation_rng(relation_composition(A,B)),relation_rng(B)) ) ),
file('theBenchmark.p',t45_relat_1) ).
fof(t45_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> B = set_union2(A,set_difference(B,A)) ),
file('theBenchmark.p',t45_xboole_1) ).
fof(t46_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(relation_rng(A),relation_dom(B))
=> relation_dom(relation_composition(A,B)) = relation_dom(A) ) ) ),
file('theBenchmark.p',t46_relat_1) ).
fof(t46_setfam_1,lemma,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ~ ( complements_of_subsets(A,B) = empty_set
& B != empty_set ) ),
file('theBenchmark.p',t46_setfam_1) ).
fof(t46_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('theBenchmark.p',t46_zfmisc_1) ).
fof(t47_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(relation_dom(A),relation_rng(B))
=> relation_rng(relation_composition(B,A)) = relation_rng(A) ) ) ),
file('theBenchmark.p',t47_relat_1) ).
fof(t47_setfam_1,lemma,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> subset_difference(A,cast_to_subset(A),union_of_subsets(A,B)) = meet_of_subsets(A,complements_of_subsets(A,B)) ) ),
file('theBenchmark.p',t47_setfam_1) ).
fof(t48_setfam_1,lemma,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> union_of_subsets(A,complements_of_subsets(A,B)) = subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B)) ) ),
file('theBenchmark.p',t48_setfam_1) ).
fof(t48_xboole_1,lemma,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
file('theBenchmark.p',t48_xboole_1) ).
fof(t4_boole,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
file('theBenchmark.p',t4_boole) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t4_xboole_0,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t4_xboole_0) ).
fof(t50_subset_1,lemma,
! [A] :
( A != empty_set
=> ! [B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,A)
=> ( ~ in(C,B)
=> in(C,subset_complement(A,B)) ) ) ) ),
file('theBenchmark.p',t50_subset_1) ).
fof(t54_funct_1,lemma,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( B = function_inverse(A)
<=> ( ! [C,D] :
( ( ( C = apply(A,D)
& in(D,relation_dom(A)) )
=> ( D = apply(B,C)
& in(C,relation_rng(A)) ) )
& ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
=> ( C = apply(A,D)
& in(D,relation_dom(A)) ) ) )
& relation_dom(B) = relation_rng(A) ) ) ) ) ),
file('theBenchmark.p',t54_funct_1) ).
fof(t54_subset_1,lemma,
! [A,B,C] :
( element(C,powerset(A))
=> ~ ( in(B,C)
& in(B,subset_complement(A,C)) ) ),
file('theBenchmark.p',t54_subset_1) ).
fof(t55_funct_1,lemma,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_dom(A) = relation_rng(function_inverse(A))
& relation_rng(A) = relation_dom(function_inverse(A)) ) ) ),
file('theBenchmark.p',t55_funct_1) ).
fof(t56_relat_1,lemma,
! [A] :
( relation(A)
=> ( ! [B,C] : ~ in(ordered_pair(B,C),A)
=> A = empty_set ) ),
file('theBenchmark.p',t56_relat_1) ).
fof(t57_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( ( in(A,relation_rng(B))
& one_to_one(B) )
=> ( A = apply(relation_composition(function_inverse(B),B),A)
& A = apply(B,apply(function_inverse(B),A)) ) ) ),
file('theBenchmark.p',t57_funct_1) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t5_wellord1,lemma,
! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> is_well_founded_in(A,relation_field(A)) ) ),
file('theBenchmark.p',t5_wellord1) ).
fof(t60_relat_1,lemma,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('theBenchmark.p',t60_relat_1) ).
fof(t60_xboole_1,lemma,
! [A,B] :
~ ( proper_subset(B,A)
& subset(A,B) ),
file('theBenchmark.p',t60_xboole_1) ).
fof(t62_funct_1,lemma,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> one_to_one(function_inverse(A)) ) ),
file('theBenchmark.p',t62_funct_1) ).
fof(t63_xboole_1,lemma,
! [A,B,C] :
( ( disjoint(B,C)
& subset(A,B) )
=> disjoint(A,C) ),
file('theBenchmark.p',t63_xboole_1) ).
fof(t64_relat_1,lemma,
! [A] :
( relation(A)
=> ( ( relation_rng(A) = empty_set
| relation_dom(A) = empty_set )
=> A = empty_set ) ),
file('theBenchmark.p',t64_relat_1) ).
fof(t65_relat_1,lemma,
! [A] :
( relation(A)
=> ( relation_dom(A) = empty_set
<=> relation_rng(A) = empty_set ) ),
file('theBenchmark.p',t65_relat_1) ).
fof(t65_zfmisc_1,lemma,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('theBenchmark.p',t65_zfmisc_1) ).
fof(t68_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( B = relation_dom_restriction(C,A)
<=> ( ! [D] :
( in(D,relation_dom(B))
=> apply(B,D) = apply(C,D) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) ) ) ) ),
file('theBenchmark.p',t68_funct_1) ).
fof(t69_enumset1,lemma,
! [A] : unordered_pair(A,A) = singleton(A),
file('theBenchmark.p',t69_enumset1) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t6_zfmisc_1,lemma,
! [A,B] :
( subset(singleton(A),singleton(B))
=> A = B ),
file('theBenchmark.p',t6_zfmisc_1) ).
fof(t70_funct_1,lemma,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
file('theBenchmark.p',t70_funct_1) ).
fof(t71_relat_1,lemma,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
file('theBenchmark.p',t71_relat_1) ).
fof(t72_funct_1,lemma,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,A)
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
file('theBenchmark.p',t72_funct_1) ).
fof(t74_relat_1,lemma,
! [A,B,C,D] :
( relation(D)
=> ( in(ordered_pair(A,B),relation_composition(identity_relation(C),D))
<=> ( in(ordered_pair(A,B),D)
& in(A,C) ) ) ),
file('theBenchmark.p',t74_relat_1) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t7_tarski,axiom,
! [A,B] :
~ ( ! [C] :
~ ( ! [D] :
~ ( in(D,C)
& in(D,B) )
& in(C,B) )
& in(A,B) ),
file('theBenchmark.p',t7_tarski) ).
fof(t7_xboole_1,lemma,
! [A,B] : subset(A,set_union2(A,B)),
file('theBenchmark.p',t7_xboole_1) ).
fof(t83_xboole_1,lemma,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('theBenchmark.p',t83_xboole_1) ).
fof(t86_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_dom(relation_dom_restriction(C,B)))
<=> ( in(A,relation_dom(C))
& in(A,B) ) ) ),
file('theBenchmark.p',t86_relat_1) ).
fof(t88_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_dom_restriction(B,A),B) ),
file('theBenchmark.p',t88_relat_1) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(t8_funct_1,lemma,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(ordered_pair(A,B),C)
<=> ( B = apply(C,A)
& in(A,relation_dom(C)) ) ) ),
file('theBenchmark.p',t8_funct_1) ).
fof(t8_wellord1,lemma,
! [A] :
( relation(A)
=> ( well_orders(A,relation_field(A))
<=> well_ordering(A) ) ),
file('theBenchmark.p',t8_wellord1) ).
fof(t8_xboole_1,lemma,
! [A,B,C] :
( ( subset(C,B)
& subset(A,B) )
=> subset(set_union2(A,C),B) ),
file('theBenchmark.p',t8_xboole_1) ).
fof(t8_zfmisc_1,lemma,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ),
file('theBenchmark.p',t8_zfmisc_1) ).
fof(t90_relat_1,lemma,
! [A,B] :
( relation(B)
=> relation_dom(relation_dom_restriction(B,A)) = set_intersection2(relation_dom(B),A) ),
file('theBenchmark.p',t90_relat_1) ).
fof(t92_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
file('theBenchmark.p',t92_zfmisc_1) ).
fof(t94_relat_1,lemma,
! [A,B] :
( relation(B)
=> relation_dom_restriction(B,A) = relation_composition(identity_relation(A),B) ),
file('theBenchmark.p',t94_relat_1) ).
fof(t99_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B)) ),
file('theBenchmark.p',t99_relat_1) ).
fof(t99_zfmisc_1,lemma,
! [A] : union(powerset(A)) = A,
file('theBenchmark.p',t99_zfmisc_1) ).
fof(t9_tarski,axiom,
! [A] :
? [B] :
( ! [C] :
~ ( ~ in(C,B)
& ~ are_equipotent(C,B)
& subset(C,B) )
& ! [C] :
~ ( ! [D] :
~ ( ! [E] :
( subset(E,C)
=> in(E,D) )
& in(D,B) )
& in(C,B) )
& ! [C,D] :
( ( subset(D,C)
& in(C,B) )
=> in(D,B) )
& in(A,B) ),
file('theBenchmark.p',t9_tarski) ).
fof(t9_zfmisc_1,lemma,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> B = C ),
file('theBenchmark.p',t9_zfmisc_1) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ proper_subset(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(f_2_2,plain,
! [U_3,U_2] :
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_3_2,plain,
! [U_4] :
( function(U_4)
| ~ empty(U_4) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( function(U_4)
| ~ empty(U_4) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[cc1_ordinal1]) ).
fof(f_4_2,plain,
! [U_5] :
( ( epsilon_connected(U_5)
& epsilon_transitive(U_5) )
| ~ ordinal(U_5) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( epsilon_transitive(U_5)
| ~ ordinal(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( epsilon_connected(U_5)
| ~ ordinal(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_5_2,plain,
! [U_6] :
( relation(U_6)
| ~ empty(U_6) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( relation(U_6)
| ~ empty(U_6) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A] :
( ( one_to_one(A)
& function(A)
& relation(A) )
| ~ function(A)
| ~ empty(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[cc2_funct_1]) ).
fof(f_6_2,plain,
! [U_7] :
( ( one_to_one(U_7)
& function(U_7)
& relation(U_7) )
| ~ function(U_7)
| ~ empty(U_7)
| ~ relation(U_7) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( relation(U_7)
| ~ function(U_7)
| ~ empty(U_7)
| ~ relation(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( function(U_7)
| ~ function(U_7)
| ~ empty(U_7)
| ~ relation(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_5,plain,
( one_to_one(U_7)
| ~ function(U_7)
| ~ empty(U_7)
| ~ relation(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A] :
( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[cc2_ordinal1]) ).
fof(f_7_2,plain,
! [U_8] :
( ordinal(U_8)
| ~ epsilon_connected(U_8)
| ~ epsilon_transitive(U_8) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( ordinal(U_8)
| ~ epsilon_connected(U_8)
| ~ epsilon_transitive(U_8) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [A] :
( ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc3_ordinal1]) ).
fof(f_8_2,plain,
! [U_9] :
( ( ordinal(U_9)
& epsilon_connected(U_9)
& epsilon_transitive(U_9) )
| ~ empty(U_9) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( epsilon_transitive(U_9)
| ~ empty(U_9) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( epsilon_connected(U_9)
| ~ empty(U_9) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_5,plain,
( ordinal(U_9)
| ~ empty(U_9) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_9_2,plain,
! [U_11,U_10] : unordered_pair(U_11,U_10) = unordered_pair(U_10,U_11),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
unordered_pair(U_11,U_10) = unordered_pair(U_10,U_11),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_10_2,plain,
! [U_13,U_12] : set_union2(U_13,U_12) = set_union2(U_12,U_13),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
set_union2(U_13,U_12) = set_union2(U_12,U_13),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_11_2,plain,
! [U_15,U_14] : set_intersection2(U_15,U_14) = set_intersection2(U_14,U_15),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
set_intersection2(U_15,U_14) = set_intersection2(U_14,U_15),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A,B] :
( ordinal_subset(B,A)
| ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[connectedness_r1_ordinal1]) ).
fof(f_12_2,plain,
! [U_17,U_16] :
( ordinal_subset(U_16,U_17)
| ordinal_subset(U_17,U_16)
| ~ ordinal(U_16)
| ~ ordinal(U_17) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( ordinal_subset(U_16,U_17)
| ordinal_subset(U_17,U_16)
| ~ ordinal(U_16)
| ~ ordinal(U_17) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [A,B] :
( ( ( B = identity_relation(A)
| ? [C,D] :
( ( ~ in(ordered_pair(C,D),B)
& C = D
& in(C,A) )
| ( ( C != D
| ~ in(C,A) )
& in(ordered_pair(C,D),B) ) ) )
& ( ! [C,D] :
( ( in(ordered_pair(C,D),B)
| C != D
| ~ in(C,A) )
& ( ( C = D
& in(C,A) )
| ~ in(ordered_pair(C,D),B) ) )
| B != identity_relation(A) ) )
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[d10_relat_1]) ).
fof(f_13_2,plain,
! [U_23,U_22] :
( ( ( U_22 = identity_relation(U_23)
| ? [U_21,U_20] :
( ( ~ in(ordered_pair(U_21,U_20),U_22)
& U_21 = U_20
& in(U_21,U_23) )
| ( ( U_21 != U_20
| ~ in(U_21,U_23) )
& in(ordered_pair(U_21,U_20),U_22) ) ) )
& ( ! [U_19,U_18] :
( ( in(ordered_pair(U_19,U_18),U_22)
| U_19 != U_18
| ~ in(U_19,U_23) )
& ( ( U_19 = U_18
& in(U_19,U_23) )
| ~ in(ordered_pair(U_19,U_18),U_22) ) )
| U_22 != identity_relation(U_23) ) )
| ~ relation(U_22) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_23,U_22] :
( ( ( U_22 = identity_relation(U_23)
| ? [U_31,U_29] :
( ~ in(ordered_pair(U_31,U_29),U_22)
& U_31 = U_29
& in(U_31,U_23) )
| ? [U_30,U_28] :
( ( U_30 != U_28
| ~ in(U_30,U_23) )
& in(ordered_pair(U_30,U_28),U_22) ) )
& ( ( ! [U_27,U_25] :
( in(ordered_pair(U_27,U_25),U_22)
| U_27 != U_25
| ~ in(U_27,U_23) )
& ! [U_26,U_24] :
( ( U_26 = U_24
& in(U_26,U_23) )
| ~ in(ordered_pair(U_26,U_24),U_22) ) )
| U_22 != identity_relation(U_23) ) )
| ~ relation(U_22) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
fof(f_13_4,plain,
! [U_23,U_22] :
( ( ( U_22 = identity_relation(U_23)
| ? [U_31,U_29] :
( ~ in(ordered_pair(U_31,U_29),U_22)
& U_31 = U_29
& in(U_31,U_23) )
| ? [U_28] :
( ( sK1(U_23,U_22) != U_28
| ~ in(sK1(U_23,U_22),U_23) )
& in(ordered_pair(sK1(U_23,U_22),U_28),U_22) ) )
& ( ( ! [U_27,U_25] :
( in(ordered_pair(U_27,U_25),U_22)
| U_27 != U_25
| ~ in(U_27,U_23) )
& ! [U_26,U_24] :
( ( U_26 = U_24
& in(U_26,U_23) )
| ~ in(ordered_pair(U_26,U_24),U_22) ) )
| U_22 != identity_relation(U_23) ) )
| ~ relation(U_22) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_30,sK1(U_23,U_22))],[f_13_3]) ).
fof(f_13_5,plain,
! [U_23,U_22] :
( ( ( U_22 = identity_relation(U_23)
| ? [U_31,U_29] :
( ~ in(ordered_pair(U_31,U_29),U_22)
& U_31 = U_29
& in(U_31,U_23) )
| ( ( sK1(U_23,U_22) != sK2(U_23,U_22)
| ~ in(sK1(U_23,U_22),U_23) )
& in(ordered_pair(sK1(U_23,U_22),sK2(U_23,U_22)),U_22) ) )
& ( ( ! [U_27,U_25] :
( in(ordered_pair(U_27,U_25),U_22)
| U_27 != U_25
| ~ in(U_27,U_23) )
& ! [U_26,U_24] :
( ( U_26 = U_24
& in(U_26,U_23) )
| ~ in(ordered_pair(U_26,U_24),U_22) ) )
| U_22 != identity_relation(U_23) ) )
| ~ relation(U_22) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_28,sK2(U_23,U_22))],[f_13_4]) ).
fof(f_13_6,plain,
! [U_23,U_22] :
( ( ( U_22 = identity_relation(U_23)
| ? [U_29] :
( ~ in(ordered_pair(sK3(U_23,U_22),U_29),U_22)
& sK3(U_23,U_22) = U_29
& in(sK3(U_23,U_22),U_23) )
| ( ( sK1(U_23,U_22) != sK2(U_23,U_22)
| ~ in(sK1(U_23,U_22),U_23) )
& in(ordered_pair(sK1(U_23,U_22),sK2(U_23,U_22)),U_22) ) )
& ( ( ! [U_27,U_25] :
( in(ordered_pair(U_27,U_25),U_22)
| U_27 != U_25
| ~ in(U_27,U_23) )
& ! [U_26,U_24] :
( ( U_26 = U_24
& in(U_26,U_23) )
| ~ in(ordered_pair(U_26,U_24),U_22) ) )
| U_22 != identity_relation(U_23) ) )
| ~ relation(U_22) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_31,sK3(U_23,U_22))],[f_13_5]) ).
fof(f_13_7,plain,
! [U_23,U_22] :
( ( ( U_22 = identity_relation(U_23)
| ( ~ in(ordered_pair(sK3(U_23,U_22),sK4(U_23,U_22)),U_22)
& sK3(U_23,U_22) = sK4(U_23,U_22)
& in(sK3(U_23,U_22),U_23) )
| ( ( sK1(U_23,U_22) != sK2(U_23,U_22)
| ~ in(sK1(U_23,U_22),U_23) )
& in(ordered_pair(sK1(U_23,U_22),sK2(U_23,U_22)),U_22) ) )
& ( ( ! [U_27,U_25] :
( in(ordered_pair(U_27,U_25),U_22)
| U_27 != U_25
| ~ in(U_27,U_23) )
& ! [U_26,U_24] :
( ( U_26 = U_24
& in(U_26,U_23) )
| ~ in(ordered_pair(U_26,U_24),U_22) ) )
| U_22 != identity_relation(U_23) ) )
| ~ relation(U_22) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_29,sK4(U_23,U_22))],[f_13_6]) ).
cnf(f_13_8,plain,
( in(U_26,U_23)
| ~ in(ordered_pair(U_26,U_24),U_22)
| U_22 != identity_relation(U_23)
| ~ relation(U_22) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_9,plain,
( U_26 = U_24
| ~ in(ordered_pair(U_26,U_24),U_22)
| U_22 != identity_relation(U_23)
| ~ relation(U_22) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_10,plain,
( in(ordered_pair(U_27,U_25),U_22)
| U_27 != U_25
| ~ in(U_27,U_23)
| U_22 != identity_relation(U_23)
| ~ relation(U_22) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_11,plain,
( in(sK3(U_23,U_22),U_23)
| in(ordered_pair(sK1(U_23,U_22),sK2(U_23,U_22)),U_22)
| U_22 = identity_relation(U_23)
| ~ relation(U_22) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_12,plain,
( sK3(U_23,U_22) = sK4(U_23,U_22)
| in(ordered_pair(sK1(U_23,U_22),sK2(U_23,U_22)),U_22)
| U_22 = identity_relation(U_23)
| ~ relation(U_22) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_13,plain,
( ~ in(ordered_pair(sK3(U_23,U_22),sK4(U_23,U_22)),U_22)
| in(ordered_pair(sK1(U_23,U_22),sK2(U_23,U_22)),U_22)
| U_22 = identity_relation(U_23)
| ~ relation(U_22) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_14,plain,
( in(sK3(U_23,U_22),U_23)
| sK1(U_23,U_22) != sK2(U_23,U_22)
| ~ in(sK1(U_23,U_22),U_23)
| U_22 = identity_relation(U_23)
| ~ relation(U_22) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_15,plain,
( sK3(U_23,U_22) = sK4(U_23,U_22)
| sK1(U_23,U_22) != sK2(U_23,U_22)
| ~ in(sK1(U_23,U_22),U_23)
| U_22 = identity_relation(U_23)
| ~ relation(U_22) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_16,plain,
( ~ in(ordered_pair(sK3(U_23,U_22),sK4(U_23,U_22)),U_22)
| sK1(U_23,U_22) != sK2(U_23,U_22)
| ~ in(sK1(U_23,U_22),U_23)
| U_22 = identity_relation(U_23)
| ~ relation(U_22) ),
inference(clausify,[status(thm)],[f_13_7]) ).
fof(f_14_1,plain,
! [A,B] :
( ( A = B
| ~ subset(B,A)
| ~ subset(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(fof_nnf,[status(thm)],[d10_xboole_0]) ).
fof(f_14_2,plain,
! [U_33,U_32] :
( ( U_33 = U_32
| ~ subset(U_32,U_33)
| ~ subset(U_33,U_32) )
& ( ( subset(U_32,U_33)
& subset(U_33,U_32) )
| U_33 != U_32 ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_37,U_35] :
( U_37 = U_35
| ~ subset(U_35,U_37)
| ~ subset(U_37,U_35) )
& ! [U_36,U_34] :
( ( subset(U_34,U_36)
& subset(U_36,U_34) )
| U_36 != U_34 ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( subset(U_36,U_34)
| U_36 != U_34 ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_5,plain,
( subset(U_34,U_36)
| U_36 != U_34 ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_6,plain,
( U_37 = U_35
| ~ subset(U_35,U_37)
| ~ subset(U_37,U_35) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [A] :
( ! [B,C] :
( ( ( C = relation_dom_restriction(A,B)
| ? [D,E] :
( ( ~ in(ordered_pair(D,E),C)
& in(ordered_pair(D,E),A)
& in(D,B) )
| ( ( ~ in(ordered_pair(D,E),A)
| ~ in(D,B) )
& in(ordered_pair(D,E),C) ) ) )
& ( ! [D,E] :
( ( in(ordered_pair(D,E),C)
| ~ in(ordered_pair(D,E),A)
| ~ in(D,B) )
& ( ( in(ordered_pair(D,E),A)
& in(D,B) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_dom_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d11_relat_1]) ).
fof(f_15_2,plain,
! [U_44] :
( ! [U_43,U_42] :
( ( ( U_42 = relation_dom_restriction(U_44,U_43)
| ? [U_41,U_40] :
( ( ~ in(ordered_pair(U_41,U_40),U_42)
& in(ordered_pair(U_41,U_40),U_44)
& in(U_41,U_43) )
| ( ( ~ in(ordered_pair(U_41,U_40),U_44)
| ~ in(U_41,U_43) )
& in(ordered_pair(U_41,U_40),U_42) ) ) )
& ( ! [U_39,U_38] :
( ( in(ordered_pair(U_39,U_38),U_42)
| ~ in(ordered_pair(U_39,U_38),U_44)
| ~ in(U_39,U_43) )
& ( ( in(ordered_pair(U_39,U_38),U_44)
& in(U_39,U_43) )
| ~ in(ordered_pair(U_39,U_38),U_42) ) )
| U_42 != relation_dom_restriction(U_44,U_43) ) )
| ~ relation(U_42) )
| ~ relation(U_44) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_44] :
( ! [U_43,U_42] :
( ( ( U_42 = relation_dom_restriction(U_44,U_43)
| ? [U_52,U_50] :
( ~ in(ordered_pair(U_52,U_50),U_42)
& in(ordered_pair(U_52,U_50),U_44)
& in(U_52,U_43) )
| ? [U_51,U_49] :
( ( ~ in(ordered_pair(U_51,U_49),U_44)
| ~ in(U_51,U_43) )
& in(ordered_pair(U_51,U_49),U_42) ) )
& ( ( ! [U_48,U_46] :
( in(ordered_pair(U_48,U_46),U_42)
| ~ in(ordered_pair(U_48,U_46),U_44)
| ~ in(U_48,U_43) )
& ! [U_47,U_45] :
( ( in(ordered_pair(U_47,U_45),U_44)
& in(U_47,U_43) )
| ~ in(ordered_pair(U_47,U_45),U_42) ) )
| U_42 != relation_dom_restriction(U_44,U_43) ) )
| ~ relation(U_42) )
| ~ relation(U_44) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
fof(f_15_4,plain,
! [U_44] :
( ! [U_43,U_42] :
( ( ( U_42 = relation_dom_restriction(U_44,U_43)
| ? [U_52,U_50] :
( ~ in(ordered_pair(U_52,U_50),U_42)
& in(ordered_pair(U_52,U_50),U_44)
& in(U_52,U_43) )
| ? [U_49] :
( ( ~ in(ordered_pair(sK5(U_44,U_43,U_42),U_49),U_44)
| ~ in(sK5(U_44,U_43,U_42),U_43) )
& in(ordered_pair(sK5(U_44,U_43,U_42),U_49),U_42) ) )
& ( ( ! [U_48,U_46] :
( in(ordered_pair(U_48,U_46),U_42)
| ~ in(ordered_pair(U_48,U_46),U_44)
| ~ in(U_48,U_43) )
& ! [U_47,U_45] :
( ( in(ordered_pair(U_47,U_45),U_44)
& in(U_47,U_43) )
| ~ in(ordered_pair(U_47,U_45),U_42) ) )
| U_42 != relation_dom_restriction(U_44,U_43) ) )
| ~ relation(U_42) )
| ~ relation(U_44) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_51,sK5(U_44,U_43,U_42))],[f_15_3]) ).
fof(f_15_5,plain,
! [U_44] :
( ! [U_43,U_42] :
( ( ( U_42 = relation_dom_restriction(U_44,U_43)
| ? [U_52,U_50] :
( ~ in(ordered_pair(U_52,U_50),U_42)
& in(ordered_pair(U_52,U_50),U_44)
& in(U_52,U_43) )
| ( ( ~ in(ordered_pair(sK5(U_44,U_43,U_42),sK6(U_44,U_43,U_42)),U_44)
| ~ in(sK5(U_44,U_43,U_42),U_43) )
& in(ordered_pair(sK5(U_44,U_43,U_42),sK6(U_44,U_43,U_42)),U_42) ) )
& ( ( ! [U_48,U_46] :
( in(ordered_pair(U_48,U_46),U_42)
| ~ in(ordered_pair(U_48,U_46),U_44)
| ~ in(U_48,U_43) )
& ! [U_47,U_45] :
( ( in(ordered_pair(U_47,U_45),U_44)
& in(U_47,U_43) )
| ~ in(ordered_pair(U_47,U_45),U_42) ) )
| U_42 != relation_dom_restriction(U_44,U_43) ) )
| ~ relation(U_42) )
| ~ relation(U_44) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_49,sK6(U_44,U_43,U_42))],[f_15_4]) ).
fof(f_15_6,plain,
! [U_44] :
( ! [U_43,U_42] :
( ( ( U_42 = relation_dom_restriction(U_44,U_43)
| ? [U_50] :
( ~ in(ordered_pair(sK7(U_44,U_43,U_42),U_50),U_42)
& in(ordered_pair(sK7(U_44,U_43,U_42),U_50),U_44)
& in(sK7(U_44,U_43,U_42),U_43) )
| ( ( ~ in(ordered_pair(sK5(U_44,U_43,U_42),sK6(U_44,U_43,U_42)),U_44)
| ~ in(sK5(U_44,U_43,U_42),U_43) )
& in(ordered_pair(sK5(U_44,U_43,U_42),sK6(U_44,U_43,U_42)),U_42) ) )
& ( ( ! [U_48,U_46] :
( in(ordered_pair(U_48,U_46),U_42)
| ~ in(ordered_pair(U_48,U_46),U_44)
| ~ in(U_48,U_43) )
& ! [U_47,U_45] :
( ( in(ordered_pair(U_47,U_45),U_44)
& in(U_47,U_43) )
| ~ in(ordered_pair(U_47,U_45),U_42) ) )
| U_42 != relation_dom_restriction(U_44,U_43) ) )
| ~ relation(U_42) )
| ~ relation(U_44) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_52,sK7(U_44,U_43,U_42))],[f_15_5]) ).
fof(f_15_7,plain,
! [U_44] :
( ! [U_43,U_42] :
( ( ( U_42 = relation_dom_restriction(U_44,U_43)
| ( ~ in(ordered_pair(sK7(U_44,U_43,U_42),sK8(U_44,U_43,U_42)),U_42)
& in(ordered_pair(sK7(U_44,U_43,U_42),sK8(U_44,U_43,U_42)),U_44)
& in(sK7(U_44,U_43,U_42),U_43) )
| ( ( ~ in(ordered_pair(sK5(U_44,U_43,U_42),sK6(U_44,U_43,U_42)),U_44)
| ~ in(sK5(U_44,U_43,U_42),U_43) )
& in(ordered_pair(sK5(U_44,U_43,U_42),sK6(U_44,U_43,U_42)),U_42) ) )
& ( ( ! [U_48,U_46] :
( in(ordered_pair(U_48,U_46),U_42)
| ~ in(ordered_pair(U_48,U_46),U_44)
| ~ in(U_48,U_43) )
& ! [U_47,U_45] :
( ( in(ordered_pair(U_47,U_45),U_44)
& in(U_47,U_43) )
| ~ in(ordered_pair(U_47,U_45),U_42) ) )
| U_42 != relation_dom_restriction(U_44,U_43) ) )
| ~ relation(U_42) )
| ~ relation(U_44) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_50,sK8(U_44,U_43,U_42))],[f_15_6]) ).
cnf(f_15_8,plain,
( in(U_47,U_43)
| ~ in(ordered_pair(U_47,U_45),U_42)
| U_42 != relation_dom_restriction(U_44,U_43)
| ~ relation(U_42)
| ~ relation(U_44) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_9,plain,
( in(ordered_pair(U_47,U_45),U_44)
| ~ in(ordered_pair(U_47,U_45),U_42)
| U_42 != relation_dom_restriction(U_44,U_43)
| ~ relation(U_42)
| ~ relation(U_44) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_10,plain,
( in(ordered_pair(U_48,U_46),U_42)
| ~ in(ordered_pair(U_48,U_46),U_44)
| ~ in(U_48,U_43)
| U_42 != relation_dom_restriction(U_44,U_43)
| ~ relation(U_42)
| ~ relation(U_44) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_11,plain,
( in(sK7(U_44,U_43,U_42),U_43)
| in(ordered_pair(sK5(U_44,U_43,U_42),sK6(U_44,U_43,U_42)),U_42)
| U_42 = relation_dom_restriction(U_44,U_43)
| ~ relation(U_42)
| ~ relation(U_44) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_12,plain,
( in(ordered_pair(sK7(U_44,U_43,U_42),sK8(U_44,U_43,U_42)),U_44)
| in(ordered_pair(sK5(U_44,U_43,U_42),sK6(U_44,U_43,U_42)),U_42)
| U_42 = relation_dom_restriction(U_44,U_43)
| ~ relation(U_42)
| ~ relation(U_44) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_13,plain,
( ~ in(ordered_pair(sK7(U_44,U_43,U_42),sK8(U_44,U_43,U_42)),U_42)
| in(ordered_pair(sK5(U_44,U_43,U_42),sK6(U_44,U_43,U_42)),U_42)
| U_42 = relation_dom_restriction(U_44,U_43)
| ~ relation(U_42)
| ~ relation(U_44) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_14,plain,
( in(sK7(U_44,U_43,U_42),U_43)
| ~ in(ordered_pair(sK5(U_44,U_43,U_42),sK6(U_44,U_43,U_42)),U_44)
| ~ in(sK5(U_44,U_43,U_42),U_43)
| U_42 = relation_dom_restriction(U_44,U_43)
| ~ relation(U_42)
| ~ relation(U_44) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_15,plain,
( in(ordered_pair(sK7(U_44,U_43,U_42),sK8(U_44,U_43,U_42)),U_44)
| ~ in(ordered_pair(sK5(U_44,U_43,U_42),sK6(U_44,U_43,U_42)),U_44)
| ~ in(sK5(U_44,U_43,U_42),U_43)
| U_42 = relation_dom_restriction(U_44,U_43)
| ~ relation(U_42)
| ~ relation(U_44) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_16,plain,
( ~ in(ordered_pair(sK7(U_44,U_43,U_42),sK8(U_44,U_43,U_42)),U_42)
| ~ in(ordered_pair(sK5(U_44,U_43,U_42),sK6(U_44,U_43,U_42)),U_44)
| ~ in(sK5(U_44,U_43,U_42),U_43)
| U_42 = relation_dom_restriction(U_44,U_43)
| ~ relation(U_42)
| ~ relation(U_44) ),
inference(clausify,[status(thm)],[f_15_7]) ).
fof(f_16_1,plain,
! [A] :
( ! [B,C] :
( ( C = relation_image(A,B)
| ? [D] :
( ( ~ in(D,C)
& ? [E] :
( D = apply(A,E)
& in(E,B)
& in(E,relation_dom(A)) ) )
| ( ! [E] :
( D != apply(A,E)
| ~ in(E,B)
| ~ in(E,relation_dom(A)) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ! [E] :
( D != apply(A,E)
| ~ in(E,B)
| ~ in(E,relation_dom(A)) ) )
& ( ? [E] :
( D = apply(A,E)
& in(E,B)
& in(E,relation_dom(A)) )
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d12_funct_1]) ).
fof(f_16_2,plain,
! [U_61] :
( ! [U_60,U_59] :
( ( U_59 = relation_image(U_61,U_60)
| ? [U_58] :
( ( ~ in(U_58,U_59)
& ? [U_57] :
( U_58 = apply(U_61,U_57)
& in(U_57,U_60)
& in(U_57,relation_dom(U_61)) ) )
| ( ! [U_56] :
( U_58 != apply(U_61,U_56)
| ~ in(U_56,U_60)
| ~ in(U_56,relation_dom(U_61)) )
& in(U_58,U_59) ) ) )
& ( ! [U_55] :
( ( in(U_55,U_59)
| ! [U_54] :
( U_55 != apply(U_61,U_54)
| ~ in(U_54,U_60)
| ~ in(U_54,relation_dom(U_61)) ) )
& ( ? [U_53] :
( U_55 = apply(U_61,U_53)
& in(U_53,U_60)
& in(U_53,relation_dom(U_61)) )
| ~ in(U_55,U_59) ) )
| U_59 != relation_image(U_61,U_60) ) )
| ~ function(U_61)
| ~ relation(U_61) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_61] :
( ( ! [U_69,U_67] :
( U_67 = relation_image(U_61,U_69)
| ? [U_65] :
( ~ in(U_65,U_67)
& ? [U_57] :
( U_65 = apply(U_61,U_57)
& in(U_57,U_69)
& in(U_57,relation_dom(U_61)) ) )
| ? [U_64] :
( ! [U_56] :
( U_64 != apply(U_61,U_56)
| ~ in(U_56,U_69)
| ~ in(U_56,relation_dom(U_61)) )
& in(U_64,U_67) ) )
& ! [U_68,U_66] :
( ( ! [U_63] :
( in(U_63,U_66)
| ! [U_54] :
( U_63 != apply(U_61,U_54)
| ~ in(U_54,U_68)
| ~ in(U_54,relation_dom(U_61)) ) )
& ! [U_62] :
( ? [U_53] :
( U_62 = apply(U_61,U_53)
& in(U_53,U_68)
& in(U_53,relation_dom(U_61)) )
| ~ in(U_62,U_66) ) )
| U_66 != relation_image(U_61,U_68) ) )
| ~ function(U_61)
| ~ relation(U_61) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
fof(f_16_4,plain,
! [U_61] :
( ( ! [U_69,U_67] :
( U_67 = relation_image(U_61,U_69)
| ? [U_65] :
( ~ in(U_65,U_67)
& ? [U_57] :
( U_65 = apply(U_61,U_57)
& in(U_57,U_69)
& in(U_57,relation_dom(U_61)) ) )
| ? [U_64] :
( ! [U_56] :
( U_64 != apply(U_61,U_56)
| ~ in(U_56,U_69)
| ~ in(U_56,relation_dom(U_61)) )
& in(U_64,U_67) ) )
& ! [U_68,U_66] :
( ( ! [U_63] :
( in(U_63,U_66)
| ! [U_54] :
( U_63 != apply(U_61,U_54)
| ~ in(U_54,U_68)
| ~ in(U_54,relation_dom(U_61)) ) )
& ! [U_62] :
( ( U_62 = apply(U_61,sK9(U_61,U_68,U_66,U_62))
& in(sK9(U_61,U_68,U_66,U_62),U_68)
& in(sK9(U_61,U_68,U_66,U_62),relation_dom(U_61)) )
| ~ in(U_62,U_66) ) )
| U_66 != relation_image(U_61,U_68) ) )
| ~ function(U_61)
| ~ relation(U_61) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_53,sK9(U_61,U_68,U_66,U_62))],[f_16_3]) ).
fof(f_16_5,plain,
! [U_61] :
( ( ! [U_69,U_67] :
( U_67 = relation_image(U_61,U_69)
| ? [U_65] :
( ~ in(U_65,U_67)
& ? [U_57] :
( U_65 = apply(U_61,U_57)
& in(U_57,U_69)
& in(U_57,relation_dom(U_61)) ) )
| ( ! [U_56] :
( sK10(U_61,U_69,U_67) != apply(U_61,U_56)
| ~ in(U_56,U_69)
| ~ in(U_56,relation_dom(U_61)) )
& in(sK10(U_61,U_69,U_67),U_67) ) )
& ! [U_68,U_66] :
( ( ! [U_63] :
( in(U_63,U_66)
| ! [U_54] :
( U_63 != apply(U_61,U_54)
| ~ in(U_54,U_68)
| ~ in(U_54,relation_dom(U_61)) ) )
& ! [U_62] :
( ( U_62 = apply(U_61,sK9(U_61,U_68,U_66,U_62))
& in(sK9(U_61,U_68,U_66,U_62),U_68)
& in(sK9(U_61,U_68,U_66,U_62),relation_dom(U_61)) )
| ~ in(U_62,U_66) ) )
| U_66 != relation_image(U_61,U_68) ) )
| ~ function(U_61)
| ~ relation(U_61) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_64,sK10(U_61,U_69,U_67))],[f_16_4]) ).
fof(f_16_6,plain,
! [U_61] :
( ( ! [U_69,U_67] :
( U_67 = relation_image(U_61,U_69)
| ( ~ in(sK11(U_61,U_69,U_67),U_67)
& ? [U_57] :
( sK11(U_61,U_69,U_67) = apply(U_61,U_57)
& in(U_57,U_69)
& in(U_57,relation_dom(U_61)) ) )
| ( ! [U_56] :
( sK10(U_61,U_69,U_67) != apply(U_61,U_56)
| ~ in(U_56,U_69)
| ~ in(U_56,relation_dom(U_61)) )
& in(sK10(U_61,U_69,U_67),U_67) ) )
& ! [U_68,U_66] :
( ( ! [U_63] :
( in(U_63,U_66)
| ! [U_54] :
( U_63 != apply(U_61,U_54)
| ~ in(U_54,U_68)
| ~ in(U_54,relation_dom(U_61)) ) )
& ! [U_62] :
( ( U_62 = apply(U_61,sK9(U_61,U_68,U_66,U_62))
& in(sK9(U_61,U_68,U_66,U_62),U_68)
& in(sK9(U_61,U_68,U_66,U_62),relation_dom(U_61)) )
| ~ in(U_62,U_66) ) )
| U_66 != relation_image(U_61,U_68) ) )
| ~ function(U_61)
| ~ relation(U_61) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_65,sK11(U_61,U_69,U_67))],[f_16_5]) ).
fof(f_16_7,plain,
! [U_61] :
( ( ! [U_69,U_67] :
( U_67 = relation_image(U_61,U_69)
| ( ~ in(sK11(U_61,U_69,U_67),U_67)
& sK11(U_61,U_69,U_67) = apply(U_61,sK12(U_61,U_69,U_67))
& in(sK12(U_61,U_69,U_67),U_69)
& in(sK12(U_61,U_69,U_67),relation_dom(U_61)) )
| ( ! [U_56] :
( sK10(U_61,U_69,U_67) != apply(U_61,U_56)
| ~ in(U_56,U_69)
| ~ in(U_56,relation_dom(U_61)) )
& in(sK10(U_61,U_69,U_67),U_67) ) )
& ! [U_68,U_66] :
( ( ! [U_63] :
( in(U_63,U_66)
| ! [U_54] :
( U_63 != apply(U_61,U_54)
| ~ in(U_54,U_68)
| ~ in(U_54,relation_dom(U_61)) ) )
& ! [U_62] :
( ( U_62 = apply(U_61,sK9(U_61,U_68,U_66,U_62))
& in(sK9(U_61,U_68,U_66,U_62),U_68)
& in(sK9(U_61,U_68,U_66,U_62),relation_dom(U_61)) )
| ~ in(U_62,U_66) ) )
| U_66 != relation_image(U_61,U_68) ) )
| ~ function(U_61)
| ~ relation(U_61) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_57,sK12(U_61,U_69,U_67))],[f_16_6]) ).
cnf(f_16_8,plain,
( in(sK9(U_61,U_68,U_66,U_62),relation_dom(U_61))
| ~ in(U_62,U_66)
| U_66 != relation_image(U_61,U_68)
| ~ function(U_61)
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_9,plain,
( in(sK9(U_61,U_68,U_66,U_62),U_68)
| ~ in(U_62,U_66)
| U_66 != relation_image(U_61,U_68)
| ~ function(U_61)
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_10,plain,
( U_62 = apply(U_61,sK9(U_61,U_68,U_66,U_62))
| ~ in(U_62,U_66)
| U_66 != relation_image(U_61,U_68)
| ~ function(U_61)
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_11,plain,
( in(U_63,U_66)
| U_63 != apply(U_61,U_54)
| ~ in(U_54,U_68)
| ~ in(U_54,relation_dom(U_61))
| U_66 != relation_image(U_61,U_68)
| ~ function(U_61)
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_12,plain,
( in(sK12(U_61,U_69,U_67),relation_dom(U_61))
| in(sK10(U_61,U_69,U_67),U_67)
| U_67 = relation_image(U_61,U_69)
| ~ function(U_61)
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_13,plain,
( in(sK12(U_61,U_69,U_67),U_69)
| in(sK10(U_61,U_69,U_67),U_67)
| U_67 = relation_image(U_61,U_69)
| ~ function(U_61)
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_14,plain,
( sK11(U_61,U_69,U_67) = apply(U_61,sK12(U_61,U_69,U_67))
| in(sK10(U_61,U_69,U_67),U_67)
| U_67 = relation_image(U_61,U_69)
| ~ function(U_61)
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_15,plain,
( ~ in(sK11(U_61,U_69,U_67),U_67)
| in(sK10(U_61,U_69,U_67),U_67)
| U_67 = relation_image(U_61,U_69)
| ~ function(U_61)
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_16,plain,
( in(sK12(U_61,U_69,U_67),relation_dom(U_61))
| sK10(U_61,U_69,U_67) != apply(U_61,U_56)
| ~ in(U_56,U_69)
| ~ in(U_56,relation_dom(U_61))
| U_67 = relation_image(U_61,U_69)
| ~ function(U_61)
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_17,plain,
( in(sK12(U_61,U_69,U_67),U_69)
| sK10(U_61,U_69,U_67) != apply(U_61,U_56)
| ~ in(U_56,U_69)
| ~ in(U_56,relation_dom(U_61))
| U_67 = relation_image(U_61,U_69)
| ~ function(U_61)
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_18,plain,
( sK11(U_61,U_69,U_67) = apply(U_61,sK12(U_61,U_69,U_67))
| sK10(U_61,U_69,U_67) != apply(U_61,U_56)
| ~ in(U_56,U_69)
| ~ in(U_56,relation_dom(U_61))
| U_67 = relation_image(U_61,U_69)
| ~ function(U_61)
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_19,plain,
( ~ in(sK11(U_61,U_69,U_67),U_67)
| sK10(U_61,U_69,U_67) != apply(U_61,U_56)
| ~ in(U_56,U_69)
| ~ in(U_56,relation_dom(U_61))
| U_67 = relation_image(U_61,U_69)
| ~ function(U_61)
| ~ relation(U_61) ),
inference(clausify,[status(thm)],[f_16_7]) ).
fof(f_17_1,plain,
! [A,B] :
( ! [C] :
( ( ( C = relation_rng_restriction(A,B)
| ? [D,E] :
( ( ~ in(ordered_pair(D,E),C)
& in(ordered_pair(D,E),B)
& in(E,A) )
| ( ( ~ in(ordered_pair(D,E),B)
| ~ in(E,A) )
& in(ordered_pair(D,E),C) ) ) )
& ( ! [D,E] :
( ( in(ordered_pair(D,E),C)
| ~ in(ordered_pair(D,E),B)
| ~ in(E,A) )
& ( ( in(ordered_pair(D,E),B)
& in(E,A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_rng_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[d12_relat_1]) ).
fof(f_17_2,plain,
! [U_76,U_75] :
( ! [U_74] :
( ( ( U_74 = relation_rng_restriction(U_76,U_75)
| ? [U_73,U_72] :
( ( ~ in(ordered_pair(U_73,U_72),U_74)
& in(ordered_pair(U_73,U_72),U_75)
& in(U_72,U_76) )
| ( ( ~ in(ordered_pair(U_73,U_72),U_75)
| ~ in(U_72,U_76) )
& in(ordered_pair(U_73,U_72),U_74) ) ) )
& ( ! [U_71,U_70] :
( ( in(ordered_pair(U_71,U_70),U_74)
| ~ in(ordered_pair(U_71,U_70),U_75)
| ~ in(U_70,U_76) )
& ( ( in(ordered_pair(U_71,U_70),U_75)
& in(U_70,U_76) )
| ~ in(ordered_pair(U_71,U_70),U_74) ) )
| U_74 != relation_rng_restriction(U_76,U_75) ) )
| ~ relation(U_74) )
| ~ relation(U_75) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_76,U_75] :
( ! [U_74] :
( ( ( U_74 = relation_rng_restriction(U_76,U_75)
| ? [U_84,U_82] :
( ~ in(ordered_pair(U_84,U_82),U_74)
& in(ordered_pair(U_84,U_82),U_75)
& in(U_82,U_76) )
| ? [U_83,U_81] :
( ( ~ in(ordered_pair(U_83,U_81),U_75)
| ~ in(U_81,U_76) )
& in(ordered_pair(U_83,U_81),U_74) ) )
& ( ( ! [U_80,U_78] :
( in(ordered_pair(U_80,U_78),U_74)
| ~ in(ordered_pair(U_80,U_78),U_75)
| ~ in(U_78,U_76) )
& ! [U_79,U_77] :
( ( in(ordered_pair(U_79,U_77),U_75)
& in(U_77,U_76) )
| ~ in(ordered_pair(U_79,U_77),U_74) ) )
| U_74 != relation_rng_restriction(U_76,U_75) ) )
| ~ relation(U_74) )
| ~ relation(U_75) ),
inference(miniscope,[status(thm)],[f_17_2]) ).
fof(f_17_4,plain,
! [U_76,U_75] :
( ! [U_74] :
( ( ( U_74 = relation_rng_restriction(U_76,U_75)
| ? [U_84,U_82] :
( ~ in(ordered_pair(U_84,U_82),U_74)
& in(ordered_pair(U_84,U_82),U_75)
& in(U_82,U_76) )
| ? [U_81] :
( ( ~ in(ordered_pair(sK13(U_76,U_75,U_74),U_81),U_75)
| ~ in(U_81,U_76) )
& in(ordered_pair(sK13(U_76,U_75,U_74),U_81),U_74) ) )
& ( ( ! [U_80,U_78] :
( in(ordered_pair(U_80,U_78),U_74)
| ~ in(ordered_pair(U_80,U_78),U_75)
| ~ in(U_78,U_76) )
& ! [U_79,U_77] :
( ( in(ordered_pair(U_79,U_77),U_75)
& in(U_77,U_76) )
| ~ in(ordered_pair(U_79,U_77),U_74) ) )
| U_74 != relation_rng_restriction(U_76,U_75) ) )
| ~ relation(U_74) )
| ~ relation(U_75) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_83,sK13(U_76,U_75,U_74))],[f_17_3]) ).
fof(f_17_5,plain,
! [U_76,U_75] :
( ! [U_74] :
( ( ( U_74 = relation_rng_restriction(U_76,U_75)
| ? [U_84,U_82] :
( ~ in(ordered_pair(U_84,U_82),U_74)
& in(ordered_pair(U_84,U_82),U_75)
& in(U_82,U_76) )
| ( ( ~ in(ordered_pair(sK13(U_76,U_75,U_74),sK14(U_76,U_75,U_74)),U_75)
| ~ in(sK14(U_76,U_75,U_74),U_76) )
& in(ordered_pair(sK13(U_76,U_75,U_74),sK14(U_76,U_75,U_74)),U_74) ) )
& ( ( ! [U_80,U_78] :
( in(ordered_pair(U_80,U_78),U_74)
| ~ in(ordered_pair(U_80,U_78),U_75)
| ~ in(U_78,U_76) )
& ! [U_79,U_77] :
( ( in(ordered_pair(U_79,U_77),U_75)
& in(U_77,U_76) )
| ~ in(ordered_pair(U_79,U_77),U_74) ) )
| U_74 != relation_rng_restriction(U_76,U_75) ) )
| ~ relation(U_74) )
| ~ relation(U_75) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_81,sK14(U_76,U_75,U_74))],[f_17_4]) ).
fof(f_17_6,plain,
! [U_76,U_75] :
( ! [U_74] :
( ( ( U_74 = relation_rng_restriction(U_76,U_75)
| ? [U_82] :
( ~ in(ordered_pair(sK15(U_76,U_75,U_74),U_82),U_74)
& in(ordered_pair(sK15(U_76,U_75,U_74),U_82),U_75)
& in(U_82,U_76) )
| ( ( ~ in(ordered_pair(sK13(U_76,U_75,U_74),sK14(U_76,U_75,U_74)),U_75)
| ~ in(sK14(U_76,U_75,U_74),U_76) )
& in(ordered_pair(sK13(U_76,U_75,U_74),sK14(U_76,U_75,U_74)),U_74) ) )
& ( ( ! [U_80,U_78] :
( in(ordered_pair(U_80,U_78),U_74)
| ~ in(ordered_pair(U_80,U_78),U_75)
| ~ in(U_78,U_76) )
& ! [U_79,U_77] :
( ( in(ordered_pair(U_79,U_77),U_75)
& in(U_77,U_76) )
| ~ in(ordered_pair(U_79,U_77),U_74) ) )
| U_74 != relation_rng_restriction(U_76,U_75) ) )
| ~ relation(U_74) )
| ~ relation(U_75) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_84,sK15(U_76,U_75,U_74))],[f_17_5]) ).
fof(f_17_7,plain,
! [U_76,U_75] :
( ! [U_74] :
( ( ( U_74 = relation_rng_restriction(U_76,U_75)
| ( ~ in(ordered_pair(sK15(U_76,U_75,U_74),sK16(U_76,U_75,U_74)),U_74)
& in(ordered_pair(sK15(U_76,U_75,U_74),sK16(U_76,U_75,U_74)),U_75)
& in(sK16(U_76,U_75,U_74),U_76) )
| ( ( ~ in(ordered_pair(sK13(U_76,U_75,U_74),sK14(U_76,U_75,U_74)),U_75)
| ~ in(sK14(U_76,U_75,U_74),U_76) )
& in(ordered_pair(sK13(U_76,U_75,U_74),sK14(U_76,U_75,U_74)),U_74) ) )
& ( ( ! [U_80,U_78] :
( in(ordered_pair(U_80,U_78),U_74)
| ~ in(ordered_pair(U_80,U_78),U_75)
| ~ in(U_78,U_76) )
& ! [U_79,U_77] :
( ( in(ordered_pair(U_79,U_77),U_75)
& in(U_77,U_76) )
| ~ in(ordered_pair(U_79,U_77),U_74) ) )
| U_74 != relation_rng_restriction(U_76,U_75) ) )
| ~ relation(U_74) )
| ~ relation(U_75) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_82,sK16(U_76,U_75,U_74))],[f_17_6]) ).
cnf(f_17_8,plain,
( in(U_77,U_76)
| ~ in(ordered_pair(U_79,U_77),U_74)
| U_74 != relation_rng_restriction(U_76,U_75)
| ~ relation(U_74)
| ~ relation(U_75) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_9,plain,
( in(ordered_pair(U_79,U_77),U_75)
| ~ in(ordered_pair(U_79,U_77),U_74)
| U_74 != relation_rng_restriction(U_76,U_75)
| ~ relation(U_74)
| ~ relation(U_75) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_10,plain,
( in(ordered_pair(U_80,U_78),U_74)
| ~ in(ordered_pair(U_80,U_78),U_75)
| ~ in(U_78,U_76)
| U_74 != relation_rng_restriction(U_76,U_75)
| ~ relation(U_74)
| ~ relation(U_75) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_11,plain,
( in(sK16(U_76,U_75,U_74),U_76)
| in(ordered_pair(sK13(U_76,U_75,U_74),sK14(U_76,U_75,U_74)),U_74)
| U_74 = relation_rng_restriction(U_76,U_75)
| ~ relation(U_74)
| ~ relation(U_75) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_12,plain,
( in(ordered_pair(sK15(U_76,U_75,U_74),sK16(U_76,U_75,U_74)),U_75)
| in(ordered_pair(sK13(U_76,U_75,U_74),sK14(U_76,U_75,U_74)),U_74)
| U_74 = relation_rng_restriction(U_76,U_75)
| ~ relation(U_74)
| ~ relation(U_75) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_13,plain,
( ~ in(ordered_pair(sK15(U_76,U_75,U_74),sK16(U_76,U_75,U_74)),U_74)
| in(ordered_pair(sK13(U_76,U_75,U_74),sK14(U_76,U_75,U_74)),U_74)
| U_74 = relation_rng_restriction(U_76,U_75)
| ~ relation(U_74)
| ~ relation(U_75) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_14,plain,
( in(sK16(U_76,U_75,U_74),U_76)
| ~ in(ordered_pair(sK13(U_76,U_75,U_74),sK14(U_76,U_75,U_74)),U_75)
| ~ in(sK14(U_76,U_75,U_74),U_76)
| U_74 = relation_rng_restriction(U_76,U_75)
| ~ relation(U_74)
| ~ relation(U_75) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_15,plain,
( in(ordered_pair(sK15(U_76,U_75,U_74),sK16(U_76,U_75,U_74)),U_75)
| ~ in(ordered_pair(sK13(U_76,U_75,U_74),sK14(U_76,U_75,U_74)),U_75)
| ~ in(sK14(U_76,U_75,U_74),U_76)
| U_74 = relation_rng_restriction(U_76,U_75)
| ~ relation(U_74)
| ~ relation(U_75) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_16,plain,
( ~ in(ordered_pair(sK15(U_76,U_75,U_74),sK16(U_76,U_75,U_74)),U_74)
| ~ in(ordered_pair(sK13(U_76,U_75,U_74),sK14(U_76,U_75,U_74)),U_75)
| ~ in(sK14(U_76,U_75,U_74),U_76)
| U_74 = relation_rng_restriction(U_76,U_75)
| ~ relation(U_74)
| ~ relation(U_75) ),
inference(clausify,[status(thm)],[f_17_7]) ).
fof(f_18_1,plain,
! [A] :
( ( ( antisymmetric(A)
| ~ is_antisymmetric_in(A,relation_field(A)) )
& ( is_antisymmetric_in(A,relation_field(A))
| ~ antisymmetric(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d12_relat_2]) ).
fof(f_18_2,plain,
! [U_85] :
( ( ( antisymmetric(U_85)
| ~ is_antisymmetric_in(U_85,relation_field(U_85)) )
& ( is_antisymmetric_in(U_85,relation_field(U_85))
| ~ antisymmetric(U_85) ) )
| ~ relation(U_85) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( is_antisymmetric_in(U_85,relation_field(U_85))
| ~ antisymmetric(U_85)
| ~ relation(U_85) ),
inference(clausify,[status(thm)],[f_18_2]) ).
cnf(f_18_4,plain,
( antisymmetric(U_85)
| ~ is_antisymmetric_in(U_85,relation_field(U_85))
| ~ relation(U_85) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [A] :
( ! [B,C] :
( ( C = relation_inverse_image(A,B)
| ? [D] :
( ( ~ in(D,C)
& in(apply(A,D),B)
& in(D,relation_dom(A)) )
| ( ( ~ in(apply(A,D),B)
| ~ in(D,relation_dom(A)) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ~ in(apply(A,D),B)
| ~ in(D,relation_dom(A)) )
& ( ( in(apply(A,D),B)
& in(D,relation_dom(A)) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d13_funct_1]) ).
fof(f_19_2,plain,
! [U_90] :
( ! [U_89,U_88] :
( ( U_88 = relation_inverse_image(U_90,U_89)
| ? [U_87] :
( ( ~ in(U_87,U_88)
& in(apply(U_90,U_87),U_89)
& in(U_87,relation_dom(U_90)) )
| ( ( ~ in(apply(U_90,U_87),U_89)
| ~ in(U_87,relation_dom(U_90)) )
& in(U_87,U_88) ) ) )
& ( ! [U_86] :
( ( in(U_86,U_88)
| ~ in(apply(U_90,U_86),U_89)
| ~ in(U_86,relation_dom(U_90)) )
& ( ( in(apply(U_90,U_86),U_89)
& in(U_86,relation_dom(U_90)) )
| ~ in(U_86,U_88) ) )
| U_88 != relation_inverse_image(U_90,U_89) ) )
| ~ function(U_90)
| ~ relation(U_90) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_90] :
( ( ! [U_98,U_96] :
( U_96 = relation_inverse_image(U_90,U_98)
| ? [U_94] :
( ~ in(U_94,U_96)
& in(apply(U_90,U_94),U_98)
& in(U_94,relation_dom(U_90)) )
| ? [U_93] :
( ( ~ in(apply(U_90,U_93),U_98)
| ~ in(U_93,relation_dom(U_90)) )
& in(U_93,U_96) ) )
& ! [U_97,U_95] :
( ( ! [U_92] :
( in(U_92,U_95)
| ~ in(apply(U_90,U_92),U_97)
| ~ in(U_92,relation_dom(U_90)) )
& ! [U_91] :
( ( in(apply(U_90,U_91),U_97)
& in(U_91,relation_dom(U_90)) )
| ~ in(U_91,U_95) ) )
| U_95 != relation_inverse_image(U_90,U_97) ) )
| ~ function(U_90)
| ~ relation(U_90) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
fof(f_19_4,plain,
! [U_90] :
( ( ! [U_98,U_96] :
( U_96 = relation_inverse_image(U_90,U_98)
| ? [U_94] :
( ~ in(U_94,U_96)
& in(apply(U_90,U_94),U_98)
& in(U_94,relation_dom(U_90)) )
| ( ( ~ in(apply(U_90,sK17(U_90,U_98,U_96)),U_98)
| ~ in(sK17(U_90,U_98,U_96),relation_dom(U_90)) )
& in(sK17(U_90,U_98,U_96),U_96) ) )
& ! [U_97,U_95] :
( ( ! [U_92] :
( in(U_92,U_95)
| ~ in(apply(U_90,U_92),U_97)
| ~ in(U_92,relation_dom(U_90)) )
& ! [U_91] :
( ( in(apply(U_90,U_91),U_97)
& in(U_91,relation_dom(U_90)) )
| ~ in(U_91,U_95) ) )
| U_95 != relation_inverse_image(U_90,U_97) ) )
| ~ function(U_90)
| ~ relation(U_90) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_93,sK17(U_90,U_98,U_96))],[f_19_3]) ).
fof(f_19_5,plain,
! [U_90] :
( ( ! [U_98,U_96] :
( U_96 = relation_inverse_image(U_90,U_98)
| ( ~ in(sK18(U_90,U_98,U_96),U_96)
& in(apply(U_90,sK18(U_90,U_98,U_96)),U_98)
& in(sK18(U_90,U_98,U_96),relation_dom(U_90)) )
| ( ( ~ in(apply(U_90,sK17(U_90,U_98,U_96)),U_98)
| ~ in(sK17(U_90,U_98,U_96),relation_dom(U_90)) )
& in(sK17(U_90,U_98,U_96),U_96) ) )
& ! [U_97,U_95] :
( ( ! [U_92] :
( in(U_92,U_95)
| ~ in(apply(U_90,U_92),U_97)
| ~ in(U_92,relation_dom(U_90)) )
& ! [U_91] :
( ( in(apply(U_90,U_91),U_97)
& in(U_91,relation_dom(U_90)) )
| ~ in(U_91,U_95) ) )
| U_95 != relation_inverse_image(U_90,U_97) ) )
| ~ function(U_90)
| ~ relation(U_90) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_94,sK18(U_90,U_98,U_96))],[f_19_4]) ).
cnf(f_19_6,plain,
( in(U_91,relation_dom(U_90))
| ~ in(U_91,U_95)
| U_95 != relation_inverse_image(U_90,U_97)
| ~ function(U_90)
| ~ relation(U_90) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_7,plain,
( in(apply(U_90,U_91),U_97)
| ~ in(U_91,U_95)
| U_95 != relation_inverse_image(U_90,U_97)
| ~ function(U_90)
| ~ relation(U_90) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_8,plain,
( in(U_92,U_95)
| ~ in(apply(U_90,U_92),U_97)
| ~ in(U_92,relation_dom(U_90))
| U_95 != relation_inverse_image(U_90,U_97)
| ~ function(U_90)
| ~ relation(U_90) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_9,plain,
( in(sK18(U_90,U_98,U_96),relation_dom(U_90))
| in(sK17(U_90,U_98,U_96),U_96)
| U_96 = relation_inverse_image(U_90,U_98)
| ~ function(U_90)
| ~ relation(U_90) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_10,plain,
( in(apply(U_90,sK18(U_90,U_98,U_96)),U_98)
| in(sK17(U_90,U_98,U_96),U_96)
| U_96 = relation_inverse_image(U_90,U_98)
| ~ function(U_90)
| ~ relation(U_90) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_11,plain,
( ~ in(sK18(U_90,U_98,U_96),U_96)
| in(sK17(U_90,U_98,U_96),U_96)
| U_96 = relation_inverse_image(U_90,U_98)
| ~ function(U_90)
| ~ relation(U_90) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_12,plain,
( in(sK18(U_90,U_98,U_96),relation_dom(U_90))
| ~ in(apply(U_90,sK17(U_90,U_98,U_96)),U_98)
| ~ in(sK17(U_90,U_98,U_96),relation_dom(U_90))
| U_96 = relation_inverse_image(U_90,U_98)
| ~ function(U_90)
| ~ relation(U_90) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_13,plain,
( in(apply(U_90,sK18(U_90,U_98,U_96)),U_98)
| ~ in(apply(U_90,sK17(U_90,U_98,U_96)),U_98)
| ~ in(sK17(U_90,U_98,U_96),relation_dom(U_90))
| U_96 = relation_inverse_image(U_90,U_98)
| ~ function(U_90)
| ~ relation(U_90) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_14,plain,
( ~ in(sK18(U_90,U_98,U_96),U_96)
| ~ in(apply(U_90,sK17(U_90,U_98,U_96)),U_98)
| ~ in(sK17(U_90,U_98,U_96),relation_dom(U_90))
| U_96 = relation_inverse_image(U_90,U_98)
| ~ function(U_90)
| ~ relation(U_90) ),
inference(clausify,[status(thm)],[f_19_5]) ).
fof(f_20_1,plain,
! [A] :
( ! [B,C] :
( ( C = relation_image(A,B)
| ? [D] :
( ( ~ in(D,C)
& ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) ) )
| ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) ) )
& ( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d13_relat_1]) ).
fof(f_20_2,plain,
! [U_107] :
( ! [U_106,U_105] :
( ( U_105 = relation_image(U_107,U_106)
| ? [U_104] :
( ( ~ in(U_104,U_105)
& ? [U_103] :
( in(U_103,U_106)
& in(ordered_pair(U_103,U_104),U_107) ) )
| ( ! [U_102] :
( ~ in(U_102,U_106)
| ~ in(ordered_pair(U_102,U_104),U_107) )
& in(U_104,U_105) ) ) )
& ( ! [U_101] :
( ( in(U_101,U_105)
| ! [U_100] :
( ~ in(U_100,U_106)
| ~ in(ordered_pair(U_100,U_101),U_107) ) )
& ( ? [U_99] :
( in(U_99,U_106)
& in(ordered_pair(U_99,U_101),U_107) )
| ~ in(U_101,U_105) ) )
| U_105 != relation_image(U_107,U_106) ) )
| ~ relation(U_107) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_107] :
( ( ! [U_115,U_113] :
( U_113 = relation_image(U_107,U_115)
| ? [U_111] :
( ~ in(U_111,U_113)
& ? [U_103] :
( in(U_103,U_115)
& in(ordered_pair(U_103,U_111),U_107) ) )
| ? [U_110] :
( ! [U_102] :
( ~ in(U_102,U_115)
| ~ in(ordered_pair(U_102,U_110),U_107) )
& in(U_110,U_113) ) )
& ! [U_114,U_112] :
( ( ! [U_109] :
( in(U_109,U_112)
| ! [U_100] :
( ~ in(U_100,U_114)
| ~ in(ordered_pair(U_100,U_109),U_107) ) )
& ! [U_108] :
( ? [U_99] :
( in(U_99,U_114)
& in(ordered_pair(U_99,U_108),U_107) )
| ~ in(U_108,U_112) ) )
| U_112 != relation_image(U_107,U_114) ) )
| ~ relation(U_107) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
fof(f_20_4,plain,
! [U_107] :
( ( ! [U_115,U_113] :
( U_113 = relation_image(U_107,U_115)
| ? [U_111] :
( ~ in(U_111,U_113)
& ? [U_103] :
( in(U_103,U_115)
& in(ordered_pair(U_103,U_111),U_107) ) )
| ? [U_110] :
( ! [U_102] :
( ~ in(U_102,U_115)
| ~ in(ordered_pair(U_102,U_110),U_107) )
& in(U_110,U_113) ) )
& ! [U_114,U_112] :
( ( ! [U_109] :
( in(U_109,U_112)
| ! [U_100] :
( ~ in(U_100,U_114)
| ~ in(ordered_pair(U_100,U_109),U_107) ) )
& ! [U_108] :
( ( in(sK19(U_107,U_114,U_112,U_108),U_114)
& in(ordered_pair(sK19(U_107,U_114,U_112,U_108),U_108),U_107) )
| ~ in(U_108,U_112) ) )
| U_112 != relation_image(U_107,U_114) ) )
| ~ relation(U_107) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_99,sK19(U_107,U_114,U_112,U_108))],[f_20_3]) ).
fof(f_20_5,plain,
! [U_107] :
( ( ! [U_115,U_113] :
( U_113 = relation_image(U_107,U_115)
| ? [U_111] :
( ~ in(U_111,U_113)
& ? [U_103] :
( in(U_103,U_115)
& in(ordered_pair(U_103,U_111),U_107) ) )
| ( ! [U_102] :
( ~ in(U_102,U_115)
| ~ in(ordered_pair(U_102,sK20(U_107,U_115,U_113)),U_107) )
& in(sK20(U_107,U_115,U_113),U_113) ) )
& ! [U_114,U_112] :
( ( ! [U_109] :
( in(U_109,U_112)
| ! [U_100] :
( ~ in(U_100,U_114)
| ~ in(ordered_pair(U_100,U_109),U_107) ) )
& ! [U_108] :
( ( in(sK19(U_107,U_114,U_112,U_108),U_114)
& in(ordered_pair(sK19(U_107,U_114,U_112,U_108),U_108),U_107) )
| ~ in(U_108,U_112) ) )
| U_112 != relation_image(U_107,U_114) ) )
| ~ relation(U_107) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_110,sK20(U_107,U_115,U_113))],[f_20_4]) ).
fof(f_20_6,plain,
! [U_107] :
( ( ! [U_115,U_113] :
( U_113 = relation_image(U_107,U_115)
| ( ~ in(sK21(U_107,U_115,U_113),U_113)
& ? [U_103] :
( in(U_103,U_115)
& in(ordered_pair(U_103,sK21(U_107,U_115,U_113)),U_107) ) )
| ( ! [U_102] :
( ~ in(U_102,U_115)
| ~ in(ordered_pair(U_102,sK20(U_107,U_115,U_113)),U_107) )
& in(sK20(U_107,U_115,U_113),U_113) ) )
& ! [U_114,U_112] :
( ( ! [U_109] :
( in(U_109,U_112)
| ! [U_100] :
( ~ in(U_100,U_114)
| ~ in(ordered_pair(U_100,U_109),U_107) ) )
& ! [U_108] :
( ( in(sK19(U_107,U_114,U_112,U_108),U_114)
& in(ordered_pair(sK19(U_107,U_114,U_112,U_108),U_108),U_107) )
| ~ in(U_108,U_112) ) )
| U_112 != relation_image(U_107,U_114) ) )
| ~ relation(U_107) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_111,sK21(U_107,U_115,U_113))],[f_20_5]) ).
fof(f_20_7,plain,
! [U_107] :
( ( ! [U_115,U_113] :
( U_113 = relation_image(U_107,U_115)
| ( ~ in(sK21(U_107,U_115,U_113),U_113)
& in(sK22(U_107,U_115,U_113),U_115)
& in(ordered_pair(sK22(U_107,U_115,U_113),sK21(U_107,U_115,U_113)),U_107) )
| ( ! [U_102] :
( ~ in(U_102,U_115)
| ~ in(ordered_pair(U_102,sK20(U_107,U_115,U_113)),U_107) )
& in(sK20(U_107,U_115,U_113),U_113) ) )
& ! [U_114,U_112] :
( ( ! [U_109] :
( in(U_109,U_112)
| ! [U_100] :
( ~ in(U_100,U_114)
| ~ in(ordered_pair(U_100,U_109),U_107) ) )
& ! [U_108] :
( ( in(sK19(U_107,U_114,U_112,U_108),U_114)
& in(ordered_pair(sK19(U_107,U_114,U_112,U_108),U_108),U_107) )
| ~ in(U_108,U_112) ) )
| U_112 != relation_image(U_107,U_114) ) )
| ~ relation(U_107) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_103,sK22(U_107,U_115,U_113))],[f_20_6]) ).
cnf(f_20_8,plain,
( in(ordered_pair(sK19(U_107,U_114,U_112,U_108),U_108),U_107)
| ~ in(U_108,U_112)
| U_112 != relation_image(U_107,U_114)
| ~ relation(U_107) ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_9,plain,
( in(sK19(U_107,U_114,U_112,U_108),U_114)
| ~ in(U_108,U_112)
| U_112 != relation_image(U_107,U_114)
| ~ relation(U_107) ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_10,plain,
( in(U_109,U_112)
| ~ in(U_100,U_114)
| ~ in(ordered_pair(U_100,U_109),U_107)
| U_112 != relation_image(U_107,U_114)
| ~ relation(U_107) ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_11,plain,
( in(ordered_pair(sK22(U_107,U_115,U_113),sK21(U_107,U_115,U_113)),U_107)
| in(sK20(U_107,U_115,U_113),U_113)
| U_113 = relation_image(U_107,U_115)
| ~ relation(U_107) ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_12,plain,
( in(sK22(U_107,U_115,U_113),U_115)
| in(sK20(U_107,U_115,U_113),U_113)
| U_113 = relation_image(U_107,U_115)
| ~ relation(U_107) ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_13,plain,
( ~ in(sK21(U_107,U_115,U_113),U_113)
| in(sK20(U_107,U_115,U_113),U_113)
| U_113 = relation_image(U_107,U_115)
| ~ relation(U_107) ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_14,plain,
( in(ordered_pair(sK22(U_107,U_115,U_113),sK21(U_107,U_115,U_113)),U_107)
| ~ in(U_102,U_115)
| ~ in(ordered_pair(U_102,sK20(U_107,U_115,U_113)),U_107)
| U_113 = relation_image(U_107,U_115)
| ~ relation(U_107) ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_15,plain,
( in(sK22(U_107,U_115,U_113),U_115)
| ~ in(U_102,U_115)
| ~ in(ordered_pair(U_102,sK20(U_107,U_115,U_113)),U_107)
| U_113 = relation_image(U_107,U_115)
| ~ relation(U_107) ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_16,plain,
( ~ in(sK21(U_107,U_115,U_113),U_113)
| ~ in(U_102,U_115)
| ~ in(ordered_pair(U_102,sK20(U_107,U_115,U_113)),U_107)
| U_113 = relation_image(U_107,U_115)
| ~ relation(U_107) ),
inference(clausify,[status(thm)],[f_20_7]) ).
fof(f_21_1,plain,
! [A] :
( ! [B,C] :
( ( C = relation_inverse_image(A,B)
| ? [D] :
( ( ~ in(D,C)
& ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) ) )
| ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) ) )
& ( ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d14_relat_1]) ).
fof(f_21_2,plain,
! [U_124] :
( ! [U_123,U_122] :
( ( U_122 = relation_inverse_image(U_124,U_123)
| ? [U_121] :
( ( ~ in(U_121,U_122)
& ? [U_120] :
( in(U_120,U_123)
& in(ordered_pair(U_121,U_120),U_124) ) )
| ( ! [U_119] :
( ~ in(U_119,U_123)
| ~ in(ordered_pair(U_121,U_119),U_124) )
& in(U_121,U_122) ) ) )
& ( ! [U_118] :
( ( in(U_118,U_122)
| ! [U_117] :
( ~ in(U_117,U_123)
| ~ in(ordered_pair(U_118,U_117),U_124) ) )
& ( ? [U_116] :
( in(U_116,U_123)
& in(ordered_pair(U_118,U_116),U_124) )
| ~ in(U_118,U_122) ) )
| U_122 != relation_inverse_image(U_124,U_123) ) )
| ~ relation(U_124) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_124] :
( ( ! [U_132,U_130] :
( U_130 = relation_inverse_image(U_124,U_132)
| ? [U_128] :
( ~ in(U_128,U_130)
& ? [U_120] :
( in(U_120,U_132)
& in(ordered_pair(U_128,U_120),U_124) ) )
| ? [U_127] :
( ! [U_119] :
( ~ in(U_119,U_132)
| ~ in(ordered_pair(U_127,U_119),U_124) )
& in(U_127,U_130) ) )
& ! [U_131,U_129] :
( ( ! [U_126] :
( in(U_126,U_129)
| ! [U_117] :
( ~ in(U_117,U_131)
| ~ in(ordered_pair(U_126,U_117),U_124) ) )
& ! [U_125] :
( ? [U_116] :
( in(U_116,U_131)
& in(ordered_pair(U_125,U_116),U_124) )
| ~ in(U_125,U_129) ) )
| U_129 != relation_inverse_image(U_124,U_131) ) )
| ~ relation(U_124) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
fof(f_21_4,plain,
! [U_124] :
( ( ! [U_132,U_130] :
( U_130 = relation_inverse_image(U_124,U_132)
| ? [U_128] :
( ~ in(U_128,U_130)
& ? [U_120] :
( in(U_120,U_132)
& in(ordered_pair(U_128,U_120),U_124) ) )
| ? [U_127] :
( ! [U_119] :
( ~ in(U_119,U_132)
| ~ in(ordered_pair(U_127,U_119),U_124) )
& in(U_127,U_130) ) )
& ! [U_131,U_129] :
( ( ! [U_126] :
( in(U_126,U_129)
| ! [U_117] :
( ~ in(U_117,U_131)
| ~ in(ordered_pair(U_126,U_117),U_124) ) )
& ! [U_125] :
( ( in(sK23(U_124,U_131,U_129,U_125),U_131)
& in(ordered_pair(U_125,sK23(U_124,U_131,U_129,U_125)),U_124) )
| ~ in(U_125,U_129) ) )
| U_129 != relation_inverse_image(U_124,U_131) ) )
| ~ relation(U_124) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_116,sK23(U_124,U_131,U_129,U_125))],[f_21_3]) ).
fof(f_21_5,plain,
! [U_124] :
( ( ! [U_132,U_130] :
( U_130 = relation_inverse_image(U_124,U_132)
| ? [U_128] :
( ~ in(U_128,U_130)
& ? [U_120] :
( in(U_120,U_132)
& in(ordered_pair(U_128,U_120),U_124) ) )
| ( ! [U_119] :
( ~ in(U_119,U_132)
| ~ in(ordered_pair(sK24(U_124,U_132,U_130),U_119),U_124) )
& in(sK24(U_124,U_132,U_130),U_130) ) )
& ! [U_131,U_129] :
( ( ! [U_126] :
( in(U_126,U_129)
| ! [U_117] :
( ~ in(U_117,U_131)
| ~ in(ordered_pair(U_126,U_117),U_124) ) )
& ! [U_125] :
( ( in(sK23(U_124,U_131,U_129,U_125),U_131)
& in(ordered_pair(U_125,sK23(U_124,U_131,U_129,U_125)),U_124) )
| ~ in(U_125,U_129) ) )
| U_129 != relation_inverse_image(U_124,U_131) ) )
| ~ relation(U_124) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_127,sK24(U_124,U_132,U_130))],[f_21_4]) ).
fof(f_21_6,plain,
! [U_124] :
( ( ! [U_132,U_130] :
( U_130 = relation_inverse_image(U_124,U_132)
| ( ~ in(sK25(U_124,U_132,U_130),U_130)
& ? [U_120] :
( in(U_120,U_132)
& in(ordered_pair(sK25(U_124,U_132,U_130),U_120),U_124) ) )
| ( ! [U_119] :
( ~ in(U_119,U_132)
| ~ in(ordered_pair(sK24(U_124,U_132,U_130),U_119),U_124) )
& in(sK24(U_124,U_132,U_130),U_130) ) )
& ! [U_131,U_129] :
( ( ! [U_126] :
( in(U_126,U_129)
| ! [U_117] :
( ~ in(U_117,U_131)
| ~ in(ordered_pair(U_126,U_117),U_124) ) )
& ! [U_125] :
( ( in(sK23(U_124,U_131,U_129,U_125),U_131)
& in(ordered_pair(U_125,sK23(U_124,U_131,U_129,U_125)),U_124) )
| ~ in(U_125,U_129) ) )
| U_129 != relation_inverse_image(U_124,U_131) ) )
| ~ relation(U_124) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_128,sK25(U_124,U_132,U_130))],[f_21_5]) ).
fof(f_21_7,plain,
! [U_124] :
( ( ! [U_132,U_130] :
( U_130 = relation_inverse_image(U_124,U_132)
| ( ~ in(sK25(U_124,U_132,U_130),U_130)
& in(sK26(U_124,U_132,U_130),U_132)
& in(ordered_pair(sK25(U_124,U_132,U_130),sK26(U_124,U_132,U_130)),U_124) )
| ( ! [U_119] :
( ~ in(U_119,U_132)
| ~ in(ordered_pair(sK24(U_124,U_132,U_130),U_119),U_124) )
& in(sK24(U_124,U_132,U_130),U_130) ) )
& ! [U_131,U_129] :
( ( ! [U_126] :
( in(U_126,U_129)
| ! [U_117] :
( ~ in(U_117,U_131)
| ~ in(ordered_pair(U_126,U_117),U_124) ) )
& ! [U_125] :
( ( in(sK23(U_124,U_131,U_129,U_125),U_131)
& in(ordered_pair(U_125,sK23(U_124,U_131,U_129,U_125)),U_124) )
| ~ in(U_125,U_129) ) )
| U_129 != relation_inverse_image(U_124,U_131) ) )
| ~ relation(U_124) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_120,sK26(U_124,U_132,U_130))],[f_21_6]) ).
cnf(f_21_8,plain,
( in(ordered_pair(U_125,sK23(U_124,U_131,U_129,U_125)),U_124)
| ~ in(U_125,U_129)
| U_129 != relation_inverse_image(U_124,U_131)
| ~ relation(U_124) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_9,plain,
( in(sK23(U_124,U_131,U_129,U_125),U_131)
| ~ in(U_125,U_129)
| U_129 != relation_inverse_image(U_124,U_131)
| ~ relation(U_124) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_10,plain,
( in(U_126,U_129)
| ~ in(U_117,U_131)
| ~ in(ordered_pair(U_126,U_117),U_124)
| U_129 != relation_inverse_image(U_124,U_131)
| ~ relation(U_124) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_11,plain,
( in(ordered_pair(sK25(U_124,U_132,U_130),sK26(U_124,U_132,U_130)),U_124)
| in(sK24(U_124,U_132,U_130),U_130)
| U_130 = relation_inverse_image(U_124,U_132)
| ~ relation(U_124) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_12,plain,
( in(sK26(U_124,U_132,U_130),U_132)
| in(sK24(U_124,U_132,U_130),U_130)
| U_130 = relation_inverse_image(U_124,U_132)
| ~ relation(U_124) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_13,plain,
( ~ in(sK25(U_124,U_132,U_130),U_130)
| in(sK24(U_124,U_132,U_130),U_130)
| U_130 = relation_inverse_image(U_124,U_132)
| ~ relation(U_124) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_14,plain,
( in(ordered_pair(sK25(U_124,U_132,U_130),sK26(U_124,U_132,U_130)),U_124)
| ~ in(U_119,U_132)
| ~ in(ordered_pair(sK24(U_124,U_132,U_130),U_119),U_124)
| U_130 = relation_inverse_image(U_124,U_132)
| ~ relation(U_124) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_15,plain,
( in(sK26(U_124,U_132,U_130),U_132)
| ~ in(U_119,U_132)
| ~ in(ordered_pair(sK24(U_124,U_132,U_130),U_119),U_124)
| U_130 = relation_inverse_image(U_124,U_132)
| ~ relation(U_124) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_16,plain,
( ~ in(sK25(U_124,U_132,U_130),U_130)
| ~ in(U_119,U_132)
| ~ in(ordered_pair(sK24(U_124,U_132,U_130),U_119),U_124)
| U_130 = relation_inverse_image(U_124,U_132)
| ~ relation(U_124) ),
inference(clausify,[status(thm)],[f_21_7]) ).
fof(f_22_1,plain,
! [A] :
( ( ( connected(A)
| ~ is_connected_in(A,relation_field(A)) )
& ( is_connected_in(A,relation_field(A))
| ~ connected(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d14_relat_2]) ).
fof(f_22_2,plain,
! [U_133] :
( ( ( connected(U_133)
| ~ is_connected_in(U_133,relation_field(U_133)) )
& ( is_connected_in(U_133,relation_field(U_133))
| ~ connected(U_133) ) )
| ~ relation(U_133) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( is_connected_in(U_133,relation_field(U_133))
| ~ connected(U_133)
| ~ relation(U_133) ),
inference(clausify,[status(thm)],[f_22_2]) ).
cnf(f_22_4,plain,
( connected(U_133)
| ~ is_connected_in(U_133,relation_field(U_133))
| ~ relation(U_133) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [A] :
( ( ( transitive(A)
| ~ is_transitive_in(A,relation_field(A)) )
& ( is_transitive_in(A,relation_field(A))
| ~ transitive(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d16_relat_2]) ).
fof(f_23_2,plain,
! [U_134] :
( ( ( transitive(U_134)
| ~ is_transitive_in(U_134,relation_field(U_134)) )
& ( is_transitive_in(U_134,relation_field(U_134))
| ~ transitive(U_134) ) )
| ~ relation(U_134) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( is_transitive_in(U_134,relation_field(U_134))
| ~ transitive(U_134)
| ~ relation(U_134) ),
inference(clausify,[status(thm)],[f_23_2]) ).
cnf(f_23_4,plain,
( transitive(U_134)
| ~ is_transitive_in(U_134,relation_field(U_134))
| ~ relation(U_134) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
! [A,B,C,D] :
( ( D = unordered_triple(A,B,C)
| ? [E] :
( ( ~ in(E,D)
& ( E = C
| E = B
| E = A ) )
| ( E != C
& E != B
& E != A
& in(E,D) ) ) )
& ( ! [E] :
( ( in(E,D)
| ( E != C
& E != B
& E != A ) )
& ( E = C
| E = B
| E = A
| ~ in(E,D) ) )
| D != unordered_triple(A,B,C) ) ),
inference(fof_nnf,[status(thm)],[d1_enumset1]) ).
fof(f_24_2,plain,
! [U_140,U_139,U_138,U_137] :
( ( U_137 = unordered_triple(U_140,U_139,U_138)
| ? [U_136] :
( ( ~ in(U_136,U_137)
& ( U_136 = U_138
| U_136 = U_139
| U_136 = U_140 ) )
| ( U_136 != U_138
& U_136 != U_139
& U_136 != U_140
& in(U_136,U_137) ) ) )
& ( ! [U_135] :
( ( in(U_135,U_137)
| ( U_135 != U_138
& U_135 != U_139
& U_135 != U_140 ) )
& ( U_135 = U_138
| U_135 = U_139
| U_135 = U_140
| ~ in(U_135,U_137) ) )
| U_137 != unordered_triple(U_140,U_139,U_138) ) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( ! [U_152,U_150,U_148,U_146] :
( U_146 = unordered_triple(U_152,U_150,U_148)
| ? [U_144] :
( ~ in(U_144,U_146)
& ( U_144 = U_148
| U_144 = U_150
| U_144 = U_152 ) )
| ? [U_143] :
( U_143 != U_148
& U_143 != U_150
& U_143 != U_152
& in(U_143,U_146) ) )
& ! [U_151,U_149,U_147,U_145] :
( ( ! [U_142] :
( in(U_142,U_145)
| ( U_142 != U_147
& U_142 != U_149
& U_142 != U_151 ) )
& ! [U_141] :
( U_141 = U_147
| U_141 = U_149
| U_141 = U_151
| ~ in(U_141,U_145) ) )
| U_145 != unordered_triple(U_151,U_149,U_147) ) ),
inference(miniscope,[status(thm)],[f_24_2]) ).
fof(f_24_4,plain,
( ! [U_152,U_150,U_148,U_146] :
( U_146 = unordered_triple(U_152,U_150,U_148)
| ? [U_144] :
( ~ in(U_144,U_146)
& ( U_144 = U_148
| U_144 = U_150
| U_144 = U_152 ) )
| ( sK27(U_152,U_150,U_148,U_146) != U_148
& sK27(U_152,U_150,U_148,U_146) != U_150
& sK27(U_152,U_150,U_148,U_146) != U_152
& in(sK27(U_152,U_150,U_148,U_146),U_146) ) )
& ! [U_151,U_149,U_147,U_145] :
( ( ! [U_142] :
( in(U_142,U_145)
| ( U_142 != U_147
& U_142 != U_149
& U_142 != U_151 ) )
& ! [U_141] :
( U_141 = U_147
| U_141 = U_149
| U_141 = U_151
| ~ in(U_141,U_145) ) )
| U_145 != unordered_triple(U_151,U_149,U_147) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_143,sK27(U_152,U_150,U_148,U_146))],[f_24_3]) ).
fof(f_24_5,plain,
( ! [U_152,U_150,U_148,U_146] :
( U_146 = unordered_triple(U_152,U_150,U_148)
| ( ~ in(sK28(U_152,U_150,U_148,U_146),U_146)
& ( sK28(U_152,U_150,U_148,U_146) = U_148
| sK28(U_152,U_150,U_148,U_146) = U_150
| sK28(U_152,U_150,U_148,U_146) = U_152 ) )
| ( sK27(U_152,U_150,U_148,U_146) != U_148
& sK27(U_152,U_150,U_148,U_146) != U_150
& sK27(U_152,U_150,U_148,U_146) != U_152
& in(sK27(U_152,U_150,U_148,U_146),U_146) ) )
& ! [U_151,U_149,U_147,U_145] :
( ( ! [U_142] :
( in(U_142,U_145)
| ( U_142 != U_147
& U_142 != U_149
& U_142 != U_151 ) )
& ! [U_141] :
( U_141 = U_147
| U_141 = U_149
| U_141 = U_151
| ~ in(U_141,U_145) ) )
| U_145 != unordered_triple(U_151,U_149,U_147) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_144,sK28(U_152,U_150,U_148,U_146))],[f_24_4]) ).
cnf(f_24_6,plain,
( U_141 = U_147
| U_141 = U_149
| U_141 = U_151
| ~ in(U_141,U_145)
| U_145 != unordered_triple(U_151,U_149,U_147) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_7,plain,
( U_142 != U_151
| in(U_142,U_145)
| U_145 != unordered_triple(U_151,U_149,U_147) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_8,plain,
( U_142 != U_149
| in(U_142,U_145)
| U_145 != unordered_triple(U_151,U_149,U_147) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_9,plain,
( U_142 != U_147
| in(U_142,U_145)
| U_145 != unordered_triple(U_151,U_149,U_147) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_10,plain,
( sK28(U_152,U_150,U_148,U_146) = U_148
| sK28(U_152,U_150,U_148,U_146) = U_150
| sK28(U_152,U_150,U_148,U_146) = U_152
| in(sK27(U_152,U_150,U_148,U_146),U_146)
| U_146 = unordered_triple(U_152,U_150,U_148) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_11,plain,
( ~ in(sK28(U_152,U_150,U_148,U_146),U_146)
| in(sK27(U_152,U_150,U_148,U_146),U_146)
| U_146 = unordered_triple(U_152,U_150,U_148) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_12,plain,
( sK27(U_152,U_150,U_148,U_146) != U_152
| sK28(U_152,U_150,U_148,U_146) = U_148
| sK28(U_152,U_150,U_148,U_146) = U_150
| sK28(U_152,U_150,U_148,U_146) = U_152
| U_146 = unordered_triple(U_152,U_150,U_148) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_13,plain,
( sK27(U_152,U_150,U_148,U_146) != U_150
| sK28(U_152,U_150,U_148,U_146) = U_148
| sK28(U_152,U_150,U_148,U_146) = U_150
| sK28(U_152,U_150,U_148,U_146) = U_152
| U_146 = unordered_triple(U_152,U_150,U_148) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_14,plain,
( sK27(U_152,U_150,U_148,U_146) != U_148
| sK28(U_152,U_150,U_148,U_146) = U_148
| sK28(U_152,U_150,U_148,U_146) = U_150
| sK28(U_152,U_150,U_148,U_146) = U_152
| U_146 = unordered_triple(U_152,U_150,U_148) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_15,plain,
( sK27(U_152,U_150,U_148,U_146) != U_152
| ~ in(sK28(U_152,U_150,U_148,U_146),U_146)
| U_146 = unordered_triple(U_152,U_150,U_148) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_16,plain,
( sK27(U_152,U_150,U_148,U_146) != U_150
| ~ in(sK28(U_152,U_150,U_148,U_146),U_146)
| U_146 = unordered_triple(U_152,U_150,U_148) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_17,plain,
( sK27(U_152,U_150,U_148,U_146) != U_148
| ~ in(sK28(U_152,U_150,U_148,U_146),U_146)
| U_146 = unordered_triple(U_152,U_150,U_148) ),
inference(clausify,[status(thm)],[f_24_5]) ).
fof(f_25_1,plain,
! [A] : succ(A) = set_union2(A,singleton(A)),
inference(fof_nnf,[status(thm)],[d1_ordinal1]) ).
fof(f_25_2,plain,
! [U_153] : succ(U_153) = set_union2(U_153,singleton(U_153)),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
succ(U_153) = set_union2(U_153,singleton(U_153)),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
! [A] :
( ( relation(A)
| ? [B] :
( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) ) )
& ( ! [B] :
( ? [C,D] : B = ordered_pair(C,D)
| ~ in(B,A) )
| ~ relation(A) ) ),
inference(fof_nnf,[status(thm)],[d1_relat_1]) ).
fof(f_26_2,plain,
! [U_160] :
( ( relation(U_160)
| ? [U_159] :
( ! [U_158,U_157] : U_159 != ordered_pair(U_158,U_157)
& in(U_159,U_160) ) )
& ( ! [U_156] :
( ? [U_155,U_154] : U_156 = ordered_pair(U_155,U_154)
| ~ in(U_156,U_160) )
| ~ relation(U_160) ) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( ! [U_162] :
( relation(U_162)
| ? [U_159] :
( ! [U_158,U_157] : U_159 != ordered_pair(U_158,U_157)
& in(U_159,U_162) ) )
& ! [U_161] :
( ! [U_156] :
( ? [U_155,U_154] : U_156 = ordered_pair(U_155,U_154)
| ~ in(U_156,U_161) )
| ~ relation(U_161) ) ),
inference(miniscope,[status(thm)],[f_26_2]) ).
fof(f_26_4,plain,
( ! [U_162] :
( relation(U_162)
| ? [U_159] :
( ! [U_158,U_157] : U_159 != ordered_pair(U_158,U_157)
& in(U_159,U_162) ) )
& ! [U_161] :
( ! [U_156] :
( ? [U_154] : U_156 = ordered_pair(sK29(U_161,U_156),U_154)
| ~ in(U_156,U_161) )
| ~ relation(U_161) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_155,sK29(U_161,U_156))],[f_26_3]) ).
fof(f_26_5,plain,
( ! [U_162] :
( relation(U_162)
| ? [U_159] :
( ! [U_158,U_157] : U_159 != ordered_pair(U_158,U_157)
& in(U_159,U_162) ) )
& ! [U_161] :
( ! [U_156] :
( U_156 = ordered_pair(sK29(U_161,U_156),sK30(U_161,U_156))
| ~ in(U_156,U_161) )
| ~ relation(U_161) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_154,sK30(U_161,U_156))],[f_26_4]) ).
fof(f_26_6,plain,
( ! [U_162] :
( relation(U_162)
| ( ! [U_158,U_157] : sK31(U_162) != ordered_pair(U_158,U_157)
& in(sK31(U_162),U_162) ) )
& ! [U_161] :
( ! [U_156] :
( U_156 = ordered_pair(sK29(U_161,U_156),sK30(U_161,U_156))
| ~ in(U_156,U_161) )
| ~ relation(U_161) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_159,sK31(U_162))],[f_26_5]) ).
cnf(f_26_7,plain,
( U_156 = ordered_pair(sK29(U_161,U_156),sK30(U_161,U_156))
| ~ in(U_156,U_161)
| ~ relation(U_161) ),
inference(clausify,[status(thm)],[f_26_6]) ).
cnf(f_26_8,plain,
( in(sK31(U_162),U_162)
| relation(U_162) ),
inference(clausify,[status(thm)],[f_26_6]) ).
cnf(f_26_9,plain,
( sK31(U_162) != ordered_pair(U_158,U_157)
| relation(U_162) ),
inference(clausify,[status(thm)],[f_26_6]) ).
fof(f_27_1,plain,
! [A] :
( ! [B] :
( ( is_reflexive_in(A,B)
| ? [C] :
( ~ in(ordered_pair(C,C),A)
& in(C,B) ) )
& ( ! [C] :
( in(ordered_pair(C,C),A)
| ~ in(C,B) )
| ~ is_reflexive_in(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d1_relat_2]) ).
fof(f_27_2,plain,
! [U_166] :
( ! [U_165] :
( ( is_reflexive_in(U_166,U_165)
| ? [U_164] :
( ~ in(ordered_pair(U_164,U_164),U_166)
& in(U_164,U_165) ) )
& ( ! [U_163] :
( in(ordered_pair(U_163,U_163),U_166)
| ~ in(U_163,U_165) )
| ~ is_reflexive_in(U_166,U_165) ) )
| ~ relation(U_166) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_166] :
( ( ! [U_168] :
( is_reflexive_in(U_166,U_168)
| ? [U_164] :
( ~ in(ordered_pair(U_164,U_164),U_166)
& in(U_164,U_168) ) )
& ! [U_167] :
( ! [U_163] :
( in(ordered_pair(U_163,U_163),U_166)
| ~ in(U_163,U_167) )
| ~ is_reflexive_in(U_166,U_167) ) )
| ~ relation(U_166) ),
inference(miniscope,[status(thm)],[f_27_2]) ).
fof(f_27_4,plain,
! [U_166] :
( ( ! [U_168] :
( is_reflexive_in(U_166,U_168)
| ( ~ in(ordered_pair(sK32(U_166,U_168),sK32(U_166,U_168)),U_166)
& in(sK32(U_166,U_168),U_168) ) )
& ! [U_167] :
( ! [U_163] :
( in(ordered_pair(U_163,U_163),U_166)
| ~ in(U_163,U_167) )
| ~ is_reflexive_in(U_166,U_167) ) )
| ~ relation(U_166) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_164,sK32(U_166,U_168))],[f_27_3]) ).
cnf(f_27_5,plain,
( in(ordered_pair(U_163,U_163),U_166)
| ~ in(U_163,U_167)
| ~ is_reflexive_in(U_166,U_167)
| ~ relation(U_166) ),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(f_27_6,plain,
( in(sK32(U_166,U_168),U_168)
| is_reflexive_in(U_166,U_168)
| ~ relation(U_166) ),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(f_27_7,plain,
( ~ in(ordered_pair(sK32(U_166,U_168),sK32(U_166,U_168)),U_166)
| is_reflexive_in(U_166,U_168)
| ~ relation(U_166) ),
inference(clausify,[status(thm)],[f_27_4]) ).
fof(f_28_1,plain,
! [A,B] :
( ( ( ( B = set_meet(A)
| B != empty_set )
& ( B = empty_set
| B != set_meet(A) ) )
| A != empty_set )
& ( ( ( B = set_meet(A)
| ? [C] :
( ( ~ in(C,B)
& ! [D] :
( in(C,D)
| ~ in(D,A) ) )
| ( ? [D] :
( ~ in(C,D)
& in(D,A) )
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ? [D] :
( ~ in(C,D)
& in(D,A) ) )
& ( ! [D] :
( in(C,D)
| ~ in(D,A) )
| ~ in(C,B) ) )
| B != set_meet(A) ) )
| A = empty_set ) ),
inference(fof_nnf,[status(thm)],[d1_setfam_1]) ).
fof(f_28_2,plain,
! [U_176,U_175] :
( ( ( ( U_175 = set_meet(U_176)
| U_175 != empty_set )
& ( U_175 = empty_set
| U_175 != set_meet(U_176) ) )
| U_176 != empty_set )
& ( ( ( U_175 = set_meet(U_176)
| ? [U_174] :
( ( ~ in(U_174,U_175)
& ! [U_173] :
( in(U_174,U_173)
| ~ in(U_173,U_176) ) )
| ( ? [U_172] :
( ~ in(U_174,U_172)
& in(U_172,U_176) )
& in(U_174,U_175) ) ) )
& ( ! [U_171] :
( ( in(U_171,U_175)
| ? [U_170] :
( ~ in(U_171,U_170)
& in(U_170,U_176) ) )
& ( ! [U_169] :
( in(U_171,U_169)
| ~ in(U_169,U_176) )
| ~ in(U_171,U_175) ) )
| U_175 != set_meet(U_176) ) )
| U_176 = empty_set ) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( ! [U_188] :
( ( ! [U_186] :
( U_186 = set_meet(U_188)
| U_186 != empty_set )
& ! [U_185] :
( U_185 = empty_set
| U_185 != set_meet(U_188) ) )
| U_188 != empty_set )
& ! [U_187] :
( ( ! [U_184] :
( U_184 = set_meet(U_187)
| ? [U_180] :
( ~ in(U_180,U_184)
& ! [U_173] :
( in(U_180,U_173)
| ~ in(U_173,U_187) ) )
| ? [U_179] :
( ? [U_172] :
( ~ in(U_179,U_172)
& in(U_172,U_187) )
& in(U_179,U_184) ) )
& ! [U_183] :
( ( ! [U_178] :
( in(U_178,U_183)
| ? [U_170] :
( ~ in(U_178,U_170)
& in(U_170,U_187) ) )
& ! [U_177] :
( ! [U_169] :
( in(U_177,U_169)
| ~ in(U_169,U_187) )
| ~ in(U_177,U_183) ) )
| U_183 != set_meet(U_187) ) )
| U_187 = empty_set ) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
fof(f_28_4,plain,
( ! [U_188] :
( ( ! [U_186] :
( U_186 = set_meet(U_188)
| U_186 != empty_set )
& ! [U_185] :
( U_185 = empty_set
| U_185 != set_meet(U_188) ) )
| U_188 != empty_set )
& ! [U_187] :
( ( ! [U_184] :
( U_184 = set_meet(U_187)
| ? [U_180] :
( ~ in(U_180,U_184)
& ! [U_173] :
( in(U_180,U_173)
| ~ in(U_173,U_187) ) )
| ? [U_179] :
( ? [U_172] :
( ~ in(U_179,U_172)
& in(U_172,U_187) )
& in(U_179,U_184) ) )
& ! [U_183] :
( ( ! [U_178] :
( in(U_178,U_183)
| ( ~ in(U_178,sK33(U_187,U_183,U_178))
& in(sK33(U_187,U_183,U_178),U_187) ) )
& ! [U_177] :
( ! [U_169] :
( in(U_177,U_169)
| ~ in(U_169,U_187) )
| ~ in(U_177,U_183) ) )
| U_183 != set_meet(U_187) ) )
| U_187 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_170,sK33(U_187,U_183,U_178))],[f_28_3]) ).
fof(f_28_5,plain,
( ! [U_188] :
( ( ! [U_186] :
( U_186 = set_meet(U_188)
| U_186 != empty_set )
& ! [U_185] :
( U_185 = empty_set
| U_185 != set_meet(U_188) ) )
| U_188 != empty_set )
& ! [U_187] :
( ( ! [U_184] :
( U_184 = set_meet(U_187)
| ? [U_180] :
( ~ in(U_180,U_184)
& ! [U_173] :
( in(U_180,U_173)
| ~ in(U_173,U_187) ) )
| ( ? [U_172] :
( ~ in(sK34(U_187,U_184),U_172)
& in(U_172,U_187) )
& in(sK34(U_187,U_184),U_184) ) )
& ! [U_183] :
( ( ! [U_178] :
( in(U_178,U_183)
| ( ~ in(U_178,sK33(U_187,U_183,U_178))
& in(sK33(U_187,U_183,U_178),U_187) ) )
& ! [U_177] :
( ! [U_169] :
( in(U_177,U_169)
| ~ in(U_169,U_187) )
| ~ in(U_177,U_183) ) )
| U_183 != set_meet(U_187) ) )
| U_187 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_179,sK34(U_187,U_184))],[f_28_4]) ).
fof(f_28_6,plain,
( ! [U_188] :
( ( ! [U_186] :
( U_186 = set_meet(U_188)
| U_186 != empty_set )
& ! [U_185] :
( U_185 = empty_set
| U_185 != set_meet(U_188) ) )
| U_188 != empty_set )
& ! [U_187] :
( ( ! [U_184] :
( U_184 = set_meet(U_187)
| ? [U_180] :
( ~ in(U_180,U_184)
& ! [U_173] :
( in(U_180,U_173)
| ~ in(U_173,U_187) ) )
| ( ~ in(sK34(U_187,U_184),sK35(U_187,U_184))
& in(sK35(U_187,U_184),U_187)
& in(sK34(U_187,U_184),U_184) ) )
& ! [U_183] :
( ( ! [U_178] :
( in(U_178,U_183)
| ( ~ in(U_178,sK33(U_187,U_183,U_178))
& in(sK33(U_187,U_183,U_178),U_187) ) )
& ! [U_177] :
( ! [U_169] :
( in(U_177,U_169)
| ~ in(U_169,U_187) )
| ~ in(U_177,U_183) ) )
| U_183 != set_meet(U_187) ) )
| U_187 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_172,sK35(U_187,U_184))],[f_28_5]) ).
fof(f_28_7,plain,
( ! [U_188] :
( ( ! [U_186] :
( U_186 = set_meet(U_188)
| U_186 != empty_set )
& ! [U_185] :
( U_185 = empty_set
| U_185 != set_meet(U_188) ) )
| U_188 != empty_set )
& ! [U_187] :
( ( ! [U_184] :
( U_184 = set_meet(U_187)
| ( ~ in(sK36(U_187,U_184),U_184)
& ! [U_173] :
( in(sK36(U_187,U_184),U_173)
| ~ in(U_173,U_187) ) )
| ( ~ in(sK34(U_187,U_184),sK35(U_187,U_184))
& in(sK35(U_187,U_184),U_187)
& in(sK34(U_187,U_184),U_184) ) )
& ! [U_183] :
( ( ! [U_178] :
( in(U_178,U_183)
| ( ~ in(U_178,sK33(U_187,U_183,U_178))
& in(sK33(U_187,U_183,U_178),U_187) ) )
& ! [U_177] :
( ! [U_169] :
( in(U_177,U_169)
| ~ in(U_169,U_187) )
| ~ in(U_177,U_183) ) )
| U_183 != set_meet(U_187) ) )
| U_187 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_180,sK36(U_187,U_184))],[f_28_6]) ).
cnf(f_28_8,plain,
( in(U_177,U_169)
| ~ in(U_169,U_187)
| ~ in(U_177,U_183)
| U_183 != set_meet(U_187)
| U_187 = empty_set ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_9,plain,
( in(sK33(U_187,U_183,U_178),U_187)
| in(U_178,U_183)
| U_183 != set_meet(U_187)
| U_187 = empty_set ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_10,plain,
( ~ in(U_178,sK33(U_187,U_183,U_178))
| in(U_178,U_183)
| U_183 != set_meet(U_187)
| U_187 = empty_set ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_11,plain,
( in(sK36(U_187,U_184),U_173)
| ~ in(U_173,U_187)
| in(sK34(U_187,U_184),U_184)
| U_184 = set_meet(U_187)
| U_187 = empty_set ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_12,plain,
( ~ in(sK36(U_187,U_184),U_184)
| in(sK34(U_187,U_184),U_184)
| U_184 = set_meet(U_187)
| U_187 = empty_set ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_13,plain,
( in(sK35(U_187,U_184),U_187)
| in(sK36(U_187,U_184),U_173)
| ~ in(U_173,U_187)
| U_184 = set_meet(U_187)
| U_187 = empty_set ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_14,plain,
( ~ in(sK34(U_187,U_184),sK35(U_187,U_184))
| in(sK36(U_187,U_184),U_173)
| ~ in(U_173,U_187)
| U_184 = set_meet(U_187)
| U_187 = empty_set ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_15,plain,
( in(sK35(U_187,U_184),U_187)
| ~ in(sK36(U_187,U_184),U_184)
| U_184 = set_meet(U_187)
| U_187 = empty_set ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_16,plain,
( ~ in(sK34(U_187,U_184),sK35(U_187,U_184))
| ~ in(sK36(U_187,U_184),U_184)
| U_184 = set_meet(U_187)
| U_187 = empty_set ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_17,plain,
( U_185 = empty_set
| U_185 != set_meet(U_188)
| U_188 != empty_set ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_18,plain,
( U_186 = set_meet(U_188)
| U_186 != empty_set
| U_188 != empty_set ),
inference(clausify,[status(thm)],[f_28_7]) ).
fof(f_29_1,plain,
! [A,B] :
( ( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
& C = A )
| ( C != A
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| C != A )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(fof_nnf,[status(thm)],[d1_tarski]) ).
fof(f_29_2,plain,
! [U_192,U_191] :
( ( U_191 = singleton(U_192)
| ? [U_190] :
( ( ~ in(U_190,U_191)
& U_190 = U_192 )
| ( U_190 != U_192
& in(U_190,U_191) ) ) )
& ( ! [U_189] :
( ( in(U_189,U_191)
| U_189 != U_192 )
& ( U_189 = U_192
| ~ in(U_189,U_191) ) )
| U_191 != singleton(U_192) ) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
( ! [U_200,U_198] :
( U_198 = singleton(U_200)
| ? [U_196] :
( ~ in(U_196,U_198)
& U_196 = U_200 )
| ? [U_195] :
( U_195 != U_200
& in(U_195,U_198) ) )
& ! [U_199,U_197] :
( ( ! [U_194] :
( in(U_194,U_197)
| U_194 != U_199 )
& ! [U_193] :
( U_193 = U_199
| ~ in(U_193,U_197) ) )
| U_197 != singleton(U_199) ) ),
inference(miniscope,[status(thm)],[f_29_2]) ).
fof(f_29_4,plain,
( ! [U_200,U_198] :
( U_198 = singleton(U_200)
| ? [U_196] :
( ~ in(U_196,U_198)
& U_196 = U_200 )
| ( sK37(U_200,U_198) != U_200
& in(sK37(U_200,U_198),U_198) ) )
& ! [U_199,U_197] :
( ( ! [U_194] :
( in(U_194,U_197)
| U_194 != U_199 )
& ! [U_193] :
( U_193 = U_199
| ~ in(U_193,U_197) ) )
| U_197 != singleton(U_199) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_195,sK37(U_200,U_198))],[f_29_3]) ).
fof(f_29_5,plain,
( ! [U_200,U_198] :
( U_198 = singleton(U_200)
| ( ~ in(sK38(U_200,U_198),U_198)
& sK38(U_200,U_198) = U_200 )
| ( sK37(U_200,U_198) != U_200
& in(sK37(U_200,U_198),U_198) ) )
& ! [U_199,U_197] :
( ( ! [U_194] :
( in(U_194,U_197)
| U_194 != U_199 )
& ! [U_193] :
( U_193 = U_199
| ~ in(U_193,U_197) ) )
| U_197 != singleton(U_199) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_196,sK38(U_200,U_198))],[f_29_4]) ).
cnf(f_29_6,plain,
( U_193 = U_199
| ~ in(U_193,U_197)
| U_197 != singleton(U_199) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_7,plain,
( in(U_194,U_197)
| U_194 != U_199
| U_197 != singleton(U_199) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_8,plain,
( sK38(U_200,U_198) = U_200
| in(sK37(U_200,U_198),U_198)
| U_198 = singleton(U_200) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_9,plain,
( ~ in(sK38(U_200,U_198),U_198)
| in(sK37(U_200,U_198),U_198)
| U_198 = singleton(U_200) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_10,plain,
( sK38(U_200,U_198) = U_200
| sK37(U_200,U_198) != U_200
| U_198 = singleton(U_200) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_11,plain,
( ~ in(sK38(U_200,U_198),U_198)
| sK37(U_200,U_198) != U_200
| U_198 = singleton(U_200) ),
inference(clausify,[status(thm)],[f_29_5]) ).
fof(f_30_1,plain,
! [A] :
( ! [B,C] :
( ( C = fiber(A,B)
| ? [D] :
( ( ~ in(D,C)
& in(ordered_pair(D,B),A)
& D != B )
| ( ( ~ in(ordered_pair(D,B),A)
| D = B )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ~ in(ordered_pair(D,B),A)
| D = B )
& ( ( in(ordered_pair(D,B),A)
& D != B )
| ~ in(D,C) ) )
| C != fiber(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d1_wellord1]) ).
fof(f_30_2,plain,
! [U_205] :
( ! [U_204,U_203] :
( ( U_203 = fiber(U_205,U_204)
| ? [U_202] :
( ( ~ in(U_202,U_203)
& in(ordered_pair(U_202,U_204),U_205)
& U_202 != U_204 )
| ( ( ~ in(ordered_pair(U_202,U_204),U_205)
| U_202 = U_204 )
& in(U_202,U_203) ) ) )
& ( ! [U_201] :
( ( in(U_201,U_203)
| ~ in(ordered_pair(U_201,U_204),U_205)
| U_201 = U_204 )
& ( ( in(ordered_pair(U_201,U_204),U_205)
& U_201 != U_204 )
| ~ in(U_201,U_203) ) )
| U_203 != fiber(U_205,U_204) ) )
| ~ relation(U_205) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_205] :
( ( ! [U_213,U_211] :
( U_211 = fiber(U_205,U_213)
| ? [U_209] :
( ~ in(U_209,U_211)
& in(ordered_pair(U_209,U_213),U_205)
& U_209 != U_213 )
| ? [U_208] :
( ( ~ in(ordered_pair(U_208,U_213),U_205)
| U_208 = U_213 )
& in(U_208,U_211) ) )
& ! [U_212,U_210] :
( ( ! [U_207] :
( in(U_207,U_210)
| ~ in(ordered_pair(U_207,U_212),U_205)
| U_207 = U_212 )
& ! [U_206] :
( ( in(ordered_pair(U_206,U_212),U_205)
& U_206 != U_212 )
| ~ in(U_206,U_210) ) )
| U_210 != fiber(U_205,U_212) ) )
| ~ relation(U_205) ),
inference(miniscope,[status(thm)],[f_30_2]) ).
fof(f_30_4,plain,
! [U_205] :
( ( ! [U_213,U_211] :
( U_211 = fiber(U_205,U_213)
| ? [U_209] :
( ~ in(U_209,U_211)
& in(ordered_pair(U_209,U_213),U_205)
& U_209 != U_213 )
| ( ( ~ in(ordered_pair(sK39(U_205,U_213,U_211),U_213),U_205)
| sK39(U_205,U_213,U_211) = U_213 )
& in(sK39(U_205,U_213,U_211),U_211) ) )
& ! [U_212,U_210] :
( ( ! [U_207] :
( in(U_207,U_210)
| ~ in(ordered_pair(U_207,U_212),U_205)
| U_207 = U_212 )
& ! [U_206] :
( ( in(ordered_pair(U_206,U_212),U_205)
& U_206 != U_212 )
| ~ in(U_206,U_210) ) )
| U_210 != fiber(U_205,U_212) ) )
| ~ relation(U_205) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_208,sK39(U_205,U_213,U_211))],[f_30_3]) ).
fof(f_30_5,plain,
! [U_205] :
( ( ! [U_213,U_211] :
( U_211 = fiber(U_205,U_213)
| ( ~ in(sK40(U_205,U_213,U_211),U_211)
& in(ordered_pair(sK40(U_205,U_213,U_211),U_213),U_205)
& sK40(U_205,U_213,U_211) != U_213 )
| ( ( ~ in(ordered_pair(sK39(U_205,U_213,U_211),U_213),U_205)
| sK39(U_205,U_213,U_211) = U_213 )
& in(sK39(U_205,U_213,U_211),U_211) ) )
& ! [U_212,U_210] :
( ( ! [U_207] :
( in(U_207,U_210)
| ~ in(ordered_pair(U_207,U_212),U_205)
| U_207 = U_212 )
& ! [U_206] :
( ( in(ordered_pair(U_206,U_212),U_205)
& U_206 != U_212 )
| ~ in(U_206,U_210) ) )
| U_210 != fiber(U_205,U_212) ) )
| ~ relation(U_205) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_209,sK40(U_205,U_213,U_211))],[f_30_4]) ).
cnf(f_30_6,plain,
( U_206 != U_212
| ~ in(U_206,U_210)
| U_210 != fiber(U_205,U_212)
| ~ relation(U_205) ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_7,plain,
( in(ordered_pair(U_206,U_212),U_205)
| ~ in(U_206,U_210)
| U_210 != fiber(U_205,U_212)
| ~ relation(U_205) ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_8,plain,
( in(U_207,U_210)
| ~ in(ordered_pair(U_207,U_212),U_205)
| U_207 = U_212
| U_210 != fiber(U_205,U_212)
| ~ relation(U_205) ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_9,plain,
( sK40(U_205,U_213,U_211) != U_213
| in(sK39(U_205,U_213,U_211),U_211)
| U_211 = fiber(U_205,U_213)
| ~ relation(U_205) ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_10,plain,
( in(ordered_pair(sK40(U_205,U_213,U_211),U_213),U_205)
| in(sK39(U_205,U_213,U_211),U_211)
| U_211 = fiber(U_205,U_213)
| ~ relation(U_205) ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_11,plain,
( ~ in(sK40(U_205,U_213,U_211),U_211)
| in(sK39(U_205,U_213,U_211),U_211)
| U_211 = fiber(U_205,U_213)
| ~ relation(U_205) ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_12,plain,
( sK40(U_205,U_213,U_211) != U_213
| ~ in(ordered_pair(sK39(U_205,U_213,U_211),U_213),U_205)
| sK39(U_205,U_213,U_211) = U_213
| U_211 = fiber(U_205,U_213)
| ~ relation(U_205) ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_13,plain,
( in(ordered_pair(sK40(U_205,U_213,U_211),U_213),U_205)
| ~ in(ordered_pair(sK39(U_205,U_213,U_211),U_213),U_205)
| sK39(U_205,U_213,U_211) = U_213
| U_211 = fiber(U_205,U_213)
| ~ relation(U_205) ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_14,plain,
( ~ in(sK40(U_205,U_213,U_211),U_211)
| ~ in(ordered_pair(sK39(U_205,U_213,U_211),U_213),U_205)
| sK39(U_205,U_213,U_211) = U_213
| U_211 = fiber(U_205,U_213)
| ~ relation(U_205) ),
inference(clausify,[status(thm)],[f_30_5]) ).
fof(f_31_1,plain,
! [A] :
( ( A = empty_set
| ? [B] : in(B,A) )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(fof_nnf,[status(thm)],[d1_xboole_0]) ).
fof(f_31_2,plain,
! [U_216] :
( ( U_216 = empty_set
| ? [U_215] : in(U_215,U_216) )
& ( ! [U_214] : ~ in(U_214,U_216)
| U_216 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( ! [U_218] :
( U_218 = empty_set
| ? [U_215] : in(U_215,U_218) )
& ! [U_217] :
( ! [U_214] : ~ in(U_214,U_217)
| U_217 != empty_set ) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
fof(f_31_4,plain,
( ! [U_218] :
( U_218 = empty_set
| in(sK41(U_218),U_218) )
& ! [U_217] :
( ! [U_214] : ~ in(U_214,U_217)
| U_217 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_215,sK41(U_218))],[f_31_3]) ).
cnf(f_31_5,plain,
( ~ in(U_214,U_217)
| U_217 != empty_set ),
inference(clausify,[status(thm)],[f_31_4]) ).
cnf(f_31_6,plain,
( U_218 = empty_set
| in(sK41(U_218),U_218) ),
inference(clausify,[status(thm)],[f_31_4]) ).
fof(f_32_1,plain,
! [A,B] :
( ( B = powerset(A)
| ? [C] :
( ( ~ in(C,B)
& subset(C,A) )
| ( ~ subset(C,A)
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ~ subset(C,A) )
& ( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(fof_nnf,[status(thm)],[d1_zfmisc_1]) ).
fof(f_32_2,plain,
! [U_222,U_221] :
( ( U_221 = powerset(U_222)
| ? [U_220] :
( ( ~ in(U_220,U_221)
& subset(U_220,U_222) )
| ( ~ subset(U_220,U_222)
& in(U_220,U_221) ) ) )
& ( ! [U_219] :
( ( in(U_219,U_221)
| ~ subset(U_219,U_222) )
& ( subset(U_219,U_222)
| ~ in(U_219,U_221) ) )
| U_221 != powerset(U_222) ) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
( ! [U_230,U_228] :
( U_228 = powerset(U_230)
| ? [U_226] :
( ~ in(U_226,U_228)
& subset(U_226,U_230) )
| ? [U_225] :
( ~ subset(U_225,U_230)
& in(U_225,U_228) ) )
& ! [U_229,U_227] :
( ( ! [U_224] :
( in(U_224,U_227)
| ~ subset(U_224,U_229) )
& ! [U_223] :
( subset(U_223,U_229)
| ~ in(U_223,U_227) ) )
| U_227 != powerset(U_229) ) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
fof(f_32_4,plain,
( ! [U_230,U_228] :
( U_228 = powerset(U_230)
| ? [U_226] :
( ~ in(U_226,U_228)
& subset(U_226,U_230) )
| ( ~ subset(sK42(U_230,U_228),U_230)
& in(sK42(U_230,U_228),U_228) ) )
& ! [U_229,U_227] :
( ( ! [U_224] :
( in(U_224,U_227)
| ~ subset(U_224,U_229) )
& ! [U_223] :
( subset(U_223,U_229)
| ~ in(U_223,U_227) ) )
| U_227 != powerset(U_229) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_225,sK42(U_230,U_228))],[f_32_3]) ).
fof(f_32_5,plain,
( ! [U_230,U_228] :
( U_228 = powerset(U_230)
| ( ~ in(sK43(U_230,U_228),U_228)
& subset(sK43(U_230,U_228),U_230) )
| ( ~ subset(sK42(U_230,U_228),U_230)
& in(sK42(U_230,U_228),U_228) ) )
& ! [U_229,U_227] :
( ( ! [U_224] :
( in(U_224,U_227)
| ~ subset(U_224,U_229) )
& ! [U_223] :
( subset(U_223,U_229)
| ~ in(U_223,U_227) ) )
| U_227 != powerset(U_229) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_226,sK43(U_230,U_228))],[f_32_4]) ).
cnf(f_32_6,plain,
( subset(U_223,U_229)
| ~ in(U_223,U_227)
| U_227 != powerset(U_229) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_7,plain,
( in(U_224,U_227)
| ~ subset(U_224,U_229)
| U_227 != powerset(U_229) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_8,plain,
( subset(sK43(U_230,U_228),U_230)
| in(sK42(U_230,U_228),U_228)
| U_228 = powerset(U_230) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_9,plain,
( ~ in(sK43(U_230,U_228),U_228)
| in(sK42(U_230,U_228),U_228)
| U_228 = powerset(U_230) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_10,plain,
( subset(sK43(U_230,U_228),U_230)
| ~ subset(sK42(U_230,U_228),U_230)
| U_228 = powerset(U_230) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_11,plain,
( ~ in(sK43(U_230,U_228),U_228)
| ~ subset(sK42(U_230,U_228),U_230)
| U_228 = powerset(U_230) ),
inference(clausify,[status(thm)],[f_32_5]) ).
fof(f_33_1,plain,
! [A] :
( ( epsilon_transitive(A)
| ? [B] :
( ~ subset(B,A)
& in(B,A) ) )
& ( ! [B] :
( subset(B,A)
| ~ in(B,A) )
| ~ epsilon_transitive(A) ) ),
inference(fof_nnf,[status(thm)],[d2_ordinal1]) ).
fof(f_33_2,plain,
! [U_233] :
( ( epsilon_transitive(U_233)
| ? [U_232] :
( ~ subset(U_232,U_233)
& in(U_232,U_233) ) )
& ( ! [U_231] :
( subset(U_231,U_233)
| ~ in(U_231,U_233) )
| ~ epsilon_transitive(U_233) ) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( ! [U_235] :
( epsilon_transitive(U_235)
| ? [U_232] :
( ~ subset(U_232,U_235)
& in(U_232,U_235) ) )
& ! [U_234] :
( ! [U_231] :
( subset(U_231,U_234)
| ~ in(U_231,U_234) )
| ~ epsilon_transitive(U_234) ) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
fof(f_33_4,plain,
( ! [U_235] :
( epsilon_transitive(U_235)
| ( ~ subset(sK44(U_235),U_235)
& in(sK44(U_235),U_235) ) )
& ! [U_234] :
( ! [U_231] :
( subset(U_231,U_234)
| ~ in(U_231,U_234) )
| ~ epsilon_transitive(U_234) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_232,sK44(U_235))],[f_33_3]) ).
cnf(f_33_5,plain,
( subset(U_231,U_234)
| ~ in(U_231,U_234)
| ~ epsilon_transitive(U_234) ),
inference(clausify,[status(thm)],[f_33_4]) ).
cnf(f_33_6,plain,
( in(sK44(U_235),U_235)
| epsilon_transitive(U_235) ),
inference(clausify,[status(thm)],[f_33_4]) ).
cnf(f_33_7,plain,
( ~ subset(sK44(U_235),U_235)
| epsilon_transitive(U_235) ),
inference(clausify,[status(thm)],[f_33_4]) ).
fof(f_34_1,plain,
! [A] :
( ! [B] :
( ( ( A = B
| ? [C,D] :
( ( ~ in(ordered_pair(C,D),A)
& in(ordered_pair(C,D),B) )
| ( ~ in(ordered_pair(C,D),B)
& in(ordered_pair(C,D),A) ) ) )
& ( ! [C,D] :
( ( in(ordered_pair(C,D),A)
| ~ in(ordered_pair(C,D),B) )
& ( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) ) )
| A != B ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d2_relat_1]) ).
fof(f_34_2,plain,
! [U_241] :
( ! [U_240] :
( ( ( U_241 = U_240
| ? [U_239,U_238] :
( ( ~ in(ordered_pair(U_239,U_238),U_241)
& in(ordered_pair(U_239,U_238),U_240) )
| ( ~ in(ordered_pair(U_239,U_238),U_240)
& in(ordered_pair(U_239,U_238),U_241) ) ) )
& ( ! [U_237,U_236] :
( ( in(ordered_pair(U_237,U_236),U_241)
| ~ in(ordered_pair(U_237,U_236),U_240) )
& ( in(ordered_pair(U_237,U_236),U_240)
| ~ in(ordered_pair(U_237,U_236),U_241) ) )
| U_241 != U_240 ) )
| ~ relation(U_240) )
| ~ relation(U_241) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_241] :
( ! [U_240] :
( ( ( U_241 = U_240
| ? [U_249,U_247] :
( ~ in(ordered_pair(U_249,U_247),U_241)
& in(ordered_pair(U_249,U_247),U_240) )
| ? [U_248,U_246] :
( ~ in(ordered_pair(U_248,U_246),U_240)
& in(ordered_pair(U_248,U_246),U_241) ) )
& ( ( ! [U_245,U_243] :
( in(ordered_pair(U_245,U_243),U_241)
| ~ in(ordered_pair(U_245,U_243),U_240) )
& ! [U_244,U_242] :
( in(ordered_pair(U_244,U_242),U_240)
| ~ in(ordered_pair(U_244,U_242),U_241) ) )
| U_241 != U_240 ) )
| ~ relation(U_240) )
| ~ relation(U_241) ),
inference(miniscope,[status(thm)],[f_34_2]) ).
fof(f_34_4,plain,
! [U_241] :
( ! [U_240] :
( ( ( U_241 = U_240
| ? [U_249,U_247] :
( ~ in(ordered_pair(U_249,U_247),U_241)
& in(ordered_pair(U_249,U_247),U_240) )
| ? [U_246] :
( ~ in(ordered_pair(sK45(U_241,U_240),U_246),U_240)
& in(ordered_pair(sK45(U_241,U_240),U_246),U_241) ) )
& ( ( ! [U_245,U_243] :
( in(ordered_pair(U_245,U_243),U_241)
| ~ in(ordered_pair(U_245,U_243),U_240) )
& ! [U_244,U_242] :
( in(ordered_pair(U_244,U_242),U_240)
| ~ in(ordered_pair(U_244,U_242),U_241) ) )
| U_241 != U_240 ) )
| ~ relation(U_240) )
| ~ relation(U_241) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_248,sK45(U_241,U_240))],[f_34_3]) ).
fof(f_34_5,plain,
! [U_241] :
( ! [U_240] :
( ( ( U_241 = U_240
| ? [U_249,U_247] :
( ~ in(ordered_pair(U_249,U_247),U_241)
& in(ordered_pair(U_249,U_247),U_240) )
| ( ~ in(ordered_pair(sK45(U_241,U_240),sK46(U_241,U_240)),U_240)
& in(ordered_pair(sK45(U_241,U_240),sK46(U_241,U_240)),U_241) ) )
& ( ( ! [U_245,U_243] :
( in(ordered_pair(U_245,U_243),U_241)
| ~ in(ordered_pair(U_245,U_243),U_240) )
& ! [U_244,U_242] :
( in(ordered_pair(U_244,U_242),U_240)
| ~ in(ordered_pair(U_244,U_242),U_241) ) )
| U_241 != U_240 ) )
| ~ relation(U_240) )
| ~ relation(U_241) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_246,sK46(U_241,U_240))],[f_34_4]) ).
fof(f_34_6,plain,
! [U_241] :
( ! [U_240] :
( ( ( U_241 = U_240
| ? [U_247] :
( ~ in(ordered_pair(sK47(U_241,U_240),U_247),U_241)
& in(ordered_pair(sK47(U_241,U_240),U_247),U_240) )
| ( ~ in(ordered_pair(sK45(U_241,U_240),sK46(U_241,U_240)),U_240)
& in(ordered_pair(sK45(U_241,U_240),sK46(U_241,U_240)),U_241) ) )
& ( ( ! [U_245,U_243] :
( in(ordered_pair(U_245,U_243),U_241)
| ~ in(ordered_pair(U_245,U_243),U_240) )
& ! [U_244,U_242] :
( in(ordered_pair(U_244,U_242),U_240)
| ~ in(ordered_pair(U_244,U_242),U_241) ) )
| U_241 != U_240 ) )
| ~ relation(U_240) )
| ~ relation(U_241) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_249,sK47(U_241,U_240))],[f_34_5]) ).
fof(f_34_7,plain,
! [U_241] :
( ! [U_240] :
( ( ( U_241 = U_240
| ( ~ in(ordered_pair(sK47(U_241,U_240),sK48(U_241,U_240)),U_241)
& in(ordered_pair(sK47(U_241,U_240),sK48(U_241,U_240)),U_240) )
| ( ~ in(ordered_pair(sK45(U_241,U_240),sK46(U_241,U_240)),U_240)
& in(ordered_pair(sK45(U_241,U_240),sK46(U_241,U_240)),U_241) ) )
& ( ( ! [U_245,U_243] :
( in(ordered_pair(U_245,U_243),U_241)
| ~ in(ordered_pair(U_245,U_243),U_240) )
& ! [U_244,U_242] :
( in(ordered_pair(U_244,U_242),U_240)
| ~ in(ordered_pair(U_244,U_242),U_241) ) )
| U_241 != U_240 ) )
| ~ relation(U_240) )
| ~ relation(U_241) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_247,sK48(U_241,U_240))],[f_34_6]) ).
cnf(f_34_8,plain,
( in(ordered_pair(U_244,U_242),U_240)
| ~ in(ordered_pair(U_244,U_242),U_241)
| U_241 != U_240
| ~ relation(U_240)
| ~ relation(U_241) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_9,plain,
( in(ordered_pair(U_245,U_243),U_241)
| ~ in(ordered_pair(U_245,U_243),U_240)
| U_241 != U_240
| ~ relation(U_240)
| ~ relation(U_241) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_10,plain,
( in(ordered_pair(sK47(U_241,U_240),sK48(U_241,U_240)),U_240)
| in(ordered_pair(sK45(U_241,U_240),sK46(U_241,U_240)),U_241)
| U_241 = U_240
| ~ relation(U_240)
| ~ relation(U_241) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_11,plain,
( ~ in(ordered_pair(sK47(U_241,U_240),sK48(U_241,U_240)),U_241)
| in(ordered_pair(sK45(U_241,U_240),sK46(U_241,U_240)),U_241)
| U_241 = U_240
| ~ relation(U_240)
| ~ relation(U_241) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_12,plain,
( in(ordered_pair(sK47(U_241,U_240),sK48(U_241,U_240)),U_240)
| ~ in(ordered_pair(sK45(U_241,U_240),sK46(U_241,U_240)),U_240)
| U_241 = U_240
| ~ relation(U_240)
| ~ relation(U_241) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_13,plain,
( ~ in(ordered_pair(sK47(U_241,U_240),sK48(U_241,U_240)),U_241)
| ~ in(ordered_pair(sK45(U_241,U_240),sK46(U_241,U_240)),U_240)
| U_241 = U_240
| ~ relation(U_240)
| ~ relation(U_241) ),
inference(clausify,[status(thm)],[f_34_7]) ).
fof(f_35_1,plain,
! [A,B] :
( ( ( ( element(B,A)
| ~ empty(B) )
& ( empty(B)
| ~ element(B,A) ) )
| ~ empty(A) )
& ( ( ( element(B,A)
| ~ in(B,A) )
& ( in(B,A)
| ~ element(B,A) ) )
| empty(A) ) ),
inference(fof_nnf,[status(thm)],[d2_subset_1]) ).
fof(f_35_2,plain,
! [U_251,U_250] :
( ( ( ( element(U_250,U_251)
| ~ empty(U_250) )
& ( empty(U_250)
| ~ element(U_250,U_251) ) )
| ~ empty(U_251) )
& ( ( ( element(U_250,U_251)
| ~ in(U_250,U_251) )
& ( in(U_250,U_251)
| ~ element(U_250,U_251) ) )
| empty(U_251) ) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( ! [U_259] :
( ( ! [U_257] :
( element(U_257,U_259)
| ~ empty(U_257) )
& ! [U_256] :
( empty(U_256)
| ~ element(U_256,U_259) ) )
| ~ empty(U_259) )
& ! [U_258] :
( ( ! [U_255] :
( element(U_255,U_258)
| ~ in(U_255,U_258) )
& ! [U_254] :
( in(U_254,U_258)
| ~ element(U_254,U_258) ) )
| empty(U_258) ) ),
inference(miniscope,[status(thm)],[f_35_2]) ).
cnf(f_35_4,plain,
( in(U_254,U_258)
| ~ element(U_254,U_258)
| empty(U_258) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_5,plain,
( element(U_255,U_258)
| ~ in(U_255,U_258)
| empty(U_258) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_6,plain,
( empty(U_256)
| ~ element(U_256,U_259)
| ~ empty(U_259) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_7,plain,
( element(U_257,U_259)
| ~ empty(U_257)
| ~ empty(U_259) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
! [A,B,C] :
( ( C = unordered_pair(A,B)
| ? [D] :
( ( ~ in(D,C)
& ( D = B
| D = A ) )
| ( D != B
& D != A
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ( D != B
& D != A ) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(fof_nnf,[status(thm)],[d2_tarski]) ).
fof(f_36_2,plain,
! [U_264,U_263,U_262] :
( ( U_262 = unordered_pair(U_264,U_263)
| ? [U_261] :
( ( ~ in(U_261,U_262)
& ( U_261 = U_263
| U_261 = U_264 ) )
| ( U_261 != U_263
& U_261 != U_264
& in(U_261,U_262) ) ) )
& ( ! [U_260] :
( ( in(U_260,U_262)
| ( U_260 != U_263
& U_260 != U_264 ) )
& ( U_260 = U_263
| U_260 = U_264
| ~ in(U_260,U_262) ) )
| U_262 != unordered_pair(U_264,U_263) ) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
( ! [U_274,U_272,U_270] :
( U_270 = unordered_pair(U_274,U_272)
| ? [U_268] :
( ~ in(U_268,U_270)
& ( U_268 = U_272
| U_268 = U_274 ) )
| ? [U_267] :
( U_267 != U_272
& U_267 != U_274
& in(U_267,U_270) ) )
& ! [U_273,U_271,U_269] :
( ( ! [U_266] :
( in(U_266,U_269)
| ( U_266 != U_271
& U_266 != U_273 ) )
& ! [U_265] :
( U_265 = U_271
| U_265 = U_273
| ~ in(U_265,U_269) ) )
| U_269 != unordered_pair(U_273,U_271) ) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
fof(f_36_4,plain,
( ! [U_274,U_272,U_270] :
( U_270 = unordered_pair(U_274,U_272)
| ? [U_268] :
( ~ in(U_268,U_270)
& ( U_268 = U_272
| U_268 = U_274 ) )
| ( sK49(U_274,U_272,U_270) != U_272
& sK49(U_274,U_272,U_270) != U_274
& in(sK49(U_274,U_272,U_270),U_270) ) )
& ! [U_273,U_271,U_269] :
( ( ! [U_266] :
( in(U_266,U_269)
| ( U_266 != U_271
& U_266 != U_273 ) )
& ! [U_265] :
( U_265 = U_271
| U_265 = U_273
| ~ in(U_265,U_269) ) )
| U_269 != unordered_pair(U_273,U_271) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_267,sK49(U_274,U_272,U_270))],[f_36_3]) ).
fof(f_36_5,plain,
( ! [U_274,U_272,U_270] :
( U_270 = unordered_pair(U_274,U_272)
| ( ~ in(sK50(U_274,U_272,U_270),U_270)
& ( sK50(U_274,U_272,U_270) = U_272
| sK50(U_274,U_272,U_270) = U_274 ) )
| ( sK49(U_274,U_272,U_270) != U_272
& sK49(U_274,U_272,U_270) != U_274
& in(sK49(U_274,U_272,U_270),U_270) ) )
& ! [U_273,U_271,U_269] :
( ( ! [U_266] :
( in(U_266,U_269)
| ( U_266 != U_271
& U_266 != U_273 ) )
& ! [U_265] :
( U_265 = U_271
| U_265 = U_273
| ~ in(U_265,U_269) ) )
| U_269 != unordered_pair(U_273,U_271) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_268,sK50(U_274,U_272,U_270))],[f_36_4]) ).
cnf(f_36_6,plain,
( U_265 = U_271
| U_265 = U_273
| ~ in(U_265,U_269)
| U_269 != unordered_pair(U_273,U_271) ),
inference(clausify,[status(thm)],[f_36_5]) ).
cnf(f_36_7,plain,
( U_266 != U_273
| in(U_266,U_269)
| U_269 != unordered_pair(U_273,U_271) ),
inference(clausify,[status(thm)],[f_36_5]) ).
cnf(f_36_8,plain,
( U_266 != U_271
| in(U_266,U_269)
| U_269 != unordered_pair(U_273,U_271) ),
inference(clausify,[status(thm)],[f_36_5]) ).
cnf(f_36_9,plain,
( sK50(U_274,U_272,U_270) = U_272
| sK50(U_274,U_272,U_270) = U_274
| in(sK49(U_274,U_272,U_270),U_270)
| U_270 = unordered_pair(U_274,U_272) ),
inference(clausify,[status(thm)],[f_36_5]) ).
cnf(f_36_10,plain,
( ~ in(sK50(U_274,U_272,U_270),U_270)
| in(sK49(U_274,U_272,U_270),U_270)
| U_270 = unordered_pair(U_274,U_272) ),
inference(clausify,[status(thm)],[f_36_5]) ).
cnf(f_36_11,plain,
( sK49(U_274,U_272,U_270) != U_274
| sK50(U_274,U_272,U_270) = U_272
| sK50(U_274,U_272,U_270) = U_274
| U_270 = unordered_pair(U_274,U_272) ),
inference(clausify,[status(thm)],[f_36_5]) ).
cnf(f_36_12,plain,
( sK49(U_274,U_272,U_270) != U_272
| sK50(U_274,U_272,U_270) = U_272
| sK50(U_274,U_272,U_270) = U_274
| U_270 = unordered_pair(U_274,U_272) ),
inference(clausify,[status(thm)],[f_36_5]) ).
cnf(f_36_13,plain,
( sK49(U_274,U_272,U_270) != U_274
| ~ in(sK50(U_274,U_272,U_270),U_270)
| U_270 = unordered_pair(U_274,U_272) ),
inference(clausify,[status(thm)],[f_36_5]) ).
cnf(f_36_14,plain,
( sK49(U_274,U_272,U_270) != U_272
| ~ in(sK50(U_274,U_272,U_270),U_270)
| U_270 = unordered_pair(U_274,U_272) ),
inference(clausify,[status(thm)],[f_36_5]) ).
fof(f_37_1,plain,
! [A] :
( ( ( well_founded_relation(A)
| ? [B] :
( ! [C] :
( ~ disjoint(fiber(A,C),B)
| ~ in(C,B) )
& B != empty_set
& subset(B,relation_field(A)) ) )
& ( ! [B] :
( ? [C] :
( disjoint(fiber(A,C),B)
& in(C,B) )
| B = empty_set
| ~ subset(B,relation_field(A)) )
| ~ well_founded_relation(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d2_wellord1]) ).
fof(f_37_2,plain,
! [U_279] :
( ( ( well_founded_relation(U_279)
| ? [U_278] :
( ! [U_277] :
( ~ disjoint(fiber(U_279,U_277),U_278)
| ~ in(U_277,U_278) )
& U_278 != empty_set
& subset(U_278,relation_field(U_279)) ) )
& ( ! [U_276] :
( ? [U_275] :
( disjoint(fiber(U_279,U_275),U_276)
& in(U_275,U_276) )
| U_276 = empty_set
| ~ subset(U_276,relation_field(U_279)) )
| ~ well_founded_relation(U_279) ) )
| ~ relation(U_279) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_279] :
( ( ( well_founded_relation(U_279)
| ? [U_278] :
( ! [U_277] :
( ~ disjoint(fiber(U_279,U_277),U_278)
| ~ in(U_277,U_278) )
& U_278 != empty_set
& subset(U_278,relation_field(U_279)) ) )
& ( ! [U_276] :
( ( disjoint(fiber(U_279,sK51(U_279,U_276)),U_276)
& in(sK51(U_279,U_276),U_276) )
| U_276 = empty_set
| ~ subset(U_276,relation_field(U_279)) )
| ~ well_founded_relation(U_279) ) )
| ~ relation(U_279) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_275,sK51(U_279,U_276))],[f_37_2]) ).
fof(f_37_4,plain,
! [U_279] :
( ( ( well_founded_relation(U_279)
| ( ! [U_277] :
( ~ disjoint(fiber(U_279,U_277),sK52(U_279))
| ~ in(U_277,sK52(U_279)) )
& sK52(U_279) != empty_set
& subset(sK52(U_279),relation_field(U_279)) ) )
& ( ! [U_276] :
( ( disjoint(fiber(U_279,sK51(U_279,U_276)),U_276)
& in(sK51(U_279,U_276),U_276) )
| U_276 = empty_set
| ~ subset(U_276,relation_field(U_279)) )
| ~ well_founded_relation(U_279) ) )
| ~ relation(U_279) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_278,sK52(U_279))],[f_37_3]) ).
cnf(f_37_5,plain,
( in(sK51(U_279,U_276),U_276)
| U_276 = empty_set
| ~ subset(U_276,relation_field(U_279))
| ~ well_founded_relation(U_279)
| ~ relation(U_279) ),
inference(clausify,[status(thm)],[f_37_4]) ).
cnf(f_37_6,plain,
( disjoint(fiber(U_279,sK51(U_279,U_276)),U_276)
| U_276 = empty_set
| ~ subset(U_276,relation_field(U_279))
| ~ well_founded_relation(U_279)
| ~ relation(U_279) ),
inference(clausify,[status(thm)],[f_37_4]) ).
cnf(f_37_7,plain,
( subset(sK52(U_279),relation_field(U_279))
| well_founded_relation(U_279)
| ~ relation(U_279) ),
inference(clausify,[status(thm)],[f_37_4]) ).
cnf(f_37_8,plain,
( sK52(U_279) != empty_set
| well_founded_relation(U_279)
| ~ relation(U_279) ),
inference(clausify,[status(thm)],[f_37_4]) ).
cnf(f_37_9,plain,
( ~ disjoint(fiber(U_279,U_277),sK52(U_279))
| ~ in(U_277,sK52(U_279))
| well_founded_relation(U_279)
| ~ relation(U_279) ),
inference(clausify,[status(thm)],[f_37_4]) ).
fof(f_38_1,plain,
! [A,B,C] :
( ( C = set_union2(A,B)
| ? [D] :
( ( ~ in(D,C)
& ( in(D,B)
| in(D,A) ) )
| ( ~ in(D,B)
& ~ in(D,A)
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ( ~ in(D,B)
& ~ in(D,A) ) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(fof_nnf,[status(thm)],[d2_xboole_0]) ).
fof(f_38_2,plain,
! [U_284,U_283,U_282] :
( ( U_282 = set_union2(U_284,U_283)
| ? [U_281] :
( ( ~ in(U_281,U_282)
& ( in(U_281,U_283)
| in(U_281,U_284) ) )
| ( ~ in(U_281,U_283)
& ~ in(U_281,U_284)
& in(U_281,U_282) ) ) )
& ( ! [U_280] :
( ( in(U_280,U_282)
| ( ~ in(U_280,U_283)
& ~ in(U_280,U_284) ) )
& ( in(U_280,U_283)
| in(U_280,U_284)
| ~ in(U_280,U_282) ) )
| U_282 != set_union2(U_284,U_283) ) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
( ! [U_294,U_292,U_290] :
( U_290 = set_union2(U_294,U_292)
| ? [U_288] :
( ~ in(U_288,U_290)
& ( in(U_288,U_292)
| in(U_288,U_294) ) )
| ? [U_287] :
( ~ in(U_287,U_292)
& ~ in(U_287,U_294)
& in(U_287,U_290) ) )
& ! [U_293,U_291,U_289] :
( ( ! [U_286] :
( in(U_286,U_289)
| ( ~ in(U_286,U_291)
& ~ in(U_286,U_293) ) )
& ! [U_285] :
( in(U_285,U_291)
| in(U_285,U_293)
| ~ in(U_285,U_289) ) )
| U_289 != set_union2(U_293,U_291) ) ),
inference(miniscope,[status(thm)],[f_38_2]) ).
fof(f_38_4,plain,
( ! [U_294,U_292,U_290] :
( U_290 = set_union2(U_294,U_292)
| ? [U_288] :
( ~ in(U_288,U_290)
& ( in(U_288,U_292)
| in(U_288,U_294) ) )
| ( ~ in(sK53(U_294,U_292,U_290),U_292)
& ~ in(sK53(U_294,U_292,U_290),U_294)
& in(sK53(U_294,U_292,U_290),U_290) ) )
& ! [U_293,U_291,U_289] :
( ( ! [U_286] :
( in(U_286,U_289)
| ( ~ in(U_286,U_291)
& ~ in(U_286,U_293) ) )
& ! [U_285] :
( in(U_285,U_291)
| in(U_285,U_293)
| ~ in(U_285,U_289) ) )
| U_289 != set_union2(U_293,U_291) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_287,sK53(U_294,U_292,U_290))],[f_38_3]) ).
fof(f_38_5,plain,
( ! [U_294,U_292,U_290] :
( U_290 = set_union2(U_294,U_292)
| ( ~ in(sK54(U_294,U_292,U_290),U_290)
& ( in(sK54(U_294,U_292,U_290),U_292)
| in(sK54(U_294,U_292,U_290),U_294) ) )
| ( ~ in(sK53(U_294,U_292,U_290),U_292)
& ~ in(sK53(U_294,U_292,U_290),U_294)
& in(sK53(U_294,U_292,U_290),U_290) ) )
& ! [U_293,U_291,U_289] :
( ( ! [U_286] :
( in(U_286,U_289)
| ( ~ in(U_286,U_291)
& ~ in(U_286,U_293) ) )
& ! [U_285] :
( in(U_285,U_291)
| in(U_285,U_293)
| ~ in(U_285,U_289) ) )
| U_289 != set_union2(U_293,U_291) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_288,sK54(U_294,U_292,U_290))],[f_38_4]) ).
cnf(f_38_6,plain,
( in(U_285,U_291)
| in(U_285,U_293)
| ~ in(U_285,U_289)
| U_289 != set_union2(U_293,U_291) ),
inference(clausify,[status(thm)],[f_38_5]) ).
cnf(f_38_7,plain,
( ~ in(U_286,U_293)
| in(U_286,U_289)
| U_289 != set_union2(U_293,U_291) ),
inference(clausify,[status(thm)],[f_38_5]) ).
cnf(f_38_8,plain,
( ~ in(U_286,U_291)
| in(U_286,U_289)
| U_289 != set_union2(U_293,U_291) ),
inference(clausify,[status(thm)],[f_38_5]) ).
cnf(f_38_9,plain,
( in(sK54(U_294,U_292,U_290),U_292)
| in(sK54(U_294,U_292,U_290),U_294)
| in(sK53(U_294,U_292,U_290),U_290)
| U_290 = set_union2(U_294,U_292) ),
inference(clausify,[status(thm)],[f_38_5]) ).
cnf(f_38_10,plain,
( ~ in(sK54(U_294,U_292,U_290),U_290)
| in(sK53(U_294,U_292,U_290),U_290)
| U_290 = set_union2(U_294,U_292) ),
inference(clausify,[status(thm)],[f_38_5]) ).
cnf(f_38_11,plain,
( ~ in(sK53(U_294,U_292,U_290),U_294)
| in(sK54(U_294,U_292,U_290),U_292)
| in(sK54(U_294,U_292,U_290),U_294)
| U_290 = set_union2(U_294,U_292) ),
inference(clausify,[status(thm)],[f_38_5]) ).
cnf(f_38_12,plain,
( ~ in(sK53(U_294,U_292,U_290),U_292)
| in(sK54(U_294,U_292,U_290),U_292)
| in(sK54(U_294,U_292,U_290),U_294)
| U_290 = set_union2(U_294,U_292) ),
inference(clausify,[status(thm)],[f_38_5]) ).
cnf(f_38_13,plain,
( ~ in(sK53(U_294,U_292,U_290),U_294)
| ~ in(sK54(U_294,U_292,U_290),U_290)
| U_290 = set_union2(U_294,U_292) ),
inference(clausify,[status(thm)],[f_38_5]) ).
cnf(f_38_14,plain,
( ~ in(sK53(U_294,U_292,U_290),U_292)
| ~ in(sK54(U_294,U_292,U_290),U_290)
| U_290 = set_union2(U_294,U_292) ),
inference(clausify,[status(thm)],[f_38_5]) ).
fof(f_39_1,plain,
! [A,B,C] :
( ( C = cartesian_product2(A,B)
| ? [D] :
( ( ~ in(D,C)
& ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) ) )
| ( ! [E,F] :
( D != ordered_pair(E,F)
| ~ in(F,B)
| ~ in(E,A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ! [E,F] :
( D != ordered_pair(E,F)
| ~ in(F,B)
| ~ in(E,A) ) )
& ( ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) )
| ~ in(D,C) ) )
| C != cartesian_product2(A,B) ) ),
inference(fof_nnf,[status(thm)],[d2_zfmisc_1]) ).
fof(f_39_2,plain,
! [U_307,U_306,U_305] :
( ( U_305 = cartesian_product2(U_307,U_306)
| ? [U_304] :
( ( ~ in(U_304,U_305)
& ? [U_303,U_302] :
( U_304 = ordered_pair(U_303,U_302)
& in(U_302,U_306)
& in(U_303,U_307) ) )
| ( ! [U_301,U_300] :
( U_304 != ordered_pair(U_301,U_300)
| ~ in(U_300,U_306)
| ~ in(U_301,U_307) )
& in(U_304,U_305) ) ) )
& ( ! [U_299] :
( ( in(U_299,U_305)
| ! [U_298,U_297] :
( U_299 != ordered_pair(U_298,U_297)
| ~ in(U_297,U_306)
| ~ in(U_298,U_307) ) )
& ( ? [U_296,U_295] :
( U_299 = ordered_pair(U_296,U_295)
& in(U_295,U_306)
& in(U_296,U_307) )
| ~ in(U_299,U_305) ) )
| U_305 != cartesian_product2(U_307,U_306) ) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
( ! [U_317,U_315,U_313] :
( U_313 = cartesian_product2(U_317,U_315)
| ? [U_311] :
( ~ in(U_311,U_313)
& ? [U_303] :
( ? [U_302] :
( U_311 = ordered_pair(U_303,U_302)
& in(U_302,U_315) )
& in(U_303,U_317) ) )
| ? [U_310] :
( ! [U_301] :
( ! [U_300] :
( U_310 != ordered_pair(U_301,U_300)
| ~ in(U_300,U_315) )
| ~ in(U_301,U_317) )
& in(U_310,U_313) ) )
& ! [U_316,U_314,U_312] :
( ( ! [U_309] :
( in(U_309,U_312)
| ! [U_298] :
( ! [U_297] :
( U_309 != ordered_pair(U_298,U_297)
| ~ in(U_297,U_314) )
| ~ in(U_298,U_316) ) )
& ! [U_308] :
( ? [U_296] :
( ? [U_295] :
( U_308 = ordered_pair(U_296,U_295)
& in(U_295,U_314) )
& in(U_296,U_316) )
| ~ in(U_308,U_312) ) )
| U_312 != cartesian_product2(U_316,U_314) ) ),
inference(miniscope,[status(thm)],[f_39_2]) ).
fof(f_39_4,plain,
( ! [U_317,U_315,U_313] :
( U_313 = cartesian_product2(U_317,U_315)
| ? [U_311] :
( ~ in(U_311,U_313)
& ? [U_303] :
( ? [U_302] :
( U_311 = ordered_pair(U_303,U_302)
& in(U_302,U_315) )
& in(U_303,U_317) ) )
| ? [U_310] :
( ! [U_301] :
( ! [U_300] :
( U_310 != ordered_pair(U_301,U_300)
| ~ in(U_300,U_315) )
| ~ in(U_301,U_317) )
& in(U_310,U_313) ) )
& ! [U_316,U_314,U_312] :
( ( ! [U_309] :
( in(U_309,U_312)
| ! [U_298] :
( ! [U_297] :
( U_309 != ordered_pair(U_298,U_297)
| ~ in(U_297,U_314) )
| ~ in(U_298,U_316) ) )
& ! [U_308] :
( ( ? [U_295] :
( U_308 = ordered_pair(sK55(U_316,U_314,U_312,U_308),U_295)
& in(U_295,U_314) )
& in(sK55(U_316,U_314,U_312,U_308),U_316) )
| ~ in(U_308,U_312) ) )
| U_312 != cartesian_product2(U_316,U_314) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_296,sK55(U_316,U_314,U_312,U_308))],[f_39_3]) ).
fof(f_39_5,plain,
( ! [U_317,U_315,U_313] :
( U_313 = cartesian_product2(U_317,U_315)
| ? [U_311] :
( ~ in(U_311,U_313)
& ? [U_303] :
( ? [U_302] :
( U_311 = ordered_pair(U_303,U_302)
& in(U_302,U_315) )
& in(U_303,U_317) ) )
| ? [U_310] :
( ! [U_301] :
( ! [U_300] :
( U_310 != ordered_pair(U_301,U_300)
| ~ in(U_300,U_315) )
| ~ in(U_301,U_317) )
& in(U_310,U_313) ) )
& ! [U_316,U_314,U_312] :
( ( ! [U_309] :
( in(U_309,U_312)
| ! [U_298] :
( ! [U_297] :
( U_309 != ordered_pair(U_298,U_297)
| ~ in(U_297,U_314) )
| ~ in(U_298,U_316) ) )
& ! [U_308] :
( ( U_308 = ordered_pair(sK55(U_316,U_314,U_312,U_308),sK56(U_316,U_314,U_312,U_308))
& in(sK56(U_316,U_314,U_312,U_308),U_314)
& in(sK55(U_316,U_314,U_312,U_308),U_316) )
| ~ in(U_308,U_312) ) )
| U_312 != cartesian_product2(U_316,U_314) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_295,sK56(U_316,U_314,U_312,U_308))],[f_39_4]) ).
fof(f_39_6,plain,
( ! [U_317,U_315,U_313] :
( U_313 = cartesian_product2(U_317,U_315)
| ? [U_311] :
( ~ in(U_311,U_313)
& ? [U_303] :
( ? [U_302] :
( U_311 = ordered_pair(U_303,U_302)
& in(U_302,U_315) )
& in(U_303,U_317) ) )
| ( ! [U_301] :
( ! [U_300] :
( sK57(U_317,U_315,U_313) != ordered_pair(U_301,U_300)
| ~ in(U_300,U_315) )
| ~ in(U_301,U_317) )
& in(sK57(U_317,U_315,U_313),U_313) ) )
& ! [U_316,U_314,U_312] :
( ( ! [U_309] :
( in(U_309,U_312)
| ! [U_298] :
( ! [U_297] :
( U_309 != ordered_pair(U_298,U_297)
| ~ in(U_297,U_314) )
| ~ in(U_298,U_316) ) )
& ! [U_308] :
( ( U_308 = ordered_pair(sK55(U_316,U_314,U_312,U_308),sK56(U_316,U_314,U_312,U_308))
& in(sK56(U_316,U_314,U_312,U_308),U_314)
& in(sK55(U_316,U_314,U_312,U_308),U_316) )
| ~ in(U_308,U_312) ) )
| U_312 != cartesian_product2(U_316,U_314) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_310,sK57(U_317,U_315,U_313))],[f_39_5]) ).
fof(f_39_7,plain,
( ! [U_317,U_315,U_313] :
( U_313 = cartesian_product2(U_317,U_315)
| ( ~ in(sK58(U_317,U_315,U_313),U_313)
& ? [U_303] :
( ? [U_302] :
( sK58(U_317,U_315,U_313) = ordered_pair(U_303,U_302)
& in(U_302,U_315) )
& in(U_303,U_317) ) )
| ( ! [U_301] :
( ! [U_300] :
( sK57(U_317,U_315,U_313) != ordered_pair(U_301,U_300)
| ~ in(U_300,U_315) )
| ~ in(U_301,U_317) )
& in(sK57(U_317,U_315,U_313),U_313) ) )
& ! [U_316,U_314,U_312] :
( ( ! [U_309] :
( in(U_309,U_312)
| ! [U_298] :
( ! [U_297] :
( U_309 != ordered_pair(U_298,U_297)
| ~ in(U_297,U_314) )
| ~ in(U_298,U_316) ) )
& ! [U_308] :
( ( U_308 = ordered_pair(sK55(U_316,U_314,U_312,U_308),sK56(U_316,U_314,U_312,U_308))
& in(sK56(U_316,U_314,U_312,U_308),U_314)
& in(sK55(U_316,U_314,U_312,U_308),U_316) )
| ~ in(U_308,U_312) ) )
| U_312 != cartesian_product2(U_316,U_314) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_311,sK58(U_317,U_315,U_313))],[f_39_6]) ).
fof(f_39_8,plain,
( ! [U_317,U_315,U_313] :
( U_313 = cartesian_product2(U_317,U_315)
| ( ~ in(sK58(U_317,U_315,U_313),U_313)
& ? [U_302] :
( sK58(U_317,U_315,U_313) = ordered_pair(sK59(U_317,U_315,U_313),U_302)
& in(U_302,U_315) )
& in(sK59(U_317,U_315,U_313),U_317) )
| ( ! [U_301] :
( ! [U_300] :
( sK57(U_317,U_315,U_313) != ordered_pair(U_301,U_300)
| ~ in(U_300,U_315) )
| ~ in(U_301,U_317) )
& in(sK57(U_317,U_315,U_313),U_313) ) )
& ! [U_316,U_314,U_312] :
( ( ! [U_309] :
( in(U_309,U_312)
| ! [U_298] :
( ! [U_297] :
( U_309 != ordered_pair(U_298,U_297)
| ~ in(U_297,U_314) )
| ~ in(U_298,U_316) ) )
& ! [U_308] :
( ( U_308 = ordered_pair(sK55(U_316,U_314,U_312,U_308),sK56(U_316,U_314,U_312,U_308))
& in(sK56(U_316,U_314,U_312,U_308),U_314)
& in(sK55(U_316,U_314,U_312,U_308),U_316) )
| ~ in(U_308,U_312) ) )
| U_312 != cartesian_product2(U_316,U_314) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_303,sK59(U_317,U_315,U_313))],[f_39_7]) ).
fof(f_39_9,plain,
( ! [U_317,U_315,U_313] :
( U_313 = cartesian_product2(U_317,U_315)
| ( ~ in(sK58(U_317,U_315,U_313),U_313)
& sK58(U_317,U_315,U_313) = ordered_pair(sK59(U_317,U_315,U_313),sK60(U_317,U_315,U_313))
& in(sK60(U_317,U_315,U_313),U_315)
& in(sK59(U_317,U_315,U_313),U_317) )
| ( ! [U_301] :
( ! [U_300] :
( sK57(U_317,U_315,U_313) != ordered_pair(U_301,U_300)
| ~ in(U_300,U_315) )
| ~ in(U_301,U_317) )
& in(sK57(U_317,U_315,U_313),U_313) ) )
& ! [U_316,U_314,U_312] :
( ( ! [U_309] :
( in(U_309,U_312)
| ! [U_298] :
( ! [U_297] :
( U_309 != ordered_pair(U_298,U_297)
| ~ in(U_297,U_314) )
| ~ in(U_298,U_316) ) )
& ! [U_308] :
( ( U_308 = ordered_pair(sK55(U_316,U_314,U_312,U_308),sK56(U_316,U_314,U_312,U_308))
& in(sK56(U_316,U_314,U_312,U_308),U_314)
& in(sK55(U_316,U_314,U_312,U_308),U_316) )
| ~ in(U_308,U_312) ) )
| U_312 != cartesian_product2(U_316,U_314) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_302,sK60(U_317,U_315,U_313))],[f_39_8]) ).
cnf(f_39_10,plain,
( in(sK55(U_316,U_314,U_312,U_308),U_316)
| ~ in(U_308,U_312)
| U_312 != cartesian_product2(U_316,U_314) ),
inference(clausify,[status(thm)],[f_39_9]) ).
cnf(f_39_11,plain,
( in(sK56(U_316,U_314,U_312,U_308),U_314)
| ~ in(U_308,U_312)
| U_312 != cartesian_product2(U_316,U_314) ),
inference(clausify,[status(thm)],[f_39_9]) ).
cnf(f_39_12,plain,
( U_308 = ordered_pair(sK55(U_316,U_314,U_312,U_308),sK56(U_316,U_314,U_312,U_308))
| ~ in(U_308,U_312)
| U_312 != cartesian_product2(U_316,U_314) ),
inference(clausify,[status(thm)],[f_39_9]) ).
cnf(f_39_13,plain,
( in(U_309,U_312)
| U_309 != ordered_pair(U_298,U_297)
| ~ in(U_297,U_314)
| ~ in(U_298,U_316)
| U_312 != cartesian_product2(U_316,U_314) ),
inference(clausify,[status(thm)],[f_39_9]) ).
cnf(f_39_14,plain,
( in(sK59(U_317,U_315,U_313),U_317)
| in(sK57(U_317,U_315,U_313),U_313)
| U_313 = cartesian_product2(U_317,U_315) ),
inference(clausify,[status(thm)],[f_39_9]) ).
cnf(f_39_15,plain,
( in(sK60(U_317,U_315,U_313),U_315)
| in(sK57(U_317,U_315,U_313),U_313)
| U_313 = cartesian_product2(U_317,U_315) ),
inference(clausify,[status(thm)],[f_39_9]) ).
cnf(f_39_16,plain,
( sK58(U_317,U_315,U_313) = ordered_pair(sK59(U_317,U_315,U_313),sK60(U_317,U_315,U_313))
| in(sK57(U_317,U_315,U_313),U_313)
| U_313 = cartesian_product2(U_317,U_315) ),
inference(clausify,[status(thm)],[f_39_9]) ).
cnf(f_39_17,plain,
( ~ in(sK58(U_317,U_315,U_313),U_313)
| in(sK57(U_317,U_315,U_313),U_313)
| U_313 = cartesian_product2(U_317,U_315) ),
inference(clausify,[status(thm)],[f_39_9]) ).
cnf(f_39_18,plain,
( in(sK59(U_317,U_315,U_313),U_317)
| sK57(U_317,U_315,U_313) != ordered_pair(U_301,U_300)
| ~ in(U_300,U_315)
| ~ in(U_301,U_317)
| U_313 = cartesian_product2(U_317,U_315) ),
inference(clausify,[status(thm)],[f_39_9]) ).
cnf(f_39_19,plain,
( in(sK60(U_317,U_315,U_313),U_315)
| sK57(U_317,U_315,U_313) != ordered_pair(U_301,U_300)
| ~ in(U_300,U_315)
| ~ in(U_301,U_317)
| U_313 = cartesian_product2(U_317,U_315) ),
inference(clausify,[status(thm)],[f_39_9]) ).
cnf(f_39_20,plain,
( sK58(U_317,U_315,U_313) = ordered_pair(sK59(U_317,U_315,U_313),sK60(U_317,U_315,U_313))
| sK57(U_317,U_315,U_313) != ordered_pair(U_301,U_300)
| ~ in(U_300,U_315)
| ~ in(U_301,U_317)
| U_313 = cartesian_product2(U_317,U_315) ),
inference(clausify,[status(thm)],[f_39_9]) ).
cnf(f_39_21,plain,
( ~ in(sK58(U_317,U_315,U_313),U_313)
| sK57(U_317,U_315,U_313) != ordered_pair(U_301,U_300)
| ~ in(U_300,U_315)
| ~ in(U_301,U_317)
| U_313 = cartesian_product2(U_317,U_315) ),
inference(clausify,[status(thm)],[f_39_9]) ).
fof(f_40_1,plain,
! [A] :
( ( epsilon_connected(A)
| ? [B,C] :
( ~ in(C,B)
& B != C
& ~ in(B,C)
& in(C,A)
& in(B,A) ) )
& ( ! [B,C] :
( in(C,B)
| B = C
| in(B,C)
| ~ in(C,A)
| ~ in(B,A) )
| ~ epsilon_connected(A) ) ),
inference(fof_nnf,[status(thm)],[d3_ordinal1]) ).
fof(f_40_2,plain,
! [U_322] :
( ( epsilon_connected(U_322)
| ? [U_321,U_320] :
( ~ in(U_320,U_321)
& U_321 != U_320
& ~ in(U_321,U_320)
& in(U_320,U_322)
& in(U_321,U_322) ) )
& ( ! [U_319,U_318] :
( in(U_318,U_319)
| U_319 = U_318
| in(U_319,U_318)
| ~ in(U_318,U_322)
| ~ in(U_319,U_322) )
| ~ epsilon_connected(U_322) ) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
( ! [U_324] :
( epsilon_connected(U_324)
| ? [U_321] :
( ? [U_320] :
( ~ in(U_320,U_321)
& U_321 != U_320
& ~ in(U_321,U_320)
& in(U_320,U_324) )
& in(U_321,U_324) ) )
& ! [U_323] :
( ! [U_319] :
( ! [U_318] :
( in(U_318,U_319)
| U_319 = U_318
| in(U_319,U_318)
| ~ in(U_318,U_323) )
| ~ in(U_319,U_323) )
| ~ epsilon_connected(U_323) ) ),
inference(miniscope,[status(thm)],[f_40_2]) ).
fof(f_40_4,plain,
( ! [U_324] :
( epsilon_connected(U_324)
| ( ? [U_320] :
( ~ in(U_320,sK61(U_324))
& sK61(U_324) != U_320
& ~ in(sK61(U_324),U_320)
& in(U_320,U_324) )
& in(sK61(U_324),U_324) ) )
& ! [U_323] :
( ! [U_319] :
( ! [U_318] :
( in(U_318,U_319)
| U_319 = U_318
| in(U_319,U_318)
| ~ in(U_318,U_323) )
| ~ in(U_319,U_323) )
| ~ epsilon_connected(U_323) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_321,sK61(U_324))],[f_40_3]) ).
fof(f_40_5,plain,
( ! [U_324] :
( epsilon_connected(U_324)
| ( ~ in(sK62(U_324),sK61(U_324))
& sK61(U_324) != sK62(U_324)
& ~ in(sK61(U_324),sK62(U_324))
& in(sK62(U_324),U_324)
& in(sK61(U_324),U_324) ) )
& ! [U_323] :
( ! [U_319] :
( ! [U_318] :
( in(U_318,U_319)
| U_319 = U_318
| in(U_319,U_318)
| ~ in(U_318,U_323) )
| ~ in(U_319,U_323) )
| ~ epsilon_connected(U_323) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_320,sK62(U_324))],[f_40_4]) ).
cnf(f_40_6,plain,
( in(U_318,U_319)
| U_319 = U_318
| in(U_319,U_318)
| ~ in(U_318,U_323)
| ~ in(U_319,U_323)
| ~ epsilon_connected(U_323) ),
inference(clausify,[status(thm)],[f_40_5]) ).
cnf(f_40_7,plain,
( in(sK61(U_324),U_324)
| epsilon_connected(U_324) ),
inference(clausify,[status(thm)],[f_40_5]) ).
cnf(f_40_8,plain,
( in(sK62(U_324),U_324)
| epsilon_connected(U_324) ),
inference(clausify,[status(thm)],[f_40_5]) ).
cnf(f_40_9,plain,
( ~ in(sK61(U_324),sK62(U_324))
| epsilon_connected(U_324) ),
inference(clausify,[status(thm)],[f_40_5]) ).
cnf(f_40_10,plain,
( sK61(U_324) != sK62(U_324)
| epsilon_connected(U_324) ),
inference(clausify,[status(thm)],[f_40_5]) ).
cnf(f_40_11,plain,
( ~ in(sK62(U_324),sK61(U_324))
| epsilon_connected(U_324) ),
inference(clausify,[status(thm)],[f_40_5]) ).
fof(f_41_1,plain,
! [A] :
( ! [B] :
( ( ( subset(A,B)
| ? [C,D] :
( ~ in(ordered_pair(C,D),B)
& in(ordered_pair(C,D),A) ) )
& ( ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) )
| ~ subset(A,B) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d3_relat_1]) ).
fof(f_41_2,plain,
! [U_330] :
( ! [U_329] :
( ( ( subset(U_330,U_329)
| ? [U_328,U_327] :
( ~ in(ordered_pair(U_328,U_327),U_329)
& in(ordered_pair(U_328,U_327),U_330) ) )
& ( ! [U_326,U_325] :
( in(ordered_pair(U_326,U_325),U_329)
| ~ in(ordered_pair(U_326,U_325),U_330) )
| ~ subset(U_330,U_329) ) )
| ~ relation(U_329) )
| ~ relation(U_330) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_330] :
( ! [U_329] :
( ( ( subset(U_330,U_329)
| ? [U_327] :
( ~ in(ordered_pair(sK63(U_330,U_329),U_327),U_329)
& in(ordered_pair(sK63(U_330,U_329),U_327),U_330) ) )
& ( ! [U_326,U_325] :
( in(ordered_pair(U_326,U_325),U_329)
| ~ in(ordered_pair(U_326,U_325),U_330) )
| ~ subset(U_330,U_329) ) )
| ~ relation(U_329) )
| ~ relation(U_330) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_328,sK63(U_330,U_329))],[f_41_2]) ).
fof(f_41_4,plain,
! [U_330] :
( ! [U_329] :
( ( ( subset(U_330,U_329)
| ( ~ in(ordered_pair(sK63(U_330,U_329),sK64(U_330,U_329)),U_329)
& in(ordered_pair(sK63(U_330,U_329),sK64(U_330,U_329)),U_330) ) )
& ( ! [U_326,U_325] :
( in(ordered_pair(U_326,U_325),U_329)
| ~ in(ordered_pair(U_326,U_325),U_330) )
| ~ subset(U_330,U_329) ) )
| ~ relation(U_329) )
| ~ relation(U_330) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_327,sK64(U_330,U_329))],[f_41_3]) ).
cnf(f_41_5,plain,
( in(ordered_pair(U_326,U_325),U_329)
| ~ in(ordered_pair(U_326,U_325),U_330)
| ~ subset(U_330,U_329)
| ~ relation(U_329)
| ~ relation(U_330) ),
inference(clausify,[status(thm)],[f_41_4]) ).
cnf(f_41_6,plain,
( in(ordered_pair(sK63(U_330,U_329),sK64(U_330,U_329)),U_330)
| subset(U_330,U_329)
| ~ relation(U_329)
| ~ relation(U_330) ),
inference(clausify,[status(thm)],[f_41_4]) ).
cnf(f_41_7,plain,
( ~ in(ordered_pair(sK63(U_330,U_329),sK64(U_330,U_329)),U_329)
| subset(U_330,U_329)
| ~ relation(U_329)
| ~ relation(U_330) ),
inference(clausify,[status(thm)],[f_41_4]) ).
fof(f_42_1,plain,
! [A,B] :
( ( subset(A,B)
| ? [C] :
( ~ in(C,B)
& in(C,A) ) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(f_42_2,plain,
! [U_334,U_333] :
( ( subset(U_334,U_333)
| ? [U_332] :
( ~ in(U_332,U_333)
& in(U_332,U_334) ) )
& ( ! [U_331] :
( in(U_331,U_333)
| ~ in(U_331,U_334) )
| ~ subset(U_334,U_333) ) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
( ! [U_338,U_336] :
( subset(U_338,U_336)
| ? [U_332] :
( ~ in(U_332,U_336)
& in(U_332,U_338) ) )
& ! [U_337,U_335] :
( ! [U_331] :
( in(U_331,U_335)
| ~ in(U_331,U_337) )
| ~ subset(U_337,U_335) ) ),
inference(miniscope,[status(thm)],[f_42_2]) ).
fof(f_42_4,plain,
( ! [U_338,U_336] :
( subset(U_338,U_336)
| ( ~ in(sK65(U_338,U_336),U_336)
& in(sK65(U_338,U_336),U_338) ) )
& ! [U_337,U_335] :
( ! [U_331] :
( in(U_331,U_335)
| ~ in(U_331,U_337) )
| ~ subset(U_337,U_335) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_332,sK65(U_338,U_336))],[f_42_3]) ).
cnf(f_42_5,plain,
( in(U_331,U_335)
| ~ in(U_331,U_337)
| ~ subset(U_337,U_335) ),
inference(clausify,[status(thm)],[f_42_4]) ).
cnf(f_42_6,plain,
( in(sK65(U_338,U_336),U_338)
| subset(U_338,U_336) ),
inference(clausify,[status(thm)],[f_42_4]) ).
cnf(f_42_7,plain,
( ~ in(sK65(U_338,U_336),U_336)
| subset(U_338,U_336) ),
inference(clausify,[status(thm)],[f_42_4]) ).
fof(f_43_1,plain,
! [A] :
( ! [B] :
( ( is_well_founded_in(A,B)
| ? [C] :
( ! [D] :
( ~ disjoint(fiber(A,D),C)
| ~ in(D,C) )
& C != empty_set
& subset(C,B) ) )
& ( ! [C] :
( ? [D] :
( disjoint(fiber(A,D),C)
& in(D,C) )
| C = empty_set
| ~ subset(C,B) )
| ~ is_well_founded_in(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d3_wellord1]) ).
fof(f_43_2,plain,
! [U_344] :
( ! [U_343] :
( ( is_well_founded_in(U_344,U_343)
| ? [U_342] :
( ! [U_341] :
( ~ disjoint(fiber(U_344,U_341),U_342)
| ~ in(U_341,U_342) )
& U_342 != empty_set
& subset(U_342,U_343) ) )
& ( ! [U_340] :
( ? [U_339] :
( disjoint(fiber(U_344,U_339),U_340)
& in(U_339,U_340) )
| U_340 = empty_set
| ~ subset(U_340,U_343) )
| ~ is_well_founded_in(U_344,U_343) ) )
| ~ relation(U_344) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_344] :
( ( ! [U_346] :
( is_well_founded_in(U_344,U_346)
| ? [U_342] :
( ! [U_341] :
( ~ disjoint(fiber(U_344,U_341),U_342)
| ~ in(U_341,U_342) )
& U_342 != empty_set
& subset(U_342,U_346) ) )
& ! [U_345] :
( ! [U_340] :
( ? [U_339] :
( disjoint(fiber(U_344,U_339),U_340)
& in(U_339,U_340) )
| U_340 = empty_set
| ~ subset(U_340,U_345) )
| ~ is_well_founded_in(U_344,U_345) ) )
| ~ relation(U_344) ),
inference(miniscope,[status(thm)],[f_43_2]) ).
fof(f_43_4,plain,
! [U_344] :
( ( ! [U_346] :
( is_well_founded_in(U_344,U_346)
| ? [U_342] :
( ! [U_341] :
( ~ disjoint(fiber(U_344,U_341),U_342)
| ~ in(U_341,U_342) )
& U_342 != empty_set
& subset(U_342,U_346) ) )
& ! [U_345] :
( ! [U_340] :
( ( disjoint(fiber(U_344,sK66(U_344,U_345,U_340)),U_340)
& in(sK66(U_344,U_345,U_340),U_340) )
| U_340 = empty_set
| ~ subset(U_340,U_345) )
| ~ is_well_founded_in(U_344,U_345) ) )
| ~ relation(U_344) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_339,sK66(U_344,U_345,U_340))],[f_43_3]) ).
fof(f_43_5,plain,
! [U_344] :
( ( ! [U_346] :
( is_well_founded_in(U_344,U_346)
| ( ! [U_341] :
( ~ disjoint(fiber(U_344,U_341),sK67(U_344,U_346))
| ~ in(U_341,sK67(U_344,U_346)) )
& sK67(U_344,U_346) != empty_set
& subset(sK67(U_344,U_346),U_346) ) )
& ! [U_345] :
( ! [U_340] :
( ( disjoint(fiber(U_344,sK66(U_344,U_345,U_340)),U_340)
& in(sK66(U_344,U_345,U_340),U_340) )
| U_340 = empty_set
| ~ subset(U_340,U_345) )
| ~ is_well_founded_in(U_344,U_345) ) )
| ~ relation(U_344) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_342,sK67(U_344,U_346))],[f_43_4]) ).
cnf(f_43_6,plain,
( in(sK66(U_344,U_345,U_340),U_340)
| U_340 = empty_set
| ~ subset(U_340,U_345)
| ~ is_well_founded_in(U_344,U_345)
| ~ relation(U_344) ),
inference(clausify,[status(thm)],[f_43_5]) ).
cnf(f_43_7,plain,
( disjoint(fiber(U_344,sK66(U_344,U_345,U_340)),U_340)
| U_340 = empty_set
| ~ subset(U_340,U_345)
| ~ is_well_founded_in(U_344,U_345)
| ~ relation(U_344) ),
inference(clausify,[status(thm)],[f_43_5]) ).
cnf(f_43_8,plain,
( subset(sK67(U_344,U_346),U_346)
| is_well_founded_in(U_344,U_346)
| ~ relation(U_344) ),
inference(clausify,[status(thm)],[f_43_5]) ).
cnf(f_43_9,plain,
( sK67(U_344,U_346) != empty_set
| is_well_founded_in(U_344,U_346)
| ~ relation(U_344) ),
inference(clausify,[status(thm)],[f_43_5]) ).
cnf(f_43_10,plain,
( ~ disjoint(fiber(U_344,U_341),sK67(U_344,U_346))
| ~ in(U_341,sK67(U_344,U_346))
| is_well_founded_in(U_344,U_346)
| ~ relation(U_344) ),
inference(clausify,[status(thm)],[f_43_5]) ).
fof(f_44_1,plain,
! [A,B,C] :
( ( C = set_intersection2(A,B)
| ? [D] :
( ( ~ in(D,C)
& in(D,B)
& in(D,A) )
| ( ( ~ in(D,B)
| ~ in(D,A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ~ in(D,B)
| ~ in(D,A) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_xboole_0]) ).
fof(f_44_2,plain,
! [U_351,U_350,U_349] :
( ( U_349 = set_intersection2(U_351,U_350)
| ? [U_348] :
( ( ~ in(U_348,U_349)
& in(U_348,U_350)
& in(U_348,U_351) )
| ( ( ~ in(U_348,U_350)
| ~ in(U_348,U_351) )
& in(U_348,U_349) ) ) )
& ( ! [U_347] :
( ( in(U_347,U_349)
| ~ in(U_347,U_350)
| ~ in(U_347,U_351) )
& ( ( in(U_347,U_350)
& in(U_347,U_351) )
| ~ in(U_347,U_349) ) )
| U_349 != set_intersection2(U_351,U_350) ) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
( ! [U_361,U_359,U_357] :
( U_357 = set_intersection2(U_361,U_359)
| ? [U_355] :
( ~ in(U_355,U_357)
& in(U_355,U_359)
& in(U_355,U_361) )
| ? [U_354] :
( ( ~ in(U_354,U_359)
| ~ in(U_354,U_361) )
& in(U_354,U_357) ) )
& ! [U_360,U_358,U_356] :
( ( ! [U_353] :
( in(U_353,U_356)
| ~ in(U_353,U_358)
| ~ in(U_353,U_360) )
& ! [U_352] :
( ( in(U_352,U_358)
& in(U_352,U_360) )
| ~ in(U_352,U_356) ) )
| U_356 != set_intersection2(U_360,U_358) ) ),
inference(miniscope,[status(thm)],[f_44_2]) ).
fof(f_44_4,plain,
( ! [U_361,U_359,U_357] :
( U_357 = set_intersection2(U_361,U_359)
| ? [U_355] :
( ~ in(U_355,U_357)
& in(U_355,U_359)
& in(U_355,U_361) )
| ( ( ~ in(sK68(U_361,U_359,U_357),U_359)
| ~ in(sK68(U_361,U_359,U_357),U_361) )
& in(sK68(U_361,U_359,U_357),U_357) ) )
& ! [U_360,U_358,U_356] :
( ( ! [U_353] :
( in(U_353,U_356)
| ~ in(U_353,U_358)
| ~ in(U_353,U_360) )
& ! [U_352] :
( ( in(U_352,U_358)
& in(U_352,U_360) )
| ~ in(U_352,U_356) ) )
| U_356 != set_intersection2(U_360,U_358) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_354,sK68(U_361,U_359,U_357))],[f_44_3]) ).
fof(f_44_5,plain,
( ! [U_361,U_359,U_357] :
( U_357 = set_intersection2(U_361,U_359)
| ( ~ in(sK69(U_361,U_359,U_357),U_357)
& in(sK69(U_361,U_359,U_357),U_359)
& in(sK69(U_361,U_359,U_357),U_361) )
| ( ( ~ in(sK68(U_361,U_359,U_357),U_359)
| ~ in(sK68(U_361,U_359,U_357),U_361) )
& in(sK68(U_361,U_359,U_357),U_357) ) )
& ! [U_360,U_358,U_356] :
( ( ! [U_353] :
( in(U_353,U_356)
| ~ in(U_353,U_358)
| ~ in(U_353,U_360) )
& ! [U_352] :
( ( in(U_352,U_358)
& in(U_352,U_360) )
| ~ in(U_352,U_356) ) )
| U_356 != set_intersection2(U_360,U_358) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_355,sK69(U_361,U_359,U_357))],[f_44_4]) ).
cnf(f_44_6,plain,
( in(U_352,U_360)
| ~ in(U_352,U_356)
| U_356 != set_intersection2(U_360,U_358) ),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(f_44_7,plain,
( in(U_352,U_358)
| ~ in(U_352,U_356)
| U_356 != set_intersection2(U_360,U_358) ),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(f_44_8,plain,
( in(U_353,U_356)
| ~ in(U_353,U_358)
| ~ in(U_353,U_360)
| U_356 != set_intersection2(U_360,U_358) ),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(f_44_9,plain,
( in(sK69(U_361,U_359,U_357),U_361)
| in(sK68(U_361,U_359,U_357),U_357)
| U_357 = set_intersection2(U_361,U_359) ),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(f_44_10,plain,
( in(sK69(U_361,U_359,U_357),U_359)
| in(sK68(U_361,U_359,U_357),U_357)
| U_357 = set_intersection2(U_361,U_359) ),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(f_44_11,plain,
( ~ in(sK69(U_361,U_359,U_357),U_357)
| in(sK68(U_361,U_359,U_357),U_357)
| U_357 = set_intersection2(U_361,U_359) ),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(f_44_12,plain,
( in(sK69(U_361,U_359,U_357),U_361)
| ~ in(sK68(U_361,U_359,U_357),U_359)
| ~ in(sK68(U_361,U_359,U_357),U_361)
| U_357 = set_intersection2(U_361,U_359) ),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(f_44_13,plain,
( in(sK69(U_361,U_359,U_357),U_359)
| ~ in(sK68(U_361,U_359,U_357),U_359)
| ~ in(sK68(U_361,U_359,U_357),U_361)
| U_357 = set_intersection2(U_361,U_359) ),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(f_44_14,plain,
( ~ in(sK69(U_361,U_359,U_357),U_357)
| ~ in(sK68(U_361,U_359,U_357),U_359)
| ~ in(sK68(U_361,U_359,U_357),U_361)
| U_357 = set_intersection2(U_361,U_359) ),
inference(clausify,[status(thm)],[f_44_5]) ).
fof(f_45_1,plain,
! [A] :
( ! [B,C] :
( ( ( ( C = apply(A,B)
| C != empty_set )
& ( C = empty_set
| C != apply(A,B) ) )
| in(B,relation_dom(A)) )
& ( ( ( C = apply(A,B)
| ~ in(ordered_pair(B,C),A) )
& ( in(ordered_pair(B,C),A)
| C != apply(A,B) ) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d4_funct_1]) ).
fof(f_45_2,plain,
! [U_364] :
( ! [U_363,U_362] :
( ( ( ( U_362 = apply(U_364,U_363)
| U_362 != empty_set )
& ( U_362 = empty_set
| U_362 != apply(U_364,U_363) ) )
| in(U_363,relation_dom(U_364)) )
& ( ( ( U_362 = apply(U_364,U_363)
| ~ in(ordered_pair(U_363,U_362),U_364) )
& ( in(ordered_pair(U_363,U_362),U_364)
| U_362 != apply(U_364,U_363) ) )
| ~ in(U_363,relation_dom(U_364)) ) )
| ~ function(U_364)
| ~ relation(U_364) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_364] :
( ( ! [U_372] :
( ( ! [U_370] :
( U_370 = apply(U_364,U_372)
| U_370 != empty_set )
& ! [U_369] :
( U_369 = empty_set
| U_369 != apply(U_364,U_372) ) )
| in(U_372,relation_dom(U_364)) )
& ! [U_371] :
( ( ! [U_368] :
( U_368 = apply(U_364,U_371)
| ~ in(ordered_pair(U_371,U_368),U_364) )
& ! [U_367] :
( in(ordered_pair(U_371,U_367),U_364)
| U_367 != apply(U_364,U_371) ) )
| ~ in(U_371,relation_dom(U_364)) ) )
| ~ function(U_364)
| ~ relation(U_364) ),
inference(miniscope,[status(thm)],[f_45_2]) ).
cnf(f_45_4,plain,
( in(ordered_pair(U_371,U_367),U_364)
| U_367 != apply(U_364,U_371)
| ~ in(U_371,relation_dom(U_364))
| ~ function(U_364)
| ~ relation(U_364) ),
inference(clausify,[status(thm)],[f_45_3]) ).
cnf(f_45_5,plain,
( U_368 = apply(U_364,U_371)
| ~ in(ordered_pair(U_371,U_368),U_364)
| ~ in(U_371,relation_dom(U_364))
| ~ function(U_364)
| ~ relation(U_364) ),
inference(clausify,[status(thm)],[f_45_3]) ).
cnf(f_45_6,plain,
( U_369 = empty_set
| U_369 != apply(U_364,U_372)
| in(U_372,relation_dom(U_364))
| ~ function(U_364)
| ~ relation(U_364) ),
inference(clausify,[status(thm)],[f_45_3]) ).
cnf(f_45_7,plain,
( U_370 = apply(U_364,U_372)
| U_370 != empty_set
| in(U_372,relation_dom(U_364))
| ~ function(U_364)
| ~ relation(U_364) ),
inference(clausify,[status(thm)],[f_45_3]) ).
fof(f_46_1,plain,
! [A] :
( ( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) )
& ( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ) ),
inference(fof_nnf,[status(thm)],[d4_ordinal1]) ).
fof(f_46_2,plain,
! [U_373] :
( ( ordinal(U_373)
| ~ epsilon_connected(U_373)
| ~ epsilon_transitive(U_373) )
& ( ( epsilon_connected(U_373)
& epsilon_transitive(U_373) )
| ~ ordinal(U_373) ) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
( ! [U_375] :
( ordinal(U_375)
| ~ epsilon_connected(U_375)
| ~ epsilon_transitive(U_375) )
& ! [U_374] :
( ( epsilon_connected(U_374)
& epsilon_transitive(U_374) )
| ~ ordinal(U_374) ) ),
inference(miniscope,[status(thm)],[f_46_2]) ).
cnf(f_46_4,plain,
( epsilon_transitive(U_374)
| ~ ordinal(U_374) ),
inference(clausify,[status(thm)],[f_46_3]) ).
cnf(f_46_5,plain,
( epsilon_connected(U_374)
| ~ ordinal(U_374) ),
inference(clausify,[status(thm)],[f_46_3]) ).
cnf(f_46_6,plain,
( ordinal(U_375)
| ~ epsilon_connected(U_375)
| ~ epsilon_transitive(U_375) ),
inference(clausify,[status(thm)],[f_46_3]) ).
fof(f_47_1,plain,
! [A] :
( ! [B] :
( ( B = relation_dom(A)
| ? [C] :
( ( ~ in(C,B)
& ? [D] : in(ordered_pair(C,D),A) )
| ( ! [D] : ~ in(ordered_pair(C,D),A)
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) )
& ( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d4_relat_1]) ).
fof(f_47_2,plain,
! [U_383] :
( ! [U_382] :
( ( U_382 = relation_dom(U_383)
| ? [U_381] :
( ( ~ in(U_381,U_382)
& ? [U_380] : in(ordered_pair(U_381,U_380),U_383) )
| ( ! [U_379] : ~ in(ordered_pair(U_381,U_379),U_383)
& in(U_381,U_382) ) ) )
& ( ! [U_378] :
( ( in(U_378,U_382)
| ! [U_377] : ~ in(ordered_pair(U_378,U_377),U_383) )
& ( ? [U_376] : in(ordered_pair(U_378,U_376),U_383)
| ~ in(U_378,U_382) ) )
| U_382 != relation_dom(U_383) ) )
| ~ relation(U_383) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_383] :
( ( ! [U_389] :
( U_389 = relation_dom(U_383)
| ? [U_387] :
( ~ in(U_387,U_389)
& ? [U_380] : in(ordered_pair(U_387,U_380),U_383) )
| ? [U_386] :
( ! [U_379] : ~ in(ordered_pair(U_386,U_379),U_383)
& in(U_386,U_389) ) )
& ! [U_388] :
( ( ! [U_385] :
( in(U_385,U_388)
| ! [U_377] : ~ in(ordered_pair(U_385,U_377),U_383) )
& ! [U_384] :
( ? [U_376] : in(ordered_pair(U_384,U_376),U_383)
| ~ in(U_384,U_388) ) )
| U_388 != relation_dom(U_383) ) )
| ~ relation(U_383) ),
inference(miniscope,[status(thm)],[f_47_2]) ).
fof(f_47_4,plain,
! [U_383] :
( ( ! [U_389] :
( U_389 = relation_dom(U_383)
| ? [U_387] :
( ~ in(U_387,U_389)
& ? [U_380] : in(ordered_pair(U_387,U_380),U_383) )
| ? [U_386] :
( ! [U_379] : ~ in(ordered_pair(U_386,U_379),U_383)
& in(U_386,U_389) ) )
& ! [U_388] :
( ( ! [U_385] :
( in(U_385,U_388)
| ! [U_377] : ~ in(ordered_pair(U_385,U_377),U_383) )
& ! [U_384] :
( in(ordered_pair(U_384,sK70(U_383,U_388,U_384)),U_383)
| ~ in(U_384,U_388) ) )
| U_388 != relation_dom(U_383) ) )
| ~ relation(U_383) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_376,sK70(U_383,U_388,U_384))],[f_47_3]) ).
fof(f_47_5,plain,
! [U_383] :
( ( ! [U_389] :
( U_389 = relation_dom(U_383)
| ? [U_387] :
( ~ in(U_387,U_389)
& ? [U_380] : in(ordered_pair(U_387,U_380),U_383) )
| ( ! [U_379] : ~ in(ordered_pair(sK71(U_383,U_389),U_379),U_383)
& in(sK71(U_383,U_389),U_389) ) )
& ! [U_388] :
( ( ! [U_385] :
( in(U_385,U_388)
| ! [U_377] : ~ in(ordered_pair(U_385,U_377),U_383) )
& ! [U_384] :
( in(ordered_pair(U_384,sK70(U_383,U_388,U_384)),U_383)
| ~ in(U_384,U_388) ) )
| U_388 != relation_dom(U_383) ) )
| ~ relation(U_383) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_386,sK71(U_383,U_389))],[f_47_4]) ).
fof(f_47_6,plain,
! [U_383] :
( ( ! [U_389] :
( U_389 = relation_dom(U_383)
| ( ~ in(sK72(U_383,U_389),U_389)
& ? [U_380] : in(ordered_pair(sK72(U_383,U_389),U_380),U_383) )
| ( ! [U_379] : ~ in(ordered_pair(sK71(U_383,U_389),U_379),U_383)
& in(sK71(U_383,U_389),U_389) ) )
& ! [U_388] :
( ( ! [U_385] :
( in(U_385,U_388)
| ! [U_377] : ~ in(ordered_pair(U_385,U_377),U_383) )
& ! [U_384] :
( in(ordered_pair(U_384,sK70(U_383,U_388,U_384)),U_383)
| ~ in(U_384,U_388) ) )
| U_388 != relation_dom(U_383) ) )
| ~ relation(U_383) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_387,sK72(U_383,U_389))],[f_47_5]) ).
fof(f_47_7,plain,
! [U_383] :
( ( ! [U_389] :
( U_389 = relation_dom(U_383)
| ( ~ in(sK72(U_383,U_389),U_389)
& in(ordered_pair(sK72(U_383,U_389),sK73(U_383,U_389)),U_383) )
| ( ! [U_379] : ~ in(ordered_pair(sK71(U_383,U_389),U_379),U_383)
& in(sK71(U_383,U_389),U_389) ) )
& ! [U_388] :
( ( ! [U_385] :
( in(U_385,U_388)
| ! [U_377] : ~ in(ordered_pair(U_385,U_377),U_383) )
& ! [U_384] :
( in(ordered_pair(U_384,sK70(U_383,U_388,U_384)),U_383)
| ~ in(U_384,U_388) ) )
| U_388 != relation_dom(U_383) ) )
| ~ relation(U_383) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_380,sK73(U_383,U_389))],[f_47_6]) ).
cnf(f_47_8,plain,
( in(ordered_pair(U_384,sK70(U_383,U_388,U_384)),U_383)
| ~ in(U_384,U_388)
| U_388 != relation_dom(U_383)
| ~ relation(U_383) ),
inference(clausify,[status(thm)],[f_47_7]) ).
cnf(f_47_9,plain,
( in(U_385,U_388)
| ~ in(ordered_pair(U_385,U_377),U_383)
| U_388 != relation_dom(U_383)
| ~ relation(U_383) ),
inference(clausify,[status(thm)],[f_47_7]) ).
cnf(f_47_10,plain,
( in(ordered_pair(sK72(U_383,U_389),sK73(U_383,U_389)),U_383)
| in(sK71(U_383,U_389),U_389)
| U_389 = relation_dom(U_383)
| ~ relation(U_383) ),
inference(clausify,[status(thm)],[f_47_7]) ).
cnf(f_47_11,plain,
( ~ in(sK72(U_383,U_389),U_389)
| in(sK71(U_383,U_389),U_389)
| U_389 = relation_dom(U_383)
| ~ relation(U_383) ),
inference(clausify,[status(thm)],[f_47_7]) ).
cnf(f_47_12,plain,
( in(ordered_pair(sK72(U_383,U_389),sK73(U_383,U_389)),U_383)
| ~ in(ordered_pair(sK71(U_383,U_389),U_379),U_383)
| U_389 = relation_dom(U_383)
| ~ relation(U_383) ),
inference(clausify,[status(thm)],[f_47_7]) ).
cnf(f_47_13,plain,
( ~ in(sK72(U_383,U_389),U_389)
| ~ in(ordered_pair(sK71(U_383,U_389),U_379),U_383)
| U_389 = relation_dom(U_383)
| ~ relation(U_383) ),
inference(clausify,[status(thm)],[f_47_7]) ).
fof(f_48_1,plain,
! [A] :
( ! [B] :
( ( is_antisymmetric_in(A,B)
| ? [C,D] :
( C != D
& in(ordered_pair(D,C),A)
& in(ordered_pair(C,D),A)
& in(D,B)
& in(C,B) ) )
& ( ! [C,D] :
( C = D
| ~ in(ordered_pair(D,C),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(D,B)
| ~ in(C,B) )
| ~ is_antisymmetric_in(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d4_relat_2]) ).
fof(f_48_2,plain,
! [U_395] :
( ! [U_394] :
( ( is_antisymmetric_in(U_395,U_394)
| ? [U_393,U_392] :
( U_393 != U_392
& in(ordered_pair(U_392,U_393),U_395)
& in(ordered_pair(U_393,U_392),U_395)
& in(U_392,U_394)
& in(U_393,U_394) ) )
& ( ! [U_391,U_390] :
( U_391 = U_390
| ~ in(ordered_pair(U_390,U_391),U_395)
| ~ in(ordered_pair(U_391,U_390),U_395)
| ~ in(U_390,U_394)
| ~ in(U_391,U_394) )
| ~ is_antisymmetric_in(U_395,U_394) ) )
| ~ relation(U_395) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
! [U_395] :
( ( ! [U_397] :
( is_antisymmetric_in(U_395,U_397)
| ? [U_393,U_392] :
( U_393 != U_392
& in(ordered_pair(U_392,U_393),U_395)
& in(ordered_pair(U_393,U_392),U_395)
& in(U_392,U_397)
& in(U_393,U_397) ) )
& ! [U_396] :
( ! [U_391,U_390] :
( U_391 = U_390
| ~ in(ordered_pair(U_390,U_391),U_395)
| ~ in(ordered_pair(U_391,U_390),U_395)
| ~ in(U_390,U_396)
| ~ in(U_391,U_396) )
| ~ is_antisymmetric_in(U_395,U_396) ) )
| ~ relation(U_395) ),
inference(miniscope,[status(thm)],[f_48_2]) ).
fof(f_48_4,plain,
! [U_395] :
( ( ! [U_397] :
( is_antisymmetric_in(U_395,U_397)
| ? [U_392] :
( sK74(U_395,U_397) != U_392
& in(ordered_pair(U_392,sK74(U_395,U_397)),U_395)
& in(ordered_pair(sK74(U_395,U_397),U_392),U_395)
& in(U_392,U_397)
& in(sK74(U_395,U_397),U_397) ) )
& ! [U_396] :
( ! [U_391,U_390] :
( U_391 = U_390
| ~ in(ordered_pair(U_390,U_391),U_395)
| ~ in(ordered_pair(U_391,U_390),U_395)
| ~ in(U_390,U_396)
| ~ in(U_391,U_396) )
| ~ is_antisymmetric_in(U_395,U_396) ) )
| ~ relation(U_395) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_393,sK74(U_395,U_397))],[f_48_3]) ).
fof(f_48_5,plain,
! [U_395] :
( ( ! [U_397] :
( is_antisymmetric_in(U_395,U_397)
| ( sK74(U_395,U_397) != sK75(U_395,U_397)
& in(ordered_pair(sK75(U_395,U_397),sK74(U_395,U_397)),U_395)
& in(ordered_pair(sK74(U_395,U_397),sK75(U_395,U_397)),U_395)
& in(sK75(U_395,U_397),U_397)
& in(sK74(U_395,U_397),U_397) ) )
& ! [U_396] :
( ! [U_391,U_390] :
( U_391 = U_390
| ~ in(ordered_pair(U_390,U_391),U_395)
| ~ in(ordered_pair(U_391,U_390),U_395)
| ~ in(U_390,U_396)
| ~ in(U_391,U_396) )
| ~ is_antisymmetric_in(U_395,U_396) ) )
| ~ relation(U_395) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_392,sK75(U_395,U_397))],[f_48_4]) ).
cnf(f_48_6,plain,
( U_391 = U_390
| ~ in(ordered_pair(U_390,U_391),U_395)
| ~ in(ordered_pair(U_391,U_390),U_395)
| ~ in(U_390,U_396)
| ~ in(U_391,U_396)
| ~ is_antisymmetric_in(U_395,U_396)
| ~ relation(U_395) ),
inference(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_7,plain,
( in(sK74(U_395,U_397),U_397)
| is_antisymmetric_in(U_395,U_397)
| ~ relation(U_395) ),
inference(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_8,plain,
( in(sK75(U_395,U_397),U_397)
| is_antisymmetric_in(U_395,U_397)
| ~ relation(U_395) ),
inference(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_9,plain,
( in(ordered_pair(sK74(U_395,U_397),sK75(U_395,U_397)),U_395)
| is_antisymmetric_in(U_395,U_397)
| ~ relation(U_395) ),
inference(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_10,plain,
( in(ordered_pair(sK75(U_395,U_397),sK74(U_395,U_397)),U_395)
| is_antisymmetric_in(U_395,U_397)
| ~ relation(U_395) ),
inference(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_11,plain,
( sK74(U_395,U_397) != sK75(U_395,U_397)
| is_antisymmetric_in(U_395,U_397)
| ~ relation(U_395) ),
inference(clausify,[status(thm)],[f_48_5]) ).
fof(f_49_1,plain,
! [A] : cast_to_subset(A) = A,
inference(fof_nnf,[status(thm)],[d4_subset_1]) ).
fof(f_49_2,plain,
! [U_398] : cast_to_subset(U_398) = U_398,
inference(variable_rename,[status(thm)],[f_49_1]) ).
cnf(f_49_3,plain,
cast_to_subset(U_398) = U_398,
inference(clausify,[status(thm)],[f_49_2]) ).
fof(f_50_1,plain,
! [A,B] :
( ( B = union(A)
| ? [C] :
( ( ~ in(C,B)
& ? [D] :
( in(D,A)
& in(C,D) ) )
| ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ! [D] :
( ~ in(D,A)
| ~ in(C,D) ) )
& ( ? [D] :
( in(D,A)
& in(C,D) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(fof_nnf,[status(thm)],[d4_tarski]) ).
fof(f_50_2,plain,
! [U_406,U_405] :
( ( U_405 = union(U_406)
| ? [U_404] :
( ( ~ in(U_404,U_405)
& ? [U_403] :
( in(U_403,U_406)
& in(U_404,U_403) ) )
| ( ! [U_402] :
( ~ in(U_402,U_406)
| ~ in(U_404,U_402) )
& in(U_404,U_405) ) ) )
& ( ! [U_401] :
( ( in(U_401,U_405)
| ! [U_400] :
( ~ in(U_400,U_406)
| ~ in(U_401,U_400) ) )
& ( ? [U_399] :
( in(U_399,U_406)
& in(U_401,U_399) )
| ~ in(U_401,U_405) ) )
| U_405 != union(U_406) ) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
( ! [U_414,U_412] :
( U_412 = union(U_414)
| ? [U_410] :
( ~ in(U_410,U_412)
& ? [U_403] :
( in(U_403,U_414)
& in(U_410,U_403) ) )
| ? [U_409] :
( ! [U_402] :
( ~ in(U_402,U_414)
| ~ in(U_409,U_402) )
& in(U_409,U_412) ) )
& ! [U_413,U_411] :
( ( ! [U_408] :
( in(U_408,U_411)
| ! [U_400] :
( ~ in(U_400,U_413)
| ~ in(U_408,U_400) ) )
& ! [U_407] :
( ? [U_399] :
( in(U_399,U_413)
& in(U_407,U_399) )
| ~ in(U_407,U_411) ) )
| U_411 != union(U_413) ) ),
inference(miniscope,[status(thm)],[f_50_2]) ).
fof(f_50_4,plain,
( ! [U_414,U_412] :
( U_412 = union(U_414)
| ? [U_410] :
( ~ in(U_410,U_412)
& ? [U_403] :
( in(U_403,U_414)
& in(U_410,U_403) ) )
| ? [U_409] :
( ! [U_402] :
( ~ in(U_402,U_414)
| ~ in(U_409,U_402) )
& in(U_409,U_412) ) )
& ! [U_413,U_411] :
( ( ! [U_408] :
( in(U_408,U_411)
| ! [U_400] :
( ~ in(U_400,U_413)
| ~ in(U_408,U_400) ) )
& ! [U_407] :
( ( in(sK76(U_413,U_411,U_407),U_413)
& in(U_407,sK76(U_413,U_411,U_407)) )
| ~ in(U_407,U_411) ) )
| U_411 != union(U_413) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_399,sK76(U_413,U_411,U_407))],[f_50_3]) ).
fof(f_50_5,plain,
( ! [U_414,U_412] :
( U_412 = union(U_414)
| ? [U_410] :
( ~ in(U_410,U_412)
& ? [U_403] :
( in(U_403,U_414)
& in(U_410,U_403) ) )
| ( ! [U_402] :
( ~ in(U_402,U_414)
| ~ in(sK77(U_414,U_412),U_402) )
& in(sK77(U_414,U_412),U_412) ) )
& ! [U_413,U_411] :
( ( ! [U_408] :
( in(U_408,U_411)
| ! [U_400] :
( ~ in(U_400,U_413)
| ~ in(U_408,U_400) ) )
& ! [U_407] :
( ( in(sK76(U_413,U_411,U_407),U_413)
& in(U_407,sK76(U_413,U_411,U_407)) )
| ~ in(U_407,U_411) ) )
| U_411 != union(U_413) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_409,sK77(U_414,U_412))],[f_50_4]) ).
fof(f_50_6,plain,
( ! [U_414,U_412] :
( U_412 = union(U_414)
| ( ~ in(sK78(U_414,U_412),U_412)
& ? [U_403] :
( in(U_403,U_414)
& in(sK78(U_414,U_412),U_403) ) )
| ( ! [U_402] :
( ~ in(U_402,U_414)
| ~ in(sK77(U_414,U_412),U_402) )
& in(sK77(U_414,U_412),U_412) ) )
& ! [U_413,U_411] :
( ( ! [U_408] :
( in(U_408,U_411)
| ! [U_400] :
( ~ in(U_400,U_413)
| ~ in(U_408,U_400) ) )
& ! [U_407] :
( ( in(sK76(U_413,U_411,U_407),U_413)
& in(U_407,sK76(U_413,U_411,U_407)) )
| ~ in(U_407,U_411) ) )
| U_411 != union(U_413) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_410,sK78(U_414,U_412))],[f_50_5]) ).
fof(f_50_7,plain,
( ! [U_414,U_412] :
( U_412 = union(U_414)
| ( ~ in(sK78(U_414,U_412),U_412)
& in(sK79(U_414,U_412),U_414)
& in(sK78(U_414,U_412),sK79(U_414,U_412)) )
| ( ! [U_402] :
( ~ in(U_402,U_414)
| ~ in(sK77(U_414,U_412),U_402) )
& in(sK77(U_414,U_412),U_412) ) )
& ! [U_413,U_411] :
( ( ! [U_408] :
( in(U_408,U_411)
| ! [U_400] :
( ~ in(U_400,U_413)
| ~ in(U_408,U_400) ) )
& ! [U_407] :
( ( in(sK76(U_413,U_411,U_407),U_413)
& in(U_407,sK76(U_413,U_411,U_407)) )
| ~ in(U_407,U_411) ) )
| U_411 != union(U_413) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_403,sK79(U_414,U_412))],[f_50_6]) ).
cnf(f_50_8,plain,
( in(U_407,sK76(U_413,U_411,U_407))
| ~ in(U_407,U_411)
| U_411 != union(U_413) ),
inference(clausify,[status(thm)],[f_50_7]) ).
cnf(f_50_9,plain,
( in(sK76(U_413,U_411,U_407),U_413)
| ~ in(U_407,U_411)
| U_411 != union(U_413) ),
inference(clausify,[status(thm)],[f_50_7]) ).
cnf(f_50_10,plain,
( in(U_408,U_411)
| ~ in(U_400,U_413)
| ~ in(U_408,U_400)
| U_411 != union(U_413) ),
inference(clausify,[status(thm)],[f_50_7]) ).
cnf(f_50_11,plain,
( in(sK78(U_414,U_412),sK79(U_414,U_412))
| in(sK77(U_414,U_412),U_412)
| U_412 = union(U_414) ),
inference(clausify,[status(thm)],[f_50_7]) ).
cnf(f_50_12,plain,
( in(sK79(U_414,U_412),U_414)
| in(sK77(U_414,U_412),U_412)
| U_412 = union(U_414) ),
inference(clausify,[status(thm)],[f_50_7]) ).
cnf(f_50_13,plain,
( ~ in(sK78(U_414,U_412),U_412)
| in(sK77(U_414,U_412),U_412)
| U_412 = union(U_414) ),
inference(clausify,[status(thm)],[f_50_7]) ).
cnf(f_50_14,plain,
( in(sK78(U_414,U_412),sK79(U_414,U_412))
| ~ in(U_402,U_414)
| ~ in(sK77(U_414,U_412),U_402)
| U_412 = union(U_414) ),
inference(clausify,[status(thm)],[f_50_7]) ).
cnf(f_50_15,plain,
( in(sK79(U_414,U_412),U_414)
| ~ in(U_402,U_414)
| ~ in(sK77(U_414,U_412),U_402)
| U_412 = union(U_414) ),
inference(clausify,[status(thm)],[f_50_7]) ).
cnf(f_50_16,plain,
( ~ in(sK78(U_414,U_412),U_412)
| ~ in(U_402,U_414)
| ~ in(sK77(U_414,U_412),U_402)
| U_412 = union(U_414) ),
inference(clausify,[status(thm)],[f_50_7]) ).
fof(f_51_1,plain,
! [A] :
( ( ( well_ordering(A)
| ~ well_founded_relation(A)
| ~ connected(A)
| ~ antisymmetric(A)
| ~ transitive(A)
| ~ reflexive(A) )
& ( ( well_founded_relation(A)
& connected(A)
& antisymmetric(A)
& transitive(A)
& reflexive(A) )
| ~ well_ordering(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d4_wellord1]) ).
fof(f_51_2,plain,
! [U_415] :
( ( ( well_ordering(U_415)
| ~ well_founded_relation(U_415)
| ~ connected(U_415)
| ~ antisymmetric(U_415)
| ~ transitive(U_415)
| ~ reflexive(U_415) )
& ( ( well_founded_relation(U_415)
& connected(U_415)
& antisymmetric(U_415)
& transitive(U_415)
& reflexive(U_415) )
| ~ well_ordering(U_415) ) )
| ~ relation(U_415) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
cnf(f_51_3,plain,
( reflexive(U_415)
| ~ well_ordering(U_415)
| ~ relation(U_415) ),
inference(clausify,[status(thm)],[f_51_2]) ).
cnf(f_51_4,plain,
( transitive(U_415)
| ~ well_ordering(U_415)
| ~ relation(U_415) ),
inference(clausify,[status(thm)],[f_51_2]) ).
cnf(f_51_5,plain,
( antisymmetric(U_415)
| ~ well_ordering(U_415)
| ~ relation(U_415) ),
inference(clausify,[status(thm)],[f_51_2]) ).
cnf(f_51_6,plain,
( connected(U_415)
| ~ well_ordering(U_415)
| ~ relation(U_415) ),
inference(clausify,[status(thm)],[f_51_2]) ).
cnf(f_51_7,plain,
( well_founded_relation(U_415)
| ~ well_ordering(U_415)
| ~ relation(U_415) ),
inference(clausify,[status(thm)],[f_51_2]) ).
cnf(f_51_8,plain,
( well_ordering(U_415)
| ~ well_founded_relation(U_415)
| ~ connected(U_415)
| ~ antisymmetric(U_415)
| ~ transitive(U_415)
| ~ reflexive(U_415)
| ~ relation(U_415) ),
inference(clausify,[status(thm)],[f_51_2]) ).
fof(f_52_1,plain,
! [A,B,C] :
( ( C = set_difference(A,B)
| ? [D] :
( ( ~ in(D,C)
& ~ in(D,B)
& in(D,A) )
| ( ( in(D,B)
| ~ in(D,A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| in(D,B)
| ~ in(D,A) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(fof_nnf,[status(thm)],[d4_xboole_0]) ).
fof(f_52_2,plain,
! [U_420,U_419,U_418] :
( ( U_418 = set_difference(U_420,U_419)
| ? [U_417] :
( ( ~ in(U_417,U_418)
& ~ in(U_417,U_419)
& in(U_417,U_420) )
| ( ( in(U_417,U_419)
| ~ in(U_417,U_420) )
& in(U_417,U_418) ) ) )
& ( ! [U_416] :
( ( in(U_416,U_418)
| in(U_416,U_419)
| ~ in(U_416,U_420) )
& ( ( ~ in(U_416,U_419)
& in(U_416,U_420) )
| ~ in(U_416,U_418) ) )
| U_418 != set_difference(U_420,U_419) ) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
( ! [U_430,U_428,U_426] :
( U_426 = set_difference(U_430,U_428)
| ? [U_424] :
( ~ in(U_424,U_426)
& ~ in(U_424,U_428)
& in(U_424,U_430) )
| ? [U_423] :
( ( in(U_423,U_428)
| ~ in(U_423,U_430) )
& in(U_423,U_426) ) )
& ! [U_429,U_427,U_425] :
( ( ! [U_422] :
( in(U_422,U_425)
| in(U_422,U_427)
| ~ in(U_422,U_429) )
& ! [U_421] :
( ( ~ in(U_421,U_427)
& in(U_421,U_429) )
| ~ in(U_421,U_425) ) )
| U_425 != set_difference(U_429,U_427) ) ),
inference(miniscope,[status(thm)],[f_52_2]) ).
fof(f_52_4,plain,
( ! [U_430,U_428,U_426] :
( U_426 = set_difference(U_430,U_428)
| ? [U_424] :
( ~ in(U_424,U_426)
& ~ in(U_424,U_428)
& in(U_424,U_430) )
| ( ( in(sK80(U_430,U_428,U_426),U_428)
| ~ in(sK80(U_430,U_428,U_426),U_430) )
& in(sK80(U_430,U_428,U_426),U_426) ) )
& ! [U_429,U_427,U_425] :
( ( ! [U_422] :
( in(U_422,U_425)
| in(U_422,U_427)
| ~ in(U_422,U_429) )
& ! [U_421] :
( ( ~ in(U_421,U_427)
& in(U_421,U_429) )
| ~ in(U_421,U_425) ) )
| U_425 != set_difference(U_429,U_427) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_423,sK80(U_430,U_428,U_426))],[f_52_3]) ).
fof(f_52_5,plain,
( ! [U_430,U_428,U_426] :
( U_426 = set_difference(U_430,U_428)
| ( ~ in(sK81(U_430,U_428,U_426),U_426)
& ~ in(sK81(U_430,U_428,U_426),U_428)
& in(sK81(U_430,U_428,U_426),U_430) )
| ( ( in(sK80(U_430,U_428,U_426),U_428)
| ~ in(sK80(U_430,U_428,U_426),U_430) )
& in(sK80(U_430,U_428,U_426),U_426) ) )
& ! [U_429,U_427,U_425] :
( ( ! [U_422] :
( in(U_422,U_425)
| in(U_422,U_427)
| ~ in(U_422,U_429) )
& ! [U_421] :
( ( ~ in(U_421,U_427)
& in(U_421,U_429) )
| ~ in(U_421,U_425) ) )
| U_425 != set_difference(U_429,U_427) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_424,sK81(U_430,U_428,U_426))],[f_52_4]) ).
cnf(f_52_6,plain,
( in(U_421,U_429)
| ~ in(U_421,U_425)
| U_425 != set_difference(U_429,U_427) ),
inference(clausify,[status(thm)],[f_52_5]) ).
cnf(f_52_7,plain,
( ~ in(U_421,U_427)
| ~ in(U_421,U_425)
| U_425 != set_difference(U_429,U_427) ),
inference(clausify,[status(thm)],[f_52_5]) ).
cnf(f_52_8,plain,
( in(U_422,U_425)
| in(U_422,U_427)
| ~ in(U_422,U_429)
| U_425 != set_difference(U_429,U_427) ),
inference(clausify,[status(thm)],[f_52_5]) ).
cnf(f_52_9,plain,
( in(sK81(U_430,U_428,U_426),U_430)
| in(sK80(U_430,U_428,U_426),U_426)
| U_426 = set_difference(U_430,U_428) ),
inference(clausify,[status(thm)],[f_52_5]) ).
cnf(f_52_10,plain,
( ~ in(sK81(U_430,U_428,U_426),U_428)
| in(sK80(U_430,U_428,U_426),U_426)
| U_426 = set_difference(U_430,U_428) ),
inference(clausify,[status(thm)],[f_52_5]) ).
cnf(f_52_11,plain,
( ~ in(sK81(U_430,U_428,U_426),U_426)
| in(sK80(U_430,U_428,U_426),U_426)
| U_426 = set_difference(U_430,U_428) ),
inference(clausify,[status(thm)],[f_52_5]) ).
cnf(f_52_12,plain,
( in(sK81(U_430,U_428,U_426),U_430)
| in(sK80(U_430,U_428,U_426),U_428)
| ~ in(sK80(U_430,U_428,U_426),U_430)
| U_426 = set_difference(U_430,U_428) ),
inference(clausify,[status(thm)],[f_52_5]) ).
cnf(f_52_13,plain,
( ~ in(sK81(U_430,U_428,U_426),U_428)
| in(sK80(U_430,U_428,U_426),U_428)
| ~ in(sK80(U_430,U_428,U_426),U_430)
| U_426 = set_difference(U_430,U_428) ),
inference(clausify,[status(thm)],[f_52_5]) ).
cnf(f_52_14,plain,
( ~ in(sK81(U_430,U_428,U_426),U_426)
| in(sK80(U_430,U_428,U_426),U_428)
| ~ in(sK80(U_430,U_428,U_426),U_430)
| U_426 = set_difference(U_430,U_428) ),
inference(clausify,[status(thm)],[f_52_5]) ).
fof(f_53_1,plain,
! [A] :
( ! [B] :
( ( B = relation_rng(A)
| ? [C] :
( ( ~ in(C,B)
& ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) )
| ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) ) )
& ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d5_funct_1]) ).
fof(f_53_2,plain,
! [U_438] :
( ! [U_437] :
( ( U_437 = relation_rng(U_438)
| ? [U_436] :
( ( ~ in(U_436,U_437)
& ? [U_435] :
( U_436 = apply(U_438,U_435)
& in(U_435,relation_dom(U_438)) ) )
| ( ! [U_434] :
( U_436 != apply(U_438,U_434)
| ~ in(U_434,relation_dom(U_438)) )
& in(U_436,U_437) ) ) )
& ( ! [U_433] :
( ( in(U_433,U_437)
| ! [U_432] :
( U_433 != apply(U_438,U_432)
| ~ in(U_432,relation_dom(U_438)) ) )
& ( ? [U_431] :
( U_433 = apply(U_438,U_431)
& in(U_431,relation_dom(U_438)) )
| ~ in(U_433,U_437) ) )
| U_437 != relation_rng(U_438) ) )
| ~ function(U_438)
| ~ relation(U_438) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
! [U_438] :
( ( ! [U_444] :
( U_444 = relation_rng(U_438)
| ? [U_442] :
( ~ in(U_442,U_444)
& ? [U_435] :
( U_442 = apply(U_438,U_435)
& in(U_435,relation_dom(U_438)) ) )
| ? [U_441] :
( ! [U_434] :
( U_441 != apply(U_438,U_434)
| ~ in(U_434,relation_dom(U_438)) )
& in(U_441,U_444) ) )
& ! [U_443] :
( ( ! [U_440] :
( in(U_440,U_443)
| ! [U_432] :
( U_440 != apply(U_438,U_432)
| ~ in(U_432,relation_dom(U_438)) ) )
& ! [U_439] :
( ? [U_431] :
( U_439 = apply(U_438,U_431)
& in(U_431,relation_dom(U_438)) )
| ~ in(U_439,U_443) ) )
| U_443 != relation_rng(U_438) ) )
| ~ function(U_438)
| ~ relation(U_438) ),
inference(miniscope,[status(thm)],[f_53_2]) ).
fof(f_53_4,plain,
! [U_438] :
( ( ! [U_444] :
( U_444 = relation_rng(U_438)
| ? [U_442] :
( ~ in(U_442,U_444)
& ? [U_435] :
( U_442 = apply(U_438,U_435)
& in(U_435,relation_dom(U_438)) ) )
| ? [U_441] :
( ! [U_434] :
( U_441 != apply(U_438,U_434)
| ~ in(U_434,relation_dom(U_438)) )
& in(U_441,U_444) ) )
& ! [U_443] :
( ( ! [U_440] :
( in(U_440,U_443)
| ! [U_432] :
( U_440 != apply(U_438,U_432)
| ~ in(U_432,relation_dom(U_438)) ) )
& ! [U_439] :
( ( U_439 = apply(U_438,sK82(U_438,U_443,U_439))
& in(sK82(U_438,U_443,U_439),relation_dom(U_438)) )
| ~ in(U_439,U_443) ) )
| U_443 != relation_rng(U_438) ) )
| ~ function(U_438)
| ~ relation(U_438) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_431,sK82(U_438,U_443,U_439))],[f_53_3]) ).
fof(f_53_5,plain,
! [U_438] :
( ( ! [U_444] :
( U_444 = relation_rng(U_438)
| ? [U_442] :
( ~ in(U_442,U_444)
& ? [U_435] :
( U_442 = apply(U_438,U_435)
& in(U_435,relation_dom(U_438)) ) )
| ( ! [U_434] :
( sK83(U_438,U_444) != apply(U_438,U_434)
| ~ in(U_434,relation_dom(U_438)) )
& in(sK83(U_438,U_444),U_444) ) )
& ! [U_443] :
( ( ! [U_440] :
( in(U_440,U_443)
| ! [U_432] :
( U_440 != apply(U_438,U_432)
| ~ in(U_432,relation_dom(U_438)) ) )
& ! [U_439] :
( ( U_439 = apply(U_438,sK82(U_438,U_443,U_439))
& in(sK82(U_438,U_443,U_439),relation_dom(U_438)) )
| ~ in(U_439,U_443) ) )
| U_443 != relation_rng(U_438) ) )
| ~ function(U_438)
| ~ relation(U_438) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_441,sK83(U_438,U_444))],[f_53_4]) ).
fof(f_53_6,plain,
! [U_438] :
( ( ! [U_444] :
( U_444 = relation_rng(U_438)
| ( ~ in(sK84(U_438,U_444),U_444)
& ? [U_435] :
( sK84(U_438,U_444) = apply(U_438,U_435)
& in(U_435,relation_dom(U_438)) ) )
| ( ! [U_434] :
( sK83(U_438,U_444) != apply(U_438,U_434)
| ~ in(U_434,relation_dom(U_438)) )
& in(sK83(U_438,U_444),U_444) ) )
& ! [U_443] :
( ( ! [U_440] :
( in(U_440,U_443)
| ! [U_432] :
( U_440 != apply(U_438,U_432)
| ~ in(U_432,relation_dom(U_438)) ) )
& ! [U_439] :
( ( U_439 = apply(U_438,sK82(U_438,U_443,U_439))
& in(sK82(U_438,U_443,U_439),relation_dom(U_438)) )
| ~ in(U_439,U_443) ) )
| U_443 != relation_rng(U_438) ) )
| ~ function(U_438)
| ~ relation(U_438) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_442,sK84(U_438,U_444))],[f_53_5]) ).
fof(f_53_7,plain,
! [U_438] :
( ( ! [U_444] :
( U_444 = relation_rng(U_438)
| ( ~ in(sK84(U_438,U_444),U_444)
& sK84(U_438,U_444) = apply(U_438,sK85(U_438,U_444))
& in(sK85(U_438,U_444),relation_dom(U_438)) )
| ( ! [U_434] :
( sK83(U_438,U_444) != apply(U_438,U_434)
| ~ in(U_434,relation_dom(U_438)) )
& in(sK83(U_438,U_444),U_444) ) )
& ! [U_443] :
( ( ! [U_440] :
( in(U_440,U_443)
| ! [U_432] :
( U_440 != apply(U_438,U_432)
| ~ in(U_432,relation_dom(U_438)) ) )
& ! [U_439] :
( ( U_439 = apply(U_438,sK82(U_438,U_443,U_439))
& in(sK82(U_438,U_443,U_439),relation_dom(U_438)) )
| ~ in(U_439,U_443) ) )
| U_443 != relation_rng(U_438) ) )
| ~ function(U_438)
| ~ relation(U_438) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_435,sK85(U_438,U_444))],[f_53_6]) ).
cnf(f_53_8,plain,
( in(sK82(U_438,U_443,U_439),relation_dom(U_438))
| ~ in(U_439,U_443)
| U_443 != relation_rng(U_438)
| ~ function(U_438)
| ~ relation(U_438) ),
inference(clausify,[status(thm)],[f_53_7]) ).
cnf(f_53_9,plain,
( U_439 = apply(U_438,sK82(U_438,U_443,U_439))
| ~ in(U_439,U_443)
| U_443 != relation_rng(U_438)
| ~ function(U_438)
| ~ relation(U_438) ),
inference(clausify,[status(thm)],[f_53_7]) ).
cnf(f_53_10,plain,
( in(U_440,U_443)
| U_440 != apply(U_438,U_432)
| ~ in(U_432,relation_dom(U_438))
| U_443 != relation_rng(U_438)
| ~ function(U_438)
| ~ relation(U_438) ),
inference(clausify,[status(thm)],[f_53_7]) ).
cnf(f_53_11,plain,
( in(sK85(U_438,U_444),relation_dom(U_438))
| in(sK83(U_438,U_444),U_444)
| U_444 = relation_rng(U_438)
| ~ function(U_438)
| ~ relation(U_438) ),
inference(clausify,[status(thm)],[f_53_7]) ).
cnf(f_53_12,plain,
( sK84(U_438,U_444) = apply(U_438,sK85(U_438,U_444))
| in(sK83(U_438,U_444),U_444)
| U_444 = relation_rng(U_438)
| ~ function(U_438)
| ~ relation(U_438) ),
inference(clausify,[status(thm)],[f_53_7]) ).
cnf(f_53_13,plain,
( ~ in(sK84(U_438,U_444),U_444)
| in(sK83(U_438,U_444),U_444)
| U_444 = relation_rng(U_438)
| ~ function(U_438)
| ~ relation(U_438) ),
inference(clausify,[status(thm)],[f_53_7]) ).
cnf(f_53_14,plain,
( in(sK85(U_438,U_444),relation_dom(U_438))
| sK83(U_438,U_444) != apply(U_438,U_434)
| ~ in(U_434,relation_dom(U_438))
| U_444 = relation_rng(U_438)
| ~ function(U_438)
| ~ relation(U_438) ),
inference(clausify,[status(thm)],[f_53_7]) ).
cnf(f_53_15,plain,
( sK84(U_438,U_444) = apply(U_438,sK85(U_438,U_444))
| sK83(U_438,U_444) != apply(U_438,U_434)
| ~ in(U_434,relation_dom(U_438))
| U_444 = relation_rng(U_438)
| ~ function(U_438)
| ~ relation(U_438) ),
inference(clausify,[status(thm)],[f_53_7]) ).
cnf(f_53_16,plain,
( ~ in(sK84(U_438,U_444),U_444)
| sK83(U_438,U_444) != apply(U_438,U_434)
| ~ in(U_434,relation_dom(U_438))
| U_444 = relation_rng(U_438)
| ~ function(U_438)
| ~ relation(U_438) ),
inference(clausify,[status(thm)],[f_53_7]) ).
fof(f_54_1,plain,
! [A] :
( ! [B] :
( ( B = relation_rng(A)
| ? [C] :
( ( ~ in(C,B)
& ? [D] : in(ordered_pair(D,C),A) )
| ( ! [D] : ~ in(ordered_pair(D,C),A)
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ! [D] : ~ in(ordered_pair(D,C),A) )
& ( ? [D] : in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d5_relat_1]) ).
fof(f_54_2,plain,
! [U_452] :
( ! [U_451] :
( ( U_451 = relation_rng(U_452)
| ? [U_450] :
( ( ~ in(U_450,U_451)
& ? [U_449] : in(ordered_pair(U_449,U_450),U_452) )
| ( ! [U_448] : ~ in(ordered_pair(U_448,U_450),U_452)
& in(U_450,U_451) ) ) )
& ( ! [U_447] :
( ( in(U_447,U_451)
| ! [U_446] : ~ in(ordered_pair(U_446,U_447),U_452) )
& ( ? [U_445] : in(ordered_pair(U_445,U_447),U_452)
| ~ in(U_447,U_451) ) )
| U_451 != relation_rng(U_452) ) )
| ~ relation(U_452) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_452] :
( ( ! [U_458] :
( U_458 = relation_rng(U_452)
| ? [U_456] :
( ~ in(U_456,U_458)
& ? [U_449] : in(ordered_pair(U_449,U_456),U_452) )
| ? [U_455] :
( ! [U_448] : ~ in(ordered_pair(U_448,U_455),U_452)
& in(U_455,U_458) ) )
& ! [U_457] :
( ( ! [U_454] :
( in(U_454,U_457)
| ! [U_446] : ~ in(ordered_pair(U_446,U_454),U_452) )
& ! [U_453] :
( ? [U_445] : in(ordered_pair(U_445,U_453),U_452)
| ~ in(U_453,U_457) ) )
| U_457 != relation_rng(U_452) ) )
| ~ relation(U_452) ),
inference(miniscope,[status(thm)],[f_54_2]) ).
fof(f_54_4,plain,
! [U_452] :
( ( ! [U_458] :
( U_458 = relation_rng(U_452)
| ? [U_456] :
( ~ in(U_456,U_458)
& ? [U_449] : in(ordered_pair(U_449,U_456),U_452) )
| ? [U_455] :
( ! [U_448] : ~ in(ordered_pair(U_448,U_455),U_452)
& in(U_455,U_458) ) )
& ! [U_457] :
( ( ! [U_454] :
( in(U_454,U_457)
| ! [U_446] : ~ in(ordered_pair(U_446,U_454),U_452) )
& ! [U_453] :
( in(ordered_pair(sK86(U_452,U_457,U_453),U_453),U_452)
| ~ in(U_453,U_457) ) )
| U_457 != relation_rng(U_452) ) )
| ~ relation(U_452) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_445,sK86(U_452,U_457,U_453))],[f_54_3]) ).
fof(f_54_5,plain,
! [U_452] :
( ( ! [U_458] :
( U_458 = relation_rng(U_452)
| ? [U_456] :
( ~ in(U_456,U_458)
& ? [U_449] : in(ordered_pair(U_449,U_456),U_452) )
| ( ! [U_448] : ~ in(ordered_pair(U_448,sK87(U_452,U_458)),U_452)
& in(sK87(U_452,U_458),U_458) ) )
& ! [U_457] :
( ( ! [U_454] :
( in(U_454,U_457)
| ! [U_446] : ~ in(ordered_pair(U_446,U_454),U_452) )
& ! [U_453] :
( in(ordered_pair(sK86(U_452,U_457,U_453),U_453),U_452)
| ~ in(U_453,U_457) ) )
| U_457 != relation_rng(U_452) ) )
| ~ relation(U_452) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_455,sK87(U_452,U_458))],[f_54_4]) ).
fof(f_54_6,plain,
! [U_452] :
( ( ! [U_458] :
( U_458 = relation_rng(U_452)
| ( ~ in(sK88(U_452,U_458),U_458)
& ? [U_449] : in(ordered_pair(U_449,sK88(U_452,U_458)),U_452) )
| ( ! [U_448] : ~ in(ordered_pair(U_448,sK87(U_452,U_458)),U_452)
& in(sK87(U_452,U_458),U_458) ) )
& ! [U_457] :
( ( ! [U_454] :
( in(U_454,U_457)
| ! [U_446] : ~ in(ordered_pair(U_446,U_454),U_452) )
& ! [U_453] :
( in(ordered_pair(sK86(U_452,U_457,U_453),U_453),U_452)
| ~ in(U_453,U_457) ) )
| U_457 != relation_rng(U_452) ) )
| ~ relation(U_452) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_456,sK88(U_452,U_458))],[f_54_5]) ).
fof(f_54_7,plain,
! [U_452] :
( ( ! [U_458] :
( U_458 = relation_rng(U_452)
| ( ~ in(sK88(U_452,U_458),U_458)
& in(ordered_pair(sK89(U_452,U_458),sK88(U_452,U_458)),U_452) )
| ( ! [U_448] : ~ in(ordered_pair(U_448,sK87(U_452,U_458)),U_452)
& in(sK87(U_452,U_458),U_458) ) )
& ! [U_457] :
( ( ! [U_454] :
( in(U_454,U_457)
| ! [U_446] : ~ in(ordered_pair(U_446,U_454),U_452) )
& ! [U_453] :
( in(ordered_pair(sK86(U_452,U_457,U_453),U_453),U_452)
| ~ in(U_453,U_457) ) )
| U_457 != relation_rng(U_452) ) )
| ~ relation(U_452) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_449,sK89(U_452,U_458))],[f_54_6]) ).
cnf(f_54_8,plain,
( in(ordered_pair(sK86(U_452,U_457,U_453),U_453),U_452)
| ~ in(U_453,U_457)
| U_457 != relation_rng(U_452)
| ~ relation(U_452) ),
inference(clausify,[status(thm)],[f_54_7]) ).
cnf(f_54_9,plain,
( in(U_454,U_457)
| ~ in(ordered_pair(U_446,U_454),U_452)
| U_457 != relation_rng(U_452)
| ~ relation(U_452) ),
inference(clausify,[status(thm)],[f_54_7]) ).
cnf(f_54_10,plain,
( in(ordered_pair(sK89(U_452,U_458),sK88(U_452,U_458)),U_452)
| in(sK87(U_452,U_458),U_458)
| U_458 = relation_rng(U_452)
| ~ relation(U_452) ),
inference(clausify,[status(thm)],[f_54_7]) ).
cnf(f_54_11,plain,
( ~ in(sK88(U_452,U_458),U_458)
| in(sK87(U_452,U_458),U_458)
| U_458 = relation_rng(U_452)
| ~ relation(U_452) ),
inference(clausify,[status(thm)],[f_54_7]) ).
cnf(f_54_12,plain,
( in(ordered_pair(sK89(U_452,U_458),sK88(U_452,U_458)),U_452)
| ~ in(ordered_pair(U_448,sK87(U_452,U_458)),U_452)
| U_458 = relation_rng(U_452)
| ~ relation(U_452) ),
inference(clausify,[status(thm)],[f_54_7]) ).
cnf(f_54_13,plain,
( ~ in(sK88(U_452,U_458),U_458)
| ~ in(ordered_pair(U_448,sK87(U_452,U_458)),U_452)
| U_458 = relation_rng(U_452)
| ~ relation(U_452) ),
inference(clausify,[status(thm)],[f_54_7]) ).
fof(f_55_1,plain,
! [A,B] :
( subset_complement(A,B) = set_difference(A,B)
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[d5_subset_1]) ).
fof(f_55_2,plain,
! [U_460,U_459] :
( subset_complement(U_460,U_459) = set_difference(U_460,U_459)
| ~ element(U_459,powerset(U_460)) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
cnf(f_55_3,plain,
( subset_complement(U_460,U_459) = set_difference(U_460,U_459)
| ~ element(U_459,powerset(U_460)) ),
inference(clausify,[status(thm)],[f_55_2]) ).
fof(f_56_1,plain,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(fof_nnf,[status(thm)],[d5_tarski]) ).
fof(f_56_2,plain,
! [U_462,U_461] : ordered_pair(U_462,U_461) = unordered_pair(unordered_pair(U_462,U_461),singleton(U_462)),
inference(variable_rename,[status(thm)],[f_56_1]) ).
cnf(f_56_3,plain,
ordered_pair(U_462,U_461) = unordered_pair(unordered_pair(U_462,U_461),singleton(U_462)),
inference(clausify,[status(thm)],[f_56_2]) ).
fof(f_57_1,plain,
! [A] :
( ! [B] :
( ( well_orders(A,B)
| ~ is_well_founded_in(A,B)
| ~ is_connected_in(A,B)
| ~ is_antisymmetric_in(A,B)
| ~ is_transitive_in(A,B)
| ~ is_reflexive_in(A,B) )
& ( ( is_well_founded_in(A,B)
& is_connected_in(A,B)
& is_antisymmetric_in(A,B)
& is_transitive_in(A,B)
& is_reflexive_in(A,B) )
| ~ well_orders(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d5_wellord1]) ).
fof(f_57_2,plain,
! [U_464] :
( ! [U_463] :
( ( well_orders(U_464,U_463)
| ~ is_well_founded_in(U_464,U_463)
| ~ is_connected_in(U_464,U_463)
| ~ is_antisymmetric_in(U_464,U_463)
| ~ is_transitive_in(U_464,U_463)
| ~ is_reflexive_in(U_464,U_463) )
& ( ( is_well_founded_in(U_464,U_463)
& is_connected_in(U_464,U_463)
& is_antisymmetric_in(U_464,U_463)
& is_transitive_in(U_464,U_463)
& is_reflexive_in(U_464,U_463) )
| ~ well_orders(U_464,U_463) ) )
| ~ relation(U_464) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
! [U_464] :
( ( ! [U_466] :
( well_orders(U_464,U_466)
| ~ is_well_founded_in(U_464,U_466)
| ~ is_connected_in(U_464,U_466)
| ~ is_antisymmetric_in(U_464,U_466)
| ~ is_transitive_in(U_464,U_466)
| ~ is_reflexive_in(U_464,U_466) )
& ! [U_465] :
( ( is_well_founded_in(U_464,U_465)
& is_connected_in(U_464,U_465)
& is_antisymmetric_in(U_464,U_465)
& is_transitive_in(U_464,U_465)
& is_reflexive_in(U_464,U_465) )
| ~ well_orders(U_464,U_465) ) )
| ~ relation(U_464) ),
inference(miniscope,[status(thm)],[f_57_2]) ).
cnf(f_57_4,plain,
( is_reflexive_in(U_464,U_465)
| ~ well_orders(U_464,U_465)
| ~ relation(U_464) ),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_5,plain,
( is_transitive_in(U_464,U_465)
| ~ well_orders(U_464,U_465)
| ~ relation(U_464) ),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_6,plain,
( is_antisymmetric_in(U_464,U_465)
| ~ well_orders(U_464,U_465)
| ~ relation(U_464) ),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_7,plain,
( is_connected_in(U_464,U_465)
| ~ well_orders(U_464,U_465)
| ~ relation(U_464) ),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_8,plain,
( is_well_founded_in(U_464,U_465)
| ~ well_orders(U_464,U_465)
| ~ relation(U_464) ),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_9,plain,
( well_orders(U_464,U_466)
| ~ is_well_founded_in(U_464,U_466)
| ~ is_connected_in(U_464,U_466)
| ~ is_antisymmetric_in(U_464,U_466)
| ~ is_transitive_in(U_464,U_466)
| ~ is_reflexive_in(U_464,U_466)
| ~ relation(U_464) ),
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_1,plain,
! [A] :
( ( being_limit_ordinal(A)
| A != union(A) )
& ( A = union(A)
| ~ being_limit_ordinal(A) ) ),
inference(fof_nnf,[status(thm)],[d6_ordinal1]) ).
fof(f_58_2,plain,
! [U_467] :
( ( being_limit_ordinal(U_467)
| U_467 != union(U_467) )
& ( U_467 = union(U_467)
| ~ being_limit_ordinal(U_467) ) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
( ! [U_469] :
( being_limit_ordinal(U_469)
| U_469 != union(U_469) )
& ! [U_468] :
( U_468 = union(U_468)
| ~ being_limit_ordinal(U_468) ) ),
inference(miniscope,[status(thm)],[f_58_2]) ).
cnf(f_58_4,plain,
( U_468 = union(U_468)
| ~ being_limit_ordinal(U_468) ),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_5,plain,
( being_limit_ordinal(U_469)
| U_469 != union(U_469) ),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_59_1,plain,
! [A] :
( relation_field(A) = set_union2(relation_dom(A),relation_rng(A))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d6_relat_1]) ).
fof(f_59_2,plain,
! [U_470] :
( relation_field(U_470) = set_union2(relation_dom(U_470),relation_rng(U_470))
| ~ relation(U_470) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
cnf(f_59_3,plain,
( relation_field(U_470) = set_union2(relation_dom(U_470),relation_rng(U_470))
| ~ relation(U_470) ),
inference(clausify,[status(thm)],[f_59_2]) ).
fof(f_60_1,plain,
! [A] :
( ! [B] :
( ( is_connected_in(A,B)
| ? [C,D] :
( ~ in(ordered_pair(D,C),A)
& ~ in(ordered_pair(C,D),A)
& C != D
& in(D,B)
& in(C,B) ) )
& ( ! [C,D] :
( in(ordered_pair(D,C),A)
| in(ordered_pair(C,D),A)
| C = D
| ~ in(D,B)
| ~ in(C,B) )
| ~ is_connected_in(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d6_relat_2]) ).
fof(f_60_2,plain,
! [U_476] :
( ! [U_475] :
( ( is_connected_in(U_476,U_475)
| ? [U_474,U_473] :
( ~ in(ordered_pair(U_473,U_474),U_476)
& ~ in(ordered_pair(U_474,U_473),U_476)
& U_474 != U_473
& in(U_473,U_475)
& in(U_474,U_475) ) )
& ( ! [U_472,U_471] :
( in(ordered_pair(U_471,U_472),U_476)
| in(ordered_pair(U_472,U_471),U_476)
| U_472 = U_471
| ~ in(U_471,U_475)
| ~ in(U_472,U_475) )
| ~ is_connected_in(U_476,U_475) ) )
| ~ relation(U_476) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
! [U_476] :
( ( ! [U_478] :
( is_connected_in(U_476,U_478)
| ? [U_474] :
( ? [U_473] :
( ~ in(ordered_pair(U_473,U_474),U_476)
& ~ in(ordered_pair(U_474,U_473),U_476)
& U_474 != U_473
& in(U_473,U_478) )
& in(U_474,U_478) ) )
& ! [U_477] :
( ! [U_472] :
( ! [U_471] :
( in(ordered_pair(U_471,U_472),U_476)
| in(ordered_pair(U_472,U_471),U_476)
| U_472 = U_471
| ~ in(U_471,U_477) )
| ~ in(U_472,U_477) )
| ~ is_connected_in(U_476,U_477) ) )
| ~ relation(U_476) ),
inference(miniscope,[status(thm)],[f_60_2]) ).
fof(f_60_4,plain,
! [U_476] :
( ( ! [U_478] :
( is_connected_in(U_476,U_478)
| ( ? [U_473] :
( ~ in(ordered_pair(U_473,sK90(U_476,U_478)),U_476)
& ~ in(ordered_pair(sK90(U_476,U_478),U_473),U_476)
& sK90(U_476,U_478) != U_473
& in(U_473,U_478) )
& in(sK90(U_476,U_478),U_478) ) )
& ! [U_477] :
( ! [U_472] :
( ! [U_471] :
( in(ordered_pair(U_471,U_472),U_476)
| in(ordered_pair(U_472,U_471),U_476)
| U_472 = U_471
| ~ in(U_471,U_477) )
| ~ in(U_472,U_477) )
| ~ is_connected_in(U_476,U_477) ) )
| ~ relation(U_476) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_474,sK90(U_476,U_478))],[f_60_3]) ).
fof(f_60_5,plain,
! [U_476] :
( ( ! [U_478] :
( is_connected_in(U_476,U_478)
| ( ~ in(ordered_pair(sK91(U_476,U_478),sK90(U_476,U_478)),U_476)
& ~ in(ordered_pair(sK90(U_476,U_478),sK91(U_476,U_478)),U_476)
& sK90(U_476,U_478) != sK91(U_476,U_478)
& in(sK91(U_476,U_478),U_478)
& in(sK90(U_476,U_478),U_478) ) )
& ! [U_477] :
( ! [U_472] :
( ! [U_471] :
( in(ordered_pair(U_471,U_472),U_476)
| in(ordered_pair(U_472,U_471),U_476)
| U_472 = U_471
| ~ in(U_471,U_477) )
| ~ in(U_472,U_477) )
| ~ is_connected_in(U_476,U_477) ) )
| ~ relation(U_476) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_473,sK91(U_476,U_478))],[f_60_4]) ).
cnf(f_60_6,plain,
( in(ordered_pair(U_471,U_472),U_476)
| in(ordered_pair(U_472,U_471),U_476)
| U_472 = U_471
| ~ in(U_471,U_477)
| ~ in(U_472,U_477)
| ~ is_connected_in(U_476,U_477)
| ~ relation(U_476) ),
inference(clausify,[status(thm)],[f_60_5]) ).
cnf(f_60_7,plain,
( in(sK90(U_476,U_478),U_478)
| is_connected_in(U_476,U_478)
| ~ relation(U_476) ),
inference(clausify,[status(thm)],[f_60_5]) ).
cnf(f_60_8,plain,
( in(sK91(U_476,U_478),U_478)
| is_connected_in(U_476,U_478)
| ~ relation(U_476) ),
inference(clausify,[status(thm)],[f_60_5]) ).
cnf(f_60_9,plain,
( sK90(U_476,U_478) != sK91(U_476,U_478)
| is_connected_in(U_476,U_478)
| ~ relation(U_476) ),
inference(clausify,[status(thm)],[f_60_5]) ).
cnf(f_60_10,plain,
( ~ in(ordered_pair(sK90(U_476,U_478),sK91(U_476,U_478)),U_476)
| is_connected_in(U_476,U_478)
| ~ relation(U_476) ),
inference(clausify,[status(thm)],[f_60_5]) ).
cnf(f_60_11,plain,
( ~ in(ordered_pair(sK91(U_476,U_478),sK90(U_476,U_478)),U_476)
| is_connected_in(U_476,U_478)
| ~ relation(U_476) ),
inference(clausify,[status(thm)],[f_60_5]) ).
fof(f_61_1,plain,
! [A] :
( ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d6_wellord1]) ).
fof(f_61_2,plain,
! [U_480] :
( ! [U_479] : relation_restriction(U_480,U_479) = set_intersection2(U_480,cartesian_product2(U_479,U_479))
| ~ relation(U_480) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
cnf(f_61_3,plain,
( relation_restriction(U_480,U_479) = set_intersection2(U_480,cartesian_product2(U_479,U_479))
| ~ relation(U_480) ),
inference(clausify,[status(thm)],[f_61_2]) ).
fof(f_62_1,plain,
! [A] :
( ! [B] :
( ( ( B = relation_inverse(A)
| ? [C,D] :
( ( ~ in(ordered_pair(C,D),B)
& in(ordered_pair(D,C),A) )
| ( ~ in(ordered_pair(D,C),A)
& in(ordered_pair(C,D),B) ) ) )
& ( ! [C,D] :
( ( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(D,C),A) )
& ( in(ordered_pair(D,C),A)
| ~ in(ordered_pair(C,D),B) ) )
| B != relation_inverse(A) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d7_relat_1]) ).
fof(f_62_2,plain,
! [U_486] :
( ! [U_485] :
( ( ( U_485 = relation_inverse(U_486)
| ? [U_484,U_483] :
( ( ~ in(ordered_pair(U_484,U_483),U_485)
& in(ordered_pair(U_483,U_484),U_486) )
| ( ~ in(ordered_pair(U_483,U_484),U_486)
& in(ordered_pair(U_484,U_483),U_485) ) ) )
& ( ! [U_482,U_481] :
( ( in(ordered_pair(U_482,U_481),U_485)
| ~ in(ordered_pair(U_481,U_482),U_486) )
& ( in(ordered_pair(U_481,U_482),U_486)
| ~ in(ordered_pair(U_482,U_481),U_485) ) )
| U_485 != relation_inverse(U_486) ) )
| ~ relation(U_485) )
| ~ relation(U_486) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
! [U_486] :
( ! [U_485] :
( ( ( U_485 = relation_inverse(U_486)
| ? [U_494,U_492] :
( ~ in(ordered_pair(U_494,U_492),U_485)
& in(ordered_pair(U_492,U_494),U_486) )
| ? [U_493,U_491] :
( ~ in(ordered_pair(U_491,U_493),U_486)
& in(ordered_pair(U_493,U_491),U_485) ) )
& ( ( ! [U_490,U_488] :
( in(ordered_pair(U_490,U_488),U_485)
| ~ in(ordered_pair(U_488,U_490),U_486) )
& ! [U_489,U_487] :
( in(ordered_pair(U_487,U_489),U_486)
| ~ in(ordered_pair(U_489,U_487),U_485) ) )
| U_485 != relation_inverse(U_486) ) )
| ~ relation(U_485) )
| ~ relation(U_486) ),
inference(miniscope,[status(thm)],[f_62_2]) ).
fof(f_62_4,plain,
! [U_486] :
( ! [U_485] :
( ( ( U_485 = relation_inverse(U_486)
| ? [U_494,U_492] :
( ~ in(ordered_pair(U_494,U_492),U_485)
& in(ordered_pair(U_492,U_494),U_486) )
| ? [U_491] :
( ~ in(ordered_pair(U_491,sK92(U_486,U_485)),U_486)
& in(ordered_pair(sK92(U_486,U_485),U_491),U_485) ) )
& ( ( ! [U_490,U_488] :
( in(ordered_pair(U_490,U_488),U_485)
| ~ in(ordered_pair(U_488,U_490),U_486) )
& ! [U_489,U_487] :
( in(ordered_pair(U_487,U_489),U_486)
| ~ in(ordered_pair(U_489,U_487),U_485) ) )
| U_485 != relation_inverse(U_486) ) )
| ~ relation(U_485) )
| ~ relation(U_486) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_493,sK92(U_486,U_485))],[f_62_3]) ).
fof(f_62_5,plain,
! [U_486] :
( ! [U_485] :
( ( ( U_485 = relation_inverse(U_486)
| ? [U_494,U_492] :
( ~ in(ordered_pair(U_494,U_492),U_485)
& in(ordered_pair(U_492,U_494),U_486) )
| ( ~ in(ordered_pair(sK93(U_486,U_485),sK92(U_486,U_485)),U_486)
& in(ordered_pair(sK92(U_486,U_485),sK93(U_486,U_485)),U_485) ) )
& ( ( ! [U_490,U_488] :
( in(ordered_pair(U_490,U_488),U_485)
| ~ in(ordered_pair(U_488,U_490),U_486) )
& ! [U_489,U_487] :
( in(ordered_pair(U_487,U_489),U_486)
| ~ in(ordered_pair(U_489,U_487),U_485) ) )
| U_485 != relation_inverse(U_486) ) )
| ~ relation(U_485) )
| ~ relation(U_486) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_491,sK93(U_486,U_485))],[f_62_4]) ).
fof(f_62_6,plain,
! [U_486] :
( ! [U_485] :
( ( ( U_485 = relation_inverse(U_486)
| ? [U_492] :
( ~ in(ordered_pair(sK94(U_486,U_485),U_492),U_485)
& in(ordered_pair(U_492,sK94(U_486,U_485)),U_486) )
| ( ~ in(ordered_pair(sK93(U_486,U_485),sK92(U_486,U_485)),U_486)
& in(ordered_pair(sK92(U_486,U_485),sK93(U_486,U_485)),U_485) ) )
& ( ( ! [U_490,U_488] :
( in(ordered_pair(U_490,U_488),U_485)
| ~ in(ordered_pair(U_488,U_490),U_486) )
& ! [U_489,U_487] :
( in(ordered_pair(U_487,U_489),U_486)
| ~ in(ordered_pair(U_489,U_487),U_485) ) )
| U_485 != relation_inverse(U_486) ) )
| ~ relation(U_485) )
| ~ relation(U_486) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_494,sK94(U_486,U_485))],[f_62_5]) ).
fof(f_62_7,plain,
! [U_486] :
( ! [U_485] :
( ( ( U_485 = relation_inverse(U_486)
| ( ~ in(ordered_pair(sK94(U_486,U_485),sK95(U_486,U_485)),U_485)
& in(ordered_pair(sK95(U_486,U_485),sK94(U_486,U_485)),U_486) )
| ( ~ in(ordered_pair(sK93(U_486,U_485),sK92(U_486,U_485)),U_486)
& in(ordered_pair(sK92(U_486,U_485),sK93(U_486,U_485)),U_485) ) )
& ( ( ! [U_490,U_488] :
( in(ordered_pair(U_490,U_488),U_485)
| ~ in(ordered_pair(U_488,U_490),U_486) )
& ! [U_489,U_487] :
( in(ordered_pair(U_487,U_489),U_486)
| ~ in(ordered_pair(U_489,U_487),U_485) ) )
| U_485 != relation_inverse(U_486) ) )
| ~ relation(U_485) )
| ~ relation(U_486) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_492,sK95(U_486,U_485))],[f_62_6]) ).
cnf(f_62_8,plain,
( in(ordered_pair(U_487,U_489),U_486)
| ~ in(ordered_pair(U_489,U_487),U_485)
| U_485 != relation_inverse(U_486)
| ~ relation(U_485)
| ~ relation(U_486) ),
inference(clausify,[status(thm)],[f_62_7]) ).
cnf(f_62_9,plain,
( in(ordered_pair(U_490,U_488),U_485)
| ~ in(ordered_pair(U_488,U_490),U_486)
| U_485 != relation_inverse(U_486)
| ~ relation(U_485)
| ~ relation(U_486) ),
inference(clausify,[status(thm)],[f_62_7]) ).
cnf(f_62_10,plain,
( in(ordered_pair(sK95(U_486,U_485),sK94(U_486,U_485)),U_486)
| in(ordered_pair(sK92(U_486,U_485),sK93(U_486,U_485)),U_485)
| U_485 = relation_inverse(U_486)
| ~ relation(U_485)
| ~ relation(U_486) ),
inference(clausify,[status(thm)],[f_62_7]) ).
cnf(f_62_11,plain,
( ~ in(ordered_pair(sK94(U_486,U_485),sK95(U_486,U_485)),U_485)
| in(ordered_pair(sK92(U_486,U_485),sK93(U_486,U_485)),U_485)
| U_485 = relation_inverse(U_486)
| ~ relation(U_485)
| ~ relation(U_486) ),
inference(clausify,[status(thm)],[f_62_7]) ).
cnf(f_62_12,plain,
( in(ordered_pair(sK95(U_486,U_485),sK94(U_486,U_485)),U_486)
| ~ in(ordered_pair(sK93(U_486,U_485),sK92(U_486,U_485)),U_486)
| U_485 = relation_inverse(U_486)
| ~ relation(U_485)
| ~ relation(U_486) ),
inference(clausify,[status(thm)],[f_62_7]) ).
cnf(f_62_13,plain,
( ~ in(ordered_pair(sK94(U_486,U_485),sK95(U_486,U_485)),U_485)
| ~ in(ordered_pair(sK93(U_486,U_485),sK92(U_486,U_485)),U_486)
| U_485 = relation_inverse(U_486)
| ~ relation(U_485)
| ~ relation(U_486) ),
inference(clausify,[status(thm)],[f_62_7]) ).
fof(f_63_1,plain,
! [A,B] :
( ( disjoint(A,B)
| set_intersection2(A,B) != empty_set )
& ( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[d7_xboole_0]) ).
fof(f_63_2,plain,
! [U_496,U_495] :
( ( disjoint(U_496,U_495)
| set_intersection2(U_496,U_495) != empty_set )
& ( set_intersection2(U_496,U_495) = empty_set
| ~ disjoint(U_496,U_495) ) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
( ! [U_500,U_498] :
( disjoint(U_500,U_498)
| set_intersection2(U_500,U_498) != empty_set )
& ! [U_499,U_497] :
( set_intersection2(U_499,U_497) = empty_set
| ~ disjoint(U_499,U_497) ) ),
inference(miniscope,[status(thm)],[f_63_2]) ).
cnf(f_63_4,plain,
( set_intersection2(U_499,U_497) = empty_set
| ~ disjoint(U_499,U_497) ),
inference(clausify,[status(thm)],[f_63_3]) ).
cnf(f_63_5,plain,
( disjoint(U_500,U_498)
| set_intersection2(U_500,U_498) != empty_set ),
inference(clausify,[status(thm)],[f_63_3]) ).
fof(f_64_1,plain,
! [A] :
( ( ( one_to_one(A)
| ? [B,C] :
( B != C
& apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) ) )
& ( ! [B,C] :
( B = C
| apply(A,B) != apply(A,C)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d8_funct_1]) ).
fof(f_64_2,plain,
! [U_505] :
( ( ( one_to_one(U_505)
| ? [U_504,U_503] :
( U_504 != U_503
& apply(U_505,U_504) = apply(U_505,U_503)
& in(U_503,relation_dom(U_505))
& in(U_504,relation_dom(U_505)) ) )
& ( ! [U_502,U_501] :
( U_502 = U_501
| apply(U_505,U_502) != apply(U_505,U_501)
| ~ in(U_501,relation_dom(U_505))
| ~ in(U_502,relation_dom(U_505)) )
| ~ one_to_one(U_505) ) )
| ~ function(U_505)
| ~ relation(U_505) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
! [U_505] :
( ( ( one_to_one(U_505)
| ? [U_503] :
( sK96(U_505) != U_503
& apply(U_505,sK96(U_505)) = apply(U_505,U_503)
& in(U_503,relation_dom(U_505))
& in(sK96(U_505),relation_dom(U_505)) ) )
& ( ! [U_502,U_501] :
( U_502 = U_501
| apply(U_505,U_502) != apply(U_505,U_501)
| ~ in(U_501,relation_dom(U_505))
| ~ in(U_502,relation_dom(U_505)) )
| ~ one_to_one(U_505) ) )
| ~ function(U_505)
| ~ relation(U_505) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_504,sK96(U_505))],[f_64_2]) ).
fof(f_64_4,plain,
! [U_505] :
( ( ( one_to_one(U_505)
| ( sK96(U_505) != sK97(U_505)
& apply(U_505,sK96(U_505)) = apply(U_505,sK97(U_505))
& in(sK97(U_505),relation_dom(U_505))
& in(sK96(U_505),relation_dom(U_505)) ) )
& ( ! [U_502,U_501] :
( U_502 = U_501
| apply(U_505,U_502) != apply(U_505,U_501)
| ~ in(U_501,relation_dom(U_505))
| ~ in(U_502,relation_dom(U_505)) )
| ~ one_to_one(U_505) ) )
| ~ function(U_505)
| ~ relation(U_505) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_503,sK97(U_505))],[f_64_3]) ).
cnf(f_64_5,plain,
( U_502 = U_501
| apply(U_505,U_502) != apply(U_505,U_501)
| ~ in(U_501,relation_dom(U_505))
| ~ in(U_502,relation_dom(U_505))
| ~ one_to_one(U_505)
| ~ function(U_505)
| ~ relation(U_505) ),
inference(clausify,[status(thm)],[f_64_4]) ).
cnf(f_64_6,plain,
( in(sK96(U_505),relation_dom(U_505))
| one_to_one(U_505)
| ~ function(U_505)
| ~ relation(U_505) ),
inference(clausify,[status(thm)],[f_64_4]) ).
cnf(f_64_7,plain,
( in(sK97(U_505),relation_dom(U_505))
| one_to_one(U_505)
| ~ function(U_505)
| ~ relation(U_505) ),
inference(clausify,[status(thm)],[f_64_4]) ).
cnf(f_64_8,plain,
( apply(U_505,sK96(U_505)) = apply(U_505,sK97(U_505))
| one_to_one(U_505)
| ~ function(U_505)
| ~ relation(U_505) ),
inference(clausify,[status(thm)],[f_64_4]) ).
cnf(f_64_9,plain,
( sK96(U_505) != sK97(U_505)
| one_to_one(U_505)
| ~ function(U_505)
| ~ relation(U_505) ),
inference(clausify,[status(thm)],[f_64_4]) ).
fof(f_65_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( C = relation_composition(A,B)
| ? [D,E] :
( ( ~ in(ordered_pair(D,E),C)
& ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) ) )
| ( ! [F] :
( ~ in(ordered_pair(F,E),B)
| ~ in(ordered_pair(D,F),A) )
& in(ordered_pair(D,E),C) ) ) )
& ( ! [D,E] :
( ( in(ordered_pair(D,E),C)
| ! [F] :
( ~ in(ordered_pair(F,E),B)
| ~ in(ordered_pair(D,F),A) ) )
& ( ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_composition(A,B) ) )
| ~ relation(C) )
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d8_relat_1]) ).
fof(f_65_2,plain,
! [U_516] :
( ! [U_515] :
( ! [U_514] :
( ( ( U_514 = relation_composition(U_516,U_515)
| ? [U_513,U_512] :
( ( ~ in(ordered_pair(U_513,U_512),U_514)
& ? [U_511] :
( in(ordered_pair(U_511,U_512),U_515)
& in(ordered_pair(U_513,U_511),U_516) ) )
| ( ! [U_510] :
( ~ in(ordered_pair(U_510,U_512),U_515)
| ~ in(ordered_pair(U_513,U_510),U_516) )
& in(ordered_pair(U_513,U_512),U_514) ) ) )
& ( ! [U_509,U_508] :
( ( in(ordered_pair(U_509,U_508),U_514)
| ! [U_507] :
( ~ in(ordered_pair(U_507,U_508),U_515)
| ~ in(ordered_pair(U_509,U_507),U_516) ) )
& ( ? [U_506] :
( in(ordered_pair(U_506,U_508),U_515)
& in(ordered_pair(U_509,U_506),U_516) )
| ~ in(ordered_pair(U_509,U_508),U_514) ) )
| U_514 != relation_composition(U_516,U_515) ) )
| ~ relation(U_514) )
| ~ relation(U_515) )
| ~ relation(U_516) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
! [U_516] :
( ! [U_515] :
( ! [U_514] :
( ( ( U_514 = relation_composition(U_516,U_515)
| ? [U_524,U_522] :
( ~ in(ordered_pair(U_524,U_522),U_514)
& ? [U_511] :
( in(ordered_pair(U_511,U_522),U_515)
& in(ordered_pair(U_524,U_511),U_516) ) )
| ? [U_523,U_521] :
( ! [U_510] :
( ~ in(ordered_pair(U_510,U_521),U_515)
| ~ in(ordered_pair(U_523,U_510),U_516) )
& in(ordered_pair(U_523,U_521),U_514) ) )
& ( ( ! [U_520,U_518] :
( in(ordered_pair(U_520,U_518),U_514)
| ! [U_507] :
( ~ in(ordered_pair(U_507,U_518),U_515)
| ~ in(ordered_pair(U_520,U_507),U_516) ) )
& ! [U_519,U_517] :
( ? [U_506] :
( in(ordered_pair(U_506,U_517),U_515)
& in(ordered_pair(U_519,U_506),U_516) )
| ~ in(ordered_pair(U_519,U_517),U_514) ) )
| U_514 != relation_composition(U_516,U_515) ) )
| ~ relation(U_514) )
| ~ relation(U_515) )
| ~ relation(U_516) ),
inference(miniscope,[status(thm)],[f_65_2]) ).
fof(f_65_4,plain,
! [U_516] :
( ! [U_515] :
( ! [U_514] :
( ( ( U_514 = relation_composition(U_516,U_515)
| ? [U_524,U_522] :
( ~ in(ordered_pair(U_524,U_522),U_514)
& ? [U_511] :
( in(ordered_pair(U_511,U_522),U_515)
& in(ordered_pair(U_524,U_511),U_516) ) )
| ? [U_523,U_521] :
( ! [U_510] :
( ~ in(ordered_pair(U_510,U_521),U_515)
| ~ in(ordered_pair(U_523,U_510),U_516) )
& in(ordered_pair(U_523,U_521),U_514) ) )
& ( ( ! [U_520,U_518] :
( in(ordered_pair(U_520,U_518),U_514)
| ! [U_507] :
( ~ in(ordered_pair(U_507,U_518),U_515)
| ~ in(ordered_pair(U_520,U_507),U_516) ) )
& ! [U_519,U_517] :
( ( in(ordered_pair(sK98(U_516,U_515,U_514,U_519,U_517),U_517),U_515)
& in(ordered_pair(U_519,sK98(U_516,U_515,U_514,U_519,U_517)),U_516) )
| ~ in(ordered_pair(U_519,U_517),U_514) ) )
| U_514 != relation_composition(U_516,U_515) ) )
| ~ relation(U_514) )
| ~ relation(U_515) )
| ~ relation(U_516) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_506,sK98(U_516,U_515,U_514,U_519,U_517))],[f_65_3]) ).
fof(f_65_5,plain,
! [U_516] :
( ! [U_515] :
( ! [U_514] :
( ( ( U_514 = relation_composition(U_516,U_515)
| ? [U_524,U_522] :
( ~ in(ordered_pair(U_524,U_522),U_514)
& ? [U_511] :
( in(ordered_pair(U_511,U_522),U_515)
& in(ordered_pair(U_524,U_511),U_516) ) )
| ? [U_521] :
( ! [U_510] :
( ~ in(ordered_pair(U_510,U_521),U_515)
| ~ in(ordered_pair(sK99(U_516,U_515,U_514),U_510),U_516) )
& in(ordered_pair(sK99(U_516,U_515,U_514),U_521),U_514) ) )
& ( ( ! [U_520,U_518] :
( in(ordered_pair(U_520,U_518),U_514)
| ! [U_507] :
( ~ in(ordered_pair(U_507,U_518),U_515)
| ~ in(ordered_pair(U_520,U_507),U_516) ) )
& ! [U_519,U_517] :
( ( in(ordered_pair(sK98(U_516,U_515,U_514,U_519,U_517),U_517),U_515)
& in(ordered_pair(U_519,sK98(U_516,U_515,U_514,U_519,U_517)),U_516) )
| ~ in(ordered_pair(U_519,U_517),U_514) ) )
| U_514 != relation_composition(U_516,U_515) ) )
| ~ relation(U_514) )
| ~ relation(U_515) )
| ~ relation(U_516) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_523,sK99(U_516,U_515,U_514))],[f_65_4]) ).
fof(f_65_6,plain,
! [U_516] :
( ! [U_515] :
( ! [U_514] :
( ( ( U_514 = relation_composition(U_516,U_515)
| ? [U_524,U_522] :
( ~ in(ordered_pair(U_524,U_522),U_514)
& ? [U_511] :
( in(ordered_pair(U_511,U_522),U_515)
& in(ordered_pair(U_524,U_511),U_516) ) )
| ( ! [U_510] :
( ~ in(ordered_pair(U_510,sK100(U_516,U_515,U_514)),U_515)
| ~ in(ordered_pair(sK99(U_516,U_515,U_514),U_510),U_516) )
& in(ordered_pair(sK99(U_516,U_515,U_514),sK100(U_516,U_515,U_514)),U_514) ) )
& ( ( ! [U_520,U_518] :
( in(ordered_pair(U_520,U_518),U_514)
| ! [U_507] :
( ~ in(ordered_pair(U_507,U_518),U_515)
| ~ in(ordered_pair(U_520,U_507),U_516) ) )
& ! [U_519,U_517] :
( ( in(ordered_pair(sK98(U_516,U_515,U_514,U_519,U_517),U_517),U_515)
& in(ordered_pair(U_519,sK98(U_516,U_515,U_514,U_519,U_517)),U_516) )
| ~ in(ordered_pair(U_519,U_517),U_514) ) )
| U_514 != relation_composition(U_516,U_515) ) )
| ~ relation(U_514) )
| ~ relation(U_515) )
| ~ relation(U_516) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_521,sK100(U_516,U_515,U_514))],[f_65_5]) ).
fof(f_65_7,plain,
! [U_516] :
( ! [U_515] :
( ! [U_514] :
( ( ( U_514 = relation_composition(U_516,U_515)
| ? [U_522] :
( ~ in(ordered_pair(sK101(U_516,U_515,U_514),U_522),U_514)
& ? [U_511] :
( in(ordered_pair(U_511,U_522),U_515)
& in(ordered_pair(sK101(U_516,U_515,U_514),U_511),U_516) ) )
| ( ! [U_510] :
( ~ in(ordered_pair(U_510,sK100(U_516,U_515,U_514)),U_515)
| ~ in(ordered_pair(sK99(U_516,U_515,U_514),U_510),U_516) )
& in(ordered_pair(sK99(U_516,U_515,U_514),sK100(U_516,U_515,U_514)),U_514) ) )
& ( ( ! [U_520,U_518] :
( in(ordered_pair(U_520,U_518),U_514)
| ! [U_507] :
( ~ in(ordered_pair(U_507,U_518),U_515)
| ~ in(ordered_pair(U_520,U_507),U_516) ) )
& ! [U_519,U_517] :
( ( in(ordered_pair(sK98(U_516,U_515,U_514,U_519,U_517),U_517),U_515)
& in(ordered_pair(U_519,sK98(U_516,U_515,U_514,U_519,U_517)),U_516) )
| ~ in(ordered_pair(U_519,U_517),U_514) ) )
| U_514 != relation_composition(U_516,U_515) ) )
| ~ relation(U_514) )
| ~ relation(U_515) )
| ~ relation(U_516) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_524,sK101(U_516,U_515,U_514))],[f_65_6]) ).
fof(f_65_8,plain,
! [U_516] :
( ! [U_515] :
( ! [U_514] :
( ( ( U_514 = relation_composition(U_516,U_515)
| ( ~ in(ordered_pair(sK101(U_516,U_515,U_514),sK102(U_516,U_515,U_514)),U_514)
& ? [U_511] :
( in(ordered_pair(U_511,sK102(U_516,U_515,U_514)),U_515)
& in(ordered_pair(sK101(U_516,U_515,U_514),U_511),U_516) ) )
| ( ! [U_510] :
( ~ in(ordered_pair(U_510,sK100(U_516,U_515,U_514)),U_515)
| ~ in(ordered_pair(sK99(U_516,U_515,U_514),U_510),U_516) )
& in(ordered_pair(sK99(U_516,U_515,U_514),sK100(U_516,U_515,U_514)),U_514) ) )
& ( ( ! [U_520,U_518] :
( in(ordered_pair(U_520,U_518),U_514)
| ! [U_507] :
( ~ in(ordered_pair(U_507,U_518),U_515)
| ~ in(ordered_pair(U_520,U_507),U_516) ) )
& ! [U_519,U_517] :
( ( in(ordered_pair(sK98(U_516,U_515,U_514,U_519,U_517),U_517),U_515)
& in(ordered_pair(U_519,sK98(U_516,U_515,U_514,U_519,U_517)),U_516) )
| ~ in(ordered_pair(U_519,U_517),U_514) ) )
| U_514 != relation_composition(U_516,U_515) ) )
| ~ relation(U_514) )
| ~ relation(U_515) )
| ~ relation(U_516) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_522,sK102(U_516,U_515,U_514))],[f_65_7]) ).
fof(f_65_9,plain,
! [U_516] :
( ! [U_515] :
( ! [U_514] :
( ( ( U_514 = relation_composition(U_516,U_515)
| ( ~ in(ordered_pair(sK101(U_516,U_515,U_514),sK102(U_516,U_515,U_514)),U_514)
& in(ordered_pair(sK103(U_516,U_515,U_514),sK102(U_516,U_515,U_514)),U_515)
& in(ordered_pair(sK101(U_516,U_515,U_514),sK103(U_516,U_515,U_514)),U_516) )
| ( ! [U_510] :
( ~ in(ordered_pair(U_510,sK100(U_516,U_515,U_514)),U_515)
| ~ in(ordered_pair(sK99(U_516,U_515,U_514),U_510),U_516) )
& in(ordered_pair(sK99(U_516,U_515,U_514),sK100(U_516,U_515,U_514)),U_514) ) )
& ( ( ! [U_520,U_518] :
( in(ordered_pair(U_520,U_518),U_514)
| ! [U_507] :
( ~ in(ordered_pair(U_507,U_518),U_515)
| ~ in(ordered_pair(U_520,U_507),U_516) ) )
& ! [U_519,U_517] :
( ( in(ordered_pair(sK98(U_516,U_515,U_514,U_519,U_517),U_517),U_515)
& in(ordered_pair(U_519,sK98(U_516,U_515,U_514,U_519,U_517)),U_516) )
| ~ in(ordered_pair(U_519,U_517),U_514) ) )
| U_514 != relation_composition(U_516,U_515) ) )
| ~ relation(U_514) )
| ~ relation(U_515) )
| ~ relation(U_516) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(U_511,sK103(U_516,U_515,U_514))],[f_65_8]) ).
cnf(f_65_10,plain,
( in(ordered_pair(U_519,sK98(U_516,U_515,U_514,U_519,U_517)),U_516)
| ~ in(ordered_pair(U_519,U_517),U_514)
| U_514 != relation_composition(U_516,U_515)
| ~ relation(U_514)
| ~ relation(U_515)
| ~ relation(U_516) ),
inference(clausify,[status(thm)],[f_65_9]) ).
cnf(f_65_11,plain,
( in(ordered_pair(sK98(U_516,U_515,U_514,U_519,U_517),U_517),U_515)
| ~ in(ordered_pair(U_519,U_517),U_514)
| U_514 != relation_composition(U_516,U_515)
| ~ relation(U_514)
| ~ relation(U_515)
| ~ relation(U_516) ),
inference(clausify,[status(thm)],[f_65_9]) ).
cnf(f_65_12,plain,
( in(ordered_pair(U_520,U_518),U_514)
| ~ in(ordered_pair(U_507,U_518),U_515)
| ~ in(ordered_pair(U_520,U_507),U_516)
| U_514 != relation_composition(U_516,U_515)
| ~ relation(U_514)
| ~ relation(U_515)
| ~ relation(U_516) ),
inference(clausify,[status(thm)],[f_65_9]) ).
cnf(f_65_13,plain,
( in(ordered_pair(sK101(U_516,U_515,U_514),sK103(U_516,U_515,U_514)),U_516)
| in(ordered_pair(sK99(U_516,U_515,U_514),sK100(U_516,U_515,U_514)),U_514)
| U_514 = relation_composition(U_516,U_515)
| ~ relation(U_514)
| ~ relation(U_515)
| ~ relation(U_516) ),
inference(clausify,[status(thm)],[f_65_9]) ).
cnf(f_65_14,plain,
( in(ordered_pair(sK103(U_516,U_515,U_514),sK102(U_516,U_515,U_514)),U_515)
| in(ordered_pair(sK99(U_516,U_515,U_514),sK100(U_516,U_515,U_514)),U_514)
| U_514 = relation_composition(U_516,U_515)
| ~ relation(U_514)
| ~ relation(U_515)
| ~ relation(U_516) ),
inference(clausify,[status(thm)],[f_65_9]) ).
cnf(f_65_15,plain,
( ~ in(ordered_pair(sK101(U_516,U_515,U_514),sK102(U_516,U_515,U_514)),U_514)
| in(ordered_pair(sK99(U_516,U_515,U_514),sK100(U_516,U_515,U_514)),U_514)
| U_514 = relation_composition(U_516,U_515)
| ~ relation(U_514)
| ~ relation(U_515)
| ~ relation(U_516) ),
inference(clausify,[status(thm)],[f_65_9]) ).
cnf(f_65_16,plain,
( in(ordered_pair(sK101(U_516,U_515,U_514),sK103(U_516,U_515,U_514)),U_516)
| ~ in(ordered_pair(U_510,sK100(U_516,U_515,U_514)),U_515)
| ~ in(ordered_pair(sK99(U_516,U_515,U_514),U_510),U_516)
| U_514 = relation_composition(U_516,U_515)
| ~ relation(U_514)
| ~ relation(U_515)
| ~ relation(U_516) ),
inference(clausify,[status(thm)],[f_65_9]) ).
cnf(f_65_17,plain,
( in(ordered_pair(sK103(U_516,U_515,U_514),sK102(U_516,U_515,U_514)),U_515)
| ~ in(ordered_pair(U_510,sK100(U_516,U_515,U_514)),U_515)
| ~ in(ordered_pair(sK99(U_516,U_515,U_514),U_510),U_516)
| U_514 = relation_composition(U_516,U_515)
| ~ relation(U_514)
| ~ relation(U_515)
| ~ relation(U_516) ),
inference(clausify,[status(thm)],[f_65_9]) ).
cnf(f_65_18,plain,
( ~ in(ordered_pair(sK101(U_516,U_515,U_514),sK102(U_516,U_515,U_514)),U_514)
| ~ in(ordered_pair(U_510,sK100(U_516,U_515,U_514)),U_515)
| ~ in(ordered_pair(sK99(U_516,U_515,U_514),U_510),U_516)
| U_514 = relation_composition(U_516,U_515)
| ~ relation(U_514)
| ~ relation(U_515)
| ~ relation(U_516) ),
inference(clausify,[status(thm)],[f_65_9]) ).
fof(f_66_1,plain,
! [A] :
( ! [B] :
( ( is_transitive_in(A,B)
| ? [C,D,E] :
( ~ in(ordered_pair(C,E),A)
& in(ordered_pair(D,E),A)
& in(ordered_pair(C,D),A)
& in(E,B)
& in(D,B)
& in(C,B) ) )
& ( ! [C,D,E] :
( in(ordered_pair(C,E),A)
| ~ in(ordered_pair(D,E),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(E,B)
| ~ in(D,B)
| ~ in(C,B) )
| ~ is_transitive_in(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d8_relat_2]) ).
fof(f_66_2,plain,
! [U_532] :
( ! [U_531] :
( ( is_transitive_in(U_532,U_531)
| ? [U_530,U_529,U_528] :
( ~ in(ordered_pair(U_530,U_528),U_532)
& in(ordered_pair(U_529,U_528),U_532)
& in(ordered_pair(U_530,U_529),U_532)
& in(U_528,U_531)
& in(U_529,U_531)
& in(U_530,U_531) ) )
& ( ! [U_527,U_526,U_525] :
( in(ordered_pair(U_527,U_525),U_532)
| ~ in(ordered_pair(U_526,U_525),U_532)
| ~ in(ordered_pair(U_527,U_526),U_532)
| ~ in(U_525,U_531)
| ~ in(U_526,U_531)
| ~ in(U_527,U_531) )
| ~ is_transitive_in(U_532,U_531) ) )
| ~ relation(U_532) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
! [U_532] :
( ( ! [U_534] :
( is_transitive_in(U_532,U_534)
| ? [U_530,U_529,U_528] :
( ~ in(ordered_pair(U_530,U_528),U_532)
& in(ordered_pair(U_529,U_528),U_532)
& in(ordered_pair(U_530,U_529),U_532)
& in(U_528,U_534)
& in(U_529,U_534)
& in(U_530,U_534) ) )
& ! [U_533] :
( ! [U_527,U_526,U_525] :
( in(ordered_pair(U_527,U_525),U_532)
| ~ in(ordered_pair(U_526,U_525),U_532)
| ~ in(ordered_pair(U_527,U_526),U_532)
| ~ in(U_525,U_533)
| ~ in(U_526,U_533)
| ~ in(U_527,U_533) )
| ~ is_transitive_in(U_532,U_533) ) )
| ~ relation(U_532) ),
inference(miniscope,[status(thm)],[f_66_2]) ).
fof(f_66_4,plain,
! [U_532] :
( ( ! [U_534] :
( is_transitive_in(U_532,U_534)
| ? [U_529,U_528] :
( ~ in(ordered_pair(sK104(U_532,U_534),U_528),U_532)
& in(ordered_pair(U_529,U_528),U_532)
& in(ordered_pair(sK104(U_532,U_534),U_529),U_532)
& in(U_528,U_534)
& in(U_529,U_534)
& in(sK104(U_532,U_534),U_534) ) )
& ! [U_533] :
( ! [U_527,U_526,U_525] :
( in(ordered_pair(U_527,U_525),U_532)
| ~ in(ordered_pair(U_526,U_525),U_532)
| ~ in(ordered_pair(U_527,U_526),U_532)
| ~ in(U_525,U_533)
| ~ in(U_526,U_533)
| ~ in(U_527,U_533) )
| ~ is_transitive_in(U_532,U_533) ) )
| ~ relation(U_532) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK104]),skolemize(U_530,sK104(U_532,U_534))],[f_66_3]) ).
fof(f_66_5,plain,
! [U_532] :
( ( ! [U_534] :
( is_transitive_in(U_532,U_534)
| ? [U_528] :
( ~ in(ordered_pair(sK104(U_532,U_534),U_528),U_532)
& in(ordered_pair(sK105(U_532,U_534),U_528),U_532)
& in(ordered_pair(sK104(U_532,U_534),sK105(U_532,U_534)),U_532)
& in(U_528,U_534)
& in(sK105(U_532,U_534),U_534)
& in(sK104(U_532,U_534),U_534) ) )
& ! [U_533] :
( ! [U_527,U_526,U_525] :
( in(ordered_pair(U_527,U_525),U_532)
| ~ in(ordered_pair(U_526,U_525),U_532)
| ~ in(ordered_pair(U_527,U_526),U_532)
| ~ in(U_525,U_533)
| ~ in(U_526,U_533)
| ~ in(U_527,U_533) )
| ~ is_transitive_in(U_532,U_533) ) )
| ~ relation(U_532) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK105]),skolemize(U_529,sK105(U_532,U_534))],[f_66_4]) ).
fof(f_66_6,plain,
! [U_532] :
( ( ! [U_534] :
( is_transitive_in(U_532,U_534)
| ( ~ in(ordered_pair(sK104(U_532,U_534),sK106(U_532,U_534)),U_532)
& in(ordered_pair(sK105(U_532,U_534),sK106(U_532,U_534)),U_532)
& in(ordered_pair(sK104(U_532,U_534),sK105(U_532,U_534)),U_532)
& in(sK106(U_532,U_534),U_534)
& in(sK105(U_532,U_534),U_534)
& in(sK104(U_532,U_534),U_534) ) )
& ! [U_533] :
( ! [U_527,U_526,U_525] :
( in(ordered_pair(U_527,U_525),U_532)
| ~ in(ordered_pair(U_526,U_525),U_532)
| ~ in(ordered_pair(U_527,U_526),U_532)
| ~ in(U_525,U_533)
| ~ in(U_526,U_533)
| ~ in(U_527,U_533) )
| ~ is_transitive_in(U_532,U_533) ) )
| ~ relation(U_532) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK106]),skolemize(U_528,sK106(U_532,U_534))],[f_66_5]) ).
cnf(f_66_7,plain,
( in(ordered_pair(U_527,U_525),U_532)
| ~ in(ordered_pair(U_526,U_525),U_532)
| ~ in(ordered_pair(U_527,U_526),U_532)
| ~ in(U_525,U_533)
| ~ in(U_526,U_533)
| ~ in(U_527,U_533)
| ~ is_transitive_in(U_532,U_533)
| ~ relation(U_532) ),
inference(clausify,[status(thm)],[f_66_6]) ).
cnf(f_66_8,plain,
( in(sK104(U_532,U_534),U_534)
| is_transitive_in(U_532,U_534)
| ~ relation(U_532) ),
inference(clausify,[status(thm)],[f_66_6]) ).
cnf(f_66_9,plain,
( in(sK105(U_532,U_534),U_534)
| is_transitive_in(U_532,U_534)
| ~ relation(U_532) ),
inference(clausify,[status(thm)],[f_66_6]) ).
cnf(f_66_10,plain,
( in(sK106(U_532,U_534),U_534)
| is_transitive_in(U_532,U_534)
| ~ relation(U_532) ),
inference(clausify,[status(thm)],[f_66_6]) ).
cnf(f_66_11,plain,
( in(ordered_pair(sK104(U_532,U_534),sK105(U_532,U_534)),U_532)
| is_transitive_in(U_532,U_534)
| ~ relation(U_532) ),
inference(clausify,[status(thm)],[f_66_6]) ).
cnf(f_66_12,plain,
( in(ordered_pair(sK105(U_532,U_534),sK106(U_532,U_534)),U_532)
| is_transitive_in(U_532,U_534)
| ~ relation(U_532) ),
inference(clausify,[status(thm)],[f_66_6]) ).
cnf(f_66_13,plain,
( ~ in(ordered_pair(sK104(U_532,U_534),sK106(U_532,U_534)),U_532)
| is_transitive_in(U_532,U_534)
| ~ relation(U_532) ),
inference(clausify,[status(thm)],[f_66_6]) ).
fof(f_67_1,plain,
! [A,B] :
( ! [C] :
( ( ( C = complements_of_subsets(A,B)
| ? [D] :
( ( ( ~ in(D,C)
& in(subset_complement(A,D),B) )
| ( ~ in(subset_complement(A,D),B)
& in(D,C) ) )
& element(D,powerset(A)) ) )
& ( ! [D] :
( ( ( in(D,C)
| ~ in(subset_complement(A,D),B) )
& ( in(subset_complement(A,D),B)
| ~ in(D,C) ) )
| ~ element(D,powerset(A)) )
| C != complements_of_subsets(A,B) ) )
| ~ element(C,powerset(powerset(A))) )
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[d8_setfam_1]) ).
fof(f_67_2,plain,
! [U_539,U_538] :
( ! [U_537] :
( ( ( U_537 = complements_of_subsets(U_539,U_538)
| ? [U_536] :
( ( ( ~ in(U_536,U_537)
& in(subset_complement(U_539,U_536),U_538) )
| ( ~ in(subset_complement(U_539,U_536),U_538)
& in(U_536,U_537) ) )
& element(U_536,powerset(U_539)) ) )
& ( ! [U_535] :
( ( ( in(U_535,U_537)
| ~ in(subset_complement(U_539,U_535),U_538) )
& ( in(subset_complement(U_539,U_535),U_538)
| ~ in(U_535,U_537) ) )
| ~ element(U_535,powerset(U_539)) )
| U_537 != complements_of_subsets(U_539,U_538) ) )
| ~ element(U_537,powerset(powerset(U_539))) )
| ~ element(U_538,powerset(powerset(U_539))) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
! [U_539,U_538] :
( ! [U_537] :
( ( ( U_537 = complements_of_subsets(U_539,U_538)
| ( ( ( ~ in(sK107(U_539,U_538,U_537),U_537)
& in(subset_complement(U_539,sK107(U_539,U_538,U_537)),U_538) )
| ( ~ in(subset_complement(U_539,sK107(U_539,U_538,U_537)),U_538)
& in(sK107(U_539,U_538,U_537),U_537) ) )
& element(sK107(U_539,U_538,U_537),powerset(U_539)) ) )
& ( ! [U_535] :
( ( ( in(U_535,U_537)
| ~ in(subset_complement(U_539,U_535),U_538) )
& ( in(subset_complement(U_539,U_535),U_538)
| ~ in(U_535,U_537) ) )
| ~ element(U_535,powerset(U_539)) )
| U_537 != complements_of_subsets(U_539,U_538) ) )
| ~ element(U_537,powerset(powerset(U_539))) )
| ~ element(U_538,powerset(powerset(U_539))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(U_536,sK107(U_539,U_538,U_537))],[f_67_2]) ).
cnf(f_67_4,plain,
( in(subset_complement(U_539,U_535),U_538)
| ~ in(U_535,U_537)
| ~ element(U_535,powerset(U_539))
| U_537 != complements_of_subsets(U_539,U_538)
| ~ element(U_537,powerset(powerset(U_539)))
| ~ element(U_538,powerset(powerset(U_539))) ),
inference(clausify,[status(thm)],[f_67_3]) ).
cnf(f_67_5,plain,
( in(U_535,U_537)
| ~ in(subset_complement(U_539,U_535),U_538)
| ~ element(U_535,powerset(U_539))
| U_537 != complements_of_subsets(U_539,U_538)
| ~ element(U_537,powerset(powerset(U_539)))
| ~ element(U_538,powerset(powerset(U_539))) ),
inference(clausify,[status(thm)],[f_67_3]) ).
cnf(f_67_6,plain,
( element(sK107(U_539,U_538,U_537),powerset(U_539))
| U_537 = complements_of_subsets(U_539,U_538)
| ~ element(U_537,powerset(powerset(U_539)))
| ~ element(U_538,powerset(powerset(U_539))) ),
inference(clausify,[status(thm)],[f_67_3]) ).
cnf(f_67_7,plain,
( in(subset_complement(U_539,sK107(U_539,U_538,U_537)),U_538)
| in(sK107(U_539,U_538,U_537),U_537)
| U_537 = complements_of_subsets(U_539,U_538)
| ~ element(U_537,powerset(powerset(U_539)))
| ~ element(U_538,powerset(powerset(U_539))) ),
inference(clausify,[status(thm)],[f_67_3]) ).
cnf(f_67_8,plain,
( ~ in(sK107(U_539,U_538,U_537),U_537)
| in(sK107(U_539,U_538,U_537),U_537)
| U_537 = complements_of_subsets(U_539,U_538)
| ~ element(U_537,powerset(powerset(U_539)))
| ~ element(U_538,powerset(powerset(U_539))) ),
inference(clausify,[status(thm)],[f_67_3]) ).
cnf(f_67_9,plain,
( in(subset_complement(U_539,sK107(U_539,U_538,U_537)),U_538)
| ~ in(subset_complement(U_539,sK107(U_539,U_538,U_537)),U_538)
| U_537 = complements_of_subsets(U_539,U_538)
| ~ element(U_537,powerset(powerset(U_539)))
| ~ element(U_538,powerset(powerset(U_539))) ),
inference(clausify,[status(thm)],[f_67_3]) ).
cnf(f_67_10,plain,
( ~ in(sK107(U_539,U_538,U_537),U_537)
| ~ in(subset_complement(U_539,sK107(U_539,U_538,U_537)),U_538)
| U_537 = complements_of_subsets(U_539,U_538)
| ~ element(U_537,powerset(powerset(U_539)))
| ~ element(U_538,powerset(powerset(U_539))) ),
inference(clausify,[status(thm)],[f_67_3]) ).
fof(f_68_1,plain,
! [A,B] :
( ( proper_subset(A,B)
| A = B
| ~ subset(A,B) )
& ( ( A != B
& subset(A,B) )
| ~ proper_subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d8_xboole_0]) ).
fof(f_68_2,plain,
! [U_541,U_540] :
( ( proper_subset(U_541,U_540)
| U_541 = U_540
| ~ subset(U_541,U_540) )
& ( ( U_541 != U_540
& subset(U_541,U_540) )
| ~ proper_subset(U_541,U_540) ) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
fof(f_68_3,plain,
( ! [U_545,U_543] :
( proper_subset(U_545,U_543)
| U_545 = U_543
| ~ subset(U_545,U_543) )
& ! [U_544,U_542] :
( ( U_544 != U_542
& subset(U_544,U_542) )
| ~ proper_subset(U_544,U_542) ) ),
inference(miniscope,[status(thm)],[f_68_2]) ).
cnf(f_68_4,plain,
( subset(U_544,U_542)
| ~ proper_subset(U_544,U_542) ),
inference(clausify,[status(thm)],[f_68_3]) ).
cnf(f_68_5,plain,
( U_544 != U_542
| ~ proper_subset(U_544,U_542) ),
inference(clausify,[status(thm)],[f_68_3]) ).
cnf(f_68_6,plain,
( proper_subset(U_545,U_543)
| U_545 = U_543
| ~ subset(U_545,U_543) ),
inference(clausify,[status(thm)],[f_68_3]) ).
fof(f_69_1,plain,
! [A] :
( function_inverse(A) = relation_inverse(A)
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d9_funct_1]) ).
fof(f_69_2,plain,
! [U_546] :
( function_inverse(U_546) = relation_inverse(U_546)
| ~ one_to_one(U_546)
| ~ function(U_546)
| ~ relation(U_546) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
cnf(f_69_3,plain,
( function_inverse(U_546) = relation_inverse(U_546)
| ~ one_to_one(U_546)
| ~ function(U_546)
| ~ relation(U_546) ),
inference(clausify,[status(thm)],[f_69_2]) ).
fof(f_70_1,plain,
! [A] :
( ( ( reflexive(A)
| ~ is_reflexive_in(A,relation_field(A)) )
& ( is_reflexive_in(A,relation_field(A))
| ~ reflexive(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d9_relat_2]) ).
fof(f_70_2,plain,
! [U_547] :
( ( ( reflexive(U_547)
| ~ is_reflexive_in(U_547,relation_field(U_547)) )
& ( is_reflexive_in(U_547,relation_field(U_547))
| ~ reflexive(U_547) ) )
| ~ relation(U_547) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
cnf(f_70_3,plain,
( is_reflexive_in(U_547,relation_field(U_547))
| ~ reflexive(U_547)
| ~ relation(U_547) ),
inference(clausify,[status(thm)],[f_70_2]) ).
cnf(f_70_4,plain,
( reflexive(U_547)
| ~ is_reflexive_in(U_547,relation_field(U_547))
| ~ relation(U_547) ),
inference(clausify,[status(thm)],[f_70_2]) ).
fof(f_71_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k10_relat_1]) ).
cnf(f_71_2,plain,
$true,
inference(clausify,[status(thm)],[f_71_1]) ).
fof(f_72_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_enumset1]) ).
cnf(f_72_2,plain,
$true,
inference(clausify,[status(thm)],[f_72_1]) ).
fof(f_73_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_funct_1]) ).
cnf(f_73_2,plain,
$true,
inference(clausify,[status(thm)],[f_73_1]) ).
fof(f_74_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_ordinal1]) ).
cnf(f_74_2,plain,
$true,
inference(clausify,[status(thm)],[f_74_1]) ).
fof(f_75_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
cnf(f_75_2,plain,
$true,
inference(clausify,[status(thm)],[f_75_1]) ).
fof(f_76_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_setfam_1]) ).
cnf(f_76_2,plain,
$true,
inference(clausify,[status(thm)],[f_76_1]) ).
fof(f_77_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
cnf(f_77_2,plain,
$true,
inference(clausify,[status(thm)],[f_77_1]) ).
fof(f_78_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_wellord1]) ).
cnf(f_78_2,plain,
$true,
inference(clausify,[status(thm)],[f_78_1]) ).
fof(f_79_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_79_2,plain,
$true,
inference(clausify,[status(thm)],[f_79_1]) ).
fof(f_80_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_80_2,plain,
$true,
inference(clausify,[status(thm)],[f_80_1]) ).
fof(f_81_1,plain,
! [A] :
( ( function(function_inverse(A))
& relation(function_inverse(A)) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_funct_1]) ).
fof(f_81_2,plain,
! [U_548] :
( ( function(function_inverse(U_548))
& relation(function_inverse(U_548)) )
| ~ function(U_548)
| ~ relation(U_548) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
cnf(f_81_3,plain,
( relation(function_inverse(U_548))
| ~ function(U_548)
| ~ relation(U_548) ),
inference(clausify,[status(thm)],[f_81_2]) ).
cnf(f_81_4,plain,
( function(function_inverse(U_548))
| ~ function(U_548)
| ~ relation(U_548) ),
inference(clausify,[status(thm)],[f_81_2]) ).
fof(f_82_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_relat_1]) ).
cnf(f_82_2,plain,
$true,
inference(clausify,[status(thm)],[f_82_1]) ).
fof(f_83_1,plain,
! [A] : element(cast_to_subset(A),powerset(A)),
inference(fof_nnf,[status(thm)],[dt_k2_subset_1]) ).
fof(f_83_2,plain,
! [U_549] : element(cast_to_subset(U_549),powerset(U_549)),
inference(variable_rename,[status(thm)],[f_83_1]) ).
cnf(f_83_3,plain,
element(cast_to_subset(U_549),powerset(U_549)),
inference(clausify,[status(thm)],[f_83_2]) ).
fof(f_84_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
cnf(f_84_2,plain,
$true,
inference(clausify,[status(thm)],[f_84_1]) ).
fof(f_85_1,plain,
! [A,B] :
( relation(relation_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_wellord1]) ).
fof(f_85_2,plain,
! [U_551,U_550] :
( relation(relation_restriction(U_551,U_550))
| ~ relation(U_551) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
fof(f_85_3,plain,
! [U_551] :
( ! [U_550] : relation(relation_restriction(U_551,U_550))
| ~ relation(U_551) ),
inference(miniscope,[status(thm)],[f_85_2]) ).
cnf(f_85_4,plain,
( relation(relation_restriction(U_551,U_550))
| ~ relation(U_551) ),
inference(clausify,[status(thm)],[f_85_3]) ).
fof(f_86_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
cnf(f_86_2,plain,
$true,
inference(clausify,[status(thm)],[f_86_1]) ).
fof(f_87_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
cnf(f_87_2,plain,
$true,
inference(clausify,[status(thm)],[f_87_1]) ).
fof(f_88_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_relat_1]) ).
cnf(f_88_2,plain,
$true,
inference(clausify,[status(thm)],[f_88_1]) ).
fof(f_89_1,plain,
! [A,B] :
( element(subset_complement(A,B),powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[dt_k3_subset_1]) ).
fof(f_89_2,plain,
! [U_553,U_552] :
( element(subset_complement(U_553,U_552),powerset(U_553))
| ~ element(U_552,powerset(U_553)) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
cnf(f_89_3,plain,
( element(subset_complement(U_553,U_552),powerset(U_553))
| ~ element(U_552,powerset(U_553)) ),
inference(clausify,[status(thm)],[f_89_2]) ).
fof(f_90_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_tarski]) ).
cnf(f_90_2,plain,
$true,
inference(clausify,[status(thm)],[f_90_1]) ).
fof(f_91_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
cnf(f_91_2,plain,
$true,
inference(clausify,[status(thm)],[f_91_1]) ).
fof(f_92_1,plain,
! [A] :
( relation(relation_inverse(A))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k4_relat_1]) ).
fof(f_92_2,plain,
! [U_554] :
( relation(relation_inverse(U_554))
| ~ relation(U_554) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
cnf(f_92_3,plain,
( relation(relation_inverse(U_554))
| ~ relation(U_554) ),
inference(clausify,[status(thm)],[f_92_2]) ).
fof(f_93_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
cnf(f_93_2,plain,
$true,
inference(clausify,[status(thm)],[f_93_1]) ).
fof(f_94_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
cnf(f_94_2,plain,
$true,
inference(clausify,[status(thm)],[f_94_1]) ).
fof(f_95_1,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_relat_1]) ).
fof(f_95_2,plain,
! [U_556,U_555] :
( relation(relation_composition(U_556,U_555))
| ~ relation(U_555)
| ~ relation(U_556) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
cnf(f_95_3,plain,
( relation(relation_composition(U_556,U_555))
| ~ relation(U_555)
| ~ relation(U_556) ),
inference(clausify,[status(thm)],[f_95_2]) ).
fof(f_96_1,plain,
! [A,B] :
( element(union_of_subsets(A,B),powerset(A))
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[dt_k5_setfam_1]) ).
fof(f_96_2,plain,
! [U_558,U_557] :
( element(union_of_subsets(U_558,U_557),powerset(U_558))
| ~ element(U_557,powerset(powerset(U_558))) ),
inference(variable_rename,[status(thm)],[f_96_1]) ).
cnf(f_96_3,plain,
( element(union_of_subsets(U_558,U_557),powerset(U_558))
| ~ element(U_557,powerset(powerset(U_558))) ),
inference(clausify,[status(thm)],[f_96_2]) ).
fof(f_97_1,plain,
! [A] : relation(identity_relation(A)),
inference(fof_nnf,[status(thm)],[dt_k6_relat_1]) ).
fof(f_97_2,plain,
! [U_559] : relation(identity_relation(U_559)),
inference(variable_rename,[status(thm)],[f_97_1]) ).
cnf(f_97_3,plain,
relation(identity_relation(U_559)),
inference(clausify,[status(thm)],[f_97_2]) ).
fof(f_98_1,plain,
! [A,B] :
( element(meet_of_subsets(A,B),powerset(A))
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[dt_k6_setfam_1]) ).
fof(f_98_2,plain,
! [U_561,U_560] :
( element(meet_of_subsets(U_561,U_560),powerset(U_561))
| ~ element(U_560,powerset(powerset(U_561))) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
cnf(f_98_3,plain,
( element(meet_of_subsets(U_561,U_560),powerset(U_561))
| ~ element(U_560,powerset(powerset(U_561))) ),
inference(clausify,[status(thm)],[f_98_2]) ).
fof(f_99_1,plain,
! [A,B,C] :
( element(subset_difference(A,B,C),powerset(A))
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[dt_k6_subset_1]) ).
fof(f_99_2,plain,
! [U_564,U_563,U_562] :
( element(subset_difference(U_564,U_563,U_562),powerset(U_564))
| ~ element(U_562,powerset(U_564))
| ~ element(U_563,powerset(U_564)) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
cnf(f_99_3,plain,
( element(subset_difference(U_564,U_563,U_562),powerset(U_564))
| ~ element(U_562,powerset(U_564))
| ~ element(U_563,powerset(U_564)) ),
inference(clausify,[status(thm)],[f_99_2]) ).
fof(f_100_1,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k7_relat_1]) ).
fof(f_100_2,plain,
! [U_566,U_565] :
( relation(relation_dom_restriction(U_566,U_565))
| ~ relation(U_566) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
fof(f_100_3,plain,
! [U_566] :
( ! [U_565] : relation(relation_dom_restriction(U_566,U_565))
| ~ relation(U_566) ),
inference(miniscope,[status(thm)],[f_100_2]) ).
cnf(f_100_4,plain,
( relation(relation_dom_restriction(U_566,U_565))
| ~ relation(U_566) ),
inference(clausify,[status(thm)],[f_100_3]) ).
fof(f_101_1,plain,
! [A,B] :
( element(complements_of_subsets(A,B),powerset(powerset(A)))
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[dt_k7_setfam_1]) ).
fof(f_101_2,plain,
! [U_568,U_567] :
( element(complements_of_subsets(U_568,U_567),powerset(powerset(U_568)))
| ~ element(U_567,powerset(powerset(U_568))) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
cnf(f_101_3,plain,
( element(complements_of_subsets(U_568,U_567),powerset(powerset(U_568)))
| ~ element(U_567,powerset(powerset(U_568))) ),
inference(clausify,[status(thm)],[f_101_2]) ).
fof(f_102_1,plain,
! [A,B] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[dt_k8_relat_1]) ).
fof(f_102_2,plain,
! [U_570,U_569] :
( relation(relation_rng_restriction(U_570,U_569))
| ~ relation(U_569) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
cnf(f_102_3,plain,
( relation(relation_rng_restriction(U_570,U_569))
| ~ relation(U_569) ),
inference(clausify,[status(thm)],[f_102_2]) ).
fof(f_103_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k9_relat_1]) ).
cnf(f_103_2,plain,
$true,
inference(clausify,[status(thm)],[f_103_1]) ).
fof(f_104_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_104_2,plain,
$true,
inference(clausify,[status(thm)],[f_104_1]) ).
fof(f_105_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_105_2,plain,
! [U_572] :
? [U_571] : element(U_571,U_572),
inference(variable_rename,[status(thm)],[f_105_1]) ).
fof(f_105_3,plain,
! [U_572] : element(sK108(U_572),U_572),
inference(skolemize,[status(esa),new_symbols(skolem,[sK108]),skolemize(U_571,sK108(U_572))],[f_105_2]) ).
cnf(f_105_4,plain,
element(sK108(U_572),U_572),
inference(clausify,[status(thm)],[f_105_3]) ).
fof(f_106_1,plain,
! [A,B] :
( ( relation(relation_composition(B,A))
& empty(relation_composition(B,A)) )
| ~ relation(B)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc10_relat_1]) ).
fof(f_106_2,plain,
! [U_574,U_573] :
( ( relation(relation_composition(U_573,U_574))
& empty(relation_composition(U_573,U_574)) )
| ~ relation(U_573)
| ~ empty(U_574) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
cnf(f_106_3,plain,
( empty(relation_composition(U_573,U_574))
| ~ relation(U_573)
| ~ empty(U_574) ),
inference(clausify,[status(thm)],[f_106_2]) ).
cnf(f_106_4,plain,
( relation(relation_composition(U_573,U_574))
| ~ relation(U_573)
| ~ empty(U_574) ),
inference(clausify,[status(thm)],[f_106_2]) ).
fof(f_107_1,plain,
! [A] :
( ( relation(relation_inverse(A))
& empty(relation_inverse(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc11_relat_1]) ).
fof(f_107_2,plain,
! [U_575] :
( ( relation(relation_inverse(U_575))
& empty(relation_inverse(U_575)) )
| ~ empty(U_575) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
cnf(f_107_3,plain,
( empty(relation_inverse(U_575))
| ~ empty(U_575) ),
inference(clausify,[status(thm)],[f_107_2]) ).
cnf(f_107_4,plain,
( relation(relation_inverse(U_575))
| ~ empty(U_575) ),
inference(clausify,[status(thm)],[f_107_2]) ).
fof(f_108_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
cnf(f_108_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_108_1]) ).
cnf(f_108_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_108_1]) ).
cnf(f_108_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_108_1]) ).
fof(f_109_1,plain,
! [A,B] :
( ( relation_empty_yielding(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) )
| ~ relation_empty_yielding(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc13_relat_1]) ).
fof(f_109_2,plain,
! [U_577,U_576] :
( ( relation_empty_yielding(relation_dom_restriction(U_577,U_576))
& relation(relation_dom_restriction(U_577,U_576)) )
| ~ relation_empty_yielding(U_577)
| ~ relation(U_577) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
fof(f_109_3,plain,
! [U_577] :
( ( ! [U_579] : relation_empty_yielding(relation_dom_restriction(U_577,U_579))
& ! [U_578] : relation(relation_dom_restriction(U_577,U_578)) )
| ~ relation_empty_yielding(U_577)
| ~ relation(U_577) ),
inference(miniscope,[status(thm)],[f_109_2]) ).
cnf(f_109_4,plain,
( relation(relation_dom_restriction(U_577,U_578))
| ~ relation_empty_yielding(U_577)
| ~ relation(U_577) ),
inference(clausify,[status(thm)],[f_109_3]) ).
cnf(f_109_5,plain,
( relation_empty_yielding(relation_dom_restriction(U_577,U_579))
| ~ relation_empty_yielding(U_577)
| ~ relation(U_577) ),
inference(clausify,[status(thm)],[f_109_3]) ).
fof(f_110_1,plain,
! [A,B] :
( ( function(relation_composition(A,B))
& relation(relation_composition(A,B)) )
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc1_funct_1]) ).
fof(f_110_2,plain,
! [U_581,U_580] :
( ( function(relation_composition(U_581,U_580))
& relation(relation_composition(U_581,U_580)) )
| ~ function(U_580)
| ~ relation(U_580)
| ~ function(U_581)
| ~ relation(U_581) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
cnf(f_110_3,plain,
( relation(relation_composition(U_581,U_580))
| ~ function(U_580)
| ~ relation(U_580)
| ~ function(U_581)
| ~ relation(U_581) ),
inference(clausify,[status(thm)],[f_110_2]) ).
cnf(f_110_4,plain,
( function(relation_composition(U_581,U_580))
| ~ function(U_580)
| ~ relation(U_580)
| ~ function(U_581)
| ~ relation(U_581) ),
inference(clausify,[status(thm)],[f_110_2]) ).
fof(f_111_1,plain,
! [A] : ~ empty(succ(A)),
inference(fof_nnf,[status(thm)],[fc1_ordinal1]) ).
fof(f_111_2,plain,
! [U_582] : ~ empty(succ(U_582)),
inference(variable_rename,[status(thm)],[f_111_1]) ).
cnf(f_111_3,plain,
~ empty(succ(U_582)),
inference(clausify,[status(thm)],[f_111_2]) ).
fof(f_112_1,plain,
! [A,B] :
( relation(set_intersection2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc1_relat_1]) ).
fof(f_112_2,plain,
! [U_584,U_583] :
( relation(set_intersection2(U_584,U_583))
| ~ relation(U_583)
| ~ relation(U_584) ),
inference(variable_rename,[status(thm)],[f_112_1]) ).
cnf(f_112_3,plain,
( relation(set_intersection2(U_584,U_583))
| ~ relation(U_583)
| ~ relation(U_584) ),
inference(clausify,[status(thm)],[f_112_2]) ).
fof(f_113_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_113_2,plain,
! [U_585] : ~ empty(powerset(U_585)),
inference(variable_rename,[status(thm)],[f_113_1]) ).
cnf(f_113_3,plain,
~ empty(powerset(U_585)),
inference(clausify,[status(thm)],[f_113_2]) ).
fof(f_114_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_114_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_114_1]) ).
fof(f_115_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_115_2,plain,
! [U_587,U_586] : ~ empty(ordered_pair(U_587,U_586)),
inference(variable_rename,[status(thm)],[f_115_1]) ).
cnf(f_115_3,plain,
~ empty(ordered_pair(U_587,U_586)),
inference(clausify,[status(thm)],[f_115_2]) ).
fof(f_116_1,plain,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
inference(fof_nnf,[status(thm)],[fc2_funct_1]) ).
fof(f_116_2,plain,
! [U_588] :
( function(identity_relation(U_588))
& relation(identity_relation(U_588)) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
fof(f_116_3,plain,
( ! [U_590] : function(identity_relation(U_590))
& ! [U_589] : relation(identity_relation(U_589)) ),
inference(miniscope,[status(thm)],[f_116_2]) ).
cnf(f_116_4,plain,
relation(identity_relation(U_589)),
inference(clausify,[status(thm)],[f_116_3]) ).
cnf(f_116_5,plain,
function(identity_relation(U_590)),
inference(clausify,[status(thm)],[f_116_3]) ).
fof(f_117_1,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
inference(fof_nnf,[status(thm)],[fc2_ordinal1]) ).
cnf(f_117_2,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_117_1]) ).
cnf(f_117_3,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_117_1]) ).
cnf(f_117_4,plain,
function(empty_set),
inference(clausify,[status(thm)],[f_117_1]) ).
cnf(f_117_5,plain,
one_to_one(empty_set),
inference(clausify,[status(thm)],[f_117_1]) ).
cnf(f_117_6,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_117_1]) ).
cnf(f_117_7,plain,
epsilon_transitive(empty_set),
inference(clausify,[status(thm)],[f_117_1]) ).
cnf(f_117_8,plain,
epsilon_connected(empty_set),
inference(clausify,[status(thm)],[f_117_1]) ).
cnf(f_117_9,plain,
ordinal(empty_set),
inference(clausify,[status(thm)],[f_117_1]) ).
fof(f_118_1,plain,
! [A,B] :
( relation(set_union2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc2_relat_1]) ).
fof(f_118_2,plain,
! [U_592,U_591] :
( relation(set_union2(U_592,U_591))
| ~ relation(U_591)
| ~ relation(U_592) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
cnf(f_118_3,plain,
( relation(set_union2(U_592,U_591))
| ~ relation(U_591)
| ~ relation(U_592) ),
inference(clausify,[status(thm)],[f_118_2]) ).
fof(f_119_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_119_2,plain,
! [U_593] : ~ empty(singleton(U_593)),
inference(variable_rename,[status(thm)],[f_119_1]) ).
cnf(f_119_3,plain,
~ empty(singleton(U_593)),
inference(clausify,[status(thm)],[f_119_2]) ).
fof(f_120_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_120_2,plain,
! [U_595,U_594] :
( ~ empty(set_union2(U_595,U_594))
| empty(U_595) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
fof(f_120_3,plain,
! [U_595] :
( ! [U_594] : ~ empty(set_union2(U_595,U_594))
| empty(U_595) ),
inference(miniscope,[status(thm)],[f_120_2]) ).
cnf(f_120_4,plain,
( ~ empty(set_union2(U_595,U_594))
| empty(U_595) ),
inference(clausify,[status(thm)],[f_120_3]) ).
fof(f_121_1,plain,
! [A] :
( ( function(relation_inverse(A))
& relation(relation_inverse(A)) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc3_funct_1]) ).
fof(f_121_2,plain,
! [U_596] :
( ( function(relation_inverse(U_596))
& relation(relation_inverse(U_596)) )
| ~ one_to_one(U_596)
| ~ function(U_596)
| ~ relation(U_596) ),
inference(variable_rename,[status(thm)],[f_121_1]) ).
cnf(f_121_3,plain,
( relation(relation_inverse(U_596))
| ~ one_to_one(U_596)
| ~ function(U_596)
| ~ relation(U_596) ),
inference(clausify,[status(thm)],[f_121_2]) ).
cnf(f_121_4,plain,
( function(relation_inverse(U_596))
| ~ one_to_one(U_596)
| ~ function(U_596)
| ~ relation(U_596) ),
inference(clausify,[status(thm)],[f_121_2]) ).
fof(f_122_1,plain,
! [A] :
( ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[fc3_ordinal1]) ).
fof(f_122_2,plain,
! [U_597] :
( ( ordinal(succ(U_597))
& epsilon_connected(succ(U_597))
& epsilon_transitive(succ(U_597))
& ~ empty(succ(U_597)) )
| ~ ordinal(U_597) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
cnf(f_122_3,plain,
( ~ empty(succ(U_597))
| ~ ordinal(U_597) ),
inference(clausify,[status(thm)],[f_122_2]) ).
cnf(f_122_4,plain,
( epsilon_transitive(succ(U_597))
| ~ ordinal(U_597) ),
inference(clausify,[status(thm)],[f_122_2]) ).
cnf(f_122_5,plain,
( epsilon_connected(succ(U_597))
| ~ ordinal(U_597) ),
inference(clausify,[status(thm)],[f_122_2]) ).
cnf(f_122_6,plain,
( ordinal(succ(U_597))
| ~ ordinal(U_597) ),
inference(clausify,[status(thm)],[f_122_2]) ).
fof(f_123_1,plain,
! [A,B] :
( relation(set_difference(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc3_relat_1]) ).
fof(f_123_2,plain,
! [U_599,U_598] :
( relation(set_difference(U_599,U_598))
| ~ relation(U_598)
| ~ relation(U_599) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
cnf(f_123_3,plain,
( relation(set_difference(U_599,U_598))
| ~ relation(U_598)
| ~ relation(U_599) ),
inference(clausify,[status(thm)],[f_123_2]) ).
fof(f_124_1,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_124_2,plain,
! [U_601,U_600] : ~ empty(unordered_pair(U_601,U_600)),
inference(variable_rename,[status(thm)],[f_124_1]) ).
cnf(f_124_3,plain,
~ empty(unordered_pair(U_601,U_600)),
inference(clausify,[status(thm)],[f_124_2]) ).
fof(f_125_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_125_2,plain,
! [U_603,U_602] :
( ~ empty(set_union2(U_602,U_603))
| empty(U_603) ),
inference(variable_rename,[status(thm)],[f_125_1]) ).
fof(f_125_3,plain,
! [U_603] :
( ! [U_602] : ~ empty(set_union2(U_602,U_603))
| empty(U_603) ),
inference(miniscope,[status(thm)],[f_125_2]) ).
cnf(f_125_4,plain,
( ~ empty(set_union2(U_602,U_603))
| empty(U_603) ),
inference(clausify,[status(thm)],[f_125_3]) ).
fof(f_126_1,plain,
! [A,B] :
( ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc4_funct_1]) ).
fof(f_126_2,plain,
! [U_605,U_604] :
( ( function(relation_dom_restriction(U_605,U_604))
& relation(relation_dom_restriction(U_605,U_604)) )
| ~ function(U_605)
| ~ relation(U_605) ),
inference(variable_rename,[status(thm)],[f_126_1]) ).
fof(f_126_3,plain,
! [U_605] :
( ( ! [U_607] : function(relation_dom_restriction(U_605,U_607))
& ! [U_606] : relation(relation_dom_restriction(U_605,U_606)) )
| ~ function(U_605)
| ~ relation(U_605) ),
inference(miniscope,[status(thm)],[f_126_2]) ).
cnf(f_126_4,plain,
( relation(relation_dom_restriction(U_605,U_606))
| ~ function(U_605)
| ~ relation(U_605) ),
inference(clausify,[status(thm)],[f_126_3]) ).
cnf(f_126_5,plain,
( function(relation_dom_restriction(U_605,U_607))
| ~ function(U_605)
| ~ relation(U_605) ),
inference(clausify,[status(thm)],[f_126_3]) ).
fof(f_127_1,plain,
! [A] :
( ( ordinal(union(A))
& epsilon_connected(union(A))
& epsilon_transitive(union(A)) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[fc4_ordinal1]) ).
fof(f_127_2,plain,
! [U_608] :
( ( ordinal(union(U_608))
& epsilon_connected(union(U_608))
& epsilon_transitive(union(U_608)) )
| ~ ordinal(U_608) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
cnf(f_127_3,plain,
( epsilon_transitive(union(U_608))
| ~ ordinal(U_608) ),
inference(clausify,[status(thm)],[f_127_2]) ).
cnf(f_127_4,plain,
( epsilon_connected(union(U_608))
| ~ ordinal(U_608) ),
inference(clausify,[status(thm)],[f_127_2]) ).
cnf(f_127_5,plain,
( ordinal(union(U_608))
| ~ ordinal(U_608) ),
inference(clausify,[status(thm)],[f_127_2]) ).
fof(f_128_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_128_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_128_1]) ).
cnf(f_128_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_128_1]) ).
fof(f_129_1,plain,
! [A,B] :
( ~ empty(cartesian_product2(A,B))
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc4_subset_1]) ).
fof(f_129_2,plain,
! [U_610,U_609] :
( ~ empty(cartesian_product2(U_610,U_609))
| empty(U_609)
| empty(U_610) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
cnf(f_129_3,plain,
( ~ empty(cartesian_product2(U_610,U_609))
| empty(U_609)
| empty(U_610) ),
inference(clausify,[status(thm)],[f_129_2]) ).
fof(f_130_1,plain,
! [A,B] :
( ( function(relation_rng_restriction(A,B))
& relation(relation_rng_restriction(A,B)) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[fc5_funct_1]) ).
fof(f_130_2,plain,
! [U_612,U_611] :
( ( function(relation_rng_restriction(U_612,U_611))
& relation(relation_rng_restriction(U_612,U_611)) )
| ~ function(U_611)
| ~ relation(U_611) ),
inference(variable_rename,[status(thm)],[f_130_1]) ).
cnf(f_130_3,plain,
( relation(relation_rng_restriction(U_612,U_611))
| ~ function(U_611)
| ~ relation(U_611) ),
inference(clausify,[status(thm)],[f_130_2]) ).
cnf(f_130_4,plain,
( function(relation_rng_restriction(U_612,U_611))
| ~ function(U_611)
| ~ relation(U_611) ),
inference(clausify,[status(thm)],[f_130_2]) ).
fof(f_131_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_131_2,plain,
! [U_613] :
( ~ empty(relation_dom(U_613))
| ~ relation(U_613)
| empty(U_613) ),
inference(variable_rename,[status(thm)],[f_131_1]) ).
cnf(f_131_3,plain,
( ~ empty(relation_dom(U_613))
| ~ relation(U_613)
| empty(U_613) ),
inference(clausify,[status(thm)],[f_131_2]) ).
fof(f_132_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_132_2,plain,
! [U_614] :
( ~ empty(relation_rng(U_614))
| ~ relation(U_614)
| empty(U_614) ),
inference(variable_rename,[status(thm)],[f_132_1]) ).
cnf(f_132_3,plain,
( ~ empty(relation_rng(U_614))
| ~ relation(U_614)
| empty(U_614) ),
inference(clausify,[status(thm)],[f_132_2]) ).
fof(f_133_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_133_2,plain,
! [U_615] :
( ( relation(relation_dom(U_615))
& empty(relation_dom(U_615)) )
| ~ empty(U_615) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
cnf(f_133_3,plain,
( empty(relation_dom(U_615))
| ~ empty(U_615) ),
inference(clausify,[status(thm)],[f_133_2]) ).
cnf(f_133_4,plain,
( relation(relation_dom(U_615))
| ~ empty(U_615) ),
inference(clausify,[status(thm)],[f_133_2]) ).
fof(f_134_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_134_2,plain,
! [U_616] :
( ( relation(relation_rng(U_616))
& empty(relation_rng(U_616)) )
| ~ empty(U_616) ),
inference(variable_rename,[status(thm)],[f_134_1]) ).
cnf(f_134_3,plain,
( empty(relation_rng(U_616))
| ~ empty(U_616) ),
inference(clausify,[status(thm)],[f_134_2]) ).
cnf(f_134_4,plain,
( relation(relation_rng(U_616))
| ~ empty(U_616) ),
inference(clausify,[status(thm)],[f_134_2]) ).
fof(f_135_1,plain,
! [A,B] :
( ( relation(relation_composition(A,B))
& empty(relation_composition(A,B)) )
| ~ relation(B)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc9_relat_1]) ).
fof(f_135_2,plain,
! [U_618,U_617] :
( ( relation(relation_composition(U_618,U_617))
& empty(relation_composition(U_618,U_617)) )
| ~ relation(U_617)
| ~ empty(U_618) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
cnf(f_135_3,plain,
( empty(relation_composition(U_618,U_617))
| ~ relation(U_617)
| ~ empty(U_618) ),
inference(clausify,[status(thm)],[f_135_2]) ).
cnf(f_135_4,plain,
( relation(relation_composition(U_618,U_617))
| ~ relation(U_617)
| ~ empty(U_618) ),
inference(clausify,[status(thm)],[f_135_2]) ).
fof(f_136_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_136_2,plain,
! [U_620,U_619] : set_union2(U_620,U_620) = U_620,
inference(variable_rename,[status(thm)],[f_136_1]) ).
fof(f_136_3,plain,
! [U_620] : set_union2(U_620,U_620) = U_620,
inference(miniscope,[status(thm)],[f_136_2]) ).
cnf(f_136_4,plain,
set_union2(U_620,U_620) = U_620,
inference(clausify,[status(thm)],[f_136_3]) ).
fof(f_137_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_137_2,plain,
! [U_622,U_621] : set_intersection2(U_622,U_622) = U_622,
inference(variable_rename,[status(thm)],[f_137_1]) ).
fof(f_137_3,plain,
! [U_622] : set_intersection2(U_622,U_622) = U_622,
inference(miniscope,[status(thm)],[f_137_2]) ).
cnf(f_137_4,plain,
set_intersection2(U_622,U_622) = U_622,
inference(clausify,[status(thm)],[f_137_3]) ).
fof(f_138_1,plain,
! [A,B] :
( subset_complement(A,subset_complement(A,B)) = B
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1]) ).
fof(f_138_2,plain,
! [U_624,U_623] :
( subset_complement(U_624,subset_complement(U_624,U_623)) = U_623
| ~ element(U_623,powerset(U_624)) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
cnf(f_138_3,plain,
( subset_complement(U_624,subset_complement(U_624,U_623)) = U_623
| ~ element(U_623,powerset(U_624)) ),
inference(clausify,[status(thm)],[f_138_2]) ).
fof(f_139_1,plain,
! [A] :
( relation_inverse(relation_inverse(A)) = A
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[involutiveness_k4_relat_1]) ).
fof(f_139_2,plain,
! [U_625] :
( relation_inverse(relation_inverse(U_625)) = U_625
| ~ relation(U_625) ),
inference(variable_rename,[status(thm)],[f_139_1]) ).
cnf(f_139_3,plain,
( relation_inverse(relation_inverse(U_625)) = U_625
| ~ relation(U_625) ),
inference(clausify,[status(thm)],[f_139_2]) ).
fof(f_140_1,plain,
! [A,B] :
( complements_of_subsets(A,complements_of_subsets(A,B)) = B
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[involutiveness_k7_setfam_1]) ).
fof(f_140_2,plain,
! [U_627,U_626] :
( complements_of_subsets(U_627,complements_of_subsets(U_627,U_626)) = U_626
| ~ element(U_626,powerset(powerset(U_627))) ),
inference(variable_rename,[status(thm)],[f_140_1]) ).
cnf(f_140_3,plain,
( complements_of_subsets(U_627,complements_of_subsets(U_627,U_626)) = U_626
| ~ element(U_626,powerset(powerset(U_627))) ),
inference(clausify,[status(thm)],[f_140_2]) ).
fof(f_141_1,plain,
! [A,B] : ~ proper_subset(A,A),
inference(fof_nnf,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(f_141_2,plain,
! [U_629,U_628] : ~ proper_subset(U_629,U_629),
inference(variable_rename,[status(thm)],[f_141_1]) ).
fof(f_141_3,plain,
! [U_629] : ~ proper_subset(U_629,U_629),
inference(miniscope,[status(thm)],[f_141_2]) ).
cnf(f_141_4,plain,
~ proper_subset(U_629,U_629),
inference(clausify,[status(thm)],[f_141_3]) ).
fof(f_142_1,plain,
! [A] :
( ( ( reflexive(A)
| ? [B] :
( ~ in(ordered_pair(B,B),A)
& in(B,relation_field(A)) ) )
& ( ! [B] :
( in(ordered_pair(B,B),A)
| ~ in(B,relation_field(A)) )
| ~ reflexive(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[l1_wellord1]) ).
fof(f_142_2,plain,
! [U_632] :
( ( ( reflexive(U_632)
| ? [U_631] :
( ~ in(ordered_pair(U_631,U_631),U_632)
& in(U_631,relation_field(U_632)) ) )
& ( ! [U_630] :
( in(ordered_pair(U_630,U_630),U_632)
| ~ in(U_630,relation_field(U_632)) )
| ~ reflexive(U_632) ) )
| ~ relation(U_632) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
fof(f_142_3,plain,
! [U_632] :
( ( ( reflexive(U_632)
| ( ~ in(ordered_pair(sK109(U_632),sK109(U_632)),U_632)
& in(sK109(U_632),relation_field(U_632)) ) )
& ( ! [U_630] :
( in(ordered_pair(U_630,U_630),U_632)
| ~ in(U_630,relation_field(U_632)) )
| ~ reflexive(U_632) ) )
| ~ relation(U_632) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK109]),skolemize(U_631,sK109(U_632))],[f_142_2]) ).
cnf(f_142_4,plain,
( in(ordered_pair(U_630,U_630),U_632)
| ~ in(U_630,relation_field(U_632))
| ~ reflexive(U_632)
| ~ relation(U_632) ),
inference(clausify,[status(thm)],[f_142_3]) ).
cnf(f_142_5,plain,
( in(sK109(U_632),relation_field(U_632))
| reflexive(U_632)
| ~ relation(U_632) ),
inference(clausify,[status(thm)],[f_142_3]) ).
cnf(f_142_6,plain,
( ~ in(ordered_pair(sK109(U_632),sK109(U_632)),U_632)
| reflexive(U_632)
| ~ relation(U_632) ),
inference(clausify,[status(thm)],[f_142_3]) ).
fof(f_143_1,plain,
! [A] : singleton(A) != empty_set,
inference(fof_nnf,[status(thm)],[l1_zfmisc_1]) ).
fof(f_143_2,plain,
! [U_633] : singleton(U_633) != empty_set,
inference(variable_rename,[status(thm)],[f_143_1]) ).
cnf(f_143_3,plain,
singleton(U_633) != empty_set,
inference(clausify,[status(thm)],[f_143_2]) ).
fof(f_144_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l23_zfmisc_1]) ).
fof(f_144_2,plain,
! [U_635,U_634] :
( set_union2(singleton(U_635),U_634) = U_634
| ~ in(U_635,U_634) ),
inference(variable_rename,[status(thm)],[f_144_1]) ).
cnf(f_144_3,plain,
( set_union2(singleton(U_635),U_634) = U_634
| ~ in(U_635,U_634) ),
inference(clausify,[status(thm)],[f_144_2]) ).
fof(f_145_1,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(fof_nnf,[status(thm)],[l25_zfmisc_1]) ).
fof(f_145_2,plain,
! [U_637,U_636] :
( ~ in(U_637,U_636)
| ~ disjoint(singleton(U_637),U_636) ),
inference(variable_rename,[status(thm)],[f_145_1]) ).
cnf(f_145_3,plain,
( ~ in(U_637,U_636)
| ~ disjoint(singleton(U_637),U_636) ),
inference(clausify,[status(thm)],[f_145_2]) ).
fof(f_146_1,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(fof_nnf,[status(thm)],[l28_zfmisc_1]) ).
fof(f_146_2,plain,
! [U_639,U_638] :
( disjoint(singleton(U_639),U_638)
| in(U_639,U_638) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
cnf(f_146_3,plain,
( disjoint(singleton(U_639),U_638)
| in(U_639,U_638) ),
inference(clausify,[status(thm)],[f_146_2]) ).
fof(f_147_1,plain,
! [A,B] :
( subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[l29_wellord1]) ).
fof(f_147_2,plain,
! [U_641,U_640] :
( subset(relation_dom(relation_rng_restriction(U_641,U_640)),relation_dom(U_640))
| ~ relation(U_640) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
cnf(f_147_3,plain,
( subset(relation_dom(relation_rng_restriction(U_641,U_640)),relation_dom(U_640))
| ~ relation(U_640) ),
inference(clausify,[status(thm)],[f_147_2]) ).
fof(f_148_1,plain,
! [A] :
( ( ( transitive(A)
| ? [B,C,D] :
( ~ in(ordered_pair(B,D),A)
& in(ordered_pair(C,D),A)
& in(ordered_pair(B,C),A) ) )
& ( ! [B,C,D] :
( in(ordered_pair(B,D),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(ordered_pair(B,C),A) )
| ~ transitive(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[l2_wellord1]) ).
fof(f_148_2,plain,
! [U_648] :
( ( ( transitive(U_648)
| ? [U_647,U_646,U_645] :
( ~ in(ordered_pair(U_647,U_645),U_648)
& in(ordered_pair(U_646,U_645),U_648)
& in(ordered_pair(U_647,U_646),U_648) ) )
& ( ! [U_644,U_643,U_642] :
( in(ordered_pair(U_644,U_642),U_648)
| ~ in(ordered_pair(U_643,U_642),U_648)
| ~ in(ordered_pair(U_644,U_643),U_648) )
| ~ transitive(U_648) ) )
| ~ relation(U_648) ),
inference(variable_rename,[status(thm)],[f_148_1]) ).
fof(f_148_3,plain,
! [U_648] :
( ( ( transitive(U_648)
| ? [U_646,U_645] :
( ~ in(ordered_pair(sK110(U_648),U_645),U_648)
& in(ordered_pair(U_646,U_645),U_648)
& in(ordered_pair(sK110(U_648),U_646),U_648) ) )
& ( ! [U_644,U_643,U_642] :
( in(ordered_pair(U_644,U_642),U_648)
| ~ in(ordered_pair(U_643,U_642),U_648)
| ~ in(ordered_pair(U_644,U_643),U_648) )
| ~ transitive(U_648) ) )
| ~ relation(U_648) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK110]),skolemize(U_647,sK110(U_648))],[f_148_2]) ).
fof(f_148_4,plain,
! [U_648] :
( ( ( transitive(U_648)
| ? [U_645] :
( ~ in(ordered_pair(sK110(U_648),U_645),U_648)
& in(ordered_pair(sK111(U_648),U_645),U_648)
& in(ordered_pair(sK110(U_648),sK111(U_648)),U_648) ) )
& ( ! [U_644,U_643,U_642] :
( in(ordered_pair(U_644,U_642),U_648)
| ~ in(ordered_pair(U_643,U_642),U_648)
| ~ in(ordered_pair(U_644,U_643),U_648) )
| ~ transitive(U_648) ) )
| ~ relation(U_648) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK111]),skolemize(U_646,sK111(U_648))],[f_148_3]) ).
fof(f_148_5,plain,
! [U_648] :
( ( ( transitive(U_648)
| ( ~ in(ordered_pair(sK110(U_648),sK112(U_648)),U_648)
& in(ordered_pair(sK111(U_648),sK112(U_648)),U_648)
& in(ordered_pair(sK110(U_648),sK111(U_648)),U_648) ) )
& ( ! [U_644,U_643,U_642] :
( in(ordered_pair(U_644,U_642),U_648)
| ~ in(ordered_pair(U_643,U_642),U_648)
| ~ in(ordered_pair(U_644,U_643),U_648) )
| ~ transitive(U_648) ) )
| ~ relation(U_648) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK112]),skolemize(U_645,sK112(U_648))],[f_148_4]) ).
cnf(f_148_6,plain,
( in(ordered_pair(U_644,U_642),U_648)
| ~ in(ordered_pair(U_643,U_642),U_648)
| ~ in(ordered_pair(U_644,U_643),U_648)
| ~ transitive(U_648)
| ~ relation(U_648) ),
inference(clausify,[status(thm)],[f_148_5]) ).
cnf(f_148_7,plain,
( in(ordered_pair(sK110(U_648),sK111(U_648)),U_648)
| transitive(U_648)
| ~ relation(U_648) ),
inference(clausify,[status(thm)],[f_148_5]) ).
cnf(f_148_8,plain,
( in(ordered_pair(sK111(U_648),sK112(U_648)),U_648)
| transitive(U_648)
| ~ relation(U_648) ),
inference(clausify,[status(thm)],[f_148_5]) ).
cnf(f_148_9,plain,
( ~ in(ordered_pair(sK110(U_648),sK112(U_648)),U_648)
| transitive(U_648)
| ~ relation(U_648) ),
inference(clausify,[status(thm)],[f_148_5]) ).
fof(f_149_1,plain,
! [A,B] :
( ( subset(singleton(A),B)
| ~ in(A,B) )
& ( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(fof_nnf,[status(thm)],[l2_zfmisc_1]) ).
fof(f_149_2,plain,
! [U_650,U_649] :
( ( subset(singleton(U_650),U_649)
| ~ in(U_650,U_649) )
& ( in(U_650,U_649)
| ~ subset(singleton(U_650),U_649) ) ),
inference(variable_rename,[status(thm)],[f_149_1]) ).
fof(f_149_3,plain,
( ! [U_654,U_652] :
( subset(singleton(U_654),U_652)
| ~ in(U_654,U_652) )
& ! [U_653,U_651] :
( in(U_653,U_651)
| ~ subset(singleton(U_653),U_651) ) ),
inference(miniscope,[status(thm)],[f_149_2]) ).
cnf(f_149_4,plain,
( in(U_653,U_651)
| ~ subset(singleton(U_653),U_651) ),
inference(clausify,[status(thm)],[f_149_3]) ).
cnf(f_149_5,plain,
( subset(singleton(U_654),U_652)
| ~ in(U_654,U_652) ),
inference(clausify,[status(thm)],[f_149_3]) ).
fof(f_150_1,plain,
! [A,B] :
( ( set_difference(A,B) = empty_set
| ~ subset(A,B) )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(fof_nnf,[status(thm)],[l32_xboole_1]) ).
fof(f_150_2,plain,
! [U_656,U_655] :
( ( set_difference(U_656,U_655) = empty_set
| ~ subset(U_656,U_655) )
& ( subset(U_656,U_655)
| set_difference(U_656,U_655) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
fof(f_150_3,plain,
( ! [U_660,U_658] :
( set_difference(U_660,U_658) = empty_set
| ~ subset(U_660,U_658) )
& ! [U_659,U_657] :
( subset(U_659,U_657)
| set_difference(U_659,U_657) != empty_set ) ),
inference(miniscope,[status(thm)],[f_150_2]) ).
cnf(f_150_4,plain,
( subset(U_659,U_657)
| set_difference(U_659,U_657) != empty_set ),
inference(clausify,[status(thm)],[f_150_3]) ).
cnf(f_150_5,plain,
( set_difference(U_660,U_658) = empty_set
| ~ subset(U_660,U_658) ),
inference(clausify,[status(thm)],[f_150_3]) ).
fof(f_151_1,plain,
! [A,B] :
( ! [C] :
( in(C,A)
| ~ in(C,B) )
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[l3_subset_1]) ).
fof(f_151_2,plain,
! [U_663,U_662] :
( ! [U_661] :
( in(U_661,U_663)
| ~ in(U_661,U_662) )
| ~ element(U_662,powerset(U_663)) ),
inference(variable_rename,[status(thm)],[f_151_1]) ).
cnf(f_151_3,plain,
( in(U_661,U_663)
| ~ in(U_661,U_662)
| ~ element(U_662,powerset(U_663)) ),
inference(clausify,[status(thm)],[f_151_2]) ).
fof(f_152_1,plain,
! [A] :
( ( ( antisymmetric(A)
| ? [B,C] :
( B != C
& in(ordered_pair(C,B),A)
& in(ordered_pair(B,C),A) ) )
& ( ! [B,C] :
( B = C
| ~ in(ordered_pair(C,B),A)
| ~ in(ordered_pair(B,C),A) )
| ~ antisymmetric(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[l3_wellord1]) ).
fof(f_152_2,plain,
! [U_668] :
( ( ( antisymmetric(U_668)
| ? [U_667,U_666] :
( U_667 != U_666
& in(ordered_pair(U_666,U_667),U_668)
& in(ordered_pair(U_667,U_666),U_668) ) )
& ( ! [U_665,U_664] :
( U_665 = U_664
| ~ in(ordered_pair(U_664,U_665),U_668)
| ~ in(ordered_pair(U_665,U_664),U_668) )
| ~ antisymmetric(U_668) ) )
| ~ relation(U_668) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
fof(f_152_3,plain,
! [U_668] :
( ( ( antisymmetric(U_668)
| ? [U_666] :
( sK113(U_668) != U_666
& in(ordered_pair(U_666,sK113(U_668)),U_668)
& in(ordered_pair(sK113(U_668),U_666),U_668) ) )
& ( ! [U_665,U_664] :
( U_665 = U_664
| ~ in(ordered_pair(U_664,U_665),U_668)
| ~ in(ordered_pair(U_665,U_664),U_668) )
| ~ antisymmetric(U_668) ) )
| ~ relation(U_668) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK113]),skolemize(U_667,sK113(U_668))],[f_152_2]) ).
fof(f_152_4,plain,
! [U_668] :
( ( ( antisymmetric(U_668)
| ( sK113(U_668) != sK114(U_668)
& in(ordered_pair(sK114(U_668),sK113(U_668)),U_668)
& in(ordered_pair(sK113(U_668),sK114(U_668)),U_668) ) )
& ( ! [U_665,U_664] :
( U_665 = U_664
| ~ in(ordered_pair(U_664,U_665),U_668)
| ~ in(ordered_pair(U_665,U_664),U_668) )
| ~ antisymmetric(U_668) ) )
| ~ relation(U_668) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK114]),skolemize(U_666,sK114(U_668))],[f_152_3]) ).
cnf(f_152_5,plain,
( U_665 = U_664
| ~ in(ordered_pair(U_664,U_665),U_668)
| ~ in(ordered_pair(U_665,U_664),U_668)
| ~ antisymmetric(U_668)
| ~ relation(U_668) ),
inference(clausify,[status(thm)],[f_152_4]) ).
cnf(f_152_6,plain,
( in(ordered_pair(sK113(U_668),sK114(U_668)),U_668)
| antisymmetric(U_668)
| ~ relation(U_668) ),
inference(clausify,[status(thm)],[f_152_4]) ).
cnf(f_152_7,plain,
( in(ordered_pair(sK114(U_668),sK113(U_668)),U_668)
| antisymmetric(U_668)
| ~ relation(U_668) ),
inference(clausify,[status(thm)],[f_152_4]) ).
cnf(f_152_8,plain,
( sK113(U_668) != sK114(U_668)
| antisymmetric(U_668)
| ~ relation(U_668) ),
inference(clausify,[status(thm)],[f_152_4]) ).
fof(f_153_1,plain,
! [A,B,C] :
( subset(A,set_difference(B,singleton(C)))
| in(C,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[l3_zfmisc_1]) ).
fof(f_153_2,plain,
! [U_671,U_670,U_669] :
( subset(U_671,set_difference(U_670,singleton(U_669)))
| in(U_669,U_671)
| ~ subset(U_671,U_670) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
fof(f_153_3,plain,
! [U_671,U_670] :
( ! [U_669] :
( subset(U_671,set_difference(U_670,singleton(U_669)))
| in(U_669,U_671) )
| ~ subset(U_671,U_670) ),
inference(miniscope,[status(thm)],[f_153_2]) ).
cnf(f_153_4,plain,
( subset(U_671,set_difference(U_670,singleton(U_669)))
| in(U_669,U_671)
| ~ subset(U_671,U_670) ),
inference(clausify,[status(thm)],[f_153_3]) ).
fof(f_154_1,plain,
! [A] :
( ( ( connected(A)
| ? [B,C] :
( ~ in(ordered_pair(C,B),A)
& ~ in(ordered_pair(B,C),A)
& B != C
& in(C,relation_field(A))
& in(B,relation_field(A)) ) )
& ( ! [B,C] :
( in(ordered_pair(C,B),A)
| in(ordered_pair(B,C),A)
| B = C
| ~ in(C,relation_field(A))
| ~ in(B,relation_field(A)) )
| ~ connected(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[l4_wellord1]) ).
fof(f_154_2,plain,
! [U_676] :
( ( ( connected(U_676)
| ? [U_675,U_674] :
( ~ in(ordered_pair(U_674,U_675),U_676)
& ~ in(ordered_pair(U_675,U_674),U_676)
& U_675 != U_674
& in(U_674,relation_field(U_676))
& in(U_675,relation_field(U_676)) ) )
& ( ! [U_673,U_672] :
( in(ordered_pair(U_672,U_673),U_676)
| in(ordered_pair(U_673,U_672),U_676)
| U_673 = U_672
| ~ in(U_672,relation_field(U_676))
| ~ in(U_673,relation_field(U_676)) )
| ~ connected(U_676) ) )
| ~ relation(U_676) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
fof(f_154_3,plain,
! [U_676] :
( ( ( connected(U_676)
| ? [U_675] :
( ? [U_674] :
( ~ in(ordered_pair(U_674,U_675),U_676)
& ~ in(ordered_pair(U_675,U_674),U_676)
& U_675 != U_674
& in(U_674,relation_field(U_676)) )
& in(U_675,relation_field(U_676)) ) )
& ( ! [U_673] :
( ! [U_672] :
( in(ordered_pair(U_672,U_673),U_676)
| in(ordered_pair(U_673,U_672),U_676)
| U_673 = U_672
| ~ in(U_672,relation_field(U_676)) )
| ~ in(U_673,relation_field(U_676)) )
| ~ connected(U_676) ) )
| ~ relation(U_676) ),
inference(miniscope,[status(thm)],[f_154_2]) ).
fof(f_154_4,plain,
! [U_676] :
( ( ( connected(U_676)
| ( ? [U_674] :
( ~ in(ordered_pair(U_674,sK115(U_676)),U_676)
& ~ in(ordered_pair(sK115(U_676),U_674),U_676)
& sK115(U_676) != U_674
& in(U_674,relation_field(U_676)) )
& in(sK115(U_676),relation_field(U_676)) ) )
& ( ! [U_673] :
( ! [U_672] :
( in(ordered_pair(U_672,U_673),U_676)
| in(ordered_pair(U_673,U_672),U_676)
| U_673 = U_672
| ~ in(U_672,relation_field(U_676)) )
| ~ in(U_673,relation_field(U_676)) )
| ~ connected(U_676) ) )
| ~ relation(U_676) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK115]),skolemize(U_675,sK115(U_676))],[f_154_3]) ).
fof(f_154_5,plain,
! [U_676] :
( ( ( connected(U_676)
| ( ~ in(ordered_pair(sK116(U_676),sK115(U_676)),U_676)
& ~ in(ordered_pair(sK115(U_676),sK116(U_676)),U_676)
& sK115(U_676) != sK116(U_676)
& in(sK116(U_676),relation_field(U_676))
& in(sK115(U_676),relation_field(U_676)) ) )
& ( ! [U_673] :
( ! [U_672] :
( in(ordered_pair(U_672,U_673),U_676)
| in(ordered_pair(U_673,U_672),U_676)
| U_673 = U_672
| ~ in(U_672,relation_field(U_676)) )
| ~ in(U_673,relation_field(U_676)) )
| ~ connected(U_676) ) )
| ~ relation(U_676) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK116]),skolemize(U_674,sK116(U_676))],[f_154_4]) ).
cnf(f_154_6,plain,
( in(ordered_pair(U_672,U_673),U_676)
| in(ordered_pair(U_673,U_672),U_676)
| U_673 = U_672
| ~ in(U_672,relation_field(U_676))
| ~ in(U_673,relation_field(U_676))
| ~ connected(U_676)
| ~ relation(U_676) ),
inference(clausify,[status(thm)],[f_154_5]) ).
cnf(f_154_7,plain,
( in(sK115(U_676),relation_field(U_676))
| connected(U_676)
| ~ relation(U_676) ),
inference(clausify,[status(thm)],[f_154_5]) ).
cnf(f_154_8,plain,
( in(sK116(U_676),relation_field(U_676))
| connected(U_676)
| ~ relation(U_676) ),
inference(clausify,[status(thm)],[f_154_5]) ).
cnf(f_154_9,plain,
( sK115(U_676) != sK116(U_676)
| connected(U_676)
| ~ relation(U_676) ),
inference(clausify,[status(thm)],[f_154_5]) ).
cnf(f_154_10,plain,
( ~ in(ordered_pair(sK115(U_676),sK116(U_676)),U_676)
| connected(U_676)
| ~ relation(U_676) ),
inference(clausify,[status(thm)],[f_154_5]) ).
cnf(f_154_11,plain,
( ~ in(ordered_pair(sK116(U_676),sK115(U_676)),U_676)
| connected(U_676)
| ~ relation(U_676) ),
inference(clausify,[status(thm)],[f_154_5]) ).
fof(f_155_1,plain,
! [A,B] :
( ( subset(A,singleton(B))
| ( A != singleton(B)
& A != empty_set ) )
& ( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(fof_nnf,[status(thm)],[l4_zfmisc_1]) ).
fof(f_155_2,plain,
! [U_678,U_677] :
( ( subset(U_678,singleton(U_677))
| ( U_678 != singleton(U_677)
& U_678 != empty_set ) )
& ( U_678 = singleton(U_677)
| U_678 = empty_set
| ~ subset(U_678,singleton(U_677)) ) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
fof(f_155_3,plain,
( ! [U_682,U_680] :
( subset(U_682,singleton(U_680))
| ( U_682 != singleton(U_680)
& U_682 != empty_set ) )
& ! [U_681,U_679] :
( U_681 = singleton(U_679)
| U_681 = empty_set
| ~ subset(U_681,singleton(U_679)) ) ),
inference(miniscope,[status(thm)],[f_155_2]) ).
cnf(f_155_4,plain,
( U_681 = singleton(U_679)
| U_681 = empty_set
| ~ subset(U_681,singleton(U_679)) ),
inference(clausify,[status(thm)],[f_155_3]) ).
cnf(f_155_5,plain,
( U_682 != empty_set
| subset(U_682,singleton(U_680)) ),
inference(clausify,[status(thm)],[f_155_3]) ).
cnf(f_155_6,plain,
( U_682 != singleton(U_680)
| subset(U_682,singleton(U_680)) ),
inference(clausify,[status(thm)],[f_155_3]) ).
fof(f_156_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l50_zfmisc_1]) ).
fof(f_156_2,plain,
! [U_684,U_683] :
( subset(U_684,union(U_683))
| ~ in(U_684,U_683) ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
cnf(f_156_3,plain,
( subset(U_684,union(U_683))
| ~ in(U_684,U_683) ),
inference(clausify,[status(thm)],[f_156_2]) ).
fof(f_157_1,plain,
! [A,B,C,D] :
( ( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(B,D)
| ~ in(A,C) )
& ( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(fof_nnf,[status(thm)],[l55_zfmisc_1]) ).
fof(f_157_2,plain,
! [U_688,U_687,U_686,U_685] :
( ( in(ordered_pair(U_688,U_687),cartesian_product2(U_686,U_685))
| ~ in(U_687,U_685)
| ~ in(U_688,U_686) )
& ( ( in(U_687,U_685)
& in(U_688,U_686) )
| ~ in(ordered_pair(U_688,U_687),cartesian_product2(U_686,U_685)) ) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
fof(f_157_3,plain,
( ! [U_696,U_694,U_692,U_690] :
( in(ordered_pair(U_696,U_694),cartesian_product2(U_692,U_690))
| ~ in(U_694,U_690)
| ~ in(U_696,U_692) )
& ! [U_695,U_693,U_691,U_689] :
( ( in(U_693,U_689)
& in(U_695,U_691) )
| ~ in(ordered_pair(U_695,U_693),cartesian_product2(U_691,U_689)) ) ),
inference(miniscope,[status(thm)],[f_157_2]) ).
cnf(f_157_4,plain,
( in(U_695,U_691)
| ~ in(ordered_pair(U_695,U_693),cartesian_product2(U_691,U_689)) ),
inference(clausify,[status(thm)],[f_157_3]) ).
cnf(f_157_5,plain,
( in(U_693,U_689)
| ~ in(ordered_pair(U_695,U_693),cartesian_product2(U_691,U_689)) ),
inference(clausify,[status(thm)],[f_157_3]) ).
cnf(f_157_6,plain,
( in(ordered_pair(U_696,U_694),cartesian_product2(U_692,U_690))
| ~ in(U_694,U_690)
| ~ in(U_696,U_692) ),
inference(clausify,[status(thm)],[f_157_3]) ).
fof(f_158_1,plain,
! [A,B] :
( element(A,powerset(B))
| ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(fof_nnf,[status(thm)],[l71_subset_1]) ).
fof(f_158_2,plain,
! [U_699,U_698] :
( element(U_699,powerset(U_698))
| ? [U_697] :
( ~ in(U_697,U_698)
& in(U_697,U_699) ) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
fof(f_158_3,plain,
! [U_699,U_698] :
( element(U_699,powerset(U_698))
| ( ~ in(sK117(U_699,U_698),U_698)
& in(sK117(U_699,U_698),U_699) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK117]),skolemize(U_697,sK117(U_699,U_698))],[f_158_2]) ).
cnf(f_158_4,plain,
( in(sK117(U_699,U_698),U_699)
| element(U_699,powerset(U_698)) ),
inference(clausify,[status(thm)],[f_158_3]) ).
cnf(f_158_5,plain,
( ~ in(sK117(U_699,U_698),U_698)
| element(U_699,powerset(U_698)) ),
inference(clausify,[status(thm)],[f_158_3]) ).
fof(f_159_1,plain,
! [A,B,C] :
( ( ( in(B,relation_dom(relation_dom_restriction(C,A)))
| ~ in(B,A)
| ~ in(B,relation_dom(C)) )
& ( ( in(B,A)
& in(B,relation_dom(C)) )
| ~ in(B,relation_dom(relation_dom_restriction(C,A))) ) )
| ~ function(C)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[l82_funct_1]) ).
fof(f_159_2,plain,
! [U_702,U_701,U_700] :
( ( ( in(U_701,relation_dom(relation_dom_restriction(U_700,U_702)))
| ~ in(U_701,U_702)
| ~ in(U_701,relation_dom(U_700)) )
& ( ( in(U_701,U_702)
& in(U_701,relation_dom(U_700)) )
| ~ in(U_701,relation_dom(relation_dom_restriction(U_700,U_702))) ) )
| ~ function(U_700)
| ~ relation(U_700) ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
cnf(f_159_3,plain,
( in(U_701,relation_dom(U_700))
| ~ in(U_701,relation_dom(relation_dom_restriction(U_700,U_702)))
| ~ function(U_700)
| ~ relation(U_700) ),
inference(clausify,[status(thm)],[f_159_2]) ).
cnf(f_159_4,plain,
( in(U_701,U_702)
| ~ in(U_701,relation_dom(relation_dom_restriction(U_700,U_702)))
| ~ function(U_700)
| ~ relation(U_700) ),
inference(clausify,[status(thm)],[f_159_2]) ).
cnf(f_159_5,plain,
( in(U_701,relation_dom(relation_dom_restriction(U_700,U_702)))
| ~ in(U_701,U_702)
| ~ in(U_701,relation_dom(U_700))
| ~ function(U_700)
| ~ relation(U_700) ),
inference(clausify,[status(thm)],[f_159_2]) ).
fof(f_160_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_160_2,plain,
? [U_703] :
( function(U_703)
& relation(U_703) ),
inference(variable_rename,[status(thm)],[f_160_1]) ).
fof(f_160_3,plain,
( function(sK118)
& relation(sK118) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK118]),skolemize(U_703,sK118)],[f_160_2]) ).
cnf(f_160_4,plain,
relation(sK118),
inference(clausify,[status(thm)],[f_160_3]) ).
cnf(f_160_5,plain,
function(sK118),
inference(clausify,[status(thm)],[f_160_3]) ).
fof(f_161_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[rc1_ordinal1]) ).
fof(f_161_2,plain,
? [U_704] :
( ordinal(U_704)
& epsilon_connected(U_704)
& epsilon_transitive(U_704) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
fof(f_161_3,plain,
( ordinal(sK119)
& epsilon_connected(sK119)
& epsilon_transitive(sK119) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK119]),skolemize(U_704,sK119)],[f_161_2]) ).
cnf(f_161_4,plain,
epsilon_transitive(sK119),
inference(clausify,[status(thm)],[f_161_3]) ).
cnf(f_161_5,plain,
epsilon_connected(sK119),
inference(clausify,[status(thm)],[f_161_3]) ).
cnf(f_161_6,plain,
ordinal(sK119),
inference(clausify,[status(thm)],[f_161_3]) ).
fof(f_162_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_162_2,plain,
? [U_705] :
( relation(U_705)
& empty(U_705) ),
inference(variable_rename,[status(thm)],[f_162_1]) ).
fof(f_162_3,plain,
( relation(sK120)
& empty(sK120) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK120]),skolemize(U_705,sK120)],[f_162_2]) ).
cnf(f_162_4,plain,
empty(sK120),
inference(clausify,[status(thm)],[f_162_3]) ).
cnf(f_162_5,plain,
relation(sK120),
inference(clausify,[status(thm)],[f_162_3]) ).
fof(f_163_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_163_2,plain,
! [U_707] :
( ? [U_706] :
( ~ empty(U_706)
& element(U_706,powerset(U_707)) )
| empty(U_707) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
fof(f_163_3,plain,
! [U_707] :
( ( ~ empty(sK121(U_707))
& element(sK121(U_707),powerset(U_707)) )
| empty(U_707) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK121]),skolemize(U_706,sK121(U_707))],[f_163_2]) ).
cnf(f_163_4,plain,
( element(sK121(U_707),powerset(U_707))
| empty(U_707) ),
inference(clausify,[status(thm)],[f_163_3]) ).
cnf(f_163_5,plain,
( ~ empty(sK121(U_707))
| empty(U_707) ),
inference(clausify,[status(thm)],[f_163_3]) ).
fof(f_164_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_164_2,plain,
? [U_708] : empty(U_708),
inference(variable_rename,[status(thm)],[f_164_1]) ).
fof(f_164_3,plain,
empty(sK122),
inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(U_708,sK122)],[f_164_2]) ).
cnf(f_164_4,plain,
empty(sK122),
inference(clausify,[status(thm)],[f_164_3]) ).
fof(f_165_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_165_2,plain,
? [U_709] :
( function(U_709)
& empty(U_709)
& relation(U_709) ),
inference(variable_rename,[status(thm)],[f_165_1]) ).
fof(f_165_3,plain,
( function(sK123)
& empty(sK123)
& relation(sK123) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK123]),skolemize(U_709,sK123)],[f_165_2]) ).
cnf(f_165_4,plain,
relation(sK123),
inference(clausify,[status(thm)],[f_165_3]) ).
cnf(f_165_5,plain,
empty(sK123),
inference(clausify,[status(thm)],[f_165_3]) ).
cnf(f_165_6,plain,
function(sK123),
inference(clausify,[status(thm)],[f_165_3]) ).
fof(f_166_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_ordinal1]) ).
fof(f_166_2,plain,
? [U_710] :
( ordinal(U_710)
& epsilon_connected(U_710)
& epsilon_transitive(U_710)
& empty(U_710)
& one_to_one(U_710)
& function(U_710)
& relation(U_710) ),
inference(variable_rename,[status(thm)],[f_166_1]) ).
fof(f_166_3,plain,
( ordinal(sK124)
& epsilon_connected(sK124)
& epsilon_transitive(sK124)
& empty(sK124)
& one_to_one(sK124)
& function(sK124)
& relation(sK124) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK124]),skolemize(U_710,sK124)],[f_166_2]) ).
cnf(f_166_4,plain,
relation(sK124),
inference(clausify,[status(thm)],[f_166_3]) ).
cnf(f_166_5,plain,
function(sK124),
inference(clausify,[status(thm)],[f_166_3]) ).
cnf(f_166_6,plain,
one_to_one(sK124),
inference(clausify,[status(thm)],[f_166_3]) ).
cnf(f_166_7,plain,
empty(sK124),
inference(clausify,[status(thm)],[f_166_3]) ).
cnf(f_166_8,plain,
epsilon_transitive(sK124),
inference(clausify,[status(thm)],[f_166_3]) ).
cnf(f_166_9,plain,
epsilon_connected(sK124),
inference(clausify,[status(thm)],[f_166_3]) ).
cnf(f_166_10,plain,
ordinal(sK124),
inference(clausify,[status(thm)],[f_166_3]) ).
fof(f_167_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_167_2,plain,
? [U_711] :
( relation(U_711)
& ~ empty(U_711) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
fof(f_167_3,plain,
( relation(sK125)
& ~ empty(sK125) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK125]),skolemize(U_711,sK125)],[f_167_2]) ).
cnf(f_167_4,plain,
~ empty(sK125),
inference(clausify,[status(thm)],[f_167_3]) ).
cnf(f_167_5,plain,
relation(sK125),
inference(clausify,[status(thm)],[f_167_3]) ).
fof(f_168_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_168_2,plain,
! [U_713] :
? [U_712] :
( empty(U_712)
& element(U_712,powerset(U_713)) ),
inference(variable_rename,[status(thm)],[f_168_1]) ).
fof(f_168_3,plain,
! [U_713] :
( empty(sK126(U_713))
& element(sK126(U_713),powerset(U_713)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK126]),skolemize(U_712,sK126(U_713))],[f_168_2]) ).
cnf(f_168_4,plain,
element(sK126(U_713),powerset(U_713)),
inference(clausify,[status(thm)],[f_168_3]) ).
cnf(f_168_5,plain,
empty(sK126(U_713)),
inference(clausify,[status(thm)],[f_168_3]) ).
fof(f_169_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_169_2,plain,
? [U_714] : ~ empty(U_714),
inference(variable_rename,[status(thm)],[f_169_1]) ).
fof(f_169_3,plain,
~ empty(sK127),
inference(skolemize,[status(esa),new_symbols(skolem,[sK127]),skolemize(U_714,sK127)],[f_169_2]) ).
cnf(f_169_4,plain,
~ empty(sK127),
inference(clausify,[status(thm)],[f_169_3]) ).
fof(f_170_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_170_2,plain,
? [U_715] :
( one_to_one(U_715)
& function(U_715)
& relation(U_715) ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
fof(f_170_3,plain,
( one_to_one(sK128)
& function(sK128)
& relation(sK128) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK128]),skolemize(U_715,sK128)],[f_170_2]) ).
cnf(f_170_4,plain,
relation(sK128),
inference(clausify,[status(thm)],[f_170_3]) ).
cnf(f_170_5,plain,
function(sK128),
inference(clausify,[status(thm)],[f_170_3]) ).
cnf(f_170_6,plain,
one_to_one(sK128),
inference(clausify,[status(thm)],[f_170_3]) ).
fof(f_171_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_ordinal1]) ).
fof(f_171_2,plain,
? [U_716] :
( ordinal(U_716)
& epsilon_connected(U_716)
& epsilon_transitive(U_716)
& ~ empty(U_716) ),
inference(variable_rename,[status(thm)],[f_171_1]) ).
fof(f_171_3,plain,
( ordinal(sK129)
& epsilon_connected(sK129)
& epsilon_transitive(sK129)
& ~ empty(sK129) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK129]),skolemize(U_716,sK129)],[f_171_2]) ).
cnf(f_171_4,plain,
~ empty(sK129),
inference(clausify,[status(thm)],[f_171_3]) ).
cnf(f_171_5,plain,
epsilon_transitive(sK129),
inference(clausify,[status(thm)],[f_171_3]) ).
cnf(f_171_6,plain,
epsilon_connected(sK129),
inference(clausify,[status(thm)],[f_171_3]) ).
cnf(f_171_7,plain,
ordinal(sK129),
inference(clausify,[status(thm)],[f_171_3]) ).
fof(f_172_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_172_2,plain,
? [U_717] :
( relation_empty_yielding(U_717)
& relation(U_717) ),
inference(variable_rename,[status(thm)],[f_172_1]) ).
fof(f_172_3,plain,
( relation_empty_yielding(sK130)
& relation(sK130) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK130]),skolemize(U_717,sK130)],[f_172_2]) ).
cnf(f_172_4,plain,
relation(sK130),
inference(clausify,[status(thm)],[f_172_3]) ).
cnf(f_172_5,plain,
relation_empty_yielding(sK130),
inference(clausify,[status(thm)],[f_172_3]) ).
fof(f_173_1,plain,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc4_funct_1]) ).
fof(f_173_2,plain,
? [U_718] :
( function(U_718)
& relation_empty_yielding(U_718)
& relation(U_718) ),
inference(variable_rename,[status(thm)],[f_173_1]) ).
fof(f_173_3,plain,
( function(sK131)
& relation_empty_yielding(sK131)
& relation(sK131) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK131]),skolemize(U_718,sK131)],[f_173_2]) ).
cnf(f_173_4,plain,
relation(sK131),
inference(clausify,[status(thm)],[f_173_3]) ).
cnf(f_173_5,plain,
relation_empty_yielding(sK131),
inference(clausify,[status(thm)],[f_173_3]) ).
cnf(f_173_6,plain,
function(sK131),
inference(clausify,[status(thm)],[f_173_3]) ).
fof(f_174_1,plain,
! [A,B] :
( union_of_subsets(A,B) = union(B)
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[redefinition_k5_setfam_1]) ).
fof(f_174_2,plain,
! [U_720,U_719] :
( union_of_subsets(U_720,U_719) = union(U_719)
| ~ element(U_719,powerset(powerset(U_720))) ),
inference(variable_rename,[status(thm)],[f_174_1]) ).
cnf(f_174_3,plain,
( union_of_subsets(U_720,U_719) = union(U_719)
| ~ element(U_719,powerset(powerset(U_720))) ),
inference(clausify,[status(thm)],[f_174_2]) ).
fof(f_175_1,plain,
! [A,B] :
( meet_of_subsets(A,B) = set_meet(B)
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[redefinition_k6_setfam_1]) ).
fof(f_175_2,plain,
! [U_722,U_721] :
( meet_of_subsets(U_722,U_721) = set_meet(U_721)
| ~ element(U_721,powerset(powerset(U_722))) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
cnf(f_175_3,plain,
( meet_of_subsets(U_722,U_721) = set_meet(U_721)
| ~ element(U_721,powerset(powerset(U_722))) ),
inference(clausify,[status(thm)],[f_175_2]) ).
fof(f_176_1,plain,
! [A,B,C] :
( subset_difference(A,B,C) = set_difference(B,C)
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[redefinition_k6_subset_1]) ).
fof(f_176_2,plain,
! [U_725,U_724,U_723] :
( subset_difference(U_725,U_724,U_723) = set_difference(U_724,U_723)
| ~ element(U_723,powerset(U_725))
| ~ element(U_724,powerset(U_725)) ),
inference(variable_rename,[status(thm)],[f_176_1]) ).
cnf(f_176_3,plain,
( subset_difference(U_725,U_724,U_723) = set_difference(U_724,U_723)
| ~ element(U_723,powerset(U_725))
| ~ element(U_724,powerset(U_725)) ),
inference(clausify,[status(thm)],[f_176_2]) ).
fof(f_177_1,plain,
! [A,B] :
( ( ( ordinal_subset(A,B)
| ~ subset(A,B) )
& ( subset(A,B)
| ~ ordinal_subset(A,B) ) )
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[redefinition_r1_ordinal1]) ).
fof(f_177_2,plain,
! [U_727,U_726] :
( ( ( ordinal_subset(U_727,U_726)
| ~ subset(U_727,U_726) )
& ( subset(U_727,U_726)
| ~ ordinal_subset(U_727,U_726) ) )
| ~ ordinal(U_726)
| ~ ordinal(U_727) ),
inference(variable_rename,[status(thm)],[f_177_1]) ).
cnf(f_177_3,plain,
( subset(U_727,U_726)
| ~ ordinal_subset(U_727,U_726)
| ~ ordinal(U_726)
| ~ ordinal(U_727) ),
inference(clausify,[status(thm)],[f_177_2]) ).
cnf(f_177_4,plain,
( ordinal_subset(U_727,U_726)
| ~ subset(U_727,U_726)
| ~ ordinal(U_726)
| ~ ordinal(U_727) ),
inference(clausify,[status(thm)],[f_177_2]) ).
fof(f_178_1,plain,
! [A,B] :
( ordinal_subset(A,A)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[reflexivity_r1_ordinal1]) ).
fof(f_178_2,plain,
! [U_729,U_728] :
( ordinal_subset(U_729,U_729)
| ~ ordinal(U_728)
| ~ ordinal(U_729) ),
inference(variable_rename,[status(thm)],[f_178_1]) ).
fof(f_178_3,plain,
! [U_729] :
( ! [U_728] : ~ ordinal(U_728)
| ~ ordinal(U_729)
| ordinal_subset(U_729,U_729) ),
inference(miniscope,[status(thm)],[f_178_2]) ).
cnf(f_178_4,plain,
( ~ ordinal(U_728)
| ~ ordinal(U_729)
| ordinal_subset(U_729,U_729) ),
inference(clausify,[status(thm)],[f_178_3]) ).
fof(f_179_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_179_2,plain,
! [U_731,U_730] : subset(U_731,U_731),
inference(variable_rename,[status(thm)],[f_179_1]) ).
fof(f_179_3,plain,
! [U_731] : subset(U_731,U_731),
inference(miniscope,[status(thm)],[f_179_2]) ).
cnf(f_179_4,plain,
subset(U_731,U_731),
inference(clausify,[status(thm)],[f_179_3]) ).
fof(f_180_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_180_2,plain,
! [U_733,U_732] :
( disjoint(U_732,U_733)
| ~ disjoint(U_733,U_732) ),
inference(variable_rename,[status(thm)],[f_180_1]) ).
cnf(f_180_3,plain,
( disjoint(U_732,U_733)
| ~ disjoint(U_733,U_732) ),
inference(clausify,[status(thm)],[f_180_2]) ).
fof(f_181_1,plain,
! [A,B,C,D] :
( ( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(B,D)
| ~ in(A,C) )
& ( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(fof_nnf,[status(thm)],[t106_zfmisc_1]) ).
fof(f_181_2,plain,
! [U_737,U_736,U_735,U_734] :
( ( in(ordered_pair(U_737,U_736),cartesian_product2(U_735,U_734))
| ~ in(U_736,U_734)
| ~ in(U_737,U_735) )
& ( ( in(U_736,U_734)
& in(U_737,U_735) )
| ~ in(ordered_pair(U_737,U_736),cartesian_product2(U_735,U_734)) ) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
fof(f_181_3,plain,
( ! [U_745,U_743,U_741,U_739] :
( in(ordered_pair(U_745,U_743),cartesian_product2(U_741,U_739))
| ~ in(U_743,U_739)
| ~ in(U_745,U_741) )
& ! [U_744,U_742,U_740,U_738] :
( ( in(U_742,U_738)
& in(U_744,U_740) )
| ~ in(ordered_pair(U_744,U_742),cartesian_product2(U_740,U_738)) ) ),
inference(miniscope,[status(thm)],[f_181_2]) ).
cnf(f_181_4,plain,
( in(U_744,U_740)
| ~ in(ordered_pair(U_744,U_742),cartesian_product2(U_740,U_738)) ),
inference(clausify,[status(thm)],[f_181_3]) ).
cnf(f_181_5,plain,
( in(U_742,U_738)
| ~ in(ordered_pair(U_744,U_742),cartesian_product2(U_740,U_738)) ),
inference(clausify,[status(thm)],[f_181_3]) ).
cnf(f_181_6,plain,
( in(ordered_pair(U_745,U_743),cartesian_product2(U_741,U_739))
| ~ in(U_743,U_739)
| ~ in(U_745,U_741) ),
inference(clausify,[status(thm)],[f_181_3]) ).
fof(f_182_1,plain,
! [A] : in(A,succ(A)),
inference(fof_nnf,[status(thm)],[t10_ordinal1]) ).
fof(f_182_2,plain,
! [U_746] : in(U_746,succ(U_746)),
inference(variable_rename,[status(thm)],[f_182_1]) ).
cnf(f_182_3,plain,
in(U_746,succ(U_746)),
inference(clausify,[status(thm)],[f_182_2]) ).
fof(f_183_1,plain,
! [A,B,C,D] :
( A = D
| A = C
| unordered_pair(A,B) != unordered_pair(C,D) ),
inference(fof_nnf,[status(thm)],[t10_zfmisc_1]) ).
fof(f_183_2,plain,
! [U_750,U_749,U_748,U_747] :
( U_750 = U_747
| U_750 = U_748
| unordered_pair(U_750,U_749) != unordered_pair(U_748,U_747) ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
fof(f_183_3,plain,
! [U_750,U_749,U_748] :
( ! [U_747] :
( U_750 = U_747
| unordered_pair(U_750,U_749) != unordered_pair(U_748,U_747) )
| U_750 = U_748 ),
inference(miniscope,[status(thm)],[f_183_2]) ).
cnf(f_183_4,plain,
( U_750 = U_747
| unordered_pair(U_750,U_749) != unordered_pair(U_748,U_747)
| U_750 = U_748 ),
inference(clausify,[status(thm)],[f_183_3]) ).
fof(f_184_1,plain,
! [A,B,C] :
( ( ( in(A,relation_rng(relation_rng_restriction(B,C)))
| ~ in(A,relation_rng(C))
| ~ in(A,B) )
& ( ( in(A,relation_rng(C))
& in(A,B) )
| ~ in(A,relation_rng(relation_rng_restriction(B,C))) ) )
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t115_relat_1]) ).
fof(f_184_2,plain,
! [U_753,U_752,U_751] :
( ( ( in(U_753,relation_rng(relation_rng_restriction(U_752,U_751)))
| ~ in(U_753,relation_rng(U_751))
| ~ in(U_753,U_752) )
& ( ( in(U_753,relation_rng(U_751))
& in(U_753,U_752) )
| ~ in(U_753,relation_rng(relation_rng_restriction(U_752,U_751))) ) )
| ~ relation(U_751) ),
inference(variable_rename,[status(thm)],[f_184_1]) ).
cnf(f_184_3,plain,
( in(U_753,U_752)
| ~ in(U_753,relation_rng(relation_rng_restriction(U_752,U_751)))
| ~ relation(U_751) ),
inference(clausify,[status(thm)],[f_184_2]) ).
cnf(f_184_4,plain,
( in(U_753,relation_rng(U_751))
| ~ in(U_753,relation_rng(relation_rng_restriction(U_752,U_751)))
| ~ relation(U_751) ),
inference(clausify,[status(thm)],[f_184_2]) ).
cnf(f_184_5,plain,
( in(U_753,relation_rng(relation_rng_restriction(U_752,U_751)))
| ~ in(U_753,relation_rng(U_751))
| ~ in(U_753,U_752)
| ~ relation(U_751) ),
inference(clausify,[status(thm)],[f_184_2]) ).
fof(f_185_1,plain,
! [A,B] :
( subset(relation_rng(relation_rng_restriction(A,B)),A)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t116_relat_1]) ).
fof(f_185_2,plain,
! [U_755,U_754] :
( subset(relation_rng(relation_rng_restriction(U_755,U_754)),U_755)
| ~ relation(U_754) ),
inference(variable_rename,[status(thm)],[f_185_1]) ).
cnf(f_185_3,plain,
( subset(relation_rng(relation_rng_restriction(U_755,U_754)),U_755)
| ~ relation(U_754) ),
inference(clausify,[status(thm)],[f_185_2]) ).
fof(f_186_1,plain,
! [A,B] :
( subset(relation_rng_restriction(A,B),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t117_relat_1]) ).
fof(f_186_2,plain,
! [U_757,U_756] :
( subset(relation_rng_restriction(U_757,U_756),U_756)
| ~ relation(U_756) ),
inference(variable_rename,[status(thm)],[f_186_1]) ).
cnf(f_186_3,plain,
( subset(relation_rng_restriction(U_757,U_756),U_756)
| ~ relation(U_756) ),
inference(clausify,[status(thm)],[f_186_2]) ).
fof(f_187_1,plain,
! [A,B] :
( subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t118_relat_1]) ).
fof(f_187_2,plain,
! [U_759,U_758] :
( subset(relation_rng(relation_rng_restriction(U_759,U_758)),relation_rng(U_758))
| ~ relation(U_758) ),
inference(variable_rename,[status(thm)],[f_187_1]) ).
cnf(f_187_3,plain,
( subset(relation_rng(relation_rng_restriction(U_759,U_758)),relation_rng(U_758))
| ~ relation(U_758) ),
inference(clausify,[status(thm)],[f_187_2]) ).
fof(f_188_1,plain,
! [A,B,C] :
( ( subset(cartesian_product2(C,A),cartesian_product2(C,B))
& subset(cartesian_product2(A,C),cartesian_product2(B,C)) )
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t118_zfmisc_1]) ).
fof(f_188_2,plain,
! [U_762,U_761,U_760] :
( ( subset(cartesian_product2(U_760,U_762),cartesian_product2(U_760,U_761))
& subset(cartesian_product2(U_762,U_760),cartesian_product2(U_761,U_760)) )
| ~ subset(U_762,U_761) ),
inference(variable_rename,[status(thm)],[f_188_1]) ).
fof(f_188_3,plain,
! [U_762,U_761] :
( ( ! [U_764] : subset(cartesian_product2(U_764,U_762),cartesian_product2(U_764,U_761))
& ! [U_763] : subset(cartesian_product2(U_762,U_763),cartesian_product2(U_761,U_763)) )
| ~ subset(U_762,U_761) ),
inference(miniscope,[status(thm)],[f_188_2]) ).
cnf(f_188_4,plain,
( subset(cartesian_product2(U_762,U_763),cartesian_product2(U_761,U_763))
| ~ subset(U_762,U_761) ),
inference(clausify,[status(thm)],[f_188_3]) ).
cnf(f_188_5,plain,
( subset(cartesian_product2(U_764,U_762),cartesian_product2(U_764,U_761))
| ~ subset(U_762,U_761) ),
inference(clausify,[status(thm)],[f_188_3]) ).
fof(f_189_1,plain,
! [A,B] :
( relation_rng(relation_rng_restriction(A,B)) = set_intersection2(relation_rng(B),A)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t119_relat_1]) ).
fof(f_189_2,plain,
! [U_766,U_765] :
( relation_rng(relation_rng_restriction(U_766,U_765)) = set_intersection2(relation_rng(U_765),U_766)
| ~ relation(U_765) ),
inference(variable_rename,[status(thm)],[f_189_1]) ).
cnf(f_189_3,plain,
( relation_rng(relation_rng_restriction(U_766,U_765)) = set_intersection2(relation_rng(U_765),U_766)
| ~ relation(U_765) ),
inference(clausify,[status(thm)],[f_189_2]) ).
fof(f_190_1,plain,
! [A,B,C,D] :
( subset(cartesian_product2(A,C),cartesian_product2(B,D))
| ~ subset(C,D)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t119_zfmisc_1]) ).
fof(f_190_2,plain,
! [U_770,U_769,U_768,U_767] :
( subset(cartesian_product2(U_770,U_768),cartesian_product2(U_769,U_767))
| ~ subset(U_768,U_767)
| ~ subset(U_770,U_769) ),
inference(variable_rename,[status(thm)],[f_190_1]) ).
cnf(f_190_3,plain,
( subset(cartesian_product2(U_770,U_768),cartesian_product2(U_769,U_767))
| ~ subset(U_768,U_767)
| ~ subset(U_770,U_769) ),
inference(clausify,[status(thm)],[f_190_2]) ).
fof(f_191_1,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t12_xboole_1]) ).
fof(f_191_2,plain,
! [U_772,U_771] :
( set_union2(U_772,U_771) = U_771
| ~ subset(U_772,U_771) ),
inference(variable_rename,[status(thm)],[f_191_1]) ).
cnf(f_191_3,plain,
( set_union2(U_772,U_771) = U_771
| ~ subset(U_772,U_771) ),
inference(clausify,[status(thm)],[f_191_2]) ).
fof(f_192_1,plain,
! [A] :
? [B] :
( ! [C] :
( in(C,B)
| are_equipotent(C,B)
| ~ subset(C,B) )
& ! [C] :
( in(powerset(C),B)
| ~ in(C,B) )
& ! [C,D] :
( in(D,B)
| ~ subset(D,C)
| ~ in(C,B) )
& in(A,B) ),
inference(fof_nnf,[status(thm)],[t136_zfmisc_1]) ).
fof(f_192_2,plain,
! [U_778] :
? [U_777] :
( ! [U_776] :
( in(U_776,U_777)
| are_equipotent(U_776,U_777)
| ~ subset(U_776,U_777) )
& ! [U_775] :
( in(powerset(U_775),U_777)
| ~ in(U_775,U_777) )
& ! [U_774,U_773] :
( in(U_773,U_777)
| ~ subset(U_773,U_774)
| ~ in(U_774,U_777) )
& in(U_778,U_777) ),
inference(variable_rename,[status(thm)],[f_192_1]) ).
fof(f_192_3,plain,
! [U_778] :
( ! [U_776] :
( in(U_776,sK132(U_778))
| are_equipotent(U_776,sK132(U_778))
| ~ subset(U_776,sK132(U_778)) )
& ! [U_775] :
( in(powerset(U_775),sK132(U_778))
| ~ in(U_775,sK132(U_778)) )
& ! [U_774,U_773] :
( in(U_773,sK132(U_778))
| ~ subset(U_773,U_774)
| ~ in(U_774,sK132(U_778)) )
& in(U_778,sK132(U_778)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK132]),skolemize(U_777,sK132(U_778))],[f_192_2]) ).
cnf(f_192_4,plain,
in(U_778,sK132(U_778)),
inference(clausify,[status(thm)],[f_192_3]) ).
cnf(f_192_5,plain,
( in(U_773,sK132(U_778))
| ~ subset(U_773,U_774)
| ~ in(U_774,sK132(U_778)) ),
inference(clausify,[status(thm)],[f_192_3]) ).
cnf(f_192_6,plain,
( in(powerset(U_775),sK132(U_778))
| ~ in(U_775,sK132(U_778)) ),
inference(clausify,[status(thm)],[f_192_3]) ).
cnf(f_192_7,plain,
( in(U_776,sK132(U_778))
| are_equipotent(U_776,sK132(U_778))
| ~ subset(U_776,sK132(U_778)) ),
inference(clausify,[status(thm)],[f_192_3]) ).
fof(f_193_1,plain,
! [A,B,C] :
( relation_dom_restriction(relation_rng_restriction(A,C),B) = relation_rng_restriction(A,relation_dom_restriction(C,B))
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t140_relat_1]) ).
fof(f_193_2,plain,
! [U_781,U_780,U_779] :
( relation_dom_restriction(relation_rng_restriction(U_781,U_779),U_780) = relation_rng_restriction(U_781,relation_dom_restriction(U_779,U_780))
| ~ relation(U_779) ),
inference(variable_rename,[status(thm)],[f_193_1]) ).
cnf(f_193_3,plain,
( relation_dom_restriction(relation_rng_restriction(U_781,U_779),U_780) = relation_rng_restriction(U_781,relation_dom_restriction(U_779,U_780))
| ~ relation(U_779) ),
inference(clausify,[status(thm)],[f_193_2]) ).
fof(f_194_1,plain,
! [A,B,C] :
( ( ( in(A,relation_image(C,B))
| ! [D] :
( ~ in(D,B)
| ~ in(ordered_pair(D,A),C)
| ~ in(D,relation_dom(C)) ) )
& ( ? [D] :
( in(D,B)
& in(ordered_pair(D,A),C)
& in(D,relation_dom(C)) )
| ~ in(A,relation_image(C,B)) ) )
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t143_relat_1]) ).
fof(f_194_2,plain,
! [U_786,U_785,U_784] :
( ( ( in(U_786,relation_image(U_784,U_785))
| ! [U_783] :
( ~ in(U_783,U_785)
| ~ in(ordered_pair(U_783,U_786),U_784)
| ~ in(U_783,relation_dom(U_784)) ) )
& ( ? [U_782] :
( in(U_782,U_785)
& in(ordered_pair(U_782,U_786),U_784)
& in(U_782,relation_dom(U_784)) )
| ~ in(U_786,relation_image(U_784,U_785)) ) )
| ~ relation(U_784) ),
inference(variable_rename,[status(thm)],[f_194_1]) ).
fof(f_194_3,plain,
! [U_786,U_785,U_784] :
( ( ( in(U_786,relation_image(U_784,U_785))
| ! [U_783] :
( ~ in(U_783,U_785)
| ~ in(ordered_pair(U_783,U_786),U_784)
| ~ in(U_783,relation_dom(U_784)) ) )
& ( ( in(sK133(U_786,U_785,U_784),U_785)
& in(ordered_pair(sK133(U_786,U_785,U_784),U_786),U_784)
& in(sK133(U_786,U_785,U_784),relation_dom(U_784)) )
| ~ in(U_786,relation_image(U_784,U_785)) ) )
| ~ relation(U_784) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK133]),skolemize(U_782,sK133(U_786,U_785,U_784))],[f_194_2]) ).
cnf(f_194_4,plain,
( in(sK133(U_786,U_785,U_784),relation_dom(U_784))
| ~ in(U_786,relation_image(U_784,U_785))
| ~ relation(U_784) ),
inference(clausify,[status(thm)],[f_194_3]) ).
cnf(f_194_5,plain,
( in(ordered_pair(sK133(U_786,U_785,U_784),U_786),U_784)
| ~ in(U_786,relation_image(U_784,U_785))
| ~ relation(U_784) ),
inference(clausify,[status(thm)],[f_194_3]) ).
cnf(f_194_6,plain,
( in(sK133(U_786,U_785,U_784),U_785)
| ~ in(U_786,relation_image(U_784,U_785))
| ~ relation(U_784) ),
inference(clausify,[status(thm)],[f_194_3]) ).
cnf(f_194_7,plain,
( in(U_786,relation_image(U_784,U_785))
| ~ in(U_783,U_785)
| ~ in(ordered_pair(U_783,U_786),U_784)
| ~ in(U_783,relation_dom(U_784))
| ~ relation(U_784) ),
inference(clausify,[status(thm)],[f_194_3]) ).
fof(f_195_1,plain,
! [A,B] :
( subset(relation_image(B,A),relation_rng(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t144_relat_1]) ).
fof(f_195_2,plain,
! [U_788,U_787] :
( subset(relation_image(U_787,U_788),relation_rng(U_787))
| ~ relation(U_787) ),
inference(variable_rename,[status(thm)],[f_195_1]) ).
cnf(f_195_3,plain,
( subset(relation_image(U_787,U_788),relation_rng(U_787))
| ~ relation(U_787) ),
inference(clausify,[status(thm)],[f_195_2]) ).
fof(f_196_1,plain,
! [A,B] :
( subset(relation_image(B,relation_inverse_image(B,A)),A)
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t145_funct_1]) ).
fof(f_196_2,plain,
! [U_790,U_789] :
( subset(relation_image(U_789,relation_inverse_image(U_789,U_790)),U_790)
| ~ function(U_789)
| ~ relation(U_789) ),
inference(variable_rename,[status(thm)],[f_196_1]) ).
cnf(f_196_3,plain,
( subset(relation_image(U_789,relation_inverse_image(U_789,U_790)),U_790)
| ~ function(U_789)
| ~ relation(U_789) ),
inference(clausify,[status(thm)],[f_196_2]) ).
fof(f_197_1,plain,
! [A,B] :
( relation_image(B,A) = relation_image(B,set_intersection2(relation_dom(B),A))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t145_relat_1]) ).
fof(f_197_2,plain,
! [U_792,U_791] :
( relation_image(U_791,U_792) = relation_image(U_791,set_intersection2(relation_dom(U_791),U_792))
| ~ relation(U_791) ),
inference(variable_rename,[status(thm)],[f_197_1]) ).
cnf(f_197_3,plain,
( relation_image(U_791,U_792) = relation_image(U_791,set_intersection2(relation_dom(U_791),U_792))
| ~ relation(U_791) ),
inference(clausify,[status(thm)],[f_197_2]) ).
fof(f_198_1,plain,
! [A,B] :
( subset(A,relation_inverse_image(B,relation_image(B,A)))
| ~ subset(A,relation_dom(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t146_funct_1]) ).
fof(f_198_2,plain,
! [U_794,U_793] :
( subset(U_794,relation_inverse_image(U_793,relation_image(U_793,U_794)))
| ~ subset(U_794,relation_dom(U_793))
| ~ relation(U_793) ),
inference(variable_rename,[status(thm)],[f_198_1]) ).
cnf(f_198_3,plain,
( subset(U_794,relation_inverse_image(U_793,relation_image(U_793,U_794)))
| ~ subset(U_794,relation_dom(U_793))
| ~ relation(U_793) ),
inference(clausify,[status(thm)],[f_198_2]) ).
fof(f_199_1,plain,
! [A] :
( relation_image(A,relation_dom(A)) = relation_rng(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t146_relat_1]) ).
fof(f_199_2,plain,
! [U_795] :
( relation_image(U_795,relation_dom(U_795)) = relation_rng(U_795)
| ~ relation(U_795) ),
inference(variable_rename,[status(thm)],[f_199_1]) ).
cnf(f_199_3,plain,
( relation_image(U_795,relation_dom(U_795)) = relation_rng(U_795)
| ~ relation(U_795) ),
inference(clausify,[status(thm)],[f_199_2]) ).
fof(f_200_1,plain,
! [A,B] :
( relation_image(B,relation_inverse_image(B,A)) = A
| ~ subset(A,relation_rng(B))
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t147_funct_1]) ).
fof(f_200_2,plain,
! [U_797,U_796] :
( relation_image(U_796,relation_inverse_image(U_796,U_797)) = U_797
| ~ subset(U_797,relation_rng(U_796))
| ~ function(U_796)
| ~ relation(U_796) ),
inference(variable_rename,[status(thm)],[f_200_1]) ).
cnf(f_200_3,plain,
( relation_image(U_796,relation_inverse_image(U_796,U_797)) = U_797
| ~ subset(U_797,relation_rng(U_796))
| ~ function(U_796)
| ~ relation(U_796) ),
inference(clausify,[status(thm)],[f_200_2]) ).
fof(f_201_1,plain,
! [A] :
( ! [B] :
( relation_rng(relation_composition(A,B)) = relation_image(B,relation_rng(A))
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t160_relat_1]) ).
fof(f_201_2,plain,
! [U_799] :
( ! [U_798] :
( relation_rng(relation_composition(U_799,U_798)) = relation_image(U_798,relation_rng(U_799))
| ~ relation(U_798) )
| ~ relation(U_799) ),
inference(variable_rename,[status(thm)],[f_201_1]) ).
cnf(f_201_3,plain,
( relation_rng(relation_composition(U_799,U_798)) = relation_image(U_798,relation_rng(U_799))
| ~ relation(U_798)
| ~ relation(U_799) ),
inference(clausify,[status(thm)],[f_201_2]) ).
fof(f_202_1,plain,
! [A,B,C] :
( ( ( in(A,relation_inverse_image(C,B))
| ! [D] :
( ~ in(D,B)
| ~ in(ordered_pair(A,D),C)
| ~ in(D,relation_rng(C)) ) )
& ( ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) )
| ~ in(A,relation_inverse_image(C,B)) ) )
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t166_relat_1]) ).
fof(f_202_2,plain,
! [U_804,U_803,U_802] :
( ( ( in(U_804,relation_inverse_image(U_802,U_803))
| ! [U_801] :
( ~ in(U_801,U_803)
| ~ in(ordered_pair(U_804,U_801),U_802)
| ~ in(U_801,relation_rng(U_802)) ) )
& ( ? [U_800] :
( in(U_800,U_803)
& in(ordered_pair(U_804,U_800),U_802)
& in(U_800,relation_rng(U_802)) )
| ~ in(U_804,relation_inverse_image(U_802,U_803)) ) )
| ~ relation(U_802) ),
inference(variable_rename,[status(thm)],[f_202_1]) ).
fof(f_202_3,plain,
! [U_804,U_803,U_802] :
( ( ( in(U_804,relation_inverse_image(U_802,U_803))
| ! [U_801] :
( ~ in(U_801,U_803)
| ~ in(ordered_pair(U_804,U_801),U_802)
| ~ in(U_801,relation_rng(U_802)) ) )
& ( ( in(sK134(U_804,U_803,U_802),U_803)
& in(ordered_pair(U_804,sK134(U_804,U_803,U_802)),U_802)
& in(sK134(U_804,U_803,U_802),relation_rng(U_802)) )
| ~ in(U_804,relation_inverse_image(U_802,U_803)) ) )
| ~ relation(U_802) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK134]),skolemize(U_800,sK134(U_804,U_803,U_802))],[f_202_2]) ).
cnf(f_202_4,plain,
( in(sK134(U_804,U_803,U_802),relation_rng(U_802))
| ~ in(U_804,relation_inverse_image(U_802,U_803))
| ~ relation(U_802) ),
inference(clausify,[status(thm)],[f_202_3]) ).
cnf(f_202_5,plain,
( in(ordered_pair(U_804,sK134(U_804,U_803,U_802)),U_802)
| ~ in(U_804,relation_inverse_image(U_802,U_803))
| ~ relation(U_802) ),
inference(clausify,[status(thm)],[f_202_3]) ).
cnf(f_202_6,plain,
( in(sK134(U_804,U_803,U_802),U_803)
| ~ in(U_804,relation_inverse_image(U_802,U_803))
| ~ relation(U_802) ),
inference(clausify,[status(thm)],[f_202_3]) ).
cnf(f_202_7,plain,
( in(U_804,relation_inverse_image(U_802,U_803))
| ~ in(U_801,U_803)
| ~ in(ordered_pair(U_804,U_801),U_802)
| ~ in(U_801,relation_rng(U_802))
| ~ relation(U_802) ),
inference(clausify,[status(thm)],[f_202_3]) ).
fof(f_203_1,plain,
! [A,B] :
( subset(relation_inverse_image(B,A),relation_dom(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t167_relat_1]) ).
fof(f_203_2,plain,
! [U_806,U_805] :
( subset(relation_inverse_image(U_805,U_806),relation_dom(U_805))
| ~ relation(U_805) ),
inference(variable_rename,[status(thm)],[f_203_1]) ).
cnf(f_203_3,plain,
( subset(relation_inverse_image(U_805,U_806),relation_dom(U_805))
| ~ relation(U_805) ),
inference(clausify,[status(thm)],[f_203_2]) ).
fof(f_204_1,plain,
! [A,B,C] :
( ( ( in(A,relation_restriction(C,B))
| ~ in(A,cartesian_product2(B,B))
| ~ in(A,C) )
& ( ( in(A,cartesian_product2(B,B))
& in(A,C) )
| ~ in(A,relation_restriction(C,B)) ) )
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t16_wellord1]) ).
fof(f_204_2,plain,
! [U_809,U_808,U_807] :
( ( ( in(U_809,relation_restriction(U_807,U_808))
| ~ in(U_809,cartesian_product2(U_808,U_808))
| ~ in(U_809,U_807) )
& ( ( in(U_809,cartesian_product2(U_808,U_808))
& in(U_809,U_807) )
| ~ in(U_809,relation_restriction(U_807,U_808)) ) )
| ~ relation(U_807) ),
inference(variable_rename,[status(thm)],[f_204_1]) ).
cnf(f_204_3,plain,
( in(U_809,U_807)
| ~ in(U_809,relation_restriction(U_807,U_808))
| ~ relation(U_807) ),
inference(clausify,[status(thm)],[f_204_2]) ).
cnf(f_204_4,plain,
( in(U_809,cartesian_product2(U_808,U_808))
| ~ in(U_809,relation_restriction(U_807,U_808))
| ~ relation(U_807) ),
inference(clausify,[status(thm)],[f_204_2]) ).
cnf(f_204_5,plain,
( in(U_809,relation_restriction(U_807,U_808))
| ~ in(U_809,cartesian_product2(U_808,U_808))
| ~ in(U_809,U_807)
| ~ relation(U_807) ),
inference(clausify,[status(thm)],[f_204_2]) ).
fof(f_205_1,plain,
! [A,B] :
( relation_inverse_image(B,A) != empty_set
| ~ subset(A,relation_rng(B))
| A = empty_set
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t174_relat_1]) ).
fof(f_205_2,plain,
! [U_811,U_810] :
( relation_inverse_image(U_810,U_811) != empty_set
| ~ subset(U_811,relation_rng(U_810))
| U_811 = empty_set
| ~ relation(U_810) ),
inference(variable_rename,[status(thm)],[f_205_1]) ).
cnf(f_205_3,plain,
( relation_inverse_image(U_810,U_811) != empty_set
| ~ subset(U_811,relation_rng(U_810))
| U_811 = empty_set
| ~ relation(U_810) ),
inference(clausify,[status(thm)],[f_205_2]) ).
fof(f_206_1,plain,
! [A,B,C] :
( subset(relation_inverse_image(C,A),relation_inverse_image(C,B))
| ~ subset(A,B)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t178_relat_1]) ).
fof(f_206_2,plain,
! [U_814,U_813,U_812] :
( subset(relation_inverse_image(U_812,U_814),relation_inverse_image(U_812,U_813))
| ~ subset(U_814,U_813)
| ~ relation(U_812) ),
inference(variable_rename,[status(thm)],[f_206_1]) ).
cnf(f_206_3,plain,
( subset(relation_inverse_image(U_812,U_814),relation_inverse_image(U_812,U_813))
| ~ subset(U_814,U_813)
| ~ relation(U_812) ),
inference(clausify,[status(thm)],[f_206_2]) ).
fof(f_207_1,plain,
! [A,B] :
( relation_restriction(B,A) = relation_dom_restriction(relation_rng_restriction(A,B),A)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t17_wellord1]) ).
fof(f_207_2,plain,
! [U_816,U_815] :
( relation_restriction(U_815,U_816) = relation_dom_restriction(relation_rng_restriction(U_816,U_815),U_816)
| ~ relation(U_815) ),
inference(variable_rename,[status(thm)],[f_207_1]) ).
cnf(f_207_3,plain,
( relation_restriction(U_815,U_816) = relation_dom_restriction(relation_rng_restriction(U_816,U_815),U_816)
| ~ relation(U_815) ),
inference(clausify,[status(thm)],[f_207_2]) ).
fof(f_208_1,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(fof_nnf,[status(thm)],[t17_xboole_1]) ).
fof(f_208_2,plain,
! [U_818,U_817] : subset(set_intersection2(U_818,U_817),U_818),
inference(variable_rename,[status(thm)],[f_208_1]) ).
cnf(f_208_3,plain,
subset(set_intersection2(U_818,U_817),U_818),
inference(clausify,[status(thm)],[f_208_2]) ).
fof(f_209_1,plain,
! [A,B] :
( relation_restriction(B,A) = relation_rng_restriction(A,relation_dom_restriction(B,A))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t18_wellord1]) ).
fof(f_209_2,plain,
! [U_820,U_819] :
( relation_restriction(U_819,U_820) = relation_rng_restriction(U_820,relation_dom_restriction(U_819,U_820))
| ~ relation(U_819) ),
inference(variable_rename,[status(thm)],[f_209_1]) ).
cnf(f_209_3,plain,
( relation_restriction(U_819,U_820) = relation_rng_restriction(U_820,relation_dom_restriction(U_819,U_820))
| ~ relation(U_819) ),
inference(clausify,[status(thm)],[f_209_2]) ).
fof(f_210_1,plain,
! [A,B,C] :
( ( in(A,B)
& in(A,relation_field(C)) )
| ~ in(A,relation_field(relation_restriction(C,B)))
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t19_wellord1]) ).
fof(f_210_2,plain,
! [U_823,U_822,U_821] :
( ( in(U_823,U_822)
& in(U_823,relation_field(U_821)) )
| ~ in(U_823,relation_field(relation_restriction(U_821,U_822)))
| ~ relation(U_821) ),
inference(variable_rename,[status(thm)],[f_210_1]) ).
cnf(f_210_3,plain,
( in(U_823,relation_field(U_821))
| ~ in(U_823,relation_field(relation_restriction(U_821,U_822)))
| ~ relation(U_821) ),
inference(clausify,[status(thm)],[f_210_2]) ).
cnf(f_210_4,plain,
( in(U_823,U_822)
| ~ in(U_823,relation_field(relation_restriction(U_821,U_822)))
| ~ relation(U_821) ),
inference(clausify,[status(thm)],[f_210_2]) ).
fof(f_211_1,plain,
! [A,B,C] :
( subset(A,set_intersection2(B,C))
| ~ subset(A,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t19_xboole_1]) ).
fof(f_211_2,plain,
! [U_826,U_825,U_824] :
( subset(U_826,set_intersection2(U_825,U_824))
| ~ subset(U_826,U_824)
| ~ subset(U_826,U_825) ),
inference(variable_rename,[status(thm)],[f_211_1]) ).
cnf(f_211_3,plain,
( subset(U_826,set_intersection2(U_825,U_824))
| ~ subset(U_826,U_824)
| ~ subset(U_826,U_825) ),
inference(clausify,[status(thm)],[f_211_2]) ).
fof(f_212_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_212_2,plain,
! [U_827] : set_union2(U_827,empty_set) = U_827,
inference(variable_rename,[status(thm)],[f_212_1]) ).
cnf(f_212_3,plain,
set_union2(U_827,empty_set) = U_827,
inference(clausify,[status(thm)],[f_212_2]) ).
fof(f_213_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_213_2,plain,
! [U_829,U_828] :
( element(U_829,U_828)
| ~ in(U_829,U_828) ),
inference(variable_rename,[status(thm)],[f_213_1]) ).
cnf(f_213_3,plain,
( element(U_829,U_828)
| ~ in(U_829,U_828) ),
inference(clausify,[status(thm)],[f_213_2]) ).
fof(f_214_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_214_2,plain,
! [U_832,U_831,U_830] :
( subset(U_832,U_830)
| ~ subset(U_831,U_830)
| ~ subset(U_832,U_831) ),
inference(variable_rename,[status(thm)],[f_214_1]) ).
cnf(f_214_3,plain,
( subset(U_832,U_830)
| ~ subset(U_831,U_830)
| ~ subset(U_832,U_831) ),
inference(clausify,[status(thm)],[f_214_2]) ).
fof(f_215_1,plain,
powerset(empty_set) = singleton(empty_set),
inference(fof_nnf,[status(thm)],[t1_zfmisc_1]) ).
cnf(f_215_2,plain,
powerset(empty_set) = singleton(empty_set),
inference(clausify,[status(thm)],[f_215_1]) ).
fof(f_216_1,plain,
! [A,B,C] :
( ( in(B,relation_rng(C))
& in(A,relation_dom(C)) )
| ~ in(ordered_pair(A,B),C)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t20_relat_1]) ).
fof(f_216_2,plain,
! [U_835,U_834,U_833] :
( ( in(U_834,relation_rng(U_833))
& in(U_835,relation_dom(U_833)) )
| ~ in(ordered_pair(U_835,U_834),U_833)
| ~ relation(U_833) ),
inference(variable_rename,[status(thm)],[f_216_1]) ).
cnf(f_216_3,plain,
( in(U_835,relation_dom(U_833))
| ~ in(ordered_pair(U_835,U_834),U_833)
| ~ relation(U_833) ),
inference(clausify,[status(thm)],[f_216_2]) ).
cnf(f_216_4,plain,
( in(U_834,relation_rng(U_833))
| ~ in(ordered_pair(U_835,U_834),U_833)
| ~ relation(U_833) ),
inference(clausify,[status(thm)],[f_216_2]) ).
fof(f_217_1,plain,
! [A,B] :
( ( subset(relation_field(relation_restriction(B,A)),A)
& subset(relation_field(relation_restriction(B,A)),relation_field(B)) )
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t20_wellord1]) ).
fof(f_217_2,plain,
! [U_837,U_836] :
( ( subset(relation_field(relation_restriction(U_836,U_837)),U_837)
& subset(relation_field(relation_restriction(U_836,U_837)),relation_field(U_836)) )
| ~ relation(U_836) ),
inference(variable_rename,[status(thm)],[f_217_1]) ).
cnf(f_217_3,plain,
( subset(relation_field(relation_restriction(U_836,U_837)),relation_field(U_836))
| ~ relation(U_836) ),
inference(clausify,[status(thm)],[f_217_2]) ).
cnf(f_217_4,plain,
( subset(relation_field(relation_restriction(U_836,U_837)),U_837)
| ~ relation(U_836) ),
inference(clausify,[status(thm)],[f_217_2]) ).
fof(f_218_1,plain,
! [A,B] :
( ! [C] :
( ( ( in(A,relation_dom(relation_composition(C,B)))
| ~ in(apply(C,A),relation_dom(B))
| ~ in(A,relation_dom(C)) )
& ( ( in(apply(C,A),relation_dom(B))
& in(A,relation_dom(C)) )
| ~ in(A,relation_dom(relation_composition(C,B))) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t21_funct_1]) ).
fof(f_218_2,plain,
! [U_840,U_839] :
( ! [U_838] :
( ( ( in(U_840,relation_dom(relation_composition(U_838,U_839)))
| ~ in(apply(U_838,U_840),relation_dom(U_839))
| ~ in(U_840,relation_dom(U_838)) )
& ( ( in(apply(U_838,U_840),relation_dom(U_839))
& in(U_840,relation_dom(U_838)) )
| ~ in(U_840,relation_dom(relation_composition(U_838,U_839))) ) )
| ~ function(U_838)
| ~ relation(U_838) )
| ~ function(U_839)
| ~ relation(U_839) ),
inference(variable_rename,[status(thm)],[f_218_1]) ).
cnf(f_218_3,plain,
( in(U_840,relation_dom(U_838))
| ~ in(U_840,relation_dom(relation_composition(U_838,U_839)))
| ~ function(U_838)
| ~ relation(U_838)
| ~ function(U_839)
| ~ relation(U_839) ),
inference(clausify,[status(thm)],[f_218_2]) ).
cnf(f_218_4,plain,
( in(apply(U_838,U_840),relation_dom(U_839))
| ~ in(U_840,relation_dom(relation_composition(U_838,U_839)))
| ~ function(U_838)
| ~ relation(U_838)
| ~ function(U_839)
| ~ relation(U_839) ),
inference(clausify,[status(thm)],[f_218_2]) ).
cnf(f_218_5,plain,
( in(U_840,relation_dom(relation_composition(U_838,U_839)))
| ~ in(apply(U_838,U_840),relation_dom(U_839))
| ~ in(U_840,relation_dom(U_838))
| ~ function(U_838)
| ~ relation(U_838)
| ~ function(U_839)
| ~ relation(U_839) ),
inference(clausify,[status(thm)],[f_218_2]) ).
fof(f_219_1,plain,
! [A] :
( ! [B] :
( in(A,B)
| ~ proper_subset(A,B)
| ~ ordinal(B) )
| ~ epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[t21_ordinal1]) ).
fof(f_219_2,plain,
! [U_842] :
( ! [U_841] :
( in(U_842,U_841)
| ~ proper_subset(U_842,U_841)
| ~ ordinal(U_841) )
| ~ epsilon_transitive(U_842) ),
inference(variable_rename,[status(thm)],[f_219_1]) ).
cnf(f_219_3,plain,
( in(U_842,U_841)
| ~ proper_subset(U_842,U_841)
| ~ ordinal(U_841)
| ~ epsilon_transitive(U_842) ),
inference(clausify,[status(thm)],[f_219_2]) ).
fof(f_220_1,plain,
! [A] :
( subset(A,cartesian_product2(relation_dom(A),relation_rng(A)))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t21_relat_1]) ).
fof(f_220_2,plain,
! [U_843] :
( subset(U_843,cartesian_product2(relation_dom(U_843),relation_rng(U_843)))
| ~ relation(U_843) ),
inference(variable_rename,[status(thm)],[f_220_1]) ).
cnf(f_220_3,plain,
( subset(U_843,cartesian_product2(relation_dom(U_843),relation_rng(U_843)))
| ~ relation(U_843) ),
inference(clausify,[status(thm)],[f_220_2]) ).
fof(f_221_1,plain,
! [A,B,C] :
( subset(fiber(relation_restriction(C,A),B),fiber(C,B))
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t21_wellord1]) ).
fof(f_221_2,plain,
! [U_846,U_845,U_844] :
( subset(fiber(relation_restriction(U_844,U_846),U_845),fiber(U_844,U_845))
| ~ relation(U_844) ),
inference(variable_rename,[status(thm)],[f_221_1]) ).
cnf(f_221_3,plain,
( subset(fiber(relation_restriction(U_844,U_846),U_845),fiber(U_844,U_845))
| ~ relation(U_844) ),
inference(clausify,[status(thm)],[f_221_2]) ).
fof(f_222_1,plain,
! [A,B] :
( ! [C] :
( apply(relation_composition(C,B),A) = apply(B,apply(C,A))
| ~ in(A,relation_dom(relation_composition(C,B)))
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t22_funct_1]) ).
fof(f_222_2,plain,
! [U_849,U_848] :
( ! [U_847] :
( apply(relation_composition(U_847,U_848),U_849) = apply(U_848,apply(U_847,U_849))
| ~ in(U_849,relation_dom(relation_composition(U_847,U_848)))
| ~ function(U_847)
| ~ relation(U_847) )
| ~ function(U_848)
| ~ relation(U_848) ),
inference(variable_rename,[status(thm)],[f_222_1]) ).
cnf(f_222_3,plain,
( apply(relation_composition(U_847,U_848),U_849) = apply(U_848,apply(U_847,U_849))
| ~ in(U_849,relation_dom(relation_composition(U_847,U_848)))
| ~ function(U_847)
| ~ relation(U_847)
| ~ function(U_848)
| ~ relation(U_848) ),
inference(clausify,[status(thm)],[f_222_2]) ).
fof(f_223_1,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> ( reflexive(B)
=> reflexive(relation_restriction(B,A)) ) ),
inference(negate,[status(cth)],[t22_wellord1]) ).
fof(f_223_2,negated_conjecture,
? [A,B] :
( ~ reflexive(relation_restriction(B,A))
& reflexive(B)
& relation(B) ),
inference(fof_nnf,[status(thm)],[f_223_1]) ).
fof(f_223_3,negated_conjecture,
? [U_851,U_850] :
( ~ reflexive(relation_restriction(U_850,U_851))
& reflexive(U_850)
& relation(U_850) ),
inference(variable_rename,[status(thm)],[f_223_2]) ).
fof(f_223_4,negated_conjecture,
? [U_850] :
( ~ reflexive(relation_restriction(U_850,sK135))
& reflexive(U_850)
& relation(U_850) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK135]),skolemize(U_851,sK135)],[f_223_3]) ).
fof(f_223_5,negated_conjecture,
( ~ reflexive(relation_restriction(sK136,sK135))
& reflexive(sK136)
& relation(sK136) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK136]),skolemize(U_850,sK136)],[f_223_4]) ).
cnf(f_223_6,negated_conjecture,
relation(sK136),
inference(clausify,[status(thm)],[f_223_5]) ).
cnf(f_223_7,negated_conjecture,
reflexive(sK136),
inference(clausify,[status(thm)],[f_223_5]) ).
cnf(f_223_8,negated_conjecture,
~ reflexive(relation_restriction(sK136,sK135)),
inference(clausify,[status(thm)],[f_223_5]) ).
fof(f_224_1,plain,
! [A,B] :
( ! [C] :
( apply(relation_composition(B,C),A) = apply(C,apply(B,A))
| ~ in(A,relation_dom(B))
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t23_funct_1]) ).
fof(f_224_2,plain,
! [U_854,U_853] :
( ! [U_852] :
( apply(relation_composition(U_853,U_852),U_854) = apply(U_852,apply(U_853,U_854))
| ~ in(U_854,relation_dom(U_853))
| ~ function(U_852)
| ~ relation(U_852) )
| ~ function(U_853)
| ~ relation(U_853) ),
inference(variable_rename,[status(thm)],[f_224_1]) ).
cnf(f_224_3,plain,
( apply(relation_composition(U_853,U_852),U_854) = apply(U_852,apply(U_853,U_854))
| ~ in(U_854,relation_dom(U_853))
| ~ function(U_852)
| ~ relation(U_852)
| ~ function(U_853)
| ~ relation(U_853) ),
inference(clausify,[status(thm)],[f_224_2]) ).
fof(f_225_1,plain,
! [A,B] :
( ordinal(A)
| ~ in(A,B)
| ~ ordinal(B) ),
inference(fof_nnf,[status(thm)],[t23_ordinal1]) ).
fof(f_225_2,plain,
! [U_856,U_855] :
( ordinal(U_856)
| ~ in(U_856,U_855)
| ~ ordinal(U_855) ),
inference(variable_rename,[status(thm)],[f_225_1]) ).
cnf(f_225_3,plain,
( ordinal(U_856)
| ~ in(U_856,U_855)
| ~ ordinal(U_855) ),
inference(clausify,[status(thm)],[f_225_2]) ).
fof(f_226_1,plain,
! [A] :
( ! [B] :
( in(B,A)
| A = B
| in(A,B)
| ~ ordinal(B) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t24_ordinal1]) ).
fof(f_226_2,plain,
! [U_858] :
( ! [U_857] :
( in(U_857,U_858)
| U_858 = U_857
| in(U_858,U_857)
| ~ ordinal(U_857) )
| ~ ordinal(U_858) ),
inference(variable_rename,[status(thm)],[f_226_1]) ).
cnf(f_226_3,plain,
( in(U_857,U_858)
| U_858 = U_857
| in(U_858,U_857)
| ~ ordinal(U_857)
| ~ ordinal(U_858) ),
inference(clausify,[status(thm)],[f_226_2]) ).
fof(f_227_1,plain,
! [A] :
( ! [B] :
( ( subset(relation_rng(A),relation_rng(B))
& subset(relation_dom(A),relation_dom(B)) )
| ~ subset(A,B)
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t25_relat_1]) ).
fof(f_227_2,plain,
! [U_860] :
( ! [U_859] :
( ( subset(relation_rng(U_860),relation_rng(U_859))
& subset(relation_dom(U_860),relation_dom(U_859)) )
| ~ subset(U_860,U_859)
| ~ relation(U_859) )
| ~ relation(U_860) ),
inference(variable_rename,[status(thm)],[f_227_1]) ).
cnf(f_227_3,plain,
( subset(relation_dom(U_860),relation_dom(U_859))
| ~ subset(U_860,U_859)
| ~ relation(U_859)
| ~ relation(U_860) ),
inference(clausify,[status(thm)],[f_227_2]) ).
cnf(f_227_4,plain,
( subset(relation_rng(U_860),relation_rng(U_859))
| ~ subset(U_860,U_859)
| ~ relation(U_859)
| ~ relation(U_860) ),
inference(clausify,[status(thm)],[f_227_2]) ).
fof(f_228_1,plain,
! [A,B,C] :
( subset(set_intersection2(A,C),set_intersection2(B,C))
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t26_xboole_1]) ).
fof(f_228_2,plain,
! [U_863,U_862,U_861] :
( subset(set_intersection2(U_863,U_861),set_intersection2(U_862,U_861))
| ~ subset(U_863,U_862) ),
inference(variable_rename,[status(thm)],[f_228_1]) ).
fof(f_228_3,plain,
! [U_863,U_862] :
( ! [U_861] : subset(set_intersection2(U_863,U_861),set_intersection2(U_862,U_861))
| ~ subset(U_863,U_862) ),
inference(miniscope,[status(thm)],[f_228_2]) ).
cnf(f_228_4,plain,
( subset(set_intersection2(U_863,U_861),set_intersection2(U_862,U_861))
| ~ subset(U_863,U_862) ),
inference(clausify,[status(thm)],[f_228_3]) ).
fof(f_229_1,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t28_xboole_1]) ).
fof(f_229_2,plain,
! [U_865,U_864] :
( set_intersection2(U_865,U_864) = U_865
| ~ subset(U_865,U_864) ),
inference(variable_rename,[status(thm)],[f_229_1]) ).
cnf(f_229_3,plain,
( set_intersection2(U_865,U_864) = U_865
| ~ subset(U_865,U_864) ),
inference(clausify,[status(thm)],[f_229_2]) ).
fof(f_230_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_230_2,plain,
! [U_866] : set_intersection2(U_866,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_230_1]) ).
cnf(f_230_3,plain,
set_intersection2(U_866,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_230_2]) ).
fof(f_231_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_231_2,plain,
! [U_868,U_867] :
( in(U_868,U_867)
| empty(U_867)
| ~ element(U_868,U_867) ),
inference(variable_rename,[status(thm)],[f_231_1]) ).
cnf(f_231_3,plain,
( in(U_868,U_867)
| empty(U_867)
| ~ element(U_868,U_867) ),
inference(clausify,[status(thm)],[f_231_2]) ).
fof(f_232_1,plain,
! [A,B] :
( A = B
| ? [C] :
( ( ~ in(C,A)
& in(C,B) )
| ( ~ in(C,B)
& in(C,A) ) ) ),
inference(fof_nnf,[status(thm)],[t2_tarski]) ).
fof(f_232_2,plain,
! [U_871,U_870] :
( U_871 = U_870
| ? [U_869] :
( ( ~ in(U_869,U_871)
& in(U_869,U_870) )
| ( ~ in(U_869,U_870)
& in(U_869,U_871) ) ) ),
inference(variable_rename,[status(thm)],[f_232_1]) ).
fof(f_232_3,plain,
! [U_871,U_870] :
( U_871 = U_870
| ? [U_873] :
( ~ in(U_873,U_871)
& in(U_873,U_870) )
| ? [U_872] :
( ~ in(U_872,U_870)
& in(U_872,U_871) ) ),
inference(miniscope,[status(thm)],[f_232_2]) ).
fof(f_232_4,plain,
! [U_871,U_870] :
( U_871 = U_870
| ? [U_873] :
( ~ in(U_873,U_871)
& in(U_873,U_870) )
| ( ~ in(sK137(U_871,U_870),U_870)
& in(sK137(U_871,U_870),U_871) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK137]),skolemize(U_872,sK137(U_871,U_870))],[f_232_3]) ).
fof(f_232_5,plain,
! [U_871,U_870] :
( U_871 = U_870
| ( ~ in(sK138(U_871,U_870),U_871)
& in(sK138(U_871,U_870),U_870) )
| ( ~ in(sK137(U_871,U_870),U_870)
& in(sK137(U_871,U_870),U_871) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK138]),skolemize(U_873,sK138(U_871,U_870))],[f_232_4]) ).
cnf(f_232_6,plain,
( in(sK138(U_871,U_870),U_870)
| in(sK137(U_871,U_870),U_871)
| U_871 = U_870 ),
inference(clausify,[status(thm)],[f_232_5]) ).
cnf(f_232_7,plain,
( ~ in(sK138(U_871,U_870),U_871)
| in(sK137(U_871,U_870),U_871)
| U_871 = U_870 ),
inference(clausify,[status(thm)],[f_232_5]) ).
cnf(f_232_8,plain,
( in(sK138(U_871,U_870),U_870)
| ~ in(sK137(U_871,U_870),U_870)
| U_871 = U_870 ),
inference(clausify,[status(thm)],[f_232_5]) ).
cnf(f_232_9,plain,
( ~ in(sK138(U_871,U_870),U_871)
| ~ in(sK137(U_871,U_870),U_870)
| U_871 = U_870 ),
inference(clausify,[status(thm)],[f_232_5]) ).
fof(f_233_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_233_2,plain,
! [U_874] : subset(empty_set,U_874),
inference(variable_rename,[status(thm)],[f_233_1]) ).
cnf(f_233_3,plain,
subset(empty_set,U_874),
inference(clausify,[status(thm)],[f_233_2]) ).
fof(f_234_1,plain,
! [A,B,C] :
( ( in(B,relation_field(C))
& in(A,relation_field(C)) )
| ~ in(ordered_pair(A,B),C)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t30_relat_1]) ).
fof(f_234_2,plain,
! [U_877,U_876,U_875] :
( ( in(U_876,relation_field(U_875))
& in(U_877,relation_field(U_875)) )
| ~ in(ordered_pair(U_877,U_876),U_875)
| ~ relation(U_875) ),
inference(variable_rename,[status(thm)],[f_234_1]) ).
cnf(f_234_3,plain,
( in(U_877,relation_field(U_875))
| ~ in(ordered_pair(U_877,U_876),U_875)
| ~ relation(U_875) ),
inference(clausify,[status(thm)],[f_234_2]) ).
cnf(f_234_4,plain,
( in(U_876,relation_field(U_875))
| ~ in(ordered_pair(U_877,U_876),U_875)
| ~ relation(U_875) ),
inference(clausify,[status(thm)],[f_234_2]) ).
fof(f_235_1,plain,
! [A] :
( ordinal(A)
| ? [B] :
( ( ~ subset(B,A)
| ~ ordinal(B) )
& in(B,A) ) ),
inference(fof_nnf,[status(thm)],[t31_ordinal1]) ).
fof(f_235_2,plain,
! [U_879] :
( ordinal(U_879)
| ? [U_878] :
( ( ~ subset(U_878,U_879)
| ~ ordinal(U_878) )
& in(U_878,U_879) ) ),
inference(variable_rename,[status(thm)],[f_235_1]) ).
fof(f_235_3,plain,
! [U_879] :
( ordinal(U_879)
| ( ( ~ subset(sK139(U_879),U_879)
| ~ ordinal(sK139(U_879)) )
& in(sK139(U_879),U_879) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK139]),skolemize(U_878,sK139(U_879))],[f_235_2]) ).
cnf(f_235_4,plain,
( in(sK139(U_879),U_879)
| ordinal(U_879) ),
inference(clausify,[status(thm)],[f_235_3]) ).
cnf(f_235_5,plain,
( ~ subset(sK139(U_879),U_879)
| ~ ordinal(sK139(U_879))
| ordinal(U_879) ),
inference(clausify,[status(thm)],[f_235_3]) ).
fof(f_236_1,plain,
! [A,B] :
( ? [C] :
( ! [D] :
( ordinal_subset(C,D)
| ~ in(D,A)
| ~ ordinal(D) )
& in(C,A)
& ordinal(C) )
| A = empty_set
| ~ subset(A,B)
| ~ ordinal(B) ),
inference(fof_nnf,[status(thm)],[t32_ordinal1]) ).
fof(f_236_2,plain,
! [U_883,U_882] :
( ? [U_881] :
( ! [U_880] :
( ordinal_subset(U_881,U_880)
| ~ in(U_880,U_883)
| ~ ordinal(U_880) )
& in(U_881,U_883)
& ordinal(U_881) )
| U_883 = empty_set
| ~ subset(U_883,U_882)
| ~ ordinal(U_882) ),
inference(variable_rename,[status(thm)],[f_236_1]) ).
fof(f_236_3,plain,
! [U_883,U_882] :
( ( ! [U_880] :
( ordinal_subset(sK140(U_883,U_882),U_880)
| ~ in(U_880,U_883)
| ~ ordinal(U_880) )
& in(sK140(U_883,U_882),U_883)
& ordinal(sK140(U_883,U_882)) )
| U_883 = empty_set
| ~ subset(U_883,U_882)
| ~ ordinal(U_882) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK140]),skolemize(U_881,sK140(U_883,U_882))],[f_236_2]) ).
cnf(f_236_4,plain,
( ordinal(sK140(U_883,U_882))
| U_883 = empty_set
| ~ subset(U_883,U_882)
| ~ ordinal(U_882) ),
inference(clausify,[status(thm)],[f_236_3]) ).
cnf(f_236_5,plain,
( in(sK140(U_883,U_882),U_883)
| U_883 = empty_set
| ~ subset(U_883,U_882)
| ~ ordinal(U_882) ),
inference(clausify,[status(thm)],[f_236_3]) ).
cnf(f_236_6,plain,
( ordinal_subset(sK140(U_883,U_882),U_880)
| ~ in(U_880,U_883)
| ~ ordinal(U_880)
| U_883 = empty_set
| ~ subset(U_883,U_882)
| ~ ordinal(U_882) ),
inference(clausify,[status(thm)],[f_236_3]) ).
fof(f_237_1,plain,
! [A] :
( ! [B] :
( ( ( in(A,B)
| ~ ordinal_subset(succ(A),B) )
& ( ordinal_subset(succ(A),B)
| ~ in(A,B) ) )
| ~ ordinal(B) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t33_ordinal1]) ).
fof(f_237_2,plain,
! [U_885] :
( ! [U_884] :
( ( ( in(U_885,U_884)
| ~ ordinal_subset(succ(U_885),U_884) )
& ( ordinal_subset(succ(U_885),U_884)
| ~ in(U_885,U_884) ) )
| ~ ordinal(U_884) )
| ~ ordinal(U_885) ),
inference(variable_rename,[status(thm)],[f_237_1]) ).
cnf(f_237_3,plain,
( ordinal_subset(succ(U_885),U_884)
| ~ in(U_885,U_884)
| ~ ordinal(U_884)
| ~ ordinal(U_885) ),
inference(clausify,[status(thm)],[f_237_2]) ).
cnf(f_237_4,plain,
( in(U_885,U_884)
| ~ ordinal_subset(succ(U_885),U_884)
| ~ ordinal(U_884)
| ~ ordinal(U_885) ),
inference(clausify,[status(thm)],[f_237_2]) ).
fof(f_238_1,plain,
! [A,B,C] :
( subset(set_difference(A,C),set_difference(B,C))
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t33_xboole_1]) ).
fof(f_238_2,plain,
! [U_888,U_887,U_886] :
( subset(set_difference(U_888,U_886),set_difference(U_887,U_886))
| ~ subset(U_888,U_887) ),
inference(variable_rename,[status(thm)],[f_238_1]) ).
fof(f_238_3,plain,
! [U_888,U_887] :
( ! [U_886] : subset(set_difference(U_888,U_886),set_difference(U_887,U_886))
| ~ subset(U_888,U_887) ),
inference(miniscope,[status(thm)],[f_238_2]) ).
cnf(f_238_4,plain,
( subset(set_difference(U_888,U_886),set_difference(U_887,U_886))
| ~ subset(U_888,U_887) ),
inference(clausify,[status(thm)],[f_238_3]) ).
fof(f_239_1,plain,
! [A,B,C,D] :
( ( B = D
& A = C )
| ordered_pair(A,B) != ordered_pair(C,D) ),
inference(fof_nnf,[status(thm)],[t33_zfmisc_1]) ).
fof(f_239_2,plain,
! [U_892,U_891,U_890,U_889] :
( ( U_891 = U_889
& U_892 = U_890 )
| ordered_pair(U_892,U_891) != ordered_pair(U_890,U_889) ),
inference(variable_rename,[status(thm)],[f_239_1]) ).
cnf(f_239_3,plain,
( U_892 = U_890
| ordered_pair(U_892,U_891) != ordered_pair(U_890,U_889) ),
inference(clausify,[status(thm)],[f_239_2]) ).
cnf(f_239_4,plain,
( U_891 = U_889
| ordered_pair(U_892,U_891) != ordered_pair(U_890,U_889) ),
inference(clausify,[status(thm)],[f_239_2]) ).
fof(f_240_1,plain,
! [A,B] :
( ( ( B = identity_relation(A)
| ? [C] :
( apply(B,C) != C
& in(C,A) )
| relation_dom(B) != A )
& ( ( ! [C] :
( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A )
| B != identity_relation(A) ) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t34_funct_1]) ).
fof(f_240_2,plain,
! [U_896,U_895] :
( ( ( U_895 = identity_relation(U_896)
| ? [U_894] :
( apply(U_895,U_894) != U_894
& in(U_894,U_896) )
| relation_dom(U_895) != U_896 )
& ( ( ! [U_893] :
( apply(U_895,U_893) = U_893
| ~ in(U_893,U_896) )
& relation_dom(U_895) = U_896 )
| U_895 != identity_relation(U_896) ) )
| ~ function(U_895)
| ~ relation(U_895) ),
inference(variable_rename,[status(thm)],[f_240_1]) ).
fof(f_240_3,plain,
! [U_896,U_895] :
( ( ( U_895 = identity_relation(U_896)
| ( apply(U_895,sK141(U_896,U_895)) != sK141(U_896,U_895)
& in(sK141(U_896,U_895),U_896) )
| relation_dom(U_895) != U_896 )
& ( ( ! [U_893] :
( apply(U_895,U_893) = U_893
| ~ in(U_893,U_896) )
& relation_dom(U_895) = U_896 )
| U_895 != identity_relation(U_896) ) )
| ~ function(U_895)
| ~ relation(U_895) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK141]),skolemize(U_894,sK141(U_896,U_895))],[f_240_2]) ).
cnf(f_240_4,plain,
( relation_dom(U_895) = U_896
| U_895 != identity_relation(U_896)
| ~ function(U_895)
| ~ relation(U_895) ),
inference(clausify,[status(thm)],[f_240_3]) ).
cnf(f_240_5,plain,
( apply(U_895,U_893) = U_893
| ~ in(U_893,U_896)
| U_895 != identity_relation(U_896)
| ~ function(U_895)
| ~ relation(U_895) ),
inference(clausify,[status(thm)],[f_240_3]) ).
cnf(f_240_6,plain,
( in(sK141(U_896,U_895),U_896)
| relation_dom(U_895) != U_896
| U_895 = identity_relation(U_896)
| ~ function(U_895)
| ~ relation(U_895) ),
inference(clausify,[status(thm)],[f_240_3]) ).
cnf(f_240_7,plain,
( apply(U_895,sK141(U_896,U_895)) != sK141(U_896,U_895)
| relation_dom(U_895) != U_896
| U_895 = identity_relation(U_896)
| ~ function(U_895)
| ~ relation(U_895) ),
inference(clausify,[status(thm)],[f_240_3]) ).
fof(f_241_1,plain,
! [A,B] :
( apply(identity_relation(A),B) = B
| ~ in(B,A) ),
inference(fof_nnf,[status(thm)],[t35_funct_1]) ).
fof(f_241_2,plain,
! [U_898,U_897] :
( apply(identity_relation(U_898),U_897) = U_897
| ~ in(U_897,U_898) ),
inference(variable_rename,[status(thm)],[f_241_1]) ).
cnf(f_241_3,plain,
( apply(identity_relation(U_898),U_897) = U_897
| ~ in(U_897,U_898) ),
inference(clausify,[status(thm)],[f_241_2]) ).
fof(f_242_1,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(fof_nnf,[status(thm)],[t36_xboole_1]) ).
fof(f_242_2,plain,
! [U_900,U_899] : subset(set_difference(U_900,U_899),U_900),
inference(variable_rename,[status(thm)],[f_242_1]) ).
cnf(f_242_3,plain,
subset(set_difference(U_900,U_899),U_900),
inference(clausify,[status(thm)],[f_242_2]) ).
fof(f_243_1,plain,
! [A] :
( ( relation_dom(A) = relation_rng(relation_inverse(A))
& relation_rng(A) = relation_dom(relation_inverse(A)) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t37_relat_1]) ).
fof(f_243_2,plain,
! [U_901] :
( ( relation_dom(U_901) = relation_rng(relation_inverse(U_901))
& relation_rng(U_901) = relation_dom(relation_inverse(U_901)) )
| ~ relation(U_901) ),
inference(variable_rename,[status(thm)],[f_243_1]) ).
cnf(f_243_3,plain,
( relation_rng(U_901) = relation_dom(relation_inverse(U_901))
| ~ relation(U_901) ),
inference(clausify,[status(thm)],[f_243_2]) ).
cnf(f_243_4,plain,
( relation_dom(U_901) = relation_rng(relation_inverse(U_901))
| ~ relation(U_901) ),
inference(clausify,[status(thm)],[f_243_2]) ).
fof(f_244_1,plain,
! [A,B] :
( ( set_difference(A,B) = empty_set
| ~ subset(A,B) )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(fof_nnf,[status(thm)],[t37_xboole_1]) ).
fof(f_244_2,plain,
! [U_903,U_902] :
( ( set_difference(U_903,U_902) = empty_set
| ~ subset(U_903,U_902) )
& ( subset(U_903,U_902)
| set_difference(U_903,U_902) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_244_1]) ).
fof(f_244_3,plain,
( ! [U_907,U_905] :
( set_difference(U_907,U_905) = empty_set
| ~ subset(U_907,U_905) )
& ! [U_906,U_904] :
( subset(U_906,U_904)
| set_difference(U_906,U_904) != empty_set ) ),
inference(miniscope,[status(thm)],[f_244_2]) ).
cnf(f_244_4,plain,
( subset(U_906,U_904)
| set_difference(U_906,U_904) != empty_set ),
inference(clausify,[status(thm)],[f_244_3]) ).
cnf(f_244_5,plain,
( set_difference(U_907,U_905) = empty_set
| ~ subset(U_907,U_905) ),
inference(clausify,[status(thm)],[f_244_3]) ).
fof(f_245_1,plain,
! [A,B] :
( ( subset(singleton(A),B)
| ~ in(A,B) )
& ( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(fof_nnf,[status(thm)],[t37_zfmisc_1]) ).
fof(f_245_2,plain,
! [U_909,U_908] :
( ( subset(singleton(U_909),U_908)
| ~ in(U_909,U_908) )
& ( in(U_909,U_908)
| ~ subset(singleton(U_909),U_908) ) ),
inference(variable_rename,[status(thm)],[f_245_1]) ).
fof(f_245_3,plain,
( ! [U_913,U_911] :
( subset(singleton(U_913),U_911)
| ~ in(U_913,U_911) )
& ! [U_912,U_910] :
( in(U_912,U_910)
| ~ subset(singleton(U_912),U_910) ) ),
inference(miniscope,[status(thm)],[f_245_2]) ).
cnf(f_245_4,plain,
( in(U_912,U_910)
| ~ subset(singleton(U_912),U_910) ),
inference(clausify,[status(thm)],[f_245_3]) ).
cnf(f_245_5,plain,
( subset(singleton(U_913),U_911)
| ~ in(U_913,U_911) ),
inference(clausify,[status(thm)],[f_245_3]) ).
fof(f_246_1,plain,
! [A,B,C] :
( ( subset(unordered_pair(A,B),C)
| ~ in(B,C)
| ~ in(A,C) )
& ( ( in(B,C)
& in(A,C) )
| ~ subset(unordered_pair(A,B),C) ) ),
inference(fof_nnf,[status(thm)],[t38_zfmisc_1]) ).
fof(f_246_2,plain,
! [U_916,U_915,U_914] :
( ( subset(unordered_pair(U_916,U_915),U_914)
| ~ in(U_915,U_914)
| ~ in(U_916,U_914) )
& ( ( in(U_915,U_914)
& in(U_916,U_914) )
| ~ subset(unordered_pair(U_916,U_915),U_914) ) ),
inference(variable_rename,[status(thm)],[f_246_1]) ).
fof(f_246_3,plain,
( ! [U_922,U_920,U_918] :
( subset(unordered_pair(U_922,U_920),U_918)
| ~ in(U_920,U_918)
| ~ in(U_922,U_918) )
& ! [U_921,U_919,U_917] :
( ( in(U_919,U_917)
& in(U_921,U_917) )
| ~ subset(unordered_pair(U_921,U_919),U_917) ) ),
inference(miniscope,[status(thm)],[f_246_2]) ).
cnf(f_246_4,plain,
( in(U_921,U_917)
| ~ subset(unordered_pair(U_921,U_919),U_917) ),
inference(clausify,[status(thm)],[f_246_3]) ).
cnf(f_246_5,plain,
( in(U_919,U_917)
| ~ subset(unordered_pair(U_921,U_919),U_917) ),
inference(clausify,[status(thm)],[f_246_3]) ).
cnf(f_246_6,plain,
( subset(unordered_pair(U_922,U_920),U_918)
| ~ in(U_920,U_918)
| ~ in(U_922,U_918) ),
inference(clausify,[status(thm)],[f_246_3]) ).
fof(f_247_1,plain,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(fof_nnf,[status(thm)],[t39_xboole_1]) ).
fof(f_247_2,plain,
! [U_924,U_923] : set_union2(U_924,set_difference(U_923,U_924)) = set_union2(U_924,U_923),
inference(variable_rename,[status(thm)],[f_247_1]) ).
cnf(f_247_3,plain,
set_union2(U_924,set_difference(U_923,U_924)) = set_union2(U_924,U_923),
inference(clausify,[status(thm)],[f_247_2]) ).
fof(f_248_1,plain,
! [A,B] :
( ( subset(A,singleton(B))
| ( A != singleton(B)
& A != empty_set ) )
& ( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(fof_nnf,[status(thm)],[t39_zfmisc_1]) ).
fof(f_248_2,plain,
! [U_926,U_925] :
( ( subset(U_926,singleton(U_925))
| ( U_926 != singleton(U_925)
& U_926 != empty_set ) )
& ( U_926 = singleton(U_925)
| U_926 = empty_set
| ~ subset(U_926,singleton(U_925)) ) ),
inference(variable_rename,[status(thm)],[f_248_1]) ).
fof(f_248_3,plain,
( ! [U_930,U_928] :
( subset(U_930,singleton(U_928))
| ( U_930 != singleton(U_928)
& U_930 != empty_set ) )
& ! [U_929,U_927] :
( U_929 = singleton(U_927)
| U_929 = empty_set
| ~ subset(U_929,singleton(U_927)) ) ),
inference(miniscope,[status(thm)],[f_248_2]) ).
cnf(f_248_4,plain,
( U_929 = singleton(U_927)
| U_929 = empty_set
| ~ subset(U_929,singleton(U_927)) ),
inference(clausify,[status(thm)],[f_248_3]) ).
cnf(f_248_5,plain,
( U_930 != empty_set
| subset(U_930,singleton(U_928)) ),
inference(clausify,[status(thm)],[f_248_3]) ).
cnf(f_248_6,plain,
( U_930 != singleton(U_928)
| subset(U_930,singleton(U_928)) ),
inference(clausify,[status(thm)],[f_248_3]) ).
fof(f_249_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_249_2,plain,
! [U_931] : set_difference(U_931,empty_set) = U_931,
inference(variable_rename,[status(thm)],[f_249_1]) ).
cnf(f_249_3,plain,
set_difference(U_931,empty_set) = U_931,
inference(clausify,[status(thm)],[f_249_2]) ).
fof(f_250_1,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ in(B,C)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t3_ordinal1]) ).
fof(f_250_2,plain,
! [U_934,U_933,U_932] :
( ~ in(U_932,U_934)
| ~ in(U_933,U_932)
| ~ in(U_934,U_933) ),
inference(variable_rename,[status(thm)],[f_250_1]) ).
fof(f_250_3,plain,
! [U_934,U_933] :
( ! [U_932] :
( ~ in(U_932,U_934)
| ~ in(U_933,U_932) )
| ~ in(U_934,U_933) ),
inference(miniscope,[status(thm)],[f_250_2]) ).
cnf(f_250_4,plain,
( ~ in(U_932,U_934)
| ~ in(U_933,U_932)
| ~ in(U_934,U_933) ),
inference(clausify,[status(thm)],[f_250_3]) ).
fof(f_251_1,plain,
! [A,B] :
( ( element(A,powerset(B))
| ~ subset(A,B) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(fof_nnf,[status(thm)],[t3_subset]) ).
fof(f_251_2,plain,
! [U_936,U_935] :
( ( element(U_936,powerset(U_935))
| ~ subset(U_936,U_935) )
& ( subset(U_936,U_935)
| ~ element(U_936,powerset(U_935)) ) ),
inference(variable_rename,[status(thm)],[f_251_1]) ).
fof(f_251_3,plain,
( ! [U_940,U_938] :
( element(U_940,powerset(U_938))
| ~ subset(U_940,U_938) )
& ! [U_939,U_937] :
( subset(U_939,U_937)
| ~ element(U_939,powerset(U_937)) ) ),
inference(miniscope,[status(thm)],[f_251_2]) ).
cnf(f_251_4,plain,
( subset(U_939,U_937)
| ~ element(U_939,powerset(U_937)) ),
inference(clausify,[status(thm)],[f_251_3]) ).
cnf(f_251_5,plain,
( element(U_940,powerset(U_938))
| ~ subset(U_940,U_938) ),
inference(clausify,[status(thm)],[f_251_3]) ).
fof(f_252_1,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] :
( ~ in(C,B)
| ~ in(C,A) ) )
& ( ? [C] :
( in(C,B)
& in(C,A) )
| disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t3_xboole_0]) ).
fof(f_252_2,plain,
! [U_944,U_943] :
( ( ~ disjoint(U_944,U_943)
| ! [U_942] :
( ~ in(U_942,U_943)
| ~ in(U_942,U_944) ) )
& ( ? [U_941] :
( in(U_941,U_943)
& in(U_941,U_944) )
| disjoint(U_944,U_943) ) ),
inference(variable_rename,[status(thm)],[f_252_1]) ).
fof(f_252_3,plain,
( ! [U_948,U_946] :
( ~ disjoint(U_948,U_946)
| ! [U_942] :
( ~ in(U_942,U_946)
| ~ in(U_942,U_948) ) )
& ! [U_947,U_945] :
( ? [U_941] :
( in(U_941,U_945)
& in(U_941,U_947) )
| disjoint(U_947,U_945) ) ),
inference(miniscope,[status(thm)],[f_252_2]) ).
fof(f_252_4,plain,
( ! [U_948,U_946] :
( ~ disjoint(U_948,U_946)
| ! [U_942] :
( ~ in(U_942,U_946)
| ~ in(U_942,U_948) ) )
& ! [U_947,U_945] :
( ( in(sK142(U_947,U_945),U_945)
& in(sK142(U_947,U_945),U_947) )
| disjoint(U_947,U_945) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK142]),skolemize(U_941,sK142(U_947,U_945))],[f_252_3]) ).
cnf(f_252_5,plain,
( in(sK142(U_947,U_945),U_947)
| disjoint(U_947,U_945) ),
inference(clausify,[status(thm)],[f_252_4]) ).
cnf(f_252_6,plain,
( in(sK142(U_947,U_945),U_945)
| disjoint(U_947,U_945) ),
inference(clausify,[status(thm)],[f_252_4]) ).
cnf(f_252_7,plain,
( ~ disjoint(U_948,U_946)
| ~ in(U_942,U_946)
| ~ in(U_942,U_948) ),
inference(clausify,[status(thm)],[f_252_4]) ).
fof(f_253_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_253_2,plain,
! [U_949] :
( U_949 = empty_set
| ~ subset(U_949,empty_set) ),
inference(variable_rename,[status(thm)],[f_253_1]) ).
cnf(f_253_3,plain,
( U_949 = empty_set
| ~ subset(U_949,empty_set) ),
inference(clausify,[status(thm)],[f_253_2]) ).
fof(f_254_1,plain,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(fof_nnf,[status(thm)],[t40_xboole_1]) ).
fof(f_254_2,plain,
! [U_951,U_950] : set_difference(set_union2(U_951,U_950),U_950) = set_difference(U_951,U_950),
inference(variable_rename,[status(thm)],[f_254_1]) ).
cnf(f_254_3,plain,
set_difference(set_union2(U_951,U_950),U_950) = set_difference(U_951,U_950),
inference(clausify,[status(thm)],[f_254_2]) ).
fof(f_255_1,plain,
! [A] :
( ( ( being_limit_ordinal(A)
| ? [B] :
( ~ in(succ(B),A)
& in(B,A)
& ordinal(B) ) )
& ( ! [B] :
( in(succ(B),A)
| ~ in(B,A)
| ~ ordinal(B) )
| ~ being_limit_ordinal(A) ) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t41_ordinal1]) ).
fof(f_255_2,plain,
! [U_954] :
( ( ( being_limit_ordinal(U_954)
| ? [U_953] :
( ~ in(succ(U_953),U_954)
& in(U_953,U_954)
& ordinal(U_953) ) )
& ( ! [U_952] :
( in(succ(U_952),U_954)
| ~ in(U_952,U_954)
| ~ ordinal(U_952) )
| ~ being_limit_ordinal(U_954) ) )
| ~ ordinal(U_954) ),
inference(variable_rename,[status(thm)],[f_255_1]) ).
fof(f_255_3,plain,
! [U_954] :
( ( ( being_limit_ordinal(U_954)
| ( ~ in(succ(sK143(U_954)),U_954)
& in(sK143(U_954),U_954)
& ordinal(sK143(U_954)) ) )
& ( ! [U_952] :
( in(succ(U_952),U_954)
| ~ in(U_952,U_954)
| ~ ordinal(U_952) )
| ~ being_limit_ordinal(U_954) ) )
| ~ ordinal(U_954) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK143]),skolemize(U_953,sK143(U_954))],[f_255_2]) ).
cnf(f_255_4,plain,
( in(succ(U_952),U_954)
| ~ in(U_952,U_954)
| ~ ordinal(U_952)
| ~ being_limit_ordinal(U_954)
| ~ ordinal(U_954) ),
inference(clausify,[status(thm)],[f_255_3]) ).
cnf(f_255_5,plain,
( ordinal(sK143(U_954))
| being_limit_ordinal(U_954)
| ~ ordinal(U_954) ),
inference(clausify,[status(thm)],[f_255_3]) ).
cnf(f_255_6,plain,
( in(sK143(U_954),U_954)
| being_limit_ordinal(U_954)
| ~ ordinal(U_954) ),
inference(clausify,[status(thm)],[f_255_3]) ).
cnf(f_255_7,plain,
( ~ in(succ(sK143(U_954)),U_954)
| being_limit_ordinal(U_954)
| ~ ordinal(U_954) ),
inference(clausify,[status(thm)],[f_255_3]) ).
fof(f_256_1,plain,
! [A] :
( ( ( ~ being_limit_ordinal(A)
| ! [B] :
( A != succ(B)
| ~ ordinal(B) ) )
& ( ? [B] :
( A = succ(B)
& ordinal(B) )
| being_limit_ordinal(A) ) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t42_ordinal1]) ).
fof(f_256_2,plain,
! [U_957] :
( ( ( ~ being_limit_ordinal(U_957)
| ! [U_956] :
( U_957 != succ(U_956)
| ~ ordinal(U_956) ) )
& ( ? [U_955] :
( U_957 = succ(U_955)
& ordinal(U_955) )
| being_limit_ordinal(U_957) ) )
| ~ ordinal(U_957) ),
inference(variable_rename,[status(thm)],[f_256_1]) ).
fof(f_256_3,plain,
! [U_957] :
( ( ( ~ being_limit_ordinal(U_957)
| ! [U_956] :
( U_957 != succ(U_956)
| ~ ordinal(U_956) ) )
& ( ( U_957 = succ(sK144(U_957))
& ordinal(sK144(U_957)) )
| being_limit_ordinal(U_957) ) )
| ~ ordinal(U_957) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK144]),skolemize(U_955,sK144(U_957))],[f_256_2]) ).
cnf(f_256_4,plain,
( ordinal(sK144(U_957))
| being_limit_ordinal(U_957)
| ~ ordinal(U_957) ),
inference(clausify,[status(thm)],[f_256_3]) ).
cnf(f_256_5,plain,
( U_957 = succ(sK144(U_957))
| being_limit_ordinal(U_957)
| ~ ordinal(U_957) ),
inference(clausify,[status(thm)],[f_256_3]) ).
cnf(f_256_6,plain,
( ~ being_limit_ordinal(U_957)
| U_957 != succ(U_956)
| ~ ordinal(U_956)
| ~ ordinal(U_957) ),
inference(clausify,[status(thm)],[f_256_3]) ).
fof(f_257_1,plain,
! [A,B] :
( ! [C] :
( ( ( disjoint(B,C)
| ~ subset(B,subset_complement(A,C)) )
& ( subset(B,subset_complement(A,C))
| ~ disjoint(B,C) ) )
| ~ element(C,powerset(A)) )
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[t43_subset_1]) ).
fof(f_257_2,plain,
! [U_960,U_959] :
( ! [U_958] :
( ( ( disjoint(U_959,U_958)
| ~ subset(U_959,subset_complement(U_960,U_958)) )
& ( subset(U_959,subset_complement(U_960,U_958))
| ~ disjoint(U_959,U_958) ) )
| ~ element(U_958,powerset(U_960)) )
| ~ element(U_959,powerset(U_960)) ),
inference(variable_rename,[status(thm)],[f_257_1]) ).
cnf(f_257_3,plain,
( subset(U_959,subset_complement(U_960,U_958))
| ~ disjoint(U_959,U_958)
| ~ element(U_958,powerset(U_960))
| ~ element(U_959,powerset(U_960)) ),
inference(clausify,[status(thm)],[f_257_2]) ).
cnf(f_257_4,plain,
( disjoint(U_959,U_958)
| ~ subset(U_959,subset_complement(U_960,U_958))
| ~ element(U_958,powerset(U_960))
| ~ element(U_959,powerset(U_960)) ),
inference(clausify,[status(thm)],[f_257_2]) ).
fof(f_258_1,plain,
! [A] :
( ! [B] :
( subset(relation_dom(relation_composition(A,B)),relation_dom(A))
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t44_relat_1]) ).
fof(f_258_2,plain,
! [U_962] :
( ! [U_961] :
( subset(relation_dom(relation_composition(U_962,U_961)),relation_dom(U_962))
| ~ relation(U_961) )
| ~ relation(U_962) ),
inference(variable_rename,[status(thm)],[f_258_1]) ).
cnf(f_258_3,plain,
( subset(relation_dom(relation_composition(U_962,U_961)),relation_dom(U_962))
| ~ relation(U_961)
| ~ relation(U_962) ),
inference(clausify,[status(thm)],[f_258_2]) ).
fof(f_259_1,plain,
! [A] :
( ! [B] :
( subset(relation_rng(relation_composition(A,B)),relation_rng(B))
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t45_relat_1]) ).
fof(f_259_2,plain,
! [U_964] :
( ! [U_963] :
( subset(relation_rng(relation_composition(U_964,U_963)),relation_rng(U_963))
| ~ relation(U_963) )
| ~ relation(U_964) ),
inference(variable_rename,[status(thm)],[f_259_1]) ).
cnf(f_259_3,plain,
( subset(relation_rng(relation_composition(U_964,U_963)),relation_rng(U_963))
| ~ relation(U_963)
| ~ relation(U_964) ),
inference(clausify,[status(thm)],[f_259_2]) ).
fof(f_260_1,plain,
! [A,B] :
( B = set_union2(A,set_difference(B,A))
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t45_xboole_1]) ).
fof(f_260_2,plain,
! [U_966,U_965] :
( U_965 = set_union2(U_966,set_difference(U_965,U_966))
| ~ subset(U_966,U_965) ),
inference(variable_rename,[status(thm)],[f_260_1]) ).
cnf(f_260_3,plain,
( U_965 = set_union2(U_966,set_difference(U_965,U_966))
| ~ subset(U_966,U_965) ),
inference(clausify,[status(thm)],[f_260_2]) ).
fof(f_261_1,plain,
! [A] :
( ! [B] :
( relation_dom(relation_composition(A,B)) = relation_dom(A)
| ~ subset(relation_rng(A),relation_dom(B))
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t46_relat_1]) ).
fof(f_261_2,plain,
! [U_968] :
( ! [U_967] :
( relation_dom(relation_composition(U_968,U_967)) = relation_dom(U_968)
| ~ subset(relation_rng(U_968),relation_dom(U_967))
| ~ relation(U_967) )
| ~ relation(U_968) ),
inference(variable_rename,[status(thm)],[f_261_1]) ).
cnf(f_261_3,plain,
( relation_dom(relation_composition(U_968,U_967)) = relation_dom(U_968)
| ~ subset(relation_rng(U_968),relation_dom(U_967))
| ~ relation(U_967)
| ~ relation(U_968) ),
inference(clausify,[status(thm)],[f_261_2]) ).
fof(f_262_1,plain,
! [A,B] :
( complements_of_subsets(A,B) != empty_set
| B = empty_set
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[t46_setfam_1]) ).
fof(f_262_2,plain,
! [U_970,U_969] :
( complements_of_subsets(U_970,U_969) != empty_set
| U_969 = empty_set
| ~ element(U_969,powerset(powerset(U_970))) ),
inference(variable_rename,[status(thm)],[f_262_1]) ).
cnf(f_262_3,plain,
( complements_of_subsets(U_970,U_969) != empty_set
| U_969 = empty_set
| ~ element(U_969,powerset(powerset(U_970))) ),
inference(clausify,[status(thm)],[f_262_2]) ).
fof(f_263_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t46_zfmisc_1]) ).
fof(f_263_2,plain,
! [U_972,U_971] :
( set_union2(singleton(U_972),U_971) = U_971
| ~ in(U_972,U_971) ),
inference(variable_rename,[status(thm)],[f_263_1]) ).
cnf(f_263_3,plain,
( set_union2(singleton(U_972),U_971) = U_971
| ~ in(U_972,U_971) ),
inference(clausify,[status(thm)],[f_263_2]) ).
fof(f_264_1,plain,
! [A] :
( ! [B] :
( relation_rng(relation_composition(B,A)) = relation_rng(A)
| ~ subset(relation_dom(A),relation_rng(B))
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t47_relat_1]) ).
fof(f_264_2,plain,
! [U_974] :
( ! [U_973] :
( relation_rng(relation_composition(U_973,U_974)) = relation_rng(U_974)
| ~ subset(relation_dom(U_974),relation_rng(U_973))
| ~ relation(U_973) )
| ~ relation(U_974) ),
inference(variable_rename,[status(thm)],[f_264_1]) ).
cnf(f_264_3,plain,
( relation_rng(relation_composition(U_973,U_974)) = relation_rng(U_974)
| ~ subset(relation_dom(U_974),relation_rng(U_973))
| ~ relation(U_973)
| ~ relation(U_974) ),
inference(clausify,[status(thm)],[f_264_2]) ).
fof(f_265_1,plain,
! [A,B] :
( subset_difference(A,cast_to_subset(A),union_of_subsets(A,B)) = meet_of_subsets(A,complements_of_subsets(A,B))
| B = empty_set
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[t47_setfam_1]) ).
fof(f_265_2,plain,
! [U_976,U_975] :
( subset_difference(U_976,cast_to_subset(U_976),union_of_subsets(U_976,U_975)) = meet_of_subsets(U_976,complements_of_subsets(U_976,U_975))
| U_975 = empty_set
| ~ element(U_975,powerset(powerset(U_976))) ),
inference(variable_rename,[status(thm)],[f_265_1]) ).
cnf(f_265_3,plain,
( subset_difference(U_976,cast_to_subset(U_976),union_of_subsets(U_976,U_975)) = meet_of_subsets(U_976,complements_of_subsets(U_976,U_975))
| U_975 = empty_set
| ~ element(U_975,powerset(powerset(U_976))) ),
inference(clausify,[status(thm)],[f_265_2]) ).
fof(f_266_1,plain,
! [A,B] :
( union_of_subsets(A,complements_of_subsets(A,B)) = subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B))
| B = empty_set
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[t48_setfam_1]) ).
fof(f_266_2,plain,
! [U_978,U_977] :
( union_of_subsets(U_978,complements_of_subsets(U_978,U_977)) = subset_difference(U_978,cast_to_subset(U_978),meet_of_subsets(U_978,U_977))
| U_977 = empty_set
| ~ element(U_977,powerset(powerset(U_978))) ),
inference(variable_rename,[status(thm)],[f_266_1]) ).
cnf(f_266_3,plain,
( union_of_subsets(U_978,complements_of_subsets(U_978,U_977)) = subset_difference(U_978,cast_to_subset(U_978),meet_of_subsets(U_978,U_977))
| U_977 = empty_set
| ~ element(U_977,powerset(powerset(U_978))) ),
inference(clausify,[status(thm)],[f_266_2]) ).
fof(f_267_1,plain,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(fof_nnf,[status(thm)],[t48_xboole_1]) ).
fof(f_267_2,plain,
! [U_980,U_979] : set_difference(U_980,set_difference(U_980,U_979)) = set_intersection2(U_980,U_979),
inference(variable_rename,[status(thm)],[f_267_1]) ).
cnf(f_267_3,plain,
set_difference(U_980,set_difference(U_980,U_979)) = set_intersection2(U_980,U_979),
inference(clausify,[status(thm)],[f_267_2]) ).
fof(f_268_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_268_2,plain,
! [U_981] : set_difference(empty_set,U_981) = empty_set,
inference(variable_rename,[status(thm)],[f_268_1]) ).
cnf(f_268_3,plain,
set_difference(empty_set,U_981) = empty_set,
inference(clausify,[status(thm)],[f_268_2]) ).
fof(f_269_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_269_2,plain,
! [U_984,U_983,U_982] :
( element(U_984,U_982)
| ~ element(U_983,powerset(U_982))
| ~ in(U_984,U_983) ),
inference(variable_rename,[status(thm)],[f_269_1]) ).
cnf(f_269_3,plain,
( element(U_984,U_982)
| ~ element(U_983,powerset(U_982))
| ~ in(U_984,U_983) ),
inference(clausify,[status(thm)],[f_269_2]) ).
fof(f_270_1,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ( ? [C] : in(C,set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t4_xboole_0]) ).
fof(f_270_2,plain,
! [U_988,U_987] :
( ( ~ disjoint(U_988,U_987)
| ! [U_986] : ~ in(U_986,set_intersection2(U_988,U_987)) )
& ( ? [U_985] : in(U_985,set_intersection2(U_988,U_987))
| disjoint(U_988,U_987) ) ),
inference(variable_rename,[status(thm)],[f_270_1]) ).
fof(f_270_3,plain,
( ! [U_992,U_990] :
( ~ disjoint(U_992,U_990)
| ! [U_986] : ~ in(U_986,set_intersection2(U_992,U_990)) )
& ! [U_991,U_989] :
( ? [U_985] : in(U_985,set_intersection2(U_991,U_989))
| disjoint(U_991,U_989) ) ),
inference(miniscope,[status(thm)],[f_270_2]) ).
fof(f_270_4,plain,
( ! [U_992,U_990] :
( ~ disjoint(U_992,U_990)
| ! [U_986] : ~ in(U_986,set_intersection2(U_992,U_990)) )
& ! [U_991,U_989] :
( in(sK145(U_991,U_989),set_intersection2(U_991,U_989))
| disjoint(U_991,U_989) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK145]),skolemize(U_985,sK145(U_991,U_989))],[f_270_3]) ).
cnf(f_270_5,plain,
( in(sK145(U_991,U_989),set_intersection2(U_991,U_989))
| disjoint(U_991,U_989) ),
inference(clausify,[status(thm)],[f_270_4]) ).
cnf(f_270_6,plain,
( ~ disjoint(U_992,U_990)
| ~ in(U_986,set_intersection2(U_992,U_990)) ),
inference(clausify,[status(thm)],[f_270_4]) ).
fof(f_271_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( in(C,subset_complement(A,B))
| in(C,B)
| ~ element(C,A) )
| ~ element(B,powerset(A)) )
| A = empty_set ),
inference(fof_nnf,[status(thm)],[t50_subset_1]) ).
fof(f_271_2,plain,
! [U_995] :
( ! [U_994] :
( ! [U_993] :
( in(U_993,subset_complement(U_995,U_994))
| in(U_993,U_994)
| ~ element(U_993,U_995) )
| ~ element(U_994,powerset(U_995)) )
| U_995 = empty_set ),
inference(variable_rename,[status(thm)],[f_271_1]) ).
cnf(f_271_3,plain,
( in(U_993,subset_complement(U_995,U_994))
| in(U_993,U_994)
| ~ element(U_993,U_995)
| ~ element(U_994,powerset(U_995))
| U_995 = empty_set ),
inference(clausify,[status(thm)],[f_271_2]) ).
fof(f_272_1,plain,
! [A] :
( ! [B] :
( ( ( B = function_inverse(A)
| ? [C,D] :
( ( ( D != apply(B,C)
| ~ in(C,relation_rng(A)) )
& C = apply(A,D)
& in(D,relation_dom(A)) )
| ( ( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& D = apply(B,C)
& in(C,relation_rng(A)) ) )
| relation_dom(B) != relation_rng(A) )
& ( ( ! [C,D] :
( ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
| C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& ( ( C = apply(A,D)
& in(D,relation_dom(A)) )
| D != apply(B,C)
| ~ in(C,relation_rng(A)) ) )
& relation_dom(B) = relation_rng(A) )
| B != function_inverse(A) ) )
| ~ function(B)
| ~ relation(B) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t54_funct_1]) ).
fof(f_272_2,plain,
! [U_1001] :
( ! [U_1000] :
( ( ( U_1000 = function_inverse(U_1001)
| ? [U_999,U_998] :
( ( ( U_998 != apply(U_1000,U_999)
| ~ in(U_999,relation_rng(U_1001)) )
& U_999 = apply(U_1001,U_998)
& in(U_998,relation_dom(U_1001)) )
| ( ( U_999 != apply(U_1001,U_998)
| ~ in(U_998,relation_dom(U_1001)) )
& U_998 = apply(U_1000,U_999)
& in(U_999,relation_rng(U_1001)) ) )
| relation_dom(U_1000) != relation_rng(U_1001) )
& ( ( ! [U_997,U_996] :
( ( ( U_996 = apply(U_1000,U_997)
& in(U_997,relation_rng(U_1001)) )
| U_997 != apply(U_1001,U_996)
| ~ in(U_996,relation_dom(U_1001)) )
& ( ( U_997 = apply(U_1001,U_996)
& in(U_996,relation_dom(U_1001)) )
| U_996 != apply(U_1000,U_997)
| ~ in(U_997,relation_rng(U_1001)) ) )
& relation_dom(U_1000) = relation_rng(U_1001) )
| U_1000 != function_inverse(U_1001) ) )
| ~ function(U_1000)
| ~ relation(U_1000) )
| ~ one_to_one(U_1001)
| ~ function(U_1001)
| ~ relation(U_1001) ),
inference(variable_rename,[status(thm)],[f_272_1]) ).
fof(f_272_3,plain,
! [U_1001] :
( ! [U_1000] :
( ( ( U_1000 = function_inverse(U_1001)
| ? [U_1009,U_1007] :
( ( U_1007 != apply(U_1000,U_1009)
| ~ in(U_1009,relation_rng(U_1001)) )
& U_1009 = apply(U_1001,U_1007)
& in(U_1007,relation_dom(U_1001)) )
| ? [U_1008,U_1006] :
( ( U_1008 != apply(U_1001,U_1006)
| ~ in(U_1006,relation_dom(U_1001)) )
& U_1006 = apply(U_1000,U_1008)
& in(U_1008,relation_rng(U_1001)) )
| relation_dom(U_1000) != relation_rng(U_1001) )
& ( ( ! [U_1005,U_1003] :
( ( U_1003 = apply(U_1000,U_1005)
& in(U_1005,relation_rng(U_1001)) )
| U_1005 != apply(U_1001,U_1003)
| ~ in(U_1003,relation_dom(U_1001)) )
& ! [U_1004,U_1002] :
( ( U_1004 = apply(U_1001,U_1002)
& in(U_1002,relation_dom(U_1001)) )
| U_1002 != apply(U_1000,U_1004)
| ~ in(U_1004,relation_rng(U_1001)) )
& relation_dom(U_1000) = relation_rng(U_1001) )
| U_1000 != function_inverse(U_1001) ) )
| ~ function(U_1000)
| ~ relation(U_1000) )
| ~ one_to_one(U_1001)
| ~ function(U_1001)
| ~ relation(U_1001) ),
inference(miniscope,[status(thm)],[f_272_2]) ).
fof(f_272_4,plain,
! [U_1001] :
( ! [U_1000] :
( ( ( U_1000 = function_inverse(U_1001)
| ? [U_1009,U_1007] :
( ( U_1007 != apply(U_1000,U_1009)
| ~ in(U_1009,relation_rng(U_1001)) )
& U_1009 = apply(U_1001,U_1007)
& in(U_1007,relation_dom(U_1001)) )
| ? [U_1006] :
( ( sK146(U_1001,U_1000) != apply(U_1001,U_1006)
| ~ in(U_1006,relation_dom(U_1001)) )
& U_1006 = apply(U_1000,sK146(U_1001,U_1000))
& in(sK146(U_1001,U_1000),relation_rng(U_1001)) )
| relation_dom(U_1000) != relation_rng(U_1001) )
& ( ( ! [U_1005,U_1003] :
( ( U_1003 = apply(U_1000,U_1005)
& in(U_1005,relation_rng(U_1001)) )
| U_1005 != apply(U_1001,U_1003)
| ~ in(U_1003,relation_dom(U_1001)) )
& ! [U_1004,U_1002] :
( ( U_1004 = apply(U_1001,U_1002)
& in(U_1002,relation_dom(U_1001)) )
| U_1002 != apply(U_1000,U_1004)
| ~ in(U_1004,relation_rng(U_1001)) )
& relation_dom(U_1000) = relation_rng(U_1001) )
| U_1000 != function_inverse(U_1001) ) )
| ~ function(U_1000)
| ~ relation(U_1000) )
| ~ one_to_one(U_1001)
| ~ function(U_1001)
| ~ relation(U_1001) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK146]),skolemize(U_1008,sK146(U_1001,U_1000))],[f_272_3]) ).
fof(f_272_5,plain,
! [U_1001] :
( ! [U_1000] :
( ( ( U_1000 = function_inverse(U_1001)
| ? [U_1009,U_1007] :
( ( U_1007 != apply(U_1000,U_1009)
| ~ in(U_1009,relation_rng(U_1001)) )
& U_1009 = apply(U_1001,U_1007)
& in(U_1007,relation_dom(U_1001)) )
| ( ( sK146(U_1001,U_1000) != apply(U_1001,sK147(U_1001,U_1000))
| ~ in(sK147(U_1001,U_1000),relation_dom(U_1001)) )
& sK147(U_1001,U_1000) = apply(U_1000,sK146(U_1001,U_1000))
& in(sK146(U_1001,U_1000),relation_rng(U_1001)) )
| relation_dom(U_1000) != relation_rng(U_1001) )
& ( ( ! [U_1005,U_1003] :
( ( U_1003 = apply(U_1000,U_1005)
& in(U_1005,relation_rng(U_1001)) )
| U_1005 != apply(U_1001,U_1003)
| ~ in(U_1003,relation_dom(U_1001)) )
& ! [U_1004,U_1002] :
( ( U_1004 = apply(U_1001,U_1002)
& in(U_1002,relation_dom(U_1001)) )
| U_1002 != apply(U_1000,U_1004)
| ~ in(U_1004,relation_rng(U_1001)) )
& relation_dom(U_1000) = relation_rng(U_1001) )
| U_1000 != function_inverse(U_1001) ) )
| ~ function(U_1000)
| ~ relation(U_1000) )
| ~ one_to_one(U_1001)
| ~ function(U_1001)
| ~ relation(U_1001) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK147]),skolemize(U_1006,sK147(U_1001,U_1000))],[f_272_4]) ).
fof(f_272_6,plain,
! [U_1001] :
( ! [U_1000] :
( ( ( U_1000 = function_inverse(U_1001)
| ? [U_1007] :
( ( U_1007 != apply(U_1000,sK148(U_1001,U_1000))
| ~ in(sK148(U_1001,U_1000),relation_rng(U_1001)) )
& sK148(U_1001,U_1000) = apply(U_1001,U_1007)
& in(U_1007,relation_dom(U_1001)) )
| ( ( sK146(U_1001,U_1000) != apply(U_1001,sK147(U_1001,U_1000))
| ~ in(sK147(U_1001,U_1000),relation_dom(U_1001)) )
& sK147(U_1001,U_1000) = apply(U_1000,sK146(U_1001,U_1000))
& in(sK146(U_1001,U_1000),relation_rng(U_1001)) )
| relation_dom(U_1000) != relation_rng(U_1001) )
& ( ( ! [U_1005,U_1003] :
( ( U_1003 = apply(U_1000,U_1005)
& in(U_1005,relation_rng(U_1001)) )
| U_1005 != apply(U_1001,U_1003)
| ~ in(U_1003,relation_dom(U_1001)) )
& ! [U_1004,U_1002] :
( ( U_1004 = apply(U_1001,U_1002)
& in(U_1002,relation_dom(U_1001)) )
| U_1002 != apply(U_1000,U_1004)
| ~ in(U_1004,relation_rng(U_1001)) )
& relation_dom(U_1000) = relation_rng(U_1001) )
| U_1000 != function_inverse(U_1001) ) )
| ~ function(U_1000)
| ~ relation(U_1000) )
| ~ one_to_one(U_1001)
| ~ function(U_1001)
| ~ relation(U_1001) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK148]),skolemize(U_1009,sK148(U_1001,U_1000))],[f_272_5]) ).
fof(f_272_7,plain,
! [U_1001] :
( ! [U_1000] :
( ( ( U_1000 = function_inverse(U_1001)
| ( ( sK149(U_1001,U_1000) != apply(U_1000,sK148(U_1001,U_1000))
| ~ in(sK148(U_1001,U_1000),relation_rng(U_1001)) )
& sK148(U_1001,U_1000) = apply(U_1001,sK149(U_1001,U_1000))
& in(sK149(U_1001,U_1000),relation_dom(U_1001)) )
| ( ( sK146(U_1001,U_1000) != apply(U_1001,sK147(U_1001,U_1000))
| ~ in(sK147(U_1001,U_1000),relation_dom(U_1001)) )
& sK147(U_1001,U_1000) = apply(U_1000,sK146(U_1001,U_1000))
& in(sK146(U_1001,U_1000),relation_rng(U_1001)) )
| relation_dom(U_1000) != relation_rng(U_1001) )
& ( ( ! [U_1005,U_1003] :
( ( U_1003 = apply(U_1000,U_1005)
& in(U_1005,relation_rng(U_1001)) )
| U_1005 != apply(U_1001,U_1003)
| ~ in(U_1003,relation_dom(U_1001)) )
& ! [U_1004,U_1002] :
( ( U_1004 = apply(U_1001,U_1002)
& in(U_1002,relation_dom(U_1001)) )
| U_1002 != apply(U_1000,U_1004)
| ~ in(U_1004,relation_rng(U_1001)) )
& relation_dom(U_1000) = relation_rng(U_1001) )
| U_1000 != function_inverse(U_1001) ) )
| ~ function(U_1000)
| ~ relation(U_1000) )
| ~ one_to_one(U_1001)
| ~ function(U_1001)
| ~ relation(U_1001) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK149]),skolemize(U_1007,sK149(U_1001,U_1000))],[f_272_6]) ).
cnf(f_272_8,plain,
( relation_dom(U_1000) = relation_rng(U_1001)
| U_1000 != function_inverse(U_1001)
| ~ function(U_1000)
| ~ relation(U_1000)
| ~ one_to_one(U_1001)
| ~ function(U_1001)
| ~ relation(U_1001) ),
inference(clausify,[status(thm)],[f_272_7]) ).
cnf(f_272_9,plain,
( in(U_1002,relation_dom(U_1001))
| U_1002 != apply(U_1000,U_1004)
| ~ in(U_1004,relation_rng(U_1001))
| U_1000 != function_inverse(U_1001)
| ~ function(U_1000)
| ~ relation(U_1000)
| ~ one_to_one(U_1001)
| ~ function(U_1001)
| ~ relation(U_1001) ),
inference(clausify,[status(thm)],[f_272_7]) ).
cnf(f_272_10,plain,
( U_1004 = apply(U_1001,U_1002)
| U_1002 != apply(U_1000,U_1004)
| ~ in(U_1004,relation_rng(U_1001))
| U_1000 != function_inverse(U_1001)
| ~ function(U_1000)
| ~ relation(U_1000)
| ~ one_to_one(U_1001)
| ~ function(U_1001)
| ~ relation(U_1001) ),
inference(clausify,[status(thm)],[f_272_7]) ).
cnf(f_272_11,plain,
( in(U_1005,relation_rng(U_1001))
| U_1005 != apply(U_1001,U_1003)
| ~ in(U_1003,relation_dom(U_1001))
| U_1000 != function_inverse(U_1001)
| ~ function(U_1000)
| ~ relation(U_1000)
| ~ one_to_one(U_1001)
| ~ function(U_1001)
| ~ relation(U_1001) ),
inference(clausify,[status(thm)],[f_272_7]) ).
cnf(f_272_12,plain,
( U_1003 = apply(U_1000,U_1005)
| U_1005 != apply(U_1001,U_1003)
| ~ in(U_1003,relation_dom(U_1001))
| U_1000 != function_inverse(U_1001)
| ~ function(U_1000)
| ~ relation(U_1000)
| ~ one_to_one(U_1001)
| ~ function(U_1001)
| ~ relation(U_1001) ),
inference(clausify,[status(thm)],[f_272_7]) ).
cnf(f_272_13,plain,
( in(sK149(U_1001,U_1000),relation_dom(U_1001))
| in(sK146(U_1001,U_1000),relation_rng(U_1001))
| relation_dom(U_1000) != relation_rng(U_1001)
| U_1000 = function_inverse(U_1001)
| ~ function(U_1000)
| ~ relation(U_1000)
| ~ one_to_one(U_1001)
| ~ function(U_1001)
| ~ relation(U_1001) ),
inference(clausify,[status(thm)],[f_272_7]) ).
cnf(f_272_14,plain,
( sK148(U_1001,U_1000) = apply(U_1001,sK149(U_1001,U_1000))
| in(sK146(U_1001,U_1000),relation_rng(U_1001))
| relation_dom(U_1000) != relation_rng(U_1001)
| U_1000 = function_inverse(U_1001)
| ~ function(U_1000)
| ~ relation(U_1000)
| ~ one_to_one(U_1001)
| ~ function(U_1001)
| ~ relation(U_1001) ),
inference(clausify,[status(thm)],[f_272_7]) ).
cnf(f_272_15,plain,
( in(sK149(U_1001,U_1000),relation_dom(U_1001))
| sK147(U_1001,U_1000) = apply(U_1000,sK146(U_1001,U_1000))
| relation_dom(U_1000) != relation_rng(U_1001)
| U_1000 = function_inverse(U_1001)
| ~ function(U_1000)
| ~ relation(U_1000)
| ~ one_to_one(U_1001)
| ~ function(U_1001)
| ~ relation(U_1001) ),
inference(clausify,[status(thm)],[f_272_7]) ).
cnf(f_272_16,plain,
( sK148(U_1001,U_1000) = apply(U_1001,sK149(U_1001,U_1000))
| sK147(U_1001,U_1000) = apply(U_1000,sK146(U_1001,U_1000))
| relation_dom(U_1000) != relation_rng(U_1001)
| U_1000 = function_inverse(U_1001)
| ~ function(U_1000)
| ~ relation(U_1000)
| ~ one_to_one(U_1001)
| ~ function(U_1001)
| ~ relation(U_1001) ),
inference(clausify,[status(thm)],[f_272_7]) ).
cnf(f_272_17,plain,
( in(sK146(U_1001,U_1000),relation_rng(U_1001))
| sK149(U_1001,U_1000) != apply(U_1000,sK148(U_1001,U_1000))
| ~ in(sK148(U_1001,U_1000),relation_rng(U_1001))
| relation_dom(U_1000) != relation_rng(U_1001)
| U_1000 = function_inverse(U_1001)
| ~ function(U_1000)
| ~ relation(U_1000)
| ~ one_to_one(U_1001)
| ~ function(U_1001)
| ~ relation(U_1001) ),
inference(clausify,[status(thm)],[f_272_7]) ).
cnf(f_272_18,plain,
( sK147(U_1001,U_1000) = apply(U_1000,sK146(U_1001,U_1000))
| sK149(U_1001,U_1000) != apply(U_1000,sK148(U_1001,U_1000))
| ~ in(sK148(U_1001,U_1000),relation_rng(U_1001))
| relation_dom(U_1000) != relation_rng(U_1001)
| U_1000 = function_inverse(U_1001)
| ~ function(U_1000)
| ~ relation(U_1000)
| ~ one_to_one(U_1001)
| ~ function(U_1001)
| ~ relation(U_1001) ),
inference(clausify,[status(thm)],[f_272_7]) ).
cnf(f_272_19,plain,
( in(sK149(U_1001,U_1000),relation_dom(U_1001))
| sK146(U_1001,U_1000) != apply(U_1001,sK147(U_1001,U_1000))
| ~ in(sK147(U_1001,U_1000),relation_dom(U_1001))
| relation_dom(U_1000) != relation_rng(U_1001)
| U_1000 = function_inverse(U_1001)
| ~ function(U_1000)
| ~ relation(U_1000)
| ~ one_to_one(U_1001)
| ~ function(U_1001)
| ~ relation(U_1001) ),
inference(clausify,[status(thm)],[f_272_7]) ).
cnf(f_272_20,plain,
( sK148(U_1001,U_1000) = apply(U_1001,sK149(U_1001,U_1000))
| sK146(U_1001,U_1000) != apply(U_1001,sK147(U_1001,U_1000))
| ~ in(sK147(U_1001,U_1000),relation_dom(U_1001))
| relation_dom(U_1000) != relation_rng(U_1001)
| U_1000 = function_inverse(U_1001)
| ~ function(U_1000)
| ~ relation(U_1000)
| ~ one_to_one(U_1001)
| ~ function(U_1001)
| ~ relation(U_1001) ),
inference(clausify,[status(thm)],[f_272_7]) ).
cnf(f_272_21,plain,
( sK149(U_1001,U_1000) != apply(U_1000,sK148(U_1001,U_1000))
| ~ in(sK148(U_1001,U_1000),relation_rng(U_1001))
| sK146(U_1001,U_1000) != apply(U_1001,sK147(U_1001,U_1000))
| ~ in(sK147(U_1001,U_1000),relation_dom(U_1001))
| relation_dom(U_1000) != relation_rng(U_1001)
| U_1000 = function_inverse(U_1001)
| ~ function(U_1000)
| ~ relation(U_1000)
| ~ one_to_one(U_1001)
| ~ function(U_1001)
| ~ relation(U_1001) ),
inference(clausify,[status(thm)],[f_272_7]) ).
fof(f_273_1,plain,
! [A,B,C] :
( ~ in(B,C)
| ~ in(B,subset_complement(A,C))
| ~ element(C,powerset(A)) ),
inference(fof_nnf,[status(thm)],[t54_subset_1]) ).
fof(f_273_2,plain,
! [U_1012,U_1011,U_1010] :
( ~ in(U_1011,U_1010)
| ~ in(U_1011,subset_complement(U_1012,U_1010))
| ~ element(U_1010,powerset(U_1012)) ),
inference(variable_rename,[status(thm)],[f_273_1]) ).
cnf(f_273_3,plain,
( ~ in(U_1011,U_1010)
| ~ in(U_1011,subset_complement(U_1012,U_1010))
| ~ element(U_1010,powerset(U_1012)) ),
inference(clausify,[status(thm)],[f_273_2]) ).
fof(f_274_1,plain,
! [A] :
( ( relation_dom(A) = relation_rng(function_inverse(A))
& relation_rng(A) = relation_dom(function_inverse(A)) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t55_funct_1]) ).
fof(f_274_2,plain,
! [U_1013] :
( ( relation_dom(U_1013) = relation_rng(function_inverse(U_1013))
& relation_rng(U_1013) = relation_dom(function_inverse(U_1013)) )
| ~ one_to_one(U_1013)
| ~ function(U_1013)
| ~ relation(U_1013) ),
inference(variable_rename,[status(thm)],[f_274_1]) ).
cnf(f_274_3,plain,
( relation_rng(U_1013) = relation_dom(function_inverse(U_1013))
| ~ one_to_one(U_1013)
| ~ function(U_1013)
| ~ relation(U_1013) ),
inference(clausify,[status(thm)],[f_274_2]) ).
cnf(f_274_4,plain,
( relation_dom(U_1013) = relation_rng(function_inverse(U_1013))
| ~ one_to_one(U_1013)
| ~ function(U_1013)
| ~ relation(U_1013) ),
inference(clausify,[status(thm)],[f_274_2]) ).
fof(f_275_1,plain,
! [A] :
( A = empty_set
| ? [B,C] : in(ordered_pair(B,C),A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t56_relat_1]) ).
fof(f_275_2,plain,
! [U_1016] :
( U_1016 = empty_set
| ? [U_1015,U_1014] : in(ordered_pair(U_1015,U_1014),U_1016)
| ~ relation(U_1016) ),
inference(variable_rename,[status(thm)],[f_275_1]) ).
fof(f_275_3,plain,
! [U_1016] :
( U_1016 = empty_set
| ? [U_1014] : in(ordered_pair(sK150(U_1016),U_1014),U_1016)
| ~ relation(U_1016) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK150]),skolemize(U_1015,sK150(U_1016))],[f_275_2]) ).
fof(f_275_4,plain,
! [U_1016] :
( U_1016 = empty_set
| in(ordered_pair(sK150(U_1016),sK151(U_1016)),U_1016)
| ~ relation(U_1016) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK151]),skolemize(U_1014,sK151(U_1016))],[f_275_3]) ).
cnf(f_275_5,plain,
( U_1016 = empty_set
| in(ordered_pair(sK150(U_1016),sK151(U_1016)),U_1016)
| ~ relation(U_1016) ),
inference(clausify,[status(thm)],[f_275_4]) ).
fof(f_276_1,plain,
! [A,B] :
( ( A = apply(relation_composition(function_inverse(B),B),A)
& A = apply(B,apply(function_inverse(B),A)) )
| ~ in(A,relation_rng(B))
| ~ one_to_one(B)
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t57_funct_1]) ).
fof(f_276_2,plain,
! [U_1018,U_1017] :
( ( U_1018 = apply(relation_composition(function_inverse(U_1017),U_1017),U_1018)
& U_1018 = apply(U_1017,apply(function_inverse(U_1017),U_1018)) )
| ~ in(U_1018,relation_rng(U_1017))
| ~ one_to_one(U_1017)
| ~ function(U_1017)
| ~ relation(U_1017) ),
inference(variable_rename,[status(thm)],[f_276_1]) ).
cnf(f_276_3,plain,
( U_1018 = apply(U_1017,apply(function_inverse(U_1017),U_1018))
| ~ in(U_1018,relation_rng(U_1017))
| ~ one_to_one(U_1017)
| ~ function(U_1017)
| ~ relation(U_1017) ),
inference(clausify,[status(thm)],[f_276_2]) ).
cnf(f_276_4,plain,
( U_1018 = apply(relation_composition(function_inverse(U_1017),U_1017),U_1018)
| ~ in(U_1018,relation_rng(U_1017))
| ~ one_to_one(U_1017)
| ~ function(U_1017)
| ~ relation(U_1017) ),
inference(clausify,[status(thm)],[f_276_2]) ).
fof(f_277_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_277_2,plain,
! [U_1021,U_1020,U_1019] :
( ~ empty(U_1019)
| ~ element(U_1020,powerset(U_1019))
| ~ in(U_1021,U_1020) ),
inference(variable_rename,[status(thm)],[f_277_1]) ).
fof(f_277_3,plain,
! [U_1021,U_1020] :
( ! [U_1019] :
( ~ empty(U_1019)
| ~ element(U_1020,powerset(U_1019)) )
| ~ in(U_1021,U_1020) ),
inference(miniscope,[status(thm)],[f_277_2]) ).
cnf(f_277_4,plain,
( ~ empty(U_1019)
| ~ element(U_1020,powerset(U_1019))
| ~ in(U_1021,U_1020) ),
inference(clausify,[status(thm)],[f_277_3]) ).
fof(f_278_1,plain,
! [A] :
( ( ( well_founded_relation(A)
| ~ is_well_founded_in(A,relation_field(A)) )
& ( is_well_founded_in(A,relation_field(A))
| ~ well_founded_relation(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t5_wellord1]) ).
fof(f_278_2,plain,
! [U_1022] :
( ( ( well_founded_relation(U_1022)
| ~ is_well_founded_in(U_1022,relation_field(U_1022)) )
& ( is_well_founded_in(U_1022,relation_field(U_1022))
| ~ well_founded_relation(U_1022) ) )
| ~ relation(U_1022) ),
inference(variable_rename,[status(thm)],[f_278_1]) ).
cnf(f_278_3,plain,
( is_well_founded_in(U_1022,relation_field(U_1022))
| ~ well_founded_relation(U_1022)
| ~ relation(U_1022) ),
inference(clausify,[status(thm)],[f_278_2]) ).
cnf(f_278_4,plain,
( well_founded_relation(U_1022)
| ~ is_well_founded_in(U_1022,relation_field(U_1022))
| ~ relation(U_1022) ),
inference(clausify,[status(thm)],[f_278_2]) ).
fof(f_279_1,plain,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(fof_nnf,[status(thm)],[t60_relat_1]) ).
cnf(f_279_2,plain,
relation_dom(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_279_1]) ).
cnf(f_279_3,plain,
relation_rng(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_279_1]) ).
fof(f_280_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t60_xboole_1]) ).
fof(f_280_2,plain,
! [U_1024,U_1023] :
( ~ proper_subset(U_1023,U_1024)
| ~ subset(U_1024,U_1023) ),
inference(variable_rename,[status(thm)],[f_280_1]) ).
cnf(f_280_3,plain,
( ~ proper_subset(U_1023,U_1024)
| ~ subset(U_1024,U_1023) ),
inference(clausify,[status(thm)],[f_280_2]) ).
fof(f_281_1,plain,
! [A] :
( one_to_one(function_inverse(A))
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t62_funct_1]) ).
fof(f_281_2,plain,
! [U_1025] :
( one_to_one(function_inverse(U_1025))
| ~ one_to_one(U_1025)
| ~ function(U_1025)
| ~ relation(U_1025) ),
inference(variable_rename,[status(thm)],[f_281_1]) ).
cnf(f_281_3,plain,
( one_to_one(function_inverse(U_1025))
| ~ one_to_one(U_1025)
| ~ function(U_1025)
| ~ relation(U_1025) ),
inference(clausify,[status(thm)],[f_281_2]) ).
fof(f_282_1,plain,
! [A,B,C] :
( disjoint(A,C)
| ~ disjoint(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t63_xboole_1]) ).
fof(f_282_2,plain,
! [U_1028,U_1027,U_1026] :
( disjoint(U_1028,U_1026)
| ~ disjoint(U_1027,U_1026)
| ~ subset(U_1028,U_1027) ),
inference(variable_rename,[status(thm)],[f_282_1]) ).
cnf(f_282_3,plain,
( disjoint(U_1028,U_1026)
| ~ disjoint(U_1027,U_1026)
| ~ subset(U_1028,U_1027) ),
inference(clausify,[status(thm)],[f_282_2]) ).
fof(f_283_1,plain,
! [A] :
( A = empty_set
| ( relation_rng(A) != empty_set
& relation_dom(A) != empty_set )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t64_relat_1]) ).
fof(f_283_2,plain,
! [U_1029] :
( U_1029 = empty_set
| ( relation_rng(U_1029) != empty_set
& relation_dom(U_1029) != empty_set )
| ~ relation(U_1029) ),
inference(variable_rename,[status(thm)],[f_283_1]) ).
cnf(f_283_3,plain,
( relation_dom(U_1029) != empty_set
| U_1029 = empty_set
| ~ relation(U_1029) ),
inference(clausify,[status(thm)],[f_283_2]) ).
cnf(f_283_4,plain,
( relation_rng(U_1029) != empty_set
| U_1029 = empty_set
| ~ relation(U_1029) ),
inference(clausify,[status(thm)],[f_283_2]) ).
fof(f_284_1,plain,
! [A] :
( ( ( relation_dom(A) = empty_set
| relation_rng(A) != empty_set )
& ( relation_rng(A) = empty_set
| relation_dom(A) != empty_set ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t65_relat_1]) ).
fof(f_284_2,plain,
! [U_1030] :
( ( ( relation_dom(U_1030) = empty_set
| relation_rng(U_1030) != empty_set )
& ( relation_rng(U_1030) = empty_set
| relation_dom(U_1030) != empty_set ) )
| ~ relation(U_1030) ),
inference(variable_rename,[status(thm)],[f_284_1]) ).
cnf(f_284_3,plain,
( relation_rng(U_1030) = empty_set
| relation_dom(U_1030) != empty_set
| ~ relation(U_1030) ),
inference(clausify,[status(thm)],[f_284_2]) ).
cnf(f_284_4,plain,
( relation_dom(U_1030) = empty_set
| relation_rng(U_1030) != empty_set
| ~ relation(U_1030) ),
inference(clausify,[status(thm)],[f_284_2]) ).
fof(f_285_1,plain,
! [A,B] :
( ( set_difference(A,singleton(B)) = A
| in(B,A) )
& ( ~ in(B,A)
| set_difference(A,singleton(B)) != A ) ),
inference(fof_nnf,[status(thm)],[t65_zfmisc_1]) ).
fof(f_285_2,plain,
! [U_1032,U_1031] :
( ( set_difference(U_1032,singleton(U_1031)) = U_1032
| in(U_1031,U_1032) )
& ( ~ in(U_1031,U_1032)
| set_difference(U_1032,singleton(U_1031)) != U_1032 ) ),
inference(variable_rename,[status(thm)],[f_285_1]) ).
fof(f_285_3,plain,
( ! [U_1036,U_1034] :
( set_difference(U_1036,singleton(U_1034)) = U_1036
| in(U_1034,U_1036) )
& ! [U_1035,U_1033] :
( ~ in(U_1033,U_1035)
| set_difference(U_1035,singleton(U_1033)) != U_1035 ) ),
inference(miniscope,[status(thm)],[f_285_2]) ).
cnf(f_285_4,plain,
( ~ in(U_1033,U_1035)
| set_difference(U_1035,singleton(U_1033)) != U_1035 ),
inference(clausify,[status(thm)],[f_285_3]) ).
cnf(f_285_5,plain,
( set_difference(U_1036,singleton(U_1034)) = U_1036
| in(U_1034,U_1036) ),
inference(clausify,[status(thm)],[f_285_3]) ).
fof(f_286_1,plain,
! [A,B] :
( ! [C] :
( ( ( B = relation_dom_restriction(C,A)
| ? [D] :
( apply(B,D) != apply(C,D)
& in(D,relation_dom(B)) )
| relation_dom(B) != set_intersection2(relation_dom(C),A) )
& ( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) )
| B != relation_dom_restriction(C,A) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t68_funct_1]) ).
fof(f_286_2,plain,
! [U_1041,U_1040] :
( ! [U_1039] :
( ( ( U_1040 = relation_dom_restriction(U_1039,U_1041)
| ? [U_1038] :
( apply(U_1040,U_1038) != apply(U_1039,U_1038)
& in(U_1038,relation_dom(U_1040)) )
| relation_dom(U_1040) != set_intersection2(relation_dom(U_1039),U_1041) )
& ( ( ! [U_1037] :
( apply(U_1040,U_1037) = apply(U_1039,U_1037)
| ~ in(U_1037,relation_dom(U_1040)) )
& relation_dom(U_1040) = set_intersection2(relation_dom(U_1039),U_1041) )
| U_1040 != relation_dom_restriction(U_1039,U_1041) ) )
| ~ function(U_1039)
| ~ relation(U_1039) )
| ~ function(U_1040)
| ~ relation(U_1040) ),
inference(variable_rename,[status(thm)],[f_286_1]) ).
fof(f_286_3,plain,
! [U_1041,U_1040] :
( ! [U_1039] :
( ( ( U_1040 = relation_dom_restriction(U_1039,U_1041)
| ( apply(U_1040,sK152(U_1041,U_1040,U_1039)) != apply(U_1039,sK152(U_1041,U_1040,U_1039))
& in(sK152(U_1041,U_1040,U_1039),relation_dom(U_1040)) )
| relation_dom(U_1040) != set_intersection2(relation_dom(U_1039),U_1041) )
& ( ( ! [U_1037] :
( apply(U_1040,U_1037) = apply(U_1039,U_1037)
| ~ in(U_1037,relation_dom(U_1040)) )
& relation_dom(U_1040) = set_intersection2(relation_dom(U_1039),U_1041) )
| U_1040 != relation_dom_restriction(U_1039,U_1041) ) )
| ~ function(U_1039)
| ~ relation(U_1039) )
| ~ function(U_1040)
| ~ relation(U_1040) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK152]),skolemize(U_1038,sK152(U_1041,U_1040,U_1039))],[f_286_2]) ).
cnf(f_286_4,plain,
( relation_dom(U_1040) = set_intersection2(relation_dom(U_1039),U_1041)
| U_1040 != relation_dom_restriction(U_1039,U_1041)
| ~ function(U_1039)
| ~ relation(U_1039)
| ~ function(U_1040)
| ~ relation(U_1040) ),
inference(clausify,[status(thm)],[f_286_3]) ).
cnf(f_286_5,plain,
( apply(U_1040,U_1037) = apply(U_1039,U_1037)
| ~ in(U_1037,relation_dom(U_1040))
| U_1040 != relation_dom_restriction(U_1039,U_1041)
| ~ function(U_1039)
| ~ relation(U_1039)
| ~ function(U_1040)
| ~ relation(U_1040) ),
inference(clausify,[status(thm)],[f_286_3]) ).
cnf(f_286_6,plain,
( in(sK152(U_1041,U_1040,U_1039),relation_dom(U_1040))
| relation_dom(U_1040) != set_intersection2(relation_dom(U_1039),U_1041)
| U_1040 = relation_dom_restriction(U_1039,U_1041)
| ~ function(U_1039)
| ~ relation(U_1039)
| ~ function(U_1040)
| ~ relation(U_1040) ),
inference(clausify,[status(thm)],[f_286_3]) ).
cnf(f_286_7,plain,
( apply(U_1040,sK152(U_1041,U_1040,U_1039)) != apply(U_1039,sK152(U_1041,U_1040,U_1039))
| relation_dom(U_1040) != set_intersection2(relation_dom(U_1039),U_1041)
| U_1040 = relation_dom_restriction(U_1039,U_1041)
| ~ function(U_1039)
| ~ relation(U_1039)
| ~ function(U_1040)
| ~ relation(U_1040) ),
inference(clausify,[status(thm)],[f_286_3]) ).
fof(f_287_1,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(fof_nnf,[status(thm)],[t69_enumset1]) ).
fof(f_287_2,plain,
! [U_1042] : unordered_pair(U_1042,U_1042) = singleton(U_1042),
inference(variable_rename,[status(thm)],[f_287_1]) ).
cnf(f_287_3,plain,
unordered_pair(U_1042,U_1042) = singleton(U_1042),
inference(clausify,[status(thm)],[f_287_2]) ).
fof(f_288_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_288_2,plain,
! [U_1043] :
( U_1043 = empty_set
| ~ empty(U_1043) ),
inference(variable_rename,[status(thm)],[f_288_1]) ).
cnf(f_288_3,plain,
( U_1043 = empty_set
| ~ empty(U_1043) ),
inference(clausify,[status(thm)],[f_288_2]) ).
fof(f_289_1,plain,
! [A,B] :
( A = B
| ~ subset(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t6_zfmisc_1]) ).
fof(f_289_2,plain,
! [U_1045,U_1044] :
( U_1045 = U_1044
| ~ subset(singleton(U_1045),singleton(U_1044)) ),
inference(variable_rename,[status(thm)],[f_289_1]) ).
cnf(f_289_3,plain,
( U_1045 = U_1044
| ~ subset(singleton(U_1045),singleton(U_1044)) ),
inference(clausify,[status(thm)],[f_289_2]) ).
fof(f_290_1,plain,
! [A,B,C] :
( apply(relation_dom_restriction(C,A),B) = apply(C,B)
| ~ in(B,relation_dom(relation_dom_restriction(C,A)))
| ~ function(C)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t70_funct_1]) ).
fof(f_290_2,plain,
! [U_1048,U_1047,U_1046] :
( apply(relation_dom_restriction(U_1046,U_1048),U_1047) = apply(U_1046,U_1047)
| ~ in(U_1047,relation_dom(relation_dom_restriction(U_1046,U_1048)))
| ~ function(U_1046)
| ~ relation(U_1046) ),
inference(variable_rename,[status(thm)],[f_290_1]) ).
cnf(f_290_3,plain,
( apply(relation_dom_restriction(U_1046,U_1048),U_1047) = apply(U_1046,U_1047)
| ~ in(U_1047,relation_dom(relation_dom_restriction(U_1046,U_1048)))
| ~ function(U_1046)
| ~ relation(U_1046) ),
inference(clausify,[status(thm)],[f_290_2]) ).
fof(f_291_1,plain,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
inference(fof_nnf,[status(thm)],[t71_relat_1]) ).
fof(f_291_2,plain,
! [U_1049] :
( relation_rng(identity_relation(U_1049)) = U_1049
& relation_dom(identity_relation(U_1049)) = U_1049 ),
inference(variable_rename,[status(thm)],[f_291_1]) ).
fof(f_291_3,plain,
( ! [U_1051] : relation_rng(identity_relation(U_1051)) = U_1051
& ! [U_1050] : relation_dom(identity_relation(U_1050)) = U_1050 ),
inference(miniscope,[status(thm)],[f_291_2]) ).
cnf(f_291_4,plain,
relation_dom(identity_relation(U_1050)) = U_1050,
inference(clausify,[status(thm)],[f_291_3]) ).
cnf(f_291_5,plain,
relation_rng(identity_relation(U_1051)) = U_1051,
inference(clausify,[status(thm)],[f_291_3]) ).
fof(f_292_1,plain,
! [A,B,C] :
( apply(relation_dom_restriction(C,A),B) = apply(C,B)
| ~ in(B,A)
| ~ function(C)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t72_funct_1]) ).
fof(f_292_2,plain,
! [U_1054,U_1053,U_1052] :
( apply(relation_dom_restriction(U_1052,U_1054),U_1053) = apply(U_1052,U_1053)
| ~ in(U_1053,U_1054)
| ~ function(U_1052)
| ~ relation(U_1052) ),
inference(variable_rename,[status(thm)],[f_292_1]) ).
cnf(f_292_3,plain,
( apply(relation_dom_restriction(U_1052,U_1054),U_1053) = apply(U_1052,U_1053)
| ~ in(U_1053,U_1054)
| ~ function(U_1052)
| ~ relation(U_1052) ),
inference(clausify,[status(thm)],[f_292_2]) ).
fof(f_293_1,plain,
! [A,B,C,D] :
( ( ( in(ordered_pair(A,B),relation_composition(identity_relation(C),D))
| ~ in(ordered_pair(A,B),D)
| ~ in(A,C) )
& ( ( in(ordered_pair(A,B),D)
& in(A,C) )
| ~ in(ordered_pair(A,B),relation_composition(identity_relation(C),D)) ) )
| ~ relation(D) ),
inference(fof_nnf,[status(thm)],[t74_relat_1]) ).
fof(f_293_2,plain,
! [U_1058,U_1057,U_1056,U_1055] :
( ( ( in(ordered_pair(U_1058,U_1057),relation_composition(identity_relation(U_1056),U_1055))
| ~ in(ordered_pair(U_1058,U_1057),U_1055)
| ~ in(U_1058,U_1056) )
& ( ( in(ordered_pair(U_1058,U_1057),U_1055)
& in(U_1058,U_1056) )
| ~ in(ordered_pair(U_1058,U_1057),relation_composition(identity_relation(U_1056),U_1055)) ) )
| ~ relation(U_1055) ),
inference(variable_rename,[status(thm)],[f_293_1]) ).
cnf(f_293_3,plain,
( in(U_1058,U_1056)
| ~ in(ordered_pair(U_1058,U_1057),relation_composition(identity_relation(U_1056),U_1055))
| ~ relation(U_1055) ),
inference(clausify,[status(thm)],[f_293_2]) ).
cnf(f_293_4,plain,
( in(ordered_pair(U_1058,U_1057),U_1055)
| ~ in(ordered_pair(U_1058,U_1057),relation_composition(identity_relation(U_1056),U_1055))
| ~ relation(U_1055) ),
inference(clausify,[status(thm)],[f_293_2]) ).
cnf(f_293_5,plain,
( in(ordered_pair(U_1058,U_1057),relation_composition(identity_relation(U_1056),U_1055))
| ~ in(ordered_pair(U_1058,U_1057),U_1055)
| ~ in(U_1058,U_1056)
| ~ relation(U_1055) ),
inference(clausify,[status(thm)],[f_293_2]) ).
fof(f_294_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_294_2,plain,
! [U_1060,U_1059] :
( ~ empty(U_1059)
| ~ in(U_1060,U_1059) ),
inference(variable_rename,[status(thm)],[f_294_1]) ).
cnf(f_294_3,plain,
( ~ empty(U_1059)
| ~ in(U_1060,U_1059) ),
inference(clausify,[status(thm)],[f_294_2]) ).
fof(f_295_1,plain,
! [A,B] :
( ? [C] :
( ! [D] :
( ~ in(D,C)
| ~ in(D,B) )
& in(C,B) )
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_tarski]) ).
fof(f_295_2,plain,
! [U_1064,U_1063] :
( ? [U_1062] :
( ! [U_1061] :
( ~ in(U_1061,U_1062)
| ~ in(U_1061,U_1063) )
& in(U_1062,U_1063) )
| ~ in(U_1064,U_1063) ),
inference(variable_rename,[status(thm)],[f_295_1]) ).
fof(f_295_3,plain,
! [U_1064,U_1063] :
( ( ! [U_1061] :
( ~ in(U_1061,sK153(U_1064,U_1063))
| ~ in(U_1061,U_1063) )
& in(sK153(U_1064,U_1063),U_1063) )
| ~ in(U_1064,U_1063) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK153]),skolemize(U_1062,sK153(U_1064,U_1063))],[f_295_2]) ).
cnf(f_295_4,plain,
( in(sK153(U_1064,U_1063),U_1063)
| ~ in(U_1064,U_1063) ),
inference(clausify,[status(thm)],[f_295_3]) ).
cnf(f_295_5,plain,
( ~ in(U_1061,sK153(U_1064,U_1063))
| ~ in(U_1061,U_1063)
| ~ in(U_1064,U_1063) ),
inference(clausify,[status(thm)],[f_295_3]) ).
fof(f_296_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1]) ).
fof(f_296_2,plain,
! [U_1066,U_1065] : subset(U_1066,set_union2(U_1066,U_1065)),
inference(variable_rename,[status(thm)],[f_296_1]) ).
cnf(f_296_3,plain,
subset(U_1066,set_union2(U_1066,U_1065)),
inference(clausify,[status(thm)],[f_296_2]) ).
fof(f_297_1,plain,
! [A,B] :
( ( disjoint(A,B)
| set_difference(A,B) != A )
& ( set_difference(A,B) = A
| ~ disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t83_xboole_1]) ).
fof(f_297_2,plain,
! [U_1068,U_1067] :
( ( disjoint(U_1068,U_1067)
| set_difference(U_1068,U_1067) != U_1068 )
& ( set_difference(U_1068,U_1067) = U_1068
| ~ disjoint(U_1068,U_1067) ) ),
inference(variable_rename,[status(thm)],[f_297_1]) ).
fof(f_297_3,plain,
( ! [U_1072,U_1070] :
( disjoint(U_1072,U_1070)
| set_difference(U_1072,U_1070) != U_1072 )
& ! [U_1071,U_1069] :
( set_difference(U_1071,U_1069) = U_1071
| ~ disjoint(U_1071,U_1069) ) ),
inference(miniscope,[status(thm)],[f_297_2]) ).
cnf(f_297_4,plain,
( set_difference(U_1071,U_1069) = U_1071
| ~ disjoint(U_1071,U_1069) ),
inference(clausify,[status(thm)],[f_297_3]) ).
cnf(f_297_5,plain,
( disjoint(U_1072,U_1070)
| set_difference(U_1072,U_1070) != U_1072 ),
inference(clausify,[status(thm)],[f_297_3]) ).
fof(f_298_1,plain,
! [A,B,C] :
( ( ( in(A,relation_dom(relation_dom_restriction(C,B)))
| ~ in(A,relation_dom(C))
| ~ in(A,B) )
& ( ( in(A,relation_dom(C))
& in(A,B) )
| ~ in(A,relation_dom(relation_dom_restriction(C,B))) ) )
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t86_relat_1]) ).
fof(f_298_2,plain,
! [U_1075,U_1074,U_1073] :
( ( ( in(U_1075,relation_dom(relation_dom_restriction(U_1073,U_1074)))
| ~ in(U_1075,relation_dom(U_1073))
| ~ in(U_1075,U_1074) )
& ( ( in(U_1075,relation_dom(U_1073))
& in(U_1075,U_1074) )
| ~ in(U_1075,relation_dom(relation_dom_restriction(U_1073,U_1074))) ) )
| ~ relation(U_1073) ),
inference(variable_rename,[status(thm)],[f_298_1]) ).
cnf(f_298_3,plain,
( in(U_1075,U_1074)
| ~ in(U_1075,relation_dom(relation_dom_restriction(U_1073,U_1074)))
| ~ relation(U_1073) ),
inference(clausify,[status(thm)],[f_298_2]) ).
cnf(f_298_4,plain,
( in(U_1075,relation_dom(U_1073))
| ~ in(U_1075,relation_dom(relation_dom_restriction(U_1073,U_1074)))
| ~ relation(U_1073) ),
inference(clausify,[status(thm)],[f_298_2]) ).
cnf(f_298_5,plain,
( in(U_1075,relation_dom(relation_dom_restriction(U_1073,U_1074)))
| ~ in(U_1075,relation_dom(U_1073))
| ~ in(U_1075,U_1074)
| ~ relation(U_1073) ),
inference(clausify,[status(thm)],[f_298_2]) ).
fof(f_299_1,plain,
! [A,B] :
( subset(relation_dom_restriction(B,A),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t88_relat_1]) ).
fof(f_299_2,plain,
! [U_1077,U_1076] :
( subset(relation_dom_restriction(U_1076,U_1077),U_1076)
| ~ relation(U_1076) ),
inference(variable_rename,[status(thm)],[f_299_1]) ).
cnf(f_299_3,plain,
( subset(relation_dom_restriction(U_1076,U_1077),U_1076)
| ~ relation(U_1076) ),
inference(clausify,[status(thm)],[f_299_2]) ).
fof(f_300_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_300_2,plain,
! [U_1079,U_1078] :
( ~ empty(U_1078)
| U_1079 = U_1078
| ~ empty(U_1079) ),
inference(variable_rename,[status(thm)],[f_300_1]) ).
fof(f_300_3,plain,
! [U_1079] :
( ! [U_1078] :
( ~ empty(U_1078)
| U_1079 = U_1078 )
| ~ empty(U_1079) ),
inference(miniscope,[status(thm)],[f_300_2]) ).
cnf(f_300_4,plain,
( ~ empty(U_1078)
| U_1079 = U_1078
| ~ empty(U_1079) ),
inference(clausify,[status(thm)],[f_300_3]) ).
fof(f_301_1,plain,
! [A,B,C] :
( ( ( in(ordered_pair(A,B),C)
| B != apply(C,A)
| ~ in(A,relation_dom(C)) )
& ( ( B = apply(C,A)
& in(A,relation_dom(C)) )
| ~ in(ordered_pair(A,B),C) ) )
| ~ function(C)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t8_funct_1]) ).
fof(f_301_2,plain,
! [U_1082,U_1081,U_1080] :
( ( ( in(ordered_pair(U_1082,U_1081),U_1080)
| U_1081 != apply(U_1080,U_1082)
| ~ in(U_1082,relation_dom(U_1080)) )
& ( ( U_1081 = apply(U_1080,U_1082)
& in(U_1082,relation_dom(U_1080)) )
| ~ in(ordered_pair(U_1082,U_1081),U_1080) ) )
| ~ function(U_1080)
| ~ relation(U_1080) ),
inference(variable_rename,[status(thm)],[f_301_1]) ).
cnf(f_301_3,plain,
( in(U_1082,relation_dom(U_1080))
| ~ in(ordered_pair(U_1082,U_1081),U_1080)
| ~ function(U_1080)
| ~ relation(U_1080) ),
inference(clausify,[status(thm)],[f_301_2]) ).
cnf(f_301_4,plain,
( U_1081 = apply(U_1080,U_1082)
| ~ in(ordered_pair(U_1082,U_1081),U_1080)
| ~ function(U_1080)
| ~ relation(U_1080) ),
inference(clausify,[status(thm)],[f_301_2]) ).
cnf(f_301_5,plain,
( in(ordered_pair(U_1082,U_1081),U_1080)
| U_1081 != apply(U_1080,U_1082)
| ~ in(U_1082,relation_dom(U_1080))
| ~ function(U_1080)
| ~ relation(U_1080) ),
inference(clausify,[status(thm)],[f_301_2]) ).
fof(f_302_1,plain,
! [A] :
( ( ( well_orders(A,relation_field(A))
| ~ well_ordering(A) )
& ( well_ordering(A)
| ~ well_orders(A,relation_field(A)) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t8_wellord1]) ).
fof(f_302_2,plain,
! [U_1083] :
( ( ( well_orders(U_1083,relation_field(U_1083))
| ~ well_ordering(U_1083) )
& ( well_ordering(U_1083)
| ~ well_orders(U_1083,relation_field(U_1083)) ) )
| ~ relation(U_1083) ),
inference(variable_rename,[status(thm)],[f_302_1]) ).
cnf(f_302_3,plain,
( well_ordering(U_1083)
| ~ well_orders(U_1083,relation_field(U_1083))
| ~ relation(U_1083) ),
inference(clausify,[status(thm)],[f_302_2]) ).
cnf(f_302_4,plain,
( well_orders(U_1083,relation_field(U_1083))
| ~ well_ordering(U_1083)
| ~ relation(U_1083) ),
inference(clausify,[status(thm)],[f_302_2]) ).
fof(f_303_1,plain,
! [A,B,C] :
( subset(set_union2(A,C),B)
| ~ subset(C,B)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t8_xboole_1]) ).
fof(f_303_2,plain,
! [U_1086,U_1085,U_1084] :
( subset(set_union2(U_1086,U_1084),U_1085)
| ~ subset(U_1084,U_1085)
| ~ subset(U_1086,U_1085) ),
inference(variable_rename,[status(thm)],[f_303_1]) ).
cnf(f_303_3,plain,
( subset(set_union2(U_1086,U_1084),U_1085)
| ~ subset(U_1084,U_1085)
| ~ subset(U_1086,U_1085) ),
inference(clausify,[status(thm)],[f_303_2]) ).
fof(f_304_1,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t8_zfmisc_1]) ).
fof(f_304_2,plain,
! [U_1089,U_1088,U_1087] :
( U_1089 = U_1088
| singleton(U_1089) != unordered_pair(U_1088,U_1087) ),
inference(variable_rename,[status(thm)],[f_304_1]) ).
fof(f_304_3,plain,
! [U_1089,U_1088] :
( ! [U_1087] : singleton(U_1089) != unordered_pair(U_1088,U_1087)
| U_1089 = U_1088 ),
inference(miniscope,[status(thm)],[f_304_2]) ).
cnf(f_304_4,plain,
( singleton(U_1089) != unordered_pair(U_1088,U_1087)
| U_1089 = U_1088 ),
inference(clausify,[status(thm)],[f_304_3]) ).
fof(f_305_1,plain,
! [A,B] :
( relation_dom(relation_dom_restriction(B,A)) = set_intersection2(relation_dom(B),A)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t90_relat_1]) ).
fof(f_305_2,plain,
! [U_1091,U_1090] :
( relation_dom(relation_dom_restriction(U_1090,U_1091)) = set_intersection2(relation_dom(U_1090),U_1091)
| ~ relation(U_1090) ),
inference(variable_rename,[status(thm)],[f_305_1]) ).
cnf(f_305_3,plain,
( relation_dom(relation_dom_restriction(U_1090,U_1091)) = set_intersection2(relation_dom(U_1090),U_1091)
| ~ relation(U_1090) ),
inference(clausify,[status(thm)],[f_305_2]) ).
fof(f_306_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t92_zfmisc_1]) ).
fof(f_306_2,plain,
! [U_1093,U_1092] :
( subset(U_1093,union(U_1092))
| ~ in(U_1093,U_1092) ),
inference(variable_rename,[status(thm)],[f_306_1]) ).
cnf(f_306_3,plain,
( subset(U_1093,union(U_1092))
| ~ in(U_1093,U_1092) ),
inference(clausify,[status(thm)],[f_306_2]) ).
fof(f_307_1,plain,
! [A,B] :
( relation_dom_restriction(B,A) = relation_composition(identity_relation(A),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t94_relat_1]) ).
fof(f_307_2,plain,
! [U_1095,U_1094] :
( relation_dom_restriction(U_1094,U_1095) = relation_composition(identity_relation(U_1095),U_1094)
| ~ relation(U_1094) ),
inference(variable_rename,[status(thm)],[f_307_1]) ).
cnf(f_307_3,plain,
( relation_dom_restriction(U_1094,U_1095) = relation_composition(identity_relation(U_1095),U_1094)
| ~ relation(U_1094) ),
inference(clausify,[status(thm)],[f_307_2]) ).
fof(f_308_1,plain,
! [A,B] :
( subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t99_relat_1]) ).
fof(f_308_2,plain,
! [U_1097,U_1096] :
( subset(relation_rng(relation_dom_restriction(U_1096,U_1097)),relation_rng(U_1096))
| ~ relation(U_1096) ),
inference(variable_rename,[status(thm)],[f_308_1]) ).
cnf(f_308_3,plain,
( subset(relation_rng(relation_dom_restriction(U_1096,U_1097)),relation_rng(U_1096))
| ~ relation(U_1096) ),
inference(clausify,[status(thm)],[f_308_2]) ).
fof(f_309_1,plain,
! [A] : union(powerset(A)) = A,
inference(fof_nnf,[status(thm)],[t99_zfmisc_1]) ).
fof(f_309_2,plain,
! [U_1098] : union(powerset(U_1098)) = U_1098,
inference(variable_rename,[status(thm)],[f_309_1]) ).
cnf(f_309_3,plain,
union(powerset(U_1098)) = U_1098,
inference(clausify,[status(thm)],[f_309_2]) ).
fof(f_310_1,plain,
! [A] :
? [B] :
( ! [C] :
( in(C,B)
| are_equipotent(C,B)
| ~ subset(C,B) )
& ! [C] :
( ? [D] :
( ! [E] :
( in(E,D)
| ~ subset(E,C) )
& in(D,B) )
| ~ in(C,B) )
& ! [C,D] :
( in(D,B)
| ~ subset(D,C)
| ~ in(C,B) )
& in(A,B) ),
inference(fof_nnf,[status(thm)],[t9_tarski]) ).
fof(f_310_2,plain,
! [U_1106] :
? [U_1105] :
( ! [U_1104] :
( in(U_1104,U_1105)
| are_equipotent(U_1104,U_1105)
| ~ subset(U_1104,U_1105) )
& ! [U_1103] :
( ? [U_1102] :
( ! [U_1101] :
( in(U_1101,U_1102)
| ~ subset(U_1101,U_1103) )
& in(U_1102,U_1105) )
| ~ in(U_1103,U_1105) )
& ! [U_1100,U_1099] :
( in(U_1099,U_1105)
| ~ subset(U_1099,U_1100)
| ~ in(U_1100,U_1105) )
& in(U_1106,U_1105) ),
inference(variable_rename,[status(thm)],[f_310_1]) ).
fof(f_310_3,plain,
! [U_1106] :
( ! [U_1104] :
( in(U_1104,sK154(U_1106))
| are_equipotent(U_1104,sK154(U_1106))
| ~ subset(U_1104,sK154(U_1106)) )
& ! [U_1103] :
( ? [U_1102] :
( ! [U_1101] :
( in(U_1101,U_1102)
| ~ subset(U_1101,U_1103) )
& in(U_1102,sK154(U_1106)) )
| ~ in(U_1103,sK154(U_1106)) )
& ! [U_1100,U_1099] :
( in(U_1099,sK154(U_1106))
| ~ subset(U_1099,U_1100)
| ~ in(U_1100,sK154(U_1106)) )
& in(U_1106,sK154(U_1106)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK154]),skolemize(U_1105,sK154(U_1106))],[f_310_2]) ).
fof(f_310_4,plain,
! [U_1106] :
( ! [U_1104] :
( in(U_1104,sK154(U_1106))
| are_equipotent(U_1104,sK154(U_1106))
| ~ subset(U_1104,sK154(U_1106)) )
& ! [U_1103] :
( ( ! [U_1101] :
( in(U_1101,sK155(U_1106,U_1103))
| ~ subset(U_1101,U_1103) )
& in(sK155(U_1106,U_1103),sK154(U_1106)) )
| ~ in(U_1103,sK154(U_1106)) )
& ! [U_1100,U_1099] :
( in(U_1099,sK154(U_1106))
| ~ subset(U_1099,U_1100)
| ~ in(U_1100,sK154(U_1106)) )
& in(U_1106,sK154(U_1106)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK155]),skolemize(U_1102,sK155(U_1106,U_1103))],[f_310_3]) ).
cnf(f_310_5,plain,
in(U_1106,sK154(U_1106)),
inference(clausify,[status(thm)],[f_310_4]) ).
cnf(f_310_6,plain,
( in(U_1099,sK154(U_1106))
| ~ subset(U_1099,U_1100)
| ~ in(U_1100,sK154(U_1106)) ),
inference(clausify,[status(thm)],[f_310_4]) ).
cnf(f_310_7,plain,
( in(sK155(U_1106,U_1103),sK154(U_1106))
| ~ in(U_1103,sK154(U_1106)) ),
inference(clausify,[status(thm)],[f_310_4]) ).
cnf(f_310_8,plain,
( in(U_1101,sK155(U_1106,U_1103))
| ~ subset(U_1101,U_1103)
| ~ in(U_1103,sK154(U_1106)) ),
inference(clausify,[status(thm)],[f_310_4]) ).
cnf(f_310_9,plain,
( in(U_1104,sK154(U_1106))
| are_equipotent(U_1104,sK154(U_1106))
| ~ subset(U_1104,sK154(U_1106)) ),
inference(clausify,[status(thm)],[f_310_4]) ).
fof(f_311_1,plain,
! [A,B,C] :
( B = C
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t9_zfmisc_1]) ).
fof(f_311_2,plain,
! [U_1109,U_1108,U_1107] :
( U_1108 = U_1107
| singleton(U_1109) != unordered_pair(U_1108,U_1107) ),
inference(variable_rename,[status(thm)],[f_311_1]) ).
cnf(f_311_3,plain,
( U_1108 = U_1107
| singleton(U_1109) != unordered_pair(U_1108,U_1107) ),
inference(clausify,[status(thm)],[f_311_2]) ).
cnf(f_6_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_3]) ).
cnf(f_6_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_4]) ).
cnf(f_67_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_67_8]) ).
cnf(f_67_9_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_67_9]) ).
cnf(f_71_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_71_2]) ).
cnf(f_72_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_72_2]) ).
cnf(f_73_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_73_2]) ).
cnf(f_74_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_74_2]) ).
cnf(f_75_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_75_2]) ).
cnf(f_76_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_76_2]) ).
cnf(f_77_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_77_2]) ).
cnf(f_78_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_78_2]) ).
cnf(f_79_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_79_2]) ).
cnf(f_80_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_80_2]) ).
cnf(f_82_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_82_2]) ).
cnf(f_84_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_84_2]) ).
cnf(f_86_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_86_2]) ).
cnf(f_87_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_87_2]) ).
cnf(f_88_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_88_2]) ).
cnf(f_90_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_90_2]) ).
cnf(f_91_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_91_2]) ).
cnf(f_93_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_93_2]) ).
cnf(f_94_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_94_2]) ).
cnf(f_103_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_103_2]) ).
cnf(f_104_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_104_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( unordered_pair(Eq_x_0,Eq_x_1) = unordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( set_union2(Eq_x_0,Eq_x_1) = set_union2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( set_intersection2(Eq_x_0,Eq_x_1) = set_intersection2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( identity_relation(Eq_x_0) = identity_relation(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( ordered_pair(Eq_x_0,Eq_x_1) = ordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( relation_dom_restriction(Eq_x_0,Eq_x_1) = relation_dom_restriction(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( relation_image(Eq_x_0,Eq_x_1) = relation_image(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( apply(Eq_x_0,Eq_x_1) = apply(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( relation_rng_restriction(Eq_x_0,Eq_x_1) = relation_rng_restriction(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( relation_field(Eq_x_0) = relation_field(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( relation_inverse_image(Eq_x_0,Eq_x_1) = relation_inverse_image(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( unordered_triple(Eq_x_0,Eq_x_1,Eq_x_2) = unordered_triple(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( succ(Eq_x_0) = succ(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( set_meet(Eq_x_0) = set_meet(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( fiber(Eq_x_0,Eq_x_1) = fiber(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( cartesian_product2(Eq_x_0,Eq_x_1) = cartesian_product2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( cast_to_subset(Eq_x_0) = cast_to_subset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,axiom,
( union(Eq_x_0) = union(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( set_difference(Eq_x_0,Eq_x_1) = set_difference(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,axiom,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_27,axiom,
( subset_complement(Eq_x_0,Eq_x_1) = subset_complement(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,axiom,
( relation_restriction(Eq_x_0,Eq_x_1) = relation_restriction(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_29,axiom,
( relation_inverse(Eq_x_0) = relation_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_30,axiom,
( relation_composition(Eq_x_0,Eq_x_1) = relation_composition(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_31,axiom,
( complements_of_subsets(Eq_x_0,Eq_x_1) = complements_of_subsets(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_32,axiom,
( function_inverse(Eq_x_0) = function_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,axiom,
( union_of_subsets(Eq_x_0,Eq_x_1) = union_of_subsets(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_34,axiom,
( meet_of_subsets(Eq_x_0,Eq_x_1) = meet_of_subsets(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_35,axiom,
( subset_difference(Eq_x_0,Eq_x_1,Eq_x_2) = subset_difference(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_36,axiom,
( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_37,axiom,
( sK2(Eq_x_0,Eq_x_1) = sK2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_38,axiom,
( sK3(Eq_x_0,Eq_x_1) = sK3(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,axiom,
( sK4(Eq_x_0,Eq_x_1) = sK4(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_40,axiom,
( sK5(Eq_x_0,Eq_x_1,Eq_x_2) = sK5(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_41,axiom,
( sK6(Eq_x_0,Eq_x_1,Eq_x_2) = sK6(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_42,axiom,
( sK7(Eq_x_0,Eq_x_1,Eq_x_2) = sK7(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_43,axiom,
( sK8(Eq_x_0,Eq_x_1,Eq_x_2) = sK8(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_44,axiom,
( sK9(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK9(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_45,axiom,
( sK10(Eq_x_0,Eq_x_1,Eq_x_2) = sK10(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_46,axiom,
( sK11(Eq_x_0,Eq_x_1,Eq_x_2) = sK11(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_47,axiom,
( sK12(Eq_x_0,Eq_x_1,Eq_x_2) = sK12(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_48,axiom,
( sK13(Eq_x_0,Eq_x_1,Eq_x_2) = sK13(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_49,axiom,
( sK14(Eq_x_0,Eq_x_1,Eq_x_2) = sK14(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_50,axiom,
( sK15(Eq_x_0,Eq_x_1,Eq_x_2) = sK15(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_51,axiom,
( sK16(Eq_x_0,Eq_x_1,Eq_x_2) = sK16(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_52,axiom,
( sK17(Eq_x_0,Eq_x_1,Eq_x_2) = sK17(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_53,axiom,
( sK18(Eq_x_0,Eq_x_1,Eq_x_2) = sK18(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_54,axiom,
( sK19(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK19(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_55,axiom,
( sK20(Eq_x_0,Eq_x_1,Eq_x_2) = sK20(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_56,axiom,
( sK21(Eq_x_0,Eq_x_1,Eq_x_2) = sK21(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_57,axiom,
( sK22(Eq_x_0,Eq_x_1,Eq_x_2) = sK22(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_58,axiom,
( sK23(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK23(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_59,axiom,
( sK24(Eq_x_0,Eq_x_1,Eq_x_2) = sK24(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_60,axiom,
( sK25(Eq_x_0,Eq_x_1,Eq_x_2) = sK25(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_61,axiom,
( sK26(Eq_x_0,Eq_x_1,Eq_x_2) = sK26(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_62,axiom,
( sK27(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK27(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_63,axiom,
( sK28(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK28(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_64,axiom,
( sK29(Eq_x_0,Eq_x_1) = sK29(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_65,axiom,
( sK30(Eq_x_0,Eq_x_1) = sK30(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_66,axiom,
( sK31(Eq_x_0) = sK31(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_67,axiom,
( sK32(Eq_x_0,Eq_x_1) = sK32(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_68,axiom,
( sK33(Eq_x_0,Eq_x_1,Eq_x_2) = sK33(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_69,axiom,
( sK34(Eq_x_0,Eq_x_1) = sK34(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_70,axiom,
( sK35(Eq_x_0,Eq_x_1) = sK35(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_71,axiom,
( sK36(Eq_x_0,Eq_x_1) = sK36(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_72,axiom,
( sK37(Eq_x_0,Eq_x_1) = sK37(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_73,axiom,
( sK38(Eq_x_0,Eq_x_1) = sK38(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_74,axiom,
( sK39(Eq_x_0,Eq_x_1,Eq_x_2) = sK39(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_75,axiom,
( sK40(Eq_x_0,Eq_x_1,Eq_x_2) = sK40(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_76,axiom,
( sK41(Eq_x_0) = sK41(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_77,axiom,
( sK42(Eq_x_0,Eq_x_1) = sK42(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_78,axiom,
( sK43(Eq_x_0,Eq_x_1) = sK43(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_79,axiom,
( sK44(Eq_x_0) = sK44(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_80,axiom,
( sK45(Eq_x_0,Eq_x_1) = sK45(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_81,axiom,
( sK46(Eq_x_0,Eq_x_1) = sK46(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_82,axiom,
( sK47(Eq_x_0,Eq_x_1) = sK47(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_83,axiom,
( sK48(Eq_x_0,Eq_x_1) = sK48(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_84,axiom,
( sK49(Eq_x_0,Eq_x_1,Eq_x_2) = sK49(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_85,axiom,
( sK50(Eq_x_0,Eq_x_1,Eq_x_2) = sK50(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_86,axiom,
( sK51(Eq_x_0,Eq_x_1) = sK51(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_87,axiom,
( sK52(Eq_x_0) = sK52(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_88,axiom,
( sK53(Eq_x_0,Eq_x_1,Eq_x_2) = sK53(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_89,axiom,
( sK54(Eq_x_0,Eq_x_1,Eq_x_2) = sK54(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_90,axiom,
( sK55(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK55(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_91,axiom,
( sK56(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK56(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_92,axiom,
( sK57(Eq_x_0,Eq_x_1,Eq_x_2) = sK57(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_93,axiom,
( sK58(Eq_x_0,Eq_x_1,Eq_x_2) = sK58(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_94,axiom,
( sK59(Eq_x_0,Eq_x_1,Eq_x_2) = sK59(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_95,axiom,
( sK60(Eq_x_0,Eq_x_1,Eq_x_2) = sK60(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_96,axiom,
( sK61(Eq_x_0) = sK61(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_97,axiom,
( sK62(Eq_x_0) = sK62(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_98,axiom,
( sK63(Eq_x_0,Eq_x_1) = sK63(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_99,axiom,
( sK64(Eq_x_0,Eq_x_1) = sK64(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_100,axiom,
( sK65(Eq_x_0,Eq_x_1) = sK65(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_101,axiom,
( sK66(Eq_x_0,Eq_x_1,Eq_x_2) = sK66(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_102,axiom,
( sK67(Eq_x_0,Eq_x_1) = sK67(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_103,axiom,
( sK68(Eq_x_0,Eq_x_1,Eq_x_2) = sK68(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_104,axiom,
( sK69(Eq_x_0,Eq_x_1,Eq_x_2) = sK69(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_105,axiom,
( sK70(Eq_x_0,Eq_x_1,Eq_x_2) = sK70(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_106,axiom,
( sK71(Eq_x_0,Eq_x_1) = sK71(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_107,axiom,
( sK72(Eq_x_0,Eq_x_1) = sK72(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_108,axiom,
( sK73(Eq_x_0,Eq_x_1) = sK73(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_109,axiom,
( sK74(Eq_x_0,Eq_x_1) = sK74(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_110,axiom,
( sK75(Eq_x_0,Eq_x_1) = sK75(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_111,axiom,
( sK76(Eq_x_0,Eq_x_1,Eq_x_2) = sK76(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_112,axiom,
( sK77(Eq_x_0,Eq_x_1) = sK77(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_113,axiom,
( sK78(Eq_x_0,Eq_x_1) = sK78(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_114,axiom,
( sK79(Eq_x_0,Eq_x_1) = sK79(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_115,axiom,
( sK80(Eq_x_0,Eq_x_1,Eq_x_2) = sK80(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_116,axiom,
( sK81(Eq_x_0,Eq_x_1,Eq_x_2) = sK81(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_117,axiom,
( sK82(Eq_x_0,Eq_x_1,Eq_x_2) = sK82(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_118,axiom,
( sK83(Eq_x_0,Eq_x_1) = sK83(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_119,axiom,
( sK84(Eq_x_0,Eq_x_1) = sK84(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_120,axiom,
( sK85(Eq_x_0,Eq_x_1) = sK85(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_121,axiom,
( sK86(Eq_x_0,Eq_x_1,Eq_x_2) = sK86(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_122,axiom,
( sK87(Eq_x_0,Eq_x_1) = sK87(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_123,axiom,
( sK88(Eq_x_0,Eq_x_1) = sK88(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_124,axiom,
( sK89(Eq_x_0,Eq_x_1) = sK89(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_125,axiom,
( sK90(Eq_x_0,Eq_x_1) = sK90(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_126,axiom,
( sK91(Eq_x_0,Eq_x_1) = sK91(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_127,axiom,
( sK92(Eq_x_0,Eq_x_1) = sK92(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_128,axiom,
( sK93(Eq_x_0,Eq_x_1) = sK93(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_129,axiom,
( sK94(Eq_x_0,Eq_x_1) = sK94(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_130,axiom,
( sK95(Eq_x_0,Eq_x_1) = sK95(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_131,axiom,
( sK96(Eq_x_0) = sK96(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_132,axiom,
( sK97(Eq_x_0) = sK97(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_133,axiom,
( sK98(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK98(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_134,axiom,
( sK99(Eq_x_0,Eq_x_1,Eq_x_2) = sK99(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_135,axiom,
( sK100(Eq_x_0,Eq_x_1,Eq_x_2) = sK100(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_136,axiom,
( sK101(Eq_x_0,Eq_x_1,Eq_x_2) = sK101(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_137,axiom,
( sK102(Eq_x_0,Eq_x_1,Eq_x_2) = sK102(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_138,axiom,
( sK103(Eq_x_0,Eq_x_1,Eq_x_2) = sK103(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_139,axiom,
( sK104(Eq_x_0,Eq_x_1) = sK104(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_140,axiom,
( sK105(Eq_x_0,Eq_x_1) = sK105(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_141,axiom,
( sK106(Eq_x_0,Eq_x_1) = sK106(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_142,axiom,
( sK107(Eq_x_0,Eq_x_1,Eq_x_2) = sK107(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_143,axiom,
( sK108(Eq_x_0) = sK108(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_144,axiom,
( sK109(Eq_x_0) = sK109(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_145,axiom,
( sK110(Eq_x_0) = sK110(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_146,axiom,
( sK111(Eq_x_0) = sK111(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_147,axiom,
( sK112(Eq_x_0) = sK112(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_148,axiom,
( sK113(Eq_x_0) = sK113(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_149,axiom,
( sK114(Eq_x_0) = sK114(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_150,axiom,
( sK115(Eq_x_0) = sK115(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_151,axiom,
( sK116(Eq_x_0) = sK116(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_152,axiom,
( sK117(Eq_x_0,Eq_x_1) = sK117(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_153,axiom,
( sK121(Eq_x_0) = sK121(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_154,axiom,
( sK126(Eq_x_0) = sK126(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_155,axiom,
( sK132(Eq_x_0) = sK132(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_156,axiom,
( sK133(Eq_x_0,Eq_x_1,Eq_x_2) = sK133(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_157,axiom,
( sK134(Eq_x_0,Eq_x_1,Eq_x_2) = sK134(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_158,axiom,
( sK137(Eq_x_0,Eq_x_1) = sK137(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_159,axiom,
( sK138(Eq_x_0,Eq_x_1) = sK138(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_160,axiom,
( sK139(Eq_x_0) = sK139(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_161,axiom,
( sK140(Eq_x_0,Eq_x_1) = sK140(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_162,axiom,
( sK141(Eq_x_0,Eq_x_1) = sK141(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_163,axiom,
( sK142(Eq_x_0,Eq_x_1) = sK142(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_164,axiom,
( sK143(Eq_x_0) = sK143(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_165,axiom,
( sK144(Eq_x_0) = sK144(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_166,axiom,
( sK145(Eq_x_0,Eq_x_1) = sK145(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_167,axiom,
( sK146(Eq_x_0,Eq_x_1) = sK146(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_168,axiom,
( sK147(Eq_x_0,Eq_x_1) = sK147(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_169,axiom,
( sK148(Eq_x_0,Eq_x_1) = sK148(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_170,axiom,
( sK149(Eq_x_0,Eq_x_1) = sK149(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_171,axiom,
( sK150(Eq_x_0) = sK150(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_172,axiom,
( sK151(Eq_x_0) = sK151(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_173,axiom,
( sK152(Eq_x_0,Eq_x_1,Eq_x_2) = sK152(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_174,axiom,
( sK153(Eq_x_0,Eq_x_1) = sK153(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_175,axiom,
( sK154(Eq_x_0) = sK154(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_176,axiom,
( sK155(Eq_x_0,Eq_x_1) = sK155(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_177,axiom,
( in(Eq_y_0,Eq_y_1)
| ~ in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_178,axiom,
( proper_subset(Eq_y_0,Eq_y_1)
| ~ proper_subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_179,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_180,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_181,axiom,
( ordinal(Eq_y_0)
| ~ ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_182,axiom,
( epsilon_transitive(Eq_y_0)
| ~ epsilon_transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_183,axiom,
( epsilon_connected(Eq_y_0)
| ~ epsilon_connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_184,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_185,axiom,
( one_to_one(Eq_y_0)
| ~ one_to_one(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_186,axiom,
( ordinal_subset(Eq_y_0,Eq_y_1)
| ~ ordinal_subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_187,axiom,
( subset(Eq_y_0,Eq_y_1)
| ~ subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_188,axiom,
( antisymmetric(Eq_y_0)
| ~ antisymmetric(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_189,axiom,
( is_antisymmetric_in(Eq_y_0,Eq_y_1)
| ~ is_antisymmetric_in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_190,axiom,
( connected(Eq_y_0)
| ~ connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_191,axiom,
( is_connected_in(Eq_y_0,Eq_y_1)
| ~ is_connected_in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_192,axiom,
( transitive(Eq_y_0)
| ~ transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_193,axiom,
( is_transitive_in(Eq_y_0,Eq_y_1)
| ~ is_transitive_in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_194,axiom,
( is_reflexive_in(Eq_y_0,Eq_y_1)
| ~ is_reflexive_in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_195,axiom,
( element(Eq_y_0,Eq_y_1)
| ~ element(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_196,axiom,
( well_founded_relation(Eq_y_0)
| ~ well_founded_relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_197,axiom,
( disjoint(Eq_y_0,Eq_y_1)
| ~ disjoint(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_198,axiom,
( is_well_founded_in(Eq_y_0,Eq_y_1)
| ~ is_well_founded_in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_199,axiom,
( well_ordering(Eq_y_0)
| ~ well_ordering(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_200,axiom,
( reflexive(Eq_y_0)
| ~ reflexive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_201,axiom,
( well_orders(Eq_y_0,Eq_y_1)
| ~ well_orders(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_202,axiom,
( being_limit_ordinal(Eq_y_0)
| ~ being_limit_ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_203,axiom,
( relation_empty_yielding(Eq_y_0)
| ~ relation_empty_yielding(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_204,axiom,
( are_equipotent(Eq_y_0,Eq_y_1)
| ~ are_equipotent(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU252+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n006.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Sat Sep 19 23:40:57 UTC 2026
% 0.11/0.36 % CPUTime :
% 165.16/165.46 % SZS status Theorem for theBenchmark
% 165.16/165.46 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------