%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU204+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 08:58:29 AM UTC 2026
% Result : Theorem 118.77s 119.06s
% Output : Proof 118.91s
% 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_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(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_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_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(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_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_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(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,conjecture,
! [A,B] :
( relation(B)
=> subset(relation_image(B,A),relation_rng(B)) ),
file('theBenchmark.p',t144_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_relat_1,lemma,
! [A] :
( relation(A)
=> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))) ),
file('theBenchmark.p',t21_relat_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(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_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] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_3_2,plain,
! [U_4] :
( relation(U_4)
| ~ empty(U_4) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( relation(U_4)
| ~ empty(U_4) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_4_2,plain,
! [U_6,U_5] : unordered_pair(U_6,U_5) = unordered_pair(U_5,U_6),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
unordered_pair(U_6,U_5) = unordered_pair(U_5,U_6),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_5_2,plain,
! [U_8,U_7] : set_union2(U_8,U_7) = set_union2(U_7,U_8),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
set_union2(U_8,U_7) = set_union2(U_7,U_8),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_6_2,plain,
! [U_10,U_9] : set_intersection2(U_10,U_9) = set_intersection2(U_9,U_10),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
set_intersection2(U_10,U_9) = set_intersection2(U_9,U_10),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_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_7_2,plain,
! [U_16,U_15] :
( ( ( U_15 = identity_relation(U_16)
| ? [U_14,U_13] :
( ( ~ in(ordered_pair(U_14,U_13),U_15)
& U_14 = U_13
& in(U_14,U_16) )
| ( ( U_14 != U_13
| ~ in(U_14,U_16) )
& in(ordered_pair(U_14,U_13),U_15) ) ) )
& ( ! [U_12,U_11] :
( ( in(ordered_pair(U_12,U_11),U_15)
| U_12 != U_11
| ~ in(U_12,U_16) )
& ( ( U_12 = U_11
& in(U_12,U_16) )
| ~ in(ordered_pair(U_12,U_11),U_15) ) )
| U_15 != identity_relation(U_16) ) )
| ~ relation(U_15) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_16,U_15] :
( ( ( U_15 = identity_relation(U_16)
| ? [U_24,U_22] :
( ~ in(ordered_pair(U_24,U_22),U_15)
& U_24 = U_22
& in(U_24,U_16) )
| ? [U_23,U_21] :
( ( U_23 != U_21
| ~ in(U_23,U_16) )
& in(ordered_pair(U_23,U_21),U_15) ) )
& ( ( ! [U_20,U_18] :
( in(ordered_pair(U_20,U_18),U_15)
| U_20 != U_18
| ~ in(U_20,U_16) )
& ! [U_19,U_17] :
( ( U_19 = U_17
& in(U_19,U_16) )
| ~ in(ordered_pair(U_19,U_17),U_15) ) )
| U_15 != identity_relation(U_16) ) )
| ~ relation(U_15) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
! [U_16,U_15] :
( ( ( U_15 = identity_relation(U_16)
| ? [U_24,U_22] :
( ~ in(ordered_pair(U_24,U_22),U_15)
& U_24 = U_22
& in(U_24,U_16) )
| ? [U_21] :
( ( sK1(U_16,U_15) != U_21
| ~ in(sK1(U_16,U_15),U_16) )
& in(ordered_pair(sK1(U_16,U_15),U_21),U_15) ) )
& ( ( ! [U_20,U_18] :
( in(ordered_pair(U_20,U_18),U_15)
| U_20 != U_18
| ~ in(U_20,U_16) )
& ! [U_19,U_17] :
( ( U_19 = U_17
& in(U_19,U_16) )
| ~ in(ordered_pair(U_19,U_17),U_15) ) )
| U_15 != identity_relation(U_16) ) )
| ~ relation(U_15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_23,sK1(U_16,U_15))],[f_7_3]) ).
fof(f_7_5,plain,
! [U_16,U_15] :
( ( ( U_15 = identity_relation(U_16)
| ? [U_24,U_22] :
( ~ in(ordered_pair(U_24,U_22),U_15)
& U_24 = U_22
& in(U_24,U_16) )
| ( ( sK1(U_16,U_15) != sK2(U_16,U_15)
| ~ in(sK1(U_16,U_15),U_16) )
& in(ordered_pair(sK1(U_16,U_15),sK2(U_16,U_15)),U_15) ) )
& ( ( ! [U_20,U_18] :
( in(ordered_pair(U_20,U_18),U_15)
| U_20 != U_18
| ~ in(U_20,U_16) )
& ! [U_19,U_17] :
( ( U_19 = U_17
& in(U_19,U_16) )
| ~ in(ordered_pair(U_19,U_17),U_15) ) )
| U_15 != identity_relation(U_16) ) )
| ~ relation(U_15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_21,sK2(U_16,U_15))],[f_7_4]) ).
fof(f_7_6,plain,
! [U_16,U_15] :
( ( ( U_15 = identity_relation(U_16)
| ? [U_22] :
( ~ in(ordered_pair(sK3(U_16,U_15),U_22),U_15)
& sK3(U_16,U_15) = U_22
& in(sK3(U_16,U_15),U_16) )
| ( ( sK1(U_16,U_15) != sK2(U_16,U_15)
| ~ in(sK1(U_16,U_15),U_16) )
& in(ordered_pair(sK1(U_16,U_15),sK2(U_16,U_15)),U_15) ) )
& ( ( ! [U_20,U_18] :
( in(ordered_pair(U_20,U_18),U_15)
| U_20 != U_18
| ~ in(U_20,U_16) )
& ! [U_19,U_17] :
( ( U_19 = U_17
& in(U_19,U_16) )
| ~ in(ordered_pair(U_19,U_17),U_15) ) )
| U_15 != identity_relation(U_16) ) )
| ~ relation(U_15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_24,sK3(U_16,U_15))],[f_7_5]) ).
fof(f_7_7,plain,
! [U_16,U_15] :
( ( ( U_15 = identity_relation(U_16)
| ( ~ in(ordered_pair(sK3(U_16,U_15),sK4(U_16,U_15)),U_15)
& sK3(U_16,U_15) = sK4(U_16,U_15)
& in(sK3(U_16,U_15),U_16) )
| ( ( sK1(U_16,U_15) != sK2(U_16,U_15)
| ~ in(sK1(U_16,U_15),U_16) )
& in(ordered_pair(sK1(U_16,U_15),sK2(U_16,U_15)),U_15) ) )
& ( ( ! [U_20,U_18] :
( in(ordered_pair(U_20,U_18),U_15)
| U_20 != U_18
| ~ in(U_20,U_16) )
& ! [U_19,U_17] :
( ( U_19 = U_17
& in(U_19,U_16) )
| ~ in(ordered_pair(U_19,U_17),U_15) ) )
| U_15 != identity_relation(U_16) ) )
| ~ relation(U_15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_22,sK4(U_16,U_15))],[f_7_6]) ).
cnf(f_7_8,plain,
( in(U_19,U_16)
| ~ in(ordered_pair(U_19,U_17),U_15)
| U_15 != identity_relation(U_16)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_9,plain,
( U_19 = U_17
| ~ in(ordered_pair(U_19,U_17),U_15)
| U_15 != identity_relation(U_16)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_10,plain,
( in(ordered_pair(U_20,U_18),U_15)
| U_20 != U_18
| ~ in(U_20,U_16)
| U_15 != identity_relation(U_16)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_11,plain,
( in(sK3(U_16,U_15),U_16)
| in(ordered_pair(sK1(U_16,U_15),sK2(U_16,U_15)),U_15)
| U_15 = identity_relation(U_16)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_12,plain,
( sK3(U_16,U_15) = sK4(U_16,U_15)
| in(ordered_pair(sK1(U_16,U_15),sK2(U_16,U_15)),U_15)
| U_15 = identity_relation(U_16)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_13,plain,
( ~ in(ordered_pair(sK3(U_16,U_15),sK4(U_16,U_15)),U_15)
| in(ordered_pair(sK1(U_16,U_15),sK2(U_16,U_15)),U_15)
| U_15 = identity_relation(U_16)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_14,plain,
( in(sK3(U_16,U_15),U_16)
| sK1(U_16,U_15) != sK2(U_16,U_15)
| ~ in(sK1(U_16,U_15),U_16)
| U_15 = identity_relation(U_16)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_15,plain,
( sK3(U_16,U_15) = sK4(U_16,U_15)
| sK1(U_16,U_15) != sK2(U_16,U_15)
| ~ in(sK1(U_16,U_15),U_16)
| U_15 = identity_relation(U_16)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_16,plain,
( ~ in(ordered_pair(sK3(U_16,U_15),sK4(U_16,U_15)),U_15)
| sK1(U_16,U_15) != sK2(U_16,U_15)
| ~ in(sK1(U_16,U_15),U_16)
| U_15 = identity_relation(U_16)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_7]) ).
fof(f_8_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_8_2,plain,
! [U_26,U_25] :
( ( U_26 = U_25
| ~ subset(U_25,U_26)
| ~ subset(U_26,U_25) )
& ( ( subset(U_25,U_26)
& subset(U_26,U_25) )
| U_26 != U_25 ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_30,U_28] :
( U_30 = U_28
| ~ subset(U_28,U_30)
| ~ subset(U_30,U_28) )
& ! [U_29,U_27] :
( ( subset(U_27,U_29)
& subset(U_29,U_27) )
| U_29 != U_27 ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( subset(U_29,U_27)
| U_29 != U_27 ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( subset(U_27,U_29)
| U_29 != U_27 ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_6,plain,
( U_30 = U_28
| ~ subset(U_28,U_30)
| ~ subset(U_30,U_28) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_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_9_2,plain,
! [U_37] :
( ! [U_36,U_35] :
( ( ( U_35 = relation_dom_restriction(U_37,U_36)
| ? [U_34,U_33] :
( ( ~ in(ordered_pair(U_34,U_33),U_35)
& in(ordered_pair(U_34,U_33),U_37)
& in(U_34,U_36) )
| ( ( ~ in(ordered_pair(U_34,U_33),U_37)
| ~ in(U_34,U_36) )
& in(ordered_pair(U_34,U_33),U_35) ) ) )
& ( ! [U_32,U_31] :
( ( in(ordered_pair(U_32,U_31),U_35)
| ~ in(ordered_pair(U_32,U_31),U_37)
| ~ in(U_32,U_36) )
& ( ( in(ordered_pair(U_32,U_31),U_37)
& in(U_32,U_36) )
| ~ in(ordered_pair(U_32,U_31),U_35) ) )
| U_35 != relation_dom_restriction(U_37,U_36) ) )
| ~ relation(U_35) )
| ~ relation(U_37) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_37] :
( ! [U_36,U_35] :
( ( ( U_35 = relation_dom_restriction(U_37,U_36)
| ? [U_45,U_43] :
( ~ in(ordered_pair(U_45,U_43),U_35)
& in(ordered_pair(U_45,U_43),U_37)
& in(U_45,U_36) )
| ? [U_44,U_42] :
( ( ~ in(ordered_pair(U_44,U_42),U_37)
| ~ in(U_44,U_36) )
& in(ordered_pair(U_44,U_42),U_35) ) )
& ( ( ! [U_41,U_39] :
( in(ordered_pair(U_41,U_39),U_35)
| ~ in(ordered_pair(U_41,U_39),U_37)
| ~ in(U_41,U_36) )
& ! [U_40,U_38] :
( ( in(ordered_pair(U_40,U_38),U_37)
& in(U_40,U_36) )
| ~ in(ordered_pair(U_40,U_38),U_35) ) )
| U_35 != relation_dom_restriction(U_37,U_36) ) )
| ~ relation(U_35) )
| ~ relation(U_37) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
fof(f_9_4,plain,
! [U_37] :
( ! [U_36,U_35] :
( ( ( U_35 = relation_dom_restriction(U_37,U_36)
| ? [U_45,U_43] :
( ~ in(ordered_pair(U_45,U_43),U_35)
& in(ordered_pair(U_45,U_43),U_37)
& in(U_45,U_36) )
| ? [U_42] :
( ( ~ in(ordered_pair(sK5(U_37,U_36,U_35),U_42),U_37)
| ~ in(sK5(U_37,U_36,U_35),U_36) )
& in(ordered_pair(sK5(U_37,U_36,U_35),U_42),U_35) ) )
& ( ( ! [U_41,U_39] :
( in(ordered_pair(U_41,U_39),U_35)
| ~ in(ordered_pair(U_41,U_39),U_37)
| ~ in(U_41,U_36) )
& ! [U_40,U_38] :
( ( in(ordered_pair(U_40,U_38),U_37)
& in(U_40,U_36) )
| ~ in(ordered_pair(U_40,U_38),U_35) ) )
| U_35 != relation_dom_restriction(U_37,U_36) ) )
| ~ relation(U_35) )
| ~ relation(U_37) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_44,sK5(U_37,U_36,U_35))],[f_9_3]) ).
fof(f_9_5,plain,
! [U_37] :
( ! [U_36,U_35] :
( ( ( U_35 = relation_dom_restriction(U_37,U_36)
| ? [U_45,U_43] :
( ~ in(ordered_pair(U_45,U_43),U_35)
& in(ordered_pair(U_45,U_43),U_37)
& in(U_45,U_36) )
| ( ( ~ in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_37)
| ~ in(sK5(U_37,U_36,U_35),U_36) )
& in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_35) ) )
& ( ( ! [U_41,U_39] :
( in(ordered_pair(U_41,U_39),U_35)
| ~ in(ordered_pair(U_41,U_39),U_37)
| ~ in(U_41,U_36) )
& ! [U_40,U_38] :
( ( in(ordered_pair(U_40,U_38),U_37)
& in(U_40,U_36) )
| ~ in(ordered_pair(U_40,U_38),U_35) ) )
| U_35 != relation_dom_restriction(U_37,U_36) ) )
| ~ relation(U_35) )
| ~ relation(U_37) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_42,sK6(U_37,U_36,U_35))],[f_9_4]) ).
fof(f_9_6,plain,
! [U_37] :
( ! [U_36,U_35] :
( ( ( U_35 = relation_dom_restriction(U_37,U_36)
| ? [U_43] :
( ~ in(ordered_pair(sK7(U_37,U_36,U_35),U_43),U_35)
& in(ordered_pair(sK7(U_37,U_36,U_35),U_43),U_37)
& in(sK7(U_37,U_36,U_35),U_36) )
| ( ( ~ in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_37)
| ~ in(sK5(U_37,U_36,U_35),U_36) )
& in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_35) ) )
& ( ( ! [U_41,U_39] :
( in(ordered_pair(U_41,U_39),U_35)
| ~ in(ordered_pair(U_41,U_39),U_37)
| ~ in(U_41,U_36) )
& ! [U_40,U_38] :
( ( in(ordered_pair(U_40,U_38),U_37)
& in(U_40,U_36) )
| ~ in(ordered_pair(U_40,U_38),U_35) ) )
| U_35 != relation_dom_restriction(U_37,U_36) ) )
| ~ relation(U_35) )
| ~ relation(U_37) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_45,sK7(U_37,U_36,U_35))],[f_9_5]) ).
fof(f_9_7,plain,
! [U_37] :
( ! [U_36,U_35] :
( ( ( U_35 = relation_dom_restriction(U_37,U_36)
| ( ~ in(ordered_pair(sK7(U_37,U_36,U_35),sK8(U_37,U_36,U_35)),U_35)
& in(ordered_pair(sK7(U_37,U_36,U_35),sK8(U_37,U_36,U_35)),U_37)
& in(sK7(U_37,U_36,U_35),U_36) )
| ( ( ~ in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_37)
| ~ in(sK5(U_37,U_36,U_35),U_36) )
& in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_35) ) )
& ( ( ! [U_41,U_39] :
( in(ordered_pair(U_41,U_39),U_35)
| ~ in(ordered_pair(U_41,U_39),U_37)
| ~ in(U_41,U_36) )
& ! [U_40,U_38] :
( ( in(ordered_pair(U_40,U_38),U_37)
& in(U_40,U_36) )
| ~ in(ordered_pair(U_40,U_38),U_35) ) )
| U_35 != relation_dom_restriction(U_37,U_36) ) )
| ~ relation(U_35) )
| ~ relation(U_37) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_43,sK8(U_37,U_36,U_35))],[f_9_6]) ).
cnf(f_9_8,plain,
( in(U_40,U_36)
| ~ in(ordered_pair(U_40,U_38),U_35)
| U_35 != relation_dom_restriction(U_37,U_36)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_9,plain,
( in(ordered_pair(U_40,U_38),U_37)
| ~ in(ordered_pair(U_40,U_38),U_35)
| U_35 != relation_dom_restriction(U_37,U_36)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_10,plain,
( in(ordered_pair(U_41,U_39),U_35)
| ~ in(ordered_pair(U_41,U_39),U_37)
| ~ in(U_41,U_36)
| U_35 != relation_dom_restriction(U_37,U_36)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_11,plain,
( in(sK7(U_37,U_36,U_35),U_36)
| in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_35)
| U_35 = relation_dom_restriction(U_37,U_36)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_12,plain,
( in(ordered_pair(sK7(U_37,U_36,U_35),sK8(U_37,U_36,U_35)),U_37)
| in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_35)
| U_35 = relation_dom_restriction(U_37,U_36)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_13,plain,
( ~ in(ordered_pair(sK7(U_37,U_36,U_35),sK8(U_37,U_36,U_35)),U_35)
| in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_35)
| U_35 = relation_dom_restriction(U_37,U_36)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_14,plain,
( in(sK7(U_37,U_36,U_35),U_36)
| ~ in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_37)
| ~ in(sK5(U_37,U_36,U_35),U_36)
| U_35 = relation_dom_restriction(U_37,U_36)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_15,plain,
( in(ordered_pair(sK7(U_37,U_36,U_35),sK8(U_37,U_36,U_35)),U_37)
| ~ in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_37)
| ~ in(sK5(U_37,U_36,U_35),U_36)
| U_35 = relation_dom_restriction(U_37,U_36)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_16,plain,
( ~ in(ordered_pair(sK7(U_37,U_36,U_35),sK8(U_37,U_36,U_35)),U_35)
| ~ in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_37)
| ~ in(sK5(U_37,U_36,U_35),U_36)
| U_35 = relation_dom_restriction(U_37,U_36)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_7]) ).
fof(f_10_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_10_2,plain,
! [U_52,U_51] :
( ! [U_50] :
( ( ( U_50 = relation_rng_restriction(U_52,U_51)
| ? [U_49,U_48] :
( ( ~ in(ordered_pair(U_49,U_48),U_50)
& in(ordered_pair(U_49,U_48),U_51)
& in(U_48,U_52) )
| ( ( ~ in(ordered_pair(U_49,U_48),U_51)
| ~ in(U_48,U_52) )
& in(ordered_pair(U_49,U_48),U_50) ) ) )
& ( ! [U_47,U_46] :
( ( in(ordered_pair(U_47,U_46),U_50)
| ~ in(ordered_pair(U_47,U_46),U_51)
| ~ in(U_46,U_52) )
& ( ( in(ordered_pair(U_47,U_46),U_51)
& in(U_46,U_52) )
| ~ in(ordered_pair(U_47,U_46),U_50) ) )
| U_50 != relation_rng_restriction(U_52,U_51) ) )
| ~ relation(U_50) )
| ~ relation(U_51) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_52,U_51] :
( ! [U_50] :
( ( ( U_50 = relation_rng_restriction(U_52,U_51)
| ? [U_60,U_58] :
( ~ in(ordered_pair(U_60,U_58),U_50)
& in(ordered_pair(U_60,U_58),U_51)
& in(U_58,U_52) )
| ? [U_59,U_57] :
( ( ~ in(ordered_pair(U_59,U_57),U_51)
| ~ in(U_57,U_52) )
& in(ordered_pair(U_59,U_57),U_50) ) )
& ( ( ! [U_56,U_54] :
( in(ordered_pair(U_56,U_54),U_50)
| ~ in(ordered_pair(U_56,U_54),U_51)
| ~ in(U_54,U_52) )
& ! [U_55,U_53] :
( ( in(ordered_pair(U_55,U_53),U_51)
& in(U_53,U_52) )
| ~ in(ordered_pair(U_55,U_53),U_50) ) )
| U_50 != relation_rng_restriction(U_52,U_51) ) )
| ~ relation(U_50) )
| ~ relation(U_51) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
fof(f_10_4,plain,
! [U_52,U_51] :
( ! [U_50] :
( ( ( U_50 = relation_rng_restriction(U_52,U_51)
| ? [U_60,U_58] :
( ~ in(ordered_pair(U_60,U_58),U_50)
& in(ordered_pair(U_60,U_58),U_51)
& in(U_58,U_52) )
| ? [U_57] :
( ( ~ in(ordered_pair(sK9(U_52,U_51,U_50),U_57),U_51)
| ~ in(U_57,U_52) )
& in(ordered_pair(sK9(U_52,U_51,U_50),U_57),U_50) ) )
& ( ( ! [U_56,U_54] :
( in(ordered_pair(U_56,U_54),U_50)
| ~ in(ordered_pair(U_56,U_54),U_51)
| ~ in(U_54,U_52) )
& ! [U_55,U_53] :
( ( in(ordered_pair(U_55,U_53),U_51)
& in(U_53,U_52) )
| ~ in(ordered_pair(U_55,U_53),U_50) ) )
| U_50 != relation_rng_restriction(U_52,U_51) ) )
| ~ relation(U_50) )
| ~ relation(U_51) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_59,sK9(U_52,U_51,U_50))],[f_10_3]) ).
fof(f_10_5,plain,
! [U_52,U_51] :
( ! [U_50] :
( ( ( U_50 = relation_rng_restriction(U_52,U_51)
| ? [U_60,U_58] :
( ~ in(ordered_pair(U_60,U_58),U_50)
& in(ordered_pair(U_60,U_58),U_51)
& in(U_58,U_52) )
| ( ( ~ in(ordered_pair(sK9(U_52,U_51,U_50),sK10(U_52,U_51,U_50)),U_51)
| ~ in(sK10(U_52,U_51,U_50),U_52) )
& in(ordered_pair(sK9(U_52,U_51,U_50),sK10(U_52,U_51,U_50)),U_50) ) )
& ( ( ! [U_56,U_54] :
( in(ordered_pair(U_56,U_54),U_50)
| ~ in(ordered_pair(U_56,U_54),U_51)
| ~ in(U_54,U_52) )
& ! [U_55,U_53] :
( ( in(ordered_pair(U_55,U_53),U_51)
& in(U_53,U_52) )
| ~ in(ordered_pair(U_55,U_53),U_50) ) )
| U_50 != relation_rng_restriction(U_52,U_51) ) )
| ~ relation(U_50) )
| ~ relation(U_51) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_57,sK10(U_52,U_51,U_50))],[f_10_4]) ).
fof(f_10_6,plain,
! [U_52,U_51] :
( ! [U_50] :
( ( ( U_50 = relation_rng_restriction(U_52,U_51)
| ? [U_58] :
( ~ in(ordered_pair(sK11(U_52,U_51,U_50),U_58),U_50)
& in(ordered_pair(sK11(U_52,U_51,U_50),U_58),U_51)
& in(U_58,U_52) )
| ( ( ~ in(ordered_pair(sK9(U_52,U_51,U_50),sK10(U_52,U_51,U_50)),U_51)
| ~ in(sK10(U_52,U_51,U_50),U_52) )
& in(ordered_pair(sK9(U_52,U_51,U_50),sK10(U_52,U_51,U_50)),U_50) ) )
& ( ( ! [U_56,U_54] :
( in(ordered_pair(U_56,U_54),U_50)
| ~ in(ordered_pair(U_56,U_54),U_51)
| ~ in(U_54,U_52) )
& ! [U_55,U_53] :
( ( in(ordered_pair(U_55,U_53),U_51)
& in(U_53,U_52) )
| ~ in(ordered_pair(U_55,U_53),U_50) ) )
| U_50 != relation_rng_restriction(U_52,U_51) ) )
| ~ relation(U_50) )
| ~ relation(U_51) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_60,sK11(U_52,U_51,U_50))],[f_10_5]) ).
fof(f_10_7,plain,
! [U_52,U_51] :
( ! [U_50] :
( ( ( U_50 = relation_rng_restriction(U_52,U_51)
| ( ~ in(ordered_pair(sK11(U_52,U_51,U_50),sK12(U_52,U_51,U_50)),U_50)
& in(ordered_pair(sK11(U_52,U_51,U_50),sK12(U_52,U_51,U_50)),U_51)
& in(sK12(U_52,U_51,U_50),U_52) )
| ( ( ~ in(ordered_pair(sK9(U_52,U_51,U_50),sK10(U_52,U_51,U_50)),U_51)
| ~ in(sK10(U_52,U_51,U_50),U_52) )
& in(ordered_pair(sK9(U_52,U_51,U_50),sK10(U_52,U_51,U_50)),U_50) ) )
& ( ( ! [U_56,U_54] :
( in(ordered_pair(U_56,U_54),U_50)
| ~ in(ordered_pair(U_56,U_54),U_51)
| ~ in(U_54,U_52) )
& ! [U_55,U_53] :
( ( in(ordered_pair(U_55,U_53),U_51)
& in(U_53,U_52) )
| ~ in(ordered_pair(U_55,U_53),U_50) ) )
| U_50 != relation_rng_restriction(U_52,U_51) ) )
| ~ relation(U_50) )
| ~ relation(U_51) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_58,sK12(U_52,U_51,U_50))],[f_10_6]) ).
cnf(f_10_8,plain,
( in(U_53,U_52)
| ~ in(ordered_pair(U_55,U_53),U_50)
| U_50 != relation_rng_restriction(U_52,U_51)
| ~ relation(U_50)
| ~ relation(U_51) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_9,plain,
( in(ordered_pair(U_55,U_53),U_51)
| ~ in(ordered_pair(U_55,U_53),U_50)
| U_50 != relation_rng_restriction(U_52,U_51)
| ~ relation(U_50)
| ~ relation(U_51) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_10,plain,
( in(ordered_pair(U_56,U_54),U_50)
| ~ in(ordered_pair(U_56,U_54),U_51)
| ~ in(U_54,U_52)
| U_50 != relation_rng_restriction(U_52,U_51)
| ~ relation(U_50)
| ~ relation(U_51) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_11,plain,
( in(sK12(U_52,U_51,U_50),U_52)
| in(ordered_pair(sK9(U_52,U_51,U_50),sK10(U_52,U_51,U_50)),U_50)
| U_50 = relation_rng_restriction(U_52,U_51)
| ~ relation(U_50)
| ~ relation(U_51) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_12,plain,
( in(ordered_pair(sK11(U_52,U_51,U_50),sK12(U_52,U_51,U_50)),U_51)
| in(ordered_pair(sK9(U_52,U_51,U_50),sK10(U_52,U_51,U_50)),U_50)
| U_50 = relation_rng_restriction(U_52,U_51)
| ~ relation(U_50)
| ~ relation(U_51) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_13,plain,
( ~ in(ordered_pair(sK11(U_52,U_51,U_50),sK12(U_52,U_51,U_50)),U_50)
| in(ordered_pair(sK9(U_52,U_51,U_50),sK10(U_52,U_51,U_50)),U_50)
| U_50 = relation_rng_restriction(U_52,U_51)
| ~ relation(U_50)
| ~ relation(U_51) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_14,plain,
( in(sK12(U_52,U_51,U_50),U_52)
| ~ in(ordered_pair(sK9(U_52,U_51,U_50),sK10(U_52,U_51,U_50)),U_51)
| ~ in(sK10(U_52,U_51,U_50),U_52)
| U_50 = relation_rng_restriction(U_52,U_51)
| ~ relation(U_50)
| ~ relation(U_51) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_15,plain,
( in(ordered_pair(sK11(U_52,U_51,U_50),sK12(U_52,U_51,U_50)),U_51)
| ~ in(ordered_pair(sK9(U_52,U_51,U_50),sK10(U_52,U_51,U_50)),U_51)
| ~ in(sK10(U_52,U_51,U_50),U_52)
| U_50 = relation_rng_restriction(U_52,U_51)
| ~ relation(U_50)
| ~ relation(U_51) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_16,plain,
( ~ in(ordered_pair(sK11(U_52,U_51,U_50),sK12(U_52,U_51,U_50)),U_50)
| ~ in(ordered_pair(sK9(U_52,U_51,U_50),sK10(U_52,U_51,U_50)),U_51)
| ~ in(sK10(U_52,U_51,U_50),U_52)
| U_50 = relation_rng_restriction(U_52,U_51)
| ~ relation(U_50)
| ~ relation(U_51) ),
inference(clausify,[status(thm)],[f_10_7]) ).
fof(f_11_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_11_2,plain,
! [U_69] :
( ! [U_68,U_67] :
( ( U_67 = relation_image(U_69,U_68)
| ? [U_66] :
( ( ~ in(U_66,U_67)
& ? [U_65] :
( in(U_65,U_68)
& in(ordered_pair(U_65,U_66),U_69) ) )
| ( ! [U_64] :
( ~ in(U_64,U_68)
| ~ in(ordered_pair(U_64,U_66),U_69) )
& in(U_66,U_67) ) ) )
& ( ! [U_63] :
( ( in(U_63,U_67)
| ! [U_62] :
( ~ in(U_62,U_68)
| ~ in(ordered_pair(U_62,U_63),U_69) ) )
& ( ? [U_61] :
( in(U_61,U_68)
& in(ordered_pair(U_61,U_63),U_69) )
| ~ in(U_63,U_67) ) )
| U_67 != relation_image(U_69,U_68) ) )
| ~ relation(U_69) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_69] :
( ( ! [U_77,U_75] :
( U_75 = relation_image(U_69,U_77)
| ? [U_73] :
( ~ in(U_73,U_75)
& ? [U_65] :
( in(U_65,U_77)
& in(ordered_pair(U_65,U_73),U_69) ) )
| ? [U_72] :
( ! [U_64] :
( ~ in(U_64,U_77)
| ~ in(ordered_pair(U_64,U_72),U_69) )
& in(U_72,U_75) ) )
& ! [U_76,U_74] :
( ( ! [U_71] :
( in(U_71,U_74)
| ! [U_62] :
( ~ in(U_62,U_76)
| ~ in(ordered_pair(U_62,U_71),U_69) ) )
& ! [U_70] :
( ? [U_61] :
( in(U_61,U_76)
& in(ordered_pair(U_61,U_70),U_69) )
| ~ in(U_70,U_74) ) )
| U_74 != relation_image(U_69,U_76) ) )
| ~ relation(U_69) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
fof(f_11_4,plain,
! [U_69] :
( ( ! [U_77,U_75] :
( U_75 = relation_image(U_69,U_77)
| ? [U_73] :
( ~ in(U_73,U_75)
& ? [U_65] :
( in(U_65,U_77)
& in(ordered_pair(U_65,U_73),U_69) ) )
| ? [U_72] :
( ! [U_64] :
( ~ in(U_64,U_77)
| ~ in(ordered_pair(U_64,U_72),U_69) )
& in(U_72,U_75) ) )
& ! [U_76,U_74] :
( ( ! [U_71] :
( in(U_71,U_74)
| ! [U_62] :
( ~ in(U_62,U_76)
| ~ in(ordered_pair(U_62,U_71),U_69) ) )
& ! [U_70] :
( ( in(sK13(U_69,U_76,U_74,U_70),U_76)
& in(ordered_pair(sK13(U_69,U_76,U_74,U_70),U_70),U_69) )
| ~ in(U_70,U_74) ) )
| U_74 != relation_image(U_69,U_76) ) )
| ~ relation(U_69) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_61,sK13(U_69,U_76,U_74,U_70))],[f_11_3]) ).
fof(f_11_5,plain,
! [U_69] :
( ( ! [U_77,U_75] :
( U_75 = relation_image(U_69,U_77)
| ? [U_73] :
( ~ in(U_73,U_75)
& ? [U_65] :
( in(U_65,U_77)
& in(ordered_pair(U_65,U_73),U_69) ) )
| ( ! [U_64] :
( ~ in(U_64,U_77)
| ~ in(ordered_pair(U_64,sK14(U_69,U_77,U_75)),U_69) )
& in(sK14(U_69,U_77,U_75),U_75) ) )
& ! [U_76,U_74] :
( ( ! [U_71] :
( in(U_71,U_74)
| ! [U_62] :
( ~ in(U_62,U_76)
| ~ in(ordered_pair(U_62,U_71),U_69) ) )
& ! [U_70] :
( ( in(sK13(U_69,U_76,U_74,U_70),U_76)
& in(ordered_pair(sK13(U_69,U_76,U_74,U_70),U_70),U_69) )
| ~ in(U_70,U_74) ) )
| U_74 != relation_image(U_69,U_76) ) )
| ~ relation(U_69) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_72,sK14(U_69,U_77,U_75))],[f_11_4]) ).
fof(f_11_6,plain,
! [U_69] :
( ( ! [U_77,U_75] :
( U_75 = relation_image(U_69,U_77)
| ( ~ in(sK15(U_69,U_77,U_75),U_75)
& ? [U_65] :
( in(U_65,U_77)
& in(ordered_pair(U_65,sK15(U_69,U_77,U_75)),U_69) ) )
| ( ! [U_64] :
( ~ in(U_64,U_77)
| ~ in(ordered_pair(U_64,sK14(U_69,U_77,U_75)),U_69) )
& in(sK14(U_69,U_77,U_75),U_75) ) )
& ! [U_76,U_74] :
( ( ! [U_71] :
( in(U_71,U_74)
| ! [U_62] :
( ~ in(U_62,U_76)
| ~ in(ordered_pair(U_62,U_71),U_69) ) )
& ! [U_70] :
( ( in(sK13(U_69,U_76,U_74,U_70),U_76)
& in(ordered_pair(sK13(U_69,U_76,U_74,U_70),U_70),U_69) )
| ~ in(U_70,U_74) ) )
| U_74 != relation_image(U_69,U_76) ) )
| ~ relation(U_69) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_73,sK15(U_69,U_77,U_75))],[f_11_5]) ).
fof(f_11_7,plain,
! [U_69] :
( ( ! [U_77,U_75] :
( U_75 = relation_image(U_69,U_77)
| ( ~ in(sK15(U_69,U_77,U_75),U_75)
& in(sK16(U_69,U_77,U_75),U_77)
& in(ordered_pair(sK16(U_69,U_77,U_75),sK15(U_69,U_77,U_75)),U_69) )
| ( ! [U_64] :
( ~ in(U_64,U_77)
| ~ in(ordered_pair(U_64,sK14(U_69,U_77,U_75)),U_69) )
& in(sK14(U_69,U_77,U_75),U_75) ) )
& ! [U_76,U_74] :
( ( ! [U_71] :
( in(U_71,U_74)
| ! [U_62] :
( ~ in(U_62,U_76)
| ~ in(ordered_pair(U_62,U_71),U_69) ) )
& ! [U_70] :
( ( in(sK13(U_69,U_76,U_74,U_70),U_76)
& in(ordered_pair(sK13(U_69,U_76,U_74,U_70),U_70),U_69) )
| ~ in(U_70,U_74) ) )
| U_74 != relation_image(U_69,U_76) ) )
| ~ relation(U_69) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_65,sK16(U_69,U_77,U_75))],[f_11_6]) ).
cnf(f_11_8,plain,
( in(ordered_pair(sK13(U_69,U_76,U_74,U_70),U_70),U_69)
| ~ in(U_70,U_74)
| U_74 != relation_image(U_69,U_76)
| ~ relation(U_69) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_9,plain,
( in(sK13(U_69,U_76,U_74,U_70),U_76)
| ~ in(U_70,U_74)
| U_74 != relation_image(U_69,U_76)
| ~ relation(U_69) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_10,plain,
( in(U_71,U_74)
| ~ in(U_62,U_76)
| ~ in(ordered_pair(U_62,U_71),U_69)
| U_74 != relation_image(U_69,U_76)
| ~ relation(U_69) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_11,plain,
( in(ordered_pair(sK16(U_69,U_77,U_75),sK15(U_69,U_77,U_75)),U_69)
| in(sK14(U_69,U_77,U_75),U_75)
| U_75 = relation_image(U_69,U_77)
| ~ relation(U_69) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_12,plain,
( in(sK16(U_69,U_77,U_75),U_77)
| in(sK14(U_69,U_77,U_75),U_75)
| U_75 = relation_image(U_69,U_77)
| ~ relation(U_69) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_13,plain,
( ~ in(sK15(U_69,U_77,U_75),U_75)
| in(sK14(U_69,U_77,U_75),U_75)
| U_75 = relation_image(U_69,U_77)
| ~ relation(U_69) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_14,plain,
( in(ordered_pair(sK16(U_69,U_77,U_75),sK15(U_69,U_77,U_75)),U_69)
| ~ in(U_64,U_77)
| ~ in(ordered_pair(U_64,sK14(U_69,U_77,U_75)),U_69)
| U_75 = relation_image(U_69,U_77)
| ~ relation(U_69) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_15,plain,
( in(sK16(U_69,U_77,U_75),U_77)
| ~ in(U_64,U_77)
| ~ in(ordered_pair(U_64,sK14(U_69,U_77,U_75)),U_69)
| U_75 = relation_image(U_69,U_77)
| ~ relation(U_69) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_16,plain,
( ~ in(sK15(U_69,U_77,U_75),U_75)
| ~ in(U_64,U_77)
| ~ in(ordered_pair(U_64,sK14(U_69,U_77,U_75)),U_69)
| U_75 = relation_image(U_69,U_77)
| ~ relation(U_69) ),
inference(clausify,[status(thm)],[f_11_7]) ).
fof(f_12_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_12_2,plain,
! [U_84] :
( ( relation(U_84)
| ? [U_83] :
( ! [U_82,U_81] : U_83 != ordered_pair(U_82,U_81)
& in(U_83,U_84) ) )
& ( ! [U_80] :
( ? [U_79,U_78] : U_80 = ordered_pair(U_79,U_78)
| ~ in(U_80,U_84) )
| ~ relation(U_84) ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_86] :
( relation(U_86)
| ? [U_83] :
( ! [U_82,U_81] : U_83 != ordered_pair(U_82,U_81)
& in(U_83,U_86) ) )
& ! [U_85] :
( ! [U_80] :
( ? [U_79,U_78] : U_80 = ordered_pair(U_79,U_78)
| ~ in(U_80,U_85) )
| ~ relation(U_85) ) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
( ! [U_86] :
( relation(U_86)
| ? [U_83] :
( ! [U_82,U_81] : U_83 != ordered_pair(U_82,U_81)
& in(U_83,U_86) ) )
& ! [U_85] :
( ! [U_80] :
( ? [U_78] : U_80 = ordered_pair(sK17(U_85,U_80),U_78)
| ~ in(U_80,U_85) )
| ~ relation(U_85) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_79,sK17(U_85,U_80))],[f_12_3]) ).
fof(f_12_5,plain,
( ! [U_86] :
( relation(U_86)
| ? [U_83] :
( ! [U_82,U_81] : U_83 != ordered_pair(U_82,U_81)
& in(U_83,U_86) ) )
& ! [U_85] :
( ! [U_80] :
( U_80 = ordered_pair(sK17(U_85,U_80),sK18(U_85,U_80))
| ~ in(U_80,U_85) )
| ~ relation(U_85) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_78,sK18(U_85,U_80))],[f_12_4]) ).
fof(f_12_6,plain,
( ! [U_86] :
( relation(U_86)
| ( ! [U_82,U_81] : sK19(U_86) != ordered_pair(U_82,U_81)
& in(sK19(U_86),U_86) ) )
& ! [U_85] :
( ! [U_80] :
( U_80 = ordered_pair(sK17(U_85,U_80),sK18(U_85,U_80))
| ~ in(U_80,U_85) )
| ~ relation(U_85) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_83,sK19(U_86))],[f_12_5]) ).
cnf(f_12_7,plain,
( U_80 = ordered_pair(sK17(U_85,U_80),sK18(U_85,U_80))
| ~ in(U_80,U_85)
| ~ relation(U_85) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_8,plain,
( in(sK19(U_86),U_86)
| relation(U_86) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_9,plain,
( sK19(U_86) != ordered_pair(U_82,U_81)
| relation(U_86) ),
inference(clausify,[status(thm)],[f_12_6]) ).
fof(f_13_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_13_2,plain,
! [U_94,U_93] :
( ( ( ( U_93 = set_meet(U_94)
| U_93 != empty_set )
& ( U_93 = empty_set
| U_93 != set_meet(U_94) ) )
| U_94 != empty_set )
& ( ( ( U_93 = set_meet(U_94)
| ? [U_92] :
( ( ~ in(U_92,U_93)
& ! [U_91] :
( in(U_92,U_91)
| ~ in(U_91,U_94) ) )
| ( ? [U_90] :
( ~ in(U_92,U_90)
& in(U_90,U_94) )
& in(U_92,U_93) ) ) )
& ( ! [U_89] :
( ( in(U_89,U_93)
| ? [U_88] :
( ~ in(U_89,U_88)
& in(U_88,U_94) ) )
& ( ! [U_87] :
( in(U_89,U_87)
| ~ in(U_87,U_94) )
| ~ in(U_89,U_93) ) )
| U_93 != set_meet(U_94) ) )
| U_94 = empty_set ) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_106] :
( ( ! [U_104] :
( U_104 = set_meet(U_106)
| U_104 != empty_set )
& ! [U_103] :
( U_103 = empty_set
| U_103 != set_meet(U_106) ) )
| U_106 != empty_set )
& ! [U_105] :
( ( ! [U_102] :
( U_102 = set_meet(U_105)
| ? [U_98] :
( ~ in(U_98,U_102)
& ! [U_91] :
( in(U_98,U_91)
| ~ in(U_91,U_105) ) )
| ? [U_97] :
( ? [U_90] :
( ~ in(U_97,U_90)
& in(U_90,U_105) )
& in(U_97,U_102) ) )
& ! [U_101] :
( ( ! [U_96] :
( in(U_96,U_101)
| ? [U_88] :
( ~ in(U_96,U_88)
& in(U_88,U_105) ) )
& ! [U_95] :
( ! [U_87] :
( in(U_95,U_87)
| ~ in(U_87,U_105) )
| ~ in(U_95,U_101) ) )
| U_101 != set_meet(U_105) ) )
| U_105 = empty_set ) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
fof(f_13_4,plain,
( ! [U_106] :
( ( ! [U_104] :
( U_104 = set_meet(U_106)
| U_104 != empty_set )
& ! [U_103] :
( U_103 = empty_set
| U_103 != set_meet(U_106) ) )
| U_106 != empty_set )
& ! [U_105] :
( ( ! [U_102] :
( U_102 = set_meet(U_105)
| ? [U_98] :
( ~ in(U_98,U_102)
& ! [U_91] :
( in(U_98,U_91)
| ~ in(U_91,U_105) ) )
| ? [U_97] :
( ? [U_90] :
( ~ in(U_97,U_90)
& in(U_90,U_105) )
& in(U_97,U_102) ) )
& ! [U_101] :
( ( ! [U_96] :
( in(U_96,U_101)
| ( ~ in(U_96,sK20(U_105,U_101,U_96))
& in(sK20(U_105,U_101,U_96),U_105) ) )
& ! [U_95] :
( ! [U_87] :
( in(U_95,U_87)
| ~ in(U_87,U_105) )
| ~ in(U_95,U_101) ) )
| U_101 != set_meet(U_105) ) )
| U_105 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_88,sK20(U_105,U_101,U_96))],[f_13_3]) ).
fof(f_13_5,plain,
( ! [U_106] :
( ( ! [U_104] :
( U_104 = set_meet(U_106)
| U_104 != empty_set )
& ! [U_103] :
( U_103 = empty_set
| U_103 != set_meet(U_106) ) )
| U_106 != empty_set )
& ! [U_105] :
( ( ! [U_102] :
( U_102 = set_meet(U_105)
| ? [U_98] :
( ~ in(U_98,U_102)
& ! [U_91] :
( in(U_98,U_91)
| ~ in(U_91,U_105) ) )
| ( ? [U_90] :
( ~ in(sK21(U_105,U_102),U_90)
& in(U_90,U_105) )
& in(sK21(U_105,U_102),U_102) ) )
& ! [U_101] :
( ( ! [U_96] :
( in(U_96,U_101)
| ( ~ in(U_96,sK20(U_105,U_101,U_96))
& in(sK20(U_105,U_101,U_96),U_105) ) )
& ! [U_95] :
( ! [U_87] :
( in(U_95,U_87)
| ~ in(U_87,U_105) )
| ~ in(U_95,U_101) ) )
| U_101 != set_meet(U_105) ) )
| U_105 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_97,sK21(U_105,U_102))],[f_13_4]) ).
fof(f_13_6,plain,
( ! [U_106] :
( ( ! [U_104] :
( U_104 = set_meet(U_106)
| U_104 != empty_set )
& ! [U_103] :
( U_103 = empty_set
| U_103 != set_meet(U_106) ) )
| U_106 != empty_set )
& ! [U_105] :
( ( ! [U_102] :
( U_102 = set_meet(U_105)
| ? [U_98] :
( ~ in(U_98,U_102)
& ! [U_91] :
( in(U_98,U_91)
| ~ in(U_91,U_105) ) )
| ( ~ in(sK21(U_105,U_102),sK22(U_105,U_102))
& in(sK22(U_105,U_102),U_105)
& in(sK21(U_105,U_102),U_102) ) )
& ! [U_101] :
( ( ! [U_96] :
( in(U_96,U_101)
| ( ~ in(U_96,sK20(U_105,U_101,U_96))
& in(sK20(U_105,U_101,U_96),U_105) ) )
& ! [U_95] :
( ! [U_87] :
( in(U_95,U_87)
| ~ in(U_87,U_105) )
| ~ in(U_95,U_101) ) )
| U_101 != set_meet(U_105) ) )
| U_105 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_90,sK22(U_105,U_102))],[f_13_5]) ).
fof(f_13_7,plain,
( ! [U_106] :
( ( ! [U_104] :
( U_104 = set_meet(U_106)
| U_104 != empty_set )
& ! [U_103] :
( U_103 = empty_set
| U_103 != set_meet(U_106) ) )
| U_106 != empty_set )
& ! [U_105] :
( ( ! [U_102] :
( U_102 = set_meet(U_105)
| ( ~ in(sK23(U_105,U_102),U_102)
& ! [U_91] :
( in(sK23(U_105,U_102),U_91)
| ~ in(U_91,U_105) ) )
| ( ~ in(sK21(U_105,U_102),sK22(U_105,U_102))
& in(sK22(U_105,U_102),U_105)
& in(sK21(U_105,U_102),U_102) ) )
& ! [U_101] :
( ( ! [U_96] :
( in(U_96,U_101)
| ( ~ in(U_96,sK20(U_105,U_101,U_96))
& in(sK20(U_105,U_101,U_96),U_105) ) )
& ! [U_95] :
( ! [U_87] :
( in(U_95,U_87)
| ~ in(U_87,U_105) )
| ~ in(U_95,U_101) ) )
| U_101 != set_meet(U_105) ) )
| U_105 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_98,sK23(U_105,U_102))],[f_13_6]) ).
cnf(f_13_8,plain,
( in(U_95,U_87)
| ~ in(U_87,U_105)
| ~ in(U_95,U_101)
| U_101 != set_meet(U_105)
| U_105 = empty_set ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_9,plain,
( in(sK20(U_105,U_101,U_96),U_105)
| in(U_96,U_101)
| U_101 != set_meet(U_105)
| U_105 = empty_set ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_10,plain,
( ~ in(U_96,sK20(U_105,U_101,U_96))
| in(U_96,U_101)
| U_101 != set_meet(U_105)
| U_105 = empty_set ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_11,plain,
( in(sK23(U_105,U_102),U_91)
| ~ in(U_91,U_105)
| in(sK21(U_105,U_102),U_102)
| U_102 = set_meet(U_105)
| U_105 = empty_set ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_12,plain,
( ~ in(sK23(U_105,U_102),U_102)
| in(sK21(U_105,U_102),U_102)
| U_102 = set_meet(U_105)
| U_105 = empty_set ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_13,plain,
( in(sK22(U_105,U_102),U_105)
| in(sK23(U_105,U_102),U_91)
| ~ in(U_91,U_105)
| U_102 = set_meet(U_105)
| U_105 = empty_set ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_14,plain,
( ~ in(sK21(U_105,U_102),sK22(U_105,U_102))
| in(sK23(U_105,U_102),U_91)
| ~ in(U_91,U_105)
| U_102 = set_meet(U_105)
| U_105 = empty_set ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_15,plain,
( in(sK22(U_105,U_102),U_105)
| ~ in(sK23(U_105,U_102),U_102)
| U_102 = set_meet(U_105)
| U_105 = empty_set ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_16,plain,
( ~ in(sK21(U_105,U_102),sK22(U_105,U_102))
| ~ in(sK23(U_105,U_102),U_102)
| U_102 = set_meet(U_105)
| U_105 = empty_set ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_17,plain,
( U_103 = empty_set
| U_103 != set_meet(U_106)
| U_106 != empty_set ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_18,plain,
( U_104 = set_meet(U_106)
| U_104 != empty_set
| U_106 != empty_set ),
inference(clausify,[status(thm)],[f_13_7]) ).
fof(f_14_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_14_2,plain,
! [U_110,U_109] :
( ( U_109 = singleton(U_110)
| ? [U_108] :
( ( ~ in(U_108,U_109)
& U_108 = U_110 )
| ( U_108 != U_110
& in(U_108,U_109) ) ) )
& ( ! [U_107] :
( ( in(U_107,U_109)
| U_107 != U_110 )
& ( U_107 = U_110
| ~ in(U_107,U_109) ) )
| U_109 != singleton(U_110) ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_118,U_116] :
( U_116 = singleton(U_118)
| ? [U_114] :
( ~ in(U_114,U_116)
& U_114 = U_118 )
| ? [U_113] :
( U_113 != U_118
& in(U_113,U_116) ) )
& ! [U_117,U_115] :
( ( ! [U_112] :
( in(U_112,U_115)
| U_112 != U_117 )
& ! [U_111] :
( U_111 = U_117
| ~ in(U_111,U_115) ) )
| U_115 != singleton(U_117) ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
fof(f_14_4,plain,
( ! [U_118,U_116] :
( U_116 = singleton(U_118)
| ? [U_114] :
( ~ in(U_114,U_116)
& U_114 = U_118 )
| ( sK24(U_118,U_116) != U_118
& in(sK24(U_118,U_116),U_116) ) )
& ! [U_117,U_115] :
( ( ! [U_112] :
( in(U_112,U_115)
| U_112 != U_117 )
& ! [U_111] :
( U_111 = U_117
| ~ in(U_111,U_115) ) )
| U_115 != singleton(U_117) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_113,sK24(U_118,U_116))],[f_14_3]) ).
fof(f_14_5,plain,
( ! [U_118,U_116] :
( U_116 = singleton(U_118)
| ( ~ in(sK25(U_118,U_116),U_116)
& sK25(U_118,U_116) = U_118 )
| ( sK24(U_118,U_116) != U_118
& in(sK24(U_118,U_116),U_116) ) )
& ! [U_117,U_115] :
( ( ! [U_112] :
( in(U_112,U_115)
| U_112 != U_117 )
& ! [U_111] :
( U_111 = U_117
| ~ in(U_111,U_115) ) )
| U_115 != singleton(U_117) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_114,sK25(U_118,U_116))],[f_14_4]) ).
cnf(f_14_6,plain,
( U_111 = U_117
| ~ in(U_111,U_115)
| U_115 != singleton(U_117) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_7,plain,
( in(U_112,U_115)
| U_112 != U_117
| U_115 != singleton(U_117) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_8,plain,
( sK25(U_118,U_116) = U_118
| in(sK24(U_118,U_116),U_116)
| U_116 = singleton(U_118) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_9,plain,
( ~ in(sK25(U_118,U_116),U_116)
| in(sK24(U_118,U_116),U_116)
| U_116 = singleton(U_118) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_10,plain,
( sK25(U_118,U_116) = U_118
| sK24(U_118,U_116) != U_118
| U_116 = singleton(U_118) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_11,plain,
( ~ in(sK25(U_118,U_116),U_116)
| sK24(U_118,U_116) != U_118
| U_116 = singleton(U_118) ),
inference(clausify,[status(thm)],[f_14_5]) ).
fof(f_15_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_15_2,plain,
! [U_121] :
( ( U_121 = empty_set
| ? [U_120] : in(U_120,U_121) )
& ( ! [U_119] : ~ in(U_119,U_121)
| U_121 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ! [U_123] :
( U_123 = empty_set
| ? [U_120] : in(U_120,U_123) )
& ! [U_122] :
( ! [U_119] : ~ in(U_119,U_122)
| U_122 != empty_set ) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
fof(f_15_4,plain,
( ! [U_123] :
( U_123 = empty_set
| in(sK26(U_123),U_123) )
& ! [U_122] :
( ! [U_119] : ~ in(U_119,U_122)
| U_122 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_120,sK26(U_123))],[f_15_3]) ).
cnf(f_15_5,plain,
( ~ in(U_119,U_122)
| U_122 != empty_set ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_6,plain,
( U_123 = empty_set
| in(sK26(U_123),U_123) ),
inference(clausify,[status(thm)],[f_15_4]) ).
fof(f_16_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_16_2,plain,
! [U_127,U_126] :
( ( U_126 = powerset(U_127)
| ? [U_125] :
( ( ~ in(U_125,U_126)
& subset(U_125,U_127) )
| ( ~ subset(U_125,U_127)
& in(U_125,U_126) ) ) )
& ( ! [U_124] :
( ( in(U_124,U_126)
| ~ subset(U_124,U_127) )
& ( subset(U_124,U_127)
| ~ in(U_124,U_126) ) )
| U_126 != powerset(U_127) ) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( ! [U_135,U_133] :
( U_133 = powerset(U_135)
| ? [U_131] :
( ~ in(U_131,U_133)
& subset(U_131,U_135) )
| ? [U_130] :
( ~ subset(U_130,U_135)
& in(U_130,U_133) ) )
& ! [U_134,U_132] :
( ( ! [U_129] :
( in(U_129,U_132)
| ~ subset(U_129,U_134) )
& ! [U_128] :
( subset(U_128,U_134)
| ~ in(U_128,U_132) ) )
| U_132 != powerset(U_134) ) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
fof(f_16_4,plain,
( ! [U_135,U_133] :
( U_133 = powerset(U_135)
| ? [U_131] :
( ~ in(U_131,U_133)
& subset(U_131,U_135) )
| ( ~ subset(sK27(U_135,U_133),U_135)
& in(sK27(U_135,U_133),U_133) ) )
& ! [U_134,U_132] :
( ( ! [U_129] :
( in(U_129,U_132)
| ~ subset(U_129,U_134) )
& ! [U_128] :
( subset(U_128,U_134)
| ~ in(U_128,U_132) ) )
| U_132 != powerset(U_134) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_130,sK27(U_135,U_133))],[f_16_3]) ).
fof(f_16_5,plain,
( ! [U_135,U_133] :
( U_133 = powerset(U_135)
| ( ~ in(sK28(U_135,U_133),U_133)
& subset(sK28(U_135,U_133),U_135) )
| ( ~ subset(sK27(U_135,U_133),U_135)
& in(sK27(U_135,U_133),U_133) ) )
& ! [U_134,U_132] :
( ( ! [U_129] :
( in(U_129,U_132)
| ~ subset(U_129,U_134) )
& ! [U_128] :
( subset(U_128,U_134)
| ~ in(U_128,U_132) ) )
| U_132 != powerset(U_134) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_131,sK28(U_135,U_133))],[f_16_4]) ).
cnf(f_16_6,plain,
( subset(U_128,U_134)
| ~ in(U_128,U_132)
| U_132 != powerset(U_134) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_7,plain,
( in(U_129,U_132)
| ~ subset(U_129,U_134)
| U_132 != powerset(U_134) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_8,plain,
( subset(sK28(U_135,U_133),U_135)
| in(sK27(U_135,U_133),U_133)
| U_133 = powerset(U_135) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_9,plain,
( ~ in(sK28(U_135,U_133),U_133)
| in(sK27(U_135,U_133),U_133)
| U_133 = powerset(U_135) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_10,plain,
( subset(sK28(U_135,U_133),U_135)
| ~ subset(sK27(U_135,U_133),U_135)
| U_133 = powerset(U_135) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_11,plain,
( ~ in(sK28(U_135,U_133),U_133)
| ~ subset(sK27(U_135,U_133),U_135)
| U_133 = powerset(U_135) ),
inference(clausify,[status(thm)],[f_16_5]) ).
fof(f_17_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_17_2,plain,
! [U_141] :
( ! [U_140] :
( ( ( U_141 = U_140
| ? [U_139,U_138] :
( ( ~ in(ordered_pair(U_139,U_138),U_141)
& in(ordered_pair(U_139,U_138),U_140) )
| ( ~ in(ordered_pair(U_139,U_138),U_140)
& in(ordered_pair(U_139,U_138),U_141) ) ) )
& ( ! [U_137,U_136] :
( ( in(ordered_pair(U_137,U_136),U_141)
| ~ in(ordered_pair(U_137,U_136),U_140) )
& ( in(ordered_pair(U_137,U_136),U_140)
| ~ in(ordered_pair(U_137,U_136),U_141) ) )
| U_141 != U_140 ) )
| ~ relation(U_140) )
| ~ relation(U_141) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_141] :
( ! [U_140] :
( ( ( U_141 = U_140
| ? [U_149,U_147] :
( ~ in(ordered_pair(U_149,U_147),U_141)
& in(ordered_pair(U_149,U_147),U_140) )
| ? [U_148,U_146] :
( ~ in(ordered_pair(U_148,U_146),U_140)
& in(ordered_pair(U_148,U_146),U_141) ) )
& ( ( ! [U_145,U_143] :
( in(ordered_pair(U_145,U_143),U_141)
| ~ in(ordered_pair(U_145,U_143),U_140) )
& ! [U_144,U_142] :
( in(ordered_pair(U_144,U_142),U_140)
| ~ in(ordered_pair(U_144,U_142),U_141) ) )
| U_141 != U_140 ) )
| ~ relation(U_140) )
| ~ relation(U_141) ),
inference(miniscope,[status(thm)],[f_17_2]) ).
fof(f_17_4,plain,
! [U_141] :
( ! [U_140] :
( ( ( U_141 = U_140
| ? [U_149,U_147] :
( ~ in(ordered_pair(U_149,U_147),U_141)
& in(ordered_pair(U_149,U_147),U_140) )
| ? [U_146] :
( ~ in(ordered_pair(sK29(U_141,U_140),U_146),U_140)
& in(ordered_pair(sK29(U_141,U_140),U_146),U_141) ) )
& ( ( ! [U_145,U_143] :
( in(ordered_pair(U_145,U_143),U_141)
| ~ in(ordered_pair(U_145,U_143),U_140) )
& ! [U_144,U_142] :
( in(ordered_pair(U_144,U_142),U_140)
| ~ in(ordered_pair(U_144,U_142),U_141) ) )
| U_141 != U_140 ) )
| ~ relation(U_140) )
| ~ relation(U_141) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_148,sK29(U_141,U_140))],[f_17_3]) ).
fof(f_17_5,plain,
! [U_141] :
( ! [U_140] :
( ( ( U_141 = U_140
| ? [U_149,U_147] :
( ~ in(ordered_pair(U_149,U_147),U_141)
& in(ordered_pair(U_149,U_147),U_140) )
| ( ~ in(ordered_pair(sK29(U_141,U_140),sK30(U_141,U_140)),U_140)
& in(ordered_pair(sK29(U_141,U_140),sK30(U_141,U_140)),U_141) ) )
& ( ( ! [U_145,U_143] :
( in(ordered_pair(U_145,U_143),U_141)
| ~ in(ordered_pair(U_145,U_143),U_140) )
& ! [U_144,U_142] :
( in(ordered_pair(U_144,U_142),U_140)
| ~ in(ordered_pair(U_144,U_142),U_141) ) )
| U_141 != U_140 ) )
| ~ relation(U_140) )
| ~ relation(U_141) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_146,sK30(U_141,U_140))],[f_17_4]) ).
fof(f_17_6,plain,
! [U_141] :
( ! [U_140] :
( ( ( U_141 = U_140
| ? [U_147] :
( ~ in(ordered_pair(sK31(U_141,U_140),U_147),U_141)
& in(ordered_pair(sK31(U_141,U_140),U_147),U_140) )
| ( ~ in(ordered_pair(sK29(U_141,U_140),sK30(U_141,U_140)),U_140)
& in(ordered_pair(sK29(U_141,U_140),sK30(U_141,U_140)),U_141) ) )
& ( ( ! [U_145,U_143] :
( in(ordered_pair(U_145,U_143),U_141)
| ~ in(ordered_pair(U_145,U_143),U_140) )
& ! [U_144,U_142] :
( in(ordered_pair(U_144,U_142),U_140)
| ~ in(ordered_pair(U_144,U_142),U_141) ) )
| U_141 != U_140 ) )
| ~ relation(U_140) )
| ~ relation(U_141) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_149,sK31(U_141,U_140))],[f_17_5]) ).
fof(f_17_7,plain,
! [U_141] :
( ! [U_140] :
( ( ( U_141 = U_140
| ( ~ in(ordered_pair(sK31(U_141,U_140),sK32(U_141,U_140)),U_141)
& in(ordered_pair(sK31(U_141,U_140),sK32(U_141,U_140)),U_140) )
| ( ~ in(ordered_pair(sK29(U_141,U_140),sK30(U_141,U_140)),U_140)
& in(ordered_pair(sK29(U_141,U_140),sK30(U_141,U_140)),U_141) ) )
& ( ( ! [U_145,U_143] :
( in(ordered_pair(U_145,U_143),U_141)
| ~ in(ordered_pair(U_145,U_143),U_140) )
& ! [U_144,U_142] :
( in(ordered_pair(U_144,U_142),U_140)
| ~ in(ordered_pair(U_144,U_142),U_141) ) )
| U_141 != U_140 ) )
| ~ relation(U_140) )
| ~ relation(U_141) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_147,sK32(U_141,U_140))],[f_17_6]) ).
cnf(f_17_8,plain,
( in(ordered_pair(U_144,U_142),U_140)
| ~ in(ordered_pair(U_144,U_142),U_141)
| U_141 != U_140
| ~ relation(U_140)
| ~ relation(U_141) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_9,plain,
( in(ordered_pair(U_145,U_143),U_141)
| ~ in(ordered_pair(U_145,U_143),U_140)
| U_141 != U_140
| ~ relation(U_140)
| ~ relation(U_141) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_10,plain,
( in(ordered_pair(sK31(U_141,U_140),sK32(U_141,U_140)),U_140)
| in(ordered_pair(sK29(U_141,U_140),sK30(U_141,U_140)),U_141)
| U_141 = U_140
| ~ relation(U_140)
| ~ relation(U_141) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_11,plain,
( ~ in(ordered_pair(sK31(U_141,U_140),sK32(U_141,U_140)),U_141)
| in(ordered_pair(sK29(U_141,U_140),sK30(U_141,U_140)),U_141)
| U_141 = U_140
| ~ relation(U_140)
| ~ relation(U_141) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_12,plain,
( in(ordered_pair(sK31(U_141,U_140),sK32(U_141,U_140)),U_140)
| ~ in(ordered_pair(sK29(U_141,U_140),sK30(U_141,U_140)),U_140)
| U_141 = U_140
| ~ relation(U_140)
| ~ relation(U_141) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_13,plain,
( ~ in(ordered_pair(sK31(U_141,U_140),sK32(U_141,U_140)),U_141)
| ~ in(ordered_pair(sK29(U_141,U_140),sK30(U_141,U_140)),U_140)
| U_141 = U_140
| ~ relation(U_140)
| ~ relation(U_141) ),
inference(clausify,[status(thm)],[f_17_7]) ).
fof(f_18_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_18_2,plain,
! [U_151,U_150] :
( ( ( ( element(U_150,U_151)
| ~ empty(U_150) )
& ( empty(U_150)
| ~ element(U_150,U_151) ) )
| ~ empty(U_151) )
& ( ( ( element(U_150,U_151)
| ~ in(U_150,U_151) )
& ( in(U_150,U_151)
| ~ element(U_150,U_151) ) )
| empty(U_151) ) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( ! [U_159] :
( ( ! [U_157] :
( element(U_157,U_159)
| ~ empty(U_157) )
& ! [U_156] :
( empty(U_156)
| ~ element(U_156,U_159) ) )
| ~ empty(U_159) )
& ! [U_158] :
( ( ! [U_155] :
( element(U_155,U_158)
| ~ in(U_155,U_158) )
& ! [U_154] :
( in(U_154,U_158)
| ~ element(U_154,U_158) ) )
| empty(U_158) ) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
cnf(f_18_4,plain,
( in(U_154,U_158)
| ~ element(U_154,U_158)
| empty(U_158) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_5,plain,
( element(U_155,U_158)
| ~ in(U_155,U_158)
| empty(U_158) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_6,plain,
( empty(U_156)
| ~ element(U_156,U_159)
| ~ empty(U_159) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_7,plain,
( element(U_157,U_159)
| ~ empty(U_157)
| ~ empty(U_159) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_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_19_2,plain,
! [U_164,U_163,U_162] :
( ( U_162 = unordered_pair(U_164,U_163)
| ? [U_161] :
( ( ~ in(U_161,U_162)
& ( U_161 = U_163
| U_161 = U_164 ) )
| ( U_161 != U_163
& U_161 != U_164
& in(U_161,U_162) ) ) )
& ( ! [U_160] :
( ( in(U_160,U_162)
| ( U_160 != U_163
& U_160 != U_164 ) )
& ( U_160 = U_163
| U_160 = U_164
| ~ in(U_160,U_162) ) )
| U_162 != unordered_pair(U_164,U_163) ) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( ! [U_174,U_172,U_170] :
( U_170 = unordered_pair(U_174,U_172)
| ? [U_168] :
( ~ in(U_168,U_170)
& ( U_168 = U_172
| U_168 = U_174 ) )
| ? [U_167] :
( U_167 != U_172
& U_167 != U_174
& in(U_167,U_170) ) )
& ! [U_173,U_171,U_169] :
( ( ! [U_166] :
( in(U_166,U_169)
| ( U_166 != U_171
& U_166 != U_173 ) )
& ! [U_165] :
( U_165 = U_171
| U_165 = U_173
| ~ in(U_165,U_169) ) )
| U_169 != unordered_pair(U_173,U_171) ) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
fof(f_19_4,plain,
( ! [U_174,U_172,U_170] :
( U_170 = unordered_pair(U_174,U_172)
| ? [U_168] :
( ~ in(U_168,U_170)
& ( U_168 = U_172
| U_168 = U_174 ) )
| ( sK33(U_174,U_172,U_170) != U_172
& sK33(U_174,U_172,U_170) != U_174
& in(sK33(U_174,U_172,U_170),U_170) ) )
& ! [U_173,U_171,U_169] :
( ( ! [U_166] :
( in(U_166,U_169)
| ( U_166 != U_171
& U_166 != U_173 ) )
& ! [U_165] :
( U_165 = U_171
| U_165 = U_173
| ~ in(U_165,U_169) ) )
| U_169 != unordered_pair(U_173,U_171) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_167,sK33(U_174,U_172,U_170))],[f_19_3]) ).
fof(f_19_5,plain,
( ! [U_174,U_172,U_170] :
( U_170 = unordered_pair(U_174,U_172)
| ( ~ in(sK34(U_174,U_172,U_170),U_170)
& ( sK34(U_174,U_172,U_170) = U_172
| sK34(U_174,U_172,U_170) = U_174 ) )
| ( sK33(U_174,U_172,U_170) != U_172
& sK33(U_174,U_172,U_170) != U_174
& in(sK33(U_174,U_172,U_170),U_170) ) )
& ! [U_173,U_171,U_169] :
( ( ! [U_166] :
( in(U_166,U_169)
| ( U_166 != U_171
& U_166 != U_173 ) )
& ! [U_165] :
( U_165 = U_171
| U_165 = U_173
| ~ in(U_165,U_169) ) )
| U_169 != unordered_pair(U_173,U_171) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_168,sK34(U_174,U_172,U_170))],[f_19_4]) ).
cnf(f_19_6,plain,
( U_165 = U_171
| U_165 = U_173
| ~ in(U_165,U_169)
| U_169 != unordered_pair(U_173,U_171) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_7,plain,
( U_166 != U_173
| in(U_166,U_169)
| U_169 != unordered_pair(U_173,U_171) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_8,plain,
( U_166 != U_171
| in(U_166,U_169)
| U_169 != unordered_pair(U_173,U_171) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_9,plain,
( sK34(U_174,U_172,U_170) = U_172
| sK34(U_174,U_172,U_170) = U_174
| in(sK33(U_174,U_172,U_170),U_170)
| U_170 = unordered_pair(U_174,U_172) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_10,plain,
( ~ in(sK34(U_174,U_172,U_170),U_170)
| in(sK33(U_174,U_172,U_170),U_170)
| U_170 = unordered_pair(U_174,U_172) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_11,plain,
( sK33(U_174,U_172,U_170) != U_174
| sK34(U_174,U_172,U_170) = U_172
| sK34(U_174,U_172,U_170) = U_174
| U_170 = unordered_pair(U_174,U_172) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_12,plain,
( sK33(U_174,U_172,U_170) != U_172
| sK34(U_174,U_172,U_170) = U_172
| sK34(U_174,U_172,U_170) = U_174
| U_170 = unordered_pair(U_174,U_172) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_13,plain,
( sK33(U_174,U_172,U_170) != U_174
| ~ in(sK34(U_174,U_172,U_170),U_170)
| U_170 = unordered_pair(U_174,U_172) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_14,plain,
( sK33(U_174,U_172,U_170) != U_172
| ~ in(sK34(U_174,U_172,U_170),U_170)
| U_170 = unordered_pair(U_174,U_172) ),
inference(clausify,[status(thm)],[f_19_5]) ).
fof(f_20_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_20_2,plain,
! [U_179,U_178,U_177] :
( ( U_177 = set_union2(U_179,U_178)
| ? [U_176] :
( ( ~ in(U_176,U_177)
& ( in(U_176,U_178)
| in(U_176,U_179) ) )
| ( ~ in(U_176,U_178)
& ~ in(U_176,U_179)
& in(U_176,U_177) ) ) )
& ( ! [U_175] :
( ( in(U_175,U_177)
| ( ~ in(U_175,U_178)
& ~ in(U_175,U_179) ) )
& ( in(U_175,U_178)
| in(U_175,U_179)
| ~ in(U_175,U_177) ) )
| U_177 != set_union2(U_179,U_178) ) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( ! [U_189,U_187,U_185] :
( U_185 = set_union2(U_189,U_187)
| ? [U_183] :
( ~ in(U_183,U_185)
& ( in(U_183,U_187)
| in(U_183,U_189) ) )
| ? [U_182] :
( ~ in(U_182,U_187)
& ~ in(U_182,U_189)
& in(U_182,U_185) ) )
& ! [U_188,U_186,U_184] :
( ( ! [U_181] :
( in(U_181,U_184)
| ( ~ in(U_181,U_186)
& ~ in(U_181,U_188) ) )
& ! [U_180] :
( in(U_180,U_186)
| in(U_180,U_188)
| ~ in(U_180,U_184) ) )
| U_184 != set_union2(U_188,U_186) ) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
fof(f_20_4,plain,
( ! [U_189,U_187,U_185] :
( U_185 = set_union2(U_189,U_187)
| ? [U_183] :
( ~ in(U_183,U_185)
& ( in(U_183,U_187)
| in(U_183,U_189) ) )
| ( ~ in(sK35(U_189,U_187,U_185),U_187)
& ~ in(sK35(U_189,U_187,U_185),U_189)
& in(sK35(U_189,U_187,U_185),U_185) ) )
& ! [U_188,U_186,U_184] :
( ( ! [U_181] :
( in(U_181,U_184)
| ( ~ in(U_181,U_186)
& ~ in(U_181,U_188) ) )
& ! [U_180] :
( in(U_180,U_186)
| in(U_180,U_188)
| ~ in(U_180,U_184) ) )
| U_184 != set_union2(U_188,U_186) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_182,sK35(U_189,U_187,U_185))],[f_20_3]) ).
fof(f_20_5,plain,
( ! [U_189,U_187,U_185] :
( U_185 = set_union2(U_189,U_187)
| ( ~ in(sK36(U_189,U_187,U_185),U_185)
& ( in(sK36(U_189,U_187,U_185),U_187)
| in(sK36(U_189,U_187,U_185),U_189) ) )
| ( ~ in(sK35(U_189,U_187,U_185),U_187)
& ~ in(sK35(U_189,U_187,U_185),U_189)
& in(sK35(U_189,U_187,U_185),U_185) ) )
& ! [U_188,U_186,U_184] :
( ( ! [U_181] :
( in(U_181,U_184)
| ( ~ in(U_181,U_186)
& ~ in(U_181,U_188) ) )
& ! [U_180] :
( in(U_180,U_186)
| in(U_180,U_188)
| ~ in(U_180,U_184) ) )
| U_184 != set_union2(U_188,U_186) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_183,sK36(U_189,U_187,U_185))],[f_20_4]) ).
cnf(f_20_6,plain,
( in(U_180,U_186)
| in(U_180,U_188)
| ~ in(U_180,U_184)
| U_184 != set_union2(U_188,U_186) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_7,plain,
( ~ in(U_181,U_188)
| in(U_181,U_184)
| U_184 != set_union2(U_188,U_186) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_8,plain,
( ~ in(U_181,U_186)
| in(U_181,U_184)
| U_184 != set_union2(U_188,U_186) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_9,plain,
( in(sK36(U_189,U_187,U_185),U_187)
| in(sK36(U_189,U_187,U_185),U_189)
| in(sK35(U_189,U_187,U_185),U_185)
| U_185 = set_union2(U_189,U_187) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_10,plain,
( ~ in(sK36(U_189,U_187,U_185),U_185)
| in(sK35(U_189,U_187,U_185),U_185)
| U_185 = set_union2(U_189,U_187) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_11,plain,
( ~ in(sK35(U_189,U_187,U_185),U_189)
| in(sK36(U_189,U_187,U_185),U_187)
| in(sK36(U_189,U_187,U_185),U_189)
| U_185 = set_union2(U_189,U_187) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_12,plain,
( ~ in(sK35(U_189,U_187,U_185),U_187)
| in(sK36(U_189,U_187,U_185),U_187)
| in(sK36(U_189,U_187,U_185),U_189)
| U_185 = set_union2(U_189,U_187) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_13,plain,
( ~ in(sK35(U_189,U_187,U_185),U_189)
| ~ in(sK36(U_189,U_187,U_185),U_185)
| U_185 = set_union2(U_189,U_187) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_14,plain,
( ~ in(sK35(U_189,U_187,U_185),U_187)
| ~ in(sK36(U_189,U_187,U_185),U_185)
| U_185 = set_union2(U_189,U_187) ),
inference(clausify,[status(thm)],[f_20_5]) ).
fof(f_21_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_21_2,plain,
! [U_202,U_201,U_200] :
( ( U_200 = cartesian_product2(U_202,U_201)
| ? [U_199] :
( ( ~ in(U_199,U_200)
& ? [U_198,U_197] :
( U_199 = ordered_pair(U_198,U_197)
& in(U_197,U_201)
& in(U_198,U_202) ) )
| ( ! [U_196,U_195] :
( U_199 != ordered_pair(U_196,U_195)
| ~ in(U_195,U_201)
| ~ in(U_196,U_202) )
& in(U_199,U_200) ) ) )
& ( ! [U_194] :
( ( in(U_194,U_200)
| ! [U_193,U_192] :
( U_194 != ordered_pair(U_193,U_192)
| ~ in(U_192,U_201)
| ~ in(U_193,U_202) ) )
& ( ? [U_191,U_190] :
( U_194 = ordered_pair(U_191,U_190)
& in(U_190,U_201)
& in(U_191,U_202) )
| ~ in(U_194,U_200) ) )
| U_200 != cartesian_product2(U_202,U_201) ) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( ! [U_212,U_210,U_208] :
( U_208 = cartesian_product2(U_212,U_210)
| ? [U_206] :
( ~ in(U_206,U_208)
& ? [U_198] :
( ? [U_197] :
( U_206 = ordered_pair(U_198,U_197)
& in(U_197,U_210) )
& in(U_198,U_212) ) )
| ? [U_205] :
( ! [U_196] :
( ! [U_195] :
( U_205 != ordered_pair(U_196,U_195)
| ~ in(U_195,U_210) )
| ~ in(U_196,U_212) )
& in(U_205,U_208) ) )
& ! [U_211,U_209,U_207] :
( ( ! [U_204] :
( in(U_204,U_207)
| ! [U_193] :
( ! [U_192] :
( U_204 != ordered_pair(U_193,U_192)
| ~ in(U_192,U_209) )
| ~ in(U_193,U_211) ) )
& ! [U_203] :
( ? [U_191] :
( ? [U_190] :
( U_203 = ordered_pair(U_191,U_190)
& in(U_190,U_209) )
& in(U_191,U_211) )
| ~ in(U_203,U_207) ) )
| U_207 != cartesian_product2(U_211,U_209) ) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
fof(f_21_4,plain,
( ! [U_212,U_210,U_208] :
( U_208 = cartesian_product2(U_212,U_210)
| ? [U_206] :
( ~ in(U_206,U_208)
& ? [U_198] :
( ? [U_197] :
( U_206 = ordered_pair(U_198,U_197)
& in(U_197,U_210) )
& in(U_198,U_212) ) )
| ? [U_205] :
( ! [U_196] :
( ! [U_195] :
( U_205 != ordered_pair(U_196,U_195)
| ~ in(U_195,U_210) )
| ~ in(U_196,U_212) )
& in(U_205,U_208) ) )
& ! [U_211,U_209,U_207] :
( ( ! [U_204] :
( in(U_204,U_207)
| ! [U_193] :
( ! [U_192] :
( U_204 != ordered_pair(U_193,U_192)
| ~ in(U_192,U_209) )
| ~ in(U_193,U_211) ) )
& ! [U_203] :
( ( ? [U_190] :
( U_203 = ordered_pair(sK37(U_211,U_209,U_207,U_203),U_190)
& in(U_190,U_209) )
& in(sK37(U_211,U_209,U_207,U_203),U_211) )
| ~ in(U_203,U_207) ) )
| U_207 != cartesian_product2(U_211,U_209) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_191,sK37(U_211,U_209,U_207,U_203))],[f_21_3]) ).
fof(f_21_5,plain,
( ! [U_212,U_210,U_208] :
( U_208 = cartesian_product2(U_212,U_210)
| ? [U_206] :
( ~ in(U_206,U_208)
& ? [U_198] :
( ? [U_197] :
( U_206 = ordered_pair(U_198,U_197)
& in(U_197,U_210) )
& in(U_198,U_212) ) )
| ? [U_205] :
( ! [U_196] :
( ! [U_195] :
( U_205 != ordered_pair(U_196,U_195)
| ~ in(U_195,U_210) )
| ~ in(U_196,U_212) )
& in(U_205,U_208) ) )
& ! [U_211,U_209,U_207] :
( ( ! [U_204] :
( in(U_204,U_207)
| ! [U_193] :
( ! [U_192] :
( U_204 != ordered_pair(U_193,U_192)
| ~ in(U_192,U_209) )
| ~ in(U_193,U_211) ) )
& ! [U_203] :
( ( U_203 = ordered_pair(sK37(U_211,U_209,U_207,U_203),sK38(U_211,U_209,U_207,U_203))
& in(sK38(U_211,U_209,U_207,U_203),U_209)
& in(sK37(U_211,U_209,U_207,U_203),U_211) )
| ~ in(U_203,U_207) ) )
| U_207 != cartesian_product2(U_211,U_209) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_190,sK38(U_211,U_209,U_207,U_203))],[f_21_4]) ).
fof(f_21_6,plain,
( ! [U_212,U_210,U_208] :
( U_208 = cartesian_product2(U_212,U_210)
| ? [U_206] :
( ~ in(U_206,U_208)
& ? [U_198] :
( ? [U_197] :
( U_206 = ordered_pair(U_198,U_197)
& in(U_197,U_210) )
& in(U_198,U_212) ) )
| ( ! [U_196] :
( ! [U_195] :
( sK39(U_212,U_210,U_208) != ordered_pair(U_196,U_195)
| ~ in(U_195,U_210) )
| ~ in(U_196,U_212) )
& in(sK39(U_212,U_210,U_208),U_208) ) )
& ! [U_211,U_209,U_207] :
( ( ! [U_204] :
( in(U_204,U_207)
| ! [U_193] :
( ! [U_192] :
( U_204 != ordered_pair(U_193,U_192)
| ~ in(U_192,U_209) )
| ~ in(U_193,U_211) ) )
& ! [U_203] :
( ( U_203 = ordered_pair(sK37(U_211,U_209,U_207,U_203),sK38(U_211,U_209,U_207,U_203))
& in(sK38(U_211,U_209,U_207,U_203),U_209)
& in(sK37(U_211,U_209,U_207,U_203),U_211) )
| ~ in(U_203,U_207) ) )
| U_207 != cartesian_product2(U_211,U_209) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_205,sK39(U_212,U_210,U_208))],[f_21_5]) ).
fof(f_21_7,plain,
( ! [U_212,U_210,U_208] :
( U_208 = cartesian_product2(U_212,U_210)
| ( ~ in(sK40(U_212,U_210,U_208),U_208)
& ? [U_198] :
( ? [U_197] :
( sK40(U_212,U_210,U_208) = ordered_pair(U_198,U_197)
& in(U_197,U_210) )
& in(U_198,U_212) ) )
| ( ! [U_196] :
( ! [U_195] :
( sK39(U_212,U_210,U_208) != ordered_pair(U_196,U_195)
| ~ in(U_195,U_210) )
| ~ in(U_196,U_212) )
& in(sK39(U_212,U_210,U_208),U_208) ) )
& ! [U_211,U_209,U_207] :
( ( ! [U_204] :
( in(U_204,U_207)
| ! [U_193] :
( ! [U_192] :
( U_204 != ordered_pair(U_193,U_192)
| ~ in(U_192,U_209) )
| ~ in(U_193,U_211) ) )
& ! [U_203] :
( ( U_203 = ordered_pair(sK37(U_211,U_209,U_207,U_203),sK38(U_211,U_209,U_207,U_203))
& in(sK38(U_211,U_209,U_207,U_203),U_209)
& in(sK37(U_211,U_209,U_207,U_203),U_211) )
| ~ in(U_203,U_207) ) )
| U_207 != cartesian_product2(U_211,U_209) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_206,sK40(U_212,U_210,U_208))],[f_21_6]) ).
fof(f_21_8,plain,
( ! [U_212,U_210,U_208] :
( U_208 = cartesian_product2(U_212,U_210)
| ( ~ in(sK40(U_212,U_210,U_208),U_208)
& ? [U_197] :
( sK40(U_212,U_210,U_208) = ordered_pair(sK41(U_212,U_210,U_208),U_197)
& in(U_197,U_210) )
& in(sK41(U_212,U_210,U_208),U_212) )
| ( ! [U_196] :
( ! [U_195] :
( sK39(U_212,U_210,U_208) != ordered_pair(U_196,U_195)
| ~ in(U_195,U_210) )
| ~ in(U_196,U_212) )
& in(sK39(U_212,U_210,U_208),U_208) ) )
& ! [U_211,U_209,U_207] :
( ( ! [U_204] :
( in(U_204,U_207)
| ! [U_193] :
( ! [U_192] :
( U_204 != ordered_pair(U_193,U_192)
| ~ in(U_192,U_209) )
| ~ in(U_193,U_211) ) )
& ! [U_203] :
( ( U_203 = ordered_pair(sK37(U_211,U_209,U_207,U_203),sK38(U_211,U_209,U_207,U_203))
& in(sK38(U_211,U_209,U_207,U_203),U_209)
& in(sK37(U_211,U_209,U_207,U_203),U_211) )
| ~ in(U_203,U_207) ) )
| U_207 != cartesian_product2(U_211,U_209) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_198,sK41(U_212,U_210,U_208))],[f_21_7]) ).
fof(f_21_9,plain,
( ! [U_212,U_210,U_208] :
( U_208 = cartesian_product2(U_212,U_210)
| ( ~ in(sK40(U_212,U_210,U_208),U_208)
& sK40(U_212,U_210,U_208) = ordered_pair(sK41(U_212,U_210,U_208),sK42(U_212,U_210,U_208))
& in(sK42(U_212,U_210,U_208),U_210)
& in(sK41(U_212,U_210,U_208),U_212) )
| ( ! [U_196] :
( ! [U_195] :
( sK39(U_212,U_210,U_208) != ordered_pair(U_196,U_195)
| ~ in(U_195,U_210) )
| ~ in(U_196,U_212) )
& in(sK39(U_212,U_210,U_208),U_208) ) )
& ! [U_211,U_209,U_207] :
( ( ! [U_204] :
( in(U_204,U_207)
| ! [U_193] :
( ! [U_192] :
( U_204 != ordered_pair(U_193,U_192)
| ~ in(U_192,U_209) )
| ~ in(U_193,U_211) ) )
& ! [U_203] :
( ( U_203 = ordered_pair(sK37(U_211,U_209,U_207,U_203),sK38(U_211,U_209,U_207,U_203))
& in(sK38(U_211,U_209,U_207,U_203),U_209)
& in(sK37(U_211,U_209,U_207,U_203),U_211) )
| ~ in(U_203,U_207) ) )
| U_207 != cartesian_product2(U_211,U_209) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_197,sK42(U_212,U_210,U_208))],[f_21_8]) ).
cnf(f_21_10,plain,
( in(sK37(U_211,U_209,U_207,U_203),U_211)
| ~ in(U_203,U_207)
| U_207 != cartesian_product2(U_211,U_209) ),
inference(clausify,[status(thm)],[f_21_9]) ).
cnf(f_21_11,plain,
( in(sK38(U_211,U_209,U_207,U_203),U_209)
| ~ in(U_203,U_207)
| U_207 != cartesian_product2(U_211,U_209) ),
inference(clausify,[status(thm)],[f_21_9]) ).
cnf(f_21_12,plain,
( U_203 = ordered_pair(sK37(U_211,U_209,U_207,U_203),sK38(U_211,U_209,U_207,U_203))
| ~ in(U_203,U_207)
| U_207 != cartesian_product2(U_211,U_209) ),
inference(clausify,[status(thm)],[f_21_9]) ).
cnf(f_21_13,plain,
( in(U_204,U_207)
| U_204 != ordered_pair(U_193,U_192)
| ~ in(U_192,U_209)
| ~ in(U_193,U_211)
| U_207 != cartesian_product2(U_211,U_209) ),
inference(clausify,[status(thm)],[f_21_9]) ).
cnf(f_21_14,plain,
( in(sK41(U_212,U_210,U_208),U_212)
| in(sK39(U_212,U_210,U_208),U_208)
| U_208 = cartesian_product2(U_212,U_210) ),
inference(clausify,[status(thm)],[f_21_9]) ).
cnf(f_21_15,plain,
( in(sK42(U_212,U_210,U_208),U_210)
| in(sK39(U_212,U_210,U_208),U_208)
| U_208 = cartesian_product2(U_212,U_210) ),
inference(clausify,[status(thm)],[f_21_9]) ).
cnf(f_21_16,plain,
( sK40(U_212,U_210,U_208) = ordered_pair(sK41(U_212,U_210,U_208),sK42(U_212,U_210,U_208))
| in(sK39(U_212,U_210,U_208),U_208)
| U_208 = cartesian_product2(U_212,U_210) ),
inference(clausify,[status(thm)],[f_21_9]) ).
cnf(f_21_17,plain,
( ~ in(sK40(U_212,U_210,U_208),U_208)
| in(sK39(U_212,U_210,U_208),U_208)
| U_208 = cartesian_product2(U_212,U_210) ),
inference(clausify,[status(thm)],[f_21_9]) ).
cnf(f_21_18,plain,
( in(sK41(U_212,U_210,U_208),U_212)
| sK39(U_212,U_210,U_208) != ordered_pair(U_196,U_195)
| ~ in(U_195,U_210)
| ~ in(U_196,U_212)
| U_208 = cartesian_product2(U_212,U_210) ),
inference(clausify,[status(thm)],[f_21_9]) ).
cnf(f_21_19,plain,
( in(sK42(U_212,U_210,U_208),U_210)
| sK39(U_212,U_210,U_208) != ordered_pair(U_196,U_195)
| ~ in(U_195,U_210)
| ~ in(U_196,U_212)
| U_208 = cartesian_product2(U_212,U_210) ),
inference(clausify,[status(thm)],[f_21_9]) ).
cnf(f_21_20,plain,
( sK40(U_212,U_210,U_208) = ordered_pair(sK41(U_212,U_210,U_208),sK42(U_212,U_210,U_208))
| sK39(U_212,U_210,U_208) != ordered_pair(U_196,U_195)
| ~ in(U_195,U_210)
| ~ in(U_196,U_212)
| U_208 = cartesian_product2(U_212,U_210) ),
inference(clausify,[status(thm)],[f_21_9]) ).
cnf(f_21_21,plain,
( ~ in(sK40(U_212,U_210,U_208),U_208)
| sK39(U_212,U_210,U_208) != ordered_pair(U_196,U_195)
| ~ in(U_195,U_210)
| ~ in(U_196,U_212)
| U_208 = cartesian_product2(U_212,U_210) ),
inference(clausify,[status(thm)],[f_21_9]) ).
fof(f_22_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_22_2,plain,
! [U_218] :
( ! [U_217] :
( ( ( subset(U_218,U_217)
| ? [U_216,U_215] :
( ~ in(ordered_pair(U_216,U_215),U_217)
& in(ordered_pair(U_216,U_215),U_218) ) )
& ( ! [U_214,U_213] :
( in(ordered_pair(U_214,U_213),U_217)
| ~ in(ordered_pair(U_214,U_213),U_218) )
| ~ subset(U_218,U_217) ) )
| ~ relation(U_217) )
| ~ relation(U_218) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_218] :
( ! [U_217] :
( ( ( subset(U_218,U_217)
| ? [U_215] :
( ~ in(ordered_pair(sK43(U_218,U_217),U_215),U_217)
& in(ordered_pair(sK43(U_218,U_217),U_215),U_218) ) )
& ( ! [U_214,U_213] :
( in(ordered_pair(U_214,U_213),U_217)
| ~ in(ordered_pair(U_214,U_213),U_218) )
| ~ subset(U_218,U_217) ) )
| ~ relation(U_217) )
| ~ relation(U_218) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_216,sK43(U_218,U_217))],[f_22_2]) ).
fof(f_22_4,plain,
! [U_218] :
( ! [U_217] :
( ( ( subset(U_218,U_217)
| ( ~ in(ordered_pair(sK43(U_218,U_217),sK44(U_218,U_217)),U_217)
& in(ordered_pair(sK43(U_218,U_217),sK44(U_218,U_217)),U_218) ) )
& ( ! [U_214,U_213] :
( in(ordered_pair(U_214,U_213),U_217)
| ~ in(ordered_pair(U_214,U_213),U_218) )
| ~ subset(U_218,U_217) ) )
| ~ relation(U_217) )
| ~ relation(U_218) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_215,sK44(U_218,U_217))],[f_22_3]) ).
cnf(f_22_5,plain,
( in(ordered_pair(U_214,U_213),U_217)
| ~ in(ordered_pair(U_214,U_213),U_218)
| ~ subset(U_218,U_217)
| ~ relation(U_217)
| ~ relation(U_218) ),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_6,plain,
( in(ordered_pair(sK43(U_218,U_217),sK44(U_218,U_217)),U_218)
| subset(U_218,U_217)
| ~ relation(U_217)
| ~ relation(U_218) ),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_7,plain,
( ~ in(ordered_pair(sK43(U_218,U_217),sK44(U_218,U_217)),U_217)
| subset(U_218,U_217)
| ~ relation(U_217)
| ~ relation(U_218) ),
inference(clausify,[status(thm)],[f_22_4]) ).
fof(f_23_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_23_2,plain,
! [U_222,U_221] :
( ( subset(U_222,U_221)
| ? [U_220] :
( ~ in(U_220,U_221)
& in(U_220,U_222) ) )
& ( ! [U_219] :
( in(U_219,U_221)
| ~ in(U_219,U_222) )
| ~ subset(U_222,U_221) ) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( ! [U_226,U_224] :
( subset(U_226,U_224)
| ? [U_220] :
( ~ in(U_220,U_224)
& in(U_220,U_226) ) )
& ! [U_225,U_223] :
( ! [U_219] :
( in(U_219,U_223)
| ~ in(U_219,U_225) )
| ~ subset(U_225,U_223) ) ),
inference(miniscope,[status(thm)],[f_23_2]) ).
fof(f_23_4,plain,
( ! [U_226,U_224] :
( subset(U_226,U_224)
| ( ~ in(sK45(U_226,U_224),U_224)
& in(sK45(U_226,U_224),U_226) ) )
& ! [U_225,U_223] :
( ! [U_219] :
( in(U_219,U_223)
| ~ in(U_219,U_225) )
| ~ subset(U_225,U_223) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_220,sK45(U_226,U_224))],[f_23_3]) ).
cnf(f_23_5,plain,
( in(U_219,U_223)
| ~ in(U_219,U_225)
| ~ subset(U_225,U_223) ),
inference(clausify,[status(thm)],[f_23_4]) ).
cnf(f_23_6,plain,
( in(sK45(U_226,U_224),U_226)
| subset(U_226,U_224) ),
inference(clausify,[status(thm)],[f_23_4]) ).
cnf(f_23_7,plain,
( ~ in(sK45(U_226,U_224),U_224)
| subset(U_226,U_224) ),
inference(clausify,[status(thm)],[f_23_4]) ).
fof(f_24_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_24_2,plain,
! [U_231,U_230,U_229] :
( ( U_229 = set_intersection2(U_231,U_230)
| ? [U_228] :
( ( ~ in(U_228,U_229)
& in(U_228,U_230)
& in(U_228,U_231) )
| ( ( ~ in(U_228,U_230)
| ~ in(U_228,U_231) )
& in(U_228,U_229) ) ) )
& ( ! [U_227] :
( ( in(U_227,U_229)
| ~ in(U_227,U_230)
| ~ in(U_227,U_231) )
& ( ( in(U_227,U_230)
& in(U_227,U_231) )
| ~ in(U_227,U_229) ) )
| U_229 != set_intersection2(U_231,U_230) ) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( ! [U_241,U_239,U_237] :
( U_237 = set_intersection2(U_241,U_239)
| ? [U_235] :
( ~ in(U_235,U_237)
& in(U_235,U_239)
& in(U_235,U_241) )
| ? [U_234] :
( ( ~ in(U_234,U_239)
| ~ in(U_234,U_241) )
& in(U_234,U_237) ) )
& ! [U_240,U_238,U_236] :
( ( ! [U_233] :
( in(U_233,U_236)
| ~ in(U_233,U_238)
| ~ in(U_233,U_240) )
& ! [U_232] :
( ( in(U_232,U_238)
& in(U_232,U_240) )
| ~ in(U_232,U_236) ) )
| U_236 != set_intersection2(U_240,U_238) ) ),
inference(miniscope,[status(thm)],[f_24_2]) ).
fof(f_24_4,plain,
( ! [U_241,U_239,U_237] :
( U_237 = set_intersection2(U_241,U_239)
| ? [U_235] :
( ~ in(U_235,U_237)
& in(U_235,U_239)
& in(U_235,U_241) )
| ( ( ~ in(sK46(U_241,U_239,U_237),U_239)
| ~ in(sK46(U_241,U_239,U_237),U_241) )
& in(sK46(U_241,U_239,U_237),U_237) ) )
& ! [U_240,U_238,U_236] :
( ( ! [U_233] :
( in(U_233,U_236)
| ~ in(U_233,U_238)
| ~ in(U_233,U_240) )
& ! [U_232] :
( ( in(U_232,U_238)
& in(U_232,U_240) )
| ~ in(U_232,U_236) ) )
| U_236 != set_intersection2(U_240,U_238) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_234,sK46(U_241,U_239,U_237))],[f_24_3]) ).
fof(f_24_5,plain,
( ! [U_241,U_239,U_237] :
( U_237 = set_intersection2(U_241,U_239)
| ( ~ in(sK47(U_241,U_239,U_237),U_237)
& in(sK47(U_241,U_239,U_237),U_239)
& in(sK47(U_241,U_239,U_237),U_241) )
| ( ( ~ in(sK46(U_241,U_239,U_237),U_239)
| ~ in(sK46(U_241,U_239,U_237),U_241) )
& in(sK46(U_241,U_239,U_237),U_237) ) )
& ! [U_240,U_238,U_236] :
( ( ! [U_233] :
( in(U_233,U_236)
| ~ in(U_233,U_238)
| ~ in(U_233,U_240) )
& ! [U_232] :
( ( in(U_232,U_238)
& in(U_232,U_240) )
| ~ in(U_232,U_236) ) )
| U_236 != set_intersection2(U_240,U_238) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_235,sK47(U_241,U_239,U_237))],[f_24_4]) ).
cnf(f_24_6,plain,
( in(U_232,U_240)
| ~ in(U_232,U_236)
| U_236 != set_intersection2(U_240,U_238) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_7,plain,
( in(U_232,U_238)
| ~ in(U_232,U_236)
| U_236 != set_intersection2(U_240,U_238) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_8,plain,
( in(U_233,U_236)
| ~ in(U_233,U_238)
| ~ in(U_233,U_240)
| U_236 != set_intersection2(U_240,U_238) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_9,plain,
( in(sK47(U_241,U_239,U_237),U_241)
| in(sK46(U_241,U_239,U_237),U_237)
| U_237 = set_intersection2(U_241,U_239) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_10,plain,
( in(sK47(U_241,U_239,U_237),U_239)
| in(sK46(U_241,U_239,U_237),U_237)
| U_237 = set_intersection2(U_241,U_239) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_11,plain,
( ~ in(sK47(U_241,U_239,U_237),U_237)
| in(sK46(U_241,U_239,U_237),U_237)
| U_237 = set_intersection2(U_241,U_239) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_12,plain,
( in(sK47(U_241,U_239,U_237),U_241)
| ~ in(sK46(U_241,U_239,U_237),U_239)
| ~ in(sK46(U_241,U_239,U_237),U_241)
| U_237 = set_intersection2(U_241,U_239) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_13,plain,
( in(sK47(U_241,U_239,U_237),U_239)
| ~ in(sK46(U_241,U_239,U_237),U_239)
| ~ in(sK46(U_241,U_239,U_237),U_241)
| U_237 = set_intersection2(U_241,U_239) ),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_14,plain,
( ~ in(sK47(U_241,U_239,U_237),U_237)
| ~ in(sK46(U_241,U_239,U_237),U_239)
| ~ in(sK46(U_241,U_239,U_237),U_241)
| U_237 = set_intersection2(U_241,U_239) ),
inference(clausify,[status(thm)],[f_24_5]) ).
fof(f_25_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_25_2,plain,
! [U_249] :
( ! [U_248] :
( ( U_248 = relation_dom(U_249)
| ? [U_247] :
( ( ~ in(U_247,U_248)
& ? [U_246] : in(ordered_pair(U_247,U_246),U_249) )
| ( ! [U_245] : ~ in(ordered_pair(U_247,U_245),U_249)
& in(U_247,U_248) ) ) )
& ( ! [U_244] :
( ( in(U_244,U_248)
| ! [U_243] : ~ in(ordered_pair(U_244,U_243),U_249) )
& ( ? [U_242] : in(ordered_pair(U_244,U_242),U_249)
| ~ in(U_244,U_248) ) )
| U_248 != relation_dom(U_249) ) )
| ~ relation(U_249) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_249] :
( ( ! [U_255] :
( U_255 = relation_dom(U_249)
| ? [U_253] :
( ~ in(U_253,U_255)
& ? [U_246] : in(ordered_pair(U_253,U_246),U_249) )
| ? [U_252] :
( ! [U_245] : ~ in(ordered_pair(U_252,U_245),U_249)
& in(U_252,U_255) ) )
& ! [U_254] :
( ( ! [U_251] :
( in(U_251,U_254)
| ! [U_243] : ~ in(ordered_pair(U_251,U_243),U_249) )
& ! [U_250] :
( ? [U_242] : in(ordered_pair(U_250,U_242),U_249)
| ~ in(U_250,U_254) ) )
| U_254 != relation_dom(U_249) ) )
| ~ relation(U_249) ),
inference(miniscope,[status(thm)],[f_25_2]) ).
fof(f_25_4,plain,
! [U_249] :
( ( ! [U_255] :
( U_255 = relation_dom(U_249)
| ? [U_253] :
( ~ in(U_253,U_255)
& ? [U_246] : in(ordered_pair(U_253,U_246),U_249) )
| ? [U_252] :
( ! [U_245] : ~ in(ordered_pair(U_252,U_245),U_249)
& in(U_252,U_255) ) )
& ! [U_254] :
( ( ! [U_251] :
( in(U_251,U_254)
| ! [U_243] : ~ in(ordered_pair(U_251,U_243),U_249) )
& ! [U_250] :
( in(ordered_pair(U_250,sK48(U_249,U_254,U_250)),U_249)
| ~ in(U_250,U_254) ) )
| U_254 != relation_dom(U_249) ) )
| ~ relation(U_249) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_242,sK48(U_249,U_254,U_250))],[f_25_3]) ).
fof(f_25_5,plain,
! [U_249] :
( ( ! [U_255] :
( U_255 = relation_dom(U_249)
| ? [U_253] :
( ~ in(U_253,U_255)
& ? [U_246] : in(ordered_pair(U_253,U_246),U_249) )
| ( ! [U_245] : ~ in(ordered_pair(sK49(U_249,U_255),U_245),U_249)
& in(sK49(U_249,U_255),U_255) ) )
& ! [U_254] :
( ( ! [U_251] :
( in(U_251,U_254)
| ! [U_243] : ~ in(ordered_pair(U_251,U_243),U_249) )
& ! [U_250] :
( in(ordered_pair(U_250,sK48(U_249,U_254,U_250)),U_249)
| ~ in(U_250,U_254) ) )
| U_254 != relation_dom(U_249) ) )
| ~ relation(U_249) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_252,sK49(U_249,U_255))],[f_25_4]) ).
fof(f_25_6,plain,
! [U_249] :
( ( ! [U_255] :
( U_255 = relation_dom(U_249)
| ( ~ in(sK50(U_249,U_255),U_255)
& ? [U_246] : in(ordered_pair(sK50(U_249,U_255),U_246),U_249) )
| ( ! [U_245] : ~ in(ordered_pair(sK49(U_249,U_255),U_245),U_249)
& in(sK49(U_249,U_255),U_255) ) )
& ! [U_254] :
( ( ! [U_251] :
( in(U_251,U_254)
| ! [U_243] : ~ in(ordered_pair(U_251,U_243),U_249) )
& ! [U_250] :
( in(ordered_pair(U_250,sK48(U_249,U_254,U_250)),U_249)
| ~ in(U_250,U_254) ) )
| U_254 != relation_dom(U_249) ) )
| ~ relation(U_249) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_253,sK50(U_249,U_255))],[f_25_5]) ).
fof(f_25_7,plain,
! [U_249] :
( ( ! [U_255] :
( U_255 = relation_dom(U_249)
| ( ~ in(sK50(U_249,U_255),U_255)
& in(ordered_pair(sK50(U_249,U_255),sK51(U_249,U_255)),U_249) )
| ( ! [U_245] : ~ in(ordered_pair(sK49(U_249,U_255),U_245),U_249)
& in(sK49(U_249,U_255),U_255) ) )
& ! [U_254] :
( ( ! [U_251] :
( in(U_251,U_254)
| ! [U_243] : ~ in(ordered_pair(U_251,U_243),U_249) )
& ! [U_250] :
( in(ordered_pair(U_250,sK48(U_249,U_254,U_250)),U_249)
| ~ in(U_250,U_254) ) )
| U_254 != relation_dom(U_249) ) )
| ~ relation(U_249) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_246,sK51(U_249,U_255))],[f_25_6]) ).
cnf(f_25_8,plain,
( in(ordered_pair(U_250,sK48(U_249,U_254,U_250)),U_249)
| ~ in(U_250,U_254)
| U_254 != relation_dom(U_249)
| ~ relation(U_249) ),
inference(clausify,[status(thm)],[f_25_7]) ).
cnf(f_25_9,plain,
( in(U_251,U_254)
| ~ in(ordered_pair(U_251,U_243),U_249)
| U_254 != relation_dom(U_249)
| ~ relation(U_249) ),
inference(clausify,[status(thm)],[f_25_7]) ).
cnf(f_25_10,plain,
( in(ordered_pair(sK50(U_249,U_255),sK51(U_249,U_255)),U_249)
| in(sK49(U_249,U_255),U_255)
| U_255 = relation_dom(U_249)
| ~ relation(U_249) ),
inference(clausify,[status(thm)],[f_25_7]) ).
cnf(f_25_11,plain,
( ~ in(sK50(U_249,U_255),U_255)
| in(sK49(U_249,U_255),U_255)
| U_255 = relation_dom(U_249)
| ~ relation(U_249) ),
inference(clausify,[status(thm)],[f_25_7]) ).
cnf(f_25_12,plain,
( in(ordered_pair(sK50(U_249,U_255),sK51(U_249,U_255)),U_249)
| ~ in(ordered_pair(sK49(U_249,U_255),U_245),U_249)
| U_255 = relation_dom(U_249)
| ~ relation(U_249) ),
inference(clausify,[status(thm)],[f_25_7]) ).
cnf(f_25_13,plain,
( ~ in(sK50(U_249,U_255),U_255)
| ~ in(ordered_pair(sK49(U_249,U_255),U_245),U_249)
| U_255 = relation_dom(U_249)
| ~ relation(U_249) ),
inference(clausify,[status(thm)],[f_25_7]) ).
fof(f_26_1,plain,
! [A] : cast_to_subset(A) = A,
inference(fof_nnf,[status(thm)],[d4_subset_1]) ).
fof(f_26_2,plain,
! [U_256] : cast_to_subset(U_256) = U_256,
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
cast_to_subset(U_256) = U_256,
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_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_27_2,plain,
! [U_264,U_263] :
( ( U_263 = union(U_264)
| ? [U_262] :
( ( ~ in(U_262,U_263)
& ? [U_261] :
( in(U_261,U_264)
& in(U_262,U_261) ) )
| ( ! [U_260] :
( ~ in(U_260,U_264)
| ~ in(U_262,U_260) )
& in(U_262,U_263) ) ) )
& ( ! [U_259] :
( ( in(U_259,U_263)
| ! [U_258] :
( ~ in(U_258,U_264)
| ~ in(U_259,U_258) ) )
& ( ? [U_257] :
( in(U_257,U_264)
& in(U_259,U_257) )
| ~ in(U_259,U_263) ) )
| U_263 != union(U_264) ) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( ! [U_272,U_270] :
( U_270 = union(U_272)
| ? [U_268] :
( ~ in(U_268,U_270)
& ? [U_261] :
( in(U_261,U_272)
& in(U_268,U_261) ) )
| ? [U_267] :
( ! [U_260] :
( ~ in(U_260,U_272)
| ~ in(U_267,U_260) )
& in(U_267,U_270) ) )
& ! [U_271,U_269] :
( ( ! [U_266] :
( in(U_266,U_269)
| ! [U_258] :
( ~ in(U_258,U_271)
| ~ in(U_266,U_258) ) )
& ! [U_265] :
( ? [U_257] :
( in(U_257,U_271)
& in(U_265,U_257) )
| ~ in(U_265,U_269) ) )
| U_269 != union(U_271) ) ),
inference(miniscope,[status(thm)],[f_27_2]) ).
fof(f_27_4,plain,
( ! [U_272,U_270] :
( U_270 = union(U_272)
| ? [U_268] :
( ~ in(U_268,U_270)
& ? [U_261] :
( in(U_261,U_272)
& in(U_268,U_261) ) )
| ? [U_267] :
( ! [U_260] :
( ~ in(U_260,U_272)
| ~ in(U_267,U_260) )
& in(U_267,U_270) ) )
& ! [U_271,U_269] :
( ( ! [U_266] :
( in(U_266,U_269)
| ! [U_258] :
( ~ in(U_258,U_271)
| ~ in(U_266,U_258) ) )
& ! [U_265] :
( ( in(sK52(U_271,U_269,U_265),U_271)
& in(U_265,sK52(U_271,U_269,U_265)) )
| ~ in(U_265,U_269) ) )
| U_269 != union(U_271) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_257,sK52(U_271,U_269,U_265))],[f_27_3]) ).
fof(f_27_5,plain,
( ! [U_272,U_270] :
( U_270 = union(U_272)
| ? [U_268] :
( ~ in(U_268,U_270)
& ? [U_261] :
( in(U_261,U_272)
& in(U_268,U_261) ) )
| ( ! [U_260] :
( ~ in(U_260,U_272)
| ~ in(sK53(U_272,U_270),U_260) )
& in(sK53(U_272,U_270),U_270) ) )
& ! [U_271,U_269] :
( ( ! [U_266] :
( in(U_266,U_269)
| ! [U_258] :
( ~ in(U_258,U_271)
| ~ in(U_266,U_258) ) )
& ! [U_265] :
( ( in(sK52(U_271,U_269,U_265),U_271)
& in(U_265,sK52(U_271,U_269,U_265)) )
| ~ in(U_265,U_269) ) )
| U_269 != union(U_271) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_267,sK53(U_272,U_270))],[f_27_4]) ).
fof(f_27_6,plain,
( ! [U_272,U_270] :
( U_270 = union(U_272)
| ( ~ in(sK54(U_272,U_270),U_270)
& ? [U_261] :
( in(U_261,U_272)
& in(sK54(U_272,U_270),U_261) ) )
| ( ! [U_260] :
( ~ in(U_260,U_272)
| ~ in(sK53(U_272,U_270),U_260) )
& in(sK53(U_272,U_270),U_270) ) )
& ! [U_271,U_269] :
( ( ! [U_266] :
( in(U_266,U_269)
| ! [U_258] :
( ~ in(U_258,U_271)
| ~ in(U_266,U_258) ) )
& ! [U_265] :
( ( in(sK52(U_271,U_269,U_265),U_271)
& in(U_265,sK52(U_271,U_269,U_265)) )
| ~ in(U_265,U_269) ) )
| U_269 != union(U_271) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_268,sK54(U_272,U_270))],[f_27_5]) ).
fof(f_27_7,plain,
( ! [U_272,U_270] :
( U_270 = union(U_272)
| ( ~ in(sK54(U_272,U_270),U_270)
& in(sK55(U_272,U_270),U_272)
& in(sK54(U_272,U_270),sK55(U_272,U_270)) )
| ( ! [U_260] :
( ~ in(U_260,U_272)
| ~ in(sK53(U_272,U_270),U_260) )
& in(sK53(U_272,U_270),U_270) ) )
& ! [U_271,U_269] :
( ( ! [U_266] :
( in(U_266,U_269)
| ! [U_258] :
( ~ in(U_258,U_271)
| ~ in(U_266,U_258) ) )
& ! [U_265] :
( ( in(sK52(U_271,U_269,U_265),U_271)
& in(U_265,sK52(U_271,U_269,U_265)) )
| ~ in(U_265,U_269) ) )
| U_269 != union(U_271) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_261,sK55(U_272,U_270))],[f_27_6]) ).
cnf(f_27_8,plain,
( in(U_265,sK52(U_271,U_269,U_265))
| ~ in(U_265,U_269)
| U_269 != union(U_271) ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_9,plain,
( in(sK52(U_271,U_269,U_265),U_271)
| ~ in(U_265,U_269)
| U_269 != union(U_271) ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_10,plain,
( in(U_266,U_269)
| ~ in(U_258,U_271)
| ~ in(U_266,U_258)
| U_269 != union(U_271) ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_11,plain,
( in(sK54(U_272,U_270),sK55(U_272,U_270))
| in(sK53(U_272,U_270),U_270)
| U_270 = union(U_272) ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_12,plain,
( in(sK55(U_272,U_270),U_272)
| in(sK53(U_272,U_270),U_270)
| U_270 = union(U_272) ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_13,plain,
( ~ in(sK54(U_272,U_270),U_270)
| in(sK53(U_272,U_270),U_270)
| U_270 = union(U_272) ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_14,plain,
( in(sK54(U_272,U_270),sK55(U_272,U_270))
| ~ in(U_260,U_272)
| ~ in(sK53(U_272,U_270),U_260)
| U_270 = union(U_272) ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_15,plain,
( in(sK55(U_272,U_270),U_272)
| ~ in(U_260,U_272)
| ~ in(sK53(U_272,U_270),U_260)
| U_270 = union(U_272) ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_16,plain,
( ~ in(sK54(U_272,U_270),U_270)
| ~ in(U_260,U_272)
| ~ in(sK53(U_272,U_270),U_260)
| U_270 = union(U_272) ),
inference(clausify,[status(thm)],[f_27_7]) ).
fof(f_28_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_28_2,plain,
! [U_277,U_276,U_275] :
( ( U_275 = set_difference(U_277,U_276)
| ? [U_274] :
( ( ~ in(U_274,U_275)
& ~ in(U_274,U_276)
& in(U_274,U_277) )
| ( ( in(U_274,U_276)
| ~ in(U_274,U_277) )
& in(U_274,U_275) ) ) )
& ( ! [U_273] :
( ( in(U_273,U_275)
| in(U_273,U_276)
| ~ in(U_273,U_277) )
& ( ( ~ in(U_273,U_276)
& in(U_273,U_277) )
| ~ in(U_273,U_275) ) )
| U_275 != set_difference(U_277,U_276) ) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( ! [U_287,U_285,U_283] :
( U_283 = set_difference(U_287,U_285)
| ? [U_281] :
( ~ in(U_281,U_283)
& ~ in(U_281,U_285)
& in(U_281,U_287) )
| ? [U_280] :
( ( in(U_280,U_285)
| ~ in(U_280,U_287) )
& in(U_280,U_283) ) )
& ! [U_286,U_284,U_282] :
( ( ! [U_279] :
( in(U_279,U_282)
| in(U_279,U_284)
| ~ in(U_279,U_286) )
& ! [U_278] :
( ( ~ in(U_278,U_284)
& in(U_278,U_286) )
| ~ in(U_278,U_282) ) )
| U_282 != set_difference(U_286,U_284) ) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
fof(f_28_4,plain,
( ! [U_287,U_285,U_283] :
( U_283 = set_difference(U_287,U_285)
| ? [U_281] :
( ~ in(U_281,U_283)
& ~ in(U_281,U_285)
& in(U_281,U_287) )
| ( ( in(sK56(U_287,U_285,U_283),U_285)
| ~ in(sK56(U_287,U_285,U_283),U_287) )
& in(sK56(U_287,U_285,U_283),U_283) ) )
& ! [U_286,U_284,U_282] :
( ( ! [U_279] :
( in(U_279,U_282)
| in(U_279,U_284)
| ~ in(U_279,U_286) )
& ! [U_278] :
( ( ~ in(U_278,U_284)
& in(U_278,U_286) )
| ~ in(U_278,U_282) ) )
| U_282 != set_difference(U_286,U_284) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_280,sK56(U_287,U_285,U_283))],[f_28_3]) ).
fof(f_28_5,plain,
( ! [U_287,U_285,U_283] :
( U_283 = set_difference(U_287,U_285)
| ( ~ in(sK57(U_287,U_285,U_283),U_283)
& ~ in(sK57(U_287,U_285,U_283),U_285)
& in(sK57(U_287,U_285,U_283),U_287) )
| ( ( in(sK56(U_287,U_285,U_283),U_285)
| ~ in(sK56(U_287,U_285,U_283),U_287) )
& in(sK56(U_287,U_285,U_283),U_283) ) )
& ! [U_286,U_284,U_282] :
( ( ! [U_279] :
( in(U_279,U_282)
| in(U_279,U_284)
| ~ in(U_279,U_286) )
& ! [U_278] :
( ( ~ in(U_278,U_284)
& in(U_278,U_286) )
| ~ in(U_278,U_282) ) )
| U_282 != set_difference(U_286,U_284) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_281,sK57(U_287,U_285,U_283))],[f_28_4]) ).
cnf(f_28_6,plain,
( in(U_278,U_286)
| ~ in(U_278,U_282)
| U_282 != set_difference(U_286,U_284) ),
inference(clausify,[status(thm)],[f_28_5]) ).
cnf(f_28_7,plain,
( ~ in(U_278,U_284)
| ~ in(U_278,U_282)
| U_282 != set_difference(U_286,U_284) ),
inference(clausify,[status(thm)],[f_28_5]) ).
cnf(f_28_8,plain,
( in(U_279,U_282)
| in(U_279,U_284)
| ~ in(U_279,U_286)
| U_282 != set_difference(U_286,U_284) ),
inference(clausify,[status(thm)],[f_28_5]) ).
cnf(f_28_9,plain,
( in(sK57(U_287,U_285,U_283),U_287)
| in(sK56(U_287,U_285,U_283),U_283)
| U_283 = set_difference(U_287,U_285) ),
inference(clausify,[status(thm)],[f_28_5]) ).
cnf(f_28_10,plain,
( ~ in(sK57(U_287,U_285,U_283),U_285)
| in(sK56(U_287,U_285,U_283),U_283)
| U_283 = set_difference(U_287,U_285) ),
inference(clausify,[status(thm)],[f_28_5]) ).
cnf(f_28_11,plain,
( ~ in(sK57(U_287,U_285,U_283),U_283)
| in(sK56(U_287,U_285,U_283),U_283)
| U_283 = set_difference(U_287,U_285) ),
inference(clausify,[status(thm)],[f_28_5]) ).
cnf(f_28_12,plain,
( in(sK57(U_287,U_285,U_283),U_287)
| in(sK56(U_287,U_285,U_283),U_285)
| ~ in(sK56(U_287,U_285,U_283),U_287)
| U_283 = set_difference(U_287,U_285) ),
inference(clausify,[status(thm)],[f_28_5]) ).
cnf(f_28_13,plain,
( ~ in(sK57(U_287,U_285,U_283),U_285)
| in(sK56(U_287,U_285,U_283),U_285)
| ~ in(sK56(U_287,U_285,U_283),U_287)
| U_283 = set_difference(U_287,U_285) ),
inference(clausify,[status(thm)],[f_28_5]) ).
cnf(f_28_14,plain,
( ~ in(sK57(U_287,U_285,U_283),U_283)
| in(sK56(U_287,U_285,U_283),U_285)
| ~ in(sK56(U_287,U_285,U_283),U_287)
| U_283 = set_difference(U_287,U_285) ),
inference(clausify,[status(thm)],[f_28_5]) ).
fof(f_29_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_29_2,plain,
! [U_295] :
( ! [U_294] :
( ( U_294 = relation_rng(U_295)
| ? [U_293] :
( ( ~ in(U_293,U_294)
& ? [U_292] : in(ordered_pair(U_292,U_293),U_295) )
| ( ! [U_291] : ~ in(ordered_pair(U_291,U_293),U_295)
& in(U_293,U_294) ) ) )
& ( ! [U_290] :
( ( in(U_290,U_294)
| ! [U_289] : ~ in(ordered_pair(U_289,U_290),U_295) )
& ( ? [U_288] : in(ordered_pair(U_288,U_290),U_295)
| ~ in(U_290,U_294) ) )
| U_294 != relation_rng(U_295) ) )
| ~ relation(U_295) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_295] :
( ( ! [U_301] :
( U_301 = relation_rng(U_295)
| ? [U_299] :
( ~ in(U_299,U_301)
& ? [U_292] : in(ordered_pair(U_292,U_299),U_295) )
| ? [U_298] :
( ! [U_291] : ~ in(ordered_pair(U_291,U_298),U_295)
& in(U_298,U_301) ) )
& ! [U_300] :
( ( ! [U_297] :
( in(U_297,U_300)
| ! [U_289] : ~ in(ordered_pair(U_289,U_297),U_295) )
& ! [U_296] :
( ? [U_288] : in(ordered_pair(U_288,U_296),U_295)
| ~ in(U_296,U_300) ) )
| U_300 != relation_rng(U_295) ) )
| ~ relation(U_295) ),
inference(miniscope,[status(thm)],[f_29_2]) ).
fof(f_29_4,plain,
! [U_295] :
( ( ! [U_301] :
( U_301 = relation_rng(U_295)
| ? [U_299] :
( ~ in(U_299,U_301)
& ? [U_292] : in(ordered_pair(U_292,U_299),U_295) )
| ? [U_298] :
( ! [U_291] : ~ in(ordered_pair(U_291,U_298),U_295)
& in(U_298,U_301) ) )
& ! [U_300] :
( ( ! [U_297] :
( in(U_297,U_300)
| ! [U_289] : ~ in(ordered_pair(U_289,U_297),U_295) )
& ! [U_296] :
( in(ordered_pair(sK58(U_295,U_300,U_296),U_296),U_295)
| ~ in(U_296,U_300) ) )
| U_300 != relation_rng(U_295) ) )
| ~ relation(U_295) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_288,sK58(U_295,U_300,U_296))],[f_29_3]) ).
fof(f_29_5,plain,
! [U_295] :
( ( ! [U_301] :
( U_301 = relation_rng(U_295)
| ? [U_299] :
( ~ in(U_299,U_301)
& ? [U_292] : in(ordered_pair(U_292,U_299),U_295) )
| ( ! [U_291] : ~ in(ordered_pair(U_291,sK59(U_295,U_301)),U_295)
& in(sK59(U_295,U_301),U_301) ) )
& ! [U_300] :
( ( ! [U_297] :
( in(U_297,U_300)
| ! [U_289] : ~ in(ordered_pair(U_289,U_297),U_295) )
& ! [U_296] :
( in(ordered_pair(sK58(U_295,U_300,U_296),U_296),U_295)
| ~ in(U_296,U_300) ) )
| U_300 != relation_rng(U_295) ) )
| ~ relation(U_295) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_298,sK59(U_295,U_301))],[f_29_4]) ).
fof(f_29_6,plain,
! [U_295] :
( ( ! [U_301] :
( U_301 = relation_rng(U_295)
| ( ~ in(sK60(U_295,U_301),U_301)
& ? [U_292] : in(ordered_pair(U_292,sK60(U_295,U_301)),U_295) )
| ( ! [U_291] : ~ in(ordered_pair(U_291,sK59(U_295,U_301)),U_295)
& in(sK59(U_295,U_301),U_301) ) )
& ! [U_300] :
( ( ! [U_297] :
( in(U_297,U_300)
| ! [U_289] : ~ in(ordered_pair(U_289,U_297),U_295) )
& ! [U_296] :
( in(ordered_pair(sK58(U_295,U_300,U_296),U_296),U_295)
| ~ in(U_296,U_300) ) )
| U_300 != relation_rng(U_295) ) )
| ~ relation(U_295) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_299,sK60(U_295,U_301))],[f_29_5]) ).
fof(f_29_7,plain,
! [U_295] :
( ( ! [U_301] :
( U_301 = relation_rng(U_295)
| ( ~ in(sK60(U_295,U_301),U_301)
& in(ordered_pair(sK61(U_295,U_301),sK60(U_295,U_301)),U_295) )
| ( ! [U_291] : ~ in(ordered_pair(U_291,sK59(U_295,U_301)),U_295)
& in(sK59(U_295,U_301),U_301) ) )
& ! [U_300] :
( ( ! [U_297] :
( in(U_297,U_300)
| ! [U_289] : ~ in(ordered_pair(U_289,U_297),U_295) )
& ! [U_296] :
( in(ordered_pair(sK58(U_295,U_300,U_296),U_296),U_295)
| ~ in(U_296,U_300) ) )
| U_300 != relation_rng(U_295) ) )
| ~ relation(U_295) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_292,sK61(U_295,U_301))],[f_29_6]) ).
cnf(f_29_8,plain,
( in(ordered_pair(sK58(U_295,U_300,U_296),U_296),U_295)
| ~ in(U_296,U_300)
| U_300 != relation_rng(U_295)
| ~ relation(U_295) ),
inference(clausify,[status(thm)],[f_29_7]) ).
cnf(f_29_9,plain,
( in(U_297,U_300)
| ~ in(ordered_pair(U_289,U_297),U_295)
| U_300 != relation_rng(U_295)
| ~ relation(U_295) ),
inference(clausify,[status(thm)],[f_29_7]) ).
cnf(f_29_10,plain,
( in(ordered_pair(sK61(U_295,U_301),sK60(U_295,U_301)),U_295)
| in(sK59(U_295,U_301),U_301)
| U_301 = relation_rng(U_295)
| ~ relation(U_295) ),
inference(clausify,[status(thm)],[f_29_7]) ).
cnf(f_29_11,plain,
( ~ in(sK60(U_295,U_301),U_301)
| in(sK59(U_295,U_301),U_301)
| U_301 = relation_rng(U_295)
| ~ relation(U_295) ),
inference(clausify,[status(thm)],[f_29_7]) ).
cnf(f_29_12,plain,
( in(ordered_pair(sK61(U_295,U_301),sK60(U_295,U_301)),U_295)
| ~ in(ordered_pair(U_291,sK59(U_295,U_301)),U_295)
| U_301 = relation_rng(U_295)
| ~ relation(U_295) ),
inference(clausify,[status(thm)],[f_29_7]) ).
cnf(f_29_13,plain,
( ~ in(sK60(U_295,U_301),U_301)
| ~ in(ordered_pair(U_291,sK59(U_295,U_301)),U_295)
| U_301 = relation_rng(U_295)
| ~ relation(U_295) ),
inference(clausify,[status(thm)],[f_29_7]) ).
fof(f_30_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_30_2,plain,
! [U_303,U_302] :
( subset_complement(U_303,U_302) = set_difference(U_303,U_302)
| ~ element(U_302,powerset(U_303)) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( subset_complement(U_303,U_302) = set_difference(U_303,U_302)
| ~ element(U_302,powerset(U_303)) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_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_31_2,plain,
! [U_305,U_304] : ordered_pair(U_305,U_304) = unordered_pair(unordered_pair(U_305,U_304),singleton(U_305)),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
ordered_pair(U_305,U_304) = unordered_pair(unordered_pair(U_305,U_304),singleton(U_305)),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_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_32_2,plain,
! [U_306] :
( relation_field(U_306) = set_union2(relation_dom(U_306),relation_rng(U_306))
| ~ relation(U_306) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( relation_field(U_306) = set_union2(relation_dom(U_306),relation_rng(U_306))
| ~ relation(U_306) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_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_33_2,plain,
! [U_312] :
( ! [U_311] :
( ( ( U_311 = relation_inverse(U_312)
| ? [U_310,U_309] :
( ( ~ in(ordered_pair(U_310,U_309),U_311)
& in(ordered_pair(U_309,U_310),U_312) )
| ( ~ in(ordered_pair(U_309,U_310),U_312)
& in(ordered_pair(U_310,U_309),U_311) ) ) )
& ( ! [U_308,U_307] :
( ( in(ordered_pair(U_308,U_307),U_311)
| ~ in(ordered_pair(U_307,U_308),U_312) )
& ( in(ordered_pair(U_307,U_308),U_312)
| ~ in(ordered_pair(U_308,U_307),U_311) ) )
| U_311 != relation_inverse(U_312) ) )
| ~ relation(U_311) )
| ~ relation(U_312) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_312] :
( ! [U_311] :
( ( ( U_311 = relation_inverse(U_312)
| ? [U_320,U_318] :
( ~ in(ordered_pair(U_320,U_318),U_311)
& in(ordered_pair(U_318,U_320),U_312) )
| ? [U_319,U_317] :
( ~ in(ordered_pair(U_317,U_319),U_312)
& in(ordered_pair(U_319,U_317),U_311) ) )
& ( ( ! [U_316,U_314] :
( in(ordered_pair(U_316,U_314),U_311)
| ~ in(ordered_pair(U_314,U_316),U_312) )
& ! [U_315,U_313] :
( in(ordered_pair(U_313,U_315),U_312)
| ~ in(ordered_pair(U_315,U_313),U_311) ) )
| U_311 != relation_inverse(U_312) ) )
| ~ relation(U_311) )
| ~ relation(U_312) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
fof(f_33_4,plain,
! [U_312] :
( ! [U_311] :
( ( ( U_311 = relation_inverse(U_312)
| ? [U_320,U_318] :
( ~ in(ordered_pair(U_320,U_318),U_311)
& in(ordered_pair(U_318,U_320),U_312) )
| ? [U_317] :
( ~ in(ordered_pair(U_317,sK62(U_312,U_311)),U_312)
& in(ordered_pair(sK62(U_312,U_311),U_317),U_311) ) )
& ( ( ! [U_316,U_314] :
( in(ordered_pair(U_316,U_314),U_311)
| ~ in(ordered_pair(U_314,U_316),U_312) )
& ! [U_315,U_313] :
( in(ordered_pair(U_313,U_315),U_312)
| ~ in(ordered_pair(U_315,U_313),U_311) ) )
| U_311 != relation_inverse(U_312) ) )
| ~ relation(U_311) )
| ~ relation(U_312) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_319,sK62(U_312,U_311))],[f_33_3]) ).
fof(f_33_5,plain,
! [U_312] :
( ! [U_311] :
( ( ( U_311 = relation_inverse(U_312)
| ? [U_320,U_318] :
( ~ in(ordered_pair(U_320,U_318),U_311)
& in(ordered_pair(U_318,U_320),U_312) )
| ( ~ in(ordered_pair(sK63(U_312,U_311),sK62(U_312,U_311)),U_312)
& in(ordered_pair(sK62(U_312,U_311),sK63(U_312,U_311)),U_311) ) )
& ( ( ! [U_316,U_314] :
( in(ordered_pair(U_316,U_314),U_311)
| ~ in(ordered_pair(U_314,U_316),U_312) )
& ! [U_315,U_313] :
( in(ordered_pair(U_313,U_315),U_312)
| ~ in(ordered_pair(U_315,U_313),U_311) ) )
| U_311 != relation_inverse(U_312) ) )
| ~ relation(U_311) )
| ~ relation(U_312) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_317,sK63(U_312,U_311))],[f_33_4]) ).
fof(f_33_6,plain,
! [U_312] :
( ! [U_311] :
( ( ( U_311 = relation_inverse(U_312)
| ? [U_318] :
( ~ in(ordered_pair(sK64(U_312,U_311),U_318),U_311)
& in(ordered_pair(U_318,sK64(U_312,U_311)),U_312) )
| ( ~ in(ordered_pair(sK63(U_312,U_311),sK62(U_312,U_311)),U_312)
& in(ordered_pair(sK62(U_312,U_311),sK63(U_312,U_311)),U_311) ) )
& ( ( ! [U_316,U_314] :
( in(ordered_pair(U_316,U_314),U_311)
| ~ in(ordered_pair(U_314,U_316),U_312) )
& ! [U_315,U_313] :
( in(ordered_pair(U_313,U_315),U_312)
| ~ in(ordered_pair(U_315,U_313),U_311) ) )
| U_311 != relation_inverse(U_312) ) )
| ~ relation(U_311) )
| ~ relation(U_312) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_320,sK64(U_312,U_311))],[f_33_5]) ).
fof(f_33_7,plain,
! [U_312] :
( ! [U_311] :
( ( ( U_311 = relation_inverse(U_312)
| ( ~ in(ordered_pair(sK64(U_312,U_311),sK65(U_312,U_311)),U_311)
& in(ordered_pair(sK65(U_312,U_311),sK64(U_312,U_311)),U_312) )
| ( ~ in(ordered_pair(sK63(U_312,U_311),sK62(U_312,U_311)),U_312)
& in(ordered_pair(sK62(U_312,U_311),sK63(U_312,U_311)),U_311) ) )
& ( ( ! [U_316,U_314] :
( in(ordered_pair(U_316,U_314),U_311)
| ~ in(ordered_pair(U_314,U_316),U_312) )
& ! [U_315,U_313] :
( in(ordered_pair(U_313,U_315),U_312)
| ~ in(ordered_pair(U_315,U_313),U_311) ) )
| U_311 != relation_inverse(U_312) ) )
| ~ relation(U_311) )
| ~ relation(U_312) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_318,sK65(U_312,U_311))],[f_33_6]) ).
cnf(f_33_8,plain,
( in(ordered_pair(U_313,U_315),U_312)
| ~ in(ordered_pair(U_315,U_313),U_311)
| U_311 != relation_inverse(U_312)
| ~ relation(U_311)
| ~ relation(U_312) ),
inference(clausify,[status(thm)],[f_33_7]) ).
cnf(f_33_9,plain,
( in(ordered_pair(U_316,U_314),U_311)
| ~ in(ordered_pair(U_314,U_316),U_312)
| U_311 != relation_inverse(U_312)
| ~ relation(U_311)
| ~ relation(U_312) ),
inference(clausify,[status(thm)],[f_33_7]) ).
cnf(f_33_10,plain,
( in(ordered_pair(sK65(U_312,U_311),sK64(U_312,U_311)),U_312)
| in(ordered_pair(sK62(U_312,U_311),sK63(U_312,U_311)),U_311)
| U_311 = relation_inverse(U_312)
| ~ relation(U_311)
| ~ relation(U_312) ),
inference(clausify,[status(thm)],[f_33_7]) ).
cnf(f_33_11,plain,
( ~ in(ordered_pair(sK64(U_312,U_311),sK65(U_312,U_311)),U_311)
| in(ordered_pair(sK62(U_312,U_311),sK63(U_312,U_311)),U_311)
| U_311 = relation_inverse(U_312)
| ~ relation(U_311)
| ~ relation(U_312) ),
inference(clausify,[status(thm)],[f_33_7]) ).
cnf(f_33_12,plain,
( in(ordered_pair(sK65(U_312,U_311),sK64(U_312,U_311)),U_312)
| ~ in(ordered_pair(sK63(U_312,U_311),sK62(U_312,U_311)),U_312)
| U_311 = relation_inverse(U_312)
| ~ relation(U_311)
| ~ relation(U_312) ),
inference(clausify,[status(thm)],[f_33_7]) ).
cnf(f_33_13,plain,
( ~ in(ordered_pair(sK64(U_312,U_311),sK65(U_312,U_311)),U_311)
| ~ in(ordered_pair(sK63(U_312,U_311),sK62(U_312,U_311)),U_312)
| U_311 = relation_inverse(U_312)
| ~ relation(U_311)
| ~ relation(U_312) ),
inference(clausify,[status(thm)],[f_33_7]) ).
fof(f_34_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_34_2,plain,
! [U_322,U_321] :
( ( disjoint(U_322,U_321)
| set_intersection2(U_322,U_321) != empty_set )
& ( set_intersection2(U_322,U_321) = empty_set
| ~ disjoint(U_322,U_321) ) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
( ! [U_326,U_324] :
( disjoint(U_326,U_324)
| set_intersection2(U_326,U_324) != empty_set )
& ! [U_325,U_323] :
( set_intersection2(U_325,U_323) = empty_set
| ~ disjoint(U_325,U_323) ) ),
inference(miniscope,[status(thm)],[f_34_2]) ).
cnf(f_34_4,plain,
( set_intersection2(U_325,U_323) = empty_set
| ~ disjoint(U_325,U_323) ),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_5,plain,
( disjoint(U_326,U_324)
| set_intersection2(U_326,U_324) != empty_set ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_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_35_2,plain,
! [U_337] :
( ! [U_336] :
( ! [U_335] :
( ( ( U_335 = relation_composition(U_337,U_336)
| ? [U_334,U_333] :
( ( ~ in(ordered_pair(U_334,U_333),U_335)
& ? [U_332] :
( in(ordered_pair(U_332,U_333),U_336)
& in(ordered_pair(U_334,U_332),U_337) ) )
| ( ! [U_331] :
( ~ in(ordered_pair(U_331,U_333),U_336)
| ~ in(ordered_pair(U_334,U_331),U_337) )
& in(ordered_pair(U_334,U_333),U_335) ) ) )
& ( ! [U_330,U_329] :
( ( in(ordered_pair(U_330,U_329),U_335)
| ! [U_328] :
( ~ in(ordered_pair(U_328,U_329),U_336)
| ~ in(ordered_pair(U_330,U_328),U_337) ) )
& ( ? [U_327] :
( in(ordered_pair(U_327,U_329),U_336)
& in(ordered_pair(U_330,U_327),U_337) )
| ~ in(ordered_pair(U_330,U_329),U_335) ) )
| U_335 != relation_composition(U_337,U_336) ) )
| ~ relation(U_335) )
| ~ relation(U_336) )
| ~ relation(U_337) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_337] :
( ! [U_336] :
( ! [U_335] :
( ( ( U_335 = relation_composition(U_337,U_336)
| ? [U_345,U_343] :
( ~ in(ordered_pair(U_345,U_343),U_335)
& ? [U_332] :
( in(ordered_pair(U_332,U_343),U_336)
& in(ordered_pair(U_345,U_332),U_337) ) )
| ? [U_344,U_342] :
( ! [U_331] :
( ~ in(ordered_pair(U_331,U_342),U_336)
| ~ in(ordered_pair(U_344,U_331),U_337) )
& in(ordered_pair(U_344,U_342),U_335) ) )
& ( ( ! [U_341,U_339] :
( in(ordered_pair(U_341,U_339),U_335)
| ! [U_328] :
( ~ in(ordered_pair(U_328,U_339),U_336)
| ~ in(ordered_pair(U_341,U_328),U_337) ) )
& ! [U_340,U_338] :
( ? [U_327] :
( in(ordered_pair(U_327,U_338),U_336)
& in(ordered_pair(U_340,U_327),U_337) )
| ~ in(ordered_pair(U_340,U_338),U_335) ) )
| U_335 != relation_composition(U_337,U_336) ) )
| ~ relation(U_335) )
| ~ relation(U_336) )
| ~ relation(U_337) ),
inference(miniscope,[status(thm)],[f_35_2]) ).
fof(f_35_4,plain,
! [U_337] :
( ! [U_336] :
( ! [U_335] :
( ( ( U_335 = relation_composition(U_337,U_336)
| ? [U_345,U_343] :
( ~ in(ordered_pair(U_345,U_343),U_335)
& ? [U_332] :
( in(ordered_pair(U_332,U_343),U_336)
& in(ordered_pair(U_345,U_332),U_337) ) )
| ? [U_344,U_342] :
( ! [U_331] :
( ~ in(ordered_pair(U_331,U_342),U_336)
| ~ in(ordered_pair(U_344,U_331),U_337) )
& in(ordered_pair(U_344,U_342),U_335) ) )
& ( ( ! [U_341,U_339] :
( in(ordered_pair(U_341,U_339),U_335)
| ! [U_328] :
( ~ in(ordered_pair(U_328,U_339),U_336)
| ~ in(ordered_pair(U_341,U_328),U_337) ) )
& ! [U_340,U_338] :
( ( in(ordered_pair(sK66(U_337,U_336,U_335,U_340,U_338),U_338),U_336)
& in(ordered_pair(U_340,sK66(U_337,U_336,U_335,U_340,U_338)),U_337) )
| ~ in(ordered_pair(U_340,U_338),U_335) ) )
| U_335 != relation_composition(U_337,U_336) ) )
| ~ relation(U_335) )
| ~ relation(U_336) )
| ~ relation(U_337) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_327,sK66(U_337,U_336,U_335,U_340,U_338))],[f_35_3]) ).
fof(f_35_5,plain,
! [U_337] :
( ! [U_336] :
( ! [U_335] :
( ( ( U_335 = relation_composition(U_337,U_336)
| ? [U_345,U_343] :
( ~ in(ordered_pair(U_345,U_343),U_335)
& ? [U_332] :
( in(ordered_pair(U_332,U_343),U_336)
& in(ordered_pair(U_345,U_332),U_337) ) )
| ? [U_342] :
( ! [U_331] :
( ~ in(ordered_pair(U_331,U_342),U_336)
| ~ in(ordered_pair(sK67(U_337,U_336,U_335),U_331),U_337) )
& in(ordered_pair(sK67(U_337,U_336,U_335),U_342),U_335) ) )
& ( ( ! [U_341,U_339] :
( in(ordered_pair(U_341,U_339),U_335)
| ! [U_328] :
( ~ in(ordered_pair(U_328,U_339),U_336)
| ~ in(ordered_pair(U_341,U_328),U_337) ) )
& ! [U_340,U_338] :
( ( in(ordered_pair(sK66(U_337,U_336,U_335,U_340,U_338),U_338),U_336)
& in(ordered_pair(U_340,sK66(U_337,U_336,U_335,U_340,U_338)),U_337) )
| ~ in(ordered_pair(U_340,U_338),U_335) ) )
| U_335 != relation_composition(U_337,U_336) ) )
| ~ relation(U_335) )
| ~ relation(U_336) )
| ~ relation(U_337) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_344,sK67(U_337,U_336,U_335))],[f_35_4]) ).
fof(f_35_6,plain,
! [U_337] :
( ! [U_336] :
( ! [U_335] :
( ( ( U_335 = relation_composition(U_337,U_336)
| ? [U_345,U_343] :
( ~ in(ordered_pair(U_345,U_343),U_335)
& ? [U_332] :
( in(ordered_pair(U_332,U_343),U_336)
& in(ordered_pair(U_345,U_332),U_337) ) )
| ( ! [U_331] :
( ~ in(ordered_pair(U_331,sK68(U_337,U_336,U_335)),U_336)
| ~ in(ordered_pair(sK67(U_337,U_336,U_335),U_331),U_337) )
& in(ordered_pair(sK67(U_337,U_336,U_335),sK68(U_337,U_336,U_335)),U_335) ) )
& ( ( ! [U_341,U_339] :
( in(ordered_pair(U_341,U_339),U_335)
| ! [U_328] :
( ~ in(ordered_pair(U_328,U_339),U_336)
| ~ in(ordered_pair(U_341,U_328),U_337) ) )
& ! [U_340,U_338] :
( ( in(ordered_pair(sK66(U_337,U_336,U_335,U_340,U_338),U_338),U_336)
& in(ordered_pair(U_340,sK66(U_337,U_336,U_335,U_340,U_338)),U_337) )
| ~ in(ordered_pair(U_340,U_338),U_335) ) )
| U_335 != relation_composition(U_337,U_336) ) )
| ~ relation(U_335) )
| ~ relation(U_336) )
| ~ relation(U_337) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_342,sK68(U_337,U_336,U_335))],[f_35_5]) ).
fof(f_35_7,plain,
! [U_337] :
( ! [U_336] :
( ! [U_335] :
( ( ( U_335 = relation_composition(U_337,U_336)
| ? [U_343] :
( ~ in(ordered_pair(sK69(U_337,U_336,U_335),U_343),U_335)
& ? [U_332] :
( in(ordered_pair(U_332,U_343),U_336)
& in(ordered_pair(sK69(U_337,U_336,U_335),U_332),U_337) ) )
| ( ! [U_331] :
( ~ in(ordered_pair(U_331,sK68(U_337,U_336,U_335)),U_336)
| ~ in(ordered_pair(sK67(U_337,U_336,U_335),U_331),U_337) )
& in(ordered_pair(sK67(U_337,U_336,U_335),sK68(U_337,U_336,U_335)),U_335) ) )
& ( ( ! [U_341,U_339] :
( in(ordered_pair(U_341,U_339),U_335)
| ! [U_328] :
( ~ in(ordered_pair(U_328,U_339),U_336)
| ~ in(ordered_pair(U_341,U_328),U_337) ) )
& ! [U_340,U_338] :
( ( in(ordered_pair(sK66(U_337,U_336,U_335,U_340,U_338),U_338),U_336)
& in(ordered_pair(U_340,sK66(U_337,U_336,U_335,U_340,U_338)),U_337) )
| ~ in(ordered_pair(U_340,U_338),U_335) ) )
| U_335 != relation_composition(U_337,U_336) ) )
| ~ relation(U_335) )
| ~ relation(U_336) )
| ~ relation(U_337) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_345,sK69(U_337,U_336,U_335))],[f_35_6]) ).
fof(f_35_8,plain,
! [U_337] :
( ! [U_336] :
( ! [U_335] :
( ( ( U_335 = relation_composition(U_337,U_336)
| ( ~ in(ordered_pair(sK69(U_337,U_336,U_335),sK70(U_337,U_336,U_335)),U_335)
& ? [U_332] :
( in(ordered_pair(U_332,sK70(U_337,U_336,U_335)),U_336)
& in(ordered_pair(sK69(U_337,U_336,U_335),U_332),U_337) ) )
| ( ! [U_331] :
( ~ in(ordered_pair(U_331,sK68(U_337,U_336,U_335)),U_336)
| ~ in(ordered_pair(sK67(U_337,U_336,U_335),U_331),U_337) )
& in(ordered_pair(sK67(U_337,U_336,U_335),sK68(U_337,U_336,U_335)),U_335) ) )
& ( ( ! [U_341,U_339] :
( in(ordered_pair(U_341,U_339),U_335)
| ! [U_328] :
( ~ in(ordered_pair(U_328,U_339),U_336)
| ~ in(ordered_pair(U_341,U_328),U_337) ) )
& ! [U_340,U_338] :
( ( in(ordered_pair(sK66(U_337,U_336,U_335,U_340,U_338),U_338),U_336)
& in(ordered_pair(U_340,sK66(U_337,U_336,U_335,U_340,U_338)),U_337) )
| ~ in(ordered_pair(U_340,U_338),U_335) ) )
| U_335 != relation_composition(U_337,U_336) ) )
| ~ relation(U_335) )
| ~ relation(U_336) )
| ~ relation(U_337) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_343,sK70(U_337,U_336,U_335))],[f_35_7]) ).
fof(f_35_9,plain,
! [U_337] :
( ! [U_336] :
( ! [U_335] :
( ( ( U_335 = relation_composition(U_337,U_336)
| ( ~ in(ordered_pair(sK69(U_337,U_336,U_335),sK70(U_337,U_336,U_335)),U_335)
& in(ordered_pair(sK71(U_337,U_336,U_335),sK70(U_337,U_336,U_335)),U_336)
& in(ordered_pair(sK69(U_337,U_336,U_335),sK71(U_337,U_336,U_335)),U_337) )
| ( ! [U_331] :
( ~ in(ordered_pair(U_331,sK68(U_337,U_336,U_335)),U_336)
| ~ in(ordered_pair(sK67(U_337,U_336,U_335),U_331),U_337) )
& in(ordered_pair(sK67(U_337,U_336,U_335),sK68(U_337,U_336,U_335)),U_335) ) )
& ( ( ! [U_341,U_339] :
( in(ordered_pair(U_341,U_339),U_335)
| ! [U_328] :
( ~ in(ordered_pair(U_328,U_339),U_336)
| ~ in(ordered_pair(U_341,U_328),U_337) ) )
& ! [U_340,U_338] :
( ( in(ordered_pair(sK66(U_337,U_336,U_335,U_340,U_338),U_338),U_336)
& in(ordered_pair(U_340,sK66(U_337,U_336,U_335,U_340,U_338)),U_337) )
| ~ in(ordered_pair(U_340,U_338),U_335) ) )
| U_335 != relation_composition(U_337,U_336) ) )
| ~ relation(U_335) )
| ~ relation(U_336) )
| ~ relation(U_337) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_332,sK71(U_337,U_336,U_335))],[f_35_8]) ).
cnf(f_35_10,plain,
( in(ordered_pair(U_340,sK66(U_337,U_336,U_335,U_340,U_338)),U_337)
| ~ in(ordered_pair(U_340,U_338),U_335)
| U_335 != relation_composition(U_337,U_336)
| ~ relation(U_335)
| ~ relation(U_336)
| ~ relation(U_337) ),
inference(clausify,[status(thm)],[f_35_9]) ).
cnf(f_35_11,plain,
( in(ordered_pair(sK66(U_337,U_336,U_335,U_340,U_338),U_338),U_336)
| ~ in(ordered_pair(U_340,U_338),U_335)
| U_335 != relation_composition(U_337,U_336)
| ~ relation(U_335)
| ~ relation(U_336)
| ~ relation(U_337) ),
inference(clausify,[status(thm)],[f_35_9]) ).
cnf(f_35_12,plain,
( in(ordered_pair(U_341,U_339),U_335)
| ~ in(ordered_pair(U_328,U_339),U_336)
| ~ in(ordered_pair(U_341,U_328),U_337)
| U_335 != relation_composition(U_337,U_336)
| ~ relation(U_335)
| ~ relation(U_336)
| ~ relation(U_337) ),
inference(clausify,[status(thm)],[f_35_9]) ).
cnf(f_35_13,plain,
( in(ordered_pair(sK69(U_337,U_336,U_335),sK71(U_337,U_336,U_335)),U_337)
| in(ordered_pair(sK67(U_337,U_336,U_335),sK68(U_337,U_336,U_335)),U_335)
| U_335 = relation_composition(U_337,U_336)
| ~ relation(U_335)
| ~ relation(U_336)
| ~ relation(U_337) ),
inference(clausify,[status(thm)],[f_35_9]) ).
cnf(f_35_14,plain,
( in(ordered_pair(sK71(U_337,U_336,U_335),sK70(U_337,U_336,U_335)),U_336)
| in(ordered_pair(sK67(U_337,U_336,U_335),sK68(U_337,U_336,U_335)),U_335)
| U_335 = relation_composition(U_337,U_336)
| ~ relation(U_335)
| ~ relation(U_336)
| ~ relation(U_337) ),
inference(clausify,[status(thm)],[f_35_9]) ).
cnf(f_35_15,plain,
( ~ in(ordered_pair(sK69(U_337,U_336,U_335),sK70(U_337,U_336,U_335)),U_335)
| in(ordered_pair(sK67(U_337,U_336,U_335),sK68(U_337,U_336,U_335)),U_335)
| U_335 = relation_composition(U_337,U_336)
| ~ relation(U_335)
| ~ relation(U_336)
| ~ relation(U_337) ),
inference(clausify,[status(thm)],[f_35_9]) ).
cnf(f_35_16,plain,
( in(ordered_pair(sK69(U_337,U_336,U_335),sK71(U_337,U_336,U_335)),U_337)
| ~ in(ordered_pair(U_331,sK68(U_337,U_336,U_335)),U_336)
| ~ in(ordered_pair(sK67(U_337,U_336,U_335),U_331),U_337)
| U_335 = relation_composition(U_337,U_336)
| ~ relation(U_335)
| ~ relation(U_336)
| ~ relation(U_337) ),
inference(clausify,[status(thm)],[f_35_9]) ).
cnf(f_35_17,plain,
( in(ordered_pair(sK71(U_337,U_336,U_335),sK70(U_337,U_336,U_335)),U_336)
| ~ in(ordered_pair(U_331,sK68(U_337,U_336,U_335)),U_336)
| ~ in(ordered_pair(sK67(U_337,U_336,U_335),U_331),U_337)
| U_335 = relation_composition(U_337,U_336)
| ~ relation(U_335)
| ~ relation(U_336)
| ~ relation(U_337) ),
inference(clausify,[status(thm)],[f_35_9]) ).
cnf(f_35_18,plain,
( ~ in(ordered_pair(sK69(U_337,U_336,U_335),sK70(U_337,U_336,U_335)),U_335)
| ~ in(ordered_pair(U_331,sK68(U_337,U_336,U_335)),U_336)
| ~ in(ordered_pair(sK67(U_337,U_336,U_335),U_331),U_337)
| U_335 = relation_composition(U_337,U_336)
| ~ relation(U_335)
| ~ relation(U_336)
| ~ relation(U_337) ),
inference(clausify,[status(thm)],[f_35_9]) ).
fof(f_36_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_36_2,plain,
! [U_350,U_349] :
( ! [U_348] :
( ( ( U_348 = complements_of_subsets(U_350,U_349)
| ? [U_347] :
( ( ( ~ in(U_347,U_348)
& in(subset_complement(U_350,U_347),U_349) )
| ( ~ in(subset_complement(U_350,U_347),U_349)
& in(U_347,U_348) ) )
& element(U_347,powerset(U_350)) ) )
& ( ! [U_346] :
( ( ( in(U_346,U_348)
| ~ in(subset_complement(U_350,U_346),U_349) )
& ( in(subset_complement(U_350,U_346),U_349)
| ~ in(U_346,U_348) ) )
| ~ element(U_346,powerset(U_350)) )
| U_348 != complements_of_subsets(U_350,U_349) ) )
| ~ element(U_348,powerset(powerset(U_350))) )
| ~ element(U_349,powerset(powerset(U_350))) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_350,U_349] :
( ! [U_348] :
( ( ( U_348 = complements_of_subsets(U_350,U_349)
| ( ( ( ~ in(sK72(U_350,U_349,U_348),U_348)
& in(subset_complement(U_350,sK72(U_350,U_349,U_348)),U_349) )
| ( ~ in(subset_complement(U_350,sK72(U_350,U_349,U_348)),U_349)
& in(sK72(U_350,U_349,U_348),U_348) ) )
& element(sK72(U_350,U_349,U_348),powerset(U_350)) ) )
& ( ! [U_346] :
( ( ( in(U_346,U_348)
| ~ in(subset_complement(U_350,U_346),U_349) )
& ( in(subset_complement(U_350,U_346),U_349)
| ~ in(U_346,U_348) ) )
| ~ element(U_346,powerset(U_350)) )
| U_348 != complements_of_subsets(U_350,U_349) ) )
| ~ element(U_348,powerset(powerset(U_350))) )
| ~ element(U_349,powerset(powerset(U_350))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_347,sK72(U_350,U_349,U_348))],[f_36_2]) ).
cnf(f_36_4,plain,
( in(subset_complement(U_350,U_346),U_349)
| ~ in(U_346,U_348)
| ~ element(U_346,powerset(U_350))
| U_348 != complements_of_subsets(U_350,U_349)
| ~ element(U_348,powerset(powerset(U_350)))
| ~ element(U_349,powerset(powerset(U_350))) ),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_5,plain,
( in(U_346,U_348)
| ~ in(subset_complement(U_350,U_346),U_349)
| ~ element(U_346,powerset(U_350))
| U_348 != complements_of_subsets(U_350,U_349)
| ~ element(U_348,powerset(powerset(U_350)))
| ~ element(U_349,powerset(powerset(U_350))) ),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_6,plain,
( element(sK72(U_350,U_349,U_348),powerset(U_350))
| U_348 = complements_of_subsets(U_350,U_349)
| ~ element(U_348,powerset(powerset(U_350)))
| ~ element(U_349,powerset(powerset(U_350))) ),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_7,plain,
( in(subset_complement(U_350,sK72(U_350,U_349,U_348)),U_349)
| in(sK72(U_350,U_349,U_348),U_348)
| U_348 = complements_of_subsets(U_350,U_349)
| ~ element(U_348,powerset(powerset(U_350)))
| ~ element(U_349,powerset(powerset(U_350))) ),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_8,plain,
( ~ in(sK72(U_350,U_349,U_348),U_348)
| in(sK72(U_350,U_349,U_348),U_348)
| U_348 = complements_of_subsets(U_350,U_349)
| ~ element(U_348,powerset(powerset(U_350)))
| ~ element(U_349,powerset(powerset(U_350))) ),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_9,plain,
( in(subset_complement(U_350,sK72(U_350,U_349,U_348)),U_349)
| ~ in(subset_complement(U_350,sK72(U_350,U_349,U_348)),U_349)
| U_348 = complements_of_subsets(U_350,U_349)
| ~ element(U_348,powerset(powerset(U_350)))
| ~ element(U_349,powerset(powerset(U_350))) ),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_10,plain,
( ~ in(sK72(U_350,U_349,U_348),U_348)
| ~ in(subset_complement(U_350,sK72(U_350,U_349,U_348)),U_349)
| U_348 = complements_of_subsets(U_350,U_349)
| ~ element(U_348,powerset(powerset(U_350)))
| ~ element(U_349,powerset(powerset(U_350))) ),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_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_37_2,plain,
! [U_352,U_351] :
( ( proper_subset(U_352,U_351)
| U_352 = U_351
| ~ subset(U_352,U_351) )
& ( ( U_352 != U_351
& subset(U_352,U_351) )
| ~ proper_subset(U_352,U_351) ) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
( ! [U_356,U_354] :
( proper_subset(U_356,U_354)
| U_356 = U_354
| ~ subset(U_356,U_354) )
& ! [U_355,U_353] :
( ( U_355 != U_353
& subset(U_355,U_353) )
| ~ proper_subset(U_355,U_353) ) ),
inference(miniscope,[status(thm)],[f_37_2]) ).
cnf(f_37_4,plain,
( subset(U_355,U_353)
| ~ proper_subset(U_355,U_353) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_5,plain,
( U_355 != U_353
| ~ proper_subset(U_355,U_353) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_6,plain,
( proper_subset(U_356,U_354)
| U_356 = U_354
| ~ subset(U_356,U_354) ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
cnf(f_38_2,plain,
$true,
inference(clausify,[status(thm)],[f_38_1]) ).
fof(f_39_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_setfam_1]) ).
cnf(f_39_2,plain,
$true,
inference(clausify,[status(thm)],[f_39_1]) ).
fof(f_40_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
cnf(f_40_2,plain,
$true,
inference(clausify,[status(thm)],[f_40_1]) ).
fof(f_41_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
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_zfmisc_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_k2_relat_1]) ).
cnf(f_43_2,plain,
$true,
inference(clausify,[status(thm)],[f_43_1]) ).
fof(f_44_1,plain,
! [A] : element(cast_to_subset(A),powerset(A)),
inference(fof_nnf,[status(thm)],[dt_k2_subset_1]) ).
fof(f_44_2,plain,
! [U_357] : element(cast_to_subset(U_357),powerset(U_357)),
inference(variable_rename,[status(thm)],[f_44_1]) ).
cnf(f_44_3,plain,
element(cast_to_subset(U_357),powerset(U_357)),
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_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_k2_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_k2_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_k3_relat_1]) ).
cnf(f_48_2,plain,
$true,
inference(clausify,[status(thm)],[f_48_1]) ).
fof(f_49_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_49_2,plain,
! [U_359,U_358] :
( element(subset_complement(U_359,U_358),powerset(U_359))
| ~ element(U_358,powerset(U_359)) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
cnf(f_49_3,plain,
( element(subset_complement(U_359,U_358),powerset(U_359))
| ~ element(U_358,powerset(U_359)) ),
inference(clausify,[status(thm)],[f_49_2]) ).
fof(f_50_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_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_k3_xboole_0]) ).
cnf(f_51_2,plain,
$true,
inference(clausify,[status(thm)],[f_51_1]) ).
fof(f_52_1,plain,
! [A] :
( relation(relation_inverse(A))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k4_relat_1]) ).
fof(f_52_2,plain,
! [U_360] :
( relation(relation_inverse(U_360))
| ~ relation(U_360) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
cnf(f_52_3,plain,
( relation(relation_inverse(U_360))
| ~ relation(U_360) ),
inference(clausify,[status(thm)],[f_52_2]) ).
fof(f_53_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
cnf(f_53_2,plain,
$true,
inference(clausify,[status(thm)],[f_53_1]) ).
fof(f_54_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
cnf(f_54_2,plain,
$true,
inference(clausify,[status(thm)],[f_54_1]) ).
fof(f_55_1,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_relat_1]) ).
fof(f_55_2,plain,
! [U_362,U_361] :
( relation(relation_composition(U_362,U_361))
| ~ relation(U_361)
| ~ relation(U_362) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
cnf(f_55_3,plain,
( relation(relation_composition(U_362,U_361))
| ~ relation(U_361)
| ~ relation(U_362) ),
inference(clausify,[status(thm)],[f_55_2]) ).
fof(f_56_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_56_2,plain,
! [U_364,U_363] :
( element(union_of_subsets(U_364,U_363),powerset(U_364))
| ~ element(U_363,powerset(powerset(U_364))) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
cnf(f_56_3,plain,
( element(union_of_subsets(U_364,U_363),powerset(U_364))
| ~ element(U_363,powerset(powerset(U_364))) ),
inference(clausify,[status(thm)],[f_56_2]) ).
fof(f_57_1,plain,
! [A] : relation(identity_relation(A)),
inference(fof_nnf,[status(thm)],[dt_k6_relat_1]) ).
fof(f_57_2,plain,
! [U_365] : relation(identity_relation(U_365)),
inference(variable_rename,[status(thm)],[f_57_1]) ).
cnf(f_57_3,plain,
relation(identity_relation(U_365)),
inference(clausify,[status(thm)],[f_57_2]) ).
fof(f_58_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_58_2,plain,
! [U_367,U_366] :
( element(meet_of_subsets(U_367,U_366),powerset(U_367))
| ~ element(U_366,powerset(powerset(U_367))) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
cnf(f_58_3,plain,
( element(meet_of_subsets(U_367,U_366),powerset(U_367))
| ~ element(U_366,powerset(powerset(U_367))) ),
inference(clausify,[status(thm)],[f_58_2]) ).
fof(f_59_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_59_2,plain,
! [U_370,U_369,U_368] :
( element(subset_difference(U_370,U_369,U_368),powerset(U_370))
| ~ element(U_368,powerset(U_370))
| ~ element(U_369,powerset(U_370)) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
cnf(f_59_3,plain,
( element(subset_difference(U_370,U_369,U_368),powerset(U_370))
| ~ element(U_368,powerset(U_370))
| ~ element(U_369,powerset(U_370)) ),
inference(clausify,[status(thm)],[f_59_2]) ).
fof(f_60_1,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k7_relat_1]) ).
fof(f_60_2,plain,
! [U_372,U_371] :
( relation(relation_dom_restriction(U_372,U_371))
| ~ relation(U_372) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
! [U_372] :
( ! [U_371] : relation(relation_dom_restriction(U_372,U_371))
| ~ relation(U_372) ),
inference(miniscope,[status(thm)],[f_60_2]) ).
cnf(f_60_4,plain,
( relation(relation_dom_restriction(U_372,U_371))
| ~ relation(U_372) ),
inference(clausify,[status(thm)],[f_60_3]) ).
fof(f_61_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_61_2,plain,
! [U_374,U_373] :
( element(complements_of_subsets(U_374,U_373),powerset(powerset(U_374)))
| ~ element(U_373,powerset(powerset(U_374))) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
cnf(f_61_3,plain,
( element(complements_of_subsets(U_374,U_373),powerset(powerset(U_374)))
| ~ element(U_373,powerset(powerset(U_374))) ),
inference(clausify,[status(thm)],[f_61_2]) ).
fof(f_62_1,plain,
! [A,B] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[dt_k8_relat_1]) ).
fof(f_62_2,plain,
! [U_376,U_375] :
( relation(relation_rng_restriction(U_376,U_375))
| ~ relation(U_375) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
cnf(f_62_3,plain,
( relation(relation_rng_restriction(U_376,U_375))
| ~ relation(U_375) ),
inference(clausify,[status(thm)],[f_62_2]) ).
fof(f_63_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k9_relat_1]) ).
cnf(f_63_2,plain,
$true,
inference(clausify,[status(thm)],[f_63_1]) ).
fof(f_64_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_64_2,plain,
$true,
inference(clausify,[status(thm)],[f_64_1]) ).
fof(f_65_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_65_2,plain,
! [U_378] :
? [U_377] : element(U_377,U_378),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
! [U_378] : element(sK73(U_378),U_378),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_377,sK73(U_378))],[f_65_2]) ).
cnf(f_65_4,plain,
element(sK73(U_378),U_378),
inference(clausify,[status(thm)],[f_65_3]) ).
fof(f_66_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_66_2,plain,
! [U_380,U_379] :
( ( relation(relation_composition(U_379,U_380))
& empty(relation_composition(U_379,U_380)) )
| ~ relation(U_379)
| ~ empty(U_380) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
cnf(f_66_3,plain,
( empty(relation_composition(U_379,U_380))
| ~ relation(U_379)
| ~ empty(U_380) ),
inference(clausify,[status(thm)],[f_66_2]) ).
cnf(f_66_4,plain,
( relation(relation_composition(U_379,U_380))
| ~ relation(U_379)
| ~ empty(U_380) ),
inference(clausify,[status(thm)],[f_66_2]) ).
fof(f_67_1,plain,
! [A,B] :
( relation(set_intersection2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc1_relat_1]) ).
fof(f_67_2,plain,
! [U_382,U_381] :
( relation(set_intersection2(U_382,U_381))
| ~ relation(U_381)
| ~ relation(U_382) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
cnf(f_67_3,plain,
( relation(set_intersection2(U_382,U_381))
| ~ relation(U_381)
| ~ relation(U_382) ),
inference(clausify,[status(thm)],[f_67_2]) ).
fof(f_68_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_68_2,plain,
! [U_383] : ~ empty(powerset(U_383)),
inference(variable_rename,[status(thm)],[f_68_1]) ).
cnf(f_68_3,plain,
~ empty(powerset(U_383)),
inference(clausify,[status(thm)],[f_68_2]) ).
fof(f_69_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_69_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_69_1]) ).
fof(f_70_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_70_2,plain,
! [U_385,U_384] : ~ empty(ordered_pair(U_385,U_384)),
inference(variable_rename,[status(thm)],[f_70_1]) ).
cnf(f_70_3,plain,
~ empty(ordered_pair(U_385,U_384)),
inference(clausify,[status(thm)],[f_70_2]) ).
fof(f_71_1,plain,
! [A,B] :
( relation(set_union2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc2_relat_1]) ).
fof(f_71_2,plain,
! [U_387,U_386] :
( relation(set_union2(U_387,U_386))
| ~ relation(U_386)
| ~ relation(U_387) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
cnf(f_71_3,plain,
( relation(set_union2(U_387,U_386))
| ~ relation(U_386)
| ~ relation(U_387) ),
inference(clausify,[status(thm)],[f_71_2]) ).
fof(f_72_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_72_2,plain,
! [U_388] : ~ empty(singleton(U_388)),
inference(variable_rename,[status(thm)],[f_72_1]) ).
cnf(f_72_3,plain,
~ empty(singleton(U_388)),
inference(clausify,[status(thm)],[f_72_2]) ).
fof(f_73_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_73_2,plain,
! [U_390,U_389] :
( ~ empty(set_union2(U_390,U_389))
| empty(U_390) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
fof(f_73_3,plain,
! [U_390] :
( ! [U_389] : ~ empty(set_union2(U_390,U_389))
| empty(U_390) ),
inference(miniscope,[status(thm)],[f_73_2]) ).
cnf(f_73_4,plain,
( ~ empty(set_union2(U_390,U_389))
| empty(U_390) ),
inference(clausify,[status(thm)],[f_73_3]) ).
fof(f_74_1,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_74_2,plain,
! [U_392,U_391] : ~ empty(unordered_pair(U_392,U_391)),
inference(variable_rename,[status(thm)],[f_74_1]) ).
cnf(f_74_3,plain,
~ empty(unordered_pair(U_392,U_391)),
inference(clausify,[status(thm)],[f_74_2]) ).
fof(f_75_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_75_2,plain,
! [U_394,U_393] :
( ~ empty(set_union2(U_393,U_394))
| empty(U_394) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
fof(f_75_3,plain,
! [U_394] :
( ! [U_393] : ~ empty(set_union2(U_393,U_394))
| empty(U_394) ),
inference(miniscope,[status(thm)],[f_75_2]) ).
cnf(f_75_4,plain,
( ~ empty(set_union2(U_393,U_394))
| empty(U_394) ),
inference(clausify,[status(thm)],[f_75_3]) ).
fof(f_76_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_76_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_76_1]) ).
cnf(f_76_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_76_1]) ).
fof(f_77_1,plain,
! [A,B] :
( ~ empty(cartesian_product2(A,B))
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc4_subset_1]) ).
fof(f_77_2,plain,
! [U_396,U_395] :
( ~ empty(cartesian_product2(U_396,U_395))
| empty(U_395)
| empty(U_396) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
cnf(f_77_3,plain,
( ~ empty(cartesian_product2(U_396,U_395))
| empty(U_395)
| empty(U_396) ),
inference(clausify,[status(thm)],[f_77_2]) ).
fof(f_78_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_78_2,plain,
! [U_397] :
( ~ empty(relation_dom(U_397))
| ~ relation(U_397)
| empty(U_397) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
cnf(f_78_3,plain,
( ~ empty(relation_dom(U_397))
| ~ relation(U_397)
| empty(U_397) ),
inference(clausify,[status(thm)],[f_78_2]) ).
fof(f_79_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_79_2,plain,
! [U_398] :
( ~ empty(relation_rng(U_398))
| ~ relation(U_398)
| empty(U_398) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
cnf(f_79_3,plain,
( ~ empty(relation_rng(U_398))
| ~ relation(U_398)
| empty(U_398) ),
inference(clausify,[status(thm)],[f_79_2]) ).
fof(f_80_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_80_2,plain,
! [U_399] :
( ( relation(relation_dom(U_399))
& empty(relation_dom(U_399)) )
| ~ empty(U_399) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
cnf(f_80_3,plain,
( empty(relation_dom(U_399))
| ~ empty(U_399) ),
inference(clausify,[status(thm)],[f_80_2]) ).
cnf(f_80_4,plain,
( relation(relation_dom(U_399))
| ~ empty(U_399) ),
inference(clausify,[status(thm)],[f_80_2]) ).
fof(f_81_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_81_2,plain,
! [U_400] :
( ( relation(relation_rng(U_400))
& empty(relation_rng(U_400)) )
| ~ empty(U_400) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
cnf(f_81_3,plain,
( empty(relation_rng(U_400))
| ~ empty(U_400) ),
inference(clausify,[status(thm)],[f_81_2]) ).
cnf(f_81_4,plain,
( relation(relation_rng(U_400))
| ~ empty(U_400) ),
inference(clausify,[status(thm)],[f_81_2]) ).
fof(f_82_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_82_2,plain,
! [U_402,U_401] :
( ( relation(relation_composition(U_402,U_401))
& empty(relation_composition(U_402,U_401)) )
| ~ relation(U_401)
| ~ empty(U_402) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
cnf(f_82_3,plain,
( empty(relation_composition(U_402,U_401))
| ~ relation(U_401)
| ~ empty(U_402) ),
inference(clausify,[status(thm)],[f_82_2]) ).
cnf(f_82_4,plain,
( relation(relation_composition(U_402,U_401))
| ~ relation(U_401)
| ~ empty(U_402) ),
inference(clausify,[status(thm)],[f_82_2]) ).
fof(f_83_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_83_2,plain,
! [U_404,U_403] : set_union2(U_404,U_404) = U_404,
inference(variable_rename,[status(thm)],[f_83_1]) ).
fof(f_83_3,plain,
! [U_404] : set_union2(U_404,U_404) = U_404,
inference(miniscope,[status(thm)],[f_83_2]) ).
cnf(f_83_4,plain,
set_union2(U_404,U_404) = U_404,
inference(clausify,[status(thm)],[f_83_3]) ).
fof(f_84_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_84_2,plain,
! [U_406,U_405] : set_intersection2(U_406,U_406) = U_406,
inference(variable_rename,[status(thm)],[f_84_1]) ).
fof(f_84_3,plain,
! [U_406] : set_intersection2(U_406,U_406) = U_406,
inference(miniscope,[status(thm)],[f_84_2]) ).
cnf(f_84_4,plain,
set_intersection2(U_406,U_406) = U_406,
inference(clausify,[status(thm)],[f_84_3]) ).
fof(f_85_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_85_2,plain,
! [U_408,U_407] :
( subset_complement(U_408,subset_complement(U_408,U_407)) = U_407
| ~ element(U_407,powerset(U_408)) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
cnf(f_85_3,plain,
( subset_complement(U_408,subset_complement(U_408,U_407)) = U_407
| ~ element(U_407,powerset(U_408)) ),
inference(clausify,[status(thm)],[f_85_2]) ).
fof(f_86_1,plain,
! [A] :
( relation_inverse(relation_inverse(A)) = A
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[involutiveness_k4_relat_1]) ).
fof(f_86_2,plain,
! [U_409] :
( relation_inverse(relation_inverse(U_409)) = U_409
| ~ relation(U_409) ),
inference(variable_rename,[status(thm)],[f_86_1]) ).
cnf(f_86_3,plain,
( relation_inverse(relation_inverse(U_409)) = U_409
| ~ relation(U_409) ),
inference(clausify,[status(thm)],[f_86_2]) ).
fof(f_87_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_87_2,plain,
! [U_411,U_410] :
( complements_of_subsets(U_411,complements_of_subsets(U_411,U_410)) = U_410
| ~ element(U_410,powerset(powerset(U_411))) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
cnf(f_87_3,plain,
( complements_of_subsets(U_411,complements_of_subsets(U_411,U_410)) = U_410
| ~ element(U_410,powerset(powerset(U_411))) ),
inference(clausify,[status(thm)],[f_87_2]) ).
fof(f_88_1,plain,
! [A,B] : ~ proper_subset(A,A),
inference(fof_nnf,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(f_88_2,plain,
! [U_413,U_412] : ~ proper_subset(U_413,U_413),
inference(variable_rename,[status(thm)],[f_88_1]) ).
fof(f_88_3,plain,
! [U_413] : ~ proper_subset(U_413,U_413),
inference(miniscope,[status(thm)],[f_88_2]) ).
cnf(f_88_4,plain,
~ proper_subset(U_413,U_413),
inference(clausify,[status(thm)],[f_88_3]) ).
fof(f_89_1,plain,
! [A] : singleton(A) != empty_set,
inference(fof_nnf,[status(thm)],[l1_zfmisc_1]) ).
fof(f_89_2,plain,
! [U_414] : singleton(U_414) != empty_set,
inference(variable_rename,[status(thm)],[f_89_1]) ).
cnf(f_89_3,plain,
singleton(U_414) != empty_set,
inference(clausify,[status(thm)],[f_89_2]) ).
fof(f_90_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l23_zfmisc_1]) ).
fof(f_90_2,plain,
! [U_416,U_415] :
( set_union2(singleton(U_416),U_415) = U_415
| ~ in(U_416,U_415) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
cnf(f_90_3,plain,
( set_union2(singleton(U_416),U_415) = U_415
| ~ in(U_416,U_415) ),
inference(clausify,[status(thm)],[f_90_2]) ).
fof(f_91_1,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(fof_nnf,[status(thm)],[l25_zfmisc_1]) ).
fof(f_91_2,plain,
! [U_418,U_417] :
( ~ in(U_418,U_417)
| ~ disjoint(singleton(U_418),U_417) ),
inference(variable_rename,[status(thm)],[f_91_1]) ).
cnf(f_91_3,plain,
( ~ in(U_418,U_417)
| ~ disjoint(singleton(U_418),U_417) ),
inference(clausify,[status(thm)],[f_91_2]) ).
fof(f_92_1,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(fof_nnf,[status(thm)],[l28_zfmisc_1]) ).
fof(f_92_2,plain,
! [U_420,U_419] :
( disjoint(singleton(U_420),U_419)
| in(U_420,U_419) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
cnf(f_92_3,plain,
( disjoint(singleton(U_420),U_419)
| in(U_420,U_419) ),
inference(clausify,[status(thm)],[f_92_2]) ).
fof(f_93_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_93_2,plain,
! [U_422,U_421] :
( ( subset(singleton(U_422),U_421)
| ~ in(U_422,U_421) )
& ( in(U_422,U_421)
| ~ subset(singleton(U_422),U_421) ) ),
inference(variable_rename,[status(thm)],[f_93_1]) ).
fof(f_93_3,plain,
( ! [U_426,U_424] :
( subset(singleton(U_426),U_424)
| ~ in(U_426,U_424) )
& ! [U_425,U_423] :
( in(U_425,U_423)
| ~ subset(singleton(U_425),U_423) ) ),
inference(miniscope,[status(thm)],[f_93_2]) ).
cnf(f_93_4,plain,
( in(U_425,U_423)
| ~ subset(singleton(U_425),U_423) ),
inference(clausify,[status(thm)],[f_93_3]) ).
cnf(f_93_5,plain,
( subset(singleton(U_426),U_424)
| ~ in(U_426,U_424) ),
inference(clausify,[status(thm)],[f_93_3]) ).
fof(f_94_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_94_2,plain,
! [U_428,U_427] :
( ( set_difference(U_428,U_427) = empty_set
| ~ subset(U_428,U_427) )
& ( subset(U_428,U_427)
| set_difference(U_428,U_427) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
fof(f_94_3,plain,
( ! [U_432,U_430] :
( set_difference(U_432,U_430) = empty_set
| ~ subset(U_432,U_430) )
& ! [U_431,U_429] :
( subset(U_431,U_429)
| set_difference(U_431,U_429) != empty_set ) ),
inference(miniscope,[status(thm)],[f_94_2]) ).
cnf(f_94_4,plain,
( subset(U_431,U_429)
| set_difference(U_431,U_429) != empty_set ),
inference(clausify,[status(thm)],[f_94_3]) ).
cnf(f_94_5,plain,
( set_difference(U_432,U_430) = empty_set
| ~ subset(U_432,U_430) ),
inference(clausify,[status(thm)],[f_94_3]) ).
fof(f_95_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_95_2,plain,
! [U_435,U_434] :
( ! [U_433] :
( in(U_433,U_435)
| ~ in(U_433,U_434) )
| ~ element(U_434,powerset(U_435)) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
cnf(f_95_3,plain,
( in(U_433,U_435)
| ~ in(U_433,U_434)
| ~ element(U_434,powerset(U_435)) ),
inference(clausify,[status(thm)],[f_95_2]) ).
fof(f_96_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_96_2,plain,
! [U_438,U_437,U_436] :
( subset(U_438,set_difference(U_437,singleton(U_436)))
| in(U_436,U_438)
| ~ subset(U_438,U_437) ),
inference(variable_rename,[status(thm)],[f_96_1]) ).
fof(f_96_3,plain,
! [U_438,U_437] :
( ! [U_436] :
( subset(U_438,set_difference(U_437,singleton(U_436)))
| in(U_436,U_438) )
| ~ subset(U_438,U_437) ),
inference(miniscope,[status(thm)],[f_96_2]) ).
cnf(f_96_4,plain,
( subset(U_438,set_difference(U_437,singleton(U_436)))
| in(U_436,U_438)
| ~ subset(U_438,U_437) ),
inference(clausify,[status(thm)],[f_96_3]) ).
fof(f_97_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_97_2,plain,
! [U_440,U_439] :
( ( subset(U_440,singleton(U_439))
| ( U_440 != singleton(U_439)
& U_440 != empty_set ) )
& ( U_440 = singleton(U_439)
| U_440 = empty_set
| ~ subset(U_440,singleton(U_439)) ) ),
inference(variable_rename,[status(thm)],[f_97_1]) ).
fof(f_97_3,plain,
( ! [U_444,U_442] :
( subset(U_444,singleton(U_442))
| ( U_444 != singleton(U_442)
& U_444 != empty_set ) )
& ! [U_443,U_441] :
( U_443 = singleton(U_441)
| U_443 = empty_set
| ~ subset(U_443,singleton(U_441)) ) ),
inference(miniscope,[status(thm)],[f_97_2]) ).
cnf(f_97_4,plain,
( U_443 = singleton(U_441)
| U_443 = empty_set
| ~ subset(U_443,singleton(U_441)) ),
inference(clausify,[status(thm)],[f_97_3]) ).
cnf(f_97_5,plain,
( U_444 != empty_set
| subset(U_444,singleton(U_442)) ),
inference(clausify,[status(thm)],[f_97_3]) ).
cnf(f_97_6,plain,
( U_444 != singleton(U_442)
| subset(U_444,singleton(U_442)) ),
inference(clausify,[status(thm)],[f_97_3]) ).
fof(f_98_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l50_zfmisc_1]) ).
fof(f_98_2,plain,
! [U_446,U_445] :
( subset(U_446,union(U_445))
| ~ in(U_446,U_445) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
cnf(f_98_3,plain,
( subset(U_446,union(U_445))
| ~ in(U_446,U_445) ),
inference(clausify,[status(thm)],[f_98_2]) ).
fof(f_99_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_99_2,plain,
! [U_450,U_449,U_448,U_447] :
( ( in(ordered_pair(U_450,U_449),cartesian_product2(U_448,U_447))
| ~ in(U_449,U_447)
| ~ in(U_450,U_448) )
& ( ( in(U_449,U_447)
& in(U_450,U_448) )
| ~ in(ordered_pair(U_450,U_449),cartesian_product2(U_448,U_447)) ) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
fof(f_99_3,plain,
( ! [U_458,U_456,U_454,U_452] :
( in(ordered_pair(U_458,U_456),cartesian_product2(U_454,U_452))
| ~ in(U_456,U_452)
| ~ in(U_458,U_454) )
& ! [U_457,U_455,U_453,U_451] :
( ( in(U_455,U_451)
& in(U_457,U_453) )
| ~ in(ordered_pair(U_457,U_455),cartesian_product2(U_453,U_451)) ) ),
inference(miniscope,[status(thm)],[f_99_2]) ).
cnf(f_99_4,plain,
( in(U_457,U_453)
| ~ in(ordered_pair(U_457,U_455),cartesian_product2(U_453,U_451)) ),
inference(clausify,[status(thm)],[f_99_3]) ).
cnf(f_99_5,plain,
( in(U_455,U_451)
| ~ in(ordered_pair(U_457,U_455),cartesian_product2(U_453,U_451)) ),
inference(clausify,[status(thm)],[f_99_3]) ).
cnf(f_99_6,plain,
( in(ordered_pair(U_458,U_456),cartesian_product2(U_454,U_452))
| ~ in(U_456,U_452)
| ~ in(U_458,U_454) ),
inference(clausify,[status(thm)],[f_99_3]) ).
fof(f_100_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_100_2,plain,
! [U_461,U_460] :
( element(U_461,powerset(U_460))
| ? [U_459] :
( ~ in(U_459,U_460)
& in(U_459,U_461) ) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
fof(f_100_3,plain,
! [U_461,U_460] :
( element(U_461,powerset(U_460))
| ( ~ in(sK74(U_461,U_460),U_460)
& in(sK74(U_461,U_460),U_461) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_459,sK74(U_461,U_460))],[f_100_2]) ).
cnf(f_100_4,plain,
( in(sK74(U_461,U_460),U_461)
| element(U_461,powerset(U_460)) ),
inference(clausify,[status(thm)],[f_100_3]) ).
cnf(f_100_5,plain,
( ~ in(sK74(U_461,U_460),U_460)
| element(U_461,powerset(U_460)) ),
inference(clausify,[status(thm)],[f_100_3]) ).
fof(f_101_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_101_2,plain,
? [U_462] :
( relation(U_462)
& empty(U_462) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
fof(f_101_3,plain,
( relation(sK75)
& empty(sK75) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_462,sK75)],[f_101_2]) ).
cnf(f_101_4,plain,
empty(sK75),
inference(clausify,[status(thm)],[f_101_3]) ).
cnf(f_101_5,plain,
relation(sK75),
inference(clausify,[status(thm)],[f_101_3]) ).
fof(f_102_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_102_2,plain,
! [U_464] :
( ? [U_463] :
( ~ empty(U_463)
& element(U_463,powerset(U_464)) )
| empty(U_464) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
fof(f_102_3,plain,
! [U_464] :
( ( ~ empty(sK76(U_464))
& element(sK76(U_464),powerset(U_464)) )
| empty(U_464) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_463,sK76(U_464))],[f_102_2]) ).
cnf(f_102_4,plain,
( element(sK76(U_464),powerset(U_464))
| empty(U_464) ),
inference(clausify,[status(thm)],[f_102_3]) ).
cnf(f_102_5,plain,
( ~ empty(sK76(U_464))
| empty(U_464) ),
inference(clausify,[status(thm)],[f_102_3]) ).
fof(f_103_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_103_2,plain,
? [U_465] : empty(U_465),
inference(variable_rename,[status(thm)],[f_103_1]) ).
fof(f_103_3,plain,
empty(sK77),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_465,sK77)],[f_103_2]) ).
cnf(f_103_4,plain,
empty(sK77),
inference(clausify,[status(thm)],[f_103_3]) ).
fof(f_104_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_104_2,plain,
? [U_466] :
( relation(U_466)
& ~ empty(U_466) ),
inference(variable_rename,[status(thm)],[f_104_1]) ).
fof(f_104_3,plain,
( relation(sK78)
& ~ empty(sK78) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_466,sK78)],[f_104_2]) ).
cnf(f_104_4,plain,
~ empty(sK78),
inference(clausify,[status(thm)],[f_104_3]) ).
cnf(f_104_5,plain,
relation(sK78),
inference(clausify,[status(thm)],[f_104_3]) ).
fof(f_105_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_105_2,plain,
! [U_468] :
? [U_467] :
( empty(U_467)
& element(U_467,powerset(U_468)) ),
inference(variable_rename,[status(thm)],[f_105_1]) ).
fof(f_105_3,plain,
! [U_468] :
( empty(sK79(U_468))
& element(sK79(U_468),powerset(U_468)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_467,sK79(U_468))],[f_105_2]) ).
cnf(f_105_4,plain,
element(sK79(U_468),powerset(U_468)),
inference(clausify,[status(thm)],[f_105_3]) ).
cnf(f_105_5,plain,
empty(sK79(U_468)),
inference(clausify,[status(thm)],[f_105_3]) ).
fof(f_106_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_106_2,plain,
? [U_469] : ~ empty(U_469),
inference(variable_rename,[status(thm)],[f_106_1]) ).
fof(f_106_3,plain,
~ empty(sK80),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_469,sK80)],[f_106_2]) ).
cnf(f_106_4,plain,
~ empty(sK80),
inference(clausify,[status(thm)],[f_106_3]) ).
fof(f_107_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_107_2,plain,
! [U_471,U_470] :
( union_of_subsets(U_471,U_470) = union(U_470)
| ~ element(U_470,powerset(powerset(U_471))) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
cnf(f_107_3,plain,
( union_of_subsets(U_471,U_470) = union(U_470)
| ~ element(U_470,powerset(powerset(U_471))) ),
inference(clausify,[status(thm)],[f_107_2]) ).
fof(f_108_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_108_2,plain,
! [U_473,U_472] :
( meet_of_subsets(U_473,U_472) = set_meet(U_472)
| ~ element(U_472,powerset(powerset(U_473))) ),
inference(variable_rename,[status(thm)],[f_108_1]) ).
cnf(f_108_3,plain,
( meet_of_subsets(U_473,U_472) = set_meet(U_472)
| ~ element(U_472,powerset(powerset(U_473))) ),
inference(clausify,[status(thm)],[f_108_2]) ).
fof(f_109_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_109_2,plain,
! [U_476,U_475,U_474] :
( subset_difference(U_476,U_475,U_474) = set_difference(U_475,U_474)
| ~ element(U_474,powerset(U_476))
| ~ element(U_475,powerset(U_476)) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
cnf(f_109_3,plain,
( subset_difference(U_476,U_475,U_474) = set_difference(U_475,U_474)
| ~ element(U_474,powerset(U_476))
| ~ element(U_475,powerset(U_476)) ),
inference(clausify,[status(thm)],[f_109_2]) ).
fof(f_110_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_110_2,plain,
! [U_478,U_477] : subset(U_478,U_478),
inference(variable_rename,[status(thm)],[f_110_1]) ).
fof(f_110_3,plain,
! [U_478] : subset(U_478,U_478),
inference(miniscope,[status(thm)],[f_110_2]) ).
cnf(f_110_4,plain,
subset(U_478,U_478),
inference(clausify,[status(thm)],[f_110_3]) ).
fof(f_111_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_111_2,plain,
! [U_480,U_479] :
( disjoint(U_479,U_480)
| ~ disjoint(U_480,U_479) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
cnf(f_111_3,plain,
( disjoint(U_479,U_480)
| ~ disjoint(U_480,U_479) ),
inference(clausify,[status(thm)],[f_111_2]) ).
fof(f_112_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_112_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_112_1]) ).
fof(f_112_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_112_2]) ).
cnf(f_112_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_112_3]) ).
cnf(f_112_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_112_3]) ).
cnf(f_112_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_112_3]) ).
fof(f_113_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_113_2,plain,
! [U_496,U_495,U_494,U_493] :
( U_496 = U_493
| U_496 = U_494
| unordered_pair(U_496,U_495) != unordered_pair(U_494,U_493) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
fof(f_113_3,plain,
! [U_496,U_495,U_494] :
( ! [U_493] :
( U_496 = U_493
| unordered_pair(U_496,U_495) != unordered_pair(U_494,U_493) )
| U_496 = U_494 ),
inference(miniscope,[status(thm)],[f_113_2]) ).
cnf(f_113_4,plain,
( U_496 = U_493
| unordered_pair(U_496,U_495) != unordered_pair(U_494,U_493)
| U_496 = U_494 ),
inference(clausify,[status(thm)],[f_113_3]) ).
fof(f_114_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_114_2,plain,
! [U_499,U_498,U_497] :
( ( ( in(U_499,relation_rng(relation_rng_restriction(U_498,U_497)))
| ~ in(U_499,relation_rng(U_497))
| ~ in(U_499,U_498) )
& ( ( in(U_499,relation_rng(U_497))
& in(U_499,U_498) )
| ~ in(U_499,relation_rng(relation_rng_restriction(U_498,U_497))) ) )
| ~ relation(U_497) ),
inference(variable_rename,[status(thm)],[f_114_1]) ).
cnf(f_114_3,plain,
( in(U_499,U_498)
| ~ in(U_499,relation_rng(relation_rng_restriction(U_498,U_497)))
| ~ relation(U_497) ),
inference(clausify,[status(thm)],[f_114_2]) ).
cnf(f_114_4,plain,
( in(U_499,relation_rng(U_497))
| ~ in(U_499,relation_rng(relation_rng_restriction(U_498,U_497)))
| ~ relation(U_497) ),
inference(clausify,[status(thm)],[f_114_2]) ).
cnf(f_114_5,plain,
( in(U_499,relation_rng(relation_rng_restriction(U_498,U_497)))
| ~ in(U_499,relation_rng(U_497))
| ~ in(U_499,U_498)
| ~ relation(U_497) ),
inference(clausify,[status(thm)],[f_114_2]) ).
fof(f_115_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_115_2,plain,
! [U_501,U_500] :
( subset(relation_rng(relation_rng_restriction(U_501,U_500)),U_501)
| ~ relation(U_500) ),
inference(variable_rename,[status(thm)],[f_115_1]) ).
cnf(f_115_3,plain,
( subset(relation_rng(relation_rng_restriction(U_501,U_500)),U_501)
| ~ relation(U_500) ),
inference(clausify,[status(thm)],[f_115_2]) ).
fof(f_116_1,plain,
! [A,B] :
( subset(relation_rng_restriction(A,B),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t117_relat_1]) ).
fof(f_116_2,plain,
! [U_503,U_502] :
( subset(relation_rng_restriction(U_503,U_502),U_502)
| ~ relation(U_502) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
cnf(f_116_3,plain,
( subset(relation_rng_restriction(U_503,U_502),U_502)
| ~ relation(U_502) ),
inference(clausify,[status(thm)],[f_116_2]) ).
fof(f_117_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_117_2,plain,
! [U_505,U_504] :
( subset(relation_rng(relation_rng_restriction(U_505,U_504)),relation_rng(U_504))
| ~ relation(U_504) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
cnf(f_117_3,plain,
( subset(relation_rng(relation_rng_restriction(U_505,U_504)),relation_rng(U_504))
| ~ relation(U_504) ),
inference(clausify,[status(thm)],[f_117_2]) ).
fof(f_118_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_118_2,plain,
! [U_508,U_507,U_506] :
( ( subset(cartesian_product2(U_506,U_508),cartesian_product2(U_506,U_507))
& subset(cartesian_product2(U_508,U_506),cartesian_product2(U_507,U_506)) )
| ~ subset(U_508,U_507) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
fof(f_118_3,plain,
! [U_508,U_507] :
( ( ! [U_510] : subset(cartesian_product2(U_510,U_508),cartesian_product2(U_510,U_507))
& ! [U_509] : subset(cartesian_product2(U_508,U_509),cartesian_product2(U_507,U_509)) )
| ~ subset(U_508,U_507) ),
inference(miniscope,[status(thm)],[f_118_2]) ).
cnf(f_118_4,plain,
( subset(cartesian_product2(U_508,U_509),cartesian_product2(U_507,U_509))
| ~ subset(U_508,U_507) ),
inference(clausify,[status(thm)],[f_118_3]) ).
cnf(f_118_5,plain,
( subset(cartesian_product2(U_510,U_508),cartesian_product2(U_510,U_507))
| ~ subset(U_508,U_507) ),
inference(clausify,[status(thm)],[f_118_3]) ).
fof(f_119_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_119_2,plain,
! [U_512,U_511] :
( relation_rng(relation_rng_restriction(U_512,U_511)) = set_intersection2(relation_rng(U_511),U_512)
| ~ relation(U_511) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
cnf(f_119_3,plain,
( relation_rng(relation_rng_restriction(U_512,U_511)) = set_intersection2(relation_rng(U_511),U_512)
| ~ relation(U_511) ),
inference(clausify,[status(thm)],[f_119_2]) ).
fof(f_120_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_120_2,plain,
! [U_516,U_515,U_514,U_513] :
( subset(cartesian_product2(U_516,U_514),cartesian_product2(U_515,U_513))
| ~ subset(U_514,U_513)
| ~ subset(U_516,U_515) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
cnf(f_120_3,plain,
( subset(cartesian_product2(U_516,U_514),cartesian_product2(U_515,U_513))
| ~ subset(U_514,U_513)
| ~ subset(U_516,U_515) ),
inference(clausify,[status(thm)],[f_120_2]) ).
fof(f_121_1,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t12_xboole_1]) ).
fof(f_121_2,plain,
! [U_518,U_517] :
( set_union2(U_518,U_517) = U_517
| ~ subset(U_518,U_517) ),
inference(variable_rename,[status(thm)],[f_121_1]) ).
cnf(f_121_3,plain,
( set_union2(U_518,U_517) = U_517
| ~ subset(U_518,U_517) ),
inference(clausify,[status(thm)],[f_121_2]) ).
fof(f_122_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_122_2,plain,
! [U_524] :
? [U_523] :
( ! [U_522] :
( in(U_522,U_523)
| are_equipotent(U_522,U_523)
| ~ subset(U_522,U_523) )
& ! [U_521] :
( in(powerset(U_521),U_523)
| ~ in(U_521,U_523) )
& ! [U_520,U_519] :
( in(U_519,U_523)
| ~ subset(U_519,U_520)
| ~ in(U_520,U_523) )
& in(U_524,U_523) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
fof(f_122_3,plain,
! [U_524] :
( ! [U_522] :
( in(U_522,sK81(U_524))
| are_equipotent(U_522,sK81(U_524))
| ~ subset(U_522,sK81(U_524)) )
& ! [U_521] :
( in(powerset(U_521),sK81(U_524))
| ~ in(U_521,sK81(U_524)) )
& ! [U_520,U_519] :
( in(U_519,sK81(U_524))
| ~ subset(U_519,U_520)
| ~ in(U_520,sK81(U_524)) )
& in(U_524,sK81(U_524)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_523,sK81(U_524))],[f_122_2]) ).
cnf(f_122_4,plain,
in(U_524,sK81(U_524)),
inference(clausify,[status(thm)],[f_122_3]) ).
cnf(f_122_5,plain,
( in(U_519,sK81(U_524))
| ~ subset(U_519,U_520)
| ~ in(U_520,sK81(U_524)) ),
inference(clausify,[status(thm)],[f_122_3]) ).
cnf(f_122_6,plain,
( in(powerset(U_521),sK81(U_524))
| ~ in(U_521,sK81(U_524)) ),
inference(clausify,[status(thm)],[f_122_3]) ).
cnf(f_122_7,plain,
( in(U_522,sK81(U_524))
| are_equipotent(U_522,sK81(U_524))
| ~ subset(U_522,sK81(U_524)) ),
inference(clausify,[status(thm)],[f_122_3]) ).
fof(f_123_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_123_2,plain,
! [U_527,U_526,U_525] :
( relation_dom_restriction(relation_rng_restriction(U_527,U_525),U_526) = relation_rng_restriction(U_527,relation_dom_restriction(U_525,U_526))
| ~ relation(U_525) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
cnf(f_123_3,plain,
( relation_dom_restriction(relation_rng_restriction(U_527,U_525),U_526) = relation_rng_restriction(U_527,relation_dom_restriction(U_525,U_526))
| ~ relation(U_525) ),
inference(clausify,[status(thm)],[f_123_2]) ).
fof(f_124_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_124_2,plain,
! [U_532,U_531,U_530] :
( ( ( in(U_532,relation_image(U_530,U_531))
| ! [U_529] :
( ~ in(U_529,U_531)
| ~ in(ordered_pair(U_529,U_532),U_530)
| ~ in(U_529,relation_dom(U_530)) ) )
& ( ? [U_528] :
( in(U_528,U_531)
& in(ordered_pair(U_528,U_532),U_530)
& in(U_528,relation_dom(U_530)) )
| ~ in(U_532,relation_image(U_530,U_531)) ) )
| ~ relation(U_530) ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
fof(f_124_3,plain,
! [U_532,U_531,U_530] :
( ( ( in(U_532,relation_image(U_530,U_531))
| ! [U_529] :
( ~ in(U_529,U_531)
| ~ in(ordered_pair(U_529,U_532),U_530)
| ~ in(U_529,relation_dom(U_530)) ) )
& ( ( in(sK82(U_532,U_531,U_530),U_531)
& in(ordered_pair(sK82(U_532,U_531,U_530),U_532),U_530)
& in(sK82(U_532,U_531,U_530),relation_dom(U_530)) )
| ~ in(U_532,relation_image(U_530,U_531)) ) )
| ~ relation(U_530) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_528,sK82(U_532,U_531,U_530))],[f_124_2]) ).
cnf(f_124_4,plain,
( in(sK82(U_532,U_531,U_530),relation_dom(U_530))
| ~ in(U_532,relation_image(U_530,U_531))
| ~ relation(U_530) ),
inference(clausify,[status(thm)],[f_124_3]) ).
cnf(f_124_5,plain,
( in(ordered_pair(sK82(U_532,U_531,U_530),U_532),U_530)
| ~ in(U_532,relation_image(U_530,U_531))
| ~ relation(U_530) ),
inference(clausify,[status(thm)],[f_124_3]) ).
cnf(f_124_6,plain,
( in(sK82(U_532,U_531,U_530),U_531)
| ~ in(U_532,relation_image(U_530,U_531))
| ~ relation(U_530) ),
inference(clausify,[status(thm)],[f_124_3]) ).
cnf(f_124_7,plain,
( in(U_532,relation_image(U_530,U_531))
| ~ in(U_529,U_531)
| ~ in(ordered_pair(U_529,U_532),U_530)
| ~ in(U_529,relation_dom(U_530))
| ~ relation(U_530) ),
inference(clausify,[status(thm)],[f_124_3]) ).
fof(f_125_1,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> subset(relation_image(B,A),relation_rng(B)) ),
inference(negate,[status(cth)],[t144_relat_1]) ).
fof(f_125_2,negated_conjecture,
? [A,B] :
( ~ subset(relation_image(B,A),relation_rng(B))
& relation(B) ),
inference(fof_nnf,[status(thm)],[f_125_1]) ).
fof(f_125_3,negated_conjecture,
? [U_534,U_533] :
( ~ subset(relation_image(U_533,U_534),relation_rng(U_533))
& relation(U_533) ),
inference(variable_rename,[status(thm)],[f_125_2]) ).
fof(f_125_4,negated_conjecture,
? [U_533] :
( ~ subset(relation_image(U_533,sK83),relation_rng(U_533))
& relation(U_533) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_534,sK83)],[f_125_3]) ).
fof(f_125_5,negated_conjecture,
( ~ subset(relation_image(sK84,sK83),relation_rng(sK84))
& relation(sK84) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_533,sK84)],[f_125_4]) ).
cnf(f_125_6,negated_conjecture,
relation(sK84),
inference(clausify,[status(thm)],[f_125_5]) ).
cnf(f_125_7,negated_conjecture,
~ subset(relation_image(sK84,sK83),relation_rng(sK84)),
inference(clausify,[status(thm)],[f_125_5]) ).
fof(f_126_1,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(fof_nnf,[status(thm)],[t17_xboole_1]) ).
fof(f_126_2,plain,
! [U_536,U_535] : subset(set_intersection2(U_536,U_535),U_536),
inference(variable_rename,[status(thm)],[f_126_1]) ).
cnf(f_126_3,plain,
subset(set_intersection2(U_536,U_535),U_536),
inference(clausify,[status(thm)],[f_126_2]) ).
fof(f_127_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_127_2,plain,
! [U_539,U_538,U_537] :
( subset(U_539,set_intersection2(U_538,U_537))
| ~ subset(U_539,U_537)
| ~ subset(U_539,U_538) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
cnf(f_127_3,plain,
( subset(U_539,set_intersection2(U_538,U_537))
| ~ subset(U_539,U_537)
| ~ subset(U_539,U_538) ),
inference(clausify,[status(thm)],[f_127_2]) ).
fof(f_128_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_128_2,plain,
! [U_540] : set_union2(U_540,empty_set) = U_540,
inference(variable_rename,[status(thm)],[f_128_1]) ).
cnf(f_128_3,plain,
set_union2(U_540,empty_set) = U_540,
inference(clausify,[status(thm)],[f_128_2]) ).
fof(f_129_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_129_2,plain,
! [U_542,U_541] :
( element(U_542,U_541)
| ~ in(U_542,U_541) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
cnf(f_129_3,plain,
( element(U_542,U_541)
| ~ in(U_542,U_541) ),
inference(clausify,[status(thm)],[f_129_2]) ).
fof(f_130_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_130_2,plain,
! [U_545,U_544,U_543] :
( subset(U_545,U_543)
| ~ subset(U_544,U_543)
| ~ subset(U_545,U_544) ),
inference(variable_rename,[status(thm)],[f_130_1]) ).
cnf(f_130_3,plain,
( subset(U_545,U_543)
| ~ subset(U_544,U_543)
| ~ subset(U_545,U_544) ),
inference(clausify,[status(thm)],[f_130_2]) ).
fof(f_131_1,plain,
powerset(empty_set) = singleton(empty_set),
inference(fof_nnf,[status(thm)],[t1_zfmisc_1]) ).
cnf(f_131_2,plain,
powerset(empty_set) = singleton(empty_set),
inference(clausify,[status(thm)],[f_131_1]) ).
fof(f_132_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_132_2,plain,
! [U_548,U_547,U_546] :
( ( in(U_547,relation_rng(U_546))
& in(U_548,relation_dom(U_546)) )
| ~ in(ordered_pair(U_548,U_547),U_546)
| ~ relation(U_546) ),
inference(variable_rename,[status(thm)],[f_132_1]) ).
cnf(f_132_3,plain,
( in(U_548,relation_dom(U_546))
| ~ in(ordered_pair(U_548,U_547),U_546)
| ~ relation(U_546) ),
inference(clausify,[status(thm)],[f_132_2]) ).
cnf(f_132_4,plain,
( in(U_547,relation_rng(U_546))
| ~ in(ordered_pair(U_548,U_547),U_546)
| ~ relation(U_546) ),
inference(clausify,[status(thm)],[f_132_2]) ).
fof(f_133_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_133_2,plain,
! [U_549] :
( subset(U_549,cartesian_product2(relation_dom(U_549),relation_rng(U_549)))
| ~ relation(U_549) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
cnf(f_133_3,plain,
( subset(U_549,cartesian_product2(relation_dom(U_549),relation_rng(U_549)))
| ~ relation(U_549) ),
inference(clausify,[status(thm)],[f_133_2]) ).
fof(f_134_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_134_2,plain,
! [U_551] :
( ! [U_550] :
( ( subset(relation_rng(U_551),relation_rng(U_550))
& subset(relation_dom(U_551),relation_dom(U_550)) )
| ~ subset(U_551,U_550)
| ~ relation(U_550) )
| ~ relation(U_551) ),
inference(variable_rename,[status(thm)],[f_134_1]) ).
cnf(f_134_3,plain,
( subset(relation_dom(U_551),relation_dom(U_550))
| ~ subset(U_551,U_550)
| ~ relation(U_550)
| ~ relation(U_551) ),
inference(clausify,[status(thm)],[f_134_2]) ).
cnf(f_134_4,plain,
( subset(relation_rng(U_551),relation_rng(U_550))
| ~ subset(U_551,U_550)
| ~ relation(U_550)
| ~ relation(U_551) ),
inference(clausify,[status(thm)],[f_134_2]) ).
fof(f_135_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_135_2,plain,
! [U_554,U_553,U_552] :
( subset(set_intersection2(U_554,U_552),set_intersection2(U_553,U_552))
| ~ subset(U_554,U_553) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
fof(f_135_3,plain,
! [U_554,U_553] :
( ! [U_552] : subset(set_intersection2(U_554,U_552),set_intersection2(U_553,U_552))
| ~ subset(U_554,U_553) ),
inference(miniscope,[status(thm)],[f_135_2]) ).
cnf(f_135_4,plain,
( subset(set_intersection2(U_554,U_552),set_intersection2(U_553,U_552))
| ~ subset(U_554,U_553) ),
inference(clausify,[status(thm)],[f_135_3]) ).
fof(f_136_1,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t28_xboole_1]) ).
fof(f_136_2,plain,
! [U_556,U_555] :
( set_intersection2(U_556,U_555) = U_556
| ~ subset(U_556,U_555) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
cnf(f_136_3,plain,
( set_intersection2(U_556,U_555) = U_556
| ~ subset(U_556,U_555) ),
inference(clausify,[status(thm)],[f_136_2]) ).
fof(f_137_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_137_2,plain,
! [U_557] : set_intersection2(U_557,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_137_1]) ).
cnf(f_137_3,plain,
set_intersection2(U_557,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_137_2]) ).
fof(f_138_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_138_2,plain,
! [U_559,U_558] :
( in(U_559,U_558)
| empty(U_558)
| ~ element(U_559,U_558) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
cnf(f_138_3,plain,
( in(U_559,U_558)
| empty(U_558)
| ~ element(U_559,U_558) ),
inference(clausify,[status(thm)],[f_138_2]) ).
fof(f_139_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_139_2,plain,
! [U_562,U_561] :
( U_562 = U_561
| ? [U_560] :
( ( ~ in(U_560,U_562)
& in(U_560,U_561) )
| ( ~ in(U_560,U_561)
& in(U_560,U_562) ) ) ),
inference(variable_rename,[status(thm)],[f_139_1]) ).
fof(f_139_3,plain,
! [U_562,U_561] :
( U_562 = U_561
| ? [U_564] :
( ~ in(U_564,U_562)
& in(U_564,U_561) )
| ? [U_563] :
( ~ in(U_563,U_561)
& in(U_563,U_562) ) ),
inference(miniscope,[status(thm)],[f_139_2]) ).
fof(f_139_4,plain,
! [U_562,U_561] :
( U_562 = U_561
| ? [U_564] :
( ~ in(U_564,U_562)
& in(U_564,U_561) )
| ( ~ in(sK85(U_562,U_561),U_561)
& in(sK85(U_562,U_561),U_562) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_563,sK85(U_562,U_561))],[f_139_3]) ).
fof(f_139_5,plain,
! [U_562,U_561] :
( U_562 = U_561
| ( ~ in(sK86(U_562,U_561),U_562)
& in(sK86(U_562,U_561),U_561) )
| ( ~ in(sK85(U_562,U_561),U_561)
& in(sK85(U_562,U_561),U_562) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_564,sK86(U_562,U_561))],[f_139_4]) ).
cnf(f_139_6,plain,
( in(sK86(U_562,U_561),U_561)
| in(sK85(U_562,U_561),U_562)
| U_562 = U_561 ),
inference(clausify,[status(thm)],[f_139_5]) ).
cnf(f_139_7,plain,
( ~ in(sK86(U_562,U_561),U_562)
| in(sK85(U_562,U_561),U_562)
| U_562 = U_561 ),
inference(clausify,[status(thm)],[f_139_5]) ).
cnf(f_139_8,plain,
( in(sK86(U_562,U_561),U_561)
| ~ in(sK85(U_562,U_561),U_561)
| U_562 = U_561 ),
inference(clausify,[status(thm)],[f_139_5]) ).
cnf(f_139_9,plain,
( ~ in(sK86(U_562,U_561),U_562)
| ~ in(sK85(U_562,U_561),U_561)
| U_562 = U_561 ),
inference(clausify,[status(thm)],[f_139_5]) ).
fof(f_140_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_140_2,plain,
! [U_565] : subset(empty_set,U_565),
inference(variable_rename,[status(thm)],[f_140_1]) ).
cnf(f_140_3,plain,
subset(empty_set,U_565),
inference(clausify,[status(thm)],[f_140_2]) ).
fof(f_141_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_141_2,plain,
! [U_568,U_567,U_566] :
( ( in(U_567,relation_field(U_566))
& in(U_568,relation_field(U_566)) )
| ~ in(ordered_pair(U_568,U_567),U_566)
| ~ relation(U_566) ),
inference(variable_rename,[status(thm)],[f_141_1]) ).
cnf(f_141_3,plain,
( in(U_568,relation_field(U_566))
| ~ in(ordered_pair(U_568,U_567),U_566)
| ~ relation(U_566) ),
inference(clausify,[status(thm)],[f_141_2]) ).
cnf(f_141_4,plain,
( in(U_567,relation_field(U_566))
| ~ in(ordered_pair(U_568,U_567),U_566)
| ~ relation(U_566) ),
inference(clausify,[status(thm)],[f_141_2]) ).
fof(f_142_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_142_2,plain,
! [U_571,U_570,U_569] :
( subset(set_difference(U_571,U_569),set_difference(U_570,U_569))
| ~ subset(U_571,U_570) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
fof(f_142_3,plain,
! [U_571,U_570] :
( ! [U_569] : subset(set_difference(U_571,U_569),set_difference(U_570,U_569))
| ~ subset(U_571,U_570) ),
inference(miniscope,[status(thm)],[f_142_2]) ).
cnf(f_142_4,plain,
( subset(set_difference(U_571,U_569),set_difference(U_570,U_569))
| ~ subset(U_571,U_570) ),
inference(clausify,[status(thm)],[f_142_3]) ).
fof(f_143_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_143_2,plain,
! [U_575,U_574,U_573,U_572] :
( ( U_574 = U_572
& U_575 = U_573 )
| ordered_pair(U_575,U_574) != ordered_pair(U_573,U_572) ),
inference(variable_rename,[status(thm)],[f_143_1]) ).
cnf(f_143_3,plain,
( U_575 = U_573
| ordered_pair(U_575,U_574) != ordered_pair(U_573,U_572) ),
inference(clausify,[status(thm)],[f_143_2]) ).
cnf(f_143_4,plain,
( U_574 = U_572
| ordered_pair(U_575,U_574) != ordered_pair(U_573,U_572) ),
inference(clausify,[status(thm)],[f_143_2]) ).
fof(f_144_1,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(fof_nnf,[status(thm)],[t36_xboole_1]) ).
fof(f_144_2,plain,
! [U_577,U_576] : subset(set_difference(U_577,U_576),U_577),
inference(variable_rename,[status(thm)],[f_144_1]) ).
cnf(f_144_3,plain,
subset(set_difference(U_577,U_576),U_577),
inference(clausify,[status(thm)],[f_144_2]) ).
fof(f_145_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_145_2,plain,
! [U_578] :
( ( relation_dom(U_578) = relation_rng(relation_inverse(U_578))
& relation_rng(U_578) = relation_dom(relation_inverse(U_578)) )
| ~ relation(U_578) ),
inference(variable_rename,[status(thm)],[f_145_1]) ).
cnf(f_145_3,plain,
( relation_rng(U_578) = relation_dom(relation_inverse(U_578))
| ~ relation(U_578) ),
inference(clausify,[status(thm)],[f_145_2]) ).
cnf(f_145_4,plain,
( relation_dom(U_578) = relation_rng(relation_inverse(U_578))
| ~ relation(U_578) ),
inference(clausify,[status(thm)],[f_145_2]) ).
fof(f_146_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_146_2,plain,
! [U_580,U_579] :
( ( set_difference(U_580,U_579) = empty_set
| ~ subset(U_580,U_579) )
& ( subset(U_580,U_579)
| set_difference(U_580,U_579) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
fof(f_146_3,plain,
( ! [U_584,U_582] :
( set_difference(U_584,U_582) = empty_set
| ~ subset(U_584,U_582) )
& ! [U_583,U_581] :
( subset(U_583,U_581)
| set_difference(U_583,U_581) != empty_set ) ),
inference(miniscope,[status(thm)],[f_146_2]) ).
cnf(f_146_4,plain,
( subset(U_583,U_581)
| set_difference(U_583,U_581) != empty_set ),
inference(clausify,[status(thm)],[f_146_3]) ).
cnf(f_146_5,plain,
( set_difference(U_584,U_582) = empty_set
| ~ subset(U_584,U_582) ),
inference(clausify,[status(thm)],[f_146_3]) ).
fof(f_147_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_147_2,plain,
! [U_586,U_585] :
( ( subset(singleton(U_586),U_585)
| ~ in(U_586,U_585) )
& ( in(U_586,U_585)
| ~ subset(singleton(U_586),U_585) ) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
fof(f_147_3,plain,
( ! [U_590,U_588] :
( subset(singleton(U_590),U_588)
| ~ in(U_590,U_588) )
& ! [U_589,U_587] :
( in(U_589,U_587)
| ~ subset(singleton(U_589),U_587) ) ),
inference(miniscope,[status(thm)],[f_147_2]) ).
cnf(f_147_4,plain,
( in(U_589,U_587)
| ~ subset(singleton(U_589),U_587) ),
inference(clausify,[status(thm)],[f_147_3]) ).
cnf(f_147_5,plain,
( subset(singleton(U_590),U_588)
| ~ in(U_590,U_588) ),
inference(clausify,[status(thm)],[f_147_3]) ).
fof(f_148_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_148_2,plain,
! [U_593,U_592,U_591] :
( ( subset(unordered_pair(U_593,U_592),U_591)
| ~ in(U_592,U_591)
| ~ in(U_593,U_591) )
& ( ( in(U_592,U_591)
& in(U_593,U_591) )
| ~ subset(unordered_pair(U_593,U_592),U_591) ) ),
inference(variable_rename,[status(thm)],[f_148_1]) ).
fof(f_148_3,plain,
( ! [U_599,U_597,U_595] :
( subset(unordered_pair(U_599,U_597),U_595)
| ~ in(U_597,U_595)
| ~ in(U_599,U_595) )
& ! [U_598,U_596,U_594] :
( ( in(U_596,U_594)
& in(U_598,U_594) )
| ~ subset(unordered_pair(U_598,U_596),U_594) ) ),
inference(miniscope,[status(thm)],[f_148_2]) ).
cnf(f_148_4,plain,
( in(U_598,U_594)
| ~ subset(unordered_pair(U_598,U_596),U_594) ),
inference(clausify,[status(thm)],[f_148_3]) ).
cnf(f_148_5,plain,
( in(U_596,U_594)
| ~ subset(unordered_pair(U_598,U_596),U_594) ),
inference(clausify,[status(thm)],[f_148_3]) ).
cnf(f_148_6,plain,
( subset(unordered_pair(U_599,U_597),U_595)
| ~ in(U_597,U_595)
| ~ in(U_599,U_595) ),
inference(clausify,[status(thm)],[f_148_3]) ).
fof(f_149_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_149_2,plain,
! [U_601,U_600] : set_union2(U_601,set_difference(U_600,U_601)) = set_union2(U_601,U_600),
inference(variable_rename,[status(thm)],[f_149_1]) ).
cnf(f_149_3,plain,
set_union2(U_601,set_difference(U_600,U_601)) = set_union2(U_601,U_600),
inference(clausify,[status(thm)],[f_149_2]) ).
fof(f_150_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_150_2,plain,
! [U_603,U_602] :
( ( subset(U_603,singleton(U_602))
| ( U_603 != singleton(U_602)
& U_603 != empty_set ) )
& ( U_603 = singleton(U_602)
| U_603 = empty_set
| ~ subset(U_603,singleton(U_602)) ) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
fof(f_150_3,plain,
( ! [U_607,U_605] :
( subset(U_607,singleton(U_605))
| ( U_607 != singleton(U_605)
& U_607 != empty_set ) )
& ! [U_606,U_604] :
( U_606 = singleton(U_604)
| U_606 = empty_set
| ~ subset(U_606,singleton(U_604)) ) ),
inference(miniscope,[status(thm)],[f_150_2]) ).
cnf(f_150_4,plain,
( U_606 = singleton(U_604)
| U_606 = empty_set
| ~ subset(U_606,singleton(U_604)) ),
inference(clausify,[status(thm)],[f_150_3]) ).
cnf(f_150_5,plain,
( U_607 != empty_set
| subset(U_607,singleton(U_605)) ),
inference(clausify,[status(thm)],[f_150_3]) ).
cnf(f_150_6,plain,
( U_607 != singleton(U_605)
| subset(U_607,singleton(U_605)) ),
inference(clausify,[status(thm)],[f_150_3]) ).
fof(f_151_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_151_2,plain,
! [U_608] : set_difference(U_608,empty_set) = U_608,
inference(variable_rename,[status(thm)],[f_151_1]) ).
cnf(f_151_3,plain,
set_difference(U_608,empty_set) = U_608,
inference(clausify,[status(thm)],[f_151_2]) ).
fof(f_152_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_152_2,plain,
! [U_610,U_609] :
( ( element(U_610,powerset(U_609))
| ~ subset(U_610,U_609) )
& ( subset(U_610,U_609)
| ~ element(U_610,powerset(U_609)) ) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
fof(f_152_3,plain,
( ! [U_614,U_612] :
( element(U_614,powerset(U_612))
| ~ subset(U_614,U_612) )
& ! [U_613,U_611] :
( subset(U_613,U_611)
| ~ element(U_613,powerset(U_611)) ) ),
inference(miniscope,[status(thm)],[f_152_2]) ).
cnf(f_152_4,plain,
( subset(U_613,U_611)
| ~ element(U_613,powerset(U_611)) ),
inference(clausify,[status(thm)],[f_152_3]) ).
cnf(f_152_5,plain,
( element(U_614,powerset(U_612))
| ~ subset(U_614,U_612) ),
inference(clausify,[status(thm)],[f_152_3]) ).
fof(f_153_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_153_2,plain,
! [U_618,U_617] :
( ( ~ disjoint(U_618,U_617)
| ! [U_616] :
( ~ in(U_616,U_617)
| ~ in(U_616,U_618) ) )
& ( ? [U_615] :
( in(U_615,U_617)
& in(U_615,U_618) )
| disjoint(U_618,U_617) ) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
fof(f_153_3,plain,
( ! [U_622,U_620] :
( ~ disjoint(U_622,U_620)
| ! [U_616] :
( ~ in(U_616,U_620)
| ~ in(U_616,U_622) ) )
& ! [U_621,U_619] :
( ? [U_615] :
( in(U_615,U_619)
& in(U_615,U_621) )
| disjoint(U_621,U_619) ) ),
inference(miniscope,[status(thm)],[f_153_2]) ).
fof(f_153_4,plain,
( ! [U_622,U_620] :
( ~ disjoint(U_622,U_620)
| ! [U_616] :
( ~ in(U_616,U_620)
| ~ in(U_616,U_622) ) )
& ! [U_621,U_619] :
( ( in(sK87(U_621,U_619),U_619)
& in(sK87(U_621,U_619),U_621) )
| disjoint(U_621,U_619) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_615,sK87(U_621,U_619))],[f_153_3]) ).
cnf(f_153_5,plain,
( in(sK87(U_621,U_619),U_621)
| disjoint(U_621,U_619) ),
inference(clausify,[status(thm)],[f_153_4]) ).
cnf(f_153_6,plain,
( in(sK87(U_621,U_619),U_619)
| disjoint(U_621,U_619) ),
inference(clausify,[status(thm)],[f_153_4]) ).
cnf(f_153_7,plain,
( ~ disjoint(U_622,U_620)
| ~ in(U_616,U_620)
| ~ in(U_616,U_622) ),
inference(clausify,[status(thm)],[f_153_4]) ).
fof(f_154_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_154_2,plain,
! [U_623] :
( U_623 = empty_set
| ~ subset(U_623,empty_set) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
cnf(f_154_3,plain,
( U_623 = empty_set
| ~ subset(U_623,empty_set) ),
inference(clausify,[status(thm)],[f_154_2]) ).
fof(f_155_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_155_2,plain,
! [U_625,U_624] : set_difference(set_union2(U_625,U_624),U_624) = set_difference(U_625,U_624),
inference(variable_rename,[status(thm)],[f_155_1]) ).
cnf(f_155_3,plain,
set_difference(set_union2(U_625,U_624),U_624) = set_difference(U_625,U_624),
inference(clausify,[status(thm)],[f_155_2]) ).
fof(f_156_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_156_2,plain,
! [U_628,U_627] :
( ! [U_626] :
( ( ( disjoint(U_627,U_626)
| ~ subset(U_627,subset_complement(U_628,U_626)) )
& ( subset(U_627,subset_complement(U_628,U_626))
| ~ disjoint(U_627,U_626) ) )
| ~ element(U_626,powerset(U_628)) )
| ~ element(U_627,powerset(U_628)) ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
cnf(f_156_3,plain,
( subset(U_627,subset_complement(U_628,U_626))
| ~ disjoint(U_627,U_626)
| ~ element(U_626,powerset(U_628))
| ~ element(U_627,powerset(U_628)) ),
inference(clausify,[status(thm)],[f_156_2]) ).
cnf(f_156_4,plain,
( disjoint(U_627,U_626)
| ~ subset(U_627,subset_complement(U_628,U_626))
| ~ element(U_626,powerset(U_628))
| ~ element(U_627,powerset(U_628)) ),
inference(clausify,[status(thm)],[f_156_2]) ).
fof(f_157_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_157_2,plain,
! [U_630] :
( ! [U_629] :
( subset(relation_dom(relation_composition(U_630,U_629)),relation_dom(U_630))
| ~ relation(U_629) )
| ~ relation(U_630) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
cnf(f_157_3,plain,
( subset(relation_dom(relation_composition(U_630,U_629)),relation_dom(U_630))
| ~ relation(U_629)
| ~ relation(U_630) ),
inference(clausify,[status(thm)],[f_157_2]) ).
fof(f_158_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_158_2,plain,
! [U_632] :
( ! [U_631] :
( subset(relation_rng(relation_composition(U_632,U_631)),relation_rng(U_631))
| ~ relation(U_631) )
| ~ relation(U_632) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
cnf(f_158_3,plain,
( subset(relation_rng(relation_composition(U_632,U_631)),relation_rng(U_631))
| ~ relation(U_631)
| ~ relation(U_632) ),
inference(clausify,[status(thm)],[f_158_2]) ).
fof(f_159_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_159_2,plain,
! [U_634,U_633] :
( U_633 = set_union2(U_634,set_difference(U_633,U_634))
| ~ subset(U_634,U_633) ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
cnf(f_159_3,plain,
( U_633 = set_union2(U_634,set_difference(U_633,U_634))
| ~ subset(U_634,U_633) ),
inference(clausify,[status(thm)],[f_159_2]) ).
fof(f_160_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_160_2,plain,
! [U_636] :
( ! [U_635] :
( relation_dom(relation_composition(U_636,U_635)) = relation_dom(U_636)
| ~ subset(relation_rng(U_636),relation_dom(U_635))
| ~ relation(U_635) )
| ~ relation(U_636) ),
inference(variable_rename,[status(thm)],[f_160_1]) ).
cnf(f_160_3,plain,
( relation_dom(relation_composition(U_636,U_635)) = relation_dom(U_636)
| ~ subset(relation_rng(U_636),relation_dom(U_635))
| ~ relation(U_635)
| ~ relation(U_636) ),
inference(clausify,[status(thm)],[f_160_2]) ).
fof(f_161_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_161_2,plain,
! [U_638,U_637] :
( complements_of_subsets(U_638,U_637) != empty_set
| U_637 = empty_set
| ~ element(U_637,powerset(powerset(U_638))) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
cnf(f_161_3,plain,
( complements_of_subsets(U_638,U_637) != empty_set
| U_637 = empty_set
| ~ element(U_637,powerset(powerset(U_638))) ),
inference(clausify,[status(thm)],[f_161_2]) ).
fof(f_162_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t46_zfmisc_1]) ).
fof(f_162_2,plain,
! [U_640,U_639] :
( set_union2(singleton(U_640),U_639) = U_639
| ~ in(U_640,U_639) ),
inference(variable_rename,[status(thm)],[f_162_1]) ).
cnf(f_162_3,plain,
( set_union2(singleton(U_640),U_639) = U_639
| ~ in(U_640,U_639) ),
inference(clausify,[status(thm)],[f_162_2]) ).
fof(f_163_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_163_2,plain,
! [U_642] :
( ! [U_641] :
( relation_rng(relation_composition(U_641,U_642)) = relation_rng(U_642)
| ~ subset(relation_dom(U_642),relation_rng(U_641))
| ~ relation(U_641) )
| ~ relation(U_642) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
cnf(f_163_3,plain,
( relation_rng(relation_composition(U_641,U_642)) = relation_rng(U_642)
| ~ subset(relation_dom(U_642),relation_rng(U_641))
| ~ relation(U_641)
| ~ relation(U_642) ),
inference(clausify,[status(thm)],[f_163_2]) ).
fof(f_164_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_164_2,plain,
! [U_644,U_643] :
( subset_difference(U_644,cast_to_subset(U_644),union_of_subsets(U_644,U_643)) = meet_of_subsets(U_644,complements_of_subsets(U_644,U_643))
| U_643 = empty_set
| ~ element(U_643,powerset(powerset(U_644))) ),
inference(variable_rename,[status(thm)],[f_164_1]) ).
cnf(f_164_3,plain,
( subset_difference(U_644,cast_to_subset(U_644),union_of_subsets(U_644,U_643)) = meet_of_subsets(U_644,complements_of_subsets(U_644,U_643))
| U_643 = empty_set
| ~ element(U_643,powerset(powerset(U_644))) ),
inference(clausify,[status(thm)],[f_164_2]) ).
fof(f_165_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_165_2,plain,
! [U_646,U_645] :
( union_of_subsets(U_646,complements_of_subsets(U_646,U_645)) = subset_difference(U_646,cast_to_subset(U_646),meet_of_subsets(U_646,U_645))
| U_645 = empty_set
| ~ element(U_645,powerset(powerset(U_646))) ),
inference(variable_rename,[status(thm)],[f_165_1]) ).
cnf(f_165_3,plain,
( union_of_subsets(U_646,complements_of_subsets(U_646,U_645)) = subset_difference(U_646,cast_to_subset(U_646),meet_of_subsets(U_646,U_645))
| U_645 = empty_set
| ~ element(U_645,powerset(powerset(U_646))) ),
inference(clausify,[status(thm)],[f_165_2]) ).
fof(f_166_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_166_2,plain,
! [U_648,U_647] : set_difference(U_648,set_difference(U_648,U_647)) = set_intersection2(U_648,U_647),
inference(variable_rename,[status(thm)],[f_166_1]) ).
cnf(f_166_3,plain,
set_difference(U_648,set_difference(U_648,U_647)) = set_intersection2(U_648,U_647),
inference(clausify,[status(thm)],[f_166_2]) ).
fof(f_167_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_167_2,plain,
! [U_649] : set_difference(empty_set,U_649) = empty_set,
inference(variable_rename,[status(thm)],[f_167_1]) ).
cnf(f_167_3,plain,
set_difference(empty_set,U_649) = empty_set,
inference(clausify,[status(thm)],[f_167_2]) ).
fof(f_168_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_168_2,plain,
! [U_652,U_651,U_650] :
( element(U_652,U_650)
| ~ element(U_651,powerset(U_650))
| ~ in(U_652,U_651) ),
inference(variable_rename,[status(thm)],[f_168_1]) ).
cnf(f_168_3,plain,
( element(U_652,U_650)
| ~ element(U_651,powerset(U_650))
| ~ in(U_652,U_651) ),
inference(clausify,[status(thm)],[f_168_2]) ).
fof(f_169_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_169_2,plain,
! [U_656,U_655] :
( ( ~ disjoint(U_656,U_655)
| ! [U_654] : ~ in(U_654,set_intersection2(U_656,U_655)) )
& ( ? [U_653] : in(U_653,set_intersection2(U_656,U_655))
| disjoint(U_656,U_655) ) ),
inference(variable_rename,[status(thm)],[f_169_1]) ).
fof(f_169_3,plain,
( ! [U_660,U_658] :
( ~ disjoint(U_660,U_658)
| ! [U_654] : ~ in(U_654,set_intersection2(U_660,U_658)) )
& ! [U_659,U_657] :
( ? [U_653] : in(U_653,set_intersection2(U_659,U_657))
| disjoint(U_659,U_657) ) ),
inference(miniscope,[status(thm)],[f_169_2]) ).
fof(f_169_4,plain,
( ! [U_660,U_658] :
( ~ disjoint(U_660,U_658)
| ! [U_654] : ~ in(U_654,set_intersection2(U_660,U_658)) )
& ! [U_659,U_657] :
( in(sK88(U_659,U_657),set_intersection2(U_659,U_657))
| disjoint(U_659,U_657) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_653,sK88(U_659,U_657))],[f_169_3]) ).
cnf(f_169_5,plain,
( in(sK88(U_659,U_657),set_intersection2(U_659,U_657))
| disjoint(U_659,U_657) ),
inference(clausify,[status(thm)],[f_169_4]) ).
cnf(f_169_6,plain,
( ~ disjoint(U_660,U_658)
| ~ in(U_654,set_intersection2(U_660,U_658)) ),
inference(clausify,[status(thm)],[f_169_4]) ).
fof(f_170_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_170_2,plain,
! [U_663] :
( ! [U_662] :
( ! [U_661] :
( in(U_661,subset_complement(U_663,U_662))
| in(U_661,U_662)
| ~ element(U_661,U_663) )
| ~ element(U_662,powerset(U_663)) )
| U_663 = empty_set ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
cnf(f_170_3,plain,
( in(U_661,subset_complement(U_663,U_662))
| in(U_661,U_662)
| ~ element(U_661,U_663)
| ~ element(U_662,powerset(U_663))
| U_663 = empty_set ),
inference(clausify,[status(thm)],[f_170_2]) ).
fof(f_171_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_171_2,plain,
! [U_666,U_665,U_664] :
( ~ in(U_665,U_664)
| ~ in(U_665,subset_complement(U_666,U_664))
| ~ element(U_664,powerset(U_666)) ),
inference(variable_rename,[status(thm)],[f_171_1]) ).
cnf(f_171_3,plain,
( ~ in(U_665,U_664)
| ~ in(U_665,subset_complement(U_666,U_664))
| ~ element(U_664,powerset(U_666)) ),
inference(clausify,[status(thm)],[f_171_2]) ).
fof(f_172_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_172_2,plain,
! [U_669] :
( U_669 = empty_set
| ? [U_668,U_667] : in(ordered_pair(U_668,U_667),U_669)
| ~ relation(U_669) ),
inference(variable_rename,[status(thm)],[f_172_1]) ).
fof(f_172_3,plain,
! [U_669] :
( U_669 = empty_set
| ? [U_667] : in(ordered_pair(sK89(U_669),U_667),U_669)
| ~ relation(U_669) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_668,sK89(U_669))],[f_172_2]) ).
fof(f_172_4,plain,
! [U_669] :
( U_669 = empty_set
| in(ordered_pair(sK89(U_669),sK90(U_669)),U_669)
| ~ relation(U_669) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_667,sK90(U_669))],[f_172_3]) ).
cnf(f_172_5,plain,
( U_669 = empty_set
| in(ordered_pair(sK89(U_669),sK90(U_669)),U_669)
| ~ relation(U_669) ),
inference(clausify,[status(thm)],[f_172_4]) ).
fof(f_173_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_173_2,plain,
! [U_672,U_671,U_670] :
( ~ empty(U_670)
| ~ element(U_671,powerset(U_670))
| ~ in(U_672,U_671) ),
inference(variable_rename,[status(thm)],[f_173_1]) ).
fof(f_173_3,plain,
! [U_672,U_671] :
( ! [U_670] :
( ~ empty(U_670)
| ~ element(U_671,powerset(U_670)) )
| ~ in(U_672,U_671) ),
inference(miniscope,[status(thm)],[f_173_2]) ).
cnf(f_173_4,plain,
( ~ empty(U_670)
| ~ element(U_671,powerset(U_670))
| ~ in(U_672,U_671) ),
inference(clausify,[status(thm)],[f_173_3]) ).
fof(f_174_1,plain,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(fof_nnf,[status(thm)],[t60_relat_1]) ).
cnf(f_174_2,plain,
relation_dom(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_174_1]) ).
cnf(f_174_3,plain,
relation_rng(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_174_1]) ).
fof(f_175_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t60_xboole_1]) ).
fof(f_175_2,plain,
! [U_674,U_673] :
( ~ proper_subset(U_673,U_674)
| ~ subset(U_674,U_673) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
cnf(f_175_3,plain,
( ~ proper_subset(U_673,U_674)
| ~ subset(U_674,U_673) ),
inference(clausify,[status(thm)],[f_175_2]) ).
fof(f_176_1,plain,
! [A,B,C] :
( disjoint(A,C)
| ~ disjoint(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t63_xboole_1]) ).
fof(f_176_2,plain,
! [U_677,U_676,U_675] :
( disjoint(U_677,U_675)
| ~ disjoint(U_676,U_675)
| ~ subset(U_677,U_676) ),
inference(variable_rename,[status(thm)],[f_176_1]) ).
cnf(f_176_3,plain,
( disjoint(U_677,U_675)
| ~ disjoint(U_676,U_675)
| ~ subset(U_677,U_676) ),
inference(clausify,[status(thm)],[f_176_2]) ).
fof(f_177_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_177_2,plain,
! [U_678] :
( U_678 = empty_set
| ( relation_rng(U_678) != empty_set
& relation_dom(U_678) != empty_set )
| ~ relation(U_678) ),
inference(variable_rename,[status(thm)],[f_177_1]) ).
cnf(f_177_3,plain,
( relation_dom(U_678) != empty_set
| U_678 = empty_set
| ~ relation(U_678) ),
inference(clausify,[status(thm)],[f_177_2]) ).
cnf(f_177_4,plain,
( relation_rng(U_678) != empty_set
| U_678 = empty_set
| ~ relation(U_678) ),
inference(clausify,[status(thm)],[f_177_2]) ).
fof(f_178_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_178_2,plain,
! [U_679] :
( ( ( relation_dom(U_679) = empty_set
| relation_rng(U_679) != empty_set )
& ( relation_rng(U_679) = empty_set
| relation_dom(U_679) != empty_set ) )
| ~ relation(U_679) ),
inference(variable_rename,[status(thm)],[f_178_1]) ).
cnf(f_178_3,plain,
( relation_rng(U_679) = empty_set
| relation_dom(U_679) != empty_set
| ~ relation(U_679) ),
inference(clausify,[status(thm)],[f_178_2]) ).
cnf(f_178_4,plain,
( relation_dom(U_679) = empty_set
| relation_rng(U_679) != empty_set
| ~ relation(U_679) ),
inference(clausify,[status(thm)],[f_178_2]) ).
fof(f_179_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_179_2,plain,
! [U_681,U_680] :
( ( set_difference(U_681,singleton(U_680)) = U_681
| in(U_680,U_681) )
& ( ~ in(U_680,U_681)
| set_difference(U_681,singleton(U_680)) != U_681 ) ),
inference(variable_rename,[status(thm)],[f_179_1]) ).
fof(f_179_3,plain,
( ! [U_685,U_683] :
( set_difference(U_685,singleton(U_683)) = U_685
| in(U_683,U_685) )
& ! [U_684,U_682] :
( ~ in(U_682,U_684)
| set_difference(U_684,singleton(U_682)) != U_684 ) ),
inference(miniscope,[status(thm)],[f_179_2]) ).
cnf(f_179_4,plain,
( ~ in(U_682,U_684)
| set_difference(U_684,singleton(U_682)) != U_684 ),
inference(clausify,[status(thm)],[f_179_3]) ).
cnf(f_179_5,plain,
( set_difference(U_685,singleton(U_683)) = U_685
| in(U_683,U_685) ),
inference(clausify,[status(thm)],[f_179_3]) ).
fof(f_180_1,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(fof_nnf,[status(thm)],[t69_enumset1]) ).
fof(f_180_2,plain,
! [U_686] : unordered_pair(U_686,U_686) = singleton(U_686),
inference(variable_rename,[status(thm)],[f_180_1]) ).
cnf(f_180_3,plain,
unordered_pair(U_686,U_686) = singleton(U_686),
inference(clausify,[status(thm)],[f_180_2]) ).
fof(f_181_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_181_2,plain,
! [U_687] :
( U_687 = empty_set
| ~ empty(U_687) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
cnf(f_181_3,plain,
( U_687 = empty_set
| ~ empty(U_687) ),
inference(clausify,[status(thm)],[f_181_2]) ).
fof(f_182_1,plain,
! [A,B] :
( A = B
| ~ subset(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t6_zfmisc_1]) ).
fof(f_182_2,plain,
! [U_689,U_688] :
( U_689 = U_688
| ~ subset(singleton(U_689),singleton(U_688)) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
cnf(f_182_3,plain,
( U_689 = U_688
| ~ subset(singleton(U_689),singleton(U_688)) ),
inference(clausify,[status(thm)],[f_182_2]) ).
fof(f_183_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_183_2,plain,
! [U_690] :
( relation_rng(identity_relation(U_690)) = U_690
& relation_dom(identity_relation(U_690)) = U_690 ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
fof(f_183_3,plain,
( ! [U_692] : relation_rng(identity_relation(U_692)) = U_692
& ! [U_691] : relation_dom(identity_relation(U_691)) = U_691 ),
inference(miniscope,[status(thm)],[f_183_2]) ).
cnf(f_183_4,plain,
relation_dom(identity_relation(U_691)) = U_691,
inference(clausify,[status(thm)],[f_183_3]) ).
cnf(f_183_5,plain,
relation_rng(identity_relation(U_692)) = U_692,
inference(clausify,[status(thm)],[f_183_3]) ).
fof(f_184_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_184_2,plain,
! [U_696,U_695,U_694,U_693] :
( ( ( in(ordered_pair(U_696,U_695),relation_composition(identity_relation(U_694),U_693))
| ~ in(ordered_pair(U_696,U_695),U_693)
| ~ in(U_696,U_694) )
& ( ( in(ordered_pair(U_696,U_695),U_693)
& in(U_696,U_694) )
| ~ in(ordered_pair(U_696,U_695),relation_composition(identity_relation(U_694),U_693)) ) )
| ~ relation(U_693) ),
inference(variable_rename,[status(thm)],[f_184_1]) ).
cnf(f_184_3,plain,
( in(U_696,U_694)
| ~ in(ordered_pair(U_696,U_695),relation_composition(identity_relation(U_694),U_693))
| ~ relation(U_693) ),
inference(clausify,[status(thm)],[f_184_2]) ).
cnf(f_184_4,plain,
( in(ordered_pair(U_696,U_695),U_693)
| ~ in(ordered_pair(U_696,U_695),relation_composition(identity_relation(U_694),U_693))
| ~ relation(U_693) ),
inference(clausify,[status(thm)],[f_184_2]) ).
cnf(f_184_5,plain,
( in(ordered_pair(U_696,U_695),relation_composition(identity_relation(U_694),U_693))
| ~ in(ordered_pair(U_696,U_695),U_693)
| ~ in(U_696,U_694)
| ~ relation(U_693) ),
inference(clausify,[status(thm)],[f_184_2]) ).
fof(f_185_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_185_2,plain,
! [U_698,U_697] :
( ~ empty(U_697)
| ~ in(U_698,U_697) ),
inference(variable_rename,[status(thm)],[f_185_1]) ).
cnf(f_185_3,plain,
( ~ empty(U_697)
| ~ in(U_698,U_697) ),
inference(clausify,[status(thm)],[f_185_2]) ).
fof(f_186_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1]) ).
fof(f_186_2,plain,
! [U_700,U_699] : subset(U_700,set_union2(U_700,U_699)),
inference(variable_rename,[status(thm)],[f_186_1]) ).
cnf(f_186_3,plain,
subset(U_700,set_union2(U_700,U_699)),
inference(clausify,[status(thm)],[f_186_2]) ).
fof(f_187_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_187_2,plain,
! [U_702,U_701] :
( ( disjoint(U_702,U_701)
| set_difference(U_702,U_701) != U_702 )
& ( set_difference(U_702,U_701) = U_702
| ~ disjoint(U_702,U_701) ) ),
inference(variable_rename,[status(thm)],[f_187_1]) ).
fof(f_187_3,plain,
( ! [U_706,U_704] :
( disjoint(U_706,U_704)
| set_difference(U_706,U_704) != U_706 )
& ! [U_705,U_703] :
( set_difference(U_705,U_703) = U_705
| ~ disjoint(U_705,U_703) ) ),
inference(miniscope,[status(thm)],[f_187_2]) ).
cnf(f_187_4,plain,
( set_difference(U_705,U_703) = U_705
| ~ disjoint(U_705,U_703) ),
inference(clausify,[status(thm)],[f_187_3]) ).
cnf(f_187_5,plain,
( disjoint(U_706,U_704)
| set_difference(U_706,U_704) != U_706 ),
inference(clausify,[status(thm)],[f_187_3]) ).
fof(f_188_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_188_2,plain,
! [U_709,U_708,U_707] :
( ( ( in(U_709,relation_dom(relation_dom_restriction(U_707,U_708)))
| ~ in(U_709,relation_dom(U_707))
| ~ in(U_709,U_708) )
& ( ( in(U_709,relation_dom(U_707))
& in(U_709,U_708) )
| ~ in(U_709,relation_dom(relation_dom_restriction(U_707,U_708))) ) )
| ~ relation(U_707) ),
inference(variable_rename,[status(thm)],[f_188_1]) ).
cnf(f_188_3,plain,
( in(U_709,U_708)
| ~ in(U_709,relation_dom(relation_dom_restriction(U_707,U_708)))
| ~ relation(U_707) ),
inference(clausify,[status(thm)],[f_188_2]) ).
cnf(f_188_4,plain,
( in(U_709,relation_dom(U_707))
| ~ in(U_709,relation_dom(relation_dom_restriction(U_707,U_708)))
| ~ relation(U_707) ),
inference(clausify,[status(thm)],[f_188_2]) ).
cnf(f_188_5,plain,
( in(U_709,relation_dom(relation_dom_restriction(U_707,U_708)))
| ~ in(U_709,relation_dom(U_707))
| ~ in(U_709,U_708)
| ~ relation(U_707) ),
inference(clausify,[status(thm)],[f_188_2]) ).
fof(f_189_1,plain,
! [A,B] :
( subset(relation_dom_restriction(B,A),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t88_relat_1]) ).
fof(f_189_2,plain,
! [U_711,U_710] :
( subset(relation_dom_restriction(U_710,U_711),U_710)
| ~ relation(U_710) ),
inference(variable_rename,[status(thm)],[f_189_1]) ).
cnf(f_189_3,plain,
( subset(relation_dom_restriction(U_710,U_711),U_710)
| ~ relation(U_710) ),
inference(clausify,[status(thm)],[f_189_2]) ).
fof(f_190_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_190_2,plain,
! [U_713,U_712] :
( ~ empty(U_712)
| U_713 = U_712
| ~ empty(U_713) ),
inference(variable_rename,[status(thm)],[f_190_1]) ).
fof(f_190_3,plain,
! [U_713] :
( ! [U_712] :
( ~ empty(U_712)
| U_713 = U_712 )
| ~ empty(U_713) ),
inference(miniscope,[status(thm)],[f_190_2]) ).
cnf(f_190_4,plain,
( ~ empty(U_712)
| U_713 = U_712
| ~ empty(U_713) ),
inference(clausify,[status(thm)],[f_190_3]) ).
fof(f_191_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_191_2,plain,
! [U_716,U_715,U_714] :
( subset(set_union2(U_716,U_714),U_715)
| ~ subset(U_714,U_715)
| ~ subset(U_716,U_715) ),
inference(variable_rename,[status(thm)],[f_191_1]) ).
cnf(f_191_3,plain,
( subset(set_union2(U_716,U_714),U_715)
| ~ subset(U_714,U_715)
| ~ subset(U_716,U_715) ),
inference(clausify,[status(thm)],[f_191_2]) ).
fof(f_192_1,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t8_zfmisc_1]) ).
fof(f_192_2,plain,
! [U_719,U_718,U_717] :
( U_719 = U_718
| singleton(U_719) != unordered_pair(U_718,U_717) ),
inference(variable_rename,[status(thm)],[f_192_1]) ).
fof(f_192_3,plain,
! [U_719,U_718] :
( ! [U_717] : singleton(U_719) != unordered_pair(U_718,U_717)
| U_719 = U_718 ),
inference(miniscope,[status(thm)],[f_192_2]) ).
cnf(f_192_4,plain,
( singleton(U_719) != unordered_pair(U_718,U_717)
| U_719 = U_718 ),
inference(clausify,[status(thm)],[f_192_3]) ).
fof(f_193_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_193_2,plain,
! [U_721,U_720] :
( relation_dom(relation_dom_restriction(U_720,U_721)) = set_intersection2(relation_dom(U_720),U_721)
| ~ relation(U_720) ),
inference(variable_rename,[status(thm)],[f_193_1]) ).
cnf(f_193_3,plain,
( relation_dom(relation_dom_restriction(U_720,U_721)) = set_intersection2(relation_dom(U_720),U_721)
| ~ relation(U_720) ),
inference(clausify,[status(thm)],[f_193_2]) ).
fof(f_194_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t92_zfmisc_1]) ).
fof(f_194_2,plain,
! [U_723,U_722] :
( subset(U_723,union(U_722))
| ~ in(U_723,U_722) ),
inference(variable_rename,[status(thm)],[f_194_1]) ).
cnf(f_194_3,plain,
( subset(U_723,union(U_722))
| ~ in(U_723,U_722) ),
inference(clausify,[status(thm)],[f_194_2]) ).
fof(f_195_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_195_2,plain,
! [U_725,U_724] :
( relation_dom_restriction(U_724,U_725) = relation_composition(identity_relation(U_725),U_724)
| ~ relation(U_724) ),
inference(variable_rename,[status(thm)],[f_195_1]) ).
cnf(f_195_3,plain,
( relation_dom_restriction(U_724,U_725) = relation_composition(identity_relation(U_725),U_724)
| ~ relation(U_724) ),
inference(clausify,[status(thm)],[f_195_2]) ).
fof(f_196_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_196_2,plain,
! [U_727,U_726] :
( subset(relation_rng(relation_dom_restriction(U_726,U_727)),relation_rng(U_726))
| ~ relation(U_726) ),
inference(variable_rename,[status(thm)],[f_196_1]) ).
cnf(f_196_3,plain,
( subset(relation_rng(relation_dom_restriction(U_726,U_727)),relation_rng(U_726))
| ~ relation(U_726) ),
inference(clausify,[status(thm)],[f_196_2]) ).
fof(f_197_1,plain,
! [A] : union(powerset(A)) = A,
inference(fof_nnf,[status(thm)],[t99_zfmisc_1]) ).
fof(f_197_2,plain,
! [U_728] : union(powerset(U_728)) = U_728,
inference(variable_rename,[status(thm)],[f_197_1]) ).
cnf(f_197_3,plain,
union(powerset(U_728)) = U_728,
inference(clausify,[status(thm)],[f_197_2]) ).
fof(f_198_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_198_2,plain,
! [U_736] :
? [U_735] :
( ! [U_734] :
( in(U_734,U_735)
| are_equipotent(U_734,U_735)
| ~ subset(U_734,U_735) )
& ! [U_733] :
( ? [U_732] :
( ! [U_731] :
( in(U_731,U_732)
| ~ subset(U_731,U_733) )
& in(U_732,U_735) )
| ~ in(U_733,U_735) )
& ! [U_730,U_729] :
( in(U_729,U_735)
| ~ subset(U_729,U_730)
| ~ in(U_730,U_735) )
& in(U_736,U_735) ),
inference(variable_rename,[status(thm)],[f_198_1]) ).
fof(f_198_3,plain,
! [U_736] :
( ! [U_734] :
( in(U_734,sK91(U_736))
| are_equipotent(U_734,sK91(U_736))
| ~ subset(U_734,sK91(U_736)) )
& ! [U_733] :
( ? [U_732] :
( ! [U_731] :
( in(U_731,U_732)
| ~ subset(U_731,U_733) )
& in(U_732,sK91(U_736)) )
| ~ in(U_733,sK91(U_736)) )
& ! [U_730,U_729] :
( in(U_729,sK91(U_736))
| ~ subset(U_729,U_730)
| ~ in(U_730,sK91(U_736)) )
& in(U_736,sK91(U_736)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_735,sK91(U_736))],[f_198_2]) ).
fof(f_198_4,plain,
! [U_736] :
( ! [U_734] :
( in(U_734,sK91(U_736))
| are_equipotent(U_734,sK91(U_736))
| ~ subset(U_734,sK91(U_736)) )
& ! [U_733] :
( ( ! [U_731] :
( in(U_731,sK92(U_736,U_733))
| ~ subset(U_731,U_733) )
& in(sK92(U_736,U_733),sK91(U_736)) )
| ~ in(U_733,sK91(U_736)) )
& ! [U_730,U_729] :
( in(U_729,sK91(U_736))
| ~ subset(U_729,U_730)
| ~ in(U_730,sK91(U_736)) )
& in(U_736,sK91(U_736)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_732,sK92(U_736,U_733))],[f_198_3]) ).
cnf(f_198_5,plain,
in(U_736,sK91(U_736)),
inference(clausify,[status(thm)],[f_198_4]) ).
cnf(f_198_6,plain,
( in(U_729,sK91(U_736))
| ~ subset(U_729,U_730)
| ~ in(U_730,sK91(U_736)) ),
inference(clausify,[status(thm)],[f_198_4]) ).
cnf(f_198_7,plain,
( in(sK92(U_736,U_733),sK91(U_736))
| ~ in(U_733,sK91(U_736)) ),
inference(clausify,[status(thm)],[f_198_4]) ).
cnf(f_198_8,plain,
( in(U_731,sK92(U_736,U_733))
| ~ subset(U_731,U_733)
| ~ in(U_733,sK91(U_736)) ),
inference(clausify,[status(thm)],[f_198_4]) ).
cnf(f_198_9,plain,
( in(U_734,sK91(U_736))
| are_equipotent(U_734,sK91(U_736))
| ~ subset(U_734,sK91(U_736)) ),
inference(clausify,[status(thm)],[f_198_4]) ).
fof(f_199_1,plain,
! [A,B,C] :
( B = C
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t9_zfmisc_1]) ).
fof(f_199_2,plain,
! [U_739,U_738,U_737] :
( U_738 = U_737
| singleton(U_739) != unordered_pair(U_738,U_737) ),
inference(variable_rename,[status(thm)],[f_199_1]) ).
cnf(f_199_3,plain,
( U_738 = U_737
| singleton(U_739) != unordered_pair(U_738,U_737) ),
inference(clausify,[status(thm)],[f_199_2]) ).
cnf(f_36_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_36_8]) ).
cnf(f_36_9_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_36_9]) ).
cnf(f_38_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_38_2]) ).
cnf(f_39_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_39_2]) ).
cnf(f_40_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_40_2]) ).
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_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_53_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_53_2]) ).
cnf(f_54_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_54_2]) ).
cnf(f_63_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_63_2]) ).
cnf(f_64_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_64_2]) ).
cnf(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,
( set_meet(Eq_x_0) = set_meet(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,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_16,axiom,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,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_18,axiom,
( union(Eq_x_0) = union(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,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_20,axiom,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,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_22,axiom,
( relation_field(Eq_x_0) = relation_field(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( relation_inverse(Eq_x_0) = relation_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,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_25,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_26,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_27,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_28,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_29,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_30,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_31,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_32,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_33,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_34,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_35,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_36,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_37,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_38,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_39,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_40,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_41,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_42,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_43,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_44,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_45,axiom,
( sK17(Eq_x_0,Eq_x_1) = sK17(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_46,axiom,
( sK18(Eq_x_0,Eq_x_1) = sK18(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_47,axiom,
( sK19(Eq_x_0) = sK19(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_48,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_49,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_50,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_51,axiom,
( sK23(Eq_x_0,Eq_x_1) = sK23(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,
( sK24(Eq_x_0,Eq_x_1) = sK24(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,
( 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_54,axiom,
( sK26(Eq_x_0) = sK26(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_55,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_56,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_57,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_58,axiom,
( sK30(Eq_x_0,Eq_x_1) = sK30(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_59,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_60,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_61,axiom,
( sK33(Eq_x_0,Eq_x_1,Eq_x_2) = sK33(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_62,axiom,
( sK34(Eq_x_0,Eq_x_1,Eq_x_2) = sK34(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_63,axiom,
( sK35(Eq_x_0,Eq_x_1,Eq_x_2) = sK35(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_64,axiom,
( sK36(Eq_x_0,Eq_x_1,Eq_x_2) = sK36(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_65,axiom,
( sK37(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK37(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_66,axiom,
( sK38(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK38(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_67,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_68,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_69,axiom,
( sK41(Eq_x_0,Eq_x_1,Eq_x_2) = sK41(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,
( sK42(Eq_x_0,Eq_x_1,Eq_x_2) = sK42(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,
( sK43(Eq_x_0,Eq_x_1) = sK43(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_72,axiom,
( sK44(Eq_x_0,Eq_x_1) = sK44(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_73,axiom,
( sK45(Eq_x_0,Eq_x_1) = sK45(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_74,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_75,axiom,
( sK47(Eq_x_0,Eq_x_1,Eq_x_2) = sK47(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_76,axiom,
( sK48(Eq_x_0,Eq_x_1,Eq_x_2) = sK48(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_77,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_78,axiom,
( sK50(Eq_x_0,Eq_x_1) = sK50(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,
( sK51(Eq_x_0,Eq_x_1) = sK51(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_80,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_81,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_82,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_83,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_84,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_85,axiom,
( sK57(Eq_x_0,Eq_x_1,Eq_x_2) = sK57(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_86,axiom,
( sK58(Eq_x_0,Eq_x_1,Eq_x_2) = sK58(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_87,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_88,axiom,
( sK60(Eq_x_0,Eq_x_1) = sK60(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_89,axiom,
( sK61(Eq_x_0,Eq_x_1) = sK61(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_90,axiom,
( sK62(Eq_x_0,Eq_x_1) = sK62(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_91,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_92,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_93,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_94,axiom,
( sK66(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK66(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_95,axiom,
( sK67(Eq_x_0,Eq_x_1,Eq_x_2) = sK67(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_96,axiom,
( sK68(Eq_x_0,Eq_x_1,Eq_x_2) = sK68(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_97,axiom,
( sK69(Eq_x_0,Eq_x_1,Eq_x_2) = sK69(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_98,axiom,
( sK70(Eq_x_0,Eq_x_1,Eq_x_2) = sK70(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_99,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_100,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_101,axiom,
( sK73(Eq_x_0) = sK73(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_102,axiom,
( sK74(Eq_x_0,Eq_x_1) = sK74(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_103,axiom,
( sK76(Eq_x_0) = sK76(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_104,axiom,
( sK79(Eq_x_0) = sK79(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_105,axiom,
( sK81(Eq_x_0) = sK81(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_106,axiom,
( sK82(Eq_x_0,Eq_x_1,Eq_x_2) = sK82(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_107,axiom,
( sK85(Eq_x_0,Eq_x_1) = sK85(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_108,axiom,
( sK86(Eq_x_0,Eq_x_1) = sK86(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_109,axiom,
( sK87(Eq_x_0,Eq_x_1) = sK87(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_110,axiom,
( sK88(Eq_x_0,Eq_x_1) = sK88(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_111,axiom,
( sK89(Eq_x_0) = sK89(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_112,axiom,
( sK90(Eq_x_0) = sK90(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_113,axiom,
( sK91(Eq_x_0) = sK91(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_114,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_115,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_116,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_117,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_118,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_119,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_120,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_121,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_122,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 : SEU204+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 23:31:38 UTC 2026
% 0.10/0.37 % CPUTime :
% 118.77/119.06 % SZS status Theorem for theBenchmark
% 118.77/119.06 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------