%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU217+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 08:58:32 AM UTC 2026
% Result : Theorem 75.88s 76.18s
% Output : Proof 75.95s
% 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_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('theBenchmark.p',cc1_relat_1) ).
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_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_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_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_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_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_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_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_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(dt_k10_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k10_relat_1) ).
fof(dt_k1_funct_1,axiom,
$true,
file('theBenchmark.p',dt_k1_funct_1) ).
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_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(fc12_relat_1,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc12_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_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_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_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_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(rc1_funct_1,axiom,
? [A] :
( function(A)
& relation(A) ),
file('theBenchmark.p',rc1_funct_1) ).
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_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_relat_1,axiom,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc3_relat_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_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_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_relat_1,lemma,
! [A] :
( relation(A)
=> relation_image(A,relation_dom(A)) = relation_rng(A) ),
file('theBenchmark.p',t146_relat_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_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(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(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,conjecture,
! [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_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_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(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(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(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(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(t71_relat_1,lemma,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
file('theBenchmark.p',t71_relat_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_xboole_1,lemma,
! [A,B] : subset(A,set_union2(A,B)),
file('theBenchmark.p',t7_xboole_1) ).
fof(t83_xboole_1,lemma,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('theBenchmark.p',t83_xboole_1) ).
fof(t86_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_dom(relation_dom_restriction(C,B)))
<=> ( in(A,relation_dom(C))
& in(A,B) ) ) ),
file('theBenchmark.p',t86_relat_1) ).
fof(t88_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_dom_restriction(B,A),B) ),
file('theBenchmark.p',t88_relat_1) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(t8_funct_1,lemma,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(ordered_pair(A,B),C)
<=> ( B = apply(C,A)
& in(A,relation_dom(C)) ) ) ),
file('theBenchmark.p',t8_funct_1) ).
fof(t8_xboole_1,lemma,
! [A,B,C] :
( ( subset(C,B)
& subset(A,B) )
=> subset(set_union2(A,C),B) ),
file('theBenchmark.p',t8_xboole_1) ).
fof(t8_zfmisc_1,lemma,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ),
file('theBenchmark.p',t8_zfmisc_1) ).
fof(t90_relat_1,lemma,
! [A,B] :
( relation(B)
=> relation_dom(relation_dom_restriction(B,A)) = set_intersection2(relation_dom(B),A) ),
file('theBenchmark.p',t90_relat_1) ).
fof(t92_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
file('theBenchmark.p',t92_zfmisc_1) ).
fof(t94_relat_1,lemma,
! [A,B] :
( relation(B)
=> relation_dom_restriction(B,A) = relation_composition(identity_relation(A),B) ),
file('theBenchmark.p',t94_relat_1) ).
fof(t99_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B)) ),
file('theBenchmark.p',t99_relat_1) ).
fof(t99_zfmisc_1,lemma,
! [A] : union(powerset(A)) = A,
file('theBenchmark.p',t99_zfmisc_1) ).
fof(t9_tarski,axiom,
! [A] :
? [B] :
( ! [C] :
~ ( ~ in(C,B)
& ~ are_equipotent(C,B)
& subset(C,B) )
& ! [C] :
~ ( ! [D] :
~ ( ! [E] :
( subset(E,C)
=> in(E,D) )
& in(D,B) )
& in(C,B) )
& ! [C,D] :
( ( subset(D,C)
& in(C,B) )
=> in(D,B) )
& in(A,B) ),
file('theBenchmark.p',t9_tarski) ).
fof(t9_zfmisc_1,lemma,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> B = C ),
file('theBenchmark.p',t9_zfmisc_1) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ proper_subset(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(f_2_2,plain,
! [U_3,U_2] :
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_3_2,plain,
! [U_4] :
( function(U_4)
| ~ empty(U_4) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( function(U_4)
| ~ empty(U_4) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_4_2,plain,
! [U_5] :
( relation(U_5)
| ~ empty(U_5) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( relation(U_5)
| ~ empty(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_5_2,plain,
! [U_7,U_6] : unordered_pair(U_7,U_6) = unordered_pair(U_6,U_7),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
unordered_pair(U_7,U_6) = unordered_pair(U_6,U_7),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_6_2,plain,
! [U_9,U_8] : set_union2(U_9,U_8) = set_union2(U_8,U_9),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
set_union2(U_9,U_8) = set_union2(U_8,U_9),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_7_2,plain,
! [U_11,U_10] : set_intersection2(U_11,U_10) = set_intersection2(U_10,U_11),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
set_intersection2(U_11,U_10) = set_intersection2(U_10,U_11),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_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_8_2,plain,
! [U_17,U_16] :
( ( ( U_16 = identity_relation(U_17)
| ? [U_15,U_14] :
( ( ~ in(ordered_pair(U_15,U_14),U_16)
& U_15 = U_14
& in(U_15,U_17) )
| ( ( U_15 != U_14
| ~ in(U_15,U_17) )
& in(ordered_pair(U_15,U_14),U_16) ) ) )
& ( ! [U_13,U_12] :
( ( in(ordered_pair(U_13,U_12),U_16)
| U_13 != U_12
| ~ in(U_13,U_17) )
& ( ( U_13 = U_12
& in(U_13,U_17) )
| ~ in(ordered_pair(U_13,U_12),U_16) ) )
| U_16 != identity_relation(U_17) ) )
| ~ relation(U_16) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_17,U_16] :
( ( ( U_16 = identity_relation(U_17)
| ? [U_25,U_23] :
( ~ in(ordered_pair(U_25,U_23),U_16)
& U_25 = U_23
& in(U_25,U_17) )
| ? [U_24,U_22] :
( ( U_24 != U_22
| ~ in(U_24,U_17) )
& in(ordered_pair(U_24,U_22),U_16) ) )
& ( ( ! [U_21,U_19] :
( in(ordered_pair(U_21,U_19),U_16)
| U_21 != U_19
| ~ in(U_21,U_17) )
& ! [U_20,U_18] :
( ( U_20 = U_18
& in(U_20,U_17) )
| ~ in(ordered_pair(U_20,U_18),U_16) ) )
| U_16 != identity_relation(U_17) ) )
| ~ relation(U_16) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
! [U_17,U_16] :
( ( ( U_16 = identity_relation(U_17)
| ? [U_25,U_23] :
( ~ in(ordered_pair(U_25,U_23),U_16)
& U_25 = U_23
& in(U_25,U_17) )
| ? [U_22] :
( ( sK1(U_17,U_16) != U_22
| ~ in(sK1(U_17,U_16),U_17) )
& in(ordered_pair(sK1(U_17,U_16),U_22),U_16) ) )
& ( ( ! [U_21,U_19] :
( in(ordered_pair(U_21,U_19),U_16)
| U_21 != U_19
| ~ in(U_21,U_17) )
& ! [U_20,U_18] :
( ( U_20 = U_18
& in(U_20,U_17) )
| ~ in(ordered_pair(U_20,U_18),U_16) ) )
| U_16 != identity_relation(U_17) ) )
| ~ relation(U_16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_24,sK1(U_17,U_16))],[f_8_3]) ).
fof(f_8_5,plain,
! [U_17,U_16] :
( ( ( U_16 = identity_relation(U_17)
| ? [U_25,U_23] :
( ~ in(ordered_pair(U_25,U_23),U_16)
& U_25 = U_23
& in(U_25,U_17) )
| ( ( sK1(U_17,U_16) != sK2(U_17,U_16)
| ~ in(sK1(U_17,U_16),U_17) )
& in(ordered_pair(sK1(U_17,U_16),sK2(U_17,U_16)),U_16) ) )
& ( ( ! [U_21,U_19] :
( in(ordered_pair(U_21,U_19),U_16)
| U_21 != U_19
| ~ in(U_21,U_17) )
& ! [U_20,U_18] :
( ( U_20 = U_18
& in(U_20,U_17) )
| ~ in(ordered_pair(U_20,U_18),U_16) ) )
| U_16 != identity_relation(U_17) ) )
| ~ relation(U_16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_22,sK2(U_17,U_16))],[f_8_4]) ).
fof(f_8_6,plain,
! [U_17,U_16] :
( ( ( U_16 = identity_relation(U_17)
| ? [U_23] :
( ~ in(ordered_pair(sK3(U_17,U_16),U_23),U_16)
& sK3(U_17,U_16) = U_23
& in(sK3(U_17,U_16),U_17) )
| ( ( sK1(U_17,U_16) != sK2(U_17,U_16)
| ~ in(sK1(U_17,U_16),U_17) )
& in(ordered_pair(sK1(U_17,U_16),sK2(U_17,U_16)),U_16) ) )
& ( ( ! [U_21,U_19] :
( in(ordered_pair(U_21,U_19),U_16)
| U_21 != U_19
| ~ in(U_21,U_17) )
& ! [U_20,U_18] :
( ( U_20 = U_18
& in(U_20,U_17) )
| ~ in(ordered_pair(U_20,U_18),U_16) ) )
| U_16 != identity_relation(U_17) ) )
| ~ relation(U_16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_25,sK3(U_17,U_16))],[f_8_5]) ).
fof(f_8_7,plain,
! [U_17,U_16] :
( ( ( U_16 = identity_relation(U_17)
| ( ~ in(ordered_pair(sK3(U_17,U_16),sK4(U_17,U_16)),U_16)
& sK3(U_17,U_16) = sK4(U_17,U_16)
& in(sK3(U_17,U_16),U_17) )
| ( ( sK1(U_17,U_16) != sK2(U_17,U_16)
| ~ in(sK1(U_17,U_16),U_17) )
& in(ordered_pair(sK1(U_17,U_16),sK2(U_17,U_16)),U_16) ) )
& ( ( ! [U_21,U_19] :
( in(ordered_pair(U_21,U_19),U_16)
| U_21 != U_19
| ~ in(U_21,U_17) )
& ! [U_20,U_18] :
( ( U_20 = U_18
& in(U_20,U_17) )
| ~ in(ordered_pair(U_20,U_18),U_16) ) )
| U_16 != identity_relation(U_17) ) )
| ~ relation(U_16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_23,sK4(U_17,U_16))],[f_8_6]) ).
cnf(f_8_8,plain,
( in(U_20,U_17)
| ~ in(ordered_pair(U_20,U_18),U_16)
| U_16 != identity_relation(U_17)
| ~ relation(U_16) ),
inference(clausify,[status(thm)],[f_8_7]) ).
cnf(f_8_9,plain,
( U_20 = U_18
| ~ in(ordered_pair(U_20,U_18),U_16)
| U_16 != identity_relation(U_17)
| ~ relation(U_16) ),
inference(clausify,[status(thm)],[f_8_7]) ).
cnf(f_8_10,plain,
( in(ordered_pair(U_21,U_19),U_16)
| U_21 != U_19
| ~ in(U_21,U_17)
| U_16 != identity_relation(U_17)
| ~ relation(U_16) ),
inference(clausify,[status(thm)],[f_8_7]) ).
cnf(f_8_11,plain,
( in(sK3(U_17,U_16),U_17)
| in(ordered_pair(sK1(U_17,U_16),sK2(U_17,U_16)),U_16)
| U_16 = identity_relation(U_17)
| ~ relation(U_16) ),
inference(clausify,[status(thm)],[f_8_7]) ).
cnf(f_8_12,plain,
( sK3(U_17,U_16) = sK4(U_17,U_16)
| in(ordered_pair(sK1(U_17,U_16),sK2(U_17,U_16)),U_16)
| U_16 = identity_relation(U_17)
| ~ relation(U_16) ),
inference(clausify,[status(thm)],[f_8_7]) ).
cnf(f_8_13,plain,
( ~ in(ordered_pair(sK3(U_17,U_16),sK4(U_17,U_16)),U_16)
| in(ordered_pair(sK1(U_17,U_16),sK2(U_17,U_16)),U_16)
| U_16 = identity_relation(U_17)
| ~ relation(U_16) ),
inference(clausify,[status(thm)],[f_8_7]) ).
cnf(f_8_14,plain,
( in(sK3(U_17,U_16),U_17)
| sK1(U_17,U_16) != sK2(U_17,U_16)
| ~ in(sK1(U_17,U_16),U_17)
| U_16 = identity_relation(U_17)
| ~ relation(U_16) ),
inference(clausify,[status(thm)],[f_8_7]) ).
cnf(f_8_15,plain,
( sK3(U_17,U_16) = sK4(U_17,U_16)
| sK1(U_17,U_16) != sK2(U_17,U_16)
| ~ in(sK1(U_17,U_16),U_17)
| U_16 = identity_relation(U_17)
| ~ relation(U_16) ),
inference(clausify,[status(thm)],[f_8_7]) ).
cnf(f_8_16,plain,
( ~ in(ordered_pair(sK3(U_17,U_16),sK4(U_17,U_16)),U_16)
| sK1(U_17,U_16) != sK2(U_17,U_16)
| ~ in(sK1(U_17,U_16),U_17)
| U_16 = identity_relation(U_17)
| ~ relation(U_16) ),
inference(clausify,[status(thm)],[f_8_7]) ).
fof(f_9_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_9_2,plain,
! [U_27,U_26] :
( ( U_27 = U_26
| ~ subset(U_26,U_27)
| ~ subset(U_27,U_26) )
& ( ( subset(U_26,U_27)
& subset(U_27,U_26) )
| U_27 != U_26 ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_31,U_29] :
( U_31 = U_29
| ~ subset(U_29,U_31)
| ~ subset(U_31,U_29) )
& ! [U_30,U_28] :
( ( subset(U_28,U_30)
& subset(U_30,U_28) )
| U_30 != U_28 ) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( subset(U_30,U_28)
| U_30 != U_28 ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( subset(U_28,U_30)
| U_30 != U_28 ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_6,plain,
( U_31 = U_29
| ~ subset(U_29,U_31)
| ~ subset(U_31,U_29) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_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_10_2,plain,
! [U_38] :
( ! [U_37,U_36] :
( ( ( U_36 = relation_dom_restriction(U_38,U_37)
| ? [U_35,U_34] :
( ( ~ in(ordered_pair(U_35,U_34),U_36)
& in(ordered_pair(U_35,U_34),U_38)
& in(U_35,U_37) )
| ( ( ~ in(ordered_pair(U_35,U_34),U_38)
| ~ in(U_35,U_37) )
& in(ordered_pair(U_35,U_34),U_36) ) ) )
& ( ! [U_33,U_32] :
( ( in(ordered_pair(U_33,U_32),U_36)
| ~ in(ordered_pair(U_33,U_32),U_38)
| ~ in(U_33,U_37) )
& ( ( in(ordered_pair(U_33,U_32),U_38)
& in(U_33,U_37) )
| ~ in(ordered_pair(U_33,U_32),U_36) ) )
| U_36 != relation_dom_restriction(U_38,U_37) ) )
| ~ relation(U_36) )
| ~ relation(U_38) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_38] :
( ! [U_37,U_36] :
( ( ( U_36 = relation_dom_restriction(U_38,U_37)
| ? [U_46,U_44] :
( ~ in(ordered_pair(U_46,U_44),U_36)
& in(ordered_pair(U_46,U_44),U_38)
& in(U_46,U_37) )
| ? [U_45,U_43] :
( ( ~ in(ordered_pair(U_45,U_43),U_38)
| ~ in(U_45,U_37) )
& in(ordered_pair(U_45,U_43),U_36) ) )
& ( ( ! [U_42,U_40] :
( in(ordered_pair(U_42,U_40),U_36)
| ~ in(ordered_pair(U_42,U_40),U_38)
| ~ in(U_42,U_37) )
& ! [U_41,U_39] :
( ( in(ordered_pair(U_41,U_39),U_38)
& in(U_41,U_37) )
| ~ in(ordered_pair(U_41,U_39),U_36) ) )
| U_36 != relation_dom_restriction(U_38,U_37) ) )
| ~ relation(U_36) )
| ~ relation(U_38) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
fof(f_10_4,plain,
! [U_38] :
( ! [U_37,U_36] :
( ( ( U_36 = relation_dom_restriction(U_38,U_37)
| ? [U_46,U_44] :
( ~ in(ordered_pair(U_46,U_44),U_36)
& in(ordered_pair(U_46,U_44),U_38)
& in(U_46,U_37) )
| ? [U_43] :
( ( ~ in(ordered_pair(sK5(U_38,U_37,U_36),U_43),U_38)
| ~ in(sK5(U_38,U_37,U_36),U_37) )
& in(ordered_pair(sK5(U_38,U_37,U_36),U_43),U_36) ) )
& ( ( ! [U_42,U_40] :
( in(ordered_pair(U_42,U_40),U_36)
| ~ in(ordered_pair(U_42,U_40),U_38)
| ~ in(U_42,U_37) )
& ! [U_41,U_39] :
( ( in(ordered_pair(U_41,U_39),U_38)
& in(U_41,U_37) )
| ~ in(ordered_pair(U_41,U_39),U_36) ) )
| U_36 != relation_dom_restriction(U_38,U_37) ) )
| ~ relation(U_36) )
| ~ relation(U_38) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_45,sK5(U_38,U_37,U_36))],[f_10_3]) ).
fof(f_10_5,plain,
! [U_38] :
( ! [U_37,U_36] :
( ( ( U_36 = relation_dom_restriction(U_38,U_37)
| ? [U_46,U_44] :
( ~ in(ordered_pair(U_46,U_44),U_36)
& in(ordered_pair(U_46,U_44),U_38)
& in(U_46,U_37) )
| ( ( ~ in(ordered_pair(sK5(U_38,U_37,U_36),sK6(U_38,U_37,U_36)),U_38)
| ~ in(sK5(U_38,U_37,U_36),U_37) )
& in(ordered_pair(sK5(U_38,U_37,U_36),sK6(U_38,U_37,U_36)),U_36) ) )
& ( ( ! [U_42,U_40] :
( in(ordered_pair(U_42,U_40),U_36)
| ~ in(ordered_pair(U_42,U_40),U_38)
| ~ in(U_42,U_37) )
& ! [U_41,U_39] :
( ( in(ordered_pair(U_41,U_39),U_38)
& in(U_41,U_37) )
| ~ in(ordered_pair(U_41,U_39),U_36) ) )
| U_36 != relation_dom_restriction(U_38,U_37) ) )
| ~ relation(U_36) )
| ~ relation(U_38) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_43,sK6(U_38,U_37,U_36))],[f_10_4]) ).
fof(f_10_6,plain,
! [U_38] :
( ! [U_37,U_36] :
( ( ( U_36 = relation_dom_restriction(U_38,U_37)
| ? [U_44] :
( ~ in(ordered_pair(sK7(U_38,U_37,U_36),U_44),U_36)
& in(ordered_pair(sK7(U_38,U_37,U_36),U_44),U_38)
& in(sK7(U_38,U_37,U_36),U_37) )
| ( ( ~ in(ordered_pair(sK5(U_38,U_37,U_36),sK6(U_38,U_37,U_36)),U_38)
| ~ in(sK5(U_38,U_37,U_36),U_37) )
& in(ordered_pair(sK5(U_38,U_37,U_36),sK6(U_38,U_37,U_36)),U_36) ) )
& ( ( ! [U_42,U_40] :
( in(ordered_pair(U_42,U_40),U_36)
| ~ in(ordered_pair(U_42,U_40),U_38)
| ~ in(U_42,U_37) )
& ! [U_41,U_39] :
( ( in(ordered_pair(U_41,U_39),U_38)
& in(U_41,U_37) )
| ~ in(ordered_pair(U_41,U_39),U_36) ) )
| U_36 != relation_dom_restriction(U_38,U_37) ) )
| ~ relation(U_36) )
| ~ relation(U_38) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_46,sK7(U_38,U_37,U_36))],[f_10_5]) ).
fof(f_10_7,plain,
! [U_38] :
( ! [U_37,U_36] :
( ( ( U_36 = relation_dom_restriction(U_38,U_37)
| ( ~ in(ordered_pair(sK7(U_38,U_37,U_36),sK8(U_38,U_37,U_36)),U_36)
& in(ordered_pair(sK7(U_38,U_37,U_36),sK8(U_38,U_37,U_36)),U_38)
& in(sK7(U_38,U_37,U_36),U_37) )
| ( ( ~ in(ordered_pair(sK5(U_38,U_37,U_36),sK6(U_38,U_37,U_36)),U_38)
| ~ in(sK5(U_38,U_37,U_36),U_37) )
& in(ordered_pair(sK5(U_38,U_37,U_36),sK6(U_38,U_37,U_36)),U_36) ) )
& ( ( ! [U_42,U_40] :
( in(ordered_pair(U_42,U_40),U_36)
| ~ in(ordered_pair(U_42,U_40),U_38)
| ~ in(U_42,U_37) )
& ! [U_41,U_39] :
( ( in(ordered_pair(U_41,U_39),U_38)
& in(U_41,U_37) )
| ~ in(ordered_pair(U_41,U_39),U_36) ) )
| U_36 != relation_dom_restriction(U_38,U_37) ) )
| ~ relation(U_36) )
| ~ relation(U_38) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_44,sK8(U_38,U_37,U_36))],[f_10_6]) ).
cnf(f_10_8,plain,
( in(U_41,U_37)
| ~ in(ordered_pair(U_41,U_39),U_36)
| U_36 != relation_dom_restriction(U_38,U_37)
| ~ relation(U_36)
| ~ relation(U_38) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_9,plain,
( in(ordered_pair(U_41,U_39),U_38)
| ~ in(ordered_pair(U_41,U_39),U_36)
| U_36 != relation_dom_restriction(U_38,U_37)
| ~ relation(U_36)
| ~ relation(U_38) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_10,plain,
( in(ordered_pair(U_42,U_40),U_36)
| ~ in(ordered_pair(U_42,U_40),U_38)
| ~ in(U_42,U_37)
| U_36 != relation_dom_restriction(U_38,U_37)
| ~ relation(U_36)
| ~ relation(U_38) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_11,plain,
( in(sK7(U_38,U_37,U_36),U_37)
| in(ordered_pair(sK5(U_38,U_37,U_36),sK6(U_38,U_37,U_36)),U_36)
| U_36 = relation_dom_restriction(U_38,U_37)
| ~ relation(U_36)
| ~ relation(U_38) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_12,plain,
( in(ordered_pair(sK7(U_38,U_37,U_36),sK8(U_38,U_37,U_36)),U_38)
| in(ordered_pair(sK5(U_38,U_37,U_36),sK6(U_38,U_37,U_36)),U_36)
| U_36 = relation_dom_restriction(U_38,U_37)
| ~ relation(U_36)
| ~ relation(U_38) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_13,plain,
( ~ in(ordered_pair(sK7(U_38,U_37,U_36),sK8(U_38,U_37,U_36)),U_36)
| in(ordered_pair(sK5(U_38,U_37,U_36),sK6(U_38,U_37,U_36)),U_36)
| U_36 = relation_dom_restriction(U_38,U_37)
| ~ relation(U_36)
| ~ relation(U_38) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_14,plain,
( in(sK7(U_38,U_37,U_36),U_37)
| ~ in(ordered_pair(sK5(U_38,U_37,U_36),sK6(U_38,U_37,U_36)),U_38)
| ~ in(sK5(U_38,U_37,U_36),U_37)
| U_36 = relation_dom_restriction(U_38,U_37)
| ~ relation(U_36)
| ~ relation(U_38) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_15,plain,
( in(ordered_pair(sK7(U_38,U_37,U_36),sK8(U_38,U_37,U_36)),U_38)
| ~ in(ordered_pair(sK5(U_38,U_37,U_36),sK6(U_38,U_37,U_36)),U_38)
| ~ in(sK5(U_38,U_37,U_36),U_37)
| U_36 = relation_dom_restriction(U_38,U_37)
| ~ relation(U_36)
| ~ relation(U_38) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_16,plain,
( ~ in(ordered_pair(sK7(U_38,U_37,U_36),sK8(U_38,U_37,U_36)),U_36)
| ~ in(ordered_pair(sK5(U_38,U_37,U_36),sK6(U_38,U_37,U_36)),U_38)
| ~ in(sK5(U_38,U_37,U_36),U_37)
| U_36 = relation_dom_restriction(U_38,U_37)
| ~ relation(U_36)
| ~ relation(U_38) ),
inference(clausify,[status(thm)],[f_10_7]) ).
fof(f_11_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_11_2,plain,
! [U_53,U_52] :
( ! [U_51] :
( ( ( U_51 = relation_rng_restriction(U_53,U_52)
| ? [U_50,U_49] :
( ( ~ in(ordered_pair(U_50,U_49),U_51)
& in(ordered_pair(U_50,U_49),U_52)
& in(U_49,U_53) )
| ( ( ~ in(ordered_pair(U_50,U_49),U_52)
| ~ in(U_49,U_53) )
& in(ordered_pair(U_50,U_49),U_51) ) ) )
& ( ! [U_48,U_47] :
( ( in(ordered_pair(U_48,U_47),U_51)
| ~ in(ordered_pair(U_48,U_47),U_52)
| ~ in(U_47,U_53) )
& ( ( in(ordered_pair(U_48,U_47),U_52)
& in(U_47,U_53) )
| ~ in(ordered_pair(U_48,U_47),U_51) ) )
| U_51 != relation_rng_restriction(U_53,U_52) ) )
| ~ relation(U_51) )
| ~ relation(U_52) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_53,U_52] :
( ! [U_51] :
( ( ( U_51 = relation_rng_restriction(U_53,U_52)
| ? [U_61,U_59] :
( ~ in(ordered_pair(U_61,U_59),U_51)
& in(ordered_pair(U_61,U_59),U_52)
& in(U_59,U_53) )
| ? [U_60,U_58] :
( ( ~ in(ordered_pair(U_60,U_58),U_52)
| ~ in(U_58,U_53) )
& in(ordered_pair(U_60,U_58),U_51) ) )
& ( ( ! [U_57,U_55] :
( in(ordered_pair(U_57,U_55),U_51)
| ~ in(ordered_pair(U_57,U_55),U_52)
| ~ in(U_55,U_53) )
& ! [U_56,U_54] :
( ( in(ordered_pair(U_56,U_54),U_52)
& in(U_54,U_53) )
| ~ in(ordered_pair(U_56,U_54),U_51) ) )
| U_51 != relation_rng_restriction(U_53,U_52) ) )
| ~ relation(U_51) )
| ~ relation(U_52) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
fof(f_11_4,plain,
! [U_53,U_52] :
( ! [U_51] :
( ( ( U_51 = relation_rng_restriction(U_53,U_52)
| ? [U_61,U_59] :
( ~ in(ordered_pair(U_61,U_59),U_51)
& in(ordered_pair(U_61,U_59),U_52)
& in(U_59,U_53) )
| ? [U_58] :
( ( ~ in(ordered_pair(sK9(U_53,U_52,U_51),U_58),U_52)
| ~ in(U_58,U_53) )
& in(ordered_pair(sK9(U_53,U_52,U_51),U_58),U_51) ) )
& ( ( ! [U_57,U_55] :
( in(ordered_pair(U_57,U_55),U_51)
| ~ in(ordered_pair(U_57,U_55),U_52)
| ~ in(U_55,U_53) )
& ! [U_56,U_54] :
( ( in(ordered_pair(U_56,U_54),U_52)
& in(U_54,U_53) )
| ~ in(ordered_pair(U_56,U_54),U_51) ) )
| U_51 != relation_rng_restriction(U_53,U_52) ) )
| ~ relation(U_51) )
| ~ relation(U_52) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_60,sK9(U_53,U_52,U_51))],[f_11_3]) ).
fof(f_11_5,plain,
! [U_53,U_52] :
( ! [U_51] :
( ( ( U_51 = relation_rng_restriction(U_53,U_52)
| ? [U_61,U_59] :
( ~ in(ordered_pair(U_61,U_59),U_51)
& in(ordered_pair(U_61,U_59),U_52)
& in(U_59,U_53) )
| ( ( ~ in(ordered_pair(sK9(U_53,U_52,U_51),sK10(U_53,U_52,U_51)),U_52)
| ~ in(sK10(U_53,U_52,U_51),U_53) )
& in(ordered_pair(sK9(U_53,U_52,U_51),sK10(U_53,U_52,U_51)),U_51) ) )
& ( ( ! [U_57,U_55] :
( in(ordered_pair(U_57,U_55),U_51)
| ~ in(ordered_pair(U_57,U_55),U_52)
| ~ in(U_55,U_53) )
& ! [U_56,U_54] :
( ( in(ordered_pair(U_56,U_54),U_52)
& in(U_54,U_53) )
| ~ in(ordered_pair(U_56,U_54),U_51) ) )
| U_51 != relation_rng_restriction(U_53,U_52) ) )
| ~ relation(U_51) )
| ~ relation(U_52) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_58,sK10(U_53,U_52,U_51))],[f_11_4]) ).
fof(f_11_6,plain,
! [U_53,U_52] :
( ! [U_51] :
( ( ( U_51 = relation_rng_restriction(U_53,U_52)
| ? [U_59] :
( ~ in(ordered_pair(sK11(U_53,U_52,U_51),U_59),U_51)
& in(ordered_pair(sK11(U_53,U_52,U_51),U_59),U_52)
& in(U_59,U_53) )
| ( ( ~ in(ordered_pair(sK9(U_53,U_52,U_51),sK10(U_53,U_52,U_51)),U_52)
| ~ in(sK10(U_53,U_52,U_51),U_53) )
& in(ordered_pair(sK9(U_53,U_52,U_51),sK10(U_53,U_52,U_51)),U_51) ) )
& ( ( ! [U_57,U_55] :
( in(ordered_pair(U_57,U_55),U_51)
| ~ in(ordered_pair(U_57,U_55),U_52)
| ~ in(U_55,U_53) )
& ! [U_56,U_54] :
( ( in(ordered_pair(U_56,U_54),U_52)
& in(U_54,U_53) )
| ~ in(ordered_pair(U_56,U_54),U_51) ) )
| U_51 != relation_rng_restriction(U_53,U_52) ) )
| ~ relation(U_51) )
| ~ relation(U_52) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_61,sK11(U_53,U_52,U_51))],[f_11_5]) ).
fof(f_11_7,plain,
! [U_53,U_52] :
( ! [U_51] :
( ( ( U_51 = relation_rng_restriction(U_53,U_52)
| ( ~ in(ordered_pair(sK11(U_53,U_52,U_51),sK12(U_53,U_52,U_51)),U_51)
& in(ordered_pair(sK11(U_53,U_52,U_51),sK12(U_53,U_52,U_51)),U_52)
& in(sK12(U_53,U_52,U_51),U_53) )
| ( ( ~ in(ordered_pair(sK9(U_53,U_52,U_51),sK10(U_53,U_52,U_51)),U_52)
| ~ in(sK10(U_53,U_52,U_51),U_53) )
& in(ordered_pair(sK9(U_53,U_52,U_51),sK10(U_53,U_52,U_51)),U_51) ) )
& ( ( ! [U_57,U_55] :
( in(ordered_pair(U_57,U_55),U_51)
| ~ in(ordered_pair(U_57,U_55),U_52)
| ~ in(U_55,U_53) )
& ! [U_56,U_54] :
( ( in(ordered_pair(U_56,U_54),U_52)
& in(U_54,U_53) )
| ~ in(ordered_pair(U_56,U_54),U_51) ) )
| U_51 != relation_rng_restriction(U_53,U_52) ) )
| ~ relation(U_51) )
| ~ relation(U_52) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_59,sK12(U_53,U_52,U_51))],[f_11_6]) ).
cnf(f_11_8,plain,
( in(U_54,U_53)
| ~ in(ordered_pair(U_56,U_54),U_51)
| U_51 != relation_rng_restriction(U_53,U_52)
| ~ relation(U_51)
| ~ relation(U_52) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_9,plain,
( in(ordered_pair(U_56,U_54),U_52)
| ~ in(ordered_pair(U_56,U_54),U_51)
| U_51 != relation_rng_restriction(U_53,U_52)
| ~ relation(U_51)
| ~ relation(U_52) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_10,plain,
( in(ordered_pair(U_57,U_55),U_51)
| ~ in(ordered_pair(U_57,U_55),U_52)
| ~ in(U_55,U_53)
| U_51 != relation_rng_restriction(U_53,U_52)
| ~ relation(U_51)
| ~ relation(U_52) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_11,plain,
( in(sK12(U_53,U_52,U_51),U_53)
| in(ordered_pair(sK9(U_53,U_52,U_51),sK10(U_53,U_52,U_51)),U_51)
| U_51 = relation_rng_restriction(U_53,U_52)
| ~ relation(U_51)
| ~ relation(U_52) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_12,plain,
( in(ordered_pair(sK11(U_53,U_52,U_51),sK12(U_53,U_52,U_51)),U_52)
| in(ordered_pair(sK9(U_53,U_52,U_51),sK10(U_53,U_52,U_51)),U_51)
| U_51 = relation_rng_restriction(U_53,U_52)
| ~ relation(U_51)
| ~ relation(U_52) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_13,plain,
( ~ in(ordered_pair(sK11(U_53,U_52,U_51),sK12(U_53,U_52,U_51)),U_51)
| in(ordered_pair(sK9(U_53,U_52,U_51),sK10(U_53,U_52,U_51)),U_51)
| U_51 = relation_rng_restriction(U_53,U_52)
| ~ relation(U_51)
| ~ relation(U_52) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_14,plain,
( in(sK12(U_53,U_52,U_51),U_53)
| ~ in(ordered_pair(sK9(U_53,U_52,U_51),sK10(U_53,U_52,U_51)),U_52)
| ~ in(sK10(U_53,U_52,U_51),U_53)
| U_51 = relation_rng_restriction(U_53,U_52)
| ~ relation(U_51)
| ~ relation(U_52) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_15,plain,
( in(ordered_pair(sK11(U_53,U_52,U_51),sK12(U_53,U_52,U_51)),U_52)
| ~ in(ordered_pair(sK9(U_53,U_52,U_51),sK10(U_53,U_52,U_51)),U_52)
| ~ in(sK10(U_53,U_52,U_51),U_53)
| U_51 = relation_rng_restriction(U_53,U_52)
| ~ relation(U_51)
| ~ relation(U_52) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_16,plain,
( ~ in(ordered_pair(sK11(U_53,U_52,U_51),sK12(U_53,U_52,U_51)),U_51)
| ~ in(ordered_pair(sK9(U_53,U_52,U_51),sK10(U_53,U_52,U_51)),U_52)
| ~ in(sK10(U_53,U_52,U_51),U_53)
| U_51 = relation_rng_restriction(U_53,U_52)
| ~ relation(U_51)
| ~ relation(U_52) ),
inference(clausify,[status(thm)],[f_11_7]) ).
fof(f_12_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_12_2,plain,
! [U_70] :
( ! [U_69,U_68] :
( ( U_68 = relation_image(U_70,U_69)
| ? [U_67] :
( ( ~ in(U_67,U_68)
& ? [U_66] :
( in(U_66,U_69)
& in(ordered_pair(U_66,U_67),U_70) ) )
| ( ! [U_65] :
( ~ in(U_65,U_69)
| ~ in(ordered_pair(U_65,U_67),U_70) )
& in(U_67,U_68) ) ) )
& ( ! [U_64] :
( ( in(U_64,U_68)
| ! [U_63] :
( ~ in(U_63,U_69)
| ~ in(ordered_pair(U_63,U_64),U_70) ) )
& ( ? [U_62] :
( in(U_62,U_69)
& in(ordered_pair(U_62,U_64),U_70) )
| ~ in(U_64,U_68) ) )
| U_68 != relation_image(U_70,U_69) ) )
| ~ relation(U_70) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_70] :
( ( ! [U_78,U_76] :
( U_76 = relation_image(U_70,U_78)
| ? [U_74] :
( ~ in(U_74,U_76)
& ? [U_66] :
( in(U_66,U_78)
& in(ordered_pair(U_66,U_74),U_70) ) )
| ? [U_73] :
( ! [U_65] :
( ~ in(U_65,U_78)
| ~ in(ordered_pair(U_65,U_73),U_70) )
& in(U_73,U_76) ) )
& ! [U_77,U_75] :
( ( ! [U_72] :
( in(U_72,U_75)
| ! [U_63] :
( ~ in(U_63,U_77)
| ~ in(ordered_pair(U_63,U_72),U_70) ) )
& ! [U_71] :
( ? [U_62] :
( in(U_62,U_77)
& in(ordered_pair(U_62,U_71),U_70) )
| ~ in(U_71,U_75) ) )
| U_75 != relation_image(U_70,U_77) ) )
| ~ relation(U_70) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
! [U_70] :
( ( ! [U_78,U_76] :
( U_76 = relation_image(U_70,U_78)
| ? [U_74] :
( ~ in(U_74,U_76)
& ? [U_66] :
( in(U_66,U_78)
& in(ordered_pair(U_66,U_74),U_70) ) )
| ? [U_73] :
( ! [U_65] :
( ~ in(U_65,U_78)
| ~ in(ordered_pair(U_65,U_73),U_70) )
& in(U_73,U_76) ) )
& ! [U_77,U_75] :
( ( ! [U_72] :
( in(U_72,U_75)
| ! [U_63] :
( ~ in(U_63,U_77)
| ~ in(ordered_pair(U_63,U_72),U_70) ) )
& ! [U_71] :
( ( in(sK13(U_70,U_77,U_75,U_71),U_77)
& in(ordered_pair(sK13(U_70,U_77,U_75,U_71),U_71),U_70) )
| ~ in(U_71,U_75) ) )
| U_75 != relation_image(U_70,U_77) ) )
| ~ relation(U_70) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_62,sK13(U_70,U_77,U_75,U_71))],[f_12_3]) ).
fof(f_12_5,plain,
! [U_70] :
( ( ! [U_78,U_76] :
( U_76 = relation_image(U_70,U_78)
| ? [U_74] :
( ~ in(U_74,U_76)
& ? [U_66] :
( in(U_66,U_78)
& in(ordered_pair(U_66,U_74),U_70) ) )
| ( ! [U_65] :
( ~ in(U_65,U_78)
| ~ in(ordered_pair(U_65,sK14(U_70,U_78,U_76)),U_70) )
& in(sK14(U_70,U_78,U_76),U_76) ) )
& ! [U_77,U_75] :
( ( ! [U_72] :
( in(U_72,U_75)
| ! [U_63] :
( ~ in(U_63,U_77)
| ~ in(ordered_pair(U_63,U_72),U_70) ) )
& ! [U_71] :
( ( in(sK13(U_70,U_77,U_75,U_71),U_77)
& in(ordered_pair(sK13(U_70,U_77,U_75,U_71),U_71),U_70) )
| ~ in(U_71,U_75) ) )
| U_75 != relation_image(U_70,U_77) ) )
| ~ relation(U_70) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_73,sK14(U_70,U_78,U_76))],[f_12_4]) ).
fof(f_12_6,plain,
! [U_70] :
( ( ! [U_78,U_76] :
( U_76 = relation_image(U_70,U_78)
| ( ~ in(sK15(U_70,U_78,U_76),U_76)
& ? [U_66] :
( in(U_66,U_78)
& in(ordered_pair(U_66,sK15(U_70,U_78,U_76)),U_70) ) )
| ( ! [U_65] :
( ~ in(U_65,U_78)
| ~ in(ordered_pair(U_65,sK14(U_70,U_78,U_76)),U_70) )
& in(sK14(U_70,U_78,U_76),U_76) ) )
& ! [U_77,U_75] :
( ( ! [U_72] :
( in(U_72,U_75)
| ! [U_63] :
( ~ in(U_63,U_77)
| ~ in(ordered_pair(U_63,U_72),U_70) ) )
& ! [U_71] :
( ( in(sK13(U_70,U_77,U_75,U_71),U_77)
& in(ordered_pair(sK13(U_70,U_77,U_75,U_71),U_71),U_70) )
| ~ in(U_71,U_75) ) )
| U_75 != relation_image(U_70,U_77) ) )
| ~ relation(U_70) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_74,sK15(U_70,U_78,U_76))],[f_12_5]) ).
fof(f_12_7,plain,
! [U_70] :
( ( ! [U_78,U_76] :
( U_76 = relation_image(U_70,U_78)
| ( ~ in(sK15(U_70,U_78,U_76),U_76)
& in(sK16(U_70,U_78,U_76),U_78)
& in(ordered_pair(sK16(U_70,U_78,U_76),sK15(U_70,U_78,U_76)),U_70) )
| ( ! [U_65] :
( ~ in(U_65,U_78)
| ~ in(ordered_pair(U_65,sK14(U_70,U_78,U_76)),U_70) )
& in(sK14(U_70,U_78,U_76),U_76) ) )
& ! [U_77,U_75] :
( ( ! [U_72] :
( in(U_72,U_75)
| ! [U_63] :
( ~ in(U_63,U_77)
| ~ in(ordered_pair(U_63,U_72),U_70) ) )
& ! [U_71] :
( ( in(sK13(U_70,U_77,U_75,U_71),U_77)
& in(ordered_pair(sK13(U_70,U_77,U_75,U_71),U_71),U_70) )
| ~ in(U_71,U_75) ) )
| U_75 != relation_image(U_70,U_77) ) )
| ~ relation(U_70) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_66,sK16(U_70,U_78,U_76))],[f_12_6]) ).
cnf(f_12_8,plain,
( in(ordered_pair(sK13(U_70,U_77,U_75,U_71),U_71),U_70)
| ~ in(U_71,U_75)
| U_75 != relation_image(U_70,U_77)
| ~ relation(U_70) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_9,plain,
( in(sK13(U_70,U_77,U_75,U_71),U_77)
| ~ in(U_71,U_75)
| U_75 != relation_image(U_70,U_77)
| ~ relation(U_70) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_10,plain,
( in(U_72,U_75)
| ~ in(U_63,U_77)
| ~ in(ordered_pair(U_63,U_72),U_70)
| U_75 != relation_image(U_70,U_77)
| ~ relation(U_70) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_11,plain,
( in(ordered_pair(sK16(U_70,U_78,U_76),sK15(U_70,U_78,U_76)),U_70)
| in(sK14(U_70,U_78,U_76),U_76)
| U_76 = relation_image(U_70,U_78)
| ~ relation(U_70) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_12,plain,
( in(sK16(U_70,U_78,U_76),U_78)
| in(sK14(U_70,U_78,U_76),U_76)
| U_76 = relation_image(U_70,U_78)
| ~ relation(U_70) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_13,plain,
( ~ in(sK15(U_70,U_78,U_76),U_76)
| in(sK14(U_70,U_78,U_76),U_76)
| U_76 = relation_image(U_70,U_78)
| ~ relation(U_70) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_14,plain,
( in(ordered_pair(sK16(U_70,U_78,U_76),sK15(U_70,U_78,U_76)),U_70)
| ~ in(U_65,U_78)
| ~ in(ordered_pair(U_65,sK14(U_70,U_78,U_76)),U_70)
| U_76 = relation_image(U_70,U_78)
| ~ relation(U_70) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_15,plain,
( in(sK16(U_70,U_78,U_76),U_78)
| ~ in(U_65,U_78)
| ~ in(ordered_pair(U_65,sK14(U_70,U_78,U_76)),U_70)
| U_76 = relation_image(U_70,U_78)
| ~ relation(U_70) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_16,plain,
( ~ in(sK15(U_70,U_78,U_76),U_76)
| ~ in(U_65,U_78)
| ~ in(ordered_pair(U_65,sK14(U_70,U_78,U_76)),U_70)
| U_76 = relation_image(U_70,U_78)
| ~ relation(U_70) ),
inference(clausify,[status(thm)],[f_12_7]) ).
fof(f_13_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_13_2,plain,
! [U_87] :
( ! [U_86,U_85] :
( ( U_85 = relation_inverse_image(U_87,U_86)
| ? [U_84] :
( ( ~ in(U_84,U_85)
& ? [U_83] :
( in(U_83,U_86)
& in(ordered_pair(U_84,U_83),U_87) ) )
| ( ! [U_82] :
( ~ in(U_82,U_86)
| ~ in(ordered_pair(U_84,U_82),U_87) )
& in(U_84,U_85) ) ) )
& ( ! [U_81] :
( ( in(U_81,U_85)
| ! [U_80] :
( ~ in(U_80,U_86)
| ~ in(ordered_pair(U_81,U_80),U_87) ) )
& ( ? [U_79] :
( in(U_79,U_86)
& in(ordered_pair(U_81,U_79),U_87) )
| ~ in(U_81,U_85) ) )
| U_85 != relation_inverse_image(U_87,U_86) ) )
| ~ relation(U_87) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_87] :
( ( ! [U_95,U_93] :
( U_93 = relation_inverse_image(U_87,U_95)
| ? [U_91] :
( ~ in(U_91,U_93)
& ? [U_83] :
( in(U_83,U_95)
& in(ordered_pair(U_91,U_83),U_87) ) )
| ? [U_90] :
( ! [U_82] :
( ~ in(U_82,U_95)
| ~ in(ordered_pair(U_90,U_82),U_87) )
& in(U_90,U_93) ) )
& ! [U_94,U_92] :
( ( ! [U_89] :
( in(U_89,U_92)
| ! [U_80] :
( ~ in(U_80,U_94)
| ~ in(ordered_pair(U_89,U_80),U_87) ) )
& ! [U_88] :
( ? [U_79] :
( in(U_79,U_94)
& in(ordered_pair(U_88,U_79),U_87) )
| ~ in(U_88,U_92) ) )
| U_92 != relation_inverse_image(U_87,U_94) ) )
| ~ relation(U_87) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
fof(f_13_4,plain,
! [U_87] :
( ( ! [U_95,U_93] :
( U_93 = relation_inverse_image(U_87,U_95)
| ? [U_91] :
( ~ in(U_91,U_93)
& ? [U_83] :
( in(U_83,U_95)
& in(ordered_pair(U_91,U_83),U_87) ) )
| ? [U_90] :
( ! [U_82] :
( ~ in(U_82,U_95)
| ~ in(ordered_pair(U_90,U_82),U_87) )
& in(U_90,U_93) ) )
& ! [U_94,U_92] :
( ( ! [U_89] :
( in(U_89,U_92)
| ! [U_80] :
( ~ in(U_80,U_94)
| ~ in(ordered_pair(U_89,U_80),U_87) ) )
& ! [U_88] :
( ( in(sK17(U_87,U_94,U_92,U_88),U_94)
& in(ordered_pair(U_88,sK17(U_87,U_94,U_92,U_88)),U_87) )
| ~ in(U_88,U_92) ) )
| U_92 != relation_inverse_image(U_87,U_94) ) )
| ~ relation(U_87) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_79,sK17(U_87,U_94,U_92,U_88))],[f_13_3]) ).
fof(f_13_5,plain,
! [U_87] :
( ( ! [U_95,U_93] :
( U_93 = relation_inverse_image(U_87,U_95)
| ? [U_91] :
( ~ in(U_91,U_93)
& ? [U_83] :
( in(U_83,U_95)
& in(ordered_pair(U_91,U_83),U_87) ) )
| ( ! [U_82] :
( ~ in(U_82,U_95)
| ~ in(ordered_pair(sK18(U_87,U_95,U_93),U_82),U_87) )
& in(sK18(U_87,U_95,U_93),U_93) ) )
& ! [U_94,U_92] :
( ( ! [U_89] :
( in(U_89,U_92)
| ! [U_80] :
( ~ in(U_80,U_94)
| ~ in(ordered_pair(U_89,U_80),U_87) ) )
& ! [U_88] :
( ( in(sK17(U_87,U_94,U_92,U_88),U_94)
& in(ordered_pair(U_88,sK17(U_87,U_94,U_92,U_88)),U_87) )
| ~ in(U_88,U_92) ) )
| U_92 != relation_inverse_image(U_87,U_94) ) )
| ~ relation(U_87) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_90,sK18(U_87,U_95,U_93))],[f_13_4]) ).
fof(f_13_6,plain,
! [U_87] :
( ( ! [U_95,U_93] :
( U_93 = relation_inverse_image(U_87,U_95)
| ( ~ in(sK19(U_87,U_95,U_93),U_93)
& ? [U_83] :
( in(U_83,U_95)
& in(ordered_pair(sK19(U_87,U_95,U_93),U_83),U_87) ) )
| ( ! [U_82] :
( ~ in(U_82,U_95)
| ~ in(ordered_pair(sK18(U_87,U_95,U_93),U_82),U_87) )
& in(sK18(U_87,U_95,U_93),U_93) ) )
& ! [U_94,U_92] :
( ( ! [U_89] :
( in(U_89,U_92)
| ! [U_80] :
( ~ in(U_80,U_94)
| ~ in(ordered_pair(U_89,U_80),U_87) ) )
& ! [U_88] :
( ( in(sK17(U_87,U_94,U_92,U_88),U_94)
& in(ordered_pair(U_88,sK17(U_87,U_94,U_92,U_88)),U_87) )
| ~ in(U_88,U_92) ) )
| U_92 != relation_inverse_image(U_87,U_94) ) )
| ~ relation(U_87) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_91,sK19(U_87,U_95,U_93))],[f_13_5]) ).
fof(f_13_7,plain,
! [U_87] :
( ( ! [U_95,U_93] :
( U_93 = relation_inverse_image(U_87,U_95)
| ( ~ in(sK19(U_87,U_95,U_93),U_93)
& in(sK20(U_87,U_95,U_93),U_95)
& in(ordered_pair(sK19(U_87,U_95,U_93),sK20(U_87,U_95,U_93)),U_87) )
| ( ! [U_82] :
( ~ in(U_82,U_95)
| ~ in(ordered_pair(sK18(U_87,U_95,U_93),U_82),U_87) )
& in(sK18(U_87,U_95,U_93),U_93) ) )
& ! [U_94,U_92] :
( ( ! [U_89] :
( in(U_89,U_92)
| ! [U_80] :
( ~ in(U_80,U_94)
| ~ in(ordered_pair(U_89,U_80),U_87) ) )
& ! [U_88] :
( ( in(sK17(U_87,U_94,U_92,U_88),U_94)
& in(ordered_pair(U_88,sK17(U_87,U_94,U_92,U_88)),U_87) )
| ~ in(U_88,U_92) ) )
| U_92 != relation_inverse_image(U_87,U_94) ) )
| ~ relation(U_87) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_83,sK20(U_87,U_95,U_93))],[f_13_6]) ).
cnf(f_13_8,plain,
( in(ordered_pair(U_88,sK17(U_87,U_94,U_92,U_88)),U_87)
| ~ in(U_88,U_92)
| U_92 != relation_inverse_image(U_87,U_94)
| ~ relation(U_87) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_9,plain,
( in(sK17(U_87,U_94,U_92,U_88),U_94)
| ~ in(U_88,U_92)
| U_92 != relation_inverse_image(U_87,U_94)
| ~ relation(U_87) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_10,plain,
( in(U_89,U_92)
| ~ in(U_80,U_94)
| ~ in(ordered_pair(U_89,U_80),U_87)
| U_92 != relation_inverse_image(U_87,U_94)
| ~ relation(U_87) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_11,plain,
( in(ordered_pair(sK19(U_87,U_95,U_93),sK20(U_87,U_95,U_93)),U_87)
| in(sK18(U_87,U_95,U_93),U_93)
| U_93 = relation_inverse_image(U_87,U_95)
| ~ relation(U_87) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_12,plain,
( in(sK20(U_87,U_95,U_93),U_95)
| in(sK18(U_87,U_95,U_93),U_93)
| U_93 = relation_inverse_image(U_87,U_95)
| ~ relation(U_87) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_13,plain,
( ~ in(sK19(U_87,U_95,U_93),U_93)
| in(sK18(U_87,U_95,U_93),U_93)
| U_93 = relation_inverse_image(U_87,U_95)
| ~ relation(U_87) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_14,plain,
( in(ordered_pair(sK19(U_87,U_95,U_93),sK20(U_87,U_95,U_93)),U_87)
| ~ in(U_82,U_95)
| ~ in(ordered_pair(sK18(U_87,U_95,U_93),U_82),U_87)
| U_93 = relation_inverse_image(U_87,U_95)
| ~ relation(U_87) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_15,plain,
( in(sK20(U_87,U_95,U_93),U_95)
| ~ in(U_82,U_95)
| ~ in(ordered_pair(sK18(U_87,U_95,U_93),U_82),U_87)
| U_93 = relation_inverse_image(U_87,U_95)
| ~ relation(U_87) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_16,plain,
( ~ in(sK19(U_87,U_95,U_93),U_93)
| ~ in(U_82,U_95)
| ~ in(ordered_pair(sK18(U_87,U_95,U_93),U_82),U_87)
| U_93 = relation_inverse_image(U_87,U_95)
| ~ relation(U_87) ),
inference(clausify,[status(thm)],[f_13_7]) ).
fof(f_14_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_14_2,plain,
! [U_102] :
( ( relation(U_102)
| ? [U_101] :
( ! [U_100,U_99] : U_101 != ordered_pair(U_100,U_99)
& in(U_101,U_102) ) )
& ( ! [U_98] :
( ? [U_97,U_96] : U_98 = ordered_pair(U_97,U_96)
| ~ in(U_98,U_102) )
| ~ relation(U_102) ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_104] :
( relation(U_104)
| ? [U_101] :
( ! [U_100,U_99] : U_101 != ordered_pair(U_100,U_99)
& in(U_101,U_104) ) )
& ! [U_103] :
( ! [U_98] :
( ? [U_97,U_96] : U_98 = ordered_pair(U_97,U_96)
| ~ in(U_98,U_103) )
| ~ relation(U_103) ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
fof(f_14_4,plain,
( ! [U_104] :
( relation(U_104)
| ? [U_101] :
( ! [U_100,U_99] : U_101 != ordered_pair(U_100,U_99)
& in(U_101,U_104) ) )
& ! [U_103] :
( ! [U_98] :
( ? [U_96] : U_98 = ordered_pair(sK21(U_103,U_98),U_96)
| ~ in(U_98,U_103) )
| ~ relation(U_103) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_97,sK21(U_103,U_98))],[f_14_3]) ).
fof(f_14_5,plain,
( ! [U_104] :
( relation(U_104)
| ? [U_101] :
( ! [U_100,U_99] : U_101 != ordered_pair(U_100,U_99)
& in(U_101,U_104) ) )
& ! [U_103] :
( ! [U_98] :
( U_98 = ordered_pair(sK21(U_103,U_98),sK22(U_103,U_98))
| ~ in(U_98,U_103) )
| ~ relation(U_103) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_96,sK22(U_103,U_98))],[f_14_4]) ).
fof(f_14_6,plain,
( ! [U_104] :
( relation(U_104)
| ( ! [U_100,U_99] : sK23(U_104) != ordered_pair(U_100,U_99)
& in(sK23(U_104),U_104) ) )
& ! [U_103] :
( ! [U_98] :
( U_98 = ordered_pair(sK21(U_103,U_98),sK22(U_103,U_98))
| ~ in(U_98,U_103) )
| ~ relation(U_103) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_101,sK23(U_104))],[f_14_5]) ).
cnf(f_14_7,plain,
( U_98 = ordered_pair(sK21(U_103,U_98),sK22(U_103,U_98))
| ~ in(U_98,U_103)
| ~ relation(U_103) ),
inference(clausify,[status(thm)],[f_14_6]) ).
cnf(f_14_8,plain,
( in(sK23(U_104),U_104)
| relation(U_104) ),
inference(clausify,[status(thm)],[f_14_6]) ).
cnf(f_14_9,plain,
( sK23(U_104) != ordered_pair(U_100,U_99)
| relation(U_104) ),
inference(clausify,[status(thm)],[f_14_6]) ).
fof(f_15_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_15_2,plain,
! [U_112,U_111] :
( ( ( ( U_111 = set_meet(U_112)
| U_111 != empty_set )
& ( U_111 = empty_set
| U_111 != set_meet(U_112) ) )
| U_112 != empty_set )
& ( ( ( U_111 = set_meet(U_112)
| ? [U_110] :
( ( ~ in(U_110,U_111)
& ! [U_109] :
( in(U_110,U_109)
| ~ in(U_109,U_112) ) )
| ( ? [U_108] :
( ~ in(U_110,U_108)
& in(U_108,U_112) )
& in(U_110,U_111) ) ) )
& ( ! [U_107] :
( ( in(U_107,U_111)
| ? [U_106] :
( ~ in(U_107,U_106)
& in(U_106,U_112) ) )
& ( ! [U_105] :
( in(U_107,U_105)
| ~ in(U_105,U_112) )
| ~ in(U_107,U_111) ) )
| U_111 != set_meet(U_112) ) )
| U_112 = empty_set ) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ! [U_124] :
( ( ! [U_122] :
( U_122 = set_meet(U_124)
| U_122 != empty_set )
& ! [U_121] :
( U_121 = empty_set
| U_121 != set_meet(U_124) ) )
| U_124 != empty_set )
& ! [U_123] :
( ( ! [U_120] :
( U_120 = set_meet(U_123)
| ? [U_116] :
( ~ in(U_116,U_120)
& ! [U_109] :
( in(U_116,U_109)
| ~ in(U_109,U_123) ) )
| ? [U_115] :
( ? [U_108] :
( ~ in(U_115,U_108)
& in(U_108,U_123) )
& in(U_115,U_120) ) )
& ! [U_119] :
( ( ! [U_114] :
( in(U_114,U_119)
| ? [U_106] :
( ~ in(U_114,U_106)
& in(U_106,U_123) ) )
& ! [U_113] :
( ! [U_105] :
( in(U_113,U_105)
| ~ in(U_105,U_123) )
| ~ in(U_113,U_119) ) )
| U_119 != set_meet(U_123) ) )
| U_123 = empty_set ) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
fof(f_15_4,plain,
( ! [U_124] :
( ( ! [U_122] :
( U_122 = set_meet(U_124)
| U_122 != empty_set )
& ! [U_121] :
( U_121 = empty_set
| U_121 != set_meet(U_124) ) )
| U_124 != empty_set )
& ! [U_123] :
( ( ! [U_120] :
( U_120 = set_meet(U_123)
| ? [U_116] :
( ~ in(U_116,U_120)
& ! [U_109] :
( in(U_116,U_109)
| ~ in(U_109,U_123) ) )
| ? [U_115] :
( ? [U_108] :
( ~ in(U_115,U_108)
& in(U_108,U_123) )
& in(U_115,U_120) ) )
& ! [U_119] :
( ( ! [U_114] :
( in(U_114,U_119)
| ( ~ in(U_114,sK24(U_123,U_119,U_114))
& in(sK24(U_123,U_119,U_114),U_123) ) )
& ! [U_113] :
( ! [U_105] :
( in(U_113,U_105)
| ~ in(U_105,U_123) )
| ~ in(U_113,U_119) ) )
| U_119 != set_meet(U_123) ) )
| U_123 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_106,sK24(U_123,U_119,U_114))],[f_15_3]) ).
fof(f_15_5,plain,
( ! [U_124] :
( ( ! [U_122] :
( U_122 = set_meet(U_124)
| U_122 != empty_set )
& ! [U_121] :
( U_121 = empty_set
| U_121 != set_meet(U_124) ) )
| U_124 != empty_set )
& ! [U_123] :
( ( ! [U_120] :
( U_120 = set_meet(U_123)
| ? [U_116] :
( ~ in(U_116,U_120)
& ! [U_109] :
( in(U_116,U_109)
| ~ in(U_109,U_123) ) )
| ( ? [U_108] :
( ~ in(sK25(U_123,U_120),U_108)
& in(U_108,U_123) )
& in(sK25(U_123,U_120),U_120) ) )
& ! [U_119] :
( ( ! [U_114] :
( in(U_114,U_119)
| ( ~ in(U_114,sK24(U_123,U_119,U_114))
& in(sK24(U_123,U_119,U_114),U_123) ) )
& ! [U_113] :
( ! [U_105] :
( in(U_113,U_105)
| ~ in(U_105,U_123) )
| ~ in(U_113,U_119) ) )
| U_119 != set_meet(U_123) ) )
| U_123 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_115,sK25(U_123,U_120))],[f_15_4]) ).
fof(f_15_6,plain,
( ! [U_124] :
( ( ! [U_122] :
( U_122 = set_meet(U_124)
| U_122 != empty_set )
& ! [U_121] :
( U_121 = empty_set
| U_121 != set_meet(U_124) ) )
| U_124 != empty_set )
& ! [U_123] :
( ( ! [U_120] :
( U_120 = set_meet(U_123)
| ? [U_116] :
( ~ in(U_116,U_120)
& ! [U_109] :
( in(U_116,U_109)
| ~ in(U_109,U_123) ) )
| ( ~ in(sK25(U_123,U_120),sK26(U_123,U_120))
& in(sK26(U_123,U_120),U_123)
& in(sK25(U_123,U_120),U_120) ) )
& ! [U_119] :
( ( ! [U_114] :
( in(U_114,U_119)
| ( ~ in(U_114,sK24(U_123,U_119,U_114))
& in(sK24(U_123,U_119,U_114),U_123) ) )
& ! [U_113] :
( ! [U_105] :
( in(U_113,U_105)
| ~ in(U_105,U_123) )
| ~ in(U_113,U_119) ) )
| U_119 != set_meet(U_123) ) )
| U_123 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_108,sK26(U_123,U_120))],[f_15_5]) ).
fof(f_15_7,plain,
( ! [U_124] :
( ( ! [U_122] :
( U_122 = set_meet(U_124)
| U_122 != empty_set )
& ! [U_121] :
( U_121 = empty_set
| U_121 != set_meet(U_124) ) )
| U_124 != empty_set )
& ! [U_123] :
( ( ! [U_120] :
( U_120 = set_meet(U_123)
| ( ~ in(sK27(U_123,U_120),U_120)
& ! [U_109] :
( in(sK27(U_123,U_120),U_109)
| ~ in(U_109,U_123) ) )
| ( ~ in(sK25(U_123,U_120),sK26(U_123,U_120))
& in(sK26(U_123,U_120),U_123)
& in(sK25(U_123,U_120),U_120) ) )
& ! [U_119] :
( ( ! [U_114] :
( in(U_114,U_119)
| ( ~ in(U_114,sK24(U_123,U_119,U_114))
& in(sK24(U_123,U_119,U_114),U_123) ) )
& ! [U_113] :
( ! [U_105] :
( in(U_113,U_105)
| ~ in(U_105,U_123) )
| ~ in(U_113,U_119) ) )
| U_119 != set_meet(U_123) ) )
| U_123 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_116,sK27(U_123,U_120))],[f_15_6]) ).
cnf(f_15_8,plain,
( in(U_113,U_105)
| ~ in(U_105,U_123)
| ~ in(U_113,U_119)
| U_119 != set_meet(U_123)
| U_123 = empty_set ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_9,plain,
( in(sK24(U_123,U_119,U_114),U_123)
| in(U_114,U_119)
| U_119 != set_meet(U_123)
| U_123 = empty_set ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_10,plain,
( ~ in(U_114,sK24(U_123,U_119,U_114))
| in(U_114,U_119)
| U_119 != set_meet(U_123)
| U_123 = empty_set ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_11,plain,
( in(sK27(U_123,U_120),U_109)
| ~ in(U_109,U_123)
| in(sK25(U_123,U_120),U_120)
| U_120 = set_meet(U_123)
| U_123 = empty_set ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_12,plain,
( ~ in(sK27(U_123,U_120),U_120)
| in(sK25(U_123,U_120),U_120)
| U_120 = set_meet(U_123)
| U_123 = empty_set ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_13,plain,
( in(sK26(U_123,U_120),U_123)
| in(sK27(U_123,U_120),U_109)
| ~ in(U_109,U_123)
| U_120 = set_meet(U_123)
| U_123 = empty_set ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_14,plain,
( ~ in(sK25(U_123,U_120),sK26(U_123,U_120))
| in(sK27(U_123,U_120),U_109)
| ~ in(U_109,U_123)
| U_120 = set_meet(U_123)
| U_123 = empty_set ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_15,plain,
( in(sK26(U_123,U_120),U_123)
| ~ in(sK27(U_123,U_120),U_120)
| U_120 = set_meet(U_123)
| U_123 = empty_set ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_16,plain,
( ~ in(sK25(U_123,U_120),sK26(U_123,U_120))
| ~ in(sK27(U_123,U_120),U_120)
| U_120 = set_meet(U_123)
| U_123 = empty_set ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_17,plain,
( U_121 = empty_set
| U_121 != set_meet(U_124)
| U_124 != empty_set ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_18,plain,
( U_122 = set_meet(U_124)
| U_122 != empty_set
| U_124 != empty_set ),
inference(clausify,[status(thm)],[f_15_7]) ).
fof(f_16_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_16_2,plain,
! [U_128,U_127] :
( ( U_127 = singleton(U_128)
| ? [U_126] :
( ( ~ in(U_126,U_127)
& U_126 = U_128 )
| ( U_126 != U_128
& in(U_126,U_127) ) ) )
& ( ! [U_125] :
( ( in(U_125,U_127)
| U_125 != U_128 )
& ( U_125 = U_128
| ~ in(U_125,U_127) ) )
| U_127 != singleton(U_128) ) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( ! [U_136,U_134] :
( U_134 = singleton(U_136)
| ? [U_132] :
( ~ in(U_132,U_134)
& U_132 = U_136 )
| ? [U_131] :
( U_131 != U_136
& in(U_131,U_134) ) )
& ! [U_135,U_133] :
( ( ! [U_130] :
( in(U_130,U_133)
| U_130 != U_135 )
& ! [U_129] :
( U_129 = U_135
| ~ in(U_129,U_133) ) )
| U_133 != singleton(U_135) ) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
fof(f_16_4,plain,
( ! [U_136,U_134] :
( U_134 = singleton(U_136)
| ? [U_132] :
( ~ in(U_132,U_134)
& U_132 = U_136 )
| ( sK28(U_136,U_134) != U_136
& in(sK28(U_136,U_134),U_134) ) )
& ! [U_135,U_133] :
( ( ! [U_130] :
( in(U_130,U_133)
| U_130 != U_135 )
& ! [U_129] :
( U_129 = U_135
| ~ in(U_129,U_133) ) )
| U_133 != singleton(U_135) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_131,sK28(U_136,U_134))],[f_16_3]) ).
fof(f_16_5,plain,
( ! [U_136,U_134] :
( U_134 = singleton(U_136)
| ( ~ in(sK29(U_136,U_134),U_134)
& sK29(U_136,U_134) = U_136 )
| ( sK28(U_136,U_134) != U_136
& in(sK28(U_136,U_134),U_134) ) )
& ! [U_135,U_133] :
( ( ! [U_130] :
( in(U_130,U_133)
| U_130 != U_135 )
& ! [U_129] :
( U_129 = U_135
| ~ in(U_129,U_133) ) )
| U_133 != singleton(U_135) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_132,sK29(U_136,U_134))],[f_16_4]) ).
cnf(f_16_6,plain,
( U_129 = U_135
| ~ in(U_129,U_133)
| U_133 != singleton(U_135) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_7,plain,
( in(U_130,U_133)
| U_130 != U_135
| U_133 != singleton(U_135) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_8,plain,
( sK29(U_136,U_134) = U_136
| in(sK28(U_136,U_134),U_134)
| U_134 = singleton(U_136) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_9,plain,
( ~ in(sK29(U_136,U_134),U_134)
| in(sK28(U_136,U_134),U_134)
| U_134 = singleton(U_136) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_10,plain,
( sK29(U_136,U_134) = U_136
| sK28(U_136,U_134) != U_136
| U_134 = singleton(U_136) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_11,plain,
( ~ in(sK29(U_136,U_134),U_134)
| sK28(U_136,U_134) != U_136
| U_134 = singleton(U_136) ),
inference(clausify,[status(thm)],[f_16_5]) ).
fof(f_17_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_17_2,plain,
! [U_139] :
( ( U_139 = empty_set
| ? [U_138] : in(U_138,U_139) )
& ( ! [U_137] : ~ in(U_137,U_139)
| U_139 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( ! [U_141] :
( U_141 = empty_set
| ? [U_138] : in(U_138,U_141) )
& ! [U_140] :
( ! [U_137] : ~ in(U_137,U_140)
| U_140 != empty_set ) ),
inference(miniscope,[status(thm)],[f_17_2]) ).
fof(f_17_4,plain,
( ! [U_141] :
( U_141 = empty_set
| in(sK30(U_141),U_141) )
& ! [U_140] :
( ! [U_137] : ~ in(U_137,U_140)
| U_140 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_138,sK30(U_141))],[f_17_3]) ).
cnf(f_17_5,plain,
( ~ in(U_137,U_140)
| U_140 != empty_set ),
inference(clausify,[status(thm)],[f_17_4]) ).
cnf(f_17_6,plain,
( U_141 = empty_set
| in(sK30(U_141),U_141) ),
inference(clausify,[status(thm)],[f_17_4]) ).
fof(f_18_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_18_2,plain,
! [U_145,U_144] :
( ( U_144 = powerset(U_145)
| ? [U_143] :
( ( ~ in(U_143,U_144)
& subset(U_143,U_145) )
| ( ~ subset(U_143,U_145)
& in(U_143,U_144) ) ) )
& ( ! [U_142] :
( ( in(U_142,U_144)
| ~ subset(U_142,U_145) )
& ( subset(U_142,U_145)
| ~ in(U_142,U_144) ) )
| U_144 != powerset(U_145) ) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( ! [U_153,U_151] :
( U_151 = powerset(U_153)
| ? [U_149] :
( ~ in(U_149,U_151)
& subset(U_149,U_153) )
| ? [U_148] :
( ~ subset(U_148,U_153)
& in(U_148,U_151) ) )
& ! [U_152,U_150] :
( ( ! [U_147] :
( in(U_147,U_150)
| ~ subset(U_147,U_152) )
& ! [U_146] :
( subset(U_146,U_152)
| ~ in(U_146,U_150) ) )
| U_150 != powerset(U_152) ) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
fof(f_18_4,plain,
( ! [U_153,U_151] :
( U_151 = powerset(U_153)
| ? [U_149] :
( ~ in(U_149,U_151)
& subset(U_149,U_153) )
| ( ~ subset(sK31(U_153,U_151),U_153)
& in(sK31(U_153,U_151),U_151) ) )
& ! [U_152,U_150] :
( ( ! [U_147] :
( in(U_147,U_150)
| ~ subset(U_147,U_152) )
& ! [U_146] :
( subset(U_146,U_152)
| ~ in(U_146,U_150) ) )
| U_150 != powerset(U_152) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_148,sK31(U_153,U_151))],[f_18_3]) ).
fof(f_18_5,plain,
( ! [U_153,U_151] :
( U_151 = powerset(U_153)
| ( ~ in(sK32(U_153,U_151),U_151)
& subset(sK32(U_153,U_151),U_153) )
| ( ~ subset(sK31(U_153,U_151),U_153)
& in(sK31(U_153,U_151),U_151) ) )
& ! [U_152,U_150] :
( ( ! [U_147] :
( in(U_147,U_150)
| ~ subset(U_147,U_152) )
& ! [U_146] :
( subset(U_146,U_152)
| ~ in(U_146,U_150) ) )
| U_150 != powerset(U_152) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_149,sK32(U_153,U_151))],[f_18_4]) ).
cnf(f_18_6,plain,
( subset(U_146,U_152)
| ~ in(U_146,U_150)
| U_150 != powerset(U_152) ),
inference(clausify,[status(thm)],[f_18_5]) ).
cnf(f_18_7,plain,
( in(U_147,U_150)
| ~ subset(U_147,U_152)
| U_150 != powerset(U_152) ),
inference(clausify,[status(thm)],[f_18_5]) ).
cnf(f_18_8,plain,
( subset(sK32(U_153,U_151),U_153)
| in(sK31(U_153,U_151),U_151)
| U_151 = powerset(U_153) ),
inference(clausify,[status(thm)],[f_18_5]) ).
cnf(f_18_9,plain,
( ~ in(sK32(U_153,U_151),U_151)
| in(sK31(U_153,U_151),U_151)
| U_151 = powerset(U_153) ),
inference(clausify,[status(thm)],[f_18_5]) ).
cnf(f_18_10,plain,
( subset(sK32(U_153,U_151),U_153)
| ~ subset(sK31(U_153,U_151),U_153)
| U_151 = powerset(U_153) ),
inference(clausify,[status(thm)],[f_18_5]) ).
cnf(f_18_11,plain,
( ~ in(sK32(U_153,U_151),U_151)
| ~ subset(sK31(U_153,U_151),U_153)
| U_151 = powerset(U_153) ),
inference(clausify,[status(thm)],[f_18_5]) ).
fof(f_19_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_19_2,plain,
! [U_159] :
( ! [U_158] :
( ( ( U_159 = U_158
| ? [U_157,U_156] :
( ( ~ in(ordered_pair(U_157,U_156),U_159)
& in(ordered_pair(U_157,U_156),U_158) )
| ( ~ in(ordered_pair(U_157,U_156),U_158)
& in(ordered_pair(U_157,U_156),U_159) ) ) )
& ( ! [U_155,U_154] :
( ( in(ordered_pair(U_155,U_154),U_159)
| ~ in(ordered_pair(U_155,U_154),U_158) )
& ( in(ordered_pair(U_155,U_154),U_158)
| ~ in(ordered_pair(U_155,U_154),U_159) ) )
| U_159 != U_158 ) )
| ~ relation(U_158) )
| ~ relation(U_159) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_159] :
( ! [U_158] :
( ( ( U_159 = U_158
| ? [U_167,U_165] :
( ~ in(ordered_pair(U_167,U_165),U_159)
& in(ordered_pair(U_167,U_165),U_158) )
| ? [U_166,U_164] :
( ~ in(ordered_pair(U_166,U_164),U_158)
& in(ordered_pair(U_166,U_164),U_159) ) )
& ( ( ! [U_163,U_161] :
( in(ordered_pair(U_163,U_161),U_159)
| ~ in(ordered_pair(U_163,U_161),U_158) )
& ! [U_162,U_160] :
( in(ordered_pair(U_162,U_160),U_158)
| ~ in(ordered_pair(U_162,U_160),U_159) ) )
| U_159 != U_158 ) )
| ~ relation(U_158) )
| ~ relation(U_159) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
fof(f_19_4,plain,
! [U_159] :
( ! [U_158] :
( ( ( U_159 = U_158
| ? [U_167,U_165] :
( ~ in(ordered_pair(U_167,U_165),U_159)
& in(ordered_pair(U_167,U_165),U_158) )
| ? [U_164] :
( ~ in(ordered_pair(sK33(U_159,U_158),U_164),U_158)
& in(ordered_pair(sK33(U_159,U_158),U_164),U_159) ) )
& ( ( ! [U_163,U_161] :
( in(ordered_pair(U_163,U_161),U_159)
| ~ in(ordered_pair(U_163,U_161),U_158) )
& ! [U_162,U_160] :
( in(ordered_pair(U_162,U_160),U_158)
| ~ in(ordered_pair(U_162,U_160),U_159) ) )
| U_159 != U_158 ) )
| ~ relation(U_158) )
| ~ relation(U_159) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_166,sK33(U_159,U_158))],[f_19_3]) ).
fof(f_19_5,plain,
! [U_159] :
( ! [U_158] :
( ( ( U_159 = U_158
| ? [U_167,U_165] :
( ~ in(ordered_pair(U_167,U_165),U_159)
& in(ordered_pair(U_167,U_165),U_158) )
| ( ~ in(ordered_pair(sK33(U_159,U_158),sK34(U_159,U_158)),U_158)
& in(ordered_pair(sK33(U_159,U_158),sK34(U_159,U_158)),U_159) ) )
& ( ( ! [U_163,U_161] :
( in(ordered_pair(U_163,U_161),U_159)
| ~ in(ordered_pair(U_163,U_161),U_158) )
& ! [U_162,U_160] :
( in(ordered_pair(U_162,U_160),U_158)
| ~ in(ordered_pair(U_162,U_160),U_159) ) )
| U_159 != U_158 ) )
| ~ relation(U_158) )
| ~ relation(U_159) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_164,sK34(U_159,U_158))],[f_19_4]) ).
fof(f_19_6,plain,
! [U_159] :
( ! [U_158] :
( ( ( U_159 = U_158
| ? [U_165] :
( ~ in(ordered_pair(sK35(U_159,U_158),U_165),U_159)
& in(ordered_pair(sK35(U_159,U_158),U_165),U_158) )
| ( ~ in(ordered_pair(sK33(U_159,U_158),sK34(U_159,U_158)),U_158)
& in(ordered_pair(sK33(U_159,U_158),sK34(U_159,U_158)),U_159) ) )
& ( ( ! [U_163,U_161] :
( in(ordered_pair(U_163,U_161),U_159)
| ~ in(ordered_pair(U_163,U_161),U_158) )
& ! [U_162,U_160] :
( in(ordered_pair(U_162,U_160),U_158)
| ~ in(ordered_pair(U_162,U_160),U_159) ) )
| U_159 != U_158 ) )
| ~ relation(U_158) )
| ~ relation(U_159) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_167,sK35(U_159,U_158))],[f_19_5]) ).
fof(f_19_7,plain,
! [U_159] :
( ! [U_158] :
( ( ( U_159 = U_158
| ( ~ in(ordered_pair(sK35(U_159,U_158),sK36(U_159,U_158)),U_159)
& in(ordered_pair(sK35(U_159,U_158),sK36(U_159,U_158)),U_158) )
| ( ~ in(ordered_pair(sK33(U_159,U_158),sK34(U_159,U_158)),U_158)
& in(ordered_pair(sK33(U_159,U_158),sK34(U_159,U_158)),U_159) ) )
& ( ( ! [U_163,U_161] :
( in(ordered_pair(U_163,U_161),U_159)
| ~ in(ordered_pair(U_163,U_161),U_158) )
& ! [U_162,U_160] :
( in(ordered_pair(U_162,U_160),U_158)
| ~ in(ordered_pair(U_162,U_160),U_159) ) )
| U_159 != U_158 ) )
| ~ relation(U_158) )
| ~ relation(U_159) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_165,sK36(U_159,U_158))],[f_19_6]) ).
cnf(f_19_8,plain,
( in(ordered_pair(U_162,U_160),U_158)
| ~ in(ordered_pair(U_162,U_160),U_159)
| U_159 != U_158
| ~ relation(U_158)
| ~ relation(U_159) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_9,plain,
( in(ordered_pair(U_163,U_161),U_159)
| ~ in(ordered_pair(U_163,U_161),U_158)
| U_159 != U_158
| ~ relation(U_158)
| ~ relation(U_159) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_10,plain,
( in(ordered_pair(sK35(U_159,U_158),sK36(U_159,U_158)),U_158)
| in(ordered_pair(sK33(U_159,U_158),sK34(U_159,U_158)),U_159)
| U_159 = U_158
| ~ relation(U_158)
| ~ relation(U_159) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_11,plain,
( ~ in(ordered_pair(sK35(U_159,U_158),sK36(U_159,U_158)),U_159)
| in(ordered_pair(sK33(U_159,U_158),sK34(U_159,U_158)),U_159)
| U_159 = U_158
| ~ relation(U_158)
| ~ relation(U_159) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_12,plain,
( in(ordered_pair(sK35(U_159,U_158),sK36(U_159,U_158)),U_158)
| ~ in(ordered_pair(sK33(U_159,U_158),sK34(U_159,U_158)),U_158)
| U_159 = U_158
| ~ relation(U_158)
| ~ relation(U_159) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_13,plain,
( ~ in(ordered_pair(sK35(U_159,U_158),sK36(U_159,U_158)),U_159)
| ~ in(ordered_pair(sK33(U_159,U_158),sK34(U_159,U_158)),U_158)
| U_159 = U_158
| ~ relation(U_158)
| ~ relation(U_159) ),
inference(clausify,[status(thm)],[f_19_7]) ).
fof(f_20_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_20_2,plain,
! [U_169,U_168] :
( ( ( ( element(U_168,U_169)
| ~ empty(U_168) )
& ( empty(U_168)
| ~ element(U_168,U_169) ) )
| ~ empty(U_169) )
& ( ( ( element(U_168,U_169)
| ~ in(U_168,U_169) )
& ( in(U_168,U_169)
| ~ element(U_168,U_169) ) )
| empty(U_169) ) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( ! [U_177] :
( ( ! [U_175] :
( element(U_175,U_177)
| ~ empty(U_175) )
& ! [U_174] :
( empty(U_174)
| ~ element(U_174,U_177) ) )
| ~ empty(U_177) )
& ! [U_176] :
( ( ! [U_173] :
( element(U_173,U_176)
| ~ in(U_173,U_176) )
& ! [U_172] :
( in(U_172,U_176)
| ~ element(U_172,U_176) ) )
| empty(U_176) ) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
cnf(f_20_4,plain,
( in(U_172,U_176)
| ~ element(U_172,U_176)
| empty(U_176) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_5,plain,
( element(U_173,U_176)
| ~ in(U_173,U_176)
| empty(U_176) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_6,plain,
( empty(U_174)
| ~ element(U_174,U_177)
| ~ empty(U_177) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_7,plain,
( element(U_175,U_177)
| ~ empty(U_175)
| ~ empty(U_177) ),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_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_21_2,plain,
! [U_182,U_181,U_180] :
( ( U_180 = unordered_pair(U_182,U_181)
| ? [U_179] :
( ( ~ in(U_179,U_180)
& ( U_179 = U_181
| U_179 = U_182 ) )
| ( U_179 != U_181
& U_179 != U_182
& in(U_179,U_180) ) ) )
& ( ! [U_178] :
( ( in(U_178,U_180)
| ( U_178 != U_181
& U_178 != U_182 ) )
& ( U_178 = U_181
| U_178 = U_182
| ~ in(U_178,U_180) ) )
| U_180 != unordered_pair(U_182,U_181) ) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( ! [U_192,U_190,U_188] :
( U_188 = unordered_pair(U_192,U_190)
| ? [U_186] :
( ~ in(U_186,U_188)
& ( U_186 = U_190
| U_186 = U_192 ) )
| ? [U_185] :
( U_185 != U_190
& U_185 != U_192
& in(U_185,U_188) ) )
& ! [U_191,U_189,U_187] :
( ( ! [U_184] :
( in(U_184,U_187)
| ( U_184 != U_189
& U_184 != U_191 ) )
& ! [U_183] :
( U_183 = U_189
| U_183 = U_191
| ~ in(U_183,U_187) ) )
| U_187 != unordered_pair(U_191,U_189) ) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
fof(f_21_4,plain,
( ! [U_192,U_190,U_188] :
( U_188 = unordered_pair(U_192,U_190)
| ? [U_186] :
( ~ in(U_186,U_188)
& ( U_186 = U_190
| U_186 = U_192 ) )
| ( sK37(U_192,U_190,U_188) != U_190
& sK37(U_192,U_190,U_188) != U_192
& in(sK37(U_192,U_190,U_188),U_188) ) )
& ! [U_191,U_189,U_187] :
( ( ! [U_184] :
( in(U_184,U_187)
| ( U_184 != U_189
& U_184 != U_191 ) )
& ! [U_183] :
( U_183 = U_189
| U_183 = U_191
| ~ in(U_183,U_187) ) )
| U_187 != unordered_pair(U_191,U_189) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_185,sK37(U_192,U_190,U_188))],[f_21_3]) ).
fof(f_21_5,plain,
( ! [U_192,U_190,U_188] :
( U_188 = unordered_pair(U_192,U_190)
| ( ~ in(sK38(U_192,U_190,U_188),U_188)
& ( sK38(U_192,U_190,U_188) = U_190
| sK38(U_192,U_190,U_188) = U_192 ) )
| ( sK37(U_192,U_190,U_188) != U_190
& sK37(U_192,U_190,U_188) != U_192
& in(sK37(U_192,U_190,U_188),U_188) ) )
& ! [U_191,U_189,U_187] :
( ( ! [U_184] :
( in(U_184,U_187)
| ( U_184 != U_189
& U_184 != U_191 ) )
& ! [U_183] :
( U_183 = U_189
| U_183 = U_191
| ~ in(U_183,U_187) ) )
| U_187 != unordered_pair(U_191,U_189) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_186,sK38(U_192,U_190,U_188))],[f_21_4]) ).
cnf(f_21_6,plain,
( U_183 = U_189
| U_183 = U_191
| ~ in(U_183,U_187)
| U_187 != unordered_pair(U_191,U_189) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_7,plain,
( U_184 != U_191
| in(U_184,U_187)
| U_187 != unordered_pair(U_191,U_189) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_8,plain,
( U_184 != U_189
| in(U_184,U_187)
| U_187 != unordered_pair(U_191,U_189) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_9,plain,
( sK38(U_192,U_190,U_188) = U_190
| sK38(U_192,U_190,U_188) = U_192
| in(sK37(U_192,U_190,U_188),U_188)
| U_188 = unordered_pair(U_192,U_190) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_10,plain,
( ~ in(sK38(U_192,U_190,U_188),U_188)
| in(sK37(U_192,U_190,U_188),U_188)
| U_188 = unordered_pair(U_192,U_190) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_11,plain,
( sK37(U_192,U_190,U_188) != U_192
| sK38(U_192,U_190,U_188) = U_190
| sK38(U_192,U_190,U_188) = U_192
| U_188 = unordered_pair(U_192,U_190) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_12,plain,
( sK37(U_192,U_190,U_188) != U_190
| sK38(U_192,U_190,U_188) = U_190
| sK38(U_192,U_190,U_188) = U_192
| U_188 = unordered_pair(U_192,U_190) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_13,plain,
( sK37(U_192,U_190,U_188) != U_192
| ~ in(sK38(U_192,U_190,U_188),U_188)
| U_188 = unordered_pair(U_192,U_190) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_14,plain,
( sK37(U_192,U_190,U_188) != U_190
| ~ in(sK38(U_192,U_190,U_188),U_188)
| U_188 = unordered_pair(U_192,U_190) ),
inference(clausify,[status(thm)],[f_21_5]) ).
fof(f_22_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_22_2,plain,
! [U_197,U_196,U_195] :
( ( U_195 = set_union2(U_197,U_196)
| ? [U_194] :
( ( ~ in(U_194,U_195)
& ( in(U_194,U_196)
| in(U_194,U_197) ) )
| ( ~ in(U_194,U_196)
& ~ in(U_194,U_197)
& in(U_194,U_195) ) ) )
& ( ! [U_193] :
( ( in(U_193,U_195)
| ( ~ in(U_193,U_196)
& ~ in(U_193,U_197) ) )
& ( in(U_193,U_196)
| in(U_193,U_197)
| ~ in(U_193,U_195) ) )
| U_195 != set_union2(U_197,U_196) ) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( ! [U_207,U_205,U_203] :
( U_203 = set_union2(U_207,U_205)
| ? [U_201] :
( ~ in(U_201,U_203)
& ( in(U_201,U_205)
| in(U_201,U_207) ) )
| ? [U_200] :
( ~ in(U_200,U_205)
& ~ in(U_200,U_207)
& in(U_200,U_203) ) )
& ! [U_206,U_204,U_202] :
( ( ! [U_199] :
( in(U_199,U_202)
| ( ~ in(U_199,U_204)
& ~ in(U_199,U_206) ) )
& ! [U_198] :
( in(U_198,U_204)
| in(U_198,U_206)
| ~ in(U_198,U_202) ) )
| U_202 != set_union2(U_206,U_204) ) ),
inference(miniscope,[status(thm)],[f_22_2]) ).
fof(f_22_4,plain,
( ! [U_207,U_205,U_203] :
( U_203 = set_union2(U_207,U_205)
| ? [U_201] :
( ~ in(U_201,U_203)
& ( in(U_201,U_205)
| in(U_201,U_207) ) )
| ( ~ in(sK39(U_207,U_205,U_203),U_205)
& ~ in(sK39(U_207,U_205,U_203),U_207)
& in(sK39(U_207,U_205,U_203),U_203) ) )
& ! [U_206,U_204,U_202] :
( ( ! [U_199] :
( in(U_199,U_202)
| ( ~ in(U_199,U_204)
& ~ in(U_199,U_206) ) )
& ! [U_198] :
( in(U_198,U_204)
| in(U_198,U_206)
| ~ in(U_198,U_202) ) )
| U_202 != set_union2(U_206,U_204) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_200,sK39(U_207,U_205,U_203))],[f_22_3]) ).
fof(f_22_5,plain,
( ! [U_207,U_205,U_203] :
( U_203 = set_union2(U_207,U_205)
| ( ~ in(sK40(U_207,U_205,U_203),U_203)
& ( in(sK40(U_207,U_205,U_203),U_205)
| in(sK40(U_207,U_205,U_203),U_207) ) )
| ( ~ in(sK39(U_207,U_205,U_203),U_205)
& ~ in(sK39(U_207,U_205,U_203),U_207)
& in(sK39(U_207,U_205,U_203),U_203) ) )
& ! [U_206,U_204,U_202] :
( ( ! [U_199] :
( in(U_199,U_202)
| ( ~ in(U_199,U_204)
& ~ in(U_199,U_206) ) )
& ! [U_198] :
( in(U_198,U_204)
| in(U_198,U_206)
| ~ in(U_198,U_202) ) )
| U_202 != set_union2(U_206,U_204) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_201,sK40(U_207,U_205,U_203))],[f_22_4]) ).
cnf(f_22_6,plain,
( in(U_198,U_204)
| in(U_198,U_206)
| ~ in(U_198,U_202)
| U_202 != set_union2(U_206,U_204) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_7,plain,
( ~ in(U_199,U_206)
| in(U_199,U_202)
| U_202 != set_union2(U_206,U_204) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_8,plain,
( ~ in(U_199,U_204)
| in(U_199,U_202)
| U_202 != set_union2(U_206,U_204) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_9,plain,
( in(sK40(U_207,U_205,U_203),U_205)
| in(sK40(U_207,U_205,U_203),U_207)
| in(sK39(U_207,U_205,U_203),U_203)
| U_203 = set_union2(U_207,U_205) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_10,plain,
( ~ in(sK40(U_207,U_205,U_203),U_203)
| in(sK39(U_207,U_205,U_203),U_203)
| U_203 = set_union2(U_207,U_205) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_11,plain,
( ~ in(sK39(U_207,U_205,U_203),U_207)
| in(sK40(U_207,U_205,U_203),U_205)
| in(sK40(U_207,U_205,U_203),U_207)
| U_203 = set_union2(U_207,U_205) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_12,plain,
( ~ in(sK39(U_207,U_205,U_203),U_205)
| in(sK40(U_207,U_205,U_203),U_205)
| in(sK40(U_207,U_205,U_203),U_207)
| U_203 = set_union2(U_207,U_205) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_13,plain,
( ~ in(sK39(U_207,U_205,U_203),U_207)
| ~ in(sK40(U_207,U_205,U_203),U_203)
| U_203 = set_union2(U_207,U_205) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_14,plain,
( ~ in(sK39(U_207,U_205,U_203),U_205)
| ~ in(sK40(U_207,U_205,U_203),U_203)
| U_203 = set_union2(U_207,U_205) ),
inference(clausify,[status(thm)],[f_22_5]) ).
fof(f_23_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_23_2,plain,
! [U_220,U_219,U_218] :
( ( U_218 = cartesian_product2(U_220,U_219)
| ? [U_217] :
( ( ~ in(U_217,U_218)
& ? [U_216,U_215] :
( U_217 = ordered_pair(U_216,U_215)
& in(U_215,U_219)
& in(U_216,U_220) ) )
| ( ! [U_214,U_213] :
( U_217 != ordered_pair(U_214,U_213)
| ~ in(U_213,U_219)
| ~ in(U_214,U_220) )
& in(U_217,U_218) ) ) )
& ( ! [U_212] :
( ( in(U_212,U_218)
| ! [U_211,U_210] :
( U_212 != ordered_pair(U_211,U_210)
| ~ in(U_210,U_219)
| ~ in(U_211,U_220) ) )
& ( ? [U_209,U_208] :
( U_212 = ordered_pair(U_209,U_208)
& in(U_208,U_219)
& in(U_209,U_220) )
| ~ in(U_212,U_218) ) )
| U_218 != cartesian_product2(U_220,U_219) ) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( ! [U_230,U_228,U_226] :
( U_226 = cartesian_product2(U_230,U_228)
| ? [U_224] :
( ~ in(U_224,U_226)
& ? [U_216] :
( ? [U_215] :
( U_224 = ordered_pair(U_216,U_215)
& in(U_215,U_228) )
& in(U_216,U_230) ) )
| ? [U_223] :
( ! [U_214] :
( ! [U_213] :
( U_223 != ordered_pair(U_214,U_213)
| ~ in(U_213,U_228) )
| ~ in(U_214,U_230) )
& in(U_223,U_226) ) )
& ! [U_229,U_227,U_225] :
( ( ! [U_222] :
( in(U_222,U_225)
| ! [U_211] :
( ! [U_210] :
( U_222 != ordered_pair(U_211,U_210)
| ~ in(U_210,U_227) )
| ~ in(U_211,U_229) ) )
& ! [U_221] :
( ? [U_209] :
( ? [U_208] :
( U_221 = ordered_pair(U_209,U_208)
& in(U_208,U_227) )
& in(U_209,U_229) )
| ~ in(U_221,U_225) ) )
| U_225 != cartesian_product2(U_229,U_227) ) ),
inference(miniscope,[status(thm)],[f_23_2]) ).
fof(f_23_4,plain,
( ! [U_230,U_228,U_226] :
( U_226 = cartesian_product2(U_230,U_228)
| ? [U_224] :
( ~ in(U_224,U_226)
& ? [U_216] :
( ? [U_215] :
( U_224 = ordered_pair(U_216,U_215)
& in(U_215,U_228) )
& in(U_216,U_230) ) )
| ? [U_223] :
( ! [U_214] :
( ! [U_213] :
( U_223 != ordered_pair(U_214,U_213)
| ~ in(U_213,U_228) )
| ~ in(U_214,U_230) )
& in(U_223,U_226) ) )
& ! [U_229,U_227,U_225] :
( ( ! [U_222] :
( in(U_222,U_225)
| ! [U_211] :
( ! [U_210] :
( U_222 != ordered_pair(U_211,U_210)
| ~ in(U_210,U_227) )
| ~ in(U_211,U_229) ) )
& ! [U_221] :
( ( ? [U_208] :
( U_221 = ordered_pair(sK41(U_229,U_227,U_225,U_221),U_208)
& in(U_208,U_227) )
& in(sK41(U_229,U_227,U_225,U_221),U_229) )
| ~ in(U_221,U_225) ) )
| U_225 != cartesian_product2(U_229,U_227) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_209,sK41(U_229,U_227,U_225,U_221))],[f_23_3]) ).
fof(f_23_5,plain,
( ! [U_230,U_228,U_226] :
( U_226 = cartesian_product2(U_230,U_228)
| ? [U_224] :
( ~ in(U_224,U_226)
& ? [U_216] :
( ? [U_215] :
( U_224 = ordered_pair(U_216,U_215)
& in(U_215,U_228) )
& in(U_216,U_230) ) )
| ? [U_223] :
( ! [U_214] :
( ! [U_213] :
( U_223 != ordered_pair(U_214,U_213)
| ~ in(U_213,U_228) )
| ~ in(U_214,U_230) )
& in(U_223,U_226) ) )
& ! [U_229,U_227,U_225] :
( ( ! [U_222] :
( in(U_222,U_225)
| ! [U_211] :
( ! [U_210] :
( U_222 != ordered_pair(U_211,U_210)
| ~ in(U_210,U_227) )
| ~ in(U_211,U_229) ) )
& ! [U_221] :
( ( U_221 = ordered_pair(sK41(U_229,U_227,U_225,U_221),sK42(U_229,U_227,U_225,U_221))
& in(sK42(U_229,U_227,U_225,U_221),U_227)
& in(sK41(U_229,U_227,U_225,U_221),U_229) )
| ~ in(U_221,U_225) ) )
| U_225 != cartesian_product2(U_229,U_227) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_208,sK42(U_229,U_227,U_225,U_221))],[f_23_4]) ).
fof(f_23_6,plain,
( ! [U_230,U_228,U_226] :
( U_226 = cartesian_product2(U_230,U_228)
| ? [U_224] :
( ~ in(U_224,U_226)
& ? [U_216] :
( ? [U_215] :
( U_224 = ordered_pair(U_216,U_215)
& in(U_215,U_228) )
& in(U_216,U_230) ) )
| ( ! [U_214] :
( ! [U_213] :
( sK43(U_230,U_228,U_226) != ordered_pair(U_214,U_213)
| ~ in(U_213,U_228) )
| ~ in(U_214,U_230) )
& in(sK43(U_230,U_228,U_226),U_226) ) )
& ! [U_229,U_227,U_225] :
( ( ! [U_222] :
( in(U_222,U_225)
| ! [U_211] :
( ! [U_210] :
( U_222 != ordered_pair(U_211,U_210)
| ~ in(U_210,U_227) )
| ~ in(U_211,U_229) ) )
& ! [U_221] :
( ( U_221 = ordered_pair(sK41(U_229,U_227,U_225,U_221),sK42(U_229,U_227,U_225,U_221))
& in(sK42(U_229,U_227,U_225,U_221),U_227)
& in(sK41(U_229,U_227,U_225,U_221),U_229) )
| ~ in(U_221,U_225) ) )
| U_225 != cartesian_product2(U_229,U_227) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_223,sK43(U_230,U_228,U_226))],[f_23_5]) ).
fof(f_23_7,plain,
( ! [U_230,U_228,U_226] :
( U_226 = cartesian_product2(U_230,U_228)
| ( ~ in(sK44(U_230,U_228,U_226),U_226)
& ? [U_216] :
( ? [U_215] :
( sK44(U_230,U_228,U_226) = ordered_pair(U_216,U_215)
& in(U_215,U_228) )
& in(U_216,U_230) ) )
| ( ! [U_214] :
( ! [U_213] :
( sK43(U_230,U_228,U_226) != ordered_pair(U_214,U_213)
| ~ in(U_213,U_228) )
| ~ in(U_214,U_230) )
& in(sK43(U_230,U_228,U_226),U_226) ) )
& ! [U_229,U_227,U_225] :
( ( ! [U_222] :
( in(U_222,U_225)
| ! [U_211] :
( ! [U_210] :
( U_222 != ordered_pair(U_211,U_210)
| ~ in(U_210,U_227) )
| ~ in(U_211,U_229) ) )
& ! [U_221] :
( ( U_221 = ordered_pair(sK41(U_229,U_227,U_225,U_221),sK42(U_229,U_227,U_225,U_221))
& in(sK42(U_229,U_227,U_225,U_221),U_227)
& in(sK41(U_229,U_227,U_225,U_221),U_229) )
| ~ in(U_221,U_225) ) )
| U_225 != cartesian_product2(U_229,U_227) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_224,sK44(U_230,U_228,U_226))],[f_23_6]) ).
fof(f_23_8,plain,
( ! [U_230,U_228,U_226] :
( U_226 = cartesian_product2(U_230,U_228)
| ( ~ in(sK44(U_230,U_228,U_226),U_226)
& ? [U_215] :
( sK44(U_230,U_228,U_226) = ordered_pair(sK45(U_230,U_228,U_226),U_215)
& in(U_215,U_228) )
& in(sK45(U_230,U_228,U_226),U_230) )
| ( ! [U_214] :
( ! [U_213] :
( sK43(U_230,U_228,U_226) != ordered_pair(U_214,U_213)
| ~ in(U_213,U_228) )
| ~ in(U_214,U_230) )
& in(sK43(U_230,U_228,U_226),U_226) ) )
& ! [U_229,U_227,U_225] :
( ( ! [U_222] :
( in(U_222,U_225)
| ! [U_211] :
( ! [U_210] :
( U_222 != ordered_pair(U_211,U_210)
| ~ in(U_210,U_227) )
| ~ in(U_211,U_229) ) )
& ! [U_221] :
( ( U_221 = ordered_pair(sK41(U_229,U_227,U_225,U_221),sK42(U_229,U_227,U_225,U_221))
& in(sK42(U_229,U_227,U_225,U_221),U_227)
& in(sK41(U_229,U_227,U_225,U_221),U_229) )
| ~ in(U_221,U_225) ) )
| U_225 != cartesian_product2(U_229,U_227) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_216,sK45(U_230,U_228,U_226))],[f_23_7]) ).
fof(f_23_9,plain,
( ! [U_230,U_228,U_226] :
( U_226 = cartesian_product2(U_230,U_228)
| ( ~ in(sK44(U_230,U_228,U_226),U_226)
& sK44(U_230,U_228,U_226) = ordered_pair(sK45(U_230,U_228,U_226),sK46(U_230,U_228,U_226))
& in(sK46(U_230,U_228,U_226),U_228)
& in(sK45(U_230,U_228,U_226),U_230) )
| ( ! [U_214] :
( ! [U_213] :
( sK43(U_230,U_228,U_226) != ordered_pair(U_214,U_213)
| ~ in(U_213,U_228) )
| ~ in(U_214,U_230) )
& in(sK43(U_230,U_228,U_226),U_226) ) )
& ! [U_229,U_227,U_225] :
( ( ! [U_222] :
( in(U_222,U_225)
| ! [U_211] :
( ! [U_210] :
( U_222 != ordered_pair(U_211,U_210)
| ~ in(U_210,U_227) )
| ~ in(U_211,U_229) ) )
& ! [U_221] :
( ( U_221 = ordered_pair(sK41(U_229,U_227,U_225,U_221),sK42(U_229,U_227,U_225,U_221))
& in(sK42(U_229,U_227,U_225,U_221),U_227)
& in(sK41(U_229,U_227,U_225,U_221),U_229) )
| ~ in(U_221,U_225) ) )
| U_225 != cartesian_product2(U_229,U_227) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_215,sK46(U_230,U_228,U_226))],[f_23_8]) ).
cnf(f_23_10,plain,
( in(sK41(U_229,U_227,U_225,U_221),U_229)
| ~ in(U_221,U_225)
| U_225 != cartesian_product2(U_229,U_227) ),
inference(clausify,[status(thm)],[f_23_9]) ).
cnf(f_23_11,plain,
( in(sK42(U_229,U_227,U_225,U_221),U_227)
| ~ in(U_221,U_225)
| U_225 != cartesian_product2(U_229,U_227) ),
inference(clausify,[status(thm)],[f_23_9]) ).
cnf(f_23_12,plain,
( U_221 = ordered_pair(sK41(U_229,U_227,U_225,U_221),sK42(U_229,U_227,U_225,U_221))
| ~ in(U_221,U_225)
| U_225 != cartesian_product2(U_229,U_227) ),
inference(clausify,[status(thm)],[f_23_9]) ).
cnf(f_23_13,plain,
( in(U_222,U_225)
| U_222 != ordered_pair(U_211,U_210)
| ~ in(U_210,U_227)
| ~ in(U_211,U_229)
| U_225 != cartesian_product2(U_229,U_227) ),
inference(clausify,[status(thm)],[f_23_9]) ).
cnf(f_23_14,plain,
( in(sK45(U_230,U_228,U_226),U_230)
| in(sK43(U_230,U_228,U_226),U_226)
| U_226 = cartesian_product2(U_230,U_228) ),
inference(clausify,[status(thm)],[f_23_9]) ).
cnf(f_23_15,plain,
( in(sK46(U_230,U_228,U_226),U_228)
| in(sK43(U_230,U_228,U_226),U_226)
| U_226 = cartesian_product2(U_230,U_228) ),
inference(clausify,[status(thm)],[f_23_9]) ).
cnf(f_23_16,plain,
( sK44(U_230,U_228,U_226) = ordered_pair(sK45(U_230,U_228,U_226),sK46(U_230,U_228,U_226))
| in(sK43(U_230,U_228,U_226),U_226)
| U_226 = cartesian_product2(U_230,U_228) ),
inference(clausify,[status(thm)],[f_23_9]) ).
cnf(f_23_17,plain,
( ~ in(sK44(U_230,U_228,U_226),U_226)
| in(sK43(U_230,U_228,U_226),U_226)
| U_226 = cartesian_product2(U_230,U_228) ),
inference(clausify,[status(thm)],[f_23_9]) ).
cnf(f_23_18,plain,
( in(sK45(U_230,U_228,U_226),U_230)
| sK43(U_230,U_228,U_226) != ordered_pair(U_214,U_213)
| ~ in(U_213,U_228)
| ~ in(U_214,U_230)
| U_226 = cartesian_product2(U_230,U_228) ),
inference(clausify,[status(thm)],[f_23_9]) ).
cnf(f_23_19,plain,
( in(sK46(U_230,U_228,U_226),U_228)
| sK43(U_230,U_228,U_226) != ordered_pair(U_214,U_213)
| ~ in(U_213,U_228)
| ~ in(U_214,U_230)
| U_226 = cartesian_product2(U_230,U_228) ),
inference(clausify,[status(thm)],[f_23_9]) ).
cnf(f_23_20,plain,
( sK44(U_230,U_228,U_226) = ordered_pair(sK45(U_230,U_228,U_226),sK46(U_230,U_228,U_226))
| sK43(U_230,U_228,U_226) != ordered_pair(U_214,U_213)
| ~ in(U_213,U_228)
| ~ in(U_214,U_230)
| U_226 = cartesian_product2(U_230,U_228) ),
inference(clausify,[status(thm)],[f_23_9]) ).
cnf(f_23_21,plain,
( ~ in(sK44(U_230,U_228,U_226),U_226)
| sK43(U_230,U_228,U_226) != ordered_pair(U_214,U_213)
| ~ in(U_213,U_228)
| ~ in(U_214,U_230)
| U_226 = cartesian_product2(U_230,U_228) ),
inference(clausify,[status(thm)],[f_23_9]) ).
fof(f_24_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_24_2,plain,
! [U_236] :
( ! [U_235] :
( ( ( subset(U_236,U_235)
| ? [U_234,U_233] :
( ~ in(ordered_pair(U_234,U_233),U_235)
& in(ordered_pair(U_234,U_233),U_236) ) )
& ( ! [U_232,U_231] :
( in(ordered_pair(U_232,U_231),U_235)
| ~ in(ordered_pair(U_232,U_231),U_236) )
| ~ subset(U_236,U_235) ) )
| ~ relation(U_235) )
| ~ relation(U_236) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_236] :
( ! [U_235] :
( ( ( subset(U_236,U_235)
| ? [U_233] :
( ~ in(ordered_pair(sK47(U_236,U_235),U_233),U_235)
& in(ordered_pair(sK47(U_236,U_235),U_233),U_236) ) )
& ( ! [U_232,U_231] :
( in(ordered_pair(U_232,U_231),U_235)
| ~ in(ordered_pair(U_232,U_231),U_236) )
| ~ subset(U_236,U_235) ) )
| ~ relation(U_235) )
| ~ relation(U_236) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_234,sK47(U_236,U_235))],[f_24_2]) ).
fof(f_24_4,plain,
! [U_236] :
( ! [U_235] :
( ( ( subset(U_236,U_235)
| ( ~ in(ordered_pair(sK47(U_236,U_235),sK48(U_236,U_235)),U_235)
& in(ordered_pair(sK47(U_236,U_235),sK48(U_236,U_235)),U_236) ) )
& ( ! [U_232,U_231] :
( in(ordered_pair(U_232,U_231),U_235)
| ~ in(ordered_pair(U_232,U_231),U_236) )
| ~ subset(U_236,U_235) ) )
| ~ relation(U_235) )
| ~ relation(U_236) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_233,sK48(U_236,U_235))],[f_24_3]) ).
cnf(f_24_5,plain,
( in(ordered_pair(U_232,U_231),U_235)
| ~ in(ordered_pair(U_232,U_231),U_236)
| ~ subset(U_236,U_235)
| ~ relation(U_235)
| ~ relation(U_236) ),
inference(clausify,[status(thm)],[f_24_4]) ).
cnf(f_24_6,plain,
( in(ordered_pair(sK47(U_236,U_235),sK48(U_236,U_235)),U_236)
| subset(U_236,U_235)
| ~ relation(U_235)
| ~ relation(U_236) ),
inference(clausify,[status(thm)],[f_24_4]) ).
cnf(f_24_7,plain,
( ~ in(ordered_pair(sK47(U_236,U_235),sK48(U_236,U_235)),U_235)
| subset(U_236,U_235)
| ~ relation(U_235)
| ~ relation(U_236) ),
inference(clausify,[status(thm)],[f_24_4]) ).
fof(f_25_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_25_2,plain,
! [U_240,U_239] :
( ( subset(U_240,U_239)
| ? [U_238] :
( ~ in(U_238,U_239)
& in(U_238,U_240) ) )
& ( ! [U_237] :
( in(U_237,U_239)
| ~ in(U_237,U_240) )
| ~ subset(U_240,U_239) ) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( ! [U_244,U_242] :
( subset(U_244,U_242)
| ? [U_238] :
( ~ in(U_238,U_242)
& in(U_238,U_244) ) )
& ! [U_243,U_241] :
( ! [U_237] :
( in(U_237,U_241)
| ~ in(U_237,U_243) )
| ~ subset(U_243,U_241) ) ),
inference(miniscope,[status(thm)],[f_25_2]) ).
fof(f_25_4,plain,
( ! [U_244,U_242] :
( subset(U_244,U_242)
| ( ~ in(sK49(U_244,U_242),U_242)
& in(sK49(U_244,U_242),U_244) ) )
& ! [U_243,U_241] :
( ! [U_237] :
( in(U_237,U_241)
| ~ in(U_237,U_243) )
| ~ subset(U_243,U_241) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_238,sK49(U_244,U_242))],[f_25_3]) ).
cnf(f_25_5,plain,
( in(U_237,U_241)
| ~ in(U_237,U_243)
| ~ subset(U_243,U_241) ),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_6,plain,
( in(sK49(U_244,U_242),U_244)
| subset(U_244,U_242) ),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_7,plain,
( ~ in(sK49(U_244,U_242),U_242)
| subset(U_244,U_242) ),
inference(clausify,[status(thm)],[f_25_4]) ).
fof(f_26_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_26_2,plain,
! [U_249,U_248,U_247] :
( ( U_247 = set_intersection2(U_249,U_248)
| ? [U_246] :
( ( ~ in(U_246,U_247)
& in(U_246,U_248)
& in(U_246,U_249) )
| ( ( ~ in(U_246,U_248)
| ~ in(U_246,U_249) )
& in(U_246,U_247) ) ) )
& ( ! [U_245] :
( ( in(U_245,U_247)
| ~ in(U_245,U_248)
| ~ in(U_245,U_249) )
& ( ( in(U_245,U_248)
& in(U_245,U_249) )
| ~ in(U_245,U_247) ) )
| U_247 != set_intersection2(U_249,U_248) ) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( ! [U_259,U_257,U_255] :
( U_255 = set_intersection2(U_259,U_257)
| ? [U_253] :
( ~ in(U_253,U_255)
& in(U_253,U_257)
& in(U_253,U_259) )
| ? [U_252] :
( ( ~ in(U_252,U_257)
| ~ in(U_252,U_259) )
& in(U_252,U_255) ) )
& ! [U_258,U_256,U_254] :
( ( ! [U_251] :
( in(U_251,U_254)
| ~ in(U_251,U_256)
| ~ in(U_251,U_258) )
& ! [U_250] :
( ( in(U_250,U_256)
& in(U_250,U_258) )
| ~ in(U_250,U_254) ) )
| U_254 != set_intersection2(U_258,U_256) ) ),
inference(miniscope,[status(thm)],[f_26_2]) ).
fof(f_26_4,plain,
( ! [U_259,U_257,U_255] :
( U_255 = set_intersection2(U_259,U_257)
| ? [U_253] :
( ~ in(U_253,U_255)
& in(U_253,U_257)
& in(U_253,U_259) )
| ( ( ~ in(sK50(U_259,U_257,U_255),U_257)
| ~ in(sK50(U_259,U_257,U_255),U_259) )
& in(sK50(U_259,U_257,U_255),U_255) ) )
& ! [U_258,U_256,U_254] :
( ( ! [U_251] :
( in(U_251,U_254)
| ~ in(U_251,U_256)
| ~ in(U_251,U_258) )
& ! [U_250] :
( ( in(U_250,U_256)
& in(U_250,U_258) )
| ~ in(U_250,U_254) ) )
| U_254 != set_intersection2(U_258,U_256) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_252,sK50(U_259,U_257,U_255))],[f_26_3]) ).
fof(f_26_5,plain,
( ! [U_259,U_257,U_255] :
( U_255 = set_intersection2(U_259,U_257)
| ( ~ in(sK51(U_259,U_257,U_255),U_255)
& in(sK51(U_259,U_257,U_255),U_257)
& in(sK51(U_259,U_257,U_255),U_259) )
| ( ( ~ in(sK50(U_259,U_257,U_255),U_257)
| ~ in(sK50(U_259,U_257,U_255),U_259) )
& in(sK50(U_259,U_257,U_255),U_255) ) )
& ! [U_258,U_256,U_254] :
( ( ! [U_251] :
( in(U_251,U_254)
| ~ in(U_251,U_256)
| ~ in(U_251,U_258) )
& ! [U_250] :
( ( in(U_250,U_256)
& in(U_250,U_258) )
| ~ in(U_250,U_254) ) )
| U_254 != set_intersection2(U_258,U_256) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_253,sK51(U_259,U_257,U_255))],[f_26_4]) ).
cnf(f_26_6,plain,
( in(U_250,U_258)
| ~ in(U_250,U_254)
| U_254 != set_intersection2(U_258,U_256) ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_7,plain,
( in(U_250,U_256)
| ~ in(U_250,U_254)
| U_254 != set_intersection2(U_258,U_256) ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_8,plain,
( in(U_251,U_254)
| ~ in(U_251,U_256)
| ~ in(U_251,U_258)
| U_254 != set_intersection2(U_258,U_256) ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_9,plain,
( in(sK51(U_259,U_257,U_255),U_259)
| in(sK50(U_259,U_257,U_255),U_255)
| U_255 = set_intersection2(U_259,U_257) ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_10,plain,
( in(sK51(U_259,U_257,U_255),U_257)
| in(sK50(U_259,U_257,U_255),U_255)
| U_255 = set_intersection2(U_259,U_257) ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_11,plain,
( ~ in(sK51(U_259,U_257,U_255),U_255)
| in(sK50(U_259,U_257,U_255),U_255)
| U_255 = set_intersection2(U_259,U_257) ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_12,plain,
( in(sK51(U_259,U_257,U_255),U_259)
| ~ in(sK50(U_259,U_257,U_255),U_257)
| ~ in(sK50(U_259,U_257,U_255),U_259)
| U_255 = set_intersection2(U_259,U_257) ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_13,plain,
( in(sK51(U_259,U_257,U_255),U_257)
| ~ in(sK50(U_259,U_257,U_255),U_257)
| ~ in(sK50(U_259,U_257,U_255),U_259)
| U_255 = set_intersection2(U_259,U_257) ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_14,plain,
( ~ in(sK51(U_259,U_257,U_255),U_255)
| ~ in(sK50(U_259,U_257,U_255),U_257)
| ~ in(sK50(U_259,U_257,U_255),U_259)
| U_255 = set_intersection2(U_259,U_257) ),
inference(clausify,[status(thm)],[f_26_5]) ).
fof(f_27_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_27_2,plain,
! [U_262] :
( ! [U_261,U_260] :
( ( ( ( U_260 = apply(U_262,U_261)
| U_260 != empty_set )
& ( U_260 = empty_set
| U_260 != apply(U_262,U_261) ) )
| in(U_261,relation_dom(U_262)) )
& ( ( ( U_260 = apply(U_262,U_261)
| ~ in(ordered_pair(U_261,U_260),U_262) )
& ( in(ordered_pair(U_261,U_260),U_262)
| U_260 != apply(U_262,U_261) ) )
| ~ in(U_261,relation_dom(U_262)) ) )
| ~ function(U_262)
| ~ relation(U_262) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_262] :
( ( ! [U_270] :
( ( ! [U_268] :
( U_268 = apply(U_262,U_270)
| U_268 != empty_set )
& ! [U_267] :
( U_267 = empty_set
| U_267 != apply(U_262,U_270) ) )
| in(U_270,relation_dom(U_262)) )
& ! [U_269] :
( ( ! [U_266] :
( U_266 = apply(U_262,U_269)
| ~ in(ordered_pair(U_269,U_266),U_262) )
& ! [U_265] :
( in(ordered_pair(U_269,U_265),U_262)
| U_265 != apply(U_262,U_269) ) )
| ~ in(U_269,relation_dom(U_262)) ) )
| ~ function(U_262)
| ~ relation(U_262) ),
inference(miniscope,[status(thm)],[f_27_2]) ).
cnf(f_27_4,plain,
( in(ordered_pair(U_269,U_265),U_262)
| U_265 != apply(U_262,U_269)
| ~ in(U_269,relation_dom(U_262))
| ~ function(U_262)
| ~ relation(U_262) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_5,plain,
( U_266 = apply(U_262,U_269)
| ~ in(ordered_pair(U_269,U_266),U_262)
| ~ in(U_269,relation_dom(U_262))
| ~ function(U_262)
| ~ relation(U_262) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_6,plain,
( U_267 = empty_set
| U_267 != apply(U_262,U_270)
| in(U_270,relation_dom(U_262))
| ~ function(U_262)
| ~ relation(U_262) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_7,plain,
( U_268 = apply(U_262,U_270)
| U_268 != empty_set
| in(U_270,relation_dom(U_262))
| ~ function(U_262)
| ~ relation(U_262) ),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_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_28_2,plain,
! [U_278] :
( ! [U_277] :
( ( U_277 = relation_dom(U_278)
| ? [U_276] :
( ( ~ in(U_276,U_277)
& ? [U_275] : in(ordered_pair(U_276,U_275),U_278) )
| ( ! [U_274] : ~ in(ordered_pair(U_276,U_274),U_278)
& in(U_276,U_277) ) ) )
& ( ! [U_273] :
( ( in(U_273,U_277)
| ! [U_272] : ~ in(ordered_pair(U_273,U_272),U_278) )
& ( ? [U_271] : in(ordered_pair(U_273,U_271),U_278)
| ~ in(U_273,U_277) ) )
| U_277 != relation_dom(U_278) ) )
| ~ relation(U_278) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_278] :
( ( ! [U_284] :
( U_284 = relation_dom(U_278)
| ? [U_282] :
( ~ in(U_282,U_284)
& ? [U_275] : in(ordered_pair(U_282,U_275),U_278) )
| ? [U_281] :
( ! [U_274] : ~ in(ordered_pair(U_281,U_274),U_278)
& in(U_281,U_284) ) )
& ! [U_283] :
( ( ! [U_280] :
( in(U_280,U_283)
| ! [U_272] : ~ in(ordered_pair(U_280,U_272),U_278) )
& ! [U_279] :
( ? [U_271] : in(ordered_pair(U_279,U_271),U_278)
| ~ in(U_279,U_283) ) )
| U_283 != relation_dom(U_278) ) )
| ~ relation(U_278) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
fof(f_28_4,plain,
! [U_278] :
( ( ! [U_284] :
( U_284 = relation_dom(U_278)
| ? [U_282] :
( ~ in(U_282,U_284)
& ? [U_275] : in(ordered_pair(U_282,U_275),U_278) )
| ? [U_281] :
( ! [U_274] : ~ in(ordered_pair(U_281,U_274),U_278)
& in(U_281,U_284) ) )
& ! [U_283] :
( ( ! [U_280] :
( in(U_280,U_283)
| ! [U_272] : ~ in(ordered_pair(U_280,U_272),U_278) )
& ! [U_279] :
( in(ordered_pair(U_279,sK52(U_278,U_283,U_279)),U_278)
| ~ in(U_279,U_283) ) )
| U_283 != relation_dom(U_278) ) )
| ~ relation(U_278) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_271,sK52(U_278,U_283,U_279))],[f_28_3]) ).
fof(f_28_5,plain,
! [U_278] :
( ( ! [U_284] :
( U_284 = relation_dom(U_278)
| ? [U_282] :
( ~ in(U_282,U_284)
& ? [U_275] : in(ordered_pair(U_282,U_275),U_278) )
| ( ! [U_274] : ~ in(ordered_pair(sK53(U_278,U_284),U_274),U_278)
& in(sK53(U_278,U_284),U_284) ) )
& ! [U_283] :
( ( ! [U_280] :
( in(U_280,U_283)
| ! [U_272] : ~ in(ordered_pair(U_280,U_272),U_278) )
& ! [U_279] :
( in(ordered_pair(U_279,sK52(U_278,U_283,U_279)),U_278)
| ~ in(U_279,U_283) ) )
| U_283 != relation_dom(U_278) ) )
| ~ relation(U_278) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_281,sK53(U_278,U_284))],[f_28_4]) ).
fof(f_28_6,plain,
! [U_278] :
( ( ! [U_284] :
( U_284 = relation_dom(U_278)
| ( ~ in(sK54(U_278,U_284),U_284)
& ? [U_275] : in(ordered_pair(sK54(U_278,U_284),U_275),U_278) )
| ( ! [U_274] : ~ in(ordered_pair(sK53(U_278,U_284),U_274),U_278)
& in(sK53(U_278,U_284),U_284) ) )
& ! [U_283] :
( ( ! [U_280] :
( in(U_280,U_283)
| ! [U_272] : ~ in(ordered_pair(U_280,U_272),U_278) )
& ! [U_279] :
( in(ordered_pair(U_279,sK52(U_278,U_283,U_279)),U_278)
| ~ in(U_279,U_283) ) )
| U_283 != relation_dom(U_278) ) )
| ~ relation(U_278) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_282,sK54(U_278,U_284))],[f_28_5]) ).
fof(f_28_7,plain,
! [U_278] :
( ( ! [U_284] :
( U_284 = relation_dom(U_278)
| ( ~ in(sK54(U_278,U_284),U_284)
& in(ordered_pair(sK54(U_278,U_284),sK55(U_278,U_284)),U_278) )
| ( ! [U_274] : ~ in(ordered_pair(sK53(U_278,U_284),U_274),U_278)
& in(sK53(U_278,U_284),U_284) ) )
& ! [U_283] :
( ( ! [U_280] :
( in(U_280,U_283)
| ! [U_272] : ~ in(ordered_pair(U_280,U_272),U_278) )
& ! [U_279] :
( in(ordered_pair(U_279,sK52(U_278,U_283,U_279)),U_278)
| ~ in(U_279,U_283) ) )
| U_283 != relation_dom(U_278) ) )
| ~ relation(U_278) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_275,sK55(U_278,U_284))],[f_28_6]) ).
cnf(f_28_8,plain,
( in(ordered_pair(U_279,sK52(U_278,U_283,U_279)),U_278)
| ~ in(U_279,U_283)
| U_283 != relation_dom(U_278)
| ~ relation(U_278) ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_9,plain,
( in(U_280,U_283)
| ~ in(ordered_pair(U_280,U_272),U_278)
| U_283 != relation_dom(U_278)
| ~ relation(U_278) ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_10,plain,
( in(ordered_pair(sK54(U_278,U_284),sK55(U_278,U_284)),U_278)
| in(sK53(U_278,U_284),U_284)
| U_284 = relation_dom(U_278)
| ~ relation(U_278) ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_11,plain,
( ~ in(sK54(U_278,U_284),U_284)
| in(sK53(U_278,U_284),U_284)
| U_284 = relation_dom(U_278)
| ~ relation(U_278) ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_12,plain,
( in(ordered_pair(sK54(U_278,U_284),sK55(U_278,U_284)),U_278)
| ~ in(ordered_pair(sK53(U_278,U_284),U_274),U_278)
| U_284 = relation_dom(U_278)
| ~ relation(U_278) ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_13,plain,
( ~ in(sK54(U_278,U_284),U_284)
| ~ in(ordered_pair(sK53(U_278,U_284),U_274),U_278)
| U_284 = relation_dom(U_278)
| ~ relation(U_278) ),
inference(clausify,[status(thm)],[f_28_7]) ).
fof(f_29_1,plain,
! [A] : cast_to_subset(A) = A,
inference(fof_nnf,[status(thm)],[d4_subset_1]) ).
fof(f_29_2,plain,
! [U_285] : cast_to_subset(U_285) = U_285,
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
cast_to_subset(U_285) = U_285,
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_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_30_2,plain,
! [U_293,U_292] :
( ( U_292 = union(U_293)
| ? [U_291] :
( ( ~ in(U_291,U_292)
& ? [U_290] :
( in(U_290,U_293)
& in(U_291,U_290) ) )
| ( ! [U_289] :
( ~ in(U_289,U_293)
| ~ in(U_291,U_289) )
& in(U_291,U_292) ) ) )
& ( ! [U_288] :
( ( in(U_288,U_292)
| ! [U_287] :
( ~ in(U_287,U_293)
| ~ in(U_288,U_287) ) )
& ( ? [U_286] :
( in(U_286,U_293)
& in(U_288,U_286) )
| ~ in(U_288,U_292) ) )
| U_292 != union(U_293) ) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( ! [U_301,U_299] :
( U_299 = union(U_301)
| ? [U_297] :
( ~ in(U_297,U_299)
& ? [U_290] :
( in(U_290,U_301)
& in(U_297,U_290) ) )
| ? [U_296] :
( ! [U_289] :
( ~ in(U_289,U_301)
| ~ in(U_296,U_289) )
& in(U_296,U_299) ) )
& ! [U_300,U_298] :
( ( ! [U_295] :
( in(U_295,U_298)
| ! [U_287] :
( ~ in(U_287,U_300)
| ~ in(U_295,U_287) ) )
& ! [U_294] :
( ? [U_286] :
( in(U_286,U_300)
& in(U_294,U_286) )
| ~ in(U_294,U_298) ) )
| U_298 != union(U_300) ) ),
inference(miniscope,[status(thm)],[f_30_2]) ).
fof(f_30_4,plain,
( ! [U_301,U_299] :
( U_299 = union(U_301)
| ? [U_297] :
( ~ in(U_297,U_299)
& ? [U_290] :
( in(U_290,U_301)
& in(U_297,U_290) ) )
| ? [U_296] :
( ! [U_289] :
( ~ in(U_289,U_301)
| ~ in(U_296,U_289) )
& in(U_296,U_299) ) )
& ! [U_300,U_298] :
( ( ! [U_295] :
( in(U_295,U_298)
| ! [U_287] :
( ~ in(U_287,U_300)
| ~ in(U_295,U_287) ) )
& ! [U_294] :
( ( in(sK56(U_300,U_298,U_294),U_300)
& in(U_294,sK56(U_300,U_298,U_294)) )
| ~ in(U_294,U_298) ) )
| U_298 != union(U_300) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_286,sK56(U_300,U_298,U_294))],[f_30_3]) ).
fof(f_30_5,plain,
( ! [U_301,U_299] :
( U_299 = union(U_301)
| ? [U_297] :
( ~ in(U_297,U_299)
& ? [U_290] :
( in(U_290,U_301)
& in(U_297,U_290) ) )
| ( ! [U_289] :
( ~ in(U_289,U_301)
| ~ in(sK57(U_301,U_299),U_289) )
& in(sK57(U_301,U_299),U_299) ) )
& ! [U_300,U_298] :
( ( ! [U_295] :
( in(U_295,U_298)
| ! [U_287] :
( ~ in(U_287,U_300)
| ~ in(U_295,U_287) ) )
& ! [U_294] :
( ( in(sK56(U_300,U_298,U_294),U_300)
& in(U_294,sK56(U_300,U_298,U_294)) )
| ~ in(U_294,U_298) ) )
| U_298 != union(U_300) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_296,sK57(U_301,U_299))],[f_30_4]) ).
fof(f_30_6,plain,
( ! [U_301,U_299] :
( U_299 = union(U_301)
| ( ~ in(sK58(U_301,U_299),U_299)
& ? [U_290] :
( in(U_290,U_301)
& in(sK58(U_301,U_299),U_290) ) )
| ( ! [U_289] :
( ~ in(U_289,U_301)
| ~ in(sK57(U_301,U_299),U_289) )
& in(sK57(U_301,U_299),U_299) ) )
& ! [U_300,U_298] :
( ( ! [U_295] :
( in(U_295,U_298)
| ! [U_287] :
( ~ in(U_287,U_300)
| ~ in(U_295,U_287) ) )
& ! [U_294] :
( ( in(sK56(U_300,U_298,U_294),U_300)
& in(U_294,sK56(U_300,U_298,U_294)) )
| ~ in(U_294,U_298) ) )
| U_298 != union(U_300) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_297,sK58(U_301,U_299))],[f_30_5]) ).
fof(f_30_7,plain,
( ! [U_301,U_299] :
( U_299 = union(U_301)
| ( ~ in(sK58(U_301,U_299),U_299)
& in(sK59(U_301,U_299),U_301)
& in(sK58(U_301,U_299),sK59(U_301,U_299)) )
| ( ! [U_289] :
( ~ in(U_289,U_301)
| ~ in(sK57(U_301,U_299),U_289) )
& in(sK57(U_301,U_299),U_299) ) )
& ! [U_300,U_298] :
( ( ! [U_295] :
( in(U_295,U_298)
| ! [U_287] :
( ~ in(U_287,U_300)
| ~ in(U_295,U_287) ) )
& ! [U_294] :
( ( in(sK56(U_300,U_298,U_294),U_300)
& in(U_294,sK56(U_300,U_298,U_294)) )
| ~ in(U_294,U_298) ) )
| U_298 != union(U_300) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_290,sK59(U_301,U_299))],[f_30_6]) ).
cnf(f_30_8,plain,
( in(U_294,sK56(U_300,U_298,U_294))
| ~ in(U_294,U_298)
| U_298 != union(U_300) ),
inference(clausify,[status(thm)],[f_30_7]) ).
cnf(f_30_9,plain,
( in(sK56(U_300,U_298,U_294),U_300)
| ~ in(U_294,U_298)
| U_298 != union(U_300) ),
inference(clausify,[status(thm)],[f_30_7]) ).
cnf(f_30_10,plain,
( in(U_295,U_298)
| ~ in(U_287,U_300)
| ~ in(U_295,U_287)
| U_298 != union(U_300) ),
inference(clausify,[status(thm)],[f_30_7]) ).
cnf(f_30_11,plain,
( in(sK58(U_301,U_299),sK59(U_301,U_299))
| in(sK57(U_301,U_299),U_299)
| U_299 = union(U_301) ),
inference(clausify,[status(thm)],[f_30_7]) ).
cnf(f_30_12,plain,
( in(sK59(U_301,U_299),U_301)
| in(sK57(U_301,U_299),U_299)
| U_299 = union(U_301) ),
inference(clausify,[status(thm)],[f_30_7]) ).
cnf(f_30_13,plain,
( ~ in(sK58(U_301,U_299),U_299)
| in(sK57(U_301,U_299),U_299)
| U_299 = union(U_301) ),
inference(clausify,[status(thm)],[f_30_7]) ).
cnf(f_30_14,plain,
( in(sK58(U_301,U_299),sK59(U_301,U_299))
| ~ in(U_289,U_301)
| ~ in(sK57(U_301,U_299),U_289)
| U_299 = union(U_301) ),
inference(clausify,[status(thm)],[f_30_7]) ).
cnf(f_30_15,plain,
( in(sK59(U_301,U_299),U_301)
| ~ in(U_289,U_301)
| ~ in(sK57(U_301,U_299),U_289)
| U_299 = union(U_301) ),
inference(clausify,[status(thm)],[f_30_7]) ).
cnf(f_30_16,plain,
( ~ in(sK58(U_301,U_299),U_299)
| ~ in(U_289,U_301)
| ~ in(sK57(U_301,U_299),U_289)
| U_299 = union(U_301) ),
inference(clausify,[status(thm)],[f_30_7]) ).
fof(f_31_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_31_2,plain,
! [U_306,U_305,U_304] :
( ( U_304 = set_difference(U_306,U_305)
| ? [U_303] :
( ( ~ in(U_303,U_304)
& ~ in(U_303,U_305)
& in(U_303,U_306) )
| ( ( in(U_303,U_305)
| ~ in(U_303,U_306) )
& in(U_303,U_304) ) ) )
& ( ! [U_302] :
( ( in(U_302,U_304)
| in(U_302,U_305)
| ~ in(U_302,U_306) )
& ( ( ~ in(U_302,U_305)
& in(U_302,U_306) )
| ~ in(U_302,U_304) ) )
| U_304 != set_difference(U_306,U_305) ) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( ! [U_316,U_314,U_312] :
( U_312 = set_difference(U_316,U_314)
| ? [U_310] :
( ~ in(U_310,U_312)
& ~ in(U_310,U_314)
& in(U_310,U_316) )
| ? [U_309] :
( ( in(U_309,U_314)
| ~ in(U_309,U_316) )
& in(U_309,U_312) ) )
& ! [U_315,U_313,U_311] :
( ( ! [U_308] :
( in(U_308,U_311)
| in(U_308,U_313)
| ~ in(U_308,U_315) )
& ! [U_307] :
( ( ~ in(U_307,U_313)
& in(U_307,U_315) )
| ~ in(U_307,U_311) ) )
| U_311 != set_difference(U_315,U_313) ) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
fof(f_31_4,plain,
( ! [U_316,U_314,U_312] :
( U_312 = set_difference(U_316,U_314)
| ? [U_310] :
( ~ in(U_310,U_312)
& ~ in(U_310,U_314)
& in(U_310,U_316) )
| ( ( in(sK60(U_316,U_314,U_312),U_314)
| ~ in(sK60(U_316,U_314,U_312),U_316) )
& in(sK60(U_316,U_314,U_312),U_312) ) )
& ! [U_315,U_313,U_311] :
( ( ! [U_308] :
( in(U_308,U_311)
| in(U_308,U_313)
| ~ in(U_308,U_315) )
& ! [U_307] :
( ( ~ in(U_307,U_313)
& in(U_307,U_315) )
| ~ in(U_307,U_311) ) )
| U_311 != set_difference(U_315,U_313) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_309,sK60(U_316,U_314,U_312))],[f_31_3]) ).
fof(f_31_5,plain,
( ! [U_316,U_314,U_312] :
( U_312 = set_difference(U_316,U_314)
| ( ~ in(sK61(U_316,U_314,U_312),U_312)
& ~ in(sK61(U_316,U_314,U_312),U_314)
& in(sK61(U_316,U_314,U_312),U_316) )
| ( ( in(sK60(U_316,U_314,U_312),U_314)
| ~ in(sK60(U_316,U_314,U_312),U_316) )
& in(sK60(U_316,U_314,U_312),U_312) ) )
& ! [U_315,U_313,U_311] :
( ( ! [U_308] :
( in(U_308,U_311)
| in(U_308,U_313)
| ~ in(U_308,U_315) )
& ! [U_307] :
( ( ~ in(U_307,U_313)
& in(U_307,U_315) )
| ~ in(U_307,U_311) ) )
| U_311 != set_difference(U_315,U_313) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_310,sK61(U_316,U_314,U_312))],[f_31_4]) ).
cnf(f_31_6,plain,
( in(U_307,U_315)
| ~ in(U_307,U_311)
| U_311 != set_difference(U_315,U_313) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_7,plain,
( ~ in(U_307,U_313)
| ~ in(U_307,U_311)
| U_311 != set_difference(U_315,U_313) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_8,plain,
( in(U_308,U_311)
| in(U_308,U_313)
| ~ in(U_308,U_315)
| U_311 != set_difference(U_315,U_313) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_9,plain,
( in(sK61(U_316,U_314,U_312),U_316)
| in(sK60(U_316,U_314,U_312),U_312)
| U_312 = set_difference(U_316,U_314) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_10,plain,
( ~ in(sK61(U_316,U_314,U_312),U_314)
| in(sK60(U_316,U_314,U_312),U_312)
| U_312 = set_difference(U_316,U_314) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_11,plain,
( ~ in(sK61(U_316,U_314,U_312),U_312)
| in(sK60(U_316,U_314,U_312),U_312)
| U_312 = set_difference(U_316,U_314) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_12,plain,
( in(sK61(U_316,U_314,U_312),U_316)
| in(sK60(U_316,U_314,U_312),U_314)
| ~ in(sK60(U_316,U_314,U_312),U_316)
| U_312 = set_difference(U_316,U_314) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_13,plain,
( ~ in(sK61(U_316,U_314,U_312),U_314)
| in(sK60(U_316,U_314,U_312),U_314)
| ~ in(sK60(U_316,U_314,U_312),U_316)
| U_312 = set_difference(U_316,U_314) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_14,plain,
( ~ in(sK61(U_316,U_314,U_312),U_312)
| in(sK60(U_316,U_314,U_312),U_314)
| ~ in(sK60(U_316,U_314,U_312),U_316)
| U_312 = set_difference(U_316,U_314) ),
inference(clausify,[status(thm)],[f_31_5]) ).
fof(f_32_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_32_2,plain,
! [U_324] :
( ! [U_323] :
( ( U_323 = relation_rng(U_324)
| ? [U_322] :
( ( ~ in(U_322,U_323)
& ? [U_321] : in(ordered_pair(U_321,U_322),U_324) )
| ( ! [U_320] : ~ in(ordered_pair(U_320,U_322),U_324)
& in(U_322,U_323) ) ) )
& ( ! [U_319] :
( ( in(U_319,U_323)
| ! [U_318] : ~ in(ordered_pair(U_318,U_319),U_324) )
& ( ? [U_317] : in(ordered_pair(U_317,U_319),U_324)
| ~ in(U_319,U_323) ) )
| U_323 != relation_rng(U_324) ) )
| ~ relation(U_324) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_324] :
( ( ! [U_330] :
( U_330 = relation_rng(U_324)
| ? [U_328] :
( ~ in(U_328,U_330)
& ? [U_321] : in(ordered_pair(U_321,U_328),U_324) )
| ? [U_327] :
( ! [U_320] : ~ in(ordered_pair(U_320,U_327),U_324)
& in(U_327,U_330) ) )
& ! [U_329] :
( ( ! [U_326] :
( in(U_326,U_329)
| ! [U_318] : ~ in(ordered_pair(U_318,U_326),U_324) )
& ! [U_325] :
( ? [U_317] : in(ordered_pair(U_317,U_325),U_324)
| ~ in(U_325,U_329) ) )
| U_329 != relation_rng(U_324) ) )
| ~ relation(U_324) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
fof(f_32_4,plain,
! [U_324] :
( ( ! [U_330] :
( U_330 = relation_rng(U_324)
| ? [U_328] :
( ~ in(U_328,U_330)
& ? [U_321] : in(ordered_pair(U_321,U_328),U_324) )
| ? [U_327] :
( ! [U_320] : ~ in(ordered_pair(U_320,U_327),U_324)
& in(U_327,U_330) ) )
& ! [U_329] :
( ( ! [U_326] :
( in(U_326,U_329)
| ! [U_318] : ~ in(ordered_pair(U_318,U_326),U_324) )
& ! [U_325] :
( in(ordered_pair(sK62(U_324,U_329,U_325),U_325),U_324)
| ~ in(U_325,U_329) ) )
| U_329 != relation_rng(U_324) ) )
| ~ relation(U_324) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_317,sK62(U_324,U_329,U_325))],[f_32_3]) ).
fof(f_32_5,plain,
! [U_324] :
( ( ! [U_330] :
( U_330 = relation_rng(U_324)
| ? [U_328] :
( ~ in(U_328,U_330)
& ? [U_321] : in(ordered_pair(U_321,U_328),U_324) )
| ( ! [U_320] : ~ in(ordered_pair(U_320,sK63(U_324,U_330)),U_324)
& in(sK63(U_324,U_330),U_330) ) )
& ! [U_329] :
( ( ! [U_326] :
( in(U_326,U_329)
| ! [U_318] : ~ in(ordered_pair(U_318,U_326),U_324) )
& ! [U_325] :
( in(ordered_pair(sK62(U_324,U_329,U_325),U_325),U_324)
| ~ in(U_325,U_329) ) )
| U_329 != relation_rng(U_324) ) )
| ~ relation(U_324) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_327,sK63(U_324,U_330))],[f_32_4]) ).
fof(f_32_6,plain,
! [U_324] :
( ( ! [U_330] :
( U_330 = relation_rng(U_324)
| ( ~ in(sK64(U_324,U_330),U_330)
& ? [U_321] : in(ordered_pair(U_321,sK64(U_324,U_330)),U_324) )
| ( ! [U_320] : ~ in(ordered_pair(U_320,sK63(U_324,U_330)),U_324)
& in(sK63(U_324,U_330),U_330) ) )
& ! [U_329] :
( ( ! [U_326] :
( in(U_326,U_329)
| ! [U_318] : ~ in(ordered_pair(U_318,U_326),U_324) )
& ! [U_325] :
( in(ordered_pair(sK62(U_324,U_329,U_325),U_325),U_324)
| ~ in(U_325,U_329) ) )
| U_329 != relation_rng(U_324) ) )
| ~ relation(U_324) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_328,sK64(U_324,U_330))],[f_32_5]) ).
fof(f_32_7,plain,
! [U_324] :
( ( ! [U_330] :
( U_330 = relation_rng(U_324)
| ( ~ in(sK64(U_324,U_330),U_330)
& in(ordered_pair(sK65(U_324,U_330),sK64(U_324,U_330)),U_324) )
| ( ! [U_320] : ~ in(ordered_pair(U_320,sK63(U_324,U_330)),U_324)
& in(sK63(U_324,U_330),U_330) ) )
& ! [U_329] :
( ( ! [U_326] :
( in(U_326,U_329)
| ! [U_318] : ~ in(ordered_pair(U_318,U_326),U_324) )
& ! [U_325] :
( in(ordered_pair(sK62(U_324,U_329,U_325),U_325),U_324)
| ~ in(U_325,U_329) ) )
| U_329 != relation_rng(U_324) ) )
| ~ relation(U_324) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_321,sK65(U_324,U_330))],[f_32_6]) ).
cnf(f_32_8,plain,
( in(ordered_pair(sK62(U_324,U_329,U_325),U_325),U_324)
| ~ in(U_325,U_329)
| U_329 != relation_rng(U_324)
| ~ relation(U_324) ),
inference(clausify,[status(thm)],[f_32_7]) ).
cnf(f_32_9,plain,
( in(U_326,U_329)
| ~ in(ordered_pair(U_318,U_326),U_324)
| U_329 != relation_rng(U_324)
| ~ relation(U_324) ),
inference(clausify,[status(thm)],[f_32_7]) ).
cnf(f_32_10,plain,
( in(ordered_pair(sK65(U_324,U_330),sK64(U_324,U_330)),U_324)
| in(sK63(U_324,U_330),U_330)
| U_330 = relation_rng(U_324)
| ~ relation(U_324) ),
inference(clausify,[status(thm)],[f_32_7]) ).
cnf(f_32_11,plain,
( ~ in(sK64(U_324,U_330),U_330)
| in(sK63(U_324,U_330),U_330)
| U_330 = relation_rng(U_324)
| ~ relation(U_324) ),
inference(clausify,[status(thm)],[f_32_7]) ).
cnf(f_32_12,plain,
( in(ordered_pair(sK65(U_324,U_330),sK64(U_324,U_330)),U_324)
| ~ in(ordered_pair(U_320,sK63(U_324,U_330)),U_324)
| U_330 = relation_rng(U_324)
| ~ relation(U_324) ),
inference(clausify,[status(thm)],[f_32_7]) ).
cnf(f_32_13,plain,
( ~ in(sK64(U_324,U_330),U_330)
| ~ in(ordered_pair(U_320,sK63(U_324,U_330)),U_324)
| U_330 = relation_rng(U_324)
| ~ relation(U_324) ),
inference(clausify,[status(thm)],[f_32_7]) ).
fof(f_33_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_33_2,plain,
! [U_332,U_331] :
( subset_complement(U_332,U_331) = set_difference(U_332,U_331)
| ~ element(U_331,powerset(U_332)) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( subset_complement(U_332,U_331) = set_difference(U_332,U_331)
| ~ element(U_331,powerset(U_332)) ),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_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_34_2,plain,
! [U_334,U_333] : ordered_pair(U_334,U_333) = unordered_pair(unordered_pair(U_334,U_333),singleton(U_334)),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
ordered_pair(U_334,U_333) = unordered_pair(unordered_pair(U_334,U_333),singleton(U_334)),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_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_35_2,plain,
! [U_335] :
( relation_field(U_335) = set_union2(relation_dom(U_335),relation_rng(U_335))
| ~ relation(U_335) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
( relation_field(U_335) = set_union2(relation_dom(U_335),relation_rng(U_335))
| ~ relation(U_335) ),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_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_36_2,plain,
! [U_341] :
( ! [U_340] :
( ( ( U_340 = relation_inverse(U_341)
| ? [U_339,U_338] :
( ( ~ in(ordered_pair(U_339,U_338),U_340)
& in(ordered_pair(U_338,U_339),U_341) )
| ( ~ in(ordered_pair(U_338,U_339),U_341)
& in(ordered_pair(U_339,U_338),U_340) ) ) )
& ( ! [U_337,U_336] :
( ( in(ordered_pair(U_337,U_336),U_340)
| ~ in(ordered_pair(U_336,U_337),U_341) )
& ( in(ordered_pair(U_336,U_337),U_341)
| ~ in(ordered_pair(U_337,U_336),U_340) ) )
| U_340 != relation_inverse(U_341) ) )
| ~ relation(U_340) )
| ~ relation(U_341) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_341] :
( ! [U_340] :
( ( ( U_340 = relation_inverse(U_341)
| ? [U_349,U_347] :
( ~ in(ordered_pair(U_349,U_347),U_340)
& in(ordered_pair(U_347,U_349),U_341) )
| ? [U_348,U_346] :
( ~ in(ordered_pair(U_346,U_348),U_341)
& in(ordered_pair(U_348,U_346),U_340) ) )
& ( ( ! [U_345,U_343] :
( in(ordered_pair(U_345,U_343),U_340)
| ~ in(ordered_pair(U_343,U_345),U_341) )
& ! [U_344,U_342] :
( in(ordered_pair(U_342,U_344),U_341)
| ~ in(ordered_pair(U_344,U_342),U_340) ) )
| U_340 != relation_inverse(U_341) ) )
| ~ relation(U_340) )
| ~ relation(U_341) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
fof(f_36_4,plain,
! [U_341] :
( ! [U_340] :
( ( ( U_340 = relation_inverse(U_341)
| ? [U_349,U_347] :
( ~ in(ordered_pair(U_349,U_347),U_340)
& in(ordered_pair(U_347,U_349),U_341) )
| ? [U_346] :
( ~ in(ordered_pair(U_346,sK66(U_341,U_340)),U_341)
& in(ordered_pair(sK66(U_341,U_340),U_346),U_340) ) )
& ( ( ! [U_345,U_343] :
( in(ordered_pair(U_345,U_343),U_340)
| ~ in(ordered_pair(U_343,U_345),U_341) )
& ! [U_344,U_342] :
( in(ordered_pair(U_342,U_344),U_341)
| ~ in(ordered_pair(U_344,U_342),U_340) ) )
| U_340 != relation_inverse(U_341) ) )
| ~ relation(U_340) )
| ~ relation(U_341) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_348,sK66(U_341,U_340))],[f_36_3]) ).
fof(f_36_5,plain,
! [U_341] :
( ! [U_340] :
( ( ( U_340 = relation_inverse(U_341)
| ? [U_349,U_347] :
( ~ in(ordered_pair(U_349,U_347),U_340)
& in(ordered_pair(U_347,U_349),U_341) )
| ( ~ in(ordered_pair(sK67(U_341,U_340),sK66(U_341,U_340)),U_341)
& in(ordered_pair(sK66(U_341,U_340),sK67(U_341,U_340)),U_340) ) )
& ( ( ! [U_345,U_343] :
( in(ordered_pair(U_345,U_343),U_340)
| ~ in(ordered_pair(U_343,U_345),U_341) )
& ! [U_344,U_342] :
( in(ordered_pair(U_342,U_344),U_341)
| ~ in(ordered_pair(U_344,U_342),U_340) ) )
| U_340 != relation_inverse(U_341) ) )
| ~ relation(U_340) )
| ~ relation(U_341) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_346,sK67(U_341,U_340))],[f_36_4]) ).
fof(f_36_6,plain,
! [U_341] :
( ! [U_340] :
( ( ( U_340 = relation_inverse(U_341)
| ? [U_347] :
( ~ in(ordered_pair(sK68(U_341,U_340),U_347),U_340)
& in(ordered_pair(U_347,sK68(U_341,U_340)),U_341) )
| ( ~ in(ordered_pair(sK67(U_341,U_340),sK66(U_341,U_340)),U_341)
& in(ordered_pair(sK66(U_341,U_340),sK67(U_341,U_340)),U_340) ) )
& ( ( ! [U_345,U_343] :
( in(ordered_pair(U_345,U_343),U_340)
| ~ in(ordered_pair(U_343,U_345),U_341) )
& ! [U_344,U_342] :
( in(ordered_pair(U_342,U_344),U_341)
| ~ in(ordered_pair(U_344,U_342),U_340) ) )
| U_340 != relation_inverse(U_341) ) )
| ~ relation(U_340) )
| ~ relation(U_341) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_349,sK68(U_341,U_340))],[f_36_5]) ).
fof(f_36_7,plain,
! [U_341] :
( ! [U_340] :
( ( ( U_340 = relation_inverse(U_341)
| ( ~ in(ordered_pair(sK68(U_341,U_340),sK69(U_341,U_340)),U_340)
& in(ordered_pair(sK69(U_341,U_340),sK68(U_341,U_340)),U_341) )
| ( ~ in(ordered_pair(sK67(U_341,U_340),sK66(U_341,U_340)),U_341)
& in(ordered_pair(sK66(U_341,U_340),sK67(U_341,U_340)),U_340) ) )
& ( ( ! [U_345,U_343] :
( in(ordered_pair(U_345,U_343),U_340)
| ~ in(ordered_pair(U_343,U_345),U_341) )
& ! [U_344,U_342] :
( in(ordered_pair(U_342,U_344),U_341)
| ~ in(ordered_pair(U_344,U_342),U_340) ) )
| U_340 != relation_inverse(U_341) ) )
| ~ relation(U_340) )
| ~ relation(U_341) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_347,sK69(U_341,U_340))],[f_36_6]) ).
cnf(f_36_8,plain,
( in(ordered_pair(U_342,U_344),U_341)
| ~ in(ordered_pair(U_344,U_342),U_340)
| U_340 != relation_inverse(U_341)
| ~ relation(U_340)
| ~ relation(U_341) ),
inference(clausify,[status(thm)],[f_36_7]) ).
cnf(f_36_9,plain,
( in(ordered_pair(U_345,U_343),U_340)
| ~ in(ordered_pair(U_343,U_345),U_341)
| U_340 != relation_inverse(U_341)
| ~ relation(U_340)
| ~ relation(U_341) ),
inference(clausify,[status(thm)],[f_36_7]) ).
cnf(f_36_10,plain,
( in(ordered_pair(sK69(U_341,U_340),sK68(U_341,U_340)),U_341)
| in(ordered_pair(sK66(U_341,U_340),sK67(U_341,U_340)),U_340)
| U_340 = relation_inverse(U_341)
| ~ relation(U_340)
| ~ relation(U_341) ),
inference(clausify,[status(thm)],[f_36_7]) ).
cnf(f_36_11,plain,
( ~ in(ordered_pair(sK68(U_341,U_340),sK69(U_341,U_340)),U_340)
| in(ordered_pair(sK66(U_341,U_340),sK67(U_341,U_340)),U_340)
| U_340 = relation_inverse(U_341)
| ~ relation(U_340)
| ~ relation(U_341) ),
inference(clausify,[status(thm)],[f_36_7]) ).
cnf(f_36_12,plain,
( in(ordered_pair(sK69(U_341,U_340),sK68(U_341,U_340)),U_341)
| ~ in(ordered_pair(sK67(U_341,U_340),sK66(U_341,U_340)),U_341)
| U_340 = relation_inverse(U_341)
| ~ relation(U_340)
| ~ relation(U_341) ),
inference(clausify,[status(thm)],[f_36_7]) ).
cnf(f_36_13,plain,
( ~ in(ordered_pair(sK68(U_341,U_340),sK69(U_341,U_340)),U_340)
| ~ in(ordered_pair(sK67(U_341,U_340),sK66(U_341,U_340)),U_341)
| U_340 = relation_inverse(U_341)
| ~ relation(U_340)
| ~ relation(U_341) ),
inference(clausify,[status(thm)],[f_36_7]) ).
fof(f_37_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_37_2,plain,
! [U_351,U_350] :
( ( disjoint(U_351,U_350)
| set_intersection2(U_351,U_350) != empty_set )
& ( set_intersection2(U_351,U_350) = empty_set
| ~ disjoint(U_351,U_350) ) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
( ! [U_355,U_353] :
( disjoint(U_355,U_353)
| set_intersection2(U_355,U_353) != empty_set )
& ! [U_354,U_352] :
( set_intersection2(U_354,U_352) = empty_set
| ~ disjoint(U_354,U_352) ) ),
inference(miniscope,[status(thm)],[f_37_2]) ).
cnf(f_37_4,plain,
( set_intersection2(U_354,U_352) = empty_set
| ~ disjoint(U_354,U_352) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_5,plain,
( disjoint(U_355,U_353)
| set_intersection2(U_355,U_353) != empty_set ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_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_38_2,plain,
! [U_366] :
( ! [U_365] :
( ! [U_364] :
( ( ( U_364 = relation_composition(U_366,U_365)
| ? [U_363,U_362] :
( ( ~ in(ordered_pair(U_363,U_362),U_364)
& ? [U_361] :
( in(ordered_pair(U_361,U_362),U_365)
& in(ordered_pair(U_363,U_361),U_366) ) )
| ( ! [U_360] :
( ~ in(ordered_pair(U_360,U_362),U_365)
| ~ in(ordered_pair(U_363,U_360),U_366) )
& in(ordered_pair(U_363,U_362),U_364) ) ) )
& ( ! [U_359,U_358] :
( ( in(ordered_pair(U_359,U_358),U_364)
| ! [U_357] :
( ~ in(ordered_pair(U_357,U_358),U_365)
| ~ in(ordered_pair(U_359,U_357),U_366) ) )
& ( ? [U_356] :
( in(ordered_pair(U_356,U_358),U_365)
& in(ordered_pair(U_359,U_356),U_366) )
| ~ in(ordered_pair(U_359,U_358),U_364) ) )
| U_364 != relation_composition(U_366,U_365) ) )
| ~ relation(U_364) )
| ~ relation(U_365) )
| ~ relation(U_366) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_366] :
( ! [U_365] :
( ! [U_364] :
( ( ( U_364 = relation_composition(U_366,U_365)
| ? [U_374,U_372] :
( ~ in(ordered_pair(U_374,U_372),U_364)
& ? [U_361] :
( in(ordered_pair(U_361,U_372),U_365)
& in(ordered_pair(U_374,U_361),U_366) ) )
| ? [U_373,U_371] :
( ! [U_360] :
( ~ in(ordered_pair(U_360,U_371),U_365)
| ~ in(ordered_pair(U_373,U_360),U_366) )
& in(ordered_pair(U_373,U_371),U_364) ) )
& ( ( ! [U_370,U_368] :
( in(ordered_pair(U_370,U_368),U_364)
| ! [U_357] :
( ~ in(ordered_pair(U_357,U_368),U_365)
| ~ in(ordered_pair(U_370,U_357),U_366) ) )
& ! [U_369,U_367] :
( ? [U_356] :
( in(ordered_pair(U_356,U_367),U_365)
& in(ordered_pair(U_369,U_356),U_366) )
| ~ in(ordered_pair(U_369,U_367),U_364) ) )
| U_364 != relation_composition(U_366,U_365) ) )
| ~ relation(U_364) )
| ~ relation(U_365) )
| ~ relation(U_366) ),
inference(miniscope,[status(thm)],[f_38_2]) ).
fof(f_38_4,plain,
! [U_366] :
( ! [U_365] :
( ! [U_364] :
( ( ( U_364 = relation_composition(U_366,U_365)
| ? [U_374,U_372] :
( ~ in(ordered_pair(U_374,U_372),U_364)
& ? [U_361] :
( in(ordered_pair(U_361,U_372),U_365)
& in(ordered_pair(U_374,U_361),U_366) ) )
| ? [U_373,U_371] :
( ! [U_360] :
( ~ in(ordered_pair(U_360,U_371),U_365)
| ~ in(ordered_pair(U_373,U_360),U_366) )
& in(ordered_pair(U_373,U_371),U_364) ) )
& ( ( ! [U_370,U_368] :
( in(ordered_pair(U_370,U_368),U_364)
| ! [U_357] :
( ~ in(ordered_pair(U_357,U_368),U_365)
| ~ in(ordered_pair(U_370,U_357),U_366) ) )
& ! [U_369,U_367] :
( ( in(ordered_pair(sK70(U_366,U_365,U_364,U_369,U_367),U_367),U_365)
& in(ordered_pair(U_369,sK70(U_366,U_365,U_364,U_369,U_367)),U_366) )
| ~ in(ordered_pair(U_369,U_367),U_364) ) )
| U_364 != relation_composition(U_366,U_365) ) )
| ~ relation(U_364) )
| ~ relation(U_365) )
| ~ relation(U_366) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_356,sK70(U_366,U_365,U_364,U_369,U_367))],[f_38_3]) ).
fof(f_38_5,plain,
! [U_366] :
( ! [U_365] :
( ! [U_364] :
( ( ( U_364 = relation_composition(U_366,U_365)
| ? [U_374,U_372] :
( ~ in(ordered_pair(U_374,U_372),U_364)
& ? [U_361] :
( in(ordered_pair(U_361,U_372),U_365)
& in(ordered_pair(U_374,U_361),U_366) ) )
| ? [U_371] :
( ! [U_360] :
( ~ in(ordered_pair(U_360,U_371),U_365)
| ~ in(ordered_pair(sK71(U_366,U_365,U_364),U_360),U_366) )
& in(ordered_pair(sK71(U_366,U_365,U_364),U_371),U_364) ) )
& ( ( ! [U_370,U_368] :
( in(ordered_pair(U_370,U_368),U_364)
| ! [U_357] :
( ~ in(ordered_pair(U_357,U_368),U_365)
| ~ in(ordered_pair(U_370,U_357),U_366) ) )
& ! [U_369,U_367] :
( ( in(ordered_pair(sK70(U_366,U_365,U_364,U_369,U_367),U_367),U_365)
& in(ordered_pair(U_369,sK70(U_366,U_365,U_364,U_369,U_367)),U_366) )
| ~ in(ordered_pair(U_369,U_367),U_364) ) )
| U_364 != relation_composition(U_366,U_365) ) )
| ~ relation(U_364) )
| ~ relation(U_365) )
| ~ relation(U_366) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_373,sK71(U_366,U_365,U_364))],[f_38_4]) ).
fof(f_38_6,plain,
! [U_366] :
( ! [U_365] :
( ! [U_364] :
( ( ( U_364 = relation_composition(U_366,U_365)
| ? [U_374,U_372] :
( ~ in(ordered_pair(U_374,U_372),U_364)
& ? [U_361] :
( in(ordered_pair(U_361,U_372),U_365)
& in(ordered_pair(U_374,U_361),U_366) ) )
| ( ! [U_360] :
( ~ in(ordered_pair(U_360,sK72(U_366,U_365,U_364)),U_365)
| ~ in(ordered_pair(sK71(U_366,U_365,U_364),U_360),U_366) )
& in(ordered_pair(sK71(U_366,U_365,U_364),sK72(U_366,U_365,U_364)),U_364) ) )
& ( ( ! [U_370,U_368] :
( in(ordered_pair(U_370,U_368),U_364)
| ! [U_357] :
( ~ in(ordered_pair(U_357,U_368),U_365)
| ~ in(ordered_pair(U_370,U_357),U_366) ) )
& ! [U_369,U_367] :
( ( in(ordered_pair(sK70(U_366,U_365,U_364,U_369,U_367),U_367),U_365)
& in(ordered_pair(U_369,sK70(U_366,U_365,U_364,U_369,U_367)),U_366) )
| ~ in(ordered_pair(U_369,U_367),U_364) ) )
| U_364 != relation_composition(U_366,U_365) ) )
| ~ relation(U_364) )
| ~ relation(U_365) )
| ~ relation(U_366) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_371,sK72(U_366,U_365,U_364))],[f_38_5]) ).
fof(f_38_7,plain,
! [U_366] :
( ! [U_365] :
( ! [U_364] :
( ( ( U_364 = relation_composition(U_366,U_365)
| ? [U_372] :
( ~ in(ordered_pair(sK73(U_366,U_365,U_364),U_372),U_364)
& ? [U_361] :
( in(ordered_pair(U_361,U_372),U_365)
& in(ordered_pair(sK73(U_366,U_365,U_364),U_361),U_366) ) )
| ( ! [U_360] :
( ~ in(ordered_pair(U_360,sK72(U_366,U_365,U_364)),U_365)
| ~ in(ordered_pair(sK71(U_366,U_365,U_364),U_360),U_366) )
& in(ordered_pair(sK71(U_366,U_365,U_364),sK72(U_366,U_365,U_364)),U_364) ) )
& ( ( ! [U_370,U_368] :
( in(ordered_pair(U_370,U_368),U_364)
| ! [U_357] :
( ~ in(ordered_pair(U_357,U_368),U_365)
| ~ in(ordered_pair(U_370,U_357),U_366) ) )
& ! [U_369,U_367] :
( ( in(ordered_pair(sK70(U_366,U_365,U_364,U_369,U_367),U_367),U_365)
& in(ordered_pair(U_369,sK70(U_366,U_365,U_364,U_369,U_367)),U_366) )
| ~ in(ordered_pair(U_369,U_367),U_364) ) )
| U_364 != relation_composition(U_366,U_365) ) )
| ~ relation(U_364) )
| ~ relation(U_365) )
| ~ relation(U_366) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_374,sK73(U_366,U_365,U_364))],[f_38_6]) ).
fof(f_38_8,plain,
! [U_366] :
( ! [U_365] :
( ! [U_364] :
( ( ( U_364 = relation_composition(U_366,U_365)
| ( ~ in(ordered_pair(sK73(U_366,U_365,U_364),sK74(U_366,U_365,U_364)),U_364)
& ? [U_361] :
( in(ordered_pair(U_361,sK74(U_366,U_365,U_364)),U_365)
& in(ordered_pair(sK73(U_366,U_365,U_364),U_361),U_366) ) )
| ( ! [U_360] :
( ~ in(ordered_pair(U_360,sK72(U_366,U_365,U_364)),U_365)
| ~ in(ordered_pair(sK71(U_366,U_365,U_364),U_360),U_366) )
& in(ordered_pair(sK71(U_366,U_365,U_364),sK72(U_366,U_365,U_364)),U_364) ) )
& ( ( ! [U_370,U_368] :
( in(ordered_pair(U_370,U_368),U_364)
| ! [U_357] :
( ~ in(ordered_pair(U_357,U_368),U_365)
| ~ in(ordered_pair(U_370,U_357),U_366) ) )
& ! [U_369,U_367] :
( ( in(ordered_pair(sK70(U_366,U_365,U_364,U_369,U_367),U_367),U_365)
& in(ordered_pair(U_369,sK70(U_366,U_365,U_364,U_369,U_367)),U_366) )
| ~ in(ordered_pair(U_369,U_367),U_364) ) )
| U_364 != relation_composition(U_366,U_365) ) )
| ~ relation(U_364) )
| ~ relation(U_365) )
| ~ relation(U_366) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_372,sK74(U_366,U_365,U_364))],[f_38_7]) ).
fof(f_38_9,plain,
! [U_366] :
( ! [U_365] :
( ! [U_364] :
( ( ( U_364 = relation_composition(U_366,U_365)
| ( ~ in(ordered_pair(sK73(U_366,U_365,U_364),sK74(U_366,U_365,U_364)),U_364)
& in(ordered_pair(sK75(U_366,U_365,U_364),sK74(U_366,U_365,U_364)),U_365)
& in(ordered_pair(sK73(U_366,U_365,U_364),sK75(U_366,U_365,U_364)),U_366) )
| ( ! [U_360] :
( ~ in(ordered_pair(U_360,sK72(U_366,U_365,U_364)),U_365)
| ~ in(ordered_pair(sK71(U_366,U_365,U_364),U_360),U_366) )
& in(ordered_pair(sK71(U_366,U_365,U_364),sK72(U_366,U_365,U_364)),U_364) ) )
& ( ( ! [U_370,U_368] :
( in(ordered_pair(U_370,U_368),U_364)
| ! [U_357] :
( ~ in(ordered_pair(U_357,U_368),U_365)
| ~ in(ordered_pair(U_370,U_357),U_366) ) )
& ! [U_369,U_367] :
( ( in(ordered_pair(sK70(U_366,U_365,U_364,U_369,U_367),U_367),U_365)
& in(ordered_pair(U_369,sK70(U_366,U_365,U_364,U_369,U_367)),U_366) )
| ~ in(ordered_pair(U_369,U_367),U_364) ) )
| U_364 != relation_composition(U_366,U_365) ) )
| ~ relation(U_364) )
| ~ relation(U_365) )
| ~ relation(U_366) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_361,sK75(U_366,U_365,U_364))],[f_38_8]) ).
cnf(f_38_10,plain,
( in(ordered_pair(U_369,sK70(U_366,U_365,U_364,U_369,U_367)),U_366)
| ~ in(ordered_pair(U_369,U_367),U_364)
| U_364 != relation_composition(U_366,U_365)
| ~ relation(U_364)
| ~ relation(U_365)
| ~ relation(U_366) ),
inference(clausify,[status(thm)],[f_38_9]) ).
cnf(f_38_11,plain,
( in(ordered_pair(sK70(U_366,U_365,U_364,U_369,U_367),U_367),U_365)
| ~ in(ordered_pair(U_369,U_367),U_364)
| U_364 != relation_composition(U_366,U_365)
| ~ relation(U_364)
| ~ relation(U_365)
| ~ relation(U_366) ),
inference(clausify,[status(thm)],[f_38_9]) ).
cnf(f_38_12,plain,
( in(ordered_pair(U_370,U_368),U_364)
| ~ in(ordered_pair(U_357,U_368),U_365)
| ~ in(ordered_pair(U_370,U_357),U_366)
| U_364 != relation_composition(U_366,U_365)
| ~ relation(U_364)
| ~ relation(U_365)
| ~ relation(U_366) ),
inference(clausify,[status(thm)],[f_38_9]) ).
cnf(f_38_13,plain,
( in(ordered_pair(sK73(U_366,U_365,U_364),sK75(U_366,U_365,U_364)),U_366)
| in(ordered_pair(sK71(U_366,U_365,U_364),sK72(U_366,U_365,U_364)),U_364)
| U_364 = relation_composition(U_366,U_365)
| ~ relation(U_364)
| ~ relation(U_365)
| ~ relation(U_366) ),
inference(clausify,[status(thm)],[f_38_9]) ).
cnf(f_38_14,plain,
( in(ordered_pair(sK75(U_366,U_365,U_364),sK74(U_366,U_365,U_364)),U_365)
| in(ordered_pair(sK71(U_366,U_365,U_364),sK72(U_366,U_365,U_364)),U_364)
| U_364 = relation_composition(U_366,U_365)
| ~ relation(U_364)
| ~ relation(U_365)
| ~ relation(U_366) ),
inference(clausify,[status(thm)],[f_38_9]) ).
cnf(f_38_15,plain,
( ~ in(ordered_pair(sK73(U_366,U_365,U_364),sK74(U_366,U_365,U_364)),U_364)
| in(ordered_pair(sK71(U_366,U_365,U_364),sK72(U_366,U_365,U_364)),U_364)
| U_364 = relation_composition(U_366,U_365)
| ~ relation(U_364)
| ~ relation(U_365)
| ~ relation(U_366) ),
inference(clausify,[status(thm)],[f_38_9]) ).
cnf(f_38_16,plain,
( in(ordered_pair(sK73(U_366,U_365,U_364),sK75(U_366,U_365,U_364)),U_366)
| ~ in(ordered_pair(U_360,sK72(U_366,U_365,U_364)),U_365)
| ~ in(ordered_pair(sK71(U_366,U_365,U_364),U_360),U_366)
| U_364 = relation_composition(U_366,U_365)
| ~ relation(U_364)
| ~ relation(U_365)
| ~ relation(U_366) ),
inference(clausify,[status(thm)],[f_38_9]) ).
cnf(f_38_17,plain,
( in(ordered_pair(sK75(U_366,U_365,U_364),sK74(U_366,U_365,U_364)),U_365)
| ~ in(ordered_pair(U_360,sK72(U_366,U_365,U_364)),U_365)
| ~ in(ordered_pair(sK71(U_366,U_365,U_364),U_360),U_366)
| U_364 = relation_composition(U_366,U_365)
| ~ relation(U_364)
| ~ relation(U_365)
| ~ relation(U_366) ),
inference(clausify,[status(thm)],[f_38_9]) ).
cnf(f_38_18,plain,
( ~ in(ordered_pair(sK73(U_366,U_365,U_364),sK74(U_366,U_365,U_364)),U_364)
| ~ in(ordered_pair(U_360,sK72(U_366,U_365,U_364)),U_365)
| ~ in(ordered_pair(sK71(U_366,U_365,U_364),U_360),U_366)
| U_364 = relation_composition(U_366,U_365)
| ~ relation(U_364)
| ~ relation(U_365)
| ~ relation(U_366) ),
inference(clausify,[status(thm)],[f_38_9]) ).
fof(f_39_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_39_2,plain,
! [U_379,U_378] :
( ! [U_377] :
( ( ( U_377 = complements_of_subsets(U_379,U_378)
| ? [U_376] :
( ( ( ~ in(U_376,U_377)
& in(subset_complement(U_379,U_376),U_378) )
| ( ~ in(subset_complement(U_379,U_376),U_378)
& in(U_376,U_377) ) )
& element(U_376,powerset(U_379)) ) )
& ( ! [U_375] :
( ( ( in(U_375,U_377)
| ~ in(subset_complement(U_379,U_375),U_378) )
& ( in(subset_complement(U_379,U_375),U_378)
| ~ in(U_375,U_377) ) )
| ~ element(U_375,powerset(U_379)) )
| U_377 != complements_of_subsets(U_379,U_378) ) )
| ~ element(U_377,powerset(powerset(U_379))) )
| ~ element(U_378,powerset(powerset(U_379))) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_379,U_378] :
( ! [U_377] :
( ( ( U_377 = complements_of_subsets(U_379,U_378)
| ( ( ( ~ in(sK76(U_379,U_378,U_377),U_377)
& in(subset_complement(U_379,sK76(U_379,U_378,U_377)),U_378) )
| ( ~ in(subset_complement(U_379,sK76(U_379,U_378,U_377)),U_378)
& in(sK76(U_379,U_378,U_377),U_377) ) )
& element(sK76(U_379,U_378,U_377),powerset(U_379)) ) )
& ( ! [U_375] :
( ( ( in(U_375,U_377)
| ~ in(subset_complement(U_379,U_375),U_378) )
& ( in(subset_complement(U_379,U_375),U_378)
| ~ in(U_375,U_377) ) )
| ~ element(U_375,powerset(U_379)) )
| U_377 != complements_of_subsets(U_379,U_378) ) )
| ~ element(U_377,powerset(powerset(U_379))) )
| ~ element(U_378,powerset(powerset(U_379))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_376,sK76(U_379,U_378,U_377))],[f_39_2]) ).
cnf(f_39_4,plain,
( in(subset_complement(U_379,U_375),U_378)
| ~ in(U_375,U_377)
| ~ element(U_375,powerset(U_379))
| U_377 != complements_of_subsets(U_379,U_378)
| ~ element(U_377,powerset(powerset(U_379)))
| ~ element(U_378,powerset(powerset(U_379))) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_5,plain,
( in(U_375,U_377)
| ~ in(subset_complement(U_379,U_375),U_378)
| ~ element(U_375,powerset(U_379))
| U_377 != complements_of_subsets(U_379,U_378)
| ~ element(U_377,powerset(powerset(U_379)))
| ~ element(U_378,powerset(powerset(U_379))) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_6,plain,
( element(sK76(U_379,U_378,U_377),powerset(U_379))
| U_377 = complements_of_subsets(U_379,U_378)
| ~ element(U_377,powerset(powerset(U_379)))
| ~ element(U_378,powerset(powerset(U_379))) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_7,plain,
( in(subset_complement(U_379,sK76(U_379,U_378,U_377)),U_378)
| in(sK76(U_379,U_378,U_377),U_377)
| U_377 = complements_of_subsets(U_379,U_378)
| ~ element(U_377,powerset(powerset(U_379)))
| ~ element(U_378,powerset(powerset(U_379))) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_8,plain,
( ~ in(sK76(U_379,U_378,U_377),U_377)
| in(sK76(U_379,U_378,U_377),U_377)
| U_377 = complements_of_subsets(U_379,U_378)
| ~ element(U_377,powerset(powerset(U_379)))
| ~ element(U_378,powerset(powerset(U_379))) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_9,plain,
( in(subset_complement(U_379,sK76(U_379,U_378,U_377)),U_378)
| ~ in(subset_complement(U_379,sK76(U_379,U_378,U_377)),U_378)
| U_377 = complements_of_subsets(U_379,U_378)
| ~ element(U_377,powerset(powerset(U_379)))
| ~ element(U_378,powerset(powerset(U_379))) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_10,plain,
( ~ in(sK76(U_379,U_378,U_377),U_377)
| ~ in(subset_complement(U_379,sK76(U_379,U_378,U_377)),U_378)
| U_377 = complements_of_subsets(U_379,U_378)
| ~ element(U_377,powerset(powerset(U_379)))
| ~ element(U_378,powerset(powerset(U_379))) ),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_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_40_2,plain,
! [U_381,U_380] :
( ( proper_subset(U_381,U_380)
| U_381 = U_380
| ~ subset(U_381,U_380) )
& ( ( U_381 != U_380
& subset(U_381,U_380) )
| ~ proper_subset(U_381,U_380) ) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
( ! [U_385,U_383] :
( proper_subset(U_385,U_383)
| U_385 = U_383
| ~ subset(U_385,U_383) )
& ! [U_384,U_382] :
( ( U_384 != U_382
& subset(U_384,U_382) )
| ~ proper_subset(U_384,U_382) ) ),
inference(miniscope,[status(thm)],[f_40_2]) ).
cnf(f_40_4,plain,
( subset(U_384,U_382)
| ~ proper_subset(U_384,U_382) ),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_40_5,plain,
( U_384 != U_382
| ~ proper_subset(U_384,U_382) ),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_40_6,plain,
( proper_subset(U_385,U_383)
| U_385 = U_383
| ~ subset(U_385,U_383) ),
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k10_relat_1]) ).
cnf(f_41_2,plain,
$true,
inference(clausify,[status(thm)],[f_41_1]) ).
fof(f_42_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_funct_1]) ).
cnf(f_42_2,plain,
$true,
inference(clausify,[status(thm)],[f_42_1]) ).
fof(f_43_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
cnf(f_43_2,plain,
$true,
inference(clausify,[status(thm)],[f_43_1]) ).
fof(f_44_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_setfam_1]) ).
cnf(f_44_2,plain,
$true,
inference(clausify,[status(thm)],[f_44_1]) ).
fof(f_45_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
cnf(f_45_2,plain,
$true,
inference(clausify,[status(thm)],[f_45_1]) ).
fof(f_46_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_46_2,plain,
$true,
inference(clausify,[status(thm)],[f_46_1]) ).
fof(f_47_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_47_2,plain,
$true,
inference(clausify,[status(thm)],[f_47_1]) ).
fof(f_48_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_relat_1]) ).
cnf(f_48_2,plain,
$true,
inference(clausify,[status(thm)],[f_48_1]) ).
fof(f_49_1,plain,
! [A] : element(cast_to_subset(A),powerset(A)),
inference(fof_nnf,[status(thm)],[dt_k2_subset_1]) ).
fof(f_49_2,plain,
! [U_386] : element(cast_to_subset(U_386),powerset(U_386)),
inference(variable_rename,[status(thm)],[f_49_1]) ).
cnf(f_49_3,plain,
element(cast_to_subset(U_386),powerset(U_386)),
inference(clausify,[status(thm)],[f_49_2]) ).
fof(f_50_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
cnf(f_50_2,plain,
$true,
inference(clausify,[status(thm)],[f_50_1]) ).
fof(f_51_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
cnf(f_51_2,plain,
$true,
inference(clausify,[status(thm)],[f_51_1]) ).
fof(f_52_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
cnf(f_52_2,plain,
$true,
inference(clausify,[status(thm)],[f_52_1]) ).
fof(f_53_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_relat_1]) ).
cnf(f_53_2,plain,
$true,
inference(clausify,[status(thm)],[f_53_1]) ).
fof(f_54_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_54_2,plain,
! [U_388,U_387] :
( element(subset_complement(U_388,U_387),powerset(U_388))
| ~ element(U_387,powerset(U_388)) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
cnf(f_54_3,plain,
( element(subset_complement(U_388,U_387),powerset(U_388))
| ~ element(U_387,powerset(U_388)) ),
inference(clausify,[status(thm)],[f_54_2]) ).
fof(f_55_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_tarski]) ).
cnf(f_55_2,plain,
$true,
inference(clausify,[status(thm)],[f_55_1]) ).
fof(f_56_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
cnf(f_56_2,plain,
$true,
inference(clausify,[status(thm)],[f_56_1]) ).
fof(f_57_1,plain,
! [A] :
( relation(relation_inverse(A))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k4_relat_1]) ).
fof(f_57_2,plain,
! [U_389] :
( relation(relation_inverse(U_389))
| ~ relation(U_389) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
cnf(f_57_3,plain,
( relation(relation_inverse(U_389))
| ~ relation(U_389) ),
inference(clausify,[status(thm)],[f_57_2]) ).
fof(f_58_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
cnf(f_58_2,plain,
$true,
inference(clausify,[status(thm)],[f_58_1]) ).
fof(f_59_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
cnf(f_59_2,plain,
$true,
inference(clausify,[status(thm)],[f_59_1]) ).
fof(f_60_1,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_relat_1]) ).
fof(f_60_2,plain,
! [U_391,U_390] :
( relation(relation_composition(U_391,U_390))
| ~ relation(U_390)
| ~ relation(U_391) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
cnf(f_60_3,plain,
( relation(relation_composition(U_391,U_390))
| ~ relation(U_390)
| ~ relation(U_391) ),
inference(clausify,[status(thm)],[f_60_2]) ).
fof(f_61_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_61_2,plain,
! [U_393,U_392] :
( element(union_of_subsets(U_393,U_392),powerset(U_393))
| ~ element(U_392,powerset(powerset(U_393))) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
cnf(f_61_3,plain,
( element(union_of_subsets(U_393,U_392),powerset(U_393))
| ~ element(U_392,powerset(powerset(U_393))) ),
inference(clausify,[status(thm)],[f_61_2]) ).
fof(f_62_1,plain,
! [A] : relation(identity_relation(A)),
inference(fof_nnf,[status(thm)],[dt_k6_relat_1]) ).
fof(f_62_2,plain,
! [U_394] : relation(identity_relation(U_394)),
inference(variable_rename,[status(thm)],[f_62_1]) ).
cnf(f_62_3,plain,
relation(identity_relation(U_394)),
inference(clausify,[status(thm)],[f_62_2]) ).
fof(f_63_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_63_2,plain,
! [U_396,U_395] :
( element(meet_of_subsets(U_396,U_395),powerset(U_396))
| ~ element(U_395,powerset(powerset(U_396))) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
cnf(f_63_3,plain,
( element(meet_of_subsets(U_396,U_395),powerset(U_396))
| ~ element(U_395,powerset(powerset(U_396))) ),
inference(clausify,[status(thm)],[f_63_2]) ).
fof(f_64_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_64_2,plain,
! [U_399,U_398,U_397] :
( element(subset_difference(U_399,U_398,U_397),powerset(U_399))
| ~ element(U_397,powerset(U_399))
| ~ element(U_398,powerset(U_399)) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
cnf(f_64_3,plain,
( element(subset_difference(U_399,U_398,U_397),powerset(U_399))
| ~ element(U_397,powerset(U_399))
| ~ element(U_398,powerset(U_399)) ),
inference(clausify,[status(thm)],[f_64_2]) ).
fof(f_65_1,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k7_relat_1]) ).
fof(f_65_2,plain,
! [U_401,U_400] :
( relation(relation_dom_restriction(U_401,U_400))
| ~ relation(U_401) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
! [U_401] :
( ! [U_400] : relation(relation_dom_restriction(U_401,U_400))
| ~ relation(U_401) ),
inference(miniscope,[status(thm)],[f_65_2]) ).
cnf(f_65_4,plain,
( relation(relation_dom_restriction(U_401,U_400))
| ~ relation(U_401) ),
inference(clausify,[status(thm)],[f_65_3]) ).
fof(f_66_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_66_2,plain,
! [U_403,U_402] :
( element(complements_of_subsets(U_403,U_402),powerset(powerset(U_403)))
| ~ element(U_402,powerset(powerset(U_403))) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
cnf(f_66_3,plain,
( element(complements_of_subsets(U_403,U_402),powerset(powerset(U_403)))
| ~ element(U_402,powerset(powerset(U_403))) ),
inference(clausify,[status(thm)],[f_66_2]) ).
fof(f_67_1,plain,
! [A,B] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[dt_k8_relat_1]) ).
fof(f_67_2,plain,
! [U_405,U_404] :
( relation(relation_rng_restriction(U_405,U_404))
| ~ relation(U_404) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
cnf(f_67_3,plain,
( relation(relation_rng_restriction(U_405,U_404))
| ~ relation(U_404) ),
inference(clausify,[status(thm)],[f_67_2]) ).
fof(f_68_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k9_relat_1]) ).
cnf(f_68_2,plain,
$true,
inference(clausify,[status(thm)],[f_68_1]) ).
fof(f_69_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_69_2,plain,
$true,
inference(clausify,[status(thm)],[f_69_1]) ).
fof(f_70_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_70_2,plain,
! [U_407] :
? [U_406] : element(U_406,U_407),
inference(variable_rename,[status(thm)],[f_70_1]) ).
fof(f_70_3,plain,
! [U_407] : element(sK77(U_407),U_407),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_406,sK77(U_407))],[f_70_2]) ).
cnf(f_70_4,plain,
element(sK77(U_407),U_407),
inference(clausify,[status(thm)],[f_70_3]) ).
fof(f_71_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_71_2,plain,
! [U_409,U_408] :
( ( relation(relation_composition(U_408,U_409))
& empty(relation_composition(U_408,U_409)) )
| ~ relation(U_408)
| ~ empty(U_409) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
cnf(f_71_3,plain,
( empty(relation_composition(U_408,U_409))
| ~ relation(U_408)
| ~ empty(U_409) ),
inference(clausify,[status(thm)],[f_71_2]) ).
cnf(f_71_4,plain,
( relation(relation_composition(U_408,U_409))
| ~ relation(U_408)
| ~ empty(U_409) ),
inference(clausify,[status(thm)],[f_71_2]) ).
fof(f_72_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
cnf(f_72_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_72_1]) ).
cnf(f_72_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_72_1]) ).
cnf(f_72_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_72_1]) ).
fof(f_73_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_73_2,plain,
! [U_411,U_410] :
( ( function(relation_composition(U_411,U_410))
& relation(relation_composition(U_411,U_410)) )
| ~ function(U_410)
| ~ relation(U_410)
| ~ function(U_411)
| ~ relation(U_411) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
cnf(f_73_3,plain,
( relation(relation_composition(U_411,U_410))
| ~ function(U_410)
| ~ relation(U_410)
| ~ function(U_411)
| ~ relation(U_411) ),
inference(clausify,[status(thm)],[f_73_2]) ).
cnf(f_73_4,plain,
( function(relation_composition(U_411,U_410))
| ~ function(U_410)
| ~ relation(U_410)
| ~ function(U_411)
| ~ relation(U_411) ),
inference(clausify,[status(thm)],[f_73_2]) ).
fof(f_74_1,plain,
! [A,B] :
( relation(set_intersection2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc1_relat_1]) ).
fof(f_74_2,plain,
! [U_413,U_412] :
( relation(set_intersection2(U_413,U_412))
| ~ relation(U_412)
| ~ relation(U_413) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
cnf(f_74_3,plain,
( relation(set_intersection2(U_413,U_412))
| ~ relation(U_412)
| ~ relation(U_413) ),
inference(clausify,[status(thm)],[f_74_2]) ).
fof(f_75_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_75_2,plain,
! [U_414] : ~ empty(powerset(U_414)),
inference(variable_rename,[status(thm)],[f_75_1]) ).
cnf(f_75_3,plain,
~ empty(powerset(U_414)),
inference(clausify,[status(thm)],[f_75_2]) ).
fof(f_76_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_76_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_76_1]) ).
fof(f_77_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_77_2,plain,
! [U_416,U_415] : ~ empty(ordered_pair(U_416,U_415)),
inference(variable_rename,[status(thm)],[f_77_1]) ).
cnf(f_77_3,plain,
~ empty(ordered_pair(U_416,U_415)),
inference(clausify,[status(thm)],[f_77_2]) ).
fof(f_78_1,plain,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
inference(fof_nnf,[status(thm)],[fc2_funct_1]) ).
fof(f_78_2,plain,
! [U_417] :
( function(identity_relation(U_417))
& relation(identity_relation(U_417)) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
fof(f_78_3,plain,
( ! [U_419] : function(identity_relation(U_419))
& ! [U_418] : relation(identity_relation(U_418)) ),
inference(miniscope,[status(thm)],[f_78_2]) ).
cnf(f_78_4,plain,
relation(identity_relation(U_418)),
inference(clausify,[status(thm)],[f_78_3]) ).
cnf(f_78_5,plain,
function(identity_relation(U_419)),
inference(clausify,[status(thm)],[f_78_3]) ).
fof(f_79_1,plain,
! [A,B] :
( relation(set_union2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc2_relat_1]) ).
fof(f_79_2,plain,
! [U_421,U_420] :
( relation(set_union2(U_421,U_420))
| ~ relation(U_420)
| ~ relation(U_421) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
cnf(f_79_3,plain,
( relation(set_union2(U_421,U_420))
| ~ relation(U_420)
| ~ relation(U_421) ),
inference(clausify,[status(thm)],[f_79_2]) ).
fof(f_80_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_80_2,plain,
! [U_422] : ~ empty(singleton(U_422)),
inference(variable_rename,[status(thm)],[f_80_1]) ).
cnf(f_80_3,plain,
~ empty(singleton(U_422)),
inference(clausify,[status(thm)],[f_80_2]) ).
fof(f_81_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_81_2,plain,
! [U_424,U_423] :
( ~ empty(set_union2(U_424,U_423))
| empty(U_424) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
fof(f_81_3,plain,
! [U_424] :
( ! [U_423] : ~ empty(set_union2(U_424,U_423))
| empty(U_424) ),
inference(miniscope,[status(thm)],[f_81_2]) ).
cnf(f_81_4,plain,
( ~ empty(set_union2(U_424,U_423))
| empty(U_424) ),
inference(clausify,[status(thm)],[f_81_3]) ).
fof(f_82_1,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_82_2,plain,
! [U_426,U_425] : ~ empty(unordered_pair(U_426,U_425)),
inference(variable_rename,[status(thm)],[f_82_1]) ).
cnf(f_82_3,plain,
~ empty(unordered_pair(U_426,U_425)),
inference(clausify,[status(thm)],[f_82_2]) ).
fof(f_83_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_83_2,plain,
! [U_428,U_427] :
( ~ empty(set_union2(U_427,U_428))
| empty(U_428) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
fof(f_83_3,plain,
! [U_428] :
( ! [U_427] : ~ empty(set_union2(U_427,U_428))
| empty(U_428) ),
inference(miniscope,[status(thm)],[f_83_2]) ).
cnf(f_83_4,plain,
( ~ empty(set_union2(U_427,U_428))
| empty(U_428) ),
inference(clausify,[status(thm)],[f_83_3]) ).
fof(f_84_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_84_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_84_1]) ).
cnf(f_84_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_84_1]) ).
fof(f_85_1,plain,
! [A,B] :
( ~ empty(cartesian_product2(A,B))
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc4_subset_1]) ).
fof(f_85_2,plain,
! [U_430,U_429] :
( ~ empty(cartesian_product2(U_430,U_429))
| empty(U_429)
| empty(U_430) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
cnf(f_85_3,plain,
( ~ empty(cartesian_product2(U_430,U_429))
| empty(U_429)
| empty(U_430) ),
inference(clausify,[status(thm)],[f_85_2]) ).
fof(f_86_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_86_2,plain,
! [U_431] :
( ~ empty(relation_dom(U_431))
| ~ relation(U_431)
| empty(U_431) ),
inference(variable_rename,[status(thm)],[f_86_1]) ).
cnf(f_86_3,plain,
( ~ empty(relation_dom(U_431))
| ~ relation(U_431)
| empty(U_431) ),
inference(clausify,[status(thm)],[f_86_2]) ).
fof(f_87_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_87_2,plain,
! [U_432] :
( ~ empty(relation_rng(U_432))
| ~ relation(U_432)
| empty(U_432) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
cnf(f_87_3,plain,
( ~ empty(relation_rng(U_432))
| ~ relation(U_432)
| empty(U_432) ),
inference(clausify,[status(thm)],[f_87_2]) ).
fof(f_88_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_88_2,plain,
! [U_433] :
( ( relation(relation_dom(U_433))
& empty(relation_dom(U_433)) )
| ~ empty(U_433) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
cnf(f_88_3,plain,
( empty(relation_dom(U_433))
| ~ empty(U_433) ),
inference(clausify,[status(thm)],[f_88_2]) ).
cnf(f_88_4,plain,
( relation(relation_dom(U_433))
| ~ empty(U_433) ),
inference(clausify,[status(thm)],[f_88_2]) ).
fof(f_89_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_89_2,plain,
! [U_434] :
( ( relation(relation_rng(U_434))
& empty(relation_rng(U_434)) )
| ~ empty(U_434) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
cnf(f_89_3,plain,
( empty(relation_rng(U_434))
| ~ empty(U_434) ),
inference(clausify,[status(thm)],[f_89_2]) ).
cnf(f_89_4,plain,
( relation(relation_rng(U_434))
| ~ empty(U_434) ),
inference(clausify,[status(thm)],[f_89_2]) ).
fof(f_90_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_90_2,plain,
! [U_436,U_435] :
( ( relation(relation_composition(U_436,U_435))
& empty(relation_composition(U_436,U_435)) )
| ~ relation(U_435)
| ~ empty(U_436) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
cnf(f_90_3,plain,
( empty(relation_composition(U_436,U_435))
| ~ relation(U_435)
| ~ empty(U_436) ),
inference(clausify,[status(thm)],[f_90_2]) ).
cnf(f_90_4,plain,
( relation(relation_composition(U_436,U_435))
| ~ relation(U_435)
| ~ empty(U_436) ),
inference(clausify,[status(thm)],[f_90_2]) ).
fof(f_91_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_91_2,plain,
! [U_438,U_437] : set_union2(U_438,U_438) = U_438,
inference(variable_rename,[status(thm)],[f_91_1]) ).
fof(f_91_3,plain,
! [U_438] : set_union2(U_438,U_438) = U_438,
inference(miniscope,[status(thm)],[f_91_2]) ).
cnf(f_91_4,plain,
set_union2(U_438,U_438) = U_438,
inference(clausify,[status(thm)],[f_91_3]) ).
fof(f_92_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_92_2,plain,
! [U_440,U_439] : set_intersection2(U_440,U_440) = U_440,
inference(variable_rename,[status(thm)],[f_92_1]) ).
fof(f_92_3,plain,
! [U_440] : set_intersection2(U_440,U_440) = U_440,
inference(miniscope,[status(thm)],[f_92_2]) ).
cnf(f_92_4,plain,
set_intersection2(U_440,U_440) = U_440,
inference(clausify,[status(thm)],[f_92_3]) ).
fof(f_93_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_93_2,plain,
! [U_442,U_441] :
( subset_complement(U_442,subset_complement(U_442,U_441)) = U_441
| ~ element(U_441,powerset(U_442)) ),
inference(variable_rename,[status(thm)],[f_93_1]) ).
cnf(f_93_3,plain,
( subset_complement(U_442,subset_complement(U_442,U_441)) = U_441
| ~ element(U_441,powerset(U_442)) ),
inference(clausify,[status(thm)],[f_93_2]) ).
fof(f_94_1,plain,
! [A] :
( relation_inverse(relation_inverse(A)) = A
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[involutiveness_k4_relat_1]) ).
fof(f_94_2,plain,
! [U_443] :
( relation_inverse(relation_inverse(U_443)) = U_443
| ~ relation(U_443) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
cnf(f_94_3,plain,
( relation_inverse(relation_inverse(U_443)) = U_443
| ~ relation(U_443) ),
inference(clausify,[status(thm)],[f_94_2]) ).
fof(f_95_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_95_2,plain,
! [U_445,U_444] :
( complements_of_subsets(U_445,complements_of_subsets(U_445,U_444)) = U_444
| ~ element(U_444,powerset(powerset(U_445))) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
cnf(f_95_3,plain,
( complements_of_subsets(U_445,complements_of_subsets(U_445,U_444)) = U_444
| ~ element(U_444,powerset(powerset(U_445))) ),
inference(clausify,[status(thm)],[f_95_2]) ).
fof(f_96_1,plain,
! [A,B] : ~ proper_subset(A,A),
inference(fof_nnf,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(f_96_2,plain,
! [U_447,U_446] : ~ proper_subset(U_447,U_447),
inference(variable_rename,[status(thm)],[f_96_1]) ).
fof(f_96_3,plain,
! [U_447] : ~ proper_subset(U_447,U_447),
inference(miniscope,[status(thm)],[f_96_2]) ).
cnf(f_96_4,plain,
~ proper_subset(U_447,U_447),
inference(clausify,[status(thm)],[f_96_3]) ).
fof(f_97_1,plain,
! [A] : singleton(A) != empty_set,
inference(fof_nnf,[status(thm)],[l1_zfmisc_1]) ).
fof(f_97_2,plain,
! [U_448] : singleton(U_448) != empty_set,
inference(variable_rename,[status(thm)],[f_97_1]) ).
cnf(f_97_3,plain,
singleton(U_448) != empty_set,
inference(clausify,[status(thm)],[f_97_2]) ).
fof(f_98_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l23_zfmisc_1]) ).
fof(f_98_2,plain,
! [U_450,U_449] :
( set_union2(singleton(U_450),U_449) = U_449
| ~ in(U_450,U_449) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
cnf(f_98_3,plain,
( set_union2(singleton(U_450),U_449) = U_449
| ~ in(U_450,U_449) ),
inference(clausify,[status(thm)],[f_98_2]) ).
fof(f_99_1,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(fof_nnf,[status(thm)],[l25_zfmisc_1]) ).
fof(f_99_2,plain,
! [U_452,U_451] :
( ~ in(U_452,U_451)
| ~ disjoint(singleton(U_452),U_451) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
cnf(f_99_3,plain,
( ~ in(U_452,U_451)
| ~ disjoint(singleton(U_452),U_451) ),
inference(clausify,[status(thm)],[f_99_2]) ).
fof(f_100_1,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(fof_nnf,[status(thm)],[l28_zfmisc_1]) ).
fof(f_100_2,plain,
! [U_454,U_453] :
( disjoint(singleton(U_454),U_453)
| in(U_454,U_453) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
cnf(f_100_3,plain,
( disjoint(singleton(U_454),U_453)
| in(U_454,U_453) ),
inference(clausify,[status(thm)],[f_100_2]) ).
fof(f_101_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_101_2,plain,
! [U_456,U_455] :
( ( subset(singleton(U_456),U_455)
| ~ in(U_456,U_455) )
& ( in(U_456,U_455)
| ~ subset(singleton(U_456),U_455) ) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
fof(f_101_3,plain,
( ! [U_460,U_458] :
( subset(singleton(U_460),U_458)
| ~ in(U_460,U_458) )
& ! [U_459,U_457] :
( in(U_459,U_457)
| ~ subset(singleton(U_459),U_457) ) ),
inference(miniscope,[status(thm)],[f_101_2]) ).
cnf(f_101_4,plain,
( in(U_459,U_457)
| ~ subset(singleton(U_459),U_457) ),
inference(clausify,[status(thm)],[f_101_3]) ).
cnf(f_101_5,plain,
( subset(singleton(U_460),U_458)
| ~ in(U_460,U_458) ),
inference(clausify,[status(thm)],[f_101_3]) ).
fof(f_102_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_102_2,plain,
! [U_462,U_461] :
( ( set_difference(U_462,U_461) = empty_set
| ~ subset(U_462,U_461) )
& ( subset(U_462,U_461)
| set_difference(U_462,U_461) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
fof(f_102_3,plain,
( ! [U_466,U_464] :
( set_difference(U_466,U_464) = empty_set
| ~ subset(U_466,U_464) )
& ! [U_465,U_463] :
( subset(U_465,U_463)
| set_difference(U_465,U_463) != empty_set ) ),
inference(miniscope,[status(thm)],[f_102_2]) ).
cnf(f_102_4,plain,
( subset(U_465,U_463)
| set_difference(U_465,U_463) != empty_set ),
inference(clausify,[status(thm)],[f_102_3]) ).
cnf(f_102_5,plain,
( set_difference(U_466,U_464) = empty_set
| ~ subset(U_466,U_464) ),
inference(clausify,[status(thm)],[f_102_3]) ).
fof(f_103_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_103_2,plain,
! [U_469,U_468] :
( ! [U_467] :
( in(U_467,U_469)
| ~ in(U_467,U_468) )
| ~ element(U_468,powerset(U_469)) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
cnf(f_103_3,plain,
( in(U_467,U_469)
| ~ in(U_467,U_468)
| ~ element(U_468,powerset(U_469)) ),
inference(clausify,[status(thm)],[f_103_2]) ).
fof(f_104_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_104_2,plain,
! [U_472,U_471,U_470] :
( subset(U_472,set_difference(U_471,singleton(U_470)))
| in(U_470,U_472)
| ~ subset(U_472,U_471) ),
inference(variable_rename,[status(thm)],[f_104_1]) ).
fof(f_104_3,plain,
! [U_472,U_471] :
( ! [U_470] :
( subset(U_472,set_difference(U_471,singleton(U_470)))
| in(U_470,U_472) )
| ~ subset(U_472,U_471) ),
inference(miniscope,[status(thm)],[f_104_2]) ).
cnf(f_104_4,plain,
( subset(U_472,set_difference(U_471,singleton(U_470)))
| in(U_470,U_472)
| ~ subset(U_472,U_471) ),
inference(clausify,[status(thm)],[f_104_3]) ).
fof(f_105_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_105_2,plain,
! [U_474,U_473] :
( ( subset(U_474,singleton(U_473))
| ( U_474 != singleton(U_473)
& U_474 != empty_set ) )
& ( U_474 = singleton(U_473)
| U_474 = empty_set
| ~ subset(U_474,singleton(U_473)) ) ),
inference(variable_rename,[status(thm)],[f_105_1]) ).
fof(f_105_3,plain,
( ! [U_478,U_476] :
( subset(U_478,singleton(U_476))
| ( U_478 != singleton(U_476)
& U_478 != empty_set ) )
& ! [U_477,U_475] :
( U_477 = singleton(U_475)
| U_477 = empty_set
| ~ subset(U_477,singleton(U_475)) ) ),
inference(miniscope,[status(thm)],[f_105_2]) ).
cnf(f_105_4,plain,
( U_477 = singleton(U_475)
| U_477 = empty_set
| ~ subset(U_477,singleton(U_475)) ),
inference(clausify,[status(thm)],[f_105_3]) ).
cnf(f_105_5,plain,
( U_478 != empty_set
| subset(U_478,singleton(U_476)) ),
inference(clausify,[status(thm)],[f_105_3]) ).
cnf(f_105_6,plain,
( U_478 != singleton(U_476)
| subset(U_478,singleton(U_476)) ),
inference(clausify,[status(thm)],[f_105_3]) ).
fof(f_106_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l50_zfmisc_1]) ).
fof(f_106_2,plain,
! [U_480,U_479] :
( subset(U_480,union(U_479))
| ~ in(U_480,U_479) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
cnf(f_106_3,plain,
( subset(U_480,union(U_479))
| ~ in(U_480,U_479) ),
inference(clausify,[status(thm)],[f_106_2]) ).
fof(f_107_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_107_2,plain,
! [U_484,U_483,U_482,U_481] :
( ( in(ordered_pair(U_484,U_483),cartesian_product2(U_482,U_481))
| ~ in(U_483,U_481)
| ~ in(U_484,U_482) )
& ( ( in(U_483,U_481)
& in(U_484,U_482) )
| ~ in(ordered_pair(U_484,U_483),cartesian_product2(U_482,U_481)) ) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
fof(f_107_3,plain,
( ! [U_492,U_490,U_488,U_486] :
( in(ordered_pair(U_492,U_490),cartesian_product2(U_488,U_486))
| ~ in(U_490,U_486)
| ~ in(U_492,U_488) )
& ! [U_491,U_489,U_487,U_485] :
( ( in(U_489,U_485)
& in(U_491,U_487) )
| ~ in(ordered_pair(U_491,U_489),cartesian_product2(U_487,U_485)) ) ),
inference(miniscope,[status(thm)],[f_107_2]) ).
cnf(f_107_4,plain,
( in(U_491,U_487)
| ~ in(ordered_pair(U_491,U_489),cartesian_product2(U_487,U_485)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_5,plain,
( in(U_489,U_485)
| ~ in(ordered_pair(U_491,U_489),cartesian_product2(U_487,U_485)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_6,plain,
( in(ordered_pair(U_492,U_490),cartesian_product2(U_488,U_486))
| ~ in(U_490,U_486)
| ~ in(U_492,U_488) ),
inference(clausify,[status(thm)],[f_107_3]) ).
fof(f_108_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_108_2,plain,
! [U_495,U_494] :
( element(U_495,powerset(U_494))
| ? [U_493] :
( ~ in(U_493,U_494)
& in(U_493,U_495) ) ),
inference(variable_rename,[status(thm)],[f_108_1]) ).
fof(f_108_3,plain,
! [U_495,U_494] :
( element(U_495,powerset(U_494))
| ( ~ in(sK78(U_495,U_494),U_494)
& in(sK78(U_495,U_494),U_495) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_493,sK78(U_495,U_494))],[f_108_2]) ).
cnf(f_108_4,plain,
( in(sK78(U_495,U_494),U_495)
| element(U_495,powerset(U_494)) ),
inference(clausify,[status(thm)],[f_108_3]) ).
cnf(f_108_5,plain,
( ~ in(sK78(U_495,U_494),U_494)
| element(U_495,powerset(U_494)) ),
inference(clausify,[status(thm)],[f_108_3]) ).
fof(f_109_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_109_2,plain,
? [U_496] :
( function(U_496)
& relation(U_496) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
fof(f_109_3,plain,
( function(sK79)
& relation(sK79) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_496,sK79)],[f_109_2]) ).
cnf(f_109_4,plain,
relation(sK79),
inference(clausify,[status(thm)],[f_109_3]) ).
cnf(f_109_5,plain,
function(sK79),
inference(clausify,[status(thm)],[f_109_3]) ).
fof(f_110_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_110_2,plain,
? [U_497] :
( relation(U_497)
& empty(U_497) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
fof(f_110_3,plain,
( relation(sK80)
& empty(sK80) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_497,sK80)],[f_110_2]) ).
cnf(f_110_4,plain,
empty(sK80),
inference(clausify,[status(thm)],[f_110_3]) ).
cnf(f_110_5,plain,
relation(sK80),
inference(clausify,[status(thm)],[f_110_3]) ).
fof(f_111_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_111_2,plain,
! [U_499] :
( ? [U_498] :
( ~ empty(U_498)
& element(U_498,powerset(U_499)) )
| empty(U_499) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
fof(f_111_3,plain,
! [U_499] :
( ( ~ empty(sK81(U_499))
& element(sK81(U_499),powerset(U_499)) )
| empty(U_499) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_498,sK81(U_499))],[f_111_2]) ).
cnf(f_111_4,plain,
( element(sK81(U_499),powerset(U_499))
| empty(U_499) ),
inference(clausify,[status(thm)],[f_111_3]) ).
cnf(f_111_5,plain,
( ~ empty(sK81(U_499))
| empty(U_499) ),
inference(clausify,[status(thm)],[f_111_3]) ).
fof(f_112_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_112_2,plain,
? [U_500] : empty(U_500),
inference(variable_rename,[status(thm)],[f_112_1]) ).
fof(f_112_3,plain,
empty(sK82),
inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_500,sK82)],[f_112_2]) ).
cnf(f_112_4,plain,
empty(sK82),
inference(clausify,[status(thm)],[f_112_3]) ).
fof(f_113_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_113_2,plain,
? [U_501] :
( relation(U_501)
& ~ empty(U_501) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
fof(f_113_3,plain,
( relation(sK83)
& ~ empty(sK83) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_501,sK83)],[f_113_2]) ).
cnf(f_113_4,plain,
~ empty(sK83),
inference(clausify,[status(thm)],[f_113_3]) ).
cnf(f_113_5,plain,
relation(sK83),
inference(clausify,[status(thm)],[f_113_3]) ).
fof(f_114_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_114_2,plain,
! [U_503] :
? [U_502] :
( empty(U_502)
& element(U_502,powerset(U_503)) ),
inference(variable_rename,[status(thm)],[f_114_1]) ).
fof(f_114_3,plain,
! [U_503] :
( empty(sK84(U_503))
& element(sK84(U_503),powerset(U_503)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_502,sK84(U_503))],[f_114_2]) ).
cnf(f_114_4,plain,
element(sK84(U_503),powerset(U_503)),
inference(clausify,[status(thm)],[f_114_3]) ).
cnf(f_114_5,plain,
empty(sK84(U_503)),
inference(clausify,[status(thm)],[f_114_3]) ).
fof(f_115_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_115_2,plain,
? [U_504] : ~ empty(U_504),
inference(variable_rename,[status(thm)],[f_115_1]) ).
fof(f_115_3,plain,
~ empty(sK85),
inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_504,sK85)],[f_115_2]) ).
cnf(f_115_4,plain,
~ empty(sK85),
inference(clausify,[status(thm)],[f_115_3]) ).
fof(f_116_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_116_2,plain,
? [U_505] :
( relation_empty_yielding(U_505)
& relation(U_505) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
fof(f_116_3,plain,
( relation_empty_yielding(sK86)
& relation(sK86) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_505,sK86)],[f_116_2]) ).
cnf(f_116_4,plain,
relation(sK86),
inference(clausify,[status(thm)],[f_116_3]) ).
cnf(f_116_5,plain,
relation_empty_yielding(sK86),
inference(clausify,[status(thm)],[f_116_3]) ).
fof(f_117_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_117_2,plain,
! [U_507,U_506] :
( union_of_subsets(U_507,U_506) = union(U_506)
| ~ element(U_506,powerset(powerset(U_507))) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
cnf(f_117_3,plain,
( union_of_subsets(U_507,U_506) = union(U_506)
| ~ element(U_506,powerset(powerset(U_507))) ),
inference(clausify,[status(thm)],[f_117_2]) ).
fof(f_118_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_118_2,plain,
! [U_509,U_508] :
( meet_of_subsets(U_509,U_508) = set_meet(U_508)
| ~ element(U_508,powerset(powerset(U_509))) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
cnf(f_118_3,plain,
( meet_of_subsets(U_509,U_508) = set_meet(U_508)
| ~ element(U_508,powerset(powerset(U_509))) ),
inference(clausify,[status(thm)],[f_118_2]) ).
fof(f_119_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_119_2,plain,
! [U_512,U_511,U_510] :
( subset_difference(U_512,U_511,U_510) = set_difference(U_511,U_510)
| ~ element(U_510,powerset(U_512))
| ~ element(U_511,powerset(U_512)) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
cnf(f_119_3,plain,
( subset_difference(U_512,U_511,U_510) = set_difference(U_511,U_510)
| ~ element(U_510,powerset(U_512))
| ~ element(U_511,powerset(U_512)) ),
inference(clausify,[status(thm)],[f_119_2]) ).
fof(f_120_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_120_2,plain,
! [U_514,U_513] : subset(U_514,U_514),
inference(variable_rename,[status(thm)],[f_120_1]) ).
fof(f_120_3,plain,
! [U_514] : subset(U_514,U_514),
inference(miniscope,[status(thm)],[f_120_2]) ).
cnf(f_120_4,plain,
subset(U_514,U_514),
inference(clausify,[status(thm)],[f_120_3]) ).
fof(f_121_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_121_2,plain,
! [U_516,U_515] :
( disjoint(U_515,U_516)
| ~ disjoint(U_516,U_515) ),
inference(variable_rename,[status(thm)],[f_121_1]) ).
cnf(f_121_3,plain,
( disjoint(U_515,U_516)
| ~ disjoint(U_516,U_515) ),
inference(clausify,[status(thm)],[f_121_2]) ).
fof(f_122_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_122_2,plain,
! [U_520,U_519,U_518,U_517] :
( ( in(ordered_pair(U_520,U_519),cartesian_product2(U_518,U_517))
| ~ in(U_519,U_517)
| ~ in(U_520,U_518) )
& ( ( in(U_519,U_517)
& in(U_520,U_518) )
| ~ in(ordered_pair(U_520,U_519),cartesian_product2(U_518,U_517)) ) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
fof(f_122_3,plain,
( ! [U_528,U_526,U_524,U_522] :
( in(ordered_pair(U_528,U_526),cartesian_product2(U_524,U_522))
| ~ in(U_526,U_522)
| ~ in(U_528,U_524) )
& ! [U_527,U_525,U_523,U_521] :
( ( in(U_525,U_521)
& in(U_527,U_523) )
| ~ in(ordered_pair(U_527,U_525),cartesian_product2(U_523,U_521)) ) ),
inference(miniscope,[status(thm)],[f_122_2]) ).
cnf(f_122_4,plain,
( in(U_527,U_523)
| ~ in(ordered_pair(U_527,U_525),cartesian_product2(U_523,U_521)) ),
inference(clausify,[status(thm)],[f_122_3]) ).
cnf(f_122_5,plain,
( in(U_525,U_521)
| ~ in(ordered_pair(U_527,U_525),cartesian_product2(U_523,U_521)) ),
inference(clausify,[status(thm)],[f_122_3]) ).
cnf(f_122_6,plain,
( in(ordered_pair(U_528,U_526),cartesian_product2(U_524,U_522))
| ~ in(U_526,U_522)
| ~ in(U_528,U_524) ),
inference(clausify,[status(thm)],[f_122_3]) ).
fof(f_123_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_123_2,plain,
! [U_532,U_531,U_530,U_529] :
( U_532 = U_529
| U_532 = U_530
| unordered_pair(U_532,U_531) != unordered_pair(U_530,U_529) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
fof(f_123_3,plain,
! [U_532,U_531,U_530] :
( ! [U_529] :
( U_532 = U_529
| unordered_pair(U_532,U_531) != unordered_pair(U_530,U_529) )
| U_532 = U_530 ),
inference(miniscope,[status(thm)],[f_123_2]) ).
cnf(f_123_4,plain,
( U_532 = U_529
| unordered_pair(U_532,U_531) != unordered_pair(U_530,U_529)
| U_532 = U_530 ),
inference(clausify,[status(thm)],[f_123_3]) ).
fof(f_124_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_124_2,plain,
! [U_535,U_534,U_533] :
( ( ( in(U_535,relation_rng(relation_rng_restriction(U_534,U_533)))
| ~ in(U_535,relation_rng(U_533))
| ~ in(U_535,U_534) )
& ( ( in(U_535,relation_rng(U_533))
& in(U_535,U_534) )
| ~ in(U_535,relation_rng(relation_rng_restriction(U_534,U_533))) ) )
| ~ relation(U_533) ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
cnf(f_124_3,plain,
( in(U_535,U_534)
| ~ in(U_535,relation_rng(relation_rng_restriction(U_534,U_533)))
| ~ relation(U_533) ),
inference(clausify,[status(thm)],[f_124_2]) ).
cnf(f_124_4,plain,
( in(U_535,relation_rng(U_533))
| ~ in(U_535,relation_rng(relation_rng_restriction(U_534,U_533)))
| ~ relation(U_533) ),
inference(clausify,[status(thm)],[f_124_2]) ).
cnf(f_124_5,plain,
( in(U_535,relation_rng(relation_rng_restriction(U_534,U_533)))
| ~ in(U_535,relation_rng(U_533))
| ~ in(U_535,U_534)
| ~ relation(U_533) ),
inference(clausify,[status(thm)],[f_124_2]) ).
fof(f_125_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_125_2,plain,
! [U_537,U_536] :
( subset(relation_rng(relation_rng_restriction(U_537,U_536)),U_537)
| ~ relation(U_536) ),
inference(variable_rename,[status(thm)],[f_125_1]) ).
cnf(f_125_3,plain,
( subset(relation_rng(relation_rng_restriction(U_537,U_536)),U_537)
| ~ relation(U_536) ),
inference(clausify,[status(thm)],[f_125_2]) ).
fof(f_126_1,plain,
! [A,B] :
( subset(relation_rng_restriction(A,B),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t117_relat_1]) ).
fof(f_126_2,plain,
! [U_539,U_538] :
( subset(relation_rng_restriction(U_539,U_538),U_538)
| ~ relation(U_538) ),
inference(variable_rename,[status(thm)],[f_126_1]) ).
cnf(f_126_3,plain,
( subset(relation_rng_restriction(U_539,U_538),U_538)
| ~ relation(U_538) ),
inference(clausify,[status(thm)],[f_126_2]) ).
fof(f_127_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_127_2,plain,
! [U_541,U_540] :
( subset(relation_rng(relation_rng_restriction(U_541,U_540)),relation_rng(U_540))
| ~ relation(U_540) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
cnf(f_127_3,plain,
( subset(relation_rng(relation_rng_restriction(U_541,U_540)),relation_rng(U_540))
| ~ relation(U_540) ),
inference(clausify,[status(thm)],[f_127_2]) ).
fof(f_128_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_128_2,plain,
! [U_544,U_543,U_542] :
( ( subset(cartesian_product2(U_542,U_544),cartesian_product2(U_542,U_543))
& subset(cartesian_product2(U_544,U_542),cartesian_product2(U_543,U_542)) )
| ~ subset(U_544,U_543) ),
inference(variable_rename,[status(thm)],[f_128_1]) ).
fof(f_128_3,plain,
! [U_544,U_543] :
( ( ! [U_546] : subset(cartesian_product2(U_546,U_544),cartesian_product2(U_546,U_543))
& ! [U_545] : subset(cartesian_product2(U_544,U_545),cartesian_product2(U_543,U_545)) )
| ~ subset(U_544,U_543) ),
inference(miniscope,[status(thm)],[f_128_2]) ).
cnf(f_128_4,plain,
( subset(cartesian_product2(U_544,U_545),cartesian_product2(U_543,U_545))
| ~ subset(U_544,U_543) ),
inference(clausify,[status(thm)],[f_128_3]) ).
cnf(f_128_5,plain,
( subset(cartesian_product2(U_546,U_544),cartesian_product2(U_546,U_543))
| ~ subset(U_544,U_543) ),
inference(clausify,[status(thm)],[f_128_3]) ).
fof(f_129_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_129_2,plain,
! [U_548,U_547] :
( relation_rng(relation_rng_restriction(U_548,U_547)) = set_intersection2(relation_rng(U_547),U_548)
| ~ relation(U_547) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
cnf(f_129_3,plain,
( relation_rng(relation_rng_restriction(U_548,U_547)) = set_intersection2(relation_rng(U_547),U_548)
| ~ relation(U_547) ),
inference(clausify,[status(thm)],[f_129_2]) ).
fof(f_130_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_130_2,plain,
! [U_552,U_551,U_550,U_549] :
( subset(cartesian_product2(U_552,U_550),cartesian_product2(U_551,U_549))
| ~ subset(U_550,U_549)
| ~ subset(U_552,U_551) ),
inference(variable_rename,[status(thm)],[f_130_1]) ).
cnf(f_130_3,plain,
( subset(cartesian_product2(U_552,U_550),cartesian_product2(U_551,U_549))
| ~ subset(U_550,U_549)
| ~ subset(U_552,U_551) ),
inference(clausify,[status(thm)],[f_130_2]) ).
fof(f_131_1,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t12_xboole_1]) ).
fof(f_131_2,plain,
! [U_554,U_553] :
( set_union2(U_554,U_553) = U_553
| ~ subset(U_554,U_553) ),
inference(variable_rename,[status(thm)],[f_131_1]) ).
cnf(f_131_3,plain,
( set_union2(U_554,U_553) = U_553
| ~ subset(U_554,U_553) ),
inference(clausify,[status(thm)],[f_131_2]) ).
fof(f_132_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_132_2,plain,
! [U_560] :
? [U_559] :
( ! [U_558] :
( in(U_558,U_559)
| are_equipotent(U_558,U_559)
| ~ subset(U_558,U_559) )
& ! [U_557] :
( in(powerset(U_557),U_559)
| ~ in(U_557,U_559) )
& ! [U_556,U_555] :
( in(U_555,U_559)
| ~ subset(U_555,U_556)
| ~ in(U_556,U_559) )
& in(U_560,U_559) ),
inference(variable_rename,[status(thm)],[f_132_1]) ).
fof(f_132_3,plain,
! [U_560] :
( ! [U_558] :
( in(U_558,sK87(U_560))
| are_equipotent(U_558,sK87(U_560))
| ~ subset(U_558,sK87(U_560)) )
& ! [U_557] :
( in(powerset(U_557),sK87(U_560))
| ~ in(U_557,sK87(U_560)) )
& ! [U_556,U_555] :
( in(U_555,sK87(U_560))
| ~ subset(U_555,U_556)
| ~ in(U_556,sK87(U_560)) )
& in(U_560,sK87(U_560)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_559,sK87(U_560))],[f_132_2]) ).
cnf(f_132_4,plain,
in(U_560,sK87(U_560)),
inference(clausify,[status(thm)],[f_132_3]) ).
cnf(f_132_5,plain,
( in(U_555,sK87(U_560))
| ~ subset(U_555,U_556)
| ~ in(U_556,sK87(U_560)) ),
inference(clausify,[status(thm)],[f_132_3]) ).
cnf(f_132_6,plain,
( in(powerset(U_557),sK87(U_560))
| ~ in(U_557,sK87(U_560)) ),
inference(clausify,[status(thm)],[f_132_3]) ).
cnf(f_132_7,plain,
( in(U_558,sK87(U_560))
| are_equipotent(U_558,sK87(U_560))
| ~ subset(U_558,sK87(U_560)) ),
inference(clausify,[status(thm)],[f_132_3]) ).
fof(f_133_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_133_2,plain,
! [U_563,U_562,U_561] :
( relation_dom_restriction(relation_rng_restriction(U_563,U_561),U_562) = relation_rng_restriction(U_563,relation_dom_restriction(U_561,U_562))
| ~ relation(U_561) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
cnf(f_133_3,plain,
( relation_dom_restriction(relation_rng_restriction(U_563,U_561),U_562) = relation_rng_restriction(U_563,relation_dom_restriction(U_561,U_562))
| ~ relation(U_561) ),
inference(clausify,[status(thm)],[f_133_2]) ).
fof(f_134_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_134_2,plain,
! [U_568,U_567,U_566] :
( ( ( in(U_568,relation_image(U_566,U_567))
| ! [U_565] :
( ~ in(U_565,U_567)
| ~ in(ordered_pair(U_565,U_568),U_566)
| ~ in(U_565,relation_dom(U_566)) ) )
& ( ? [U_564] :
( in(U_564,U_567)
& in(ordered_pair(U_564,U_568),U_566)
& in(U_564,relation_dom(U_566)) )
| ~ in(U_568,relation_image(U_566,U_567)) ) )
| ~ relation(U_566) ),
inference(variable_rename,[status(thm)],[f_134_1]) ).
fof(f_134_3,plain,
! [U_568,U_567,U_566] :
( ( ( in(U_568,relation_image(U_566,U_567))
| ! [U_565] :
( ~ in(U_565,U_567)
| ~ in(ordered_pair(U_565,U_568),U_566)
| ~ in(U_565,relation_dom(U_566)) ) )
& ( ( in(sK88(U_568,U_567,U_566),U_567)
& in(ordered_pair(sK88(U_568,U_567,U_566),U_568),U_566)
& in(sK88(U_568,U_567,U_566),relation_dom(U_566)) )
| ~ in(U_568,relation_image(U_566,U_567)) ) )
| ~ relation(U_566) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_564,sK88(U_568,U_567,U_566))],[f_134_2]) ).
cnf(f_134_4,plain,
( in(sK88(U_568,U_567,U_566),relation_dom(U_566))
| ~ in(U_568,relation_image(U_566,U_567))
| ~ relation(U_566) ),
inference(clausify,[status(thm)],[f_134_3]) ).
cnf(f_134_5,plain,
( in(ordered_pair(sK88(U_568,U_567,U_566),U_568),U_566)
| ~ in(U_568,relation_image(U_566,U_567))
| ~ relation(U_566) ),
inference(clausify,[status(thm)],[f_134_3]) ).
cnf(f_134_6,plain,
( in(sK88(U_568,U_567,U_566),U_567)
| ~ in(U_568,relation_image(U_566,U_567))
| ~ relation(U_566) ),
inference(clausify,[status(thm)],[f_134_3]) ).
cnf(f_134_7,plain,
( in(U_568,relation_image(U_566,U_567))
| ~ in(U_565,U_567)
| ~ in(ordered_pair(U_565,U_568),U_566)
| ~ in(U_565,relation_dom(U_566))
| ~ relation(U_566) ),
inference(clausify,[status(thm)],[f_134_3]) ).
fof(f_135_1,plain,
! [A,B] :
( subset(relation_image(B,A),relation_rng(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t144_relat_1]) ).
fof(f_135_2,plain,
! [U_570,U_569] :
( subset(relation_image(U_569,U_570),relation_rng(U_569))
| ~ relation(U_569) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
cnf(f_135_3,plain,
( subset(relation_image(U_569,U_570),relation_rng(U_569))
| ~ relation(U_569) ),
inference(clausify,[status(thm)],[f_135_2]) ).
fof(f_136_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_136_2,plain,
! [U_572,U_571] :
( relation_image(U_571,U_572) = relation_image(U_571,set_intersection2(relation_dom(U_571),U_572))
| ~ relation(U_571) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
cnf(f_136_3,plain,
( relation_image(U_571,U_572) = relation_image(U_571,set_intersection2(relation_dom(U_571),U_572))
| ~ relation(U_571) ),
inference(clausify,[status(thm)],[f_136_2]) ).
fof(f_137_1,plain,
! [A] :
( relation_image(A,relation_dom(A)) = relation_rng(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t146_relat_1]) ).
fof(f_137_2,plain,
! [U_573] :
( relation_image(U_573,relation_dom(U_573)) = relation_rng(U_573)
| ~ relation(U_573) ),
inference(variable_rename,[status(thm)],[f_137_1]) ).
cnf(f_137_3,plain,
( relation_image(U_573,relation_dom(U_573)) = relation_rng(U_573)
| ~ relation(U_573) ),
inference(clausify,[status(thm)],[f_137_2]) ).
fof(f_138_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_138_2,plain,
! [U_575] :
( ! [U_574] :
( relation_rng(relation_composition(U_575,U_574)) = relation_image(U_574,relation_rng(U_575))
| ~ relation(U_574) )
| ~ relation(U_575) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
cnf(f_138_3,plain,
( relation_rng(relation_composition(U_575,U_574)) = relation_image(U_574,relation_rng(U_575))
| ~ relation(U_574)
| ~ relation(U_575) ),
inference(clausify,[status(thm)],[f_138_2]) ).
fof(f_139_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_139_2,plain,
! [U_580,U_579,U_578] :
( ( ( in(U_580,relation_inverse_image(U_578,U_579))
| ! [U_577] :
( ~ in(U_577,U_579)
| ~ in(ordered_pair(U_580,U_577),U_578)
| ~ in(U_577,relation_rng(U_578)) ) )
& ( ? [U_576] :
( in(U_576,U_579)
& in(ordered_pair(U_580,U_576),U_578)
& in(U_576,relation_rng(U_578)) )
| ~ in(U_580,relation_inverse_image(U_578,U_579)) ) )
| ~ relation(U_578) ),
inference(variable_rename,[status(thm)],[f_139_1]) ).
fof(f_139_3,plain,
! [U_580,U_579,U_578] :
( ( ( in(U_580,relation_inverse_image(U_578,U_579))
| ! [U_577] :
( ~ in(U_577,U_579)
| ~ in(ordered_pair(U_580,U_577),U_578)
| ~ in(U_577,relation_rng(U_578)) ) )
& ( ( in(sK89(U_580,U_579,U_578),U_579)
& in(ordered_pair(U_580,sK89(U_580,U_579,U_578)),U_578)
& in(sK89(U_580,U_579,U_578),relation_rng(U_578)) )
| ~ in(U_580,relation_inverse_image(U_578,U_579)) ) )
| ~ relation(U_578) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_576,sK89(U_580,U_579,U_578))],[f_139_2]) ).
cnf(f_139_4,plain,
( in(sK89(U_580,U_579,U_578),relation_rng(U_578))
| ~ in(U_580,relation_inverse_image(U_578,U_579))
| ~ relation(U_578) ),
inference(clausify,[status(thm)],[f_139_3]) ).
cnf(f_139_5,plain,
( in(ordered_pair(U_580,sK89(U_580,U_579,U_578)),U_578)
| ~ in(U_580,relation_inverse_image(U_578,U_579))
| ~ relation(U_578) ),
inference(clausify,[status(thm)],[f_139_3]) ).
cnf(f_139_6,plain,
( in(sK89(U_580,U_579,U_578),U_579)
| ~ in(U_580,relation_inverse_image(U_578,U_579))
| ~ relation(U_578) ),
inference(clausify,[status(thm)],[f_139_3]) ).
cnf(f_139_7,plain,
( in(U_580,relation_inverse_image(U_578,U_579))
| ~ in(U_577,U_579)
| ~ in(ordered_pair(U_580,U_577),U_578)
| ~ in(U_577,relation_rng(U_578))
| ~ relation(U_578) ),
inference(clausify,[status(thm)],[f_139_3]) ).
fof(f_140_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_140_2,plain,
! [U_582,U_581] :
( subset(relation_inverse_image(U_581,U_582),relation_dom(U_581))
| ~ relation(U_581) ),
inference(variable_rename,[status(thm)],[f_140_1]) ).
cnf(f_140_3,plain,
( subset(relation_inverse_image(U_581,U_582),relation_dom(U_581))
| ~ relation(U_581) ),
inference(clausify,[status(thm)],[f_140_2]) ).
fof(f_141_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_141_2,plain,
! [U_584,U_583] :
( relation_inverse_image(U_583,U_584) != empty_set
| ~ subset(U_584,relation_rng(U_583))
| U_584 = empty_set
| ~ relation(U_583) ),
inference(variable_rename,[status(thm)],[f_141_1]) ).
cnf(f_141_3,plain,
( relation_inverse_image(U_583,U_584) != empty_set
| ~ subset(U_584,relation_rng(U_583))
| U_584 = empty_set
| ~ relation(U_583) ),
inference(clausify,[status(thm)],[f_141_2]) ).
fof(f_142_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_142_2,plain,
! [U_587,U_586,U_585] :
( subset(relation_inverse_image(U_585,U_587),relation_inverse_image(U_585,U_586))
| ~ subset(U_587,U_586)
| ~ relation(U_585) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
cnf(f_142_3,plain,
( subset(relation_inverse_image(U_585,U_587),relation_inverse_image(U_585,U_586))
| ~ subset(U_587,U_586)
| ~ relation(U_585) ),
inference(clausify,[status(thm)],[f_142_2]) ).
fof(f_143_1,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(fof_nnf,[status(thm)],[t17_xboole_1]) ).
fof(f_143_2,plain,
! [U_589,U_588] : subset(set_intersection2(U_589,U_588),U_589),
inference(variable_rename,[status(thm)],[f_143_1]) ).
cnf(f_143_3,plain,
subset(set_intersection2(U_589,U_588),U_589),
inference(clausify,[status(thm)],[f_143_2]) ).
fof(f_144_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_144_2,plain,
! [U_592,U_591,U_590] :
( subset(U_592,set_intersection2(U_591,U_590))
| ~ subset(U_592,U_590)
| ~ subset(U_592,U_591) ),
inference(variable_rename,[status(thm)],[f_144_1]) ).
cnf(f_144_3,plain,
( subset(U_592,set_intersection2(U_591,U_590))
| ~ subset(U_592,U_590)
| ~ subset(U_592,U_591) ),
inference(clausify,[status(thm)],[f_144_2]) ).
fof(f_145_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_145_2,plain,
! [U_593] : set_union2(U_593,empty_set) = U_593,
inference(variable_rename,[status(thm)],[f_145_1]) ).
cnf(f_145_3,plain,
set_union2(U_593,empty_set) = U_593,
inference(clausify,[status(thm)],[f_145_2]) ).
fof(f_146_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_146_2,plain,
! [U_595,U_594] :
( element(U_595,U_594)
| ~ in(U_595,U_594) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
cnf(f_146_3,plain,
( element(U_595,U_594)
| ~ in(U_595,U_594) ),
inference(clausify,[status(thm)],[f_146_2]) ).
fof(f_147_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_147_2,plain,
! [U_598,U_597,U_596] :
( subset(U_598,U_596)
| ~ subset(U_597,U_596)
| ~ subset(U_598,U_597) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
cnf(f_147_3,plain,
( subset(U_598,U_596)
| ~ subset(U_597,U_596)
| ~ subset(U_598,U_597) ),
inference(clausify,[status(thm)],[f_147_2]) ).
fof(f_148_1,plain,
powerset(empty_set) = singleton(empty_set),
inference(fof_nnf,[status(thm)],[t1_zfmisc_1]) ).
cnf(f_148_2,plain,
powerset(empty_set) = singleton(empty_set),
inference(clausify,[status(thm)],[f_148_1]) ).
fof(f_149_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_149_2,plain,
! [U_601,U_600,U_599] :
( ( in(U_600,relation_rng(U_599))
& in(U_601,relation_dom(U_599)) )
| ~ in(ordered_pair(U_601,U_600),U_599)
| ~ relation(U_599) ),
inference(variable_rename,[status(thm)],[f_149_1]) ).
cnf(f_149_3,plain,
( in(U_601,relation_dom(U_599))
| ~ in(ordered_pair(U_601,U_600),U_599)
| ~ relation(U_599) ),
inference(clausify,[status(thm)],[f_149_2]) ).
cnf(f_149_4,plain,
( in(U_600,relation_rng(U_599))
| ~ in(ordered_pair(U_601,U_600),U_599)
| ~ relation(U_599) ),
inference(clausify,[status(thm)],[f_149_2]) ).
fof(f_150_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_150_2,plain,
! [U_604,U_603] :
( ! [U_602] :
( ( ( in(U_604,relation_dom(relation_composition(U_602,U_603)))
| ~ in(apply(U_602,U_604),relation_dom(U_603))
| ~ in(U_604,relation_dom(U_602)) )
& ( ( in(apply(U_602,U_604),relation_dom(U_603))
& in(U_604,relation_dom(U_602)) )
| ~ in(U_604,relation_dom(relation_composition(U_602,U_603))) ) )
| ~ function(U_602)
| ~ relation(U_602) )
| ~ function(U_603)
| ~ relation(U_603) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
cnf(f_150_3,plain,
( in(U_604,relation_dom(U_602))
| ~ in(U_604,relation_dom(relation_composition(U_602,U_603)))
| ~ function(U_602)
| ~ relation(U_602)
| ~ function(U_603)
| ~ relation(U_603) ),
inference(clausify,[status(thm)],[f_150_2]) ).
cnf(f_150_4,plain,
( in(apply(U_602,U_604),relation_dom(U_603))
| ~ in(U_604,relation_dom(relation_composition(U_602,U_603)))
| ~ function(U_602)
| ~ relation(U_602)
| ~ function(U_603)
| ~ relation(U_603) ),
inference(clausify,[status(thm)],[f_150_2]) ).
cnf(f_150_5,plain,
( in(U_604,relation_dom(relation_composition(U_602,U_603)))
| ~ in(apply(U_602,U_604),relation_dom(U_603))
| ~ in(U_604,relation_dom(U_602))
| ~ function(U_602)
| ~ relation(U_602)
| ~ function(U_603)
| ~ relation(U_603) ),
inference(clausify,[status(thm)],[f_150_2]) ).
fof(f_151_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_151_2,plain,
! [U_605] :
( subset(U_605,cartesian_product2(relation_dom(U_605),relation_rng(U_605)))
| ~ relation(U_605) ),
inference(variable_rename,[status(thm)],[f_151_1]) ).
cnf(f_151_3,plain,
( subset(U_605,cartesian_product2(relation_dom(U_605),relation_rng(U_605)))
| ~ relation(U_605) ),
inference(clausify,[status(thm)],[f_151_2]) ).
fof(f_152_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_152_2,plain,
! [U_608,U_607] :
( ! [U_606] :
( apply(relation_composition(U_606,U_607),U_608) = apply(U_607,apply(U_606,U_608))
| ~ in(U_608,relation_dom(relation_composition(U_606,U_607)))
| ~ function(U_606)
| ~ relation(U_606) )
| ~ function(U_607)
| ~ relation(U_607) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
cnf(f_152_3,plain,
( apply(relation_composition(U_606,U_607),U_608) = apply(U_607,apply(U_606,U_608))
| ~ in(U_608,relation_dom(relation_composition(U_606,U_607)))
| ~ function(U_606)
| ~ relation(U_606)
| ~ function(U_607)
| ~ relation(U_607) ),
inference(clausify,[status(thm)],[f_152_2]) ).
fof(f_153_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_153_2,plain,
! [U_611,U_610] :
( ! [U_609] :
( apply(relation_composition(U_610,U_609),U_611) = apply(U_609,apply(U_610,U_611))
| ~ in(U_611,relation_dom(U_610))
| ~ function(U_609)
| ~ relation(U_609) )
| ~ function(U_610)
| ~ relation(U_610) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
cnf(f_153_3,plain,
( apply(relation_composition(U_610,U_609),U_611) = apply(U_609,apply(U_610,U_611))
| ~ in(U_611,relation_dom(U_610))
| ~ function(U_609)
| ~ relation(U_609)
| ~ function(U_610)
| ~ relation(U_610) ),
inference(clausify,[status(thm)],[f_153_2]) ).
fof(f_154_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_154_2,plain,
! [U_613] :
( ! [U_612] :
( ( subset(relation_rng(U_613),relation_rng(U_612))
& subset(relation_dom(U_613),relation_dom(U_612)) )
| ~ subset(U_613,U_612)
| ~ relation(U_612) )
| ~ relation(U_613) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
cnf(f_154_3,plain,
( subset(relation_dom(U_613),relation_dom(U_612))
| ~ subset(U_613,U_612)
| ~ relation(U_612)
| ~ relation(U_613) ),
inference(clausify,[status(thm)],[f_154_2]) ).
cnf(f_154_4,plain,
( subset(relation_rng(U_613),relation_rng(U_612))
| ~ subset(U_613,U_612)
| ~ relation(U_612)
| ~ relation(U_613) ),
inference(clausify,[status(thm)],[f_154_2]) ).
fof(f_155_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_155_2,plain,
! [U_616,U_615,U_614] :
( subset(set_intersection2(U_616,U_614),set_intersection2(U_615,U_614))
| ~ subset(U_616,U_615) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
fof(f_155_3,plain,
! [U_616,U_615] :
( ! [U_614] : subset(set_intersection2(U_616,U_614),set_intersection2(U_615,U_614))
| ~ subset(U_616,U_615) ),
inference(miniscope,[status(thm)],[f_155_2]) ).
cnf(f_155_4,plain,
( subset(set_intersection2(U_616,U_614),set_intersection2(U_615,U_614))
| ~ subset(U_616,U_615) ),
inference(clausify,[status(thm)],[f_155_3]) ).
fof(f_156_1,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t28_xboole_1]) ).
fof(f_156_2,plain,
! [U_618,U_617] :
( set_intersection2(U_618,U_617) = U_618
| ~ subset(U_618,U_617) ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
cnf(f_156_3,plain,
( set_intersection2(U_618,U_617) = U_618
| ~ subset(U_618,U_617) ),
inference(clausify,[status(thm)],[f_156_2]) ).
fof(f_157_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_157_2,plain,
! [U_619] : set_intersection2(U_619,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_157_1]) ).
cnf(f_157_3,plain,
set_intersection2(U_619,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_157_2]) ).
fof(f_158_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_158_2,plain,
! [U_621,U_620] :
( in(U_621,U_620)
| empty(U_620)
| ~ element(U_621,U_620) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
cnf(f_158_3,plain,
( in(U_621,U_620)
| empty(U_620)
| ~ element(U_621,U_620) ),
inference(clausify,[status(thm)],[f_158_2]) ).
fof(f_159_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_159_2,plain,
! [U_624,U_623] :
( U_624 = U_623
| ? [U_622] :
( ( ~ in(U_622,U_624)
& in(U_622,U_623) )
| ( ~ in(U_622,U_623)
& in(U_622,U_624) ) ) ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
fof(f_159_3,plain,
! [U_624,U_623] :
( U_624 = U_623
| ? [U_626] :
( ~ in(U_626,U_624)
& in(U_626,U_623) )
| ? [U_625] :
( ~ in(U_625,U_623)
& in(U_625,U_624) ) ),
inference(miniscope,[status(thm)],[f_159_2]) ).
fof(f_159_4,plain,
! [U_624,U_623] :
( U_624 = U_623
| ? [U_626] :
( ~ in(U_626,U_624)
& in(U_626,U_623) )
| ( ~ in(sK90(U_624,U_623),U_623)
& in(sK90(U_624,U_623),U_624) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_625,sK90(U_624,U_623))],[f_159_3]) ).
fof(f_159_5,plain,
! [U_624,U_623] :
( U_624 = U_623
| ( ~ in(sK91(U_624,U_623),U_624)
& in(sK91(U_624,U_623),U_623) )
| ( ~ in(sK90(U_624,U_623),U_623)
& in(sK90(U_624,U_623),U_624) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_626,sK91(U_624,U_623))],[f_159_4]) ).
cnf(f_159_6,plain,
( in(sK91(U_624,U_623),U_623)
| in(sK90(U_624,U_623),U_624)
| U_624 = U_623 ),
inference(clausify,[status(thm)],[f_159_5]) ).
cnf(f_159_7,plain,
( ~ in(sK91(U_624,U_623),U_624)
| in(sK90(U_624,U_623),U_624)
| U_624 = U_623 ),
inference(clausify,[status(thm)],[f_159_5]) ).
cnf(f_159_8,plain,
( in(sK91(U_624,U_623),U_623)
| ~ in(sK90(U_624,U_623),U_623)
| U_624 = U_623 ),
inference(clausify,[status(thm)],[f_159_5]) ).
cnf(f_159_9,plain,
( ~ in(sK91(U_624,U_623),U_624)
| ~ in(sK90(U_624,U_623),U_623)
| U_624 = U_623 ),
inference(clausify,[status(thm)],[f_159_5]) ).
fof(f_160_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_160_2,plain,
! [U_627] : subset(empty_set,U_627),
inference(variable_rename,[status(thm)],[f_160_1]) ).
cnf(f_160_3,plain,
subset(empty_set,U_627),
inference(clausify,[status(thm)],[f_160_2]) ).
fof(f_161_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_161_2,plain,
! [U_630,U_629,U_628] :
( ( in(U_629,relation_field(U_628))
& in(U_630,relation_field(U_628)) )
| ~ in(ordered_pair(U_630,U_629),U_628)
| ~ relation(U_628) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
cnf(f_161_3,plain,
( in(U_630,relation_field(U_628))
| ~ in(ordered_pair(U_630,U_629),U_628)
| ~ relation(U_628) ),
inference(clausify,[status(thm)],[f_161_2]) ).
cnf(f_161_4,plain,
( in(U_629,relation_field(U_628))
| ~ in(ordered_pair(U_630,U_629),U_628)
| ~ relation(U_628) ),
inference(clausify,[status(thm)],[f_161_2]) ).
fof(f_162_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_162_2,plain,
! [U_633,U_632,U_631] :
( subset(set_difference(U_633,U_631),set_difference(U_632,U_631))
| ~ subset(U_633,U_632) ),
inference(variable_rename,[status(thm)],[f_162_1]) ).
fof(f_162_3,plain,
! [U_633,U_632] :
( ! [U_631] : subset(set_difference(U_633,U_631),set_difference(U_632,U_631))
| ~ subset(U_633,U_632) ),
inference(miniscope,[status(thm)],[f_162_2]) ).
cnf(f_162_4,plain,
( subset(set_difference(U_633,U_631),set_difference(U_632,U_631))
| ~ subset(U_633,U_632) ),
inference(clausify,[status(thm)],[f_162_3]) ).
fof(f_163_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_163_2,plain,
! [U_637,U_636,U_635,U_634] :
( ( U_636 = U_634
& U_637 = U_635 )
| ordered_pair(U_637,U_636) != ordered_pair(U_635,U_634) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
cnf(f_163_3,plain,
( U_637 = U_635
| ordered_pair(U_637,U_636) != ordered_pair(U_635,U_634) ),
inference(clausify,[status(thm)],[f_163_2]) ).
cnf(f_163_4,plain,
( U_636 = U_634
| ordered_pair(U_637,U_636) != ordered_pair(U_635,U_634) ),
inference(clausify,[status(thm)],[f_163_2]) ).
fof(f_164_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_164_2,plain,
! [U_641,U_640] :
( ( ( U_640 = identity_relation(U_641)
| ? [U_639] :
( apply(U_640,U_639) != U_639
& in(U_639,U_641) )
| relation_dom(U_640) != U_641 )
& ( ( ! [U_638] :
( apply(U_640,U_638) = U_638
| ~ in(U_638,U_641) )
& relation_dom(U_640) = U_641 )
| U_640 != identity_relation(U_641) ) )
| ~ function(U_640)
| ~ relation(U_640) ),
inference(variable_rename,[status(thm)],[f_164_1]) ).
fof(f_164_3,plain,
! [U_641,U_640] :
( ( ( U_640 = identity_relation(U_641)
| ( apply(U_640,sK92(U_641,U_640)) != sK92(U_641,U_640)
& in(sK92(U_641,U_640),U_641) )
| relation_dom(U_640) != U_641 )
& ( ( ! [U_638] :
( apply(U_640,U_638) = U_638
| ~ in(U_638,U_641) )
& relation_dom(U_640) = U_641 )
| U_640 != identity_relation(U_641) ) )
| ~ function(U_640)
| ~ relation(U_640) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_639,sK92(U_641,U_640))],[f_164_2]) ).
cnf(f_164_4,plain,
( relation_dom(U_640) = U_641
| U_640 != identity_relation(U_641)
| ~ function(U_640)
| ~ relation(U_640) ),
inference(clausify,[status(thm)],[f_164_3]) ).
cnf(f_164_5,plain,
( apply(U_640,U_638) = U_638
| ~ in(U_638,U_641)
| U_640 != identity_relation(U_641)
| ~ function(U_640)
| ~ relation(U_640) ),
inference(clausify,[status(thm)],[f_164_3]) ).
cnf(f_164_6,plain,
( in(sK92(U_641,U_640),U_641)
| relation_dom(U_640) != U_641
| U_640 = identity_relation(U_641)
| ~ function(U_640)
| ~ relation(U_640) ),
inference(clausify,[status(thm)],[f_164_3]) ).
cnf(f_164_7,plain,
( apply(U_640,sK92(U_641,U_640)) != sK92(U_641,U_640)
| relation_dom(U_640) != U_641
| U_640 = identity_relation(U_641)
| ~ function(U_640)
| ~ relation(U_640) ),
inference(clausify,[status(thm)],[f_164_3]) ).
fof(f_165_1,negated_conjecture,
~ ! [A,B] :
( in(B,A)
=> apply(identity_relation(A),B) = B ),
inference(negate,[status(cth)],[t35_funct_1]) ).
fof(f_165_2,negated_conjecture,
? [A,B] :
( apply(identity_relation(A),B) != B
& in(B,A) ),
inference(fof_nnf,[status(thm)],[f_165_1]) ).
fof(f_165_3,negated_conjecture,
? [U_643,U_642] :
( apply(identity_relation(U_643),U_642) != U_642
& in(U_642,U_643) ),
inference(variable_rename,[status(thm)],[f_165_2]) ).
fof(f_165_4,negated_conjecture,
? [U_642] :
( apply(identity_relation(sK93),U_642) != U_642
& in(U_642,sK93) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_643,sK93)],[f_165_3]) ).
fof(f_165_5,negated_conjecture,
( apply(identity_relation(sK93),sK94) != sK94
& in(sK94,sK93) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_642,sK94)],[f_165_4]) ).
cnf(f_165_6,negated_conjecture,
in(sK94,sK93),
inference(clausify,[status(thm)],[f_165_5]) ).
cnf(f_165_7,negated_conjecture,
apply(identity_relation(sK93),sK94) != sK94,
inference(clausify,[status(thm)],[f_165_5]) ).
fof(f_166_1,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(fof_nnf,[status(thm)],[t36_xboole_1]) ).
fof(f_166_2,plain,
! [U_645,U_644] : subset(set_difference(U_645,U_644),U_645),
inference(variable_rename,[status(thm)],[f_166_1]) ).
cnf(f_166_3,plain,
subset(set_difference(U_645,U_644),U_645),
inference(clausify,[status(thm)],[f_166_2]) ).
fof(f_167_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_167_2,plain,
! [U_646] :
( ( relation_dom(U_646) = relation_rng(relation_inverse(U_646))
& relation_rng(U_646) = relation_dom(relation_inverse(U_646)) )
| ~ relation(U_646) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
cnf(f_167_3,plain,
( relation_rng(U_646) = relation_dom(relation_inverse(U_646))
| ~ relation(U_646) ),
inference(clausify,[status(thm)],[f_167_2]) ).
cnf(f_167_4,plain,
( relation_dom(U_646) = relation_rng(relation_inverse(U_646))
| ~ relation(U_646) ),
inference(clausify,[status(thm)],[f_167_2]) ).
fof(f_168_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_168_2,plain,
! [U_648,U_647] :
( ( set_difference(U_648,U_647) = empty_set
| ~ subset(U_648,U_647) )
& ( subset(U_648,U_647)
| set_difference(U_648,U_647) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_168_1]) ).
fof(f_168_3,plain,
( ! [U_652,U_650] :
( set_difference(U_652,U_650) = empty_set
| ~ subset(U_652,U_650) )
& ! [U_651,U_649] :
( subset(U_651,U_649)
| set_difference(U_651,U_649) != empty_set ) ),
inference(miniscope,[status(thm)],[f_168_2]) ).
cnf(f_168_4,plain,
( subset(U_651,U_649)
| set_difference(U_651,U_649) != empty_set ),
inference(clausify,[status(thm)],[f_168_3]) ).
cnf(f_168_5,plain,
( set_difference(U_652,U_650) = empty_set
| ~ subset(U_652,U_650) ),
inference(clausify,[status(thm)],[f_168_3]) ).
fof(f_169_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_169_2,plain,
! [U_654,U_653] :
( ( subset(singleton(U_654),U_653)
| ~ in(U_654,U_653) )
& ( in(U_654,U_653)
| ~ subset(singleton(U_654),U_653) ) ),
inference(variable_rename,[status(thm)],[f_169_1]) ).
fof(f_169_3,plain,
( ! [U_658,U_656] :
( subset(singleton(U_658),U_656)
| ~ in(U_658,U_656) )
& ! [U_657,U_655] :
( in(U_657,U_655)
| ~ subset(singleton(U_657),U_655) ) ),
inference(miniscope,[status(thm)],[f_169_2]) ).
cnf(f_169_4,plain,
( in(U_657,U_655)
| ~ subset(singleton(U_657),U_655) ),
inference(clausify,[status(thm)],[f_169_3]) ).
cnf(f_169_5,plain,
( subset(singleton(U_658),U_656)
| ~ in(U_658,U_656) ),
inference(clausify,[status(thm)],[f_169_3]) ).
fof(f_170_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_170_2,plain,
! [U_661,U_660,U_659] :
( ( subset(unordered_pair(U_661,U_660),U_659)
| ~ in(U_660,U_659)
| ~ in(U_661,U_659) )
& ( ( in(U_660,U_659)
& in(U_661,U_659) )
| ~ subset(unordered_pair(U_661,U_660),U_659) ) ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
fof(f_170_3,plain,
( ! [U_667,U_665,U_663] :
( subset(unordered_pair(U_667,U_665),U_663)
| ~ in(U_665,U_663)
| ~ in(U_667,U_663) )
& ! [U_666,U_664,U_662] :
( ( in(U_664,U_662)
& in(U_666,U_662) )
| ~ subset(unordered_pair(U_666,U_664),U_662) ) ),
inference(miniscope,[status(thm)],[f_170_2]) ).
cnf(f_170_4,plain,
( in(U_666,U_662)
| ~ subset(unordered_pair(U_666,U_664),U_662) ),
inference(clausify,[status(thm)],[f_170_3]) ).
cnf(f_170_5,plain,
( in(U_664,U_662)
| ~ subset(unordered_pair(U_666,U_664),U_662) ),
inference(clausify,[status(thm)],[f_170_3]) ).
cnf(f_170_6,plain,
( subset(unordered_pair(U_667,U_665),U_663)
| ~ in(U_665,U_663)
| ~ in(U_667,U_663) ),
inference(clausify,[status(thm)],[f_170_3]) ).
fof(f_171_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_171_2,plain,
! [U_669,U_668] : set_union2(U_669,set_difference(U_668,U_669)) = set_union2(U_669,U_668),
inference(variable_rename,[status(thm)],[f_171_1]) ).
cnf(f_171_3,plain,
set_union2(U_669,set_difference(U_668,U_669)) = set_union2(U_669,U_668),
inference(clausify,[status(thm)],[f_171_2]) ).
fof(f_172_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_172_2,plain,
! [U_671,U_670] :
( ( subset(U_671,singleton(U_670))
| ( U_671 != singleton(U_670)
& U_671 != empty_set ) )
& ( U_671 = singleton(U_670)
| U_671 = empty_set
| ~ subset(U_671,singleton(U_670)) ) ),
inference(variable_rename,[status(thm)],[f_172_1]) ).
fof(f_172_3,plain,
( ! [U_675,U_673] :
( subset(U_675,singleton(U_673))
| ( U_675 != singleton(U_673)
& U_675 != empty_set ) )
& ! [U_674,U_672] :
( U_674 = singleton(U_672)
| U_674 = empty_set
| ~ subset(U_674,singleton(U_672)) ) ),
inference(miniscope,[status(thm)],[f_172_2]) ).
cnf(f_172_4,plain,
( U_674 = singleton(U_672)
| U_674 = empty_set
| ~ subset(U_674,singleton(U_672)) ),
inference(clausify,[status(thm)],[f_172_3]) ).
cnf(f_172_5,plain,
( U_675 != empty_set
| subset(U_675,singleton(U_673)) ),
inference(clausify,[status(thm)],[f_172_3]) ).
cnf(f_172_6,plain,
( U_675 != singleton(U_673)
| subset(U_675,singleton(U_673)) ),
inference(clausify,[status(thm)],[f_172_3]) ).
fof(f_173_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_173_2,plain,
! [U_676] : set_difference(U_676,empty_set) = U_676,
inference(variable_rename,[status(thm)],[f_173_1]) ).
cnf(f_173_3,plain,
set_difference(U_676,empty_set) = U_676,
inference(clausify,[status(thm)],[f_173_2]) ).
fof(f_174_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_174_2,plain,
! [U_678,U_677] :
( ( element(U_678,powerset(U_677))
| ~ subset(U_678,U_677) )
& ( subset(U_678,U_677)
| ~ element(U_678,powerset(U_677)) ) ),
inference(variable_rename,[status(thm)],[f_174_1]) ).
fof(f_174_3,plain,
( ! [U_682,U_680] :
( element(U_682,powerset(U_680))
| ~ subset(U_682,U_680) )
& ! [U_681,U_679] :
( subset(U_681,U_679)
| ~ element(U_681,powerset(U_679)) ) ),
inference(miniscope,[status(thm)],[f_174_2]) ).
cnf(f_174_4,plain,
( subset(U_681,U_679)
| ~ element(U_681,powerset(U_679)) ),
inference(clausify,[status(thm)],[f_174_3]) ).
cnf(f_174_5,plain,
( element(U_682,powerset(U_680))
| ~ subset(U_682,U_680) ),
inference(clausify,[status(thm)],[f_174_3]) ).
fof(f_175_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_175_2,plain,
! [U_686,U_685] :
( ( ~ disjoint(U_686,U_685)
| ! [U_684] :
( ~ in(U_684,U_685)
| ~ in(U_684,U_686) ) )
& ( ? [U_683] :
( in(U_683,U_685)
& in(U_683,U_686) )
| disjoint(U_686,U_685) ) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
fof(f_175_3,plain,
( ! [U_690,U_688] :
( ~ disjoint(U_690,U_688)
| ! [U_684] :
( ~ in(U_684,U_688)
| ~ in(U_684,U_690) ) )
& ! [U_689,U_687] :
( ? [U_683] :
( in(U_683,U_687)
& in(U_683,U_689) )
| disjoint(U_689,U_687) ) ),
inference(miniscope,[status(thm)],[f_175_2]) ).
fof(f_175_4,plain,
( ! [U_690,U_688] :
( ~ disjoint(U_690,U_688)
| ! [U_684] :
( ~ in(U_684,U_688)
| ~ in(U_684,U_690) ) )
& ! [U_689,U_687] :
( ( in(sK95(U_689,U_687),U_687)
& in(sK95(U_689,U_687),U_689) )
| disjoint(U_689,U_687) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_683,sK95(U_689,U_687))],[f_175_3]) ).
cnf(f_175_5,plain,
( in(sK95(U_689,U_687),U_689)
| disjoint(U_689,U_687) ),
inference(clausify,[status(thm)],[f_175_4]) ).
cnf(f_175_6,plain,
( in(sK95(U_689,U_687),U_687)
| disjoint(U_689,U_687) ),
inference(clausify,[status(thm)],[f_175_4]) ).
cnf(f_175_7,plain,
( ~ disjoint(U_690,U_688)
| ~ in(U_684,U_688)
| ~ in(U_684,U_690) ),
inference(clausify,[status(thm)],[f_175_4]) ).
fof(f_176_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_176_2,plain,
! [U_691] :
( U_691 = empty_set
| ~ subset(U_691,empty_set) ),
inference(variable_rename,[status(thm)],[f_176_1]) ).
cnf(f_176_3,plain,
( U_691 = empty_set
| ~ subset(U_691,empty_set) ),
inference(clausify,[status(thm)],[f_176_2]) ).
fof(f_177_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_177_2,plain,
! [U_693,U_692] : set_difference(set_union2(U_693,U_692),U_692) = set_difference(U_693,U_692),
inference(variable_rename,[status(thm)],[f_177_1]) ).
cnf(f_177_3,plain,
set_difference(set_union2(U_693,U_692),U_692) = set_difference(U_693,U_692),
inference(clausify,[status(thm)],[f_177_2]) ).
fof(f_178_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_178_2,plain,
! [U_696,U_695] :
( ! [U_694] :
( ( ( disjoint(U_695,U_694)
| ~ subset(U_695,subset_complement(U_696,U_694)) )
& ( subset(U_695,subset_complement(U_696,U_694))
| ~ disjoint(U_695,U_694) ) )
| ~ element(U_694,powerset(U_696)) )
| ~ element(U_695,powerset(U_696)) ),
inference(variable_rename,[status(thm)],[f_178_1]) ).
cnf(f_178_3,plain,
( subset(U_695,subset_complement(U_696,U_694))
| ~ disjoint(U_695,U_694)
| ~ element(U_694,powerset(U_696))
| ~ element(U_695,powerset(U_696)) ),
inference(clausify,[status(thm)],[f_178_2]) ).
cnf(f_178_4,plain,
( disjoint(U_695,U_694)
| ~ subset(U_695,subset_complement(U_696,U_694))
| ~ element(U_694,powerset(U_696))
| ~ element(U_695,powerset(U_696)) ),
inference(clausify,[status(thm)],[f_178_2]) ).
fof(f_179_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_179_2,plain,
! [U_698] :
( ! [U_697] :
( subset(relation_dom(relation_composition(U_698,U_697)),relation_dom(U_698))
| ~ relation(U_697) )
| ~ relation(U_698) ),
inference(variable_rename,[status(thm)],[f_179_1]) ).
cnf(f_179_3,plain,
( subset(relation_dom(relation_composition(U_698,U_697)),relation_dom(U_698))
| ~ relation(U_697)
| ~ relation(U_698) ),
inference(clausify,[status(thm)],[f_179_2]) ).
fof(f_180_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_180_2,plain,
! [U_700] :
( ! [U_699] :
( subset(relation_rng(relation_composition(U_700,U_699)),relation_rng(U_699))
| ~ relation(U_699) )
| ~ relation(U_700) ),
inference(variable_rename,[status(thm)],[f_180_1]) ).
cnf(f_180_3,plain,
( subset(relation_rng(relation_composition(U_700,U_699)),relation_rng(U_699))
| ~ relation(U_699)
| ~ relation(U_700) ),
inference(clausify,[status(thm)],[f_180_2]) ).
fof(f_181_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_181_2,plain,
! [U_702,U_701] :
( U_701 = set_union2(U_702,set_difference(U_701,U_702))
| ~ subset(U_702,U_701) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
cnf(f_181_3,plain,
( U_701 = set_union2(U_702,set_difference(U_701,U_702))
| ~ subset(U_702,U_701) ),
inference(clausify,[status(thm)],[f_181_2]) ).
fof(f_182_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_182_2,plain,
! [U_704] :
( ! [U_703] :
( relation_dom(relation_composition(U_704,U_703)) = relation_dom(U_704)
| ~ subset(relation_rng(U_704),relation_dom(U_703))
| ~ relation(U_703) )
| ~ relation(U_704) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
cnf(f_182_3,plain,
( relation_dom(relation_composition(U_704,U_703)) = relation_dom(U_704)
| ~ subset(relation_rng(U_704),relation_dom(U_703))
| ~ relation(U_703)
| ~ relation(U_704) ),
inference(clausify,[status(thm)],[f_182_2]) ).
fof(f_183_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_183_2,plain,
! [U_706,U_705] :
( complements_of_subsets(U_706,U_705) != empty_set
| U_705 = empty_set
| ~ element(U_705,powerset(powerset(U_706))) ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
cnf(f_183_3,plain,
( complements_of_subsets(U_706,U_705) != empty_set
| U_705 = empty_set
| ~ element(U_705,powerset(powerset(U_706))) ),
inference(clausify,[status(thm)],[f_183_2]) ).
fof(f_184_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t46_zfmisc_1]) ).
fof(f_184_2,plain,
! [U_708,U_707] :
( set_union2(singleton(U_708),U_707) = U_707
| ~ in(U_708,U_707) ),
inference(variable_rename,[status(thm)],[f_184_1]) ).
cnf(f_184_3,plain,
( set_union2(singleton(U_708),U_707) = U_707
| ~ in(U_708,U_707) ),
inference(clausify,[status(thm)],[f_184_2]) ).
fof(f_185_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_185_2,plain,
! [U_710] :
( ! [U_709] :
( relation_rng(relation_composition(U_709,U_710)) = relation_rng(U_710)
| ~ subset(relation_dom(U_710),relation_rng(U_709))
| ~ relation(U_709) )
| ~ relation(U_710) ),
inference(variable_rename,[status(thm)],[f_185_1]) ).
cnf(f_185_3,plain,
( relation_rng(relation_composition(U_709,U_710)) = relation_rng(U_710)
| ~ subset(relation_dom(U_710),relation_rng(U_709))
| ~ relation(U_709)
| ~ relation(U_710) ),
inference(clausify,[status(thm)],[f_185_2]) ).
fof(f_186_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_186_2,plain,
! [U_712,U_711] :
( subset_difference(U_712,cast_to_subset(U_712),union_of_subsets(U_712,U_711)) = meet_of_subsets(U_712,complements_of_subsets(U_712,U_711))
| U_711 = empty_set
| ~ element(U_711,powerset(powerset(U_712))) ),
inference(variable_rename,[status(thm)],[f_186_1]) ).
cnf(f_186_3,plain,
( subset_difference(U_712,cast_to_subset(U_712),union_of_subsets(U_712,U_711)) = meet_of_subsets(U_712,complements_of_subsets(U_712,U_711))
| U_711 = empty_set
| ~ element(U_711,powerset(powerset(U_712))) ),
inference(clausify,[status(thm)],[f_186_2]) ).
fof(f_187_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_187_2,plain,
! [U_714,U_713] :
( union_of_subsets(U_714,complements_of_subsets(U_714,U_713)) = subset_difference(U_714,cast_to_subset(U_714),meet_of_subsets(U_714,U_713))
| U_713 = empty_set
| ~ element(U_713,powerset(powerset(U_714))) ),
inference(variable_rename,[status(thm)],[f_187_1]) ).
cnf(f_187_3,plain,
( union_of_subsets(U_714,complements_of_subsets(U_714,U_713)) = subset_difference(U_714,cast_to_subset(U_714),meet_of_subsets(U_714,U_713))
| U_713 = empty_set
| ~ element(U_713,powerset(powerset(U_714))) ),
inference(clausify,[status(thm)],[f_187_2]) ).
fof(f_188_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_188_2,plain,
! [U_716,U_715] : set_difference(U_716,set_difference(U_716,U_715)) = set_intersection2(U_716,U_715),
inference(variable_rename,[status(thm)],[f_188_1]) ).
cnf(f_188_3,plain,
set_difference(U_716,set_difference(U_716,U_715)) = set_intersection2(U_716,U_715),
inference(clausify,[status(thm)],[f_188_2]) ).
fof(f_189_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_189_2,plain,
! [U_717] : set_difference(empty_set,U_717) = empty_set,
inference(variable_rename,[status(thm)],[f_189_1]) ).
cnf(f_189_3,plain,
set_difference(empty_set,U_717) = empty_set,
inference(clausify,[status(thm)],[f_189_2]) ).
fof(f_190_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_190_2,plain,
! [U_720,U_719,U_718] :
( element(U_720,U_718)
| ~ element(U_719,powerset(U_718))
| ~ in(U_720,U_719) ),
inference(variable_rename,[status(thm)],[f_190_1]) ).
cnf(f_190_3,plain,
( element(U_720,U_718)
| ~ element(U_719,powerset(U_718))
| ~ in(U_720,U_719) ),
inference(clausify,[status(thm)],[f_190_2]) ).
fof(f_191_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_191_2,plain,
! [U_724,U_723] :
( ( ~ disjoint(U_724,U_723)
| ! [U_722] : ~ in(U_722,set_intersection2(U_724,U_723)) )
& ( ? [U_721] : in(U_721,set_intersection2(U_724,U_723))
| disjoint(U_724,U_723) ) ),
inference(variable_rename,[status(thm)],[f_191_1]) ).
fof(f_191_3,plain,
( ! [U_728,U_726] :
( ~ disjoint(U_728,U_726)
| ! [U_722] : ~ in(U_722,set_intersection2(U_728,U_726)) )
& ! [U_727,U_725] :
( ? [U_721] : in(U_721,set_intersection2(U_727,U_725))
| disjoint(U_727,U_725) ) ),
inference(miniscope,[status(thm)],[f_191_2]) ).
fof(f_191_4,plain,
( ! [U_728,U_726] :
( ~ disjoint(U_728,U_726)
| ! [U_722] : ~ in(U_722,set_intersection2(U_728,U_726)) )
& ! [U_727,U_725] :
( in(sK96(U_727,U_725),set_intersection2(U_727,U_725))
| disjoint(U_727,U_725) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_721,sK96(U_727,U_725))],[f_191_3]) ).
cnf(f_191_5,plain,
( in(sK96(U_727,U_725),set_intersection2(U_727,U_725))
| disjoint(U_727,U_725) ),
inference(clausify,[status(thm)],[f_191_4]) ).
cnf(f_191_6,plain,
( ~ disjoint(U_728,U_726)
| ~ in(U_722,set_intersection2(U_728,U_726)) ),
inference(clausify,[status(thm)],[f_191_4]) ).
fof(f_192_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_192_2,plain,
! [U_731] :
( ! [U_730] :
( ! [U_729] :
( in(U_729,subset_complement(U_731,U_730))
| in(U_729,U_730)
| ~ element(U_729,U_731) )
| ~ element(U_730,powerset(U_731)) )
| U_731 = empty_set ),
inference(variable_rename,[status(thm)],[f_192_1]) ).
cnf(f_192_3,plain,
( in(U_729,subset_complement(U_731,U_730))
| in(U_729,U_730)
| ~ element(U_729,U_731)
| ~ element(U_730,powerset(U_731))
| U_731 = empty_set ),
inference(clausify,[status(thm)],[f_192_2]) ).
fof(f_193_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_193_2,plain,
! [U_734,U_733,U_732] :
( ~ in(U_733,U_732)
| ~ in(U_733,subset_complement(U_734,U_732))
| ~ element(U_732,powerset(U_734)) ),
inference(variable_rename,[status(thm)],[f_193_1]) ).
cnf(f_193_3,plain,
( ~ in(U_733,U_732)
| ~ in(U_733,subset_complement(U_734,U_732))
| ~ element(U_732,powerset(U_734)) ),
inference(clausify,[status(thm)],[f_193_2]) ).
fof(f_194_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_194_2,plain,
! [U_737] :
( U_737 = empty_set
| ? [U_736,U_735] : in(ordered_pair(U_736,U_735),U_737)
| ~ relation(U_737) ),
inference(variable_rename,[status(thm)],[f_194_1]) ).
fof(f_194_3,plain,
! [U_737] :
( U_737 = empty_set
| ? [U_735] : in(ordered_pair(sK97(U_737),U_735),U_737)
| ~ relation(U_737) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_736,sK97(U_737))],[f_194_2]) ).
fof(f_194_4,plain,
! [U_737] :
( U_737 = empty_set
| in(ordered_pair(sK97(U_737),sK98(U_737)),U_737)
| ~ relation(U_737) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_735,sK98(U_737))],[f_194_3]) ).
cnf(f_194_5,plain,
( U_737 = empty_set
| in(ordered_pair(sK97(U_737),sK98(U_737)),U_737)
| ~ relation(U_737) ),
inference(clausify,[status(thm)],[f_194_4]) ).
fof(f_195_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_195_2,plain,
! [U_740,U_739,U_738] :
( ~ empty(U_738)
| ~ element(U_739,powerset(U_738))
| ~ in(U_740,U_739) ),
inference(variable_rename,[status(thm)],[f_195_1]) ).
fof(f_195_3,plain,
! [U_740,U_739] :
( ! [U_738] :
( ~ empty(U_738)
| ~ element(U_739,powerset(U_738)) )
| ~ in(U_740,U_739) ),
inference(miniscope,[status(thm)],[f_195_2]) ).
cnf(f_195_4,plain,
( ~ empty(U_738)
| ~ element(U_739,powerset(U_738))
| ~ in(U_740,U_739) ),
inference(clausify,[status(thm)],[f_195_3]) ).
fof(f_196_1,plain,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(fof_nnf,[status(thm)],[t60_relat_1]) ).
cnf(f_196_2,plain,
relation_dom(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_196_1]) ).
cnf(f_196_3,plain,
relation_rng(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_196_1]) ).
fof(f_197_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t60_xboole_1]) ).
fof(f_197_2,plain,
! [U_742,U_741] :
( ~ proper_subset(U_741,U_742)
| ~ subset(U_742,U_741) ),
inference(variable_rename,[status(thm)],[f_197_1]) ).
cnf(f_197_3,plain,
( ~ proper_subset(U_741,U_742)
| ~ subset(U_742,U_741) ),
inference(clausify,[status(thm)],[f_197_2]) ).
fof(f_198_1,plain,
! [A,B,C] :
( disjoint(A,C)
| ~ disjoint(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t63_xboole_1]) ).
fof(f_198_2,plain,
! [U_745,U_744,U_743] :
( disjoint(U_745,U_743)
| ~ disjoint(U_744,U_743)
| ~ subset(U_745,U_744) ),
inference(variable_rename,[status(thm)],[f_198_1]) ).
cnf(f_198_3,plain,
( disjoint(U_745,U_743)
| ~ disjoint(U_744,U_743)
| ~ subset(U_745,U_744) ),
inference(clausify,[status(thm)],[f_198_2]) ).
fof(f_199_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_199_2,plain,
! [U_746] :
( U_746 = empty_set
| ( relation_rng(U_746) != empty_set
& relation_dom(U_746) != empty_set )
| ~ relation(U_746) ),
inference(variable_rename,[status(thm)],[f_199_1]) ).
cnf(f_199_3,plain,
( relation_dom(U_746) != empty_set
| U_746 = empty_set
| ~ relation(U_746) ),
inference(clausify,[status(thm)],[f_199_2]) ).
cnf(f_199_4,plain,
( relation_rng(U_746) != empty_set
| U_746 = empty_set
| ~ relation(U_746) ),
inference(clausify,[status(thm)],[f_199_2]) ).
fof(f_200_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_200_2,plain,
! [U_747] :
( ( ( relation_dom(U_747) = empty_set
| relation_rng(U_747) != empty_set )
& ( relation_rng(U_747) = empty_set
| relation_dom(U_747) != empty_set ) )
| ~ relation(U_747) ),
inference(variable_rename,[status(thm)],[f_200_1]) ).
cnf(f_200_3,plain,
( relation_rng(U_747) = empty_set
| relation_dom(U_747) != empty_set
| ~ relation(U_747) ),
inference(clausify,[status(thm)],[f_200_2]) ).
cnf(f_200_4,plain,
( relation_dom(U_747) = empty_set
| relation_rng(U_747) != empty_set
| ~ relation(U_747) ),
inference(clausify,[status(thm)],[f_200_2]) ).
fof(f_201_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_201_2,plain,
! [U_749,U_748] :
( ( set_difference(U_749,singleton(U_748)) = U_749
| in(U_748,U_749) )
& ( ~ in(U_748,U_749)
| set_difference(U_749,singleton(U_748)) != U_749 ) ),
inference(variable_rename,[status(thm)],[f_201_1]) ).
fof(f_201_3,plain,
( ! [U_753,U_751] :
( set_difference(U_753,singleton(U_751)) = U_753
| in(U_751,U_753) )
& ! [U_752,U_750] :
( ~ in(U_750,U_752)
| set_difference(U_752,singleton(U_750)) != U_752 ) ),
inference(miniscope,[status(thm)],[f_201_2]) ).
cnf(f_201_4,plain,
( ~ in(U_750,U_752)
| set_difference(U_752,singleton(U_750)) != U_752 ),
inference(clausify,[status(thm)],[f_201_3]) ).
cnf(f_201_5,plain,
( set_difference(U_753,singleton(U_751)) = U_753
| in(U_751,U_753) ),
inference(clausify,[status(thm)],[f_201_3]) ).
fof(f_202_1,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(fof_nnf,[status(thm)],[t69_enumset1]) ).
fof(f_202_2,plain,
! [U_754] : unordered_pair(U_754,U_754) = singleton(U_754),
inference(variable_rename,[status(thm)],[f_202_1]) ).
cnf(f_202_3,plain,
unordered_pair(U_754,U_754) = singleton(U_754),
inference(clausify,[status(thm)],[f_202_2]) ).
fof(f_203_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_203_2,plain,
! [U_755] :
( U_755 = empty_set
| ~ empty(U_755) ),
inference(variable_rename,[status(thm)],[f_203_1]) ).
cnf(f_203_3,plain,
( U_755 = empty_set
| ~ empty(U_755) ),
inference(clausify,[status(thm)],[f_203_2]) ).
fof(f_204_1,plain,
! [A,B] :
( A = B
| ~ subset(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t6_zfmisc_1]) ).
fof(f_204_2,plain,
! [U_757,U_756] :
( U_757 = U_756
| ~ subset(singleton(U_757),singleton(U_756)) ),
inference(variable_rename,[status(thm)],[f_204_1]) ).
cnf(f_204_3,plain,
( U_757 = U_756
| ~ subset(singleton(U_757),singleton(U_756)) ),
inference(clausify,[status(thm)],[f_204_2]) ).
fof(f_205_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_205_2,plain,
! [U_758] :
( relation_rng(identity_relation(U_758)) = U_758
& relation_dom(identity_relation(U_758)) = U_758 ),
inference(variable_rename,[status(thm)],[f_205_1]) ).
fof(f_205_3,plain,
( ! [U_760] : relation_rng(identity_relation(U_760)) = U_760
& ! [U_759] : relation_dom(identity_relation(U_759)) = U_759 ),
inference(miniscope,[status(thm)],[f_205_2]) ).
cnf(f_205_4,plain,
relation_dom(identity_relation(U_759)) = U_759,
inference(clausify,[status(thm)],[f_205_3]) ).
cnf(f_205_5,plain,
relation_rng(identity_relation(U_760)) = U_760,
inference(clausify,[status(thm)],[f_205_3]) ).
fof(f_206_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_206_2,plain,
! [U_764,U_763,U_762,U_761] :
( ( ( in(ordered_pair(U_764,U_763),relation_composition(identity_relation(U_762),U_761))
| ~ in(ordered_pair(U_764,U_763),U_761)
| ~ in(U_764,U_762) )
& ( ( in(ordered_pair(U_764,U_763),U_761)
& in(U_764,U_762) )
| ~ in(ordered_pair(U_764,U_763),relation_composition(identity_relation(U_762),U_761)) ) )
| ~ relation(U_761) ),
inference(variable_rename,[status(thm)],[f_206_1]) ).
cnf(f_206_3,plain,
( in(U_764,U_762)
| ~ in(ordered_pair(U_764,U_763),relation_composition(identity_relation(U_762),U_761))
| ~ relation(U_761) ),
inference(clausify,[status(thm)],[f_206_2]) ).
cnf(f_206_4,plain,
( in(ordered_pair(U_764,U_763),U_761)
| ~ in(ordered_pair(U_764,U_763),relation_composition(identity_relation(U_762),U_761))
| ~ relation(U_761) ),
inference(clausify,[status(thm)],[f_206_2]) ).
cnf(f_206_5,plain,
( in(ordered_pair(U_764,U_763),relation_composition(identity_relation(U_762),U_761))
| ~ in(ordered_pair(U_764,U_763),U_761)
| ~ in(U_764,U_762)
| ~ relation(U_761) ),
inference(clausify,[status(thm)],[f_206_2]) ).
fof(f_207_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_207_2,plain,
! [U_766,U_765] :
( ~ empty(U_765)
| ~ in(U_766,U_765) ),
inference(variable_rename,[status(thm)],[f_207_1]) ).
cnf(f_207_3,plain,
( ~ empty(U_765)
| ~ in(U_766,U_765) ),
inference(clausify,[status(thm)],[f_207_2]) ).
fof(f_208_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1]) ).
fof(f_208_2,plain,
! [U_768,U_767] : subset(U_768,set_union2(U_768,U_767)),
inference(variable_rename,[status(thm)],[f_208_1]) ).
cnf(f_208_3,plain,
subset(U_768,set_union2(U_768,U_767)),
inference(clausify,[status(thm)],[f_208_2]) ).
fof(f_209_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_209_2,plain,
! [U_770,U_769] :
( ( disjoint(U_770,U_769)
| set_difference(U_770,U_769) != U_770 )
& ( set_difference(U_770,U_769) = U_770
| ~ disjoint(U_770,U_769) ) ),
inference(variable_rename,[status(thm)],[f_209_1]) ).
fof(f_209_3,plain,
( ! [U_774,U_772] :
( disjoint(U_774,U_772)
| set_difference(U_774,U_772) != U_774 )
& ! [U_773,U_771] :
( set_difference(U_773,U_771) = U_773
| ~ disjoint(U_773,U_771) ) ),
inference(miniscope,[status(thm)],[f_209_2]) ).
cnf(f_209_4,plain,
( set_difference(U_773,U_771) = U_773
| ~ disjoint(U_773,U_771) ),
inference(clausify,[status(thm)],[f_209_3]) ).
cnf(f_209_5,plain,
( disjoint(U_774,U_772)
| set_difference(U_774,U_772) != U_774 ),
inference(clausify,[status(thm)],[f_209_3]) ).
fof(f_210_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_210_2,plain,
! [U_777,U_776,U_775] :
( ( ( in(U_777,relation_dom(relation_dom_restriction(U_775,U_776)))
| ~ in(U_777,relation_dom(U_775))
| ~ in(U_777,U_776) )
& ( ( in(U_777,relation_dom(U_775))
& in(U_777,U_776) )
| ~ in(U_777,relation_dom(relation_dom_restriction(U_775,U_776))) ) )
| ~ relation(U_775) ),
inference(variable_rename,[status(thm)],[f_210_1]) ).
cnf(f_210_3,plain,
( in(U_777,U_776)
| ~ in(U_777,relation_dom(relation_dom_restriction(U_775,U_776)))
| ~ relation(U_775) ),
inference(clausify,[status(thm)],[f_210_2]) ).
cnf(f_210_4,plain,
( in(U_777,relation_dom(U_775))
| ~ in(U_777,relation_dom(relation_dom_restriction(U_775,U_776)))
| ~ relation(U_775) ),
inference(clausify,[status(thm)],[f_210_2]) ).
cnf(f_210_5,plain,
( in(U_777,relation_dom(relation_dom_restriction(U_775,U_776)))
| ~ in(U_777,relation_dom(U_775))
| ~ in(U_777,U_776)
| ~ relation(U_775) ),
inference(clausify,[status(thm)],[f_210_2]) ).
fof(f_211_1,plain,
! [A,B] :
( subset(relation_dom_restriction(B,A),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t88_relat_1]) ).
fof(f_211_2,plain,
! [U_779,U_778] :
( subset(relation_dom_restriction(U_778,U_779),U_778)
| ~ relation(U_778) ),
inference(variable_rename,[status(thm)],[f_211_1]) ).
cnf(f_211_3,plain,
( subset(relation_dom_restriction(U_778,U_779),U_778)
| ~ relation(U_778) ),
inference(clausify,[status(thm)],[f_211_2]) ).
fof(f_212_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_212_2,plain,
! [U_781,U_780] :
( ~ empty(U_780)
| U_781 = U_780
| ~ empty(U_781) ),
inference(variable_rename,[status(thm)],[f_212_1]) ).
fof(f_212_3,plain,
! [U_781] :
( ! [U_780] :
( ~ empty(U_780)
| U_781 = U_780 )
| ~ empty(U_781) ),
inference(miniscope,[status(thm)],[f_212_2]) ).
cnf(f_212_4,plain,
( ~ empty(U_780)
| U_781 = U_780
| ~ empty(U_781) ),
inference(clausify,[status(thm)],[f_212_3]) ).
fof(f_213_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_213_2,plain,
! [U_784,U_783,U_782] :
( ( ( in(ordered_pair(U_784,U_783),U_782)
| U_783 != apply(U_782,U_784)
| ~ in(U_784,relation_dom(U_782)) )
& ( ( U_783 = apply(U_782,U_784)
& in(U_784,relation_dom(U_782)) )
| ~ in(ordered_pair(U_784,U_783),U_782) ) )
| ~ function(U_782)
| ~ relation(U_782) ),
inference(variable_rename,[status(thm)],[f_213_1]) ).
cnf(f_213_3,plain,
( in(U_784,relation_dom(U_782))
| ~ in(ordered_pair(U_784,U_783),U_782)
| ~ function(U_782)
| ~ relation(U_782) ),
inference(clausify,[status(thm)],[f_213_2]) ).
cnf(f_213_4,plain,
( U_783 = apply(U_782,U_784)
| ~ in(ordered_pair(U_784,U_783),U_782)
| ~ function(U_782)
| ~ relation(U_782) ),
inference(clausify,[status(thm)],[f_213_2]) ).
cnf(f_213_5,plain,
( in(ordered_pair(U_784,U_783),U_782)
| U_783 != apply(U_782,U_784)
| ~ in(U_784,relation_dom(U_782))
| ~ function(U_782)
| ~ relation(U_782) ),
inference(clausify,[status(thm)],[f_213_2]) ).
fof(f_214_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_214_2,plain,
! [U_787,U_786,U_785] :
( subset(set_union2(U_787,U_785),U_786)
| ~ subset(U_785,U_786)
| ~ subset(U_787,U_786) ),
inference(variable_rename,[status(thm)],[f_214_1]) ).
cnf(f_214_3,plain,
( subset(set_union2(U_787,U_785),U_786)
| ~ subset(U_785,U_786)
| ~ subset(U_787,U_786) ),
inference(clausify,[status(thm)],[f_214_2]) ).
fof(f_215_1,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t8_zfmisc_1]) ).
fof(f_215_2,plain,
! [U_790,U_789,U_788] :
( U_790 = U_789
| singleton(U_790) != unordered_pair(U_789,U_788) ),
inference(variable_rename,[status(thm)],[f_215_1]) ).
fof(f_215_3,plain,
! [U_790,U_789] :
( ! [U_788] : singleton(U_790) != unordered_pair(U_789,U_788)
| U_790 = U_789 ),
inference(miniscope,[status(thm)],[f_215_2]) ).
cnf(f_215_4,plain,
( singleton(U_790) != unordered_pair(U_789,U_788)
| U_790 = U_789 ),
inference(clausify,[status(thm)],[f_215_3]) ).
fof(f_216_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_216_2,plain,
! [U_792,U_791] :
( relation_dom(relation_dom_restriction(U_791,U_792)) = set_intersection2(relation_dom(U_791),U_792)
| ~ relation(U_791) ),
inference(variable_rename,[status(thm)],[f_216_1]) ).
cnf(f_216_3,plain,
( relation_dom(relation_dom_restriction(U_791,U_792)) = set_intersection2(relation_dom(U_791),U_792)
| ~ relation(U_791) ),
inference(clausify,[status(thm)],[f_216_2]) ).
fof(f_217_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t92_zfmisc_1]) ).
fof(f_217_2,plain,
! [U_794,U_793] :
( subset(U_794,union(U_793))
| ~ in(U_794,U_793) ),
inference(variable_rename,[status(thm)],[f_217_1]) ).
cnf(f_217_3,plain,
( subset(U_794,union(U_793))
| ~ in(U_794,U_793) ),
inference(clausify,[status(thm)],[f_217_2]) ).
fof(f_218_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_218_2,plain,
! [U_796,U_795] :
( relation_dom_restriction(U_795,U_796) = relation_composition(identity_relation(U_796),U_795)
| ~ relation(U_795) ),
inference(variable_rename,[status(thm)],[f_218_1]) ).
cnf(f_218_3,plain,
( relation_dom_restriction(U_795,U_796) = relation_composition(identity_relation(U_796),U_795)
| ~ relation(U_795) ),
inference(clausify,[status(thm)],[f_218_2]) ).
fof(f_219_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_219_2,plain,
! [U_798,U_797] :
( subset(relation_rng(relation_dom_restriction(U_797,U_798)),relation_rng(U_797))
| ~ relation(U_797) ),
inference(variable_rename,[status(thm)],[f_219_1]) ).
cnf(f_219_3,plain,
( subset(relation_rng(relation_dom_restriction(U_797,U_798)),relation_rng(U_797))
| ~ relation(U_797) ),
inference(clausify,[status(thm)],[f_219_2]) ).
fof(f_220_1,plain,
! [A] : union(powerset(A)) = A,
inference(fof_nnf,[status(thm)],[t99_zfmisc_1]) ).
fof(f_220_2,plain,
! [U_799] : union(powerset(U_799)) = U_799,
inference(variable_rename,[status(thm)],[f_220_1]) ).
cnf(f_220_3,plain,
union(powerset(U_799)) = U_799,
inference(clausify,[status(thm)],[f_220_2]) ).
fof(f_221_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_221_2,plain,
! [U_807] :
? [U_806] :
( ! [U_805] :
( in(U_805,U_806)
| are_equipotent(U_805,U_806)
| ~ subset(U_805,U_806) )
& ! [U_804] :
( ? [U_803] :
( ! [U_802] :
( in(U_802,U_803)
| ~ subset(U_802,U_804) )
& in(U_803,U_806) )
| ~ in(U_804,U_806) )
& ! [U_801,U_800] :
( in(U_800,U_806)
| ~ subset(U_800,U_801)
| ~ in(U_801,U_806) )
& in(U_807,U_806) ),
inference(variable_rename,[status(thm)],[f_221_1]) ).
fof(f_221_3,plain,
! [U_807] :
( ! [U_805] :
( in(U_805,sK99(U_807))
| are_equipotent(U_805,sK99(U_807))
| ~ subset(U_805,sK99(U_807)) )
& ! [U_804] :
( ? [U_803] :
( ! [U_802] :
( in(U_802,U_803)
| ~ subset(U_802,U_804) )
& in(U_803,sK99(U_807)) )
| ~ in(U_804,sK99(U_807)) )
& ! [U_801,U_800] :
( in(U_800,sK99(U_807))
| ~ subset(U_800,U_801)
| ~ in(U_801,sK99(U_807)) )
& in(U_807,sK99(U_807)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_806,sK99(U_807))],[f_221_2]) ).
fof(f_221_4,plain,
! [U_807] :
( ! [U_805] :
( in(U_805,sK99(U_807))
| are_equipotent(U_805,sK99(U_807))
| ~ subset(U_805,sK99(U_807)) )
& ! [U_804] :
( ( ! [U_802] :
( in(U_802,sK100(U_807,U_804))
| ~ subset(U_802,U_804) )
& in(sK100(U_807,U_804),sK99(U_807)) )
| ~ in(U_804,sK99(U_807)) )
& ! [U_801,U_800] :
( in(U_800,sK99(U_807))
| ~ subset(U_800,U_801)
| ~ in(U_801,sK99(U_807)) )
& in(U_807,sK99(U_807)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_803,sK100(U_807,U_804))],[f_221_3]) ).
cnf(f_221_5,plain,
in(U_807,sK99(U_807)),
inference(clausify,[status(thm)],[f_221_4]) ).
cnf(f_221_6,plain,
( in(U_800,sK99(U_807))
| ~ subset(U_800,U_801)
| ~ in(U_801,sK99(U_807)) ),
inference(clausify,[status(thm)],[f_221_4]) ).
cnf(f_221_7,plain,
( in(sK100(U_807,U_804),sK99(U_807))
| ~ in(U_804,sK99(U_807)) ),
inference(clausify,[status(thm)],[f_221_4]) ).
cnf(f_221_8,plain,
( in(U_802,sK100(U_807,U_804))
| ~ subset(U_802,U_804)
| ~ in(U_804,sK99(U_807)) ),
inference(clausify,[status(thm)],[f_221_4]) ).
cnf(f_221_9,plain,
( in(U_805,sK99(U_807))
| are_equipotent(U_805,sK99(U_807))
| ~ subset(U_805,sK99(U_807)) ),
inference(clausify,[status(thm)],[f_221_4]) ).
fof(f_222_1,plain,
! [A,B,C] :
( B = C
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t9_zfmisc_1]) ).
fof(f_222_2,plain,
! [U_810,U_809,U_808] :
( U_809 = U_808
| singleton(U_810) != unordered_pair(U_809,U_808) ),
inference(variable_rename,[status(thm)],[f_222_1]) ).
cnf(f_222_3,plain,
( U_809 = U_808
| singleton(U_810) != unordered_pair(U_809,U_808) ),
inference(clausify,[status(thm)],[f_222_2]) ).
cnf(f_39_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_39_8]) ).
cnf(f_39_9_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_39_9]) ).
cnf(f_41_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_41_2]) ).
cnf(f_42_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_42_2]) ).
cnf(f_43_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_43_2]) ).
cnf(f_44_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_44_2]) ).
cnf(f_45_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_45_2]) ).
cnf(f_46_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_46_2]) ).
cnf(f_47_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_47_2]) ).
cnf(f_48_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_48_2]) ).
cnf(f_50_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_50_2]) ).
cnf(f_51_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_51_2]) ).
cnf(f_52_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_52_2]) ).
cnf(f_53_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_53_2]) ).
cnf(f_55_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_55_2]) ).
cnf(f_56_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_56_2]) ).
cnf(f_58_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_58_2]) ).
cnf(f_59_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_59_2]) ).
cnf(f_68_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_68_2]) ).
cnf(f_69_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_69_2]) ).
cnf(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_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_11,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_12,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_13,axiom,
( set_meet(Eq_x_0) = set_meet(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,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_17,axiom,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,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_19,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_20,axiom,
( union(Eq_x_0) = union(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,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_22,axiom,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,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_24,axiom,
( relation_field(Eq_x_0) = relation_field(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( relation_inverse(Eq_x_0) = relation_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,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_27,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_28,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_29,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_30,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_31,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_32,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_33,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_34,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_35,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_36,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_37,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_38,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_39,axiom,
( sK9(Eq_x_0,Eq_x_1,Eq_x_2) = sK9(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,
( 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_41,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_42,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_43,axiom,
( sK13(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK13(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_44,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_45,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_46,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_47,axiom,
( sK17(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK17(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_48,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_49,axiom,
( sK19(Eq_x_0,Eq_x_1,Eq_x_2) = sK19(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,
( 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_51,axiom,
( sK21(Eq_x_0,Eq_x_1) = sK21(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_52,axiom,
( sK22(Eq_x_0,Eq_x_1) = sK22(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_53,axiom,
( sK23(Eq_x_0) = sK23(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_54,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_55,axiom,
( sK25(Eq_x_0,Eq_x_1) = sK25(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_56,axiom,
( sK26(Eq_x_0,Eq_x_1) = sK26(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_57,axiom,
( sK27(Eq_x_0,Eq_x_1) = sK27(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_58,axiom,
( sK28(Eq_x_0,Eq_x_1) = sK28(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_59,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_60,axiom,
( sK30(Eq_x_0) = sK30(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_61,axiom,
( sK31(Eq_x_0,Eq_x_1) = sK31(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_62,axiom,
( sK32(Eq_x_0,Eq_x_1) = sK32(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_63,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_64,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_65,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_66,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_67,axiom,
( sK37(Eq_x_0,Eq_x_1,Eq_x_2) = sK37(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_68,axiom,
( sK38(Eq_x_0,Eq_x_1,Eq_x_2) = sK38(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_69,axiom,
( sK39(Eq_x_0,Eq_x_1,Eq_x_2) = sK39(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_70,axiom,
( sK40(Eq_x_0,Eq_x_1,Eq_x_2) = sK40(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_71,axiom,
( sK41(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK41(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_72,axiom,
( sK42(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK42(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_73,axiom,
( sK43(Eq_x_0,Eq_x_1,Eq_x_2) = sK43(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_74,axiom,
( sK44(Eq_x_0,Eq_x_1,Eq_x_2) = sK44(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_75,axiom,
( sK45(Eq_x_0,Eq_x_1,Eq_x_2) = sK45(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_76,axiom,
( 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_77,axiom,
( sK47(Eq_x_0,Eq_x_1) = sK47(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_78,axiom,
( sK48(Eq_x_0,Eq_x_1) = sK48(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_79,axiom,
( sK49(Eq_x_0,Eq_x_1) = sK49(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_80,axiom,
( sK50(Eq_x_0,Eq_x_1,Eq_x_2) = sK50(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_81,axiom,
( sK51(Eq_x_0,Eq_x_1,Eq_x_2) = sK51(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,
( 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_83,axiom,
( sK53(Eq_x_0,Eq_x_1) = sK53(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_84,axiom,
( sK54(Eq_x_0,Eq_x_1) = sK54(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_85,axiom,
( sK55(Eq_x_0,Eq_x_1) = sK55(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_86,axiom,
( sK56(Eq_x_0,Eq_x_1,Eq_x_2) = sK56(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_87,axiom,
( sK57(Eq_x_0,Eq_x_1) = sK57(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_88,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_89,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_90,axiom,
( sK60(Eq_x_0,Eq_x_1,Eq_x_2) = sK60(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_91,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_92,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_93,axiom,
( sK63(Eq_x_0,Eq_x_1) = sK63(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_94,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_95,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_96,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_97,axiom,
( sK67(Eq_x_0,Eq_x_1) = sK67(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_98,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_99,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_100,axiom,
( sK70(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK70(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_101,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_102,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_103,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_104,axiom,
( sK74(Eq_x_0,Eq_x_1,Eq_x_2) = sK74(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_105,axiom,
( sK75(Eq_x_0,Eq_x_1,Eq_x_2) = sK75(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_106,axiom,
( sK76(Eq_x_0,Eq_x_1,Eq_x_2) = sK76(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_107,axiom,
( sK77(Eq_x_0) = sK77(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_108,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_109,axiom,
( sK81(Eq_x_0) = sK81(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_110,axiom,
( sK84(Eq_x_0) = sK84(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_111,axiom,
( sK87(Eq_x_0) = sK87(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_112,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_113,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_114,axiom,
( sK90(Eq_x_0,Eq_x_1) = sK90(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_115,axiom,
( sK91(Eq_x_0,Eq_x_1) = sK91(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_116,axiom,
( sK92(Eq_x_0,Eq_x_1) = sK92(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_117,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_118,axiom,
( sK96(Eq_x_0,Eq_x_1) = sK96(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_119,axiom,
( sK97(Eq_x_0) = sK97(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_120,axiom,
( sK98(Eq_x_0) = sK98(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_121,axiom,
( sK99(Eq_x_0) = sK99(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_122,axiom,
( sK100(Eq_x_0,Eq_x_1) = sK100(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_123,axiom,
( 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_124,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_125,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_126,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_127,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_128,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_129,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_130,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_131,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_132,axiom,
( are_equipotent(Eq_y_0,Eq_y_1)
| ~ are_equipotent(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU217+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 23:34:14 UTC 2026
% 0.09/0.35 % CPUTime :
% 75.88/76.18 % SZS status Theorem for theBenchmark
% 75.88/76.18 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------