%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU187+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:58:23 AM UTC 2026
% Result : Theorem 158.04s 158.30s
% Output : Proof 158.19s
% 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_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
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_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_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_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_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(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(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,conjecture,
( 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(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(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(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(t92_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
file('theBenchmark.p',t92_zfmisc_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] :
( ( 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_7_2,plain,
! [U_12,U_11] :
( ( U_12 = U_11
| ~ subset(U_11,U_12)
| ~ subset(U_12,U_11) )
& ( ( subset(U_11,U_12)
& subset(U_12,U_11) )
| U_12 != U_11 ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_16,U_14] :
( U_16 = U_14
| ~ subset(U_14,U_16)
| ~ subset(U_16,U_14) )
& ! [U_15,U_13] :
( ( subset(U_13,U_15)
& subset(U_15,U_13) )
| U_15 != U_13 ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
( ! [U_15,U_13] :
( subset(U_13,U_15)
| ~ sP0(U_15,U_13) )
& ! [U_15,U_13] :
( subset(U_15,U_13)
| ~ sP0(U_15,U_13) )
& ! [U_14,U_16] :
( U_16 = U_14
| ~ subset(U_14,U_16)
| ~ subset(U_16,U_14) )
& ! [U_15,U_13] :
( sP0(U_15,U_13)
| U_15 != U_13 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_7_3]) ).
cnf(f_7_5,plain,
( sP0(U_15,U_13)
| U_15 != U_13 ),
inference(clausify,[status(thm)],[f_7_4]) ).
cnf(f_7_6,plain,
( U_16 = U_14
| ~ subset(U_14,U_16)
| ~ subset(U_16,U_14) ),
inference(clausify,[status(thm)],[f_7_4]) ).
cnf(f_7_7,plain,
( subset(U_15,U_13)
| ~ sP0(U_15,U_13) ),
inference(clausify,[status(thm)],[f_7_4]) ).
cnf(f_7_8,plain,
( subset(U_13,U_15)
| ~ sP0(U_15,U_13) ),
inference(clausify,[status(thm)],[f_7_4]) ).
fof(f_8_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_8_2,plain,
! [U_23] :
( ( relation(U_23)
| ? [U_22] :
( ! [U_21,U_20] : U_22 != ordered_pair(U_21,U_20)
& in(U_22,U_23) ) )
& ( ! [U_19] :
( ? [U_18,U_17] : U_19 = ordered_pair(U_18,U_17)
| ~ in(U_19,U_23) )
| ~ relation(U_23) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_25] :
( relation(U_25)
| ? [U_22] :
( ! [U_21,U_20] : U_22 != ordered_pair(U_21,U_20)
& in(U_22,U_25) ) )
& ! [U_24] :
( ! [U_19] :
( ? [U_18,U_17] : U_19 = ordered_pair(U_18,U_17)
| ~ in(U_19,U_24) )
| ~ relation(U_24) ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
( ! [U_25] :
( relation(U_25)
| ? [U_22] :
( ! [U_21,U_20] : U_22 != ordered_pair(U_21,U_20)
& in(U_22,U_25) ) )
& ! [U_24] :
( ! [U_19] :
( ? [U_17] : U_19 = ordered_pair(sK1(U_24,U_19),U_17)
| ~ in(U_19,U_24) )
| ~ relation(U_24) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_18,sK1(U_24,U_19))],[f_8_3]) ).
fof(f_8_5,plain,
( ! [U_25] :
( relation(U_25)
| ? [U_22] :
( ! [U_21,U_20] : U_22 != ordered_pair(U_21,U_20)
& in(U_22,U_25) ) )
& ! [U_24] :
( ! [U_19] :
( U_19 = ordered_pair(sK1(U_24,U_19),sK2(U_24,U_19))
| ~ in(U_19,U_24) )
| ~ relation(U_24) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_17,sK2(U_24,U_19))],[f_8_4]) ).
fof(f_8_6,plain,
( ! [U_25] :
( relation(U_25)
| ( ! [U_21,U_20] : sK3(U_25) != ordered_pair(U_21,U_20)
& in(sK3(U_25),U_25) ) )
& ! [U_24] :
( ! [U_19] :
( U_19 = ordered_pair(sK1(U_24,U_19),sK2(U_24,U_19))
| ~ in(U_19,U_24) )
| ~ relation(U_24) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_22,sK3(U_25))],[f_8_5]) ).
fof(f_8_7,plain,
( ! [U_25,U_20,U_21] :
( sK3(U_25) != ordered_pair(U_21,U_20)
| ~ sP1(U_25,U_20,U_21) )
& ! [U_25,U_20,U_21] :
( in(sK3(U_25),U_25)
| ~ sP1(U_25,U_20,U_21) )
& ! [U_25,U_20,U_21] :
( relation(U_25)
| sP1(U_25,U_20,U_21) )
& ! [U_24,U_19] :
( U_19 = ordered_pair(sK1(U_24,U_19),sK2(U_24,U_19))
| ~ in(U_19,U_24)
| ~ relation(U_24) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_8_6]) ).
cnf(f_8_8,plain,
( U_19 = ordered_pair(sK1(U_24,U_19),sK2(U_24,U_19))
| ~ in(U_19,U_24)
| ~ relation(U_24) ),
inference(clausify,[status(thm)],[f_8_7]) ).
cnf(f_8_9,plain,
( relation(U_25)
| sP1(U_25,U_20,U_21) ),
inference(clausify,[status(thm)],[f_8_7]) ).
cnf(f_8_10,plain,
( in(sK3(U_25),U_25)
| ~ sP1(U_25,U_20,U_21) ),
inference(clausify,[status(thm)],[f_8_7]) ).
cnf(f_8_11,plain,
( sK3(U_25) != ordered_pair(U_21,U_20)
| ~ sP1(U_25,U_20,U_21) ),
inference(clausify,[status(thm)],[f_8_7]) ).
fof(f_9_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_9_2,plain,
! [U_33,U_32] :
( ( ( ( U_32 = set_meet(U_33)
| U_32 != empty_set )
& ( U_32 = empty_set
| U_32 != set_meet(U_33) ) )
| U_33 != empty_set )
& ( ( ( U_32 = set_meet(U_33)
| ? [U_31] :
( ( ~ in(U_31,U_32)
& ! [U_30] :
( in(U_31,U_30)
| ~ in(U_30,U_33) ) )
| ( ? [U_29] :
( ~ in(U_31,U_29)
& in(U_29,U_33) )
& in(U_31,U_32) ) ) )
& ( ! [U_28] :
( ( in(U_28,U_32)
| ? [U_27] :
( ~ in(U_28,U_27)
& in(U_27,U_33) ) )
& ( ! [U_26] :
( in(U_28,U_26)
| ~ in(U_26,U_33) )
| ~ in(U_28,U_32) ) )
| U_32 != set_meet(U_33) ) )
| U_33 = empty_set ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_45] :
( ( ! [U_43] :
( U_43 = set_meet(U_45)
| U_43 != empty_set )
& ! [U_42] :
( U_42 = empty_set
| U_42 != set_meet(U_45) ) )
| U_45 != empty_set )
& ! [U_44] :
( ( ! [U_41] :
( U_41 = set_meet(U_44)
| ? [U_37] :
( ~ in(U_37,U_41)
& ! [U_30] :
( in(U_37,U_30)
| ~ in(U_30,U_44) ) )
| ? [U_36] :
( ? [U_29] :
( ~ in(U_36,U_29)
& in(U_29,U_44) )
& in(U_36,U_41) ) )
& ! [U_40] :
( ( ! [U_35] :
( in(U_35,U_40)
| ? [U_27] :
( ~ in(U_35,U_27)
& in(U_27,U_44) ) )
& ! [U_34] :
( ! [U_26] :
( in(U_34,U_26)
| ~ in(U_26,U_44) )
| ~ in(U_34,U_40) ) )
| U_40 != set_meet(U_44) ) )
| U_44 = empty_set ) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
fof(f_9_4,plain,
( ! [U_45] :
( ( ! [U_43] :
( U_43 = set_meet(U_45)
| U_43 != empty_set )
& ! [U_42] :
( U_42 = empty_set
| U_42 != set_meet(U_45) ) )
| U_45 != empty_set )
& ! [U_44] :
( ( ! [U_41] :
( U_41 = set_meet(U_44)
| ? [U_37] :
( ~ in(U_37,U_41)
& ! [U_30] :
( in(U_37,U_30)
| ~ in(U_30,U_44) ) )
| ? [U_36] :
( ? [U_29] :
( ~ in(U_36,U_29)
& in(U_29,U_44) )
& in(U_36,U_41) ) )
& ! [U_40] :
( ( ! [U_35] :
( in(U_35,U_40)
| ( ~ in(U_35,sK4(U_44,U_40,U_35))
& in(sK4(U_44,U_40,U_35),U_44) ) )
& ! [U_34] :
( ! [U_26] :
( in(U_34,U_26)
| ~ in(U_26,U_44) )
| ~ in(U_34,U_40) ) )
| U_40 != set_meet(U_44) ) )
| U_44 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_27,sK4(U_44,U_40,U_35))],[f_9_3]) ).
fof(f_9_5,plain,
( ! [U_45] :
( ( ! [U_43] :
( U_43 = set_meet(U_45)
| U_43 != empty_set )
& ! [U_42] :
( U_42 = empty_set
| U_42 != set_meet(U_45) ) )
| U_45 != empty_set )
& ! [U_44] :
( ( ! [U_41] :
( U_41 = set_meet(U_44)
| ? [U_37] :
( ~ in(U_37,U_41)
& ! [U_30] :
( in(U_37,U_30)
| ~ in(U_30,U_44) ) )
| ( ? [U_29] :
( ~ in(sK5(U_44,U_41),U_29)
& in(U_29,U_44) )
& in(sK5(U_44,U_41),U_41) ) )
& ! [U_40] :
( ( ! [U_35] :
( in(U_35,U_40)
| ( ~ in(U_35,sK4(U_44,U_40,U_35))
& in(sK4(U_44,U_40,U_35),U_44) ) )
& ! [U_34] :
( ! [U_26] :
( in(U_34,U_26)
| ~ in(U_26,U_44) )
| ~ in(U_34,U_40) ) )
| U_40 != set_meet(U_44) ) )
| U_44 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_36,sK5(U_44,U_41))],[f_9_4]) ).
fof(f_9_6,plain,
( ! [U_45] :
( ( ! [U_43] :
( U_43 = set_meet(U_45)
| U_43 != empty_set )
& ! [U_42] :
( U_42 = empty_set
| U_42 != set_meet(U_45) ) )
| U_45 != empty_set )
& ! [U_44] :
( ( ! [U_41] :
( U_41 = set_meet(U_44)
| ? [U_37] :
( ~ in(U_37,U_41)
& ! [U_30] :
( in(U_37,U_30)
| ~ in(U_30,U_44) ) )
| ( ~ in(sK5(U_44,U_41),sK6(U_44,U_41))
& in(sK6(U_44,U_41),U_44)
& in(sK5(U_44,U_41),U_41) ) )
& ! [U_40] :
( ( ! [U_35] :
( in(U_35,U_40)
| ( ~ in(U_35,sK4(U_44,U_40,U_35))
& in(sK4(U_44,U_40,U_35),U_44) ) )
& ! [U_34] :
( ! [U_26] :
( in(U_34,U_26)
| ~ in(U_26,U_44) )
| ~ in(U_34,U_40) ) )
| U_40 != set_meet(U_44) ) )
| U_44 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_29,sK6(U_44,U_41))],[f_9_5]) ).
fof(f_9_7,plain,
( ! [U_45] :
( ( ! [U_43] :
( U_43 = set_meet(U_45)
| U_43 != empty_set )
& ! [U_42] :
( U_42 = empty_set
| U_42 != set_meet(U_45) ) )
| U_45 != empty_set )
& ! [U_44] :
( ( ! [U_41] :
( U_41 = set_meet(U_44)
| ( ~ in(sK7(U_44,U_41),U_41)
& ! [U_30] :
( in(sK7(U_44,U_41),U_30)
| ~ in(U_30,U_44) ) )
| ( ~ in(sK5(U_44,U_41),sK6(U_44,U_41))
& in(sK6(U_44,U_41),U_44)
& in(sK5(U_44,U_41),U_41) ) )
& ! [U_40] :
( ( ! [U_35] :
( in(U_35,U_40)
| ( ~ in(U_35,sK4(U_44,U_40,U_35))
& in(sK4(U_44,U_40,U_35),U_44) ) )
& ! [U_34] :
( ! [U_26] :
( in(U_34,U_26)
| ~ in(U_26,U_44) )
| ~ in(U_34,U_40) ) )
| U_40 != set_meet(U_44) ) )
| U_44 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_37,sK7(U_44,U_41))],[f_9_6]) ).
fof(f_9_8,plain,
( ! [U_42,U_45,U_43] :
( U_43 = set_meet(U_45)
| U_43 != empty_set
| ~ sP7(U_42,U_45,U_43) )
& ! [U_42,U_45,U_43] :
( U_42 = empty_set
| U_42 != set_meet(U_45)
| ~ sP7(U_42,U_45,U_43) )
& ! [U_41,U_30,U_44] :
( ~ in(sK7(U_44,U_41),U_41)
| ~ sP5(U_41,U_30,U_44) )
& ! [U_41,U_30,U_44] :
( in(sK7(U_44,U_41),U_30)
| ~ in(U_30,U_44)
| ~ sP5(U_41,U_30,U_44) )
& ! [U_41,U_44] :
( ~ in(sK5(U_44,U_41),sK6(U_44,U_41))
| ~ sP4(U_41,U_44) )
& ! [U_41,U_44] :
( in(sK6(U_44,U_41),U_44)
| ~ sP4(U_41,U_44) )
& ! [U_41,U_44] :
( in(sK5(U_44,U_41),U_41)
| ~ sP4(U_41,U_44) )
& ! [U_35,U_44,U_40] :
( ~ in(U_35,sK4(U_44,U_40,U_35))
| ~ sP2(U_35,U_44,U_40) )
& ! [U_35,U_44,U_40] :
( in(sK4(U_44,U_40,U_35),U_44)
| ~ sP2(U_35,U_44,U_40) )
& ! [U_26,U_35,U_34,U_44,U_40] :
( in(U_35,U_40)
| sP2(U_35,U_44,U_40)
| ~ sP3(U_26,U_35,U_34,U_44,U_40) )
& ! [U_26,U_35,U_34,U_44,U_40] :
( in(U_34,U_26)
| ~ in(U_26,U_44)
| ~ in(U_34,U_40)
| ~ sP3(U_26,U_35,U_34,U_44,U_40) )
& ! [U_41,U_30,U_26,U_35,U_34,U_44,U_40] :
( U_41 = set_meet(U_44)
| sP5(U_41,U_30,U_44)
| sP4(U_41,U_44)
| ~ sP6(U_41,U_30,U_26,U_35,U_34,U_44,U_40) )
& ! [U_41,U_30,U_26,U_35,U_34,U_44,U_40] :
( sP3(U_26,U_35,U_34,U_44,U_40)
| U_40 != set_meet(U_44)
| ~ sP6(U_41,U_30,U_26,U_35,U_34,U_44,U_40) )
& ! [U_42,U_45,U_43] :
( sP7(U_42,U_45,U_43)
| U_45 != empty_set )
& ! [U_41,U_30,U_26,U_35,U_34,U_44,U_40] :
( sP6(U_41,U_30,U_26,U_35,U_34,U_44,U_40)
| U_44 = empty_set ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2,sP3,sP4,sP5,sP6,sP7])],[f_9_7]) ).
cnf(f_9_9,plain,
( sP6(U_41,U_30,U_26,U_35,U_34,U_44,U_40)
| U_44 = empty_set ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_10,plain,
( sP7(U_42,U_45,U_43)
| U_45 != empty_set ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_11,plain,
( sP3(U_26,U_35,U_34,U_44,U_40)
| U_40 != set_meet(U_44)
| ~ sP6(U_41,U_30,U_26,U_35,U_34,U_44,U_40) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_12,plain,
( U_41 = set_meet(U_44)
| sP5(U_41,U_30,U_44)
| sP4(U_41,U_44)
| ~ sP6(U_41,U_30,U_26,U_35,U_34,U_44,U_40) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_13,plain,
( in(U_34,U_26)
| ~ in(U_26,U_44)
| ~ in(U_34,U_40)
| ~ sP3(U_26,U_35,U_34,U_44,U_40) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_14,plain,
( in(U_35,U_40)
| sP2(U_35,U_44,U_40)
| ~ sP3(U_26,U_35,U_34,U_44,U_40) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_15,plain,
( in(sK4(U_44,U_40,U_35),U_44)
| ~ sP2(U_35,U_44,U_40) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_16,plain,
( ~ in(U_35,sK4(U_44,U_40,U_35))
| ~ sP2(U_35,U_44,U_40) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_17,plain,
( in(sK5(U_44,U_41),U_41)
| ~ sP4(U_41,U_44) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_18,plain,
( in(sK6(U_44,U_41),U_44)
| ~ sP4(U_41,U_44) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_19,plain,
( ~ in(sK5(U_44,U_41),sK6(U_44,U_41))
| ~ sP4(U_41,U_44) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_20,plain,
( in(sK7(U_44,U_41),U_30)
| ~ in(U_30,U_44)
| ~ sP5(U_41,U_30,U_44) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_21,plain,
( ~ in(sK7(U_44,U_41),U_41)
| ~ sP5(U_41,U_30,U_44) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_22,plain,
( U_42 = empty_set
| U_42 != set_meet(U_45)
| ~ sP7(U_42,U_45,U_43) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_23,plain,
( U_43 = set_meet(U_45)
| U_43 != empty_set
| ~ sP7(U_42,U_45,U_43) ),
inference(clausify,[status(thm)],[f_9_8]) ).
fof(f_10_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_10_2,plain,
! [U_49,U_48] :
( ( U_48 = singleton(U_49)
| ? [U_47] :
( ( ~ in(U_47,U_48)
& U_47 = U_49 )
| ( U_47 != U_49
& in(U_47,U_48) ) ) )
& ( ! [U_46] :
( ( in(U_46,U_48)
| U_46 != U_49 )
& ( U_46 = U_49
| ~ in(U_46,U_48) ) )
| U_48 != singleton(U_49) ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_57,U_55] :
( U_55 = singleton(U_57)
| ? [U_53] :
( ~ in(U_53,U_55)
& U_53 = U_57 )
| ? [U_52] :
( U_52 != U_57
& in(U_52,U_55) ) )
& ! [U_56,U_54] :
( ( ! [U_51] :
( in(U_51,U_54)
| U_51 != U_56 )
& ! [U_50] :
( U_50 = U_56
| ~ in(U_50,U_54) ) )
| U_54 != singleton(U_56) ) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
fof(f_10_4,plain,
( ! [U_57,U_55] :
( U_55 = singleton(U_57)
| ? [U_53] :
( ~ in(U_53,U_55)
& U_53 = U_57 )
| ( sK8(U_57,U_55) != U_57
& in(sK8(U_57,U_55),U_55) ) )
& ! [U_56,U_54] :
( ( ! [U_51] :
( in(U_51,U_54)
| U_51 != U_56 )
& ! [U_50] :
( U_50 = U_56
| ~ in(U_50,U_54) ) )
| U_54 != singleton(U_56) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_52,sK8(U_57,U_55))],[f_10_3]) ).
fof(f_10_5,plain,
( ! [U_57,U_55] :
( U_55 = singleton(U_57)
| ( ~ in(sK9(U_57,U_55),U_55)
& sK9(U_57,U_55) = U_57 )
| ( sK8(U_57,U_55) != U_57
& in(sK8(U_57,U_55),U_55) ) )
& ! [U_56,U_54] :
( ( ! [U_51] :
( in(U_51,U_54)
| U_51 != U_56 )
& ! [U_50] :
( U_50 = U_56
| ~ in(U_50,U_54) ) )
| U_54 != singleton(U_56) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_53,sK9(U_57,U_55))],[f_10_4]) ).
fof(f_10_6,plain,
( ! [U_55,U_57] :
( ~ in(sK9(U_57,U_55),U_55)
| ~ sP10(U_55,U_57) )
& ! [U_55,U_57] :
( sK9(U_57,U_55) = U_57
| ~ sP10(U_55,U_57) )
& ! [U_55,U_57] :
( sK8(U_57,U_55) != U_57
| ~ sP9(U_55,U_57) )
& ! [U_55,U_57] :
( in(sK8(U_57,U_55),U_55)
| ~ sP9(U_55,U_57) )
& ! [U_56,U_50,U_51,U_54] :
( in(U_51,U_54)
| U_51 != U_56
| ~ sP8(U_56,U_50,U_51,U_54) )
& ! [U_56,U_50,U_51,U_54] :
( U_50 = U_56
| ~ in(U_50,U_54)
| ~ sP8(U_56,U_50,U_51,U_54) )
& ! [U_55,U_57] :
( U_55 = singleton(U_57)
| sP10(U_55,U_57)
| sP9(U_55,U_57) )
& ! [U_56,U_50,U_51,U_54] :
( sP8(U_56,U_50,U_51,U_54)
| U_54 != singleton(U_56) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8,sP9,sP10])],[f_10_5]) ).
cnf(f_10_7,plain,
( sP8(U_56,U_50,U_51,U_54)
| U_54 != singleton(U_56) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_8,plain,
( U_55 = singleton(U_57)
| sP10(U_55,U_57)
| sP9(U_55,U_57) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_9,plain,
( U_50 = U_56
| ~ in(U_50,U_54)
| ~ sP8(U_56,U_50,U_51,U_54) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_10,plain,
( in(U_51,U_54)
| U_51 != U_56
| ~ sP8(U_56,U_50,U_51,U_54) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_11,plain,
( in(sK8(U_57,U_55),U_55)
| ~ sP9(U_55,U_57) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_12,plain,
( sK8(U_57,U_55) != U_57
| ~ sP9(U_55,U_57) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_13,plain,
( sK9(U_57,U_55) = U_57
| ~ sP10(U_55,U_57) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_14,plain,
( ~ in(sK9(U_57,U_55),U_55)
| ~ sP10(U_55,U_57) ),
inference(clausify,[status(thm)],[f_10_6]) ).
fof(f_11_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_11_2,plain,
! [U_60] :
( ( U_60 = empty_set
| ? [U_59] : in(U_59,U_60) )
& ( ! [U_58] : ~ in(U_58,U_60)
| U_60 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
( ! [U_62] :
( U_62 = empty_set
| ? [U_59] : in(U_59,U_62) )
& ! [U_61] :
( ! [U_58] : ~ in(U_58,U_61)
| U_61 != empty_set ) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
fof(f_11_4,plain,
( ! [U_62] :
( U_62 = empty_set
| in(sK10(U_62),U_62) )
& ! [U_61] :
( ! [U_58] : ~ in(U_58,U_61)
| U_61 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_59,sK10(U_62))],[f_11_3]) ).
fof(f_11_5,plain,
( ! [U_62] :
( U_62 = empty_set
| in(sK10(U_62),U_62) )
& ! [U_58,U_61] :
( ~ in(U_58,U_61)
| U_61 != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_11_4]) ).
cnf(f_11_6,plain,
( ~ in(U_58,U_61)
| U_61 != empty_set ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_7,plain,
( U_62 = empty_set
| in(sK10(U_62),U_62) ),
inference(clausify,[status(thm)],[f_11_5]) ).
fof(f_12_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_12_2,plain,
! [U_66,U_65] :
( ( U_65 = powerset(U_66)
| ? [U_64] :
( ( ~ in(U_64,U_65)
& subset(U_64,U_66) )
| ( ~ subset(U_64,U_66)
& in(U_64,U_65) ) ) )
& ( ! [U_63] :
( ( in(U_63,U_65)
| ~ subset(U_63,U_66) )
& ( subset(U_63,U_66)
| ~ in(U_63,U_65) ) )
| U_65 != powerset(U_66) ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_74,U_72] :
( U_72 = powerset(U_74)
| ? [U_70] :
( ~ in(U_70,U_72)
& subset(U_70,U_74) )
| ? [U_69] :
( ~ subset(U_69,U_74)
& in(U_69,U_72) ) )
& ! [U_73,U_71] :
( ( ! [U_68] :
( in(U_68,U_71)
| ~ subset(U_68,U_73) )
& ! [U_67] :
( subset(U_67,U_73)
| ~ in(U_67,U_71) ) )
| U_71 != powerset(U_73) ) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
( ! [U_74,U_72] :
( U_72 = powerset(U_74)
| ? [U_70] :
( ~ in(U_70,U_72)
& subset(U_70,U_74) )
| ( ~ subset(sK11(U_74,U_72),U_74)
& in(sK11(U_74,U_72),U_72) ) )
& ! [U_73,U_71] :
( ( ! [U_68] :
( in(U_68,U_71)
| ~ subset(U_68,U_73) )
& ! [U_67] :
( subset(U_67,U_73)
| ~ in(U_67,U_71) ) )
| U_71 != powerset(U_73) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_69,sK11(U_74,U_72))],[f_12_3]) ).
fof(f_12_5,plain,
( ! [U_74,U_72] :
( U_72 = powerset(U_74)
| ( ~ in(sK12(U_74,U_72),U_72)
& subset(sK12(U_74,U_72),U_74) )
| ( ~ subset(sK11(U_74,U_72),U_74)
& in(sK11(U_74,U_72),U_72) ) )
& ! [U_73,U_71] :
( ( ! [U_68] :
( in(U_68,U_71)
| ~ subset(U_68,U_73) )
& ! [U_67] :
( subset(U_67,U_73)
| ~ in(U_67,U_71) ) )
| U_71 != powerset(U_73) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_70,sK12(U_74,U_72))],[f_12_4]) ).
fof(f_12_6,plain,
( ! [U_74,U_72] :
( ~ in(sK12(U_74,U_72),U_72)
| ~ sP13(U_74,U_72) )
& ! [U_74,U_72] :
( subset(sK12(U_74,U_72),U_74)
| ~ sP13(U_74,U_72) )
& ! [U_74,U_72] :
( ~ subset(sK11(U_74,U_72),U_74)
| ~ sP12(U_74,U_72) )
& ! [U_74,U_72] :
( in(sK11(U_74,U_72),U_72)
| ~ sP12(U_74,U_72) )
& ! [U_67,U_68,U_71,U_73] :
( in(U_68,U_71)
| ~ subset(U_68,U_73)
| ~ sP11(U_67,U_68,U_71,U_73) )
& ! [U_67,U_68,U_71,U_73] :
( subset(U_67,U_73)
| ~ in(U_67,U_71)
| ~ sP11(U_67,U_68,U_71,U_73) )
& ! [U_74,U_72] :
( U_72 = powerset(U_74)
| sP13(U_74,U_72)
| sP12(U_74,U_72) )
& ! [U_67,U_68,U_71,U_73] :
( sP11(U_67,U_68,U_71,U_73)
| U_71 != powerset(U_73) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11,sP12,sP13])],[f_12_5]) ).
cnf(f_12_7,plain,
( sP11(U_67,U_68,U_71,U_73)
| U_71 != powerset(U_73) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_8,plain,
( U_72 = powerset(U_74)
| sP13(U_74,U_72)
| sP12(U_74,U_72) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_9,plain,
( subset(U_67,U_73)
| ~ in(U_67,U_71)
| ~ sP11(U_67,U_68,U_71,U_73) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_10,plain,
( in(U_68,U_71)
| ~ subset(U_68,U_73)
| ~ sP11(U_67,U_68,U_71,U_73) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_11,plain,
( in(sK11(U_74,U_72),U_72)
| ~ sP12(U_74,U_72) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_12,plain,
( ~ subset(sK11(U_74,U_72),U_74)
| ~ sP12(U_74,U_72) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_13,plain,
( subset(sK12(U_74,U_72),U_74)
| ~ sP13(U_74,U_72) ),
inference(clausify,[status(thm)],[f_12_6]) ).
cnf(f_12_14,plain,
( ~ in(sK12(U_74,U_72),U_72)
| ~ sP13(U_74,U_72) ),
inference(clausify,[status(thm)],[f_12_6]) ).
fof(f_13_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_13_2,plain,
! [U_76,U_75] :
( ( ( ( element(U_75,U_76)
| ~ empty(U_75) )
& ( empty(U_75)
| ~ element(U_75,U_76) ) )
| ~ empty(U_76) )
& ( ( ( element(U_75,U_76)
| ~ in(U_75,U_76) )
& ( in(U_75,U_76)
| ~ element(U_75,U_76) ) )
| empty(U_76) ) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_84] :
( ( ! [U_82] :
( element(U_82,U_84)
| ~ empty(U_82) )
& ! [U_81] :
( empty(U_81)
| ~ element(U_81,U_84) ) )
| ~ empty(U_84) )
& ! [U_83] :
( ( ! [U_80] :
( element(U_80,U_83)
| ~ in(U_80,U_83) )
& ! [U_79] :
( in(U_79,U_83)
| ~ element(U_79,U_83) ) )
| empty(U_83) ) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
fof(f_13_4,plain,
( ! [U_82,U_81,U_84] :
( element(U_82,U_84)
| ~ empty(U_82)
| ~ sP15(U_82,U_81,U_84) )
& ! [U_82,U_81,U_84] :
( empty(U_81)
| ~ element(U_81,U_84)
| ~ sP15(U_82,U_81,U_84) )
& ! [U_79,U_80,U_83] :
( element(U_80,U_83)
| ~ in(U_80,U_83)
| ~ sP14(U_79,U_80,U_83) )
& ! [U_79,U_80,U_83] :
( in(U_79,U_83)
| ~ element(U_79,U_83)
| ~ sP14(U_79,U_80,U_83) )
& ! [U_82,U_81,U_84] :
( sP15(U_82,U_81,U_84)
| ~ empty(U_84) )
& ! [U_79,U_80,U_83] :
( sP14(U_79,U_80,U_83)
| empty(U_83) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14,sP15])],[f_13_3]) ).
cnf(f_13_5,plain,
( sP14(U_79,U_80,U_83)
| empty(U_83) ),
inference(clausify,[status(thm)],[f_13_4]) ).
cnf(f_13_6,plain,
( sP15(U_82,U_81,U_84)
| ~ empty(U_84) ),
inference(clausify,[status(thm)],[f_13_4]) ).
cnf(f_13_7,plain,
( in(U_79,U_83)
| ~ element(U_79,U_83)
| ~ sP14(U_79,U_80,U_83) ),
inference(clausify,[status(thm)],[f_13_4]) ).
cnf(f_13_8,plain,
( element(U_80,U_83)
| ~ in(U_80,U_83)
| ~ sP14(U_79,U_80,U_83) ),
inference(clausify,[status(thm)],[f_13_4]) ).
cnf(f_13_9,plain,
( empty(U_81)
| ~ element(U_81,U_84)
| ~ sP15(U_82,U_81,U_84) ),
inference(clausify,[status(thm)],[f_13_4]) ).
cnf(f_13_10,plain,
( element(U_82,U_84)
| ~ empty(U_82)
| ~ sP15(U_82,U_81,U_84) ),
inference(clausify,[status(thm)],[f_13_4]) ).
fof(f_14_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_14_2,plain,
! [U_89,U_88,U_87] :
( ( U_87 = unordered_pair(U_89,U_88)
| ? [U_86] :
( ( ~ in(U_86,U_87)
& ( U_86 = U_88
| U_86 = U_89 ) )
| ( U_86 != U_88
& U_86 != U_89
& in(U_86,U_87) ) ) )
& ( ! [U_85] :
( ( in(U_85,U_87)
| ( U_85 != U_88
& U_85 != U_89 ) )
& ( U_85 = U_88
| U_85 = U_89
| ~ in(U_85,U_87) ) )
| U_87 != unordered_pair(U_89,U_88) ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_99,U_97,U_95] :
( U_95 = unordered_pair(U_99,U_97)
| ? [U_93] :
( ~ in(U_93,U_95)
& ( U_93 = U_97
| U_93 = U_99 ) )
| ? [U_92] :
( U_92 != U_97
& U_92 != U_99
& in(U_92,U_95) ) )
& ! [U_98,U_96,U_94] :
( ( ! [U_91] :
( in(U_91,U_94)
| ( U_91 != U_96
& U_91 != U_98 ) )
& ! [U_90] :
( U_90 = U_96
| U_90 = U_98
| ~ in(U_90,U_94) ) )
| U_94 != unordered_pair(U_98,U_96) ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
fof(f_14_4,plain,
( ! [U_99,U_97,U_95] :
( U_95 = unordered_pair(U_99,U_97)
| ? [U_93] :
( ~ in(U_93,U_95)
& ( U_93 = U_97
| U_93 = U_99 ) )
| ( sK13(U_99,U_97,U_95) != U_97
& sK13(U_99,U_97,U_95) != U_99
& in(sK13(U_99,U_97,U_95),U_95) ) )
& ! [U_98,U_96,U_94] :
( ( ! [U_91] :
( in(U_91,U_94)
| ( U_91 != U_96
& U_91 != U_98 ) )
& ! [U_90] :
( U_90 = U_96
| U_90 = U_98
| ~ in(U_90,U_94) ) )
| U_94 != unordered_pair(U_98,U_96) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_92,sK13(U_99,U_97,U_95))],[f_14_3]) ).
fof(f_14_5,plain,
( ! [U_99,U_97,U_95] :
( U_95 = unordered_pair(U_99,U_97)
| ( ~ in(sK14(U_99,U_97,U_95),U_95)
& ( sK14(U_99,U_97,U_95) = U_97
| sK14(U_99,U_97,U_95) = U_99 ) )
| ( sK13(U_99,U_97,U_95) != U_97
& sK13(U_99,U_97,U_95) != U_99
& in(sK13(U_99,U_97,U_95),U_95) ) )
& ! [U_98,U_96,U_94] :
( ( ! [U_91] :
( in(U_91,U_94)
| ( U_91 != U_96
& U_91 != U_98 ) )
& ! [U_90] :
( U_90 = U_96
| U_90 = U_98
| ~ in(U_90,U_94) ) )
| U_94 != unordered_pair(U_98,U_96) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_93,sK14(U_99,U_97,U_95))],[f_14_4]) ).
fof(f_14_6,plain,
( ! [U_97,U_95,U_99] :
( ~ in(sK14(U_99,U_97,U_95),U_95)
| ~ sP19(U_97,U_95,U_99) )
& ! [U_97,U_95,U_99] :
( sK14(U_99,U_97,U_95) = U_97
| sK14(U_99,U_97,U_95) = U_99
| ~ sP19(U_97,U_95,U_99) )
& ! [U_97,U_95,U_99] :
( sK13(U_99,U_97,U_95) != U_97
| ~ sP18(U_97,U_95,U_99) )
& ! [U_97,U_95,U_99] :
( sK13(U_99,U_97,U_95) != U_99
| ~ sP18(U_97,U_95,U_99) )
& ! [U_97,U_95,U_99] :
( in(sK13(U_99,U_97,U_95),U_95)
| ~ sP18(U_97,U_95,U_99) )
& ! [U_98,U_96,U_91] :
( U_91 != U_96
| ~ sP16(U_98,U_96,U_91) )
& ! [U_98,U_96,U_91] :
( U_91 != U_98
| ~ sP16(U_98,U_96,U_91) )
& ! [U_98,U_90,U_96,U_94,U_91] :
( in(U_91,U_94)
| sP16(U_98,U_96,U_91)
| ~ sP17(U_98,U_90,U_96,U_94,U_91) )
& ! [U_98,U_90,U_96,U_94,U_91] :
( U_90 = U_96
| U_90 = U_98
| ~ in(U_90,U_94)
| ~ sP17(U_98,U_90,U_96,U_94,U_91) )
& ! [U_97,U_95,U_99] :
( U_95 = unordered_pair(U_99,U_97)
| sP19(U_97,U_95,U_99)
| sP18(U_97,U_95,U_99) )
& ! [U_98,U_90,U_96,U_94,U_91] :
( sP17(U_98,U_90,U_96,U_94,U_91)
| U_94 != unordered_pair(U_98,U_96) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16,sP17,sP18,sP19])],[f_14_5]) ).
cnf(f_14_7,plain,
( sP17(U_98,U_90,U_96,U_94,U_91)
| U_94 != unordered_pair(U_98,U_96) ),
inference(clausify,[status(thm)],[f_14_6]) ).
cnf(f_14_8,plain,
( U_95 = unordered_pair(U_99,U_97)
| sP19(U_97,U_95,U_99)
| sP18(U_97,U_95,U_99) ),
inference(clausify,[status(thm)],[f_14_6]) ).
cnf(f_14_9,plain,
( U_90 = U_96
| U_90 = U_98
| ~ in(U_90,U_94)
| ~ sP17(U_98,U_90,U_96,U_94,U_91) ),
inference(clausify,[status(thm)],[f_14_6]) ).
cnf(f_14_10,plain,
( in(U_91,U_94)
| sP16(U_98,U_96,U_91)
| ~ sP17(U_98,U_90,U_96,U_94,U_91) ),
inference(clausify,[status(thm)],[f_14_6]) ).
cnf(f_14_11,plain,
( U_91 != U_98
| ~ sP16(U_98,U_96,U_91) ),
inference(clausify,[status(thm)],[f_14_6]) ).
cnf(f_14_12,plain,
( U_91 != U_96
| ~ sP16(U_98,U_96,U_91) ),
inference(clausify,[status(thm)],[f_14_6]) ).
cnf(f_14_13,plain,
( in(sK13(U_99,U_97,U_95),U_95)
| ~ sP18(U_97,U_95,U_99) ),
inference(clausify,[status(thm)],[f_14_6]) ).
cnf(f_14_14,plain,
( sK13(U_99,U_97,U_95) != U_99
| ~ sP18(U_97,U_95,U_99) ),
inference(clausify,[status(thm)],[f_14_6]) ).
cnf(f_14_15,plain,
( sK13(U_99,U_97,U_95) != U_97
| ~ sP18(U_97,U_95,U_99) ),
inference(clausify,[status(thm)],[f_14_6]) ).
cnf(f_14_16,plain,
( sK14(U_99,U_97,U_95) = U_97
| sK14(U_99,U_97,U_95) = U_99
| ~ sP19(U_97,U_95,U_99) ),
inference(clausify,[status(thm)],[f_14_6]) ).
cnf(f_14_17,plain,
( ~ in(sK14(U_99,U_97,U_95),U_95)
| ~ sP19(U_97,U_95,U_99) ),
inference(clausify,[status(thm)],[f_14_6]) ).
fof(f_15_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_15_2,plain,
! [U_104,U_103,U_102] :
( ( U_102 = set_union2(U_104,U_103)
| ? [U_101] :
( ( ~ in(U_101,U_102)
& ( in(U_101,U_103)
| in(U_101,U_104) ) )
| ( ~ in(U_101,U_103)
& ~ in(U_101,U_104)
& in(U_101,U_102) ) ) )
& ( ! [U_100] :
( ( in(U_100,U_102)
| ( ~ in(U_100,U_103)
& ~ in(U_100,U_104) ) )
& ( in(U_100,U_103)
| in(U_100,U_104)
| ~ in(U_100,U_102) ) )
| U_102 != set_union2(U_104,U_103) ) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ! [U_114,U_112,U_110] :
( U_110 = set_union2(U_114,U_112)
| ? [U_108] :
( ~ in(U_108,U_110)
& ( in(U_108,U_112)
| in(U_108,U_114) ) )
| ? [U_107] :
( ~ in(U_107,U_112)
& ~ in(U_107,U_114)
& in(U_107,U_110) ) )
& ! [U_113,U_111,U_109] :
( ( ! [U_106] :
( in(U_106,U_109)
| ( ~ in(U_106,U_111)
& ~ in(U_106,U_113) ) )
& ! [U_105] :
( in(U_105,U_111)
| in(U_105,U_113)
| ~ in(U_105,U_109) ) )
| U_109 != set_union2(U_113,U_111) ) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
fof(f_15_4,plain,
( ! [U_114,U_112,U_110] :
( U_110 = set_union2(U_114,U_112)
| ? [U_108] :
( ~ in(U_108,U_110)
& ( in(U_108,U_112)
| in(U_108,U_114) ) )
| ( ~ in(sK15(U_114,U_112,U_110),U_112)
& ~ in(sK15(U_114,U_112,U_110),U_114)
& in(sK15(U_114,U_112,U_110),U_110) ) )
& ! [U_113,U_111,U_109] :
( ( ! [U_106] :
( in(U_106,U_109)
| ( ~ in(U_106,U_111)
& ~ in(U_106,U_113) ) )
& ! [U_105] :
( in(U_105,U_111)
| in(U_105,U_113)
| ~ in(U_105,U_109) ) )
| U_109 != set_union2(U_113,U_111) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_107,sK15(U_114,U_112,U_110))],[f_15_3]) ).
fof(f_15_5,plain,
( ! [U_114,U_112,U_110] :
( U_110 = set_union2(U_114,U_112)
| ( ~ in(sK16(U_114,U_112,U_110),U_110)
& ( in(sK16(U_114,U_112,U_110),U_112)
| in(sK16(U_114,U_112,U_110),U_114) ) )
| ( ~ in(sK15(U_114,U_112,U_110),U_112)
& ~ in(sK15(U_114,U_112,U_110),U_114)
& in(sK15(U_114,U_112,U_110),U_110) ) )
& ! [U_113,U_111,U_109] :
( ( ! [U_106] :
( in(U_106,U_109)
| ( ~ in(U_106,U_111)
& ~ in(U_106,U_113) ) )
& ! [U_105] :
( in(U_105,U_111)
| in(U_105,U_113)
| ~ in(U_105,U_109) ) )
| U_109 != set_union2(U_113,U_111) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_108,sK16(U_114,U_112,U_110))],[f_15_4]) ).
fof(f_15_6,plain,
( ! [U_110,U_112,U_114] :
( ~ in(sK16(U_114,U_112,U_110),U_110)
| ~ sP23(U_110,U_112,U_114) )
& ! [U_110,U_112,U_114] :
( in(sK16(U_114,U_112,U_110),U_112)
| in(sK16(U_114,U_112,U_110),U_114)
| ~ sP23(U_110,U_112,U_114) )
& ! [U_110,U_112,U_114] :
( ~ in(sK15(U_114,U_112,U_110),U_112)
| ~ sP22(U_110,U_112,U_114) )
& ! [U_110,U_112,U_114] :
( ~ in(sK15(U_114,U_112,U_110),U_114)
| ~ sP22(U_110,U_112,U_114) )
& ! [U_110,U_112,U_114] :
( in(sK15(U_114,U_112,U_110),U_110)
| ~ sP22(U_110,U_112,U_114) )
& ! [U_111,U_113,U_106] :
( ~ in(U_106,U_111)
| ~ sP20(U_111,U_113,U_106) )
& ! [U_111,U_113,U_106] :
( ~ in(U_106,U_113)
| ~ sP20(U_111,U_113,U_106) )
& ! [U_111,U_113,U_109,U_105,U_106] :
( in(U_106,U_109)
| sP20(U_111,U_113,U_106)
| ~ sP21(U_111,U_113,U_109,U_105,U_106) )
& ! [U_111,U_113,U_109,U_105,U_106] :
( in(U_105,U_111)
| in(U_105,U_113)
| ~ in(U_105,U_109)
| ~ sP21(U_111,U_113,U_109,U_105,U_106) )
& ! [U_110,U_112,U_114] :
( U_110 = set_union2(U_114,U_112)
| sP23(U_110,U_112,U_114)
| sP22(U_110,U_112,U_114) )
& ! [U_111,U_113,U_109,U_105,U_106] :
( sP21(U_111,U_113,U_109,U_105,U_106)
| U_109 != set_union2(U_113,U_111) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP20,sP21,sP22,sP23])],[f_15_5]) ).
cnf(f_15_7,plain,
( sP21(U_111,U_113,U_109,U_105,U_106)
| U_109 != set_union2(U_113,U_111) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_8,plain,
( U_110 = set_union2(U_114,U_112)
| sP23(U_110,U_112,U_114)
| sP22(U_110,U_112,U_114) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_9,plain,
( in(U_105,U_111)
| in(U_105,U_113)
| ~ in(U_105,U_109)
| ~ sP21(U_111,U_113,U_109,U_105,U_106) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_10,plain,
( in(U_106,U_109)
| sP20(U_111,U_113,U_106)
| ~ sP21(U_111,U_113,U_109,U_105,U_106) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_11,plain,
( ~ in(U_106,U_113)
| ~ sP20(U_111,U_113,U_106) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_12,plain,
( ~ in(U_106,U_111)
| ~ sP20(U_111,U_113,U_106) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_13,plain,
( in(sK15(U_114,U_112,U_110),U_110)
| ~ sP22(U_110,U_112,U_114) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_14,plain,
( ~ in(sK15(U_114,U_112,U_110),U_114)
| ~ sP22(U_110,U_112,U_114) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_15,plain,
( ~ in(sK15(U_114,U_112,U_110),U_112)
| ~ sP22(U_110,U_112,U_114) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_16,plain,
( in(sK16(U_114,U_112,U_110),U_112)
| in(sK16(U_114,U_112,U_110),U_114)
| ~ sP23(U_110,U_112,U_114) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_17,plain,
( ~ in(sK16(U_114,U_112,U_110),U_110)
| ~ sP23(U_110,U_112,U_114) ),
inference(clausify,[status(thm)],[f_15_6]) ).
fof(f_16_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_16_2,plain,
! [U_127,U_126,U_125] :
( ( U_125 = cartesian_product2(U_127,U_126)
| ? [U_124] :
( ( ~ in(U_124,U_125)
& ? [U_123,U_122] :
( U_124 = ordered_pair(U_123,U_122)
& in(U_122,U_126)
& in(U_123,U_127) ) )
| ( ! [U_121,U_120] :
( U_124 != ordered_pair(U_121,U_120)
| ~ in(U_120,U_126)
| ~ in(U_121,U_127) )
& in(U_124,U_125) ) ) )
& ( ! [U_119] :
( ( in(U_119,U_125)
| ! [U_118,U_117] :
( U_119 != ordered_pair(U_118,U_117)
| ~ in(U_117,U_126)
| ~ in(U_118,U_127) ) )
& ( ? [U_116,U_115] :
( U_119 = ordered_pair(U_116,U_115)
& in(U_115,U_126)
& in(U_116,U_127) )
| ~ in(U_119,U_125) ) )
| U_125 != cartesian_product2(U_127,U_126) ) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( ! [U_137,U_135,U_133] :
( U_133 = cartesian_product2(U_137,U_135)
| ? [U_131] :
( ~ in(U_131,U_133)
& ? [U_123] :
( ? [U_122] :
( U_131 = ordered_pair(U_123,U_122)
& in(U_122,U_135) )
& in(U_123,U_137) ) )
| ? [U_130] :
( ! [U_121] :
( ! [U_120] :
( U_130 != ordered_pair(U_121,U_120)
| ~ in(U_120,U_135) )
| ~ in(U_121,U_137) )
& in(U_130,U_133) ) )
& ! [U_136,U_134,U_132] :
( ( ! [U_129] :
( in(U_129,U_132)
| ! [U_118] :
( ! [U_117] :
( U_129 != ordered_pair(U_118,U_117)
| ~ in(U_117,U_134) )
| ~ in(U_118,U_136) ) )
& ! [U_128] :
( ? [U_116] :
( ? [U_115] :
( U_128 = ordered_pair(U_116,U_115)
& in(U_115,U_134) )
& in(U_116,U_136) )
| ~ in(U_128,U_132) ) )
| U_132 != cartesian_product2(U_136,U_134) ) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
fof(f_16_4,plain,
( ! [U_137,U_135,U_133] :
( U_133 = cartesian_product2(U_137,U_135)
| ? [U_131] :
( ~ in(U_131,U_133)
& ? [U_123] :
( ? [U_122] :
( U_131 = ordered_pair(U_123,U_122)
& in(U_122,U_135) )
& in(U_123,U_137) ) )
| ? [U_130] :
( ! [U_121] :
( ! [U_120] :
( U_130 != ordered_pair(U_121,U_120)
| ~ in(U_120,U_135) )
| ~ in(U_121,U_137) )
& in(U_130,U_133) ) )
& ! [U_136,U_134,U_132] :
( ( ! [U_129] :
( in(U_129,U_132)
| ! [U_118] :
( ! [U_117] :
( U_129 != ordered_pair(U_118,U_117)
| ~ in(U_117,U_134) )
| ~ in(U_118,U_136) ) )
& ! [U_128] :
( ( ? [U_115] :
( U_128 = ordered_pair(sK17(U_136,U_134,U_132,U_128),U_115)
& in(U_115,U_134) )
& in(sK17(U_136,U_134,U_132,U_128),U_136) )
| ~ in(U_128,U_132) ) )
| U_132 != cartesian_product2(U_136,U_134) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_116,sK17(U_136,U_134,U_132,U_128))],[f_16_3]) ).
fof(f_16_5,plain,
( ! [U_137,U_135,U_133] :
( U_133 = cartesian_product2(U_137,U_135)
| ? [U_131] :
( ~ in(U_131,U_133)
& ? [U_123] :
( ? [U_122] :
( U_131 = ordered_pair(U_123,U_122)
& in(U_122,U_135) )
& in(U_123,U_137) ) )
| ? [U_130] :
( ! [U_121] :
( ! [U_120] :
( U_130 != ordered_pair(U_121,U_120)
| ~ in(U_120,U_135) )
| ~ in(U_121,U_137) )
& in(U_130,U_133) ) )
& ! [U_136,U_134,U_132] :
( ( ! [U_129] :
( in(U_129,U_132)
| ! [U_118] :
( ! [U_117] :
( U_129 != ordered_pair(U_118,U_117)
| ~ in(U_117,U_134) )
| ~ in(U_118,U_136) ) )
& ! [U_128] :
( ( U_128 = ordered_pair(sK17(U_136,U_134,U_132,U_128),sK18(U_136,U_134,U_132,U_128))
& in(sK18(U_136,U_134,U_132,U_128),U_134)
& in(sK17(U_136,U_134,U_132,U_128),U_136) )
| ~ in(U_128,U_132) ) )
| U_132 != cartesian_product2(U_136,U_134) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_115,sK18(U_136,U_134,U_132,U_128))],[f_16_4]) ).
fof(f_16_6,plain,
( ! [U_137,U_135,U_133] :
( U_133 = cartesian_product2(U_137,U_135)
| ? [U_131] :
( ~ in(U_131,U_133)
& ? [U_123] :
( ? [U_122] :
( U_131 = ordered_pair(U_123,U_122)
& in(U_122,U_135) )
& in(U_123,U_137) ) )
| ( ! [U_121] :
( ! [U_120] :
( sK19(U_137,U_135,U_133) != ordered_pair(U_121,U_120)
| ~ in(U_120,U_135) )
| ~ in(U_121,U_137) )
& in(sK19(U_137,U_135,U_133),U_133) ) )
& ! [U_136,U_134,U_132] :
( ( ! [U_129] :
( in(U_129,U_132)
| ! [U_118] :
( ! [U_117] :
( U_129 != ordered_pair(U_118,U_117)
| ~ in(U_117,U_134) )
| ~ in(U_118,U_136) ) )
& ! [U_128] :
( ( U_128 = ordered_pair(sK17(U_136,U_134,U_132,U_128),sK18(U_136,U_134,U_132,U_128))
& in(sK18(U_136,U_134,U_132,U_128),U_134)
& in(sK17(U_136,U_134,U_132,U_128),U_136) )
| ~ in(U_128,U_132) ) )
| U_132 != cartesian_product2(U_136,U_134) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_130,sK19(U_137,U_135,U_133))],[f_16_5]) ).
fof(f_16_7,plain,
( ! [U_137,U_135,U_133] :
( U_133 = cartesian_product2(U_137,U_135)
| ( ~ in(sK20(U_137,U_135,U_133),U_133)
& ? [U_123] :
( ? [U_122] :
( sK20(U_137,U_135,U_133) = ordered_pair(U_123,U_122)
& in(U_122,U_135) )
& in(U_123,U_137) ) )
| ( ! [U_121] :
( ! [U_120] :
( sK19(U_137,U_135,U_133) != ordered_pair(U_121,U_120)
| ~ in(U_120,U_135) )
| ~ in(U_121,U_137) )
& in(sK19(U_137,U_135,U_133),U_133) ) )
& ! [U_136,U_134,U_132] :
( ( ! [U_129] :
( in(U_129,U_132)
| ! [U_118] :
( ! [U_117] :
( U_129 != ordered_pair(U_118,U_117)
| ~ in(U_117,U_134) )
| ~ in(U_118,U_136) ) )
& ! [U_128] :
( ( U_128 = ordered_pair(sK17(U_136,U_134,U_132,U_128),sK18(U_136,U_134,U_132,U_128))
& in(sK18(U_136,U_134,U_132,U_128),U_134)
& in(sK17(U_136,U_134,U_132,U_128),U_136) )
| ~ in(U_128,U_132) ) )
| U_132 != cartesian_product2(U_136,U_134) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_131,sK20(U_137,U_135,U_133))],[f_16_6]) ).
fof(f_16_8,plain,
( ! [U_137,U_135,U_133] :
( U_133 = cartesian_product2(U_137,U_135)
| ( ~ in(sK20(U_137,U_135,U_133),U_133)
& ? [U_122] :
( sK20(U_137,U_135,U_133) = ordered_pair(sK21(U_137,U_135,U_133),U_122)
& in(U_122,U_135) )
& in(sK21(U_137,U_135,U_133),U_137) )
| ( ! [U_121] :
( ! [U_120] :
( sK19(U_137,U_135,U_133) != ordered_pair(U_121,U_120)
| ~ in(U_120,U_135) )
| ~ in(U_121,U_137) )
& in(sK19(U_137,U_135,U_133),U_133) ) )
& ! [U_136,U_134,U_132] :
( ( ! [U_129] :
( in(U_129,U_132)
| ! [U_118] :
( ! [U_117] :
( U_129 != ordered_pair(U_118,U_117)
| ~ in(U_117,U_134) )
| ~ in(U_118,U_136) ) )
& ! [U_128] :
( ( U_128 = ordered_pair(sK17(U_136,U_134,U_132,U_128),sK18(U_136,U_134,U_132,U_128))
& in(sK18(U_136,U_134,U_132,U_128),U_134)
& in(sK17(U_136,U_134,U_132,U_128),U_136) )
| ~ in(U_128,U_132) ) )
| U_132 != cartesian_product2(U_136,U_134) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_123,sK21(U_137,U_135,U_133))],[f_16_7]) ).
fof(f_16_9,plain,
( ! [U_137,U_135,U_133] :
( U_133 = cartesian_product2(U_137,U_135)
| ( ~ in(sK20(U_137,U_135,U_133),U_133)
& sK20(U_137,U_135,U_133) = ordered_pair(sK21(U_137,U_135,U_133),sK22(U_137,U_135,U_133))
& in(sK22(U_137,U_135,U_133),U_135)
& in(sK21(U_137,U_135,U_133),U_137) )
| ( ! [U_121] :
( ! [U_120] :
( sK19(U_137,U_135,U_133) != ordered_pair(U_121,U_120)
| ~ in(U_120,U_135) )
| ~ in(U_121,U_137) )
& in(sK19(U_137,U_135,U_133),U_133) ) )
& ! [U_136,U_134,U_132] :
( ( ! [U_129] :
( in(U_129,U_132)
| ! [U_118] :
( ! [U_117] :
( U_129 != ordered_pair(U_118,U_117)
| ~ in(U_117,U_134) )
| ~ in(U_118,U_136) ) )
& ! [U_128] :
( ( U_128 = ordered_pair(sK17(U_136,U_134,U_132,U_128),sK18(U_136,U_134,U_132,U_128))
& in(sK18(U_136,U_134,U_132,U_128),U_134)
& in(sK17(U_136,U_134,U_132,U_128),U_136) )
| ~ in(U_128,U_132) ) )
| U_132 != cartesian_product2(U_136,U_134) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_122,sK22(U_137,U_135,U_133))],[f_16_8]) ).
fof(f_16_10,plain,
( ! [U_135,U_137,U_133] :
( ~ in(sK20(U_137,U_135,U_133),U_133)
| ~ sP27(U_135,U_137,U_133) )
& ! [U_135,U_137,U_133] :
( sK20(U_137,U_135,U_133) = ordered_pair(sK21(U_137,U_135,U_133),sK22(U_137,U_135,U_133))
| ~ sP27(U_135,U_137,U_133) )
& ! [U_135,U_137,U_133] :
( in(sK22(U_137,U_135,U_133),U_135)
| ~ sP27(U_135,U_137,U_133) )
& ! [U_135,U_137,U_133] :
( in(sK21(U_137,U_135,U_133),U_137)
| ~ sP27(U_135,U_137,U_133) )
& ! [U_121,U_135,U_137,U_133,U_120] :
( sK19(U_137,U_135,U_133) != ordered_pair(U_121,U_120)
| ~ in(U_120,U_135)
| ~ in(U_121,U_137)
| ~ sP26(U_121,U_135,U_137,U_133,U_120) )
& ! [U_121,U_135,U_137,U_133,U_120] :
( in(sK19(U_137,U_135,U_133),U_133)
| ~ sP26(U_121,U_135,U_137,U_133,U_120) )
& ! [U_132,U_134,U_136,U_128] :
( U_128 = ordered_pair(sK17(U_136,U_134,U_132,U_128),sK18(U_136,U_134,U_132,U_128))
| ~ sP24(U_132,U_134,U_136,U_128) )
& ! [U_132,U_134,U_136,U_128] :
( in(sK18(U_136,U_134,U_132,U_128),U_134)
| ~ sP24(U_132,U_134,U_136,U_128) )
& ! [U_132,U_134,U_136,U_128] :
( in(sK17(U_136,U_134,U_132,U_128),U_136)
| ~ sP24(U_132,U_134,U_136,U_128) )
& ! [U_118,U_117,U_132,U_134,U_136,U_128,U_129] :
( in(U_129,U_132)
| U_129 != ordered_pair(U_118,U_117)
| ~ in(U_117,U_134)
| ~ in(U_118,U_136)
| ~ sP25(U_118,U_117,U_132,U_134,U_136,U_128,U_129) )
& ! [U_118,U_117,U_132,U_134,U_136,U_128,U_129] :
( sP24(U_132,U_134,U_136,U_128)
| ~ in(U_128,U_132)
| ~ sP25(U_118,U_117,U_132,U_134,U_136,U_128,U_129) )
& ! [U_121,U_135,U_137,U_133,U_120] :
( U_133 = cartesian_product2(U_137,U_135)
| sP27(U_135,U_137,U_133)
| sP26(U_121,U_135,U_137,U_133,U_120) )
& ! [U_118,U_117,U_132,U_134,U_136,U_128,U_129] :
( sP25(U_118,U_117,U_132,U_134,U_136,U_128,U_129)
| U_132 != cartesian_product2(U_136,U_134) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP24,sP25,sP26,sP27])],[f_16_9]) ).
cnf(f_16_11,plain,
( sP25(U_118,U_117,U_132,U_134,U_136,U_128,U_129)
| U_132 != cartesian_product2(U_136,U_134) ),
inference(clausify,[status(thm)],[f_16_10]) ).
cnf(f_16_12,plain,
( U_133 = cartesian_product2(U_137,U_135)
| sP27(U_135,U_137,U_133)
| sP26(U_121,U_135,U_137,U_133,U_120) ),
inference(clausify,[status(thm)],[f_16_10]) ).
cnf(f_16_13,plain,
( sP24(U_132,U_134,U_136,U_128)
| ~ in(U_128,U_132)
| ~ sP25(U_118,U_117,U_132,U_134,U_136,U_128,U_129) ),
inference(clausify,[status(thm)],[f_16_10]) ).
cnf(f_16_14,plain,
( in(U_129,U_132)
| U_129 != ordered_pair(U_118,U_117)
| ~ in(U_117,U_134)
| ~ in(U_118,U_136)
| ~ sP25(U_118,U_117,U_132,U_134,U_136,U_128,U_129) ),
inference(clausify,[status(thm)],[f_16_10]) ).
cnf(f_16_15,plain,
( in(sK17(U_136,U_134,U_132,U_128),U_136)
| ~ sP24(U_132,U_134,U_136,U_128) ),
inference(clausify,[status(thm)],[f_16_10]) ).
cnf(f_16_16,plain,
( in(sK18(U_136,U_134,U_132,U_128),U_134)
| ~ sP24(U_132,U_134,U_136,U_128) ),
inference(clausify,[status(thm)],[f_16_10]) ).
cnf(f_16_17,plain,
( U_128 = ordered_pair(sK17(U_136,U_134,U_132,U_128),sK18(U_136,U_134,U_132,U_128))
| ~ sP24(U_132,U_134,U_136,U_128) ),
inference(clausify,[status(thm)],[f_16_10]) ).
cnf(f_16_18,plain,
( in(sK19(U_137,U_135,U_133),U_133)
| ~ sP26(U_121,U_135,U_137,U_133,U_120) ),
inference(clausify,[status(thm)],[f_16_10]) ).
cnf(f_16_19,plain,
( sK19(U_137,U_135,U_133) != ordered_pair(U_121,U_120)
| ~ in(U_120,U_135)
| ~ in(U_121,U_137)
| ~ sP26(U_121,U_135,U_137,U_133,U_120) ),
inference(clausify,[status(thm)],[f_16_10]) ).
cnf(f_16_20,plain,
( in(sK21(U_137,U_135,U_133),U_137)
| ~ sP27(U_135,U_137,U_133) ),
inference(clausify,[status(thm)],[f_16_10]) ).
cnf(f_16_21,plain,
( in(sK22(U_137,U_135,U_133),U_135)
| ~ sP27(U_135,U_137,U_133) ),
inference(clausify,[status(thm)],[f_16_10]) ).
cnf(f_16_22,plain,
( sK20(U_137,U_135,U_133) = ordered_pair(sK21(U_137,U_135,U_133),sK22(U_137,U_135,U_133))
| ~ sP27(U_135,U_137,U_133) ),
inference(clausify,[status(thm)],[f_16_10]) ).
cnf(f_16_23,plain,
( ~ in(sK20(U_137,U_135,U_133),U_133)
| ~ sP27(U_135,U_137,U_133) ),
inference(clausify,[status(thm)],[f_16_10]) ).
fof(f_17_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_17_2,plain,
! [U_141,U_140] :
( ( subset(U_141,U_140)
| ? [U_139] :
( ~ in(U_139,U_140)
& in(U_139,U_141) ) )
& ( ! [U_138] :
( in(U_138,U_140)
| ~ in(U_138,U_141) )
| ~ subset(U_141,U_140) ) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( ! [U_145,U_143] :
( subset(U_145,U_143)
| ? [U_139] :
( ~ in(U_139,U_143)
& in(U_139,U_145) ) )
& ! [U_144,U_142] :
( ! [U_138] :
( in(U_138,U_142)
| ~ in(U_138,U_144) )
| ~ subset(U_144,U_142) ) ),
inference(miniscope,[status(thm)],[f_17_2]) ).
fof(f_17_4,plain,
( ! [U_145,U_143] :
( subset(U_145,U_143)
| ( ~ in(sK23(U_145,U_143),U_143)
& in(sK23(U_145,U_143),U_145) ) )
& ! [U_144,U_142] :
( ! [U_138] :
( in(U_138,U_142)
| ~ in(U_138,U_144) )
| ~ subset(U_144,U_142) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_139,sK23(U_145,U_143))],[f_17_3]) ).
fof(f_17_5,plain,
( ! [U_143,U_145] :
( ~ in(sK23(U_145,U_143),U_143)
| ~ sP28(U_143,U_145) )
& ! [U_143,U_145] :
( in(sK23(U_145,U_143),U_145)
| ~ sP28(U_143,U_145) )
& ! [U_143,U_145] :
( subset(U_145,U_143)
| sP28(U_143,U_145) )
& ! [U_142,U_144,U_138] :
( in(U_138,U_142)
| ~ in(U_138,U_144)
| ~ subset(U_144,U_142) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP28])],[f_17_4]) ).
cnf(f_17_6,plain,
( in(U_138,U_142)
| ~ in(U_138,U_144)
| ~ subset(U_144,U_142) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_7,plain,
( subset(U_145,U_143)
| sP28(U_143,U_145) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_8,plain,
( in(sK23(U_145,U_143),U_145)
| ~ sP28(U_143,U_145) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_9,plain,
( ~ in(sK23(U_145,U_143),U_143)
| ~ sP28(U_143,U_145) ),
inference(clausify,[status(thm)],[f_17_5]) ).
fof(f_18_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_18_2,plain,
! [U_150,U_149,U_148] :
( ( U_148 = set_intersection2(U_150,U_149)
| ? [U_147] :
( ( ~ in(U_147,U_148)
& in(U_147,U_149)
& in(U_147,U_150) )
| ( ( ~ in(U_147,U_149)
| ~ in(U_147,U_150) )
& in(U_147,U_148) ) ) )
& ( ! [U_146] :
( ( in(U_146,U_148)
| ~ in(U_146,U_149)
| ~ in(U_146,U_150) )
& ( ( in(U_146,U_149)
& in(U_146,U_150) )
| ~ in(U_146,U_148) ) )
| U_148 != set_intersection2(U_150,U_149) ) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( ! [U_160,U_158,U_156] :
( U_156 = set_intersection2(U_160,U_158)
| ? [U_154] :
( ~ in(U_154,U_156)
& in(U_154,U_158)
& in(U_154,U_160) )
| ? [U_153] :
( ( ~ in(U_153,U_158)
| ~ in(U_153,U_160) )
& in(U_153,U_156) ) )
& ! [U_159,U_157,U_155] :
( ( ! [U_152] :
( in(U_152,U_155)
| ~ in(U_152,U_157)
| ~ in(U_152,U_159) )
& ! [U_151] :
( ( in(U_151,U_157)
& in(U_151,U_159) )
| ~ in(U_151,U_155) ) )
| U_155 != set_intersection2(U_159,U_157) ) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
fof(f_18_4,plain,
( ! [U_160,U_158,U_156] :
( U_156 = set_intersection2(U_160,U_158)
| ? [U_154] :
( ~ in(U_154,U_156)
& in(U_154,U_158)
& in(U_154,U_160) )
| ( ( ~ in(sK24(U_160,U_158,U_156),U_158)
| ~ in(sK24(U_160,U_158,U_156),U_160) )
& in(sK24(U_160,U_158,U_156),U_156) ) )
& ! [U_159,U_157,U_155] :
( ( ! [U_152] :
( in(U_152,U_155)
| ~ in(U_152,U_157)
| ~ in(U_152,U_159) )
& ! [U_151] :
( ( in(U_151,U_157)
& in(U_151,U_159) )
| ~ in(U_151,U_155) ) )
| U_155 != set_intersection2(U_159,U_157) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_153,sK24(U_160,U_158,U_156))],[f_18_3]) ).
fof(f_18_5,plain,
( ! [U_160,U_158,U_156] :
( U_156 = set_intersection2(U_160,U_158)
| ( ~ in(sK25(U_160,U_158,U_156),U_156)
& in(sK25(U_160,U_158,U_156),U_158)
& in(sK25(U_160,U_158,U_156),U_160) )
| ( ( ~ in(sK24(U_160,U_158,U_156),U_158)
| ~ in(sK24(U_160,U_158,U_156),U_160) )
& in(sK24(U_160,U_158,U_156),U_156) ) )
& ! [U_159,U_157,U_155] :
( ( ! [U_152] :
( in(U_152,U_155)
| ~ in(U_152,U_157)
| ~ in(U_152,U_159) )
& ! [U_151] :
( ( in(U_151,U_157)
& in(U_151,U_159) )
| ~ in(U_151,U_155) ) )
| U_155 != set_intersection2(U_159,U_157) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_154,sK25(U_160,U_158,U_156))],[f_18_4]) ).
fof(f_18_6,plain,
( ! [U_160,U_156,U_158] :
( ~ in(sK25(U_160,U_158,U_156),U_156)
| ~ sP32(U_160,U_156,U_158) )
& ! [U_160,U_156,U_158] :
( in(sK25(U_160,U_158,U_156),U_158)
| ~ sP32(U_160,U_156,U_158) )
& ! [U_160,U_156,U_158] :
( in(sK25(U_160,U_158,U_156),U_160)
| ~ sP32(U_160,U_156,U_158) )
& ! [U_160,U_156,U_158] :
( ~ in(sK24(U_160,U_158,U_156),U_158)
| ~ in(sK24(U_160,U_158,U_156),U_160)
| ~ sP31(U_160,U_156,U_158) )
& ! [U_160,U_156,U_158] :
( in(sK24(U_160,U_158,U_156),U_156)
| ~ sP31(U_160,U_156,U_158) )
& ! [U_159,U_151,U_157] :
( in(U_151,U_157)
| ~ sP29(U_159,U_151,U_157) )
& ! [U_159,U_151,U_157] :
( in(U_151,U_159)
| ~ sP29(U_159,U_151,U_157) )
& ! [U_155,U_159,U_152,U_151,U_157] :
( in(U_152,U_155)
| ~ in(U_152,U_157)
| ~ in(U_152,U_159)
| ~ sP30(U_155,U_159,U_152,U_151,U_157) )
& ! [U_155,U_159,U_152,U_151,U_157] :
( sP29(U_159,U_151,U_157)
| ~ in(U_151,U_155)
| ~ sP30(U_155,U_159,U_152,U_151,U_157) )
& ! [U_160,U_156,U_158] :
( U_156 = set_intersection2(U_160,U_158)
| sP32(U_160,U_156,U_158)
| sP31(U_160,U_156,U_158) )
& ! [U_155,U_159,U_152,U_151,U_157] :
( sP30(U_155,U_159,U_152,U_151,U_157)
| U_155 != set_intersection2(U_159,U_157) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP29,sP30,sP31,sP32])],[f_18_5]) ).
cnf(f_18_7,plain,
( sP30(U_155,U_159,U_152,U_151,U_157)
| U_155 != set_intersection2(U_159,U_157) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_8,plain,
( U_156 = set_intersection2(U_160,U_158)
| sP32(U_160,U_156,U_158)
| sP31(U_160,U_156,U_158) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_9,plain,
( sP29(U_159,U_151,U_157)
| ~ in(U_151,U_155)
| ~ sP30(U_155,U_159,U_152,U_151,U_157) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_10,plain,
( in(U_152,U_155)
| ~ in(U_152,U_157)
| ~ in(U_152,U_159)
| ~ sP30(U_155,U_159,U_152,U_151,U_157) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_11,plain,
( in(U_151,U_159)
| ~ sP29(U_159,U_151,U_157) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_12,plain,
( in(U_151,U_157)
| ~ sP29(U_159,U_151,U_157) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_13,plain,
( in(sK24(U_160,U_158,U_156),U_156)
| ~ sP31(U_160,U_156,U_158) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_14,plain,
( ~ in(sK24(U_160,U_158,U_156),U_158)
| ~ in(sK24(U_160,U_158,U_156),U_160)
| ~ sP31(U_160,U_156,U_158) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_15,plain,
( in(sK25(U_160,U_158,U_156),U_160)
| ~ sP32(U_160,U_156,U_158) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_16,plain,
( in(sK25(U_160,U_158,U_156),U_158)
| ~ sP32(U_160,U_156,U_158) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_17,plain,
( ~ in(sK25(U_160,U_158,U_156),U_156)
| ~ sP32(U_160,U_156,U_158) ),
inference(clausify,[status(thm)],[f_18_6]) ).
fof(f_19_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_19_2,plain,
! [U_168] :
( ! [U_167] :
( ( U_167 = relation_dom(U_168)
| ? [U_166] :
( ( ~ in(U_166,U_167)
& ? [U_165] : in(ordered_pair(U_166,U_165),U_168) )
| ( ! [U_164] : ~ in(ordered_pair(U_166,U_164),U_168)
& in(U_166,U_167) ) ) )
& ( ! [U_163] :
( ( in(U_163,U_167)
| ! [U_162] : ~ in(ordered_pair(U_163,U_162),U_168) )
& ( ? [U_161] : in(ordered_pair(U_163,U_161),U_168)
| ~ in(U_163,U_167) ) )
| U_167 != relation_dom(U_168) ) )
| ~ relation(U_168) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_168] :
( ( ! [U_174] :
( U_174 = relation_dom(U_168)
| ? [U_172] :
( ~ in(U_172,U_174)
& ? [U_165] : in(ordered_pair(U_172,U_165),U_168) )
| ? [U_171] :
( ! [U_164] : ~ in(ordered_pair(U_171,U_164),U_168)
& in(U_171,U_174) ) )
& ! [U_173] :
( ( ! [U_170] :
( in(U_170,U_173)
| ! [U_162] : ~ in(ordered_pair(U_170,U_162),U_168) )
& ! [U_169] :
( ? [U_161] : in(ordered_pair(U_169,U_161),U_168)
| ~ in(U_169,U_173) ) )
| U_173 != relation_dom(U_168) ) )
| ~ relation(U_168) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
fof(f_19_4,plain,
! [U_168] :
( ( ! [U_174] :
( U_174 = relation_dom(U_168)
| ? [U_172] :
( ~ in(U_172,U_174)
& ? [U_165] : in(ordered_pair(U_172,U_165),U_168) )
| ? [U_171] :
( ! [U_164] : ~ in(ordered_pair(U_171,U_164),U_168)
& in(U_171,U_174) ) )
& ! [U_173] :
( ( ! [U_170] :
( in(U_170,U_173)
| ! [U_162] : ~ in(ordered_pair(U_170,U_162),U_168) )
& ! [U_169] :
( in(ordered_pair(U_169,sK26(U_168,U_173,U_169)),U_168)
| ~ in(U_169,U_173) ) )
| U_173 != relation_dom(U_168) ) )
| ~ relation(U_168) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_161,sK26(U_168,U_173,U_169))],[f_19_3]) ).
fof(f_19_5,plain,
! [U_168] :
( ( ! [U_174] :
( U_174 = relation_dom(U_168)
| ? [U_172] :
( ~ in(U_172,U_174)
& ? [U_165] : in(ordered_pair(U_172,U_165),U_168) )
| ( ! [U_164] : ~ in(ordered_pair(sK27(U_168,U_174),U_164),U_168)
& in(sK27(U_168,U_174),U_174) ) )
& ! [U_173] :
( ( ! [U_170] :
( in(U_170,U_173)
| ! [U_162] : ~ in(ordered_pair(U_170,U_162),U_168) )
& ! [U_169] :
( in(ordered_pair(U_169,sK26(U_168,U_173,U_169)),U_168)
| ~ in(U_169,U_173) ) )
| U_173 != relation_dom(U_168) ) )
| ~ relation(U_168) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_171,sK27(U_168,U_174))],[f_19_4]) ).
fof(f_19_6,plain,
! [U_168] :
( ( ! [U_174] :
( U_174 = relation_dom(U_168)
| ( ~ in(sK28(U_168,U_174),U_174)
& ? [U_165] : in(ordered_pair(sK28(U_168,U_174),U_165),U_168) )
| ( ! [U_164] : ~ in(ordered_pair(sK27(U_168,U_174),U_164),U_168)
& in(sK27(U_168,U_174),U_174) ) )
& ! [U_173] :
( ( ! [U_170] :
( in(U_170,U_173)
| ! [U_162] : ~ in(ordered_pair(U_170,U_162),U_168) )
& ! [U_169] :
( in(ordered_pair(U_169,sK26(U_168,U_173,U_169)),U_168)
| ~ in(U_169,U_173) ) )
| U_173 != relation_dom(U_168) ) )
| ~ relation(U_168) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_172,sK28(U_168,U_174))],[f_19_5]) ).
fof(f_19_7,plain,
! [U_168] :
( ( ! [U_174] :
( U_174 = relation_dom(U_168)
| ( ~ in(sK28(U_168,U_174),U_174)
& in(ordered_pair(sK28(U_168,U_174),sK29(U_168,U_174)),U_168) )
| ( ! [U_164] : ~ in(ordered_pair(sK27(U_168,U_174),U_164),U_168)
& in(sK27(U_168,U_174),U_174) ) )
& ! [U_173] :
( ( ! [U_170] :
( in(U_170,U_173)
| ! [U_162] : ~ in(ordered_pair(U_170,U_162),U_168) )
& ! [U_169] :
( in(ordered_pair(U_169,sK26(U_168,U_173,U_169)),U_168)
| ~ in(U_169,U_173) ) )
| U_173 != relation_dom(U_168) ) )
| ~ relation(U_168) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_165,sK29(U_168,U_174))],[f_19_6]) ).
fof(f_19_8,plain,
( ! [U_168,U_174] :
( ~ in(sK28(U_168,U_174),U_174)
| ~ sP35(U_168,U_174) )
& ! [U_168,U_174] :
( in(ordered_pair(sK28(U_168,U_174),sK29(U_168,U_174)),U_168)
| ~ sP35(U_168,U_174) )
& ! [U_168,U_174,U_164] :
( ~ in(ordered_pair(sK27(U_168,U_174),U_164),U_168)
| ~ sP34(U_168,U_174,U_164) )
& ! [U_168,U_174,U_164] :
( in(sK27(U_168,U_174),U_174)
| ~ sP34(U_168,U_174,U_164) )
& ! [U_168,U_170,U_169,U_173,U_162] :
( in(U_170,U_173)
| ~ in(ordered_pair(U_170,U_162),U_168)
| ~ sP33(U_168,U_170,U_169,U_173,U_162) )
& ! [U_168,U_170,U_169,U_173,U_162] :
( in(ordered_pair(U_169,sK26(U_168,U_173,U_169)),U_168)
| ~ in(U_169,U_173)
| ~ sP33(U_168,U_170,U_169,U_173,U_162) )
& ! [U_168,U_170,U_174,U_169,U_164,U_173,U_162] :
( U_174 = relation_dom(U_168)
| sP35(U_168,U_174)
| sP34(U_168,U_174,U_164)
| ~ sP36(U_168,U_170,U_174,U_169,U_164,U_173,U_162) )
& ! [U_168,U_170,U_174,U_169,U_164,U_173,U_162] :
( sP33(U_168,U_170,U_169,U_173,U_162)
| U_173 != relation_dom(U_168)
| ~ sP36(U_168,U_170,U_174,U_169,U_164,U_173,U_162) )
& ! [U_168,U_170,U_174,U_169,U_164,U_173,U_162] :
( sP36(U_168,U_170,U_174,U_169,U_164,U_173,U_162)
| ~ relation(U_168) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP33,sP34,sP35,sP36])],[f_19_7]) ).
cnf(f_19_9,plain,
( sP36(U_168,U_170,U_174,U_169,U_164,U_173,U_162)
| ~ relation(U_168) ),
inference(clausify,[status(thm)],[f_19_8]) ).
cnf(f_19_10,plain,
( sP33(U_168,U_170,U_169,U_173,U_162)
| U_173 != relation_dom(U_168)
| ~ sP36(U_168,U_170,U_174,U_169,U_164,U_173,U_162) ),
inference(clausify,[status(thm)],[f_19_8]) ).
cnf(f_19_11,plain,
( U_174 = relation_dom(U_168)
| sP35(U_168,U_174)
| sP34(U_168,U_174,U_164)
| ~ sP36(U_168,U_170,U_174,U_169,U_164,U_173,U_162) ),
inference(clausify,[status(thm)],[f_19_8]) ).
cnf(f_19_12,plain,
( in(ordered_pair(U_169,sK26(U_168,U_173,U_169)),U_168)
| ~ in(U_169,U_173)
| ~ sP33(U_168,U_170,U_169,U_173,U_162) ),
inference(clausify,[status(thm)],[f_19_8]) ).
cnf(f_19_13,plain,
( in(U_170,U_173)
| ~ in(ordered_pair(U_170,U_162),U_168)
| ~ sP33(U_168,U_170,U_169,U_173,U_162) ),
inference(clausify,[status(thm)],[f_19_8]) ).
cnf(f_19_14,plain,
( in(sK27(U_168,U_174),U_174)
| ~ sP34(U_168,U_174,U_164) ),
inference(clausify,[status(thm)],[f_19_8]) ).
cnf(f_19_15,plain,
( ~ in(ordered_pair(sK27(U_168,U_174),U_164),U_168)
| ~ sP34(U_168,U_174,U_164) ),
inference(clausify,[status(thm)],[f_19_8]) ).
cnf(f_19_16,plain,
( in(ordered_pair(sK28(U_168,U_174),sK29(U_168,U_174)),U_168)
| ~ sP35(U_168,U_174) ),
inference(clausify,[status(thm)],[f_19_8]) ).
cnf(f_19_17,plain,
( ~ in(sK28(U_168,U_174),U_174)
| ~ sP35(U_168,U_174) ),
inference(clausify,[status(thm)],[f_19_8]) ).
fof(f_20_1,plain,
! [A] : cast_to_subset(A) = A,
inference(fof_nnf,[status(thm)],[d4_subset_1]) ).
fof(f_20_2,plain,
! [U_175] : cast_to_subset(U_175) = U_175,
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_175] : cast_to_subset(U_175) = U_175,
inference(definitional_conversion,[status(esa)],[f_20_2]) ).
cnf(f_20_4,plain,
cast_to_subset(U_175) = U_175,
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_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_21_2,plain,
! [U_183,U_182] :
( ( U_182 = union(U_183)
| ? [U_181] :
( ( ~ in(U_181,U_182)
& ? [U_180] :
( in(U_180,U_183)
& in(U_181,U_180) ) )
| ( ! [U_179] :
( ~ in(U_179,U_183)
| ~ in(U_181,U_179) )
& in(U_181,U_182) ) ) )
& ( ! [U_178] :
( ( in(U_178,U_182)
| ! [U_177] :
( ~ in(U_177,U_183)
| ~ in(U_178,U_177) ) )
& ( ? [U_176] :
( in(U_176,U_183)
& in(U_178,U_176) )
| ~ in(U_178,U_182) ) )
| U_182 != union(U_183) ) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( ! [U_191,U_189] :
( U_189 = union(U_191)
| ? [U_187] :
( ~ in(U_187,U_189)
& ? [U_180] :
( in(U_180,U_191)
& in(U_187,U_180) ) )
| ? [U_186] :
( ! [U_179] :
( ~ in(U_179,U_191)
| ~ in(U_186,U_179) )
& in(U_186,U_189) ) )
& ! [U_190,U_188] :
( ( ! [U_185] :
( in(U_185,U_188)
| ! [U_177] :
( ~ in(U_177,U_190)
| ~ in(U_185,U_177) ) )
& ! [U_184] :
( ? [U_176] :
( in(U_176,U_190)
& in(U_184,U_176) )
| ~ in(U_184,U_188) ) )
| U_188 != union(U_190) ) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
fof(f_21_4,plain,
( ! [U_191,U_189] :
( U_189 = union(U_191)
| ? [U_187] :
( ~ in(U_187,U_189)
& ? [U_180] :
( in(U_180,U_191)
& in(U_187,U_180) ) )
| ? [U_186] :
( ! [U_179] :
( ~ in(U_179,U_191)
| ~ in(U_186,U_179) )
& in(U_186,U_189) ) )
& ! [U_190,U_188] :
( ( ! [U_185] :
( in(U_185,U_188)
| ! [U_177] :
( ~ in(U_177,U_190)
| ~ in(U_185,U_177) ) )
& ! [U_184] :
( ( in(sK30(U_190,U_188,U_184),U_190)
& in(U_184,sK30(U_190,U_188,U_184)) )
| ~ in(U_184,U_188) ) )
| U_188 != union(U_190) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_176,sK30(U_190,U_188,U_184))],[f_21_3]) ).
fof(f_21_5,plain,
( ! [U_191,U_189] :
( U_189 = union(U_191)
| ? [U_187] :
( ~ in(U_187,U_189)
& ? [U_180] :
( in(U_180,U_191)
& in(U_187,U_180) ) )
| ( ! [U_179] :
( ~ in(U_179,U_191)
| ~ in(sK31(U_191,U_189),U_179) )
& in(sK31(U_191,U_189),U_189) ) )
& ! [U_190,U_188] :
( ( ! [U_185] :
( in(U_185,U_188)
| ! [U_177] :
( ~ in(U_177,U_190)
| ~ in(U_185,U_177) ) )
& ! [U_184] :
( ( in(sK30(U_190,U_188,U_184),U_190)
& in(U_184,sK30(U_190,U_188,U_184)) )
| ~ in(U_184,U_188) ) )
| U_188 != union(U_190) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_186,sK31(U_191,U_189))],[f_21_4]) ).
fof(f_21_6,plain,
( ! [U_191,U_189] :
( U_189 = union(U_191)
| ( ~ in(sK32(U_191,U_189),U_189)
& ? [U_180] :
( in(U_180,U_191)
& in(sK32(U_191,U_189),U_180) ) )
| ( ! [U_179] :
( ~ in(U_179,U_191)
| ~ in(sK31(U_191,U_189),U_179) )
& in(sK31(U_191,U_189),U_189) ) )
& ! [U_190,U_188] :
( ( ! [U_185] :
( in(U_185,U_188)
| ! [U_177] :
( ~ in(U_177,U_190)
| ~ in(U_185,U_177) ) )
& ! [U_184] :
( ( in(sK30(U_190,U_188,U_184),U_190)
& in(U_184,sK30(U_190,U_188,U_184)) )
| ~ in(U_184,U_188) ) )
| U_188 != union(U_190) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_187,sK32(U_191,U_189))],[f_21_5]) ).
fof(f_21_7,plain,
( ! [U_191,U_189] :
( U_189 = union(U_191)
| ( ~ in(sK32(U_191,U_189),U_189)
& in(sK33(U_191,U_189),U_191)
& in(sK32(U_191,U_189),sK33(U_191,U_189)) )
| ( ! [U_179] :
( ~ in(U_179,U_191)
| ~ in(sK31(U_191,U_189),U_179) )
& in(sK31(U_191,U_189),U_189) ) )
& ! [U_190,U_188] :
( ( ! [U_185] :
( in(U_185,U_188)
| ! [U_177] :
( ~ in(U_177,U_190)
| ~ in(U_185,U_177) ) )
& ! [U_184] :
( ( in(sK30(U_190,U_188,U_184),U_190)
& in(U_184,sK30(U_190,U_188,U_184)) )
| ~ in(U_184,U_188) ) )
| U_188 != union(U_190) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_180,sK33(U_191,U_189))],[f_21_6]) ).
fof(f_21_8,plain,
( ! [U_189,U_191] :
( ~ in(sK32(U_191,U_189),U_189)
| ~ sP40(U_189,U_191) )
& ! [U_189,U_191] :
( in(sK33(U_191,U_189),U_191)
| ~ sP40(U_189,U_191) )
& ! [U_189,U_191] :
( in(sK32(U_191,U_189),sK33(U_191,U_189))
| ~ sP40(U_189,U_191) )
& ! [U_189,U_179,U_191] :
( ~ in(U_179,U_191)
| ~ in(sK31(U_191,U_189),U_179)
| ~ sP39(U_189,U_179,U_191) )
& ! [U_189,U_179,U_191] :
( in(sK31(U_191,U_189),U_189)
| ~ sP39(U_189,U_179,U_191) )
& ! [U_184,U_190,U_188] :
( in(sK30(U_190,U_188,U_184),U_190)
| ~ sP37(U_184,U_190,U_188) )
& ! [U_184,U_190,U_188] :
( in(U_184,sK30(U_190,U_188,U_184))
| ~ sP37(U_184,U_190,U_188) )
& ! [U_177,U_185,U_184,U_190,U_188] :
( in(U_185,U_188)
| ~ in(U_177,U_190)
| ~ in(U_185,U_177)
| ~ sP38(U_177,U_185,U_184,U_190,U_188) )
& ! [U_177,U_185,U_184,U_190,U_188] :
( sP37(U_184,U_190,U_188)
| ~ in(U_184,U_188)
| ~ sP38(U_177,U_185,U_184,U_190,U_188) )
& ! [U_189,U_179,U_191] :
( U_189 = union(U_191)
| sP40(U_189,U_191)
| sP39(U_189,U_179,U_191) )
& ! [U_177,U_185,U_184,U_190,U_188] :
( sP38(U_177,U_185,U_184,U_190,U_188)
| U_188 != union(U_190) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP37,sP38,sP39,sP40])],[f_21_7]) ).
cnf(f_21_9,plain,
( sP38(U_177,U_185,U_184,U_190,U_188)
| U_188 != union(U_190) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_10,plain,
( U_189 = union(U_191)
| sP40(U_189,U_191)
| sP39(U_189,U_179,U_191) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_11,plain,
( sP37(U_184,U_190,U_188)
| ~ in(U_184,U_188)
| ~ sP38(U_177,U_185,U_184,U_190,U_188) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_12,plain,
( in(U_185,U_188)
| ~ in(U_177,U_190)
| ~ in(U_185,U_177)
| ~ sP38(U_177,U_185,U_184,U_190,U_188) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_13,plain,
( in(U_184,sK30(U_190,U_188,U_184))
| ~ sP37(U_184,U_190,U_188) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_14,plain,
( in(sK30(U_190,U_188,U_184),U_190)
| ~ sP37(U_184,U_190,U_188) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_15,plain,
( in(sK31(U_191,U_189),U_189)
| ~ sP39(U_189,U_179,U_191) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_16,plain,
( ~ in(U_179,U_191)
| ~ in(sK31(U_191,U_189),U_179)
| ~ sP39(U_189,U_179,U_191) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_17,plain,
( in(sK32(U_191,U_189),sK33(U_191,U_189))
| ~ sP40(U_189,U_191) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_18,plain,
( in(sK33(U_191,U_189),U_191)
| ~ sP40(U_189,U_191) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_19,plain,
( ~ in(sK32(U_191,U_189),U_189)
| ~ sP40(U_189,U_191) ),
inference(clausify,[status(thm)],[f_21_8]) ).
fof(f_22_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_22_2,plain,
! [U_196,U_195,U_194] :
( ( U_194 = set_difference(U_196,U_195)
| ? [U_193] :
( ( ~ in(U_193,U_194)
& ~ in(U_193,U_195)
& in(U_193,U_196) )
| ( ( in(U_193,U_195)
| ~ in(U_193,U_196) )
& in(U_193,U_194) ) ) )
& ( ! [U_192] :
( ( in(U_192,U_194)
| in(U_192,U_195)
| ~ in(U_192,U_196) )
& ( ( ~ in(U_192,U_195)
& in(U_192,U_196) )
| ~ in(U_192,U_194) ) )
| U_194 != set_difference(U_196,U_195) ) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( ! [U_206,U_204,U_202] :
( U_202 = set_difference(U_206,U_204)
| ? [U_200] :
( ~ in(U_200,U_202)
& ~ in(U_200,U_204)
& in(U_200,U_206) )
| ? [U_199] :
( ( in(U_199,U_204)
| ~ in(U_199,U_206) )
& in(U_199,U_202) ) )
& ! [U_205,U_203,U_201] :
( ( ! [U_198] :
( in(U_198,U_201)
| in(U_198,U_203)
| ~ in(U_198,U_205) )
& ! [U_197] :
( ( ~ in(U_197,U_203)
& in(U_197,U_205) )
| ~ in(U_197,U_201) ) )
| U_201 != set_difference(U_205,U_203) ) ),
inference(miniscope,[status(thm)],[f_22_2]) ).
fof(f_22_4,plain,
( ! [U_206,U_204,U_202] :
( U_202 = set_difference(U_206,U_204)
| ? [U_200] :
( ~ in(U_200,U_202)
& ~ in(U_200,U_204)
& in(U_200,U_206) )
| ( ( in(sK34(U_206,U_204,U_202),U_204)
| ~ in(sK34(U_206,U_204,U_202),U_206) )
& in(sK34(U_206,U_204,U_202),U_202) ) )
& ! [U_205,U_203,U_201] :
( ( ! [U_198] :
( in(U_198,U_201)
| in(U_198,U_203)
| ~ in(U_198,U_205) )
& ! [U_197] :
( ( ~ in(U_197,U_203)
& in(U_197,U_205) )
| ~ in(U_197,U_201) ) )
| U_201 != set_difference(U_205,U_203) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_199,sK34(U_206,U_204,U_202))],[f_22_3]) ).
fof(f_22_5,plain,
( ! [U_206,U_204,U_202] :
( U_202 = set_difference(U_206,U_204)
| ( ~ in(sK35(U_206,U_204,U_202),U_202)
& ~ in(sK35(U_206,U_204,U_202),U_204)
& in(sK35(U_206,U_204,U_202),U_206) )
| ( ( in(sK34(U_206,U_204,U_202),U_204)
| ~ in(sK34(U_206,U_204,U_202),U_206) )
& in(sK34(U_206,U_204,U_202),U_202) ) )
& ! [U_205,U_203,U_201] :
( ( ! [U_198] :
( in(U_198,U_201)
| in(U_198,U_203)
| ~ in(U_198,U_205) )
& ! [U_197] :
( ( ~ in(U_197,U_203)
& in(U_197,U_205) )
| ~ in(U_197,U_201) ) )
| U_201 != set_difference(U_205,U_203) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_200,sK35(U_206,U_204,U_202))],[f_22_4]) ).
fof(f_22_6,plain,
( ! [U_202,U_204,U_206] :
( ~ in(sK35(U_206,U_204,U_202),U_202)
| ~ sP44(U_202,U_204,U_206) )
& ! [U_202,U_204,U_206] :
( ~ in(sK35(U_206,U_204,U_202),U_204)
| ~ sP44(U_202,U_204,U_206) )
& ! [U_202,U_204,U_206] :
( in(sK35(U_206,U_204,U_202),U_206)
| ~ sP44(U_202,U_204,U_206) )
& ! [U_202,U_204,U_206] :
( in(sK34(U_206,U_204,U_202),U_204)
| ~ in(sK34(U_206,U_204,U_202),U_206)
| ~ sP43(U_202,U_204,U_206) )
& ! [U_202,U_204,U_206] :
( in(sK34(U_206,U_204,U_202),U_202)
| ~ sP43(U_202,U_204,U_206) )
& ! [U_197,U_203,U_205] :
( ~ in(U_197,U_203)
| ~ sP41(U_197,U_203,U_205) )
& ! [U_197,U_203,U_205] :
( in(U_197,U_205)
| ~ sP41(U_197,U_203,U_205) )
& ! [U_197,U_201,U_198,U_203,U_205] :
( in(U_198,U_201)
| in(U_198,U_203)
| ~ in(U_198,U_205)
| ~ sP42(U_197,U_201,U_198,U_203,U_205) )
& ! [U_197,U_201,U_198,U_203,U_205] :
( sP41(U_197,U_203,U_205)
| ~ in(U_197,U_201)
| ~ sP42(U_197,U_201,U_198,U_203,U_205) )
& ! [U_202,U_204,U_206] :
( U_202 = set_difference(U_206,U_204)
| sP44(U_202,U_204,U_206)
| sP43(U_202,U_204,U_206) )
& ! [U_197,U_201,U_198,U_203,U_205] :
( sP42(U_197,U_201,U_198,U_203,U_205)
| U_201 != set_difference(U_205,U_203) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP41,sP42,sP43,sP44])],[f_22_5]) ).
cnf(f_22_7,plain,
( sP42(U_197,U_201,U_198,U_203,U_205)
| U_201 != set_difference(U_205,U_203) ),
inference(clausify,[status(thm)],[f_22_6]) ).
cnf(f_22_8,plain,
( U_202 = set_difference(U_206,U_204)
| sP44(U_202,U_204,U_206)
| sP43(U_202,U_204,U_206) ),
inference(clausify,[status(thm)],[f_22_6]) ).
cnf(f_22_9,plain,
( sP41(U_197,U_203,U_205)
| ~ in(U_197,U_201)
| ~ sP42(U_197,U_201,U_198,U_203,U_205) ),
inference(clausify,[status(thm)],[f_22_6]) ).
cnf(f_22_10,plain,
( in(U_198,U_201)
| in(U_198,U_203)
| ~ in(U_198,U_205)
| ~ sP42(U_197,U_201,U_198,U_203,U_205) ),
inference(clausify,[status(thm)],[f_22_6]) ).
cnf(f_22_11,plain,
( in(U_197,U_205)
| ~ sP41(U_197,U_203,U_205) ),
inference(clausify,[status(thm)],[f_22_6]) ).
cnf(f_22_12,plain,
( ~ in(U_197,U_203)
| ~ sP41(U_197,U_203,U_205) ),
inference(clausify,[status(thm)],[f_22_6]) ).
cnf(f_22_13,plain,
( in(sK34(U_206,U_204,U_202),U_202)
| ~ sP43(U_202,U_204,U_206) ),
inference(clausify,[status(thm)],[f_22_6]) ).
cnf(f_22_14,plain,
( in(sK34(U_206,U_204,U_202),U_204)
| ~ in(sK34(U_206,U_204,U_202),U_206)
| ~ sP43(U_202,U_204,U_206) ),
inference(clausify,[status(thm)],[f_22_6]) ).
cnf(f_22_15,plain,
( in(sK35(U_206,U_204,U_202),U_206)
| ~ sP44(U_202,U_204,U_206) ),
inference(clausify,[status(thm)],[f_22_6]) ).
cnf(f_22_16,plain,
( ~ in(sK35(U_206,U_204,U_202),U_204)
| ~ sP44(U_202,U_204,U_206) ),
inference(clausify,[status(thm)],[f_22_6]) ).
cnf(f_22_17,plain,
( ~ in(sK35(U_206,U_204,U_202),U_202)
| ~ sP44(U_202,U_204,U_206) ),
inference(clausify,[status(thm)],[f_22_6]) ).
fof(f_23_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_23_2,plain,
! [U_214] :
( ! [U_213] :
( ( U_213 = relation_rng(U_214)
| ? [U_212] :
( ( ~ in(U_212,U_213)
& ? [U_211] : in(ordered_pair(U_211,U_212),U_214) )
| ( ! [U_210] : ~ in(ordered_pair(U_210,U_212),U_214)
& in(U_212,U_213) ) ) )
& ( ! [U_209] :
( ( in(U_209,U_213)
| ! [U_208] : ~ in(ordered_pair(U_208,U_209),U_214) )
& ( ? [U_207] : in(ordered_pair(U_207,U_209),U_214)
| ~ in(U_209,U_213) ) )
| U_213 != relation_rng(U_214) ) )
| ~ relation(U_214) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_214] :
( ( ! [U_220] :
( U_220 = relation_rng(U_214)
| ? [U_218] :
( ~ in(U_218,U_220)
& ? [U_211] : in(ordered_pair(U_211,U_218),U_214) )
| ? [U_217] :
( ! [U_210] : ~ in(ordered_pair(U_210,U_217),U_214)
& in(U_217,U_220) ) )
& ! [U_219] :
( ( ! [U_216] :
( in(U_216,U_219)
| ! [U_208] : ~ in(ordered_pair(U_208,U_216),U_214) )
& ! [U_215] :
( ? [U_207] : in(ordered_pair(U_207,U_215),U_214)
| ~ in(U_215,U_219) ) )
| U_219 != relation_rng(U_214) ) )
| ~ relation(U_214) ),
inference(miniscope,[status(thm)],[f_23_2]) ).
fof(f_23_4,plain,
! [U_214] :
( ( ! [U_220] :
( U_220 = relation_rng(U_214)
| ? [U_218] :
( ~ in(U_218,U_220)
& ? [U_211] : in(ordered_pair(U_211,U_218),U_214) )
| ? [U_217] :
( ! [U_210] : ~ in(ordered_pair(U_210,U_217),U_214)
& in(U_217,U_220) ) )
& ! [U_219] :
( ( ! [U_216] :
( in(U_216,U_219)
| ! [U_208] : ~ in(ordered_pair(U_208,U_216),U_214) )
& ! [U_215] :
( in(ordered_pair(sK36(U_214,U_219,U_215),U_215),U_214)
| ~ in(U_215,U_219) ) )
| U_219 != relation_rng(U_214) ) )
| ~ relation(U_214) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_207,sK36(U_214,U_219,U_215))],[f_23_3]) ).
fof(f_23_5,plain,
! [U_214] :
( ( ! [U_220] :
( U_220 = relation_rng(U_214)
| ? [U_218] :
( ~ in(U_218,U_220)
& ? [U_211] : in(ordered_pair(U_211,U_218),U_214) )
| ( ! [U_210] : ~ in(ordered_pair(U_210,sK37(U_214,U_220)),U_214)
& in(sK37(U_214,U_220),U_220) ) )
& ! [U_219] :
( ( ! [U_216] :
( in(U_216,U_219)
| ! [U_208] : ~ in(ordered_pair(U_208,U_216),U_214) )
& ! [U_215] :
( in(ordered_pair(sK36(U_214,U_219,U_215),U_215),U_214)
| ~ in(U_215,U_219) ) )
| U_219 != relation_rng(U_214) ) )
| ~ relation(U_214) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_217,sK37(U_214,U_220))],[f_23_4]) ).
fof(f_23_6,plain,
! [U_214] :
( ( ! [U_220] :
( U_220 = relation_rng(U_214)
| ( ~ in(sK38(U_214,U_220),U_220)
& ? [U_211] : in(ordered_pair(U_211,sK38(U_214,U_220)),U_214) )
| ( ! [U_210] : ~ in(ordered_pair(U_210,sK37(U_214,U_220)),U_214)
& in(sK37(U_214,U_220),U_220) ) )
& ! [U_219] :
( ( ! [U_216] :
( in(U_216,U_219)
| ! [U_208] : ~ in(ordered_pair(U_208,U_216),U_214) )
& ! [U_215] :
( in(ordered_pair(sK36(U_214,U_219,U_215),U_215),U_214)
| ~ in(U_215,U_219) ) )
| U_219 != relation_rng(U_214) ) )
| ~ relation(U_214) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_218,sK38(U_214,U_220))],[f_23_5]) ).
fof(f_23_7,plain,
! [U_214] :
( ( ! [U_220] :
( U_220 = relation_rng(U_214)
| ( ~ in(sK38(U_214,U_220),U_220)
& in(ordered_pair(sK39(U_214,U_220),sK38(U_214,U_220)),U_214) )
| ( ! [U_210] : ~ in(ordered_pair(U_210,sK37(U_214,U_220)),U_214)
& in(sK37(U_214,U_220),U_220) ) )
& ! [U_219] :
( ( ! [U_216] :
( in(U_216,U_219)
| ! [U_208] : ~ in(ordered_pair(U_208,U_216),U_214) )
& ! [U_215] :
( in(ordered_pair(sK36(U_214,U_219,U_215),U_215),U_214)
| ~ in(U_215,U_219) ) )
| U_219 != relation_rng(U_214) ) )
| ~ relation(U_214) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_211,sK39(U_214,U_220))],[f_23_6]) ).
fof(f_23_8,plain,
( ! [U_214,U_220] :
( ~ in(sK38(U_214,U_220),U_220)
| ~ sP47(U_214,U_220) )
& ! [U_214,U_220] :
( in(ordered_pair(sK39(U_214,U_220),sK38(U_214,U_220)),U_214)
| ~ sP47(U_214,U_220) )
& ! [U_210,U_214,U_220] :
( ~ in(ordered_pair(U_210,sK37(U_214,U_220)),U_214)
| ~ sP46(U_210,U_214,U_220) )
& ! [U_210,U_214,U_220] :
( in(sK37(U_214,U_220),U_220)
| ~ sP46(U_210,U_214,U_220) )
& ! [U_208,U_215,U_216,U_214,U_219] :
( in(U_216,U_219)
| ~ in(ordered_pair(U_208,U_216),U_214)
| ~ sP45(U_208,U_215,U_216,U_214,U_219) )
& ! [U_208,U_215,U_216,U_214,U_219] :
( in(ordered_pair(sK36(U_214,U_219,U_215),U_215),U_214)
| ~ in(U_215,U_219)
| ~ sP45(U_208,U_215,U_216,U_214,U_219) )
& ! [U_208,U_210,U_215,U_216,U_214,U_220,U_219] :
( U_220 = relation_rng(U_214)
| sP47(U_214,U_220)
| sP46(U_210,U_214,U_220)
| ~ sP48(U_208,U_210,U_215,U_216,U_214,U_220,U_219) )
& ! [U_208,U_210,U_215,U_216,U_214,U_220,U_219] :
( sP45(U_208,U_215,U_216,U_214,U_219)
| U_219 != relation_rng(U_214)
| ~ sP48(U_208,U_210,U_215,U_216,U_214,U_220,U_219) )
& ! [U_208,U_210,U_215,U_216,U_214,U_220,U_219] :
( sP48(U_208,U_210,U_215,U_216,U_214,U_220,U_219)
| ~ relation(U_214) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP45,sP46,sP47,sP48])],[f_23_7]) ).
cnf(f_23_9,plain,
( sP48(U_208,U_210,U_215,U_216,U_214,U_220,U_219)
| ~ relation(U_214) ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_10,plain,
( sP45(U_208,U_215,U_216,U_214,U_219)
| U_219 != relation_rng(U_214)
| ~ sP48(U_208,U_210,U_215,U_216,U_214,U_220,U_219) ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_11,plain,
( U_220 = relation_rng(U_214)
| sP47(U_214,U_220)
| sP46(U_210,U_214,U_220)
| ~ sP48(U_208,U_210,U_215,U_216,U_214,U_220,U_219) ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_12,plain,
( in(ordered_pair(sK36(U_214,U_219,U_215),U_215),U_214)
| ~ in(U_215,U_219)
| ~ sP45(U_208,U_215,U_216,U_214,U_219) ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_13,plain,
( in(U_216,U_219)
| ~ in(ordered_pair(U_208,U_216),U_214)
| ~ sP45(U_208,U_215,U_216,U_214,U_219) ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_14,plain,
( in(sK37(U_214,U_220),U_220)
| ~ sP46(U_210,U_214,U_220) ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_15,plain,
( ~ in(ordered_pair(U_210,sK37(U_214,U_220)),U_214)
| ~ sP46(U_210,U_214,U_220) ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_16,plain,
( in(ordered_pair(sK39(U_214,U_220),sK38(U_214,U_220)),U_214)
| ~ sP47(U_214,U_220) ),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_17,plain,
( ~ in(sK38(U_214,U_220),U_220)
| ~ sP47(U_214,U_220) ),
inference(clausify,[status(thm)],[f_23_8]) ).
fof(f_24_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_24_2,plain,
! [U_222,U_221] :
( subset_complement(U_222,U_221) = set_difference(U_222,U_221)
| ~ element(U_221,powerset(U_222)) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_222,U_221] :
( subset_complement(U_222,U_221) = set_difference(U_222,U_221)
| ~ element(U_221,powerset(U_222)) ),
inference(definitional_conversion,[status(esa)],[f_24_2]) ).
cnf(f_24_4,plain,
( subset_complement(U_222,U_221) = set_difference(U_222,U_221)
| ~ element(U_221,powerset(U_222)) ),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_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_25_2,plain,
! [U_224,U_223] : ordered_pair(U_224,U_223) = unordered_pair(unordered_pair(U_224,U_223),singleton(U_224)),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_224,U_223] : ordered_pair(U_224,U_223) = unordered_pair(unordered_pair(U_224,U_223),singleton(U_224)),
inference(definitional_conversion,[status(esa)],[f_25_2]) ).
cnf(f_25_4,plain,
ordered_pair(U_224,U_223) = unordered_pair(unordered_pair(U_224,U_223),singleton(U_224)),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_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_26_2,plain,
! [U_225] :
( relation_field(U_225) = set_union2(relation_dom(U_225),relation_rng(U_225))
| ~ relation(U_225) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_225] :
( relation_field(U_225) = set_union2(relation_dom(U_225),relation_rng(U_225))
| ~ relation(U_225) ),
inference(definitional_conversion,[status(esa)],[f_26_2]) ).
cnf(f_26_4,plain,
( relation_field(U_225) = set_union2(relation_dom(U_225),relation_rng(U_225))
| ~ relation(U_225) ),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_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_27_2,plain,
! [U_231] :
( ! [U_230] :
( ( ( U_230 = relation_inverse(U_231)
| ? [U_229,U_228] :
( ( ~ in(ordered_pair(U_229,U_228),U_230)
& in(ordered_pair(U_228,U_229),U_231) )
| ( ~ in(ordered_pair(U_228,U_229),U_231)
& in(ordered_pair(U_229,U_228),U_230) ) ) )
& ( ! [U_227,U_226] :
( ( in(ordered_pair(U_227,U_226),U_230)
| ~ in(ordered_pair(U_226,U_227),U_231) )
& ( in(ordered_pair(U_226,U_227),U_231)
| ~ in(ordered_pair(U_227,U_226),U_230) ) )
| U_230 != relation_inverse(U_231) ) )
| ~ relation(U_230) )
| ~ relation(U_231) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_231] :
( ! [U_230] :
( ( ( U_230 = relation_inverse(U_231)
| ? [U_239,U_237] :
( ~ in(ordered_pair(U_239,U_237),U_230)
& in(ordered_pair(U_237,U_239),U_231) )
| ? [U_238,U_236] :
( ~ in(ordered_pair(U_236,U_238),U_231)
& in(ordered_pair(U_238,U_236),U_230) ) )
& ( ( ! [U_235,U_233] :
( in(ordered_pair(U_235,U_233),U_230)
| ~ in(ordered_pair(U_233,U_235),U_231) )
& ! [U_234,U_232] :
( in(ordered_pair(U_232,U_234),U_231)
| ~ in(ordered_pair(U_234,U_232),U_230) ) )
| U_230 != relation_inverse(U_231) ) )
| ~ relation(U_230) )
| ~ relation(U_231) ),
inference(miniscope,[status(thm)],[f_27_2]) ).
fof(f_27_4,plain,
! [U_231] :
( ! [U_230] :
( ( ( U_230 = relation_inverse(U_231)
| ? [U_239,U_237] :
( ~ in(ordered_pair(U_239,U_237),U_230)
& in(ordered_pair(U_237,U_239),U_231) )
| ? [U_236] :
( ~ in(ordered_pair(U_236,sK40(U_231,U_230)),U_231)
& in(ordered_pair(sK40(U_231,U_230),U_236),U_230) ) )
& ( ( ! [U_235,U_233] :
( in(ordered_pair(U_235,U_233),U_230)
| ~ in(ordered_pair(U_233,U_235),U_231) )
& ! [U_234,U_232] :
( in(ordered_pair(U_232,U_234),U_231)
| ~ in(ordered_pair(U_234,U_232),U_230) ) )
| U_230 != relation_inverse(U_231) ) )
| ~ relation(U_230) )
| ~ relation(U_231) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_238,sK40(U_231,U_230))],[f_27_3]) ).
fof(f_27_5,plain,
! [U_231] :
( ! [U_230] :
( ( ( U_230 = relation_inverse(U_231)
| ? [U_239,U_237] :
( ~ in(ordered_pair(U_239,U_237),U_230)
& in(ordered_pair(U_237,U_239),U_231) )
| ( ~ in(ordered_pair(sK41(U_231,U_230),sK40(U_231,U_230)),U_231)
& in(ordered_pair(sK40(U_231,U_230),sK41(U_231,U_230)),U_230) ) )
& ( ( ! [U_235,U_233] :
( in(ordered_pair(U_235,U_233),U_230)
| ~ in(ordered_pair(U_233,U_235),U_231) )
& ! [U_234,U_232] :
( in(ordered_pair(U_232,U_234),U_231)
| ~ in(ordered_pair(U_234,U_232),U_230) ) )
| U_230 != relation_inverse(U_231) ) )
| ~ relation(U_230) )
| ~ relation(U_231) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_236,sK41(U_231,U_230))],[f_27_4]) ).
fof(f_27_6,plain,
! [U_231] :
( ! [U_230] :
( ( ( U_230 = relation_inverse(U_231)
| ? [U_237] :
( ~ in(ordered_pair(sK42(U_231,U_230),U_237),U_230)
& in(ordered_pair(U_237,sK42(U_231,U_230)),U_231) )
| ( ~ in(ordered_pair(sK41(U_231,U_230),sK40(U_231,U_230)),U_231)
& in(ordered_pair(sK40(U_231,U_230),sK41(U_231,U_230)),U_230) ) )
& ( ( ! [U_235,U_233] :
( in(ordered_pair(U_235,U_233),U_230)
| ~ in(ordered_pair(U_233,U_235),U_231) )
& ! [U_234,U_232] :
( in(ordered_pair(U_232,U_234),U_231)
| ~ in(ordered_pair(U_234,U_232),U_230) ) )
| U_230 != relation_inverse(U_231) ) )
| ~ relation(U_230) )
| ~ relation(U_231) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_239,sK42(U_231,U_230))],[f_27_5]) ).
fof(f_27_7,plain,
! [U_231] :
( ! [U_230] :
( ( ( U_230 = relation_inverse(U_231)
| ( ~ in(ordered_pair(sK42(U_231,U_230),sK43(U_231,U_230)),U_230)
& in(ordered_pair(sK43(U_231,U_230),sK42(U_231,U_230)),U_231) )
| ( ~ in(ordered_pair(sK41(U_231,U_230),sK40(U_231,U_230)),U_231)
& in(ordered_pair(sK40(U_231,U_230),sK41(U_231,U_230)),U_230) ) )
& ( ( ! [U_235,U_233] :
( in(ordered_pair(U_235,U_233),U_230)
| ~ in(ordered_pair(U_233,U_235),U_231) )
& ! [U_234,U_232] :
( in(ordered_pair(U_232,U_234),U_231)
| ~ in(ordered_pair(U_234,U_232),U_230) ) )
| U_230 != relation_inverse(U_231) ) )
| ~ relation(U_230) )
| ~ relation(U_231) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_237,sK43(U_231,U_230))],[f_27_6]) ).
fof(f_27_8,plain,
( ! [U_230,U_231] :
( ~ in(ordered_pair(sK42(U_231,U_230),sK43(U_231,U_230)),U_230)
| ~ sP51(U_230,U_231) )
& ! [U_230,U_231] :
( in(ordered_pair(sK43(U_231,U_230),sK42(U_231,U_230)),U_231)
| ~ sP51(U_230,U_231) )
& ! [U_230,U_231] :
( ~ in(ordered_pair(sK41(U_231,U_230),sK40(U_231,U_230)),U_231)
| ~ sP50(U_230,U_231) )
& ! [U_230,U_231] :
( in(ordered_pair(sK40(U_231,U_230),sK41(U_231,U_230)),U_230)
| ~ sP50(U_230,U_231) )
& ! [U_234,U_232,U_233,U_230,U_231,U_235] :
( in(ordered_pair(U_235,U_233),U_230)
| ~ in(ordered_pair(U_233,U_235),U_231)
| ~ sP49(U_234,U_232,U_233,U_230,U_231,U_235) )
& ! [U_234,U_232,U_233,U_230,U_231,U_235] :
( in(ordered_pair(U_232,U_234),U_231)
| ~ in(ordered_pair(U_234,U_232),U_230)
| ~ sP49(U_234,U_232,U_233,U_230,U_231,U_235) )
& ! [U_234,U_232,U_233,U_230,U_231,U_235] :
( U_230 = relation_inverse(U_231)
| sP51(U_230,U_231)
| sP50(U_230,U_231)
| ~ sP52(U_234,U_232,U_233,U_230,U_231,U_235) )
& ! [U_234,U_232,U_233,U_230,U_231,U_235] :
( sP49(U_234,U_232,U_233,U_230,U_231,U_235)
| U_230 != relation_inverse(U_231)
| ~ sP52(U_234,U_232,U_233,U_230,U_231,U_235) )
& ! [U_234,U_232,U_233,U_230,U_231,U_235] :
( sP52(U_234,U_232,U_233,U_230,U_231,U_235)
| ~ relation(U_230)
| ~ relation(U_231) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP49,sP50,sP51,sP52])],[f_27_7]) ).
cnf(f_27_9,plain,
( sP52(U_234,U_232,U_233,U_230,U_231,U_235)
| ~ relation(U_230)
| ~ relation(U_231) ),
inference(clausify,[status(thm)],[f_27_8]) ).
cnf(f_27_10,plain,
( sP49(U_234,U_232,U_233,U_230,U_231,U_235)
| U_230 != relation_inverse(U_231)
| ~ sP52(U_234,U_232,U_233,U_230,U_231,U_235) ),
inference(clausify,[status(thm)],[f_27_8]) ).
cnf(f_27_11,plain,
( U_230 = relation_inverse(U_231)
| sP51(U_230,U_231)
| sP50(U_230,U_231)
| ~ sP52(U_234,U_232,U_233,U_230,U_231,U_235) ),
inference(clausify,[status(thm)],[f_27_8]) ).
cnf(f_27_12,plain,
( in(ordered_pair(U_232,U_234),U_231)
| ~ in(ordered_pair(U_234,U_232),U_230)
| ~ sP49(U_234,U_232,U_233,U_230,U_231,U_235) ),
inference(clausify,[status(thm)],[f_27_8]) ).
cnf(f_27_13,plain,
( in(ordered_pair(U_235,U_233),U_230)
| ~ in(ordered_pair(U_233,U_235),U_231)
| ~ sP49(U_234,U_232,U_233,U_230,U_231,U_235) ),
inference(clausify,[status(thm)],[f_27_8]) ).
cnf(f_27_14,plain,
( in(ordered_pair(sK40(U_231,U_230),sK41(U_231,U_230)),U_230)
| ~ sP50(U_230,U_231) ),
inference(clausify,[status(thm)],[f_27_8]) ).
cnf(f_27_15,plain,
( ~ in(ordered_pair(sK41(U_231,U_230),sK40(U_231,U_230)),U_231)
| ~ sP50(U_230,U_231) ),
inference(clausify,[status(thm)],[f_27_8]) ).
cnf(f_27_16,plain,
( in(ordered_pair(sK43(U_231,U_230),sK42(U_231,U_230)),U_231)
| ~ sP51(U_230,U_231) ),
inference(clausify,[status(thm)],[f_27_8]) ).
cnf(f_27_17,plain,
( ~ in(ordered_pair(sK42(U_231,U_230),sK43(U_231,U_230)),U_230)
| ~ sP51(U_230,U_231) ),
inference(clausify,[status(thm)],[f_27_8]) ).
fof(f_28_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_28_2,plain,
! [U_241,U_240] :
( ( disjoint(U_241,U_240)
| set_intersection2(U_241,U_240) != empty_set )
& ( set_intersection2(U_241,U_240) = empty_set
| ~ disjoint(U_241,U_240) ) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( ! [U_245,U_243] :
( disjoint(U_245,U_243)
| set_intersection2(U_245,U_243) != empty_set )
& ! [U_244,U_242] :
( set_intersection2(U_244,U_242) = empty_set
| ~ disjoint(U_244,U_242) ) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
fof(f_28_4,plain,
( ! [U_243,U_245] :
( disjoint(U_245,U_243)
| set_intersection2(U_245,U_243) != empty_set )
& ! [U_242,U_244] :
( set_intersection2(U_244,U_242) = empty_set
| ~ disjoint(U_244,U_242) ) ),
inference(definitional_conversion,[status(esa)],[f_28_3]) ).
cnf(f_28_5,plain,
( set_intersection2(U_244,U_242) = empty_set
| ~ disjoint(U_244,U_242) ),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_6,plain,
( disjoint(U_245,U_243)
| set_intersection2(U_245,U_243) != empty_set ),
inference(clausify,[status(thm)],[f_28_4]) ).
fof(f_29_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_29_2,plain,
! [U_256] :
( ! [U_255] :
( ! [U_254] :
( ( ( U_254 = relation_composition(U_256,U_255)
| ? [U_253,U_252] :
( ( ~ in(ordered_pair(U_253,U_252),U_254)
& ? [U_251] :
( in(ordered_pair(U_251,U_252),U_255)
& in(ordered_pair(U_253,U_251),U_256) ) )
| ( ! [U_250] :
( ~ in(ordered_pair(U_250,U_252),U_255)
| ~ in(ordered_pair(U_253,U_250),U_256) )
& in(ordered_pair(U_253,U_252),U_254) ) ) )
& ( ! [U_249,U_248] :
( ( in(ordered_pair(U_249,U_248),U_254)
| ! [U_247] :
( ~ in(ordered_pair(U_247,U_248),U_255)
| ~ in(ordered_pair(U_249,U_247),U_256) ) )
& ( ? [U_246] :
( in(ordered_pair(U_246,U_248),U_255)
& in(ordered_pair(U_249,U_246),U_256) )
| ~ in(ordered_pair(U_249,U_248),U_254) ) )
| U_254 != relation_composition(U_256,U_255) ) )
| ~ relation(U_254) )
| ~ relation(U_255) )
| ~ relation(U_256) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_256] :
( ! [U_255] :
( ! [U_254] :
( ( ( U_254 = relation_composition(U_256,U_255)
| ? [U_264,U_262] :
( ~ in(ordered_pair(U_264,U_262),U_254)
& ? [U_251] :
( in(ordered_pair(U_251,U_262),U_255)
& in(ordered_pair(U_264,U_251),U_256) ) )
| ? [U_263,U_261] :
( ! [U_250] :
( ~ in(ordered_pair(U_250,U_261),U_255)
| ~ in(ordered_pair(U_263,U_250),U_256) )
& in(ordered_pair(U_263,U_261),U_254) ) )
& ( ( ! [U_260,U_258] :
( in(ordered_pair(U_260,U_258),U_254)
| ! [U_247] :
( ~ in(ordered_pair(U_247,U_258),U_255)
| ~ in(ordered_pair(U_260,U_247),U_256) ) )
& ! [U_259,U_257] :
( ? [U_246] :
( in(ordered_pair(U_246,U_257),U_255)
& in(ordered_pair(U_259,U_246),U_256) )
| ~ in(ordered_pair(U_259,U_257),U_254) ) )
| U_254 != relation_composition(U_256,U_255) ) )
| ~ relation(U_254) )
| ~ relation(U_255) )
| ~ relation(U_256) ),
inference(miniscope,[status(thm)],[f_29_2]) ).
fof(f_29_4,plain,
! [U_256] :
( ! [U_255] :
( ! [U_254] :
( ( ( U_254 = relation_composition(U_256,U_255)
| ? [U_264,U_262] :
( ~ in(ordered_pair(U_264,U_262),U_254)
& ? [U_251] :
( in(ordered_pair(U_251,U_262),U_255)
& in(ordered_pair(U_264,U_251),U_256) ) )
| ? [U_263,U_261] :
( ! [U_250] :
( ~ in(ordered_pair(U_250,U_261),U_255)
| ~ in(ordered_pair(U_263,U_250),U_256) )
& in(ordered_pair(U_263,U_261),U_254) ) )
& ( ( ! [U_260,U_258] :
( in(ordered_pair(U_260,U_258),U_254)
| ! [U_247] :
( ~ in(ordered_pair(U_247,U_258),U_255)
| ~ in(ordered_pair(U_260,U_247),U_256) ) )
& ! [U_259,U_257] :
( ( in(ordered_pair(sK44(U_256,U_255,U_254,U_259,U_257),U_257),U_255)
& in(ordered_pair(U_259,sK44(U_256,U_255,U_254,U_259,U_257)),U_256) )
| ~ in(ordered_pair(U_259,U_257),U_254) ) )
| U_254 != relation_composition(U_256,U_255) ) )
| ~ relation(U_254) )
| ~ relation(U_255) )
| ~ relation(U_256) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_246,sK44(U_256,U_255,U_254,U_259,U_257))],[f_29_3]) ).
fof(f_29_5,plain,
! [U_256] :
( ! [U_255] :
( ! [U_254] :
( ( ( U_254 = relation_composition(U_256,U_255)
| ? [U_264,U_262] :
( ~ in(ordered_pair(U_264,U_262),U_254)
& ? [U_251] :
( in(ordered_pair(U_251,U_262),U_255)
& in(ordered_pair(U_264,U_251),U_256) ) )
| ? [U_261] :
( ! [U_250] :
( ~ in(ordered_pair(U_250,U_261),U_255)
| ~ in(ordered_pair(sK45(U_256,U_255,U_254),U_250),U_256) )
& in(ordered_pair(sK45(U_256,U_255,U_254),U_261),U_254) ) )
& ( ( ! [U_260,U_258] :
( in(ordered_pair(U_260,U_258),U_254)
| ! [U_247] :
( ~ in(ordered_pair(U_247,U_258),U_255)
| ~ in(ordered_pair(U_260,U_247),U_256) ) )
& ! [U_259,U_257] :
( ( in(ordered_pair(sK44(U_256,U_255,U_254,U_259,U_257),U_257),U_255)
& in(ordered_pair(U_259,sK44(U_256,U_255,U_254,U_259,U_257)),U_256) )
| ~ in(ordered_pair(U_259,U_257),U_254) ) )
| U_254 != relation_composition(U_256,U_255) ) )
| ~ relation(U_254) )
| ~ relation(U_255) )
| ~ relation(U_256) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_263,sK45(U_256,U_255,U_254))],[f_29_4]) ).
fof(f_29_6,plain,
! [U_256] :
( ! [U_255] :
( ! [U_254] :
( ( ( U_254 = relation_composition(U_256,U_255)
| ? [U_264,U_262] :
( ~ in(ordered_pair(U_264,U_262),U_254)
& ? [U_251] :
( in(ordered_pair(U_251,U_262),U_255)
& in(ordered_pair(U_264,U_251),U_256) ) )
| ( ! [U_250] :
( ~ in(ordered_pair(U_250,sK46(U_256,U_255,U_254)),U_255)
| ~ in(ordered_pair(sK45(U_256,U_255,U_254),U_250),U_256) )
& in(ordered_pair(sK45(U_256,U_255,U_254),sK46(U_256,U_255,U_254)),U_254) ) )
& ( ( ! [U_260,U_258] :
( in(ordered_pair(U_260,U_258),U_254)
| ! [U_247] :
( ~ in(ordered_pair(U_247,U_258),U_255)
| ~ in(ordered_pair(U_260,U_247),U_256) ) )
& ! [U_259,U_257] :
( ( in(ordered_pair(sK44(U_256,U_255,U_254,U_259,U_257),U_257),U_255)
& in(ordered_pair(U_259,sK44(U_256,U_255,U_254,U_259,U_257)),U_256) )
| ~ in(ordered_pair(U_259,U_257),U_254) ) )
| U_254 != relation_composition(U_256,U_255) ) )
| ~ relation(U_254) )
| ~ relation(U_255) )
| ~ relation(U_256) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_261,sK46(U_256,U_255,U_254))],[f_29_5]) ).
fof(f_29_7,plain,
! [U_256] :
( ! [U_255] :
( ! [U_254] :
( ( ( U_254 = relation_composition(U_256,U_255)
| ? [U_262] :
( ~ in(ordered_pair(sK47(U_256,U_255,U_254),U_262),U_254)
& ? [U_251] :
( in(ordered_pair(U_251,U_262),U_255)
& in(ordered_pair(sK47(U_256,U_255,U_254),U_251),U_256) ) )
| ( ! [U_250] :
( ~ in(ordered_pair(U_250,sK46(U_256,U_255,U_254)),U_255)
| ~ in(ordered_pair(sK45(U_256,U_255,U_254),U_250),U_256) )
& in(ordered_pair(sK45(U_256,U_255,U_254),sK46(U_256,U_255,U_254)),U_254) ) )
& ( ( ! [U_260,U_258] :
( in(ordered_pair(U_260,U_258),U_254)
| ! [U_247] :
( ~ in(ordered_pair(U_247,U_258),U_255)
| ~ in(ordered_pair(U_260,U_247),U_256) ) )
& ! [U_259,U_257] :
( ( in(ordered_pair(sK44(U_256,U_255,U_254,U_259,U_257),U_257),U_255)
& in(ordered_pair(U_259,sK44(U_256,U_255,U_254,U_259,U_257)),U_256) )
| ~ in(ordered_pair(U_259,U_257),U_254) ) )
| U_254 != relation_composition(U_256,U_255) ) )
| ~ relation(U_254) )
| ~ relation(U_255) )
| ~ relation(U_256) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_264,sK47(U_256,U_255,U_254))],[f_29_6]) ).
fof(f_29_8,plain,
! [U_256] :
( ! [U_255] :
( ! [U_254] :
( ( ( U_254 = relation_composition(U_256,U_255)
| ( ~ in(ordered_pair(sK47(U_256,U_255,U_254),sK48(U_256,U_255,U_254)),U_254)
& ? [U_251] :
( in(ordered_pair(U_251,sK48(U_256,U_255,U_254)),U_255)
& in(ordered_pair(sK47(U_256,U_255,U_254),U_251),U_256) ) )
| ( ! [U_250] :
( ~ in(ordered_pair(U_250,sK46(U_256,U_255,U_254)),U_255)
| ~ in(ordered_pair(sK45(U_256,U_255,U_254),U_250),U_256) )
& in(ordered_pair(sK45(U_256,U_255,U_254),sK46(U_256,U_255,U_254)),U_254) ) )
& ( ( ! [U_260,U_258] :
( in(ordered_pair(U_260,U_258),U_254)
| ! [U_247] :
( ~ in(ordered_pair(U_247,U_258),U_255)
| ~ in(ordered_pair(U_260,U_247),U_256) ) )
& ! [U_259,U_257] :
( ( in(ordered_pair(sK44(U_256,U_255,U_254,U_259,U_257),U_257),U_255)
& in(ordered_pair(U_259,sK44(U_256,U_255,U_254,U_259,U_257)),U_256) )
| ~ in(ordered_pair(U_259,U_257),U_254) ) )
| U_254 != relation_composition(U_256,U_255) ) )
| ~ relation(U_254) )
| ~ relation(U_255) )
| ~ relation(U_256) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_262,sK48(U_256,U_255,U_254))],[f_29_7]) ).
fof(f_29_9,plain,
! [U_256] :
( ! [U_255] :
( ! [U_254] :
( ( ( U_254 = relation_composition(U_256,U_255)
| ( ~ in(ordered_pair(sK47(U_256,U_255,U_254),sK48(U_256,U_255,U_254)),U_254)
& in(ordered_pair(sK49(U_256,U_255,U_254),sK48(U_256,U_255,U_254)),U_255)
& in(ordered_pair(sK47(U_256,U_255,U_254),sK49(U_256,U_255,U_254)),U_256) )
| ( ! [U_250] :
( ~ in(ordered_pair(U_250,sK46(U_256,U_255,U_254)),U_255)
| ~ in(ordered_pair(sK45(U_256,U_255,U_254),U_250),U_256) )
& in(ordered_pair(sK45(U_256,U_255,U_254),sK46(U_256,U_255,U_254)),U_254) ) )
& ( ( ! [U_260,U_258] :
( in(ordered_pair(U_260,U_258),U_254)
| ! [U_247] :
( ~ in(ordered_pair(U_247,U_258),U_255)
| ~ in(ordered_pair(U_260,U_247),U_256) ) )
& ! [U_259,U_257] :
( ( in(ordered_pair(sK44(U_256,U_255,U_254,U_259,U_257),U_257),U_255)
& in(ordered_pair(U_259,sK44(U_256,U_255,U_254,U_259,U_257)),U_256) )
| ~ in(ordered_pair(U_259,U_257),U_254) ) )
| U_254 != relation_composition(U_256,U_255) ) )
| ~ relation(U_254) )
| ~ relation(U_255) )
| ~ relation(U_256) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_251,sK49(U_256,U_255,U_254))],[f_29_8]) ).
fof(f_29_10,plain,
( ! [U_254,U_255,U_256] :
( ~ in(ordered_pair(sK47(U_256,U_255,U_254),sK48(U_256,U_255,U_254)),U_254)
| ~ sP56(U_254,U_255,U_256) )
& ! [U_254,U_255,U_256] :
( in(ordered_pair(sK49(U_256,U_255,U_254),sK48(U_256,U_255,U_254)),U_255)
| ~ sP56(U_254,U_255,U_256) )
& ! [U_254,U_255,U_256] :
( in(ordered_pair(sK47(U_256,U_255,U_254),sK49(U_256,U_255,U_254)),U_256)
| ~ sP56(U_254,U_255,U_256) )
& ! [U_254,U_255,U_256,U_250] :
( ~ in(ordered_pair(U_250,sK46(U_256,U_255,U_254)),U_255)
| ~ in(ordered_pair(sK45(U_256,U_255,U_254),U_250),U_256)
| ~ sP55(U_254,U_255,U_256,U_250) )
& ! [U_254,U_255,U_256,U_250] :
( in(ordered_pair(sK45(U_256,U_255,U_254),sK46(U_256,U_255,U_254)),U_254)
| ~ sP55(U_254,U_255,U_256,U_250) )
& ! [U_254,U_255,U_259,U_256,U_257] :
( in(ordered_pair(sK44(U_256,U_255,U_254,U_259,U_257),U_257),U_255)
| ~ sP53(U_254,U_255,U_259,U_256,U_257) )
& ! [U_254,U_255,U_259,U_256,U_257] :
( in(ordered_pair(U_259,sK44(U_256,U_255,U_254,U_259,U_257)),U_256)
| ~ sP53(U_254,U_255,U_259,U_256,U_257) )
& ! [U_254,U_255,U_260,U_258,U_247,U_259,U_256,U_257] :
( in(ordered_pair(U_260,U_258),U_254)
| ~ in(ordered_pair(U_247,U_258),U_255)
| ~ in(ordered_pair(U_260,U_247),U_256)
| ~ sP54(U_254,U_255,U_260,U_258,U_247,U_259,U_256,U_257) )
& ! [U_254,U_255,U_260,U_258,U_247,U_259,U_256,U_257] :
( sP53(U_254,U_255,U_259,U_256,U_257)
| ~ in(ordered_pair(U_259,U_257),U_254)
| ~ sP54(U_254,U_255,U_260,U_258,U_247,U_259,U_256,U_257) )
& ! [U_254,U_255,U_260,U_258,U_247,U_259,U_256,U_257,U_250] :
( U_254 = relation_composition(U_256,U_255)
| sP56(U_254,U_255,U_256)
| sP55(U_254,U_255,U_256,U_250)
| ~ sP57(U_254,U_255,U_260,U_258,U_247,U_259,U_256,U_257,U_250) )
& ! [U_254,U_255,U_260,U_258,U_247,U_259,U_256,U_257,U_250] :
( sP54(U_254,U_255,U_260,U_258,U_247,U_259,U_256,U_257)
| U_254 != relation_composition(U_256,U_255)
| ~ sP57(U_254,U_255,U_260,U_258,U_247,U_259,U_256,U_257,U_250) )
& ! [U_254,U_255,U_260,U_258,U_247,U_259,U_256,U_257,U_250] :
( sP57(U_254,U_255,U_260,U_258,U_247,U_259,U_256,U_257,U_250)
| ~ relation(U_254)
| ~ relation(U_255)
| ~ relation(U_256) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP53,sP54,sP55,sP56,sP57])],[f_29_9]) ).
cnf(f_29_11,plain,
( sP57(U_254,U_255,U_260,U_258,U_247,U_259,U_256,U_257,U_250)
| ~ relation(U_254)
| ~ relation(U_255)
| ~ relation(U_256) ),
inference(clausify,[status(thm)],[f_29_10]) ).
cnf(f_29_12,plain,
( sP54(U_254,U_255,U_260,U_258,U_247,U_259,U_256,U_257)
| U_254 != relation_composition(U_256,U_255)
| ~ sP57(U_254,U_255,U_260,U_258,U_247,U_259,U_256,U_257,U_250) ),
inference(clausify,[status(thm)],[f_29_10]) ).
cnf(f_29_13,plain,
( U_254 = relation_composition(U_256,U_255)
| sP56(U_254,U_255,U_256)
| sP55(U_254,U_255,U_256,U_250)
| ~ sP57(U_254,U_255,U_260,U_258,U_247,U_259,U_256,U_257,U_250) ),
inference(clausify,[status(thm)],[f_29_10]) ).
cnf(f_29_14,plain,
( sP53(U_254,U_255,U_259,U_256,U_257)
| ~ in(ordered_pair(U_259,U_257),U_254)
| ~ sP54(U_254,U_255,U_260,U_258,U_247,U_259,U_256,U_257) ),
inference(clausify,[status(thm)],[f_29_10]) ).
cnf(f_29_15,plain,
( in(ordered_pair(U_260,U_258),U_254)
| ~ in(ordered_pair(U_247,U_258),U_255)
| ~ in(ordered_pair(U_260,U_247),U_256)
| ~ sP54(U_254,U_255,U_260,U_258,U_247,U_259,U_256,U_257) ),
inference(clausify,[status(thm)],[f_29_10]) ).
cnf(f_29_16,plain,
( in(ordered_pair(U_259,sK44(U_256,U_255,U_254,U_259,U_257)),U_256)
| ~ sP53(U_254,U_255,U_259,U_256,U_257) ),
inference(clausify,[status(thm)],[f_29_10]) ).
cnf(f_29_17,plain,
( in(ordered_pair(sK44(U_256,U_255,U_254,U_259,U_257),U_257),U_255)
| ~ sP53(U_254,U_255,U_259,U_256,U_257) ),
inference(clausify,[status(thm)],[f_29_10]) ).
cnf(f_29_18,plain,
( in(ordered_pair(sK45(U_256,U_255,U_254),sK46(U_256,U_255,U_254)),U_254)
| ~ sP55(U_254,U_255,U_256,U_250) ),
inference(clausify,[status(thm)],[f_29_10]) ).
cnf(f_29_19,plain,
( ~ in(ordered_pair(U_250,sK46(U_256,U_255,U_254)),U_255)
| ~ in(ordered_pair(sK45(U_256,U_255,U_254),U_250),U_256)
| ~ sP55(U_254,U_255,U_256,U_250) ),
inference(clausify,[status(thm)],[f_29_10]) ).
cnf(f_29_20,plain,
( in(ordered_pair(sK47(U_256,U_255,U_254),sK49(U_256,U_255,U_254)),U_256)
| ~ sP56(U_254,U_255,U_256) ),
inference(clausify,[status(thm)],[f_29_10]) ).
cnf(f_29_21,plain,
( in(ordered_pair(sK49(U_256,U_255,U_254),sK48(U_256,U_255,U_254)),U_255)
| ~ sP56(U_254,U_255,U_256) ),
inference(clausify,[status(thm)],[f_29_10]) ).
cnf(f_29_22,plain,
( ~ in(ordered_pair(sK47(U_256,U_255,U_254),sK48(U_256,U_255,U_254)),U_254)
| ~ sP56(U_254,U_255,U_256) ),
inference(clausify,[status(thm)],[f_29_10]) ).
fof(f_30_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_30_2,plain,
! [U_269,U_268] :
( ! [U_267] :
( ( ( U_267 = complements_of_subsets(U_269,U_268)
| ? [U_266] :
( ( ( ~ in(U_266,U_267)
& in(subset_complement(U_269,U_266),U_268) )
| ( ~ in(subset_complement(U_269,U_266),U_268)
& in(U_266,U_267) ) )
& element(U_266,powerset(U_269)) ) )
& ( ! [U_265] :
( ( ( in(U_265,U_267)
| ~ in(subset_complement(U_269,U_265),U_268) )
& ( in(subset_complement(U_269,U_265),U_268)
| ~ in(U_265,U_267) ) )
| ~ element(U_265,powerset(U_269)) )
| U_267 != complements_of_subsets(U_269,U_268) ) )
| ~ element(U_267,powerset(powerset(U_269))) )
| ~ element(U_268,powerset(powerset(U_269))) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_269,U_268] :
( ! [U_267] :
( ( ( U_267 = complements_of_subsets(U_269,U_268)
| ( ( ( ~ in(sK50(U_269,U_268,U_267),U_267)
& in(subset_complement(U_269,sK50(U_269,U_268,U_267)),U_268) )
| ( ~ in(subset_complement(U_269,sK50(U_269,U_268,U_267)),U_268)
& in(sK50(U_269,U_268,U_267),U_267) ) )
& element(sK50(U_269,U_268,U_267),powerset(U_269)) ) )
& ( ! [U_265] :
( ( ( in(U_265,U_267)
| ~ in(subset_complement(U_269,U_265),U_268) )
& ( in(subset_complement(U_269,U_265),U_268)
| ~ in(U_265,U_267) ) )
| ~ element(U_265,powerset(U_269)) )
| U_267 != complements_of_subsets(U_269,U_268) ) )
| ~ element(U_267,powerset(powerset(U_269))) )
| ~ element(U_268,powerset(powerset(U_269))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_266,sK50(U_269,U_268,U_267))],[f_30_2]) ).
fof(f_30_4,plain,
( ! [U_269,U_268,U_267] :
( ~ in(sK50(U_269,U_268,U_267),U_267)
| ~ sP60(U_269,U_268,U_267) )
& ! [U_269,U_268,U_267] :
( in(subset_complement(U_269,sK50(U_269,U_268,U_267)),U_268)
| ~ sP60(U_269,U_268,U_267) )
& ! [U_269,U_268,U_267] :
( ~ in(subset_complement(U_269,sK50(U_269,U_268,U_267)),U_268)
| ~ sP59(U_269,U_268,U_267) )
& ! [U_269,U_268,U_267] :
( in(sK50(U_269,U_268,U_267),U_267)
| ~ sP59(U_269,U_268,U_267) )
& ! [U_269,U_268,U_267] :
( sP60(U_269,U_268,U_267)
| sP59(U_269,U_268,U_267)
| ~ sP61(U_269,U_268,U_267) )
& ! [U_269,U_268,U_267] :
( element(sK50(U_269,U_268,U_267),powerset(U_269))
| ~ sP61(U_269,U_268,U_267) )
& ! [U_265,U_269,U_268,U_267] :
( in(U_265,U_267)
| ~ in(subset_complement(U_269,U_265),U_268)
| ~ sP58(U_265,U_269,U_268,U_267) )
& ! [U_265,U_269,U_268,U_267] :
( in(subset_complement(U_269,U_265),U_268)
| ~ in(U_265,U_267)
| ~ sP58(U_265,U_269,U_268,U_267) )
& ! [U_265,U_269,U_268,U_267] :
( U_267 = complements_of_subsets(U_269,U_268)
| sP61(U_269,U_268,U_267)
| ~ sP62(U_265,U_269,U_268,U_267) )
& ! [U_265,U_269,U_268,U_267] :
( sP58(U_265,U_269,U_268,U_267)
| ~ element(U_265,powerset(U_269))
| U_267 != complements_of_subsets(U_269,U_268)
| ~ sP62(U_265,U_269,U_268,U_267) )
& ! [U_265,U_269,U_268,U_267] :
( sP62(U_265,U_269,U_268,U_267)
| ~ element(U_267,powerset(powerset(U_269)))
| ~ element(U_268,powerset(powerset(U_269))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP58,sP59,sP60,sP61,sP62])],[f_30_3]) ).
cnf(f_30_5,plain,
( sP62(U_265,U_269,U_268,U_267)
| ~ element(U_267,powerset(powerset(U_269)))
| ~ element(U_268,powerset(powerset(U_269))) ),
inference(clausify,[status(thm)],[f_30_4]) ).
cnf(f_30_6,plain,
( sP58(U_265,U_269,U_268,U_267)
| ~ element(U_265,powerset(U_269))
| U_267 != complements_of_subsets(U_269,U_268)
| ~ sP62(U_265,U_269,U_268,U_267) ),
inference(clausify,[status(thm)],[f_30_4]) ).
cnf(f_30_7,plain,
( U_267 = complements_of_subsets(U_269,U_268)
| sP61(U_269,U_268,U_267)
| ~ sP62(U_265,U_269,U_268,U_267) ),
inference(clausify,[status(thm)],[f_30_4]) ).
cnf(f_30_8,plain,
( in(subset_complement(U_269,U_265),U_268)
| ~ in(U_265,U_267)
| ~ sP58(U_265,U_269,U_268,U_267) ),
inference(clausify,[status(thm)],[f_30_4]) ).
cnf(f_30_9,plain,
( in(U_265,U_267)
| ~ in(subset_complement(U_269,U_265),U_268)
| ~ sP58(U_265,U_269,U_268,U_267) ),
inference(clausify,[status(thm)],[f_30_4]) ).
cnf(f_30_10,plain,
( element(sK50(U_269,U_268,U_267),powerset(U_269))
| ~ sP61(U_269,U_268,U_267) ),
inference(clausify,[status(thm)],[f_30_4]) ).
cnf(f_30_11,plain,
( sP60(U_269,U_268,U_267)
| sP59(U_269,U_268,U_267)
| ~ sP61(U_269,U_268,U_267) ),
inference(clausify,[status(thm)],[f_30_4]) ).
cnf(f_30_12,plain,
( in(sK50(U_269,U_268,U_267),U_267)
| ~ sP59(U_269,U_268,U_267) ),
inference(clausify,[status(thm)],[f_30_4]) ).
cnf(f_30_13,plain,
( ~ in(subset_complement(U_269,sK50(U_269,U_268,U_267)),U_268)
| ~ sP59(U_269,U_268,U_267) ),
inference(clausify,[status(thm)],[f_30_4]) ).
cnf(f_30_14,plain,
( in(subset_complement(U_269,sK50(U_269,U_268,U_267)),U_268)
| ~ sP60(U_269,U_268,U_267) ),
inference(clausify,[status(thm)],[f_30_4]) ).
cnf(f_30_15,plain,
( ~ in(sK50(U_269,U_268,U_267),U_267)
| ~ sP60(U_269,U_268,U_267) ),
inference(clausify,[status(thm)],[f_30_4]) ).
fof(f_31_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_31_2,plain,
! [U_271,U_270] :
( ( proper_subset(U_271,U_270)
| U_271 = U_270
| ~ subset(U_271,U_270) )
& ( ( U_271 != U_270
& subset(U_271,U_270) )
| ~ proper_subset(U_271,U_270) ) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( ! [U_275,U_273] :
( proper_subset(U_275,U_273)
| U_275 = U_273
| ~ subset(U_275,U_273) )
& ! [U_274,U_272] :
( ( U_274 != U_272
& subset(U_274,U_272) )
| ~ proper_subset(U_274,U_272) ) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
fof(f_31_4,plain,
( ! [U_274,U_272] :
( U_274 != U_272
| ~ sP63(U_274,U_272) )
& ! [U_274,U_272] :
( subset(U_274,U_272)
| ~ sP63(U_274,U_272) )
& ! [U_273,U_275] :
( proper_subset(U_275,U_273)
| U_275 = U_273
| ~ subset(U_275,U_273) )
& ! [U_274,U_272] :
( sP63(U_274,U_272)
| ~ proper_subset(U_274,U_272) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP63])],[f_31_3]) ).
cnf(f_31_5,plain,
( sP63(U_274,U_272)
| ~ proper_subset(U_274,U_272) ),
inference(clausify,[status(thm)],[f_31_4]) ).
cnf(f_31_6,plain,
( proper_subset(U_275,U_273)
| U_275 = U_273
| ~ subset(U_275,U_273) ),
inference(clausify,[status(thm)],[f_31_4]) ).
cnf(f_31_7,plain,
( subset(U_274,U_272)
| ~ sP63(U_274,U_272) ),
inference(clausify,[status(thm)],[f_31_4]) ).
cnf(f_31_8,plain,
( U_274 != U_272
| ~ sP63(U_274,U_272) ),
inference(clausify,[status(thm)],[f_31_4]) ).
fof(f_32_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
fof(f_32_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_32_1]) ).
cnf(f_32_3,plain,
$true,
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_setfam_1]) ).
fof(f_33_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_33_1]) ).
cnf(f_33_3,plain,
$true,
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
fof(f_34_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_34_1]) ).
cnf(f_34_3,plain,
$true,
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
fof(f_35_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_35_1]) ).
cnf(f_35_3,plain,
$true,
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_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_k2_relat_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,
! [A] : element(cast_to_subset(A),powerset(A)),
inference(fof_nnf,[status(thm)],[dt_k2_subset_1]) ).
fof(f_38_2,plain,
! [U_276] : element(cast_to_subset(U_276),powerset(U_276)),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_276] : element(cast_to_subset(U_276),powerset(U_276)),
inference(definitional_conversion,[status(esa)],[f_38_2]) ).
cnf(f_38_4,plain,
element(cast_to_subset(U_276),powerset(U_276)),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
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_k2_xboole_0]) ).
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_zfmisc_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,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_relat_1]) ).
fof(f_42_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_42_1]) ).
cnf(f_42_3,plain,
$true,
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_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_43_2,plain,
! [U_278,U_277] :
( element(subset_complement(U_278,U_277),powerset(U_278))
| ~ element(U_277,powerset(U_278)) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_277,U_278] :
( element(subset_complement(U_278,U_277),powerset(U_278))
| ~ element(U_277,powerset(U_278)) ),
inference(definitional_conversion,[status(esa)],[f_43_2]) ).
cnf(f_43_4,plain,
( element(subset_complement(U_278,U_277),powerset(U_278))
| ~ element(U_277,powerset(U_278)) ),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_tarski]) ).
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_k3_xboole_0]) ).
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,
! [A] :
( relation(relation_inverse(A))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k4_relat_1]) ).
fof(f_46_2,plain,
! [U_279] :
( relation(relation_inverse(U_279))
| ~ relation(U_279) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_279] :
( relation(relation_inverse(U_279))
| ~ relation(U_279) ),
inference(definitional_conversion,[status(esa)],[f_46_2]) ).
cnf(f_46_4,plain,
( relation(relation_inverse(U_279))
| ~ relation(U_279) ),
inference(clausify,[status(thm)],[f_46_3]) ).
fof(f_47_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
fof(f_47_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_47_1]) ).
cnf(f_47_3,plain,
$true,
inference(clausify,[status(thm)],[f_47_2]) ).
fof(f_48_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
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,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_relat_1]) ).
fof(f_49_2,plain,
! [U_281,U_280] :
( relation(relation_composition(U_281,U_280))
| ~ relation(U_280)
| ~ relation(U_281) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
! [U_281,U_280] :
( relation(relation_composition(U_281,U_280))
| ~ relation(U_280)
| ~ relation(U_281) ),
inference(definitional_conversion,[status(esa)],[f_49_2]) ).
cnf(f_49_4,plain,
( relation(relation_composition(U_281,U_280))
| ~ relation(U_280)
| ~ relation(U_281) ),
inference(clausify,[status(thm)],[f_49_3]) ).
fof(f_50_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_50_2,plain,
! [U_283,U_282] :
( element(union_of_subsets(U_283,U_282),powerset(U_283))
| ~ element(U_282,powerset(powerset(U_283))) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_283,U_282] :
( element(union_of_subsets(U_283,U_282),powerset(U_283))
| ~ element(U_282,powerset(powerset(U_283))) ),
inference(definitional_conversion,[status(esa)],[f_50_2]) ).
cnf(f_50_4,plain,
( element(union_of_subsets(U_283,U_282),powerset(U_283))
| ~ element(U_282,powerset(powerset(U_283))) ),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_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_51_2,plain,
! [U_285,U_284] :
( element(meet_of_subsets(U_285,U_284),powerset(U_285))
| ~ element(U_284,powerset(powerset(U_285))) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
! [U_284,U_285] :
( element(meet_of_subsets(U_285,U_284),powerset(U_285))
| ~ element(U_284,powerset(powerset(U_285))) ),
inference(definitional_conversion,[status(esa)],[f_51_2]) ).
cnf(f_51_4,plain,
( element(meet_of_subsets(U_285,U_284),powerset(U_285))
| ~ element(U_284,powerset(powerset(U_285))) ),
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_52_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_52_2,plain,
! [U_288,U_287,U_286] :
( element(subset_difference(U_288,U_287,U_286),powerset(U_288))
| ~ element(U_286,powerset(U_288))
| ~ element(U_287,powerset(U_288)) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
! [U_287,U_286,U_288] :
( element(subset_difference(U_288,U_287,U_286),powerset(U_288))
| ~ element(U_286,powerset(U_288))
| ~ element(U_287,powerset(U_288)) ),
inference(definitional_conversion,[status(esa)],[f_52_2]) ).
cnf(f_52_4,plain,
( element(subset_difference(U_288,U_287,U_286),powerset(U_288))
| ~ element(U_286,powerset(U_288))
| ~ element(U_287,powerset(U_288)) ),
inference(clausify,[status(thm)],[f_52_3]) ).
fof(f_53_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_53_2,plain,
! [U_290,U_289] :
( element(complements_of_subsets(U_290,U_289),powerset(powerset(U_290)))
| ~ element(U_289,powerset(powerset(U_290))) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
! [U_290,U_289] :
( element(complements_of_subsets(U_290,U_289),powerset(powerset(U_290)))
| ~ element(U_289,powerset(powerset(U_290))) ),
inference(definitional_conversion,[status(esa)],[f_53_2]) ).
cnf(f_53_4,plain,
( element(complements_of_subsets(U_290,U_289),powerset(powerset(U_290)))
| ~ element(U_289,powerset(powerset(U_290))) ),
inference(clausify,[status(thm)],[f_53_3]) ).
fof(f_54_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
fof(f_54_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_54_1]) ).
cnf(f_54_3,plain,
$true,
inference(clausify,[status(thm)],[f_54_2]) ).
fof(f_55_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_55_2,plain,
! [U_292] :
? [U_291] : element(U_291,U_292),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
! [U_292] : element(sK51(U_292),U_292),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_291,sK51(U_292))],[f_55_2]) ).
fof(f_55_4,plain,
! [U_292] : element(sK51(U_292),U_292),
inference(definitional_conversion,[status(esa)],[f_55_3]) ).
cnf(f_55_5,plain,
element(sK51(U_292),U_292),
inference(clausify,[status(thm)],[f_55_4]) ).
fof(f_56_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_56_2,plain,
! [U_293] : ~ empty(powerset(U_293)),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
! [U_293] : ~ empty(powerset(U_293)),
inference(definitional_conversion,[status(esa)],[f_56_2]) ).
cnf(f_56_4,plain,
~ empty(powerset(U_293)),
inference(clausify,[status(thm)],[f_56_3]) ).
fof(f_57_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_57_2,plain,
empty(empty_set),
inference(definitional_conversion,[status(esa)],[f_57_1]) ).
cnf(f_57_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_57_2]) ).
fof(f_58_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_58_2,plain,
! [U_295,U_294] : ~ empty(ordered_pair(U_295,U_294)),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
! [U_294,U_295] : ~ empty(ordered_pair(U_295,U_294)),
inference(definitional_conversion,[status(esa)],[f_58_2]) ).
cnf(f_58_4,plain,
~ empty(ordered_pair(U_295,U_294)),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_59_1,plain,
! [A,B] :
( relation(set_union2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc2_relat_1]) ).
fof(f_59_2,plain,
! [U_297,U_296] :
( relation(set_union2(U_297,U_296))
| ~ relation(U_296)
| ~ relation(U_297) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
! [U_296,U_297] :
( relation(set_union2(U_297,U_296))
| ~ relation(U_296)
| ~ relation(U_297) ),
inference(definitional_conversion,[status(esa)],[f_59_2]) ).
cnf(f_59_4,plain,
( relation(set_union2(U_297,U_296))
| ~ relation(U_296)
| ~ relation(U_297) ),
inference(clausify,[status(thm)],[f_59_3]) ).
fof(f_60_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_60_2,plain,
! [U_298] : ~ empty(singleton(U_298)),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
! [U_298] : ~ empty(singleton(U_298)),
inference(definitional_conversion,[status(esa)],[f_60_2]) ).
cnf(f_60_4,plain,
~ empty(singleton(U_298)),
inference(clausify,[status(thm)],[f_60_3]) ).
fof(f_61_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_61_2,plain,
! [U_300,U_299] :
( ~ empty(set_union2(U_300,U_299))
| empty(U_300) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
! [U_300] :
( ! [U_299] : ~ empty(set_union2(U_300,U_299))
| empty(U_300) ),
inference(miniscope,[status(thm)],[f_61_2]) ).
fof(f_61_4,plain,
! [U_299,U_300] :
( ~ empty(set_union2(U_300,U_299))
| empty(U_300) ),
inference(definitional_conversion,[status(esa)],[f_61_3]) ).
cnf(f_61_5,plain,
( ~ empty(set_union2(U_300,U_299))
| empty(U_300) ),
inference(clausify,[status(thm)],[f_61_4]) ).
fof(f_62_1,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_62_2,plain,
! [U_302,U_301] : ~ empty(unordered_pair(U_302,U_301)),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
! [U_301,U_302] : ~ empty(unordered_pair(U_302,U_301)),
inference(definitional_conversion,[status(esa)],[f_62_2]) ).
cnf(f_62_4,plain,
~ empty(unordered_pair(U_302,U_301)),
inference(clausify,[status(thm)],[f_62_3]) ).
fof(f_63_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_63_2,plain,
! [U_304,U_303] :
( ~ empty(set_union2(U_303,U_304))
| empty(U_304) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
! [U_304] :
( ! [U_303] : ~ empty(set_union2(U_303,U_304))
| empty(U_304) ),
inference(miniscope,[status(thm)],[f_63_2]) ).
fof(f_63_4,plain,
! [U_303,U_304] :
( ~ empty(set_union2(U_303,U_304))
| empty(U_304) ),
inference(definitional_conversion,[status(esa)],[f_63_3]) ).
cnf(f_63_5,plain,
( ~ empty(set_union2(U_303,U_304))
| empty(U_304) ),
inference(clausify,[status(thm)],[f_63_4]) ).
fof(f_64_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
fof(f_64_2,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_64_1]) ).
cnf(f_64_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_64_2]) ).
cnf(f_64_4,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_64_2]) ).
fof(f_65_1,plain,
! [A,B] :
( ~ empty(cartesian_product2(A,B))
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc4_subset_1]) ).
fof(f_65_2,plain,
! [U_306,U_305] :
( ~ empty(cartesian_product2(U_306,U_305))
| empty(U_305)
| empty(U_306) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
! [U_305,U_306] :
( ~ empty(cartesian_product2(U_306,U_305))
| empty(U_305)
| empty(U_306) ),
inference(definitional_conversion,[status(esa)],[f_65_2]) ).
cnf(f_65_4,plain,
( ~ empty(cartesian_product2(U_306,U_305))
| empty(U_305)
| empty(U_306) ),
inference(clausify,[status(thm)],[f_65_3]) ).
fof(f_66_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_66_2,plain,
! [U_307] :
( ~ empty(relation_dom(U_307))
| ~ relation(U_307)
| empty(U_307) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
! [U_307] :
( ~ empty(relation_dom(U_307))
| ~ relation(U_307)
| empty(U_307) ),
inference(definitional_conversion,[status(esa)],[f_66_2]) ).
cnf(f_66_4,plain,
( ~ empty(relation_dom(U_307))
| ~ relation(U_307)
| empty(U_307) ),
inference(clausify,[status(thm)],[f_66_3]) ).
fof(f_67_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_67_2,plain,
! [U_308] :
( ~ empty(relation_rng(U_308))
| ~ relation(U_308)
| empty(U_308) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
! [U_308] :
( ~ empty(relation_rng(U_308))
| ~ relation(U_308)
| empty(U_308) ),
inference(definitional_conversion,[status(esa)],[f_67_2]) ).
cnf(f_67_4,plain,
( ~ empty(relation_rng(U_308))
| ~ relation(U_308)
| empty(U_308) ),
inference(clausify,[status(thm)],[f_67_3]) ).
fof(f_68_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_68_2,plain,
! [U_310,U_309] : set_union2(U_310,U_310) = U_310,
inference(variable_rename,[status(thm)],[f_68_1]) ).
fof(f_68_3,plain,
! [U_310] : set_union2(U_310,U_310) = U_310,
inference(miniscope,[status(thm)],[f_68_2]) ).
fof(f_68_4,plain,
! [U_310] : set_union2(U_310,U_310) = U_310,
inference(definitional_conversion,[status(esa)],[f_68_3]) ).
cnf(f_68_5,plain,
set_union2(U_310,U_310) = U_310,
inference(clausify,[status(thm)],[f_68_4]) ).
fof(f_69_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_69_2,plain,
! [U_312,U_311] : set_intersection2(U_312,U_312) = U_312,
inference(variable_rename,[status(thm)],[f_69_1]) ).
fof(f_69_3,plain,
! [U_312] : set_intersection2(U_312,U_312) = U_312,
inference(miniscope,[status(thm)],[f_69_2]) ).
fof(f_69_4,plain,
! [U_312] : set_intersection2(U_312,U_312) = U_312,
inference(definitional_conversion,[status(esa)],[f_69_3]) ).
cnf(f_69_5,plain,
set_intersection2(U_312,U_312) = U_312,
inference(clausify,[status(thm)],[f_69_4]) ).
fof(f_70_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_70_2,plain,
! [U_314,U_313] :
( subset_complement(U_314,subset_complement(U_314,U_313)) = U_313
| ~ element(U_313,powerset(U_314)) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
fof(f_70_3,plain,
! [U_313,U_314] :
( subset_complement(U_314,subset_complement(U_314,U_313)) = U_313
| ~ element(U_313,powerset(U_314)) ),
inference(definitional_conversion,[status(esa)],[f_70_2]) ).
cnf(f_70_4,plain,
( subset_complement(U_314,subset_complement(U_314,U_313)) = U_313
| ~ element(U_313,powerset(U_314)) ),
inference(clausify,[status(thm)],[f_70_3]) ).
fof(f_71_1,plain,
! [A] :
( relation_inverse(relation_inverse(A)) = A
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[involutiveness_k4_relat_1]) ).
fof(f_71_2,plain,
! [U_315] :
( relation_inverse(relation_inverse(U_315)) = U_315
| ~ relation(U_315) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
fof(f_71_3,plain,
! [U_315] :
( relation_inverse(relation_inverse(U_315)) = U_315
| ~ relation(U_315) ),
inference(definitional_conversion,[status(esa)],[f_71_2]) ).
cnf(f_71_4,plain,
( relation_inverse(relation_inverse(U_315)) = U_315
| ~ relation(U_315) ),
inference(clausify,[status(thm)],[f_71_3]) ).
fof(f_72_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_72_2,plain,
! [U_317,U_316] :
( complements_of_subsets(U_317,complements_of_subsets(U_317,U_316)) = U_316
| ~ element(U_316,powerset(powerset(U_317))) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
fof(f_72_3,plain,
! [U_316,U_317] :
( complements_of_subsets(U_317,complements_of_subsets(U_317,U_316)) = U_316
| ~ element(U_316,powerset(powerset(U_317))) ),
inference(definitional_conversion,[status(esa)],[f_72_2]) ).
cnf(f_72_4,plain,
( complements_of_subsets(U_317,complements_of_subsets(U_317,U_316)) = U_316
| ~ element(U_316,powerset(powerset(U_317))) ),
inference(clausify,[status(thm)],[f_72_3]) ).
fof(f_73_1,plain,
! [A,B] : ~ proper_subset(A,A),
inference(fof_nnf,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(f_73_2,plain,
! [U_319,U_318] : ~ proper_subset(U_319,U_319),
inference(variable_rename,[status(thm)],[f_73_1]) ).
fof(f_73_3,plain,
! [U_319] : ~ proper_subset(U_319,U_319),
inference(miniscope,[status(thm)],[f_73_2]) ).
fof(f_73_4,plain,
! [U_319] : ~ proper_subset(U_319,U_319),
inference(definitional_conversion,[status(esa)],[f_73_3]) ).
cnf(f_73_5,plain,
~ proper_subset(U_319,U_319),
inference(clausify,[status(thm)],[f_73_4]) ).
fof(f_74_1,plain,
! [A] : singleton(A) != empty_set,
inference(fof_nnf,[status(thm)],[l1_zfmisc_1]) ).
fof(f_74_2,plain,
! [U_320] : singleton(U_320) != empty_set,
inference(variable_rename,[status(thm)],[f_74_1]) ).
fof(f_74_3,plain,
! [U_320] : singleton(U_320) != empty_set,
inference(definitional_conversion,[status(esa)],[f_74_2]) ).
cnf(f_74_4,plain,
singleton(U_320) != empty_set,
inference(clausify,[status(thm)],[f_74_3]) ).
fof(f_75_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l23_zfmisc_1]) ).
fof(f_75_2,plain,
! [U_322,U_321] :
( set_union2(singleton(U_322),U_321) = U_321
| ~ in(U_322,U_321) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
fof(f_75_3,plain,
! [U_321,U_322] :
( set_union2(singleton(U_322),U_321) = U_321
| ~ in(U_322,U_321) ),
inference(definitional_conversion,[status(esa)],[f_75_2]) ).
cnf(f_75_4,plain,
( set_union2(singleton(U_322),U_321) = U_321
| ~ in(U_322,U_321) ),
inference(clausify,[status(thm)],[f_75_3]) ).
fof(f_76_1,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(fof_nnf,[status(thm)],[l25_zfmisc_1]) ).
fof(f_76_2,plain,
! [U_324,U_323] :
( ~ in(U_324,U_323)
| ~ disjoint(singleton(U_324),U_323) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
fof(f_76_3,plain,
! [U_324,U_323] :
( ~ in(U_324,U_323)
| ~ disjoint(singleton(U_324),U_323) ),
inference(definitional_conversion,[status(esa)],[f_76_2]) ).
cnf(f_76_4,plain,
( ~ in(U_324,U_323)
| ~ disjoint(singleton(U_324),U_323) ),
inference(clausify,[status(thm)],[f_76_3]) ).
fof(f_77_1,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(fof_nnf,[status(thm)],[l28_zfmisc_1]) ).
fof(f_77_2,plain,
! [U_326,U_325] :
( disjoint(singleton(U_326),U_325)
| in(U_326,U_325) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
fof(f_77_3,plain,
! [U_325,U_326] :
( disjoint(singleton(U_326),U_325)
| in(U_326,U_325) ),
inference(definitional_conversion,[status(esa)],[f_77_2]) ).
cnf(f_77_4,plain,
( disjoint(singleton(U_326),U_325)
| in(U_326,U_325) ),
inference(clausify,[status(thm)],[f_77_3]) ).
fof(f_78_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_78_2,plain,
! [U_328,U_327] :
( ( subset(singleton(U_328),U_327)
| ~ in(U_328,U_327) )
& ( in(U_328,U_327)
| ~ subset(singleton(U_328),U_327) ) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
fof(f_78_3,plain,
( ! [U_332,U_330] :
( subset(singleton(U_332),U_330)
| ~ in(U_332,U_330) )
& ! [U_331,U_329] :
( in(U_331,U_329)
| ~ subset(singleton(U_331),U_329) ) ),
inference(miniscope,[status(thm)],[f_78_2]) ).
fof(f_78_4,plain,
( ! [U_330,U_332] :
( subset(singleton(U_332),U_330)
| ~ in(U_332,U_330) )
& ! [U_329,U_331] :
( in(U_331,U_329)
| ~ subset(singleton(U_331),U_329) ) ),
inference(definitional_conversion,[status(esa)],[f_78_3]) ).
cnf(f_78_5,plain,
( in(U_331,U_329)
| ~ subset(singleton(U_331),U_329) ),
inference(clausify,[status(thm)],[f_78_4]) ).
cnf(f_78_6,plain,
( subset(singleton(U_332),U_330)
| ~ in(U_332,U_330) ),
inference(clausify,[status(thm)],[f_78_4]) ).
fof(f_79_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_79_2,plain,
! [U_334,U_333] :
( ( set_difference(U_334,U_333) = empty_set
| ~ subset(U_334,U_333) )
& ( subset(U_334,U_333)
| set_difference(U_334,U_333) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
fof(f_79_3,plain,
( ! [U_338,U_336] :
( set_difference(U_338,U_336) = empty_set
| ~ subset(U_338,U_336) )
& ! [U_337,U_335] :
( subset(U_337,U_335)
| set_difference(U_337,U_335) != empty_set ) ),
inference(miniscope,[status(thm)],[f_79_2]) ).
fof(f_79_4,plain,
( ! [U_336,U_338] :
( set_difference(U_338,U_336) = empty_set
| ~ subset(U_338,U_336) )
& ! [U_335,U_337] :
( subset(U_337,U_335)
| set_difference(U_337,U_335) != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_79_3]) ).
cnf(f_79_5,plain,
( subset(U_337,U_335)
| set_difference(U_337,U_335) != empty_set ),
inference(clausify,[status(thm)],[f_79_4]) ).
cnf(f_79_6,plain,
( set_difference(U_338,U_336) = empty_set
| ~ subset(U_338,U_336) ),
inference(clausify,[status(thm)],[f_79_4]) ).
fof(f_80_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_80_2,plain,
! [U_341,U_340] :
( ! [U_339] :
( in(U_339,U_341)
| ~ in(U_339,U_340) )
| ~ element(U_340,powerset(U_341)) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
fof(f_80_3,plain,
! [U_341,U_339,U_340] :
( in(U_339,U_341)
| ~ in(U_339,U_340)
| ~ element(U_340,powerset(U_341)) ),
inference(definitional_conversion,[status(esa)],[f_80_2]) ).
cnf(f_80_4,plain,
( in(U_339,U_341)
| ~ in(U_339,U_340)
| ~ element(U_340,powerset(U_341)) ),
inference(clausify,[status(thm)],[f_80_3]) ).
fof(f_81_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_81_2,plain,
! [U_344,U_343,U_342] :
( subset(U_344,set_difference(U_343,singleton(U_342)))
| in(U_342,U_344)
| ~ subset(U_344,U_343) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
fof(f_81_3,plain,
! [U_344,U_343] :
( ! [U_342] :
( subset(U_344,set_difference(U_343,singleton(U_342)))
| in(U_342,U_344) )
| ~ subset(U_344,U_343) ),
inference(miniscope,[status(thm)],[f_81_2]) ).
fof(f_81_4,plain,
! [U_342,U_343,U_344] :
( subset(U_344,set_difference(U_343,singleton(U_342)))
| in(U_342,U_344)
| ~ subset(U_344,U_343) ),
inference(definitional_conversion,[status(esa)],[f_81_3]) ).
cnf(f_81_5,plain,
( subset(U_344,set_difference(U_343,singleton(U_342)))
| in(U_342,U_344)
| ~ subset(U_344,U_343) ),
inference(clausify,[status(thm)],[f_81_4]) ).
fof(f_82_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_82_2,plain,
! [U_346,U_345] :
( ( subset(U_346,singleton(U_345))
| ( U_346 != singleton(U_345)
& U_346 != empty_set ) )
& ( U_346 = singleton(U_345)
| U_346 = empty_set
| ~ subset(U_346,singleton(U_345)) ) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
fof(f_82_3,plain,
( ! [U_350,U_348] :
( subset(U_350,singleton(U_348))
| ( U_350 != singleton(U_348)
& U_350 != empty_set ) )
& ! [U_349,U_347] :
( U_349 = singleton(U_347)
| U_349 = empty_set
| ~ subset(U_349,singleton(U_347)) ) ),
inference(miniscope,[status(thm)],[f_82_2]) ).
fof(f_82_4,plain,
( ! [U_348,U_350] :
( U_350 != singleton(U_348)
| ~ sP64(U_348,U_350) )
& ! [U_348,U_350] :
( U_350 != empty_set
| ~ sP64(U_348,U_350) )
& ! [U_348,U_350] :
( subset(U_350,singleton(U_348))
| sP64(U_348,U_350) )
& ! [U_349,U_347] :
( U_349 = singleton(U_347)
| U_349 = empty_set
| ~ subset(U_349,singleton(U_347)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP64])],[f_82_3]) ).
cnf(f_82_5,plain,
( U_349 = singleton(U_347)
| U_349 = empty_set
| ~ subset(U_349,singleton(U_347)) ),
inference(clausify,[status(thm)],[f_82_4]) ).
cnf(f_82_6,plain,
( subset(U_350,singleton(U_348))
| sP64(U_348,U_350) ),
inference(clausify,[status(thm)],[f_82_4]) ).
cnf(f_82_7,plain,
( U_350 != empty_set
| ~ sP64(U_348,U_350) ),
inference(clausify,[status(thm)],[f_82_4]) ).
cnf(f_82_8,plain,
( U_350 != singleton(U_348)
| ~ sP64(U_348,U_350) ),
inference(clausify,[status(thm)],[f_82_4]) ).
fof(f_83_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l50_zfmisc_1]) ).
fof(f_83_2,plain,
! [U_352,U_351] :
( subset(U_352,union(U_351))
| ~ in(U_352,U_351) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
fof(f_83_3,plain,
! [U_352,U_351] :
( subset(U_352,union(U_351))
| ~ in(U_352,U_351) ),
inference(definitional_conversion,[status(esa)],[f_83_2]) ).
cnf(f_83_4,plain,
( subset(U_352,union(U_351))
| ~ in(U_352,U_351) ),
inference(clausify,[status(thm)],[f_83_3]) ).
fof(f_84_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_84_2,plain,
! [U_356,U_355,U_354,U_353] :
( ( in(ordered_pair(U_356,U_355),cartesian_product2(U_354,U_353))
| ~ in(U_355,U_353)
| ~ in(U_356,U_354) )
& ( ( in(U_355,U_353)
& in(U_356,U_354) )
| ~ in(ordered_pair(U_356,U_355),cartesian_product2(U_354,U_353)) ) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
fof(f_84_3,plain,
( ! [U_364,U_362,U_360,U_358] :
( in(ordered_pair(U_364,U_362),cartesian_product2(U_360,U_358))
| ~ in(U_362,U_358)
| ~ in(U_364,U_360) )
& ! [U_363,U_361,U_359,U_357] :
( ( in(U_361,U_357)
& in(U_363,U_359) )
| ~ in(ordered_pair(U_363,U_361),cartesian_product2(U_359,U_357)) ) ),
inference(miniscope,[status(thm)],[f_84_2]) ).
fof(f_84_4,plain,
( ! [U_359,U_363,U_357,U_361] :
( in(U_361,U_357)
| ~ sP65(U_359,U_363,U_357,U_361) )
& ! [U_359,U_363,U_357,U_361] :
( in(U_363,U_359)
| ~ sP65(U_359,U_363,U_357,U_361) )
& ! [U_358,U_362,U_360,U_364] :
( in(ordered_pair(U_364,U_362),cartesian_product2(U_360,U_358))
| ~ in(U_362,U_358)
| ~ in(U_364,U_360) )
& ! [U_359,U_363,U_357,U_361] :
( sP65(U_359,U_363,U_357,U_361)
| ~ in(ordered_pair(U_363,U_361),cartesian_product2(U_359,U_357)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP65])],[f_84_3]) ).
cnf(f_84_5,plain,
( sP65(U_359,U_363,U_357,U_361)
| ~ in(ordered_pair(U_363,U_361),cartesian_product2(U_359,U_357)) ),
inference(clausify,[status(thm)],[f_84_4]) ).
cnf(f_84_6,plain,
( in(ordered_pair(U_364,U_362),cartesian_product2(U_360,U_358))
| ~ in(U_362,U_358)
| ~ in(U_364,U_360) ),
inference(clausify,[status(thm)],[f_84_4]) ).
cnf(f_84_7,plain,
( in(U_363,U_359)
| ~ sP65(U_359,U_363,U_357,U_361) ),
inference(clausify,[status(thm)],[f_84_4]) ).
cnf(f_84_8,plain,
( in(U_361,U_357)
| ~ sP65(U_359,U_363,U_357,U_361) ),
inference(clausify,[status(thm)],[f_84_4]) ).
fof(f_85_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_85_2,plain,
! [U_367,U_366] :
( element(U_367,powerset(U_366))
| ? [U_365] :
( ~ in(U_365,U_366)
& in(U_365,U_367) ) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
fof(f_85_3,plain,
! [U_367,U_366] :
( element(U_367,powerset(U_366))
| ( ~ in(sK52(U_367,U_366),U_366)
& in(sK52(U_367,U_366),U_367) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_365,sK52(U_367,U_366))],[f_85_2]) ).
fof(f_85_4,plain,
( ! [U_367,U_366] :
( ~ in(sK52(U_367,U_366),U_366)
| ~ sP66(U_367,U_366) )
& ! [U_367,U_366] :
( in(sK52(U_367,U_366),U_367)
| ~ sP66(U_367,U_366) )
& ! [U_367,U_366] :
( element(U_367,powerset(U_366))
| sP66(U_367,U_366) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP66])],[f_85_3]) ).
cnf(f_85_5,plain,
( element(U_367,powerset(U_366))
| sP66(U_367,U_366) ),
inference(clausify,[status(thm)],[f_85_4]) ).
cnf(f_85_6,plain,
( in(sK52(U_367,U_366),U_367)
| ~ sP66(U_367,U_366) ),
inference(clausify,[status(thm)],[f_85_4]) ).
cnf(f_85_7,plain,
( ~ in(sK52(U_367,U_366),U_366)
| ~ sP66(U_367,U_366) ),
inference(clausify,[status(thm)],[f_85_4]) ).
fof(f_86_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_86_2,plain,
? [U_368] :
( relation(U_368)
& empty(U_368) ),
inference(variable_rename,[status(thm)],[f_86_1]) ).
fof(f_86_3,plain,
( relation(sK53)
& empty(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_368,sK53)],[f_86_2]) ).
fof(f_86_4,plain,
( relation(sK53)
& empty(sK53) ),
inference(definitional_conversion,[status(esa)],[f_86_3]) ).
cnf(f_86_5,plain,
empty(sK53),
inference(clausify,[status(thm)],[f_86_4]) ).
cnf(f_86_6,plain,
relation(sK53),
inference(clausify,[status(thm)],[f_86_4]) ).
fof(f_87_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_87_2,plain,
! [U_370] :
( ? [U_369] :
( ~ empty(U_369)
& element(U_369,powerset(U_370)) )
| empty(U_370) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
fof(f_87_3,plain,
! [U_370] :
( ( ~ empty(sK54(U_370))
& element(sK54(U_370),powerset(U_370)) )
| empty(U_370) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_369,sK54(U_370))],[f_87_2]) ).
fof(f_87_4,plain,
( ! [U_370] :
( ~ empty(sK54(U_370))
| ~ sP67(U_370) )
& ! [U_370] :
( element(sK54(U_370),powerset(U_370))
| ~ sP67(U_370) )
& ! [U_370] :
( sP67(U_370)
| empty(U_370) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP67])],[f_87_3]) ).
cnf(f_87_5,plain,
( sP67(U_370)
| empty(U_370) ),
inference(clausify,[status(thm)],[f_87_4]) ).
cnf(f_87_6,plain,
( element(sK54(U_370),powerset(U_370))
| ~ sP67(U_370) ),
inference(clausify,[status(thm)],[f_87_4]) ).
cnf(f_87_7,plain,
( ~ empty(sK54(U_370))
| ~ sP67(U_370) ),
inference(clausify,[status(thm)],[f_87_4]) ).
fof(f_88_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_88_2,plain,
? [U_371] : empty(U_371),
inference(variable_rename,[status(thm)],[f_88_1]) ).
fof(f_88_3,plain,
empty(sK55),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_371,sK55)],[f_88_2]) ).
fof(f_88_4,plain,
empty(sK55),
inference(definitional_conversion,[status(esa)],[f_88_3]) ).
cnf(f_88_5,plain,
empty(sK55),
inference(clausify,[status(thm)],[f_88_4]) ).
fof(f_89_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_89_2,plain,
? [U_372] :
( relation(U_372)
& ~ empty(U_372) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
fof(f_89_3,plain,
( relation(sK56)
& ~ empty(sK56) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_372,sK56)],[f_89_2]) ).
fof(f_89_4,plain,
( relation(sK56)
& ~ empty(sK56) ),
inference(definitional_conversion,[status(esa)],[f_89_3]) ).
cnf(f_89_5,plain,
~ empty(sK56),
inference(clausify,[status(thm)],[f_89_4]) ).
cnf(f_89_6,plain,
relation(sK56),
inference(clausify,[status(thm)],[f_89_4]) ).
fof(f_90_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_90_2,plain,
! [U_374] :
? [U_373] :
( empty(U_373)
& element(U_373,powerset(U_374)) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
fof(f_90_3,plain,
! [U_374] :
( empty(sK57(U_374))
& element(sK57(U_374),powerset(U_374)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_373,sK57(U_374))],[f_90_2]) ).
fof(f_90_4,plain,
( ! [U_374] : empty(sK57(U_374))
& ! [U_374] : element(sK57(U_374),powerset(U_374)) ),
inference(definitional_conversion,[status(esa)],[f_90_3]) ).
cnf(f_90_5,plain,
element(sK57(U_374),powerset(U_374)),
inference(clausify,[status(thm)],[f_90_4]) ).
cnf(f_90_6,plain,
empty(sK57(U_374)),
inference(clausify,[status(thm)],[f_90_4]) ).
fof(f_91_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_91_2,plain,
? [U_375] : ~ empty(U_375),
inference(variable_rename,[status(thm)],[f_91_1]) ).
fof(f_91_3,plain,
~ empty(sK58),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_375,sK58)],[f_91_2]) ).
fof(f_91_4,plain,
~ empty(sK58),
inference(definitional_conversion,[status(esa)],[f_91_3]) ).
cnf(f_91_5,plain,
~ empty(sK58),
inference(clausify,[status(thm)],[f_91_4]) ).
fof(f_92_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_92_2,plain,
! [U_377,U_376] :
( union_of_subsets(U_377,U_376) = union(U_376)
| ~ element(U_376,powerset(powerset(U_377))) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
fof(f_92_3,plain,
! [U_376,U_377] :
( union_of_subsets(U_377,U_376) = union(U_376)
| ~ element(U_376,powerset(powerset(U_377))) ),
inference(definitional_conversion,[status(esa)],[f_92_2]) ).
cnf(f_92_4,plain,
( union_of_subsets(U_377,U_376) = union(U_376)
| ~ element(U_376,powerset(powerset(U_377))) ),
inference(clausify,[status(thm)],[f_92_3]) ).
fof(f_93_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_93_2,plain,
! [U_379,U_378] :
( meet_of_subsets(U_379,U_378) = set_meet(U_378)
| ~ element(U_378,powerset(powerset(U_379))) ),
inference(variable_rename,[status(thm)],[f_93_1]) ).
fof(f_93_3,plain,
! [U_378,U_379] :
( meet_of_subsets(U_379,U_378) = set_meet(U_378)
| ~ element(U_378,powerset(powerset(U_379))) ),
inference(definitional_conversion,[status(esa)],[f_93_2]) ).
cnf(f_93_4,plain,
( meet_of_subsets(U_379,U_378) = set_meet(U_378)
| ~ element(U_378,powerset(powerset(U_379))) ),
inference(clausify,[status(thm)],[f_93_3]) ).
fof(f_94_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_94_2,plain,
! [U_382,U_381,U_380] :
( subset_difference(U_382,U_381,U_380) = set_difference(U_381,U_380)
| ~ element(U_380,powerset(U_382))
| ~ element(U_381,powerset(U_382)) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
fof(f_94_3,plain,
! [U_380,U_381,U_382] :
( subset_difference(U_382,U_381,U_380) = set_difference(U_381,U_380)
| ~ element(U_380,powerset(U_382))
| ~ element(U_381,powerset(U_382)) ),
inference(definitional_conversion,[status(esa)],[f_94_2]) ).
cnf(f_94_4,plain,
( subset_difference(U_382,U_381,U_380) = set_difference(U_381,U_380)
| ~ element(U_380,powerset(U_382))
| ~ element(U_381,powerset(U_382)) ),
inference(clausify,[status(thm)],[f_94_3]) ).
fof(f_95_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_95_2,plain,
! [U_384,U_383] : subset(U_384,U_384),
inference(variable_rename,[status(thm)],[f_95_1]) ).
fof(f_95_3,plain,
! [U_384] : subset(U_384,U_384),
inference(miniscope,[status(thm)],[f_95_2]) ).
fof(f_95_4,plain,
! [U_384] : subset(U_384,U_384),
inference(definitional_conversion,[status(esa)],[f_95_3]) ).
cnf(f_95_5,plain,
subset(U_384,U_384),
inference(clausify,[status(thm)],[f_95_4]) ).
fof(f_96_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_96_2,plain,
! [U_386,U_385] :
( disjoint(U_385,U_386)
| ~ disjoint(U_386,U_385) ),
inference(variable_rename,[status(thm)],[f_96_1]) ).
fof(f_96_3,plain,
! [U_385,U_386] :
( disjoint(U_385,U_386)
| ~ disjoint(U_386,U_385) ),
inference(definitional_conversion,[status(esa)],[f_96_2]) ).
cnf(f_96_4,plain,
( disjoint(U_385,U_386)
| ~ disjoint(U_386,U_385) ),
inference(clausify,[status(thm)],[f_96_3]) ).
fof(f_97_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_97_2,plain,
! [U_390,U_389,U_388,U_387] :
( ( in(ordered_pair(U_390,U_389),cartesian_product2(U_388,U_387))
| ~ in(U_389,U_387)
| ~ in(U_390,U_388) )
& ( ( in(U_389,U_387)
& in(U_390,U_388) )
| ~ in(ordered_pair(U_390,U_389),cartesian_product2(U_388,U_387)) ) ),
inference(variable_rename,[status(thm)],[f_97_1]) ).
fof(f_97_3,plain,
( ! [U_398,U_396,U_394,U_392] :
( in(ordered_pair(U_398,U_396),cartesian_product2(U_394,U_392))
| ~ in(U_396,U_392)
| ~ in(U_398,U_394) )
& ! [U_397,U_395,U_393,U_391] :
( ( in(U_395,U_391)
& in(U_397,U_393) )
| ~ in(ordered_pair(U_397,U_395),cartesian_product2(U_393,U_391)) ) ),
inference(miniscope,[status(thm)],[f_97_2]) ).
fof(f_97_4,plain,
( ! [U_393,U_395,U_391,U_397] :
( in(U_395,U_391)
| ~ sP68(U_393,U_395,U_391,U_397) )
& ! [U_393,U_395,U_391,U_397] :
( in(U_397,U_393)
| ~ sP68(U_393,U_395,U_391,U_397) )
& ! [U_398,U_392,U_396,U_394] :
( in(ordered_pair(U_398,U_396),cartesian_product2(U_394,U_392))
| ~ in(U_396,U_392)
| ~ in(U_398,U_394) )
& ! [U_393,U_395,U_391,U_397] :
( sP68(U_393,U_395,U_391,U_397)
| ~ in(ordered_pair(U_397,U_395),cartesian_product2(U_393,U_391)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP68])],[f_97_3]) ).
cnf(f_97_5,plain,
( sP68(U_393,U_395,U_391,U_397)
| ~ in(ordered_pair(U_397,U_395),cartesian_product2(U_393,U_391)) ),
inference(clausify,[status(thm)],[f_97_4]) ).
cnf(f_97_6,plain,
( in(ordered_pair(U_398,U_396),cartesian_product2(U_394,U_392))
| ~ in(U_396,U_392)
| ~ in(U_398,U_394) ),
inference(clausify,[status(thm)],[f_97_4]) ).
cnf(f_97_7,plain,
( in(U_397,U_393)
| ~ sP68(U_393,U_395,U_391,U_397) ),
inference(clausify,[status(thm)],[f_97_4]) ).
cnf(f_97_8,plain,
( in(U_395,U_391)
| ~ sP68(U_393,U_395,U_391,U_397) ),
inference(clausify,[status(thm)],[f_97_4]) ).
fof(f_98_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_98_2,plain,
! [U_402,U_401,U_400,U_399] :
( U_402 = U_399
| U_402 = U_400
| unordered_pair(U_402,U_401) != unordered_pair(U_400,U_399) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
fof(f_98_3,plain,
! [U_402,U_401,U_400] :
( ! [U_399] :
( U_402 = U_399
| unordered_pair(U_402,U_401) != unordered_pair(U_400,U_399) )
| U_402 = U_400 ),
inference(miniscope,[status(thm)],[f_98_2]) ).
fof(f_98_4,plain,
! [U_400,U_399,U_402,U_401] :
( U_402 = U_399
| unordered_pair(U_402,U_401) != unordered_pair(U_400,U_399)
| U_402 = U_400 ),
inference(definitional_conversion,[status(esa)],[f_98_3]) ).
cnf(f_98_5,plain,
( U_402 = U_399
| unordered_pair(U_402,U_401) != unordered_pair(U_400,U_399)
| U_402 = U_400 ),
inference(clausify,[status(thm)],[f_98_4]) ).
fof(f_99_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_99_2,plain,
! [U_405,U_404,U_403] :
( ( subset(cartesian_product2(U_403,U_405),cartesian_product2(U_403,U_404))
& subset(cartesian_product2(U_405,U_403),cartesian_product2(U_404,U_403)) )
| ~ subset(U_405,U_404) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
fof(f_99_3,plain,
! [U_405,U_404] :
( ( ! [U_407] : subset(cartesian_product2(U_407,U_405),cartesian_product2(U_407,U_404))
& ! [U_406] : subset(cartesian_product2(U_405,U_406),cartesian_product2(U_404,U_406)) )
| ~ subset(U_405,U_404) ),
inference(miniscope,[status(thm)],[f_99_2]) ).
fof(f_99_4,plain,
( ! [U_404,U_405,U_406,U_407] :
( subset(cartesian_product2(U_407,U_405),cartesian_product2(U_407,U_404))
| ~ sP69(U_404,U_405,U_406,U_407) )
& ! [U_404,U_405,U_406,U_407] :
( subset(cartesian_product2(U_405,U_406),cartesian_product2(U_404,U_406))
| ~ sP69(U_404,U_405,U_406,U_407) )
& ! [U_404,U_405,U_406,U_407] :
( sP69(U_404,U_405,U_406,U_407)
| ~ subset(U_405,U_404) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP69])],[f_99_3]) ).
cnf(f_99_5,plain,
( sP69(U_404,U_405,U_406,U_407)
| ~ subset(U_405,U_404) ),
inference(clausify,[status(thm)],[f_99_4]) ).
cnf(f_99_6,plain,
( subset(cartesian_product2(U_405,U_406),cartesian_product2(U_404,U_406))
| ~ sP69(U_404,U_405,U_406,U_407) ),
inference(clausify,[status(thm)],[f_99_4]) ).
cnf(f_99_7,plain,
( subset(cartesian_product2(U_407,U_405),cartesian_product2(U_407,U_404))
| ~ sP69(U_404,U_405,U_406,U_407) ),
inference(clausify,[status(thm)],[f_99_4]) ).
fof(f_100_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_100_2,plain,
! [U_411,U_410,U_409,U_408] :
( subset(cartesian_product2(U_411,U_409),cartesian_product2(U_410,U_408))
| ~ subset(U_409,U_408)
| ~ subset(U_411,U_410) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
fof(f_100_3,plain,
! [U_408,U_411,U_410,U_409] :
( subset(cartesian_product2(U_411,U_409),cartesian_product2(U_410,U_408))
| ~ subset(U_409,U_408)
| ~ subset(U_411,U_410) ),
inference(definitional_conversion,[status(esa)],[f_100_2]) ).
cnf(f_100_4,plain,
( subset(cartesian_product2(U_411,U_409),cartesian_product2(U_410,U_408))
| ~ subset(U_409,U_408)
| ~ subset(U_411,U_410) ),
inference(clausify,[status(thm)],[f_100_3]) ).
fof(f_101_1,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t12_xboole_1]) ).
fof(f_101_2,plain,
! [U_413,U_412] :
( set_union2(U_413,U_412) = U_412
| ~ subset(U_413,U_412) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
fof(f_101_3,plain,
! [U_413,U_412] :
( set_union2(U_413,U_412) = U_412
| ~ subset(U_413,U_412) ),
inference(definitional_conversion,[status(esa)],[f_101_2]) ).
cnf(f_101_4,plain,
( set_union2(U_413,U_412) = U_412
| ~ subset(U_413,U_412) ),
inference(clausify,[status(thm)],[f_101_3]) ).
fof(f_102_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_102_2,plain,
! [U_419] :
? [U_418] :
( ! [U_417] :
( in(U_417,U_418)
| are_equipotent(U_417,U_418)
| ~ subset(U_417,U_418) )
& ! [U_416] :
( in(powerset(U_416),U_418)
| ~ in(U_416,U_418) )
& ! [U_415,U_414] :
( in(U_414,U_418)
| ~ subset(U_414,U_415)
| ~ in(U_415,U_418) )
& in(U_419,U_418) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
fof(f_102_3,plain,
! [U_419] :
( ! [U_417] :
( in(U_417,sK59(U_419))
| are_equipotent(U_417,sK59(U_419))
| ~ subset(U_417,sK59(U_419)) )
& ! [U_416] :
( in(powerset(U_416),sK59(U_419))
| ~ in(U_416,sK59(U_419)) )
& ! [U_415,U_414] :
( in(U_414,sK59(U_419))
| ~ subset(U_414,U_415)
| ~ in(U_415,sK59(U_419)) )
& in(U_419,sK59(U_419)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_418,sK59(U_419))],[f_102_2]) ).
fof(f_102_4,plain,
( ! [U_417,U_419] :
( in(U_417,sK59(U_419))
| are_equipotent(U_417,sK59(U_419))
| ~ subset(U_417,sK59(U_419)) )
& ! [U_416,U_419] :
( in(powerset(U_416),sK59(U_419))
| ~ in(U_416,sK59(U_419)) )
& ! [U_415,U_414,U_419] :
( in(U_414,sK59(U_419))
| ~ subset(U_414,U_415)
| ~ in(U_415,sK59(U_419)) )
& ! [U_419] : in(U_419,sK59(U_419)) ),
inference(definitional_conversion,[status(esa)],[f_102_3]) ).
cnf(f_102_5,plain,
in(U_419,sK59(U_419)),
inference(clausify,[status(thm)],[f_102_4]) ).
cnf(f_102_6,plain,
( in(U_414,sK59(U_419))
| ~ subset(U_414,U_415)
| ~ in(U_415,sK59(U_419)) ),
inference(clausify,[status(thm)],[f_102_4]) ).
cnf(f_102_7,plain,
( in(powerset(U_416),sK59(U_419))
| ~ in(U_416,sK59(U_419)) ),
inference(clausify,[status(thm)],[f_102_4]) ).
cnf(f_102_8,plain,
( in(U_417,sK59(U_419))
| are_equipotent(U_417,sK59(U_419))
| ~ subset(U_417,sK59(U_419)) ),
inference(clausify,[status(thm)],[f_102_4]) ).
fof(f_103_1,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(fof_nnf,[status(thm)],[t17_xboole_1]) ).
fof(f_103_2,plain,
! [U_421,U_420] : subset(set_intersection2(U_421,U_420),U_421),
inference(variable_rename,[status(thm)],[f_103_1]) ).
fof(f_103_3,plain,
! [U_420,U_421] : subset(set_intersection2(U_421,U_420),U_421),
inference(definitional_conversion,[status(esa)],[f_103_2]) ).
cnf(f_103_4,plain,
subset(set_intersection2(U_421,U_420),U_421),
inference(clausify,[status(thm)],[f_103_3]) ).
fof(f_104_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_104_2,plain,
! [U_424,U_423,U_422] :
( subset(U_424,set_intersection2(U_423,U_422))
| ~ subset(U_424,U_422)
| ~ subset(U_424,U_423) ),
inference(variable_rename,[status(thm)],[f_104_1]) ).
fof(f_104_3,plain,
! [U_422,U_423,U_424] :
( subset(U_424,set_intersection2(U_423,U_422))
| ~ subset(U_424,U_422)
| ~ subset(U_424,U_423) ),
inference(definitional_conversion,[status(esa)],[f_104_2]) ).
cnf(f_104_4,plain,
( subset(U_424,set_intersection2(U_423,U_422))
| ~ subset(U_424,U_422)
| ~ subset(U_424,U_423) ),
inference(clausify,[status(thm)],[f_104_3]) ).
fof(f_105_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_105_2,plain,
! [U_425] : set_union2(U_425,empty_set) = U_425,
inference(variable_rename,[status(thm)],[f_105_1]) ).
fof(f_105_3,plain,
! [U_425] : set_union2(U_425,empty_set) = U_425,
inference(definitional_conversion,[status(esa)],[f_105_2]) ).
cnf(f_105_4,plain,
set_union2(U_425,empty_set) = U_425,
inference(clausify,[status(thm)],[f_105_3]) ).
fof(f_106_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_106_2,plain,
! [U_427,U_426] :
( element(U_427,U_426)
| ~ in(U_427,U_426) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
fof(f_106_3,plain,
! [U_427,U_426] :
( element(U_427,U_426)
| ~ in(U_427,U_426) ),
inference(definitional_conversion,[status(esa)],[f_106_2]) ).
cnf(f_106_4,plain,
( element(U_427,U_426)
| ~ in(U_427,U_426) ),
inference(clausify,[status(thm)],[f_106_3]) ).
fof(f_107_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_107_2,plain,
! [U_430,U_429,U_428] :
( subset(U_430,U_428)
| ~ subset(U_429,U_428)
| ~ subset(U_430,U_429) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
fof(f_107_3,plain,
! [U_429,U_428,U_430] :
( subset(U_430,U_428)
| ~ subset(U_429,U_428)
| ~ subset(U_430,U_429) ),
inference(definitional_conversion,[status(esa)],[f_107_2]) ).
cnf(f_107_4,plain,
( subset(U_430,U_428)
| ~ subset(U_429,U_428)
| ~ subset(U_430,U_429) ),
inference(clausify,[status(thm)],[f_107_3]) ).
fof(f_108_1,plain,
powerset(empty_set) = singleton(empty_set),
inference(fof_nnf,[status(thm)],[t1_zfmisc_1]) ).
fof(f_108_2,plain,
powerset(empty_set) = singleton(empty_set),
inference(definitional_conversion,[status(esa)],[f_108_1]) ).
cnf(f_108_3,plain,
powerset(empty_set) = singleton(empty_set),
inference(clausify,[status(thm)],[f_108_2]) ).
fof(f_109_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_109_2,plain,
! [U_433,U_432,U_431] :
( ( in(U_432,relation_rng(U_431))
& in(U_433,relation_dom(U_431)) )
| ~ in(ordered_pair(U_433,U_432),U_431)
| ~ relation(U_431) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
fof(f_109_3,plain,
( ! [U_431,U_432,U_433] :
( in(U_432,relation_rng(U_431))
| ~ sP70(U_431,U_432,U_433) )
& ! [U_431,U_432,U_433] :
( in(U_433,relation_dom(U_431))
| ~ sP70(U_431,U_432,U_433) )
& ! [U_431,U_432,U_433] :
( sP70(U_431,U_432,U_433)
| ~ in(ordered_pair(U_433,U_432),U_431)
| ~ relation(U_431) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP70])],[f_109_2]) ).
cnf(f_109_4,plain,
( sP70(U_431,U_432,U_433)
| ~ in(ordered_pair(U_433,U_432),U_431)
| ~ relation(U_431) ),
inference(clausify,[status(thm)],[f_109_3]) ).
cnf(f_109_5,plain,
( in(U_433,relation_dom(U_431))
| ~ sP70(U_431,U_432,U_433) ),
inference(clausify,[status(thm)],[f_109_3]) ).
cnf(f_109_6,plain,
( in(U_432,relation_rng(U_431))
| ~ sP70(U_431,U_432,U_433) ),
inference(clausify,[status(thm)],[f_109_3]) ).
fof(f_110_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_110_2,plain,
! [U_434] :
( subset(U_434,cartesian_product2(relation_dom(U_434),relation_rng(U_434)))
| ~ relation(U_434) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
fof(f_110_3,plain,
! [U_434] :
( subset(U_434,cartesian_product2(relation_dom(U_434),relation_rng(U_434)))
| ~ relation(U_434) ),
inference(definitional_conversion,[status(esa)],[f_110_2]) ).
cnf(f_110_4,plain,
( subset(U_434,cartesian_product2(relation_dom(U_434),relation_rng(U_434)))
| ~ relation(U_434) ),
inference(clausify,[status(thm)],[f_110_3]) ).
fof(f_111_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_111_2,plain,
! [U_436] :
( ! [U_435] :
( ( subset(relation_rng(U_436),relation_rng(U_435))
& subset(relation_dom(U_436),relation_dom(U_435)) )
| ~ subset(U_436,U_435)
| ~ relation(U_435) )
| ~ relation(U_436) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
fof(f_111_3,plain,
( ! [U_435,U_436] :
( subset(relation_rng(U_436),relation_rng(U_435))
| ~ sP71(U_435,U_436) )
& ! [U_435,U_436] :
( subset(relation_dom(U_436),relation_dom(U_435))
| ~ sP71(U_435,U_436) )
& ! [U_435,U_436] :
( sP71(U_435,U_436)
| ~ subset(U_436,U_435)
| ~ relation(U_435)
| ~ relation(U_436) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP71])],[f_111_2]) ).
cnf(f_111_4,plain,
( sP71(U_435,U_436)
| ~ subset(U_436,U_435)
| ~ relation(U_435)
| ~ relation(U_436) ),
inference(clausify,[status(thm)],[f_111_3]) ).
cnf(f_111_5,plain,
( subset(relation_dom(U_436),relation_dom(U_435))
| ~ sP71(U_435,U_436) ),
inference(clausify,[status(thm)],[f_111_3]) ).
cnf(f_111_6,plain,
( subset(relation_rng(U_436),relation_rng(U_435))
| ~ sP71(U_435,U_436) ),
inference(clausify,[status(thm)],[f_111_3]) ).
fof(f_112_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_112_2,plain,
! [U_439,U_438,U_437] :
( subset(set_intersection2(U_439,U_437),set_intersection2(U_438,U_437))
| ~ subset(U_439,U_438) ),
inference(variable_rename,[status(thm)],[f_112_1]) ).
fof(f_112_3,plain,
! [U_439,U_438] :
( ! [U_437] : subset(set_intersection2(U_439,U_437),set_intersection2(U_438,U_437))
| ~ subset(U_439,U_438) ),
inference(miniscope,[status(thm)],[f_112_2]) ).
fof(f_112_4,plain,
! [U_439,U_438,U_437] :
( subset(set_intersection2(U_439,U_437),set_intersection2(U_438,U_437))
| ~ subset(U_439,U_438) ),
inference(definitional_conversion,[status(esa)],[f_112_3]) ).
cnf(f_112_5,plain,
( subset(set_intersection2(U_439,U_437),set_intersection2(U_438,U_437))
| ~ subset(U_439,U_438) ),
inference(clausify,[status(thm)],[f_112_4]) ).
fof(f_113_1,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t28_xboole_1]) ).
fof(f_113_2,plain,
! [U_441,U_440] :
( set_intersection2(U_441,U_440) = U_441
| ~ subset(U_441,U_440) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
fof(f_113_3,plain,
! [U_440,U_441] :
( set_intersection2(U_441,U_440) = U_441
| ~ subset(U_441,U_440) ),
inference(definitional_conversion,[status(esa)],[f_113_2]) ).
cnf(f_113_4,plain,
( set_intersection2(U_441,U_440) = U_441
| ~ subset(U_441,U_440) ),
inference(clausify,[status(thm)],[f_113_3]) ).
fof(f_114_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_114_2,plain,
! [U_442] : set_intersection2(U_442,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_114_1]) ).
fof(f_114_3,plain,
! [U_442] : set_intersection2(U_442,empty_set) = empty_set,
inference(definitional_conversion,[status(esa)],[f_114_2]) ).
cnf(f_114_4,plain,
set_intersection2(U_442,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_114_3]) ).
fof(f_115_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_115_2,plain,
! [U_444,U_443] :
( in(U_444,U_443)
| empty(U_443)
| ~ element(U_444,U_443) ),
inference(variable_rename,[status(thm)],[f_115_1]) ).
fof(f_115_3,plain,
! [U_444,U_443] :
( in(U_444,U_443)
| empty(U_443)
| ~ element(U_444,U_443) ),
inference(definitional_conversion,[status(esa)],[f_115_2]) ).
cnf(f_115_4,plain,
( in(U_444,U_443)
| empty(U_443)
| ~ element(U_444,U_443) ),
inference(clausify,[status(thm)],[f_115_3]) ).
fof(f_116_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_116_2,plain,
! [U_447,U_446] :
( U_447 = U_446
| ? [U_445] :
( ( ~ in(U_445,U_447)
& in(U_445,U_446) )
| ( ~ in(U_445,U_446)
& in(U_445,U_447) ) ) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
fof(f_116_3,plain,
! [U_447,U_446] :
( U_447 = U_446
| ? [U_449] :
( ~ in(U_449,U_447)
& in(U_449,U_446) )
| ? [U_448] :
( ~ in(U_448,U_446)
& in(U_448,U_447) ) ),
inference(miniscope,[status(thm)],[f_116_2]) ).
fof(f_116_4,plain,
! [U_447,U_446] :
( U_447 = U_446
| ? [U_449] :
( ~ in(U_449,U_447)
& in(U_449,U_446) )
| ( ~ in(sK60(U_447,U_446),U_446)
& in(sK60(U_447,U_446),U_447) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_448,sK60(U_447,U_446))],[f_116_3]) ).
fof(f_116_5,plain,
! [U_447,U_446] :
( U_447 = U_446
| ( ~ in(sK61(U_447,U_446),U_447)
& in(sK61(U_447,U_446),U_446) )
| ( ~ in(sK60(U_447,U_446),U_446)
& in(sK60(U_447,U_446),U_447) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_449,sK61(U_447,U_446))],[f_116_4]) ).
fof(f_116_6,plain,
( ! [U_446,U_447] :
( ~ in(sK61(U_447,U_446),U_447)
| ~ sP73(U_446,U_447) )
& ! [U_446,U_447] :
( in(sK61(U_447,U_446),U_446)
| ~ sP73(U_446,U_447) )
& ! [U_446,U_447] :
( ~ in(sK60(U_447,U_446),U_446)
| ~ sP72(U_446,U_447) )
& ! [U_446,U_447] :
( in(sK60(U_447,U_446),U_447)
| ~ sP72(U_446,U_447) )
& ! [U_446,U_447] :
( U_447 = U_446
| sP73(U_446,U_447)
| sP72(U_446,U_447) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP72,sP73])],[f_116_5]) ).
cnf(f_116_7,plain,
( U_447 = U_446
| sP73(U_446,U_447)
| sP72(U_446,U_447) ),
inference(clausify,[status(thm)],[f_116_6]) ).
cnf(f_116_8,plain,
( in(sK60(U_447,U_446),U_447)
| ~ sP72(U_446,U_447) ),
inference(clausify,[status(thm)],[f_116_6]) ).
cnf(f_116_9,plain,
( ~ in(sK60(U_447,U_446),U_446)
| ~ sP72(U_446,U_447) ),
inference(clausify,[status(thm)],[f_116_6]) ).
cnf(f_116_10,plain,
( in(sK61(U_447,U_446),U_446)
| ~ sP73(U_446,U_447) ),
inference(clausify,[status(thm)],[f_116_6]) ).
cnf(f_116_11,plain,
( ~ in(sK61(U_447,U_446),U_447)
| ~ sP73(U_446,U_447) ),
inference(clausify,[status(thm)],[f_116_6]) ).
fof(f_117_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_117_2,plain,
! [U_450] : subset(empty_set,U_450),
inference(variable_rename,[status(thm)],[f_117_1]) ).
fof(f_117_3,plain,
! [U_450] : subset(empty_set,U_450),
inference(definitional_conversion,[status(esa)],[f_117_2]) ).
cnf(f_117_4,plain,
subset(empty_set,U_450),
inference(clausify,[status(thm)],[f_117_3]) ).
fof(f_118_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_118_2,plain,
! [U_453,U_452,U_451] :
( ( in(U_452,relation_field(U_451))
& in(U_453,relation_field(U_451)) )
| ~ in(ordered_pair(U_453,U_452),U_451)
| ~ relation(U_451) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
fof(f_118_3,plain,
( ! [U_451,U_453,U_452] :
( in(U_452,relation_field(U_451))
| ~ sP74(U_451,U_453,U_452) )
& ! [U_451,U_453,U_452] :
( in(U_453,relation_field(U_451))
| ~ sP74(U_451,U_453,U_452) )
& ! [U_451,U_453,U_452] :
( sP74(U_451,U_453,U_452)
| ~ in(ordered_pair(U_453,U_452),U_451)
| ~ relation(U_451) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP74])],[f_118_2]) ).
cnf(f_118_4,plain,
( sP74(U_451,U_453,U_452)
| ~ in(ordered_pair(U_453,U_452),U_451)
| ~ relation(U_451) ),
inference(clausify,[status(thm)],[f_118_3]) ).
cnf(f_118_5,plain,
( in(U_453,relation_field(U_451))
| ~ sP74(U_451,U_453,U_452) ),
inference(clausify,[status(thm)],[f_118_3]) ).
cnf(f_118_6,plain,
( in(U_452,relation_field(U_451))
| ~ sP74(U_451,U_453,U_452) ),
inference(clausify,[status(thm)],[f_118_3]) ).
fof(f_119_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_119_2,plain,
! [U_456,U_455,U_454] :
( subset(set_difference(U_456,U_454),set_difference(U_455,U_454))
| ~ subset(U_456,U_455) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
fof(f_119_3,plain,
! [U_456,U_455] :
( ! [U_454] : subset(set_difference(U_456,U_454),set_difference(U_455,U_454))
| ~ subset(U_456,U_455) ),
inference(miniscope,[status(thm)],[f_119_2]) ).
fof(f_119_4,plain,
! [U_455,U_456,U_454] :
( subset(set_difference(U_456,U_454),set_difference(U_455,U_454))
| ~ subset(U_456,U_455) ),
inference(definitional_conversion,[status(esa)],[f_119_3]) ).
cnf(f_119_5,plain,
( subset(set_difference(U_456,U_454),set_difference(U_455,U_454))
| ~ subset(U_456,U_455) ),
inference(clausify,[status(thm)],[f_119_4]) ).
fof(f_120_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_120_2,plain,
! [U_460,U_459,U_458,U_457] :
( ( U_459 = U_457
& U_460 = U_458 )
| ordered_pair(U_460,U_459) != ordered_pair(U_458,U_457) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
fof(f_120_3,plain,
( ! [U_457,U_458,U_459,U_460] :
( U_459 = U_457
| ~ sP75(U_457,U_458,U_459,U_460) )
& ! [U_457,U_458,U_459,U_460] :
( U_460 = U_458
| ~ sP75(U_457,U_458,U_459,U_460) )
& ! [U_457,U_458,U_459,U_460] :
( sP75(U_457,U_458,U_459,U_460)
| ordered_pair(U_460,U_459) != ordered_pair(U_458,U_457) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP75])],[f_120_2]) ).
cnf(f_120_4,plain,
( sP75(U_457,U_458,U_459,U_460)
| ordered_pair(U_460,U_459) != ordered_pair(U_458,U_457) ),
inference(clausify,[status(thm)],[f_120_3]) ).
cnf(f_120_5,plain,
( U_460 = U_458
| ~ sP75(U_457,U_458,U_459,U_460) ),
inference(clausify,[status(thm)],[f_120_3]) ).
cnf(f_120_6,plain,
( U_459 = U_457
| ~ sP75(U_457,U_458,U_459,U_460) ),
inference(clausify,[status(thm)],[f_120_3]) ).
fof(f_121_1,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(fof_nnf,[status(thm)],[t36_xboole_1]) ).
fof(f_121_2,plain,
! [U_462,U_461] : subset(set_difference(U_462,U_461),U_462),
inference(variable_rename,[status(thm)],[f_121_1]) ).
fof(f_121_3,plain,
! [U_462,U_461] : subset(set_difference(U_462,U_461),U_462),
inference(definitional_conversion,[status(esa)],[f_121_2]) ).
cnf(f_121_4,plain,
subset(set_difference(U_462,U_461),U_462),
inference(clausify,[status(thm)],[f_121_3]) ).
fof(f_122_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_122_2,plain,
! [U_463] :
( ( relation_dom(U_463) = relation_rng(relation_inverse(U_463))
& relation_rng(U_463) = relation_dom(relation_inverse(U_463)) )
| ~ relation(U_463) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
fof(f_122_3,plain,
( ! [U_463] :
( relation_dom(U_463) = relation_rng(relation_inverse(U_463))
| ~ sP76(U_463) )
& ! [U_463] :
( relation_rng(U_463) = relation_dom(relation_inverse(U_463))
| ~ sP76(U_463) )
& ! [U_463] :
( sP76(U_463)
| ~ relation(U_463) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP76])],[f_122_2]) ).
cnf(f_122_4,plain,
( sP76(U_463)
| ~ relation(U_463) ),
inference(clausify,[status(thm)],[f_122_3]) ).
cnf(f_122_5,plain,
( relation_rng(U_463) = relation_dom(relation_inverse(U_463))
| ~ sP76(U_463) ),
inference(clausify,[status(thm)],[f_122_3]) ).
cnf(f_122_6,plain,
( relation_dom(U_463) = relation_rng(relation_inverse(U_463))
| ~ sP76(U_463) ),
inference(clausify,[status(thm)],[f_122_3]) ).
fof(f_123_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_123_2,plain,
! [U_465,U_464] :
( ( set_difference(U_465,U_464) = empty_set
| ~ subset(U_465,U_464) )
& ( subset(U_465,U_464)
| set_difference(U_465,U_464) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
fof(f_123_3,plain,
( ! [U_469,U_467] :
( set_difference(U_469,U_467) = empty_set
| ~ subset(U_469,U_467) )
& ! [U_468,U_466] :
( subset(U_468,U_466)
| set_difference(U_468,U_466) != empty_set ) ),
inference(miniscope,[status(thm)],[f_123_2]) ).
fof(f_123_4,plain,
( ! [U_469,U_467] :
( set_difference(U_469,U_467) = empty_set
| ~ subset(U_469,U_467) )
& ! [U_468,U_466] :
( subset(U_468,U_466)
| set_difference(U_468,U_466) != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_123_3]) ).
cnf(f_123_5,plain,
( subset(U_468,U_466)
| set_difference(U_468,U_466) != empty_set ),
inference(clausify,[status(thm)],[f_123_4]) ).
cnf(f_123_6,plain,
( set_difference(U_469,U_467) = empty_set
| ~ subset(U_469,U_467) ),
inference(clausify,[status(thm)],[f_123_4]) ).
fof(f_124_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_124_2,plain,
! [U_471,U_470] :
( ( subset(singleton(U_471),U_470)
| ~ in(U_471,U_470) )
& ( in(U_471,U_470)
| ~ subset(singleton(U_471),U_470) ) ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
fof(f_124_3,plain,
( ! [U_475,U_473] :
( subset(singleton(U_475),U_473)
| ~ in(U_475,U_473) )
& ! [U_474,U_472] :
( in(U_474,U_472)
| ~ subset(singleton(U_474),U_472) ) ),
inference(miniscope,[status(thm)],[f_124_2]) ).
fof(f_124_4,plain,
( ! [U_473,U_475] :
( subset(singleton(U_475),U_473)
| ~ in(U_475,U_473) )
& ! [U_472,U_474] :
( in(U_474,U_472)
| ~ subset(singleton(U_474),U_472) ) ),
inference(definitional_conversion,[status(esa)],[f_124_3]) ).
cnf(f_124_5,plain,
( in(U_474,U_472)
| ~ subset(singleton(U_474),U_472) ),
inference(clausify,[status(thm)],[f_124_4]) ).
cnf(f_124_6,plain,
( subset(singleton(U_475),U_473)
| ~ in(U_475,U_473) ),
inference(clausify,[status(thm)],[f_124_4]) ).
fof(f_125_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_125_2,plain,
! [U_478,U_477,U_476] :
( ( subset(unordered_pair(U_478,U_477),U_476)
| ~ in(U_477,U_476)
| ~ in(U_478,U_476) )
& ( ( in(U_477,U_476)
& in(U_478,U_476) )
| ~ subset(unordered_pair(U_478,U_477),U_476) ) ),
inference(variable_rename,[status(thm)],[f_125_1]) ).
fof(f_125_3,plain,
( ! [U_484,U_482,U_480] :
( subset(unordered_pair(U_484,U_482),U_480)
| ~ in(U_482,U_480)
| ~ in(U_484,U_480) )
& ! [U_483,U_481,U_479] :
( ( in(U_481,U_479)
& in(U_483,U_479) )
| ~ subset(unordered_pair(U_483,U_481),U_479) ) ),
inference(miniscope,[status(thm)],[f_125_2]) ).
fof(f_125_4,plain,
( ! [U_479,U_481,U_483] :
( in(U_481,U_479)
| ~ sP77(U_479,U_481,U_483) )
& ! [U_479,U_481,U_483] :
( in(U_483,U_479)
| ~ sP77(U_479,U_481,U_483) )
& ! [U_482,U_480,U_484] :
( subset(unordered_pair(U_484,U_482),U_480)
| ~ in(U_482,U_480)
| ~ in(U_484,U_480) )
& ! [U_479,U_481,U_483] :
( sP77(U_479,U_481,U_483)
| ~ subset(unordered_pair(U_483,U_481),U_479) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP77])],[f_125_3]) ).
cnf(f_125_5,plain,
( sP77(U_479,U_481,U_483)
| ~ subset(unordered_pair(U_483,U_481),U_479) ),
inference(clausify,[status(thm)],[f_125_4]) ).
cnf(f_125_6,plain,
( subset(unordered_pair(U_484,U_482),U_480)
| ~ in(U_482,U_480)
| ~ in(U_484,U_480) ),
inference(clausify,[status(thm)],[f_125_4]) ).
cnf(f_125_7,plain,
( in(U_483,U_479)
| ~ sP77(U_479,U_481,U_483) ),
inference(clausify,[status(thm)],[f_125_4]) ).
cnf(f_125_8,plain,
( in(U_481,U_479)
| ~ sP77(U_479,U_481,U_483) ),
inference(clausify,[status(thm)],[f_125_4]) ).
fof(f_126_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_126_2,plain,
! [U_486,U_485] : set_union2(U_486,set_difference(U_485,U_486)) = set_union2(U_486,U_485),
inference(variable_rename,[status(thm)],[f_126_1]) ).
fof(f_126_3,plain,
! [U_485,U_486] : set_union2(U_486,set_difference(U_485,U_486)) = set_union2(U_486,U_485),
inference(definitional_conversion,[status(esa)],[f_126_2]) ).
cnf(f_126_4,plain,
set_union2(U_486,set_difference(U_485,U_486)) = set_union2(U_486,U_485),
inference(clausify,[status(thm)],[f_126_3]) ).
fof(f_127_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_127_2,plain,
! [U_488,U_487] :
( ( subset(U_488,singleton(U_487))
| ( U_488 != singleton(U_487)
& U_488 != empty_set ) )
& ( U_488 = singleton(U_487)
| U_488 = empty_set
| ~ subset(U_488,singleton(U_487)) ) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
fof(f_127_3,plain,
( ! [U_492,U_490] :
( subset(U_492,singleton(U_490))
| ( U_492 != singleton(U_490)
& U_492 != empty_set ) )
& ! [U_491,U_489] :
( U_491 = singleton(U_489)
| U_491 = empty_set
| ~ subset(U_491,singleton(U_489)) ) ),
inference(miniscope,[status(thm)],[f_127_2]) ).
fof(f_127_4,plain,
( ! [U_490,U_492] :
( U_492 != singleton(U_490)
| ~ sP78(U_490,U_492) )
& ! [U_490,U_492] :
( U_492 != empty_set
| ~ sP78(U_490,U_492) )
& ! [U_490,U_492] :
( subset(U_492,singleton(U_490))
| sP78(U_490,U_492) )
& ! [U_491,U_489] :
( U_491 = singleton(U_489)
| U_491 = empty_set
| ~ subset(U_491,singleton(U_489)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP78])],[f_127_3]) ).
cnf(f_127_5,plain,
( U_491 = singleton(U_489)
| U_491 = empty_set
| ~ subset(U_491,singleton(U_489)) ),
inference(clausify,[status(thm)],[f_127_4]) ).
cnf(f_127_6,plain,
( subset(U_492,singleton(U_490))
| sP78(U_490,U_492) ),
inference(clausify,[status(thm)],[f_127_4]) ).
cnf(f_127_7,plain,
( U_492 != empty_set
| ~ sP78(U_490,U_492) ),
inference(clausify,[status(thm)],[f_127_4]) ).
cnf(f_127_8,plain,
( U_492 != singleton(U_490)
| ~ sP78(U_490,U_492) ),
inference(clausify,[status(thm)],[f_127_4]) ).
fof(f_128_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_128_2,plain,
! [U_493] : set_difference(U_493,empty_set) = U_493,
inference(variable_rename,[status(thm)],[f_128_1]) ).
fof(f_128_3,plain,
! [U_493] : set_difference(U_493,empty_set) = U_493,
inference(definitional_conversion,[status(esa)],[f_128_2]) ).
cnf(f_128_4,plain,
set_difference(U_493,empty_set) = U_493,
inference(clausify,[status(thm)],[f_128_3]) ).
fof(f_129_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_129_2,plain,
! [U_495,U_494] :
( ( element(U_495,powerset(U_494))
| ~ subset(U_495,U_494) )
& ( subset(U_495,U_494)
| ~ element(U_495,powerset(U_494)) ) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
fof(f_129_3,plain,
( ! [U_499,U_497] :
( element(U_499,powerset(U_497))
| ~ subset(U_499,U_497) )
& ! [U_498,U_496] :
( subset(U_498,U_496)
| ~ element(U_498,powerset(U_496)) ) ),
inference(miniscope,[status(thm)],[f_129_2]) ).
fof(f_129_4,plain,
( ! [U_499,U_497] :
( element(U_499,powerset(U_497))
| ~ subset(U_499,U_497) )
& ! [U_498,U_496] :
( subset(U_498,U_496)
| ~ element(U_498,powerset(U_496)) ) ),
inference(definitional_conversion,[status(esa)],[f_129_3]) ).
cnf(f_129_5,plain,
( subset(U_498,U_496)
| ~ element(U_498,powerset(U_496)) ),
inference(clausify,[status(thm)],[f_129_4]) ).
cnf(f_129_6,plain,
( element(U_499,powerset(U_497))
| ~ subset(U_499,U_497) ),
inference(clausify,[status(thm)],[f_129_4]) ).
fof(f_130_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_130_2,plain,
! [U_503,U_502] :
( ( ~ disjoint(U_503,U_502)
| ! [U_501] :
( ~ in(U_501,U_502)
| ~ in(U_501,U_503) ) )
& ( ? [U_500] :
( in(U_500,U_502)
& in(U_500,U_503) )
| disjoint(U_503,U_502) ) ),
inference(variable_rename,[status(thm)],[f_130_1]) ).
fof(f_130_3,plain,
( ! [U_507,U_505] :
( ~ disjoint(U_507,U_505)
| ! [U_501] :
( ~ in(U_501,U_505)
| ~ in(U_501,U_507) ) )
& ! [U_506,U_504] :
( ? [U_500] :
( in(U_500,U_504)
& in(U_500,U_506) )
| disjoint(U_506,U_504) ) ),
inference(miniscope,[status(thm)],[f_130_2]) ).
fof(f_130_4,plain,
( ! [U_507,U_505] :
( ~ disjoint(U_507,U_505)
| ! [U_501] :
( ~ in(U_501,U_505)
| ~ in(U_501,U_507) ) )
& ! [U_506,U_504] :
( ( in(sK62(U_506,U_504),U_504)
& in(sK62(U_506,U_504),U_506) )
| disjoint(U_506,U_504) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_500,sK62(U_506,U_504))],[f_130_3]) ).
fof(f_130_5,plain,
( ! [U_504,U_506] :
( in(sK62(U_506,U_504),U_504)
| ~ sP79(U_504,U_506) )
& ! [U_504,U_506] :
( in(sK62(U_506,U_504),U_506)
| ~ sP79(U_504,U_506) )
& ! [U_507,U_505,U_501] :
( ~ disjoint(U_507,U_505)
| ~ in(U_501,U_505)
| ~ in(U_501,U_507) )
& ! [U_504,U_506] :
( sP79(U_504,U_506)
| disjoint(U_506,U_504) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP79])],[f_130_4]) ).
cnf(f_130_6,plain,
( sP79(U_504,U_506)
| disjoint(U_506,U_504) ),
inference(clausify,[status(thm)],[f_130_5]) ).
cnf(f_130_7,plain,
( ~ disjoint(U_507,U_505)
| ~ in(U_501,U_505)
| ~ in(U_501,U_507) ),
inference(clausify,[status(thm)],[f_130_5]) ).
cnf(f_130_8,plain,
( in(sK62(U_506,U_504),U_506)
| ~ sP79(U_504,U_506) ),
inference(clausify,[status(thm)],[f_130_5]) ).
cnf(f_130_9,plain,
( in(sK62(U_506,U_504),U_504)
| ~ sP79(U_504,U_506) ),
inference(clausify,[status(thm)],[f_130_5]) ).
fof(f_131_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_131_2,plain,
! [U_508] :
( U_508 = empty_set
| ~ subset(U_508,empty_set) ),
inference(variable_rename,[status(thm)],[f_131_1]) ).
fof(f_131_3,plain,
! [U_508] :
( U_508 = empty_set
| ~ subset(U_508,empty_set) ),
inference(definitional_conversion,[status(esa)],[f_131_2]) ).
cnf(f_131_4,plain,
( U_508 = empty_set
| ~ subset(U_508,empty_set) ),
inference(clausify,[status(thm)],[f_131_3]) ).
fof(f_132_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_132_2,plain,
! [U_510,U_509] : set_difference(set_union2(U_510,U_509),U_509) = set_difference(U_510,U_509),
inference(variable_rename,[status(thm)],[f_132_1]) ).
fof(f_132_3,plain,
! [U_509,U_510] : set_difference(set_union2(U_510,U_509),U_509) = set_difference(U_510,U_509),
inference(definitional_conversion,[status(esa)],[f_132_2]) ).
cnf(f_132_4,plain,
set_difference(set_union2(U_510,U_509),U_509) = set_difference(U_510,U_509),
inference(clausify,[status(thm)],[f_132_3]) ).
fof(f_133_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_133_2,plain,
! [U_513,U_512] :
( ! [U_511] :
( ( ( disjoint(U_512,U_511)
| ~ subset(U_512,subset_complement(U_513,U_511)) )
& ( subset(U_512,subset_complement(U_513,U_511))
| ~ disjoint(U_512,U_511) ) )
| ~ element(U_511,powerset(U_513)) )
| ~ element(U_512,powerset(U_513)) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
fof(f_133_3,plain,
( ! [U_512,U_513,U_511] :
( disjoint(U_512,U_511)
| ~ subset(U_512,subset_complement(U_513,U_511))
| ~ sP80(U_512,U_513,U_511) )
& ! [U_512,U_513,U_511] :
( subset(U_512,subset_complement(U_513,U_511))
| ~ disjoint(U_512,U_511)
| ~ sP80(U_512,U_513,U_511) )
& ! [U_512,U_513,U_511] :
( sP80(U_512,U_513,U_511)
| ~ element(U_511,powerset(U_513))
| ~ element(U_512,powerset(U_513)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP80])],[f_133_2]) ).
cnf(f_133_4,plain,
( sP80(U_512,U_513,U_511)
| ~ element(U_511,powerset(U_513))
| ~ element(U_512,powerset(U_513)) ),
inference(clausify,[status(thm)],[f_133_3]) ).
cnf(f_133_5,plain,
( subset(U_512,subset_complement(U_513,U_511))
| ~ disjoint(U_512,U_511)
| ~ sP80(U_512,U_513,U_511) ),
inference(clausify,[status(thm)],[f_133_3]) ).
cnf(f_133_6,plain,
( disjoint(U_512,U_511)
| ~ subset(U_512,subset_complement(U_513,U_511))
| ~ sP80(U_512,U_513,U_511) ),
inference(clausify,[status(thm)],[f_133_3]) ).
fof(f_134_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_134_2,plain,
! [U_515] :
( ! [U_514] :
( subset(relation_dom(relation_composition(U_515,U_514)),relation_dom(U_515))
| ~ relation(U_514) )
| ~ relation(U_515) ),
inference(variable_rename,[status(thm)],[f_134_1]) ).
fof(f_134_3,plain,
! [U_514,U_515] :
( subset(relation_dom(relation_composition(U_515,U_514)),relation_dom(U_515))
| ~ relation(U_514)
| ~ relation(U_515) ),
inference(definitional_conversion,[status(esa)],[f_134_2]) ).
cnf(f_134_4,plain,
( subset(relation_dom(relation_composition(U_515,U_514)),relation_dom(U_515))
| ~ relation(U_514)
| ~ relation(U_515) ),
inference(clausify,[status(thm)],[f_134_3]) ).
fof(f_135_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_135_2,plain,
! [U_517] :
( ! [U_516] :
( subset(relation_rng(relation_composition(U_517,U_516)),relation_rng(U_516))
| ~ relation(U_516) )
| ~ relation(U_517) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
fof(f_135_3,plain,
! [U_517,U_516] :
( subset(relation_rng(relation_composition(U_517,U_516)),relation_rng(U_516))
| ~ relation(U_516)
| ~ relation(U_517) ),
inference(definitional_conversion,[status(esa)],[f_135_2]) ).
cnf(f_135_4,plain,
( subset(relation_rng(relation_composition(U_517,U_516)),relation_rng(U_516))
| ~ relation(U_516)
| ~ relation(U_517) ),
inference(clausify,[status(thm)],[f_135_3]) ).
fof(f_136_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_136_2,plain,
! [U_519,U_518] :
( U_518 = set_union2(U_519,set_difference(U_518,U_519))
| ~ subset(U_519,U_518) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
fof(f_136_3,plain,
! [U_519,U_518] :
( U_518 = set_union2(U_519,set_difference(U_518,U_519))
| ~ subset(U_519,U_518) ),
inference(definitional_conversion,[status(esa)],[f_136_2]) ).
cnf(f_136_4,plain,
( U_518 = set_union2(U_519,set_difference(U_518,U_519))
| ~ subset(U_519,U_518) ),
inference(clausify,[status(thm)],[f_136_3]) ).
fof(f_137_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_137_2,plain,
! [U_521] :
( ! [U_520] :
( relation_dom(relation_composition(U_521,U_520)) = relation_dom(U_521)
| ~ subset(relation_rng(U_521),relation_dom(U_520))
| ~ relation(U_520) )
| ~ relation(U_521) ),
inference(variable_rename,[status(thm)],[f_137_1]) ).
fof(f_137_3,plain,
! [U_520,U_521] :
( relation_dom(relation_composition(U_521,U_520)) = relation_dom(U_521)
| ~ subset(relation_rng(U_521),relation_dom(U_520))
| ~ relation(U_520)
| ~ relation(U_521) ),
inference(definitional_conversion,[status(esa)],[f_137_2]) ).
cnf(f_137_4,plain,
( relation_dom(relation_composition(U_521,U_520)) = relation_dom(U_521)
| ~ subset(relation_rng(U_521),relation_dom(U_520))
| ~ relation(U_520)
| ~ relation(U_521) ),
inference(clausify,[status(thm)],[f_137_3]) ).
fof(f_138_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_138_2,plain,
! [U_523,U_522] :
( complements_of_subsets(U_523,U_522) != empty_set
| U_522 = empty_set
| ~ element(U_522,powerset(powerset(U_523))) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
fof(f_138_3,plain,
! [U_523,U_522] :
( complements_of_subsets(U_523,U_522) != empty_set
| U_522 = empty_set
| ~ element(U_522,powerset(powerset(U_523))) ),
inference(definitional_conversion,[status(esa)],[f_138_2]) ).
cnf(f_138_4,plain,
( complements_of_subsets(U_523,U_522) != empty_set
| U_522 = empty_set
| ~ element(U_522,powerset(powerset(U_523))) ),
inference(clausify,[status(thm)],[f_138_3]) ).
fof(f_139_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t46_zfmisc_1]) ).
fof(f_139_2,plain,
! [U_525,U_524] :
( set_union2(singleton(U_525),U_524) = U_524
| ~ in(U_525,U_524) ),
inference(variable_rename,[status(thm)],[f_139_1]) ).
fof(f_139_3,plain,
! [U_525,U_524] :
( set_union2(singleton(U_525),U_524) = U_524
| ~ in(U_525,U_524) ),
inference(definitional_conversion,[status(esa)],[f_139_2]) ).
cnf(f_139_4,plain,
( set_union2(singleton(U_525),U_524) = U_524
| ~ in(U_525,U_524) ),
inference(clausify,[status(thm)],[f_139_3]) ).
fof(f_140_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_140_2,plain,
! [U_527] :
( ! [U_526] :
( relation_rng(relation_composition(U_526,U_527)) = relation_rng(U_527)
| ~ subset(relation_dom(U_527),relation_rng(U_526))
| ~ relation(U_526) )
| ~ relation(U_527) ),
inference(variable_rename,[status(thm)],[f_140_1]) ).
fof(f_140_3,plain,
! [U_526,U_527] :
( relation_rng(relation_composition(U_526,U_527)) = relation_rng(U_527)
| ~ subset(relation_dom(U_527),relation_rng(U_526))
| ~ relation(U_526)
| ~ relation(U_527) ),
inference(definitional_conversion,[status(esa)],[f_140_2]) ).
cnf(f_140_4,plain,
( relation_rng(relation_composition(U_526,U_527)) = relation_rng(U_527)
| ~ subset(relation_dom(U_527),relation_rng(U_526))
| ~ relation(U_526)
| ~ relation(U_527) ),
inference(clausify,[status(thm)],[f_140_3]) ).
fof(f_141_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_141_2,plain,
! [U_529,U_528] :
( subset_difference(U_529,cast_to_subset(U_529),union_of_subsets(U_529,U_528)) = meet_of_subsets(U_529,complements_of_subsets(U_529,U_528))
| U_528 = empty_set
| ~ element(U_528,powerset(powerset(U_529))) ),
inference(variable_rename,[status(thm)],[f_141_1]) ).
fof(f_141_3,plain,
! [U_529,U_528] :
( subset_difference(U_529,cast_to_subset(U_529),union_of_subsets(U_529,U_528)) = meet_of_subsets(U_529,complements_of_subsets(U_529,U_528))
| U_528 = empty_set
| ~ element(U_528,powerset(powerset(U_529))) ),
inference(definitional_conversion,[status(esa)],[f_141_2]) ).
cnf(f_141_4,plain,
( subset_difference(U_529,cast_to_subset(U_529),union_of_subsets(U_529,U_528)) = meet_of_subsets(U_529,complements_of_subsets(U_529,U_528))
| U_528 = empty_set
| ~ element(U_528,powerset(powerset(U_529))) ),
inference(clausify,[status(thm)],[f_141_3]) ).
fof(f_142_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_142_2,plain,
! [U_531,U_530] :
( union_of_subsets(U_531,complements_of_subsets(U_531,U_530)) = subset_difference(U_531,cast_to_subset(U_531),meet_of_subsets(U_531,U_530))
| U_530 = empty_set
| ~ element(U_530,powerset(powerset(U_531))) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
fof(f_142_3,plain,
! [U_531,U_530] :
( union_of_subsets(U_531,complements_of_subsets(U_531,U_530)) = subset_difference(U_531,cast_to_subset(U_531),meet_of_subsets(U_531,U_530))
| U_530 = empty_set
| ~ element(U_530,powerset(powerset(U_531))) ),
inference(definitional_conversion,[status(esa)],[f_142_2]) ).
cnf(f_142_4,plain,
( union_of_subsets(U_531,complements_of_subsets(U_531,U_530)) = subset_difference(U_531,cast_to_subset(U_531),meet_of_subsets(U_531,U_530))
| U_530 = empty_set
| ~ element(U_530,powerset(powerset(U_531))) ),
inference(clausify,[status(thm)],[f_142_3]) ).
fof(f_143_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_143_2,plain,
! [U_533,U_532] : set_difference(U_533,set_difference(U_533,U_532)) = set_intersection2(U_533,U_532),
inference(variable_rename,[status(thm)],[f_143_1]) ).
fof(f_143_3,plain,
! [U_532,U_533] : set_difference(U_533,set_difference(U_533,U_532)) = set_intersection2(U_533,U_532),
inference(definitional_conversion,[status(esa)],[f_143_2]) ).
cnf(f_143_4,plain,
set_difference(U_533,set_difference(U_533,U_532)) = set_intersection2(U_533,U_532),
inference(clausify,[status(thm)],[f_143_3]) ).
fof(f_144_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_144_2,plain,
! [U_534] : set_difference(empty_set,U_534) = empty_set,
inference(variable_rename,[status(thm)],[f_144_1]) ).
fof(f_144_3,plain,
! [U_534] : set_difference(empty_set,U_534) = empty_set,
inference(definitional_conversion,[status(esa)],[f_144_2]) ).
cnf(f_144_4,plain,
set_difference(empty_set,U_534) = empty_set,
inference(clausify,[status(thm)],[f_144_3]) ).
fof(f_145_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_145_2,plain,
! [U_537,U_536,U_535] :
( element(U_537,U_535)
| ~ element(U_536,powerset(U_535))
| ~ in(U_537,U_536) ),
inference(variable_rename,[status(thm)],[f_145_1]) ).
fof(f_145_3,plain,
! [U_536,U_537,U_535] :
( element(U_537,U_535)
| ~ element(U_536,powerset(U_535))
| ~ in(U_537,U_536) ),
inference(definitional_conversion,[status(esa)],[f_145_2]) ).
cnf(f_145_4,plain,
( element(U_537,U_535)
| ~ element(U_536,powerset(U_535))
| ~ in(U_537,U_536) ),
inference(clausify,[status(thm)],[f_145_3]) ).
fof(f_146_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_146_2,plain,
! [U_541,U_540] :
( ( ~ disjoint(U_541,U_540)
| ! [U_539] : ~ in(U_539,set_intersection2(U_541,U_540)) )
& ( ? [U_538] : in(U_538,set_intersection2(U_541,U_540))
| disjoint(U_541,U_540) ) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
fof(f_146_3,plain,
( ! [U_545,U_543] :
( ~ disjoint(U_545,U_543)
| ! [U_539] : ~ in(U_539,set_intersection2(U_545,U_543)) )
& ! [U_544,U_542] :
( ? [U_538] : in(U_538,set_intersection2(U_544,U_542))
| disjoint(U_544,U_542) ) ),
inference(miniscope,[status(thm)],[f_146_2]) ).
fof(f_146_4,plain,
( ! [U_545,U_543] :
( ~ disjoint(U_545,U_543)
| ! [U_539] : ~ in(U_539,set_intersection2(U_545,U_543)) )
& ! [U_544,U_542] :
( in(sK63(U_544,U_542),set_intersection2(U_544,U_542))
| disjoint(U_544,U_542) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_538,sK63(U_544,U_542))],[f_146_3]) ).
fof(f_146_5,plain,
( ! [U_539,U_545,U_543] :
( ~ disjoint(U_545,U_543)
| ~ in(U_539,set_intersection2(U_545,U_543)) )
& ! [U_542,U_544] :
( in(sK63(U_544,U_542),set_intersection2(U_544,U_542))
| disjoint(U_544,U_542) ) ),
inference(definitional_conversion,[status(esa)],[f_146_4]) ).
cnf(f_146_6,plain,
( in(sK63(U_544,U_542),set_intersection2(U_544,U_542))
| disjoint(U_544,U_542) ),
inference(clausify,[status(thm)],[f_146_5]) ).
cnf(f_146_7,plain,
( ~ disjoint(U_545,U_543)
| ~ in(U_539,set_intersection2(U_545,U_543)) ),
inference(clausify,[status(thm)],[f_146_5]) ).
fof(f_147_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_147_2,plain,
! [U_548] :
( ! [U_547] :
( ! [U_546] :
( in(U_546,subset_complement(U_548,U_547))
| in(U_546,U_547)
| ~ element(U_546,U_548) )
| ~ element(U_547,powerset(U_548)) )
| U_548 = empty_set ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
fof(f_147_3,plain,
! [U_548,U_547,U_546] :
( in(U_546,subset_complement(U_548,U_547))
| in(U_546,U_547)
| ~ element(U_546,U_548)
| ~ element(U_547,powerset(U_548))
| U_548 = empty_set ),
inference(definitional_conversion,[status(esa)],[f_147_2]) ).
cnf(f_147_4,plain,
( in(U_546,subset_complement(U_548,U_547))
| in(U_546,U_547)
| ~ element(U_546,U_548)
| ~ element(U_547,powerset(U_548))
| U_548 = empty_set ),
inference(clausify,[status(thm)],[f_147_3]) ).
fof(f_148_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_148_2,plain,
! [U_551,U_550,U_549] :
( ~ in(U_550,U_549)
| ~ in(U_550,subset_complement(U_551,U_549))
| ~ element(U_549,powerset(U_551)) ),
inference(variable_rename,[status(thm)],[f_148_1]) ).
fof(f_148_3,plain,
! [U_550,U_551,U_549] :
( ~ in(U_550,U_549)
| ~ in(U_550,subset_complement(U_551,U_549))
| ~ element(U_549,powerset(U_551)) ),
inference(definitional_conversion,[status(esa)],[f_148_2]) ).
cnf(f_148_4,plain,
( ~ in(U_550,U_549)
| ~ in(U_550,subset_complement(U_551,U_549))
| ~ element(U_549,powerset(U_551)) ),
inference(clausify,[status(thm)],[f_148_3]) ).
fof(f_149_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_149_2,plain,
! [U_554] :
( U_554 = empty_set
| ? [U_553,U_552] : in(ordered_pair(U_553,U_552),U_554)
| ~ relation(U_554) ),
inference(variable_rename,[status(thm)],[f_149_1]) ).
fof(f_149_3,plain,
! [U_554] :
( U_554 = empty_set
| ? [U_552] : in(ordered_pair(sK64(U_554),U_552),U_554)
| ~ relation(U_554) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_553,sK64(U_554))],[f_149_2]) ).
fof(f_149_4,plain,
! [U_554] :
( U_554 = empty_set
| in(ordered_pair(sK64(U_554),sK65(U_554)),U_554)
| ~ relation(U_554) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_552,sK65(U_554))],[f_149_3]) ).
fof(f_149_5,plain,
! [U_554] :
( U_554 = empty_set
| in(ordered_pair(sK64(U_554),sK65(U_554)),U_554)
| ~ relation(U_554) ),
inference(definitional_conversion,[status(esa)],[f_149_4]) ).
cnf(f_149_6,plain,
( U_554 = empty_set
| in(ordered_pair(sK64(U_554),sK65(U_554)),U_554)
| ~ relation(U_554) ),
inference(clausify,[status(thm)],[f_149_5]) ).
fof(f_150_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_150_2,plain,
! [U_557,U_556,U_555] :
( ~ empty(U_555)
| ~ element(U_556,powerset(U_555))
| ~ in(U_557,U_556) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
fof(f_150_3,plain,
! [U_557,U_556] :
( ! [U_555] :
( ~ empty(U_555)
| ~ element(U_556,powerset(U_555)) )
| ~ in(U_557,U_556) ),
inference(miniscope,[status(thm)],[f_150_2]) ).
fof(f_150_4,plain,
! [U_555,U_556,U_557] :
( ~ empty(U_555)
| ~ element(U_556,powerset(U_555))
| ~ in(U_557,U_556) ),
inference(definitional_conversion,[status(esa)],[f_150_3]) ).
cnf(f_150_5,plain,
( ~ empty(U_555)
| ~ element(U_556,powerset(U_555))
| ~ in(U_557,U_556) ),
inference(clausify,[status(thm)],[f_150_4]) ).
fof(f_151_1,negated_conjecture,
~ ( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(negate,[status(cth)],[t60_relat_1]) ).
fof(f_151_2,negated_conjecture,
( relation_rng(empty_set) != empty_set
| relation_dom(empty_set) != empty_set ),
inference(fof_nnf,[status(thm)],[f_151_1]) ).
fof(f_151_3,negated_conjecture,
( relation_rng(empty_set) != empty_set
| relation_dom(empty_set) != empty_set ),
inference(definitional_conversion,[status(esa)],[f_151_2]) ).
cnf(f_151_4,negated_conjecture,
( relation_rng(empty_set) != empty_set
| relation_dom(empty_set) != empty_set ),
inference(clausify,[status(thm)],[f_151_3]) ).
fof(f_152_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t60_xboole_1]) ).
fof(f_152_2,plain,
! [U_559,U_558] :
( ~ proper_subset(U_558,U_559)
| ~ subset(U_559,U_558) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
fof(f_152_3,plain,
! [U_558,U_559] :
( ~ proper_subset(U_558,U_559)
| ~ subset(U_559,U_558) ),
inference(definitional_conversion,[status(esa)],[f_152_2]) ).
cnf(f_152_4,plain,
( ~ proper_subset(U_558,U_559)
| ~ subset(U_559,U_558) ),
inference(clausify,[status(thm)],[f_152_3]) ).
fof(f_153_1,plain,
! [A,B,C] :
( disjoint(A,C)
| ~ disjoint(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t63_xboole_1]) ).
fof(f_153_2,plain,
! [U_562,U_561,U_560] :
( disjoint(U_562,U_560)
| ~ disjoint(U_561,U_560)
| ~ subset(U_562,U_561) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
fof(f_153_3,plain,
! [U_561,U_560,U_562] :
( disjoint(U_562,U_560)
| ~ disjoint(U_561,U_560)
| ~ subset(U_562,U_561) ),
inference(definitional_conversion,[status(esa)],[f_153_2]) ).
cnf(f_153_4,plain,
( disjoint(U_562,U_560)
| ~ disjoint(U_561,U_560)
| ~ subset(U_562,U_561) ),
inference(clausify,[status(thm)],[f_153_3]) ).
fof(f_154_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_154_2,plain,
! [U_564,U_563] :
( ( set_difference(U_564,singleton(U_563)) = U_564
| in(U_563,U_564) )
& ( ~ in(U_563,U_564)
| set_difference(U_564,singleton(U_563)) != U_564 ) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
fof(f_154_3,plain,
( ! [U_568,U_566] :
( set_difference(U_568,singleton(U_566)) = U_568
| in(U_566,U_568) )
& ! [U_567,U_565] :
( ~ in(U_565,U_567)
| set_difference(U_567,singleton(U_565)) != U_567 ) ),
inference(miniscope,[status(thm)],[f_154_2]) ).
fof(f_154_4,plain,
( ! [U_566,U_568] :
( set_difference(U_568,singleton(U_566)) = U_568
| in(U_566,U_568) )
& ! [U_567,U_565] :
( ~ in(U_565,U_567)
| set_difference(U_567,singleton(U_565)) != U_567 ) ),
inference(definitional_conversion,[status(esa)],[f_154_3]) ).
cnf(f_154_5,plain,
( ~ in(U_565,U_567)
| set_difference(U_567,singleton(U_565)) != U_567 ),
inference(clausify,[status(thm)],[f_154_4]) ).
cnf(f_154_6,plain,
( set_difference(U_568,singleton(U_566)) = U_568
| in(U_566,U_568) ),
inference(clausify,[status(thm)],[f_154_4]) ).
fof(f_155_1,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(fof_nnf,[status(thm)],[t69_enumset1]) ).
fof(f_155_2,plain,
! [U_569] : unordered_pair(U_569,U_569) = singleton(U_569),
inference(variable_rename,[status(thm)],[f_155_1]) ).
fof(f_155_3,plain,
! [U_569] : unordered_pair(U_569,U_569) = singleton(U_569),
inference(definitional_conversion,[status(esa)],[f_155_2]) ).
cnf(f_155_4,plain,
unordered_pair(U_569,U_569) = singleton(U_569),
inference(clausify,[status(thm)],[f_155_3]) ).
fof(f_156_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_156_2,plain,
! [U_570] :
( U_570 = empty_set
| ~ empty(U_570) ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
fof(f_156_3,plain,
! [U_570] :
( U_570 = empty_set
| ~ empty(U_570) ),
inference(definitional_conversion,[status(esa)],[f_156_2]) ).
cnf(f_156_4,plain,
( U_570 = empty_set
| ~ empty(U_570) ),
inference(clausify,[status(thm)],[f_156_3]) ).
fof(f_157_1,plain,
! [A,B] :
( A = B
| ~ subset(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t6_zfmisc_1]) ).
fof(f_157_2,plain,
! [U_572,U_571] :
( U_572 = U_571
| ~ subset(singleton(U_572),singleton(U_571)) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
fof(f_157_3,plain,
! [U_571,U_572] :
( U_572 = U_571
| ~ subset(singleton(U_572),singleton(U_571)) ),
inference(definitional_conversion,[status(esa)],[f_157_2]) ).
cnf(f_157_4,plain,
( U_572 = U_571
| ~ subset(singleton(U_572),singleton(U_571)) ),
inference(clausify,[status(thm)],[f_157_3]) ).
fof(f_158_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_158_2,plain,
! [U_574,U_573] :
( ~ empty(U_573)
| ~ in(U_574,U_573) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
fof(f_158_3,plain,
! [U_574,U_573] :
( ~ empty(U_573)
| ~ in(U_574,U_573) ),
inference(definitional_conversion,[status(esa)],[f_158_2]) ).
cnf(f_158_4,plain,
( ~ empty(U_573)
| ~ in(U_574,U_573) ),
inference(clausify,[status(thm)],[f_158_3]) ).
fof(f_159_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1]) ).
fof(f_159_2,plain,
! [U_576,U_575] : subset(U_576,set_union2(U_576,U_575)),
inference(variable_rename,[status(thm)],[f_159_1]) ).
fof(f_159_3,plain,
! [U_575,U_576] : subset(U_576,set_union2(U_576,U_575)),
inference(definitional_conversion,[status(esa)],[f_159_2]) ).
cnf(f_159_4,plain,
subset(U_576,set_union2(U_576,U_575)),
inference(clausify,[status(thm)],[f_159_3]) ).
fof(f_160_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_160_2,plain,
! [U_578,U_577] :
( ( disjoint(U_578,U_577)
| set_difference(U_578,U_577) != U_578 )
& ( set_difference(U_578,U_577) = U_578
| ~ disjoint(U_578,U_577) ) ),
inference(variable_rename,[status(thm)],[f_160_1]) ).
fof(f_160_3,plain,
( ! [U_582,U_580] :
( disjoint(U_582,U_580)
| set_difference(U_582,U_580) != U_582 )
& ! [U_581,U_579] :
( set_difference(U_581,U_579) = U_581
| ~ disjoint(U_581,U_579) ) ),
inference(miniscope,[status(thm)],[f_160_2]) ).
fof(f_160_4,plain,
( ! [U_580,U_582] :
( disjoint(U_582,U_580)
| set_difference(U_582,U_580) != U_582 )
& ! [U_581,U_579] :
( set_difference(U_581,U_579) = U_581
| ~ disjoint(U_581,U_579) ) ),
inference(definitional_conversion,[status(esa)],[f_160_3]) ).
cnf(f_160_5,plain,
( set_difference(U_581,U_579) = U_581
| ~ disjoint(U_581,U_579) ),
inference(clausify,[status(thm)],[f_160_4]) ).
cnf(f_160_6,plain,
( disjoint(U_582,U_580)
| set_difference(U_582,U_580) != U_582 ),
inference(clausify,[status(thm)],[f_160_4]) ).
fof(f_161_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_161_2,plain,
! [U_584,U_583] :
( ~ empty(U_583)
| U_584 = U_583
| ~ empty(U_584) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
fof(f_161_3,plain,
! [U_584] :
( ! [U_583] :
( ~ empty(U_583)
| U_584 = U_583 )
| ~ empty(U_584) ),
inference(miniscope,[status(thm)],[f_161_2]) ).
fof(f_161_4,plain,
! [U_584,U_583] :
( ~ empty(U_583)
| U_584 = U_583
| ~ empty(U_584) ),
inference(definitional_conversion,[status(esa)],[f_161_3]) ).
cnf(f_161_5,plain,
( ~ empty(U_583)
| U_584 = U_583
| ~ empty(U_584) ),
inference(clausify,[status(thm)],[f_161_4]) ).
fof(f_162_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_162_2,plain,
! [U_587,U_586,U_585] :
( subset(set_union2(U_587,U_585),U_586)
| ~ subset(U_585,U_586)
| ~ subset(U_587,U_586) ),
inference(variable_rename,[status(thm)],[f_162_1]) ).
fof(f_162_3,plain,
! [U_585,U_586,U_587] :
( subset(set_union2(U_587,U_585),U_586)
| ~ subset(U_585,U_586)
| ~ subset(U_587,U_586) ),
inference(definitional_conversion,[status(esa)],[f_162_2]) ).
cnf(f_162_4,plain,
( subset(set_union2(U_587,U_585),U_586)
| ~ subset(U_585,U_586)
| ~ subset(U_587,U_586) ),
inference(clausify,[status(thm)],[f_162_3]) ).
fof(f_163_1,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t8_zfmisc_1]) ).
fof(f_163_2,plain,
! [U_590,U_589,U_588] :
( U_590 = U_589
| singleton(U_590) != unordered_pair(U_589,U_588) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
fof(f_163_3,plain,
! [U_590,U_589] :
( ! [U_588] : singleton(U_590) != unordered_pair(U_589,U_588)
| U_590 = U_589 ),
inference(miniscope,[status(thm)],[f_163_2]) ).
fof(f_163_4,plain,
! [U_589,U_588,U_590] :
( singleton(U_590) != unordered_pair(U_589,U_588)
| U_590 = U_589 ),
inference(definitional_conversion,[status(esa)],[f_163_3]) ).
cnf(f_163_5,plain,
( singleton(U_590) != unordered_pair(U_589,U_588)
| U_590 = U_589 ),
inference(clausify,[status(thm)],[f_163_4]) ).
fof(f_164_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t92_zfmisc_1]) ).
fof(f_164_2,plain,
! [U_592,U_591] :
( subset(U_592,union(U_591))
| ~ in(U_592,U_591) ),
inference(variable_rename,[status(thm)],[f_164_1]) ).
fof(f_164_3,plain,
! [U_591,U_592] :
( subset(U_592,union(U_591))
| ~ in(U_592,U_591) ),
inference(definitional_conversion,[status(esa)],[f_164_2]) ).
cnf(f_164_4,plain,
( subset(U_592,union(U_591))
| ~ in(U_592,U_591) ),
inference(clausify,[status(thm)],[f_164_3]) ).
fof(f_165_1,plain,
! [A] : union(powerset(A)) = A,
inference(fof_nnf,[status(thm)],[t99_zfmisc_1]) ).
fof(f_165_2,plain,
! [U_593] : union(powerset(U_593)) = U_593,
inference(variable_rename,[status(thm)],[f_165_1]) ).
fof(f_165_3,plain,
! [U_593] : union(powerset(U_593)) = U_593,
inference(definitional_conversion,[status(esa)],[f_165_2]) ).
cnf(f_165_4,plain,
union(powerset(U_593)) = U_593,
inference(clausify,[status(thm)],[f_165_3]) ).
fof(f_166_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_166_2,plain,
! [U_601] :
? [U_600] :
( ! [U_599] :
( in(U_599,U_600)
| are_equipotent(U_599,U_600)
| ~ subset(U_599,U_600) )
& ! [U_598] :
( ? [U_597] :
( ! [U_596] :
( in(U_596,U_597)
| ~ subset(U_596,U_598) )
& in(U_597,U_600) )
| ~ in(U_598,U_600) )
& ! [U_595,U_594] :
( in(U_594,U_600)
| ~ subset(U_594,U_595)
| ~ in(U_595,U_600) )
& in(U_601,U_600) ),
inference(variable_rename,[status(thm)],[f_166_1]) ).
fof(f_166_3,plain,
! [U_601] :
( ! [U_599] :
( in(U_599,sK66(U_601))
| are_equipotent(U_599,sK66(U_601))
| ~ subset(U_599,sK66(U_601)) )
& ! [U_598] :
( ? [U_597] :
( ! [U_596] :
( in(U_596,U_597)
| ~ subset(U_596,U_598) )
& in(U_597,sK66(U_601)) )
| ~ in(U_598,sK66(U_601)) )
& ! [U_595,U_594] :
( in(U_594,sK66(U_601))
| ~ subset(U_594,U_595)
| ~ in(U_595,sK66(U_601)) )
& in(U_601,sK66(U_601)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_600,sK66(U_601))],[f_166_2]) ).
fof(f_166_4,plain,
! [U_601] :
( ! [U_599] :
( in(U_599,sK66(U_601))
| are_equipotent(U_599,sK66(U_601))
| ~ subset(U_599,sK66(U_601)) )
& ! [U_598] :
( ( ! [U_596] :
( in(U_596,sK67(U_601,U_598))
| ~ subset(U_596,U_598) )
& in(sK67(U_601,U_598),sK66(U_601)) )
| ~ in(U_598,sK66(U_601)) )
& ! [U_595,U_594] :
( in(U_594,sK66(U_601))
| ~ subset(U_594,U_595)
| ~ in(U_595,sK66(U_601)) )
& in(U_601,sK66(U_601)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_597,sK67(U_601,U_598))],[f_166_3]) ).
fof(f_166_5,plain,
( ! [U_596,U_598,U_601] :
( in(U_596,sK67(U_601,U_598))
| ~ subset(U_596,U_598)
| ~ sP81(U_596,U_598,U_601) )
& ! [U_596,U_598,U_601] :
( in(sK67(U_601,U_598),sK66(U_601))
| ~ sP81(U_596,U_598,U_601) )
& ! [U_599,U_601] :
( in(U_599,sK66(U_601))
| are_equipotent(U_599,sK66(U_601))
| ~ subset(U_599,sK66(U_601)) )
& ! [U_596,U_598,U_601] :
( sP81(U_596,U_598,U_601)
| ~ in(U_598,sK66(U_601)) )
& ! [U_595,U_594,U_601] :
( in(U_594,sK66(U_601))
| ~ subset(U_594,U_595)
| ~ in(U_595,sK66(U_601)) )
& ! [U_601] : in(U_601,sK66(U_601)) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP81])],[f_166_4]) ).
cnf(f_166_6,plain,
in(U_601,sK66(U_601)),
inference(clausify,[status(thm)],[f_166_5]) ).
cnf(f_166_7,plain,
( in(U_594,sK66(U_601))
| ~ subset(U_594,U_595)
| ~ in(U_595,sK66(U_601)) ),
inference(clausify,[status(thm)],[f_166_5]) ).
cnf(f_166_8,plain,
( sP81(U_596,U_598,U_601)
| ~ in(U_598,sK66(U_601)) ),
inference(clausify,[status(thm)],[f_166_5]) ).
cnf(f_166_9,plain,
( in(U_599,sK66(U_601))
| are_equipotent(U_599,sK66(U_601))
| ~ subset(U_599,sK66(U_601)) ),
inference(clausify,[status(thm)],[f_166_5]) ).
cnf(f_166_10,plain,
( in(sK67(U_601,U_598),sK66(U_601))
| ~ sP81(U_596,U_598,U_601) ),
inference(clausify,[status(thm)],[f_166_5]) ).
cnf(f_166_11,plain,
( in(U_596,sK67(U_601,U_598))
| ~ subset(U_596,U_598)
| ~ sP81(U_596,U_598,U_601) ),
inference(clausify,[status(thm)],[f_166_5]) ).
fof(f_167_1,plain,
! [A,B,C] :
( B = C
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t9_zfmisc_1]) ).
fof(f_167_2,plain,
! [U_604,U_603,U_602] :
( U_603 = U_602
| singleton(U_604) != unordered_pair(U_603,U_602) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
fof(f_167_3,plain,
! [U_604,U_603,U_602] :
( U_603 = U_602
| singleton(U_604) != unordered_pair(U_603,U_602) ),
inference(definitional_conversion,[status(esa)],[f_167_2]) ).
cnf(f_167_4,plain,
( U_603 = U_602
| singleton(U_604) != unordered_pair(U_603,U_602) ),
inference(clausify,[status(thm)],[f_167_3]) ).
cnf(f_32_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_32_3]) ).
cnf(f_33_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_33_3]) ).
cnf(f_34_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_34_3]) ).
cnf(f_35_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_35_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_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_42_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_42_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_47_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_47_3]) ).
cnf(f_48_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_48_3]) ).
cnf(f_54_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_54_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,
( 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_8,axiom,
( set_meet(Eq_x_0) = set_meet(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,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_12,axiom,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,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_14,axiom,
( union(Eq_x_0) = union(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,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_16,axiom,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,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_18,axiom,
( relation_field(Eq_x_0) = relation_field(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( relation_inverse(Eq_x_0) = relation_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,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_21,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_22,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_23,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_24,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_25,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_26,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_27,axiom,
( sK3(Eq_x_0) = sK3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,axiom,
( sK4(Eq_x_0,Eq_x_1,Eq_x_2) = sK4(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_29,axiom,
( sK5(Eq_x_0,Eq_x_1) = sK5(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,
( sK6(Eq_x_0,Eq_x_1) = sK6(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,
( sK7(Eq_x_0,Eq_x_1) = sK7(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_32,axiom,
( sK8(Eq_x_0,Eq_x_1) = sK8(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,axiom,
( 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_34,axiom,
( sK10(Eq_x_0) = sK10(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_35,axiom,
( sK11(Eq_x_0,Eq_x_1) = sK11(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,
( sK12(Eq_x_0,Eq_x_1) = sK12(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,
( sK13(Eq_x_0,Eq_x_1,Eq_x_2) = sK13(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_38,axiom,
( sK14(Eq_x_0,Eq_x_1,Eq_x_2) = sK14(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,axiom,
( sK15(Eq_x_0,Eq_x_1,Eq_x_2) = sK15(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_40,axiom,
( sK16(Eq_x_0,Eq_x_1,Eq_x_2) = sK16(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_41,axiom,
( sK17(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK17(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_42,axiom,
( sK18(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK18(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_43,axiom,
( sK19(Eq_x_0,Eq_x_1,Eq_x_2) = sK19(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_44,axiom,
( sK20(Eq_x_0,Eq_x_1,Eq_x_2) = sK20(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_45,axiom,
( sK21(Eq_x_0,Eq_x_1,Eq_x_2) = sK21(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_46,axiom,
( sK22(Eq_x_0,Eq_x_1,Eq_x_2) = sK22(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_47,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_48,axiom,
( sK24(Eq_x_0,Eq_x_1,Eq_x_2) = sK24(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_49,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_50,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_51,axiom,
( sK27(Eq_x_0,Eq_x_1) = sK27(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_52,axiom,
( sK28(Eq_x_0,Eq_x_1) = sK28(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_53,axiom,
( sK29(Eq_x_0,Eq_x_1) = sK29(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_54,axiom,
( sK30(Eq_x_0,Eq_x_1,Eq_x_2) = sK30(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,
( sK31(Eq_x_0,Eq_x_1) = sK31(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_56,axiom,
( sK32(Eq_x_0,Eq_x_1) = sK32(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_57,axiom,
( sK33(Eq_x_0,Eq_x_1) = sK33(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_58,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_59,axiom,
( sK35(Eq_x_0,Eq_x_1,Eq_x_2) = sK35(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_60,axiom,
( sK36(Eq_x_0,Eq_x_1,Eq_x_2) = sK36(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_61,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_62,axiom,
( sK38(Eq_x_0,Eq_x_1) = sK38(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_63,axiom,
( sK39(Eq_x_0,Eq_x_1) = sK39(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_64,axiom,
( sK40(Eq_x_0,Eq_x_1) = sK40(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_65,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_66,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_67,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_68,axiom,
( sK44(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK44(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_69,axiom,
( sK45(Eq_x_0,Eq_x_1,Eq_x_2) = sK45(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_70,axiom,
( sK46(Eq_x_0,Eq_x_1,Eq_x_2) = sK46(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_71,axiom,
( sK47(Eq_x_0,Eq_x_1,Eq_x_2) = sK47(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_72,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_73,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_74,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_75,axiom,
( sK51(Eq_x_0) = sK51(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_76,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_77,axiom,
( sK54(Eq_x_0) = sK54(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_78,axiom,
( sK57(Eq_x_0) = sK57(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_79,axiom,
( sK59(Eq_x_0) = sK59(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_80,axiom,
( sK60(Eq_x_0,Eq_x_1) = sK60(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_81,axiom,
( sK61(Eq_x_0,Eq_x_1) = sK61(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_82,axiom,
( sK62(Eq_x_0,Eq_x_1) = sK62(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_83,axiom,
( sK63(Eq_x_0,Eq_x_1) = sK63(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_84,axiom,
( sK64(Eq_x_0) = sK64(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_85,axiom,
( sK65(Eq_x_0) = sK65(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_86,axiom,
( sK66(Eq_x_0) = sK66(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_87,axiom,
( sK67(Eq_x_0,Eq_x_1) = sK67(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_88,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_89,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_90,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_91,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_92,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_93,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_94,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_95,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_96,axiom,
( sP0(Eq_y_0,Eq_y_1)
| ~ sP0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_97,axiom,
( sP1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP1(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_98,axiom,
( sP2(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP2(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_99,axiom,
( sP3(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP3(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_100,axiom,
( sP4(Eq_y_0,Eq_y_1)
| ~ sP4(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_101,axiom,
( sP5(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP5(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_102,axiom,
( sP6(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP6(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_103,axiom,
( sP7(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP7(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_104,axiom,
( sP8(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP8(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_105,axiom,
( sP9(Eq_y_0,Eq_y_1)
| ~ sP9(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,
( sP10(Eq_y_0,Eq_y_1)
| ~ sP10(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_107,axiom,
( sP11(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP11(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_108,axiom,
( sP12(Eq_y_0,Eq_y_1)
| ~ sP12(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,
( sP13(Eq_y_0,Eq_y_1)
| ~ sP13(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,
( sP14(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP14(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_111,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_112,axiom,
( sP16(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP16(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,
( sP17(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP17(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_114,axiom,
( sP18(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP18(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_115,axiom,
( sP19(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP19(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_116,axiom,
( sP20(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP20(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_117,axiom,
( sP21(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP21(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_118,axiom,
( sP22(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP22(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_119,axiom,
( sP23(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP23(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_120,axiom,
( sP24(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP24(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_121,axiom,
( sP25(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP25(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_122,axiom,
( sP26(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP26(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_123,axiom,
( sP27(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP27(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_124,axiom,
( sP28(Eq_y_0,Eq_y_1)
| ~ sP28(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_125,axiom,
( 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_126,axiom,
( sP30(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP30(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_127,axiom,
( sP31(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP31(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,
( 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_129,axiom,
( sP33(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP33(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_130,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_131,axiom,
( sP35(Eq_y_0,Eq_y_1)
| ~ sP35(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,
( sP36(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP36(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_133,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_134,axiom,
( sP38(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP38(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_135,axiom,
( sP39(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP39(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_136,axiom,
( sP40(Eq_y_0,Eq_y_1)
| ~ sP40(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_137,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_138,axiom,
( sP42(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP42(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_139,axiom,
( sP43(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP43(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_140,axiom,
( sP44(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP44(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_141,axiom,
( sP45(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP45(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_142,axiom,
( sP46(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP46(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,
( sP47(Eq_y_0,Eq_y_1)
| ~ sP47(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_144,axiom,
( sP48(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP48(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_145,axiom,
( sP49(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP49(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_146,axiom,
( sP50(Eq_y_0,Eq_y_1)
| ~ sP50(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_147,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_148,axiom,
( sP52(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP52(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_149,axiom,
( sP53(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP53(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_150,axiom,
( sP54(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| ~ sP54(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_151,axiom,
( sP55(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP55(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_152,axiom,
( sP56(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP56(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_153,axiom,
( sP57(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)
| ~ sP57(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_154,axiom,
( sP58(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP58(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_155,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_156,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_157,axiom,
( sP61(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP61(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_158,axiom,
( sP62(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP62(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_159,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_160,axiom,
( sP64(Eq_y_0,Eq_y_1)
| ~ sP64(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_161,axiom,
( sP65(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP65(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_162,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_163,axiom,
( sP67(Eq_y_0)
| ~ sP67(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_164,axiom,
( sP68(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP68(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_165,axiom,
( sP69(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP69(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_166,axiom,
( sP70(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP70(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_167,axiom,
( sP71(Eq_y_0,Eq_y_1)
| ~ sP71(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_168,axiom,
( sP72(Eq_y_0,Eq_y_1)
| ~ sP72(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,
( sP73(Eq_y_0,Eq_y_1)
| ~ sP73(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_170,axiom,
( sP74(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP74(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_171,axiom,
( sP75(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP75(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_172,axiom,
( sP76(Eq_y_0)
| ~ sP76(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_173,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_174,axiom,
( sP78(Eq_y_0,Eq_y_1)
| ~ sP78(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_175,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_176,axiom,
( sP80(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP80(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_177,axiom,
( sP81(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP81(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU187+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 : n008.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
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 23:28:46 UTC 2026
% 0.10/0.37 % CPUTime :
% 158.04/158.30 % SZS status Theorem for theBenchmark
% 158.04/158.30 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------