%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU234+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 : n012.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 08:58:37 AM UTC 2026
% Result : Theorem 251.55s 251.98s
% Output : Proof 251.80s
% 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(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(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(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_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_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_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_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(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_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_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_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_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_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(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,conjecture,
! [A] :
( ! [B] :
( in(B,A)
=> ( subset(B,A)
& ordinal(B) ) )
=> ordinal(A) ),
file('theBenchmark.p',t31_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(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]) ).
fof(f_1_3,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(definitional_conversion,[status(esa)],[f_1_2]) ).
cnf(f_1_4,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_3]) ).
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]) ).
fof(f_2_3,plain,
! [U_2,U_3] :
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(clausify,[status(thm)],[f_2_3]) ).
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]) ).
fof(f_3_3,plain,
! [U_4] :
( function(U_4)
| ~ empty(U_4) ),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
( function(U_4)
| ~ empty(U_4) ),
inference(clausify,[status(thm)],[f_3_3]) ).
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]) ).
fof(f_4_3,plain,
( ! [U_5] :
( epsilon_connected(U_5)
| ~ sP0(U_5) )
& ! [U_5] :
( epsilon_transitive(U_5)
| ~ sP0(U_5) )
& ! [U_5] :
( sP0(U_5)
| ~ ordinal(U_5) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_4_2]) ).
cnf(f_4_4,plain,
( sP0(U_5)
| ~ ordinal(U_5) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( epsilon_transitive(U_5)
| ~ sP0(U_5) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( epsilon_connected(U_5)
| ~ sP0(U_5) ),
inference(clausify,[status(thm)],[f_4_3]) ).
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]) ).
fof(f_5_3,plain,
! [U_6] :
( relation(U_6)
| ~ empty(U_6) ),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
( relation(U_6)
| ~ empty(U_6) ),
inference(clausify,[status(thm)],[f_5_3]) ).
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]) ).
fof(f_6_3,plain,
( ! [U_7] :
( one_to_one(U_7)
| ~ sP1(U_7) )
& ! [U_7] :
( function(U_7)
| ~ sP1(U_7) )
& ! [U_7] :
( relation(U_7)
| ~ sP1(U_7) )
& ! [U_7] :
( sP1(U_7)
| ~ function(U_7)
| ~ empty(U_7)
| ~ relation(U_7) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_6_2]) ).
cnf(f_6_4,plain,
( sP1(U_7)
| ~ function(U_7)
| ~ empty(U_7)
| ~ relation(U_7) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( relation(U_7)
| ~ sP1(U_7) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
( function(U_7)
| ~ sP1(U_7) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_7,plain,
( one_to_one(U_7)
| ~ sP1(U_7) ),
inference(clausify,[status(thm)],[f_6_3]) ).
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]) ).
fof(f_7_3,plain,
! [U_8] :
( ordinal(U_8)
| ~ epsilon_connected(U_8)
| ~ epsilon_transitive(U_8) ),
inference(definitional_conversion,[status(esa)],[f_7_2]) ).
cnf(f_7_4,plain,
( ordinal(U_8)
| ~ epsilon_connected(U_8)
| ~ epsilon_transitive(U_8) ),
inference(clausify,[status(thm)],[f_7_3]) ).
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]) ).
fof(f_8_3,plain,
( ! [U_9] :
( ordinal(U_9)
| ~ sP2(U_9) )
& ! [U_9] :
( epsilon_connected(U_9)
| ~ sP2(U_9) )
& ! [U_9] :
( epsilon_transitive(U_9)
| ~ sP2(U_9) )
& ! [U_9] :
( sP2(U_9)
| ~ empty(U_9) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_8_2]) ).
cnf(f_8_4,plain,
( sP2(U_9)
| ~ empty(U_9) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( epsilon_transitive(U_9)
| ~ sP2(U_9) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_6,plain,
( epsilon_connected(U_9)
| ~ sP2(U_9) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_7,plain,
( ordinal(U_9)
| ~ sP2(U_9) ),
inference(clausify,[status(thm)],[f_8_3]) ).
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]) ).
fof(f_9_3,plain,
! [U_11,U_10] : unordered_pair(U_11,U_10) = unordered_pair(U_10,U_11),
inference(definitional_conversion,[status(esa)],[f_9_2]) ).
cnf(f_9_4,plain,
unordered_pair(U_11,U_10) = unordered_pair(U_10,U_11),
inference(clausify,[status(thm)],[f_9_3]) ).
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]) ).
fof(f_10_3,plain,
! [U_12,U_13] : set_union2(U_13,U_12) = set_union2(U_12,U_13),
inference(definitional_conversion,[status(esa)],[f_10_2]) ).
cnf(f_10_4,plain,
set_union2(U_13,U_12) = set_union2(U_12,U_13),
inference(clausify,[status(thm)],[f_10_3]) ).
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]) ).
fof(f_11_3,plain,
! [U_14,U_15] : set_intersection2(U_15,U_14) = set_intersection2(U_14,U_15),
inference(definitional_conversion,[status(esa)],[f_11_2]) ).
cnf(f_11_4,plain,
set_intersection2(U_15,U_14) = set_intersection2(U_14,U_15),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_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_12_2,plain,
! [U_21,U_20] :
( ( ( U_20 = identity_relation(U_21)
| ? [U_19,U_18] :
( ( ~ in(ordered_pair(U_19,U_18),U_20)
& U_19 = U_18
& in(U_19,U_21) )
| ( ( U_19 != U_18
| ~ in(U_19,U_21) )
& in(ordered_pair(U_19,U_18),U_20) ) ) )
& ( ! [U_17,U_16] :
( ( in(ordered_pair(U_17,U_16),U_20)
| U_17 != U_16
| ~ in(U_17,U_21) )
& ( ( U_17 = U_16
& in(U_17,U_21) )
| ~ in(ordered_pair(U_17,U_16),U_20) ) )
| U_20 != identity_relation(U_21) ) )
| ~ relation(U_20) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_21,U_20] :
( ( ( U_20 = identity_relation(U_21)
| ? [U_29,U_27] :
( ~ in(ordered_pair(U_29,U_27),U_20)
& U_29 = U_27
& in(U_29,U_21) )
| ? [U_28,U_26] :
( ( U_28 != U_26
| ~ in(U_28,U_21) )
& in(ordered_pair(U_28,U_26),U_20) ) )
& ( ( ! [U_25,U_23] :
( in(ordered_pair(U_25,U_23),U_20)
| U_25 != U_23
| ~ in(U_25,U_21) )
& ! [U_24,U_22] :
( ( U_24 = U_22
& in(U_24,U_21) )
| ~ in(ordered_pair(U_24,U_22),U_20) ) )
| U_20 != identity_relation(U_21) ) )
| ~ relation(U_20) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
! [U_21,U_20] :
( ( ( U_20 = identity_relation(U_21)
| ? [U_29,U_27] :
( ~ in(ordered_pair(U_29,U_27),U_20)
& U_29 = U_27
& in(U_29,U_21) )
| ? [U_26] :
( ( sK1(U_21,U_20) != U_26
| ~ in(sK1(U_21,U_20),U_21) )
& in(ordered_pair(sK1(U_21,U_20),U_26),U_20) ) )
& ( ( ! [U_25,U_23] :
( in(ordered_pair(U_25,U_23),U_20)
| U_25 != U_23
| ~ in(U_25,U_21) )
& ! [U_24,U_22] :
( ( U_24 = U_22
& in(U_24,U_21) )
| ~ in(ordered_pair(U_24,U_22),U_20) ) )
| U_20 != identity_relation(U_21) ) )
| ~ relation(U_20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_28,sK1(U_21,U_20))],[f_12_3]) ).
fof(f_12_5,plain,
! [U_21,U_20] :
( ( ( U_20 = identity_relation(U_21)
| ? [U_29,U_27] :
( ~ in(ordered_pair(U_29,U_27),U_20)
& U_29 = U_27
& in(U_29,U_21) )
| ( ( sK1(U_21,U_20) != sK2(U_21,U_20)
| ~ in(sK1(U_21,U_20),U_21) )
& in(ordered_pair(sK1(U_21,U_20),sK2(U_21,U_20)),U_20) ) )
& ( ( ! [U_25,U_23] :
( in(ordered_pair(U_25,U_23),U_20)
| U_25 != U_23
| ~ in(U_25,U_21) )
& ! [U_24,U_22] :
( ( U_24 = U_22
& in(U_24,U_21) )
| ~ in(ordered_pair(U_24,U_22),U_20) ) )
| U_20 != identity_relation(U_21) ) )
| ~ relation(U_20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_26,sK2(U_21,U_20))],[f_12_4]) ).
fof(f_12_6,plain,
! [U_21,U_20] :
( ( ( U_20 = identity_relation(U_21)
| ? [U_27] :
( ~ in(ordered_pair(sK3(U_21,U_20),U_27),U_20)
& sK3(U_21,U_20) = U_27
& in(sK3(U_21,U_20),U_21) )
| ( ( sK1(U_21,U_20) != sK2(U_21,U_20)
| ~ in(sK1(U_21,U_20),U_21) )
& in(ordered_pair(sK1(U_21,U_20),sK2(U_21,U_20)),U_20) ) )
& ( ( ! [U_25,U_23] :
( in(ordered_pair(U_25,U_23),U_20)
| U_25 != U_23
| ~ in(U_25,U_21) )
& ! [U_24,U_22] :
( ( U_24 = U_22
& in(U_24,U_21) )
| ~ in(ordered_pair(U_24,U_22),U_20) ) )
| U_20 != identity_relation(U_21) ) )
| ~ relation(U_20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_29,sK3(U_21,U_20))],[f_12_5]) ).
fof(f_12_7,plain,
! [U_21,U_20] :
( ( ( U_20 = identity_relation(U_21)
| ( ~ in(ordered_pair(sK3(U_21,U_20),sK4(U_21,U_20)),U_20)
& sK3(U_21,U_20) = sK4(U_21,U_20)
& in(sK3(U_21,U_20),U_21) )
| ( ( sK1(U_21,U_20) != sK2(U_21,U_20)
| ~ in(sK1(U_21,U_20),U_21) )
& in(ordered_pair(sK1(U_21,U_20),sK2(U_21,U_20)),U_20) ) )
& ( ( ! [U_25,U_23] :
( in(ordered_pair(U_25,U_23),U_20)
| U_25 != U_23
| ~ in(U_25,U_21) )
& ! [U_24,U_22] :
( ( U_24 = U_22
& in(U_24,U_21) )
| ~ in(ordered_pair(U_24,U_22),U_20) ) )
| U_20 != identity_relation(U_21) ) )
| ~ relation(U_20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_27,sK4(U_21,U_20))],[f_12_6]) ).
fof(f_12_8,plain,
( ! [U_20,U_21] :
( ~ in(ordered_pair(sK3(U_21,U_20),sK4(U_21,U_20)),U_20)
| ~ sP6(U_20,U_21) )
& ! [U_20,U_21] :
( sK3(U_21,U_20) = sK4(U_21,U_20)
| ~ sP6(U_20,U_21) )
& ! [U_20,U_21] :
( in(sK3(U_21,U_20),U_21)
| ~ sP6(U_20,U_21) )
& ! [U_20,U_21] :
( sK1(U_21,U_20) != sK2(U_21,U_20)
| ~ in(sK1(U_21,U_20),U_21)
| ~ sP5(U_20,U_21) )
& ! [U_20,U_21] :
( in(ordered_pair(sK1(U_21,U_20),sK2(U_21,U_20)),U_20)
| ~ sP5(U_20,U_21) )
& ! [U_24,U_21,U_22] :
( U_24 = U_22
| ~ sP3(U_24,U_21,U_22) )
& ! [U_24,U_21,U_22] :
( in(U_24,U_21)
| ~ sP3(U_24,U_21,U_22) )
& ! [U_24,U_20,U_21,U_22,U_23,U_25] :
( in(ordered_pair(U_25,U_23),U_20)
| U_25 != U_23
| ~ in(U_25,U_21)
| ~ sP4(U_24,U_20,U_21,U_22,U_23,U_25) )
& ! [U_24,U_20,U_21,U_22,U_23,U_25] :
( sP3(U_24,U_21,U_22)
| ~ in(ordered_pair(U_24,U_22),U_20)
| ~ sP4(U_24,U_20,U_21,U_22,U_23,U_25) )
& ! [U_24,U_20,U_21,U_22,U_23,U_25] :
( U_20 = identity_relation(U_21)
| sP6(U_20,U_21)
| sP5(U_20,U_21)
| ~ sP7(U_24,U_20,U_21,U_22,U_23,U_25) )
& ! [U_24,U_20,U_21,U_22,U_23,U_25] :
( sP4(U_24,U_20,U_21,U_22,U_23,U_25)
| U_20 != identity_relation(U_21)
| ~ sP7(U_24,U_20,U_21,U_22,U_23,U_25) )
& ! [U_24,U_20,U_21,U_22,U_23,U_25] :
( sP7(U_24,U_20,U_21,U_22,U_23,U_25)
| ~ relation(U_20) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3,sP4,sP5,sP6,sP7])],[f_12_7]) ).
cnf(f_12_9,plain,
( sP7(U_24,U_20,U_21,U_22,U_23,U_25)
| ~ relation(U_20) ),
inference(clausify,[status(thm)],[f_12_8]) ).
cnf(f_12_10,plain,
( sP4(U_24,U_20,U_21,U_22,U_23,U_25)
| U_20 != identity_relation(U_21)
| ~ sP7(U_24,U_20,U_21,U_22,U_23,U_25) ),
inference(clausify,[status(thm)],[f_12_8]) ).
cnf(f_12_11,plain,
( U_20 = identity_relation(U_21)
| sP6(U_20,U_21)
| sP5(U_20,U_21)
| ~ sP7(U_24,U_20,U_21,U_22,U_23,U_25) ),
inference(clausify,[status(thm)],[f_12_8]) ).
cnf(f_12_12,plain,
( sP3(U_24,U_21,U_22)
| ~ in(ordered_pair(U_24,U_22),U_20)
| ~ sP4(U_24,U_20,U_21,U_22,U_23,U_25) ),
inference(clausify,[status(thm)],[f_12_8]) ).
cnf(f_12_13,plain,
( in(ordered_pair(U_25,U_23),U_20)
| U_25 != U_23
| ~ in(U_25,U_21)
| ~ sP4(U_24,U_20,U_21,U_22,U_23,U_25) ),
inference(clausify,[status(thm)],[f_12_8]) ).
cnf(f_12_14,plain,
( in(U_24,U_21)
| ~ sP3(U_24,U_21,U_22) ),
inference(clausify,[status(thm)],[f_12_8]) ).
cnf(f_12_15,plain,
( U_24 = U_22
| ~ sP3(U_24,U_21,U_22) ),
inference(clausify,[status(thm)],[f_12_8]) ).
cnf(f_12_16,plain,
( in(ordered_pair(sK1(U_21,U_20),sK2(U_21,U_20)),U_20)
| ~ sP5(U_20,U_21) ),
inference(clausify,[status(thm)],[f_12_8]) ).
cnf(f_12_17,plain,
( sK1(U_21,U_20) != sK2(U_21,U_20)
| ~ in(sK1(U_21,U_20),U_21)
| ~ sP5(U_20,U_21) ),
inference(clausify,[status(thm)],[f_12_8]) ).
cnf(f_12_18,plain,
( in(sK3(U_21,U_20),U_21)
| ~ sP6(U_20,U_21) ),
inference(clausify,[status(thm)],[f_12_8]) ).
cnf(f_12_19,plain,
( sK3(U_21,U_20) = sK4(U_21,U_20)
| ~ sP6(U_20,U_21) ),
inference(clausify,[status(thm)],[f_12_8]) ).
cnf(f_12_20,plain,
( ~ in(ordered_pair(sK3(U_21,U_20),sK4(U_21,U_20)),U_20)
| ~ sP6(U_20,U_21) ),
inference(clausify,[status(thm)],[f_12_8]) ).
fof(f_13_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_13_2,plain,
! [U_31,U_30] :
( ( U_31 = U_30
| ~ subset(U_30,U_31)
| ~ subset(U_31,U_30) )
& ( ( subset(U_30,U_31)
& subset(U_31,U_30) )
| U_31 != U_30 ) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_35,U_33] :
( U_35 = U_33
| ~ subset(U_33,U_35)
| ~ subset(U_35,U_33) )
& ! [U_34,U_32] :
( ( subset(U_32,U_34)
& subset(U_34,U_32) )
| U_34 != U_32 ) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
fof(f_13_4,plain,
( ! [U_32,U_34] :
( subset(U_32,U_34)
| ~ sP8(U_32,U_34) )
& ! [U_32,U_34] :
( subset(U_34,U_32)
| ~ sP8(U_32,U_34) )
& ! [U_35,U_33] :
( U_35 = U_33
| ~ subset(U_33,U_35)
| ~ subset(U_35,U_33) )
& ! [U_32,U_34] :
( sP8(U_32,U_34)
| U_34 != U_32 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_13_3]) ).
cnf(f_13_5,plain,
( sP8(U_32,U_34)
| U_34 != U_32 ),
inference(clausify,[status(thm)],[f_13_4]) ).
cnf(f_13_6,plain,
( U_35 = U_33
| ~ subset(U_33,U_35)
| ~ subset(U_35,U_33) ),
inference(clausify,[status(thm)],[f_13_4]) ).
cnf(f_13_7,plain,
( subset(U_34,U_32)
| ~ sP8(U_32,U_34) ),
inference(clausify,[status(thm)],[f_13_4]) ).
cnf(f_13_8,plain,
( subset(U_32,U_34)
| ~ sP8(U_32,U_34) ),
inference(clausify,[status(thm)],[f_13_4]) ).
fof(f_14_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_14_2,plain,
! [U_42] :
( ! [U_41,U_40] :
( ( ( U_40 = relation_dom_restriction(U_42,U_41)
| ? [U_39,U_38] :
( ( ~ in(ordered_pair(U_39,U_38),U_40)
& in(ordered_pair(U_39,U_38),U_42)
& in(U_39,U_41) )
| ( ( ~ in(ordered_pair(U_39,U_38),U_42)
| ~ in(U_39,U_41) )
& in(ordered_pair(U_39,U_38),U_40) ) ) )
& ( ! [U_37,U_36] :
( ( in(ordered_pair(U_37,U_36),U_40)
| ~ in(ordered_pair(U_37,U_36),U_42)
| ~ in(U_37,U_41) )
& ( ( in(ordered_pair(U_37,U_36),U_42)
& in(U_37,U_41) )
| ~ in(ordered_pair(U_37,U_36),U_40) ) )
| U_40 != relation_dom_restriction(U_42,U_41) ) )
| ~ relation(U_40) )
| ~ relation(U_42) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_42] :
( ! [U_41,U_40] :
( ( ( U_40 = relation_dom_restriction(U_42,U_41)
| ? [U_50,U_48] :
( ~ in(ordered_pair(U_50,U_48),U_40)
& in(ordered_pair(U_50,U_48),U_42)
& in(U_50,U_41) )
| ? [U_49,U_47] :
( ( ~ in(ordered_pair(U_49,U_47),U_42)
| ~ in(U_49,U_41) )
& in(ordered_pair(U_49,U_47),U_40) ) )
& ( ( ! [U_46,U_44] :
( in(ordered_pair(U_46,U_44),U_40)
| ~ in(ordered_pair(U_46,U_44),U_42)
| ~ in(U_46,U_41) )
& ! [U_45,U_43] :
( ( in(ordered_pair(U_45,U_43),U_42)
& in(U_45,U_41) )
| ~ in(ordered_pair(U_45,U_43),U_40) ) )
| U_40 != relation_dom_restriction(U_42,U_41) ) )
| ~ relation(U_40) )
| ~ relation(U_42) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
fof(f_14_4,plain,
! [U_42] :
( ! [U_41,U_40] :
( ( ( U_40 = relation_dom_restriction(U_42,U_41)
| ? [U_50,U_48] :
( ~ in(ordered_pair(U_50,U_48),U_40)
& in(ordered_pair(U_50,U_48),U_42)
& in(U_50,U_41) )
| ? [U_47] :
( ( ~ in(ordered_pair(sK5(U_42,U_41,U_40),U_47),U_42)
| ~ in(sK5(U_42,U_41,U_40),U_41) )
& in(ordered_pair(sK5(U_42,U_41,U_40),U_47),U_40) ) )
& ( ( ! [U_46,U_44] :
( in(ordered_pair(U_46,U_44),U_40)
| ~ in(ordered_pair(U_46,U_44),U_42)
| ~ in(U_46,U_41) )
& ! [U_45,U_43] :
( ( in(ordered_pair(U_45,U_43),U_42)
& in(U_45,U_41) )
| ~ in(ordered_pair(U_45,U_43),U_40) ) )
| U_40 != relation_dom_restriction(U_42,U_41) ) )
| ~ relation(U_40) )
| ~ relation(U_42) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_49,sK5(U_42,U_41,U_40))],[f_14_3]) ).
fof(f_14_5,plain,
! [U_42] :
( ! [U_41,U_40] :
( ( ( U_40 = relation_dom_restriction(U_42,U_41)
| ? [U_50,U_48] :
( ~ in(ordered_pair(U_50,U_48),U_40)
& in(ordered_pair(U_50,U_48),U_42)
& in(U_50,U_41) )
| ( ( ~ in(ordered_pair(sK5(U_42,U_41,U_40),sK6(U_42,U_41,U_40)),U_42)
| ~ in(sK5(U_42,U_41,U_40),U_41) )
& in(ordered_pair(sK5(U_42,U_41,U_40),sK6(U_42,U_41,U_40)),U_40) ) )
& ( ( ! [U_46,U_44] :
( in(ordered_pair(U_46,U_44),U_40)
| ~ in(ordered_pair(U_46,U_44),U_42)
| ~ in(U_46,U_41) )
& ! [U_45,U_43] :
( ( in(ordered_pair(U_45,U_43),U_42)
& in(U_45,U_41) )
| ~ in(ordered_pair(U_45,U_43),U_40) ) )
| U_40 != relation_dom_restriction(U_42,U_41) ) )
| ~ relation(U_40) )
| ~ relation(U_42) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_47,sK6(U_42,U_41,U_40))],[f_14_4]) ).
fof(f_14_6,plain,
! [U_42] :
( ! [U_41,U_40] :
( ( ( U_40 = relation_dom_restriction(U_42,U_41)
| ? [U_48] :
( ~ in(ordered_pair(sK7(U_42,U_41,U_40),U_48),U_40)
& in(ordered_pair(sK7(U_42,U_41,U_40),U_48),U_42)
& in(sK7(U_42,U_41,U_40),U_41) )
| ( ( ~ in(ordered_pair(sK5(U_42,U_41,U_40),sK6(U_42,U_41,U_40)),U_42)
| ~ in(sK5(U_42,U_41,U_40),U_41) )
& in(ordered_pair(sK5(U_42,U_41,U_40),sK6(U_42,U_41,U_40)),U_40) ) )
& ( ( ! [U_46,U_44] :
( in(ordered_pair(U_46,U_44),U_40)
| ~ in(ordered_pair(U_46,U_44),U_42)
| ~ in(U_46,U_41) )
& ! [U_45,U_43] :
( ( in(ordered_pair(U_45,U_43),U_42)
& in(U_45,U_41) )
| ~ in(ordered_pair(U_45,U_43),U_40) ) )
| U_40 != relation_dom_restriction(U_42,U_41) ) )
| ~ relation(U_40) )
| ~ relation(U_42) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_50,sK7(U_42,U_41,U_40))],[f_14_5]) ).
fof(f_14_7,plain,
! [U_42] :
( ! [U_41,U_40] :
( ( ( U_40 = relation_dom_restriction(U_42,U_41)
| ( ~ in(ordered_pair(sK7(U_42,U_41,U_40),sK8(U_42,U_41,U_40)),U_40)
& in(ordered_pair(sK7(U_42,U_41,U_40),sK8(U_42,U_41,U_40)),U_42)
& in(sK7(U_42,U_41,U_40),U_41) )
| ( ( ~ in(ordered_pair(sK5(U_42,U_41,U_40),sK6(U_42,U_41,U_40)),U_42)
| ~ in(sK5(U_42,U_41,U_40),U_41) )
& in(ordered_pair(sK5(U_42,U_41,U_40),sK6(U_42,U_41,U_40)),U_40) ) )
& ( ( ! [U_46,U_44] :
( in(ordered_pair(U_46,U_44),U_40)
| ~ in(ordered_pair(U_46,U_44),U_42)
| ~ in(U_46,U_41) )
& ! [U_45,U_43] :
( ( in(ordered_pair(U_45,U_43),U_42)
& in(U_45,U_41) )
| ~ in(ordered_pair(U_45,U_43),U_40) ) )
| U_40 != relation_dom_restriction(U_42,U_41) ) )
| ~ relation(U_40) )
| ~ relation(U_42) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_48,sK8(U_42,U_41,U_40))],[f_14_6]) ).
fof(f_14_8,plain,
( ! [U_41,U_42,U_40] :
( ~ in(ordered_pair(sK7(U_42,U_41,U_40),sK8(U_42,U_41,U_40)),U_40)
| ~ sP12(U_41,U_42,U_40) )
& ! [U_41,U_42,U_40] :
( in(ordered_pair(sK7(U_42,U_41,U_40),sK8(U_42,U_41,U_40)),U_42)
| ~ sP12(U_41,U_42,U_40) )
& ! [U_41,U_42,U_40] :
( in(sK7(U_42,U_41,U_40),U_41)
| ~ sP12(U_41,U_42,U_40) )
& ! [U_41,U_42,U_40] :
( ~ in(ordered_pair(sK5(U_42,U_41,U_40),sK6(U_42,U_41,U_40)),U_42)
| ~ in(sK5(U_42,U_41,U_40),U_41)
| ~ sP11(U_41,U_42,U_40) )
& ! [U_41,U_42,U_40] :
( in(ordered_pair(sK5(U_42,U_41,U_40),sK6(U_42,U_41,U_40)),U_40)
| ~ sP11(U_41,U_42,U_40) )
& ! [U_41,U_42,U_43,U_45] :
( in(ordered_pair(U_45,U_43),U_42)
| ~ sP9(U_41,U_42,U_43,U_45) )
& ! [U_41,U_42,U_43,U_45] :
( in(U_45,U_41)
| ~ sP9(U_41,U_42,U_43,U_45) )
& ! [U_41,U_46,U_42,U_43,U_45,U_40,U_44] :
( in(ordered_pair(U_46,U_44),U_40)
| ~ in(ordered_pair(U_46,U_44),U_42)
| ~ in(U_46,U_41)
| ~ sP10(U_41,U_46,U_42,U_43,U_45,U_40,U_44) )
& ! [U_41,U_46,U_42,U_43,U_45,U_40,U_44] :
( sP9(U_41,U_42,U_43,U_45)
| ~ in(ordered_pair(U_45,U_43),U_40)
| ~ sP10(U_41,U_46,U_42,U_43,U_45,U_40,U_44) )
& ! [U_41,U_46,U_42,U_43,U_45,U_40,U_44] :
( U_40 = relation_dom_restriction(U_42,U_41)
| sP12(U_41,U_42,U_40)
| sP11(U_41,U_42,U_40)
| ~ sP13(U_41,U_46,U_42,U_43,U_45,U_40,U_44) )
& ! [U_41,U_46,U_42,U_43,U_45,U_40,U_44] :
( sP10(U_41,U_46,U_42,U_43,U_45,U_40,U_44)
| U_40 != relation_dom_restriction(U_42,U_41)
| ~ sP13(U_41,U_46,U_42,U_43,U_45,U_40,U_44) )
& ! [U_41,U_46,U_42,U_43,U_45,U_40,U_44] :
( sP13(U_41,U_46,U_42,U_43,U_45,U_40,U_44)
| ~ relation(U_40)
| ~ relation(U_42) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9,sP10,sP11,sP12,sP13])],[f_14_7]) ).
cnf(f_14_9,plain,
( sP13(U_41,U_46,U_42,U_43,U_45,U_40,U_44)
| ~ relation(U_40)
| ~ relation(U_42) ),
inference(clausify,[status(thm)],[f_14_8]) ).
cnf(f_14_10,plain,
( sP10(U_41,U_46,U_42,U_43,U_45,U_40,U_44)
| U_40 != relation_dom_restriction(U_42,U_41)
| ~ sP13(U_41,U_46,U_42,U_43,U_45,U_40,U_44) ),
inference(clausify,[status(thm)],[f_14_8]) ).
cnf(f_14_11,plain,
( U_40 = relation_dom_restriction(U_42,U_41)
| sP12(U_41,U_42,U_40)
| sP11(U_41,U_42,U_40)
| ~ sP13(U_41,U_46,U_42,U_43,U_45,U_40,U_44) ),
inference(clausify,[status(thm)],[f_14_8]) ).
cnf(f_14_12,plain,
( sP9(U_41,U_42,U_43,U_45)
| ~ in(ordered_pair(U_45,U_43),U_40)
| ~ sP10(U_41,U_46,U_42,U_43,U_45,U_40,U_44) ),
inference(clausify,[status(thm)],[f_14_8]) ).
cnf(f_14_13,plain,
( in(ordered_pair(U_46,U_44),U_40)
| ~ in(ordered_pair(U_46,U_44),U_42)
| ~ in(U_46,U_41)
| ~ sP10(U_41,U_46,U_42,U_43,U_45,U_40,U_44) ),
inference(clausify,[status(thm)],[f_14_8]) ).
cnf(f_14_14,plain,
( in(U_45,U_41)
| ~ sP9(U_41,U_42,U_43,U_45) ),
inference(clausify,[status(thm)],[f_14_8]) ).
cnf(f_14_15,plain,
( in(ordered_pair(U_45,U_43),U_42)
| ~ sP9(U_41,U_42,U_43,U_45) ),
inference(clausify,[status(thm)],[f_14_8]) ).
cnf(f_14_16,plain,
( in(ordered_pair(sK5(U_42,U_41,U_40),sK6(U_42,U_41,U_40)),U_40)
| ~ sP11(U_41,U_42,U_40) ),
inference(clausify,[status(thm)],[f_14_8]) ).
cnf(f_14_17,plain,
( ~ in(ordered_pair(sK5(U_42,U_41,U_40),sK6(U_42,U_41,U_40)),U_42)
| ~ in(sK5(U_42,U_41,U_40),U_41)
| ~ sP11(U_41,U_42,U_40) ),
inference(clausify,[status(thm)],[f_14_8]) ).
cnf(f_14_18,plain,
( in(sK7(U_42,U_41,U_40),U_41)
| ~ sP12(U_41,U_42,U_40) ),
inference(clausify,[status(thm)],[f_14_8]) ).
cnf(f_14_19,plain,
( in(ordered_pair(sK7(U_42,U_41,U_40),sK8(U_42,U_41,U_40)),U_42)
| ~ sP12(U_41,U_42,U_40) ),
inference(clausify,[status(thm)],[f_14_8]) ).
cnf(f_14_20,plain,
( ~ in(ordered_pair(sK7(U_42,U_41,U_40),sK8(U_42,U_41,U_40)),U_40)
| ~ sP12(U_41,U_42,U_40) ),
inference(clausify,[status(thm)],[f_14_8]) ).
fof(f_15_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_15_2,plain,
! [U_59] :
( ! [U_58,U_57] :
( ( U_57 = relation_image(U_59,U_58)
| ? [U_56] :
( ( ~ in(U_56,U_57)
& ? [U_55] :
( U_56 = apply(U_59,U_55)
& in(U_55,U_58)
& in(U_55,relation_dom(U_59)) ) )
| ( ! [U_54] :
( U_56 != apply(U_59,U_54)
| ~ in(U_54,U_58)
| ~ in(U_54,relation_dom(U_59)) )
& in(U_56,U_57) ) ) )
& ( ! [U_53] :
( ( in(U_53,U_57)
| ! [U_52] :
( U_53 != apply(U_59,U_52)
| ~ in(U_52,U_58)
| ~ in(U_52,relation_dom(U_59)) ) )
& ( ? [U_51] :
( U_53 = apply(U_59,U_51)
& in(U_51,U_58)
& in(U_51,relation_dom(U_59)) )
| ~ in(U_53,U_57) ) )
| U_57 != relation_image(U_59,U_58) ) )
| ~ function(U_59)
| ~ relation(U_59) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_59] :
( ( ! [U_67,U_65] :
( U_65 = relation_image(U_59,U_67)
| ? [U_63] :
( ~ in(U_63,U_65)
& ? [U_55] :
( U_63 = apply(U_59,U_55)
& in(U_55,U_67)
& in(U_55,relation_dom(U_59)) ) )
| ? [U_62] :
( ! [U_54] :
( U_62 != apply(U_59,U_54)
| ~ in(U_54,U_67)
| ~ in(U_54,relation_dom(U_59)) )
& in(U_62,U_65) ) )
& ! [U_66,U_64] :
( ( ! [U_61] :
( in(U_61,U_64)
| ! [U_52] :
( U_61 != apply(U_59,U_52)
| ~ in(U_52,U_66)
| ~ in(U_52,relation_dom(U_59)) ) )
& ! [U_60] :
( ? [U_51] :
( U_60 = apply(U_59,U_51)
& in(U_51,U_66)
& in(U_51,relation_dom(U_59)) )
| ~ in(U_60,U_64) ) )
| U_64 != relation_image(U_59,U_66) ) )
| ~ function(U_59)
| ~ relation(U_59) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
fof(f_15_4,plain,
! [U_59] :
( ( ! [U_67,U_65] :
( U_65 = relation_image(U_59,U_67)
| ? [U_63] :
( ~ in(U_63,U_65)
& ? [U_55] :
( U_63 = apply(U_59,U_55)
& in(U_55,U_67)
& in(U_55,relation_dom(U_59)) ) )
| ? [U_62] :
( ! [U_54] :
( U_62 != apply(U_59,U_54)
| ~ in(U_54,U_67)
| ~ in(U_54,relation_dom(U_59)) )
& in(U_62,U_65) ) )
& ! [U_66,U_64] :
( ( ! [U_61] :
( in(U_61,U_64)
| ! [U_52] :
( U_61 != apply(U_59,U_52)
| ~ in(U_52,U_66)
| ~ in(U_52,relation_dom(U_59)) ) )
& ! [U_60] :
( ( U_60 = apply(U_59,sK9(U_59,U_66,U_64,U_60))
& in(sK9(U_59,U_66,U_64,U_60),U_66)
& in(sK9(U_59,U_66,U_64,U_60),relation_dom(U_59)) )
| ~ in(U_60,U_64) ) )
| U_64 != relation_image(U_59,U_66) ) )
| ~ function(U_59)
| ~ relation(U_59) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_51,sK9(U_59,U_66,U_64,U_60))],[f_15_3]) ).
fof(f_15_5,plain,
! [U_59] :
( ( ! [U_67,U_65] :
( U_65 = relation_image(U_59,U_67)
| ? [U_63] :
( ~ in(U_63,U_65)
& ? [U_55] :
( U_63 = apply(U_59,U_55)
& in(U_55,U_67)
& in(U_55,relation_dom(U_59)) ) )
| ( ! [U_54] :
( sK10(U_59,U_67,U_65) != apply(U_59,U_54)
| ~ in(U_54,U_67)
| ~ in(U_54,relation_dom(U_59)) )
& in(sK10(U_59,U_67,U_65),U_65) ) )
& ! [U_66,U_64] :
( ( ! [U_61] :
( in(U_61,U_64)
| ! [U_52] :
( U_61 != apply(U_59,U_52)
| ~ in(U_52,U_66)
| ~ in(U_52,relation_dom(U_59)) ) )
& ! [U_60] :
( ( U_60 = apply(U_59,sK9(U_59,U_66,U_64,U_60))
& in(sK9(U_59,U_66,U_64,U_60),U_66)
& in(sK9(U_59,U_66,U_64,U_60),relation_dom(U_59)) )
| ~ in(U_60,U_64) ) )
| U_64 != relation_image(U_59,U_66) ) )
| ~ function(U_59)
| ~ relation(U_59) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_62,sK10(U_59,U_67,U_65))],[f_15_4]) ).
fof(f_15_6,plain,
! [U_59] :
( ( ! [U_67,U_65] :
( U_65 = relation_image(U_59,U_67)
| ( ~ in(sK11(U_59,U_67,U_65),U_65)
& ? [U_55] :
( sK11(U_59,U_67,U_65) = apply(U_59,U_55)
& in(U_55,U_67)
& in(U_55,relation_dom(U_59)) ) )
| ( ! [U_54] :
( sK10(U_59,U_67,U_65) != apply(U_59,U_54)
| ~ in(U_54,U_67)
| ~ in(U_54,relation_dom(U_59)) )
& in(sK10(U_59,U_67,U_65),U_65) ) )
& ! [U_66,U_64] :
( ( ! [U_61] :
( in(U_61,U_64)
| ! [U_52] :
( U_61 != apply(U_59,U_52)
| ~ in(U_52,U_66)
| ~ in(U_52,relation_dom(U_59)) ) )
& ! [U_60] :
( ( U_60 = apply(U_59,sK9(U_59,U_66,U_64,U_60))
& in(sK9(U_59,U_66,U_64,U_60),U_66)
& in(sK9(U_59,U_66,U_64,U_60),relation_dom(U_59)) )
| ~ in(U_60,U_64) ) )
| U_64 != relation_image(U_59,U_66) ) )
| ~ function(U_59)
| ~ relation(U_59) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_63,sK11(U_59,U_67,U_65))],[f_15_5]) ).
fof(f_15_7,plain,
! [U_59] :
( ( ! [U_67,U_65] :
( U_65 = relation_image(U_59,U_67)
| ( ~ in(sK11(U_59,U_67,U_65),U_65)
& sK11(U_59,U_67,U_65) = apply(U_59,sK12(U_59,U_67,U_65))
& in(sK12(U_59,U_67,U_65),U_67)
& in(sK12(U_59,U_67,U_65),relation_dom(U_59)) )
| ( ! [U_54] :
( sK10(U_59,U_67,U_65) != apply(U_59,U_54)
| ~ in(U_54,U_67)
| ~ in(U_54,relation_dom(U_59)) )
& in(sK10(U_59,U_67,U_65),U_65) ) )
& ! [U_66,U_64] :
( ( ! [U_61] :
( in(U_61,U_64)
| ! [U_52] :
( U_61 != apply(U_59,U_52)
| ~ in(U_52,U_66)
| ~ in(U_52,relation_dom(U_59)) ) )
& ! [U_60] :
( ( U_60 = apply(U_59,sK9(U_59,U_66,U_64,U_60))
& in(sK9(U_59,U_66,U_64,U_60),U_66)
& in(sK9(U_59,U_66,U_64,U_60),relation_dom(U_59)) )
| ~ in(U_60,U_64) ) )
| U_64 != relation_image(U_59,U_66) ) )
| ~ function(U_59)
| ~ relation(U_59) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_55,sK12(U_59,U_67,U_65))],[f_15_6]) ).
fof(f_15_8,plain,
( ! [U_67,U_59,U_65] :
( ~ in(sK11(U_59,U_67,U_65),U_65)
| ~ sP17(U_67,U_59,U_65) )
& ! [U_67,U_59,U_65] :
( sK11(U_59,U_67,U_65) = apply(U_59,sK12(U_59,U_67,U_65))
| ~ sP17(U_67,U_59,U_65) )
& ! [U_67,U_59,U_65] :
( in(sK12(U_59,U_67,U_65),U_67)
| ~ sP17(U_67,U_59,U_65) )
& ! [U_67,U_59,U_65] :
( in(sK12(U_59,U_67,U_65),relation_dom(U_59))
| ~ sP17(U_67,U_59,U_65) )
& ! [U_54,U_67,U_59,U_65] :
( sK10(U_59,U_67,U_65) != apply(U_59,U_54)
| ~ in(U_54,U_67)
| ~ in(U_54,relation_dom(U_59))
| ~ sP16(U_54,U_67,U_59,U_65) )
& ! [U_54,U_67,U_59,U_65] :
( in(sK10(U_59,U_67,U_65),U_65)
| ~ sP16(U_54,U_67,U_59,U_65) )
& ! [U_66,U_60,U_59,U_64] :
( U_60 = apply(U_59,sK9(U_59,U_66,U_64,U_60))
| ~ sP14(U_66,U_60,U_59,U_64) )
& ! [U_66,U_60,U_59,U_64] :
( in(sK9(U_59,U_66,U_64,U_60),U_66)
| ~ sP14(U_66,U_60,U_59,U_64) )
& ! [U_66,U_60,U_59,U_64] :
( in(sK9(U_59,U_66,U_64,U_60),relation_dom(U_59))
| ~ sP14(U_66,U_60,U_59,U_64) )
& ! [U_66,U_52,U_61,U_60,U_59,U_64] :
( in(U_61,U_64)
| U_61 != apply(U_59,U_52)
| ~ in(U_52,U_66)
| ~ in(U_52,relation_dom(U_59))
| ~ sP15(U_66,U_52,U_61,U_60,U_59,U_64) )
& ! [U_66,U_52,U_61,U_60,U_59,U_64] :
( sP14(U_66,U_60,U_59,U_64)
| ~ in(U_60,U_64)
| ~ sP15(U_66,U_52,U_61,U_60,U_59,U_64) )
& ! [U_54,U_66,U_52,U_61,U_60,U_67,U_59,U_65,U_64] :
( U_65 = relation_image(U_59,U_67)
| sP17(U_67,U_59,U_65)
| sP16(U_54,U_67,U_59,U_65)
| ~ sP18(U_54,U_66,U_52,U_61,U_60,U_67,U_59,U_65,U_64) )
& ! [U_54,U_66,U_52,U_61,U_60,U_67,U_59,U_65,U_64] :
( sP15(U_66,U_52,U_61,U_60,U_59,U_64)
| U_64 != relation_image(U_59,U_66)
| ~ sP18(U_54,U_66,U_52,U_61,U_60,U_67,U_59,U_65,U_64) )
& ! [U_54,U_66,U_52,U_61,U_60,U_67,U_59,U_65,U_64] :
( sP18(U_54,U_66,U_52,U_61,U_60,U_67,U_59,U_65,U_64)
| ~ function(U_59)
| ~ relation(U_59) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14,sP15,sP16,sP17,sP18])],[f_15_7]) ).
cnf(f_15_9,plain,
( sP18(U_54,U_66,U_52,U_61,U_60,U_67,U_59,U_65,U_64)
| ~ function(U_59)
| ~ relation(U_59) ),
inference(clausify,[status(thm)],[f_15_8]) ).
cnf(f_15_10,plain,
( sP15(U_66,U_52,U_61,U_60,U_59,U_64)
| U_64 != relation_image(U_59,U_66)
| ~ sP18(U_54,U_66,U_52,U_61,U_60,U_67,U_59,U_65,U_64) ),
inference(clausify,[status(thm)],[f_15_8]) ).
cnf(f_15_11,plain,
( U_65 = relation_image(U_59,U_67)
| sP17(U_67,U_59,U_65)
| sP16(U_54,U_67,U_59,U_65)
| ~ sP18(U_54,U_66,U_52,U_61,U_60,U_67,U_59,U_65,U_64) ),
inference(clausify,[status(thm)],[f_15_8]) ).
cnf(f_15_12,plain,
( sP14(U_66,U_60,U_59,U_64)
| ~ in(U_60,U_64)
| ~ sP15(U_66,U_52,U_61,U_60,U_59,U_64) ),
inference(clausify,[status(thm)],[f_15_8]) ).
cnf(f_15_13,plain,
( in(U_61,U_64)
| U_61 != apply(U_59,U_52)
| ~ in(U_52,U_66)
| ~ in(U_52,relation_dom(U_59))
| ~ sP15(U_66,U_52,U_61,U_60,U_59,U_64) ),
inference(clausify,[status(thm)],[f_15_8]) ).
cnf(f_15_14,plain,
( in(sK9(U_59,U_66,U_64,U_60),relation_dom(U_59))
| ~ sP14(U_66,U_60,U_59,U_64) ),
inference(clausify,[status(thm)],[f_15_8]) ).
cnf(f_15_15,plain,
( in(sK9(U_59,U_66,U_64,U_60),U_66)
| ~ sP14(U_66,U_60,U_59,U_64) ),
inference(clausify,[status(thm)],[f_15_8]) ).
cnf(f_15_16,plain,
( U_60 = apply(U_59,sK9(U_59,U_66,U_64,U_60))
| ~ sP14(U_66,U_60,U_59,U_64) ),
inference(clausify,[status(thm)],[f_15_8]) ).
cnf(f_15_17,plain,
( in(sK10(U_59,U_67,U_65),U_65)
| ~ sP16(U_54,U_67,U_59,U_65) ),
inference(clausify,[status(thm)],[f_15_8]) ).
cnf(f_15_18,plain,
( sK10(U_59,U_67,U_65) != apply(U_59,U_54)
| ~ in(U_54,U_67)
| ~ in(U_54,relation_dom(U_59))
| ~ sP16(U_54,U_67,U_59,U_65) ),
inference(clausify,[status(thm)],[f_15_8]) ).
cnf(f_15_19,plain,
( in(sK12(U_59,U_67,U_65),relation_dom(U_59))
| ~ sP17(U_67,U_59,U_65) ),
inference(clausify,[status(thm)],[f_15_8]) ).
cnf(f_15_20,plain,
( in(sK12(U_59,U_67,U_65),U_67)
| ~ sP17(U_67,U_59,U_65) ),
inference(clausify,[status(thm)],[f_15_8]) ).
cnf(f_15_21,plain,
( sK11(U_59,U_67,U_65) = apply(U_59,sK12(U_59,U_67,U_65))
| ~ sP17(U_67,U_59,U_65) ),
inference(clausify,[status(thm)],[f_15_8]) ).
cnf(f_15_22,plain,
( ~ in(sK11(U_59,U_67,U_65),U_65)
| ~ sP17(U_67,U_59,U_65) ),
inference(clausify,[status(thm)],[f_15_8]) ).
fof(f_16_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_16_2,plain,
! [U_74,U_73] :
( ! [U_72] :
( ( ( U_72 = relation_rng_restriction(U_74,U_73)
| ? [U_71,U_70] :
( ( ~ in(ordered_pair(U_71,U_70),U_72)
& in(ordered_pair(U_71,U_70),U_73)
& in(U_70,U_74) )
| ( ( ~ in(ordered_pair(U_71,U_70),U_73)
| ~ in(U_70,U_74) )
& in(ordered_pair(U_71,U_70),U_72) ) ) )
& ( ! [U_69,U_68] :
( ( in(ordered_pair(U_69,U_68),U_72)
| ~ in(ordered_pair(U_69,U_68),U_73)
| ~ in(U_68,U_74) )
& ( ( in(ordered_pair(U_69,U_68),U_73)
& in(U_68,U_74) )
| ~ in(ordered_pair(U_69,U_68),U_72) ) )
| U_72 != relation_rng_restriction(U_74,U_73) ) )
| ~ relation(U_72) )
| ~ relation(U_73) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_74,U_73] :
( ! [U_72] :
( ( ( U_72 = relation_rng_restriction(U_74,U_73)
| ? [U_82,U_80] :
( ~ in(ordered_pair(U_82,U_80),U_72)
& in(ordered_pair(U_82,U_80),U_73)
& in(U_80,U_74) )
| ? [U_81,U_79] :
( ( ~ in(ordered_pair(U_81,U_79),U_73)
| ~ in(U_79,U_74) )
& in(ordered_pair(U_81,U_79),U_72) ) )
& ( ( ! [U_78,U_76] :
( in(ordered_pair(U_78,U_76),U_72)
| ~ in(ordered_pair(U_78,U_76),U_73)
| ~ in(U_76,U_74) )
& ! [U_77,U_75] :
( ( in(ordered_pair(U_77,U_75),U_73)
& in(U_75,U_74) )
| ~ in(ordered_pair(U_77,U_75),U_72) ) )
| U_72 != relation_rng_restriction(U_74,U_73) ) )
| ~ relation(U_72) )
| ~ relation(U_73) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
fof(f_16_4,plain,
! [U_74,U_73] :
( ! [U_72] :
( ( ( U_72 = relation_rng_restriction(U_74,U_73)
| ? [U_82,U_80] :
( ~ in(ordered_pair(U_82,U_80),U_72)
& in(ordered_pair(U_82,U_80),U_73)
& in(U_80,U_74) )
| ? [U_79] :
( ( ~ in(ordered_pair(sK13(U_74,U_73,U_72),U_79),U_73)
| ~ in(U_79,U_74) )
& in(ordered_pair(sK13(U_74,U_73,U_72),U_79),U_72) ) )
& ( ( ! [U_78,U_76] :
( in(ordered_pair(U_78,U_76),U_72)
| ~ in(ordered_pair(U_78,U_76),U_73)
| ~ in(U_76,U_74) )
& ! [U_77,U_75] :
( ( in(ordered_pair(U_77,U_75),U_73)
& in(U_75,U_74) )
| ~ in(ordered_pair(U_77,U_75),U_72) ) )
| U_72 != relation_rng_restriction(U_74,U_73) ) )
| ~ relation(U_72) )
| ~ relation(U_73) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_81,sK13(U_74,U_73,U_72))],[f_16_3]) ).
fof(f_16_5,plain,
! [U_74,U_73] :
( ! [U_72] :
( ( ( U_72 = relation_rng_restriction(U_74,U_73)
| ? [U_82,U_80] :
( ~ in(ordered_pair(U_82,U_80),U_72)
& in(ordered_pair(U_82,U_80),U_73)
& in(U_80,U_74) )
| ( ( ~ in(ordered_pair(sK13(U_74,U_73,U_72),sK14(U_74,U_73,U_72)),U_73)
| ~ in(sK14(U_74,U_73,U_72),U_74) )
& in(ordered_pair(sK13(U_74,U_73,U_72),sK14(U_74,U_73,U_72)),U_72) ) )
& ( ( ! [U_78,U_76] :
( in(ordered_pair(U_78,U_76),U_72)
| ~ in(ordered_pair(U_78,U_76),U_73)
| ~ in(U_76,U_74) )
& ! [U_77,U_75] :
( ( in(ordered_pair(U_77,U_75),U_73)
& in(U_75,U_74) )
| ~ in(ordered_pair(U_77,U_75),U_72) ) )
| U_72 != relation_rng_restriction(U_74,U_73) ) )
| ~ relation(U_72) )
| ~ relation(U_73) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_79,sK14(U_74,U_73,U_72))],[f_16_4]) ).
fof(f_16_6,plain,
! [U_74,U_73] :
( ! [U_72] :
( ( ( U_72 = relation_rng_restriction(U_74,U_73)
| ? [U_80] :
( ~ in(ordered_pair(sK15(U_74,U_73,U_72),U_80),U_72)
& in(ordered_pair(sK15(U_74,U_73,U_72),U_80),U_73)
& in(U_80,U_74) )
| ( ( ~ in(ordered_pair(sK13(U_74,U_73,U_72),sK14(U_74,U_73,U_72)),U_73)
| ~ in(sK14(U_74,U_73,U_72),U_74) )
& in(ordered_pair(sK13(U_74,U_73,U_72),sK14(U_74,U_73,U_72)),U_72) ) )
& ( ( ! [U_78,U_76] :
( in(ordered_pair(U_78,U_76),U_72)
| ~ in(ordered_pair(U_78,U_76),U_73)
| ~ in(U_76,U_74) )
& ! [U_77,U_75] :
( ( in(ordered_pair(U_77,U_75),U_73)
& in(U_75,U_74) )
| ~ in(ordered_pair(U_77,U_75),U_72) ) )
| U_72 != relation_rng_restriction(U_74,U_73) ) )
| ~ relation(U_72) )
| ~ relation(U_73) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_82,sK15(U_74,U_73,U_72))],[f_16_5]) ).
fof(f_16_7,plain,
! [U_74,U_73] :
( ! [U_72] :
( ( ( U_72 = relation_rng_restriction(U_74,U_73)
| ( ~ in(ordered_pair(sK15(U_74,U_73,U_72),sK16(U_74,U_73,U_72)),U_72)
& in(ordered_pair(sK15(U_74,U_73,U_72),sK16(U_74,U_73,U_72)),U_73)
& in(sK16(U_74,U_73,U_72),U_74) )
| ( ( ~ in(ordered_pair(sK13(U_74,U_73,U_72),sK14(U_74,U_73,U_72)),U_73)
| ~ in(sK14(U_74,U_73,U_72),U_74) )
& in(ordered_pair(sK13(U_74,U_73,U_72),sK14(U_74,U_73,U_72)),U_72) ) )
& ( ( ! [U_78,U_76] :
( in(ordered_pair(U_78,U_76),U_72)
| ~ in(ordered_pair(U_78,U_76),U_73)
| ~ in(U_76,U_74) )
& ! [U_77,U_75] :
( ( in(ordered_pair(U_77,U_75),U_73)
& in(U_75,U_74) )
| ~ in(ordered_pair(U_77,U_75),U_72) ) )
| U_72 != relation_rng_restriction(U_74,U_73) ) )
| ~ relation(U_72) )
| ~ relation(U_73) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_80,sK16(U_74,U_73,U_72))],[f_16_6]) ).
fof(f_16_8,plain,
( ! [U_72,U_73,U_74] :
( ~ in(ordered_pair(sK15(U_74,U_73,U_72),sK16(U_74,U_73,U_72)),U_72)
| ~ sP22(U_72,U_73,U_74) )
& ! [U_72,U_73,U_74] :
( in(ordered_pair(sK15(U_74,U_73,U_72),sK16(U_74,U_73,U_72)),U_73)
| ~ sP22(U_72,U_73,U_74) )
& ! [U_72,U_73,U_74] :
( in(sK16(U_74,U_73,U_72),U_74)
| ~ sP22(U_72,U_73,U_74) )
& ! [U_72,U_73,U_74] :
( ~ in(ordered_pair(sK13(U_74,U_73,U_72),sK14(U_74,U_73,U_72)),U_73)
| ~ in(sK14(U_74,U_73,U_72),U_74)
| ~ sP21(U_72,U_73,U_74) )
& ! [U_72,U_73,U_74] :
( in(ordered_pair(sK13(U_74,U_73,U_72),sK14(U_74,U_73,U_72)),U_72)
| ~ sP21(U_72,U_73,U_74) )
& ! [U_75,U_77,U_73,U_74] :
( in(ordered_pair(U_77,U_75),U_73)
| ~ sP19(U_75,U_77,U_73,U_74) )
& ! [U_75,U_77,U_73,U_74] :
( in(U_75,U_74)
| ~ sP19(U_75,U_77,U_73,U_74) )
& ! [U_75,U_78,U_76,U_77,U_72,U_73,U_74] :
( in(ordered_pair(U_78,U_76),U_72)
| ~ in(ordered_pair(U_78,U_76),U_73)
| ~ in(U_76,U_74)
| ~ sP20(U_75,U_78,U_76,U_77,U_72,U_73,U_74) )
& ! [U_75,U_78,U_76,U_77,U_72,U_73,U_74] :
( sP19(U_75,U_77,U_73,U_74)
| ~ in(ordered_pair(U_77,U_75),U_72)
| ~ sP20(U_75,U_78,U_76,U_77,U_72,U_73,U_74) )
& ! [U_75,U_78,U_76,U_77,U_72,U_73,U_74] :
( U_72 = relation_rng_restriction(U_74,U_73)
| sP22(U_72,U_73,U_74)
| sP21(U_72,U_73,U_74)
| ~ sP23(U_75,U_78,U_76,U_77,U_72,U_73,U_74) )
& ! [U_75,U_78,U_76,U_77,U_72,U_73,U_74] :
( sP20(U_75,U_78,U_76,U_77,U_72,U_73,U_74)
| U_72 != relation_rng_restriction(U_74,U_73)
| ~ sP23(U_75,U_78,U_76,U_77,U_72,U_73,U_74) )
& ! [U_75,U_78,U_76,U_77,U_72,U_73,U_74] :
( sP23(U_75,U_78,U_76,U_77,U_72,U_73,U_74)
| ~ relation(U_72)
| ~ relation(U_73) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP19,sP20,sP21,sP22,sP23])],[f_16_7]) ).
cnf(f_16_9,plain,
( sP23(U_75,U_78,U_76,U_77,U_72,U_73,U_74)
| ~ relation(U_72)
| ~ relation(U_73) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_10,plain,
( sP20(U_75,U_78,U_76,U_77,U_72,U_73,U_74)
| U_72 != relation_rng_restriction(U_74,U_73)
| ~ sP23(U_75,U_78,U_76,U_77,U_72,U_73,U_74) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_11,plain,
( U_72 = relation_rng_restriction(U_74,U_73)
| sP22(U_72,U_73,U_74)
| sP21(U_72,U_73,U_74)
| ~ sP23(U_75,U_78,U_76,U_77,U_72,U_73,U_74) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_12,plain,
( sP19(U_75,U_77,U_73,U_74)
| ~ in(ordered_pair(U_77,U_75),U_72)
| ~ sP20(U_75,U_78,U_76,U_77,U_72,U_73,U_74) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_13,plain,
( in(ordered_pair(U_78,U_76),U_72)
| ~ in(ordered_pair(U_78,U_76),U_73)
| ~ in(U_76,U_74)
| ~ sP20(U_75,U_78,U_76,U_77,U_72,U_73,U_74) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_14,plain,
( in(U_75,U_74)
| ~ sP19(U_75,U_77,U_73,U_74) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_15,plain,
( in(ordered_pair(U_77,U_75),U_73)
| ~ sP19(U_75,U_77,U_73,U_74) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_16,plain,
( in(ordered_pair(sK13(U_74,U_73,U_72),sK14(U_74,U_73,U_72)),U_72)
| ~ sP21(U_72,U_73,U_74) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_17,plain,
( ~ in(ordered_pair(sK13(U_74,U_73,U_72),sK14(U_74,U_73,U_72)),U_73)
| ~ in(sK14(U_74,U_73,U_72),U_74)
| ~ sP21(U_72,U_73,U_74) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_18,plain,
( in(sK16(U_74,U_73,U_72),U_74)
| ~ sP22(U_72,U_73,U_74) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_19,plain,
( in(ordered_pair(sK15(U_74,U_73,U_72),sK16(U_74,U_73,U_72)),U_73)
| ~ sP22(U_72,U_73,U_74) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_20,plain,
( ~ in(ordered_pair(sK15(U_74,U_73,U_72),sK16(U_74,U_73,U_72)),U_72)
| ~ sP22(U_72,U_73,U_74) ),
inference(clausify,[status(thm)],[f_16_8]) ).
fof(f_17_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_17_2,plain,
! [U_87] :
( ! [U_86,U_85] :
( ( U_85 = relation_inverse_image(U_87,U_86)
| ? [U_84] :
( ( ~ in(U_84,U_85)
& in(apply(U_87,U_84),U_86)
& in(U_84,relation_dom(U_87)) )
| ( ( ~ in(apply(U_87,U_84),U_86)
| ~ in(U_84,relation_dom(U_87)) )
& in(U_84,U_85) ) ) )
& ( ! [U_83] :
( ( in(U_83,U_85)
| ~ in(apply(U_87,U_83),U_86)
| ~ in(U_83,relation_dom(U_87)) )
& ( ( in(apply(U_87,U_83),U_86)
& in(U_83,relation_dom(U_87)) )
| ~ in(U_83,U_85) ) )
| U_85 != relation_inverse_image(U_87,U_86) ) )
| ~ function(U_87)
| ~ relation(U_87) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_87] :
( ( ! [U_95,U_93] :
( U_93 = relation_inverse_image(U_87,U_95)
| ? [U_91] :
( ~ in(U_91,U_93)
& in(apply(U_87,U_91),U_95)
& in(U_91,relation_dom(U_87)) )
| ? [U_90] :
( ( ~ in(apply(U_87,U_90),U_95)
| ~ in(U_90,relation_dom(U_87)) )
& in(U_90,U_93) ) )
& ! [U_94,U_92] :
( ( ! [U_89] :
( in(U_89,U_92)
| ~ in(apply(U_87,U_89),U_94)
| ~ in(U_89,relation_dom(U_87)) )
& ! [U_88] :
( ( in(apply(U_87,U_88),U_94)
& in(U_88,relation_dom(U_87)) )
| ~ in(U_88,U_92) ) )
| U_92 != relation_inverse_image(U_87,U_94) ) )
| ~ function(U_87)
| ~ relation(U_87) ),
inference(miniscope,[status(thm)],[f_17_2]) ).
fof(f_17_4,plain,
! [U_87] :
( ( ! [U_95,U_93] :
( U_93 = relation_inverse_image(U_87,U_95)
| ? [U_91] :
( ~ in(U_91,U_93)
& in(apply(U_87,U_91),U_95)
& in(U_91,relation_dom(U_87)) )
| ( ( ~ in(apply(U_87,sK17(U_87,U_95,U_93)),U_95)
| ~ in(sK17(U_87,U_95,U_93),relation_dom(U_87)) )
& in(sK17(U_87,U_95,U_93),U_93) ) )
& ! [U_94,U_92] :
( ( ! [U_89] :
( in(U_89,U_92)
| ~ in(apply(U_87,U_89),U_94)
| ~ in(U_89,relation_dom(U_87)) )
& ! [U_88] :
( ( in(apply(U_87,U_88),U_94)
& in(U_88,relation_dom(U_87)) )
| ~ in(U_88,U_92) ) )
| U_92 != relation_inverse_image(U_87,U_94) ) )
| ~ function(U_87)
| ~ relation(U_87) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_90,sK17(U_87,U_95,U_93))],[f_17_3]) ).
fof(f_17_5,plain,
! [U_87] :
( ( ! [U_95,U_93] :
( U_93 = relation_inverse_image(U_87,U_95)
| ( ~ in(sK18(U_87,U_95,U_93),U_93)
& in(apply(U_87,sK18(U_87,U_95,U_93)),U_95)
& in(sK18(U_87,U_95,U_93),relation_dom(U_87)) )
| ( ( ~ in(apply(U_87,sK17(U_87,U_95,U_93)),U_95)
| ~ in(sK17(U_87,U_95,U_93),relation_dom(U_87)) )
& in(sK17(U_87,U_95,U_93),U_93) ) )
& ! [U_94,U_92] :
( ( ! [U_89] :
( in(U_89,U_92)
| ~ in(apply(U_87,U_89),U_94)
| ~ in(U_89,relation_dom(U_87)) )
& ! [U_88] :
( ( in(apply(U_87,U_88),U_94)
& in(U_88,relation_dom(U_87)) )
| ~ in(U_88,U_92) ) )
| U_92 != relation_inverse_image(U_87,U_94) ) )
| ~ function(U_87)
| ~ relation(U_87) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_91,sK18(U_87,U_95,U_93))],[f_17_4]) ).
fof(f_17_6,plain,
( ! [U_95,U_87,U_93] :
( ~ in(sK18(U_87,U_95,U_93),U_93)
| ~ sP27(U_95,U_87,U_93) )
& ! [U_95,U_87,U_93] :
( in(apply(U_87,sK18(U_87,U_95,U_93)),U_95)
| ~ sP27(U_95,U_87,U_93) )
& ! [U_95,U_87,U_93] :
( in(sK18(U_87,U_95,U_93),relation_dom(U_87))
| ~ sP27(U_95,U_87,U_93) )
& ! [U_95,U_87,U_93] :
( ~ in(apply(U_87,sK17(U_87,U_95,U_93)),U_95)
| ~ in(sK17(U_87,U_95,U_93),relation_dom(U_87))
| ~ sP26(U_95,U_87,U_93) )
& ! [U_95,U_87,U_93] :
( in(sK17(U_87,U_95,U_93),U_93)
| ~ sP26(U_95,U_87,U_93) )
& ! [U_87,U_88,U_94] :
( in(apply(U_87,U_88),U_94)
| ~ sP24(U_87,U_88,U_94) )
& ! [U_87,U_88,U_94] :
( in(U_88,relation_dom(U_87))
| ~ sP24(U_87,U_88,U_94) )
& ! [U_87,U_89,U_88,U_94,U_92] :
( in(U_89,U_92)
| ~ in(apply(U_87,U_89),U_94)
| ~ in(U_89,relation_dom(U_87))
| ~ sP25(U_87,U_89,U_88,U_94,U_92) )
& ! [U_87,U_89,U_88,U_94,U_92] :
( sP24(U_87,U_88,U_94)
| ~ in(U_88,U_92)
| ~ sP25(U_87,U_89,U_88,U_94,U_92) )
& ! [U_95,U_87,U_89,U_88,U_93,U_94,U_92] :
( U_93 = relation_inverse_image(U_87,U_95)
| sP27(U_95,U_87,U_93)
| sP26(U_95,U_87,U_93)
| ~ sP28(U_95,U_87,U_89,U_88,U_93,U_94,U_92) )
& ! [U_95,U_87,U_89,U_88,U_93,U_94,U_92] :
( sP25(U_87,U_89,U_88,U_94,U_92)
| U_92 != relation_inverse_image(U_87,U_94)
| ~ sP28(U_95,U_87,U_89,U_88,U_93,U_94,U_92) )
& ! [U_95,U_87,U_89,U_88,U_93,U_94,U_92] :
( sP28(U_95,U_87,U_89,U_88,U_93,U_94,U_92)
| ~ function(U_87)
| ~ relation(U_87) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP24,sP25,sP26,sP27,sP28])],[f_17_5]) ).
cnf(f_17_7,plain,
( sP28(U_95,U_87,U_89,U_88,U_93,U_94,U_92)
| ~ function(U_87)
| ~ relation(U_87) ),
inference(clausify,[status(thm)],[f_17_6]) ).
cnf(f_17_8,plain,
( sP25(U_87,U_89,U_88,U_94,U_92)
| U_92 != relation_inverse_image(U_87,U_94)
| ~ sP28(U_95,U_87,U_89,U_88,U_93,U_94,U_92) ),
inference(clausify,[status(thm)],[f_17_6]) ).
cnf(f_17_9,plain,
( U_93 = relation_inverse_image(U_87,U_95)
| sP27(U_95,U_87,U_93)
| sP26(U_95,U_87,U_93)
| ~ sP28(U_95,U_87,U_89,U_88,U_93,U_94,U_92) ),
inference(clausify,[status(thm)],[f_17_6]) ).
cnf(f_17_10,plain,
( sP24(U_87,U_88,U_94)
| ~ in(U_88,U_92)
| ~ sP25(U_87,U_89,U_88,U_94,U_92) ),
inference(clausify,[status(thm)],[f_17_6]) ).
cnf(f_17_11,plain,
( in(U_89,U_92)
| ~ in(apply(U_87,U_89),U_94)
| ~ in(U_89,relation_dom(U_87))
| ~ sP25(U_87,U_89,U_88,U_94,U_92) ),
inference(clausify,[status(thm)],[f_17_6]) ).
cnf(f_17_12,plain,
( in(U_88,relation_dom(U_87))
| ~ sP24(U_87,U_88,U_94) ),
inference(clausify,[status(thm)],[f_17_6]) ).
cnf(f_17_13,plain,
( in(apply(U_87,U_88),U_94)
| ~ sP24(U_87,U_88,U_94) ),
inference(clausify,[status(thm)],[f_17_6]) ).
cnf(f_17_14,plain,
( in(sK17(U_87,U_95,U_93),U_93)
| ~ sP26(U_95,U_87,U_93) ),
inference(clausify,[status(thm)],[f_17_6]) ).
cnf(f_17_15,plain,
( ~ in(apply(U_87,sK17(U_87,U_95,U_93)),U_95)
| ~ in(sK17(U_87,U_95,U_93),relation_dom(U_87))
| ~ sP26(U_95,U_87,U_93) ),
inference(clausify,[status(thm)],[f_17_6]) ).
cnf(f_17_16,plain,
( in(sK18(U_87,U_95,U_93),relation_dom(U_87))
| ~ sP27(U_95,U_87,U_93) ),
inference(clausify,[status(thm)],[f_17_6]) ).
cnf(f_17_17,plain,
( in(apply(U_87,sK18(U_87,U_95,U_93)),U_95)
| ~ sP27(U_95,U_87,U_93) ),
inference(clausify,[status(thm)],[f_17_6]) ).
cnf(f_17_18,plain,
( ~ in(sK18(U_87,U_95,U_93),U_93)
| ~ sP27(U_95,U_87,U_93) ),
inference(clausify,[status(thm)],[f_17_6]) ).
fof(f_18_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_18_2,plain,
! [U_104] :
( ! [U_103,U_102] :
( ( U_102 = relation_image(U_104,U_103)
| ? [U_101] :
( ( ~ in(U_101,U_102)
& ? [U_100] :
( in(U_100,U_103)
& in(ordered_pair(U_100,U_101),U_104) ) )
| ( ! [U_99] :
( ~ in(U_99,U_103)
| ~ in(ordered_pair(U_99,U_101),U_104) )
& in(U_101,U_102) ) ) )
& ( ! [U_98] :
( ( in(U_98,U_102)
| ! [U_97] :
( ~ in(U_97,U_103)
| ~ in(ordered_pair(U_97,U_98),U_104) ) )
& ( ? [U_96] :
( in(U_96,U_103)
& in(ordered_pair(U_96,U_98),U_104) )
| ~ in(U_98,U_102) ) )
| U_102 != relation_image(U_104,U_103) ) )
| ~ relation(U_104) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_104] :
( ( ! [U_112,U_110] :
( U_110 = relation_image(U_104,U_112)
| ? [U_108] :
( ~ in(U_108,U_110)
& ? [U_100] :
( in(U_100,U_112)
& in(ordered_pair(U_100,U_108),U_104) ) )
| ? [U_107] :
( ! [U_99] :
( ~ in(U_99,U_112)
| ~ in(ordered_pair(U_99,U_107),U_104) )
& in(U_107,U_110) ) )
& ! [U_111,U_109] :
( ( ! [U_106] :
( in(U_106,U_109)
| ! [U_97] :
( ~ in(U_97,U_111)
| ~ in(ordered_pair(U_97,U_106),U_104) ) )
& ! [U_105] :
( ? [U_96] :
( in(U_96,U_111)
& in(ordered_pair(U_96,U_105),U_104) )
| ~ in(U_105,U_109) ) )
| U_109 != relation_image(U_104,U_111) ) )
| ~ relation(U_104) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
fof(f_18_4,plain,
! [U_104] :
( ( ! [U_112,U_110] :
( U_110 = relation_image(U_104,U_112)
| ? [U_108] :
( ~ in(U_108,U_110)
& ? [U_100] :
( in(U_100,U_112)
& in(ordered_pair(U_100,U_108),U_104) ) )
| ? [U_107] :
( ! [U_99] :
( ~ in(U_99,U_112)
| ~ in(ordered_pair(U_99,U_107),U_104) )
& in(U_107,U_110) ) )
& ! [U_111,U_109] :
( ( ! [U_106] :
( in(U_106,U_109)
| ! [U_97] :
( ~ in(U_97,U_111)
| ~ in(ordered_pair(U_97,U_106),U_104) ) )
& ! [U_105] :
( ( in(sK19(U_104,U_111,U_109,U_105),U_111)
& in(ordered_pair(sK19(U_104,U_111,U_109,U_105),U_105),U_104) )
| ~ in(U_105,U_109) ) )
| U_109 != relation_image(U_104,U_111) ) )
| ~ relation(U_104) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_96,sK19(U_104,U_111,U_109,U_105))],[f_18_3]) ).
fof(f_18_5,plain,
! [U_104] :
( ( ! [U_112,U_110] :
( U_110 = relation_image(U_104,U_112)
| ? [U_108] :
( ~ in(U_108,U_110)
& ? [U_100] :
( in(U_100,U_112)
& in(ordered_pair(U_100,U_108),U_104) ) )
| ( ! [U_99] :
( ~ in(U_99,U_112)
| ~ in(ordered_pair(U_99,sK20(U_104,U_112,U_110)),U_104) )
& in(sK20(U_104,U_112,U_110),U_110) ) )
& ! [U_111,U_109] :
( ( ! [U_106] :
( in(U_106,U_109)
| ! [U_97] :
( ~ in(U_97,U_111)
| ~ in(ordered_pair(U_97,U_106),U_104) ) )
& ! [U_105] :
( ( in(sK19(U_104,U_111,U_109,U_105),U_111)
& in(ordered_pair(sK19(U_104,U_111,U_109,U_105),U_105),U_104) )
| ~ in(U_105,U_109) ) )
| U_109 != relation_image(U_104,U_111) ) )
| ~ relation(U_104) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_107,sK20(U_104,U_112,U_110))],[f_18_4]) ).
fof(f_18_6,plain,
! [U_104] :
( ( ! [U_112,U_110] :
( U_110 = relation_image(U_104,U_112)
| ( ~ in(sK21(U_104,U_112,U_110),U_110)
& ? [U_100] :
( in(U_100,U_112)
& in(ordered_pair(U_100,sK21(U_104,U_112,U_110)),U_104) ) )
| ( ! [U_99] :
( ~ in(U_99,U_112)
| ~ in(ordered_pair(U_99,sK20(U_104,U_112,U_110)),U_104) )
& in(sK20(U_104,U_112,U_110),U_110) ) )
& ! [U_111,U_109] :
( ( ! [U_106] :
( in(U_106,U_109)
| ! [U_97] :
( ~ in(U_97,U_111)
| ~ in(ordered_pair(U_97,U_106),U_104) ) )
& ! [U_105] :
( ( in(sK19(U_104,U_111,U_109,U_105),U_111)
& in(ordered_pair(sK19(U_104,U_111,U_109,U_105),U_105),U_104) )
| ~ in(U_105,U_109) ) )
| U_109 != relation_image(U_104,U_111) ) )
| ~ relation(U_104) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_108,sK21(U_104,U_112,U_110))],[f_18_5]) ).
fof(f_18_7,plain,
! [U_104] :
( ( ! [U_112,U_110] :
( U_110 = relation_image(U_104,U_112)
| ( ~ in(sK21(U_104,U_112,U_110),U_110)
& in(sK22(U_104,U_112,U_110),U_112)
& in(ordered_pair(sK22(U_104,U_112,U_110),sK21(U_104,U_112,U_110)),U_104) )
| ( ! [U_99] :
( ~ in(U_99,U_112)
| ~ in(ordered_pair(U_99,sK20(U_104,U_112,U_110)),U_104) )
& in(sK20(U_104,U_112,U_110),U_110) ) )
& ! [U_111,U_109] :
( ( ! [U_106] :
( in(U_106,U_109)
| ! [U_97] :
( ~ in(U_97,U_111)
| ~ in(ordered_pair(U_97,U_106),U_104) ) )
& ! [U_105] :
( ( in(sK19(U_104,U_111,U_109,U_105),U_111)
& in(ordered_pair(sK19(U_104,U_111,U_109,U_105),U_105),U_104) )
| ~ in(U_105,U_109) ) )
| U_109 != relation_image(U_104,U_111) ) )
| ~ relation(U_104) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_100,sK22(U_104,U_112,U_110))],[f_18_6]) ).
fof(f_18_8,plain,
( ! [U_110,U_112,U_104] :
( ~ in(sK21(U_104,U_112,U_110),U_110)
| ~ sP32(U_110,U_112,U_104) )
& ! [U_110,U_112,U_104] :
( in(sK22(U_104,U_112,U_110),U_112)
| ~ sP32(U_110,U_112,U_104) )
& ! [U_110,U_112,U_104] :
( in(ordered_pair(sK22(U_104,U_112,U_110),sK21(U_104,U_112,U_110)),U_104)
| ~ sP32(U_110,U_112,U_104) )
& ! [U_110,U_99,U_112,U_104] :
( ~ in(U_99,U_112)
| ~ in(ordered_pair(U_99,sK20(U_104,U_112,U_110)),U_104)
| ~ sP31(U_110,U_99,U_112,U_104) )
& ! [U_110,U_99,U_112,U_104] :
( in(sK20(U_104,U_112,U_110),U_110)
| ~ sP31(U_110,U_99,U_112,U_104) )
& ! [U_104,U_111,U_109,U_105] :
( in(sK19(U_104,U_111,U_109,U_105),U_111)
| ~ sP29(U_104,U_111,U_109,U_105) )
& ! [U_104,U_111,U_109,U_105] :
( in(ordered_pair(sK19(U_104,U_111,U_109,U_105),U_105),U_104)
| ~ sP29(U_104,U_111,U_109,U_105) )
& ! [U_106,U_104,U_111,U_97,U_109,U_105] :
( in(U_106,U_109)
| ~ in(U_97,U_111)
| ~ in(ordered_pair(U_97,U_106),U_104)
| ~ sP30(U_106,U_104,U_111,U_97,U_109,U_105) )
& ! [U_106,U_104,U_111,U_97,U_109,U_105] :
( sP29(U_104,U_111,U_109,U_105)
| ~ in(U_105,U_109)
| ~ sP30(U_106,U_104,U_111,U_97,U_109,U_105) )
& ! [U_110,U_99,U_106,U_112,U_104,U_111,U_97,U_109,U_105] :
( U_110 = relation_image(U_104,U_112)
| sP32(U_110,U_112,U_104)
| sP31(U_110,U_99,U_112,U_104)
| ~ sP33(U_110,U_99,U_106,U_112,U_104,U_111,U_97,U_109,U_105) )
& ! [U_110,U_99,U_106,U_112,U_104,U_111,U_97,U_109,U_105] :
( sP30(U_106,U_104,U_111,U_97,U_109,U_105)
| U_109 != relation_image(U_104,U_111)
| ~ sP33(U_110,U_99,U_106,U_112,U_104,U_111,U_97,U_109,U_105) )
& ! [U_110,U_99,U_106,U_112,U_104,U_111,U_97,U_109,U_105] :
( sP33(U_110,U_99,U_106,U_112,U_104,U_111,U_97,U_109,U_105)
| ~ relation(U_104) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP29,sP30,sP31,sP32,sP33])],[f_18_7]) ).
cnf(f_18_9,plain,
( sP33(U_110,U_99,U_106,U_112,U_104,U_111,U_97,U_109,U_105)
| ~ relation(U_104) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_10,plain,
( sP30(U_106,U_104,U_111,U_97,U_109,U_105)
| U_109 != relation_image(U_104,U_111)
| ~ sP33(U_110,U_99,U_106,U_112,U_104,U_111,U_97,U_109,U_105) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_11,plain,
( U_110 = relation_image(U_104,U_112)
| sP32(U_110,U_112,U_104)
| sP31(U_110,U_99,U_112,U_104)
| ~ sP33(U_110,U_99,U_106,U_112,U_104,U_111,U_97,U_109,U_105) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_12,plain,
( sP29(U_104,U_111,U_109,U_105)
| ~ in(U_105,U_109)
| ~ sP30(U_106,U_104,U_111,U_97,U_109,U_105) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_13,plain,
( in(U_106,U_109)
| ~ in(U_97,U_111)
| ~ in(ordered_pair(U_97,U_106),U_104)
| ~ sP30(U_106,U_104,U_111,U_97,U_109,U_105) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_14,plain,
( in(ordered_pair(sK19(U_104,U_111,U_109,U_105),U_105),U_104)
| ~ sP29(U_104,U_111,U_109,U_105) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_15,plain,
( in(sK19(U_104,U_111,U_109,U_105),U_111)
| ~ sP29(U_104,U_111,U_109,U_105) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_16,plain,
( in(sK20(U_104,U_112,U_110),U_110)
| ~ sP31(U_110,U_99,U_112,U_104) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_17,plain,
( ~ in(U_99,U_112)
| ~ in(ordered_pair(U_99,sK20(U_104,U_112,U_110)),U_104)
| ~ sP31(U_110,U_99,U_112,U_104) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_18,plain,
( in(ordered_pair(sK22(U_104,U_112,U_110),sK21(U_104,U_112,U_110)),U_104)
| ~ sP32(U_110,U_112,U_104) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_19,plain,
( in(sK22(U_104,U_112,U_110),U_112)
| ~ sP32(U_110,U_112,U_104) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_20,plain,
( ~ in(sK21(U_104,U_112,U_110),U_110)
| ~ sP32(U_110,U_112,U_104) ),
inference(clausify,[status(thm)],[f_18_8]) ).
fof(f_19_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_19_2,plain,
! [U_121] :
( ! [U_120,U_119] :
( ( U_119 = relation_inverse_image(U_121,U_120)
| ? [U_118] :
( ( ~ in(U_118,U_119)
& ? [U_117] :
( in(U_117,U_120)
& in(ordered_pair(U_118,U_117),U_121) ) )
| ( ! [U_116] :
( ~ in(U_116,U_120)
| ~ in(ordered_pair(U_118,U_116),U_121) )
& in(U_118,U_119) ) ) )
& ( ! [U_115] :
( ( in(U_115,U_119)
| ! [U_114] :
( ~ in(U_114,U_120)
| ~ in(ordered_pair(U_115,U_114),U_121) ) )
& ( ? [U_113] :
( in(U_113,U_120)
& in(ordered_pair(U_115,U_113),U_121) )
| ~ in(U_115,U_119) ) )
| U_119 != relation_inverse_image(U_121,U_120) ) )
| ~ relation(U_121) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_121] :
( ( ! [U_129,U_127] :
( U_127 = relation_inverse_image(U_121,U_129)
| ? [U_125] :
( ~ in(U_125,U_127)
& ? [U_117] :
( in(U_117,U_129)
& in(ordered_pair(U_125,U_117),U_121) ) )
| ? [U_124] :
( ! [U_116] :
( ~ in(U_116,U_129)
| ~ in(ordered_pair(U_124,U_116),U_121) )
& in(U_124,U_127) ) )
& ! [U_128,U_126] :
( ( ! [U_123] :
( in(U_123,U_126)
| ! [U_114] :
( ~ in(U_114,U_128)
| ~ in(ordered_pair(U_123,U_114),U_121) ) )
& ! [U_122] :
( ? [U_113] :
( in(U_113,U_128)
& in(ordered_pair(U_122,U_113),U_121) )
| ~ in(U_122,U_126) ) )
| U_126 != relation_inverse_image(U_121,U_128) ) )
| ~ relation(U_121) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
fof(f_19_4,plain,
! [U_121] :
( ( ! [U_129,U_127] :
( U_127 = relation_inverse_image(U_121,U_129)
| ? [U_125] :
( ~ in(U_125,U_127)
& ? [U_117] :
( in(U_117,U_129)
& in(ordered_pair(U_125,U_117),U_121) ) )
| ? [U_124] :
( ! [U_116] :
( ~ in(U_116,U_129)
| ~ in(ordered_pair(U_124,U_116),U_121) )
& in(U_124,U_127) ) )
& ! [U_128,U_126] :
( ( ! [U_123] :
( in(U_123,U_126)
| ! [U_114] :
( ~ in(U_114,U_128)
| ~ in(ordered_pair(U_123,U_114),U_121) ) )
& ! [U_122] :
( ( in(sK23(U_121,U_128,U_126,U_122),U_128)
& in(ordered_pair(U_122,sK23(U_121,U_128,U_126,U_122)),U_121) )
| ~ in(U_122,U_126) ) )
| U_126 != relation_inverse_image(U_121,U_128) ) )
| ~ relation(U_121) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_113,sK23(U_121,U_128,U_126,U_122))],[f_19_3]) ).
fof(f_19_5,plain,
! [U_121] :
( ( ! [U_129,U_127] :
( U_127 = relation_inverse_image(U_121,U_129)
| ? [U_125] :
( ~ in(U_125,U_127)
& ? [U_117] :
( in(U_117,U_129)
& in(ordered_pair(U_125,U_117),U_121) ) )
| ( ! [U_116] :
( ~ in(U_116,U_129)
| ~ in(ordered_pair(sK24(U_121,U_129,U_127),U_116),U_121) )
& in(sK24(U_121,U_129,U_127),U_127) ) )
& ! [U_128,U_126] :
( ( ! [U_123] :
( in(U_123,U_126)
| ! [U_114] :
( ~ in(U_114,U_128)
| ~ in(ordered_pair(U_123,U_114),U_121) ) )
& ! [U_122] :
( ( in(sK23(U_121,U_128,U_126,U_122),U_128)
& in(ordered_pair(U_122,sK23(U_121,U_128,U_126,U_122)),U_121) )
| ~ in(U_122,U_126) ) )
| U_126 != relation_inverse_image(U_121,U_128) ) )
| ~ relation(U_121) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_124,sK24(U_121,U_129,U_127))],[f_19_4]) ).
fof(f_19_6,plain,
! [U_121] :
( ( ! [U_129,U_127] :
( U_127 = relation_inverse_image(U_121,U_129)
| ( ~ in(sK25(U_121,U_129,U_127),U_127)
& ? [U_117] :
( in(U_117,U_129)
& in(ordered_pair(sK25(U_121,U_129,U_127),U_117),U_121) ) )
| ( ! [U_116] :
( ~ in(U_116,U_129)
| ~ in(ordered_pair(sK24(U_121,U_129,U_127),U_116),U_121) )
& in(sK24(U_121,U_129,U_127),U_127) ) )
& ! [U_128,U_126] :
( ( ! [U_123] :
( in(U_123,U_126)
| ! [U_114] :
( ~ in(U_114,U_128)
| ~ in(ordered_pair(U_123,U_114),U_121) ) )
& ! [U_122] :
( ( in(sK23(U_121,U_128,U_126,U_122),U_128)
& in(ordered_pair(U_122,sK23(U_121,U_128,U_126,U_122)),U_121) )
| ~ in(U_122,U_126) ) )
| U_126 != relation_inverse_image(U_121,U_128) ) )
| ~ relation(U_121) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_125,sK25(U_121,U_129,U_127))],[f_19_5]) ).
fof(f_19_7,plain,
! [U_121] :
( ( ! [U_129,U_127] :
( U_127 = relation_inverse_image(U_121,U_129)
| ( ~ in(sK25(U_121,U_129,U_127),U_127)
& in(sK26(U_121,U_129,U_127),U_129)
& in(ordered_pair(sK25(U_121,U_129,U_127),sK26(U_121,U_129,U_127)),U_121) )
| ( ! [U_116] :
( ~ in(U_116,U_129)
| ~ in(ordered_pair(sK24(U_121,U_129,U_127),U_116),U_121) )
& in(sK24(U_121,U_129,U_127),U_127) ) )
& ! [U_128,U_126] :
( ( ! [U_123] :
( in(U_123,U_126)
| ! [U_114] :
( ~ in(U_114,U_128)
| ~ in(ordered_pair(U_123,U_114),U_121) ) )
& ! [U_122] :
( ( in(sK23(U_121,U_128,U_126,U_122),U_128)
& in(ordered_pair(U_122,sK23(U_121,U_128,U_126,U_122)),U_121) )
| ~ in(U_122,U_126) ) )
| U_126 != relation_inverse_image(U_121,U_128) ) )
| ~ relation(U_121) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_117,sK26(U_121,U_129,U_127))],[f_19_6]) ).
fof(f_19_8,plain,
( ! [U_129,U_127,U_121] :
( ~ in(sK25(U_121,U_129,U_127),U_127)
| ~ sP37(U_129,U_127,U_121) )
& ! [U_129,U_127,U_121] :
( in(sK26(U_121,U_129,U_127),U_129)
| ~ sP37(U_129,U_127,U_121) )
& ! [U_129,U_127,U_121] :
( in(ordered_pair(sK25(U_121,U_129,U_127),sK26(U_121,U_129,U_127)),U_121)
| ~ sP37(U_129,U_127,U_121) )
& ! [U_129,U_127,U_116,U_121] :
( ~ in(U_116,U_129)
| ~ in(ordered_pair(sK24(U_121,U_129,U_127),U_116),U_121)
| ~ sP36(U_129,U_127,U_116,U_121) )
& ! [U_129,U_127,U_116,U_121] :
( in(sK24(U_121,U_129,U_127),U_127)
| ~ sP36(U_129,U_127,U_116,U_121) )
& ! [U_122,U_128,U_126,U_121] :
( in(sK23(U_121,U_128,U_126,U_122),U_128)
| ~ sP34(U_122,U_128,U_126,U_121) )
& ! [U_122,U_128,U_126,U_121] :
( in(ordered_pair(U_122,sK23(U_121,U_128,U_126,U_122)),U_121)
| ~ sP34(U_122,U_128,U_126,U_121) )
& ! [U_123,U_122,U_114,U_128,U_126,U_121] :
( in(U_123,U_126)
| ~ in(U_114,U_128)
| ~ in(ordered_pair(U_123,U_114),U_121)
| ~ sP35(U_123,U_122,U_114,U_128,U_126,U_121) )
& ! [U_123,U_122,U_114,U_128,U_126,U_121] :
( sP34(U_122,U_128,U_126,U_121)
| ~ in(U_122,U_126)
| ~ sP35(U_123,U_122,U_114,U_128,U_126,U_121) )
& ! [U_123,U_122,U_129,U_127,U_116,U_114,U_128,U_126,U_121] :
( U_127 = relation_inverse_image(U_121,U_129)
| sP37(U_129,U_127,U_121)
| sP36(U_129,U_127,U_116,U_121)
| ~ sP38(U_123,U_122,U_129,U_127,U_116,U_114,U_128,U_126,U_121) )
& ! [U_123,U_122,U_129,U_127,U_116,U_114,U_128,U_126,U_121] :
( sP35(U_123,U_122,U_114,U_128,U_126,U_121)
| U_126 != relation_inverse_image(U_121,U_128)
| ~ sP38(U_123,U_122,U_129,U_127,U_116,U_114,U_128,U_126,U_121) )
& ! [U_123,U_122,U_129,U_127,U_116,U_114,U_128,U_126,U_121] :
( sP38(U_123,U_122,U_129,U_127,U_116,U_114,U_128,U_126,U_121)
| ~ relation(U_121) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP34,sP35,sP36,sP37,sP38])],[f_19_7]) ).
cnf(f_19_9,plain,
( sP38(U_123,U_122,U_129,U_127,U_116,U_114,U_128,U_126,U_121)
| ~ relation(U_121) ),
inference(clausify,[status(thm)],[f_19_8]) ).
cnf(f_19_10,plain,
( sP35(U_123,U_122,U_114,U_128,U_126,U_121)
| U_126 != relation_inverse_image(U_121,U_128)
| ~ sP38(U_123,U_122,U_129,U_127,U_116,U_114,U_128,U_126,U_121) ),
inference(clausify,[status(thm)],[f_19_8]) ).
cnf(f_19_11,plain,
( U_127 = relation_inverse_image(U_121,U_129)
| sP37(U_129,U_127,U_121)
| sP36(U_129,U_127,U_116,U_121)
| ~ sP38(U_123,U_122,U_129,U_127,U_116,U_114,U_128,U_126,U_121) ),
inference(clausify,[status(thm)],[f_19_8]) ).
cnf(f_19_12,plain,
( sP34(U_122,U_128,U_126,U_121)
| ~ in(U_122,U_126)
| ~ sP35(U_123,U_122,U_114,U_128,U_126,U_121) ),
inference(clausify,[status(thm)],[f_19_8]) ).
cnf(f_19_13,plain,
( in(U_123,U_126)
| ~ in(U_114,U_128)
| ~ in(ordered_pair(U_123,U_114),U_121)
| ~ sP35(U_123,U_122,U_114,U_128,U_126,U_121) ),
inference(clausify,[status(thm)],[f_19_8]) ).
cnf(f_19_14,plain,
( in(ordered_pair(U_122,sK23(U_121,U_128,U_126,U_122)),U_121)
| ~ sP34(U_122,U_128,U_126,U_121) ),
inference(clausify,[status(thm)],[f_19_8]) ).
cnf(f_19_15,plain,
( in(sK23(U_121,U_128,U_126,U_122),U_128)
| ~ sP34(U_122,U_128,U_126,U_121) ),
inference(clausify,[status(thm)],[f_19_8]) ).
cnf(f_19_16,plain,
( in(sK24(U_121,U_129,U_127),U_127)
| ~ sP36(U_129,U_127,U_116,U_121) ),
inference(clausify,[status(thm)],[f_19_8]) ).
cnf(f_19_17,plain,
( ~ in(U_116,U_129)
| ~ in(ordered_pair(sK24(U_121,U_129,U_127),U_116),U_121)
| ~ sP36(U_129,U_127,U_116,U_121) ),
inference(clausify,[status(thm)],[f_19_8]) ).
cnf(f_19_18,plain,
( in(ordered_pair(sK25(U_121,U_129,U_127),sK26(U_121,U_129,U_127)),U_121)
| ~ sP37(U_129,U_127,U_121) ),
inference(clausify,[status(thm)],[f_19_8]) ).
cnf(f_19_19,plain,
( in(sK26(U_121,U_129,U_127),U_129)
| ~ sP37(U_129,U_127,U_121) ),
inference(clausify,[status(thm)],[f_19_8]) ).
cnf(f_19_20,plain,
( ~ in(sK25(U_121,U_129,U_127),U_127)
| ~ sP37(U_129,U_127,U_121) ),
inference(clausify,[status(thm)],[f_19_8]) ).
fof(f_20_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_20_2,plain,
! [U_135,U_134,U_133,U_132] :
( ( U_132 = unordered_triple(U_135,U_134,U_133)
| ? [U_131] :
( ( ~ in(U_131,U_132)
& ( U_131 = U_133
| U_131 = U_134
| U_131 = U_135 ) )
| ( U_131 != U_133
& U_131 != U_134
& U_131 != U_135
& in(U_131,U_132) ) ) )
& ( ! [U_130] :
( ( in(U_130,U_132)
| ( U_130 != U_133
& U_130 != U_134
& U_130 != U_135 ) )
& ( U_130 = U_133
| U_130 = U_134
| U_130 = U_135
| ~ in(U_130,U_132) ) )
| U_132 != unordered_triple(U_135,U_134,U_133) ) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( ! [U_147,U_145,U_143,U_141] :
( U_141 = unordered_triple(U_147,U_145,U_143)
| ? [U_139] :
( ~ in(U_139,U_141)
& ( U_139 = U_143
| U_139 = U_145
| U_139 = U_147 ) )
| ? [U_138] :
( U_138 != U_143
& U_138 != U_145
& U_138 != U_147
& in(U_138,U_141) ) )
& ! [U_146,U_144,U_142,U_140] :
( ( ! [U_137] :
( in(U_137,U_140)
| ( U_137 != U_142
& U_137 != U_144
& U_137 != U_146 ) )
& ! [U_136] :
( U_136 = U_142
| U_136 = U_144
| U_136 = U_146
| ~ in(U_136,U_140) ) )
| U_140 != unordered_triple(U_146,U_144,U_142) ) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
fof(f_20_4,plain,
( ! [U_147,U_145,U_143,U_141] :
( U_141 = unordered_triple(U_147,U_145,U_143)
| ? [U_139] :
( ~ in(U_139,U_141)
& ( U_139 = U_143
| U_139 = U_145
| U_139 = U_147 ) )
| ( sK27(U_147,U_145,U_143,U_141) != U_143
& sK27(U_147,U_145,U_143,U_141) != U_145
& sK27(U_147,U_145,U_143,U_141) != U_147
& in(sK27(U_147,U_145,U_143,U_141),U_141) ) )
& ! [U_146,U_144,U_142,U_140] :
( ( ! [U_137] :
( in(U_137,U_140)
| ( U_137 != U_142
& U_137 != U_144
& U_137 != U_146 ) )
& ! [U_136] :
( U_136 = U_142
| U_136 = U_144
| U_136 = U_146
| ~ in(U_136,U_140) ) )
| U_140 != unordered_triple(U_146,U_144,U_142) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_138,sK27(U_147,U_145,U_143,U_141))],[f_20_3]) ).
fof(f_20_5,plain,
( ! [U_147,U_145,U_143,U_141] :
( U_141 = unordered_triple(U_147,U_145,U_143)
| ( ~ in(sK28(U_147,U_145,U_143,U_141),U_141)
& ( sK28(U_147,U_145,U_143,U_141) = U_143
| sK28(U_147,U_145,U_143,U_141) = U_145
| sK28(U_147,U_145,U_143,U_141) = U_147 ) )
| ( sK27(U_147,U_145,U_143,U_141) != U_143
& sK27(U_147,U_145,U_143,U_141) != U_145
& sK27(U_147,U_145,U_143,U_141) != U_147
& in(sK27(U_147,U_145,U_143,U_141),U_141) ) )
& ! [U_146,U_144,U_142,U_140] :
( ( ! [U_137] :
( in(U_137,U_140)
| ( U_137 != U_142
& U_137 != U_144
& U_137 != U_146 ) )
& ! [U_136] :
( U_136 = U_142
| U_136 = U_144
| U_136 = U_146
| ~ in(U_136,U_140) ) )
| U_140 != unordered_triple(U_146,U_144,U_142) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_139,sK28(U_147,U_145,U_143,U_141))],[f_20_4]) ).
fof(f_20_6,plain,
( ! [U_147,U_145,U_141,U_143] :
( ~ in(sK28(U_147,U_145,U_143,U_141),U_141)
| ~ sP42(U_147,U_145,U_141,U_143) )
& ! [U_147,U_145,U_141,U_143] :
( sK28(U_147,U_145,U_143,U_141) = U_143
| sK28(U_147,U_145,U_143,U_141) = U_145
| sK28(U_147,U_145,U_143,U_141) = U_147
| ~ sP42(U_147,U_145,U_141,U_143) )
& ! [U_147,U_145,U_141,U_143] :
( sK27(U_147,U_145,U_143,U_141) != U_143
| ~ sP41(U_147,U_145,U_141,U_143) )
& ! [U_147,U_145,U_141,U_143] :
( sK27(U_147,U_145,U_143,U_141) != U_145
| ~ sP41(U_147,U_145,U_141,U_143) )
& ! [U_147,U_145,U_141,U_143] :
( sK27(U_147,U_145,U_143,U_141) != U_147
| ~ sP41(U_147,U_145,U_141,U_143) )
& ! [U_147,U_145,U_141,U_143] :
( in(sK27(U_147,U_145,U_143,U_141),U_141)
| ~ sP41(U_147,U_145,U_141,U_143) )
& ! [U_142,U_146,U_144,U_137] :
( U_137 != U_142
| ~ sP39(U_142,U_146,U_144,U_137) )
& ! [U_142,U_146,U_144,U_137] :
( U_137 != U_144
| ~ sP39(U_142,U_146,U_144,U_137) )
& ! [U_142,U_146,U_144,U_137] :
( U_137 != U_146
| ~ sP39(U_142,U_146,U_144,U_137) )
& ! [U_136,U_142,U_146,U_140,U_144,U_137] :
( in(U_137,U_140)
| sP39(U_142,U_146,U_144,U_137)
| ~ sP40(U_136,U_142,U_146,U_140,U_144,U_137) )
& ! [U_136,U_142,U_146,U_140,U_144,U_137] :
( U_136 = U_142
| U_136 = U_144
| U_136 = U_146
| ~ in(U_136,U_140)
| ~ sP40(U_136,U_142,U_146,U_140,U_144,U_137) )
& ! [U_147,U_145,U_141,U_143] :
( U_141 = unordered_triple(U_147,U_145,U_143)
| sP42(U_147,U_145,U_141,U_143)
| sP41(U_147,U_145,U_141,U_143) )
& ! [U_136,U_142,U_146,U_140,U_144,U_137] :
( sP40(U_136,U_142,U_146,U_140,U_144,U_137)
| U_140 != unordered_triple(U_146,U_144,U_142) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP39,sP40,sP41,sP42])],[f_20_5]) ).
cnf(f_20_7,plain,
( sP40(U_136,U_142,U_146,U_140,U_144,U_137)
| U_140 != unordered_triple(U_146,U_144,U_142) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_8,plain,
( U_141 = unordered_triple(U_147,U_145,U_143)
| sP42(U_147,U_145,U_141,U_143)
| sP41(U_147,U_145,U_141,U_143) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_9,plain,
( U_136 = U_142
| U_136 = U_144
| U_136 = U_146
| ~ in(U_136,U_140)
| ~ sP40(U_136,U_142,U_146,U_140,U_144,U_137) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_10,plain,
( in(U_137,U_140)
| sP39(U_142,U_146,U_144,U_137)
| ~ sP40(U_136,U_142,U_146,U_140,U_144,U_137) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_11,plain,
( U_137 != U_146
| ~ sP39(U_142,U_146,U_144,U_137) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_12,plain,
( U_137 != U_144
| ~ sP39(U_142,U_146,U_144,U_137) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_13,plain,
( U_137 != U_142
| ~ sP39(U_142,U_146,U_144,U_137) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_14,plain,
( in(sK27(U_147,U_145,U_143,U_141),U_141)
| ~ sP41(U_147,U_145,U_141,U_143) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_15,plain,
( sK27(U_147,U_145,U_143,U_141) != U_147
| ~ sP41(U_147,U_145,U_141,U_143) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_16,plain,
( sK27(U_147,U_145,U_143,U_141) != U_145
| ~ sP41(U_147,U_145,U_141,U_143) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_17,plain,
( sK27(U_147,U_145,U_143,U_141) != U_143
| ~ sP41(U_147,U_145,U_141,U_143) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_18,plain,
( sK28(U_147,U_145,U_143,U_141) = U_143
| sK28(U_147,U_145,U_143,U_141) = U_145
| sK28(U_147,U_145,U_143,U_141) = U_147
| ~ sP42(U_147,U_145,U_141,U_143) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_19,plain,
( ~ in(sK28(U_147,U_145,U_143,U_141),U_141)
| ~ sP42(U_147,U_145,U_141,U_143) ),
inference(clausify,[status(thm)],[f_20_6]) ).
fof(f_21_1,plain,
! [A] : succ(A) = set_union2(A,singleton(A)),
inference(fof_nnf,[status(thm)],[d1_ordinal1]) ).
fof(f_21_2,plain,
! [U_148] : succ(U_148) = set_union2(U_148,singleton(U_148)),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_148] : succ(U_148) = set_union2(U_148,singleton(U_148)),
inference(definitional_conversion,[status(esa)],[f_21_2]) ).
cnf(f_21_4,plain,
succ(U_148) = set_union2(U_148,singleton(U_148)),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_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_22_2,plain,
! [U_155] :
( ( relation(U_155)
| ? [U_154] :
( ! [U_153,U_152] : U_154 != ordered_pair(U_153,U_152)
& in(U_154,U_155) ) )
& ( ! [U_151] :
( ? [U_150,U_149] : U_151 = ordered_pair(U_150,U_149)
| ~ in(U_151,U_155) )
| ~ relation(U_155) ) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( ! [U_157] :
( relation(U_157)
| ? [U_154] :
( ! [U_153,U_152] : U_154 != ordered_pair(U_153,U_152)
& in(U_154,U_157) ) )
& ! [U_156] :
( ! [U_151] :
( ? [U_150,U_149] : U_151 = ordered_pair(U_150,U_149)
| ~ in(U_151,U_156) )
| ~ relation(U_156) ) ),
inference(miniscope,[status(thm)],[f_22_2]) ).
fof(f_22_4,plain,
( ! [U_157] :
( relation(U_157)
| ? [U_154] :
( ! [U_153,U_152] : U_154 != ordered_pair(U_153,U_152)
& in(U_154,U_157) ) )
& ! [U_156] :
( ! [U_151] :
( ? [U_149] : U_151 = ordered_pair(sK29(U_156,U_151),U_149)
| ~ in(U_151,U_156) )
| ~ relation(U_156) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_150,sK29(U_156,U_151))],[f_22_3]) ).
fof(f_22_5,plain,
( ! [U_157] :
( relation(U_157)
| ? [U_154] :
( ! [U_153,U_152] : U_154 != ordered_pair(U_153,U_152)
& in(U_154,U_157) ) )
& ! [U_156] :
( ! [U_151] :
( U_151 = ordered_pair(sK29(U_156,U_151),sK30(U_156,U_151))
| ~ in(U_151,U_156) )
| ~ relation(U_156) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_149,sK30(U_156,U_151))],[f_22_4]) ).
fof(f_22_6,plain,
( ! [U_157] :
( relation(U_157)
| ( ! [U_153,U_152] : sK31(U_157) != ordered_pair(U_153,U_152)
& in(sK31(U_157),U_157) ) )
& ! [U_156] :
( ! [U_151] :
( U_151 = ordered_pair(sK29(U_156,U_151),sK30(U_156,U_151))
| ~ in(U_151,U_156) )
| ~ relation(U_156) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_154,sK31(U_157))],[f_22_5]) ).
fof(f_22_7,plain,
( ! [U_153,U_157,U_152] :
( sK31(U_157) != ordered_pair(U_153,U_152)
| ~ sP43(U_153,U_157,U_152) )
& ! [U_153,U_157,U_152] :
( in(sK31(U_157),U_157)
| ~ sP43(U_153,U_157,U_152) )
& ! [U_153,U_157,U_152] :
( relation(U_157)
| sP43(U_153,U_157,U_152) )
& ! [U_156,U_151] :
( U_151 = ordered_pair(sK29(U_156,U_151),sK30(U_156,U_151))
| ~ in(U_151,U_156)
| ~ relation(U_156) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP43])],[f_22_6]) ).
cnf(f_22_8,plain,
( U_151 = ordered_pair(sK29(U_156,U_151),sK30(U_156,U_151))
| ~ in(U_151,U_156)
| ~ relation(U_156) ),
inference(clausify,[status(thm)],[f_22_7]) ).
cnf(f_22_9,plain,
( relation(U_157)
| sP43(U_153,U_157,U_152) ),
inference(clausify,[status(thm)],[f_22_7]) ).
cnf(f_22_10,plain,
( in(sK31(U_157),U_157)
| ~ sP43(U_153,U_157,U_152) ),
inference(clausify,[status(thm)],[f_22_7]) ).
cnf(f_22_11,plain,
( sK31(U_157) != ordered_pair(U_153,U_152)
| ~ sP43(U_153,U_157,U_152) ),
inference(clausify,[status(thm)],[f_22_7]) ).
fof(f_23_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_23_2,plain,
! [U_165,U_164] :
( ( ( ( U_164 = set_meet(U_165)
| U_164 != empty_set )
& ( U_164 = empty_set
| U_164 != set_meet(U_165) ) )
| U_165 != empty_set )
& ( ( ( U_164 = set_meet(U_165)
| ? [U_163] :
( ( ~ in(U_163,U_164)
& ! [U_162] :
( in(U_163,U_162)
| ~ in(U_162,U_165) ) )
| ( ? [U_161] :
( ~ in(U_163,U_161)
& in(U_161,U_165) )
& in(U_163,U_164) ) ) )
& ( ! [U_160] :
( ( in(U_160,U_164)
| ? [U_159] :
( ~ in(U_160,U_159)
& in(U_159,U_165) ) )
& ( ! [U_158] :
( in(U_160,U_158)
| ~ in(U_158,U_165) )
| ~ in(U_160,U_164) ) )
| U_164 != set_meet(U_165) ) )
| U_165 = empty_set ) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( ! [U_177] :
( ( ! [U_175] :
( U_175 = set_meet(U_177)
| U_175 != empty_set )
& ! [U_174] :
( U_174 = empty_set
| U_174 != set_meet(U_177) ) )
| U_177 != empty_set )
& ! [U_176] :
( ( ! [U_173] :
( U_173 = set_meet(U_176)
| ? [U_169] :
( ~ in(U_169,U_173)
& ! [U_162] :
( in(U_169,U_162)
| ~ in(U_162,U_176) ) )
| ? [U_168] :
( ? [U_161] :
( ~ in(U_168,U_161)
& in(U_161,U_176) )
& in(U_168,U_173) ) )
& ! [U_172] :
( ( ! [U_167] :
( in(U_167,U_172)
| ? [U_159] :
( ~ in(U_167,U_159)
& in(U_159,U_176) ) )
& ! [U_166] :
( ! [U_158] :
( in(U_166,U_158)
| ~ in(U_158,U_176) )
| ~ in(U_166,U_172) ) )
| U_172 != set_meet(U_176) ) )
| U_176 = empty_set ) ),
inference(miniscope,[status(thm)],[f_23_2]) ).
fof(f_23_4,plain,
( ! [U_177] :
( ( ! [U_175] :
( U_175 = set_meet(U_177)
| U_175 != empty_set )
& ! [U_174] :
( U_174 = empty_set
| U_174 != set_meet(U_177) ) )
| U_177 != empty_set )
& ! [U_176] :
( ( ! [U_173] :
( U_173 = set_meet(U_176)
| ? [U_169] :
( ~ in(U_169,U_173)
& ! [U_162] :
( in(U_169,U_162)
| ~ in(U_162,U_176) ) )
| ? [U_168] :
( ? [U_161] :
( ~ in(U_168,U_161)
& in(U_161,U_176) )
& in(U_168,U_173) ) )
& ! [U_172] :
( ( ! [U_167] :
( in(U_167,U_172)
| ( ~ in(U_167,sK32(U_176,U_172,U_167))
& in(sK32(U_176,U_172,U_167),U_176) ) )
& ! [U_166] :
( ! [U_158] :
( in(U_166,U_158)
| ~ in(U_158,U_176) )
| ~ in(U_166,U_172) ) )
| U_172 != set_meet(U_176) ) )
| U_176 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_159,sK32(U_176,U_172,U_167))],[f_23_3]) ).
fof(f_23_5,plain,
( ! [U_177] :
( ( ! [U_175] :
( U_175 = set_meet(U_177)
| U_175 != empty_set )
& ! [U_174] :
( U_174 = empty_set
| U_174 != set_meet(U_177) ) )
| U_177 != empty_set )
& ! [U_176] :
( ( ! [U_173] :
( U_173 = set_meet(U_176)
| ? [U_169] :
( ~ in(U_169,U_173)
& ! [U_162] :
( in(U_169,U_162)
| ~ in(U_162,U_176) ) )
| ( ? [U_161] :
( ~ in(sK33(U_176,U_173),U_161)
& in(U_161,U_176) )
& in(sK33(U_176,U_173),U_173) ) )
& ! [U_172] :
( ( ! [U_167] :
( in(U_167,U_172)
| ( ~ in(U_167,sK32(U_176,U_172,U_167))
& in(sK32(U_176,U_172,U_167),U_176) ) )
& ! [U_166] :
( ! [U_158] :
( in(U_166,U_158)
| ~ in(U_158,U_176) )
| ~ in(U_166,U_172) ) )
| U_172 != set_meet(U_176) ) )
| U_176 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_168,sK33(U_176,U_173))],[f_23_4]) ).
fof(f_23_6,plain,
( ! [U_177] :
( ( ! [U_175] :
( U_175 = set_meet(U_177)
| U_175 != empty_set )
& ! [U_174] :
( U_174 = empty_set
| U_174 != set_meet(U_177) ) )
| U_177 != empty_set )
& ! [U_176] :
( ( ! [U_173] :
( U_173 = set_meet(U_176)
| ? [U_169] :
( ~ in(U_169,U_173)
& ! [U_162] :
( in(U_169,U_162)
| ~ in(U_162,U_176) ) )
| ( ~ in(sK33(U_176,U_173),sK34(U_176,U_173))
& in(sK34(U_176,U_173),U_176)
& in(sK33(U_176,U_173),U_173) ) )
& ! [U_172] :
( ( ! [U_167] :
( in(U_167,U_172)
| ( ~ in(U_167,sK32(U_176,U_172,U_167))
& in(sK32(U_176,U_172,U_167),U_176) ) )
& ! [U_166] :
( ! [U_158] :
( in(U_166,U_158)
| ~ in(U_158,U_176) )
| ~ in(U_166,U_172) ) )
| U_172 != set_meet(U_176) ) )
| U_176 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_161,sK34(U_176,U_173))],[f_23_5]) ).
fof(f_23_7,plain,
( ! [U_177] :
( ( ! [U_175] :
( U_175 = set_meet(U_177)
| U_175 != empty_set )
& ! [U_174] :
( U_174 = empty_set
| U_174 != set_meet(U_177) ) )
| U_177 != empty_set )
& ! [U_176] :
( ( ! [U_173] :
( U_173 = set_meet(U_176)
| ( ~ in(sK35(U_176,U_173),U_173)
& ! [U_162] :
( in(sK35(U_176,U_173),U_162)
| ~ in(U_162,U_176) ) )
| ( ~ in(sK33(U_176,U_173),sK34(U_176,U_173))
& in(sK34(U_176,U_173),U_176)
& in(sK33(U_176,U_173),U_173) ) )
& ! [U_172] :
( ( ! [U_167] :
( in(U_167,U_172)
| ( ~ in(U_167,sK32(U_176,U_172,U_167))
& in(sK32(U_176,U_172,U_167),U_176) ) )
& ! [U_166] :
( ! [U_158] :
( in(U_166,U_158)
| ~ in(U_158,U_176) )
| ~ in(U_166,U_172) ) )
| U_172 != set_meet(U_176) ) )
| U_176 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_169,sK35(U_176,U_173))],[f_23_6]) ).
fof(f_23_8,plain,
( ! [U_174,U_177,U_175] :
( U_175 = set_meet(U_177)
| U_175 != empty_set
| ~ sP49(U_174,U_177,U_175) )
& ! [U_174,U_177,U_175] :
( U_174 = empty_set
| U_174 != set_meet(U_177)
| ~ sP49(U_174,U_177,U_175) )
& ! [U_173,U_162,U_176] :
( ~ in(sK35(U_176,U_173),U_173)
| ~ sP47(U_173,U_162,U_176) )
& ! [U_173,U_162,U_176] :
( in(sK35(U_176,U_173),U_162)
| ~ in(U_162,U_176)
| ~ sP47(U_173,U_162,U_176) )
& ! [U_173,U_176] :
( ~ in(sK33(U_176,U_173),sK34(U_176,U_173))
| ~ sP46(U_173,U_176) )
& ! [U_173,U_176] :
( in(sK34(U_176,U_173),U_176)
| ~ sP46(U_173,U_176) )
& ! [U_173,U_176] :
( in(sK33(U_176,U_173),U_173)
| ~ sP46(U_173,U_176) )
& ! [U_167,U_176,U_172] :
( ~ in(U_167,sK32(U_176,U_172,U_167))
| ~ sP44(U_167,U_176,U_172) )
& ! [U_167,U_176,U_172] :
( in(sK32(U_176,U_172,U_167),U_176)
| ~ sP44(U_167,U_176,U_172) )
& ! [U_158,U_166,U_167,U_176,U_172] :
( in(U_167,U_172)
| sP44(U_167,U_176,U_172)
| ~ sP45(U_158,U_166,U_167,U_176,U_172) )
& ! [U_158,U_166,U_167,U_176,U_172] :
( in(U_166,U_158)
| ~ in(U_158,U_176)
| ~ in(U_166,U_172)
| ~ sP45(U_158,U_166,U_167,U_176,U_172) )
& ! [U_158,U_173,U_162,U_166,U_167,U_176,U_172] :
( U_173 = set_meet(U_176)
| sP47(U_173,U_162,U_176)
| sP46(U_173,U_176)
| ~ sP48(U_158,U_173,U_162,U_166,U_167,U_176,U_172) )
& ! [U_158,U_173,U_162,U_166,U_167,U_176,U_172] :
( sP45(U_158,U_166,U_167,U_176,U_172)
| U_172 != set_meet(U_176)
| ~ sP48(U_158,U_173,U_162,U_166,U_167,U_176,U_172) )
& ! [U_174,U_177,U_175] :
( sP49(U_174,U_177,U_175)
| U_177 != empty_set )
& ! [U_158,U_173,U_162,U_166,U_167,U_176,U_172] :
( sP48(U_158,U_173,U_162,U_166,U_167,U_176,U_172)
| U_176 = empty_set ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP44,sP45,sP46,sP47,sP48,sP49])],[f_23_7]) ).
cnf(f_23_9,plain,
( sP48(U_158,U_173,U_162,U_166,U_167,U_176,U_172)
| U_176 = empty_set ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_10,plain,
( sP49(U_174,U_177,U_175)
| U_177 != empty_set ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_11,plain,
( sP45(U_158,U_166,U_167,U_176,U_172)
| U_172 != set_meet(U_176)
| ~ sP48(U_158,U_173,U_162,U_166,U_167,U_176,U_172) ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_12,plain,
( U_173 = set_meet(U_176)
| sP47(U_173,U_162,U_176)
| sP46(U_173,U_176)
| ~ sP48(U_158,U_173,U_162,U_166,U_167,U_176,U_172) ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_13,plain,
( in(U_166,U_158)
| ~ in(U_158,U_176)
| ~ in(U_166,U_172)
| ~ sP45(U_158,U_166,U_167,U_176,U_172) ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_14,plain,
( in(U_167,U_172)
| sP44(U_167,U_176,U_172)
| ~ sP45(U_158,U_166,U_167,U_176,U_172) ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_15,plain,
( in(sK32(U_176,U_172,U_167),U_176)
| ~ sP44(U_167,U_176,U_172) ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_16,plain,
( ~ in(U_167,sK32(U_176,U_172,U_167))
| ~ sP44(U_167,U_176,U_172) ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_17,plain,
( in(sK33(U_176,U_173),U_173)
| ~ sP46(U_173,U_176) ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_18,plain,
( in(sK34(U_176,U_173),U_176)
| ~ sP46(U_173,U_176) ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_19,plain,
( ~ in(sK33(U_176,U_173),sK34(U_176,U_173))
| ~ sP46(U_173,U_176) ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_20,plain,
( in(sK35(U_176,U_173),U_162)
| ~ in(U_162,U_176)
| ~ sP47(U_173,U_162,U_176) ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_21,plain,
( ~ in(sK35(U_176,U_173),U_173)
| ~ sP47(U_173,U_162,U_176) ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_22,plain,
( U_174 = empty_set
| U_174 != set_meet(U_177)
| ~ sP49(U_174,U_177,U_175) ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_23,plain,
( U_175 = set_meet(U_177)
| U_175 != empty_set
| ~ sP49(U_174,U_177,U_175) ),
inference(clausify,[status(thm)],[f_23_8]) ).
fof(f_24_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_24_2,plain,
! [U_181,U_180] :
( ( U_180 = singleton(U_181)
| ? [U_179] :
( ( ~ in(U_179,U_180)
& U_179 = U_181 )
| ( U_179 != U_181
& in(U_179,U_180) ) ) )
& ( ! [U_178] :
( ( in(U_178,U_180)
| U_178 != U_181 )
& ( U_178 = U_181
| ~ in(U_178,U_180) ) )
| U_180 != singleton(U_181) ) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( ! [U_189,U_187] :
( U_187 = singleton(U_189)
| ? [U_185] :
( ~ in(U_185,U_187)
& U_185 = U_189 )
| ? [U_184] :
( U_184 != U_189
& in(U_184,U_187) ) )
& ! [U_188,U_186] :
( ( ! [U_183] :
( in(U_183,U_186)
| U_183 != U_188 )
& ! [U_182] :
( U_182 = U_188
| ~ in(U_182,U_186) ) )
| U_186 != singleton(U_188) ) ),
inference(miniscope,[status(thm)],[f_24_2]) ).
fof(f_24_4,plain,
( ! [U_189,U_187] :
( U_187 = singleton(U_189)
| ? [U_185] :
( ~ in(U_185,U_187)
& U_185 = U_189 )
| ( sK36(U_189,U_187) != U_189
& in(sK36(U_189,U_187),U_187) ) )
& ! [U_188,U_186] :
( ( ! [U_183] :
( in(U_183,U_186)
| U_183 != U_188 )
& ! [U_182] :
( U_182 = U_188
| ~ in(U_182,U_186) ) )
| U_186 != singleton(U_188) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_184,sK36(U_189,U_187))],[f_24_3]) ).
fof(f_24_5,plain,
( ! [U_189,U_187] :
( U_187 = singleton(U_189)
| ( ~ in(sK37(U_189,U_187),U_187)
& sK37(U_189,U_187) = U_189 )
| ( sK36(U_189,U_187) != U_189
& in(sK36(U_189,U_187),U_187) ) )
& ! [U_188,U_186] :
( ( ! [U_183] :
( in(U_183,U_186)
| U_183 != U_188 )
& ! [U_182] :
( U_182 = U_188
| ~ in(U_182,U_186) ) )
| U_186 != singleton(U_188) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_185,sK37(U_189,U_187))],[f_24_4]) ).
fof(f_24_6,plain,
( ! [U_189,U_187] :
( ~ in(sK37(U_189,U_187),U_187)
| ~ sP52(U_189,U_187) )
& ! [U_189,U_187] :
( sK37(U_189,U_187) = U_189
| ~ sP52(U_189,U_187) )
& ! [U_189,U_187] :
( sK36(U_189,U_187) != U_189
| ~ sP51(U_189,U_187) )
& ! [U_189,U_187] :
( in(sK36(U_189,U_187),U_187)
| ~ sP51(U_189,U_187) )
& ! [U_186,U_183,U_182,U_188] :
( in(U_183,U_186)
| U_183 != U_188
| ~ sP50(U_186,U_183,U_182,U_188) )
& ! [U_186,U_183,U_182,U_188] :
( U_182 = U_188
| ~ in(U_182,U_186)
| ~ sP50(U_186,U_183,U_182,U_188) )
& ! [U_189,U_187] :
( U_187 = singleton(U_189)
| sP52(U_189,U_187)
| sP51(U_189,U_187) )
& ! [U_186,U_183,U_182,U_188] :
( sP50(U_186,U_183,U_182,U_188)
| U_186 != singleton(U_188) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP50,sP51,sP52])],[f_24_5]) ).
cnf(f_24_7,plain,
( sP50(U_186,U_183,U_182,U_188)
| U_186 != singleton(U_188) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_8,plain,
( U_187 = singleton(U_189)
| sP52(U_189,U_187)
| sP51(U_189,U_187) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_9,plain,
( U_182 = U_188
| ~ in(U_182,U_186)
| ~ sP50(U_186,U_183,U_182,U_188) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_10,plain,
( in(U_183,U_186)
| U_183 != U_188
| ~ sP50(U_186,U_183,U_182,U_188) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_11,plain,
( in(sK36(U_189,U_187),U_187)
| ~ sP51(U_189,U_187) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_12,plain,
( sK36(U_189,U_187) != U_189
| ~ sP51(U_189,U_187) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_13,plain,
( sK37(U_189,U_187) = U_189
| ~ sP52(U_189,U_187) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_14,plain,
( ~ in(sK37(U_189,U_187),U_187)
| ~ sP52(U_189,U_187) ),
inference(clausify,[status(thm)],[f_24_6]) ).
fof(f_25_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_25_2,plain,
! [U_192] :
( ( U_192 = empty_set
| ? [U_191] : in(U_191,U_192) )
& ( ! [U_190] : ~ in(U_190,U_192)
| U_192 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( ! [U_194] :
( U_194 = empty_set
| ? [U_191] : in(U_191,U_194) )
& ! [U_193] :
( ! [U_190] : ~ in(U_190,U_193)
| U_193 != empty_set ) ),
inference(miniscope,[status(thm)],[f_25_2]) ).
fof(f_25_4,plain,
( ! [U_194] :
( U_194 = empty_set
| in(sK38(U_194),U_194) )
& ! [U_193] :
( ! [U_190] : ~ in(U_190,U_193)
| U_193 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_191,sK38(U_194))],[f_25_3]) ).
fof(f_25_5,plain,
( ! [U_194] :
( U_194 = empty_set
| in(sK38(U_194),U_194) )
& ! [U_193,U_190] :
( ~ in(U_190,U_193)
| U_193 != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_25_4]) ).
cnf(f_25_6,plain,
( ~ in(U_190,U_193)
| U_193 != empty_set ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_7,plain,
( U_194 = empty_set
| in(sK38(U_194),U_194) ),
inference(clausify,[status(thm)],[f_25_5]) ).
fof(f_26_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_26_2,plain,
! [U_198,U_197] :
( ( U_197 = powerset(U_198)
| ? [U_196] :
( ( ~ in(U_196,U_197)
& subset(U_196,U_198) )
| ( ~ subset(U_196,U_198)
& in(U_196,U_197) ) ) )
& ( ! [U_195] :
( ( in(U_195,U_197)
| ~ subset(U_195,U_198) )
& ( subset(U_195,U_198)
| ~ in(U_195,U_197) ) )
| U_197 != powerset(U_198) ) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( ! [U_206,U_204] :
( U_204 = powerset(U_206)
| ? [U_202] :
( ~ in(U_202,U_204)
& subset(U_202,U_206) )
| ? [U_201] :
( ~ subset(U_201,U_206)
& in(U_201,U_204) ) )
& ! [U_205,U_203] :
( ( ! [U_200] :
( in(U_200,U_203)
| ~ subset(U_200,U_205) )
& ! [U_199] :
( subset(U_199,U_205)
| ~ in(U_199,U_203) ) )
| U_203 != powerset(U_205) ) ),
inference(miniscope,[status(thm)],[f_26_2]) ).
fof(f_26_4,plain,
( ! [U_206,U_204] :
( U_204 = powerset(U_206)
| ? [U_202] :
( ~ in(U_202,U_204)
& subset(U_202,U_206) )
| ( ~ subset(sK39(U_206,U_204),U_206)
& in(sK39(U_206,U_204),U_204) ) )
& ! [U_205,U_203] :
( ( ! [U_200] :
( in(U_200,U_203)
| ~ subset(U_200,U_205) )
& ! [U_199] :
( subset(U_199,U_205)
| ~ in(U_199,U_203) ) )
| U_203 != powerset(U_205) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_201,sK39(U_206,U_204))],[f_26_3]) ).
fof(f_26_5,plain,
( ! [U_206,U_204] :
( U_204 = powerset(U_206)
| ( ~ in(sK40(U_206,U_204),U_204)
& subset(sK40(U_206,U_204),U_206) )
| ( ~ subset(sK39(U_206,U_204),U_206)
& in(sK39(U_206,U_204),U_204) ) )
& ! [U_205,U_203] :
( ( ! [U_200] :
( in(U_200,U_203)
| ~ subset(U_200,U_205) )
& ! [U_199] :
( subset(U_199,U_205)
| ~ in(U_199,U_203) ) )
| U_203 != powerset(U_205) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_202,sK40(U_206,U_204))],[f_26_4]) ).
fof(f_26_6,plain,
( ! [U_206,U_204] :
( ~ in(sK40(U_206,U_204),U_204)
| ~ sP55(U_206,U_204) )
& ! [U_206,U_204] :
( subset(sK40(U_206,U_204),U_206)
| ~ sP55(U_206,U_204) )
& ! [U_206,U_204] :
( ~ subset(sK39(U_206,U_204),U_206)
| ~ sP54(U_206,U_204) )
& ! [U_206,U_204] :
( in(sK39(U_206,U_204),U_204)
| ~ sP54(U_206,U_204) )
& ! [U_200,U_203,U_205,U_199] :
( in(U_200,U_203)
| ~ subset(U_200,U_205)
| ~ sP53(U_200,U_203,U_205,U_199) )
& ! [U_200,U_203,U_205,U_199] :
( subset(U_199,U_205)
| ~ in(U_199,U_203)
| ~ sP53(U_200,U_203,U_205,U_199) )
& ! [U_206,U_204] :
( U_204 = powerset(U_206)
| sP55(U_206,U_204)
| sP54(U_206,U_204) )
& ! [U_200,U_203,U_205,U_199] :
( sP53(U_200,U_203,U_205,U_199)
| U_203 != powerset(U_205) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP53,sP54,sP55])],[f_26_5]) ).
cnf(f_26_7,plain,
( sP53(U_200,U_203,U_205,U_199)
| U_203 != powerset(U_205) ),
inference(clausify,[status(thm)],[f_26_6]) ).
cnf(f_26_8,plain,
( U_204 = powerset(U_206)
| sP55(U_206,U_204)
| sP54(U_206,U_204) ),
inference(clausify,[status(thm)],[f_26_6]) ).
cnf(f_26_9,plain,
( subset(U_199,U_205)
| ~ in(U_199,U_203)
| ~ sP53(U_200,U_203,U_205,U_199) ),
inference(clausify,[status(thm)],[f_26_6]) ).
cnf(f_26_10,plain,
( in(U_200,U_203)
| ~ subset(U_200,U_205)
| ~ sP53(U_200,U_203,U_205,U_199) ),
inference(clausify,[status(thm)],[f_26_6]) ).
cnf(f_26_11,plain,
( in(sK39(U_206,U_204),U_204)
| ~ sP54(U_206,U_204) ),
inference(clausify,[status(thm)],[f_26_6]) ).
cnf(f_26_12,plain,
( ~ subset(sK39(U_206,U_204),U_206)
| ~ sP54(U_206,U_204) ),
inference(clausify,[status(thm)],[f_26_6]) ).
cnf(f_26_13,plain,
( subset(sK40(U_206,U_204),U_206)
| ~ sP55(U_206,U_204) ),
inference(clausify,[status(thm)],[f_26_6]) ).
cnf(f_26_14,plain,
( ~ in(sK40(U_206,U_204),U_204)
| ~ sP55(U_206,U_204) ),
inference(clausify,[status(thm)],[f_26_6]) ).
fof(f_27_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_27_2,plain,
! [U_209] :
( ( epsilon_transitive(U_209)
| ? [U_208] :
( ~ subset(U_208,U_209)
& in(U_208,U_209) ) )
& ( ! [U_207] :
( subset(U_207,U_209)
| ~ in(U_207,U_209) )
| ~ epsilon_transitive(U_209) ) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( ! [U_211] :
( epsilon_transitive(U_211)
| ? [U_208] :
( ~ subset(U_208,U_211)
& in(U_208,U_211) ) )
& ! [U_210] :
( ! [U_207] :
( subset(U_207,U_210)
| ~ in(U_207,U_210) )
| ~ epsilon_transitive(U_210) ) ),
inference(miniscope,[status(thm)],[f_27_2]) ).
fof(f_27_4,plain,
( ! [U_211] :
( epsilon_transitive(U_211)
| ( ~ subset(sK41(U_211),U_211)
& in(sK41(U_211),U_211) ) )
& ! [U_210] :
( ! [U_207] :
( subset(U_207,U_210)
| ~ in(U_207,U_210) )
| ~ epsilon_transitive(U_210) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_208,sK41(U_211))],[f_27_3]) ).
fof(f_27_5,plain,
( ! [U_211] :
( ~ subset(sK41(U_211),U_211)
| ~ sP56(U_211) )
& ! [U_211] :
( in(sK41(U_211),U_211)
| ~ sP56(U_211) )
& ! [U_211] :
( epsilon_transitive(U_211)
| sP56(U_211) )
& ! [U_210,U_207] :
( subset(U_207,U_210)
| ~ in(U_207,U_210)
| ~ epsilon_transitive(U_210) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP56])],[f_27_4]) ).
cnf(f_27_6,plain,
( subset(U_207,U_210)
| ~ in(U_207,U_210)
| ~ epsilon_transitive(U_210) ),
inference(clausify,[status(thm)],[f_27_5]) ).
cnf(f_27_7,plain,
( epsilon_transitive(U_211)
| sP56(U_211) ),
inference(clausify,[status(thm)],[f_27_5]) ).
cnf(f_27_8,plain,
( in(sK41(U_211),U_211)
| ~ sP56(U_211) ),
inference(clausify,[status(thm)],[f_27_5]) ).
cnf(f_27_9,plain,
( ~ subset(sK41(U_211),U_211)
| ~ sP56(U_211) ),
inference(clausify,[status(thm)],[f_27_5]) ).
fof(f_28_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_28_2,plain,
! [U_217] :
( ! [U_216] :
( ( ( U_217 = U_216
| ? [U_215,U_214] :
( ( ~ in(ordered_pair(U_215,U_214),U_217)
& in(ordered_pair(U_215,U_214),U_216) )
| ( ~ in(ordered_pair(U_215,U_214),U_216)
& in(ordered_pair(U_215,U_214),U_217) ) ) )
& ( ! [U_213,U_212] :
( ( in(ordered_pair(U_213,U_212),U_217)
| ~ in(ordered_pair(U_213,U_212),U_216) )
& ( in(ordered_pair(U_213,U_212),U_216)
| ~ in(ordered_pair(U_213,U_212),U_217) ) )
| U_217 != U_216 ) )
| ~ relation(U_216) )
| ~ relation(U_217) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_217] :
( ! [U_216] :
( ( ( U_217 = U_216
| ? [U_225,U_223] :
( ~ in(ordered_pair(U_225,U_223),U_217)
& in(ordered_pair(U_225,U_223),U_216) )
| ? [U_224,U_222] :
( ~ in(ordered_pair(U_224,U_222),U_216)
& in(ordered_pair(U_224,U_222),U_217) ) )
& ( ( ! [U_221,U_219] :
( in(ordered_pair(U_221,U_219),U_217)
| ~ in(ordered_pair(U_221,U_219),U_216) )
& ! [U_220,U_218] :
( in(ordered_pair(U_220,U_218),U_216)
| ~ in(ordered_pair(U_220,U_218),U_217) ) )
| U_217 != U_216 ) )
| ~ relation(U_216) )
| ~ relation(U_217) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
fof(f_28_4,plain,
! [U_217] :
( ! [U_216] :
( ( ( U_217 = U_216
| ? [U_225,U_223] :
( ~ in(ordered_pair(U_225,U_223),U_217)
& in(ordered_pair(U_225,U_223),U_216) )
| ? [U_222] :
( ~ in(ordered_pair(sK42(U_217,U_216),U_222),U_216)
& in(ordered_pair(sK42(U_217,U_216),U_222),U_217) ) )
& ( ( ! [U_221,U_219] :
( in(ordered_pair(U_221,U_219),U_217)
| ~ in(ordered_pair(U_221,U_219),U_216) )
& ! [U_220,U_218] :
( in(ordered_pair(U_220,U_218),U_216)
| ~ in(ordered_pair(U_220,U_218),U_217) ) )
| U_217 != U_216 ) )
| ~ relation(U_216) )
| ~ relation(U_217) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_224,sK42(U_217,U_216))],[f_28_3]) ).
fof(f_28_5,plain,
! [U_217] :
( ! [U_216] :
( ( ( U_217 = U_216
| ? [U_225,U_223] :
( ~ in(ordered_pair(U_225,U_223),U_217)
& in(ordered_pair(U_225,U_223),U_216) )
| ( ~ in(ordered_pair(sK42(U_217,U_216),sK43(U_217,U_216)),U_216)
& in(ordered_pair(sK42(U_217,U_216),sK43(U_217,U_216)),U_217) ) )
& ( ( ! [U_221,U_219] :
( in(ordered_pair(U_221,U_219),U_217)
| ~ in(ordered_pair(U_221,U_219),U_216) )
& ! [U_220,U_218] :
( in(ordered_pair(U_220,U_218),U_216)
| ~ in(ordered_pair(U_220,U_218),U_217) ) )
| U_217 != U_216 ) )
| ~ relation(U_216) )
| ~ relation(U_217) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_222,sK43(U_217,U_216))],[f_28_4]) ).
fof(f_28_6,plain,
! [U_217] :
( ! [U_216] :
( ( ( U_217 = U_216
| ? [U_223] :
( ~ in(ordered_pair(sK44(U_217,U_216),U_223),U_217)
& in(ordered_pair(sK44(U_217,U_216),U_223),U_216) )
| ( ~ in(ordered_pair(sK42(U_217,U_216),sK43(U_217,U_216)),U_216)
& in(ordered_pair(sK42(U_217,U_216),sK43(U_217,U_216)),U_217) ) )
& ( ( ! [U_221,U_219] :
( in(ordered_pair(U_221,U_219),U_217)
| ~ in(ordered_pair(U_221,U_219),U_216) )
& ! [U_220,U_218] :
( in(ordered_pair(U_220,U_218),U_216)
| ~ in(ordered_pair(U_220,U_218),U_217) ) )
| U_217 != U_216 ) )
| ~ relation(U_216) )
| ~ relation(U_217) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_225,sK44(U_217,U_216))],[f_28_5]) ).
fof(f_28_7,plain,
! [U_217] :
( ! [U_216] :
( ( ( U_217 = U_216
| ( ~ in(ordered_pair(sK44(U_217,U_216),sK45(U_217,U_216)),U_217)
& in(ordered_pair(sK44(U_217,U_216),sK45(U_217,U_216)),U_216) )
| ( ~ in(ordered_pair(sK42(U_217,U_216),sK43(U_217,U_216)),U_216)
& in(ordered_pair(sK42(U_217,U_216),sK43(U_217,U_216)),U_217) ) )
& ( ( ! [U_221,U_219] :
( in(ordered_pair(U_221,U_219),U_217)
| ~ in(ordered_pair(U_221,U_219),U_216) )
& ! [U_220,U_218] :
( in(ordered_pair(U_220,U_218),U_216)
| ~ in(ordered_pair(U_220,U_218),U_217) ) )
| U_217 != U_216 ) )
| ~ relation(U_216) )
| ~ relation(U_217) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_223,sK45(U_217,U_216))],[f_28_6]) ).
fof(f_28_8,plain,
( ! [U_216,U_217] :
( ~ in(ordered_pair(sK44(U_217,U_216),sK45(U_217,U_216)),U_217)
| ~ sP59(U_216,U_217) )
& ! [U_216,U_217] :
( in(ordered_pair(sK44(U_217,U_216),sK45(U_217,U_216)),U_216)
| ~ sP59(U_216,U_217) )
& ! [U_216,U_217] :
( ~ in(ordered_pair(sK42(U_217,U_216),sK43(U_217,U_216)),U_216)
| ~ sP58(U_216,U_217) )
& ! [U_216,U_217] :
( in(ordered_pair(sK42(U_217,U_216),sK43(U_217,U_216)),U_217)
| ~ sP58(U_216,U_217) )
& ! [U_218,U_219,U_216,U_217,U_221,U_220] :
( in(ordered_pair(U_221,U_219),U_217)
| ~ in(ordered_pair(U_221,U_219),U_216)
| ~ sP57(U_218,U_219,U_216,U_217,U_221,U_220) )
& ! [U_218,U_219,U_216,U_217,U_221,U_220] :
( in(ordered_pair(U_220,U_218),U_216)
| ~ in(ordered_pair(U_220,U_218),U_217)
| ~ sP57(U_218,U_219,U_216,U_217,U_221,U_220) )
& ! [U_218,U_219,U_216,U_217,U_221,U_220] :
( U_217 = U_216
| sP59(U_216,U_217)
| sP58(U_216,U_217)
| ~ sP60(U_218,U_219,U_216,U_217,U_221,U_220) )
& ! [U_218,U_219,U_216,U_217,U_221,U_220] :
( sP57(U_218,U_219,U_216,U_217,U_221,U_220)
| U_217 != U_216
| ~ sP60(U_218,U_219,U_216,U_217,U_221,U_220) )
& ! [U_218,U_219,U_216,U_217,U_221,U_220] :
( sP60(U_218,U_219,U_216,U_217,U_221,U_220)
| ~ relation(U_216)
| ~ relation(U_217) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP57,sP58,sP59,sP60])],[f_28_7]) ).
cnf(f_28_9,plain,
( sP60(U_218,U_219,U_216,U_217,U_221,U_220)
| ~ relation(U_216)
| ~ relation(U_217) ),
inference(clausify,[status(thm)],[f_28_8]) ).
cnf(f_28_10,plain,
( sP57(U_218,U_219,U_216,U_217,U_221,U_220)
| U_217 != U_216
| ~ sP60(U_218,U_219,U_216,U_217,U_221,U_220) ),
inference(clausify,[status(thm)],[f_28_8]) ).
cnf(f_28_11,plain,
( U_217 = U_216
| sP59(U_216,U_217)
| sP58(U_216,U_217)
| ~ sP60(U_218,U_219,U_216,U_217,U_221,U_220) ),
inference(clausify,[status(thm)],[f_28_8]) ).
cnf(f_28_12,plain,
( in(ordered_pair(U_220,U_218),U_216)
| ~ in(ordered_pair(U_220,U_218),U_217)
| ~ sP57(U_218,U_219,U_216,U_217,U_221,U_220) ),
inference(clausify,[status(thm)],[f_28_8]) ).
cnf(f_28_13,plain,
( in(ordered_pair(U_221,U_219),U_217)
| ~ in(ordered_pair(U_221,U_219),U_216)
| ~ sP57(U_218,U_219,U_216,U_217,U_221,U_220) ),
inference(clausify,[status(thm)],[f_28_8]) ).
cnf(f_28_14,plain,
( in(ordered_pair(sK42(U_217,U_216),sK43(U_217,U_216)),U_217)
| ~ sP58(U_216,U_217) ),
inference(clausify,[status(thm)],[f_28_8]) ).
cnf(f_28_15,plain,
( ~ in(ordered_pair(sK42(U_217,U_216),sK43(U_217,U_216)),U_216)
| ~ sP58(U_216,U_217) ),
inference(clausify,[status(thm)],[f_28_8]) ).
cnf(f_28_16,plain,
( in(ordered_pair(sK44(U_217,U_216),sK45(U_217,U_216)),U_216)
| ~ sP59(U_216,U_217) ),
inference(clausify,[status(thm)],[f_28_8]) ).
cnf(f_28_17,plain,
( ~ in(ordered_pair(sK44(U_217,U_216),sK45(U_217,U_216)),U_217)
| ~ sP59(U_216,U_217) ),
inference(clausify,[status(thm)],[f_28_8]) ).
fof(f_29_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_29_2,plain,
! [U_227,U_226] :
( ( ( ( element(U_226,U_227)
| ~ empty(U_226) )
& ( empty(U_226)
| ~ element(U_226,U_227) ) )
| ~ empty(U_227) )
& ( ( ( element(U_226,U_227)
| ~ in(U_226,U_227) )
& ( in(U_226,U_227)
| ~ element(U_226,U_227) ) )
| empty(U_227) ) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
( ! [U_235] :
( ( ! [U_233] :
( element(U_233,U_235)
| ~ empty(U_233) )
& ! [U_232] :
( empty(U_232)
| ~ element(U_232,U_235) ) )
| ~ empty(U_235) )
& ! [U_234] :
( ( ! [U_231] :
( element(U_231,U_234)
| ~ in(U_231,U_234) )
& ! [U_230] :
( in(U_230,U_234)
| ~ element(U_230,U_234) ) )
| empty(U_234) ) ),
inference(miniscope,[status(thm)],[f_29_2]) ).
fof(f_29_4,plain,
( ! [U_235,U_233,U_232] :
( element(U_233,U_235)
| ~ empty(U_233)
| ~ sP62(U_235,U_233,U_232) )
& ! [U_235,U_233,U_232] :
( empty(U_232)
| ~ element(U_232,U_235)
| ~ sP62(U_235,U_233,U_232) )
& ! [U_231,U_234,U_230] :
( element(U_231,U_234)
| ~ in(U_231,U_234)
| ~ sP61(U_231,U_234,U_230) )
& ! [U_231,U_234,U_230] :
( in(U_230,U_234)
| ~ element(U_230,U_234)
| ~ sP61(U_231,U_234,U_230) )
& ! [U_235,U_233,U_232] :
( sP62(U_235,U_233,U_232)
| ~ empty(U_235) )
& ! [U_231,U_234,U_230] :
( sP61(U_231,U_234,U_230)
| empty(U_234) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP61,sP62])],[f_29_3]) ).
cnf(f_29_5,plain,
( sP61(U_231,U_234,U_230)
| empty(U_234) ),
inference(clausify,[status(thm)],[f_29_4]) ).
cnf(f_29_6,plain,
( sP62(U_235,U_233,U_232)
| ~ empty(U_235) ),
inference(clausify,[status(thm)],[f_29_4]) ).
cnf(f_29_7,plain,
( in(U_230,U_234)
| ~ element(U_230,U_234)
| ~ sP61(U_231,U_234,U_230) ),
inference(clausify,[status(thm)],[f_29_4]) ).
cnf(f_29_8,plain,
( element(U_231,U_234)
| ~ in(U_231,U_234)
| ~ sP61(U_231,U_234,U_230) ),
inference(clausify,[status(thm)],[f_29_4]) ).
cnf(f_29_9,plain,
( empty(U_232)
| ~ element(U_232,U_235)
| ~ sP62(U_235,U_233,U_232) ),
inference(clausify,[status(thm)],[f_29_4]) ).
cnf(f_29_10,plain,
( element(U_233,U_235)
| ~ empty(U_233)
| ~ sP62(U_235,U_233,U_232) ),
inference(clausify,[status(thm)],[f_29_4]) ).
fof(f_30_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_30_2,plain,
! [U_240,U_239,U_238] :
( ( U_238 = unordered_pair(U_240,U_239)
| ? [U_237] :
( ( ~ in(U_237,U_238)
& ( U_237 = U_239
| U_237 = U_240 ) )
| ( U_237 != U_239
& U_237 != U_240
& in(U_237,U_238) ) ) )
& ( ! [U_236] :
( ( in(U_236,U_238)
| ( U_236 != U_239
& U_236 != U_240 ) )
& ( U_236 = U_239
| U_236 = U_240
| ~ in(U_236,U_238) ) )
| U_238 != unordered_pair(U_240,U_239) ) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( ! [U_250,U_248,U_246] :
( U_246 = unordered_pair(U_250,U_248)
| ? [U_244] :
( ~ in(U_244,U_246)
& ( U_244 = U_248
| U_244 = U_250 ) )
| ? [U_243] :
( U_243 != U_248
& U_243 != U_250
& in(U_243,U_246) ) )
& ! [U_249,U_247,U_245] :
( ( ! [U_242] :
( in(U_242,U_245)
| ( U_242 != U_247
& U_242 != U_249 ) )
& ! [U_241] :
( U_241 = U_247
| U_241 = U_249
| ~ in(U_241,U_245) ) )
| U_245 != unordered_pair(U_249,U_247) ) ),
inference(miniscope,[status(thm)],[f_30_2]) ).
fof(f_30_4,plain,
( ! [U_250,U_248,U_246] :
( U_246 = unordered_pair(U_250,U_248)
| ? [U_244] :
( ~ in(U_244,U_246)
& ( U_244 = U_248
| U_244 = U_250 ) )
| ( sK46(U_250,U_248,U_246) != U_248
& sK46(U_250,U_248,U_246) != U_250
& in(sK46(U_250,U_248,U_246),U_246) ) )
& ! [U_249,U_247,U_245] :
( ( ! [U_242] :
( in(U_242,U_245)
| ( U_242 != U_247
& U_242 != U_249 ) )
& ! [U_241] :
( U_241 = U_247
| U_241 = U_249
| ~ in(U_241,U_245) ) )
| U_245 != unordered_pair(U_249,U_247) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_243,sK46(U_250,U_248,U_246))],[f_30_3]) ).
fof(f_30_5,plain,
( ! [U_250,U_248,U_246] :
( U_246 = unordered_pair(U_250,U_248)
| ( ~ in(sK47(U_250,U_248,U_246),U_246)
& ( sK47(U_250,U_248,U_246) = U_248
| sK47(U_250,U_248,U_246) = U_250 ) )
| ( sK46(U_250,U_248,U_246) != U_248
& sK46(U_250,U_248,U_246) != U_250
& in(sK46(U_250,U_248,U_246),U_246) ) )
& ! [U_249,U_247,U_245] :
( ( ! [U_242] :
( in(U_242,U_245)
| ( U_242 != U_247
& U_242 != U_249 ) )
& ! [U_241] :
( U_241 = U_247
| U_241 = U_249
| ~ in(U_241,U_245) ) )
| U_245 != unordered_pair(U_249,U_247) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_244,sK47(U_250,U_248,U_246))],[f_30_4]) ).
fof(f_30_6,plain,
( ! [U_246,U_248,U_250] :
( ~ in(sK47(U_250,U_248,U_246),U_246)
| ~ sP66(U_246,U_248,U_250) )
& ! [U_246,U_248,U_250] :
( sK47(U_250,U_248,U_246) = U_248
| sK47(U_250,U_248,U_246) = U_250
| ~ sP66(U_246,U_248,U_250) )
& ! [U_246,U_248,U_250] :
( sK46(U_250,U_248,U_246) != U_248
| ~ sP65(U_246,U_248,U_250) )
& ! [U_246,U_248,U_250] :
( sK46(U_250,U_248,U_246) != U_250
| ~ sP65(U_246,U_248,U_250) )
& ! [U_246,U_248,U_250] :
( in(sK46(U_250,U_248,U_246),U_246)
| ~ sP65(U_246,U_248,U_250) )
& ! [U_242,U_247,U_249] :
( U_242 != U_247
| ~ sP63(U_242,U_247,U_249) )
& ! [U_242,U_247,U_249] :
( U_242 != U_249
| ~ sP63(U_242,U_247,U_249) )
& ! [U_242,U_241,U_245,U_247,U_249] :
( in(U_242,U_245)
| sP63(U_242,U_247,U_249)
| ~ sP64(U_242,U_241,U_245,U_247,U_249) )
& ! [U_242,U_241,U_245,U_247,U_249] :
( U_241 = U_247
| U_241 = U_249
| ~ in(U_241,U_245)
| ~ sP64(U_242,U_241,U_245,U_247,U_249) )
& ! [U_246,U_248,U_250] :
( U_246 = unordered_pair(U_250,U_248)
| sP66(U_246,U_248,U_250)
| sP65(U_246,U_248,U_250) )
& ! [U_242,U_241,U_245,U_247,U_249] :
( sP64(U_242,U_241,U_245,U_247,U_249)
| U_245 != unordered_pair(U_249,U_247) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP63,sP64,sP65,sP66])],[f_30_5]) ).
cnf(f_30_7,plain,
( sP64(U_242,U_241,U_245,U_247,U_249)
| U_245 != unordered_pair(U_249,U_247) ),
inference(clausify,[status(thm)],[f_30_6]) ).
cnf(f_30_8,plain,
( U_246 = unordered_pair(U_250,U_248)
| sP66(U_246,U_248,U_250)
| sP65(U_246,U_248,U_250) ),
inference(clausify,[status(thm)],[f_30_6]) ).
cnf(f_30_9,plain,
( U_241 = U_247
| U_241 = U_249
| ~ in(U_241,U_245)
| ~ sP64(U_242,U_241,U_245,U_247,U_249) ),
inference(clausify,[status(thm)],[f_30_6]) ).
cnf(f_30_10,plain,
( in(U_242,U_245)
| sP63(U_242,U_247,U_249)
| ~ sP64(U_242,U_241,U_245,U_247,U_249) ),
inference(clausify,[status(thm)],[f_30_6]) ).
cnf(f_30_11,plain,
( U_242 != U_249
| ~ sP63(U_242,U_247,U_249) ),
inference(clausify,[status(thm)],[f_30_6]) ).
cnf(f_30_12,plain,
( U_242 != U_247
| ~ sP63(U_242,U_247,U_249) ),
inference(clausify,[status(thm)],[f_30_6]) ).
cnf(f_30_13,plain,
( in(sK46(U_250,U_248,U_246),U_246)
| ~ sP65(U_246,U_248,U_250) ),
inference(clausify,[status(thm)],[f_30_6]) ).
cnf(f_30_14,plain,
( sK46(U_250,U_248,U_246) != U_250
| ~ sP65(U_246,U_248,U_250) ),
inference(clausify,[status(thm)],[f_30_6]) ).
cnf(f_30_15,plain,
( sK46(U_250,U_248,U_246) != U_248
| ~ sP65(U_246,U_248,U_250) ),
inference(clausify,[status(thm)],[f_30_6]) ).
cnf(f_30_16,plain,
( sK47(U_250,U_248,U_246) = U_248
| sK47(U_250,U_248,U_246) = U_250
| ~ sP66(U_246,U_248,U_250) ),
inference(clausify,[status(thm)],[f_30_6]) ).
cnf(f_30_17,plain,
( ~ in(sK47(U_250,U_248,U_246),U_246)
| ~ sP66(U_246,U_248,U_250) ),
inference(clausify,[status(thm)],[f_30_6]) ).
fof(f_31_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_31_2,plain,
! [U_255,U_254,U_253] :
( ( U_253 = set_union2(U_255,U_254)
| ? [U_252] :
( ( ~ in(U_252,U_253)
& ( in(U_252,U_254)
| in(U_252,U_255) ) )
| ( ~ in(U_252,U_254)
& ~ in(U_252,U_255)
& in(U_252,U_253) ) ) )
& ( ! [U_251] :
( ( in(U_251,U_253)
| ( ~ in(U_251,U_254)
& ~ in(U_251,U_255) ) )
& ( in(U_251,U_254)
| in(U_251,U_255)
| ~ in(U_251,U_253) ) )
| U_253 != set_union2(U_255,U_254) ) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( ! [U_265,U_263,U_261] :
( U_261 = set_union2(U_265,U_263)
| ? [U_259] :
( ~ in(U_259,U_261)
& ( in(U_259,U_263)
| in(U_259,U_265) ) )
| ? [U_258] :
( ~ in(U_258,U_263)
& ~ in(U_258,U_265)
& in(U_258,U_261) ) )
& ! [U_264,U_262,U_260] :
( ( ! [U_257] :
( in(U_257,U_260)
| ( ~ in(U_257,U_262)
& ~ in(U_257,U_264) ) )
& ! [U_256] :
( in(U_256,U_262)
| in(U_256,U_264)
| ~ in(U_256,U_260) ) )
| U_260 != set_union2(U_264,U_262) ) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
fof(f_31_4,plain,
( ! [U_265,U_263,U_261] :
( U_261 = set_union2(U_265,U_263)
| ? [U_259] :
( ~ in(U_259,U_261)
& ( in(U_259,U_263)
| in(U_259,U_265) ) )
| ( ~ in(sK48(U_265,U_263,U_261),U_263)
& ~ in(sK48(U_265,U_263,U_261),U_265)
& in(sK48(U_265,U_263,U_261),U_261) ) )
& ! [U_264,U_262,U_260] :
( ( ! [U_257] :
( in(U_257,U_260)
| ( ~ in(U_257,U_262)
& ~ in(U_257,U_264) ) )
& ! [U_256] :
( in(U_256,U_262)
| in(U_256,U_264)
| ~ in(U_256,U_260) ) )
| U_260 != set_union2(U_264,U_262) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_258,sK48(U_265,U_263,U_261))],[f_31_3]) ).
fof(f_31_5,plain,
( ! [U_265,U_263,U_261] :
( U_261 = set_union2(U_265,U_263)
| ( ~ in(sK49(U_265,U_263,U_261),U_261)
& ( in(sK49(U_265,U_263,U_261),U_263)
| in(sK49(U_265,U_263,U_261),U_265) ) )
| ( ~ in(sK48(U_265,U_263,U_261),U_263)
& ~ in(sK48(U_265,U_263,U_261),U_265)
& in(sK48(U_265,U_263,U_261),U_261) ) )
& ! [U_264,U_262,U_260] :
( ( ! [U_257] :
( in(U_257,U_260)
| ( ~ in(U_257,U_262)
& ~ in(U_257,U_264) ) )
& ! [U_256] :
( in(U_256,U_262)
| in(U_256,U_264)
| ~ in(U_256,U_260) ) )
| U_260 != set_union2(U_264,U_262) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_259,sK49(U_265,U_263,U_261))],[f_31_4]) ).
fof(f_31_6,plain,
( ! [U_263,U_265,U_261] :
( ~ in(sK49(U_265,U_263,U_261),U_261)
| ~ sP70(U_263,U_265,U_261) )
& ! [U_263,U_265,U_261] :
( in(sK49(U_265,U_263,U_261),U_263)
| in(sK49(U_265,U_263,U_261),U_265)
| ~ sP70(U_263,U_265,U_261) )
& ! [U_263,U_265,U_261] :
( ~ in(sK48(U_265,U_263,U_261),U_263)
| ~ sP69(U_263,U_265,U_261) )
& ! [U_263,U_265,U_261] :
( ~ in(sK48(U_265,U_263,U_261),U_265)
| ~ sP69(U_263,U_265,U_261) )
& ! [U_263,U_265,U_261] :
( in(sK48(U_265,U_263,U_261),U_261)
| ~ sP69(U_263,U_265,U_261) )
& ! [U_264,U_262,U_257] :
( ~ in(U_257,U_262)
| ~ sP67(U_264,U_262,U_257) )
& ! [U_264,U_262,U_257] :
( ~ in(U_257,U_264)
| ~ sP67(U_264,U_262,U_257) )
& ! [U_256,U_260,U_264,U_262,U_257] :
( in(U_257,U_260)
| sP67(U_264,U_262,U_257)
| ~ sP68(U_256,U_260,U_264,U_262,U_257) )
& ! [U_256,U_260,U_264,U_262,U_257] :
( in(U_256,U_262)
| in(U_256,U_264)
| ~ in(U_256,U_260)
| ~ sP68(U_256,U_260,U_264,U_262,U_257) )
& ! [U_263,U_265,U_261] :
( U_261 = set_union2(U_265,U_263)
| sP70(U_263,U_265,U_261)
| sP69(U_263,U_265,U_261) )
& ! [U_256,U_260,U_264,U_262,U_257] :
( sP68(U_256,U_260,U_264,U_262,U_257)
| U_260 != set_union2(U_264,U_262) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP67,sP68,sP69,sP70])],[f_31_5]) ).
cnf(f_31_7,plain,
( sP68(U_256,U_260,U_264,U_262,U_257)
| U_260 != set_union2(U_264,U_262) ),
inference(clausify,[status(thm)],[f_31_6]) ).
cnf(f_31_8,plain,
( U_261 = set_union2(U_265,U_263)
| sP70(U_263,U_265,U_261)
| sP69(U_263,U_265,U_261) ),
inference(clausify,[status(thm)],[f_31_6]) ).
cnf(f_31_9,plain,
( in(U_256,U_262)
| in(U_256,U_264)
| ~ in(U_256,U_260)
| ~ sP68(U_256,U_260,U_264,U_262,U_257) ),
inference(clausify,[status(thm)],[f_31_6]) ).
cnf(f_31_10,plain,
( in(U_257,U_260)
| sP67(U_264,U_262,U_257)
| ~ sP68(U_256,U_260,U_264,U_262,U_257) ),
inference(clausify,[status(thm)],[f_31_6]) ).
cnf(f_31_11,plain,
( ~ in(U_257,U_264)
| ~ sP67(U_264,U_262,U_257) ),
inference(clausify,[status(thm)],[f_31_6]) ).
cnf(f_31_12,plain,
( ~ in(U_257,U_262)
| ~ sP67(U_264,U_262,U_257) ),
inference(clausify,[status(thm)],[f_31_6]) ).
cnf(f_31_13,plain,
( in(sK48(U_265,U_263,U_261),U_261)
| ~ sP69(U_263,U_265,U_261) ),
inference(clausify,[status(thm)],[f_31_6]) ).
cnf(f_31_14,plain,
( ~ in(sK48(U_265,U_263,U_261),U_265)
| ~ sP69(U_263,U_265,U_261) ),
inference(clausify,[status(thm)],[f_31_6]) ).
cnf(f_31_15,plain,
( ~ in(sK48(U_265,U_263,U_261),U_263)
| ~ sP69(U_263,U_265,U_261) ),
inference(clausify,[status(thm)],[f_31_6]) ).
cnf(f_31_16,plain,
( in(sK49(U_265,U_263,U_261),U_263)
| in(sK49(U_265,U_263,U_261),U_265)
| ~ sP70(U_263,U_265,U_261) ),
inference(clausify,[status(thm)],[f_31_6]) ).
cnf(f_31_17,plain,
( ~ in(sK49(U_265,U_263,U_261),U_261)
| ~ sP70(U_263,U_265,U_261) ),
inference(clausify,[status(thm)],[f_31_6]) ).
fof(f_32_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_32_2,plain,
! [U_278,U_277,U_276] :
( ( U_276 = cartesian_product2(U_278,U_277)
| ? [U_275] :
( ( ~ in(U_275,U_276)
& ? [U_274,U_273] :
( U_275 = ordered_pair(U_274,U_273)
& in(U_273,U_277)
& in(U_274,U_278) ) )
| ( ! [U_272,U_271] :
( U_275 != ordered_pair(U_272,U_271)
| ~ in(U_271,U_277)
| ~ in(U_272,U_278) )
& in(U_275,U_276) ) ) )
& ( ! [U_270] :
( ( in(U_270,U_276)
| ! [U_269,U_268] :
( U_270 != ordered_pair(U_269,U_268)
| ~ in(U_268,U_277)
| ~ in(U_269,U_278) ) )
& ( ? [U_267,U_266] :
( U_270 = ordered_pair(U_267,U_266)
& in(U_266,U_277)
& in(U_267,U_278) )
| ~ in(U_270,U_276) ) )
| U_276 != cartesian_product2(U_278,U_277) ) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
( ! [U_288,U_286,U_284] :
( U_284 = cartesian_product2(U_288,U_286)
| ? [U_282] :
( ~ in(U_282,U_284)
& ? [U_274] :
( ? [U_273] :
( U_282 = ordered_pair(U_274,U_273)
& in(U_273,U_286) )
& in(U_274,U_288) ) )
| ? [U_281] :
( ! [U_272] :
( ! [U_271] :
( U_281 != ordered_pair(U_272,U_271)
| ~ in(U_271,U_286) )
| ~ in(U_272,U_288) )
& in(U_281,U_284) ) )
& ! [U_287,U_285,U_283] :
( ( ! [U_280] :
( in(U_280,U_283)
| ! [U_269] :
( ! [U_268] :
( U_280 != ordered_pair(U_269,U_268)
| ~ in(U_268,U_285) )
| ~ in(U_269,U_287) ) )
& ! [U_279] :
( ? [U_267] :
( ? [U_266] :
( U_279 = ordered_pair(U_267,U_266)
& in(U_266,U_285) )
& in(U_267,U_287) )
| ~ in(U_279,U_283) ) )
| U_283 != cartesian_product2(U_287,U_285) ) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
fof(f_32_4,plain,
( ! [U_288,U_286,U_284] :
( U_284 = cartesian_product2(U_288,U_286)
| ? [U_282] :
( ~ in(U_282,U_284)
& ? [U_274] :
( ? [U_273] :
( U_282 = ordered_pair(U_274,U_273)
& in(U_273,U_286) )
& in(U_274,U_288) ) )
| ? [U_281] :
( ! [U_272] :
( ! [U_271] :
( U_281 != ordered_pair(U_272,U_271)
| ~ in(U_271,U_286) )
| ~ in(U_272,U_288) )
& in(U_281,U_284) ) )
& ! [U_287,U_285,U_283] :
( ( ! [U_280] :
( in(U_280,U_283)
| ! [U_269] :
( ! [U_268] :
( U_280 != ordered_pair(U_269,U_268)
| ~ in(U_268,U_285) )
| ~ in(U_269,U_287) ) )
& ! [U_279] :
( ( ? [U_266] :
( U_279 = ordered_pair(sK50(U_287,U_285,U_283,U_279),U_266)
& in(U_266,U_285) )
& in(sK50(U_287,U_285,U_283,U_279),U_287) )
| ~ in(U_279,U_283) ) )
| U_283 != cartesian_product2(U_287,U_285) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_267,sK50(U_287,U_285,U_283,U_279))],[f_32_3]) ).
fof(f_32_5,plain,
( ! [U_288,U_286,U_284] :
( U_284 = cartesian_product2(U_288,U_286)
| ? [U_282] :
( ~ in(U_282,U_284)
& ? [U_274] :
( ? [U_273] :
( U_282 = ordered_pair(U_274,U_273)
& in(U_273,U_286) )
& in(U_274,U_288) ) )
| ? [U_281] :
( ! [U_272] :
( ! [U_271] :
( U_281 != ordered_pair(U_272,U_271)
| ~ in(U_271,U_286) )
| ~ in(U_272,U_288) )
& in(U_281,U_284) ) )
& ! [U_287,U_285,U_283] :
( ( ! [U_280] :
( in(U_280,U_283)
| ! [U_269] :
( ! [U_268] :
( U_280 != ordered_pair(U_269,U_268)
| ~ in(U_268,U_285) )
| ~ in(U_269,U_287) ) )
& ! [U_279] :
( ( U_279 = ordered_pair(sK50(U_287,U_285,U_283,U_279),sK51(U_287,U_285,U_283,U_279))
& in(sK51(U_287,U_285,U_283,U_279),U_285)
& in(sK50(U_287,U_285,U_283,U_279),U_287) )
| ~ in(U_279,U_283) ) )
| U_283 != cartesian_product2(U_287,U_285) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_266,sK51(U_287,U_285,U_283,U_279))],[f_32_4]) ).
fof(f_32_6,plain,
( ! [U_288,U_286,U_284] :
( U_284 = cartesian_product2(U_288,U_286)
| ? [U_282] :
( ~ in(U_282,U_284)
& ? [U_274] :
( ? [U_273] :
( U_282 = ordered_pair(U_274,U_273)
& in(U_273,U_286) )
& in(U_274,U_288) ) )
| ( ! [U_272] :
( ! [U_271] :
( sK52(U_288,U_286,U_284) != ordered_pair(U_272,U_271)
| ~ in(U_271,U_286) )
| ~ in(U_272,U_288) )
& in(sK52(U_288,U_286,U_284),U_284) ) )
& ! [U_287,U_285,U_283] :
( ( ! [U_280] :
( in(U_280,U_283)
| ! [U_269] :
( ! [U_268] :
( U_280 != ordered_pair(U_269,U_268)
| ~ in(U_268,U_285) )
| ~ in(U_269,U_287) ) )
& ! [U_279] :
( ( U_279 = ordered_pair(sK50(U_287,U_285,U_283,U_279),sK51(U_287,U_285,U_283,U_279))
& in(sK51(U_287,U_285,U_283,U_279),U_285)
& in(sK50(U_287,U_285,U_283,U_279),U_287) )
| ~ in(U_279,U_283) ) )
| U_283 != cartesian_product2(U_287,U_285) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_281,sK52(U_288,U_286,U_284))],[f_32_5]) ).
fof(f_32_7,plain,
( ! [U_288,U_286,U_284] :
( U_284 = cartesian_product2(U_288,U_286)
| ( ~ in(sK53(U_288,U_286,U_284),U_284)
& ? [U_274] :
( ? [U_273] :
( sK53(U_288,U_286,U_284) = ordered_pair(U_274,U_273)
& in(U_273,U_286) )
& in(U_274,U_288) ) )
| ( ! [U_272] :
( ! [U_271] :
( sK52(U_288,U_286,U_284) != ordered_pair(U_272,U_271)
| ~ in(U_271,U_286) )
| ~ in(U_272,U_288) )
& in(sK52(U_288,U_286,U_284),U_284) ) )
& ! [U_287,U_285,U_283] :
( ( ! [U_280] :
( in(U_280,U_283)
| ! [U_269] :
( ! [U_268] :
( U_280 != ordered_pair(U_269,U_268)
| ~ in(U_268,U_285) )
| ~ in(U_269,U_287) ) )
& ! [U_279] :
( ( U_279 = ordered_pair(sK50(U_287,U_285,U_283,U_279),sK51(U_287,U_285,U_283,U_279))
& in(sK51(U_287,U_285,U_283,U_279),U_285)
& in(sK50(U_287,U_285,U_283,U_279),U_287) )
| ~ in(U_279,U_283) ) )
| U_283 != cartesian_product2(U_287,U_285) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_282,sK53(U_288,U_286,U_284))],[f_32_6]) ).
fof(f_32_8,plain,
( ! [U_288,U_286,U_284] :
( U_284 = cartesian_product2(U_288,U_286)
| ( ~ in(sK53(U_288,U_286,U_284),U_284)
& ? [U_273] :
( sK53(U_288,U_286,U_284) = ordered_pair(sK54(U_288,U_286,U_284),U_273)
& in(U_273,U_286) )
& in(sK54(U_288,U_286,U_284),U_288) )
| ( ! [U_272] :
( ! [U_271] :
( sK52(U_288,U_286,U_284) != ordered_pair(U_272,U_271)
| ~ in(U_271,U_286) )
| ~ in(U_272,U_288) )
& in(sK52(U_288,U_286,U_284),U_284) ) )
& ! [U_287,U_285,U_283] :
( ( ! [U_280] :
( in(U_280,U_283)
| ! [U_269] :
( ! [U_268] :
( U_280 != ordered_pair(U_269,U_268)
| ~ in(U_268,U_285) )
| ~ in(U_269,U_287) ) )
& ! [U_279] :
( ( U_279 = ordered_pair(sK50(U_287,U_285,U_283,U_279),sK51(U_287,U_285,U_283,U_279))
& in(sK51(U_287,U_285,U_283,U_279),U_285)
& in(sK50(U_287,U_285,U_283,U_279),U_287) )
| ~ in(U_279,U_283) ) )
| U_283 != cartesian_product2(U_287,U_285) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_274,sK54(U_288,U_286,U_284))],[f_32_7]) ).
fof(f_32_9,plain,
( ! [U_288,U_286,U_284] :
( U_284 = cartesian_product2(U_288,U_286)
| ( ~ in(sK53(U_288,U_286,U_284),U_284)
& sK53(U_288,U_286,U_284) = ordered_pair(sK54(U_288,U_286,U_284),sK55(U_288,U_286,U_284))
& in(sK55(U_288,U_286,U_284),U_286)
& in(sK54(U_288,U_286,U_284),U_288) )
| ( ! [U_272] :
( ! [U_271] :
( sK52(U_288,U_286,U_284) != ordered_pair(U_272,U_271)
| ~ in(U_271,U_286) )
| ~ in(U_272,U_288) )
& in(sK52(U_288,U_286,U_284),U_284) ) )
& ! [U_287,U_285,U_283] :
( ( ! [U_280] :
( in(U_280,U_283)
| ! [U_269] :
( ! [U_268] :
( U_280 != ordered_pair(U_269,U_268)
| ~ in(U_268,U_285) )
| ~ in(U_269,U_287) ) )
& ! [U_279] :
( ( U_279 = ordered_pair(sK50(U_287,U_285,U_283,U_279),sK51(U_287,U_285,U_283,U_279))
& in(sK51(U_287,U_285,U_283,U_279),U_285)
& in(sK50(U_287,U_285,U_283,U_279),U_287) )
| ~ in(U_279,U_283) ) )
| U_283 != cartesian_product2(U_287,U_285) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_273,sK55(U_288,U_286,U_284))],[f_32_8]) ).
fof(f_32_10,plain,
( ! [U_284,U_286,U_288] :
( ~ in(sK53(U_288,U_286,U_284),U_284)
| ~ sP74(U_284,U_286,U_288) )
& ! [U_284,U_286,U_288] :
( sK53(U_288,U_286,U_284) = ordered_pair(sK54(U_288,U_286,U_284),sK55(U_288,U_286,U_284))
| ~ sP74(U_284,U_286,U_288) )
& ! [U_284,U_286,U_288] :
( in(sK55(U_288,U_286,U_284),U_286)
| ~ sP74(U_284,U_286,U_288) )
& ! [U_284,U_286,U_288] :
( in(sK54(U_288,U_286,U_284),U_288)
| ~ sP74(U_284,U_286,U_288) )
& ! [U_284,U_272,U_271,U_286,U_288] :
( sK52(U_288,U_286,U_284) != ordered_pair(U_272,U_271)
| ~ in(U_271,U_286)
| ~ in(U_272,U_288)
| ~ sP73(U_284,U_272,U_271,U_286,U_288) )
& ! [U_284,U_272,U_271,U_286,U_288] :
( in(sK52(U_288,U_286,U_284),U_284)
| ~ sP73(U_284,U_272,U_271,U_286,U_288) )
& ! [U_283,U_285,U_279,U_287] :
( U_279 = ordered_pair(sK50(U_287,U_285,U_283,U_279),sK51(U_287,U_285,U_283,U_279))
| ~ sP71(U_283,U_285,U_279,U_287) )
& ! [U_283,U_285,U_279,U_287] :
( in(sK51(U_287,U_285,U_283,U_279),U_285)
| ~ sP71(U_283,U_285,U_279,U_287) )
& ! [U_283,U_285,U_279,U_287] :
( in(sK50(U_287,U_285,U_283,U_279),U_287)
| ~ sP71(U_283,U_285,U_279,U_287) )
& ! [U_283,U_285,U_268,U_280,U_279,U_269,U_287] :
( in(U_280,U_283)
| U_280 != ordered_pair(U_269,U_268)
| ~ in(U_268,U_285)
| ~ in(U_269,U_287)
| ~ sP72(U_283,U_285,U_268,U_280,U_279,U_269,U_287) )
& ! [U_283,U_285,U_268,U_280,U_279,U_269,U_287] :
( sP71(U_283,U_285,U_279,U_287)
| ~ in(U_279,U_283)
| ~ sP72(U_283,U_285,U_268,U_280,U_279,U_269,U_287) )
& ! [U_284,U_272,U_271,U_286,U_288] :
( U_284 = cartesian_product2(U_288,U_286)
| sP74(U_284,U_286,U_288)
| sP73(U_284,U_272,U_271,U_286,U_288) )
& ! [U_283,U_285,U_268,U_280,U_279,U_269,U_287] :
( sP72(U_283,U_285,U_268,U_280,U_279,U_269,U_287)
| U_283 != cartesian_product2(U_287,U_285) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP71,sP72,sP73,sP74])],[f_32_9]) ).
cnf(f_32_11,plain,
( sP72(U_283,U_285,U_268,U_280,U_279,U_269,U_287)
| U_283 != cartesian_product2(U_287,U_285) ),
inference(clausify,[status(thm)],[f_32_10]) ).
cnf(f_32_12,plain,
( U_284 = cartesian_product2(U_288,U_286)
| sP74(U_284,U_286,U_288)
| sP73(U_284,U_272,U_271,U_286,U_288) ),
inference(clausify,[status(thm)],[f_32_10]) ).
cnf(f_32_13,plain,
( sP71(U_283,U_285,U_279,U_287)
| ~ in(U_279,U_283)
| ~ sP72(U_283,U_285,U_268,U_280,U_279,U_269,U_287) ),
inference(clausify,[status(thm)],[f_32_10]) ).
cnf(f_32_14,plain,
( in(U_280,U_283)
| U_280 != ordered_pair(U_269,U_268)
| ~ in(U_268,U_285)
| ~ in(U_269,U_287)
| ~ sP72(U_283,U_285,U_268,U_280,U_279,U_269,U_287) ),
inference(clausify,[status(thm)],[f_32_10]) ).
cnf(f_32_15,plain,
( in(sK50(U_287,U_285,U_283,U_279),U_287)
| ~ sP71(U_283,U_285,U_279,U_287) ),
inference(clausify,[status(thm)],[f_32_10]) ).
cnf(f_32_16,plain,
( in(sK51(U_287,U_285,U_283,U_279),U_285)
| ~ sP71(U_283,U_285,U_279,U_287) ),
inference(clausify,[status(thm)],[f_32_10]) ).
cnf(f_32_17,plain,
( U_279 = ordered_pair(sK50(U_287,U_285,U_283,U_279),sK51(U_287,U_285,U_283,U_279))
| ~ sP71(U_283,U_285,U_279,U_287) ),
inference(clausify,[status(thm)],[f_32_10]) ).
cnf(f_32_18,plain,
( in(sK52(U_288,U_286,U_284),U_284)
| ~ sP73(U_284,U_272,U_271,U_286,U_288) ),
inference(clausify,[status(thm)],[f_32_10]) ).
cnf(f_32_19,plain,
( sK52(U_288,U_286,U_284) != ordered_pair(U_272,U_271)
| ~ in(U_271,U_286)
| ~ in(U_272,U_288)
| ~ sP73(U_284,U_272,U_271,U_286,U_288) ),
inference(clausify,[status(thm)],[f_32_10]) ).
cnf(f_32_20,plain,
( in(sK54(U_288,U_286,U_284),U_288)
| ~ sP74(U_284,U_286,U_288) ),
inference(clausify,[status(thm)],[f_32_10]) ).
cnf(f_32_21,plain,
( in(sK55(U_288,U_286,U_284),U_286)
| ~ sP74(U_284,U_286,U_288) ),
inference(clausify,[status(thm)],[f_32_10]) ).
cnf(f_32_22,plain,
( sK53(U_288,U_286,U_284) = ordered_pair(sK54(U_288,U_286,U_284),sK55(U_288,U_286,U_284))
| ~ sP74(U_284,U_286,U_288) ),
inference(clausify,[status(thm)],[f_32_10]) ).
cnf(f_32_23,plain,
( ~ in(sK53(U_288,U_286,U_284),U_284)
| ~ sP74(U_284,U_286,U_288) ),
inference(clausify,[status(thm)],[f_32_10]) ).
fof(f_33_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_33_2,plain,
! [U_293] :
( ( epsilon_connected(U_293)
| ? [U_292,U_291] :
( ~ in(U_291,U_292)
& U_292 != U_291
& ~ in(U_292,U_291)
& in(U_291,U_293)
& in(U_292,U_293) ) )
& ( ! [U_290,U_289] :
( in(U_289,U_290)
| U_290 = U_289
| in(U_290,U_289)
| ~ in(U_289,U_293)
| ~ in(U_290,U_293) )
| ~ epsilon_connected(U_293) ) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( ! [U_295] :
( epsilon_connected(U_295)
| ? [U_292] :
( ? [U_291] :
( ~ in(U_291,U_292)
& U_292 != U_291
& ~ in(U_292,U_291)
& in(U_291,U_295) )
& in(U_292,U_295) ) )
& ! [U_294] :
( ! [U_290] :
( ! [U_289] :
( in(U_289,U_290)
| U_290 = U_289
| in(U_290,U_289)
| ~ in(U_289,U_294) )
| ~ in(U_290,U_294) )
| ~ epsilon_connected(U_294) ) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
fof(f_33_4,plain,
( ! [U_295] :
( epsilon_connected(U_295)
| ( ? [U_291] :
( ~ in(U_291,sK56(U_295))
& sK56(U_295) != U_291
& ~ in(sK56(U_295),U_291)
& in(U_291,U_295) )
& in(sK56(U_295),U_295) ) )
& ! [U_294] :
( ! [U_290] :
( ! [U_289] :
( in(U_289,U_290)
| U_290 = U_289
| in(U_290,U_289)
| ~ in(U_289,U_294) )
| ~ in(U_290,U_294) )
| ~ epsilon_connected(U_294) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_292,sK56(U_295))],[f_33_3]) ).
fof(f_33_5,plain,
( ! [U_295] :
( epsilon_connected(U_295)
| ( ~ in(sK57(U_295),sK56(U_295))
& sK56(U_295) != sK57(U_295)
& ~ in(sK56(U_295),sK57(U_295))
& in(sK57(U_295),U_295)
& in(sK56(U_295),U_295) ) )
& ! [U_294] :
( ! [U_290] :
( ! [U_289] :
( in(U_289,U_290)
| U_290 = U_289
| in(U_290,U_289)
| ~ in(U_289,U_294) )
| ~ in(U_290,U_294) )
| ~ epsilon_connected(U_294) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_291,sK57(U_295))],[f_33_4]) ).
fof(f_33_6,plain,
( ! [U_295] :
( ~ in(sK57(U_295),sK56(U_295))
| ~ sP75(U_295) )
& ! [U_295] :
( sK56(U_295) != sK57(U_295)
| ~ sP75(U_295) )
& ! [U_295] :
( ~ in(sK56(U_295),sK57(U_295))
| ~ sP75(U_295) )
& ! [U_295] :
( in(sK57(U_295),U_295)
| ~ sP75(U_295) )
& ! [U_295] :
( in(sK56(U_295),U_295)
| ~ sP75(U_295) )
& ! [U_295] :
( epsilon_connected(U_295)
| sP75(U_295) )
& ! [U_289,U_290,U_294] :
( in(U_289,U_290)
| U_290 = U_289
| in(U_290,U_289)
| ~ in(U_289,U_294)
| ~ in(U_290,U_294)
| ~ epsilon_connected(U_294) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP75])],[f_33_5]) ).
cnf(f_33_7,plain,
( in(U_289,U_290)
| U_290 = U_289
| in(U_290,U_289)
| ~ in(U_289,U_294)
| ~ in(U_290,U_294)
| ~ epsilon_connected(U_294) ),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_33_8,plain,
( epsilon_connected(U_295)
| sP75(U_295) ),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_33_9,plain,
( in(sK56(U_295),U_295)
| ~ sP75(U_295) ),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_33_10,plain,
( in(sK57(U_295),U_295)
| ~ sP75(U_295) ),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_33_11,plain,
( ~ in(sK56(U_295),sK57(U_295))
| ~ sP75(U_295) ),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_33_12,plain,
( sK56(U_295) != sK57(U_295)
| ~ sP75(U_295) ),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_33_13,plain,
( ~ in(sK57(U_295),sK56(U_295))
| ~ sP75(U_295) ),
inference(clausify,[status(thm)],[f_33_6]) ).
fof(f_34_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_34_2,plain,
! [U_301] :
( ! [U_300] :
( ( ( subset(U_301,U_300)
| ? [U_299,U_298] :
( ~ in(ordered_pair(U_299,U_298),U_300)
& in(ordered_pair(U_299,U_298),U_301) ) )
& ( ! [U_297,U_296] :
( in(ordered_pair(U_297,U_296),U_300)
| ~ in(ordered_pair(U_297,U_296),U_301) )
| ~ subset(U_301,U_300) ) )
| ~ relation(U_300) )
| ~ relation(U_301) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_301] :
( ! [U_300] :
( ( ( subset(U_301,U_300)
| ? [U_298] :
( ~ in(ordered_pair(sK58(U_301,U_300),U_298),U_300)
& in(ordered_pair(sK58(U_301,U_300),U_298),U_301) ) )
& ( ! [U_297,U_296] :
( in(ordered_pair(U_297,U_296),U_300)
| ~ in(ordered_pair(U_297,U_296),U_301) )
| ~ subset(U_301,U_300) ) )
| ~ relation(U_300) )
| ~ relation(U_301) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_299,sK58(U_301,U_300))],[f_34_2]) ).
fof(f_34_4,plain,
! [U_301] :
( ! [U_300] :
( ( ( subset(U_301,U_300)
| ( ~ in(ordered_pair(sK58(U_301,U_300),sK59(U_301,U_300)),U_300)
& in(ordered_pair(sK58(U_301,U_300),sK59(U_301,U_300)),U_301) ) )
& ( ! [U_297,U_296] :
( in(ordered_pair(U_297,U_296),U_300)
| ~ in(ordered_pair(U_297,U_296),U_301) )
| ~ subset(U_301,U_300) ) )
| ~ relation(U_300) )
| ~ relation(U_301) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_298,sK59(U_301,U_300))],[f_34_3]) ).
fof(f_34_5,plain,
( ! [U_300,U_301] :
( ~ in(ordered_pair(sK58(U_301,U_300),sK59(U_301,U_300)),U_300)
| ~ sP76(U_300,U_301) )
& ! [U_300,U_301] :
( in(ordered_pair(sK58(U_301,U_300),sK59(U_301,U_300)),U_301)
| ~ sP76(U_300,U_301) )
& ! [U_300,U_296,U_301,U_297] :
( subset(U_301,U_300)
| sP76(U_300,U_301)
| ~ sP77(U_300,U_296,U_301,U_297) )
& ! [U_300,U_296,U_301,U_297] :
( in(ordered_pair(U_297,U_296),U_300)
| ~ in(ordered_pair(U_297,U_296),U_301)
| ~ subset(U_301,U_300)
| ~ sP77(U_300,U_296,U_301,U_297) )
& ! [U_300,U_296,U_301,U_297] :
( sP77(U_300,U_296,U_301,U_297)
| ~ relation(U_300)
| ~ relation(U_301) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP76,sP77])],[f_34_4]) ).
cnf(f_34_6,plain,
( sP77(U_300,U_296,U_301,U_297)
| ~ relation(U_300)
| ~ relation(U_301) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_7,plain,
( in(ordered_pair(U_297,U_296),U_300)
| ~ in(ordered_pair(U_297,U_296),U_301)
| ~ subset(U_301,U_300)
| ~ sP77(U_300,U_296,U_301,U_297) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_8,plain,
( subset(U_301,U_300)
| sP76(U_300,U_301)
| ~ sP77(U_300,U_296,U_301,U_297) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_9,plain,
( in(ordered_pair(sK58(U_301,U_300),sK59(U_301,U_300)),U_301)
| ~ sP76(U_300,U_301) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_10,plain,
( ~ in(ordered_pair(sK58(U_301,U_300),sK59(U_301,U_300)),U_300)
| ~ sP76(U_300,U_301) ),
inference(clausify,[status(thm)],[f_34_5]) ).
fof(f_35_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_35_2,plain,
! [U_305,U_304] :
( ( subset(U_305,U_304)
| ? [U_303] :
( ~ in(U_303,U_304)
& in(U_303,U_305) ) )
& ( ! [U_302] :
( in(U_302,U_304)
| ~ in(U_302,U_305) )
| ~ subset(U_305,U_304) ) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( ! [U_309,U_307] :
( subset(U_309,U_307)
| ? [U_303] :
( ~ in(U_303,U_307)
& in(U_303,U_309) ) )
& ! [U_308,U_306] :
( ! [U_302] :
( in(U_302,U_306)
| ~ in(U_302,U_308) )
| ~ subset(U_308,U_306) ) ),
inference(miniscope,[status(thm)],[f_35_2]) ).
fof(f_35_4,plain,
( ! [U_309,U_307] :
( subset(U_309,U_307)
| ( ~ in(sK60(U_309,U_307),U_307)
& in(sK60(U_309,U_307),U_309) ) )
& ! [U_308,U_306] :
( ! [U_302] :
( in(U_302,U_306)
| ~ in(U_302,U_308) )
| ~ subset(U_308,U_306) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_303,sK60(U_309,U_307))],[f_35_3]) ).
fof(f_35_5,plain,
( ! [U_307,U_309] :
( ~ in(sK60(U_309,U_307),U_307)
| ~ sP78(U_307,U_309) )
& ! [U_307,U_309] :
( in(sK60(U_309,U_307),U_309)
| ~ sP78(U_307,U_309) )
& ! [U_307,U_309] :
( subset(U_309,U_307)
| sP78(U_307,U_309) )
& ! [U_302,U_308,U_306] :
( in(U_302,U_306)
| ~ in(U_302,U_308)
| ~ subset(U_308,U_306) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP78])],[f_35_4]) ).
cnf(f_35_6,plain,
( in(U_302,U_306)
| ~ in(U_302,U_308)
| ~ subset(U_308,U_306) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_7,plain,
( subset(U_309,U_307)
| sP78(U_307,U_309) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_8,plain,
( in(sK60(U_309,U_307),U_309)
| ~ sP78(U_307,U_309) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_9,plain,
( ~ in(sK60(U_309,U_307),U_307)
| ~ sP78(U_307,U_309) ),
inference(clausify,[status(thm)],[f_35_5]) ).
fof(f_36_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_36_2,plain,
! [U_314,U_313,U_312] :
( ( U_312 = set_intersection2(U_314,U_313)
| ? [U_311] :
( ( ~ in(U_311,U_312)
& in(U_311,U_313)
& in(U_311,U_314) )
| ( ( ~ in(U_311,U_313)
| ~ in(U_311,U_314) )
& in(U_311,U_312) ) ) )
& ( ! [U_310] :
( ( in(U_310,U_312)
| ~ in(U_310,U_313)
| ~ in(U_310,U_314) )
& ( ( in(U_310,U_313)
& in(U_310,U_314) )
| ~ in(U_310,U_312) ) )
| U_312 != set_intersection2(U_314,U_313) ) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
( ! [U_324,U_322,U_320] :
( U_320 = set_intersection2(U_324,U_322)
| ? [U_318] :
( ~ in(U_318,U_320)
& in(U_318,U_322)
& in(U_318,U_324) )
| ? [U_317] :
( ( ~ in(U_317,U_322)
| ~ in(U_317,U_324) )
& in(U_317,U_320) ) )
& ! [U_323,U_321,U_319] :
( ( ! [U_316] :
( in(U_316,U_319)
| ~ in(U_316,U_321)
| ~ in(U_316,U_323) )
& ! [U_315] :
( ( in(U_315,U_321)
& in(U_315,U_323) )
| ~ in(U_315,U_319) ) )
| U_319 != set_intersection2(U_323,U_321) ) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
fof(f_36_4,plain,
( ! [U_324,U_322,U_320] :
( U_320 = set_intersection2(U_324,U_322)
| ? [U_318] :
( ~ in(U_318,U_320)
& in(U_318,U_322)
& in(U_318,U_324) )
| ( ( ~ in(sK61(U_324,U_322,U_320),U_322)
| ~ in(sK61(U_324,U_322,U_320),U_324) )
& in(sK61(U_324,U_322,U_320),U_320) ) )
& ! [U_323,U_321,U_319] :
( ( ! [U_316] :
( in(U_316,U_319)
| ~ in(U_316,U_321)
| ~ in(U_316,U_323) )
& ! [U_315] :
( ( in(U_315,U_321)
& in(U_315,U_323) )
| ~ in(U_315,U_319) ) )
| U_319 != set_intersection2(U_323,U_321) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_317,sK61(U_324,U_322,U_320))],[f_36_3]) ).
fof(f_36_5,plain,
( ! [U_324,U_322,U_320] :
( U_320 = set_intersection2(U_324,U_322)
| ( ~ in(sK62(U_324,U_322,U_320),U_320)
& in(sK62(U_324,U_322,U_320),U_322)
& in(sK62(U_324,U_322,U_320),U_324) )
| ( ( ~ in(sK61(U_324,U_322,U_320),U_322)
| ~ in(sK61(U_324,U_322,U_320),U_324) )
& in(sK61(U_324,U_322,U_320),U_320) ) )
& ! [U_323,U_321,U_319] :
( ( ! [U_316] :
( in(U_316,U_319)
| ~ in(U_316,U_321)
| ~ in(U_316,U_323) )
& ! [U_315] :
( ( in(U_315,U_321)
& in(U_315,U_323) )
| ~ in(U_315,U_319) ) )
| U_319 != set_intersection2(U_323,U_321) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_318,sK62(U_324,U_322,U_320))],[f_36_4]) ).
fof(f_36_6,plain,
( ! [U_320,U_322,U_324] :
( ~ in(sK62(U_324,U_322,U_320),U_320)
| ~ sP82(U_320,U_322,U_324) )
& ! [U_320,U_322,U_324] :
( in(sK62(U_324,U_322,U_320),U_322)
| ~ sP82(U_320,U_322,U_324) )
& ! [U_320,U_322,U_324] :
( in(sK62(U_324,U_322,U_320),U_324)
| ~ sP82(U_320,U_322,U_324) )
& ! [U_320,U_322,U_324] :
( ~ in(sK61(U_324,U_322,U_320),U_322)
| ~ in(sK61(U_324,U_322,U_320),U_324)
| ~ sP81(U_320,U_322,U_324) )
& ! [U_320,U_322,U_324] :
( in(sK61(U_324,U_322,U_320),U_320)
| ~ sP81(U_320,U_322,U_324) )
& ! [U_315,U_321,U_323] :
( in(U_315,U_321)
| ~ sP79(U_315,U_321,U_323) )
& ! [U_315,U_321,U_323] :
( in(U_315,U_323)
| ~ sP79(U_315,U_321,U_323) )
& ! [U_319,U_316,U_315,U_321,U_323] :
( in(U_316,U_319)
| ~ in(U_316,U_321)
| ~ in(U_316,U_323)
| ~ sP80(U_319,U_316,U_315,U_321,U_323) )
& ! [U_319,U_316,U_315,U_321,U_323] :
( sP79(U_315,U_321,U_323)
| ~ in(U_315,U_319)
| ~ sP80(U_319,U_316,U_315,U_321,U_323) )
& ! [U_320,U_322,U_324] :
( U_320 = set_intersection2(U_324,U_322)
| sP82(U_320,U_322,U_324)
| sP81(U_320,U_322,U_324) )
& ! [U_319,U_316,U_315,U_321,U_323] :
( sP80(U_319,U_316,U_315,U_321,U_323)
| U_319 != set_intersection2(U_323,U_321) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP79,sP80,sP81,sP82])],[f_36_5]) ).
cnf(f_36_7,plain,
( sP80(U_319,U_316,U_315,U_321,U_323)
| U_319 != set_intersection2(U_323,U_321) ),
inference(clausify,[status(thm)],[f_36_6]) ).
cnf(f_36_8,plain,
( U_320 = set_intersection2(U_324,U_322)
| sP82(U_320,U_322,U_324)
| sP81(U_320,U_322,U_324) ),
inference(clausify,[status(thm)],[f_36_6]) ).
cnf(f_36_9,plain,
( sP79(U_315,U_321,U_323)
| ~ in(U_315,U_319)
| ~ sP80(U_319,U_316,U_315,U_321,U_323) ),
inference(clausify,[status(thm)],[f_36_6]) ).
cnf(f_36_10,plain,
( in(U_316,U_319)
| ~ in(U_316,U_321)
| ~ in(U_316,U_323)
| ~ sP80(U_319,U_316,U_315,U_321,U_323) ),
inference(clausify,[status(thm)],[f_36_6]) ).
cnf(f_36_11,plain,
( in(U_315,U_323)
| ~ sP79(U_315,U_321,U_323) ),
inference(clausify,[status(thm)],[f_36_6]) ).
cnf(f_36_12,plain,
( in(U_315,U_321)
| ~ sP79(U_315,U_321,U_323) ),
inference(clausify,[status(thm)],[f_36_6]) ).
cnf(f_36_13,plain,
( in(sK61(U_324,U_322,U_320),U_320)
| ~ sP81(U_320,U_322,U_324) ),
inference(clausify,[status(thm)],[f_36_6]) ).
cnf(f_36_14,plain,
( ~ in(sK61(U_324,U_322,U_320),U_322)
| ~ in(sK61(U_324,U_322,U_320),U_324)
| ~ sP81(U_320,U_322,U_324) ),
inference(clausify,[status(thm)],[f_36_6]) ).
cnf(f_36_15,plain,
( in(sK62(U_324,U_322,U_320),U_324)
| ~ sP82(U_320,U_322,U_324) ),
inference(clausify,[status(thm)],[f_36_6]) ).
cnf(f_36_16,plain,
( in(sK62(U_324,U_322,U_320),U_322)
| ~ sP82(U_320,U_322,U_324) ),
inference(clausify,[status(thm)],[f_36_6]) ).
cnf(f_36_17,plain,
( ~ in(sK62(U_324,U_322,U_320),U_320)
| ~ sP82(U_320,U_322,U_324) ),
inference(clausify,[status(thm)],[f_36_6]) ).
fof(f_37_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_37_2,plain,
! [U_327] :
( ! [U_326,U_325] :
( ( ( ( U_325 = apply(U_327,U_326)
| U_325 != empty_set )
& ( U_325 = empty_set
| U_325 != apply(U_327,U_326) ) )
| in(U_326,relation_dom(U_327)) )
& ( ( ( U_325 = apply(U_327,U_326)
| ~ in(ordered_pair(U_326,U_325),U_327) )
& ( in(ordered_pair(U_326,U_325),U_327)
| U_325 != apply(U_327,U_326) ) )
| ~ in(U_326,relation_dom(U_327)) ) )
| ~ function(U_327)
| ~ relation(U_327) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_327] :
( ( ! [U_335] :
( ( ! [U_333] :
( U_333 = apply(U_327,U_335)
| U_333 != empty_set )
& ! [U_332] :
( U_332 = empty_set
| U_332 != apply(U_327,U_335) ) )
| in(U_335,relation_dom(U_327)) )
& ! [U_334] :
( ( ! [U_331] :
( U_331 = apply(U_327,U_334)
| ~ in(ordered_pair(U_334,U_331),U_327) )
& ! [U_330] :
( in(ordered_pair(U_334,U_330),U_327)
| U_330 != apply(U_327,U_334) ) )
| ~ in(U_334,relation_dom(U_327)) ) )
| ~ function(U_327)
| ~ relation(U_327) ),
inference(miniscope,[status(thm)],[f_37_2]) ).
fof(f_37_4,plain,
( ! [U_332,U_335,U_333,U_327] :
( U_333 = apply(U_327,U_335)
| U_333 != empty_set
| ~ sP84(U_332,U_335,U_333,U_327) )
& ! [U_332,U_335,U_333,U_327] :
( U_332 = empty_set
| U_332 != apply(U_327,U_335)
| ~ sP84(U_332,U_335,U_333,U_327) )
& ! [U_330,U_334,U_331,U_327] :
( U_331 = apply(U_327,U_334)
| ~ in(ordered_pair(U_334,U_331),U_327)
| ~ sP83(U_330,U_334,U_331,U_327) )
& ! [U_330,U_334,U_331,U_327] :
( in(ordered_pair(U_334,U_330),U_327)
| U_330 != apply(U_327,U_334)
| ~ sP83(U_330,U_334,U_331,U_327) )
& ! [U_330,U_332,U_335,U_334,U_333,U_331,U_327] :
( sP84(U_332,U_335,U_333,U_327)
| in(U_335,relation_dom(U_327))
| ~ sP85(U_330,U_332,U_335,U_334,U_333,U_331,U_327) )
& ! [U_330,U_332,U_335,U_334,U_333,U_331,U_327] :
( sP83(U_330,U_334,U_331,U_327)
| ~ in(U_334,relation_dom(U_327))
| ~ sP85(U_330,U_332,U_335,U_334,U_333,U_331,U_327) )
& ! [U_330,U_332,U_335,U_334,U_333,U_331,U_327] :
( sP85(U_330,U_332,U_335,U_334,U_333,U_331,U_327)
| ~ function(U_327)
| ~ relation(U_327) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP83,sP84,sP85])],[f_37_3]) ).
cnf(f_37_5,plain,
( sP85(U_330,U_332,U_335,U_334,U_333,U_331,U_327)
| ~ function(U_327)
| ~ relation(U_327) ),
inference(clausify,[status(thm)],[f_37_4]) ).
cnf(f_37_6,plain,
( sP83(U_330,U_334,U_331,U_327)
| ~ in(U_334,relation_dom(U_327))
| ~ sP85(U_330,U_332,U_335,U_334,U_333,U_331,U_327) ),
inference(clausify,[status(thm)],[f_37_4]) ).
cnf(f_37_7,plain,
( sP84(U_332,U_335,U_333,U_327)
| in(U_335,relation_dom(U_327))
| ~ sP85(U_330,U_332,U_335,U_334,U_333,U_331,U_327) ),
inference(clausify,[status(thm)],[f_37_4]) ).
cnf(f_37_8,plain,
( in(ordered_pair(U_334,U_330),U_327)
| U_330 != apply(U_327,U_334)
| ~ sP83(U_330,U_334,U_331,U_327) ),
inference(clausify,[status(thm)],[f_37_4]) ).
cnf(f_37_9,plain,
( U_331 = apply(U_327,U_334)
| ~ in(ordered_pair(U_334,U_331),U_327)
| ~ sP83(U_330,U_334,U_331,U_327) ),
inference(clausify,[status(thm)],[f_37_4]) ).
cnf(f_37_10,plain,
( U_332 = empty_set
| U_332 != apply(U_327,U_335)
| ~ sP84(U_332,U_335,U_333,U_327) ),
inference(clausify,[status(thm)],[f_37_4]) ).
cnf(f_37_11,plain,
( U_333 = apply(U_327,U_335)
| U_333 != empty_set
| ~ sP84(U_332,U_335,U_333,U_327) ),
inference(clausify,[status(thm)],[f_37_4]) ).
fof(f_38_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_38_2,plain,
! [U_336] :
( ( ordinal(U_336)
| ~ epsilon_connected(U_336)
| ~ epsilon_transitive(U_336) )
& ( ( epsilon_connected(U_336)
& epsilon_transitive(U_336) )
| ~ ordinal(U_336) ) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
( ! [U_338] :
( ordinal(U_338)
| ~ epsilon_connected(U_338)
| ~ epsilon_transitive(U_338) )
& ! [U_337] :
( ( epsilon_connected(U_337)
& epsilon_transitive(U_337) )
| ~ ordinal(U_337) ) ),
inference(miniscope,[status(thm)],[f_38_2]) ).
fof(f_38_4,plain,
( ! [U_337] :
( epsilon_connected(U_337)
| ~ sP86(U_337) )
& ! [U_337] :
( epsilon_transitive(U_337)
| ~ sP86(U_337) )
& ! [U_338] :
( ordinal(U_338)
| ~ epsilon_connected(U_338)
| ~ epsilon_transitive(U_338) )
& ! [U_337] :
( sP86(U_337)
| ~ ordinal(U_337) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP86])],[f_38_3]) ).
cnf(f_38_5,plain,
( sP86(U_337)
| ~ ordinal(U_337) ),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_38_6,plain,
( ordinal(U_338)
| ~ epsilon_connected(U_338)
| ~ epsilon_transitive(U_338) ),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_38_7,plain,
( epsilon_transitive(U_337)
| ~ sP86(U_337) ),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_38_8,plain,
( epsilon_connected(U_337)
| ~ sP86(U_337) ),
inference(clausify,[status(thm)],[f_38_4]) ).
fof(f_39_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_39_2,plain,
! [U_346] :
( ! [U_345] :
( ( U_345 = relation_dom(U_346)
| ? [U_344] :
( ( ~ in(U_344,U_345)
& ? [U_343] : in(ordered_pair(U_344,U_343),U_346) )
| ( ! [U_342] : ~ in(ordered_pair(U_344,U_342),U_346)
& in(U_344,U_345) ) ) )
& ( ! [U_341] :
( ( in(U_341,U_345)
| ! [U_340] : ~ in(ordered_pair(U_341,U_340),U_346) )
& ( ? [U_339] : in(ordered_pair(U_341,U_339),U_346)
| ~ in(U_341,U_345) ) )
| U_345 != relation_dom(U_346) ) )
| ~ relation(U_346) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_346] :
( ( ! [U_352] :
( U_352 = relation_dom(U_346)
| ? [U_350] :
( ~ in(U_350,U_352)
& ? [U_343] : in(ordered_pair(U_350,U_343),U_346) )
| ? [U_349] :
( ! [U_342] : ~ in(ordered_pair(U_349,U_342),U_346)
& in(U_349,U_352) ) )
& ! [U_351] :
( ( ! [U_348] :
( in(U_348,U_351)
| ! [U_340] : ~ in(ordered_pair(U_348,U_340),U_346) )
& ! [U_347] :
( ? [U_339] : in(ordered_pair(U_347,U_339),U_346)
| ~ in(U_347,U_351) ) )
| U_351 != relation_dom(U_346) ) )
| ~ relation(U_346) ),
inference(miniscope,[status(thm)],[f_39_2]) ).
fof(f_39_4,plain,
! [U_346] :
( ( ! [U_352] :
( U_352 = relation_dom(U_346)
| ? [U_350] :
( ~ in(U_350,U_352)
& ? [U_343] : in(ordered_pair(U_350,U_343),U_346) )
| ? [U_349] :
( ! [U_342] : ~ in(ordered_pair(U_349,U_342),U_346)
& in(U_349,U_352) ) )
& ! [U_351] :
( ( ! [U_348] :
( in(U_348,U_351)
| ! [U_340] : ~ in(ordered_pair(U_348,U_340),U_346) )
& ! [U_347] :
( in(ordered_pair(U_347,sK63(U_346,U_351,U_347)),U_346)
| ~ in(U_347,U_351) ) )
| U_351 != relation_dom(U_346) ) )
| ~ relation(U_346) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_339,sK63(U_346,U_351,U_347))],[f_39_3]) ).
fof(f_39_5,plain,
! [U_346] :
( ( ! [U_352] :
( U_352 = relation_dom(U_346)
| ? [U_350] :
( ~ in(U_350,U_352)
& ? [U_343] : in(ordered_pair(U_350,U_343),U_346) )
| ( ! [U_342] : ~ in(ordered_pair(sK64(U_346,U_352),U_342),U_346)
& in(sK64(U_346,U_352),U_352) ) )
& ! [U_351] :
( ( ! [U_348] :
( in(U_348,U_351)
| ! [U_340] : ~ in(ordered_pair(U_348,U_340),U_346) )
& ! [U_347] :
( in(ordered_pair(U_347,sK63(U_346,U_351,U_347)),U_346)
| ~ in(U_347,U_351) ) )
| U_351 != relation_dom(U_346) ) )
| ~ relation(U_346) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_349,sK64(U_346,U_352))],[f_39_4]) ).
fof(f_39_6,plain,
! [U_346] :
( ( ! [U_352] :
( U_352 = relation_dom(U_346)
| ( ~ in(sK65(U_346,U_352),U_352)
& ? [U_343] : in(ordered_pair(sK65(U_346,U_352),U_343),U_346) )
| ( ! [U_342] : ~ in(ordered_pair(sK64(U_346,U_352),U_342),U_346)
& in(sK64(U_346,U_352),U_352) ) )
& ! [U_351] :
( ( ! [U_348] :
( in(U_348,U_351)
| ! [U_340] : ~ in(ordered_pair(U_348,U_340),U_346) )
& ! [U_347] :
( in(ordered_pair(U_347,sK63(U_346,U_351,U_347)),U_346)
| ~ in(U_347,U_351) ) )
| U_351 != relation_dom(U_346) ) )
| ~ relation(U_346) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_350,sK65(U_346,U_352))],[f_39_5]) ).
fof(f_39_7,plain,
! [U_346] :
( ( ! [U_352] :
( U_352 = relation_dom(U_346)
| ( ~ in(sK65(U_346,U_352),U_352)
& in(ordered_pair(sK65(U_346,U_352),sK66(U_346,U_352)),U_346) )
| ( ! [U_342] : ~ in(ordered_pair(sK64(U_346,U_352),U_342),U_346)
& in(sK64(U_346,U_352),U_352) ) )
& ! [U_351] :
( ( ! [U_348] :
( in(U_348,U_351)
| ! [U_340] : ~ in(ordered_pair(U_348,U_340),U_346) )
& ! [U_347] :
( in(ordered_pair(U_347,sK63(U_346,U_351,U_347)),U_346)
| ~ in(U_347,U_351) ) )
| U_351 != relation_dom(U_346) ) )
| ~ relation(U_346) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_343,sK66(U_346,U_352))],[f_39_6]) ).
fof(f_39_8,plain,
( ! [U_346,U_352] :
( ~ in(sK65(U_346,U_352),U_352)
| ~ sP89(U_346,U_352) )
& ! [U_346,U_352] :
( in(ordered_pair(sK65(U_346,U_352),sK66(U_346,U_352)),U_346)
| ~ sP89(U_346,U_352) )
& ! [U_342,U_346,U_352] :
( ~ in(ordered_pair(sK64(U_346,U_352),U_342),U_346)
| ~ sP88(U_342,U_346,U_352) )
& ! [U_342,U_346,U_352] :
( in(sK64(U_346,U_352),U_352)
| ~ sP88(U_342,U_346,U_352) )
& ! [U_346,U_348,U_340,U_351,U_347] :
( in(U_348,U_351)
| ~ in(ordered_pair(U_348,U_340),U_346)
| ~ sP87(U_346,U_348,U_340,U_351,U_347) )
& ! [U_346,U_348,U_340,U_351,U_347] :
( in(ordered_pair(U_347,sK63(U_346,U_351,U_347)),U_346)
| ~ in(U_347,U_351)
| ~ sP87(U_346,U_348,U_340,U_351,U_347) )
& ! [U_342,U_346,U_348,U_340,U_352,U_351,U_347] :
( U_352 = relation_dom(U_346)
| sP89(U_346,U_352)
| sP88(U_342,U_346,U_352)
| ~ sP90(U_342,U_346,U_348,U_340,U_352,U_351,U_347) )
& ! [U_342,U_346,U_348,U_340,U_352,U_351,U_347] :
( sP87(U_346,U_348,U_340,U_351,U_347)
| U_351 != relation_dom(U_346)
| ~ sP90(U_342,U_346,U_348,U_340,U_352,U_351,U_347) )
& ! [U_342,U_346,U_348,U_340,U_352,U_351,U_347] :
( sP90(U_342,U_346,U_348,U_340,U_352,U_351,U_347)
| ~ relation(U_346) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP87,sP88,sP89,sP90])],[f_39_7]) ).
cnf(f_39_9,plain,
( sP90(U_342,U_346,U_348,U_340,U_352,U_351,U_347)
| ~ relation(U_346) ),
inference(clausify,[status(thm)],[f_39_8]) ).
cnf(f_39_10,plain,
( sP87(U_346,U_348,U_340,U_351,U_347)
| U_351 != relation_dom(U_346)
| ~ sP90(U_342,U_346,U_348,U_340,U_352,U_351,U_347) ),
inference(clausify,[status(thm)],[f_39_8]) ).
cnf(f_39_11,plain,
( U_352 = relation_dom(U_346)
| sP89(U_346,U_352)
| sP88(U_342,U_346,U_352)
| ~ sP90(U_342,U_346,U_348,U_340,U_352,U_351,U_347) ),
inference(clausify,[status(thm)],[f_39_8]) ).
cnf(f_39_12,plain,
( in(ordered_pair(U_347,sK63(U_346,U_351,U_347)),U_346)
| ~ in(U_347,U_351)
| ~ sP87(U_346,U_348,U_340,U_351,U_347) ),
inference(clausify,[status(thm)],[f_39_8]) ).
cnf(f_39_13,plain,
( in(U_348,U_351)
| ~ in(ordered_pair(U_348,U_340),U_346)
| ~ sP87(U_346,U_348,U_340,U_351,U_347) ),
inference(clausify,[status(thm)],[f_39_8]) ).
cnf(f_39_14,plain,
( in(sK64(U_346,U_352),U_352)
| ~ sP88(U_342,U_346,U_352) ),
inference(clausify,[status(thm)],[f_39_8]) ).
cnf(f_39_15,plain,
( ~ in(ordered_pair(sK64(U_346,U_352),U_342),U_346)
| ~ sP88(U_342,U_346,U_352) ),
inference(clausify,[status(thm)],[f_39_8]) ).
cnf(f_39_16,plain,
( in(ordered_pair(sK65(U_346,U_352),sK66(U_346,U_352)),U_346)
| ~ sP89(U_346,U_352) ),
inference(clausify,[status(thm)],[f_39_8]) ).
cnf(f_39_17,plain,
( ~ in(sK65(U_346,U_352),U_352)
| ~ sP89(U_346,U_352) ),
inference(clausify,[status(thm)],[f_39_8]) ).
fof(f_40_1,plain,
! [A] : cast_to_subset(A) = A,
inference(fof_nnf,[status(thm)],[d4_subset_1]) ).
fof(f_40_2,plain,
! [U_353] : cast_to_subset(U_353) = U_353,
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_353] : cast_to_subset(U_353) = U_353,
inference(definitional_conversion,[status(esa)],[f_40_2]) ).
cnf(f_40_4,plain,
cast_to_subset(U_353) = U_353,
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_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_41_2,plain,
! [U_361,U_360] :
( ( U_360 = union(U_361)
| ? [U_359] :
( ( ~ in(U_359,U_360)
& ? [U_358] :
( in(U_358,U_361)
& in(U_359,U_358) ) )
| ( ! [U_357] :
( ~ in(U_357,U_361)
| ~ in(U_359,U_357) )
& in(U_359,U_360) ) ) )
& ( ! [U_356] :
( ( in(U_356,U_360)
| ! [U_355] :
( ~ in(U_355,U_361)
| ~ in(U_356,U_355) ) )
& ( ? [U_354] :
( in(U_354,U_361)
& in(U_356,U_354) )
| ~ in(U_356,U_360) ) )
| U_360 != union(U_361) ) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
( ! [U_369,U_367] :
( U_367 = union(U_369)
| ? [U_365] :
( ~ in(U_365,U_367)
& ? [U_358] :
( in(U_358,U_369)
& in(U_365,U_358) ) )
| ? [U_364] :
( ! [U_357] :
( ~ in(U_357,U_369)
| ~ in(U_364,U_357) )
& in(U_364,U_367) ) )
& ! [U_368,U_366] :
( ( ! [U_363] :
( in(U_363,U_366)
| ! [U_355] :
( ~ in(U_355,U_368)
| ~ in(U_363,U_355) ) )
& ! [U_362] :
( ? [U_354] :
( in(U_354,U_368)
& in(U_362,U_354) )
| ~ in(U_362,U_366) ) )
| U_366 != union(U_368) ) ),
inference(miniscope,[status(thm)],[f_41_2]) ).
fof(f_41_4,plain,
( ! [U_369,U_367] :
( U_367 = union(U_369)
| ? [U_365] :
( ~ in(U_365,U_367)
& ? [U_358] :
( in(U_358,U_369)
& in(U_365,U_358) ) )
| ? [U_364] :
( ! [U_357] :
( ~ in(U_357,U_369)
| ~ in(U_364,U_357) )
& in(U_364,U_367) ) )
& ! [U_368,U_366] :
( ( ! [U_363] :
( in(U_363,U_366)
| ! [U_355] :
( ~ in(U_355,U_368)
| ~ in(U_363,U_355) ) )
& ! [U_362] :
( ( in(sK67(U_368,U_366,U_362),U_368)
& in(U_362,sK67(U_368,U_366,U_362)) )
| ~ in(U_362,U_366) ) )
| U_366 != union(U_368) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_354,sK67(U_368,U_366,U_362))],[f_41_3]) ).
fof(f_41_5,plain,
( ! [U_369,U_367] :
( U_367 = union(U_369)
| ? [U_365] :
( ~ in(U_365,U_367)
& ? [U_358] :
( in(U_358,U_369)
& in(U_365,U_358) ) )
| ( ! [U_357] :
( ~ in(U_357,U_369)
| ~ in(sK68(U_369,U_367),U_357) )
& in(sK68(U_369,U_367),U_367) ) )
& ! [U_368,U_366] :
( ( ! [U_363] :
( in(U_363,U_366)
| ! [U_355] :
( ~ in(U_355,U_368)
| ~ in(U_363,U_355) ) )
& ! [U_362] :
( ( in(sK67(U_368,U_366,U_362),U_368)
& in(U_362,sK67(U_368,U_366,U_362)) )
| ~ in(U_362,U_366) ) )
| U_366 != union(U_368) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_364,sK68(U_369,U_367))],[f_41_4]) ).
fof(f_41_6,plain,
( ! [U_369,U_367] :
( U_367 = union(U_369)
| ( ~ in(sK69(U_369,U_367),U_367)
& ? [U_358] :
( in(U_358,U_369)
& in(sK69(U_369,U_367),U_358) ) )
| ( ! [U_357] :
( ~ in(U_357,U_369)
| ~ in(sK68(U_369,U_367),U_357) )
& in(sK68(U_369,U_367),U_367) ) )
& ! [U_368,U_366] :
( ( ! [U_363] :
( in(U_363,U_366)
| ! [U_355] :
( ~ in(U_355,U_368)
| ~ in(U_363,U_355) ) )
& ! [U_362] :
( ( in(sK67(U_368,U_366,U_362),U_368)
& in(U_362,sK67(U_368,U_366,U_362)) )
| ~ in(U_362,U_366) ) )
| U_366 != union(U_368) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_365,sK69(U_369,U_367))],[f_41_5]) ).
fof(f_41_7,plain,
( ! [U_369,U_367] :
( U_367 = union(U_369)
| ( ~ in(sK69(U_369,U_367),U_367)
& in(sK70(U_369,U_367),U_369)
& in(sK69(U_369,U_367),sK70(U_369,U_367)) )
| ( ! [U_357] :
( ~ in(U_357,U_369)
| ~ in(sK68(U_369,U_367),U_357) )
& in(sK68(U_369,U_367),U_367) ) )
& ! [U_368,U_366] :
( ( ! [U_363] :
( in(U_363,U_366)
| ! [U_355] :
( ~ in(U_355,U_368)
| ~ in(U_363,U_355) ) )
& ! [U_362] :
( ( in(sK67(U_368,U_366,U_362),U_368)
& in(U_362,sK67(U_368,U_366,U_362)) )
| ~ in(U_362,U_366) ) )
| U_366 != union(U_368) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_358,sK70(U_369,U_367))],[f_41_6]) ).
fof(f_41_8,plain,
( ! [U_367,U_369] :
( ~ in(sK69(U_369,U_367),U_367)
| ~ sP94(U_367,U_369) )
& ! [U_367,U_369] :
( in(sK70(U_369,U_367),U_369)
| ~ sP94(U_367,U_369) )
& ! [U_367,U_369] :
( in(sK69(U_369,U_367),sK70(U_369,U_367))
| ~ sP94(U_367,U_369) )
& ! [U_357,U_367,U_369] :
( ~ in(U_357,U_369)
| ~ in(sK68(U_369,U_367),U_357)
| ~ sP93(U_357,U_367,U_369) )
& ! [U_357,U_367,U_369] :
( in(sK68(U_369,U_367),U_367)
| ~ sP93(U_357,U_367,U_369) )
& ! [U_362,U_366,U_368] :
( in(sK67(U_368,U_366,U_362),U_368)
| ~ sP91(U_362,U_366,U_368) )
& ! [U_362,U_366,U_368] :
( in(U_362,sK67(U_368,U_366,U_362))
| ~ sP91(U_362,U_366,U_368) )
& ! [U_363,U_362,U_355,U_366,U_368] :
( in(U_363,U_366)
| ~ in(U_355,U_368)
| ~ in(U_363,U_355)
| ~ sP92(U_363,U_362,U_355,U_366,U_368) )
& ! [U_363,U_362,U_355,U_366,U_368] :
( sP91(U_362,U_366,U_368)
| ~ in(U_362,U_366)
| ~ sP92(U_363,U_362,U_355,U_366,U_368) )
& ! [U_357,U_367,U_369] :
( U_367 = union(U_369)
| sP94(U_367,U_369)
| sP93(U_357,U_367,U_369) )
& ! [U_363,U_362,U_355,U_366,U_368] :
( sP92(U_363,U_362,U_355,U_366,U_368)
| U_366 != union(U_368) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP91,sP92,sP93,sP94])],[f_41_7]) ).
cnf(f_41_9,plain,
( sP92(U_363,U_362,U_355,U_366,U_368)
| U_366 != union(U_368) ),
inference(clausify,[status(thm)],[f_41_8]) ).
cnf(f_41_10,plain,
( U_367 = union(U_369)
| sP94(U_367,U_369)
| sP93(U_357,U_367,U_369) ),
inference(clausify,[status(thm)],[f_41_8]) ).
cnf(f_41_11,plain,
( sP91(U_362,U_366,U_368)
| ~ in(U_362,U_366)
| ~ sP92(U_363,U_362,U_355,U_366,U_368) ),
inference(clausify,[status(thm)],[f_41_8]) ).
cnf(f_41_12,plain,
( in(U_363,U_366)
| ~ in(U_355,U_368)
| ~ in(U_363,U_355)
| ~ sP92(U_363,U_362,U_355,U_366,U_368) ),
inference(clausify,[status(thm)],[f_41_8]) ).
cnf(f_41_13,plain,
( in(U_362,sK67(U_368,U_366,U_362))
| ~ sP91(U_362,U_366,U_368) ),
inference(clausify,[status(thm)],[f_41_8]) ).
cnf(f_41_14,plain,
( in(sK67(U_368,U_366,U_362),U_368)
| ~ sP91(U_362,U_366,U_368) ),
inference(clausify,[status(thm)],[f_41_8]) ).
cnf(f_41_15,plain,
( in(sK68(U_369,U_367),U_367)
| ~ sP93(U_357,U_367,U_369) ),
inference(clausify,[status(thm)],[f_41_8]) ).
cnf(f_41_16,plain,
( ~ in(U_357,U_369)
| ~ in(sK68(U_369,U_367),U_357)
| ~ sP93(U_357,U_367,U_369) ),
inference(clausify,[status(thm)],[f_41_8]) ).
cnf(f_41_17,plain,
( in(sK69(U_369,U_367),sK70(U_369,U_367))
| ~ sP94(U_367,U_369) ),
inference(clausify,[status(thm)],[f_41_8]) ).
cnf(f_41_18,plain,
( in(sK70(U_369,U_367),U_369)
| ~ sP94(U_367,U_369) ),
inference(clausify,[status(thm)],[f_41_8]) ).
cnf(f_41_19,plain,
( ~ in(sK69(U_369,U_367),U_367)
| ~ sP94(U_367,U_369) ),
inference(clausify,[status(thm)],[f_41_8]) ).
fof(f_42_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_42_2,plain,
! [U_374,U_373,U_372] :
( ( U_372 = set_difference(U_374,U_373)
| ? [U_371] :
( ( ~ in(U_371,U_372)
& ~ in(U_371,U_373)
& in(U_371,U_374) )
| ( ( in(U_371,U_373)
| ~ in(U_371,U_374) )
& in(U_371,U_372) ) ) )
& ( ! [U_370] :
( ( in(U_370,U_372)
| in(U_370,U_373)
| ~ in(U_370,U_374) )
& ( ( ~ in(U_370,U_373)
& in(U_370,U_374) )
| ~ in(U_370,U_372) ) )
| U_372 != set_difference(U_374,U_373) ) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
( ! [U_384,U_382,U_380] :
( U_380 = set_difference(U_384,U_382)
| ? [U_378] :
( ~ in(U_378,U_380)
& ~ in(U_378,U_382)
& in(U_378,U_384) )
| ? [U_377] :
( ( in(U_377,U_382)
| ~ in(U_377,U_384) )
& in(U_377,U_380) ) )
& ! [U_383,U_381,U_379] :
( ( ! [U_376] :
( in(U_376,U_379)
| in(U_376,U_381)
| ~ in(U_376,U_383) )
& ! [U_375] :
( ( ~ in(U_375,U_381)
& in(U_375,U_383) )
| ~ in(U_375,U_379) ) )
| U_379 != set_difference(U_383,U_381) ) ),
inference(miniscope,[status(thm)],[f_42_2]) ).
fof(f_42_4,plain,
( ! [U_384,U_382,U_380] :
( U_380 = set_difference(U_384,U_382)
| ? [U_378] :
( ~ in(U_378,U_380)
& ~ in(U_378,U_382)
& in(U_378,U_384) )
| ( ( in(sK71(U_384,U_382,U_380),U_382)
| ~ in(sK71(U_384,U_382,U_380),U_384) )
& in(sK71(U_384,U_382,U_380),U_380) ) )
& ! [U_383,U_381,U_379] :
( ( ! [U_376] :
( in(U_376,U_379)
| in(U_376,U_381)
| ~ in(U_376,U_383) )
& ! [U_375] :
( ( ~ in(U_375,U_381)
& in(U_375,U_383) )
| ~ in(U_375,U_379) ) )
| U_379 != set_difference(U_383,U_381) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_377,sK71(U_384,U_382,U_380))],[f_42_3]) ).
fof(f_42_5,plain,
( ! [U_384,U_382,U_380] :
( U_380 = set_difference(U_384,U_382)
| ( ~ in(sK72(U_384,U_382,U_380),U_380)
& ~ in(sK72(U_384,U_382,U_380),U_382)
& in(sK72(U_384,U_382,U_380),U_384) )
| ( ( in(sK71(U_384,U_382,U_380),U_382)
| ~ in(sK71(U_384,U_382,U_380),U_384) )
& in(sK71(U_384,U_382,U_380),U_380) ) )
& ! [U_383,U_381,U_379] :
( ( ! [U_376] :
( in(U_376,U_379)
| in(U_376,U_381)
| ~ in(U_376,U_383) )
& ! [U_375] :
( ( ~ in(U_375,U_381)
& in(U_375,U_383) )
| ~ in(U_375,U_379) ) )
| U_379 != set_difference(U_383,U_381) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_378,sK72(U_384,U_382,U_380))],[f_42_4]) ).
fof(f_42_6,plain,
( ! [U_384,U_380,U_382] :
( ~ in(sK72(U_384,U_382,U_380),U_380)
| ~ sP98(U_384,U_380,U_382) )
& ! [U_384,U_380,U_382] :
( ~ in(sK72(U_384,U_382,U_380),U_382)
| ~ sP98(U_384,U_380,U_382) )
& ! [U_384,U_380,U_382] :
( in(sK72(U_384,U_382,U_380),U_384)
| ~ sP98(U_384,U_380,U_382) )
& ! [U_384,U_380,U_382] :
( in(sK71(U_384,U_382,U_380),U_382)
| ~ in(sK71(U_384,U_382,U_380),U_384)
| ~ sP97(U_384,U_380,U_382) )
& ! [U_384,U_380,U_382] :
( in(sK71(U_384,U_382,U_380),U_380)
| ~ sP97(U_384,U_380,U_382) )
& ! [U_383,U_381,U_375] :
( ~ in(U_375,U_381)
| ~ sP95(U_383,U_381,U_375) )
& ! [U_383,U_381,U_375] :
( in(U_375,U_383)
| ~ sP95(U_383,U_381,U_375) )
& ! [U_376,U_383,U_379,U_381,U_375] :
( in(U_376,U_379)
| in(U_376,U_381)
| ~ in(U_376,U_383)
| ~ sP96(U_376,U_383,U_379,U_381,U_375) )
& ! [U_376,U_383,U_379,U_381,U_375] :
( sP95(U_383,U_381,U_375)
| ~ in(U_375,U_379)
| ~ sP96(U_376,U_383,U_379,U_381,U_375) )
& ! [U_384,U_380,U_382] :
( U_380 = set_difference(U_384,U_382)
| sP98(U_384,U_380,U_382)
| sP97(U_384,U_380,U_382) )
& ! [U_376,U_383,U_379,U_381,U_375] :
( sP96(U_376,U_383,U_379,U_381,U_375)
| U_379 != set_difference(U_383,U_381) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP95,sP96,sP97,sP98])],[f_42_5]) ).
cnf(f_42_7,plain,
( sP96(U_376,U_383,U_379,U_381,U_375)
| U_379 != set_difference(U_383,U_381) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_8,plain,
( U_380 = set_difference(U_384,U_382)
| sP98(U_384,U_380,U_382)
| sP97(U_384,U_380,U_382) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_9,plain,
( sP95(U_383,U_381,U_375)
| ~ in(U_375,U_379)
| ~ sP96(U_376,U_383,U_379,U_381,U_375) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_10,plain,
( in(U_376,U_379)
| in(U_376,U_381)
| ~ in(U_376,U_383)
| ~ sP96(U_376,U_383,U_379,U_381,U_375) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_11,plain,
( in(U_375,U_383)
| ~ sP95(U_383,U_381,U_375) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_12,plain,
( ~ in(U_375,U_381)
| ~ sP95(U_383,U_381,U_375) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_13,plain,
( in(sK71(U_384,U_382,U_380),U_380)
| ~ sP97(U_384,U_380,U_382) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_14,plain,
( in(sK71(U_384,U_382,U_380),U_382)
| ~ in(sK71(U_384,U_382,U_380),U_384)
| ~ sP97(U_384,U_380,U_382) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_15,plain,
( in(sK72(U_384,U_382,U_380),U_384)
| ~ sP98(U_384,U_380,U_382) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_16,plain,
( ~ in(sK72(U_384,U_382,U_380),U_382)
| ~ sP98(U_384,U_380,U_382) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_17,plain,
( ~ in(sK72(U_384,U_382,U_380),U_380)
| ~ sP98(U_384,U_380,U_382) ),
inference(clausify,[status(thm)],[f_42_6]) ).
fof(f_43_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_43_2,plain,
! [U_392] :
( ! [U_391] :
( ( U_391 = relation_rng(U_392)
| ? [U_390] :
( ( ~ in(U_390,U_391)
& ? [U_389] :
( U_390 = apply(U_392,U_389)
& in(U_389,relation_dom(U_392)) ) )
| ( ! [U_388] :
( U_390 != apply(U_392,U_388)
| ~ in(U_388,relation_dom(U_392)) )
& in(U_390,U_391) ) ) )
& ( ! [U_387] :
( ( in(U_387,U_391)
| ! [U_386] :
( U_387 != apply(U_392,U_386)
| ~ in(U_386,relation_dom(U_392)) ) )
& ( ? [U_385] :
( U_387 = apply(U_392,U_385)
& in(U_385,relation_dom(U_392)) )
| ~ in(U_387,U_391) ) )
| U_391 != relation_rng(U_392) ) )
| ~ function(U_392)
| ~ relation(U_392) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_392] :
( ( ! [U_398] :
( U_398 = relation_rng(U_392)
| ? [U_396] :
( ~ in(U_396,U_398)
& ? [U_389] :
( U_396 = apply(U_392,U_389)
& in(U_389,relation_dom(U_392)) ) )
| ? [U_395] :
( ! [U_388] :
( U_395 != apply(U_392,U_388)
| ~ in(U_388,relation_dom(U_392)) )
& in(U_395,U_398) ) )
& ! [U_397] :
( ( ! [U_394] :
( in(U_394,U_397)
| ! [U_386] :
( U_394 != apply(U_392,U_386)
| ~ in(U_386,relation_dom(U_392)) ) )
& ! [U_393] :
( ? [U_385] :
( U_393 = apply(U_392,U_385)
& in(U_385,relation_dom(U_392)) )
| ~ in(U_393,U_397) ) )
| U_397 != relation_rng(U_392) ) )
| ~ function(U_392)
| ~ relation(U_392) ),
inference(miniscope,[status(thm)],[f_43_2]) ).
fof(f_43_4,plain,
! [U_392] :
( ( ! [U_398] :
( U_398 = relation_rng(U_392)
| ? [U_396] :
( ~ in(U_396,U_398)
& ? [U_389] :
( U_396 = apply(U_392,U_389)
& in(U_389,relation_dom(U_392)) ) )
| ? [U_395] :
( ! [U_388] :
( U_395 != apply(U_392,U_388)
| ~ in(U_388,relation_dom(U_392)) )
& in(U_395,U_398) ) )
& ! [U_397] :
( ( ! [U_394] :
( in(U_394,U_397)
| ! [U_386] :
( U_394 != apply(U_392,U_386)
| ~ in(U_386,relation_dom(U_392)) ) )
& ! [U_393] :
( ( U_393 = apply(U_392,sK73(U_392,U_397,U_393))
& in(sK73(U_392,U_397,U_393),relation_dom(U_392)) )
| ~ in(U_393,U_397) ) )
| U_397 != relation_rng(U_392) ) )
| ~ function(U_392)
| ~ relation(U_392) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_385,sK73(U_392,U_397,U_393))],[f_43_3]) ).
fof(f_43_5,plain,
! [U_392] :
( ( ! [U_398] :
( U_398 = relation_rng(U_392)
| ? [U_396] :
( ~ in(U_396,U_398)
& ? [U_389] :
( U_396 = apply(U_392,U_389)
& in(U_389,relation_dom(U_392)) ) )
| ( ! [U_388] :
( sK74(U_392,U_398) != apply(U_392,U_388)
| ~ in(U_388,relation_dom(U_392)) )
& in(sK74(U_392,U_398),U_398) ) )
& ! [U_397] :
( ( ! [U_394] :
( in(U_394,U_397)
| ! [U_386] :
( U_394 != apply(U_392,U_386)
| ~ in(U_386,relation_dom(U_392)) ) )
& ! [U_393] :
( ( U_393 = apply(U_392,sK73(U_392,U_397,U_393))
& in(sK73(U_392,U_397,U_393),relation_dom(U_392)) )
| ~ in(U_393,U_397) ) )
| U_397 != relation_rng(U_392) ) )
| ~ function(U_392)
| ~ relation(U_392) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_395,sK74(U_392,U_398))],[f_43_4]) ).
fof(f_43_6,plain,
! [U_392] :
( ( ! [U_398] :
( U_398 = relation_rng(U_392)
| ( ~ in(sK75(U_392,U_398),U_398)
& ? [U_389] :
( sK75(U_392,U_398) = apply(U_392,U_389)
& in(U_389,relation_dom(U_392)) ) )
| ( ! [U_388] :
( sK74(U_392,U_398) != apply(U_392,U_388)
| ~ in(U_388,relation_dom(U_392)) )
& in(sK74(U_392,U_398),U_398) ) )
& ! [U_397] :
( ( ! [U_394] :
( in(U_394,U_397)
| ! [U_386] :
( U_394 != apply(U_392,U_386)
| ~ in(U_386,relation_dom(U_392)) ) )
& ! [U_393] :
( ( U_393 = apply(U_392,sK73(U_392,U_397,U_393))
& in(sK73(U_392,U_397,U_393),relation_dom(U_392)) )
| ~ in(U_393,U_397) ) )
| U_397 != relation_rng(U_392) ) )
| ~ function(U_392)
| ~ relation(U_392) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_396,sK75(U_392,U_398))],[f_43_5]) ).
fof(f_43_7,plain,
! [U_392] :
( ( ! [U_398] :
( U_398 = relation_rng(U_392)
| ( ~ in(sK75(U_392,U_398),U_398)
& sK75(U_392,U_398) = apply(U_392,sK76(U_392,U_398))
& in(sK76(U_392,U_398),relation_dom(U_392)) )
| ( ! [U_388] :
( sK74(U_392,U_398) != apply(U_392,U_388)
| ~ in(U_388,relation_dom(U_392)) )
& in(sK74(U_392,U_398),U_398) ) )
& ! [U_397] :
( ( ! [U_394] :
( in(U_394,U_397)
| ! [U_386] :
( U_394 != apply(U_392,U_386)
| ~ in(U_386,relation_dom(U_392)) ) )
& ! [U_393] :
( ( U_393 = apply(U_392,sK73(U_392,U_397,U_393))
& in(sK73(U_392,U_397,U_393),relation_dom(U_392)) )
| ~ in(U_393,U_397) ) )
| U_397 != relation_rng(U_392) ) )
| ~ function(U_392)
| ~ relation(U_392) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_389,sK76(U_392,U_398))],[f_43_6]) ).
fof(f_43_8,plain,
( ! [U_398,U_392] :
( ~ in(sK75(U_392,U_398),U_398)
| ~ sP102(U_398,U_392) )
& ! [U_398,U_392] :
( sK75(U_392,U_398) = apply(U_392,sK76(U_392,U_398))
| ~ sP102(U_398,U_392) )
& ! [U_398,U_392] :
( in(sK76(U_392,U_398),relation_dom(U_392))
| ~ sP102(U_398,U_392) )
& ! [U_388,U_398,U_392] :
( sK74(U_392,U_398) != apply(U_392,U_388)
| ~ in(U_388,relation_dom(U_392))
| ~ sP101(U_388,U_398,U_392) )
& ! [U_388,U_398,U_392] :
( in(sK74(U_392,U_398),U_398)
| ~ sP101(U_388,U_398,U_392) )
& ! [U_397,U_393,U_392] :
( U_393 = apply(U_392,sK73(U_392,U_397,U_393))
| ~ sP99(U_397,U_393,U_392) )
& ! [U_397,U_393,U_392] :
( in(sK73(U_392,U_397,U_393),relation_dom(U_392))
| ~ sP99(U_397,U_393,U_392) )
& ! [U_397,U_393,U_394,U_386,U_392] :
( in(U_394,U_397)
| U_394 != apply(U_392,U_386)
| ~ in(U_386,relation_dom(U_392))
| ~ sP100(U_397,U_393,U_394,U_386,U_392) )
& ! [U_397,U_393,U_394,U_386,U_392] :
( sP99(U_397,U_393,U_392)
| ~ in(U_393,U_397)
| ~ sP100(U_397,U_393,U_394,U_386,U_392) )
& ! [U_397,U_393,U_394,U_386,U_388,U_398,U_392] :
( U_398 = relation_rng(U_392)
| sP102(U_398,U_392)
| sP101(U_388,U_398,U_392)
| ~ sP103(U_397,U_393,U_394,U_386,U_388,U_398,U_392) )
& ! [U_397,U_393,U_394,U_386,U_388,U_398,U_392] :
( sP100(U_397,U_393,U_394,U_386,U_392)
| U_397 != relation_rng(U_392)
| ~ sP103(U_397,U_393,U_394,U_386,U_388,U_398,U_392) )
& ! [U_397,U_393,U_394,U_386,U_388,U_398,U_392] :
( sP103(U_397,U_393,U_394,U_386,U_388,U_398,U_392)
| ~ function(U_392)
| ~ relation(U_392) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP99,sP100,sP101,sP102,sP103])],[f_43_7]) ).
cnf(f_43_9,plain,
( sP103(U_397,U_393,U_394,U_386,U_388,U_398,U_392)
| ~ function(U_392)
| ~ relation(U_392) ),
inference(clausify,[status(thm)],[f_43_8]) ).
cnf(f_43_10,plain,
( sP100(U_397,U_393,U_394,U_386,U_392)
| U_397 != relation_rng(U_392)
| ~ sP103(U_397,U_393,U_394,U_386,U_388,U_398,U_392) ),
inference(clausify,[status(thm)],[f_43_8]) ).
cnf(f_43_11,plain,
( U_398 = relation_rng(U_392)
| sP102(U_398,U_392)
| sP101(U_388,U_398,U_392)
| ~ sP103(U_397,U_393,U_394,U_386,U_388,U_398,U_392) ),
inference(clausify,[status(thm)],[f_43_8]) ).
cnf(f_43_12,plain,
( sP99(U_397,U_393,U_392)
| ~ in(U_393,U_397)
| ~ sP100(U_397,U_393,U_394,U_386,U_392) ),
inference(clausify,[status(thm)],[f_43_8]) ).
cnf(f_43_13,plain,
( in(U_394,U_397)
| U_394 != apply(U_392,U_386)
| ~ in(U_386,relation_dom(U_392))
| ~ sP100(U_397,U_393,U_394,U_386,U_392) ),
inference(clausify,[status(thm)],[f_43_8]) ).
cnf(f_43_14,plain,
( in(sK73(U_392,U_397,U_393),relation_dom(U_392))
| ~ sP99(U_397,U_393,U_392) ),
inference(clausify,[status(thm)],[f_43_8]) ).
cnf(f_43_15,plain,
( U_393 = apply(U_392,sK73(U_392,U_397,U_393))
| ~ sP99(U_397,U_393,U_392) ),
inference(clausify,[status(thm)],[f_43_8]) ).
cnf(f_43_16,plain,
( in(sK74(U_392,U_398),U_398)
| ~ sP101(U_388,U_398,U_392) ),
inference(clausify,[status(thm)],[f_43_8]) ).
cnf(f_43_17,plain,
( sK74(U_392,U_398) != apply(U_392,U_388)
| ~ in(U_388,relation_dom(U_392))
| ~ sP101(U_388,U_398,U_392) ),
inference(clausify,[status(thm)],[f_43_8]) ).
cnf(f_43_18,plain,
( in(sK76(U_392,U_398),relation_dom(U_392))
| ~ sP102(U_398,U_392) ),
inference(clausify,[status(thm)],[f_43_8]) ).
cnf(f_43_19,plain,
( sK75(U_392,U_398) = apply(U_392,sK76(U_392,U_398))
| ~ sP102(U_398,U_392) ),
inference(clausify,[status(thm)],[f_43_8]) ).
cnf(f_43_20,plain,
( ~ in(sK75(U_392,U_398),U_398)
| ~ sP102(U_398,U_392) ),
inference(clausify,[status(thm)],[f_43_8]) ).
fof(f_44_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_44_2,plain,
! [U_406] :
( ! [U_405] :
( ( U_405 = relation_rng(U_406)
| ? [U_404] :
( ( ~ in(U_404,U_405)
& ? [U_403] : in(ordered_pair(U_403,U_404),U_406) )
| ( ! [U_402] : ~ in(ordered_pair(U_402,U_404),U_406)
& in(U_404,U_405) ) ) )
& ( ! [U_401] :
( ( in(U_401,U_405)
| ! [U_400] : ~ in(ordered_pair(U_400,U_401),U_406) )
& ( ? [U_399] : in(ordered_pair(U_399,U_401),U_406)
| ~ in(U_401,U_405) ) )
| U_405 != relation_rng(U_406) ) )
| ~ relation(U_406) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_406] :
( ( ! [U_412] :
( U_412 = relation_rng(U_406)
| ? [U_410] :
( ~ in(U_410,U_412)
& ? [U_403] : in(ordered_pair(U_403,U_410),U_406) )
| ? [U_409] :
( ! [U_402] : ~ in(ordered_pair(U_402,U_409),U_406)
& in(U_409,U_412) ) )
& ! [U_411] :
( ( ! [U_408] :
( in(U_408,U_411)
| ! [U_400] : ~ in(ordered_pair(U_400,U_408),U_406) )
& ! [U_407] :
( ? [U_399] : in(ordered_pair(U_399,U_407),U_406)
| ~ in(U_407,U_411) ) )
| U_411 != relation_rng(U_406) ) )
| ~ relation(U_406) ),
inference(miniscope,[status(thm)],[f_44_2]) ).
fof(f_44_4,plain,
! [U_406] :
( ( ! [U_412] :
( U_412 = relation_rng(U_406)
| ? [U_410] :
( ~ in(U_410,U_412)
& ? [U_403] : in(ordered_pair(U_403,U_410),U_406) )
| ? [U_409] :
( ! [U_402] : ~ in(ordered_pair(U_402,U_409),U_406)
& in(U_409,U_412) ) )
& ! [U_411] :
( ( ! [U_408] :
( in(U_408,U_411)
| ! [U_400] : ~ in(ordered_pair(U_400,U_408),U_406) )
& ! [U_407] :
( in(ordered_pair(sK77(U_406,U_411,U_407),U_407),U_406)
| ~ in(U_407,U_411) ) )
| U_411 != relation_rng(U_406) ) )
| ~ relation(U_406) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_399,sK77(U_406,U_411,U_407))],[f_44_3]) ).
fof(f_44_5,plain,
! [U_406] :
( ( ! [U_412] :
( U_412 = relation_rng(U_406)
| ? [U_410] :
( ~ in(U_410,U_412)
& ? [U_403] : in(ordered_pair(U_403,U_410),U_406) )
| ( ! [U_402] : ~ in(ordered_pair(U_402,sK78(U_406,U_412)),U_406)
& in(sK78(U_406,U_412),U_412) ) )
& ! [U_411] :
( ( ! [U_408] :
( in(U_408,U_411)
| ! [U_400] : ~ in(ordered_pair(U_400,U_408),U_406) )
& ! [U_407] :
( in(ordered_pair(sK77(U_406,U_411,U_407),U_407),U_406)
| ~ in(U_407,U_411) ) )
| U_411 != relation_rng(U_406) ) )
| ~ relation(U_406) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_409,sK78(U_406,U_412))],[f_44_4]) ).
fof(f_44_6,plain,
! [U_406] :
( ( ! [U_412] :
( U_412 = relation_rng(U_406)
| ( ~ in(sK79(U_406,U_412),U_412)
& ? [U_403] : in(ordered_pair(U_403,sK79(U_406,U_412)),U_406) )
| ( ! [U_402] : ~ in(ordered_pair(U_402,sK78(U_406,U_412)),U_406)
& in(sK78(U_406,U_412),U_412) ) )
& ! [U_411] :
( ( ! [U_408] :
( in(U_408,U_411)
| ! [U_400] : ~ in(ordered_pair(U_400,U_408),U_406) )
& ! [U_407] :
( in(ordered_pair(sK77(U_406,U_411,U_407),U_407),U_406)
| ~ in(U_407,U_411) ) )
| U_411 != relation_rng(U_406) ) )
| ~ relation(U_406) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_410,sK79(U_406,U_412))],[f_44_5]) ).
fof(f_44_7,plain,
! [U_406] :
( ( ! [U_412] :
( U_412 = relation_rng(U_406)
| ( ~ in(sK79(U_406,U_412),U_412)
& in(ordered_pair(sK80(U_406,U_412),sK79(U_406,U_412)),U_406) )
| ( ! [U_402] : ~ in(ordered_pair(U_402,sK78(U_406,U_412)),U_406)
& in(sK78(U_406,U_412),U_412) ) )
& ! [U_411] :
( ( ! [U_408] :
( in(U_408,U_411)
| ! [U_400] : ~ in(ordered_pair(U_400,U_408),U_406) )
& ! [U_407] :
( in(ordered_pair(sK77(U_406,U_411,U_407),U_407),U_406)
| ~ in(U_407,U_411) ) )
| U_411 != relation_rng(U_406) ) )
| ~ relation(U_406) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_403,sK80(U_406,U_412))],[f_44_6]) ).
fof(f_44_8,plain,
( ! [U_406,U_412] :
( ~ in(sK79(U_406,U_412),U_412)
| ~ sP106(U_406,U_412) )
& ! [U_406,U_412] :
( in(ordered_pair(sK80(U_406,U_412),sK79(U_406,U_412)),U_406)
| ~ sP106(U_406,U_412) )
& ! [U_406,U_402,U_412] :
( ~ in(ordered_pair(U_402,sK78(U_406,U_412)),U_406)
| ~ sP105(U_406,U_402,U_412) )
& ! [U_406,U_402,U_412] :
( in(sK78(U_406,U_412),U_412)
| ~ sP105(U_406,U_402,U_412) )
& ! [U_406,U_400,U_411,U_408,U_407] :
( in(U_408,U_411)
| ~ in(ordered_pair(U_400,U_408),U_406)
| ~ sP104(U_406,U_400,U_411,U_408,U_407) )
& ! [U_406,U_400,U_411,U_408,U_407] :
( in(ordered_pair(sK77(U_406,U_411,U_407),U_407),U_406)
| ~ in(U_407,U_411)
| ~ sP104(U_406,U_400,U_411,U_408,U_407) )
& ! [U_406,U_400,U_402,U_411,U_408,U_407,U_412] :
( U_412 = relation_rng(U_406)
| sP106(U_406,U_412)
| sP105(U_406,U_402,U_412)
| ~ sP107(U_406,U_400,U_402,U_411,U_408,U_407,U_412) )
& ! [U_406,U_400,U_402,U_411,U_408,U_407,U_412] :
( sP104(U_406,U_400,U_411,U_408,U_407)
| U_411 != relation_rng(U_406)
| ~ sP107(U_406,U_400,U_402,U_411,U_408,U_407,U_412) )
& ! [U_406,U_400,U_402,U_411,U_408,U_407,U_412] :
( sP107(U_406,U_400,U_402,U_411,U_408,U_407,U_412)
| ~ relation(U_406) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP104,sP105,sP106,sP107])],[f_44_7]) ).
cnf(f_44_9,plain,
( sP107(U_406,U_400,U_402,U_411,U_408,U_407,U_412)
| ~ relation(U_406) ),
inference(clausify,[status(thm)],[f_44_8]) ).
cnf(f_44_10,plain,
( sP104(U_406,U_400,U_411,U_408,U_407)
| U_411 != relation_rng(U_406)
| ~ sP107(U_406,U_400,U_402,U_411,U_408,U_407,U_412) ),
inference(clausify,[status(thm)],[f_44_8]) ).
cnf(f_44_11,plain,
( U_412 = relation_rng(U_406)
| sP106(U_406,U_412)
| sP105(U_406,U_402,U_412)
| ~ sP107(U_406,U_400,U_402,U_411,U_408,U_407,U_412) ),
inference(clausify,[status(thm)],[f_44_8]) ).
cnf(f_44_12,plain,
( in(ordered_pair(sK77(U_406,U_411,U_407),U_407),U_406)
| ~ in(U_407,U_411)
| ~ sP104(U_406,U_400,U_411,U_408,U_407) ),
inference(clausify,[status(thm)],[f_44_8]) ).
cnf(f_44_13,plain,
( in(U_408,U_411)
| ~ in(ordered_pair(U_400,U_408),U_406)
| ~ sP104(U_406,U_400,U_411,U_408,U_407) ),
inference(clausify,[status(thm)],[f_44_8]) ).
cnf(f_44_14,plain,
( in(sK78(U_406,U_412),U_412)
| ~ sP105(U_406,U_402,U_412) ),
inference(clausify,[status(thm)],[f_44_8]) ).
cnf(f_44_15,plain,
( ~ in(ordered_pair(U_402,sK78(U_406,U_412)),U_406)
| ~ sP105(U_406,U_402,U_412) ),
inference(clausify,[status(thm)],[f_44_8]) ).
cnf(f_44_16,plain,
( in(ordered_pair(sK80(U_406,U_412),sK79(U_406,U_412)),U_406)
| ~ sP106(U_406,U_412) ),
inference(clausify,[status(thm)],[f_44_8]) ).
cnf(f_44_17,plain,
( ~ in(sK79(U_406,U_412),U_412)
| ~ sP106(U_406,U_412) ),
inference(clausify,[status(thm)],[f_44_8]) ).
fof(f_45_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_45_2,plain,
! [U_414,U_413] :
( subset_complement(U_414,U_413) = set_difference(U_414,U_413)
| ~ element(U_413,powerset(U_414)) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_414,U_413] :
( subset_complement(U_414,U_413) = set_difference(U_414,U_413)
| ~ element(U_413,powerset(U_414)) ),
inference(definitional_conversion,[status(esa)],[f_45_2]) ).
cnf(f_45_4,plain,
( subset_complement(U_414,U_413) = set_difference(U_414,U_413)
| ~ element(U_413,powerset(U_414)) ),
inference(clausify,[status(thm)],[f_45_3]) ).
fof(f_46_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_46_2,plain,
! [U_416,U_415] : ordered_pair(U_416,U_415) = unordered_pair(unordered_pair(U_416,U_415),singleton(U_416)),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_416,U_415] : ordered_pair(U_416,U_415) = unordered_pair(unordered_pair(U_416,U_415),singleton(U_416)),
inference(definitional_conversion,[status(esa)],[f_46_2]) ).
cnf(f_46_4,plain,
ordered_pair(U_416,U_415) = unordered_pair(unordered_pair(U_416,U_415),singleton(U_416)),
inference(clausify,[status(thm)],[f_46_3]) ).
fof(f_47_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_47_2,plain,
! [U_417] :
( relation_field(U_417) = set_union2(relation_dom(U_417),relation_rng(U_417))
| ~ relation(U_417) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_417] :
( relation_field(U_417) = set_union2(relation_dom(U_417),relation_rng(U_417))
| ~ relation(U_417) ),
inference(definitional_conversion,[status(esa)],[f_47_2]) ).
cnf(f_47_4,plain,
( relation_field(U_417) = set_union2(relation_dom(U_417),relation_rng(U_417))
| ~ relation(U_417) ),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_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_48_2,plain,
! [U_423] :
( ! [U_422] :
( ( ( U_422 = relation_inverse(U_423)
| ? [U_421,U_420] :
( ( ~ in(ordered_pair(U_421,U_420),U_422)
& in(ordered_pair(U_420,U_421),U_423) )
| ( ~ in(ordered_pair(U_420,U_421),U_423)
& in(ordered_pair(U_421,U_420),U_422) ) ) )
& ( ! [U_419,U_418] :
( ( in(ordered_pair(U_419,U_418),U_422)
| ~ in(ordered_pair(U_418,U_419),U_423) )
& ( in(ordered_pair(U_418,U_419),U_423)
| ~ in(ordered_pair(U_419,U_418),U_422) ) )
| U_422 != relation_inverse(U_423) ) )
| ~ relation(U_422) )
| ~ relation(U_423) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
! [U_423] :
( ! [U_422] :
( ( ( U_422 = relation_inverse(U_423)
| ? [U_431,U_429] :
( ~ in(ordered_pair(U_431,U_429),U_422)
& in(ordered_pair(U_429,U_431),U_423) )
| ? [U_430,U_428] :
( ~ in(ordered_pair(U_428,U_430),U_423)
& in(ordered_pair(U_430,U_428),U_422) ) )
& ( ( ! [U_427,U_425] :
( in(ordered_pair(U_427,U_425),U_422)
| ~ in(ordered_pair(U_425,U_427),U_423) )
& ! [U_426,U_424] :
( in(ordered_pair(U_424,U_426),U_423)
| ~ in(ordered_pair(U_426,U_424),U_422) ) )
| U_422 != relation_inverse(U_423) ) )
| ~ relation(U_422) )
| ~ relation(U_423) ),
inference(miniscope,[status(thm)],[f_48_2]) ).
fof(f_48_4,plain,
! [U_423] :
( ! [U_422] :
( ( ( U_422 = relation_inverse(U_423)
| ? [U_431,U_429] :
( ~ in(ordered_pair(U_431,U_429),U_422)
& in(ordered_pair(U_429,U_431),U_423) )
| ? [U_428] :
( ~ in(ordered_pair(U_428,sK81(U_423,U_422)),U_423)
& in(ordered_pair(sK81(U_423,U_422),U_428),U_422) ) )
& ( ( ! [U_427,U_425] :
( in(ordered_pair(U_427,U_425),U_422)
| ~ in(ordered_pair(U_425,U_427),U_423) )
& ! [U_426,U_424] :
( in(ordered_pair(U_424,U_426),U_423)
| ~ in(ordered_pair(U_426,U_424),U_422) ) )
| U_422 != relation_inverse(U_423) ) )
| ~ relation(U_422) )
| ~ relation(U_423) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_430,sK81(U_423,U_422))],[f_48_3]) ).
fof(f_48_5,plain,
! [U_423] :
( ! [U_422] :
( ( ( U_422 = relation_inverse(U_423)
| ? [U_431,U_429] :
( ~ in(ordered_pair(U_431,U_429),U_422)
& in(ordered_pair(U_429,U_431),U_423) )
| ( ~ in(ordered_pair(sK82(U_423,U_422),sK81(U_423,U_422)),U_423)
& in(ordered_pair(sK81(U_423,U_422),sK82(U_423,U_422)),U_422) ) )
& ( ( ! [U_427,U_425] :
( in(ordered_pair(U_427,U_425),U_422)
| ~ in(ordered_pair(U_425,U_427),U_423) )
& ! [U_426,U_424] :
( in(ordered_pair(U_424,U_426),U_423)
| ~ in(ordered_pair(U_426,U_424),U_422) ) )
| U_422 != relation_inverse(U_423) ) )
| ~ relation(U_422) )
| ~ relation(U_423) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_428,sK82(U_423,U_422))],[f_48_4]) ).
fof(f_48_6,plain,
! [U_423] :
( ! [U_422] :
( ( ( U_422 = relation_inverse(U_423)
| ? [U_429] :
( ~ in(ordered_pair(sK83(U_423,U_422),U_429),U_422)
& in(ordered_pair(U_429,sK83(U_423,U_422)),U_423) )
| ( ~ in(ordered_pair(sK82(U_423,U_422),sK81(U_423,U_422)),U_423)
& in(ordered_pair(sK81(U_423,U_422),sK82(U_423,U_422)),U_422) ) )
& ( ( ! [U_427,U_425] :
( in(ordered_pair(U_427,U_425),U_422)
| ~ in(ordered_pair(U_425,U_427),U_423) )
& ! [U_426,U_424] :
( in(ordered_pair(U_424,U_426),U_423)
| ~ in(ordered_pair(U_426,U_424),U_422) ) )
| U_422 != relation_inverse(U_423) ) )
| ~ relation(U_422) )
| ~ relation(U_423) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_431,sK83(U_423,U_422))],[f_48_5]) ).
fof(f_48_7,plain,
! [U_423] :
( ! [U_422] :
( ( ( U_422 = relation_inverse(U_423)
| ( ~ in(ordered_pair(sK83(U_423,U_422),sK84(U_423,U_422)),U_422)
& in(ordered_pair(sK84(U_423,U_422),sK83(U_423,U_422)),U_423) )
| ( ~ in(ordered_pair(sK82(U_423,U_422),sK81(U_423,U_422)),U_423)
& in(ordered_pair(sK81(U_423,U_422),sK82(U_423,U_422)),U_422) ) )
& ( ( ! [U_427,U_425] :
( in(ordered_pair(U_427,U_425),U_422)
| ~ in(ordered_pair(U_425,U_427),U_423) )
& ! [U_426,U_424] :
( in(ordered_pair(U_424,U_426),U_423)
| ~ in(ordered_pair(U_426,U_424),U_422) ) )
| U_422 != relation_inverse(U_423) ) )
| ~ relation(U_422) )
| ~ relation(U_423) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_429,sK84(U_423,U_422))],[f_48_6]) ).
fof(f_48_8,plain,
( ! [U_422,U_423] :
( ~ in(ordered_pair(sK83(U_423,U_422),sK84(U_423,U_422)),U_422)
| ~ sP110(U_422,U_423) )
& ! [U_422,U_423] :
( in(ordered_pair(sK84(U_423,U_422),sK83(U_423,U_422)),U_423)
| ~ sP110(U_422,U_423) )
& ! [U_422,U_423] :
( ~ in(ordered_pair(sK82(U_423,U_422),sK81(U_423,U_422)),U_423)
| ~ sP109(U_422,U_423) )
& ! [U_422,U_423] :
( in(ordered_pair(sK81(U_423,U_422),sK82(U_423,U_422)),U_422)
| ~ sP109(U_422,U_423) )
& ! [U_427,U_422,U_423,U_426,U_424,U_425] :
( in(ordered_pair(U_427,U_425),U_422)
| ~ in(ordered_pair(U_425,U_427),U_423)
| ~ sP108(U_427,U_422,U_423,U_426,U_424,U_425) )
& ! [U_427,U_422,U_423,U_426,U_424,U_425] :
( in(ordered_pair(U_424,U_426),U_423)
| ~ in(ordered_pair(U_426,U_424),U_422)
| ~ sP108(U_427,U_422,U_423,U_426,U_424,U_425) )
& ! [U_427,U_422,U_423,U_426,U_424,U_425] :
( U_422 = relation_inverse(U_423)
| sP110(U_422,U_423)
| sP109(U_422,U_423)
| ~ sP111(U_427,U_422,U_423,U_426,U_424,U_425) )
& ! [U_427,U_422,U_423,U_426,U_424,U_425] :
( sP108(U_427,U_422,U_423,U_426,U_424,U_425)
| U_422 != relation_inverse(U_423)
| ~ sP111(U_427,U_422,U_423,U_426,U_424,U_425) )
& ! [U_427,U_422,U_423,U_426,U_424,U_425] :
( sP111(U_427,U_422,U_423,U_426,U_424,U_425)
| ~ relation(U_422)
| ~ relation(U_423) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP108,sP109,sP110,sP111])],[f_48_7]) ).
cnf(f_48_9,plain,
( sP111(U_427,U_422,U_423,U_426,U_424,U_425)
| ~ relation(U_422)
| ~ relation(U_423) ),
inference(clausify,[status(thm)],[f_48_8]) ).
cnf(f_48_10,plain,
( sP108(U_427,U_422,U_423,U_426,U_424,U_425)
| U_422 != relation_inverse(U_423)
| ~ sP111(U_427,U_422,U_423,U_426,U_424,U_425) ),
inference(clausify,[status(thm)],[f_48_8]) ).
cnf(f_48_11,plain,
( U_422 = relation_inverse(U_423)
| sP110(U_422,U_423)
| sP109(U_422,U_423)
| ~ sP111(U_427,U_422,U_423,U_426,U_424,U_425) ),
inference(clausify,[status(thm)],[f_48_8]) ).
cnf(f_48_12,plain,
( in(ordered_pair(U_424,U_426),U_423)
| ~ in(ordered_pair(U_426,U_424),U_422)
| ~ sP108(U_427,U_422,U_423,U_426,U_424,U_425) ),
inference(clausify,[status(thm)],[f_48_8]) ).
cnf(f_48_13,plain,
( in(ordered_pair(U_427,U_425),U_422)
| ~ in(ordered_pair(U_425,U_427),U_423)
| ~ sP108(U_427,U_422,U_423,U_426,U_424,U_425) ),
inference(clausify,[status(thm)],[f_48_8]) ).
cnf(f_48_14,plain,
( in(ordered_pair(sK81(U_423,U_422),sK82(U_423,U_422)),U_422)
| ~ sP109(U_422,U_423) ),
inference(clausify,[status(thm)],[f_48_8]) ).
cnf(f_48_15,plain,
( ~ in(ordered_pair(sK82(U_423,U_422),sK81(U_423,U_422)),U_423)
| ~ sP109(U_422,U_423) ),
inference(clausify,[status(thm)],[f_48_8]) ).
cnf(f_48_16,plain,
( in(ordered_pair(sK84(U_423,U_422),sK83(U_423,U_422)),U_423)
| ~ sP110(U_422,U_423) ),
inference(clausify,[status(thm)],[f_48_8]) ).
cnf(f_48_17,plain,
( ~ in(ordered_pair(sK83(U_423,U_422),sK84(U_423,U_422)),U_422)
| ~ sP110(U_422,U_423) ),
inference(clausify,[status(thm)],[f_48_8]) ).
fof(f_49_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_49_2,plain,
! [U_433,U_432] :
( ( disjoint(U_433,U_432)
| set_intersection2(U_433,U_432) != empty_set )
& ( set_intersection2(U_433,U_432) = empty_set
| ~ disjoint(U_433,U_432) ) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
( ! [U_437,U_435] :
( disjoint(U_437,U_435)
| set_intersection2(U_437,U_435) != empty_set )
& ! [U_436,U_434] :
( set_intersection2(U_436,U_434) = empty_set
| ~ disjoint(U_436,U_434) ) ),
inference(miniscope,[status(thm)],[f_49_2]) ).
fof(f_49_4,plain,
( ! [U_435,U_437] :
( disjoint(U_437,U_435)
| set_intersection2(U_437,U_435) != empty_set )
& ! [U_434,U_436] :
( set_intersection2(U_436,U_434) = empty_set
| ~ disjoint(U_436,U_434) ) ),
inference(definitional_conversion,[status(esa)],[f_49_3]) ).
cnf(f_49_5,plain,
( set_intersection2(U_436,U_434) = empty_set
| ~ disjoint(U_436,U_434) ),
inference(clausify,[status(thm)],[f_49_4]) ).
cnf(f_49_6,plain,
( disjoint(U_437,U_435)
| set_intersection2(U_437,U_435) != empty_set ),
inference(clausify,[status(thm)],[f_49_4]) ).
fof(f_50_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_50_2,plain,
! [U_442] :
( ( ( one_to_one(U_442)
| ? [U_441,U_440] :
( U_441 != U_440
& apply(U_442,U_441) = apply(U_442,U_440)
& in(U_440,relation_dom(U_442))
& in(U_441,relation_dom(U_442)) ) )
& ( ! [U_439,U_438] :
( U_439 = U_438
| apply(U_442,U_439) != apply(U_442,U_438)
| ~ in(U_438,relation_dom(U_442))
| ~ in(U_439,relation_dom(U_442)) )
| ~ one_to_one(U_442) ) )
| ~ function(U_442)
| ~ relation(U_442) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_442] :
( ( ( one_to_one(U_442)
| ? [U_440] :
( sK85(U_442) != U_440
& apply(U_442,sK85(U_442)) = apply(U_442,U_440)
& in(U_440,relation_dom(U_442))
& in(sK85(U_442),relation_dom(U_442)) ) )
& ( ! [U_439,U_438] :
( U_439 = U_438
| apply(U_442,U_439) != apply(U_442,U_438)
| ~ in(U_438,relation_dom(U_442))
| ~ in(U_439,relation_dom(U_442)) )
| ~ one_to_one(U_442) ) )
| ~ function(U_442)
| ~ relation(U_442) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_441,sK85(U_442))],[f_50_2]) ).
fof(f_50_4,plain,
! [U_442] :
( ( ( one_to_one(U_442)
| ( sK85(U_442) != sK86(U_442)
& apply(U_442,sK85(U_442)) = apply(U_442,sK86(U_442))
& in(sK86(U_442),relation_dom(U_442))
& in(sK85(U_442),relation_dom(U_442)) ) )
& ( ! [U_439,U_438] :
( U_439 = U_438
| apply(U_442,U_439) != apply(U_442,U_438)
| ~ in(U_438,relation_dom(U_442))
| ~ in(U_439,relation_dom(U_442)) )
| ~ one_to_one(U_442) ) )
| ~ function(U_442)
| ~ relation(U_442) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_440,sK86(U_442))],[f_50_3]) ).
fof(f_50_5,plain,
( ! [U_442] :
( sK85(U_442) != sK86(U_442)
| ~ sP112(U_442) )
& ! [U_442] :
( apply(U_442,sK85(U_442)) = apply(U_442,sK86(U_442))
| ~ sP112(U_442) )
& ! [U_442] :
( in(sK86(U_442),relation_dom(U_442))
| ~ sP112(U_442) )
& ! [U_442] :
( in(sK85(U_442),relation_dom(U_442))
| ~ sP112(U_442) )
& ! [U_439,U_438,U_442] :
( one_to_one(U_442)
| sP112(U_442)
| ~ sP113(U_439,U_438,U_442) )
& ! [U_439,U_438,U_442] :
( U_439 = U_438
| apply(U_442,U_439) != apply(U_442,U_438)
| ~ in(U_438,relation_dom(U_442))
| ~ in(U_439,relation_dom(U_442))
| ~ one_to_one(U_442)
| ~ sP113(U_439,U_438,U_442) )
& ! [U_439,U_438,U_442] :
( sP113(U_439,U_438,U_442)
| ~ function(U_442)
| ~ relation(U_442) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP112,sP113])],[f_50_4]) ).
cnf(f_50_6,plain,
( sP113(U_439,U_438,U_442)
| ~ function(U_442)
| ~ relation(U_442) ),
inference(clausify,[status(thm)],[f_50_5]) ).
cnf(f_50_7,plain,
( U_439 = U_438
| apply(U_442,U_439) != apply(U_442,U_438)
| ~ in(U_438,relation_dom(U_442))
| ~ in(U_439,relation_dom(U_442))
| ~ one_to_one(U_442)
| ~ sP113(U_439,U_438,U_442) ),
inference(clausify,[status(thm)],[f_50_5]) ).
cnf(f_50_8,plain,
( one_to_one(U_442)
| sP112(U_442)
| ~ sP113(U_439,U_438,U_442) ),
inference(clausify,[status(thm)],[f_50_5]) ).
cnf(f_50_9,plain,
( in(sK85(U_442),relation_dom(U_442))
| ~ sP112(U_442) ),
inference(clausify,[status(thm)],[f_50_5]) ).
cnf(f_50_10,plain,
( in(sK86(U_442),relation_dom(U_442))
| ~ sP112(U_442) ),
inference(clausify,[status(thm)],[f_50_5]) ).
cnf(f_50_11,plain,
( apply(U_442,sK85(U_442)) = apply(U_442,sK86(U_442))
| ~ sP112(U_442) ),
inference(clausify,[status(thm)],[f_50_5]) ).
cnf(f_50_12,plain,
( sK85(U_442) != sK86(U_442)
| ~ sP112(U_442) ),
inference(clausify,[status(thm)],[f_50_5]) ).
fof(f_51_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_51_2,plain,
! [U_453] :
( ! [U_452] :
( ! [U_451] :
( ( ( U_451 = relation_composition(U_453,U_452)
| ? [U_450,U_449] :
( ( ~ in(ordered_pair(U_450,U_449),U_451)
& ? [U_448] :
( in(ordered_pair(U_448,U_449),U_452)
& in(ordered_pair(U_450,U_448),U_453) ) )
| ( ! [U_447] :
( ~ in(ordered_pair(U_447,U_449),U_452)
| ~ in(ordered_pair(U_450,U_447),U_453) )
& in(ordered_pair(U_450,U_449),U_451) ) ) )
& ( ! [U_446,U_445] :
( ( in(ordered_pair(U_446,U_445),U_451)
| ! [U_444] :
( ~ in(ordered_pair(U_444,U_445),U_452)
| ~ in(ordered_pair(U_446,U_444),U_453) ) )
& ( ? [U_443] :
( in(ordered_pair(U_443,U_445),U_452)
& in(ordered_pair(U_446,U_443),U_453) )
| ~ in(ordered_pair(U_446,U_445),U_451) ) )
| U_451 != relation_composition(U_453,U_452) ) )
| ~ relation(U_451) )
| ~ relation(U_452) )
| ~ relation(U_453) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
! [U_453] :
( ! [U_452] :
( ! [U_451] :
( ( ( U_451 = relation_composition(U_453,U_452)
| ? [U_461,U_459] :
( ~ in(ordered_pair(U_461,U_459),U_451)
& ? [U_448] :
( in(ordered_pair(U_448,U_459),U_452)
& in(ordered_pair(U_461,U_448),U_453) ) )
| ? [U_460,U_458] :
( ! [U_447] :
( ~ in(ordered_pair(U_447,U_458),U_452)
| ~ in(ordered_pair(U_460,U_447),U_453) )
& in(ordered_pair(U_460,U_458),U_451) ) )
& ( ( ! [U_457,U_455] :
( in(ordered_pair(U_457,U_455),U_451)
| ! [U_444] :
( ~ in(ordered_pair(U_444,U_455),U_452)
| ~ in(ordered_pair(U_457,U_444),U_453) ) )
& ! [U_456,U_454] :
( ? [U_443] :
( in(ordered_pair(U_443,U_454),U_452)
& in(ordered_pair(U_456,U_443),U_453) )
| ~ in(ordered_pair(U_456,U_454),U_451) ) )
| U_451 != relation_composition(U_453,U_452) ) )
| ~ relation(U_451) )
| ~ relation(U_452) )
| ~ relation(U_453) ),
inference(miniscope,[status(thm)],[f_51_2]) ).
fof(f_51_4,plain,
! [U_453] :
( ! [U_452] :
( ! [U_451] :
( ( ( U_451 = relation_composition(U_453,U_452)
| ? [U_461,U_459] :
( ~ in(ordered_pair(U_461,U_459),U_451)
& ? [U_448] :
( in(ordered_pair(U_448,U_459),U_452)
& in(ordered_pair(U_461,U_448),U_453) ) )
| ? [U_460,U_458] :
( ! [U_447] :
( ~ in(ordered_pair(U_447,U_458),U_452)
| ~ in(ordered_pair(U_460,U_447),U_453) )
& in(ordered_pair(U_460,U_458),U_451) ) )
& ( ( ! [U_457,U_455] :
( in(ordered_pair(U_457,U_455),U_451)
| ! [U_444] :
( ~ in(ordered_pair(U_444,U_455),U_452)
| ~ in(ordered_pair(U_457,U_444),U_453) ) )
& ! [U_456,U_454] :
( ( in(ordered_pair(sK87(U_453,U_452,U_451,U_456,U_454),U_454),U_452)
& in(ordered_pair(U_456,sK87(U_453,U_452,U_451,U_456,U_454)),U_453) )
| ~ in(ordered_pair(U_456,U_454),U_451) ) )
| U_451 != relation_composition(U_453,U_452) ) )
| ~ relation(U_451) )
| ~ relation(U_452) )
| ~ relation(U_453) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_443,sK87(U_453,U_452,U_451,U_456,U_454))],[f_51_3]) ).
fof(f_51_5,plain,
! [U_453] :
( ! [U_452] :
( ! [U_451] :
( ( ( U_451 = relation_composition(U_453,U_452)
| ? [U_461,U_459] :
( ~ in(ordered_pair(U_461,U_459),U_451)
& ? [U_448] :
( in(ordered_pair(U_448,U_459),U_452)
& in(ordered_pair(U_461,U_448),U_453) ) )
| ? [U_458] :
( ! [U_447] :
( ~ in(ordered_pair(U_447,U_458),U_452)
| ~ in(ordered_pair(sK88(U_453,U_452,U_451),U_447),U_453) )
& in(ordered_pair(sK88(U_453,U_452,U_451),U_458),U_451) ) )
& ( ( ! [U_457,U_455] :
( in(ordered_pair(U_457,U_455),U_451)
| ! [U_444] :
( ~ in(ordered_pair(U_444,U_455),U_452)
| ~ in(ordered_pair(U_457,U_444),U_453) ) )
& ! [U_456,U_454] :
( ( in(ordered_pair(sK87(U_453,U_452,U_451,U_456,U_454),U_454),U_452)
& in(ordered_pair(U_456,sK87(U_453,U_452,U_451,U_456,U_454)),U_453) )
| ~ in(ordered_pair(U_456,U_454),U_451) ) )
| U_451 != relation_composition(U_453,U_452) ) )
| ~ relation(U_451) )
| ~ relation(U_452) )
| ~ relation(U_453) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_460,sK88(U_453,U_452,U_451))],[f_51_4]) ).
fof(f_51_6,plain,
! [U_453] :
( ! [U_452] :
( ! [U_451] :
( ( ( U_451 = relation_composition(U_453,U_452)
| ? [U_461,U_459] :
( ~ in(ordered_pair(U_461,U_459),U_451)
& ? [U_448] :
( in(ordered_pair(U_448,U_459),U_452)
& in(ordered_pair(U_461,U_448),U_453) ) )
| ( ! [U_447] :
( ~ in(ordered_pair(U_447,sK89(U_453,U_452,U_451)),U_452)
| ~ in(ordered_pair(sK88(U_453,U_452,U_451),U_447),U_453) )
& in(ordered_pair(sK88(U_453,U_452,U_451),sK89(U_453,U_452,U_451)),U_451) ) )
& ( ( ! [U_457,U_455] :
( in(ordered_pair(U_457,U_455),U_451)
| ! [U_444] :
( ~ in(ordered_pair(U_444,U_455),U_452)
| ~ in(ordered_pair(U_457,U_444),U_453) ) )
& ! [U_456,U_454] :
( ( in(ordered_pair(sK87(U_453,U_452,U_451,U_456,U_454),U_454),U_452)
& in(ordered_pair(U_456,sK87(U_453,U_452,U_451,U_456,U_454)),U_453) )
| ~ in(ordered_pair(U_456,U_454),U_451) ) )
| U_451 != relation_composition(U_453,U_452) ) )
| ~ relation(U_451) )
| ~ relation(U_452) )
| ~ relation(U_453) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_458,sK89(U_453,U_452,U_451))],[f_51_5]) ).
fof(f_51_7,plain,
! [U_453] :
( ! [U_452] :
( ! [U_451] :
( ( ( U_451 = relation_composition(U_453,U_452)
| ? [U_459] :
( ~ in(ordered_pair(sK90(U_453,U_452,U_451),U_459),U_451)
& ? [U_448] :
( in(ordered_pair(U_448,U_459),U_452)
& in(ordered_pair(sK90(U_453,U_452,U_451),U_448),U_453) ) )
| ( ! [U_447] :
( ~ in(ordered_pair(U_447,sK89(U_453,U_452,U_451)),U_452)
| ~ in(ordered_pair(sK88(U_453,U_452,U_451),U_447),U_453) )
& in(ordered_pair(sK88(U_453,U_452,U_451),sK89(U_453,U_452,U_451)),U_451) ) )
& ( ( ! [U_457,U_455] :
( in(ordered_pair(U_457,U_455),U_451)
| ! [U_444] :
( ~ in(ordered_pair(U_444,U_455),U_452)
| ~ in(ordered_pair(U_457,U_444),U_453) ) )
& ! [U_456,U_454] :
( ( in(ordered_pair(sK87(U_453,U_452,U_451,U_456,U_454),U_454),U_452)
& in(ordered_pair(U_456,sK87(U_453,U_452,U_451,U_456,U_454)),U_453) )
| ~ in(ordered_pair(U_456,U_454),U_451) ) )
| U_451 != relation_composition(U_453,U_452) ) )
| ~ relation(U_451) )
| ~ relation(U_452) )
| ~ relation(U_453) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_461,sK90(U_453,U_452,U_451))],[f_51_6]) ).
fof(f_51_8,plain,
! [U_453] :
( ! [U_452] :
( ! [U_451] :
( ( ( U_451 = relation_composition(U_453,U_452)
| ( ~ in(ordered_pair(sK90(U_453,U_452,U_451),sK91(U_453,U_452,U_451)),U_451)
& ? [U_448] :
( in(ordered_pair(U_448,sK91(U_453,U_452,U_451)),U_452)
& in(ordered_pair(sK90(U_453,U_452,U_451),U_448),U_453) ) )
| ( ! [U_447] :
( ~ in(ordered_pair(U_447,sK89(U_453,U_452,U_451)),U_452)
| ~ in(ordered_pair(sK88(U_453,U_452,U_451),U_447),U_453) )
& in(ordered_pair(sK88(U_453,U_452,U_451),sK89(U_453,U_452,U_451)),U_451) ) )
& ( ( ! [U_457,U_455] :
( in(ordered_pair(U_457,U_455),U_451)
| ! [U_444] :
( ~ in(ordered_pair(U_444,U_455),U_452)
| ~ in(ordered_pair(U_457,U_444),U_453) ) )
& ! [U_456,U_454] :
( ( in(ordered_pair(sK87(U_453,U_452,U_451,U_456,U_454),U_454),U_452)
& in(ordered_pair(U_456,sK87(U_453,U_452,U_451,U_456,U_454)),U_453) )
| ~ in(ordered_pair(U_456,U_454),U_451) ) )
| U_451 != relation_composition(U_453,U_452) ) )
| ~ relation(U_451) )
| ~ relation(U_452) )
| ~ relation(U_453) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_459,sK91(U_453,U_452,U_451))],[f_51_7]) ).
fof(f_51_9,plain,
! [U_453] :
( ! [U_452] :
( ! [U_451] :
( ( ( U_451 = relation_composition(U_453,U_452)
| ( ~ in(ordered_pair(sK90(U_453,U_452,U_451),sK91(U_453,U_452,U_451)),U_451)
& in(ordered_pair(sK92(U_453,U_452,U_451),sK91(U_453,U_452,U_451)),U_452)
& in(ordered_pair(sK90(U_453,U_452,U_451),sK92(U_453,U_452,U_451)),U_453) )
| ( ! [U_447] :
( ~ in(ordered_pair(U_447,sK89(U_453,U_452,U_451)),U_452)
| ~ in(ordered_pair(sK88(U_453,U_452,U_451),U_447),U_453) )
& in(ordered_pair(sK88(U_453,U_452,U_451),sK89(U_453,U_452,U_451)),U_451) ) )
& ( ( ! [U_457,U_455] :
( in(ordered_pair(U_457,U_455),U_451)
| ! [U_444] :
( ~ in(ordered_pair(U_444,U_455),U_452)
| ~ in(ordered_pair(U_457,U_444),U_453) ) )
& ! [U_456,U_454] :
( ( in(ordered_pair(sK87(U_453,U_452,U_451,U_456,U_454),U_454),U_452)
& in(ordered_pair(U_456,sK87(U_453,U_452,U_451,U_456,U_454)),U_453) )
| ~ in(ordered_pair(U_456,U_454),U_451) ) )
| U_451 != relation_composition(U_453,U_452) ) )
| ~ relation(U_451) )
| ~ relation(U_452) )
| ~ relation(U_453) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_448,sK92(U_453,U_452,U_451))],[f_51_8]) ).
fof(f_51_10,plain,
( ! [U_451,U_452,U_453] :
( ~ in(ordered_pair(sK90(U_453,U_452,U_451),sK91(U_453,U_452,U_451)),U_451)
| ~ sP117(U_451,U_452,U_453) )
& ! [U_451,U_452,U_453] :
( in(ordered_pair(sK92(U_453,U_452,U_451),sK91(U_453,U_452,U_451)),U_452)
| ~ sP117(U_451,U_452,U_453) )
& ! [U_451,U_452,U_453] :
( in(ordered_pair(sK90(U_453,U_452,U_451),sK92(U_453,U_452,U_451)),U_453)
| ~ sP117(U_451,U_452,U_453) )
& ! [U_451,U_447,U_452,U_453] :
( ~ in(ordered_pair(U_447,sK89(U_453,U_452,U_451)),U_452)
| ~ in(ordered_pair(sK88(U_453,U_452,U_451),U_447),U_453)
| ~ sP116(U_451,U_447,U_452,U_453) )
& ! [U_451,U_447,U_452,U_453] :
( in(ordered_pair(sK88(U_453,U_452,U_451),sK89(U_453,U_452,U_451)),U_451)
| ~ sP116(U_451,U_447,U_452,U_453) )
& ! [U_456,U_451,U_452,U_453,U_454] :
( in(ordered_pair(sK87(U_453,U_452,U_451,U_456,U_454),U_454),U_452)
| ~ sP114(U_456,U_451,U_452,U_453,U_454) )
& ! [U_456,U_451,U_452,U_453,U_454] :
( in(ordered_pair(U_456,sK87(U_453,U_452,U_451,U_456,U_454)),U_453)
| ~ sP114(U_456,U_451,U_452,U_453,U_454) )
& ! [U_457,U_455,U_444,U_456,U_451,U_452,U_453,U_454] :
( in(ordered_pair(U_457,U_455),U_451)
| ~ in(ordered_pair(U_444,U_455),U_452)
| ~ in(ordered_pair(U_457,U_444),U_453)
| ~ sP115(U_457,U_455,U_444,U_456,U_451,U_452,U_453,U_454) )
& ! [U_457,U_455,U_444,U_456,U_451,U_452,U_453,U_454] :
( sP114(U_456,U_451,U_452,U_453,U_454)
| ~ in(ordered_pair(U_456,U_454),U_451)
| ~ sP115(U_457,U_455,U_444,U_456,U_451,U_452,U_453,U_454) )
& ! [U_457,U_455,U_444,U_456,U_451,U_447,U_452,U_453,U_454] :
( U_451 = relation_composition(U_453,U_452)
| sP117(U_451,U_452,U_453)
| sP116(U_451,U_447,U_452,U_453)
| ~ sP118(U_457,U_455,U_444,U_456,U_451,U_447,U_452,U_453,U_454) )
& ! [U_457,U_455,U_444,U_456,U_451,U_447,U_452,U_453,U_454] :
( sP115(U_457,U_455,U_444,U_456,U_451,U_452,U_453,U_454)
| U_451 != relation_composition(U_453,U_452)
| ~ sP118(U_457,U_455,U_444,U_456,U_451,U_447,U_452,U_453,U_454) )
& ! [U_457,U_455,U_444,U_456,U_451,U_447,U_452,U_453,U_454] :
( sP118(U_457,U_455,U_444,U_456,U_451,U_447,U_452,U_453,U_454)
| ~ relation(U_451)
| ~ relation(U_452)
| ~ relation(U_453) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP114,sP115,sP116,sP117,sP118])],[f_51_9]) ).
cnf(f_51_11,plain,
( sP118(U_457,U_455,U_444,U_456,U_451,U_447,U_452,U_453,U_454)
| ~ relation(U_451)
| ~ relation(U_452)
| ~ relation(U_453) ),
inference(clausify,[status(thm)],[f_51_10]) ).
cnf(f_51_12,plain,
( sP115(U_457,U_455,U_444,U_456,U_451,U_452,U_453,U_454)
| U_451 != relation_composition(U_453,U_452)
| ~ sP118(U_457,U_455,U_444,U_456,U_451,U_447,U_452,U_453,U_454) ),
inference(clausify,[status(thm)],[f_51_10]) ).
cnf(f_51_13,plain,
( U_451 = relation_composition(U_453,U_452)
| sP117(U_451,U_452,U_453)
| sP116(U_451,U_447,U_452,U_453)
| ~ sP118(U_457,U_455,U_444,U_456,U_451,U_447,U_452,U_453,U_454) ),
inference(clausify,[status(thm)],[f_51_10]) ).
cnf(f_51_14,plain,
( sP114(U_456,U_451,U_452,U_453,U_454)
| ~ in(ordered_pair(U_456,U_454),U_451)
| ~ sP115(U_457,U_455,U_444,U_456,U_451,U_452,U_453,U_454) ),
inference(clausify,[status(thm)],[f_51_10]) ).
cnf(f_51_15,plain,
( in(ordered_pair(U_457,U_455),U_451)
| ~ in(ordered_pair(U_444,U_455),U_452)
| ~ in(ordered_pair(U_457,U_444),U_453)
| ~ sP115(U_457,U_455,U_444,U_456,U_451,U_452,U_453,U_454) ),
inference(clausify,[status(thm)],[f_51_10]) ).
cnf(f_51_16,plain,
( in(ordered_pair(U_456,sK87(U_453,U_452,U_451,U_456,U_454)),U_453)
| ~ sP114(U_456,U_451,U_452,U_453,U_454) ),
inference(clausify,[status(thm)],[f_51_10]) ).
cnf(f_51_17,plain,
( in(ordered_pair(sK87(U_453,U_452,U_451,U_456,U_454),U_454),U_452)
| ~ sP114(U_456,U_451,U_452,U_453,U_454) ),
inference(clausify,[status(thm)],[f_51_10]) ).
cnf(f_51_18,plain,
( in(ordered_pair(sK88(U_453,U_452,U_451),sK89(U_453,U_452,U_451)),U_451)
| ~ sP116(U_451,U_447,U_452,U_453) ),
inference(clausify,[status(thm)],[f_51_10]) ).
cnf(f_51_19,plain,
( ~ in(ordered_pair(U_447,sK89(U_453,U_452,U_451)),U_452)
| ~ in(ordered_pair(sK88(U_453,U_452,U_451),U_447),U_453)
| ~ sP116(U_451,U_447,U_452,U_453) ),
inference(clausify,[status(thm)],[f_51_10]) ).
cnf(f_51_20,plain,
( in(ordered_pair(sK90(U_453,U_452,U_451),sK92(U_453,U_452,U_451)),U_453)
| ~ sP117(U_451,U_452,U_453) ),
inference(clausify,[status(thm)],[f_51_10]) ).
cnf(f_51_21,plain,
( in(ordered_pair(sK92(U_453,U_452,U_451),sK91(U_453,U_452,U_451)),U_452)
| ~ sP117(U_451,U_452,U_453) ),
inference(clausify,[status(thm)],[f_51_10]) ).
cnf(f_51_22,plain,
( ~ in(ordered_pair(sK90(U_453,U_452,U_451),sK91(U_453,U_452,U_451)),U_451)
| ~ sP117(U_451,U_452,U_453) ),
inference(clausify,[status(thm)],[f_51_10]) ).
fof(f_52_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_52_2,plain,
! [U_466,U_465] :
( ! [U_464] :
( ( ( U_464 = complements_of_subsets(U_466,U_465)
| ? [U_463] :
( ( ( ~ in(U_463,U_464)
& in(subset_complement(U_466,U_463),U_465) )
| ( ~ in(subset_complement(U_466,U_463),U_465)
& in(U_463,U_464) ) )
& element(U_463,powerset(U_466)) ) )
& ( ! [U_462] :
( ( ( in(U_462,U_464)
| ~ in(subset_complement(U_466,U_462),U_465) )
& ( in(subset_complement(U_466,U_462),U_465)
| ~ in(U_462,U_464) ) )
| ~ element(U_462,powerset(U_466)) )
| U_464 != complements_of_subsets(U_466,U_465) ) )
| ~ element(U_464,powerset(powerset(U_466))) )
| ~ element(U_465,powerset(powerset(U_466))) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
! [U_466,U_465] :
( ! [U_464] :
( ( ( U_464 = complements_of_subsets(U_466,U_465)
| ( ( ( ~ in(sK93(U_466,U_465,U_464),U_464)
& in(subset_complement(U_466,sK93(U_466,U_465,U_464)),U_465) )
| ( ~ in(subset_complement(U_466,sK93(U_466,U_465,U_464)),U_465)
& in(sK93(U_466,U_465,U_464),U_464) ) )
& element(sK93(U_466,U_465,U_464),powerset(U_466)) ) )
& ( ! [U_462] :
( ( ( in(U_462,U_464)
| ~ in(subset_complement(U_466,U_462),U_465) )
& ( in(subset_complement(U_466,U_462),U_465)
| ~ in(U_462,U_464) ) )
| ~ element(U_462,powerset(U_466)) )
| U_464 != complements_of_subsets(U_466,U_465) ) )
| ~ element(U_464,powerset(powerset(U_466))) )
| ~ element(U_465,powerset(powerset(U_466))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_463,sK93(U_466,U_465,U_464))],[f_52_2]) ).
fof(f_52_4,plain,
( ! [U_464,U_465,U_466] :
( ~ in(sK93(U_466,U_465,U_464),U_464)
| ~ sP121(U_464,U_465,U_466) )
& ! [U_464,U_465,U_466] :
( in(subset_complement(U_466,sK93(U_466,U_465,U_464)),U_465)
| ~ sP121(U_464,U_465,U_466) )
& ! [U_464,U_465,U_466] :
( ~ in(subset_complement(U_466,sK93(U_466,U_465,U_464)),U_465)
| ~ sP120(U_464,U_465,U_466) )
& ! [U_464,U_465,U_466] :
( in(sK93(U_466,U_465,U_464),U_464)
| ~ sP120(U_464,U_465,U_466) )
& ! [U_464,U_465,U_466] :
( sP121(U_464,U_465,U_466)
| sP120(U_464,U_465,U_466)
| ~ sP122(U_464,U_465,U_466) )
& ! [U_464,U_465,U_466] :
( element(sK93(U_466,U_465,U_464),powerset(U_466))
| ~ sP122(U_464,U_465,U_466) )
& ! [U_464,U_465,U_466,U_462] :
( in(U_462,U_464)
| ~ in(subset_complement(U_466,U_462),U_465)
| ~ sP119(U_464,U_465,U_466,U_462) )
& ! [U_464,U_465,U_466,U_462] :
( in(subset_complement(U_466,U_462),U_465)
| ~ in(U_462,U_464)
| ~ sP119(U_464,U_465,U_466,U_462) )
& ! [U_464,U_465,U_466,U_462] :
( U_464 = complements_of_subsets(U_466,U_465)
| sP122(U_464,U_465,U_466)
| ~ sP123(U_464,U_465,U_466,U_462) )
& ! [U_464,U_465,U_466,U_462] :
( sP119(U_464,U_465,U_466,U_462)
| ~ element(U_462,powerset(U_466))
| U_464 != complements_of_subsets(U_466,U_465)
| ~ sP123(U_464,U_465,U_466,U_462) )
& ! [U_464,U_465,U_466,U_462] :
( sP123(U_464,U_465,U_466,U_462)
| ~ element(U_464,powerset(powerset(U_466)))
| ~ element(U_465,powerset(powerset(U_466))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP119,sP120,sP121,sP122,sP123])],[f_52_3]) ).
cnf(f_52_5,plain,
( sP123(U_464,U_465,U_466,U_462)
| ~ element(U_464,powerset(powerset(U_466)))
| ~ element(U_465,powerset(powerset(U_466))) ),
inference(clausify,[status(thm)],[f_52_4]) ).
cnf(f_52_6,plain,
( sP119(U_464,U_465,U_466,U_462)
| ~ element(U_462,powerset(U_466))
| U_464 != complements_of_subsets(U_466,U_465)
| ~ sP123(U_464,U_465,U_466,U_462) ),
inference(clausify,[status(thm)],[f_52_4]) ).
cnf(f_52_7,plain,
( U_464 = complements_of_subsets(U_466,U_465)
| sP122(U_464,U_465,U_466)
| ~ sP123(U_464,U_465,U_466,U_462) ),
inference(clausify,[status(thm)],[f_52_4]) ).
cnf(f_52_8,plain,
( in(subset_complement(U_466,U_462),U_465)
| ~ in(U_462,U_464)
| ~ sP119(U_464,U_465,U_466,U_462) ),
inference(clausify,[status(thm)],[f_52_4]) ).
cnf(f_52_9,plain,
( in(U_462,U_464)
| ~ in(subset_complement(U_466,U_462),U_465)
| ~ sP119(U_464,U_465,U_466,U_462) ),
inference(clausify,[status(thm)],[f_52_4]) ).
cnf(f_52_10,plain,
( element(sK93(U_466,U_465,U_464),powerset(U_466))
| ~ sP122(U_464,U_465,U_466) ),
inference(clausify,[status(thm)],[f_52_4]) ).
cnf(f_52_11,plain,
( sP121(U_464,U_465,U_466)
| sP120(U_464,U_465,U_466)
| ~ sP122(U_464,U_465,U_466) ),
inference(clausify,[status(thm)],[f_52_4]) ).
cnf(f_52_12,plain,
( in(sK93(U_466,U_465,U_464),U_464)
| ~ sP120(U_464,U_465,U_466) ),
inference(clausify,[status(thm)],[f_52_4]) ).
cnf(f_52_13,plain,
( ~ in(subset_complement(U_466,sK93(U_466,U_465,U_464)),U_465)
| ~ sP120(U_464,U_465,U_466) ),
inference(clausify,[status(thm)],[f_52_4]) ).
cnf(f_52_14,plain,
( in(subset_complement(U_466,sK93(U_466,U_465,U_464)),U_465)
| ~ sP121(U_464,U_465,U_466) ),
inference(clausify,[status(thm)],[f_52_4]) ).
cnf(f_52_15,plain,
( ~ in(sK93(U_466,U_465,U_464),U_464)
| ~ sP121(U_464,U_465,U_466) ),
inference(clausify,[status(thm)],[f_52_4]) ).
fof(f_53_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_53_2,plain,
! [U_468,U_467] :
( ( proper_subset(U_468,U_467)
| U_468 = U_467
| ~ subset(U_468,U_467) )
& ( ( U_468 != U_467
& subset(U_468,U_467) )
| ~ proper_subset(U_468,U_467) ) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
( ! [U_472,U_470] :
( proper_subset(U_472,U_470)
| U_472 = U_470
| ~ subset(U_472,U_470) )
& ! [U_471,U_469] :
( ( U_471 != U_469
& subset(U_471,U_469) )
| ~ proper_subset(U_471,U_469) ) ),
inference(miniscope,[status(thm)],[f_53_2]) ).
fof(f_53_4,plain,
( ! [U_469,U_471] :
( U_471 != U_469
| ~ sP124(U_469,U_471) )
& ! [U_469,U_471] :
( subset(U_471,U_469)
| ~ sP124(U_469,U_471) )
& ! [U_470,U_472] :
( proper_subset(U_472,U_470)
| U_472 = U_470
| ~ subset(U_472,U_470) )
& ! [U_469,U_471] :
( sP124(U_469,U_471)
| ~ proper_subset(U_471,U_469) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP124])],[f_53_3]) ).
cnf(f_53_5,plain,
( sP124(U_469,U_471)
| ~ proper_subset(U_471,U_469) ),
inference(clausify,[status(thm)],[f_53_4]) ).
cnf(f_53_6,plain,
( proper_subset(U_472,U_470)
| U_472 = U_470
| ~ subset(U_472,U_470) ),
inference(clausify,[status(thm)],[f_53_4]) ).
cnf(f_53_7,plain,
( subset(U_471,U_469)
| ~ sP124(U_469,U_471) ),
inference(clausify,[status(thm)],[f_53_4]) ).
cnf(f_53_8,plain,
( U_471 != U_469
| ~ sP124(U_469,U_471) ),
inference(clausify,[status(thm)],[f_53_4]) ).
fof(f_54_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_54_2,plain,
! [U_473] :
( function_inverse(U_473) = relation_inverse(U_473)
| ~ one_to_one(U_473)
| ~ function(U_473)
| ~ relation(U_473) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_473] :
( function_inverse(U_473) = relation_inverse(U_473)
| ~ one_to_one(U_473)
| ~ function(U_473)
| ~ relation(U_473) ),
inference(definitional_conversion,[status(esa)],[f_54_2]) ).
cnf(f_54_4,plain,
( function_inverse(U_473) = relation_inverse(U_473)
| ~ one_to_one(U_473)
| ~ function(U_473)
| ~ relation(U_473) ),
inference(clausify,[status(thm)],[f_54_3]) ).
fof(f_55_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k10_relat_1]) ).
fof(f_55_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_55_1]) ).
cnf(f_55_3,plain,
$true,
inference(clausify,[status(thm)],[f_55_2]) ).
fof(f_56_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_enumset1]) ).
fof(f_56_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_56_1]) ).
cnf(f_56_3,plain,
$true,
inference(clausify,[status(thm)],[f_56_2]) ).
fof(f_57_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_funct_1]) ).
fof(f_57_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_57_1]) ).
cnf(f_57_3,plain,
$true,
inference(clausify,[status(thm)],[f_57_2]) ).
fof(f_58_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_ordinal1]) ).
fof(f_58_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_58_1]) ).
cnf(f_58_3,plain,
$true,
inference(clausify,[status(thm)],[f_58_2]) ).
fof(f_59_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
fof(f_59_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_59_1]) ).
cnf(f_59_3,plain,
$true,
inference(clausify,[status(thm)],[f_59_2]) ).
fof(f_60_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_setfam_1]) ).
fof(f_60_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_60_1]) ).
cnf(f_60_3,plain,
$true,
inference(clausify,[status(thm)],[f_60_2]) ).
fof(f_61_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
fof(f_61_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_61_1]) ).
cnf(f_61_3,plain,
$true,
inference(clausify,[status(thm)],[f_61_2]) ).
fof(f_62_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
fof(f_62_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_62_1]) ).
cnf(f_62_3,plain,
$true,
inference(clausify,[status(thm)],[f_62_2]) ).
fof(f_63_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
fof(f_63_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_63_1]) ).
cnf(f_63_3,plain,
$true,
inference(clausify,[status(thm)],[f_63_2]) ).
fof(f_64_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_64_2,plain,
! [U_474] :
( ( function(function_inverse(U_474))
& relation(function_inverse(U_474)) )
| ~ function(U_474)
| ~ relation(U_474) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
( ! [U_474] :
( function(function_inverse(U_474))
| ~ sP125(U_474) )
& ! [U_474] :
( relation(function_inverse(U_474))
| ~ sP125(U_474) )
& ! [U_474] :
( sP125(U_474)
| ~ function(U_474)
| ~ relation(U_474) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP125])],[f_64_2]) ).
cnf(f_64_4,plain,
( sP125(U_474)
| ~ function(U_474)
| ~ relation(U_474) ),
inference(clausify,[status(thm)],[f_64_3]) ).
cnf(f_64_5,plain,
( relation(function_inverse(U_474))
| ~ sP125(U_474) ),
inference(clausify,[status(thm)],[f_64_3]) ).
cnf(f_64_6,plain,
( function(function_inverse(U_474))
| ~ sP125(U_474) ),
inference(clausify,[status(thm)],[f_64_3]) ).
fof(f_65_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_relat_1]) ).
fof(f_65_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_65_1]) ).
cnf(f_65_3,plain,
$true,
inference(clausify,[status(thm)],[f_65_2]) ).
fof(f_66_1,plain,
! [A] : element(cast_to_subset(A),powerset(A)),
inference(fof_nnf,[status(thm)],[dt_k2_subset_1]) ).
fof(f_66_2,plain,
! [U_475] : element(cast_to_subset(U_475),powerset(U_475)),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
! [U_475] : element(cast_to_subset(U_475),powerset(U_475)),
inference(definitional_conversion,[status(esa)],[f_66_2]) ).
cnf(f_66_4,plain,
element(cast_to_subset(U_475),powerset(U_475)),
inference(clausify,[status(thm)],[f_66_3]) ).
fof(f_67_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
fof(f_67_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_67_1]) ).
cnf(f_67_3,plain,
$true,
inference(clausify,[status(thm)],[f_67_2]) ).
fof(f_68_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
fof(f_68_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_68_1]) ).
cnf(f_68_3,plain,
$true,
inference(clausify,[status(thm)],[f_68_2]) ).
fof(f_69_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
fof(f_69_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_69_1]) ).
cnf(f_69_3,plain,
$true,
inference(clausify,[status(thm)],[f_69_2]) ).
fof(f_70_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_relat_1]) ).
fof(f_70_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_70_1]) ).
cnf(f_70_3,plain,
$true,
inference(clausify,[status(thm)],[f_70_2]) ).
fof(f_71_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_71_2,plain,
! [U_477,U_476] :
( element(subset_complement(U_477,U_476),powerset(U_477))
| ~ element(U_476,powerset(U_477)) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
fof(f_71_3,plain,
! [U_477,U_476] :
( element(subset_complement(U_477,U_476),powerset(U_477))
| ~ element(U_476,powerset(U_477)) ),
inference(definitional_conversion,[status(esa)],[f_71_2]) ).
cnf(f_71_4,plain,
( element(subset_complement(U_477,U_476),powerset(U_477))
| ~ element(U_476,powerset(U_477)) ),
inference(clausify,[status(thm)],[f_71_3]) ).
fof(f_72_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_tarski]) ).
fof(f_72_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_72_1]) ).
cnf(f_72_3,plain,
$true,
inference(clausify,[status(thm)],[f_72_2]) ).
fof(f_73_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
fof(f_73_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_73_1]) ).
cnf(f_73_3,plain,
$true,
inference(clausify,[status(thm)],[f_73_2]) ).
fof(f_74_1,plain,
! [A] :
( relation(relation_inverse(A))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k4_relat_1]) ).
fof(f_74_2,plain,
! [U_478] :
( relation(relation_inverse(U_478))
| ~ relation(U_478) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
fof(f_74_3,plain,
! [U_478] :
( relation(relation_inverse(U_478))
| ~ relation(U_478) ),
inference(definitional_conversion,[status(esa)],[f_74_2]) ).
cnf(f_74_4,plain,
( relation(relation_inverse(U_478))
| ~ relation(U_478) ),
inference(clausify,[status(thm)],[f_74_3]) ).
fof(f_75_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
fof(f_75_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_75_1]) ).
cnf(f_75_3,plain,
$true,
inference(clausify,[status(thm)],[f_75_2]) ).
fof(f_76_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
fof(f_76_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_76_1]) ).
cnf(f_76_3,plain,
$true,
inference(clausify,[status(thm)],[f_76_2]) ).
fof(f_77_1,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_relat_1]) ).
fof(f_77_2,plain,
! [U_480,U_479] :
( relation(relation_composition(U_480,U_479))
| ~ relation(U_479)
| ~ relation(U_480) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
fof(f_77_3,plain,
! [U_480,U_479] :
( relation(relation_composition(U_480,U_479))
| ~ relation(U_479)
| ~ relation(U_480) ),
inference(definitional_conversion,[status(esa)],[f_77_2]) ).
cnf(f_77_4,plain,
( relation(relation_composition(U_480,U_479))
| ~ relation(U_479)
| ~ relation(U_480) ),
inference(clausify,[status(thm)],[f_77_3]) ).
fof(f_78_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_78_2,plain,
! [U_482,U_481] :
( element(union_of_subsets(U_482,U_481),powerset(U_482))
| ~ element(U_481,powerset(powerset(U_482))) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
fof(f_78_3,plain,
! [U_482,U_481] :
( element(union_of_subsets(U_482,U_481),powerset(U_482))
| ~ element(U_481,powerset(powerset(U_482))) ),
inference(definitional_conversion,[status(esa)],[f_78_2]) ).
cnf(f_78_4,plain,
( element(union_of_subsets(U_482,U_481),powerset(U_482))
| ~ element(U_481,powerset(powerset(U_482))) ),
inference(clausify,[status(thm)],[f_78_3]) ).
fof(f_79_1,plain,
! [A] : relation(identity_relation(A)),
inference(fof_nnf,[status(thm)],[dt_k6_relat_1]) ).
fof(f_79_2,plain,
! [U_483] : relation(identity_relation(U_483)),
inference(variable_rename,[status(thm)],[f_79_1]) ).
fof(f_79_3,plain,
! [U_483] : relation(identity_relation(U_483)),
inference(definitional_conversion,[status(esa)],[f_79_2]) ).
cnf(f_79_4,plain,
relation(identity_relation(U_483)),
inference(clausify,[status(thm)],[f_79_3]) ).
fof(f_80_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_80_2,plain,
! [U_485,U_484] :
( element(meet_of_subsets(U_485,U_484),powerset(U_485))
| ~ element(U_484,powerset(powerset(U_485))) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
fof(f_80_3,plain,
! [U_484,U_485] :
( element(meet_of_subsets(U_485,U_484),powerset(U_485))
| ~ element(U_484,powerset(powerset(U_485))) ),
inference(definitional_conversion,[status(esa)],[f_80_2]) ).
cnf(f_80_4,plain,
( element(meet_of_subsets(U_485,U_484),powerset(U_485))
| ~ element(U_484,powerset(powerset(U_485))) ),
inference(clausify,[status(thm)],[f_80_3]) ).
fof(f_81_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_81_2,plain,
! [U_488,U_487,U_486] :
( element(subset_difference(U_488,U_487,U_486),powerset(U_488))
| ~ element(U_486,powerset(U_488))
| ~ element(U_487,powerset(U_488)) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
fof(f_81_3,plain,
! [U_487,U_486,U_488] :
( element(subset_difference(U_488,U_487,U_486),powerset(U_488))
| ~ element(U_486,powerset(U_488))
| ~ element(U_487,powerset(U_488)) ),
inference(definitional_conversion,[status(esa)],[f_81_2]) ).
cnf(f_81_4,plain,
( element(subset_difference(U_488,U_487,U_486),powerset(U_488))
| ~ element(U_486,powerset(U_488))
| ~ element(U_487,powerset(U_488)) ),
inference(clausify,[status(thm)],[f_81_3]) ).
fof(f_82_1,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k7_relat_1]) ).
fof(f_82_2,plain,
! [U_490,U_489] :
( relation(relation_dom_restriction(U_490,U_489))
| ~ relation(U_490) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
fof(f_82_3,plain,
! [U_490] :
( ! [U_489] : relation(relation_dom_restriction(U_490,U_489))
| ~ relation(U_490) ),
inference(miniscope,[status(thm)],[f_82_2]) ).
fof(f_82_4,plain,
! [U_490,U_489] :
( relation(relation_dom_restriction(U_490,U_489))
| ~ relation(U_490) ),
inference(definitional_conversion,[status(esa)],[f_82_3]) ).
cnf(f_82_5,plain,
( relation(relation_dom_restriction(U_490,U_489))
| ~ relation(U_490) ),
inference(clausify,[status(thm)],[f_82_4]) ).
fof(f_83_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_83_2,plain,
! [U_492,U_491] :
( element(complements_of_subsets(U_492,U_491),powerset(powerset(U_492)))
| ~ element(U_491,powerset(powerset(U_492))) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
fof(f_83_3,plain,
! [U_491,U_492] :
( element(complements_of_subsets(U_492,U_491),powerset(powerset(U_492)))
| ~ element(U_491,powerset(powerset(U_492))) ),
inference(definitional_conversion,[status(esa)],[f_83_2]) ).
cnf(f_83_4,plain,
( element(complements_of_subsets(U_492,U_491),powerset(powerset(U_492)))
| ~ element(U_491,powerset(powerset(U_492))) ),
inference(clausify,[status(thm)],[f_83_3]) ).
fof(f_84_1,plain,
! [A,B] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[dt_k8_relat_1]) ).
fof(f_84_2,plain,
! [U_494,U_493] :
( relation(relation_rng_restriction(U_494,U_493))
| ~ relation(U_493) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
fof(f_84_3,plain,
! [U_493,U_494] :
( relation(relation_rng_restriction(U_494,U_493))
| ~ relation(U_493) ),
inference(definitional_conversion,[status(esa)],[f_84_2]) ).
cnf(f_84_4,plain,
( relation(relation_rng_restriction(U_494,U_493))
| ~ relation(U_493) ),
inference(clausify,[status(thm)],[f_84_3]) ).
fof(f_85_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k9_relat_1]) ).
fof(f_85_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_85_1]) ).
cnf(f_85_3,plain,
$true,
inference(clausify,[status(thm)],[f_85_2]) ).
fof(f_86_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
fof(f_86_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_86_1]) ).
cnf(f_86_3,plain,
$true,
inference(clausify,[status(thm)],[f_86_2]) ).
fof(f_87_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_87_2,plain,
! [U_496] :
? [U_495] : element(U_495,U_496),
inference(variable_rename,[status(thm)],[f_87_1]) ).
fof(f_87_3,plain,
! [U_496] : element(sK94(U_496),U_496),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_495,sK94(U_496))],[f_87_2]) ).
fof(f_87_4,plain,
! [U_496] : element(sK94(U_496),U_496),
inference(definitional_conversion,[status(esa)],[f_87_3]) ).
cnf(f_87_5,plain,
element(sK94(U_496),U_496),
inference(clausify,[status(thm)],[f_87_4]) ).
fof(f_88_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_88_2,plain,
! [U_498,U_497] :
( ( relation(relation_composition(U_497,U_498))
& empty(relation_composition(U_497,U_498)) )
| ~ relation(U_497)
| ~ empty(U_498) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
fof(f_88_3,plain,
( ! [U_498,U_497] :
( relation(relation_composition(U_497,U_498))
| ~ sP126(U_498,U_497) )
& ! [U_498,U_497] :
( empty(relation_composition(U_497,U_498))
| ~ sP126(U_498,U_497) )
& ! [U_498,U_497] :
( sP126(U_498,U_497)
| ~ relation(U_497)
| ~ empty(U_498) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP126])],[f_88_2]) ).
cnf(f_88_4,plain,
( sP126(U_498,U_497)
| ~ relation(U_497)
| ~ empty(U_498) ),
inference(clausify,[status(thm)],[f_88_3]) ).
cnf(f_88_5,plain,
( empty(relation_composition(U_497,U_498))
| ~ sP126(U_498,U_497) ),
inference(clausify,[status(thm)],[f_88_3]) ).
cnf(f_88_6,plain,
( relation(relation_composition(U_497,U_498))
| ~ sP126(U_498,U_497) ),
inference(clausify,[status(thm)],[f_88_3]) ).
fof(f_89_1,plain,
! [A] :
( ( relation(relation_inverse(A))
& empty(relation_inverse(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc11_relat_1]) ).
fof(f_89_2,plain,
! [U_499] :
( ( relation(relation_inverse(U_499))
& empty(relation_inverse(U_499)) )
| ~ empty(U_499) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
fof(f_89_3,plain,
( ! [U_499] :
( relation(relation_inverse(U_499))
| ~ sP127(U_499) )
& ! [U_499] :
( empty(relation_inverse(U_499))
| ~ sP127(U_499) )
& ! [U_499] :
( sP127(U_499)
| ~ empty(U_499) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP127])],[f_89_2]) ).
cnf(f_89_4,plain,
( sP127(U_499)
| ~ empty(U_499) ),
inference(clausify,[status(thm)],[f_89_3]) ).
cnf(f_89_5,plain,
( empty(relation_inverse(U_499))
| ~ sP127(U_499) ),
inference(clausify,[status(thm)],[f_89_3]) ).
cnf(f_89_6,plain,
( relation(relation_inverse(U_499))
| ~ sP127(U_499) ),
inference(clausify,[status(thm)],[f_89_3]) ).
fof(f_90_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
fof(f_90_2,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_90_1]) ).
cnf(f_90_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_90_2]) ).
cnf(f_90_4,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_90_2]) ).
cnf(f_90_5,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_90_2]) ).
fof(f_91_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_91_2,plain,
! [U_501,U_500] :
( ( relation_empty_yielding(relation_dom_restriction(U_501,U_500))
& relation(relation_dom_restriction(U_501,U_500)) )
| ~ relation_empty_yielding(U_501)
| ~ relation(U_501) ),
inference(variable_rename,[status(thm)],[f_91_1]) ).
fof(f_91_3,plain,
! [U_501] :
( ( ! [U_503] : relation_empty_yielding(relation_dom_restriction(U_501,U_503))
& ! [U_502] : relation(relation_dom_restriction(U_501,U_502)) )
| ~ relation_empty_yielding(U_501)
| ~ relation(U_501) ),
inference(miniscope,[status(thm)],[f_91_2]) ).
fof(f_91_4,plain,
( ! [U_501,U_503,U_502] :
( relation_empty_yielding(relation_dom_restriction(U_501,U_503))
| ~ sP128(U_501,U_503,U_502) )
& ! [U_501,U_503,U_502] :
( relation(relation_dom_restriction(U_501,U_502))
| ~ sP128(U_501,U_503,U_502) )
& ! [U_501,U_503,U_502] :
( sP128(U_501,U_503,U_502)
| ~ relation_empty_yielding(U_501)
| ~ relation(U_501) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP128])],[f_91_3]) ).
cnf(f_91_5,plain,
( sP128(U_501,U_503,U_502)
| ~ relation_empty_yielding(U_501)
| ~ relation(U_501) ),
inference(clausify,[status(thm)],[f_91_4]) ).
cnf(f_91_6,plain,
( relation(relation_dom_restriction(U_501,U_502))
| ~ sP128(U_501,U_503,U_502) ),
inference(clausify,[status(thm)],[f_91_4]) ).
cnf(f_91_7,plain,
( relation_empty_yielding(relation_dom_restriction(U_501,U_503))
| ~ sP128(U_501,U_503,U_502) ),
inference(clausify,[status(thm)],[f_91_4]) ).
fof(f_92_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_92_2,plain,
! [U_505,U_504] :
( ( function(relation_composition(U_505,U_504))
& relation(relation_composition(U_505,U_504)) )
| ~ function(U_504)
| ~ relation(U_504)
| ~ function(U_505)
| ~ relation(U_505) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
fof(f_92_3,plain,
( ! [U_505,U_504] :
( function(relation_composition(U_505,U_504))
| ~ sP129(U_505,U_504) )
& ! [U_505,U_504] :
( relation(relation_composition(U_505,U_504))
| ~ sP129(U_505,U_504) )
& ! [U_505,U_504] :
( sP129(U_505,U_504)
| ~ function(U_504)
| ~ relation(U_504)
| ~ function(U_505)
| ~ relation(U_505) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP129])],[f_92_2]) ).
cnf(f_92_4,plain,
( sP129(U_505,U_504)
| ~ function(U_504)
| ~ relation(U_504)
| ~ function(U_505)
| ~ relation(U_505) ),
inference(clausify,[status(thm)],[f_92_3]) ).
cnf(f_92_5,plain,
( relation(relation_composition(U_505,U_504))
| ~ sP129(U_505,U_504) ),
inference(clausify,[status(thm)],[f_92_3]) ).
cnf(f_92_6,plain,
( function(relation_composition(U_505,U_504))
| ~ sP129(U_505,U_504) ),
inference(clausify,[status(thm)],[f_92_3]) ).
fof(f_93_1,plain,
! [A] : ~ empty(succ(A)),
inference(fof_nnf,[status(thm)],[fc1_ordinal1]) ).
fof(f_93_2,plain,
! [U_506] : ~ empty(succ(U_506)),
inference(variable_rename,[status(thm)],[f_93_1]) ).
fof(f_93_3,plain,
! [U_506] : ~ empty(succ(U_506)),
inference(definitional_conversion,[status(esa)],[f_93_2]) ).
cnf(f_93_4,plain,
~ empty(succ(U_506)),
inference(clausify,[status(thm)],[f_93_3]) ).
fof(f_94_1,plain,
! [A,B] :
( relation(set_intersection2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc1_relat_1]) ).
fof(f_94_2,plain,
! [U_508,U_507] :
( relation(set_intersection2(U_508,U_507))
| ~ relation(U_507)
| ~ relation(U_508) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
fof(f_94_3,plain,
! [U_508,U_507] :
( relation(set_intersection2(U_508,U_507))
| ~ relation(U_507)
| ~ relation(U_508) ),
inference(definitional_conversion,[status(esa)],[f_94_2]) ).
cnf(f_94_4,plain,
( relation(set_intersection2(U_508,U_507))
| ~ relation(U_507)
| ~ relation(U_508) ),
inference(clausify,[status(thm)],[f_94_3]) ).
fof(f_95_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_95_2,plain,
! [U_509] : ~ empty(powerset(U_509)),
inference(variable_rename,[status(thm)],[f_95_1]) ).
fof(f_95_3,plain,
! [U_509] : ~ empty(powerset(U_509)),
inference(definitional_conversion,[status(esa)],[f_95_2]) ).
cnf(f_95_4,plain,
~ empty(powerset(U_509)),
inference(clausify,[status(thm)],[f_95_3]) ).
fof(f_96_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_96_2,plain,
empty(empty_set),
inference(definitional_conversion,[status(esa)],[f_96_1]) ).
cnf(f_96_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_96_2]) ).
fof(f_97_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_97_2,plain,
! [U_511,U_510] : ~ empty(ordered_pair(U_511,U_510)),
inference(variable_rename,[status(thm)],[f_97_1]) ).
fof(f_97_3,plain,
! [U_511,U_510] : ~ empty(ordered_pair(U_511,U_510)),
inference(definitional_conversion,[status(esa)],[f_97_2]) ).
cnf(f_97_4,plain,
~ empty(ordered_pair(U_511,U_510)),
inference(clausify,[status(thm)],[f_97_3]) ).
fof(f_98_1,plain,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
inference(fof_nnf,[status(thm)],[fc2_funct_1]) ).
fof(f_98_2,plain,
! [U_512] :
( function(identity_relation(U_512))
& relation(identity_relation(U_512)) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
fof(f_98_3,plain,
( ! [U_514] : function(identity_relation(U_514))
& ! [U_513] : relation(identity_relation(U_513)) ),
inference(miniscope,[status(thm)],[f_98_2]) ).
fof(f_98_4,plain,
( ! [U_514] : function(identity_relation(U_514))
& ! [U_513] : relation(identity_relation(U_513)) ),
inference(definitional_conversion,[status(esa)],[f_98_3]) ).
cnf(f_98_5,plain,
relation(identity_relation(U_513)),
inference(clausify,[status(thm)],[f_98_4]) ).
cnf(f_98_6,plain,
function(identity_relation(U_514)),
inference(clausify,[status(thm)],[f_98_4]) ).
fof(f_99_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]) ).
fof(f_99_2,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(definitional_conversion,[status(esa)],[f_99_1]) ).
cnf(f_99_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_99_2]) ).
cnf(f_99_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_99_2]) ).
cnf(f_99_5,plain,
function(empty_set),
inference(clausify,[status(thm)],[f_99_2]) ).
cnf(f_99_6,plain,
one_to_one(empty_set),
inference(clausify,[status(thm)],[f_99_2]) ).
cnf(f_99_7,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_99_2]) ).
cnf(f_99_8,plain,
epsilon_transitive(empty_set),
inference(clausify,[status(thm)],[f_99_2]) ).
cnf(f_99_9,plain,
epsilon_connected(empty_set),
inference(clausify,[status(thm)],[f_99_2]) ).
cnf(f_99_10,plain,
ordinal(empty_set),
inference(clausify,[status(thm)],[f_99_2]) ).
fof(f_100_1,plain,
! [A,B] :
( relation(set_union2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc2_relat_1]) ).
fof(f_100_2,plain,
! [U_516,U_515] :
( relation(set_union2(U_516,U_515))
| ~ relation(U_515)
| ~ relation(U_516) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
fof(f_100_3,plain,
! [U_515,U_516] :
( relation(set_union2(U_516,U_515))
| ~ relation(U_515)
| ~ relation(U_516) ),
inference(definitional_conversion,[status(esa)],[f_100_2]) ).
cnf(f_100_4,plain,
( relation(set_union2(U_516,U_515))
| ~ relation(U_515)
| ~ relation(U_516) ),
inference(clausify,[status(thm)],[f_100_3]) ).
fof(f_101_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_101_2,plain,
! [U_517] : ~ empty(singleton(U_517)),
inference(variable_rename,[status(thm)],[f_101_1]) ).
fof(f_101_3,plain,
! [U_517] : ~ empty(singleton(U_517)),
inference(definitional_conversion,[status(esa)],[f_101_2]) ).
cnf(f_101_4,plain,
~ empty(singleton(U_517)),
inference(clausify,[status(thm)],[f_101_3]) ).
fof(f_102_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_102_2,plain,
! [U_519,U_518] :
( ~ empty(set_union2(U_519,U_518))
| empty(U_519) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
fof(f_102_3,plain,
! [U_519] :
( ! [U_518] : ~ empty(set_union2(U_519,U_518))
| empty(U_519) ),
inference(miniscope,[status(thm)],[f_102_2]) ).
fof(f_102_4,plain,
! [U_518,U_519] :
( ~ empty(set_union2(U_519,U_518))
| empty(U_519) ),
inference(definitional_conversion,[status(esa)],[f_102_3]) ).
cnf(f_102_5,plain,
( ~ empty(set_union2(U_519,U_518))
| empty(U_519) ),
inference(clausify,[status(thm)],[f_102_4]) ).
fof(f_103_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_103_2,plain,
! [U_520] :
( ( function(relation_inverse(U_520))
& relation(relation_inverse(U_520)) )
| ~ one_to_one(U_520)
| ~ function(U_520)
| ~ relation(U_520) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
fof(f_103_3,plain,
( ! [U_520] :
( function(relation_inverse(U_520))
| ~ sP130(U_520) )
& ! [U_520] :
( relation(relation_inverse(U_520))
| ~ sP130(U_520) )
& ! [U_520] :
( sP130(U_520)
| ~ one_to_one(U_520)
| ~ function(U_520)
| ~ relation(U_520) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP130])],[f_103_2]) ).
cnf(f_103_4,plain,
( sP130(U_520)
| ~ one_to_one(U_520)
| ~ function(U_520)
| ~ relation(U_520) ),
inference(clausify,[status(thm)],[f_103_3]) ).
cnf(f_103_5,plain,
( relation(relation_inverse(U_520))
| ~ sP130(U_520) ),
inference(clausify,[status(thm)],[f_103_3]) ).
cnf(f_103_6,plain,
( function(relation_inverse(U_520))
| ~ sP130(U_520) ),
inference(clausify,[status(thm)],[f_103_3]) ).
fof(f_104_1,plain,
! [A,B] :
( relation(set_difference(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc3_relat_1]) ).
fof(f_104_2,plain,
! [U_522,U_521] :
( relation(set_difference(U_522,U_521))
| ~ relation(U_521)
| ~ relation(U_522) ),
inference(variable_rename,[status(thm)],[f_104_1]) ).
fof(f_104_3,plain,
! [U_521,U_522] :
( relation(set_difference(U_522,U_521))
| ~ relation(U_521)
| ~ relation(U_522) ),
inference(definitional_conversion,[status(esa)],[f_104_2]) ).
cnf(f_104_4,plain,
( relation(set_difference(U_522,U_521))
| ~ relation(U_521)
| ~ relation(U_522) ),
inference(clausify,[status(thm)],[f_104_3]) ).
fof(f_105_1,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_105_2,plain,
! [U_524,U_523] : ~ empty(unordered_pair(U_524,U_523)),
inference(variable_rename,[status(thm)],[f_105_1]) ).
fof(f_105_3,plain,
! [U_524,U_523] : ~ empty(unordered_pair(U_524,U_523)),
inference(definitional_conversion,[status(esa)],[f_105_2]) ).
cnf(f_105_4,plain,
~ empty(unordered_pair(U_524,U_523)),
inference(clausify,[status(thm)],[f_105_3]) ).
fof(f_106_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_106_2,plain,
! [U_526,U_525] :
( ~ empty(set_union2(U_525,U_526))
| empty(U_526) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
fof(f_106_3,plain,
! [U_526] :
( ! [U_525] : ~ empty(set_union2(U_525,U_526))
| empty(U_526) ),
inference(miniscope,[status(thm)],[f_106_2]) ).
fof(f_106_4,plain,
! [U_525,U_526] :
( ~ empty(set_union2(U_525,U_526))
| empty(U_526) ),
inference(definitional_conversion,[status(esa)],[f_106_3]) ).
cnf(f_106_5,plain,
( ~ empty(set_union2(U_525,U_526))
| empty(U_526) ),
inference(clausify,[status(thm)],[f_106_4]) ).
fof(f_107_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_107_2,plain,
! [U_528,U_527] :
( ( function(relation_dom_restriction(U_528,U_527))
& relation(relation_dom_restriction(U_528,U_527)) )
| ~ function(U_528)
| ~ relation(U_528) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
fof(f_107_3,plain,
! [U_528] :
( ( ! [U_530] : function(relation_dom_restriction(U_528,U_530))
& ! [U_529] : relation(relation_dom_restriction(U_528,U_529)) )
| ~ function(U_528)
| ~ relation(U_528) ),
inference(miniscope,[status(thm)],[f_107_2]) ).
fof(f_107_4,plain,
( ! [U_528,U_529,U_530] :
( function(relation_dom_restriction(U_528,U_530))
| ~ sP131(U_528,U_529,U_530) )
& ! [U_528,U_529,U_530] :
( relation(relation_dom_restriction(U_528,U_529))
| ~ sP131(U_528,U_529,U_530) )
& ! [U_528,U_529,U_530] :
( sP131(U_528,U_529,U_530)
| ~ function(U_528)
| ~ relation(U_528) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP131])],[f_107_3]) ).
cnf(f_107_5,plain,
( sP131(U_528,U_529,U_530)
| ~ function(U_528)
| ~ relation(U_528) ),
inference(clausify,[status(thm)],[f_107_4]) ).
cnf(f_107_6,plain,
( relation(relation_dom_restriction(U_528,U_529))
| ~ sP131(U_528,U_529,U_530) ),
inference(clausify,[status(thm)],[f_107_4]) ).
cnf(f_107_7,plain,
( function(relation_dom_restriction(U_528,U_530))
| ~ sP131(U_528,U_529,U_530) ),
inference(clausify,[status(thm)],[f_107_4]) ).
fof(f_108_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
fof(f_108_2,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_108_1]) ).
cnf(f_108_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_108_2]) ).
cnf(f_108_4,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_108_2]) ).
fof(f_109_1,plain,
! [A,B] :
( ~ empty(cartesian_product2(A,B))
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc4_subset_1]) ).
fof(f_109_2,plain,
! [U_532,U_531] :
( ~ empty(cartesian_product2(U_532,U_531))
| empty(U_531)
| empty(U_532) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
fof(f_109_3,plain,
! [U_531,U_532] :
( ~ empty(cartesian_product2(U_532,U_531))
| empty(U_531)
| empty(U_532) ),
inference(definitional_conversion,[status(esa)],[f_109_2]) ).
cnf(f_109_4,plain,
( ~ empty(cartesian_product2(U_532,U_531))
| empty(U_531)
| empty(U_532) ),
inference(clausify,[status(thm)],[f_109_3]) ).
fof(f_110_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_110_2,plain,
! [U_533] :
( ~ empty(relation_dom(U_533))
| ~ relation(U_533)
| empty(U_533) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
fof(f_110_3,plain,
! [U_533] :
( ~ empty(relation_dom(U_533))
| ~ relation(U_533)
| empty(U_533) ),
inference(definitional_conversion,[status(esa)],[f_110_2]) ).
cnf(f_110_4,plain,
( ~ empty(relation_dom(U_533))
| ~ relation(U_533)
| empty(U_533) ),
inference(clausify,[status(thm)],[f_110_3]) ).
fof(f_111_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_111_2,plain,
! [U_534] :
( ~ empty(relation_rng(U_534))
| ~ relation(U_534)
| empty(U_534) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
fof(f_111_3,plain,
! [U_534] :
( ~ empty(relation_rng(U_534))
| ~ relation(U_534)
| empty(U_534) ),
inference(definitional_conversion,[status(esa)],[f_111_2]) ).
cnf(f_111_4,plain,
( ~ empty(relation_rng(U_534))
| ~ relation(U_534)
| empty(U_534) ),
inference(clausify,[status(thm)],[f_111_3]) ).
fof(f_112_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_112_2,plain,
! [U_535] :
( ( relation(relation_dom(U_535))
& empty(relation_dom(U_535)) )
| ~ empty(U_535) ),
inference(variable_rename,[status(thm)],[f_112_1]) ).
fof(f_112_3,plain,
( ! [U_535] :
( relation(relation_dom(U_535))
| ~ sP132(U_535) )
& ! [U_535] :
( empty(relation_dom(U_535))
| ~ sP132(U_535) )
& ! [U_535] :
( sP132(U_535)
| ~ empty(U_535) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP132])],[f_112_2]) ).
cnf(f_112_4,plain,
( sP132(U_535)
| ~ empty(U_535) ),
inference(clausify,[status(thm)],[f_112_3]) ).
cnf(f_112_5,plain,
( empty(relation_dom(U_535))
| ~ sP132(U_535) ),
inference(clausify,[status(thm)],[f_112_3]) ).
cnf(f_112_6,plain,
( relation(relation_dom(U_535))
| ~ sP132(U_535) ),
inference(clausify,[status(thm)],[f_112_3]) ).
fof(f_113_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_113_2,plain,
! [U_536] :
( ( relation(relation_rng(U_536))
& empty(relation_rng(U_536)) )
| ~ empty(U_536) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
fof(f_113_3,plain,
( ! [U_536] :
( relation(relation_rng(U_536))
| ~ sP133(U_536) )
& ! [U_536] :
( empty(relation_rng(U_536))
| ~ sP133(U_536) )
& ! [U_536] :
( sP133(U_536)
| ~ empty(U_536) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP133])],[f_113_2]) ).
cnf(f_113_4,plain,
( sP133(U_536)
| ~ empty(U_536) ),
inference(clausify,[status(thm)],[f_113_3]) ).
cnf(f_113_5,plain,
( empty(relation_rng(U_536))
| ~ sP133(U_536) ),
inference(clausify,[status(thm)],[f_113_3]) ).
cnf(f_113_6,plain,
( relation(relation_rng(U_536))
| ~ sP133(U_536) ),
inference(clausify,[status(thm)],[f_113_3]) ).
fof(f_114_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_114_2,plain,
! [U_538,U_537] :
( ( relation(relation_composition(U_538,U_537))
& empty(relation_composition(U_538,U_537)) )
| ~ relation(U_537)
| ~ empty(U_538) ),
inference(variable_rename,[status(thm)],[f_114_1]) ).
fof(f_114_3,plain,
( ! [U_538,U_537] :
( relation(relation_composition(U_538,U_537))
| ~ sP134(U_538,U_537) )
& ! [U_538,U_537] :
( empty(relation_composition(U_538,U_537))
| ~ sP134(U_538,U_537) )
& ! [U_538,U_537] :
( sP134(U_538,U_537)
| ~ relation(U_537)
| ~ empty(U_538) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP134])],[f_114_2]) ).
cnf(f_114_4,plain,
( sP134(U_538,U_537)
| ~ relation(U_537)
| ~ empty(U_538) ),
inference(clausify,[status(thm)],[f_114_3]) ).
cnf(f_114_5,plain,
( empty(relation_composition(U_538,U_537))
| ~ sP134(U_538,U_537) ),
inference(clausify,[status(thm)],[f_114_3]) ).
cnf(f_114_6,plain,
( relation(relation_composition(U_538,U_537))
| ~ sP134(U_538,U_537) ),
inference(clausify,[status(thm)],[f_114_3]) ).
fof(f_115_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_115_2,plain,
! [U_540,U_539] : set_union2(U_540,U_540) = U_540,
inference(variable_rename,[status(thm)],[f_115_1]) ).
fof(f_115_3,plain,
! [U_540] : set_union2(U_540,U_540) = U_540,
inference(miniscope,[status(thm)],[f_115_2]) ).
fof(f_115_4,plain,
! [U_540] : set_union2(U_540,U_540) = U_540,
inference(definitional_conversion,[status(esa)],[f_115_3]) ).
cnf(f_115_5,plain,
set_union2(U_540,U_540) = U_540,
inference(clausify,[status(thm)],[f_115_4]) ).
fof(f_116_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_116_2,plain,
! [U_542,U_541] : set_intersection2(U_542,U_542) = U_542,
inference(variable_rename,[status(thm)],[f_116_1]) ).
fof(f_116_3,plain,
! [U_542] : set_intersection2(U_542,U_542) = U_542,
inference(miniscope,[status(thm)],[f_116_2]) ).
fof(f_116_4,plain,
! [U_542] : set_intersection2(U_542,U_542) = U_542,
inference(definitional_conversion,[status(esa)],[f_116_3]) ).
cnf(f_116_5,plain,
set_intersection2(U_542,U_542) = U_542,
inference(clausify,[status(thm)],[f_116_4]) ).
fof(f_117_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_117_2,plain,
! [U_544,U_543] :
( subset_complement(U_544,subset_complement(U_544,U_543)) = U_543
| ~ element(U_543,powerset(U_544)) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
fof(f_117_3,plain,
! [U_543,U_544] :
( subset_complement(U_544,subset_complement(U_544,U_543)) = U_543
| ~ element(U_543,powerset(U_544)) ),
inference(definitional_conversion,[status(esa)],[f_117_2]) ).
cnf(f_117_4,plain,
( subset_complement(U_544,subset_complement(U_544,U_543)) = U_543
| ~ element(U_543,powerset(U_544)) ),
inference(clausify,[status(thm)],[f_117_3]) ).
fof(f_118_1,plain,
! [A] :
( relation_inverse(relation_inverse(A)) = A
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[involutiveness_k4_relat_1]) ).
fof(f_118_2,plain,
! [U_545] :
( relation_inverse(relation_inverse(U_545)) = U_545
| ~ relation(U_545) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
fof(f_118_3,plain,
! [U_545] :
( relation_inverse(relation_inverse(U_545)) = U_545
| ~ relation(U_545) ),
inference(definitional_conversion,[status(esa)],[f_118_2]) ).
cnf(f_118_4,plain,
( relation_inverse(relation_inverse(U_545)) = U_545
| ~ relation(U_545) ),
inference(clausify,[status(thm)],[f_118_3]) ).
fof(f_119_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_119_2,plain,
! [U_547,U_546] :
( complements_of_subsets(U_547,complements_of_subsets(U_547,U_546)) = U_546
| ~ element(U_546,powerset(powerset(U_547))) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
fof(f_119_3,plain,
! [U_546,U_547] :
( complements_of_subsets(U_547,complements_of_subsets(U_547,U_546)) = U_546
| ~ element(U_546,powerset(powerset(U_547))) ),
inference(definitional_conversion,[status(esa)],[f_119_2]) ).
cnf(f_119_4,plain,
( complements_of_subsets(U_547,complements_of_subsets(U_547,U_546)) = U_546
| ~ element(U_546,powerset(powerset(U_547))) ),
inference(clausify,[status(thm)],[f_119_3]) ).
fof(f_120_1,plain,
! [A,B] : ~ proper_subset(A,A),
inference(fof_nnf,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(f_120_2,plain,
! [U_549,U_548] : ~ proper_subset(U_549,U_549),
inference(variable_rename,[status(thm)],[f_120_1]) ).
fof(f_120_3,plain,
! [U_549] : ~ proper_subset(U_549,U_549),
inference(miniscope,[status(thm)],[f_120_2]) ).
fof(f_120_4,plain,
! [U_549] : ~ proper_subset(U_549,U_549),
inference(definitional_conversion,[status(esa)],[f_120_3]) ).
cnf(f_120_5,plain,
~ proper_subset(U_549,U_549),
inference(clausify,[status(thm)],[f_120_4]) ).
fof(f_121_1,plain,
! [A] : singleton(A) != empty_set,
inference(fof_nnf,[status(thm)],[l1_zfmisc_1]) ).
fof(f_121_2,plain,
! [U_550] : singleton(U_550) != empty_set,
inference(variable_rename,[status(thm)],[f_121_1]) ).
fof(f_121_3,plain,
! [U_550] : singleton(U_550) != empty_set,
inference(definitional_conversion,[status(esa)],[f_121_2]) ).
cnf(f_121_4,plain,
singleton(U_550) != empty_set,
inference(clausify,[status(thm)],[f_121_3]) ).
fof(f_122_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l23_zfmisc_1]) ).
fof(f_122_2,plain,
! [U_552,U_551] :
( set_union2(singleton(U_552),U_551) = U_551
| ~ in(U_552,U_551) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
fof(f_122_3,plain,
! [U_551,U_552] :
( set_union2(singleton(U_552),U_551) = U_551
| ~ in(U_552,U_551) ),
inference(definitional_conversion,[status(esa)],[f_122_2]) ).
cnf(f_122_4,plain,
( set_union2(singleton(U_552),U_551) = U_551
| ~ in(U_552,U_551) ),
inference(clausify,[status(thm)],[f_122_3]) ).
fof(f_123_1,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(fof_nnf,[status(thm)],[l25_zfmisc_1]) ).
fof(f_123_2,plain,
! [U_554,U_553] :
( ~ in(U_554,U_553)
| ~ disjoint(singleton(U_554),U_553) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
fof(f_123_3,plain,
! [U_554,U_553] :
( ~ in(U_554,U_553)
| ~ disjoint(singleton(U_554),U_553) ),
inference(definitional_conversion,[status(esa)],[f_123_2]) ).
cnf(f_123_4,plain,
( ~ in(U_554,U_553)
| ~ disjoint(singleton(U_554),U_553) ),
inference(clausify,[status(thm)],[f_123_3]) ).
fof(f_124_1,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(fof_nnf,[status(thm)],[l28_zfmisc_1]) ).
fof(f_124_2,plain,
! [U_556,U_555] :
( disjoint(singleton(U_556),U_555)
| in(U_556,U_555) ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
fof(f_124_3,plain,
! [U_555,U_556] :
( disjoint(singleton(U_556),U_555)
| in(U_556,U_555) ),
inference(definitional_conversion,[status(esa)],[f_124_2]) ).
cnf(f_124_4,plain,
( disjoint(singleton(U_556),U_555)
| in(U_556,U_555) ),
inference(clausify,[status(thm)],[f_124_3]) ).
fof(f_125_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_125_2,plain,
! [U_558,U_557] :
( ( subset(singleton(U_558),U_557)
| ~ in(U_558,U_557) )
& ( in(U_558,U_557)
| ~ subset(singleton(U_558),U_557) ) ),
inference(variable_rename,[status(thm)],[f_125_1]) ).
fof(f_125_3,plain,
( ! [U_562,U_560] :
( subset(singleton(U_562),U_560)
| ~ in(U_562,U_560) )
& ! [U_561,U_559] :
( in(U_561,U_559)
| ~ subset(singleton(U_561),U_559) ) ),
inference(miniscope,[status(thm)],[f_125_2]) ).
fof(f_125_4,plain,
( ! [U_560,U_562] :
( subset(singleton(U_562),U_560)
| ~ in(U_562,U_560) )
& ! [U_559,U_561] :
( in(U_561,U_559)
| ~ subset(singleton(U_561),U_559) ) ),
inference(definitional_conversion,[status(esa)],[f_125_3]) ).
cnf(f_125_5,plain,
( in(U_561,U_559)
| ~ subset(singleton(U_561),U_559) ),
inference(clausify,[status(thm)],[f_125_4]) ).
cnf(f_125_6,plain,
( subset(singleton(U_562),U_560)
| ~ in(U_562,U_560) ),
inference(clausify,[status(thm)],[f_125_4]) ).
fof(f_126_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_126_2,plain,
! [U_564,U_563] :
( ( set_difference(U_564,U_563) = empty_set
| ~ subset(U_564,U_563) )
& ( subset(U_564,U_563)
| set_difference(U_564,U_563) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_126_1]) ).
fof(f_126_3,plain,
( ! [U_568,U_566] :
( set_difference(U_568,U_566) = empty_set
| ~ subset(U_568,U_566) )
& ! [U_567,U_565] :
( subset(U_567,U_565)
| set_difference(U_567,U_565) != empty_set ) ),
inference(miniscope,[status(thm)],[f_126_2]) ).
fof(f_126_4,plain,
( ! [U_566,U_568] :
( set_difference(U_568,U_566) = empty_set
| ~ subset(U_568,U_566) )
& ! [U_565,U_567] :
( subset(U_567,U_565)
| set_difference(U_567,U_565) != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_126_3]) ).
cnf(f_126_5,plain,
( subset(U_567,U_565)
| set_difference(U_567,U_565) != empty_set ),
inference(clausify,[status(thm)],[f_126_4]) ).
cnf(f_126_6,plain,
( set_difference(U_568,U_566) = empty_set
| ~ subset(U_568,U_566) ),
inference(clausify,[status(thm)],[f_126_4]) ).
fof(f_127_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_127_2,plain,
! [U_571,U_570] :
( ! [U_569] :
( in(U_569,U_571)
| ~ in(U_569,U_570) )
| ~ element(U_570,powerset(U_571)) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
fof(f_127_3,plain,
! [U_571,U_569,U_570] :
( in(U_569,U_571)
| ~ in(U_569,U_570)
| ~ element(U_570,powerset(U_571)) ),
inference(definitional_conversion,[status(esa)],[f_127_2]) ).
cnf(f_127_4,plain,
( in(U_569,U_571)
| ~ in(U_569,U_570)
| ~ element(U_570,powerset(U_571)) ),
inference(clausify,[status(thm)],[f_127_3]) ).
fof(f_128_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_128_2,plain,
! [U_574,U_573,U_572] :
( subset(U_574,set_difference(U_573,singleton(U_572)))
| in(U_572,U_574)
| ~ subset(U_574,U_573) ),
inference(variable_rename,[status(thm)],[f_128_1]) ).
fof(f_128_3,plain,
! [U_574,U_573] :
( ! [U_572] :
( subset(U_574,set_difference(U_573,singleton(U_572)))
| in(U_572,U_574) )
| ~ subset(U_574,U_573) ),
inference(miniscope,[status(thm)],[f_128_2]) ).
fof(f_128_4,plain,
! [U_572,U_573,U_574] :
( subset(U_574,set_difference(U_573,singleton(U_572)))
| in(U_572,U_574)
| ~ subset(U_574,U_573) ),
inference(definitional_conversion,[status(esa)],[f_128_3]) ).
cnf(f_128_5,plain,
( subset(U_574,set_difference(U_573,singleton(U_572)))
| in(U_572,U_574)
| ~ subset(U_574,U_573) ),
inference(clausify,[status(thm)],[f_128_4]) ).
fof(f_129_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_129_2,plain,
! [U_576,U_575] :
( ( subset(U_576,singleton(U_575))
| ( U_576 != singleton(U_575)
& U_576 != empty_set ) )
& ( U_576 = singleton(U_575)
| U_576 = empty_set
| ~ subset(U_576,singleton(U_575)) ) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
fof(f_129_3,plain,
( ! [U_580,U_578] :
( subset(U_580,singleton(U_578))
| ( U_580 != singleton(U_578)
& U_580 != empty_set ) )
& ! [U_579,U_577] :
( U_579 = singleton(U_577)
| U_579 = empty_set
| ~ subset(U_579,singleton(U_577)) ) ),
inference(miniscope,[status(thm)],[f_129_2]) ).
fof(f_129_4,plain,
( ! [U_578,U_580] :
( U_580 != singleton(U_578)
| ~ sP135(U_578,U_580) )
& ! [U_578,U_580] :
( U_580 != empty_set
| ~ sP135(U_578,U_580) )
& ! [U_578,U_580] :
( subset(U_580,singleton(U_578))
| sP135(U_578,U_580) )
& ! [U_579,U_577] :
( U_579 = singleton(U_577)
| U_579 = empty_set
| ~ subset(U_579,singleton(U_577)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP135])],[f_129_3]) ).
cnf(f_129_5,plain,
( U_579 = singleton(U_577)
| U_579 = empty_set
| ~ subset(U_579,singleton(U_577)) ),
inference(clausify,[status(thm)],[f_129_4]) ).
cnf(f_129_6,plain,
( subset(U_580,singleton(U_578))
| sP135(U_578,U_580) ),
inference(clausify,[status(thm)],[f_129_4]) ).
cnf(f_129_7,plain,
( U_580 != empty_set
| ~ sP135(U_578,U_580) ),
inference(clausify,[status(thm)],[f_129_4]) ).
cnf(f_129_8,plain,
( U_580 != singleton(U_578)
| ~ sP135(U_578,U_580) ),
inference(clausify,[status(thm)],[f_129_4]) ).
fof(f_130_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l50_zfmisc_1]) ).
fof(f_130_2,plain,
! [U_582,U_581] :
( subset(U_582,union(U_581))
| ~ in(U_582,U_581) ),
inference(variable_rename,[status(thm)],[f_130_1]) ).
fof(f_130_3,plain,
! [U_582,U_581] :
( subset(U_582,union(U_581))
| ~ in(U_582,U_581) ),
inference(definitional_conversion,[status(esa)],[f_130_2]) ).
cnf(f_130_4,plain,
( subset(U_582,union(U_581))
| ~ in(U_582,U_581) ),
inference(clausify,[status(thm)],[f_130_3]) ).
fof(f_131_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_131_2,plain,
! [U_586,U_585,U_584,U_583] :
( ( in(ordered_pair(U_586,U_585),cartesian_product2(U_584,U_583))
| ~ in(U_585,U_583)
| ~ in(U_586,U_584) )
& ( ( in(U_585,U_583)
& in(U_586,U_584) )
| ~ in(ordered_pair(U_586,U_585),cartesian_product2(U_584,U_583)) ) ),
inference(variable_rename,[status(thm)],[f_131_1]) ).
fof(f_131_3,plain,
( ! [U_594,U_592,U_590,U_588] :
( in(ordered_pair(U_594,U_592),cartesian_product2(U_590,U_588))
| ~ in(U_592,U_588)
| ~ in(U_594,U_590) )
& ! [U_593,U_591,U_589,U_587] :
( ( in(U_591,U_587)
& in(U_593,U_589) )
| ~ in(ordered_pair(U_593,U_591),cartesian_product2(U_589,U_587)) ) ),
inference(miniscope,[status(thm)],[f_131_2]) ).
fof(f_131_4,plain,
( ! [U_591,U_589,U_587,U_593] :
( in(U_591,U_587)
| ~ sP136(U_591,U_589,U_587,U_593) )
& ! [U_591,U_589,U_587,U_593] :
( in(U_593,U_589)
| ~ sP136(U_591,U_589,U_587,U_593) )
& ! [U_588,U_592,U_590,U_594] :
( in(ordered_pair(U_594,U_592),cartesian_product2(U_590,U_588))
| ~ in(U_592,U_588)
| ~ in(U_594,U_590) )
& ! [U_591,U_589,U_587,U_593] :
( sP136(U_591,U_589,U_587,U_593)
| ~ in(ordered_pair(U_593,U_591),cartesian_product2(U_589,U_587)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP136])],[f_131_3]) ).
cnf(f_131_5,plain,
( sP136(U_591,U_589,U_587,U_593)
| ~ in(ordered_pair(U_593,U_591),cartesian_product2(U_589,U_587)) ),
inference(clausify,[status(thm)],[f_131_4]) ).
cnf(f_131_6,plain,
( in(ordered_pair(U_594,U_592),cartesian_product2(U_590,U_588))
| ~ in(U_592,U_588)
| ~ in(U_594,U_590) ),
inference(clausify,[status(thm)],[f_131_4]) ).
cnf(f_131_7,plain,
( in(U_593,U_589)
| ~ sP136(U_591,U_589,U_587,U_593) ),
inference(clausify,[status(thm)],[f_131_4]) ).
cnf(f_131_8,plain,
( in(U_591,U_587)
| ~ sP136(U_591,U_589,U_587,U_593) ),
inference(clausify,[status(thm)],[f_131_4]) ).
fof(f_132_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_132_2,plain,
! [U_597,U_596] :
( element(U_597,powerset(U_596))
| ? [U_595] :
( ~ in(U_595,U_596)
& in(U_595,U_597) ) ),
inference(variable_rename,[status(thm)],[f_132_1]) ).
fof(f_132_3,plain,
! [U_597,U_596] :
( element(U_597,powerset(U_596))
| ( ~ in(sK95(U_597,U_596),U_596)
& in(sK95(U_597,U_596),U_597) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_595,sK95(U_597,U_596))],[f_132_2]) ).
fof(f_132_4,plain,
( ! [U_596,U_597] :
( ~ in(sK95(U_597,U_596),U_596)
| ~ sP137(U_596,U_597) )
& ! [U_596,U_597] :
( in(sK95(U_597,U_596),U_597)
| ~ sP137(U_596,U_597) )
& ! [U_596,U_597] :
( element(U_597,powerset(U_596))
| sP137(U_596,U_597) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP137])],[f_132_3]) ).
cnf(f_132_5,plain,
( element(U_597,powerset(U_596))
| sP137(U_596,U_597) ),
inference(clausify,[status(thm)],[f_132_4]) ).
cnf(f_132_6,plain,
( in(sK95(U_597,U_596),U_597)
| ~ sP137(U_596,U_597) ),
inference(clausify,[status(thm)],[f_132_4]) ).
cnf(f_132_7,plain,
( ~ in(sK95(U_597,U_596),U_596)
| ~ sP137(U_596,U_597) ),
inference(clausify,[status(thm)],[f_132_4]) ).
fof(f_133_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_133_2,plain,
! [U_600,U_599,U_598] :
( ( ( in(U_599,relation_dom(relation_dom_restriction(U_598,U_600)))
| ~ in(U_599,U_600)
| ~ in(U_599,relation_dom(U_598)) )
& ( ( in(U_599,U_600)
& in(U_599,relation_dom(U_598)) )
| ~ in(U_599,relation_dom(relation_dom_restriction(U_598,U_600))) ) )
| ~ function(U_598)
| ~ relation(U_598) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
fof(f_133_3,plain,
( ! [U_598,U_600,U_599] :
( in(U_599,U_600)
| ~ sP138(U_598,U_600,U_599) )
& ! [U_598,U_600,U_599] :
( in(U_599,relation_dom(U_598))
| ~ sP138(U_598,U_600,U_599) )
& ! [U_598,U_600,U_599] :
( in(U_599,relation_dom(relation_dom_restriction(U_598,U_600)))
| ~ in(U_599,U_600)
| ~ in(U_599,relation_dom(U_598))
| ~ sP139(U_598,U_600,U_599) )
& ! [U_598,U_600,U_599] :
( sP138(U_598,U_600,U_599)
| ~ in(U_599,relation_dom(relation_dom_restriction(U_598,U_600)))
| ~ sP139(U_598,U_600,U_599) )
& ! [U_598,U_600,U_599] :
( sP139(U_598,U_600,U_599)
| ~ function(U_598)
| ~ relation(U_598) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP138,sP139])],[f_133_2]) ).
cnf(f_133_4,plain,
( sP139(U_598,U_600,U_599)
| ~ function(U_598)
| ~ relation(U_598) ),
inference(clausify,[status(thm)],[f_133_3]) ).
cnf(f_133_5,plain,
( sP138(U_598,U_600,U_599)
| ~ in(U_599,relation_dom(relation_dom_restriction(U_598,U_600)))
| ~ sP139(U_598,U_600,U_599) ),
inference(clausify,[status(thm)],[f_133_3]) ).
cnf(f_133_6,plain,
( in(U_599,relation_dom(relation_dom_restriction(U_598,U_600)))
| ~ in(U_599,U_600)
| ~ in(U_599,relation_dom(U_598))
| ~ sP139(U_598,U_600,U_599) ),
inference(clausify,[status(thm)],[f_133_3]) ).
cnf(f_133_7,plain,
( in(U_599,relation_dom(U_598))
| ~ sP138(U_598,U_600,U_599) ),
inference(clausify,[status(thm)],[f_133_3]) ).
cnf(f_133_8,plain,
( in(U_599,U_600)
| ~ sP138(U_598,U_600,U_599) ),
inference(clausify,[status(thm)],[f_133_3]) ).
fof(f_134_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_134_2,plain,
? [U_601] :
( function(U_601)
& relation(U_601) ),
inference(variable_rename,[status(thm)],[f_134_1]) ).
fof(f_134_3,plain,
( function(sK96)
& relation(sK96) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_601,sK96)],[f_134_2]) ).
fof(f_134_4,plain,
( function(sK96)
& relation(sK96) ),
inference(definitional_conversion,[status(esa)],[f_134_3]) ).
cnf(f_134_5,plain,
relation(sK96),
inference(clausify,[status(thm)],[f_134_4]) ).
cnf(f_134_6,plain,
function(sK96),
inference(clausify,[status(thm)],[f_134_4]) ).
fof(f_135_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[rc1_ordinal1]) ).
fof(f_135_2,plain,
? [U_602] :
( ordinal(U_602)
& epsilon_connected(U_602)
& epsilon_transitive(U_602) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
fof(f_135_3,plain,
( ordinal(sK97)
& epsilon_connected(sK97)
& epsilon_transitive(sK97) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_602,sK97)],[f_135_2]) ).
fof(f_135_4,plain,
( ordinal(sK97)
& epsilon_connected(sK97)
& epsilon_transitive(sK97) ),
inference(definitional_conversion,[status(esa)],[f_135_3]) ).
cnf(f_135_5,plain,
epsilon_transitive(sK97),
inference(clausify,[status(thm)],[f_135_4]) ).
cnf(f_135_6,plain,
epsilon_connected(sK97),
inference(clausify,[status(thm)],[f_135_4]) ).
cnf(f_135_7,plain,
ordinal(sK97),
inference(clausify,[status(thm)],[f_135_4]) ).
fof(f_136_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_136_2,plain,
? [U_603] :
( relation(U_603)
& empty(U_603) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
fof(f_136_3,plain,
( relation(sK98)
& empty(sK98) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_603,sK98)],[f_136_2]) ).
fof(f_136_4,plain,
( relation(sK98)
& empty(sK98) ),
inference(definitional_conversion,[status(esa)],[f_136_3]) ).
cnf(f_136_5,plain,
empty(sK98),
inference(clausify,[status(thm)],[f_136_4]) ).
cnf(f_136_6,plain,
relation(sK98),
inference(clausify,[status(thm)],[f_136_4]) ).
fof(f_137_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_137_2,plain,
! [U_605] :
( ? [U_604] :
( ~ empty(U_604)
& element(U_604,powerset(U_605)) )
| empty(U_605) ),
inference(variable_rename,[status(thm)],[f_137_1]) ).
fof(f_137_3,plain,
! [U_605] :
( ( ~ empty(sK99(U_605))
& element(sK99(U_605),powerset(U_605)) )
| empty(U_605) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_604,sK99(U_605))],[f_137_2]) ).
fof(f_137_4,plain,
( ! [U_605] :
( ~ empty(sK99(U_605))
| ~ sP140(U_605) )
& ! [U_605] :
( element(sK99(U_605),powerset(U_605))
| ~ sP140(U_605) )
& ! [U_605] :
( sP140(U_605)
| empty(U_605) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP140])],[f_137_3]) ).
cnf(f_137_5,plain,
( sP140(U_605)
| empty(U_605) ),
inference(clausify,[status(thm)],[f_137_4]) ).
cnf(f_137_6,plain,
( element(sK99(U_605),powerset(U_605))
| ~ sP140(U_605) ),
inference(clausify,[status(thm)],[f_137_4]) ).
cnf(f_137_7,plain,
( ~ empty(sK99(U_605))
| ~ sP140(U_605) ),
inference(clausify,[status(thm)],[f_137_4]) ).
fof(f_138_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_138_2,plain,
? [U_606] : empty(U_606),
inference(variable_rename,[status(thm)],[f_138_1]) ).
fof(f_138_3,plain,
empty(sK100),
inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_606,sK100)],[f_138_2]) ).
fof(f_138_4,plain,
empty(sK100),
inference(definitional_conversion,[status(esa)],[f_138_3]) ).
cnf(f_138_5,plain,
empty(sK100),
inference(clausify,[status(thm)],[f_138_4]) ).
fof(f_139_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_139_2,plain,
? [U_607] :
( function(U_607)
& empty(U_607)
& relation(U_607) ),
inference(variable_rename,[status(thm)],[f_139_1]) ).
fof(f_139_3,plain,
( function(sK101)
& empty(sK101)
& relation(sK101) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_607,sK101)],[f_139_2]) ).
fof(f_139_4,plain,
( function(sK101)
& empty(sK101)
& relation(sK101) ),
inference(definitional_conversion,[status(esa)],[f_139_3]) ).
cnf(f_139_5,plain,
relation(sK101),
inference(clausify,[status(thm)],[f_139_4]) ).
cnf(f_139_6,plain,
empty(sK101),
inference(clausify,[status(thm)],[f_139_4]) ).
cnf(f_139_7,plain,
function(sK101),
inference(clausify,[status(thm)],[f_139_4]) ).
fof(f_140_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_140_2,plain,
? [U_608] :
( ordinal(U_608)
& epsilon_connected(U_608)
& epsilon_transitive(U_608)
& empty(U_608)
& one_to_one(U_608)
& function(U_608)
& relation(U_608) ),
inference(variable_rename,[status(thm)],[f_140_1]) ).
fof(f_140_3,plain,
( ordinal(sK102)
& epsilon_connected(sK102)
& epsilon_transitive(sK102)
& empty(sK102)
& one_to_one(sK102)
& function(sK102)
& relation(sK102) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_608,sK102)],[f_140_2]) ).
fof(f_140_4,plain,
( ordinal(sK102)
& epsilon_connected(sK102)
& epsilon_transitive(sK102)
& empty(sK102)
& one_to_one(sK102)
& function(sK102)
& relation(sK102) ),
inference(definitional_conversion,[status(esa)],[f_140_3]) ).
cnf(f_140_5,plain,
relation(sK102),
inference(clausify,[status(thm)],[f_140_4]) ).
cnf(f_140_6,plain,
function(sK102),
inference(clausify,[status(thm)],[f_140_4]) ).
cnf(f_140_7,plain,
one_to_one(sK102),
inference(clausify,[status(thm)],[f_140_4]) ).
cnf(f_140_8,plain,
empty(sK102),
inference(clausify,[status(thm)],[f_140_4]) ).
cnf(f_140_9,plain,
epsilon_transitive(sK102),
inference(clausify,[status(thm)],[f_140_4]) ).
cnf(f_140_10,plain,
epsilon_connected(sK102),
inference(clausify,[status(thm)],[f_140_4]) ).
cnf(f_140_11,plain,
ordinal(sK102),
inference(clausify,[status(thm)],[f_140_4]) ).
fof(f_141_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_141_2,plain,
? [U_609] :
( relation(U_609)
& ~ empty(U_609) ),
inference(variable_rename,[status(thm)],[f_141_1]) ).
fof(f_141_3,plain,
( relation(sK103)
& ~ empty(sK103) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(U_609,sK103)],[f_141_2]) ).
fof(f_141_4,plain,
( relation(sK103)
& ~ empty(sK103) ),
inference(definitional_conversion,[status(esa)],[f_141_3]) ).
cnf(f_141_5,plain,
~ empty(sK103),
inference(clausify,[status(thm)],[f_141_4]) ).
cnf(f_141_6,plain,
relation(sK103),
inference(clausify,[status(thm)],[f_141_4]) ).
fof(f_142_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_142_2,plain,
! [U_611] :
? [U_610] :
( empty(U_610)
& element(U_610,powerset(U_611)) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
fof(f_142_3,plain,
! [U_611] :
( empty(sK104(U_611))
& element(sK104(U_611),powerset(U_611)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK104]),skolemize(U_610,sK104(U_611))],[f_142_2]) ).
fof(f_142_4,plain,
( ! [U_611] : empty(sK104(U_611))
& ! [U_611] : element(sK104(U_611),powerset(U_611)) ),
inference(definitional_conversion,[status(esa)],[f_142_3]) ).
cnf(f_142_5,plain,
element(sK104(U_611),powerset(U_611)),
inference(clausify,[status(thm)],[f_142_4]) ).
cnf(f_142_6,plain,
empty(sK104(U_611)),
inference(clausify,[status(thm)],[f_142_4]) ).
fof(f_143_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_143_2,plain,
? [U_612] : ~ empty(U_612),
inference(variable_rename,[status(thm)],[f_143_1]) ).
fof(f_143_3,plain,
~ empty(sK105),
inference(skolemize,[status(esa),new_symbols(skolem,[sK105]),skolemize(U_612,sK105)],[f_143_2]) ).
fof(f_143_4,plain,
~ empty(sK105),
inference(definitional_conversion,[status(esa)],[f_143_3]) ).
cnf(f_143_5,plain,
~ empty(sK105),
inference(clausify,[status(thm)],[f_143_4]) ).
fof(f_144_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_144_2,plain,
? [U_613] :
( one_to_one(U_613)
& function(U_613)
& relation(U_613) ),
inference(variable_rename,[status(thm)],[f_144_1]) ).
fof(f_144_3,plain,
( one_to_one(sK106)
& function(sK106)
& relation(sK106) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK106]),skolemize(U_613,sK106)],[f_144_2]) ).
fof(f_144_4,plain,
( one_to_one(sK106)
& function(sK106)
& relation(sK106) ),
inference(definitional_conversion,[status(esa)],[f_144_3]) ).
cnf(f_144_5,plain,
relation(sK106),
inference(clausify,[status(thm)],[f_144_4]) ).
cnf(f_144_6,plain,
function(sK106),
inference(clausify,[status(thm)],[f_144_4]) ).
cnf(f_144_7,plain,
one_to_one(sK106),
inference(clausify,[status(thm)],[f_144_4]) ).
fof(f_145_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_ordinal1]) ).
fof(f_145_2,plain,
? [U_614] :
( ordinal(U_614)
& epsilon_connected(U_614)
& epsilon_transitive(U_614)
& ~ empty(U_614) ),
inference(variable_rename,[status(thm)],[f_145_1]) ).
fof(f_145_3,plain,
( ordinal(sK107)
& epsilon_connected(sK107)
& epsilon_transitive(sK107)
& ~ empty(sK107) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(U_614,sK107)],[f_145_2]) ).
fof(f_145_4,plain,
( ordinal(sK107)
& epsilon_connected(sK107)
& epsilon_transitive(sK107)
& ~ empty(sK107) ),
inference(definitional_conversion,[status(esa)],[f_145_3]) ).
cnf(f_145_5,plain,
~ empty(sK107),
inference(clausify,[status(thm)],[f_145_4]) ).
cnf(f_145_6,plain,
epsilon_transitive(sK107),
inference(clausify,[status(thm)],[f_145_4]) ).
cnf(f_145_7,plain,
epsilon_connected(sK107),
inference(clausify,[status(thm)],[f_145_4]) ).
cnf(f_145_8,plain,
ordinal(sK107),
inference(clausify,[status(thm)],[f_145_4]) ).
fof(f_146_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_146_2,plain,
? [U_615] :
( relation_empty_yielding(U_615)
& relation(U_615) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
fof(f_146_3,plain,
( relation_empty_yielding(sK108)
& relation(sK108) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK108]),skolemize(U_615,sK108)],[f_146_2]) ).
fof(f_146_4,plain,
( relation_empty_yielding(sK108)
& relation(sK108) ),
inference(definitional_conversion,[status(esa)],[f_146_3]) ).
cnf(f_146_5,plain,
relation(sK108),
inference(clausify,[status(thm)],[f_146_4]) ).
cnf(f_146_6,plain,
relation_empty_yielding(sK108),
inference(clausify,[status(thm)],[f_146_4]) ).
fof(f_147_1,plain,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc4_funct_1]) ).
fof(f_147_2,plain,
? [U_616] :
( function(U_616)
& relation_empty_yielding(U_616)
& relation(U_616) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
fof(f_147_3,plain,
( function(sK109)
& relation_empty_yielding(sK109)
& relation(sK109) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK109]),skolemize(U_616,sK109)],[f_147_2]) ).
fof(f_147_4,plain,
( function(sK109)
& relation_empty_yielding(sK109)
& relation(sK109) ),
inference(definitional_conversion,[status(esa)],[f_147_3]) ).
cnf(f_147_5,plain,
relation(sK109),
inference(clausify,[status(thm)],[f_147_4]) ).
cnf(f_147_6,plain,
relation_empty_yielding(sK109),
inference(clausify,[status(thm)],[f_147_4]) ).
cnf(f_147_7,plain,
function(sK109),
inference(clausify,[status(thm)],[f_147_4]) ).
fof(f_148_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_148_2,plain,
! [U_618,U_617] :
( union_of_subsets(U_618,U_617) = union(U_617)
| ~ element(U_617,powerset(powerset(U_618))) ),
inference(variable_rename,[status(thm)],[f_148_1]) ).
fof(f_148_3,plain,
! [U_617,U_618] :
( union_of_subsets(U_618,U_617) = union(U_617)
| ~ element(U_617,powerset(powerset(U_618))) ),
inference(definitional_conversion,[status(esa)],[f_148_2]) ).
cnf(f_148_4,plain,
( union_of_subsets(U_618,U_617) = union(U_617)
| ~ element(U_617,powerset(powerset(U_618))) ),
inference(clausify,[status(thm)],[f_148_3]) ).
fof(f_149_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_149_2,plain,
! [U_620,U_619] :
( meet_of_subsets(U_620,U_619) = set_meet(U_619)
| ~ element(U_619,powerset(powerset(U_620))) ),
inference(variable_rename,[status(thm)],[f_149_1]) ).
fof(f_149_3,plain,
! [U_619,U_620] :
( meet_of_subsets(U_620,U_619) = set_meet(U_619)
| ~ element(U_619,powerset(powerset(U_620))) ),
inference(definitional_conversion,[status(esa)],[f_149_2]) ).
cnf(f_149_4,plain,
( meet_of_subsets(U_620,U_619) = set_meet(U_619)
| ~ element(U_619,powerset(powerset(U_620))) ),
inference(clausify,[status(thm)],[f_149_3]) ).
fof(f_150_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_150_2,plain,
! [U_623,U_622,U_621] :
( subset_difference(U_623,U_622,U_621) = set_difference(U_622,U_621)
| ~ element(U_621,powerset(U_623))
| ~ element(U_622,powerset(U_623)) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
fof(f_150_3,plain,
! [U_621,U_622,U_623] :
( subset_difference(U_623,U_622,U_621) = set_difference(U_622,U_621)
| ~ element(U_621,powerset(U_623))
| ~ element(U_622,powerset(U_623)) ),
inference(definitional_conversion,[status(esa)],[f_150_2]) ).
cnf(f_150_4,plain,
( subset_difference(U_623,U_622,U_621) = set_difference(U_622,U_621)
| ~ element(U_621,powerset(U_623))
| ~ element(U_622,powerset(U_623)) ),
inference(clausify,[status(thm)],[f_150_3]) ).
fof(f_151_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_151_2,plain,
! [U_625,U_624] : subset(U_625,U_625),
inference(variable_rename,[status(thm)],[f_151_1]) ).
fof(f_151_3,plain,
! [U_625] : subset(U_625,U_625),
inference(miniscope,[status(thm)],[f_151_2]) ).
fof(f_151_4,plain,
! [U_625] : subset(U_625,U_625),
inference(definitional_conversion,[status(esa)],[f_151_3]) ).
cnf(f_151_5,plain,
subset(U_625,U_625),
inference(clausify,[status(thm)],[f_151_4]) ).
fof(f_152_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_152_2,plain,
! [U_627,U_626] :
( disjoint(U_626,U_627)
| ~ disjoint(U_627,U_626) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
fof(f_152_3,plain,
! [U_626,U_627] :
( disjoint(U_626,U_627)
| ~ disjoint(U_627,U_626) ),
inference(definitional_conversion,[status(esa)],[f_152_2]) ).
cnf(f_152_4,plain,
( disjoint(U_626,U_627)
| ~ disjoint(U_627,U_626) ),
inference(clausify,[status(thm)],[f_152_3]) ).
fof(f_153_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_153_2,plain,
! [U_631,U_630,U_629,U_628] :
( ( in(ordered_pair(U_631,U_630),cartesian_product2(U_629,U_628))
| ~ in(U_630,U_628)
| ~ in(U_631,U_629) )
& ( ( in(U_630,U_628)
& in(U_631,U_629) )
| ~ in(ordered_pair(U_631,U_630),cartesian_product2(U_629,U_628)) ) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
fof(f_153_3,plain,
( ! [U_639,U_637,U_635,U_633] :
( in(ordered_pair(U_639,U_637),cartesian_product2(U_635,U_633))
| ~ in(U_637,U_633)
| ~ in(U_639,U_635) )
& ! [U_638,U_636,U_634,U_632] :
( ( in(U_636,U_632)
& in(U_638,U_634) )
| ~ in(ordered_pair(U_638,U_636),cartesian_product2(U_634,U_632)) ) ),
inference(miniscope,[status(thm)],[f_153_2]) ).
fof(f_153_4,plain,
( ! [U_634,U_636,U_632,U_638] :
( in(U_636,U_632)
| ~ sP141(U_634,U_636,U_632,U_638) )
& ! [U_634,U_636,U_632,U_638] :
( in(U_638,U_634)
| ~ sP141(U_634,U_636,U_632,U_638) )
& ! [U_639,U_633,U_637,U_635] :
( in(ordered_pair(U_639,U_637),cartesian_product2(U_635,U_633))
| ~ in(U_637,U_633)
| ~ in(U_639,U_635) )
& ! [U_634,U_636,U_632,U_638] :
( sP141(U_634,U_636,U_632,U_638)
| ~ in(ordered_pair(U_638,U_636),cartesian_product2(U_634,U_632)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP141])],[f_153_3]) ).
cnf(f_153_5,plain,
( sP141(U_634,U_636,U_632,U_638)
| ~ in(ordered_pair(U_638,U_636),cartesian_product2(U_634,U_632)) ),
inference(clausify,[status(thm)],[f_153_4]) ).
cnf(f_153_6,plain,
( in(ordered_pair(U_639,U_637),cartesian_product2(U_635,U_633))
| ~ in(U_637,U_633)
| ~ in(U_639,U_635) ),
inference(clausify,[status(thm)],[f_153_4]) ).
cnf(f_153_7,plain,
( in(U_638,U_634)
| ~ sP141(U_634,U_636,U_632,U_638) ),
inference(clausify,[status(thm)],[f_153_4]) ).
cnf(f_153_8,plain,
( in(U_636,U_632)
| ~ sP141(U_634,U_636,U_632,U_638) ),
inference(clausify,[status(thm)],[f_153_4]) ).
fof(f_154_1,plain,
! [A] : in(A,succ(A)),
inference(fof_nnf,[status(thm)],[t10_ordinal1]) ).
fof(f_154_2,plain,
! [U_640] : in(U_640,succ(U_640)),
inference(variable_rename,[status(thm)],[f_154_1]) ).
fof(f_154_3,plain,
! [U_640] : in(U_640,succ(U_640)),
inference(definitional_conversion,[status(esa)],[f_154_2]) ).
cnf(f_154_4,plain,
in(U_640,succ(U_640)),
inference(clausify,[status(thm)],[f_154_3]) ).
fof(f_155_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_155_2,plain,
! [U_644,U_643,U_642,U_641] :
( U_644 = U_641
| U_644 = U_642
| unordered_pair(U_644,U_643) != unordered_pair(U_642,U_641) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
fof(f_155_3,plain,
! [U_644,U_643,U_642] :
( ! [U_641] :
( U_644 = U_641
| unordered_pair(U_644,U_643) != unordered_pair(U_642,U_641) )
| U_644 = U_642 ),
inference(miniscope,[status(thm)],[f_155_2]) ).
fof(f_155_4,plain,
! [U_641,U_643,U_642,U_644] :
( U_644 = U_641
| unordered_pair(U_644,U_643) != unordered_pair(U_642,U_641)
| U_644 = U_642 ),
inference(definitional_conversion,[status(esa)],[f_155_3]) ).
cnf(f_155_5,plain,
( U_644 = U_641
| unordered_pair(U_644,U_643) != unordered_pair(U_642,U_641)
| U_644 = U_642 ),
inference(clausify,[status(thm)],[f_155_4]) ).
fof(f_156_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_156_2,plain,
! [U_647,U_646,U_645] :
( ( ( in(U_647,relation_rng(relation_rng_restriction(U_646,U_645)))
| ~ in(U_647,relation_rng(U_645))
| ~ in(U_647,U_646) )
& ( ( in(U_647,relation_rng(U_645))
& in(U_647,U_646) )
| ~ in(U_647,relation_rng(relation_rng_restriction(U_646,U_645))) ) )
| ~ relation(U_645) ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
fof(f_156_3,plain,
( ! [U_645,U_646,U_647] :
( in(U_647,relation_rng(U_645))
| ~ sP142(U_645,U_646,U_647) )
& ! [U_645,U_646,U_647] :
( in(U_647,U_646)
| ~ sP142(U_645,U_646,U_647) )
& ! [U_645,U_646,U_647] :
( in(U_647,relation_rng(relation_rng_restriction(U_646,U_645)))
| ~ in(U_647,relation_rng(U_645))
| ~ in(U_647,U_646)
| ~ sP143(U_645,U_646,U_647) )
& ! [U_645,U_646,U_647] :
( sP142(U_645,U_646,U_647)
| ~ in(U_647,relation_rng(relation_rng_restriction(U_646,U_645)))
| ~ sP143(U_645,U_646,U_647) )
& ! [U_645,U_646,U_647] :
( sP143(U_645,U_646,U_647)
| ~ relation(U_645) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP142,sP143])],[f_156_2]) ).
cnf(f_156_4,plain,
( sP143(U_645,U_646,U_647)
| ~ relation(U_645) ),
inference(clausify,[status(thm)],[f_156_3]) ).
cnf(f_156_5,plain,
( sP142(U_645,U_646,U_647)
| ~ in(U_647,relation_rng(relation_rng_restriction(U_646,U_645)))
| ~ sP143(U_645,U_646,U_647) ),
inference(clausify,[status(thm)],[f_156_3]) ).
cnf(f_156_6,plain,
( in(U_647,relation_rng(relation_rng_restriction(U_646,U_645)))
| ~ in(U_647,relation_rng(U_645))
| ~ in(U_647,U_646)
| ~ sP143(U_645,U_646,U_647) ),
inference(clausify,[status(thm)],[f_156_3]) ).
cnf(f_156_7,plain,
( in(U_647,U_646)
| ~ sP142(U_645,U_646,U_647) ),
inference(clausify,[status(thm)],[f_156_3]) ).
cnf(f_156_8,plain,
( in(U_647,relation_rng(U_645))
| ~ sP142(U_645,U_646,U_647) ),
inference(clausify,[status(thm)],[f_156_3]) ).
fof(f_157_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_157_2,plain,
! [U_649,U_648] :
( subset(relation_rng(relation_rng_restriction(U_649,U_648)),U_649)
| ~ relation(U_648) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
fof(f_157_3,plain,
! [U_649,U_648] :
( subset(relation_rng(relation_rng_restriction(U_649,U_648)),U_649)
| ~ relation(U_648) ),
inference(definitional_conversion,[status(esa)],[f_157_2]) ).
cnf(f_157_4,plain,
( subset(relation_rng(relation_rng_restriction(U_649,U_648)),U_649)
| ~ relation(U_648) ),
inference(clausify,[status(thm)],[f_157_3]) ).
fof(f_158_1,plain,
! [A,B] :
( subset(relation_rng_restriction(A,B),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t117_relat_1]) ).
fof(f_158_2,plain,
! [U_651,U_650] :
( subset(relation_rng_restriction(U_651,U_650),U_650)
| ~ relation(U_650) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
fof(f_158_3,plain,
! [U_651,U_650] :
( subset(relation_rng_restriction(U_651,U_650),U_650)
| ~ relation(U_650) ),
inference(definitional_conversion,[status(esa)],[f_158_2]) ).
cnf(f_158_4,plain,
( subset(relation_rng_restriction(U_651,U_650),U_650)
| ~ relation(U_650) ),
inference(clausify,[status(thm)],[f_158_3]) ).
fof(f_159_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_159_2,plain,
! [U_653,U_652] :
( subset(relation_rng(relation_rng_restriction(U_653,U_652)),relation_rng(U_652))
| ~ relation(U_652) ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
fof(f_159_3,plain,
! [U_652,U_653] :
( subset(relation_rng(relation_rng_restriction(U_653,U_652)),relation_rng(U_652))
| ~ relation(U_652) ),
inference(definitional_conversion,[status(esa)],[f_159_2]) ).
cnf(f_159_4,plain,
( subset(relation_rng(relation_rng_restriction(U_653,U_652)),relation_rng(U_652))
| ~ relation(U_652) ),
inference(clausify,[status(thm)],[f_159_3]) ).
fof(f_160_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_160_2,plain,
! [U_656,U_655,U_654] :
( ( subset(cartesian_product2(U_654,U_656),cartesian_product2(U_654,U_655))
& subset(cartesian_product2(U_656,U_654),cartesian_product2(U_655,U_654)) )
| ~ subset(U_656,U_655) ),
inference(variable_rename,[status(thm)],[f_160_1]) ).
fof(f_160_3,plain,
! [U_656,U_655] :
( ( ! [U_658] : subset(cartesian_product2(U_658,U_656),cartesian_product2(U_658,U_655))
& ! [U_657] : subset(cartesian_product2(U_656,U_657),cartesian_product2(U_655,U_657)) )
| ~ subset(U_656,U_655) ),
inference(miniscope,[status(thm)],[f_160_2]) ).
fof(f_160_4,plain,
( ! [U_655,U_656,U_657,U_658] :
( subset(cartesian_product2(U_658,U_656),cartesian_product2(U_658,U_655))
| ~ sP144(U_655,U_656,U_657,U_658) )
& ! [U_655,U_656,U_657,U_658] :
( subset(cartesian_product2(U_656,U_657),cartesian_product2(U_655,U_657))
| ~ sP144(U_655,U_656,U_657,U_658) )
& ! [U_655,U_656,U_657,U_658] :
( sP144(U_655,U_656,U_657,U_658)
| ~ subset(U_656,U_655) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP144])],[f_160_3]) ).
cnf(f_160_5,plain,
( sP144(U_655,U_656,U_657,U_658)
| ~ subset(U_656,U_655) ),
inference(clausify,[status(thm)],[f_160_4]) ).
cnf(f_160_6,plain,
( subset(cartesian_product2(U_656,U_657),cartesian_product2(U_655,U_657))
| ~ sP144(U_655,U_656,U_657,U_658) ),
inference(clausify,[status(thm)],[f_160_4]) ).
cnf(f_160_7,plain,
( subset(cartesian_product2(U_658,U_656),cartesian_product2(U_658,U_655))
| ~ sP144(U_655,U_656,U_657,U_658) ),
inference(clausify,[status(thm)],[f_160_4]) ).
fof(f_161_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_161_2,plain,
! [U_660,U_659] :
( relation_rng(relation_rng_restriction(U_660,U_659)) = set_intersection2(relation_rng(U_659),U_660)
| ~ relation(U_659) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
fof(f_161_3,plain,
! [U_659,U_660] :
( relation_rng(relation_rng_restriction(U_660,U_659)) = set_intersection2(relation_rng(U_659),U_660)
| ~ relation(U_659) ),
inference(definitional_conversion,[status(esa)],[f_161_2]) ).
cnf(f_161_4,plain,
( relation_rng(relation_rng_restriction(U_660,U_659)) = set_intersection2(relation_rng(U_659),U_660)
| ~ relation(U_659) ),
inference(clausify,[status(thm)],[f_161_3]) ).
fof(f_162_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_162_2,plain,
! [U_664,U_663,U_662,U_661] :
( subset(cartesian_product2(U_664,U_662),cartesian_product2(U_663,U_661))
| ~ subset(U_662,U_661)
| ~ subset(U_664,U_663) ),
inference(variable_rename,[status(thm)],[f_162_1]) ).
fof(f_162_3,plain,
! [U_661,U_662,U_663,U_664] :
( subset(cartesian_product2(U_664,U_662),cartesian_product2(U_663,U_661))
| ~ subset(U_662,U_661)
| ~ subset(U_664,U_663) ),
inference(definitional_conversion,[status(esa)],[f_162_2]) ).
cnf(f_162_4,plain,
( subset(cartesian_product2(U_664,U_662),cartesian_product2(U_663,U_661))
| ~ subset(U_662,U_661)
| ~ subset(U_664,U_663) ),
inference(clausify,[status(thm)],[f_162_3]) ).
fof(f_163_1,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t12_xboole_1]) ).
fof(f_163_2,plain,
! [U_666,U_665] :
( set_union2(U_666,U_665) = U_665
| ~ subset(U_666,U_665) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
fof(f_163_3,plain,
! [U_666,U_665] :
( set_union2(U_666,U_665) = U_665
| ~ subset(U_666,U_665) ),
inference(definitional_conversion,[status(esa)],[f_163_2]) ).
cnf(f_163_4,plain,
( set_union2(U_666,U_665) = U_665
| ~ subset(U_666,U_665) ),
inference(clausify,[status(thm)],[f_163_3]) ).
fof(f_164_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_164_2,plain,
! [U_672] :
? [U_671] :
( ! [U_670] :
( in(U_670,U_671)
| are_equipotent(U_670,U_671)
| ~ subset(U_670,U_671) )
& ! [U_669] :
( in(powerset(U_669),U_671)
| ~ in(U_669,U_671) )
& ! [U_668,U_667] :
( in(U_667,U_671)
| ~ subset(U_667,U_668)
| ~ in(U_668,U_671) )
& in(U_672,U_671) ),
inference(variable_rename,[status(thm)],[f_164_1]) ).
fof(f_164_3,plain,
! [U_672] :
( ! [U_670] :
( in(U_670,sK110(U_672))
| are_equipotent(U_670,sK110(U_672))
| ~ subset(U_670,sK110(U_672)) )
& ! [U_669] :
( in(powerset(U_669),sK110(U_672))
| ~ in(U_669,sK110(U_672)) )
& ! [U_668,U_667] :
( in(U_667,sK110(U_672))
| ~ subset(U_667,U_668)
| ~ in(U_668,sK110(U_672)) )
& in(U_672,sK110(U_672)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK110]),skolemize(U_671,sK110(U_672))],[f_164_2]) ).
fof(f_164_4,plain,
( ! [U_670,U_672] :
( in(U_670,sK110(U_672))
| are_equipotent(U_670,sK110(U_672))
| ~ subset(U_670,sK110(U_672)) )
& ! [U_669,U_672] :
( in(powerset(U_669),sK110(U_672))
| ~ in(U_669,sK110(U_672)) )
& ! [U_668,U_667,U_672] :
( in(U_667,sK110(U_672))
| ~ subset(U_667,U_668)
| ~ in(U_668,sK110(U_672)) )
& ! [U_672] : in(U_672,sK110(U_672)) ),
inference(definitional_conversion,[status(esa)],[f_164_3]) ).
cnf(f_164_5,plain,
in(U_672,sK110(U_672)),
inference(clausify,[status(thm)],[f_164_4]) ).
cnf(f_164_6,plain,
( in(U_667,sK110(U_672))
| ~ subset(U_667,U_668)
| ~ in(U_668,sK110(U_672)) ),
inference(clausify,[status(thm)],[f_164_4]) ).
cnf(f_164_7,plain,
( in(powerset(U_669),sK110(U_672))
| ~ in(U_669,sK110(U_672)) ),
inference(clausify,[status(thm)],[f_164_4]) ).
cnf(f_164_8,plain,
( in(U_670,sK110(U_672))
| are_equipotent(U_670,sK110(U_672))
| ~ subset(U_670,sK110(U_672)) ),
inference(clausify,[status(thm)],[f_164_4]) ).
fof(f_165_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_165_2,plain,
! [U_675,U_674,U_673] :
( relation_dom_restriction(relation_rng_restriction(U_675,U_673),U_674) = relation_rng_restriction(U_675,relation_dom_restriction(U_673,U_674))
| ~ relation(U_673) ),
inference(variable_rename,[status(thm)],[f_165_1]) ).
fof(f_165_3,plain,
! [U_675,U_673,U_674] :
( relation_dom_restriction(relation_rng_restriction(U_675,U_673),U_674) = relation_rng_restriction(U_675,relation_dom_restriction(U_673,U_674))
| ~ relation(U_673) ),
inference(definitional_conversion,[status(esa)],[f_165_2]) ).
cnf(f_165_4,plain,
( relation_dom_restriction(relation_rng_restriction(U_675,U_673),U_674) = relation_rng_restriction(U_675,relation_dom_restriction(U_673,U_674))
| ~ relation(U_673) ),
inference(clausify,[status(thm)],[f_165_3]) ).
fof(f_166_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_166_2,plain,
! [U_680,U_679,U_678] :
( ( ( in(U_680,relation_image(U_678,U_679))
| ! [U_677] :
( ~ in(U_677,U_679)
| ~ in(ordered_pair(U_677,U_680),U_678)
| ~ in(U_677,relation_dom(U_678)) ) )
& ( ? [U_676] :
( in(U_676,U_679)
& in(ordered_pair(U_676,U_680),U_678)
& in(U_676,relation_dom(U_678)) )
| ~ in(U_680,relation_image(U_678,U_679)) ) )
| ~ relation(U_678) ),
inference(variable_rename,[status(thm)],[f_166_1]) ).
fof(f_166_3,plain,
! [U_680,U_679,U_678] :
( ( ( in(U_680,relation_image(U_678,U_679))
| ! [U_677] :
( ~ in(U_677,U_679)
| ~ in(ordered_pair(U_677,U_680),U_678)
| ~ in(U_677,relation_dom(U_678)) ) )
& ( ( in(sK111(U_680,U_679,U_678),U_679)
& in(ordered_pair(sK111(U_680,U_679,U_678),U_680),U_678)
& in(sK111(U_680,U_679,U_678),relation_dom(U_678)) )
| ~ in(U_680,relation_image(U_678,U_679)) ) )
| ~ relation(U_678) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK111]),skolemize(U_676,sK111(U_680,U_679,U_678))],[f_166_2]) ).
fof(f_166_4,plain,
( ! [U_678,U_679,U_680] :
( in(sK111(U_680,U_679,U_678),U_679)
| ~ sP145(U_678,U_679,U_680) )
& ! [U_678,U_679,U_680] :
( in(ordered_pair(sK111(U_680,U_679,U_678),U_680),U_678)
| ~ sP145(U_678,U_679,U_680) )
& ! [U_678,U_679,U_680] :
( in(sK111(U_680,U_679,U_678),relation_dom(U_678))
| ~ sP145(U_678,U_679,U_680) )
& ! [U_677,U_678,U_679,U_680] :
( in(U_680,relation_image(U_678,U_679))
| ~ in(U_677,U_679)
| ~ in(ordered_pair(U_677,U_680),U_678)
| ~ in(U_677,relation_dom(U_678))
| ~ sP146(U_677,U_678,U_679,U_680) )
& ! [U_677,U_678,U_679,U_680] :
( sP145(U_678,U_679,U_680)
| ~ in(U_680,relation_image(U_678,U_679))
| ~ sP146(U_677,U_678,U_679,U_680) )
& ! [U_677,U_678,U_679,U_680] :
( sP146(U_677,U_678,U_679,U_680)
| ~ relation(U_678) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP145,sP146])],[f_166_3]) ).
cnf(f_166_5,plain,
( sP146(U_677,U_678,U_679,U_680)
| ~ relation(U_678) ),
inference(clausify,[status(thm)],[f_166_4]) ).
cnf(f_166_6,plain,
( sP145(U_678,U_679,U_680)
| ~ in(U_680,relation_image(U_678,U_679))
| ~ sP146(U_677,U_678,U_679,U_680) ),
inference(clausify,[status(thm)],[f_166_4]) ).
cnf(f_166_7,plain,
( in(U_680,relation_image(U_678,U_679))
| ~ in(U_677,U_679)
| ~ in(ordered_pair(U_677,U_680),U_678)
| ~ in(U_677,relation_dom(U_678))
| ~ sP146(U_677,U_678,U_679,U_680) ),
inference(clausify,[status(thm)],[f_166_4]) ).
cnf(f_166_8,plain,
( in(sK111(U_680,U_679,U_678),relation_dom(U_678))
| ~ sP145(U_678,U_679,U_680) ),
inference(clausify,[status(thm)],[f_166_4]) ).
cnf(f_166_9,plain,
( in(ordered_pair(sK111(U_680,U_679,U_678),U_680),U_678)
| ~ sP145(U_678,U_679,U_680) ),
inference(clausify,[status(thm)],[f_166_4]) ).
cnf(f_166_10,plain,
( in(sK111(U_680,U_679,U_678),U_679)
| ~ sP145(U_678,U_679,U_680) ),
inference(clausify,[status(thm)],[f_166_4]) ).
fof(f_167_1,plain,
! [A,B] :
( subset(relation_image(B,A),relation_rng(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t144_relat_1]) ).
fof(f_167_2,plain,
! [U_682,U_681] :
( subset(relation_image(U_681,U_682),relation_rng(U_681))
| ~ relation(U_681) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
fof(f_167_3,plain,
! [U_682,U_681] :
( subset(relation_image(U_681,U_682),relation_rng(U_681))
| ~ relation(U_681) ),
inference(definitional_conversion,[status(esa)],[f_167_2]) ).
cnf(f_167_4,plain,
( subset(relation_image(U_681,U_682),relation_rng(U_681))
| ~ relation(U_681) ),
inference(clausify,[status(thm)],[f_167_3]) ).
fof(f_168_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_168_2,plain,
! [U_684,U_683] :
( subset(relation_image(U_683,relation_inverse_image(U_683,U_684)),U_684)
| ~ function(U_683)
| ~ relation(U_683) ),
inference(variable_rename,[status(thm)],[f_168_1]) ).
fof(f_168_3,plain,
! [U_684,U_683] :
( subset(relation_image(U_683,relation_inverse_image(U_683,U_684)),U_684)
| ~ function(U_683)
| ~ relation(U_683) ),
inference(definitional_conversion,[status(esa)],[f_168_2]) ).
cnf(f_168_4,plain,
( subset(relation_image(U_683,relation_inverse_image(U_683,U_684)),U_684)
| ~ function(U_683)
| ~ relation(U_683) ),
inference(clausify,[status(thm)],[f_168_3]) ).
fof(f_169_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_169_2,plain,
! [U_686,U_685] :
( relation_image(U_685,U_686) = relation_image(U_685,set_intersection2(relation_dom(U_685),U_686))
| ~ relation(U_685) ),
inference(variable_rename,[status(thm)],[f_169_1]) ).
fof(f_169_3,plain,
! [U_685,U_686] :
( relation_image(U_685,U_686) = relation_image(U_685,set_intersection2(relation_dom(U_685),U_686))
| ~ relation(U_685) ),
inference(definitional_conversion,[status(esa)],[f_169_2]) ).
cnf(f_169_4,plain,
( relation_image(U_685,U_686) = relation_image(U_685,set_intersection2(relation_dom(U_685),U_686))
| ~ relation(U_685) ),
inference(clausify,[status(thm)],[f_169_3]) ).
fof(f_170_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_170_2,plain,
! [U_688,U_687] :
( subset(U_688,relation_inverse_image(U_687,relation_image(U_687,U_688)))
| ~ subset(U_688,relation_dom(U_687))
| ~ relation(U_687) ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
fof(f_170_3,plain,
! [U_688,U_687] :
( subset(U_688,relation_inverse_image(U_687,relation_image(U_687,U_688)))
| ~ subset(U_688,relation_dom(U_687))
| ~ relation(U_687) ),
inference(definitional_conversion,[status(esa)],[f_170_2]) ).
cnf(f_170_4,plain,
( subset(U_688,relation_inverse_image(U_687,relation_image(U_687,U_688)))
| ~ subset(U_688,relation_dom(U_687))
| ~ relation(U_687) ),
inference(clausify,[status(thm)],[f_170_3]) ).
fof(f_171_1,plain,
! [A] :
( relation_image(A,relation_dom(A)) = relation_rng(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t146_relat_1]) ).
fof(f_171_2,plain,
! [U_689] :
( relation_image(U_689,relation_dom(U_689)) = relation_rng(U_689)
| ~ relation(U_689) ),
inference(variable_rename,[status(thm)],[f_171_1]) ).
fof(f_171_3,plain,
! [U_689] :
( relation_image(U_689,relation_dom(U_689)) = relation_rng(U_689)
| ~ relation(U_689) ),
inference(definitional_conversion,[status(esa)],[f_171_2]) ).
cnf(f_171_4,plain,
( relation_image(U_689,relation_dom(U_689)) = relation_rng(U_689)
| ~ relation(U_689) ),
inference(clausify,[status(thm)],[f_171_3]) ).
fof(f_172_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_172_2,plain,
! [U_691,U_690] :
( relation_image(U_690,relation_inverse_image(U_690,U_691)) = U_691
| ~ subset(U_691,relation_rng(U_690))
| ~ function(U_690)
| ~ relation(U_690) ),
inference(variable_rename,[status(thm)],[f_172_1]) ).
fof(f_172_3,plain,
! [U_690,U_691] :
( relation_image(U_690,relation_inverse_image(U_690,U_691)) = U_691
| ~ subset(U_691,relation_rng(U_690))
| ~ function(U_690)
| ~ relation(U_690) ),
inference(definitional_conversion,[status(esa)],[f_172_2]) ).
cnf(f_172_4,plain,
( relation_image(U_690,relation_inverse_image(U_690,U_691)) = U_691
| ~ subset(U_691,relation_rng(U_690))
| ~ function(U_690)
| ~ relation(U_690) ),
inference(clausify,[status(thm)],[f_172_3]) ).
fof(f_173_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_173_2,plain,
! [U_693] :
( ! [U_692] :
( relation_rng(relation_composition(U_693,U_692)) = relation_image(U_692,relation_rng(U_693))
| ~ relation(U_692) )
| ~ relation(U_693) ),
inference(variable_rename,[status(thm)],[f_173_1]) ).
fof(f_173_3,plain,
! [U_692,U_693] :
( relation_rng(relation_composition(U_693,U_692)) = relation_image(U_692,relation_rng(U_693))
| ~ relation(U_692)
| ~ relation(U_693) ),
inference(definitional_conversion,[status(esa)],[f_173_2]) ).
cnf(f_173_4,plain,
( relation_rng(relation_composition(U_693,U_692)) = relation_image(U_692,relation_rng(U_693))
| ~ relation(U_692)
| ~ relation(U_693) ),
inference(clausify,[status(thm)],[f_173_3]) ).
fof(f_174_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_174_2,plain,
! [U_698,U_697,U_696] :
( ( ( in(U_698,relation_inverse_image(U_696,U_697))
| ! [U_695] :
( ~ in(U_695,U_697)
| ~ in(ordered_pair(U_698,U_695),U_696)
| ~ in(U_695,relation_rng(U_696)) ) )
& ( ? [U_694] :
( in(U_694,U_697)
& in(ordered_pair(U_698,U_694),U_696)
& in(U_694,relation_rng(U_696)) )
| ~ in(U_698,relation_inverse_image(U_696,U_697)) ) )
| ~ relation(U_696) ),
inference(variable_rename,[status(thm)],[f_174_1]) ).
fof(f_174_3,plain,
! [U_698,U_697,U_696] :
( ( ( in(U_698,relation_inverse_image(U_696,U_697))
| ! [U_695] :
( ~ in(U_695,U_697)
| ~ in(ordered_pair(U_698,U_695),U_696)
| ~ in(U_695,relation_rng(U_696)) ) )
& ( ( in(sK112(U_698,U_697,U_696),U_697)
& in(ordered_pair(U_698,sK112(U_698,U_697,U_696)),U_696)
& in(sK112(U_698,U_697,U_696),relation_rng(U_696)) )
| ~ in(U_698,relation_inverse_image(U_696,U_697)) ) )
| ~ relation(U_696) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK112]),skolemize(U_694,sK112(U_698,U_697,U_696))],[f_174_2]) ).
fof(f_174_4,plain,
( ! [U_696,U_697,U_698] :
( in(sK112(U_698,U_697,U_696),U_697)
| ~ sP147(U_696,U_697,U_698) )
& ! [U_696,U_697,U_698] :
( in(ordered_pair(U_698,sK112(U_698,U_697,U_696)),U_696)
| ~ sP147(U_696,U_697,U_698) )
& ! [U_696,U_697,U_698] :
( in(sK112(U_698,U_697,U_696),relation_rng(U_696))
| ~ sP147(U_696,U_697,U_698) )
& ! [U_695,U_696,U_697,U_698] :
( in(U_698,relation_inverse_image(U_696,U_697))
| ~ in(U_695,U_697)
| ~ in(ordered_pair(U_698,U_695),U_696)
| ~ in(U_695,relation_rng(U_696))
| ~ sP148(U_695,U_696,U_697,U_698) )
& ! [U_695,U_696,U_697,U_698] :
( sP147(U_696,U_697,U_698)
| ~ in(U_698,relation_inverse_image(U_696,U_697))
| ~ sP148(U_695,U_696,U_697,U_698) )
& ! [U_695,U_696,U_697,U_698] :
( sP148(U_695,U_696,U_697,U_698)
| ~ relation(U_696) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP147,sP148])],[f_174_3]) ).
cnf(f_174_5,plain,
( sP148(U_695,U_696,U_697,U_698)
| ~ relation(U_696) ),
inference(clausify,[status(thm)],[f_174_4]) ).
cnf(f_174_6,plain,
( sP147(U_696,U_697,U_698)
| ~ in(U_698,relation_inverse_image(U_696,U_697))
| ~ sP148(U_695,U_696,U_697,U_698) ),
inference(clausify,[status(thm)],[f_174_4]) ).
cnf(f_174_7,plain,
( in(U_698,relation_inverse_image(U_696,U_697))
| ~ in(U_695,U_697)
| ~ in(ordered_pair(U_698,U_695),U_696)
| ~ in(U_695,relation_rng(U_696))
| ~ sP148(U_695,U_696,U_697,U_698) ),
inference(clausify,[status(thm)],[f_174_4]) ).
cnf(f_174_8,plain,
( in(sK112(U_698,U_697,U_696),relation_rng(U_696))
| ~ sP147(U_696,U_697,U_698) ),
inference(clausify,[status(thm)],[f_174_4]) ).
cnf(f_174_9,plain,
( in(ordered_pair(U_698,sK112(U_698,U_697,U_696)),U_696)
| ~ sP147(U_696,U_697,U_698) ),
inference(clausify,[status(thm)],[f_174_4]) ).
cnf(f_174_10,plain,
( in(sK112(U_698,U_697,U_696),U_697)
| ~ sP147(U_696,U_697,U_698) ),
inference(clausify,[status(thm)],[f_174_4]) ).
fof(f_175_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_175_2,plain,
! [U_700,U_699] :
( subset(relation_inverse_image(U_699,U_700),relation_dom(U_699))
| ~ relation(U_699) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
fof(f_175_3,plain,
! [U_699,U_700] :
( subset(relation_inverse_image(U_699,U_700),relation_dom(U_699))
| ~ relation(U_699) ),
inference(definitional_conversion,[status(esa)],[f_175_2]) ).
cnf(f_175_4,plain,
( subset(relation_inverse_image(U_699,U_700),relation_dom(U_699))
| ~ relation(U_699) ),
inference(clausify,[status(thm)],[f_175_3]) ).
fof(f_176_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_176_2,plain,
! [U_702,U_701] :
( relation_inverse_image(U_701,U_702) != empty_set
| ~ subset(U_702,relation_rng(U_701))
| U_702 = empty_set
| ~ relation(U_701) ),
inference(variable_rename,[status(thm)],[f_176_1]) ).
fof(f_176_3,plain,
! [U_701,U_702] :
( relation_inverse_image(U_701,U_702) != empty_set
| ~ subset(U_702,relation_rng(U_701))
| U_702 = empty_set
| ~ relation(U_701) ),
inference(definitional_conversion,[status(esa)],[f_176_2]) ).
cnf(f_176_4,plain,
( relation_inverse_image(U_701,U_702) != empty_set
| ~ subset(U_702,relation_rng(U_701))
| U_702 = empty_set
| ~ relation(U_701) ),
inference(clausify,[status(thm)],[f_176_3]) ).
fof(f_177_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_177_2,plain,
! [U_705,U_704,U_703] :
( subset(relation_inverse_image(U_703,U_705),relation_inverse_image(U_703,U_704))
| ~ subset(U_705,U_704)
| ~ relation(U_703) ),
inference(variable_rename,[status(thm)],[f_177_1]) ).
fof(f_177_3,plain,
! [U_703,U_705,U_704] :
( subset(relation_inverse_image(U_703,U_705),relation_inverse_image(U_703,U_704))
| ~ subset(U_705,U_704)
| ~ relation(U_703) ),
inference(definitional_conversion,[status(esa)],[f_177_2]) ).
cnf(f_177_4,plain,
( subset(relation_inverse_image(U_703,U_705),relation_inverse_image(U_703,U_704))
| ~ subset(U_705,U_704)
| ~ relation(U_703) ),
inference(clausify,[status(thm)],[f_177_3]) ).
fof(f_178_1,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(fof_nnf,[status(thm)],[t17_xboole_1]) ).
fof(f_178_2,plain,
! [U_707,U_706] : subset(set_intersection2(U_707,U_706),U_707),
inference(variable_rename,[status(thm)],[f_178_1]) ).
fof(f_178_3,plain,
! [U_707,U_706] : subset(set_intersection2(U_707,U_706),U_707),
inference(definitional_conversion,[status(esa)],[f_178_2]) ).
cnf(f_178_4,plain,
subset(set_intersection2(U_707,U_706),U_707),
inference(clausify,[status(thm)],[f_178_3]) ).
fof(f_179_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_179_2,plain,
! [U_710,U_709,U_708] :
( subset(U_710,set_intersection2(U_709,U_708))
| ~ subset(U_710,U_708)
| ~ subset(U_710,U_709) ),
inference(variable_rename,[status(thm)],[f_179_1]) ).
fof(f_179_3,plain,
! [U_708,U_709,U_710] :
( subset(U_710,set_intersection2(U_709,U_708))
| ~ subset(U_710,U_708)
| ~ subset(U_710,U_709) ),
inference(definitional_conversion,[status(esa)],[f_179_2]) ).
cnf(f_179_4,plain,
( subset(U_710,set_intersection2(U_709,U_708))
| ~ subset(U_710,U_708)
| ~ subset(U_710,U_709) ),
inference(clausify,[status(thm)],[f_179_3]) ).
fof(f_180_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_180_2,plain,
! [U_711] : set_union2(U_711,empty_set) = U_711,
inference(variable_rename,[status(thm)],[f_180_1]) ).
fof(f_180_3,plain,
! [U_711] : set_union2(U_711,empty_set) = U_711,
inference(definitional_conversion,[status(esa)],[f_180_2]) ).
cnf(f_180_4,plain,
set_union2(U_711,empty_set) = U_711,
inference(clausify,[status(thm)],[f_180_3]) ).
fof(f_181_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_181_2,plain,
! [U_713,U_712] :
( element(U_713,U_712)
| ~ in(U_713,U_712) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
fof(f_181_3,plain,
! [U_713,U_712] :
( element(U_713,U_712)
| ~ in(U_713,U_712) ),
inference(definitional_conversion,[status(esa)],[f_181_2]) ).
cnf(f_181_4,plain,
( element(U_713,U_712)
| ~ in(U_713,U_712) ),
inference(clausify,[status(thm)],[f_181_3]) ).
fof(f_182_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_182_2,plain,
! [U_716,U_715,U_714] :
( subset(U_716,U_714)
| ~ subset(U_715,U_714)
| ~ subset(U_716,U_715) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
fof(f_182_3,plain,
! [U_715,U_714,U_716] :
( subset(U_716,U_714)
| ~ subset(U_715,U_714)
| ~ subset(U_716,U_715) ),
inference(definitional_conversion,[status(esa)],[f_182_2]) ).
cnf(f_182_4,plain,
( subset(U_716,U_714)
| ~ subset(U_715,U_714)
| ~ subset(U_716,U_715) ),
inference(clausify,[status(thm)],[f_182_3]) ).
fof(f_183_1,plain,
powerset(empty_set) = singleton(empty_set),
inference(fof_nnf,[status(thm)],[t1_zfmisc_1]) ).
fof(f_183_2,plain,
powerset(empty_set) = singleton(empty_set),
inference(definitional_conversion,[status(esa)],[f_183_1]) ).
cnf(f_183_3,plain,
powerset(empty_set) = singleton(empty_set),
inference(clausify,[status(thm)],[f_183_2]) ).
fof(f_184_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_184_2,plain,
! [U_719,U_718,U_717] :
( ( in(U_718,relation_rng(U_717))
& in(U_719,relation_dom(U_717)) )
| ~ in(ordered_pair(U_719,U_718),U_717)
| ~ relation(U_717) ),
inference(variable_rename,[status(thm)],[f_184_1]) ).
fof(f_184_3,plain,
( ! [U_717,U_718,U_719] :
( in(U_718,relation_rng(U_717))
| ~ sP149(U_717,U_718,U_719) )
& ! [U_717,U_718,U_719] :
( in(U_719,relation_dom(U_717))
| ~ sP149(U_717,U_718,U_719) )
& ! [U_717,U_718,U_719] :
( sP149(U_717,U_718,U_719)
| ~ in(ordered_pair(U_719,U_718),U_717)
| ~ relation(U_717) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP149])],[f_184_2]) ).
cnf(f_184_4,plain,
( sP149(U_717,U_718,U_719)
| ~ in(ordered_pair(U_719,U_718),U_717)
| ~ relation(U_717) ),
inference(clausify,[status(thm)],[f_184_3]) ).
cnf(f_184_5,plain,
( in(U_719,relation_dom(U_717))
| ~ sP149(U_717,U_718,U_719) ),
inference(clausify,[status(thm)],[f_184_3]) ).
cnf(f_184_6,plain,
( in(U_718,relation_rng(U_717))
| ~ sP149(U_717,U_718,U_719) ),
inference(clausify,[status(thm)],[f_184_3]) ).
fof(f_185_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_185_2,plain,
! [U_722,U_721] :
( ! [U_720] :
( ( ( in(U_722,relation_dom(relation_composition(U_720,U_721)))
| ~ in(apply(U_720,U_722),relation_dom(U_721))
| ~ in(U_722,relation_dom(U_720)) )
& ( ( in(apply(U_720,U_722),relation_dom(U_721))
& in(U_722,relation_dom(U_720)) )
| ~ in(U_722,relation_dom(relation_composition(U_720,U_721))) ) )
| ~ function(U_720)
| ~ relation(U_720) )
| ~ function(U_721)
| ~ relation(U_721) ),
inference(variable_rename,[status(thm)],[f_185_1]) ).
fof(f_185_3,plain,
( ! [U_721,U_720,U_722] :
( in(apply(U_720,U_722),relation_dom(U_721))
| ~ sP150(U_721,U_720,U_722) )
& ! [U_721,U_720,U_722] :
( in(U_722,relation_dom(U_720))
| ~ sP150(U_721,U_720,U_722) )
& ! [U_721,U_720,U_722] :
( in(U_722,relation_dom(relation_composition(U_720,U_721)))
| ~ in(apply(U_720,U_722),relation_dom(U_721))
| ~ in(U_722,relation_dom(U_720))
| ~ sP151(U_721,U_720,U_722) )
& ! [U_721,U_720,U_722] :
( sP150(U_721,U_720,U_722)
| ~ in(U_722,relation_dom(relation_composition(U_720,U_721)))
| ~ sP151(U_721,U_720,U_722) )
& ! [U_721,U_720,U_722] :
( sP151(U_721,U_720,U_722)
| ~ function(U_720)
| ~ relation(U_720)
| ~ function(U_721)
| ~ relation(U_721) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP150,sP151])],[f_185_2]) ).
cnf(f_185_4,plain,
( sP151(U_721,U_720,U_722)
| ~ function(U_720)
| ~ relation(U_720)
| ~ function(U_721)
| ~ relation(U_721) ),
inference(clausify,[status(thm)],[f_185_3]) ).
cnf(f_185_5,plain,
( sP150(U_721,U_720,U_722)
| ~ in(U_722,relation_dom(relation_composition(U_720,U_721)))
| ~ sP151(U_721,U_720,U_722) ),
inference(clausify,[status(thm)],[f_185_3]) ).
cnf(f_185_6,plain,
( in(U_722,relation_dom(relation_composition(U_720,U_721)))
| ~ in(apply(U_720,U_722),relation_dom(U_721))
| ~ in(U_722,relation_dom(U_720))
| ~ sP151(U_721,U_720,U_722) ),
inference(clausify,[status(thm)],[f_185_3]) ).
cnf(f_185_7,plain,
( in(U_722,relation_dom(U_720))
| ~ sP150(U_721,U_720,U_722) ),
inference(clausify,[status(thm)],[f_185_3]) ).
cnf(f_185_8,plain,
( in(apply(U_720,U_722),relation_dom(U_721))
| ~ sP150(U_721,U_720,U_722) ),
inference(clausify,[status(thm)],[f_185_3]) ).
fof(f_186_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_186_2,plain,
! [U_724] :
( ! [U_723] :
( in(U_724,U_723)
| ~ proper_subset(U_724,U_723)
| ~ ordinal(U_723) )
| ~ epsilon_transitive(U_724) ),
inference(variable_rename,[status(thm)],[f_186_1]) ).
fof(f_186_3,plain,
! [U_724,U_723] :
( in(U_724,U_723)
| ~ proper_subset(U_724,U_723)
| ~ ordinal(U_723)
| ~ epsilon_transitive(U_724) ),
inference(definitional_conversion,[status(esa)],[f_186_2]) ).
cnf(f_186_4,plain,
( in(U_724,U_723)
| ~ proper_subset(U_724,U_723)
| ~ ordinal(U_723)
| ~ epsilon_transitive(U_724) ),
inference(clausify,[status(thm)],[f_186_3]) ).
fof(f_187_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_187_2,plain,
! [U_725] :
( subset(U_725,cartesian_product2(relation_dom(U_725),relation_rng(U_725)))
| ~ relation(U_725) ),
inference(variable_rename,[status(thm)],[f_187_1]) ).
fof(f_187_3,plain,
! [U_725] :
( subset(U_725,cartesian_product2(relation_dom(U_725),relation_rng(U_725)))
| ~ relation(U_725) ),
inference(definitional_conversion,[status(esa)],[f_187_2]) ).
cnf(f_187_4,plain,
( subset(U_725,cartesian_product2(relation_dom(U_725),relation_rng(U_725)))
| ~ relation(U_725) ),
inference(clausify,[status(thm)],[f_187_3]) ).
fof(f_188_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_188_2,plain,
! [U_728,U_727] :
( ! [U_726] :
( apply(relation_composition(U_726,U_727),U_728) = apply(U_727,apply(U_726,U_728))
| ~ in(U_728,relation_dom(relation_composition(U_726,U_727)))
| ~ function(U_726)
| ~ relation(U_726) )
| ~ function(U_727)
| ~ relation(U_727) ),
inference(variable_rename,[status(thm)],[f_188_1]) ).
fof(f_188_3,plain,
! [U_726,U_728,U_727] :
( apply(relation_composition(U_726,U_727),U_728) = apply(U_727,apply(U_726,U_728))
| ~ in(U_728,relation_dom(relation_composition(U_726,U_727)))
| ~ function(U_726)
| ~ relation(U_726)
| ~ function(U_727)
| ~ relation(U_727) ),
inference(definitional_conversion,[status(esa)],[f_188_2]) ).
cnf(f_188_4,plain,
( apply(relation_composition(U_726,U_727),U_728) = apply(U_727,apply(U_726,U_728))
| ~ in(U_728,relation_dom(relation_composition(U_726,U_727)))
| ~ function(U_726)
| ~ relation(U_726)
| ~ function(U_727)
| ~ relation(U_727) ),
inference(clausify,[status(thm)],[f_188_3]) ).
fof(f_189_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_189_2,plain,
! [U_731,U_730] :
( ! [U_729] :
( apply(relation_composition(U_730,U_729),U_731) = apply(U_729,apply(U_730,U_731))
| ~ in(U_731,relation_dom(U_730))
| ~ function(U_729)
| ~ relation(U_729) )
| ~ function(U_730)
| ~ relation(U_730) ),
inference(variable_rename,[status(thm)],[f_189_1]) ).
fof(f_189_3,plain,
! [U_729,U_731,U_730] :
( apply(relation_composition(U_730,U_729),U_731) = apply(U_729,apply(U_730,U_731))
| ~ in(U_731,relation_dom(U_730))
| ~ function(U_729)
| ~ relation(U_729)
| ~ function(U_730)
| ~ relation(U_730) ),
inference(definitional_conversion,[status(esa)],[f_189_2]) ).
cnf(f_189_4,plain,
( apply(relation_composition(U_730,U_729),U_731) = apply(U_729,apply(U_730,U_731))
| ~ in(U_731,relation_dom(U_730))
| ~ function(U_729)
| ~ relation(U_729)
| ~ function(U_730)
| ~ relation(U_730) ),
inference(clausify,[status(thm)],[f_189_3]) ).
fof(f_190_1,plain,
! [A,B] :
( ordinal(A)
| ~ in(A,B)
| ~ ordinal(B) ),
inference(fof_nnf,[status(thm)],[t23_ordinal1]) ).
fof(f_190_2,plain,
! [U_733,U_732] :
( ordinal(U_733)
| ~ in(U_733,U_732)
| ~ ordinal(U_732) ),
inference(variable_rename,[status(thm)],[f_190_1]) ).
fof(f_190_3,plain,
! [U_732,U_733] :
( ordinal(U_733)
| ~ in(U_733,U_732)
| ~ ordinal(U_732) ),
inference(definitional_conversion,[status(esa)],[f_190_2]) ).
cnf(f_190_4,plain,
( ordinal(U_733)
| ~ in(U_733,U_732)
| ~ ordinal(U_732) ),
inference(clausify,[status(thm)],[f_190_3]) ).
fof(f_191_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_191_2,plain,
! [U_735] :
( ! [U_734] :
( in(U_734,U_735)
| U_735 = U_734
| in(U_735,U_734)
| ~ ordinal(U_734) )
| ~ ordinal(U_735) ),
inference(variable_rename,[status(thm)],[f_191_1]) ).
fof(f_191_3,plain,
! [U_735,U_734] :
( in(U_734,U_735)
| U_735 = U_734
| in(U_735,U_734)
| ~ ordinal(U_734)
| ~ ordinal(U_735) ),
inference(definitional_conversion,[status(esa)],[f_191_2]) ).
cnf(f_191_4,plain,
( in(U_734,U_735)
| U_735 = U_734
| in(U_735,U_734)
| ~ ordinal(U_734)
| ~ ordinal(U_735) ),
inference(clausify,[status(thm)],[f_191_3]) ).
fof(f_192_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_192_2,plain,
! [U_737] :
( ! [U_736] :
( ( subset(relation_rng(U_737),relation_rng(U_736))
& subset(relation_dom(U_737),relation_dom(U_736)) )
| ~ subset(U_737,U_736)
| ~ relation(U_736) )
| ~ relation(U_737) ),
inference(variable_rename,[status(thm)],[f_192_1]) ).
fof(f_192_3,plain,
( ! [U_737,U_736] :
( subset(relation_rng(U_737),relation_rng(U_736))
| ~ sP152(U_737,U_736) )
& ! [U_737,U_736] :
( subset(relation_dom(U_737),relation_dom(U_736))
| ~ sP152(U_737,U_736) )
& ! [U_737,U_736] :
( sP152(U_737,U_736)
| ~ subset(U_737,U_736)
| ~ relation(U_736)
| ~ relation(U_737) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP152])],[f_192_2]) ).
cnf(f_192_4,plain,
( sP152(U_737,U_736)
| ~ subset(U_737,U_736)
| ~ relation(U_736)
| ~ relation(U_737) ),
inference(clausify,[status(thm)],[f_192_3]) ).
cnf(f_192_5,plain,
( subset(relation_dom(U_737),relation_dom(U_736))
| ~ sP152(U_737,U_736) ),
inference(clausify,[status(thm)],[f_192_3]) ).
cnf(f_192_6,plain,
( subset(relation_rng(U_737),relation_rng(U_736))
| ~ sP152(U_737,U_736) ),
inference(clausify,[status(thm)],[f_192_3]) ).
fof(f_193_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_193_2,plain,
! [U_740,U_739,U_738] :
( subset(set_intersection2(U_740,U_738),set_intersection2(U_739,U_738))
| ~ subset(U_740,U_739) ),
inference(variable_rename,[status(thm)],[f_193_1]) ).
fof(f_193_3,plain,
! [U_740,U_739] :
( ! [U_738] : subset(set_intersection2(U_740,U_738),set_intersection2(U_739,U_738))
| ~ subset(U_740,U_739) ),
inference(miniscope,[status(thm)],[f_193_2]) ).
fof(f_193_4,plain,
! [U_739,U_740,U_738] :
( subset(set_intersection2(U_740,U_738),set_intersection2(U_739,U_738))
| ~ subset(U_740,U_739) ),
inference(definitional_conversion,[status(esa)],[f_193_3]) ).
cnf(f_193_5,plain,
( subset(set_intersection2(U_740,U_738),set_intersection2(U_739,U_738))
| ~ subset(U_740,U_739) ),
inference(clausify,[status(thm)],[f_193_4]) ).
fof(f_194_1,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t28_xboole_1]) ).
fof(f_194_2,plain,
! [U_742,U_741] :
( set_intersection2(U_742,U_741) = U_742
| ~ subset(U_742,U_741) ),
inference(variable_rename,[status(thm)],[f_194_1]) ).
fof(f_194_3,plain,
! [U_741,U_742] :
( set_intersection2(U_742,U_741) = U_742
| ~ subset(U_742,U_741) ),
inference(definitional_conversion,[status(esa)],[f_194_2]) ).
cnf(f_194_4,plain,
( set_intersection2(U_742,U_741) = U_742
| ~ subset(U_742,U_741) ),
inference(clausify,[status(thm)],[f_194_3]) ).
fof(f_195_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_195_2,plain,
! [U_743] : set_intersection2(U_743,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_195_1]) ).
fof(f_195_3,plain,
! [U_743] : set_intersection2(U_743,empty_set) = empty_set,
inference(definitional_conversion,[status(esa)],[f_195_2]) ).
cnf(f_195_4,plain,
set_intersection2(U_743,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_195_3]) ).
fof(f_196_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_196_2,plain,
! [U_745,U_744] :
( in(U_745,U_744)
| empty(U_744)
| ~ element(U_745,U_744) ),
inference(variable_rename,[status(thm)],[f_196_1]) ).
fof(f_196_3,plain,
! [U_745,U_744] :
( in(U_745,U_744)
| empty(U_744)
| ~ element(U_745,U_744) ),
inference(definitional_conversion,[status(esa)],[f_196_2]) ).
cnf(f_196_4,plain,
( in(U_745,U_744)
| empty(U_744)
| ~ element(U_745,U_744) ),
inference(clausify,[status(thm)],[f_196_3]) ).
fof(f_197_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_197_2,plain,
! [U_748,U_747] :
( U_748 = U_747
| ? [U_746] :
( ( ~ in(U_746,U_748)
& in(U_746,U_747) )
| ( ~ in(U_746,U_747)
& in(U_746,U_748) ) ) ),
inference(variable_rename,[status(thm)],[f_197_1]) ).
fof(f_197_3,plain,
! [U_748,U_747] :
( U_748 = U_747
| ? [U_750] :
( ~ in(U_750,U_748)
& in(U_750,U_747) )
| ? [U_749] :
( ~ in(U_749,U_747)
& in(U_749,U_748) ) ),
inference(miniscope,[status(thm)],[f_197_2]) ).
fof(f_197_4,plain,
! [U_748,U_747] :
( U_748 = U_747
| ? [U_750] :
( ~ in(U_750,U_748)
& in(U_750,U_747) )
| ( ~ in(sK113(U_748,U_747),U_747)
& in(sK113(U_748,U_747),U_748) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK113]),skolemize(U_749,sK113(U_748,U_747))],[f_197_3]) ).
fof(f_197_5,plain,
! [U_748,U_747] :
( U_748 = U_747
| ( ~ in(sK114(U_748,U_747),U_748)
& in(sK114(U_748,U_747),U_747) )
| ( ~ in(sK113(U_748,U_747),U_747)
& in(sK113(U_748,U_747),U_748) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK114]),skolemize(U_750,sK114(U_748,U_747))],[f_197_4]) ).
fof(f_197_6,plain,
( ! [U_747,U_748] :
( ~ in(sK114(U_748,U_747),U_748)
| ~ sP154(U_747,U_748) )
& ! [U_747,U_748] :
( in(sK114(U_748,U_747),U_747)
| ~ sP154(U_747,U_748) )
& ! [U_747,U_748] :
( ~ in(sK113(U_748,U_747),U_747)
| ~ sP153(U_747,U_748) )
& ! [U_747,U_748] :
( in(sK113(U_748,U_747),U_748)
| ~ sP153(U_747,U_748) )
& ! [U_747,U_748] :
( U_748 = U_747
| sP154(U_747,U_748)
| sP153(U_747,U_748) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP153,sP154])],[f_197_5]) ).
cnf(f_197_7,plain,
( U_748 = U_747
| sP154(U_747,U_748)
| sP153(U_747,U_748) ),
inference(clausify,[status(thm)],[f_197_6]) ).
cnf(f_197_8,plain,
( in(sK113(U_748,U_747),U_748)
| ~ sP153(U_747,U_748) ),
inference(clausify,[status(thm)],[f_197_6]) ).
cnf(f_197_9,plain,
( ~ in(sK113(U_748,U_747),U_747)
| ~ sP153(U_747,U_748) ),
inference(clausify,[status(thm)],[f_197_6]) ).
cnf(f_197_10,plain,
( in(sK114(U_748,U_747),U_747)
| ~ sP154(U_747,U_748) ),
inference(clausify,[status(thm)],[f_197_6]) ).
cnf(f_197_11,plain,
( ~ in(sK114(U_748,U_747),U_748)
| ~ sP154(U_747,U_748) ),
inference(clausify,[status(thm)],[f_197_6]) ).
fof(f_198_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_198_2,plain,
! [U_751] : subset(empty_set,U_751),
inference(variable_rename,[status(thm)],[f_198_1]) ).
fof(f_198_3,plain,
! [U_751] : subset(empty_set,U_751),
inference(definitional_conversion,[status(esa)],[f_198_2]) ).
cnf(f_198_4,plain,
subset(empty_set,U_751),
inference(clausify,[status(thm)],[f_198_3]) ).
fof(f_199_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_199_2,plain,
! [U_754,U_753,U_752] :
( ( in(U_753,relation_field(U_752))
& in(U_754,relation_field(U_752)) )
| ~ in(ordered_pair(U_754,U_753),U_752)
| ~ relation(U_752) ),
inference(variable_rename,[status(thm)],[f_199_1]) ).
fof(f_199_3,plain,
( ! [U_753,U_754,U_752] :
( in(U_753,relation_field(U_752))
| ~ sP155(U_753,U_754,U_752) )
& ! [U_753,U_754,U_752] :
( in(U_754,relation_field(U_752))
| ~ sP155(U_753,U_754,U_752) )
& ! [U_753,U_754,U_752] :
( sP155(U_753,U_754,U_752)
| ~ in(ordered_pair(U_754,U_753),U_752)
| ~ relation(U_752) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP155])],[f_199_2]) ).
cnf(f_199_4,plain,
( sP155(U_753,U_754,U_752)
| ~ in(ordered_pair(U_754,U_753),U_752)
| ~ relation(U_752) ),
inference(clausify,[status(thm)],[f_199_3]) ).
cnf(f_199_5,plain,
( in(U_754,relation_field(U_752))
| ~ sP155(U_753,U_754,U_752) ),
inference(clausify,[status(thm)],[f_199_3]) ).
cnf(f_199_6,plain,
( in(U_753,relation_field(U_752))
| ~ sP155(U_753,U_754,U_752) ),
inference(clausify,[status(thm)],[f_199_3]) ).
fof(f_200_1,negated_conjecture,
~ ! [A] :
( ! [B] :
( in(B,A)
=> ( subset(B,A)
& ordinal(B) ) )
=> ordinal(A) ),
inference(negate,[status(cth)],[t31_ordinal1]) ).
fof(f_200_2,negated_conjecture,
? [A] :
( ~ ordinal(A)
& ! [B] :
( ( subset(B,A)
& ordinal(B) )
| ~ in(B,A) ) ),
inference(fof_nnf,[status(thm)],[f_200_1]) ).
fof(f_200_3,negated_conjecture,
? [U_756] :
( ~ ordinal(U_756)
& ! [U_755] :
( ( subset(U_755,U_756)
& ordinal(U_755) )
| ~ in(U_755,U_756) ) ),
inference(variable_rename,[status(thm)],[f_200_2]) ).
fof(f_200_4,negated_conjecture,
( ~ ordinal(sK115)
& ! [U_755] :
( ( subset(U_755,sK115)
& ordinal(U_755) )
| ~ in(U_755,sK115) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK115]),skolemize(U_756,sK115)],[f_200_3]) ).
fof(f_200_5,negated_conjecture,
( ! [U_755] :
( subset(U_755,sK115)
| ~ sP156(U_755) )
& ! [U_755] :
( ordinal(U_755)
| ~ sP156(U_755) )
& ~ ordinal(sK115)
& ! [U_755] :
( sP156(U_755)
| ~ in(U_755,sK115) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP156])],[f_200_4]) ).
cnf(f_200_6,negated_conjecture,
( sP156(U_755)
| ~ in(U_755,sK115) ),
inference(clausify,[status(thm)],[f_200_5]) ).
cnf(f_200_7,negated_conjecture,
~ ordinal(sK115),
inference(clausify,[status(thm)],[f_200_5]) ).
cnf(f_200_8,negated_conjecture,
( ordinal(U_755)
| ~ sP156(U_755) ),
inference(clausify,[status(thm)],[f_200_5]) ).
cnf(f_200_9,negated_conjecture,
( subset(U_755,sK115)
| ~ sP156(U_755) ),
inference(clausify,[status(thm)],[f_200_5]) ).
fof(f_201_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_201_2,plain,
! [U_759,U_758,U_757] :
( subset(set_difference(U_759,U_757),set_difference(U_758,U_757))
| ~ subset(U_759,U_758) ),
inference(variable_rename,[status(thm)],[f_201_1]) ).
fof(f_201_3,plain,
! [U_759,U_758] :
( ! [U_757] : subset(set_difference(U_759,U_757),set_difference(U_758,U_757))
| ~ subset(U_759,U_758) ),
inference(miniscope,[status(thm)],[f_201_2]) ).
fof(f_201_4,plain,
! [U_758,U_759,U_757] :
( subset(set_difference(U_759,U_757),set_difference(U_758,U_757))
| ~ subset(U_759,U_758) ),
inference(definitional_conversion,[status(esa)],[f_201_3]) ).
cnf(f_201_5,plain,
( subset(set_difference(U_759,U_757),set_difference(U_758,U_757))
| ~ subset(U_759,U_758) ),
inference(clausify,[status(thm)],[f_201_4]) ).
fof(f_202_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_202_2,plain,
! [U_763,U_762,U_761,U_760] :
( ( U_762 = U_760
& U_763 = U_761 )
| ordered_pair(U_763,U_762) != ordered_pair(U_761,U_760) ),
inference(variable_rename,[status(thm)],[f_202_1]) ).
fof(f_202_3,plain,
( ! [U_760,U_761,U_762,U_763] :
( U_762 = U_760
| ~ sP157(U_760,U_761,U_762,U_763) )
& ! [U_760,U_761,U_762,U_763] :
( U_763 = U_761
| ~ sP157(U_760,U_761,U_762,U_763) )
& ! [U_760,U_761,U_762,U_763] :
( sP157(U_760,U_761,U_762,U_763)
| ordered_pair(U_763,U_762) != ordered_pair(U_761,U_760) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP157])],[f_202_2]) ).
cnf(f_202_4,plain,
( sP157(U_760,U_761,U_762,U_763)
| ordered_pair(U_763,U_762) != ordered_pair(U_761,U_760) ),
inference(clausify,[status(thm)],[f_202_3]) ).
cnf(f_202_5,plain,
( U_763 = U_761
| ~ sP157(U_760,U_761,U_762,U_763) ),
inference(clausify,[status(thm)],[f_202_3]) ).
cnf(f_202_6,plain,
( U_762 = U_760
| ~ sP157(U_760,U_761,U_762,U_763) ),
inference(clausify,[status(thm)],[f_202_3]) ).
fof(f_203_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_203_2,plain,
! [U_767,U_766] :
( ( ( U_766 = identity_relation(U_767)
| ? [U_765] :
( apply(U_766,U_765) != U_765
& in(U_765,U_767) )
| relation_dom(U_766) != U_767 )
& ( ( ! [U_764] :
( apply(U_766,U_764) = U_764
| ~ in(U_764,U_767) )
& relation_dom(U_766) = U_767 )
| U_766 != identity_relation(U_767) ) )
| ~ function(U_766)
| ~ relation(U_766) ),
inference(variable_rename,[status(thm)],[f_203_1]) ).
fof(f_203_3,plain,
! [U_767,U_766] :
( ( ( U_766 = identity_relation(U_767)
| ( apply(U_766,sK116(U_767,U_766)) != sK116(U_767,U_766)
& in(sK116(U_767,U_766),U_767) )
| relation_dom(U_766) != U_767 )
& ( ( ! [U_764] :
( apply(U_766,U_764) = U_764
| ~ in(U_764,U_767) )
& relation_dom(U_766) = U_767 )
| U_766 != identity_relation(U_767) ) )
| ~ function(U_766)
| ~ relation(U_766) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK116]),skolemize(U_765,sK116(U_767,U_766))],[f_203_2]) ).
fof(f_203_4,plain,
( ! [U_766,U_767] :
( apply(U_766,sK116(U_767,U_766)) != sK116(U_767,U_766)
| ~ sP159(U_766,U_767) )
& ! [U_766,U_767] :
( in(sK116(U_767,U_766),U_767)
| ~ sP159(U_766,U_767) )
& ! [U_764,U_766,U_767] :
( apply(U_766,U_764) = U_764
| ~ in(U_764,U_767)
| ~ sP158(U_764,U_766,U_767) )
& ! [U_764,U_766,U_767] :
( relation_dom(U_766) = U_767
| ~ sP158(U_764,U_766,U_767) )
& ! [U_764,U_766,U_767] :
( U_766 = identity_relation(U_767)
| sP159(U_766,U_767)
| relation_dom(U_766) != U_767
| ~ sP160(U_764,U_766,U_767) )
& ! [U_764,U_766,U_767] :
( sP158(U_764,U_766,U_767)
| U_766 != identity_relation(U_767)
| ~ sP160(U_764,U_766,U_767) )
& ! [U_764,U_766,U_767] :
( sP160(U_764,U_766,U_767)
| ~ function(U_766)
| ~ relation(U_766) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP158,sP159,sP160])],[f_203_3]) ).
cnf(f_203_5,plain,
( sP160(U_764,U_766,U_767)
| ~ function(U_766)
| ~ relation(U_766) ),
inference(clausify,[status(thm)],[f_203_4]) ).
cnf(f_203_6,plain,
( sP158(U_764,U_766,U_767)
| U_766 != identity_relation(U_767)
| ~ sP160(U_764,U_766,U_767) ),
inference(clausify,[status(thm)],[f_203_4]) ).
cnf(f_203_7,plain,
( U_766 = identity_relation(U_767)
| sP159(U_766,U_767)
| relation_dom(U_766) != U_767
| ~ sP160(U_764,U_766,U_767) ),
inference(clausify,[status(thm)],[f_203_4]) ).
cnf(f_203_8,plain,
( relation_dom(U_766) = U_767
| ~ sP158(U_764,U_766,U_767) ),
inference(clausify,[status(thm)],[f_203_4]) ).
cnf(f_203_9,plain,
( apply(U_766,U_764) = U_764
| ~ in(U_764,U_767)
| ~ sP158(U_764,U_766,U_767) ),
inference(clausify,[status(thm)],[f_203_4]) ).
cnf(f_203_10,plain,
( in(sK116(U_767,U_766),U_767)
| ~ sP159(U_766,U_767) ),
inference(clausify,[status(thm)],[f_203_4]) ).
cnf(f_203_11,plain,
( apply(U_766,sK116(U_767,U_766)) != sK116(U_767,U_766)
| ~ sP159(U_766,U_767) ),
inference(clausify,[status(thm)],[f_203_4]) ).
fof(f_204_1,plain,
! [A,B] :
( apply(identity_relation(A),B) = B
| ~ in(B,A) ),
inference(fof_nnf,[status(thm)],[t35_funct_1]) ).
fof(f_204_2,plain,
! [U_769,U_768] :
( apply(identity_relation(U_769),U_768) = U_768
| ~ in(U_768,U_769) ),
inference(variable_rename,[status(thm)],[f_204_1]) ).
fof(f_204_3,plain,
! [U_768,U_769] :
( apply(identity_relation(U_769),U_768) = U_768
| ~ in(U_768,U_769) ),
inference(definitional_conversion,[status(esa)],[f_204_2]) ).
cnf(f_204_4,plain,
( apply(identity_relation(U_769),U_768) = U_768
| ~ in(U_768,U_769) ),
inference(clausify,[status(thm)],[f_204_3]) ).
fof(f_205_1,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(fof_nnf,[status(thm)],[t36_xboole_1]) ).
fof(f_205_2,plain,
! [U_771,U_770] : subset(set_difference(U_771,U_770),U_771),
inference(variable_rename,[status(thm)],[f_205_1]) ).
fof(f_205_3,plain,
! [U_771,U_770] : subset(set_difference(U_771,U_770),U_771),
inference(definitional_conversion,[status(esa)],[f_205_2]) ).
cnf(f_205_4,plain,
subset(set_difference(U_771,U_770),U_771),
inference(clausify,[status(thm)],[f_205_3]) ).
fof(f_206_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_206_2,plain,
! [U_772] :
( ( relation_dom(U_772) = relation_rng(relation_inverse(U_772))
& relation_rng(U_772) = relation_dom(relation_inverse(U_772)) )
| ~ relation(U_772) ),
inference(variable_rename,[status(thm)],[f_206_1]) ).
fof(f_206_3,plain,
( ! [U_772] :
( relation_dom(U_772) = relation_rng(relation_inverse(U_772))
| ~ sP161(U_772) )
& ! [U_772] :
( relation_rng(U_772) = relation_dom(relation_inverse(U_772))
| ~ sP161(U_772) )
& ! [U_772] :
( sP161(U_772)
| ~ relation(U_772) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP161])],[f_206_2]) ).
cnf(f_206_4,plain,
( sP161(U_772)
| ~ relation(U_772) ),
inference(clausify,[status(thm)],[f_206_3]) ).
cnf(f_206_5,plain,
( relation_rng(U_772) = relation_dom(relation_inverse(U_772))
| ~ sP161(U_772) ),
inference(clausify,[status(thm)],[f_206_3]) ).
cnf(f_206_6,plain,
( relation_dom(U_772) = relation_rng(relation_inverse(U_772))
| ~ sP161(U_772) ),
inference(clausify,[status(thm)],[f_206_3]) ).
fof(f_207_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_207_2,plain,
! [U_774,U_773] :
( ( set_difference(U_774,U_773) = empty_set
| ~ subset(U_774,U_773) )
& ( subset(U_774,U_773)
| set_difference(U_774,U_773) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_207_1]) ).
fof(f_207_3,plain,
( ! [U_778,U_776] :
( set_difference(U_778,U_776) = empty_set
| ~ subset(U_778,U_776) )
& ! [U_777,U_775] :
( subset(U_777,U_775)
| set_difference(U_777,U_775) != empty_set ) ),
inference(miniscope,[status(thm)],[f_207_2]) ).
fof(f_207_4,plain,
( ! [U_778,U_776] :
( set_difference(U_778,U_776) = empty_set
| ~ subset(U_778,U_776) )
& ! [U_775,U_777] :
( subset(U_777,U_775)
| set_difference(U_777,U_775) != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_207_3]) ).
cnf(f_207_5,plain,
( subset(U_777,U_775)
| set_difference(U_777,U_775) != empty_set ),
inference(clausify,[status(thm)],[f_207_4]) ).
cnf(f_207_6,plain,
( set_difference(U_778,U_776) = empty_set
| ~ subset(U_778,U_776) ),
inference(clausify,[status(thm)],[f_207_4]) ).
fof(f_208_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_208_2,plain,
! [U_780,U_779] :
( ( subset(singleton(U_780),U_779)
| ~ in(U_780,U_779) )
& ( in(U_780,U_779)
| ~ subset(singleton(U_780),U_779) ) ),
inference(variable_rename,[status(thm)],[f_208_1]) ).
fof(f_208_3,plain,
( ! [U_784,U_782] :
( subset(singleton(U_784),U_782)
| ~ in(U_784,U_782) )
& ! [U_783,U_781] :
( in(U_783,U_781)
| ~ subset(singleton(U_783),U_781) ) ),
inference(miniscope,[status(thm)],[f_208_2]) ).
fof(f_208_4,plain,
( ! [U_782,U_784] :
( subset(singleton(U_784),U_782)
| ~ in(U_784,U_782) )
& ! [U_781,U_783] :
( in(U_783,U_781)
| ~ subset(singleton(U_783),U_781) ) ),
inference(definitional_conversion,[status(esa)],[f_208_3]) ).
cnf(f_208_5,plain,
( in(U_783,U_781)
| ~ subset(singleton(U_783),U_781) ),
inference(clausify,[status(thm)],[f_208_4]) ).
cnf(f_208_6,plain,
( subset(singleton(U_784),U_782)
| ~ in(U_784,U_782) ),
inference(clausify,[status(thm)],[f_208_4]) ).
fof(f_209_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_209_2,plain,
! [U_787,U_786,U_785] :
( ( subset(unordered_pair(U_787,U_786),U_785)
| ~ in(U_786,U_785)
| ~ in(U_787,U_785) )
& ( ( in(U_786,U_785)
& in(U_787,U_785) )
| ~ subset(unordered_pair(U_787,U_786),U_785) ) ),
inference(variable_rename,[status(thm)],[f_209_1]) ).
fof(f_209_3,plain,
( ! [U_793,U_791,U_789] :
( subset(unordered_pair(U_793,U_791),U_789)
| ~ in(U_791,U_789)
| ~ in(U_793,U_789) )
& ! [U_792,U_790,U_788] :
( ( in(U_790,U_788)
& in(U_792,U_788) )
| ~ subset(unordered_pair(U_792,U_790),U_788) ) ),
inference(miniscope,[status(thm)],[f_209_2]) ).
fof(f_209_4,plain,
( ! [U_788,U_790,U_792] :
( in(U_790,U_788)
| ~ sP162(U_788,U_790,U_792) )
& ! [U_788,U_790,U_792] :
( in(U_792,U_788)
| ~ sP162(U_788,U_790,U_792) )
& ! [U_793,U_791,U_789] :
( subset(unordered_pair(U_793,U_791),U_789)
| ~ in(U_791,U_789)
| ~ in(U_793,U_789) )
& ! [U_788,U_790,U_792] :
( sP162(U_788,U_790,U_792)
| ~ subset(unordered_pair(U_792,U_790),U_788) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP162])],[f_209_3]) ).
cnf(f_209_5,plain,
( sP162(U_788,U_790,U_792)
| ~ subset(unordered_pair(U_792,U_790),U_788) ),
inference(clausify,[status(thm)],[f_209_4]) ).
cnf(f_209_6,plain,
( subset(unordered_pair(U_793,U_791),U_789)
| ~ in(U_791,U_789)
| ~ in(U_793,U_789) ),
inference(clausify,[status(thm)],[f_209_4]) ).
cnf(f_209_7,plain,
( in(U_792,U_788)
| ~ sP162(U_788,U_790,U_792) ),
inference(clausify,[status(thm)],[f_209_4]) ).
cnf(f_209_8,plain,
( in(U_790,U_788)
| ~ sP162(U_788,U_790,U_792) ),
inference(clausify,[status(thm)],[f_209_4]) ).
fof(f_210_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_210_2,plain,
! [U_795,U_794] : set_union2(U_795,set_difference(U_794,U_795)) = set_union2(U_795,U_794),
inference(variable_rename,[status(thm)],[f_210_1]) ).
fof(f_210_3,plain,
! [U_795,U_794] : set_union2(U_795,set_difference(U_794,U_795)) = set_union2(U_795,U_794),
inference(definitional_conversion,[status(esa)],[f_210_2]) ).
cnf(f_210_4,plain,
set_union2(U_795,set_difference(U_794,U_795)) = set_union2(U_795,U_794),
inference(clausify,[status(thm)],[f_210_3]) ).
fof(f_211_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_211_2,plain,
! [U_797,U_796] :
( ( subset(U_797,singleton(U_796))
| ( U_797 != singleton(U_796)
& U_797 != empty_set ) )
& ( U_797 = singleton(U_796)
| U_797 = empty_set
| ~ subset(U_797,singleton(U_796)) ) ),
inference(variable_rename,[status(thm)],[f_211_1]) ).
fof(f_211_3,plain,
( ! [U_801,U_799] :
( subset(U_801,singleton(U_799))
| ( U_801 != singleton(U_799)
& U_801 != empty_set ) )
& ! [U_800,U_798] :
( U_800 = singleton(U_798)
| U_800 = empty_set
| ~ subset(U_800,singleton(U_798)) ) ),
inference(miniscope,[status(thm)],[f_211_2]) ).
fof(f_211_4,plain,
( ! [U_799,U_801] :
( U_801 != singleton(U_799)
| ~ sP163(U_799,U_801) )
& ! [U_799,U_801] :
( U_801 != empty_set
| ~ sP163(U_799,U_801) )
& ! [U_799,U_801] :
( subset(U_801,singleton(U_799))
| sP163(U_799,U_801) )
& ! [U_800,U_798] :
( U_800 = singleton(U_798)
| U_800 = empty_set
| ~ subset(U_800,singleton(U_798)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP163])],[f_211_3]) ).
cnf(f_211_5,plain,
( U_800 = singleton(U_798)
| U_800 = empty_set
| ~ subset(U_800,singleton(U_798)) ),
inference(clausify,[status(thm)],[f_211_4]) ).
cnf(f_211_6,plain,
( subset(U_801,singleton(U_799))
| sP163(U_799,U_801) ),
inference(clausify,[status(thm)],[f_211_4]) ).
cnf(f_211_7,plain,
( U_801 != empty_set
| ~ sP163(U_799,U_801) ),
inference(clausify,[status(thm)],[f_211_4]) ).
cnf(f_211_8,plain,
( U_801 != singleton(U_799)
| ~ sP163(U_799,U_801) ),
inference(clausify,[status(thm)],[f_211_4]) ).
fof(f_212_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_212_2,plain,
! [U_802] : set_difference(U_802,empty_set) = U_802,
inference(variable_rename,[status(thm)],[f_212_1]) ).
fof(f_212_3,plain,
! [U_802] : set_difference(U_802,empty_set) = U_802,
inference(definitional_conversion,[status(esa)],[f_212_2]) ).
cnf(f_212_4,plain,
set_difference(U_802,empty_set) = U_802,
inference(clausify,[status(thm)],[f_212_3]) ).
fof(f_213_1,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ in(B,C)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t3_ordinal1]) ).
fof(f_213_2,plain,
! [U_805,U_804,U_803] :
( ~ in(U_803,U_805)
| ~ in(U_804,U_803)
| ~ in(U_805,U_804) ),
inference(variable_rename,[status(thm)],[f_213_1]) ).
fof(f_213_3,plain,
! [U_805,U_804] :
( ! [U_803] :
( ~ in(U_803,U_805)
| ~ in(U_804,U_803) )
| ~ in(U_805,U_804) ),
inference(miniscope,[status(thm)],[f_213_2]) ).
fof(f_213_4,plain,
! [U_804,U_803,U_805] :
( ~ in(U_803,U_805)
| ~ in(U_804,U_803)
| ~ in(U_805,U_804) ),
inference(definitional_conversion,[status(esa)],[f_213_3]) ).
cnf(f_213_5,plain,
( ~ in(U_803,U_805)
| ~ in(U_804,U_803)
| ~ in(U_805,U_804) ),
inference(clausify,[status(thm)],[f_213_4]) ).
fof(f_214_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_214_2,plain,
! [U_807,U_806] :
( ( element(U_807,powerset(U_806))
| ~ subset(U_807,U_806) )
& ( subset(U_807,U_806)
| ~ element(U_807,powerset(U_806)) ) ),
inference(variable_rename,[status(thm)],[f_214_1]) ).
fof(f_214_3,plain,
( ! [U_811,U_809] :
( element(U_811,powerset(U_809))
| ~ subset(U_811,U_809) )
& ! [U_810,U_808] :
( subset(U_810,U_808)
| ~ element(U_810,powerset(U_808)) ) ),
inference(miniscope,[status(thm)],[f_214_2]) ).
fof(f_214_4,plain,
( ! [U_811,U_809] :
( element(U_811,powerset(U_809))
| ~ subset(U_811,U_809) )
& ! [U_810,U_808] :
( subset(U_810,U_808)
| ~ element(U_810,powerset(U_808)) ) ),
inference(definitional_conversion,[status(esa)],[f_214_3]) ).
cnf(f_214_5,plain,
( subset(U_810,U_808)
| ~ element(U_810,powerset(U_808)) ),
inference(clausify,[status(thm)],[f_214_4]) ).
cnf(f_214_6,plain,
( element(U_811,powerset(U_809))
| ~ subset(U_811,U_809) ),
inference(clausify,[status(thm)],[f_214_4]) ).
fof(f_215_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_215_2,plain,
! [U_815,U_814] :
( ( ~ disjoint(U_815,U_814)
| ! [U_813] :
( ~ in(U_813,U_814)
| ~ in(U_813,U_815) ) )
& ( ? [U_812] :
( in(U_812,U_814)
& in(U_812,U_815) )
| disjoint(U_815,U_814) ) ),
inference(variable_rename,[status(thm)],[f_215_1]) ).
fof(f_215_3,plain,
( ! [U_819,U_817] :
( ~ disjoint(U_819,U_817)
| ! [U_813] :
( ~ in(U_813,U_817)
| ~ in(U_813,U_819) ) )
& ! [U_818,U_816] :
( ? [U_812] :
( in(U_812,U_816)
& in(U_812,U_818) )
| disjoint(U_818,U_816) ) ),
inference(miniscope,[status(thm)],[f_215_2]) ).
fof(f_215_4,plain,
( ! [U_819,U_817] :
( ~ disjoint(U_819,U_817)
| ! [U_813] :
( ~ in(U_813,U_817)
| ~ in(U_813,U_819) ) )
& ! [U_818,U_816] :
( ( in(sK117(U_818,U_816),U_816)
& in(sK117(U_818,U_816),U_818) )
| disjoint(U_818,U_816) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK117]),skolemize(U_812,sK117(U_818,U_816))],[f_215_3]) ).
fof(f_215_5,plain,
( ! [U_816,U_818] :
( in(sK117(U_818,U_816),U_816)
| ~ sP164(U_816,U_818) )
& ! [U_816,U_818] :
( in(sK117(U_818,U_816),U_818)
| ~ sP164(U_816,U_818) )
& ! [U_813,U_817,U_819] :
( ~ disjoint(U_819,U_817)
| ~ in(U_813,U_817)
| ~ in(U_813,U_819) )
& ! [U_816,U_818] :
( sP164(U_816,U_818)
| disjoint(U_818,U_816) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP164])],[f_215_4]) ).
cnf(f_215_6,plain,
( sP164(U_816,U_818)
| disjoint(U_818,U_816) ),
inference(clausify,[status(thm)],[f_215_5]) ).
cnf(f_215_7,plain,
( ~ disjoint(U_819,U_817)
| ~ in(U_813,U_817)
| ~ in(U_813,U_819) ),
inference(clausify,[status(thm)],[f_215_5]) ).
cnf(f_215_8,plain,
( in(sK117(U_818,U_816),U_818)
| ~ sP164(U_816,U_818) ),
inference(clausify,[status(thm)],[f_215_5]) ).
cnf(f_215_9,plain,
( in(sK117(U_818,U_816),U_816)
| ~ sP164(U_816,U_818) ),
inference(clausify,[status(thm)],[f_215_5]) ).
fof(f_216_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_216_2,plain,
! [U_820] :
( U_820 = empty_set
| ~ subset(U_820,empty_set) ),
inference(variable_rename,[status(thm)],[f_216_1]) ).
fof(f_216_3,plain,
! [U_820] :
( U_820 = empty_set
| ~ subset(U_820,empty_set) ),
inference(definitional_conversion,[status(esa)],[f_216_2]) ).
cnf(f_216_4,plain,
( U_820 = empty_set
| ~ subset(U_820,empty_set) ),
inference(clausify,[status(thm)],[f_216_3]) ).
fof(f_217_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_217_2,plain,
! [U_822,U_821] : set_difference(set_union2(U_822,U_821),U_821) = set_difference(U_822,U_821),
inference(variable_rename,[status(thm)],[f_217_1]) ).
fof(f_217_3,plain,
! [U_821,U_822] : set_difference(set_union2(U_822,U_821),U_821) = set_difference(U_822,U_821),
inference(definitional_conversion,[status(esa)],[f_217_2]) ).
cnf(f_217_4,plain,
set_difference(set_union2(U_822,U_821),U_821) = set_difference(U_822,U_821),
inference(clausify,[status(thm)],[f_217_3]) ).
fof(f_218_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_218_2,plain,
! [U_825,U_824] :
( ! [U_823] :
( ( ( disjoint(U_824,U_823)
| ~ subset(U_824,subset_complement(U_825,U_823)) )
& ( subset(U_824,subset_complement(U_825,U_823))
| ~ disjoint(U_824,U_823) ) )
| ~ element(U_823,powerset(U_825)) )
| ~ element(U_824,powerset(U_825)) ),
inference(variable_rename,[status(thm)],[f_218_1]) ).
fof(f_218_3,plain,
( ! [U_823,U_824,U_825] :
( disjoint(U_824,U_823)
| ~ subset(U_824,subset_complement(U_825,U_823))
| ~ sP165(U_823,U_824,U_825) )
& ! [U_823,U_824,U_825] :
( subset(U_824,subset_complement(U_825,U_823))
| ~ disjoint(U_824,U_823)
| ~ sP165(U_823,U_824,U_825) )
& ! [U_823,U_824,U_825] :
( sP165(U_823,U_824,U_825)
| ~ element(U_823,powerset(U_825))
| ~ element(U_824,powerset(U_825)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP165])],[f_218_2]) ).
cnf(f_218_4,plain,
( sP165(U_823,U_824,U_825)
| ~ element(U_823,powerset(U_825))
| ~ element(U_824,powerset(U_825)) ),
inference(clausify,[status(thm)],[f_218_3]) ).
cnf(f_218_5,plain,
( subset(U_824,subset_complement(U_825,U_823))
| ~ disjoint(U_824,U_823)
| ~ sP165(U_823,U_824,U_825) ),
inference(clausify,[status(thm)],[f_218_3]) ).
cnf(f_218_6,plain,
( disjoint(U_824,U_823)
| ~ subset(U_824,subset_complement(U_825,U_823))
| ~ sP165(U_823,U_824,U_825) ),
inference(clausify,[status(thm)],[f_218_3]) ).
fof(f_219_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_219_2,plain,
! [U_827] :
( ! [U_826] :
( subset(relation_dom(relation_composition(U_827,U_826)),relation_dom(U_827))
| ~ relation(U_826) )
| ~ relation(U_827) ),
inference(variable_rename,[status(thm)],[f_219_1]) ).
fof(f_219_3,plain,
! [U_827,U_826] :
( subset(relation_dom(relation_composition(U_827,U_826)),relation_dom(U_827))
| ~ relation(U_826)
| ~ relation(U_827) ),
inference(definitional_conversion,[status(esa)],[f_219_2]) ).
cnf(f_219_4,plain,
( subset(relation_dom(relation_composition(U_827,U_826)),relation_dom(U_827))
| ~ relation(U_826)
| ~ relation(U_827) ),
inference(clausify,[status(thm)],[f_219_3]) ).
fof(f_220_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_220_2,plain,
! [U_829] :
( ! [U_828] :
( subset(relation_rng(relation_composition(U_829,U_828)),relation_rng(U_828))
| ~ relation(U_828) )
| ~ relation(U_829) ),
inference(variable_rename,[status(thm)],[f_220_1]) ).
fof(f_220_3,plain,
! [U_828,U_829] :
( subset(relation_rng(relation_composition(U_829,U_828)),relation_rng(U_828))
| ~ relation(U_828)
| ~ relation(U_829) ),
inference(definitional_conversion,[status(esa)],[f_220_2]) ).
cnf(f_220_4,plain,
( subset(relation_rng(relation_composition(U_829,U_828)),relation_rng(U_828))
| ~ relation(U_828)
| ~ relation(U_829) ),
inference(clausify,[status(thm)],[f_220_3]) ).
fof(f_221_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_221_2,plain,
! [U_831,U_830] :
( U_830 = set_union2(U_831,set_difference(U_830,U_831))
| ~ subset(U_831,U_830) ),
inference(variable_rename,[status(thm)],[f_221_1]) ).
fof(f_221_3,plain,
! [U_831,U_830] :
( U_830 = set_union2(U_831,set_difference(U_830,U_831))
| ~ subset(U_831,U_830) ),
inference(definitional_conversion,[status(esa)],[f_221_2]) ).
cnf(f_221_4,plain,
( U_830 = set_union2(U_831,set_difference(U_830,U_831))
| ~ subset(U_831,U_830) ),
inference(clausify,[status(thm)],[f_221_3]) ).
fof(f_222_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_222_2,plain,
! [U_833] :
( ! [U_832] :
( relation_dom(relation_composition(U_833,U_832)) = relation_dom(U_833)
| ~ subset(relation_rng(U_833),relation_dom(U_832))
| ~ relation(U_832) )
| ~ relation(U_833) ),
inference(variable_rename,[status(thm)],[f_222_1]) ).
fof(f_222_3,plain,
! [U_832,U_833] :
( relation_dom(relation_composition(U_833,U_832)) = relation_dom(U_833)
| ~ subset(relation_rng(U_833),relation_dom(U_832))
| ~ relation(U_832)
| ~ relation(U_833) ),
inference(definitional_conversion,[status(esa)],[f_222_2]) ).
cnf(f_222_4,plain,
( relation_dom(relation_composition(U_833,U_832)) = relation_dom(U_833)
| ~ subset(relation_rng(U_833),relation_dom(U_832))
| ~ relation(U_832)
| ~ relation(U_833) ),
inference(clausify,[status(thm)],[f_222_3]) ).
fof(f_223_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_223_2,plain,
! [U_835,U_834] :
( complements_of_subsets(U_835,U_834) != empty_set
| U_834 = empty_set
| ~ element(U_834,powerset(powerset(U_835))) ),
inference(variable_rename,[status(thm)],[f_223_1]) ).
fof(f_223_3,plain,
! [U_835,U_834] :
( complements_of_subsets(U_835,U_834) != empty_set
| U_834 = empty_set
| ~ element(U_834,powerset(powerset(U_835))) ),
inference(definitional_conversion,[status(esa)],[f_223_2]) ).
cnf(f_223_4,plain,
( complements_of_subsets(U_835,U_834) != empty_set
| U_834 = empty_set
| ~ element(U_834,powerset(powerset(U_835))) ),
inference(clausify,[status(thm)],[f_223_3]) ).
fof(f_224_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t46_zfmisc_1]) ).
fof(f_224_2,plain,
! [U_837,U_836] :
( set_union2(singleton(U_837),U_836) = U_836
| ~ in(U_837,U_836) ),
inference(variable_rename,[status(thm)],[f_224_1]) ).
fof(f_224_3,plain,
! [U_837,U_836] :
( set_union2(singleton(U_837),U_836) = U_836
| ~ in(U_837,U_836) ),
inference(definitional_conversion,[status(esa)],[f_224_2]) ).
cnf(f_224_4,plain,
( set_union2(singleton(U_837),U_836) = U_836
| ~ in(U_837,U_836) ),
inference(clausify,[status(thm)],[f_224_3]) ).
fof(f_225_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_225_2,plain,
! [U_839] :
( ! [U_838] :
( relation_rng(relation_composition(U_838,U_839)) = relation_rng(U_839)
| ~ subset(relation_dom(U_839),relation_rng(U_838))
| ~ relation(U_838) )
| ~ relation(U_839) ),
inference(variable_rename,[status(thm)],[f_225_1]) ).
fof(f_225_3,plain,
! [U_838,U_839] :
( relation_rng(relation_composition(U_838,U_839)) = relation_rng(U_839)
| ~ subset(relation_dom(U_839),relation_rng(U_838))
| ~ relation(U_838)
| ~ relation(U_839) ),
inference(definitional_conversion,[status(esa)],[f_225_2]) ).
cnf(f_225_4,plain,
( relation_rng(relation_composition(U_838,U_839)) = relation_rng(U_839)
| ~ subset(relation_dom(U_839),relation_rng(U_838))
| ~ relation(U_838)
| ~ relation(U_839) ),
inference(clausify,[status(thm)],[f_225_3]) ).
fof(f_226_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_226_2,plain,
! [U_841,U_840] :
( subset_difference(U_841,cast_to_subset(U_841),union_of_subsets(U_841,U_840)) = meet_of_subsets(U_841,complements_of_subsets(U_841,U_840))
| U_840 = empty_set
| ~ element(U_840,powerset(powerset(U_841))) ),
inference(variable_rename,[status(thm)],[f_226_1]) ).
fof(f_226_3,plain,
! [U_841,U_840] :
( subset_difference(U_841,cast_to_subset(U_841),union_of_subsets(U_841,U_840)) = meet_of_subsets(U_841,complements_of_subsets(U_841,U_840))
| U_840 = empty_set
| ~ element(U_840,powerset(powerset(U_841))) ),
inference(definitional_conversion,[status(esa)],[f_226_2]) ).
cnf(f_226_4,plain,
( subset_difference(U_841,cast_to_subset(U_841),union_of_subsets(U_841,U_840)) = meet_of_subsets(U_841,complements_of_subsets(U_841,U_840))
| U_840 = empty_set
| ~ element(U_840,powerset(powerset(U_841))) ),
inference(clausify,[status(thm)],[f_226_3]) ).
fof(f_227_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_227_2,plain,
! [U_843,U_842] :
( union_of_subsets(U_843,complements_of_subsets(U_843,U_842)) = subset_difference(U_843,cast_to_subset(U_843),meet_of_subsets(U_843,U_842))
| U_842 = empty_set
| ~ element(U_842,powerset(powerset(U_843))) ),
inference(variable_rename,[status(thm)],[f_227_1]) ).
fof(f_227_3,plain,
! [U_843,U_842] :
( union_of_subsets(U_843,complements_of_subsets(U_843,U_842)) = subset_difference(U_843,cast_to_subset(U_843),meet_of_subsets(U_843,U_842))
| U_842 = empty_set
| ~ element(U_842,powerset(powerset(U_843))) ),
inference(definitional_conversion,[status(esa)],[f_227_2]) ).
cnf(f_227_4,plain,
( union_of_subsets(U_843,complements_of_subsets(U_843,U_842)) = subset_difference(U_843,cast_to_subset(U_843),meet_of_subsets(U_843,U_842))
| U_842 = empty_set
| ~ element(U_842,powerset(powerset(U_843))) ),
inference(clausify,[status(thm)],[f_227_3]) ).
fof(f_228_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_228_2,plain,
! [U_845,U_844] : set_difference(U_845,set_difference(U_845,U_844)) = set_intersection2(U_845,U_844),
inference(variable_rename,[status(thm)],[f_228_1]) ).
fof(f_228_3,plain,
! [U_845,U_844] : set_difference(U_845,set_difference(U_845,U_844)) = set_intersection2(U_845,U_844),
inference(definitional_conversion,[status(esa)],[f_228_2]) ).
cnf(f_228_4,plain,
set_difference(U_845,set_difference(U_845,U_844)) = set_intersection2(U_845,U_844),
inference(clausify,[status(thm)],[f_228_3]) ).
fof(f_229_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_229_2,plain,
! [U_846] : set_difference(empty_set,U_846) = empty_set,
inference(variable_rename,[status(thm)],[f_229_1]) ).
fof(f_229_3,plain,
! [U_846] : set_difference(empty_set,U_846) = empty_set,
inference(definitional_conversion,[status(esa)],[f_229_2]) ).
cnf(f_229_4,plain,
set_difference(empty_set,U_846) = empty_set,
inference(clausify,[status(thm)],[f_229_3]) ).
fof(f_230_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_230_2,plain,
! [U_849,U_848,U_847] :
( element(U_849,U_847)
| ~ element(U_848,powerset(U_847))
| ~ in(U_849,U_848) ),
inference(variable_rename,[status(thm)],[f_230_1]) ).
fof(f_230_3,plain,
! [U_847,U_848,U_849] :
( element(U_849,U_847)
| ~ element(U_848,powerset(U_847))
| ~ in(U_849,U_848) ),
inference(definitional_conversion,[status(esa)],[f_230_2]) ).
cnf(f_230_4,plain,
( element(U_849,U_847)
| ~ element(U_848,powerset(U_847))
| ~ in(U_849,U_848) ),
inference(clausify,[status(thm)],[f_230_3]) ).
fof(f_231_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_231_2,plain,
! [U_853,U_852] :
( ( ~ disjoint(U_853,U_852)
| ! [U_851] : ~ in(U_851,set_intersection2(U_853,U_852)) )
& ( ? [U_850] : in(U_850,set_intersection2(U_853,U_852))
| disjoint(U_853,U_852) ) ),
inference(variable_rename,[status(thm)],[f_231_1]) ).
fof(f_231_3,plain,
( ! [U_857,U_855] :
( ~ disjoint(U_857,U_855)
| ! [U_851] : ~ in(U_851,set_intersection2(U_857,U_855)) )
& ! [U_856,U_854] :
( ? [U_850] : in(U_850,set_intersection2(U_856,U_854))
| disjoint(U_856,U_854) ) ),
inference(miniscope,[status(thm)],[f_231_2]) ).
fof(f_231_4,plain,
( ! [U_857,U_855] :
( ~ disjoint(U_857,U_855)
| ! [U_851] : ~ in(U_851,set_intersection2(U_857,U_855)) )
& ! [U_856,U_854] :
( in(sK118(U_856,U_854),set_intersection2(U_856,U_854))
| disjoint(U_856,U_854) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK118]),skolemize(U_850,sK118(U_856,U_854))],[f_231_3]) ).
fof(f_231_5,plain,
( ! [U_851,U_855,U_857] :
( ~ disjoint(U_857,U_855)
| ~ in(U_851,set_intersection2(U_857,U_855)) )
& ! [U_856,U_854] :
( in(sK118(U_856,U_854),set_intersection2(U_856,U_854))
| disjoint(U_856,U_854) ) ),
inference(definitional_conversion,[status(esa)],[f_231_4]) ).
cnf(f_231_6,plain,
( in(sK118(U_856,U_854),set_intersection2(U_856,U_854))
| disjoint(U_856,U_854) ),
inference(clausify,[status(thm)],[f_231_5]) ).
cnf(f_231_7,plain,
( ~ disjoint(U_857,U_855)
| ~ in(U_851,set_intersection2(U_857,U_855)) ),
inference(clausify,[status(thm)],[f_231_5]) ).
fof(f_232_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_232_2,plain,
! [U_860] :
( ! [U_859] :
( ! [U_858] :
( in(U_858,subset_complement(U_860,U_859))
| in(U_858,U_859)
| ~ element(U_858,U_860) )
| ~ element(U_859,powerset(U_860)) )
| U_860 = empty_set ),
inference(variable_rename,[status(thm)],[f_232_1]) ).
fof(f_232_3,plain,
! [U_860,U_858,U_859] :
( in(U_858,subset_complement(U_860,U_859))
| in(U_858,U_859)
| ~ element(U_858,U_860)
| ~ element(U_859,powerset(U_860))
| U_860 = empty_set ),
inference(definitional_conversion,[status(esa)],[f_232_2]) ).
cnf(f_232_4,plain,
( in(U_858,subset_complement(U_860,U_859))
| in(U_858,U_859)
| ~ element(U_858,U_860)
| ~ element(U_859,powerset(U_860))
| U_860 = empty_set ),
inference(clausify,[status(thm)],[f_232_3]) ).
fof(f_233_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_233_2,plain,
! [U_866] :
( ! [U_865] :
( ( ( U_865 = function_inverse(U_866)
| ? [U_864,U_863] :
( ( ( U_863 != apply(U_865,U_864)
| ~ in(U_864,relation_rng(U_866)) )
& U_864 = apply(U_866,U_863)
& in(U_863,relation_dom(U_866)) )
| ( ( U_864 != apply(U_866,U_863)
| ~ in(U_863,relation_dom(U_866)) )
& U_863 = apply(U_865,U_864)
& in(U_864,relation_rng(U_866)) ) )
| relation_dom(U_865) != relation_rng(U_866) )
& ( ( ! [U_862,U_861] :
( ( ( U_861 = apply(U_865,U_862)
& in(U_862,relation_rng(U_866)) )
| U_862 != apply(U_866,U_861)
| ~ in(U_861,relation_dom(U_866)) )
& ( ( U_862 = apply(U_866,U_861)
& in(U_861,relation_dom(U_866)) )
| U_861 != apply(U_865,U_862)
| ~ in(U_862,relation_rng(U_866)) ) )
& relation_dom(U_865) = relation_rng(U_866) )
| U_865 != function_inverse(U_866) ) )
| ~ function(U_865)
| ~ relation(U_865) )
| ~ one_to_one(U_866)
| ~ function(U_866)
| ~ relation(U_866) ),
inference(variable_rename,[status(thm)],[f_233_1]) ).
fof(f_233_3,plain,
! [U_866] :
( ! [U_865] :
( ( ( U_865 = function_inverse(U_866)
| ? [U_874,U_872] :
( ( U_872 != apply(U_865,U_874)
| ~ in(U_874,relation_rng(U_866)) )
& U_874 = apply(U_866,U_872)
& in(U_872,relation_dom(U_866)) )
| ? [U_873,U_871] :
( ( U_873 != apply(U_866,U_871)
| ~ in(U_871,relation_dom(U_866)) )
& U_871 = apply(U_865,U_873)
& in(U_873,relation_rng(U_866)) )
| relation_dom(U_865) != relation_rng(U_866) )
& ( ( ! [U_870,U_868] :
( ( U_868 = apply(U_865,U_870)
& in(U_870,relation_rng(U_866)) )
| U_870 != apply(U_866,U_868)
| ~ in(U_868,relation_dom(U_866)) )
& ! [U_869,U_867] :
( ( U_869 = apply(U_866,U_867)
& in(U_867,relation_dom(U_866)) )
| U_867 != apply(U_865,U_869)
| ~ in(U_869,relation_rng(U_866)) )
& relation_dom(U_865) = relation_rng(U_866) )
| U_865 != function_inverse(U_866) ) )
| ~ function(U_865)
| ~ relation(U_865) )
| ~ one_to_one(U_866)
| ~ function(U_866)
| ~ relation(U_866) ),
inference(miniscope,[status(thm)],[f_233_2]) ).
fof(f_233_4,plain,
! [U_866] :
( ! [U_865] :
( ( ( U_865 = function_inverse(U_866)
| ? [U_874,U_872] :
( ( U_872 != apply(U_865,U_874)
| ~ in(U_874,relation_rng(U_866)) )
& U_874 = apply(U_866,U_872)
& in(U_872,relation_dom(U_866)) )
| ? [U_871] :
( ( sK119(U_866,U_865) != apply(U_866,U_871)
| ~ in(U_871,relation_dom(U_866)) )
& U_871 = apply(U_865,sK119(U_866,U_865))
& in(sK119(U_866,U_865),relation_rng(U_866)) )
| relation_dom(U_865) != relation_rng(U_866) )
& ( ( ! [U_870,U_868] :
( ( U_868 = apply(U_865,U_870)
& in(U_870,relation_rng(U_866)) )
| U_870 != apply(U_866,U_868)
| ~ in(U_868,relation_dom(U_866)) )
& ! [U_869,U_867] :
( ( U_869 = apply(U_866,U_867)
& in(U_867,relation_dom(U_866)) )
| U_867 != apply(U_865,U_869)
| ~ in(U_869,relation_rng(U_866)) )
& relation_dom(U_865) = relation_rng(U_866) )
| U_865 != function_inverse(U_866) ) )
| ~ function(U_865)
| ~ relation(U_865) )
| ~ one_to_one(U_866)
| ~ function(U_866)
| ~ relation(U_866) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK119]),skolemize(U_873,sK119(U_866,U_865))],[f_233_3]) ).
fof(f_233_5,plain,
! [U_866] :
( ! [U_865] :
( ( ( U_865 = function_inverse(U_866)
| ? [U_874,U_872] :
( ( U_872 != apply(U_865,U_874)
| ~ in(U_874,relation_rng(U_866)) )
& U_874 = apply(U_866,U_872)
& in(U_872,relation_dom(U_866)) )
| ( ( sK119(U_866,U_865) != apply(U_866,sK120(U_866,U_865))
| ~ in(sK120(U_866,U_865),relation_dom(U_866)) )
& sK120(U_866,U_865) = apply(U_865,sK119(U_866,U_865))
& in(sK119(U_866,U_865),relation_rng(U_866)) )
| relation_dom(U_865) != relation_rng(U_866) )
& ( ( ! [U_870,U_868] :
( ( U_868 = apply(U_865,U_870)
& in(U_870,relation_rng(U_866)) )
| U_870 != apply(U_866,U_868)
| ~ in(U_868,relation_dom(U_866)) )
& ! [U_869,U_867] :
( ( U_869 = apply(U_866,U_867)
& in(U_867,relation_dom(U_866)) )
| U_867 != apply(U_865,U_869)
| ~ in(U_869,relation_rng(U_866)) )
& relation_dom(U_865) = relation_rng(U_866) )
| U_865 != function_inverse(U_866) ) )
| ~ function(U_865)
| ~ relation(U_865) )
| ~ one_to_one(U_866)
| ~ function(U_866)
| ~ relation(U_866) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK120]),skolemize(U_871,sK120(U_866,U_865))],[f_233_4]) ).
fof(f_233_6,plain,
! [U_866] :
( ! [U_865] :
( ( ( U_865 = function_inverse(U_866)
| ? [U_872] :
( ( U_872 != apply(U_865,sK121(U_866,U_865))
| ~ in(sK121(U_866,U_865),relation_rng(U_866)) )
& sK121(U_866,U_865) = apply(U_866,U_872)
& in(U_872,relation_dom(U_866)) )
| ( ( sK119(U_866,U_865) != apply(U_866,sK120(U_866,U_865))
| ~ in(sK120(U_866,U_865),relation_dom(U_866)) )
& sK120(U_866,U_865) = apply(U_865,sK119(U_866,U_865))
& in(sK119(U_866,U_865),relation_rng(U_866)) )
| relation_dom(U_865) != relation_rng(U_866) )
& ( ( ! [U_870,U_868] :
( ( U_868 = apply(U_865,U_870)
& in(U_870,relation_rng(U_866)) )
| U_870 != apply(U_866,U_868)
| ~ in(U_868,relation_dom(U_866)) )
& ! [U_869,U_867] :
( ( U_869 = apply(U_866,U_867)
& in(U_867,relation_dom(U_866)) )
| U_867 != apply(U_865,U_869)
| ~ in(U_869,relation_rng(U_866)) )
& relation_dom(U_865) = relation_rng(U_866) )
| U_865 != function_inverse(U_866) ) )
| ~ function(U_865)
| ~ relation(U_865) )
| ~ one_to_one(U_866)
| ~ function(U_866)
| ~ relation(U_866) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK121]),skolemize(U_874,sK121(U_866,U_865))],[f_233_5]) ).
fof(f_233_7,plain,
! [U_866] :
( ! [U_865] :
( ( ( U_865 = function_inverse(U_866)
| ( ( sK122(U_866,U_865) != apply(U_865,sK121(U_866,U_865))
| ~ in(sK121(U_866,U_865),relation_rng(U_866)) )
& sK121(U_866,U_865) = apply(U_866,sK122(U_866,U_865))
& in(sK122(U_866,U_865),relation_dom(U_866)) )
| ( ( sK119(U_866,U_865) != apply(U_866,sK120(U_866,U_865))
| ~ in(sK120(U_866,U_865),relation_dom(U_866)) )
& sK120(U_866,U_865) = apply(U_865,sK119(U_866,U_865))
& in(sK119(U_866,U_865),relation_rng(U_866)) )
| relation_dom(U_865) != relation_rng(U_866) )
& ( ( ! [U_870,U_868] :
( ( U_868 = apply(U_865,U_870)
& in(U_870,relation_rng(U_866)) )
| U_870 != apply(U_866,U_868)
| ~ in(U_868,relation_dom(U_866)) )
& ! [U_869,U_867] :
( ( U_869 = apply(U_866,U_867)
& in(U_867,relation_dom(U_866)) )
| U_867 != apply(U_865,U_869)
| ~ in(U_869,relation_rng(U_866)) )
& relation_dom(U_865) = relation_rng(U_866) )
| U_865 != function_inverse(U_866) ) )
| ~ function(U_865)
| ~ relation(U_865) )
| ~ one_to_one(U_866)
| ~ function(U_866)
| ~ relation(U_866) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(U_872,sK122(U_866,U_865))],[f_233_6]) ).
fof(f_233_8,plain,
( ! [U_865,U_866] :
( sK122(U_866,U_865) != apply(U_865,sK121(U_866,U_865))
| ~ in(sK121(U_866,U_865),relation_rng(U_866))
| ~ sP170(U_865,U_866) )
& ! [U_865,U_866] :
( sK121(U_866,U_865) = apply(U_866,sK122(U_866,U_865))
| ~ sP170(U_865,U_866) )
& ! [U_865,U_866] :
( in(sK122(U_866,U_865),relation_dom(U_866))
| ~ sP170(U_865,U_866) )
& ! [U_865,U_866] :
( sK119(U_866,U_865) != apply(U_866,sK120(U_866,U_865))
| ~ in(sK120(U_866,U_865),relation_dom(U_866))
| ~ sP169(U_865,U_866) )
& ! [U_865,U_866] :
( sK120(U_866,U_865) = apply(U_865,sK119(U_866,U_865))
| ~ sP169(U_865,U_866) )
& ! [U_865,U_866] :
( in(sK119(U_866,U_865),relation_rng(U_866))
| ~ sP169(U_865,U_866) )
& ! [U_865,U_866,U_868,U_870] :
( U_868 = apply(U_865,U_870)
| ~ sP167(U_865,U_866,U_868,U_870) )
& ! [U_865,U_866,U_868,U_870] :
( in(U_870,relation_rng(U_866))
| ~ sP167(U_865,U_866,U_868,U_870) )
& ! [U_869,U_866,U_867] :
( U_869 = apply(U_866,U_867)
| ~ sP166(U_869,U_866,U_867) )
& ! [U_869,U_866,U_867] :
( in(U_867,relation_dom(U_866))
| ~ sP166(U_869,U_866,U_867) )
& ! [U_865,U_869,U_866,U_867,U_868,U_870] :
( sP167(U_865,U_866,U_868,U_870)
| U_870 != apply(U_866,U_868)
| ~ in(U_868,relation_dom(U_866))
| ~ sP168(U_865,U_869,U_866,U_867,U_868,U_870) )
& ! [U_865,U_869,U_866,U_867,U_868,U_870] :
( sP166(U_869,U_866,U_867)
| U_867 != apply(U_865,U_869)
| ~ in(U_869,relation_rng(U_866))
| ~ sP168(U_865,U_869,U_866,U_867,U_868,U_870) )
& ! [U_865,U_869,U_866,U_867,U_868,U_870] :
( relation_dom(U_865) = relation_rng(U_866)
| ~ sP168(U_865,U_869,U_866,U_867,U_868,U_870) )
& ! [U_865,U_869,U_866,U_867,U_868,U_870] :
( U_865 = function_inverse(U_866)
| sP170(U_865,U_866)
| sP169(U_865,U_866)
| relation_dom(U_865) != relation_rng(U_866)
| ~ sP171(U_865,U_869,U_866,U_867,U_868,U_870) )
& ! [U_865,U_869,U_866,U_867,U_868,U_870] :
( sP168(U_865,U_869,U_866,U_867,U_868,U_870)
| U_865 != function_inverse(U_866)
| ~ sP171(U_865,U_869,U_866,U_867,U_868,U_870) )
& ! [U_865,U_869,U_866,U_867,U_868,U_870] :
( sP171(U_865,U_869,U_866,U_867,U_868,U_870)
| ~ function(U_865)
| ~ relation(U_865)
| ~ one_to_one(U_866)
| ~ function(U_866)
| ~ relation(U_866) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP166,sP167,sP168,sP169,sP170,sP171])],[f_233_7]) ).
cnf(f_233_9,plain,
( sP171(U_865,U_869,U_866,U_867,U_868,U_870)
| ~ function(U_865)
| ~ relation(U_865)
| ~ one_to_one(U_866)
| ~ function(U_866)
| ~ relation(U_866) ),
inference(clausify,[status(thm)],[f_233_8]) ).
cnf(f_233_10,plain,
( sP168(U_865,U_869,U_866,U_867,U_868,U_870)
| U_865 != function_inverse(U_866)
| ~ sP171(U_865,U_869,U_866,U_867,U_868,U_870) ),
inference(clausify,[status(thm)],[f_233_8]) ).
cnf(f_233_11,plain,
( U_865 = function_inverse(U_866)
| sP170(U_865,U_866)
| sP169(U_865,U_866)
| relation_dom(U_865) != relation_rng(U_866)
| ~ sP171(U_865,U_869,U_866,U_867,U_868,U_870) ),
inference(clausify,[status(thm)],[f_233_8]) ).
cnf(f_233_12,plain,
( relation_dom(U_865) = relation_rng(U_866)
| ~ sP168(U_865,U_869,U_866,U_867,U_868,U_870) ),
inference(clausify,[status(thm)],[f_233_8]) ).
cnf(f_233_13,plain,
( sP166(U_869,U_866,U_867)
| U_867 != apply(U_865,U_869)
| ~ in(U_869,relation_rng(U_866))
| ~ sP168(U_865,U_869,U_866,U_867,U_868,U_870) ),
inference(clausify,[status(thm)],[f_233_8]) ).
cnf(f_233_14,plain,
( sP167(U_865,U_866,U_868,U_870)
| U_870 != apply(U_866,U_868)
| ~ in(U_868,relation_dom(U_866))
| ~ sP168(U_865,U_869,U_866,U_867,U_868,U_870) ),
inference(clausify,[status(thm)],[f_233_8]) ).
cnf(f_233_15,plain,
( in(U_867,relation_dom(U_866))
| ~ sP166(U_869,U_866,U_867) ),
inference(clausify,[status(thm)],[f_233_8]) ).
cnf(f_233_16,plain,
( U_869 = apply(U_866,U_867)
| ~ sP166(U_869,U_866,U_867) ),
inference(clausify,[status(thm)],[f_233_8]) ).
cnf(f_233_17,plain,
( in(U_870,relation_rng(U_866))
| ~ sP167(U_865,U_866,U_868,U_870) ),
inference(clausify,[status(thm)],[f_233_8]) ).
cnf(f_233_18,plain,
( U_868 = apply(U_865,U_870)
| ~ sP167(U_865,U_866,U_868,U_870) ),
inference(clausify,[status(thm)],[f_233_8]) ).
cnf(f_233_19,plain,
( in(sK119(U_866,U_865),relation_rng(U_866))
| ~ sP169(U_865,U_866) ),
inference(clausify,[status(thm)],[f_233_8]) ).
cnf(f_233_20,plain,
( sK120(U_866,U_865) = apply(U_865,sK119(U_866,U_865))
| ~ sP169(U_865,U_866) ),
inference(clausify,[status(thm)],[f_233_8]) ).
cnf(f_233_21,plain,
( sK119(U_866,U_865) != apply(U_866,sK120(U_866,U_865))
| ~ in(sK120(U_866,U_865),relation_dom(U_866))
| ~ sP169(U_865,U_866) ),
inference(clausify,[status(thm)],[f_233_8]) ).
cnf(f_233_22,plain,
( in(sK122(U_866,U_865),relation_dom(U_866))
| ~ sP170(U_865,U_866) ),
inference(clausify,[status(thm)],[f_233_8]) ).
cnf(f_233_23,plain,
( sK121(U_866,U_865) = apply(U_866,sK122(U_866,U_865))
| ~ sP170(U_865,U_866) ),
inference(clausify,[status(thm)],[f_233_8]) ).
cnf(f_233_24,plain,
( sK122(U_866,U_865) != apply(U_865,sK121(U_866,U_865))
| ~ in(sK121(U_866,U_865),relation_rng(U_866))
| ~ sP170(U_865,U_866) ),
inference(clausify,[status(thm)],[f_233_8]) ).
fof(f_234_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_234_2,plain,
! [U_877,U_876,U_875] :
( ~ in(U_876,U_875)
| ~ in(U_876,subset_complement(U_877,U_875))
| ~ element(U_875,powerset(U_877)) ),
inference(variable_rename,[status(thm)],[f_234_1]) ).
fof(f_234_3,plain,
! [U_877,U_876,U_875] :
( ~ in(U_876,U_875)
| ~ in(U_876,subset_complement(U_877,U_875))
| ~ element(U_875,powerset(U_877)) ),
inference(definitional_conversion,[status(esa)],[f_234_2]) ).
cnf(f_234_4,plain,
( ~ in(U_876,U_875)
| ~ in(U_876,subset_complement(U_877,U_875))
| ~ element(U_875,powerset(U_877)) ),
inference(clausify,[status(thm)],[f_234_3]) ).
fof(f_235_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_235_2,plain,
! [U_878] :
( ( relation_dom(U_878) = relation_rng(function_inverse(U_878))
& relation_rng(U_878) = relation_dom(function_inverse(U_878)) )
| ~ one_to_one(U_878)
| ~ function(U_878)
| ~ relation(U_878) ),
inference(variable_rename,[status(thm)],[f_235_1]) ).
fof(f_235_3,plain,
( ! [U_878] :
( relation_dom(U_878) = relation_rng(function_inverse(U_878))
| ~ sP172(U_878) )
& ! [U_878] :
( relation_rng(U_878) = relation_dom(function_inverse(U_878))
| ~ sP172(U_878) )
& ! [U_878] :
( sP172(U_878)
| ~ one_to_one(U_878)
| ~ function(U_878)
| ~ relation(U_878) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP172])],[f_235_2]) ).
cnf(f_235_4,plain,
( sP172(U_878)
| ~ one_to_one(U_878)
| ~ function(U_878)
| ~ relation(U_878) ),
inference(clausify,[status(thm)],[f_235_3]) ).
cnf(f_235_5,plain,
( relation_rng(U_878) = relation_dom(function_inverse(U_878))
| ~ sP172(U_878) ),
inference(clausify,[status(thm)],[f_235_3]) ).
cnf(f_235_6,plain,
( relation_dom(U_878) = relation_rng(function_inverse(U_878))
| ~ sP172(U_878) ),
inference(clausify,[status(thm)],[f_235_3]) ).
fof(f_236_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_236_2,plain,
! [U_881] :
( U_881 = empty_set
| ? [U_880,U_879] : in(ordered_pair(U_880,U_879),U_881)
| ~ relation(U_881) ),
inference(variable_rename,[status(thm)],[f_236_1]) ).
fof(f_236_3,plain,
! [U_881] :
( U_881 = empty_set
| ? [U_879] : in(ordered_pair(sK123(U_881),U_879),U_881)
| ~ relation(U_881) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK123]),skolemize(U_880,sK123(U_881))],[f_236_2]) ).
fof(f_236_4,plain,
! [U_881] :
( U_881 = empty_set
| in(ordered_pair(sK123(U_881),sK124(U_881)),U_881)
| ~ relation(U_881) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK124]),skolemize(U_879,sK124(U_881))],[f_236_3]) ).
fof(f_236_5,plain,
! [U_881] :
( U_881 = empty_set
| in(ordered_pair(sK123(U_881),sK124(U_881)),U_881)
| ~ relation(U_881) ),
inference(definitional_conversion,[status(esa)],[f_236_4]) ).
cnf(f_236_6,plain,
( U_881 = empty_set
| in(ordered_pair(sK123(U_881),sK124(U_881)),U_881)
| ~ relation(U_881) ),
inference(clausify,[status(thm)],[f_236_5]) ).
fof(f_237_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_237_2,plain,
! [U_883,U_882] :
( ( U_883 = apply(relation_composition(function_inverse(U_882),U_882),U_883)
& U_883 = apply(U_882,apply(function_inverse(U_882),U_883)) )
| ~ in(U_883,relation_rng(U_882))
| ~ one_to_one(U_882)
| ~ function(U_882)
| ~ relation(U_882) ),
inference(variable_rename,[status(thm)],[f_237_1]) ).
fof(f_237_3,plain,
( ! [U_883,U_882] :
( U_883 = apply(relation_composition(function_inverse(U_882),U_882),U_883)
| ~ sP173(U_883,U_882) )
& ! [U_883,U_882] :
( U_883 = apply(U_882,apply(function_inverse(U_882),U_883))
| ~ sP173(U_883,U_882) )
& ! [U_883,U_882] :
( sP173(U_883,U_882)
| ~ in(U_883,relation_rng(U_882))
| ~ one_to_one(U_882)
| ~ function(U_882)
| ~ relation(U_882) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP173])],[f_237_2]) ).
cnf(f_237_4,plain,
( sP173(U_883,U_882)
| ~ in(U_883,relation_rng(U_882))
| ~ one_to_one(U_882)
| ~ function(U_882)
| ~ relation(U_882) ),
inference(clausify,[status(thm)],[f_237_3]) ).
cnf(f_237_5,plain,
( U_883 = apply(U_882,apply(function_inverse(U_882),U_883))
| ~ sP173(U_883,U_882) ),
inference(clausify,[status(thm)],[f_237_3]) ).
cnf(f_237_6,plain,
( U_883 = apply(relation_composition(function_inverse(U_882),U_882),U_883)
| ~ sP173(U_883,U_882) ),
inference(clausify,[status(thm)],[f_237_3]) ).
fof(f_238_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_238_2,plain,
! [U_886,U_885,U_884] :
( ~ empty(U_884)
| ~ element(U_885,powerset(U_884))
| ~ in(U_886,U_885) ),
inference(variable_rename,[status(thm)],[f_238_1]) ).
fof(f_238_3,plain,
! [U_886,U_885] :
( ! [U_884] :
( ~ empty(U_884)
| ~ element(U_885,powerset(U_884)) )
| ~ in(U_886,U_885) ),
inference(miniscope,[status(thm)],[f_238_2]) ).
fof(f_238_4,plain,
! [U_884,U_885,U_886] :
( ~ empty(U_884)
| ~ element(U_885,powerset(U_884))
| ~ in(U_886,U_885) ),
inference(definitional_conversion,[status(esa)],[f_238_3]) ).
cnf(f_238_5,plain,
( ~ empty(U_884)
| ~ element(U_885,powerset(U_884))
| ~ in(U_886,U_885) ),
inference(clausify,[status(thm)],[f_238_4]) ).
fof(f_239_1,plain,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(fof_nnf,[status(thm)],[t60_relat_1]) ).
fof(f_239_2,plain,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(definitional_conversion,[status(esa)],[f_239_1]) ).
cnf(f_239_3,plain,
relation_dom(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_239_2]) ).
cnf(f_239_4,plain,
relation_rng(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_239_2]) ).
fof(f_240_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t60_xboole_1]) ).
fof(f_240_2,plain,
! [U_888,U_887] :
( ~ proper_subset(U_887,U_888)
| ~ subset(U_888,U_887) ),
inference(variable_rename,[status(thm)],[f_240_1]) ).
fof(f_240_3,plain,
! [U_888,U_887] :
( ~ proper_subset(U_887,U_888)
| ~ subset(U_888,U_887) ),
inference(definitional_conversion,[status(esa)],[f_240_2]) ).
cnf(f_240_4,plain,
( ~ proper_subset(U_887,U_888)
| ~ subset(U_888,U_887) ),
inference(clausify,[status(thm)],[f_240_3]) ).
fof(f_241_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_241_2,plain,
! [U_889] :
( one_to_one(function_inverse(U_889))
| ~ one_to_one(U_889)
| ~ function(U_889)
| ~ relation(U_889) ),
inference(variable_rename,[status(thm)],[f_241_1]) ).
fof(f_241_3,plain,
! [U_889] :
( one_to_one(function_inverse(U_889))
| ~ one_to_one(U_889)
| ~ function(U_889)
| ~ relation(U_889) ),
inference(definitional_conversion,[status(esa)],[f_241_2]) ).
cnf(f_241_4,plain,
( one_to_one(function_inverse(U_889))
| ~ one_to_one(U_889)
| ~ function(U_889)
| ~ relation(U_889) ),
inference(clausify,[status(thm)],[f_241_3]) ).
fof(f_242_1,plain,
! [A,B,C] :
( disjoint(A,C)
| ~ disjoint(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t63_xboole_1]) ).
fof(f_242_2,plain,
! [U_892,U_891,U_890] :
( disjoint(U_892,U_890)
| ~ disjoint(U_891,U_890)
| ~ subset(U_892,U_891) ),
inference(variable_rename,[status(thm)],[f_242_1]) ).
fof(f_242_3,plain,
! [U_892,U_890,U_891] :
( disjoint(U_892,U_890)
| ~ disjoint(U_891,U_890)
| ~ subset(U_892,U_891) ),
inference(definitional_conversion,[status(esa)],[f_242_2]) ).
cnf(f_242_4,plain,
( disjoint(U_892,U_890)
| ~ disjoint(U_891,U_890)
| ~ subset(U_892,U_891) ),
inference(clausify,[status(thm)],[f_242_3]) ).
fof(f_243_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_243_2,plain,
! [U_893] :
( U_893 = empty_set
| ( relation_rng(U_893) != empty_set
& relation_dom(U_893) != empty_set )
| ~ relation(U_893) ),
inference(variable_rename,[status(thm)],[f_243_1]) ).
fof(f_243_3,plain,
( ! [U_893] :
( relation_rng(U_893) != empty_set
| ~ sP174(U_893) )
& ! [U_893] :
( relation_dom(U_893) != empty_set
| ~ sP174(U_893) )
& ! [U_893] :
( U_893 = empty_set
| sP174(U_893)
| ~ relation(U_893) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP174])],[f_243_2]) ).
cnf(f_243_4,plain,
( U_893 = empty_set
| sP174(U_893)
| ~ relation(U_893) ),
inference(clausify,[status(thm)],[f_243_3]) ).
cnf(f_243_5,plain,
( relation_dom(U_893) != empty_set
| ~ sP174(U_893) ),
inference(clausify,[status(thm)],[f_243_3]) ).
cnf(f_243_6,plain,
( relation_rng(U_893) != empty_set
| ~ sP174(U_893) ),
inference(clausify,[status(thm)],[f_243_3]) ).
fof(f_244_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_244_2,plain,
! [U_894] :
( ( ( relation_dom(U_894) = empty_set
| relation_rng(U_894) != empty_set )
& ( relation_rng(U_894) = empty_set
| relation_dom(U_894) != empty_set ) )
| ~ relation(U_894) ),
inference(variable_rename,[status(thm)],[f_244_1]) ).
fof(f_244_3,plain,
( ! [U_894] :
( relation_dom(U_894) = empty_set
| relation_rng(U_894) != empty_set
| ~ sP175(U_894) )
& ! [U_894] :
( relation_rng(U_894) = empty_set
| relation_dom(U_894) != empty_set
| ~ sP175(U_894) )
& ! [U_894] :
( sP175(U_894)
| ~ relation(U_894) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP175])],[f_244_2]) ).
cnf(f_244_4,plain,
( sP175(U_894)
| ~ relation(U_894) ),
inference(clausify,[status(thm)],[f_244_3]) ).
cnf(f_244_5,plain,
( relation_rng(U_894) = empty_set
| relation_dom(U_894) != empty_set
| ~ sP175(U_894) ),
inference(clausify,[status(thm)],[f_244_3]) ).
cnf(f_244_6,plain,
( relation_dom(U_894) = empty_set
| relation_rng(U_894) != empty_set
| ~ sP175(U_894) ),
inference(clausify,[status(thm)],[f_244_3]) ).
fof(f_245_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_245_2,plain,
! [U_896,U_895] :
( ( set_difference(U_896,singleton(U_895)) = U_896
| in(U_895,U_896) )
& ( ~ in(U_895,U_896)
| set_difference(U_896,singleton(U_895)) != U_896 ) ),
inference(variable_rename,[status(thm)],[f_245_1]) ).
fof(f_245_3,plain,
( ! [U_900,U_898] :
( set_difference(U_900,singleton(U_898)) = U_900
| in(U_898,U_900) )
& ! [U_899,U_897] :
( ~ in(U_897,U_899)
| set_difference(U_899,singleton(U_897)) != U_899 ) ),
inference(miniscope,[status(thm)],[f_245_2]) ).
fof(f_245_4,plain,
( ! [U_900,U_898] :
( set_difference(U_900,singleton(U_898)) = U_900
| in(U_898,U_900) )
& ! [U_897,U_899] :
( ~ in(U_897,U_899)
| set_difference(U_899,singleton(U_897)) != U_899 ) ),
inference(definitional_conversion,[status(esa)],[f_245_3]) ).
cnf(f_245_5,plain,
( ~ in(U_897,U_899)
| set_difference(U_899,singleton(U_897)) != U_899 ),
inference(clausify,[status(thm)],[f_245_4]) ).
cnf(f_245_6,plain,
( set_difference(U_900,singleton(U_898)) = U_900
| in(U_898,U_900) ),
inference(clausify,[status(thm)],[f_245_4]) ).
fof(f_246_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_246_2,plain,
! [U_905,U_904] :
( ! [U_903] :
( ( ( U_904 = relation_dom_restriction(U_903,U_905)
| ? [U_902] :
( apply(U_904,U_902) != apply(U_903,U_902)
& in(U_902,relation_dom(U_904)) )
| relation_dom(U_904) != set_intersection2(relation_dom(U_903),U_905) )
& ( ( ! [U_901] :
( apply(U_904,U_901) = apply(U_903,U_901)
| ~ in(U_901,relation_dom(U_904)) )
& relation_dom(U_904) = set_intersection2(relation_dom(U_903),U_905) )
| U_904 != relation_dom_restriction(U_903,U_905) ) )
| ~ function(U_903)
| ~ relation(U_903) )
| ~ function(U_904)
| ~ relation(U_904) ),
inference(variable_rename,[status(thm)],[f_246_1]) ).
fof(f_246_3,plain,
! [U_905,U_904] :
( ! [U_903] :
( ( ( U_904 = relation_dom_restriction(U_903,U_905)
| ( apply(U_904,sK125(U_905,U_904,U_903)) != apply(U_903,sK125(U_905,U_904,U_903))
& in(sK125(U_905,U_904,U_903),relation_dom(U_904)) )
| relation_dom(U_904) != set_intersection2(relation_dom(U_903),U_905) )
& ( ( ! [U_901] :
( apply(U_904,U_901) = apply(U_903,U_901)
| ~ in(U_901,relation_dom(U_904)) )
& relation_dom(U_904) = set_intersection2(relation_dom(U_903),U_905) )
| U_904 != relation_dom_restriction(U_903,U_905) ) )
| ~ function(U_903)
| ~ relation(U_903) )
| ~ function(U_904)
| ~ relation(U_904) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK125]),skolemize(U_902,sK125(U_905,U_904,U_903))],[f_246_2]) ).
fof(f_246_4,plain,
( ! [U_903,U_904,U_905] :
( apply(U_904,sK125(U_905,U_904,U_903)) != apply(U_903,sK125(U_905,U_904,U_903))
| ~ sP177(U_903,U_904,U_905) )
& ! [U_903,U_904,U_905] :
( in(sK125(U_905,U_904,U_903),relation_dom(U_904))
| ~ sP177(U_903,U_904,U_905) )
& ! [U_903,U_904,U_905,U_901] :
( apply(U_904,U_901) = apply(U_903,U_901)
| ~ in(U_901,relation_dom(U_904))
| ~ sP176(U_903,U_904,U_905,U_901) )
& ! [U_903,U_904,U_905,U_901] :
( relation_dom(U_904) = set_intersection2(relation_dom(U_903),U_905)
| ~ sP176(U_903,U_904,U_905,U_901) )
& ! [U_903,U_904,U_905,U_901] :
( U_904 = relation_dom_restriction(U_903,U_905)
| sP177(U_903,U_904,U_905)
| relation_dom(U_904) != set_intersection2(relation_dom(U_903),U_905)
| ~ sP178(U_903,U_904,U_905,U_901) )
& ! [U_903,U_904,U_905,U_901] :
( sP176(U_903,U_904,U_905,U_901)
| U_904 != relation_dom_restriction(U_903,U_905)
| ~ sP178(U_903,U_904,U_905,U_901) )
& ! [U_903,U_904,U_905,U_901] :
( sP178(U_903,U_904,U_905,U_901)
| ~ function(U_903)
| ~ relation(U_903)
| ~ function(U_904)
| ~ relation(U_904) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP176,sP177,sP178])],[f_246_3]) ).
cnf(f_246_5,plain,
( sP178(U_903,U_904,U_905,U_901)
| ~ function(U_903)
| ~ relation(U_903)
| ~ function(U_904)
| ~ relation(U_904) ),
inference(clausify,[status(thm)],[f_246_4]) ).
cnf(f_246_6,plain,
( sP176(U_903,U_904,U_905,U_901)
| U_904 != relation_dom_restriction(U_903,U_905)
| ~ sP178(U_903,U_904,U_905,U_901) ),
inference(clausify,[status(thm)],[f_246_4]) ).
cnf(f_246_7,plain,
( U_904 = relation_dom_restriction(U_903,U_905)
| sP177(U_903,U_904,U_905)
| relation_dom(U_904) != set_intersection2(relation_dom(U_903),U_905)
| ~ sP178(U_903,U_904,U_905,U_901) ),
inference(clausify,[status(thm)],[f_246_4]) ).
cnf(f_246_8,plain,
( relation_dom(U_904) = set_intersection2(relation_dom(U_903),U_905)
| ~ sP176(U_903,U_904,U_905,U_901) ),
inference(clausify,[status(thm)],[f_246_4]) ).
cnf(f_246_9,plain,
( apply(U_904,U_901) = apply(U_903,U_901)
| ~ in(U_901,relation_dom(U_904))
| ~ sP176(U_903,U_904,U_905,U_901) ),
inference(clausify,[status(thm)],[f_246_4]) ).
cnf(f_246_10,plain,
( in(sK125(U_905,U_904,U_903),relation_dom(U_904))
| ~ sP177(U_903,U_904,U_905) ),
inference(clausify,[status(thm)],[f_246_4]) ).
cnf(f_246_11,plain,
( apply(U_904,sK125(U_905,U_904,U_903)) != apply(U_903,sK125(U_905,U_904,U_903))
| ~ sP177(U_903,U_904,U_905) ),
inference(clausify,[status(thm)],[f_246_4]) ).
fof(f_247_1,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(fof_nnf,[status(thm)],[t69_enumset1]) ).
fof(f_247_2,plain,
! [U_906] : unordered_pair(U_906,U_906) = singleton(U_906),
inference(variable_rename,[status(thm)],[f_247_1]) ).
fof(f_247_3,plain,
! [U_906] : unordered_pair(U_906,U_906) = singleton(U_906),
inference(definitional_conversion,[status(esa)],[f_247_2]) ).
cnf(f_247_4,plain,
unordered_pair(U_906,U_906) = singleton(U_906),
inference(clausify,[status(thm)],[f_247_3]) ).
fof(f_248_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_248_2,plain,
! [U_907] :
( U_907 = empty_set
| ~ empty(U_907) ),
inference(variable_rename,[status(thm)],[f_248_1]) ).
fof(f_248_3,plain,
! [U_907] :
( U_907 = empty_set
| ~ empty(U_907) ),
inference(definitional_conversion,[status(esa)],[f_248_2]) ).
cnf(f_248_4,plain,
( U_907 = empty_set
| ~ empty(U_907) ),
inference(clausify,[status(thm)],[f_248_3]) ).
fof(f_249_1,plain,
! [A,B] :
( A = B
| ~ subset(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t6_zfmisc_1]) ).
fof(f_249_2,plain,
! [U_909,U_908] :
( U_909 = U_908
| ~ subset(singleton(U_909),singleton(U_908)) ),
inference(variable_rename,[status(thm)],[f_249_1]) ).
fof(f_249_3,plain,
! [U_909,U_908] :
( U_909 = U_908
| ~ subset(singleton(U_909),singleton(U_908)) ),
inference(definitional_conversion,[status(esa)],[f_249_2]) ).
cnf(f_249_4,plain,
( U_909 = U_908
| ~ subset(singleton(U_909),singleton(U_908)) ),
inference(clausify,[status(thm)],[f_249_3]) ).
fof(f_250_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_250_2,plain,
! [U_912,U_911,U_910] :
( apply(relation_dom_restriction(U_910,U_912),U_911) = apply(U_910,U_911)
| ~ in(U_911,relation_dom(relation_dom_restriction(U_910,U_912)))
| ~ function(U_910)
| ~ relation(U_910) ),
inference(variable_rename,[status(thm)],[f_250_1]) ).
fof(f_250_3,plain,
! [U_911,U_910,U_912] :
( apply(relation_dom_restriction(U_910,U_912),U_911) = apply(U_910,U_911)
| ~ in(U_911,relation_dom(relation_dom_restriction(U_910,U_912)))
| ~ function(U_910)
| ~ relation(U_910) ),
inference(definitional_conversion,[status(esa)],[f_250_2]) ).
cnf(f_250_4,plain,
( apply(relation_dom_restriction(U_910,U_912),U_911) = apply(U_910,U_911)
| ~ in(U_911,relation_dom(relation_dom_restriction(U_910,U_912)))
| ~ function(U_910)
| ~ relation(U_910) ),
inference(clausify,[status(thm)],[f_250_3]) ).
fof(f_251_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_251_2,plain,
! [U_913] :
( relation_rng(identity_relation(U_913)) = U_913
& relation_dom(identity_relation(U_913)) = U_913 ),
inference(variable_rename,[status(thm)],[f_251_1]) ).
fof(f_251_3,plain,
( ! [U_915] : relation_rng(identity_relation(U_915)) = U_915
& ! [U_914] : relation_dom(identity_relation(U_914)) = U_914 ),
inference(miniscope,[status(thm)],[f_251_2]) ).
fof(f_251_4,plain,
( ! [U_915] : relation_rng(identity_relation(U_915)) = U_915
& ! [U_914] : relation_dom(identity_relation(U_914)) = U_914 ),
inference(definitional_conversion,[status(esa)],[f_251_3]) ).
cnf(f_251_5,plain,
relation_dom(identity_relation(U_914)) = U_914,
inference(clausify,[status(thm)],[f_251_4]) ).
cnf(f_251_6,plain,
relation_rng(identity_relation(U_915)) = U_915,
inference(clausify,[status(thm)],[f_251_4]) ).
fof(f_252_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_252_2,plain,
! [U_918,U_917,U_916] :
( apply(relation_dom_restriction(U_916,U_918),U_917) = apply(U_916,U_917)
| ~ in(U_917,U_918)
| ~ function(U_916)
| ~ relation(U_916) ),
inference(variable_rename,[status(thm)],[f_252_1]) ).
fof(f_252_3,plain,
! [U_917,U_916,U_918] :
( apply(relation_dom_restriction(U_916,U_918),U_917) = apply(U_916,U_917)
| ~ in(U_917,U_918)
| ~ function(U_916)
| ~ relation(U_916) ),
inference(definitional_conversion,[status(esa)],[f_252_2]) ).
cnf(f_252_4,plain,
( apply(relation_dom_restriction(U_916,U_918),U_917) = apply(U_916,U_917)
| ~ in(U_917,U_918)
| ~ function(U_916)
| ~ relation(U_916) ),
inference(clausify,[status(thm)],[f_252_3]) ).
fof(f_253_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_253_2,plain,
! [U_922,U_921,U_920,U_919] :
( ( ( in(ordered_pair(U_922,U_921),relation_composition(identity_relation(U_920),U_919))
| ~ in(ordered_pair(U_922,U_921),U_919)
| ~ in(U_922,U_920) )
& ( ( in(ordered_pair(U_922,U_921),U_919)
& in(U_922,U_920) )
| ~ in(ordered_pair(U_922,U_921),relation_composition(identity_relation(U_920),U_919)) ) )
| ~ relation(U_919) ),
inference(variable_rename,[status(thm)],[f_253_1]) ).
fof(f_253_3,plain,
( ! [U_921,U_922,U_919,U_920] :
( in(ordered_pair(U_922,U_921),U_919)
| ~ sP179(U_921,U_922,U_919,U_920) )
& ! [U_921,U_922,U_919,U_920] :
( in(U_922,U_920)
| ~ sP179(U_921,U_922,U_919,U_920) )
& ! [U_921,U_922,U_919,U_920] :
( in(ordered_pair(U_922,U_921),relation_composition(identity_relation(U_920),U_919))
| ~ in(ordered_pair(U_922,U_921),U_919)
| ~ in(U_922,U_920)
| ~ sP180(U_921,U_922,U_919,U_920) )
& ! [U_921,U_922,U_919,U_920] :
( sP179(U_921,U_922,U_919,U_920)
| ~ in(ordered_pair(U_922,U_921),relation_composition(identity_relation(U_920),U_919))
| ~ sP180(U_921,U_922,U_919,U_920) )
& ! [U_921,U_922,U_919,U_920] :
( sP180(U_921,U_922,U_919,U_920)
| ~ relation(U_919) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP179,sP180])],[f_253_2]) ).
cnf(f_253_4,plain,
( sP180(U_921,U_922,U_919,U_920)
| ~ relation(U_919) ),
inference(clausify,[status(thm)],[f_253_3]) ).
cnf(f_253_5,plain,
( sP179(U_921,U_922,U_919,U_920)
| ~ in(ordered_pair(U_922,U_921),relation_composition(identity_relation(U_920),U_919))
| ~ sP180(U_921,U_922,U_919,U_920) ),
inference(clausify,[status(thm)],[f_253_3]) ).
cnf(f_253_6,plain,
( in(ordered_pair(U_922,U_921),relation_composition(identity_relation(U_920),U_919))
| ~ in(ordered_pair(U_922,U_921),U_919)
| ~ in(U_922,U_920)
| ~ sP180(U_921,U_922,U_919,U_920) ),
inference(clausify,[status(thm)],[f_253_3]) ).
cnf(f_253_7,plain,
( in(U_922,U_920)
| ~ sP179(U_921,U_922,U_919,U_920) ),
inference(clausify,[status(thm)],[f_253_3]) ).
cnf(f_253_8,plain,
( in(ordered_pair(U_922,U_921),U_919)
| ~ sP179(U_921,U_922,U_919,U_920) ),
inference(clausify,[status(thm)],[f_253_3]) ).
fof(f_254_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_254_2,plain,
! [U_924,U_923] :
( ~ empty(U_923)
| ~ in(U_924,U_923) ),
inference(variable_rename,[status(thm)],[f_254_1]) ).
fof(f_254_3,plain,
! [U_924,U_923] :
( ~ empty(U_923)
| ~ in(U_924,U_923) ),
inference(definitional_conversion,[status(esa)],[f_254_2]) ).
cnf(f_254_4,plain,
( ~ empty(U_923)
| ~ in(U_924,U_923) ),
inference(clausify,[status(thm)],[f_254_3]) ).
fof(f_255_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_255_2,plain,
! [U_928,U_927] :
( ? [U_926] :
( ! [U_925] :
( ~ in(U_925,U_926)
| ~ in(U_925,U_927) )
& in(U_926,U_927) )
| ~ in(U_928,U_927) ),
inference(variable_rename,[status(thm)],[f_255_1]) ).
fof(f_255_3,plain,
! [U_928,U_927] :
( ( ! [U_925] :
( ~ in(U_925,sK126(U_928,U_927))
| ~ in(U_925,U_927) )
& in(sK126(U_928,U_927),U_927) )
| ~ in(U_928,U_927) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK126]),skolemize(U_926,sK126(U_928,U_927))],[f_255_2]) ).
fof(f_255_4,plain,
( ! [U_927,U_928,U_925] :
( ~ in(U_925,sK126(U_928,U_927))
| ~ in(U_925,U_927)
| ~ sP181(U_927,U_928,U_925) )
& ! [U_927,U_928,U_925] :
( in(sK126(U_928,U_927),U_927)
| ~ sP181(U_927,U_928,U_925) )
& ! [U_927,U_928,U_925] :
( sP181(U_927,U_928,U_925)
| ~ in(U_928,U_927) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP181])],[f_255_3]) ).
cnf(f_255_5,plain,
( sP181(U_927,U_928,U_925)
| ~ in(U_928,U_927) ),
inference(clausify,[status(thm)],[f_255_4]) ).
cnf(f_255_6,plain,
( in(sK126(U_928,U_927),U_927)
| ~ sP181(U_927,U_928,U_925) ),
inference(clausify,[status(thm)],[f_255_4]) ).
cnf(f_255_7,plain,
( ~ in(U_925,sK126(U_928,U_927))
| ~ in(U_925,U_927)
| ~ sP181(U_927,U_928,U_925) ),
inference(clausify,[status(thm)],[f_255_4]) ).
fof(f_256_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1]) ).
fof(f_256_2,plain,
! [U_930,U_929] : subset(U_930,set_union2(U_930,U_929)),
inference(variable_rename,[status(thm)],[f_256_1]) ).
fof(f_256_3,plain,
! [U_929,U_930] : subset(U_930,set_union2(U_930,U_929)),
inference(definitional_conversion,[status(esa)],[f_256_2]) ).
cnf(f_256_4,plain,
subset(U_930,set_union2(U_930,U_929)),
inference(clausify,[status(thm)],[f_256_3]) ).
fof(f_257_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_257_2,plain,
! [U_932,U_931] :
( ( disjoint(U_932,U_931)
| set_difference(U_932,U_931) != U_932 )
& ( set_difference(U_932,U_931) = U_932
| ~ disjoint(U_932,U_931) ) ),
inference(variable_rename,[status(thm)],[f_257_1]) ).
fof(f_257_3,plain,
( ! [U_936,U_934] :
( disjoint(U_936,U_934)
| set_difference(U_936,U_934) != U_936 )
& ! [U_935,U_933] :
( set_difference(U_935,U_933) = U_935
| ~ disjoint(U_935,U_933) ) ),
inference(miniscope,[status(thm)],[f_257_2]) ).
fof(f_257_4,plain,
( ! [U_934,U_936] :
( disjoint(U_936,U_934)
| set_difference(U_936,U_934) != U_936 )
& ! [U_935,U_933] :
( set_difference(U_935,U_933) = U_935
| ~ disjoint(U_935,U_933) ) ),
inference(definitional_conversion,[status(esa)],[f_257_3]) ).
cnf(f_257_5,plain,
( set_difference(U_935,U_933) = U_935
| ~ disjoint(U_935,U_933) ),
inference(clausify,[status(thm)],[f_257_4]) ).
cnf(f_257_6,plain,
( disjoint(U_936,U_934)
| set_difference(U_936,U_934) != U_936 ),
inference(clausify,[status(thm)],[f_257_4]) ).
fof(f_258_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_258_2,plain,
! [U_939,U_938,U_937] :
( ( ( in(U_939,relation_dom(relation_dom_restriction(U_937,U_938)))
| ~ in(U_939,relation_dom(U_937))
| ~ in(U_939,U_938) )
& ( ( in(U_939,relation_dom(U_937))
& in(U_939,U_938) )
| ~ in(U_939,relation_dom(relation_dom_restriction(U_937,U_938))) ) )
| ~ relation(U_937) ),
inference(variable_rename,[status(thm)],[f_258_1]) ).
fof(f_258_3,plain,
( ! [U_937,U_939,U_938] :
( in(U_939,relation_dom(U_937))
| ~ sP182(U_937,U_939,U_938) )
& ! [U_937,U_939,U_938] :
( in(U_939,U_938)
| ~ sP182(U_937,U_939,U_938) )
& ! [U_937,U_939,U_938] :
( in(U_939,relation_dom(relation_dom_restriction(U_937,U_938)))
| ~ in(U_939,relation_dom(U_937))
| ~ in(U_939,U_938)
| ~ sP183(U_937,U_939,U_938) )
& ! [U_937,U_939,U_938] :
( sP182(U_937,U_939,U_938)
| ~ in(U_939,relation_dom(relation_dom_restriction(U_937,U_938)))
| ~ sP183(U_937,U_939,U_938) )
& ! [U_937,U_939,U_938] :
( sP183(U_937,U_939,U_938)
| ~ relation(U_937) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP182,sP183])],[f_258_2]) ).
cnf(f_258_4,plain,
( sP183(U_937,U_939,U_938)
| ~ relation(U_937) ),
inference(clausify,[status(thm)],[f_258_3]) ).
cnf(f_258_5,plain,
( sP182(U_937,U_939,U_938)
| ~ in(U_939,relation_dom(relation_dom_restriction(U_937,U_938)))
| ~ sP183(U_937,U_939,U_938) ),
inference(clausify,[status(thm)],[f_258_3]) ).
cnf(f_258_6,plain,
( in(U_939,relation_dom(relation_dom_restriction(U_937,U_938)))
| ~ in(U_939,relation_dom(U_937))
| ~ in(U_939,U_938)
| ~ sP183(U_937,U_939,U_938) ),
inference(clausify,[status(thm)],[f_258_3]) ).
cnf(f_258_7,plain,
( in(U_939,U_938)
| ~ sP182(U_937,U_939,U_938) ),
inference(clausify,[status(thm)],[f_258_3]) ).
cnf(f_258_8,plain,
( in(U_939,relation_dom(U_937))
| ~ sP182(U_937,U_939,U_938) ),
inference(clausify,[status(thm)],[f_258_3]) ).
fof(f_259_1,plain,
! [A,B] :
( subset(relation_dom_restriction(B,A),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t88_relat_1]) ).
fof(f_259_2,plain,
! [U_941,U_940] :
( subset(relation_dom_restriction(U_940,U_941),U_940)
| ~ relation(U_940) ),
inference(variable_rename,[status(thm)],[f_259_1]) ).
fof(f_259_3,plain,
! [U_940,U_941] :
( subset(relation_dom_restriction(U_940,U_941),U_940)
| ~ relation(U_940) ),
inference(definitional_conversion,[status(esa)],[f_259_2]) ).
cnf(f_259_4,plain,
( subset(relation_dom_restriction(U_940,U_941),U_940)
| ~ relation(U_940) ),
inference(clausify,[status(thm)],[f_259_3]) ).
fof(f_260_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_260_2,plain,
! [U_943,U_942] :
( ~ empty(U_942)
| U_943 = U_942
| ~ empty(U_943) ),
inference(variable_rename,[status(thm)],[f_260_1]) ).
fof(f_260_3,plain,
! [U_943] :
( ! [U_942] :
( ~ empty(U_942)
| U_943 = U_942 )
| ~ empty(U_943) ),
inference(miniscope,[status(thm)],[f_260_2]) ).
fof(f_260_4,plain,
! [U_942,U_943] :
( ~ empty(U_942)
| U_943 = U_942
| ~ empty(U_943) ),
inference(definitional_conversion,[status(esa)],[f_260_3]) ).
cnf(f_260_5,plain,
( ~ empty(U_942)
| U_943 = U_942
| ~ empty(U_943) ),
inference(clausify,[status(thm)],[f_260_4]) ).
fof(f_261_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_261_2,plain,
! [U_946,U_945,U_944] :
( ( ( in(ordered_pair(U_946,U_945),U_944)
| U_945 != apply(U_944,U_946)
| ~ in(U_946,relation_dom(U_944)) )
& ( ( U_945 = apply(U_944,U_946)
& in(U_946,relation_dom(U_944)) )
| ~ in(ordered_pair(U_946,U_945),U_944) ) )
| ~ function(U_944)
| ~ relation(U_944) ),
inference(variable_rename,[status(thm)],[f_261_1]) ).
fof(f_261_3,plain,
( ! [U_946,U_944,U_945] :
( U_945 = apply(U_944,U_946)
| ~ sP184(U_946,U_944,U_945) )
& ! [U_946,U_944,U_945] :
( in(U_946,relation_dom(U_944))
| ~ sP184(U_946,U_944,U_945) )
& ! [U_946,U_944,U_945] :
( in(ordered_pair(U_946,U_945),U_944)
| U_945 != apply(U_944,U_946)
| ~ in(U_946,relation_dom(U_944))
| ~ sP185(U_946,U_944,U_945) )
& ! [U_946,U_944,U_945] :
( sP184(U_946,U_944,U_945)
| ~ in(ordered_pair(U_946,U_945),U_944)
| ~ sP185(U_946,U_944,U_945) )
& ! [U_946,U_944,U_945] :
( sP185(U_946,U_944,U_945)
| ~ function(U_944)
| ~ relation(U_944) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP184,sP185])],[f_261_2]) ).
cnf(f_261_4,plain,
( sP185(U_946,U_944,U_945)
| ~ function(U_944)
| ~ relation(U_944) ),
inference(clausify,[status(thm)],[f_261_3]) ).
cnf(f_261_5,plain,
( sP184(U_946,U_944,U_945)
| ~ in(ordered_pair(U_946,U_945),U_944)
| ~ sP185(U_946,U_944,U_945) ),
inference(clausify,[status(thm)],[f_261_3]) ).
cnf(f_261_6,plain,
( in(ordered_pair(U_946,U_945),U_944)
| U_945 != apply(U_944,U_946)
| ~ in(U_946,relation_dom(U_944))
| ~ sP185(U_946,U_944,U_945) ),
inference(clausify,[status(thm)],[f_261_3]) ).
cnf(f_261_7,plain,
( in(U_946,relation_dom(U_944))
| ~ sP184(U_946,U_944,U_945) ),
inference(clausify,[status(thm)],[f_261_3]) ).
cnf(f_261_8,plain,
( U_945 = apply(U_944,U_946)
| ~ sP184(U_946,U_944,U_945) ),
inference(clausify,[status(thm)],[f_261_3]) ).
fof(f_262_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_262_2,plain,
! [U_949,U_948,U_947] :
( subset(set_union2(U_949,U_947),U_948)
| ~ subset(U_947,U_948)
| ~ subset(U_949,U_948) ),
inference(variable_rename,[status(thm)],[f_262_1]) ).
fof(f_262_3,plain,
! [U_948,U_949,U_947] :
( subset(set_union2(U_949,U_947),U_948)
| ~ subset(U_947,U_948)
| ~ subset(U_949,U_948) ),
inference(definitional_conversion,[status(esa)],[f_262_2]) ).
cnf(f_262_4,plain,
( subset(set_union2(U_949,U_947),U_948)
| ~ subset(U_947,U_948)
| ~ subset(U_949,U_948) ),
inference(clausify,[status(thm)],[f_262_3]) ).
fof(f_263_1,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t8_zfmisc_1]) ).
fof(f_263_2,plain,
! [U_952,U_951,U_950] :
( U_952 = U_951
| singleton(U_952) != unordered_pair(U_951,U_950) ),
inference(variable_rename,[status(thm)],[f_263_1]) ).
fof(f_263_3,plain,
! [U_952,U_951] :
( ! [U_950] : singleton(U_952) != unordered_pair(U_951,U_950)
| U_952 = U_951 ),
inference(miniscope,[status(thm)],[f_263_2]) ).
fof(f_263_4,plain,
! [U_952,U_951,U_950] :
( singleton(U_952) != unordered_pair(U_951,U_950)
| U_952 = U_951 ),
inference(definitional_conversion,[status(esa)],[f_263_3]) ).
cnf(f_263_5,plain,
( singleton(U_952) != unordered_pair(U_951,U_950)
| U_952 = U_951 ),
inference(clausify,[status(thm)],[f_263_4]) ).
fof(f_264_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_264_2,plain,
! [U_954,U_953] :
( relation_dom(relation_dom_restriction(U_953,U_954)) = set_intersection2(relation_dom(U_953),U_954)
| ~ relation(U_953) ),
inference(variable_rename,[status(thm)],[f_264_1]) ).
fof(f_264_3,plain,
! [U_954,U_953] :
( relation_dom(relation_dom_restriction(U_953,U_954)) = set_intersection2(relation_dom(U_953),U_954)
| ~ relation(U_953) ),
inference(definitional_conversion,[status(esa)],[f_264_2]) ).
cnf(f_264_4,plain,
( relation_dom(relation_dom_restriction(U_953,U_954)) = set_intersection2(relation_dom(U_953),U_954)
| ~ relation(U_953) ),
inference(clausify,[status(thm)],[f_264_3]) ).
fof(f_265_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t92_zfmisc_1]) ).
fof(f_265_2,plain,
! [U_956,U_955] :
( subset(U_956,union(U_955))
| ~ in(U_956,U_955) ),
inference(variable_rename,[status(thm)],[f_265_1]) ).
fof(f_265_3,plain,
! [U_955,U_956] :
( subset(U_956,union(U_955))
| ~ in(U_956,U_955) ),
inference(definitional_conversion,[status(esa)],[f_265_2]) ).
cnf(f_265_4,plain,
( subset(U_956,union(U_955))
| ~ in(U_956,U_955) ),
inference(clausify,[status(thm)],[f_265_3]) ).
fof(f_266_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_266_2,plain,
! [U_958,U_957] :
( relation_dom_restriction(U_957,U_958) = relation_composition(identity_relation(U_958),U_957)
| ~ relation(U_957) ),
inference(variable_rename,[status(thm)],[f_266_1]) ).
fof(f_266_3,plain,
! [U_957,U_958] :
( relation_dom_restriction(U_957,U_958) = relation_composition(identity_relation(U_958),U_957)
| ~ relation(U_957) ),
inference(definitional_conversion,[status(esa)],[f_266_2]) ).
cnf(f_266_4,plain,
( relation_dom_restriction(U_957,U_958) = relation_composition(identity_relation(U_958),U_957)
| ~ relation(U_957) ),
inference(clausify,[status(thm)],[f_266_3]) ).
fof(f_267_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_267_2,plain,
! [U_960,U_959] :
( subset(relation_rng(relation_dom_restriction(U_959,U_960)),relation_rng(U_959))
| ~ relation(U_959) ),
inference(variable_rename,[status(thm)],[f_267_1]) ).
fof(f_267_3,plain,
! [U_959,U_960] :
( subset(relation_rng(relation_dom_restriction(U_959,U_960)),relation_rng(U_959))
| ~ relation(U_959) ),
inference(definitional_conversion,[status(esa)],[f_267_2]) ).
cnf(f_267_4,plain,
( subset(relation_rng(relation_dom_restriction(U_959,U_960)),relation_rng(U_959))
| ~ relation(U_959) ),
inference(clausify,[status(thm)],[f_267_3]) ).
fof(f_268_1,plain,
! [A] : union(powerset(A)) = A,
inference(fof_nnf,[status(thm)],[t99_zfmisc_1]) ).
fof(f_268_2,plain,
! [U_961] : union(powerset(U_961)) = U_961,
inference(variable_rename,[status(thm)],[f_268_1]) ).
fof(f_268_3,plain,
! [U_961] : union(powerset(U_961)) = U_961,
inference(definitional_conversion,[status(esa)],[f_268_2]) ).
cnf(f_268_4,plain,
union(powerset(U_961)) = U_961,
inference(clausify,[status(thm)],[f_268_3]) ).
fof(f_269_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_269_2,plain,
! [U_969] :
? [U_968] :
( ! [U_967] :
( in(U_967,U_968)
| are_equipotent(U_967,U_968)
| ~ subset(U_967,U_968) )
& ! [U_966] :
( ? [U_965] :
( ! [U_964] :
( in(U_964,U_965)
| ~ subset(U_964,U_966) )
& in(U_965,U_968) )
| ~ in(U_966,U_968) )
& ! [U_963,U_962] :
( in(U_962,U_968)
| ~ subset(U_962,U_963)
| ~ in(U_963,U_968) )
& in(U_969,U_968) ),
inference(variable_rename,[status(thm)],[f_269_1]) ).
fof(f_269_3,plain,
! [U_969] :
( ! [U_967] :
( in(U_967,sK127(U_969))
| are_equipotent(U_967,sK127(U_969))
| ~ subset(U_967,sK127(U_969)) )
& ! [U_966] :
( ? [U_965] :
( ! [U_964] :
( in(U_964,U_965)
| ~ subset(U_964,U_966) )
& in(U_965,sK127(U_969)) )
| ~ in(U_966,sK127(U_969)) )
& ! [U_963,U_962] :
( in(U_962,sK127(U_969))
| ~ subset(U_962,U_963)
| ~ in(U_963,sK127(U_969)) )
& in(U_969,sK127(U_969)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK127]),skolemize(U_968,sK127(U_969))],[f_269_2]) ).
fof(f_269_4,plain,
! [U_969] :
( ! [U_967] :
( in(U_967,sK127(U_969))
| are_equipotent(U_967,sK127(U_969))
| ~ subset(U_967,sK127(U_969)) )
& ! [U_966] :
( ( ! [U_964] :
( in(U_964,sK128(U_969,U_966))
| ~ subset(U_964,U_966) )
& in(sK128(U_969,U_966),sK127(U_969)) )
| ~ in(U_966,sK127(U_969)) )
& ! [U_963,U_962] :
( in(U_962,sK127(U_969))
| ~ subset(U_962,U_963)
| ~ in(U_963,sK127(U_969)) )
& in(U_969,sK127(U_969)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK128]),skolemize(U_965,sK128(U_969,U_966))],[f_269_3]) ).
fof(f_269_5,plain,
( ! [U_964,U_966,U_969] :
( in(U_964,sK128(U_969,U_966))
| ~ subset(U_964,U_966)
| ~ sP186(U_964,U_966,U_969) )
& ! [U_964,U_966,U_969] :
( in(sK128(U_969,U_966),sK127(U_969))
| ~ sP186(U_964,U_966,U_969) )
& ! [U_967,U_969] :
( in(U_967,sK127(U_969))
| are_equipotent(U_967,sK127(U_969))
| ~ subset(U_967,sK127(U_969)) )
& ! [U_964,U_966,U_969] :
( sP186(U_964,U_966,U_969)
| ~ in(U_966,sK127(U_969)) )
& ! [U_963,U_962,U_969] :
( in(U_962,sK127(U_969))
| ~ subset(U_962,U_963)
| ~ in(U_963,sK127(U_969)) )
& ! [U_969] : in(U_969,sK127(U_969)) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP186])],[f_269_4]) ).
cnf(f_269_6,plain,
in(U_969,sK127(U_969)),
inference(clausify,[status(thm)],[f_269_5]) ).
cnf(f_269_7,plain,
( in(U_962,sK127(U_969))
| ~ subset(U_962,U_963)
| ~ in(U_963,sK127(U_969)) ),
inference(clausify,[status(thm)],[f_269_5]) ).
cnf(f_269_8,plain,
( sP186(U_964,U_966,U_969)
| ~ in(U_966,sK127(U_969)) ),
inference(clausify,[status(thm)],[f_269_5]) ).
cnf(f_269_9,plain,
( in(U_967,sK127(U_969))
| are_equipotent(U_967,sK127(U_969))
| ~ subset(U_967,sK127(U_969)) ),
inference(clausify,[status(thm)],[f_269_5]) ).
cnf(f_269_10,plain,
( in(sK128(U_969,U_966),sK127(U_969))
| ~ sP186(U_964,U_966,U_969) ),
inference(clausify,[status(thm)],[f_269_5]) ).
cnf(f_269_11,plain,
( in(U_964,sK128(U_969,U_966))
| ~ subset(U_964,U_966)
| ~ sP186(U_964,U_966,U_969) ),
inference(clausify,[status(thm)],[f_269_5]) ).
fof(f_270_1,plain,
! [A,B,C] :
( B = C
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t9_zfmisc_1]) ).
fof(f_270_2,plain,
! [U_972,U_971,U_970] :
( U_971 = U_970
| singleton(U_972) != unordered_pair(U_971,U_970) ),
inference(variable_rename,[status(thm)],[f_270_1]) ).
fof(f_270_3,plain,
! [U_970,U_971,U_972] :
( U_971 = U_970
| singleton(U_972) != unordered_pair(U_971,U_970) ),
inference(definitional_conversion,[status(esa)],[f_270_2]) ).
cnf(f_270_4,plain,
( U_971 = U_970
| singleton(U_972) != unordered_pair(U_971,U_970) ),
inference(clausify,[status(thm)],[f_270_3]) ).
cnf(f_55_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_55_3]) ).
cnf(f_56_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_56_3]) ).
cnf(f_57_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_57_3]) ).
cnf(f_58_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_58_3]) ).
cnf(f_59_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_59_3]) ).
cnf(f_60_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_60_3]) ).
cnf(f_61_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_61_3]) ).
cnf(f_62_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_62_3]) ).
cnf(f_63_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_63_3]) ).
cnf(f_65_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_65_3]) ).
cnf(f_67_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_67_3]) ).
cnf(f_68_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_68_3]) ).
cnf(f_69_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_69_3]) ).
cnf(f_70_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_70_3]) ).
cnf(f_72_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_72_3]) ).
cnf(f_73_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_73_3]) ).
cnf(f_75_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_75_3]) ).
cnf(f_76_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_76_3]) ).
cnf(f_85_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_85_3]) ).
cnf(f_86_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_86_3]) ).
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_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_15,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_16,axiom,
( succ(Eq_x_0) = succ(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( set_meet(Eq_x_0) = set_meet(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,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_21,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_22,axiom,
( union(Eq_x_0) = union(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,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_24,axiom,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,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_26,axiom,
( relation_field(Eq_x_0) = relation_field(Eq_y_0)
| 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,Eq_x_2) = sK32(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_66,axiom,
( sK33(Eq_x_0,Eq_x_1) = sK33(Eq_y_0,Eq_y_1)
| 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) = sK38(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_72,axiom,
( sK39(Eq_x_0,Eq_x_1) = sK39(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_73,axiom,
( 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) = sK41(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_75,axiom,
( sK42(Eq_x_0,Eq_x_1) = sK42(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_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,Eq_x_2) = sK46(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_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,Eq_x_3) = sK50(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_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) = sK52(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_86,axiom,
( 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) = sK56(Eq_y_0)
| 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,Eq_x_1) = sK58(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| 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,Eq_x_2) = sK61(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_95,axiom,
( 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) = sK64(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_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,Eq_x_2) = sK67(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_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) = sK70(Eq_y_0,Eq_y_1)
| 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,Eq_x_2) = sK71(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_105,axiom,
( sK72(Eq_x_0,Eq_x_1,Eq_x_2) = sK72(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_106,axiom,
( sK73(Eq_x_0,Eq_x_1,Eq_x_2) = sK73(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_107,axiom,
( sK74(Eq_x_0,Eq_x_1) = sK74(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_108,axiom,
( sK75(Eq_x_0,Eq_x_1) = sK75(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_109,axiom,
( sK76(Eq_x_0,Eq_x_1) = sK76(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_110,axiom,
( sK77(Eq_x_0,Eq_x_1,Eq_x_2) = sK77(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_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) = sK80(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_114,axiom,
( 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) = sK85(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_119,axiom,
( sK86(Eq_x_0) = sK86(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_120,axiom,
( sK87(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK87(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_121,axiom,
( sK88(Eq_x_0,Eq_x_1,Eq_x_2) = sK88(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_122,axiom,
( sK89(Eq_x_0,Eq_x_1,Eq_x_2) = sK89(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_123,axiom,
( sK90(Eq_x_0,Eq_x_1,Eq_x_2) = sK90(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_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) = sK94(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_128,axiom,
( sK95(Eq_x_0,Eq_x_1) = sK95(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_129,axiom,
( sK99(Eq_x_0) = sK99(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_130,axiom,
( sK104(Eq_x_0) = sK104(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_131,axiom,
( sK110(Eq_x_0) = sK110(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_132,axiom,
( sK111(Eq_x_0,Eq_x_1,Eq_x_2) = sK111(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,
( sK112(Eq_x_0,Eq_x_1,Eq_x_2) = sK112(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_134,axiom,
( sK113(Eq_x_0,Eq_x_1) = sK113(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_135,axiom,
( sK114(Eq_x_0,Eq_x_1) = sK114(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_136,axiom,
( sK116(Eq_x_0,Eq_x_1) = sK116(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_137,axiom,
( sK117(Eq_x_0,Eq_x_1) = sK117(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_138,axiom,
( sK118(Eq_x_0,Eq_x_1) = sK118(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,
( sK119(Eq_x_0,Eq_x_1) = sK119(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_140,axiom,
( sK120(Eq_x_0,Eq_x_1) = sK120(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_141,axiom,
( sK121(Eq_x_0,Eq_x_1) = sK121(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_142,axiom,
( sK122(Eq_x_0,Eq_x_1) = sK122(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_143,axiom,
( sK123(Eq_x_0) = sK123(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_144,axiom,
( sK124(Eq_x_0) = sK124(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_145,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_146,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_147,axiom,
( sK127(Eq_x_0) = sK127(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_148,axiom,
( sK128(Eq_x_0,Eq_x_1) = sK128(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,
( 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_150,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_151,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_152,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_153,axiom,
( ordinal(Eq_y_0)
| ~ ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_154,axiom,
( epsilon_transitive(Eq_y_0)
| ~ epsilon_transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_155,axiom,
( epsilon_connected(Eq_y_0)
| ~ epsilon_connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_156,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_157,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_158,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_159,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_160,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_161,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_162,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(equality_163,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_164,axiom,
( sP1(Eq_y_0)
| ~ sP1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_165,axiom,
( sP2(Eq_y_0)
| ~ sP2(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_166,axiom,
( sP3(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP3(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_167,axiom,
( sP4(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP4(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| 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_predicates]) ).
cnf(equality_168,axiom,
( sP5(Eq_y_0,Eq_y_1)
| ~ sP5(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_169,axiom,
( sP6(Eq_y_0,Eq_y_1)
| ~ sP6(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_170,axiom,
( sP7(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP7(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| 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_predicates]) ).
cnf(equality_171,axiom,
( sP8(Eq_y_0,Eq_y_1)
| ~ sP8(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_172,axiom,
( sP9(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP9(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_173,axiom,
( sP10(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP10(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| 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_predicates]) ).
cnf(equality_174,axiom,
( sP11(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP11(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_175,axiom,
( sP12(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP12(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_176,axiom,
( sP13(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP13(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| 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_predicates]) ).
cnf(equality_177,axiom,
( sP14(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP14(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_178,axiom,
( sP15(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP15(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| 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_predicates]) ).
cnf(equality_179,axiom,
( sP16(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP16(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_180,axiom,
( sP17(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP17(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_181,axiom,
( sP18(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8)
| ~ sP18(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8)
| Eq_x_8 != Eq_y_8
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| 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_predicates]) ).
cnf(equality_182,axiom,
( sP19(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP19(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_183,axiom,
( sP20(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP20(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| 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_predicates]) ).
cnf(equality_184,axiom,
( sP21(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP21(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_185,axiom,
( sP22(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP22(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_186,axiom,
( sP23(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP23(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| 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_predicates]) ).
cnf(equality_187,axiom,
( sP24(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP24(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_188,axiom,
( sP25(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP25(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_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_predicates]) ).
cnf(equality_189,axiom,
( sP26(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP26(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_190,axiom,
( sP27(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP27(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_191,axiom,
( sP28(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP28(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| 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_predicates]) ).
cnf(equality_192,axiom,
( sP29(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP29(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_193,axiom,
( sP30(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP30(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| 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_predicates]) ).
cnf(equality_194,axiom,
( sP31(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP31(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_195,axiom,
( sP32(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP32(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_196,axiom,
( sP33(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8)
| ~ sP33(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8)
| Eq_x_8 != Eq_y_8
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| 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_predicates]) ).
cnf(equality_197,axiom,
( sP34(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP34(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_198,axiom,
( sP35(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP35(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| 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_predicates]) ).
cnf(equality_199,axiom,
( sP36(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP36(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_200,axiom,
( sP37(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP37(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_201,axiom,
( sP38(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8)
| ~ sP38(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8)
| Eq_x_8 != Eq_y_8
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| 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_predicates]) ).
cnf(equality_202,axiom,
( sP39(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP39(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_203,axiom,
( sP40(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP40(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| 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_predicates]) ).
cnf(equality_204,axiom,
( sP41(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP41(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_205,axiom,
( sP42(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP42(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_206,axiom,
( sP43(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP43(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_207,axiom,
( sP44(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP44(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_208,axiom,
( sP45(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP45(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_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_predicates]) ).
cnf(equality_209,axiom,
( sP46(Eq_y_0,Eq_y_1)
| ~ sP46(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_210,axiom,
( sP47(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP47(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_211,axiom,
( sP48(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP48(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| 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_predicates]) ).
cnf(equality_212,axiom,
( sP49(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP49(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_213,axiom,
( sP50(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP50(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_214,axiom,
( sP51(Eq_y_0,Eq_y_1)
| ~ sP51(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_215,axiom,
( sP52(Eq_y_0,Eq_y_1)
| ~ sP52(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_216,axiom,
( sP53(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP53(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_217,axiom,
( sP54(Eq_y_0,Eq_y_1)
| ~ sP54(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_218,axiom,
( sP55(Eq_y_0,Eq_y_1)
| ~ sP55(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_219,axiom,
( sP56(Eq_y_0)
| ~ sP56(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_220,axiom,
( sP57(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP57(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| 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_predicates]) ).
cnf(equality_221,axiom,
( sP58(Eq_y_0,Eq_y_1)
| ~ sP58(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_222,axiom,
( sP59(Eq_y_0,Eq_y_1)
| ~ sP59(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_223,axiom,
( sP60(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP60(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| 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_predicates]) ).
cnf(equality_224,axiom,
( sP61(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP61(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_225,axiom,
( sP62(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP62(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_226,axiom,
( sP63(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP63(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_227,axiom,
( sP64(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP64(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_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_predicates]) ).
cnf(equality_228,axiom,
( sP65(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP65(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_229,axiom,
( sP66(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP66(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_230,axiom,
( sP67(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP67(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_231,axiom,
( sP68(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP68(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_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_predicates]) ).
cnf(equality_232,axiom,
( sP69(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP69(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_233,axiom,
( sP70(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP70(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_234,axiom,
( sP71(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP71(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_235,axiom,
( sP72(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP72(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| 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_predicates]) ).
cnf(equality_236,axiom,
( sP73(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP73(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_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_predicates]) ).
cnf(equality_237,axiom,
( sP74(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP74(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_238,axiom,
( sP75(Eq_y_0)
| ~ sP75(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_239,axiom,
( sP76(Eq_y_0,Eq_y_1)
| ~ sP76(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_240,axiom,
( sP77(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP77(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_241,axiom,
( sP78(Eq_y_0,Eq_y_1)
| ~ sP78(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_242,axiom,
( sP79(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP79(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_243,axiom,
( sP80(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP80(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_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_predicates]) ).
cnf(equality_244,axiom,
( sP81(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP81(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_245,axiom,
( sP82(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP82(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_246,axiom,
( sP83(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP83(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_247,axiom,
( sP84(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP84(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_248,axiom,
( sP85(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP85(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| 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_predicates]) ).
cnf(equality_249,axiom,
( sP86(Eq_y_0)
| ~ sP86(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_250,axiom,
( sP87(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP87(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_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_predicates]) ).
cnf(equality_251,axiom,
( sP88(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP88(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_252,axiom,
( sP89(Eq_y_0,Eq_y_1)
| ~ sP89(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_253,axiom,
( sP90(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP90(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| 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_predicates]) ).
cnf(equality_254,axiom,
( sP91(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP91(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_255,axiom,
( sP92(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP92(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_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_predicates]) ).
cnf(equality_256,axiom,
( sP93(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP93(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_257,axiom,
( sP94(Eq_y_0,Eq_y_1)
| ~ sP94(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_258,axiom,
( sP95(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP95(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_259,axiom,
( sP96(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP96(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_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_predicates]) ).
cnf(equality_260,axiom,
( sP97(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP97(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_261,axiom,
( sP98(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP98(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_262,axiom,
( sP99(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP99(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_263,axiom,
( sP100(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP100(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_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_predicates]) ).
cnf(equality_264,axiom,
( sP101(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP101(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_265,axiom,
( sP102(Eq_y_0,Eq_y_1)
| ~ sP102(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_266,axiom,
( sP103(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP103(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| 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_predicates]) ).
cnf(equality_267,axiom,
( sP104(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP104(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_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_predicates]) ).
cnf(equality_268,axiom,
( sP105(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP105(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_269,axiom,
( sP106(Eq_y_0,Eq_y_1)
| ~ sP106(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_270,axiom,
( sP107(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP107(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| 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_predicates]) ).
cnf(equality_271,axiom,
( sP108(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP108(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| 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_predicates]) ).
cnf(equality_272,axiom,
( sP109(Eq_y_0,Eq_y_1)
| ~ sP109(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_273,axiom,
( sP110(Eq_y_0,Eq_y_1)
| ~ sP110(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_274,axiom,
( sP111(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP111(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| 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_predicates]) ).
cnf(equality_275,axiom,
( sP112(Eq_y_0)
| ~ sP112(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_276,axiom,
( sP113(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP113(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_277,axiom,
( sP114(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP114(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_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_predicates]) ).
cnf(equality_278,axiom,
( sP115(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| ~ sP115(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7)
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| 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_predicates]) ).
cnf(equality_279,axiom,
( sP116(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP116(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_280,axiom,
( sP117(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP117(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_281,axiom,
( sP118(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8)
| ~ sP118(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8)
| Eq_x_8 != Eq_y_8
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| 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_predicates]) ).
cnf(equality_282,axiom,
( sP119(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP119(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_283,axiom,
( sP120(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP120(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_284,axiom,
( sP121(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP121(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_285,axiom,
( sP122(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP122(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_286,axiom,
( sP123(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP123(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_287,axiom,
( sP124(Eq_y_0,Eq_y_1)
| ~ sP124(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_288,axiom,
( sP125(Eq_y_0)
| ~ sP125(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_289,axiom,
( sP126(Eq_y_0,Eq_y_1)
| ~ sP126(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_290,axiom,
( sP127(Eq_y_0)
| ~ sP127(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_291,axiom,
( sP128(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP128(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_292,axiom,
( sP129(Eq_y_0,Eq_y_1)
| ~ sP129(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_293,axiom,
( sP130(Eq_y_0)
| ~ sP130(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_294,axiom,
( sP131(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP131(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_295,axiom,
( sP132(Eq_y_0)
| ~ sP132(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_296,axiom,
( sP133(Eq_y_0)
| ~ sP133(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_297,axiom,
( sP134(Eq_y_0,Eq_y_1)
| ~ sP134(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_298,axiom,
( sP135(Eq_y_0,Eq_y_1)
| ~ sP135(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_299,axiom,
( sP136(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP136(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_300,axiom,
( sP137(Eq_y_0,Eq_y_1)
| ~ sP137(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_301,axiom,
( sP138(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP138(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_302,axiom,
( sP139(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP139(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_303,axiom,
( sP140(Eq_y_0)
| ~ sP140(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_304,axiom,
( sP141(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP141(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_305,axiom,
( sP142(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP142(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_306,axiom,
( sP143(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP143(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_307,axiom,
( sP144(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP144(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_308,axiom,
( sP145(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP145(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_309,axiom,
( sP146(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP146(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_310,axiom,
( sP147(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP147(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_311,axiom,
( sP148(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP148(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_312,axiom,
( sP149(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP149(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_313,axiom,
( sP150(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP150(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_314,axiom,
( sP151(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP151(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_315,axiom,
( sP152(Eq_y_0,Eq_y_1)
| ~ sP152(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_316,axiom,
( sP153(Eq_y_0,Eq_y_1)
| ~ sP153(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_317,axiom,
( sP154(Eq_y_0,Eq_y_1)
| ~ sP154(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_318,axiom,
( sP155(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP155(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_319,axiom,
( sP156(Eq_y_0)
| ~ sP156(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_320,axiom,
( sP157(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP157(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_321,axiom,
( sP158(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP158(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_322,axiom,
( sP159(Eq_y_0,Eq_y_1)
| ~ sP159(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_323,axiom,
( sP160(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP160(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_324,axiom,
( sP161(Eq_y_0)
| ~ sP161(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_325,axiom,
( sP162(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP162(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_326,axiom,
( sP163(Eq_y_0,Eq_y_1)
| ~ sP163(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_327,axiom,
( sP164(Eq_y_0,Eq_y_1)
| ~ sP164(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_328,axiom,
( sP165(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP165(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_329,axiom,
( sP166(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP166(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_330,axiom,
( sP167(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP167(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_331,axiom,
( sP168(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP168(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| 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_predicates]) ).
cnf(equality_332,axiom,
( sP169(Eq_y_0,Eq_y_1)
| ~ sP169(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_333,axiom,
( sP170(Eq_y_0,Eq_y_1)
| ~ sP170(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_334,axiom,
( sP171(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP171(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| 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_predicates]) ).
cnf(equality_335,axiom,
( sP172(Eq_y_0)
| ~ sP172(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_336,axiom,
( sP173(Eq_y_0,Eq_y_1)
| ~ sP173(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_337,axiom,
( sP174(Eq_y_0)
| ~ sP174(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_338,axiom,
( sP175(Eq_y_0)
| ~ sP175(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_339,axiom,
( sP176(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP176(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_340,axiom,
( sP177(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP177(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_341,axiom,
( sP178(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP178(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_342,axiom,
( sP179(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP179(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_343,axiom,
( sP180(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP180(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_344,axiom,
( sP181(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP181(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_345,axiom,
( sP182(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP182(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_346,axiom,
( sP183(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP183(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_347,axiom,
( sP184(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP184(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_348,axiom,
( sP185(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP185(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_349,axiom,
( sP186(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP186(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| 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
% 0.00/0.01 % Problem : SEU234+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.01 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.02 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.32 % Computer : n012.cluster.edu
% 0.03/0.32 % Model : x86_64 x86_64
% 0.03/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.32 % Memory : 8046.5625MB
% 0.03/0.32 % OS : Linux 6.8.0-71-generic
% 0.03/0.32 % CPULimit : 300
% 0.03/0.32 % WCLimit : 300
% 0.03/0.32 % DateTime : Sat Sep 19 23:37:07 UTC 2026
% 0.03/0.32 % CPUTime :
% 251.55/251.98 % SZS status Theorem for theBenchmark
% 251.55/251.98 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------