%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU241+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 : n026.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 08:58:39 AM UTC 2026
% Result : Theorem 264.21s 264.51s
% Output : Proof 264.42s
% 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(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_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_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_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_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(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(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_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_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_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(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,conjecture,
! [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_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(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_xboole_1,lemma,
! [A,B] : subset(set_intersection2(A,B),A),
file('theBenchmark.p',t17_xboole_1) ).
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(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(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(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(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_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] :
( ( ( 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_22_2,plain,
! [U_133] :
( ( ( transitive(U_133)
| ~ is_transitive_in(U_133,relation_field(U_133)) )
& ( is_transitive_in(U_133,relation_field(U_133))
| ~ transitive(U_133) ) )
| ~ relation(U_133) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( is_transitive_in(U_133,relation_field(U_133))
| ~ transitive(U_133)
| ~ relation(U_133) ),
inference(clausify,[status(thm)],[f_22_2]) ).
cnf(f_22_4,plain,
( transitive(U_133)
| ~ is_transitive_in(U_133,relation_field(U_133))
| ~ relation(U_133) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_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_23_2,plain,
! [U_139,U_138,U_137,U_136] :
( ( U_136 = unordered_triple(U_139,U_138,U_137)
| ? [U_135] :
( ( ~ in(U_135,U_136)
& ( U_135 = U_137
| U_135 = U_138
| U_135 = U_139 ) )
| ( U_135 != U_137
& U_135 != U_138
& U_135 != U_139
& in(U_135,U_136) ) ) )
& ( ! [U_134] :
( ( in(U_134,U_136)
| ( U_134 != U_137
& U_134 != U_138
& U_134 != U_139 ) )
& ( U_134 = U_137
| U_134 = U_138
| U_134 = U_139
| ~ in(U_134,U_136) ) )
| U_136 != unordered_triple(U_139,U_138,U_137) ) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( ! [U_151,U_149,U_147,U_145] :
( U_145 = unordered_triple(U_151,U_149,U_147)
| ? [U_143] :
( ~ in(U_143,U_145)
& ( U_143 = U_147
| U_143 = U_149
| U_143 = U_151 ) )
| ? [U_142] :
( U_142 != U_147
& U_142 != U_149
& U_142 != U_151
& in(U_142,U_145) ) )
& ! [U_150,U_148,U_146,U_144] :
( ( ! [U_141] :
( in(U_141,U_144)
| ( U_141 != U_146
& U_141 != U_148
& U_141 != U_150 ) )
& ! [U_140] :
( U_140 = U_146
| U_140 = U_148
| U_140 = U_150
| ~ in(U_140,U_144) ) )
| U_144 != unordered_triple(U_150,U_148,U_146) ) ),
inference(miniscope,[status(thm)],[f_23_2]) ).
fof(f_23_4,plain,
( ! [U_151,U_149,U_147,U_145] :
( U_145 = unordered_triple(U_151,U_149,U_147)
| ? [U_143] :
( ~ in(U_143,U_145)
& ( U_143 = U_147
| U_143 = U_149
| U_143 = U_151 ) )
| ( sK27(U_151,U_149,U_147,U_145) != U_147
& sK27(U_151,U_149,U_147,U_145) != U_149
& sK27(U_151,U_149,U_147,U_145) != U_151
& in(sK27(U_151,U_149,U_147,U_145),U_145) ) )
& ! [U_150,U_148,U_146,U_144] :
( ( ! [U_141] :
( in(U_141,U_144)
| ( U_141 != U_146
& U_141 != U_148
& U_141 != U_150 ) )
& ! [U_140] :
( U_140 = U_146
| U_140 = U_148
| U_140 = U_150
| ~ in(U_140,U_144) ) )
| U_144 != unordered_triple(U_150,U_148,U_146) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_142,sK27(U_151,U_149,U_147,U_145))],[f_23_3]) ).
fof(f_23_5,plain,
( ! [U_151,U_149,U_147,U_145] :
( U_145 = unordered_triple(U_151,U_149,U_147)
| ( ~ in(sK28(U_151,U_149,U_147,U_145),U_145)
& ( sK28(U_151,U_149,U_147,U_145) = U_147
| sK28(U_151,U_149,U_147,U_145) = U_149
| sK28(U_151,U_149,U_147,U_145) = U_151 ) )
| ( sK27(U_151,U_149,U_147,U_145) != U_147
& sK27(U_151,U_149,U_147,U_145) != U_149
& sK27(U_151,U_149,U_147,U_145) != U_151
& in(sK27(U_151,U_149,U_147,U_145),U_145) ) )
& ! [U_150,U_148,U_146,U_144] :
( ( ! [U_141] :
( in(U_141,U_144)
| ( U_141 != U_146
& U_141 != U_148
& U_141 != U_150 ) )
& ! [U_140] :
( U_140 = U_146
| U_140 = U_148
| U_140 = U_150
| ~ in(U_140,U_144) ) )
| U_144 != unordered_triple(U_150,U_148,U_146) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_143,sK28(U_151,U_149,U_147,U_145))],[f_23_4]) ).
cnf(f_23_6,plain,
( U_140 = U_146
| U_140 = U_148
| U_140 = U_150
| ~ in(U_140,U_144)
| U_144 != unordered_triple(U_150,U_148,U_146) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_7,plain,
( U_141 != U_150
| in(U_141,U_144)
| U_144 != unordered_triple(U_150,U_148,U_146) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_8,plain,
( U_141 != U_148
| in(U_141,U_144)
| U_144 != unordered_triple(U_150,U_148,U_146) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_9,plain,
( U_141 != U_146
| in(U_141,U_144)
| U_144 != unordered_triple(U_150,U_148,U_146) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_10,plain,
( sK28(U_151,U_149,U_147,U_145) = U_147
| sK28(U_151,U_149,U_147,U_145) = U_149
| sK28(U_151,U_149,U_147,U_145) = U_151
| in(sK27(U_151,U_149,U_147,U_145),U_145)
| U_145 = unordered_triple(U_151,U_149,U_147) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_11,plain,
( ~ in(sK28(U_151,U_149,U_147,U_145),U_145)
| in(sK27(U_151,U_149,U_147,U_145),U_145)
| U_145 = unordered_triple(U_151,U_149,U_147) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_12,plain,
( sK27(U_151,U_149,U_147,U_145) != U_151
| sK28(U_151,U_149,U_147,U_145) = U_147
| sK28(U_151,U_149,U_147,U_145) = U_149
| sK28(U_151,U_149,U_147,U_145) = U_151
| U_145 = unordered_triple(U_151,U_149,U_147) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_13,plain,
( sK27(U_151,U_149,U_147,U_145) != U_149
| sK28(U_151,U_149,U_147,U_145) = U_147
| sK28(U_151,U_149,U_147,U_145) = U_149
| sK28(U_151,U_149,U_147,U_145) = U_151
| U_145 = unordered_triple(U_151,U_149,U_147) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_14,plain,
( sK27(U_151,U_149,U_147,U_145) != U_147
| sK28(U_151,U_149,U_147,U_145) = U_147
| sK28(U_151,U_149,U_147,U_145) = U_149
| sK28(U_151,U_149,U_147,U_145) = U_151
| U_145 = unordered_triple(U_151,U_149,U_147) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_15,plain,
( sK27(U_151,U_149,U_147,U_145) != U_151
| ~ in(sK28(U_151,U_149,U_147,U_145),U_145)
| U_145 = unordered_triple(U_151,U_149,U_147) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_16,plain,
( sK27(U_151,U_149,U_147,U_145) != U_149
| ~ in(sK28(U_151,U_149,U_147,U_145),U_145)
| U_145 = unordered_triple(U_151,U_149,U_147) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_17,plain,
( sK27(U_151,U_149,U_147,U_145) != U_147
| ~ in(sK28(U_151,U_149,U_147,U_145),U_145)
| U_145 = unordered_triple(U_151,U_149,U_147) ),
inference(clausify,[status(thm)],[f_23_5]) ).
fof(f_24_1,plain,
! [A] : succ(A) = set_union2(A,singleton(A)),
inference(fof_nnf,[status(thm)],[d1_ordinal1]) ).
fof(f_24_2,plain,
! [U_152] : succ(U_152) = set_union2(U_152,singleton(U_152)),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
succ(U_152) = set_union2(U_152,singleton(U_152)),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_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_25_2,plain,
! [U_159] :
( ( relation(U_159)
| ? [U_158] :
( ! [U_157,U_156] : U_158 != ordered_pair(U_157,U_156)
& in(U_158,U_159) ) )
& ( ! [U_155] :
( ? [U_154,U_153] : U_155 = ordered_pair(U_154,U_153)
| ~ in(U_155,U_159) )
| ~ relation(U_159) ) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( ! [U_161] :
( relation(U_161)
| ? [U_158] :
( ! [U_157,U_156] : U_158 != ordered_pair(U_157,U_156)
& in(U_158,U_161) ) )
& ! [U_160] :
( ! [U_155] :
( ? [U_154,U_153] : U_155 = ordered_pair(U_154,U_153)
| ~ in(U_155,U_160) )
| ~ relation(U_160) ) ),
inference(miniscope,[status(thm)],[f_25_2]) ).
fof(f_25_4,plain,
( ! [U_161] :
( relation(U_161)
| ? [U_158] :
( ! [U_157,U_156] : U_158 != ordered_pair(U_157,U_156)
& in(U_158,U_161) ) )
& ! [U_160] :
( ! [U_155] :
( ? [U_153] : U_155 = ordered_pair(sK29(U_160,U_155),U_153)
| ~ in(U_155,U_160) )
| ~ relation(U_160) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_154,sK29(U_160,U_155))],[f_25_3]) ).
fof(f_25_5,plain,
( ! [U_161] :
( relation(U_161)
| ? [U_158] :
( ! [U_157,U_156] : U_158 != ordered_pair(U_157,U_156)
& in(U_158,U_161) ) )
& ! [U_160] :
( ! [U_155] :
( U_155 = ordered_pair(sK29(U_160,U_155),sK30(U_160,U_155))
| ~ in(U_155,U_160) )
| ~ relation(U_160) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_153,sK30(U_160,U_155))],[f_25_4]) ).
fof(f_25_6,plain,
( ! [U_161] :
( relation(U_161)
| ( ! [U_157,U_156] : sK31(U_161) != ordered_pair(U_157,U_156)
& in(sK31(U_161),U_161) ) )
& ! [U_160] :
( ! [U_155] :
( U_155 = ordered_pair(sK29(U_160,U_155),sK30(U_160,U_155))
| ~ in(U_155,U_160) )
| ~ relation(U_160) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_158,sK31(U_161))],[f_25_5]) ).
cnf(f_25_7,plain,
( U_155 = ordered_pair(sK29(U_160,U_155),sK30(U_160,U_155))
| ~ in(U_155,U_160)
| ~ relation(U_160) ),
inference(clausify,[status(thm)],[f_25_6]) ).
cnf(f_25_8,plain,
( in(sK31(U_161),U_161)
| relation(U_161) ),
inference(clausify,[status(thm)],[f_25_6]) ).
cnf(f_25_9,plain,
( sK31(U_161) != ordered_pair(U_157,U_156)
| relation(U_161) ),
inference(clausify,[status(thm)],[f_25_6]) ).
fof(f_26_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_26_2,plain,
! [U_165] :
( ! [U_164] :
( ( is_reflexive_in(U_165,U_164)
| ? [U_163] :
( ~ in(ordered_pair(U_163,U_163),U_165)
& in(U_163,U_164) ) )
& ( ! [U_162] :
( in(ordered_pair(U_162,U_162),U_165)
| ~ in(U_162,U_164) )
| ~ is_reflexive_in(U_165,U_164) ) )
| ~ relation(U_165) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_165] :
( ( ! [U_167] :
( is_reflexive_in(U_165,U_167)
| ? [U_163] :
( ~ in(ordered_pair(U_163,U_163),U_165)
& in(U_163,U_167) ) )
& ! [U_166] :
( ! [U_162] :
( in(ordered_pair(U_162,U_162),U_165)
| ~ in(U_162,U_166) )
| ~ is_reflexive_in(U_165,U_166) ) )
| ~ relation(U_165) ),
inference(miniscope,[status(thm)],[f_26_2]) ).
fof(f_26_4,plain,
! [U_165] :
( ( ! [U_167] :
( is_reflexive_in(U_165,U_167)
| ( ~ in(ordered_pair(sK32(U_165,U_167),sK32(U_165,U_167)),U_165)
& in(sK32(U_165,U_167),U_167) ) )
& ! [U_166] :
( ! [U_162] :
( in(ordered_pair(U_162,U_162),U_165)
| ~ in(U_162,U_166) )
| ~ is_reflexive_in(U_165,U_166) ) )
| ~ relation(U_165) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_163,sK32(U_165,U_167))],[f_26_3]) ).
cnf(f_26_5,plain,
( in(ordered_pair(U_162,U_162),U_165)
| ~ in(U_162,U_166)
| ~ is_reflexive_in(U_165,U_166)
| ~ relation(U_165) ),
inference(clausify,[status(thm)],[f_26_4]) ).
cnf(f_26_6,plain,
( in(sK32(U_165,U_167),U_167)
| is_reflexive_in(U_165,U_167)
| ~ relation(U_165) ),
inference(clausify,[status(thm)],[f_26_4]) ).
cnf(f_26_7,plain,
( ~ in(ordered_pair(sK32(U_165,U_167),sK32(U_165,U_167)),U_165)
| is_reflexive_in(U_165,U_167)
| ~ relation(U_165) ),
inference(clausify,[status(thm)],[f_26_4]) ).
fof(f_27_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_27_2,plain,
! [U_175,U_174] :
( ( ( ( U_174 = set_meet(U_175)
| U_174 != empty_set )
& ( U_174 = empty_set
| U_174 != set_meet(U_175) ) )
| U_175 != empty_set )
& ( ( ( U_174 = set_meet(U_175)
| ? [U_173] :
( ( ~ in(U_173,U_174)
& ! [U_172] :
( in(U_173,U_172)
| ~ in(U_172,U_175) ) )
| ( ? [U_171] :
( ~ in(U_173,U_171)
& in(U_171,U_175) )
& in(U_173,U_174) ) ) )
& ( ! [U_170] :
( ( in(U_170,U_174)
| ? [U_169] :
( ~ in(U_170,U_169)
& in(U_169,U_175) ) )
& ( ! [U_168] :
( in(U_170,U_168)
| ~ in(U_168,U_175) )
| ~ in(U_170,U_174) ) )
| U_174 != set_meet(U_175) ) )
| U_175 = empty_set ) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( ! [U_187] :
( ( ! [U_185] :
( U_185 = set_meet(U_187)
| U_185 != empty_set )
& ! [U_184] :
( U_184 = empty_set
| U_184 != set_meet(U_187) ) )
| U_187 != empty_set )
& ! [U_186] :
( ( ! [U_183] :
( U_183 = set_meet(U_186)
| ? [U_179] :
( ~ in(U_179,U_183)
& ! [U_172] :
( in(U_179,U_172)
| ~ in(U_172,U_186) ) )
| ? [U_178] :
( ? [U_171] :
( ~ in(U_178,U_171)
& in(U_171,U_186) )
& in(U_178,U_183) ) )
& ! [U_182] :
( ( ! [U_177] :
( in(U_177,U_182)
| ? [U_169] :
( ~ in(U_177,U_169)
& in(U_169,U_186) ) )
& ! [U_176] :
( ! [U_168] :
( in(U_176,U_168)
| ~ in(U_168,U_186) )
| ~ in(U_176,U_182) ) )
| U_182 != set_meet(U_186) ) )
| U_186 = empty_set ) ),
inference(miniscope,[status(thm)],[f_27_2]) ).
fof(f_27_4,plain,
( ! [U_187] :
( ( ! [U_185] :
( U_185 = set_meet(U_187)
| U_185 != empty_set )
& ! [U_184] :
( U_184 = empty_set
| U_184 != set_meet(U_187) ) )
| U_187 != empty_set )
& ! [U_186] :
( ( ! [U_183] :
( U_183 = set_meet(U_186)
| ? [U_179] :
( ~ in(U_179,U_183)
& ! [U_172] :
( in(U_179,U_172)
| ~ in(U_172,U_186) ) )
| ? [U_178] :
( ? [U_171] :
( ~ in(U_178,U_171)
& in(U_171,U_186) )
& in(U_178,U_183) ) )
& ! [U_182] :
( ( ! [U_177] :
( in(U_177,U_182)
| ( ~ in(U_177,sK33(U_186,U_182,U_177))
& in(sK33(U_186,U_182,U_177),U_186) ) )
& ! [U_176] :
( ! [U_168] :
( in(U_176,U_168)
| ~ in(U_168,U_186) )
| ~ in(U_176,U_182) ) )
| U_182 != set_meet(U_186) ) )
| U_186 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_169,sK33(U_186,U_182,U_177))],[f_27_3]) ).
fof(f_27_5,plain,
( ! [U_187] :
( ( ! [U_185] :
( U_185 = set_meet(U_187)
| U_185 != empty_set )
& ! [U_184] :
( U_184 = empty_set
| U_184 != set_meet(U_187) ) )
| U_187 != empty_set )
& ! [U_186] :
( ( ! [U_183] :
( U_183 = set_meet(U_186)
| ? [U_179] :
( ~ in(U_179,U_183)
& ! [U_172] :
( in(U_179,U_172)
| ~ in(U_172,U_186) ) )
| ( ? [U_171] :
( ~ in(sK34(U_186,U_183),U_171)
& in(U_171,U_186) )
& in(sK34(U_186,U_183),U_183) ) )
& ! [U_182] :
( ( ! [U_177] :
( in(U_177,U_182)
| ( ~ in(U_177,sK33(U_186,U_182,U_177))
& in(sK33(U_186,U_182,U_177),U_186) ) )
& ! [U_176] :
( ! [U_168] :
( in(U_176,U_168)
| ~ in(U_168,U_186) )
| ~ in(U_176,U_182) ) )
| U_182 != set_meet(U_186) ) )
| U_186 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_178,sK34(U_186,U_183))],[f_27_4]) ).
fof(f_27_6,plain,
( ! [U_187] :
( ( ! [U_185] :
( U_185 = set_meet(U_187)
| U_185 != empty_set )
& ! [U_184] :
( U_184 = empty_set
| U_184 != set_meet(U_187) ) )
| U_187 != empty_set )
& ! [U_186] :
( ( ! [U_183] :
( U_183 = set_meet(U_186)
| ? [U_179] :
( ~ in(U_179,U_183)
& ! [U_172] :
( in(U_179,U_172)
| ~ in(U_172,U_186) ) )
| ( ~ in(sK34(U_186,U_183),sK35(U_186,U_183))
& in(sK35(U_186,U_183),U_186)
& in(sK34(U_186,U_183),U_183) ) )
& ! [U_182] :
( ( ! [U_177] :
( in(U_177,U_182)
| ( ~ in(U_177,sK33(U_186,U_182,U_177))
& in(sK33(U_186,U_182,U_177),U_186) ) )
& ! [U_176] :
( ! [U_168] :
( in(U_176,U_168)
| ~ in(U_168,U_186) )
| ~ in(U_176,U_182) ) )
| U_182 != set_meet(U_186) ) )
| U_186 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_171,sK35(U_186,U_183))],[f_27_5]) ).
fof(f_27_7,plain,
( ! [U_187] :
( ( ! [U_185] :
( U_185 = set_meet(U_187)
| U_185 != empty_set )
& ! [U_184] :
( U_184 = empty_set
| U_184 != set_meet(U_187) ) )
| U_187 != empty_set )
& ! [U_186] :
( ( ! [U_183] :
( U_183 = set_meet(U_186)
| ( ~ in(sK36(U_186,U_183),U_183)
& ! [U_172] :
( in(sK36(U_186,U_183),U_172)
| ~ in(U_172,U_186) ) )
| ( ~ in(sK34(U_186,U_183),sK35(U_186,U_183))
& in(sK35(U_186,U_183),U_186)
& in(sK34(U_186,U_183),U_183) ) )
& ! [U_182] :
( ( ! [U_177] :
( in(U_177,U_182)
| ( ~ in(U_177,sK33(U_186,U_182,U_177))
& in(sK33(U_186,U_182,U_177),U_186) ) )
& ! [U_176] :
( ! [U_168] :
( in(U_176,U_168)
| ~ in(U_168,U_186) )
| ~ in(U_176,U_182) ) )
| U_182 != set_meet(U_186) ) )
| U_186 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_179,sK36(U_186,U_183))],[f_27_6]) ).
cnf(f_27_8,plain,
( in(U_176,U_168)
| ~ in(U_168,U_186)
| ~ in(U_176,U_182)
| U_182 != set_meet(U_186)
| U_186 = empty_set ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_9,plain,
( in(sK33(U_186,U_182,U_177),U_186)
| in(U_177,U_182)
| U_182 != set_meet(U_186)
| U_186 = empty_set ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_10,plain,
( ~ in(U_177,sK33(U_186,U_182,U_177))
| in(U_177,U_182)
| U_182 != set_meet(U_186)
| U_186 = empty_set ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_11,plain,
( in(sK36(U_186,U_183),U_172)
| ~ in(U_172,U_186)
| in(sK34(U_186,U_183),U_183)
| U_183 = set_meet(U_186)
| U_186 = empty_set ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_12,plain,
( ~ in(sK36(U_186,U_183),U_183)
| in(sK34(U_186,U_183),U_183)
| U_183 = set_meet(U_186)
| U_186 = empty_set ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_13,plain,
( in(sK35(U_186,U_183),U_186)
| in(sK36(U_186,U_183),U_172)
| ~ in(U_172,U_186)
| U_183 = set_meet(U_186)
| U_186 = empty_set ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_14,plain,
( ~ in(sK34(U_186,U_183),sK35(U_186,U_183))
| in(sK36(U_186,U_183),U_172)
| ~ in(U_172,U_186)
| U_183 = set_meet(U_186)
| U_186 = empty_set ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_15,plain,
( in(sK35(U_186,U_183),U_186)
| ~ in(sK36(U_186,U_183),U_183)
| U_183 = set_meet(U_186)
| U_186 = empty_set ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_16,plain,
( ~ in(sK34(U_186,U_183),sK35(U_186,U_183))
| ~ in(sK36(U_186,U_183),U_183)
| U_183 = set_meet(U_186)
| U_186 = empty_set ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_17,plain,
( U_184 = empty_set
| U_184 != set_meet(U_187)
| U_187 != empty_set ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_18,plain,
( U_185 = set_meet(U_187)
| U_185 != empty_set
| U_187 != empty_set ),
inference(clausify,[status(thm)],[f_27_7]) ).
fof(f_28_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_28_2,plain,
! [U_191,U_190] :
( ( U_190 = singleton(U_191)
| ? [U_189] :
( ( ~ in(U_189,U_190)
& U_189 = U_191 )
| ( U_189 != U_191
& in(U_189,U_190) ) ) )
& ( ! [U_188] :
( ( in(U_188,U_190)
| U_188 != U_191 )
& ( U_188 = U_191
| ~ in(U_188,U_190) ) )
| U_190 != singleton(U_191) ) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( ! [U_199,U_197] :
( U_197 = singleton(U_199)
| ? [U_195] :
( ~ in(U_195,U_197)
& U_195 = U_199 )
| ? [U_194] :
( U_194 != U_199
& in(U_194,U_197) ) )
& ! [U_198,U_196] :
( ( ! [U_193] :
( in(U_193,U_196)
| U_193 != U_198 )
& ! [U_192] :
( U_192 = U_198
| ~ in(U_192,U_196) ) )
| U_196 != singleton(U_198) ) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
fof(f_28_4,plain,
( ! [U_199,U_197] :
( U_197 = singleton(U_199)
| ? [U_195] :
( ~ in(U_195,U_197)
& U_195 = U_199 )
| ( sK37(U_199,U_197) != U_199
& in(sK37(U_199,U_197),U_197) ) )
& ! [U_198,U_196] :
( ( ! [U_193] :
( in(U_193,U_196)
| U_193 != U_198 )
& ! [U_192] :
( U_192 = U_198
| ~ in(U_192,U_196) ) )
| U_196 != singleton(U_198) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_194,sK37(U_199,U_197))],[f_28_3]) ).
fof(f_28_5,plain,
( ! [U_199,U_197] :
( U_197 = singleton(U_199)
| ( ~ in(sK38(U_199,U_197),U_197)
& sK38(U_199,U_197) = U_199 )
| ( sK37(U_199,U_197) != U_199
& in(sK37(U_199,U_197),U_197) ) )
& ! [U_198,U_196] :
( ( ! [U_193] :
( in(U_193,U_196)
| U_193 != U_198 )
& ! [U_192] :
( U_192 = U_198
| ~ in(U_192,U_196) ) )
| U_196 != singleton(U_198) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_195,sK38(U_199,U_197))],[f_28_4]) ).
cnf(f_28_6,plain,
( U_192 = U_198
| ~ in(U_192,U_196)
| U_196 != singleton(U_198) ),
inference(clausify,[status(thm)],[f_28_5]) ).
cnf(f_28_7,plain,
( in(U_193,U_196)
| U_193 != U_198
| U_196 != singleton(U_198) ),
inference(clausify,[status(thm)],[f_28_5]) ).
cnf(f_28_8,plain,
( sK38(U_199,U_197) = U_199
| in(sK37(U_199,U_197),U_197)
| U_197 = singleton(U_199) ),
inference(clausify,[status(thm)],[f_28_5]) ).
cnf(f_28_9,plain,
( ~ in(sK38(U_199,U_197),U_197)
| in(sK37(U_199,U_197),U_197)
| U_197 = singleton(U_199) ),
inference(clausify,[status(thm)],[f_28_5]) ).
cnf(f_28_10,plain,
( sK38(U_199,U_197) = U_199
| sK37(U_199,U_197) != U_199
| U_197 = singleton(U_199) ),
inference(clausify,[status(thm)],[f_28_5]) ).
cnf(f_28_11,plain,
( ~ in(sK38(U_199,U_197),U_197)
| sK37(U_199,U_197) != U_199
| U_197 = singleton(U_199) ),
inference(clausify,[status(thm)],[f_28_5]) ).
fof(f_29_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_29_2,plain,
! [U_202] :
( ( U_202 = empty_set
| ? [U_201] : in(U_201,U_202) )
& ( ! [U_200] : ~ in(U_200,U_202)
| U_202 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
( ! [U_204] :
( U_204 = empty_set
| ? [U_201] : in(U_201,U_204) )
& ! [U_203] :
( ! [U_200] : ~ in(U_200,U_203)
| U_203 != empty_set ) ),
inference(miniscope,[status(thm)],[f_29_2]) ).
fof(f_29_4,plain,
( ! [U_204] :
( U_204 = empty_set
| in(sK39(U_204),U_204) )
& ! [U_203] :
( ! [U_200] : ~ in(U_200,U_203)
| U_203 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_201,sK39(U_204))],[f_29_3]) ).
cnf(f_29_5,plain,
( ~ in(U_200,U_203)
| U_203 != empty_set ),
inference(clausify,[status(thm)],[f_29_4]) ).
cnf(f_29_6,plain,
( U_204 = empty_set
| in(sK39(U_204),U_204) ),
inference(clausify,[status(thm)],[f_29_4]) ).
fof(f_30_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_30_2,plain,
! [U_208,U_207] :
( ( U_207 = powerset(U_208)
| ? [U_206] :
( ( ~ in(U_206,U_207)
& subset(U_206,U_208) )
| ( ~ subset(U_206,U_208)
& in(U_206,U_207) ) ) )
& ( ! [U_205] :
( ( in(U_205,U_207)
| ~ subset(U_205,U_208) )
& ( subset(U_205,U_208)
| ~ in(U_205,U_207) ) )
| U_207 != powerset(U_208) ) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( ! [U_216,U_214] :
( U_214 = powerset(U_216)
| ? [U_212] :
( ~ in(U_212,U_214)
& subset(U_212,U_216) )
| ? [U_211] :
( ~ subset(U_211,U_216)
& in(U_211,U_214) ) )
& ! [U_215,U_213] :
( ( ! [U_210] :
( in(U_210,U_213)
| ~ subset(U_210,U_215) )
& ! [U_209] :
( subset(U_209,U_215)
| ~ in(U_209,U_213) ) )
| U_213 != powerset(U_215) ) ),
inference(miniscope,[status(thm)],[f_30_2]) ).
fof(f_30_4,plain,
( ! [U_216,U_214] :
( U_214 = powerset(U_216)
| ? [U_212] :
( ~ in(U_212,U_214)
& subset(U_212,U_216) )
| ( ~ subset(sK40(U_216,U_214),U_216)
& in(sK40(U_216,U_214),U_214) ) )
& ! [U_215,U_213] :
( ( ! [U_210] :
( in(U_210,U_213)
| ~ subset(U_210,U_215) )
& ! [U_209] :
( subset(U_209,U_215)
| ~ in(U_209,U_213) ) )
| U_213 != powerset(U_215) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_211,sK40(U_216,U_214))],[f_30_3]) ).
fof(f_30_5,plain,
( ! [U_216,U_214] :
( U_214 = powerset(U_216)
| ( ~ in(sK41(U_216,U_214),U_214)
& subset(sK41(U_216,U_214),U_216) )
| ( ~ subset(sK40(U_216,U_214),U_216)
& in(sK40(U_216,U_214),U_214) ) )
& ! [U_215,U_213] :
( ( ! [U_210] :
( in(U_210,U_213)
| ~ subset(U_210,U_215) )
& ! [U_209] :
( subset(U_209,U_215)
| ~ in(U_209,U_213) ) )
| U_213 != powerset(U_215) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_212,sK41(U_216,U_214))],[f_30_4]) ).
cnf(f_30_6,plain,
( subset(U_209,U_215)
| ~ in(U_209,U_213)
| U_213 != powerset(U_215) ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_7,plain,
( in(U_210,U_213)
| ~ subset(U_210,U_215)
| U_213 != powerset(U_215) ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_8,plain,
( subset(sK41(U_216,U_214),U_216)
| in(sK40(U_216,U_214),U_214)
| U_214 = powerset(U_216) ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_9,plain,
( ~ in(sK41(U_216,U_214),U_214)
| in(sK40(U_216,U_214),U_214)
| U_214 = powerset(U_216) ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_10,plain,
( subset(sK41(U_216,U_214),U_216)
| ~ subset(sK40(U_216,U_214),U_216)
| U_214 = powerset(U_216) ),
inference(clausify,[status(thm)],[f_30_5]) ).
cnf(f_30_11,plain,
( ~ in(sK41(U_216,U_214),U_214)
| ~ subset(sK40(U_216,U_214),U_216)
| U_214 = powerset(U_216) ),
inference(clausify,[status(thm)],[f_30_5]) ).
fof(f_31_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_31_2,plain,
! [U_219] :
( ( epsilon_transitive(U_219)
| ? [U_218] :
( ~ subset(U_218,U_219)
& in(U_218,U_219) ) )
& ( ! [U_217] :
( subset(U_217,U_219)
| ~ in(U_217,U_219) )
| ~ epsilon_transitive(U_219) ) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( ! [U_221] :
( epsilon_transitive(U_221)
| ? [U_218] :
( ~ subset(U_218,U_221)
& in(U_218,U_221) ) )
& ! [U_220] :
( ! [U_217] :
( subset(U_217,U_220)
| ~ in(U_217,U_220) )
| ~ epsilon_transitive(U_220) ) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
fof(f_31_4,plain,
( ! [U_221] :
( epsilon_transitive(U_221)
| ( ~ subset(sK42(U_221),U_221)
& in(sK42(U_221),U_221) ) )
& ! [U_220] :
( ! [U_217] :
( subset(U_217,U_220)
| ~ in(U_217,U_220) )
| ~ epsilon_transitive(U_220) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_218,sK42(U_221))],[f_31_3]) ).
cnf(f_31_5,plain,
( subset(U_217,U_220)
| ~ in(U_217,U_220)
| ~ epsilon_transitive(U_220) ),
inference(clausify,[status(thm)],[f_31_4]) ).
cnf(f_31_6,plain,
( in(sK42(U_221),U_221)
| epsilon_transitive(U_221) ),
inference(clausify,[status(thm)],[f_31_4]) ).
cnf(f_31_7,plain,
( ~ subset(sK42(U_221),U_221)
| epsilon_transitive(U_221) ),
inference(clausify,[status(thm)],[f_31_4]) ).
fof(f_32_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_32_2,plain,
! [U_227] :
( ! [U_226] :
( ( ( U_227 = U_226
| ? [U_225,U_224] :
( ( ~ in(ordered_pair(U_225,U_224),U_227)
& in(ordered_pair(U_225,U_224),U_226) )
| ( ~ in(ordered_pair(U_225,U_224),U_226)
& in(ordered_pair(U_225,U_224),U_227) ) ) )
& ( ! [U_223,U_222] :
( ( in(ordered_pair(U_223,U_222),U_227)
| ~ in(ordered_pair(U_223,U_222),U_226) )
& ( in(ordered_pair(U_223,U_222),U_226)
| ~ in(ordered_pair(U_223,U_222),U_227) ) )
| U_227 != U_226 ) )
| ~ relation(U_226) )
| ~ relation(U_227) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_227] :
( ! [U_226] :
( ( ( U_227 = U_226
| ? [U_235,U_233] :
( ~ in(ordered_pair(U_235,U_233),U_227)
& in(ordered_pair(U_235,U_233),U_226) )
| ? [U_234,U_232] :
( ~ in(ordered_pair(U_234,U_232),U_226)
& in(ordered_pair(U_234,U_232),U_227) ) )
& ( ( ! [U_231,U_229] :
( in(ordered_pair(U_231,U_229),U_227)
| ~ in(ordered_pair(U_231,U_229),U_226) )
& ! [U_230,U_228] :
( in(ordered_pair(U_230,U_228),U_226)
| ~ in(ordered_pair(U_230,U_228),U_227) ) )
| U_227 != U_226 ) )
| ~ relation(U_226) )
| ~ relation(U_227) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
fof(f_32_4,plain,
! [U_227] :
( ! [U_226] :
( ( ( U_227 = U_226
| ? [U_235,U_233] :
( ~ in(ordered_pair(U_235,U_233),U_227)
& in(ordered_pair(U_235,U_233),U_226) )
| ? [U_232] :
( ~ in(ordered_pair(sK43(U_227,U_226),U_232),U_226)
& in(ordered_pair(sK43(U_227,U_226),U_232),U_227) ) )
& ( ( ! [U_231,U_229] :
( in(ordered_pair(U_231,U_229),U_227)
| ~ in(ordered_pair(U_231,U_229),U_226) )
& ! [U_230,U_228] :
( in(ordered_pair(U_230,U_228),U_226)
| ~ in(ordered_pair(U_230,U_228),U_227) ) )
| U_227 != U_226 ) )
| ~ relation(U_226) )
| ~ relation(U_227) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_234,sK43(U_227,U_226))],[f_32_3]) ).
fof(f_32_5,plain,
! [U_227] :
( ! [U_226] :
( ( ( U_227 = U_226
| ? [U_235,U_233] :
( ~ in(ordered_pair(U_235,U_233),U_227)
& in(ordered_pair(U_235,U_233),U_226) )
| ( ~ in(ordered_pair(sK43(U_227,U_226),sK44(U_227,U_226)),U_226)
& in(ordered_pair(sK43(U_227,U_226),sK44(U_227,U_226)),U_227) ) )
& ( ( ! [U_231,U_229] :
( in(ordered_pair(U_231,U_229),U_227)
| ~ in(ordered_pair(U_231,U_229),U_226) )
& ! [U_230,U_228] :
( in(ordered_pair(U_230,U_228),U_226)
| ~ in(ordered_pair(U_230,U_228),U_227) ) )
| U_227 != U_226 ) )
| ~ relation(U_226) )
| ~ relation(U_227) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_232,sK44(U_227,U_226))],[f_32_4]) ).
fof(f_32_6,plain,
! [U_227] :
( ! [U_226] :
( ( ( U_227 = U_226
| ? [U_233] :
( ~ in(ordered_pair(sK45(U_227,U_226),U_233),U_227)
& in(ordered_pair(sK45(U_227,U_226),U_233),U_226) )
| ( ~ in(ordered_pair(sK43(U_227,U_226),sK44(U_227,U_226)),U_226)
& in(ordered_pair(sK43(U_227,U_226),sK44(U_227,U_226)),U_227) ) )
& ( ( ! [U_231,U_229] :
( in(ordered_pair(U_231,U_229),U_227)
| ~ in(ordered_pair(U_231,U_229),U_226) )
& ! [U_230,U_228] :
( in(ordered_pair(U_230,U_228),U_226)
| ~ in(ordered_pair(U_230,U_228),U_227) ) )
| U_227 != U_226 ) )
| ~ relation(U_226) )
| ~ relation(U_227) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_235,sK45(U_227,U_226))],[f_32_5]) ).
fof(f_32_7,plain,
! [U_227] :
( ! [U_226] :
( ( ( U_227 = U_226
| ( ~ in(ordered_pair(sK45(U_227,U_226),sK46(U_227,U_226)),U_227)
& in(ordered_pair(sK45(U_227,U_226),sK46(U_227,U_226)),U_226) )
| ( ~ in(ordered_pair(sK43(U_227,U_226),sK44(U_227,U_226)),U_226)
& in(ordered_pair(sK43(U_227,U_226),sK44(U_227,U_226)),U_227) ) )
& ( ( ! [U_231,U_229] :
( in(ordered_pair(U_231,U_229),U_227)
| ~ in(ordered_pair(U_231,U_229),U_226) )
& ! [U_230,U_228] :
( in(ordered_pair(U_230,U_228),U_226)
| ~ in(ordered_pair(U_230,U_228),U_227) ) )
| U_227 != U_226 ) )
| ~ relation(U_226) )
| ~ relation(U_227) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_233,sK46(U_227,U_226))],[f_32_6]) ).
cnf(f_32_8,plain,
( in(ordered_pair(U_230,U_228),U_226)
| ~ in(ordered_pair(U_230,U_228),U_227)
| U_227 != U_226
| ~ relation(U_226)
| ~ relation(U_227) ),
inference(clausify,[status(thm)],[f_32_7]) ).
cnf(f_32_9,plain,
( in(ordered_pair(U_231,U_229),U_227)
| ~ in(ordered_pair(U_231,U_229),U_226)
| U_227 != U_226
| ~ relation(U_226)
| ~ relation(U_227) ),
inference(clausify,[status(thm)],[f_32_7]) ).
cnf(f_32_10,plain,
( in(ordered_pair(sK45(U_227,U_226),sK46(U_227,U_226)),U_226)
| in(ordered_pair(sK43(U_227,U_226),sK44(U_227,U_226)),U_227)
| U_227 = U_226
| ~ relation(U_226)
| ~ relation(U_227) ),
inference(clausify,[status(thm)],[f_32_7]) ).
cnf(f_32_11,plain,
( ~ in(ordered_pair(sK45(U_227,U_226),sK46(U_227,U_226)),U_227)
| in(ordered_pair(sK43(U_227,U_226),sK44(U_227,U_226)),U_227)
| U_227 = U_226
| ~ relation(U_226)
| ~ relation(U_227) ),
inference(clausify,[status(thm)],[f_32_7]) ).
cnf(f_32_12,plain,
( in(ordered_pair(sK45(U_227,U_226),sK46(U_227,U_226)),U_226)
| ~ in(ordered_pair(sK43(U_227,U_226),sK44(U_227,U_226)),U_226)
| U_227 = U_226
| ~ relation(U_226)
| ~ relation(U_227) ),
inference(clausify,[status(thm)],[f_32_7]) ).
cnf(f_32_13,plain,
( ~ in(ordered_pair(sK45(U_227,U_226),sK46(U_227,U_226)),U_227)
| ~ in(ordered_pair(sK43(U_227,U_226),sK44(U_227,U_226)),U_226)
| U_227 = U_226
| ~ relation(U_226)
| ~ relation(U_227) ),
inference(clausify,[status(thm)],[f_32_7]) ).
fof(f_33_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_33_2,plain,
! [U_237,U_236] :
( ( ( ( element(U_236,U_237)
| ~ empty(U_236) )
& ( empty(U_236)
| ~ element(U_236,U_237) ) )
| ~ empty(U_237) )
& ( ( ( element(U_236,U_237)
| ~ in(U_236,U_237) )
& ( in(U_236,U_237)
| ~ element(U_236,U_237) ) )
| empty(U_237) ) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( ! [U_245] :
( ( ! [U_243] :
( element(U_243,U_245)
| ~ empty(U_243) )
& ! [U_242] :
( empty(U_242)
| ~ element(U_242,U_245) ) )
| ~ empty(U_245) )
& ! [U_244] :
( ( ! [U_241] :
( element(U_241,U_244)
| ~ in(U_241,U_244) )
& ! [U_240] :
( in(U_240,U_244)
| ~ element(U_240,U_244) ) )
| empty(U_244) ) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
cnf(f_33_4,plain,
( in(U_240,U_244)
| ~ element(U_240,U_244)
| empty(U_244) ),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_5,plain,
( element(U_241,U_244)
| ~ in(U_241,U_244)
| empty(U_244) ),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_6,plain,
( empty(U_242)
| ~ element(U_242,U_245)
| ~ empty(U_245) ),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_7,plain,
( element(U_243,U_245)
| ~ empty(U_243)
| ~ empty(U_245) ),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_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_34_2,plain,
! [U_250,U_249,U_248] :
( ( U_248 = unordered_pair(U_250,U_249)
| ? [U_247] :
( ( ~ in(U_247,U_248)
& ( U_247 = U_249
| U_247 = U_250 ) )
| ( U_247 != U_249
& U_247 != U_250
& in(U_247,U_248) ) ) )
& ( ! [U_246] :
( ( in(U_246,U_248)
| ( U_246 != U_249
& U_246 != U_250 ) )
& ( U_246 = U_249
| U_246 = U_250
| ~ in(U_246,U_248) ) )
| U_248 != unordered_pair(U_250,U_249) ) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
( ! [U_260,U_258,U_256] :
( U_256 = unordered_pair(U_260,U_258)
| ? [U_254] :
( ~ in(U_254,U_256)
& ( U_254 = U_258
| U_254 = U_260 ) )
| ? [U_253] :
( U_253 != U_258
& U_253 != U_260
& in(U_253,U_256) ) )
& ! [U_259,U_257,U_255] :
( ( ! [U_252] :
( in(U_252,U_255)
| ( U_252 != U_257
& U_252 != U_259 ) )
& ! [U_251] :
( U_251 = U_257
| U_251 = U_259
| ~ in(U_251,U_255) ) )
| U_255 != unordered_pair(U_259,U_257) ) ),
inference(miniscope,[status(thm)],[f_34_2]) ).
fof(f_34_4,plain,
( ! [U_260,U_258,U_256] :
( U_256 = unordered_pair(U_260,U_258)
| ? [U_254] :
( ~ in(U_254,U_256)
& ( U_254 = U_258
| U_254 = U_260 ) )
| ( sK47(U_260,U_258,U_256) != U_258
& sK47(U_260,U_258,U_256) != U_260
& in(sK47(U_260,U_258,U_256),U_256) ) )
& ! [U_259,U_257,U_255] :
( ( ! [U_252] :
( in(U_252,U_255)
| ( U_252 != U_257
& U_252 != U_259 ) )
& ! [U_251] :
( U_251 = U_257
| U_251 = U_259
| ~ in(U_251,U_255) ) )
| U_255 != unordered_pair(U_259,U_257) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_253,sK47(U_260,U_258,U_256))],[f_34_3]) ).
fof(f_34_5,plain,
( ! [U_260,U_258,U_256] :
( U_256 = unordered_pair(U_260,U_258)
| ( ~ in(sK48(U_260,U_258,U_256),U_256)
& ( sK48(U_260,U_258,U_256) = U_258
| sK48(U_260,U_258,U_256) = U_260 ) )
| ( sK47(U_260,U_258,U_256) != U_258
& sK47(U_260,U_258,U_256) != U_260
& in(sK47(U_260,U_258,U_256),U_256) ) )
& ! [U_259,U_257,U_255] :
( ( ! [U_252] :
( in(U_252,U_255)
| ( U_252 != U_257
& U_252 != U_259 ) )
& ! [U_251] :
( U_251 = U_257
| U_251 = U_259
| ~ in(U_251,U_255) ) )
| U_255 != unordered_pair(U_259,U_257) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_254,sK48(U_260,U_258,U_256))],[f_34_4]) ).
cnf(f_34_6,plain,
( U_251 = U_257
| U_251 = U_259
| ~ in(U_251,U_255)
| U_255 != unordered_pair(U_259,U_257) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_7,plain,
( U_252 != U_259
| in(U_252,U_255)
| U_255 != unordered_pair(U_259,U_257) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_8,plain,
( U_252 != U_257
| in(U_252,U_255)
| U_255 != unordered_pair(U_259,U_257) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_9,plain,
( sK48(U_260,U_258,U_256) = U_258
| sK48(U_260,U_258,U_256) = U_260
| in(sK47(U_260,U_258,U_256),U_256)
| U_256 = unordered_pair(U_260,U_258) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_10,plain,
( ~ in(sK48(U_260,U_258,U_256),U_256)
| in(sK47(U_260,U_258,U_256),U_256)
| U_256 = unordered_pair(U_260,U_258) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_11,plain,
( sK47(U_260,U_258,U_256) != U_260
| sK48(U_260,U_258,U_256) = U_258
| sK48(U_260,U_258,U_256) = U_260
| U_256 = unordered_pair(U_260,U_258) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_12,plain,
( sK47(U_260,U_258,U_256) != U_258
| sK48(U_260,U_258,U_256) = U_258
| sK48(U_260,U_258,U_256) = U_260
| U_256 = unordered_pair(U_260,U_258) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_13,plain,
( sK47(U_260,U_258,U_256) != U_260
| ~ in(sK48(U_260,U_258,U_256),U_256)
| U_256 = unordered_pair(U_260,U_258) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_14,plain,
( sK47(U_260,U_258,U_256) != U_258
| ~ in(sK48(U_260,U_258,U_256),U_256)
| U_256 = unordered_pair(U_260,U_258) ),
inference(clausify,[status(thm)],[f_34_5]) ).
fof(f_35_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_35_2,plain,
! [U_265,U_264,U_263] :
( ( U_263 = set_union2(U_265,U_264)
| ? [U_262] :
( ( ~ in(U_262,U_263)
& ( in(U_262,U_264)
| in(U_262,U_265) ) )
| ( ~ in(U_262,U_264)
& ~ in(U_262,U_265)
& in(U_262,U_263) ) ) )
& ( ! [U_261] :
( ( in(U_261,U_263)
| ( ~ in(U_261,U_264)
& ~ in(U_261,U_265) ) )
& ( in(U_261,U_264)
| in(U_261,U_265)
| ~ in(U_261,U_263) ) )
| U_263 != set_union2(U_265,U_264) ) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( ! [U_275,U_273,U_271] :
( U_271 = set_union2(U_275,U_273)
| ? [U_269] :
( ~ in(U_269,U_271)
& ( in(U_269,U_273)
| in(U_269,U_275) ) )
| ? [U_268] :
( ~ in(U_268,U_273)
& ~ in(U_268,U_275)
& in(U_268,U_271) ) )
& ! [U_274,U_272,U_270] :
( ( ! [U_267] :
( in(U_267,U_270)
| ( ~ in(U_267,U_272)
& ~ in(U_267,U_274) ) )
& ! [U_266] :
( in(U_266,U_272)
| in(U_266,U_274)
| ~ in(U_266,U_270) ) )
| U_270 != set_union2(U_274,U_272) ) ),
inference(miniscope,[status(thm)],[f_35_2]) ).
fof(f_35_4,plain,
( ! [U_275,U_273,U_271] :
( U_271 = set_union2(U_275,U_273)
| ? [U_269] :
( ~ in(U_269,U_271)
& ( in(U_269,U_273)
| in(U_269,U_275) ) )
| ( ~ in(sK49(U_275,U_273,U_271),U_273)
& ~ in(sK49(U_275,U_273,U_271),U_275)
& in(sK49(U_275,U_273,U_271),U_271) ) )
& ! [U_274,U_272,U_270] :
( ( ! [U_267] :
( in(U_267,U_270)
| ( ~ in(U_267,U_272)
& ~ in(U_267,U_274) ) )
& ! [U_266] :
( in(U_266,U_272)
| in(U_266,U_274)
| ~ in(U_266,U_270) ) )
| U_270 != set_union2(U_274,U_272) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_268,sK49(U_275,U_273,U_271))],[f_35_3]) ).
fof(f_35_5,plain,
( ! [U_275,U_273,U_271] :
( U_271 = set_union2(U_275,U_273)
| ( ~ in(sK50(U_275,U_273,U_271),U_271)
& ( in(sK50(U_275,U_273,U_271),U_273)
| in(sK50(U_275,U_273,U_271),U_275) ) )
| ( ~ in(sK49(U_275,U_273,U_271),U_273)
& ~ in(sK49(U_275,U_273,U_271),U_275)
& in(sK49(U_275,U_273,U_271),U_271) ) )
& ! [U_274,U_272,U_270] :
( ( ! [U_267] :
( in(U_267,U_270)
| ( ~ in(U_267,U_272)
& ~ in(U_267,U_274) ) )
& ! [U_266] :
( in(U_266,U_272)
| in(U_266,U_274)
| ~ in(U_266,U_270) ) )
| U_270 != set_union2(U_274,U_272) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_269,sK50(U_275,U_273,U_271))],[f_35_4]) ).
cnf(f_35_6,plain,
( in(U_266,U_272)
| in(U_266,U_274)
| ~ in(U_266,U_270)
| U_270 != set_union2(U_274,U_272) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_7,plain,
( ~ in(U_267,U_274)
| in(U_267,U_270)
| U_270 != set_union2(U_274,U_272) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_8,plain,
( ~ in(U_267,U_272)
| in(U_267,U_270)
| U_270 != set_union2(U_274,U_272) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_9,plain,
( in(sK50(U_275,U_273,U_271),U_273)
| in(sK50(U_275,U_273,U_271),U_275)
| in(sK49(U_275,U_273,U_271),U_271)
| U_271 = set_union2(U_275,U_273) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_10,plain,
( ~ in(sK50(U_275,U_273,U_271),U_271)
| in(sK49(U_275,U_273,U_271),U_271)
| U_271 = set_union2(U_275,U_273) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_11,plain,
( ~ in(sK49(U_275,U_273,U_271),U_275)
| in(sK50(U_275,U_273,U_271),U_273)
| in(sK50(U_275,U_273,U_271),U_275)
| U_271 = set_union2(U_275,U_273) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_12,plain,
( ~ in(sK49(U_275,U_273,U_271),U_273)
| in(sK50(U_275,U_273,U_271),U_273)
| in(sK50(U_275,U_273,U_271),U_275)
| U_271 = set_union2(U_275,U_273) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_13,plain,
( ~ in(sK49(U_275,U_273,U_271),U_275)
| ~ in(sK50(U_275,U_273,U_271),U_271)
| U_271 = set_union2(U_275,U_273) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_14,plain,
( ~ in(sK49(U_275,U_273,U_271),U_273)
| ~ in(sK50(U_275,U_273,U_271),U_271)
| U_271 = set_union2(U_275,U_273) ),
inference(clausify,[status(thm)],[f_35_5]) ).
fof(f_36_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_36_2,plain,
! [U_288,U_287,U_286] :
( ( U_286 = cartesian_product2(U_288,U_287)
| ? [U_285] :
( ( ~ in(U_285,U_286)
& ? [U_284,U_283] :
( U_285 = ordered_pair(U_284,U_283)
& in(U_283,U_287)
& in(U_284,U_288) ) )
| ( ! [U_282,U_281] :
( U_285 != ordered_pair(U_282,U_281)
| ~ in(U_281,U_287)
| ~ in(U_282,U_288) )
& in(U_285,U_286) ) ) )
& ( ! [U_280] :
( ( in(U_280,U_286)
| ! [U_279,U_278] :
( U_280 != ordered_pair(U_279,U_278)
| ~ in(U_278,U_287)
| ~ in(U_279,U_288) ) )
& ( ? [U_277,U_276] :
( U_280 = ordered_pair(U_277,U_276)
& in(U_276,U_287)
& in(U_277,U_288) )
| ~ in(U_280,U_286) ) )
| U_286 != cartesian_product2(U_288,U_287) ) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
( ! [U_298,U_296,U_294] :
( U_294 = cartesian_product2(U_298,U_296)
| ? [U_292] :
( ~ in(U_292,U_294)
& ? [U_284] :
( ? [U_283] :
( U_292 = ordered_pair(U_284,U_283)
& in(U_283,U_296) )
& in(U_284,U_298) ) )
| ? [U_291] :
( ! [U_282] :
( ! [U_281] :
( U_291 != ordered_pair(U_282,U_281)
| ~ in(U_281,U_296) )
| ~ in(U_282,U_298) )
& in(U_291,U_294) ) )
& ! [U_297,U_295,U_293] :
( ( ! [U_290] :
( in(U_290,U_293)
| ! [U_279] :
( ! [U_278] :
( U_290 != ordered_pair(U_279,U_278)
| ~ in(U_278,U_295) )
| ~ in(U_279,U_297) ) )
& ! [U_289] :
( ? [U_277] :
( ? [U_276] :
( U_289 = ordered_pair(U_277,U_276)
& in(U_276,U_295) )
& in(U_277,U_297) )
| ~ in(U_289,U_293) ) )
| U_293 != cartesian_product2(U_297,U_295) ) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
fof(f_36_4,plain,
( ! [U_298,U_296,U_294] :
( U_294 = cartesian_product2(U_298,U_296)
| ? [U_292] :
( ~ in(U_292,U_294)
& ? [U_284] :
( ? [U_283] :
( U_292 = ordered_pair(U_284,U_283)
& in(U_283,U_296) )
& in(U_284,U_298) ) )
| ? [U_291] :
( ! [U_282] :
( ! [U_281] :
( U_291 != ordered_pair(U_282,U_281)
| ~ in(U_281,U_296) )
| ~ in(U_282,U_298) )
& in(U_291,U_294) ) )
& ! [U_297,U_295,U_293] :
( ( ! [U_290] :
( in(U_290,U_293)
| ! [U_279] :
( ! [U_278] :
( U_290 != ordered_pair(U_279,U_278)
| ~ in(U_278,U_295) )
| ~ in(U_279,U_297) ) )
& ! [U_289] :
( ( ? [U_276] :
( U_289 = ordered_pair(sK51(U_297,U_295,U_293,U_289),U_276)
& in(U_276,U_295) )
& in(sK51(U_297,U_295,U_293,U_289),U_297) )
| ~ in(U_289,U_293) ) )
| U_293 != cartesian_product2(U_297,U_295) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_277,sK51(U_297,U_295,U_293,U_289))],[f_36_3]) ).
fof(f_36_5,plain,
( ! [U_298,U_296,U_294] :
( U_294 = cartesian_product2(U_298,U_296)
| ? [U_292] :
( ~ in(U_292,U_294)
& ? [U_284] :
( ? [U_283] :
( U_292 = ordered_pair(U_284,U_283)
& in(U_283,U_296) )
& in(U_284,U_298) ) )
| ? [U_291] :
( ! [U_282] :
( ! [U_281] :
( U_291 != ordered_pair(U_282,U_281)
| ~ in(U_281,U_296) )
| ~ in(U_282,U_298) )
& in(U_291,U_294) ) )
& ! [U_297,U_295,U_293] :
( ( ! [U_290] :
( in(U_290,U_293)
| ! [U_279] :
( ! [U_278] :
( U_290 != ordered_pair(U_279,U_278)
| ~ in(U_278,U_295) )
| ~ in(U_279,U_297) ) )
& ! [U_289] :
( ( U_289 = ordered_pair(sK51(U_297,U_295,U_293,U_289),sK52(U_297,U_295,U_293,U_289))
& in(sK52(U_297,U_295,U_293,U_289),U_295)
& in(sK51(U_297,U_295,U_293,U_289),U_297) )
| ~ in(U_289,U_293) ) )
| U_293 != cartesian_product2(U_297,U_295) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_276,sK52(U_297,U_295,U_293,U_289))],[f_36_4]) ).
fof(f_36_6,plain,
( ! [U_298,U_296,U_294] :
( U_294 = cartesian_product2(U_298,U_296)
| ? [U_292] :
( ~ in(U_292,U_294)
& ? [U_284] :
( ? [U_283] :
( U_292 = ordered_pair(U_284,U_283)
& in(U_283,U_296) )
& in(U_284,U_298) ) )
| ( ! [U_282] :
( ! [U_281] :
( sK53(U_298,U_296,U_294) != ordered_pair(U_282,U_281)
| ~ in(U_281,U_296) )
| ~ in(U_282,U_298) )
& in(sK53(U_298,U_296,U_294),U_294) ) )
& ! [U_297,U_295,U_293] :
( ( ! [U_290] :
( in(U_290,U_293)
| ! [U_279] :
( ! [U_278] :
( U_290 != ordered_pair(U_279,U_278)
| ~ in(U_278,U_295) )
| ~ in(U_279,U_297) ) )
& ! [U_289] :
( ( U_289 = ordered_pair(sK51(U_297,U_295,U_293,U_289),sK52(U_297,U_295,U_293,U_289))
& in(sK52(U_297,U_295,U_293,U_289),U_295)
& in(sK51(U_297,U_295,U_293,U_289),U_297) )
| ~ in(U_289,U_293) ) )
| U_293 != cartesian_product2(U_297,U_295) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_291,sK53(U_298,U_296,U_294))],[f_36_5]) ).
fof(f_36_7,plain,
( ! [U_298,U_296,U_294] :
( U_294 = cartesian_product2(U_298,U_296)
| ( ~ in(sK54(U_298,U_296,U_294),U_294)
& ? [U_284] :
( ? [U_283] :
( sK54(U_298,U_296,U_294) = ordered_pair(U_284,U_283)
& in(U_283,U_296) )
& in(U_284,U_298) ) )
| ( ! [U_282] :
( ! [U_281] :
( sK53(U_298,U_296,U_294) != ordered_pair(U_282,U_281)
| ~ in(U_281,U_296) )
| ~ in(U_282,U_298) )
& in(sK53(U_298,U_296,U_294),U_294) ) )
& ! [U_297,U_295,U_293] :
( ( ! [U_290] :
( in(U_290,U_293)
| ! [U_279] :
( ! [U_278] :
( U_290 != ordered_pair(U_279,U_278)
| ~ in(U_278,U_295) )
| ~ in(U_279,U_297) ) )
& ! [U_289] :
( ( U_289 = ordered_pair(sK51(U_297,U_295,U_293,U_289),sK52(U_297,U_295,U_293,U_289))
& in(sK52(U_297,U_295,U_293,U_289),U_295)
& in(sK51(U_297,U_295,U_293,U_289),U_297) )
| ~ in(U_289,U_293) ) )
| U_293 != cartesian_product2(U_297,U_295) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_292,sK54(U_298,U_296,U_294))],[f_36_6]) ).
fof(f_36_8,plain,
( ! [U_298,U_296,U_294] :
( U_294 = cartesian_product2(U_298,U_296)
| ( ~ in(sK54(U_298,U_296,U_294),U_294)
& ? [U_283] :
( sK54(U_298,U_296,U_294) = ordered_pair(sK55(U_298,U_296,U_294),U_283)
& in(U_283,U_296) )
& in(sK55(U_298,U_296,U_294),U_298) )
| ( ! [U_282] :
( ! [U_281] :
( sK53(U_298,U_296,U_294) != ordered_pair(U_282,U_281)
| ~ in(U_281,U_296) )
| ~ in(U_282,U_298) )
& in(sK53(U_298,U_296,U_294),U_294) ) )
& ! [U_297,U_295,U_293] :
( ( ! [U_290] :
( in(U_290,U_293)
| ! [U_279] :
( ! [U_278] :
( U_290 != ordered_pair(U_279,U_278)
| ~ in(U_278,U_295) )
| ~ in(U_279,U_297) ) )
& ! [U_289] :
( ( U_289 = ordered_pair(sK51(U_297,U_295,U_293,U_289),sK52(U_297,U_295,U_293,U_289))
& in(sK52(U_297,U_295,U_293,U_289),U_295)
& in(sK51(U_297,U_295,U_293,U_289),U_297) )
| ~ in(U_289,U_293) ) )
| U_293 != cartesian_product2(U_297,U_295) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_284,sK55(U_298,U_296,U_294))],[f_36_7]) ).
fof(f_36_9,plain,
( ! [U_298,U_296,U_294] :
( U_294 = cartesian_product2(U_298,U_296)
| ( ~ in(sK54(U_298,U_296,U_294),U_294)
& sK54(U_298,U_296,U_294) = ordered_pair(sK55(U_298,U_296,U_294),sK56(U_298,U_296,U_294))
& in(sK56(U_298,U_296,U_294),U_296)
& in(sK55(U_298,U_296,U_294),U_298) )
| ( ! [U_282] :
( ! [U_281] :
( sK53(U_298,U_296,U_294) != ordered_pair(U_282,U_281)
| ~ in(U_281,U_296) )
| ~ in(U_282,U_298) )
& in(sK53(U_298,U_296,U_294),U_294) ) )
& ! [U_297,U_295,U_293] :
( ( ! [U_290] :
( in(U_290,U_293)
| ! [U_279] :
( ! [U_278] :
( U_290 != ordered_pair(U_279,U_278)
| ~ in(U_278,U_295) )
| ~ in(U_279,U_297) ) )
& ! [U_289] :
( ( U_289 = ordered_pair(sK51(U_297,U_295,U_293,U_289),sK52(U_297,U_295,U_293,U_289))
& in(sK52(U_297,U_295,U_293,U_289),U_295)
& in(sK51(U_297,U_295,U_293,U_289),U_297) )
| ~ in(U_289,U_293) ) )
| U_293 != cartesian_product2(U_297,U_295) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_283,sK56(U_298,U_296,U_294))],[f_36_8]) ).
cnf(f_36_10,plain,
( in(sK51(U_297,U_295,U_293,U_289),U_297)
| ~ in(U_289,U_293)
| U_293 != cartesian_product2(U_297,U_295) ),
inference(clausify,[status(thm)],[f_36_9]) ).
cnf(f_36_11,plain,
( in(sK52(U_297,U_295,U_293,U_289),U_295)
| ~ in(U_289,U_293)
| U_293 != cartesian_product2(U_297,U_295) ),
inference(clausify,[status(thm)],[f_36_9]) ).
cnf(f_36_12,plain,
( U_289 = ordered_pair(sK51(U_297,U_295,U_293,U_289),sK52(U_297,U_295,U_293,U_289))
| ~ in(U_289,U_293)
| U_293 != cartesian_product2(U_297,U_295) ),
inference(clausify,[status(thm)],[f_36_9]) ).
cnf(f_36_13,plain,
( in(U_290,U_293)
| U_290 != ordered_pair(U_279,U_278)
| ~ in(U_278,U_295)
| ~ in(U_279,U_297)
| U_293 != cartesian_product2(U_297,U_295) ),
inference(clausify,[status(thm)],[f_36_9]) ).
cnf(f_36_14,plain,
( in(sK55(U_298,U_296,U_294),U_298)
| in(sK53(U_298,U_296,U_294),U_294)
| U_294 = cartesian_product2(U_298,U_296) ),
inference(clausify,[status(thm)],[f_36_9]) ).
cnf(f_36_15,plain,
( in(sK56(U_298,U_296,U_294),U_296)
| in(sK53(U_298,U_296,U_294),U_294)
| U_294 = cartesian_product2(U_298,U_296) ),
inference(clausify,[status(thm)],[f_36_9]) ).
cnf(f_36_16,plain,
( sK54(U_298,U_296,U_294) = ordered_pair(sK55(U_298,U_296,U_294),sK56(U_298,U_296,U_294))
| in(sK53(U_298,U_296,U_294),U_294)
| U_294 = cartesian_product2(U_298,U_296) ),
inference(clausify,[status(thm)],[f_36_9]) ).
cnf(f_36_17,plain,
( ~ in(sK54(U_298,U_296,U_294),U_294)
| in(sK53(U_298,U_296,U_294),U_294)
| U_294 = cartesian_product2(U_298,U_296) ),
inference(clausify,[status(thm)],[f_36_9]) ).
cnf(f_36_18,plain,
( in(sK55(U_298,U_296,U_294),U_298)
| sK53(U_298,U_296,U_294) != ordered_pair(U_282,U_281)
| ~ in(U_281,U_296)
| ~ in(U_282,U_298)
| U_294 = cartesian_product2(U_298,U_296) ),
inference(clausify,[status(thm)],[f_36_9]) ).
cnf(f_36_19,plain,
( in(sK56(U_298,U_296,U_294),U_296)
| sK53(U_298,U_296,U_294) != ordered_pair(U_282,U_281)
| ~ in(U_281,U_296)
| ~ in(U_282,U_298)
| U_294 = cartesian_product2(U_298,U_296) ),
inference(clausify,[status(thm)],[f_36_9]) ).
cnf(f_36_20,plain,
( sK54(U_298,U_296,U_294) = ordered_pair(sK55(U_298,U_296,U_294),sK56(U_298,U_296,U_294))
| sK53(U_298,U_296,U_294) != ordered_pair(U_282,U_281)
| ~ in(U_281,U_296)
| ~ in(U_282,U_298)
| U_294 = cartesian_product2(U_298,U_296) ),
inference(clausify,[status(thm)],[f_36_9]) ).
cnf(f_36_21,plain,
( ~ in(sK54(U_298,U_296,U_294),U_294)
| sK53(U_298,U_296,U_294) != ordered_pair(U_282,U_281)
| ~ in(U_281,U_296)
| ~ in(U_282,U_298)
| U_294 = cartesian_product2(U_298,U_296) ),
inference(clausify,[status(thm)],[f_36_9]) ).
fof(f_37_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_37_2,plain,
! [U_303] :
( ( epsilon_connected(U_303)
| ? [U_302,U_301] :
( ~ in(U_301,U_302)
& U_302 != U_301
& ~ in(U_302,U_301)
& in(U_301,U_303)
& in(U_302,U_303) ) )
& ( ! [U_300,U_299] :
( in(U_299,U_300)
| U_300 = U_299
| in(U_300,U_299)
| ~ in(U_299,U_303)
| ~ in(U_300,U_303) )
| ~ epsilon_connected(U_303) ) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
( ! [U_305] :
( epsilon_connected(U_305)
| ? [U_302] :
( ? [U_301] :
( ~ in(U_301,U_302)
& U_302 != U_301
& ~ in(U_302,U_301)
& in(U_301,U_305) )
& in(U_302,U_305) ) )
& ! [U_304] :
( ! [U_300] :
( ! [U_299] :
( in(U_299,U_300)
| U_300 = U_299
| in(U_300,U_299)
| ~ in(U_299,U_304) )
| ~ in(U_300,U_304) )
| ~ epsilon_connected(U_304) ) ),
inference(miniscope,[status(thm)],[f_37_2]) ).
fof(f_37_4,plain,
( ! [U_305] :
( epsilon_connected(U_305)
| ( ? [U_301] :
( ~ in(U_301,sK57(U_305))
& sK57(U_305) != U_301
& ~ in(sK57(U_305),U_301)
& in(U_301,U_305) )
& in(sK57(U_305),U_305) ) )
& ! [U_304] :
( ! [U_300] :
( ! [U_299] :
( in(U_299,U_300)
| U_300 = U_299
| in(U_300,U_299)
| ~ in(U_299,U_304) )
| ~ in(U_300,U_304) )
| ~ epsilon_connected(U_304) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_302,sK57(U_305))],[f_37_3]) ).
fof(f_37_5,plain,
( ! [U_305] :
( epsilon_connected(U_305)
| ( ~ in(sK58(U_305),sK57(U_305))
& sK57(U_305) != sK58(U_305)
& ~ in(sK57(U_305),sK58(U_305))
& in(sK58(U_305),U_305)
& in(sK57(U_305),U_305) ) )
& ! [U_304] :
( ! [U_300] :
( ! [U_299] :
( in(U_299,U_300)
| U_300 = U_299
| in(U_300,U_299)
| ~ in(U_299,U_304) )
| ~ in(U_300,U_304) )
| ~ epsilon_connected(U_304) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_301,sK58(U_305))],[f_37_4]) ).
cnf(f_37_6,plain,
( in(U_299,U_300)
| U_300 = U_299
| in(U_300,U_299)
| ~ in(U_299,U_304)
| ~ in(U_300,U_304)
| ~ epsilon_connected(U_304) ),
inference(clausify,[status(thm)],[f_37_5]) ).
cnf(f_37_7,plain,
( in(sK57(U_305),U_305)
| epsilon_connected(U_305) ),
inference(clausify,[status(thm)],[f_37_5]) ).
cnf(f_37_8,plain,
( in(sK58(U_305),U_305)
| epsilon_connected(U_305) ),
inference(clausify,[status(thm)],[f_37_5]) ).
cnf(f_37_9,plain,
( ~ in(sK57(U_305),sK58(U_305))
| epsilon_connected(U_305) ),
inference(clausify,[status(thm)],[f_37_5]) ).
cnf(f_37_10,plain,
( sK57(U_305) != sK58(U_305)
| epsilon_connected(U_305) ),
inference(clausify,[status(thm)],[f_37_5]) ).
cnf(f_37_11,plain,
( ~ in(sK58(U_305),sK57(U_305))
| epsilon_connected(U_305) ),
inference(clausify,[status(thm)],[f_37_5]) ).
fof(f_38_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_38_2,plain,
! [U_311] :
( ! [U_310] :
( ( ( subset(U_311,U_310)
| ? [U_309,U_308] :
( ~ in(ordered_pair(U_309,U_308),U_310)
& in(ordered_pair(U_309,U_308),U_311) ) )
& ( ! [U_307,U_306] :
( in(ordered_pair(U_307,U_306),U_310)
| ~ in(ordered_pair(U_307,U_306),U_311) )
| ~ subset(U_311,U_310) ) )
| ~ relation(U_310) )
| ~ relation(U_311) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_311] :
( ! [U_310] :
( ( ( subset(U_311,U_310)
| ? [U_308] :
( ~ in(ordered_pair(sK59(U_311,U_310),U_308),U_310)
& in(ordered_pair(sK59(U_311,U_310),U_308),U_311) ) )
& ( ! [U_307,U_306] :
( in(ordered_pair(U_307,U_306),U_310)
| ~ in(ordered_pair(U_307,U_306),U_311) )
| ~ subset(U_311,U_310) ) )
| ~ relation(U_310) )
| ~ relation(U_311) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_309,sK59(U_311,U_310))],[f_38_2]) ).
fof(f_38_4,plain,
! [U_311] :
( ! [U_310] :
( ( ( subset(U_311,U_310)
| ( ~ in(ordered_pair(sK59(U_311,U_310),sK60(U_311,U_310)),U_310)
& in(ordered_pair(sK59(U_311,U_310),sK60(U_311,U_310)),U_311) ) )
& ( ! [U_307,U_306] :
( in(ordered_pair(U_307,U_306),U_310)
| ~ in(ordered_pair(U_307,U_306),U_311) )
| ~ subset(U_311,U_310) ) )
| ~ relation(U_310) )
| ~ relation(U_311) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_308,sK60(U_311,U_310))],[f_38_3]) ).
cnf(f_38_5,plain,
( in(ordered_pair(U_307,U_306),U_310)
| ~ in(ordered_pair(U_307,U_306),U_311)
| ~ subset(U_311,U_310)
| ~ relation(U_310)
| ~ relation(U_311) ),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_38_6,plain,
( in(ordered_pair(sK59(U_311,U_310),sK60(U_311,U_310)),U_311)
| subset(U_311,U_310)
| ~ relation(U_310)
| ~ relation(U_311) ),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_38_7,plain,
( ~ in(ordered_pair(sK59(U_311,U_310),sK60(U_311,U_310)),U_310)
| subset(U_311,U_310)
| ~ relation(U_310)
| ~ relation(U_311) ),
inference(clausify,[status(thm)],[f_38_4]) ).
fof(f_39_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_39_2,plain,
! [U_315,U_314] :
( ( subset(U_315,U_314)
| ? [U_313] :
( ~ in(U_313,U_314)
& in(U_313,U_315) ) )
& ( ! [U_312] :
( in(U_312,U_314)
| ~ in(U_312,U_315) )
| ~ subset(U_315,U_314) ) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
( ! [U_319,U_317] :
( subset(U_319,U_317)
| ? [U_313] :
( ~ in(U_313,U_317)
& in(U_313,U_319) ) )
& ! [U_318,U_316] :
( ! [U_312] :
( in(U_312,U_316)
| ~ in(U_312,U_318) )
| ~ subset(U_318,U_316) ) ),
inference(miniscope,[status(thm)],[f_39_2]) ).
fof(f_39_4,plain,
( ! [U_319,U_317] :
( subset(U_319,U_317)
| ( ~ in(sK61(U_319,U_317),U_317)
& in(sK61(U_319,U_317),U_319) ) )
& ! [U_318,U_316] :
( ! [U_312] :
( in(U_312,U_316)
| ~ in(U_312,U_318) )
| ~ subset(U_318,U_316) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_313,sK61(U_319,U_317))],[f_39_3]) ).
cnf(f_39_5,plain,
( in(U_312,U_316)
| ~ in(U_312,U_318)
| ~ subset(U_318,U_316) ),
inference(clausify,[status(thm)],[f_39_4]) ).
cnf(f_39_6,plain,
( in(sK61(U_319,U_317),U_319)
| subset(U_319,U_317) ),
inference(clausify,[status(thm)],[f_39_4]) ).
cnf(f_39_7,plain,
( ~ in(sK61(U_319,U_317),U_317)
| subset(U_319,U_317) ),
inference(clausify,[status(thm)],[f_39_4]) ).
fof(f_40_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_40_2,plain,
! [U_324,U_323,U_322] :
( ( U_322 = set_intersection2(U_324,U_323)
| ? [U_321] :
( ( ~ in(U_321,U_322)
& in(U_321,U_323)
& in(U_321,U_324) )
| ( ( ~ in(U_321,U_323)
| ~ in(U_321,U_324) )
& in(U_321,U_322) ) ) )
& ( ! [U_320] :
( ( in(U_320,U_322)
| ~ in(U_320,U_323)
| ~ in(U_320,U_324) )
& ( ( in(U_320,U_323)
& in(U_320,U_324) )
| ~ in(U_320,U_322) ) )
| U_322 != set_intersection2(U_324,U_323) ) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
( ! [U_334,U_332,U_330] :
( U_330 = set_intersection2(U_334,U_332)
| ? [U_328] :
( ~ in(U_328,U_330)
& in(U_328,U_332)
& in(U_328,U_334) )
| ? [U_327] :
( ( ~ in(U_327,U_332)
| ~ in(U_327,U_334) )
& in(U_327,U_330) ) )
& ! [U_333,U_331,U_329] :
( ( ! [U_326] :
( in(U_326,U_329)
| ~ in(U_326,U_331)
| ~ in(U_326,U_333) )
& ! [U_325] :
( ( in(U_325,U_331)
& in(U_325,U_333) )
| ~ in(U_325,U_329) ) )
| U_329 != set_intersection2(U_333,U_331) ) ),
inference(miniscope,[status(thm)],[f_40_2]) ).
fof(f_40_4,plain,
( ! [U_334,U_332,U_330] :
( U_330 = set_intersection2(U_334,U_332)
| ? [U_328] :
( ~ in(U_328,U_330)
& in(U_328,U_332)
& in(U_328,U_334) )
| ( ( ~ in(sK62(U_334,U_332,U_330),U_332)
| ~ in(sK62(U_334,U_332,U_330),U_334) )
& in(sK62(U_334,U_332,U_330),U_330) ) )
& ! [U_333,U_331,U_329] :
( ( ! [U_326] :
( in(U_326,U_329)
| ~ in(U_326,U_331)
| ~ in(U_326,U_333) )
& ! [U_325] :
( ( in(U_325,U_331)
& in(U_325,U_333) )
| ~ in(U_325,U_329) ) )
| U_329 != set_intersection2(U_333,U_331) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_327,sK62(U_334,U_332,U_330))],[f_40_3]) ).
fof(f_40_5,plain,
( ! [U_334,U_332,U_330] :
( U_330 = set_intersection2(U_334,U_332)
| ( ~ in(sK63(U_334,U_332,U_330),U_330)
& in(sK63(U_334,U_332,U_330),U_332)
& in(sK63(U_334,U_332,U_330),U_334) )
| ( ( ~ in(sK62(U_334,U_332,U_330),U_332)
| ~ in(sK62(U_334,U_332,U_330),U_334) )
& in(sK62(U_334,U_332,U_330),U_330) ) )
& ! [U_333,U_331,U_329] :
( ( ! [U_326] :
( in(U_326,U_329)
| ~ in(U_326,U_331)
| ~ in(U_326,U_333) )
& ! [U_325] :
( ( in(U_325,U_331)
& in(U_325,U_333) )
| ~ in(U_325,U_329) ) )
| U_329 != set_intersection2(U_333,U_331) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_328,sK63(U_334,U_332,U_330))],[f_40_4]) ).
cnf(f_40_6,plain,
( in(U_325,U_333)
| ~ in(U_325,U_329)
| U_329 != set_intersection2(U_333,U_331) ),
inference(clausify,[status(thm)],[f_40_5]) ).
cnf(f_40_7,plain,
( in(U_325,U_331)
| ~ in(U_325,U_329)
| U_329 != set_intersection2(U_333,U_331) ),
inference(clausify,[status(thm)],[f_40_5]) ).
cnf(f_40_8,plain,
( in(U_326,U_329)
| ~ in(U_326,U_331)
| ~ in(U_326,U_333)
| U_329 != set_intersection2(U_333,U_331) ),
inference(clausify,[status(thm)],[f_40_5]) ).
cnf(f_40_9,plain,
( in(sK63(U_334,U_332,U_330),U_334)
| in(sK62(U_334,U_332,U_330),U_330)
| U_330 = set_intersection2(U_334,U_332) ),
inference(clausify,[status(thm)],[f_40_5]) ).
cnf(f_40_10,plain,
( in(sK63(U_334,U_332,U_330),U_332)
| in(sK62(U_334,U_332,U_330),U_330)
| U_330 = set_intersection2(U_334,U_332) ),
inference(clausify,[status(thm)],[f_40_5]) ).
cnf(f_40_11,plain,
( ~ in(sK63(U_334,U_332,U_330),U_330)
| in(sK62(U_334,U_332,U_330),U_330)
| U_330 = set_intersection2(U_334,U_332) ),
inference(clausify,[status(thm)],[f_40_5]) ).
cnf(f_40_12,plain,
( in(sK63(U_334,U_332,U_330),U_334)
| ~ in(sK62(U_334,U_332,U_330),U_332)
| ~ in(sK62(U_334,U_332,U_330),U_334)
| U_330 = set_intersection2(U_334,U_332) ),
inference(clausify,[status(thm)],[f_40_5]) ).
cnf(f_40_13,plain,
( in(sK63(U_334,U_332,U_330),U_332)
| ~ in(sK62(U_334,U_332,U_330),U_332)
| ~ in(sK62(U_334,U_332,U_330),U_334)
| U_330 = set_intersection2(U_334,U_332) ),
inference(clausify,[status(thm)],[f_40_5]) ).
cnf(f_40_14,plain,
( ~ in(sK63(U_334,U_332,U_330),U_330)
| ~ in(sK62(U_334,U_332,U_330),U_332)
| ~ in(sK62(U_334,U_332,U_330),U_334)
| U_330 = set_intersection2(U_334,U_332) ),
inference(clausify,[status(thm)],[f_40_5]) ).
fof(f_41_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_41_2,plain,
! [U_337] :
( ! [U_336,U_335] :
( ( ( ( U_335 = apply(U_337,U_336)
| U_335 != empty_set )
& ( U_335 = empty_set
| U_335 != apply(U_337,U_336) ) )
| in(U_336,relation_dom(U_337)) )
& ( ( ( U_335 = apply(U_337,U_336)
| ~ in(ordered_pair(U_336,U_335),U_337) )
& ( in(ordered_pair(U_336,U_335),U_337)
| U_335 != apply(U_337,U_336) ) )
| ~ in(U_336,relation_dom(U_337)) ) )
| ~ function(U_337)
| ~ relation(U_337) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_337] :
( ( ! [U_345] :
( ( ! [U_343] :
( U_343 = apply(U_337,U_345)
| U_343 != empty_set )
& ! [U_342] :
( U_342 = empty_set
| U_342 != apply(U_337,U_345) ) )
| in(U_345,relation_dom(U_337)) )
& ! [U_344] :
( ( ! [U_341] :
( U_341 = apply(U_337,U_344)
| ~ in(ordered_pair(U_344,U_341),U_337) )
& ! [U_340] :
( in(ordered_pair(U_344,U_340),U_337)
| U_340 != apply(U_337,U_344) ) )
| ~ in(U_344,relation_dom(U_337)) ) )
| ~ function(U_337)
| ~ relation(U_337) ),
inference(miniscope,[status(thm)],[f_41_2]) ).
cnf(f_41_4,plain,
( in(ordered_pair(U_344,U_340),U_337)
| U_340 != apply(U_337,U_344)
| ~ in(U_344,relation_dom(U_337))
| ~ function(U_337)
| ~ relation(U_337) ),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_5,plain,
( U_341 = apply(U_337,U_344)
| ~ in(ordered_pair(U_344,U_341),U_337)
| ~ in(U_344,relation_dom(U_337))
| ~ function(U_337)
| ~ relation(U_337) ),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_6,plain,
( U_342 = empty_set
| U_342 != apply(U_337,U_345)
| in(U_345,relation_dom(U_337))
| ~ function(U_337)
| ~ relation(U_337) ),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_7,plain,
( U_343 = apply(U_337,U_345)
| U_343 != empty_set
| in(U_345,relation_dom(U_337))
| ~ function(U_337)
| ~ relation(U_337) ),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_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_42_2,plain,
! [U_346] :
( ( ordinal(U_346)
| ~ epsilon_connected(U_346)
| ~ epsilon_transitive(U_346) )
& ( ( epsilon_connected(U_346)
& epsilon_transitive(U_346) )
| ~ ordinal(U_346) ) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
( ! [U_348] :
( ordinal(U_348)
| ~ epsilon_connected(U_348)
| ~ epsilon_transitive(U_348) )
& ! [U_347] :
( ( epsilon_connected(U_347)
& epsilon_transitive(U_347) )
| ~ ordinal(U_347) ) ),
inference(miniscope,[status(thm)],[f_42_2]) ).
cnf(f_42_4,plain,
( epsilon_transitive(U_347)
| ~ ordinal(U_347) ),
inference(clausify,[status(thm)],[f_42_3]) ).
cnf(f_42_5,plain,
( epsilon_connected(U_347)
| ~ ordinal(U_347) ),
inference(clausify,[status(thm)],[f_42_3]) ).
cnf(f_42_6,plain,
( ordinal(U_348)
| ~ epsilon_connected(U_348)
| ~ epsilon_transitive(U_348) ),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_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_43_2,plain,
! [U_356] :
( ! [U_355] :
( ( U_355 = relation_dom(U_356)
| ? [U_354] :
( ( ~ in(U_354,U_355)
& ? [U_353] : in(ordered_pair(U_354,U_353),U_356) )
| ( ! [U_352] : ~ in(ordered_pair(U_354,U_352),U_356)
& in(U_354,U_355) ) ) )
& ( ! [U_351] :
( ( in(U_351,U_355)
| ! [U_350] : ~ in(ordered_pair(U_351,U_350),U_356) )
& ( ? [U_349] : in(ordered_pair(U_351,U_349),U_356)
| ~ in(U_351,U_355) ) )
| U_355 != relation_dom(U_356) ) )
| ~ relation(U_356) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_356] :
( ( ! [U_362] :
( U_362 = relation_dom(U_356)
| ? [U_360] :
( ~ in(U_360,U_362)
& ? [U_353] : in(ordered_pair(U_360,U_353),U_356) )
| ? [U_359] :
( ! [U_352] : ~ in(ordered_pair(U_359,U_352),U_356)
& in(U_359,U_362) ) )
& ! [U_361] :
( ( ! [U_358] :
( in(U_358,U_361)
| ! [U_350] : ~ in(ordered_pair(U_358,U_350),U_356) )
& ! [U_357] :
( ? [U_349] : in(ordered_pair(U_357,U_349),U_356)
| ~ in(U_357,U_361) ) )
| U_361 != relation_dom(U_356) ) )
| ~ relation(U_356) ),
inference(miniscope,[status(thm)],[f_43_2]) ).
fof(f_43_4,plain,
! [U_356] :
( ( ! [U_362] :
( U_362 = relation_dom(U_356)
| ? [U_360] :
( ~ in(U_360,U_362)
& ? [U_353] : in(ordered_pair(U_360,U_353),U_356) )
| ? [U_359] :
( ! [U_352] : ~ in(ordered_pair(U_359,U_352),U_356)
& in(U_359,U_362) ) )
& ! [U_361] :
( ( ! [U_358] :
( in(U_358,U_361)
| ! [U_350] : ~ in(ordered_pair(U_358,U_350),U_356) )
& ! [U_357] :
( in(ordered_pair(U_357,sK64(U_356,U_361,U_357)),U_356)
| ~ in(U_357,U_361) ) )
| U_361 != relation_dom(U_356) ) )
| ~ relation(U_356) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_349,sK64(U_356,U_361,U_357))],[f_43_3]) ).
fof(f_43_5,plain,
! [U_356] :
( ( ! [U_362] :
( U_362 = relation_dom(U_356)
| ? [U_360] :
( ~ in(U_360,U_362)
& ? [U_353] : in(ordered_pair(U_360,U_353),U_356) )
| ( ! [U_352] : ~ in(ordered_pair(sK65(U_356,U_362),U_352),U_356)
& in(sK65(U_356,U_362),U_362) ) )
& ! [U_361] :
( ( ! [U_358] :
( in(U_358,U_361)
| ! [U_350] : ~ in(ordered_pair(U_358,U_350),U_356) )
& ! [U_357] :
( in(ordered_pair(U_357,sK64(U_356,U_361,U_357)),U_356)
| ~ in(U_357,U_361) ) )
| U_361 != relation_dom(U_356) ) )
| ~ relation(U_356) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_359,sK65(U_356,U_362))],[f_43_4]) ).
fof(f_43_6,plain,
! [U_356] :
( ( ! [U_362] :
( U_362 = relation_dom(U_356)
| ( ~ in(sK66(U_356,U_362),U_362)
& ? [U_353] : in(ordered_pair(sK66(U_356,U_362),U_353),U_356) )
| ( ! [U_352] : ~ in(ordered_pair(sK65(U_356,U_362),U_352),U_356)
& in(sK65(U_356,U_362),U_362) ) )
& ! [U_361] :
( ( ! [U_358] :
( in(U_358,U_361)
| ! [U_350] : ~ in(ordered_pair(U_358,U_350),U_356) )
& ! [U_357] :
( in(ordered_pair(U_357,sK64(U_356,U_361,U_357)),U_356)
| ~ in(U_357,U_361) ) )
| U_361 != relation_dom(U_356) ) )
| ~ relation(U_356) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_360,sK66(U_356,U_362))],[f_43_5]) ).
fof(f_43_7,plain,
! [U_356] :
( ( ! [U_362] :
( U_362 = relation_dom(U_356)
| ( ~ in(sK66(U_356,U_362),U_362)
& in(ordered_pair(sK66(U_356,U_362),sK67(U_356,U_362)),U_356) )
| ( ! [U_352] : ~ in(ordered_pair(sK65(U_356,U_362),U_352),U_356)
& in(sK65(U_356,U_362),U_362) ) )
& ! [U_361] :
( ( ! [U_358] :
( in(U_358,U_361)
| ! [U_350] : ~ in(ordered_pair(U_358,U_350),U_356) )
& ! [U_357] :
( in(ordered_pair(U_357,sK64(U_356,U_361,U_357)),U_356)
| ~ in(U_357,U_361) ) )
| U_361 != relation_dom(U_356) ) )
| ~ relation(U_356) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_353,sK67(U_356,U_362))],[f_43_6]) ).
cnf(f_43_8,plain,
( in(ordered_pair(U_357,sK64(U_356,U_361,U_357)),U_356)
| ~ in(U_357,U_361)
| U_361 != relation_dom(U_356)
| ~ relation(U_356) ),
inference(clausify,[status(thm)],[f_43_7]) ).
cnf(f_43_9,plain,
( in(U_358,U_361)
| ~ in(ordered_pair(U_358,U_350),U_356)
| U_361 != relation_dom(U_356)
| ~ relation(U_356) ),
inference(clausify,[status(thm)],[f_43_7]) ).
cnf(f_43_10,plain,
( in(ordered_pair(sK66(U_356,U_362),sK67(U_356,U_362)),U_356)
| in(sK65(U_356,U_362),U_362)
| U_362 = relation_dom(U_356)
| ~ relation(U_356) ),
inference(clausify,[status(thm)],[f_43_7]) ).
cnf(f_43_11,plain,
( ~ in(sK66(U_356,U_362),U_362)
| in(sK65(U_356,U_362),U_362)
| U_362 = relation_dom(U_356)
| ~ relation(U_356) ),
inference(clausify,[status(thm)],[f_43_7]) ).
cnf(f_43_12,plain,
( in(ordered_pair(sK66(U_356,U_362),sK67(U_356,U_362)),U_356)
| ~ in(ordered_pair(sK65(U_356,U_362),U_352),U_356)
| U_362 = relation_dom(U_356)
| ~ relation(U_356) ),
inference(clausify,[status(thm)],[f_43_7]) ).
cnf(f_43_13,plain,
( ~ in(sK66(U_356,U_362),U_362)
| ~ in(ordered_pair(sK65(U_356,U_362),U_352),U_356)
| U_362 = relation_dom(U_356)
| ~ relation(U_356) ),
inference(clausify,[status(thm)],[f_43_7]) ).
fof(f_44_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_44_2,plain,
! [U_368] :
( ! [U_367] :
( ( is_antisymmetric_in(U_368,U_367)
| ? [U_366,U_365] :
( U_366 != U_365
& in(ordered_pair(U_365,U_366),U_368)
& in(ordered_pair(U_366,U_365),U_368)
& in(U_365,U_367)
& in(U_366,U_367) ) )
& ( ! [U_364,U_363] :
( U_364 = U_363
| ~ in(ordered_pair(U_363,U_364),U_368)
| ~ in(ordered_pair(U_364,U_363),U_368)
| ~ in(U_363,U_367)
| ~ in(U_364,U_367) )
| ~ is_antisymmetric_in(U_368,U_367) ) )
| ~ relation(U_368) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_368] :
( ( ! [U_370] :
( is_antisymmetric_in(U_368,U_370)
| ? [U_366,U_365] :
( U_366 != U_365
& in(ordered_pair(U_365,U_366),U_368)
& in(ordered_pair(U_366,U_365),U_368)
& in(U_365,U_370)
& in(U_366,U_370) ) )
& ! [U_369] :
( ! [U_364,U_363] :
( U_364 = U_363
| ~ in(ordered_pair(U_363,U_364),U_368)
| ~ in(ordered_pair(U_364,U_363),U_368)
| ~ in(U_363,U_369)
| ~ in(U_364,U_369) )
| ~ is_antisymmetric_in(U_368,U_369) ) )
| ~ relation(U_368) ),
inference(miniscope,[status(thm)],[f_44_2]) ).
fof(f_44_4,plain,
! [U_368] :
( ( ! [U_370] :
( is_antisymmetric_in(U_368,U_370)
| ? [U_365] :
( sK68(U_368,U_370) != U_365
& in(ordered_pair(U_365,sK68(U_368,U_370)),U_368)
& in(ordered_pair(sK68(U_368,U_370),U_365),U_368)
& in(U_365,U_370)
& in(sK68(U_368,U_370),U_370) ) )
& ! [U_369] :
( ! [U_364,U_363] :
( U_364 = U_363
| ~ in(ordered_pair(U_363,U_364),U_368)
| ~ in(ordered_pair(U_364,U_363),U_368)
| ~ in(U_363,U_369)
| ~ in(U_364,U_369) )
| ~ is_antisymmetric_in(U_368,U_369) ) )
| ~ relation(U_368) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_366,sK68(U_368,U_370))],[f_44_3]) ).
fof(f_44_5,plain,
! [U_368] :
( ( ! [U_370] :
( is_antisymmetric_in(U_368,U_370)
| ( sK68(U_368,U_370) != sK69(U_368,U_370)
& in(ordered_pair(sK69(U_368,U_370),sK68(U_368,U_370)),U_368)
& in(ordered_pair(sK68(U_368,U_370),sK69(U_368,U_370)),U_368)
& in(sK69(U_368,U_370),U_370)
& in(sK68(U_368,U_370),U_370) ) )
& ! [U_369] :
( ! [U_364,U_363] :
( U_364 = U_363
| ~ in(ordered_pair(U_363,U_364),U_368)
| ~ in(ordered_pair(U_364,U_363),U_368)
| ~ in(U_363,U_369)
| ~ in(U_364,U_369) )
| ~ is_antisymmetric_in(U_368,U_369) ) )
| ~ relation(U_368) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_365,sK69(U_368,U_370))],[f_44_4]) ).
cnf(f_44_6,plain,
( U_364 = U_363
| ~ in(ordered_pair(U_363,U_364),U_368)
| ~ in(ordered_pair(U_364,U_363),U_368)
| ~ in(U_363,U_369)
| ~ in(U_364,U_369)
| ~ is_antisymmetric_in(U_368,U_369)
| ~ relation(U_368) ),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(f_44_7,plain,
( in(sK68(U_368,U_370),U_370)
| is_antisymmetric_in(U_368,U_370)
| ~ relation(U_368) ),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(f_44_8,plain,
( in(sK69(U_368,U_370),U_370)
| is_antisymmetric_in(U_368,U_370)
| ~ relation(U_368) ),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(f_44_9,plain,
( in(ordered_pair(sK68(U_368,U_370),sK69(U_368,U_370)),U_368)
| is_antisymmetric_in(U_368,U_370)
| ~ relation(U_368) ),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(f_44_10,plain,
( in(ordered_pair(sK69(U_368,U_370),sK68(U_368,U_370)),U_368)
| is_antisymmetric_in(U_368,U_370)
| ~ relation(U_368) ),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(f_44_11,plain,
( sK68(U_368,U_370) != sK69(U_368,U_370)
| is_antisymmetric_in(U_368,U_370)
| ~ relation(U_368) ),
inference(clausify,[status(thm)],[f_44_5]) ).
fof(f_45_1,plain,
! [A] : cast_to_subset(A) = A,
inference(fof_nnf,[status(thm)],[d4_subset_1]) ).
fof(f_45_2,plain,
! [U_371] : cast_to_subset(U_371) = U_371,
inference(variable_rename,[status(thm)],[f_45_1]) ).
cnf(f_45_3,plain,
cast_to_subset(U_371) = U_371,
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_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_46_2,plain,
! [U_379,U_378] :
( ( U_378 = union(U_379)
| ? [U_377] :
( ( ~ in(U_377,U_378)
& ? [U_376] :
( in(U_376,U_379)
& in(U_377,U_376) ) )
| ( ! [U_375] :
( ~ in(U_375,U_379)
| ~ in(U_377,U_375) )
& in(U_377,U_378) ) ) )
& ( ! [U_374] :
( ( in(U_374,U_378)
| ! [U_373] :
( ~ in(U_373,U_379)
| ~ in(U_374,U_373) ) )
& ( ? [U_372] :
( in(U_372,U_379)
& in(U_374,U_372) )
| ~ in(U_374,U_378) ) )
| U_378 != union(U_379) ) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
( ! [U_387,U_385] :
( U_385 = union(U_387)
| ? [U_383] :
( ~ in(U_383,U_385)
& ? [U_376] :
( in(U_376,U_387)
& in(U_383,U_376) ) )
| ? [U_382] :
( ! [U_375] :
( ~ in(U_375,U_387)
| ~ in(U_382,U_375) )
& in(U_382,U_385) ) )
& ! [U_386,U_384] :
( ( ! [U_381] :
( in(U_381,U_384)
| ! [U_373] :
( ~ in(U_373,U_386)
| ~ in(U_381,U_373) ) )
& ! [U_380] :
( ? [U_372] :
( in(U_372,U_386)
& in(U_380,U_372) )
| ~ in(U_380,U_384) ) )
| U_384 != union(U_386) ) ),
inference(miniscope,[status(thm)],[f_46_2]) ).
fof(f_46_4,plain,
( ! [U_387,U_385] :
( U_385 = union(U_387)
| ? [U_383] :
( ~ in(U_383,U_385)
& ? [U_376] :
( in(U_376,U_387)
& in(U_383,U_376) ) )
| ? [U_382] :
( ! [U_375] :
( ~ in(U_375,U_387)
| ~ in(U_382,U_375) )
& in(U_382,U_385) ) )
& ! [U_386,U_384] :
( ( ! [U_381] :
( in(U_381,U_384)
| ! [U_373] :
( ~ in(U_373,U_386)
| ~ in(U_381,U_373) ) )
& ! [U_380] :
( ( in(sK70(U_386,U_384,U_380),U_386)
& in(U_380,sK70(U_386,U_384,U_380)) )
| ~ in(U_380,U_384) ) )
| U_384 != union(U_386) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_372,sK70(U_386,U_384,U_380))],[f_46_3]) ).
fof(f_46_5,plain,
( ! [U_387,U_385] :
( U_385 = union(U_387)
| ? [U_383] :
( ~ in(U_383,U_385)
& ? [U_376] :
( in(U_376,U_387)
& in(U_383,U_376) ) )
| ( ! [U_375] :
( ~ in(U_375,U_387)
| ~ in(sK71(U_387,U_385),U_375) )
& in(sK71(U_387,U_385),U_385) ) )
& ! [U_386,U_384] :
( ( ! [U_381] :
( in(U_381,U_384)
| ! [U_373] :
( ~ in(U_373,U_386)
| ~ in(U_381,U_373) ) )
& ! [U_380] :
( ( in(sK70(U_386,U_384,U_380),U_386)
& in(U_380,sK70(U_386,U_384,U_380)) )
| ~ in(U_380,U_384) ) )
| U_384 != union(U_386) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_382,sK71(U_387,U_385))],[f_46_4]) ).
fof(f_46_6,plain,
( ! [U_387,U_385] :
( U_385 = union(U_387)
| ( ~ in(sK72(U_387,U_385),U_385)
& ? [U_376] :
( in(U_376,U_387)
& in(sK72(U_387,U_385),U_376) ) )
| ( ! [U_375] :
( ~ in(U_375,U_387)
| ~ in(sK71(U_387,U_385),U_375) )
& in(sK71(U_387,U_385),U_385) ) )
& ! [U_386,U_384] :
( ( ! [U_381] :
( in(U_381,U_384)
| ! [U_373] :
( ~ in(U_373,U_386)
| ~ in(U_381,U_373) ) )
& ! [U_380] :
( ( in(sK70(U_386,U_384,U_380),U_386)
& in(U_380,sK70(U_386,U_384,U_380)) )
| ~ in(U_380,U_384) ) )
| U_384 != union(U_386) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_383,sK72(U_387,U_385))],[f_46_5]) ).
fof(f_46_7,plain,
( ! [U_387,U_385] :
( U_385 = union(U_387)
| ( ~ in(sK72(U_387,U_385),U_385)
& in(sK73(U_387,U_385),U_387)
& in(sK72(U_387,U_385),sK73(U_387,U_385)) )
| ( ! [U_375] :
( ~ in(U_375,U_387)
| ~ in(sK71(U_387,U_385),U_375) )
& in(sK71(U_387,U_385),U_385) ) )
& ! [U_386,U_384] :
( ( ! [U_381] :
( in(U_381,U_384)
| ! [U_373] :
( ~ in(U_373,U_386)
| ~ in(U_381,U_373) ) )
& ! [U_380] :
( ( in(sK70(U_386,U_384,U_380),U_386)
& in(U_380,sK70(U_386,U_384,U_380)) )
| ~ in(U_380,U_384) ) )
| U_384 != union(U_386) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_376,sK73(U_387,U_385))],[f_46_6]) ).
cnf(f_46_8,plain,
( in(U_380,sK70(U_386,U_384,U_380))
| ~ in(U_380,U_384)
| U_384 != union(U_386) ),
inference(clausify,[status(thm)],[f_46_7]) ).
cnf(f_46_9,plain,
( in(sK70(U_386,U_384,U_380),U_386)
| ~ in(U_380,U_384)
| U_384 != union(U_386) ),
inference(clausify,[status(thm)],[f_46_7]) ).
cnf(f_46_10,plain,
( in(U_381,U_384)
| ~ in(U_373,U_386)
| ~ in(U_381,U_373)
| U_384 != union(U_386) ),
inference(clausify,[status(thm)],[f_46_7]) ).
cnf(f_46_11,plain,
( in(sK72(U_387,U_385),sK73(U_387,U_385))
| in(sK71(U_387,U_385),U_385)
| U_385 = union(U_387) ),
inference(clausify,[status(thm)],[f_46_7]) ).
cnf(f_46_12,plain,
( in(sK73(U_387,U_385),U_387)
| in(sK71(U_387,U_385),U_385)
| U_385 = union(U_387) ),
inference(clausify,[status(thm)],[f_46_7]) ).
cnf(f_46_13,plain,
( ~ in(sK72(U_387,U_385),U_385)
| in(sK71(U_387,U_385),U_385)
| U_385 = union(U_387) ),
inference(clausify,[status(thm)],[f_46_7]) ).
cnf(f_46_14,plain,
( in(sK72(U_387,U_385),sK73(U_387,U_385))
| ~ in(U_375,U_387)
| ~ in(sK71(U_387,U_385),U_375)
| U_385 = union(U_387) ),
inference(clausify,[status(thm)],[f_46_7]) ).
cnf(f_46_15,plain,
( in(sK73(U_387,U_385),U_387)
| ~ in(U_375,U_387)
| ~ in(sK71(U_387,U_385),U_375)
| U_385 = union(U_387) ),
inference(clausify,[status(thm)],[f_46_7]) ).
cnf(f_46_16,plain,
( ~ in(sK72(U_387,U_385),U_385)
| ~ in(U_375,U_387)
| ~ in(sK71(U_387,U_385),U_375)
| U_385 = union(U_387) ),
inference(clausify,[status(thm)],[f_46_7]) ).
fof(f_47_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_47_2,plain,
! [U_392,U_391,U_390] :
( ( U_390 = set_difference(U_392,U_391)
| ? [U_389] :
( ( ~ in(U_389,U_390)
& ~ in(U_389,U_391)
& in(U_389,U_392) )
| ( ( in(U_389,U_391)
| ~ in(U_389,U_392) )
& in(U_389,U_390) ) ) )
& ( ! [U_388] :
( ( in(U_388,U_390)
| in(U_388,U_391)
| ~ in(U_388,U_392) )
& ( ( ~ in(U_388,U_391)
& in(U_388,U_392) )
| ~ in(U_388,U_390) ) )
| U_390 != set_difference(U_392,U_391) ) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
( ! [U_402,U_400,U_398] :
( U_398 = set_difference(U_402,U_400)
| ? [U_396] :
( ~ in(U_396,U_398)
& ~ in(U_396,U_400)
& in(U_396,U_402) )
| ? [U_395] :
( ( in(U_395,U_400)
| ~ in(U_395,U_402) )
& in(U_395,U_398) ) )
& ! [U_401,U_399,U_397] :
( ( ! [U_394] :
( in(U_394,U_397)
| in(U_394,U_399)
| ~ in(U_394,U_401) )
& ! [U_393] :
( ( ~ in(U_393,U_399)
& in(U_393,U_401) )
| ~ in(U_393,U_397) ) )
| U_397 != set_difference(U_401,U_399) ) ),
inference(miniscope,[status(thm)],[f_47_2]) ).
fof(f_47_4,plain,
( ! [U_402,U_400,U_398] :
( U_398 = set_difference(U_402,U_400)
| ? [U_396] :
( ~ in(U_396,U_398)
& ~ in(U_396,U_400)
& in(U_396,U_402) )
| ( ( in(sK74(U_402,U_400,U_398),U_400)
| ~ in(sK74(U_402,U_400,U_398),U_402) )
& in(sK74(U_402,U_400,U_398),U_398) ) )
& ! [U_401,U_399,U_397] :
( ( ! [U_394] :
( in(U_394,U_397)
| in(U_394,U_399)
| ~ in(U_394,U_401) )
& ! [U_393] :
( ( ~ in(U_393,U_399)
& in(U_393,U_401) )
| ~ in(U_393,U_397) ) )
| U_397 != set_difference(U_401,U_399) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_395,sK74(U_402,U_400,U_398))],[f_47_3]) ).
fof(f_47_5,plain,
( ! [U_402,U_400,U_398] :
( U_398 = set_difference(U_402,U_400)
| ( ~ in(sK75(U_402,U_400,U_398),U_398)
& ~ in(sK75(U_402,U_400,U_398),U_400)
& in(sK75(U_402,U_400,U_398),U_402) )
| ( ( in(sK74(U_402,U_400,U_398),U_400)
| ~ in(sK74(U_402,U_400,U_398),U_402) )
& in(sK74(U_402,U_400,U_398),U_398) ) )
& ! [U_401,U_399,U_397] :
( ( ! [U_394] :
( in(U_394,U_397)
| in(U_394,U_399)
| ~ in(U_394,U_401) )
& ! [U_393] :
( ( ~ in(U_393,U_399)
& in(U_393,U_401) )
| ~ in(U_393,U_397) ) )
| U_397 != set_difference(U_401,U_399) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_396,sK75(U_402,U_400,U_398))],[f_47_4]) ).
cnf(f_47_6,plain,
( in(U_393,U_401)
| ~ in(U_393,U_397)
| U_397 != set_difference(U_401,U_399) ),
inference(clausify,[status(thm)],[f_47_5]) ).
cnf(f_47_7,plain,
( ~ in(U_393,U_399)
| ~ in(U_393,U_397)
| U_397 != set_difference(U_401,U_399) ),
inference(clausify,[status(thm)],[f_47_5]) ).
cnf(f_47_8,plain,
( in(U_394,U_397)
| in(U_394,U_399)
| ~ in(U_394,U_401)
| U_397 != set_difference(U_401,U_399) ),
inference(clausify,[status(thm)],[f_47_5]) ).
cnf(f_47_9,plain,
( in(sK75(U_402,U_400,U_398),U_402)
| in(sK74(U_402,U_400,U_398),U_398)
| U_398 = set_difference(U_402,U_400) ),
inference(clausify,[status(thm)],[f_47_5]) ).
cnf(f_47_10,plain,
( ~ in(sK75(U_402,U_400,U_398),U_400)
| in(sK74(U_402,U_400,U_398),U_398)
| U_398 = set_difference(U_402,U_400) ),
inference(clausify,[status(thm)],[f_47_5]) ).
cnf(f_47_11,plain,
( ~ in(sK75(U_402,U_400,U_398),U_398)
| in(sK74(U_402,U_400,U_398),U_398)
| U_398 = set_difference(U_402,U_400) ),
inference(clausify,[status(thm)],[f_47_5]) ).
cnf(f_47_12,plain,
( in(sK75(U_402,U_400,U_398),U_402)
| in(sK74(U_402,U_400,U_398),U_400)
| ~ in(sK74(U_402,U_400,U_398),U_402)
| U_398 = set_difference(U_402,U_400) ),
inference(clausify,[status(thm)],[f_47_5]) ).
cnf(f_47_13,plain,
( ~ in(sK75(U_402,U_400,U_398),U_400)
| in(sK74(U_402,U_400,U_398),U_400)
| ~ in(sK74(U_402,U_400,U_398),U_402)
| U_398 = set_difference(U_402,U_400) ),
inference(clausify,[status(thm)],[f_47_5]) ).
cnf(f_47_14,plain,
( ~ in(sK75(U_402,U_400,U_398),U_398)
| in(sK74(U_402,U_400,U_398),U_400)
| ~ in(sK74(U_402,U_400,U_398),U_402)
| U_398 = set_difference(U_402,U_400) ),
inference(clausify,[status(thm)],[f_47_5]) ).
fof(f_48_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_48_2,plain,
! [U_410] :
( ! [U_409] :
( ( U_409 = relation_rng(U_410)
| ? [U_408] :
( ( ~ in(U_408,U_409)
& ? [U_407] :
( U_408 = apply(U_410,U_407)
& in(U_407,relation_dom(U_410)) ) )
| ( ! [U_406] :
( U_408 != apply(U_410,U_406)
| ~ in(U_406,relation_dom(U_410)) )
& in(U_408,U_409) ) ) )
& ( ! [U_405] :
( ( in(U_405,U_409)
| ! [U_404] :
( U_405 != apply(U_410,U_404)
| ~ in(U_404,relation_dom(U_410)) ) )
& ( ? [U_403] :
( U_405 = apply(U_410,U_403)
& in(U_403,relation_dom(U_410)) )
| ~ in(U_405,U_409) ) )
| U_409 != relation_rng(U_410) ) )
| ~ function(U_410)
| ~ relation(U_410) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
! [U_410] :
( ( ! [U_416] :
( U_416 = relation_rng(U_410)
| ? [U_414] :
( ~ in(U_414,U_416)
& ? [U_407] :
( U_414 = apply(U_410,U_407)
& in(U_407,relation_dom(U_410)) ) )
| ? [U_413] :
( ! [U_406] :
( U_413 != apply(U_410,U_406)
| ~ in(U_406,relation_dom(U_410)) )
& in(U_413,U_416) ) )
& ! [U_415] :
( ( ! [U_412] :
( in(U_412,U_415)
| ! [U_404] :
( U_412 != apply(U_410,U_404)
| ~ in(U_404,relation_dom(U_410)) ) )
& ! [U_411] :
( ? [U_403] :
( U_411 = apply(U_410,U_403)
& in(U_403,relation_dom(U_410)) )
| ~ in(U_411,U_415) ) )
| U_415 != relation_rng(U_410) ) )
| ~ function(U_410)
| ~ relation(U_410) ),
inference(miniscope,[status(thm)],[f_48_2]) ).
fof(f_48_4,plain,
! [U_410] :
( ( ! [U_416] :
( U_416 = relation_rng(U_410)
| ? [U_414] :
( ~ in(U_414,U_416)
& ? [U_407] :
( U_414 = apply(U_410,U_407)
& in(U_407,relation_dom(U_410)) ) )
| ? [U_413] :
( ! [U_406] :
( U_413 != apply(U_410,U_406)
| ~ in(U_406,relation_dom(U_410)) )
& in(U_413,U_416) ) )
& ! [U_415] :
( ( ! [U_412] :
( in(U_412,U_415)
| ! [U_404] :
( U_412 != apply(U_410,U_404)
| ~ in(U_404,relation_dom(U_410)) ) )
& ! [U_411] :
( ( U_411 = apply(U_410,sK76(U_410,U_415,U_411))
& in(sK76(U_410,U_415,U_411),relation_dom(U_410)) )
| ~ in(U_411,U_415) ) )
| U_415 != relation_rng(U_410) ) )
| ~ function(U_410)
| ~ relation(U_410) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_403,sK76(U_410,U_415,U_411))],[f_48_3]) ).
fof(f_48_5,plain,
! [U_410] :
( ( ! [U_416] :
( U_416 = relation_rng(U_410)
| ? [U_414] :
( ~ in(U_414,U_416)
& ? [U_407] :
( U_414 = apply(U_410,U_407)
& in(U_407,relation_dom(U_410)) ) )
| ( ! [U_406] :
( sK77(U_410,U_416) != apply(U_410,U_406)
| ~ in(U_406,relation_dom(U_410)) )
& in(sK77(U_410,U_416),U_416) ) )
& ! [U_415] :
( ( ! [U_412] :
( in(U_412,U_415)
| ! [U_404] :
( U_412 != apply(U_410,U_404)
| ~ in(U_404,relation_dom(U_410)) ) )
& ! [U_411] :
( ( U_411 = apply(U_410,sK76(U_410,U_415,U_411))
& in(sK76(U_410,U_415,U_411),relation_dom(U_410)) )
| ~ in(U_411,U_415) ) )
| U_415 != relation_rng(U_410) ) )
| ~ function(U_410)
| ~ relation(U_410) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_413,sK77(U_410,U_416))],[f_48_4]) ).
fof(f_48_6,plain,
! [U_410] :
( ( ! [U_416] :
( U_416 = relation_rng(U_410)
| ( ~ in(sK78(U_410,U_416),U_416)
& ? [U_407] :
( sK78(U_410,U_416) = apply(U_410,U_407)
& in(U_407,relation_dom(U_410)) ) )
| ( ! [U_406] :
( sK77(U_410,U_416) != apply(U_410,U_406)
| ~ in(U_406,relation_dom(U_410)) )
& in(sK77(U_410,U_416),U_416) ) )
& ! [U_415] :
( ( ! [U_412] :
( in(U_412,U_415)
| ! [U_404] :
( U_412 != apply(U_410,U_404)
| ~ in(U_404,relation_dom(U_410)) ) )
& ! [U_411] :
( ( U_411 = apply(U_410,sK76(U_410,U_415,U_411))
& in(sK76(U_410,U_415,U_411),relation_dom(U_410)) )
| ~ in(U_411,U_415) ) )
| U_415 != relation_rng(U_410) ) )
| ~ function(U_410)
| ~ relation(U_410) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_414,sK78(U_410,U_416))],[f_48_5]) ).
fof(f_48_7,plain,
! [U_410] :
( ( ! [U_416] :
( U_416 = relation_rng(U_410)
| ( ~ in(sK78(U_410,U_416),U_416)
& sK78(U_410,U_416) = apply(U_410,sK79(U_410,U_416))
& in(sK79(U_410,U_416),relation_dom(U_410)) )
| ( ! [U_406] :
( sK77(U_410,U_416) != apply(U_410,U_406)
| ~ in(U_406,relation_dom(U_410)) )
& in(sK77(U_410,U_416),U_416) ) )
& ! [U_415] :
( ( ! [U_412] :
( in(U_412,U_415)
| ! [U_404] :
( U_412 != apply(U_410,U_404)
| ~ in(U_404,relation_dom(U_410)) ) )
& ! [U_411] :
( ( U_411 = apply(U_410,sK76(U_410,U_415,U_411))
& in(sK76(U_410,U_415,U_411),relation_dom(U_410)) )
| ~ in(U_411,U_415) ) )
| U_415 != relation_rng(U_410) ) )
| ~ function(U_410)
| ~ relation(U_410) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_407,sK79(U_410,U_416))],[f_48_6]) ).
cnf(f_48_8,plain,
( in(sK76(U_410,U_415,U_411),relation_dom(U_410))
| ~ in(U_411,U_415)
| U_415 != relation_rng(U_410)
| ~ function(U_410)
| ~ relation(U_410) ),
inference(clausify,[status(thm)],[f_48_7]) ).
cnf(f_48_9,plain,
( U_411 = apply(U_410,sK76(U_410,U_415,U_411))
| ~ in(U_411,U_415)
| U_415 != relation_rng(U_410)
| ~ function(U_410)
| ~ relation(U_410) ),
inference(clausify,[status(thm)],[f_48_7]) ).
cnf(f_48_10,plain,
( in(U_412,U_415)
| U_412 != apply(U_410,U_404)
| ~ in(U_404,relation_dom(U_410))
| U_415 != relation_rng(U_410)
| ~ function(U_410)
| ~ relation(U_410) ),
inference(clausify,[status(thm)],[f_48_7]) ).
cnf(f_48_11,plain,
( in(sK79(U_410,U_416),relation_dom(U_410))
| in(sK77(U_410,U_416),U_416)
| U_416 = relation_rng(U_410)
| ~ function(U_410)
| ~ relation(U_410) ),
inference(clausify,[status(thm)],[f_48_7]) ).
cnf(f_48_12,plain,
( sK78(U_410,U_416) = apply(U_410,sK79(U_410,U_416))
| in(sK77(U_410,U_416),U_416)
| U_416 = relation_rng(U_410)
| ~ function(U_410)
| ~ relation(U_410) ),
inference(clausify,[status(thm)],[f_48_7]) ).
cnf(f_48_13,plain,
( ~ in(sK78(U_410,U_416),U_416)
| in(sK77(U_410,U_416),U_416)
| U_416 = relation_rng(U_410)
| ~ function(U_410)
| ~ relation(U_410) ),
inference(clausify,[status(thm)],[f_48_7]) ).
cnf(f_48_14,plain,
( in(sK79(U_410,U_416),relation_dom(U_410))
| sK77(U_410,U_416) != apply(U_410,U_406)
| ~ in(U_406,relation_dom(U_410))
| U_416 = relation_rng(U_410)
| ~ function(U_410)
| ~ relation(U_410) ),
inference(clausify,[status(thm)],[f_48_7]) ).
cnf(f_48_15,plain,
( sK78(U_410,U_416) = apply(U_410,sK79(U_410,U_416))
| sK77(U_410,U_416) != apply(U_410,U_406)
| ~ in(U_406,relation_dom(U_410))
| U_416 = relation_rng(U_410)
| ~ function(U_410)
| ~ relation(U_410) ),
inference(clausify,[status(thm)],[f_48_7]) ).
cnf(f_48_16,plain,
( ~ in(sK78(U_410,U_416),U_416)
| sK77(U_410,U_416) != apply(U_410,U_406)
| ~ in(U_406,relation_dom(U_410))
| U_416 = relation_rng(U_410)
| ~ function(U_410)
| ~ relation(U_410) ),
inference(clausify,[status(thm)],[f_48_7]) ).
fof(f_49_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_49_2,plain,
! [U_424] :
( ! [U_423] :
( ( U_423 = relation_rng(U_424)
| ? [U_422] :
( ( ~ in(U_422,U_423)
& ? [U_421] : in(ordered_pair(U_421,U_422),U_424) )
| ( ! [U_420] : ~ in(ordered_pair(U_420,U_422),U_424)
& in(U_422,U_423) ) ) )
& ( ! [U_419] :
( ( in(U_419,U_423)
| ! [U_418] : ~ in(ordered_pair(U_418,U_419),U_424) )
& ( ? [U_417] : in(ordered_pair(U_417,U_419),U_424)
| ~ in(U_419,U_423) ) )
| U_423 != relation_rng(U_424) ) )
| ~ relation(U_424) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
! [U_424] :
( ( ! [U_430] :
( U_430 = relation_rng(U_424)
| ? [U_428] :
( ~ in(U_428,U_430)
& ? [U_421] : in(ordered_pair(U_421,U_428),U_424) )
| ? [U_427] :
( ! [U_420] : ~ in(ordered_pair(U_420,U_427),U_424)
& in(U_427,U_430) ) )
& ! [U_429] :
( ( ! [U_426] :
( in(U_426,U_429)
| ! [U_418] : ~ in(ordered_pair(U_418,U_426),U_424) )
& ! [U_425] :
( ? [U_417] : in(ordered_pair(U_417,U_425),U_424)
| ~ in(U_425,U_429) ) )
| U_429 != relation_rng(U_424) ) )
| ~ relation(U_424) ),
inference(miniscope,[status(thm)],[f_49_2]) ).
fof(f_49_4,plain,
! [U_424] :
( ( ! [U_430] :
( U_430 = relation_rng(U_424)
| ? [U_428] :
( ~ in(U_428,U_430)
& ? [U_421] : in(ordered_pair(U_421,U_428),U_424) )
| ? [U_427] :
( ! [U_420] : ~ in(ordered_pair(U_420,U_427),U_424)
& in(U_427,U_430) ) )
& ! [U_429] :
( ( ! [U_426] :
( in(U_426,U_429)
| ! [U_418] : ~ in(ordered_pair(U_418,U_426),U_424) )
& ! [U_425] :
( in(ordered_pair(sK80(U_424,U_429,U_425),U_425),U_424)
| ~ in(U_425,U_429) ) )
| U_429 != relation_rng(U_424) ) )
| ~ relation(U_424) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_417,sK80(U_424,U_429,U_425))],[f_49_3]) ).
fof(f_49_5,plain,
! [U_424] :
( ( ! [U_430] :
( U_430 = relation_rng(U_424)
| ? [U_428] :
( ~ in(U_428,U_430)
& ? [U_421] : in(ordered_pair(U_421,U_428),U_424) )
| ( ! [U_420] : ~ in(ordered_pair(U_420,sK81(U_424,U_430)),U_424)
& in(sK81(U_424,U_430),U_430) ) )
& ! [U_429] :
( ( ! [U_426] :
( in(U_426,U_429)
| ! [U_418] : ~ in(ordered_pair(U_418,U_426),U_424) )
& ! [U_425] :
( in(ordered_pair(sK80(U_424,U_429,U_425),U_425),U_424)
| ~ in(U_425,U_429) ) )
| U_429 != relation_rng(U_424) ) )
| ~ relation(U_424) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_427,sK81(U_424,U_430))],[f_49_4]) ).
fof(f_49_6,plain,
! [U_424] :
( ( ! [U_430] :
( U_430 = relation_rng(U_424)
| ( ~ in(sK82(U_424,U_430),U_430)
& ? [U_421] : in(ordered_pair(U_421,sK82(U_424,U_430)),U_424) )
| ( ! [U_420] : ~ in(ordered_pair(U_420,sK81(U_424,U_430)),U_424)
& in(sK81(U_424,U_430),U_430) ) )
& ! [U_429] :
( ( ! [U_426] :
( in(U_426,U_429)
| ! [U_418] : ~ in(ordered_pair(U_418,U_426),U_424) )
& ! [U_425] :
( in(ordered_pair(sK80(U_424,U_429,U_425),U_425),U_424)
| ~ in(U_425,U_429) ) )
| U_429 != relation_rng(U_424) ) )
| ~ relation(U_424) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_428,sK82(U_424,U_430))],[f_49_5]) ).
fof(f_49_7,plain,
! [U_424] :
( ( ! [U_430] :
( U_430 = relation_rng(U_424)
| ( ~ in(sK82(U_424,U_430),U_430)
& in(ordered_pair(sK83(U_424,U_430),sK82(U_424,U_430)),U_424) )
| ( ! [U_420] : ~ in(ordered_pair(U_420,sK81(U_424,U_430)),U_424)
& in(sK81(U_424,U_430),U_430) ) )
& ! [U_429] :
( ( ! [U_426] :
( in(U_426,U_429)
| ! [U_418] : ~ in(ordered_pair(U_418,U_426),U_424) )
& ! [U_425] :
( in(ordered_pair(sK80(U_424,U_429,U_425),U_425),U_424)
| ~ in(U_425,U_429) ) )
| U_429 != relation_rng(U_424) ) )
| ~ relation(U_424) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_421,sK83(U_424,U_430))],[f_49_6]) ).
cnf(f_49_8,plain,
( in(ordered_pair(sK80(U_424,U_429,U_425),U_425),U_424)
| ~ in(U_425,U_429)
| U_429 != relation_rng(U_424)
| ~ relation(U_424) ),
inference(clausify,[status(thm)],[f_49_7]) ).
cnf(f_49_9,plain,
( in(U_426,U_429)
| ~ in(ordered_pair(U_418,U_426),U_424)
| U_429 != relation_rng(U_424)
| ~ relation(U_424) ),
inference(clausify,[status(thm)],[f_49_7]) ).
cnf(f_49_10,plain,
( in(ordered_pair(sK83(U_424,U_430),sK82(U_424,U_430)),U_424)
| in(sK81(U_424,U_430),U_430)
| U_430 = relation_rng(U_424)
| ~ relation(U_424) ),
inference(clausify,[status(thm)],[f_49_7]) ).
cnf(f_49_11,plain,
( ~ in(sK82(U_424,U_430),U_430)
| in(sK81(U_424,U_430),U_430)
| U_430 = relation_rng(U_424)
| ~ relation(U_424) ),
inference(clausify,[status(thm)],[f_49_7]) ).
cnf(f_49_12,plain,
( in(ordered_pair(sK83(U_424,U_430),sK82(U_424,U_430)),U_424)
| ~ in(ordered_pair(U_420,sK81(U_424,U_430)),U_424)
| U_430 = relation_rng(U_424)
| ~ relation(U_424) ),
inference(clausify,[status(thm)],[f_49_7]) ).
cnf(f_49_13,plain,
( ~ in(sK82(U_424,U_430),U_430)
| ~ in(ordered_pair(U_420,sK81(U_424,U_430)),U_424)
| U_430 = relation_rng(U_424)
| ~ relation(U_424) ),
inference(clausify,[status(thm)],[f_49_7]) ).
fof(f_50_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_50_2,plain,
! [U_432,U_431] :
( subset_complement(U_432,U_431) = set_difference(U_432,U_431)
| ~ element(U_431,powerset(U_432)) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
cnf(f_50_3,plain,
( subset_complement(U_432,U_431) = set_difference(U_432,U_431)
| ~ element(U_431,powerset(U_432)) ),
inference(clausify,[status(thm)],[f_50_2]) ).
fof(f_51_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_51_2,plain,
! [U_434,U_433] : ordered_pair(U_434,U_433) = unordered_pair(unordered_pair(U_434,U_433),singleton(U_434)),
inference(variable_rename,[status(thm)],[f_51_1]) ).
cnf(f_51_3,plain,
ordered_pair(U_434,U_433) = unordered_pair(unordered_pair(U_434,U_433),singleton(U_434)),
inference(clausify,[status(thm)],[f_51_2]) ).
fof(f_52_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_52_2,plain,
! [U_435] :
( ( being_limit_ordinal(U_435)
| U_435 != union(U_435) )
& ( U_435 = union(U_435)
| ~ being_limit_ordinal(U_435) ) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
( ! [U_437] :
( being_limit_ordinal(U_437)
| U_437 != union(U_437) )
& ! [U_436] :
( U_436 = union(U_436)
| ~ being_limit_ordinal(U_436) ) ),
inference(miniscope,[status(thm)],[f_52_2]) ).
cnf(f_52_4,plain,
( U_436 = union(U_436)
| ~ being_limit_ordinal(U_436) ),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_5,plain,
( being_limit_ordinal(U_437)
| U_437 != union(U_437) ),
inference(clausify,[status(thm)],[f_52_3]) ).
fof(f_53_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_53_2,plain,
! [U_438] :
( relation_field(U_438) = set_union2(relation_dom(U_438),relation_rng(U_438))
| ~ relation(U_438) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
cnf(f_53_3,plain,
( relation_field(U_438) = set_union2(relation_dom(U_438),relation_rng(U_438))
| ~ relation(U_438) ),
inference(clausify,[status(thm)],[f_53_2]) ).
fof(f_54_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_54_2,plain,
! [U_444] :
( ! [U_443] :
( ( ( U_443 = relation_inverse(U_444)
| ? [U_442,U_441] :
( ( ~ in(ordered_pair(U_442,U_441),U_443)
& in(ordered_pair(U_441,U_442),U_444) )
| ( ~ in(ordered_pair(U_441,U_442),U_444)
& in(ordered_pair(U_442,U_441),U_443) ) ) )
& ( ! [U_440,U_439] :
( ( in(ordered_pair(U_440,U_439),U_443)
| ~ in(ordered_pair(U_439,U_440),U_444) )
& ( in(ordered_pair(U_439,U_440),U_444)
| ~ in(ordered_pair(U_440,U_439),U_443) ) )
| U_443 != relation_inverse(U_444) ) )
| ~ relation(U_443) )
| ~ relation(U_444) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_444] :
( ! [U_443] :
( ( ( U_443 = relation_inverse(U_444)
| ? [U_452,U_450] :
( ~ in(ordered_pair(U_452,U_450),U_443)
& in(ordered_pair(U_450,U_452),U_444) )
| ? [U_451,U_449] :
( ~ in(ordered_pair(U_449,U_451),U_444)
& in(ordered_pair(U_451,U_449),U_443) ) )
& ( ( ! [U_448,U_446] :
( in(ordered_pair(U_448,U_446),U_443)
| ~ in(ordered_pair(U_446,U_448),U_444) )
& ! [U_447,U_445] :
( in(ordered_pair(U_445,U_447),U_444)
| ~ in(ordered_pair(U_447,U_445),U_443) ) )
| U_443 != relation_inverse(U_444) ) )
| ~ relation(U_443) )
| ~ relation(U_444) ),
inference(miniscope,[status(thm)],[f_54_2]) ).
fof(f_54_4,plain,
! [U_444] :
( ! [U_443] :
( ( ( U_443 = relation_inverse(U_444)
| ? [U_452,U_450] :
( ~ in(ordered_pair(U_452,U_450),U_443)
& in(ordered_pair(U_450,U_452),U_444) )
| ? [U_449] :
( ~ in(ordered_pair(U_449,sK84(U_444,U_443)),U_444)
& in(ordered_pair(sK84(U_444,U_443),U_449),U_443) ) )
& ( ( ! [U_448,U_446] :
( in(ordered_pair(U_448,U_446),U_443)
| ~ in(ordered_pair(U_446,U_448),U_444) )
& ! [U_447,U_445] :
( in(ordered_pair(U_445,U_447),U_444)
| ~ in(ordered_pair(U_447,U_445),U_443) ) )
| U_443 != relation_inverse(U_444) ) )
| ~ relation(U_443) )
| ~ relation(U_444) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_451,sK84(U_444,U_443))],[f_54_3]) ).
fof(f_54_5,plain,
! [U_444] :
( ! [U_443] :
( ( ( U_443 = relation_inverse(U_444)
| ? [U_452,U_450] :
( ~ in(ordered_pair(U_452,U_450),U_443)
& in(ordered_pair(U_450,U_452),U_444) )
| ( ~ in(ordered_pair(sK85(U_444,U_443),sK84(U_444,U_443)),U_444)
& in(ordered_pair(sK84(U_444,U_443),sK85(U_444,U_443)),U_443) ) )
& ( ( ! [U_448,U_446] :
( in(ordered_pair(U_448,U_446),U_443)
| ~ in(ordered_pair(U_446,U_448),U_444) )
& ! [U_447,U_445] :
( in(ordered_pair(U_445,U_447),U_444)
| ~ in(ordered_pair(U_447,U_445),U_443) ) )
| U_443 != relation_inverse(U_444) ) )
| ~ relation(U_443) )
| ~ relation(U_444) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_449,sK85(U_444,U_443))],[f_54_4]) ).
fof(f_54_6,plain,
! [U_444] :
( ! [U_443] :
( ( ( U_443 = relation_inverse(U_444)
| ? [U_450] :
( ~ in(ordered_pair(sK86(U_444,U_443),U_450),U_443)
& in(ordered_pair(U_450,sK86(U_444,U_443)),U_444) )
| ( ~ in(ordered_pair(sK85(U_444,U_443),sK84(U_444,U_443)),U_444)
& in(ordered_pair(sK84(U_444,U_443),sK85(U_444,U_443)),U_443) ) )
& ( ( ! [U_448,U_446] :
( in(ordered_pair(U_448,U_446),U_443)
| ~ in(ordered_pair(U_446,U_448),U_444) )
& ! [U_447,U_445] :
( in(ordered_pair(U_445,U_447),U_444)
| ~ in(ordered_pair(U_447,U_445),U_443) ) )
| U_443 != relation_inverse(U_444) ) )
| ~ relation(U_443) )
| ~ relation(U_444) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_452,sK86(U_444,U_443))],[f_54_5]) ).
fof(f_54_7,plain,
! [U_444] :
( ! [U_443] :
( ( ( U_443 = relation_inverse(U_444)
| ( ~ in(ordered_pair(sK86(U_444,U_443),sK87(U_444,U_443)),U_443)
& in(ordered_pair(sK87(U_444,U_443),sK86(U_444,U_443)),U_444) )
| ( ~ in(ordered_pair(sK85(U_444,U_443),sK84(U_444,U_443)),U_444)
& in(ordered_pair(sK84(U_444,U_443),sK85(U_444,U_443)),U_443) ) )
& ( ( ! [U_448,U_446] :
( in(ordered_pair(U_448,U_446),U_443)
| ~ in(ordered_pair(U_446,U_448),U_444) )
& ! [U_447,U_445] :
( in(ordered_pair(U_445,U_447),U_444)
| ~ in(ordered_pair(U_447,U_445),U_443) ) )
| U_443 != relation_inverse(U_444) ) )
| ~ relation(U_443) )
| ~ relation(U_444) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_450,sK87(U_444,U_443))],[f_54_6]) ).
cnf(f_54_8,plain,
( in(ordered_pair(U_445,U_447),U_444)
| ~ in(ordered_pair(U_447,U_445),U_443)
| U_443 != relation_inverse(U_444)
| ~ relation(U_443)
| ~ relation(U_444) ),
inference(clausify,[status(thm)],[f_54_7]) ).
cnf(f_54_9,plain,
( in(ordered_pair(U_448,U_446),U_443)
| ~ in(ordered_pair(U_446,U_448),U_444)
| U_443 != relation_inverse(U_444)
| ~ relation(U_443)
| ~ relation(U_444) ),
inference(clausify,[status(thm)],[f_54_7]) ).
cnf(f_54_10,plain,
( in(ordered_pair(sK87(U_444,U_443),sK86(U_444,U_443)),U_444)
| in(ordered_pair(sK84(U_444,U_443),sK85(U_444,U_443)),U_443)
| U_443 = relation_inverse(U_444)
| ~ relation(U_443)
| ~ relation(U_444) ),
inference(clausify,[status(thm)],[f_54_7]) ).
cnf(f_54_11,plain,
( ~ in(ordered_pair(sK86(U_444,U_443),sK87(U_444,U_443)),U_443)
| in(ordered_pair(sK84(U_444,U_443),sK85(U_444,U_443)),U_443)
| U_443 = relation_inverse(U_444)
| ~ relation(U_443)
| ~ relation(U_444) ),
inference(clausify,[status(thm)],[f_54_7]) ).
cnf(f_54_12,plain,
( in(ordered_pair(sK87(U_444,U_443),sK86(U_444,U_443)),U_444)
| ~ in(ordered_pair(sK85(U_444,U_443),sK84(U_444,U_443)),U_444)
| U_443 = relation_inverse(U_444)
| ~ relation(U_443)
| ~ relation(U_444) ),
inference(clausify,[status(thm)],[f_54_7]) ).
cnf(f_54_13,plain,
( ~ in(ordered_pair(sK86(U_444,U_443),sK87(U_444,U_443)),U_443)
| ~ in(ordered_pair(sK85(U_444,U_443),sK84(U_444,U_443)),U_444)
| U_443 = relation_inverse(U_444)
| ~ relation(U_443)
| ~ relation(U_444) ),
inference(clausify,[status(thm)],[f_54_7]) ).
fof(f_55_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_55_2,plain,
! [U_454,U_453] :
( ( disjoint(U_454,U_453)
| set_intersection2(U_454,U_453) != empty_set )
& ( set_intersection2(U_454,U_453) = empty_set
| ~ disjoint(U_454,U_453) ) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
( ! [U_458,U_456] :
( disjoint(U_458,U_456)
| set_intersection2(U_458,U_456) != empty_set )
& ! [U_457,U_455] :
( set_intersection2(U_457,U_455) = empty_set
| ~ disjoint(U_457,U_455) ) ),
inference(miniscope,[status(thm)],[f_55_2]) ).
cnf(f_55_4,plain,
( set_intersection2(U_457,U_455) = empty_set
| ~ disjoint(U_457,U_455) ),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_5,plain,
( disjoint(U_458,U_456)
| set_intersection2(U_458,U_456) != empty_set ),
inference(clausify,[status(thm)],[f_55_3]) ).
fof(f_56_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_56_2,plain,
! [U_463] :
( ( ( one_to_one(U_463)
| ? [U_462,U_461] :
( U_462 != U_461
& apply(U_463,U_462) = apply(U_463,U_461)
& in(U_461,relation_dom(U_463))
& in(U_462,relation_dom(U_463)) ) )
& ( ! [U_460,U_459] :
( U_460 = U_459
| apply(U_463,U_460) != apply(U_463,U_459)
| ~ in(U_459,relation_dom(U_463))
| ~ in(U_460,relation_dom(U_463)) )
| ~ one_to_one(U_463) ) )
| ~ function(U_463)
| ~ relation(U_463) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
! [U_463] :
( ( ( one_to_one(U_463)
| ? [U_461] :
( sK88(U_463) != U_461
& apply(U_463,sK88(U_463)) = apply(U_463,U_461)
& in(U_461,relation_dom(U_463))
& in(sK88(U_463),relation_dom(U_463)) ) )
& ( ! [U_460,U_459] :
( U_460 = U_459
| apply(U_463,U_460) != apply(U_463,U_459)
| ~ in(U_459,relation_dom(U_463))
| ~ in(U_460,relation_dom(U_463)) )
| ~ one_to_one(U_463) ) )
| ~ function(U_463)
| ~ relation(U_463) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_462,sK88(U_463))],[f_56_2]) ).
fof(f_56_4,plain,
! [U_463] :
( ( ( one_to_one(U_463)
| ( sK88(U_463) != sK89(U_463)
& apply(U_463,sK88(U_463)) = apply(U_463,sK89(U_463))
& in(sK89(U_463),relation_dom(U_463))
& in(sK88(U_463),relation_dom(U_463)) ) )
& ( ! [U_460,U_459] :
( U_460 = U_459
| apply(U_463,U_460) != apply(U_463,U_459)
| ~ in(U_459,relation_dom(U_463))
| ~ in(U_460,relation_dom(U_463)) )
| ~ one_to_one(U_463) ) )
| ~ function(U_463)
| ~ relation(U_463) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_461,sK89(U_463))],[f_56_3]) ).
cnf(f_56_5,plain,
( U_460 = U_459
| apply(U_463,U_460) != apply(U_463,U_459)
| ~ in(U_459,relation_dom(U_463))
| ~ in(U_460,relation_dom(U_463))
| ~ one_to_one(U_463)
| ~ function(U_463)
| ~ relation(U_463) ),
inference(clausify,[status(thm)],[f_56_4]) ).
cnf(f_56_6,plain,
( in(sK88(U_463),relation_dom(U_463))
| one_to_one(U_463)
| ~ function(U_463)
| ~ relation(U_463) ),
inference(clausify,[status(thm)],[f_56_4]) ).
cnf(f_56_7,plain,
( in(sK89(U_463),relation_dom(U_463))
| one_to_one(U_463)
| ~ function(U_463)
| ~ relation(U_463) ),
inference(clausify,[status(thm)],[f_56_4]) ).
cnf(f_56_8,plain,
( apply(U_463,sK88(U_463)) = apply(U_463,sK89(U_463))
| one_to_one(U_463)
| ~ function(U_463)
| ~ relation(U_463) ),
inference(clausify,[status(thm)],[f_56_4]) ).
cnf(f_56_9,plain,
( sK88(U_463) != sK89(U_463)
| one_to_one(U_463)
| ~ function(U_463)
| ~ relation(U_463) ),
inference(clausify,[status(thm)],[f_56_4]) ).
fof(f_57_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_57_2,plain,
! [U_474] :
( ! [U_473] :
( ! [U_472] :
( ( ( U_472 = relation_composition(U_474,U_473)
| ? [U_471,U_470] :
( ( ~ in(ordered_pair(U_471,U_470),U_472)
& ? [U_469] :
( in(ordered_pair(U_469,U_470),U_473)
& in(ordered_pair(U_471,U_469),U_474) ) )
| ( ! [U_468] :
( ~ in(ordered_pair(U_468,U_470),U_473)
| ~ in(ordered_pair(U_471,U_468),U_474) )
& in(ordered_pair(U_471,U_470),U_472) ) ) )
& ( ! [U_467,U_466] :
( ( in(ordered_pair(U_467,U_466),U_472)
| ! [U_465] :
( ~ in(ordered_pair(U_465,U_466),U_473)
| ~ in(ordered_pair(U_467,U_465),U_474) ) )
& ( ? [U_464] :
( in(ordered_pair(U_464,U_466),U_473)
& in(ordered_pair(U_467,U_464),U_474) )
| ~ in(ordered_pair(U_467,U_466),U_472) ) )
| U_472 != relation_composition(U_474,U_473) ) )
| ~ relation(U_472) )
| ~ relation(U_473) )
| ~ relation(U_474) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
! [U_474] :
( ! [U_473] :
( ! [U_472] :
( ( ( U_472 = relation_composition(U_474,U_473)
| ? [U_482,U_480] :
( ~ in(ordered_pair(U_482,U_480),U_472)
& ? [U_469] :
( in(ordered_pair(U_469,U_480),U_473)
& in(ordered_pair(U_482,U_469),U_474) ) )
| ? [U_481,U_479] :
( ! [U_468] :
( ~ in(ordered_pair(U_468,U_479),U_473)
| ~ in(ordered_pair(U_481,U_468),U_474) )
& in(ordered_pair(U_481,U_479),U_472) ) )
& ( ( ! [U_478,U_476] :
( in(ordered_pair(U_478,U_476),U_472)
| ! [U_465] :
( ~ in(ordered_pair(U_465,U_476),U_473)
| ~ in(ordered_pair(U_478,U_465),U_474) ) )
& ! [U_477,U_475] :
( ? [U_464] :
( in(ordered_pair(U_464,U_475),U_473)
& in(ordered_pair(U_477,U_464),U_474) )
| ~ in(ordered_pair(U_477,U_475),U_472) ) )
| U_472 != relation_composition(U_474,U_473) ) )
| ~ relation(U_472) )
| ~ relation(U_473) )
| ~ relation(U_474) ),
inference(miniscope,[status(thm)],[f_57_2]) ).
fof(f_57_4,plain,
! [U_474] :
( ! [U_473] :
( ! [U_472] :
( ( ( U_472 = relation_composition(U_474,U_473)
| ? [U_482,U_480] :
( ~ in(ordered_pair(U_482,U_480),U_472)
& ? [U_469] :
( in(ordered_pair(U_469,U_480),U_473)
& in(ordered_pair(U_482,U_469),U_474) ) )
| ? [U_481,U_479] :
( ! [U_468] :
( ~ in(ordered_pair(U_468,U_479),U_473)
| ~ in(ordered_pair(U_481,U_468),U_474) )
& in(ordered_pair(U_481,U_479),U_472) ) )
& ( ( ! [U_478,U_476] :
( in(ordered_pair(U_478,U_476),U_472)
| ! [U_465] :
( ~ in(ordered_pair(U_465,U_476),U_473)
| ~ in(ordered_pair(U_478,U_465),U_474) ) )
& ! [U_477,U_475] :
( ( in(ordered_pair(sK90(U_474,U_473,U_472,U_477,U_475),U_475),U_473)
& in(ordered_pair(U_477,sK90(U_474,U_473,U_472,U_477,U_475)),U_474) )
| ~ in(ordered_pair(U_477,U_475),U_472) ) )
| U_472 != relation_composition(U_474,U_473) ) )
| ~ relation(U_472) )
| ~ relation(U_473) )
| ~ relation(U_474) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_464,sK90(U_474,U_473,U_472,U_477,U_475))],[f_57_3]) ).
fof(f_57_5,plain,
! [U_474] :
( ! [U_473] :
( ! [U_472] :
( ( ( U_472 = relation_composition(U_474,U_473)
| ? [U_482,U_480] :
( ~ in(ordered_pair(U_482,U_480),U_472)
& ? [U_469] :
( in(ordered_pair(U_469,U_480),U_473)
& in(ordered_pair(U_482,U_469),U_474) ) )
| ? [U_479] :
( ! [U_468] :
( ~ in(ordered_pair(U_468,U_479),U_473)
| ~ in(ordered_pair(sK91(U_474,U_473,U_472),U_468),U_474) )
& in(ordered_pair(sK91(U_474,U_473,U_472),U_479),U_472) ) )
& ( ( ! [U_478,U_476] :
( in(ordered_pair(U_478,U_476),U_472)
| ! [U_465] :
( ~ in(ordered_pair(U_465,U_476),U_473)
| ~ in(ordered_pair(U_478,U_465),U_474) ) )
& ! [U_477,U_475] :
( ( in(ordered_pair(sK90(U_474,U_473,U_472,U_477,U_475),U_475),U_473)
& in(ordered_pair(U_477,sK90(U_474,U_473,U_472,U_477,U_475)),U_474) )
| ~ in(ordered_pair(U_477,U_475),U_472) ) )
| U_472 != relation_composition(U_474,U_473) ) )
| ~ relation(U_472) )
| ~ relation(U_473) )
| ~ relation(U_474) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_481,sK91(U_474,U_473,U_472))],[f_57_4]) ).
fof(f_57_6,plain,
! [U_474] :
( ! [U_473] :
( ! [U_472] :
( ( ( U_472 = relation_composition(U_474,U_473)
| ? [U_482,U_480] :
( ~ in(ordered_pair(U_482,U_480),U_472)
& ? [U_469] :
( in(ordered_pair(U_469,U_480),U_473)
& in(ordered_pair(U_482,U_469),U_474) ) )
| ( ! [U_468] :
( ~ in(ordered_pair(U_468,sK92(U_474,U_473,U_472)),U_473)
| ~ in(ordered_pair(sK91(U_474,U_473,U_472),U_468),U_474) )
& in(ordered_pair(sK91(U_474,U_473,U_472),sK92(U_474,U_473,U_472)),U_472) ) )
& ( ( ! [U_478,U_476] :
( in(ordered_pair(U_478,U_476),U_472)
| ! [U_465] :
( ~ in(ordered_pair(U_465,U_476),U_473)
| ~ in(ordered_pair(U_478,U_465),U_474) ) )
& ! [U_477,U_475] :
( ( in(ordered_pair(sK90(U_474,U_473,U_472,U_477,U_475),U_475),U_473)
& in(ordered_pair(U_477,sK90(U_474,U_473,U_472,U_477,U_475)),U_474) )
| ~ in(ordered_pair(U_477,U_475),U_472) ) )
| U_472 != relation_composition(U_474,U_473) ) )
| ~ relation(U_472) )
| ~ relation(U_473) )
| ~ relation(U_474) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_479,sK92(U_474,U_473,U_472))],[f_57_5]) ).
fof(f_57_7,plain,
! [U_474] :
( ! [U_473] :
( ! [U_472] :
( ( ( U_472 = relation_composition(U_474,U_473)
| ? [U_480] :
( ~ in(ordered_pair(sK93(U_474,U_473,U_472),U_480),U_472)
& ? [U_469] :
( in(ordered_pair(U_469,U_480),U_473)
& in(ordered_pair(sK93(U_474,U_473,U_472),U_469),U_474) ) )
| ( ! [U_468] :
( ~ in(ordered_pair(U_468,sK92(U_474,U_473,U_472)),U_473)
| ~ in(ordered_pair(sK91(U_474,U_473,U_472),U_468),U_474) )
& in(ordered_pair(sK91(U_474,U_473,U_472),sK92(U_474,U_473,U_472)),U_472) ) )
& ( ( ! [U_478,U_476] :
( in(ordered_pair(U_478,U_476),U_472)
| ! [U_465] :
( ~ in(ordered_pair(U_465,U_476),U_473)
| ~ in(ordered_pair(U_478,U_465),U_474) ) )
& ! [U_477,U_475] :
( ( in(ordered_pair(sK90(U_474,U_473,U_472,U_477,U_475),U_475),U_473)
& in(ordered_pair(U_477,sK90(U_474,U_473,U_472,U_477,U_475)),U_474) )
| ~ in(ordered_pair(U_477,U_475),U_472) ) )
| U_472 != relation_composition(U_474,U_473) ) )
| ~ relation(U_472) )
| ~ relation(U_473) )
| ~ relation(U_474) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_482,sK93(U_474,U_473,U_472))],[f_57_6]) ).
fof(f_57_8,plain,
! [U_474] :
( ! [U_473] :
( ! [U_472] :
( ( ( U_472 = relation_composition(U_474,U_473)
| ( ~ in(ordered_pair(sK93(U_474,U_473,U_472),sK94(U_474,U_473,U_472)),U_472)
& ? [U_469] :
( in(ordered_pair(U_469,sK94(U_474,U_473,U_472)),U_473)
& in(ordered_pair(sK93(U_474,U_473,U_472),U_469),U_474) ) )
| ( ! [U_468] :
( ~ in(ordered_pair(U_468,sK92(U_474,U_473,U_472)),U_473)
| ~ in(ordered_pair(sK91(U_474,U_473,U_472),U_468),U_474) )
& in(ordered_pair(sK91(U_474,U_473,U_472),sK92(U_474,U_473,U_472)),U_472) ) )
& ( ( ! [U_478,U_476] :
( in(ordered_pair(U_478,U_476),U_472)
| ! [U_465] :
( ~ in(ordered_pair(U_465,U_476),U_473)
| ~ in(ordered_pair(U_478,U_465),U_474) ) )
& ! [U_477,U_475] :
( ( in(ordered_pair(sK90(U_474,U_473,U_472,U_477,U_475),U_475),U_473)
& in(ordered_pair(U_477,sK90(U_474,U_473,U_472,U_477,U_475)),U_474) )
| ~ in(ordered_pair(U_477,U_475),U_472) ) )
| U_472 != relation_composition(U_474,U_473) ) )
| ~ relation(U_472) )
| ~ relation(U_473) )
| ~ relation(U_474) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_480,sK94(U_474,U_473,U_472))],[f_57_7]) ).
fof(f_57_9,plain,
! [U_474] :
( ! [U_473] :
( ! [U_472] :
( ( ( U_472 = relation_composition(U_474,U_473)
| ( ~ in(ordered_pair(sK93(U_474,U_473,U_472),sK94(U_474,U_473,U_472)),U_472)
& in(ordered_pair(sK95(U_474,U_473,U_472),sK94(U_474,U_473,U_472)),U_473)
& in(ordered_pair(sK93(U_474,U_473,U_472),sK95(U_474,U_473,U_472)),U_474) )
| ( ! [U_468] :
( ~ in(ordered_pair(U_468,sK92(U_474,U_473,U_472)),U_473)
| ~ in(ordered_pair(sK91(U_474,U_473,U_472),U_468),U_474) )
& in(ordered_pair(sK91(U_474,U_473,U_472),sK92(U_474,U_473,U_472)),U_472) ) )
& ( ( ! [U_478,U_476] :
( in(ordered_pair(U_478,U_476),U_472)
| ! [U_465] :
( ~ in(ordered_pair(U_465,U_476),U_473)
| ~ in(ordered_pair(U_478,U_465),U_474) ) )
& ! [U_477,U_475] :
( ( in(ordered_pair(sK90(U_474,U_473,U_472,U_477,U_475),U_475),U_473)
& in(ordered_pair(U_477,sK90(U_474,U_473,U_472,U_477,U_475)),U_474) )
| ~ in(ordered_pair(U_477,U_475),U_472) ) )
| U_472 != relation_composition(U_474,U_473) ) )
| ~ relation(U_472) )
| ~ relation(U_473) )
| ~ relation(U_474) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_469,sK95(U_474,U_473,U_472))],[f_57_8]) ).
cnf(f_57_10,plain,
( in(ordered_pair(U_477,sK90(U_474,U_473,U_472,U_477,U_475)),U_474)
| ~ in(ordered_pair(U_477,U_475),U_472)
| U_472 != relation_composition(U_474,U_473)
| ~ relation(U_472)
| ~ relation(U_473)
| ~ relation(U_474) ),
inference(clausify,[status(thm)],[f_57_9]) ).
cnf(f_57_11,plain,
( in(ordered_pair(sK90(U_474,U_473,U_472,U_477,U_475),U_475),U_473)
| ~ in(ordered_pair(U_477,U_475),U_472)
| U_472 != relation_composition(U_474,U_473)
| ~ relation(U_472)
| ~ relation(U_473)
| ~ relation(U_474) ),
inference(clausify,[status(thm)],[f_57_9]) ).
cnf(f_57_12,plain,
( in(ordered_pair(U_478,U_476),U_472)
| ~ in(ordered_pair(U_465,U_476),U_473)
| ~ in(ordered_pair(U_478,U_465),U_474)
| U_472 != relation_composition(U_474,U_473)
| ~ relation(U_472)
| ~ relation(U_473)
| ~ relation(U_474) ),
inference(clausify,[status(thm)],[f_57_9]) ).
cnf(f_57_13,plain,
( in(ordered_pair(sK93(U_474,U_473,U_472),sK95(U_474,U_473,U_472)),U_474)
| in(ordered_pair(sK91(U_474,U_473,U_472),sK92(U_474,U_473,U_472)),U_472)
| U_472 = relation_composition(U_474,U_473)
| ~ relation(U_472)
| ~ relation(U_473)
| ~ relation(U_474) ),
inference(clausify,[status(thm)],[f_57_9]) ).
cnf(f_57_14,plain,
( in(ordered_pair(sK95(U_474,U_473,U_472),sK94(U_474,U_473,U_472)),U_473)
| in(ordered_pair(sK91(U_474,U_473,U_472),sK92(U_474,U_473,U_472)),U_472)
| U_472 = relation_composition(U_474,U_473)
| ~ relation(U_472)
| ~ relation(U_473)
| ~ relation(U_474) ),
inference(clausify,[status(thm)],[f_57_9]) ).
cnf(f_57_15,plain,
( ~ in(ordered_pair(sK93(U_474,U_473,U_472),sK94(U_474,U_473,U_472)),U_472)
| in(ordered_pair(sK91(U_474,U_473,U_472),sK92(U_474,U_473,U_472)),U_472)
| U_472 = relation_composition(U_474,U_473)
| ~ relation(U_472)
| ~ relation(U_473)
| ~ relation(U_474) ),
inference(clausify,[status(thm)],[f_57_9]) ).
cnf(f_57_16,plain,
( in(ordered_pair(sK93(U_474,U_473,U_472),sK95(U_474,U_473,U_472)),U_474)
| ~ in(ordered_pair(U_468,sK92(U_474,U_473,U_472)),U_473)
| ~ in(ordered_pair(sK91(U_474,U_473,U_472),U_468),U_474)
| U_472 = relation_composition(U_474,U_473)
| ~ relation(U_472)
| ~ relation(U_473)
| ~ relation(U_474) ),
inference(clausify,[status(thm)],[f_57_9]) ).
cnf(f_57_17,plain,
( in(ordered_pair(sK95(U_474,U_473,U_472),sK94(U_474,U_473,U_472)),U_473)
| ~ in(ordered_pair(U_468,sK92(U_474,U_473,U_472)),U_473)
| ~ in(ordered_pair(sK91(U_474,U_473,U_472),U_468),U_474)
| U_472 = relation_composition(U_474,U_473)
| ~ relation(U_472)
| ~ relation(U_473)
| ~ relation(U_474) ),
inference(clausify,[status(thm)],[f_57_9]) ).
cnf(f_57_18,plain,
( ~ in(ordered_pair(sK93(U_474,U_473,U_472),sK94(U_474,U_473,U_472)),U_472)
| ~ in(ordered_pair(U_468,sK92(U_474,U_473,U_472)),U_473)
| ~ in(ordered_pair(sK91(U_474,U_473,U_472),U_468),U_474)
| U_472 = relation_composition(U_474,U_473)
| ~ relation(U_472)
| ~ relation(U_473)
| ~ relation(U_474) ),
inference(clausify,[status(thm)],[f_57_9]) ).
fof(f_58_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_58_2,plain,
! [U_490] :
( ! [U_489] :
( ( is_transitive_in(U_490,U_489)
| ? [U_488,U_487,U_486] :
( ~ in(ordered_pair(U_488,U_486),U_490)
& in(ordered_pair(U_487,U_486),U_490)
& in(ordered_pair(U_488,U_487),U_490)
& in(U_486,U_489)
& in(U_487,U_489)
& in(U_488,U_489) ) )
& ( ! [U_485,U_484,U_483] :
( in(ordered_pair(U_485,U_483),U_490)
| ~ in(ordered_pair(U_484,U_483),U_490)
| ~ in(ordered_pair(U_485,U_484),U_490)
| ~ in(U_483,U_489)
| ~ in(U_484,U_489)
| ~ in(U_485,U_489) )
| ~ is_transitive_in(U_490,U_489) ) )
| ~ relation(U_490) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
! [U_490] :
( ( ! [U_492] :
( is_transitive_in(U_490,U_492)
| ? [U_488,U_487,U_486] :
( ~ in(ordered_pair(U_488,U_486),U_490)
& in(ordered_pair(U_487,U_486),U_490)
& in(ordered_pair(U_488,U_487),U_490)
& in(U_486,U_492)
& in(U_487,U_492)
& in(U_488,U_492) ) )
& ! [U_491] :
( ! [U_485,U_484,U_483] :
( in(ordered_pair(U_485,U_483),U_490)
| ~ in(ordered_pair(U_484,U_483),U_490)
| ~ in(ordered_pair(U_485,U_484),U_490)
| ~ in(U_483,U_491)
| ~ in(U_484,U_491)
| ~ in(U_485,U_491) )
| ~ is_transitive_in(U_490,U_491) ) )
| ~ relation(U_490) ),
inference(miniscope,[status(thm)],[f_58_2]) ).
fof(f_58_4,plain,
! [U_490] :
( ( ! [U_492] :
( is_transitive_in(U_490,U_492)
| ? [U_487,U_486] :
( ~ in(ordered_pair(sK96(U_490,U_492),U_486),U_490)
& in(ordered_pair(U_487,U_486),U_490)
& in(ordered_pair(sK96(U_490,U_492),U_487),U_490)
& in(U_486,U_492)
& in(U_487,U_492)
& in(sK96(U_490,U_492),U_492) ) )
& ! [U_491] :
( ! [U_485,U_484,U_483] :
( in(ordered_pair(U_485,U_483),U_490)
| ~ in(ordered_pair(U_484,U_483),U_490)
| ~ in(ordered_pair(U_485,U_484),U_490)
| ~ in(U_483,U_491)
| ~ in(U_484,U_491)
| ~ in(U_485,U_491) )
| ~ is_transitive_in(U_490,U_491) ) )
| ~ relation(U_490) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_488,sK96(U_490,U_492))],[f_58_3]) ).
fof(f_58_5,plain,
! [U_490] :
( ( ! [U_492] :
( is_transitive_in(U_490,U_492)
| ? [U_486] :
( ~ in(ordered_pair(sK96(U_490,U_492),U_486),U_490)
& in(ordered_pair(sK97(U_490,U_492),U_486),U_490)
& in(ordered_pair(sK96(U_490,U_492),sK97(U_490,U_492)),U_490)
& in(U_486,U_492)
& in(sK97(U_490,U_492),U_492)
& in(sK96(U_490,U_492),U_492) ) )
& ! [U_491] :
( ! [U_485,U_484,U_483] :
( in(ordered_pair(U_485,U_483),U_490)
| ~ in(ordered_pair(U_484,U_483),U_490)
| ~ in(ordered_pair(U_485,U_484),U_490)
| ~ in(U_483,U_491)
| ~ in(U_484,U_491)
| ~ in(U_485,U_491) )
| ~ is_transitive_in(U_490,U_491) ) )
| ~ relation(U_490) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_487,sK97(U_490,U_492))],[f_58_4]) ).
fof(f_58_6,plain,
! [U_490] :
( ( ! [U_492] :
( is_transitive_in(U_490,U_492)
| ( ~ in(ordered_pair(sK96(U_490,U_492),sK98(U_490,U_492)),U_490)
& in(ordered_pair(sK97(U_490,U_492),sK98(U_490,U_492)),U_490)
& in(ordered_pair(sK96(U_490,U_492),sK97(U_490,U_492)),U_490)
& in(sK98(U_490,U_492),U_492)
& in(sK97(U_490,U_492),U_492)
& in(sK96(U_490,U_492),U_492) ) )
& ! [U_491] :
( ! [U_485,U_484,U_483] :
( in(ordered_pair(U_485,U_483),U_490)
| ~ in(ordered_pair(U_484,U_483),U_490)
| ~ in(ordered_pair(U_485,U_484),U_490)
| ~ in(U_483,U_491)
| ~ in(U_484,U_491)
| ~ in(U_485,U_491) )
| ~ is_transitive_in(U_490,U_491) ) )
| ~ relation(U_490) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_486,sK98(U_490,U_492))],[f_58_5]) ).
cnf(f_58_7,plain,
( in(ordered_pair(U_485,U_483),U_490)
| ~ in(ordered_pair(U_484,U_483),U_490)
| ~ in(ordered_pair(U_485,U_484),U_490)
| ~ in(U_483,U_491)
| ~ in(U_484,U_491)
| ~ in(U_485,U_491)
| ~ is_transitive_in(U_490,U_491)
| ~ relation(U_490) ),
inference(clausify,[status(thm)],[f_58_6]) ).
cnf(f_58_8,plain,
( in(sK96(U_490,U_492),U_492)
| is_transitive_in(U_490,U_492)
| ~ relation(U_490) ),
inference(clausify,[status(thm)],[f_58_6]) ).
cnf(f_58_9,plain,
( in(sK97(U_490,U_492),U_492)
| is_transitive_in(U_490,U_492)
| ~ relation(U_490) ),
inference(clausify,[status(thm)],[f_58_6]) ).
cnf(f_58_10,plain,
( in(sK98(U_490,U_492),U_492)
| is_transitive_in(U_490,U_492)
| ~ relation(U_490) ),
inference(clausify,[status(thm)],[f_58_6]) ).
cnf(f_58_11,plain,
( in(ordered_pair(sK96(U_490,U_492),sK97(U_490,U_492)),U_490)
| is_transitive_in(U_490,U_492)
| ~ relation(U_490) ),
inference(clausify,[status(thm)],[f_58_6]) ).
cnf(f_58_12,plain,
( in(ordered_pair(sK97(U_490,U_492),sK98(U_490,U_492)),U_490)
| is_transitive_in(U_490,U_492)
| ~ relation(U_490) ),
inference(clausify,[status(thm)],[f_58_6]) ).
cnf(f_58_13,plain,
( ~ in(ordered_pair(sK96(U_490,U_492),sK98(U_490,U_492)),U_490)
| is_transitive_in(U_490,U_492)
| ~ relation(U_490) ),
inference(clausify,[status(thm)],[f_58_6]) ).
fof(f_59_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_59_2,plain,
! [U_497,U_496] :
( ! [U_495] :
( ( ( U_495 = complements_of_subsets(U_497,U_496)
| ? [U_494] :
( ( ( ~ in(U_494,U_495)
& in(subset_complement(U_497,U_494),U_496) )
| ( ~ in(subset_complement(U_497,U_494),U_496)
& in(U_494,U_495) ) )
& element(U_494,powerset(U_497)) ) )
& ( ! [U_493] :
( ( ( in(U_493,U_495)
| ~ in(subset_complement(U_497,U_493),U_496) )
& ( in(subset_complement(U_497,U_493),U_496)
| ~ in(U_493,U_495) ) )
| ~ element(U_493,powerset(U_497)) )
| U_495 != complements_of_subsets(U_497,U_496) ) )
| ~ element(U_495,powerset(powerset(U_497))) )
| ~ element(U_496,powerset(powerset(U_497))) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
! [U_497,U_496] :
( ! [U_495] :
( ( ( U_495 = complements_of_subsets(U_497,U_496)
| ( ( ( ~ in(sK99(U_497,U_496,U_495),U_495)
& in(subset_complement(U_497,sK99(U_497,U_496,U_495)),U_496) )
| ( ~ in(subset_complement(U_497,sK99(U_497,U_496,U_495)),U_496)
& in(sK99(U_497,U_496,U_495),U_495) ) )
& element(sK99(U_497,U_496,U_495),powerset(U_497)) ) )
& ( ! [U_493] :
( ( ( in(U_493,U_495)
| ~ in(subset_complement(U_497,U_493),U_496) )
& ( in(subset_complement(U_497,U_493),U_496)
| ~ in(U_493,U_495) ) )
| ~ element(U_493,powerset(U_497)) )
| U_495 != complements_of_subsets(U_497,U_496) ) )
| ~ element(U_495,powerset(powerset(U_497))) )
| ~ element(U_496,powerset(powerset(U_497))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_494,sK99(U_497,U_496,U_495))],[f_59_2]) ).
cnf(f_59_4,plain,
( in(subset_complement(U_497,U_493),U_496)
| ~ in(U_493,U_495)
| ~ element(U_493,powerset(U_497))
| U_495 != complements_of_subsets(U_497,U_496)
| ~ element(U_495,powerset(powerset(U_497)))
| ~ element(U_496,powerset(powerset(U_497))) ),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_5,plain,
( in(U_493,U_495)
| ~ in(subset_complement(U_497,U_493),U_496)
| ~ element(U_493,powerset(U_497))
| U_495 != complements_of_subsets(U_497,U_496)
| ~ element(U_495,powerset(powerset(U_497)))
| ~ element(U_496,powerset(powerset(U_497))) ),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_6,plain,
( element(sK99(U_497,U_496,U_495),powerset(U_497))
| U_495 = complements_of_subsets(U_497,U_496)
| ~ element(U_495,powerset(powerset(U_497)))
| ~ element(U_496,powerset(powerset(U_497))) ),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_7,plain,
( in(subset_complement(U_497,sK99(U_497,U_496,U_495)),U_496)
| in(sK99(U_497,U_496,U_495),U_495)
| U_495 = complements_of_subsets(U_497,U_496)
| ~ element(U_495,powerset(powerset(U_497)))
| ~ element(U_496,powerset(powerset(U_497))) ),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_8,plain,
( ~ in(sK99(U_497,U_496,U_495),U_495)
| in(sK99(U_497,U_496,U_495),U_495)
| U_495 = complements_of_subsets(U_497,U_496)
| ~ element(U_495,powerset(powerset(U_497)))
| ~ element(U_496,powerset(powerset(U_497))) ),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_9,plain,
( in(subset_complement(U_497,sK99(U_497,U_496,U_495)),U_496)
| ~ in(subset_complement(U_497,sK99(U_497,U_496,U_495)),U_496)
| U_495 = complements_of_subsets(U_497,U_496)
| ~ element(U_495,powerset(powerset(U_497)))
| ~ element(U_496,powerset(powerset(U_497))) ),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_10,plain,
( ~ in(sK99(U_497,U_496,U_495),U_495)
| ~ in(subset_complement(U_497,sK99(U_497,U_496,U_495)),U_496)
| U_495 = complements_of_subsets(U_497,U_496)
| ~ element(U_495,powerset(powerset(U_497)))
| ~ element(U_496,powerset(powerset(U_497))) ),
inference(clausify,[status(thm)],[f_59_3]) ).
fof(f_60_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_60_2,plain,
! [U_499,U_498] :
( ( proper_subset(U_499,U_498)
| U_499 = U_498
| ~ subset(U_499,U_498) )
& ( ( U_499 != U_498
& subset(U_499,U_498) )
| ~ proper_subset(U_499,U_498) ) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
( ! [U_503,U_501] :
( proper_subset(U_503,U_501)
| U_503 = U_501
| ~ subset(U_503,U_501) )
& ! [U_502,U_500] :
( ( U_502 != U_500
& subset(U_502,U_500) )
| ~ proper_subset(U_502,U_500) ) ),
inference(miniscope,[status(thm)],[f_60_2]) ).
cnf(f_60_4,plain,
( subset(U_502,U_500)
| ~ proper_subset(U_502,U_500) ),
inference(clausify,[status(thm)],[f_60_3]) ).
cnf(f_60_5,plain,
( U_502 != U_500
| ~ proper_subset(U_502,U_500) ),
inference(clausify,[status(thm)],[f_60_3]) ).
cnf(f_60_6,plain,
( proper_subset(U_503,U_501)
| U_503 = U_501
| ~ subset(U_503,U_501) ),
inference(clausify,[status(thm)],[f_60_3]) ).
fof(f_61_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_61_2,plain,
! [U_504] :
( function_inverse(U_504) = relation_inverse(U_504)
| ~ one_to_one(U_504)
| ~ function(U_504)
| ~ relation(U_504) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
cnf(f_61_3,plain,
( function_inverse(U_504) = relation_inverse(U_504)
| ~ one_to_one(U_504)
| ~ function(U_504)
| ~ relation(U_504) ),
inference(clausify,[status(thm)],[f_61_2]) ).
fof(f_62_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_62_2,plain,
! [U_505] :
( ( ( reflexive(U_505)
| ~ is_reflexive_in(U_505,relation_field(U_505)) )
& ( is_reflexive_in(U_505,relation_field(U_505))
| ~ reflexive(U_505) ) )
| ~ relation(U_505) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
cnf(f_62_3,plain,
( is_reflexive_in(U_505,relation_field(U_505))
| ~ reflexive(U_505)
| ~ relation(U_505) ),
inference(clausify,[status(thm)],[f_62_2]) ).
cnf(f_62_4,plain,
( reflexive(U_505)
| ~ is_reflexive_in(U_505,relation_field(U_505))
| ~ relation(U_505) ),
inference(clausify,[status(thm)],[f_62_2]) ).
fof(f_63_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k10_relat_1]) ).
cnf(f_63_2,plain,
$true,
inference(clausify,[status(thm)],[f_63_1]) ).
fof(f_64_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_enumset1]) ).
cnf(f_64_2,plain,
$true,
inference(clausify,[status(thm)],[f_64_1]) ).
fof(f_65_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_funct_1]) ).
cnf(f_65_2,plain,
$true,
inference(clausify,[status(thm)],[f_65_1]) ).
fof(f_66_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_ordinal1]) ).
cnf(f_66_2,plain,
$true,
inference(clausify,[status(thm)],[f_66_1]) ).
fof(f_67_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
cnf(f_67_2,plain,
$true,
inference(clausify,[status(thm)],[f_67_1]) ).
fof(f_68_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_setfam_1]) ).
cnf(f_68_2,plain,
$true,
inference(clausify,[status(thm)],[f_68_1]) ).
fof(f_69_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
cnf(f_69_2,plain,
$true,
inference(clausify,[status(thm)],[f_69_1]) ).
fof(f_70_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_70_2,plain,
$true,
inference(clausify,[status(thm)],[f_70_1]) ).
fof(f_71_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_71_2,plain,
$true,
inference(clausify,[status(thm)],[f_71_1]) ).
fof(f_72_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_72_2,plain,
! [U_506] :
( ( function(function_inverse(U_506))
& relation(function_inverse(U_506)) )
| ~ function(U_506)
| ~ relation(U_506) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
cnf(f_72_3,plain,
( relation(function_inverse(U_506))
| ~ function(U_506)
| ~ relation(U_506) ),
inference(clausify,[status(thm)],[f_72_2]) ).
cnf(f_72_4,plain,
( function(function_inverse(U_506))
| ~ function(U_506)
| ~ relation(U_506) ),
inference(clausify,[status(thm)],[f_72_2]) ).
fof(f_73_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_relat_1]) ).
cnf(f_73_2,plain,
$true,
inference(clausify,[status(thm)],[f_73_1]) ).
fof(f_74_1,plain,
! [A] : element(cast_to_subset(A),powerset(A)),
inference(fof_nnf,[status(thm)],[dt_k2_subset_1]) ).
fof(f_74_2,plain,
! [U_507] : element(cast_to_subset(U_507),powerset(U_507)),
inference(variable_rename,[status(thm)],[f_74_1]) ).
cnf(f_74_3,plain,
element(cast_to_subset(U_507),powerset(U_507)),
inference(clausify,[status(thm)],[f_74_2]) ).
fof(f_75_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
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_k2_xboole_0]) ).
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_k2_zfmisc_1]) ).
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_k3_relat_1]) ).
cnf(f_78_2,plain,
$true,
inference(clausify,[status(thm)],[f_78_1]) ).
fof(f_79_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_79_2,plain,
! [U_509,U_508] :
( element(subset_complement(U_509,U_508),powerset(U_509))
| ~ element(U_508,powerset(U_509)) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
cnf(f_79_3,plain,
( element(subset_complement(U_509,U_508),powerset(U_509))
| ~ element(U_508,powerset(U_509)) ),
inference(clausify,[status(thm)],[f_79_2]) ).
fof(f_80_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_tarski]) ).
cnf(f_80_2,plain,
$true,
inference(clausify,[status(thm)],[f_80_1]) ).
fof(f_81_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
cnf(f_81_2,plain,
$true,
inference(clausify,[status(thm)],[f_81_1]) ).
fof(f_82_1,plain,
! [A] :
( relation(relation_inverse(A))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k4_relat_1]) ).
fof(f_82_2,plain,
! [U_510] :
( relation(relation_inverse(U_510))
| ~ relation(U_510) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
cnf(f_82_3,plain,
( relation(relation_inverse(U_510))
| ~ relation(U_510) ),
inference(clausify,[status(thm)],[f_82_2]) ).
fof(f_83_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
cnf(f_83_2,plain,
$true,
inference(clausify,[status(thm)],[f_83_1]) ).
fof(f_84_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
cnf(f_84_2,plain,
$true,
inference(clausify,[status(thm)],[f_84_1]) ).
fof(f_85_1,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_relat_1]) ).
fof(f_85_2,plain,
! [U_512,U_511] :
( relation(relation_composition(U_512,U_511))
| ~ relation(U_511)
| ~ relation(U_512) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
cnf(f_85_3,plain,
( relation(relation_composition(U_512,U_511))
| ~ relation(U_511)
| ~ relation(U_512) ),
inference(clausify,[status(thm)],[f_85_2]) ).
fof(f_86_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_86_2,plain,
! [U_514,U_513] :
( element(union_of_subsets(U_514,U_513),powerset(U_514))
| ~ element(U_513,powerset(powerset(U_514))) ),
inference(variable_rename,[status(thm)],[f_86_1]) ).
cnf(f_86_3,plain,
( element(union_of_subsets(U_514,U_513),powerset(U_514))
| ~ element(U_513,powerset(powerset(U_514))) ),
inference(clausify,[status(thm)],[f_86_2]) ).
fof(f_87_1,plain,
! [A] : relation(identity_relation(A)),
inference(fof_nnf,[status(thm)],[dt_k6_relat_1]) ).
fof(f_87_2,plain,
! [U_515] : relation(identity_relation(U_515)),
inference(variable_rename,[status(thm)],[f_87_1]) ).
cnf(f_87_3,plain,
relation(identity_relation(U_515)),
inference(clausify,[status(thm)],[f_87_2]) ).
fof(f_88_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_88_2,plain,
! [U_517,U_516] :
( element(meet_of_subsets(U_517,U_516),powerset(U_517))
| ~ element(U_516,powerset(powerset(U_517))) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
cnf(f_88_3,plain,
( element(meet_of_subsets(U_517,U_516),powerset(U_517))
| ~ element(U_516,powerset(powerset(U_517))) ),
inference(clausify,[status(thm)],[f_88_2]) ).
fof(f_89_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_89_2,plain,
! [U_520,U_519,U_518] :
( element(subset_difference(U_520,U_519,U_518),powerset(U_520))
| ~ element(U_518,powerset(U_520))
| ~ element(U_519,powerset(U_520)) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
cnf(f_89_3,plain,
( element(subset_difference(U_520,U_519,U_518),powerset(U_520))
| ~ element(U_518,powerset(U_520))
| ~ element(U_519,powerset(U_520)) ),
inference(clausify,[status(thm)],[f_89_2]) ).
fof(f_90_1,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k7_relat_1]) ).
fof(f_90_2,plain,
! [U_522,U_521] :
( relation(relation_dom_restriction(U_522,U_521))
| ~ relation(U_522) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
fof(f_90_3,plain,
! [U_522] :
( ! [U_521] : relation(relation_dom_restriction(U_522,U_521))
| ~ relation(U_522) ),
inference(miniscope,[status(thm)],[f_90_2]) ).
cnf(f_90_4,plain,
( relation(relation_dom_restriction(U_522,U_521))
| ~ relation(U_522) ),
inference(clausify,[status(thm)],[f_90_3]) ).
fof(f_91_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_91_2,plain,
! [U_524,U_523] :
( element(complements_of_subsets(U_524,U_523),powerset(powerset(U_524)))
| ~ element(U_523,powerset(powerset(U_524))) ),
inference(variable_rename,[status(thm)],[f_91_1]) ).
cnf(f_91_3,plain,
( element(complements_of_subsets(U_524,U_523),powerset(powerset(U_524)))
| ~ element(U_523,powerset(powerset(U_524))) ),
inference(clausify,[status(thm)],[f_91_2]) ).
fof(f_92_1,plain,
! [A,B] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[dt_k8_relat_1]) ).
fof(f_92_2,plain,
! [U_526,U_525] :
( relation(relation_rng_restriction(U_526,U_525))
| ~ relation(U_525) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
cnf(f_92_3,plain,
( relation(relation_rng_restriction(U_526,U_525))
| ~ relation(U_525) ),
inference(clausify,[status(thm)],[f_92_2]) ).
fof(f_93_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k9_relat_1]) ).
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_m1_subset_1]) ).
cnf(f_94_2,plain,
$true,
inference(clausify,[status(thm)],[f_94_1]) ).
fof(f_95_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_95_2,plain,
! [U_528] :
? [U_527] : element(U_527,U_528),
inference(variable_rename,[status(thm)],[f_95_1]) ).
fof(f_95_3,plain,
! [U_528] : element(sK100(U_528),U_528),
inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_527,sK100(U_528))],[f_95_2]) ).
cnf(f_95_4,plain,
element(sK100(U_528),U_528),
inference(clausify,[status(thm)],[f_95_3]) ).
fof(f_96_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_96_2,plain,
! [U_530,U_529] :
( ( relation(relation_composition(U_529,U_530))
& empty(relation_composition(U_529,U_530)) )
| ~ relation(U_529)
| ~ empty(U_530) ),
inference(variable_rename,[status(thm)],[f_96_1]) ).
cnf(f_96_3,plain,
( empty(relation_composition(U_529,U_530))
| ~ relation(U_529)
| ~ empty(U_530) ),
inference(clausify,[status(thm)],[f_96_2]) ).
cnf(f_96_4,plain,
( relation(relation_composition(U_529,U_530))
| ~ relation(U_529)
| ~ empty(U_530) ),
inference(clausify,[status(thm)],[f_96_2]) ).
fof(f_97_1,plain,
! [A] :
( ( relation(relation_inverse(A))
& empty(relation_inverse(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc11_relat_1]) ).
fof(f_97_2,plain,
! [U_531] :
( ( relation(relation_inverse(U_531))
& empty(relation_inverse(U_531)) )
| ~ empty(U_531) ),
inference(variable_rename,[status(thm)],[f_97_1]) ).
cnf(f_97_3,plain,
( empty(relation_inverse(U_531))
| ~ empty(U_531) ),
inference(clausify,[status(thm)],[f_97_2]) ).
cnf(f_97_4,plain,
( relation(relation_inverse(U_531))
| ~ empty(U_531) ),
inference(clausify,[status(thm)],[f_97_2]) ).
fof(f_98_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
cnf(f_98_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_98_1]) ).
cnf(f_98_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_98_1]) ).
cnf(f_98_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_98_1]) ).
fof(f_99_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_99_2,plain,
! [U_533,U_532] :
( ( relation_empty_yielding(relation_dom_restriction(U_533,U_532))
& relation(relation_dom_restriction(U_533,U_532)) )
| ~ relation_empty_yielding(U_533)
| ~ relation(U_533) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
fof(f_99_3,plain,
! [U_533] :
( ( ! [U_535] : relation_empty_yielding(relation_dom_restriction(U_533,U_535))
& ! [U_534] : relation(relation_dom_restriction(U_533,U_534)) )
| ~ relation_empty_yielding(U_533)
| ~ relation(U_533) ),
inference(miniscope,[status(thm)],[f_99_2]) ).
cnf(f_99_4,plain,
( relation(relation_dom_restriction(U_533,U_534))
| ~ relation_empty_yielding(U_533)
| ~ relation(U_533) ),
inference(clausify,[status(thm)],[f_99_3]) ).
cnf(f_99_5,plain,
( relation_empty_yielding(relation_dom_restriction(U_533,U_535))
| ~ relation_empty_yielding(U_533)
| ~ relation(U_533) ),
inference(clausify,[status(thm)],[f_99_3]) ).
fof(f_100_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_100_2,plain,
! [U_537,U_536] :
( ( function(relation_composition(U_537,U_536))
& relation(relation_composition(U_537,U_536)) )
| ~ function(U_536)
| ~ relation(U_536)
| ~ function(U_537)
| ~ relation(U_537) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
cnf(f_100_3,plain,
( relation(relation_composition(U_537,U_536))
| ~ function(U_536)
| ~ relation(U_536)
| ~ function(U_537)
| ~ relation(U_537) ),
inference(clausify,[status(thm)],[f_100_2]) ).
cnf(f_100_4,plain,
( function(relation_composition(U_537,U_536))
| ~ function(U_536)
| ~ relation(U_536)
| ~ function(U_537)
| ~ relation(U_537) ),
inference(clausify,[status(thm)],[f_100_2]) ).
fof(f_101_1,plain,
! [A] : ~ empty(succ(A)),
inference(fof_nnf,[status(thm)],[fc1_ordinal1]) ).
fof(f_101_2,plain,
! [U_538] : ~ empty(succ(U_538)),
inference(variable_rename,[status(thm)],[f_101_1]) ).
cnf(f_101_3,plain,
~ empty(succ(U_538)),
inference(clausify,[status(thm)],[f_101_2]) ).
fof(f_102_1,plain,
! [A,B] :
( relation(set_intersection2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc1_relat_1]) ).
fof(f_102_2,plain,
! [U_540,U_539] :
( relation(set_intersection2(U_540,U_539))
| ~ relation(U_539)
| ~ relation(U_540) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
cnf(f_102_3,plain,
( relation(set_intersection2(U_540,U_539))
| ~ relation(U_539)
| ~ relation(U_540) ),
inference(clausify,[status(thm)],[f_102_2]) ).
fof(f_103_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_103_2,plain,
! [U_541] : ~ empty(powerset(U_541)),
inference(variable_rename,[status(thm)],[f_103_1]) ).
cnf(f_103_3,plain,
~ empty(powerset(U_541)),
inference(clausify,[status(thm)],[f_103_2]) ).
fof(f_104_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_104_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_104_1]) ).
fof(f_105_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_105_2,plain,
! [U_543,U_542] : ~ empty(ordered_pair(U_543,U_542)),
inference(variable_rename,[status(thm)],[f_105_1]) ).
cnf(f_105_3,plain,
~ empty(ordered_pair(U_543,U_542)),
inference(clausify,[status(thm)],[f_105_2]) ).
fof(f_106_1,plain,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
inference(fof_nnf,[status(thm)],[fc2_funct_1]) ).
fof(f_106_2,plain,
! [U_544] :
( function(identity_relation(U_544))
& relation(identity_relation(U_544)) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
fof(f_106_3,plain,
( ! [U_546] : function(identity_relation(U_546))
& ! [U_545] : relation(identity_relation(U_545)) ),
inference(miniscope,[status(thm)],[f_106_2]) ).
cnf(f_106_4,plain,
relation(identity_relation(U_545)),
inference(clausify,[status(thm)],[f_106_3]) ).
cnf(f_106_5,plain,
function(identity_relation(U_546)),
inference(clausify,[status(thm)],[f_106_3]) ).
fof(f_107_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_107_2,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_107_1]) ).
cnf(f_107_3,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_107_1]) ).
cnf(f_107_4,plain,
function(empty_set),
inference(clausify,[status(thm)],[f_107_1]) ).
cnf(f_107_5,plain,
one_to_one(empty_set),
inference(clausify,[status(thm)],[f_107_1]) ).
cnf(f_107_6,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_107_1]) ).
cnf(f_107_7,plain,
epsilon_transitive(empty_set),
inference(clausify,[status(thm)],[f_107_1]) ).
cnf(f_107_8,plain,
epsilon_connected(empty_set),
inference(clausify,[status(thm)],[f_107_1]) ).
cnf(f_107_9,plain,
ordinal(empty_set),
inference(clausify,[status(thm)],[f_107_1]) ).
fof(f_108_1,plain,
! [A,B] :
( relation(set_union2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc2_relat_1]) ).
fof(f_108_2,plain,
! [U_548,U_547] :
( relation(set_union2(U_548,U_547))
| ~ relation(U_547)
| ~ relation(U_548) ),
inference(variable_rename,[status(thm)],[f_108_1]) ).
cnf(f_108_3,plain,
( relation(set_union2(U_548,U_547))
| ~ relation(U_547)
| ~ relation(U_548) ),
inference(clausify,[status(thm)],[f_108_2]) ).
fof(f_109_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_109_2,plain,
! [U_549] : ~ empty(singleton(U_549)),
inference(variable_rename,[status(thm)],[f_109_1]) ).
cnf(f_109_3,plain,
~ empty(singleton(U_549)),
inference(clausify,[status(thm)],[f_109_2]) ).
fof(f_110_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_110_2,plain,
! [U_551,U_550] :
( ~ empty(set_union2(U_551,U_550))
| empty(U_551) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
fof(f_110_3,plain,
! [U_551] :
( ! [U_550] : ~ empty(set_union2(U_551,U_550))
| empty(U_551) ),
inference(miniscope,[status(thm)],[f_110_2]) ).
cnf(f_110_4,plain,
( ~ empty(set_union2(U_551,U_550))
| empty(U_551) ),
inference(clausify,[status(thm)],[f_110_3]) ).
fof(f_111_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_111_2,plain,
! [U_552] :
( ( function(relation_inverse(U_552))
& relation(relation_inverse(U_552)) )
| ~ one_to_one(U_552)
| ~ function(U_552)
| ~ relation(U_552) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
cnf(f_111_3,plain,
( relation(relation_inverse(U_552))
| ~ one_to_one(U_552)
| ~ function(U_552)
| ~ relation(U_552) ),
inference(clausify,[status(thm)],[f_111_2]) ).
cnf(f_111_4,plain,
( function(relation_inverse(U_552))
| ~ one_to_one(U_552)
| ~ function(U_552)
| ~ relation(U_552) ),
inference(clausify,[status(thm)],[f_111_2]) ).
fof(f_112_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_112_2,plain,
! [U_553] :
( ( ordinal(succ(U_553))
& epsilon_connected(succ(U_553))
& epsilon_transitive(succ(U_553))
& ~ empty(succ(U_553)) )
| ~ ordinal(U_553) ),
inference(variable_rename,[status(thm)],[f_112_1]) ).
cnf(f_112_3,plain,
( ~ empty(succ(U_553))
| ~ ordinal(U_553) ),
inference(clausify,[status(thm)],[f_112_2]) ).
cnf(f_112_4,plain,
( epsilon_transitive(succ(U_553))
| ~ ordinal(U_553) ),
inference(clausify,[status(thm)],[f_112_2]) ).
cnf(f_112_5,plain,
( epsilon_connected(succ(U_553))
| ~ ordinal(U_553) ),
inference(clausify,[status(thm)],[f_112_2]) ).
cnf(f_112_6,plain,
( ordinal(succ(U_553))
| ~ ordinal(U_553) ),
inference(clausify,[status(thm)],[f_112_2]) ).
fof(f_113_1,plain,
! [A,B] :
( relation(set_difference(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc3_relat_1]) ).
fof(f_113_2,plain,
! [U_555,U_554] :
( relation(set_difference(U_555,U_554))
| ~ relation(U_554)
| ~ relation(U_555) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
cnf(f_113_3,plain,
( relation(set_difference(U_555,U_554))
| ~ relation(U_554)
| ~ relation(U_555) ),
inference(clausify,[status(thm)],[f_113_2]) ).
fof(f_114_1,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_114_2,plain,
! [U_557,U_556] : ~ empty(unordered_pair(U_557,U_556)),
inference(variable_rename,[status(thm)],[f_114_1]) ).
cnf(f_114_3,plain,
~ empty(unordered_pair(U_557,U_556)),
inference(clausify,[status(thm)],[f_114_2]) ).
fof(f_115_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_115_2,plain,
! [U_559,U_558] :
( ~ empty(set_union2(U_558,U_559))
| empty(U_559) ),
inference(variable_rename,[status(thm)],[f_115_1]) ).
fof(f_115_3,plain,
! [U_559] :
( ! [U_558] : ~ empty(set_union2(U_558,U_559))
| empty(U_559) ),
inference(miniscope,[status(thm)],[f_115_2]) ).
cnf(f_115_4,plain,
( ~ empty(set_union2(U_558,U_559))
| empty(U_559) ),
inference(clausify,[status(thm)],[f_115_3]) ).
fof(f_116_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_116_2,plain,
! [U_561,U_560] :
( ( function(relation_dom_restriction(U_561,U_560))
& relation(relation_dom_restriction(U_561,U_560)) )
| ~ function(U_561)
| ~ relation(U_561) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
fof(f_116_3,plain,
! [U_561] :
( ( ! [U_563] : function(relation_dom_restriction(U_561,U_563))
& ! [U_562] : relation(relation_dom_restriction(U_561,U_562)) )
| ~ function(U_561)
| ~ relation(U_561) ),
inference(miniscope,[status(thm)],[f_116_2]) ).
cnf(f_116_4,plain,
( relation(relation_dom_restriction(U_561,U_562))
| ~ function(U_561)
| ~ relation(U_561) ),
inference(clausify,[status(thm)],[f_116_3]) ).
cnf(f_116_5,plain,
( function(relation_dom_restriction(U_561,U_563))
| ~ function(U_561)
| ~ relation(U_561) ),
inference(clausify,[status(thm)],[f_116_3]) ).
fof(f_117_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_117_2,plain,
! [U_564] :
( ( ordinal(union(U_564))
& epsilon_connected(union(U_564))
& epsilon_transitive(union(U_564)) )
| ~ ordinal(U_564) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
cnf(f_117_3,plain,
( epsilon_transitive(union(U_564))
| ~ ordinal(U_564) ),
inference(clausify,[status(thm)],[f_117_2]) ).
cnf(f_117_4,plain,
( epsilon_connected(union(U_564))
| ~ ordinal(U_564) ),
inference(clausify,[status(thm)],[f_117_2]) ).
cnf(f_117_5,plain,
( ordinal(union(U_564))
| ~ ordinal(U_564) ),
inference(clausify,[status(thm)],[f_117_2]) ).
fof(f_118_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_118_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_118_1]) ).
cnf(f_118_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_118_1]) ).
fof(f_119_1,plain,
! [A,B] :
( ~ empty(cartesian_product2(A,B))
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc4_subset_1]) ).
fof(f_119_2,plain,
! [U_566,U_565] :
( ~ empty(cartesian_product2(U_566,U_565))
| empty(U_565)
| empty(U_566) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
cnf(f_119_3,plain,
( ~ empty(cartesian_product2(U_566,U_565))
| empty(U_565)
| empty(U_566) ),
inference(clausify,[status(thm)],[f_119_2]) ).
fof(f_120_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_120_2,plain,
! [U_567] :
( ~ empty(relation_dom(U_567))
| ~ relation(U_567)
| empty(U_567) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
cnf(f_120_3,plain,
( ~ empty(relation_dom(U_567))
| ~ relation(U_567)
| empty(U_567) ),
inference(clausify,[status(thm)],[f_120_2]) ).
fof(f_121_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_121_2,plain,
! [U_568] :
( ~ empty(relation_rng(U_568))
| ~ relation(U_568)
| empty(U_568) ),
inference(variable_rename,[status(thm)],[f_121_1]) ).
cnf(f_121_3,plain,
( ~ empty(relation_rng(U_568))
| ~ relation(U_568)
| empty(U_568) ),
inference(clausify,[status(thm)],[f_121_2]) ).
fof(f_122_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_122_2,plain,
! [U_569] :
( ( relation(relation_dom(U_569))
& empty(relation_dom(U_569)) )
| ~ empty(U_569) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
cnf(f_122_3,plain,
( empty(relation_dom(U_569))
| ~ empty(U_569) ),
inference(clausify,[status(thm)],[f_122_2]) ).
cnf(f_122_4,plain,
( relation(relation_dom(U_569))
| ~ empty(U_569) ),
inference(clausify,[status(thm)],[f_122_2]) ).
fof(f_123_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_123_2,plain,
! [U_570] :
( ( relation(relation_rng(U_570))
& empty(relation_rng(U_570)) )
| ~ empty(U_570) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
cnf(f_123_3,plain,
( empty(relation_rng(U_570))
| ~ empty(U_570) ),
inference(clausify,[status(thm)],[f_123_2]) ).
cnf(f_123_4,plain,
( relation(relation_rng(U_570))
| ~ empty(U_570) ),
inference(clausify,[status(thm)],[f_123_2]) ).
fof(f_124_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_124_2,plain,
! [U_572,U_571] :
( ( relation(relation_composition(U_572,U_571))
& empty(relation_composition(U_572,U_571)) )
| ~ relation(U_571)
| ~ empty(U_572) ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
cnf(f_124_3,plain,
( empty(relation_composition(U_572,U_571))
| ~ relation(U_571)
| ~ empty(U_572) ),
inference(clausify,[status(thm)],[f_124_2]) ).
cnf(f_124_4,plain,
( relation(relation_composition(U_572,U_571))
| ~ relation(U_571)
| ~ empty(U_572) ),
inference(clausify,[status(thm)],[f_124_2]) ).
fof(f_125_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_125_2,plain,
! [U_574,U_573] : set_union2(U_574,U_574) = U_574,
inference(variable_rename,[status(thm)],[f_125_1]) ).
fof(f_125_3,plain,
! [U_574] : set_union2(U_574,U_574) = U_574,
inference(miniscope,[status(thm)],[f_125_2]) ).
cnf(f_125_4,plain,
set_union2(U_574,U_574) = U_574,
inference(clausify,[status(thm)],[f_125_3]) ).
fof(f_126_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_126_2,plain,
! [U_576,U_575] : set_intersection2(U_576,U_576) = U_576,
inference(variable_rename,[status(thm)],[f_126_1]) ).
fof(f_126_3,plain,
! [U_576] : set_intersection2(U_576,U_576) = U_576,
inference(miniscope,[status(thm)],[f_126_2]) ).
cnf(f_126_4,plain,
set_intersection2(U_576,U_576) = U_576,
inference(clausify,[status(thm)],[f_126_3]) ).
fof(f_127_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_127_2,plain,
! [U_578,U_577] :
( subset_complement(U_578,subset_complement(U_578,U_577)) = U_577
| ~ element(U_577,powerset(U_578)) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
cnf(f_127_3,plain,
( subset_complement(U_578,subset_complement(U_578,U_577)) = U_577
| ~ element(U_577,powerset(U_578)) ),
inference(clausify,[status(thm)],[f_127_2]) ).
fof(f_128_1,plain,
! [A] :
( relation_inverse(relation_inverse(A)) = A
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[involutiveness_k4_relat_1]) ).
fof(f_128_2,plain,
! [U_579] :
( relation_inverse(relation_inverse(U_579)) = U_579
| ~ relation(U_579) ),
inference(variable_rename,[status(thm)],[f_128_1]) ).
cnf(f_128_3,plain,
( relation_inverse(relation_inverse(U_579)) = U_579
| ~ relation(U_579) ),
inference(clausify,[status(thm)],[f_128_2]) ).
fof(f_129_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_129_2,plain,
! [U_581,U_580] :
( complements_of_subsets(U_581,complements_of_subsets(U_581,U_580)) = U_580
| ~ element(U_580,powerset(powerset(U_581))) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
cnf(f_129_3,plain,
( complements_of_subsets(U_581,complements_of_subsets(U_581,U_580)) = U_580
| ~ element(U_580,powerset(powerset(U_581))) ),
inference(clausify,[status(thm)],[f_129_2]) ).
fof(f_130_1,plain,
! [A,B] : ~ proper_subset(A,A),
inference(fof_nnf,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(f_130_2,plain,
! [U_583,U_582] : ~ proper_subset(U_583,U_583),
inference(variable_rename,[status(thm)],[f_130_1]) ).
fof(f_130_3,plain,
! [U_583] : ~ proper_subset(U_583,U_583),
inference(miniscope,[status(thm)],[f_130_2]) ).
cnf(f_130_4,plain,
~ proper_subset(U_583,U_583),
inference(clausify,[status(thm)],[f_130_3]) ).
fof(f_131_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_131_2,plain,
! [U_586] :
( ( ( reflexive(U_586)
| ? [U_585] :
( ~ in(ordered_pair(U_585,U_585),U_586)
& in(U_585,relation_field(U_586)) ) )
& ( ! [U_584] :
( in(ordered_pair(U_584,U_584),U_586)
| ~ in(U_584,relation_field(U_586)) )
| ~ reflexive(U_586) ) )
| ~ relation(U_586) ),
inference(variable_rename,[status(thm)],[f_131_1]) ).
fof(f_131_3,plain,
! [U_586] :
( ( ( reflexive(U_586)
| ( ~ in(ordered_pair(sK101(U_586),sK101(U_586)),U_586)
& in(sK101(U_586),relation_field(U_586)) ) )
& ( ! [U_584] :
( in(ordered_pair(U_584,U_584),U_586)
| ~ in(U_584,relation_field(U_586)) )
| ~ reflexive(U_586) ) )
| ~ relation(U_586) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_585,sK101(U_586))],[f_131_2]) ).
cnf(f_131_4,plain,
( in(ordered_pair(U_584,U_584),U_586)
| ~ in(U_584,relation_field(U_586))
| ~ reflexive(U_586)
| ~ relation(U_586) ),
inference(clausify,[status(thm)],[f_131_3]) ).
cnf(f_131_5,plain,
( in(sK101(U_586),relation_field(U_586))
| reflexive(U_586)
| ~ relation(U_586) ),
inference(clausify,[status(thm)],[f_131_3]) ).
cnf(f_131_6,plain,
( ~ in(ordered_pair(sK101(U_586),sK101(U_586)),U_586)
| reflexive(U_586)
| ~ relation(U_586) ),
inference(clausify,[status(thm)],[f_131_3]) ).
fof(f_132_1,plain,
! [A] : singleton(A) != empty_set,
inference(fof_nnf,[status(thm)],[l1_zfmisc_1]) ).
fof(f_132_2,plain,
! [U_587] : singleton(U_587) != empty_set,
inference(variable_rename,[status(thm)],[f_132_1]) ).
cnf(f_132_3,plain,
singleton(U_587) != empty_set,
inference(clausify,[status(thm)],[f_132_2]) ).
fof(f_133_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l23_zfmisc_1]) ).
fof(f_133_2,plain,
! [U_589,U_588] :
( set_union2(singleton(U_589),U_588) = U_588
| ~ in(U_589,U_588) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
cnf(f_133_3,plain,
( set_union2(singleton(U_589),U_588) = U_588
| ~ in(U_589,U_588) ),
inference(clausify,[status(thm)],[f_133_2]) ).
fof(f_134_1,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(fof_nnf,[status(thm)],[l25_zfmisc_1]) ).
fof(f_134_2,plain,
! [U_591,U_590] :
( ~ in(U_591,U_590)
| ~ disjoint(singleton(U_591),U_590) ),
inference(variable_rename,[status(thm)],[f_134_1]) ).
cnf(f_134_3,plain,
( ~ in(U_591,U_590)
| ~ disjoint(singleton(U_591),U_590) ),
inference(clausify,[status(thm)],[f_134_2]) ).
fof(f_135_1,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(fof_nnf,[status(thm)],[l28_zfmisc_1]) ).
fof(f_135_2,plain,
! [U_593,U_592] :
( disjoint(singleton(U_593),U_592)
| in(U_593,U_592) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
cnf(f_135_3,plain,
( disjoint(singleton(U_593),U_592)
| in(U_593,U_592) ),
inference(clausify,[status(thm)],[f_135_2]) ).
fof(f_136_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_136_2,plain,
! [U_600] :
( ( ( transitive(U_600)
| ? [U_599,U_598,U_597] :
( ~ in(ordered_pair(U_599,U_597),U_600)
& in(ordered_pair(U_598,U_597),U_600)
& in(ordered_pair(U_599,U_598),U_600) ) )
& ( ! [U_596,U_595,U_594] :
( in(ordered_pair(U_596,U_594),U_600)
| ~ in(ordered_pair(U_595,U_594),U_600)
| ~ in(ordered_pair(U_596,U_595),U_600) )
| ~ transitive(U_600) ) )
| ~ relation(U_600) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
fof(f_136_3,plain,
! [U_600] :
( ( ( transitive(U_600)
| ? [U_598,U_597] :
( ~ in(ordered_pair(sK102(U_600),U_597),U_600)
& in(ordered_pair(U_598,U_597),U_600)
& in(ordered_pair(sK102(U_600),U_598),U_600) ) )
& ( ! [U_596,U_595,U_594] :
( in(ordered_pair(U_596,U_594),U_600)
| ~ in(ordered_pair(U_595,U_594),U_600)
| ~ in(ordered_pair(U_596,U_595),U_600) )
| ~ transitive(U_600) ) )
| ~ relation(U_600) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_599,sK102(U_600))],[f_136_2]) ).
fof(f_136_4,plain,
! [U_600] :
( ( ( transitive(U_600)
| ? [U_597] :
( ~ in(ordered_pair(sK102(U_600),U_597),U_600)
& in(ordered_pair(sK103(U_600),U_597),U_600)
& in(ordered_pair(sK102(U_600),sK103(U_600)),U_600) ) )
& ( ! [U_596,U_595,U_594] :
( in(ordered_pair(U_596,U_594),U_600)
| ~ in(ordered_pair(U_595,U_594),U_600)
| ~ in(ordered_pair(U_596,U_595),U_600) )
| ~ transitive(U_600) ) )
| ~ relation(U_600) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(U_598,sK103(U_600))],[f_136_3]) ).
fof(f_136_5,plain,
! [U_600] :
( ( ( transitive(U_600)
| ( ~ in(ordered_pair(sK102(U_600),sK104(U_600)),U_600)
& in(ordered_pair(sK103(U_600),sK104(U_600)),U_600)
& in(ordered_pair(sK102(U_600),sK103(U_600)),U_600) ) )
& ( ! [U_596,U_595,U_594] :
( in(ordered_pair(U_596,U_594),U_600)
| ~ in(ordered_pair(U_595,U_594),U_600)
| ~ in(ordered_pair(U_596,U_595),U_600) )
| ~ transitive(U_600) ) )
| ~ relation(U_600) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK104]),skolemize(U_597,sK104(U_600))],[f_136_4]) ).
cnf(f_136_6,plain,
( in(ordered_pair(U_596,U_594),U_600)
| ~ in(ordered_pair(U_595,U_594),U_600)
| ~ in(ordered_pair(U_596,U_595),U_600)
| ~ transitive(U_600)
| ~ relation(U_600) ),
inference(clausify,[status(thm)],[f_136_5]) ).
cnf(f_136_7,plain,
( in(ordered_pair(sK102(U_600),sK103(U_600)),U_600)
| transitive(U_600)
| ~ relation(U_600) ),
inference(clausify,[status(thm)],[f_136_5]) ).
cnf(f_136_8,plain,
( in(ordered_pair(sK103(U_600),sK104(U_600)),U_600)
| transitive(U_600)
| ~ relation(U_600) ),
inference(clausify,[status(thm)],[f_136_5]) ).
cnf(f_136_9,plain,
( ~ in(ordered_pair(sK102(U_600),sK104(U_600)),U_600)
| transitive(U_600)
| ~ relation(U_600) ),
inference(clausify,[status(thm)],[f_136_5]) ).
fof(f_137_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_137_2,plain,
! [U_602,U_601] :
( ( subset(singleton(U_602),U_601)
| ~ in(U_602,U_601) )
& ( in(U_602,U_601)
| ~ subset(singleton(U_602),U_601) ) ),
inference(variable_rename,[status(thm)],[f_137_1]) ).
fof(f_137_3,plain,
( ! [U_606,U_604] :
( subset(singleton(U_606),U_604)
| ~ in(U_606,U_604) )
& ! [U_605,U_603] :
( in(U_605,U_603)
| ~ subset(singleton(U_605),U_603) ) ),
inference(miniscope,[status(thm)],[f_137_2]) ).
cnf(f_137_4,plain,
( in(U_605,U_603)
| ~ subset(singleton(U_605),U_603) ),
inference(clausify,[status(thm)],[f_137_3]) ).
cnf(f_137_5,plain,
( subset(singleton(U_606),U_604)
| ~ in(U_606,U_604) ),
inference(clausify,[status(thm)],[f_137_3]) ).
fof(f_138_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_138_2,plain,
! [U_608,U_607] :
( ( set_difference(U_608,U_607) = empty_set
| ~ subset(U_608,U_607) )
& ( subset(U_608,U_607)
| set_difference(U_608,U_607) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
fof(f_138_3,plain,
( ! [U_612,U_610] :
( set_difference(U_612,U_610) = empty_set
| ~ subset(U_612,U_610) )
& ! [U_611,U_609] :
( subset(U_611,U_609)
| set_difference(U_611,U_609) != empty_set ) ),
inference(miniscope,[status(thm)],[f_138_2]) ).
cnf(f_138_4,plain,
( subset(U_611,U_609)
| set_difference(U_611,U_609) != empty_set ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_5,plain,
( set_difference(U_612,U_610) = empty_set
| ~ subset(U_612,U_610) ),
inference(clausify,[status(thm)],[f_138_3]) ).
fof(f_139_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_139_2,plain,
! [U_615,U_614] :
( ! [U_613] :
( in(U_613,U_615)
| ~ in(U_613,U_614) )
| ~ element(U_614,powerset(U_615)) ),
inference(variable_rename,[status(thm)],[f_139_1]) ).
cnf(f_139_3,plain,
( in(U_613,U_615)
| ~ in(U_613,U_614)
| ~ element(U_614,powerset(U_615)) ),
inference(clausify,[status(thm)],[f_139_2]) ).
fof(f_140_1,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( antisymmetric(A)
<=> ! [B,C] :
( ( in(ordered_pair(C,B),A)
& in(ordered_pair(B,C),A) )
=> B = C ) ) ),
inference(negate,[status(cth)],[l3_wellord1]) ).
fof(f_140_2,negated_conjecture,
? [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)],[f_140_1]) ).
fof(f_140_3,negated_conjecture,
? [U_620] :
( ( ( ~ antisymmetric(U_620)
& ! [U_619,U_618] :
( U_619 = U_618
| ~ in(ordered_pair(U_618,U_619),U_620)
| ~ in(ordered_pair(U_619,U_618),U_620) ) )
| ( ? [U_617,U_616] :
( U_617 != U_616
& in(ordered_pair(U_616,U_617),U_620)
& in(ordered_pair(U_617,U_616),U_620) )
& antisymmetric(U_620) ) )
& relation(U_620) ),
inference(variable_rename,[status(thm)],[f_140_2]) ).
fof(f_140_4,negated_conjecture,
( ( ( ~ antisymmetric(sK105)
& ! [U_619,U_618] :
( U_619 = U_618
| ~ in(ordered_pair(U_618,U_619),sK105)
| ~ in(ordered_pair(U_619,U_618),sK105) ) )
| ( ? [U_617,U_616] :
( U_617 != U_616
& in(ordered_pair(U_616,U_617),sK105)
& in(ordered_pair(U_617,U_616),sK105) )
& antisymmetric(sK105) ) )
& relation(sK105) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK105]),skolemize(U_620,sK105)],[f_140_3]) ).
fof(f_140_5,negated_conjecture,
( ( ( ~ antisymmetric(sK105)
& ! [U_619,U_618] :
( U_619 = U_618
| ~ in(ordered_pair(U_618,U_619),sK105)
| ~ in(ordered_pair(U_619,U_618),sK105) ) )
| ( ? [U_616] :
( sK106 != U_616
& in(ordered_pair(U_616,sK106),sK105)
& in(ordered_pair(sK106,U_616),sK105) )
& antisymmetric(sK105) ) )
& relation(sK105) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK106]),skolemize(U_617,sK106)],[f_140_4]) ).
fof(f_140_6,negated_conjecture,
( ( ( ~ antisymmetric(sK105)
& ! [U_619,U_618] :
( U_619 = U_618
| ~ in(ordered_pair(U_618,U_619),sK105)
| ~ in(ordered_pair(U_619,U_618),sK105) ) )
| ( sK106 != sK107
& in(ordered_pair(sK107,sK106),sK105)
& in(ordered_pair(sK106,sK107),sK105)
& antisymmetric(sK105) ) )
& relation(sK105) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(U_616,sK107)],[f_140_5]) ).
cnf(f_140_7,negated_conjecture,
relation(sK105),
inference(clausify,[status(thm)],[f_140_6]) ).
cnf(f_140_8,negated_conjecture,
( U_619 = U_618
| ~ in(ordered_pair(U_618,U_619),sK105)
| ~ in(ordered_pair(U_619,U_618),sK105)
| antisymmetric(sK105) ),
inference(clausify,[status(thm)],[f_140_6]) ).
cnf(f_140_9,negated_conjecture,
( ~ antisymmetric(sK105)
| antisymmetric(sK105) ),
inference(clausify,[status(thm)],[f_140_6]) ).
cnf(f_140_10,negated_conjecture,
( in(ordered_pair(sK106,sK107),sK105)
| U_619 = U_618
| ~ in(ordered_pair(U_618,U_619),sK105)
| ~ in(ordered_pair(U_619,U_618),sK105) ),
inference(clausify,[status(thm)],[f_140_6]) ).
cnf(f_140_11,negated_conjecture,
( in(ordered_pair(sK107,sK106),sK105)
| U_619 = U_618
| ~ in(ordered_pair(U_618,U_619),sK105)
| ~ in(ordered_pair(U_619,U_618),sK105) ),
inference(clausify,[status(thm)],[f_140_6]) ).
cnf(f_140_12,negated_conjecture,
( sK106 != sK107
| U_619 = U_618
| ~ in(ordered_pair(U_618,U_619),sK105)
| ~ in(ordered_pair(U_619,U_618),sK105) ),
inference(clausify,[status(thm)],[f_140_6]) ).
cnf(f_140_13,negated_conjecture,
( in(ordered_pair(sK106,sK107),sK105)
| ~ antisymmetric(sK105) ),
inference(clausify,[status(thm)],[f_140_6]) ).
cnf(f_140_14,negated_conjecture,
( in(ordered_pair(sK107,sK106),sK105)
| ~ antisymmetric(sK105) ),
inference(clausify,[status(thm)],[f_140_6]) ).
cnf(f_140_15,negated_conjecture,
( sK106 != sK107
| ~ antisymmetric(sK105) ),
inference(clausify,[status(thm)],[f_140_6]) ).
fof(f_141_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_141_2,plain,
! [U_623,U_622,U_621] :
( subset(U_623,set_difference(U_622,singleton(U_621)))
| in(U_621,U_623)
| ~ subset(U_623,U_622) ),
inference(variable_rename,[status(thm)],[f_141_1]) ).
fof(f_141_3,plain,
! [U_623,U_622] :
( ! [U_621] :
( subset(U_623,set_difference(U_622,singleton(U_621)))
| in(U_621,U_623) )
| ~ subset(U_623,U_622) ),
inference(miniscope,[status(thm)],[f_141_2]) ).
cnf(f_141_4,plain,
( subset(U_623,set_difference(U_622,singleton(U_621)))
| in(U_621,U_623)
| ~ subset(U_623,U_622) ),
inference(clausify,[status(thm)],[f_141_3]) ).
fof(f_142_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_142_2,plain,
! [U_625,U_624] :
( ( subset(U_625,singleton(U_624))
| ( U_625 != singleton(U_624)
& U_625 != empty_set ) )
& ( U_625 = singleton(U_624)
| U_625 = empty_set
| ~ subset(U_625,singleton(U_624)) ) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
fof(f_142_3,plain,
( ! [U_629,U_627] :
( subset(U_629,singleton(U_627))
| ( U_629 != singleton(U_627)
& U_629 != empty_set ) )
& ! [U_628,U_626] :
( U_628 = singleton(U_626)
| U_628 = empty_set
| ~ subset(U_628,singleton(U_626)) ) ),
inference(miniscope,[status(thm)],[f_142_2]) ).
cnf(f_142_4,plain,
( U_628 = singleton(U_626)
| U_628 = empty_set
| ~ subset(U_628,singleton(U_626)) ),
inference(clausify,[status(thm)],[f_142_3]) ).
cnf(f_142_5,plain,
( U_629 != empty_set
| subset(U_629,singleton(U_627)) ),
inference(clausify,[status(thm)],[f_142_3]) ).
cnf(f_142_6,plain,
( U_629 != singleton(U_627)
| subset(U_629,singleton(U_627)) ),
inference(clausify,[status(thm)],[f_142_3]) ).
fof(f_143_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l50_zfmisc_1]) ).
fof(f_143_2,plain,
! [U_631,U_630] :
( subset(U_631,union(U_630))
| ~ in(U_631,U_630) ),
inference(variable_rename,[status(thm)],[f_143_1]) ).
cnf(f_143_3,plain,
( subset(U_631,union(U_630))
| ~ in(U_631,U_630) ),
inference(clausify,[status(thm)],[f_143_2]) ).
fof(f_144_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_144_2,plain,
! [U_635,U_634,U_633,U_632] :
( ( in(ordered_pair(U_635,U_634),cartesian_product2(U_633,U_632))
| ~ in(U_634,U_632)
| ~ in(U_635,U_633) )
& ( ( in(U_634,U_632)
& in(U_635,U_633) )
| ~ in(ordered_pair(U_635,U_634),cartesian_product2(U_633,U_632)) ) ),
inference(variable_rename,[status(thm)],[f_144_1]) ).
fof(f_144_3,plain,
( ! [U_643,U_641,U_639,U_637] :
( in(ordered_pair(U_643,U_641),cartesian_product2(U_639,U_637))
| ~ in(U_641,U_637)
| ~ in(U_643,U_639) )
& ! [U_642,U_640,U_638,U_636] :
( ( in(U_640,U_636)
& in(U_642,U_638) )
| ~ in(ordered_pair(U_642,U_640),cartesian_product2(U_638,U_636)) ) ),
inference(miniscope,[status(thm)],[f_144_2]) ).
cnf(f_144_4,plain,
( in(U_642,U_638)
| ~ in(ordered_pair(U_642,U_640),cartesian_product2(U_638,U_636)) ),
inference(clausify,[status(thm)],[f_144_3]) ).
cnf(f_144_5,plain,
( in(U_640,U_636)
| ~ in(ordered_pair(U_642,U_640),cartesian_product2(U_638,U_636)) ),
inference(clausify,[status(thm)],[f_144_3]) ).
cnf(f_144_6,plain,
( in(ordered_pair(U_643,U_641),cartesian_product2(U_639,U_637))
| ~ in(U_641,U_637)
| ~ in(U_643,U_639) ),
inference(clausify,[status(thm)],[f_144_3]) ).
fof(f_145_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_145_2,plain,
! [U_646,U_645] :
( element(U_646,powerset(U_645))
| ? [U_644] :
( ~ in(U_644,U_645)
& in(U_644,U_646) ) ),
inference(variable_rename,[status(thm)],[f_145_1]) ).
fof(f_145_3,plain,
! [U_646,U_645] :
( element(U_646,powerset(U_645))
| ( ~ in(sK108(U_646,U_645),U_645)
& in(sK108(U_646,U_645),U_646) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK108]),skolemize(U_644,sK108(U_646,U_645))],[f_145_2]) ).
cnf(f_145_4,plain,
( in(sK108(U_646,U_645),U_646)
| element(U_646,powerset(U_645)) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_5,plain,
( ~ in(sK108(U_646,U_645),U_645)
| element(U_646,powerset(U_645)) ),
inference(clausify,[status(thm)],[f_145_3]) ).
fof(f_146_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_146_2,plain,
! [U_649,U_648,U_647] :
( ( ( in(U_648,relation_dom(relation_dom_restriction(U_647,U_649)))
| ~ in(U_648,U_649)
| ~ in(U_648,relation_dom(U_647)) )
& ( ( in(U_648,U_649)
& in(U_648,relation_dom(U_647)) )
| ~ in(U_648,relation_dom(relation_dom_restriction(U_647,U_649))) ) )
| ~ function(U_647)
| ~ relation(U_647) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
cnf(f_146_3,plain,
( in(U_648,relation_dom(U_647))
| ~ in(U_648,relation_dom(relation_dom_restriction(U_647,U_649)))
| ~ function(U_647)
| ~ relation(U_647) ),
inference(clausify,[status(thm)],[f_146_2]) ).
cnf(f_146_4,plain,
( in(U_648,U_649)
| ~ in(U_648,relation_dom(relation_dom_restriction(U_647,U_649)))
| ~ function(U_647)
| ~ relation(U_647) ),
inference(clausify,[status(thm)],[f_146_2]) ).
cnf(f_146_5,plain,
( in(U_648,relation_dom(relation_dom_restriction(U_647,U_649)))
| ~ in(U_648,U_649)
| ~ in(U_648,relation_dom(U_647))
| ~ function(U_647)
| ~ relation(U_647) ),
inference(clausify,[status(thm)],[f_146_2]) ).
fof(f_147_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_147_2,plain,
? [U_650] :
( function(U_650)
& relation(U_650) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
fof(f_147_3,plain,
( function(sK109)
& relation(sK109) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK109]),skolemize(U_650,sK109)],[f_147_2]) ).
cnf(f_147_4,plain,
relation(sK109),
inference(clausify,[status(thm)],[f_147_3]) ).
cnf(f_147_5,plain,
function(sK109),
inference(clausify,[status(thm)],[f_147_3]) ).
fof(f_148_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[rc1_ordinal1]) ).
fof(f_148_2,plain,
? [U_651] :
( ordinal(U_651)
& epsilon_connected(U_651)
& epsilon_transitive(U_651) ),
inference(variable_rename,[status(thm)],[f_148_1]) ).
fof(f_148_3,plain,
( ordinal(sK110)
& epsilon_connected(sK110)
& epsilon_transitive(sK110) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK110]),skolemize(U_651,sK110)],[f_148_2]) ).
cnf(f_148_4,plain,
epsilon_transitive(sK110),
inference(clausify,[status(thm)],[f_148_3]) ).
cnf(f_148_5,plain,
epsilon_connected(sK110),
inference(clausify,[status(thm)],[f_148_3]) ).
cnf(f_148_6,plain,
ordinal(sK110),
inference(clausify,[status(thm)],[f_148_3]) ).
fof(f_149_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_149_2,plain,
? [U_652] :
( relation(U_652)
& empty(U_652) ),
inference(variable_rename,[status(thm)],[f_149_1]) ).
fof(f_149_3,plain,
( relation(sK111)
& empty(sK111) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK111]),skolemize(U_652,sK111)],[f_149_2]) ).
cnf(f_149_4,plain,
empty(sK111),
inference(clausify,[status(thm)],[f_149_3]) ).
cnf(f_149_5,plain,
relation(sK111),
inference(clausify,[status(thm)],[f_149_3]) ).
fof(f_150_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_150_2,plain,
! [U_654] :
( ? [U_653] :
( ~ empty(U_653)
& element(U_653,powerset(U_654)) )
| empty(U_654) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
fof(f_150_3,plain,
! [U_654] :
( ( ~ empty(sK112(U_654))
& element(sK112(U_654),powerset(U_654)) )
| empty(U_654) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK112]),skolemize(U_653,sK112(U_654))],[f_150_2]) ).
cnf(f_150_4,plain,
( element(sK112(U_654),powerset(U_654))
| empty(U_654) ),
inference(clausify,[status(thm)],[f_150_3]) ).
cnf(f_150_5,plain,
( ~ empty(sK112(U_654))
| empty(U_654) ),
inference(clausify,[status(thm)],[f_150_3]) ).
fof(f_151_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_151_2,plain,
? [U_655] : empty(U_655),
inference(variable_rename,[status(thm)],[f_151_1]) ).
fof(f_151_3,plain,
empty(sK113),
inference(skolemize,[status(esa),new_symbols(skolem,[sK113]),skolemize(U_655,sK113)],[f_151_2]) ).
cnf(f_151_4,plain,
empty(sK113),
inference(clausify,[status(thm)],[f_151_3]) ).
fof(f_152_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_152_2,plain,
? [U_656] :
( function(U_656)
& empty(U_656)
& relation(U_656) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
fof(f_152_3,plain,
( function(sK114)
& empty(sK114)
& relation(sK114) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK114]),skolemize(U_656,sK114)],[f_152_2]) ).
cnf(f_152_4,plain,
relation(sK114),
inference(clausify,[status(thm)],[f_152_3]) ).
cnf(f_152_5,plain,
empty(sK114),
inference(clausify,[status(thm)],[f_152_3]) ).
cnf(f_152_6,plain,
function(sK114),
inference(clausify,[status(thm)],[f_152_3]) ).
fof(f_153_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_153_2,plain,
? [U_657] :
( ordinal(U_657)
& epsilon_connected(U_657)
& epsilon_transitive(U_657)
& empty(U_657)
& one_to_one(U_657)
& function(U_657)
& relation(U_657) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
fof(f_153_3,plain,
( ordinal(sK115)
& epsilon_connected(sK115)
& epsilon_transitive(sK115)
& empty(sK115)
& one_to_one(sK115)
& function(sK115)
& relation(sK115) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK115]),skolemize(U_657,sK115)],[f_153_2]) ).
cnf(f_153_4,plain,
relation(sK115),
inference(clausify,[status(thm)],[f_153_3]) ).
cnf(f_153_5,plain,
function(sK115),
inference(clausify,[status(thm)],[f_153_3]) ).
cnf(f_153_6,plain,
one_to_one(sK115),
inference(clausify,[status(thm)],[f_153_3]) ).
cnf(f_153_7,plain,
empty(sK115),
inference(clausify,[status(thm)],[f_153_3]) ).
cnf(f_153_8,plain,
epsilon_transitive(sK115),
inference(clausify,[status(thm)],[f_153_3]) ).
cnf(f_153_9,plain,
epsilon_connected(sK115),
inference(clausify,[status(thm)],[f_153_3]) ).
cnf(f_153_10,plain,
ordinal(sK115),
inference(clausify,[status(thm)],[f_153_3]) ).
fof(f_154_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_154_2,plain,
? [U_658] :
( relation(U_658)
& ~ empty(U_658) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
fof(f_154_3,plain,
( relation(sK116)
& ~ empty(sK116) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK116]),skolemize(U_658,sK116)],[f_154_2]) ).
cnf(f_154_4,plain,
~ empty(sK116),
inference(clausify,[status(thm)],[f_154_3]) ).
cnf(f_154_5,plain,
relation(sK116),
inference(clausify,[status(thm)],[f_154_3]) ).
fof(f_155_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_155_2,plain,
! [U_660] :
? [U_659] :
( empty(U_659)
& element(U_659,powerset(U_660)) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
fof(f_155_3,plain,
! [U_660] :
( empty(sK117(U_660))
& element(sK117(U_660),powerset(U_660)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK117]),skolemize(U_659,sK117(U_660))],[f_155_2]) ).
cnf(f_155_4,plain,
element(sK117(U_660),powerset(U_660)),
inference(clausify,[status(thm)],[f_155_3]) ).
cnf(f_155_5,plain,
empty(sK117(U_660)),
inference(clausify,[status(thm)],[f_155_3]) ).
fof(f_156_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_156_2,plain,
? [U_661] : ~ empty(U_661),
inference(variable_rename,[status(thm)],[f_156_1]) ).
fof(f_156_3,plain,
~ empty(sK118),
inference(skolemize,[status(esa),new_symbols(skolem,[sK118]),skolemize(U_661,sK118)],[f_156_2]) ).
cnf(f_156_4,plain,
~ empty(sK118),
inference(clausify,[status(thm)],[f_156_3]) ).
fof(f_157_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_157_2,plain,
? [U_662] :
( one_to_one(U_662)
& function(U_662)
& relation(U_662) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
fof(f_157_3,plain,
( one_to_one(sK119)
& function(sK119)
& relation(sK119) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK119]),skolemize(U_662,sK119)],[f_157_2]) ).
cnf(f_157_4,plain,
relation(sK119),
inference(clausify,[status(thm)],[f_157_3]) ).
cnf(f_157_5,plain,
function(sK119),
inference(clausify,[status(thm)],[f_157_3]) ).
cnf(f_157_6,plain,
one_to_one(sK119),
inference(clausify,[status(thm)],[f_157_3]) ).
fof(f_158_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_ordinal1]) ).
fof(f_158_2,plain,
? [U_663] :
( ordinal(U_663)
& epsilon_connected(U_663)
& epsilon_transitive(U_663)
& ~ empty(U_663) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
fof(f_158_3,plain,
( ordinal(sK120)
& epsilon_connected(sK120)
& epsilon_transitive(sK120)
& ~ empty(sK120) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK120]),skolemize(U_663,sK120)],[f_158_2]) ).
cnf(f_158_4,plain,
~ empty(sK120),
inference(clausify,[status(thm)],[f_158_3]) ).
cnf(f_158_5,plain,
epsilon_transitive(sK120),
inference(clausify,[status(thm)],[f_158_3]) ).
cnf(f_158_6,plain,
epsilon_connected(sK120),
inference(clausify,[status(thm)],[f_158_3]) ).
cnf(f_158_7,plain,
ordinal(sK120),
inference(clausify,[status(thm)],[f_158_3]) ).
fof(f_159_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_159_2,plain,
? [U_664] :
( relation_empty_yielding(U_664)
& relation(U_664) ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
fof(f_159_3,plain,
( relation_empty_yielding(sK121)
& relation(sK121) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK121]),skolemize(U_664,sK121)],[f_159_2]) ).
cnf(f_159_4,plain,
relation(sK121),
inference(clausify,[status(thm)],[f_159_3]) ).
cnf(f_159_5,plain,
relation_empty_yielding(sK121),
inference(clausify,[status(thm)],[f_159_3]) ).
fof(f_160_1,plain,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc4_funct_1]) ).
fof(f_160_2,plain,
? [U_665] :
( function(U_665)
& relation_empty_yielding(U_665)
& relation(U_665) ),
inference(variable_rename,[status(thm)],[f_160_1]) ).
fof(f_160_3,plain,
( function(sK122)
& relation_empty_yielding(sK122)
& relation(sK122) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(U_665,sK122)],[f_160_2]) ).
cnf(f_160_4,plain,
relation(sK122),
inference(clausify,[status(thm)],[f_160_3]) ).
cnf(f_160_5,plain,
relation_empty_yielding(sK122),
inference(clausify,[status(thm)],[f_160_3]) ).
cnf(f_160_6,plain,
function(sK122),
inference(clausify,[status(thm)],[f_160_3]) ).
fof(f_161_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_161_2,plain,
! [U_667,U_666] :
( union_of_subsets(U_667,U_666) = union(U_666)
| ~ element(U_666,powerset(powerset(U_667))) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
cnf(f_161_3,plain,
( union_of_subsets(U_667,U_666) = union(U_666)
| ~ element(U_666,powerset(powerset(U_667))) ),
inference(clausify,[status(thm)],[f_161_2]) ).
fof(f_162_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_162_2,plain,
! [U_669,U_668] :
( meet_of_subsets(U_669,U_668) = set_meet(U_668)
| ~ element(U_668,powerset(powerset(U_669))) ),
inference(variable_rename,[status(thm)],[f_162_1]) ).
cnf(f_162_3,plain,
( meet_of_subsets(U_669,U_668) = set_meet(U_668)
| ~ element(U_668,powerset(powerset(U_669))) ),
inference(clausify,[status(thm)],[f_162_2]) ).
fof(f_163_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_163_2,plain,
! [U_672,U_671,U_670] :
( subset_difference(U_672,U_671,U_670) = set_difference(U_671,U_670)
| ~ element(U_670,powerset(U_672))
| ~ element(U_671,powerset(U_672)) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
cnf(f_163_3,plain,
( subset_difference(U_672,U_671,U_670) = set_difference(U_671,U_670)
| ~ element(U_670,powerset(U_672))
| ~ element(U_671,powerset(U_672)) ),
inference(clausify,[status(thm)],[f_163_2]) ).
fof(f_164_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_164_2,plain,
! [U_674,U_673] :
( ( ( ordinal_subset(U_674,U_673)
| ~ subset(U_674,U_673) )
& ( subset(U_674,U_673)
| ~ ordinal_subset(U_674,U_673) ) )
| ~ ordinal(U_673)
| ~ ordinal(U_674) ),
inference(variable_rename,[status(thm)],[f_164_1]) ).
cnf(f_164_3,plain,
( subset(U_674,U_673)
| ~ ordinal_subset(U_674,U_673)
| ~ ordinal(U_673)
| ~ ordinal(U_674) ),
inference(clausify,[status(thm)],[f_164_2]) ).
cnf(f_164_4,plain,
( ordinal_subset(U_674,U_673)
| ~ subset(U_674,U_673)
| ~ ordinal(U_673)
| ~ ordinal(U_674) ),
inference(clausify,[status(thm)],[f_164_2]) ).
fof(f_165_1,plain,
! [A,B] :
( ordinal_subset(A,A)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[reflexivity_r1_ordinal1]) ).
fof(f_165_2,plain,
! [U_676,U_675] :
( ordinal_subset(U_676,U_676)
| ~ ordinal(U_675)
| ~ ordinal(U_676) ),
inference(variable_rename,[status(thm)],[f_165_1]) ).
fof(f_165_3,plain,
! [U_676] :
( ! [U_675] : ~ ordinal(U_675)
| ~ ordinal(U_676)
| ordinal_subset(U_676,U_676) ),
inference(miniscope,[status(thm)],[f_165_2]) ).
cnf(f_165_4,plain,
( ~ ordinal(U_675)
| ~ ordinal(U_676)
| ordinal_subset(U_676,U_676) ),
inference(clausify,[status(thm)],[f_165_3]) ).
fof(f_166_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_166_2,plain,
! [U_678,U_677] : subset(U_678,U_678),
inference(variable_rename,[status(thm)],[f_166_1]) ).
fof(f_166_3,plain,
! [U_678] : subset(U_678,U_678),
inference(miniscope,[status(thm)],[f_166_2]) ).
cnf(f_166_4,plain,
subset(U_678,U_678),
inference(clausify,[status(thm)],[f_166_3]) ).
fof(f_167_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_167_2,plain,
! [U_680,U_679] :
( disjoint(U_679,U_680)
| ~ disjoint(U_680,U_679) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
cnf(f_167_3,plain,
( disjoint(U_679,U_680)
| ~ disjoint(U_680,U_679) ),
inference(clausify,[status(thm)],[f_167_2]) ).
fof(f_168_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_168_2,plain,
! [U_684,U_683,U_682,U_681] :
( ( in(ordered_pair(U_684,U_683),cartesian_product2(U_682,U_681))
| ~ in(U_683,U_681)
| ~ in(U_684,U_682) )
& ( ( in(U_683,U_681)
& in(U_684,U_682) )
| ~ in(ordered_pair(U_684,U_683),cartesian_product2(U_682,U_681)) ) ),
inference(variable_rename,[status(thm)],[f_168_1]) ).
fof(f_168_3,plain,
( ! [U_692,U_690,U_688,U_686] :
( in(ordered_pair(U_692,U_690),cartesian_product2(U_688,U_686))
| ~ in(U_690,U_686)
| ~ in(U_692,U_688) )
& ! [U_691,U_689,U_687,U_685] :
( ( in(U_689,U_685)
& in(U_691,U_687) )
| ~ in(ordered_pair(U_691,U_689),cartesian_product2(U_687,U_685)) ) ),
inference(miniscope,[status(thm)],[f_168_2]) ).
cnf(f_168_4,plain,
( in(U_691,U_687)
| ~ in(ordered_pair(U_691,U_689),cartesian_product2(U_687,U_685)) ),
inference(clausify,[status(thm)],[f_168_3]) ).
cnf(f_168_5,plain,
( in(U_689,U_685)
| ~ in(ordered_pair(U_691,U_689),cartesian_product2(U_687,U_685)) ),
inference(clausify,[status(thm)],[f_168_3]) ).
cnf(f_168_6,plain,
( in(ordered_pair(U_692,U_690),cartesian_product2(U_688,U_686))
| ~ in(U_690,U_686)
| ~ in(U_692,U_688) ),
inference(clausify,[status(thm)],[f_168_3]) ).
fof(f_169_1,plain,
! [A] : in(A,succ(A)),
inference(fof_nnf,[status(thm)],[t10_ordinal1]) ).
fof(f_169_2,plain,
! [U_693] : in(U_693,succ(U_693)),
inference(variable_rename,[status(thm)],[f_169_1]) ).
cnf(f_169_3,plain,
in(U_693,succ(U_693)),
inference(clausify,[status(thm)],[f_169_2]) ).
fof(f_170_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_170_2,plain,
! [U_697,U_696,U_695,U_694] :
( U_697 = U_694
| U_697 = U_695
| unordered_pair(U_697,U_696) != unordered_pair(U_695,U_694) ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
fof(f_170_3,plain,
! [U_697,U_696,U_695] :
( ! [U_694] :
( U_697 = U_694
| unordered_pair(U_697,U_696) != unordered_pair(U_695,U_694) )
| U_697 = U_695 ),
inference(miniscope,[status(thm)],[f_170_2]) ).
cnf(f_170_4,plain,
( U_697 = U_694
| unordered_pair(U_697,U_696) != unordered_pair(U_695,U_694)
| U_697 = U_695 ),
inference(clausify,[status(thm)],[f_170_3]) ).
fof(f_171_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_171_2,plain,
! [U_700,U_699,U_698] :
( ( ( in(U_700,relation_rng(relation_rng_restriction(U_699,U_698)))
| ~ in(U_700,relation_rng(U_698))
| ~ in(U_700,U_699) )
& ( ( in(U_700,relation_rng(U_698))
& in(U_700,U_699) )
| ~ in(U_700,relation_rng(relation_rng_restriction(U_699,U_698))) ) )
| ~ relation(U_698) ),
inference(variable_rename,[status(thm)],[f_171_1]) ).
cnf(f_171_3,plain,
( in(U_700,U_699)
| ~ in(U_700,relation_rng(relation_rng_restriction(U_699,U_698)))
| ~ relation(U_698) ),
inference(clausify,[status(thm)],[f_171_2]) ).
cnf(f_171_4,plain,
( in(U_700,relation_rng(U_698))
| ~ in(U_700,relation_rng(relation_rng_restriction(U_699,U_698)))
| ~ relation(U_698) ),
inference(clausify,[status(thm)],[f_171_2]) ).
cnf(f_171_5,plain,
( in(U_700,relation_rng(relation_rng_restriction(U_699,U_698)))
| ~ in(U_700,relation_rng(U_698))
| ~ in(U_700,U_699)
| ~ relation(U_698) ),
inference(clausify,[status(thm)],[f_171_2]) ).
fof(f_172_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_172_2,plain,
! [U_702,U_701] :
( subset(relation_rng(relation_rng_restriction(U_702,U_701)),U_702)
| ~ relation(U_701) ),
inference(variable_rename,[status(thm)],[f_172_1]) ).
cnf(f_172_3,plain,
( subset(relation_rng(relation_rng_restriction(U_702,U_701)),U_702)
| ~ relation(U_701) ),
inference(clausify,[status(thm)],[f_172_2]) ).
fof(f_173_1,plain,
! [A,B] :
( subset(relation_rng_restriction(A,B),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t117_relat_1]) ).
fof(f_173_2,plain,
! [U_704,U_703] :
( subset(relation_rng_restriction(U_704,U_703),U_703)
| ~ relation(U_703) ),
inference(variable_rename,[status(thm)],[f_173_1]) ).
cnf(f_173_3,plain,
( subset(relation_rng_restriction(U_704,U_703),U_703)
| ~ relation(U_703) ),
inference(clausify,[status(thm)],[f_173_2]) ).
fof(f_174_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_174_2,plain,
! [U_706,U_705] :
( subset(relation_rng(relation_rng_restriction(U_706,U_705)),relation_rng(U_705))
| ~ relation(U_705) ),
inference(variable_rename,[status(thm)],[f_174_1]) ).
cnf(f_174_3,plain,
( subset(relation_rng(relation_rng_restriction(U_706,U_705)),relation_rng(U_705))
| ~ relation(U_705) ),
inference(clausify,[status(thm)],[f_174_2]) ).
fof(f_175_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_175_2,plain,
! [U_709,U_708,U_707] :
( ( subset(cartesian_product2(U_707,U_709),cartesian_product2(U_707,U_708))
& subset(cartesian_product2(U_709,U_707),cartesian_product2(U_708,U_707)) )
| ~ subset(U_709,U_708) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
fof(f_175_3,plain,
! [U_709,U_708] :
( ( ! [U_711] : subset(cartesian_product2(U_711,U_709),cartesian_product2(U_711,U_708))
& ! [U_710] : subset(cartesian_product2(U_709,U_710),cartesian_product2(U_708,U_710)) )
| ~ subset(U_709,U_708) ),
inference(miniscope,[status(thm)],[f_175_2]) ).
cnf(f_175_4,plain,
( subset(cartesian_product2(U_709,U_710),cartesian_product2(U_708,U_710))
| ~ subset(U_709,U_708) ),
inference(clausify,[status(thm)],[f_175_3]) ).
cnf(f_175_5,plain,
( subset(cartesian_product2(U_711,U_709),cartesian_product2(U_711,U_708))
| ~ subset(U_709,U_708) ),
inference(clausify,[status(thm)],[f_175_3]) ).
fof(f_176_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_176_2,plain,
! [U_713,U_712] :
( relation_rng(relation_rng_restriction(U_713,U_712)) = set_intersection2(relation_rng(U_712),U_713)
| ~ relation(U_712) ),
inference(variable_rename,[status(thm)],[f_176_1]) ).
cnf(f_176_3,plain,
( relation_rng(relation_rng_restriction(U_713,U_712)) = set_intersection2(relation_rng(U_712),U_713)
| ~ relation(U_712) ),
inference(clausify,[status(thm)],[f_176_2]) ).
fof(f_177_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_177_2,plain,
! [U_717,U_716,U_715,U_714] :
( subset(cartesian_product2(U_717,U_715),cartesian_product2(U_716,U_714))
| ~ subset(U_715,U_714)
| ~ subset(U_717,U_716) ),
inference(variable_rename,[status(thm)],[f_177_1]) ).
cnf(f_177_3,plain,
( subset(cartesian_product2(U_717,U_715),cartesian_product2(U_716,U_714))
| ~ subset(U_715,U_714)
| ~ subset(U_717,U_716) ),
inference(clausify,[status(thm)],[f_177_2]) ).
fof(f_178_1,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t12_xboole_1]) ).
fof(f_178_2,plain,
! [U_719,U_718] :
( set_union2(U_719,U_718) = U_718
| ~ subset(U_719,U_718) ),
inference(variable_rename,[status(thm)],[f_178_1]) ).
cnf(f_178_3,plain,
( set_union2(U_719,U_718) = U_718
| ~ subset(U_719,U_718) ),
inference(clausify,[status(thm)],[f_178_2]) ).
fof(f_179_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_179_2,plain,
! [U_725] :
? [U_724] :
( ! [U_723] :
( in(U_723,U_724)
| are_equipotent(U_723,U_724)
| ~ subset(U_723,U_724) )
& ! [U_722] :
( in(powerset(U_722),U_724)
| ~ in(U_722,U_724) )
& ! [U_721,U_720] :
( in(U_720,U_724)
| ~ subset(U_720,U_721)
| ~ in(U_721,U_724) )
& in(U_725,U_724) ),
inference(variable_rename,[status(thm)],[f_179_1]) ).
fof(f_179_3,plain,
! [U_725] :
( ! [U_723] :
( in(U_723,sK123(U_725))
| are_equipotent(U_723,sK123(U_725))
| ~ subset(U_723,sK123(U_725)) )
& ! [U_722] :
( in(powerset(U_722),sK123(U_725))
| ~ in(U_722,sK123(U_725)) )
& ! [U_721,U_720] :
( in(U_720,sK123(U_725))
| ~ subset(U_720,U_721)
| ~ in(U_721,sK123(U_725)) )
& in(U_725,sK123(U_725)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK123]),skolemize(U_724,sK123(U_725))],[f_179_2]) ).
cnf(f_179_4,plain,
in(U_725,sK123(U_725)),
inference(clausify,[status(thm)],[f_179_3]) ).
cnf(f_179_5,plain,
( in(U_720,sK123(U_725))
| ~ subset(U_720,U_721)
| ~ in(U_721,sK123(U_725)) ),
inference(clausify,[status(thm)],[f_179_3]) ).
cnf(f_179_6,plain,
( in(powerset(U_722),sK123(U_725))
| ~ in(U_722,sK123(U_725)) ),
inference(clausify,[status(thm)],[f_179_3]) ).
cnf(f_179_7,plain,
( in(U_723,sK123(U_725))
| are_equipotent(U_723,sK123(U_725))
| ~ subset(U_723,sK123(U_725)) ),
inference(clausify,[status(thm)],[f_179_3]) ).
fof(f_180_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_180_2,plain,
! [U_728,U_727,U_726] :
( relation_dom_restriction(relation_rng_restriction(U_728,U_726),U_727) = relation_rng_restriction(U_728,relation_dom_restriction(U_726,U_727))
| ~ relation(U_726) ),
inference(variable_rename,[status(thm)],[f_180_1]) ).
cnf(f_180_3,plain,
( relation_dom_restriction(relation_rng_restriction(U_728,U_726),U_727) = relation_rng_restriction(U_728,relation_dom_restriction(U_726,U_727))
| ~ relation(U_726) ),
inference(clausify,[status(thm)],[f_180_2]) ).
fof(f_181_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_181_2,plain,
! [U_733,U_732,U_731] :
( ( ( in(U_733,relation_image(U_731,U_732))
| ! [U_730] :
( ~ in(U_730,U_732)
| ~ in(ordered_pair(U_730,U_733),U_731)
| ~ in(U_730,relation_dom(U_731)) ) )
& ( ? [U_729] :
( in(U_729,U_732)
& in(ordered_pair(U_729,U_733),U_731)
& in(U_729,relation_dom(U_731)) )
| ~ in(U_733,relation_image(U_731,U_732)) ) )
| ~ relation(U_731) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
fof(f_181_3,plain,
! [U_733,U_732,U_731] :
( ( ( in(U_733,relation_image(U_731,U_732))
| ! [U_730] :
( ~ in(U_730,U_732)
| ~ in(ordered_pair(U_730,U_733),U_731)
| ~ in(U_730,relation_dom(U_731)) ) )
& ( ( in(sK124(U_733,U_732,U_731),U_732)
& in(ordered_pair(sK124(U_733,U_732,U_731),U_733),U_731)
& in(sK124(U_733,U_732,U_731),relation_dom(U_731)) )
| ~ in(U_733,relation_image(U_731,U_732)) ) )
| ~ relation(U_731) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK124]),skolemize(U_729,sK124(U_733,U_732,U_731))],[f_181_2]) ).
cnf(f_181_4,plain,
( in(sK124(U_733,U_732,U_731),relation_dom(U_731))
| ~ in(U_733,relation_image(U_731,U_732))
| ~ relation(U_731) ),
inference(clausify,[status(thm)],[f_181_3]) ).
cnf(f_181_5,plain,
( in(ordered_pair(sK124(U_733,U_732,U_731),U_733),U_731)
| ~ in(U_733,relation_image(U_731,U_732))
| ~ relation(U_731) ),
inference(clausify,[status(thm)],[f_181_3]) ).
cnf(f_181_6,plain,
( in(sK124(U_733,U_732,U_731),U_732)
| ~ in(U_733,relation_image(U_731,U_732))
| ~ relation(U_731) ),
inference(clausify,[status(thm)],[f_181_3]) ).
cnf(f_181_7,plain,
( in(U_733,relation_image(U_731,U_732))
| ~ in(U_730,U_732)
| ~ in(ordered_pair(U_730,U_733),U_731)
| ~ in(U_730,relation_dom(U_731))
| ~ relation(U_731) ),
inference(clausify,[status(thm)],[f_181_3]) ).
fof(f_182_1,plain,
! [A,B] :
( subset(relation_image(B,A),relation_rng(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t144_relat_1]) ).
fof(f_182_2,plain,
! [U_735,U_734] :
( subset(relation_image(U_734,U_735),relation_rng(U_734))
| ~ relation(U_734) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
cnf(f_182_3,plain,
( subset(relation_image(U_734,U_735),relation_rng(U_734))
| ~ relation(U_734) ),
inference(clausify,[status(thm)],[f_182_2]) ).
fof(f_183_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_183_2,plain,
! [U_737,U_736] :
( subset(relation_image(U_736,relation_inverse_image(U_736,U_737)),U_737)
| ~ function(U_736)
| ~ relation(U_736) ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
cnf(f_183_3,plain,
( subset(relation_image(U_736,relation_inverse_image(U_736,U_737)),U_737)
| ~ function(U_736)
| ~ relation(U_736) ),
inference(clausify,[status(thm)],[f_183_2]) ).
fof(f_184_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_184_2,plain,
! [U_739,U_738] :
( relation_image(U_738,U_739) = relation_image(U_738,set_intersection2(relation_dom(U_738),U_739))
| ~ relation(U_738) ),
inference(variable_rename,[status(thm)],[f_184_1]) ).
cnf(f_184_3,plain,
( relation_image(U_738,U_739) = relation_image(U_738,set_intersection2(relation_dom(U_738),U_739))
| ~ relation(U_738) ),
inference(clausify,[status(thm)],[f_184_2]) ).
fof(f_185_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_185_2,plain,
! [U_741,U_740] :
( subset(U_741,relation_inverse_image(U_740,relation_image(U_740,U_741)))
| ~ subset(U_741,relation_dom(U_740))
| ~ relation(U_740) ),
inference(variable_rename,[status(thm)],[f_185_1]) ).
cnf(f_185_3,plain,
( subset(U_741,relation_inverse_image(U_740,relation_image(U_740,U_741)))
| ~ subset(U_741,relation_dom(U_740))
| ~ relation(U_740) ),
inference(clausify,[status(thm)],[f_185_2]) ).
fof(f_186_1,plain,
! [A] :
( relation_image(A,relation_dom(A)) = relation_rng(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t146_relat_1]) ).
fof(f_186_2,plain,
! [U_742] :
( relation_image(U_742,relation_dom(U_742)) = relation_rng(U_742)
| ~ relation(U_742) ),
inference(variable_rename,[status(thm)],[f_186_1]) ).
cnf(f_186_3,plain,
( relation_image(U_742,relation_dom(U_742)) = relation_rng(U_742)
| ~ relation(U_742) ),
inference(clausify,[status(thm)],[f_186_2]) ).
fof(f_187_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_187_2,plain,
! [U_744,U_743] :
( relation_image(U_743,relation_inverse_image(U_743,U_744)) = U_744
| ~ subset(U_744,relation_rng(U_743))
| ~ function(U_743)
| ~ relation(U_743) ),
inference(variable_rename,[status(thm)],[f_187_1]) ).
cnf(f_187_3,plain,
( relation_image(U_743,relation_inverse_image(U_743,U_744)) = U_744
| ~ subset(U_744,relation_rng(U_743))
| ~ function(U_743)
| ~ relation(U_743) ),
inference(clausify,[status(thm)],[f_187_2]) ).
fof(f_188_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_188_2,plain,
! [U_746] :
( ! [U_745] :
( relation_rng(relation_composition(U_746,U_745)) = relation_image(U_745,relation_rng(U_746))
| ~ relation(U_745) )
| ~ relation(U_746) ),
inference(variable_rename,[status(thm)],[f_188_1]) ).
cnf(f_188_3,plain,
( relation_rng(relation_composition(U_746,U_745)) = relation_image(U_745,relation_rng(U_746))
| ~ relation(U_745)
| ~ relation(U_746) ),
inference(clausify,[status(thm)],[f_188_2]) ).
fof(f_189_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_189_2,plain,
! [U_751,U_750,U_749] :
( ( ( in(U_751,relation_inverse_image(U_749,U_750))
| ! [U_748] :
( ~ in(U_748,U_750)
| ~ in(ordered_pair(U_751,U_748),U_749)
| ~ in(U_748,relation_rng(U_749)) ) )
& ( ? [U_747] :
( in(U_747,U_750)
& in(ordered_pair(U_751,U_747),U_749)
& in(U_747,relation_rng(U_749)) )
| ~ in(U_751,relation_inverse_image(U_749,U_750)) ) )
| ~ relation(U_749) ),
inference(variable_rename,[status(thm)],[f_189_1]) ).
fof(f_189_3,plain,
! [U_751,U_750,U_749] :
( ( ( in(U_751,relation_inverse_image(U_749,U_750))
| ! [U_748] :
( ~ in(U_748,U_750)
| ~ in(ordered_pair(U_751,U_748),U_749)
| ~ in(U_748,relation_rng(U_749)) ) )
& ( ( in(sK125(U_751,U_750,U_749),U_750)
& in(ordered_pair(U_751,sK125(U_751,U_750,U_749)),U_749)
& in(sK125(U_751,U_750,U_749),relation_rng(U_749)) )
| ~ in(U_751,relation_inverse_image(U_749,U_750)) ) )
| ~ relation(U_749) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK125]),skolemize(U_747,sK125(U_751,U_750,U_749))],[f_189_2]) ).
cnf(f_189_4,plain,
( in(sK125(U_751,U_750,U_749),relation_rng(U_749))
| ~ in(U_751,relation_inverse_image(U_749,U_750))
| ~ relation(U_749) ),
inference(clausify,[status(thm)],[f_189_3]) ).
cnf(f_189_5,plain,
( in(ordered_pair(U_751,sK125(U_751,U_750,U_749)),U_749)
| ~ in(U_751,relation_inverse_image(U_749,U_750))
| ~ relation(U_749) ),
inference(clausify,[status(thm)],[f_189_3]) ).
cnf(f_189_6,plain,
( in(sK125(U_751,U_750,U_749),U_750)
| ~ in(U_751,relation_inverse_image(U_749,U_750))
| ~ relation(U_749) ),
inference(clausify,[status(thm)],[f_189_3]) ).
cnf(f_189_7,plain,
( in(U_751,relation_inverse_image(U_749,U_750))
| ~ in(U_748,U_750)
| ~ in(ordered_pair(U_751,U_748),U_749)
| ~ in(U_748,relation_rng(U_749))
| ~ relation(U_749) ),
inference(clausify,[status(thm)],[f_189_3]) ).
fof(f_190_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_190_2,plain,
! [U_753,U_752] :
( subset(relation_inverse_image(U_752,U_753),relation_dom(U_752))
| ~ relation(U_752) ),
inference(variable_rename,[status(thm)],[f_190_1]) ).
cnf(f_190_3,plain,
( subset(relation_inverse_image(U_752,U_753),relation_dom(U_752))
| ~ relation(U_752) ),
inference(clausify,[status(thm)],[f_190_2]) ).
fof(f_191_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_191_2,plain,
! [U_755,U_754] :
( relation_inverse_image(U_754,U_755) != empty_set
| ~ subset(U_755,relation_rng(U_754))
| U_755 = empty_set
| ~ relation(U_754) ),
inference(variable_rename,[status(thm)],[f_191_1]) ).
cnf(f_191_3,plain,
( relation_inverse_image(U_754,U_755) != empty_set
| ~ subset(U_755,relation_rng(U_754))
| U_755 = empty_set
| ~ relation(U_754) ),
inference(clausify,[status(thm)],[f_191_2]) ).
fof(f_192_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_192_2,plain,
! [U_758,U_757,U_756] :
( subset(relation_inverse_image(U_756,U_758),relation_inverse_image(U_756,U_757))
| ~ subset(U_758,U_757)
| ~ relation(U_756) ),
inference(variable_rename,[status(thm)],[f_192_1]) ).
cnf(f_192_3,plain,
( subset(relation_inverse_image(U_756,U_758),relation_inverse_image(U_756,U_757))
| ~ subset(U_758,U_757)
| ~ relation(U_756) ),
inference(clausify,[status(thm)],[f_192_2]) ).
fof(f_193_1,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(fof_nnf,[status(thm)],[t17_xboole_1]) ).
fof(f_193_2,plain,
! [U_760,U_759] : subset(set_intersection2(U_760,U_759),U_760),
inference(variable_rename,[status(thm)],[f_193_1]) ).
cnf(f_193_3,plain,
subset(set_intersection2(U_760,U_759),U_760),
inference(clausify,[status(thm)],[f_193_2]) ).
fof(f_194_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_194_2,plain,
! [U_763,U_762,U_761] :
( subset(U_763,set_intersection2(U_762,U_761))
| ~ subset(U_763,U_761)
| ~ subset(U_763,U_762) ),
inference(variable_rename,[status(thm)],[f_194_1]) ).
cnf(f_194_3,plain,
( subset(U_763,set_intersection2(U_762,U_761))
| ~ subset(U_763,U_761)
| ~ subset(U_763,U_762) ),
inference(clausify,[status(thm)],[f_194_2]) ).
fof(f_195_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_195_2,plain,
! [U_764] : set_union2(U_764,empty_set) = U_764,
inference(variable_rename,[status(thm)],[f_195_1]) ).
cnf(f_195_3,plain,
set_union2(U_764,empty_set) = U_764,
inference(clausify,[status(thm)],[f_195_2]) ).
fof(f_196_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_196_2,plain,
! [U_766,U_765] :
( element(U_766,U_765)
| ~ in(U_766,U_765) ),
inference(variable_rename,[status(thm)],[f_196_1]) ).
cnf(f_196_3,plain,
( element(U_766,U_765)
| ~ in(U_766,U_765) ),
inference(clausify,[status(thm)],[f_196_2]) ).
fof(f_197_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_197_2,plain,
! [U_769,U_768,U_767] :
( subset(U_769,U_767)
| ~ subset(U_768,U_767)
| ~ subset(U_769,U_768) ),
inference(variable_rename,[status(thm)],[f_197_1]) ).
cnf(f_197_3,plain,
( subset(U_769,U_767)
| ~ subset(U_768,U_767)
| ~ subset(U_769,U_768) ),
inference(clausify,[status(thm)],[f_197_2]) ).
fof(f_198_1,plain,
powerset(empty_set) = singleton(empty_set),
inference(fof_nnf,[status(thm)],[t1_zfmisc_1]) ).
cnf(f_198_2,plain,
powerset(empty_set) = singleton(empty_set),
inference(clausify,[status(thm)],[f_198_1]) ).
fof(f_199_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_199_2,plain,
! [U_772,U_771,U_770] :
( ( in(U_771,relation_rng(U_770))
& in(U_772,relation_dom(U_770)) )
| ~ in(ordered_pair(U_772,U_771),U_770)
| ~ relation(U_770) ),
inference(variable_rename,[status(thm)],[f_199_1]) ).
cnf(f_199_3,plain,
( in(U_772,relation_dom(U_770))
| ~ in(ordered_pair(U_772,U_771),U_770)
| ~ relation(U_770) ),
inference(clausify,[status(thm)],[f_199_2]) ).
cnf(f_199_4,plain,
( in(U_771,relation_rng(U_770))
| ~ in(ordered_pair(U_772,U_771),U_770)
| ~ relation(U_770) ),
inference(clausify,[status(thm)],[f_199_2]) ).
fof(f_200_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_200_2,plain,
! [U_775,U_774] :
( ! [U_773] :
( ( ( in(U_775,relation_dom(relation_composition(U_773,U_774)))
| ~ in(apply(U_773,U_775),relation_dom(U_774))
| ~ in(U_775,relation_dom(U_773)) )
& ( ( in(apply(U_773,U_775),relation_dom(U_774))
& in(U_775,relation_dom(U_773)) )
| ~ in(U_775,relation_dom(relation_composition(U_773,U_774))) ) )
| ~ function(U_773)
| ~ relation(U_773) )
| ~ function(U_774)
| ~ relation(U_774) ),
inference(variable_rename,[status(thm)],[f_200_1]) ).
cnf(f_200_3,plain,
( in(U_775,relation_dom(U_773))
| ~ in(U_775,relation_dom(relation_composition(U_773,U_774)))
| ~ function(U_773)
| ~ relation(U_773)
| ~ function(U_774)
| ~ relation(U_774) ),
inference(clausify,[status(thm)],[f_200_2]) ).
cnf(f_200_4,plain,
( in(apply(U_773,U_775),relation_dom(U_774))
| ~ in(U_775,relation_dom(relation_composition(U_773,U_774)))
| ~ function(U_773)
| ~ relation(U_773)
| ~ function(U_774)
| ~ relation(U_774) ),
inference(clausify,[status(thm)],[f_200_2]) ).
cnf(f_200_5,plain,
( in(U_775,relation_dom(relation_composition(U_773,U_774)))
| ~ in(apply(U_773,U_775),relation_dom(U_774))
| ~ in(U_775,relation_dom(U_773))
| ~ function(U_773)
| ~ relation(U_773)
| ~ function(U_774)
| ~ relation(U_774) ),
inference(clausify,[status(thm)],[f_200_2]) ).
fof(f_201_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_201_2,plain,
! [U_777] :
( ! [U_776] :
( in(U_777,U_776)
| ~ proper_subset(U_777,U_776)
| ~ ordinal(U_776) )
| ~ epsilon_transitive(U_777) ),
inference(variable_rename,[status(thm)],[f_201_1]) ).
cnf(f_201_3,plain,
( in(U_777,U_776)
| ~ proper_subset(U_777,U_776)
| ~ ordinal(U_776)
| ~ epsilon_transitive(U_777) ),
inference(clausify,[status(thm)],[f_201_2]) ).
fof(f_202_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_202_2,plain,
! [U_778] :
( subset(U_778,cartesian_product2(relation_dom(U_778),relation_rng(U_778)))
| ~ relation(U_778) ),
inference(variable_rename,[status(thm)],[f_202_1]) ).
cnf(f_202_3,plain,
( subset(U_778,cartesian_product2(relation_dom(U_778),relation_rng(U_778)))
| ~ relation(U_778) ),
inference(clausify,[status(thm)],[f_202_2]) ).
fof(f_203_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_203_2,plain,
! [U_781,U_780] :
( ! [U_779] :
( apply(relation_composition(U_779,U_780),U_781) = apply(U_780,apply(U_779,U_781))
| ~ in(U_781,relation_dom(relation_composition(U_779,U_780)))
| ~ function(U_779)
| ~ relation(U_779) )
| ~ function(U_780)
| ~ relation(U_780) ),
inference(variable_rename,[status(thm)],[f_203_1]) ).
cnf(f_203_3,plain,
( apply(relation_composition(U_779,U_780),U_781) = apply(U_780,apply(U_779,U_781))
| ~ in(U_781,relation_dom(relation_composition(U_779,U_780)))
| ~ function(U_779)
| ~ relation(U_779)
| ~ function(U_780)
| ~ relation(U_780) ),
inference(clausify,[status(thm)],[f_203_2]) ).
fof(f_204_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_204_2,plain,
! [U_784,U_783] :
( ! [U_782] :
( apply(relation_composition(U_783,U_782),U_784) = apply(U_782,apply(U_783,U_784))
| ~ in(U_784,relation_dom(U_783))
| ~ function(U_782)
| ~ relation(U_782) )
| ~ function(U_783)
| ~ relation(U_783) ),
inference(variable_rename,[status(thm)],[f_204_1]) ).
cnf(f_204_3,plain,
( apply(relation_composition(U_783,U_782),U_784) = apply(U_782,apply(U_783,U_784))
| ~ in(U_784,relation_dom(U_783))
| ~ function(U_782)
| ~ relation(U_782)
| ~ function(U_783)
| ~ relation(U_783) ),
inference(clausify,[status(thm)],[f_204_2]) ).
fof(f_205_1,plain,
! [A,B] :
( ordinal(A)
| ~ in(A,B)
| ~ ordinal(B) ),
inference(fof_nnf,[status(thm)],[t23_ordinal1]) ).
fof(f_205_2,plain,
! [U_786,U_785] :
( ordinal(U_786)
| ~ in(U_786,U_785)
| ~ ordinal(U_785) ),
inference(variable_rename,[status(thm)],[f_205_1]) ).
cnf(f_205_3,plain,
( ordinal(U_786)
| ~ in(U_786,U_785)
| ~ ordinal(U_785) ),
inference(clausify,[status(thm)],[f_205_2]) ).
fof(f_206_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_206_2,plain,
! [U_788] :
( ! [U_787] :
( in(U_787,U_788)
| U_788 = U_787
| in(U_788,U_787)
| ~ ordinal(U_787) )
| ~ ordinal(U_788) ),
inference(variable_rename,[status(thm)],[f_206_1]) ).
cnf(f_206_3,plain,
( in(U_787,U_788)
| U_788 = U_787
| in(U_788,U_787)
| ~ ordinal(U_787)
| ~ ordinal(U_788) ),
inference(clausify,[status(thm)],[f_206_2]) ).
fof(f_207_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_207_2,plain,
! [U_790] :
( ! [U_789] :
( ( subset(relation_rng(U_790),relation_rng(U_789))
& subset(relation_dom(U_790),relation_dom(U_789)) )
| ~ subset(U_790,U_789)
| ~ relation(U_789) )
| ~ relation(U_790) ),
inference(variable_rename,[status(thm)],[f_207_1]) ).
cnf(f_207_3,plain,
( subset(relation_dom(U_790),relation_dom(U_789))
| ~ subset(U_790,U_789)
| ~ relation(U_789)
| ~ relation(U_790) ),
inference(clausify,[status(thm)],[f_207_2]) ).
cnf(f_207_4,plain,
( subset(relation_rng(U_790),relation_rng(U_789))
| ~ subset(U_790,U_789)
| ~ relation(U_789)
| ~ relation(U_790) ),
inference(clausify,[status(thm)],[f_207_2]) ).
fof(f_208_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_208_2,plain,
! [U_793,U_792,U_791] :
( subset(set_intersection2(U_793,U_791),set_intersection2(U_792,U_791))
| ~ subset(U_793,U_792) ),
inference(variable_rename,[status(thm)],[f_208_1]) ).
fof(f_208_3,plain,
! [U_793,U_792] :
( ! [U_791] : subset(set_intersection2(U_793,U_791),set_intersection2(U_792,U_791))
| ~ subset(U_793,U_792) ),
inference(miniscope,[status(thm)],[f_208_2]) ).
cnf(f_208_4,plain,
( subset(set_intersection2(U_793,U_791),set_intersection2(U_792,U_791))
| ~ subset(U_793,U_792) ),
inference(clausify,[status(thm)],[f_208_3]) ).
fof(f_209_1,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t28_xboole_1]) ).
fof(f_209_2,plain,
! [U_795,U_794] :
( set_intersection2(U_795,U_794) = U_795
| ~ subset(U_795,U_794) ),
inference(variable_rename,[status(thm)],[f_209_1]) ).
cnf(f_209_3,plain,
( set_intersection2(U_795,U_794) = U_795
| ~ subset(U_795,U_794) ),
inference(clausify,[status(thm)],[f_209_2]) ).
fof(f_210_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_210_2,plain,
! [U_796] : set_intersection2(U_796,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_210_1]) ).
cnf(f_210_3,plain,
set_intersection2(U_796,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_210_2]) ).
fof(f_211_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_211_2,plain,
! [U_798,U_797] :
( in(U_798,U_797)
| empty(U_797)
| ~ element(U_798,U_797) ),
inference(variable_rename,[status(thm)],[f_211_1]) ).
cnf(f_211_3,plain,
( in(U_798,U_797)
| empty(U_797)
| ~ element(U_798,U_797) ),
inference(clausify,[status(thm)],[f_211_2]) ).
fof(f_212_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_212_2,plain,
! [U_801,U_800] :
( U_801 = U_800
| ? [U_799] :
( ( ~ in(U_799,U_801)
& in(U_799,U_800) )
| ( ~ in(U_799,U_800)
& in(U_799,U_801) ) ) ),
inference(variable_rename,[status(thm)],[f_212_1]) ).
fof(f_212_3,plain,
! [U_801,U_800] :
( U_801 = U_800
| ? [U_803] :
( ~ in(U_803,U_801)
& in(U_803,U_800) )
| ? [U_802] :
( ~ in(U_802,U_800)
& in(U_802,U_801) ) ),
inference(miniscope,[status(thm)],[f_212_2]) ).
fof(f_212_4,plain,
! [U_801,U_800] :
( U_801 = U_800
| ? [U_803] :
( ~ in(U_803,U_801)
& in(U_803,U_800) )
| ( ~ in(sK126(U_801,U_800),U_800)
& in(sK126(U_801,U_800),U_801) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK126]),skolemize(U_802,sK126(U_801,U_800))],[f_212_3]) ).
fof(f_212_5,plain,
! [U_801,U_800] :
( U_801 = U_800
| ( ~ in(sK127(U_801,U_800),U_801)
& in(sK127(U_801,U_800),U_800) )
| ( ~ in(sK126(U_801,U_800),U_800)
& in(sK126(U_801,U_800),U_801) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK127]),skolemize(U_803,sK127(U_801,U_800))],[f_212_4]) ).
cnf(f_212_6,plain,
( in(sK127(U_801,U_800),U_800)
| in(sK126(U_801,U_800),U_801)
| U_801 = U_800 ),
inference(clausify,[status(thm)],[f_212_5]) ).
cnf(f_212_7,plain,
( ~ in(sK127(U_801,U_800),U_801)
| in(sK126(U_801,U_800),U_801)
| U_801 = U_800 ),
inference(clausify,[status(thm)],[f_212_5]) ).
cnf(f_212_8,plain,
( in(sK127(U_801,U_800),U_800)
| ~ in(sK126(U_801,U_800),U_800)
| U_801 = U_800 ),
inference(clausify,[status(thm)],[f_212_5]) ).
cnf(f_212_9,plain,
( ~ in(sK127(U_801,U_800),U_801)
| ~ in(sK126(U_801,U_800),U_800)
| U_801 = U_800 ),
inference(clausify,[status(thm)],[f_212_5]) ).
fof(f_213_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_213_2,plain,
! [U_804] : subset(empty_set,U_804),
inference(variable_rename,[status(thm)],[f_213_1]) ).
cnf(f_213_3,plain,
subset(empty_set,U_804),
inference(clausify,[status(thm)],[f_213_2]) ).
fof(f_214_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_214_2,plain,
! [U_807,U_806,U_805] :
( ( in(U_806,relation_field(U_805))
& in(U_807,relation_field(U_805)) )
| ~ in(ordered_pair(U_807,U_806),U_805)
| ~ relation(U_805) ),
inference(variable_rename,[status(thm)],[f_214_1]) ).
cnf(f_214_3,plain,
( in(U_807,relation_field(U_805))
| ~ in(ordered_pair(U_807,U_806),U_805)
| ~ relation(U_805) ),
inference(clausify,[status(thm)],[f_214_2]) ).
cnf(f_214_4,plain,
( in(U_806,relation_field(U_805))
| ~ in(ordered_pair(U_807,U_806),U_805)
| ~ relation(U_805) ),
inference(clausify,[status(thm)],[f_214_2]) ).
fof(f_215_1,plain,
! [A] :
( ordinal(A)
| ? [B] :
( ( ~ subset(B,A)
| ~ ordinal(B) )
& in(B,A) ) ),
inference(fof_nnf,[status(thm)],[t31_ordinal1]) ).
fof(f_215_2,plain,
! [U_809] :
( ordinal(U_809)
| ? [U_808] :
( ( ~ subset(U_808,U_809)
| ~ ordinal(U_808) )
& in(U_808,U_809) ) ),
inference(variable_rename,[status(thm)],[f_215_1]) ).
fof(f_215_3,plain,
! [U_809] :
( ordinal(U_809)
| ( ( ~ subset(sK128(U_809),U_809)
| ~ ordinal(sK128(U_809)) )
& in(sK128(U_809),U_809) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK128]),skolemize(U_808,sK128(U_809))],[f_215_2]) ).
cnf(f_215_4,plain,
( in(sK128(U_809),U_809)
| ordinal(U_809) ),
inference(clausify,[status(thm)],[f_215_3]) ).
cnf(f_215_5,plain,
( ~ subset(sK128(U_809),U_809)
| ~ ordinal(sK128(U_809))
| ordinal(U_809) ),
inference(clausify,[status(thm)],[f_215_3]) ).
fof(f_216_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_216_2,plain,
! [U_813,U_812] :
( ? [U_811] :
( ! [U_810] :
( ordinal_subset(U_811,U_810)
| ~ in(U_810,U_813)
| ~ ordinal(U_810) )
& in(U_811,U_813)
& ordinal(U_811) )
| U_813 = empty_set
| ~ subset(U_813,U_812)
| ~ ordinal(U_812) ),
inference(variable_rename,[status(thm)],[f_216_1]) ).
fof(f_216_3,plain,
! [U_813,U_812] :
( ( ! [U_810] :
( ordinal_subset(sK129(U_813,U_812),U_810)
| ~ in(U_810,U_813)
| ~ ordinal(U_810) )
& in(sK129(U_813,U_812),U_813)
& ordinal(sK129(U_813,U_812)) )
| U_813 = empty_set
| ~ subset(U_813,U_812)
| ~ ordinal(U_812) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK129]),skolemize(U_811,sK129(U_813,U_812))],[f_216_2]) ).
cnf(f_216_4,plain,
( ordinal(sK129(U_813,U_812))
| U_813 = empty_set
| ~ subset(U_813,U_812)
| ~ ordinal(U_812) ),
inference(clausify,[status(thm)],[f_216_3]) ).
cnf(f_216_5,plain,
( in(sK129(U_813,U_812),U_813)
| U_813 = empty_set
| ~ subset(U_813,U_812)
| ~ ordinal(U_812) ),
inference(clausify,[status(thm)],[f_216_3]) ).
cnf(f_216_6,plain,
( ordinal_subset(sK129(U_813,U_812),U_810)
| ~ in(U_810,U_813)
| ~ ordinal(U_810)
| U_813 = empty_set
| ~ subset(U_813,U_812)
| ~ ordinal(U_812) ),
inference(clausify,[status(thm)],[f_216_3]) ).
fof(f_217_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_217_2,plain,
! [U_815] :
( ! [U_814] :
( ( ( in(U_815,U_814)
| ~ ordinal_subset(succ(U_815),U_814) )
& ( ordinal_subset(succ(U_815),U_814)
| ~ in(U_815,U_814) ) )
| ~ ordinal(U_814) )
| ~ ordinal(U_815) ),
inference(variable_rename,[status(thm)],[f_217_1]) ).
cnf(f_217_3,plain,
( ordinal_subset(succ(U_815),U_814)
| ~ in(U_815,U_814)
| ~ ordinal(U_814)
| ~ ordinal(U_815) ),
inference(clausify,[status(thm)],[f_217_2]) ).
cnf(f_217_4,plain,
( in(U_815,U_814)
| ~ ordinal_subset(succ(U_815),U_814)
| ~ ordinal(U_814)
| ~ ordinal(U_815) ),
inference(clausify,[status(thm)],[f_217_2]) ).
fof(f_218_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_218_2,plain,
! [U_818,U_817,U_816] :
( subset(set_difference(U_818,U_816),set_difference(U_817,U_816))
| ~ subset(U_818,U_817) ),
inference(variable_rename,[status(thm)],[f_218_1]) ).
fof(f_218_3,plain,
! [U_818,U_817] :
( ! [U_816] : subset(set_difference(U_818,U_816),set_difference(U_817,U_816))
| ~ subset(U_818,U_817) ),
inference(miniscope,[status(thm)],[f_218_2]) ).
cnf(f_218_4,plain,
( subset(set_difference(U_818,U_816),set_difference(U_817,U_816))
| ~ subset(U_818,U_817) ),
inference(clausify,[status(thm)],[f_218_3]) ).
fof(f_219_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_219_2,plain,
! [U_822,U_821,U_820,U_819] :
( ( U_821 = U_819
& U_822 = U_820 )
| ordered_pair(U_822,U_821) != ordered_pair(U_820,U_819) ),
inference(variable_rename,[status(thm)],[f_219_1]) ).
cnf(f_219_3,plain,
( U_822 = U_820
| ordered_pair(U_822,U_821) != ordered_pair(U_820,U_819) ),
inference(clausify,[status(thm)],[f_219_2]) ).
cnf(f_219_4,plain,
( U_821 = U_819
| ordered_pair(U_822,U_821) != ordered_pair(U_820,U_819) ),
inference(clausify,[status(thm)],[f_219_2]) ).
fof(f_220_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_220_2,plain,
! [U_826,U_825] :
( ( ( U_825 = identity_relation(U_826)
| ? [U_824] :
( apply(U_825,U_824) != U_824
& in(U_824,U_826) )
| relation_dom(U_825) != U_826 )
& ( ( ! [U_823] :
( apply(U_825,U_823) = U_823
| ~ in(U_823,U_826) )
& relation_dom(U_825) = U_826 )
| U_825 != identity_relation(U_826) ) )
| ~ function(U_825)
| ~ relation(U_825) ),
inference(variable_rename,[status(thm)],[f_220_1]) ).
fof(f_220_3,plain,
! [U_826,U_825] :
( ( ( U_825 = identity_relation(U_826)
| ( apply(U_825,sK130(U_826,U_825)) != sK130(U_826,U_825)
& in(sK130(U_826,U_825),U_826) )
| relation_dom(U_825) != U_826 )
& ( ( ! [U_823] :
( apply(U_825,U_823) = U_823
| ~ in(U_823,U_826) )
& relation_dom(U_825) = U_826 )
| U_825 != identity_relation(U_826) ) )
| ~ function(U_825)
| ~ relation(U_825) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK130]),skolemize(U_824,sK130(U_826,U_825))],[f_220_2]) ).
cnf(f_220_4,plain,
( relation_dom(U_825) = U_826
| U_825 != identity_relation(U_826)
| ~ function(U_825)
| ~ relation(U_825) ),
inference(clausify,[status(thm)],[f_220_3]) ).
cnf(f_220_5,plain,
( apply(U_825,U_823) = U_823
| ~ in(U_823,U_826)
| U_825 != identity_relation(U_826)
| ~ function(U_825)
| ~ relation(U_825) ),
inference(clausify,[status(thm)],[f_220_3]) ).
cnf(f_220_6,plain,
( in(sK130(U_826,U_825),U_826)
| relation_dom(U_825) != U_826
| U_825 = identity_relation(U_826)
| ~ function(U_825)
| ~ relation(U_825) ),
inference(clausify,[status(thm)],[f_220_3]) ).
cnf(f_220_7,plain,
( apply(U_825,sK130(U_826,U_825)) != sK130(U_826,U_825)
| relation_dom(U_825) != U_826
| U_825 = identity_relation(U_826)
| ~ function(U_825)
| ~ relation(U_825) ),
inference(clausify,[status(thm)],[f_220_3]) ).
fof(f_221_1,plain,
! [A,B] :
( apply(identity_relation(A),B) = B
| ~ in(B,A) ),
inference(fof_nnf,[status(thm)],[t35_funct_1]) ).
fof(f_221_2,plain,
! [U_828,U_827] :
( apply(identity_relation(U_828),U_827) = U_827
| ~ in(U_827,U_828) ),
inference(variable_rename,[status(thm)],[f_221_1]) ).
cnf(f_221_3,plain,
( apply(identity_relation(U_828),U_827) = U_827
| ~ in(U_827,U_828) ),
inference(clausify,[status(thm)],[f_221_2]) ).
fof(f_222_1,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(fof_nnf,[status(thm)],[t36_xboole_1]) ).
fof(f_222_2,plain,
! [U_830,U_829] : subset(set_difference(U_830,U_829),U_830),
inference(variable_rename,[status(thm)],[f_222_1]) ).
cnf(f_222_3,plain,
subset(set_difference(U_830,U_829),U_830),
inference(clausify,[status(thm)],[f_222_2]) ).
fof(f_223_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_223_2,plain,
! [U_831] :
( ( relation_dom(U_831) = relation_rng(relation_inverse(U_831))
& relation_rng(U_831) = relation_dom(relation_inverse(U_831)) )
| ~ relation(U_831) ),
inference(variable_rename,[status(thm)],[f_223_1]) ).
cnf(f_223_3,plain,
( relation_rng(U_831) = relation_dom(relation_inverse(U_831))
| ~ relation(U_831) ),
inference(clausify,[status(thm)],[f_223_2]) ).
cnf(f_223_4,plain,
( relation_dom(U_831) = relation_rng(relation_inverse(U_831))
| ~ relation(U_831) ),
inference(clausify,[status(thm)],[f_223_2]) ).
fof(f_224_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_224_2,plain,
! [U_833,U_832] :
( ( set_difference(U_833,U_832) = empty_set
| ~ subset(U_833,U_832) )
& ( subset(U_833,U_832)
| set_difference(U_833,U_832) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_224_1]) ).
fof(f_224_3,plain,
( ! [U_837,U_835] :
( set_difference(U_837,U_835) = empty_set
| ~ subset(U_837,U_835) )
& ! [U_836,U_834] :
( subset(U_836,U_834)
| set_difference(U_836,U_834) != empty_set ) ),
inference(miniscope,[status(thm)],[f_224_2]) ).
cnf(f_224_4,plain,
( subset(U_836,U_834)
| set_difference(U_836,U_834) != empty_set ),
inference(clausify,[status(thm)],[f_224_3]) ).
cnf(f_224_5,plain,
( set_difference(U_837,U_835) = empty_set
| ~ subset(U_837,U_835) ),
inference(clausify,[status(thm)],[f_224_3]) ).
fof(f_225_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_225_2,plain,
! [U_839,U_838] :
( ( subset(singleton(U_839),U_838)
| ~ in(U_839,U_838) )
& ( in(U_839,U_838)
| ~ subset(singleton(U_839),U_838) ) ),
inference(variable_rename,[status(thm)],[f_225_1]) ).
fof(f_225_3,plain,
( ! [U_843,U_841] :
( subset(singleton(U_843),U_841)
| ~ in(U_843,U_841) )
& ! [U_842,U_840] :
( in(U_842,U_840)
| ~ subset(singleton(U_842),U_840) ) ),
inference(miniscope,[status(thm)],[f_225_2]) ).
cnf(f_225_4,plain,
( in(U_842,U_840)
| ~ subset(singleton(U_842),U_840) ),
inference(clausify,[status(thm)],[f_225_3]) ).
cnf(f_225_5,plain,
( subset(singleton(U_843),U_841)
| ~ in(U_843,U_841) ),
inference(clausify,[status(thm)],[f_225_3]) ).
fof(f_226_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_226_2,plain,
! [U_846,U_845,U_844] :
( ( subset(unordered_pair(U_846,U_845),U_844)
| ~ in(U_845,U_844)
| ~ in(U_846,U_844) )
& ( ( in(U_845,U_844)
& in(U_846,U_844) )
| ~ subset(unordered_pair(U_846,U_845),U_844) ) ),
inference(variable_rename,[status(thm)],[f_226_1]) ).
fof(f_226_3,plain,
( ! [U_852,U_850,U_848] :
( subset(unordered_pair(U_852,U_850),U_848)
| ~ in(U_850,U_848)
| ~ in(U_852,U_848) )
& ! [U_851,U_849,U_847] :
( ( in(U_849,U_847)
& in(U_851,U_847) )
| ~ subset(unordered_pair(U_851,U_849),U_847) ) ),
inference(miniscope,[status(thm)],[f_226_2]) ).
cnf(f_226_4,plain,
( in(U_851,U_847)
| ~ subset(unordered_pair(U_851,U_849),U_847) ),
inference(clausify,[status(thm)],[f_226_3]) ).
cnf(f_226_5,plain,
( in(U_849,U_847)
| ~ subset(unordered_pair(U_851,U_849),U_847) ),
inference(clausify,[status(thm)],[f_226_3]) ).
cnf(f_226_6,plain,
( subset(unordered_pair(U_852,U_850),U_848)
| ~ in(U_850,U_848)
| ~ in(U_852,U_848) ),
inference(clausify,[status(thm)],[f_226_3]) ).
fof(f_227_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_227_2,plain,
! [U_854,U_853] : set_union2(U_854,set_difference(U_853,U_854)) = set_union2(U_854,U_853),
inference(variable_rename,[status(thm)],[f_227_1]) ).
cnf(f_227_3,plain,
set_union2(U_854,set_difference(U_853,U_854)) = set_union2(U_854,U_853),
inference(clausify,[status(thm)],[f_227_2]) ).
fof(f_228_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_228_2,plain,
! [U_856,U_855] :
( ( subset(U_856,singleton(U_855))
| ( U_856 != singleton(U_855)
& U_856 != empty_set ) )
& ( U_856 = singleton(U_855)
| U_856 = empty_set
| ~ subset(U_856,singleton(U_855)) ) ),
inference(variable_rename,[status(thm)],[f_228_1]) ).
fof(f_228_3,plain,
( ! [U_860,U_858] :
( subset(U_860,singleton(U_858))
| ( U_860 != singleton(U_858)
& U_860 != empty_set ) )
& ! [U_859,U_857] :
( U_859 = singleton(U_857)
| U_859 = empty_set
| ~ subset(U_859,singleton(U_857)) ) ),
inference(miniscope,[status(thm)],[f_228_2]) ).
cnf(f_228_4,plain,
( U_859 = singleton(U_857)
| U_859 = empty_set
| ~ subset(U_859,singleton(U_857)) ),
inference(clausify,[status(thm)],[f_228_3]) ).
cnf(f_228_5,plain,
( U_860 != empty_set
| subset(U_860,singleton(U_858)) ),
inference(clausify,[status(thm)],[f_228_3]) ).
cnf(f_228_6,plain,
( U_860 != singleton(U_858)
| subset(U_860,singleton(U_858)) ),
inference(clausify,[status(thm)],[f_228_3]) ).
fof(f_229_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_229_2,plain,
! [U_861] : set_difference(U_861,empty_set) = U_861,
inference(variable_rename,[status(thm)],[f_229_1]) ).
cnf(f_229_3,plain,
set_difference(U_861,empty_set) = U_861,
inference(clausify,[status(thm)],[f_229_2]) ).
fof(f_230_1,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ in(B,C)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t3_ordinal1]) ).
fof(f_230_2,plain,
! [U_864,U_863,U_862] :
( ~ in(U_862,U_864)
| ~ in(U_863,U_862)
| ~ in(U_864,U_863) ),
inference(variable_rename,[status(thm)],[f_230_1]) ).
fof(f_230_3,plain,
! [U_864,U_863] :
( ! [U_862] :
( ~ in(U_862,U_864)
| ~ in(U_863,U_862) )
| ~ in(U_864,U_863) ),
inference(miniscope,[status(thm)],[f_230_2]) ).
cnf(f_230_4,plain,
( ~ in(U_862,U_864)
| ~ in(U_863,U_862)
| ~ in(U_864,U_863) ),
inference(clausify,[status(thm)],[f_230_3]) ).
fof(f_231_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_231_2,plain,
! [U_866,U_865] :
( ( element(U_866,powerset(U_865))
| ~ subset(U_866,U_865) )
& ( subset(U_866,U_865)
| ~ element(U_866,powerset(U_865)) ) ),
inference(variable_rename,[status(thm)],[f_231_1]) ).
fof(f_231_3,plain,
( ! [U_870,U_868] :
( element(U_870,powerset(U_868))
| ~ subset(U_870,U_868) )
& ! [U_869,U_867] :
( subset(U_869,U_867)
| ~ element(U_869,powerset(U_867)) ) ),
inference(miniscope,[status(thm)],[f_231_2]) ).
cnf(f_231_4,plain,
( subset(U_869,U_867)
| ~ element(U_869,powerset(U_867)) ),
inference(clausify,[status(thm)],[f_231_3]) ).
cnf(f_231_5,plain,
( element(U_870,powerset(U_868))
| ~ subset(U_870,U_868) ),
inference(clausify,[status(thm)],[f_231_3]) ).
fof(f_232_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_232_2,plain,
! [U_874,U_873] :
( ( ~ disjoint(U_874,U_873)
| ! [U_872] :
( ~ in(U_872,U_873)
| ~ in(U_872,U_874) ) )
& ( ? [U_871] :
( in(U_871,U_873)
& in(U_871,U_874) )
| disjoint(U_874,U_873) ) ),
inference(variable_rename,[status(thm)],[f_232_1]) ).
fof(f_232_3,plain,
( ! [U_878,U_876] :
( ~ disjoint(U_878,U_876)
| ! [U_872] :
( ~ in(U_872,U_876)
| ~ in(U_872,U_878) ) )
& ! [U_877,U_875] :
( ? [U_871] :
( in(U_871,U_875)
& in(U_871,U_877) )
| disjoint(U_877,U_875) ) ),
inference(miniscope,[status(thm)],[f_232_2]) ).
fof(f_232_4,plain,
( ! [U_878,U_876] :
( ~ disjoint(U_878,U_876)
| ! [U_872] :
( ~ in(U_872,U_876)
| ~ in(U_872,U_878) ) )
& ! [U_877,U_875] :
( ( in(sK131(U_877,U_875),U_875)
& in(sK131(U_877,U_875),U_877) )
| disjoint(U_877,U_875) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK131]),skolemize(U_871,sK131(U_877,U_875))],[f_232_3]) ).
cnf(f_232_5,plain,
( in(sK131(U_877,U_875),U_877)
| disjoint(U_877,U_875) ),
inference(clausify,[status(thm)],[f_232_4]) ).
cnf(f_232_6,plain,
( in(sK131(U_877,U_875),U_875)
| disjoint(U_877,U_875) ),
inference(clausify,[status(thm)],[f_232_4]) ).
cnf(f_232_7,plain,
( ~ disjoint(U_878,U_876)
| ~ in(U_872,U_876)
| ~ in(U_872,U_878) ),
inference(clausify,[status(thm)],[f_232_4]) ).
fof(f_233_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_233_2,plain,
! [U_879] :
( U_879 = empty_set
| ~ subset(U_879,empty_set) ),
inference(variable_rename,[status(thm)],[f_233_1]) ).
cnf(f_233_3,plain,
( U_879 = empty_set
| ~ subset(U_879,empty_set) ),
inference(clausify,[status(thm)],[f_233_2]) ).
fof(f_234_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_234_2,plain,
! [U_881,U_880] : set_difference(set_union2(U_881,U_880),U_880) = set_difference(U_881,U_880),
inference(variable_rename,[status(thm)],[f_234_1]) ).
cnf(f_234_3,plain,
set_difference(set_union2(U_881,U_880),U_880) = set_difference(U_881,U_880),
inference(clausify,[status(thm)],[f_234_2]) ).
fof(f_235_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_235_2,plain,
! [U_884] :
( ( ( being_limit_ordinal(U_884)
| ? [U_883] :
( ~ in(succ(U_883),U_884)
& in(U_883,U_884)
& ordinal(U_883) ) )
& ( ! [U_882] :
( in(succ(U_882),U_884)
| ~ in(U_882,U_884)
| ~ ordinal(U_882) )
| ~ being_limit_ordinal(U_884) ) )
| ~ ordinal(U_884) ),
inference(variable_rename,[status(thm)],[f_235_1]) ).
fof(f_235_3,plain,
! [U_884] :
( ( ( being_limit_ordinal(U_884)
| ( ~ in(succ(sK132(U_884)),U_884)
& in(sK132(U_884),U_884)
& ordinal(sK132(U_884)) ) )
& ( ! [U_882] :
( in(succ(U_882),U_884)
| ~ in(U_882,U_884)
| ~ ordinal(U_882) )
| ~ being_limit_ordinal(U_884) ) )
| ~ ordinal(U_884) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK132]),skolemize(U_883,sK132(U_884))],[f_235_2]) ).
cnf(f_235_4,plain,
( in(succ(U_882),U_884)
| ~ in(U_882,U_884)
| ~ ordinal(U_882)
| ~ being_limit_ordinal(U_884)
| ~ ordinal(U_884) ),
inference(clausify,[status(thm)],[f_235_3]) ).
cnf(f_235_5,plain,
( ordinal(sK132(U_884))
| being_limit_ordinal(U_884)
| ~ ordinal(U_884) ),
inference(clausify,[status(thm)],[f_235_3]) ).
cnf(f_235_6,plain,
( in(sK132(U_884),U_884)
| being_limit_ordinal(U_884)
| ~ ordinal(U_884) ),
inference(clausify,[status(thm)],[f_235_3]) ).
cnf(f_235_7,plain,
( ~ in(succ(sK132(U_884)),U_884)
| being_limit_ordinal(U_884)
| ~ ordinal(U_884) ),
inference(clausify,[status(thm)],[f_235_3]) ).
fof(f_236_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_236_2,plain,
! [U_887] :
( ( ( ~ being_limit_ordinal(U_887)
| ! [U_886] :
( U_887 != succ(U_886)
| ~ ordinal(U_886) ) )
& ( ? [U_885] :
( U_887 = succ(U_885)
& ordinal(U_885) )
| being_limit_ordinal(U_887) ) )
| ~ ordinal(U_887) ),
inference(variable_rename,[status(thm)],[f_236_1]) ).
fof(f_236_3,plain,
! [U_887] :
( ( ( ~ being_limit_ordinal(U_887)
| ! [U_886] :
( U_887 != succ(U_886)
| ~ ordinal(U_886) ) )
& ( ( U_887 = succ(sK133(U_887))
& ordinal(sK133(U_887)) )
| being_limit_ordinal(U_887) ) )
| ~ ordinal(U_887) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK133]),skolemize(U_885,sK133(U_887))],[f_236_2]) ).
cnf(f_236_4,plain,
( ordinal(sK133(U_887))
| being_limit_ordinal(U_887)
| ~ ordinal(U_887) ),
inference(clausify,[status(thm)],[f_236_3]) ).
cnf(f_236_5,plain,
( U_887 = succ(sK133(U_887))
| being_limit_ordinal(U_887)
| ~ ordinal(U_887) ),
inference(clausify,[status(thm)],[f_236_3]) ).
cnf(f_236_6,plain,
( ~ being_limit_ordinal(U_887)
| U_887 != succ(U_886)
| ~ ordinal(U_886)
| ~ ordinal(U_887) ),
inference(clausify,[status(thm)],[f_236_3]) ).
fof(f_237_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_237_2,plain,
! [U_890,U_889] :
( ! [U_888] :
( ( ( disjoint(U_889,U_888)
| ~ subset(U_889,subset_complement(U_890,U_888)) )
& ( subset(U_889,subset_complement(U_890,U_888))
| ~ disjoint(U_889,U_888) ) )
| ~ element(U_888,powerset(U_890)) )
| ~ element(U_889,powerset(U_890)) ),
inference(variable_rename,[status(thm)],[f_237_1]) ).
cnf(f_237_3,plain,
( subset(U_889,subset_complement(U_890,U_888))
| ~ disjoint(U_889,U_888)
| ~ element(U_888,powerset(U_890))
| ~ element(U_889,powerset(U_890)) ),
inference(clausify,[status(thm)],[f_237_2]) ).
cnf(f_237_4,plain,
( disjoint(U_889,U_888)
| ~ subset(U_889,subset_complement(U_890,U_888))
| ~ element(U_888,powerset(U_890))
| ~ element(U_889,powerset(U_890)) ),
inference(clausify,[status(thm)],[f_237_2]) ).
fof(f_238_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_238_2,plain,
! [U_892] :
( ! [U_891] :
( subset(relation_dom(relation_composition(U_892,U_891)),relation_dom(U_892))
| ~ relation(U_891) )
| ~ relation(U_892) ),
inference(variable_rename,[status(thm)],[f_238_1]) ).
cnf(f_238_3,plain,
( subset(relation_dom(relation_composition(U_892,U_891)),relation_dom(U_892))
| ~ relation(U_891)
| ~ relation(U_892) ),
inference(clausify,[status(thm)],[f_238_2]) ).
fof(f_239_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_239_2,plain,
! [U_894] :
( ! [U_893] :
( subset(relation_rng(relation_composition(U_894,U_893)),relation_rng(U_893))
| ~ relation(U_893) )
| ~ relation(U_894) ),
inference(variable_rename,[status(thm)],[f_239_1]) ).
cnf(f_239_3,plain,
( subset(relation_rng(relation_composition(U_894,U_893)),relation_rng(U_893))
| ~ relation(U_893)
| ~ relation(U_894) ),
inference(clausify,[status(thm)],[f_239_2]) ).
fof(f_240_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_240_2,plain,
! [U_896,U_895] :
( U_895 = set_union2(U_896,set_difference(U_895,U_896))
| ~ subset(U_896,U_895) ),
inference(variable_rename,[status(thm)],[f_240_1]) ).
cnf(f_240_3,plain,
( U_895 = set_union2(U_896,set_difference(U_895,U_896))
| ~ subset(U_896,U_895) ),
inference(clausify,[status(thm)],[f_240_2]) ).
fof(f_241_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_241_2,plain,
! [U_898] :
( ! [U_897] :
( relation_dom(relation_composition(U_898,U_897)) = relation_dom(U_898)
| ~ subset(relation_rng(U_898),relation_dom(U_897))
| ~ relation(U_897) )
| ~ relation(U_898) ),
inference(variable_rename,[status(thm)],[f_241_1]) ).
cnf(f_241_3,plain,
( relation_dom(relation_composition(U_898,U_897)) = relation_dom(U_898)
| ~ subset(relation_rng(U_898),relation_dom(U_897))
| ~ relation(U_897)
| ~ relation(U_898) ),
inference(clausify,[status(thm)],[f_241_2]) ).
fof(f_242_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_242_2,plain,
! [U_900,U_899] :
( complements_of_subsets(U_900,U_899) != empty_set
| U_899 = empty_set
| ~ element(U_899,powerset(powerset(U_900))) ),
inference(variable_rename,[status(thm)],[f_242_1]) ).
cnf(f_242_3,plain,
( complements_of_subsets(U_900,U_899) != empty_set
| U_899 = empty_set
| ~ element(U_899,powerset(powerset(U_900))) ),
inference(clausify,[status(thm)],[f_242_2]) ).
fof(f_243_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t46_zfmisc_1]) ).
fof(f_243_2,plain,
! [U_902,U_901] :
( set_union2(singleton(U_902),U_901) = U_901
| ~ in(U_902,U_901) ),
inference(variable_rename,[status(thm)],[f_243_1]) ).
cnf(f_243_3,plain,
( set_union2(singleton(U_902),U_901) = U_901
| ~ in(U_902,U_901) ),
inference(clausify,[status(thm)],[f_243_2]) ).
fof(f_244_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_244_2,plain,
! [U_904] :
( ! [U_903] :
( relation_rng(relation_composition(U_903,U_904)) = relation_rng(U_904)
| ~ subset(relation_dom(U_904),relation_rng(U_903))
| ~ relation(U_903) )
| ~ relation(U_904) ),
inference(variable_rename,[status(thm)],[f_244_1]) ).
cnf(f_244_3,plain,
( relation_rng(relation_composition(U_903,U_904)) = relation_rng(U_904)
| ~ subset(relation_dom(U_904),relation_rng(U_903))
| ~ relation(U_903)
| ~ relation(U_904) ),
inference(clausify,[status(thm)],[f_244_2]) ).
fof(f_245_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_245_2,plain,
! [U_906,U_905] :
( subset_difference(U_906,cast_to_subset(U_906),union_of_subsets(U_906,U_905)) = meet_of_subsets(U_906,complements_of_subsets(U_906,U_905))
| U_905 = empty_set
| ~ element(U_905,powerset(powerset(U_906))) ),
inference(variable_rename,[status(thm)],[f_245_1]) ).
cnf(f_245_3,plain,
( subset_difference(U_906,cast_to_subset(U_906),union_of_subsets(U_906,U_905)) = meet_of_subsets(U_906,complements_of_subsets(U_906,U_905))
| U_905 = empty_set
| ~ element(U_905,powerset(powerset(U_906))) ),
inference(clausify,[status(thm)],[f_245_2]) ).
fof(f_246_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_246_2,plain,
! [U_908,U_907] :
( union_of_subsets(U_908,complements_of_subsets(U_908,U_907)) = subset_difference(U_908,cast_to_subset(U_908),meet_of_subsets(U_908,U_907))
| U_907 = empty_set
| ~ element(U_907,powerset(powerset(U_908))) ),
inference(variable_rename,[status(thm)],[f_246_1]) ).
cnf(f_246_3,plain,
( union_of_subsets(U_908,complements_of_subsets(U_908,U_907)) = subset_difference(U_908,cast_to_subset(U_908),meet_of_subsets(U_908,U_907))
| U_907 = empty_set
| ~ element(U_907,powerset(powerset(U_908))) ),
inference(clausify,[status(thm)],[f_246_2]) ).
fof(f_247_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_247_2,plain,
! [U_910,U_909] : set_difference(U_910,set_difference(U_910,U_909)) = set_intersection2(U_910,U_909),
inference(variable_rename,[status(thm)],[f_247_1]) ).
cnf(f_247_3,plain,
set_difference(U_910,set_difference(U_910,U_909)) = set_intersection2(U_910,U_909),
inference(clausify,[status(thm)],[f_247_2]) ).
fof(f_248_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_248_2,plain,
! [U_911] : set_difference(empty_set,U_911) = empty_set,
inference(variable_rename,[status(thm)],[f_248_1]) ).
cnf(f_248_3,plain,
set_difference(empty_set,U_911) = empty_set,
inference(clausify,[status(thm)],[f_248_2]) ).
fof(f_249_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_249_2,plain,
! [U_914,U_913,U_912] :
( element(U_914,U_912)
| ~ element(U_913,powerset(U_912))
| ~ in(U_914,U_913) ),
inference(variable_rename,[status(thm)],[f_249_1]) ).
cnf(f_249_3,plain,
( element(U_914,U_912)
| ~ element(U_913,powerset(U_912))
| ~ in(U_914,U_913) ),
inference(clausify,[status(thm)],[f_249_2]) ).
fof(f_250_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_250_2,plain,
! [U_918,U_917] :
( ( ~ disjoint(U_918,U_917)
| ! [U_916] : ~ in(U_916,set_intersection2(U_918,U_917)) )
& ( ? [U_915] : in(U_915,set_intersection2(U_918,U_917))
| disjoint(U_918,U_917) ) ),
inference(variable_rename,[status(thm)],[f_250_1]) ).
fof(f_250_3,plain,
( ! [U_922,U_920] :
( ~ disjoint(U_922,U_920)
| ! [U_916] : ~ in(U_916,set_intersection2(U_922,U_920)) )
& ! [U_921,U_919] :
( ? [U_915] : in(U_915,set_intersection2(U_921,U_919))
| disjoint(U_921,U_919) ) ),
inference(miniscope,[status(thm)],[f_250_2]) ).
fof(f_250_4,plain,
( ! [U_922,U_920] :
( ~ disjoint(U_922,U_920)
| ! [U_916] : ~ in(U_916,set_intersection2(U_922,U_920)) )
& ! [U_921,U_919] :
( in(sK134(U_921,U_919),set_intersection2(U_921,U_919))
| disjoint(U_921,U_919) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK134]),skolemize(U_915,sK134(U_921,U_919))],[f_250_3]) ).
cnf(f_250_5,plain,
( in(sK134(U_921,U_919),set_intersection2(U_921,U_919))
| disjoint(U_921,U_919) ),
inference(clausify,[status(thm)],[f_250_4]) ).
cnf(f_250_6,plain,
( ~ disjoint(U_922,U_920)
| ~ in(U_916,set_intersection2(U_922,U_920)) ),
inference(clausify,[status(thm)],[f_250_4]) ).
fof(f_251_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_251_2,plain,
! [U_925] :
( ! [U_924] :
( ! [U_923] :
( in(U_923,subset_complement(U_925,U_924))
| in(U_923,U_924)
| ~ element(U_923,U_925) )
| ~ element(U_924,powerset(U_925)) )
| U_925 = empty_set ),
inference(variable_rename,[status(thm)],[f_251_1]) ).
cnf(f_251_3,plain,
( in(U_923,subset_complement(U_925,U_924))
| in(U_923,U_924)
| ~ element(U_923,U_925)
| ~ element(U_924,powerset(U_925))
| U_925 = empty_set ),
inference(clausify,[status(thm)],[f_251_2]) ).
fof(f_252_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_252_2,plain,
! [U_931] :
( ! [U_930] :
( ( ( U_930 = function_inverse(U_931)
| ? [U_929,U_928] :
( ( ( U_928 != apply(U_930,U_929)
| ~ in(U_929,relation_rng(U_931)) )
& U_929 = apply(U_931,U_928)
& in(U_928,relation_dom(U_931)) )
| ( ( U_929 != apply(U_931,U_928)
| ~ in(U_928,relation_dom(U_931)) )
& U_928 = apply(U_930,U_929)
& in(U_929,relation_rng(U_931)) ) )
| relation_dom(U_930) != relation_rng(U_931) )
& ( ( ! [U_927,U_926] :
( ( ( U_926 = apply(U_930,U_927)
& in(U_927,relation_rng(U_931)) )
| U_927 != apply(U_931,U_926)
| ~ in(U_926,relation_dom(U_931)) )
& ( ( U_927 = apply(U_931,U_926)
& in(U_926,relation_dom(U_931)) )
| U_926 != apply(U_930,U_927)
| ~ in(U_927,relation_rng(U_931)) ) )
& relation_dom(U_930) = relation_rng(U_931) )
| U_930 != function_inverse(U_931) ) )
| ~ function(U_930)
| ~ relation(U_930) )
| ~ one_to_one(U_931)
| ~ function(U_931)
| ~ relation(U_931) ),
inference(variable_rename,[status(thm)],[f_252_1]) ).
fof(f_252_3,plain,
! [U_931] :
( ! [U_930] :
( ( ( U_930 = function_inverse(U_931)
| ? [U_939,U_937] :
( ( U_937 != apply(U_930,U_939)
| ~ in(U_939,relation_rng(U_931)) )
& U_939 = apply(U_931,U_937)
& in(U_937,relation_dom(U_931)) )
| ? [U_938,U_936] :
( ( U_938 != apply(U_931,U_936)
| ~ in(U_936,relation_dom(U_931)) )
& U_936 = apply(U_930,U_938)
& in(U_938,relation_rng(U_931)) )
| relation_dom(U_930) != relation_rng(U_931) )
& ( ( ! [U_935,U_933] :
( ( U_933 = apply(U_930,U_935)
& in(U_935,relation_rng(U_931)) )
| U_935 != apply(U_931,U_933)
| ~ in(U_933,relation_dom(U_931)) )
& ! [U_934,U_932] :
( ( U_934 = apply(U_931,U_932)
& in(U_932,relation_dom(U_931)) )
| U_932 != apply(U_930,U_934)
| ~ in(U_934,relation_rng(U_931)) )
& relation_dom(U_930) = relation_rng(U_931) )
| U_930 != function_inverse(U_931) ) )
| ~ function(U_930)
| ~ relation(U_930) )
| ~ one_to_one(U_931)
| ~ function(U_931)
| ~ relation(U_931) ),
inference(miniscope,[status(thm)],[f_252_2]) ).
fof(f_252_4,plain,
! [U_931] :
( ! [U_930] :
( ( ( U_930 = function_inverse(U_931)
| ? [U_939,U_937] :
( ( U_937 != apply(U_930,U_939)
| ~ in(U_939,relation_rng(U_931)) )
& U_939 = apply(U_931,U_937)
& in(U_937,relation_dom(U_931)) )
| ? [U_936] :
( ( sK135(U_931,U_930) != apply(U_931,U_936)
| ~ in(U_936,relation_dom(U_931)) )
& U_936 = apply(U_930,sK135(U_931,U_930))
& in(sK135(U_931,U_930),relation_rng(U_931)) )
| relation_dom(U_930) != relation_rng(U_931) )
& ( ( ! [U_935,U_933] :
( ( U_933 = apply(U_930,U_935)
& in(U_935,relation_rng(U_931)) )
| U_935 != apply(U_931,U_933)
| ~ in(U_933,relation_dom(U_931)) )
& ! [U_934,U_932] :
( ( U_934 = apply(U_931,U_932)
& in(U_932,relation_dom(U_931)) )
| U_932 != apply(U_930,U_934)
| ~ in(U_934,relation_rng(U_931)) )
& relation_dom(U_930) = relation_rng(U_931) )
| U_930 != function_inverse(U_931) ) )
| ~ function(U_930)
| ~ relation(U_930) )
| ~ one_to_one(U_931)
| ~ function(U_931)
| ~ relation(U_931) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK135]),skolemize(U_938,sK135(U_931,U_930))],[f_252_3]) ).
fof(f_252_5,plain,
! [U_931] :
( ! [U_930] :
( ( ( U_930 = function_inverse(U_931)
| ? [U_939,U_937] :
( ( U_937 != apply(U_930,U_939)
| ~ in(U_939,relation_rng(U_931)) )
& U_939 = apply(U_931,U_937)
& in(U_937,relation_dom(U_931)) )
| ( ( sK135(U_931,U_930) != apply(U_931,sK136(U_931,U_930))
| ~ in(sK136(U_931,U_930),relation_dom(U_931)) )
& sK136(U_931,U_930) = apply(U_930,sK135(U_931,U_930))
& in(sK135(U_931,U_930),relation_rng(U_931)) )
| relation_dom(U_930) != relation_rng(U_931) )
& ( ( ! [U_935,U_933] :
( ( U_933 = apply(U_930,U_935)
& in(U_935,relation_rng(U_931)) )
| U_935 != apply(U_931,U_933)
| ~ in(U_933,relation_dom(U_931)) )
& ! [U_934,U_932] :
( ( U_934 = apply(U_931,U_932)
& in(U_932,relation_dom(U_931)) )
| U_932 != apply(U_930,U_934)
| ~ in(U_934,relation_rng(U_931)) )
& relation_dom(U_930) = relation_rng(U_931) )
| U_930 != function_inverse(U_931) ) )
| ~ function(U_930)
| ~ relation(U_930) )
| ~ one_to_one(U_931)
| ~ function(U_931)
| ~ relation(U_931) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK136]),skolemize(U_936,sK136(U_931,U_930))],[f_252_4]) ).
fof(f_252_6,plain,
! [U_931] :
( ! [U_930] :
( ( ( U_930 = function_inverse(U_931)
| ? [U_937] :
( ( U_937 != apply(U_930,sK137(U_931,U_930))
| ~ in(sK137(U_931,U_930),relation_rng(U_931)) )
& sK137(U_931,U_930) = apply(U_931,U_937)
& in(U_937,relation_dom(U_931)) )
| ( ( sK135(U_931,U_930) != apply(U_931,sK136(U_931,U_930))
| ~ in(sK136(U_931,U_930),relation_dom(U_931)) )
& sK136(U_931,U_930) = apply(U_930,sK135(U_931,U_930))
& in(sK135(U_931,U_930),relation_rng(U_931)) )
| relation_dom(U_930) != relation_rng(U_931) )
& ( ( ! [U_935,U_933] :
( ( U_933 = apply(U_930,U_935)
& in(U_935,relation_rng(U_931)) )
| U_935 != apply(U_931,U_933)
| ~ in(U_933,relation_dom(U_931)) )
& ! [U_934,U_932] :
( ( U_934 = apply(U_931,U_932)
& in(U_932,relation_dom(U_931)) )
| U_932 != apply(U_930,U_934)
| ~ in(U_934,relation_rng(U_931)) )
& relation_dom(U_930) = relation_rng(U_931) )
| U_930 != function_inverse(U_931) ) )
| ~ function(U_930)
| ~ relation(U_930) )
| ~ one_to_one(U_931)
| ~ function(U_931)
| ~ relation(U_931) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK137]),skolemize(U_939,sK137(U_931,U_930))],[f_252_5]) ).
fof(f_252_7,plain,
! [U_931] :
( ! [U_930] :
( ( ( U_930 = function_inverse(U_931)
| ( ( sK138(U_931,U_930) != apply(U_930,sK137(U_931,U_930))
| ~ in(sK137(U_931,U_930),relation_rng(U_931)) )
& sK137(U_931,U_930) = apply(U_931,sK138(U_931,U_930))
& in(sK138(U_931,U_930),relation_dom(U_931)) )
| ( ( sK135(U_931,U_930) != apply(U_931,sK136(U_931,U_930))
| ~ in(sK136(U_931,U_930),relation_dom(U_931)) )
& sK136(U_931,U_930) = apply(U_930,sK135(U_931,U_930))
& in(sK135(U_931,U_930),relation_rng(U_931)) )
| relation_dom(U_930) != relation_rng(U_931) )
& ( ( ! [U_935,U_933] :
( ( U_933 = apply(U_930,U_935)
& in(U_935,relation_rng(U_931)) )
| U_935 != apply(U_931,U_933)
| ~ in(U_933,relation_dom(U_931)) )
& ! [U_934,U_932] :
( ( U_934 = apply(U_931,U_932)
& in(U_932,relation_dom(U_931)) )
| U_932 != apply(U_930,U_934)
| ~ in(U_934,relation_rng(U_931)) )
& relation_dom(U_930) = relation_rng(U_931) )
| U_930 != function_inverse(U_931) ) )
| ~ function(U_930)
| ~ relation(U_930) )
| ~ one_to_one(U_931)
| ~ function(U_931)
| ~ relation(U_931) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK138]),skolemize(U_937,sK138(U_931,U_930))],[f_252_6]) ).
cnf(f_252_8,plain,
( relation_dom(U_930) = relation_rng(U_931)
| U_930 != function_inverse(U_931)
| ~ function(U_930)
| ~ relation(U_930)
| ~ one_to_one(U_931)
| ~ function(U_931)
| ~ relation(U_931) ),
inference(clausify,[status(thm)],[f_252_7]) ).
cnf(f_252_9,plain,
( in(U_932,relation_dom(U_931))
| U_932 != apply(U_930,U_934)
| ~ in(U_934,relation_rng(U_931))
| U_930 != function_inverse(U_931)
| ~ function(U_930)
| ~ relation(U_930)
| ~ one_to_one(U_931)
| ~ function(U_931)
| ~ relation(U_931) ),
inference(clausify,[status(thm)],[f_252_7]) ).
cnf(f_252_10,plain,
( U_934 = apply(U_931,U_932)
| U_932 != apply(U_930,U_934)
| ~ in(U_934,relation_rng(U_931))
| U_930 != function_inverse(U_931)
| ~ function(U_930)
| ~ relation(U_930)
| ~ one_to_one(U_931)
| ~ function(U_931)
| ~ relation(U_931) ),
inference(clausify,[status(thm)],[f_252_7]) ).
cnf(f_252_11,plain,
( in(U_935,relation_rng(U_931))
| U_935 != apply(U_931,U_933)
| ~ in(U_933,relation_dom(U_931))
| U_930 != function_inverse(U_931)
| ~ function(U_930)
| ~ relation(U_930)
| ~ one_to_one(U_931)
| ~ function(U_931)
| ~ relation(U_931) ),
inference(clausify,[status(thm)],[f_252_7]) ).
cnf(f_252_12,plain,
( U_933 = apply(U_930,U_935)
| U_935 != apply(U_931,U_933)
| ~ in(U_933,relation_dom(U_931))
| U_930 != function_inverse(U_931)
| ~ function(U_930)
| ~ relation(U_930)
| ~ one_to_one(U_931)
| ~ function(U_931)
| ~ relation(U_931) ),
inference(clausify,[status(thm)],[f_252_7]) ).
cnf(f_252_13,plain,
( in(sK138(U_931,U_930),relation_dom(U_931))
| in(sK135(U_931,U_930),relation_rng(U_931))
| relation_dom(U_930) != relation_rng(U_931)
| U_930 = function_inverse(U_931)
| ~ function(U_930)
| ~ relation(U_930)
| ~ one_to_one(U_931)
| ~ function(U_931)
| ~ relation(U_931) ),
inference(clausify,[status(thm)],[f_252_7]) ).
cnf(f_252_14,plain,
( sK137(U_931,U_930) = apply(U_931,sK138(U_931,U_930))
| in(sK135(U_931,U_930),relation_rng(U_931))
| relation_dom(U_930) != relation_rng(U_931)
| U_930 = function_inverse(U_931)
| ~ function(U_930)
| ~ relation(U_930)
| ~ one_to_one(U_931)
| ~ function(U_931)
| ~ relation(U_931) ),
inference(clausify,[status(thm)],[f_252_7]) ).
cnf(f_252_15,plain,
( in(sK138(U_931,U_930),relation_dom(U_931))
| sK136(U_931,U_930) = apply(U_930,sK135(U_931,U_930))
| relation_dom(U_930) != relation_rng(U_931)
| U_930 = function_inverse(U_931)
| ~ function(U_930)
| ~ relation(U_930)
| ~ one_to_one(U_931)
| ~ function(U_931)
| ~ relation(U_931) ),
inference(clausify,[status(thm)],[f_252_7]) ).
cnf(f_252_16,plain,
( sK137(U_931,U_930) = apply(U_931,sK138(U_931,U_930))
| sK136(U_931,U_930) = apply(U_930,sK135(U_931,U_930))
| relation_dom(U_930) != relation_rng(U_931)
| U_930 = function_inverse(U_931)
| ~ function(U_930)
| ~ relation(U_930)
| ~ one_to_one(U_931)
| ~ function(U_931)
| ~ relation(U_931) ),
inference(clausify,[status(thm)],[f_252_7]) ).
cnf(f_252_17,plain,
( in(sK135(U_931,U_930),relation_rng(U_931))
| sK138(U_931,U_930) != apply(U_930,sK137(U_931,U_930))
| ~ in(sK137(U_931,U_930),relation_rng(U_931))
| relation_dom(U_930) != relation_rng(U_931)
| U_930 = function_inverse(U_931)
| ~ function(U_930)
| ~ relation(U_930)
| ~ one_to_one(U_931)
| ~ function(U_931)
| ~ relation(U_931) ),
inference(clausify,[status(thm)],[f_252_7]) ).
cnf(f_252_18,plain,
( sK136(U_931,U_930) = apply(U_930,sK135(U_931,U_930))
| sK138(U_931,U_930) != apply(U_930,sK137(U_931,U_930))
| ~ in(sK137(U_931,U_930),relation_rng(U_931))
| relation_dom(U_930) != relation_rng(U_931)
| U_930 = function_inverse(U_931)
| ~ function(U_930)
| ~ relation(U_930)
| ~ one_to_one(U_931)
| ~ function(U_931)
| ~ relation(U_931) ),
inference(clausify,[status(thm)],[f_252_7]) ).
cnf(f_252_19,plain,
( in(sK138(U_931,U_930),relation_dom(U_931))
| sK135(U_931,U_930) != apply(U_931,sK136(U_931,U_930))
| ~ in(sK136(U_931,U_930),relation_dom(U_931))
| relation_dom(U_930) != relation_rng(U_931)
| U_930 = function_inverse(U_931)
| ~ function(U_930)
| ~ relation(U_930)
| ~ one_to_one(U_931)
| ~ function(U_931)
| ~ relation(U_931) ),
inference(clausify,[status(thm)],[f_252_7]) ).
cnf(f_252_20,plain,
( sK137(U_931,U_930) = apply(U_931,sK138(U_931,U_930))
| sK135(U_931,U_930) != apply(U_931,sK136(U_931,U_930))
| ~ in(sK136(U_931,U_930),relation_dom(U_931))
| relation_dom(U_930) != relation_rng(U_931)
| U_930 = function_inverse(U_931)
| ~ function(U_930)
| ~ relation(U_930)
| ~ one_to_one(U_931)
| ~ function(U_931)
| ~ relation(U_931) ),
inference(clausify,[status(thm)],[f_252_7]) ).
cnf(f_252_21,plain,
( sK138(U_931,U_930) != apply(U_930,sK137(U_931,U_930))
| ~ in(sK137(U_931,U_930),relation_rng(U_931))
| sK135(U_931,U_930) != apply(U_931,sK136(U_931,U_930))
| ~ in(sK136(U_931,U_930),relation_dom(U_931))
| relation_dom(U_930) != relation_rng(U_931)
| U_930 = function_inverse(U_931)
| ~ function(U_930)
| ~ relation(U_930)
| ~ one_to_one(U_931)
| ~ function(U_931)
| ~ relation(U_931) ),
inference(clausify,[status(thm)],[f_252_7]) ).
fof(f_253_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_253_2,plain,
! [U_942,U_941,U_940] :
( ~ in(U_941,U_940)
| ~ in(U_941,subset_complement(U_942,U_940))
| ~ element(U_940,powerset(U_942)) ),
inference(variable_rename,[status(thm)],[f_253_1]) ).
cnf(f_253_3,plain,
( ~ in(U_941,U_940)
| ~ in(U_941,subset_complement(U_942,U_940))
| ~ element(U_940,powerset(U_942)) ),
inference(clausify,[status(thm)],[f_253_2]) ).
fof(f_254_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_254_2,plain,
! [U_943] :
( ( relation_dom(U_943) = relation_rng(function_inverse(U_943))
& relation_rng(U_943) = relation_dom(function_inverse(U_943)) )
| ~ one_to_one(U_943)
| ~ function(U_943)
| ~ relation(U_943) ),
inference(variable_rename,[status(thm)],[f_254_1]) ).
cnf(f_254_3,plain,
( relation_rng(U_943) = relation_dom(function_inverse(U_943))
| ~ one_to_one(U_943)
| ~ function(U_943)
| ~ relation(U_943) ),
inference(clausify,[status(thm)],[f_254_2]) ).
cnf(f_254_4,plain,
( relation_dom(U_943) = relation_rng(function_inverse(U_943))
| ~ one_to_one(U_943)
| ~ function(U_943)
| ~ relation(U_943) ),
inference(clausify,[status(thm)],[f_254_2]) ).
fof(f_255_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_255_2,plain,
! [U_946] :
( U_946 = empty_set
| ? [U_945,U_944] : in(ordered_pair(U_945,U_944),U_946)
| ~ relation(U_946) ),
inference(variable_rename,[status(thm)],[f_255_1]) ).
fof(f_255_3,plain,
! [U_946] :
( U_946 = empty_set
| ? [U_944] : in(ordered_pair(sK139(U_946),U_944),U_946)
| ~ relation(U_946) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK139]),skolemize(U_945,sK139(U_946))],[f_255_2]) ).
fof(f_255_4,plain,
! [U_946] :
( U_946 = empty_set
| in(ordered_pair(sK139(U_946),sK140(U_946)),U_946)
| ~ relation(U_946) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK140]),skolemize(U_944,sK140(U_946))],[f_255_3]) ).
cnf(f_255_5,plain,
( U_946 = empty_set
| in(ordered_pair(sK139(U_946),sK140(U_946)),U_946)
| ~ relation(U_946) ),
inference(clausify,[status(thm)],[f_255_4]) ).
fof(f_256_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_256_2,plain,
! [U_948,U_947] :
( ( U_948 = apply(relation_composition(function_inverse(U_947),U_947),U_948)
& U_948 = apply(U_947,apply(function_inverse(U_947),U_948)) )
| ~ in(U_948,relation_rng(U_947))
| ~ one_to_one(U_947)
| ~ function(U_947)
| ~ relation(U_947) ),
inference(variable_rename,[status(thm)],[f_256_1]) ).
cnf(f_256_3,plain,
( U_948 = apply(U_947,apply(function_inverse(U_947),U_948))
| ~ in(U_948,relation_rng(U_947))
| ~ one_to_one(U_947)
| ~ function(U_947)
| ~ relation(U_947) ),
inference(clausify,[status(thm)],[f_256_2]) ).
cnf(f_256_4,plain,
( U_948 = apply(relation_composition(function_inverse(U_947),U_947),U_948)
| ~ in(U_948,relation_rng(U_947))
| ~ one_to_one(U_947)
| ~ function(U_947)
| ~ relation(U_947) ),
inference(clausify,[status(thm)],[f_256_2]) ).
fof(f_257_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_257_2,plain,
! [U_951,U_950,U_949] :
( ~ empty(U_949)
| ~ element(U_950,powerset(U_949))
| ~ in(U_951,U_950) ),
inference(variable_rename,[status(thm)],[f_257_1]) ).
fof(f_257_3,plain,
! [U_951,U_950] :
( ! [U_949] :
( ~ empty(U_949)
| ~ element(U_950,powerset(U_949)) )
| ~ in(U_951,U_950) ),
inference(miniscope,[status(thm)],[f_257_2]) ).
cnf(f_257_4,plain,
( ~ empty(U_949)
| ~ element(U_950,powerset(U_949))
| ~ in(U_951,U_950) ),
inference(clausify,[status(thm)],[f_257_3]) ).
fof(f_258_1,plain,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(fof_nnf,[status(thm)],[t60_relat_1]) ).
cnf(f_258_2,plain,
relation_dom(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_258_1]) ).
cnf(f_258_3,plain,
relation_rng(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_258_1]) ).
fof(f_259_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t60_xboole_1]) ).
fof(f_259_2,plain,
! [U_953,U_952] :
( ~ proper_subset(U_952,U_953)
| ~ subset(U_953,U_952) ),
inference(variable_rename,[status(thm)],[f_259_1]) ).
cnf(f_259_3,plain,
( ~ proper_subset(U_952,U_953)
| ~ subset(U_953,U_952) ),
inference(clausify,[status(thm)],[f_259_2]) ).
fof(f_260_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_260_2,plain,
! [U_954] :
( one_to_one(function_inverse(U_954))
| ~ one_to_one(U_954)
| ~ function(U_954)
| ~ relation(U_954) ),
inference(variable_rename,[status(thm)],[f_260_1]) ).
cnf(f_260_3,plain,
( one_to_one(function_inverse(U_954))
| ~ one_to_one(U_954)
| ~ function(U_954)
| ~ relation(U_954) ),
inference(clausify,[status(thm)],[f_260_2]) ).
fof(f_261_1,plain,
! [A,B,C] :
( disjoint(A,C)
| ~ disjoint(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t63_xboole_1]) ).
fof(f_261_2,plain,
! [U_957,U_956,U_955] :
( disjoint(U_957,U_955)
| ~ disjoint(U_956,U_955)
| ~ subset(U_957,U_956) ),
inference(variable_rename,[status(thm)],[f_261_1]) ).
cnf(f_261_3,plain,
( disjoint(U_957,U_955)
| ~ disjoint(U_956,U_955)
| ~ subset(U_957,U_956) ),
inference(clausify,[status(thm)],[f_261_2]) ).
fof(f_262_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_262_2,plain,
! [U_958] :
( U_958 = empty_set
| ( relation_rng(U_958) != empty_set
& relation_dom(U_958) != empty_set )
| ~ relation(U_958) ),
inference(variable_rename,[status(thm)],[f_262_1]) ).
cnf(f_262_3,plain,
( relation_dom(U_958) != empty_set
| U_958 = empty_set
| ~ relation(U_958) ),
inference(clausify,[status(thm)],[f_262_2]) ).
cnf(f_262_4,plain,
( relation_rng(U_958) != empty_set
| U_958 = empty_set
| ~ relation(U_958) ),
inference(clausify,[status(thm)],[f_262_2]) ).
fof(f_263_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_263_2,plain,
! [U_959] :
( ( ( relation_dom(U_959) = empty_set
| relation_rng(U_959) != empty_set )
& ( relation_rng(U_959) = empty_set
| relation_dom(U_959) != empty_set ) )
| ~ relation(U_959) ),
inference(variable_rename,[status(thm)],[f_263_1]) ).
cnf(f_263_3,plain,
( relation_rng(U_959) = empty_set
| relation_dom(U_959) != empty_set
| ~ relation(U_959) ),
inference(clausify,[status(thm)],[f_263_2]) ).
cnf(f_263_4,plain,
( relation_dom(U_959) = empty_set
| relation_rng(U_959) != empty_set
| ~ relation(U_959) ),
inference(clausify,[status(thm)],[f_263_2]) ).
fof(f_264_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_264_2,plain,
! [U_961,U_960] :
( ( set_difference(U_961,singleton(U_960)) = U_961
| in(U_960,U_961) )
& ( ~ in(U_960,U_961)
| set_difference(U_961,singleton(U_960)) != U_961 ) ),
inference(variable_rename,[status(thm)],[f_264_1]) ).
fof(f_264_3,plain,
( ! [U_965,U_963] :
( set_difference(U_965,singleton(U_963)) = U_965
| in(U_963,U_965) )
& ! [U_964,U_962] :
( ~ in(U_962,U_964)
| set_difference(U_964,singleton(U_962)) != U_964 ) ),
inference(miniscope,[status(thm)],[f_264_2]) ).
cnf(f_264_4,plain,
( ~ in(U_962,U_964)
| set_difference(U_964,singleton(U_962)) != U_964 ),
inference(clausify,[status(thm)],[f_264_3]) ).
cnf(f_264_5,plain,
( set_difference(U_965,singleton(U_963)) = U_965
| in(U_963,U_965) ),
inference(clausify,[status(thm)],[f_264_3]) ).
fof(f_265_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_265_2,plain,
! [U_970,U_969] :
( ! [U_968] :
( ( ( U_969 = relation_dom_restriction(U_968,U_970)
| ? [U_967] :
( apply(U_969,U_967) != apply(U_968,U_967)
& in(U_967,relation_dom(U_969)) )
| relation_dom(U_969) != set_intersection2(relation_dom(U_968),U_970) )
& ( ( ! [U_966] :
( apply(U_969,U_966) = apply(U_968,U_966)
| ~ in(U_966,relation_dom(U_969)) )
& relation_dom(U_969) = set_intersection2(relation_dom(U_968),U_970) )
| U_969 != relation_dom_restriction(U_968,U_970) ) )
| ~ function(U_968)
| ~ relation(U_968) )
| ~ function(U_969)
| ~ relation(U_969) ),
inference(variable_rename,[status(thm)],[f_265_1]) ).
fof(f_265_3,plain,
! [U_970,U_969] :
( ! [U_968] :
( ( ( U_969 = relation_dom_restriction(U_968,U_970)
| ( apply(U_969,sK141(U_970,U_969,U_968)) != apply(U_968,sK141(U_970,U_969,U_968))
& in(sK141(U_970,U_969,U_968),relation_dom(U_969)) )
| relation_dom(U_969) != set_intersection2(relation_dom(U_968),U_970) )
& ( ( ! [U_966] :
( apply(U_969,U_966) = apply(U_968,U_966)
| ~ in(U_966,relation_dom(U_969)) )
& relation_dom(U_969) = set_intersection2(relation_dom(U_968),U_970) )
| U_969 != relation_dom_restriction(U_968,U_970) ) )
| ~ function(U_968)
| ~ relation(U_968) )
| ~ function(U_969)
| ~ relation(U_969) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK141]),skolemize(U_967,sK141(U_970,U_969,U_968))],[f_265_2]) ).
cnf(f_265_4,plain,
( relation_dom(U_969) = set_intersection2(relation_dom(U_968),U_970)
| U_969 != relation_dom_restriction(U_968,U_970)
| ~ function(U_968)
| ~ relation(U_968)
| ~ function(U_969)
| ~ relation(U_969) ),
inference(clausify,[status(thm)],[f_265_3]) ).
cnf(f_265_5,plain,
( apply(U_969,U_966) = apply(U_968,U_966)
| ~ in(U_966,relation_dom(U_969))
| U_969 != relation_dom_restriction(U_968,U_970)
| ~ function(U_968)
| ~ relation(U_968)
| ~ function(U_969)
| ~ relation(U_969) ),
inference(clausify,[status(thm)],[f_265_3]) ).
cnf(f_265_6,plain,
( in(sK141(U_970,U_969,U_968),relation_dom(U_969))
| relation_dom(U_969) != set_intersection2(relation_dom(U_968),U_970)
| U_969 = relation_dom_restriction(U_968,U_970)
| ~ function(U_968)
| ~ relation(U_968)
| ~ function(U_969)
| ~ relation(U_969) ),
inference(clausify,[status(thm)],[f_265_3]) ).
cnf(f_265_7,plain,
( apply(U_969,sK141(U_970,U_969,U_968)) != apply(U_968,sK141(U_970,U_969,U_968))
| relation_dom(U_969) != set_intersection2(relation_dom(U_968),U_970)
| U_969 = relation_dom_restriction(U_968,U_970)
| ~ function(U_968)
| ~ relation(U_968)
| ~ function(U_969)
| ~ relation(U_969) ),
inference(clausify,[status(thm)],[f_265_3]) ).
fof(f_266_1,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(fof_nnf,[status(thm)],[t69_enumset1]) ).
fof(f_266_2,plain,
! [U_971] : unordered_pair(U_971,U_971) = singleton(U_971),
inference(variable_rename,[status(thm)],[f_266_1]) ).
cnf(f_266_3,plain,
unordered_pair(U_971,U_971) = singleton(U_971),
inference(clausify,[status(thm)],[f_266_2]) ).
fof(f_267_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_267_2,plain,
! [U_972] :
( U_972 = empty_set
| ~ empty(U_972) ),
inference(variable_rename,[status(thm)],[f_267_1]) ).
cnf(f_267_3,plain,
( U_972 = empty_set
| ~ empty(U_972) ),
inference(clausify,[status(thm)],[f_267_2]) ).
fof(f_268_1,plain,
! [A,B] :
( A = B
| ~ subset(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t6_zfmisc_1]) ).
fof(f_268_2,plain,
! [U_974,U_973] :
( U_974 = U_973
| ~ subset(singleton(U_974),singleton(U_973)) ),
inference(variable_rename,[status(thm)],[f_268_1]) ).
cnf(f_268_3,plain,
( U_974 = U_973
| ~ subset(singleton(U_974),singleton(U_973)) ),
inference(clausify,[status(thm)],[f_268_2]) ).
fof(f_269_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_269_2,plain,
! [U_977,U_976,U_975] :
( apply(relation_dom_restriction(U_975,U_977),U_976) = apply(U_975,U_976)
| ~ in(U_976,relation_dom(relation_dom_restriction(U_975,U_977)))
| ~ function(U_975)
| ~ relation(U_975) ),
inference(variable_rename,[status(thm)],[f_269_1]) ).
cnf(f_269_3,plain,
( apply(relation_dom_restriction(U_975,U_977),U_976) = apply(U_975,U_976)
| ~ in(U_976,relation_dom(relation_dom_restriction(U_975,U_977)))
| ~ function(U_975)
| ~ relation(U_975) ),
inference(clausify,[status(thm)],[f_269_2]) ).
fof(f_270_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_270_2,plain,
! [U_978] :
( relation_rng(identity_relation(U_978)) = U_978
& relation_dom(identity_relation(U_978)) = U_978 ),
inference(variable_rename,[status(thm)],[f_270_1]) ).
fof(f_270_3,plain,
( ! [U_980] : relation_rng(identity_relation(U_980)) = U_980
& ! [U_979] : relation_dom(identity_relation(U_979)) = U_979 ),
inference(miniscope,[status(thm)],[f_270_2]) ).
cnf(f_270_4,plain,
relation_dom(identity_relation(U_979)) = U_979,
inference(clausify,[status(thm)],[f_270_3]) ).
cnf(f_270_5,plain,
relation_rng(identity_relation(U_980)) = U_980,
inference(clausify,[status(thm)],[f_270_3]) ).
fof(f_271_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_271_2,plain,
! [U_983,U_982,U_981] :
( apply(relation_dom_restriction(U_981,U_983),U_982) = apply(U_981,U_982)
| ~ in(U_982,U_983)
| ~ function(U_981)
| ~ relation(U_981) ),
inference(variable_rename,[status(thm)],[f_271_1]) ).
cnf(f_271_3,plain,
( apply(relation_dom_restriction(U_981,U_983),U_982) = apply(U_981,U_982)
| ~ in(U_982,U_983)
| ~ function(U_981)
| ~ relation(U_981) ),
inference(clausify,[status(thm)],[f_271_2]) ).
fof(f_272_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_272_2,plain,
! [U_987,U_986,U_985,U_984] :
( ( ( in(ordered_pair(U_987,U_986),relation_composition(identity_relation(U_985),U_984))
| ~ in(ordered_pair(U_987,U_986),U_984)
| ~ in(U_987,U_985) )
& ( ( in(ordered_pair(U_987,U_986),U_984)
& in(U_987,U_985) )
| ~ in(ordered_pair(U_987,U_986),relation_composition(identity_relation(U_985),U_984)) ) )
| ~ relation(U_984) ),
inference(variable_rename,[status(thm)],[f_272_1]) ).
cnf(f_272_3,plain,
( in(U_987,U_985)
| ~ in(ordered_pair(U_987,U_986),relation_composition(identity_relation(U_985),U_984))
| ~ relation(U_984) ),
inference(clausify,[status(thm)],[f_272_2]) ).
cnf(f_272_4,plain,
( in(ordered_pair(U_987,U_986),U_984)
| ~ in(ordered_pair(U_987,U_986),relation_composition(identity_relation(U_985),U_984))
| ~ relation(U_984) ),
inference(clausify,[status(thm)],[f_272_2]) ).
cnf(f_272_5,plain,
( in(ordered_pair(U_987,U_986),relation_composition(identity_relation(U_985),U_984))
| ~ in(ordered_pair(U_987,U_986),U_984)
| ~ in(U_987,U_985)
| ~ relation(U_984) ),
inference(clausify,[status(thm)],[f_272_2]) ).
fof(f_273_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_273_2,plain,
! [U_989,U_988] :
( ~ empty(U_988)
| ~ in(U_989,U_988) ),
inference(variable_rename,[status(thm)],[f_273_1]) ).
cnf(f_273_3,plain,
( ~ empty(U_988)
| ~ in(U_989,U_988) ),
inference(clausify,[status(thm)],[f_273_2]) ).
fof(f_274_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_274_2,plain,
! [U_993,U_992] :
( ? [U_991] :
( ! [U_990] :
( ~ in(U_990,U_991)
| ~ in(U_990,U_992) )
& in(U_991,U_992) )
| ~ in(U_993,U_992) ),
inference(variable_rename,[status(thm)],[f_274_1]) ).
fof(f_274_3,plain,
! [U_993,U_992] :
( ( ! [U_990] :
( ~ in(U_990,sK142(U_993,U_992))
| ~ in(U_990,U_992) )
& in(sK142(U_993,U_992),U_992) )
| ~ in(U_993,U_992) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK142]),skolemize(U_991,sK142(U_993,U_992))],[f_274_2]) ).
cnf(f_274_4,plain,
( in(sK142(U_993,U_992),U_992)
| ~ in(U_993,U_992) ),
inference(clausify,[status(thm)],[f_274_3]) ).
cnf(f_274_5,plain,
( ~ in(U_990,sK142(U_993,U_992))
| ~ in(U_990,U_992)
| ~ in(U_993,U_992) ),
inference(clausify,[status(thm)],[f_274_3]) ).
fof(f_275_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1]) ).
fof(f_275_2,plain,
! [U_995,U_994] : subset(U_995,set_union2(U_995,U_994)),
inference(variable_rename,[status(thm)],[f_275_1]) ).
cnf(f_275_3,plain,
subset(U_995,set_union2(U_995,U_994)),
inference(clausify,[status(thm)],[f_275_2]) ).
fof(f_276_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_276_2,plain,
! [U_997,U_996] :
( ( disjoint(U_997,U_996)
| set_difference(U_997,U_996) != U_997 )
& ( set_difference(U_997,U_996) = U_997
| ~ disjoint(U_997,U_996) ) ),
inference(variable_rename,[status(thm)],[f_276_1]) ).
fof(f_276_3,plain,
( ! [U_1001,U_999] :
( disjoint(U_1001,U_999)
| set_difference(U_1001,U_999) != U_1001 )
& ! [U_1000,U_998] :
( set_difference(U_1000,U_998) = U_1000
| ~ disjoint(U_1000,U_998) ) ),
inference(miniscope,[status(thm)],[f_276_2]) ).
cnf(f_276_4,plain,
( set_difference(U_1000,U_998) = U_1000
| ~ disjoint(U_1000,U_998) ),
inference(clausify,[status(thm)],[f_276_3]) ).
cnf(f_276_5,plain,
( disjoint(U_1001,U_999)
| set_difference(U_1001,U_999) != U_1001 ),
inference(clausify,[status(thm)],[f_276_3]) ).
fof(f_277_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_277_2,plain,
! [U_1004,U_1003,U_1002] :
( ( ( in(U_1004,relation_dom(relation_dom_restriction(U_1002,U_1003)))
| ~ in(U_1004,relation_dom(U_1002))
| ~ in(U_1004,U_1003) )
& ( ( in(U_1004,relation_dom(U_1002))
& in(U_1004,U_1003) )
| ~ in(U_1004,relation_dom(relation_dom_restriction(U_1002,U_1003))) ) )
| ~ relation(U_1002) ),
inference(variable_rename,[status(thm)],[f_277_1]) ).
cnf(f_277_3,plain,
( in(U_1004,U_1003)
| ~ in(U_1004,relation_dom(relation_dom_restriction(U_1002,U_1003)))
| ~ relation(U_1002) ),
inference(clausify,[status(thm)],[f_277_2]) ).
cnf(f_277_4,plain,
( in(U_1004,relation_dom(U_1002))
| ~ in(U_1004,relation_dom(relation_dom_restriction(U_1002,U_1003)))
| ~ relation(U_1002) ),
inference(clausify,[status(thm)],[f_277_2]) ).
cnf(f_277_5,plain,
( in(U_1004,relation_dom(relation_dom_restriction(U_1002,U_1003)))
| ~ in(U_1004,relation_dom(U_1002))
| ~ in(U_1004,U_1003)
| ~ relation(U_1002) ),
inference(clausify,[status(thm)],[f_277_2]) ).
fof(f_278_1,plain,
! [A,B] :
( subset(relation_dom_restriction(B,A),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t88_relat_1]) ).
fof(f_278_2,plain,
! [U_1006,U_1005] :
( subset(relation_dom_restriction(U_1005,U_1006),U_1005)
| ~ relation(U_1005) ),
inference(variable_rename,[status(thm)],[f_278_1]) ).
cnf(f_278_3,plain,
( subset(relation_dom_restriction(U_1005,U_1006),U_1005)
| ~ relation(U_1005) ),
inference(clausify,[status(thm)],[f_278_2]) ).
fof(f_279_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_279_2,plain,
! [U_1008,U_1007] :
( ~ empty(U_1007)
| U_1008 = U_1007
| ~ empty(U_1008) ),
inference(variable_rename,[status(thm)],[f_279_1]) ).
fof(f_279_3,plain,
! [U_1008] :
( ! [U_1007] :
( ~ empty(U_1007)
| U_1008 = U_1007 )
| ~ empty(U_1008) ),
inference(miniscope,[status(thm)],[f_279_2]) ).
cnf(f_279_4,plain,
( ~ empty(U_1007)
| U_1008 = U_1007
| ~ empty(U_1008) ),
inference(clausify,[status(thm)],[f_279_3]) ).
fof(f_280_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_280_2,plain,
! [U_1011,U_1010,U_1009] :
( ( ( in(ordered_pair(U_1011,U_1010),U_1009)
| U_1010 != apply(U_1009,U_1011)
| ~ in(U_1011,relation_dom(U_1009)) )
& ( ( U_1010 = apply(U_1009,U_1011)
& in(U_1011,relation_dom(U_1009)) )
| ~ in(ordered_pair(U_1011,U_1010),U_1009) ) )
| ~ function(U_1009)
| ~ relation(U_1009) ),
inference(variable_rename,[status(thm)],[f_280_1]) ).
cnf(f_280_3,plain,
( in(U_1011,relation_dom(U_1009))
| ~ in(ordered_pair(U_1011,U_1010),U_1009)
| ~ function(U_1009)
| ~ relation(U_1009) ),
inference(clausify,[status(thm)],[f_280_2]) ).
cnf(f_280_4,plain,
( U_1010 = apply(U_1009,U_1011)
| ~ in(ordered_pair(U_1011,U_1010),U_1009)
| ~ function(U_1009)
| ~ relation(U_1009) ),
inference(clausify,[status(thm)],[f_280_2]) ).
cnf(f_280_5,plain,
( in(ordered_pair(U_1011,U_1010),U_1009)
| U_1010 != apply(U_1009,U_1011)
| ~ in(U_1011,relation_dom(U_1009))
| ~ function(U_1009)
| ~ relation(U_1009) ),
inference(clausify,[status(thm)],[f_280_2]) ).
fof(f_281_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_281_2,plain,
! [U_1014,U_1013,U_1012] :
( subset(set_union2(U_1014,U_1012),U_1013)
| ~ subset(U_1012,U_1013)
| ~ subset(U_1014,U_1013) ),
inference(variable_rename,[status(thm)],[f_281_1]) ).
cnf(f_281_3,plain,
( subset(set_union2(U_1014,U_1012),U_1013)
| ~ subset(U_1012,U_1013)
| ~ subset(U_1014,U_1013) ),
inference(clausify,[status(thm)],[f_281_2]) ).
fof(f_282_1,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t8_zfmisc_1]) ).
fof(f_282_2,plain,
! [U_1017,U_1016,U_1015] :
( U_1017 = U_1016
| singleton(U_1017) != unordered_pair(U_1016,U_1015) ),
inference(variable_rename,[status(thm)],[f_282_1]) ).
fof(f_282_3,plain,
! [U_1017,U_1016] :
( ! [U_1015] : singleton(U_1017) != unordered_pair(U_1016,U_1015)
| U_1017 = U_1016 ),
inference(miniscope,[status(thm)],[f_282_2]) ).
cnf(f_282_4,plain,
( singleton(U_1017) != unordered_pair(U_1016,U_1015)
| U_1017 = U_1016 ),
inference(clausify,[status(thm)],[f_282_3]) ).
fof(f_283_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_283_2,plain,
! [U_1019,U_1018] :
( relation_dom(relation_dom_restriction(U_1018,U_1019)) = set_intersection2(relation_dom(U_1018),U_1019)
| ~ relation(U_1018) ),
inference(variable_rename,[status(thm)],[f_283_1]) ).
cnf(f_283_3,plain,
( relation_dom(relation_dom_restriction(U_1018,U_1019)) = set_intersection2(relation_dom(U_1018),U_1019)
| ~ relation(U_1018) ),
inference(clausify,[status(thm)],[f_283_2]) ).
fof(f_284_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t92_zfmisc_1]) ).
fof(f_284_2,plain,
! [U_1021,U_1020] :
( subset(U_1021,union(U_1020))
| ~ in(U_1021,U_1020) ),
inference(variable_rename,[status(thm)],[f_284_1]) ).
cnf(f_284_3,plain,
( subset(U_1021,union(U_1020))
| ~ in(U_1021,U_1020) ),
inference(clausify,[status(thm)],[f_284_2]) ).
fof(f_285_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_285_2,plain,
! [U_1023,U_1022] :
( relation_dom_restriction(U_1022,U_1023) = relation_composition(identity_relation(U_1023),U_1022)
| ~ relation(U_1022) ),
inference(variable_rename,[status(thm)],[f_285_1]) ).
cnf(f_285_3,plain,
( relation_dom_restriction(U_1022,U_1023) = relation_composition(identity_relation(U_1023),U_1022)
| ~ relation(U_1022) ),
inference(clausify,[status(thm)],[f_285_2]) ).
fof(f_286_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_286_2,plain,
! [U_1025,U_1024] :
( subset(relation_rng(relation_dom_restriction(U_1024,U_1025)),relation_rng(U_1024))
| ~ relation(U_1024) ),
inference(variable_rename,[status(thm)],[f_286_1]) ).
cnf(f_286_3,plain,
( subset(relation_rng(relation_dom_restriction(U_1024,U_1025)),relation_rng(U_1024))
| ~ relation(U_1024) ),
inference(clausify,[status(thm)],[f_286_2]) ).
fof(f_287_1,plain,
! [A] : union(powerset(A)) = A,
inference(fof_nnf,[status(thm)],[t99_zfmisc_1]) ).
fof(f_287_2,plain,
! [U_1026] : union(powerset(U_1026)) = U_1026,
inference(variable_rename,[status(thm)],[f_287_1]) ).
cnf(f_287_3,plain,
union(powerset(U_1026)) = U_1026,
inference(clausify,[status(thm)],[f_287_2]) ).
fof(f_288_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_288_2,plain,
! [U_1034] :
? [U_1033] :
( ! [U_1032] :
( in(U_1032,U_1033)
| are_equipotent(U_1032,U_1033)
| ~ subset(U_1032,U_1033) )
& ! [U_1031] :
( ? [U_1030] :
( ! [U_1029] :
( in(U_1029,U_1030)
| ~ subset(U_1029,U_1031) )
& in(U_1030,U_1033) )
| ~ in(U_1031,U_1033) )
& ! [U_1028,U_1027] :
( in(U_1027,U_1033)
| ~ subset(U_1027,U_1028)
| ~ in(U_1028,U_1033) )
& in(U_1034,U_1033) ),
inference(variable_rename,[status(thm)],[f_288_1]) ).
fof(f_288_3,plain,
! [U_1034] :
( ! [U_1032] :
( in(U_1032,sK143(U_1034))
| are_equipotent(U_1032,sK143(U_1034))
| ~ subset(U_1032,sK143(U_1034)) )
& ! [U_1031] :
( ? [U_1030] :
( ! [U_1029] :
( in(U_1029,U_1030)
| ~ subset(U_1029,U_1031) )
& in(U_1030,sK143(U_1034)) )
| ~ in(U_1031,sK143(U_1034)) )
& ! [U_1028,U_1027] :
( in(U_1027,sK143(U_1034))
| ~ subset(U_1027,U_1028)
| ~ in(U_1028,sK143(U_1034)) )
& in(U_1034,sK143(U_1034)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK143]),skolemize(U_1033,sK143(U_1034))],[f_288_2]) ).
fof(f_288_4,plain,
! [U_1034] :
( ! [U_1032] :
( in(U_1032,sK143(U_1034))
| are_equipotent(U_1032,sK143(U_1034))
| ~ subset(U_1032,sK143(U_1034)) )
& ! [U_1031] :
( ( ! [U_1029] :
( in(U_1029,sK144(U_1034,U_1031))
| ~ subset(U_1029,U_1031) )
& in(sK144(U_1034,U_1031),sK143(U_1034)) )
| ~ in(U_1031,sK143(U_1034)) )
& ! [U_1028,U_1027] :
( in(U_1027,sK143(U_1034))
| ~ subset(U_1027,U_1028)
| ~ in(U_1028,sK143(U_1034)) )
& in(U_1034,sK143(U_1034)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK144]),skolemize(U_1030,sK144(U_1034,U_1031))],[f_288_3]) ).
cnf(f_288_5,plain,
in(U_1034,sK143(U_1034)),
inference(clausify,[status(thm)],[f_288_4]) ).
cnf(f_288_6,plain,
( in(U_1027,sK143(U_1034))
| ~ subset(U_1027,U_1028)
| ~ in(U_1028,sK143(U_1034)) ),
inference(clausify,[status(thm)],[f_288_4]) ).
cnf(f_288_7,plain,
( in(sK144(U_1034,U_1031),sK143(U_1034))
| ~ in(U_1031,sK143(U_1034)) ),
inference(clausify,[status(thm)],[f_288_4]) ).
cnf(f_288_8,plain,
( in(U_1029,sK144(U_1034,U_1031))
| ~ subset(U_1029,U_1031)
| ~ in(U_1031,sK143(U_1034)) ),
inference(clausify,[status(thm)],[f_288_4]) ).
cnf(f_288_9,plain,
( in(U_1032,sK143(U_1034))
| are_equipotent(U_1032,sK143(U_1034))
| ~ subset(U_1032,sK143(U_1034)) ),
inference(clausify,[status(thm)],[f_288_4]) ).
fof(f_289_1,plain,
! [A,B,C] :
( B = C
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t9_zfmisc_1]) ).
fof(f_289_2,plain,
! [U_1037,U_1036,U_1035] :
( U_1036 = U_1035
| singleton(U_1037) != unordered_pair(U_1036,U_1035) ),
inference(variable_rename,[status(thm)],[f_289_1]) ).
cnf(f_289_3,plain,
( U_1036 = U_1035
| singleton(U_1037) != unordered_pair(U_1036,U_1035) ),
inference(clausify,[status(thm)],[f_289_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_59_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_59_8]) ).
cnf(f_59_9_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_59_9]) ).
cnf(f_63_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_63_2]) ).
cnf(f_64_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_64_2]) ).
cnf(f_65_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_65_2]) ).
cnf(f_66_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_66_2]) ).
cnf(f_67_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_67_2]) ).
cnf(f_68_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_68_2]) ).
cnf(f_69_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_69_2]) ).
cnf(f_70_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_70_2]) ).
cnf(f_71_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_71_2]) ).
cnf(f_73_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_73_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_80_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_80_2]) ).
cnf(f_81_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_81_2]) ).
cnf(f_83_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_83_2]) ).
cnf(f_84_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_84_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_140_9_true,negated_conjecture,
$true,
inference(clause_is_true,[status(thm)],[f_140_9]) ).
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,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,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_22,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_23,axiom,
( union(Eq_x_0) = union(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,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_25,axiom,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,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_27,axiom,
( relation_inverse(Eq_x_0) = relation_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,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_29,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_30,axiom,
( function_inverse(Eq_x_0) = function_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_31,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_32,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_33,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_34,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_35,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_36,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_37,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_38,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_39,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_40,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_41,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_42,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_43,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_44,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_45,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_46,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_47,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_48,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_49,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_50,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_51,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_52,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_53,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_54,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_55,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_56,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_57,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_58,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_59,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_60,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_61,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_62,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_63,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_64,axiom,
( sK31(Eq_x_0) = sK31(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_65,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_66,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_67,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_68,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_69,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_70,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_71,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_72,axiom,
( sK39(Eq_x_0) = sK39(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_73,axiom,
( sK40(Eq_x_0,Eq_x_1) = sK40(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,
( sK41(Eq_x_0,Eq_x_1) = sK41(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_75,axiom,
( sK42(Eq_x_0) = sK42(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_76,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_77,axiom,
( sK44(Eq_x_0,Eq_x_1) = sK44(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,
( 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_79,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_80,axiom,
( sK47(Eq_x_0,Eq_x_1,Eq_x_2) = sK47(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_81,axiom,
( sK48(Eq_x_0,Eq_x_1,Eq_x_2) = sK48(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_82,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_83,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_84,axiom,
( sK51(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK51(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_85,axiom,
( sK52(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK52(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_86,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_87,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_88,axiom,
( sK55(Eq_x_0,Eq_x_1,Eq_x_2) = sK55(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,
( sK56(Eq_x_0,Eq_x_1,Eq_x_2) = sK56(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,
( sK57(Eq_x_0) = sK57(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_91,axiom,
( sK58(Eq_x_0) = sK58(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_92,axiom,
( sK59(Eq_x_0,Eq_x_1) = sK59(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_93,axiom,
( sK60(Eq_x_0,Eq_x_1) = sK60(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_94,axiom,
( sK61(Eq_x_0,Eq_x_1) = sK61(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_95,axiom,
( sK62(Eq_x_0,Eq_x_1,Eq_x_2) = sK62(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,
( sK63(Eq_x_0,Eq_x_1,Eq_x_2) = sK63(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_97,axiom,
( sK64(Eq_x_0,Eq_x_1,Eq_x_2) = sK64(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_98,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_99,axiom,
( sK66(Eq_x_0,Eq_x_1) = sK66(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,
( 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_101,axiom,
( sK68(Eq_x_0,Eq_x_1) = sK68(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_102,axiom,
( sK69(Eq_x_0,Eq_x_1) = sK69(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,
( 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_104,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_105,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_106,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_107,axiom,
( sK74(Eq_x_0,Eq_x_1,Eq_x_2) = sK74(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_108,axiom,
( sK75(Eq_x_0,Eq_x_1,Eq_x_2) = sK75(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_109,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_110,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_111,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_112,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_113,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_114,axiom,
( sK81(Eq_x_0,Eq_x_1) = sK81(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,
( sK82(Eq_x_0,Eq_x_1) = sK82(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_116,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_117,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_118,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_119,axiom,
( sK86(Eq_x_0,Eq_x_1) = sK86(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,
( 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_121,axiom,
( sK88(Eq_x_0) = sK88(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_122,axiom,
( sK89(Eq_x_0) = sK89(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_123,axiom,
( sK90(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK90(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_124,axiom,
( sK91(Eq_x_0,Eq_x_1,Eq_x_2) = sK91(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_125,axiom,
( sK92(Eq_x_0,Eq_x_1,Eq_x_2) = sK92(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_126,axiom,
( sK93(Eq_x_0,Eq_x_1,Eq_x_2) = sK93(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_127,axiom,
( sK94(Eq_x_0,Eq_x_1,Eq_x_2) = sK94(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_128,axiom,
( sK95(Eq_x_0,Eq_x_1,Eq_x_2) = sK95(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_129,axiom,
( sK96(Eq_x_0,Eq_x_1) = sK96(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,
( sK97(Eq_x_0,Eq_x_1) = sK97(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,
( sK98(Eq_x_0,Eq_x_1) = sK98(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_132,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_133,axiom,
( sK100(Eq_x_0) = sK100(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_134,axiom,
( sK101(Eq_x_0) = sK101(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_135,axiom,
( sK102(Eq_x_0) = sK102(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_136,axiom,
( sK103(Eq_x_0) = sK103(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_137,axiom,
( sK104(Eq_x_0) = sK104(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_138,axiom,
( sK108(Eq_x_0,Eq_x_1) = sK108(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_139,axiom,
( sK112(Eq_x_0) = sK112(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_140,axiom,
( sK117(Eq_x_0) = sK117(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_141,axiom,
( sK123(Eq_x_0) = sK123(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_142,axiom,
( sK124(Eq_x_0,Eq_x_1,Eq_x_2) = sK124(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,
( sK125(Eq_x_0,Eq_x_1,Eq_x_2) = sK125(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_144,axiom,
( sK126(Eq_x_0,Eq_x_1) = sK126(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_145,axiom,
( sK127(Eq_x_0,Eq_x_1) = sK127(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_146,axiom,
( sK128(Eq_x_0) = sK128(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_147,axiom,
( sK129(Eq_x_0,Eq_x_1) = sK129(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_148,axiom,
( sK130(Eq_x_0,Eq_x_1) = sK130(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_149,axiom,
( sK131(Eq_x_0,Eq_x_1) = sK131(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_150,axiom,
( sK132(Eq_x_0) = sK132(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_151,axiom,
( sK133(Eq_x_0) = sK133(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_152,axiom,
( sK134(Eq_x_0,Eq_x_1) = sK134(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,
( sK135(Eq_x_0,Eq_x_1) = sK135(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_154,axiom,
( sK136(Eq_x_0,Eq_x_1) = sK136(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_155,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_156,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_157,axiom,
( sK139(Eq_x_0) = sK139(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_158,axiom,
( sK140(Eq_x_0) = sK140(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_159,axiom,
( sK141(Eq_x_0,Eq_x_1,Eq_x_2) = sK141(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_160,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_161,axiom,
( sK143(Eq_x_0) = sK143(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_162,axiom,
( sK144(Eq_x_0,Eq_x_1) = sK144(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,
( 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_164,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_165,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_166,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_167,axiom,
( ordinal(Eq_y_0)
| ~ ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_168,axiom,
( epsilon_transitive(Eq_y_0)
| ~ epsilon_transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_169,axiom,
( epsilon_connected(Eq_y_0)
| ~ epsilon_connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_170,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_171,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_172,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_173,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_174,axiom,
( antisymmetric(Eq_y_0)
| ~ antisymmetric(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_175,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_176,axiom,
( transitive(Eq_y_0)
| ~ transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_177,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_178,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_179,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_180,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_181,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_182,axiom,
( reflexive(Eq_y_0)
| ~ reflexive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_183,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_184,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
% 0.00/0.03 % Problem : SEU241+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
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 23:41:07 UTC 2026
% 0.10/0.37 % CPUTime :
% 264.21/264.51 % SZS status Theorem for theBenchmark
% 264.21/264.51 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------