%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU193+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 : n018.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 08:58:25 AM UTC 2026
% Result : Theorem 284.45s 284.71s
% Output : Proof 284.74s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(antisymmetry_r2_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
=> ~ proper_subset(B,A) ),
file('theBenchmark.p',antisymmetry_r2_xboole_0) ).
fof(cc1_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('theBenchmark.p',cc1_relat_1) ).
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d10_relat_1,axiom,
! [A,B] :
( relation(B)
=> ( B = identity_relation(A)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> ( C = D
& in(C,A) ) ) ) ),
file('theBenchmark.p',d10_relat_1) ).
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
fof(d11_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( relation(C)
=> ( C = relation_dom_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),A)
& in(D,B) ) ) ) ) ),
file('theBenchmark.p',d11_relat_1) ).
fof(d1_relat_1,axiom,
! [A] :
( relation(A)
<=> ! [B] :
~ ( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) ) ),
file('theBenchmark.p',d1_relat_1) ).
fof(d1_setfam_1,axiom,
! [A,B] :
( ( A = empty_set
=> ( B = set_meet(A)
<=> B = empty_set ) )
& ( A != empty_set
=> ( B = set_meet(A)
<=> ! [C] :
( in(C,B)
<=> ! [D] :
( in(D,A)
=> in(C,D) ) ) ) ) ),
file('theBenchmark.p',d1_setfam_1) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
fof(d1_zfmisc_1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('theBenchmark.p',d1_zfmisc_1) ).
fof(d2_subset_1,axiom,
! [A,B] :
( ( empty(A)
=> ( element(B,A)
<=> empty(B) ) )
& ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) ) ),
file('theBenchmark.p',d2_subset_1) ).
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('theBenchmark.p',d2_tarski) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('theBenchmark.p',d2_xboole_0) ).
fof(d2_zfmisc_1,axiom,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) ) ) ),
file('theBenchmark.p',d2_zfmisc_1) ).
fof(d3_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(A,B)
<=> ! [C,D] :
( in(ordered_pair(C,D),A)
=> in(ordered_pair(C,D),B) ) ) ) ),
file('theBenchmark.p',d3_relat_1) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(d3_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d3_xboole_0) ).
fof(d4_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('theBenchmark.p',d4_relat_1) ).
fof(d4_subset_1,axiom,
! [A] : cast_to_subset(A) = A,
file('theBenchmark.p',d4_subset_1) ).
fof(d4_tarski,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(D,A)
& in(C,D) ) ) ),
file('theBenchmark.p',d4_tarski) ).
fof(d4_xboole_0,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d4_xboole_0) ).
fof(d5_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('theBenchmark.p',d5_relat_1) ).
fof(d5_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,B) = set_difference(A,B) ),
file('theBenchmark.p',d5_subset_1) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(d6_relat_1,axiom,
! [A] :
( relation(A)
=> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
file('theBenchmark.p',d6_relat_1) ).
fof(d7_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( B = relation_inverse(A)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> in(ordered_pair(D,C),A) ) ) ) ),
file('theBenchmark.p',d7_relat_1) ).
fof(d7_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('theBenchmark.p',d7_xboole_0) ).
fof(d8_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( relation(C)
=> ( C = relation_composition(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) ) ) ) ) ) ),
file('theBenchmark.p',d8_relat_1) ).
fof(d8_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ! [C] :
( element(C,powerset(powerset(A)))
=> ( C = complements_of_subsets(A,B)
<=> ! [D] :
( element(D,powerset(A))
=> ( in(D,C)
<=> in(subset_complement(A,D),B) ) ) ) ) ),
file('theBenchmark.p',d8_setfam_1) ).
fof(d8_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('theBenchmark.p',d8_xboole_0) ).
fof(dt_k1_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k1_relat_1) ).
fof(dt_k1_setfam_1,axiom,
$true,
file('theBenchmark.p',dt_k1_setfam_1) ).
fof(dt_k1_tarski,axiom,
$true,
file('theBenchmark.p',dt_k1_tarski) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(dt_k2_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k2_relat_1) ).
fof(dt_k2_subset_1,axiom,
! [A] : element(cast_to_subset(A),powerset(A)),
file('theBenchmark.p',dt_k2_subset_1) ).
fof(dt_k2_tarski,axiom,
$true,
file('theBenchmark.p',dt_k2_tarski) ).
fof(dt_k2_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k2_xboole_0) ).
fof(dt_k2_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k2_zfmisc_1) ).
fof(dt_k3_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k3_relat_1) ).
fof(dt_k3_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> element(subset_complement(A,B),powerset(A)) ),
file('theBenchmark.p',dt_k3_subset_1) ).
fof(dt_k3_tarski,axiom,
$true,
file('theBenchmark.p',dt_k3_tarski) ).
fof(dt_k3_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k3_xboole_0) ).
fof(dt_k4_relat_1,axiom,
! [A] :
( relation(A)
=> relation(relation_inverse(A)) ),
file('theBenchmark.p',dt_k4_relat_1) ).
fof(dt_k4_tarski,axiom,
$true,
file('theBenchmark.p',dt_k4_tarski) ).
fof(dt_k4_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k4_xboole_0) ).
fof(dt_k5_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(relation_composition(A,B)) ),
file('theBenchmark.p',dt_k5_relat_1) ).
fof(dt_k5_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(union_of_subsets(A,B),powerset(A)) ),
file('theBenchmark.p',dt_k5_setfam_1) ).
fof(dt_k6_relat_1,axiom,
! [A] : relation(identity_relation(A)),
file('theBenchmark.p',dt_k6_relat_1) ).
fof(dt_k6_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(meet_of_subsets(A,B),powerset(A)) ),
file('theBenchmark.p',dt_k6_setfam_1) ).
fof(dt_k6_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> element(subset_difference(A,B,C),powerset(A)) ),
file('theBenchmark.p',dt_k6_subset_1) ).
fof(dt_k7_relat_1,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('theBenchmark.p',dt_k7_relat_1) ).
fof(dt_k7_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(complements_of_subsets(A,B),powerset(powerset(A))) ),
file('theBenchmark.p',dt_k7_setfam_1) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc10_relat_1,axiom,
! [A,B] :
( ( relation(B)
& empty(A) )
=> ( relation(relation_composition(B,A))
& empty(relation_composition(B,A)) ) ),
file('theBenchmark.p',fc10_relat_1) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc1_zfmisc_1,axiom,
! [A,B] : ~ empty(ordered_pair(A,B)),
file('theBenchmark.p',fc1_zfmisc_1) ).
fof(fc2_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(set_union2(A,B)) ),
file('theBenchmark.p',fc2_relat_1) ).
fof(fc2_subset_1,axiom,
! [A] : ~ empty(singleton(A)),
file('theBenchmark.p',fc2_subset_1) ).
fof(fc2_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(A,B)) ),
file('theBenchmark.p',fc2_xboole_0) ).
fof(fc3_subset_1,axiom,
! [A,B] : ~ empty(unordered_pair(A,B)),
file('theBenchmark.p',fc3_subset_1) ).
fof(fc3_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(B,A)) ),
file('theBenchmark.p',fc3_xboole_0) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(fc4_subset_1,axiom,
! [A,B] :
( ( ~ empty(B)
& ~ empty(A) )
=> ~ empty(cartesian_product2(A,B)) ),
file('theBenchmark.p',fc4_subset_1) ).
fof(fc5_relat_1,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_dom(A)) ),
file('theBenchmark.p',fc5_relat_1) ).
fof(fc6_relat_1,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_rng(A)) ),
file('theBenchmark.p',fc6_relat_1) ).
fof(fc7_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_dom(A))
& empty(relation_dom(A)) ) ),
file('theBenchmark.p',fc7_relat_1) ).
fof(fc8_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_rng(A))
& empty(relation_rng(A)) ) ),
file('theBenchmark.p',fc8_relat_1) ).
fof(fc9_relat_1,axiom,
! [A,B] :
( ( relation(B)
& empty(A) )
=> ( relation(relation_composition(A,B))
& empty(relation_composition(A,B)) ) ),
file('theBenchmark.p',fc9_relat_1) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('theBenchmark.p',idempotence_k3_xboole_0) ).
fof(involutiveness_k3_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,subset_complement(A,B)) = B ),
file('theBenchmark.p',involutiveness_k3_subset_1) ).
fof(involutiveness_k4_relat_1,axiom,
! [A] :
( relation(A)
=> relation_inverse(relation_inverse(A)) = A ),
file('theBenchmark.p',involutiveness_k4_relat_1) ).
fof(involutiveness_k7_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> complements_of_subsets(A,complements_of_subsets(A,B)) = B ),
file('theBenchmark.p',involutiveness_k7_setfam_1) ).
fof(irreflexivity_r2_xboole_0,axiom,
! [A,B] : ~ proper_subset(A,A),
file('theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(l1_zfmisc_1,lemma,
! [A] : singleton(A) != empty_set,
file('theBenchmark.p',l1_zfmisc_1) ).
fof(l23_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('theBenchmark.p',l23_zfmisc_1) ).
fof(l25_zfmisc_1,lemma,
! [A,B] :
~ ( in(A,B)
& disjoint(singleton(A),B) ),
file('theBenchmark.p',l25_zfmisc_1) ).
fof(l28_zfmisc_1,lemma,
! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
file('theBenchmark.p',l28_zfmisc_1) ).
fof(l2_zfmisc_1,lemma,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('theBenchmark.p',l2_zfmisc_1) ).
fof(l32_xboole_1,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',l32_xboole_1) ).
fof(l3_subset_1,lemma,
! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( in(C,B)
=> in(C,A) ) ),
file('theBenchmark.p',l3_subset_1) ).
fof(l3_zfmisc_1,lemma,
! [A,B,C] :
( subset(A,B)
=> ( subset(A,set_difference(B,singleton(C)))
| in(C,A) ) ),
file('theBenchmark.p',l3_zfmisc_1) ).
fof(l4_zfmisc_1,lemma,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',l4_zfmisc_1) ).
fof(l50_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
file('theBenchmark.p',l50_zfmisc_1) ).
fof(l55_zfmisc_1,lemma,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('theBenchmark.p',l55_zfmisc_1) ).
fof(l71_subset_1,lemma,
! [A,B] :
( ! [C] :
( in(C,A)
=> in(C,B) )
=> element(A,powerset(B)) ),
file('theBenchmark.p',l71_subset_1) ).
fof(rc1_relat_1,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('theBenchmark.p',rc1_relat_1) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc1_subset_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_relat_1,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('theBenchmark.p',rc2_relat_1) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(redefinition_k5_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> union_of_subsets(A,B) = union(B) ),
file('theBenchmark.p',redefinition_k5_setfam_1) ).
fof(redefinition_k6_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> meet_of_subsets(A,B) = set_meet(B) ),
file('theBenchmark.p',redefinition_k6_setfam_1) ).
fof(redefinition_k6_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> subset_difference(A,B,C) = set_difference(B,C) ),
file('theBenchmark.p',redefinition_k6_subset_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t106_zfmisc_1,lemma,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('theBenchmark.p',t106_zfmisc_1) ).
fof(t10_zfmisc_1,lemma,
! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
file('theBenchmark.p',t10_zfmisc_1) ).
fof(t118_zfmisc_1,lemma,
! [A,B,C] :
( subset(A,B)
=> ( subset(cartesian_product2(C,A),cartesian_product2(C,B))
& subset(cartesian_product2(A,C),cartesian_product2(B,C)) ) ),
file('theBenchmark.p',t118_zfmisc_1) ).
fof(t119_zfmisc_1,lemma,
! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('theBenchmark.p',t119_zfmisc_1) ).
fof(t12_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
file('theBenchmark.p',t12_xboole_1) ).
fof(t136_zfmisc_1,lemma,
! [A] :
? [B] :
( ! [C] :
~ ( ~ in(C,B)
& ~ are_equipotent(C,B)
& subset(C,B) )
& ! [C] :
( in(C,B)
=> in(powerset(C),B) )
& ! [C,D] :
( ( subset(D,C)
& in(C,B) )
=> in(D,B) )
& in(A,B) ),
file('theBenchmark.p',t136_zfmisc_1) ).
fof(t17_xboole_1,lemma,
! [A,B] : subset(set_intersection2(A,B),A),
file('theBenchmark.p',t17_xboole_1) ).
fof(t19_xboole_1,lemma,
! [A,B,C] :
( ( subset(A,C)
& subset(A,B) )
=> subset(A,set_intersection2(B,C)) ),
file('theBenchmark.p',t19_xboole_1) ).
fof(t1_boole,axiom,
! [A] : set_union2(A,empty_set) = A,
file('theBenchmark.p',t1_boole) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t1_xboole_1,lemma,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('theBenchmark.p',t1_xboole_1) ).
fof(t1_zfmisc_1,lemma,
powerset(empty_set) = singleton(empty_set),
file('theBenchmark.p',t1_zfmisc_1) ).
fof(t20_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_rng(C))
& in(A,relation_dom(C)) ) ) ),
file('theBenchmark.p',t20_relat_1) ).
fof(t21_relat_1,lemma,
! [A] :
( relation(A)
=> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))) ),
file('theBenchmark.p',t21_relat_1) ).
fof(t25_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(A,B)
=> ( subset(relation_rng(A),relation_rng(B))
& subset(relation_dom(A),relation_dom(B)) ) ) ) ),
file('theBenchmark.p',t25_relat_1) ).
fof(t26_xboole_1,lemma,
! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ),
file('theBenchmark.p',t26_xboole_1) ).
fof(t28_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('theBenchmark.p',t28_xboole_1) ).
fof(t2_boole,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
file('theBenchmark.p',t2_boole) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('theBenchmark.p',t2_tarski) ).
fof(t2_xboole_1,lemma,
! [A] : subset(empty_set,A),
file('theBenchmark.p',t2_xboole_1) ).
fof(t30_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_field(C))
& in(A,relation_field(C)) ) ) ),
file('theBenchmark.p',t30_relat_1) ).
fof(t33_xboole_1,lemma,
! [A,B,C] :
( subset(A,B)
=> subset(set_difference(A,C),set_difference(B,C)) ),
file('theBenchmark.p',t33_xboole_1) ).
fof(t33_zfmisc_1,lemma,
! [A,B,C,D] :
( ordered_pair(A,B) = ordered_pair(C,D)
=> ( B = D
& A = C ) ),
file('theBenchmark.p',t33_zfmisc_1) ).
fof(t36_xboole_1,lemma,
! [A,B] : subset(set_difference(A,B),A),
file('theBenchmark.p',t36_xboole_1) ).
fof(t37_relat_1,lemma,
! [A] :
( relation(A)
=> ( relation_dom(A) = relation_rng(relation_inverse(A))
& relation_rng(A) = relation_dom(relation_inverse(A)) ) ),
file('theBenchmark.p',t37_relat_1) ).
fof(t37_xboole_1,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',t37_xboole_1) ).
fof(t37_zfmisc_1,lemma,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('theBenchmark.p',t37_zfmisc_1) ).
fof(t38_zfmisc_1,lemma,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(B,C)
& in(A,C) ) ),
file('theBenchmark.p',t38_zfmisc_1) ).
fof(t39_xboole_1,lemma,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
file('theBenchmark.p',t39_xboole_1) ).
fof(t39_zfmisc_1,lemma,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',t39_zfmisc_1) ).
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
file('theBenchmark.p',t3_boole) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t3_xboole_0,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t3_xboole_0) ).
fof(t3_xboole_1,lemma,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('theBenchmark.p',t3_xboole_1) ).
fof(t40_xboole_1,lemma,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
file('theBenchmark.p',t40_xboole_1) ).
fof(t43_subset_1,lemma,
! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,powerset(A))
=> ( disjoint(B,C)
<=> subset(B,subset_complement(A,C)) ) ) ),
file('theBenchmark.p',t43_subset_1) ).
fof(t44_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> subset(relation_dom(relation_composition(A,B)),relation_dom(A)) ) ),
file('theBenchmark.p',t44_relat_1) ).
fof(t45_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> subset(relation_rng(relation_composition(A,B)),relation_rng(B)) ) ),
file('theBenchmark.p',t45_relat_1) ).
fof(t45_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> B = set_union2(A,set_difference(B,A)) ),
file('theBenchmark.p',t45_xboole_1) ).
fof(t46_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(relation_rng(A),relation_dom(B))
=> relation_dom(relation_composition(A,B)) = relation_dom(A) ) ) ),
file('theBenchmark.p',t46_relat_1) ).
fof(t46_setfam_1,lemma,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ~ ( complements_of_subsets(A,B) = empty_set
& B != empty_set ) ),
file('theBenchmark.p',t46_setfam_1) ).
fof(t46_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('theBenchmark.p',t46_zfmisc_1) ).
fof(t47_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(relation_dom(A),relation_rng(B))
=> relation_rng(relation_composition(B,A)) = relation_rng(A) ) ) ),
file('theBenchmark.p',t47_relat_1) ).
fof(t47_setfam_1,lemma,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> subset_difference(A,cast_to_subset(A),union_of_subsets(A,B)) = meet_of_subsets(A,complements_of_subsets(A,B)) ) ),
file('theBenchmark.p',t47_setfam_1) ).
fof(t48_setfam_1,lemma,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> union_of_subsets(A,complements_of_subsets(A,B)) = subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B)) ) ),
file('theBenchmark.p',t48_setfam_1) ).
fof(t48_xboole_1,lemma,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
file('theBenchmark.p',t48_xboole_1) ).
fof(t4_boole,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
file('theBenchmark.p',t4_boole) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t4_xboole_0,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t4_xboole_0) ).
fof(t50_subset_1,lemma,
! [A] :
( A != empty_set
=> ! [B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,A)
=> ( ~ in(C,B)
=> in(C,subset_complement(A,B)) ) ) ) ),
file('theBenchmark.p',t50_subset_1) ).
fof(t54_subset_1,lemma,
! [A,B,C] :
( element(C,powerset(A))
=> ~ ( in(B,C)
& in(B,subset_complement(A,C)) ) ),
file('theBenchmark.p',t54_subset_1) ).
fof(t56_relat_1,lemma,
! [A] :
( relation(A)
=> ( ! [B,C] : ~ in(ordered_pair(B,C),A)
=> A = empty_set ) ),
file('theBenchmark.p',t56_relat_1) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t60_relat_1,lemma,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('theBenchmark.p',t60_relat_1) ).
fof(t60_xboole_1,lemma,
! [A,B] :
~ ( proper_subset(B,A)
& subset(A,B) ),
file('theBenchmark.p',t60_xboole_1) ).
fof(t63_xboole_1,lemma,
! [A,B,C] :
( ( disjoint(B,C)
& subset(A,B) )
=> disjoint(A,C) ),
file('theBenchmark.p',t63_xboole_1) ).
fof(t64_relat_1,lemma,
! [A] :
( relation(A)
=> ( ( relation_rng(A) = empty_set
| relation_dom(A) = empty_set )
=> A = empty_set ) ),
file('theBenchmark.p',t64_relat_1) ).
fof(t65_relat_1,lemma,
! [A] :
( relation(A)
=> ( relation_dom(A) = empty_set
<=> relation_rng(A) = empty_set ) ),
file('theBenchmark.p',t65_relat_1) ).
fof(t65_zfmisc_1,lemma,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('theBenchmark.p',t65_zfmisc_1) ).
fof(t69_enumset1,lemma,
! [A] : unordered_pair(A,A) = singleton(A),
file('theBenchmark.p',t69_enumset1) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t6_zfmisc_1,lemma,
! [A,B] :
( subset(singleton(A),singleton(B))
=> A = B ),
file('theBenchmark.p',t6_zfmisc_1) ).
fof(t71_relat_1,lemma,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
file('theBenchmark.p',t71_relat_1) ).
fof(t74_relat_1,lemma,
! [A,B,C,D] :
( relation(D)
=> ( in(ordered_pair(A,B),relation_composition(identity_relation(C),D))
<=> ( in(ordered_pair(A,B),D)
& in(A,C) ) ) ),
file('theBenchmark.p',t74_relat_1) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t7_xboole_1,lemma,
! [A,B] : subset(A,set_union2(A,B)),
file('theBenchmark.p',t7_xboole_1) ).
fof(t83_xboole_1,lemma,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('theBenchmark.p',t83_xboole_1) ).
fof(t86_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_dom(relation_dom_restriction(C,B)))
<=> ( in(A,relation_dom(C))
& in(A,B) ) ) ),
file('theBenchmark.p',t86_relat_1) ).
fof(t88_relat_1,conjecture,
! [A,B] :
( relation(B)
=> subset(relation_dom_restriction(B,A),B) ),
file('theBenchmark.p',t88_relat_1) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(t8_xboole_1,lemma,
! [A,B,C] :
( ( subset(C,B)
& subset(A,B) )
=> subset(set_union2(A,C),B) ),
file('theBenchmark.p',t8_xboole_1) ).
fof(t8_zfmisc_1,lemma,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ),
file('theBenchmark.p',t8_zfmisc_1) ).
fof(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] :
( ( ( B = identity_relation(A)
| ? [C,D] :
( ( ~ in(ordered_pair(C,D),B)
& C = D
& in(C,A) )
| ( ( C != D
| ~ in(C,A) )
& in(ordered_pair(C,D),B) ) ) )
& ( ! [C,D] :
( ( in(ordered_pair(C,D),B)
| C != D
| ~ in(C,A) )
& ( ( C = D
& in(C,A) )
| ~ in(ordered_pair(C,D),B) ) )
| B != identity_relation(A) ) )
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[d10_relat_1]) ).
fof(f_7_2,plain,
! [U_16,U_15] :
( ( ( U_15 = identity_relation(U_16)
| ? [U_14,U_13] :
( ( ~ in(ordered_pair(U_14,U_13),U_15)
& U_14 = U_13
& in(U_14,U_16) )
| ( ( U_14 != U_13
| ~ in(U_14,U_16) )
& in(ordered_pair(U_14,U_13),U_15) ) ) )
& ( ! [U_12,U_11] :
( ( in(ordered_pair(U_12,U_11),U_15)
| U_12 != U_11
| ~ in(U_12,U_16) )
& ( ( U_12 = U_11
& in(U_12,U_16) )
| ~ in(ordered_pair(U_12,U_11),U_15) ) )
| U_15 != identity_relation(U_16) ) )
| ~ relation(U_15) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_16,U_15] :
( ( ( U_15 = identity_relation(U_16)
| ? [U_24,U_22] :
( ~ in(ordered_pair(U_24,U_22),U_15)
& U_24 = U_22
& in(U_24,U_16) )
| ? [U_23,U_21] :
( ( U_23 != U_21
| ~ in(U_23,U_16) )
& in(ordered_pair(U_23,U_21),U_15) ) )
& ( ( ! [U_20,U_18] :
( in(ordered_pair(U_20,U_18),U_15)
| U_20 != U_18
| ~ in(U_20,U_16) )
& ! [U_19,U_17] :
( ( U_19 = U_17
& in(U_19,U_16) )
| ~ in(ordered_pair(U_19,U_17),U_15) ) )
| U_15 != identity_relation(U_16) ) )
| ~ relation(U_15) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
! [U_16,U_15] :
( ( ( U_15 = identity_relation(U_16)
| ? [U_24,U_22] :
( ~ in(ordered_pair(U_24,U_22),U_15)
& U_24 = U_22
& in(U_24,U_16) )
| ? [U_21] :
( ( sK1(U_16,U_15) != U_21
| ~ in(sK1(U_16,U_15),U_16) )
& in(ordered_pair(sK1(U_16,U_15),U_21),U_15) ) )
& ( ( ! [U_20,U_18] :
( in(ordered_pair(U_20,U_18),U_15)
| U_20 != U_18
| ~ in(U_20,U_16) )
& ! [U_19,U_17] :
( ( U_19 = U_17
& in(U_19,U_16) )
| ~ in(ordered_pair(U_19,U_17),U_15) ) )
| U_15 != identity_relation(U_16) ) )
| ~ relation(U_15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_23,sK1(U_16,U_15))],[f_7_3]) ).
fof(f_7_5,plain,
! [U_16,U_15] :
( ( ( U_15 = identity_relation(U_16)
| ? [U_24,U_22] :
( ~ in(ordered_pair(U_24,U_22),U_15)
& U_24 = U_22
& in(U_24,U_16) )
| ( ( sK1(U_16,U_15) != sK2(U_16,U_15)
| ~ in(sK1(U_16,U_15),U_16) )
& in(ordered_pair(sK1(U_16,U_15),sK2(U_16,U_15)),U_15) ) )
& ( ( ! [U_20,U_18] :
( in(ordered_pair(U_20,U_18),U_15)
| U_20 != U_18
| ~ in(U_20,U_16) )
& ! [U_19,U_17] :
( ( U_19 = U_17
& in(U_19,U_16) )
| ~ in(ordered_pair(U_19,U_17),U_15) ) )
| U_15 != identity_relation(U_16) ) )
| ~ relation(U_15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_21,sK2(U_16,U_15))],[f_7_4]) ).
fof(f_7_6,plain,
! [U_16,U_15] :
( ( ( U_15 = identity_relation(U_16)
| ? [U_22] :
( ~ in(ordered_pair(sK3(U_16,U_15),U_22),U_15)
& sK3(U_16,U_15) = U_22
& in(sK3(U_16,U_15),U_16) )
| ( ( sK1(U_16,U_15) != sK2(U_16,U_15)
| ~ in(sK1(U_16,U_15),U_16) )
& in(ordered_pair(sK1(U_16,U_15),sK2(U_16,U_15)),U_15) ) )
& ( ( ! [U_20,U_18] :
( in(ordered_pair(U_20,U_18),U_15)
| U_20 != U_18
| ~ in(U_20,U_16) )
& ! [U_19,U_17] :
( ( U_19 = U_17
& in(U_19,U_16) )
| ~ in(ordered_pair(U_19,U_17),U_15) ) )
| U_15 != identity_relation(U_16) ) )
| ~ relation(U_15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_24,sK3(U_16,U_15))],[f_7_5]) ).
fof(f_7_7,plain,
! [U_16,U_15] :
( ( ( U_15 = identity_relation(U_16)
| ( ~ in(ordered_pair(sK3(U_16,U_15),sK4(U_16,U_15)),U_15)
& sK3(U_16,U_15) = sK4(U_16,U_15)
& in(sK3(U_16,U_15),U_16) )
| ( ( sK1(U_16,U_15) != sK2(U_16,U_15)
| ~ in(sK1(U_16,U_15),U_16) )
& in(ordered_pair(sK1(U_16,U_15),sK2(U_16,U_15)),U_15) ) )
& ( ( ! [U_20,U_18] :
( in(ordered_pair(U_20,U_18),U_15)
| U_20 != U_18
| ~ in(U_20,U_16) )
& ! [U_19,U_17] :
( ( U_19 = U_17
& in(U_19,U_16) )
| ~ in(ordered_pair(U_19,U_17),U_15) ) )
| U_15 != identity_relation(U_16) ) )
| ~ relation(U_15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_22,sK4(U_16,U_15))],[f_7_6]) ).
cnf(f_7_8,plain,
( in(U_19,U_16)
| ~ in(ordered_pair(U_19,U_17),U_15)
| U_15 != identity_relation(U_16)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_9,plain,
( U_19 = U_17
| ~ in(ordered_pair(U_19,U_17),U_15)
| U_15 != identity_relation(U_16)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_10,plain,
( in(ordered_pair(U_20,U_18),U_15)
| U_20 != U_18
| ~ in(U_20,U_16)
| U_15 != identity_relation(U_16)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_11,plain,
( in(sK3(U_16,U_15),U_16)
| in(ordered_pair(sK1(U_16,U_15),sK2(U_16,U_15)),U_15)
| U_15 = identity_relation(U_16)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_12,plain,
( sK3(U_16,U_15) = sK4(U_16,U_15)
| in(ordered_pair(sK1(U_16,U_15),sK2(U_16,U_15)),U_15)
| U_15 = identity_relation(U_16)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_13,plain,
( ~ in(ordered_pair(sK3(U_16,U_15),sK4(U_16,U_15)),U_15)
| in(ordered_pair(sK1(U_16,U_15),sK2(U_16,U_15)),U_15)
| U_15 = identity_relation(U_16)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_14,plain,
( in(sK3(U_16,U_15),U_16)
| sK1(U_16,U_15) != sK2(U_16,U_15)
| ~ in(sK1(U_16,U_15),U_16)
| U_15 = identity_relation(U_16)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_15,plain,
( sK3(U_16,U_15) = sK4(U_16,U_15)
| sK1(U_16,U_15) != sK2(U_16,U_15)
| ~ in(sK1(U_16,U_15),U_16)
| U_15 = identity_relation(U_16)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_16,plain,
( ~ in(ordered_pair(sK3(U_16,U_15),sK4(U_16,U_15)),U_15)
| sK1(U_16,U_15) != sK2(U_16,U_15)
| ~ in(sK1(U_16,U_15),U_16)
| U_15 = identity_relation(U_16)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_7]) ).
fof(f_8_1,plain,
! [A,B] :
( ( A = B
| ~ subset(B,A)
| ~ subset(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(fof_nnf,[status(thm)],[d10_xboole_0]) ).
fof(f_8_2,plain,
! [U_26,U_25] :
( ( U_26 = U_25
| ~ subset(U_25,U_26)
| ~ subset(U_26,U_25) )
& ( ( subset(U_25,U_26)
& subset(U_26,U_25) )
| U_26 != U_25 ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_30,U_28] :
( U_30 = U_28
| ~ subset(U_28,U_30)
| ~ subset(U_30,U_28) )
& ! [U_29,U_27] :
( ( subset(U_27,U_29)
& subset(U_29,U_27) )
| U_29 != U_27 ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( subset(U_29,U_27)
| U_29 != U_27 ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( subset(U_27,U_29)
| U_29 != U_27 ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_6,plain,
( U_30 = U_28
| ~ subset(U_28,U_30)
| ~ subset(U_30,U_28) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [A] :
( ! [B,C] :
( ( ( C = relation_dom_restriction(A,B)
| ? [D,E] :
( ( ~ in(ordered_pair(D,E),C)
& in(ordered_pair(D,E),A)
& in(D,B) )
| ( ( ~ in(ordered_pair(D,E),A)
| ~ in(D,B) )
& in(ordered_pair(D,E),C) ) ) )
& ( ! [D,E] :
( ( in(ordered_pair(D,E),C)
| ~ in(ordered_pair(D,E),A)
| ~ in(D,B) )
& ( ( in(ordered_pair(D,E),A)
& in(D,B) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_dom_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d11_relat_1]) ).
fof(f_9_2,plain,
! [U_37] :
( ! [U_36,U_35] :
( ( ( U_35 = relation_dom_restriction(U_37,U_36)
| ? [U_34,U_33] :
( ( ~ in(ordered_pair(U_34,U_33),U_35)
& in(ordered_pair(U_34,U_33),U_37)
& in(U_34,U_36) )
| ( ( ~ in(ordered_pair(U_34,U_33),U_37)
| ~ in(U_34,U_36) )
& in(ordered_pair(U_34,U_33),U_35) ) ) )
& ( ! [U_32,U_31] :
( ( in(ordered_pair(U_32,U_31),U_35)
| ~ in(ordered_pair(U_32,U_31),U_37)
| ~ in(U_32,U_36) )
& ( ( in(ordered_pair(U_32,U_31),U_37)
& in(U_32,U_36) )
| ~ in(ordered_pair(U_32,U_31),U_35) ) )
| U_35 != relation_dom_restriction(U_37,U_36) ) )
| ~ relation(U_35) )
| ~ relation(U_37) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_37] :
( ! [U_36,U_35] :
( ( ( U_35 = relation_dom_restriction(U_37,U_36)
| ? [U_45,U_43] :
( ~ in(ordered_pair(U_45,U_43),U_35)
& in(ordered_pair(U_45,U_43),U_37)
& in(U_45,U_36) )
| ? [U_44,U_42] :
( ( ~ in(ordered_pair(U_44,U_42),U_37)
| ~ in(U_44,U_36) )
& in(ordered_pair(U_44,U_42),U_35) ) )
& ( ( ! [U_41,U_39] :
( in(ordered_pair(U_41,U_39),U_35)
| ~ in(ordered_pair(U_41,U_39),U_37)
| ~ in(U_41,U_36) )
& ! [U_40,U_38] :
( ( in(ordered_pair(U_40,U_38),U_37)
& in(U_40,U_36) )
| ~ in(ordered_pair(U_40,U_38),U_35) ) )
| U_35 != relation_dom_restriction(U_37,U_36) ) )
| ~ relation(U_35) )
| ~ relation(U_37) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
fof(f_9_4,plain,
! [U_37] :
( ! [U_36,U_35] :
( ( ( U_35 = relation_dom_restriction(U_37,U_36)
| ? [U_45,U_43] :
( ~ in(ordered_pair(U_45,U_43),U_35)
& in(ordered_pair(U_45,U_43),U_37)
& in(U_45,U_36) )
| ? [U_42] :
( ( ~ in(ordered_pair(sK5(U_37,U_36,U_35),U_42),U_37)
| ~ in(sK5(U_37,U_36,U_35),U_36) )
& in(ordered_pair(sK5(U_37,U_36,U_35),U_42),U_35) ) )
& ( ( ! [U_41,U_39] :
( in(ordered_pair(U_41,U_39),U_35)
| ~ in(ordered_pair(U_41,U_39),U_37)
| ~ in(U_41,U_36) )
& ! [U_40,U_38] :
( ( in(ordered_pair(U_40,U_38),U_37)
& in(U_40,U_36) )
| ~ in(ordered_pair(U_40,U_38),U_35) ) )
| U_35 != relation_dom_restriction(U_37,U_36) ) )
| ~ relation(U_35) )
| ~ relation(U_37) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_44,sK5(U_37,U_36,U_35))],[f_9_3]) ).
fof(f_9_5,plain,
! [U_37] :
( ! [U_36,U_35] :
( ( ( U_35 = relation_dom_restriction(U_37,U_36)
| ? [U_45,U_43] :
( ~ in(ordered_pair(U_45,U_43),U_35)
& in(ordered_pair(U_45,U_43),U_37)
& in(U_45,U_36) )
| ( ( ~ in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_37)
| ~ in(sK5(U_37,U_36,U_35),U_36) )
& in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_35) ) )
& ( ( ! [U_41,U_39] :
( in(ordered_pair(U_41,U_39),U_35)
| ~ in(ordered_pair(U_41,U_39),U_37)
| ~ in(U_41,U_36) )
& ! [U_40,U_38] :
( ( in(ordered_pair(U_40,U_38),U_37)
& in(U_40,U_36) )
| ~ in(ordered_pair(U_40,U_38),U_35) ) )
| U_35 != relation_dom_restriction(U_37,U_36) ) )
| ~ relation(U_35) )
| ~ relation(U_37) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_42,sK6(U_37,U_36,U_35))],[f_9_4]) ).
fof(f_9_6,plain,
! [U_37] :
( ! [U_36,U_35] :
( ( ( U_35 = relation_dom_restriction(U_37,U_36)
| ? [U_43] :
( ~ in(ordered_pair(sK7(U_37,U_36,U_35),U_43),U_35)
& in(ordered_pair(sK7(U_37,U_36,U_35),U_43),U_37)
& in(sK7(U_37,U_36,U_35),U_36) )
| ( ( ~ in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_37)
| ~ in(sK5(U_37,U_36,U_35),U_36) )
& in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_35) ) )
& ( ( ! [U_41,U_39] :
( in(ordered_pair(U_41,U_39),U_35)
| ~ in(ordered_pair(U_41,U_39),U_37)
| ~ in(U_41,U_36) )
& ! [U_40,U_38] :
( ( in(ordered_pair(U_40,U_38),U_37)
& in(U_40,U_36) )
| ~ in(ordered_pair(U_40,U_38),U_35) ) )
| U_35 != relation_dom_restriction(U_37,U_36) ) )
| ~ relation(U_35) )
| ~ relation(U_37) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_45,sK7(U_37,U_36,U_35))],[f_9_5]) ).
fof(f_9_7,plain,
! [U_37] :
( ! [U_36,U_35] :
( ( ( U_35 = relation_dom_restriction(U_37,U_36)
| ( ~ in(ordered_pair(sK7(U_37,U_36,U_35),sK8(U_37,U_36,U_35)),U_35)
& in(ordered_pair(sK7(U_37,U_36,U_35),sK8(U_37,U_36,U_35)),U_37)
& in(sK7(U_37,U_36,U_35),U_36) )
| ( ( ~ in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_37)
| ~ in(sK5(U_37,U_36,U_35),U_36) )
& in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_35) ) )
& ( ( ! [U_41,U_39] :
( in(ordered_pair(U_41,U_39),U_35)
| ~ in(ordered_pair(U_41,U_39),U_37)
| ~ in(U_41,U_36) )
& ! [U_40,U_38] :
( ( in(ordered_pair(U_40,U_38),U_37)
& in(U_40,U_36) )
| ~ in(ordered_pair(U_40,U_38),U_35) ) )
| U_35 != relation_dom_restriction(U_37,U_36) ) )
| ~ relation(U_35) )
| ~ relation(U_37) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_43,sK8(U_37,U_36,U_35))],[f_9_6]) ).
cnf(f_9_8,plain,
( in(U_40,U_36)
| ~ in(ordered_pair(U_40,U_38),U_35)
| U_35 != relation_dom_restriction(U_37,U_36)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_9,plain,
( in(ordered_pair(U_40,U_38),U_37)
| ~ in(ordered_pair(U_40,U_38),U_35)
| U_35 != relation_dom_restriction(U_37,U_36)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_10,plain,
( in(ordered_pair(U_41,U_39),U_35)
| ~ in(ordered_pair(U_41,U_39),U_37)
| ~ in(U_41,U_36)
| U_35 != relation_dom_restriction(U_37,U_36)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_11,plain,
( in(sK7(U_37,U_36,U_35),U_36)
| in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_35)
| U_35 = relation_dom_restriction(U_37,U_36)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_12,plain,
( in(ordered_pair(sK7(U_37,U_36,U_35),sK8(U_37,U_36,U_35)),U_37)
| in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_35)
| U_35 = relation_dom_restriction(U_37,U_36)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_13,plain,
( ~ in(ordered_pair(sK7(U_37,U_36,U_35),sK8(U_37,U_36,U_35)),U_35)
| in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_35)
| U_35 = relation_dom_restriction(U_37,U_36)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_14,plain,
( in(sK7(U_37,U_36,U_35),U_36)
| ~ in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_37)
| ~ in(sK5(U_37,U_36,U_35),U_36)
| U_35 = relation_dom_restriction(U_37,U_36)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_15,plain,
( in(ordered_pair(sK7(U_37,U_36,U_35),sK8(U_37,U_36,U_35)),U_37)
| ~ in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_37)
| ~ in(sK5(U_37,U_36,U_35),U_36)
| U_35 = relation_dom_restriction(U_37,U_36)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_16,plain,
( ~ in(ordered_pair(sK7(U_37,U_36,U_35),sK8(U_37,U_36,U_35)),U_35)
| ~ in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_37)
| ~ in(sK5(U_37,U_36,U_35),U_36)
| U_35 = relation_dom_restriction(U_37,U_36)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_7]) ).
fof(f_10_1,plain,
! [A] :
( ( relation(A)
| ? [B] :
( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) ) )
& ( ! [B] :
( ? [C,D] : B = ordered_pair(C,D)
| ~ in(B,A) )
| ~ relation(A) ) ),
inference(fof_nnf,[status(thm)],[d1_relat_1]) ).
fof(f_10_2,plain,
! [U_52] :
( ( relation(U_52)
| ? [U_51] :
( ! [U_50,U_49] : U_51 != ordered_pair(U_50,U_49)
& in(U_51,U_52) ) )
& ( ! [U_48] :
( ? [U_47,U_46] : U_48 = ordered_pair(U_47,U_46)
| ~ in(U_48,U_52) )
| ~ relation(U_52) ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_54] :
( relation(U_54)
| ? [U_51] :
( ! [U_50,U_49] : U_51 != ordered_pair(U_50,U_49)
& in(U_51,U_54) ) )
& ! [U_53] :
( ! [U_48] :
( ? [U_47,U_46] : U_48 = ordered_pair(U_47,U_46)
| ~ in(U_48,U_53) )
| ~ relation(U_53) ) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
fof(f_10_4,plain,
( ! [U_54] :
( relation(U_54)
| ? [U_51] :
( ! [U_50,U_49] : U_51 != ordered_pair(U_50,U_49)
& in(U_51,U_54) ) )
& ! [U_53] :
( ! [U_48] :
( ? [U_46] : U_48 = ordered_pair(sK9(U_53,U_48),U_46)
| ~ in(U_48,U_53) )
| ~ relation(U_53) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_47,sK9(U_53,U_48))],[f_10_3]) ).
fof(f_10_5,plain,
( ! [U_54] :
( relation(U_54)
| ? [U_51] :
( ! [U_50,U_49] : U_51 != ordered_pair(U_50,U_49)
& in(U_51,U_54) ) )
& ! [U_53] :
( ! [U_48] :
( U_48 = ordered_pair(sK9(U_53,U_48),sK10(U_53,U_48))
| ~ in(U_48,U_53) )
| ~ relation(U_53) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_46,sK10(U_53,U_48))],[f_10_4]) ).
fof(f_10_6,plain,
( ! [U_54] :
( relation(U_54)
| ( ! [U_50,U_49] : sK11(U_54) != ordered_pair(U_50,U_49)
& in(sK11(U_54),U_54) ) )
& ! [U_53] :
( ! [U_48] :
( U_48 = ordered_pair(sK9(U_53,U_48),sK10(U_53,U_48))
| ~ in(U_48,U_53) )
| ~ relation(U_53) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_51,sK11(U_54))],[f_10_5]) ).
cnf(f_10_7,plain,
( U_48 = ordered_pair(sK9(U_53,U_48),sK10(U_53,U_48))
| ~ in(U_48,U_53)
| ~ relation(U_53) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_8,plain,
( in(sK11(U_54),U_54)
| relation(U_54) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_9,plain,
( sK11(U_54) != ordered_pair(U_50,U_49)
| relation(U_54) ),
inference(clausify,[status(thm)],[f_10_6]) ).
fof(f_11_1,plain,
! [A,B] :
( ( ( ( B = set_meet(A)
| B != empty_set )
& ( B = empty_set
| B != set_meet(A) ) )
| A != empty_set )
& ( ( ( B = set_meet(A)
| ? [C] :
( ( ~ in(C,B)
& ! [D] :
( in(C,D)
| ~ in(D,A) ) )
| ( ? [D] :
( ~ in(C,D)
& in(D,A) )
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ? [D] :
( ~ in(C,D)
& in(D,A) ) )
& ( ! [D] :
( in(C,D)
| ~ in(D,A) )
| ~ in(C,B) ) )
| B != set_meet(A) ) )
| A = empty_set ) ),
inference(fof_nnf,[status(thm)],[d1_setfam_1]) ).
fof(f_11_2,plain,
! [U_62,U_61] :
( ( ( ( U_61 = set_meet(U_62)
| U_61 != empty_set )
& ( U_61 = empty_set
| U_61 != set_meet(U_62) ) )
| U_62 != empty_set )
& ( ( ( U_61 = set_meet(U_62)
| ? [U_60] :
( ( ~ in(U_60,U_61)
& ! [U_59] :
( in(U_60,U_59)
| ~ in(U_59,U_62) ) )
| ( ? [U_58] :
( ~ in(U_60,U_58)
& in(U_58,U_62) )
& in(U_60,U_61) ) ) )
& ( ! [U_57] :
( ( in(U_57,U_61)
| ? [U_56] :
( ~ in(U_57,U_56)
& in(U_56,U_62) ) )
& ( ! [U_55] :
( in(U_57,U_55)
| ~ in(U_55,U_62) )
| ~ in(U_57,U_61) ) )
| U_61 != set_meet(U_62) ) )
| U_62 = empty_set ) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
( ! [U_74] :
( ( ! [U_72] :
( U_72 = set_meet(U_74)
| U_72 != empty_set )
& ! [U_71] :
( U_71 = empty_set
| U_71 != set_meet(U_74) ) )
| U_74 != empty_set )
& ! [U_73] :
( ( ! [U_70] :
( U_70 = set_meet(U_73)
| ? [U_66] :
( ~ in(U_66,U_70)
& ! [U_59] :
( in(U_66,U_59)
| ~ in(U_59,U_73) ) )
| ? [U_65] :
( ? [U_58] :
( ~ in(U_65,U_58)
& in(U_58,U_73) )
& in(U_65,U_70) ) )
& ! [U_69] :
( ( ! [U_64] :
( in(U_64,U_69)
| ? [U_56] :
( ~ in(U_64,U_56)
& in(U_56,U_73) ) )
& ! [U_63] :
( ! [U_55] :
( in(U_63,U_55)
| ~ in(U_55,U_73) )
| ~ in(U_63,U_69) ) )
| U_69 != set_meet(U_73) ) )
| U_73 = empty_set ) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
fof(f_11_4,plain,
( ! [U_74] :
( ( ! [U_72] :
( U_72 = set_meet(U_74)
| U_72 != empty_set )
& ! [U_71] :
( U_71 = empty_set
| U_71 != set_meet(U_74) ) )
| U_74 != empty_set )
& ! [U_73] :
( ( ! [U_70] :
( U_70 = set_meet(U_73)
| ? [U_66] :
( ~ in(U_66,U_70)
& ! [U_59] :
( in(U_66,U_59)
| ~ in(U_59,U_73) ) )
| ? [U_65] :
( ? [U_58] :
( ~ in(U_65,U_58)
& in(U_58,U_73) )
& in(U_65,U_70) ) )
& ! [U_69] :
( ( ! [U_64] :
( in(U_64,U_69)
| ( ~ in(U_64,sK12(U_73,U_69,U_64))
& in(sK12(U_73,U_69,U_64),U_73) ) )
& ! [U_63] :
( ! [U_55] :
( in(U_63,U_55)
| ~ in(U_55,U_73) )
| ~ in(U_63,U_69) ) )
| U_69 != set_meet(U_73) ) )
| U_73 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_56,sK12(U_73,U_69,U_64))],[f_11_3]) ).
fof(f_11_5,plain,
( ! [U_74] :
( ( ! [U_72] :
( U_72 = set_meet(U_74)
| U_72 != empty_set )
& ! [U_71] :
( U_71 = empty_set
| U_71 != set_meet(U_74) ) )
| U_74 != empty_set )
& ! [U_73] :
( ( ! [U_70] :
( U_70 = set_meet(U_73)
| ? [U_66] :
( ~ in(U_66,U_70)
& ! [U_59] :
( in(U_66,U_59)
| ~ in(U_59,U_73) ) )
| ( ? [U_58] :
( ~ in(sK13(U_73,U_70),U_58)
& in(U_58,U_73) )
& in(sK13(U_73,U_70),U_70) ) )
& ! [U_69] :
( ( ! [U_64] :
( in(U_64,U_69)
| ( ~ in(U_64,sK12(U_73,U_69,U_64))
& in(sK12(U_73,U_69,U_64),U_73) ) )
& ! [U_63] :
( ! [U_55] :
( in(U_63,U_55)
| ~ in(U_55,U_73) )
| ~ in(U_63,U_69) ) )
| U_69 != set_meet(U_73) ) )
| U_73 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_65,sK13(U_73,U_70))],[f_11_4]) ).
fof(f_11_6,plain,
( ! [U_74] :
( ( ! [U_72] :
( U_72 = set_meet(U_74)
| U_72 != empty_set )
& ! [U_71] :
( U_71 = empty_set
| U_71 != set_meet(U_74) ) )
| U_74 != empty_set )
& ! [U_73] :
( ( ! [U_70] :
( U_70 = set_meet(U_73)
| ? [U_66] :
( ~ in(U_66,U_70)
& ! [U_59] :
( in(U_66,U_59)
| ~ in(U_59,U_73) ) )
| ( ~ in(sK13(U_73,U_70),sK14(U_73,U_70))
& in(sK14(U_73,U_70),U_73)
& in(sK13(U_73,U_70),U_70) ) )
& ! [U_69] :
( ( ! [U_64] :
( in(U_64,U_69)
| ( ~ in(U_64,sK12(U_73,U_69,U_64))
& in(sK12(U_73,U_69,U_64),U_73) ) )
& ! [U_63] :
( ! [U_55] :
( in(U_63,U_55)
| ~ in(U_55,U_73) )
| ~ in(U_63,U_69) ) )
| U_69 != set_meet(U_73) ) )
| U_73 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_58,sK14(U_73,U_70))],[f_11_5]) ).
fof(f_11_7,plain,
( ! [U_74] :
( ( ! [U_72] :
( U_72 = set_meet(U_74)
| U_72 != empty_set )
& ! [U_71] :
( U_71 = empty_set
| U_71 != set_meet(U_74) ) )
| U_74 != empty_set )
& ! [U_73] :
( ( ! [U_70] :
( U_70 = set_meet(U_73)
| ( ~ in(sK15(U_73,U_70),U_70)
& ! [U_59] :
( in(sK15(U_73,U_70),U_59)
| ~ in(U_59,U_73) ) )
| ( ~ in(sK13(U_73,U_70),sK14(U_73,U_70))
& in(sK14(U_73,U_70),U_73)
& in(sK13(U_73,U_70),U_70) ) )
& ! [U_69] :
( ( ! [U_64] :
( in(U_64,U_69)
| ( ~ in(U_64,sK12(U_73,U_69,U_64))
& in(sK12(U_73,U_69,U_64),U_73) ) )
& ! [U_63] :
( ! [U_55] :
( in(U_63,U_55)
| ~ in(U_55,U_73) )
| ~ in(U_63,U_69) ) )
| U_69 != set_meet(U_73) ) )
| U_73 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_66,sK15(U_73,U_70))],[f_11_6]) ).
cnf(f_11_8,plain,
( in(U_63,U_55)
| ~ in(U_55,U_73)
| ~ in(U_63,U_69)
| U_69 != set_meet(U_73)
| U_73 = empty_set ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_9,plain,
( in(sK12(U_73,U_69,U_64),U_73)
| in(U_64,U_69)
| U_69 != set_meet(U_73)
| U_73 = empty_set ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_10,plain,
( ~ in(U_64,sK12(U_73,U_69,U_64))
| in(U_64,U_69)
| U_69 != set_meet(U_73)
| U_73 = empty_set ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_11,plain,
( in(sK15(U_73,U_70),U_59)
| ~ in(U_59,U_73)
| in(sK13(U_73,U_70),U_70)
| U_70 = set_meet(U_73)
| U_73 = empty_set ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_12,plain,
( ~ in(sK15(U_73,U_70),U_70)
| in(sK13(U_73,U_70),U_70)
| U_70 = set_meet(U_73)
| U_73 = empty_set ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_13,plain,
( in(sK14(U_73,U_70),U_73)
| in(sK15(U_73,U_70),U_59)
| ~ in(U_59,U_73)
| U_70 = set_meet(U_73)
| U_73 = empty_set ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_14,plain,
( ~ in(sK13(U_73,U_70),sK14(U_73,U_70))
| in(sK15(U_73,U_70),U_59)
| ~ in(U_59,U_73)
| U_70 = set_meet(U_73)
| U_73 = empty_set ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_15,plain,
( in(sK14(U_73,U_70),U_73)
| ~ in(sK15(U_73,U_70),U_70)
| U_70 = set_meet(U_73)
| U_73 = empty_set ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_16,plain,
( ~ in(sK13(U_73,U_70),sK14(U_73,U_70))
| ~ in(sK15(U_73,U_70),U_70)
| U_70 = set_meet(U_73)
| U_73 = empty_set ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_17,plain,
( U_71 = empty_set
| U_71 != set_meet(U_74)
| U_74 != empty_set ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_18,plain,
( U_72 = set_meet(U_74)
| U_72 != empty_set
| U_74 != empty_set ),
inference(clausify,[status(thm)],[f_11_7]) ).
fof(f_12_1,plain,
! [A,B] :
( ( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
& C = A )
| ( C != A
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| C != A )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(fof_nnf,[status(thm)],[d1_tarski]) ).
fof(f_12_2,plain,
! [U_78,U_77] :
( ( U_77 = singleton(U_78)
| ? [U_76] :
( ( ~ in(U_76,U_77)
& U_76 = U_78 )
| ( U_76 != U_78
& in(U_76,U_77) ) ) )
& ( ! [U_75] :
( ( in(U_75,U_77)
| U_75 != U_78 )
& ( U_75 = U_78
| ~ in(U_75,U_77) ) )
| U_77 != singleton(U_78) ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_86,U_84] :
( U_84 = singleton(U_86)
| ? [U_82] :
( ~ in(U_82,U_84)
& U_82 = U_86 )
| ? [U_81] :
( U_81 != U_86
& in(U_81,U_84) ) )
& ! [U_85,U_83] :
( ( ! [U_80] :
( in(U_80,U_83)
| U_80 != U_85 )
& ! [U_79] :
( U_79 = U_85
| ~ in(U_79,U_83) ) )
| U_83 != singleton(U_85) ) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
( ! [U_86,U_84] :
( U_84 = singleton(U_86)
| ? [U_82] :
( ~ in(U_82,U_84)
& U_82 = U_86 )
| ( sK16(U_86,U_84) != U_86
& in(sK16(U_86,U_84),U_84) ) )
& ! [U_85,U_83] :
( ( ! [U_80] :
( in(U_80,U_83)
| U_80 != U_85 )
& ! [U_79] :
( U_79 = U_85
| ~ in(U_79,U_83) ) )
| U_83 != singleton(U_85) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_81,sK16(U_86,U_84))],[f_12_3]) ).
fof(f_12_5,plain,
( ! [U_86,U_84] :
( U_84 = singleton(U_86)
| ( ~ in(sK17(U_86,U_84),U_84)
& sK17(U_86,U_84) = U_86 )
| ( sK16(U_86,U_84) != U_86
& in(sK16(U_86,U_84),U_84) ) )
& ! [U_85,U_83] :
( ( ! [U_80] :
( in(U_80,U_83)
| U_80 != U_85 )
& ! [U_79] :
( U_79 = U_85
| ~ in(U_79,U_83) ) )
| U_83 != singleton(U_85) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_82,sK17(U_86,U_84))],[f_12_4]) ).
cnf(f_12_6,plain,
( U_79 = U_85
| ~ in(U_79,U_83)
| U_83 != singleton(U_85) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_7,plain,
( in(U_80,U_83)
| U_80 != U_85
| U_83 != singleton(U_85) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_8,plain,
( sK17(U_86,U_84) = U_86
| in(sK16(U_86,U_84),U_84)
| U_84 = singleton(U_86) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_9,plain,
( ~ in(sK17(U_86,U_84),U_84)
| in(sK16(U_86,U_84),U_84)
| U_84 = singleton(U_86) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_10,plain,
( sK17(U_86,U_84) = U_86
| sK16(U_86,U_84) != U_86
| U_84 = singleton(U_86) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_11,plain,
( ~ in(sK17(U_86,U_84),U_84)
| sK16(U_86,U_84) != U_86
| U_84 = singleton(U_86) ),
inference(clausify,[status(thm)],[f_12_5]) ).
fof(f_13_1,plain,
! [A] :
( ( A = empty_set
| ? [B] : in(B,A) )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(fof_nnf,[status(thm)],[d1_xboole_0]) ).
fof(f_13_2,plain,
! [U_89] :
( ( U_89 = empty_set
| ? [U_88] : in(U_88,U_89) )
& ( ! [U_87] : ~ in(U_87,U_89)
| U_89 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_91] :
( U_91 = empty_set
| ? [U_88] : in(U_88,U_91) )
& ! [U_90] :
( ! [U_87] : ~ in(U_87,U_90)
| U_90 != empty_set ) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
fof(f_13_4,plain,
( ! [U_91] :
( U_91 = empty_set
| in(sK18(U_91),U_91) )
& ! [U_90] :
( ! [U_87] : ~ in(U_87,U_90)
| U_90 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_88,sK18(U_91))],[f_13_3]) ).
cnf(f_13_5,plain,
( ~ in(U_87,U_90)
| U_90 != empty_set ),
inference(clausify,[status(thm)],[f_13_4]) ).
cnf(f_13_6,plain,
( U_91 = empty_set
| in(sK18(U_91),U_91) ),
inference(clausify,[status(thm)],[f_13_4]) ).
fof(f_14_1,plain,
! [A,B] :
( ( B = powerset(A)
| ? [C] :
( ( ~ in(C,B)
& subset(C,A) )
| ( ~ subset(C,A)
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ~ subset(C,A) )
& ( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(fof_nnf,[status(thm)],[d1_zfmisc_1]) ).
fof(f_14_2,plain,
! [U_95,U_94] :
( ( U_94 = powerset(U_95)
| ? [U_93] :
( ( ~ in(U_93,U_94)
& subset(U_93,U_95) )
| ( ~ subset(U_93,U_95)
& in(U_93,U_94) ) ) )
& ( ! [U_92] :
( ( in(U_92,U_94)
| ~ subset(U_92,U_95) )
& ( subset(U_92,U_95)
| ~ in(U_92,U_94) ) )
| U_94 != powerset(U_95) ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_103,U_101] :
( U_101 = powerset(U_103)
| ? [U_99] :
( ~ in(U_99,U_101)
& subset(U_99,U_103) )
| ? [U_98] :
( ~ subset(U_98,U_103)
& in(U_98,U_101) ) )
& ! [U_102,U_100] :
( ( ! [U_97] :
( in(U_97,U_100)
| ~ subset(U_97,U_102) )
& ! [U_96] :
( subset(U_96,U_102)
| ~ in(U_96,U_100) ) )
| U_100 != powerset(U_102) ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
fof(f_14_4,plain,
( ! [U_103,U_101] :
( U_101 = powerset(U_103)
| ? [U_99] :
( ~ in(U_99,U_101)
& subset(U_99,U_103) )
| ( ~ subset(sK19(U_103,U_101),U_103)
& in(sK19(U_103,U_101),U_101) ) )
& ! [U_102,U_100] :
( ( ! [U_97] :
( in(U_97,U_100)
| ~ subset(U_97,U_102) )
& ! [U_96] :
( subset(U_96,U_102)
| ~ in(U_96,U_100) ) )
| U_100 != powerset(U_102) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_98,sK19(U_103,U_101))],[f_14_3]) ).
fof(f_14_5,plain,
( ! [U_103,U_101] :
( U_101 = powerset(U_103)
| ( ~ in(sK20(U_103,U_101),U_101)
& subset(sK20(U_103,U_101),U_103) )
| ( ~ subset(sK19(U_103,U_101),U_103)
& in(sK19(U_103,U_101),U_101) ) )
& ! [U_102,U_100] :
( ( ! [U_97] :
( in(U_97,U_100)
| ~ subset(U_97,U_102) )
& ! [U_96] :
( subset(U_96,U_102)
| ~ in(U_96,U_100) ) )
| U_100 != powerset(U_102) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_99,sK20(U_103,U_101))],[f_14_4]) ).
cnf(f_14_6,plain,
( subset(U_96,U_102)
| ~ in(U_96,U_100)
| U_100 != powerset(U_102) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_7,plain,
( in(U_97,U_100)
| ~ subset(U_97,U_102)
| U_100 != powerset(U_102) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_8,plain,
( subset(sK20(U_103,U_101),U_103)
| in(sK19(U_103,U_101),U_101)
| U_101 = powerset(U_103) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_9,plain,
( ~ in(sK20(U_103,U_101),U_101)
| in(sK19(U_103,U_101),U_101)
| U_101 = powerset(U_103) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_10,plain,
( subset(sK20(U_103,U_101),U_103)
| ~ subset(sK19(U_103,U_101),U_103)
| U_101 = powerset(U_103) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_11,plain,
( ~ in(sK20(U_103,U_101),U_101)
| ~ subset(sK19(U_103,U_101),U_103)
| U_101 = powerset(U_103) ),
inference(clausify,[status(thm)],[f_14_5]) ).
fof(f_15_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_15_2,plain,
! [U_105,U_104] :
( ( ( ( element(U_104,U_105)
| ~ empty(U_104) )
& ( empty(U_104)
| ~ element(U_104,U_105) ) )
| ~ empty(U_105) )
& ( ( ( element(U_104,U_105)
| ~ in(U_104,U_105) )
& ( in(U_104,U_105)
| ~ element(U_104,U_105) ) )
| empty(U_105) ) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ! [U_113] :
( ( ! [U_111] :
( element(U_111,U_113)
| ~ empty(U_111) )
& ! [U_110] :
( empty(U_110)
| ~ element(U_110,U_113) ) )
| ~ empty(U_113) )
& ! [U_112] :
( ( ! [U_109] :
( element(U_109,U_112)
| ~ in(U_109,U_112) )
& ! [U_108] :
( in(U_108,U_112)
| ~ element(U_108,U_112) ) )
| empty(U_112) ) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( in(U_108,U_112)
| ~ element(U_108,U_112)
| empty(U_112) ),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_5,plain,
( element(U_109,U_112)
| ~ in(U_109,U_112)
| empty(U_112) ),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_6,plain,
( empty(U_110)
| ~ element(U_110,U_113)
| ~ empty(U_113) ),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_7,plain,
( element(U_111,U_113)
| ~ empty(U_111)
| ~ empty(U_113) ),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_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_16_2,plain,
! [U_118,U_117,U_116] :
( ( U_116 = unordered_pair(U_118,U_117)
| ? [U_115] :
( ( ~ in(U_115,U_116)
& ( U_115 = U_117
| U_115 = U_118 ) )
| ( U_115 != U_117
& U_115 != U_118
& in(U_115,U_116) ) ) )
& ( ! [U_114] :
( ( in(U_114,U_116)
| ( U_114 != U_117
& U_114 != U_118 ) )
& ( U_114 = U_117
| U_114 = U_118
| ~ in(U_114,U_116) ) )
| U_116 != unordered_pair(U_118,U_117) ) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( ! [U_128,U_126,U_124] :
( U_124 = unordered_pair(U_128,U_126)
| ? [U_122] :
( ~ in(U_122,U_124)
& ( U_122 = U_126
| U_122 = U_128 ) )
| ? [U_121] :
( U_121 != U_126
& U_121 != U_128
& in(U_121,U_124) ) )
& ! [U_127,U_125,U_123] :
( ( ! [U_120] :
( in(U_120,U_123)
| ( U_120 != U_125
& U_120 != U_127 ) )
& ! [U_119] :
( U_119 = U_125
| U_119 = U_127
| ~ in(U_119,U_123) ) )
| U_123 != unordered_pair(U_127,U_125) ) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
fof(f_16_4,plain,
( ! [U_128,U_126,U_124] :
( U_124 = unordered_pair(U_128,U_126)
| ? [U_122] :
( ~ in(U_122,U_124)
& ( U_122 = U_126
| U_122 = U_128 ) )
| ( sK21(U_128,U_126,U_124) != U_126
& sK21(U_128,U_126,U_124) != U_128
& in(sK21(U_128,U_126,U_124),U_124) ) )
& ! [U_127,U_125,U_123] :
( ( ! [U_120] :
( in(U_120,U_123)
| ( U_120 != U_125
& U_120 != U_127 ) )
& ! [U_119] :
( U_119 = U_125
| U_119 = U_127
| ~ in(U_119,U_123) ) )
| U_123 != unordered_pair(U_127,U_125) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_121,sK21(U_128,U_126,U_124))],[f_16_3]) ).
fof(f_16_5,plain,
( ! [U_128,U_126,U_124] :
( U_124 = unordered_pair(U_128,U_126)
| ( ~ in(sK22(U_128,U_126,U_124),U_124)
& ( sK22(U_128,U_126,U_124) = U_126
| sK22(U_128,U_126,U_124) = U_128 ) )
| ( sK21(U_128,U_126,U_124) != U_126
& sK21(U_128,U_126,U_124) != U_128
& in(sK21(U_128,U_126,U_124),U_124) ) )
& ! [U_127,U_125,U_123] :
( ( ! [U_120] :
( in(U_120,U_123)
| ( U_120 != U_125
& U_120 != U_127 ) )
& ! [U_119] :
( U_119 = U_125
| U_119 = U_127
| ~ in(U_119,U_123) ) )
| U_123 != unordered_pair(U_127,U_125) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_122,sK22(U_128,U_126,U_124))],[f_16_4]) ).
cnf(f_16_6,plain,
( U_119 = U_125
| U_119 = U_127
| ~ in(U_119,U_123)
| U_123 != unordered_pair(U_127,U_125) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_7,plain,
( U_120 != U_127
| in(U_120,U_123)
| U_123 != unordered_pair(U_127,U_125) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_8,plain,
( U_120 != U_125
| in(U_120,U_123)
| U_123 != unordered_pair(U_127,U_125) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_9,plain,
( sK22(U_128,U_126,U_124) = U_126
| sK22(U_128,U_126,U_124) = U_128
| in(sK21(U_128,U_126,U_124),U_124)
| U_124 = unordered_pair(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_10,plain,
( ~ in(sK22(U_128,U_126,U_124),U_124)
| in(sK21(U_128,U_126,U_124),U_124)
| U_124 = unordered_pair(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_11,plain,
( sK21(U_128,U_126,U_124) != U_128
| sK22(U_128,U_126,U_124) = U_126
| sK22(U_128,U_126,U_124) = U_128
| U_124 = unordered_pair(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_12,plain,
( sK21(U_128,U_126,U_124) != U_126
| sK22(U_128,U_126,U_124) = U_126
| sK22(U_128,U_126,U_124) = U_128
| U_124 = unordered_pair(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_13,plain,
( sK21(U_128,U_126,U_124) != U_128
| ~ in(sK22(U_128,U_126,U_124),U_124)
| U_124 = unordered_pair(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_14,plain,
( sK21(U_128,U_126,U_124) != U_126
| ~ in(sK22(U_128,U_126,U_124),U_124)
| U_124 = unordered_pair(U_128,U_126) ),
inference(clausify,[status(thm)],[f_16_5]) ).
fof(f_17_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_17_2,plain,
! [U_133,U_132,U_131] :
( ( U_131 = set_union2(U_133,U_132)
| ? [U_130] :
( ( ~ in(U_130,U_131)
& ( in(U_130,U_132)
| in(U_130,U_133) ) )
| ( ~ in(U_130,U_132)
& ~ in(U_130,U_133)
& in(U_130,U_131) ) ) )
& ( ! [U_129] :
( ( in(U_129,U_131)
| ( ~ in(U_129,U_132)
& ~ in(U_129,U_133) ) )
& ( in(U_129,U_132)
| in(U_129,U_133)
| ~ in(U_129,U_131) ) )
| U_131 != set_union2(U_133,U_132) ) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( ! [U_143,U_141,U_139] :
( U_139 = set_union2(U_143,U_141)
| ? [U_137] :
( ~ in(U_137,U_139)
& ( in(U_137,U_141)
| in(U_137,U_143) ) )
| ? [U_136] :
( ~ in(U_136,U_141)
& ~ in(U_136,U_143)
& in(U_136,U_139) ) )
& ! [U_142,U_140,U_138] :
( ( ! [U_135] :
( in(U_135,U_138)
| ( ~ in(U_135,U_140)
& ~ in(U_135,U_142) ) )
& ! [U_134] :
( in(U_134,U_140)
| in(U_134,U_142)
| ~ in(U_134,U_138) ) )
| U_138 != set_union2(U_142,U_140) ) ),
inference(miniscope,[status(thm)],[f_17_2]) ).
fof(f_17_4,plain,
( ! [U_143,U_141,U_139] :
( U_139 = set_union2(U_143,U_141)
| ? [U_137] :
( ~ in(U_137,U_139)
& ( in(U_137,U_141)
| in(U_137,U_143) ) )
| ( ~ in(sK23(U_143,U_141,U_139),U_141)
& ~ in(sK23(U_143,U_141,U_139),U_143)
& in(sK23(U_143,U_141,U_139),U_139) ) )
& ! [U_142,U_140,U_138] :
( ( ! [U_135] :
( in(U_135,U_138)
| ( ~ in(U_135,U_140)
& ~ in(U_135,U_142) ) )
& ! [U_134] :
( in(U_134,U_140)
| in(U_134,U_142)
| ~ in(U_134,U_138) ) )
| U_138 != set_union2(U_142,U_140) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_136,sK23(U_143,U_141,U_139))],[f_17_3]) ).
fof(f_17_5,plain,
( ! [U_143,U_141,U_139] :
( U_139 = set_union2(U_143,U_141)
| ( ~ in(sK24(U_143,U_141,U_139),U_139)
& ( in(sK24(U_143,U_141,U_139),U_141)
| in(sK24(U_143,U_141,U_139),U_143) ) )
| ( ~ in(sK23(U_143,U_141,U_139),U_141)
& ~ in(sK23(U_143,U_141,U_139),U_143)
& in(sK23(U_143,U_141,U_139),U_139) ) )
& ! [U_142,U_140,U_138] :
( ( ! [U_135] :
( in(U_135,U_138)
| ( ~ in(U_135,U_140)
& ~ in(U_135,U_142) ) )
& ! [U_134] :
( in(U_134,U_140)
| in(U_134,U_142)
| ~ in(U_134,U_138) ) )
| U_138 != set_union2(U_142,U_140) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_137,sK24(U_143,U_141,U_139))],[f_17_4]) ).
cnf(f_17_6,plain,
( in(U_134,U_140)
| in(U_134,U_142)
| ~ in(U_134,U_138)
| U_138 != set_union2(U_142,U_140) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_7,plain,
( ~ in(U_135,U_142)
| in(U_135,U_138)
| U_138 != set_union2(U_142,U_140) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_8,plain,
( ~ in(U_135,U_140)
| in(U_135,U_138)
| U_138 != set_union2(U_142,U_140) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_9,plain,
( in(sK24(U_143,U_141,U_139),U_141)
| in(sK24(U_143,U_141,U_139),U_143)
| in(sK23(U_143,U_141,U_139),U_139)
| U_139 = set_union2(U_143,U_141) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_10,plain,
( ~ in(sK24(U_143,U_141,U_139),U_139)
| in(sK23(U_143,U_141,U_139),U_139)
| U_139 = set_union2(U_143,U_141) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_11,plain,
( ~ in(sK23(U_143,U_141,U_139),U_143)
| in(sK24(U_143,U_141,U_139),U_141)
| in(sK24(U_143,U_141,U_139),U_143)
| U_139 = set_union2(U_143,U_141) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_12,plain,
( ~ in(sK23(U_143,U_141,U_139),U_141)
| in(sK24(U_143,U_141,U_139),U_141)
| in(sK24(U_143,U_141,U_139),U_143)
| U_139 = set_union2(U_143,U_141) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_13,plain,
( ~ in(sK23(U_143,U_141,U_139),U_143)
| ~ in(sK24(U_143,U_141,U_139),U_139)
| U_139 = set_union2(U_143,U_141) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_14,plain,
( ~ in(sK23(U_143,U_141,U_139),U_141)
| ~ in(sK24(U_143,U_141,U_139),U_139)
| U_139 = set_union2(U_143,U_141) ),
inference(clausify,[status(thm)],[f_17_5]) ).
fof(f_18_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_18_2,plain,
! [U_156,U_155,U_154] :
( ( U_154 = cartesian_product2(U_156,U_155)
| ? [U_153] :
( ( ~ in(U_153,U_154)
& ? [U_152,U_151] :
( U_153 = ordered_pair(U_152,U_151)
& in(U_151,U_155)
& in(U_152,U_156) ) )
| ( ! [U_150,U_149] :
( U_153 != ordered_pair(U_150,U_149)
| ~ in(U_149,U_155)
| ~ in(U_150,U_156) )
& in(U_153,U_154) ) ) )
& ( ! [U_148] :
( ( in(U_148,U_154)
| ! [U_147,U_146] :
( U_148 != ordered_pair(U_147,U_146)
| ~ in(U_146,U_155)
| ~ in(U_147,U_156) ) )
& ( ? [U_145,U_144] :
( U_148 = ordered_pair(U_145,U_144)
& in(U_144,U_155)
& in(U_145,U_156) )
| ~ in(U_148,U_154) ) )
| U_154 != cartesian_product2(U_156,U_155) ) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( ! [U_166,U_164,U_162] :
( U_162 = cartesian_product2(U_166,U_164)
| ? [U_160] :
( ~ in(U_160,U_162)
& ? [U_152] :
( ? [U_151] :
( U_160 = ordered_pair(U_152,U_151)
& in(U_151,U_164) )
& in(U_152,U_166) ) )
| ? [U_159] :
( ! [U_150] :
( ! [U_149] :
( U_159 != ordered_pair(U_150,U_149)
| ~ in(U_149,U_164) )
| ~ in(U_150,U_166) )
& in(U_159,U_162) ) )
& ! [U_165,U_163,U_161] :
( ( ! [U_158] :
( in(U_158,U_161)
| ! [U_147] :
( ! [U_146] :
( U_158 != ordered_pair(U_147,U_146)
| ~ in(U_146,U_163) )
| ~ in(U_147,U_165) ) )
& ! [U_157] :
( ? [U_145] :
( ? [U_144] :
( U_157 = ordered_pair(U_145,U_144)
& in(U_144,U_163) )
& in(U_145,U_165) )
| ~ in(U_157,U_161) ) )
| U_161 != cartesian_product2(U_165,U_163) ) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
fof(f_18_4,plain,
( ! [U_166,U_164,U_162] :
( U_162 = cartesian_product2(U_166,U_164)
| ? [U_160] :
( ~ in(U_160,U_162)
& ? [U_152] :
( ? [U_151] :
( U_160 = ordered_pair(U_152,U_151)
& in(U_151,U_164) )
& in(U_152,U_166) ) )
| ? [U_159] :
( ! [U_150] :
( ! [U_149] :
( U_159 != ordered_pair(U_150,U_149)
| ~ in(U_149,U_164) )
| ~ in(U_150,U_166) )
& in(U_159,U_162) ) )
& ! [U_165,U_163,U_161] :
( ( ! [U_158] :
( in(U_158,U_161)
| ! [U_147] :
( ! [U_146] :
( U_158 != ordered_pair(U_147,U_146)
| ~ in(U_146,U_163) )
| ~ in(U_147,U_165) ) )
& ! [U_157] :
( ( ? [U_144] :
( U_157 = ordered_pair(sK25(U_165,U_163,U_161,U_157),U_144)
& in(U_144,U_163) )
& in(sK25(U_165,U_163,U_161,U_157),U_165) )
| ~ in(U_157,U_161) ) )
| U_161 != cartesian_product2(U_165,U_163) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_145,sK25(U_165,U_163,U_161,U_157))],[f_18_3]) ).
fof(f_18_5,plain,
( ! [U_166,U_164,U_162] :
( U_162 = cartesian_product2(U_166,U_164)
| ? [U_160] :
( ~ in(U_160,U_162)
& ? [U_152] :
( ? [U_151] :
( U_160 = ordered_pair(U_152,U_151)
& in(U_151,U_164) )
& in(U_152,U_166) ) )
| ? [U_159] :
( ! [U_150] :
( ! [U_149] :
( U_159 != ordered_pair(U_150,U_149)
| ~ in(U_149,U_164) )
| ~ in(U_150,U_166) )
& in(U_159,U_162) ) )
& ! [U_165,U_163,U_161] :
( ( ! [U_158] :
( in(U_158,U_161)
| ! [U_147] :
( ! [U_146] :
( U_158 != ordered_pair(U_147,U_146)
| ~ in(U_146,U_163) )
| ~ in(U_147,U_165) ) )
& ! [U_157] :
( ( U_157 = ordered_pair(sK25(U_165,U_163,U_161,U_157),sK26(U_165,U_163,U_161,U_157))
& in(sK26(U_165,U_163,U_161,U_157),U_163)
& in(sK25(U_165,U_163,U_161,U_157),U_165) )
| ~ in(U_157,U_161) ) )
| U_161 != cartesian_product2(U_165,U_163) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_144,sK26(U_165,U_163,U_161,U_157))],[f_18_4]) ).
fof(f_18_6,plain,
( ! [U_166,U_164,U_162] :
( U_162 = cartesian_product2(U_166,U_164)
| ? [U_160] :
( ~ in(U_160,U_162)
& ? [U_152] :
( ? [U_151] :
( U_160 = ordered_pair(U_152,U_151)
& in(U_151,U_164) )
& in(U_152,U_166) ) )
| ( ! [U_150] :
( ! [U_149] :
( sK27(U_166,U_164,U_162) != ordered_pair(U_150,U_149)
| ~ in(U_149,U_164) )
| ~ in(U_150,U_166) )
& in(sK27(U_166,U_164,U_162),U_162) ) )
& ! [U_165,U_163,U_161] :
( ( ! [U_158] :
( in(U_158,U_161)
| ! [U_147] :
( ! [U_146] :
( U_158 != ordered_pair(U_147,U_146)
| ~ in(U_146,U_163) )
| ~ in(U_147,U_165) ) )
& ! [U_157] :
( ( U_157 = ordered_pair(sK25(U_165,U_163,U_161,U_157),sK26(U_165,U_163,U_161,U_157))
& in(sK26(U_165,U_163,U_161,U_157),U_163)
& in(sK25(U_165,U_163,U_161,U_157),U_165) )
| ~ in(U_157,U_161) ) )
| U_161 != cartesian_product2(U_165,U_163) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_159,sK27(U_166,U_164,U_162))],[f_18_5]) ).
fof(f_18_7,plain,
( ! [U_166,U_164,U_162] :
( U_162 = cartesian_product2(U_166,U_164)
| ( ~ in(sK28(U_166,U_164,U_162),U_162)
& ? [U_152] :
( ? [U_151] :
( sK28(U_166,U_164,U_162) = ordered_pair(U_152,U_151)
& in(U_151,U_164) )
& in(U_152,U_166) ) )
| ( ! [U_150] :
( ! [U_149] :
( sK27(U_166,U_164,U_162) != ordered_pair(U_150,U_149)
| ~ in(U_149,U_164) )
| ~ in(U_150,U_166) )
& in(sK27(U_166,U_164,U_162),U_162) ) )
& ! [U_165,U_163,U_161] :
( ( ! [U_158] :
( in(U_158,U_161)
| ! [U_147] :
( ! [U_146] :
( U_158 != ordered_pair(U_147,U_146)
| ~ in(U_146,U_163) )
| ~ in(U_147,U_165) ) )
& ! [U_157] :
( ( U_157 = ordered_pair(sK25(U_165,U_163,U_161,U_157),sK26(U_165,U_163,U_161,U_157))
& in(sK26(U_165,U_163,U_161,U_157),U_163)
& in(sK25(U_165,U_163,U_161,U_157),U_165) )
| ~ in(U_157,U_161) ) )
| U_161 != cartesian_product2(U_165,U_163) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_160,sK28(U_166,U_164,U_162))],[f_18_6]) ).
fof(f_18_8,plain,
( ! [U_166,U_164,U_162] :
( U_162 = cartesian_product2(U_166,U_164)
| ( ~ in(sK28(U_166,U_164,U_162),U_162)
& ? [U_151] :
( sK28(U_166,U_164,U_162) = ordered_pair(sK29(U_166,U_164,U_162),U_151)
& in(U_151,U_164) )
& in(sK29(U_166,U_164,U_162),U_166) )
| ( ! [U_150] :
( ! [U_149] :
( sK27(U_166,U_164,U_162) != ordered_pair(U_150,U_149)
| ~ in(U_149,U_164) )
| ~ in(U_150,U_166) )
& in(sK27(U_166,U_164,U_162),U_162) ) )
& ! [U_165,U_163,U_161] :
( ( ! [U_158] :
( in(U_158,U_161)
| ! [U_147] :
( ! [U_146] :
( U_158 != ordered_pair(U_147,U_146)
| ~ in(U_146,U_163) )
| ~ in(U_147,U_165) ) )
& ! [U_157] :
( ( U_157 = ordered_pair(sK25(U_165,U_163,U_161,U_157),sK26(U_165,U_163,U_161,U_157))
& in(sK26(U_165,U_163,U_161,U_157),U_163)
& in(sK25(U_165,U_163,U_161,U_157),U_165) )
| ~ in(U_157,U_161) ) )
| U_161 != cartesian_product2(U_165,U_163) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_152,sK29(U_166,U_164,U_162))],[f_18_7]) ).
fof(f_18_9,plain,
( ! [U_166,U_164,U_162] :
( U_162 = cartesian_product2(U_166,U_164)
| ( ~ in(sK28(U_166,U_164,U_162),U_162)
& sK28(U_166,U_164,U_162) = ordered_pair(sK29(U_166,U_164,U_162),sK30(U_166,U_164,U_162))
& in(sK30(U_166,U_164,U_162),U_164)
& in(sK29(U_166,U_164,U_162),U_166) )
| ( ! [U_150] :
( ! [U_149] :
( sK27(U_166,U_164,U_162) != ordered_pair(U_150,U_149)
| ~ in(U_149,U_164) )
| ~ in(U_150,U_166) )
& in(sK27(U_166,U_164,U_162),U_162) ) )
& ! [U_165,U_163,U_161] :
( ( ! [U_158] :
( in(U_158,U_161)
| ! [U_147] :
( ! [U_146] :
( U_158 != ordered_pair(U_147,U_146)
| ~ in(U_146,U_163) )
| ~ in(U_147,U_165) ) )
& ! [U_157] :
( ( U_157 = ordered_pair(sK25(U_165,U_163,U_161,U_157),sK26(U_165,U_163,U_161,U_157))
& in(sK26(U_165,U_163,U_161,U_157),U_163)
& in(sK25(U_165,U_163,U_161,U_157),U_165) )
| ~ in(U_157,U_161) ) )
| U_161 != cartesian_product2(U_165,U_163) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_151,sK30(U_166,U_164,U_162))],[f_18_8]) ).
cnf(f_18_10,plain,
( in(sK25(U_165,U_163,U_161,U_157),U_165)
| ~ in(U_157,U_161)
| U_161 != cartesian_product2(U_165,U_163) ),
inference(clausify,[status(thm)],[f_18_9]) ).
cnf(f_18_11,plain,
( in(sK26(U_165,U_163,U_161,U_157),U_163)
| ~ in(U_157,U_161)
| U_161 != cartesian_product2(U_165,U_163) ),
inference(clausify,[status(thm)],[f_18_9]) ).
cnf(f_18_12,plain,
( U_157 = ordered_pair(sK25(U_165,U_163,U_161,U_157),sK26(U_165,U_163,U_161,U_157))
| ~ in(U_157,U_161)
| U_161 != cartesian_product2(U_165,U_163) ),
inference(clausify,[status(thm)],[f_18_9]) ).
cnf(f_18_13,plain,
( in(U_158,U_161)
| U_158 != ordered_pair(U_147,U_146)
| ~ in(U_146,U_163)
| ~ in(U_147,U_165)
| U_161 != cartesian_product2(U_165,U_163) ),
inference(clausify,[status(thm)],[f_18_9]) ).
cnf(f_18_14,plain,
( in(sK29(U_166,U_164,U_162),U_166)
| in(sK27(U_166,U_164,U_162),U_162)
| U_162 = cartesian_product2(U_166,U_164) ),
inference(clausify,[status(thm)],[f_18_9]) ).
cnf(f_18_15,plain,
( in(sK30(U_166,U_164,U_162),U_164)
| in(sK27(U_166,U_164,U_162),U_162)
| U_162 = cartesian_product2(U_166,U_164) ),
inference(clausify,[status(thm)],[f_18_9]) ).
cnf(f_18_16,plain,
( sK28(U_166,U_164,U_162) = ordered_pair(sK29(U_166,U_164,U_162),sK30(U_166,U_164,U_162))
| in(sK27(U_166,U_164,U_162),U_162)
| U_162 = cartesian_product2(U_166,U_164) ),
inference(clausify,[status(thm)],[f_18_9]) ).
cnf(f_18_17,plain,
( ~ in(sK28(U_166,U_164,U_162),U_162)
| in(sK27(U_166,U_164,U_162),U_162)
| U_162 = cartesian_product2(U_166,U_164) ),
inference(clausify,[status(thm)],[f_18_9]) ).
cnf(f_18_18,plain,
( in(sK29(U_166,U_164,U_162),U_166)
| sK27(U_166,U_164,U_162) != ordered_pair(U_150,U_149)
| ~ in(U_149,U_164)
| ~ in(U_150,U_166)
| U_162 = cartesian_product2(U_166,U_164) ),
inference(clausify,[status(thm)],[f_18_9]) ).
cnf(f_18_19,plain,
( in(sK30(U_166,U_164,U_162),U_164)
| sK27(U_166,U_164,U_162) != ordered_pair(U_150,U_149)
| ~ in(U_149,U_164)
| ~ in(U_150,U_166)
| U_162 = cartesian_product2(U_166,U_164) ),
inference(clausify,[status(thm)],[f_18_9]) ).
cnf(f_18_20,plain,
( sK28(U_166,U_164,U_162) = ordered_pair(sK29(U_166,U_164,U_162),sK30(U_166,U_164,U_162))
| sK27(U_166,U_164,U_162) != ordered_pair(U_150,U_149)
| ~ in(U_149,U_164)
| ~ in(U_150,U_166)
| U_162 = cartesian_product2(U_166,U_164) ),
inference(clausify,[status(thm)],[f_18_9]) ).
cnf(f_18_21,plain,
( ~ in(sK28(U_166,U_164,U_162),U_162)
| sK27(U_166,U_164,U_162) != ordered_pair(U_150,U_149)
| ~ in(U_149,U_164)
| ~ in(U_150,U_166)
| U_162 = cartesian_product2(U_166,U_164) ),
inference(clausify,[status(thm)],[f_18_9]) ).
fof(f_19_1,plain,
! [A] :
( ! [B] :
( ( ( subset(A,B)
| ? [C,D] :
( ~ in(ordered_pair(C,D),B)
& in(ordered_pair(C,D),A) ) )
& ( ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) )
| ~ subset(A,B) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d3_relat_1]) ).
fof(f_19_2,plain,
! [U_172] :
( ! [U_171] :
( ( ( subset(U_172,U_171)
| ? [U_170,U_169] :
( ~ in(ordered_pair(U_170,U_169),U_171)
& in(ordered_pair(U_170,U_169),U_172) ) )
& ( ! [U_168,U_167] :
( in(ordered_pair(U_168,U_167),U_171)
| ~ in(ordered_pair(U_168,U_167),U_172) )
| ~ subset(U_172,U_171) ) )
| ~ relation(U_171) )
| ~ relation(U_172) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_172] :
( ! [U_171] :
( ( ( subset(U_172,U_171)
| ? [U_169] :
( ~ in(ordered_pair(sK31(U_172,U_171),U_169),U_171)
& in(ordered_pair(sK31(U_172,U_171),U_169),U_172) ) )
& ( ! [U_168,U_167] :
( in(ordered_pair(U_168,U_167),U_171)
| ~ in(ordered_pair(U_168,U_167),U_172) )
| ~ subset(U_172,U_171) ) )
| ~ relation(U_171) )
| ~ relation(U_172) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_170,sK31(U_172,U_171))],[f_19_2]) ).
fof(f_19_4,plain,
! [U_172] :
( ! [U_171] :
( ( ( subset(U_172,U_171)
| ( ~ in(ordered_pair(sK31(U_172,U_171),sK32(U_172,U_171)),U_171)
& in(ordered_pair(sK31(U_172,U_171),sK32(U_172,U_171)),U_172) ) )
& ( ! [U_168,U_167] :
( in(ordered_pair(U_168,U_167),U_171)
| ~ in(ordered_pair(U_168,U_167),U_172) )
| ~ subset(U_172,U_171) ) )
| ~ relation(U_171) )
| ~ relation(U_172) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_169,sK32(U_172,U_171))],[f_19_3]) ).
cnf(f_19_5,plain,
( in(ordered_pair(U_168,U_167),U_171)
| ~ in(ordered_pair(U_168,U_167),U_172)
| ~ subset(U_172,U_171)
| ~ relation(U_171)
| ~ relation(U_172) ),
inference(clausify,[status(thm)],[f_19_4]) ).
cnf(f_19_6,plain,
( in(ordered_pair(sK31(U_172,U_171),sK32(U_172,U_171)),U_172)
| subset(U_172,U_171)
| ~ relation(U_171)
| ~ relation(U_172) ),
inference(clausify,[status(thm)],[f_19_4]) ).
cnf(f_19_7,plain,
( ~ in(ordered_pair(sK31(U_172,U_171),sK32(U_172,U_171)),U_171)
| subset(U_172,U_171)
| ~ relation(U_171)
| ~ relation(U_172) ),
inference(clausify,[status(thm)],[f_19_4]) ).
fof(f_20_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_20_2,plain,
! [U_176,U_175] :
( ( subset(U_176,U_175)
| ? [U_174] :
( ~ in(U_174,U_175)
& in(U_174,U_176) ) )
& ( ! [U_173] :
( in(U_173,U_175)
| ~ in(U_173,U_176) )
| ~ subset(U_176,U_175) ) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( ! [U_180,U_178] :
( subset(U_180,U_178)
| ? [U_174] :
( ~ in(U_174,U_178)
& in(U_174,U_180) ) )
& ! [U_179,U_177] :
( ! [U_173] :
( in(U_173,U_177)
| ~ in(U_173,U_179) )
| ~ subset(U_179,U_177) ) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
fof(f_20_4,plain,
( ! [U_180,U_178] :
( subset(U_180,U_178)
| ( ~ in(sK33(U_180,U_178),U_178)
& in(sK33(U_180,U_178),U_180) ) )
& ! [U_179,U_177] :
( ! [U_173] :
( in(U_173,U_177)
| ~ in(U_173,U_179) )
| ~ subset(U_179,U_177) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_174,sK33(U_180,U_178))],[f_20_3]) ).
cnf(f_20_5,plain,
( in(U_173,U_177)
| ~ in(U_173,U_179)
| ~ subset(U_179,U_177) ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_6,plain,
( in(sK33(U_180,U_178),U_180)
| subset(U_180,U_178) ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_7,plain,
( ~ in(sK33(U_180,U_178),U_178)
| subset(U_180,U_178) ),
inference(clausify,[status(thm)],[f_20_4]) ).
fof(f_21_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_21_2,plain,
! [U_185,U_184,U_183] :
( ( U_183 = set_intersection2(U_185,U_184)
| ? [U_182] :
( ( ~ in(U_182,U_183)
& in(U_182,U_184)
& in(U_182,U_185) )
| ( ( ~ in(U_182,U_184)
| ~ in(U_182,U_185) )
& in(U_182,U_183) ) ) )
& ( ! [U_181] :
( ( in(U_181,U_183)
| ~ in(U_181,U_184)
| ~ in(U_181,U_185) )
& ( ( in(U_181,U_184)
& in(U_181,U_185) )
| ~ in(U_181,U_183) ) )
| U_183 != set_intersection2(U_185,U_184) ) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( ! [U_195,U_193,U_191] :
( U_191 = set_intersection2(U_195,U_193)
| ? [U_189] :
( ~ in(U_189,U_191)
& in(U_189,U_193)
& in(U_189,U_195) )
| ? [U_188] :
( ( ~ in(U_188,U_193)
| ~ in(U_188,U_195) )
& in(U_188,U_191) ) )
& ! [U_194,U_192,U_190] :
( ( ! [U_187] :
( in(U_187,U_190)
| ~ in(U_187,U_192)
| ~ in(U_187,U_194) )
& ! [U_186] :
( ( in(U_186,U_192)
& in(U_186,U_194) )
| ~ in(U_186,U_190) ) )
| U_190 != set_intersection2(U_194,U_192) ) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
fof(f_21_4,plain,
( ! [U_195,U_193,U_191] :
( U_191 = set_intersection2(U_195,U_193)
| ? [U_189] :
( ~ in(U_189,U_191)
& in(U_189,U_193)
& in(U_189,U_195) )
| ( ( ~ in(sK34(U_195,U_193,U_191),U_193)
| ~ in(sK34(U_195,U_193,U_191),U_195) )
& in(sK34(U_195,U_193,U_191),U_191) ) )
& ! [U_194,U_192,U_190] :
( ( ! [U_187] :
( in(U_187,U_190)
| ~ in(U_187,U_192)
| ~ in(U_187,U_194) )
& ! [U_186] :
( ( in(U_186,U_192)
& in(U_186,U_194) )
| ~ in(U_186,U_190) ) )
| U_190 != set_intersection2(U_194,U_192) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_188,sK34(U_195,U_193,U_191))],[f_21_3]) ).
fof(f_21_5,plain,
( ! [U_195,U_193,U_191] :
( U_191 = set_intersection2(U_195,U_193)
| ( ~ in(sK35(U_195,U_193,U_191),U_191)
& in(sK35(U_195,U_193,U_191),U_193)
& in(sK35(U_195,U_193,U_191),U_195) )
| ( ( ~ in(sK34(U_195,U_193,U_191),U_193)
| ~ in(sK34(U_195,U_193,U_191),U_195) )
& in(sK34(U_195,U_193,U_191),U_191) ) )
& ! [U_194,U_192,U_190] :
( ( ! [U_187] :
( in(U_187,U_190)
| ~ in(U_187,U_192)
| ~ in(U_187,U_194) )
& ! [U_186] :
( ( in(U_186,U_192)
& in(U_186,U_194) )
| ~ in(U_186,U_190) ) )
| U_190 != set_intersection2(U_194,U_192) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_189,sK35(U_195,U_193,U_191))],[f_21_4]) ).
cnf(f_21_6,plain,
( in(U_186,U_194)
| ~ in(U_186,U_190)
| U_190 != set_intersection2(U_194,U_192) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_7,plain,
( in(U_186,U_192)
| ~ in(U_186,U_190)
| U_190 != set_intersection2(U_194,U_192) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_8,plain,
( in(U_187,U_190)
| ~ in(U_187,U_192)
| ~ in(U_187,U_194)
| U_190 != set_intersection2(U_194,U_192) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_9,plain,
( in(sK35(U_195,U_193,U_191),U_195)
| in(sK34(U_195,U_193,U_191),U_191)
| U_191 = set_intersection2(U_195,U_193) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_10,plain,
( in(sK35(U_195,U_193,U_191),U_193)
| in(sK34(U_195,U_193,U_191),U_191)
| U_191 = set_intersection2(U_195,U_193) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_11,plain,
( ~ in(sK35(U_195,U_193,U_191),U_191)
| in(sK34(U_195,U_193,U_191),U_191)
| U_191 = set_intersection2(U_195,U_193) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_12,plain,
( in(sK35(U_195,U_193,U_191),U_195)
| ~ in(sK34(U_195,U_193,U_191),U_193)
| ~ in(sK34(U_195,U_193,U_191),U_195)
| U_191 = set_intersection2(U_195,U_193) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_13,plain,
( in(sK35(U_195,U_193,U_191),U_193)
| ~ in(sK34(U_195,U_193,U_191),U_193)
| ~ in(sK34(U_195,U_193,U_191),U_195)
| U_191 = set_intersection2(U_195,U_193) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_14,plain,
( ~ in(sK35(U_195,U_193,U_191),U_191)
| ~ in(sK34(U_195,U_193,U_191),U_193)
| ~ in(sK34(U_195,U_193,U_191),U_195)
| U_191 = set_intersection2(U_195,U_193) ),
inference(clausify,[status(thm)],[f_21_5]) ).
fof(f_22_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_22_2,plain,
! [U_203] :
( ! [U_202] :
( ( U_202 = relation_dom(U_203)
| ? [U_201] :
( ( ~ in(U_201,U_202)
& ? [U_200] : in(ordered_pair(U_201,U_200),U_203) )
| ( ! [U_199] : ~ in(ordered_pair(U_201,U_199),U_203)
& in(U_201,U_202) ) ) )
& ( ! [U_198] :
( ( in(U_198,U_202)
| ! [U_197] : ~ in(ordered_pair(U_198,U_197),U_203) )
& ( ? [U_196] : in(ordered_pair(U_198,U_196),U_203)
| ~ in(U_198,U_202) ) )
| U_202 != relation_dom(U_203) ) )
| ~ relation(U_203) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_203] :
( ( ! [U_209] :
( U_209 = relation_dom(U_203)
| ? [U_207] :
( ~ in(U_207,U_209)
& ? [U_200] : in(ordered_pair(U_207,U_200),U_203) )
| ? [U_206] :
( ! [U_199] : ~ in(ordered_pair(U_206,U_199),U_203)
& in(U_206,U_209) ) )
& ! [U_208] :
( ( ! [U_205] :
( in(U_205,U_208)
| ! [U_197] : ~ in(ordered_pair(U_205,U_197),U_203) )
& ! [U_204] :
( ? [U_196] : in(ordered_pair(U_204,U_196),U_203)
| ~ in(U_204,U_208) ) )
| U_208 != relation_dom(U_203) ) )
| ~ relation(U_203) ),
inference(miniscope,[status(thm)],[f_22_2]) ).
fof(f_22_4,plain,
! [U_203] :
( ( ! [U_209] :
( U_209 = relation_dom(U_203)
| ? [U_207] :
( ~ in(U_207,U_209)
& ? [U_200] : in(ordered_pair(U_207,U_200),U_203) )
| ? [U_206] :
( ! [U_199] : ~ in(ordered_pair(U_206,U_199),U_203)
& in(U_206,U_209) ) )
& ! [U_208] :
( ( ! [U_205] :
( in(U_205,U_208)
| ! [U_197] : ~ in(ordered_pair(U_205,U_197),U_203) )
& ! [U_204] :
( in(ordered_pair(U_204,sK36(U_203,U_208,U_204)),U_203)
| ~ in(U_204,U_208) ) )
| U_208 != relation_dom(U_203) ) )
| ~ relation(U_203) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_196,sK36(U_203,U_208,U_204))],[f_22_3]) ).
fof(f_22_5,plain,
! [U_203] :
( ( ! [U_209] :
( U_209 = relation_dom(U_203)
| ? [U_207] :
( ~ in(U_207,U_209)
& ? [U_200] : in(ordered_pair(U_207,U_200),U_203) )
| ( ! [U_199] : ~ in(ordered_pair(sK37(U_203,U_209),U_199),U_203)
& in(sK37(U_203,U_209),U_209) ) )
& ! [U_208] :
( ( ! [U_205] :
( in(U_205,U_208)
| ! [U_197] : ~ in(ordered_pair(U_205,U_197),U_203) )
& ! [U_204] :
( in(ordered_pair(U_204,sK36(U_203,U_208,U_204)),U_203)
| ~ in(U_204,U_208) ) )
| U_208 != relation_dom(U_203) ) )
| ~ relation(U_203) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_206,sK37(U_203,U_209))],[f_22_4]) ).
fof(f_22_6,plain,
! [U_203] :
( ( ! [U_209] :
( U_209 = relation_dom(U_203)
| ( ~ in(sK38(U_203,U_209),U_209)
& ? [U_200] : in(ordered_pair(sK38(U_203,U_209),U_200),U_203) )
| ( ! [U_199] : ~ in(ordered_pair(sK37(U_203,U_209),U_199),U_203)
& in(sK37(U_203,U_209),U_209) ) )
& ! [U_208] :
( ( ! [U_205] :
( in(U_205,U_208)
| ! [U_197] : ~ in(ordered_pair(U_205,U_197),U_203) )
& ! [U_204] :
( in(ordered_pair(U_204,sK36(U_203,U_208,U_204)),U_203)
| ~ in(U_204,U_208) ) )
| U_208 != relation_dom(U_203) ) )
| ~ relation(U_203) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_207,sK38(U_203,U_209))],[f_22_5]) ).
fof(f_22_7,plain,
! [U_203] :
( ( ! [U_209] :
( U_209 = relation_dom(U_203)
| ( ~ in(sK38(U_203,U_209),U_209)
& in(ordered_pair(sK38(U_203,U_209),sK39(U_203,U_209)),U_203) )
| ( ! [U_199] : ~ in(ordered_pair(sK37(U_203,U_209),U_199),U_203)
& in(sK37(U_203,U_209),U_209) ) )
& ! [U_208] :
( ( ! [U_205] :
( in(U_205,U_208)
| ! [U_197] : ~ in(ordered_pair(U_205,U_197),U_203) )
& ! [U_204] :
( in(ordered_pair(U_204,sK36(U_203,U_208,U_204)),U_203)
| ~ in(U_204,U_208) ) )
| U_208 != relation_dom(U_203) ) )
| ~ relation(U_203) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_200,sK39(U_203,U_209))],[f_22_6]) ).
cnf(f_22_8,plain,
( in(ordered_pair(U_204,sK36(U_203,U_208,U_204)),U_203)
| ~ in(U_204,U_208)
| U_208 != relation_dom(U_203)
| ~ relation(U_203) ),
inference(clausify,[status(thm)],[f_22_7]) ).
cnf(f_22_9,plain,
( in(U_205,U_208)
| ~ in(ordered_pair(U_205,U_197),U_203)
| U_208 != relation_dom(U_203)
| ~ relation(U_203) ),
inference(clausify,[status(thm)],[f_22_7]) ).
cnf(f_22_10,plain,
( in(ordered_pair(sK38(U_203,U_209),sK39(U_203,U_209)),U_203)
| in(sK37(U_203,U_209),U_209)
| U_209 = relation_dom(U_203)
| ~ relation(U_203) ),
inference(clausify,[status(thm)],[f_22_7]) ).
cnf(f_22_11,plain,
( ~ in(sK38(U_203,U_209),U_209)
| in(sK37(U_203,U_209),U_209)
| U_209 = relation_dom(U_203)
| ~ relation(U_203) ),
inference(clausify,[status(thm)],[f_22_7]) ).
cnf(f_22_12,plain,
( in(ordered_pair(sK38(U_203,U_209),sK39(U_203,U_209)),U_203)
| ~ in(ordered_pair(sK37(U_203,U_209),U_199),U_203)
| U_209 = relation_dom(U_203)
| ~ relation(U_203) ),
inference(clausify,[status(thm)],[f_22_7]) ).
cnf(f_22_13,plain,
( ~ in(sK38(U_203,U_209),U_209)
| ~ in(ordered_pair(sK37(U_203,U_209),U_199),U_203)
| U_209 = relation_dom(U_203)
| ~ relation(U_203) ),
inference(clausify,[status(thm)],[f_22_7]) ).
fof(f_23_1,plain,
! [A] : cast_to_subset(A) = A,
inference(fof_nnf,[status(thm)],[d4_subset_1]) ).
fof(f_23_2,plain,
! [U_210] : cast_to_subset(U_210) = U_210,
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
cast_to_subset(U_210) = U_210,
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_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_24_2,plain,
! [U_218,U_217] :
( ( U_217 = union(U_218)
| ? [U_216] :
( ( ~ in(U_216,U_217)
& ? [U_215] :
( in(U_215,U_218)
& in(U_216,U_215) ) )
| ( ! [U_214] :
( ~ in(U_214,U_218)
| ~ in(U_216,U_214) )
& in(U_216,U_217) ) ) )
& ( ! [U_213] :
( ( in(U_213,U_217)
| ! [U_212] :
( ~ in(U_212,U_218)
| ~ in(U_213,U_212) ) )
& ( ? [U_211] :
( in(U_211,U_218)
& in(U_213,U_211) )
| ~ in(U_213,U_217) ) )
| U_217 != union(U_218) ) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( ! [U_226,U_224] :
( U_224 = union(U_226)
| ? [U_222] :
( ~ in(U_222,U_224)
& ? [U_215] :
( in(U_215,U_226)
& in(U_222,U_215) ) )
| ? [U_221] :
( ! [U_214] :
( ~ in(U_214,U_226)
| ~ in(U_221,U_214) )
& in(U_221,U_224) ) )
& ! [U_225,U_223] :
( ( ! [U_220] :
( in(U_220,U_223)
| ! [U_212] :
( ~ in(U_212,U_225)
| ~ in(U_220,U_212) ) )
& ! [U_219] :
( ? [U_211] :
( in(U_211,U_225)
& in(U_219,U_211) )
| ~ in(U_219,U_223) ) )
| U_223 != union(U_225) ) ),
inference(miniscope,[status(thm)],[f_24_2]) ).
fof(f_24_4,plain,
( ! [U_226,U_224] :
( U_224 = union(U_226)
| ? [U_222] :
( ~ in(U_222,U_224)
& ? [U_215] :
( in(U_215,U_226)
& in(U_222,U_215) ) )
| ? [U_221] :
( ! [U_214] :
( ~ in(U_214,U_226)
| ~ in(U_221,U_214) )
& in(U_221,U_224) ) )
& ! [U_225,U_223] :
( ( ! [U_220] :
( in(U_220,U_223)
| ! [U_212] :
( ~ in(U_212,U_225)
| ~ in(U_220,U_212) ) )
& ! [U_219] :
( ( in(sK40(U_225,U_223,U_219),U_225)
& in(U_219,sK40(U_225,U_223,U_219)) )
| ~ in(U_219,U_223) ) )
| U_223 != union(U_225) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_211,sK40(U_225,U_223,U_219))],[f_24_3]) ).
fof(f_24_5,plain,
( ! [U_226,U_224] :
( U_224 = union(U_226)
| ? [U_222] :
( ~ in(U_222,U_224)
& ? [U_215] :
( in(U_215,U_226)
& in(U_222,U_215) ) )
| ( ! [U_214] :
( ~ in(U_214,U_226)
| ~ in(sK41(U_226,U_224),U_214) )
& in(sK41(U_226,U_224),U_224) ) )
& ! [U_225,U_223] :
( ( ! [U_220] :
( in(U_220,U_223)
| ! [U_212] :
( ~ in(U_212,U_225)
| ~ in(U_220,U_212) ) )
& ! [U_219] :
( ( in(sK40(U_225,U_223,U_219),U_225)
& in(U_219,sK40(U_225,U_223,U_219)) )
| ~ in(U_219,U_223) ) )
| U_223 != union(U_225) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_221,sK41(U_226,U_224))],[f_24_4]) ).
fof(f_24_6,plain,
( ! [U_226,U_224] :
( U_224 = union(U_226)
| ( ~ in(sK42(U_226,U_224),U_224)
& ? [U_215] :
( in(U_215,U_226)
& in(sK42(U_226,U_224),U_215) ) )
| ( ! [U_214] :
( ~ in(U_214,U_226)
| ~ in(sK41(U_226,U_224),U_214) )
& in(sK41(U_226,U_224),U_224) ) )
& ! [U_225,U_223] :
( ( ! [U_220] :
( in(U_220,U_223)
| ! [U_212] :
( ~ in(U_212,U_225)
| ~ in(U_220,U_212) ) )
& ! [U_219] :
( ( in(sK40(U_225,U_223,U_219),U_225)
& in(U_219,sK40(U_225,U_223,U_219)) )
| ~ in(U_219,U_223) ) )
| U_223 != union(U_225) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_222,sK42(U_226,U_224))],[f_24_5]) ).
fof(f_24_7,plain,
( ! [U_226,U_224] :
( U_224 = union(U_226)
| ( ~ in(sK42(U_226,U_224),U_224)
& in(sK43(U_226,U_224),U_226)
& in(sK42(U_226,U_224),sK43(U_226,U_224)) )
| ( ! [U_214] :
( ~ in(U_214,U_226)
| ~ in(sK41(U_226,U_224),U_214) )
& in(sK41(U_226,U_224),U_224) ) )
& ! [U_225,U_223] :
( ( ! [U_220] :
( in(U_220,U_223)
| ! [U_212] :
( ~ in(U_212,U_225)
| ~ in(U_220,U_212) ) )
& ! [U_219] :
( ( in(sK40(U_225,U_223,U_219),U_225)
& in(U_219,sK40(U_225,U_223,U_219)) )
| ~ in(U_219,U_223) ) )
| U_223 != union(U_225) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_215,sK43(U_226,U_224))],[f_24_6]) ).
cnf(f_24_8,plain,
( in(U_219,sK40(U_225,U_223,U_219))
| ~ in(U_219,U_223)
| U_223 != union(U_225) ),
inference(clausify,[status(thm)],[f_24_7]) ).
cnf(f_24_9,plain,
( in(sK40(U_225,U_223,U_219),U_225)
| ~ in(U_219,U_223)
| U_223 != union(U_225) ),
inference(clausify,[status(thm)],[f_24_7]) ).
cnf(f_24_10,plain,
( in(U_220,U_223)
| ~ in(U_212,U_225)
| ~ in(U_220,U_212)
| U_223 != union(U_225) ),
inference(clausify,[status(thm)],[f_24_7]) ).
cnf(f_24_11,plain,
( in(sK42(U_226,U_224),sK43(U_226,U_224))
| in(sK41(U_226,U_224),U_224)
| U_224 = union(U_226) ),
inference(clausify,[status(thm)],[f_24_7]) ).
cnf(f_24_12,plain,
( in(sK43(U_226,U_224),U_226)
| in(sK41(U_226,U_224),U_224)
| U_224 = union(U_226) ),
inference(clausify,[status(thm)],[f_24_7]) ).
cnf(f_24_13,plain,
( ~ in(sK42(U_226,U_224),U_224)
| in(sK41(U_226,U_224),U_224)
| U_224 = union(U_226) ),
inference(clausify,[status(thm)],[f_24_7]) ).
cnf(f_24_14,plain,
( in(sK42(U_226,U_224),sK43(U_226,U_224))
| ~ in(U_214,U_226)
| ~ in(sK41(U_226,U_224),U_214)
| U_224 = union(U_226) ),
inference(clausify,[status(thm)],[f_24_7]) ).
cnf(f_24_15,plain,
( in(sK43(U_226,U_224),U_226)
| ~ in(U_214,U_226)
| ~ in(sK41(U_226,U_224),U_214)
| U_224 = union(U_226) ),
inference(clausify,[status(thm)],[f_24_7]) ).
cnf(f_24_16,plain,
( ~ in(sK42(U_226,U_224),U_224)
| ~ in(U_214,U_226)
| ~ in(sK41(U_226,U_224),U_214)
| U_224 = union(U_226) ),
inference(clausify,[status(thm)],[f_24_7]) ).
fof(f_25_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_25_2,plain,
! [U_231,U_230,U_229] :
( ( U_229 = set_difference(U_231,U_230)
| ? [U_228] :
( ( ~ in(U_228,U_229)
& ~ in(U_228,U_230)
& in(U_228,U_231) )
| ( ( in(U_228,U_230)
| ~ in(U_228,U_231) )
& in(U_228,U_229) ) ) )
& ( ! [U_227] :
( ( in(U_227,U_229)
| in(U_227,U_230)
| ~ in(U_227,U_231) )
& ( ( ~ in(U_227,U_230)
& in(U_227,U_231) )
| ~ in(U_227,U_229) ) )
| U_229 != set_difference(U_231,U_230) ) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( ! [U_241,U_239,U_237] :
( U_237 = set_difference(U_241,U_239)
| ? [U_235] :
( ~ in(U_235,U_237)
& ~ in(U_235,U_239)
& in(U_235,U_241) )
| ? [U_234] :
( ( in(U_234,U_239)
| ~ in(U_234,U_241) )
& in(U_234,U_237) ) )
& ! [U_240,U_238,U_236] :
( ( ! [U_233] :
( in(U_233,U_236)
| in(U_233,U_238)
| ~ in(U_233,U_240) )
& ! [U_232] :
( ( ~ in(U_232,U_238)
& in(U_232,U_240) )
| ~ in(U_232,U_236) ) )
| U_236 != set_difference(U_240,U_238) ) ),
inference(miniscope,[status(thm)],[f_25_2]) ).
fof(f_25_4,plain,
( ! [U_241,U_239,U_237] :
( U_237 = set_difference(U_241,U_239)
| ? [U_235] :
( ~ in(U_235,U_237)
& ~ in(U_235,U_239)
& in(U_235,U_241) )
| ( ( in(sK44(U_241,U_239,U_237),U_239)
| ~ in(sK44(U_241,U_239,U_237),U_241) )
& in(sK44(U_241,U_239,U_237),U_237) ) )
& ! [U_240,U_238,U_236] :
( ( ! [U_233] :
( in(U_233,U_236)
| in(U_233,U_238)
| ~ in(U_233,U_240) )
& ! [U_232] :
( ( ~ in(U_232,U_238)
& in(U_232,U_240) )
| ~ in(U_232,U_236) ) )
| U_236 != set_difference(U_240,U_238) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_234,sK44(U_241,U_239,U_237))],[f_25_3]) ).
fof(f_25_5,plain,
( ! [U_241,U_239,U_237] :
( U_237 = set_difference(U_241,U_239)
| ( ~ in(sK45(U_241,U_239,U_237),U_237)
& ~ in(sK45(U_241,U_239,U_237),U_239)
& in(sK45(U_241,U_239,U_237),U_241) )
| ( ( in(sK44(U_241,U_239,U_237),U_239)
| ~ in(sK44(U_241,U_239,U_237),U_241) )
& in(sK44(U_241,U_239,U_237),U_237) ) )
& ! [U_240,U_238,U_236] :
( ( ! [U_233] :
( in(U_233,U_236)
| in(U_233,U_238)
| ~ in(U_233,U_240) )
& ! [U_232] :
( ( ~ in(U_232,U_238)
& in(U_232,U_240) )
| ~ in(U_232,U_236) ) )
| U_236 != set_difference(U_240,U_238) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_235,sK45(U_241,U_239,U_237))],[f_25_4]) ).
cnf(f_25_6,plain,
( in(U_232,U_240)
| ~ in(U_232,U_236)
| U_236 != set_difference(U_240,U_238) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_7,plain,
( ~ in(U_232,U_238)
| ~ in(U_232,U_236)
| U_236 != set_difference(U_240,U_238) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_8,plain,
( in(U_233,U_236)
| in(U_233,U_238)
| ~ in(U_233,U_240)
| U_236 != set_difference(U_240,U_238) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_9,plain,
( in(sK45(U_241,U_239,U_237),U_241)
| in(sK44(U_241,U_239,U_237),U_237)
| U_237 = set_difference(U_241,U_239) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_10,plain,
( ~ in(sK45(U_241,U_239,U_237),U_239)
| in(sK44(U_241,U_239,U_237),U_237)
| U_237 = set_difference(U_241,U_239) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_11,plain,
( ~ in(sK45(U_241,U_239,U_237),U_237)
| in(sK44(U_241,U_239,U_237),U_237)
| U_237 = set_difference(U_241,U_239) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_12,plain,
( in(sK45(U_241,U_239,U_237),U_241)
| in(sK44(U_241,U_239,U_237),U_239)
| ~ in(sK44(U_241,U_239,U_237),U_241)
| U_237 = set_difference(U_241,U_239) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_13,plain,
( ~ in(sK45(U_241,U_239,U_237),U_239)
| in(sK44(U_241,U_239,U_237),U_239)
| ~ in(sK44(U_241,U_239,U_237),U_241)
| U_237 = set_difference(U_241,U_239) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_14,plain,
( ~ in(sK45(U_241,U_239,U_237),U_237)
| in(sK44(U_241,U_239,U_237),U_239)
| ~ in(sK44(U_241,U_239,U_237),U_241)
| U_237 = set_difference(U_241,U_239) ),
inference(clausify,[status(thm)],[f_25_5]) ).
fof(f_26_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_26_2,plain,
! [U_249] :
( ! [U_248] :
( ( U_248 = relation_rng(U_249)
| ? [U_247] :
( ( ~ in(U_247,U_248)
& ? [U_246] : in(ordered_pair(U_246,U_247),U_249) )
| ( ! [U_245] : ~ in(ordered_pair(U_245,U_247),U_249)
& in(U_247,U_248) ) ) )
& ( ! [U_244] :
( ( in(U_244,U_248)
| ! [U_243] : ~ in(ordered_pair(U_243,U_244),U_249) )
& ( ? [U_242] : in(ordered_pair(U_242,U_244),U_249)
| ~ in(U_244,U_248) ) )
| U_248 != relation_rng(U_249) ) )
| ~ relation(U_249) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_249] :
( ( ! [U_255] :
( U_255 = relation_rng(U_249)
| ? [U_253] :
( ~ in(U_253,U_255)
& ? [U_246] : in(ordered_pair(U_246,U_253),U_249) )
| ? [U_252] :
( ! [U_245] : ~ in(ordered_pair(U_245,U_252),U_249)
& in(U_252,U_255) ) )
& ! [U_254] :
( ( ! [U_251] :
( in(U_251,U_254)
| ! [U_243] : ~ in(ordered_pair(U_243,U_251),U_249) )
& ! [U_250] :
( ? [U_242] : in(ordered_pair(U_242,U_250),U_249)
| ~ in(U_250,U_254) ) )
| U_254 != relation_rng(U_249) ) )
| ~ relation(U_249) ),
inference(miniscope,[status(thm)],[f_26_2]) ).
fof(f_26_4,plain,
! [U_249] :
( ( ! [U_255] :
( U_255 = relation_rng(U_249)
| ? [U_253] :
( ~ in(U_253,U_255)
& ? [U_246] : in(ordered_pair(U_246,U_253),U_249) )
| ? [U_252] :
( ! [U_245] : ~ in(ordered_pair(U_245,U_252),U_249)
& in(U_252,U_255) ) )
& ! [U_254] :
( ( ! [U_251] :
( in(U_251,U_254)
| ! [U_243] : ~ in(ordered_pair(U_243,U_251),U_249) )
& ! [U_250] :
( in(ordered_pair(sK46(U_249,U_254,U_250),U_250),U_249)
| ~ in(U_250,U_254) ) )
| U_254 != relation_rng(U_249) ) )
| ~ relation(U_249) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_242,sK46(U_249,U_254,U_250))],[f_26_3]) ).
fof(f_26_5,plain,
! [U_249] :
( ( ! [U_255] :
( U_255 = relation_rng(U_249)
| ? [U_253] :
( ~ in(U_253,U_255)
& ? [U_246] : in(ordered_pair(U_246,U_253),U_249) )
| ( ! [U_245] : ~ in(ordered_pair(U_245,sK47(U_249,U_255)),U_249)
& in(sK47(U_249,U_255),U_255) ) )
& ! [U_254] :
( ( ! [U_251] :
( in(U_251,U_254)
| ! [U_243] : ~ in(ordered_pair(U_243,U_251),U_249) )
& ! [U_250] :
( in(ordered_pair(sK46(U_249,U_254,U_250),U_250),U_249)
| ~ in(U_250,U_254) ) )
| U_254 != relation_rng(U_249) ) )
| ~ relation(U_249) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_252,sK47(U_249,U_255))],[f_26_4]) ).
fof(f_26_6,plain,
! [U_249] :
( ( ! [U_255] :
( U_255 = relation_rng(U_249)
| ( ~ in(sK48(U_249,U_255),U_255)
& ? [U_246] : in(ordered_pair(U_246,sK48(U_249,U_255)),U_249) )
| ( ! [U_245] : ~ in(ordered_pair(U_245,sK47(U_249,U_255)),U_249)
& in(sK47(U_249,U_255),U_255) ) )
& ! [U_254] :
( ( ! [U_251] :
( in(U_251,U_254)
| ! [U_243] : ~ in(ordered_pair(U_243,U_251),U_249) )
& ! [U_250] :
( in(ordered_pair(sK46(U_249,U_254,U_250),U_250),U_249)
| ~ in(U_250,U_254) ) )
| U_254 != relation_rng(U_249) ) )
| ~ relation(U_249) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_253,sK48(U_249,U_255))],[f_26_5]) ).
fof(f_26_7,plain,
! [U_249] :
( ( ! [U_255] :
( U_255 = relation_rng(U_249)
| ( ~ in(sK48(U_249,U_255),U_255)
& in(ordered_pair(sK49(U_249,U_255),sK48(U_249,U_255)),U_249) )
| ( ! [U_245] : ~ in(ordered_pair(U_245,sK47(U_249,U_255)),U_249)
& in(sK47(U_249,U_255),U_255) ) )
& ! [U_254] :
( ( ! [U_251] :
( in(U_251,U_254)
| ! [U_243] : ~ in(ordered_pair(U_243,U_251),U_249) )
& ! [U_250] :
( in(ordered_pair(sK46(U_249,U_254,U_250),U_250),U_249)
| ~ in(U_250,U_254) ) )
| U_254 != relation_rng(U_249) ) )
| ~ relation(U_249) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_246,sK49(U_249,U_255))],[f_26_6]) ).
cnf(f_26_8,plain,
( in(ordered_pair(sK46(U_249,U_254,U_250),U_250),U_249)
| ~ in(U_250,U_254)
| U_254 != relation_rng(U_249)
| ~ relation(U_249) ),
inference(clausify,[status(thm)],[f_26_7]) ).
cnf(f_26_9,plain,
( in(U_251,U_254)
| ~ in(ordered_pair(U_243,U_251),U_249)
| U_254 != relation_rng(U_249)
| ~ relation(U_249) ),
inference(clausify,[status(thm)],[f_26_7]) ).
cnf(f_26_10,plain,
( in(ordered_pair(sK49(U_249,U_255),sK48(U_249,U_255)),U_249)
| in(sK47(U_249,U_255),U_255)
| U_255 = relation_rng(U_249)
| ~ relation(U_249) ),
inference(clausify,[status(thm)],[f_26_7]) ).
cnf(f_26_11,plain,
( ~ in(sK48(U_249,U_255),U_255)
| in(sK47(U_249,U_255),U_255)
| U_255 = relation_rng(U_249)
| ~ relation(U_249) ),
inference(clausify,[status(thm)],[f_26_7]) ).
cnf(f_26_12,plain,
( in(ordered_pair(sK49(U_249,U_255),sK48(U_249,U_255)),U_249)
| ~ in(ordered_pair(U_245,sK47(U_249,U_255)),U_249)
| U_255 = relation_rng(U_249)
| ~ relation(U_249) ),
inference(clausify,[status(thm)],[f_26_7]) ).
cnf(f_26_13,plain,
( ~ in(sK48(U_249,U_255),U_255)
| ~ in(ordered_pair(U_245,sK47(U_249,U_255)),U_249)
| U_255 = relation_rng(U_249)
| ~ relation(U_249) ),
inference(clausify,[status(thm)],[f_26_7]) ).
fof(f_27_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_27_2,plain,
! [U_257,U_256] :
( subset_complement(U_257,U_256) = set_difference(U_257,U_256)
| ~ element(U_256,powerset(U_257)) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( subset_complement(U_257,U_256) = set_difference(U_257,U_256)
| ~ element(U_256,powerset(U_257)) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_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_28_2,plain,
! [U_259,U_258] : ordered_pair(U_259,U_258) = unordered_pair(unordered_pair(U_259,U_258),singleton(U_259)),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
ordered_pair(U_259,U_258) = unordered_pair(unordered_pair(U_259,U_258),singleton(U_259)),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_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_29_2,plain,
! [U_260] :
( relation_field(U_260) = set_union2(relation_dom(U_260),relation_rng(U_260))
| ~ relation(U_260) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( relation_field(U_260) = set_union2(relation_dom(U_260),relation_rng(U_260))
| ~ relation(U_260) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_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_30_2,plain,
! [U_266] :
( ! [U_265] :
( ( ( U_265 = relation_inverse(U_266)
| ? [U_264,U_263] :
( ( ~ in(ordered_pair(U_264,U_263),U_265)
& in(ordered_pair(U_263,U_264),U_266) )
| ( ~ in(ordered_pair(U_263,U_264),U_266)
& in(ordered_pair(U_264,U_263),U_265) ) ) )
& ( ! [U_262,U_261] :
( ( in(ordered_pair(U_262,U_261),U_265)
| ~ in(ordered_pair(U_261,U_262),U_266) )
& ( in(ordered_pair(U_261,U_262),U_266)
| ~ in(ordered_pair(U_262,U_261),U_265) ) )
| U_265 != relation_inverse(U_266) ) )
| ~ relation(U_265) )
| ~ relation(U_266) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_266] :
( ! [U_265] :
( ( ( U_265 = relation_inverse(U_266)
| ? [U_274,U_272] :
( ~ in(ordered_pair(U_274,U_272),U_265)
& in(ordered_pair(U_272,U_274),U_266) )
| ? [U_273,U_271] :
( ~ in(ordered_pair(U_271,U_273),U_266)
& in(ordered_pair(U_273,U_271),U_265) ) )
& ( ( ! [U_270,U_268] :
( in(ordered_pair(U_270,U_268),U_265)
| ~ in(ordered_pair(U_268,U_270),U_266) )
& ! [U_269,U_267] :
( in(ordered_pair(U_267,U_269),U_266)
| ~ in(ordered_pair(U_269,U_267),U_265) ) )
| U_265 != relation_inverse(U_266) ) )
| ~ relation(U_265) )
| ~ relation(U_266) ),
inference(miniscope,[status(thm)],[f_30_2]) ).
fof(f_30_4,plain,
! [U_266] :
( ! [U_265] :
( ( ( U_265 = relation_inverse(U_266)
| ? [U_274,U_272] :
( ~ in(ordered_pair(U_274,U_272),U_265)
& in(ordered_pair(U_272,U_274),U_266) )
| ? [U_271] :
( ~ in(ordered_pair(U_271,sK50(U_266,U_265)),U_266)
& in(ordered_pair(sK50(U_266,U_265),U_271),U_265) ) )
& ( ( ! [U_270,U_268] :
( in(ordered_pair(U_270,U_268),U_265)
| ~ in(ordered_pair(U_268,U_270),U_266) )
& ! [U_269,U_267] :
( in(ordered_pair(U_267,U_269),U_266)
| ~ in(ordered_pair(U_269,U_267),U_265) ) )
| U_265 != relation_inverse(U_266) ) )
| ~ relation(U_265) )
| ~ relation(U_266) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_273,sK50(U_266,U_265))],[f_30_3]) ).
fof(f_30_5,plain,
! [U_266] :
( ! [U_265] :
( ( ( U_265 = relation_inverse(U_266)
| ? [U_274,U_272] :
( ~ in(ordered_pair(U_274,U_272),U_265)
& in(ordered_pair(U_272,U_274),U_266) )
| ( ~ in(ordered_pair(sK51(U_266,U_265),sK50(U_266,U_265)),U_266)
& in(ordered_pair(sK50(U_266,U_265),sK51(U_266,U_265)),U_265) ) )
& ( ( ! [U_270,U_268] :
( in(ordered_pair(U_270,U_268),U_265)
| ~ in(ordered_pair(U_268,U_270),U_266) )
& ! [U_269,U_267] :
( in(ordered_pair(U_267,U_269),U_266)
| ~ in(ordered_pair(U_269,U_267),U_265) ) )
| U_265 != relation_inverse(U_266) ) )
| ~ relation(U_265) )
| ~ relation(U_266) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_271,sK51(U_266,U_265))],[f_30_4]) ).
fof(f_30_6,plain,
! [U_266] :
( ! [U_265] :
( ( ( U_265 = relation_inverse(U_266)
| ? [U_272] :
( ~ in(ordered_pair(sK52(U_266,U_265),U_272),U_265)
& in(ordered_pair(U_272,sK52(U_266,U_265)),U_266) )
| ( ~ in(ordered_pair(sK51(U_266,U_265),sK50(U_266,U_265)),U_266)
& in(ordered_pair(sK50(U_266,U_265),sK51(U_266,U_265)),U_265) ) )
& ( ( ! [U_270,U_268] :
( in(ordered_pair(U_270,U_268),U_265)
| ~ in(ordered_pair(U_268,U_270),U_266) )
& ! [U_269,U_267] :
( in(ordered_pair(U_267,U_269),U_266)
| ~ in(ordered_pair(U_269,U_267),U_265) ) )
| U_265 != relation_inverse(U_266) ) )
| ~ relation(U_265) )
| ~ relation(U_266) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_274,sK52(U_266,U_265))],[f_30_5]) ).
fof(f_30_7,plain,
! [U_266] :
( ! [U_265] :
( ( ( U_265 = relation_inverse(U_266)
| ( ~ in(ordered_pair(sK52(U_266,U_265),sK53(U_266,U_265)),U_265)
& in(ordered_pair(sK53(U_266,U_265),sK52(U_266,U_265)),U_266) )
| ( ~ in(ordered_pair(sK51(U_266,U_265),sK50(U_266,U_265)),U_266)
& in(ordered_pair(sK50(U_266,U_265),sK51(U_266,U_265)),U_265) ) )
& ( ( ! [U_270,U_268] :
( in(ordered_pair(U_270,U_268),U_265)
| ~ in(ordered_pair(U_268,U_270),U_266) )
& ! [U_269,U_267] :
( in(ordered_pair(U_267,U_269),U_266)
| ~ in(ordered_pair(U_269,U_267),U_265) ) )
| U_265 != relation_inverse(U_266) ) )
| ~ relation(U_265) )
| ~ relation(U_266) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_272,sK53(U_266,U_265))],[f_30_6]) ).
cnf(f_30_8,plain,
( in(ordered_pair(U_267,U_269),U_266)
| ~ in(ordered_pair(U_269,U_267),U_265)
| U_265 != relation_inverse(U_266)
| ~ relation(U_265)
| ~ relation(U_266) ),
inference(clausify,[status(thm)],[f_30_7]) ).
cnf(f_30_9,plain,
( in(ordered_pair(U_270,U_268),U_265)
| ~ in(ordered_pair(U_268,U_270),U_266)
| U_265 != relation_inverse(U_266)
| ~ relation(U_265)
| ~ relation(U_266) ),
inference(clausify,[status(thm)],[f_30_7]) ).
cnf(f_30_10,plain,
( in(ordered_pair(sK53(U_266,U_265),sK52(U_266,U_265)),U_266)
| in(ordered_pair(sK50(U_266,U_265),sK51(U_266,U_265)),U_265)
| U_265 = relation_inverse(U_266)
| ~ relation(U_265)
| ~ relation(U_266) ),
inference(clausify,[status(thm)],[f_30_7]) ).
cnf(f_30_11,plain,
( ~ in(ordered_pair(sK52(U_266,U_265),sK53(U_266,U_265)),U_265)
| in(ordered_pair(sK50(U_266,U_265),sK51(U_266,U_265)),U_265)
| U_265 = relation_inverse(U_266)
| ~ relation(U_265)
| ~ relation(U_266) ),
inference(clausify,[status(thm)],[f_30_7]) ).
cnf(f_30_12,plain,
( in(ordered_pair(sK53(U_266,U_265),sK52(U_266,U_265)),U_266)
| ~ in(ordered_pair(sK51(U_266,U_265),sK50(U_266,U_265)),U_266)
| U_265 = relation_inverse(U_266)
| ~ relation(U_265)
| ~ relation(U_266) ),
inference(clausify,[status(thm)],[f_30_7]) ).
cnf(f_30_13,plain,
( ~ in(ordered_pair(sK52(U_266,U_265),sK53(U_266,U_265)),U_265)
| ~ in(ordered_pair(sK51(U_266,U_265),sK50(U_266,U_265)),U_266)
| U_265 = relation_inverse(U_266)
| ~ relation(U_265)
| ~ relation(U_266) ),
inference(clausify,[status(thm)],[f_30_7]) ).
fof(f_31_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_31_2,plain,
! [U_276,U_275] :
( ( disjoint(U_276,U_275)
| set_intersection2(U_276,U_275) != empty_set )
& ( set_intersection2(U_276,U_275) = empty_set
| ~ disjoint(U_276,U_275) ) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( ! [U_280,U_278] :
( disjoint(U_280,U_278)
| set_intersection2(U_280,U_278) != empty_set )
& ! [U_279,U_277] :
( set_intersection2(U_279,U_277) = empty_set
| ~ disjoint(U_279,U_277) ) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
cnf(f_31_4,plain,
( set_intersection2(U_279,U_277) = empty_set
| ~ disjoint(U_279,U_277) ),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_5,plain,
( disjoint(U_280,U_278)
| set_intersection2(U_280,U_278) != empty_set ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_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_32_2,plain,
! [U_291] :
( ! [U_290] :
( ! [U_289] :
( ( ( U_289 = relation_composition(U_291,U_290)
| ? [U_288,U_287] :
( ( ~ in(ordered_pair(U_288,U_287),U_289)
& ? [U_286] :
( in(ordered_pair(U_286,U_287),U_290)
& in(ordered_pair(U_288,U_286),U_291) ) )
| ( ! [U_285] :
( ~ in(ordered_pair(U_285,U_287),U_290)
| ~ in(ordered_pair(U_288,U_285),U_291) )
& in(ordered_pair(U_288,U_287),U_289) ) ) )
& ( ! [U_284,U_283] :
( ( in(ordered_pair(U_284,U_283),U_289)
| ! [U_282] :
( ~ in(ordered_pair(U_282,U_283),U_290)
| ~ in(ordered_pair(U_284,U_282),U_291) ) )
& ( ? [U_281] :
( in(ordered_pair(U_281,U_283),U_290)
& in(ordered_pair(U_284,U_281),U_291) )
| ~ in(ordered_pair(U_284,U_283),U_289) ) )
| U_289 != relation_composition(U_291,U_290) ) )
| ~ relation(U_289) )
| ~ relation(U_290) )
| ~ relation(U_291) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_291] :
( ! [U_290] :
( ! [U_289] :
( ( ( U_289 = relation_composition(U_291,U_290)
| ? [U_299,U_297] :
( ~ in(ordered_pair(U_299,U_297),U_289)
& ? [U_286] :
( in(ordered_pair(U_286,U_297),U_290)
& in(ordered_pair(U_299,U_286),U_291) ) )
| ? [U_298,U_296] :
( ! [U_285] :
( ~ in(ordered_pair(U_285,U_296),U_290)
| ~ in(ordered_pair(U_298,U_285),U_291) )
& in(ordered_pair(U_298,U_296),U_289) ) )
& ( ( ! [U_295,U_293] :
( in(ordered_pair(U_295,U_293),U_289)
| ! [U_282] :
( ~ in(ordered_pair(U_282,U_293),U_290)
| ~ in(ordered_pair(U_295,U_282),U_291) ) )
& ! [U_294,U_292] :
( ? [U_281] :
( in(ordered_pair(U_281,U_292),U_290)
& in(ordered_pair(U_294,U_281),U_291) )
| ~ in(ordered_pair(U_294,U_292),U_289) ) )
| U_289 != relation_composition(U_291,U_290) ) )
| ~ relation(U_289) )
| ~ relation(U_290) )
| ~ relation(U_291) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
fof(f_32_4,plain,
! [U_291] :
( ! [U_290] :
( ! [U_289] :
( ( ( U_289 = relation_composition(U_291,U_290)
| ? [U_299,U_297] :
( ~ in(ordered_pair(U_299,U_297),U_289)
& ? [U_286] :
( in(ordered_pair(U_286,U_297),U_290)
& in(ordered_pair(U_299,U_286),U_291) ) )
| ? [U_298,U_296] :
( ! [U_285] :
( ~ in(ordered_pair(U_285,U_296),U_290)
| ~ in(ordered_pair(U_298,U_285),U_291) )
& in(ordered_pair(U_298,U_296),U_289) ) )
& ( ( ! [U_295,U_293] :
( in(ordered_pair(U_295,U_293),U_289)
| ! [U_282] :
( ~ in(ordered_pair(U_282,U_293),U_290)
| ~ in(ordered_pair(U_295,U_282),U_291) ) )
& ! [U_294,U_292] :
( ( in(ordered_pair(sK54(U_291,U_290,U_289,U_294,U_292),U_292),U_290)
& in(ordered_pair(U_294,sK54(U_291,U_290,U_289,U_294,U_292)),U_291) )
| ~ in(ordered_pair(U_294,U_292),U_289) ) )
| U_289 != relation_composition(U_291,U_290) ) )
| ~ relation(U_289) )
| ~ relation(U_290) )
| ~ relation(U_291) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_281,sK54(U_291,U_290,U_289,U_294,U_292))],[f_32_3]) ).
fof(f_32_5,plain,
! [U_291] :
( ! [U_290] :
( ! [U_289] :
( ( ( U_289 = relation_composition(U_291,U_290)
| ? [U_299,U_297] :
( ~ in(ordered_pair(U_299,U_297),U_289)
& ? [U_286] :
( in(ordered_pair(U_286,U_297),U_290)
& in(ordered_pair(U_299,U_286),U_291) ) )
| ? [U_296] :
( ! [U_285] :
( ~ in(ordered_pair(U_285,U_296),U_290)
| ~ in(ordered_pair(sK55(U_291,U_290,U_289),U_285),U_291) )
& in(ordered_pair(sK55(U_291,U_290,U_289),U_296),U_289) ) )
& ( ( ! [U_295,U_293] :
( in(ordered_pair(U_295,U_293),U_289)
| ! [U_282] :
( ~ in(ordered_pair(U_282,U_293),U_290)
| ~ in(ordered_pair(U_295,U_282),U_291) ) )
& ! [U_294,U_292] :
( ( in(ordered_pair(sK54(U_291,U_290,U_289,U_294,U_292),U_292),U_290)
& in(ordered_pair(U_294,sK54(U_291,U_290,U_289,U_294,U_292)),U_291) )
| ~ in(ordered_pair(U_294,U_292),U_289) ) )
| U_289 != relation_composition(U_291,U_290) ) )
| ~ relation(U_289) )
| ~ relation(U_290) )
| ~ relation(U_291) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_298,sK55(U_291,U_290,U_289))],[f_32_4]) ).
fof(f_32_6,plain,
! [U_291] :
( ! [U_290] :
( ! [U_289] :
( ( ( U_289 = relation_composition(U_291,U_290)
| ? [U_299,U_297] :
( ~ in(ordered_pair(U_299,U_297),U_289)
& ? [U_286] :
( in(ordered_pair(U_286,U_297),U_290)
& in(ordered_pair(U_299,U_286),U_291) ) )
| ( ! [U_285] :
( ~ in(ordered_pair(U_285,sK56(U_291,U_290,U_289)),U_290)
| ~ in(ordered_pair(sK55(U_291,U_290,U_289),U_285),U_291) )
& in(ordered_pair(sK55(U_291,U_290,U_289),sK56(U_291,U_290,U_289)),U_289) ) )
& ( ( ! [U_295,U_293] :
( in(ordered_pair(U_295,U_293),U_289)
| ! [U_282] :
( ~ in(ordered_pair(U_282,U_293),U_290)
| ~ in(ordered_pair(U_295,U_282),U_291) ) )
& ! [U_294,U_292] :
( ( in(ordered_pair(sK54(U_291,U_290,U_289,U_294,U_292),U_292),U_290)
& in(ordered_pair(U_294,sK54(U_291,U_290,U_289,U_294,U_292)),U_291) )
| ~ in(ordered_pair(U_294,U_292),U_289) ) )
| U_289 != relation_composition(U_291,U_290) ) )
| ~ relation(U_289) )
| ~ relation(U_290) )
| ~ relation(U_291) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_296,sK56(U_291,U_290,U_289))],[f_32_5]) ).
fof(f_32_7,plain,
! [U_291] :
( ! [U_290] :
( ! [U_289] :
( ( ( U_289 = relation_composition(U_291,U_290)
| ? [U_297] :
( ~ in(ordered_pair(sK57(U_291,U_290,U_289),U_297),U_289)
& ? [U_286] :
( in(ordered_pair(U_286,U_297),U_290)
& in(ordered_pair(sK57(U_291,U_290,U_289),U_286),U_291) ) )
| ( ! [U_285] :
( ~ in(ordered_pair(U_285,sK56(U_291,U_290,U_289)),U_290)
| ~ in(ordered_pair(sK55(U_291,U_290,U_289),U_285),U_291) )
& in(ordered_pair(sK55(U_291,U_290,U_289),sK56(U_291,U_290,U_289)),U_289) ) )
& ( ( ! [U_295,U_293] :
( in(ordered_pair(U_295,U_293),U_289)
| ! [U_282] :
( ~ in(ordered_pair(U_282,U_293),U_290)
| ~ in(ordered_pair(U_295,U_282),U_291) ) )
& ! [U_294,U_292] :
( ( in(ordered_pair(sK54(U_291,U_290,U_289,U_294,U_292),U_292),U_290)
& in(ordered_pair(U_294,sK54(U_291,U_290,U_289,U_294,U_292)),U_291) )
| ~ in(ordered_pair(U_294,U_292),U_289) ) )
| U_289 != relation_composition(U_291,U_290) ) )
| ~ relation(U_289) )
| ~ relation(U_290) )
| ~ relation(U_291) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_299,sK57(U_291,U_290,U_289))],[f_32_6]) ).
fof(f_32_8,plain,
! [U_291] :
( ! [U_290] :
( ! [U_289] :
( ( ( U_289 = relation_composition(U_291,U_290)
| ( ~ in(ordered_pair(sK57(U_291,U_290,U_289),sK58(U_291,U_290,U_289)),U_289)
& ? [U_286] :
( in(ordered_pair(U_286,sK58(U_291,U_290,U_289)),U_290)
& in(ordered_pair(sK57(U_291,U_290,U_289),U_286),U_291) ) )
| ( ! [U_285] :
( ~ in(ordered_pair(U_285,sK56(U_291,U_290,U_289)),U_290)
| ~ in(ordered_pair(sK55(U_291,U_290,U_289),U_285),U_291) )
& in(ordered_pair(sK55(U_291,U_290,U_289),sK56(U_291,U_290,U_289)),U_289) ) )
& ( ( ! [U_295,U_293] :
( in(ordered_pair(U_295,U_293),U_289)
| ! [U_282] :
( ~ in(ordered_pair(U_282,U_293),U_290)
| ~ in(ordered_pair(U_295,U_282),U_291) ) )
& ! [U_294,U_292] :
( ( in(ordered_pair(sK54(U_291,U_290,U_289,U_294,U_292),U_292),U_290)
& in(ordered_pair(U_294,sK54(U_291,U_290,U_289,U_294,U_292)),U_291) )
| ~ in(ordered_pair(U_294,U_292),U_289) ) )
| U_289 != relation_composition(U_291,U_290) ) )
| ~ relation(U_289) )
| ~ relation(U_290) )
| ~ relation(U_291) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_297,sK58(U_291,U_290,U_289))],[f_32_7]) ).
fof(f_32_9,plain,
! [U_291] :
( ! [U_290] :
( ! [U_289] :
( ( ( U_289 = relation_composition(U_291,U_290)
| ( ~ in(ordered_pair(sK57(U_291,U_290,U_289),sK58(U_291,U_290,U_289)),U_289)
& in(ordered_pair(sK59(U_291,U_290,U_289),sK58(U_291,U_290,U_289)),U_290)
& in(ordered_pair(sK57(U_291,U_290,U_289),sK59(U_291,U_290,U_289)),U_291) )
| ( ! [U_285] :
( ~ in(ordered_pair(U_285,sK56(U_291,U_290,U_289)),U_290)
| ~ in(ordered_pair(sK55(U_291,U_290,U_289),U_285),U_291) )
& in(ordered_pair(sK55(U_291,U_290,U_289),sK56(U_291,U_290,U_289)),U_289) ) )
& ( ( ! [U_295,U_293] :
( in(ordered_pair(U_295,U_293),U_289)
| ! [U_282] :
( ~ in(ordered_pair(U_282,U_293),U_290)
| ~ in(ordered_pair(U_295,U_282),U_291) ) )
& ! [U_294,U_292] :
( ( in(ordered_pair(sK54(U_291,U_290,U_289,U_294,U_292),U_292),U_290)
& in(ordered_pair(U_294,sK54(U_291,U_290,U_289,U_294,U_292)),U_291) )
| ~ in(ordered_pair(U_294,U_292),U_289) ) )
| U_289 != relation_composition(U_291,U_290) ) )
| ~ relation(U_289) )
| ~ relation(U_290) )
| ~ relation(U_291) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_286,sK59(U_291,U_290,U_289))],[f_32_8]) ).
cnf(f_32_10,plain,
( in(ordered_pair(U_294,sK54(U_291,U_290,U_289,U_294,U_292)),U_291)
| ~ in(ordered_pair(U_294,U_292),U_289)
| U_289 != relation_composition(U_291,U_290)
| ~ relation(U_289)
| ~ relation(U_290)
| ~ relation(U_291) ),
inference(clausify,[status(thm)],[f_32_9]) ).
cnf(f_32_11,plain,
( in(ordered_pair(sK54(U_291,U_290,U_289,U_294,U_292),U_292),U_290)
| ~ in(ordered_pair(U_294,U_292),U_289)
| U_289 != relation_composition(U_291,U_290)
| ~ relation(U_289)
| ~ relation(U_290)
| ~ relation(U_291) ),
inference(clausify,[status(thm)],[f_32_9]) ).
cnf(f_32_12,plain,
( in(ordered_pair(U_295,U_293),U_289)
| ~ in(ordered_pair(U_282,U_293),U_290)
| ~ in(ordered_pair(U_295,U_282),U_291)
| U_289 != relation_composition(U_291,U_290)
| ~ relation(U_289)
| ~ relation(U_290)
| ~ relation(U_291) ),
inference(clausify,[status(thm)],[f_32_9]) ).
cnf(f_32_13,plain,
( in(ordered_pair(sK57(U_291,U_290,U_289),sK59(U_291,U_290,U_289)),U_291)
| in(ordered_pair(sK55(U_291,U_290,U_289),sK56(U_291,U_290,U_289)),U_289)
| U_289 = relation_composition(U_291,U_290)
| ~ relation(U_289)
| ~ relation(U_290)
| ~ relation(U_291) ),
inference(clausify,[status(thm)],[f_32_9]) ).
cnf(f_32_14,plain,
( in(ordered_pair(sK59(U_291,U_290,U_289),sK58(U_291,U_290,U_289)),U_290)
| in(ordered_pair(sK55(U_291,U_290,U_289),sK56(U_291,U_290,U_289)),U_289)
| U_289 = relation_composition(U_291,U_290)
| ~ relation(U_289)
| ~ relation(U_290)
| ~ relation(U_291) ),
inference(clausify,[status(thm)],[f_32_9]) ).
cnf(f_32_15,plain,
( ~ in(ordered_pair(sK57(U_291,U_290,U_289),sK58(U_291,U_290,U_289)),U_289)
| in(ordered_pair(sK55(U_291,U_290,U_289),sK56(U_291,U_290,U_289)),U_289)
| U_289 = relation_composition(U_291,U_290)
| ~ relation(U_289)
| ~ relation(U_290)
| ~ relation(U_291) ),
inference(clausify,[status(thm)],[f_32_9]) ).
cnf(f_32_16,plain,
( in(ordered_pair(sK57(U_291,U_290,U_289),sK59(U_291,U_290,U_289)),U_291)
| ~ in(ordered_pair(U_285,sK56(U_291,U_290,U_289)),U_290)
| ~ in(ordered_pair(sK55(U_291,U_290,U_289),U_285),U_291)
| U_289 = relation_composition(U_291,U_290)
| ~ relation(U_289)
| ~ relation(U_290)
| ~ relation(U_291) ),
inference(clausify,[status(thm)],[f_32_9]) ).
cnf(f_32_17,plain,
( in(ordered_pair(sK59(U_291,U_290,U_289),sK58(U_291,U_290,U_289)),U_290)
| ~ in(ordered_pair(U_285,sK56(U_291,U_290,U_289)),U_290)
| ~ in(ordered_pair(sK55(U_291,U_290,U_289),U_285),U_291)
| U_289 = relation_composition(U_291,U_290)
| ~ relation(U_289)
| ~ relation(U_290)
| ~ relation(U_291) ),
inference(clausify,[status(thm)],[f_32_9]) ).
cnf(f_32_18,plain,
( ~ in(ordered_pair(sK57(U_291,U_290,U_289),sK58(U_291,U_290,U_289)),U_289)
| ~ in(ordered_pair(U_285,sK56(U_291,U_290,U_289)),U_290)
| ~ in(ordered_pair(sK55(U_291,U_290,U_289),U_285),U_291)
| U_289 = relation_composition(U_291,U_290)
| ~ relation(U_289)
| ~ relation(U_290)
| ~ relation(U_291) ),
inference(clausify,[status(thm)],[f_32_9]) ).
fof(f_33_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_33_2,plain,
! [U_304,U_303] :
( ! [U_302] :
( ( ( U_302 = complements_of_subsets(U_304,U_303)
| ? [U_301] :
( ( ( ~ in(U_301,U_302)
& in(subset_complement(U_304,U_301),U_303) )
| ( ~ in(subset_complement(U_304,U_301),U_303)
& in(U_301,U_302) ) )
& element(U_301,powerset(U_304)) ) )
& ( ! [U_300] :
( ( ( in(U_300,U_302)
| ~ in(subset_complement(U_304,U_300),U_303) )
& ( in(subset_complement(U_304,U_300),U_303)
| ~ in(U_300,U_302) ) )
| ~ element(U_300,powerset(U_304)) )
| U_302 != complements_of_subsets(U_304,U_303) ) )
| ~ element(U_302,powerset(powerset(U_304))) )
| ~ element(U_303,powerset(powerset(U_304))) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_304,U_303] :
( ! [U_302] :
( ( ( U_302 = complements_of_subsets(U_304,U_303)
| ( ( ( ~ in(sK60(U_304,U_303,U_302),U_302)
& in(subset_complement(U_304,sK60(U_304,U_303,U_302)),U_303) )
| ( ~ in(subset_complement(U_304,sK60(U_304,U_303,U_302)),U_303)
& in(sK60(U_304,U_303,U_302),U_302) ) )
& element(sK60(U_304,U_303,U_302),powerset(U_304)) ) )
& ( ! [U_300] :
( ( ( in(U_300,U_302)
| ~ in(subset_complement(U_304,U_300),U_303) )
& ( in(subset_complement(U_304,U_300),U_303)
| ~ in(U_300,U_302) ) )
| ~ element(U_300,powerset(U_304)) )
| U_302 != complements_of_subsets(U_304,U_303) ) )
| ~ element(U_302,powerset(powerset(U_304))) )
| ~ element(U_303,powerset(powerset(U_304))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_301,sK60(U_304,U_303,U_302))],[f_33_2]) ).
cnf(f_33_4,plain,
( in(subset_complement(U_304,U_300),U_303)
| ~ in(U_300,U_302)
| ~ element(U_300,powerset(U_304))
| U_302 != complements_of_subsets(U_304,U_303)
| ~ element(U_302,powerset(powerset(U_304)))
| ~ element(U_303,powerset(powerset(U_304))) ),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_5,plain,
( in(U_300,U_302)
| ~ in(subset_complement(U_304,U_300),U_303)
| ~ element(U_300,powerset(U_304))
| U_302 != complements_of_subsets(U_304,U_303)
| ~ element(U_302,powerset(powerset(U_304)))
| ~ element(U_303,powerset(powerset(U_304))) ),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_6,plain,
( element(sK60(U_304,U_303,U_302),powerset(U_304))
| U_302 = complements_of_subsets(U_304,U_303)
| ~ element(U_302,powerset(powerset(U_304)))
| ~ element(U_303,powerset(powerset(U_304))) ),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_7,plain,
( in(subset_complement(U_304,sK60(U_304,U_303,U_302)),U_303)
| in(sK60(U_304,U_303,U_302),U_302)
| U_302 = complements_of_subsets(U_304,U_303)
| ~ element(U_302,powerset(powerset(U_304)))
| ~ element(U_303,powerset(powerset(U_304))) ),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_8,plain,
( ~ in(sK60(U_304,U_303,U_302),U_302)
| in(sK60(U_304,U_303,U_302),U_302)
| U_302 = complements_of_subsets(U_304,U_303)
| ~ element(U_302,powerset(powerset(U_304)))
| ~ element(U_303,powerset(powerset(U_304))) ),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_9,plain,
( in(subset_complement(U_304,sK60(U_304,U_303,U_302)),U_303)
| ~ in(subset_complement(U_304,sK60(U_304,U_303,U_302)),U_303)
| U_302 = complements_of_subsets(U_304,U_303)
| ~ element(U_302,powerset(powerset(U_304)))
| ~ element(U_303,powerset(powerset(U_304))) ),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_10,plain,
( ~ in(sK60(U_304,U_303,U_302),U_302)
| ~ in(subset_complement(U_304,sK60(U_304,U_303,U_302)),U_303)
| U_302 = complements_of_subsets(U_304,U_303)
| ~ element(U_302,powerset(powerset(U_304)))
| ~ element(U_303,powerset(powerset(U_304))) ),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_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_34_2,plain,
! [U_306,U_305] :
( ( proper_subset(U_306,U_305)
| U_306 = U_305
| ~ subset(U_306,U_305) )
& ( ( U_306 != U_305
& subset(U_306,U_305) )
| ~ proper_subset(U_306,U_305) ) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
( ! [U_310,U_308] :
( proper_subset(U_310,U_308)
| U_310 = U_308
| ~ subset(U_310,U_308) )
& ! [U_309,U_307] :
( ( U_309 != U_307
& subset(U_309,U_307) )
| ~ proper_subset(U_309,U_307) ) ),
inference(miniscope,[status(thm)],[f_34_2]) ).
cnf(f_34_4,plain,
( subset(U_309,U_307)
| ~ proper_subset(U_309,U_307) ),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_5,plain,
( U_309 != U_307
| ~ proper_subset(U_309,U_307) ),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_6,plain,
( proper_subset(U_310,U_308)
| U_310 = U_308
| ~ subset(U_310,U_308) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
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_setfam_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_k1_tarski]) ).
cnf(f_37_2,plain,
$true,
inference(clausify,[status(thm)],[f_37_1]) ).
fof(f_38_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_38_2,plain,
$true,
inference(clausify,[status(thm)],[f_38_1]) ).
fof(f_39_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_39_2,plain,
$true,
inference(clausify,[status(thm)],[f_39_1]) ).
fof(f_40_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_relat_1]) ).
cnf(f_40_2,plain,
$true,
inference(clausify,[status(thm)],[f_40_1]) ).
fof(f_41_1,plain,
! [A] : element(cast_to_subset(A),powerset(A)),
inference(fof_nnf,[status(thm)],[dt_k2_subset_1]) ).
fof(f_41_2,plain,
! [U_311] : element(cast_to_subset(U_311),powerset(U_311)),
inference(variable_rename,[status(thm)],[f_41_1]) ).
cnf(f_41_3,plain,
element(cast_to_subset(U_311),powerset(U_311)),
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
cnf(f_42_2,plain,
$true,
inference(clausify,[status(thm)],[f_42_1]) ).
fof(f_43_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
cnf(f_43_2,plain,
$true,
inference(clausify,[status(thm)],[f_43_1]) ).
fof(f_44_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
cnf(f_44_2,plain,
$true,
inference(clausify,[status(thm)],[f_44_1]) ).
fof(f_45_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_relat_1]) ).
cnf(f_45_2,plain,
$true,
inference(clausify,[status(thm)],[f_45_1]) ).
fof(f_46_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_46_2,plain,
! [U_313,U_312] :
( element(subset_complement(U_313,U_312),powerset(U_313))
| ~ element(U_312,powerset(U_313)) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
cnf(f_46_3,plain,
( element(subset_complement(U_313,U_312),powerset(U_313))
| ~ element(U_312,powerset(U_313)) ),
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_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_k3_xboole_0]) ).
cnf(f_48_2,plain,
$true,
inference(clausify,[status(thm)],[f_48_1]) ).
fof(f_49_1,plain,
! [A] :
( relation(relation_inverse(A))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k4_relat_1]) ).
fof(f_49_2,plain,
! [U_314] :
( relation(relation_inverse(U_314))
| ~ relation(U_314) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
cnf(f_49_3,plain,
( relation(relation_inverse(U_314))
| ~ relation(U_314) ),
inference(clausify,[status(thm)],[f_49_2]) ).
fof(f_50_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
cnf(f_50_2,plain,
$true,
inference(clausify,[status(thm)],[f_50_1]) ).
fof(f_51_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
cnf(f_51_2,plain,
$true,
inference(clausify,[status(thm)],[f_51_1]) ).
fof(f_52_1,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_relat_1]) ).
fof(f_52_2,plain,
! [U_316,U_315] :
( relation(relation_composition(U_316,U_315))
| ~ relation(U_315)
| ~ relation(U_316) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
cnf(f_52_3,plain,
( relation(relation_composition(U_316,U_315))
| ~ relation(U_315)
| ~ relation(U_316) ),
inference(clausify,[status(thm)],[f_52_2]) ).
fof(f_53_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_53_2,plain,
! [U_318,U_317] :
( element(union_of_subsets(U_318,U_317),powerset(U_318))
| ~ element(U_317,powerset(powerset(U_318))) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
cnf(f_53_3,plain,
( element(union_of_subsets(U_318,U_317),powerset(U_318))
| ~ element(U_317,powerset(powerset(U_318))) ),
inference(clausify,[status(thm)],[f_53_2]) ).
fof(f_54_1,plain,
! [A] : relation(identity_relation(A)),
inference(fof_nnf,[status(thm)],[dt_k6_relat_1]) ).
fof(f_54_2,plain,
! [U_319] : relation(identity_relation(U_319)),
inference(variable_rename,[status(thm)],[f_54_1]) ).
cnf(f_54_3,plain,
relation(identity_relation(U_319)),
inference(clausify,[status(thm)],[f_54_2]) ).
fof(f_55_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_55_2,plain,
! [U_321,U_320] :
( element(meet_of_subsets(U_321,U_320),powerset(U_321))
| ~ element(U_320,powerset(powerset(U_321))) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
cnf(f_55_3,plain,
( element(meet_of_subsets(U_321,U_320),powerset(U_321))
| ~ element(U_320,powerset(powerset(U_321))) ),
inference(clausify,[status(thm)],[f_55_2]) ).
fof(f_56_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_56_2,plain,
! [U_324,U_323,U_322] :
( element(subset_difference(U_324,U_323,U_322),powerset(U_324))
| ~ element(U_322,powerset(U_324))
| ~ element(U_323,powerset(U_324)) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
cnf(f_56_3,plain,
( element(subset_difference(U_324,U_323,U_322),powerset(U_324))
| ~ element(U_322,powerset(U_324))
| ~ element(U_323,powerset(U_324)) ),
inference(clausify,[status(thm)],[f_56_2]) ).
fof(f_57_1,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k7_relat_1]) ).
fof(f_57_2,plain,
! [U_326,U_325] :
( relation(relation_dom_restriction(U_326,U_325))
| ~ relation(U_326) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
! [U_326] :
( ! [U_325] : relation(relation_dom_restriction(U_326,U_325))
| ~ relation(U_326) ),
inference(miniscope,[status(thm)],[f_57_2]) ).
cnf(f_57_4,plain,
( relation(relation_dom_restriction(U_326,U_325))
| ~ relation(U_326) ),
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_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_58_2,plain,
! [U_328,U_327] :
( element(complements_of_subsets(U_328,U_327),powerset(powerset(U_328)))
| ~ element(U_327,powerset(powerset(U_328))) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
cnf(f_58_3,plain,
( element(complements_of_subsets(U_328,U_327),powerset(powerset(U_328)))
| ~ element(U_327,powerset(powerset(U_328))) ),
inference(clausify,[status(thm)],[f_58_2]) ).
fof(f_59_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_59_2,plain,
$true,
inference(clausify,[status(thm)],[f_59_1]) ).
fof(f_60_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_60_2,plain,
! [U_330] :
? [U_329] : element(U_329,U_330),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
! [U_330] : element(sK61(U_330),U_330),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_329,sK61(U_330))],[f_60_2]) ).
cnf(f_60_4,plain,
element(sK61(U_330),U_330),
inference(clausify,[status(thm)],[f_60_3]) ).
fof(f_61_1,plain,
! [A,B] :
( ( relation(relation_composition(B,A))
& empty(relation_composition(B,A)) )
| ~ relation(B)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc10_relat_1]) ).
fof(f_61_2,plain,
! [U_332,U_331] :
( ( relation(relation_composition(U_331,U_332))
& empty(relation_composition(U_331,U_332)) )
| ~ relation(U_331)
| ~ empty(U_332) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
cnf(f_61_3,plain,
( empty(relation_composition(U_331,U_332))
| ~ relation(U_331)
| ~ empty(U_332) ),
inference(clausify,[status(thm)],[f_61_2]) ).
cnf(f_61_4,plain,
( relation(relation_composition(U_331,U_332))
| ~ relation(U_331)
| ~ empty(U_332) ),
inference(clausify,[status(thm)],[f_61_2]) ).
fof(f_62_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_62_2,plain,
! [U_333] : ~ empty(powerset(U_333)),
inference(variable_rename,[status(thm)],[f_62_1]) ).
cnf(f_62_3,plain,
~ empty(powerset(U_333)),
inference(clausify,[status(thm)],[f_62_2]) ).
fof(f_63_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_63_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_63_1]) ).
fof(f_64_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_64_2,plain,
! [U_335,U_334] : ~ empty(ordered_pair(U_335,U_334)),
inference(variable_rename,[status(thm)],[f_64_1]) ).
cnf(f_64_3,plain,
~ empty(ordered_pair(U_335,U_334)),
inference(clausify,[status(thm)],[f_64_2]) ).
fof(f_65_1,plain,
! [A,B] :
( relation(set_union2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc2_relat_1]) ).
fof(f_65_2,plain,
! [U_337,U_336] :
( relation(set_union2(U_337,U_336))
| ~ relation(U_336)
| ~ relation(U_337) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
cnf(f_65_3,plain,
( relation(set_union2(U_337,U_336))
| ~ relation(U_336)
| ~ relation(U_337) ),
inference(clausify,[status(thm)],[f_65_2]) ).
fof(f_66_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_66_2,plain,
! [U_338] : ~ empty(singleton(U_338)),
inference(variable_rename,[status(thm)],[f_66_1]) ).
cnf(f_66_3,plain,
~ empty(singleton(U_338)),
inference(clausify,[status(thm)],[f_66_2]) ).
fof(f_67_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_67_2,plain,
! [U_340,U_339] :
( ~ empty(set_union2(U_340,U_339))
| empty(U_340) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
! [U_340] :
( ! [U_339] : ~ empty(set_union2(U_340,U_339))
| empty(U_340) ),
inference(miniscope,[status(thm)],[f_67_2]) ).
cnf(f_67_4,plain,
( ~ empty(set_union2(U_340,U_339))
| empty(U_340) ),
inference(clausify,[status(thm)],[f_67_3]) ).
fof(f_68_1,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_68_2,plain,
! [U_342,U_341] : ~ empty(unordered_pair(U_342,U_341)),
inference(variable_rename,[status(thm)],[f_68_1]) ).
cnf(f_68_3,plain,
~ empty(unordered_pair(U_342,U_341)),
inference(clausify,[status(thm)],[f_68_2]) ).
fof(f_69_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_69_2,plain,
! [U_344,U_343] :
( ~ empty(set_union2(U_343,U_344))
| empty(U_344) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
fof(f_69_3,plain,
! [U_344] :
( ! [U_343] : ~ empty(set_union2(U_343,U_344))
| empty(U_344) ),
inference(miniscope,[status(thm)],[f_69_2]) ).
cnf(f_69_4,plain,
( ~ empty(set_union2(U_343,U_344))
| empty(U_344) ),
inference(clausify,[status(thm)],[f_69_3]) ).
fof(f_70_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_70_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_70_1]) ).
cnf(f_70_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_70_1]) ).
fof(f_71_1,plain,
! [A,B] :
( ~ empty(cartesian_product2(A,B))
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc4_subset_1]) ).
fof(f_71_2,plain,
! [U_346,U_345] :
( ~ empty(cartesian_product2(U_346,U_345))
| empty(U_345)
| empty(U_346) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
cnf(f_71_3,plain,
( ~ empty(cartesian_product2(U_346,U_345))
| empty(U_345)
| empty(U_346) ),
inference(clausify,[status(thm)],[f_71_2]) ).
fof(f_72_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_72_2,plain,
! [U_347] :
( ~ empty(relation_dom(U_347))
| ~ relation(U_347)
| empty(U_347) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
cnf(f_72_3,plain,
( ~ empty(relation_dom(U_347))
| ~ relation(U_347)
| empty(U_347) ),
inference(clausify,[status(thm)],[f_72_2]) ).
fof(f_73_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_73_2,plain,
! [U_348] :
( ~ empty(relation_rng(U_348))
| ~ relation(U_348)
| empty(U_348) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
cnf(f_73_3,plain,
( ~ empty(relation_rng(U_348))
| ~ relation(U_348)
| empty(U_348) ),
inference(clausify,[status(thm)],[f_73_2]) ).
fof(f_74_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_74_2,plain,
! [U_349] :
( ( relation(relation_dom(U_349))
& empty(relation_dom(U_349)) )
| ~ empty(U_349) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
cnf(f_74_3,plain,
( empty(relation_dom(U_349))
| ~ empty(U_349) ),
inference(clausify,[status(thm)],[f_74_2]) ).
cnf(f_74_4,plain,
( relation(relation_dom(U_349))
| ~ empty(U_349) ),
inference(clausify,[status(thm)],[f_74_2]) ).
fof(f_75_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_75_2,plain,
! [U_350] :
( ( relation(relation_rng(U_350))
& empty(relation_rng(U_350)) )
| ~ empty(U_350) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
cnf(f_75_3,plain,
( empty(relation_rng(U_350))
| ~ empty(U_350) ),
inference(clausify,[status(thm)],[f_75_2]) ).
cnf(f_75_4,plain,
( relation(relation_rng(U_350))
| ~ empty(U_350) ),
inference(clausify,[status(thm)],[f_75_2]) ).
fof(f_76_1,plain,
! [A,B] :
( ( relation(relation_composition(A,B))
& empty(relation_composition(A,B)) )
| ~ relation(B)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc9_relat_1]) ).
fof(f_76_2,plain,
! [U_352,U_351] :
( ( relation(relation_composition(U_352,U_351))
& empty(relation_composition(U_352,U_351)) )
| ~ relation(U_351)
| ~ empty(U_352) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
cnf(f_76_3,plain,
( empty(relation_composition(U_352,U_351))
| ~ relation(U_351)
| ~ empty(U_352) ),
inference(clausify,[status(thm)],[f_76_2]) ).
cnf(f_76_4,plain,
( relation(relation_composition(U_352,U_351))
| ~ relation(U_351)
| ~ empty(U_352) ),
inference(clausify,[status(thm)],[f_76_2]) ).
fof(f_77_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_77_2,plain,
! [U_354,U_353] : set_union2(U_354,U_354) = U_354,
inference(variable_rename,[status(thm)],[f_77_1]) ).
fof(f_77_3,plain,
! [U_354] : set_union2(U_354,U_354) = U_354,
inference(miniscope,[status(thm)],[f_77_2]) ).
cnf(f_77_4,plain,
set_union2(U_354,U_354) = U_354,
inference(clausify,[status(thm)],[f_77_3]) ).
fof(f_78_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_78_2,plain,
! [U_356,U_355] : set_intersection2(U_356,U_356) = U_356,
inference(variable_rename,[status(thm)],[f_78_1]) ).
fof(f_78_3,plain,
! [U_356] : set_intersection2(U_356,U_356) = U_356,
inference(miniscope,[status(thm)],[f_78_2]) ).
cnf(f_78_4,plain,
set_intersection2(U_356,U_356) = U_356,
inference(clausify,[status(thm)],[f_78_3]) ).
fof(f_79_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_79_2,plain,
! [U_358,U_357] :
( subset_complement(U_358,subset_complement(U_358,U_357)) = U_357
| ~ element(U_357,powerset(U_358)) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
cnf(f_79_3,plain,
( subset_complement(U_358,subset_complement(U_358,U_357)) = U_357
| ~ element(U_357,powerset(U_358)) ),
inference(clausify,[status(thm)],[f_79_2]) ).
fof(f_80_1,plain,
! [A] :
( relation_inverse(relation_inverse(A)) = A
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[involutiveness_k4_relat_1]) ).
fof(f_80_2,plain,
! [U_359] :
( relation_inverse(relation_inverse(U_359)) = U_359
| ~ relation(U_359) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
cnf(f_80_3,plain,
( relation_inverse(relation_inverse(U_359)) = U_359
| ~ relation(U_359) ),
inference(clausify,[status(thm)],[f_80_2]) ).
fof(f_81_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_81_2,plain,
! [U_361,U_360] :
( complements_of_subsets(U_361,complements_of_subsets(U_361,U_360)) = U_360
| ~ element(U_360,powerset(powerset(U_361))) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
cnf(f_81_3,plain,
( complements_of_subsets(U_361,complements_of_subsets(U_361,U_360)) = U_360
| ~ element(U_360,powerset(powerset(U_361))) ),
inference(clausify,[status(thm)],[f_81_2]) ).
fof(f_82_1,plain,
! [A,B] : ~ proper_subset(A,A),
inference(fof_nnf,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(f_82_2,plain,
! [U_363,U_362] : ~ proper_subset(U_363,U_363),
inference(variable_rename,[status(thm)],[f_82_1]) ).
fof(f_82_3,plain,
! [U_363] : ~ proper_subset(U_363,U_363),
inference(miniscope,[status(thm)],[f_82_2]) ).
cnf(f_82_4,plain,
~ proper_subset(U_363,U_363),
inference(clausify,[status(thm)],[f_82_3]) ).
fof(f_83_1,plain,
! [A] : singleton(A) != empty_set,
inference(fof_nnf,[status(thm)],[l1_zfmisc_1]) ).
fof(f_83_2,plain,
! [U_364] : singleton(U_364) != empty_set,
inference(variable_rename,[status(thm)],[f_83_1]) ).
cnf(f_83_3,plain,
singleton(U_364) != empty_set,
inference(clausify,[status(thm)],[f_83_2]) ).
fof(f_84_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l23_zfmisc_1]) ).
fof(f_84_2,plain,
! [U_366,U_365] :
( set_union2(singleton(U_366),U_365) = U_365
| ~ in(U_366,U_365) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
cnf(f_84_3,plain,
( set_union2(singleton(U_366),U_365) = U_365
| ~ in(U_366,U_365) ),
inference(clausify,[status(thm)],[f_84_2]) ).
fof(f_85_1,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(fof_nnf,[status(thm)],[l25_zfmisc_1]) ).
fof(f_85_2,plain,
! [U_368,U_367] :
( ~ in(U_368,U_367)
| ~ disjoint(singleton(U_368),U_367) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
cnf(f_85_3,plain,
( ~ in(U_368,U_367)
| ~ disjoint(singleton(U_368),U_367) ),
inference(clausify,[status(thm)],[f_85_2]) ).
fof(f_86_1,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(fof_nnf,[status(thm)],[l28_zfmisc_1]) ).
fof(f_86_2,plain,
! [U_370,U_369] :
( disjoint(singleton(U_370),U_369)
| in(U_370,U_369) ),
inference(variable_rename,[status(thm)],[f_86_1]) ).
cnf(f_86_3,plain,
( disjoint(singleton(U_370),U_369)
| in(U_370,U_369) ),
inference(clausify,[status(thm)],[f_86_2]) ).
fof(f_87_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_87_2,plain,
! [U_372,U_371] :
( ( subset(singleton(U_372),U_371)
| ~ in(U_372,U_371) )
& ( in(U_372,U_371)
| ~ subset(singleton(U_372),U_371) ) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
fof(f_87_3,plain,
( ! [U_376,U_374] :
( subset(singleton(U_376),U_374)
| ~ in(U_376,U_374) )
& ! [U_375,U_373] :
( in(U_375,U_373)
| ~ subset(singleton(U_375),U_373) ) ),
inference(miniscope,[status(thm)],[f_87_2]) ).
cnf(f_87_4,plain,
( in(U_375,U_373)
| ~ subset(singleton(U_375),U_373) ),
inference(clausify,[status(thm)],[f_87_3]) ).
cnf(f_87_5,plain,
( subset(singleton(U_376),U_374)
| ~ in(U_376,U_374) ),
inference(clausify,[status(thm)],[f_87_3]) ).
fof(f_88_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_88_2,plain,
! [U_378,U_377] :
( ( set_difference(U_378,U_377) = empty_set
| ~ subset(U_378,U_377) )
& ( subset(U_378,U_377)
| set_difference(U_378,U_377) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
fof(f_88_3,plain,
( ! [U_382,U_380] :
( set_difference(U_382,U_380) = empty_set
| ~ subset(U_382,U_380) )
& ! [U_381,U_379] :
( subset(U_381,U_379)
| set_difference(U_381,U_379) != empty_set ) ),
inference(miniscope,[status(thm)],[f_88_2]) ).
cnf(f_88_4,plain,
( subset(U_381,U_379)
| set_difference(U_381,U_379) != empty_set ),
inference(clausify,[status(thm)],[f_88_3]) ).
cnf(f_88_5,plain,
( set_difference(U_382,U_380) = empty_set
| ~ subset(U_382,U_380) ),
inference(clausify,[status(thm)],[f_88_3]) ).
fof(f_89_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_89_2,plain,
! [U_385,U_384] :
( ! [U_383] :
( in(U_383,U_385)
| ~ in(U_383,U_384) )
| ~ element(U_384,powerset(U_385)) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
cnf(f_89_3,plain,
( in(U_383,U_385)
| ~ in(U_383,U_384)
| ~ element(U_384,powerset(U_385)) ),
inference(clausify,[status(thm)],[f_89_2]) ).
fof(f_90_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_90_2,plain,
! [U_388,U_387,U_386] :
( subset(U_388,set_difference(U_387,singleton(U_386)))
| in(U_386,U_388)
| ~ subset(U_388,U_387) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
fof(f_90_3,plain,
! [U_388,U_387] :
( ! [U_386] :
( subset(U_388,set_difference(U_387,singleton(U_386)))
| in(U_386,U_388) )
| ~ subset(U_388,U_387) ),
inference(miniscope,[status(thm)],[f_90_2]) ).
cnf(f_90_4,plain,
( subset(U_388,set_difference(U_387,singleton(U_386)))
| in(U_386,U_388)
| ~ subset(U_388,U_387) ),
inference(clausify,[status(thm)],[f_90_3]) ).
fof(f_91_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_91_2,plain,
! [U_390,U_389] :
( ( subset(U_390,singleton(U_389))
| ( U_390 != singleton(U_389)
& U_390 != empty_set ) )
& ( U_390 = singleton(U_389)
| U_390 = empty_set
| ~ subset(U_390,singleton(U_389)) ) ),
inference(variable_rename,[status(thm)],[f_91_1]) ).
fof(f_91_3,plain,
( ! [U_394,U_392] :
( subset(U_394,singleton(U_392))
| ( U_394 != singleton(U_392)
& U_394 != empty_set ) )
& ! [U_393,U_391] :
( U_393 = singleton(U_391)
| U_393 = empty_set
| ~ subset(U_393,singleton(U_391)) ) ),
inference(miniscope,[status(thm)],[f_91_2]) ).
cnf(f_91_4,plain,
( U_393 = singleton(U_391)
| U_393 = empty_set
| ~ subset(U_393,singleton(U_391)) ),
inference(clausify,[status(thm)],[f_91_3]) ).
cnf(f_91_5,plain,
( U_394 != empty_set
| subset(U_394,singleton(U_392)) ),
inference(clausify,[status(thm)],[f_91_3]) ).
cnf(f_91_6,plain,
( U_394 != singleton(U_392)
| subset(U_394,singleton(U_392)) ),
inference(clausify,[status(thm)],[f_91_3]) ).
fof(f_92_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l50_zfmisc_1]) ).
fof(f_92_2,plain,
! [U_396,U_395] :
( subset(U_396,union(U_395))
| ~ in(U_396,U_395) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
cnf(f_92_3,plain,
( subset(U_396,union(U_395))
| ~ in(U_396,U_395) ),
inference(clausify,[status(thm)],[f_92_2]) ).
fof(f_93_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_93_2,plain,
! [U_400,U_399,U_398,U_397] :
( ( in(ordered_pair(U_400,U_399),cartesian_product2(U_398,U_397))
| ~ in(U_399,U_397)
| ~ in(U_400,U_398) )
& ( ( in(U_399,U_397)
& in(U_400,U_398) )
| ~ in(ordered_pair(U_400,U_399),cartesian_product2(U_398,U_397)) ) ),
inference(variable_rename,[status(thm)],[f_93_1]) ).
fof(f_93_3,plain,
( ! [U_408,U_406,U_404,U_402] :
( in(ordered_pair(U_408,U_406),cartesian_product2(U_404,U_402))
| ~ in(U_406,U_402)
| ~ in(U_408,U_404) )
& ! [U_407,U_405,U_403,U_401] :
( ( in(U_405,U_401)
& in(U_407,U_403) )
| ~ in(ordered_pair(U_407,U_405),cartesian_product2(U_403,U_401)) ) ),
inference(miniscope,[status(thm)],[f_93_2]) ).
cnf(f_93_4,plain,
( in(U_407,U_403)
| ~ in(ordered_pair(U_407,U_405),cartesian_product2(U_403,U_401)) ),
inference(clausify,[status(thm)],[f_93_3]) ).
cnf(f_93_5,plain,
( in(U_405,U_401)
| ~ in(ordered_pair(U_407,U_405),cartesian_product2(U_403,U_401)) ),
inference(clausify,[status(thm)],[f_93_3]) ).
cnf(f_93_6,plain,
( in(ordered_pair(U_408,U_406),cartesian_product2(U_404,U_402))
| ~ in(U_406,U_402)
| ~ in(U_408,U_404) ),
inference(clausify,[status(thm)],[f_93_3]) ).
fof(f_94_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_94_2,plain,
! [U_411,U_410] :
( element(U_411,powerset(U_410))
| ? [U_409] :
( ~ in(U_409,U_410)
& in(U_409,U_411) ) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
fof(f_94_3,plain,
! [U_411,U_410] :
( element(U_411,powerset(U_410))
| ( ~ in(sK62(U_411,U_410),U_410)
& in(sK62(U_411,U_410),U_411) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_409,sK62(U_411,U_410))],[f_94_2]) ).
cnf(f_94_4,plain,
( in(sK62(U_411,U_410),U_411)
| element(U_411,powerset(U_410)) ),
inference(clausify,[status(thm)],[f_94_3]) ).
cnf(f_94_5,plain,
( ~ in(sK62(U_411,U_410),U_410)
| element(U_411,powerset(U_410)) ),
inference(clausify,[status(thm)],[f_94_3]) ).
fof(f_95_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_95_2,plain,
? [U_412] :
( relation(U_412)
& empty(U_412) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
fof(f_95_3,plain,
( relation(sK63)
& empty(sK63) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_412,sK63)],[f_95_2]) ).
cnf(f_95_4,plain,
empty(sK63),
inference(clausify,[status(thm)],[f_95_3]) ).
cnf(f_95_5,plain,
relation(sK63),
inference(clausify,[status(thm)],[f_95_3]) ).
fof(f_96_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_96_2,plain,
! [U_414] :
( ? [U_413] :
( ~ empty(U_413)
& element(U_413,powerset(U_414)) )
| empty(U_414) ),
inference(variable_rename,[status(thm)],[f_96_1]) ).
fof(f_96_3,plain,
! [U_414] :
( ( ~ empty(sK64(U_414))
& element(sK64(U_414),powerset(U_414)) )
| empty(U_414) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_413,sK64(U_414))],[f_96_2]) ).
cnf(f_96_4,plain,
( element(sK64(U_414),powerset(U_414))
| empty(U_414) ),
inference(clausify,[status(thm)],[f_96_3]) ).
cnf(f_96_5,plain,
( ~ empty(sK64(U_414))
| empty(U_414) ),
inference(clausify,[status(thm)],[f_96_3]) ).
fof(f_97_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_97_2,plain,
? [U_415] : empty(U_415),
inference(variable_rename,[status(thm)],[f_97_1]) ).
fof(f_97_3,plain,
empty(sK65),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_415,sK65)],[f_97_2]) ).
cnf(f_97_4,plain,
empty(sK65),
inference(clausify,[status(thm)],[f_97_3]) ).
fof(f_98_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_98_2,plain,
? [U_416] :
( relation(U_416)
& ~ empty(U_416) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
fof(f_98_3,plain,
( relation(sK66)
& ~ empty(sK66) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_416,sK66)],[f_98_2]) ).
cnf(f_98_4,plain,
~ empty(sK66),
inference(clausify,[status(thm)],[f_98_3]) ).
cnf(f_98_5,plain,
relation(sK66),
inference(clausify,[status(thm)],[f_98_3]) ).
fof(f_99_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_99_2,plain,
! [U_418] :
? [U_417] :
( empty(U_417)
& element(U_417,powerset(U_418)) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
fof(f_99_3,plain,
! [U_418] :
( empty(sK67(U_418))
& element(sK67(U_418),powerset(U_418)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_417,sK67(U_418))],[f_99_2]) ).
cnf(f_99_4,plain,
element(sK67(U_418),powerset(U_418)),
inference(clausify,[status(thm)],[f_99_3]) ).
cnf(f_99_5,plain,
empty(sK67(U_418)),
inference(clausify,[status(thm)],[f_99_3]) ).
fof(f_100_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_100_2,plain,
? [U_419] : ~ empty(U_419),
inference(variable_rename,[status(thm)],[f_100_1]) ).
fof(f_100_3,plain,
~ empty(sK68),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_419,sK68)],[f_100_2]) ).
cnf(f_100_4,plain,
~ empty(sK68),
inference(clausify,[status(thm)],[f_100_3]) ).
fof(f_101_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_101_2,plain,
! [U_421,U_420] :
( union_of_subsets(U_421,U_420) = union(U_420)
| ~ element(U_420,powerset(powerset(U_421))) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
cnf(f_101_3,plain,
( union_of_subsets(U_421,U_420) = union(U_420)
| ~ element(U_420,powerset(powerset(U_421))) ),
inference(clausify,[status(thm)],[f_101_2]) ).
fof(f_102_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_102_2,plain,
! [U_423,U_422] :
( meet_of_subsets(U_423,U_422) = set_meet(U_422)
| ~ element(U_422,powerset(powerset(U_423))) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
cnf(f_102_3,plain,
( meet_of_subsets(U_423,U_422) = set_meet(U_422)
| ~ element(U_422,powerset(powerset(U_423))) ),
inference(clausify,[status(thm)],[f_102_2]) ).
fof(f_103_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_103_2,plain,
! [U_426,U_425,U_424] :
( subset_difference(U_426,U_425,U_424) = set_difference(U_425,U_424)
| ~ element(U_424,powerset(U_426))
| ~ element(U_425,powerset(U_426)) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
cnf(f_103_3,plain,
( subset_difference(U_426,U_425,U_424) = set_difference(U_425,U_424)
| ~ element(U_424,powerset(U_426))
| ~ element(U_425,powerset(U_426)) ),
inference(clausify,[status(thm)],[f_103_2]) ).
fof(f_104_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_104_2,plain,
! [U_428,U_427] : subset(U_428,U_428),
inference(variable_rename,[status(thm)],[f_104_1]) ).
fof(f_104_3,plain,
! [U_428] : subset(U_428,U_428),
inference(miniscope,[status(thm)],[f_104_2]) ).
cnf(f_104_4,plain,
subset(U_428,U_428),
inference(clausify,[status(thm)],[f_104_3]) ).
fof(f_105_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_105_2,plain,
! [U_430,U_429] :
( disjoint(U_429,U_430)
| ~ disjoint(U_430,U_429) ),
inference(variable_rename,[status(thm)],[f_105_1]) ).
cnf(f_105_3,plain,
( disjoint(U_429,U_430)
| ~ disjoint(U_430,U_429) ),
inference(clausify,[status(thm)],[f_105_2]) ).
fof(f_106_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_106_2,plain,
! [U_434,U_433,U_432,U_431] :
( ( in(ordered_pair(U_434,U_433),cartesian_product2(U_432,U_431))
| ~ in(U_433,U_431)
| ~ in(U_434,U_432) )
& ( ( in(U_433,U_431)
& in(U_434,U_432) )
| ~ in(ordered_pair(U_434,U_433),cartesian_product2(U_432,U_431)) ) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
fof(f_106_3,plain,
( ! [U_442,U_440,U_438,U_436] :
( in(ordered_pair(U_442,U_440),cartesian_product2(U_438,U_436))
| ~ in(U_440,U_436)
| ~ in(U_442,U_438) )
& ! [U_441,U_439,U_437,U_435] :
( ( in(U_439,U_435)
& in(U_441,U_437) )
| ~ in(ordered_pair(U_441,U_439),cartesian_product2(U_437,U_435)) ) ),
inference(miniscope,[status(thm)],[f_106_2]) ).
cnf(f_106_4,plain,
( in(U_441,U_437)
| ~ in(ordered_pair(U_441,U_439),cartesian_product2(U_437,U_435)) ),
inference(clausify,[status(thm)],[f_106_3]) ).
cnf(f_106_5,plain,
( in(U_439,U_435)
| ~ in(ordered_pair(U_441,U_439),cartesian_product2(U_437,U_435)) ),
inference(clausify,[status(thm)],[f_106_3]) ).
cnf(f_106_6,plain,
( in(ordered_pair(U_442,U_440),cartesian_product2(U_438,U_436))
| ~ in(U_440,U_436)
| ~ in(U_442,U_438) ),
inference(clausify,[status(thm)],[f_106_3]) ).
fof(f_107_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_107_2,plain,
! [U_446,U_445,U_444,U_443] :
( U_446 = U_443
| U_446 = U_444
| unordered_pair(U_446,U_445) != unordered_pair(U_444,U_443) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
fof(f_107_3,plain,
! [U_446,U_445,U_444] :
( ! [U_443] :
( U_446 = U_443
| unordered_pair(U_446,U_445) != unordered_pair(U_444,U_443) )
| U_446 = U_444 ),
inference(miniscope,[status(thm)],[f_107_2]) ).
cnf(f_107_4,plain,
( U_446 = U_443
| unordered_pair(U_446,U_445) != unordered_pair(U_444,U_443)
| U_446 = U_444 ),
inference(clausify,[status(thm)],[f_107_3]) ).
fof(f_108_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_108_2,plain,
! [U_449,U_448,U_447] :
( ( subset(cartesian_product2(U_447,U_449),cartesian_product2(U_447,U_448))
& subset(cartesian_product2(U_449,U_447),cartesian_product2(U_448,U_447)) )
| ~ subset(U_449,U_448) ),
inference(variable_rename,[status(thm)],[f_108_1]) ).
fof(f_108_3,plain,
! [U_449,U_448] :
( ( ! [U_451] : subset(cartesian_product2(U_451,U_449),cartesian_product2(U_451,U_448))
& ! [U_450] : subset(cartesian_product2(U_449,U_450),cartesian_product2(U_448,U_450)) )
| ~ subset(U_449,U_448) ),
inference(miniscope,[status(thm)],[f_108_2]) ).
cnf(f_108_4,plain,
( subset(cartesian_product2(U_449,U_450),cartesian_product2(U_448,U_450))
| ~ subset(U_449,U_448) ),
inference(clausify,[status(thm)],[f_108_3]) ).
cnf(f_108_5,plain,
( subset(cartesian_product2(U_451,U_449),cartesian_product2(U_451,U_448))
| ~ subset(U_449,U_448) ),
inference(clausify,[status(thm)],[f_108_3]) ).
fof(f_109_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_109_2,plain,
! [U_455,U_454,U_453,U_452] :
( subset(cartesian_product2(U_455,U_453),cartesian_product2(U_454,U_452))
| ~ subset(U_453,U_452)
| ~ subset(U_455,U_454) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
cnf(f_109_3,plain,
( subset(cartesian_product2(U_455,U_453),cartesian_product2(U_454,U_452))
| ~ subset(U_453,U_452)
| ~ subset(U_455,U_454) ),
inference(clausify,[status(thm)],[f_109_2]) ).
fof(f_110_1,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t12_xboole_1]) ).
fof(f_110_2,plain,
! [U_457,U_456] :
( set_union2(U_457,U_456) = U_456
| ~ subset(U_457,U_456) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
cnf(f_110_3,plain,
( set_union2(U_457,U_456) = U_456
| ~ subset(U_457,U_456) ),
inference(clausify,[status(thm)],[f_110_2]) ).
fof(f_111_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_111_2,plain,
! [U_463] :
? [U_462] :
( ! [U_461] :
( in(U_461,U_462)
| are_equipotent(U_461,U_462)
| ~ subset(U_461,U_462) )
& ! [U_460] :
( in(powerset(U_460),U_462)
| ~ in(U_460,U_462) )
& ! [U_459,U_458] :
( in(U_458,U_462)
| ~ subset(U_458,U_459)
| ~ in(U_459,U_462) )
& in(U_463,U_462) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
fof(f_111_3,plain,
! [U_463] :
( ! [U_461] :
( in(U_461,sK69(U_463))
| are_equipotent(U_461,sK69(U_463))
| ~ subset(U_461,sK69(U_463)) )
& ! [U_460] :
( in(powerset(U_460),sK69(U_463))
| ~ in(U_460,sK69(U_463)) )
& ! [U_459,U_458] :
( in(U_458,sK69(U_463))
| ~ subset(U_458,U_459)
| ~ in(U_459,sK69(U_463)) )
& in(U_463,sK69(U_463)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_462,sK69(U_463))],[f_111_2]) ).
cnf(f_111_4,plain,
in(U_463,sK69(U_463)),
inference(clausify,[status(thm)],[f_111_3]) ).
cnf(f_111_5,plain,
( in(U_458,sK69(U_463))
| ~ subset(U_458,U_459)
| ~ in(U_459,sK69(U_463)) ),
inference(clausify,[status(thm)],[f_111_3]) ).
cnf(f_111_6,plain,
( in(powerset(U_460),sK69(U_463))
| ~ in(U_460,sK69(U_463)) ),
inference(clausify,[status(thm)],[f_111_3]) ).
cnf(f_111_7,plain,
( in(U_461,sK69(U_463))
| are_equipotent(U_461,sK69(U_463))
| ~ subset(U_461,sK69(U_463)) ),
inference(clausify,[status(thm)],[f_111_3]) ).
fof(f_112_1,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(fof_nnf,[status(thm)],[t17_xboole_1]) ).
fof(f_112_2,plain,
! [U_465,U_464] : subset(set_intersection2(U_465,U_464),U_465),
inference(variable_rename,[status(thm)],[f_112_1]) ).
cnf(f_112_3,plain,
subset(set_intersection2(U_465,U_464),U_465),
inference(clausify,[status(thm)],[f_112_2]) ).
fof(f_113_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_113_2,plain,
! [U_468,U_467,U_466] :
( subset(U_468,set_intersection2(U_467,U_466))
| ~ subset(U_468,U_466)
| ~ subset(U_468,U_467) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
cnf(f_113_3,plain,
( subset(U_468,set_intersection2(U_467,U_466))
| ~ subset(U_468,U_466)
| ~ subset(U_468,U_467) ),
inference(clausify,[status(thm)],[f_113_2]) ).
fof(f_114_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_114_2,plain,
! [U_469] : set_union2(U_469,empty_set) = U_469,
inference(variable_rename,[status(thm)],[f_114_1]) ).
cnf(f_114_3,plain,
set_union2(U_469,empty_set) = U_469,
inference(clausify,[status(thm)],[f_114_2]) ).
fof(f_115_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_115_2,plain,
! [U_471,U_470] :
( element(U_471,U_470)
| ~ in(U_471,U_470) ),
inference(variable_rename,[status(thm)],[f_115_1]) ).
cnf(f_115_3,plain,
( element(U_471,U_470)
| ~ in(U_471,U_470) ),
inference(clausify,[status(thm)],[f_115_2]) ).
fof(f_116_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_116_2,plain,
! [U_474,U_473,U_472] :
( subset(U_474,U_472)
| ~ subset(U_473,U_472)
| ~ subset(U_474,U_473) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
cnf(f_116_3,plain,
( subset(U_474,U_472)
| ~ subset(U_473,U_472)
| ~ subset(U_474,U_473) ),
inference(clausify,[status(thm)],[f_116_2]) ).
fof(f_117_1,plain,
powerset(empty_set) = singleton(empty_set),
inference(fof_nnf,[status(thm)],[t1_zfmisc_1]) ).
cnf(f_117_2,plain,
powerset(empty_set) = singleton(empty_set),
inference(clausify,[status(thm)],[f_117_1]) ).
fof(f_118_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_118_2,plain,
! [U_477,U_476,U_475] :
( ( in(U_476,relation_rng(U_475))
& in(U_477,relation_dom(U_475)) )
| ~ in(ordered_pair(U_477,U_476),U_475)
| ~ relation(U_475) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
cnf(f_118_3,plain,
( in(U_477,relation_dom(U_475))
| ~ in(ordered_pair(U_477,U_476),U_475)
| ~ relation(U_475) ),
inference(clausify,[status(thm)],[f_118_2]) ).
cnf(f_118_4,plain,
( in(U_476,relation_rng(U_475))
| ~ in(ordered_pair(U_477,U_476),U_475)
| ~ relation(U_475) ),
inference(clausify,[status(thm)],[f_118_2]) ).
fof(f_119_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_119_2,plain,
! [U_478] :
( subset(U_478,cartesian_product2(relation_dom(U_478),relation_rng(U_478)))
| ~ relation(U_478) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
cnf(f_119_3,plain,
( subset(U_478,cartesian_product2(relation_dom(U_478),relation_rng(U_478)))
| ~ relation(U_478) ),
inference(clausify,[status(thm)],[f_119_2]) ).
fof(f_120_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_120_2,plain,
! [U_480] :
( ! [U_479] :
( ( subset(relation_rng(U_480),relation_rng(U_479))
& subset(relation_dom(U_480),relation_dom(U_479)) )
| ~ subset(U_480,U_479)
| ~ relation(U_479) )
| ~ relation(U_480) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
cnf(f_120_3,plain,
( subset(relation_dom(U_480),relation_dom(U_479))
| ~ subset(U_480,U_479)
| ~ relation(U_479)
| ~ relation(U_480) ),
inference(clausify,[status(thm)],[f_120_2]) ).
cnf(f_120_4,plain,
( subset(relation_rng(U_480),relation_rng(U_479))
| ~ subset(U_480,U_479)
| ~ relation(U_479)
| ~ relation(U_480) ),
inference(clausify,[status(thm)],[f_120_2]) ).
fof(f_121_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_121_2,plain,
! [U_483,U_482,U_481] :
( subset(set_intersection2(U_483,U_481),set_intersection2(U_482,U_481))
| ~ subset(U_483,U_482) ),
inference(variable_rename,[status(thm)],[f_121_1]) ).
fof(f_121_3,plain,
! [U_483,U_482] :
( ! [U_481] : subset(set_intersection2(U_483,U_481),set_intersection2(U_482,U_481))
| ~ subset(U_483,U_482) ),
inference(miniscope,[status(thm)],[f_121_2]) ).
cnf(f_121_4,plain,
( subset(set_intersection2(U_483,U_481),set_intersection2(U_482,U_481))
| ~ subset(U_483,U_482) ),
inference(clausify,[status(thm)],[f_121_3]) ).
fof(f_122_1,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t28_xboole_1]) ).
fof(f_122_2,plain,
! [U_485,U_484] :
( set_intersection2(U_485,U_484) = U_485
| ~ subset(U_485,U_484) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
cnf(f_122_3,plain,
( set_intersection2(U_485,U_484) = U_485
| ~ subset(U_485,U_484) ),
inference(clausify,[status(thm)],[f_122_2]) ).
fof(f_123_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_123_2,plain,
! [U_486] : set_intersection2(U_486,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_123_1]) ).
cnf(f_123_3,plain,
set_intersection2(U_486,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_123_2]) ).
fof(f_124_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_124_2,plain,
! [U_488,U_487] :
( in(U_488,U_487)
| empty(U_487)
| ~ element(U_488,U_487) ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
cnf(f_124_3,plain,
( in(U_488,U_487)
| empty(U_487)
| ~ element(U_488,U_487) ),
inference(clausify,[status(thm)],[f_124_2]) ).
fof(f_125_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_125_2,plain,
! [U_491,U_490] :
( U_491 = U_490
| ? [U_489] :
( ( ~ in(U_489,U_491)
& in(U_489,U_490) )
| ( ~ in(U_489,U_490)
& in(U_489,U_491) ) ) ),
inference(variable_rename,[status(thm)],[f_125_1]) ).
fof(f_125_3,plain,
! [U_491,U_490] :
( U_491 = U_490
| ? [U_493] :
( ~ in(U_493,U_491)
& in(U_493,U_490) )
| ? [U_492] :
( ~ in(U_492,U_490)
& in(U_492,U_491) ) ),
inference(miniscope,[status(thm)],[f_125_2]) ).
fof(f_125_4,plain,
! [U_491,U_490] :
( U_491 = U_490
| ? [U_493] :
( ~ in(U_493,U_491)
& in(U_493,U_490) )
| ( ~ in(sK70(U_491,U_490),U_490)
& in(sK70(U_491,U_490),U_491) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_492,sK70(U_491,U_490))],[f_125_3]) ).
fof(f_125_5,plain,
! [U_491,U_490] :
( U_491 = U_490
| ( ~ in(sK71(U_491,U_490),U_491)
& in(sK71(U_491,U_490),U_490) )
| ( ~ in(sK70(U_491,U_490),U_490)
& in(sK70(U_491,U_490),U_491) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_493,sK71(U_491,U_490))],[f_125_4]) ).
cnf(f_125_6,plain,
( in(sK71(U_491,U_490),U_490)
| in(sK70(U_491,U_490),U_491)
| U_491 = U_490 ),
inference(clausify,[status(thm)],[f_125_5]) ).
cnf(f_125_7,plain,
( ~ in(sK71(U_491,U_490),U_491)
| in(sK70(U_491,U_490),U_491)
| U_491 = U_490 ),
inference(clausify,[status(thm)],[f_125_5]) ).
cnf(f_125_8,plain,
( in(sK71(U_491,U_490),U_490)
| ~ in(sK70(U_491,U_490),U_490)
| U_491 = U_490 ),
inference(clausify,[status(thm)],[f_125_5]) ).
cnf(f_125_9,plain,
( ~ in(sK71(U_491,U_490),U_491)
| ~ in(sK70(U_491,U_490),U_490)
| U_491 = U_490 ),
inference(clausify,[status(thm)],[f_125_5]) ).
fof(f_126_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_126_2,plain,
! [U_494] : subset(empty_set,U_494),
inference(variable_rename,[status(thm)],[f_126_1]) ).
cnf(f_126_3,plain,
subset(empty_set,U_494),
inference(clausify,[status(thm)],[f_126_2]) ).
fof(f_127_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_127_2,plain,
! [U_497,U_496,U_495] :
( ( in(U_496,relation_field(U_495))
& in(U_497,relation_field(U_495)) )
| ~ in(ordered_pair(U_497,U_496),U_495)
| ~ relation(U_495) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
cnf(f_127_3,plain,
( in(U_497,relation_field(U_495))
| ~ in(ordered_pair(U_497,U_496),U_495)
| ~ relation(U_495) ),
inference(clausify,[status(thm)],[f_127_2]) ).
cnf(f_127_4,plain,
( in(U_496,relation_field(U_495))
| ~ in(ordered_pair(U_497,U_496),U_495)
| ~ relation(U_495) ),
inference(clausify,[status(thm)],[f_127_2]) ).
fof(f_128_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_128_2,plain,
! [U_500,U_499,U_498] :
( subset(set_difference(U_500,U_498),set_difference(U_499,U_498))
| ~ subset(U_500,U_499) ),
inference(variable_rename,[status(thm)],[f_128_1]) ).
fof(f_128_3,plain,
! [U_500,U_499] :
( ! [U_498] : subset(set_difference(U_500,U_498),set_difference(U_499,U_498))
| ~ subset(U_500,U_499) ),
inference(miniscope,[status(thm)],[f_128_2]) ).
cnf(f_128_4,plain,
( subset(set_difference(U_500,U_498),set_difference(U_499,U_498))
| ~ subset(U_500,U_499) ),
inference(clausify,[status(thm)],[f_128_3]) ).
fof(f_129_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_129_2,plain,
! [U_504,U_503,U_502,U_501] :
( ( U_503 = U_501
& U_504 = U_502 )
| ordered_pair(U_504,U_503) != ordered_pair(U_502,U_501) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
cnf(f_129_3,plain,
( U_504 = U_502
| ordered_pair(U_504,U_503) != ordered_pair(U_502,U_501) ),
inference(clausify,[status(thm)],[f_129_2]) ).
cnf(f_129_4,plain,
( U_503 = U_501
| ordered_pair(U_504,U_503) != ordered_pair(U_502,U_501) ),
inference(clausify,[status(thm)],[f_129_2]) ).
fof(f_130_1,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(fof_nnf,[status(thm)],[t36_xboole_1]) ).
fof(f_130_2,plain,
! [U_506,U_505] : subset(set_difference(U_506,U_505),U_506),
inference(variable_rename,[status(thm)],[f_130_1]) ).
cnf(f_130_3,plain,
subset(set_difference(U_506,U_505),U_506),
inference(clausify,[status(thm)],[f_130_2]) ).
fof(f_131_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_131_2,plain,
! [U_507] :
( ( relation_dom(U_507) = relation_rng(relation_inverse(U_507))
& relation_rng(U_507) = relation_dom(relation_inverse(U_507)) )
| ~ relation(U_507) ),
inference(variable_rename,[status(thm)],[f_131_1]) ).
cnf(f_131_3,plain,
( relation_rng(U_507) = relation_dom(relation_inverse(U_507))
| ~ relation(U_507) ),
inference(clausify,[status(thm)],[f_131_2]) ).
cnf(f_131_4,plain,
( relation_dom(U_507) = relation_rng(relation_inverse(U_507))
| ~ relation(U_507) ),
inference(clausify,[status(thm)],[f_131_2]) ).
fof(f_132_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_132_2,plain,
! [U_509,U_508] :
( ( set_difference(U_509,U_508) = empty_set
| ~ subset(U_509,U_508) )
& ( subset(U_509,U_508)
| set_difference(U_509,U_508) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_132_1]) ).
fof(f_132_3,plain,
( ! [U_513,U_511] :
( set_difference(U_513,U_511) = empty_set
| ~ subset(U_513,U_511) )
& ! [U_512,U_510] :
( subset(U_512,U_510)
| set_difference(U_512,U_510) != empty_set ) ),
inference(miniscope,[status(thm)],[f_132_2]) ).
cnf(f_132_4,plain,
( subset(U_512,U_510)
| set_difference(U_512,U_510) != empty_set ),
inference(clausify,[status(thm)],[f_132_3]) ).
cnf(f_132_5,plain,
( set_difference(U_513,U_511) = empty_set
| ~ subset(U_513,U_511) ),
inference(clausify,[status(thm)],[f_132_3]) ).
fof(f_133_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_133_2,plain,
! [U_515,U_514] :
( ( subset(singleton(U_515),U_514)
| ~ in(U_515,U_514) )
& ( in(U_515,U_514)
| ~ subset(singleton(U_515),U_514) ) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
fof(f_133_3,plain,
( ! [U_519,U_517] :
( subset(singleton(U_519),U_517)
| ~ in(U_519,U_517) )
& ! [U_518,U_516] :
( in(U_518,U_516)
| ~ subset(singleton(U_518),U_516) ) ),
inference(miniscope,[status(thm)],[f_133_2]) ).
cnf(f_133_4,plain,
( in(U_518,U_516)
| ~ subset(singleton(U_518),U_516) ),
inference(clausify,[status(thm)],[f_133_3]) ).
cnf(f_133_5,plain,
( subset(singleton(U_519),U_517)
| ~ in(U_519,U_517) ),
inference(clausify,[status(thm)],[f_133_3]) ).
fof(f_134_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_134_2,plain,
! [U_522,U_521,U_520] :
( ( subset(unordered_pair(U_522,U_521),U_520)
| ~ in(U_521,U_520)
| ~ in(U_522,U_520) )
& ( ( in(U_521,U_520)
& in(U_522,U_520) )
| ~ subset(unordered_pair(U_522,U_521),U_520) ) ),
inference(variable_rename,[status(thm)],[f_134_1]) ).
fof(f_134_3,plain,
( ! [U_528,U_526,U_524] :
( subset(unordered_pair(U_528,U_526),U_524)
| ~ in(U_526,U_524)
| ~ in(U_528,U_524) )
& ! [U_527,U_525,U_523] :
( ( in(U_525,U_523)
& in(U_527,U_523) )
| ~ subset(unordered_pair(U_527,U_525),U_523) ) ),
inference(miniscope,[status(thm)],[f_134_2]) ).
cnf(f_134_4,plain,
( in(U_527,U_523)
| ~ subset(unordered_pair(U_527,U_525),U_523) ),
inference(clausify,[status(thm)],[f_134_3]) ).
cnf(f_134_5,plain,
( in(U_525,U_523)
| ~ subset(unordered_pair(U_527,U_525),U_523) ),
inference(clausify,[status(thm)],[f_134_3]) ).
cnf(f_134_6,plain,
( subset(unordered_pair(U_528,U_526),U_524)
| ~ in(U_526,U_524)
| ~ in(U_528,U_524) ),
inference(clausify,[status(thm)],[f_134_3]) ).
fof(f_135_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_135_2,plain,
! [U_530,U_529] : set_union2(U_530,set_difference(U_529,U_530)) = set_union2(U_530,U_529),
inference(variable_rename,[status(thm)],[f_135_1]) ).
cnf(f_135_3,plain,
set_union2(U_530,set_difference(U_529,U_530)) = set_union2(U_530,U_529),
inference(clausify,[status(thm)],[f_135_2]) ).
fof(f_136_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_136_2,plain,
! [U_532,U_531] :
( ( subset(U_532,singleton(U_531))
| ( U_532 != singleton(U_531)
& U_532 != empty_set ) )
& ( U_532 = singleton(U_531)
| U_532 = empty_set
| ~ subset(U_532,singleton(U_531)) ) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
fof(f_136_3,plain,
( ! [U_536,U_534] :
( subset(U_536,singleton(U_534))
| ( U_536 != singleton(U_534)
& U_536 != empty_set ) )
& ! [U_535,U_533] :
( U_535 = singleton(U_533)
| U_535 = empty_set
| ~ subset(U_535,singleton(U_533)) ) ),
inference(miniscope,[status(thm)],[f_136_2]) ).
cnf(f_136_4,plain,
( U_535 = singleton(U_533)
| U_535 = empty_set
| ~ subset(U_535,singleton(U_533)) ),
inference(clausify,[status(thm)],[f_136_3]) ).
cnf(f_136_5,plain,
( U_536 != empty_set
| subset(U_536,singleton(U_534)) ),
inference(clausify,[status(thm)],[f_136_3]) ).
cnf(f_136_6,plain,
( U_536 != singleton(U_534)
| subset(U_536,singleton(U_534)) ),
inference(clausify,[status(thm)],[f_136_3]) ).
fof(f_137_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_137_2,plain,
! [U_537] : set_difference(U_537,empty_set) = U_537,
inference(variable_rename,[status(thm)],[f_137_1]) ).
cnf(f_137_3,plain,
set_difference(U_537,empty_set) = U_537,
inference(clausify,[status(thm)],[f_137_2]) ).
fof(f_138_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_138_2,plain,
! [U_539,U_538] :
( ( element(U_539,powerset(U_538))
| ~ subset(U_539,U_538) )
& ( subset(U_539,U_538)
| ~ element(U_539,powerset(U_538)) ) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
fof(f_138_3,plain,
( ! [U_543,U_541] :
( element(U_543,powerset(U_541))
| ~ subset(U_543,U_541) )
& ! [U_542,U_540] :
( subset(U_542,U_540)
| ~ element(U_542,powerset(U_540)) ) ),
inference(miniscope,[status(thm)],[f_138_2]) ).
cnf(f_138_4,plain,
( subset(U_542,U_540)
| ~ element(U_542,powerset(U_540)) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_5,plain,
( element(U_543,powerset(U_541))
| ~ subset(U_543,U_541) ),
inference(clausify,[status(thm)],[f_138_3]) ).
fof(f_139_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_139_2,plain,
! [U_547,U_546] :
( ( ~ disjoint(U_547,U_546)
| ! [U_545] :
( ~ in(U_545,U_546)
| ~ in(U_545,U_547) ) )
& ( ? [U_544] :
( in(U_544,U_546)
& in(U_544,U_547) )
| disjoint(U_547,U_546) ) ),
inference(variable_rename,[status(thm)],[f_139_1]) ).
fof(f_139_3,plain,
( ! [U_551,U_549] :
( ~ disjoint(U_551,U_549)
| ! [U_545] :
( ~ in(U_545,U_549)
| ~ in(U_545,U_551) ) )
& ! [U_550,U_548] :
( ? [U_544] :
( in(U_544,U_548)
& in(U_544,U_550) )
| disjoint(U_550,U_548) ) ),
inference(miniscope,[status(thm)],[f_139_2]) ).
fof(f_139_4,plain,
( ! [U_551,U_549] :
( ~ disjoint(U_551,U_549)
| ! [U_545] :
( ~ in(U_545,U_549)
| ~ in(U_545,U_551) ) )
& ! [U_550,U_548] :
( ( in(sK72(U_550,U_548),U_548)
& in(sK72(U_550,U_548),U_550) )
| disjoint(U_550,U_548) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_544,sK72(U_550,U_548))],[f_139_3]) ).
cnf(f_139_5,plain,
( in(sK72(U_550,U_548),U_550)
| disjoint(U_550,U_548) ),
inference(clausify,[status(thm)],[f_139_4]) ).
cnf(f_139_6,plain,
( in(sK72(U_550,U_548),U_548)
| disjoint(U_550,U_548) ),
inference(clausify,[status(thm)],[f_139_4]) ).
cnf(f_139_7,plain,
( ~ disjoint(U_551,U_549)
| ~ in(U_545,U_549)
| ~ in(U_545,U_551) ),
inference(clausify,[status(thm)],[f_139_4]) ).
fof(f_140_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_140_2,plain,
! [U_552] :
( U_552 = empty_set
| ~ subset(U_552,empty_set) ),
inference(variable_rename,[status(thm)],[f_140_1]) ).
cnf(f_140_3,plain,
( U_552 = empty_set
| ~ subset(U_552,empty_set) ),
inference(clausify,[status(thm)],[f_140_2]) ).
fof(f_141_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_141_2,plain,
! [U_554,U_553] : set_difference(set_union2(U_554,U_553),U_553) = set_difference(U_554,U_553),
inference(variable_rename,[status(thm)],[f_141_1]) ).
cnf(f_141_3,plain,
set_difference(set_union2(U_554,U_553),U_553) = set_difference(U_554,U_553),
inference(clausify,[status(thm)],[f_141_2]) ).
fof(f_142_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_142_2,plain,
! [U_557,U_556] :
( ! [U_555] :
( ( ( disjoint(U_556,U_555)
| ~ subset(U_556,subset_complement(U_557,U_555)) )
& ( subset(U_556,subset_complement(U_557,U_555))
| ~ disjoint(U_556,U_555) ) )
| ~ element(U_555,powerset(U_557)) )
| ~ element(U_556,powerset(U_557)) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
cnf(f_142_3,plain,
( subset(U_556,subset_complement(U_557,U_555))
| ~ disjoint(U_556,U_555)
| ~ element(U_555,powerset(U_557))
| ~ element(U_556,powerset(U_557)) ),
inference(clausify,[status(thm)],[f_142_2]) ).
cnf(f_142_4,plain,
( disjoint(U_556,U_555)
| ~ subset(U_556,subset_complement(U_557,U_555))
| ~ element(U_555,powerset(U_557))
| ~ element(U_556,powerset(U_557)) ),
inference(clausify,[status(thm)],[f_142_2]) ).
fof(f_143_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_143_2,plain,
! [U_559] :
( ! [U_558] :
( subset(relation_dom(relation_composition(U_559,U_558)),relation_dom(U_559))
| ~ relation(U_558) )
| ~ relation(U_559) ),
inference(variable_rename,[status(thm)],[f_143_1]) ).
cnf(f_143_3,plain,
( subset(relation_dom(relation_composition(U_559,U_558)),relation_dom(U_559))
| ~ relation(U_558)
| ~ relation(U_559) ),
inference(clausify,[status(thm)],[f_143_2]) ).
fof(f_144_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_144_2,plain,
! [U_561] :
( ! [U_560] :
( subset(relation_rng(relation_composition(U_561,U_560)),relation_rng(U_560))
| ~ relation(U_560) )
| ~ relation(U_561) ),
inference(variable_rename,[status(thm)],[f_144_1]) ).
cnf(f_144_3,plain,
( subset(relation_rng(relation_composition(U_561,U_560)),relation_rng(U_560))
| ~ relation(U_560)
| ~ relation(U_561) ),
inference(clausify,[status(thm)],[f_144_2]) ).
fof(f_145_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_145_2,plain,
! [U_563,U_562] :
( U_562 = set_union2(U_563,set_difference(U_562,U_563))
| ~ subset(U_563,U_562) ),
inference(variable_rename,[status(thm)],[f_145_1]) ).
cnf(f_145_3,plain,
( U_562 = set_union2(U_563,set_difference(U_562,U_563))
| ~ subset(U_563,U_562) ),
inference(clausify,[status(thm)],[f_145_2]) ).
fof(f_146_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_146_2,plain,
! [U_565] :
( ! [U_564] :
( relation_dom(relation_composition(U_565,U_564)) = relation_dom(U_565)
| ~ subset(relation_rng(U_565),relation_dom(U_564))
| ~ relation(U_564) )
| ~ relation(U_565) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
cnf(f_146_3,plain,
( relation_dom(relation_composition(U_565,U_564)) = relation_dom(U_565)
| ~ subset(relation_rng(U_565),relation_dom(U_564))
| ~ relation(U_564)
| ~ relation(U_565) ),
inference(clausify,[status(thm)],[f_146_2]) ).
fof(f_147_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_147_2,plain,
! [U_567,U_566] :
( complements_of_subsets(U_567,U_566) != empty_set
| U_566 = empty_set
| ~ element(U_566,powerset(powerset(U_567))) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
cnf(f_147_3,plain,
( complements_of_subsets(U_567,U_566) != empty_set
| U_566 = empty_set
| ~ element(U_566,powerset(powerset(U_567))) ),
inference(clausify,[status(thm)],[f_147_2]) ).
fof(f_148_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t46_zfmisc_1]) ).
fof(f_148_2,plain,
! [U_569,U_568] :
( set_union2(singleton(U_569),U_568) = U_568
| ~ in(U_569,U_568) ),
inference(variable_rename,[status(thm)],[f_148_1]) ).
cnf(f_148_3,plain,
( set_union2(singleton(U_569),U_568) = U_568
| ~ in(U_569,U_568) ),
inference(clausify,[status(thm)],[f_148_2]) ).
fof(f_149_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_149_2,plain,
! [U_571] :
( ! [U_570] :
( relation_rng(relation_composition(U_570,U_571)) = relation_rng(U_571)
| ~ subset(relation_dom(U_571),relation_rng(U_570))
| ~ relation(U_570) )
| ~ relation(U_571) ),
inference(variable_rename,[status(thm)],[f_149_1]) ).
cnf(f_149_3,plain,
( relation_rng(relation_composition(U_570,U_571)) = relation_rng(U_571)
| ~ subset(relation_dom(U_571),relation_rng(U_570))
| ~ relation(U_570)
| ~ relation(U_571) ),
inference(clausify,[status(thm)],[f_149_2]) ).
fof(f_150_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_150_2,plain,
! [U_573,U_572] :
( subset_difference(U_573,cast_to_subset(U_573),union_of_subsets(U_573,U_572)) = meet_of_subsets(U_573,complements_of_subsets(U_573,U_572))
| U_572 = empty_set
| ~ element(U_572,powerset(powerset(U_573))) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
cnf(f_150_3,plain,
( subset_difference(U_573,cast_to_subset(U_573),union_of_subsets(U_573,U_572)) = meet_of_subsets(U_573,complements_of_subsets(U_573,U_572))
| U_572 = empty_set
| ~ element(U_572,powerset(powerset(U_573))) ),
inference(clausify,[status(thm)],[f_150_2]) ).
fof(f_151_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_151_2,plain,
! [U_575,U_574] :
( union_of_subsets(U_575,complements_of_subsets(U_575,U_574)) = subset_difference(U_575,cast_to_subset(U_575),meet_of_subsets(U_575,U_574))
| U_574 = empty_set
| ~ element(U_574,powerset(powerset(U_575))) ),
inference(variable_rename,[status(thm)],[f_151_1]) ).
cnf(f_151_3,plain,
( union_of_subsets(U_575,complements_of_subsets(U_575,U_574)) = subset_difference(U_575,cast_to_subset(U_575),meet_of_subsets(U_575,U_574))
| U_574 = empty_set
| ~ element(U_574,powerset(powerset(U_575))) ),
inference(clausify,[status(thm)],[f_151_2]) ).
fof(f_152_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_152_2,plain,
! [U_577,U_576] : set_difference(U_577,set_difference(U_577,U_576)) = set_intersection2(U_577,U_576),
inference(variable_rename,[status(thm)],[f_152_1]) ).
cnf(f_152_3,plain,
set_difference(U_577,set_difference(U_577,U_576)) = set_intersection2(U_577,U_576),
inference(clausify,[status(thm)],[f_152_2]) ).
fof(f_153_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_153_2,plain,
! [U_578] : set_difference(empty_set,U_578) = empty_set,
inference(variable_rename,[status(thm)],[f_153_1]) ).
cnf(f_153_3,plain,
set_difference(empty_set,U_578) = empty_set,
inference(clausify,[status(thm)],[f_153_2]) ).
fof(f_154_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_154_2,plain,
! [U_581,U_580,U_579] :
( element(U_581,U_579)
| ~ element(U_580,powerset(U_579))
| ~ in(U_581,U_580) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
cnf(f_154_3,plain,
( element(U_581,U_579)
| ~ element(U_580,powerset(U_579))
| ~ in(U_581,U_580) ),
inference(clausify,[status(thm)],[f_154_2]) ).
fof(f_155_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_155_2,plain,
! [U_585,U_584] :
( ( ~ disjoint(U_585,U_584)
| ! [U_583] : ~ in(U_583,set_intersection2(U_585,U_584)) )
& ( ? [U_582] : in(U_582,set_intersection2(U_585,U_584))
| disjoint(U_585,U_584) ) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
fof(f_155_3,plain,
( ! [U_589,U_587] :
( ~ disjoint(U_589,U_587)
| ! [U_583] : ~ in(U_583,set_intersection2(U_589,U_587)) )
& ! [U_588,U_586] :
( ? [U_582] : in(U_582,set_intersection2(U_588,U_586))
| disjoint(U_588,U_586) ) ),
inference(miniscope,[status(thm)],[f_155_2]) ).
fof(f_155_4,plain,
( ! [U_589,U_587] :
( ~ disjoint(U_589,U_587)
| ! [U_583] : ~ in(U_583,set_intersection2(U_589,U_587)) )
& ! [U_588,U_586] :
( in(sK73(U_588,U_586),set_intersection2(U_588,U_586))
| disjoint(U_588,U_586) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_582,sK73(U_588,U_586))],[f_155_3]) ).
cnf(f_155_5,plain,
( in(sK73(U_588,U_586),set_intersection2(U_588,U_586))
| disjoint(U_588,U_586) ),
inference(clausify,[status(thm)],[f_155_4]) ).
cnf(f_155_6,plain,
( ~ disjoint(U_589,U_587)
| ~ in(U_583,set_intersection2(U_589,U_587)) ),
inference(clausify,[status(thm)],[f_155_4]) ).
fof(f_156_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_156_2,plain,
! [U_592] :
( ! [U_591] :
( ! [U_590] :
( in(U_590,subset_complement(U_592,U_591))
| in(U_590,U_591)
| ~ element(U_590,U_592) )
| ~ element(U_591,powerset(U_592)) )
| U_592 = empty_set ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
cnf(f_156_3,plain,
( in(U_590,subset_complement(U_592,U_591))
| in(U_590,U_591)
| ~ element(U_590,U_592)
| ~ element(U_591,powerset(U_592))
| U_592 = empty_set ),
inference(clausify,[status(thm)],[f_156_2]) ).
fof(f_157_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_157_2,plain,
! [U_595,U_594,U_593] :
( ~ in(U_594,U_593)
| ~ in(U_594,subset_complement(U_595,U_593))
| ~ element(U_593,powerset(U_595)) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
cnf(f_157_3,plain,
( ~ in(U_594,U_593)
| ~ in(U_594,subset_complement(U_595,U_593))
| ~ element(U_593,powerset(U_595)) ),
inference(clausify,[status(thm)],[f_157_2]) ).
fof(f_158_1,plain,
! [A] :
( A = empty_set
| ? [B,C] : in(ordered_pair(B,C),A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t56_relat_1]) ).
fof(f_158_2,plain,
! [U_598] :
( U_598 = empty_set
| ? [U_597,U_596] : in(ordered_pair(U_597,U_596),U_598)
| ~ relation(U_598) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
fof(f_158_3,plain,
! [U_598] :
( U_598 = empty_set
| ? [U_596] : in(ordered_pair(sK74(U_598),U_596),U_598)
| ~ relation(U_598) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_597,sK74(U_598))],[f_158_2]) ).
fof(f_158_4,plain,
! [U_598] :
( U_598 = empty_set
| in(ordered_pair(sK74(U_598),sK75(U_598)),U_598)
| ~ relation(U_598) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_596,sK75(U_598))],[f_158_3]) ).
cnf(f_158_5,plain,
( U_598 = empty_set
| in(ordered_pair(sK74(U_598),sK75(U_598)),U_598)
| ~ relation(U_598) ),
inference(clausify,[status(thm)],[f_158_4]) ).
fof(f_159_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_159_2,plain,
! [U_601,U_600,U_599] :
( ~ empty(U_599)
| ~ element(U_600,powerset(U_599))
| ~ in(U_601,U_600) ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
fof(f_159_3,plain,
! [U_601,U_600] :
( ! [U_599] :
( ~ empty(U_599)
| ~ element(U_600,powerset(U_599)) )
| ~ in(U_601,U_600) ),
inference(miniscope,[status(thm)],[f_159_2]) ).
cnf(f_159_4,plain,
( ~ empty(U_599)
| ~ element(U_600,powerset(U_599))
| ~ in(U_601,U_600) ),
inference(clausify,[status(thm)],[f_159_3]) ).
fof(f_160_1,plain,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(fof_nnf,[status(thm)],[t60_relat_1]) ).
cnf(f_160_2,plain,
relation_dom(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_160_1]) ).
cnf(f_160_3,plain,
relation_rng(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_160_1]) ).
fof(f_161_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t60_xboole_1]) ).
fof(f_161_2,plain,
! [U_603,U_602] :
( ~ proper_subset(U_602,U_603)
| ~ subset(U_603,U_602) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
cnf(f_161_3,plain,
( ~ proper_subset(U_602,U_603)
| ~ subset(U_603,U_602) ),
inference(clausify,[status(thm)],[f_161_2]) ).
fof(f_162_1,plain,
! [A,B,C] :
( disjoint(A,C)
| ~ disjoint(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t63_xboole_1]) ).
fof(f_162_2,plain,
! [U_606,U_605,U_604] :
( disjoint(U_606,U_604)
| ~ disjoint(U_605,U_604)
| ~ subset(U_606,U_605) ),
inference(variable_rename,[status(thm)],[f_162_1]) ).
cnf(f_162_3,plain,
( disjoint(U_606,U_604)
| ~ disjoint(U_605,U_604)
| ~ subset(U_606,U_605) ),
inference(clausify,[status(thm)],[f_162_2]) ).
fof(f_163_1,plain,
! [A] :
( A = empty_set
| ( relation_rng(A) != empty_set
& relation_dom(A) != empty_set )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t64_relat_1]) ).
fof(f_163_2,plain,
! [U_607] :
( U_607 = empty_set
| ( relation_rng(U_607) != empty_set
& relation_dom(U_607) != empty_set )
| ~ relation(U_607) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
cnf(f_163_3,plain,
( relation_dom(U_607) != empty_set
| U_607 = empty_set
| ~ relation(U_607) ),
inference(clausify,[status(thm)],[f_163_2]) ).
cnf(f_163_4,plain,
( relation_rng(U_607) != empty_set
| U_607 = empty_set
| ~ relation(U_607) ),
inference(clausify,[status(thm)],[f_163_2]) ).
fof(f_164_1,plain,
! [A] :
( ( ( relation_dom(A) = empty_set
| relation_rng(A) != empty_set )
& ( relation_rng(A) = empty_set
| relation_dom(A) != empty_set ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t65_relat_1]) ).
fof(f_164_2,plain,
! [U_608] :
( ( ( relation_dom(U_608) = empty_set
| relation_rng(U_608) != empty_set )
& ( relation_rng(U_608) = empty_set
| relation_dom(U_608) != empty_set ) )
| ~ relation(U_608) ),
inference(variable_rename,[status(thm)],[f_164_1]) ).
cnf(f_164_3,plain,
( relation_rng(U_608) = empty_set
| relation_dom(U_608) != empty_set
| ~ relation(U_608) ),
inference(clausify,[status(thm)],[f_164_2]) ).
cnf(f_164_4,plain,
( relation_dom(U_608) = empty_set
| relation_rng(U_608) != empty_set
| ~ relation(U_608) ),
inference(clausify,[status(thm)],[f_164_2]) ).
fof(f_165_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_165_2,plain,
! [U_610,U_609] :
( ( set_difference(U_610,singleton(U_609)) = U_610
| in(U_609,U_610) )
& ( ~ in(U_609,U_610)
| set_difference(U_610,singleton(U_609)) != U_610 ) ),
inference(variable_rename,[status(thm)],[f_165_1]) ).
fof(f_165_3,plain,
( ! [U_614,U_612] :
( set_difference(U_614,singleton(U_612)) = U_614
| in(U_612,U_614) )
& ! [U_613,U_611] :
( ~ in(U_611,U_613)
| set_difference(U_613,singleton(U_611)) != U_613 ) ),
inference(miniscope,[status(thm)],[f_165_2]) ).
cnf(f_165_4,plain,
( ~ in(U_611,U_613)
| set_difference(U_613,singleton(U_611)) != U_613 ),
inference(clausify,[status(thm)],[f_165_3]) ).
cnf(f_165_5,plain,
( set_difference(U_614,singleton(U_612)) = U_614
| in(U_612,U_614) ),
inference(clausify,[status(thm)],[f_165_3]) ).
fof(f_166_1,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(fof_nnf,[status(thm)],[t69_enumset1]) ).
fof(f_166_2,plain,
! [U_615] : unordered_pair(U_615,U_615) = singleton(U_615),
inference(variable_rename,[status(thm)],[f_166_1]) ).
cnf(f_166_3,plain,
unordered_pair(U_615,U_615) = singleton(U_615),
inference(clausify,[status(thm)],[f_166_2]) ).
fof(f_167_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_167_2,plain,
! [U_616] :
( U_616 = empty_set
| ~ empty(U_616) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
cnf(f_167_3,plain,
( U_616 = empty_set
| ~ empty(U_616) ),
inference(clausify,[status(thm)],[f_167_2]) ).
fof(f_168_1,plain,
! [A,B] :
( A = B
| ~ subset(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t6_zfmisc_1]) ).
fof(f_168_2,plain,
! [U_618,U_617] :
( U_618 = U_617
| ~ subset(singleton(U_618),singleton(U_617)) ),
inference(variable_rename,[status(thm)],[f_168_1]) ).
cnf(f_168_3,plain,
( U_618 = U_617
| ~ subset(singleton(U_618),singleton(U_617)) ),
inference(clausify,[status(thm)],[f_168_2]) ).
fof(f_169_1,plain,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
inference(fof_nnf,[status(thm)],[t71_relat_1]) ).
fof(f_169_2,plain,
! [U_619] :
( relation_rng(identity_relation(U_619)) = U_619
& relation_dom(identity_relation(U_619)) = U_619 ),
inference(variable_rename,[status(thm)],[f_169_1]) ).
fof(f_169_3,plain,
( ! [U_621] : relation_rng(identity_relation(U_621)) = U_621
& ! [U_620] : relation_dom(identity_relation(U_620)) = U_620 ),
inference(miniscope,[status(thm)],[f_169_2]) ).
cnf(f_169_4,plain,
relation_dom(identity_relation(U_620)) = U_620,
inference(clausify,[status(thm)],[f_169_3]) ).
cnf(f_169_5,plain,
relation_rng(identity_relation(U_621)) = U_621,
inference(clausify,[status(thm)],[f_169_3]) ).
fof(f_170_1,plain,
! [A,B,C,D] :
( ( ( in(ordered_pair(A,B),relation_composition(identity_relation(C),D))
| ~ in(ordered_pair(A,B),D)
| ~ in(A,C) )
& ( ( in(ordered_pair(A,B),D)
& in(A,C) )
| ~ in(ordered_pair(A,B),relation_composition(identity_relation(C),D)) ) )
| ~ relation(D) ),
inference(fof_nnf,[status(thm)],[t74_relat_1]) ).
fof(f_170_2,plain,
! [U_625,U_624,U_623,U_622] :
( ( ( in(ordered_pair(U_625,U_624),relation_composition(identity_relation(U_623),U_622))
| ~ in(ordered_pair(U_625,U_624),U_622)
| ~ in(U_625,U_623) )
& ( ( in(ordered_pair(U_625,U_624),U_622)
& in(U_625,U_623) )
| ~ in(ordered_pair(U_625,U_624),relation_composition(identity_relation(U_623),U_622)) ) )
| ~ relation(U_622) ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
cnf(f_170_3,plain,
( in(U_625,U_623)
| ~ in(ordered_pair(U_625,U_624),relation_composition(identity_relation(U_623),U_622))
| ~ relation(U_622) ),
inference(clausify,[status(thm)],[f_170_2]) ).
cnf(f_170_4,plain,
( in(ordered_pair(U_625,U_624),U_622)
| ~ in(ordered_pair(U_625,U_624),relation_composition(identity_relation(U_623),U_622))
| ~ relation(U_622) ),
inference(clausify,[status(thm)],[f_170_2]) ).
cnf(f_170_5,plain,
( in(ordered_pair(U_625,U_624),relation_composition(identity_relation(U_623),U_622))
| ~ in(ordered_pair(U_625,U_624),U_622)
| ~ in(U_625,U_623)
| ~ relation(U_622) ),
inference(clausify,[status(thm)],[f_170_2]) ).
fof(f_171_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_171_2,plain,
! [U_627,U_626] :
( ~ empty(U_626)
| ~ in(U_627,U_626) ),
inference(variable_rename,[status(thm)],[f_171_1]) ).
cnf(f_171_3,plain,
( ~ empty(U_626)
| ~ in(U_627,U_626) ),
inference(clausify,[status(thm)],[f_171_2]) ).
fof(f_172_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1]) ).
fof(f_172_2,plain,
! [U_629,U_628] : subset(U_629,set_union2(U_629,U_628)),
inference(variable_rename,[status(thm)],[f_172_1]) ).
cnf(f_172_3,plain,
subset(U_629,set_union2(U_629,U_628)),
inference(clausify,[status(thm)],[f_172_2]) ).
fof(f_173_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_173_2,plain,
! [U_631,U_630] :
( ( disjoint(U_631,U_630)
| set_difference(U_631,U_630) != U_631 )
& ( set_difference(U_631,U_630) = U_631
| ~ disjoint(U_631,U_630) ) ),
inference(variable_rename,[status(thm)],[f_173_1]) ).
fof(f_173_3,plain,
( ! [U_635,U_633] :
( disjoint(U_635,U_633)
| set_difference(U_635,U_633) != U_635 )
& ! [U_634,U_632] :
( set_difference(U_634,U_632) = U_634
| ~ disjoint(U_634,U_632) ) ),
inference(miniscope,[status(thm)],[f_173_2]) ).
cnf(f_173_4,plain,
( set_difference(U_634,U_632) = U_634
| ~ disjoint(U_634,U_632) ),
inference(clausify,[status(thm)],[f_173_3]) ).
cnf(f_173_5,plain,
( disjoint(U_635,U_633)
| set_difference(U_635,U_633) != U_635 ),
inference(clausify,[status(thm)],[f_173_3]) ).
fof(f_174_1,plain,
! [A,B,C] :
( ( ( in(A,relation_dom(relation_dom_restriction(C,B)))
| ~ in(A,relation_dom(C))
| ~ in(A,B) )
& ( ( in(A,relation_dom(C))
& in(A,B) )
| ~ in(A,relation_dom(relation_dom_restriction(C,B))) ) )
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t86_relat_1]) ).
fof(f_174_2,plain,
! [U_638,U_637,U_636] :
( ( ( in(U_638,relation_dom(relation_dom_restriction(U_636,U_637)))
| ~ in(U_638,relation_dom(U_636))
| ~ in(U_638,U_637) )
& ( ( in(U_638,relation_dom(U_636))
& in(U_638,U_637) )
| ~ in(U_638,relation_dom(relation_dom_restriction(U_636,U_637))) ) )
| ~ relation(U_636) ),
inference(variable_rename,[status(thm)],[f_174_1]) ).
cnf(f_174_3,plain,
( in(U_638,U_637)
| ~ in(U_638,relation_dom(relation_dom_restriction(U_636,U_637)))
| ~ relation(U_636) ),
inference(clausify,[status(thm)],[f_174_2]) ).
cnf(f_174_4,plain,
( in(U_638,relation_dom(U_636))
| ~ in(U_638,relation_dom(relation_dom_restriction(U_636,U_637)))
| ~ relation(U_636) ),
inference(clausify,[status(thm)],[f_174_2]) ).
cnf(f_174_5,plain,
( in(U_638,relation_dom(relation_dom_restriction(U_636,U_637)))
| ~ in(U_638,relation_dom(U_636))
| ~ in(U_638,U_637)
| ~ relation(U_636) ),
inference(clausify,[status(thm)],[f_174_2]) ).
fof(f_175_1,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> subset(relation_dom_restriction(B,A),B) ),
inference(negate,[status(cth)],[t88_relat_1]) ).
fof(f_175_2,negated_conjecture,
? [A,B] :
( ~ subset(relation_dom_restriction(B,A),B)
& relation(B) ),
inference(fof_nnf,[status(thm)],[f_175_1]) ).
fof(f_175_3,negated_conjecture,
? [U_640,U_639] :
( ~ subset(relation_dom_restriction(U_639,U_640),U_639)
& relation(U_639) ),
inference(variable_rename,[status(thm)],[f_175_2]) ).
fof(f_175_4,negated_conjecture,
? [U_639] :
( ~ subset(relation_dom_restriction(U_639,sK76),U_639)
& relation(U_639) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_640,sK76)],[f_175_3]) ).
fof(f_175_5,negated_conjecture,
( ~ subset(relation_dom_restriction(sK77,sK76),sK77)
& relation(sK77) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_639,sK77)],[f_175_4]) ).
cnf(f_175_6,negated_conjecture,
relation(sK77),
inference(clausify,[status(thm)],[f_175_5]) ).
cnf(f_175_7,negated_conjecture,
~ subset(relation_dom_restriction(sK77,sK76),sK77),
inference(clausify,[status(thm)],[f_175_5]) ).
fof(f_176_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_176_2,plain,
! [U_642,U_641] :
( ~ empty(U_641)
| U_642 = U_641
| ~ empty(U_642) ),
inference(variable_rename,[status(thm)],[f_176_1]) ).
fof(f_176_3,plain,
! [U_642] :
( ! [U_641] :
( ~ empty(U_641)
| U_642 = U_641 )
| ~ empty(U_642) ),
inference(miniscope,[status(thm)],[f_176_2]) ).
cnf(f_176_4,plain,
( ~ empty(U_641)
| U_642 = U_641
| ~ empty(U_642) ),
inference(clausify,[status(thm)],[f_176_3]) ).
fof(f_177_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_177_2,plain,
! [U_645,U_644,U_643] :
( subset(set_union2(U_645,U_643),U_644)
| ~ subset(U_643,U_644)
| ~ subset(U_645,U_644) ),
inference(variable_rename,[status(thm)],[f_177_1]) ).
cnf(f_177_3,plain,
( subset(set_union2(U_645,U_643),U_644)
| ~ subset(U_643,U_644)
| ~ subset(U_645,U_644) ),
inference(clausify,[status(thm)],[f_177_2]) ).
fof(f_178_1,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t8_zfmisc_1]) ).
fof(f_178_2,plain,
! [U_648,U_647,U_646] :
( U_648 = U_647
| singleton(U_648) != unordered_pair(U_647,U_646) ),
inference(variable_rename,[status(thm)],[f_178_1]) ).
fof(f_178_3,plain,
! [U_648,U_647] :
( ! [U_646] : singleton(U_648) != unordered_pair(U_647,U_646)
| U_648 = U_647 ),
inference(miniscope,[status(thm)],[f_178_2]) ).
cnf(f_178_4,plain,
( singleton(U_648) != unordered_pair(U_647,U_646)
| U_648 = U_647 ),
inference(clausify,[status(thm)],[f_178_3]) ).
fof(f_179_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t92_zfmisc_1]) ).
fof(f_179_2,plain,
! [U_650,U_649] :
( subset(U_650,union(U_649))
| ~ in(U_650,U_649) ),
inference(variable_rename,[status(thm)],[f_179_1]) ).
cnf(f_179_3,plain,
( subset(U_650,union(U_649))
| ~ in(U_650,U_649) ),
inference(clausify,[status(thm)],[f_179_2]) ).
fof(f_180_1,plain,
! [A] : union(powerset(A)) = A,
inference(fof_nnf,[status(thm)],[t99_zfmisc_1]) ).
fof(f_180_2,plain,
! [U_651] : union(powerset(U_651)) = U_651,
inference(variable_rename,[status(thm)],[f_180_1]) ).
cnf(f_180_3,plain,
union(powerset(U_651)) = U_651,
inference(clausify,[status(thm)],[f_180_2]) ).
fof(f_181_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_181_2,plain,
! [U_659] :
? [U_658] :
( ! [U_657] :
( in(U_657,U_658)
| are_equipotent(U_657,U_658)
| ~ subset(U_657,U_658) )
& ! [U_656] :
( ? [U_655] :
( ! [U_654] :
( in(U_654,U_655)
| ~ subset(U_654,U_656) )
& in(U_655,U_658) )
| ~ in(U_656,U_658) )
& ! [U_653,U_652] :
( in(U_652,U_658)
| ~ subset(U_652,U_653)
| ~ in(U_653,U_658) )
& in(U_659,U_658) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
fof(f_181_3,plain,
! [U_659] :
( ! [U_657] :
( in(U_657,sK78(U_659))
| are_equipotent(U_657,sK78(U_659))
| ~ subset(U_657,sK78(U_659)) )
& ! [U_656] :
( ? [U_655] :
( ! [U_654] :
( in(U_654,U_655)
| ~ subset(U_654,U_656) )
& in(U_655,sK78(U_659)) )
| ~ in(U_656,sK78(U_659)) )
& ! [U_653,U_652] :
( in(U_652,sK78(U_659))
| ~ subset(U_652,U_653)
| ~ in(U_653,sK78(U_659)) )
& in(U_659,sK78(U_659)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_658,sK78(U_659))],[f_181_2]) ).
fof(f_181_4,plain,
! [U_659] :
( ! [U_657] :
( in(U_657,sK78(U_659))
| are_equipotent(U_657,sK78(U_659))
| ~ subset(U_657,sK78(U_659)) )
& ! [U_656] :
( ( ! [U_654] :
( in(U_654,sK79(U_659,U_656))
| ~ subset(U_654,U_656) )
& in(sK79(U_659,U_656),sK78(U_659)) )
| ~ in(U_656,sK78(U_659)) )
& ! [U_653,U_652] :
( in(U_652,sK78(U_659))
| ~ subset(U_652,U_653)
| ~ in(U_653,sK78(U_659)) )
& in(U_659,sK78(U_659)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_655,sK79(U_659,U_656))],[f_181_3]) ).
cnf(f_181_5,plain,
in(U_659,sK78(U_659)),
inference(clausify,[status(thm)],[f_181_4]) ).
cnf(f_181_6,plain,
( in(U_652,sK78(U_659))
| ~ subset(U_652,U_653)
| ~ in(U_653,sK78(U_659)) ),
inference(clausify,[status(thm)],[f_181_4]) ).
cnf(f_181_7,plain,
( in(sK79(U_659,U_656),sK78(U_659))
| ~ in(U_656,sK78(U_659)) ),
inference(clausify,[status(thm)],[f_181_4]) ).
cnf(f_181_8,plain,
( in(U_654,sK79(U_659,U_656))
| ~ subset(U_654,U_656)
| ~ in(U_656,sK78(U_659)) ),
inference(clausify,[status(thm)],[f_181_4]) ).
cnf(f_181_9,plain,
( in(U_657,sK78(U_659))
| are_equipotent(U_657,sK78(U_659))
| ~ subset(U_657,sK78(U_659)) ),
inference(clausify,[status(thm)],[f_181_4]) ).
fof(f_182_1,plain,
! [A,B,C] :
( B = C
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t9_zfmisc_1]) ).
fof(f_182_2,plain,
! [U_662,U_661,U_660] :
( U_661 = U_660
| singleton(U_662) != unordered_pair(U_661,U_660) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
cnf(f_182_3,plain,
( U_661 = U_660
| singleton(U_662) != unordered_pair(U_661,U_660) ),
inference(clausify,[status(thm)],[f_182_2]) ).
cnf(f_33_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_33_8]) ).
cnf(f_33_9_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_33_9]) ).
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_38_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_38_2]) ).
cnf(f_39_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_39_2]) ).
cnf(f_40_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_40_2]) ).
cnf(f_42_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_42_2]) ).
cnf(f_43_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_43_2]) ).
cnf(f_44_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_44_2]) ).
cnf(f_45_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_45_2]) ).
cnf(f_47_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_47_2]) ).
cnf(f_48_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_48_2]) ).
cnf(f_50_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_50_2]) ).
cnf(f_51_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_51_2]) ).
cnf(f_59_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_59_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( unordered_pair(Eq_x_0,Eq_x_1) = unordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( set_union2(Eq_x_0,Eq_x_1) = set_union2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( set_intersection2(Eq_x_0,Eq_x_1) = set_intersection2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( identity_relation(Eq_x_0) = identity_relation(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( ordered_pair(Eq_x_0,Eq_x_1) = ordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( relation_dom_restriction(Eq_x_0,Eq_x_1) = relation_dom_restriction(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( set_meet(Eq_x_0) = set_meet(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( cartesian_product2(Eq_x_0,Eq_x_1) = cartesian_product2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( cast_to_subset(Eq_x_0) = cast_to_subset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( union(Eq_x_0) = union(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( set_difference(Eq_x_0,Eq_x_1) = set_difference(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( subset_complement(Eq_x_0,Eq_x_1) = subset_complement(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( relation_field(Eq_x_0) = relation_field(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( relation_inverse(Eq_x_0) = relation_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( relation_composition(Eq_x_0,Eq_x_1) = relation_composition(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( complements_of_subsets(Eq_x_0,Eq_x_1) = complements_of_subsets(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,axiom,
( union_of_subsets(Eq_x_0,Eq_x_1) = union_of_subsets(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( meet_of_subsets(Eq_x_0,Eq_x_1) = meet_of_subsets(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,axiom,
( subset_difference(Eq_x_0,Eq_x_1,Eq_x_2) = subset_difference(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_27,axiom,
( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,axiom,
( sK2(Eq_x_0,Eq_x_1) = sK2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_29,axiom,
( sK3(Eq_x_0,Eq_x_1) = sK3(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_30,axiom,
( sK4(Eq_x_0,Eq_x_1) = sK4(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_31,axiom,
( sK5(Eq_x_0,Eq_x_1,Eq_x_2) = sK5(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_32,axiom,
( sK6(Eq_x_0,Eq_x_1,Eq_x_2) = sK6(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,axiom,
( sK7(Eq_x_0,Eq_x_1,Eq_x_2) = sK7(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_34,axiom,
( sK8(Eq_x_0,Eq_x_1,Eq_x_2) = sK8(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_35,axiom,
( sK9(Eq_x_0,Eq_x_1) = sK9(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_36,axiom,
( sK10(Eq_x_0,Eq_x_1) = sK10(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_37,axiom,
( sK11(Eq_x_0) = sK11(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_38,axiom,
( sK12(Eq_x_0,Eq_x_1,Eq_x_2) = sK12(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,axiom,
( sK13(Eq_x_0,Eq_x_1) = sK13(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_40,axiom,
( sK14(Eq_x_0,Eq_x_1) = sK14(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_41,axiom,
( sK15(Eq_x_0,Eq_x_1) = sK15(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_42,axiom,
( sK16(Eq_x_0,Eq_x_1) = sK16(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_43,axiom,
( sK17(Eq_x_0,Eq_x_1) = sK17(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_44,axiom,
( sK18(Eq_x_0) = sK18(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_45,axiom,
( sK19(Eq_x_0,Eq_x_1) = sK19(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_46,axiom,
( sK20(Eq_x_0,Eq_x_1) = sK20(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_47,axiom,
( sK21(Eq_x_0,Eq_x_1,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_48,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_49,axiom,
( sK23(Eq_x_0,Eq_x_1,Eq_x_2) = sK23(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,
( 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_51,axiom,
( sK25(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK25(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_52,axiom,
( sK26(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK26(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_53,axiom,
( sK27(Eq_x_0,Eq_x_1,Eq_x_2) = sK27(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_54,axiom,
( sK28(Eq_x_0,Eq_x_1,Eq_x_2) = sK28(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_55,axiom,
( sK29(Eq_x_0,Eq_x_1,Eq_x_2) = sK29(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_56,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_57,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_58,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_59,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_60,axiom,
( sK34(Eq_x_0,Eq_x_1,Eq_x_2) = sK34(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_61,axiom,
( sK35(Eq_x_0,Eq_x_1,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_62,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_63,axiom,
( sK37(Eq_x_0,Eq_x_1) = sK37(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_64,axiom,
( sK38(Eq_x_0,Eq_x_1) = 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_65,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_66,axiom,
( sK40(Eq_x_0,Eq_x_1,Eq_x_2) = sK40(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_67,axiom,
( sK41(Eq_x_0,Eq_x_1) = sK41(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_68,axiom,
( sK42(Eq_x_0,Eq_x_1) = sK42(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_69,axiom,
( sK43(Eq_x_0,Eq_x_1) = sK43(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_70,axiom,
( sK44(Eq_x_0,Eq_x_1,Eq_x_2) = sK44(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_71,axiom,
( sK45(Eq_x_0,Eq_x_1,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_72,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_73,axiom,
( sK47(Eq_x_0,Eq_x_1) = sK47(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_74,axiom,
( sK48(Eq_x_0,Eq_x_1) = sK48(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_75,axiom,
( sK49(Eq_x_0,Eq_x_1) = sK49(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_76,axiom,
( sK50(Eq_x_0,Eq_x_1) = sK50(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_77,axiom,
( sK51(Eq_x_0,Eq_x_1) = sK51(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_78,axiom,
( sK52(Eq_x_0,Eq_x_1) = sK52(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_79,axiom,
( sK53(Eq_x_0,Eq_x_1) = sK53(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_80,axiom,
( sK54(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK54(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_81,axiom,
( sK55(Eq_x_0,Eq_x_1,Eq_x_2) = sK55(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_82,axiom,
( sK56(Eq_x_0,Eq_x_1,Eq_x_2) = sK56(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_83,axiom,
( sK57(Eq_x_0,Eq_x_1,Eq_x_2) = sK57(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_84,axiom,
( sK58(Eq_x_0,Eq_x_1,Eq_x_2) = sK58(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_85,axiom,
( sK59(Eq_x_0,Eq_x_1,Eq_x_2) = sK59(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_86,axiom,
( sK60(Eq_x_0,Eq_x_1,Eq_x_2) = sK60(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_87,axiom,
( sK61(Eq_x_0) = sK61(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_88,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_89,axiom,
( sK64(Eq_x_0) = sK64(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_90,axiom,
( sK67(Eq_x_0) = sK67(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_91,axiom,
( sK69(Eq_x_0) = sK69(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_92,axiom,
( sK70(Eq_x_0,Eq_x_1) = sK70(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_93,axiom,
( sK71(Eq_x_0,Eq_x_1) = sK71(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_94,axiom,
( sK72(Eq_x_0,Eq_x_1) = sK72(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_95,axiom,
( sK73(Eq_x_0,Eq_x_1) = sK73(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_96,axiom,
( sK74(Eq_x_0) = sK74(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_97,axiom,
( sK75(Eq_x_0) = sK75(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_98,axiom,
( sK78(Eq_x_0) = sK78(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_99,axiom,
( sK79(Eq_x_0,Eq_x_1) = sK79(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_100,axiom,
( 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_101,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_102,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_103,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_104,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_105,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_106,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_107,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 : SEU193+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
% 0.10/0.38 % Computer : n018.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 19 23:31:14 UTC 2026
% 0.10/0.38 % CPUTime :
% 284.45/284.71 % SZS status Theorem for theBenchmark
% 284.45/284.71 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------