%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU186+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 24.06s 24.38s
% Output : Proof 24.23s
% 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(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,conjecture,
! [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_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]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ proper_subset(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(f_2_2,plain,
! [U_3,U_2] :
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_3_2,plain,
! [U_4] :
( relation(U_4)
| ~ empty(U_4) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( relation(U_4)
| ~ empty(U_4) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_4_2,plain,
! [U_6,U_5] : unordered_pair(U_6,U_5) = unordered_pair(U_5,U_6),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
unordered_pair(U_6,U_5) = unordered_pair(U_5,U_6),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_5_2,plain,
! [U_8,U_7] : set_union2(U_8,U_7) = set_union2(U_7,U_8),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
set_union2(U_8,U_7) = set_union2(U_7,U_8),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_6_2,plain,
! [U_10,U_9] : set_intersection2(U_10,U_9) = set_intersection2(U_9,U_10),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
set_intersection2(U_10,U_9) = set_intersection2(U_9,U_10),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A,B] :
( ( 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]) ).
cnf(f_7_4,plain,
( subset(U_15,U_13)
| U_15 != U_13 ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( subset(U_13,U_15)
| U_15 != U_13 ),
inference(clausify,[status(thm)],[f_7_3]) ).
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_3]) ).
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]) ).
cnf(f_8_7,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_6]) ).
cnf(f_8_8,plain,
( in(sK3(U_25),U_25)
| relation(U_25) ),
inference(clausify,[status(thm)],[f_8_6]) ).
cnf(f_8_9,plain,
( sK3(U_25) != ordered_pair(U_21,U_20)
| relation(U_25) ),
inference(clausify,[status(thm)],[f_8_6]) ).
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]) ).
cnf(f_9_8,plain,
( 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(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_9,plain,
( in(sK4(U_44,U_40,U_35),U_44)
| in(U_35,U_40)
| U_40 != set_meet(U_44)
| U_44 = empty_set ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_10,plain,
( ~ in(U_35,sK4(U_44,U_40,U_35))
| in(U_35,U_40)
| U_40 != set_meet(U_44)
| U_44 = empty_set ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_11,plain,
( in(sK7(U_44,U_41),U_30)
| ~ in(U_30,U_44)
| in(sK5(U_44,U_41),U_41)
| U_41 = set_meet(U_44)
| U_44 = empty_set ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_12,plain,
( ~ in(sK7(U_44,U_41),U_41)
| in(sK5(U_44,U_41),U_41)
| U_41 = set_meet(U_44)
| U_44 = empty_set ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_13,plain,
( in(sK6(U_44,U_41),U_44)
| in(sK7(U_44,U_41),U_30)
| ~ in(U_30,U_44)
| U_41 = set_meet(U_44)
| U_44 = empty_set ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_14,plain,
( ~ in(sK5(U_44,U_41),sK6(U_44,U_41))
| in(sK7(U_44,U_41),U_30)
| ~ in(U_30,U_44)
| U_41 = set_meet(U_44)
| U_44 = empty_set ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_15,plain,
( in(sK6(U_44,U_41),U_44)
| ~ in(sK7(U_44,U_41),U_41)
| U_41 = set_meet(U_44)
| U_44 = empty_set ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_16,plain,
( ~ in(sK5(U_44,U_41),sK6(U_44,U_41))
| ~ in(sK7(U_44,U_41),U_41)
| U_41 = set_meet(U_44)
| U_44 = empty_set ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_17,plain,
( U_42 = empty_set
| U_42 != set_meet(U_45)
| U_45 != empty_set ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_18,plain,
( U_43 = set_meet(U_45)
| U_43 != empty_set
| U_45 != empty_set ),
inference(clausify,[status(thm)],[f_9_7]) ).
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]) ).
cnf(f_10_6,plain,
( U_50 = U_56
| ~ in(U_50,U_54)
| U_54 != singleton(U_56) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_7,plain,
( in(U_51,U_54)
| U_51 != U_56
| U_54 != singleton(U_56) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_8,plain,
( sK9(U_57,U_55) = U_57
| in(sK8(U_57,U_55),U_55)
| U_55 = singleton(U_57) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_9,plain,
( ~ in(sK9(U_57,U_55),U_55)
| in(sK8(U_57,U_55),U_55)
| U_55 = singleton(U_57) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_10,plain,
( sK9(U_57,U_55) = U_57
| sK8(U_57,U_55) != U_57
| U_55 = singleton(U_57) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_11,plain,
( ~ in(sK9(U_57,U_55),U_55)
| sK8(U_57,U_55) != U_57
| U_55 = singleton(U_57) ),
inference(clausify,[status(thm)],[f_10_5]) ).
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]) ).
cnf(f_11_5,plain,
( ~ in(U_58,U_61)
| U_61 != empty_set ),
inference(clausify,[status(thm)],[f_11_4]) ).
cnf(f_11_6,plain,
( U_62 = empty_set
| in(sK10(U_62),U_62) ),
inference(clausify,[status(thm)],[f_11_4]) ).
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]) ).
cnf(f_12_6,plain,
( subset(U_67,U_73)
| ~ in(U_67,U_71)
| U_71 != powerset(U_73) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_7,plain,
( in(U_68,U_71)
| ~ subset(U_68,U_73)
| U_71 != powerset(U_73) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_8,plain,
( subset(sK12(U_74,U_72),U_74)
| in(sK11(U_74,U_72),U_72)
| U_72 = powerset(U_74) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_9,plain,
( ~ in(sK12(U_74,U_72),U_72)
| in(sK11(U_74,U_72),U_72)
| U_72 = powerset(U_74) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_10,plain,
( subset(sK12(U_74,U_72),U_74)
| ~ subset(sK11(U_74,U_72),U_74)
| U_72 = powerset(U_74) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_11,plain,
( ~ in(sK12(U_74,U_72),U_72)
| ~ subset(sK11(U_74,U_72),U_74)
| U_72 = powerset(U_74) ),
inference(clausify,[status(thm)],[f_12_5]) ).
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]) ).
cnf(f_13_4,plain,
( in(U_79,U_83)
| ~ element(U_79,U_83)
| empty(U_83) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_5,plain,
( element(U_80,U_83)
| ~ in(U_80,U_83)
| empty(U_83) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_6,plain,
( empty(U_81)
| ~ element(U_81,U_84)
| ~ empty(U_84) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_7,plain,
( element(U_82,U_84)
| ~ empty(U_82)
| ~ empty(U_84) ),
inference(clausify,[status(thm)],[f_13_3]) ).
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]) ).
cnf(f_14_6,plain,
( U_90 = U_96
| U_90 = U_98
| ~ in(U_90,U_94)
| U_94 != unordered_pair(U_98,U_96) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_7,plain,
( U_91 != U_98
| in(U_91,U_94)
| U_94 != unordered_pair(U_98,U_96) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_8,plain,
( U_91 != U_96
| in(U_91,U_94)
| U_94 != unordered_pair(U_98,U_96) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_9,plain,
( sK14(U_99,U_97,U_95) = U_97
| sK14(U_99,U_97,U_95) = U_99
| in(sK13(U_99,U_97,U_95),U_95)
| U_95 = unordered_pair(U_99,U_97) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_10,plain,
( ~ in(sK14(U_99,U_97,U_95),U_95)
| in(sK13(U_99,U_97,U_95),U_95)
| U_95 = unordered_pair(U_99,U_97) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_11,plain,
( sK13(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
| U_95 = unordered_pair(U_99,U_97) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_12,plain,
( sK13(U_99,U_97,U_95) != U_97
| sK14(U_99,U_97,U_95) = U_97
| sK14(U_99,U_97,U_95) = U_99
| U_95 = unordered_pair(U_99,U_97) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_13,plain,
( sK13(U_99,U_97,U_95) != U_99
| ~ in(sK14(U_99,U_97,U_95),U_95)
| U_95 = unordered_pair(U_99,U_97) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_14,plain,
( sK13(U_99,U_97,U_95) != U_97
| ~ in(sK14(U_99,U_97,U_95),U_95)
| U_95 = unordered_pair(U_99,U_97) ),
inference(clausify,[status(thm)],[f_14_5]) ).
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]) ).
cnf(f_15_6,plain,
( in(U_105,U_111)
| in(U_105,U_113)
| ~ in(U_105,U_109)
| U_109 != set_union2(U_113,U_111) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_7,plain,
( ~ in(U_106,U_113)
| in(U_106,U_109)
| U_109 != set_union2(U_113,U_111) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_8,plain,
( ~ in(U_106,U_111)
| in(U_106,U_109)
| U_109 != set_union2(U_113,U_111) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_9,plain,
( 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_110)
| U_110 = set_union2(U_114,U_112) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_10,plain,
( ~ in(sK16(U_114,U_112,U_110),U_110)
| in(sK15(U_114,U_112,U_110),U_110)
| U_110 = set_union2(U_114,U_112) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_11,plain,
( ~ in(sK15(U_114,U_112,U_110),U_114)
| in(sK16(U_114,U_112,U_110),U_112)
| in(sK16(U_114,U_112,U_110),U_114)
| U_110 = set_union2(U_114,U_112) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_12,plain,
( ~ in(sK15(U_114,U_112,U_110),U_112)
| in(sK16(U_114,U_112,U_110),U_112)
| in(sK16(U_114,U_112,U_110),U_114)
| U_110 = set_union2(U_114,U_112) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_13,plain,
( ~ in(sK15(U_114,U_112,U_110),U_114)
| ~ in(sK16(U_114,U_112,U_110),U_110)
| U_110 = set_union2(U_114,U_112) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_14,plain,
( ~ in(sK15(U_114,U_112,U_110),U_112)
| ~ in(sK16(U_114,U_112,U_110),U_110)
| U_110 = set_union2(U_114,U_112) ),
inference(clausify,[status(thm)],[f_15_5]) ).
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]) ).
cnf(f_16_10,plain,
( 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(clausify,[status(thm)],[f_16_9]) ).
cnf(f_16_11,plain,
( in(sK18(U_136,U_134,U_132,U_128),U_134)
| ~ in(U_128,U_132)
| U_132 != cartesian_product2(U_136,U_134) ),
inference(clausify,[status(thm)],[f_16_9]) ).
cnf(f_16_12,plain,
( U_128 = ordered_pair(sK17(U_136,U_134,U_132,U_128),sK18(U_136,U_134,U_132,U_128))
| ~ in(U_128,U_132)
| U_132 != cartesian_product2(U_136,U_134) ),
inference(clausify,[status(thm)],[f_16_9]) ).
cnf(f_16_13,plain,
( in(U_129,U_132)
| U_129 != ordered_pair(U_118,U_117)
| ~ in(U_117,U_134)
| ~ in(U_118,U_136)
| U_132 != cartesian_product2(U_136,U_134) ),
inference(clausify,[status(thm)],[f_16_9]) ).
cnf(f_16_14,plain,
( in(sK21(U_137,U_135,U_133),U_137)
| in(sK19(U_137,U_135,U_133),U_133)
| U_133 = cartesian_product2(U_137,U_135) ),
inference(clausify,[status(thm)],[f_16_9]) ).
cnf(f_16_15,plain,
( in(sK22(U_137,U_135,U_133),U_135)
| in(sK19(U_137,U_135,U_133),U_133)
| U_133 = cartesian_product2(U_137,U_135) ),
inference(clausify,[status(thm)],[f_16_9]) ).
cnf(f_16_16,plain,
( sK20(U_137,U_135,U_133) = ordered_pair(sK21(U_137,U_135,U_133),sK22(U_137,U_135,U_133))
| in(sK19(U_137,U_135,U_133),U_133)
| U_133 = cartesian_product2(U_137,U_135) ),
inference(clausify,[status(thm)],[f_16_9]) ).
cnf(f_16_17,plain,
( ~ in(sK20(U_137,U_135,U_133),U_133)
| in(sK19(U_137,U_135,U_133),U_133)
| U_133 = cartesian_product2(U_137,U_135) ),
inference(clausify,[status(thm)],[f_16_9]) ).
cnf(f_16_18,plain,
( in(sK21(U_137,U_135,U_133),U_137)
| sK19(U_137,U_135,U_133) != ordered_pair(U_121,U_120)
| ~ in(U_120,U_135)
| ~ in(U_121,U_137)
| U_133 = cartesian_product2(U_137,U_135) ),
inference(clausify,[status(thm)],[f_16_9]) ).
cnf(f_16_19,plain,
( in(sK22(U_137,U_135,U_133),U_135)
| sK19(U_137,U_135,U_133) != ordered_pair(U_121,U_120)
| ~ in(U_120,U_135)
| ~ in(U_121,U_137)
| U_133 = cartesian_product2(U_137,U_135) ),
inference(clausify,[status(thm)],[f_16_9]) ).
cnf(f_16_20,plain,
( sK20(U_137,U_135,U_133) = ordered_pair(sK21(U_137,U_135,U_133),sK22(U_137,U_135,U_133))
| sK19(U_137,U_135,U_133) != ordered_pair(U_121,U_120)
| ~ in(U_120,U_135)
| ~ in(U_121,U_137)
| U_133 = cartesian_product2(U_137,U_135) ),
inference(clausify,[status(thm)],[f_16_9]) ).
cnf(f_16_21,plain,
( ~ in(sK20(U_137,U_135,U_133),U_133)
| sK19(U_137,U_135,U_133) != ordered_pair(U_121,U_120)
| ~ in(U_120,U_135)
| ~ in(U_121,U_137)
| U_133 = cartesian_product2(U_137,U_135) ),
inference(clausify,[status(thm)],[f_16_9]) ).
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]) ).
cnf(f_17_5,plain,
( in(U_138,U_142)
| ~ in(U_138,U_144)
| ~ subset(U_144,U_142) ),
inference(clausify,[status(thm)],[f_17_4]) ).
cnf(f_17_6,plain,
( in(sK23(U_145,U_143),U_145)
| subset(U_145,U_143) ),
inference(clausify,[status(thm)],[f_17_4]) ).
cnf(f_17_7,plain,
( ~ in(sK23(U_145,U_143),U_143)
| subset(U_145,U_143) ),
inference(clausify,[status(thm)],[f_17_4]) ).
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]) ).
cnf(f_18_6,plain,
( in(U_151,U_159)
| ~ in(U_151,U_155)
| U_155 != set_intersection2(U_159,U_157) ),
inference(clausify,[status(thm)],[f_18_5]) ).
cnf(f_18_7,plain,
( in(U_151,U_157)
| ~ in(U_151,U_155)
| U_155 != set_intersection2(U_159,U_157) ),
inference(clausify,[status(thm)],[f_18_5]) ).
cnf(f_18_8,plain,
( in(U_152,U_155)
| ~ in(U_152,U_157)
| ~ in(U_152,U_159)
| U_155 != set_intersection2(U_159,U_157) ),
inference(clausify,[status(thm)],[f_18_5]) ).
cnf(f_18_9,plain,
( in(sK25(U_160,U_158,U_156),U_160)
| in(sK24(U_160,U_158,U_156),U_156)
| U_156 = set_intersection2(U_160,U_158) ),
inference(clausify,[status(thm)],[f_18_5]) ).
cnf(f_18_10,plain,
( in(sK25(U_160,U_158,U_156),U_158)
| in(sK24(U_160,U_158,U_156),U_156)
| U_156 = set_intersection2(U_160,U_158) ),
inference(clausify,[status(thm)],[f_18_5]) ).
cnf(f_18_11,plain,
( ~ in(sK25(U_160,U_158,U_156),U_156)
| in(sK24(U_160,U_158,U_156),U_156)
| U_156 = set_intersection2(U_160,U_158) ),
inference(clausify,[status(thm)],[f_18_5]) ).
cnf(f_18_12,plain,
( 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)
| U_156 = set_intersection2(U_160,U_158) ),
inference(clausify,[status(thm)],[f_18_5]) ).
cnf(f_18_13,plain,
( in(sK25(U_160,U_158,U_156),U_158)
| ~ in(sK24(U_160,U_158,U_156),U_158)
| ~ in(sK24(U_160,U_158,U_156),U_160)
| U_156 = set_intersection2(U_160,U_158) ),
inference(clausify,[status(thm)],[f_18_5]) ).
cnf(f_18_14,plain,
( ~ in(sK25(U_160,U_158,U_156),U_156)
| ~ in(sK24(U_160,U_158,U_156),U_158)
| ~ in(sK24(U_160,U_158,U_156),U_160)
| U_156 = set_intersection2(U_160,U_158) ),
inference(clausify,[status(thm)],[f_18_5]) ).
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]) ).
cnf(f_19_8,plain,
( 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(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_9,plain,
( in(U_170,U_173)
| ~ in(ordered_pair(U_170,U_162),U_168)
| U_173 != relation_dom(U_168)
| ~ relation(U_168) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_10,plain,
( in(ordered_pair(sK28(U_168,U_174),sK29(U_168,U_174)),U_168)
| in(sK27(U_168,U_174),U_174)
| U_174 = relation_dom(U_168)
| ~ relation(U_168) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_11,plain,
( ~ in(sK28(U_168,U_174),U_174)
| in(sK27(U_168,U_174),U_174)
| U_174 = relation_dom(U_168)
| ~ relation(U_168) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_12,plain,
( in(ordered_pair(sK28(U_168,U_174),sK29(U_168,U_174)),U_168)
| ~ in(ordered_pair(sK27(U_168,U_174),U_164),U_168)
| U_174 = relation_dom(U_168)
| ~ relation(U_168) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_13,plain,
( ~ in(sK28(U_168,U_174),U_174)
| ~ in(ordered_pair(sK27(U_168,U_174),U_164),U_168)
| U_174 = relation_dom(U_168)
| ~ relation(U_168) ),
inference(clausify,[status(thm)],[f_19_7]) ).
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]) ).
cnf(f_20_3,plain,
cast_to_subset(U_175) = U_175,
inference(clausify,[status(thm)],[f_20_2]) ).
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]) ).
cnf(f_21_8,plain,
( in(U_184,sK30(U_190,U_188,U_184))
| ~ in(U_184,U_188)
| U_188 != union(U_190) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_9,plain,
( in(sK30(U_190,U_188,U_184),U_190)
| ~ in(U_184,U_188)
| U_188 != union(U_190) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_10,plain,
( in(U_185,U_188)
| ~ in(U_177,U_190)
| ~ in(U_185,U_177)
| U_188 != union(U_190) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_11,plain,
( in(sK32(U_191,U_189),sK33(U_191,U_189))
| in(sK31(U_191,U_189),U_189)
| U_189 = union(U_191) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_12,plain,
( in(sK33(U_191,U_189),U_191)
| in(sK31(U_191,U_189),U_189)
| U_189 = union(U_191) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_13,plain,
( ~ in(sK32(U_191,U_189),U_189)
| in(sK31(U_191,U_189),U_189)
| U_189 = union(U_191) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_14,plain,
( in(sK32(U_191,U_189),sK33(U_191,U_189))
| ~ in(U_179,U_191)
| ~ in(sK31(U_191,U_189),U_179)
| U_189 = union(U_191) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_15,plain,
( in(sK33(U_191,U_189),U_191)
| ~ in(U_179,U_191)
| ~ in(sK31(U_191,U_189),U_179)
| U_189 = union(U_191) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_16,plain,
( ~ in(sK32(U_191,U_189),U_189)
| ~ in(U_179,U_191)
| ~ in(sK31(U_191,U_189),U_179)
| U_189 = union(U_191) ),
inference(clausify,[status(thm)],[f_21_7]) ).
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]) ).
cnf(f_22_6,plain,
( in(U_197,U_205)
| ~ in(U_197,U_201)
| U_201 != set_difference(U_205,U_203) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_7,plain,
( ~ in(U_197,U_203)
| ~ in(U_197,U_201)
| U_201 != set_difference(U_205,U_203) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_8,plain,
( in(U_198,U_201)
| in(U_198,U_203)
| ~ in(U_198,U_205)
| U_201 != set_difference(U_205,U_203) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_9,plain,
( in(sK35(U_206,U_204,U_202),U_206)
| in(sK34(U_206,U_204,U_202),U_202)
| U_202 = set_difference(U_206,U_204) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_10,plain,
( ~ in(sK35(U_206,U_204,U_202),U_204)
| in(sK34(U_206,U_204,U_202),U_202)
| U_202 = set_difference(U_206,U_204) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_11,plain,
( ~ in(sK35(U_206,U_204,U_202),U_202)
| in(sK34(U_206,U_204,U_202),U_202)
| U_202 = set_difference(U_206,U_204) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_12,plain,
( 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)
| U_202 = set_difference(U_206,U_204) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_13,plain,
( ~ in(sK35(U_206,U_204,U_202),U_204)
| in(sK34(U_206,U_204,U_202),U_204)
| ~ in(sK34(U_206,U_204,U_202),U_206)
| U_202 = set_difference(U_206,U_204) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_14,plain,
( ~ in(sK35(U_206,U_204,U_202),U_202)
| in(sK34(U_206,U_204,U_202),U_204)
| ~ in(sK34(U_206,U_204,U_202),U_206)
| U_202 = set_difference(U_206,U_204) ),
inference(clausify,[status(thm)],[f_22_5]) ).
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]) ).
cnf(f_23_8,plain,
( 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(clausify,[status(thm)],[f_23_7]) ).
cnf(f_23_9,plain,
( in(U_216,U_219)
| ~ in(ordered_pair(U_208,U_216),U_214)
| U_219 != relation_rng(U_214)
| ~ relation(U_214) ),
inference(clausify,[status(thm)],[f_23_7]) ).
cnf(f_23_10,plain,
( in(ordered_pair(sK39(U_214,U_220),sK38(U_214,U_220)),U_214)
| in(sK37(U_214,U_220),U_220)
| U_220 = relation_rng(U_214)
| ~ relation(U_214) ),
inference(clausify,[status(thm)],[f_23_7]) ).
cnf(f_23_11,plain,
( ~ in(sK38(U_214,U_220),U_220)
| in(sK37(U_214,U_220),U_220)
| U_220 = relation_rng(U_214)
| ~ relation(U_214) ),
inference(clausify,[status(thm)],[f_23_7]) ).
cnf(f_23_12,plain,
( in(ordered_pair(sK39(U_214,U_220),sK38(U_214,U_220)),U_214)
| ~ in(ordered_pair(U_210,sK37(U_214,U_220)),U_214)
| U_220 = relation_rng(U_214)
| ~ relation(U_214) ),
inference(clausify,[status(thm)],[f_23_7]) ).
cnf(f_23_13,plain,
( ~ in(sK38(U_214,U_220),U_220)
| ~ in(ordered_pair(U_210,sK37(U_214,U_220)),U_214)
| U_220 = relation_rng(U_214)
| ~ relation(U_214) ),
inference(clausify,[status(thm)],[f_23_7]) ).
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]) ).
cnf(f_24_3,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_2]) ).
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]) ).
cnf(f_25_3,plain,
ordered_pair(U_224,U_223) = unordered_pair(unordered_pair(U_224,U_223),singleton(U_224)),
inference(clausify,[status(thm)],[f_25_2]) ).
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]) ).
cnf(f_26_3,plain,
( relation_field(U_225) = set_union2(relation_dom(U_225),relation_rng(U_225))
| ~ relation(U_225) ),
inference(clausify,[status(thm)],[f_26_2]) ).
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]) ).
cnf(f_27_8,plain,
( 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(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_9,plain,
( in(ordered_pair(U_235,U_233),U_230)
| ~ in(ordered_pair(U_233,U_235),U_231)
| U_230 != relation_inverse(U_231)
| ~ relation(U_230)
| ~ relation(U_231) ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_10,plain,
( in(ordered_pair(sK43(U_231,U_230),sK42(U_231,U_230)),U_231)
| in(ordered_pair(sK40(U_231,U_230),sK41(U_231,U_230)),U_230)
| U_230 = relation_inverse(U_231)
| ~ relation(U_230)
| ~ relation(U_231) ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_11,plain,
( ~ in(ordered_pair(sK42(U_231,U_230),sK43(U_231,U_230)),U_230)
| in(ordered_pair(sK40(U_231,U_230),sK41(U_231,U_230)),U_230)
| U_230 = relation_inverse(U_231)
| ~ relation(U_230)
| ~ relation(U_231) ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_12,plain,
( 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)
| U_230 = relation_inverse(U_231)
| ~ relation(U_230)
| ~ relation(U_231) ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_13,plain,
( ~ in(ordered_pair(sK42(U_231,U_230),sK43(U_231,U_230)),U_230)
| ~ in(ordered_pair(sK41(U_231,U_230),sK40(U_231,U_230)),U_231)
| U_230 = relation_inverse(U_231)
| ~ relation(U_230)
| ~ relation(U_231) ),
inference(clausify,[status(thm)],[f_27_7]) ).
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]) ).
cnf(f_28_4,plain,
( set_intersection2(U_244,U_242) = empty_set
| ~ disjoint(U_244,U_242) ),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_5,plain,
( disjoint(U_245,U_243)
| set_intersection2(U_245,U_243) != empty_set ),
inference(clausify,[status(thm)],[f_28_3]) ).
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]) ).
cnf(f_29_10,plain,
( 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(clausify,[status(thm)],[f_29_9]) ).
cnf(f_29_11,plain,
( in(ordered_pair(sK44(U_256,U_255,U_254,U_259,U_257),U_257),U_255)
| ~ 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(clausify,[status(thm)],[f_29_9]) ).
cnf(f_29_12,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)
| U_254 != relation_composition(U_256,U_255)
| ~ relation(U_254)
| ~ relation(U_255)
| ~ relation(U_256) ),
inference(clausify,[status(thm)],[f_29_9]) ).
cnf(f_29_13,plain,
( in(ordered_pair(sK47(U_256,U_255,U_254),sK49(U_256,U_255,U_254)),U_256)
| in(ordered_pair(sK45(U_256,U_255,U_254),sK46(U_256,U_255,U_254)),U_254)
| U_254 = relation_composition(U_256,U_255)
| ~ relation(U_254)
| ~ relation(U_255)
| ~ relation(U_256) ),
inference(clausify,[status(thm)],[f_29_9]) ).
cnf(f_29_14,plain,
( in(ordered_pair(sK49(U_256,U_255,U_254),sK48(U_256,U_255,U_254)),U_255)
| in(ordered_pair(sK45(U_256,U_255,U_254),sK46(U_256,U_255,U_254)),U_254)
| U_254 = relation_composition(U_256,U_255)
| ~ relation(U_254)
| ~ relation(U_255)
| ~ relation(U_256) ),
inference(clausify,[status(thm)],[f_29_9]) ).
cnf(f_29_15,plain,
( ~ in(ordered_pair(sK47(U_256,U_255,U_254),sK48(U_256,U_255,U_254)),U_254)
| in(ordered_pair(sK45(U_256,U_255,U_254),sK46(U_256,U_255,U_254)),U_254)
| U_254 = relation_composition(U_256,U_255)
| ~ relation(U_254)
| ~ relation(U_255)
| ~ relation(U_256) ),
inference(clausify,[status(thm)],[f_29_9]) ).
cnf(f_29_16,plain,
( in(ordered_pair(sK47(U_256,U_255,U_254),sK49(U_256,U_255,U_254)),U_256)
| ~ 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)
| U_254 = relation_composition(U_256,U_255)
| ~ relation(U_254)
| ~ relation(U_255)
| ~ relation(U_256) ),
inference(clausify,[status(thm)],[f_29_9]) ).
cnf(f_29_17,plain,
( in(ordered_pair(sK49(U_256,U_255,U_254),sK48(U_256,U_255,U_254)),U_255)
| ~ 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)
| U_254 = relation_composition(U_256,U_255)
| ~ relation(U_254)
| ~ relation(U_255)
| ~ relation(U_256) ),
inference(clausify,[status(thm)],[f_29_9]) ).
cnf(f_29_18,plain,
( ~ in(ordered_pair(sK47(U_256,U_255,U_254),sK48(U_256,U_255,U_254)),U_254)
| ~ 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)
| U_254 = relation_composition(U_256,U_255)
| ~ relation(U_254)
| ~ relation(U_255)
| ~ relation(U_256) ),
inference(clausify,[status(thm)],[f_29_9]) ).
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]) ).
cnf(f_30_4,plain,
( 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(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_5,plain,
( in(U_265,U_267)
| ~ in(subset_complement(U_269,U_265),U_268)
| ~ 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(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_6,plain,
( element(sK50(U_269,U_268,U_267),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(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_7,plain,
( in(subset_complement(U_269,sK50(U_269,U_268,U_267)),U_268)
| in(sK50(U_269,U_268,U_267),U_267)
| U_267 = complements_of_subsets(U_269,U_268)
| ~ element(U_267,powerset(powerset(U_269)))
| ~ element(U_268,powerset(powerset(U_269))) ),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_8,plain,
( ~ in(sK50(U_269,U_268,U_267),U_267)
| in(sK50(U_269,U_268,U_267),U_267)
| U_267 = complements_of_subsets(U_269,U_268)
| ~ element(U_267,powerset(powerset(U_269)))
| ~ element(U_268,powerset(powerset(U_269))) ),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_9,plain,
( 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)
| U_267 = complements_of_subsets(U_269,U_268)
| ~ element(U_267,powerset(powerset(U_269)))
| ~ element(U_268,powerset(powerset(U_269))) ),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_10,plain,
( ~ in(sK50(U_269,U_268,U_267),U_267)
| ~ in(subset_complement(U_269,sK50(U_269,U_268,U_267)),U_268)
| U_267 = complements_of_subsets(U_269,U_268)
| ~ element(U_267,powerset(powerset(U_269)))
| ~ element(U_268,powerset(powerset(U_269))) ),
inference(clausify,[status(thm)],[f_30_3]) ).
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]) ).
cnf(f_31_4,plain,
( subset(U_274,U_272)
| ~ proper_subset(U_274,U_272) ),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_5,plain,
( U_274 != U_272
| ~ proper_subset(U_274,U_272) ),
inference(clausify,[status(thm)],[f_31_3]) ).
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_3]) ).
fof(f_32_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
cnf(f_32_2,plain,
$true,
inference(clausify,[status(thm)],[f_32_1]) ).
fof(f_33_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_setfam_1]) ).
cnf(f_33_2,plain,
$true,
inference(clausify,[status(thm)],[f_33_1]) ).
fof(f_34_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
cnf(f_34_2,plain,
$true,
inference(clausify,[status(thm)],[f_34_1]) ).
fof(f_35_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_35_2,plain,
$true,
inference(clausify,[status(thm)],[f_35_1]) ).
fof(f_36_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_36_2,plain,
$true,
inference(clausify,[status(thm)],[f_36_1]) ).
fof(f_37_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_relat_1]) ).
cnf(f_37_2,plain,
$true,
inference(clausify,[status(thm)],[f_37_1]) ).
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]) ).
cnf(f_38_3,plain,
element(cast_to_subset(U_276),powerset(U_276)),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
cnf(f_39_2,plain,
$true,
inference(clausify,[status(thm)],[f_39_1]) ).
fof(f_40_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
cnf(f_40_2,plain,
$true,
inference(clausify,[status(thm)],[f_40_1]) ).
fof(f_41_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
cnf(f_41_2,plain,
$true,
inference(clausify,[status(thm)],[f_41_1]) ).
fof(f_42_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_relat_1]) ).
cnf(f_42_2,plain,
$true,
inference(clausify,[status(thm)],[f_42_1]) ).
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]) ).
cnf(f_43_3,plain,
( element(subset_complement(U_278,U_277),powerset(U_278))
| ~ element(U_277,powerset(U_278)) ),
inference(clausify,[status(thm)],[f_43_2]) ).
fof(f_44_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_tarski]) ).
cnf(f_44_2,plain,
$true,
inference(clausify,[status(thm)],[f_44_1]) ).
fof(f_45_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
cnf(f_45_2,plain,
$true,
inference(clausify,[status(thm)],[f_45_1]) ).
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]) ).
cnf(f_46_3,plain,
( relation(relation_inverse(U_279))
| ~ relation(U_279) ),
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
cnf(f_47_2,plain,
$true,
inference(clausify,[status(thm)],[f_47_1]) ).
fof(f_48_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
cnf(f_48_2,plain,
$true,
inference(clausify,[status(thm)],[f_48_1]) ).
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]) ).
cnf(f_49_3,plain,
( relation(relation_composition(U_281,U_280))
| ~ relation(U_280)
| ~ relation(U_281) ),
inference(clausify,[status(thm)],[f_49_2]) ).
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]) ).
cnf(f_50_3,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_2]) ).
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]) ).
cnf(f_51_3,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_2]) ).
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]) ).
cnf(f_52_3,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_2]) ).
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]) ).
cnf(f_53_3,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_2]) ).
fof(f_54_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_54_2,plain,
$true,
inference(clausify,[status(thm)],[f_54_1]) ).
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]) ).
cnf(f_55_4,plain,
element(sK51(U_292),U_292),
inference(clausify,[status(thm)],[f_55_3]) ).
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]) ).
cnf(f_56_3,plain,
~ empty(powerset(U_293)),
inference(clausify,[status(thm)],[f_56_2]) ).
fof(f_57_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_57_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_57_1]) ).
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]) ).
cnf(f_58_3,plain,
~ empty(ordered_pair(U_295,U_294)),
inference(clausify,[status(thm)],[f_58_2]) ).
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]) ).
cnf(f_59_3,plain,
( relation(set_union2(U_297,U_296))
| ~ relation(U_296)
| ~ relation(U_297) ),
inference(clausify,[status(thm)],[f_59_2]) ).
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]) ).
cnf(f_60_3,plain,
~ empty(singleton(U_298)),
inference(clausify,[status(thm)],[f_60_2]) ).
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]) ).
cnf(f_61_4,plain,
( ~ empty(set_union2(U_300,U_299))
| empty(U_300) ),
inference(clausify,[status(thm)],[f_61_3]) ).
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]) ).
cnf(f_62_3,plain,
~ empty(unordered_pair(U_302,U_301)),
inference(clausify,[status(thm)],[f_62_2]) ).
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]) ).
cnf(f_63_4,plain,
( ~ empty(set_union2(U_303,U_304))
| empty(U_304) ),
inference(clausify,[status(thm)],[f_63_3]) ).
fof(f_64_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_64_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_64_1]) ).
cnf(f_64_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_64_1]) ).
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]) ).
cnf(f_65_3,plain,
( ~ empty(cartesian_product2(U_306,U_305))
| empty(U_305)
| empty(U_306) ),
inference(clausify,[status(thm)],[f_65_2]) ).
fof(f_66_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_66_2,plain,
! [U_308,U_307] : set_union2(U_308,U_308) = U_308,
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
! [U_308] : set_union2(U_308,U_308) = U_308,
inference(miniscope,[status(thm)],[f_66_2]) ).
cnf(f_66_4,plain,
set_union2(U_308,U_308) = U_308,
inference(clausify,[status(thm)],[f_66_3]) ).
fof(f_67_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_67_2,plain,
! [U_310,U_309] : set_intersection2(U_310,U_310) = U_310,
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
! [U_310] : set_intersection2(U_310,U_310) = U_310,
inference(miniscope,[status(thm)],[f_67_2]) ).
cnf(f_67_4,plain,
set_intersection2(U_310,U_310) = U_310,
inference(clausify,[status(thm)],[f_67_3]) ).
fof(f_68_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_68_2,plain,
! [U_312,U_311] :
( subset_complement(U_312,subset_complement(U_312,U_311)) = U_311
| ~ element(U_311,powerset(U_312)) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
cnf(f_68_3,plain,
( subset_complement(U_312,subset_complement(U_312,U_311)) = U_311
| ~ element(U_311,powerset(U_312)) ),
inference(clausify,[status(thm)],[f_68_2]) ).
fof(f_69_1,plain,
! [A] :
( relation_inverse(relation_inverse(A)) = A
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[involutiveness_k4_relat_1]) ).
fof(f_69_2,plain,
! [U_313] :
( relation_inverse(relation_inverse(U_313)) = U_313
| ~ relation(U_313) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
cnf(f_69_3,plain,
( relation_inverse(relation_inverse(U_313)) = U_313
| ~ relation(U_313) ),
inference(clausify,[status(thm)],[f_69_2]) ).
fof(f_70_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_70_2,plain,
! [U_315,U_314] :
( complements_of_subsets(U_315,complements_of_subsets(U_315,U_314)) = U_314
| ~ element(U_314,powerset(powerset(U_315))) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
cnf(f_70_3,plain,
( complements_of_subsets(U_315,complements_of_subsets(U_315,U_314)) = U_314
| ~ element(U_314,powerset(powerset(U_315))) ),
inference(clausify,[status(thm)],[f_70_2]) ).
fof(f_71_1,plain,
! [A,B] : ~ proper_subset(A,A),
inference(fof_nnf,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(f_71_2,plain,
! [U_317,U_316] : ~ proper_subset(U_317,U_317),
inference(variable_rename,[status(thm)],[f_71_1]) ).
fof(f_71_3,plain,
! [U_317] : ~ proper_subset(U_317,U_317),
inference(miniscope,[status(thm)],[f_71_2]) ).
cnf(f_71_4,plain,
~ proper_subset(U_317,U_317),
inference(clausify,[status(thm)],[f_71_3]) ).
fof(f_72_1,plain,
! [A] : singleton(A) != empty_set,
inference(fof_nnf,[status(thm)],[l1_zfmisc_1]) ).
fof(f_72_2,plain,
! [U_318] : singleton(U_318) != empty_set,
inference(variable_rename,[status(thm)],[f_72_1]) ).
cnf(f_72_3,plain,
singleton(U_318) != empty_set,
inference(clausify,[status(thm)],[f_72_2]) ).
fof(f_73_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l23_zfmisc_1]) ).
fof(f_73_2,plain,
! [U_320,U_319] :
( set_union2(singleton(U_320),U_319) = U_319
| ~ in(U_320,U_319) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
cnf(f_73_3,plain,
( set_union2(singleton(U_320),U_319) = U_319
| ~ in(U_320,U_319) ),
inference(clausify,[status(thm)],[f_73_2]) ).
fof(f_74_1,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(fof_nnf,[status(thm)],[l25_zfmisc_1]) ).
fof(f_74_2,plain,
! [U_322,U_321] :
( ~ in(U_322,U_321)
| ~ disjoint(singleton(U_322),U_321) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
cnf(f_74_3,plain,
( ~ in(U_322,U_321)
| ~ disjoint(singleton(U_322),U_321) ),
inference(clausify,[status(thm)],[f_74_2]) ).
fof(f_75_1,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(fof_nnf,[status(thm)],[l28_zfmisc_1]) ).
fof(f_75_2,plain,
! [U_324,U_323] :
( disjoint(singleton(U_324),U_323)
| in(U_324,U_323) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
cnf(f_75_3,plain,
( disjoint(singleton(U_324),U_323)
| in(U_324,U_323) ),
inference(clausify,[status(thm)],[f_75_2]) ).
fof(f_76_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_76_2,plain,
! [U_326,U_325] :
( ( subset(singleton(U_326),U_325)
| ~ in(U_326,U_325) )
& ( in(U_326,U_325)
| ~ subset(singleton(U_326),U_325) ) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
fof(f_76_3,plain,
( ! [U_330,U_328] :
( subset(singleton(U_330),U_328)
| ~ in(U_330,U_328) )
& ! [U_329,U_327] :
( in(U_329,U_327)
| ~ subset(singleton(U_329),U_327) ) ),
inference(miniscope,[status(thm)],[f_76_2]) ).
cnf(f_76_4,plain,
( in(U_329,U_327)
| ~ subset(singleton(U_329),U_327) ),
inference(clausify,[status(thm)],[f_76_3]) ).
cnf(f_76_5,plain,
( subset(singleton(U_330),U_328)
| ~ in(U_330,U_328) ),
inference(clausify,[status(thm)],[f_76_3]) ).
fof(f_77_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_77_2,plain,
! [U_332,U_331] :
( ( set_difference(U_332,U_331) = empty_set
| ~ subset(U_332,U_331) )
& ( subset(U_332,U_331)
| set_difference(U_332,U_331) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
fof(f_77_3,plain,
( ! [U_336,U_334] :
( set_difference(U_336,U_334) = empty_set
| ~ subset(U_336,U_334) )
& ! [U_335,U_333] :
( subset(U_335,U_333)
| set_difference(U_335,U_333) != empty_set ) ),
inference(miniscope,[status(thm)],[f_77_2]) ).
cnf(f_77_4,plain,
( subset(U_335,U_333)
| set_difference(U_335,U_333) != empty_set ),
inference(clausify,[status(thm)],[f_77_3]) ).
cnf(f_77_5,plain,
( set_difference(U_336,U_334) = empty_set
| ~ subset(U_336,U_334) ),
inference(clausify,[status(thm)],[f_77_3]) ).
fof(f_78_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_78_2,plain,
! [U_339,U_338] :
( ! [U_337] :
( in(U_337,U_339)
| ~ in(U_337,U_338) )
| ~ element(U_338,powerset(U_339)) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
cnf(f_78_3,plain,
( in(U_337,U_339)
| ~ in(U_337,U_338)
| ~ element(U_338,powerset(U_339)) ),
inference(clausify,[status(thm)],[f_78_2]) ).
fof(f_79_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_79_2,plain,
! [U_342,U_341,U_340] :
( subset(U_342,set_difference(U_341,singleton(U_340)))
| in(U_340,U_342)
| ~ subset(U_342,U_341) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
fof(f_79_3,plain,
! [U_342,U_341] :
( ! [U_340] :
( subset(U_342,set_difference(U_341,singleton(U_340)))
| in(U_340,U_342) )
| ~ subset(U_342,U_341) ),
inference(miniscope,[status(thm)],[f_79_2]) ).
cnf(f_79_4,plain,
( subset(U_342,set_difference(U_341,singleton(U_340)))
| in(U_340,U_342)
| ~ subset(U_342,U_341) ),
inference(clausify,[status(thm)],[f_79_3]) ).
fof(f_80_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_80_2,plain,
! [U_344,U_343] :
( ( subset(U_344,singleton(U_343))
| ( U_344 != singleton(U_343)
& U_344 != empty_set ) )
& ( U_344 = singleton(U_343)
| U_344 = empty_set
| ~ subset(U_344,singleton(U_343)) ) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
fof(f_80_3,plain,
( ! [U_348,U_346] :
( subset(U_348,singleton(U_346))
| ( U_348 != singleton(U_346)
& U_348 != empty_set ) )
& ! [U_347,U_345] :
( U_347 = singleton(U_345)
| U_347 = empty_set
| ~ subset(U_347,singleton(U_345)) ) ),
inference(miniscope,[status(thm)],[f_80_2]) ).
cnf(f_80_4,plain,
( U_347 = singleton(U_345)
| U_347 = empty_set
| ~ subset(U_347,singleton(U_345)) ),
inference(clausify,[status(thm)],[f_80_3]) ).
cnf(f_80_5,plain,
( U_348 != empty_set
| subset(U_348,singleton(U_346)) ),
inference(clausify,[status(thm)],[f_80_3]) ).
cnf(f_80_6,plain,
( U_348 != singleton(U_346)
| subset(U_348,singleton(U_346)) ),
inference(clausify,[status(thm)],[f_80_3]) ).
fof(f_81_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l50_zfmisc_1]) ).
fof(f_81_2,plain,
! [U_350,U_349] :
( subset(U_350,union(U_349))
| ~ in(U_350,U_349) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
cnf(f_81_3,plain,
( subset(U_350,union(U_349))
| ~ in(U_350,U_349) ),
inference(clausify,[status(thm)],[f_81_2]) ).
fof(f_82_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_82_2,plain,
! [U_354,U_353,U_352,U_351] :
( ( in(ordered_pair(U_354,U_353),cartesian_product2(U_352,U_351))
| ~ in(U_353,U_351)
| ~ in(U_354,U_352) )
& ( ( in(U_353,U_351)
& in(U_354,U_352) )
| ~ in(ordered_pair(U_354,U_353),cartesian_product2(U_352,U_351)) ) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
fof(f_82_3,plain,
( ! [U_362,U_360,U_358,U_356] :
( in(ordered_pair(U_362,U_360),cartesian_product2(U_358,U_356))
| ~ in(U_360,U_356)
| ~ in(U_362,U_358) )
& ! [U_361,U_359,U_357,U_355] :
( ( in(U_359,U_355)
& in(U_361,U_357) )
| ~ in(ordered_pair(U_361,U_359),cartesian_product2(U_357,U_355)) ) ),
inference(miniscope,[status(thm)],[f_82_2]) ).
cnf(f_82_4,plain,
( in(U_361,U_357)
| ~ in(ordered_pair(U_361,U_359),cartesian_product2(U_357,U_355)) ),
inference(clausify,[status(thm)],[f_82_3]) ).
cnf(f_82_5,plain,
( in(U_359,U_355)
| ~ in(ordered_pair(U_361,U_359),cartesian_product2(U_357,U_355)) ),
inference(clausify,[status(thm)],[f_82_3]) ).
cnf(f_82_6,plain,
( in(ordered_pair(U_362,U_360),cartesian_product2(U_358,U_356))
| ~ in(U_360,U_356)
| ~ in(U_362,U_358) ),
inference(clausify,[status(thm)],[f_82_3]) ).
fof(f_83_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_83_2,plain,
! [U_365,U_364] :
( element(U_365,powerset(U_364))
| ? [U_363] :
( ~ in(U_363,U_364)
& in(U_363,U_365) ) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
fof(f_83_3,plain,
! [U_365,U_364] :
( element(U_365,powerset(U_364))
| ( ~ in(sK52(U_365,U_364),U_364)
& in(sK52(U_365,U_364),U_365) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_363,sK52(U_365,U_364))],[f_83_2]) ).
cnf(f_83_4,plain,
( in(sK52(U_365,U_364),U_365)
| element(U_365,powerset(U_364)) ),
inference(clausify,[status(thm)],[f_83_3]) ).
cnf(f_83_5,plain,
( ~ in(sK52(U_365,U_364),U_364)
| element(U_365,powerset(U_364)) ),
inference(clausify,[status(thm)],[f_83_3]) ).
fof(f_84_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_84_2,plain,
? [U_366] :
( relation(U_366)
& empty(U_366) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
fof(f_84_3,plain,
( relation(sK53)
& empty(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_366,sK53)],[f_84_2]) ).
cnf(f_84_4,plain,
empty(sK53),
inference(clausify,[status(thm)],[f_84_3]) ).
cnf(f_84_5,plain,
relation(sK53),
inference(clausify,[status(thm)],[f_84_3]) ).
fof(f_85_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_85_2,plain,
! [U_368] :
( ? [U_367] :
( ~ empty(U_367)
& element(U_367,powerset(U_368)) )
| empty(U_368) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
fof(f_85_3,plain,
! [U_368] :
( ( ~ empty(sK54(U_368))
& element(sK54(U_368),powerset(U_368)) )
| empty(U_368) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_367,sK54(U_368))],[f_85_2]) ).
cnf(f_85_4,plain,
( element(sK54(U_368),powerset(U_368))
| empty(U_368) ),
inference(clausify,[status(thm)],[f_85_3]) ).
cnf(f_85_5,plain,
( ~ empty(sK54(U_368))
| empty(U_368) ),
inference(clausify,[status(thm)],[f_85_3]) ).
fof(f_86_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_86_2,plain,
? [U_369] : empty(U_369),
inference(variable_rename,[status(thm)],[f_86_1]) ).
fof(f_86_3,plain,
empty(sK55),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_369,sK55)],[f_86_2]) ).
cnf(f_86_4,plain,
empty(sK55),
inference(clausify,[status(thm)],[f_86_3]) ).
fof(f_87_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_87_2,plain,
? [U_370] :
( relation(U_370)
& ~ empty(U_370) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
fof(f_87_3,plain,
( relation(sK56)
& ~ empty(sK56) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_370,sK56)],[f_87_2]) ).
cnf(f_87_4,plain,
~ empty(sK56),
inference(clausify,[status(thm)],[f_87_3]) ).
cnf(f_87_5,plain,
relation(sK56),
inference(clausify,[status(thm)],[f_87_3]) ).
fof(f_88_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_88_2,plain,
! [U_372] :
? [U_371] :
( empty(U_371)
& element(U_371,powerset(U_372)) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
fof(f_88_3,plain,
! [U_372] :
( empty(sK57(U_372))
& element(sK57(U_372),powerset(U_372)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_371,sK57(U_372))],[f_88_2]) ).
cnf(f_88_4,plain,
element(sK57(U_372),powerset(U_372)),
inference(clausify,[status(thm)],[f_88_3]) ).
cnf(f_88_5,plain,
empty(sK57(U_372)),
inference(clausify,[status(thm)],[f_88_3]) ).
fof(f_89_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_89_2,plain,
? [U_373] : ~ empty(U_373),
inference(variable_rename,[status(thm)],[f_89_1]) ).
fof(f_89_3,plain,
~ empty(sK58),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_373,sK58)],[f_89_2]) ).
cnf(f_89_4,plain,
~ empty(sK58),
inference(clausify,[status(thm)],[f_89_3]) ).
fof(f_90_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_90_2,plain,
! [U_375,U_374] :
( union_of_subsets(U_375,U_374) = union(U_374)
| ~ element(U_374,powerset(powerset(U_375))) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
cnf(f_90_3,plain,
( union_of_subsets(U_375,U_374) = union(U_374)
| ~ element(U_374,powerset(powerset(U_375))) ),
inference(clausify,[status(thm)],[f_90_2]) ).
fof(f_91_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_91_2,plain,
! [U_377,U_376] :
( meet_of_subsets(U_377,U_376) = set_meet(U_376)
| ~ element(U_376,powerset(powerset(U_377))) ),
inference(variable_rename,[status(thm)],[f_91_1]) ).
cnf(f_91_3,plain,
( meet_of_subsets(U_377,U_376) = set_meet(U_376)
| ~ element(U_376,powerset(powerset(U_377))) ),
inference(clausify,[status(thm)],[f_91_2]) ).
fof(f_92_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_92_2,plain,
! [U_380,U_379,U_378] :
( subset_difference(U_380,U_379,U_378) = set_difference(U_379,U_378)
| ~ element(U_378,powerset(U_380))
| ~ element(U_379,powerset(U_380)) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
cnf(f_92_3,plain,
( subset_difference(U_380,U_379,U_378) = set_difference(U_379,U_378)
| ~ element(U_378,powerset(U_380))
| ~ element(U_379,powerset(U_380)) ),
inference(clausify,[status(thm)],[f_92_2]) ).
fof(f_93_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_93_2,plain,
! [U_382,U_381] : subset(U_382,U_382),
inference(variable_rename,[status(thm)],[f_93_1]) ).
fof(f_93_3,plain,
! [U_382] : subset(U_382,U_382),
inference(miniscope,[status(thm)],[f_93_2]) ).
cnf(f_93_4,plain,
subset(U_382,U_382),
inference(clausify,[status(thm)],[f_93_3]) ).
fof(f_94_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_94_2,plain,
! [U_384,U_383] :
( disjoint(U_383,U_384)
| ~ disjoint(U_384,U_383) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
cnf(f_94_3,plain,
( disjoint(U_383,U_384)
| ~ disjoint(U_384,U_383) ),
inference(clausify,[status(thm)],[f_94_2]) ).
fof(f_95_1,plain,
! [A,B,C,D] :
( ( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(B,D)
| ~ in(A,C) )
& ( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(fof_nnf,[status(thm)],[t106_zfmisc_1]) ).
fof(f_95_2,plain,
! [U_388,U_387,U_386,U_385] :
( ( in(ordered_pair(U_388,U_387),cartesian_product2(U_386,U_385))
| ~ in(U_387,U_385)
| ~ in(U_388,U_386) )
& ( ( in(U_387,U_385)
& in(U_388,U_386) )
| ~ in(ordered_pair(U_388,U_387),cartesian_product2(U_386,U_385)) ) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
fof(f_95_3,plain,
( ! [U_396,U_394,U_392,U_390] :
( in(ordered_pair(U_396,U_394),cartesian_product2(U_392,U_390))
| ~ in(U_394,U_390)
| ~ in(U_396,U_392) )
& ! [U_395,U_393,U_391,U_389] :
( ( in(U_393,U_389)
& in(U_395,U_391) )
| ~ in(ordered_pair(U_395,U_393),cartesian_product2(U_391,U_389)) ) ),
inference(miniscope,[status(thm)],[f_95_2]) ).
cnf(f_95_4,plain,
( in(U_395,U_391)
| ~ in(ordered_pair(U_395,U_393),cartesian_product2(U_391,U_389)) ),
inference(clausify,[status(thm)],[f_95_3]) ).
cnf(f_95_5,plain,
( in(U_393,U_389)
| ~ in(ordered_pair(U_395,U_393),cartesian_product2(U_391,U_389)) ),
inference(clausify,[status(thm)],[f_95_3]) ).
cnf(f_95_6,plain,
( in(ordered_pair(U_396,U_394),cartesian_product2(U_392,U_390))
| ~ in(U_394,U_390)
| ~ in(U_396,U_392) ),
inference(clausify,[status(thm)],[f_95_3]) ).
fof(f_96_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_96_2,plain,
! [U_400,U_399,U_398,U_397] :
( U_400 = U_397
| U_400 = U_398
| unordered_pair(U_400,U_399) != unordered_pair(U_398,U_397) ),
inference(variable_rename,[status(thm)],[f_96_1]) ).
fof(f_96_3,plain,
! [U_400,U_399,U_398] :
( ! [U_397] :
( U_400 = U_397
| unordered_pair(U_400,U_399) != unordered_pair(U_398,U_397) )
| U_400 = U_398 ),
inference(miniscope,[status(thm)],[f_96_2]) ).
cnf(f_96_4,plain,
( U_400 = U_397
| unordered_pair(U_400,U_399) != unordered_pair(U_398,U_397)
| U_400 = U_398 ),
inference(clausify,[status(thm)],[f_96_3]) ).
fof(f_97_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_97_2,plain,
! [U_403,U_402,U_401] :
( ( subset(cartesian_product2(U_401,U_403),cartesian_product2(U_401,U_402))
& subset(cartesian_product2(U_403,U_401),cartesian_product2(U_402,U_401)) )
| ~ subset(U_403,U_402) ),
inference(variable_rename,[status(thm)],[f_97_1]) ).
fof(f_97_3,plain,
! [U_403,U_402] :
( ( ! [U_405] : subset(cartesian_product2(U_405,U_403),cartesian_product2(U_405,U_402))
& ! [U_404] : subset(cartesian_product2(U_403,U_404),cartesian_product2(U_402,U_404)) )
| ~ subset(U_403,U_402) ),
inference(miniscope,[status(thm)],[f_97_2]) ).
cnf(f_97_4,plain,
( subset(cartesian_product2(U_403,U_404),cartesian_product2(U_402,U_404))
| ~ subset(U_403,U_402) ),
inference(clausify,[status(thm)],[f_97_3]) ).
cnf(f_97_5,plain,
( subset(cartesian_product2(U_405,U_403),cartesian_product2(U_405,U_402))
| ~ subset(U_403,U_402) ),
inference(clausify,[status(thm)],[f_97_3]) ).
fof(f_98_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_98_2,plain,
! [U_409,U_408,U_407,U_406] :
( subset(cartesian_product2(U_409,U_407),cartesian_product2(U_408,U_406))
| ~ subset(U_407,U_406)
| ~ subset(U_409,U_408) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
cnf(f_98_3,plain,
( subset(cartesian_product2(U_409,U_407),cartesian_product2(U_408,U_406))
| ~ subset(U_407,U_406)
| ~ subset(U_409,U_408) ),
inference(clausify,[status(thm)],[f_98_2]) ).
fof(f_99_1,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t12_xboole_1]) ).
fof(f_99_2,plain,
! [U_411,U_410] :
( set_union2(U_411,U_410) = U_410
| ~ subset(U_411,U_410) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
cnf(f_99_3,plain,
( set_union2(U_411,U_410) = U_410
| ~ subset(U_411,U_410) ),
inference(clausify,[status(thm)],[f_99_2]) ).
fof(f_100_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_100_2,plain,
! [U_417] :
? [U_416] :
( ! [U_415] :
( in(U_415,U_416)
| are_equipotent(U_415,U_416)
| ~ subset(U_415,U_416) )
& ! [U_414] :
( in(powerset(U_414),U_416)
| ~ in(U_414,U_416) )
& ! [U_413,U_412] :
( in(U_412,U_416)
| ~ subset(U_412,U_413)
| ~ in(U_413,U_416) )
& in(U_417,U_416) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
fof(f_100_3,plain,
! [U_417] :
( ! [U_415] :
( in(U_415,sK59(U_417))
| are_equipotent(U_415,sK59(U_417))
| ~ subset(U_415,sK59(U_417)) )
& ! [U_414] :
( in(powerset(U_414),sK59(U_417))
| ~ in(U_414,sK59(U_417)) )
& ! [U_413,U_412] :
( in(U_412,sK59(U_417))
| ~ subset(U_412,U_413)
| ~ in(U_413,sK59(U_417)) )
& in(U_417,sK59(U_417)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_416,sK59(U_417))],[f_100_2]) ).
cnf(f_100_4,plain,
in(U_417,sK59(U_417)),
inference(clausify,[status(thm)],[f_100_3]) ).
cnf(f_100_5,plain,
( in(U_412,sK59(U_417))
| ~ subset(U_412,U_413)
| ~ in(U_413,sK59(U_417)) ),
inference(clausify,[status(thm)],[f_100_3]) ).
cnf(f_100_6,plain,
( in(powerset(U_414),sK59(U_417))
| ~ in(U_414,sK59(U_417)) ),
inference(clausify,[status(thm)],[f_100_3]) ).
cnf(f_100_7,plain,
( in(U_415,sK59(U_417))
| are_equipotent(U_415,sK59(U_417))
| ~ subset(U_415,sK59(U_417)) ),
inference(clausify,[status(thm)],[f_100_3]) ).
fof(f_101_1,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(fof_nnf,[status(thm)],[t17_xboole_1]) ).
fof(f_101_2,plain,
! [U_419,U_418] : subset(set_intersection2(U_419,U_418),U_419),
inference(variable_rename,[status(thm)],[f_101_1]) ).
cnf(f_101_3,plain,
subset(set_intersection2(U_419,U_418),U_419),
inference(clausify,[status(thm)],[f_101_2]) ).
fof(f_102_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_102_2,plain,
! [U_422,U_421,U_420] :
( subset(U_422,set_intersection2(U_421,U_420))
| ~ subset(U_422,U_420)
| ~ subset(U_422,U_421) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
cnf(f_102_3,plain,
( subset(U_422,set_intersection2(U_421,U_420))
| ~ subset(U_422,U_420)
| ~ subset(U_422,U_421) ),
inference(clausify,[status(thm)],[f_102_2]) ).
fof(f_103_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_103_2,plain,
! [U_423] : set_union2(U_423,empty_set) = U_423,
inference(variable_rename,[status(thm)],[f_103_1]) ).
cnf(f_103_3,plain,
set_union2(U_423,empty_set) = U_423,
inference(clausify,[status(thm)],[f_103_2]) ).
fof(f_104_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_104_2,plain,
! [U_425,U_424] :
( element(U_425,U_424)
| ~ in(U_425,U_424) ),
inference(variable_rename,[status(thm)],[f_104_1]) ).
cnf(f_104_3,plain,
( element(U_425,U_424)
| ~ in(U_425,U_424) ),
inference(clausify,[status(thm)],[f_104_2]) ).
fof(f_105_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_105_2,plain,
! [U_428,U_427,U_426] :
( subset(U_428,U_426)
| ~ subset(U_427,U_426)
| ~ subset(U_428,U_427) ),
inference(variable_rename,[status(thm)],[f_105_1]) ).
cnf(f_105_3,plain,
( subset(U_428,U_426)
| ~ subset(U_427,U_426)
| ~ subset(U_428,U_427) ),
inference(clausify,[status(thm)],[f_105_2]) ).
fof(f_106_1,plain,
powerset(empty_set) = singleton(empty_set),
inference(fof_nnf,[status(thm)],[t1_zfmisc_1]) ).
cnf(f_106_2,plain,
powerset(empty_set) = singleton(empty_set),
inference(clausify,[status(thm)],[f_106_1]) ).
fof(f_107_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_107_2,plain,
! [U_431,U_430,U_429] :
( ( in(U_430,relation_rng(U_429))
& in(U_431,relation_dom(U_429)) )
| ~ in(ordered_pair(U_431,U_430),U_429)
| ~ relation(U_429) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
cnf(f_107_3,plain,
( in(U_431,relation_dom(U_429))
| ~ in(ordered_pair(U_431,U_430),U_429)
| ~ relation(U_429) ),
inference(clausify,[status(thm)],[f_107_2]) ).
cnf(f_107_4,plain,
( in(U_430,relation_rng(U_429))
| ~ in(ordered_pair(U_431,U_430),U_429)
| ~ relation(U_429) ),
inference(clausify,[status(thm)],[f_107_2]) ).
fof(f_108_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_108_2,plain,
! [U_432] :
( subset(U_432,cartesian_product2(relation_dom(U_432),relation_rng(U_432)))
| ~ relation(U_432) ),
inference(variable_rename,[status(thm)],[f_108_1]) ).
cnf(f_108_3,plain,
( subset(U_432,cartesian_product2(relation_dom(U_432),relation_rng(U_432)))
| ~ relation(U_432) ),
inference(clausify,[status(thm)],[f_108_2]) ).
fof(f_109_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_109_2,plain,
! [U_434] :
( ! [U_433] :
( ( subset(relation_rng(U_434),relation_rng(U_433))
& subset(relation_dom(U_434),relation_dom(U_433)) )
| ~ subset(U_434,U_433)
| ~ relation(U_433) )
| ~ relation(U_434) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
cnf(f_109_3,plain,
( subset(relation_dom(U_434),relation_dom(U_433))
| ~ subset(U_434,U_433)
| ~ relation(U_433)
| ~ relation(U_434) ),
inference(clausify,[status(thm)],[f_109_2]) ).
cnf(f_109_4,plain,
( subset(relation_rng(U_434),relation_rng(U_433))
| ~ subset(U_434,U_433)
| ~ relation(U_433)
| ~ relation(U_434) ),
inference(clausify,[status(thm)],[f_109_2]) ).
fof(f_110_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_110_2,plain,
! [U_437,U_436,U_435] :
( subset(set_intersection2(U_437,U_435),set_intersection2(U_436,U_435))
| ~ subset(U_437,U_436) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
fof(f_110_3,plain,
! [U_437,U_436] :
( ! [U_435] : subset(set_intersection2(U_437,U_435),set_intersection2(U_436,U_435))
| ~ subset(U_437,U_436) ),
inference(miniscope,[status(thm)],[f_110_2]) ).
cnf(f_110_4,plain,
( subset(set_intersection2(U_437,U_435),set_intersection2(U_436,U_435))
| ~ subset(U_437,U_436) ),
inference(clausify,[status(thm)],[f_110_3]) ).
fof(f_111_1,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t28_xboole_1]) ).
fof(f_111_2,plain,
! [U_439,U_438] :
( set_intersection2(U_439,U_438) = U_439
| ~ subset(U_439,U_438) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
cnf(f_111_3,plain,
( set_intersection2(U_439,U_438) = U_439
| ~ subset(U_439,U_438) ),
inference(clausify,[status(thm)],[f_111_2]) ).
fof(f_112_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_112_2,plain,
! [U_440] : set_intersection2(U_440,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_112_1]) ).
cnf(f_112_3,plain,
set_intersection2(U_440,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_112_2]) ).
fof(f_113_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_113_2,plain,
! [U_442,U_441] :
( in(U_442,U_441)
| empty(U_441)
| ~ element(U_442,U_441) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
cnf(f_113_3,plain,
( in(U_442,U_441)
| empty(U_441)
| ~ element(U_442,U_441) ),
inference(clausify,[status(thm)],[f_113_2]) ).
fof(f_114_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_114_2,plain,
! [U_445,U_444] :
( U_445 = U_444
| ? [U_443] :
( ( ~ in(U_443,U_445)
& in(U_443,U_444) )
| ( ~ in(U_443,U_444)
& in(U_443,U_445) ) ) ),
inference(variable_rename,[status(thm)],[f_114_1]) ).
fof(f_114_3,plain,
! [U_445,U_444] :
( U_445 = U_444
| ? [U_447] :
( ~ in(U_447,U_445)
& in(U_447,U_444) )
| ? [U_446] :
( ~ in(U_446,U_444)
& in(U_446,U_445) ) ),
inference(miniscope,[status(thm)],[f_114_2]) ).
fof(f_114_4,plain,
! [U_445,U_444] :
( U_445 = U_444
| ? [U_447] :
( ~ in(U_447,U_445)
& in(U_447,U_444) )
| ( ~ in(sK60(U_445,U_444),U_444)
& in(sK60(U_445,U_444),U_445) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_446,sK60(U_445,U_444))],[f_114_3]) ).
fof(f_114_5,plain,
! [U_445,U_444] :
( U_445 = U_444
| ( ~ in(sK61(U_445,U_444),U_445)
& in(sK61(U_445,U_444),U_444) )
| ( ~ in(sK60(U_445,U_444),U_444)
& in(sK60(U_445,U_444),U_445) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_447,sK61(U_445,U_444))],[f_114_4]) ).
cnf(f_114_6,plain,
( in(sK61(U_445,U_444),U_444)
| in(sK60(U_445,U_444),U_445)
| U_445 = U_444 ),
inference(clausify,[status(thm)],[f_114_5]) ).
cnf(f_114_7,plain,
( ~ in(sK61(U_445,U_444),U_445)
| in(sK60(U_445,U_444),U_445)
| U_445 = U_444 ),
inference(clausify,[status(thm)],[f_114_5]) ).
cnf(f_114_8,plain,
( in(sK61(U_445,U_444),U_444)
| ~ in(sK60(U_445,U_444),U_444)
| U_445 = U_444 ),
inference(clausify,[status(thm)],[f_114_5]) ).
cnf(f_114_9,plain,
( ~ in(sK61(U_445,U_444),U_445)
| ~ in(sK60(U_445,U_444),U_444)
| U_445 = U_444 ),
inference(clausify,[status(thm)],[f_114_5]) ).
fof(f_115_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_115_2,plain,
! [U_448] : subset(empty_set,U_448),
inference(variable_rename,[status(thm)],[f_115_1]) ).
cnf(f_115_3,plain,
subset(empty_set,U_448),
inference(clausify,[status(thm)],[f_115_2]) ).
fof(f_116_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_116_2,plain,
! [U_451,U_450,U_449] :
( ( in(U_450,relation_field(U_449))
& in(U_451,relation_field(U_449)) )
| ~ in(ordered_pair(U_451,U_450),U_449)
| ~ relation(U_449) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
cnf(f_116_3,plain,
( in(U_451,relation_field(U_449))
| ~ in(ordered_pair(U_451,U_450),U_449)
| ~ relation(U_449) ),
inference(clausify,[status(thm)],[f_116_2]) ).
cnf(f_116_4,plain,
( in(U_450,relation_field(U_449))
| ~ in(ordered_pair(U_451,U_450),U_449)
| ~ relation(U_449) ),
inference(clausify,[status(thm)],[f_116_2]) ).
fof(f_117_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_117_2,plain,
! [U_454,U_453,U_452] :
( subset(set_difference(U_454,U_452),set_difference(U_453,U_452))
| ~ subset(U_454,U_453) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
fof(f_117_3,plain,
! [U_454,U_453] :
( ! [U_452] : subset(set_difference(U_454,U_452),set_difference(U_453,U_452))
| ~ subset(U_454,U_453) ),
inference(miniscope,[status(thm)],[f_117_2]) ).
cnf(f_117_4,plain,
( subset(set_difference(U_454,U_452),set_difference(U_453,U_452))
| ~ subset(U_454,U_453) ),
inference(clausify,[status(thm)],[f_117_3]) ).
fof(f_118_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_118_2,plain,
! [U_458,U_457,U_456,U_455] :
( ( U_457 = U_455
& U_458 = U_456 )
| ordered_pair(U_458,U_457) != ordered_pair(U_456,U_455) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
cnf(f_118_3,plain,
( U_458 = U_456
| ordered_pair(U_458,U_457) != ordered_pair(U_456,U_455) ),
inference(clausify,[status(thm)],[f_118_2]) ).
cnf(f_118_4,plain,
( U_457 = U_455
| ordered_pair(U_458,U_457) != ordered_pair(U_456,U_455) ),
inference(clausify,[status(thm)],[f_118_2]) ).
fof(f_119_1,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(fof_nnf,[status(thm)],[t36_xboole_1]) ).
fof(f_119_2,plain,
! [U_460,U_459] : subset(set_difference(U_460,U_459),U_460),
inference(variable_rename,[status(thm)],[f_119_1]) ).
cnf(f_119_3,plain,
subset(set_difference(U_460,U_459),U_460),
inference(clausify,[status(thm)],[f_119_2]) ).
fof(f_120_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_120_2,plain,
! [U_461] :
( ( relation_dom(U_461) = relation_rng(relation_inverse(U_461))
& relation_rng(U_461) = relation_dom(relation_inverse(U_461)) )
| ~ relation(U_461) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
cnf(f_120_3,plain,
( relation_rng(U_461) = relation_dom(relation_inverse(U_461))
| ~ relation(U_461) ),
inference(clausify,[status(thm)],[f_120_2]) ).
cnf(f_120_4,plain,
( relation_dom(U_461) = relation_rng(relation_inverse(U_461))
| ~ relation(U_461) ),
inference(clausify,[status(thm)],[f_120_2]) ).
fof(f_121_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_121_2,plain,
! [U_463,U_462] :
( ( set_difference(U_463,U_462) = empty_set
| ~ subset(U_463,U_462) )
& ( subset(U_463,U_462)
| set_difference(U_463,U_462) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_121_1]) ).
fof(f_121_3,plain,
( ! [U_467,U_465] :
( set_difference(U_467,U_465) = empty_set
| ~ subset(U_467,U_465) )
& ! [U_466,U_464] :
( subset(U_466,U_464)
| set_difference(U_466,U_464) != empty_set ) ),
inference(miniscope,[status(thm)],[f_121_2]) ).
cnf(f_121_4,plain,
( subset(U_466,U_464)
| set_difference(U_466,U_464) != empty_set ),
inference(clausify,[status(thm)],[f_121_3]) ).
cnf(f_121_5,plain,
( set_difference(U_467,U_465) = empty_set
| ~ subset(U_467,U_465) ),
inference(clausify,[status(thm)],[f_121_3]) ).
fof(f_122_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_122_2,plain,
! [U_469,U_468] :
( ( subset(singleton(U_469),U_468)
| ~ in(U_469,U_468) )
& ( in(U_469,U_468)
| ~ subset(singleton(U_469),U_468) ) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
fof(f_122_3,plain,
( ! [U_473,U_471] :
( subset(singleton(U_473),U_471)
| ~ in(U_473,U_471) )
& ! [U_472,U_470] :
( in(U_472,U_470)
| ~ subset(singleton(U_472),U_470) ) ),
inference(miniscope,[status(thm)],[f_122_2]) ).
cnf(f_122_4,plain,
( in(U_472,U_470)
| ~ subset(singleton(U_472),U_470) ),
inference(clausify,[status(thm)],[f_122_3]) ).
cnf(f_122_5,plain,
( subset(singleton(U_473),U_471)
| ~ in(U_473,U_471) ),
inference(clausify,[status(thm)],[f_122_3]) ).
fof(f_123_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_123_2,plain,
! [U_476,U_475,U_474] :
( ( subset(unordered_pair(U_476,U_475),U_474)
| ~ in(U_475,U_474)
| ~ in(U_476,U_474) )
& ( ( in(U_475,U_474)
& in(U_476,U_474) )
| ~ subset(unordered_pair(U_476,U_475),U_474) ) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
fof(f_123_3,plain,
( ! [U_482,U_480,U_478] :
( subset(unordered_pair(U_482,U_480),U_478)
| ~ in(U_480,U_478)
| ~ in(U_482,U_478) )
& ! [U_481,U_479,U_477] :
( ( in(U_479,U_477)
& in(U_481,U_477) )
| ~ subset(unordered_pair(U_481,U_479),U_477) ) ),
inference(miniscope,[status(thm)],[f_123_2]) ).
cnf(f_123_4,plain,
( in(U_481,U_477)
| ~ subset(unordered_pair(U_481,U_479),U_477) ),
inference(clausify,[status(thm)],[f_123_3]) ).
cnf(f_123_5,plain,
( in(U_479,U_477)
| ~ subset(unordered_pair(U_481,U_479),U_477) ),
inference(clausify,[status(thm)],[f_123_3]) ).
cnf(f_123_6,plain,
( subset(unordered_pair(U_482,U_480),U_478)
| ~ in(U_480,U_478)
| ~ in(U_482,U_478) ),
inference(clausify,[status(thm)],[f_123_3]) ).
fof(f_124_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_124_2,plain,
! [U_484,U_483] : set_union2(U_484,set_difference(U_483,U_484)) = set_union2(U_484,U_483),
inference(variable_rename,[status(thm)],[f_124_1]) ).
cnf(f_124_3,plain,
set_union2(U_484,set_difference(U_483,U_484)) = set_union2(U_484,U_483),
inference(clausify,[status(thm)],[f_124_2]) ).
fof(f_125_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_125_2,plain,
! [U_486,U_485] :
( ( subset(U_486,singleton(U_485))
| ( U_486 != singleton(U_485)
& U_486 != empty_set ) )
& ( U_486 = singleton(U_485)
| U_486 = empty_set
| ~ subset(U_486,singleton(U_485)) ) ),
inference(variable_rename,[status(thm)],[f_125_1]) ).
fof(f_125_3,plain,
( ! [U_490,U_488] :
( subset(U_490,singleton(U_488))
| ( U_490 != singleton(U_488)
& U_490 != empty_set ) )
& ! [U_489,U_487] :
( U_489 = singleton(U_487)
| U_489 = empty_set
| ~ subset(U_489,singleton(U_487)) ) ),
inference(miniscope,[status(thm)],[f_125_2]) ).
cnf(f_125_4,plain,
( U_489 = singleton(U_487)
| U_489 = empty_set
| ~ subset(U_489,singleton(U_487)) ),
inference(clausify,[status(thm)],[f_125_3]) ).
cnf(f_125_5,plain,
( U_490 != empty_set
| subset(U_490,singleton(U_488)) ),
inference(clausify,[status(thm)],[f_125_3]) ).
cnf(f_125_6,plain,
( U_490 != singleton(U_488)
| subset(U_490,singleton(U_488)) ),
inference(clausify,[status(thm)],[f_125_3]) ).
fof(f_126_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_126_2,plain,
! [U_491] : set_difference(U_491,empty_set) = U_491,
inference(variable_rename,[status(thm)],[f_126_1]) ).
cnf(f_126_3,plain,
set_difference(U_491,empty_set) = U_491,
inference(clausify,[status(thm)],[f_126_2]) ).
fof(f_127_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_127_2,plain,
! [U_493,U_492] :
( ( element(U_493,powerset(U_492))
| ~ subset(U_493,U_492) )
& ( subset(U_493,U_492)
| ~ element(U_493,powerset(U_492)) ) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
fof(f_127_3,plain,
( ! [U_497,U_495] :
( element(U_497,powerset(U_495))
| ~ subset(U_497,U_495) )
& ! [U_496,U_494] :
( subset(U_496,U_494)
| ~ element(U_496,powerset(U_494)) ) ),
inference(miniscope,[status(thm)],[f_127_2]) ).
cnf(f_127_4,plain,
( subset(U_496,U_494)
| ~ element(U_496,powerset(U_494)) ),
inference(clausify,[status(thm)],[f_127_3]) ).
cnf(f_127_5,plain,
( element(U_497,powerset(U_495))
| ~ subset(U_497,U_495) ),
inference(clausify,[status(thm)],[f_127_3]) ).
fof(f_128_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_128_2,plain,
! [U_501,U_500] :
( ( ~ disjoint(U_501,U_500)
| ! [U_499] :
( ~ in(U_499,U_500)
| ~ in(U_499,U_501) ) )
& ( ? [U_498] :
( in(U_498,U_500)
& in(U_498,U_501) )
| disjoint(U_501,U_500) ) ),
inference(variable_rename,[status(thm)],[f_128_1]) ).
fof(f_128_3,plain,
( ! [U_505,U_503] :
( ~ disjoint(U_505,U_503)
| ! [U_499] :
( ~ in(U_499,U_503)
| ~ in(U_499,U_505) ) )
& ! [U_504,U_502] :
( ? [U_498] :
( in(U_498,U_502)
& in(U_498,U_504) )
| disjoint(U_504,U_502) ) ),
inference(miniscope,[status(thm)],[f_128_2]) ).
fof(f_128_4,plain,
( ! [U_505,U_503] :
( ~ disjoint(U_505,U_503)
| ! [U_499] :
( ~ in(U_499,U_503)
| ~ in(U_499,U_505) ) )
& ! [U_504,U_502] :
( ( in(sK62(U_504,U_502),U_502)
& in(sK62(U_504,U_502),U_504) )
| disjoint(U_504,U_502) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_498,sK62(U_504,U_502))],[f_128_3]) ).
cnf(f_128_5,plain,
( in(sK62(U_504,U_502),U_504)
| disjoint(U_504,U_502) ),
inference(clausify,[status(thm)],[f_128_4]) ).
cnf(f_128_6,plain,
( in(sK62(U_504,U_502),U_502)
| disjoint(U_504,U_502) ),
inference(clausify,[status(thm)],[f_128_4]) ).
cnf(f_128_7,plain,
( ~ disjoint(U_505,U_503)
| ~ in(U_499,U_503)
| ~ in(U_499,U_505) ),
inference(clausify,[status(thm)],[f_128_4]) ).
fof(f_129_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_129_2,plain,
! [U_506] :
( U_506 = empty_set
| ~ subset(U_506,empty_set) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
cnf(f_129_3,plain,
( U_506 = empty_set
| ~ subset(U_506,empty_set) ),
inference(clausify,[status(thm)],[f_129_2]) ).
fof(f_130_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_130_2,plain,
! [U_508,U_507] : set_difference(set_union2(U_508,U_507),U_507) = set_difference(U_508,U_507),
inference(variable_rename,[status(thm)],[f_130_1]) ).
cnf(f_130_3,plain,
set_difference(set_union2(U_508,U_507),U_507) = set_difference(U_508,U_507),
inference(clausify,[status(thm)],[f_130_2]) ).
fof(f_131_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_131_2,plain,
! [U_511,U_510] :
( ! [U_509] :
( ( ( disjoint(U_510,U_509)
| ~ subset(U_510,subset_complement(U_511,U_509)) )
& ( subset(U_510,subset_complement(U_511,U_509))
| ~ disjoint(U_510,U_509) ) )
| ~ element(U_509,powerset(U_511)) )
| ~ element(U_510,powerset(U_511)) ),
inference(variable_rename,[status(thm)],[f_131_1]) ).
cnf(f_131_3,plain,
( subset(U_510,subset_complement(U_511,U_509))
| ~ disjoint(U_510,U_509)
| ~ element(U_509,powerset(U_511))
| ~ element(U_510,powerset(U_511)) ),
inference(clausify,[status(thm)],[f_131_2]) ).
cnf(f_131_4,plain,
( disjoint(U_510,U_509)
| ~ subset(U_510,subset_complement(U_511,U_509))
| ~ element(U_509,powerset(U_511))
| ~ element(U_510,powerset(U_511)) ),
inference(clausify,[status(thm)],[f_131_2]) ).
fof(f_132_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_132_2,plain,
! [U_513] :
( ! [U_512] :
( subset(relation_dom(relation_composition(U_513,U_512)),relation_dom(U_513))
| ~ relation(U_512) )
| ~ relation(U_513) ),
inference(variable_rename,[status(thm)],[f_132_1]) ).
cnf(f_132_3,plain,
( subset(relation_dom(relation_composition(U_513,U_512)),relation_dom(U_513))
| ~ relation(U_512)
| ~ relation(U_513) ),
inference(clausify,[status(thm)],[f_132_2]) ).
fof(f_133_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_133_2,plain,
! [U_515] :
( ! [U_514] :
( subset(relation_rng(relation_composition(U_515,U_514)),relation_rng(U_514))
| ~ relation(U_514) )
| ~ relation(U_515) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
cnf(f_133_3,plain,
( subset(relation_rng(relation_composition(U_515,U_514)),relation_rng(U_514))
| ~ relation(U_514)
| ~ relation(U_515) ),
inference(clausify,[status(thm)],[f_133_2]) ).
fof(f_134_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_134_2,plain,
! [U_517,U_516] :
( U_516 = set_union2(U_517,set_difference(U_516,U_517))
| ~ subset(U_517,U_516) ),
inference(variable_rename,[status(thm)],[f_134_1]) ).
cnf(f_134_3,plain,
( U_516 = set_union2(U_517,set_difference(U_516,U_517))
| ~ subset(U_517,U_516) ),
inference(clausify,[status(thm)],[f_134_2]) ).
fof(f_135_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_135_2,plain,
! [U_519] :
( ! [U_518] :
( relation_dom(relation_composition(U_519,U_518)) = relation_dom(U_519)
| ~ subset(relation_rng(U_519),relation_dom(U_518))
| ~ relation(U_518) )
| ~ relation(U_519) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
cnf(f_135_3,plain,
( relation_dom(relation_composition(U_519,U_518)) = relation_dom(U_519)
| ~ subset(relation_rng(U_519),relation_dom(U_518))
| ~ relation(U_518)
| ~ relation(U_519) ),
inference(clausify,[status(thm)],[f_135_2]) ).
fof(f_136_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_136_2,plain,
! [U_521,U_520] :
( complements_of_subsets(U_521,U_520) != empty_set
| U_520 = empty_set
| ~ element(U_520,powerset(powerset(U_521))) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
cnf(f_136_3,plain,
( complements_of_subsets(U_521,U_520) != empty_set
| U_520 = empty_set
| ~ element(U_520,powerset(powerset(U_521))) ),
inference(clausify,[status(thm)],[f_136_2]) ).
fof(f_137_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t46_zfmisc_1]) ).
fof(f_137_2,plain,
! [U_523,U_522] :
( set_union2(singleton(U_523),U_522) = U_522
| ~ in(U_523,U_522) ),
inference(variable_rename,[status(thm)],[f_137_1]) ).
cnf(f_137_3,plain,
( set_union2(singleton(U_523),U_522) = U_522
| ~ in(U_523,U_522) ),
inference(clausify,[status(thm)],[f_137_2]) ).
fof(f_138_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_138_2,plain,
! [U_525] :
( ! [U_524] :
( relation_rng(relation_composition(U_524,U_525)) = relation_rng(U_525)
| ~ subset(relation_dom(U_525),relation_rng(U_524))
| ~ relation(U_524) )
| ~ relation(U_525) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
cnf(f_138_3,plain,
( relation_rng(relation_composition(U_524,U_525)) = relation_rng(U_525)
| ~ subset(relation_dom(U_525),relation_rng(U_524))
| ~ relation(U_524)
| ~ relation(U_525) ),
inference(clausify,[status(thm)],[f_138_2]) ).
fof(f_139_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_139_2,plain,
! [U_527,U_526] :
( subset_difference(U_527,cast_to_subset(U_527),union_of_subsets(U_527,U_526)) = meet_of_subsets(U_527,complements_of_subsets(U_527,U_526))
| U_526 = empty_set
| ~ element(U_526,powerset(powerset(U_527))) ),
inference(variable_rename,[status(thm)],[f_139_1]) ).
cnf(f_139_3,plain,
( subset_difference(U_527,cast_to_subset(U_527),union_of_subsets(U_527,U_526)) = meet_of_subsets(U_527,complements_of_subsets(U_527,U_526))
| U_526 = empty_set
| ~ element(U_526,powerset(powerset(U_527))) ),
inference(clausify,[status(thm)],[f_139_2]) ).
fof(f_140_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_140_2,plain,
! [U_529,U_528] :
( union_of_subsets(U_529,complements_of_subsets(U_529,U_528)) = subset_difference(U_529,cast_to_subset(U_529),meet_of_subsets(U_529,U_528))
| U_528 = empty_set
| ~ element(U_528,powerset(powerset(U_529))) ),
inference(variable_rename,[status(thm)],[f_140_1]) ).
cnf(f_140_3,plain,
( union_of_subsets(U_529,complements_of_subsets(U_529,U_528)) = subset_difference(U_529,cast_to_subset(U_529),meet_of_subsets(U_529,U_528))
| U_528 = empty_set
| ~ element(U_528,powerset(powerset(U_529))) ),
inference(clausify,[status(thm)],[f_140_2]) ).
fof(f_141_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_141_2,plain,
! [U_531,U_530] : set_difference(U_531,set_difference(U_531,U_530)) = set_intersection2(U_531,U_530),
inference(variable_rename,[status(thm)],[f_141_1]) ).
cnf(f_141_3,plain,
set_difference(U_531,set_difference(U_531,U_530)) = set_intersection2(U_531,U_530),
inference(clausify,[status(thm)],[f_141_2]) ).
fof(f_142_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_142_2,plain,
! [U_532] : set_difference(empty_set,U_532) = empty_set,
inference(variable_rename,[status(thm)],[f_142_1]) ).
cnf(f_142_3,plain,
set_difference(empty_set,U_532) = empty_set,
inference(clausify,[status(thm)],[f_142_2]) ).
fof(f_143_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_143_2,plain,
! [U_535,U_534,U_533] :
( element(U_535,U_533)
| ~ element(U_534,powerset(U_533))
| ~ in(U_535,U_534) ),
inference(variable_rename,[status(thm)],[f_143_1]) ).
cnf(f_143_3,plain,
( element(U_535,U_533)
| ~ element(U_534,powerset(U_533))
| ~ in(U_535,U_534) ),
inference(clausify,[status(thm)],[f_143_2]) ).
fof(f_144_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_144_2,plain,
! [U_539,U_538] :
( ( ~ disjoint(U_539,U_538)
| ! [U_537] : ~ in(U_537,set_intersection2(U_539,U_538)) )
& ( ? [U_536] : in(U_536,set_intersection2(U_539,U_538))
| disjoint(U_539,U_538) ) ),
inference(variable_rename,[status(thm)],[f_144_1]) ).
fof(f_144_3,plain,
( ! [U_543,U_541] :
( ~ disjoint(U_543,U_541)
| ! [U_537] : ~ in(U_537,set_intersection2(U_543,U_541)) )
& ! [U_542,U_540] :
( ? [U_536] : in(U_536,set_intersection2(U_542,U_540))
| disjoint(U_542,U_540) ) ),
inference(miniscope,[status(thm)],[f_144_2]) ).
fof(f_144_4,plain,
( ! [U_543,U_541] :
( ~ disjoint(U_543,U_541)
| ! [U_537] : ~ in(U_537,set_intersection2(U_543,U_541)) )
& ! [U_542,U_540] :
( in(sK63(U_542,U_540),set_intersection2(U_542,U_540))
| disjoint(U_542,U_540) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_536,sK63(U_542,U_540))],[f_144_3]) ).
cnf(f_144_5,plain,
( in(sK63(U_542,U_540),set_intersection2(U_542,U_540))
| disjoint(U_542,U_540) ),
inference(clausify,[status(thm)],[f_144_4]) ).
cnf(f_144_6,plain,
( ~ disjoint(U_543,U_541)
| ~ in(U_537,set_intersection2(U_543,U_541)) ),
inference(clausify,[status(thm)],[f_144_4]) ).
fof(f_145_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_145_2,plain,
! [U_546] :
( ! [U_545] :
( ! [U_544] :
( in(U_544,subset_complement(U_546,U_545))
| in(U_544,U_545)
| ~ element(U_544,U_546) )
| ~ element(U_545,powerset(U_546)) )
| U_546 = empty_set ),
inference(variable_rename,[status(thm)],[f_145_1]) ).
cnf(f_145_3,plain,
( in(U_544,subset_complement(U_546,U_545))
| in(U_544,U_545)
| ~ element(U_544,U_546)
| ~ element(U_545,powerset(U_546))
| U_546 = empty_set ),
inference(clausify,[status(thm)],[f_145_2]) ).
fof(f_146_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_146_2,plain,
! [U_549,U_548,U_547] :
( ~ in(U_548,U_547)
| ~ in(U_548,subset_complement(U_549,U_547))
| ~ element(U_547,powerset(U_549)) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
cnf(f_146_3,plain,
( ~ in(U_548,U_547)
| ~ in(U_548,subset_complement(U_549,U_547))
| ~ element(U_547,powerset(U_549)) ),
inference(clausify,[status(thm)],[f_146_2]) ).
fof(f_147_1,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( ! [B,C] : ~ in(ordered_pair(B,C),A)
=> A = empty_set ) ),
inference(negate,[status(cth)],[t56_relat_1]) ).
fof(f_147_2,negated_conjecture,
? [A] :
( A != empty_set
& ! [B,C] : ~ in(ordered_pair(B,C),A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[f_147_1]) ).
fof(f_147_3,negated_conjecture,
? [U_552] :
( U_552 != empty_set
& ! [U_551,U_550] : ~ in(ordered_pair(U_551,U_550),U_552)
& relation(U_552) ),
inference(variable_rename,[status(thm)],[f_147_2]) ).
fof(f_147_4,negated_conjecture,
( sK64 != empty_set
& ! [U_551,U_550] : ~ in(ordered_pair(U_551,U_550),sK64)
& relation(sK64) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_552,sK64)],[f_147_3]) ).
fof(f_147_5,negated_conjecture,
( sK64 != empty_set
& ! [U_550,U_551] : ~ in(ordered_pair(U_551,U_550),sK64)
& relation(sK64) ),
inference(definitional_conversion,[status(esa)],[f_147_4]) ).
cnf(f_147_6,negated_conjecture,
relation(sK64),
inference(clausify,[status(thm)],[f_147_5]) ).
cnf(f_147_7,negated_conjecture,
~ in(ordered_pair(U_551,U_550),sK64),
inference(clausify,[status(thm)],[f_147_5]) ).
cnf(f_147_8,negated_conjecture,
sK64 != empty_set,
inference(clausify,[status(thm)],[f_147_5]) ).
fof(f_148_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_148_2,plain,
! [U_555,U_554,U_553] :
( ~ empty(U_553)
| ~ element(U_554,powerset(U_553))
| ~ in(U_555,U_554) ),
inference(variable_rename,[status(thm)],[f_148_1]) ).
fof(f_148_3,plain,
! [U_555,U_554] :
( ! [U_553] :
( ~ empty(U_553)
| ~ element(U_554,powerset(U_553)) )
| ~ in(U_555,U_554) ),
inference(miniscope,[status(thm)],[f_148_2]) ).
cnf(f_148_4,plain,
( ~ empty(U_553)
| ~ element(U_554,powerset(U_553))
| ~ in(U_555,U_554) ),
inference(clausify,[status(thm)],[f_148_3]) ).
fof(f_149_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t60_xboole_1]) ).
fof(f_149_2,plain,
! [U_557,U_556] :
( ~ proper_subset(U_556,U_557)
| ~ subset(U_557,U_556) ),
inference(variable_rename,[status(thm)],[f_149_1]) ).
cnf(f_149_3,plain,
( ~ proper_subset(U_556,U_557)
| ~ subset(U_557,U_556) ),
inference(clausify,[status(thm)],[f_149_2]) ).
fof(f_150_1,plain,
! [A,B,C] :
( disjoint(A,C)
| ~ disjoint(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t63_xboole_1]) ).
fof(f_150_2,plain,
! [U_560,U_559,U_558] :
( disjoint(U_560,U_558)
| ~ disjoint(U_559,U_558)
| ~ subset(U_560,U_559) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
cnf(f_150_3,plain,
( disjoint(U_560,U_558)
| ~ disjoint(U_559,U_558)
| ~ subset(U_560,U_559) ),
inference(clausify,[status(thm)],[f_150_2]) ).
fof(f_151_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_151_2,plain,
! [U_562,U_561] :
( ( set_difference(U_562,singleton(U_561)) = U_562
| in(U_561,U_562) )
& ( ~ in(U_561,U_562)
| set_difference(U_562,singleton(U_561)) != U_562 ) ),
inference(variable_rename,[status(thm)],[f_151_1]) ).
fof(f_151_3,plain,
( ! [U_566,U_564] :
( set_difference(U_566,singleton(U_564)) = U_566
| in(U_564,U_566) )
& ! [U_565,U_563] :
( ~ in(U_563,U_565)
| set_difference(U_565,singleton(U_563)) != U_565 ) ),
inference(miniscope,[status(thm)],[f_151_2]) ).
cnf(f_151_4,plain,
( ~ in(U_563,U_565)
| set_difference(U_565,singleton(U_563)) != U_565 ),
inference(clausify,[status(thm)],[f_151_3]) ).
cnf(f_151_5,plain,
( set_difference(U_566,singleton(U_564)) = U_566
| in(U_564,U_566) ),
inference(clausify,[status(thm)],[f_151_3]) ).
fof(f_152_1,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(fof_nnf,[status(thm)],[t69_enumset1]) ).
fof(f_152_2,plain,
! [U_567] : unordered_pair(U_567,U_567) = singleton(U_567),
inference(variable_rename,[status(thm)],[f_152_1]) ).
cnf(f_152_3,plain,
unordered_pair(U_567,U_567) = singleton(U_567),
inference(clausify,[status(thm)],[f_152_2]) ).
fof(f_153_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_153_2,plain,
! [U_568] :
( U_568 = empty_set
| ~ empty(U_568) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
cnf(f_153_3,plain,
( U_568 = empty_set
| ~ empty(U_568) ),
inference(clausify,[status(thm)],[f_153_2]) ).
fof(f_154_1,plain,
! [A,B] :
( A = B
| ~ subset(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t6_zfmisc_1]) ).
fof(f_154_2,plain,
! [U_570,U_569] :
( U_570 = U_569
| ~ subset(singleton(U_570),singleton(U_569)) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
cnf(f_154_3,plain,
( U_570 = U_569
| ~ subset(singleton(U_570),singleton(U_569)) ),
inference(clausify,[status(thm)],[f_154_2]) ).
fof(f_155_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_155_2,plain,
! [U_572,U_571] :
( ~ empty(U_571)
| ~ in(U_572,U_571) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
cnf(f_155_3,plain,
( ~ empty(U_571)
| ~ in(U_572,U_571) ),
inference(clausify,[status(thm)],[f_155_2]) ).
fof(f_156_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1]) ).
fof(f_156_2,plain,
! [U_574,U_573] : subset(U_574,set_union2(U_574,U_573)),
inference(variable_rename,[status(thm)],[f_156_1]) ).
cnf(f_156_3,plain,
subset(U_574,set_union2(U_574,U_573)),
inference(clausify,[status(thm)],[f_156_2]) ).
fof(f_157_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_157_2,plain,
! [U_576,U_575] :
( ( disjoint(U_576,U_575)
| set_difference(U_576,U_575) != U_576 )
& ( set_difference(U_576,U_575) = U_576
| ~ disjoint(U_576,U_575) ) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
fof(f_157_3,plain,
( ! [U_580,U_578] :
( disjoint(U_580,U_578)
| set_difference(U_580,U_578) != U_580 )
& ! [U_579,U_577] :
( set_difference(U_579,U_577) = U_579
| ~ disjoint(U_579,U_577) ) ),
inference(miniscope,[status(thm)],[f_157_2]) ).
cnf(f_157_4,plain,
( set_difference(U_579,U_577) = U_579
| ~ disjoint(U_579,U_577) ),
inference(clausify,[status(thm)],[f_157_3]) ).
cnf(f_157_5,plain,
( disjoint(U_580,U_578)
| set_difference(U_580,U_578) != U_580 ),
inference(clausify,[status(thm)],[f_157_3]) ).
fof(f_158_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_158_2,plain,
! [U_582,U_581] :
( ~ empty(U_581)
| U_582 = U_581
| ~ empty(U_582) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
fof(f_158_3,plain,
! [U_582] :
( ! [U_581] :
( ~ empty(U_581)
| U_582 = U_581 )
| ~ empty(U_582) ),
inference(miniscope,[status(thm)],[f_158_2]) ).
cnf(f_158_4,plain,
( ~ empty(U_581)
| U_582 = U_581
| ~ empty(U_582) ),
inference(clausify,[status(thm)],[f_158_3]) ).
fof(f_159_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_159_2,plain,
! [U_585,U_584,U_583] :
( subset(set_union2(U_585,U_583),U_584)
| ~ subset(U_583,U_584)
| ~ subset(U_585,U_584) ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
cnf(f_159_3,plain,
( subset(set_union2(U_585,U_583),U_584)
| ~ subset(U_583,U_584)
| ~ subset(U_585,U_584) ),
inference(clausify,[status(thm)],[f_159_2]) ).
fof(f_160_1,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t8_zfmisc_1]) ).
fof(f_160_2,plain,
! [U_588,U_587,U_586] :
( U_588 = U_587
| singleton(U_588) != unordered_pair(U_587,U_586) ),
inference(variable_rename,[status(thm)],[f_160_1]) ).
fof(f_160_3,plain,
! [U_588,U_587] :
( ! [U_586] : singleton(U_588) != unordered_pair(U_587,U_586)
| U_588 = U_587 ),
inference(miniscope,[status(thm)],[f_160_2]) ).
cnf(f_160_4,plain,
( singleton(U_588) != unordered_pair(U_587,U_586)
| U_588 = U_587 ),
inference(clausify,[status(thm)],[f_160_3]) ).
fof(f_161_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t92_zfmisc_1]) ).
fof(f_161_2,plain,
! [U_590,U_589] :
( subset(U_590,union(U_589))
| ~ in(U_590,U_589) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
cnf(f_161_3,plain,
( subset(U_590,union(U_589))
| ~ in(U_590,U_589) ),
inference(clausify,[status(thm)],[f_161_2]) ).
fof(f_162_1,plain,
! [A] : union(powerset(A)) = A,
inference(fof_nnf,[status(thm)],[t99_zfmisc_1]) ).
fof(f_162_2,plain,
! [U_591] : union(powerset(U_591)) = U_591,
inference(variable_rename,[status(thm)],[f_162_1]) ).
cnf(f_162_3,plain,
union(powerset(U_591)) = U_591,
inference(clausify,[status(thm)],[f_162_2]) ).
fof(f_163_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_163_2,plain,
! [U_599] :
? [U_598] :
( ! [U_597] :
( in(U_597,U_598)
| are_equipotent(U_597,U_598)
| ~ subset(U_597,U_598) )
& ! [U_596] :
( ? [U_595] :
( ! [U_594] :
( in(U_594,U_595)
| ~ subset(U_594,U_596) )
& in(U_595,U_598) )
| ~ in(U_596,U_598) )
& ! [U_593,U_592] :
( in(U_592,U_598)
| ~ subset(U_592,U_593)
| ~ in(U_593,U_598) )
& in(U_599,U_598) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
fof(f_163_3,plain,
! [U_599] :
( ! [U_597] :
( in(U_597,sK65(U_599))
| are_equipotent(U_597,sK65(U_599))
| ~ subset(U_597,sK65(U_599)) )
& ! [U_596] :
( ? [U_595] :
( ! [U_594] :
( in(U_594,U_595)
| ~ subset(U_594,U_596) )
& in(U_595,sK65(U_599)) )
| ~ in(U_596,sK65(U_599)) )
& ! [U_593,U_592] :
( in(U_592,sK65(U_599))
| ~ subset(U_592,U_593)
| ~ in(U_593,sK65(U_599)) )
& in(U_599,sK65(U_599)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_598,sK65(U_599))],[f_163_2]) ).
fof(f_163_4,plain,
! [U_599] :
( ! [U_597] :
( in(U_597,sK65(U_599))
| are_equipotent(U_597,sK65(U_599))
| ~ subset(U_597,sK65(U_599)) )
& ! [U_596] :
( ( ! [U_594] :
( in(U_594,sK66(U_599,U_596))
| ~ subset(U_594,U_596) )
& in(sK66(U_599,U_596),sK65(U_599)) )
| ~ in(U_596,sK65(U_599)) )
& ! [U_593,U_592] :
( in(U_592,sK65(U_599))
| ~ subset(U_592,U_593)
| ~ in(U_593,sK65(U_599)) )
& in(U_599,sK65(U_599)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_595,sK66(U_599,U_596))],[f_163_3]) ).
cnf(f_163_5,plain,
in(U_599,sK65(U_599)),
inference(clausify,[status(thm)],[f_163_4]) ).
cnf(f_163_6,plain,
( in(U_592,sK65(U_599))
| ~ subset(U_592,U_593)
| ~ in(U_593,sK65(U_599)) ),
inference(clausify,[status(thm)],[f_163_4]) ).
cnf(f_163_7,plain,
( in(sK66(U_599,U_596),sK65(U_599))
| ~ in(U_596,sK65(U_599)) ),
inference(clausify,[status(thm)],[f_163_4]) ).
cnf(f_163_8,plain,
( in(U_594,sK66(U_599,U_596))
| ~ subset(U_594,U_596)
| ~ in(U_596,sK65(U_599)) ),
inference(clausify,[status(thm)],[f_163_4]) ).
cnf(f_163_9,plain,
( in(U_597,sK65(U_599))
| are_equipotent(U_597,sK65(U_599))
| ~ subset(U_597,sK65(U_599)) ),
inference(clausify,[status(thm)],[f_163_4]) ).
fof(f_164_1,plain,
! [A,B,C] :
( B = C
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t9_zfmisc_1]) ).
fof(f_164_2,plain,
! [U_602,U_601,U_600] :
( U_601 = U_600
| singleton(U_602) != unordered_pair(U_601,U_600) ),
inference(variable_rename,[status(thm)],[f_164_1]) ).
cnf(f_164_3,plain,
( U_601 = U_600
| singleton(U_602) != unordered_pair(U_601,U_600) ),
inference(clausify,[status(thm)],[f_164_2]) ).
cnf(f_30_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_30_8]) ).
cnf(f_30_9_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_30_9]) ).
cnf(f_32_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_32_2]) ).
cnf(f_33_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_33_2]) ).
cnf(f_34_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_34_2]) ).
cnf(f_35_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_35_2]) ).
cnf(f_36_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_36_2]) ).
cnf(f_37_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_37_2]) ).
cnf(f_39_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_39_2]) ).
cnf(f_40_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_40_2]) ).
cnf(f_41_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_41_2]) ).
cnf(f_42_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_42_2]) ).
cnf(f_44_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_44_2]) ).
cnf(f_45_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_45_2]) ).
cnf(f_47_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_47_2]) ).
cnf(f_48_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_48_2]) ).
cnf(f_54_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_54_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( unordered_pair(Eq_x_0,Eq_x_1) = unordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( set_union2(Eq_x_0,Eq_x_1) = set_union2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( set_intersection2(Eq_x_0,Eq_x_1) = set_intersection2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( 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,
( sK65(Eq_x_0) = sK65(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_85,axiom,
( sK66(Eq_x_0,Eq_x_1) = sK66(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_86,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_87,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_88,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_89,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_90,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_91,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_92,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_93,axiom,
( are_equipotent(Eq_y_0,Eq_y_1)
| ~ are_equipotent(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU186+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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Sep 19 23:32:20 UTC 2026
% 0.13/0.36 % CPUTime :
% 24.06/24.38 % SZS status Theorem for theBenchmark
% 24.06/24.38 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------