%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU196+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:58:26 AM UTC 2026
% Result : Theorem 43.79s 44.03s
% Output : Proof 43.85s
% 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(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_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(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_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(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,conjecture,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B)) ),
file('theBenchmark.p',t99_relat_1) ).
fof(t99_zfmisc_1,lemma,
! [A] : union(powerset(A)) = A,
file('theBenchmark.p',t99_zfmisc_1) ).
fof(t9_tarski,axiom,
! [A] :
? [B] :
( ! [C] :
~ ( ~ in(C,B)
& ~ are_equipotent(C,B)
& subset(C,B) )
& ! [C] :
~ ( ! [D] :
~ ( ! [E] :
( subset(E,C)
=> in(E,D) )
& in(D,B) )
& in(C,B) )
& ! [C,D] :
( ( subset(D,C)
& in(C,B) )
=> in(D,B) )
& in(A,B) ),
file('theBenchmark.p',t9_tarski) ).
fof(t9_zfmisc_1,lemma,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> B = C ),
file('theBenchmark.p',t9_zfmisc_1) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(definitional_conversion,[status(esa)],[f_1_2]) ).
cnf(f_1_4,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ proper_subset(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(f_2_2,plain,
! [U_3,U_2] :
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_3,U_2] :
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A] :
( 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]) ).
fof(f_3_3,plain,
! [U_4] :
( relation(U_4)
| ~ empty(U_4) ),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
( relation(U_4)
| ~ empty(U_4) ),
inference(clausify,[status(thm)],[f_3_3]) ).
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]) ).
fof(f_4_3,plain,
! [U_6,U_5] : unordered_pair(U_6,U_5) = unordered_pair(U_5,U_6),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
unordered_pair(U_6,U_5) = unordered_pair(U_5,U_6),
inference(clausify,[status(thm)],[f_4_3]) ).
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]) ).
fof(f_5_3,plain,
! [U_7,U_8] : set_union2(U_8,U_7) = set_union2(U_7,U_8),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
set_union2(U_8,U_7) = set_union2(U_7,U_8),
inference(clausify,[status(thm)],[f_5_3]) ).
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]) ).
fof(f_6_3,plain,
! [U_9,U_10] : set_intersection2(U_10,U_9) = set_intersection2(U_9,U_10),
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
set_intersection2(U_10,U_9) = set_intersection2(U_9,U_10),
inference(clausify,[status(thm)],[f_6_3]) ).
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]) ).
fof(f_7_8,plain,
( ! [U_15,U_16] :
( ~ in(ordered_pair(sK3(U_16,U_15),sK4(U_16,U_15)),U_15)
| ~ sP3(U_15,U_16) )
& ! [U_15,U_16] :
( sK3(U_16,U_15) = sK4(U_16,U_15)
| ~ sP3(U_15,U_16) )
& ! [U_15,U_16] :
( in(sK3(U_16,U_15),U_16)
| ~ sP3(U_15,U_16) )
& ! [U_15,U_16] :
( sK1(U_16,U_15) != sK2(U_16,U_15)
| ~ in(sK1(U_16,U_15),U_16)
| ~ sP2(U_15,U_16) )
& ! [U_15,U_16] :
( in(ordered_pair(sK1(U_16,U_15),sK2(U_16,U_15)),U_15)
| ~ sP2(U_15,U_16) )
& ! [U_19,U_16,U_17] :
( U_19 = U_17
| ~ sP0(U_19,U_16,U_17) )
& ! [U_19,U_16,U_17] :
( in(U_19,U_16)
| ~ sP0(U_19,U_16,U_17) )
& ! [U_19,U_15,U_16,U_17,U_18,U_20] :
( in(ordered_pair(U_20,U_18),U_15)
| U_20 != U_18
| ~ in(U_20,U_16)
| ~ sP1(U_19,U_15,U_16,U_17,U_18,U_20) )
& ! [U_19,U_15,U_16,U_17,U_18,U_20] :
( sP0(U_19,U_16,U_17)
| ~ in(ordered_pair(U_19,U_17),U_15)
| ~ sP1(U_19,U_15,U_16,U_17,U_18,U_20) )
& ! [U_19,U_15,U_16,U_17,U_18,U_20] :
( U_15 = identity_relation(U_16)
| sP3(U_15,U_16)
| sP2(U_15,U_16)
| ~ sP4(U_19,U_15,U_16,U_17,U_18,U_20) )
& ! [U_19,U_15,U_16,U_17,U_18,U_20] :
( sP1(U_19,U_15,U_16,U_17,U_18,U_20)
| U_15 != identity_relation(U_16)
| ~ sP4(U_19,U_15,U_16,U_17,U_18,U_20) )
& ! [U_19,U_15,U_16,U_17,U_18,U_20] :
( sP4(U_19,U_15,U_16,U_17,U_18,U_20)
| ~ relation(U_15) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1,sP2,sP3,sP4])],[f_7_7]) ).
cnf(f_7_9,plain,
( sP4(U_19,U_15,U_16,U_17,U_18,U_20)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_10,plain,
( sP1(U_19,U_15,U_16,U_17,U_18,U_20)
| U_15 != identity_relation(U_16)
| ~ sP4(U_19,U_15,U_16,U_17,U_18,U_20) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_11,plain,
( U_15 = identity_relation(U_16)
| sP3(U_15,U_16)
| sP2(U_15,U_16)
| ~ sP4(U_19,U_15,U_16,U_17,U_18,U_20) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_12,plain,
( sP0(U_19,U_16,U_17)
| ~ in(ordered_pair(U_19,U_17),U_15)
| ~ sP1(U_19,U_15,U_16,U_17,U_18,U_20) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_13,plain,
( in(ordered_pair(U_20,U_18),U_15)
| U_20 != U_18
| ~ in(U_20,U_16)
| ~ sP1(U_19,U_15,U_16,U_17,U_18,U_20) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_14,plain,
( in(U_19,U_16)
| ~ sP0(U_19,U_16,U_17) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_15,plain,
( U_19 = U_17
| ~ sP0(U_19,U_16,U_17) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_16,plain,
( in(ordered_pair(sK1(U_16,U_15),sK2(U_16,U_15)),U_15)
| ~ sP2(U_15,U_16) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_17,plain,
( sK1(U_16,U_15) != sK2(U_16,U_15)
| ~ in(sK1(U_16,U_15),U_16)
| ~ sP2(U_15,U_16) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_18,plain,
( in(sK3(U_16,U_15),U_16)
| ~ sP3(U_15,U_16) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_19,plain,
( sK3(U_16,U_15) = sK4(U_16,U_15)
| ~ sP3(U_15,U_16) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_20,plain,
( ~ in(ordered_pair(sK3(U_16,U_15),sK4(U_16,U_15)),U_15)
| ~ sP3(U_15,U_16) ),
inference(clausify,[status(thm)],[f_7_8]) ).
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]) ).
fof(f_8_4,plain,
( ! [U_27,U_29] :
( subset(U_27,U_29)
| ~ sP5(U_27,U_29) )
& ! [U_27,U_29] :
( subset(U_29,U_27)
| ~ sP5(U_27,U_29) )
& ! [U_28,U_30] :
( U_30 = U_28
| ~ subset(U_28,U_30)
| ~ subset(U_30,U_28) )
& ! [U_27,U_29] :
( sP5(U_27,U_29)
| U_29 != U_27 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_8_3]) ).
cnf(f_8_5,plain,
( sP5(U_27,U_29)
| U_29 != U_27 ),
inference(clausify,[status(thm)],[f_8_4]) ).
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_4]) ).
cnf(f_8_7,plain,
( subset(U_29,U_27)
| ~ sP5(U_27,U_29) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_8,plain,
( subset(U_27,U_29)
| ~ sP5(U_27,U_29) ),
inference(clausify,[status(thm)],[f_8_4]) ).
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]) ).
fof(f_9_8,plain,
( ! [U_35,U_36,U_37] :
( ~ in(ordered_pair(sK7(U_37,U_36,U_35),sK8(U_37,U_36,U_35)),U_35)
| ~ sP9(U_35,U_36,U_37) )
& ! [U_35,U_36,U_37] :
( in(ordered_pair(sK7(U_37,U_36,U_35),sK8(U_37,U_36,U_35)),U_37)
| ~ sP9(U_35,U_36,U_37) )
& ! [U_35,U_36,U_37] :
( in(sK7(U_37,U_36,U_35),U_36)
| ~ sP9(U_35,U_36,U_37) )
& ! [U_35,U_36,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)
| ~ sP8(U_35,U_36,U_37) )
& ! [U_35,U_36,U_37] :
( in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_35)
| ~ sP8(U_35,U_36,U_37) )
& ! [U_38,U_36,U_37,U_40] :
( in(ordered_pair(U_40,U_38),U_37)
| ~ sP6(U_38,U_36,U_37,U_40) )
& ! [U_38,U_36,U_37,U_40] :
( in(U_40,U_36)
| ~ sP6(U_38,U_36,U_37,U_40) )
& ! [U_38,U_41,U_35,U_36,U_37,U_40,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)
| ~ sP7(U_38,U_41,U_35,U_36,U_37,U_40,U_39) )
& ! [U_38,U_41,U_35,U_36,U_37,U_40,U_39] :
( sP6(U_38,U_36,U_37,U_40)
| ~ in(ordered_pair(U_40,U_38),U_35)
| ~ sP7(U_38,U_41,U_35,U_36,U_37,U_40,U_39) )
& ! [U_38,U_41,U_35,U_36,U_37,U_40,U_39] :
( U_35 = relation_dom_restriction(U_37,U_36)
| sP9(U_35,U_36,U_37)
| sP8(U_35,U_36,U_37)
| ~ sP10(U_38,U_41,U_35,U_36,U_37,U_40,U_39) )
& ! [U_38,U_41,U_35,U_36,U_37,U_40,U_39] :
( sP7(U_38,U_41,U_35,U_36,U_37,U_40,U_39)
| U_35 != relation_dom_restriction(U_37,U_36)
| ~ sP10(U_38,U_41,U_35,U_36,U_37,U_40,U_39) )
& ! [U_38,U_41,U_35,U_36,U_37,U_40,U_39] :
( sP10(U_38,U_41,U_35,U_36,U_37,U_40,U_39)
| ~ relation(U_35)
| ~ relation(U_37) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6,sP7,sP8,sP9,sP10])],[f_9_7]) ).
cnf(f_9_9,plain,
( sP10(U_38,U_41,U_35,U_36,U_37,U_40,U_39)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_10,plain,
( sP7(U_38,U_41,U_35,U_36,U_37,U_40,U_39)
| U_35 != relation_dom_restriction(U_37,U_36)
| ~ sP10(U_38,U_41,U_35,U_36,U_37,U_40,U_39) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_11,plain,
( U_35 = relation_dom_restriction(U_37,U_36)
| sP9(U_35,U_36,U_37)
| sP8(U_35,U_36,U_37)
| ~ sP10(U_38,U_41,U_35,U_36,U_37,U_40,U_39) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_12,plain,
( sP6(U_38,U_36,U_37,U_40)
| ~ in(ordered_pair(U_40,U_38),U_35)
| ~ sP7(U_38,U_41,U_35,U_36,U_37,U_40,U_39) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_13,plain,
( in(ordered_pair(U_41,U_39),U_35)
| ~ in(ordered_pair(U_41,U_39),U_37)
| ~ in(U_41,U_36)
| ~ sP7(U_38,U_41,U_35,U_36,U_37,U_40,U_39) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_14,plain,
( in(U_40,U_36)
| ~ sP6(U_38,U_36,U_37,U_40) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_15,plain,
( in(ordered_pair(U_40,U_38),U_37)
| ~ sP6(U_38,U_36,U_37,U_40) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_16,plain,
( in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_35)
| ~ sP8(U_35,U_36,U_37) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_17,plain,
( ~ 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)
| ~ sP8(U_35,U_36,U_37) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_18,plain,
( in(sK7(U_37,U_36,U_35),U_36)
| ~ sP9(U_35,U_36,U_37) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_19,plain,
( in(ordered_pair(sK7(U_37,U_36,U_35),sK8(U_37,U_36,U_35)),U_37)
| ~ sP9(U_35,U_36,U_37) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_20,plain,
( ~ in(ordered_pair(sK7(U_37,U_36,U_35),sK8(U_37,U_36,U_35)),U_35)
| ~ sP9(U_35,U_36,U_37) ),
inference(clausify,[status(thm)],[f_9_8]) ).
fof(f_10_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_10_2,plain,
! [U_52] :
( ( relation(U_52)
| ? [U_51] :
( ! [U_50,U_49] : U_51 != ordered_pair(U_50,U_49)
& in(U_51,U_52) ) )
& ( ! [U_48] :
( ? [U_47,U_46] : U_48 = ordered_pair(U_47,U_46)
| ~ in(U_48,U_52) )
| ~ relation(U_52) ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_54] :
( relation(U_54)
| ? [U_51] :
( ! [U_50,U_49] : U_51 != ordered_pair(U_50,U_49)
& in(U_51,U_54) ) )
& ! [U_53] :
( ! [U_48] :
( ? [U_47,U_46] : U_48 = ordered_pair(U_47,U_46)
| ~ in(U_48,U_53) )
| ~ relation(U_53) ) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
fof(f_10_4,plain,
( ! [U_54] :
( relation(U_54)
| ? [U_51] :
( ! [U_50,U_49] : U_51 != ordered_pair(U_50,U_49)
& in(U_51,U_54) ) )
& ! [U_53] :
( ! [U_48] :
( ? [U_46] : U_48 = ordered_pair(sK9(U_53,U_48),U_46)
| ~ in(U_48,U_53) )
| ~ relation(U_53) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_47,sK9(U_53,U_48))],[f_10_3]) ).
fof(f_10_5,plain,
( ! [U_54] :
( relation(U_54)
| ? [U_51] :
( ! [U_50,U_49] : U_51 != ordered_pair(U_50,U_49)
& in(U_51,U_54) ) )
& ! [U_53] :
( ! [U_48] :
( U_48 = ordered_pair(sK9(U_53,U_48),sK10(U_53,U_48))
| ~ in(U_48,U_53) )
| ~ relation(U_53) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_46,sK10(U_53,U_48))],[f_10_4]) ).
fof(f_10_6,plain,
( ! [U_54] :
( relation(U_54)
| ( ! [U_50,U_49] : sK11(U_54) != ordered_pair(U_50,U_49)
& in(sK11(U_54),U_54) ) )
& ! [U_53] :
( ! [U_48] :
( U_48 = ordered_pair(sK9(U_53,U_48),sK10(U_53,U_48))
| ~ in(U_48,U_53) )
| ~ relation(U_53) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_51,sK11(U_54))],[f_10_5]) ).
fof(f_10_7,plain,
( ! [U_54,U_50,U_49] :
( sK11(U_54) != ordered_pair(U_50,U_49)
| ~ sP11(U_54,U_50,U_49) )
& ! [U_54,U_50,U_49] :
( in(sK11(U_54),U_54)
| ~ sP11(U_54,U_50,U_49) )
& ! [U_54,U_50,U_49] :
( relation(U_54)
| sP11(U_54,U_50,U_49) )
& ! [U_53,U_48] :
( U_48 = ordered_pair(sK9(U_53,U_48),sK10(U_53,U_48))
| ~ in(U_48,U_53)
| ~ relation(U_53) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11])],[f_10_6]) ).
cnf(f_10_8,plain,
( U_48 = ordered_pair(sK9(U_53,U_48),sK10(U_53,U_48))
| ~ in(U_48,U_53)
| ~ relation(U_53) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_9,plain,
( relation(U_54)
| sP11(U_54,U_50,U_49) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_10,plain,
( in(sK11(U_54),U_54)
| ~ sP11(U_54,U_50,U_49) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_11,plain,
( sK11(U_54) != ordered_pair(U_50,U_49)
| ~ sP11(U_54,U_50,U_49) ),
inference(clausify,[status(thm)],[f_10_7]) ).
fof(f_11_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_11_2,plain,
! [U_62,U_61] :
( ( ( ( U_61 = set_meet(U_62)
| U_61 != empty_set )
& ( U_61 = empty_set
| U_61 != set_meet(U_62) ) )
| U_62 != empty_set )
& ( ( ( U_61 = set_meet(U_62)
| ? [U_60] :
( ( ~ in(U_60,U_61)
& ! [U_59] :
( in(U_60,U_59)
| ~ in(U_59,U_62) ) )
| ( ? [U_58] :
( ~ in(U_60,U_58)
& in(U_58,U_62) )
& in(U_60,U_61) ) ) )
& ( ! [U_57] :
( ( in(U_57,U_61)
| ? [U_56] :
( ~ in(U_57,U_56)
& in(U_56,U_62) ) )
& ( ! [U_55] :
( in(U_57,U_55)
| ~ in(U_55,U_62) )
| ~ in(U_57,U_61) ) )
| U_61 != set_meet(U_62) ) )
| U_62 = empty_set ) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
( ! [U_74] :
( ( ! [U_72] :
( U_72 = set_meet(U_74)
| U_72 != empty_set )
& ! [U_71] :
( U_71 = empty_set
| U_71 != set_meet(U_74) ) )
| U_74 != empty_set )
& ! [U_73] :
( ( ! [U_70] :
( U_70 = set_meet(U_73)
| ? [U_66] :
( ~ in(U_66,U_70)
& ! [U_59] :
( in(U_66,U_59)
| ~ in(U_59,U_73) ) )
| ? [U_65] :
( ? [U_58] :
( ~ in(U_65,U_58)
& in(U_58,U_73) )
& in(U_65,U_70) ) )
& ! [U_69] :
( ( ! [U_64] :
( in(U_64,U_69)
| ? [U_56] :
( ~ in(U_64,U_56)
& in(U_56,U_73) ) )
& ! [U_63] :
( ! [U_55] :
( in(U_63,U_55)
| ~ in(U_55,U_73) )
| ~ in(U_63,U_69) ) )
| U_69 != set_meet(U_73) ) )
| U_73 = empty_set ) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
fof(f_11_4,plain,
( ! [U_74] :
( ( ! [U_72] :
( U_72 = set_meet(U_74)
| U_72 != empty_set )
& ! [U_71] :
( U_71 = empty_set
| U_71 != set_meet(U_74) ) )
| U_74 != empty_set )
& ! [U_73] :
( ( ! [U_70] :
( U_70 = set_meet(U_73)
| ? [U_66] :
( ~ in(U_66,U_70)
& ! [U_59] :
( in(U_66,U_59)
| ~ in(U_59,U_73) ) )
| ? [U_65] :
( ? [U_58] :
( ~ in(U_65,U_58)
& in(U_58,U_73) )
& in(U_65,U_70) ) )
& ! [U_69] :
( ( ! [U_64] :
( in(U_64,U_69)
| ( ~ in(U_64,sK12(U_73,U_69,U_64))
& in(sK12(U_73,U_69,U_64),U_73) ) )
& ! [U_63] :
( ! [U_55] :
( in(U_63,U_55)
| ~ in(U_55,U_73) )
| ~ in(U_63,U_69) ) )
| U_69 != set_meet(U_73) ) )
| U_73 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_56,sK12(U_73,U_69,U_64))],[f_11_3]) ).
fof(f_11_5,plain,
( ! [U_74] :
( ( ! [U_72] :
( U_72 = set_meet(U_74)
| U_72 != empty_set )
& ! [U_71] :
( U_71 = empty_set
| U_71 != set_meet(U_74) ) )
| U_74 != empty_set )
& ! [U_73] :
( ( ! [U_70] :
( U_70 = set_meet(U_73)
| ? [U_66] :
( ~ in(U_66,U_70)
& ! [U_59] :
( in(U_66,U_59)
| ~ in(U_59,U_73) ) )
| ( ? [U_58] :
( ~ in(sK13(U_73,U_70),U_58)
& in(U_58,U_73) )
& in(sK13(U_73,U_70),U_70) ) )
& ! [U_69] :
( ( ! [U_64] :
( in(U_64,U_69)
| ( ~ in(U_64,sK12(U_73,U_69,U_64))
& in(sK12(U_73,U_69,U_64),U_73) ) )
& ! [U_63] :
( ! [U_55] :
( in(U_63,U_55)
| ~ in(U_55,U_73) )
| ~ in(U_63,U_69) ) )
| U_69 != set_meet(U_73) ) )
| U_73 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_65,sK13(U_73,U_70))],[f_11_4]) ).
fof(f_11_6,plain,
( ! [U_74] :
( ( ! [U_72] :
( U_72 = set_meet(U_74)
| U_72 != empty_set )
& ! [U_71] :
( U_71 = empty_set
| U_71 != set_meet(U_74) ) )
| U_74 != empty_set )
& ! [U_73] :
( ( ! [U_70] :
( U_70 = set_meet(U_73)
| ? [U_66] :
( ~ in(U_66,U_70)
& ! [U_59] :
( in(U_66,U_59)
| ~ in(U_59,U_73) ) )
| ( ~ in(sK13(U_73,U_70),sK14(U_73,U_70))
& in(sK14(U_73,U_70),U_73)
& in(sK13(U_73,U_70),U_70) ) )
& ! [U_69] :
( ( ! [U_64] :
( in(U_64,U_69)
| ( ~ in(U_64,sK12(U_73,U_69,U_64))
& in(sK12(U_73,U_69,U_64),U_73) ) )
& ! [U_63] :
( ! [U_55] :
( in(U_63,U_55)
| ~ in(U_55,U_73) )
| ~ in(U_63,U_69) ) )
| U_69 != set_meet(U_73) ) )
| U_73 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_58,sK14(U_73,U_70))],[f_11_5]) ).
fof(f_11_7,plain,
( ! [U_74] :
( ( ! [U_72] :
( U_72 = set_meet(U_74)
| U_72 != empty_set )
& ! [U_71] :
( U_71 = empty_set
| U_71 != set_meet(U_74) ) )
| U_74 != empty_set )
& ! [U_73] :
( ( ! [U_70] :
( U_70 = set_meet(U_73)
| ( ~ in(sK15(U_73,U_70),U_70)
& ! [U_59] :
( in(sK15(U_73,U_70),U_59)
| ~ in(U_59,U_73) ) )
| ( ~ in(sK13(U_73,U_70),sK14(U_73,U_70))
& in(sK14(U_73,U_70),U_73)
& in(sK13(U_73,U_70),U_70) ) )
& ! [U_69] :
( ( ! [U_64] :
( in(U_64,U_69)
| ( ~ in(U_64,sK12(U_73,U_69,U_64))
& in(sK12(U_73,U_69,U_64),U_73) ) )
& ! [U_63] :
( ! [U_55] :
( in(U_63,U_55)
| ~ in(U_55,U_73) )
| ~ in(U_63,U_69) ) )
| U_69 != set_meet(U_73) ) )
| U_73 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_66,sK15(U_73,U_70))],[f_11_6]) ).
fof(f_11_8,plain,
( ! [U_71,U_72,U_74] :
( U_72 = set_meet(U_74)
| U_72 != empty_set
| ~ sP17(U_71,U_72,U_74) )
& ! [U_71,U_72,U_74] :
( U_71 = empty_set
| U_71 != set_meet(U_74)
| ~ sP17(U_71,U_72,U_74) )
& ! [U_59,U_73,U_70] :
( ~ in(sK15(U_73,U_70),U_70)
| ~ sP15(U_59,U_73,U_70) )
& ! [U_59,U_73,U_70] :
( in(sK15(U_73,U_70),U_59)
| ~ in(U_59,U_73)
| ~ sP15(U_59,U_73,U_70) )
& ! [U_73,U_70] :
( ~ in(sK13(U_73,U_70),sK14(U_73,U_70))
| ~ sP14(U_73,U_70) )
& ! [U_73,U_70] :
( in(sK14(U_73,U_70),U_73)
| ~ sP14(U_73,U_70) )
& ! [U_73,U_70] :
( in(sK13(U_73,U_70),U_70)
| ~ sP14(U_73,U_70) )
& ! [U_69,U_64,U_73] :
( ~ in(U_64,sK12(U_73,U_69,U_64))
| ~ sP12(U_69,U_64,U_73) )
& ! [U_69,U_64,U_73] :
( in(sK12(U_73,U_69,U_64),U_73)
| ~ sP12(U_69,U_64,U_73) )
& ! [U_69,U_64,U_63,U_73,U_55] :
( in(U_64,U_69)
| sP12(U_69,U_64,U_73)
| ~ sP13(U_69,U_64,U_63,U_73,U_55) )
& ! [U_69,U_64,U_63,U_73,U_55] :
( in(U_63,U_55)
| ~ in(U_55,U_73)
| ~ in(U_63,U_69)
| ~ sP13(U_69,U_64,U_63,U_73,U_55) )
& ! [U_69,U_64,U_63,U_59,U_73,U_70,U_55] :
( U_70 = set_meet(U_73)
| sP15(U_59,U_73,U_70)
| sP14(U_73,U_70)
| ~ sP16(U_69,U_64,U_63,U_59,U_73,U_70,U_55) )
& ! [U_69,U_64,U_63,U_59,U_73,U_70,U_55] :
( sP13(U_69,U_64,U_63,U_73,U_55)
| U_69 != set_meet(U_73)
| ~ sP16(U_69,U_64,U_63,U_59,U_73,U_70,U_55) )
& ! [U_71,U_72,U_74] :
( sP17(U_71,U_72,U_74)
| U_74 != empty_set )
& ! [U_69,U_64,U_63,U_59,U_73,U_70,U_55] :
( sP16(U_69,U_64,U_63,U_59,U_73,U_70,U_55)
| U_73 = empty_set ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12,sP13,sP14,sP15,sP16,sP17])],[f_11_7]) ).
cnf(f_11_9,plain,
( sP16(U_69,U_64,U_63,U_59,U_73,U_70,U_55)
| U_73 = empty_set ),
inference(clausify,[status(thm)],[f_11_8]) ).
cnf(f_11_10,plain,
( sP17(U_71,U_72,U_74)
| U_74 != empty_set ),
inference(clausify,[status(thm)],[f_11_8]) ).
cnf(f_11_11,plain,
( sP13(U_69,U_64,U_63,U_73,U_55)
| U_69 != set_meet(U_73)
| ~ sP16(U_69,U_64,U_63,U_59,U_73,U_70,U_55) ),
inference(clausify,[status(thm)],[f_11_8]) ).
cnf(f_11_12,plain,
( U_70 = set_meet(U_73)
| sP15(U_59,U_73,U_70)
| sP14(U_73,U_70)
| ~ sP16(U_69,U_64,U_63,U_59,U_73,U_70,U_55) ),
inference(clausify,[status(thm)],[f_11_8]) ).
cnf(f_11_13,plain,
( in(U_63,U_55)
| ~ in(U_55,U_73)
| ~ in(U_63,U_69)
| ~ sP13(U_69,U_64,U_63,U_73,U_55) ),
inference(clausify,[status(thm)],[f_11_8]) ).
cnf(f_11_14,plain,
( in(U_64,U_69)
| sP12(U_69,U_64,U_73)
| ~ sP13(U_69,U_64,U_63,U_73,U_55) ),
inference(clausify,[status(thm)],[f_11_8]) ).
cnf(f_11_15,plain,
( in(sK12(U_73,U_69,U_64),U_73)
| ~ sP12(U_69,U_64,U_73) ),
inference(clausify,[status(thm)],[f_11_8]) ).
cnf(f_11_16,plain,
( ~ in(U_64,sK12(U_73,U_69,U_64))
| ~ sP12(U_69,U_64,U_73) ),
inference(clausify,[status(thm)],[f_11_8]) ).
cnf(f_11_17,plain,
( in(sK13(U_73,U_70),U_70)
| ~ sP14(U_73,U_70) ),
inference(clausify,[status(thm)],[f_11_8]) ).
cnf(f_11_18,plain,
( in(sK14(U_73,U_70),U_73)
| ~ sP14(U_73,U_70) ),
inference(clausify,[status(thm)],[f_11_8]) ).
cnf(f_11_19,plain,
( ~ in(sK13(U_73,U_70),sK14(U_73,U_70))
| ~ sP14(U_73,U_70) ),
inference(clausify,[status(thm)],[f_11_8]) ).
cnf(f_11_20,plain,
( in(sK15(U_73,U_70),U_59)
| ~ in(U_59,U_73)
| ~ sP15(U_59,U_73,U_70) ),
inference(clausify,[status(thm)],[f_11_8]) ).
cnf(f_11_21,plain,
( ~ in(sK15(U_73,U_70),U_70)
| ~ sP15(U_59,U_73,U_70) ),
inference(clausify,[status(thm)],[f_11_8]) ).
cnf(f_11_22,plain,
( U_71 = empty_set
| U_71 != set_meet(U_74)
| ~ sP17(U_71,U_72,U_74) ),
inference(clausify,[status(thm)],[f_11_8]) ).
cnf(f_11_23,plain,
( U_72 = set_meet(U_74)
| U_72 != empty_set
| ~ sP17(U_71,U_72,U_74) ),
inference(clausify,[status(thm)],[f_11_8]) ).
fof(f_12_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_12_2,plain,
! [U_78,U_77] :
( ( U_77 = singleton(U_78)
| ? [U_76] :
( ( ~ in(U_76,U_77)
& U_76 = U_78 )
| ( U_76 != U_78
& in(U_76,U_77) ) ) )
& ( ! [U_75] :
( ( in(U_75,U_77)
| U_75 != U_78 )
& ( U_75 = U_78
| ~ in(U_75,U_77) ) )
| U_77 != singleton(U_78) ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_86,U_84] :
( U_84 = singleton(U_86)
| ? [U_82] :
( ~ in(U_82,U_84)
& U_82 = U_86 )
| ? [U_81] :
( U_81 != U_86
& in(U_81,U_84) ) )
& ! [U_85,U_83] :
( ( ! [U_80] :
( in(U_80,U_83)
| U_80 != U_85 )
& ! [U_79] :
( U_79 = U_85
| ~ in(U_79,U_83) ) )
| U_83 != singleton(U_85) ) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
( ! [U_86,U_84] :
( U_84 = singleton(U_86)
| ? [U_82] :
( ~ in(U_82,U_84)
& U_82 = U_86 )
| ( sK16(U_86,U_84) != U_86
& in(sK16(U_86,U_84),U_84) ) )
& ! [U_85,U_83] :
( ( ! [U_80] :
( in(U_80,U_83)
| U_80 != U_85 )
& ! [U_79] :
( U_79 = U_85
| ~ in(U_79,U_83) ) )
| U_83 != singleton(U_85) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_81,sK16(U_86,U_84))],[f_12_3]) ).
fof(f_12_5,plain,
( ! [U_86,U_84] :
( U_84 = singleton(U_86)
| ( ~ in(sK17(U_86,U_84),U_84)
& sK17(U_86,U_84) = U_86 )
| ( sK16(U_86,U_84) != U_86
& in(sK16(U_86,U_84),U_84) ) )
& ! [U_85,U_83] :
( ( ! [U_80] :
( in(U_80,U_83)
| U_80 != U_85 )
& ! [U_79] :
( U_79 = U_85
| ~ in(U_79,U_83) ) )
| U_83 != singleton(U_85) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_82,sK17(U_86,U_84))],[f_12_4]) ).
fof(f_12_6,plain,
( ! [U_86,U_84] :
( ~ in(sK17(U_86,U_84),U_84)
| ~ sP20(U_86,U_84) )
& ! [U_86,U_84] :
( sK17(U_86,U_84) = U_86
| ~ sP20(U_86,U_84) )
& ! [U_86,U_84] :
( sK16(U_86,U_84) != U_86
| ~ sP19(U_86,U_84) )
& ! [U_86,U_84] :
( in(sK16(U_86,U_84),U_84)
| ~ sP19(U_86,U_84) )
& ! [U_79,U_85,U_80,U_83] :
( in(U_80,U_83)
| U_80 != U_85
| ~ sP18(U_79,U_85,U_80,U_83) )
& ! [U_79,U_85,U_80,U_83] :
( U_79 = U_85
| ~ in(U_79,U_83)
| ~ sP18(U_79,U_85,U_80,U_83) )
& ! [U_86,U_84] :
( U_84 = singleton(U_86)
| sP20(U_86,U_84)
| sP19(U_86,U_84) )
& ! [U_79,U_85,U_80,U_83] :
( sP18(U_79,U_85,U_80,U_83)
| U_83 != singleton(U_85) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP18,sP19,sP20])],[f_12_5]) ).
cnf(f_12_7,plain,
( sP18(U_79,U_85,U_80,U_83)
| U_83 != singleton(U_85) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_8,plain,
( U_84 = singleton(U_86)
| sP20(U_86,U_84)
| sP19(U_86,U_84) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_9,plain,
( U_79 = U_85
| ~ in(U_79,U_83)
| ~ sP18(U_79,U_85,U_80,U_83) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_10,plain,
( in(U_80,U_83)
| U_80 != U_85
| ~ sP18(U_79,U_85,U_80,U_83) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_11,plain,
( in(sK16(U_86,U_84),U_84)
| ~ sP19(U_86,U_84) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_12,plain,
( sK16(U_86,U_84) != U_86
| ~ sP19(U_86,U_84) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_13,plain,
( sK17(U_86,U_84) = U_86
| ~ sP20(U_86,U_84) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_14,plain,
( ~ in(sK17(U_86,U_84),U_84)
| ~ sP20(U_86,U_84) ),
inference(clausify,[status(thm)],[f_12_6]) ).
fof(f_13_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_13_2,plain,
! [U_89] :
( ( U_89 = empty_set
| ? [U_88] : in(U_88,U_89) )
& ( ! [U_87] : ~ in(U_87,U_89)
| U_89 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_91] :
( U_91 = empty_set
| ? [U_88] : in(U_88,U_91) )
& ! [U_90] :
( ! [U_87] : ~ in(U_87,U_90)
| U_90 != empty_set ) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
fof(f_13_4,plain,
( ! [U_91] :
( U_91 = empty_set
| in(sK18(U_91),U_91) )
& ! [U_90] :
( ! [U_87] : ~ in(U_87,U_90)
| U_90 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_88,sK18(U_91))],[f_13_3]) ).
fof(f_13_5,plain,
( ! [U_91] :
( U_91 = empty_set
| in(sK18(U_91),U_91) )
& ! [U_87,U_90] :
( ~ in(U_87,U_90)
| U_90 != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_13_4]) ).
cnf(f_13_6,plain,
( ~ in(U_87,U_90)
| U_90 != empty_set ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_7,plain,
( U_91 = empty_set
| in(sK18(U_91),U_91) ),
inference(clausify,[status(thm)],[f_13_5]) ).
fof(f_14_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_14_2,plain,
! [U_95,U_94] :
( ( U_94 = powerset(U_95)
| ? [U_93] :
( ( ~ in(U_93,U_94)
& subset(U_93,U_95) )
| ( ~ subset(U_93,U_95)
& in(U_93,U_94) ) ) )
& ( ! [U_92] :
( ( in(U_92,U_94)
| ~ subset(U_92,U_95) )
& ( subset(U_92,U_95)
| ~ in(U_92,U_94) ) )
| U_94 != powerset(U_95) ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_103,U_101] :
( U_101 = powerset(U_103)
| ? [U_99] :
( ~ in(U_99,U_101)
& subset(U_99,U_103) )
| ? [U_98] :
( ~ subset(U_98,U_103)
& in(U_98,U_101) ) )
& ! [U_102,U_100] :
( ( ! [U_97] :
( in(U_97,U_100)
| ~ subset(U_97,U_102) )
& ! [U_96] :
( subset(U_96,U_102)
| ~ in(U_96,U_100) ) )
| U_100 != powerset(U_102) ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
fof(f_14_4,plain,
( ! [U_103,U_101] :
( U_101 = powerset(U_103)
| ? [U_99] :
( ~ in(U_99,U_101)
& subset(U_99,U_103) )
| ( ~ subset(sK19(U_103,U_101),U_103)
& in(sK19(U_103,U_101),U_101) ) )
& ! [U_102,U_100] :
( ( ! [U_97] :
( in(U_97,U_100)
| ~ subset(U_97,U_102) )
& ! [U_96] :
( subset(U_96,U_102)
| ~ in(U_96,U_100) ) )
| U_100 != powerset(U_102) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_98,sK19(U_103,U_101))],[f_14_3]) ).
fof(f_14_5,plain,
( ! [U_103,U_101] :
( U_101 = powerset(U_103)
| ( ~ in(sK20(U_103,U_101),U_101)
& subset(sK20(U_103,U_101),U_103) )
| ( ~ subset(sK19(U_103,U_101),U_103)
& in(sK19(U_103,U_101),U_101) ) )
& ! [U_102,U_100] :
( ( ! [U_97] :
( in(U_97,U_100)
| ~ subset(U_97,U_102) )
& ! [U_96] :
( subset(U_96,U_102)
| ~ in(U_96,U_100) ) )
| U_100 != powerset(U_102) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_99,sK20(U_103,U_101))],[f_14_4]) ).
fof(f_14_6,plain,
( ! [U_101,U_103] :
( ~ in(sK20(U_103,U_101),U_101)
| ~ sP23(U_101,U_103) )
& ! [U_101,U_103] :
( subset(sK20(U_103,U_101),U_103)
| ~ sP23(U_101,U_103) )
& ! [U_101,U_103] :
( ~ subset(sK19(U_103,U_101),U_103)
| ~ sP22(U_101,U_103) )
& ! [U_101,U_103] :
( in(sK19(U_103,U_101),U_101)
| ~ sP22(U_101,U_103) )
& ! [U_102,U_96,U_100,U_97] :
( in(U_97,U_100)
| ~ subset(U_97,U_102)
| ~ sP21(U_102,U_96,U_100,U_97) )
& ! [U_102,U_96,U_100,U_97] :
( subset(U_96,U_102)
| ~ in(U_96,U_100)
| ~ sP21(U_102,U_96,U_100,U_97) )
& ! [U_101,U_103] :
( U_101 = powerset(U_103)
| sP23(U_101,U_103)
| sP22(U_101,U_103) )
& ! [U_102,U_96,U_100,U_97] :
( sP21(U_102,U_96,U_100,U_97)
| U_100 != powerset(U_102) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP21,sP22,sP23])],[f_14_5]) ).
cnf(f_14_7,plain,
( sP21(U_102,U_96,U_100,U_97)
| U_100 != powerset(U_102) ),
inference(clausify,[status(thm)],[f_14_6]) ).
cnf(f_14_8,plain,
( U_101 = powerset(U_103)
| sP23(U_101,U_103)
| sP22(U_101,U_103) ),
inference(clausify,[status(thm)],[f_14_6]) ).
cnf(f_14_9,plain,
( subset(U_96,U_102)
| ~ in(U_96,U_100)
| ~ sP21(U_102,U_96,U_100,U_97) ),
inference(clausify,[status(thm)],[f_14_6]) ).
cnf(f_14_10,plain,
( in(U_97,U_100)
| ~ subset(U_97,U_102)
| ~ sP21(U_102,U_96,U_100,U_97) ),
inference(clausify,[status(thm)],[f_14_6]) ).
cnf(f_14_11,plain,
( in(sK19(U_103,U_101),U_101)
| ~ sP22(U_101,U_103) ),
inference(clausify,[status(thm)],[f_14_6]) ).
cnf(f_14_12,plain,
( ~ subset(sK19(U_103,U_101),U_103)
| ~ sP22(U_101,U_103) ),
inference(clausify,[status(thm)],[f_14_6]) ).
cnf(f_14_13,plain,
( subset(sK20(U_103,U_101),U_103)
| ~ sP23(U_101,U_103) ),
inference(clausify,[status(thm)],[f_14_6]) ).
cnf(f_14_14,plain,
( ~ in(sK20(U_103,U_101),U_101)
| ~ sP23(U_101,U_103) ),
inference(clausify,[status(thm)],[f_14_6]) ).
fof(f_15_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_15_2,plain,
! [U_109] :
( ! [U_108] :
( ( ( U_109 = U_108
| ? [U_107,U_106] :
( ( ~ in(ordered_pair(U_107,U_106),U_109)
& in(ordered_pair(U_107,U_106),U_108) )
| ( ~ in(ordered_pair(U_107,U_106),U_108)
& in(ordered_pair(U_107,U_106),U_109) ) ) )
& ( ! [U_105,U_104] :
( ( in(ordered_pair(U_105,U_104),U_109)
| ~ in(ordered_pair(U_105,U_104),U_108) )
& ( in(ordered_pair(U_105,U_104),U_108)
| ~ in(ordered_pair(U_105,U_104),U_109) ) )
| U_109 != U_108 ) )
| ~ relation(U_108) )
| ~ relation(U_109) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_109] :
( ! [U_108] :
( ( ( U_109 = U_108
| ? [U_117,U_115] :
( ~ in(ordered_pair(U_117,U_115),U_109)
& in(ordered_pair(U_117,U_115),U_108) )
| ? [U_116,U_114] :
( ~ in(ordered_pair(U_116,U_114),U_108)
& in(ordered_pair(U_116,U_114),U_109) ) )
& ( ( ! [U_113,U_111] :
( in(ordered_pair(U_113,U_111),U_109)
| ~ in(ordered_pair(U_113,U_111),U_108) )
& ! [U_112,U_110] :
( in(ordered_pair(U_112,U_110),U_108)
| ~ in(ordered_pair(U_112,U_110),U_109) ) )
| U_109 != U_108 ) )
| ~ relation(U_108) )
| ~ relation(U_109) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
fof(f_15_4,plain,
! [U_109] :
( ! [U_108] :
( ( ( U_109 = U_108
| ? [U_117,U_115] :
( ~ in(ordered_pair(U_117,U_115),U_109)
& in(ordered_pair(U_117,U_115),U_108) )
| ? [U_114] :
( ~ in(ordered_pair(sK21(U_109,U_108),U_114),U_108)
& in(ordered_pair(sK21(U_109,U_108),U_114),U_109) ) )
& ( ( ! [U_113,U_111] :
( in(ordered_pair(U_113,U_111),U_109)
| ~ in(ordered_pair(U_113,U_111),U_108) )
& ! [U_112,U_110] :
( in(ordered_pair(U_112,U_110),U_108)
| ~ in(ordered_pair(U_112,U_110),U_109) ) )
| U_109 != U_108 ) )
| ~ relation(U_108) )
| ~ relation(U_109) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_116,sK21(U_109,U_108))],[f_15_3]) ).
fof(f_15_5,plain,
! [U_109] :
( ! [U_108] :
( ( ( U_109 = U_108
| ? [U_117,U_115] :
( ~ in(ordered_pair(U_117,U_115),U_109)
& in(ordered_pair(U_117,U_115),U_108) )
| ( ~ in(ordered_pair(sK21(U_109,U_108),sK22(U_109,U_108)),U_108)
& in(ordered_pair(sK21(U_109,U_108),sK22(U_109,U_108)),U_109) ) )
& ( ( ! [U_113,U_111] :
( in(ordered_pair(U_113,U_111),U_109)
| ~ in(ordered_pair(U_113,U_111),U_108) )
& ! [U_112,U_110] :
( in(ordered_pair(U_112,U_110),U_108)
| ~ in(ordered_pair(U_112,U_110),U_109) ) )
| U_109 != U_108 ) )
| ~ relation(U_108) )
| ~ relation(U_109) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_114,sK22(U_109,U_108))],[f_15_4]) ).
fof(f_15_6,plain,
! [U_109] :
( ! [U_108] :
( ( ( U_109 = U_108
| ? [U_115] :
( ~ in(ordered_pair(sK23(U_109,U_108),U_115),U_109)
& in(ordered_pair(sK23(U_109,U_108),U_115),U_108) )
| ( ~ in(ordered_pair(sK21(U_109,U_108),sK22(U_109,U_108)),U_108)
& in(ordered_pair(sK21(U_109,U_108),sK22(U_109,U_108)),U_109) ) )
& ( ( ! [U_113,U_111] :
( in(ordered_pair(U_113,U_111),U_109)
| ~ in(ordered_pair(U_113,U_111),U_108) )
& ! [U_112,U_110] :
( in(ordered_pair(U_112,U_110),U_108)
| ~ in(ordered_pair(U_112,U_110),U_109) ) )
| U_109 != U_108 ) )
| ~ relation(U_108) )
| ~ relation(U_109) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_117,sK23(U_109,U_108))],[f_15_5]) ).
fof(f_15_7,plain,
! [U_109] :
( ! [U_108] :
( ( ( U_109 = U_108
| ( ~ in(ordered_pair(sK23(U_109,U_108),sK24(U_109,U_108)),U_109)
& in(ordered_pair(sK23(U_109,U_108),sK24(U_109,U_108)),U_108) )
| ( ~ in(ordered_pair(sK21(U_109,U_108),sK22(U_109,U_108)),U_108)
& in(ordered_pair(sK21(U_109,U_108),sK22(U_109,U_108)),U_109) ) )
& ( ( ! [U_113,U_111] :
( in(ordered_pair(U_113,U_111),U_109)
| ~ in(ordered_pair(U_113,U_111),U_108) )
& ! [U_112,U_110] :
( in(ordered_pair(U_112,U_110),U_108)
| ~ in(ordered_pair(U_112,U_110),U_109) ) )
| U_109 != U_108 ) )
| ~ relation(U_108) )
| ~ relation(U_109) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_115,sK24(U_109,U_108))],[f_15_6]) ).
fof(f_15_8,plain,
( ! [U_109,U_108] :
( ~ in(ordered_pair(sK23(U_109,U_108),sK24(U_109,U_108)),U_109)
| ~ sP26(U_109,U_108) )
& ! [U_109,U_108] :
( in(ordered_pair(sK23(U_109,U_108),sK24(U_109,U_108)),U_108)
| ~ sP26(U_109,U_108) )
& ! [U_109,U_108] :
( ~ in(ordered_pair(sK21(U_109,U_108),sK22(U_109,U_108)),U_108)
| ~ sP25(U_109,U_108) )
& ! [U_109,U_108] :
( in(ordered_pair(sK21(U_109,U_108),sK22(U_109,U_108)),U_109)
| ~ sP25(U_109,U_108) )
& ! [U_109,U_108,U_113,U_110,U_111,U_112] :
( in(ordered_pair(U_113,U_111),U_109)
| ~ in(ordered_pair(U_113,U_111),U_108)
| ~ sP24(U_109,U_108,U_113,U_110,U_111,U_112) )
& ! [U_109,U_108,U_113,U_110,U_111,U_112] :
( in(ordered_pair(U_112,U_110),U_108)
| ~ in(ordered_pair(U_112,U_110),U_109)
| ~ sP24(U_109,U_108,U_113,U_110,U_111,U_112) )
& ! [U_109,U_108,U_113,U_110,U_111,U_112] :
( U_109 = U_108
| sP26(U_109,U_108)
| sP25(U_109,U_108)
| ~ sP27(U_109,U_108,U_113,U_110,U_111,U_112) )
& ! [U_109,U_108,U_113,U_110,U_111,U_112] :
( sP24(U_109,U_108,U_113,U_110,U_111,U_112)
| U_109 != U_108
| ~ sP27(U_109,U_108,U_113,U_110,U_111,U_112) )
& ! [U_109,U_108,U_113,U_110,U_111,U_112] :
( sP27(U_109,U_108,U_113,U_110,U_111,U_112)
| ~ relation(U_108)
| ~ relation(U_109) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP24,sP25,sP26,sP27])],[f_15_7]) ).
cnf(f_15_9,plain,
( sP27(U_109,U_108,U_113,U_110,U_111,U_112)
| ~ relation(U_108)
| ~ relation(U_109) ),
inference(clausify,[status(thm)],[f_15_8]) ).
cnf(f_15_10,plain,
( sP24(U_109,U_108,U_113,U_110,U_111,U_112)
| U_109 != U_108
| ~ sP27(U_109,U_108,U_113,U_110,U_111,U_112) ),
inference(clausify,[status(thm)],[f_15_8]) ).
cnf(f_15_11,plain,
( U_109 = U_108
| sP26(U_109,U_108)
| sP25(U_109,U_108)
| ~ sP27(U_109,U_108,U_113,U_110,U_111,U_112) ),
inference(clausify,[status(thm)],[f_15_8]) ).
cnf(f_15_12,plain,
( in(ordered_pair(U_112,U_110),U_108)
| ~ in(ordered_pair(U_112,U_110),U_109)
| ~ sP24(U_109,U_108,U_113,U_110,U_111,U_112) ),
inference(clausify,[status(thm)],[f_15_8]) ).
cnf(f_15_13,plain,
( in(ordered_pair(U_113,U_111),U_109)
| ~ in(ordered_pair(U_113,U_111),U_108)
| ~ sP24(U_109,U_108,U_113,U_110,U_111,U_112) ),
inference(clausify,[status(thm)],[f_15_8]) ).
cnf(f_15_14,plain,
( in(ordered_pair(sK21(U_109,U_108),sK22(U_109,U_108)),U_109)
| ~ sP25(U_109,U_108) ),
inference(clausify,[status(thm)],[f_15_8]) ).
cnf(f_15_15,plain,
( ~ in(ordered_pair(sK21(U_109,U_108),sK22(U_109,U_108)),U_108)
| ~ sP25(U_109,U_108) ),
inference(clausify,[status(thm)],[f_15_8]) ).
cnf(f_15_16,plain,
( in(ordered_pair(sK23(U_109,U_108),sK24(U_109,U_108)),U_108)
| ~ sP26(U_109,U_108) ),
inference(clausify,[status(thm)],[f_15_8]) ).
cnf(f_15_17,plain,
( ~ in(ordered_pair(sK23(U_109,U_108),sK24(U_109,U_108)),U_109)
| ~ sP26(U_109,U_108) ),
inference(clausify,[status(thm)],[f_15_8]) ).
fof(f_16_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_16_2,plain,
! [U_119,U_118] :
( ( ( ( element(U_118,U_119)
| ~ empty(U_118) )
& ( empty(U_118)
| ~ element(U_118,U_119) ) )
| ~ empty(U_119) )
& ( ( ( element(U_118,U_119)
| ~ in(U_118,U_119) )
& ( in(U_118,U_119)
| ~ element(U_118,U_119) ) )
| empty(U_119) ) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( ! [U_127] :
( ( ! [U_125] :
( element(U_125,U_127)
| ~ empty(U_125) )
& ! [U_124] :
( empty(U_124)
| ~ element(U_124,U_127) ) )
| ~ empty(U_127) )
& ! [U_126] :
( ( ! [U_123] :
( element(U_123,U_126)
| ~ in(U_123,U_126) )
& ! [U_122] :
( in(U_122,U_126)
| ~ element(U_122,U_126) ) )
| empty(U_126) ) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
fof(f_16_4,plain,
( ! [U_127,U_125,U_124] :
( element(U_125,U_127)
| ~ empty(U_125)
| ~ sP29(U_127,U_125,U_124) )
& ! [U_127,U_125,U_124] :
( empty(U_124)
| ~ element(U_124,U_127)
| ~ sP29(U_127,U_125,U_124) )
& ! [U_126,U_123,U_122] :
( element(U_123,U_126)
| ~ in(U_123,U_126)
| ~ sP28(U_126,U_123,U_122) )
& ! [U_126,U_123,U_122] :
( in(U_122,U_126)
| ~ element(U_122,U_126)
| ~ sP28(U_126,U_123,U_122) )
& ! [U_127,U_125,U_124] :
( sP29(U_127,U_125,U_124)
| ~ empty(U_127) )
& ! [U_126,U_123,U_122] :
( sP28(U_126,U_123,U_122)
| empty(U_126) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP28,sP29])],[f_16_3]) ).
cnf(f_16_5,plain,
( sP28(U_126,U_123,U_122)
| empty(U_126) ),
inference(clausify,[status(thm)],[f_16_4]) ).
cnf(f_16_6,plain,
( sP29(U_127,U_125,U_124)
| ~ empty(U_127) ),
inference(clausify,[status(thm)],[f_16_4]) ).
cnf(f_16_7,plain,
( in(U_122,U_126)
| ~ element(U_122,U_126)
| ~ sP28(U_126,U_123,U_122) ),
inference(clausify,[status(thm)],[f_16_4]) ).
cnf(f_16_8,plain,
( element(U_123,U_126)
| ~ in(U_123,U_126)
| ~ sP28(U_126,U_123,U_122) ),
inference(clausify,[status(thm)],[f_16_4]) ).
cnf(f_16_9,plain,
( empty(U_124)
| ~ element(U_124,U_127)
| ~ sP29(U_127,U_125,U_124) ),
inference(clausify,[status(thm)],[f_16_4]) ).
cnf(f_16_10,plain,
( element(U_125,U_127)
| ~ empty(U_125)
| ~ sP29(U_127,U_125,U_124) ),
inference(clausify,[status(thm)],[f_16_4]) ).
fof(f_17_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_17_2,plain,
! [U_132,U_131,U_130] :
( ( U_130 = unordered_pair(U_132,U_131)
| ? [U_129] :
( ( ~ in(U_129,U_130)
& ( U_129 = U_131
| U_129 = U_132 ) )
| ( U_129 != U_131
& U_129 != U_132
& in(U_129,U_130) ) ) )
& ( ! [U_128] :
( ( in(U_128,U_130)
| ( U_128 != U_131
& U_128 != U_132 ) )
& ( U_128 = U_131
| U_128 = U_132
| ~ in(U_128,U_130) ) )
| U_130 != unordered_pair(U_132,U_131) ) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( ! [U_142,U_140,U_138] :
( U_138 = unordered_pair(U_142,U_140)
| ? [U_136] :
( ~ in(U_136,U_138)
& ( U_136 = U_140
| U_136 = U_142 ) )
| ? [U_135] :
( U_135 != U_140
& U_135 != U_142
& in(U_135,U_138) ) )
& ! [U_141,U_139,U_137] :
( ( ! [U_134] :
( in(U_134,U_137)
| ( U_134 != U_139
& U_134 != U_141 ) )
& ! [U_133] :
( U_133 = U_139
| U_133 = U_141
| ~ in(U_133,U_137) ) )
| U_137 != unordered_pair(U_141,U_139) ) ),
inference(miniscope,[status(thm)],[f_17_2]) ).
fof(f_17_4,plain,
( ! [U_142,U_140,U_138] :
( U_138 = unordered_pair(U_142,U_140)
| ? [U_136] :
( ~ in(U_136,U_138)
& ( U_136 = U_140
| U_136 = U_142 ) )
| ( sK25(U_142,U_140,U_138) != U_140
& sK25(U_142,U_140,U_138) != U_142
& in(sK25(U_142,U_140,U_138),U_138) ) )
& ! [U_141,U_139,U_137] :
( ( ! [U_134] :
( in(U_134,U_137)
| ( U_134 != U_139
& U_134 != U_141 ) )
& ! [U_133] :
( U_133 = U_139
| U_133 = U_141
| ~ in(U_133,U_137) ) )
| U_137 != unordered_pair(U_141,U_139) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_135,sK25(U_142,U_140,U_138))],[f_17_3]) ).
fof(f_17_5,plain,
( ! [U_142,U_140,U_138] :
( U_138 = unordered_pair(U_142,U_140)
| ( ~ in(sK26(U_142,U_140,U_138),U_138)
& ( sK26(U_142,U_140,U_138) = U_140
| sK26(U_142,U_140,U_138) = U_142 ) )
| ( sK25(U_142,U_140,U_138) != U_140
& sK25(U_142,U_140,U_138) != U_142
& in(sK25(U_142,U_140,U_138),U_138) ) )
& ! [U_141,U_139,U_137] :
( ( ! [U_134] :
( in(U_134,U_137)
| ( U_134 != U_139
& U_134 != U_141 ) )
& ! [U_133] :
( U_133 = U_139
| U_133 = U_141
| ~ in(U_133,U_137) ) )
| U_137 != unordered_pair(U_141,U_139) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_136,sK26(U_142,U_140,U_138))],[f_17_4]) ).
fof(f_17_6,plain,
( ! [U_138,U_142,U_140] :
( ~ in(sK26(U_142,U_140,U_138),U_138)
| ~ sP33(U_138,U_142,U_140) )
& ! [U_138,U_142,U_140] :
( sK26(U_142,U_140,U_138) = U_140
| sK26(U_142,U_140,U_138) = U_142
| ~ sP33(U_138,U_142,U_140) )
& ! [U_138,U_142,U_140] :
( sK25(U_142,U_140,U_138) != U_140
| ~ sP32(U_138,U_142,U_140) )
& ! [U_138,U_142,U_140] :
( sK25(U_142,U_140,U_138) != U_142
| ~ sP32(U_138,U_142,U_140) )
& ! [U_138,U_142,U_140] :
( in(sK25(U_142,U_140,U_138),U_138)
| ~ sP32(U_138,U_142,U_140) )
& ! [U_134,U_139,U_141] :
( U_134 != U_139
| ~ sP30(U_134,U_139,U_141) )
& ! [U_134,U_139,U_141] :
( U_134 != U_141
| ~ sP30(U_134,U_139,U_141) )
& ! [U_134,U_139,U_141,U_133,U_137] :
( in(U_134,U_137)
| sP30(U_134,U_139,U_141)
| ~ sP31(U_134,U_139,U_141,U_133,U_137) )
& ! [U_134,U_139,U_141,U_133,U_137] :
( U_133 = U_139
| U_133 = U_141
| ~ in(U_133,U_137)
| ~ sP31(U_134,U_139,U_141,U_133,U_137) )
& ! [U_138,U_142,U_140] :
( U_138 = unordered_pair(U_142,U_140)
| sP33(U_138,U_142,U_140)
| sP32(U_138,U_142,U_140) )
& ! [U_134,U_139,U_141,U_133,U_137] :
( sP31(U_134,U_139,U_141,U_133,U_137)
| U_137 != unordered_pair(U_141,U_139) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP30,sP31,sP32,sP33])],[f_17_5]) ).
cnf(f_17_7,plain,
( sP31(U_134,U_139,U_141,U_133,U_137)
| U_137 != unordered_pair(U_141,U_139) ),
inference(clausify,[status(thm)],[f_17_6]) ).
cnf(f_17_8,plain,
( U_138 = unordered_pair(U_142,U_140)
| sP33(U_138,U_142,U_140)
| sP32(U_138,U_142,U_140) ),
inference(clausify,[status(thm)],[f_17_6]) ).
cnf(f_17_9,plain,
( U_133 = U_139
| U_133 = U_141
| ~ in(U_133,U_137)
| ~ sP31(U_134,U_139,U_141,U_133,U_137) ),
inference(clausify,[status(thm)],[f_17_6]) ).
cnf(f_17_10,plain,
( in(U_134,U_137)
| sP30(U_134,U_139,U_141)
| ~ sP31(U_134,U_139,U_141,U_133,U_137) ),
inference(clausify,[status(thm)],[f_17_6]) ).
cnf(f_17_11,plain,
( U_134 != U_141
| ~ sP30(U_134,U_139,U_141) ),
inference(clausify,[status(thm)],[f_17_6]) ).
cnf(f_17_12,plain,
( U_134 != U_139
| ~ sP30(U_134,U_139,U_141) ),
inference(clausify,[status(thm)],[f_17_6]) ).
cnf(f_17_13,plain,
( in(sK25(U_142,U_140,U_138),U_138)
| ~ sP32(U_138,U_142,U_140) ),
inference(clausify,[status(thm)],[f_17_6]) ).
cnf(f_17_14,plain,
( sK25(U_142,U_140,U_138) != U_142
| ~ sP32(U_138,U_142,U_140) ),
inference(clausify,[status(thm)],[f_17_6]) ).
cnf(f_17_15,plain,
( sK25(U_142,U_140,U_138) != U_140
| ~ sP32(U_138,U_142,U_140) ),
inference(clausify,[status(thm)],[f_17_6]) ).
cnf(f_17_16,plain,
( sK26(U_142,U_140,U_138) = U_140
| sK26(U_142,U_140,U_138) = U_142
| ~ sP33(U_138,U_142,U_140) ),
inference(clausify,[status(thm)],[f_17_6]) ).
cnf(f_17_17,plain,
( ~ in(sK26(U_142,U_140,U_138),U_138)
| ~ sP33(U_138,U_142,U_140) ),
inference(clausify,[status(thm)],[f_17_6]) ).
fof(f_18_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_18_2,plain,
! [U_147,U_146,U_145] :
( ( U_145 = set_union2(U_147,U_146)
| ? [U_144] :
( ( ~ in(U_144,U_145)
& ( in(U_144,U_146)
| in(U_144,U_147) ) )
| ( ~ in(U_144,U_146)
& ~ in(U_144,U_147)
& in(U_144,U_145) ) ) )
& ( ! [U_143] :
( ( in(U_143,U_145)
| ( ~ in(U_143,U_146)
& ~ in(U_143,U_147) ) )
& ( in(U_143,U_146)
| in(U_143,U_147)
| ~ in(U_143,U_145) ) )
| U_145 != set_union2(U_147,U_146) ) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( ! [U_157,U_155,U_153] :
( U_153 = set_union2(U_157,U_155)
| ? [U_151] :
( ~ in(U_151,U_153)
& ( in(U_151,U_155)
| in(U_151,U_157) ) )
| ? [U_150] :
( ~ in(U_150,U_155)
& ~ in(U_150,U_157)
& in(U_150,U_153) ) )
& ! [U_156,U_154,U_152] :
( ( ! [U_149] :
( in(U_149,U_152)
| ( ~ in(U_149,U_154)
& ~ in(U_149,U_156) ) )
& ! [U_148] :
( in(U_148,U_154)
| in(U_148,U_156)
| ~ in(U_148,U_152) ) )
| U_152 != set_union2(U_156,U_154) ) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
fof(f_18_4,plain,
( ! [U_157,U_155,U_153] :
( U_153 = set_union2(U_157,U_155)
| ? [U_151] :
( ~ in(U_151,U_153)
& ( in(U_151,U_155)
| in(U_151,U_157) ) )
| ( ~ in(sK27(U_157,U_155,U_153),U_155)
& ~ in(sK27(U_157,U_155,U_153),U_157)
& in(sK27(U_157,U_155,U_153),U_153) ) )
& ! [U_156,U_154,U_152] :
( ( ! [U_149] :
( in(U_149,U_152)
| ( ~ in(U_149,U_154)
& ~ in(U_149,U_156) ) )
& ! [U_148] :
( in(U_148,U_154)
| in(U_148,U_156)
| ~ in(U_148,U_152) ) )
| U_152 != set_union2(U_156,U_154) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_150,sK27(U_157,U_155,U_153))],[f_18_3]) ).
fof(f_18_5,plain,
( ! [U_157,U_155,U_153] :
( U_153 = set_union2(U_157,U_155)
| ( ~ in(sK28(U_157,U_155,U_153),U_153)
& ( in(sK28(U_157,U_155,U_153),U_155)
| in(sK28(U_157,U_155,U_153),U_157) ) )
| ( ~ in(sK27(U_157,U_155,U_153),U_155)
& ~ in(sK27(U_157,U_155,U_153),U_157)
& in(sK27(U_157,U_155,U_153),U_153) ) )
& ! [U_156,U_154,U_152] :
( ( ! [U_149] :
( in(U_149,U_152)
| ( ~ in(U_149,U_154)
& ~ in(U_149,U_156) ) )
& ! [U_148] :
( in(U_148,U_154)
| in(U_148,U_156)
| ~ in(U_148,U_152) ) )
| U_152 != set_union2(U_156,U_154) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_151,sK28(U_157,U_155,U_153))],[f_18_4]) ).
fof(f_18_6,plain,
( ! [U_157,U_155,U_153] :
( ~ in(sK28(U_157,U_155,U_153),U_153)
| ~ sP37(U_157,U_155,U_153) )
& ! [U_157,U_155,U_153] :
( in(sK28(U_157,U_155,U_153),U_155)
| in(sK28(U_157,U_155,U_153),U_157)
| ~ sP37(U_157,U_155,U_153) )
& ! [U_157,U_155,U_153] :
( ~ in(sK27(U_157,U_155,U_153),U_155)
| ~ sP36(U_157,U_155,U_153) )
& ! [U_157,U_155,U_153] :
( ~ in(sK27(U_157,U_155,U_153),U_157)
| ~ sP36(U_157,U_155,U_153) )
& ! [U_157,U_155,U_153] :
( in(sK27(U_157,U_155,U_153),U_153)
| ~ sP36(U_157,U_155,U_153) )
& ! [U_156,U_149,U_154] :
( ~ in(U_149,U_154)
| ~ sP34(U_156,U_149,U_154) )
& ! [U_156,U_149,U_154] :
( ~ in(U_149,U_156)
| ~ sP34(U_156,U_149,U_154) )
& ! [U_148,U_156,U_149,U_152,U_154] :
( in(U_149,U_152)
| sP34(U_156,U_149,U_154)
| ~ sP35(U_148,U_156,U_149,U_152,U_154) )
& ! [U_148,U_156,U_149,U_152,U_154] :
( in(U_148,U_154)
| in(U_148,U_156)
| ~ in(U_148,U_152)
| ~ sP35(U_148,U_156,U_149,U_152,U_154) )
& ! [U_157,U_155,U_153] :
( U_153 = set_union2(U_157,U_155)
| sP37(U_157,U_155,U_153)
| sP36(U_157,U_155,U_153) )
& ! [U_148,U_156,U_149,U_152,U_154] :
( sP35(U_148,U_156,U_149,U_152,U_154)
| U_152 != set_union2(U_156,U_154) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP34,sP35,sP36,sP37])],[f_18_5]) ).
cnf(f_18_7,plain,
( sP35(U_148,U_156,U_149,U_152,U_154)
| U_152 != set_union2(U_156,U_154) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_8,plain,
( U_153 = set_union2(U_157,U_155)
| sP37(U_157,U_155,U_153)
| sP36(U_157,U_155,U_153) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_9,plain,
( in(U_148,U_154)
| in(U_148,U_156)
| ~ in(U_148,U_152)
| ~ sP35(U_148,U_156,U_149,U_152,U_154) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_10,plain,
( in(U_149,U_152)
| sP34(U_156,U_149,U_154)
| ~ sP35(U_148,U_156,U_149,U_152,U_154) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_11,plain,
( ~ in(U_149,U_156)
| ~ sP34(U_156,U_149,U_154) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_12,plain,
( ~ in(U_149,U_154)
| ~ sP34(U_156,U_149,U_154) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_13,plain,
( in(sK27(U_157,U_155,U_153),U_153)
| ~ sP36(U_157,U_155,U_153) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_14,plain,
( ~ in(sK27(U_157,U_155,U_153),U_157)
| ~ sP36(U_157,U_155,U_153) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_15,plain,
( ~ in(sK27(U_157,U_155,U_153),U_155)
| ~ sP36(U_157,U_155,U_153) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_16,plain,
( in(sK28(U_157,U_155,U_153),U_155)
| in(sK28(U_157,U_155,U_153),U_157)
| ~ sP37(U_157,U_155,U_153) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_17,plain,
( ~ in(sK28(U_157,U_155,U_153),U_153)
| ~ sP37(U_157,U_155,U_153) ),
inference(clausify,[status(thm)],[f_18_6]) ).
fof(f_19_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_19_2,plain,
! [U_170,U_169,U_168] :
( ( U_168 = cartesian_product2(U_170,U_169)
| ? [U_167] :
( ( ~ in(U_167,U_168)
& ? [U_166,U_165] :
( U_167 = ordered_pair(U_166,U_165)
& in(U_165,U_169)
& in(U_166,U_170) ) )
| ( ! [U_164,U_163] :
( U_167 != ordered_pair(U_164,U_163)
| ~ in(U_163,U_169)
| ~ in(U_164,U_170) )
& in(U_167,U_168) ) ) )
& ( ! [U_162] :
( ( in(U_162,U_168)
| ! [U_161,U_160] :
( U_162 != ordered_pair(U_161,U_160)
| ~ in(U_160,U_169)
| ~ in(U_161,U_170) ) )
& ( ? [U_159,U_158] :
( U_162 = ordered_pair(U_159,U_158)
& in(U_158,U_169)
& in(U_159,U_170) )
| ~ in(U_162,U_168) ) )
| U_168 != cartesian_product2(U_170,U_169) ) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( ! [U_180,U_178,U_176] :
( U_176 = cartesian_product2(U_180,U_178)
| ? [U_174] :
( ~ in(U_174,U_176)
& ? [U_166] :
( ? [U_165] :
( U_174 = ordered_pair(U_166,U_165)
& in(U_165,U_178) )
& in(U_166,U_180) ) )
| ? [U_173] :
( ! [U_164] :
( ! [U_163] :
( U_173 != ordered_pair(U_164,U_163)
| ~ in(U_163,U_178) )
| ~ in(U_164,U_180) )
& in(U_173,U_176) ) )
& ! [U_179,U_177,U_175] :
( ( ! [U_172] :
( in(U_172,U_175)
| ! [U_161] :
( ! [U_160] :
( U_172 != ordered_pair(U_161,U_160)
| ~ in(U_160,U_177) )
| ~ in(U_161,U_179) ) )
& ! [U_171] :
( ? [U_159] :
( ? [U_158] :
( U_171 = ordered_pair(U_159,U_158)
& in(U_158,U_177) )
& in(U_159,U_179) )
| ~ in(U_171,U_175) ) )
| U_175 != cartesian_product2(U_179,U_177) ) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
fof(f_19_4,plain,
( ! [U_180,U_178,U_176] :
( U_176 = cartesian_product2(U_180,U_178)
| ? [U_174] :
( ~ in(U_174,U_176)
& ? [U_166] :
( ? [U_165] :
( U_174 = ordered_pair(U_166,U_165)
& in(U_165,U_178) )
& in(U_166,U_180) ) )
| ? [U_173] :
( ! [U_164] :
( ! [U_163] :
( U_173 != ordered_pair(U_164,U_163)
| ~ in(U_163,U_178) )
| ~ in(U_164,U_180) )
& in(U_173,U_176) ) )
& ! [U_179,U_177,U_175] :
( ( ! [U_172] :
( in(U_172,U_175)
| ! [U_161] :
( ! [U_160] :
( U_172 != ordered_pair(U_161,U_160)
| ~ in(U_160,U_177) )
| ~ in(U_161,U_179) ) )
& ! [U_171] :
( ( ? [U_158] :
( U_171 = ordered_pair(sK29(U_179,U_177,U_175,U_171),U_158)
& in(U_158,U_177) )
& in(sK29(U_179,U_177,U_175,U_171),U_179) )
| ~ in(U_171,U_175) ) )
| U_175 != cartesian_product2(U_179,U_177) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_159,sK29(U_179,U_177,U_175,U_171))],[f_19_3]) ).
fof(f_19_5,plain,
( ! [U_180,U_178,U_176] :
( U_176 = cartesian_product2(U_180,U_178)
| ? [U_174] :
( ~ in(U_174,U_176)
& ? [U_166] :
( ? [U_165] :
( U_174 = ordered_pair(U_166,U_165)
& in(U_165,U_178) )
& in(U_166,U_180) ) )
| ? [U_173] :
( ! [U_164] :
( ! [U_163] :
( U_173 != ordered_pair(U_164,U_163)
| ~ in(U_163,U_178) )
| ~ in(U_164,U_180) )
& in(U_173,U_176) ) )
& ! [U_179,U_177,U_175] :
( ( ! [U_172] :
( in(U_172,U_175)
| ! [U_161] :
( ! [U_160] :
( U_172 != ordered_pair(U_161,U_160)
| ~ in(U_160,U_177) )
| ~ in(U_161,U_179) ) )
& ! [U_171] :
( ( U_171 = ordered_pair(sK29(U_179,U_177,U_175,U_171),sK30(U_179,U_177,U_175,U_171))
& in(sK30(U_179,U_177,U_175,U_171),U_177)
& in(sK29(U_179,U_177,U_175,U_171),U_179) )
| ~ in(U_171,U_175) ) )
| U_175 != cartesian_product2(U_179,U_177) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_158,sK30(U_179,U_177,U_175,U_171))],[f_19_4]) ).
fof(f_19_6,plain,
( ! [U_180,U_178,U_176] :
( U_176 = cartesian_product2(U_180,U_178)
| ? [U_174] :
( ~ in(U_174,U_176)
& ? [U_166] :
( ? [U_165] :
( U_174 = ordered_pair(U_166,U_165)
& in(U_165,U_178) )
& in(U_166,U_180) ) )
| ( ! [U_164] :
( ! [U_163] :
( sK31(U_180,U_178,U_176) != ordered_pair(U_164,U_163)
| ~ in(U_163,U_178) )
| ~ in(U_164,U_180) )
& in(sK31(U_180,U_178,U_176),U_176) ) )
& ! [U_179,U_177,U_175] :
( ( ! [U_172] :
( in(U_172,U_175)
| ! [U_161] :
( ! [U_160] :
( U_172 != ordered_pair(U_161,U_160)
| ~ in(U_160,U_177) )
| ~ in(U_161,U_179) ) )
& ! [U_171] :
( ( U_171 = ordered_pair(sK29(U_179,U_177,U_175,U_171),sK30(U_179,U_177,U_175,U_171))
& in(sK30(U_179,U_177,U_175,U_171),U_177)
& in(sK29(U_179,U_177,U_175,U_171),U_179) )
| ~ in(U_171,U_175) ) )
| U_175 != cartesian_product2(U_179,U_177) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_173,sK31(U_180,U_178,U_176))],[f_19_5]) ).
fof(f_19_7,plain,
( ! [U_180,U_178,U_176] :
( U_176 = cartesian_product2(U_180,U_178)
| ( ~ in(sK32(U_180,U_178,U_176),U_176)
& ? [U_166] :
( ? [U_165] :
( sK32(U_180,U_178,U_176) = ordered_pair(U_166,U_165)
& in(U_165,U_178) )
& in(U_166,U_180) ) )
| ( ! [U_164] :
( ! [U_163] :
( sK31(U_180,U_178,U_176) != ordered_pair(U_164,U_163)
| ~ in(U_163,U_178) )
| ~ in(U_164,U_180) )
& in(sK31(U_180,U_178,U_176),U_176) ) )
& ! [U_179,U_177,U_175] :
( ( ! [U_172] :
( in(U_172,U_175)
| ! [U_161] :
( ! [U_160] :
( U_172 != ordered_pair(U_161,U_160)
| ~ in(U_160,U_177) )
| ~ in(U_161,U_179) ) )
& ! [U_171] :
( ( U_171 = ordered_pair(sK29(U_179,U_177,U_175,U_171),sK30(U_179,U_177,U_175,U_171))
& in(sK30(U_179,U_177,U_175,U_171),U_177)
& in(sK29(U_179,U_177,U_175,U_171),U_179) )
| ~ in(U_171,U_175) ) )
| U_175 != cartesian_product2(U_179,U_177) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_174,sK32(U_180,U_178,U_176))],[f_19_6]) ).
fof(f_19_8,plain,
( ! [U_180,U_178,U_176] :
( U_176 = cartesian_product2(U_180,U_178)
| ( ~ in(sK32(U_180,U_178,U_176),U_176)
& ? [U_165] :
( sK32(U_180,U_178,U_176) = ordered_pair(sK33(U_180,U_178,U_176),U_165)
& in(U_165,U_178) )
& in(sK33(U_180,U_178,U_176),U_180) )
| ( ! [U_164] :
( ! [U_163] :
( sK31(U_180,U_178,U_176) != ordered_pair(U_164,U_163)
| ~ in(U_163,U_178) )
| ~ in(U_164,U_180) )
& in(sK31(U_180,U_178,U_176),U_176) ) )
& ! [U_179,U_177,U_175] :
( ( ! [U_172] :
( in(U_172,U_175)
| ! [U_161] :
( ! [U_160] :
( U_172 != ordered_pair(U_161,U_160)
| ~ in(U_160,U_177) )
| ~ in(U_161,U_179) ) )
& ! [U_171] :
( ( U_171 = ordered_pair(sK29(U_179,U_177,U_175,U_171),sK30(U_179,U_177,U_175,U_171))
& in(sK30(U_179,U_177,U_175,U_171),U_177)
& in(sK29(U_179,U_177,U_175,U_171),U_179) )
| ~ in(U_171,U_175) ) )
| U_175 != cartesian_product2(U_179,U_177) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_166,sK33(U_180,U_178,U_176))],[f_19_7]) ).
fof(f_19_9,plain,
( ! [U_180,U_178,U_176] :
( U_176 = cartesian_product2(U_180,U_178)
| ( ~ in(sK32(U_180,U_178,U_176),U_176)
& sK32(U_180,U_178,U_176) = ordered_pair(sK33(U_180,U_178,U_176),sK34(U_180,U_178,U_176))
& in(sK34(U_180,U_178,U_176),U_178)
& in(sK33(U_180,U_178,U_176),U_180) )
| ( ! [U_164] :
( ! [U_163] :
( sK31(U_180,U_178,U_176) != ordered_pair(U_164,U_163)
| ~ in(U_163,U_178) )
| ~ in(U_164,U_180) )
& in(sK31(U_180,U_178,U_176),U_176) ) )
& ! [U_179,U_177,U_175] :
( ( ! [U_172] :
( in(U_172,U_175)
| ! [U_161] :
( ! [U_160] :
( U_172 != ordered_pair(U_161,U_160)
| ~ in(U_160,U_177) )
| ~ in(U_161,U_179) ) )
& ! [U_171] :
( ( U_171 = ordered_pair(sK29(U_179,U_177,U_175,U_171),sK30(U_179,U_177,U_175,U_171))
& in(sK30(U_179,U_177,U_175,U_171),U_177)
& in(sK29(U_179,U_177,U_175,U_171),U_179) )
| ~ in(U_171,U_175) ) )
| U_175 != cartesian_product2(U_179,U_177) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_165,sK34(U_180,U_178,U_176))],[f_19_8]) ).
fof(f_19_10,plain,
( ! [U_178,U_180,U_176] :
( ~ in(sK32(U_180,U_178,U_176),U_176)
| ~ sP41(U_178,U_180,U_176) )
& ! [U_178,U_180,U_176] :
( sK32(U_180,U_178,U_176) = ordered_pair(sK33(U_180,U_178,U_176),sK34(U_180,U_178,U_176))
| ~ sP41(U_178,U_180,U_176) )
& ! [U_178,U_180,U_176] :
( in(sK34(U_180,U_178,U_176),U_178)
| ~ sP41(U_178,U_180,U_176) )
& ! [U_178,U_180,U_176] :
( in(sK33(U_180,U_178,U_176),U_180)
| ~ sP41(U_178,U_180,U_176) )
& ! [U_164,U_163,U_178,U_180,U_176] :
( sK31(U_180,U_178,U_176) != ordered_pair(U_164,U_163)
| ~ in(U_163,U_178)
| ~ in(U_164,U_180)
| ~ sP40(U_164,U_163,U_178,U_180,U_176) )
& ! [U_164,U_163,U_178,U_180,U_176] :
( in(sK31(U_180,U_178,U_176),U_176)
| ~ sP40(U_164,U_163,U_178,U_180,U_176) )
& ! [U_175,U_177,U_179,U_171] :
( U_171 = ordered_pair(sK29(U_179,U_177,U_175,U_171),sK30(U_179,U_177,U_175,U_171))
| ~ sP38(U_175,U_177,U_179,U_171) )
& ! [U_175,U_177,U_179,U_171] :
( in(sK30(U_179,U_177,U_175,U_171),U_177)
| ~ sP38(U_175,U_177,U_179,U_171) )
& ! [U_175,U_177,U_179,U_171] :
( in(sK29(U_179,U_177,U_175,U_171),U_179)
| ~ sP38(U_175,U_177,U_179,U_171) )
& ! [U_175,U_161,U_177,U_179,U_171,U_160,U_172] :
( in(U_172,U_175)
| U_172 != ordered_pair(U_161,U_160)
| ~ in(U_160,U_177)
| ~ in(U_161,U_179)
| ~ sP39(U_175,U_161,U_177,U_179,U_171,U_160,U_172) )
& ! [U_175,U_161,U_177,U_179,U_171,U_160,U_172] :
( sP38(U_175,U_177,U_179,U_171)
| ~ in(U_171,U_175)
| ~ sP39(U_175,U_161,U_177,U_179,U_171,U_160,U_172) )
& ! [U_164,U_163,U_178,U_180,U_176] :
( U_176 = cartesian_product2(U_180,U_178)
| sP41(U_178,U_180,U_176)
| sP40(U_164,U_163,U_178,U_180,U_176) )
& ! [U_175,U_161,U_177,U_179,U_171,U_160,U_172] :
( sP39(U_175,U_161,U_177,U_179,U_171,U_160,U_172)
| U_175 != cartesian_product2(U_179,U_177) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP38,sP39,sP40,sP41])],[f_19_9]) ).
cnf(f_19_11,plain,
( sP39(U_175,U_161,U_177,U_179,U_171,U_160,U_172)
| U_175 != cartesian_product2(U_179,U_177) ),
inference(clausify,[status(thm)],[f_19_10]) ).
cnf(f_19_12,plain,
( U_176 = cartesian_product2(U_180,U_178)
| sP41(U_178,U_180,U_176)
| sP40(U_164,U_163,U_178,U_180,U_176) ),
inference(clausify,[status(thm)],[f_19_10]) ).
cnf(f_19_13,plain,
( sP38(U_175,U_177,U_179,U_171)
| ~ in(U_171,U_175)
| ~ sP39(U_175,U_161,U_177,U_179,U_171,U_160,U_172) ),
inference(clausify,[status(thm)],[f_19_10]) ).
cnf(f_19_14,plain,
( in(U_172,U_175)
| U_172 != ordered_pair(U_161,U_160)
| ~ in(U_160,U_177)
| ~ in(U_161,U_179)
| ~ sP39(U_175,U_161,U_177,U_179,U_171,U_160,U_172) ),
inference(clausify,[status(thm)],[f_19_10]) ).
cnf(f_19_15,plain,
( in(sK29(U_179,U_177,U_175,U_171),U_179)
| ~ sP38(U_175,U_177,U_179,U_171) ),
inference(clausify,[status(thm)],[f_19_10]) ).
cnf(f_19_16,plain,
( in(sK30(U_179,U_177,U_175,U_171),U_177)
| ~ sP38(U_175,U_177,U_179,U_171) ),
inference(clausify,[status(thm)],[f_19_10]) ).
cnf(f_19_17,plain,
( U_171 = ordered_pair(sK29(U_179,U_177,U_175,U_171),sK30(U_179,U_177,U_175,U_171))
| ~ sP38(U_175,U_177,U_179,U_171) ),
inference(clausify,[status(thm)],[f_19_10]) ).
cnf(f_19_18,plain,
( in(sK31(U_180,U_178,U_176),U_176)
| ~ sP40(U_164,U_163,U_178,U_180,U_176) ),
inference(clausify,[status(thm)],[f_19_10]) ).
cnf(f_19_19,plain,
( sK31(U_180,U_178,U_176) != ordered_pair(U_164,U_163)
| ~ in(U_163,U_178)
| ~ in(U_164,U_180)
| ~ sP40(U_164,U_163,U_178,U_180,U_176) ),
inference(clausify,[status(thm)],[f_19_10]) ).
cnf(f_19_20,plain,
( in(sK33(U_180,U_178,U_176),U_180)
| ~ sP41(U_178,U_180,U_176) ),
inference(clausify,[status(thm)],[f_19_10]) ).
cnf(f_19_21,plain,
( in(sK34(U_180,U_178,U_176),U_178)
| ~ sP41(U_178,U_180,U_176) ),
inference(clausify,[status(thm)],[f_19_10]) ).
cnf(f_19_22,plain,
( sK32(U_180,U_178,U_176) = ordered_pair(sK33(U_180,U_178,U_176),sK34(U_180,U_178,U_176))
| ~ sP41(U_178,U_180,U_176) ),
inference(clausify,[status(thm)],[f_19_10]) ).
cnf(f_19_23,plain,
( ~ in(sK32(U_180,U_178,U_176),U_176)
| ~ sP41(U_178,U_180,U_176) ),
inference(clausify,[status(thm)],[f_19_10]) ).
fof(f_20_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_20_2,plain,
! [U_186] :
( ! [U_185] :
( ( ( subset(U_186,U_185)
| ? [U_184,U_183] :
( ~ in(ordered_pair(U_184,U_183),U_185)
& in(ordered_pair(U_184,U_183),U_186) ) )
& ( ! [U_182,U_181] :
( in(ordered_pair(U_182,U_181),U_185)
| ~ in(ordered_pair(U_182,U_181),U_186) )
| ~ subset(U_186,U_185) ) )
| ~ relation(U_185) )
| ~ relation(U_186) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_186] :
( ! [U_185] :
( ( ( subset(U_186,U_185)
| ? [U_183] :
( ~ in(ordered_pair(sK35(U_186,U_185),U_183),U_185)
& in(ordered_pair(sK35(U_186,U_185),U_183),U_186) ) )
& ( ! [U_182,U_181] :
( in(ordered_pair(U_182,U_181),U_185)
| ~ in(ordered_pair(U_182,U_181),U_186) )
| ~ subset(U_186,U_185) ) )
| ~ relation(U_185) )
| ~ relation(U_186) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_184,sK35(U_186,U_185))],[f_20_2]) ).
fof(f_20_4,plain,
! [U_186] :
( ! [U_185] :
( ( ( subset(U_186,U_185)
| ( ~ in(ordered_pair(sK35(U_186,U_185),sK36(U_186,U_185)),U_185)
& in(ordered_pair(sK35(U_186,U_185),sK36(U_186,U_185)),U_186) ) )
& ( ! [U_182,U_181] :
( in(ordered_pair(U_182,U_181),U_185)
| ~ in(ordered_pair(U_182,U_181),U_186) )
| ~ subset(U_186,U_185) ) )
| ~ relation(U_185) )
| ~ relation(U_186) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_183,sK36(U_186,U_185))],[f_20_3]) ).
fof(f_20_5,plain,
( ! [U_185,U_186] :
( ~ in(ordered_pair(sK35(U_186,U_185),sK36(U_186,U_185)),U_185)
| ~ sP42(U_185,U_186) )
& ! [U_185,U_186] :
( in(ordered_pair(sK35(U_186,U_185),sK36(U_186,U_185)),U_186)
| ~ sP42(U_185,U_186) )
& ! [U_182,U_185,U_186,U_181] :
( subset(U_186,U_185)
| sP42(U_185,U_186)
| ~ sP43(U_182,U_185,U_186,U_181) )
& ! [U_182,U_185,U_186,U_181] :
( in(ordered_pair(U_182,U_181),U_185)
| ~ in(ordered_pair(U_182,U_181),U_186)
| ~ subset(U_186,U_185)
| ~ sP43(U_182,U_185,U_186,U_181) )
& ! [U_182,U_185,U_186,U_181] :
( sP43(U_182,U_185,U_186,U_181)
| ~ relation(U_185)
| ~ relation(U_186) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP42,sP43])],[f_20_4]) ).
cnf(f_20_6,plain,
( sP43(U_182,U_185,U_186,U_181)
| ~ relation(U_185)
| ~ relation(U_186) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_7,plain,
( in(ordered_pair(U_182,U_181),U_185)
| ~ in(ordered_pair(U_182,U_181),U_186)
| ~ subset(U_186,U_185)
| ~ sP43(U_182,U_185,U_186,U_181) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_8,plain,
( subset(U_186,U_185)
| sP42(U_185,U_186)
| ~ sP43(U_182,U_185,U_186,U_181) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_9,plain,
( in(ordered_pair(sK35(U_186,U_185),sK36(U_186,U_185)),U_186)
| ~ sP42(U_185,U_186) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_10,plain,
( ~ in(ordered_pair(sK35(U_186,U_185),sK36(U_186,U_185)),U_185)
| ~ sP42(U_185,U_186) ),
inference(clausify,[status(thm)],[f_20_5]) ).
fof(f_21_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_21_2,plain,
! [U_190,U_189] :
( ( subset(U_190,U_189)
| ? [U_188] :
( ~ in(U_188,U_189)
& in(U_188,U_190) ) )
& ( ! [U_187] :
( in(U_187,U_189)
| ~ in(U_187,U_190) )
| ~ subset(U_190,U_189) ) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( ! [U_194,U_192] :
( subset(U_194,U_192)
| ? [U_188] :
( ~ in(U_188,U_192)
& in(U_188,U_194) ) )
& ! [U_193,U_191] :
( ! [U_187] :
( in(U_187,U_191)
| ~ in(U_187,U_193) )
| ~ subset(U_193,U_191) ) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
fof(f_21_4,plain,
( ! [U_194,U_192] :
( subset(U_194,U_192)
| ( ~ in(sK37(U_194,U_192),U_192)
& in(sK37(U_194,U_192),U_194) ) )
& ! [U_193,U_191] :
( ! [U_187] :
( in(U_187,U_191)
| ~ in(U_187,U_193) )
| ~ subset(U_193,U_191) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_188,sK37(U_194,U_192))],[f_21_3]) ).
fof(f_21_5,plain,
( ! [U_194,U_192] :
( ~ in(sK37(U_194,U_192),U_192)
| ~ sP44(U_194,U_192) )
& ! [U_194,U_192] :
( in(sK37(U_194,U_192),U_194)
| ~ sP44(U_194,U_192) )
& ! [U_194,U_192] :
( subset(U_194,U_192)
| sP44(U_194,U_192) )
& ! [U_187,U_191,U_193] :
( in(U_187,U_191)
| ~ in(U_187,U_193)
| ~ subset(U_193,U_191) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP44])],[f_21_4]) ).
cnf(f_21_6,plain,
( in(U_187,U_191)
| ~ in(U_187,U_193)
| ~ subset(U_193,U_191) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_7,plain,
( subset(U_194,U_192)
| sP44(U_194,U_192) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_8,plain,
( in(sK37(U_194,U_192),U_194)
| ~ sP44(U_194,U_192) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_9,plain,
( ~ in(sK37(U_194,U_192),U_192)
| ~ sP44(U_194,U_192) ),
inference(clausify,[status(thm)],[f_21_5]) ).
fof(f_22_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_22_2,plain,
! [U_199,U_198,U_197] :
( ( U_197 = set_intersection2(U_199,U_198)
| ? [U_196] :
( ( ~ in(U_196,U_197)
& in(U_196,U_198)
& in(U_196,U_199) )
| ( ( ~ in(U_196,U_198)
| ~ in(U_196,U_199) )
& in(U_196,U_197) ) ) )
& ( ! [U_195] :
( ( in(U_195,U_197)
| ~ in(U_195,U_198)
| ~ in(U_195,U_199) )
& ( ( in(U_195,U_198)
& in(U_195,U_199) )
| ~ in(U_195,U_197) ) )
| U_197 != set_intersection2(U_199,U_198) ) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( ! [U_209,U_207,U_205] :
( U_205 = set_intersection2(U_209,U_207)
| ? [U_203] :
( ~ in(U_203,U_205)
& in(U_203,U_207)
& in(U_203,U_209) )
| ? [U_202] :
( ( ~ in(U_202,U_207)
| ~ in(U_202,U_209) )
& in(U_202,U_205) ) )
& ! [U_208,U_206,U_204] :
( ( ! [U_201] :
( in(U_201,U_204)
| ~ in(U_201,U_206)
| ~ in(U_201,U_208) )
& ! [U_200] :
( ( in(U_200,U_206)
& in(U_200,U_208) )
| ~ in(U_200,U_204) ) )
| U_204 != set_intersection2(U_208,U_206) ) ),
inference(miniscope,[status(thm)],[f_22_2]) ).
fof(f_22_4,plain,
( ! [U_209,U_207,U_205] :
( U_205 = set_intersection2(U_209,U_207)
| ? [U_203] :
( ~ in(U_203,U_205)
& in(U_203,U_207)
& in(U_203,U_209) )
| ( ( ~ in(sK38(U_209,U_207,U_205),U_207)
| ~ in(sK38(U_209,U_207,U_205),U_209) )
& in(sK38(U_209,U_207,U_205),U_205) ) )
& ! [U_208,U_206,U_204] :
( ( ! [U_201] :
( in(U_201,U_204)
| ~ in(U_201,U_206)
| ~ in(U_201,U_208) )
& ! [U_200] :
( ( in(U_200,U_206)
& in(U_200,U_208) )
| ~ in(U_200,U_204) ) )
| U_204 != set_intersection2(U_208,U_206) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_202,sK38(U_209,U_207,U_205))],[f_22_3]) ).
fof(f_22_5,plain,
( ! [U_209,U_207,U_205] :
( U_205 = set_intersection2(U_209,U_207)
| ( ~ in(sK39(U_209,U_207,U_205),U_205)
& in(sK39(U_209,U_207,U_205),U_207)
& in(sK39(U_209,U_207,U_205),U_209) )
| ( ( ~ in(sK38(U_209,U_207,U_205),U_207)
| ~ in(sK38(U_209,U_207,U_205),U_209) )
& in(sK38(U_209,U_207,U_205),U_205) ) )
& ! [U_208,U_206,U_204] :
( ( ! [U_201] :
( in(U_201,U_204)
| ~ in(U_201,U_206)
| ~ in(U_201,U_208) )
& ! [U_200] :
( ( in(U_200,U_206)
& in(U_200,U_208) )
| ~ in(U_200,U_204) ) )
| U_204 != set_intersection2(U_208,U_206) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_203,sK39(U_209,U_207,U_205))],[f_22_4]) ).
fof(f_22_6,plain,
( ! [U_209,U_205,U_207] :
( ~ in(sK39(U_209,U_207,U_205),U_205)
| ~ sP48(U_209,U_205,U_207) )
& ! [U_209,U_205,U_207] :
( in(sK39(U_209,U_207,U_205),U_207)
| ~ sP48(U_209,U_205,U_207) )
& ! [U_209,U_205,U_207] :
( in(sK39(U_209,U_207,U_205),U_209)
| ~ sP48(U_209,U_205,U_207) )
& ! [U_209,U_205,U_207] :
( ~ in(sK38(U_209,U_207,U_205),U_207)
| ~ in(sK38(U_209,U_207,U_205),U_209)
| ~ sP47(U_209,U_205,U_207) )
& ! [U_209,U_205,U_207] :
( in(sK38(U_209,U_207,U_205),U_205)
| ~ sP47(U_209,U_205,U_207) )
& ! [U_200,U_206,U_208] :
( in(U_200,U_206)
| ~ sP45(U_200,U_206,U_208) )
& ! [U_200,U_206,U_208] :
( in(U_200,U_208)
| ~ sP45(U_200,U_206,U_208) )
& ! [U_204,U_201,U_200,U_206,U_208] :
( in(U_201,U_204)
| ~ in(U_201,U_206)
| ~ in(U_201,U_208)
| ~ sP46(U_204,U_201,U_200,U_206,U_208) )
& ! [U_204,U_201,U_200,U_206,U_208] :
( sP45(U_200,U_206,U_208)
| ~ in(U_200,U_204)
| ~ sP46(U_204,U_201,U_200,U_206,U_208) )
& ! [U_209,U_205,U_207] :
( U_205 = set_intersection2(U_209,U_207)
| sP48(U_209,U_205,U_207)
| sP47(U_209,U_205,U_207) )
& ! [U_204,U_201,U_200,U_206,U_208] :
( sP46(U_204,U_201,U_200,U_206,U_208)
| U_204 != set_intersection2(U_208,U_206) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP45,sP46,sP47,sP48])],[f_22_5]) ).
cnf(f_22_7,plain,
( sP46(U_204,U_201,U_200,U_206,U_208)
| U_204 != set_intersection2(U_208,U_206) ),
inference(clausify,[status(thm)],[f_22_6]) ).
cnf(f_22_8,plain,
( U_205 = set_intersection2(U_209,U_207)
| sP48(U_209,U_205,U_207)
| sP47(U_209,U_205,U_207) ),
inference(clausify,[status(thm)],[f_22_6]) ).
cnf(f_22_9,plain,
( sP45(U_200,U_206,U_208)
| ~ in(U_200,U_204)
| ~ sP46(U_204,U_201,U_200,U_206,U_208) ),
inference(clausify,[status(thm)],[f_22_6]) ).
cnf(f_22_10,plain,
( in(U_201,U_204)
| ~ in(U_201,U_206)
| ~ in(U_201,U_208)
| ~ sP46(U_204,U_201,U_200,U_206,U_208) ),
inference(clausify,[status(thm)],[f_22_6]) ).
cnf(f_22_11,plain,
( in(U_200,U_208)
| ~ sP45(U_200,U_206,U_208) ),
inference(clausify,[status(thm)],[f_22_6]) ).
cnf(f_22_12,plain,
( in(U_200,U_206)
| ~ sP45(U_200,U_206,U_208) ),
inference(clausify,[status(thm)],[f_22_6]) ).
cnf(f_22_13,plain,
( in(sK38(U_209,U_207,U_205),U_205)
| ~ sP47(U_209,U_205,U_207) ),
inference(clausify,[status(thm)],[f_22_6]) ).
cnf(f_22_14,plain,
( ~ in(sK38(U_209,U_207,U_205),U_207)
| ~ in(sK38(U_209,U_207,U_205),U_209)
| ~ sP47(U_209,U_205,U_207) ),
inference(clausify,[status(thm)],[f_22_6]) ).
cnf(f_22_15,plain,
( in(sK39(U_209,U_207,U_205),U_209)
| ~ sP48(U_209,U_205,U_207) ),
inference(clausify,[status(thm)],[f_22_6]) ).
cnf(f_22_16,plain,
( in(sK39(U_209,U_207,U_205),U_207)
| ~ sP48(U_209,U_205,U_207) ),
inference(clausify,[status(thm)],[f_22_6]) ).
cnf(f_22_17,plain,
( ~ in(sK39(U_209,U_207,U_205),U_205)
| ~ sP48(U_209,U_205,U_207) ),
inference(clausify,[status(thm)],[f_22_6]) ).
fof(f_23_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_23_2,plain,
! [U_217] :
( ! [U_216] :
( ( U_216 = relation_dom(U_217)
| ? [U_215] :
( ( ~ in(U_215,U_216)
& ? [U_214] : in(ordered_pair(U_215,U_214),U_217) )
| ( ! [U_213] : ~ in(ordered_pair(U_215,U_213),U_217)
& in(U_215,U_216) ) ) )
& ( ! [U_212] :
( ( in(U_212,U_216)
| ! [U_211] : ~ in(ordered_pair(U_212,U_211),U_217) )
& ( ? [U_210] : in(ordered_pair(U_212,U_210),U_217)
| ~ in(U_212,U_216) ) )
| U_216 != relation_dom(U_217) ) )
| ~ relation(U_217) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_217] :
( ( ! [U_223] :
( U_223 = relation_dom(U_217)
| ? [U_221] :
( ~ in(U_221,U_223)
& ? [U_214] : in(ordered_pair(U_221,U_214),U_217) )
| ? [U_220] :
( ! [U_213] : ~ in(ordered_pair(U_220,U_213),U_217)
& in(U_220,U_223) ) )
& ! [U_222] :
( ( ! [U_219] :
( in(U_219,U_222)
| ! [U_211] : ~ in(ordered_pair(U_219,U_211),U_217) )
& ! [U_218] :
( ? [U_210] : in(ordered_pair(U_218,U_210),U_217)
| ~ in(U_218,U_222) ) )
| U_222 != relation_dom(U_217) ) )
| ~ relation(U_217) ),
inference(miniscope,[status(thm)],[f_23_2]) ).
fof(f_23_4,plain,
! [U_217] :
( ( ! [U_223] :
( U_223 = relation_dom(U_217)
| ? [U_221] :
( ~ in(U_221,U_223)
& ? [U_214] : in(ordered_pair(U_221,U_214),U_217) )
| ? [U_220] :
( ! [U_213] : ~ in(ordered_pair(U_220,U_213),U_217)
& in(U_220,U_223) ) )
& ! [U_222] :
( ( ! [U_219] :
( in(U_219,U_222)
| ! [U_211] : ~ in(ordered_pair(U_219,U_211),U_217) )
& ! [U_218] :
( in(ordered_pair(U_218,sK40(U_217,U_222,U_218)),U_217)
| ~ in(U_218,U_222) ) )
| U_222 != relation_dom(U_217) ) )
| ~ relation(U_217) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_210,sK40(U_217,U_222,U_218))],[f_23_3]) ).
fof(f_23_5,plain,
! [U_217] :
( ( ! [U_223] :
( U_223 = relation_dom(U_217)
| ? [U_221] :
( ~ in(U_221,U_223)
& ? [U_214] : in(ordered_pair(U_221,U_214),U_217) )
| ( ! [U_213] : ~ in(ordered_pair(sK41(U_217,U_223),U_213),U_217)
& in(sK41(U_217,U_223),U_223) ) )
& ! [U_222] :
( ( ! [U_219] :
( in(U_219,U_222)
| ! [U_211] : ~ in(ordered_pair(U_219,U_211),U_217) )
& ! [U_218] :
( in(ordered_pair(U_218,sK40(U_217,U_222,U_218)),U_217)
| ~ in(U_218,U_222) ) )
| U_222 != relation_dom(U_217) ) )
| ~ relation(U_217) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_220,sK41(U_217,U_223))],[f_23_4]) ).
fof(f_23_6,plain,
! [U_217] :
( ( ! [U_223] :
( U_223 = relation_dom(U_217)
| ( ~ in(sK42(U_217,U_223),U_223)
& ? [U_214] : in(ordered_pair(sK42(U_217,U_223),U_214),U_217) )
| ( ! [U_213] : ~ in(ordered_pair(sK41(U_217,U_223),U_213),U_217)
& in(sK41(U_217,U_223),U_223) ) )
& ! [U_222] :
( ( ! [U_219] :
( in(U_219,U_222)
| ! [U_211] : ~ in(ordered_pair(U_219,U_211),U_217) )
& ! [U_218] :
( in(ordered_pair(U_218,sK40(U_217,U_222,U_218)),U_217)
| ~ in(U_218,U_222) ) )
| U_222 != relation_dom(U_217) ) )
| ~ relation(U_217) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_221,sK42(U_217,U_223))],[f_23_5]) ).
fof(f_23_7,plain,
! [U_217] :
( ( ! [U_223] :
( U_223 = relation_dom(U_217)
| ( ~ in(sK42(U_217,U_223),U_223)
& in(ordered_pair(sK42(U_217,U_223),sK43(U_217,U_223)),U_217) )
| ( ! [U_213] : ~ in(ordered_pair(sK41(U_217,U_223),U_213),U_217)
& in(sK41(U_217,U_223),U_223) ) )
& ! [U_222] :
( ( ! [U_219] :
( in(U_219,U_222)
| ! [U_211] : ~ in(ordered_pair(U_219,U_211),U_217) )
& ! [U_218] :
( in(ordered_pair(U_218,sK40(U_217,U_222,U_218)),U_217)
| ~ in(U_218,U_222) ) )
| U_222 != relation_dom(U_217) ) )
| ~ relation(U_217) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_214,sK43(U_217,U_223))],[f_23_6]) ).
fof(f_23_8,plain,
( ! [U_217,U_223] :
( ~ in(sK42(U_217,U_223),U_223)
| ~ sP51(U_217,U_223) )
& ! [U_217,U_223] :
( in(ordered_pair(sK42(U_217,U_223),sK43(U_217,U_223)),U_217)
| ~ sP51(U_217,U_223) )
& ! [U_217,U_213,U_223] :
( ~ in(ordered_pair(sK41(U_217,U_223),U_213),U_217)
| ~ sP50(U_217,U_213,U_223) )
& ! [U_217,U_213,U_223] :
( in(sK41(U_217,U_223),U_223)
| ~ sP50(U_217,U_213,U_223) )
& ! [U_218,U_219,U_217,U_222,U_211] :
( in(U_219,U_222)
| ~ in(ordered_pair(U_219,U_211),U_217)
| ~ sP49(U_218,U_219,U_217,U_222,U_211) )
& ! [U_218,U_219,U_217,U_222,U_211] :
( in(ordered_pair(U_218,sK40(U_217,U_222,U_218)),U_217)
| ~ in(U_218,U_222)
| ~ sP49(U_218,U_219,U_217,U_222,U_211) )
& ! [U_218,U_219,U_217,U_213,U_222,U_223,U_211] :
( U_223 = relation_dom(U_217)
| sP51(U_217,U_223)
| sP50(U_217,U_213,U_223)
| ~ sP52(U_218,U_219,U_217,U_213,U_222,U_223,U_211) )
& ! [U_218,U_219,U_217,U_213,U_222,U_223,U_211] :
( sP49(U_218,U_219,U_217,U_222,U_211)
| U_222 != relation_dom(U_217)
| ~ sP52(U_218,U_219,U_217,U_213,U_222,U_223,U_211) )
& ! [U_218,U_219,U_217,U_213,U_222,U_223,U_211] :
( sP52(U_218,U_219,U_217,U_213,U_222,U_223,U_211)
| ~ relation(U_217) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP49,sP50,sP51,sP52])],[f_23_7]) ).
cnf(f_23_9,plain,
( sP52(U_218,U_219,U_217,U_213,U_222,U_223,U_211)
| ~ relation(U_217) ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_10,plain,
( sP49(U_218,U_219,U_217,U_222,U_211)
| U_222 != relation_dom(U_217)
| ~ sP52(U_218,U_219,U_217,U_213,U_222,U_223,U_211) ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_11,plain,
( U_223 = relation_dom(U_217)
| sP51(U_217,U_223)
| sP50(U_217,U_213,U_223)
| ~ sP52(U_218,U_219,U_217,U_213,U_222,U_223,U_211) ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_12,plain,
( in(ordered_pair(U_218,sK40(U_217,U_222,U_218)),U_217)
| ~ in(U_218,U_222)
| ~ sP49(U_218,U_219,U_217,U_222,U_211) ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_13,plain,
( in(U_219,U_222)
| ~ in(ordered_pair(U_219,U_211),U_217)
| ~ sP49(U_218,U_219,U_217,U_222,U_211) ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_14,plain,
( in(sK41(U_217,U_223),U_223)
| ~ sP50(U_217,U_213,U_223) ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_15,plain,
( ~ in(ordered_pair(sK41(U_217,U_223),U_213),U_217)
| ~ sP50(U_217,U_213,U_223) ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_16,plain,
( in(ordered_pair(sK42(U_217,U_223),sK43(U_217,U_223)),U_217)
| ~ sP51(U_217,U_223) ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_17,plain,
( ~ in(sK42(U_217,U_223),U_223)
| ~ sP51(U_217,U_223) ),
inference(clausify,[status(thm)],[f_23_8]) ).
fof(f_24_1,plain,
! [A] : cast_to_subset(A) = A,
inference(fof_nnf,[status(thm)],[d4_subset_1]) ).
fof(f_24_2,plain,
! [U_224] : cast_to_subset(U_224) = U_224,
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_224] : cast_to_subset(U_224) = U_224,
inference(definitional_conversion,[status(esa)],[f_24_2]) ).
cnf(f_24_4,plain,
cast_to_subset(U_224) = U_224,
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_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_25_2,plain,
! [U_232,U_231] :
( ( U_231 = union(U_232)
| ? [U_230] :
( ( ~ in(U_230,U_231)
& ? [U_229] :
( in(U_229,U_232)
& in(U_230,U_229) ) )
| ( ! [U_228] :
( ~ in(U_228,U_232)
| ~ in(U_230,U_228) )
& in(U_230,U_231) ) ) )
& ( ! [U_227] :
( ( in(U_227,U_231)
| ! [U_226] :
( ~ in(U_226,U_232)
| ~ in(U_227,U_226) ) )
& ( ? [U_225] :
( in(U_225,U_232)
& in(U_227,U_225) )
| ~ in(U_227,U_231) ) )
| U_231 != union(U_232) ) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( ! [U_240,U_238] :
( U_238 = union(U_240)
| ? [U_236] :
( ~ in(U_236,U_238)
& ? [U_229] :
( in(U_229,U_240)
& in(U_236,U_229) ) )
| ? [U_235] :
( ! [U_228] :
( ~ in(U_228,U_240)
| ~ in(U_235,U_228) )
& in(U_235,U_238) ) )
& ! [U_239,U_237] :
( ( ! [U_234] :
( in(U_234,U_237)
| ! [U_226] :
( ~ in(U_226,U_239)
| ~ in(U_234,U_226) ) )
& ! [U_233] :
( ? [U_225] :
( in(U_225,U_239)
& in(U_233,U_225) )
| ~ in(U_233,U_237) ) )
| U_237 != union(U_239) ) ),
inference(miniscope,[status(thm)],[f_25_2]) ).
fof(f_25_4,plain,
( ! [U_240,U_238] :
( U_238 = union(U_240)
| ? [U_236] :
( ~ in(U_236,U_238)
& ? [U_229] :
( in(U_229,U_240)
& in(U_236,U_229) ) )
| ? [U_235] :
( ! [U_228] :
( ~ in(U_228,U_240)
| ~ in(U_235,U_228) )
& in(U_235,U_238) ) )
& ! [U_239,U_237] :
( ( ! [U_234] :
( in(U_234,U_237)
| ! [U_226] :
( ~ in(U_226,U_239)
| ~ in(U_234,U_226) ) )
& ! [U_233] :
( ( in(sK44(U_239,U_237,U_233),U_239)
& in(U_233,sK44(U_239,U_237,U_233)) )
| ~ in(U_233,U_237) ) )
| U_237 != union(U_239) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_225,sK44(U_239,U_237,U_233))],[f_25_3]) ).
fof(f_25_5,plain,
( ! [U_240,U_238] :
( U_238 = union(U_240)
| ? [U_236] :
( ~ in(U_236,U_238)
& ? [U_229] :
( in(U_229,U_240)
& in(U_236,U_229) ) )
| ( ! [U_228] :
( ~ in(U_228,U_240)
| ~ in(sK45(U_240,U_238),U_228) )
& in(sK45(U_240,U_238),U_238) ) )
& ! [U_239,U_237] :
( ( ! [U_234] :
( in(U_234,U_237)
| ! [U_226] :
( ~ in(U_226,U_239)
| ~ in(U_234,U_226) ) )
& ! [U_233] :
( ( in(sK44(U_239,U_237,U_233),U_239)
& in(U_233,sK44(U_239,U_237,U_233)) )
| ~ in(U_233,U_237) ) )
| U_237 != union(U_239) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_235,sK45(U_240,U_238))],[f_25_4]) ).
fof(f_25_6,plain,
( ! [U_240,U_238] :
( U_238 = union(U_240)
| ( ~ in(sK46(U_240,U_238),U_238)
& ? [U_229] :
( in(U_229,U_240)
& in(sK46(U_240,U_238),U_229) ) )
| ( ! [U_228] :
( ~ in(U_228,U_240)
| ~ in(sK45(U_240,U_238),U_228) )
& in(sK45(U_240,U_238),U_238) ) )
& ! [U_239,U_237] :
( ( ! [U_234] :
( in(U_234,U_237)
| ! [U_226] :
( ~ in(U_226,U_239)
| ~ in(U_234,U_226) ) )
& ! [U_233] :
( ( in(sK44(U_239,U_237,U_233),U_239)
& in(U_233,sK44(U_239,U_237,U_233)) )
| ~ in(U_233,U_237) ) )
| U_237 != union(U_239) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_236,sK46(U_240,U_238))],[f_25_5]) ).
fof(f_25_7,plain,
( ! [U_240,U_238] :
( U_238 = union(U_240)
| ( ~ in(sK46(U_240,U_238),U_238)
& in(sK47(U_240,U_238),U_240)
& in(sK46(U_240,U_238),sK47(U_240,U_238)) )
| ( ! [U_228] :
( ~ in(U_228,U_240)
| ~ in(sK45(U_240,U_238),U_228) )
& in(sK45(U_240,U_238),U_238) ) )
& ! [U_239,U_237] :
( ( ! [U_234] :
( in(U_234,U_237)
| ! [U_226] :
( ~ in(U_226,U_239)
| ~ in(U_234,U_226) ) )
& ! [U_233] :
( ( in(sK44(U_239,U_237,U_233),U_239)
& in(U_233,sK44(U_239,U_237,U_233)) )
| ~ in(U_233,U_237) ) )
| U_237 != union(U_239) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_229,sK47(U_240,U_238))],[f_25_6]) ).
fof(f_25_8,plain,
( ! [U_238,U_240] :
( ~ in(sK46(U_240,U_238),U_238)
| ~ sP56(U_238,U_240) )
& ! [U_238,U_240] :
( in(sK47(U_240,U_238),U_240)
| ~ sP56(U_238,U_240) )
& ! [U_238,U_240] :
( in(sK46(U_240,U_238),sK47(U_240,U_238))
| ~ sP56(U_238,U_240) )
& ! [U_228,U_238,U_240] :
( ~ in(U_228,U_240)
| ~ in(sK45(U_240,U_238),U_228)
| ~ sP55(U_228,U_238,U_240) )
& ! [U_228,U_238,U_240] :
( in(sK45(U_240,U_238),U_238)
| ~ sP55(U_228,U_238,U_240) )
& ! [U_233,U_237,U_239] :
( in(sK44(U_239,U_237,U_233),U_239)
| ~ sP53(U_233,U_237,U_239) )
& ! [U_233,U_237,U_239] :
( in(U_233,sK44(U_239,U_237,U_233))
| ~ sP53(U_233,U_237,U_239) )
& ! [U_234,U_233,U_237,U_226,U_239] :
( in(U_234,U_237)
| ~ in(U_226,U_239)
| ~ in(U_234,U_226)
| ~ sP54(U_234,U_233,U_237,U_226,U_239) )
& ! [U_234,U_233,U_237,U_226,U_239] :
( sP53(U_233,U_237,U_239)
| ~ in(U_233,U_237)
| ~ sP54(U_234,U_233,U_237,U_226,U_239) )
& ! [U_228,U_238,U_240] :
( U_238 = union(U_240)
| sP56(U_238,U_240)
| sP55(U_228,U_238,U_240) )
& ! [U_234,U_233,U_237,U_226,U_239] :
( sP54(U_234,U_233,U_237,U_226,U_239)
| U_237 != union(U_239) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP53,sP54,sP55,sP56])],[f_25_7]) ).
cnf(f_25_9,plain,
( sP54(U_234,U_233,U_237,U_226,U_239)
| U_237 != union(U_239) ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_10,plain,
( U_238 = union(U_240)
| sP56(U_238,U_240)
| sP55(U_228,U_238,U_240) ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_11,plain,
( sP53(U_233,U_237,U_239)
| ~ in(U_233,U_237)
| ~ sP54(U_234,U_233,U_237,U_226,U_239) ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_12,plain,
( in(U_234,U_237)
| ~ in(U_226,U_239)
| ~ in(U_234,U_226)
| ~ sP54(U_234,U_233,U_237,U_226,U_239) ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_13,plain,
( in(U_233,sK44(U_239,U_237,U_233))
| ~ sP53(U_233,U_237,U_239) ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_14,plain,
( in(sK44(U_239,U_237,U_233),U_239)
| ~ sP53(U_233,U_237,U_239) ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_15,plain,
( in(sK45(U_240,U_238),U_238)
| ~ sP55(U_228,U_238,U_240) ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_16,plain,
( ~ in(U_228,U_240)
| ~ in(sK45(U_240,U_238),U_228)
| ~ sP55(U_228,U_238,U_240) ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_17,plain,
( in(sK46(U_240,U_238),sK47(U_240,U_238))
| ~ sP56(U_238,U_240) ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_18,plain,
( in(sK47(U_240,U_238),U_240)
| ~ sP56(U_238,U_240) ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_19,plain,
( ~ in(sK46(U_240,U_238),U_238)
| ~ sP56(U_238,U_240) ),
inference(clausify,[status(thm)],[f_25_8]) ).
fof(f_26_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_26_2,plain,
! [U_245,U_244,U_243] :
( ( U_243 = set_difference(U_245,U_244)
| ? [U_242] :
( ( ~ in(U_242,U_243)
& ~ in(U_242,U_244)
& in(U_242,U_245) )
| ( ( in(U_242,U_244)
| ~ in(U_242,U_245) )
& in(U_242,U_243) ) ) )
& ( ! [U_241] :
( ( in(U_241,U_243)
| in(U_241,U_244)
| ~ in(U_241,U_245) )
& ( ( ~ in(U_241,U_244)
& in(U_241,U_245) )
| ~ in(U_241,U_243) ) )
| U_243 != set_difference(U_245,U_244) ) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( ! [U_255,U_253,U_251] :
( U_251 = set_difference(U_255,U_253)
| ? [U_249] :
( ~ in(U_249,U_251)
& ~ in(U_249,U_253)
& in(U_249,U_255) )
| ? [U_248] :
( ( in(U_248,U_253)
| ~ in(U_248,U_255) )
& in(U_248,U_251) ) )
& ! [U_254,U_252,U_250] :
( ( ! [U_247] :
( in(U_247,U_250)
| in(U_247,U_252)
| ~ in(U_247,U_254) )
& ! [U_246] :
( ( ~ in(U_246,U_252)
& in(U_246,U_254) )
| ~ in(U_246,U_250) ) )
| U_250 != set_difference(U_254,U_252) ) ),
inference(miniscope,[status(thm)],[f_26_2]) ).
fof(f_26_4,plain,
( ! [U_255,U_253,U_251] :
( U_251 = set_difference(U_255,U_253)
| ? [U_249] :
( ~ in(U_249,U_251)
& ~ in(U_249,U_253)
& in(U_249,U_255) )
| ( ( in(sK48(U_255,U_253,U_251),U_253)
| ~ in(sK48(U_255,U_253,U_251),U_255) )
& in(sK48(U_255,U_253,U_251),U_251) ) )
& ! [U_254,U_252,U_250] :
( ( ! [U_247] :
( in(U_247,U_250)
| in(U_247,U_252)
| ~ in(U_247,U_254) )
& ! [U_246] :
( ( ~ in(U_246,U_252)
& in(U_246,U_254) )
| ~ in(U_246,U_250) ) )
| U_250 != set_difference(U_254,U_252) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_248,sK48(U_255,U_253,U_251))],[f_26_3]) ).
fof(f_26_5,plain,
( ! [U_255,U_253,U_251] :
( U_251 = set_difference(U_255,U_253)
| ( ~ in(sK49(U_255,U_253,U_251),U_251)
& ~ in(sK49(U_255,U_253,U_251),U_253)
& in(sK49(U_255,U_253,U_251),U_255) )
| ( ( in(sK48(U_255,U_253,U_251),U_253)
| ~ in(sK48(U_255,U_253,U_251),U_255) )
& in(sK48(U_255,U_253,U_251),U_251) ) )
& ! [U_254,U_252,U_250] :
( ( ! [U_247] :
( in(U_247,U_250)
| in(U_247,U_252)
| ~ in(U_247,U_254) )
& ! [U_246] :
( ( ~ in(U_246,U_252)
& in(U_246,U_254) )
| ~ in(U_246,U_250) ) )
| U_250 != set_difference(U_254,U_252) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_249,sK49(U_255,U_253,U_251))],[f_26_4]) ).
fof(f_26_6,plain,
( ! [U_251,U_253,U_255] :
( ~ in(sK49(U_255,U_253,U_251),U_251)
| ~ sP60(U_251,U_253,U_255) )
& ! [U_251,U_253,U_255] :
( ~ in(sK49(U_255,U_253,U_251),U_253)
| ~ sP60(U_251,U_253,U_255) )
& ! [U_251,U_253,U_255] :
( in(sK49(U_255,U_253,U_251),U_255)
| ~ sP60(U_251,U_253,U_255) )
& ! [U_251,U_253,U_255] :
( in(sK48(U_255,U_253,U_251),U_253)
| ~ in(sK48(U_255,U_253,U_251),U_255)
| ~ sP59(U_251,U_253,U_255) )
& ! [U_251,U_253,U_255] :
( in(sK48(U_255,U_253,U_251),U_251)
| ~ sP59(U_251,U_253,U_255) )
& ! [U_252,U_246,U_254] :
( ~ in(U_246,U_252)
| ~ sP57(U_252,U_246,U_254) )
& ! [U_252,U_246,U_254] :
( in(U_246,U_254)
| ~ sP57(U_252,U_246,U_254) )
& ! [U_252,U_246,U_247,U_250,U_254] :
( in(U_247,U_250)
| in(U_247,U_252)
| ~ in(U_247,U_254)
| ~ sP58(U_252,U_246,U_247,U_250,U_254) )
& ! [U_252,U_246,U_247,U_250,U_254] :
( sP57(U_252,U_246,U_254)
| ~ in(U_246,U_250)
| ~ sP58(U_252,U_246,U_247,U_250,U_254) )
& ! [U_251,U_253,U_255] :
( U_251 = set_difference(U_255,U_253)
| sP60(U_251,U_253,U_255)
| sP59(U_251,U_253,U_255) )
& ! [U_252,U_246,U_247,U_250,U_254] :
( sP58(U_252,U_246,U_247,U_250,U_254)
| U_250 != set_difference(U_254,U_252) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP57,sP58,sP59,sP60])],[f_26_5]) ).
cnf(f_26_7,plain,
( sP58(U_252,U_246,U_247,U_250,U_254)
| U_250 != set_difference(U_254,U_252) ),
inference(clausify,[status(thm)],[f_26_6]) ).
cnf(f_26_8,plain,
( U_251 = set_difference(U_255,U_253)
| sP60(U_251,U_253,U_255)
| sP59(U_251,U_253,U_255) ),
inference(clausify,[status(thm)],[f_26_6]) ).
cnf(f_26_9,plain,
( sP57(U_252,U_246,U_254)
| ~ in(U_246,U_250)
| ~ sP58(U_252,U_246,U_247,U_250,U_254) ),
inference(clausify,[status(thm)],[f_26_6]) ).
cnf(f_26_10,plain,
( in(U_247,U_250)
| in(U_247,U_252)
| ~ in(U_247,U_254)
| ~ sP58(U_252,U_246,U_247,U_250,U_254) ),
inference(clausify,[status(thm)],[f_26_6]) ).
cnf(f_26_11,plain,
( in(U_246,U_254)
| ~ sP57(U_252,U_246,U_254) ),
inference(clausify,[status(thm)],[f_26_6]) ).
cnf(f_26_12,plain,
( ~ in(U_246,U_252)
| ~ sP57(U_252,U_246,U_254) ),
inference(clausify,[status(thm)],[f_26_6]) ).
cnf(f_26_13,plain,
( in(sK48(U_255,U_253,U_251),U_251)
| ~ sP59(U_251,U_253,U_255) ),
inference(clausify,[status(thm)],[f_26_6]) ).
cnf(f_26_14,plain,
( in(sK48(U_255,U_253,U_251),U_253)
| ~ in(sK48(U_255,U_253,U_251),U_255)
| ~ sP59(U_251,U_253,U_255) ),
inference(clausify,[status(thm)],[f_26_6]) ).
cnf(f_26_15,plain,
( in(sK49(U_255,U_253,U_251),U_255)
| ~ sP60(U_251,U_253,U_255) ),
inference(clausify,[status(thm)],[f_26_6]) ).
cnf(f_26_16,plain,
( ~ in(sK49(U_255,U_253,U_251),U_253)
| ~ sP60(U_251,U_253,U_255) ),
inference(clausify,[status(thm)],[f_26_6]) ).
cnf(f_26_17,plain,
( ~ in(sK49(U_255,U_253,U_251),U_251)
| ~ sP60(U_251,U_253,U_255) ),
inference(clausify,[status(thm)],[f_26_6]) ).
fof(f_27_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_27_2,plain,
! [U_263] :
( ! [U_262] :
( ( U_262 = relation_rng(U_263)
| ? [U_261] :
( ( ~ in(U_261,U_262)
& ? [U_260] : in(ordered_pair(U_260,U_261),U_263) )
| ( ! [U_259] : ~ in(ordered_pair(U_259,U_261),U_263)
& in(U_261,U_262) ) ) )
& ( ! [U_258] :
( ( in(U_258,U_262)
| ! [U_257] : ~ in(ordered_pair(U_257,U_258),U_263) )
& ( ? [U_256] : in(ordered_pair(U_256,U_258),U_263)
| ~ in(U_258,U_262) ) )
| U_262 != relation_rng(U_263) ) )
| ~ relation(U_263) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_263] :
( ( ! [U_269] :
( U_269 = relation_rng(U_263)
| ? [U_267] :
( ~ in(U_267,U_269)
& ? [U_260] : in(ordered_pair(U_260,U_267),U_263) )
| ? [U_266] :
( ! [U_259] : ~ in(ordered_pair(U_259,U_266),U_263)
& in(U_266,U_269) ) )
& ! [U_268] :
( ( ! [U_265] :
( in(U_265,U_268)
| ! [U_257] : ~ in(ordered_pair(U_257,U_265),U_263) )
& ! [U_264] :
( ? [U_256] : in(ordered_pair(U_256,U_264),U_263)
| ~ in(U_264,U_268) ) )
| U_268 != relation_rng(U_263) ) )
| ~ relation(U_263) ),
inference(miniscope,[status(thm)],[f_27_2]) ).
fof(f_27_4,plain,
! [U_263] :
( ( ! [U_269] :
( U_269 = relation_rng(U_263)
| ? [U_267] :
( ~ in(U_267,U_269)
& ? [U_260] : in(ordered_pair(U_260,U_267),U_263) )
| ? [U_266] :
( ! [U_259] : ~ in(ordered_pair(U_259,U_266),U_263)
& in(U_266,U_269) ) )
& ! [U_268] :
( ( ! [U_265] :
( in(U_265,U_268)
| ! [U_257] : ~ in(ordered_pair(U_257,U_265),U_263) )
& ! [U_264] :
( in(ordered_pair(sK50(U_263,U_268,U_264),U_264),U_263)
| ~ in(U_264,U_268) ) )
| U_268 != relation_rng(U_263) ) )
| ~ relation(U_263) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_256,sK50(U_263,U_268,U_264))],[f_27_3]) ).
fof(f_27_5,plain,
! [U_263] :
( ( ! [U_269] :
( U_269 = relation_rng(U_263)
| ? [U_267] :
( ~ in(U_267,U_269)
& ? [U_260] : in(ordered_pair(U_260,U_267),U_263) )
| ( ! [U_259] : ~ in(ordered_pair(U_259,sK51(U_263,U_269)),U_263)
& in(sK51(U_263,U_269),U_269) ) )
& ! [U_268] :
( ( ! [U_265] :
( in(U_265,U_268)
| ! [U_257] : ~ in(ordered_pair(U_257,U_265),U_263) )
& ! [U_264] :
( in(ordered_pair(sK50(U_263,U_268,U_264),U_264),U_263)
| ~ in(U_264,U_268) ) )
| U_268 != relation_rng(U_263) ) )
| ~ relation(U_263) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_266,sK51(U_263,U_269))],[f_27_4]) ).
fof(f_27_6,plain,
! [U_263] :
( ( ! [U_269] :
( U_269 = relation_rng(U_263)
| ( ~ in(sK52(U_263,U_269),U_269)
& ? [U_260] : in(ordered_pair(U_260,sK52(U_263,U_269)),U_263) )
| ( ! [U_259] : ~ in(ordered_pair(U_259,sK51(U_263,U_269)),U_263)
& in(sK51(U_263,U_269),U_269) ) )
& ! [U_268] :
( ( ! [U_265] :
( in(U_265,U_268)
| ! [U_257] : ~ in(ordered_pair(U_257,U_265),U_263) )
& ! [U_264] :
( in(ordered_pair(sK50(U_263,U_268,U_264),U_264),U_263)
| ~ in(U_264,U_268) ) )
| U_268 != relation_rng(U_263) ) )
| ~ relation(U_263) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_267,sK52(U_263,U_269))],[f_27_5]) ).
fof(f_27_7,plain,
! [U_263] :
( ( ! [U_269] :
( U_269 = relation_rng(U_263)
| ( ~ in(sK52(U_263,U_269),U_269)
& in(ordered_pair(sK53(U_263,U_269),sK52(U_263,U_269)),U_263) )
| ( ! [U_259] : ~ in(ordered_pair(U_259,sK51(U_263,U_269)),U_263)
& in(sK51(U_263,U_269),U_269) ) )
& ! [U_268] :
( ( ! [U_265] :
( in(U_265,U_268)
| ! [U_257] : ~ in(ordered_pair(U_257,U_265),U_263) )
& ! [U_264] :
( in(ordered_pair(sK50(U_263,U_268,U_264),U_264),U_263)
| ~ in(U_264,U_268) ) )
| U_268 != relation_rng(U_263) ) )
| ~ relation(U_263) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_260,sK53(U_263,U_269))],[f_27_6]) ).
fof(f_27_8,plain,
( ! [U_263,U_269] :
( ~ in(sK52(U_263,U_269),U_269)
| ~ sP63(U_263,U_269) )
& ! [U_263,U_269] :
( in(ordered_pair(sK53(U_263,U_269),sK52(U_263,U_269)),U_263)
| ~ sP63(U_263,U_269) )
& ! [U_263,U_259,U_269] :
( ~ in(ordered_pair(U_259,sK51(U_263,U_269)),U_263)
| ~ sP62(U_263,U_259,U_269) )
& ! [U_263,U_259,U_269] :
( in(sK51(U_263,U_269),U_269)
| ~ sP62(U_263,U_259,U_269) )
& ! [U_264,U_265,U_263,U_257,U_268] :
( in(U_265,U_268)
| ~ in(ordered_pair(U_257,U_265),U_263)
| ~ sP61(U_264,U_265,U_263,U_257,U_268) )
& ! [U_264,U_265,U_263,U_257,U_268] :
( in(ordered_pair(sK50(U_263,U_268,U_264),U_264),U_263)
| ~ in(U_264,U_268)
| ~ sP61(U_264,U_265,U_263,U_257,U_268) )
& ! [U_264,U_265,U_263,U_257,U_259,U_269,U_268] :
( U_269 = relation_rng(U_263)
| sP63(U_263,U_269)
| sP62(U_263,U_259,U_269)
| ~ sP64(U_264,U_265,U_263,U_257,U_259,U_269,U_268) )
& ! [U_264,U_265,U_263,U_257,U_259,U_269,U_268] :
( sP61(U_264,U_265,U_263,U_257,U_268)
| U_268 != relation_rng(U_263)
| ~ sP64(U_264,U_265,U_263,U_257,U_259,U_269,U_268) )
& ! [U_264,U_265,U_263,U_257,U_259,U_269,U_268] :
( sP64(U_264,U_265,U_263,U_257,U_259,U_269,U_268)
| ~ relation(U_263) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP61,sP62,sP63,sP64])],[f_27_7]) ).
cnf(f_27_9,plain,
( sP64(U_264,U_265,U_263,U_257,U_259,U_269,U_268)
| ~ relation(U_263) ),
inference(clausify,[status(thm)],[f_27_8]) ).
cnf(f_27_10,plain,
( sP61(U_264,U_265,U_263,U_257,U_268)
| U_268 != relation_rng(U_263)
| ~ sP64(U_264,U_265,U_263,U_257,U_259,U_269,U_268) ),
inference(clausify,[status(thm)],[f_27_8]) ).
cnf(f_27_11,plain,
( U_269 = relation_rng(U_263)
| sP63(U_263,U_269)
| sP62(U_263,U_259,U_269)
| ~ sP64(U_264,U_265,U_263,U_257,U_259,U_269,U_268) ),
inference(clausify,[status(thm)],[f_27_8]) ).
cnf(f_27_12,plain,
( in(ordered_pair(sK50(U_263,U_268,U_264),U_264),U_263)
| ~ in(U_264,U_268)
| ~ sP61(U_264,U_265,U_263,U_257,U_268) ),
inference(clausify,[status(thm)],[f_27_8]) ).
cnf(f_27_13,plain,
( in(U_265,U_268)
| ~ in(ordered_pair(U_257,U_265),U_263)
| ~ sP61(U_264,U_265,U_263,U_257,U_268) ),
inference(clausify,[status(thm)],[f_27_8]) ).
cnf(f_27_14,plain,
( in(sK51(U_263,U_269),U_269)
| ~ sP62(U_263,U_259,U_269) ),
inference(clausify,[status(thm)],[f_27_8]) ).
cnf(f_27_15,plain,
( ~ in(ordered_pair(U_259,sK51(U_263,U_269)),U_263)
| ~ sP62(U_263,U_259,U_269) ),
inference(clausify,[status(thm)],[f_27_8]) ).
cnf(f_27_16,plain,
( in(ordered_pair(sK53(U_263,U_269),sK52(U_263,U_269)),U_263)
| ~ sP63(U_263,U_269) ),
inference(clausify,[status(thm)],[f_27_8]) ).
cnf(f_27_17,plain,
( ~ in(sK52(U_263,U_269),U_269)
| ~ sP63(U_263,U_269) ),
inference(clausify,[status(thm)],[f_27_8]) ).
fof(f_28_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_28_2,plain,
! [U_271,U_270] :
( subset_complement(U_271,U_270) = set_difference(U_271,U_270)
| ~ element(U_270,powerset(U_271)) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_271,U_270] :
( subset_complement(U_271,U_270) = set_difference(U_271,U_270)
| ~ element(U_270,powerset(U_271)) ),
inference(definitional_conversion,[status(esa)],[f_28_2]) ).
cnf(f_28_4,plain,
( subset_complement(U_271,U_270) = set_difference(U_271,U_270)
| ~ element(U_270,powerset(U_271)) ),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_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_29_2,plain,
! [U_273,U_272] : ordered_pair(U_273,U_272) = unordered_pair(unordered_pair(U_273,U_272),singleton(U_273)),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_272,U_273] : ordered_pair(U_273,U_272) = unordered_pair(unordered_pair(U_273,U_272),singleton(U_273)),
inference(definitional_conversion,[status(esa)],[f_29_2]) ).
cnf(f_29_4,plain,
ordered_pair(U_273,U_272) = unordered_pair(unordered_pair(U_273,U_272),singleton(U_273)),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_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_30_2,plain,
! [U_274] :
( relation_field(U_274) = set_union2(relation_dom(U_274),relation_rng(U_274))
| ~ relation(U_274) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_274] :
( relation_field(U_274) = set_union2(relation_dom(U_274),relation_rng(U_274))
| ~ relation(U_274) ),
inference(definitional_conversion,[status(esa)],[f_30_2]) ).
cnf(f_30_4,plain,
( relation_field(U_274) = set_union2(relation_dom(U_274),relation_rng(U_274))
| ~ relation(U_274) ),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_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_31_2,plain,
! [U_280] :
( ! [U_279] :
( ( ( U_279 = relation_inverse(U_280)
| ? [U_278,U_277] :
( ( ~ in(ordered_pair(U_278,U_277),U_279)
& in(ordered_pair(U_277,U_278),U_280) )
| ( ~ in(ordered_pair(U_277,U_278),U_280)
& in(ordered_pair(U_278,U_277),U_279) ) ) )
& ( ! [U_276,U_275] :
( ( in(ordered_pair(U_276,U_275),U_279)
| ~ in(ordered_pair(U_275,U_276),U_280) )
& ( in(ordered_pair(U_275,U_276),U_280)
| ~ in(ordered_pair(U_276,U_275),U_279) ) )
| U_279 != relation_inverse(U_280) ) )
| ~ relation(U_279) )
| ~ relation(U_280) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_280] :
( ! [U_279] :
( ( ( U_279 = relation_inverse(U_280)
| ? [U_288,U_286] :
( ~ in(ordered_pair(U_288,U_286),U_279)
& in(ordered_pair(U_286,U_288),U_280) )
| ? [U_287,U_285] :
( ~ in(ordered_pair(U_285,U_287),U_280)
& in(ordered_pair(U_287,U_285),U_279) ) )
& ( ( ! [U_284,U_282] :
( in(ordered_pair(U_284,U_282),U_279)
| ~ in(ordered_pair(U_282,U_284),U_280) )
& ! [U_283,U_281] :
( in(ordered_pair(U_281,U_283),U_280)
| ~ in(ordered_pair(U_283,U_281),U_279) ) )
| U_279 != relation_inverse(U_280) ) )
| ~ relation(U_279) )
| ~ relation(U_280) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
fof(f_31_4,plain,
! [U_280] :
( ! [U_279] :
( ( ( U_279 = relation_inverse(U_280)
| ? [U_288,U_286] :
( ~ in(ordered_pair(U_288,U_286),U_279)
& in(ordered_pair(U_286,U_288),U_280) )
| ? [U_285] :
( ~ in(ordered_pair(U_285,sK54(U_280,U_279)),U_280)
& in(ordered_pair(sK54(U_280,U_279),U_285),U_279) ) )
& ( ( ! [U_284,U_282] :
( in(ordered_pair(U_284,U_282),U_279)
| ~ in(ordered_pair(U_282,U_284),U_280) )
& ! [U_283,U_281] :
( in(ordered_pair(U_281,U_283),U_280)
| ~ in(ordered_pair(U_283,U_281),U_279) ) )
| U_279 != relation_inverse(U_280) ) )
| ~ relation(U_279) )
| ~ relation(U_280) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_287,sK54(U_280,U_279))],[f_31_3]) ).
fof(f_31_5,plain,
! [U_280] :
( ! [U_279] :
( ( ( U_279 = relation_inverse(U_280)
| ? [U_288,U_286] :
( ~ in(ordered_pair(U_288,U_286),U_279)
& in(ordered_pair(U_286,U_288),U_280) )
| ( ~ in(ordered_pair(sK55(U_280,U_279),sK54(U_280,U_279)),U_280)
& in(ordered_pair(sK54(U_280,U_279),sK55(U_280,U_279)),U_279) ) )
& ( ( ! [U_284,U_282] :
( in(ordered_pair(U_284,U_282),U_279)
| ~ in(ordered_pair(U_282,U_284),U_280) )
& ! [U_283,U_281] :
( in(ordered_pair(U_281,U_283),U_280)
| ~ in(ordered_pair(U_283,U_281),U_279) ) )
| U_279 != relation_inverse(U_280) ) )
| ~ relation(U_279) )
| ~ relation(U_280) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_285,sK55(U_280,U_279))],[f_31_4]) ).
fof(f_31_6,plain,
! [U_280] :
( ! [U_279] :
( ( ( U_279 = relation_inverse(U_280)
| ? [U_286] :
( ~ in(ordered_pair(sK56(U_280,U_279),U_286),U_279)
& in(ordered_pair(U_286,sK56(U_280,U_279)),U_280) )
| ( ~ in(ordered_pair(sK55(U_280,U_279),sK54(U_280,U_279)),U_280)
& in(ordered_pair(sK54(U_280,U_279),sK55(U_280,U_279)),U_279) ) )
& ( ( ! [U_284,U_282] :
( in(ordered_pair(U_284,U_282),U_279)
| ~ in(ordered_pair(U_282,U_284),U_280) )
& ! [U_283,U_281] :
( in(ordered_pair(U_281,U_283),U_280)
| ~ in(ordered_pair(U_283,U_281),U_279) ) )
| U_279 != relation_inverse(U_280) ) )
| ~ relation(U_279) )
| ~ relation(U_280) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_288,sK56(U_280,U_279))],[f_31_5]) ).
fof(f_31_7,plain,
! [U_280] :
( ! [U_279] :
( ( ( U_279 = relation_inverse(U_280)
| ( ~ in(ordered_pair(sK56(U_280,U_279),sK57(U_280,U_279)),U_279)
& in(ordered_pair(sK57(U_280,U_279),sK56(U_280,U_279)),U_280) )
| ( ~ in(ordered_pair(sK55(U_280,U_279),sK54(U_280,U_279)),U_280)
& in(ordered_pair(sK54(U_280,U_279),sK55(U_280,U_279)),U_279) ) )
& ( ( ! [U_284,U_282] :
( in(ordered_pair(U_284,U_282),U_279)
| ~ in(ordered_pair(U_282,U_284),U_280) )
& ! [U_283,U_281] :
( in(ordered_pair(U_281,U_283),U_280)
| ~ in(ordered_pair(U_283,U_281),U_279) ) )
| U_279 != relation_inverse(U_280) ) )
| ~ relation(U_279) )
| ~ relation(U_280) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_286,sK57(U_280,U_279))],[f_31_6]) ).
fof(f_31_8,plain,
( ! [U_280,U_279] :
( ~ in(ordered_pair(sK56(U_280,U_279),sK57(U_280,U_279)),U_279)
| ~ sP67(U_280,U_279) )
& ! [U_280,U_279] :
( in(ordered_pair(sK57(U_280,U_279),sK56(U_280,U_279)),U_280)
| ~ sP67(U_280,U_279) )
& ! [U_280,U_279] :
( ~ in(ordered_pair(sK55(U_280,U_279),sK54(U_280,U_279)),U_280)
| ~ sP66(U_280,U_279) )
& ! [U_280,U_279] :
( in(ordered_pair(sK54(U_280,U_279),sK55(U_280,U_279)),U_279)
| ~ sP66(U_280,U_279) )
& ! [U_284,U_280,U_281,U_282,U_279,U_283] :
( in(ordered_pair(U_284,U_282),U_279)
| ~ in(ordered_pair(U_282,U_284),U_280)
| ~ sP65(U_284,U_280,U_281,U_282,U_279,U_283) )
& ! [U_284,U_280,U_281,U_282,U_279,U_283] :
( in(ordered_pair(U_281,U_283),U_280)
| ~ in(ordered_pair(U_283,U_281),U_279)
| ~ sP65(U_284,U_280,U_281,U_282,U_279,U_283) )
& ! [U_284,U_280,U_281,U_282,U_279,U_283] :
( U_279 = relation_inverse(U_280)
| sP67(U_280,U_279)
| sP66(U_280,U_279)
| ~ sP68(U_284,U_280,U_281,U_282,U_279,U_283) )
& ! [U_284,U_280,U_281,U_282,U_279,U_283] :
( sP65(U_284,U_280,U_281,U_282,U_279,U_283)
| U_279 != relation_inverse(U_280)
| ~ sP68(U_284,U_280,U_281,U_282,U_279,U_283) )
& ! [U_284,U_280,U_281,U_282,U_279,U_283] :
( sP68(U_284,U_280,U_281,U_282,U_279,U_283)
| ~ relation(U_279)
| ~ relation(U_280) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP65,sP66,sP67,sP68])],[f_31_7]) ).
cnf(f_31_9,plain,
( sP68(U_284,U_280,U_281,U_282,U_279,U_283)
| ~ relation(U_279)
| ~ relation(U_280) ),
inference(clausify,[status(thm)],[f_31_8]) ).
cnf(f_31_10,plain,
( sP65(U_284,U_280,U_281,U_282,U_279,U_283)
| U_279 != relation_inverse(U_280)
| ~ sP68(U_284,U_280,U_281,U_282,U_279,U_283) ),
inference(clausify,[status(thm)],[f_31_8]) ).
cnf(f_31_11,plain,
( U_279 = relation_inverse(U_280)
| sP67(U_280,U_279)
| sP66(U_280,U_279)
| ~ sP68(U_284,U_280,U_281,U_282,U_279,U_283) ),
inference(clausify,[status(thm)],[f_31_8]) ).
cnf(f_31_12,plain,
( in(ordered_pair(U_281,U_283),U_280)
| ~ in(ordered_pair(U_283,U_281),U_279)
| ~ sP65(U_284,U_280,U_281,U_282,U_279,U_283) ),
inference(clausify,[status(thm)],[f_31_8]) ).
cnf(f_31_13,plain,
( in(ordered_pair(U_284,U_282),U_279)
| ~ in(ordered_pair(U_282,U_284),U_280)
| ~ sP65(U_284,U_280,U_281,U_282,U_279,U_283) ),
inference(clausify,[status(thm)],[f_31_8]) ).
cnf(f_31_14,plain,
( in(ordered_pair(sK54(U_280,U_279),sK55(U_280,U_279)),U_279)
| ~ sP66(U_280,U_279) ),
inference(clausify,[status(thm)],[f_31_8]) ).
cnf(f_31_15,plain,
( ~ in(ordered_pair(sK55(U_280,U_279),sK54(U_280,U_279)),U_280)
| ~ sP66(U_280,U_279) ),
inference(clausify,[status(thm)],[f_31_8]) ).
cnf(f_31_16,plain,
( in(ordered_pair(sK57(U_280,U_279),sK56(U_280,U_279)),U_280)
| ~ sP67(U_280,U_279) ),
inference(clausify,[status(thm)],[f_31_8]) ).
cnf(f_31_17,plain,
( ~ in(ordered_pair(sK56(U_280,U_279),sK57(U_280,U_279)),U_279)
| ~ sP67(U_280,U_279) ),
inference(clausify,[status(thm)],[f_31_8]) ).
fof(f_32_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_32_2,plain,
! [U_290,U_289] :
( ( disjoint(U_290,U_289)
| set_intersection2(U_290,U_289) != empty_set )
& ( set_intersection2(U_290,U_289) = empty_set
| ~ disjoint(U_290,U_289) ) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
( ! [U_294,U_292] :
( disjoint(U_294,U_292)
| set_intersection2(U_294,U_292) != empty_set )
& ! [U_293,U_291] :
( set_intersection2(U_293,U_291) = empty_set
| ~ disjoint(U_293,U_291) ) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
fof(f_32_4,plain,
( ! [U_292,U_294] :
( disjoint(U_294,U_292)
| set_intersection2(U_294,U_292) != empty_set )
& ! [U_291,U_293] :
( set_intersection2(U_293,U_291) = empty_set
| ~ disjoint(U_293,U_291) ) ),
inference(definitional_conversion,[status(esa)],[f_32_3]) ).
cnf(f_32_5,plain,
( set_intersection2(U_293,U_291) = empty_set
| ~ disjoint(U_293,U_291) ),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_6,plain,
( disjoint(U_294,U_292)
| set_intersection2(U_294,U_292) != empty_set ),
inference(clausify,[status(thm)],[f_32_4]) ).
fof(f_33_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_33_2,plain,
! [U_305] :
( ! [U_304] :
( ! [U_303] :
( ( ( U_303 = relation_composition(U_305,U_304)
| ? [U_302,U_301] :
( ( ~ in(ordered_pair(U_302,U_301),U_303)
& ? [U_300] :
( in(ordered_pair(U_300,U_301),U_304)
& in(ordered_pair(U_302,U_300),U_305) ) )
| ( ! [U_299] :
( ~ in(ordered_pair(U_299,U_301),U_304)
| ~ in(ordered_pair(U_302,U_299),U_305) )
& in(ordered_pair(U_302,U_301),U_303) ) ) )
& ( ! [U_298,U_297] :
( ( in(ordered_pair(U_298,U_297),U_303)
| ! [U_296] :
( ~ in(ordered_pair(U_296,U_297),U_304)
| ~ in(ordered_pair(U_298,U_296),U_305) ) )
& ( ? [U_295] :
( in(ordered_pair(U_295,U_297),U_304)
& in(ordered_pair(U_298,U_295),U_305) )
| ~ in(ordered_pair(U_298,U_297),U_303) ) )
| U_303 != relation_composition(U_305,U_304) ) )
| ~ relation(U_303) )
| ~ relation(U_304) )
| ~ relation(U_305) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_305] :
( ! [U_304] :
( ! [U_303] :
( ( ( U_303 = relation_composition(U_305,U_304)
| ? [U_313,U_311] :
( ~ in(ordered_pair(U_313,U_311),U_303)
& ? [U_300] :
( in(ordered_pair(U_300,U_311),U_304)
& in(ordered_pair(U_313,U_300),U_305) ) )
| ? [U_312,U_310] :
( ! [U_299] :
( ~ in(ordered_pair(U_299,U_310),U_304)
| ~ in(ordered_pair(U_312,U_299),U_305) )
& in(ordered_pair(U_312,U_310),U_303) ) )
& ( ( ! [U_309,U_307] :
( in(ordered_pair(U_309,U_307),U_303)
| ! [U_296] :
( ~ in(ordered_pair(U_296,U_307),U_304)
| ~ in(ordered_pair(U_309,U_296),U_305) ) )
& ! [U_308,U_306] :
( ? [U_295] :
( in(ordered_pair(U_295,U_306),U_304)
& in(ordered_pair(U_308,U_295),U_305) )
| ~ in(ordered_pair(U_308,U_306),U_303) ) )
| U_303 != relation_composition(U_305,U_304) ) )
| ~ relation(U_303) )
| ~ relation(U_304) )
| ~ relation(U_305) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
fof(f_33_4,plain,
! [U_305] :
( ! [U_304] :
( ! [U_303] :
( ( ( U_303 = relation_composition(U_305,U_304)
| ? [U_313,U_311] :
( ~ in(ordered_pair(U_313,U_311),U_303)
& ? [U_300] :
( in(ordered_pair(U_300,U_311),U_304)
& in(ordered_pair(U_313,U_300),U_305) ) )
| ? [U_312,U_310] :
( ! [U_299] :
( ~ in(ordered_pair(U_299,U_310),U_304)
| ~ in(ordered_pair(U_312,U_299),U_305) )
& in(ordered_pair(U_312,U_310),U_303) ) )
& ( ( ! [U_309,U_307] :
( in(ordered_pair(U_309,U_307),U_303)
| ! [U_296] :
( ~ in(ordered_pair(U_296,U_307),U_304)
| ~ in(ordered_pair(U_309,U_296),U_305) ) )
& ! [U_308,U_306] :
( ( in(ordered_pair(sK58(U_305,U_304,U_303,U_308,U_306),U_306),U_304)
& in(ordered_pair(U_308,sK58(U_305,U_304,U_303,U_308,U_306)),U_305) )
| ~ in(ordered_pair(U_308,U_306),U_303) ) )
| U_303 != relation_composition(U_305,U_304) ) )
| ~ relation(U_303) )
| ~ relation(U_304) )
| ~ relation(U_305) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_295,sK58(U_305,U_304,U_303,U_308,U_306))],[f_33_3]) ).
fof(f_33_5,plain,
! [U_305] :
( ! [U_304] :
( ! [U_303] :
( ( ( U_303 = relation_composition(U_305,U_304)
| ? [U_313,U_311] :
( ~ in(ordered_pair(U_313,U_311),U_303)
& ? [U_300] :
( in(ordered_pair(U_300,U_311),U_304)
& in(ordered_pair(U_313,U_300),U_305) ) )
| ? [U_310] :
( ! [U_299] :
( ~ in(ordered_pair(U_299,U_310),U_304)
| ~ in(ordered_pair(sK59(U_305,U_304,U_303),U_299),U_305) )
& in(ordered_pair(sK59(U_305,U_304,U_303),U_310),U_303) ) )
& ( ( ! [U_309,U_307] :
( in(ordered_pair(U_309,U_307),U_303)
| ! [U_296] :
( ~ in(ordered_pair(U_296,U_307),U_304)
| ~ in(ordered_pair(U_309,U_296),U_305) ) )
& ! [U_308,U_306] :
( ( in(ordered_pair(sK58(U_305,U_304,U_303,U_308,U_306),U_306),U_304)
& in(ordered_pair(U_308,sK58(U_305,U_304,U_303,U_308,U_306)),U_305) )
| ~ in(ordered_pair(U_308,U_306),U_303) ) )
| U_303 != relation_composition(U_305,U_304) ) )
| ~ relation(U_303) )
| ~ relation(U_304) )
| ~ relation(U_305) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_312,sK59(U_305,U_304,U_303))],[f_33_4]) ).
fof(f_33_6,plain,
! [U_305] :
( ! [U_304] :
( ! [U_303] :
( ( ( U_303 = relation_composition(U_305,U_304)
| ? [U_313,U_311] :
( ~ in(ordered_pair(U_313,U_311),U_303)
& ? [U_300] :
( in(ordered_pair(U_300,U_311),U_304)
& in(ordered_pair(U_313,U_300),U_305) ) )
| ( ! [U_299] :
( ~ in(ordered_pair(U_299,sK60(U_305,U_304,U_303)),U_304)
| ~ in(ordered_pair(sK59(U_305,U_304,U_303),U_299),U_305) )
& in(ordered_pair(sK59(U_305,U_304,U_303),sK60(U_305,U_304,U_303)),U_303) ) )
& ( ( ! [U_309,U_307] :
( in(ordered_pair(U_309,U_307),U_303)
| ! [U_296] :
( ~ in(ordered_pair(U_296,U_307),U_304)
| ~ in(ordered_pair(U_309,U_296),U_305) ) )
& ! [U_308,U_306] :
( ( in(ordered_pair(sK58(U_305,U_304,U_303,U_308,U_306),U_306),U_304)
& in(ordered_pair(U_308,sK58(U_305,U_304,U_303,U_308,U_306)),U_305) )
| ~ in(ordered_pair(U_308,U_306),U_303) ) )
| U_303 != relation_composition(U_305,U_304) ) )
| ~ relation(U_303) )
| ~ relation(U_304) )
| ~ relation(U_305) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_310,sK60(U_305,U_304,U_303))],[f_33_5]) ).
fof(f_33_7,plain,
! [U_305] :
( ! [U_304] :
( ! [U_303] :
( ( ( U_303 = relation_composition(U_305,U_304)
| ? [U_311] :
( ~ in(ordered_pair(sK61(U_305,U_304,U_303),U_311),U_303)
& ? [U_300] :
( in(ordered_pair(U_300,U_311),U_304)
& in(ordered_pair(sK61(U_305,U_304,U_303),U_300),U_305) ) )
| ( ! [U_299] :
( ~ in(ordered_pair(U_299,sK60(U_305,U_304,U_303)),U_304)
| ~ in(ordered_pair(sK59(U_305,U_304,U_303),U_299),U_305) )
& in(ordered_pair(sK59(U_305,U_304,U_303),sK60(U_305,U_304,U_303)),U_303) ) )
& ( ( ! [U_309,U_307] :
( in(ordered_pair(U_309,U_307),U_303)
| ! [U_296] :
( ~ in(ordered_pair(U_296,U_307),U_304)
| ~ in(ordered_pair(U_309,U_296),U_305) ) )
& ! [U_308,U_306] :
( ( in(ordered_pair(sK58(U_305,U_304,U_303,U_308,U_306),U_306),U_304)
& in(ordered_pair(U_308,sK58(U_305,U_304,U_303,U_308,U_306)),U_305) )
| ~ in(ordered_pair(U_308,U_306),U_303) ) )
| U_303 != relation_composition(U_305,U_304) ) )
| ~ relation(U_303) )
| ~ relation(U_304) )
| ~ relation(U_305) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_313,sK61(U_305,U_304,U_303))],[f_33_6]) ).
fof(f_33_8,plain,
! [U_305] :
( ! [U_304] :
( ! [U_303] :
( ( ( U_303 = relation_composition(U_305,U_304)
| ( ~ in(ordered_pair(sK61(U_305,U_304,U_303),sK62(U_305,U_304,U_303)),U_303)
& ? [U_300] :
( in(ordered_pair(U_300,sK62(U_305,U_304,U_303)),U_304)
& in(ordered_pair(sK61(U_305,U_304,U_303),U_300),U_305) ) )
| ( ! [U_299] :
( ~ in(ordered_pair(U_299,sK60(U_305,U_304,U_303)),U_304)
| ~ in(ordered_pair(sK59(U_305,U_304,U_303),U_299),U_305) )
& in(ordered_pair(sK59(U_305,U_304,U_303),sK60(U_305,U_304,U_303)),U_303) ) )
& ( ( ! [U_309,U_307] :
( in(ordered_pair(U_309,U_307),U_303)
| ! [U_296] :
( ~ in(ordered_pair(U_296,U_307),U_304)
| ~ in(ordered_pair(U_309,U_296),U_305) ) )
& ! [U_308,U_306] :
( ( in(ordered_pair(sK58(U_305,U_304,U_303,U_308,U_306),U_306),U_304)
& in(ordered_pair(U_308,sK58(U_305,U_304,U_303,U_308,U_306)),U_305) )
| ~ in(ordered_pair(U_308,U_306),U_303) ) )
| U_303 != relation_composition(U_305,U_304) ) )
| ~ relation(U_303) )
| ~ relation(U_304) )
| ~ relation(U_305) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_311,sK62(U_305,U_304,U_303))],[f_33_7]) ).
fof(f_33_9,plain,
! [U_305] :
( ! [U_304] :
( ! [U_303] :
( ( ( U_303 = relation_composition(U_305,U_304)
| ( ~ in(ordered_pair(sK61(U_305,U_304,U_303),sK62(U_305,U_304,U_303)),U_303)
& in(ordered_pair(sK63(U_305,U_304,U_303),sK62(U_305,U_304,U_303)),U_304)
& in(ordered_pair(sK61(U_305,U_304,U_303),sK63(U_305,U_304,U_303)),U_305) )
| ( ! [U_299] :
( ~ in(ordered_pair(U_299,sK60(U_305,U_304,U_303)),U_304)
| ~ in(ordered_pair(sK59(U_305,U_304,U_303),U_299),U_305) )
& in(ordered_pair(sK59(U_305,U_304,U_303),sK60(U_305,U_304,U_303)),U_303) ) )
& ( ( ! [U_309,U_307] :
( in(ordered_pair(U_309,U_307),U_303)
| ! [U_296] :
( ~ in(ordered_pair(U_296,U_307),U_304)
| ~ in(ordered_pair(U_309,U_296),U_305) ) )
& ! [U_308,U_306] :
( ( in(ordered_pair(sK58(U_305,U_304,U_303,U_308,U_306),U_306),U_304)
& in(ordered_pair(U_308,sK58(U_305,U_304,U_303,U_308,U_306)),U_305) )
| ~ in(ordered_pair(U_308,U_306),U_303) ) )
| U_303 != relation_composition(U_305,U_304) ) )
| ~ relation(U_303) )
| ~ relation(U_304) )
| ~ relation(U_305) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_300,sK63(U_305,U_304,U_303))],[f_33_8]) ).
fof(f_33_10,plain,
( ! [U_303,U_304,U_305] :
( ~ in(ordered_pair(sK61(U_305,U_304,U_303),sK62(U_305,U_304,U_303)),U_303)
| ~ sP72(U_303,U_304,U_305) )
& ! [U_303,U_304,U_305] :
( in(ordered_pair(sK63(U_305,U_304,U_303),sK62(U_305,U_304,U_303)),U_304)
| ~ sP72(U_303,U_304,U_305) )
& ! [U_303,U_304,U_305] :
( in(ordered_pair(sK61(U_305,U_304,U_303),sK63(U_305,U_304,U_303)),U_305)
| ~ sP72(U_303,U_304,U_305) )
& ! [U_299,U_303,U_304,U_305] :
( ~ in(ordered_pair(U_299,sK60(U_305,U_304,U_303)),U_304)
| ~ in(ordered_pair(sK59(U_305,U_304,U_303),U_299),U_305)
| ~ sP71(U_299,U_303,U_304,U_305) )
& ! [U_299,U_303,U_304,U_305] :
( in(ordered_pair(sK59(U_305,U_304,U_303),sK60(U_305,U_304,U_303)),U_303)
| ~ sP71(U_299,U_303,U_304,U_305) )
& ! [U_308,U_306,U_303,U_304,U_305] :
( in(ordered_pair(sK58(U_305,U_304,U_303,U_308,U_306),U_306),U_304)
| ~ sP69(U_308,U_306,U_303,U_304,U_305) )
& ! [U_308,U_306,U_303,U_304,U_305] :
( in(ordered_pair(U_308,sK58(U_305,U_304,U_303,U_308,U_306)),U_305)
| ~ sP69(U_308,U_306,U_303,U_304,U_305) )
& ! [U_296,U_308,U_309,U_307,U_306,U_303,U_304,U_305] :
( in(ordered_pair(U_309,U_307),U_303)
| ~ in(ordered_pair(U_296,U_307),U_304)
| ~ in(ordered_pair(U_309,U_296),U_305)
| ~ sP70(U_296,U_308,U_309,U_307,U_306,U_303,U_304,U_305) )
& ! [U_296,U_308,U_309,U_307,U_306,U_303,U_304,U_305] :
( sP69(U_308,U_306,U_303,U_304,U_305)
| ~ in(ordered_pair(U_308,U_306),U_303)
| ~ sP70(U_296,U_308,U_309,U_307,U_306,U_303,U_304,U_305) )
& ! [U_296,U_308,U_309,U_307,U_306,U_299,U_303,U_304,U_305] :
( U_303 = relation_composition(U_305,U_304)
| sP72(U_303,U_304,U_305)
| sP71(U_299,U_303,U_304,U_305)
| ~ sP73(U_296,U_308,U_309,U_307,U_306,U_299,U_303,U_304,U_305) )
& ! [U_296,U_308,U_309,U_307,U_306,U_299,U_303,U_304,U_305] :
( sP70(U_296,U_308,U_309,U_307,U_306,U_303,U_304,U_305)
| U_303 != relation_composition(U_305,U_304)
| ~ sP73(U_296,U_308,U_309,U_307,U_306,U_299,U_303,U_304,U_305) )
& ! [U_296,U_308,U_309,U_307,U_306,U_299,U_303,U_304,U_305] :
( sP73(U_296,U_308,U_309,U_307,U_306,U_299,U_303,U_304,U_305)
| ~ relation(U_303)
| ~ relation(U_304)
| ~ relation(U_305) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP69,sP70,sP71,sP72,sP73])],[f_33_9]) ).
cnf(f_33_11,plain,
( sP73(U_296,U_308,U_309,U_307,U_306,U_299,U_303,U_304,U_305)
| ~ relation(U_303)
| ~ relation(U_304)
| ~ relation(U_305) ),
inference(clausify,[status(thm)],[f_33_10]) ).
cnf(f_33_12,plain,
( sP70(U_296,U_308,U_309,U_307,U_306,U_303,U_304,U_305)
| U_303 != relation_composition(U_305,U_304)
| ~ sP73(U_296,U_308,U_309,U_307,U_306,U_299,U_303,U_304,U_305) ),
inference(clausify,[status(thm)],[f_33_10]) ).
cnf(f_33_13,plain,
( U_303 = relation_composition(U_305,U_304)
| sP72(U_303,U_304,U_305)
| sP71(U_299,U_303,U_304,U_305)
| ~ sP73(U_296,U_308,U_309,U_307,U_306,U_299,U_303,U_304,U_305) ),
inference(clausify,[status(thm)],[f_33_10]) ).
cnf(f_33_14,plain,
( sP69(U_308,U_306,U_303,U_304,U_305)
| ~ in(ordered_pair(U_308,U_306),U_303)
| ~ sP70(U_296,U_308,U_309,U_307,U_306,U_303,U_304,U_305) ),
inference(clausify,[status(thm)],[f_33_10]) ).
cnf(f_33_15,plain,
( in(ordered_pair(U_309,U_307),U_303)
| ~ in(ordered_pair(U_296,U_307),U_304)
| ~ in(ordered_pair(U_309,U_296),U_305)
| ~ sP70(U_296,U_308,U_309,U_307,U_306,U_303,U_304,U_305) ),
inference(clausify,[status(thm)],[f_33_10]) ).
cnf(f_33_16,plain,
( in(ordered_pair(U_308,sK58(U_305,U_304,U_303,U_308,U_306)),U_305)
| ~ sP69(U_308,U_306,U_303,U_304,U_305) ),
inference(clausify,[status(thm)],[f_33_10]) ).
cnf(f_33_17,plain,
( in(ordered_pair(sK58(U_305,U_304,U_303,U_308,U_306),U_306),U_304)
| ~ sP69(U_308,U_306,U_303,U_304,U_305) ),
inference(clausify,[status(thm)],[f_33_10]) ).
cnf(f_33_18,plain,
( in(ordered_pair(sK59(U_305,U_304,U_303),sK60(U_305,U_304,U_303)),U_303)
| ~ sP71(U_299,U_303,U_304,U_305) ),
inference(clausify,[status(thm)],[f_33_10]) ).
cnf(f_33_19,plain,
( ~ in(ordered_pair(U_299,sK60(U_305,U_304,U_303)),U_304)
| ~ in(ordered_pair(sK59(U_305,U_304,U_303),U_299),U_305)
| ~ sP71(U_299,U_303,U_304,U_305) ),
inference(clausify,[status(thm)],[f_33_10]) ).
cnf(f_33_20,plain,
( in(ordered_pair(sK61(U_305,U_304,U_303),sK63(U_305,U_304,U_303)),U_305)
| ~ sP72(U_303,U_304,U_305) ),
inference(clausify,[status(thm)],[f_33_10]) ).
cnf(f_33_21,plain,
( in(ordered_pair(sK63(U_305,U_304,U_303),sK62(U_305,U_304,U_303)),U_304)
| ~ sP72(U_303,U_304,U_305) ),
inference(clausify,[status(thm)],[f_33_10]) ).
cnf(f_33_22,plain,
( ~ in(ordered_pair(sK61(U_305,U_304,U_303),sK62(U_305,U_304,U_303)),U_303)
| ~ sP72(U_303,U_304,U_305) ),
inference(clausify,[status(thm)],[f_33_10]) ).
fof(f_34_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_34_2,plain,
! [U_318,U_317] :
( ! [U_316] :
( ( ( U_316 = complements_of_subsets(U_318,U_317)
| ? [U_315] :
( ( ( ~ in(U_315,U_316)
& in(subset_complement(U_318,U_315),U_317) )
| ( ~ in(subset_complement(U_318,U_315),U_317)
& in(U_315,U_316) ) )
& element(U_315,powerset(U_318)) ) )
& ( ! [U_314] :
( ( ( in(U_314,U_316)
| ~ in(subset_complement(U_318,U_314),U_317) )
& ( in(subset_complement(U_318,U_314),U_317)
| ~ in(U_314,U_316) ) )
| ~ element(U_314,powerset(U_318)) )
| U_316 != complements_of_subsets(U_318,U_317) ) )
| ~ element(U_316,powerset(powerset(U_318))) )
| ~ element(U_317,powerset(powerset(U_318))) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_318,U_317] :
( ! [U_316] :
( ( ( U_316 = complements_of_subsets(U_318,U_317)
| ( ( ( ~ in(sK64(U_318,U_317,U_316),U_316)
& in(subset_complement(U_318,sK64(U_318,U_317,U_316)),U_317) )
| ( ~ in(subset_complement(U_318,sK64(U_318,U_317,U_316)),U_317)
& in(sK64(U_318,U_317,U_316),U_316) ) )
& element(sK64(U_318,U_317,U_316),powerset(U_318)) ) )
& ( ! [U_314] :
( ( ( in(U_314,U_316)
| ~ in(subset_complement(U_318,U_314),U_317) )
& ( in(subset_complement(U_318,U_314),U_317)
| ~ in(U_314,U_316) ) )
| ~ element(U_314,powerset(U_318)) )
| U_316 != complements_of_subsets(U_318,U_317) ) )
| ~ element(U_316,powerset(powerset(U_318))) )
| ~ element(U_317,powerset(powerset(U_318))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_315,sK64(U_318,U_317,U_316))],[f_34_2]) ).
fof(f_34_4,plain,
( ! [U_318,U_316,U_317] :
( ~ in(sK64(U_318,U_317,U_316),U_316)
| ~ sP76(U_318,U_316,U_317) )
& ! [U_318,U_316,U_317] :
( in(subset_complement(U_318,sK64(U_318,U_317,U_316)),U_317)
| ~ sP76(U_318,U_316,U_317) )
& ! [U_318,U_316,U_317] :
( ~ in(subset_complement(U_318,sK64(U_318,U_317,U_316)),U_317)
| ~ sP75(U_318,U_316,U_317) )
& ! [U_318,U_316,U_317] :
( in(sK64(U_318,U_317,U_316),U_316)
| ~ sP75(U_318,U_316,U_317) )
& ! [U_318,U_316,U_317] :
( sP76(U_318,U_316,U_317)
| sP75(U_318,U_316,U_317)
| ~ sP77(U_318,U_316,U_317) )
& ! [U_318,U_316,U_317] :
( element(sK64(U_318,U_317,U_316),powerset(U_318))
| ~ sP77(U_318,U_316,U_317) )
& ! [U_318,U_316,U_317,U_314] :
( in(U_314,U_316)
| ~ in(subset_complement(U_318,U_314),U_317)
| ~ sP74(U_318,U_316,U_317,U_314) )
& ! [U_318,U_316,U_317,U_314] :
( in(subset_complement(U_318,U_314),U_317)
| ~ in(U_314,U_316)
| ~ sP74(U_318,U_316,U_317,U_314) )
& ! [U_318,U_316,U_317,U_314] :
( U_316 = complements_of_subsets(U_318,U_317)
| sP77(U_318,U_316,U_317)
| ~ sP78(U_318,U_316,U_317,U_314) )
& ! [U_318,U_316,U_317,U_314] :
( sP74(U_318,U_316,U_317,U_314)
| ~ element(U_314,powerset(U_318))
| U_316 != complements_of_subsets(U_318,U_317)
| ~ sP78(U_318,U_316,U_317,U_314) )
& ! [U_318,U_316,U_317,U_314] :
( sP78(U_318,U_316,U_317,U_314)
| ~ element(U_316,powerset(powerset(U_318)))
| ~ element(U_317,powerset(powerset(U_318))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP74,sP75,sP76,sP77,sP78])],[f_34_3]) ).
cnf(f_34_5,plain,
( sP78(U_318,U_316,U_317,U_314)
| ~ element(U_316,powerset(powerset(U_318)))
| ~ element(U_317,powerset(powerset(U_318))) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_6,plain,
( sP74(U_318,U_316,U_317,U_314)
| ~ element(U_314,powerset(U_318))
| U_316 != complements_of_subsets(U_318,U_317)
| ~ sP78(U_318,U_316,U_317,U_314) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_7,plain,
( U_316 = complements_of_subsets(U_318,U_317)
| sP77(U_318,U_316,U_317)
| ~ sP78(U_318,U_316,U_317,U_314) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_8,plain,
( in(subset_complement(U_318,U_314),U_317)
| ~ in(U_314,U_316)
| ~ sP74(U_318,U_316,U_317,U_314) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_9,plain,
( in(U_314,U_316)
| ~ in(subset_complement(U_318,U_314),U_317)
| ~ sP74(U_318,U_316,U_317,U_314) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_10,plain,
( element(sK64(U_318,U_317,U_316),powerset(U_318))
| ~ sP77(U_318,U_316,U_317) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_11,plain,
( sP76(U_318,U_316,U_317)
| sP75(U_318,U_316,U_317)
| ~ sP77(U_318,U_316,U_317) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_12,plain,
( in(sK64(U_318,U_317,U_316),U_316)
| ~ sP75(U_318,U_316,U_317) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_13,plain,
( ~ in(subset_complement(U_318,sK64(U_318,U_317,U_316)),U_317)
| ~ sP75(U_318,U_316,U_317) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_14,plain,
( in(subset_complement(U_318,sK64(U_318,U_317,U_316)),U_317)
| ~ sP76(U_318,U_316,U_317) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_15,plain,
( ~ in(sK64(U_318,U_317,U_316),U_316)
| ~ sP76(U_318,U_316,U_317) ),
inference(clausify,[status(thm)],[f_34_4]) ).
fof(f_35_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_35_2,plain,
! [U_320,U_319] :
( ( proper_subset(U_320,U_319)
| U_320 = U_319
| ~ subset(U_320,U_319) )
& ( ( U_320 != U_319
& subset(U_320,U_319) )
| ~ proper_subset(U_320,U_319) ) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( ! [U_324,U_322] :
( proper_subset(U_324,U_322)
| U_324 = U_322
| ~ subset(U_324,U_322) )
& ! [U_323,U_321] :
( ( U_323 != U_321
& subset(U_323,U_321) )
| ~ proper_subset(U_323,U_321) ) ),
inference(miniscope,[status(thm)],[f_35_2]) ).
fof(f_35_4,plain,
( ! [U_323,U_321] :
( U_323 != U_321
| ~ sP79(U_323,U_321) )
& ! [U_323,U_321] :
( subset(U_323,U_321)
| ~ sP79(U_323,U_321) )
& ! [U_322,U_324] :
( proper_subset(U_324,U_322)
| U_324 = U_322
| ~ subset(U_324,U_322) )
& ! [U_323,U_321] :
( sP79(U_323,U_321)
| ~ proper_subset(U_323,U_321) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP79])],[f_35_3]) ).
cnf(f_35_5,plain,
( sP79(U_323,U_321)
| ~ proper_subset(U_323,U_321) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_6,plain,
( proper_subset(U_324,U_322)
| U_324 = U_322
| ~ subset(U_324,U_322) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_7,plain,
( subset(U_323,U_321)
| ~ sP79(U_323,U_321) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_8,plain,
( U_323 != U_321
| ~ sP79(U_323,U_321) ),
inference(clausify,[status(thm)],[f_35_4]) ).
fof(f_36_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
fof(f_36_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_36_1]) ).
cnf(f_36_3,plain,
$true,
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_setfam_1]) ).
fof(f_37_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_37_1]) ).
cnf(f_37_3,plain,
$true,
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
fof(f_38_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_38_1]) ).
cnf(f_38_3,plain,
$true,
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
fof(f_39_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_39_1]) ).
cnf(f_39_3,plain,
$true,
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
fof(f_40_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_40_1]) ).
cnf(f_40_3,plain,
$true,
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_relat_1]) ).
fof(f_41_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_41_1]) ).
cnf(f_41_3,plain,
$true,
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_1,plain,
! [A] : element(cast_to_subset(A),powerset(A)),
inference(fof_nnf,[status(thm)],[dt_k2_subset_1]) ).
fof(f_42_2,plain,
! [U_325] : element(cast_to_subset(U_325),powerset(U_325)),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_325] : element(cast_to_subset(U_325),powerset(U_325)),
inference(definitional_conversion,[status(esa)],[f_42_2]) ).
cnf(f_42_4,plain,
element(cast_to_subset(U_325),powerset(U_325)),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
fof(f_43_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_43_1]) ).
cnf(f_43_3,plain,
$true,
inference(clausify,[status(thm)],[f_43_2]) ).
fof(f_44_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
fof(f_44_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_44_1]) ).
cnf(f_44_3,plain,
$true,
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
fof(f_45_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_45_1]) ).
cnf(f_45_3,plain,
$true,
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_relat_1]) ).
fof(f_46_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_46_1]) ).
cnf(f_46_3,plain,
$true,
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_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_47_2,plain,
! [U_327,U_326] :
( element(subset_complement(U_327,U_326),powerset(U_327))
| ~ element(U_326,powerset(U_327)) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_327,U_326] :
( element(subset_complement(U_327,U_326),powerset(U_327))
| ~ element(U_326,powerset(U_327)) ),
inference(definitional_conversion,[status(esa)],[f_47_2]) ).
cnf(f_47_4,plain,
( element(subset_complement(U_327,U_326),powerset(U_327))
| ~ element(U_326,powerset(U_327)) ),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_tarski]) ).
fof(f_48_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_48_1]) ).
cnf(f_48_3,plain,
$true,
inference(clausify,[status(thm)],[f_48_2]) ).
fof(f_49_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
fof(f_49_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_49_1]) ).
cnf(f_49_3,plain,
$true,
inference(clausify,[status(thm)],[f_49_2]) ).
fof(f_50_1,plain,
! [A] :
( relation(relation_inverse(A))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k4_relat_1]) ).
fof(f_50_2,plain,
! [U_328] :
( relation(relation_inverse(U_328))
| ~ relation(U_328) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_328] :
( relation(relation_inverse(U_328))
| ~ relation(U_328) ),
inference(definitional_conversion,[status(esa)],[f_50_2]) ).
cnf(f_50_4,plain,
( relation(relation_inverse(U_328))
| ~ relation(U_328) ),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
fof(f_51_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_51_1]) ).
cnf(f_51_3,plain,
$true,
inference(clausify,[status(thm)],[f_51_2]) ).
fof(f_52_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
fof(f_52_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_52_1]) ).
cnf(f_52_3,plain,
$true,
inference(clausify,[status(thm)],[f_52_2]) ).
fof(f_53_1,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_relat_1]) ).
fof(f_53_2,plain,
! [U_330,U_329] :
( relation(relation_composition(U_330,U_329))
| ~ relation(U_329)
| ~ relation(U_330) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
! [U_330,U_329] :
( relation(relation_composition(U_330,U_329))
| ~ relation(U_329)
| ~ relation(U_330) ),
inference(definitional_conversion,[status(esa)],[f_53_2]) ).
cnf(f_53_4,plain,
( relation(relation_composition(U_330,U_329))
| ~ relation(U_329)
| ~ relation(U_330) ),
inference(clausify,[status(thm)],[f_53_3]) ).
fof(f_54_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_54_2,plain,
! [U_332,U_331] :
( element(union_of_subsets(U_332,U_331),powerset(U_332))
| ~ element(U_331,powerset(powerset(U_332))) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_332,U_331] :
( element(union_of_subsets(U_332,U_331),powerset(U_332))
| ~ element(U_331,powerset(powerset(U_332))) ),
inference(definitional_conversion,[status(esa)],[f_54_2]) ).
cnf(f_54_4,plain,
( element(union_of_subsets(U_332,U_331),powerset(U_332))
| ~ element(U_331,powerset(powerset(U_332))) ),
inference(clausify,[status(thm)],[f_54_3]) ).
fof(f_55_1,plain,
! [A] : relation(identity_relation(A)),
inference(fof_nnf,[status(thm)],[dt_k6_relat_1]) ).
fof(f_55_2,plain,
! [U_333] : relation(identity_relation(U_333)),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
! [U_333] : relation(identity_relation(U_333)),
inference(definitional_conversion,[status(esa)],[f_55_2]) ).
cnf(f_55_4,plain,
relation(identity_relation(U_333)),
inference(clausify,[status(thm)],[f_55_3]) ).
fof(f_56_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_56_2,plain,
! [U_335,U_334] :
( element(meet_of_subsets(U_335,U_334),powerset(U_335))
| ~ element(U_334,powerset(powerset(U_335))) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
! [U_334,U_335] :
( element(meet_of_subsets(U_335,U_334),powerset(U_335))
| ~ element(U_334,powerset(powerset(U_335))) ),
inference(definitional_conversion,[status(esa)],[f_56_2]) ).
cnf(f_56_4,plain,
( element(meet_of_subsets(U_335,U_334),powerset(U_335))
| ~ element(U_334,powerset(powerset(U_335))) ),
inference(clausify,[status(thm)],[f_56_3]) ).
fof(f_57_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_57_2,plain,
! [U_338,U_337,U_336] :
( element(subset_difference(U_338,U_337,U_336),powerset(U_338))
| ~ element(U_336,powerset(U_338))
| ~ element(U_337,powerset(U_338)) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
! [U_337,U_336,U_338] :
( element(subset_difference(U_338,U_337,U_336),powerset(U_338))
| ~ element(U_336,powerset(U_338))
| ~ element(U_337,powerset(U_338)) ),
inference(definitional_conversion,[status(esa)],[f_57_2]) ).
cnf(f_57_4,plain,
( element(subset_difference(U_338,U_337,U_336),powerset(U_338))
| ~ element(U_336,powerset(U_338))
| ~ element(U_337,powerset(U_338)) ),
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_1,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k7_relat_1]) ).
fof(f_58_2,plain,
! [U_340,U_339] :
( relation(relation_dom_restriction(U_340,U_339))
| ~ relation(U_340) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
! [U_340] :
( ! [U_339] : relation(relation_dom_restriction(U_340,U_339))
| ~ relation(U_340) ),
inference(miniscope,[status(thm)],[f_58_2]) ).
fof(f_58_4,plain,
! [U_340,U_339] :
( relation(relation_dom_restriction(U_340,U_339))
| ~ relation(U_340) ),
inference(definitional_conversion,[status(esa)],[f_58_3]) ).
cnf(f_58_5,plain,
( relation(relation_dom_restriction(U_340,U_339))
| ~ relation(U_340) ),
inference(clausify,[status(thm)],[f_58_4]) ).
fof(f_59_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_59_2,plain,
! [U_342,U_341] :
( element(complements_of_subsets(U_342,U_341),powerset(powerset(U_342)))
| ~ element(U_341,powerset(powerset(U_342))) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
! [U_341,U_342] :
( element(complements_of_subsets(U_342,U_341),powerset(powerset(U_342)))
| ~ element(U_341,powerset(powerset(U_342))) ),
inference(definitional_conversion,[status(esa)],[f_59_2]) ).
cnf(f_59_4,plain,
( element(complements_of_subsets(U_342,U_341),powerset(powerset(U_342)))
| ~ element(U_341,powerset(powerset(U_342))) ),
inference(clausify,[status(thm)],[f_59_3]) ).
fof(f_60_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
fof(f_60_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_60_1]) ).
cnf(f_60_3,plain,
$true,
inference(clausify,[status(thm)],[f_60_2]) ).
fof(f_61_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_61_2,plain,
! [U_344] :
? [U_343] : element(U_343,U_344),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
! [U_344] : element(sK65(U_344),U_344),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_343,sK65(U_344))],[f_61_2]) ).
fof(f_61_4,plain,
! [U_344] : element(sK65(U_344),U_344),
inference(definitional_conversion,[status(esa)],[f_61_3]) ).
cnf(f_61_5,plain,
element(sK65(U_344),U_344),
inference(clausify,[status(thm)],[f_61_4]) ).
fof(f_62_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_62_2,plain,
! [U_346,U_345] :
( ( relation(relation_composition(U_345,U_346))
& empty(relation_composition(U_345,U_346)) )
| ~ relation(U_345)
| ~ empty(U_346) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
( ! [U_345,U_346] :
( relation(relation_composition(U_345,U_346))
| ~ sP80(U_345,U_346) )
& ! [U_345,U_346] :
( empty(relation_composition(U_345,U_346))
| ~ sP80(U_345,U_346) )
& ! [U_345,U_346] :
( sP80(U_345,U_346)
| ~ relation(U_345)
| ~ empty(U_346) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP80])],[f_62_2]) ).
cnf(f_62_4,plain,
( sP80(U_345,U_346)
| ~ relation(U_345)
| ~ empty(U_346) ),
inference(clausify,[status(thm)],[f_62_3]) ).
cnf(f_62_5,plain,
( empty(relation_composition(U_345,U_346))
| ~ sP80(U_345,U_346) ),
inference(clausify,[status(thm)],[f_62_3]) ).
cnf(f_62_6,plain,
( relation(relation_composition(U_345,U_346))
| ~ sP80(U_345,U_346) ),
inference(clausify,[status(thm)],[f_62_3]) ).
fof(f_63_1,plain,
! [A,B] :
( relation(set_intersection2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc1_relat_1]) ).
fof(f_63_2,plain,
! [U_348,U_347] :
( relation(set_intersection2(U_348,U_347))
| ~ relation(U_347)
| ~ relation(U_348) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
! [U_348,U_347] :
( relation(set_intersection2(U_348,U_347))
| ~ relation(U_347)
| ~ relation(U_348) ),
inference(definitional_conversion,[status(esa)],[f_63_2]) ).
cnf(f_63_4,plain,
( relation(set_intersection2(U_348,U_347))
| ~ relation(U_347)
| ~ relation(U_348) ),
inference(clausify,[status(thm)],[f_63_3]) ).
fof(f_64_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_64_2,plain,
! [U_349] : ~ empty(powerset(U_349)),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
! [U_349] : ~ empty(powerset(U_349)),
inference(definitional_conversion,[status(esa)],[f_64_2]) ).
cnf(f_64_4,plain,
~ empty(powerset(U_349)),
inference(clausify,[status(thm)],[f_64_3]) ).
fof(f_65_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_65_2,plain,
empty(empty_set),
inference(definitional_conversion,[status(esa)],[f_65_1]) ).
cnf(f_65_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_65_2]) ).
fof(f_66_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_66_2,plain,
! [U_351,U_350] : ~ empty(ordered_pair(U_351,U_350)),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
! [U_351,U_350] : ~ empty(ordered_pair(U_351,U_350)),
inference(definitional_conversion,[status(esa)],[f_66_2]) ).
cnf(f_66_4,plain,
~ empty(ordered_pair(U_351,U_350)),
inference(clausify,[status(thm)],[f_66_3]) ).
fof(f_67_1,plain,
! [A,B] :
( relation(set_union2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc2_relat_1]) ).
fof(f_67_2,plain,
! [U_353,U_352] :
( relation(set_union2(U_353,U_352))
| ~ relation(U_352)
| ~ relation(U_353) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
! [U_352,U_353] :
( relation(set_union2(U_353,U_352))
| ~ relation(U_352)
| ~ relation(U_353) ),
inference(definitional_conversion,[status(esa)],[f_67_2]) ).
cnf(f_67_4,plain,
( relation(set_union2(U_353,U_352))
| ~ relation(U_352)
| ~ relation(U_353) ),
inference(clausify,[status(thm)],[f_67_3]) ).
fof(f_68_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_68_2,plain,
! [U_354] : ~ empty(singleton(U_354)),
inference(variable_rename,[status(thm)],[f_68_1]) ).
fof(f_68_3,plain,
! [U_354] : ~ empty(singleton(U_354)),
inference(definitional_conversion,[status(esa)],[f_68_2]) ).
cnf(f_68_4,plain,
~ empty(singleton(U_354)),
inference(clausify,[status(thm)],[f_68_3]) ).
fof(f_69_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_69_2,plain,
! [U_356,U_355] :
( ~ empty(set_union2(U_356,U_355))
| empty(U_356) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
fof(f_69_3,plain,
! [U_356] :
( ! [U_355] : ~ empty(set_union2(U_356,U_355))
| empty(U_356) ),
inference(miniscope,[status(thm)],[f_69_2]) ).
fof(f_69_4,plain,
! [U_355,U_356] :
( ~ empty(set_union2(U_356,U_355))
| empty(U_356) ),
inference(definitional_conversion,[status(esa)],[f_69_3]) ).
cnf(f_69_5,plain,
( ~ empty(set_union2(U_356,U_355))
| empty(U_356) ),
inference(clausify,[status(thm)],[f_69_4]) ).
fof(f_70_1,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_70_2,plain,
! [U_358,U_357] : ~ empty(unordered_pair(U_358,U_357)),
inference(variable_rename,[status(thm)],[f_70_1]) ).
fof(f_70_3,plain,
! [U_357,U_358] : ~ empty(unordered_pair(U_358,U_357)),
inference(definitional_conversion,[status(esa)],[f_70_2]) ).
cnf(f_70_4,plain,
~ empty(unordered_pair(U_358,U_357)),
inference(clausify,[status(thm)],[f_70_3]) ).
fof(f_71_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_71_2,plain,
! [U_360,U_359] :
( ~ empty(set_union2(U_359,U_360))
| empty(U_360) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
fof(f_71_3,plain,
! [U_360] :
( ! [U_359] : ~ empty(set_union2(U_359,U_360))
| empty(U_360) ),
inference(miniscope,[status(thm)],[f_71_2]) ).
fof(f_71_4,plain,
! [U_359,U_360] :
( ~ empty(set_union2(U_359,U_360))
| empty(U_360) ),
inference(definitional_conversion,[status(esa)],[f_71_3]) ).
cnf(f_71_5,plain,
( ~ empty(set_union2(U_359,U_360))
| empty(U_360) ),
inference(clausify,[status(thm)],[f_71_4]) ).
fof(f_72_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
fof(f_72_2,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_72_1]) ).
cnf(f_72_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_72_2]) ).
cnf(f_72_4,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_72_2]) ).
fof(f_73_1,plain,
! [A,B] :
( ~ empty(cartesian_product2(A,B))
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc4_subset_1]) ).
fof(f_73_2,plain,
! [U_362,U_361] :
( ~ empty(cartesian_product2(U_362,U_361))
| empty(U_361)
| empty(U_362) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
fof(f_73_3,plain,
! [U_361,U_362] :
( ~ empty(cartesian_product2(U_362,U_361))
| empty(U_361)
| empty(U_362) ),
inference(definitional_conversion,[status(esa)],[f_73_2]) ).
cnf(f_73_4,plain,
( ~ empty(cartesian_product2(U_362,U_361))
| empty(U_361)
| empty(U_362) ),
inference(clausify,[status(thm)],[f_73_3]) ).
fof(f_74_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_74_2,plain,
! [U_363] :
( ~ empty(relation_dom(U_363))
| ~ relation(U_363)
| empty(U_363) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
fof(f_74_3,plain,
! [U_363] :
( ~ empty(relation_dom(U_363))
| ~ relation(U_363)
| empty(U_363) ),
inference(definitional_conversion,[status(esa)],[f_74_2]) ).
cnf(f_74_4,plain,
( ~ empty(relation_dom(U_363))
| ~ relation(U_363)
| empty(U_363) ),
inference(clausify,[status(thm)],[f_74_3]) ).
fof(f_75_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_75_2,plain,
! [U_364] :
( ~ empty(relation_rng(U_364))
| ~ relation(U_364)
| empty(U_364) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
fof(f_75_3,plain,
! [U_364] :
( ~ empty(relation_rng(U_364))
| ~ relation(U_364)
| empty(U_364) ),
inference(definitional_conversion,[status(esa)],[f_75_2]) ).
cnf(f_75_4,plain,
( ~ empty(relation_rng(U_364))
| ~ relation(U_364)
| empty(U_364) ),
inference(clausify,[status(thm)],[f_75_3]) ).
fof(f_76_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_76_2,plain,
! [U_365] :
( ( relation(relation_dom(U_365))
& empty(relation_dom(U_365)) )
| ~ empty(U_365) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
fof(f_76_3,plain,
( ! [U_365] :
( relation(relation_dom(U_365))
| ~ sP81(U_365) )
& ! [U_365] :
( empty(relation_dom(U_365))
| ~ sP81(U_365) )
& ! [U_365] :
( sP81(U_365)
| ~ empty(U_365) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP81])],[f_76_2]) ).
cnf(f_76_4,plain,
( sP81(U_365)
| ~ empty(U_365) ),
inference(clausify,[status(thm)],[f_76_3]) ).
cnf(f_76_5,plain,
( empty(relation_dom(U_365))
| ~ sP81(U_365) ),
inference(clausify,[status(thm)],[f_76_3]) ).
cnf(f_76_6,plain,
( relation(relation_dom(U_365))
| ~ sP81(U_365) ),
inference(clausify,[status(thm)],[f_76_3]) ).
fof(f_77_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_77_2,plain,
! [U_366] :
( ( relation(relation_rng(U_366))
& empty(relation_rng(U_366)) )
| ~ empty(U_366) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
fof(f_77_3,plain,
( ! [U_366] :
( relation(relation_rng(U_366))
| ~ sP82(U_366) )
& ! [U_366] :
( empty(relation_rng(U_366))
| ~ sP82(U_366) )
& ! [U_366] :
( sP82(U_366)
| ~ empty(U_366) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP82])],[f_77_2]) ).
cnf(f_77_4,plain,
( sP82(U_366)
| ~ empty(U_366) ),
inference(clausify,[status(thm)],[f_77_3]) ).
cnf(f_77_5,plain,
( empty(relation_rng(U_366))
| ~ sP82(U_366) ),
inference(clausify,[status(thm)],[f_77_3]) ).
cnf(f_77_6,plain,
( relation(relation_rng(U_366))
| ~ sP82(U_366) ),
inference(clausify,[status(thm)],[f_77_3]) ).
fof(f_78_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_78_2,plain,
! [U_368,U_367] :
( ( relation(relation_composition(U_368,U_367))
& empty(relation_composition(U_368,U_367)) )
| ~ relation(U_367)
| ~ empty(U_368) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
fof(f_78_3,plain,
( ! [U_368,U_367] :
( relation(relation_composition(U_368,U_367))
| ~ sP83(U_368,U_367) )
& ! [U_368,U_367] :
( empty(relation_composition(U_368,U_367))
| ~ sP83(U_368,U_367) )
& ! [U_368,U_367] :
( sP83(U_368,U_367)
| ~ relation(U_367)
| ~ empty(U_368) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP83])],[f_78_2]) ).
cnf(f_78_4,plain,
( sP83(U_368,U_367)
| ~ relation(U_367)
| ~ empty(U_368) ),
inference(clausify,[status(thm)],[f_78_3]) ).
cnf(f_78_5,plain,
( empty(relation_composition(U_368,U_367))
| ~ sP83(U_368,U_367) ),
inference(clausify,[status(thm)],[f_78_3]) ).
cnf(f_78_6,plain,
( relation(relation_composition(U_368,U_367))
| ~ sP83(U_368,U_367) ),
inference(clausify,[status(thm)],[f_78_3]) ).
fof(f_79_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_79_2,plain,
! [U_370,U_369] : set_union2(U_370,U_370) = U_370,
inference(variable_rename,[status(thm)],[f_79_1]) ).
fof(f_79_3,plain,
! [U_370] : set_union2(U_370,U_370) = U_370,
inference(miniscope,[status(thm)],[f_79_2]) ).
fof(f_79_4,plain,
! [U_370] : set_union2(U_370,U_370) = U_370,
inference(definitional_conversion,[status(esa)],[f_79_3]) ).
cnf(f_79_5,plain,
set_union2(U_370,U_370) = U_370,
inference(clausify,[status(thm)],[f_79_4]) ).
fof(f_80_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_80_2,plain,
! [U_372,U_371] : set_intersection2(U_372,U_372) = U_372,
inference(variable_rename,[status(thm)],[f_80_1]) ).
fof(f_80_3,plain,
! [U_372] : set_intersection2(U_372,U_372) = U_372,
inference(miniscope,[status(thm)],[f_80_2]) ).
fof(f_80_4,plain,
! [U_372] : set_intersection2(U_372,U_372) = U_372,
inference(definitional_conversion,[status(esa)],[f_80_3]) ).
cnf(f_80_5,plain,
set_intersection2(U_372,U_372) = U_372,
inference(clausify,[status(thm)],[f_80_4]) ).
fof(f_81_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_81_2,plain,
! [U_374,U_373] :
( subset_complement(U_374,subset_complement(U_374,U_373)) = U_373
| ~ element(U_373,powerset(U_374)) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
fof(f_81_3,plain,
! [U_373,U_374] :
( subset_complement(U_374,subset_complement(U_374,U_373)) = U_373
| ~ element(U_373,powerset(U_374)) ),
inference(definitional_conversion,[status(esa)],[f_81_2]) ).
cnf(f_81_4,plain,
( subset_complement(U_374,subset_complement(U_374,U_373)) = U_373
| ~ element(U_373,powerset(U_374)) ),
inference(clausify,[status(thm)],[f_81_3]) ).
fof(f_82_1,plain,
! [A] :
( relation_inverse(relation_inverse(A)) = A
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[involutiveness_k4_relat_1]) ).
fof(f_82_2,plain,
! [U_375] :
( relation_inverse(relation_inverse(U_375)) = U_375
| ~ relation(U_375) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
fof(f_82_3,plain,
! [U_375] :
( relation_inverse(relation_inverse(U_375)) = U_375
| ~ relation(U_375) ),
inference(definitional_conversion,[status(esa)],[f_82_2]) ).
cnf(f_82_4,plain,
( relation_inverse(relation_inverse(U_375)) = U_375
| ~ relation(U_375) ),
inference(clausify,[status(thm)],[f_82_3]) ).
fof(f_83_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_83_2,plain,
! [U_377,U_376] :
( complements_of_subsets(U_377,complements_of_subsets(U_377,U_376)) = U_376
| ~ element(U_376,powerset(powerset(U_377))) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
fof(f_83_3,plain,
! [U_376,U_377] :
( complements_of_subsets(U_377,complements_of_subsets(U_377,U_376)) = U_376
| ~ element(U_376,powerset(powerset(U_377))) ),
inference(definitional_conversion,[status(esa)],[f_83_2]) ).
cnf(f_83_4,plain,
( complements_of_subsets(U_377,complements_of_subsets(U_377,U_376)) = U_376
| ~ element(U_376,powerset(powerset(U_377))) ),
inference(clausify,[status(thm)],[f_83_3]) ).
fof(f_84_1,plain,
! [A,B] : ~ proper_subset(A,A),
inference(fof_nnf,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(f_84_2,plain,
! [U_379,U_378] : ~ proper_subset(U_379,U_379),
inference(variable_rename,[status(thm)],[f_84_1]) ).
fof(f_84_3,plain,
! [U_379] : ~ proper_subset(U_379,U_379),
inference(miniscope,[status(thm)],[f_84_2]) ).
fof(f_84_4,plain,
! [U_379] : ~ proper_subset(U_379,U_379),
inference(definitional_conversion,[status(esa)],[f_84_3]) ).
cnf(f_84_5,plain,
~ proper_subset(U_379,U_379),
inference(clausify,[status(thm)],[f_84_4]) ).
fof(f_85_1,plain,
! [A] : singleton(A) != empty_set,
inference(fof_nnf,[status(thm)],[l1_zfmisc_1]) ).
fof(f_85_2,plain,
! [U_380] : singleton(U_380) != empty_set,
inference(variable_rename,[status(thm)],[f_85_1]) ).
fof(f_85_3,plain,
! [U_380] : singleton(U_380) != empty_set,
inference(definitional_conversion,[status(esa)],[f_85_2]) ).
cnf(f_85_4,plain,
singleton(U_380) != empty_set,
inference(clausify,[status(thm)],[f_85_3]) ).
fof(f_86_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l23_zfmisc_1]) ).
fof(f_86_2,plain,
! [U_382,U_381] :
( set_union2(singleton(U_382),U_381) = U_381
| ~ in(U_382,U_381) ),
inference(variable_rename,[status(thm)],[f_86_1]) ).
fof(f_86_3,plain,
! [U_381,U_382] :
( set_union2(singleton(U_382),U_381) = U_381
| ~ in(U_382,U_381) ),
inference(definitional_conversion,[status(esa)],[f_86_2]) ).
cnf(f_86_4,plain,
( set_union2(singleton(U_382),U_381) = U_381
| ~ in(U_382,U_381) ),
inference(clausify,[status(thm)],[f_86_3]) ).
fof(f_87_1,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(fof_nnf,[status(thm)],[l25_zfmisc_1]) ).
fof(f_87_2,plain,
! [U_384,U_383] :
( ~ in(U_384,U_383)
| ~ disjoint(singleton(U_384),U_383) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
fof(f_87_3,plain,
! [U_384,U_383] :
( ~ in(U_384,U_383)
| ~ disjoint(singleton(U_384),U_383) ),
inference(definitional_conversion,[status(esa)],[f_87_2]) ).
cnf(f_87_4,plain,
( ~ in(U_384,U_383)
| ~ disjoint(singleton(U_384),U_383) ),
inference(clausify,[status(thm)],[f_87_3]) ).
fof(f_88_1,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(fof_nnf,[status(thm)],[l28_zfmisc_1]) ).
fof(f_88_2,plain,
! [U_386,U_385] :
( disjoint(singleton(U_386),U_385)
| in(U_386,U_385) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
fof(f_88_3,plain,
! [U_385,U_386] :
( disjoint(singleton(U_386),U_385)
| in(U_386,U_385) ),
inference(definitional_conversion,[status(esa)],[f_88_2]) ).
cnf(f_88_4,plain,
( disjoint(singleton(U_386),U_385)
| in(U_386,U_385) ),
inference(clausify,[status(thm)],[f_88_3]) ).
fof(f_89_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_89_2,plain,
! [U_388,U_387] :
( ( subset(singleton(U_388),U_387)
| ~ in(U_388,U_387) )
& ( in(U_388,U_387)
| ~ subset(singleton(U_388),U_387) ) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
fof(f_89_3,plain,
( ! [U_392,U_390] :
( subset(singleton(U_392),U_390)
| ~ in(U_392,U_390) )
& ! [U_391,U_389] :
( in(U_391,U_389)
| ~ subset(singleton(U_391),U_389) ) ),
inference(miniscope,[status(thm)],[f_89_2]) ).
fof(f_89_4,plain,
( ! [U_390,U_392] :
( subset(singleton(U_392),U_390)
| ~ in(U_392,U_390) )
& ! [U_389,U_391] :
( in(U_391,U_389)
| ~ subset(singleton(U_391),U_389) ) ),
inference(definitional_conversion,[status(esa)],[f_89_3]) ).
cnf(f_89_5,plain,
( in(U_391,U_389)
| ~ subset(singleton(U_391),U_389) ),
inference(clausify,[status(thm)],[f_89_4]) ).
cnf(f_89_6,plain,
( subset(singleton(U_392),U_390)
| ~ in(U_392,U_390) ),
inference(clausify,[status(thm)],[f_89_4]) ).
fof(f_90_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_90_2,plain,
! [U_394,U_393] :
( ( set_difference(U_394,U_393) = empty_set
| ~ subset(U_394,U_393) )
& ( subset(U_394,U_393)
| set_difference(U_394,U_393) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
fof(f_90_3,plain,
( ! [U_398,U_396] :
( set_difference(U_398,U_396) = empty_set
| ~ subset(U_398,U_396) )
& ! [U_397,U_395] :
( subset(U_397,U_395)
| set_difference(U_397,U_395) != empty_set ) ),
inference(miniscope,[status(thm)],[f_90_2]) ).
fof(f_90_4,plain,
( ! [U_396,U_398] :
( set_difference(U_398,U_396) = empty_set
| ~ subset(U_398,U_396) )
& ! [U_395,U_397] :
( subset(U_397,U_395)
| set_difference(U_397,U_395) != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_90_3]) ).
cnf(f_90_5,plain,
( subset(U_397,U_395)
| set_difference(U_397,U_395) != empty_set ),
inference(clausify,[status(thm)],[f_90_4]) ).
cnf(f_90_6,plain,
( set_difference(U_398,U_396) = empty_set
| ~ subset(U_398,U_396) ),
inference(clausify,[status(thm)],[f_90_4]) ).
fof(f_91_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_91_2,plain,
! [U_401,U_400] :
( ! [U_399] :
( in(U_399,U_401)
| ~ in(U_399,U_400) )
| ~ element(U_400,powerset(U_401)) ),
inference(variable_rename,[status(thm)],[f_91_1]) ).
fof(f_91_3,plain,
! [U_401,U_399,U_400] :
( in(U_399,U_401)
| ~ in(U_399,U_400)
| ~ element(U_400,powerset(U_401)) ),
inference(definitional_conversion,[status(esa)],[f_91_2]) ).
cnf(f_91_4,plain,
( in(U_399,U_401)
| ~ in(U_399,U_400)
| ~ element(U_400,powerset(U_401)) ),
inference(clausify,[status(thm)],[f_91_3]) ).
fof(f_92_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_92_2,plain,
! [U_404,U_403,U_402] :
( subset(U_404,set_difference(U_403,singleton(U_402)))
| in(U_402,U_404)
| ~ subset(U_404,U_403) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
fof(f_92_3,plain,
! [U_404,U_403] :
( ! [U_402] :
( subset(U_404,set_difference(U_403,singleton(U_402)))
| in(U_402,U_404) )
| ~ subset(U_404,U_403) ),
inference(miniscope,[status(thm)],[f_92_2]) ).
fof(f_92_4,plain,
! [U_402,U_403,U_404] :
( subset(U_404,set_difference(U_403,singleton(U_402)))
| in(U_402,U_404)
| ~ subset(U_404,U_403) ),
inference(definitional_conversion,[status(esa)],[f_92_3]) ).
cnf(f_92_5,plain,
( subset(U_404,set_difference(U_403,singleton(U_402)))
| in(U_402,U_404)
| ~ subset(U_404,U_403) ),
inference(clausify,[status(thm)],[f_92_4]) ).
fof(f_93_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_93_2,plain,
! [U_406,U_405] :
( ( subset(U_406,singleton(U_405))
| ( U_406 != singleton(U_405)
& U_406 != empty_set ) )
& ( U_406 = singleton(U_405)
| U_406 = empty_set
| ~ subset(U_406,singleton(U_405)) ) ),
inference(variable_rename,[status(thm)],[f_93_1]) ).
fof(f_93_3,plain,
( ! [U_410,U_408] :
( subset(U_410,singleton(U_408))
| ( U_410 != singleton(U_408)
& U_410 != empty_set ) )
& ! [U_409,U_407] :
( U_409 = singleton(U_407)
| U_409 = empty_set
| ~ subset(U_409,singleton(U_407)) ) ),
inference(miniscope,[status(thm)],[f_93_2]) ).
fof(f_93_4,plain,
( ! [U_408,U_410] :
( U_410 != singleton(U_408)
| ~ sP84(U_408,U_410) )
& ! [U_408,U_410] :
( U_410 != empty_set
| ~ sP84(U_408,U_410) )
& ! [U_408,U_410] :
( subset(U_410,singleton(U_408))
| sP84(U_408,U_410) )
& ! [U_409,U_407] :
( U_409 = singleton(U_407)
| U_409 = empty_set
| ~ subset(U_409,singleton(U_407)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP84])],[f_93_3]) ).
cnf(f_93_5,plain,
( U_409 = singleton(U_407)
| U_409 = empty_set
| ~ subset(U_409,singleton(U_407)) ),
inference(clausify,[status(thm)],[f_93_4]) ).
cnf(f_93_6,plain,
( subset(U_410,singleton(U_408))
| sP84(U_408,U_410) ),
inference(clausify,[status(thm)],[f_93_4]) ).
cnf(f_93_7,plain,
( U_410 != empty_set
| ~ sP84(U_408,U_410) ),
inference(clausify,[status(thm)],[f_93_4]) ).
cnf(f_93_8,plain,
( U_410 != singleton(U_408)
| ~ sP84(U_408,U_410) ),
inference(clausify,[status(thm)],[f_93_4]) ).
fof(f_94_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l50_zfmisc_1]) ).
fof(f_94_2,plain,
! [U_412,U_411] :
( subset(U_412,union(U_411))
| ~ in(U_412,U_411) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
fof(f_94_3,plain,
! [U_411,U_412] :
( subset(U_412,union(U_411))
| ~ in(U_412,U_411) ),
inference(definitional_conversion,[status(esa)],[f_94_2]) ).
cnf(f_94_4,plain,
( subset(U_412,union(U_411))
| ~ in(U_412,U_411) ),
inference(clausify,[status(thm)],[f_94_3]) ).
fof(f_95_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_95_2,plain,
! [U_416,U_415,U_414,U_413] :
( ( in(ordered_pair(U_416,U_415),cartesian_product2(U_414,U_413))
| ~ in(U_415,U_413)
| ~ in(U_416,U_414) )
& ( ( in(U_415,U_413)
& in(U_416,U_414) )
| ~ in(ordered_pair(U_416,U_415),cartesian_product2(U_414,U_413)) ) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
fof(f_95_3,plain,
( ! [U_424,U_422,U_420,U_418] :
( in(ordered_pair(U_424,U_422),cartesian_product2(U_420,U_418))
| ~ in(U_422,U_418)
| ~ in(U_424,U_420) )
& ! [U_423,U_421,U_419,U_417] :
( ( in(U_421,U_417)
& in(U_423,U_419) )
| ~ in(ordered_pair(U_423,U_421),cartesian_product2(U_419,U_417)) ) ),
inference(miniscope,[status(thm)],[f_95_2]) ).
fof(f_95_4,plain,
( ! [U_419,U_423,U_417,U_421] :
( in(U_421,U_417)
| ~ sP85(U_419,U_423,U_417,U_421) )
& ! [U_419,U_423,U_417,U_421] :
( in(U_423,U_419)
| ~ sP85(U_419,U_423,U_417,U_421) )
& ! [U_422,U_418,U_420,U_424] :
( in(ordered_pair(U_424,U_422),cartesian_product2(U_420,U_418))
| ~ in(U_422,U_418)
| ~ in(U_424,U_420) )
& ! [U_419,U_423,U_417,U_421] :
( sP85(U_419,U_423,U_417,U_421)
| ~ in(ordered_pair(U_423,U_421),cartesian_product2(U_419,U_417)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP85])],[f_95_3]) ).
cnf(f_95_5,plain,
( sP85(U_419,U_423,U_417,U_421)
| ~ in(ordered_pair(U_423,U_421),cartesian_product2(U_419,U_417)) ),
inference(clausify,[status(thm)],[f_95_4]) ).
cnf(f_95_6,plain,
( in(ordered_pair(U_424,U_422),cartesian_product2(U_420,U_418))
| ~ in(U_422,U_418)
| ~ in(U_424,U_420) ),
inference(clausify,[status(thm)],[f_95_4]) ).
cnf(f_95_7,plain,
( in(U_423,U_419)
| ~ sP85(U_419,U_423,U_417,U_421) ),
inference(clausify,[status(thm)],[f_95_4]) ).
cnf(f_95_8,plain,
( in(U_421,U_417)
| ~ sP85(U_419,U_423,U_417,U_421) ),
inference(clausify,[status(thm)],[f_95_4]) ).
fof(f_96_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_96_2,plain,
! [U_427,U_426] :
( element(U_427,powerset(U_426))
| ? [U_425] :
( ~ in(U_425,U_426)
& in(U_425,U_427) ) ),
inference(variable_rename,[status(thm)],[f_96_1]) ).
fof(f_96_3,plain,
! [U_427,U_426] :
( element(U_427,powerset(U_426))
| ( ~ in(sK66(U_427,U_426),U_426)
& in(sK66(U_427,U_426),U_427) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_425,sK66(U_427,U_426))],[f_96_2]) ).
fof(f_96_4,plain,
( ! [U_427,U_426] :
( ~ in(sK66(U_427,U_426),U_426)
| ~ sP86(U_427,U_426) )
& ! [U_427,U_426] :
( in(sK66(U_427,U_426),U_427)
| ~ sP86(U_427,U_426) )
& ! [U_427,U_426] :
( element(U_427,powerset(U_426))
| sP86(U_427,U_426) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP86])],[f_96_3]) ).
cnf(f_96_5,plain,
( element(U_427,powerset(U_426))
| sP86(U_427,U_426) ),
inference(clausify,[status(thm)],[f_96_4]) ).
cnf(f_96_6,plain,
( in(sK66(U_427,U_426),U_427)
| ~ sP86(U_427,U_426) ),
inference(clausify,[status(thm)],[f_96_4]) ).
cnf(f_96_7,plain,
( ~ in(sK66(U_427,U_426),U_426)
| ~ sP86(U_427,U_426) ),
inference(clausify,[status(thm)],[f_96_4]) ).
fof(f_97_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_97_2,plain,
? [U_428] :
( relation(U_428)
& empty(U_428) ),
inference(variable_rename,[status(thm)],[f_97_1]) ).
fof(f_97_3,plain,
( relation(sK67)
& empty(sK67) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_428,sK67)],[f_97_2]) ).
fof(f_97_4,plain,
( relation(sK67)
& empty(sK67) ),
inference(definitional_conversion,[status(esa)],[f_97_3]) ).
cnf(f_97_5,plain,
empty(sK67),
inference(clausify,[status(thm)],[f_97_4]) ).
cnf(f_97_6,plain,
relation(sK67),
inference(clausify,[status(thm)],[f_97_4]) ).
fof(f_98_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_98_2,plain,
! [U_430] :
( ? [U_429] :
( ~ empty(U_429)
& element(U_429,powerset(U_430)) )
| empty(U_430) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
fof(f_98_3,plain,
! [U_430] :
( ( ~ empty(sK68(U_430))
& element(sK68(U_430),powerset(U_430)) )
| empty(U_430) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_429,sK68(U_430))],[f_98_2]) ).
fof(f_98_4,plain,
( ! [U_430] :
( ~ empty(sK68(U_430))
| ~ sP87(U_430) )
& ! [U_430] :
( element(sK68(U_430),powerset(U_430))
| ~ sP87(U_430) )
& ! [U_430] :
( sP87(U_430)
| empty(U_430) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP87])],[f_98_3]) ).
cnf(f_98_5,plain,
( sP87(U_430)
| empty(U_430) ),
inference(clausify,[status(thm)],[f_98_4]) ).
cnf(f_98_6,plain,
( element(sK68(U_430),powerset(U_430))
| ~ sP87(U_430) ),
inference(clausify,[status(thm)],[f_98_4]) ).
cnf(f_98_7,plain,
( ~ empty(sK68(U_430))
| ~ sP87(U_430) ),
inference(clausify,[status(thm)],[f_98_4]) ).
fof(f_99_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_99_2,plain,
? [U_431] : empty(U_431),
inference(variable_rename,[status(thm)],[f_99_1]) ).
fof(f_99_3,plain,
empty(sK69),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_431,sK69)],[f_99_2]) ).
fof(f_99_4,plain,
empty(sK69),
inference(definitional_conversion,[status(esa)],[f_99_3]) ).
cnf(f_99_5,plain,
empty(sK69),
inference(clausify,[status(thm)],[f_99_4]) ).
fof(f_100_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_100_2,plain,
? [U_432] :
( relation(U_432)
& ~ empty(U_432) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
fof(f_100_3,plain,
( relation(sK70)
& ~ empty(sK70) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_432,sK70)],[f_100_2]) ).
fof(f_100_4,plain,
( relation(sK70)
& ~ empty(sK70) ),
inference(definitional_conversion,[status(esa)],[f_100_3]) ).
cnf(f_100_5,plain,
~ empty(sK70),
inference(clausify,[status(thm)],[f_100_4]) ).
cnf(f_100_6,plain,
relation(sK70),
inference(clausify,[status(thm)],[f_100_4]) ).
fof(f_101_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_101_2,plain,
! [U_434] :
? [U_433] :
( empty(U_433)
& element(U_433,powerset(U_434)) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
fof(f_101_3,plain,
! [U_434] :
( empty(sK71(U_434))
& element(sK71(U_434),powerset(U_434)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_433,sK71(U_434))],[f_101_2]) ).
fof(f_101_4,plain,
( ! [U_434] : empty(sK71(U_434))
& ! [U_434] : element(sK71(U_434),powerset(U_434)) ),
inference(definitional_conversion,[status(esa)],[f_101_3]) ).
cnf(f_101_5,plain,
element(sK71(U_434),powerset(U_434)),
inference(clausify,[status(thm)],[f_101_4]) ).
cnf(f_101_6,plain,
empty(sK71(U_434)),
inference(clausify,[status(thm)],[f_101_4]) ).
fof(f_102_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_102_2,plain,
? [U_435] : ~ empty(U_435),
inference(variable_rename,[status(thm)],[f_102_1]) ).
fof(f_102_3,plain,
~ empty(sK72),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_435,sK72)],[f_102_2]) ).
fof(f_102_4,plain,
~ empty(sK72),
inference(definitional_conversion,[status(esa)],[f_102_3]) ).
cnf(f_102_5,plain,
~ empty(sK72),
inference(clausify,[status(thm)],[f_102_4]) ).
fof(f_103_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_103_2,plain,
! [U_437,U_436] :
( union_of_subsets(U_437,U_436) = union(U_436)
| ~ element(U_436,powerset(powerset(U_437))) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
fof(f_103_3,plain,
! [U_436,U_437] :
( union_of_subsets(U_437,U_436) = union(U_436)
| ~ element(U_436,powerset(powerset(U_437))) ),
inference(definitional_conversion,[status(esa)],[f_103_2]) ).
cnf(f_103_4,plain,
( union_of_subsets(U_437,U_436) = union(U_436)
| ~ element(U_436,powerset(powerset(U_437))) ),
inference(clausify,[status(thm)],[f_103_3]) ).
fof(f_104_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_104_2,plain,
! [U_439,U_438] :
( meet_of_subsets(U_439,U_438) = set_meet(U_438)
| ~ element(U_438,powerset(powerset(U_439))) ),
inference(variable_rename,[status(thm)],[f_104_1]) ).
fof(f_104_3,plain,
! [U_438,U_439] :
( meet_of_subsets(U_439,U_438) = set_meet(U_438)
| ~ element(U_438,powerset(powerset(U_439))) ),
inference(definitional_conversion,[status(esa)],[f_104_2]) ).
cnf(f_104_4,plain,
( meet_of_subsets(U_439,U_438) = set_meet(U_438)
| ~ element(U_438,powerset(powerset(U_439))) ),
inference(clausify,[status(thm)],[f_104_3]) ).
fof(f_105_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_105_2,plain,
! [U_442,U_441,U_440] :
( subset_difference(U_442,U_441,U_440) = set_difference(U_441,U_440)
| ~ element(U_440,powerset(U_442))
| ~ element(U_441,powerset(U_442)) ),
inference(variable_rename,[status(thm)],[f_105_1]) ).
fof(f_105_3,plain,
! [U_440,U_441,U_442] :
( subset_difference(U_442,U_441,U_440) = set_difference(U_441,U_440)
| ~ element(U_440,powerset(U_442))
| ~ element(U_441,powerset(U_442)) ),
inference(definitional_conversion,[status(esa)],[f_105_2]) ).
cnf(f_105_4,plain,
( subset_difference(U_442,U_441,U_440) = set_difference(U_441,U_440)
| ~ element(U_440,powerset(U_442))
| ~ element(U_441,powerset(U_442)) ),
inference(clausify,[status(thm)],[f_105_3]) ).
fof(f_106_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_106_2,plain,
! [U_444,U_443] : subset(U_444,U_444),
inference(variable_rename,[status(thm)],[f_106_1]) ).
fof(f_106_3,plain,
! [U_444] : subset(U_444,U_444),
inference(miniscope,[status(thm)],[f_106_2]) ).
fof(f_106_4,plain,
! [U_444] : subset(U_444,U_444),
inference(definitional_conversion,[status(esa)],[f_106_3]) ).
cnf(f_106_5,plain,
subset(U_444,U_444),
inference(clausify,[status(thm)],[f_106_4]) ).
fof(f_107_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_107_2,plain,
! [U_446,U_445] :
( disjoint(U_445,U_446)
| ~ disjoint(U_446,U_445) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
fof(f_107_3,plain,
! [U_445,U_446] :
( disjoint(U_445,U_446)
| ~ disjoint(U_446,U_445) ),
inference(definitional_conversion,[status(esa)],[f_107_2]) ).
cnf(f_107_4,plain,
( disjoint(U_445,U_446)
| ~ disjoint(U_446,U_445) ),
inference(clausify,[status(thm)],[f_107_3]) ).
fof(f_108_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_108_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_108_1]) ).
fof(f_108_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_108_2]) ).
fof(f_108_4,plain,
( ! [U_451,U_455,U_453,U_457] :
( in(U_455,U_451)
| ~ sP88(U_451,U_455,U_453,U_457) )
& ! [U_451,U_455,U_453,U_457] :
( in(U_457,U_453)
| ~ sP88(U_451,U_455,U_453,U_457) )
& ! [U_452,U_458,U_454,U_456] :
( in(ordered_pair(U_458,U_456),cartesian_product2(U_454,U_452))
| ~ in(U_456,U_452)
| ~ in(U_458,U_454) )
& ! [U_451,U_455,U_453,U_457] :
( sP88(U_451,U_455,U_453,U_457)
| ~ in(ordered_pair(U_457,U_455),cartesian_product2(U_453,U_451)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP88])],[f_108_3]) ).
cnf(f_108_5,plain,
( sP88(U_451,U_455,U_453,U_457)
| ~ in(ordered_pair(U_457,U_455),cartesian_product2(U_453,U_451)) ),
inference(clausify,[status(thm)],[f_108_4]) ).
cnf(f_108_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_108_4]) ).
cnf(f_108_7,plain,
( in(U_457,U_453)
| ~ sP88(U_451,U_455,U_453,U_457) ),
inference(clausify,[status(thm)],[f_108_4]) ).
cnf(f_108_8,plain,
( in(U_455,U_451)
| ~ sP88(U_451,U_455,U_453,U_457) ),
inference(clausify,[status(thm)],[f_108_4]) ).
fof(f_109_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_109_2,plain,
! [U_462,U_461,U_460,U_459] :
( U_462 = U_459
| U_462 = U_460
| unordered_pair(U_462,U_461) != unordered_pair(U_460,U_459) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
fof(f_109_3,plain,
! [U_462,U_461,U_460] :
( ! [U_459] :
( U_462 = U_459
| unordered_pair(U_462,U_461) != unordered_pair(U_460,U_459) )
| U_462 = U_460 ),
inference(miniscope,[status(thm)],[f_109_2]) ).
fof(f_109_4,plain,
! [U_460,U_462,U_461,U_459] :
( U_462 = U_459
| unordered_pair(U_462,U_461) != unordered_pair(U_460,U_459)
| U_462 = U_460 ),
inference(definitional_conversion,[status(esa)],[f_109_3]) ).
cnf(f_109_5,plain,
( U_462 = U_459
| unordered_pair(U_462,U_461) != unordered_pair(U_460,U_459)
| U_462 = U_460 ),
inference(clausify,[status(thm)],[f_109_4]) ).
fof(f_110_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_110_2,plain,
! [U_465,U_464,U_463] :
( ( subset(cartesian_product2(U_463,U_465),cartesian_product2(U_463,U_464))
& subset(cartesian_product2(U_465,U_463),cartesian_product2(U_464,U_463)) )
| ~ subset(U_465,U_464) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
fof(f_110_3,plain,
! [U_465,U_464] :
( ( ! [U_467] : subset(cartesian_product2(U_467,U_465),cartesian_product2(U_467,U_464))
& ! [U_466] : subset(cartesian_product2(U_465,U_466),cartesian_product2(U_464,U_466)) )
| ~ subset(U_465,U_464) ),
inference(miniscope,[status(thm)],[f_110_2]) ).
fof(f_110_4,plain,
( ! [U_464,U_465,U_466,U_467] :
( subset(cartesian_product2(U_467,U_465),cartesian_product2(U_467,U_464))
| ~ sP89(U_464,U_465,U_466,U_467) )
& ! [U_464,U_465,U_466,U_467] :
( subset(cartesian_product2(U_465,U_466),cartesian_product2(U_464,U_466))
| ~ sP89(U_464,U_465,U_466,U_467) )
& ! [U_464,U_465,U_466,U_467] :
( sP89(U_464,U_465,U_466,U_467)
| ~ subset(U_465,U_464) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP89])],[f_110_3]) ).
cnf(f_110_5,plain,
( sP89(U_464,U_465,U_466,U_467)
| ~ subset(U_465,U_464) ),
inference(clausify,[status(thm)],[f_110_4]) ).
cnf(f_110_6,plain,
( subset(cartesian_product2(U_465,U_466),cartesian_product2(U_464,U_466))
| ~ sP89(U_464,U_465,U_466,U_467) ),
inference(clausify,[status(thm)],[f_110_4]) ).
cnf(f_110_7,plain,
( subset(cartesian_product2(U_467,U_465),cartesian_product2(U_467,U_464))
| ~ sP89(U_464,U_465,U_466,U_467) ),
inference(clausify,[status(thm)],[f_110_4]) ).
fof(f_111_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_111_2,plain,
! [U_471,U_470,U_469,U_468] :
( subset(cartesian_product2(U_471,U_469),cartesian_product2(U_470,U_468))
| ~ subset(U_469,U_468)
| ~ subset(U_471,U_470) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
fof(f_111_3,plain,
! [U_468,U_471,U_470,U_469] :
( subset(cartesian_product2(U_471,U_469),cartesian_product2(U_470,U_468))
| ~ subset(U_469,U_468)
| ~ subset(U_471,U_470) ),
inference(definitional_conversion,[status(esa)],[f_111_2]) ).
cnf(f_111_4,plain,
( subset(cartesian_product2(U_471,U_469),cartesian_product2(U_470,U_468))
| ~ subset(U_469,U_468)
| ~ subset(U_471,U_470) ),
inference(clausify,[status(thm)],[f_111_3]) ).
fof(f_112_1,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t12_xboole_1]) ).
fof(f_112_2,plain,
! [U_473,U_472] :
( set_union2(U_473,U_472) = U_472
| ~ subset(U_473,U_472) ),
inference(variable_rename,[status(thm)],[f_112_1]) ).
fof(f_112_3,plain,
! [U_473,U_472] :
( set_union2(U_473,U_472) = U_472
| ~ subset(U_473,U_472) ),
inference(definitional_conversion,[status(esa)],[f_112_2]) ).
cnf(f_112_4,plain,
( set_union2(U_473,U_472) = U_472
| ~ subset(U_473,U_472) ),
inference(clausify,[status(thm)],[f_112_3]) ).
fof(f_113_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_113_2,plain,
! [U_479] :
? [U_478] :
( ! [U_477] :
( in(U_477,U_478)
| are_equipotent(U_477,U_478)
| ~ subset(U_477,U_478) )
& ! [U_476] :
( in(powerset(U_476),U_478)
| ~ in(U_476,U_478) )
& ! [U_475,U_474] :
( in(U_474,U_478)
| ~ subset(U_474,U_475)
| ~ in(U_475,U_478) )
& in(U_479,U_478) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
fof(f_113_3,plain,
! [U_479] :
( ! [U_477] :
( in(U_477,sK73(U_479))
| are_equipotent(U_477,sK73(U_479))
| ~ subset(U_477,sK73(U_479)) )
& ! [U_476] :
( in(powerset(U_476),sK73(U_479))
| ~ in(U_476,sK73(U_479)) )
& ! [U_475,U_474] :
( in(U_474,sK73(U_479))
| ~ subset(U_474,U_475)
| ~ in(U_475,sK73(U_479)) )
& in(U_479,sK73(U_479)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_478,sK73(U_479))],[f_113_2]) ).
fof(f_113_4,plain,
( ! [U_477,U_479] :
( in(U_477,sK73(U_479))
| are_equipotent(U_477,sK73(U_479))
| ~ subset(U_477,sK73(U_479)) )
& ! [U_476,U_479] :
( in(powerset(U_476),sK73(U_479))
| ~ in(U_476,sK73(U_479)) )
& ! [U_475,U_474,U_479] :
( in(U_474,sK73(U_479))
| ~ subset(U_474,U_475)
| ~ in(U_475,sK73(U_479)) )
& ! [U_479] : in(U_479,sK73(U_479)) ),
inference(definitional_conversion,[status(esa)],[f_113_3]) ).
cnf(f_113_5,plain,
in(U_479,sK73(U_479)),
inference(clausify,[status(thm)],[f_113_4]) ).
cnf(f_113_6,plain,
( in(U_474,sK73(U_479))
| ~ subset(U_474,U_475)
| ~ in(U_475,sK73(U_479)) ),
inference(clausify,[status(thm)],[f_113_4]) ).
cnf(f_113_7,plain,
( in(powerset(U_476),sK73(U_479))
| ~ in(U_476,sK73(U_479)) ),
inference(clausify,[status(thm)],[f_113_4]) ).
cnf(f_113_8,plain,
( in(U_477,sK73(U_479))
| are_equipotent(U_477,sK73(U_479))
| ~ subset(U_477,sK73(U_479)) ),
inference(clausify,[status(thm)],[f_113_4]) ).
fof(f_114_1,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(fof_nnf,[status(thm)],[t17_xboole_1]) ).
fof(f_114_2,plain,
! [U_481,U_480] : subset(set_intersection2(U_481,U_480),U_481),
inference(variable_rename,[status(thm)],[f_114_1]) ).
fof(f_114_3,plain,
! [U_480,U_481] : subset(set_intersection2(U_481,U_480),U_481),
inference(definitional_conversion,[status(esa)],[f_114_2]) ).
cnf(f_114_4,plain,
subset(set_intersection2(U_481,U_480),U_481),
inference(clausify,[status(thm)],[f_114_3]) ).
fof(f_115_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_115_2,plain,
! [U_484,U_483,U_482] :
( subset(U_484,set_intersection2(U_483,U_482))
| ~ subset(U_484,U_482)
| ~ subset(U_484,U_483) ),
inference(variable_rename,[status(thm)],[f_115_1]) ).
fof(f_115_3,plain,
! [U_482,U_483,U_484] :
( subset(U_484,set_intersection2(U_483,U_482))
| ~ subset(U_484,U_482)
| ~ subset(U_484,U_483) ),
inference(definitional_conversion,[status(esa)],[f_115_2]) ).
cnf(f_115_4,plain,
( subset(U_484,set_intersection2(U_483,U_482))
| ~ subset(U_484,U_482)
| ~ subset(U_484,U_483) ),
inference(clausify,[status(thm)],[f_115_3]) ).
fof(f_116_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_116_2,plain,
! [U_485] : set_union2(U_485,empty_set) = U_485,
inference(variable_rename,[status(thm)],[f_116_1]) ).
fof(f_116_3,plain,
! [U_485] : set_union2(U_485,empty_set) = U_485,
inference(definitional_conversion,[status(esa)],[f_116_2]) ).
cnf(f_116_4,plain,
set_union2(U_485,empty_set) = U_485,
inference(clausify,[status(thm)],[f_116_3]) ).
fof(f_117_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_117_2,plain,
! [U_487,U_486] :
( element(U_487,U_486)
| ~ in(U_487,U_486) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
fof(f_117_3,plain,
! [U_487,U_486] :
( element(U_487,U_486)
| ~ in(U_487,U_486) ),
inference(definitional_conversion,[status(esa)],[f_117_2]) ).
cnf(f_117_4,plain,
( element(U_487,U_486)
| ~ in(U_487,U_486) ),
inference(clausify,[status(thm)],[f_117_3]) ).
fof(f_118_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_118_2,plain,
! [U_490,U_489,U_488] :
( subset(U_490,U_488)
| ~ subset(U_489,U_488)
| ~ subset(U_490,U_489) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
fof(f_118_3,plain,
! [U_490,U_489,U_488] :
( subset(U_490,U_488)
| ~ subset(U_489,U_488)
| ~ subset(U_490,U_489) ),
inference(definitional_conversion,[status(esa)],[f_118_2]) ).
cnf(f_118_4,plain,
( subset(U_490,U_488)
| ~ subset(U_489,U_488)
| ~ subset(U_490,U_489) ),
inference(clausify,[status(thm)],[f_118_3]) ).
fof(f_119_1,plain,
powerset(empty_set) = singleton(empty_set),
inference(fof_nnf,[status(thm)],[t1_zfmisc_1]) ).
fof(f_119_2,plain,
powerset(empty_set) = singleton(empty_set),
inference(definitional_conversion,[status(esa)],[f_119_1]) ).
cnf(f_119_3,plain,
powerset(empty_set) = singleton(empty_set),
inference(clausify,[status(thm)],[f_119_2]) ).
fof(f_120_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_120_2,plain,
! [U_493,U_492,U_491] :
( ( in(U_492,relation_rng(U_491))
& in(U_493,relation_dom(U_491)) )
| ~ in(ordered_pair(U_493,U_492),U_491)
| ~ relation(U_491) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
fof(f_120_3,plain,
( ! [U_491,U_492,U_493] :
( in(U_492,relation_rng(U_491))
| ~ sP90(U_491,U_492,U_493) )
& ! [U_491,U_492,U_493] :
( in(U_493,relation_dom(U_491))
| ~ sP90(U_491,U_492,U_493) )
& ! [U_491,U_492,U_493] :
( sP90(U_491,U_492,U_493)
| ~ in(ordered_pair(U_493,U_492),U_491)
| ~ relation(U_491) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP90])],[f_120_2]) ).
cnf(f_120_4,plain,
( sP90(U_491,U_492,U_493)
| ~ in(ordered_pair(U_493,U_492),U_491)
| ~ relation(U_491) ),
inference(clausify,[status(thm)],[f_120_3]) ).
cnf(f_120_5,plain,
( in(U_493,relation_dom(U_491))
| ~ sP90(U_491,U_492,U_493) ),
inference(clausify,[status(thm)],[f_120_3]) ).
cnf(f_120_6,plain,
( in(U_492,relation_rng(U_491))
| ~ sP90(U_491,U_492,U_493) ),
inference(clausify,[status(thm)],[f_120_3]) ).
fof(f_121_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_121_2,plain,
! [U_494] :
( subset(U_494,cartesian_product2(relation_dom(U_494),relation_rng(U_494)))
| ~ relation(U_494) ),
inference(variable_rename,[status(thm)],[f_121_1]) ).
fof(f_121_3,plain,
! [U_494] :
( subset(U_494,cartesian_product2(relation_dom(U_494),relation_rng(U_494)))
| ~ relation(U_494) ),
inference(definitional_conversion,[status(esa)],[f_121_2]) ).
cnf(f_121_4,plain,
( subset(U_494,cartesian_product2(relation_dom(U_494),relation_rng(U_494)))
| ~ relation(U_494) ),
inference(clausify,[status(thm)],[f_121_3]) ).
fof(f_122_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_122_2,plain,
! [U_496] :
( ! [U_495] :
( ( subset(relation_rng(U_496),relation_rng(U_495))
& subset(relation_dom(U_496),relation_dom(U_495)) )
| ~ subset(U_496,U_495)
| ~ relation(U_495) )
| ~ relation(U_496) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
fof(f_122_3,plain,
( ! [U_495,U_496] :
( subset(relation_rng(U_496),relation_rng(U_495))
| ~ sP91(U_495,U_496) )
& ! [U_495,U_496] :
( subset(relation_dom(U_496),relation_dom(U_495))
| ~ sP91(U_495,U_496) )
& ! [U_495,U_496] :
( sP91(U_495,U_496)
| ~ subset(U_496,U_495)
| ~ relation(U_495)
| ~ relation(U_496) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP91])],[f_122_2]) ).
cnf(f_122_4,plain,
( sP91(U_495,U_496)
| ~ subset(U_496,U_495)
| ~ relation(U_495)
| ~ relation(U_496) ),
inference(clausify,[status(thm)],[f_122_3]) ).
cnf(f_122_5,plain,
( subset(relation_dom(U_496),relation_dom(U_495))
| ~ sP91(U_495,U_496) ),
inference(clausify,[status(thm)],[f_122_3]) ).
cnf(f_122_6,plain,
( subset(relation_rng(U_496),relation_rng(U_495))
| ~ sP91(U_495,U_496) ),
inference(clausify,[status(thm)],[f_122_3]) ).
fof(f_123_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_123_2,plain,
! [U_499,U_498,U_497] :
( subset(set_intersection2(U_499,U_497),set_intersection2(U_498,U_497))
| ~ subset(U_499,U_498) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
fof(f_123_3,plain,
! [U_499,U_498] :
( ! [U_497] : subset(set_intersection2(U_499,U_497),set_intersection2(U_498,U_497))
| ~ subset(U_499,U_498) ),
inference(miniscope,[status(thm)],[f_123_2]) ).
fof(f_123_4,plain,
! [U_499,U_497,U_498] :
( subset(set_intersection2(U_499,U_497),set_intersection2(U_498,U_497))
| ~ subset(U_499,U_498) ),
inference(definitional_conversion,[status(esa)],[f_123_3]) ).
cnf(f_123_5,plain,
( subset(set_intersection2(U_499,U_497),set_intersection2(U_498,U_497))
| ~ subset(U_499,U_498) ),
inference(clausify,[status(thm)],[f_123_4]) ).
fof(f_124_1,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t28_xboole_1]) ).
fof(f_124_2,plain,
! [U_501,U_500] :
( set_intersection2(U_501,U_500) = U_501
| ~ subset(U_501,U_500) ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
fof(f_124_3,plain,
! [U_501,U_500] :
( set_intersection2(U_501,U_500) = U_501
| ~ subset(U_501,U_500) ),
inference(definitional_conversion,[status(esa)],[f_124_2]) ).
cnf(f_124_4,plain,
( set_intersection2(U_501,U_500) = U_501
| ~ subset(U_501,U_500) ),
inference(clausify,[status(thm)],[f_124_3]) ).
fof(f_125_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_125_2,plain,
! [U_502] : set_intersection2(U_502,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_125_1]) ).
fof(f_125_3,plain,
! [U_502] : set_intersection2(U_502,empty_set) = empty_set,
inference(definitional_conversion,[status(esa)],[f_125_2]) ).
cnf(f_125_4,plain,
set_intersection2(U_502,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_125_3]) ).
fof(f_126_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_126_2,plain,
! [U_504,U_503] :
( in(U_504,U_503)
| empty(U_503)
| ~ element(U_504,U_503) ),
inference(variable_rename,[status(thm)],[f_126_1]) ).
fof(f_126_3,plain,
! [U_504,U_503] :
( in(U_504,U_503)
| empty(U_503)
| ~ element(U_504,U_503) ),
inference(definitional_conversion,[status(esa)],[f_126_2]) ).
cnf(f_126_4,plain,
( in(U_504,U_503)
| empty(U_503)
| ~ element(U_504,U_503) ),
inference(clausify,[status(thm)],[f_126_3]) ).
fof(f_127_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_127_2,plain,
! [U_507,U_506] :
( U_507 = U_506
| ? [U_505] :
( ( ~ in(U_505,U_507)
& in(U_505,U_506) )
| ( ~ in(U_505,U_506)
& in(U_505,U_507) ) ) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
fof(f_127_3,plain,
! [U_507,U_506] :
( U_507 = U_506
| ? [U_509] :
( ~ in(U_509,U_507)
& in(U_509,U_506) )
| ? [U_508] :
( ~ in(U_508,U_506)
& in(U_508,U_507) ) ),
inference(miniscope,[status(thm)],[f_127_2]) ).
fof(f_127_4,plain,
! [U_507,U_506] :
( U_507 = U_506
| ? [U_509] :
( ~ in(U_509,U_507)
& in(U_509,U_506) )
| ( ~ in(sK74(U_507,U_506),U_506)
& in(sK74(U_507,U_506),U_507) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_508,sK74(U_507,U_506))],[f_127_3]) ).
fof(f_127_5,plain,
! [U_507,U_506] :
( U_507 = U_506
| ( ~ in(sK75(U_507,U_506),U_507)
& in(sK75(U_507,U_506),U_506) )
| ( ~ in(sK74(U_507,U_506),U_506)
& in(sK74(U_507,U_506),U_507) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_509,sK75(U_507,U_506))],[f_127_4]) ).
fof(f_127_6,plain,
( ! [U_507,U_506] :
( ~ in(sK75(U_507,U_506),U_507)
| ~ sP93(U_507,U_506) )
& ! [U_507,U_506] :
( in(sK75(U_507,U_506),U_506)
| ~ sP93(U_507,U_506) )
& ! [U_507,U_506] :
( ~ in(sK74(U_507,U_506),U_506)
| ~ sP92(U_507,U_506) )
& ! [U_507,U_506] :
( in(sK74(U_507,U_506),U_507)
| ~ sP92(U_507,U_506) )
& ! [U_507,U_506] :
( U_507 = U_506
| sP93(U_507,U_506)
| sP92(U_507,U_506) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP92,sP93])],[f_127_5]) ).
cnf(f_127_7,plain,
( U_507 = U_506
| sP93(U_507,U_506)
| sP92(U_507,U_506) ),
inference(clausify,[status(thm)],[f_127_6]) ).
cnf(f_127_8,plain,
( in(sK74(U_507,U_506),U_507)
| ~ sP92(U_507,U_506) ),
inference(clausify,[status(thm)],[f_127_6]) ).
cnf(f_127_9,plain,
( ~ in(sK74(U_507,U_506),U_506)
| ~ sP92(U_507,U_506) ),
inference(clausify,[status(thm)],[f_127_6]) ).
cnf(f_127_10,plain,
( in(sK75(U_507,U_506),U_506)
| ~ sP93(U_507,U_506) ),
inference(clausify,[status(thm)],[f_127_6]) ).
cnf(f_127_11,plain,
( ~ in(sK75(U_507,U_506),U_507)
| ~ sP93(U_507,U_506) ),
inference(clausify,[status(thm)],[f_127_6]) ).
fof(f_128_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_128_2,plain,
! [U_510] : subset(empty_set,U_510),
inference(variable_rename,[status(thm)],[f_128_1]) ).
fof(f_128_3,plain,
! [U_510] : subset(empty_set,U_510),
inference(definitional_conversion,[status(esa)],[f_128_2]) ).
cnf(f_128_4,plain,
subset(empty_set,U_510),
inference(clausify,[status(thm)],[f_128_3]) ).
fof(f_129_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_129_2,plain,
! [U_513,U_512,U_511] :
( ( in(U_512,relation_field(U_511))
& in(U_513,relation_field(U_511)) )
| ~ in(ordered_pair(U_513,U_512),U_511)
| ~ relation(U_511) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
fof(f_129_3,plain,
( ! [U_512,U_513,U_511] :
( in(U_512,relation_field(U_511))
| ~ sP94(U_512,U_513,U_511) )
& ! [U_512,U_513,U_511] :
( in(U_513,relation_field(U_511))
| ~ sP94(U_512,U_513,U_511) )
& ! [U_512,U_513,U_511] :
( sP94(U_512,U_513,U_511)
| ~ in(ordered_pair(U_513,U_512),U_511)
| ~ relation(U_511) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP94])],[f_129_2]) ).
cnf(f_129_4,plain,
( sP94(U_512,U_513,U_511)
| ~ in(ordered_pair(U_513,U_512),U_511)
| ~ relation(U_511) ),
inference(clausify,[status(thm)],[f_129_3]) ).
cnf(f_129_5,plain,
( in(U_513,relation_field(U_511))
| ~ sP94(U_512,U_513,U_511) ),
inference(clausify,[status(thm)],[f_129_3]) ).
cnf(f_129_6,plain,
( in(U_512,relation_field(U_511))
| ~ sP94(U_512,U_513,U_511) ),
inference(clausify,[status(thm)],[f_129_3]) ).
fof(f_130_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_130_2,plain,
! [U_516,U_515,U_514] :
( subset(set_difference(U_516,U_514),set_difference(U_515,U_514))
| ~ subset(U_516,U_515) ),
inference(variable_rename,[status(thm)],[f_130_1]) ).
fof(f_130_3,plain,
! [U_516,U_515] :
( ! [U_514] : subset(set_difference(U_516,U_514),set_difference(U_515,U_514))
| ~ subset(U_516,U_515) ),
inference(miniscope,[status(thm)],[f_130_2]) ).
fof(f_130_4,plain,
! [U_514,U_516,U_515] :
( subset(set_difference(U_516,U_514),set_difference(U_515,U_514))
| ~ subset(U_516,U_515) ),
inference(definitional_conversion,[status(esa)],[f_130_3]) ).
cnf(f_130_5,plain,
( subset(set_difference(U_516,U_514),set_difference(U_515,U_514))
| ~ subset(U_516,U_515) ),
inference(clausify,[status(thm)],[f_130_4]) ).
fof(f_131_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_131_2,plain,
! [U_520,U_519,U_518,U_517] :
( ( U_519 = U_517
& U_520 = U_518 )
| ordered_pair(U_520,U_519) != ordered_pair(U_518,U_517) ),
inference(variable_rename,[status(thm)],[f_131_1]) ).
fof(f_131_3,plain,
( ! [U_520,U_518,U_519,U_517] :
( U_519 = U_517
| ~ sP95(U_520,U_518,U_519,U_517) )
& ! [U_520,U_518,U_519,U_517] :
( U_520 = U_518
| ~ sP95(U_520,U_518,U_519,U_517) )
& ! [U_520,U_518,U_519,U_517] :
( sP95(U_520,U_518,U_519,U_517)
| ordered_pair(U_520,U_519) != ordered_pair(U_518,U_517) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP95])],[f_131_2]) ).
cnf(f_131_4,plain,
( sP95(U_520,U_518,U_519,U_517)
| ordered_pair(U_520,U_519) != ordered_pair(U_518,U_517) ),
inference(clausify,[status(thm)],[f_131_3]) ).
cnf(f_131_5,plain,
( U_520 = U_518
| ~ sP95(U_520,U_518,U_519,U_517) ),
inference(clausify,[status(thm)],[f_131_3]) ).
cnf(f_131_6,plain,
( U_519 = U_517
| ~ sP95(U_520,U_518,U_519,U_517) ),
inference(clausify,[status(thm)],[f_131_3]) ).
fof(f_132_1,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(fof_nnf,[status(thm)],[t36_xboole_1]) ).
fof(f_132_2,plain,
! [U_522,U_521] : subset(set_difference(U_522,U_521),U_522),
inference(variable_rename,[status(thm)],[f_132_1]) ).
fof(f_132_3,plain,
! [U_522,U_521] : subset(set_difference(U_522,U_521),U_522),
inference(definitional_conversion,[status(esa)],[f_132_2]) ).
cnf(f_132_4,plain,
subset(set_difference(U_522,U_521),U_522),
inference(clausify,[status(thm)],[f_132_3]) ).
fof(f_133_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_133_2,plain,
! [U_523] :
( ( relation_dom(U_523) = relation_rng(relation_inverse(U_523))
& relation_rng(U_523) = relation_dom(relation_inverse(U_523)) )
| ~ relation(U_523) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
fof(f_133_3,plain,
( ! [U_523] :
( relation_dom(U_523) = relation_rng(relation_inverse(U_523))
| ~ sP96(U_523) )
& ! [U_523] :
( relation_rng(U_523) = relation_dom(relation_inverse(U_523))
| ~ sP96(U_523) )
& ! [U_523] :
( sP96(U_523)
| ~ relation(U_523) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP96])],[f_133_2]) ).
cnf(f_133_4,plain,
( sP96(U_523)
| ~ relation(U_523) ),
inference(clausify,[status(thm)],[f_133_3]) ).
cnf(f_133_5,plain,
( relation_rng(U_523) = relation_dom(relation_inverse(U_523))
| ~ sP96(U_523) ),
inference(clausify,[status(thm)],[f_133_3]) ).
cnf(f_133_6,plain,
( relation_dom(U_523) = relation_rng(relation_inverse(U_523))
| ~ sP96(U_523) ),
inference(clausify,[status(thm)],[f_133_3]) ).
fof(f_134_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_134_2,plain,
! [U_525,U_524] :
( ( set_difference(U_525,U_524) = empty_set
| ~ subset(U_525,U_524) )
& ( subset(U_525,U_524)
| set_difference(U_525,U_524) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_134_1]) ).
fof(f_134_3,plain,
( ! [U_529,U_527] :
( set_difference(U_529,U_527) = empty_set
| ~ subset(U_529,U_527) )
& ! [U_528,U_526] :
( subset(U_528,U_526)
| set_difference(U_528,U_526) != empty_set ) ),
inference(miniscope,[status(thm)],[f_134_2]) ).
fof(f_134_4,plain,
( ! [U_529,U_527] :
( set_difference(U_529,U_527) = empty_set
| ~ subset(U_529,U_527) )
& ! [U_528,U_526] :
( subset(U_528,U_526)
| set_difference(U_528,U_526) != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_134_3]) ).
cnf(f_134_5,plain,
( subset(U_528,U_526)
| set_difference(U_528,U_526) != empty_set ),
inference(clausify,[status(thm)],[f_134_4]) ).
cnf(f_134_6,plain,
( set_difference(U_529,U_527) = empty_set
| ~ subset(U_529,U_527) ),
inference(clausify,[status(thm)],[f_134_4]) ).
fof(f_135_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_135_2,plain,
! [U_531,U_530] :
( ( subset(singleton(U_531),U_530)
| ~ in(U_531,U_530) )
& ( in(U_531,U_530)
| ~ subset(singleton(U_531),U_530) ) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
fof(f_135_3,plain,
( ! [U_535,U_533] :
( subset(singleton(U_535),U_533)
| ~ in(U_535,U_533) )
& ! [U_534,U_532] :
( in(U_534,U_532)
| ~ subset(singleton(U_534),U_532) ) ),
inference(miniscope,[status(thm)],[f_135_2]) ).
fof(f_135_4,plain,
( ! [U_533,U_535] :
( subset(singleton(U_535),U_533)
| ~ in(U_535,U_533) )
& ! [U_532,U_534] :
( in(U_534,U_532)
| ~ subset(singleton(U_534),U_532) ) ),
inference(definitional_conversion,[status(esa)],[f_135_3]) ).
cnf(f_135_5,plain,
( in(U_534,U_532)
| ~ subset(singleton(U_534),U_532) ),
inference(clausify,[status(thm)],[f_135_4]) ).
cnf(f_135_6,plain,
( subset(singleton(U_535),U_533)
| ~ in(U_535,U_533) ),
inference(clausify,[status(thm)],[f_135_4]) ).
fof(f_136_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_136_2,plain,
! [U_538,U_537,U_536] :
( ( subset(unordered_pair(U_538,U_537),U_536)
| ~ in(U_537,U_536)
| ~ in(U_538,U_536) )
& ( ( in(U_537,U_536)
& in(U_538,U_536) )
| ~ subset(unordered_pair(U_538,U_537),U_536) ) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
fof(f_136_3,plain,
( ! [U_544,U_542,U_540] :
( subset(unordered_pair(U_544,U_542),U_540)
| ~ in(U_542,U_540)
| ~ in(U_544,U_540) )
& ! [U_543,U_541,U_539] :
( ( in(U_541,U_539)
& in(U_543,U_539) )
| ~ subset(unordered_pair(U_543,U_541),U_539) ) ),
inference(miniscope,[status(thm)],[f_136_2]) ).
fof(f_136_4,plain,
( ! [U_539,U_541,U_543] :
( in(U_541,U_539)
| ~ sP97(U_539,U_541,U_543) )
& ! [U_539,U_541,U_543] :
( in(U_543,U_539)
| ~ sP97(U_539,U_541,U_543) )
& ! [U_540,U_542,U_544] :
( subset(unordered_pair(U_544,U_542),U_540)
| ~ in(U_542,U_540)
| ~ in(U_544,U_540) )
& ! [U_539,U_541,U_543] :
( sP97(U_539,U_541,U_543)
| ~ subset(unordered_pair(U_543,U_541),U_539) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP97])],[f_136_3]) ).
cnf(f_136_5,plain,
( sP97(U_539,U_541,U_543)
| ~ subset(unordered_pair(U_543,U_541),U_539) ),
inference(clausify,[status(thm)],[f_136_4]) ).
cnf(f_136_6,plain,
( subset(unordered_pair(U_544,U_542),U_540)
| ~ in(U_542,U_540)
| ~ in(U_544,U_540) ),
inference(clausify,[status(thm)],[f_136_4]) ).
cnf(f_136_7,plain,
( in(U_543,U_539)
| ~ sP97(U_539,U_541,U_543) ),
inference(clausify,[status(thm)],[f_136_4]) ).
cnf(f_136_8,plain,
( in(U_541,U_539)
| ~ sP97(U_539,U_541,U_543) ),
inference(clausify,[status(thm)],[f_136_4]) ).
fof(f_137_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_137_2,plain,
! [U_546,U_545] : set_union2(U_546,set_difference(U_545,U_546)) = set_union2(U_546,U_545),
inference(variable_rename,[status(thm)],[f_137_1]) ).
fof(f_137_3,plain,
! [U_546,U_545] : set_union2(U_546,set_difference(U_545,U_546)) = set_union2(U_546,U_545),
inference(definitional_conversion,[status(esa)],[f_137_2]) ).
cnf(f_137_4,plain,
set_union2(U_546,set_difference(U_545,U_546)) = set_union2(U_546,U_545),
inference(clausify,[status(thm)],[f_137_3]) ).
fof(f_138_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_138_2,plain,
! [U_548,U_547] :
( ( subset(U_548,singleton(U_547))
| ( U_548 != singleton(U_547)
& U_548 != empty_set ) )
& ( U_548 = singleton(U_547)
| U_548 = empty_set
| ~ subset(U_548,singleton(U_547)) ) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
fof(f_138_3,plain,
( ! [U_552,U_550] :
( subset(U_552,singleton(U_550))
| ( U_552 != singleton(U_550)
& U_552 != empty_set ) )
& ! [U_551,U_549] :
( U_551 = singleton(U_549)
| U_551 = empty_set
| ~ subset(U_551,singleton(U_549)) ) ),
inference(miniscope,[status(thm)],[f_138_2]) ).
fof(f_138_4,plain,
( ! [U_550,U_552] :
( U_552 != singleton(U_550)
| ~ sP98(U_550,U_552) )
& ! [U_550,U_552] :
( U_552 != empty_set
| ~ sP98(U_550,U_552) )
& ! [U_550,U_552] :
( subset(U_552,singleton(U_550))
| sP98(U_550,U_552) )
& ! [U_551,U_549] :
( U_551 = singleton(U_549)
| U_551 = empty_set
| ~ subset(U_551,singleton(U_549)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP98])],[f_138_3]) ).
cnf(f_138_5,plain,
( U_551 = singleton(U_549)
| U_551 = empty_set
| ~ subset(U_551,singleton(U_549)) ),
inference(clausify,[status(thm)],[f_138_4]) ).
cnf(f_138_6,plain,
( subset(U_552,singleton(U_550))
| sP98(U_550,U_552) ),
inference(clausify,[status(thm)],[f_138_4]) ).
cnf(f_138_7,plain,
( U_552 != empty_set
| ~ sP98(U_550,U_552) ),
inference(clausify,[status(thm)],[f_138_4]) ).
cnf(f_138_8,plain,
( U_552 != singleton(U_550)
| ~ sP98(U_550,U_552) ),
inference(clausify,[status(thm)],[f_138_4]) ).
fof(f_139_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_139_2,plain,
! [U_553] : set_difference(U_553,empty_set) = U_553,
inference(variable_rename,[status(thm)],[f_139_1]) ).
fof(f_139_3,plain,
! [U_553] : set_difference(U_553,empty_set) = U_553,
inference(definitional_conversion,[status(esa)],[f_139_2]) ).
cnf(f_139_4,plain,
set_difference(U_553,empty_set) = U_553,
inference(clausify,[status(thm)],[f_139_3]) ).
fof(f_140_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_140_2,plain,
! [U_555,U_554] :
( ( element(U_555,powerset(U_554))
| ~ subset(U_555,U_554) )
& ( subset(U_555,U_554)
| ~ element(U_555,powerset(U_554)) ) ),
inference(variable_rename,[status(thm)],[f_140_1]) ).
fof(f_140_3,plain,
( ! [U_559,U_557] :
( element(U_559,powerset(U_557))
| ~ subset(U_559,U_557) )
& ! [U_558,U_556] :
( subset(U_558,U_556)
| ~ element(U_558,powerset(U_556)) ) ),
inference(miniscope,[status(thm)],[f_140_2]) ).
fof(f_140_4,plain,
( ! [U_559,U_557] :
( element(U_559,powerset(U_557))
| ~ subset(U_559,U_557) )
& ! [U_558,U_556] :
( subset(U_558,U_556)
| ~ element(U_558,powerset(U_556)) ) ),
inference(definitional_conversion,[status(esa)],[f_140_3]) ).
cnf(f_140_5,plain,
( subset(U_558,U_556)
| ~ element(U_558,powerset(U_556)) ),
inference(clausify,[status(thm)],[f_140_4]) ).
cnf(f_140_6,plain,
( element(U_559,powerset(U_557))
| ~ subset(U_559,U_557) ),
inference(clausify,[status(thm)],[f_140_4]) ).
fof(f_141_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_141_2,plain,
! [U_563,U_562] :
( ( ~ disjoint(U_563,U_562)
| ! [U_561] :
( ~ in(U_561,U_562)
| ~ in(U_561,U_563) ) )
& ( ? [U_560] :
( in(U_560,U_562)
& in(U_560,U_563) )
| disjoint(U_563,U_562) ) ),
inference(variable_rename,[status(thm)],[f_141_1]) ).
fof(f_141_3,plain,
( ! [U_567,U_565] :
( ~ disjoint(U_567,U_565)
| ! [U_561] :
( ~ in(U_561,U_565)
| ~ in(U_561,U_567) ) )
& ! [U_566,U_564] :
( ? [U_560] :
( in(U_560,U_564)
& in(U_560,U_566) )
| disjoint(U_566,U_564) ) ),
inference(miniscope,[status(thm)],[f_141_2]) ).
fof(f_141_4,plain,
( ! [U_567,U_565] :
( ~ disjoint(U_567,U_565)
| ! [U_561] :
( ~ in(U_561,U_565)
| ~ in(U_561,U_567) ) )
& ! [U_566,U_564] :
( ( in(sK76(U_566,U_564),U_564)
& in(sK76(U_566,U_564),U_566) )
| disjoint(U_566,U_564) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_560,sK76(U_566,U_564))],[f_141_3]) ).
fof(f_141_5,plain,
( ! [U_564,U_566] :
( in(sK76(U_566,U_564),U_564)
| ~ sP99(U_564,U_566) )
& ! [U_564,U_566] :
( in(sK76(U_566,U_564),U_566)
| ~ sP99(U_564,U_566) )
& ! [U_567,U_565,U_561] :
( ~ disjoint(U_567,U_565)
| ~ in(U_561,U_565)
| ~ in(U_561,U_567) )
& ! [U_564,U_566] :
( sP99(U_564,U_566)
| disjoint(U_566,U_564) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP99])],[f_141_4]) ).
cnf(f_141_6,plain,
( sP99(U_564,U_566)
| disjoint(U_566,U_564) ),
inference(clausify,[status(thm)],[f_141_5]) ).
cnf(f_141_7,plain,
( ~ disjoint(U_567,U_565)
| ~ in(U_561,U_565)
| ~ in(U_561,U_567) ),
inference(clausify,[status(thm)],[f_141_5]) ).
cnf(f_141_8,plain,
( in(sK76(U_566,U_564),U_566)
| ~ sP99(U_564,U_566) ),
inference(clausify,[status(thm)],[f_141_5]) ).
cnf(f_141_9,plain,
( in(sK76(U_566,U_564),U_564)
| ~ sP99(U_564,U_566) ),
inference(clausify,[status(thm)],[f_141_5]) ).
fof(f_142_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_142_2,plain,
! [U_568] :
( U_568 = empty_set
| ~ subset(U_568,empty_set) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
fof(f_142_3,plain,
! [U_568] :
( U_568 = empty_set
| ~ subset(U_568,empty_set) ),
inference(definitional_conversion,[status(esa)],[f_142_2]) ).
cnf(f_142_4,plain,
( U_568 = empty_set
| ~ subset(U_568,empty_set) ),
inference(clausify,[status(thm)],[f_142_3]) ).
fof(f_143_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_143_2,plain,
! [U_570,U_569] : set_difference(set_union2(U_570,U_569),U_569) = set_difference(U_570,U_569),
inference(variable_rename,[status(thm)],[f_143_1]) ).
fof(f_143_3,plain,
! [U_569,U_570] : set_difference(set_union2(U_570,U_569),U_569) = set_difference(U_570,U_569),
inference(definitional_conversion,[status(esa)],[f_143_2]) ).
cnf(f_143_4,plain,
set_difference(set_union2(U_570,U_569),U_569) = set_difference(U_570,U_569),
inference(clausify,[status(thm)],[f_143_3]) ).
fof(f_144_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_144_2,plain,
! [U_573,U_572] :
( ! [U_571] :
( ( ( disjoint(U_572,U_571)
| ~ subset(U_572,subset_complement(U_573,U_571)) )
& ( subset(U_572,subset_complement(U_573,U_571))
| ~ disjoint(U_572,U_571) ) )
| ~ element(U_571,powerset(U_573)) )
| ~ element(U_572,powerset(U_573)) ),
inference(variable_rename,[status(thm)],[f_144_1]) ).
fof(f_144_3,plain,
( ! [U_571,U_572,U_573] :
( disjoint(U_572,U_571)
| ~ subset(U_572,subset_complement(U_573,U_571))
| ~ sP100(U_571,U_572,U_573) )
& ! [U_571,U_572,U_573] :
( subset(U_572,subset_complement(U_573,U_571))
| ~ disjoint(U_572,U_571)
| ~ sP100(U_571,U_572,U_573) )
& ! [U_571,U_572,U_573] :
( sP100(U_571,U_572,U_573)
| ~ element(U_571,powerset(U_573))
| ~ element(U_572,powerset(U_573)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP100])],[f_144_2]) ).
cnf(f_144_4,plain,
( sP100(U_571,U_572,U_573)
| ~ element(U_571,powerset(U_573))
| ~ element(U_572,powerset(U_573)) ),
inference(clausify,[status(thm)],[f_144_3]) ).
cnf(f_144_5,plain,
( subset(U_572,subset_complement(U_573,U_571))
| ~ disjoint(U_572,U_571)
| ~ sP100(U_571,U_572,U_573) ),
inference(clausify,[status(thm)],[f_144_3]) ).
cnf(f_144_6,plain,
( disjoint(U_572,U_571)
| ~ subset(U_572,subset_complement(U_573,U_571))
| ~ sP100(U_571,U_572,U_573) ),
inference(clausify,[status(thm)],[f_144_3]) ).
fof(f_145_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_145_2,plain,
! [U_575] :
( ! [U_574] :
( subset(relation_dom(relation_composition(U_575,U_574)),relation_dom(U_575))
| ~ relation(U_574) )
| ~ relation(U_575) ),
inference(variable_rename,[status(thm)],[f_145_1]) ).
fof(f_145_3,plain,
! [U_575,U_574] :
( subset(relation_dom(relation_composition(U_575,U_574)),relation_dom(U_575))
| ~ relation(U_574)
| ~ relation(U_575) ),
inference(definitional_conversion,[status(esa)],[f_145_2]) ).
cnf(f_145_4,plain,
( subset(relation_dom(relation_composition(U_575,U_574)),relation_dom(U_575))
| ~ relation(U_574)
| ~ relation(U_575) ),
inference(clausify,[status(thm)],[f_145_3]) ).
fof(f_146_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_146_2,plain,
! [U_577] :
( ! [U_576] :
( subset(relation_rng(relation_composition(U_577,U_576)),relation_rng(U_576))
| ~ relation(U_576) )
| ~ relation(U_577) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
fof(f_146_3,plain,
! [U_576,U_577] :
( subset(relation_rng(relation_composition(U_577,U_576)),relation_rng(U_576))
| ~ relation(U_576)
| ~ relation(U_577) ),
inference(definitional_conversion,[status(esa)],[f_146_2]) ).
cnf(f_146_4,plain,
( subset(relation_rng(relation_composition(U_577,U_576)),relation_rng(U_576))
| ~ relation(U_576)
| ~ relation(U_577) ),
inference(clausify,[status(thm)],[f_146_3]) ).
fof(f_147_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_147_2,plain,
! [U_579,U_578] :
( U_578 = set_union2(U_579,set_difference(U_578,U_579))
| ~ subset(U_579,U_578) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
fof(f_147_3,plain,
! [U_578,U_579] :
( U_578 = set_union2(U_579,set_difference(U_578,U_579))
| ~ subset(U_579,U_578) ),
inference(definitional_conversion,[status(esa)],[f_147_2]) ).
cnf(f_147_4,plain,
( U_578 = set_union2(U_579,set_difference(U_578,U_579))
| ~ subset(U_579,U_578) ),
inference(clausify,[status(thm)],[f_147_3]) ).
fof(f_148_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_148_2,plain,
! [U_581] :
( ! [U_580] :
( relation_dom(relation_composition(U_581,U_580)) = relation_dom(U_581)
| ~ subset(relation_rng(U_581),relation_dom(U_580))
| ~ relation(U_580) )
| ~ relation(U_581) ),
inference(variable_rename,[status(thm)],[f_148_1]) ).
fof(f_148_3,plain,
! [U_580,U_581] :
( relation_dom(relation_composition(U_581,U_580)) = relation_dom(U_581)
| ~ subset(relation_rng(U_581),relation_dom(U_580))
| ~ relation(U_580)
| ~ relation(U_581) ),
inference(definitional_conversion,[status(esa)],[f_148_2]) ).
cnf(f_148_4,plain,
( relation_dom(relation_composition(U_581,U_580)) = relation_dom(U_581)
| ~ subset(relation_rng(U_581),relation_dom(U_580))
| ~ relation(U_580)
| ~ relation(U_581) ),
inference(clausify,[status(thm)],[f_148_3]) ).
fof(f_149_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_149_2,plain,
! [U_583,U_582] :
( complements_of_subsets(U_583,U_582) != empty_set
| U_582 = empty_set
| ~ element(U_582,powerset(powerset(U_583))) ),
inference(variable_rename,[status(thm)],[f_149_1]) ).
fof(f_149_3,plain,
! [U_583,U_582] :
( complements_of_subsets(U_583,U_582) != empty_set
| U_582 = empty_set
| ~ element(U_582,powerset(powerset(U_583))) ),
inference(definitional_conversion,[status(esa)],[f_149_2]) ).
cnf(f_149_4,plain,
( complements_of_subsets(U_583,U_582) != empty_set
| U_582 = empty_set
| ~ element(U_582,powerset(powerset(U_583))) ),
inference(clausify,[status(thm)],[f_149_3]) ).
fof(f_150_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t46_zfmisc_1]) ).
fof(f_150_2,plain,
! [U_585,U_584] :
( set_union2(singleton(U_585),U_584) = U_584
| ~ in(U_585,U_584) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
fof(f_150_3,plain,
! [U_584,U_585] :
( set_union2(singleton(U_585),U_584) = U_584
| ~ in(U_585,U_584) ),
inference(definitional_conversion,[status(esa)],[f_150_2]) ).
cnf(f_150_4,plain,
( set_union2(singleton(U_585),U_584) = U_584
| ~ in(U_585,U_584) ),
inference(clausify,[status(thm)],[f_150_3]) ).
fof(f_151_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_151_2,plain,
! [U_587] :
( ! [U_586] :
( relation_rng(relation_composition(U_586,U_587)) = relation_rng(U_587)
| ~ subset(relation_dom(U_587),relation_rng(U_586))
| ~ relation(U_586) )
| ~ relation(U_587) ),
inference(variable_rename,[status(thm)],[f_151_1]) ).
fof(f_151_3,plain,
! [U_586,U_587] :
( relation_rng(relation_composition(U_586,U_587)) = relation_rng(U_587)
| ~ subset(relation_dom(U_587),relation_rng(U_586))
| ~ relation(U_586)
| ~ relation(U_587) ),
inference(definitional_conversion,[status(esa)],[f_151_2]) ).
cnf(f_151_4,plain,
( relation_rng(relation_composition(U_586,U_587)) = relation_rng(U_587)
| ~ subset(relation_dom(U_587),relation_rng(U_586))
| ~ relation(U_586)
| ~ relation(U_587) ),
inference(clausify,[status(thm)],[f_151_3]) ).
fof(f_152_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_152_2,plain,
! [U_589,U_588] :
( subset_difference(U_589,cast_to_subset(U_589),union_of_subsets(U_589,U_588)) = meet_of_subsets(U_589,complements_of_subsets(U_589,U_588))
| U_588 = empty_set
| ~ element(U_588,powerset(powerset(U_589))) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
fof(f_152_3,plain,
! [U_588,U_589] :
( subset_difference(U_589,cast_to_subset(U_589),union_of_subsets(U_589,U_588)) = meet_of_subsets(U_589,complements_of_subsets(U_589,U_588))
| U_588 = empty_set
| ~ element(U_588,powerset(powerset(U_589))) ),
inference(definitional_conversion,[status(esa)],[f_152_2]) ).
cnf(f_152_4,plain,
( subset_difference(U_589,cast_to_subset(U_589),union_of_subsets(U_589,U_588)) = meet_of_subsets(U_589,complements_of_subsets(U_589,U_588))
| U_588 = empty_set
| ~ element(U_588,powerset(powerset(U_589))) ),
inference(clausify,[status(thm)],[f_152_3]) ).
fof(f_153_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_153_2,plain,
! [U_591,U_590] :
( union_of_subsets(U_591,complements_of_subsets(U_591,U_590)) = subset_difference(U_591,cast_to_subset(U_591),meet_of_subsets(U_591,U_590))
| U_590 = empty_set
| ~ element(U_590,powerset(powerset(U_591))) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
fof(f_153_3,plain,
! [U_590,U_591] :
( union_of_subsets(U_591,complements_of_subsets(U_591,U_590)) = subset_difference(U_591,cast_to_subset(U_591),meet_of_subsets(U_591,U_590))
| U_590 = empty_set
| ~ element(U_590,powerset(powerset(U_591))) ),
inference(definitional_conversion,[status(esa)],[f_153_2]) ).
cnf(f_153_4,plain,
( union_of_subsets(U_591,complements_of_subsets(U_591,U_590)) = subset_difference(U_591,cast_to_subset(U_591),meet_of_subsets(U_591,U_590))
| U_590 = empty_set
| ~ element(U_590,powerset(powerset(U_591))) ),
inference(clausify,[status(thm)],[f_153_3]) ).
fof(f_154_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_154_2,plain,
! [U_593,U_592] : set_difference(U_593,set_difference(U_593,U_592)) = set_intersection2(U_593,U_592),
inference(variable_rename,[status(thm)],[f_154_1]) ).
fof(f_154_3,plain,
! [U_592,U_593] : set_difference(U_593,set_difference(U_593,U_592)) = set_intersection2(U_593,U_592),
inference(definitional_conversion,[status(esa)],[f_154_2]) ).
cnf(f_154_4,plain,
set_difference(U_593,set_difference(U_593,U_592)) = set_intersection2(U_593,U_592),
inference(clausify,[status(thm)],[f_154_3]) ).
fof(f_155_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_155_2,plain,
! [U_594] : set_difference(empty_set,U_594) = empty_set,
inference(variable_rename,[status(thm)],[f_155_1]) ).
fof(f_155_3,plain,
! [U_594] : set_difference(empty_set,U_594) = empty_set,
inference(definitional_conversion,[status(esa)],[f_155_2]) ).
cnf(f_155_4,plain,
set_difference(empty_set,U_594) = empty_set,
inference(clausify,[status(thm)],[f_155_3]) ).
fof(f_156_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_156_2,plain,
! [U_597,U_596,U_595] :
( element(U_597,U_595)
| ~ element(U_596,powerset(U_595))
| ~ in(U_597,U_596) ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
fof(f_156_3,plain,
! [U_595,U_596,U_597] :
( element(U_597,U_595)
| ~ element(U_596,powerset(U_595))
| ~ in(U_597,U_596) ),
inference(definitional_conversion,[status(esa)],[f_156_2]) ).
cnf(f_156_4,plain,
( element(U_597,U_595)
| ~ element(U_596,powerset(U_595))
| ~ in(U_597,U_596) ),
inference(clausify,[status(thm)],[f_156_3]) ).
fof(f_157_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_157_2,plain,
! [U_601,U_600] :
( ( ~ disjoint(U_601,U_600)
| ! [U_599] : ~ in(U_599,set_intersection2(U_601,U_600)) )
& ( ? [U_598] : in(U_598,set_intersection2(U_601,U_600))
| disjoint(U_601,U_600) ) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
fof(f_157_3,plain,
( ! [U_605,U_603] :
( ~ disjoint(U_605,U_603)
| ! [U_599] : ~ in(U_599,set_intersection2(U_605,U_603)) )
& ! [U_604,U_602] :
( ? [U_598] : in(U_598,set_intersection2(U_604,U_602))
| disjoint(U_604,U_602) ) ),
inference(miniscope,[status(thm)],[f_157_2]) ).
fof(f_157_4,plain,
( ! [U_605,U_603] :
( ~ disjoint(U_605,U_603)
| ! [U_599] : ~ in(U_599,set_intersection2(U_605,U_603)) )
& ! [U_604,U_602] :
( in(sK77(U_604,U_602),set_intersection2(U_604,U_602))
| disjoint(U_604,U_602) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_598,sK77(U_604,U_602))],[f_157_3]) ).
fof(f_157_5,plain,
( ! [U_599,U_605,U_603] :
( ~ disjoint(U_605,U_603)
| ~ in(U_599,set_intersection2(U_605,U_603)) )
& ! [U_604,U_602] :
( in(sK77(U_604,U_602),set_intersection2(U_604,U_602))
| disjoint(U_604,U_602) ) ),
inference(definitional_conversion,[status(esa)],[f_157_4]) ).
cnf(f_157_6,plain,
( in(sK77(U_604,U_602),set_intersection2(U_604,U_602))
| disjoint(U_604,U_602) ),
inference(clausify,[status(thm)],[f_157_5]) ).
cnf(f_157_7,plain,
( ~ disjoint(U_605,U_603)
| ~ in(U_599,set_intersection2(U_605,U_603)) ),
inference(clausify,[status(thm)],[f_157_5]) ).
fof(f_158_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_158_2,plain,
! [U_608] :
( ! [U_607] :
( ! [U_606] :
( in(U_606,subset_complement(U_608,U_607))
| in(U_606,U_607)
| ~ element(U_606,U_608) )
| ~ element(U_607,powerset(U_608)) )
| U_608 = empty_set ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
fof(f_158_3,plain,
! [U_608,U_606,U_607] :
( in(U_606,subset_complement(U_608,U_607))
| in(U_606,U_607)
| ~ element(U_606,U_608)
| ~ element(U_607,powerset(U_608))
| U_608 = empty_set ),
inference(definitional_conversion,[status(esa)],[f_158_2]) ).
cnf(f_158_4,plain,
( in(U_606,subset_complement(U_608,U_607))
| in(U_606,U_607)
| ~ element(U_606,U_608)
| ~ element(U_607,powerset(U_608))
| U_608 = empty_set ),
inference(clausify,[status(thm)],[f_158_3]) ).
fof(f_159_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_159_2,plain,
! [U_611,U_610,U_609] :
( ~ in(U_610,U_609)
| ~ in(U_610,subset_complement(U_611,U_609))
| ~ element(U_609,powerset(U_611)) ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
fof(f_159_3,plain,
! [U_610,U_611,U_609] :
( ~ in(U_610,U_609)
| ~ in(U_610,subset_complement(U_611,U_609))
| ~ element(U_609,powerset(U_611)) ),
inference(definitional_conversion,[status(esa)],[f_159_2]) ).
cnf(f_159_4,plain,
( ~ in(U_610,U_609)
| ~ in(U_610,subset_complement(U_611,U_609))
| ~ element(U_609,powerset(U_611)) ),
inference(clausify,[status(thm)],[f_159_3]) ).
fof(f_160_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_160_2,plain,
! [U_614] :
( U_614 = empty_set
| ? [U_613,U_612] : in(ordered_pair(U_613,U_612),U_614)
| ~ relation(U_614) ),
inference(variable_rename,[status(thm)],[f_160_1]) ).
fof(f_160_3,plain,
! [U_614] :
( U_614 = empty_set
| ? [U_612] : in(ordered_pair(sK78(U_614),U_612),U_614)
| ~ relation(U_614) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_613,sK78(U_614))],[f_160_2]) ).
fof(f_160_4,plain,
! [U_614] :
( U_614 = empty_set
| in(ordered_pair(sK78(U_614),sK79(U_614)),U_614)
| ~ relation(U_614) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_612,sK79(U_614))],[f_160_3]) ).
fof(f_160_5,plain,
! [U_614] :
( U_614 = empty_set
| in(ordered_pair(sK78(U_614),sK79(U_614)),U_614)
| ~ relation(U_614) ),
inference(definitional_conversion,[status(esa)],[f_160_4]) ).
cnf(f_160_6,plain,
( U_614 = empty_set
| in(ordered_pair(sK78(U_614),sK79(U_614)),U_614)
| ~ relation(U_614) ),
inference(clausify,[status(thm)],[f_160_5]) ).
fof(f_161_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_161_2,plain,
! [U_617,U_616,U_615] :
( ~ empty(U_615)
| ~ element(U_616,powerset(U_615))
| ~ in(U_617,U_616) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
fof(f_161_3,plain,
! [U_617,U_616] :
( ! [U_615] :
( ~ empty(U_615)
| ~ element(U_616,powerset(U_615)) )
| ~ in(U_617,U_616) ),
inference(miniscope,[status(thm)],[f_161_2]) ).
fof(f_161_4,plain,
! [U_615,U_616,U_617] :
( ~ empty(U_615)
| ~ element(U_616,powerset(U_615))
| ~ in(U_617,U_616) ),
inference(definitional_conversion,[status(esa)],[f_161_3]) ).
cnf(f_161_5,plain,
( ~ empty(U_615)
| ~ element(U_616,powerset(U_615))
| ~ in(U_617,U_616) ),
inference(clausify,[status(thm)],[f_161_4]) ).
fof(f_162_1,plain,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(fof_nnf,[status(thm)],[t60_relat_1]) ).
fof(f_162_2,plain,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(definitional_conversion,[status(esa)],[f_162_1]) ).
cnf(f_162_3,plain,
relation_dom(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_162_2]) ).
cnf(f_162_4,plain,
relation_rng(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_162_2]) ).
fof(f_163_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t60_xboole_1]) ).
fof(f_163_2,plain,
! [U_619,U_618] :
( ~ proper_subset(U_618,U_619)
| ~ subset(U_619,U_618) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
fof(f_163_3,plain,
! [U_618,U_619] :
( ~ proper_subset(U_618,U_619)
| ~ subset(U_619,U_618) ),
inference(definitional_conversion,[status(esa)],[f_163_2]) ).
cnf(f_163_4,plain,
( ~ proper_subset(U_618,U_619)
| ~ subset(U_619,U_618) ),
inference(clausify,[status(thm)],[f_163_3]) ).
fof(f_164_1,plain,
! [A,B,C] :
( disjoint(A,C)
| ~ disjoint(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t63_xboole_1]) ).
fof(f_164_2,plain,
! [U_622,U_621,U_620] :
( disjoint(U_622,U_620)
| ~ disjoint(U_621,U_620)
| ~ subset(U_622,U_621) ),
inference(variable_rename,[status(thm)],[f_164_1]) ).
fof(f_164_3,plain,
! [U_621,U_620,U_622] :
( disjoint(U_622,U_620)
| ~ disjoint(U_621,U_620)
| ~ subset(U_622,U_621) ),
inference(definitional_conversion,[status(esa)],[f_164_2]) ).
cnf(f_164_4,plain,
( disjoint(U_622,U_620)
| ~ disjoint(U_621,U_620)
| ~ subset(U_622,U_621) ),
inference(clausify,[status(thm)],[f_164_3]) ).
fof(f_165_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_165_2,plain,
! [U_623] :
( U_623 = empty_set
| ( relation_rng(U_623) != empty_set
& relation_dom(U_623) != empty_set )
| ~ relation(U_623) ),
inference(variable_rename,[status(thm)],[f_165_1]) ).
fof(f_165_3,plain,
( ! [U_623] :
( relation_rng(U_623) != empty_set
| ~ sP101(U_623) )
& ! [U_623] :
( relation_dom(U_623) != empty_set
| ~ sP101(U_623) )
& ! [U_623] :
( U_623 = empty_set
| sP101(U_623)
| ~ relation(U_623) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP101])],[f_165_2]) ).
cnf(f_165_4,plain,
( U_623 = empty_set
| sP101(U_623)
| ~ relation(U_623) ),
inference(clausify,[status(thm)],[f_165_3]) ).
cnf(f_165_5,plain,
( relation_dom(U_623) != empty_set
| ~ sP101(U_623) ),
inference(clausify,[status(thm)],[f_165_3]) ).
cnf(f_165_6,plain,
( relation_rng(U_623) != empty_set
| ~ sP101(U_623) ),
inference(clausify,[status(thm)],[f_165_3]) ).
fof(f_166_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_166_2,plain,
! [U_624] :
( ( ( relation_dom(U_624) = empty_set
| relation_rng(U_624) != empty_set )
& ( relation_rng(U_624) = empty_set
| relation_dom(U_624) != empty_set ) )
| ~ relation(U_624) ),
inference(variable_rename,[status(thm)],[f_166_1]) ).
fof(f_166_3,plain,
( ! [U_624] :
( relation_dom(U_624) = empty_set
| relation_rng(U_624) != empty_set
| ~ sP102(U_624) )
& ! [U_624] :
( relation_rng(U_624) = empty_set
| relation_dom(U_624) != empty_set
| ~ sP102(U_624) )
& ! [U_624] :
( sP102(U_624)
| ~ relation(U_624) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP102])],[f_166_2]) ).
cnf(f_166_4,plain,
( sP102(U_624)
| ~ relation(U_624) ),
inference(clausify,[status(thm)],[f_166_3]) ).
cnf(f_166_5,plain,
( relation_rng(U_624) = empty_set
| relation_dom(U_624) != empty_set
| ~ sP102(U_624) ),
inference(clausify,[status(thm)],[f_166_3]) ).
cnf(f_166_6,plain,
( relation_dom(U_624) = empty_set
| relation_rng(U_624) != empty_set
| ~ sP102(U_624) ),
inference(clausify,[status(thm)],[f_166_3]) ).
fof(f_167_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_167_2,plain,
! [U_626,U_625] :
( ( set_difference(U_626,singleton(U_625)) = U_626
| in(U_625,U_626) )
& ( ~ in(U_625,U_626)
| set_difference(U_626,singleton(U_625)) != U_626 ) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
fof(f_167_3,plain,
( ! [U_630,U_628] :
( set_difference(U_630,singleton(U_628)) = U_630
| in(U_628,U_630) )
& ! [U_629,U_627] :
( ~ in(U_627,U_629)
| set_difference(U_629,singleton(U_627)) != U_629 ) ),
inference(miniscope,[status(thm)],[f_167_2]) ).
fof(f_167_4,plain,
( ! [U_630,U_628] :
( set_difference(U_630,singleton(U_628)) = U_630
| in(U_628,U_630) )
& ! [U_627,U_629] :
( ~ in(U_627,U_629)
| set_difference(U_629,singleton(U_627)) != U_629 ) ),
inference(definitional_conversion,[status(esa)],[f_167_3]) ).
cnf(f_167_5,plain,
( ~ in(U_627,U_629)
| set_difference(U_629,singleton(U_627)) != U_629 ),
inference(clausify,[status(thm)],[f_167_4]) ).
cnf(f_167_6,plain,
( set_difference(U_630,singleton(U_628)) = U_630
| in(U_628,U_630) ),
inference(clausify,[status(thm)],[f_167_4]) ).
fof(f_168_1,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(fof_nnf,[status(thm)],[t69_enumset1]) ).
fof(f_168_2,plain,
! [U_631] : unordered_pair(U_631,U_631) = singleton(U_631),
inference(variable_rename,[status(thm)],[f_168_1]) ).
fof(f_168_3,plain,
! [U_631] : unordered_pair(U_631,U_631) = singleton(U_631),
inference(definitional_conversion,[status(esa)],[f_168_2]) ).
cnf(f_168_4,plain,
unordered_pair(U_631,U_631) = singleton(U_631),
inference(clausify,[status(thm)],[f_168_3]) ).
fof(f_169_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_169_2,plain,
! [U_632] :
( U_632 = empty_set
| ~ empty(U_632) ),
inference(variable_rename,[status(thm)],[f_169_1]) ).
fof(f_169_3,plain,
! [U_632] :
( U_632 = empty_set
| ~ empty(U_632) ),
inference(definitional_conversion,[status(esa)],[f_169_2]) ).
cnf(f_169_4,plain,
( U_632 = empty_set
| ~ empty(U_632) ),
inference(clausify,[status(thm)],[f_169_3]) ).
fof(f_170_1,plain,
! [A,B] :
( A = B
| ~ subset(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t6_zfmisc_1]) ).
fof(f_170_2,plain,
! [U_634,U_633] :
( U_634 = U_633
| ~ subset(singleton(U_634),singleton(U_633)) ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
fof(f_170_3,plain,
! [U_633,U_634] :
( U_634 = U_633
| ~ subset(singleton(U_634),singleton(U_633)) ),
inference(definitional_conversion,[status(esa)],[f_170_2]) ).
cnf(f_170_4,plain,
( U_634 = U_633
| ~ subset(singleton(U_634),singleton(U_633)) ),
inference(clausify,[status(thm)],[f_170_3]) ).
fof(f_171_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_171_2,plain,
! [U_635] :
( relation_rng(identity_relation(U_635)) = U_635
& relation_dom(identity_relation(U_635)) = U_635 ),
inference(variable_rename,[status(thm)],[f_171_1]) ).
fof(f_171_3,plain,
( ! [U_637] : relation_rng(identity_relation(U_637)) = U_637
& ! [U_636] : relation_dom(identity_relation(U_636)) = U_636 ),
inference(miniscope,[status(thm)],[f_171_2]) ).
fof(f_171_4,plain,
( ! [U_637] : relation_rng(identity_relation(U_637)) = U_637
& ! [U_636] : relation_dom(identity_relation(U_636)) = U_636 ),
inference(definitional_conversion,[status(esa)],[f_171_3]) ).
cnf(f_171_5,plain,
relation_dom(identity_relation(U_636)) = U_636,
inference(clausify,[status(thm)],[f_171_4]) ).
cnf(f_171_6,plain,
relation_rng(identity_relation(U_637)) = U_637,
inference(clausify,[status(thm)],[f_171_4]) ).
fof(f_172_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_172_2,plain,
! [U_641,U_640,U_639,U_638] :
( ( ( in(ordered_pair(U_641,U_640),relation_composition(identity_relation(U_639),U_638))
| ~ in(ordered_pair(U_641,U_640),U_638)
| ~ in(U_641,U_639) )
& ( ( in(ordered_pair(U_641,U_640),U_638)
& in(U_641,U_639) )
| ~ in(ordered_pair(U_641,U_640),relation_composition(identity_relation(U_639),U_638)) ) )
| ~ relation(U_638) ),
inference(variable_rename,[status(thm)],[f_172_1]) ).
fof(f_172_3,plain,
( ! [U_638,U_639,U_640,U_641] :
( in(ordered_pair(U_641,U_640),U_638)
| ~ sP103(U_638,U_639,U_640,U_641) )
& ! [U_638,U_639,U_640,U_641] :
( in(U_641,U_639)
| ~ sP103(U_638,U_639,U_640,U_641) )
& ! [U_638,U_639,U_640,U_641] :
( in(ordered_pair(U_641,U_640),relation_composition(identity_relation(U_639),U_638))
| ~ in(ordered_pair(U_641,U_640),U_638)
| ~ in(U_641,U_639)
| ~ sP104(U_638,U_639,U_640,U_641) )
& ! [U_638,U_639,U_640,U_641] :
( sP103(U_638,U_639,U_640,U_641)
| ~ in(ordered_pair(U_641,U_640),relation_composition(identity_relation(U_639),U_638))
| ~ sP104(U_638,U_639,U_640,U_641) )
& ! [U_638,U_639,U_640,U_641] :
( sP104(U_638,U_639,U_640,U_641)
| ~ relation(U_638) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP103,sP104])],[f_172_2]) ).
cnf(f_172_4,plain,
( sP104(U_638,U_639,U_640,U_641)
| ~ relation(U_638) ),
inference(clausify,[status(thm)],[f_172_3]) ).
cnf(f_172_5,plain,
( sP103(U_638,U_639,U_640,U_641)
| ~ in(ordered_pair(U_641,U_640),relation_composition(identity_relation(U_639),U_638))
| ~ sP104(U_638,U_639,U_640,U_641) ),
inference(clausify,[status(thm)],[f_172_3]) ).
cnf(f_172_6,plain,
( in(ordered_pair(U_641,U_640),relation_composition(identity_relation(U_639),U_638))
| ~ in(ordered_pair(U_641,U_640),U_638)
| ~ in(U_641,U_639)
| ~ sP104(U_638,U_639,U_640,U_641) ),
inference(clausify,[status(thm)],[f_172_3]) ).
cnf(f_172_7,plain,
( in(U_641,U_639)
| ~ sP103(U_638,U_639,U_640,U_641) ),
inference(clausify,[status(thm)],[f_172_3]) ).
cnf(f_172_8,plain,
( in(ordered_pair(U_641,U_640),U_638)
| ~ sP103(U_638,U_639,U_640,U_641) ),
inference(clausify,[status(thm)],[f_172_3]) ).
fof(f_173_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_173_2,plain,
! [U_643,U_642] :
( ~ empty(U_642)
| ~ in(U_643,U_642) ),
inference(variable_rename,[status(thm)],[f_173_1]) ).
fof(f_173_3,plain,
! [U_642,U_643] :
( ~ empty(U_642)
| ~ in(U_643,U_642) ),
inference(definitional_conversion,[status(esa)],[f_173_2]) ).
cnf(f_173_4,plain,
( ~ empty(U_642)
| ~ in(U_643,U_642) ),
inference(clausify,[status(thm)],[f_173_3]) ).
fof(f_174_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1]) ).
fof(f_174_2,plain,
! [U_645,U_644] : subset(U_645,set_union2(U_645,U_644)),
inference(variable_rename,[status(thm)],[f_174_1]) ).
fof(f_174_3,plain,
! [U_645,U_644] : subset(U_645,set_union2(U_645,U_644)),
inference(definitional_conversion,[status(esa)],[f_174_2]) ).
cnf(f_174_4,plain,
subset(U_645,set_union2(U_645,U_644)),
inference(clausify,[status(thm)],[f_174_3]) ).
fof(f_175_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_175_2,plain,
! [U_647,U_646] :
( ( disjoint(U_647,U_646)
| set_difference(U_647,U_646) != U_647 )
& ( set_difference(U_647,U_646) = U_647
| ~ disjoint(U_647,U_646) ) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
fof(f_175_3,plain,
( ! [U_651,U_649] :
( disjoint(U_651,U_649)
| set_difference(U_651,U_649) != U_651 )
& ! [U_650,U_648] :
( set_difference(U_650,U_648) = U_650
| ~ disjoint(U_650,U_648) ) ),
inference(miniscope,[status(thm)],[f_175_2]) ).
fof(f_175_4,plain,
( ! [U_651,U_649] :
( disjoint(U_651,U_649)
| set_difference(U_651,U_649) != U_651 )
& ! [U_650,U_648] :
( set_difference(U_650,U_648) = U_650
| ~ disjoint(U_650,U_648) ) ),
inference(definitional_conversion,[status(esa)],[f_175_3]) ).
cnf(f_175_5,plain,
( set_difference(U_650,U_648) = U_650
| ~ disjoint(U_650,U_648) ),
inference(clausify,[status(thm)],[f_175_4]) ).
cnf(f_175_6,plain,
( disjoint(U_651,U_649)
| set_difference(U_651,U_649) != U_651 ),
inference(clausify,[status(thm)],[f_175_4]) ).
fof(f_176_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_176_2,plain,
! [U_654,U_653,U_652] :
( ( ( in(U_654,relation_dom(relation_dom_restriction(U_652,U_653)))
| ~ in(U_654,relation_dom(U_652))
| ~ in(U_654,U_653) )
& ( ( in(U_654,relation_dom(U_652))
& in(U_654,U_653) )
| ~ in(U_654,relation_dom(relation_dom_restriction(U_652,U_653))) ) )
| ~ relation(U_652) ),
inference(variable_rename,[status(thm)],[f_176_1]) ).
fof(f_176_3,plain,
( ! [U_652,U_653,U_654] :
( in(U_654,relation_dom(U_652))
| ~ sP105(U_652,U_653,U_654) )
& ! [U_652,U_653,U_654] :
( in(U_654,U_653)
| ~ sP105(U_652,U_653,U_654) )
& ! [U_652,U_653,U_654] :
( in(U_654,relation_dom(relation_dom_restriction(U_652,U_653)))
| ~ in(U_654,relation_dom(U_652))
| ~ in(U_654,U_653)
| ~ sP106(U_652,U_653,U_654) )
& ! [U_652,U_653,U_654] :
( sP105(U_652,U_653,U_654)
| ~ in(U_654,relation_dom(relation_dom_restriction(U_652,U_653)))
| ~ sP106(U_652,U_653,U_654) )
& ! [U_652,U_653,U_654] :
( sP106(U_652,U_653,U_654)
| ~ relation(U_652) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP105,sP106])],[f_176_2]) ).
cnf(f_176_4,plain,
( sP106(U_652,U_653,U_654)
| ~ relation(U_652) ),
inference(clausify,[status(thm)],[f_176_3]) ).
cnf(f_176_5,plain,
( sP105(U_652,U_653,U_654)
| ~ in(U_654,relation_dom(relation_dom_restriction(U_652,U_653)))
| ~ sP106(U_652,U_653,U_654) ),
inference(clausify,[status(thm)],[f_176_3]) ).
cnf(f_176_6,plain,
( in(U_654,relation_dom(relation_dom_restriction(U_652,U_653)))
| ~ in(U_654,relation_dom(U_652))
| ~ in(U_654,U_653)
| ~ sP106(U_652,U_653,U_654) ),
inference(clausify,[status(thm)],[f_176_3]) ).
cnf(f_176_7,plain,
( in(U_654,U_653)
| ~ sP105(U_652,U_653,U_654) ),
inference(clausify,[status(thm)],[f_176_3]) ).
cnf(f_176_8,plain,
( in(U_654,relation_dom(U_652))
| ~ sP105(U_652,U_653,U_654) ),
inference(clausify,[status(thm)],[f_176_3]) ).
fof(f_177_1,plain,
! [A,B] :
( subset(relation_dom_restriction(B,A),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t88_relat_1]) ).
fof(f_177_2,plain,
! [U_656,U_655] :
( subset(relation_dom_restriction(U_655,U_656),U_655)
| ~ relation(U_655) ),
inference(variable_rename,[status(thm)],[f_177_1]) ).
fof(f_177_3,plain,
! [U_655,U_656] :
( subset(relation_dom_restriction(U_655,U_656),U_655)
| ~ relation(U_655) ),
inference(definitional_conversion,[status(esa)],[f_177_2]) ).
cnf(f_177_4,plain,
( subset(relation_dom_restriction(U_655,U_656),U_655)
| ~ relation(U_655) ),
inference(clausify,[status(thm)],[f_177_3]) ).
fof(f_178_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_178_2,plain,
! [U_658,U_657] :
( ~ empty(U_657)
| U_658 = U_657
| ~ empty(U_658) ),
inference(variable_rename,[status(thm)],[f_178_1]) ).
fof(f_178_3,plain,
! [U_658] :
( ! [U_657] :
( ~ empty(U_657)
| U_658 = U_657 )
| ~ empty(U_658) ),
inference(miniscope,[status(thm)],[f_178_2]) ).
fof(f_178_4,plain,
! [U_657,U_658] :
( ~ empty(U_657)
| U_658 = U_657
| ~ empty(U_658) ),
inference(definitional_conversion,[status(esa)],[f_178_3]) ).
cnf(f_178_5,plain,
( ~ empty(U_657)
| U_658 = U_657
| ~ empty(U_658) ),
inference(clausify,[status(thm)],[f_178_4]) ).
fof(f_179_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_179_2,plain,
! [U_661,U_660,U_659] :
( subset(set_union2(U_661,U_659),U_660)
| ~ subset(U_659,U_660)
| ~ subset(U_661,U_660) ),
inference(variable_rename,[status(thm)],[f_179_1]) ).
fof(f_179_3,plain,
! [U_659,U_660,U_661] :
( subset(set_union2(U_661,U_659),U_660)
| ~ subset(U_659,U_660)
| ~ subset(U_661,U_660) ),
inference(definitional_conversion,[status(esa)],[f_179_2]) ).
cnf(f_179_4,plain,
( subset(set_union2(U_661,U_659),U_660)
| ~ subset(U_659,U_660)
| ~ subset(U_661,U_660) ),
inference(clausify,[status(thm)],[f_179_3]) ).
fof(f_180_1,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t8_zfmisc_1]) ).
fof(f_180_2,plain,
! [U_664,U_663,U_662] :
( U_664 = U_663
| singleton(U_664) != unordered_pair(U_663,U_662) ),
inference(variable_rename,[status(thm)],[f_180_1]) ).
fof(f_180_3,plain,
! [U_664,U_663] :
( ! [U_662] : singleton(U_664) != unordered_pair(U_663,U_662)
| U_664 = U_663 ),
inference(miniscope,[status(thm)],[f_180_2]) ).
fof(f_180_4,plain,
! [U_664,U_662,U_663] :
( singleton(U_664) != unordered_pair(U_663,U_662)
| U_664 = U_663 ),
inference(definitional_conversion,[status(esa)],[f_180_3]) ).
cnf(f_180_5,plain,
( singleton(U_664) != unordered_pair(U_663,U_662)
| U_664 = U_663 ),
inference(clausify,[status(thm)],[f_180_4]) ).
fof(f_181_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_181_2,plain,
! [U_666,U_665] :
( relation_dom(relation_dom_restriction(U_665,U_666)) = set_intersection2(relation_dom(U_665),U_666)
| ~ relation(U_665) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
fof(f_181_3,plain,
! [U_665,U_666] :
( relation_dom(relation_dom_restriction(U_665,U_666)) = set_intersection2(relation_dom(U_665),U_666)
| ~ relation(U_665) ),
inference(definitional_conversion,[status(esa)],[f_181_2]) ).
cnf(f_181_4,plain,
( relation_dom(relation_dom_restriction(U_665,U_666)) = set_intersection2(relation_dom(U_665),U_666)
| ~ relation(U_665) ),
inference(clausify,[status(thm)],[f_181_3]) ).
fof(f_182_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t92_zfmisc_1]) ).
fof(f_182_2,plain,
! [U_668,U_667] :
( subset(U_668,union(U_667))
| ~ in(U_668,U_667) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
fof(f_182_3,plain,
! [U_667,U_668] :
( subset(U_668,union(U_667))
| ~ in(U_668,U_667) ),
inference(definitional_conversion,[status(esa)],[f_182_2]) ).
cnf(f_182_4,plain,
( subset(U_668,union(U_667))
| ~ in(U_668,U_667) ),
inference(clausify,[status(thm)],[f_182_3]) ).
fof(f_183_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_183_2,plain,
! [U_670,U_669] :
( relation_dom_restriction(U_669,U_670) = relation_composition(identity_relation(U_670),U_669)
| ~ relation(U_669) ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
fof(f_183_3,plain,
! [U_669,U_670] :
( relation_dom_restriction(U_669,U_670) = relation_composition(identity_relation(U_670),U_669)
| ~ relation(U_669) ),
inference(definitional_conversion,[status(esa)],[f_183_2]) ).
cnf(f_183_4,plain,
( relation_dom_restriction(U_669,U_670) = relation_composition(identity_relation(U_670),U_669)
| ~ relation(U_669) ),
inference(clausify,[status(thm)],[f_183_3]) ).
fof(f_184_1,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B)) ),
inference(negate,[status(cth)],[t99_relat_1]) ).
fof(f_184_2,negated_conjecture,
? [A,B] :
( ~ subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B))
& relation(B) ),
inference(fof_nnf,[status(thm)],[f_184_1]) ).
fof(f_184_3,negated_conjecture,
? [U_672,U_671] :
( ~ subset(relation_rng(relation_dom_restriction(U_671,U_672)),relation_rng(U_671))
& relation(U_671) ),
inference(variable_rename,[status(thm)],[f_184_2]) ).
fof(f_184_4,negated_conjecture,
? [U_671] :
( ~ subset(relation_rng(relation_dom_restriction(U_671,sK80)),relation_rng(U_671))
& relation(U_671) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_672,sK80)],[f_184_3]) ).
fof(f_184_5,negated_conjecture,
( ~ subset(relation_rng(relation_dom_restriction(sK81,sK80)),relation_rng(sK81))
& relation(sK81) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_671,sK81)],[f_184_4]) ).
fof(f_184_6,negated_conjecture,
( ~ subset(relation_rng(relation_dom_restriction(sK81,sK80)),relation_rng(sK81))
& relation(sK81) ),
inference(definitional_conversion,[status(esa)],[f_184_5]) ).
cnf(f_184_7,negated_conjecture,
relation(sK81),
inference(clausify,[status(thm)],[f_184_6]) ).
cnf(f_184_8,negated_conjecture,
~ subset(relation_rng(relation_dom_restriction(sK81,sK80)),relation_rng(sK81)),
inference(clausify,[status(thm)],[f_184_6]) ).
fof(f_185_1,plain,
! [A] : union(powerset(A)) = A,
inference(fof_nnf,[status(thm)],[t99_zfmisc_1]) ).
fof(f_185_2,plain,
! [U_673] : union(powerset(U_673)) = U_673,
inference(variable_rename,[status(thm)],[f_185_1]) ).
fof(f_185_3,plain,
! [U_673] : union(powerset(U_673)) = U_673,
inference(definitional_conversion,[status(esa)],[f_185_2]) ).
cnf(f_185_4,plain,
union(powerset(U_673)) = U_673,
inference(clausify,[status(thm)],[f_185_3]) ).
fof(f_186_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_186_2,plain,
! [U_681] :
? [U_680] :
( ! [U_679] :
( in(U_679,U_680)
| are_equipotent(U_679,U_680)
| ~ subset(U_679,U_680) )
& ! [U_678] :
( ? [U_677] :
( ! [U_676] :
( in(U_676,U_677)
| ~ subset(U_676,U_678) )
& in(U_677,U_680) )
| ~ in(U_678,U_680) )
& ! [U_675,U_674] :
( in(U_674,U_680)
| ~ subset(U_674,U_675)
| ~ in(U_675,U_680) )
& in(U_681,U_680) ),
inference(variable_rename,[status(thm)],[f_186_1]) ).
fof(f_186_3,plain,
! [U_681] :
( ! [U_679] :
( in(U_679,sK82(U_681))
| are_equipotent(U_679,sK82(U_681))
| ~ subset(U_679,sK82(U_681)) )
& ! [U_678] :
( ? [U_677] :
( ! [U_676] :
( in(U_676,U_677)
| ~ subset(U_676,U_678) )
& in(U_677,sK82(U_681)) )
| ~ in(U_678,sK82(U_681)) )
& ! [U_675,U_674] :
( in(U_674,sK82(U_681))
| ~ subset(U_674,U_675)
| ~ in(U_675,sK82(U_681)) )
& in(U_681,sK82(U_681)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_680,sK82(U_681))],[f_186_2]) ).
fof(f_186_4,plain,
! [U_681] :
( ! [U_679] :
( in(U_679,sK82(U_681))
| are_equipotent(U_679,sK82(U_681))
| ~ subset(U_679,sK82(U_681)) )
& ! [U_678] :
( ( ! [U_676] :
( in(U_676,sK83(U_681,U_678))
| ~ subset(U_676,U_678) )
& in(sK83(U_681,U_678),sK82(U_681)) )
| ~ in(U_678,sK82(U_681)) )
& ! [U_675,U_674] :
( in(U_674,sK82(U_681))
| ~ subset(U_674,U_675)
| ~ in(U_675,sK82(U_681)) )
& in(U_681,sK82(U_681)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_677,sK83(U_681,U_678))],[f_186_3]) ).
fof(f_186_5,plain,
( ! [U_676,U_678,U_681] :
( in(U_676,sK83(U_681,U_678))
| ~ subset(U_676,U_678)
| ~ sP107(U_676,U_678,U_681) )
& ! [U_676,U_678,U_681] :
( in(sK83(U_681,U_678),sK82(U_681))
| ~ sP107(U_676,U_678,U_681) )
& ! [U_679,U_681] :
( in(U_679,sK82(U_681))
| are_equipotent(U_679,sK82(U_681))
| ~ subset(U_679,sK82(U_681)) )
& ! [U_676,U_678,U_681] :
( sP107(U_676,U_678,U_681)
| ~ in(U_678,sK82(U_681)) )
& ! [U_675,U_674,U_681] :
( in(U_674,sK82(U_681))
| ~ subset(U_674,U_675)
| ~ in(U_675,sK82(U_681)) )
& ! [U_681] : in(U_681,sK82(U_681)) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP107])],[f_186_4]) ).
cnf(f_186_6,plain,
in(U_681,sK82(U_681)),
inference(clausify,[status(thm)],[f_186_5]) ).
cnf(f_186_7,plain,
( in(U_674,sK82(U_681))
| ~ subset(U_674,U_675)
| ~ in(U_675,sK82(U_681)) ),
inference(clausify,[status(thm)],[f_186_5]) ).
cnf(f_186_8,plain,
( sP107(U_676,U_678,U_681)
| ~ in(U_678,sK82(U_681)) ),
inference(clausify,[status(thm)],[f_186_5]) ).
cnf(f_186_9,plain,
( in(U_679,sK82(U_681))
| are_equipotent(U_679,sK82(U_681))
| ~ subset(U_679,sK82(U_681)) ),
inference(clausify,[status(thm)],[f_186_5]) ).
cnf(f_186_10,plain,
( in(sK83(U_681,U_678),sK82(U_681))
| ~ sP107(U_676,U_678,U_681) ),
inference(clausify,[status(thm)],[f_186_5]) ).
cnf(f_186_11,plain,
( in(U_676,sK83(U_681,U_678))
| ~ subset(U_676,U_678)
| ~ sP107(U_676,U_678,U_681) ),
inference(clausify,[status(thm)],[f_186_5]) ).
fof(f_187_1,plain,
! [A,B,C] :
( B = C
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t9_zfmisc_1]) ).
fof(f_187_2,plain,
! [U_684,U_683,U_682] :
( U_683 = U_682
| singleton(U_684) != unordered_pair(U_683,U_682) ),
inference(variable_rename,[status(thm)],[f_187_1]) ).
fof(f_187_3,plain,
! [U_682,U_683,U_684] :
( U_683 = U_682
| singleton(U_684) != unordered_pair(U_683,U_682) ),
inference(definitional_conversion,[status(esa)],[f_187_2]) ).
cnf(f_187_4,plain,
( U_683 = U_682
| singleton(U_684) != unordered_pair(U_683,U_682) ),
inference(clausify,[status(thm)],[f_187_3]) ).
cnf(f_36_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_36_3]) ).
cnf(f_37_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_37_3]) ).
cnf(f_38_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_38_3]) ).
cnf(f_39_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_39_3]) ).
cnf(f_40_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_40_3]) ).
cnf(f_41_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_41_3]) ).
cnf(f_43_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_43_3]) ).
cnf(f_44_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_44_3]) ).
cnf(f_45_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_45_3]) ).
cnf(f_46_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_46_3]) ).
cnf(f_48_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_48_3]) ).
cnf(f_49_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_49_3]) ).
cnf(f_51_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_51_3]) ).
cnf(f_52_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_52_3]) ).
cnf(f_60_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_60_3]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( unordered_pair(Eq_x_0,Eq_x_1) = unordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( set_union2(Eq_x_0,Eq_x_1) = set_union2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( set_intersection2(Eq_x_0,Eq_x_1) = set_intersection2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( identity_relation(Eq_x_0) = identity_relation(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( ordered_pair(Eq_x_0,Eq_x_1) = ordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( relation_dom_restriction(Eq_x_0,Eq_x_1) = relation_dom_restriction(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( set_meet(Eq_x_0) = set_meet(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,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_14,axiom,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,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_16,axiom,
( union(Eq_x_0) = union(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,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_18,axiom,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,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_20,axiom,
( relation_field(Eq_x_0) = relation_field(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( relation_inverse(Eq_x_0) = relation_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,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_23,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_24,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_25,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_26,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_27,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_28,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_29,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_30,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_31,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_32,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_33,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_34,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_35,axiom,
( sK9(Eq_x_0,Eq_x_1) = sK9(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_36,axiom,
( sK10(Eq_x_0,Eq_x_1) = sK10(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_37,axiom,
( sK11(Eq_x_0) = sK11(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_38,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_39,axiom,
( sK13(Eq_x_0,Eq_x_1) = sK13(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_40,axiom,
( sK14(Eq_x_0,Eq_x_1) = sK14(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_41,axiom,
( sK15(Eq_x_0,Eq_x_1) = sK15(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_42,axiom,
( sK16(Eq_x_0,Eq_x_1) = sK16(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_43,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_44,axiom,
( sK18(Eq_x_0) = sK18(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_45,axiom,
( sK19(Eq_x_0,Eq_x_1) = sK19(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,
( sK20(Eq_x_0,Eq_x_1) = sK20(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,
( 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_48,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_49,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_50,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_51,axiom,
( sK25(Eq_x_0,Eq_x_1,Eq_x_2) = sK25(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_52,axiom,
( sK26(Eq_x_0,Eq_x_1,Eq_x_2) = sK26(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_53,axiom,
( sK27(Eq_x_0,Eq_x_1,Eq_x_2) = sK27(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_54,axiom,
( sK28(Eq_x_0,Eq_x_1,Eq_x_2) = sK28(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_55,axiom,
( sK29(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK29(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_56,axiom,
( sK30(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK30(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_57,axiom,
( sK31(Eq_x_0,Eq_x_1,Eq_x_2) = sK31(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_58,axiom,
( sK32(Eq_x_0,Eq_x_1,Eq_x_2) = sK32(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_59,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_60,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_61,axiom,
( sK35(Eq_x_0,Eq_x_1) = sK35(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_62,axiom,
( sK36(Eq_x_0,Eq_x_1) = sK36(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_63,axiom,
( sK37(Eq_x_0,Eq_x_1) = sK37(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_64,axiom,
( sK38(Eq_x_0,Eq_x_1,Eq_x_2) = sK38(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_65,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_66,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_67,axiom,
( sK41(Eq_x_0,Eq_x_1) = sK41(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_68,axiom,
( sK42(Eq_x_0,Eq_x_1) = sK42(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_69,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_70,axiom,
( sK44(Eq_x_0,Eq_x_1,Eq_x_2) = sK44(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_71,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_72,axiom,
( sK46(Eq_x_0,Eq_x_1) = sK46(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_73,axiom,
( sK47(Eq_x_0,Eq_x_1) = sK47(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_74,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_75,axiom,
( sK49(Eq_x_0,Eq_x_1,Eq_x_2) = sK49(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_76,axiom,
( sK50(Eq_x_0,Eq_x_1,Eq_x_2) = sK50(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_77,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_78,axiom,
( sK52(Eq_x_0,Eq_x_1) = sK52(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,
( 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_80,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_81,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_82,axiom,
( sK56(Eq_x_0,Eq_x_1) = sK56(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,
( sK57(Eq_x_0,Eq_x_1) = sK57(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_84,axiom,
( sK58(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK58(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_85,axiom,
( sK59(Eq_x_0,Eq_x_1,Eq_x_2) = sK59(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_86,axiom,
( sK60(Eq_x_0,Eq_x_1,Eq_x_2) = sK60(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_87,axiom,
( sK61(Eq_x_0,Eq_x_1,Eq_x_2) = sK61(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_88,axiom,
( sK62(Eq_x_0,Eq_x_1,Eq_x_2) = sK62(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_89,axiom,
( sK63(Eq_x_0,Eq_x_1,Eq_x_2) = sK63(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_90,axiom,
( sK64(Eq_x_0,Eq_x_1,Eq_x_2) = sK64(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_91,axiom,
( sK65(Eq_x_0) = sK65(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_92,axiom,
( sK66(Eq_x_0,Eq_x_1) = sK66(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_93,axiom,
( sK68(Eq_x_0) = sK68(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_94,axiom,
( sK71(Eq_x_0) = sK71(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_95,axiom,
( sK73(Eq_x_0) = sK73(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_96,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_97,axiom,
( sK75(Eq_x_0,Eq_x_1) = sK75(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_98,axiom,
( sK76(Eq_x_0,Eq_x_1) = sK76(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_99,axiom,
( sK77(Eq_x_0,Eq_x_1) = sK77(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_100,axiom,
( sK78(Eq_x_0) = sK78(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_101,axiom,
( sK79(Eq_x_0) = sK79(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_102,axiom,
( sK82(Eq_x_0) = sK82(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_103,axiom,
( sK83(Eq_x_0,Eq_x_1) = sK83(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_104,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_105,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_106,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_107,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_108,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_109,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_110,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_111,axiom,
( are_equipotent(Eq_y_0,Eq_y_1)
| ~ are_equipotent(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_112,axiom,
( sP0(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP0(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_113,axiom,
( sP1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_114,axiom,
( sP2(Eq_y_0,Eq_y_1)
| ~ sP2(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_115,axiom,
( sP3(Eq_y_0,Eq_y_1)
| ~ sP3(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,
( sP4(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP4(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_117,axiom,
( sP5(Eq_y_0,Eq_y_1)
| ~ sP5(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_118,axiom,
( sP6(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP6(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_119,axiom,
( sP7(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP7(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_120,axiom,
( sP8(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP8(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_121,axiom,
( sP9(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP9(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_122,axiom,
( sP10(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP10(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_123,axiom,
( sP11(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP11(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_124,axiom,
( sP12(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP12(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_125,axiom,
( sP13(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP13(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_126,axiom,
( sP14(Eq_y_0,Eq_y_1)
| ~ sP14(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_127,axiom,
( sP15(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP15(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_128,axiom,
( sP16(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP16(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_129,axiom,
( sP17(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP17(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_130,axiom,
( sP18(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP18(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_131,axiom,
( sP19(Eq_y_0,Eq_y_1)
| ~ sP19(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_132,axiom,
( sP20(Eq_y_0,Eq_y_1)
| ~ sP20(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_133,axiom,
( sP21(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP21(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_134,axiom,
( sP22(Eq_y_0,Eq_y_1)
| ~ sP22(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_135,axiom,
( sP23(Eq_y_0,Eq_y_1)
| ~ sP23(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_136,axiom,
( sP24(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP24(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_137,axiom,
( sP25(Eq_y_0,Eq_y_1)
| ~ sP25(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_138,axiom,
( sP26(Eq_y_0,Eq_y_1)
| ~ sP26(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_139,axiom,
( sP27(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP27(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_140,axiom,
( sP28(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP28(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_141,axiom,
( sP29(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP29(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_142,axiom,
( sP30(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP30(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_143,axiom,
( sP31(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP31(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_144,axiom,
( sP32(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP32(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_145,axiom,
( sP33(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP33(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_146,axiom,
( sP34(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP34(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_147,axiom,
( sP35(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP35(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_148,axiom,
( sP36(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP36(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_149,axiom,
( sP37(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP37(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_150,axiom,
( sP38(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP38(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_151,axiom,
( sP39(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP39(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_152,axiom,
( sP40(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP40(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_153,axiom,
( sP41(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP41(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_154,axiom,
( sP42(Eq_y_0,Eq_y_1)
| ~ sP42(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_155,axiom,
( sP43(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP43(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_156,axiom,
( sP44(Eq_y_0,Eq_y_1)
| ~ sP44(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_157,axiom,
( sP45(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP45(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_158,axiom,
( sP46(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP46(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_159,axiom,
( sP47(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP47(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_160,axiom,
( sP48(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP48(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_161,axiom,
( sP49(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP49(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_162,axiom,
( sP50(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP50(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_163,axiom,
( sP51(Eq_y_0,Eq_y_1)
| ~ sP51(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_164,axiom,
( sP52(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP52(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_165,axiom,
( sP53(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP53(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_166,axiom,
( sP54(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP54(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_167,axiom,
( sP55(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP55(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_168,axiom,
( sP56(Eq_y_0,Eq_y_1)
| ~ sP56(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_169,axiom,
( sP57(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP57(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_170,axiom,
( sP58(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP58(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_171,axiom,
( sP59(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP59(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_172,axiom,
( sP60(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP60(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_173,axiom,
( sP61(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP61(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_174,axiom,
( sP62(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP62(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_175,axiom,
( sP63(Eq_y_0,Eq_y_1)
| ~ sP63(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_176,axiom,
( sP64(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP64(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_177,axiom,
( sP65(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP65(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_178,axiom,
( sP66(Eq_y_0,Eq_y_1)
| ~ sP66(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_179,axiom,
( sP67(Eq_y_0,Eq_y_1)
| ~ sP67(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_180,axiom,
( sP68(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP68(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_181,axiom,
( sP69(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP69(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_182,axiom,
( sP70(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| ~ sP70(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7)
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_183,axiom,
( sP71(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP71(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_184,axiom,
( sP72(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP72(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_185,axiom,
( sP73(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8)
| ~ sP73(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8)
| Eq_x_8 != Eq_y_8
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_186,axiom,
( sP74(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP74(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_187,axiom,
( sP75(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP75(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_188,axiom,
( sP76(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP76(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_189,axiom,
( sP77(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP77(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_190,axiom,
( sP78(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP78(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_191,axiom,
( sP79(Eq_y_0,Eq_y_1)
| ~ sP79(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_192,axiom,
( sP80(Eq_y_0,Eq_y_1)
| ~ sP80(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_193,axiom,
( sP81(Eq_y_0)
| ~ sP81(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_194,axiom,
( sP82(Eq_y_0)
| ~ sP82(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_195,axiom,
( sP83(Eq_y_0,Eq_y_1)
| ~ sP83(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_196,axiom,
( sP84(Eq_y_0,Eq_y_1)
| ~ sP84(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_197,axiom,
( sP85(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP85(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_198,axiom,
( sP86(Eq_y_0,Eq_y_1)
| ~ sP86(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_199,axiom,
( sP87(Eq_y_0)
| ~ sP87(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_200,axiom,
( sP88(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP88(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_201,axiom,
( sP89(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP89(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_202,axiom,
( sP90(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP90(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_203,axiom,
( sP91(Eq_y_0,Eq_y_1)
| ~ sP91(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_204,axiom,
( sP92(Eq_y_0,Eq_y_1)
| ~ sP92(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_205,axiom,
( sP93(Eq_y_0,Eq_y_1)
| ~ sP93(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_206,axiom,
( sP94(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP94(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_207,axiom,
( sP95(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP95(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_208,axiom,
( sP96(Eq_y_0)
| ~ sP96(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_209,axiom,
( sP97(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP97(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_210,axiom,
( sP98(Eq_y_0,Eq_y_1)
| ~ sP98(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_211,axiom,
( sP99(Eq_y_0,Eq_y_1)
| ~ sP99(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_212,axiom,
( sP100(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP100(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_213,axiom,
( sP101(Eq_y_0)
| ~ sP101(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_214,axiom,
( sP102(Eq_y_0)
| ~ sP102(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_215,axiom,
( sP103(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP103(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_216,axiom,
( sP104(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP104(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_217,axiom,
( sP105(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP105(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_218,axiom,
( sP106(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP106(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_219,axiom,
( sP107(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP107(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU196+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n006.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 23:29:12 UTC 2026
% 0.10/0.37 % CPUTime :
% 43.79/44.03 % SZS status Theorem for theBenchmark
% 43.79/44.03 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------