%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU200+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 : n009.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 08:58:28 AM UTC 2026
% Result : Theorem 45.55s 45.81s
% Output : Proof 45.61s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(antisymmetry_r2_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
=> ~ proper_subset(B,A) ),
file('theBenchmark.p',antisymmetry_r2_xboole_0) ).
fof(cc1_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('theBenchmark.p',cc1_relat_1) ).
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d10_relat_1,axiom,
! [A,B] :
( relation(B)
=> ( B = identity_relation(A)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> ( C = D
& in(C,A) ) ) ) ),
file('theBenchmark.p',d10_relat_1) ).
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
fof(d11_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( relation(C)
=> ( C = relation_dom_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),A)
& in(D,B) ) ) ) ) ),
file('theBenchmark.p',d11_relat_1) ).
fof(d12_relat_1,axiom,
! [A,B] :
( relation(B)
=> ! [C] :
( relation(C)
=> ( C = relation_rng_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),B)
& in(E,A) ) ) ) ) ),
file('theBenchmark.p',d12_relat_1) ).
fof(d1_relat_1,axiom,
! [A] :
( relation(A)
<=> ! [B] :
~ ( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) ) ),
file('theBenchmark.p',d1_relat_1) ).
fof(d1_setfam_1,axiom,
! [A,B] :
( ( A = empty_set
=> ( B = set_meet(A)
<=> B = empty_set ) )
& ( A != empty_set
=> ( B = set_meet(A)
<=> ! [C] :
( in(C,B)
<=> ! [D] :
( in(D,A)
=> in(C,D) ) ) ) ) ),
file('theBenchmark.p',d1_setfam_1) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
fof(d1_zfmisc_1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('theBenchmark.p',d1_zfmisc_1) ).
fof(d2_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( A = B
<=> ! [C,D] :
( in(ordered_pair(C,D),A)
<=> in(ordered_pair(C,D),B) ) ) ) ),
file('theBenchmark.p',d2_relat_1) ).
fof(d2_subset_1,axiom,
! [A,B] :
( ( empty(A)
=> ( element(B,A)
<=> empty(B) ) )
& ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) ) ),
file('theBenchmark.p',d2_subset_1) ).
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('theBenchmark.p',d2_tarski) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('theBenchmark.p',d2_xboole_0) ).
fof(d2_zfmisc_1,axiom,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) ) ) ),
file('theBenchmark.p',d2_zfmisc_1) ).
fof(d3_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(A,B)
<=> ! [C,D] :
( in(ordered_pair(C,D),A)
=> in(ordered_pair(C,D),B) ) ) ) ),
file('theBenchmark.p',d3_relat_1) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(d3_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d3_xboole_0) ).
fof(d4_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('theBenchmark.p',d4_relat_1) ).
fof(d4_subset_1,axiom,
! [A] : cast_to_subset(A) = A,
file('theBenchmark.p',d4_subset_1) ).
fof(d4_tarski,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(D,A)
& in(C,D) ) ) ),
file('theBenchmark.p',d4_tarski) ).
fof(d4_xboole_0,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d4_xboole_0) ).
fof(d5_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('theBenchmark.p',d5_relat_1) ).
fof(d5_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,B) = set_difference(A,B) ),
file('theBenchmark.p',d5_subset_1) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(d6_relat_1,axiom,
! [A] :
( relation(A)
=> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
file('theBenchmark.p',d6_relat_1) ).
fof(d7_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( B = relation_inverse(A)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> in(ordered_pair(D,C),A) ) ) ) ),
file('theBenchmark.p',d7_relat_1) ).
fof(d7_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('theBenchmark.p',d7_xboole_0) ).
fof(d8_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( relation(C)
=> ( C = relation_composition(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) ) ) ) ) ) ),
file('theBenchmark.p',d8_relat_1) ).
fof(d8_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ! [C] :
( element(C,powerset(powerset(A)))
=> ( C = complements_of_subsets(A,B)
<=> ! [D] :
( element(D,powerset(A))
=> ( in(D,C)
<=> in(subset_complement(A,D),B) ) ) ) ) ),
file('theBenchmark.p',d8_setfam_1) ).
fof(d8_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('theBenchmark.p',d8_xboole_0) ).
fof(dt_k1_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k1_relat_1) ).
fof(dt_k1_setfam_1,axiom,
$true,
file('theBenchmark.p',dt_k1_setfam_1) ).
fof(dt_k1_tarski,axiom,
$true,
file('theBenchmark.p',dt_k1_tarski) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(dt_k2_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k2_relat_1) ).
fof(dt_k2_subset_1,axiom,
! [A] : element(cast_to_subset(A),powerset(A)),
file('theBenchmark.p',dt_k2_subset_1) ).
fof(dt_k2_tarski,axiom,
$true,
file('theBenchmark.p',dt_k2_tarski) ).
fof(dt_k2_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k2_xboole_0) ).
fof(dt_k2_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k2_zfmisc_1) ).
fof(dt_k3_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k3_relat_1) ).
fof(dt_k3_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> element(subset_complement(A,B),powerset(A)) ),
file('theBenchmark.p',dt_k3_subset_1) ).
fof(dt_k3_tarski,axiom,
$true,
file('theBenchmark.p',dt_k3_tarski) ).
fof(dt_k3_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k3_xboole_0) ).
fof(dt_k4_relat_1,axiom,
! [A] :
( relation(A)
=> relation(relation_inverse(A)) ),
file('theBenchmark.p',dt_k4_relat_1) ).
fof(dt_k4_tarski,axiom,
$true,
file('theBenchmark.p',dt_k4_tarski) ).
fof(dt_k4_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k4_xboole_0) ).
fof(dt_k5_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(relation_composition(A,B)) ),
file('theBenchmark.p',dt_k5_relat_1) ).
fof(dt_k5_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(union_of_subsets(A,B),powerset(A)) ),
file('theBenchmark.p',dt_k5_setfam_1) ).
fof(dt_k6_relat_1,axiom,
! [A] : relation(identity_relation(A)),
file('theBenchmark.p',dt_k6_relat_1) ).
fof(dt_k6_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(meet_of_subsets(A,B),powerset(A)) ),
file('theBenchmark.p',dt_k6_setfam_1) ).
fof(dt_k6_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> element(subset_difference(A,B,C),powerset(A)) ),
file('theBenchmark.p',dt_k6_subset_1) ).
fof(dt_k7_relat_1,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('theBenchmark.p',dt_k7_relat_1) ).
fof(dt_k7_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(complements_of_subsets(A,B),powerset(powerset(A))) ),
file('theBenchmark.p',dt_k7_setfam_1) ).
fof(dt_k8_relat_1,axiom,
! [A,B] :
( relation(B)
=> relation(relation_rng_restriction(A,B)) ),
file('theBenchmark.p',dt_k8_relat_1) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc10_relat_1,axiom,
! [A,B] :
( ( relation(B)
& empty(A) )
=> ( relation(relation_composition(B,A))
& empty(relation_composition(B,A)) ) ),
file('theBenchmark.p',fc10_relat_1) ).
fof(fc1_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(set_intersection2(A,B)) ),
file('theBenchmark.p',fc1_relat_1) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc1_zfmisc_1,axiom,
! [A,B] : ~ empty(ordered_pair(A,B)),
file('theBenchmark.p',fc1_zfmisc_1) ).
fof(fc2_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(set_union2(A,B)) ),
file('theBenchmark.p',fc2_relat_1) ).
fof(fc2_subset_1,axiom,
! [A] : ~ empty(singleton(A)),
file('theBenchmark.p',fc2_subset_1) ).
fof(fc2_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(A,B)) ),
file('theBenchmark.p',fc2_xboole_0) ).
fof(fc3_subset_1,axiom,
! [A,B] : ~ empty(unordered_pair(A,B)),
file('theBenchmark.p',fc3_subset_1) ).
fof(fc3_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(B,A)) ),
file('theBenchmark.p',fc3_xboole_0) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(fc4_subset_1,axiom,
! [A,B] :
( ( ~ empty(B)
& ~ empty(A) )
=> ~ empty(cartesian_product2(A,B)) ),
file('theBenchmark.p',fc4_subset_1) ).
fof(fc5_relat_1,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_dom(A)) ),
file('theBenchmark.p',fc5_relat_1) ).
fof(fc6_relat_1,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_rng(A)) ),
file('theBenchmark.p',fc6_relat_1) ).
fof(fc7_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_dom(A))
& empty(relation_dom(A)) ) ),
file('theBenchmark.p',fc7_relat_1) ).
fof(fc8_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_rng(A))
& empty(relation_rng(A)) ) ),
file('theBenchmark.p',fc8_relat_1) ).
fof(fc9_relat_1,axiom,
! [A,B] :
( ( relation(B)
& empty(A) )
=> ( relation(relation_composition(A,B))
& empty(relation_composition(A,B)) ) ),
file('theBenchmark.p',fc9_relat_1) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('theBenchmark.p',idempotence_k3_xboole_0) ).
fof(involutiveness_k3_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,subset_complement(A,B)) = B ),
file('theBenchmark.p',involutiveness_k3_subset_1) ).
fof(involutiveness_k4_relat_1,axiom,
! [A] :
( relation(A)
=> relation_inverse(relation_inverse(A)) = A ),
file('theBenchmark.p',involutiveness_k4_relat_1) ).
fof(involutiveness_k7_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> complements_of_subsets(A,complements_of_subsets(A,B)) = B ),
file('theBenchmark.p',involutiveness_k7_setfam_1) ).
fof(irreflexivity_r2_xboole_0,axiom,
! [A,B] : ~ proper_subset(A,A),
file('theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(l1_zfmisc_1,lemma,
! [A] : singleton(A) != empty_set,
file('theBenchmark.p',l1_zfmisc_1) ).
fof(l23_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('theBenchmark.p',l23_zfmisc_1) ).
fof(l25_zfmisc_1,lemma,
! [A,B] :
~ ( in(A,B)
& disjoint(singleton(A),B) ),
file('theBenchmark.p',l25_zfmisc_1) ).
fof(l28_zfmisc_1,lemma,
! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
file('theBenchmark.p',l28_zfmisc_1) ).
fof(l2_zfmisc_1,lemma,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('theBenchmark.p',l2_zfmisc_1) ).
fof(l32_xboole_1,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',l32_xboole_1) ).
fof(l3_subset_1,lemma,
! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( in(C,B)
=> in(C,A) ) ),
file('theBenchmark.p',l3_subset_1) ).
fof(l3_zfmisc_1,lemma,
! [A,B,C] :
( subset(A,B)
=> ( subset(A,set_difference(B,singleton(C)))
| in(C,A) ) ),
file('theBenchmark.p',l3_zfmisc_1) ).
fof(l4_zfmisc_1,lemma,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',l4_zfmisc_1) ).
fof(l50_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
file('theBenchmark.p',l50_zfmisc_1) ).
fof(l55_zfmisc_1,lemma,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('theBenchmark.p',l55_zfmisc_1) ).
fof(l71_subset_1,lemma,
! [A,B] :
( ! [C] :
( in(C,A)
=> in(C,B) )
=> element(A,powerset(B)) ),
file('theBenchmark.p',l71_subset_1) ).
fof(rc1_relat_1,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('theBenchmark.p',rc1_relat_1) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc1_subset_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_relat_1,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('theBenchmark.p',rc2_relat_1) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(redefinition_k5_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> union_of_subsets(A,B) = union(B) ),
file('theBenchmark.p',redefinition_k5_setfam_1) ).
fof(redefinition_k6_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> meet_of_subsets(A,B) = set_meet(B) ),
file('theBenchmark.p',redefinition_k6_setfam_1) ).
fof(redefinition_k6_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> subset_difference(A,B,C) = set_difference(B,C) ),
file('theBenchmark.p',redefinition_k6_subset_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t106_zfmisc_1,lemma,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('theBenchmark.p',t106_zfmisc_1) ).
fof(t10_zfmisc_1,lemma,
! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
file('theBenchmark.p',t10_zfmisc_1) ).
fof(t115_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_rng(relation_rng_restriction(B,C)))
<=> ( in(A,relation_rng(C))
& in(A,B) ) ) ),
file('theBenchmark.p',t115_relat_1) ).
fof(t116_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),A) ),
file('theBenchmark.p',t116_relat_1) ).
fof(t117_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng_restriction(A,B),B) ),
file('theBenchmark.p',t117_relat_1) ).
fof(t118_relat_1,conjecture,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ),
file('theBenchmark.p',t118_relat_1) ).
fof(t118_zfmisc_1,lemma,
! [A,B,C] :
( subset(A,B)
=> ( subset(cartesian_product2(C,A),cartesian_product2(C,B))
& subset(cartesian_product2(A,C),cartesian_product2(B,C)) ) ),
file('theBenchmark.p',t118_zfmisc_1) ).
fof(t119_zfmisc_1,lemma,
! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('theBenchmark.p',t119_zfmisc_1) ).
fof(t12_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
file('theBenchmark.p',t12_xboole_1) ).
fof(t136_zfmisc_1,lemma,
! [A] :
? [B] :
( ! [C] :
~ ( ~ in(C,B)
& ~ are_equipotent(C,B)
& subset(C,B) )
& ! [C] :
( in(C,B)
=> in(powerset(C),B) )
& ! [C,D] :
( ( subset(D,C)
& in(C,B) )
=> in(D,B) )
& in(A,B) ),
file('theBenchmark.p',t136_zfmisc_1) ).
fof(t17_xboole_1,lemma,
! [A,B] : subset(set_intersection2(A,B),A),
file('theBenchmark.p',t17_xboole_1) ).
fof(t19_xboole_1,lemma,
! [A,B,C] :
( ( subset(A,C)
& subset(A,B) )
=> subset(A,set_intersection2(B,C)) ),
file('theBenchmark.p',t19_xboole_1) ).
fof(t1_boole,axiom,
! [A] : set_union2(A,empty_set) = A,
file('theBenchmark.p',t1_boole) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t1_xboole_1,lemma,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('theBenchmark.p',t1_xboole_1) ).
fof(t1_zfmisc_1,lemma,
powerset(empty_set) = singleton(empty_set),
file('theBenchmark.p',t1_zfmisc_1) ).
fof(t20_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_rng(C))
& in(A,relation_dom(C)) ) ) ),
file('theBenchmark.p',t20_relat_1) ).
fof(t21_relat_1,lemma,
! [A] :
( relation(A)
=> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))) ),
file('theBenchmark.p',t21_relat_1) ).
fof(t25_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(A,B)
=> ( subset(relation_rng(A),relation_rng(B))
& subset(relation_dom(A),relation_dom(B)) ) ) ) ),
file('theBenchmark.p',t25_relat_1) ).
fof(t26_xboole_1,lemma,
! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ),
file('theBenchmark.p',t26_xboole_1) ).
fof(t28_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('theBenchmark.p',t28_xboole_1) ).
fof(t2_boole,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
file('theBenchmark.p',t2_boole) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('theBenchmark.p',t2_tarski) ).
fof(t2_xboole_1,lemma,
! [A] : subset(empty_set,A),
file('theBenchmark.p',t2_xboole_1) ).
fof(t30_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_field(C))
& in(A,relation_field(C)) ) ) ),
file('theBenchmark.p',t30_relat_1) ).
fof(t33_xboole_1,lemma,
! [A,B,C] :
( subset(A,B)
=> subset(set_difference(A,C),set_difference(B,C)) ),
file('theBenchmark.p',t33_xboole_1) ).
fof(t33_zfmisc_1,lemma,
! [A,B,C,D] :
( ordered_pair(A,B) = ordered_pair(C,D)
=> ( B = D
& A = C ) ),
file('theBenchmark.p',t33_zfmisc_1) ).
fof(t36_xboole_1,lemma,
! [A,B] : subset(set_difference(A,B),A),
file('theBenchmark.p',t36_xboole_1) ).
fof(t37_relat_1,lemma,
! [A] :
( relation(A)
=> ( relation_dom(A) = relation_rng(relation_inverse(A))
& relation_rng(A) = relation_dom(relation_inverse(A)) ) ),
file('theBenchmark.p',t37_relat_1) ).
fof(t37_xboole_1,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',t37_xboole_1) ).
fof(t37_zfmisc_1,lemma,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('theBenchmark.p',t37_zfmisc_1) ).
fof(t38_zfmisc_1,lemma,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(B,C)
& in(A,C) ) ),
file('theBenchmark.p',t38_zfmisc_1) ).
fof(t39_xboole_1,lemma,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
file('theBenchmark.p',t39_xboole_1) ).
fof(t39_zfmisc_1,lemma,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',t39_zfmisc_1) ).
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
file('theBenchmark.p',t3_boole) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t3_xboole_0,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t3_xboole_0) ).
fof(t3_xboole_1,lemma,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('theBenchmark.p',t3_xboole_1) ).
fof(t40_xboole_1,lemma,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
file('theBenchmark.p',t40_xboole_1) ).
fof(t43_subset_1,lemma,
! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,powerset(A))
=> ( disjoint(B,C)
<=> subset(B,subset_complement(A,C)) ) ) ),
file('theBenchmark.p',t43_subset_1) ).
fof(t44_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> subset(relation_dom(relation_composition(A,B)),relation_dom(A)) ) ),
file('theBenchmark.p',t44_relat_1) ).
fof(t45_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> subset(relation_rng(relation_composition(A,B)),relation_rng(B)) ) ),
file('theBenchmark.p',t45_relat_1) ).
fof(t45_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> B = set_union2(A,set_difference(B,A)) ),
file('theBenchmark.p',t45_xboole_1) ).
fof(t46_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(relation_rng(A),relation_dom(B))
=> relation_dom(relation_composition(A,B)) = relation_dom(A) ) ) ),
file('theBenchmark.p',t46_relat_1) ).
fof(t46_setfam_1,lemma,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ~ ( complements_of_subsets(A,B) = empty_set
& B != empty_set ) ),
file('theBenchmark.p',t46_setfam_1) ).
fof(t46_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('theBenchmark.p',t46_zfmisc_1) ).
fof(t47_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(relation_dom(A),relation_rng(B))
=> relation_rng(relation_composition(B,A)) = relation_rng(A) ) ) ),
file('theBenchmark.p',t47_relat_1) ).
fof(t47_setfam_1,lemma,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> subset_difference(A,cast_to_subset(A),union_of_subsets(A,B)) = meet_of_subsets(A,complements_of_subsets(A,B)) ) ),
file('theBenchmark.p',t47_setfam_1) ).
fof(t48_setfam_1,lemma,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> union_of_subsets(A,complements_of_subsets(A,B)) = subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B)) ) ),
file('theBenchmark.p',t48_setfam_1) ).
fof(t48_xboole_1,lemma,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
file('theBenchmark.p',t48_xboole_1) ).
fof(t4_boole,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
file('theBenchmark.p',t4_boole) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t4_xboole_0,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t4_xboole_0) ).
fof(t50_subset_1,lemma,
! [A] :
( A != empty_set
=> ! [B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,A)
=> ( ~ in(C,B)
=> in(C,subset_complement(A,B)) ) ) ) ),
file('theBenchmark.p',t50_subset_1) ).
fof(t54_subset_1,lemma,
! [A,B,C] :
( element(C,powerset(A))
=> ~ ( in(B,C)
& in(B,subset_complement(A,C)) ) ),
file('theBenchmark.p',t54_subset_1) ).
fof(t56_relat_1,lemma,
! [A] :
( relation(A)
=> ( ! [B,C] : ~ in(ordered_pair(B,C),A)
=> A = empty_set ) ),
file('theBenchmark.p',t56_relat_1) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t60_relat_1,lemma,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('theBenchmark.p',t60_relat_1) ).
fof(t60_xboole_1,lemma,
! [A,B] :
~ ( proper_subset(B,A)
& subset(A,B) ),
file('theBenchmark.p',t60_xboole_1) ).
fof(t63_xboole_1,lemma,
! [A,B,C] :
( ( disjoint(B,C)
& subset(A,B) )
=> disjoint(A,C) ),
file('theBenchmark.p',t63_xboole_1) ).
fof(t64_relat_1,lemma,
! [A] :
( relation(A)
=> ( ( relation_rng(A) = empty_set
| relation_dom(A) = empty_set )
=> A = empty_set ) ),
file('theBenchmark.p',t64_relat_1) ).
fof(t65_relat_1,lemma,
! [A] :
( relation(A)
=> ( relation_dom(A) = empty_set
<=> relation_rng(A) = empty_set ) ),
file('theBenchmark.p',t65_relat_1) ).
fof(t65_zfmisc_1,lemma,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('theBenchmark.p',t65_zfmisc_1) ).
fof(t69_enumset1,lemma,
! [A] : unordered_pair(A,A) = singleton(A),
file('theBenchmark.p',t69_enumset1) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t6_zfmisc_1,lemma,
! [A,B] :
( subset(singleton(A),singleton(B))
=> A = B ),
file('theBenchmark.p',t6_zfmisc_1) ).
fof(t71_relat_1,lemma,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
file('theBenchmark.p',t71_relat_1) ).
fof(t74_relat_1,lemma,
! [A,B,C,D] :
( relation(D)
=> ( in(ordered_pair(A,B),relation_composition(identity_relation(C),D))
<=> ( in(ordered_pair(A,B),D)
& in(A,C) ) ) ),
file('theBenchmark.p',t74_relat_1) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t7_xboole_1,lemma,
! [A,B] : subset(A,set_union2(A,B)),
file('theBenchmark.p',t7_xboole_1) ).
fof(t83_xboole_1,lemma,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('theBenchmark.p',t83_xboole_1) ).
fof(t86_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_dom(relation_dom_restriction(C,B)))
<=> ( in(A,relation_dom(C))
& in(A,B) ) ) ),
file('theBenchmark.p',t86_relat_1) ).
fof(t88_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_dom_restriction(B,A),B) ),
file('theBenchmark.p',t88_relat_1) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(t8_xboole_1,lemma,
! [A,B,C] :
( ( subset(C,B)
& subset(A,B) )
=> subset(set_union2(A,C),B) ),
file('theBenchmark.p',t8_xboole_1) ).
fof(t8_zfmisc_1,lemma,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ),
file('theBenchmark.p',t8_zfmisc_1) ).
fof(t90_relat_1,lemma,
! [A,B] :
( relation(B)
=> relation_dom(relation_dom_restriction(B,A)) = set_intersection2(relation_dom(B),A) ),
file('theBenchmark.p',t90_relat_1) ).
fof(t92_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
file('theBenchmark.p',t92_zfmisc_1) ).
fof(t94_relat_1,lemma,
! [A,B] :
( relation(B)
=> relation_dom_restriction(B,A) = relation_composition(identity_relation(A),B) ),
file('theBenchmark.p',t94_relat_1) ).
fof(t99_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B)) ),
file('theBenchmark.p',t99_relat_1) ).
fof(t99_zfmisc_1,lemma,
! [A] : union(powerset(A)) = A,
file('theBenchmark.p',t99_zfmisc_1) ).
fof(t9_tarski,axiom,
! [A] :
? [B] :
( ! [C] :
~ ( ~ in(C,B)
& ~ are_equipotent(C,B)
& subset(C,B) )
& ! [C] :
~ ( ! [D] :
~ ( ! [E] :
( subset(E,C)
=> in(E,D) )
& in(D,B) )
& in(C,B) )
& ! [C,D] :
( ( subset(D,C)
& in(C,B) )
=> in(D,B) )
& in(A,B) ),
file('theBenchmark.p',t9_tarski) ).
fof(t9_zfmisc_1,lemma,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> B = C ),
file('theBenchmark.p',t9_zfmisc_1) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(definitional_conversion,[status(esa)],[f_1_2]) ).
cnf(f_1_4,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ proper_subset(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(f_2_2,plain,
! [U_3,U_2] :
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_3,U_2] :
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_3_2,plain,
! [U_4] :
( relation(U_4)
| ~ empty(U_4) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_4] :
( relation(U_4)
| ~ empty(U_4) ),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
( relation(U_4)
| ~ empty(U_4) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_4_2,plain,
! [U_6,U_5] : unordered_pair(U_6,U_5) = unordered_pair(U_5,U_6),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_5,U_6] : unordered_pair(U_6,U_5) = unordered_pair(U_5,U_6),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
unordered_pair(U_6,U_5) = unordered_pair(U_5,U_6),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_5_2,plain,
! [U_8,U_7] : set_union2(U_8,U_7) = set_union2(U_7,U_8),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_7,U_8] : set_union2(U_8,U_7) = set_union2(U_7,U_8),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
set_union2(U_8,U_7) = set_union2(U_7,U_8),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_6_2,plain,
! [U_10,U_9] : set_intersection2(U_10,U_9) = set_intersection2(U_9,U_10),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_9,U_10] : set_intersection2(U_10,U_9) = set_intersection2(U_9,U_10),
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
set_intersection2(U_10,U_9) = set_intersection2(U_9,U_10),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [A,B] :
( ( ( B = identity_relation(A)
| ? [C,D] :
( ( ~ in(ordered_pair(C,D),B)
& C = D
& in(C,A) )
| ( ( C != D
| ~ in(C,A) )
& in(ordered_pair(C,D),B) ) ) )
& ( ! [C,D] :
( ( in(ordered_pair(C,D),B)
| C != D
| ~ in(C,A) )
& ( ( C = D
& in(C,A) )
| ~ in(ordered_pair(C,D),B) ) )
| B != identity_relation(A) ) )
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[d10_relat_1]) ).
fof(f_7_2,plain,
! [U_16,U_15] :
( ( ( U_15 = identity_relation(U_16)
| ? [U_14,U_13] :
( ( ~ in(ordered_pair(U_14,U_13),U_15)
& U_14 = U_13
& in(U_14,U_16) )
| ( ( U_14 != U_13
| ~ in(U_14,U_16) )
& in(ordered_pair(U_14,U_13),U_15) ) ) )
& ( ! [U_12,U_11] :
( ( in(ordered_pair(U_12,U_11),U_15)
| U_12 != U_11
| ~ in(U_12,U_16) )
& ( ( U_12 = U_11
& in(U_12,U_16) )
| ~ in(ordered_pair(U_12,U_11),U_15) ) )
| U_15 != identity_relation(U_16) ) )
| ~ relation(U_15) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_16,U_15] :
( ( ( U_15 = identity_relation(U_16)
| ? [U_24,U_22] :
( ~ in(ordered_pair(U_24,U_22),U_15)
& U_24 = U_22
& in(U_24,U_16) )
| ? [U_23,U_21] :
( ( U_23 != U_21
| ~ in(U_23,U_16) )
& in(ordered_pair(U_23,U_21),U_15) ) )
& ( ( ! [U_20,U_18] :
( in(ordered_pair(U_20,U_18),U_15)
| U_20 != U_18
| ~ in(U_20,U_16) )
& ! [U_19,U_17] :
( ( U_19 = U_17
& in(U_19,U_16) )
| ~ in(ordered_pair(U_19,U_17),U_15) ) )
| U_15 != identity_relation(U_16) ) )
| ~ relation(U_15) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
! [U_16,U_15] :
( ( ( U_15 = identity_relation(U_16)
| ? [U_24,U_22] :
( ~ in(ordered_pair(U_24,U_22),U_15)
& U_24 = U_22
& in(U_24,U_16) )
| ? [U_21] :
( ( sK1(U_16,U_15) != U_21
| ~ in(sK1(U_16,U_15),U_16) )
& in(ordered_pair(sK1(U_16,U_15),U_21),U_15) ) )
& ( ( ! [U_20,U_18] :
( in(ordered_pair(U_20,U_18),U_15)
| U_20 != U_18
| ~ in(U_20,U_16) )
& ! [U_19,U_17] :
( ( U_19 = U_17
& in(U_19,U_16) )
| ~ in(ordered_pair(U_19,U_17),U_15) ) )
| U_15 != identity_relation(U_16) ) )
| ~ relation(U_15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_23,sK1(U_16,U_15))],[f_7_3]) ).
fof(f_7_5,plain,
! [U_16,U_15] :
( ( ( U_15 = identity_relation(U_16)
| ? [U_24,U_22] :
( ~ in(ordered_pair(U_24,U_22),U_15)
& U_24 = U_22
& in(U_24,U_16) )
| ( ( sK1(U_16,U_15) != sK2(U_16,U_15)
| ~ in(sK1(U_16,U_15),U_16) )
& in(ordered_pair(sK1(U_16,U_15),sK2(U_16,U_15)),U_15) ) )
& ( ( ! [U_20,U_18] :
( in(ordered_pair(U_20,U_18),U_15)
| U_20 != U_18
| ~ in(U_20,U_16) )
& ! [U_19,U_17] :
( ( U_19 = U_17
& in(U_19,U_16) )
| ~ in(ordered_pair(U_19,U_17),U_15) ) )
| U_15 != identity_relation(U_16) ) )
| ~ relation(U_15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_21,sK2(U_16,U_15))],[f_7_4]) ).
fof(f_7_6,plain,
! [U_16,U_15] :
( ( ( U_15 = identity_relation(U_16)
| ? [U_22] :
( ~ in(ordered_pair(sK3(U_16,U_15),U_22),U_15)
& sK3(U_16,U_15) = U_22
& in(sK3(U_16,U_15),U_16) )
| ( ( sK1(U_16,U_15) != sK2(U_16,U_15)
| ~ in(sK1(U_16,U_15),U_16) )
& in(ordered_pair(sK1(U_16,U_15),sK2(U_16,U_15)),U_15) ) )
& ( ( ! [U_20,U_18] :
( in(ordered_pair(U_20,U_18),U_15)
| U_20 != U_18
| ~ in(U_20,U_16) )
& ! [U_19,U_17] :
( ( U_19 = U_17
& in(U_19,U_16) )
| ~ in(ordered_pair(U_19,U_17),U_15) ) )
| U_15 != identity_relation(U_16) ) )
| ~ relation(U_15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_24,sK3(U_16,U_15))],[f_7_5]) ).
fof(f_7_7,plain,
! [U_16,U_15] :
( ( ( U_15 = identity_relation(U_16)
| ( ~ in(ordered_pair(sK3(U_16,U_15),sK4(U_16,U_15)),U_15)
& sK3(U_16,U_15) = sK4(U_16,U_15)
& in(sK3(U_16,U_15),U_16) )
| ( ( sK1(U_16,U_15) != sK2(U_16,U_15)
| ~ in(sK1(U_16,U_15),U_16) )
& in(ordered_pair(sK1(U_16,U_15),sK2(U_16,U_15)),U_15) ) )
& ( ( ! [U_20,U_18] :
( in(ordered_pair(U_20,U_18),U_15)
| U_20 != U_18
| ~ in(U_20,U_16) )
& ! [U_19,U_17] :
( ( U_19 = U_17
& in(U_19,U_16) )
| ~ in(ordered_pair(U_19,U_17),U_15) ) )
| U_15 != identity_relation(U_16) ) )
| ~ relation(U_15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_22,sK4(U_16,U_15))],[f_7_6]) ).
fof(f_7_8,plain,
( ! [U_15,U_16] :
( ~ in(ordered_pair(sK3(U_16,U_15),sK4(U_16,U_15)),U_15)
| ~ sP3(U_15,U_16) )
& ! [U_15,U_16] :
( sK3(U_16,U_15) = sK4(U_16,U_15)
| ~ sP3(U_15,U_16) )
& ! [U_15,U_16] :
( in(sK3(U_16,U_15),U_16)
| ~ sP3(U_15,U_16) )
& ! [U_15,U_16] :
( sK1(U_16,U_15) != sK2(U_16,U_15)
| ~ in(sK1(U_16,U_15),U_16)
| ~ sP2(U_15,U_16) )
& ! [U_15,U_16] :
( in(ordered_pair(sK1(U_16,U_15),sK2(U_16,U_15)),U_15)
| ~ sP2(U_15,U_16) )
& ! [U_19,U_16,U_17] :
( U_19 = U_17
| ~ sP0(U_19,U_16,U_17) )
& ! [U_19,U_16,U_17] :
( in(U_19,U_16)
| ~ sP0(U_19,U_16,U_17) )
& ! [U_19,U_15,U_16,U_17,U_18,U_20] :
( in(ordered_pair(U_20,U_18),U_15)
| U_20 != U_18
| ~ in(U_20,U_16)
| ~ sP1(U_19,U_15,U_16,U_17,U_18,U_20) )
& ! [U_19,U_15,U_16,U_17,U_18,U_20] :
( sP0(U_19,U_16,U_17)
| ~ in(ordered_pair(U_19,U_17),U_15)
| ~ sP1(U_19,U_15,U_16,U_17,U_18,U_20) )
& ! [U_19,U_15,U_16,U_17,U_18,U_20] :
( U_15 = identity_relation(U_16)
| sP3(U_15,U_16)
| sP2(U_15,U_16)
| ~ sP4(U_19,U_15,U_16,U_17,U_18,U_20) )
& ! [U_19,U_15,U_16,U_17,U_18,U_20] :
( sP1(U_19,U_15,U_16,U_17,U_18,U_20)
| U_15 != identity_relation(U_16)
| ~ sP4(U_19,U_15,U_16,U_17,U_18,U_20) )
& ! [U_19,U_15,U_16,U_17,U_18,U_20] :
( sP4(U_19,U_15,U_16,U_17,U_18,U_20)
| ~ relation(U_15) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1,sP2,sP3,sP4])],[f_7_7]) ).
cnf(f_7_9,plain,
( sP4(U_19,U_15,U_16,U_17,U_18,U_20)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_10,plain,
( sP1(U_19,U_15,U_16,U_17,U_18,U_20)
| U_15 != identity_relation(U_16)
| ~ sP4(U_19,U_15,U_16,U_17,U_18,U_20) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_11,plain,
( U_15 = identity_relation(U_16)
| sP3(U_15,U_16)
| sP2(U_15,U_16)
| ~ sP4(U_19,U_15,U_16,U_17,U_18,U_20) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_12,plain,
( sP0(U_19,U_16,U_17)
| ~ in(ordered_pair(U_19,U_17),U_15)
| ~ sP1(U_19,U_15,U_16,U_17,U_18,U_20) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_13,plain,
( in(ordered_pair(U_20,U_18),U_15)
| U_20 != U_18
| ~ in(U_20,U_16)
| ~ sP1(U_19,U_15,U_16,U_17,U_18,U_20) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_14,plain,
( in(U_19,U_16)
| ~ sP0(U_19,U_16,U_17) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_15,plain,
( U_19 = U_17
| ~ sP0(U_19,U_16,U_17) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_16,plain,
( in(ordered_pair(sK1(U_16,U_15),sK2(U_16,U_15)),U_15)
| ~ sP2(U_15,U_16) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_17,plain,
( sK1(U_16,U_15) != sK2(U_16,U_15)
| ~ in(sK1(U_16,U_15),U_16)
| ~ sP2(U_15,U_16) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_18,plain,
( in(sK3(U_16,U_15),U_16)
| ~ sP3(U_15,U_16) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_19,plain,
( sK3(U_16,U_15) = sK4(U_16,U_15)
| ~ sP3(U_15,U_16) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_20,plain,
( ~ in(ordered_pair(sK3(U_16,U_15),sK4(U_16,U_15)),U_15)
| ~ sP3(U_15,U_16) ),
inference(clausify,[status(thm)],[f_7_8]) ).
fof(f_8_1,plain,
! [A,B] :
( ( A = B
| ~ subset(B,A)
| ~ subset(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(fof_nnf,[status(thm)],[d10_xboole_0]) ).
fof(f_8_2,plain,
! [U_26,U_25] :
( ( U_26 = U_25
| ~ subset(U_25,U_26)
| ~ subset(U_26,U_25) )
& ( ( subset(U_25,U_26)
& subset(U_26,U_25) )
| U_26 != U_25 ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_30,U_28] :
( U_30 = U_28
| ~ subset(U_28,U_30)
| ~ subset(U_30,U_28) )
& ! [U_29,U_27] :
( ( subset(U_27,U_29)
& subset(U_29,U_27) )
| U_29 != U_27 ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
( ! [U_29,U_27] :
( subset(U_27,U_29)
| ~ sP5(U_29,U_27) )
& ! [U_29,U_27] :
( subset(U_29,U_27)
| ~ sP5(U_29,U_27) )
& ! [U_30,U_28] :
( U_30 = U_28
| ~ subset(U_28,U_30)
| ~ subset(U_30,U_28) )
& ! [U_29,U_27] :
( sP5(U_29,U_27)
| U_29 != U_27 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_8_3]) ).
cnf(f_8_5,plain,
( sP5(U_29,U_27)
| U_29 != U_27 ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_6,plain,
( U_30 = U_28
| ~ subset(U_28,U_30)
| ~ subset(U_30,U_28) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_7,plain,
( subset(U_29,U_27)
| ~ sP5(U_29,U_27) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_8,plain,
( subset(U_27,U_29)
| ~ sP5(U_29,U_27) ),
inference(clausify,[status(thm)],[f_8_4]) ).
fof(f_9_1,plain,
! [A] :
( ! [B,C] :
( ( ( C = relation_dom_restriction(A,B)
| ? [D,E] :
( ( ~ in(ordered_pair(D,E),C)
& in(ordered_pair(D,E),A)
& in(D,B) )
| ( ( ~ in(ordered_pair(D,E),A)
| ~ in(D,B) )
& in(ordered_pair(D,E),C) ) ) )
& ( ! [D,E] :
( ( in(ordered_pair(D,E),C)
| ~ in(ordered_pair(D,E),A)
| ~ in(D,B) )
& ( ( in(ordered_pair(D,E),A)
& in(D,B) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_dom_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d11_relat_1]) ).
fof(f_9_2,plain,
! [U_37] :
( ! [U_36,U_35] :
( ( ( U_35 = relation_dom_restriction(U_37,U_36)
| ? [U_34,U_33] :
( ( ~ in(ordered_pair(U_34,U_33),U_35)
& in(ordered_pair(U_34,U_33),U_37)
& in(U_34,U_36) )
| ( ( ~ in(ordered_pair(U_34,U_33),U_37)
| ~ in(U_34,U_36) )
& in(ordered_pair(U_34,U_33),U_35) ) ) )
& ( ! [U_32,U_31] :
( ( in(ordered_pair(U_32,U_31),U_35)
| ~ in(ordered_pair(U_32,U_31),U_37)
| ~ in(U_32,U_36) )
& ( ( in(ordered_pair(U_32,U_31),U_37)
& in(U_32,U_36) )
| ~ in(ordered_pair(U_32,U_31),U_35) ) )
| U_35 != relation_dom_restriction(U_37,U_36) ) )
| ~ relation(U_35) )
| ~ relation(U_37) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_37] :
( ! [U_36,U_35] :
( ( ( U_35 = relation_dom_restriction(U_37,U_36)
| ? [U_45,U_43] :
( ~ in(ordered_pair(U_45,U_43),U_35)
& in(ordered_pair(U_45,U_43),U_37)
& in(U_45,U_36) )
| ? [U_44,U_42] :
( ( ~ in(ordered_pair(U_44,U_42),U_37)
| ~ in(U_44,U_36) )
& in(ordered_pair(U_44,U_42),U_35) ) )
& ( ( ! [U_41,U_39] :
( in(ordered_pair(U_41,U_39),U_35)
| ~ in(ordered_pair(U_41,U_39),U_37)
| ~ in(U_41,U_36) )
& ! [U_40,U_38] :
( ( in(ordered_pair(U_40,U_38),U_37)
& in(U_40,U_36) )
| ~ in(ordered_pair(U_40,U_38),U_35) ) )
| U_35 != relation_dom_restriction(U_37,U_36) ) )
| ~ relation(U_35) )
| ~ relation(U_37) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
fof(f_9_4,plain,
! [U_37] :
( ! [U_36,U_35] :
( ( ( U_35 = relation_dom_restriction(U_37,U_36)
| ? [U_45,U_43] :
( ~ in(ordered_pair(U_45,U_43),U_35)
& in(ordered_pair(U_45,U_43),U_37)
& in(U_45,U_36) )
| ? [U_42] :
( ( ~ in(ordered_pair(sK5(U_37,U_36,U_35),U_42),U_37)
| ~ in(sK5(U_37,U_36,U_35),U_36) )
& in(ordered_pair(sK5(U_37,U_36,U_35),U_42),U_35) ) )
& ( ( ! [U_41,U_39] :
( in(ordered_pair(U_41,U_39),U_35)
| ~ in(ordered_pair(U_41,U_39),U_37)
| ~ in(U_41,U_36) )
& ! [U_40,U_38] :
( ( in(ordered_pair(U_40,U_38),U_37)
& in(U_40,U_36) )
| ~ in(ordered_pair(U_40,U_38),U_35) ) )
| U_35 != relation_dom_restriction(U_37,U_36) ) )
| ~ relation(U_35) )
| ~ relation(U_37) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_44,sK5(U_37,U_36,U_35))],[f_9_3]) ).
fof(f_9_5,plain,
! [U_37] :
( ! [U_36,U_35] :
( ( ( U_35 = relation_dom_restriction(U_37,U_36)
| ? [U_45,U_43] :
( ~ in(ordered_pair(U_45,U_43),U_35)
& in(ordered_pair(U_45,U_43),U_37)
& in(U_45,U_36) )
| ( ( ~ in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_37)
| ~ in(sK5(U_37,U_36,U_35),U_36) )
& in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_35) ) )
& ( ( ! [U_41,U_39] :
( in(ordered_pair(U_41,U_39),U_35)
| ~ in(ordered_pair(U_41,U_39),U_37)
| ~ in(U_41,U_36) )
& ! [U_40,U_38] :
( ( in(ordered_pair(U_40,U_38),U_37)
& in(U_40,U_36) )
| ~ in(ordered_pair(U_40,U_38),U_35) ) )
| U_35 != relation_dom_restriction(U_37,U_36) ) )
| ~ relation(U_35) )
| ~ relation(U_37) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_42,sK6(U_37,U_36,U_35))],[f_9_4]) ).
fof(f_9_6,plain,
! [U_37] :
( ! [U_36,U_35] :
( ( ( U_35 = relation_dom_restriction(U_37,U_36)
| ? [U_43] :
( ~ in(ordered_pair(sK7(U_37,U_36,U_35),U_43),U_35)
& in(ordered_pair(sK7(U_37,U_36,U_35),U_43),U_37)
& in(sK7(U_37,U_36,U_35),U_36) )
| ( ( ~ in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_37)
| ~ in(sK5(U_37,U_36,U_35),U_36) )
& in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_35) ) )
& ( ( ! [U_41,U_39] :
( in(ordered_pair(U_41,U_39),U_35)
| ~ in(ordered_pair(U_41,U_39),U_37)
| ~ in(U_41,U_36) )
& ! [U_40,U_38] :
( ( in(ordered_pair(U_40,U_38),U_37)
& in(U_40,U_36) )
| ~ in(ordered_pair(U_40,U_38),U_35) ) )
| U_35 != relation_dom_restriction(U_37,U_36) ) )
| ~ relation(U_35) )
| ~ relation(U_37) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_45,sK7(U_37,U_36,U_35))],[f_9_5]) ).
fof(f_9_7,plain,
! [U_37] :
( ! [U_36,U_35] :
( ( ( U_35 = relation_dom_restriction(U_37,U_36)
| ( ~ in(ordered_pair(sK7(U_37,U_36,U_35),sK8(U_37,U_36,U_35)),U_35)
& in(ordered_pair(sK7(U_37,U_36,U_35),sK8(U_37,U_36,U_35)),U_37)
& in(sK7(U_37,U_36,U_35),U_36) )
| ( ( ~ in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_37)
| ~ in(sK5(U_37,U_36,U_35),U_36) )
& in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_35) ) )
& ( ( ! [U_41,U_39] :
( in(ordered_pair(U_41,U_39),U_35)
| ~ in(ordered_pair(U_41,U_39),U_37)
| ~ in(U_41,U_36) )
& ! [U_40,U_38] :
( ( in(ordered_pair(U_40,U_38),U_37)
& in(U_40,U_36) )
| ~ in(ordered_pair(U_40,U_38),U_35) ) )
| U_35 != relation_dom_restriction(U_37,U_36) ) )
| ~ relation(U_35) )
| ~ relation(U_37) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_43,sK8(U_37,U_36,U_35))],[f_9_6]) ).
fof(f_9_8,plain,
( ! [U_35,U_36,U_37] :
( ~ in(ordered_pair(sK7(U_37,U_36,U_35),sK8(U_37,U_36,U_35)),U_35)
| ~ sP9(U_35,U_36,U_37) )
& ! [U_35,U_36,U_37] :
( in(ordered_pair(sK7(U_37,U_36,U_35),sK8(U_37,U_36,U_35)),U_37)
| ~ sP9(U_35,U_36,U_37) )
& ! [U_35,U_36,U_37] :
( in(sK7(U_37,U_36,U_35),U_36)
| ~ sP9(U_35,U_36,U_37) )
& ! [U_35,U_36,U_37] :
( ~ in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_37)
| ~ in(sK5(U_37,U_36,U_35),U_36)
| ~ sP8(U_35,U_36,U_37) )
& ! [U_35,U_36,U_37] :
( in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_35)
| ~ sP8(U_35,U_36,U_37) )
& ! [U_36,U_37,U_40,U_38] :
( in(ordered_pair(U_40,U_38),U_37)
| ~ sP6(U_36,U_37,U_40,U_38) )
& ! [U_36,U_37,U_40,U_38] :
( in(U_40,U_36)
| ~ sP6(U_36,U_37,U_40,U_38) )
& ! [U_35,U_36,U_37,U_40,U_41,U_38,U_39] :
( in(ordered_pair(U_41,U_39),U_35)
| ~ in(ordered_pair(U_41,U_39),U_37)
| ~ in(U_41,U_36)
| ~ sP7(U_35,U_36,U_37,U_40,U_41,U_38,U_39) )
& ! [U_35,U_36,U_37,U_40,U_41,U_38,U_39] :
( sP6(U_36,U_37,U_40,U_38)
| ~ in(ordered_pair(U_40,U_38),U_35)
| ~ sP7(U_35,U_36,U_37,U_40,U_41,U_38,U_39) )
& ! [U_35,U_36,U_37,U_40,U_41,U_38,U_39] :
( U_35 = relation_dom_restriction(U_37,U_36)
| sP9(U_35,U_36,U_37)
| sP8(U_35,U_36,U_37)
| ~ sP10(U_35,U_36,U_37,U_40,U_41,U_38,U_39) )
& ! [U_35,U_36,U_37,U_40,U_41,U_38,U_39] :
( sP7(U_35,U_36,U_37,U_40,U_41,U_38,U_39)
| U_35 != relation_dom_restriction(U_37,U_36)
| ~ sP10(U_35,U_36,U_37,U_40,U_41,U_38,U_39) )
& ! [U_35,U_36,U_37,U_40,U_41,U_38,U_39] :
( sP10(U_35,U_36,U_37,U_40,U_41,U_38,U_39)
| ~ relation(U_35)
| ~ relation(U_37) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6,sP7,sP8,sP9,sP10])],[f_9_7]) ).
cnf(f_9_9,plain,
( sP10(U_35,U_36,U_37,U_40,U_41,U_38,U_39)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_10,plain,
( sP7(U_35,U_36,U_37,U_40,U_41,U_38,U_39)
| U_35 != relation_dom_restriction(U_37,U_36)
| ~ sP10(U_35,U_36,U_37,U_40,U_41,U_38,U_39) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_11,plain,
( U_35 = relation_dom_restriction(U_37,U_36)
| sP9(U_35,U_36,U_37)
| sP8(U_35,U_36,U_37)
| ~ sP10(U_35,U_36,U_37,U_40,U_41,U_38,U_39) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_12,plain,
( sP6(U_36,U_37,U_40,U_38)
| ~ in(ordered_pair(U_40,U_38),U_35)
| ~ sP7(U_35,U_36,U_37,U_40,U_41,U_38,U_39) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_13,plain,
( in(ordered_pair(U_41,U_39),U_35)
| ~ in(ordered_pair(U_41,U_39),U_37)
| ~ in(U_41,U_36)
| ~ sP7(U_35,U_36,U_37,U_40,U_41,U_38,U_39) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_14,plain,
( in(U_40,U_36)
| ~ sP6(U_36,U_37,U_40,U_38) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_15,plain,
( in(ordered_pair(U_40,U_38),U_37)
| ~ sP6(U_36,U_37,U_40,U_38) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_16,plain,
( in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_35)
| ~ sP8(U_35,U_36,U_37) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_17,plain,
( ~ in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_37)
| ~ in(sK5(U_37,U_36,U_35),U_36)
| ~ sP8(U_35,U_36,U_37) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_18,plain,
( in(sK7(U_37,U_36,U_35),U_36)
| ~ sP9(U_35,U_36,U_37) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_19,plain,
( in(ordered_pair(sK7(U_37,U_36,U_35),sK8(U_37,U_36,U_35)),U_37)
| ~ sP9(U_35,U_36,U_37) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_20,plain,
( ~ in(ordered_pair(sK7(U_37,U_36,U_35),sK8(U_37,U_36,U_35)),U_35)
| ~ sP9(U_35,U_36,U_37) ),
inference(clausify,[status(thm)],[f_9_8]) ).
fof(f_10_1,plain,
! [A,B] :
( ! [C] :
( ( ( C = relation_rng_restriction(A,B)
| ? [D,E] :
( ( ~ in(ordered_pair(D,E),C)
& in(ordered_pair(D,E),B)
& in(E,A) )
| ( ( ~ in(ordered_pair(D,E),B)
| ~ in(E,A) )
& in(ordered_pair(D,E),C) ) ) )
& ( ! [D,E] :
( ( in(ordered_pair(D,E),C)
| ~ in(ordered_pair(D,E),B)
| ~ in(E,A) )
& ( ( in(ordered_pair(D,E),B)
& in(E,A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_rng_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[d12_relat_1]) ).
fof(f_10_2,plain,
! [U_52,U_51] :
( ! [U_50] :
( ( ( U_50 = relation_rng_restriction(U_52,U_51)
| ? [U_49,U_48] :
( ( ~ in(ordered_pair(U_49,U_48),U_50)
& in(ordered_pair(U_49,U_48),U_51)
& in(U_48,U_52) )
| ( ( ~ in(ordered_pair(U_49,U_48),U_51)
| ~ in(U_48,U_52) )
& in(ordered_pair(U_49,U_48),U_50) ) ) )
& ( ! [U_47,U_46] :
( ( in(ordered_pair(U_47,U_46),U_50)
| ~ in(ordered_pair(U_47,U_46),U_51)
| ~ in(U_46,U_52) )
& ( ( in(ordered_pair(U_47,U_46),U_51)
& in(U_46,U_52) )
| ~ in(ordered_pair(U_47,U_46),U_50) ) )
| U_50 != relation_rng_restriction(U_52,U_51) ) )
| ~ relation(U_50) )
| ~ relation(U_51) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_52,U_51] :
( ! [U_50] :
( ( ( U_50 = relation_rng_restriction(U_52,U_51)
| ? [U_60,U_58] :
( ~ in(ordered_pair(U_60,U_58),U_50)
& in(ordered_pair(U_60,U_58),U_51)
& in(U_58,U_52) )
| ? [U_59,U_57] :
( ( ~ in(ordered_pair(U_59,U_57),U_51)
| ~ in(U_57,U_52) )
& in(ordered_pair(U_59,U_57),U_50) ) )
& ( ( ! [U_56,U_54] :
( in(ordered_pair(U_56,U_54),U_50)
| ~ in(ordered_pair(U_56,U_54),U_51)
| ~ in(U_54,U_52) )
& ! [U_55,U_53] :
( ( in(ordered_pair(U_55,U_53),U_51)
& in(U_53,U_52) )
| ~ in(ordered_pair(U_55,U_53),U_50) ) )
| U_50 != relation_rng_restriction(U_52,U_51) ) )
| ~ relation(U_50) )
| ~ relation(U_51) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
fof(f_10_4,plain,
! [U_52,U_51] :
( ! [U_50] :
( ( ( U_50 = relation_rng_restriction(U_52,U_51)
| ? [U_60,U_58] :
( ~ in(ordered_pair(U_60,U_58),U_50)
& in(ordered_pair(U_60,U_58),U_51)
& in(U_58,U_52) )
| ? [U_57] :
( ( ~ in(ordered_pair(sK9(U_52,U_51,U_50),U_57),U_51)
| ~ in(U_57,U_52) )
& in(ordered_pair(sK9(U_52,U_51,U_50),U_57),U_50) ) )
& ( ( ! [U_56,U_54] :
( in(ordered_pair(U_56,U_54),U_50)
| ~ in(ordered_pair(U_56,U_54),U_51)
| ~ in(U_54,U_52) )
& ! [U_55,U_53] :
( ( in(ordered_pair(U_55,U_53),U_51)
& in(U_53,U_52) )
| ~ in(ordered_pair(U_55,U_53),U_50) ) )
| U_50 != relation_rng_restriction(U_52,U_51) ) )
| ~ relation(U_50) )
| ~ relation(U_51) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_59,sK9(U_52,U_51,U_50))],[f_10_3]) ).
fof(f_10_5,plain,
! [U_52,U_51] :
( ! [U_50] :
( ( ( U_50 = relation_rng_restriction(U_52,U_51)
| ? [U_60,U_58] :
( ~ in(ordered_pair(U_60,U_58),U_50)
& in(ordered_pair(U_60,U_58),U_51)
& in(U_58,U_52) )
| ( ( ~ in(ordered_pair(sK9(U_52,U_51,U_50),sK10(U_52,U_51,U_50)),U_51)
| ~ in(sK10(U_52,U_51,U_50),U_52) )
& in(ordered_pair(sK9(U_52,U_51,U_50),sK10(U_52,U_51,U_50)),U_50) ) )
& ( ( ! [U_56,U_54] :
( in(ordered_pair(U_56,U_54),U_50)
| ~ in(ordered_pair(U_56,U_54),U_51)
| ~ in(U_54,U_52) )
& ! [U_55,U_53] :
( ( in(ordered_pair(U_55,U_53),U_51)
& in(U_53,U_52) )
| ~ in(ordered_pair(U_55,U_53),U_50) ) )
| U_50 != relation_rng_restriction(U_52,U_51) ) )
| ~ relation(U_50) )
| ~ relation(U_51) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_57,sK10(U_52,U_51,U_50))],[f_10_4]) ).
fof(f_10_6,plain,
! [U_52,U_51] :
( ! [U_50] :
( ( ( U_50 = relation_rng_restriction(U_52,U_51)
| ? [U_58] :
( ~ in(ordered_pair(sK11(U_52,U_51,U_50),U_58),U_50)
& in(ordered_pair(sK11(U_52,U_51,U_50),U_58),U_51)
& in(U_58,U_52) )
| ( ( ~ in(ordered_pair(sK9(U_52,U_51,U_50),sK10(U_52,U_51,U_50)),U_51)
| ~ in(sK10(U_52,U_51,U_50),U_52) )
& in(ordered_pair(sK9(U_52,U_51,U_50),sK10(U_52,U_51,U_50)),U_50) ) )
& ( ( ! [U_56,U_54] :
( in(ordered_pair(U_56,U_54),U_50)
| ~ in(ordered_pair(U_56,U_54),U_51)
| ~ in(U_54,U_52) )
& ! [U_55,U_53] :
( ( in(ordered_pair(U_55,U_53),U_51)
& in(U_53,U_52) )
| ~ in(ordered_pair(U_55,U_53),U_50) ) )
| U_50 != relation_rng_restriction(U_52,U_51) ) )
| ~ relation(U_50) )
| ~ relation(U_51) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_60,sK11(U_52,U_51,U_50))],[f_10_5]) ).
fof(f_10_7,plain,
! [U_52,U_51] :
( ! [U_50] :
( ( ( U_50 = relation_rng_restriction(U_52,U_51)
| ( ~ in(ordered_pair(sK11(U_52,U_51,U_50),sK12(U_52,U_51,U_50)),U_50)
& in(ordered_pair(sK11(U_52,U_51,U_50),sK12(U_52,U_51,U_50)),U_51)
& in(sK12(U_52,U_51,U_50),U_52) )
| ( ( ~ in(ordered_pair(sK9(U_52,U_51,U_50),sK10(U_52,U_51,U_50)),U_51)
| ~ in(sK10(U_52,U_51,U_50),U_52) )
& in(ordered_pair(sK9(U_52,U_51,U_50),sK10(U_52,U_51,U_50)),U_50) ) )
& ( ( ! [U_56,U_54] :
( in(ordered_pair(U_56,U_54),U_50)
| ~ in(ordered_pair(U_56,U_54),U_51)
| ~ in(U_54,U_52) )
& ! [U_55,U_53] :
( ( in(ordered_pair(U_55,U_53),U_51)
& in(U_53,U_52) )
| ~ in(ordered_pair(U_55,U_53),U_50) ) )
| U_50 != relation_rng_restriction(U_52,U_51) ) )
| ~ relation(U_50) )
| ~ relation(U_51) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_58,sK12(U_52,U_51,U_50))],[f_10_6]) ).
fof(f_10_8,plain,
( ! [U_52,U_51,U_50] :
( ~ in(ordered_pair(sK11(U_52,U_51,U_50),sK12(U_52,U_51,U_50)),U_50)
| ~ sP14(U_52,U_51,U_50) )
& ! [U_52,U_51,U_50] :
( in(ordered_pair(sK11(U_52,U_51,U_50),sK12(U_52,U_51,U_50)),U_51)
| ~ sP14(U_52,U_51,U_50) )
& ! [U_52,U_51,U_50] :
( in(sK12(U_52,U_51,U_50),U_52)
| ~ sP14(U_52,U_51,U_50) )
& ! [U_52,U_51,U_50] :
( ~ in(ordered_pair(sK9(U_52,U_51,U_50),sK10(U_52,U_51,U_50)),U_51)
| ~ in(sK10(U_52,U_51,U_50),U_52)
| ~ sP13(U_52,U_51,U_50) )
& ! [U_52,U_51,U_50] :
( in(ordered_pair(sK9(U_52,U_51,U_50),sK10(U_52,U_51,U_50)),U_50)
| ~ sP13(U_52,U_51,U_50) )
& ! [U_52,U_51,U_55,U_53] :
( in(ordered_pair(U_55,U_53),U_51)
| ~ sP11(U_52,U_51,U_55,U_53) )
& ! [U_52,U_51,U_55,U_53] :
( in(U_53,U_52)
| ~ sP11(U_52,U_51,U_55,U_53) )
& ! [U_52,U_51,U_50,U_55,U_53,U_54,U_56] :
( in(ordered_pair(U_56,U_54),U_50)
| ~ in(ordered_pair(U_56,U_54),U_51)
| ~ in(U_54,U_52)
| ~ sP12(U_52,U_51,U_50,U_55,U_53,U_54,U_56) )
& ! [U_52,U_51,U_50,U_55,U_53,U_54,U_56] :
( sP11(U_52,U_51,U_55,U_53)
| ~ in(ordered_pair(U_55,U_53),U_50)
| ~ sP12(U_52,U_51,U_50,U_55,U_53,U_54,U_56) )
& ! [U_52,U_51,U_50,U_55,U_53,U_54,U_56] :
( U_50 = relation_rng_restriction(U_52,U_51)
| sP14(U_52,U_51,U_50)
| sP13(U_52,U_51,U_50)
| ~ sP15(U_52,U_51,U_50,U_55,U_53,U_54,U_56) )
& ! [U_52,U_51,U_50,U_55,U_53,U_54,U_56] :
( sP12(U_52,U_51,U_50,U_55,U_53,U_54,U_56)
| U_50 != relation_rng_restriction(U_52,U_51)
| ~ sP15(U_52,U_51,U_50,U_55,U_53,U_54,U_56) )
& ! [U_52,U_51,U_50,U_55,U_53,U_54,U_56] :
( sP15(U_52,U_51,U_50,U_55,U_53,U_54,U_56)
| ~ relation(U_50)
| ~ relation(U_51) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11,sP12,sP13,sP14,sP15])],[f_10_7]) ).
cnf(f_10_9,plain,
( sP15(U_52,U_51,U_50,U_55,U_53,U_54,U_56)
| ~ relation(U_50)
| ~ relation(U_51) ),
inference(clausify,[status(thm)],[f_10_8]) ).
cnf(f_10_10,plain,
( sP12(U_52,U_51,U_50,U_55,U_53,U_54,U_56)
| U_50 != relation_rng_restriction(U_52,U_51)
| ~ sP15(U_52,U_51,U_50,U_55,U_53,U_54,U_56) ),
inference(clausify,[status(thm)],[f_10_8]) ).
cnf(f_10_11,plain,
( U_50 = relation_rng_restriction(U_52,U_51)
| sP14(U_52,U_51,U_50)
| sP13(U_52,U_51,U_50)
| ~ sP15(U_52,U_51,U_50,U_55,U_53,U_54,U_56) ),
inference(clausify,[status(thm)],[f_10_8]) ).
cnf(f_10_12,plain,
( sP11(U_52,U_51,U_55,U_53)
| ~ in(ordered_pair(U_55,U_53),U_50)
| ~ sP12(U_52,U_51,U_50,U_55,U_53,U_54,U_56) ),
inference(clausify,[status(thm)],[f_10_8]) ).
cnf(f_10_13,plain,
( in(ordered_pair(U_56,U_54),U_50)
| ~ in(ordered_pair(U_56,U_54),U_51)
| ~ in(U_54,U_52)
| ~ sP12(U_52,U_51,U_50,U_55,U_53,U_54,U_56) ),
inference(clausify,[status(thm)],[f_10_8]) ).
cnf(f_10_14,plain,
( in(U_53,U_52)
| ~ sP11(U_52,U_51,U_55,U_53) ),
inference(clausify,[status(thm)],[f_10_8]) ).
cnf(f_10_15,plain,
( in(ordered_pair(U_55,U_53),U_51)
| ~ sP11(U_52,U_51,U_55,U_53) ),
inference(clausify,[status(thm)],[f_10_8]) ).
cnf(f_10_16,plain,
( in(ordered_pair(sK9(U_52,U_51,U_50),sK10(U_52,U_51,U_50)),U_50)
| ~ sP13(U_52,U_51,U_50) ),
inference(clausify,[status(thm)],[f_10_8]) ).
cnf(f_10_17,plain,
( ~ in(ordered_pair(sK9(U_52,U_51,U_50),sK10(U_52,U_51,U_50)),U_51)
| ~ in(sK10(U_52,U_51,U_50),U_52)
| ~ sP13(U_52,U_51,U_50) ),
inference(clausify,[status(thm)],[f_10_8]) ).
cnf(f_10_18,plain,
( in(sK12(U_52,U_51,U_50),U_52)
| ~ sP14(U_52,U_51,U_50) ),
inference(clausify,[status(thm)],[f_10_8]) ).
cnf(f_10_19,plain,
( in(ordered_pair(sK11(U_52,U_51,U_50),sK12(U_52,U_51,U_50)),U_51)
| ~ sP14(U_52,U_51,U_50) ),
inference(clausify,[status(thm)],[f_10_8]) ).
cnf(f_10_20,plain,
( ~ in(ordered_pair(sK11(U_52,U_51,U_50),sK12(U_52,U_51,U_50)),U_50)
| ~ sP14(U_52,U_51,U_50) ),
inference(clausify,[status(thm)],[f_10_8]) ).
fof(f_11_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_11_2,plain,
! [U_67] :
( ( relation(U_67)
| ? [U_66] :
( ! [U_65,U_64] : U_66 != ordered_pair(U_65,U_64)
& in(U_66,U_67) ) )
& ( ! [U_63] :
( ? [U_62,U_61] : U_63 = ordered_pair(U_62,U_61)
| ~ in(U_63,U_67) )
| ~ relation(U_67) ) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
( ! [U_69] :
( relation(U_69)
| ? [U_66] :
( ! [U_65,U_64] : U_66 != ordered_pair(U_65,U_64)
& in(U_66,U_69) ) )
& ! [U_68] :
( ! [U_63] :
( ? [U_62,U_61] : U_63 = ordered_pair(U_62,U_61)
| ~ in(U_63,U_68) )
| ~ relation(U_68) ) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
fof(f_11_4,plain,
( ! [U_69] :
( relation(U_69)
| ? [U_66] :
( ! [U_65,U_64] : U_66 != ordered_pair(U_65,U_64)
& in(U_66,U_69) ) )
& ! [U_68] :
( ! [U_63] :
( ? [U_61] : U_63 = ordered_pair(sK13(U_68,U_63),U_61)
| ~ in(U_63,U_68) )
| ~ relation(U_68) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_62,sK13(U_68,U_63))],[f_11_3]) ).
fof(f_11_5,plain,
( ! [U_69] :
( relation(U_69)
| ? [U_66] :
( ! [U_65,U_64] : U_66 != ordered_pair(U_65,U_64)
& in(U_66,U_69) ) )
& ! [U_68] :
( ! [U_63] :
( U_63 = ordered_pair(sK13(U_68,U_63),sK14(U_68,U_63))
| ~ in(U_63,U_68) )
| ~ relation(U_68) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_61,sK14(U_68,U_63))],[f_11_4]) ).
fof(f_11_6,plain,
( ! [U_69] :
( relation(U_69)
| ( ! [U_65,U_64] : sK15(U_69) != ordered_pair(U_65,U_64)
& in(sK15(U_69),U_69) ) )
& ! [U_68] :
( ! [U_63] :
( U_63 = ordered_pair(sK13(U_68,U_63),sK14(U_68,U_63))
| ~ in(U_63,U_68) )
| ~ relation(U_68) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_66,sK15(U_69))],[f_11_5]) ).
fof(f_11_7,plain,
( ! [U_64,U_65,U_69] :
( sK15(U_69) != ordered_pair(U_65,U_64)
| ~ sP16(U_64,U_65,U_69) )
& ! [U_64,U_65,U_69] :
( in(sK15(U_69),U_69)
| ~ sP16(U_64,U_65,U_69) )
& ! [U_64,U_65,U_69] :
( relation(U_69)
| sP16(U_64,U_65,U_69) )
& ! [U_63,U_68] :
( U_63 = ordered_pair(sK13(U_68,U_63),sK14(U_68,U_63))
| ~ in(U_63,U_68)
| ~ relation(U_68) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16])],[f_11_6]) ).
cnf(f_11_8,plain,
( U_63 = ordered_pair(sK13(U_68,U_63),sK14(U_68,U_63))
| ~ in(U_63,U_68)
| ~ relation(U_68) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_9,plain,
( relation(U_69)
| sP16(U_64,U_65,U_69) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_10,plain,
( in(sK15(U_69),U_69)
| ~ sP16(U_64,U_65,U_69) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_11,plain,
( sK15(U_69) != ordered_pair(U_65,U_64)
| ~ sP16(U_64,U_65,U_69) ),
inference(clausify,[status(thm)],[f_11_7]) ).
fof(f_12_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_12_2,plain,
! [U_77,U_76] :
( ( ( ( U_76 = set_meet(U_77)
| U_76 != empty_set )
& ( U_76 = empty_set
| U_76 != set_meet(U_77) ) )
| U_77 != empty_set )
& ( ( ( U_76 = set_meet(U_77)
| ? [U_75] :
( ( ~ in(U_75,U_76)
& ! [U_74] :
( in(U_75,U_74)
| ~ in(U_74,U_77) ) )
| ( ? [U_73] :
( ~ in(U_75,U_73)
& in(U_73,U_77) )
& in(U_75,U_76) ) ) )
& ( ! [U_72] :
( ( in(U_72,U_76)
| ? [U_71] :
( ~ in(U_72,U_71)
& in(U_71,U_77) ) )
& ( ! [U_70] :
( in(U_72,U_70)
| ~ in(U_70,U_77) )
| ~ in(U_72,U_76) ) )
| U_76 != set_meet(U_77) ) )
| U_77 = empty_set ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_89] :
( ( ! [U_87] :
( U_87 = set_meet(U_89)
| U_87 != empty_set )
& ! [U_86] :
( U_86 = empty_set
| U_86 != set_meet(U_89) ) )
| U_89 != empty_set )
& ! [U_88] :
( ( ! [U_85] :
( U_85 = set_meet(U_88)
| ? [U_81] :
( ~ in(U_81,U_85)
& ! [U_74] :
( in(U_81,U_74)
| ~ in(U_74,U_88) ) )
| ? [U_80] :
( ? [U_73] :
( ~ in(U_80,U_73)
& in(U_73,U_88) )
& in(U_80,U_85) ) )
& ! [U_84] :
( ( ! [U_79] :
( in(U_79,U_84)
| ? [U_71] :
( ~ in(U_79,U_71)
& in(U_71,U_88) ) )
& ! [U_78] :
( ! [U_70] :
( in(U_78,U_70)
| ~ in(U_70,U_88) )
| ~ in(U_78,U_84) ) )
| U_84 != set_meet(U_88) ) )
| U_88 = empty_set ) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
( ! [U_89] :
( ( ! [U_87] :
( U_87 = set_meet(U_89)
| U_87 != empty_set )
& ! [U_86] :
( U_86 = empty_set
| U_86 != set_meet(U_89) ) )
| U_89 != empty_set )
& ! [U_88] :
( ( ! [U_85] :
( U_85 = set_meet(U_88)
| ? [U_81] :
( ~ in(U_81,U_85)
& ! [U_74] :
( in(U_81,U_74)
| ~ in(U_74,U_88) ) )
| ? [U_80] :
( ? [U_73] :
( ~ in(U_80,U_73)
& in(U_73,U_88) )
& in(U_80,U_85) ) )
& ! [U_84] :
( ( ! [U_79] :
( in(U_79,U_84)
| ( ~ in(U_79,sK16(U_88,U_84,U_79))
& in(sK16(U_88,U_84,U_79),U_88) ) )
& ! [U_78] :
( ! [U_70] :
( in(U_78,U_70)
| ~ in(U_70,U_88) )
| ~ in(U_78,U_84) ) )
| U_84 != set_meet(U_88) ) )
| U_88 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_71,sK16(U_88,U_84,U_79))],[f_12_3]) ).
fof(f_12_5,plain,
( ! [U_89] :
( ( ! [U_87] :
( U_87 = set_meet(U_89)
| U_87 != empty_set )
& ! [U_86] :
( U_86 = empty_set
| U_86 != set_meet(U_89) ) )
| U_89 != empty_set )
& ! [U_88] :
( ( ! [U_85] :
( U_85 = set_meet(U_88)
| ? [U_81] :
( ~ in(U_81,U_85)
& ! [U_74] :
( in(U_81,U_74)
| ~ in(U_74,U_88) ) )
| ( ? [U_73] :
( ~ in(sK17(U_88,U_85),U_73)
& in(U_73,U_88) )
& in(sK17(U_88,U_85),U_85) ) )
& ! [U_84] :
( ( ! [U_79] :
( in(U_79,U_84)
| ( ~ in(U_79,sK16(U_88,U_84,U_79))
& in(sK16(U_88,U_84,U_79),U_88) ) )
& ! [U_78] :
( ! [U_70] :
( in(U_78,U_70)
| ~ in(U_70,U_88) )
| ~ in(U_78,U_84) ) )
| U_84 != set_meet(U_88) ) )
| U_88 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_80,sK17(U_88,U_85))],[f_12_4]) ).
fof(f_12_6,plain,
( ! [U_89] :
( ( ! [U_87] :
( U_87 = set_meet(U_89)
| U_87 != empty_set )
& ! [U_86] :
( U_86 = empty_set
| U_86 != set_meet(U_89) ) )
| U_89 != empty_set )
& ! [U_88] :
( ( ! [U_85] :
( U_85 = set_meet(U_88)
| ? [U_81] :
( ~ in(U_81,U_85)
& ! [U_74] :
( in(U_81,U_74)
| ~ in(U_74,U_88) ) )
| ( ~ in(sK17(U_88,U_85),sK18(U_88,U_85))
& in(sK18(U_88,U_85),U_88)
& in(sK17(U_88,U_85),U_85) ) )
& ! [U_84] :
( ( ! [U_79] :
( in(U_79,U_84)
| ( ~ in(U_79,sK16(U_88,U_84,U_79))
& in(sK16(U_88,U_84,U_79),U_88) ) )
& ! [U_78] :
( ! [U_70] :
( in(U_78,U_70)
| ~ in(U_70,U_88) )
| ~ in(U_78,U_84) ) )
| U_84 != set_meet(U_88) ) )
| U_88 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_73,sK18(U_88,U_85))],[f_12_5]) ).
fof(f_12_7,plain,
( ! [U_89] :
( ( ! [U_87] :
( U_87 = set_meet(U_89)
| U_87 != empty_set )
& ! [U_86] :
( U_86 = empty_set
| U_86 != set_meet(U_89) ) )
| U_89 != empty_set )
& ! [U_88] :
( ( ! [U_85] :
( U_85 = set_meet(U_88)
| ( ~ in(sK19(U_88,U_85),U_85)
& ! [U_74] :
( in(sK19(U_88,U_85),U_74)
| ~ in(U_74,U_88) ) )
| ( ~ in(sK17(U_88,U_85),sK18(U_88,U_85))
& in(sK18(U_88,U_85),U_88)
& in(sK17(U_88,U_85),U_85) ) )
& ! [U_84] :
( ( ! [U_79] :
( in(U_79,U_84)
| ( ~ in(U_79,sK16(U_88,U_84,U_79))
& in(sK16(U_88,U_84,U_79),U_88) ) )
& ! [U_78] :
( ! [U_70] :
( in(U_78,U_70)
| ~ in(U_70,U_88) )
| ~ in(U_78,U_84) ) )
| U_84 != set_meet(U_88) ) )
| U_88 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_81,sK19(U_88,U_85))],[f_12_6]) ).
fof(f_12_8,plain,
( ! [U_89,U_86,U_87] :
( U_87 = set_meet(U_89)
| U_87 != empty_set
| ~ sP22(U_89,U_86,U_87) )
& ! [U_89,U_86,U_87] :
( U_86 = empty_set
| U_86 != set_meet(U_89)
| ~ sP22(U_89,U_86,U_87) )
& ! [U_74,U_88,U_85] :
( ~ in(sK19(U_88,U_85),U_85)
| ~ sP20(U_74,U_88,U_85) )
& ! [U_74,U_88,U_85] :
( in(sK19(U_88,U_85),U_74)
| ~ in(U_74,U_88)
| ~ sP20(U_74,U_88,U_85) )
& ! [U_88,U_85] :
( ~ in(sK17(U_88,U_85),sK18(U_88,U_85))
| ~ sP19(U_88,U_85) )
& ! [U_88,U_85] :
( in(sK18(U_88,U_85),U_88)
| ~ sP19(U_88,U_85) )
& ! [U_88,U_85] :
( in(sK17(U_88,U_85),U_85)
| ~ sP19(U_88,U_85) )
& ! [U_84,U_88,U_79] :
( ~ in(U_79,sK16(U_88,U_84,U_79))
| ~ sP17(U_84,U_88,U_79) )
& ! [U_84,U_88,U_79] :
( in(sK16(U_88,U_84,U_79),U_88)
| ~ sP17(U_84,U_88,U_79) )
& ! [U_84,U_88,U_78,U_79,U_70] :
( in(U_79,U_84)
| sP17(U_84,U_88,U_79)
| ~ sP18(U_84,U_88,U_78,U_79,U_70) )
& ! [U_84,U_88,U_78,U_79,U_70] :
( in(U_78,U_70)
| ~ in(U_70,U_88)
| ~ in(U_78,U_84)
| ~ sP18(U_84,U_88,U_78,U_79,U_70) )
& ! [U_84,U_74,U_88,U_78,U_79,U_70,U_85] :
( U_85 = set_meet(U_88)
| sP20(U_74,U_88,U_85)
| sP19(U_88,U_85)
| ~ sP21(U_84,U_74,U_88,U_78,U_79,U_70,U_85) )
& ! [U_84,U_74,U_88,U_78,U_79,U_70,U_85] :
( sP18(U_84,U_88,U_78,U_79,U_70)
| U_84 != set_meet(U_88)
| ~ sP21(U_84,U_74,U_88,U_78,U_79,U_70,U_85) )
& ! [U_89,U_86,U_87] :
( sP22(U_89,U_86,U_87)
| U_89 != empty_set )
& ! [U_84,U_74,U_88,U_78,U_79,U_70,U_85] :
( sP21(U_84,U_74,U_88,U_78,U_79,U_70,U_85)
| U_88 = empty_set ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP17,sP18,sP19,sP20,sP21,sP22])],[f_12_7]) ).
cnf(f_12_9,plain,
( sP21(U_84,U_74,U_88,U_78,U_79,U_70,U_85)
| U_88 = empty_set ),
inference(clausify,[status(thm)],[f_12_8]) ).
cnf(f_12_10,plain,
( sP22(U_89,U_86,U_87)
| U_89 != empty_set ),
inference(clausify,[status(thm)],[f_12_8]) ).
cnf(f_12_11,plain,
( sP18(U_84,U_88,U_78,U_79,U_70)
| U_84 != set_meet(U_88)
| ~ sP21(U_84,U_74,U_88,U_78,U_79,U_70,U_85) ),
inference(clausify,[status(thm)],[f_12_8]) ).
cnf(f_12_12,plain,
( U_85 = set_meet(U_88)
| sP20(U_74,U_88,U_85)
| sP19(U_88,U_85)
| ~ sP21(U_84,U_74,U_88,U_78,U_79,U_70,U_85) ),
inference(clausify,[status(thm)],[f_12_8]) ).
cnf(f_12_13,plain,
( in(U_78,U_70)
| ~ in(U_70,U_88)
| ~ in(U_78,U_84)
| ~ sP18(U_84,U_88,U_78,U_79,U_70) ),
inference(clausify,[status(thm)],[f_12_8]) ).
cnf(f_12_14,plain,
( in(U_79,U_84)
| sP17(U_84,U_88,U_79)
| ~ sP18(U_84,U_88,U_78,U_79,U_70) ),
inference(clausify,[status(thm)],[f_12_8]) ).
cnf(f_12_15,plain,
( in(sK16(U_88,U_84,U_79),U_88)
| ~ sP17(U_84,U_88,U_79) ),
inference(clausify,[status(thm)],[f_12_8]) ).
cnf(f_12_16,plain,
( ~ in(U_79,sK16(U_88,U_84,U_79))
| ~ sP17(U_84,U_88,U_79) ),
inference(clausify,[status(thm)],[f_12_8]) ).
cnf(f_12_17,plain,
( in(sK17(U_88,U_85),U_85)
| ~ sP19(U_88,U_85) ),
inference(clausify,[status(thm)],[f_12_8]) ).
cnf(f_12_18,plain,
( in(sK18(U_88,U_85),U_88)
| ~ sP19(U_88,U_85) ),
inference(clausify,[status(thm)],[f_12_8]) ).
cnf(f_12_19,plain,
( ~ in(sK17(U_88,U_85),sK18(U_88,U_85))
| ~ sP19(U_88,U_85) ),
inference(clausify,[status(thm)],[f_12_8]) ).
cnf(f_12_20,plain,
( in(sK19(U_88,U_85),U_74)
| ~ in(U_74,U_88)
| ~ sP20(U_74,U_88,U_85) ),
inference(clausify,[status(thm)],[f_12_8]) ).
cnf(f_12_21,plain,
( ~ in(sK19(U_88,U_85),U_85)
| ~ sP20(U_74,U_88,U_85) ),
inference(clausify,[status(thm)],[f_12_8]) ).
cnf(f_12_22,plain,
( U_86 = empty_set
| U_86 != set_meet(U_89)
| ~ sP22(U_89,U_86,U_87) ),
inference(clausify,[status(thm)],[f_12_8]) ).
cnf(f_12_23,plain,
( U_87 = set_meet(U_89)
| U_87 != empty_set
| ~ sP22(U_89,U_86,U_87) ),
inference(clausify,[status(thm)],[f_12_8]) ).
fof(f_13_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_13_2,plain,
! [U_93,U_92] :
( ( U_92 = singleton(U_93)
| ? [U_91] :
( ( ~ in(U_91,U_92)
& U_91 = U_93 )
| ( U_91 != U_93
& in(U_91,U_92) ) ) )
& ( ! [U_90] :
( ( in(U_90,U_92)
| U_90 != U_93 )
& ( U_90 = U_93
| ~ in(U_90,U_92) ) )
| U_92 != singleton(U_93) ) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_101,U_99] :
( U_99 = singleton(U_101)
| ? [U_97] :
( ~ in(U_97,U_99)
& U_97 = U_101 )
| ? [U_96] :
( U_96 != U_101
& in(U_96,U_99) ) )
& ! [U_100,U_98] :
( ( ! [U_95] :
( in(U_95,U_98)
| U_95 != U_100 )
& ! [U_94] :
( U_94 = U_100
| ~ in(U_94,U_98) ) )
| U_98 != singleton(U_100) ) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
fof(f_13_4,plain,
( ! [U_101,U_99] :
( U_99 = singleton(U_101)
| ? [U_97] :
( ~ in(U_97,U_99)
& U_97 = U_101 )
| ( sK20(U_101,U_99) != U_101
& in(sK20(U_101,U_99),U_99) ) )
& ! [U_100,U_98] :
( ( ! [U_95] :
( in(U_95,U_98)
| U_95 != U_100 )
& ! [U_94] :
( U_94 = U_100
| ~ in(U_94,U_98) ) )
| U_98 != singleton(U_100) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_96,sK20(U_101,U_99))],[f_13_3]) ).
fof(f_13_5,plain,
( ! [U_101,U_99] :
( U_99 = singleton(U_101)
| ( ~ in(sK21(U_101,U_99),U_99)
& sK21(U_101,U_99) = U_101 )
| ( sK20(U_101,U_99) != U_101
& in(sK20(U_101,U_99),U_99) ) )
& ! [U_100,U_98] :
( ( ! [U_95] :
( in(U_95,U_98)
| U_95 != U_100 )
& ! [U_94] :
( U_94 = U_100
| ~ in(U_94,U_98) ) )
| U_98 != singleton(U_100) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_97,sK21(U_101,U_99))],[f_13_4]) ).
fof(f_13_6,plain,
( ! [U_99,U_101] :
( ~ in(sK21(U_101,U_99),U_99)
| ~ sP25(U_99,U_101) )
& ! [U_99,U_101] :
( sK21(U_101,U_99) = U_101
| ~ sP25(U_99,U_101) )
& ! [U_99,U_101] :
( sK20(U_101,U_99) != U_101
| ~ sP24(U_99,U_101) )
& ! [U_99,U_101] :
( in(sK20(U_101,U_99),U_99)
| ~ sP24(U_99,U_101) )
& ! [U_100,U_94,U_98,U_95] :
( in(U_95,U_98)
| U_95 != U_100
| ~ sP23(U_100,U_94,U_98,U_95) )
& ! [U_100,U_94,U_98,U_95] :
( U_94 = U_100
| ~ in(U_94,U_98)
| ~ sP23(U_100,U_94,U_98,U_95) )
& ! [U_99,U_101] :
( U_99 = singleton(U_101)
| sP25(U_99,U_101)
| sP24(U_99,U_101) )
& ! [U_100,U_94,U_98,U_95] :
( sP23(U_100,U_94,U_98,U_95)
| U_98 != singleton(U_100) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP23,sP24,sP25])],[f_13_5]) ).
cnf(f_13_7,plain,
( sP23(U_100,U_94,U_98,U_95)
| U_98 != singleton(U_100) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_8,plain,
( U_99 = singleton(U_101)
| sP25(U_99,U_101)
| sP24(U_99,U_101) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_9,plain,
( U_94 = U_100
| ~ in(U_94,U_98)
| ~ sP23(U_100,U_94,U_98,U_95) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_10,plain,
( in(U_95,U_98)
| U_95 != U_100
| ~ sP23(U_100,U_94,U_98,U_95) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_11,plain,
( in(sK20(U_101,U_99),U_99)
| ~ sP24(U_99,U_101) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_12,plain,
( sK20(U_101,U_99) != U_101
| ~ sP24(U_99,U_101) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_13,plain,
( sK21(U_101,U_99) = U_101
| ~ sP25(U_99,U_101) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_14,plain,
( ~ in(sK21(U_101,U_99),U_99)
| ~ sP25(U_99,U_101) ),
inference(clausify,[status(thm)],[f_13_6]) ).
fof(f_14_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_14_2,plain,
! [U_104] :
( ( U_104 = empty_set
| ? [U_103] : in(U_103,U_104) )
& ( ! [U_102] : ~ in(U_102,U_104)
| U_104 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_106] :
( U_106 = empty_set
| ? [U_103] : in(U_103,U_106) )
& ! [U_105] :
( ! [U_102] : ~ in(U_102,U_105)
| U_105 != empty_set ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
fof(f_14_4,plain,
( ! [U_106] :
( U_106 = empty_set
| in(sK22(U_106),U_106) )
& ! [U_105] :
( ! [U_102] : ~ in(U_102,U_105)
| U_105 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_103,sK22(U_106))],[f_14_3]) ).
fof(f_14_5,plain,
( ! [U_106] :
( U_106 = empty_set
| in(sK22(U_106),U_106) )
& ! [U_102,U_105] :
( ~ in(U_102,U_105)
| U_105 != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_14_4]) ).
cnf(f_14_6,plain,
( ~ in(U_102,U_105)
| U_105 != empty_set ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_7,plain,
( U_106 = empty_set
| in(sK22(U_106),U_106) ),
inference(clausify,[status(thm)],[f_14_5]) ).
fof(f_15_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_15_2,plain,
! [U_110,U_109] :
( ( U_109 = powerset(U_110)
| ? [U_108] :
( ( ~ in(U_108,U_109)
& subset(U_108,U_110) )
| ( ~ subset(U_108,U_110)
& in(U_108,U_109) ) ) )
& ( ! [U_107] :
( ( in(U_107,U_109)
| ~ subset(U_107,U_110) )
& ( subset(U_107,U_110)
| ~ in(U_107,U_109) ) )
| U_109 != powerset(U_110) ) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ! [U_118,U_116] :
( U_116 = powerset(U_118)
| ? [U_114] :
( ~ in(U_114,U_116)
& subset(U_114,U_118) )
| ? [U_113] :
( ~ subset(U_113,U_118)
& in(U_113,U_116) ) )
& ! [U_117,U_115] :
( ( ! [U_112] :
( in(U_112,U_115)
| ~ subset(U_112,U_117) )
& ! [U_111] :
( subset(U_111,U_117)
| ~ in(U_111,U_115) ) )
| U_115 != powerset(U_117) ) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
fof(f_15_4,plain,
( ! [U_118,U_116] :
( U_116 = powerset(U_118)
| ? [U_114] :
( ~ in(U_114,U_116)
& subset(U_114,U_118) )
| ( ~ subset(sK23(U_118,U_116),U_118)
& in(sK23(U_118,U_116),U_116) ) )
& ! [U_117,U_115] :
( ( ! [U_112] :
( in(U_112,U_115)
| ~ subset(U_112,U_117) )
& ! [U_111] :
( subset(U_111,U_117)
| ~ in(U_111,U_115) ) )
| U_115 != powerset(U_117) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_113,sK23(U_118,U_116))],[f_15_3]) ).
fof(f_15_5,plain,
( ! [U_118,U_116] :
( U_116 = powerset(U_118)
| ( ~ in(sK24(U_118,U_116),U_116)
& subset(sK24(U_118,U_116),U_118) )
| ( ~ subset(sK23(U_118,U_116),U_118)
& in(sK23(U_118,U_116),U_116) ) )
& ! [U_117,U_115] :
( ( ! [U_112] :
( in(U_112,U_115)
| ~ subset(U_112,U_117) )
& ! [U_111] :
( subset(U_111,U_117)
| ~ in(U_111,U_115) ) )
| U_115 != powerset(U_117) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_114,sK24(U_118,U_116))],[f_15_4]) ).
fof(f_15_6,plain,
( ! [U_116,U_118] :
( ~ in(sK24(U_118,U_116),U_116)
| ~ sP28(U_116,U_118) )
& ! [U_116,U_118] :
( subset(sK24(U_118,U_116),U_118)
| ~ sP28(U_116,U_118) )
& ! [U_116,U_118] :
( ~ subset(sK23(U_118,U_116),U_118)
| ~ sP27(U_116,U_118) )
& ! [U_116,U_118] :
( in(sK23(U_118,U_116),U_116)
| ~ sP27(U_116,U_118) )
& ! [U_115,U_111,U_112,U_117] :
( in(U_112,U_115)
| ~ subset(U_112,U_117)
| ~ sP26(U_115,U_111,U_112,U_117) )
& ! [U_115,U_111,U_112,U_117] :
( subset(U_111,U_117)
| ~ in(U_111,U_115)
| ~ sP26(U_115,U_111,U_112,U_117) )
& ! [U_116,U_118] :
( U_116 = powerset(U_118)
| sP28(U_116,U_118)
| sP27(U_116,U_118) )
& ! [U_115,U_111,U_112,U_117] :
( sP26(U_115,U_111,U_112,U_117)
| U_115 != powerset(U_117) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP26,sP27,sP28])],[f_15_5]) ).
cnf(f_15_7,plain,
( sP26(U_115,U_111,U_112,U_117)
| U_115 != powerset(U_117) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_8,plain,
( U_116 = powerset(U_118)
| sP28(U_116,U_118)
| sP27(U_116,U_118) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_9,plain,
( subset(U_111,U_117)
| ~ in(U_111,U_115)
| ~ sP26(U_115,U_111,U_112,U_117) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_10,plain,
( in(U_112,U_115)
| ~ subset(U_112,U_117)
| ~ sP26(U_115,U_111,U_112,U_117) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_11,plain,
( in(sK23(U_118,U_116),U_116)
| ~ sP27(U_116,U_118) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_12,plain,
( ~ subset(sK23(U_118,U_116),U_118)
| ~ sP27(U_116,U_118) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_13,plain,
( subset(sK24(U_118,U_116),U_118)
| ~ sP28(U_116,U_118) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_14,plain,
( ~ in(sK24(U_118,U_116),U_116)
| ~ sP28(U_116,U_118) ),
inference(clausify,[status(thm)],[f_15_6]) ).
fof(f_16_1,plain,
! [A] :
( ! [B] :
( ( ( A = B
| ? [C,D] :
( ( ~ in(ordered_pair(C,D),A)
& in(ordered_pair(C,D),B) )
| ( ~ in(ordered_pair(C,D),B)
& in(ordered_pair(C,D),A) ) ) )
& ( ! [C,D] :
( ( in(ordered_pair(C,D),A)
| ~ in(ordered_pair(C,D),B) )
& ( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) ) )
| A != B ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d2_relat_1]) ).
fof(f_16_2,plain,
! [U_124] :
( ! [U_123] :
( ( ( U_124 = U_123
| ? [U_122,U_121] :
( ( ~ in(ordered_pair(U_122,U_121),U_124)
& in(ordered_pair(U_122,U_121),U_123) )
| ( ~ in(ordered_pair(U_122,U_121),U_123)
& in(ordered_pair(U_122,U_121),U_124) ) ) )
& ( ! [U_120,U_119] :
( ( in(ordered_pair(U_120,U_119),U_124)
| ~ in(ordered_pair(U_120,U_119),U_123) )
& ( in(ordered_pair(U_120,U_119),U_123)
| ~ in(ordered_pair(U_120,U_119),U_124) ) )
| U_124 != U_123 ) )
| ~ relation(U_123) )
| ~ relation(U_124) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_124] :
( ! [U_123] :
( ( ( U_124 = U_123
| ? [U_132,U_130] :
( ~ in(ordered_pair(U_132,U_130),U_124)
& in(ordered_pair(U_132,U_130),U_123) )
| ? [U_131,U_129] :
( ~ in(ordered_pair(U_131,U_129),U_123)
& in(ordered_pair(U_131,U_129),U_124) ) )
& ( ( ! [U_128,U_126] :
( in(ordered_pair(U_128,U_126),U_124)
| ~ in(ordered_pair(U_128,U_126),U_123) )
& ! [U_127,U_125] :
( in(ordered_pair(U_127,U_125),U_123)
| ~ in(ordered_pair(U_127,U_125),U_124) ) )
| U_124 != U_123 ) )
| ~ relation(U_123) )
| ~ relation(U_124) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
fof(f_16_4,plain,
! [U_124] :
( ! [U_123] :
( ( ( U_124 = U_123
| ? [U_132,U_130] :
( ~ in(ordered_pair(U_132,U_130),U_124)
& in(ordered_pair(U_132,U_130),U_123) )
| ? [U_129] :
( ~ in(ordered_pair(sK25(U_124,U_123),U_129),U_123)
& in(ordered_pair(sK25(U_124,U_123),U_129),U_124) ) )
& ( ( ! [U_128,U_126] :
( in(ordered_pair(U_128,U_126),U_124)
| ~ in(ordered_pair(U_128,U_126),U_123) )
& ! [U_127,U_125] :
( in(ordered_pair(U_127,U_125),U_123)
| ~ in(ordered_pair(U_127,U_125),U_124) ) )
| U_124 != U_123 ) )
| ~ relation(U_123) )
| ~ relation(U_124) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_131,sK25(U_124,U_123))],[f_16_3]) ).
fof(f_16_5,plain,
! [U_124] :
( ! [U_123] :
( ( ( U_124 = U_123
| ? [U_132,U_130] :
( ~ in(ordered_pair(U_132,U_130),U_124)
& in(ordered_pair(U_132,U_130),U_123) )
| ( ~ in(ordered_pair(sK25(U_124,U_123),sK26(U_124,U_123)),U_123)
& in(ordered_pair(sK25(U_124,U_123),sK26(U_124,U_123)),U_124) ) )
& ( ( ! [U_128,U_126] :
( in(ordered_pair(U_128,U_126),U_124)
| ~ in(ordered_pair(U_128,U_126),U_123) )
& ! [U_127,U_125] :
( in(ordered_pair(U_127,U_125),U_123)
| ~ in(ordered_pair(U_127,U_125),U_124) ) )
| U_124 != U_123 ) )
| ~ relation(U_123) )
| ~ relation(U_124) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_129,sK26(U_124,U_123))],[f_16_4]) ).
fof(f_16_6,plain,
! [U_124] :
( ! [U_123] :
( ( ( U_124 = U_123
| ? [U_130] :
( ~ in(ordered_pair(sK27(U_124,U_123),U_130),U_124)
& in(ordered_pair(sK27(U_124,U_123),U_130),U_123) )
| ( ~ in(ordered_pair(sK25(U_124,U_123),sK26(U_124,U_123)),U_123)
& in(ordered_pair(sK25(U_124,U_123),sK26(U_124,U_123)),U_124) ) )
& ( ( ! [U_128,U_126] :
( in(ordered_pair(U_128,U_126),U_124)
| ~ in(ordered_pair(U_128,U_126),U_123) )
& ! [U_127,U_125] :
( in(ordered_pair(U_127,U_125),U_123)
| ~ in(ordered_pair(U_127,U_125),U_124) ) )
| U_124 != U_123 ) )
| ~ relation(U_123) )
| ~ relation(U_124) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_132,sK27(U_124,U_123))],[f_16_5]) ).
fof(f_16_7,plain,
! [U_124] :
( ! [U_123] :
( ( ( U_124 = U_123
| ( ~ in(ordered_pair(sK27(U_124,U_123),sK28(U_124,U_123)),U_124)
& in(ordered_pair(sK27(U_124,U_123),sK28(U_124,U_123)),U_123) )
| ( ~ in(ordered_pair(sK25(U_124,U_123),sK26(U_124,U_123)),U_123)
& in(ordered_pair(sK25(U_124,U_123),sK26(U_124,U_123)),U_124) ) )
& ( ( ! [U_128,U_126] :
( in(ordered_pair(U_128,U_126),U_124)
| ~ in(ordered_pair(U_128,U_126),U_123) )
& ! [U_127,U_125] :
( in(ordered_pair(U_127,U_125),U_123)
| ~ in(ordered_pair(U_127,U_125),U_124) ) )
| U_124 != U_123 ) )
| ~ relation(U_123) )
| ~ relation(U_124) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_130,sK28(U_124,U_123))],[f_16_6]) ).
fof(f_16_8,plain,
( ! [U_124,U_123] :
( ~ in(ordered_pair(sK27(U_124,U_123),sK28(U_124,U_123)),U_124)
| ~ sP31(U_124,U_123) )
& ! [U_124,U_123] :
( in(ordered_pair(sK27(U_124,U_123),sK28(U_124,U_123)),U_123)
| ~ sP31(U_124,U_123) )
& ! [U_124,U_123] :
( ~ in(ordered_pair(sK25(U_124,U_123),sK26(U_124,U_123)),U_123)
| ~ sP30(U_124,U_123) )
& ! [U_124,U_123] :
( in(ordered_pair(sK25(U_124,U_123),sK26(U_124,U_123)),U_124)
| ~ sP30(U_124,U_123) )
& ! [U_127,U_124,U_123,U_128,U_125,U_126] :
( in(ordered_pair(U_128,U_126),U_124)
| ~ in(ordered_pair(U_128,U_126),U_123)
| ~ sP29(U_127,U_124,U_123,U_128,U_125,U_126) )
& ! [U_127,U_124,U_123,U_128,U_125,U_126] :
( in(ordered_pair(U_127,U_125),U_123)
| ~ in(ordered_pair(U_127,U_125),U_124)
| ~ sP29(U_127,U_124,U_123,U_128,U_125,U_126) )
& ! [U_127,U_124,U_123,U_128,U_125,U_126] :
( U_124 = U_123
| sP31(U_124,U_123)
| sP30(U_124,U_123)
| ~ sP32(U_127,U_124,U_123,U_128,U_125,U_126) )
& ! [U_127,U_124,U_123,U_128,U_125,U_126] :
( sP29(U_127,U_124,U_123,U_128,U_125,U_126)
| U_124 != U_123
| ~ sP32(U_127,U_124,U_123,U_128,U_125,U_126) )
& ! [U_127,U_124,U_123,U_128,U_125,U_126] :
( sP32(U_127,U_124,U_123,U_128,U_125,U_126)
| ~ relation(U_123)
| ~ relation(U_124) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP29,sP30,sP31,sP32])],[f_16_7]) ).
cnf(f_16_9,plain,
( sP32(U_127,U_124,U_123,U_128,U_125,U_126)
| ~ relation(U_123)
| ~ relation(U_124) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_10,plain,
( sP29(U_127,U_124,U_123,U_128,U_125,U_126)
| U_124 != U_123
| ~ sP32(U_127,U_124,U_123,U_128,U_125,U_126) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_11,plain,
( U_124 = U_123
| sP31(U_124,U_123)
| sP30(U_124,U_123)
| ~ sP32(U_127,U_124,U_123,U_128,U_125,U_126) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_12,plain,
( in(ordered_pair(U_127,U_125),U_123)
| ~ in(ordered_pair(U_127,U_125),U_124)
| ~ sP29(U_127,U_124,U_123,U_128,U_125,U_126) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_13,plain,
( in(ordered_pair(U_128,U_126),U_124)
| ~ in(ordered_pair(U_128,U_126),U_123)
| ~ sP29(U_127,U_124,U_123,U_128,U_125,U_126) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_14,plain,
( in(ordered_pair(sK25(U_124,U_123),sK26(U_124,U_123)),U_124)
| ~ sP30(U_124,U_123) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_15,plain,
( ~ in(ordered_pair(sK25(U_124,U_123),sK26(U_124,U_123)),U_123)
| ~ sP30(U_124,U_123) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_16,plain,
( in(ordered_pair(sK27(U_124,U_123),sK28(U_124,U_123)),U_123)
| ~ sP31(U_124,U_123) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_17,plain,
( ~ in(ordered_pair(sK27(U_124,U_123),sK28(U_124,U_123)),U_124)
| ~ sP31(U_124,U_123) ),
inference(clausify,[status(thm)],[f_16_8]) ).
fof(f_17_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_17_2,plain,
! [U_134,U_133] :
( ( ( ( element(U_133,U_134)
| ~ empty(U_133) )
& ( empty(U_133)
| ~ element(U_133,U_134) ) )
| ~ empty(U_134) )
& ( ( ( element(U_133,U_134)
| ~ in(U_133,U_134) )
& ( in(U_133,U_134)
| ~ element(U_133,U_134) ) )
| empty(U_134) ) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( ! [U_142] :
( ( ! [U_140] :
( element(U_140,U_142)
| ~ empty(U_140) )
& ! [U_139] :
( empty(U_139)
| ~ element(U_139,U_142) ) )
| ~ empty(U_142) )
& ! [U_141] :
( ( ! [U_138] :
( element(U_138,U_141)
| ~ in(U_138,U_141) )
& ! [U_137] :
( in(U_137,U_141)
| ~ element(U_137,U_141) ) )
| empty(U_141) ) ),
inference(miniscope,[status(thm)],[f_17_2]) ).
fof(f_17_4,plain,
( ! [U_139,U_142,U_140] :
( element(U_140,U_142)
| ~ empty(U_140)
| ~ sP34(U_139,U_142,U_140) )
& ! [U_139,U_142,U_140] :
( empty(U_139)
| ~ element(U_139,U_142)
| ~ sP34(U_139,U_142,U_140) )
& ! [U_138,U_137,U_141] :
( element(U_138,U_141)
| ~ in(U_138,U_141)
| ~ sP33(U_138,U_137,U_141) )
& ! [U_138,U_137,U_141] :
( in(U_137,U_141)
| ~ element(U_137,U_141)
| ~ sP33(U_138,U_137,U_141) )
& ! [U_139,U_142,U_140] :
( sP34(U_139,U_142,U_140)
| ~ empty(U_142) )
& ! [U_138,U_137,U_141] :
( sP33(U_138,U_137,U_141)
| empty(U_141) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP33,sP34])],[f_17_3]) ).
cnf(f_17_5,plain,
( sP33(U_138,U_137,U_141)
| empty(U_141) ),
inference(clausify,[status(thm)],[f_17_4]) ).
cnf(f_17_6,plain,
( sP34(U_139,U_142,U_140)
| ~ empty(U_142) ),
inference(clausify,[status(thm)],[f_17_4]) ).
cnf(f_17_7,plain,
( in(U_137,U_141)
| ~ element(U_137,U_141)
| ~ sP33(U_138,U_137,U_141) ),
inference(clausify,[status(thm)],[f_17_4]) ).
cnf(f_17_8,plain,
( element(U_138,U_141)
| ~ in(U_138,U_141)
| ~ sP33(U_138,U_137,U_141) ),
inference(clausify,[status(thm)],[f_17_4]) ).
cnf(f_17_9,plain,
( empty(U_139)
| ~ element(U_139,U_142)
| ~ sP34(U_139,U_142,U_140) ),
inference(clausify,[status(thm)],[f_17_4]) ).
cnf(f_17_10,plain,
( element(U_140,U_142)
| ~ empty(U_140)
| ~ sP34(U_139,U_142,U_140) ),
inference(clausify,[status(thm)],[f_17_4]) ).
fof(f_18_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_18_2,plain,
! [U_147,U_146,U_145] :
( ( U_145 = unordered_pair(U_147,U_146)
| ? [U_144] :
( ( ~ in(U_144,U_145)
& ( U_144 = U_146
| U_144 = U_147 ) )
| ( U_144 != U_146
& U_144 != U_147
& in(U_144,U_145) ) ) )
& ( ! [U_143] :
( ( in(U_143,U_145)
| ( U_143 != U_146
& U_143 != U_147 ) )
& ( U_143 = U_146
| U_143 = U_147
| ~ in(U_143,U_145) ) )
| U_145 != unordered_pair(U_147,U_146) ) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( ! [U_157,U_155,U_153] :
( U_153 = unordered_pair(U_157,U_155)
| ? [U_151] :
( ~ in(U_151,U_153)
& ( U_151 = U_155
| U_151 = U_157 ) )
| ? [U_150] :
( U_150 != U_155
& U_150 != U_157
& in(U_150,U_153) ) )
& ! [U_156,U_154,U_152] :
( ( ! [U_149] :
( in(U_149,U_152)
| ( U_149 != U_154
& U_149 != U_156 ) )
& ! [U_148] :
( U_148 = U_154
| U_148 = U_156
| ~ in(U_148,U_152) ) )
| U_152 != unordered_pair(U_156,U_154) ) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
fof(f_18_4,plain,
( ! [U_157,U_155,U_153] :
( U_153 = unordered_pair(U_157,U_155)
| ? [U_151] :
( ~ in(U_151,U_153)
& ( U_151 = U_155
| U_151 = U_157 ) )
| ( sK29(U_157,U_155,U_153) != U_155
& sK29(U_157,U_155,U_153) != U_157
& in(sK29(U_157,U_155,U_153),U_153) ) )
& ! [U_156,U_154,U_152] :
( ( ! [U_149] :
( in(U_149,U_152)
| ( U_149 != U_154
& U_149 != U_156 ) )
& ! [U_148] :
( U_148 = U_154
| U_148 = U_156
| ~ in(U_148,U_152) ) )
| U_152 != unordered_pair(U_156,U_154) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_150,sK29(U_157,U_155,U_153))],[f_18_3]) ).
fof(f_18_5,plain,
( ! [U_157,U_155,U_153] :
( U_153 = unordered_pair(U_157,U_155)
| ( ~ in(sK30(U_157,U_155,U_153),U_153)
& ( sK30(U_157,U_155,U_153) = U_155
| sK30(U_157,U_155,U_153) = U_157 ) )
| ( sK29(U_157,U_155,U_153) != U_155
& sK29(U_157,U_155,U_153) != U_157
& in(sK29(U_157,U_155,U_153),U_153) ) )
& ! [U_156,U_154,U_152] :
( ( ! [U_149] :
( in(U_149,U_152)
| ( U_149 != U_154
& U_149 != U_156 ) )
& ! [U_148] :
( U_148 = U_154
| U_148 = U_156
| ~ in(U_148,U_152) ) )
| U_152 != unordered_pair(U_156,U_154) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_151,sK30(U_157,U_155,U_153))],[f_18_4]) ).
fof(f_18_6,plain,
( ! [U_157,U_153,U_155] :
( ~ in(sK30(U_157,U_155,U_153),U_153)
| ~ sP38(U_157,U_153,U_155) )
& ! [U_157,U_153,U_155] :
( sK30(U_157,U_155,U_153) = U_155
| sK30(U_157,U_155,U_153) = U_157
| ~ sP38(U_157,U_153,U_155) )
& ! [U_157,U_153,U_155] :
( sK29(U_157,U_155,U_153) != U_155
| ~ sP37(U_157,U_153,U_155) )
& ! [U_157,U_153,U_155] :
( sK29(U_157,U_155,U_153) != U_157
| ~ sP37(U_157,U_153,U_155) )
& ! [U_157,U_153,U_155] :
( in(sK29(U_157,U_155,U_153),U_153)
| ~ sP37(U_157,U_153,U_155) )
& ! [U_154,U_149,U_156] :
( U_149 != U_154
| ~ sP35(U_154,U_149,U_156) )
& ! [U_154,U_149,U_156] :
( U_149 != U_156
| ~ sP35(U_154,U_149,U_156) )
& ! [U_152,U_148,U_154,U_149,U_156] :
( in(U_149,U_152)
| sP35(U_154,U_149,U_156)
| ~ sP36(U_152,U_148,U_154,U_149,U_156) )
& ! [U_152,U_148,U_154,U_149,U_156] :
( U_148 = U_154
| U_148 = U_156
| ~ in(U_148,U_152)
| ~ sP36(U_152,U_148,U_154,U_149,U_156) )
& ! [U_157,U_153,U_155] :
( U_153 = unordered_pair(U_157,U_155)
| sP38(U_157,U_153,U_155)
| sP37(U_157,U_153,U_155) )
& ! [U_152,U_148,U_154,U_149,U_156] :
( sP36(U_152,U_148,U_154,U_149,U_156)
| U_152 != unordered_pair(U_156,U_154) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP35,sP36,sP37,sP38])],[f_18_5]) ).
cnf(f_18_7,plain,
( sP36(U_152,U_148,U_154,U_149,U_156)
| U_152 != unordered_pair(U_156,U_154) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_8,plain,
( U_153 = unordered_pair(U_157,U_155)
| sP38(U_157,U_153,U_155)
| sP37(U_157,U_153,U_155) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_9,plain,
( U_148 = U_154
| U_148 = U_156
| ~ in(U_148,U_152)
| ~ sP36(U_152,U_148,U_154,U_149,U_156) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_10,plain,
( in(U_149,U_152)
| sP35(U_154,U_149,U_156)
| ~ sP36(U_152,U_148,U_154,U_149,U_156) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_11,plain,
( U_149 != U_156
| ~ sP35(U_154,U_149,U_156) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_12,plain,
( U_149 != U_154
| ~ sP35(U_154,U_149,U_156) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_13,plain,
( in(sK29(U_157,U_155,U_153),U_153)
| ~ sP37(U_157,U_153,U_155) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_14,plain,
( sK29(U_157,U_155,U_153) != U_157
| ~ sP37(U_157,U_153,U_155) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_15,plain,
( sK29(U_157,U_155,U_153) != U_155
| ~ sP37(U_157,U_153,U_155) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_16,plain,
( sK30(U_157,U_155,U_153) = U_155
| sK30(U_157,U_155,U_153) = U_157
| ~ sP38(U_157,U_153,U_155) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_17,plain,
( ~ in(sK30(U_157,U_155,U_153),U_153)
| ~ sP38(U_157,U_153,U_155) ),
inference(clausify,[status(thm)],[f_18_6]) ).
fof(f_19_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_19_2,plain,
! [U_162,U_161,U_160] :
( ( U_160 = set_union2(U_162,U_161)
| ? [U_159] :
( ( ~ in(U_159,U_160)
& ( in(U_159,U_161)
| in(U_159,U_162) ) )
| ( ~ in(U_159,U_161)
& ~ in(U_159,U_162)
& in(U_159,U_160) ) ) )
& ( ! [U_158] :
( ( in(U_158,U_160)
| ( ~ in(U_158,U_161)
& ~ in(U_158,U_162) ) )
& ( in(U_158,U_161)
| in(U_158,U_162)
| ~ in(U_158,U_160) ) )
| U_160 != set_union2(U_162,U_161) ) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( ! [U_172,U_170,U_168] :
( U_168 = set_union2(U_172,U_170)
| ? [U_166] :
( ~ in(U_166,U_168)
& ( in(U_166,U_170)
| in(U_166,U_172) ) )
| ? [U_165] :
( ~ in(U_165,U_170)
& ~ in(U_165,U_172)
& in(U_165,U_168) ) )
& ! [U_171,U_169,U_167] :
( ( ! [U_164] :
( in(U_164,U_167)
| ( ~ in(U_164,U_169)
& ~ in(U_164,U_171) ) )
& ! [U_163] :
( in(U_163,U_169)
| in(U_163,U_171)
| ~ in(U_163,U_167) ) )
| U_167 != set_union2(U_171,U_169) ) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
fof(f_19_4,plain,
( ! [U_172,U_170,U_168] :
( U_168 = set_union2(U_172,U_170)
| ? [U_166] :
( ~ in(U_166,U_168)
& ( in(U_166,U_170)
| in(U_166,U_172) ) )
| ( ~ in(sK31(U_172,U_170,U_168),U_170)
& ~ in(sK31(U_172,U_170,U_168),U_172)
& in(sK31(U_172,U_170,U_168),U_168) ) )
& ! [U_171,U_169,U_167] :
( ( ! [U_164] :
( in(U_164,U_167)
| ( ~ in(U_164,U_169)
& ~ in(U_164,U_171) ) )
& ! [U_163] :
( in(U_163,U_169)
| in(U_163,U_171)
| ~ in(U_163,U_167) ) )
| U_167 != set_union2(U_171,U_169) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_165,sK31(U_172,U_170,U_168))],[f_19_3]) ).
fof(f_19_5,plain,
( ! [U_172,U_170,U_168] :
( U_168 = set_union2(U_172,U_170)
| ( ~ in(sK32(U_172,U_170,U_168),U_168)
& ( in(sK32(U_172,U_170,U_168),U_170)
| in(sK32(U_172,U_170,U_168),U_172) ) )
| ( ~ in(sK31(U_172,U_170,U_168),U_170)
& ~ in(sK31(U_172,U_170,U_168),U_172)
& in(sK31(U_172,U_170,U_168),U_168) ) )
& ! [U_171,U_169,U_167] :
( ( ! [U_164] :
( in(U_164,U_167)
| ( ~ in(U_164,U_169)
& ~ in(U_164,U_171) ) )
& ! [U_163] :
( in(U_163,U_169)
| in(U_163,U_171)
| ~ in(U_163,U_167) ) )
| U_167 != set_union2(U_171,U_169) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_166,sK32(U_172,U_170,U_168))],[f_19_4]) ).
fof(f_19_6,plain,
( ! [U_168,U_170,U_172] :
( ~ in(sK32(U_172,U_170,U_168),U_168)
| ~ sP42(U_168,U_170,U_172) )
& ! [U_168,U_170,U_172] :
( in(sK32(U_172,U_170,U_168),U_170)
| in(sK32(U_172,U_170,U_168),U_172)
| ~ sP42(U_168,U_170,U_172) )
& ! [U_168,U_170,U_172] :
( ~ in(sK31(U_172,U_170,U_168),U_170)
| ~ sP41(U_168,U_170,U_172) )
& ! [U_168,U_170,U_172] :
( ~ in(sK31(U_172,U_170,U_168),U_172)
| ~ sP41(U_168,U_170,U_172) )
& ! [U_168,U_170,U_172] :
( in(sK31(U_172,U_170,U_168),U_168)
| ~ sP41(U_168,U_170,U_172) )
& ! [U_164,U_169,U_171] :
( ~ in(U_164,U_169)
| ~ sP39(U_164,U_169,U_171) )
& ! [U_164,U_169,U_171] :
( ~ in(U_164,U_171)
| ~ sP39(U_164,U_169,U_171) )
& ! [U_164,U_169,U_163,U_171,U_167] :
( in(U_164,U_167)
| sP39(U_164,U_169,U_171)
| ~ sP40(U_164,U_169,U_163,U_171,U_167) )
& ! [U_164,U_169,U_163,U_171,U_167] :
( in(U_163,U_169)
| in(U_163,U_171)
| ~ in(U_163,U_167)
| ~ sP40(U_164,U_169,U_163,U_171,U_167) )
& ! [U_168,U_170,U_172] :
( U_168 = set_union2(U_172,U_170)
| sP42(U_168,U_170,U_172)
| sP41(U_168,U_170,U_172) )
& ! [U_164,U_169,U_163,U_171,U_167] :
( sP40(U_164,U_169,U_163,U_171,U_167)
| U_167 != set_union2(U_171,U_169) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP39,sP40,sP41,sP42])],[f_19_5]) ).
cnf(f_19_7,plain,
( sP40(U_164,U_169,U_163,U_171,U_167)
| U_167 != set_union2(U_171,U_169) ),
inference(clausify,[status(thm)],[f_19_6]) ).
cnf(f_19_8,plain,
( U_168 = set_union2(U_172,U_170)
| sP42(U_168,U_170,U_172)
| sP41(U_168,U_170,U_172) ),
inference(clausify,[status(thm)],[f_19_6]) ).
cnf(f_19_9,plain,
( in(U_163,U_169)
| in(U_163,U_171)
| ~ in(U_163,U_167)
| ~ sP40(U_164,U_169,U_163,U_171,U_167) ),
inference(clausify,[status(thm)],[f_19_6]) ).
cnf(f_19_10,plain,
( in(U_164,U_167)
| sP39(U_164,U_169,U_171)
| ~ sP40(U_164,U_169,U_163,U_171,U_167) ),
inference(clausify,[status(thm)],[f_19_6]) ).
cnf(f_19_11,plain,
( ~ in(U_164,U_171)
| ~ sP39(U_164,U_169,U_171) ),
inference(clausify,[status(thm)],[f_19_6]) ).
cnf(f_19_12,plain,
( ~ in(U_164,U_169)
| ~ sP39(U_164,U_169,U_171) ),
inference(clausify,[status(thm)],[f_19_6]) ).
cnf(f_19_13,plain,
( in(sK31(U_172,U_170,U_168),U_168)
| ~ sP41(U_168,U_170,U_172) ),
inference(clausify,[status(thm)],[f_19_6]) ).
cnf(f_19_14,plain,
( ~ in(sK31(U_172,U_170,U_168),U_172)
| ~ sP41(U_168,U_170,U_172) ),
inference(clausify,[status(thm)],[f_19_6]) ).
cnf(f_19_15,plain,
( ~ in(sK31(U_172,U_170,U_168),U_170)
| ~ sP41(U_168,U_170,U_172) ),
inference(clausify,[status(thm)],[f_19_6]) ).
cnf(f_19_16,plain,
( in(sK32(U_172,U_170,U_168),U_170)
| in(sK32(U_172,U_170,U_168),U_172)
| ~ sP42(U_168,U_170,U_172) ),
inference(clausify,[status(thm)],[f_19_6]) ).
cnf(f_19_17,plain,
( ~ in(sK32(U_172,U_170,U_168),U_168)
| ~ sP42(U_168,U_170,U_172) ),
inference(clausify,[status(thm)],[f_19_6]) ).
fof(f_20_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_20_2,plain,
! [U_185,U_184,U_183] :
( ( U_183 = cartesian_product2(U_185,U_184)
| ? [U_182] :
( ( ~ in(U_182,U_183)
& ? [U_181,U_180] :
( U_182 = ordered_pair(U_181,U_180)
& in(U_180,U_184)
& in(U_181,U_185) ) )
| ( ! [U_179,U_178] :
( U_182 != ordered_pair(U_179,U_178)
| ~ in(U_178,U_184)
| ~ in(U_179,U_185) )
& in(U_182,U_183) ) ) )
& ( ! [U_177] :
( ( in(U_177,U_183)
| ! [U_176,U_175] :
( U_177 != ordered_pair(U_176,U_175)
| ~ in(U_175,U_184)
| ~ in(U_176,U_185) ) )
& ( ? [U_174,U_173] :
( U_177 = ordered_pair(U_174,U_173)
& in(U_173,U_184)
& in(U_174,U_185) )
| ~ in(U_177,U_183) ) )
| U_183 != cartesian_product2(U_185,U_184) ) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( ! [U_195,U_193,U_191] :
( U_191 = cartesian_product2(U_195,U_193)
| ? [U_189] :
( ~ in(U_189,U_191)
& ? [U_181] :
( ? [U_180] :
( U_189 = ordered_pair(U_181,U_180)
& in(U_180,U_193) )
& in(U_181,U_195) ) )
| ? [U_188] :
( ! [U_179] :
( ! [U_178] :
( U_188 != ordered_pair(U_179,U_178)
| ~ in(U_178,U_193) )
| ~ in(U_179,U_195) )
& in(U_188,U_191) ) )
& ! [U_194,U_192,U_190] :
( ( ! [U_187] :
( in(U_187,U_190)
| ! [U_176] :
( ! [U_175] :
( U_187 != ordered_pair(U_176,U_175)
| ~ in(U_175,U_192) )
| ~ in(U_176,U_194) ) )
& ! [U_186] :
( ? [U_174] :
( ? [U_173] :
( U_186 = ordered_pair(U_174,U_173)
& in(U_173,U_192) )
& in(U_174,U_194) )
| ~ in(U_186,U_190) ) )
| U_190 != cartesian_product2(U_194,U_192) ) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
fof(f_20_4,plain,
( ! [U_195,U_193,U_191] :
( U_191 = cartesian_product2(U_195,U_193)
| ? [U_189] :
( ~ in(U_189,U_191)
& ? [U_181] :
( ? [U_180] :
( U_189 = ordered_pair(U_181,U_180)
& in(U_180,U_193) )
& in(U_181,U_195) ) )
| ? [U_188] :
( ! [U_179] :
( ! [U_178] :
( U_188 != ordered_pair(U_179,U_178)
| ~ in(U_178,U_193) )
| ~ in(U_179,U_195) )
& in(U_188,U_191) ) )
& ! [U_194,U_192,U_190] :
( ( ! [U_187] :
( in(U_187,U_190)
| ! [U_176] :
( ! [U_175] :
( U_187 != ordered_pair(U_176,U_175)
| ~ in(U_175,U_192) )
| ~ in(U_176,U_194) ) )
& ! [U_186] :
( ( ? [U_173] :
( U_186 = ordered_pair(sK33(U_194,U_192,U_190,U_186),U_173)
& in(U_173,U_192) )
& in(sK33(U_194,U_192,U_190,U_186),U_194) )
| ~ in(U_186,U_190) ) )
| U_190 != cartesian_product2(U_194,U_192) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_174,sK33(U_194,U_192,U_190,U_186))],[f_20_3]) ).
fof(f_20_5,plain,
( ! [U_195,U_193,U_191] :
( U_191 = cartesian_product2(U_195,U_193)
| ? [U_189] :
( ~ in(U_189,U_191)
& ? [U_181] :
( ? [U_180] :
( U_189 = ordered_pair(U_181,U_180)
& in(U_180,U_193) )
& in(U_181,U_195) ) )
| ? [U_188] :
( ! [U_179] :
( ! [U_178] :
( U_188 != ordered_pair(U_179,U_178)
| ~ in(U_178,U_193) )
| ~ in(U_179,U_195) )
& in(U_188,U_191) ) )
& ! [U_194,U_192,U_190] :
( ( ! [U_187] :
( in(U_187,U_190)
| ! [U_176] :
( ! [U_175] :
( U_187 != ordered_pair(U_176,U_175)
| ~ in(U_175,U_192) )
| ~ in(U_176,U_194) ) )
& ! [U_186] :
( ( U_186 = ordered_pair(sK33(U_194,U_192,U_190,U_186),sK34(U_194,U_192,U_190,U_186))
& in(sK34(U_194,U_192,U_190,U_186),U_192)
& in(sK33(U_194,U_192,U_190,U_186),U_194) )
| ~ in(U_186,U_190) ) )
| U_190 != cartesian_product2(U_194,U_192) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_173,sK34(U_194,U_192,U_190,U_186))],[f_20_4]) ).
fof(f_20_6,plain,
( ! [U_195,U_193,U_191] :
( U_191 = cartesian_product2(U_195,U_193)
| ? [U_189] :
( ~ in(U_189,U_191)
& ? [U_181] :
( ? [U_180] :
( U_189 = ordered_pair(U_181,U_180)
& in(U_180,U_193) )
& in(U_181,U_195) ) )
| ( ! [U_179] :
( ! [U_178] :
( sK35(U_195,U_193,U_191) != ordered_pair(U_179,U_178)
| ~ in(U_178,U_193) )
| ~ in(U_179,U_195) )
& in(sK35(U_195,U_193,U_191),U_191) ) )
& ! [U_194,U_192,U_190] :
( ( ! [U_187] :
( in(U_187,U_190)
| ! [U_176] :
( ! [U_175] :
( U_187 != ordered_pair(U_176,U_175)
| ~ in(U_175,U_192) )
| ~ in(U_176,U_194) ) )
& ! [U_186] :
( ( U_186 = ordered_pair(sK33(U_194,U_192,U_190,U_186),sK34(U_194,U_192,U_190,U_186))
& in(sK34(U_194,U_192,U_190,U_186),U_192)
& in(sK33(U_194,U_192,U_190,U_186),U_194) )
| ~ in(U_186,U_190) ) )
| U_190 != cartesian_product2(U_194,U_192) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_188,sK35(U_195,U_193,U_191))],[f_20_5]) ).
fof(f_20_7,plain,
( ! [U_195,U_193,U_191] :
( U_191 = cartesian_product2(U_195,U_193)
| ( ~ in(sK36(U_195,U_193,U_191),U_191)
& ? [U_181] :
( ? [U_180] :
( sK36(U_195,U_193,U_191) = ordered_pair(U_181,U_180)
& in(U_180,U_193) )
& in(U_181,U_195) ) )
| ( ! [U_179] :
( ! [U_178] :
( sK35(U_195,U_193,U_191) != ordered_pair(U_179,U_178)
| ~ in(U_178,U_193) )
| ~ in(U_179,U_195) )
& in(sK35(U_195,U_193,U_191),U_191) ) )
& ! [U_194,U_192,U_190] :
( ( ! [U_187] :
( in(U_187,U_190)
| ! [U_176] :
( ! [U_175] :
( U_187 != ordered_pair(U_176,U_175)
| ~ in(U_175,U_192) )
| ~ in(U_176,U_194) ) )
& ! [U_186] :
( ( U_186 = ordered_pair(sK33(U_194,U_192,U_190,U_186),sK34(U_194,U_192,U_190,U_186))
& in(sK34(U_194,U_192,U_190,U_186),U_192)
& in(sK33(U_194,U_192,U_190,U_186),U_194) )
| ~ in(U_186,U_190) ) )
| U_190 != cartesian_product2(U_194,U_192) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_189,sK36(U_195,U_193,U_191))],[f_20_6]) ).
fof(f_20_8,plain,
( ! [U_195,U_193,U_191] :
( U_191 = cartesian_product2(U_195,U_193)
| ( ~ in(sK36(U_195,U_193,U_191),U_191)
& ? [U_180] :
( sK36(U_195,U_193,U_191) = ordered_pair(sK37(U_195,U_193,U_191),U_180)
& in(U_180,U_193) )
& in(sK37(U_195,U_193,U_191),U_195) )
| ( ! [U_179] :
( ! [U_178] :
( sK35(U_195,U_193,U_191) != ordered_pair(U_179,U_178)
| ~ in(U_178,U_193) )
| ~ in(U_179,U_195) )
& in(sK35(U_195,U_193,U_191),U_191) ) )
& ! [U_194,U_192,U_190] :
( ( ! [U_187] :
( in(U_187,U_190)
| ! [U_176] :
( ! [U_175] :
( U_187 != ordered_pair(U_176,U_175)
| ~ in(U_175,U_192) )
| ~ in(U_176,U_194) ) )
& ! [U_186] :
( ( U_186 = ordered_pair(sK33(U_194,U_192,U_190,U_186),sK34(U_194,U_192,U_190,U_186))
& in(sK34(U_194,U_192,U_190,U_186),U_192)
& in(sK33(U_194,U_192,U_190,U_186),U_194) )
| ~ in(U_186,U_190) ) )
| U_190 != cartesian_product2(U_194,U_192) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_181,sK37(U_195,U_193,U_191))],[f_20_7]) ).
fof(f_20_9,plain,
( ! [U_195,U_193,U_191] :
( U_191 = cartesian_product2(U_195,U_193)
| ( ~ in(sK36(U_195,U_193,U_191),U_191)
& sK36(U_195,U_193,U_191) = ordered_pair(sK37(U_195,U_193,U_191),sK38(U_195,U_193,U_191))
& in(sK38(U_195,U_193,U_191),U_193)
& in(sK37(U_195,U_193,U_191),U_195) )
| ( ! [U_179] :
( ! [U_178] :
( sK35(U_195,U_193,U_191) != ordered_pair(U_179,U_178)
| ~ in(U_178,U_193) )
| ~ in(U_179,U_195) )
& in(sK35(U_195,U_193,U_191),U_191) ) )
& ! [U_194,U_192,U_190] :
( ( ! [U_187] :
( in(U_187,U_190)
| ! [U_176] :
( ! [U_175] :
( U_187 != ordered_pair(U_176,U_175)
| ~ in(U_175,U_192) )
| ~ in(U_176,U_194) ) )
& ! [U_186] :
( ( U_186 = ordered_pair(sK33(U_194,U_192,U_190,U_186),sK34(U_194,U_192,U_190,U_186))
& in(sK34(U_194,U_192,U_190,U_186),U_192)
& in(sK33(U_194,U_192,U_190,U_186),U_194) )
| ~ in(U_186,U_190) ) )
| U_190 != cartesian_product2(U_194,U_192) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_180,sK38(U_195,U_193,U_191))],[f_20_8]) ).
fof(f_20_10,plain,
( ! [U_193,U_195,U_191] :
( ~ in(sK36(U_195,U_193,U_191),U_191)
| ~ sP46(U_193,U_195,U_191) )
& ! [U_193,U_195,U_191] :
( sK36(U_195,U_193,U_191) = ordered_pair(sK37(U_195,U_193,U_191),sK38(U_195,U_193,U_191))
| ~ sP46(U_193,U_195,U_191) )
& ! [U_193,U_195,U_191] :
( in(sK38(U_195,U_193,U_191),U_193)
| ~ sP46(U_193,U_195,U_191) )
& ! [U_193,U_195,U_191] :
( in(sK37(U_195,U_193,U_191),U_195)
| ~ sP46(U_193,U_195,U_191) )
& ! [U_178,U_193,U_195,U_179,U_191] :
( sK35(U_195,U_193,U_191) != ordered_pair(U_179,U_178)
| ~ in(U_178,U_193)
| ~ in(U_179,U_195)
| ~ sP45(U_178,U_193,U_195,U_179,U_191) )
& ! [U_178,U_193,U_195,U_179,U_191] :
( in(sK35(U_195,U_193,U_191),U_191)
| ~ sP45(U_178,U_193,U_195,U_179,U_191) )
& ! [U_186,U_192,U_190,U_194] :
( U_186 = ordered_pair(sK33(U_194,U_192,U_190,U_186),sK34(U_194,U_192,U_190,U_186))
| ~ sP43(U_186,U_192,U_190,U_194) )
& ! [U_186,U_192,U_190,U_194] :
( in(sK34(U_194,U_192,U_190,U_186),U_192)
| ~ sP43(U_186,U_192,U_190,U_194) )
& ! [U_186,U_192,U_190,U_194] :
( in(sK33(U_194,U_192,U_190,U_186),U_194)
| ~ sP43(U_186,U_192,U_190,U_194) )
& ! [U_175,U_186,U_187,U_176,U_192,U_190,U_194] :
( in(U_187,U_190)
| U_187 != ordered_pair(U_176,U_175)
| ~ in(U_175,U_192)
| ~ in(U_176,U_194)
| ~ sP44(U_175,U_186,U_187,U_176,U_192,U_190,U_194) )
& ! [U_175,U_186,U_187,U_176,U_192,U_190,U_194] :
( sP43(U_186,U_192,U_190,U_194)
| ~ in(U_186,U_190)
| ~ sP44(U_175,U_186,U_187,U_176,U_192,U_190,U_194) )
& ! [U_178,U_193,U_195,U_179,U_191] :
( U_191 = cartesian_product2(U_195,U_193)
| sP46(U_193,U_195,U_191)
| sP45(U_178,U_193,U_195,U_179,U_191) )
& ! [U_175,U_186,U_187,U_176,U_192,U_190,U_194] :
( sP44(U_175,U_186,U_187,U_176,U_192,U_190,U_194)
| U_190 != cartesian_product2(U_194,U_192) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP43,sP44,sP45,sP46])],[f_20_9]) ).
cnf(f_20_11,plain,
( sP44(U_175,U_186,U_187,U_176,U_192,U_190,U_194)
| U_190 != cartesian_product2(U_194,U_192) ),
inference(clausify,[status(thm)],[f_20_10]) ).
cnf(f_20_12,plain,
( U_191 = cartesian_product2(U_195,U_193)
| sP46(U_193,U_195,U_191)
| sP45(U_178,U_193,U_195,U_179,U_191) ),
inference(clausify,[status(thm)],[f_20_10]) ).
cnf(f_20_13,plain,
( sP43(U_186,U_192,U_190,U_194)
| ~ in(U_186,U_190)
| ~ sP44(U_175,U_186,U_187,U_176,U_192,U_190,U_194) ),
inference(clausify,[status(thm)],[f_20_10]) ).
cnf(f_20_14,plain,
( in(U_187,U_190)
| U_187 != ordered_pair(U_176,U_175)
| ~ in(U_175,U_192)
| ~ in(U_176,U_194)
| ~ sP44(U_175,U_186,U_187,U_176,U_192,U_190,U_194) ),
inference(clausify,[status(thm)],[f_20_10]) ).
cnf(f_20_15,plain,
( in(sK33(U_194,U_192,U_190,U_186),U_194)
| ~ sP43(U_186,U_192,U_190,U_194) ),
inference(clausify,[status(thm)],[f_20_10]) ).
cnf(f_20_16,plain,
( in(sK34(U_194,U_192,U_190,U_186),U_192)
| ~ sP43(U_186,U_192,U_190,U_194) ),
inference(clausify,[status(thm)],[f_20_10]) ).
cnf(f_20_17,plain,
( U_186 = ordered_pair(sK33(U_194,U_192,U_190,U_186),sK34(U_194,U_192,U_190,U_186))
| ~ sP43(U_186,U_192,U_190,U_194) ),
inference(clausify,[status(thm)],[f_20_10]) ).
cnf(f_20_18,plain,
( in(sK35(U_195,U_193,U_191),U_191)
| ~ sP45(U_178,U_193,U_195,U_179,U_191) ),
inference(clausify,[status(thm)],[f_20_10]) ).
cnf(f_20_19,plain,
( sK35(U_195,U_193,U_191) != ordered_pair(U_179,U_178)
| ~ in(U_178,U_193)
| ~ in(U_179,U_195)
| ~ sP45(U_178,U_193,U_195,U_179,U_191) ),
inference(clausify,[status(thm)],[f_20_10]) ).
cnf(f_20_20,plain,
( in(sK37(U_195,U_193,U_191),U_195)
| ~ sP46(U_193,U_195,U_191) ),
inference(clausify,[status(thm)],[f_20_10]) ).
cnf(f_20_21,plain,
( in(sK38(U_195,U_193,U_191),U_193)
| ~ sP46(U_193,U_195,U_191) ),
inference(clausify,[status(thm)],[f_20_10]) ).
cnf(f_20_22,plain,
( sK36(U_195,U_193,U_191) = ordered_pair(sK37(U_195,U_193,U_191),sK38(U_195,U_193,U_191))
| ~ sP46(U_193,U_195,U_191) ),
inference(clausify,[status(thm)],[f_20_10]) ).
cnf(f_20_23,plain,
( ~ in(sK36(U_195,U_193,U_191),U_191)
| ~ sP46(U_193,U_195,U_191) ),
inference(clausify,[status(thm)],[f_20_10]) ).
fof(f_21_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_21_2,plain,
! [U_201] :
( ! [U_200] :
( ( ( subset(U_201,U_200)
| ? [U_199,U_198] :
( ~ in(ordered_pair(U_199,U_198),U_200)
& in(ordered_pair(U_199,U_198),U_201) ) )
& ( ! [U_197,U_196] :
( in(ordered_pair(U_197,U_196),U_200)
| ~ in(ordered_pair(U_197,U_196),U_201) )
| ~ subset(U_201,U_200) ) )
| ~ relation(U_200) )
| ~ relation(U_201) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_201] :
( ! [U_200] :
( ( ( subset(U_201,U_200)
| ? [U_198] :
( ~ in(ordered_pair(sK39(U_201,U_200),U_198),U_200)
& in(ordered_pair(sK39(U_201,U_200),U_198),U_201) ) )
& ( ! [U_197,U_196] :
( in(ordered_pair(U_197,U_196),U_200)
| ~ in(ordered_pair(U_197,U_196),U_201) )
| ~ subset(U_201,U_200) ) )
| ~ relation(U_200) )
| ~ relation(U_201) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_199,sK39(U_201,U_200))],[f_21_2]) ).
fof(f_21_4,plain,
! [U_201] :
( ! [U_200] :
( ( ( subset(U_201,U_200)
| ( ~ in(ordered_pair(sK39(U_201,U_200),sK40(U_201,U_200)),U_200)
& in(ordered_pair(sK39(U_201,U_200),sK40(U_201,U_200)),U_201) ) )
& ( ! [U_197,U_196] :
( in(ordered_pair(U_197,U_196),U_200)
| ~ in(ordered_pair(U_197,U_196),U_201) )
| ~ subset(U_201,U_200) ) )
| ~ relation(U_200) )
| ~ relation(U_201) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_198,sK40(U_201,U_200))],[f_21_3]) ).
fof(f_21_5,plain,
( ! [U_200,U_201] :
( ~ in(ordered_pair(sK39(U_201,U_200),sK40(U_201,U_200)),U_200)
| ~ sP47(U_200,U_201) )
& ! [U_200,U_201] :
( in(ordered_pair(sK39(U_201,U_200),sK40(U_201,U_200)),U_201)
| ~ sP47(U_200,U_201) )
& ! [U_197,U_200,U_196,U_201] :
( subset(U_201,U_200)
| sP47(U_200,U_201)
| ~ sP48(U_197,U_200,U_196,U_201) )
& ! [U_197,U_200,U_196,U_201] :
( in(ordered_pair(U_197,U_196),U_200)
| ~ in(ordered_pair(U_197,U_196),U_201)
| ~ subset(U_201,U_200)
| ~ sP48(U_197,U_200,U_196,U_201) )
& ! [U_197,U_200,U_196,U_201] :
( sP48(U_197,U_200,U_196,U_201)
| ~ relation(U_200)
| ~ relation(U_201) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP47,sP48])],[f_21_4]) ).
cnf(f_21_6,plain,
( sP48(U_197,U_200,U_196,U_201)
| ~ relation(U_200)
| ~ relation(U_201) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_7,plain,
( in(ordered_pair(U_197,U_196),U_200)
| ~ in(ordered_pair(U_197,U_196),U_201)
| ~ subset(U_201,U_200)
| ~ sP48(U_197,U_200,U_196,U_201) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_8,plain,
( subset(U_201,U_200)
| sP47(U_200,U_201)
| ~ sP48(U_197,U_200,U_196,U_201) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_9,plain,
( in(ordered_pair(sK39(U_201,U_200),sK40(U_201,U_200)),U_201)
| ~ sP47(U_200,U_201) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_10,plain,
( ~ in(ordered_pair(sK39(U_201,U_200),sK40(U_201,U_200)),U_200)
| ~ sP47(U_200,U_201) ),
inference(clausify,[status(thm)],[f_21_5]) ).
fof(f_22_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_22_2,plain,
! [U_205,U_204] :
( ( subset(U_205,U_204)
| ? [U_203] :
( ~ in(U_203,U_204)
& in(U_203,U_205) ) )
& ( ! [U_202] :
( in(U_202,U_204)
| ~ in(U_202,U_205) )
| ~ subset(U_205,U_204) ) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( ! [U_209,U_207] :
( subset(U_209,U_207)
| ? [U_203] :
( ~ in(U_203,U_207)
& in(U_203,U_209) ) )
& ! [U_208,U_206] :
( ! [U_202] :
( in(U_202,U_206)
| ~ in(U_202,U_208) )
| ~ subset(U_208,U_206) ) ),
inference(miniscope,[status(thm)],[f_22_2]) ).
fof(f_22_4,plain,
( ! [U_209,U_207] :
( subset(U_209,U_207)
| ( ~ in(sK41(U_209,U_207),U_207)
& in(sK41(U_209,U_207),U_209) ) )
& ! [U_208,U_206] :
( ! [U_202] :
( in(U_202,U_206)
| ~ in(U_202,U_208) )
| ~ subset(U_208,U_206) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_203,sK41(U_209,U_207))],[f_22_3]) ).
fof(f_22_5,plain,
( ! [U_207,U_209] :
( ~ in(sK41(U_209,U_207),U_207)
| ~ sP49(U_207,U_209) )
& ! [U_207,U_209] :
( in(sK41(U_209,U_207),U_209)
| ~ sP49(U_207,U_209) )
& ! [U_207,U_209] :
( subset(U_209,U_207)
| sP49(U_207,U_209) )
& ! [U_202,U_208,U_206] :
( in(U_202,U_206)
| ~ in(U_202,U_208)
| ~ subset(U_208,U_206) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP49])],[f_22_4]) ).
cnf(f_22_6,plain,
( in(U_202,U_206)
| ~ in(U_202,U_208)
| ~ subset(U_208,U_206) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_7,plain,
( subset(U_209,U_207)
| sP49(U_207,U_209) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_8,plain,
( in(sK41(U_209,U_207),U_209)
| ~ sP49(U_207,U_209) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_9,plain,
( ~ in(sK41(U_209,U_207),U_207)
| ~ sP49(U_207,U_209) ),
inference(clausify,[status(thm)],[f_22_5]) ).
fof(f_23_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_23_2,plain,
! [U_214,U_213,U_212] :
( ( U_212 = set_intersection2(U_214,U_213)
| ? [U_211] :
( ( ~ in(U_211,U_212)
& in(U_211,U_213)
& in(U_211,U_214) )
| ( ( ~ in(U_211,U_213)
| ~ in(U_211,U_214) )
& in(U_211,U_212) ) ) )
& ( ! [U_210] :
( ( in(U_210,U_212)
| ~ in(U_210,U_213)
| ~ in(U_210,U_214) )
& ( ( in(U_210,U_213)
& in(U_210,U_214) )
| ~ in(U_210,U_212) ) )
| U_212 != set_intersection2(U_214,U_213) ) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( ! [U_224,U_222,U_220] :
( U_220 = set_intersection2(U_224,U_222)
| ? [U_218] :
( ~ in(U_218,U_220)
& in(U_218,U_222)
& in(U_218,U_224) )
| ? [U_217] :
( ( ~ in(U_217,U_222)
| ~ in(U_217,U_224) )
& in(U_217,U_220) ) )
& ! [U_223,U_221,U_219] :
( ( ! [U_216] :
( in(U_216,U_219)
| ~ in(U_216,U_221)
| ~ in(U_216,U_223) )
& ! [U_215] :
( ( in(U_215,U_221)
& in(U_215,U_223) )
| ~ in(U_215,U_219) ) )
| U_219 != set_intersection2(U_223,U_221) ) ),
inference(miniscope,[status(thm)],[f_23_2]) ).
fof(f_23_4,plain,
( ! [U_224,U_222,U_220] :
( U_220 = set_intersection2(U_224,U_222)
| ? [U_218] :
( ~ in(U_218,U_220)
& in(U_218,U_222)
& in(U_218,U_224) )
| ( ( ~ in(sK42(U_224,U_222,U_220),U_222)
| ~ in(sK42(U_224,U_222,U_220),U_224) )
& in(sK42(U_224,U_222,U_220),U_220) ) )
& ! [U_223,U_221,U_219] :
( ( ! [U_216] :
( in(U_216,U_219)
| ~ in(U_216,U_221)
| ~ in(U_216,U_223) )
& ! [U_215] :
( ( in(U_215,U_221)
& in(U_215,U_223) )
| ~ in(U_215,U_219) ) )
| U_219 != set_intersection2(U_223,U_221) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_217,sK42(U_224,U_222,U_220))],[f_23_3]) ).
fof(f_23_5,plain,
( ! [U_224,U_222,U_220] :
( U_220 = set_intersection2(U_224,U_222)
| ( ~ in(sK43(U_224,U_222,U_220),U_220)
& in(sK43(U_224,U_222,U_220),U_222)
& in(sK43(U_224,U_222,U_220),U_224) )
| ( ( ~ in(sK42(U_224,U_222,U_220),U_222)
| ~ in(sK42(U_224,U_222,U_220),U_224) )
& in(sK42(U_224,U_222,U_220),U_220) ) )
& ! [U_223,U_221,U_219] :
( ( ! [U_216] :
( in(U_216,U_219)
| ~ in(U_216,U_221)
| ~ in(U_216,U_223) )
& ! [U_215] :
( ( in(U_215,U_221)
& in(U_215,U_223) )
| ~ in(U_215,U_219) ) )
| U_219 != set_intersection2(U_223,U_221) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_218,sK43(U_224,U_222,U_220))],[f_23_4]) ).
fof(f_23_6,plain,
( ! [U_224,U_220,U_222] :
( ~ in(sK43(U_224,U_222,U_220),U_220)
| ~ sP53(U_224,U_220,U_222) )
& ! [U_224,U_220,U_222] :
( in(sK43(U_224,U_222,U_220),U_222)
| ~ sP53(U_224,U_220,U_222) )
& ! [U_224,U_220,U_222] :
( in(sK43(U_224,U_222,U_220),U_224)
| ~ sP53(U_224,U_220,U_222) )
& ! [U_224,U_220,U_222] :
( ~ in(sK42(U_224,U_222,U_220),U_222)
| ~ in(sK42(U_224,U_222,U_220),U_224)
| ~ sP52(U_224,U_220,U_222) )
& ! [U_224,U_220,U_222] :
( in(sK42(U_224,U_222,U_220),U_220)
| ~ sP52(U_224,U_220,U_222) )
& ! [U_223,U_221,U_215] :
( in(U_215,U_221)
| ~ sP50(U_223,U_221,U_215) )
& ! [U_223,U_221,U_215] :
( in(U_215,U_223)
| ~ sP50(U_223,U_221,U_215) )
& ! [U_223,U_221,U_216,U_215,U_219] :
( in(U_216,U_219)
| ~ in(U_216,U_221)
| ~ in(U_216,U_223)
| ~ sP51(U_223,U_221,U_216,U_215,U_219) )
& ! [U_223,U_221,U_216,U_215,U_219] :
( sP50(U_223,U_221,U_215)
| ~ in(U_215,U_219)
| ~ sP51(U_223,U_221,U_216,U_215,U_219) )
& ! [U_224,U_220,U_222] :
( U_220 = set_intersection2(U_224,U_222)
| sP53(U_224,U_220,U_222)
| sP52(U_224,U_220,U_222) )
& ! [U_223,U_221,U_216,U_215,U_219] :
( sP51(U_223,U_221,U_216,U_215,U_219)
| U_219 != set_intersection2(U_223,U_221) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP50,sP51,sP52,sP53])],[f_23_5]) ).
cnf(f_23_7,plain,
( sP51(U_223,U_221,U_216,U_215,U_219)
| U_219 != set_intersection2(U_223,U_221) ),
inference(clausify,[status(thm)],[f_23_6]) ).
cnf(f_23_8,plain,
( U_220 = set_intersection2(U_224,U_222)
| sP53(U_224,U_220,U_222)
| sP52(U_224,U_220,U_222) ),
inference(clausify,[status(thm)],[f_23_6]) ).
cnf(f_23_9,plain,
( sP50(U_223,U_221,U_215)
| ~ in(U_215,U_219)
| ~ sP51(U_223,U_221,U_216,U_215,U_219) ),
inference(clausify,[status(thm)],[f_23_6]) ).
cnf(f_23_10,plain,
( in(U_216,U_219)
| ~ in(U_216,U_221)
| ~ in(U_216,U_223)
| ~ sP51(U_223,U_221,U_216,U_215,U_219) ),
inference(clausify,[status(thm)],[f_23_6]) ).
cnf(f_23_11,plain,
( in(U_215,U_223)
| ~ sP50(U_223,U_221,U_215) ),
inference(clausify,[status(thm)],[f_23_6]) ).
cnf(f_23_12,plain,
( in(U_215,U_221)
| ~ sP50(U_223,U_221,U_215) ),
inference(clausify,[status(thm)],[f_23_6]) ).
cnf(f_23_13,plain,
( in(sK42(U_224,U_222,U_220),U_220)
| ~ sP52(U_224,U_220,U_222) ),
inference(clausify,[status(thm)],[f_23_6]) ).
cnf(f_23_14,plain,
( ~ in(sK42(U_224,U_222,U_220),U_222)
| ~ in(sK42(U_224,U_222,U_220),U_224)
| ~ sP52(U_224,U_220,U_222) ),
inference(clausify,[status(thm)],[f_23_6]) ).
cnf(f_23_15,plain,
( in(sK43(U_224,U_222,U_220),U_224)
| ~ sP53(U_224,U_220,U_222) ),
inference(clausify,[status(thm)],[f_23_6]) ).
cnf(f_23_16,plain,
( in(sK43(U_224,U_222,U_220),U_222)
| ~ sP53(U_224,U_220,U_222) ),
inference(clausify,[status(thm)],[f_23_6]) ).
cnf(f_23_17,plain,
( ~ in(sK43(U_224,U_222,U_220),U_220)
| ~ sP53(U_224,U_220,U_222) ),
inference(clausify,[status(thm)],[f_23_6]) ).
fof(f_24_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_24_2,plain,
! [U_232] :
( ! [U_231] :
( ( U_231 = relation_dom(U_232)
| ? [U_230] :
( ( ~ in(U_230,U_231)
& ? [U_229] : in(ordered_pair(U_230,U_229),U_232) )
| ( ! [U_228] : ~ in(ordered_pair(U_230,U_228),U_232)
& in(U_230,U_231) ) ) )
& ( ! [U_227] :
( ( in(U_227,U_231)
| ! [U_226] : ~ in(ordered_pair(U_227,U_226),U_232) )
& ( ? [U_225] : in(ordered_pair(U_227,U_225),U_232)
| ~ in(U_227,U_231) ) )
| U_231 != relation_dom(U_232) ) )
| ~ relation(U_232) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_232] :
( ( ! [U_238] :
( U_238 = relation_dom(U_232)
| ? [U_236] :
( ~ in(U_236,U_238)
& ? [U_229] : in(ordered_pair(U_236,U_229),U_232) )
| ? [U_235] :
( ! [U_228] : ~ in(ordered_pair(U_235,U_228),U_232)
& in(U_235,U_238) ) )
& ! [U_237] :
( ( ! [U_234] :
( in(U_234,U_237)
| ! [U_226] : ~ in(ordered_pair(U_234,U_226),U_232) )
& ! [U_233] :
( ? [U_225] : in(ordered_pair(U_233,U_225),U_232)
| ~ in(U_233,U_237) ) )
| U_237 != relation_dom(U_232) ) )
| ~ relation(U_232) ),
inference(miniscope,[status(thm)],[f_24_2]) ).
fof(f_24_4,plain,
! [U_232] :
( ( ! [U_238] :
( U_238 = relation_dom(U_232)
| ? [U_236] :
( ~ in(U_236,U_238)
& ? [U_229] : in(ordered_pair(U_236,U_229),U_232) )
| ? [U_235] :
( ! [U_228] : ~ in(ordered_pair(U_235,U_228),U_232)
& in(U_235,U_238) ) )
& ! [U_237] :
( ( ! [U_234] :
( in(U_234,U_237)
| ! [U_226] : ~ in(ordered_pair(U_234,U_226),U_232) )
& ! [U_233] :
( in(ordered_pair(U_233,sK44(U_232,U_237,U_233)),U_232)
| ~ in(U_233,U_237) ) )
| U_237 != relation_dom(U_232) ) )
| ~ relation(U_232) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_225,sK44(U_232,U_237,U_233))],[f_24_3]) ).
fof(f_24_5,plain,
! [U_232] :
( ( ! [U_238] :
( U_238 = relation_dom(U_232)
| ? [U_236] :
( ~ in(U_236,U_238)
& ? [U_229] : in(ordered_pair(U_236,U_229),U_232) )
| ( ! [U_228] : ~ in(ordered_pair(sK45(U_232,U_238),U_228),U_232)
& in(sK45(U_232,U_238),U_238) ) )
& ! [U_237] :
( ( ! [U_234] :
( in(U_234,U_237)
| ! [U_226] : ~ in(ordered_pair(U_234,U_226),U_232) )
& ! [U_233] :
( in(ordered_pair(U_233,sK44(U_232,U_237,U_233)),U_232)
| ~ in(U_233,U_237) ) )
| U_237 != relation_dom(U_232) ) )
| ~ relation(U_232) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_235,sK45(U_232,U_238))],[f_24_4]) ).
fof(f_24_6,plain,
! [U_232] :
( ( ! [U_238] :
( U_238 = relation_dom(U_232)
| ( ~ in(sK46(U_232,U_238),U_238)
& ? [U_229] : in(ordered_pair(sK46(U_232,U_238),U_229),U_232) )
| ( ! [U_228] : ~ in(ordered_pair(sK45(U_232,U_238),U_228),U_232)
& in(sK45(U_232,U_238),U_238) ) )
& ! [U_237] :
( ( ! [U_234] :
( in(U_234,U_237)
| ! [U_226] : ~ in(ordered_pair(U_234,U_226),U_232) )
& ! [U_233] :
( in(ordered_pair(U_233,sK44(U_232,U_237,U_233)),U_232)
| ~ in(U_233,U_237) ) )
| U_237 != relation_dom(U_232) ) )
| ~ relation(U_232) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_236,sK46(U_232,U_238))],[f_24_5]) ).
fof(f_24_7,plain,
! [U_232] :
( ( ! [U_238] :
( U_238 = relation_dom(U_232)
| ( ~ in(sK46(U_232,U_238),U_238)
& in(ordered_pair(sK46(U_232,U_238),sK47(U_232,U_238)),U_232) )
| ( ! [U_228] : ~ in(ordered_pair(sK45(U_232,U_238),U_228),U_232)
& in(sK45(U_232,U_238),U_238) ) )
& ! [U_237] :
( ( ! [U_234] :
( in(U_234,U_237)
| ! [U_226] : ~ in(ordered_pair(U_234,U_226),U_232) )
& ! [U_233] :
( in(ordered_pair(U_233,sK44(U_232,U_237,U_233)),U_232)
| ~ in(U_233,U_237) ) )
| U_237 != relation_dom(U_232) ) )
| ~ relation(U_232) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_229,sK47(U_232,U_238))],[f_24_6]) ).
fof(f_24_8,plain,
( ! [U_238,U_232] :
( ~ in(sK46(U_232,U_238),U_238)
| ~ sP56(U_238,U_232) )
& ! [U_238,U_232] :
( in(ordered_pair(sK46(U_232,U_238),sK47(U_232,U_238)),U_232)
| ~ sP56(U_238,U_232) )
& ! [U_228,U_238,U_232] :
( ~ in(ordered_pair(sK45(U_232,U_238),U_228),U_232)
| ~ sP55(U_228,U_238,U_232) )
& ! [U_228,U_238,U_232] :
( in(sK45(U_232,U_238),U_238)
| ~ sP55(U_228,U_238,U_232) )
& ! [U_237,U_233,U_234,U_226,U_232] :
( in(U_234,U_237)
| ~ in(ordered_pair(U_234,U_226),U_232)
| ~ sP54(U_237,U_233,U_234,U_226,U_232) )
& ! [U_237,U_233,U_234,U_226,U_232] :
( in(ordered_pair(U_233,sK44(U_232,U_237,U_233)),U_232)
| ~ in(U_233,U_237)
| ~ sP54(U_237,U_233,U_234,U_226,U_232) )
& ! [U_228,U_237,U_233,U_234,U_238,U_226,U_232] :
( U_238 = relation_dom(U_232)
| sP56(U_238,U_232)
| sP55(U_228,U_238,U_232)
| ~ sP57(U_228,U_237,U_233,U_234,U_238,U_226,U_232) )
& ! [U_228,U_237,U_233,U_234,U_238,U_226,U_232] :
( sP54(U_237,U_233,U_234,U_226,U_232)
| U_237 != relation_dom(U_232)
| ~ sP57(U_228,U_237,U_233,U_234,U_238,U_226,U_232) )
& ! [U_228,U_237,U_233,U_234,U_238,U_226,U_232] :
( sP57(U_228,U_237,U_233,U_234,U_238,U_226,U_232)
| ~ relation(U_232) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP54,sP55,sP56,sP57])],[f_24_7]) ).
cnf(f_24_9,plain,
( sP57(U_228,U_237,U_233,U_234,U_238,U_226,U_232)
| ~ relation(U_232) ),
inference(clausify,[status(thm)],[f_24_8]) ).
cnf(f_24_10,plain,
( sP54(U_237,U_233,U_234,U_226,U_232)
| U_237 != relation_dom(U_232)
| ~ sP57(U_228,U_237,U_233,U_234,U_238,U_226,U_232) ),
inference(clausify,[status(thm)],[f_24_8]) ).
cnf(f_24_11,plain,
( U_238 = relation_dom(U_232)
| sP56(U_238,U_232)
| sP55(U_228,U_238,U_232)
| ~ sP57(U_228,U_237,U_233,U_234,U_238,U_226,U_232) ),
inference(clausify,[status(thm)],[f_24_8]) ).
cnf(f_24_12,plain,
( in(ordered_pair(U_233,sK44(U_232,U_237,U_233)),U_232)
| ~ in(U_233,U_237)
| ~ sP54(U_237,U_233,U_234,U_226,U_232) ),
inference(clausify,[status(thm)],[f_24_8]) ).
cnf(f_24_13,plain,
( in(U_234,U_237)
| ~ in(ordered_pair(U_234,U_226),U_232)
| ~ sP54(U_237,U_233,U_234,U_226,U_232) ),
inference(clausify,[status(thm)],[f_24_8]) ).
cnf(f_24_14,plain,
( in(sK45(U_232,U_238),U_238)
| ~ sP55(U_228,U_238,U_232) ),
inference(clausify,[status(thm)],[f_24_8]) ).
cnf(f_24_15,plain,
( ~ in(ordered_pair(sK45(U_232,U_238),U_228),U_232)
| ~ sP55(U_228,U_238,U_232) ),
inference(clausify,[status(thm)],[f_24_8]) ).
cnf(f_24_16,plain,
( in(ordered_pair(sK46(U_232,U_238),sK47(U_232,U_238)),U_232)
| ~ sP56(U_238,U_232) ),
inference(clausify,[status(thm)],[f_24_8]) ).
cnf(f_24_17,plain,
( ~ in(sK46(U_232,U_238),U_238)
| ~ sP56(U_238,U_232) ),
inference(clausify,[status(thm)],[f_24_8]) ).
fof(f_25_1,plain,
! [A] : cast_to_subset(A) = A,
inference(fof_nnf,[status(thm)],[d4_subset_1]) ).
fof(f_25_2,plain,
! [U_239] : cast_to_subset(U_239) = U_239,
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_239] : cast_to_subset(U_239) = U_239,
inference(definitional_conversion,[status(esa)],[f_25_2]) ).
cnf(f_25_4,plain,
cast_to_subset(U_239) = U_239,
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_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_26_2,plain,
! [U_247,U_246] :
( ( U_246 = union(U_247)
| ? [U_245] :
( ( ~ in(U_245,U_246)
& ? [U_244] :
( in(U_244,U_247)
& in(U_245,U_244) ) )
| ( ! [U_243] :
( ~ in(U_243,U_247)
| ~ in(U_245,U_243) )
& in(U_245,U_246) ) ) )
& ( ! [U_242] :
( ( in(U_242,U_246)
| ! [U_241] :
( ~ in(U_241,U_247)
| ~ in(U_242,U_241) ) )
& ( ? [U_240] :
( in(U_240,U_247)
& in(U_242,U_240) )
| ~ in(U_242,U_246) ) )
| U_246 != union(U_247) ) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( ! [U_255,U_253] :
( U_253 = union(U_255)
| ? [U_251] :
( ~ in(U_251,U_253)
& ? [U_244] :
( in(U_244,U_255)
& in(U_251,U_244) ) )
| ? [U_250] :
( ! [U_243] :
( ~ in(U_243,U_255)
| ~ in(U_250,U_243) )
& in(U_250,U_253) ) )
& ! [U_254,U_252] :
( ( ! [U_249] :
( in(U_249,U_252)
| ! [U_241] :
( ~ in(U_241,U_254)
| ~ in(U_249,U_241) ) )
& ! [U_248] :
( ? [U_240] :
( in(U_240,U_254)
& in(U_248,U_240) )
| ~ in(U_248,U_252) ) )
| U_252 != union(U_254) ) ),
inference(miniscope,[status(thm)],[f_26_2]) ).
fof(f_26_4,plain,
( ! [U_255,U_253] :
( U_253 = union(U_255)
| ? [U_251] :
( ~ in(U_251,U_253)
& ? [U_244] :
( in(U_244,U_255)
& in(U_251,U_244) ) )
| ? [U_250] :
( ! [U_243] :
( ~ in(U_243,U_255)
| ~ in(U_250,U_243) )
& in(U_250,U_253) ) )
& ! [U_254,U_252] :
( ( ! [U_249] :
( in(U_249,U_252)
| ! [U_241] :
( ~ in(U_241,U_254)
| ~ in(U_249,U_241) ) )
& ! [U_248] :
( ( in(sK48(U_254,U_252,U_248),U_254)
& in(U_248,sK48(U_254,U_252,U_248)) )
| ~ in(U_248,U_252) ) )
| U_252 != union(U_254) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_240,sK48(U_254,U_252,U_248))],[f_26_3]) ).
fof(f_26_5,plain,
( ! [U_255,U_253] :
( U_253 = union(U_255)
| ? [U_251] :
( ~ in(U_251,U_253)
& ? [U_244] :
( in(U_244,U_255)
& in(U_251,U_244) ) )
| ( ! [U_243] :
( ~ in(U_243,U_255)
| ~ in(sK49(U_255,U_253),U_243) )
& in(sK49(U_255,U_253),U_253) ) )
& ! [U_254,U_252] :
( ( ! [U_249] :
( in(U_249,U_252)
| ! [U_241] :
( ~ in(U_241,U_254)
| ~ in(U_249,U_241) ) )
& ! [U_248] :
( ( in(sK48(U_254,U_252,U_248),U_254)
& in(U_248,sK48(U_254,U_252,U_248)) )
| ~ in(U_248,U_252) ) )
| U_252 != union(U_254) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_250,sK49(U_255,U_253))],[f_26_4]) ).
fof(f_26_6,plain,
( ! [U_255,U_253] :
( U_253 = union(U_255)
| ( ~ in(sK50(U_255,U_253),U_253)
& ? [U_244] :
( in(U_244,U_255)
& in(sK50(U_255,U_253),U_244) ) )
| ( ! [U_243] :
( ~ in(U_243,U_255)
| ~ in(sK49(U_255,U_253),U_243) )
& in(sK49(U_255,U_253),U_253) ) )
& ! [U_254,U_252] :
( ( ! [U_249] :
( in(U_249,U_252)
| ! [U_241] :
( ~ in(U_241,U_254)
| ~ in(U_249,U_241) ) )
& ! [U_248] :
( ( in(sK48(U_254,U_252,U_248),U_254)
& in(U_248,sK48(U_254,U_252,U_248)) )
| ~ in(U_248,U_252) ) )
| U_252 != union(U_254) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_251,sK50(U_255,U_253))],[f_26_5]) ).
fof(f_26_7,plain,
( ! [U_255,U_253] :
( U_253 = union(U_255)
| ( ~ in(sK50(U_255,U_253),U_253)
& in(sK51(U_255,U_253),U_255)
& in(sK50(U_255,U_253),sK51(U_255,U_253)) )
| ( ! [U_243] :
( ~ in(U_243,U_255)
| ~ in(sK49(U_255,U_253),U_243) )
& in(sK49(U_255,U_253),U_253) ) )
& ! [U_254,U_252] :
( ( ! [U_249] :
( in(U_249,U_252)
| ! [U_241] :
( ~ in(U_241,U_254)
| ~ in(U_249,U_241) ) )
& ! [U_248] :
( ( in(sK48(U_254,U_252,U_248),U_254)
& in(U_248,sK48(U_254,U_252,U_248)) )
| ~ in(U_248,U_252) ) )
| U_252 != union(U_254) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_244,sK51(U_255,U_253))],[f_26_6]) ).
fof(f_26_8,plain,
( ! [U_253,U_255] :
( ~ in(sK50(U_255,U_253),U_253)
| ~ sP61(U_253,U_255) )
& ! [U_253,U_255] :
( in(sK51(U_255,U_253),U_255)
| ~ sP61(U_253,U_255) )
& ! [U_253,U_255] :
( in(sK50(U_255,U_253),sK51(U_255,U_253))
| ~ sP61(U_253,U_255) )
& ! [U_243,U_253,U_255] :
( ~ in(U_243,U_255)
| ~ in(sK49(U_255,U_253),U_243)
| ~ sP60(U_243,U_253,U_255) )
& ! [U_243,U_253,U_255] :
( in(sK49(U_255,U_253),U_253)
| ~ sP60(U_243,U_253,U_255) )
& ! [U_254,U_252,U_248] :
( in(sK48(U_254,U_252,U_248),U_254)
| ~ sP58(U_254,U_252,U_248) )
& ! [U_254,U_252,U_248] :
( in(U_248,sK48(U_254,U_252,U_248))
| ~ sP58(U_254,U_252,U_248) )
& ! [U_241,U_249,U_254,U_252,U_248] :
( in(U_249,U_252)
| ~ in(U_241,U_254)
| ~ in(U_249,U_241)
| ~ sP59(U_241,U_249,U_254,U_252,U_248) )
& ! [U_241,U_249,U_254,U_252,U_248] :
( sP58(U_254,U_252,U_248)
| ~ in(U_248,U_252)
| ~ sP59(U_241,U_249,U_254,U_252,U_248) )
& ! [U_243,U_253,U_255] :
( U_253 = union(U_255)
| sP61(U_253,U_255)
| sP60(U_243,U_253,U_255) )
& ! [U_241,U_249,U_254,U_252,U_248] :
( sP59(U_241,U_249,U_254,U_252,U_248)
| U_252 != union(U_254) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP58,sP59,sP60,sP61])],[f_26_7]) ).
cnf(f_26_9,plain,
( sP59(U_241,U_249,U_254,U_252,U_248)
| U_252 != union(U_254) ),
inference(clausify,[status(thm)],[f_26_8]) ).
cnf(f_26_10,plain,
( U_253 = union(U_255)
| sP61(U_253,U_255)
| sP60(U_243,U_253,U_255) ),
inference(clausify,[status(thm)],[f_26_8]) ).
cnf(f_26_11,plain,
( sP58(U_254,U_252,U_248)
| ~ in(U_248,U_252)
| ~ sP59(U_241,U_249,U_254,U_252,U_248) ),
inference(clausify,[status(thm)],[f_26_8]) ).
cnf(f_26_12,plain,
( in(U_249,U_252)
| ~ in(U_241,U_254)
| ~ in(U_249,U_241)
| ~ sP59(U_241,U_249,U_254,U_252,U_248) ),
inference(clausify,[status(thm)],[f_26_8]) ).
cnf(f_26_13,plain,
( in(U_248,sK48(U_254,U_252,U_248))
| ~ sP58(U_254,U_252,U_248) ),
inference(clausify,[status(thm)],[f_26_8]) ).
cnf(f_26_14,plain,
( in(sK48(U_254,U_252,U_248),U_254)
| ~ sP58(U_254,U_252,U_248) ),
inference(clausify,[status(thm)],[f_26_8]) ).
cnf(f_26_15,plain,
( in(sK49(U_255,U_253),U_253)
| ~ sP60(U_243,U_253,U_255) ),
inference(clausify,[status(thm)],[f_26_8]) ).
cnf(f_26_16,plain,
( ~ in(U_243,U_255)
| ~ in(sK49(U_255,U_253),U_243)
| ~ sP60(U_243,U_253,U_255) ),
inference(clausify,[status(thm)],[f_26_8]) ).
cnf(f_26_17,plain,
( in(sK50(U_255,U_253),sK51(U_255,U_253))
| ~ sP61(U_253,U_255) ),
inference(clausify,[status(thm)],[f_26_8]) ).
cnf(f_26_18,plain,
( in(sK51(U_255,U_253),U_255)
| ~ sP61(U_253,U_255) ),
inference(clausify,[status(thm)],[f_26_8]) ).
cnf(f_26_19,plain,
( ~ in(sK50(U_255,U_253),U_253)
| ~ sP61(U_253,U_255) ),
inference(clausify,[status(thm)],[f_26_8]) ).
fof(f_27_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_27_2,plain,
! [U_260,U_259,U_258] :
( ( U_258 = set_difference(U_260,U_259)
| ? [U_257] :
( ( ~ in(U_257,U_258)
& ~ in(U_257,U_259)
& in(U_257,U_260) )
| ( ( in(U_257,U_259)
| ~ in(U_257,U_260) )
& in(U_257,U_258) ) ) )
& ( ! [U_256] :
( ( in(U_256,U_258)
| in(U_256,U_259)
| ~ in(U_256,U_260) )
& ( ( ~ in(U_256,U_259)
& in(U_256,U_260) )
| ~ in(U_256,U_258) ) )
| U_258 != set_difference(U_260,U_259) ) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( ! [U_270,U_268,U_266] :
( U_266 = set_difference(U_270,U_268)
| ? [U_264] :
( ~ in(U_264,U_266)
& ~ in(U_264,U_268)
& in(U_264,U_270) )
| ? [U_263] :
( ( in(U_263,U_268)
| ~ in(U_263,U_270) )
& in(U_263,U_266) ) )
& ! [U_269,U_267,U_265] :
( ( ! [U_262] :
( in(U_262,U_265)
| in(U_262,U_267)
| ~ in(U_262,U_269) )
& ! [U_261] :
( ( ~ in(U_261,U_267)
& in(U_261,U_269) )
| ~ in(U_261,U_265) ) )
| U_265 != set_difference(U_269,U_267) ) ),
inference(miniscope,[status(thm)],[f_27_2]) ).
fof(f_27_4,plain,
( ! [U_270,U_268,U_266] :
( U_266 = set_difference(U_270,U_268)
| ? [U_264] :
( ~ in(U_264,U_266)
& ~ in(U_264,U_268)
& in(U_264,U_270) )
| ( ( in(sK52(U_270,U_268,U_266),U_268)
| ~ in(sK52(U_270,U_268,U_266),U_270) )
& in(sK52(U_270,U_268,U_266),U_266) ) )
& ! [U_269,U_267,U_265] :
( ( ! [U_262] :
( in(U_262,U_265)
| in(U_262,U_267)
| ~ in(U_262,U_269) )
& ! [U_261] :
( ( ~ in(U_261,U_267)
& in(U_261,U_269) )
| ~ in(U_261,U_265) ) )
| U_265 != set_difference(U_269,U_267) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_263,sK52(U_270,U_268,U_266))],[f_27_3]) ).
fof(f_27_5,plain,
( ! [U_270,U_268,U_266] :
( U_266 = set_difference(U_270,U_268)
| ( ~ in(sK53(U_270,U_268,U_266),U_266)
& ~ in(sK53(U_270,U_268,U_266),U_268)
& in(sK53(U_270,U_268,U_266),U_270) )
| ( ( in(sK52(U_270,U_268,U_266),U_268)
| ~ in(sK52(U_270,U_268,U_266),U_270) )
& in(sK52(U_270,U_268,U_266),U_266) ) )
& ! [U_269,U_267,U_265] :
( ( ! [U_262] :
( in(U_262,U_265)
| in(U_262,U_267)
| ~ in(U_262,U_269) )
& ! [U_261] :
( ( ~ in(U_261,U_267)
& in(U_261,U_269) )
| ~ in(U_261,U_265) ) )
| U_265 != set_difference(U_269,U_267) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_264,sK53(U_270,U_268,U_266))],[f_27_4]) ).
fof(f_27_6,plain,
( ! [U_268,U_266,U_270] :
( ~ in(sK53(U_270,U_268,U_266),U_266)
| ~ sP65(U_268,U_266,U_270) )
& ! [U_268,U_266,U_270] :
( ~ in(sK53(U_270,U_268,U_266),U_268)
| ~ sP65(U_268,U_266,U_270) )
& ! [U_268,U_266,U_270] :
( in(sK53(U_270,U_268,U_266),U_270)
| ~ sP65(U_268,U_266,U_270) )
& ! [U_268,U_266,U_270] :
( in(sK52(U_270,U_268,U_266),U_268)
| ~ in(sK52(U_270,U_268,U_266),U_270)
| ~ sP64(U_268,U_266,U_270) )
& ! [U_268,U_266,U_270] :
( in(sK52(U_270,U_268,U_266),U_266)
| ~ sP64(U_268,U_266,U_270) )
& ! [U_267,U_261,U_269] :
( ~ in(U_261,U_267)
| ~ sP62(U_267,U_261,U_269) )
& ! [U_267,U_261,U_269] :
( in(U_261,U_269)
| ~ sP62(U_267,U_261,U_269) )
& ! [U_267,U_261,U_265,U_262,U_269] :
( in(U_262,U_265)
| in(U_262,U_267)
| ~ in(U_262,U_269)
| ~ sP63(U_267,U_261,U_265,U_262,U_269) )
& ! [U_267,U_261,U_265,U_262,U_269] :
( sP62(U_267,U_261,U_269)
| ~ in(U_261,U_265)
| ~ sP63(U_267,U_261,U_265,U_262,U_269) )
& ! [U_268,U_266,U_270] :
( U_266 = set_difference(U_270,U_268)
| sP65(U_268,U_266,U_270)
| sP64(U_268,U_266,U_270) )
& ! [U_267,U_261,U_265,U_262,U_269] :
( sP63(U_267,U_261,U_265,U_262,U_269)
| U_265 != set_difference(U_269,U_267) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP62,sP63,sP64,sP65])],[f_27_5]) ).
cnf(f_27_7,plain,
( sP63(U_267,U_261,U_265,U_262,U_269)
| U_265 != set_difference(U_269,U_267) ),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_8,plain,
( U_266 = set_difference(U_270,U_268)
| sP65(U_268,U_266,U_270)
| sP64(U_268,U_266,U_270) ),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_9,plain,
( sP62(U_267,U_261,U_269)
| ~ in(U_261,U_265)
| ~ sP63(U_267,U_261,U_265,U_262,U_269) ),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_10,plain,
( in(U_262,U_265)
| in(U_262,U_267)
| ~ in(U_262,U_269)
| ~ sP63(U_267,U_261,U_265,U_262,U_269) ),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_11,plain,
( in(U_261,U_269)
| ~ sP62(U_267,U_261,U_269) ),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_12,plain,
( ~ in(U_261,U_267)
| ~ sP62(U_267,U_261,U_269) ),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_13,plain,
( in(sK52(U_270,U_268,U_266),U_266)
| ~ sP64(U_268,U_266,U_270) ),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_14,plain,
( in(sK52(U_270,U_268,U_266),U_268)
| ~ in(sK52(U_270,U_268,U_266),U_270)
| ~ sP64(U_268,U_266,U_270) ),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_15,plain,
( in(sK53(U_270,U_268,U_266),U_270)
| ~ sP65(U_268,U_266,U_270) ),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_16,plain,
( ~ in(sK53(U_270,U_268,U_266),U_268)
| ~ sP65(U_268,U_266,U_270) ),
inference(clausify,[status(thm)],[f_27_6]) ).
cnf(f_27_17,plain,
( ~ in(sK53(U_270,U_268,U_266),U_266)
| ~ sP65(U_268,U_266,U_270) ),
inference(clausify,[status(thm)],[f_27_6]) ).
fof(f_28_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_28_2,plain,
! [U_278] :
( ! [U_277] :
( ( U_277 = relation_rng(U_278)
| ? [U_276] :
( ( ~ in(U_276,U_277)
& ? [U_275] : in(ordered_pair(U_275,U_276),U_278) )
| ( ! [U_274] : ~ in(ordered_pair(U_274,U_276),U_278)
& in(U_276,U_277) ) ) )
& ( ! [U_273] :
( ( in(U_273,U_277)
| ! [U_272] : ~ in(ordered_pair(U_272,U_273),U_278) )
& ( ? [U_271] : in(ordered_pair(U_271,U_273),U_278)
| ~ in(U_273,U_277) ) )
| U_277 != relation_rng(U_278) ) )
| ~ relation(U_278) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_278] :
( ( ! [U_284] :
( U_284 = relation_rng(U_278)
| ? [U_282] :
( ~ in(U_282,U_284)
& ? [U_275] : in(ordered_pair(U_275,U_282),U_278) )
| ? [U_281] :
( ! [U_274] : ~ in(ordered_pair(U_274,U_281),U_278)
& in(U_281,U_284) ) )
& ! [U_283] :
( ( ! [U_280] :
( in(U_280,U_283)
| ! [U_272] : ~ in(ordered_pair(U_272,U_280),U_278) )
& ! [U_279] :
( ? [U_271] : in(ordered_pair(U_271,U_279),U_278)
| ~ in(U_279,U_283) ) )
| U_283 != relation_rng(U_278) ) )
| ~ relation(U_278) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
fof(f_28_4,plain,
! [U_278] :
( ( ! [U_284] :
( U_284 = relation_rng(U_278)
| ? [U_282] :
( ~ in(U_282,U_284)
& ? [U_275] : in(ordered_pair(U_275,U_282),U_278) )
| ? [U_281] :
( ! [U_274] : ~ in(ordered_pair(U_274,U_281),U_278)
& in(U_281,U_284) ) )
& ! [U_283] :
( ( ! [U_280] :
( in(U_280,U_283)
| ! [U_272] : ~ in(ordered_pair(U_272,U_280),U_278) )
& ! [U_279] :
( in(ordered_pair(sK54(U_278,U_283,U_279),U_279),U_278)
| ~ in(U_279,U_283) ) )
| U_283 != relation_rng(U_278) ) )
| ~ relation(U_278) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_271,sK54(U_278,U_283,U_279))],[f_28_3]) ).
fof(f_28_5,plain,
! [U_278] :
( ( ! [U_284] :
( U_284 = relation_rng(U_278)
| ? [U_282] :
( ~ in(U_282,U_284)
& ? [U_275] : in(ordered_pair(U_275,U_282),U_278) )
| ( ! [U_274] : ~ in(ordered_pair(U_274,sK55(U_278,U_284)),U_278)
& in(sK55(U_278,U_284),U_284) ) )
& ! [U_283] :
( ( ! [U_280] :
( in(U_280,U_283)
| ! [U_272] : ~ in(ordered_pair(U_272,U_280),U_278) )
& ! [U_279] :
( in(ordered_pair(sK54(U_278,U_283,U_279),U_279),U_278)
| ~ in(U_279,U_283) ) )
| U_283 != relation_rng(U_278) ) )
| ~ relation(U_278) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_281,sK55(U_278,U_284))],[f_28_4]) ).
fof(f_28_6,plain,
! [U_278] :
( ( ! [U_284] :
( U_284 = relation_rng(U_278)
| ( ~ in(sK56(U_278,U_284),U_284)
& ? [U_275] : in(ordered_pair(U_275,sK56(U_278,U_284)),U_278) )
| ( ! [U_274] : ~ in(ordered_pair(U_274,sK55(U_278,U_284)),U_278)
& in(sK55(U_278,U_284),U_284) ) )
& ! [U_283] :
( ( ! [U_280] :
( in(U_280,U_283)
| ! [U_272] : ~ in(ordered_pair(U_272,U_280),U_278) )
& ! [U_279] :
( in(ordered_pair(sK54(U_278,U_283,U_279),U_279),U_278)
| ~ in(U_279,U_283) ) )
| U_283 != relation_rng(U_278) ) )
| ~ relation(U_278) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_282,sK56(U_278,U_284))],[f_28_5]) ).
fof(f_28_7,plain,
! [U_278] :
( ( ! [U_284] :
( U_284 = relation_rng(U_278)
| ( ~ in(sK56(U_278,U_284),U_284)
& in(ordered_pair(sK57(U_278,U_284),sK56(U_278,U_284)),U_278) )
| ( ! [U_274] : ~ in(ordered_pair(U_274,sK55(U_278,U_284)),U_278)
& in(sK55(U_278,U_284),U_284) ) )
& ! [U_283] :
( ( ! [U_280] :
( in(U_280,U_283)
| ! [U_272] : ~ in(ordered_pair(U_272,U_280),U_278) )
& ! [U_279] :
( in(ordered_pair(sK54(U_278,U_283,U_279),U_279),U_278)
| ~ in(U_279,U_283) ) )
| U_283 != relation_rng(U_278) ) )
| ~ relation(U_278) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_275,sK57(U_278,U_284))],[f_28_6]) ).
fof(f_28_8,plain,
( ! [U_284,U_278] :
( ~ in(sK56(U_278,U_284),U_284)
| ~ sP68(U_284,U_278) )
& ! [U_284,U_278] :
( in(ordered_pair(sK57(U_278,U_284),sK56(U_278,U_284)),U_278)
| ~ sP68(U_284,U_278) )
& ! [U_284,U_274,U_278] :
( ~ in(ordered_pair(U_274,sK55(U_278,U_284)),U_278)
| ~ sP67(U_284,U_274,U_278) )
& ! [U_284,U_274,U_278] :
( in(sK55(U_278,U_284),U_284)
| ~ sP67(U_284,U_274,U_278) )
& ! [U_283,U_279,U_280,U_278,U_272] :
( in(U_280,U_283)
| ~ in(ordered_pair(U_272,U_280),U_278)
| ~ sP66(U_283,U_279,U_280,U_278,U_272) )
& ! [U_283,U_279,U_280,U_278,U_272] :
( in(ordered_pair(sK54(U_278,U_283,U_279),U_279),U_278)
| ~ in(U_279,U_283)
| ~ sP66(U_283,U_279,U_280,U_278,U_272) )
& ! [U_283,U_284,U_279,U_280,U_274,U_278,U_272] :
( U_284 = relation_rng(U_278)
| sP68(U_284,U_278)
| sP67(U_284,U_274,U_278)
| ~ sP69(U_283,U_284,U_279,U_280,U_274,U_278,U_272) )
& ! [U_283,U_284,U_279,U_280,U_274,U_278,U_272] :
( sP66(U_283,U_279,U_280,U_278,U_272)
| U_283 != relation_rng(U_278)
| ~ sP69(U_283,U_284,U_279,U_280,U_274,U_278,U_272) )
& ! [U_283,U_284,U_279,U_280,U_274,U_278,U_272] :
( sP69(U_283,U_284,U_279,U_280,U_274,U_278,U_272)
| ~ relation(U_278) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP66,sP67,sP68,sP69])],[f_28_7]) ).
cnf(f_28_9,plain,
( sP69(U_283,U_284,U_279,U_280,U_274,U_278,U_272)
| ~ relation(U_278) ),
inference(clausify,[status(thm)],[f_28_8]) ).
cnf(f_28_10,plain,
( sP66(U_283,U_279,U_280,U_278,U_272)
| U_283 != relation_rng(U_278)
| ~ sP69(U_283,U_284,U_279,U_280,U_274,U_278,U_272) ),
inference(clausify,[status(thm)],[f_28_8]) ).
cnf(f_28_11,plain,
( U_284 = relation_rng(U_278)
| sP68(U_284,U_278)
| sP67(U_284,U_274,U_278)
| ~ sP69(U_283,U_284,U_279,U_280,U_274,U_278,U_272) ),
inference(clausify,[status(thm)],[f_28_8]) ).
cnf(f_28_12,plain,
( in(ordered_pair(sK54(U_278,U_283,U_279),U_279),U_278)
| ~ in(U_279,U_283)
| ~ sP66(U_283,U_279,U_280,U_278,U_272) ),
inference(clausify,[status(thm)],[f_28_8]) ).
cnf(f_28_13,plain,
( in(U_280,U_283)
| ~ in(ordered_pair(U_272,U_280),U_278)
| ~ sP66(U_283,U_279,U_280,U_278,U_272) ),
inference(clausify,[status(thm)],[f_28_8]) ).
cnf(f_28_14,plain,
( in(sK55(U_278,U_284),U_284)
| ~ sP67(U_284,U_274,U_278) ),
inference(clausify,[status(thm)],[f_28_8]) ).
cnf(f_28_15,plain,
( ~ in(ordered_pair(U_274,sK55(U_278,U_284)),U_278)
| ~ sP67(U_284,U_274,U_278) ),
inference(clausify,[status(thm)],[f_28_8]) ).
cnf(f_28_16,plain,
( in(ordered_pair(sK57(U_278,U_284),sK56(U_278,U_284)),U_278)
| ~ sP68(U_284,U_278) ),
inference(clausify,[status(thm)],[f_28_8]) ).
cnf(f_28_17,plain,
( ~ in(sK56(U_278,U_284),U_284)
| ~ sP68(U_284,U_278) ),
inference(clausify,[status(thm)],[f_28_8]) ).
fof(f_29_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_29_2,plain,
! [U_286,U_285] :
( subset_complement(U_286,U_285) = set_difference(U_286,U_285)
| ~ element(U_285,powerset(U_286)) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_286,U_285] :
( subset_complement(U_286,U_285) = set_difference(U_286,U_285)
| ~ element(U_285,powerset(U_286)) ),
inference(definitional_conversion,[status(esa)],[f_29_2]) ).
cnf(f_29_4,plain,
( subset_complement(U_286,U_285) = set_difference(U_286,U_285)
| ~ element(U_285,powerset(U_286)) ),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_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_30_2,plain,
! [U_288,U_287] : ordered_pair(U_288,U_287) = unordered_pair(unordered_pair(U_288,U_287),singleton(U_288)),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_288,U_287] : ordered_pair(U_288,U_287) = unordered_pair(unordered_pair(U_288,U_287),singleton(U_288)),
inference(definitional_conversion,[status(esa)],[f_30_2]) ).
cnf(f_30_4,plain,
ordered_pair(U_288,U_287) = unordered_pair(unordered_pair(U_288,U_287),singleton(U_288)),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_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_31_2,plain,
! [U_289] :
( relation_field(U_289) = set_union2(relation_dom(U_289),relation_rng(U_289))
| ~ relation(U_289) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_289] :
( relation_field(U_289) = set_union2(relation_dom(U_289),relation_rng(U_289))
| ~ relation(U_289) ),
inference(definitional_conversion,[status(esa)],[f_31_2]) ).
cnf(f_31_4,plain,
( relation_field(U_289) = set_union2(relation_dom(U_289),relation_rng(U_289))
| ~ relation(U_289) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_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_32_2,plain,
! [U_295] :
( ! [U_294] :
( ( ( U_294 = relation_inverse(U_295)
| ? [U_293,U_292] :
( ( ~ in(ordered_pair(U_293,U_292),U_294)
& in(ordered_pair(U_292,U_293),U_295) )
| ( ~ in(ordered_pair(U_292,U_293),U_295)
& in(ordered_pair(U_293,U_292),U_294) ) ) )
& ( ! [U_291,U_290] :
( ( in(ordered_pair(U_291,U_290),U_294)
| ~ in(ordered_pair(U_290,U_291),U_295) )
& ( in(ordered_pair(U_290,U_291),U_295)
| ~ in(ordered_pair(U_291,U_290),U_294) ) )
| U_294 != relation_inverse(U_295) ) )
| ~ relation(U_294) )
| ~ relation(U_295) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_295] :
( ! [U_294] :
( ( ( U_294 = relation_inverse(U_295)
| ? [U_303,U_301] :
( ~ in(ordered_pair(U_303,U_301),U_294)
& in(ordered_pair(U_301,U_303),U_295) )
| ? [U_302,U_300] :
( ~ in(ordered_pair(U_300,U_302),U_295)
& in(ordered_pair(U_302,U_300),U_294) ) )
& ( ( ! [U_299,U_297] :
( in(ordered_pair(U_299,U_297),U_294)
| ~ in(ordered_pair(U_297,U_299),U_295) )
& ! [U_298,U_296] :
( in(ordered_pair(U_296,U_298),U_295)
| ~ in(ordered_pair(U_298,U_296),U_294) ) )
| U_294 != relation_inverse(U_295) ) )
| ~ relation(U_294) )
| ~ relation(U_295) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
fof(f_32_4,plain,
! [U_295] :
( ! [U_294] :
( ( ( U_294 = relation_inverse(U_295)
| ? [U_303,U_301] :
( ~ in(ordered_pair(U_303,U_301),U_294)
& in(ordered_pair(U_301,U_303),U_295) )
| ? [U_300] :
( ~ in(ordered_pair(U_300,sK58(U_295,U_294)),U_295)
& in(ordered_pair(sK58(U_295,U_294),U_300),U_294) ) )
& ( ( ! [U_299,U_297] :
( in(ordered_pair(U_299,U_297),U_294)
| ~ in(ordered_pair(U_297,U_299),U_295) )
& ! [U_298,U_296] :
( in(ordered_pair(U_296,U_298),U_295)
| ~ in(ordered_pair(U_298,U_296),U_294) ) )
| U_294 != relation_inverse(U_295) ) )
| ~ relation(U_294) )
| ~ relation(U_295) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_302,sK58(U_295,U_294))],[f_32_3]) ).
fof(f_32_5,plain,
! [U_295] :
( ! [U_294] :
( ( ( U_294 = relation_inverse(U_295)
| ? [U_303,U_301] :
( ~ in(ordered_pair(U_303,U_301),U_294)
& in(ordered_pair(U_301,U_303),U_295) )
| ( ~ in(ordered_pair(sK59(U_295,U_294),sK58(U_295,U_294)),U_295)
& in(ordered_pair(sK58(U_295,U_294),sK59(U_295,U_294)),U_294) ) )
& ( ( ! [U_299,U_297] :
( in(ordered_pair(U_299,U_297),U_294)
| ~ in(ordered_pair(U_297,U_299),U_295) )
& ! [U_298,U_296] :
( in(ordered_pair(U_296,U_298),U_295)
| ~ in(ordered_pair(U_298,U_296),U_294) ) )
| U_294 != relation_inverse(U_295) ) )
| ~ relation(U_294) )
| ~ relation(U_295) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_300,sK59(U_295,U_294))],[f_32_4]) ).
fof(f_32_6,plain,
! [U_295] :
( ! [U_294] :
( ( ( U_294 = relation_inverse(U_295)
| ? [U_301] :
( ~ in(ordered_pair(sK60(U_295,U_294),U_301),U_294)
& in(ordered_pair(U_301,sK60(U_295,U_294)),U_295) )
| ( ~ in(ordered_pair(sK59(U_295,U_294),sK58(U_295,U_294)),U_295)
& in(ordered_pair(sK58(U_295,U_294),sK59(U_295,U_294)),U_294) ) )
& ( ( ! [U_299,U_297] :
( in(ordered_pair(U_299,U_297),U_294)
| ~ in(ordered_pair(U_297,U_299),U_295) )
& ! [U_298,U_296] :
( in(ordered_pair(U_296,U_298),U_295)
| ~ in(ordered_pair(U_298,U_296),U_294) ) )
| U_294 != relation_inverse(U_295) ) )
| ~ relation(U_294) )
| ~ relation(U_295) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_303,sK60(U_295,U_294))],[f_32_5]) ).
fof(f_32_7,plain,
! [U_295] :
( ! [U_294] :
( ( ( U_294 = relation_inverse(U_295)
| ( ~ in(ordered_pair(sK60(U_295,U_294),sK61(U_295,U_294)),U_294)
& in(ordered_pair(sK61(U_295,U_294),sK60(U_295,U_294)),U_295) )
| ( ~ in(ordered_pair(sK59(U_295,U_294),sK58(U_295,U_294)),U_295)
& in(ordered_pair(sK58(U_295,U_294),sK59(U_295,U_294)),U_294) ) )
& ( ( ! [U_299,U_297] :
( in(ordered_pair(U_299,U_297),U_294)
| ~ in(ordered_pair(U_297,U_299),U_295) )
& ! [U_298,U_296] :
( in(ordered_pair(U_296,U_298),U_295)
| ~ in(ordered_pair(U_298,U_296),U_294) ) )
| U_294 != relation_inverse(U_295) ) )
| ~ relation(U_294) )
| ~ relation(U_295) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_301,sK61(U_295,U_294))],[f_32_6]) ).
fof(f_32_8,plain,
( ! [U_294,U_295] :
( ~ in(ordered_pair(sK60(U_295,U_294),sK61(U_295,U_294)),U_294)
| ~ sP72(U_294,U_295) )
& ! [U_294,U_295] :
( in(ordered_pair(sK61(U_295,U_294),sK60(U_295,U_294)),U_295)
| ~ sP72(U_294,U_295) )
& ! [U_294,U_295] :
( ~ in(ordered_pair(sK59(U_295,U_294),sK58(U_295,U_294)),U_295)
| ~ sP71(U_294,U_295) )
& ! [U_294,U_295] :
( in(ordered_pair(sK58(U_295,U_294),sK59(U_295,U_294)),U_294)
| ~ sP71(U_294,U_295) )
& ! [U_299,U_298,U_294,U_295,U_296,U_297] :
( in(ordered_pair(U_299,U_297),U_294)
| ~ in(ordered_pair(U_297,U_299),U_295)
| ~ sP70(U_299,U_298,U_294,U_295,U_296,U_297) )
& ! [U_299,U_298,U_294,U_295,U_296,U_297] :
( in(ordered_pair(U_296,U_298),U_295)
| ~ in(ordered_pair(U_298,U_296),U_294)
| ~ sP70(U_299,U_298,U_294,U_295,U_296,U_297) )
& ! [U_299,U_298,U_294,U_295,U_296,U_297] :
( U_294 = relation_inverse(U_295)
| sP72(U_294,U_295)
| sP71(U_294,U_295)
| ~ sP73(U_299,U_298,U_294,U_295,U_296,U_297) )
& ! [U_299,U_298,U_294,U_295,U_296,U_297] :
( sP70(U_299,U_298,U_294,U_295,U_296,U_297)
| U_294 != relation_inverse(U_295)
| ~ sP73(U_299,U_298,U_294,U_295,U_296,U_297) )
& ! [U_299,U_298,U_294,U_295,U_296,U_297] :
( sP73(U_299,U_298,U_294,U_295,U_296,U_297)
| ~ relation(U_294)
| ~ relation(U_295) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP70,sP71,sP72,sP73])],[f_32_7]) ).
cnf(f_32_9,plain,
( sP73(U_299,U_298,U_294,U_295,U_296,U_297)
| ~ relation(U_294)
| ~ relation(U_295) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_10,plain,
( sP70(U_299,U_298,U_294,U_295,U_296,U_297)
| U_294 != relation_inverse(U_295)
| ~ sP73(U_299,U_298,U_294,U_295,U_296,U_297) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_11,plain,
( U_294 = relation_inverse(U_295)
| sP72(U_294,U_295)
| sP71(U_294,U_295)
| ~ sP73(U_299,U_298,U_294,U_295,U_296,U_297) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_12,plain,
( in(ordered_pair(U_296,U_298),U_295)
| ~ in(ordered_pair(U_298,U_296),U_294)
| ~ sP70(U_299,U_298,U_294,U_295,U_296,U_297) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_13,plain,
( in(ordered_pair(U_299,U_297),U_294)
| ~ in(ordered_pair(U_297,U_299),U_295)
| ~ sP70(U_299,U_298,U_294,U_295,U_296,U_297) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_14,plain,
( in(ordered_pair(sK58(U_295,U_294),sK59(U_295,U_294)),U_294)
| ~ sP71(U_294,U_295) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_15,plain,
( ~ in(ordered_pair(sK59(U_295,U_294),sK58(U_295,U_294)),U_295)
| ~ sP71(U_294,U_295) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_16,plain,
( in(ordered_pair(sK61(U_295,U_294),sK60(U_295,U_294)),U_295)
| ~ sP72(U_294,U_295) ),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(f_32_17,plain,
( ~ in(ordered_pair(sK60(U_295,U_294),sK61(U_295,U_294)),U_294)
| ~ sP72(U_294,U_295) ),
inference(clausify,[status(thm)],[f_32_8]) ).
fof(f_33_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_33_2,plain,
! [U_305,U_304] :
( ( disjoint(U_305,U_304)
| set_intersection2(U_305,U_304) != empty_set )
& ( set_intersection2(U_305,U_304) = empty_set
| ~ disjoint(U_305,U_304) ) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( ! [U_309,U_307] :
( disjoint(U_309,U_307)
| set_intersection2(U_309,U_307) != empty_set )
& ! [U_308,U_306] :
( set_intersection2(U_308,U_306) = empty_set
| ~ disjoint(U_308,U_306) ) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
fof(f_33_4,plain,
( ! [U_309,U_307] :
( disjoint(U_309,U_307)
| set_intersection2(U_309,U_307) != empty_set )
& ! [U_308,U_306] :
( set_intersection2(U_308,U_306) = empty_set
| ~ disjoint(U_308,U_306) ) ),
inference(definitional_conversion,[status(esa)],[f_33_3]) ).
cnf(f_33_5,plain,
( set_intersection2(U_308,U_306) = empty_set
| ~ disjoint(U_308,U_306) ),
inference(clausify,[status(thm)],[f_33_4]) ).
cnf(f_33_6,plain,
( disjoint(U_309,U_307)
| set_intersection2(U_309,U_307) != empty_set ),
inference(clausify,[status(thm)],[f_33_4]) ).
fof(f_34_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_34_2,plain,
! [U_320] :
( ! [U_319] :
( ! [U_318] :
( ( ( U_318 = relation_composition(U_320,U_319)
| ? [U_317,U_316] :
( ( ~ in(ordered_pair(U_317,U_316),U_318)
& ? [U_315] :
( in(ordered_pair(U_315,U_316),U_319)
& in(ordered_pair(U_317,U_315),U_320) ) )
| ( ! [U_314] :
( ~ in(ordered_pair(U_314,U_316),U_319)
| ~ in(ordered_pair(U_317,U_314),U_320) )
& in(ordered_pair(U_317,U_316),U_318) ) ) )
& ( ! [U_313,U_312] :
( ( in(ordered_pair(U_313,U_312),U_318)
| ! [U_311] :
( ~ in(ordered_pair(U_311,U_312),U_319)
| ~ in(ordered_pair(U_313,U_311),U_320) ) )
& ( ? [U_310] :
( in(ordered_pair(U_310,U_312),U_319)
& in(ordered_pair(U_313,U_310),U_320) )
| ~ in(ordered_pair(U_313,U_312),U_318) ) )
| U_318 != relation_composition(U_320,U_319) ) )
| ~ relation(U_318) )
| ~ relation(U_319) )
| ~ relation(U_320) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_320] :
( ! [U_319] :
( ! [U_318] :
( ( ( U_318 = relation_composition(U_320,U_319)
| ? [U_328,U_326] :
( ~ in(ordered_pair(U_328,U_326),U_318)
& ? [U_315] :
( in(ordered_pair(U_315,U_326),U_319)
& in(ordered_pair(U_328,U_315),U_320) ) )
| ? [U_327,U_325] :
( ! [U_314] :
( ~ in(ordered_pair(U_314,U_325),U_319)
| ~ in(ordered_pair(U_327,U_314),U_320) )
& in(ordered_pair(U_327,U_325),U_318) ) )
& ( ( ! [U_324,U_322] :
( in(ordered_pair(U_324,U_322),U_318)
| ! [U_311] :
( ~ in(ordered_pair(U_311,U_322),U_319)
| ~ in(ordered_pair(U_324,U_311),U_320) ) )
& ! [U_323,U_321] :
( ? [U_310] :
( in(ordered_pair(U_310,U_321),U_319)
& in(ordered_pair(U_323,U_310),U_320) )
| ~ in(ordered_pair(U_323,U_321),U_318) ) )
| U_318 != relation_composition(U_320,U_319) ) )
| ~ relation(U_318) )
| ~ relation(U_319) )
| ~ relation(U_320) ),
inference(miniscope,[status(thm)],[f_34_2]) ).
fof(f_34_4,plain,
! [U_320] :
( ! [U_319] :
( ! [U_318] :
( ( ( U_318 = relation_composition(U_320,U_319)
| ? [U_328,U_326] :
( ~ in(ordered_pair(U_328,U_326),U_318)
& ? [U_315] :
( in(ordered_pair(U_315,U_326),U_319)
& in(ordered_pair(U_328,U_315),U_320) ) )
| ? [U_327,U_325] :
( ! [U_314] :
( ~ in(ordered_pair(U_314,U_325),U_319)
| ~ in(ordered_pair(U_327,U_314),U_320) )
& in(ordered_pair(U_327,U_325),U_318) ) )
& ( ( ! [U_324,U_322] :
( in(ordered_pair(U_324,U_322),U_318)
| ! [U_311] :
( ~ in(ordered_pair(U_311,U_322),U_319)
| ~ in(ordered_pair(U_324,U_311),U_320) ) )
& ! [U_323,U_321] :
( ( in(ordered_pair(sK62(U_320,U_319,U_318,U_323,U_321),U_321),U_319)
& in(ordered_pair(U_323,sK62(U_320,U_319,U_318,U_323,U_321)),U_320) )
| ~ in(ordered_pair(U_323,U_321),U_318) ) )
| U_318 != relation_composition(U_320,U_319) ) )
| ~ relation(U_318) )
| ~ relation(U_319) )
| ~ relation(U_320) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_310,sK62(U_320,U_319,U_318,U_323,U_321))],[f_34_3]) ).
fof(f_34_5,plain,
! [U_320] :
( ! [U_319] :
( ! [U_318] :
( ( ( U_318 = relation_composition(U_320,U_319)
| ? [U_328,U_326] :
( ~ in(ordered_pair(U_328,U_326),U_318)
& ? [U_315] :
( in(ordered_pair(U_315,U_326),U_319)
& in(ordered_pair(U_328,U_315),U_320) ) )
| ? [U_325] :
( ! [U_314] :
( ~ in(ordered_pair(U_314,U_325),U_319)
| ~ in(ordered_pair(sK63(U_320,U_319,U_318),U_314),U_320) )
& in(ordered_pair(sK63(U_320,U_319,U_318),U_325),U_318) ) )
& ( ( ! [U_324,U_322] :
( in(ordered_pair(U_324,U_322),U_318)
| ! [U_311] :
( ~ in(ordered_pair(U_311,U_322),U_319)
| ~ in(ordered_pair(U_324,U_311),U_320) ) )
& ! [U_323,U_321] :
( ( in(ordered_pair(sK62(U_320,U_319,U_318,U_323,U_321),U_321),U_319)
& in(ordered_pair(U_323,sK62(U_320,U_319,U_318,U_323,U_321)),U_320) )
| ~ in(ordered_pair(U_323,U_321),U_318) ) )
| U_318 != relation_composition(U_320,U_319) ) )
| ~ relation(U_318) )
| ~ relation(U_319) )
| ~ relation(U_320) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_327,sK63(U_320,U_319,U_318))],[f_34_4]) ).
fof(f_34_6,plain,
! [U_320] :
( ! [U_319] :
( ! [U_318] :
( ( ( U_318 = relation_composition(U_320,U_319)
| ? [U_328,U_326] :
( ~ in(ordered_pair(U_328,U_326),U_318)
& ? [U_315] :
( in(ordered_pair(U_315,U_326),U_319)
& in(ordered_pair(U_328,U_315),U_320) ) )
| ( ! [U_314] :
( ~ in(ordered_pair(U_314,sK64(U_320,U_319,U_318)),U_319)
| ~ in(ordered_pair(sK63(U_320,U_319,U_318),U_314),U_320) )
& in(ordered_pair(sK63(U_320,U_319,U_318),sK64(U_320,U_319,U_318)),U_318) ) )
& ( ( ! [U_324,U_322] :
( in(ordered_pair(U_324,U_322),U_318)
| ! [U_311] :
( ~ in(ordered_pair(U_311,U_322),U_319)
| ~ in(ordered_pair(U_324,U_311),U_320) ) )
& ! [U_323,U_321] :
( ( in(ordered_pair(sK62(U_320,U_319,U_318,U_323,U_321),U_321),U_319)
& in(ordered_pair(U_323,sK62(U_320,U_319,U_318,U_323,U_321)),U_320) )
| ~ in(ordered_pair(U_323,U_321),U_318) ) )
| U_318 != relation_composition(U_320,U_319) ) )
| ~ relation(U_318) )
| ~ relation(U_319) )
| ~ relation(U_320) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_325,sK64(U_320,U_319,U_318))],[f_34_5]) ).
fof(f_34_7,plain,
! [U_320] :
( ! [U_319] :
( ! [U_318] :
( ( ( U_318 = relation_composition(U_320,U_319)
| ? [U_326] :
( ~ in(ordered_pair(sK65(U_320,U_319,U_318),U_326),U_318)
& ? [U_315] :
( in(ordered_pair(U_315,U_326),U_319)
& in(ordered_pair(sK65(U_320,U_319,U_318),U_315),U_320) ) )
| ( ! [U_314] :
( ~ in(ordered_pair(U_314,sK64(U_320,U_319,U_318)),U_319)
| ~ in(ordered_pair(sK63(U_320,U_319,U_318),U_314),U_320) )
& in(ordered_pair(sK63(U_320,U_319,U_318),sK64(U_320,U_319,U_318)),U_318) ) )
& ( ( ! [U_324,U_322] :
( in(ordered_pair(U_324,U_322),U_318)
| ! [U_311] :
( ~ in(ordered_pair(U_311,U_322),U_319)
| ~ in(ordered_pair(U_324,U_311),U_320) ) )
& ! [U_323,U_321] :
( ( in(ordered_pair(sK62(U_320,U_319,U_318,U_323,U_321),U_321),U_319)
& in(ordered_pair(U_323,sK62(U_320,U_319,U_318,U_323,U_321)),U_320) )
| ~ in(ordered_pair(U_323,U_321),U_318) ) )
| U_318 != relation_composition(U_320,U_319) ) )
| ~ relation(U_318) )
| ~ relation(U_319) )
| ~ relation(U_320) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_328,sK65(U_320,U_319,U_318))],[f_34_6]) ).
fof(f_34_8,plain,
! [U_320] :
( ! [U_319] :
( ! [U_318] :
( ( ( U_318 = relation_composition(U_320,U_319)
| ( ~ in(ordered_pair(sK65(U_320,U_319,U_318),sK66(U_320,U_319,U_318)),U_318)
& ? [U_315] :
( in(ordered_pair(U_315,sK66(U_320,U_319,U_318)),U_319)
& in(ordered_pair(sK65(U_320,U_319,U_318),U_315),U_320) ) )
| ( ! [U_314] :
( ~ in(ordered_pair(U_314,sK64(U_320,U_319,U_318)),U_319)
| ~ in(ordered_pair(sK63(U_320,U_319,U_318),U_314),U_320) )
& in(ordered_pair(sK63(U_320,U_319,U_318),sK64(U_320,U_319,U_318)),U_318) ) )
& ( ( ! [U_324,U_322] :
( in(ordered_pair(U_324,U_322),U_318)
| ! [U_311] :
( ~ in(ordered_pair(U_311,U_322),U_319)
| ~ in(ordered_pair(U_324,U_311),U_320) ) )
& ! [U_323,U_321] :
( ( in(ordered_pair(sK62(U_320,U_319,U_318,U_323,U_321),U_321),U_319)
& in(ordered_pair(U_323,sK62(U_320,U_319,U_318,U_323,U_321)),U_320) )
| ~ in(ordered_pair(U_323,U_321),U_318) ) )
| U_318 != relation_composition(U_320,U_319) ) )
| ~ relation(U_318) )
| ~ relation(U_319) )
| ~ relation(U_320) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_326,sK66(U_320,U_319,U_318))],[f_34_7]) ).
fof(f_34_9,plain,
! [U_320] :
( ! [U_319] :
( ! [U_318] :
( ( ( U_318 = relation_composition(U_320,U_319)
| ( ~ in(ordered_pair(sK65(U_320,U_319,U_318),sK66(U_320,U_319,U_318)),U_318)
& in(ordered_pair(sK67(U_320,U_319,U_318),sK66(U_320,U_319,U_318)),U_319)
& in(ordered_pair(sK65(U_320,U_319,U_318),sK67(U_320,U_319,U_318)),U_320) )
| ( ! [U_314] :
( ~ in(ordered_pair(U_314,sK64(U_320,U_319,U_318)),U_319)
| ~ in(ordered_pair(sK63(U_320,U_319,U_318),U_314),U_320) )
& in(ordered_pair(sK63(U_320,U_319,U_318),sK64(U_320,U_319,U_318)),U_318) ) )
& ( ( ! [U_324,U_322] :
( in(ordered_pair(U_324,U_322),U_318)
| ! [U_311] :
( ~ in(ordered_pair(U_311,U_322),U_319)
| ~ in(ordered_pair(U_324,U_311),U_320) ) )
& ! [U_323,U_321] :
( ( in(ordered_pair(sK62(U_320,U_319,U_318,U_323,U_321),U_321),U_319)
& in(ordered_pair(U_323,sK62(U_320,U_319,U_318,U_323,U_321)),U_320) )
| ~ in(ordered_pair(U_323,U_321),U_318) ) )
| U_318 != relation_composition(U_320,U_319) ) )
| ~ relation(U_318) )
| ~ relation(U_319) )
| ~ relation(U_320) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_315,sK67(U_320,U_319,U_318))],[f_34_8]) ).
fof(f_34_10,plain,
( ! [U_318,U_319,U_320] :
( ~ in(ordered_pair(sK65(U_320,U_319,U_318),sK66(U_320,U_319,U_318)),U_318)
| ~ sP77(U_318,U_319,U_320) )
& ! [U_318,U_319,U_320] :
( in(ordered_pair(sK67(U_320,U_319,U_318),sK66(U_320,U_319,U_318)),U_319)
| ~ sP77(U_318,U_319,U_320) )
& ! [U_318,U_319,U_320] :
( in(ordered_pair(sK65(U_320,U_319,U_318),sK67(U_320,U_319,U_318)),U_320)
| ~ sP77(U_318,U_319,U_320) )
& ! [U_314,U_318,U_319,U_320] :
( ~ in(ordered_pair(U_314,sK64(U_320,U_319,U_318)),U_319)
| ~ in(ordered_pair(sK63(U_320,U_319,U_318),U_314),U_320)
| ~ sP76(U_314,U_318,U_319,U_320) )
& ! [U_314,U_318,U_319,U_320] :
( in(ordered_pair(sK63(U_320,U_319,U_318),sK64(U_320,U_319,U_318)),U_318)
| ~ sP76(U_314,U_318,U_319,U_320) )
& ! [U_321,U_318,U_319,U_320,U_323] :
( in(ordered_pair(sK62(U_320,U_319,U_318,U_323,U_321),U_321),U_319)
| ~ sP74(U_321,U_318,U_319,U_320,U_323) )
& ! [U_321,U_318,U_319,U_320,U_323] :
( in(ordered_pair(U_323,sK62(U_320,U_319,U_318,U_323,U_321)),U_320)
| ~ sP74(U_321,U_318,U_319,U_320,U_323) )
& ! [U_321,U_322,U_318,U_319,U_320,U_311,U_324,U_323] :
( in(ordered_pair(U_324,U_322),U_318)
| ~ in(ordered_pair(U_311,U_322),U_319)
| ~ in(ordered_pair(U_324,U_311),U_320)
| ~ sP75(U_321,U_322,U_318,U_319,U_320,U_311,U_324,U_323) )
& ! [U_321,U_322,U_318,U_319,U_320,U_311,U_324,U_323] :
( sP74(U_321,U_318,U_319,U_320,U_323)
| ~ in(ordered_pair(U_323,U_321),U_318)
| ~ sP75(U_321,U_322,U_318,U_319,U_320,U_311,U_324,U_323) )
& ! [U_321,U_314,U_322,U_318,U_319,U_320,U_311,U_324,U_323] :
( U_318 = relation_composition(U_320,U_319)
| sP77(U_318,U_319,U_320)
| sP76(U_314,U_318,U_319,U_320)
| ~ sP78(U_321,U_314,U_322,U_318,U_319,U_320,U_311,U_324,U_323) )
& ! [U_321,U_314,U_322,U_318,U_319,U_320,U_311,U_324,U_323] :
( sP75(U_321,U_322,U_318,U_319,U_320,U_311,U_324,U_323)
| U_318 != relation_composition(U_320,U_319)
| ~ sP78(U_321,U_314,U_322,U_318,U_319,U_320,U_311,U_324,U_323) )
& ! [U_321,U_314,U_322,U_318,U_319,U_320,U_311,U_324,U_323] :
( sP78(U_321,U_314,U_322,U_318,U_319,U_320,U_311,U_324,U_323)
| ~ relation(U_318)
| ~ relation(U_319)
| ~ relation(U_320) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP74,sP75,sP76,sP77,sP78])],[f_34_9]) ).
cnf(f_34_11,plain,
( sP78(U_321,U_314,U_322,U_318,U_319,U_320,U_311,U_324,U_323)
| ~ relation(U_318)
| ~ relation(U_319)
| ~ relation(U_320) ),
inference(clausify,[status(thm)],[f_34_10]) ).
cnf(f_34_12,plain,
( sP75(U_321,U_322,U_318,U_319,U_320,U_311,U_324,U_323)
| U_318 != relation_composition(U_320,U_319)
| ~ sP78(U_321,U_314,U_322,U_318,U_319,U_320,U_311,U_324,U_323) ),
inference(clausify,[status(thm)],[f_34_10]) ).
cnf(f_34_13,plain,
( U_318 = relation_composition(U_320,U_319)
| sP77(U_318,U_319,U_320)
| sP76(U_314,U_318,U_319,U_320)
| ~ sP78(U_321,U_314,U_322,U_318,U_319,U_320,U_311,U_324,U_323) ),
inference(clausify,[status(thm)],[f_34_10]) ).
cnf(f_34_14,plain,
( sP74(U_321,U_318,U_319,U_320,U_323)
| ~ in(ordered_pair(U_323,U_321),U_318)
| ~ sP75(U_321,U_322,U_318,U_319,U_320,U_311,U_324,U_323) ),
inference(clausify,[status(thm)],[f_34_10]) ).
cnf(f_34_15,plain,
( in(ordered_pair(U_324,U_322),U_318)
| ~ in(ordered_pair(U_311,U_322),U_319)
| ~ in(ordered_pair(U_324,U_311),U_320)
| ~ sP75(U_321,U_322,U_318,U_319,U_320,U_311,U_324,U_323) ),
inference(clausify,[status(thm)],[f_34_10]) ).
cnf(f_34_16,plain,
( in(ordered_pair(U_323,sK62(U_320,U_319,U_318,U_323,U_321)),U_320)
| ~ sP74(U_321,U_318,U_319,U_320,U_323) ),
inference(clausify,[status(thm)],[f_34_10]) ).
cnf(f_34_17,plain,
( in(ordered_pair(sK62(U_320,U_319,U_318,U_323,U_321),U_321),U_319)
| ~ sP74(U_321,U_318,U_319,U_320,U_323) ),
inference(clausify,[status(thm)],[f_34_10]) ).
cnf(f_34_18,plain,
( in(ordered_pair(sK63(U_320,U_319,U_318),sK64(U_320,U_319,U_318)),U_318)
| ~ sP76(U_314,U_318,U_319,U_320) ),
inference(clausify,[status(thm)],[f_34_10]) ).
cnf(f_34_19,plain,
( ~ in(ordered_pair(U_314,sK64(U_320,U_319,U_318)),U_319)
| ~ in(ordered_pair(sK63(U_320,U_319,U_318),U_314),U_320)
| ~ sP76(U_314,U_318,U_319,U_320) ),
inference(clausify,[status(thm)],[f_34_10]) ).
cnf(f_34_20,plain,
( in(ordered_pair(sK65(U_320,U_319,U_318),sK67(U_320,U_319,U_318)),U_320)
| ~ sP77(U_318,U_319,U_320) ),
inference(clausify,[status(thm)],[f_34_10]) ).
cnf(f_34_21,plain,
( in(ordered_pair(sK67(U_320,U_319,U_318),sK66(U_320,U_319,U_318)),U_319)
| ~ sP77(U_318,U_319,U_320) ),
inference(clausify,[status(thm)],[f_34_10]) ).
cnf(f_34_22,plain,
( ~ in(ordered_pair(sK65(U_320,U_319,U_318),sK66(U_320,U_319,U_318)),U_318)
| ~ sP77(U_318,U_319,U_320) ),
inference(clausify,[status(thm)],[f_34_10]) ).
fof(f_35_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_35_2,plain,
! [U_333,U_332] :
( ! [U_331] :
( ( ( U_331 = complements_of_subsets(U_333,U_332)
| ? [U_330] :
( ( ( ~ in(U_330,U_331)
& in(subset_complement(U_333,U_330),U_332) )
| ( ~ in(subset_complement(U_333,U_330),U_332)
& in(U_330,U_331) ) )
& element(U_330,powerset(U_333)) ) )
& ( ! [U_329] :
( ( ( in(U_329,U_331)
| ~ in(subset_complement(U_333,U_329),U_332) )
& ( in(subset_complement(U_333,U_329),U_332)
| ~ in(U_329,U_331) ) )
| ~ element(U_329,powerset(U_333)) )
| U_331 != complements_of_subsets(U_333,U_332) ) )
| ~ element(U_331,powerset(powerset(U_333))) )
| ~ element(U_332,powerset(powerset(U_333))) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_333,U_332] :
( ! [U_331] :
( ( ( U_331 = complements_of_subsets(U_333,U_332)
| ( ( ( ~ in(sK68(U_333,U_332,U_331),U_331)
& in(subset_complement(U_333,sK68(U_333,U_332,U_331)),U_332) )
| ( ~ in(subset_complement(U_333,sK68(U_333,U_332,U_331)),U_332)
& in(sK68(U_333,U_332,U_331),U_331) ) )
& element(sK68(U_333,U_332,U_331),powerset(U_333)) ) )
& ( ! [U_329] :
( ( ( in(U_329,U_331)
| ~ in(subset_complement(U_333,U_329),U_332) )
& ( in(subset_complement(U_333,U_329),U_332)
| ~ in(U_329,U_331) ) )
| ~ element(U_329,powerset(U_333)) )
| U_331 != complements_of_subsets(U_333,U_332) ) )
| ~ element(U_331,powerset(powerset(U_333))) )
| ~ element(U_332,powerset(powerset(U_333))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_330,sK68(U_333,U_332,U_331))],[f_35_2]) ).
fof(f_35_4,plain,
( ! [U_333,U_332,U_331] :
( ~ in(sK68(U_333,U_332,U_331),U_331)
| ~ sP81(U_333,U_332,U_331) )
& ! [U_333,U_332,U_331] :
( in(subset_complement(U_333,sK68(U_333,U_332,U_331)),U_332)
| ~ sP81(U_333,U_332,U_331) )
& ! [U_333,U_332,U_331] :
( ~ in(subset_complement(U_333,sK68(U_333,U_332,U_331)),U_332)
| ~ sP80(U_333,U_332,U_331) )
& ! [U_333,U_332,U_331] :
( in(sK68(U_333,U_332,U_331),U_331)
| ~ sP80(U_333,U_332,U_331) )
& ! [U_333,U_332,U_331] :
( sP81(U_333,U_332,U_331)
| sP80(U_333,U_332,U_331)
| ~ sP82(U_333,U_332,U_331) )
& ! [U_333,U_332,U_331] :
( element(sK68(U_333,U_332,U_331),powerset(U_333))
| ~ sP82(U_333,U_332,U_331) )
& ! [U_333,U_332,U_329,U_331] :
( in(U_329,U_331)
| ~ in(subset_complement(U_333,U_329),U_332)
| ~ sP79(U_333,U_332,U_329,U_331) )
& ! [U_333,U_332,U_329,U_331] :
( in(subset_complement(U_333,U_329),U_332)
| ~ in(U_329,U_331)
| ~ sP79(U_333,U_332,U_329,U_331) )
& ! [U_333,U_332,U_329,U_331] :
( U_331 = complements_of_subsets(U_333,U_332)
| sP82(U_333,U_332,U_331)
| ~ sP83(U_333,U_332,U_329,U_331) )
& ! [U_333,U_332,U_329,U_331] :
( sP79(U_333,U_332,U_329,U_331)
| ~ element(U_329,powerset(U_333))
| U_331 != complements_of_subsets(U_333,U_332)
| ~ sP83(U_333,U_332,U_329,U_331) )
& ! [U_333,U_332,U_329,U_331] :
( sP83(U_333,U_332,U_329,U_331)
| ~ element(U_331,powerset(powerset(U_333)))
| ~ element(U_332,powerset(powerset(U_333))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP79,sP80,sP81,sP82,sP83])],[f_35_3]) ).
cnf(f_35_5,plain,
( sP83(U_333,U_332,U_329,U_331)
| ~ element(U_331,powerset(powerset(U_333)))
| ~ element(U_332,powerset(powerset(U_333))) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_6,plain,
( sP79(U_333,U_332,U_329,U_331)
| ~ element(U_329,powerset(U_333))
| U_331 != complements_of_subsets(U_333,U_332)
| ~ sP83(U_333,U_332,U_329,U_331) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_7,plain,
( U_331 = complements_of_subsets(U_333,U_332)
| sP82(U_333,U_332,U_331)
| ~ sP83(U_333,U_332,U_329,U_331) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_8,plain,
( in(subset_complement(U_333,U_329),U_332)
| ~ in(U_329,U_331)
| ~ sP79(U_333,U_332,U_329,U_331) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_9,plain,
( in(U_329,U_331)
| ~ in(subset_complement(U_333,U_329),U_332)
| ~ sP79(U_333,U_332,U_329,U_331) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_10,plain,
( element(sK68(U_333,U_332,U_331),powerset(U_333))
| ~ sP82(U_333,U_332,U_331) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_11,plain,
( sP81(U_333,U_332,U_331)
| sP80(U_333,U_332,U_331)
| ~ sP82(U_333,U_332,U_331) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_12,plain,
( in(sK68(U_333,U_332,U_331),U_331)
| ~ sP80(U_333,U_332,U_331) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_13,plain,
( ~ in(subset_complement(U_333,sK68(U_333,U_332,U_331)),U_332)
| ~ sP80(U_333,U_332,U_331) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_14,plain,
( in(subset_complement(U_333,sK68(U_333,U_332,U_331)),U_332)
| ~ sP81(U_333,U_332,U_331) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_15,plain,
( ~ in(sK68(U_333,U_332,U_331),U_331)
| ~ sP81(U_333,U_332,U_331) ),
inference(clausify,[status(thm)],[f_35_4]) ).
fof(f_36_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_36_2,plain,
! [U_335,U_334] :
( ( proper_subset(U_335,U_334)
| U_335 = U_334
| ~ subset(U_335,U_334) )
& ( ( U_335 != U_334
& subset(U_335,U_334) )
| ~ proper_subset(U_335,U_334) ) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
( ! [U_339,U_337] :
( proper_subset(U_339,U_337)
| U_339 = U_337
| ~ subset(U_339,U_337) )
& ! [U_338,U_336] :
( ( U_338 != U_336
& subset(U_338,U_336) )
| ~ proper_subset(U_338,U_336) ) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
fof(f_36_4,plain,
( ! [U_336,U_338] :
( U_338 != U_336
| ~ sP84(U_336,U_338) )
& ! [U_336,U_338] :
( subset(U_338,U_336)
| ~ sP84(U_336,U_338) )
& ! [U_337,U_339] :
( proper_subset(U_339,U_337)
| U_339 = U_337
| ~ subset(U_339,U_337) )
& ! [U_336,U_338] :
( sP84(U_336,U_338)
| ~ proper_subset(U_338,U_336) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP84])],[f_36_3]) ).
cnf(f_36_5,plain,
( sP84(U_336,U_338)
| ~ proper_subset(U_338,U_336) ),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_6,plain,
( proper_subset(U_339,U_337)
| U_339 = U_337
| ~ subset(U_339,U_337) ),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_7,plain,
( subset(U_338,U_336)
| ~ sP84(U_336,U_338) ),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_8,plain,
( U_338 != U_336
| ~ sP84(U_336,U_338) ),
inference(clausify,[status(thm)],[f_36_4]) ).
fof(f_37_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
fof(f_37_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_37_1]) ).
cnf(f_37_3,plain,
$true,
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_setfam_1]) ).
fof(f_38_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_38_1]) ).
cnf(f_38_3,plain,
$true,
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
fof(f_39_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_39_1]) ).
cnf(f_39_3,plain,
$true,
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
fof(f_40_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_40_1]) ).
cnf(f_40_3,plain,
$true,
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
fof(f_41_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_41_1]) ).
cnf(f_41_3,plain,
$true,
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_relat_1]) ).
fof(f_42_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_42_1]) ).
cnf(f_42_3,plain,
$true,
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_1,plain,
! [A] : element(cast_to_subset(A),powerset(A)),
inference(fof_nnf,[status(thm)],[dt_k2_subset_1]) ).
fof(f_43_2,plain,
! [U_340] : element(cast_to_subset(U_340),powerset(U_340)),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_340] : element(cast_to_subset(U_340),powerset(U_340)),
inference(definitional_conversion,[status(esa)],[f_43_2]) ).
cnf(f_43_4,plain,
element(cast_to_subset(U_340),powerset(U_340)),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
fof(f_44_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_44_1]) ).
cnf(f_44_3,plain,
$true,
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
fof(f_45_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_45_1]) ).
cnf(f_45_3,plain,
$true,
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
fof(f_46_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_46_1]) ).
cnf(f_46_3,plain,
$true,
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_relat_1]) ).
fof(f_47_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_47_1]) ).
cnf(f_47_3,plain,
$true,
inference(clausify,[status(thm)],[f_47_2]) ).
fof(f_48_1,plain,
! [A,B] :
( element(subset_complement(A,B),powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[dt_k3_subset_1]) ).
fof(f_48_2,plain,
! [U_342,U_341] :
( element(subset_complement(U_342,U_341),powerset(U_342))
| ~ element(U_341,powerset(U_342)) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
! [U_342,U_341] :
( element(subset_complement(U_342,U_341),powerset(U_342))
| ~ element(U_341,powerset(U_342)) ),
inference(definitional_conversion,[status(esa)],[f_48_2]) ).
cnf(f_48_4,plain,
( element(subset_complement(U_342,U_341),powerset(U_342))
| ~ element(U_341,powerset(U_342)) ),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_tarski]) ).
fof(f_49_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_49_1]) ).
cnf(f_49_3,plain,
$true,
inference(clausify,[status(thm)],[f_49_2]) ).
fof(f_50_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
fof(f_50_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_50_1]) ).
cnf(f_50_3,plain,
$true,
inference(clausify,[status(thm)],[f_50_2]) ).
fof(f_51_1,plain,
! [A] :
( relation(relation_inverse(A))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k4_relat_1]) ).
fof(f_51_2,plain,
! [U_343] :
( relation(relation_inverse(U_343))
| ~ relation(U_343) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
! [U_343] :
( relation(relation_inverse(U_343))
| ~ relation(U_343) ),
inference(definitional_conversion,[status(esa)],[f_51_2]) ).
cnf(f_51_4,plain,
( relation(relation_inverse(U_343))
| ~ relation(U_343) ),
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_52_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
fof(f_52_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_52_1]) ).
cnf(f_52_3,plain,
$true,
inference(clausify,[status(thm)],[f_52_2]) ).
fof(f_53_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
fof(f_53_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_53_1]) ).
cnf(f_53_3,plain,
$true,
inference(clausify,[status(thm)],[f_53_2]) ).
fof(f_54_1,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_relat_1]) ).
fof(f_54_2,plain,
! [U_345,U_344] :
( relation(relation_composition(U_345,U_344))
| ~ relation(U_344)
| ~ relation(U_345) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_344,U_345] :
( relation(relation_composition(U_345,U_344))
| ~ relation(U_344)
| ~ relation(U_345) ),
inference(definitional_conversion,[status(esa)],[f_54_2]) ).
cnf(f_54_4,plain,
( relation(relation_composition(U_345,U_344))
| ~ relation(U_344)
| ~ relation(U_345) ),
inference(clausify,[status(thm)],[f_54_3]) ).
fof(f_55_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_55_2,plain,
! [U_347,U_346] :
( element(union_of_subsets(U_347,U_346),powerset(U_347))
| ~ element(U_346,powerset(powerset(U_347))) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
! [U_347,U_346] :
( element(union_of_subsets(U_347,U_346),powerset(U_347))
| ~ element(U_346,powerset(powerset(U_347))) ),
inference(definitional_conversion,[status(esa)],[f_55_2]) ).
cnf(f_55_4,plain,
( element(union_of_subsets(U_347,U_346),powerset(U_347))
| ~ element(U_346,powerset(powerset(U_347))) ),
inference(clausify,[status(thm)],[f_55_3]) ).
fof(f_56_1,plain,
! [A] : relation(identity_relation(A)),
inference(fof_nnf,[status(thm)],[dt_k6_relat_1]) ).
fof(f_56_2,plain,
! [U_348] : relation(identity_relation(U_348)),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
! [U_348] : relation(identity_relation(U_348)),
inference(definitional_conversion,[status(esa)],[f_56_2]) ).
cnf(f_56_4,plain,
relation(identity_relation(U_348)),
inference(clausify,[status(thm)],[f_56_3]) ).
fof(f_57_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_57_2,plain,
! [U_350,U_349] :
( element(meet_of_subsets(U_350,U_349),powerset(U_350))
| ~ element(U_349,powerset(powerset(U_350))) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
! [U_349,U_350] :
( element(meet_of_subsets(U_350,U_349),powerset(U_350))
| ~ element(U_349,powerset(powerset(U_350))) ),
inference(definitional_conversion,[status(esa)],[f_57_2]) ).
cnf(f_57_4,plain,
( element(meet_of_subsets(U_350,U_349),powerset(U_350))
| ~ element(U_349,powerset(powerset(U_350))) ),
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_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_58_2,plain,
! [U_353,U_352,U_351] :
( element(subset_difference(U_353,U_352,U_351),powerset(U_353))
| ~ element(U_351,powerset(U_353))
| ~ element(U_352,powerset(U_353)) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
! [U_352,U_351,U_353] :
( element(subset_difference(U_353,U_352,U_351),powerset(U_353))
| ~ element(U_351,powerset(U_353))
| ~ element(U_352,powerset(U_353)) ),
inference(definitional_conversion,[status(esa)],[f_58_2]) ).
cnf(f_58_4,plain,
( element(subset_difference(U_353,U_352,U_351),powerset(U_353))
| ~ element(U_351,powerset(U_353))
| ~ element(U_352,powerset(U_353)) ),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_59_1,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k7_relat_1]) ).
fof(f_59_2,plain,
! [U_355,U_354] :
( relation(relation_dom_restriction(U_355,U_354))
| ~ relation(U_355) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
! [U_355] :
( ! [U_354] : relation(relation_dom_restriction(U_355,U_354))
| ~ relation(U_355) ),
inference(miniscope,[status(thm)],[f_59_2]) ).
fof(f_59_4,plain,
! [U_355,U_354] :
( relation(relation_dom_restriction(U_355,U_354))
| ~ relation(U_355) ),
inference(definitional_conversion,[status(esa)],[f_59_3]) ).
cnf(f_59_5,plain,
( relation(relation_dom_restriction(U_355,U_354))
| ~ relation(U_355) ),
inference(clausify,[status(thm)],[f_59_4]) ).
fof(f_60_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_60_2,plain,
! [U_357,U_356] :
( element(complements_of_subsets(U_357,U_356),powerset(powerset(U_357)))
| ~ element(U_356,powerset(powerset(U_357))) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
! [U_356,U_357] :
( element(complements_of_subsets(U_357,U_356),powerset(powerset(U_357)))
| ~ element(U_356,powerset(powerset(U_357))) ),
inference(definitional_conversion,[status(esa)],[f_60_2]) ).
cnf(f_60_4,plain,
( element(complements_of_subsets(U_357,U_356),powerset(powerset(U_357)))
| ~ element(U_356,powerset(powerset(U_357))) ),
inference(clausify,[status(thm)],[f_60_3]) ).
fof(f_61_1,plain,
! [A,B] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[dt_k8_relat_1]) ).
fof(f_61_2,plain,
! [U_359,U_358] :
( relation(relation_rng_restriction(U_359,U_358))
| ~ relation(U_358) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
! [U_358,U_359] :
( relation(relation_rng_restriction(U_359,U_358))
| ~ relation(U_358) ),
inference(definitional_conversion,[status(esa)],[f_61_2]) ).
cnf(f_61_4,plain,
( relation(relation_rng_restriction(U_359,U_358))
| ~ relation(U_358) ),
inference(clausify,[status(thm)],[f_61_3]) ).
fof(f_62_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
fof(f_62_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_62_1]) ).
cnf(f_62_3,plain,
$true,
inference(clausify,[status(thm)],[f_62_2]) ).
fof(f_63_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_63_2,plain,
! [U_361] :
? [U_360] : element(U_360,U_361),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
! [U_361] : element(sK69(U_361),U_361),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_360,sK69(U_361))],[f_63_2]) ).
fof(f_63_4,plain,
! [U_361] : element(sK69(U_361),U_361),
inference(definitional_conversion,[status(esa)],[f_63_3]) ).
cnf(f_63_5,plain,
element(sK69(U_361),U_361),
inference(clausify,[status(thm)],[f_63_4]) ).
fof(f_64_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_64_2,plain,
! [U_363,U_362] :
( ( relation(relation_composition(U_362,U_363))
& empty(relation_composition(U_362,U_363)) )
| ~ relation(U_362)
| ~ empty(U_363) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
( ! [U_362,U_363] :
( relation(relation_composition(U_362,U_363))
| ~ sP85(U_362,U_363) )
& ! [U_362,U_363] :
( empty(relation_composition(U_362,U_363))
| ~ sP85(U_362,U_363) )
& ! [U_362,U_363] :
( sP85(U_362,U_363)
| ~ relation(U_362)
| ~ empty(U_363) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP85])],[f_64_2]) ).
cnf(f_64_4,plain,
( sP85(U_362,U_363)
| ~ relation(U_362)
| ~ empty(U_363) ),
inference(clausify,[status(thm)],[f_64_3]) ).
cnf(f_64_5,plain,
( empty(relation_composition(U_362,U_363))
| ~ sP85(U_362,U_363) ),
inference(clausify,[status(thm)],[f_64_3]) ).
cnf(f_64_6,plain,
( relation(relation_composition(U_362,U_363))
| ~ sP85(U_362,U_363) ),
inference(clausify,[status(thm)],[f_64_3]) ).
fof(f_65_1,plain,
! [A,B] :
( relation(set_intersection2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc1_relat_1]) ).
fof(f_65_2,plain,
! [U_365,U_364] :
( relation(set_intersection2(U_365,U_364))
| ~ relation(U_364)
| ~ relation(U_365) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
! [U_365,U_364] :
( relation(set_intersection2(U_365,U_364))
| ~ relation(U_364)
| ~ relation(U_365) ),
inference(definitional_conversion,[status(esa)],[f_65_2]) ).
cnf(f_65_4,plain,
( relation(set_intersection2(U_365,U_364))
| ~ relation(U_364)
| ~ relation(U_365) ),
inference(clausify,[status(thm)],[f_65_3]) ).
fof(f_66_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_66_2,plain,
! [U_366] : ~ empty(powerset(U_366)),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
! [U_366] : ~ empty(powerset(U_366)),
inference(definitional_conversion,[status(esa)],[f_66_2]) ).
cnf(f_66_4,plain,
~ empty(powerset(U_366)),
inference(clausify,[status(thm)],[f_66_3]) ).
fof(f_67_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_67_2,plain,
empty(empty_set),
inference(definitional_conversion,[status(esa)],[f_67_1]) ).
cnf(f_67_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_67_2]) ).
fof(f_68_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_68_2,plain,
! [U_368,U_367] : ~ empty(ordered_pair(U_368,U_367)),
inference(variable_rename,[status(thm)],[f_68_1]) ).
fof(f_68_3,plain,
! [U_367,U_368] : ~ empty(ordered_pair(U_368,U_367)),
inference(definitional_conversion,[status(esa)],[f_68_2]) ).
cnf(f_68_4,plain,
~ empty(ordered_pair(U_368,U_367)),
inference(clausify,[status(thm)],[f_68_3]) ).
fof(f_69_1,plain,
! [A,B] :
( relation(set_union2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc2_relat_1]) ).
fof(f_69_2,plain,
! [U_370,U_369] :
( relation(set_union2(U_370,U_369))
| ~ relation(U_369)
| ~ relation(U_370) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
fof(f_69_3,plain,
! [U_369,U_370] :
( relation(set_union2(U_370,U_369))
| ~ relation(U_369)
| ~ relation(U_370) ),
inference(definitional_conversion,[status(esa)],[f_69_2]) ).
cnf(f_69_4,plain,
( relation(set_union2(U_370,U_369))
| ~ relation(U_369)
| ~ relation(U_370) ),
inference(clausify,[status(thm)],[f_69_3]) ).
fof(f_70_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_70_2,plain,
! [U_371] : ~ empty(singleton(U_371)),
inference(variable_rename,[status(thm)],[f_70_1]) ).
fof(f_70_3,plain,
! [U_371] : ~ empty(singleton(U_371)),
inference(definitional_conversion,[status(esa)],[f_70_2]) ).
cnf(f_70_4,plain,
~ empty(singleton(U_371)),
inference(clausify,[status(thm)],[f_70_3]) ).
fof(f_71_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_71_2,plain,
! [U_373,U_372] :
( ~ empty(set_union2(U_373,U_372))
| empty(U_373) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
fof(f_71_3,plain,
! [U_373] :
( ! [U_372] : ~ empty(set_union2(U_373,U_372))
| empty(U_373) ),
inference(miniscope,[status(thm)],[f_71_2]) ).
fof(f_71_4,plain,
! [U_372,U_373] :
( ~ empty(set_union2(U_373,U_372))
| empty(U_373) ),
inference(definitional_conversion,[status(esa)],[f_71_3]) ).
cnf(f_71_5,plain,
( ~ empty(set_union2(U_373,U_372))
| empty(U_373) ),
inference(clausify,[status(thm)],[f_71_4]) ).
fof(f_72_1,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_72_2,plain,
! [U_375,U_374] : ~ empty(unordered_pair(U_375,U_374)),
inference(variable_rename,[status(thm)],[f_72_1]) ).
fof(f_72_3,plain,
! [U_374,U_375] : ~ empty(unordered_pair(U_375,U_374)),
inference(definitional_conversion,[status(esa)],[f_72_2]) ).
cnf(f_72_4,plain,
~ empty(unordered_pair(U_375,U_374)),
inference(clausify,[status(thm)],[f_72_3]) ).
fof(f_73_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_73_2,plain,
! [U_377,U_376] :
( ~ empty(set_union2(U_376,U_377))
| empty(U_377) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
fof(f_73_3,plain,
! [U_377] :
( ! [U_376] : ~ empty(set_union2(U_376,U_377))
| empty(U_377) ),
inference(miniscope,[status(thm)],[f_73_2]) ).
fof(f_73_4,plain,
! [U_376,U_377] :
( ~ empty(set_union2(U_376,U_377))
| empty(U_377) ),
inference(definitional_conversion,[status(esa)],[f_73_3]) ).
cnf(f_73_5,plain,
( ~ empty(set_union2(U_376,U_377))
| empty(U_377) ),
inference(clausify,[status(thm)],[f_73_4]) ).
fof(f_74_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
fof(f_74_2,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_74_1]) ).
cnf(f_74_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_74_2]) ).
cnf(f_74_4,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_74_2]) ).
fof(f_75_1,plain,
! [A,B] :
( ~ empty(cartesian_product2(A,B))
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc4_subset_1]) ).
fof(f_75_2,plain,
! [U_379,U_378] :
( ~ empty(cartesian_product2(U_379,U_378))
| empty(U_378)
| empty(U_379) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
fof(f_75_3,plain,
! [U_378,U_379] :
( ~ empty(cartesian_product2(U_379,U_378))
| empty(U_378)
| empty(U_379) ),
inference(definitional_conversion,[status(esa)],[f_75_2]) ).
cnf(f_75_4,plain,
( ~ empty(cartesian_product2(U_379,U_378))
| empty(U_378)
| empty(U_379) ),
inference(clausify,[status(thm)],[f_75_3]) ).
fof(f_76_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_76_2,plain,
! [U_380] :
( ~ empty(relation_dom(U_380))
| ~ relation(U_380)
| empty(U_380) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
fof(f_76_3,plain,
! [U_380] :
( ~ empty(relation_dom(U_380))
| ~ relation(U_380)
| empty(U_380) ),
inference(definitional_conversion,[status(esa)],[f_76_2]) ).
cnf(f_76_4,plain,
( ~ empty(relation_dom(U_380))
| ~ relation(U_380)
| empty(U_380) ),
inference(clausify,[status(thm)],[f_76_3]) ).
fof(f_77_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_77_2,plain,
! [U_381] :
( ~ empty(relation_rng(U_381))
| ~ relation(U_381)
| empty(U_381) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
fof(f_77_3,plain,
! [U_381] :
( ~ empty(relation_rng(U_381))
| ~ relation(U_381)
| empty(U_381) ),
inference(definitional_conversion,[status(esa)],[f_77_2]) ).
cnf(f_77_4,plain,
( ~ empty(relation_rng(U_381))
| ~ relation(U_381)
| empty(U_381) ),
inference(clausify,[status(thm)],[f_77_3]) ).
fof(f_78_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_78_2,plain,
! [U_382] :
( ( relation(relation_dom(U_382))
& empty(relation_dom(U_382)) )
| ~ empty(U_382) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
fof(f_78_3,plain,
( ! [U_382] :
( relation(relation_dom(U_382))
| ~ sP86(U_382) )
& ! [U_382] :
( empty(relation_dom(U_382))
| ~ sP86(U_382) )
& ! [U_382] :
( sP86(U_382)
| ~ empty(U_382) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP86])],[f_78_2]) ).
cnf(f_78_4,plain,
( sP86(U_382)
| ~ empty(U_382) ),
inference(clausify,[status(thm)],[f_78_3]) ).
cnf(f_78_5,plain,
( empty(relation_dom(U_382))
| ~ sP86(U_382) ),
inference(clausify,[status(thm)],[f_78_3]) ).
cnf(f_78_6,plain,
( relation(relation_dom(U_382))
| ~ sP86(U_382) ),
inference(clausify,[status(thm)],[f_78_3]) ).
fof(f_79_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_79_2,plain,
! [U_383] :
( ( relation(relation_rng(U_383))
& empty(relation_rng(U_383)) )
| ~ empty(U_383) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
fof(f_79_3,plain,
( ! [U_383] :
( relation(relation_rng(U_383))
| ~ sP87(U_383) )
& ! [U_383] :
( empty(relation_rng(U_383))
| ~ sP87(U_383) )
& ! [U_383] :
( sP87(U_383)
| ~ empty(U_383) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP87])],[f_79_2]) ).
cnf(f_79_4,plain,
( sP87(U_383)
| ~ empty(U_383) ),
inference(clausify,[status(thm)],[f_79_3]) ).
cnf(f_79_5,plain,
( empty(relation_rng(U_383))
| ~ sP87(U_383) ),
inference(clausify,[status(thm)],[f_79_3]) ).
cnf(f_79_6,plain,
( relation(relation_rng(U_383))
| ~ sP87(U_383) ),
inference(clausify,[status(thm)],[f_79_3]) ).
fof(f_80_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_80_2,plain,
! [U_385,U_384] :
( ( relation(relation_composition(U_385,U_384))
& empty(relation_composition(U_385,U_384)) )
| ~ relation(U_384)
| ~ empty(U_385) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
fof(f_80_3,plain,
( ! [U_385,U_384] :
( relation(relation_composition(U_385,U_384))
| ~ sP88(U_385,U_384) )
& ! [U_385,U_384] :
( empty(relation_composition(U_385,U_384))
| ~ sP88(U_385,U_384) )
& ! [U_385,U_384] :
( sP88(U_385,U_384)
| ~ relation(U_384)
| ~ empty(U_385) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP88])],[f_80_2]) ).
cnf(f_80_4,plain,
( sP88(U_385,U_384)
| ~ relation(U_384)
| ~ empty(U_385) ),
inference(clausify,[status(thm)],[f_80_3]) ).
cnf(f_80_5,plain,
( empty(relation_composition(U_385,U_384))
| ~ sP88(U_385,U_384) ),
inference(clausify,[status(thm)],[f_80_3]) ).
cnf(f_80_6,plain,
( relation(relation_composition(U_385,U_384))
| ~ sP88(U_385,U_384) ),
inference(clausify,[status(thm)],[f_80_3]) ).
fof(f_81_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_81_2,plain,
! [U_387,U_386] : set_union2(U_387,U_387) = U_387,
inference(variable_rename,[status(thm)],[f_81_1]) ).
fof(f_81_3,plain,
! [U_387] : set_union2(U_387,U_387) = U_387,
inference(miniscope,[status(thm)],[f_81_2]) ).
fof(f_81_4,plain,
! [U_387] : set_union2(U_387,U_387) = U_387,
inference(definitional_conversion,[status(esa)],[f_81_3]) ).
cnf(f_81_5,plain,
set_union2(U_387,U_387) = U_387,
inference(clausify,[status(thm)],[f_81_4]) ).
fof(f_82_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_82_2,plain,
! [U_389,U_388] : set_intersection2(U_389,U_389) = U_389,
inference(variable_rename,[status(thm)],[f_82_1]) ).
fof(f_82_3,plain,
! [U_389] : set_intersection2(U_389,U_389) = U_389,
inference(miniscope,[status(thm)],[f_82_2]) ).
fof(f_82_4,plain,
! [U_389] : set_intersection2(U_389,U_389) = U_389,
inference(definitional_conversion,[status(esa)],[f_82_3]) ).
cnf(f_82_5,plain,
set_intersection2(U_389,U_389) = U_389,
inference(clausify,[status(thm)],[f_82_4]) ).
fof(f_83_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_83_2,plain,
! [U_391,U_390] :
( subset_complement(U_391,subset_complement(U_391,U_390)) = U_390
| ~ element(U_390,powerset(U_391)) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
fof(f_83_3,plain,
! [U_390,U_391] :
( subset_complement(U_391,subset_complement(U_391,U_390)) = U_390
| ~ element(U_390,powerset(U_391)) ),
inference(definitional_conversion,[status(esa)],[f_83_2]) ).
cnf(f_83_4,plain,
( subset_complement(U_391,subset_complement(U_391,U_390)) = U_390
| ~ element(U_390,powerset(U_391)) ),
inference(clausify,[status(thm)],[f_83_3]) ).
fof(f_84_1,plain,
! [A] :
( relation_inverse(relation_inverse(A)) = A
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[involutiveness_k4_relat_1]) ).
fof(f_84_2,plain,
! [U_392] :
( relation_inverse(relation_inverse(U_392)) = U_392
| ~ relation(U_392) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
fof(f_84_3,plain,
! [U_392] :
( relation_inverse(relation_inverse(U_392)) = U_392
| ~ relation(U_392) ),
inference(definitional_conversion,[status(esa)],[f_84_2]) ).
cnf(f_84_4,plain,
( relation_inverse(relation_inverse(U_392)) = U_392
| ~ relation(U_392) ),
inference(clausify,[status(thm)],[f_84_3]) ).
fof(f_85_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_85_2,plain,
! [U_394,U_393] :
( complements_of_subsets(U_394,complements_of_subsets(U_394,U_393)) = U_393
| ~ element(U_393,powerset(powerset(U_394))) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
fof(f_85_3,plain,
! [U_393,U_394] :
( complements_of_subsets(U_394,complements_of_subsets(U_394,U_393)) = U_393
| ~ element(U_393,powerset(powerset(U_394))) ),
inference(definitional_conversion,[status(esa)],[f_85_2]) ).
cnf(f_85_4,plain,
( complements_of_subsets(U_394,complements_of_subsets(U_394,U_393)) = U_393
| ~ element(U_393,powerset(powerset(U_394))) ),
inference(clausify,[status(thm)],[f_85_3]) ).
fof(f_86_1,plain,
! [A,B] : ~ proper_subset(A,A),
inference(fof_nnf,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(f_86_2,plain,
! [U_396,U_395] : ~ proper_subset(U_396,U_396),
inference(variable_rename,[status(thm)],[f_86_1]) ).
fof(f_86_3,plain,
! [U_396] : ~ proper_subset(U_396,U_396),
inference(miniscope,[status(thm)],[f_86_2]) ).
fof(f_86_4,plain,
! [U_396] : ~ proper_subset(U_396,U_396),
inference(definitional_conversion,[status(esa)],[f_86_3]) ).
cnf(f_86_5,plain,
~ proper_subset(U_396,U_396),
inference(clausify,[status(thm)],[f_86_4]) ).
fof(f_87_1,plain,
! [A] : singleton(A) != empty_set,
inference(fof_nnf,[status(thm)],[l1_zfmisc_1]) ).
fof(f_87_2,plain,
! [U_397] : singleton(U_397) != empty_set,
inference(variable_rename,[status(thm)],[f_87_1]) ).
fof(f_87_3,plain,
! [U_397] : singleton(U_397) != empty_set,
inference(definitional_conversion,[status(esa)],[f_87_2]) ).
cnf(f_87_4,plain,
singleton(U_397) != empty_set,
inference(clausify,[status(thm)],[f_87_3]) ).
fof(f_88_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l23_zfmisc_1]) ).
fof(f_88_2,plain,
! [U_399,U_398] :
( set_union2(singleton(U_399),U_398) = U_398
| ~ in(U_399,U_398) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
fof(f_88_3,plain,
! [U_398,U_399] :
( set_union2(singleton(U_399),U_398) = U_398
| ~ in(U_399,U_398) ),
inference(definitional_conversion,[status(esa)],[f_88_2]) ).
cnf(f_88_4,plain,
( set_union2(singleton(U_399),U_398) = U_398
| ~ in(U_399,U_398) ),
inference(clausify,[status(thm)],[f_88_3]) ).
fof(f_89_1,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(fof_nnf,[status(thm)],[l25_zfmisc_1]) ).
fof(f_89_2,plain,
! [U_401,U_400] :
( ~ in(U_401,U_400)
| ~ disjoint(singleton(U_401),U_400) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
fof(f_89_3,plain,
! [U_401,U_400] :
( ~ in(U_401,U_400)
| ~ disjoint(singleton(U_401),U_400) ),
inference(definitional_conversion,[status(esa)],[f_89_2]) ).
cnf(f_89_4,plain,
( ~ in(U_401,U_400)
| ~ disjoint(singleton(U_401),U_400) ),
inference(clausify,[status(thm)],[f_89_3]) ).
fof(f_90_1,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(fof_nnf,[status(thm)],[l28_zfmisc_1]) ).
fof(f_90_2,plain,
! [U_403,U_402] :
( disjoint(singleton(U_403),U_402)
| in(U_403,U_402) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
fof(f_90_3,plain,
! [U_402,U_403] :
( disjoint(singleton(U_403),U_402)
| in(U_403,U_402) ),
inference(definitional_conversion,[status(esa)],[f_90_2]) ).
cnf(f_90_4,plain,
( disjoint(singleton(U_403),U_402)
| in(U_403,U_402) ),
inference(clausify,[status(thm)],[f_90_3]) ).
fof(f_91_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_91_2,plain,
! [U_405,U_404] :
( ( subset(singleton(U_405),U_404)
| ~ in(U_405,U_404) )
& ( in(U_405,U_404)
| ~ subset(singleton(U_405),U_404) ) ),
inference(variable_rename,[status(thm)],[f_91_1]) ).
fof(f_91_3,plain,
( ! [U_409,U_407] :
( subset(singleton(U_409),U_407)
| ~ in(U_409,U_407) )
& ! [U_408,U_406] :
( in(U_408,U_406)
| ~ subset(singleton(U_408),U_406) ) ),
inference(miniscope,[status(thm)],[f_91_2]) ).
fof(f_91_4,plain,
( ! [U_407,U_409] :
( subset(singleton(U_409),U_407)
| ~ in(U_409,U_407) )
& ! [U_406,U_408] :
( in(U_408,U_406)
| ~ subset(singleton(U_408),U_406) ) ),
inference(definitional_conversion,[status(esa)],[f_91_3]) ).
cnf(f_91_5,plain,
( in(U_408,U_406)
| ~ subset(singleton(U_408),U_406) ),
inference(clausify,[status(thm)],[f_91_4]) ).
cnf(f_91_6,plain,
( subset(singleton(U_409),U_407)
| ~ in(U_409,U_407) ),
inference(clausify,[status(thm)],[f_91_4]) ).
fof(f_92_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_92_2,plain,
! [U_411,U_410] :
( ( set_difference(U_411,U_410) = empty_set
| ~ subset(U_411,U_410) )
& ( subset(U_411,U_410)
| set_difference(U_411,U_410) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
fof(f_92_3,plain,
( ! [U_415,U_413] :
( set_difference(U_415,U_413) = empty_set
| ~ subset(U_415,U_413) )
& ! [U_414,U_412] :
( subset(U_414,U_412)
| set_difference(U_414,U_412) != empty_set ) ),
inference(miniscope,[status(thm)],[f_92_2]) ).
fof(f_92_4,plain,
( ! [U_413,U_415] :
( set_difference(U_415,U_413) = empty_set
| ~ subset(U_415,U_413) )
& ! [U_412,U_414] :
( subset(U_414,U_412)
| set_difference(U_414,U_412) != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_92_3]) ).
cnf(f_92_5,plain,
( subset(U_414,U_412)
| set_difference(U_414,U_412) != empty_set ),
inference(clausify,[status(thm)],[f_92_4]) ).
cnf(f_92_6,plain,
( set_difference(U_415,U_413) = empty_set
| ~ subset(U_415,U_413) ),
inference(clausify,[status(thm)],[f_92_4]) ).
fof(f_93_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_93_2,plain,
! [U_418,U_417] :
( ! [U_416] :
( in(U_416,U_418)
| ~ in(U_416,U_417) )
| ~ element(U_417,powerset(U_418)) ),
inference(variable_rename,[status(thm)],[f_93_1]) ).
fof(f_93_3,plain,
! [U_418,U_416,U_417] :
( in(U_416,U_418)
| ~ in(U_416,U_417)
| ~ element(U_417,powerset(U_418)) ),
inference(definitional_conversion,[status(esa)],[f_93_2]) ).
cnf(f_93_4,plain,
( in(U_416,U_418)
| ~ in(U_416,U_417)
| ~ element(U_417,powerset(U_418)) ),
inference(clausify,[status(thm)],[f_93_3]) ).
fof(f_94_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_94_2,plain,
! [U_421,U_420,U_419] :
( subset(U_421,set_difference(U_420,singleton(U_419)))
| in(U_419,U_421)
| ~ subset(U_421,U_420) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
fof(f_94_3,plain,
! [U_421,U_420] :
( ! [U_419] :
( subset(U_421,set_difference(U_420,singleton(U_419)))
| in(U_419,U_421) )
| ~ subset(U_421,U_420) ),
inference(miniscope,[status(thm)],[f_94_2]) ).
fof(f_94_4,plain,
! [U_419,U_420,U_421] :
( subset(U_421,set_difference(U_420,singleton(U_419)))
| in(U_419,U_421)
| ~ subset(U_421,U_420) ),
inference(definitional_conversion,[status(esa)],[f_94_3]) ).
cnf(f_94_5,plain,
( subset(U_421,set_difference(U_420,singleton(U_419)))
| in(U_419,U_421)
| ~ subset(U_421,U_420) ),
inference(clausify,[status(thm)],[f_94_4]) ).
fof(f_95_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_95_2,plain,
! [U_423,U_422] :
( ( subset(U_423,singleton(U_422))
| ( U_423 != singleton(U_422)
& U_423 != empty_set ) )
& ( U_423 = singleton(U_422)
| U_423 = empty_set
| ~ subset(U_423,singleton(U_422)) ) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
fof(f_95_3,plain,
( ! [U_427,U_425] :
( subset(U_427,singleton(U_425))
| ( U_427 != singleton(U_425)
& U_427 != empty_set ) )
& ! [U_426,U_424] :
( U_426 = singleton(U_424)
| U_426 = empty_set
| ~ subset(U_426,singleton(U_424)) ) ),
inference(miniscope,[status(thm)],[f_95_2]) ).
fof(f_95_4,plain,
( ! [U_425,U_427] :
( U_427 != singleton(U_425)
| ~ sP89(U_425,U_427) )
& ! [U_425,U_427] :
( U_427 != empty_set
| ~ sP89(U_425,U_427) )
& ! [U_425,U_427] :
( subset(U_427,singleton(U_425))
| sP89(U_425,U_427) )
& ! [U_426,U_424] :
( U_426 = singleton(U_424)
| U_426 = empty_set
| ~ subset(U_426,singleton(U_424)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP89])],[f_95_3]) ).
cnf(f_95_5,plain,
( U_426 = singleton(U_424)
| U_426 = empty_set
| ~ subset(U_426,singleton(U_424)) ),
inference(clausify,[status(thm)],[f_95_4]) ).
cnf(f_95_6,plain,
( subset(U_427,singleton(U_425))
| sP89(U_425,U_427) ),
inference(clausify,[status(thm)],[f_95_4]) ).
cnf(f_95_7,plain,
( U_427 != empty_set
| ~ sP89(U_425,U_427) ),
inference(clausify,[status(thm)],[f_95_4]) ).
cnf(f_95_8,plain,
( U_427 != singleton(U_425)
| ~ sP89(U_425,U_427) ),
inference(clausify,[status(thm)],[f_95_4]) ).
fof(f_96_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l50_zfmisc_1]) ).
fof(f_96_2,plain,
! [U_429,U_428] :
( subset(U_429,union(U_428))
| ~ in(U_429,U_428) ),
inference(variable_rename,[status(thm)],[f_96_1]) ).
fof(f_96_3,plain,
! [U_428,U_429] :
( subset(U_429,union(U_428))
| ~ in(U_429,U_428) ),
inference(definitional_conversion,[status(esa)],[f_96_2]) ).
cnf(f_96_4,plain,
( subset(U_429,union(U_428))
| ~ in(U_429,U_428) ),
inference(clausify,[status(thm)],[f_96_3]) ).
fof(f_97_1,plain,
! [A,B,C,D] :
( ( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(B,D)
| ~ in(A,C) )
& ( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(fof_nnf,[status(thm)],[l55_zfmisc_1]) ).
fof(f_97_2,plain,
! [U_433,U_432,U_431,U_430] :
( ( in(ordered_pair(U_433,U_432),cartesian_product2(U_431,U_430))
| ~ in(U_432,U_430)
| ~ in(U_433,U_431) )
& ( ( in(U_432,U_430)
& in(U_433,U_431) )
| ~ in(ordered_pair(U_433,U_432),cartesian_product2(U_431,U_430)) ) ),
inference(variable_rename,[status(thm)],[f_97_1]) ).
fof(f_97_3,plain,
( ! [U_441,U_439,U_437,U_435] :
( in(ordered_pair(U_441,U_439),cartesian_product2(U_437,U_435))
| ~ in(U_439,U_435)
| ~ in(U_441,U_437) )
& ! [U_440,U_438,U_436,U_434] :
( ( in(U_438,U_434)
& in(U_440,U_436) )
| ~ in(ordered_pair(U_440,U_438),cartesian_product2(U_436,U_434)) ) ),
inference(miniscope,[status(thm)],[f_97_2]) ).
fof(f_97_4,plain,
( ! [U_436,U_440,U_434,U_438] :
( in(U_438,U_434)
| ~ sP90(U_436,U_440,U_434,U_438) )
& ! [U_436,U_440,U_434,U_438] :
( in(U_440,U_436)
| ~ sP90(U_436,U_440,U_434,U_438) )
& ! [U_439,U_435,U_437,U_441] :
( in(ordered_pair(U_441,U_439),cartesian_product2(U_437,U_435))
| ~ in(U_439,U_435)
| ~ in(U_441,U_437) )
& ! [U_436,U_440,U_434,U_438] :
( sP90(U_436,U_440,U_434,U_438)
| ~ in(ordered_pair(U_440,U_438),cartesian_product2(U_436,U_434)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP90])],[f_97_3]) ).
cnf(f_97_5,plain,
( sP90(U_436,U_440,U_434,U_438)
| ~ in(ordered_pair(U_440,U_438),cartesian_product2(U_436,U_434)) ),
inference(clausify,[status(thm)],[f_97_4]) ).
cnf(f_97_6,plain,
( in(ordered_pair(U_441,U_439),cartesian_product2(U_437,U_435))
| ~ in(U_439,U_435)
| ~ in(U_441,U_437) ),
inference(clausify,[status(thm)],[f_97_4]) ).
cnf(f_97_7,plain,
( in(U_440,U_436)
| ~ sP90(U_436,U_440,U_434,U_438) ),
inference(clausify,[status(thm)],[f_97_4]) ).
cnf(f_97_8,plain,
( in(U_438,U_434)
| ~ sP90(U_436,U_440,U_434,U_438) ),
inference(clausify,[status(thm)],[f_97_4]) ).
fof(f_98_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_98_2,plain,
! [U_444,U_443] :
( element(U_444,powerset(U_443))
| ? [U_442] :
( ~ in(U_442,U_443)
& in(U_442,U_444) ) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
fof(f_98_3,plain,
! [U_444,U_443] :
( element(U_444,powerset(U_443))
| ( ~ in(sK70(U_444,U_443),U_443)
& in(sK70(U_444,U_443),U_444) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_442,sK70(U_444,U_443))],[f_98_2]) ).
fof(f_98_4,plain,
( ! [U_444,U_443] :
( ~ in(sK70(U_444,U_443),U_443)
| ~ sP91(U_444,U_443) )
& ! [U_444,U_443] :
( in(sK70(U_444,U_443),U_444)
| ~ sP91(U_444,U_443) )
& ! [U_444,U_443] :
( element(U_444,powerset(U_443))
| sP91(U_444,U_443) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP91])],[f_98_3]) ).
cnf(f_98_5,plain,
( element(U_444,powerset(U_443))
| sP91(U_444,U_443) ),
inference(clausify,[status(thm)],[f_98_4]) ).
cnf(f_98_6,plain,
( in(sK70(U_444,U_443),U_444)
| ~ sP91(U_444,U_443) ),
inference(clausify,[status(thm)],[f_98_4]) ).
cnf(f_98_7,plain,
( ~ in(sK70(U_444,U_443),U_443)
| ~ sP91(U_444,U_443) ),
inference(clausify,[status(thm)],[f_98_4]) ).
fof(f_99_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_99_2,plain,
? [U_445] :
( relation(U_445)
& empty(U_445) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
fof(f_99_3,plain,
( relation(sK71)
& empty(sK71) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_445,sK71)],[f_99_2]) ).
fof(f_99_4,plain,
( relation(sK71)
& empty(sK71) ),
inference(definitional_conversion,[status(esa)],[f_99_3]) ).
cnf(f_99_5,plain,
empty(sK71),
inference(clausify,[status(thm)],[f_99_4]) ).
cnf(f_99_6,plain,
relation(sK71),
inference(clausify,[status(thm)],[f_99_4]) ).
fof(f_100_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_100_2,plain,
! [U_447] :
( ? [U_446] :
( ~ empty(U_446)
& element(U_446,powerset(U_447)) )
| empty(U_447) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
fof(f_100_3,plain,
! [U_447] :
( ( ~ empty(sK72(U_447))
& element(sK72(U_447),powerset(U_447)) )
| empty(U_447) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_446,sK72(U_447))],[f_100_2]) ).
fof(f_100_4,plain,
( ! [U_447] :
( ~ empty(sK72(U_447))
| ~ sP92(U_447) )
& ! [U_447] :
( element(sK72(U_447),powerset(U_447))
| ~ sP92(U_447) )
& ! [U_447] :
( sP92(U_447)
| empty(U_447) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP92])],[f_100_3]) ).
cnf(f_100_5,plain,
( sP92(U_447)
| empty(U_447) ),
inference(clausify,[status(thm)],[f_100_4]) ).
cnf(f_100_6,plain,
( element(sK72(U_447),powerset(U_447))
| ~ sP92(U_447) ),
inference(clausify,[status(thm)],[f_100_4]) ).
cnf(f_100_7,plain,
( ~ empty(sK72(U_447))
| ~ sP92(U_447) ),
inference(clausify,[status(thm)],[f_100_4]) ).
fof(f_101_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_101_2,plain,
? [U_448] : empty(U_448),
inference(variable_rename,[status(thm)],[f_101_1]) ).
fof(f_101_3,plain,
empty(sK73),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_448,sK73)],[f_101_2]) ).
fof(f_101_4,plain,
empty(sK73),
inference(definitional_conversion,[status(esa)],[f_101_3]) ).
cnf(f_101_5,plain,
empty(sK73),
inference(clausify,[status(thm)],[f_101_4]) ).
fof(f_102_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_102_2,plain,
? [U_449] :
( relation(U_449)
& ~ empty(U_449) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
fof(f_102_3,plain,
( relation(sK74)
& ~ empty(sK74) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_449,sK74)],[f_102_2]) ).
fof(f_102_4,plain,
( relation(sK74)
& ~ empty(sK74) ),
inference(definitional_conversion,[status(esa)],[f_102_3]) ).
cnf(f_102_5,plain,
~ empty(sK74),
inference(clausify,[status(thm)],[f_102_4]) ).
cnf(f_102_6,plain,
relation(sK74),
inference(clausify,[status(thm)],[f_102_4]) ).
fof(f_103_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_103_2,plain,
! [U_451] :
? [U_450] :
( empty(U_450)
& element(U_450,powerset(U_451)) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
fof(f_103_3,plain,
! [U_451] :
( empty(sK75(U_451))
& element(sK75(U_451),powerset(U_451)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_450,sK75(U_451))],[f_103_2]) ).
fof(f_103_4,plain,
( ! [U_451] : empty(sK75(U_451))
& ! [U_451] : element(sK75(U_451),powerset(U_451)) ),
inference(definitional_conversion,[status(esa)],[f_103_3]) ).
cnf(f_103_5,plain,
element(sK75(U_451),powerset(U_451)),
inference(clausify,[status(thm)],[f_103_4]) ).
cnf(f_103_6,plain,
empty(sK75(U_451)),
inference(clausify,[status(thm)],[f_103_4]) ).
fof(f_104_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_104_2,plain,
? [U_452] : ~ empty(U_452),
inference(variable_rename,[status(thm)],[f_104_1]) ).
fof(f_104_3,plain,
~ empty(sK76),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_452,sK76)],[f_104_2]) ).
fof(f_104_4,plain,
~ empty(sK76),
inference(definitional_conversion,[status(esa)],[f_104_3]) ).
cnf(f_104_5,plain,
~ empty(sK76),
inference(clausify,[status(thm)],[f_104_4]) ).
fof(f_105_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_105_2,plain,
! [U_454,U_453] :
( union_of_subsets(U_454,U_453) = union(U_453)
| ~ element(U_453,powerset(powerset(U_454))) ),
inference(variable_rename,[status(thm)],[f_105_1]) ).
fof(f_105_3,plain,
! [U_453,U_454] :
( union_of_subsets(U_454,U_453) = union(U_453)
| ~ element(U_453,powerset(powerset(U_454))) ),
inference(definitional_conversion,[status(esa)],[f_105_2]) ).
cnf(f_105_4,plain,
( union_of_subsets(U_454,U_453) = union(U_453)
| ~ element(U_453,powerset(powerset(U_454))) ),
inference(clausify,[status(thm)],[f_105_3]) ).
fof(f_106_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_106_2,plain,
! [U_456,U_455] :
( meet_of_subsets(U_456,U_455) = set_meet(U_455)
| ~ element(U_455,powerset(powerset(U_456))) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
fof(f_106_3,plain,
! [U_455,U_456] :
( meet_of_subsets(U_456,U_455) = set_meet(U_455)
| ~ element(U_455,powerset(powerset(U_456))) ),
inference(definitional_conversion,[status(esa)],[f_106_2]) ).
cnf(f_106_4,plain,
( meet_of_subsets(U_456,U_455) = set_meet(U_455)
| ~ element(U_455,powerset(powerset(U_456))) ),
inference(clausify,[status(thm)],[f_106_3]) ).
fof(f_107_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_107_2,plain,
! [U_459,U_458,U_457] :
( subset_difference(U_459,U_458,U_457) = set_difference(U_458,U_457)
| ~ element(U_457,powerset(U_459))
| ~ element(U_458,powerset(U_459)) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
fof(f_107_3,plain,
! [U_457,U_458,U_459] :
( subset_difference(U_459,U_458,U_457) = set_difference(U_458,U_457)
| ~ element(U_457,powerset(U_459))
| ~ element(U_458,powerset(U_459)) ),
inference(definitional_conversion,[status(esa)],[f_107_2]) ).
cnf(f_107_4,plain,
( subset_difference(U_459,U_458,U_457) = set_difference(U_458,U_457)
| ~ element(U_457,powerset(U_459))
| ~ element(U_458,powerset(U_459)) ),
inference(clausify,[status(thm)],[f_107_3]) ).
fof(f_108_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_108_2,plain,
! [U_461,U_460] : subset(U_461,U_461),
inference(variable_rename,[status(thm)],[f_108_1]) ).
fof(f_108_3,plain,
! [U_461] : subset(U_461,U_461),
inference(miniscope,[status(thm)],[f_108_2]) ).
fof(f_108_4,plain,
! [U_461] : subset(U_461,U_461),
inference(definitional_conversion,[status(esa)],[f_108_3]) ).
cnf(f_108_5,plain,
subset(U_461,U_461),
inference(clausify,[status(thm)],[f_108_4]) ).
fof(f_109_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_109_2,plain,
! [U_463,U_462] :
( disjoint(U_462,U_463)
| ~ disjoint(U_463,U_462) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
fof(f_109_3,plain,
! [U_462,U_463] :
( disjoint(U_462,U_463)
| ~ disjoint(U_463,U_462) ),
inference(definitional_conversion,[status(esa)],[f_109_2]) ).
cnf(f_109_4,plain,
( disjoint(U_462,U_463)
| ~ disjoint(U_463,U_462) ),
inference(clausify,[status(thm)],[f_109_3]) ).
fof(f_110_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_110_2,plain,
! [U_467,U_466,U_465,U_464] :
( ( in(ordered_pair(U_467,U_466),cartesian_product2(U_465,U_464))
| ~ in(U_466,U_464)
| ~ in(U_467,U_465) )
& ( ( in(U_466,U_464)
& in(U_467,U_465) )
| ~ in(ordered_pair(U_467,U_466),cartesian_product2(U_465,U_464)) ) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
fof(f_110_3,plain,
( ! [U_475,U_473,U_471,U_469] :
( in(ordered_pair(U_475,U_473),cartesian_product2(U_471,U_469))
| ~ in(U_473,U_469)
| ~ in(U_475,U_471) )
& ! [U_474,U_472,U_470,U_468] :
( ( in(U_472,U_468)
& in(U_474,U_470) )
| ~ in(ordered_pair(U_474,U_472),cartesian_product2(U_470,U_468)) ) ),
inference(miniscope,[status(thm)],[f_110_2]) ).
fof(f_110_4,plain,
( ! [U_474,U_470,U_468,U_472] :
( in(U_472,U_468)
| ~ sP93(U_474,U_470,U_468,U_472) )
& ! [U_474,U_470,U_468,U_472] :
( in(U_474,U_470)
| ~ sP93(U_474,U_470,U_468,U_472) )
& ! [U_475,U_469,U_473,U_471] :
( in(ordered_pair(U_475,U_473),cartesian_product2(U_471,U_469))
| ~ in(U_473,U_469)
| ~ in(U_475,U_471) )
& ! [U_474,U_470,U_468,U_472] :
( sP93(U_474,U_470,U_468,U_472)
| ~ in(ordered_pair(U_474,U_472),cartesian_product2(U_470,U_468)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP93])],[f_110_3]) ).
cnf(f_110_5,plain,
( sP93(U_474,U_470,U_468,U_472)
| ~ in(ordered_pair(U_474,U_472),cartesian_product2(U_470,U_468)) ),
inference(clausify,[status(thm)],[f_110_4]) ).
cnf(f_110_6,plain,
( in(ordered_pair(U_475,U_473),cartesian_product2(U_471,U_469))
| ~ in(U_473,U_469)
| ~ in(U_475,U_471) ),
inference(clausify,[status(thm)],[f_110_4]) ).
cnf(f_110_7,plain,
( in(U_474,U_470)
| ~ sP93(U_474,U_470,U_468,U_472) ),
inference(clausify,[status(thm)],[f_110_4]) ).
cnf(f_110_8,plain,
( in(U_472,U_468)
| ~ sP93(U_474,U_470,U_468,U_472) ),
inference(clausify,[status(thm)],[f_110_4]) ).
fof(f_111_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_111_2,plain,
! [U_479,U_478,U_477,U_476] :
( U_479 = U_476
| U_479 = U_477
| unordered_pair(U_479,U_478) != unordered_pair(U_477,U_476) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
fof(f_111_3,plain,
! [U_479,U_478,U_477] :
( ! [U_476] :
( U_479 = U_476
| unordered_pair(U_479,U_478) != unordered_pair(U_477,U_476) )
| U_479 = U_477 ),
inference(miniscope,[status(thm)],[f_111_2]) ).
fof(f_111_4,plain,
! [U_479,U_477,U_478,U_476] :
( U_479 = U_476
| unordered_pair(U_479,U_478) != unordered_pair(U_477,U_476)
| U_479 = U_477 ),
inference(definitional_conversion,[status(esa)],[f_111_3]) ).
cnf(f_111_5,plain,
( U_479 = U_476
| unordered_pair(U_479,U_478) != unordered_pair(U_477,U_476)
| U_479 = U_477 ),
inference(clausify,[status(thm)],[f_111_4]) ).
fof(f_112_1,plain,
! [A,B,C] :
( ( ( in(A,relation_rng(relation_rng_restriction(B,C)))
| ~ in(A,relation_rng(C))
| ~ in(A,B) )
& ( ( in(A,relation_rng(C))
& in(A,B) )
| ~ in(A,relation_rng(relation_rng_restriction(B,C))) ) )
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t115_relat_1]) ).
fof(f_112_2,plain,
! [U_482,U_481,U_480] :
( ( ( in(U_482,relation_rng(relation_rng_restriction(U_481,U_480)))
| ~ in(U_482,relation_rng(U_480))
| ~ in(U_482,U_481) )
& ( ( in(U_482,relation_rng(U_480))
& in(U_482,U_481) )
| ~ in(U_482,relation_rng(relation_rng_restriction(U_481,U_480))) ) )
| ~ relation(U_480) ),
inference(variable_rename,[status(thm)],[f_112_1]) ).
fof(f_112_3,plain,
( ! [U_482,U_480,U_481] :
( in(U_482,relation_rng(U_480))
| ~ sP94(U_482,U_480,U_481) )
& ! [U_482,U_480,U_481] :
( in(U_482,U_481)
| ~ sP94(U_482,U_480,U_481) )
& ! [U_482,U_480,U_481] :
( in(U_482,relation_rng(relation_rng_restriction(U_481,U_480)))
| ~ in(U_482,relation_rng(U_480))
| ~ in(U_482,U_481)
| ~ sP95(U_482,U_480,U_481) )
& ! [U_482,U_480,U_481] :
( sP94(U_482,U_480,U_481)
| ~ in(U_482,relation_rng(relation_rng_restriction(U_481,U_480)))
| ~ sP95(U_482,U_480,U_481) )
& ! [U_482,U_480,U_481] :
( sP95(U_482,U_480,U_481)
| ~ relation(U_480) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP94,sP95])],[f_112_2]) ).
cnf(f_112_4,plain,
( sP95(U_482,U_480,U_481)
| ~ relation(U_480) ),
inference(clausify,[status(thm)],[f_112_3]) ).
cnf(f_112_5,plain,
( sP94(U_482,U_480,U_481)
| ~ in(U_482,relation_rng(relation_rng_restriction(U_481,U_480)))
| ~ sP95(U_482,U_480,U_481) ),
inference(clausify,[status(thm)],[f_112_3]) ).
cnf(f_112_6,plain,
( in(U_482,relation_rng(relation_rng_restriction(U_481,U_480)))
| ~ in(U_482,relation_rng(U_480))
| ~ in(U_482,U_481)
| ~ sP95(U_482,U_480,U_481) ),
inference(clausify,[status(thm)],[f_112_3]) ).
cnf(f_112_7,plain,
( in(U_482,U_481)
| ~ sP94(U_482,U_480,U_481) ),
inference(clausify,[status(thm)],[f_112_3]) ).
cnf(f_112_8,plain,
( in(U_482,relation_rng(U_480))
| ~ sP94(U_482,U_480,U_481) ),
inference(clausify,[status(thm)],[f_112_3]) ).
fof(f_113_1,plain,
! [A,B] :
( subset(relation_rng(relation_rng_restriction(A,B)),A)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t116_relat_1]) ).
fof(f_113_2,plain,
! [U_484,U_483] :
( subset(relation_rng(relation_rng_restriction(U_484,U_483)),U_484)
| ~ relation(U_483) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
fof(f_113_3,plain,
! [U_484,U_483] :
( subset(relation_rng(relation_rng_restriction(U_484,U_483)),U_484)
| ~ relation(U_483) ),
inference(definitional_conversion,[status(esa)],[f_113_2]) ).
cnf(f_113_4,plain,
( subset(relation_rng(relation_rng_restriction(U_484,U_483)),U_484)
| ~ relation(U_483) ),
inference(clausify,[status(thm)],[f_113_3]) ).
fof(f_114_1,plain,
! [A,B] :
( subset(relation_rng_restriction(A,B),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t117_relat_1]) ).
fof(f_114_2,plain,
! [U_486,U_485] :
( subset(relation_rng_restriction(U_486,U_485),U_485)
| ~ relation(U_485) ),
inference(variable_rename,[status(thm)],[f_114_1]) ).
fof(f_114_3,plain,
! [U_485,U_486] :
( subset(relation_rng_restriction(U_486,U_485),U_485)
| ~ relation(U_485) ),
inference(definitional_conversion,[status(esa)],[f_114_2]) ).
cnf(f_114_4,plain,
( subset(relation_rng_restriction(U_486,U_485),U_485)
| ~ relation(U_485) ),
inference(clausify,[status(thm)],[f_114_3]) ).
fof(f_115_1,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ),
inference(negate,[status(cth)],[t118_relat_1]) ).
fof(f_115_2,negated_conjecture,
? [A,B] :
( ~ subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B))
& relation(B) ),
inference(fof_nnf,[status(thm)],[f_115_1]) ).
fof(f_115_3,negated_conjecture,
? [U_488,U_487] :
( ~ subset(relation_rng(relation_rng_restriction(U_488,U_487)),relation_rng(U_487))
& relation(U_487) ),
inference(variable_rename,[status(thm)],[f_115_2]) ).
fof(f_115_4,negated_conjecture,
? [U_487] :
( ~ subset(relation_rng(relation_rng_restriction(sK77,U_487)),relation_rng(U_487))
& relation(U_487) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_488,sK77)],[f_115_3]) ).
fof(f_115_5,negated_conjecture,
( ~ subset(relation_rng(relation_rng_restriction(sK77,sK78)),relation_rng(sK78))
& relation(sK78) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_487,sK78)],[f_115_4]) ).
fof(f_115_6,negated_conjecture,
( ~ subset(relation_rng(relation_rng_restriction(sK77,sK78)),relation_rng(sK78))
& relation(sK78) ),
inference(definitional_conversion,[status(esa)],[f_115_5]) ).
cnf(f_115_7,negated_conjecture,
relation(sK78),
inference(clausify,[status(thm)],[f_115_6]) ).
cnf(f_115_8,negated_conjecture,
~ subset(relation_rng(relation_rng_restriction(sK77,sK78)),relation_rng(sK78)),
inference(clausify,[status(thm)],[f_115_6]) ).
fof(f_116_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_116_2,plain,
! [U_491,U_490,U_489] :
( ( subset(cartesian_product2(U_489,U_491),cartesian_product2(U_489,U_490))
& subset(cartesian_product2(U_491,U_489),cartesian_product2(U_490,U_489)) )
| ~ subset(U_491,U_490) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
fof(f_116_3,plain,
! [U_491,U_490] :
( ( ! [U_493] : subset(cartesian_product2(U_493,U_491),cartesian_product2(U_493,U_490))
& ! [U_492] : subset(cartesian_product2(U_491,U_492),cartesian_product2(U_490,U_492)) )
| ~ subset(U_491,U_490) ),
inference(miniscope,[status(thm)],[f_116_2]) ).
fof(f_116_4,plain,
( ! [U_490,U_491,U_492,U_493] :
( subset(cartesian_product2(U_493,U_491),cartesian_product2(U_493,U_490))
| ~ sP96(U_490,U_491,U_492,U_493) )
& ! [U_490,U_491,U_492,U_493] :
( subset(cartesian_product2(U_491,U_492),cartesian_product2(U_490,U_492))
| ~ sP96(U_490,U_491,U_492,U_493) )
& ! [U_490,U_491,U_492,U_493] :
( sP96(U_490,U_491,U_492,U_493)
| ~ subset(U_491,U_490) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP96])],[f_116_3]) ).
cnf(f_116_5,plain,
( sP96(U_490,U_491,U_492,U_493)
| ~ subset(U_491,U_490) ),
inference(clausify,[status(thm)],[f_116_4]) ).
cnf(f_116_6,plain,
( subset(cartesian_product2(U_491,U_492),cartesian_product2(U_490,U_492))
| ~ sP96(U_490,U_491,U_492,U_493) ),
inference(clausify,[status(thm)],[f_116_4]) ).
cnf(f_116_7,plain,
( subset(cartesian_product2(U_493,U_491),cartesian_product2(U_493,U_490))
| ~ sP96(U_490,U_491,U_492,U_493) ),
inference(clausify,[status(thm)],[f_116_4]) ).
fof(f_117_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_117_2,plain,
! [U_497,U_496,U_495,U_494] :
( subset(cartesian_product2(U_497,U_495),cartesian_product2(U_496,U_494))
| ~ subset(U_495,U_494)
| ~ subset(U_497,U_496) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
fof(f_117_3,plain,
! [U_494,U_497,U_496,U_495] :
( subset(cartesian_product2(U_497,U_495),cartesian_product2(U_496,U_494))
| ~ subset(U_495,U_494)
| ~ subset(U_497,U_496) ),
inference(definitional_conversion,[status(esa)],[f_117_2]) ).
cnf(f_117_4,plain,
( subset(cartesian_product2(U_497,U_495),cartesian_product2(U_496,U_494))
| ~ subset(U_495,U_494)
| ~ subset(U_497,U_496) ),
inference(clausify,[status(thm)],[f_117_3]) ).
fof(f_118_1,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t12_xboole_1]) ).
fof(f_118_2,plain,
! [U_499,U_498] :
( set_union2(U_499,U_498) = U_498
| ~ subset(U_499,U_498) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
fof(f_118_3,plain,
! [U_499,U_498] :
( set_union2(U_499,U_498) = U_498
| ~ subset(U_499,U_498) ),
inference(definitional_conversion,[status(esa)],[f_118_2]) ).
cnf(f_118_4,plain,
( set_union2(U_499,U_498) = U_498
| ~ subset(U_499,U_498) ),
inference(clausify,[status(thm)],[f_118_3]) ).
fof(f_119_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_119_2,plain,
! [U_505] :
? [U_504] :
( ! [U_503] :
( in(U_503,U_504)
| are_equipotent(U_503,U_504)
| ~ subset(U_503,U_504) )
& ! [U_502] :
( in(powerset(U_502),U_504)
| ~ in(U_502,U_504) )
& ! [U_501,U_500] :
( in(U_500,U_504)
| ~ subset(U_500,U_501)
| ~ in(U_501,U_504) )
& in(U_505,U_504) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
fof(f_119_3,plain,
! [U_505] :
( ! [U_503] :
( in(U_503,sK79(U_505))
| are_equipotent(U_503,sK79(U_505))
| ~ subset(U_503,sK79(U_505)) )
& ! [U_502] :
( in(powerset(U_502),sK79(U_505))
| ~ in(U_502,sK79(U_505)) )
& ! [U_501,U_500] :
( in(U_500,sK79(U_505))
| ~ subset(U_500,U_501)
| ~ in(U_501,sK79(U_505)) )
& in(U_505,sK79(U_505)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_504,sK79(U_505))],[f_119_2]) ).
fof(f_119_4,plain,
( ! [U_503,U_505] :
( in(U_503,sK79(U_505))
| are_equipotent(U_503,sK79(U_505))
| ~ subset(U_503,sK79(U_505)) )
& ! [U_502,U_505] :
( in(powerset(U_502),sK79(U_505))
| ~ in(U_502,sK79(U_505)) )
& ! [U_501,U_500,U_505] :
( in(U_500,sK79(U_505))
| ~ subset(U_500,U_501)
| ~ in(U_501,sK79(U_505)) )
& ! [U_505] : in(U_505,sK79(U_505)) ),
inference(definitional_conversion,[status(esa)],[f_119_3]) ).
cnf(f_119_5,plain,
in(U_505,sK79(U_505)),
inference(clausify,[status(thm)],[f_119_4]) ).
cnf(f_119_6,plain,
( in(U_500,sK79(U_505))
| ~ subset(U_500,U_501)
| ~ in(U_501,sK79(U_505)) ),
inference(clausify,[status(thm)],[f_119_4]) ).
cnf(f_119_7,plain,
( in(powerset(U_502),sK79(U_505))
| ~ in(U_502,sK79(U_505)) ),
inference(clausify,[status(thm)],[f_119_4]) ).
cnf(f_119_8,plain,
( in(U_503,sK79(U_505))
| are_equipotent(U_503,sK79(U_505))
| ~ subset(U_503,sK79(U_505)) ),
inference(clausify,[status(thm)],[f_119_4]) ).
fof(f_120_1,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(fof_nnf,[status(thm)],[t17_xboole_1]) ).
fof(f_120_2,plain,
! [U_507,U_506] : subset(set_intersection2(U_507,U_506),U_507),
inference(variable_rename,[status(thm)],[f_120_1]) ).
fof(f_120_3,plain,
! [U_506,U_507] : subset(set_intersection2(U_507,U_506),U_507),
inference(definitional_conversion,[status(esa)],[f_120_2]) ).
cnf(f_120_4,plain,
subset(set_intersection2(U_507,U_506),U_507),
inference(clausify,[status(thm)],[f_120_3]) ).
fof(f_121_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_121_2,plain,
! [U_510,U_509,U_508] :
( subset(U_510,set_intersection2(U_509,U_508))
| ~ subset(U_510,U_508)
| ~ subset(U_510,U_509) ),
inference(variable_rename,[status(thm)],[f_121_1]) ).
fof(f_121_3,plain,
! [U_508,U_510,U_509] :
( subset(U_510,set_intersection2(U_509,U_508))
| ~ subset(U_510,U_508)
| ~ subset(U_510,U_509) ),
inference(definitional_conversion,[status(esa)],[f_121_2]) ).
cnf(f_121_4,plain,
( subset(U_510,set_intersection2(U_509,U_508))
| ~ subset(U_510,U_508)
| ~ subset(U_510,U_509) ),
inference(clausify,[status(thm)],[f_121_3]) ).
fof(f_122_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_122_2,plain,
! [U_511] : set_union2(U_511,empty_set) = U_511,
inference(variable_rename,[status(thm)],[f_122_1]) ).
fof(f_122_3,plain,
! [U_511] : set_union2(U_511,empty_set) = U_511,
inference(definitional_conversion,[status(esa)],[f_122_2]) ).
cnf(f_122_4,plain,
set_union2(U_511,empty_set) = U_511,
inference(clausify,[status(thm)],[f_122_3]) ).
fof(f_123_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_123_2,plain,
! [U_513,U_512] :
( element(U_513,U_512)
| ~ in(U_513,U_512) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
fof(f_123_3,plain,
! [U_513,U_512] :
( element(U_513,U_512)
| ~ in(U_513,U_512) ),
inference(definitional_conversion,[status(esa)],[f_123_2]) ).
cnf(f_123_4,plain,
( element(U_513,U_512)
| ~ in(U_513,U_512) ),
inference(clausify,[status(thm)],[f_123_3]) ).
fof(f_124_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_124_2,plain,
! [U_516,U_515,U_514] :
( subset(U_516,U_514)
| ~ subset(U_515,U_514)
| ~ subset(U_516,U_515) ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
fof(f_124_3,plain,
! [U_515,U_514,U_516] :
( subset(U_516,U_514)
| ~ subset(U_515,U_514)
| ~ subset(U_516,U_515) ),
inference(definitional_conversion,[status(esa)],[f_124_2]) ).
cnf(f_124_4,plain,
( subset(U_516,U_514)
| ~ subset(U_515,U_514)
| ~ subset(U_516,U_515) ),
inference(clausify,[status(thm)],[f_124_3]) ).
fof(f_125_1,plain,
powerset(empty_set) = singleton(empty_set),
inference(fof_nnf,[status(thm)],[t1_zfmisc_1]) ).
fof(f_125_2,plain,
powerset(empty_set) = singleton(empty_set),
inference(definitional_conversion,[status(esa)],[f_125_1]) ).
cnf(f_125_3,plain,
powerset(empty_set) = singleton(empty_set),
inference(clausify,[status(thm)],[f_125_2]) ).
fof(f_126_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_126_2,plain,
! [U_519,U_518,U_517] :
( ( in(U_518,relation_rng(U_517))
& in(U_519,relation_dom(U_517)) )
| ~ in(ordered_pair(U_519,U_518),U_517)
| ~ relation(U_517) ),
inference(variable_rename,[status(thm)],[f_126_1]) ).
fof(f_126_3,plain,
( ! [U_517,U_518,U_519] :
( in(U_518,relation_rng(U_517))
| ~ sP97(U_517,U_518,U_519) )
& ! [U_517,U_518,U_519] :
( in(U_519,relation_dom(U_517))
| ~ sP97(U_517,U_518,U_519) )
& ! [U_517,U_518,U_519] :
( sP97(U_517,U_518,U_519)
| ~ in(ordered_pair(U_519,U_518),U_517)
| ~ relation(U_517) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP97])],[f_126_2]) ).
cnf(f_126_4,plain,
( sP97(U_517,U_518,U_519)
| ~ in(ordered_pair(U_519,U_518),U_517)
| ~ relation(U_517) ),
inference(clausify,[status(thm)],[f_126_3]) ).
cnf(f_126_5,plain,
( in(U_519,relation_dom(U_517))
| ~ sP97(U_517,U_518,U_519) ),
inference(clausify,[status(thm)],[f_126_3]) ).
cnf(f_126_6,plain,
( in(U_518,relation_rng(U_517))
| ~ sP97(U_517,U_518,U_519) ),
inference(clausify,[status(thm)],[f_126_3]) ).
fof(f_127_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_127_2,plain,
! [U_520] :
( subset(U_520,cartesian_product2(relation_dom(U_520),relation_rng(U_520)))
| ~ relation(U_520) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
fof(f_127_3,plain,
! [U_520] :
( subset(U_520,cartesian_product2(relation_dom(U_520),relation_rng(U_520)))
| ~ relation(U_520) ),
inference(definitional_conversion,[status(esa)],[f_127_2]) ).
cnf(f_127_4,plain,
( subset(U_520,cartesian_product2(relation_dom(U_520),relation_rng(U_520)))
| ~ relation(U_520) ),
inference(clausify,[status(thm)],[f_127_3]) ).
fof(f_128_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_128_2,plain,
! [U_522] :
( ! [U_521] :
( ( subset(relation_rng(U_522),relation_rng(U_521))
& subset(relation_dom(U_522),relation_dom(U_521)) )
| ~ subset(U_522,U_521)
| ~ relation(U_521) )
| ~ relation(U_522) ),
inference(variable_rename,[status(thm)],[f_128_1]) ).
fof(f_128_3,plain,
( ! [U_521,U_522] :
( subset(relation_rng(U_522),relation_rng(U_521))
| ~ sP98(U_521,U_522) )
& ! [U_521,U_522] :
( subset(relation_dom(U_522),relation_dom(U_521))
| ~ sP98(U_521,U_522) )
& ! [U_521,U_522] :
( sP98(U_521,U_522)
| ~ subset(U_522,U_521)
| ~ relation(U_521)
| ~ relation(U_522) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP98])],[f_128_2]) ).
cnf(f_128_4,plain,
( sP98(U_521,U_522)
| ~ subset(U_522,U_521)
| ~ relation(U_521)
| ~ relation(U_522) ),
inference(clausify,[status(thm)],[f_128_3]) ).
cnf(f_128_5,plain,
( subset(relation_dom(U_522),relation_dom(U_521))
| ~ sP98(U_521,U_522) ),
inference(clausify,[status(thm)],[f_128_3]) ).
cnf(f_128_6,plain,
( subset(relation_rng(U_522),relation_rng(U_521))
| ~ sP98(U_521,U_522) ),
inference(clausify,[status(thm)],[f_128_3]) ).
fof(f_129_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_129_2,plain,
! [U_525,U_524,U_523] :
( subset(set_intersection2(U_525,U_523),set_intersection2(U_524,U_523))
| ~ subset(U_525,U_524) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
fof(f_129_3,plain,
! [U_525,U_524] :
( ! [U_523] : subset(set_intersection2(U_525,U_523),set_intersection2(U_524,U_523))
| ~ subset(U_525,U_524) ),
inference(miniscope,[status(thm)],[f_129_2]) ).
fof(f_129_4,plain,
! [U_525,U_524,U_523] :
( subset(set_intersection2(U_525,U_523),set_intersection2(U_524,U_523))
| ~ subset(U_525,U_524) ),
inference(definitional_conversion,[status(esa)],[f_129_3]) ).
cnf(f_129_5,plain,
( subset(set_intersection2(U_525,U_523),set_intersection2(U_524,U_523))
| ~ subset(U_525,U_524) ),
inference(clausify,[status(thm)],[f_129_4]) ).
fof(f_130_1,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t28_xboole_1]) ).
fof(f_130_2,plain,
! [U_527,U_526] :
( set_intersection2(U_527,U_526) = U_527
| ~ subset(U_527,U_526) ),
inference(variable_rename,[status(thm)],[f_130_1]) ).
fof(f_130_3,plain,
! [U_526,U_527] :
( set_intersection2(U_527,U_526) = U_527
| ~ subset(U_527,U_526) ),
inference(definitional_conversion,[status(esa)],[f_130_2]) ).
cnf(f_130_4,plain,
( set_intersection2(U_527,U_526) = U_527
| ~ subset(U_527,U_526) ),
inference(clausify,[status(thm)],[f_130_3]) ).
fof(f_131_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_131_2,plain,
! [U_528] : set_intersection2(U_528,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_131_1]) ).
fof(f_131_3,plain,
! [U_528] : set_intersection2(U_528,empty_set) = empty_set,
inference(definitional_conversion,[status(esa)],[f_131_2]) ).
cnf(f_131_4,plain,
set_intersection2(U_528,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_131_3]) ).
fof(f_132_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_132_2,plain,
! [U_530,U_529] :
( in(U_530,U_529)
| empty(U_529)
| ~ element(U_530,U_529) ),
inference(variable_rename,[status(thm)],[f_132_1]) ).
fof(f_132_3,plain,
! [U_530,U_529] :
( in(U_530,U_529)
| empty(U_529)
| ~ element(U_530,U_529) ),
inference(definitional_conversion,[status(esa)],[f_132_2]) ).
cnf(f_132_4,plain,
( in(U_530,U_529)
| empty(U_529)
| ~ element(U_530,U_529) ),
inference(clausify,[status(thm)],[f_132_3]) ).
fof(f_133_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_133_2,plain,
! [U_533,U_532] :
( U_533 = U_532
| ? [U_531] :
( ( ~ in(U_531,U_533)
& in(U_531,U_532) )
| ( ~ in(U_531,U_532)
& in(U_531,U_533) ) ) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
fof(f_133_3,plain,
! [U_533,U_532] :
( U_533 = U_532
| ? [U_535] :
( ~ in(U_535,U_533)
& in(U_535,U_532) )
| ? [U_534] :
( ~ in(U_534,U_532)
& in(U_534,U_533) ) ),
inference(miniscope,[status(thm)],[f_133_2]) ).
fof(f_133_4,plain,
! [U_533,U_532] :
( U_533 = U_532
| ? [U_535] :
( ~ in(U_535,U_533)
& in(U_535,U_532) )
| ( ~ in(sK80(U_533,U_532),U_532)
& in(sK80(U_533,U_532),U_533) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_534,sK80(U_533,U_532))],[f_133_3]) ).
fof(f_133_5,plain,
! [U_533,U_532] :
( U_533 = U_532
| ( ~ in(sK81(U_533,U_532),U_533)
& in(sK81(U_533,U_532),U_532) )
| ( ~ in(sK80(U_533,U_532),U_532)
& in(sK80(U_533,U_532),U_533) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_535,sK81(U_533,U_532))],[f_133_4]) ).
fof(f_133_6,plain,
( ! [U_532,U_533] :
( ~ in(sK81(U_533,U_532),U_533)
| ~ sP100(U_532,U_533) )
& ! [U_532,U_533] :
( in(sK81(U_533,U_532),U_532)
| ~ sP100(U_532,U_533) )
& ! [U_532,U_533] :
( ~ in(sK80(U_533,U_532),U_532)
| ~ sP99(U_532,U_533) )
& ! [U_532,U_533] :
( in(sK80(U_533,U_532),U_533)
| ~ sP99(U_532,U_533) )
& ! [U_532,U_533] :
( U_533 = U_532
| sP100(U_532,U_533)
| sP99(U_532,U_533) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP99,sP100])],[f_133_5]) ).
cnf(f_133_7,plain,
( U_533 = U_532
| sP100(U_532,U_533)
| sP99(U_532,U_533) ),
inference(clausify,[status(thm)],[f_133_6]) ).
cnf(f_133_8,plain,
( in(sK80(U_533,U_532),U_533)
| ~ sP99(U_532,U_533) ),
inference(clausify,[status(thm)],[f_133_6]) ).
cnf(f_133_9,plain,
( ~ in(sK80(U_533,U_532),U_532)
| ~ sP99(U_532,U_533) ),
inference(clausify,[status(thm)],[f_133_6]) ).
cnf(f_133_10,plain,
( in(sK81(U_533,U_532),U_532)
| ~ sP100(U_532,U_533) ),
inference(clausify,[status(thm)],[f_133_6]) ).
cnf(f_133_11,plain,
( ~ in(sK81(U_533,U_532),U_533)
| ~ sP100(U_532,U_533) ),
inference(clausify,[status(thm)],[f_133_6]) ).
fof(f_134_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_134_2,plain,
! [U_536] : subset(empty_set,U_536),
inference(variable_rename,[status(thm)],[f_134_1]) ).
fof(f_134_3,plain,
! [U_536] : subset(empty_set,U_536),
inference(definitional_conversion,[status(esa)],[f_134_2]) ).
cnf(f_134_4,plain,
subset(empty_set,U_536),
inference(clausify,[status(thm)],[f_134_3]) ).
fof(f_135_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_135_2,plain,
! [U_539,U_538,U_537] :
( ( in(U_538,relation_field(U_537))
& in(U_539,relation_field(U_537)) )
| ~ in(ordered_pair(U_539,U_538),U_537)
| ~ relation(U_537) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
fof(f_135_3,plain,
( ! [U_539,U_537,U_538] :
( in(U_538,relation_field(U_537))
| ~ sP101(U_539,U_537,U_538) )
& ! [U_539,U_537,U_538] :
( in(U_539,relation_field(U_537))
| ~ sP101(U_539,U_537,U_538) )
& ! [U_539,U_537,U_538] :
( sP101(U_539,U_537,U_538)
| ~ in(ordered_pair(U_539,U_538),U_537)
| ~ relation(U_537) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP101])],[f_135_2]) ).
cnf(f_135_4,plain,
( sP101(U_539,U_537,U_538)
| ~ in(ordered_pair(U_539,U_538),U_537)
| ~ relation(U_537) ),
inference(clausify,[status(thm)],[f_135_3]) ).
cnf(f_135_5,plain,
( in(U_539,relation_field(U_537))
| ~ sP101(U_539,U_537,U_538) ),
inference(clausify,[status(thm)],[f_135_3]) ).
cnf(f_135_6,plain,
( in(U_538,relation_field(U_537))
| ~ sP101(U_539,U_537,U_538) ),
inference(clausify,[status(thm)],[f_135_3]) ).
fof(f_136_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_136_2,plain,
! [U_542,U_541,U_540] :
( subset(set_difference(U_542,U_540),set_difference(U_541,U_540))
| ~ subset(U_542,U_541) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
fof(f_136_3,plain,
! [U_542,U_541] :
( ! [U_540] : subset(set_difference(U_542,U_540),set_difference(U_541,U_540))
| ~ subset(U_542,U_541) ),
inference(miniscope,[status(thm)],[f_136_2]) ).
fof(f_136_4,plain,
! [U_541,U_540,U_542] :
( subset(set_difference(U_542,U_540),set_difference(U_541,U_540))
| ~ subset(U_542,U_541) ),
inference(definitional_conversion,[status(esa)],[f_136_3]) ).
cnf(f_136_5,plain,
( subset(set_difference(U_542,U_540),set_difference(U_541,U_540))
| ~ subset(U_542,U_541) ),
inference(clausify,[status(thm)],[f_136_4]) ).
fof(f_137_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_137_2,plain,
! [U_546,U_545,U_544,U_543] :
( ( U_545 = U_543
& U_546 = U_544 )
| ordered_pair(U_546,U_545) != ordered_pair(U_544,U_543) ),
inference(variable_rename,[status(thm)],[f_137_1]) ).
fof(f_137_3,plain,
( ! [U_543,U_544,U_545,U_546] :
( U_545 = U_543
| ~ sP102(U_543,U_544,U_545,U_546) )
& ! [U_543,U_544,U_545,U_546] :
( U_546 = U_544
| ~ sP102(U_543,U_544,U_545,U_546) )
& ! [U_543,U_544,U_545,U_546] :
( sP102(U_543,U_544,U_545,U_546)
| ordered_pair(U_546,U_545) != ordered_pair(U_544,U_543) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP102])],[f_137_2]) ).
cnf(f_137_4,plain,
( sP102(U_543,U_544,U_545,U_546)
| ordered_pair(U_546,U_545) != ordered_pair(U_544,U_543) ),
inference(clausify,[status(thm)],[f_137_3]) ).
cnf(f_137_5,plain,
( U_546 = U_544
| ~ sP102(U_543,U_544,U_545,U_546) ),
inference(clausify,[status(thm)],[f_137_3]) ).
cnf(f_137_6,plain,
( U_545 = U_543
| ~ sP102(U_543,U_544,U_545,U_546) ),
inference(clausify,[status(thm)],[f_137_3]) ).
fof(f_138_1,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(fof_nnf,[status(thm)],[t36_xboole_1]) ).
fof(f_138_2,plain,
! [U_548,U_547] : subset(set_difference(U_548,U_547),U_548),
inference(variable_rename,[status(thm)],[f_138_1]) ).
fof(f_138_3,plain,
! [U_548,U_547] : subset(set_difference(U_548,U_547),U_548),
inference(definitional_conversion,[status(esa)],[f_138_2]) ).
cnf(f_138_4,plain,
subset(set_difference(U_548,U_547),U_548),
inference(clausify,[status(thm)],[f_138_3]) ).
fof(f_139_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_139_2,plain,
! [U_549] :
( ( relation_dom(U_549) = relation_rng(relation_inverse(U_549))
& relation_rng(U_549) = relation_dom(relation_inverse(U_549)) )
| ~ relation(U_549) ),
inference(variable_rename,[status(thm)],[f_139_1]) ).
fof(f_139_3,plain,
( ! [U_549] :
( relation_dom(U_549) = relation_rng(relation_inverse(U_549))
| ~ sP103(U_549) )
& ! [U_549] :
( relation_rng(U_549) = relation_dom(relation_inverse(U_549))
| ~ sP103(U_549) )
& ! [U_549] :
( sP103(U_549)
| ~ relation(U_549) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP103])],[f_139_2]) ).
cnf(f_139_4,plain,
( sP103(U_549)
| ~ relation(U_549) ),
inference(clausify,[status(thm)],[f_139_3]) ).
cnf(f_139_5,plain,
( relation_rng(U_549) = relation_dom(relation_inverse(U_549))
| ~ sP103(U_549) ),
inference(clausify,[status(thm)],[f_139_3]) ).
cnf(f_139_6,plain,
( relation_dom(U_549) = relation_rng(relation_inverse(U_549))
| ~ sP103(U_549) ),
inference(clausify,[status(thm)],[f_139_3]) ).
fof(f_140_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_140_2,plain,
! [U_551,U_550] :
( ( set_difference(U_551,U_550) = empty_set
| ~ subset(U_551,U_550) )
& ( subset(U_551,U_550)
| set_difference(U_551,U_550) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_140_1]) ).
fof(f_140_3,plain,
( ! [U_555,U_553] :
( set_difference(U_555,U_553) = empty_set
| ~ subset(U_555,U_553) )
& ! [U_554,U_552] :
( subset(U_554,U_552)
| set_difference(U_554,U_552) != empty_set ) ),
inference(miniscope,[status(thm)],[f_140_2]) ).
fof(f_140_4,plain,
( ! [U_555,U_553] :
( set_difference(U_555,U_553) = empty_set
| ~ subset(U_555,U_553) )
& ! [U_554,U_552] :
( subset(U_554,U_552)
| set_difference(U_554,U_552) != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_140_3]) ).
cnf(f_140_5,plain,
( subset(U_554,U_552)
| set_difference(U_554,U_552) != empty_set ),
inference(clausify,[status(thm)],[f_140_4]) ).
cnf(f_140_6,plain,
( set_difference(U_555,U_553) = empty_set
| ~ subset(U_555,U_553) ),
inference(clausify,[status(thm)],[f_140_4]) ).
fof(f_141_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_141_2,plain,
! [U_557,U_556] :
( ( subset(singleton(U_557),U_556)
| ~ in(U_557,U_556) )
& ( in(U_557,U_556)
| ~ subset(singleton(U_557),U_556) ) ),
inference(variable_rename,[status(thm)],[f_141_1]) ).
fof(f_141_3,plain,
( ! [U_561,U_559] :
( subset(singleton(U_561),U_559)
| ~ in(U_561,U_559) )
& ! [U_560,U_558] :
( in(U_560,U_558)
| ~ subset(singleton(U_560),U_558) ) ),
inference(miniscope,[status(thm)],[f_141_2]) ).
fof(f_141_4,plain,
( ! [U_559,U_561] :
( subset(singleton(U_561),U_559)
| ~ in(U_561,U_559) )
& ! [U_558,U_560] :
( in(U_560,U_558)
| ~ subset(singleton(U_560),U_558) ) ),
inference(definitional_conversion,[status(esa)],[f_141_3]) ).
cnf(f_141_5,plain,
( in(U_560,U_558)
| ~ subset(singleton(U_560),U_558) ),
inference(clausify,[status(thm)],[f_141_4]) ).
cnf(f_141_6,plain,
( subset(singleton(U_561),U_559)
| ~ in(U_561,U_559) ),
inference(clausify,[status(thm)],[f_141_4]) ).
fof(f_142_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_142_2,plain,
! [U_564,U_563,U_562] :
( ( subset(unordered_pair(U_564,U_563),U_562)
| ~ in(U_563,U_562)
| ~ in(U_564,U_562) )
& ( ( in(U_563,U_562)
& in(U_564,U_562) )
| ~ subset(unordered_pair(U_564,U_563),U_562) ) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
fof(f_142_3,plain,
( ! [U_570,U_568,U_566] :
( subset(unordered_pair(U_570,U_568),U_566)
| ~ in(U_568,U_566)
| ~ in(U_570,U_566) )
& ! [U_569,U_567,U_565] :
( ( in(U_567,U_565)
& in(U_569,U_565) )
| ~ subset(unordered_pair(U_569,U_567),U_565) ) ),
inference(miniscope,[status(thm)],[f_142_2]) ).
fof(f_142_4,plain,
( ! [U_569,U_565,U_567] :
( in(U_567,U_565)
| ~ sP104(U_569,U_565,U_567) )
& ! [U_569,U_565,U_567] :
( in(U_569,U_565)
| ~ sP104(U_569,U_565,U_567) )
& ! [U_568,U_566,U_570] :
( subset(unordered_pair(U_570,U_568),U_566)
| ~ in(U_568,U_566)
| ~ in(U_570,U_566) )
& ! [U_569,U_565,U_567] :
( sP104(U_569,U_565,U_567)
| ~ subset(unordered_pair(U_569,U_567),U_565) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP104])],[f_142_3]) ).
cnf(f_142_5,plain,
( sP104(U_569,U_565,U_567)
| ~ subset(unordered_pair(U_569,U_567),U_565) ),
inference(clausify,[status(thm)],[f_142_4]) ).
cnf(f_142_6,plain,
( subset(unordered_pair(U_570,U_568),U_566)
| ~ in(U_568,U_566)
| ~ in(U_570,U_566) ),
inference(clausify,[status(thm)],[f_142_4]) ).
cnf(f_142_7,plain,
( in(U_569,U_565)
| ~ sP104(U_569,U_565,U_567) ),
inference(clausify,[status(thm)],[f_142_4]) ).
cnf(f_142_8,plain,
( in(U_567,U_565)
| ~ sP104(U_569,U_565,U_567) ),
inference(clausify,[status(thm)],[f_142_4]) ).
fof(f_143_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_143_2,plain,
! [U_572,U_571] : set_union2(U_572,set_difference(U_571,U_572)) = set_union2(U_572,U_571),
inference(variable_rename,[status(thm)],[f_143_1]) ).
fof(f_143_3,plain,
! [U_571,U_572] : set_union2(U_572,set_difference(U_571,U_572)) = set_union2(U_572,U_571),
inference(definitional_conversion,[status(esa)],[f_143_2]) ).
cnf(f_143_4,plain,
set_union2(U_572,set_difference(U_571,U_572)) = set_union2(U_572,U_571),
inference(clausify,[status(thm)],[f_143_3]) ).
fof(f_144_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_144_2,plain,
! [U_574,U_573] :
( ( subset(U_574,singleton(U_573))
| ( U_574 != singleton(U_573)
& U_574 != empty_set ) )
& ( U_574 = singleton(U_573)
| U_574 = empty_set
| ~ subset(U_574,singleton(U_573)) ) ),
inference(variable_rename,[status(thm)],[f_144_1]) ).
fof(f_144_3,plain,
( ! [U_578,U_576] :
( subset(U_578,singleton(U_576))
| ( U_578 != singleton(U_576)
& U_578 != empty_set ) )
& ! [U_577,U_575] :
( U_577 = singleton(U_575)
| U_577 = empty_set
| ~ subset(U_577,singleton(U_575)) ) ),
inference(miniscope,[status(thm)],[f_144_2]) ).
fof(f_144_4,plain,
( ! [U_576,U_578] :
( U_578 != singleton(U_576)
| ~ sP105(U_576,U_578) )
& ! [U_576,U_578] :
( U_578 != empty_set
| ~ sP105(U_576,U_578) )
& ! [U_576,U_578] :
( subset(U_578,singleton(U_576))
| sP105(U_576,U_578) )
& ! [U_577,U_575] :
( U_577 = singleton(U_575)
| U_577 = empty_set
| ~ subset(U_577,singleton(U_575)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP105])],[f_144_3]) ).
cnf(f_144_5,plain,
( U_577 = singleton(U_575)
| U_577 = empty_set
| ~ subset(U_577,singleton(U_575)) ),
inference(clausify,[status(thm)],[f_144_4]) ).
cnf(f_144_6,plain,
( subset(U_578,singleton(U_576))
| sP105(U_576,U_578) ),
inference(clausify,[status(thm)],[f_144_4]) ).
cnf(f_144_7,plain,
( U_578 != empty_set
| ~ sP105(U_576,U_578) ),
inference(clausify,[status(thm)],[f_144_4]) ).
cnf(f_144_8,plain,
( U_578 != singleton(U_576)
| ~ sP105(U_576,U_578) ),
inference(clausify,[status(thm)],[f_144_4]) ).
fof(f_145_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_145_2,plain,
! [U_579] : set_difference(U_579,empty_set) = U_579,
inference(variable_rename,[status(thm)],[f_145_1]) ).
fof(f_145_3,plain,
! [U_579] : set_difference(U_579,empty_set) = U_579,
inference(definitional_conversion,[status(esa)],[f_145_2]) ).
cnf(f_145_4,plain,
set_difference(U_579,empty_set) = U_579,
inference(clausify,[status(thm)],[f_145_3]) ).
fof(f_146_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_146_2,plain,
! [U_581,U_580] :
( ( element(U_581,powerset(U_580))
| ~ subset(U_581,U_580) )
& ( subset(U_581,U_580)
| ~ element(U_581,powerset(U_580)) ) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
fof(f_146_3,plain,
( ! [U_585,U_583] :
( element(U_585,powerset(U_583))
| ~ subset(U_585,U_583) )
& ! [U_584,U_582] :
( subset(U_584,U_582)
| ~ element(U_584,powerset(U_582)) ) ),
inference(miniscope,[status(thm)],[f_146_2]) ).
fof(f_146_4,plain,
( ! [U_585,U_583] :
( element(U_585,powerset(U_583))
| ~ subset(U_585,U_583) )
& ! [U_584,U_582] :
( subset(U_584,U_582)
| ~ element(U_584,powerset(U_582)) ) ),
inference(definitional_conversion,[status(esa)],[f_146_3]) ).
cnf(f_146_5,plain,
( subset(U_584,U_582)
| ~ element(U_584,powerset(U_582)) ),
inference(clausify,[status(thm)],[f_146_4]) ).
cnf(f_146_6,plain,
( element(U_585,powerset(U_583))
| ~ subset(U_585,U_583) ),
inference(clausify,[status(thm)],[f_146_4]) ).
fof(f_147_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_147_2,plain,
! [U_589,U_588] :
( ( ~ disjoint(U_589,U_588)
| ! [U_587] :
( ~ in(U_587,U_588)
| ~ in(U_587,U_589) ) )
& ( ? [U_586] :
( in(U_586,U_588)
& in(U_586,U_589) )
| disjoint(U_589,U_588) ) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
fof(f_147_3,plain,
( ! [U_593,U_591] :
( ~ disjoint(U_593,U_591)
| ! [U_587] :
( ~ in(U_587,U_591)
| ~ in(U_587,U_593) ) )
& ! [U_592,U_590] :
( ? [U_586] :
( in(U_586,U_590)
& in(U_586,U_592) )
| disjoint(U_592,U_590) ) ),
inference(miniscope,[status(thm)],[f_147_2]) ).
fof(f_147_4,plain,
( ! [U_593,U_591] :
( ~ disjoint(U_593,U_591)
| ! [U_587] :
( ~ in(U_587,U_591)
| ~ in(U_587,U_593) ) )
& ! [U_592,U_590] :
( ( in(sK82(U_592,U_590),U_590)
& in(sK82(U_592,U_590),U_592) )
| disjoint(U_592,U_590) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_586,sK82(U_592,U_590))],[f_147_3]) ).
fof(f_147_5,plain,
( ! [U_590,U_592] :
( in(sK82(U_592,U_590),U_590)
| ~ sP106(U_590,U_592) )
& ! [U_590,U_592] :
( in(sK82(U_592,U_590),U_592)
| ~ sP106(U_590,U_592) )
& ! [U_591,U_593,U_587] :
( ~ disjoint(U_593,U_591)
| ~ in(U_587,U_591)
| ~ in(U_587,U_593) )
& ! [U_590,U_592] :
( sP106(U_590,U_592)
| disjoint(U_592,U_590) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP106])],[f_147_4]) ).
cnf(f_147_6,plain,
( sP106(U_590,U_592)
| disjoint(U_592,U_590) ),
inference(clausify,[status(thm)],[f_147_5]) ).
cnf(f_147_7,plain,
( ~ disjoint(U_593,U_591)
| ~ in(U_587,U_591)
| ~ in(U_587,U_593) ),
inference(clausify,[status(thm)],[f_147_5]) ).
cnf(f_147_8,plain,
( in(sK82(U_592,U_590),U_592)
| ~ sP106(U_590,U_592) ),
inference(clausify,[status(thm)],[f_147_5]) ).
cnf(f_147_9,plain,
( in(sK82(U_592,U_590),U_590)
| ~ sP106(U_590,U_592) ),
inference(clausify,[status(thm)],[f_147_5]) ).
fof(f_148_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_148_2,plain,
! [U_594] :
( U_594 = empty_set
| ~ subset(U_594,empty_set) ),
inference(variable_rename,[status(thm)],[f_148_1]) ).
fof(f_148_3,plain,
! [U_594] :
( U_594 = empty_set
| ~ subset(U_594,empty_set) ),
inference(definitional_conversion,[status(esa)],[f_148_2]) ).
cnf(f_148_4,plain,
( U_594 = empty_set
| ~ subset(U_594,empty_set) ),
inference(clausify,[status(thm)],[f_148_3]) ).
fof(f_149_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_149_2,plain,
! [U_596,U_595] : set_difference(set_union2(U_596,U_595),U_595) = set_difference(U_596,U_595),
inference(variable_rename,[status(thm)],[f_149_1]) ).
fof(f_149_3,plain,
! [U_595,U_596] : set_difference(set_union2(U_596,U_595),U_595) = set_difference(U_596,U_595),
inference(definitional_conversion,[status(esa)],[f_149_2]) ).
cnf(f_149_4,plain,
set_difference(set_union2(U_596,U_595),U_595) = set_difference(U_596,U_595),
inference(clausify,[status(thm)],[f_149_3]) ).
fof(f_150_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_150_2,plain,
! [U_599,U_598] :
( ! [U_597] :
( ( ( disjoint(U_598,U_597)
| ~ subset(U_598,subset_complement(U_599,U_597)) )
& ( subset(U_598,subset_complement(U_599,U_597))
| ~ disjoint(U_598,U_597) ) )
| ~ element(U_597,powerset(U_599)) )
| ~ element(U_598,powerset(U_599)) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
fof(f_150_3,plain,
( ! [U_597,U_598,U_599] :
( disjoint(U_598,U_597)
| ~ subset(U_598,subset_complement(U_599,U_597))
| ~ sP107(U_597,U_598,U_599) )
& ! [U_597,U_598,U_599] :
( subset(U_598,subset_complement(U_599,U_597))
| ~ disjoint(U_598,U_597)
| ~ sP107(U_597,U_598,U_599) )
& ! [U_597,U_598,U_599] :
( sP107(U_597,U_598,U_599)
| ~ element(U_597,powerset(U_599))
| ~ element(U_598,powerset(U_599)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP107])],[f_150_2]) ).
cnf(f_150_4,plain,
( sP107(U_597,U_598,U_599)
| ~ element(U_597,powerset(U_599))
| ~ element(U_598,powerset(U_599)) ),
inference(clausify,[status(thm)],[f_150_3]) ).
cnf(f_150_5,plain,
( subset(U_598,subset_complement(U_599,U_597))
| ~ disjoint(U_598,U_597)
| ~ sP107(U_597,U_598,U_599) ),
inference(clausify,[status(thm)],[f_150_3]) ).
cnf(f_150_6,plain,
( disjoint(U_598,U_597)
| ~ subset(U_598,subset_complement(U_599,U_597))
| ~ sP107(U_597,U_598,U_599) ),
inference(clausify,[status(thm)],[f_150_3]) ).
fof(f_151_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_151_2,plain,
! [U_601] :
( ! [U_600] :
( subset(relation_dom(relation_composition(U_601,U_600)),relation_dom(U_601))
| ~ relation(U_600) )
| ~ relation(U_601) ),
inference(variable_rename,[status(thm)],[f_151_1]) ).
fof(f_151_3,plain,
! [U_601,U_600] :
( subset(relation_dom(relation_composition(U_601,U_600)),relation_dom(U_601))
| ~ relation(U_600)
| ~ relation(U_601) ),
inference(definitional_conversion,[status(esa)],[f_151_2]) ).
cnf(f_151_4,plain,
( subset(relation_dom(relation_composition(U_601,U_600)),relation_dom(U_601))
| ~ relation(U_600)
| ~ relation(U_601) ),
inference(clausify,[status(thm)],[f_151_3]) ).
fof(f_152_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_152_2,plain,
! [U_603] :
( ! [U_602] :
( subset(relation_rng(relation_composition(U_603,U_602)),relation_rng(U_602))
| ~ relation(U_602) )
| ~ relation(U_603) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
fof(f_152_3,plain,
! [U_602,U_603] :
( subset(relation_rng(relation_composition(U_603,U_602)),relation_rng(U_602))
| ~ relation(U_602)
| ~ relation(U_603) ),
inference(definitional_conversion,[status(esa)],[f_152_2]) ).
cnf(f_152_4,plain,
( subset(relation_rng(relation_composition(U_603,U_602)),relation_rng(U_602))
| ~ relation(U_602)
| ~ relation(U_603) ),
inference(clausify,[status(thm)],[f_152_3]) ).
fof(f_153_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_153_2,plain,
! [U_605,U_604] :
( U_604 = set_union2(U_605,set_difference(U_604,U_605))
| ~ subset(U_605,U_604) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
fof(f_153_3,plain,
! [U_604,U_605] :
( U_604 = set_union2(U_605,set_difference(U_604,U_605))
| ~ subset(U_605,U_604) ),
inference(definitional_conversion,[status(esa)],[f_153_2]) ).
cnf(f_153_4,plain,
( U_604 = set_union2(U_605,set_difference(U_604,U_605))
| ~ subset(U_605,U_604) ),
inference(clausify,[status(thm)],[f_153_3]) ).
fof(f_154_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_154_2,plain,
! [U_607] :
( ! [U_606] :
( relation_dom(relation_composition(U_607,U_606)) = relation_dom(U_607)
| ~ subset(relation_rng(U_607),relation_dom(U_606))
| ~ relation(U_606) )
| ~ relation(U_607) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
fof(f_154_3,plain,
! [U_606,U_607] :
( relation_dom(relation_composition(U_607,U_606)) = relation_dom(U_607)
| ~ subset(relation_rng(U_607),relation_dom(U_606))
| ~ relation(U_606)
| ~ relation(U_607) ),
inference(definitional_conversion,[status(esa)],[f_154_2]) ).
cnf(f_154_4,plain,
( relation_dom(relation_composition(U_607,U_606)) = relation_dom(U_607)
| ~ subset(relation_rng(U_607),relation_dom(U_606))
| ~ relation(U_606)
| ~ relation(U_607) ),
inference(clausify,[status(thm)],[f_154_3]) ).
fof(f_155_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_155_2,plain,
! [U_609,U_608] :
( complements_of_subsets(U_609,U_608) != empty_set
| U_608 = empty_set
| ~ element(U_608,powerset(powerset(U_609))) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
fof(f_155_3,plain,
! [U_609,U_608] :
( complements_of_subsets(U_609,U_608) != empty_set
| U_608 = empty_set
| ~ element(U_608,powerset(powerset(U_609))) ),
inference(definitional_conversion,[status(esa)],[f_155_2]) ).
cnf(f_155_4,plain,
( complements_of_subsets(U_609,U_608) != empty_set
| U_608 = empty_set
| ~ element(U_608,powerset(powerset(U_609))) ),
inference(clausify,[status(thm)],[f_155_3]) ).
fof(f_156_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t46_zfmisc_1]) ).
fof(f_156_2,plain,
! [U_611,U_610] :
( set_union2(singleton(U_611),U_610) = U_610
| ~ in(U_611,U_610) ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
fof(f_156_3,plain,
! [U_610,U_611] :
( set_union2(singleton(U_611),U_610) = U_610
| ~ in(U_611,U_610) ),
inference(definitional_conversion,[status(esa)],[f_156_2]) ).
cnf(f_156_4,plain,
( set_union2(singleton(U_611),U_610) = U_610
| ~ in(U_611,U_610) ),
inference(clausify,[status(thm)],[f_156_3]) ).
fof(f_157_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_157_2,plain,
! [U_613] :
( ! [U_612] :
( relation_rng(relation_composition(U_612,U_613)) = relation_rng(U_613)
| ~ subset(relation_dom(U_613),relation_rng(U_612))
| ~ relation(U_612) )
| ~ relation(U_613) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
fof(f_157_3,plain,
! [U_612,U_613] :
( relation_rng(relation_composition(U_612,U_613)) = relation_rng(U_613)
| ~ subset(relation_dom(U_613),relation_rng(U_612))
| ~ relation(U_612)
| ~ relation(U_613) ),
inference(definitional_conversion,[status(esa)],[f_157_2]) ).
cnf(f_157_4,plain,
( relation_rng(relation_composition(U_612,U_613)) = relation_rng(U_613)
| ~ subset(relation_dom(U_613),relation_rng(U_612))
| ~ relation(U_612)
| ~ relation(U_613) ),
inference(clausify,[status(thm)],[f_157_3]) ).
fof(f_158_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_158_2,plain,
! [U_615,U_614] :
( subset_difference(U_615,cast_to_subset(U_615),union_of_subsets(U_615,U_614)) = meet_of_subsets(U_615,complements_of_subsets(U_615,U_614))
| U_614 = empty_set
| ~ element(U_614,powerset(powerset(U_615))) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
fof(f_158_3,plain,
! [U_614,U_615] :
( subset_difference(U_615,cast_to_subset(U_615),union_of_subsets(U_615,U_614)) = meet_of_subsets(U_615,complements_of_subsets(U_615,U_614))
| U_614 = empty_set
| ~ element(U_614,powerset(powerset(U_615))) ),
inference(definitional_conversion,[status(esa)],[f_158_2]) ).
cnf(f_158_4,plain,
( subset_difference(U_615,cast_to_subset(U_615),union_of_subsets(U_615,U_614)) = meet_of_subsets(U_615,complements_of_subsets(U_615,U_614))
| U_614 = empty_set
| ~ element(U_614,powerset(powerset(U_615))) ),
inference(clausify,[status(thm)],[f_158_3]) ).
fof(f_159_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_159_2,plain,
! [U_617,U_616] :
( union_of_subsets(U_617,complements_of_subsets(U_617,U_616)) = subset_difference(U_617,cast_to_subset(U_617),meet_of_subsets(U_617,U_616))
| U_616 = empty_set
| ~ element(U_616,powerset(powerset(U_617))) ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
fof(f_159_3,plain,
! [U_616,U_617] :
( union_of_subsets(U_617,complements_of_subsets(U_617,U_616)) = subset_difference(U_617,cast_to_subset(U_617),meet_of_subsets(U_617,U_616))
| U_616 = empty_set
| ~ element(U_616,powerset(powerset(U_617))) ),
inference(definitional_conversion,[status(esa)],[f_159_2]) ).
cnf(f_159_4,plain,
( union_of_subsets(U_617,complements_of_subsets(U_617,U_616)) = subset_difference(U_617,cast_to_subset(U_617),meet_of_subsets(U_617,U_616))
| U_616 = empty_set
| ~ element(U_616,powerset(powerset(U_617))) ),
inference(clausify,[status(thm)],[f_159_3]) ).
fof(f_160_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_160_2,plain,
! [U_619,U_618] : set_difference(U_619,set_difference(U_619,U_618)) = set_intersection2(U_619,U_618),
inference(variable_rename,[status(thm)],[f_160_1]) ).
fof(f_160_3,plain,
! [U_618,U_619] : set_difference(U_619,set_difference(U_619,U_618)) = set_intersection2(U_619,U_618),
inference(definitional_conversion,[status(esa)],[f_160_2]) ).
cnf(f_160_4,plain,
set_difference(U_619,set_difference(U_619,U_618)) = set_intersection2(U_619,U_618),
inference(clausify,[status(thm)],[f_160_3]) ).
fof(f_161_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_161_2,plain,
! [U_620] : set_difference(empty_set,U_620) = empty_set,
inference(variable_rename,[status(thm)],[f_161_1]) ).
fof(f_161_3,plain,
! [U_620] : set_difference(empty_set,U_620) = empty_set,
inference(definitional_conversion,[status(esa)],[f_161_2]) ).
cnf(f_161_4,plain,
set_difference(empty_set,U_620) = empty_set,
inference(clausify,[status(thm)],[f_161_3]) ).
fof(f_162_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_162_2,plain,
! [U_623,U_622,U_621] :
( element(U_623,U_621)
| ~ element(U_622,powerset(U_621))
| ~ in(U_623,U_622) ),
inference(variable_rename,[status(thm)],[f_162_1]) ).
fof(f_162_3,plain,
! [U_621,U_622,U_623] :
( element(U_623,U_621)
| ~ element(U_622,powerset(U_621))
| ~ in(U_623,U_622) ),
inference(definitional_conversion,[status(esa)],[f_162_2]) ).
cnf(f_162_4,plain,
( element(U_623,U_621)
| ~ element(U_622,powerset(U_621))
| ~ in(U_623,U_622) ),
inference(clausify,[status(thm)],[f_162_3]) ).
fof(f_163_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_163_2,plain,
! [U_627,U_626] :
( ( ~ disjoint(U_627,U_626)
| ! [U_625] : ~ in(U_625,set_intersection2(U_627,U_626)) )
& ( ? [U_624] : in(U_624,set_intersection2(U_627,U_626))
| disjoint(U_627,U_626) ) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
fof(f_163_3,plain,
( ! [U_631,U_629] :
( ~ disjoint(U_631,U_629)
| ! [U_625] : ~ in(U_625,set_intersection2(U_631,U_629)) )
& ! [U_630,U_628] :
( ? [U_624] : in(U_624,set_intersection2(U_630,U_628))
| disjoint(U_630,U_628) ) ),
inference(miniscope,[status(thm)],[f_163_2]) ).
fof(f_163_4,plain,
( ! [U_631,U_629] :
( ~ disjoint(U_631,U_629)
| ! [U_625] : ~ in(U_625,set_intersection2(U_631,U_629)) )
& ! [U_630,U_628] :
( in(sK83(U_630,U_628),set_intersection2(U_630,U_628))
| disjoint(U_630,U_628) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_624,sK83(U_630,U_628))],[f_163_3]) ).
fof(f_163_5,plain,
( ! [U_625,U_631,U_629] :
( ~ disjoint(U_631,U_629)
| ~ in(U_625,set_intersection2(U_631,U_629)) )
& ! [U_630,U_628] :
( in(sK83(U_630,U_628),set_intersection2(U_630,U_628))
| disjoint(U_630,U_628) ) ),
inference(definitional_conversion,[status(esa)],[f_163_4]) ).
cnf(f_163_6,plain,
( in(sK83(U_630,U_628),set_intersection2(U_630,U_628))
| disjoint(U_630,U_628) ),
inference(clausify,[status(thm)],[f_163_5]) ).
cnf(f_163_7,plain,
( ~ disjoint(U_631,U_629)
| ~ in(U_625,set_intersection2(U_631,U_629)) ),
inference(clausify,[status(thm)],[f_163_5]) ).
fof(f_164_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_164_2,plain,
! [U_634] :
( ! [U_633] :
( ! [U_632] :
( in(U_632,subset_complement(U_634,U_633))
| in(U_632,U_633)
| ~ element(U_632,U_634) )
| ~ element(U_633,powerset(U_634)) )
| U_634 = empty_set ),
inference(variable_rename,[status(thm)],[f_164_1]) ).
fof(f_164_3,plain,
! [U_634,U_632,U_633] :
( in(U_632,subset_complement(U_634,U_633))
| in(U_632,U_633)
| ~ element(U_632,U_634)
| ~ element(U_633,powerset(U_634))
| U_634 = empty_set ),
inference(definitional_conversion,[status(esa)],[f_164_2]) ).
cnf(f_164_4,plain,
( in(U_632,subset_complement(U_634,U_633))
| in(U_632,U_633)
| ~ element(U_632,U_634)
| ~ element(U_633,powerset(U_634))
| U_634 = empty_set ),
inference(clausify,[status(thm)],[f_164_3]) ).
fof(f_165_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_165_2,plain,
! [U_637,U_636,U_635] :
( ~ in(U_636,U_635)
| ~ in(U_636,subset_complement(U_637,U_635))
| ~ element(U_635,powerset(U_637)) ),
inference(variable_rename,[status(thm)],[f_165_1]) ).
fof(f_165_3,plain,
! [U_636,U_637,U_635] :
( ~ in(U_636,U_635)
| ~ in(U_636,subset_complement(U_637,U_635))
| ~ element(U_635,powerset(U_637)) ),
inference(definitional_conversion,[status(esa)],[f_165_2]) ).
cnf(f_165_4,plain,
( ~ in(U_636,U_635)
| ~ in(U_636,subset_complement(U_637,U_635))
| ~ element(U_635,powerset(U_637)) ),
inference(clausify,[status(thm)],[f_165_3]) ).
fof(f_166_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_166_2,plain,
! [U_640] :
( U_640 = empty_set
| ? [U_639,U_638] : in(ordered_pair(U_639,U_638),U_640)
| ~ relation(U_640) ),
inference(variable_rename,[status(thm)],[f_166_1]) ).
fof(f_166_3,plain,
! [U_640] :
( U_640 = empty_set
| ? [U_638] : in(ordered_pair(sK84(U_640),U_638),U_640)
| ~ relation(U_640) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_639,sK84(U_640))],[f_166_2]) ).
fof(f_166_4,plain,
! [U_640] :
( U_640 = empty_set
| in(ordered_pair(sK84(U_640),sK85(U_640)),U_640)
| ~ relation(U_640) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_638,sK85(U_640))],[f_166_3]) ).
fof(f_166_5,plain,
! [U_640] :
( U_640 = empty_set
| in(ordered_pair(sK84(U_640),sK85(U_640)),U_640)
| ~ relation(U_640) ),
inference(definitional_conversion,[status(esa)],[f_166_4]) ).
cnf(f_166_6,plain,
( U_640 = empty_set
| in(ordered_pair(sK84(U_640),sK85(U_640)),U_640)
| ~ relation(U_640) ),
inference(clausify,[status(thm)],[f_166_5]) ).
fof(f_167_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_167_2,plain,
! [U_643,U_642,U_641] :
( ~ empty(U_641)
| ~ element(U_642,powerset(U_641))
| ~ in(U_643,U_642) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
fof(f_167_3,plain,
! [U_643,U_642] :
( ! [U_641] :
( ~ empty(U_641)
| ~ element(U_642,powerset(U_641)) )
| ~ in(U_643,U_642) ),
inference(miniscope,[status(thm)],[f_167_2]) ).
fof(f_167_4,plain,
! [U_641,U_642,U_643] :
( ~ empty(U_641)
| ~ element(U_642,powerset(U_641))
| ~ in(U_643,U_642) ),
inference(definitional_conversion,[status(esa)],[f_167_3]) ).
cnf(f_167_5,plain,
( ~ empty(U_641)
| ~ element(U_642,powerset(U_641))
| ~ in(U_643,U_642) ),
inference(clausify,[status(thm)],[f_167_4]) ).
fof(f_168_1,plain,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(fof_nnf,[status(thm)],[t60_relat_1]) ).
fof(f_168_2,plain,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(definitional_conversion,[status(esa)],[f_168_1]) ).
cnf(f_168_3,plain,
relation_dom(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_168_2]) ).
cnf(f_168_4,plain,
relation_rng(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_168_2]) ).
fof(f_169_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t60_xboole_1]) ).
fof(f_169_2,plain,
! [U_645,U_644] :
( ~ proper_subset(U_644,U_645)
| ~ subset(U_645,U_644) ),
inference(variable_rename,[status(thm)],[f_169_1]) ).
fof(f_169_3,plain,
! [U_644,U_645] :
( ~ proper_subset(U_644,U_645)
| ~ subset(U_645,U_644) ),
inference(definitional_conversion,[status(esa)],[f_169_2]) ).
cnf(f_169_4,plain,
( ~ proper_subset(U_644,U_645)
| ~ subset(U_645,U_644) ),
inference(clausify,[status(thm)],[f_169_3]) ).
fof(f_170_1,plain,
! [A,B,C] :
( disjoint(A,C)
| ~ disjoint(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t63_xboole_1]) ).
fof(f_170_2,plain,
! [U_648,U_647,U_646] :
( disjoint(U_648,U_646)
| ~ disjoint(U_647,U_646)
| ~ subset(U_648,U_647) ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
fof(f_170_3,plain,
! [U_647,U_646,U_648] :
( disjoint(U_648,U_646)
| ~ disjoint(U_647,U_646)
| ~ subset(U_648,U_647) ),
inference(definitional_conversion,[status(esa)],[f_170_2]) ).
cnf(f_170_4,plain,
( disjoint(U_648,U_646)
| ~ disjoint(U_647,U_646)
| ~ subset(U_648,U_647) ),
inference(clausify,[status(thm)],[f_170_3]) ).
fof(f_171_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_171_2,plain,
! [U_649] :
( U_649 = empty_set
| ( relation_rng(U_649) != empty_set
& relation_dom(U_649) != empty_set )
| ~ relation(U_649) ),
inference(variable_rename,[status(thm)],[f_171_1]) ).
fof(f_171_3,plain,
( ! [U_649] :
( relation_rng(U_649) != empty_set
| ~ sP108(U_649) )
& ! [U_649] :
( relation_dom(U_649) != empty_set
| ~ sP108(U_649) )
& ! [U_649] :
( U_649 = empty_set
| sP108(U_649)
| ~ relation(U_649) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP108])],[f_171_2]) ).
cnf(f_171_4,plain,
( U_649 = empty_set
| sP108(U_649)
| ~ relation(U_649) ),
inference(clausify,[status(thm)],[f_171_3]) ).
cnf(f_171_5,plain,
( relation_dom(U_649) != empty_set
| ~ sP108(U_649) ),
inference(clausify,[status(thm)],[f_171_3]) ).
cnf(f_171_6,plain,
( relation_rng(U_649) != empty_set
| ~ sP108(U_649) ),
inference(clausify,[status(thm)],[f_171_3]) ).
fof(f_172_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_172_2,plain,
! [U_650] :
( ( ( relation_dom(U_650) = empty_set
| relation_rng(U_650) != empty_set )
& ( relation_rng(U_650) = empty_set
| relation_dom(U_650) != empty_set ) )
| ~ relation(U_650) ),
inference(variable_rename,[status(thm)],[f_172_1]) ).
fof(f_172_3,plain,
( ! [U_650] :
( relation_dom(U_650) = empty_set
| relation_rng(U_650) != empty_set
| ~ sP109(U_650) )
& ! [U_650] :
( relation_rng(U_650) = empty_set
| relation_dom(U_650) != empty_set
| ~ sP109(U_650) )
& ! [U_650] :
( sP109(U_650)
| ~ relation(U_650) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP109])],[f_172_2]) ).
cnf(f_172_4,plain,
( sP109(U_650)
| ~ relation(U_650) ),
inference(clausify,[status(thm)],[f_172_3]) ).
cnf(f_172_5,plain,
( relation_rng(U_650) = empty_set
| relation_dom(U_650) != empty_set
| ~ sP109(U_650) ),
inference(clausify,[status(thm)],[f_172_3]) ).
cnf(f_172_6,plain,
( relation_dom(U_650) = empty_set
| relation_rng(U_650) != empty_set
| ~ sP109(U_650) ),
inference(clausify,[status(thm)],[f_172_3]) ).
fof(f_173_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_173_2,plain,
! [U_652,U_651] :
( ( set_difference(U_652,singleton(U_651)) = U_652
| in(U_651,U_652) )
& ( ~ in(U_651,U_652)
| set_difference(U_652,singleton(U_651)) != U_652 ) ),
inference(variable_rename,[status(thm)],[f_173_1]) ).
fof(f_173_3,plain,
( ! [U_656,U_654] :
( set_difference(U_656,singleton(U_654)) = U_656
| in(U_654,U_656) )
& ! [U_655,U_653] :
( ~ in(U_653,U_655)
| set_difference(U_655,singleton(U_653)) != U_655 ) ),
inference(miniscope,[status(thm)],[f_173_2]) ).
fof(f_173_4,plain,
( ! [U_656,U_654] :
( set_difference(U_656,singleton(U_654)) = U_656
| in(U_654,U_656) )
& ! [U_653,U_655] :
( ~ in(U_653,U_655)
| set_difference(U_655,singleton(U_653)) != U_655 ) ),
inference(definitional_conversion,[status(esa)],[f_173_3]) ).
cnf(f_173_5,plain,
( ~ in(U_653,U_655)
| set_difference(U_655,singleton(U_653)) != U_655 ),
inference(clausify,[status(thm)],[f_173_4]) ).
cnf(f_173_6,plain,
( set_difference(U_656,singleton(U_654)) = U_656
| in(U_654,U_656) ),
inference(clausify,[status(thm)],[f_173_4]) ).
fof(f_174_1,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(fof_nnf,[status(thm)],[t69_enumset1]) ).
fof(f_174_2,plain,
! [U_657] : unordered_pair(U_657,U_657) = singleton(U_657),
inference(variable_rename,[status(thm)],[f_174_1]) ).
fof(f_174_3,plain,
! [U_657] : unordered_pair(U_657,U_657) = singleton(U_657),
inference(definitional_conversion,[status(esa)],[f_174_2]) ).
cnf(f_174_4,plain,
unordered_pair(U_657,U_657) = singleton(U_657),
inference(clausify,[status(thm)],[f_174_3]) ).
fof(f_175_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_175_2,plain,
! [U_658] :
( U_658 = empty_set
| ~ empty(U_658) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
fof(f_175_3,plain,
! [U_658] :
( U_658 = empty_set
| ~ empty(U_658) ),
inference(definitional_conversion,[status(esa)],[f_175_2]) ).
cnf(f_175_4,plain,
( U_658 = empty_set
| ~ empty(U_658) ),
inference(clausify,[status(thm)],[f_175_3]) ).
fof(f_176_1,plain,
! [A,B] :
( A = B
| ~ subset(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t6_zfmisc_1]) ).
fof(f_176_2,plain,
! [U_660,U_659] :
( U_660 = U_659
| ~ subset(singleton(U_660),singleton(U_659)) ),
inference(variable_rename,[status(thm)],[f_176_1]) ).
fof(f_176_3,plain,
! [U_659,U_660] :
( U_660 = U_659
| ~ subset(singleton(U_660),singleton(U_659)) ),
inference(definitional_conversion,[status(esa)],[f_176_2]) ).
cnf(f_176_4,plain,
( U_660 = U_659
| ~ subset(singleton(U_660),singleton(U_659)) ),
inference(clausify,[status(thm)],[f_176_3]) ).
fof(f_177_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_177_2,plain,
! [U_661] :
( relation_rng(identity_relation(U_661)) = U_661
& relation_dom(identity_relation(U_661)) = U_661 ),
inference(variable_rename,[status(thm)],[f_177_1]) ).
fof(f_177_3,plain,
( ! [U_663] : relation_rng(identity_relation(U_663)) = U_663
& ! [U_662] : relation_dom(identity_relation(U_662)) = U_662 ),
inference(miniscope,[status(thm)],[f_177_2]) ).
fof(f_177_4,plain,
( ! [U_663] : relation_rng(identity_relation(U_663)) = U_663
& ! [U_662] : relation_dom(identity_relation(U_662)) = U_662 ),
inference(definitional_conversion,[status(esa)],[f_177_3]) ).
cnf(f_177_5,plain,
relation_dom(identity_relation(U_662)) = U_662,
inference(clausify,[status(thm)],[f_177_4]) ).
cnf(f_177_6,plain,
relation_rng(identity_relation(U_663)) = U_663,
inference(clausify,[status(thm)],[f_177_4]) ).
fof(f_178_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_178_2,plain,
! [U_667,U_666,U_665,U_664] :
( ( ( in(ordered_pair(U_667,U_666),relation_composition(identity_relation(U_665),U_664))
| ~ in(ordered_pair(U_667,U_666),U_664)
| ~ in(U_667,U_665) )
& ( ( in(ordered_pair(U_667,U_666),U_664)
& in(U_667,U_665) )
| ~ in(ordered_pair(U_667,U_666),relation_composition(identity_relation(U_665),U_664)) ) )
| ~ relation(U_664) ),
inference(variable_rename,[status(thm)],[f_178_1]) ).
fof(f_178_3,plain,
( ! [U_664,U_665,U_666,U_667] :
( in(ordered_pair(U_667,U_666),U_664)
| ~ sP110(U_664,U_665,U_666,U_667) )
& ! [U_664,U_665,U_666,U_667] :
( in(U_667,U_665)
| ~ sP110(U_664,U_665,U_666,U_667) )
& ! [U_664,U_665,U_666,U_667] :
( in(ordered_pair(U_667,U_666),relation_composition(identity_relation(U_665),U_664))
| ~ in(ordered_pair(U_667,U_666),U_664)
| ~ in(U_667,U_665)
| ~ sP111(U_664,U_665,U_666,U_667) )
& ! [U_664,U_665,U_666,U_667] :
( sP110(U_664,U_665,U_666,U_667)
| ~ in(ordered_pair(U_667,U_666),relation_composition(identity_relation(U_665),U_664))
| ~ sP111(U_664,U_665,U_666,U_667) )
& ! [U_664,U_665,U_666,U_667] :
( sP111(U_664,U_665,U_666,U_667)
| ~ relation(U_664) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP110,sP111])],[f_178_2]) ).
cnf(f_178_4,plain,
( sP111(U_664,U_665,U_666,U_667)
| ~ relation(U_664) ),
inference(clausify,[status(thm)],[f_178_3]) ).
cnf(f_178_5,plain,
( sP110(U_664,U_665,U_666,U_667)
| ~ in(ordered_pair(U_667,U_666),relation_composition(identity_relation(U_665),U_664))
| ~ sP111(U_664,U_665,U_666,U_667) ),
inference(clausify,[status(thm)],[f_178_3]) ).
cnf(f_178_6,plain,
( in(ordered_pair(U_667,U_666),relation_composition(identity_relation(U_665),U_664))
| ~ in(ordered_pair(U_667,U_666),U_664)
| ~ in(U_667,U_665)
| ~ sP111(U_664,U_665,U_666,U_667) ),
inference(clausify,[status(thm)],[f_178_3]) ).
cnf(f_178_7,plain,
( in(U_667,U_665)
| ~ sP110(U_664,U_665,U_666,U_667) ),
inference(clausify,[status(thm)],[f_178_3]) ).
cnf(f_178_8,plain,
( in(ordered_pair(U_667,U_666),U_664)
| ~ sP110(U_664,U_665,U_666,U_667) ),
inference(clausify,[status(thm)],[f_178_3]) ).
fof(f_179_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_179_2,plain,
! [U_669,U_668] :
( ~ empty(U_668)
| ~ in(U_669,U_668) ),
inference(variable_rename,[status(thm)],[f_179_1]) ).
fof(f_179_3,plain,
! [U_668,U_669] :
( ~ empty(U_668)
| ~ in(U_669,U_668) ),
inference(definitional_conversion,[status(esa)],[f_179_2]) ).
cnf(f_179_4,plain,
( ~ empty(U_668)
| ~ in(U_669,U_668) ),
inference(clausify,[status(thm)],[f_179_3]) ).
fof(f_180_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1]) ).
fof(f_180_2,plain,
! [U_671,U_670] : subset(U_671,set_union2(U_671,U_670)),
inference(variable_rename,[status(thm)],[f_180_1]) ).
fof(f_180_3,plain,
! [U_671,U_670] : subset(U_671,set_union2(U_671,U_670)),
inference(definitional_conversion,[status(esa)],[f_180_2]) ).
cnf(f_180_4,plain,
subset(U_671,set_union2(U_671,U_670)),
inference(clausify,[status(thm)],[f_180_3]) ).
fof(f_181_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_181_2,plain,
! [U_673,U_672] :
( ( disjoint(U_673,U_672)
| set_difference(U_673,U_672) != U_673 )
& ( set_difference(U_673,U_672) = U_673
| ~ disjoint(U_673,U_672) ) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
fof(f_181_3,plain,
( ! [U_677,U_675] :
( disjoint(U_677,U_675)
| set_difference(U_677,U_675) != U_677 )
& ! [U_676,U_674] :
( set_difference(U_676,U_674) = U_676
| ~ disjoint(U_676,U_674) ) ),
inference(miniscope,[status(thm)],[f_181_2]) ).
fof(f_181_4,plain,
( ! [U_677,U_675] :
( disjoint(U_677,U_675)
| set_difference(U_677,U_675) != U_677 )
& ! [U_676,U_674] :
( set_difference(U_676,U_674) = U_676
| ~ disjoint(U_676,U_674) ) ),
inference(definitional_conversion,[status(esa)],[f_181_3]) ).
cnf(f_181_5,plain,
( set_difference(U_676,U_674) = U_676
| ~ disjoint(U_676,U_674) ),
inference(clausify,[status(thm)],[f_181_4]) ).
cnf(f_181_6,plain,
( disjoint(U_677,U_675)
| set_difference(U_677,U_675) != U_677 ),
inference(clausify,[status(thm)],[f_181_4]) ).
fof(f_182_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_182_2,plain,
! [U_680,U_679,U_678] :
( ( ( in(U_680,relation_dom(relation_dom_restriction(U_678,U_679)))
| ~ in(U_680,relation_dom(U_678))
| ~ in(U_680,U_679) )
& ( ( in(U_680,relation_dom(U_678))
& in(U_680,U_679) )
| ~ in(U_680,relation_dom(relation_dom_restriction(U_678,U_679))) ) )
| ~ relation(U_678) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
fof(f_182_3,plain,
( ! [U_678,U_679,U_680] :
( in(U_680,relation_dom(U_678))
| ~ sP112(U_678,U_679,U_680) )
& ! [U_678,U_679,U_680] :
( in(U_680,U_679)
| ~ sP112(U_678,U_679,U_680) )
& ! [U_678,U_679,U_680] :
( in(U_680,relation_dom(relation_dom_restriction(U_678,U_679)))
| ~ in(U_680,relation_dom(U_678))
| ~ in(U_680,U_679)
| ~ sP113(U_678,U_679,U_680) )
& ! [U_678,U_679,U_680] :
( sP112(U_678,U_679,U_680)
| ~ in(U_680,relation_dom(relation_dom_restriction(U_678,U_679)))
| ~ sP113(U_678,U_679,U_680) )
& ! [U_678,U_679,U_680] :
( sP113(U_678,U_679,U_680)
| ~ relation(U_678) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP112,sP113])],[f_182_2]) ).
cnf(f_182_4,plain,
( sP113(U_678,U_679,U_680)
| ~ relation(U_678) ),
inference(clausify,[status(thm)],[f_182_3]) ).
cnf(f_182_5,plain,
( sP112(U_678,U_679,U_680)
| ~ in(U_680,relation_dom(relation_dom_restriction(U_678,U_679)))
| ~ sP113(U_678,U_679,U_680) ),
inference(clausify,[status(thm)],[f_182_3]) ).
cnf(f_182_6,plain,
( in(U_680,relation_dom(relation_dom_restriction(U_678,U_679)))
| ~ in(U_680,relation_dom(U_678))
| ~ in(U_680,U_679)
| ~ sP113(U_678,U_679,U_680) ),
inference(clausify,[status(thm)],[f_182_3]) ).
cnf(f_182_7,plain,
( in(U_680,U_679)
| ~ sP112(U_678,U_679,U_680) ),
inference(clausify,[status(thm)],[f_182_3]) ).
cnf(f_182_8,plain,
( in(U_680,relation_dom(U_678))
| ~ sP112(U_678,U_679,U_680) ),
inference(clausify,[status(thm)],[f_182_3]) ).
fof(f_183_1,plain,
! [A,B] :
( subset(relation_dom_restriction(B,A),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t88_relat_1]) ).
fof(f_183_2,plain,
! [U_682,U_681] :
( subset(relation_dom_restriction(U_681,U_682),U_681)
| ~ relation(U_681) ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
fof(f_183_3,plain,
! [U_681,U_682] :
( subset(relation_dom_restriction(U_681,U_682),U_681)
| ~ relation(U_681) ),
inference(definitional_conversion,[status(esa)],[f_183_2]) ).
cnf(f_183_4,plain,
( subset(relation_dom_restriction(U_681,U_682),U_681)
| ~ relation(U_681) ),
inference(clausify,[status(thm)],[f_183_3]) ).
fof(f_184_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_184_2,plain,
! [U_684,U_683] :
( ~ empty(U_683)
| U_684 = U_683
| ~ empty(U_684) ),
inference(variable_rename,[status(thm)],[f_184_1]) ).
fof(f_184_3,plain,
! [U_684] :
( ! [U_683] :
( ~ empty(U_683)
| U_684 = U_683 )
| ~ empty(U_684) ),
inference(miniscope,[status(thm)],[f_184_2]) ).
fof(f_184_4,plain,
! [U_683,U_684] :
( ~ empty(U_683)
| U_684 = U_683
| ~ empty(U_684) ),
inference(definitional_conversion,[status(esa)],[f_184_3]) ).
cnf(f_184_5,plain,
( ~ empty(U_683)
| U_684 = U_683
| ~ empty(U_684) ),
inference(clausify,[status(thm)],[f_184_4]) ).
fof(f_185_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_185_2,plain,
! [U_687,U_686,U_685] :
( subset(set_union2(U_687,U_685),U_686)
| ~ subset(U_685,U_686)
| ~ subset(U_687,U_686) ),
inference(variable_rename,[status(thm)],[f_185_1]) ).
fof(f_185_3,plain,
! [U_687,U_685,U_686] :
( subset(set_union2(U_687,U_685),U_686)
| ~ subset(U_685,U_686)
| ~ subset(U_687,U_686) ),
inference(definitional_conversion,[status(esa)],[f_185_2]) ).
cnf(f_185_4,plain,
( subset(set_union2(U_687,U_685),U_686)
| ~ subset(U_685,U_686)
| ~ subset(U_687,U_686) ),
inference(clausify,[status(thm)],[f_185_3]) ).
fof(f_186_1,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t8_zfmisc_1]) ).
fof(f_186_2,plain,
! [U_690,U_689,U_688] :
( U_690 = U_689
| singleton(U_690) != unordered_pair(U_689,U_688) ),
inference(variable_rename,[status(thm)],[f_186_1]) ).
fof(f_186_3,plain,
! [U_690,U_689] :
( ! [U_688] : singleton(U_690) != unordered_pair(U_689,U_688)
| U_690 = U_689 ),
inference(miniscope,[status(thm)],[f_186_2]) ).
fof(f_186_4,plain,
! [U_688,U_690,U_689] :
( singleton(U_690) != unordered_pair(U_689,U_688)
| U_690 = U_689 ),
inference(definitional_conversion,[status(esa)],[f_186_3]) ).
cnf(f_186_5,plain,
( singleton(U_690) != unordered_pair(U_689,U_688)
| U_690 = U_689 ),
inference(clausify,[status(thm)],[f_186_4]) ).
fof(f_187_1,plain,
! [A,B] :
( relation_dom(relation_dom_restriction(B,A)) = set_intersection2(relation_dom(B),A)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t90_relat_1]) ).
fof(f_187_2,plain,
! [U_692,U_691] :
( relation_dom(relation_dom_restriction(U_691,U_692)) = set_intersection2(relation_dom(U_691),U_692)
| ~ relation(U_691) ),
inference(variable_rename,[status(thm)],[f_187_1]) ).
fof(f_187_3,plain,
! [U_691,U_692] :
( relation_dom(relation_dom_restriction(U_691,U_692)) = set_intersection2(relation_dom(U_691),U_692)
| ~ relation(U_691) ),
inference(definitional_conversion,[status(esa)],[f_187_2]) ).
cnf(f_187_4,plain,
( relation_dom(relation_dom_restriction(U_691,U_692)) = set_intersection2(relation_dom(U_691),U_692)
| ~ relation(U_691) ),
inference(clausify,[status(thm)],[f_187_3]) ).
fof(f_188_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t92_zfmisc_1]) ).
fof(f_188_2,plain,
! [U_694,U_693] :
( subset(U_694,union(U_693))
| ~ in(U_694,U_693) ),
inference(variable_rename,[status(thm)],[f_188_1]) ).
fof(f_188_3,plain,
! [U_693,U_694] :
( subset(U_694,union(U_693))
| ~ in(U_694,U_693) ),
inference(definitional_conversion,[status(esa)],[f_188_2]) ).
cnf(f_188_4,plain,
( subset(U_694,union(U_693))
| ~ in(U_694,U_693) ),
inference(clausify,[status(thm)],[f_188_3]) ).
fof(f_189_1,plain,
! [A,B] :
( relation_dom_restriction(B,A) = relation_composition(identity_relation(A),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t94_relat_1]) ).
fof(f_189_2,plain,
! [U_696,U_695] :
( relation_dom_restriction(U_695,U_696) = relation_composition(identity_relation(U_696),U_695)
| ~ relation(U_695) ),
inference(variable_rename,[status(thm)],[f_189_1]) ).
fof(f_189_3,plain,
! [U_695,U_696] :
( relation_dom_restriction(U_695,U_696) = relation_composition(identity_relation(U_696),U_695)
| ~ relation(U_695) ),
inference(definitional_conversion,[status(esa)],[f_189_2]) ).
cnf(f_189_4,plain,
( relation_dom_restriction(U_695,U_696) = relation_composition(identity_relation(U_696),U_695)
| ~ relation(U_695) ),
inference(clausify,[status(thm)],[f_189_3]) ).
fof(f_190_1,plain,
! [A,B] :
( subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t99_relat_1]) ).
fof(f_190_2,plain,
! [U_698,U_697] :
( subset(relation_rng(relation_dom_restriction(U_697,U_698)),relation_rng(U_697))
| ~ relation(U_697) ),
inference(variable_rename,[status(thm)],[f_190_1]) ).
fof(f_190_3,plain,
! [U_697,U_698] :
( subset(relation_rng(relation_dom_restriction(U_697,U_698)),relation_rng(U_697))
| ~ relation(U_697) ),
inference(definitional_conversion,[status(esa)],[f_190_2]) ).
cnf(f_190_4,plain,
( subset(relation_rng(relation_dom_restriction(U_697,U_698)),relation_rng(U_697))
| ~ relation(U_697) ),
inference(clausify,[status(thm)],[f_190_3]) ).
fof(f_191_1,plain,
! [A] : union(powerset(A)) = A,
inference(fof_nnf,[status(thm)],[t99_zfmisc_1]) ).
fof(f_191_2,plain,
! [U_699] : union(powerset(U_699)) = U_699,
inference(variable_rename,[status(thm)],[f_191_1]) ).
fof(f_191_3,plain,
! [U_699] : union(powerset(U_699)) = U_699,
inference(definitional_conversion,[status(esa)],[f_191_2]) ).
cnf(f_191_4,plain,
union(powerset(U_699)) = U_699,
inference(clausify,[status(thm)],[f_191_3]) ).
fof(f_192_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_192_2,plain,
! [U_707] :
? [U_706] :
( ! [U_705] :
( in(U_705,U_706)
| are_equipotent(U_705,U_706)
| ~ subset(U_705,U_706) )
& ! [U_704] :
( ? [U_703] :
( ! [U_702] :
( in(U_702,U_703)
| ~ subset(U_702,U_704) )
& in(U_703,U_706) )
| ~ in(U_704,U_706) )
& ! [U_701,U_700] :
( in(U_700,U_706)
| ~ subset(U_700,U_701)
| ~ in(U_701,U_706) )
& in(U_707,U_706) ),
inference(variable_rename,[status(thm)],[f_192_1]) ).
fof(f_192_3,plain,
! [U_707] :
( ! [U_705] :
( in(U_705,sK86(U_707))
| are_equipotent(U_705,sK86(U_707))
| ~ subset(U_705,sK86(U_707)) )
& ! [U_704] :
( ? [U_703] :
( ! [U_702] :
( in(U_702,U_703)
| ~ subset(U_702,U_704) )
& in(U_703,sK86(U_707)) )
| ~ in(U_704,sK86(U_707)) )
& ! [U_701,U_700] :
( in(U_700,sK86(U_707))
| ~ subset(U_700,U_701)
| ~ in(U_701,sK86(U_707)) )
& in(U_707,sK86(U_707)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_706,sK86(U_707))],[f_192_2]) ).
fof(f_192_4,plain,
! [U_707] :
( ! [U_705] :
( in(U_705,sK86(U_707))
| are_equipotent(U_705,sK86(U_707))
| ~ subset(U_705,sK86(U_707)) )
& ! [U_704] :
( ( ! [U_702] :
( in(U_702,sK87(U_707,U_704))
| ~ subset(U_702,U_704) )
& in(sK87(U_707,U_704),sK86(U_707)) )
| ~ in(U_704,sK86(U_707)) )
& ! [U_701,U_700] :
( in(U_700,sK86(U_707))
| ~ subset(U_700,U_701)
| ~ in(U_701,sK86(U_707)) )
& in(U_707,sK86(U_707)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_703,sK87(U_707,U_704))],[f_192_3]) ).
fof(f_192_5,plain,
( ! [U_702,U_704,U_707] :
( in(U_702,sK87(U_707,U_704))
| ~ subset(U_702,U_704)
| ~ sP114(U_702,U_704,U_707) )
& ! [U_702,U_704,U_707] :
( in(sK87(U_707,U_704),sK86(U_707))
| ~ sP114(U_702,U_704,U_707) )
& ! [U_705,U_707] :
( in(U_705,sK86(U_707))
| are_equipotent(U_705,sK86(U_707))
| ~ subset(U_705,sK86(U_707)) )
& ! [U_702,U_704,U_707] :
( sP114(U_702,U_704,U_707)
| ~ in(U_704,sK86(U_707)) )
& ! [U_701,U_700,U_707] :
( in(U_700,sK86(U_707))
| ~ subset(U_700,U_701)
| ~ in(U_701,sK86(U_707)) )
& ! [U_707] : in(U_707,sK86(U_707)) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP114])],[f_192_4]) ).
cnf(f_192_6,plain,
in(U_707,sK86(U_707)),
inference(clausify,[status(thm)],[f_192_5]) ).
cnf(f_192_7,plain,
( in(U_700,sK86(U_707))
| ~ subset(U_700,U_701)
| ~ in(U_701,sK86(U_707)) ),
inference(clausify,[status(thm)],[f_192_5]) ).
cnf(f_192_8,plain,
( sP114(U_702,U_704,U_707)
| ~ in(U_704,sK86(U_707)) ),
inference(clausify,[status(thm)],[f_192_5]) ).
cnf(f_192_9,plain,
( in(U_705,sK86(U_707))
| are_equipotent(U_705,sK86(U_707))
| ~ subset(U_705,sK86(U_707)) ),
inference(clausify,[status(thm)],[f_192_5]) ).
cnf(f_192_10,plain,
( in(sK87(U_707,U_704),sK86(U_707))
| ~ sP114(U_702,U_704,U_707) ),
inference(clausify,[status(thm)],[f_192_5]) ).
cnf(f_192_11,plain,
( in(U_702,sK87(U_707,U_704))
| ~ subset(U_702,U_704)
| ~ sP114(U_702,U_704,U_707) ),
inference(clausify,[status(thm)],[f_192_5]) ).
fof(f_193_1,plain,
! [A,B,C] :
( B = C
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t9_zfmisc_1]) ).
fof(f_193_2,plain,
! [U_710,U_709,U_708] :
( U_709 = U_708
| singleton(U_710) != unordered_pair(U_709,U_708) ),
inference(variable_rename,[status(thm)],[f_193_1]) ).
fof(f_193_3,plain,
! [U_710,U_708,U_709] :
( U_709 = U_708
| singleton(U_710) != unordered_pair(U_709,U_708) ),
inference(definitional_conversion,[status(esa)],[f_193_2]) ).
cnf(f_193_4,plain,
( U_709 = U_708
| singleton(U_710) != unordered_pair(U_709,U_708) ),
inference(clausify,[status(thm)],[f_193_3]) ).
cnf(f_37_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_37_3]) ).
cnf(f_38_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_38_3]) ).
cnf(f_39_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_39_3]) ).
cnf(f_40_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_40_3]) ).
cnf(f_41_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_41_3]) ).
cnf(f_42_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_42_3]) ).
cnf(f_44_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_44_3]) ).
cnf(f_45_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_45_3]) ).
cnf(f_46_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_46_3]) ).
cnf(f_47_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_47_3]) ).
cnf(f_49_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_49_3]) ).
cnf(f_50_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_50_3]) ).
cnf(f_52_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_52_3]) ).
cnf(f_53_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_53_3]) ).
cnf(f_62_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_62_3]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( unordered_pair(Eq_x_0,Eq_x_1) = unordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( set_union2(Eq_x_0,Eq_x_1) = set_union2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( set_intersection2(Eq_x_0,Eq_x_1) = set_intersection2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( identity_relation(Eq_x_0) = identity_relation(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( ordered_pair(Eq_x_0,Eq_x_1) = ordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( relation_dom_restriction(Eq_x_0,Eq_x_1) = relation_dom_restriction(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( relation_rng_restriction(Eq_x_0,Eq_x_1) = relation_rng_restriction(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( set_meet(Eq_x_0) = set_meet(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,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_15,axiom,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,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_17,axiom,
( union(Eq_x_0) = union(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,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_19,axiom,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,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_21,axiom,
( relation_field(Eq_x_0) = relation_field(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( relation_inverse(Eq_x_0) = relation_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,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_24,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_25,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_26,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_27,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_28,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_29,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_30,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_31,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_32,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_33,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_34,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_35,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_36,axiom,
( sK9(Eq_x_0,Eq_x_1,Eq_x_2) = sK9(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_37,axiom,
( sK10(Eq_x_0,Eq_x_1,Eq_x_2) = sK10(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_38,axiom,
( sK11(Eq_x_0,Eq_x_1,Eq_x_2) = sK11(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,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_40,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_41,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_42,axiom,
( sK15(Eq_x_0) = sK15(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_43,axiom,
( sK16(Eq_x_0,Eq_x_1,Eq_x_2) = sK16(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_44,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_45,axiom,
( sK18(Eq_x_0,Eq_x_1) = sK18(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_46,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_47,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_48,axiom,
( sK21(Eq_x_0,Eq_x_1) = sK21(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_49,axiom,
( sK22(Eq_x_0) = sK22(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_50,axiom,
( sK23(Eq_x_0,Eq_x_1) = sK23(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_51,axiom,
( sK24(Eq_x_0,Eq_x_1) = sK24(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_52,axiom,
( sK25(Eq_x_0,Eq_x_1) = sK25(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_53,axiom,
( sK26(Eq_x_0,Eq_x_1) = sK26(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_54,axiom,
( sK27(Eq_x_0,Eq_x_1) = sK27(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_55,axiom,
( sK28(Eq_x_0,Eq_x_1) = sK28(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_56,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_57,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_58,axiom,
( sK31(Eq_x_0,Eq_x_1,Eq_x_2) = sK31(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_59,axiom,
( sK32(Eq_x_0,Eq_x_1,Eq_x_2) = sK32(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_60,axiom,
( sK33(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK33(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_61,axiom,
( sK34(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK34(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_62,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_63,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_64,axiom,
( sK37(Eq_x_0,Eq_x_1,Eq_x_2) = sK37(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_65,axiom,
( sK38(Eq_x_0,Eq_x_1,Eq_x_2) = sK38(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_66,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_67,axiom,
( sK40(Eq_x_0,Eq_x_1) = sK40(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_68,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_69,axiom,
( sK42(Eq_x_0,Eq_x_1,Eq_x_2) = sK42(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_70,axiom,
( sK43(Eq_x_0,Eq_x_1,Eq_x_2) = sK43(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,
( 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_72,axiom,
( sK45(Eq_x_0,Eq_x_1) = sK45(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_73,axiom,
( sK46(Eq_x_0,Eq_x_1) = sK46(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_74,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_75,axiom,
( sK48(Eq_x_0,Eq_x_1,Eq_x_2) = sK48(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_76,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_77,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_78,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_79,axiom,
( sK52(Eq_x_0,Eq_x_1,Eq_x_2) = sK52(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_80,axiom,
( sK53(Eq_x_0,Eq_x_1,Eq_x_2) = sK53(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_81,axiom,
( sK54(Eq_x_0,Eq_x_1,Eq_x_2) = sK54(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,
( sK55(Eq_x_0,Eq_x_1) = sK55(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_83,axiom,
( sK56(Eq_x_0,Eq_x_1) = sK56(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_84,axiom,
( sK57(Eq_x_0,Eq_x_1) = sK57(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_85,axiom,
( sK58(Eq_x_0,Eq_x_1) = sK58(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_86,axiom,
( sK59(Eq_x_0,Eq_x_1) = sK59(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_87,axiom,
( sK60(Eq_x_0,Eq_x_1) = sK60(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_88,axiom,
( sK61(Eq_x_0,Eq_x_1) = sK61(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_89,axiom,
( sK62(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK62(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_90,axiom,
( sK63(Eq_x_0,Eq_x_1,Eq_x_2) = sK63(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_91,axiom,
( sK64(Eq_x_0,Eq_x_1,Eq_x_2) = sK64(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_92,axiom,
( sK65(Eq_x_0,Eq_x_1,Eq_x_2) = sK65(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_93,axiom,
( sK66(Eq_x_0,Eq_x_1,Eq_x_2) = sK66(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_94,axiom,
( sK67(Eq_x_0,Eq_x_1,Eq_x_2) = sK67(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_95,axiom,
( sK68(Eq_x_0,Eq_x_1,Eq_x_2) = sK68(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_96,axiom,
( sK69(Eq_x_0) = sK69(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_97,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_98,axiom,
( sK72(Eq_x_0) = sK72(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_99,axiom,
( sK75(Eq_x_0) = sK75(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_100,axiom,
( sK79(Eq_x_0) = sK79(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_101,axiom,
( sK80(Eq_x_0,Eq_x_1) = sK80(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_102,axiom,
( sK81(Eq_x_0,Eq_x_1) = sK81(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_103,axiom,
( sK82(Eq_x_0,Eq_x_1) = sK82(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_104,axiom,
( sK83(Eq_x_0,Eq_x_1) = sK83(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_105,axiom,
( sK84(Eq_x_0) = sK84(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_106,axiom,
( sK85(Eq_x_0) = sK85(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_107,axiom,
( sK86(Eq_x_0) = sK86(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_108,axiom,
( sK87(Eq_x_0,Eq_x_1) = sK87(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_109,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_110,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_111,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_112,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_113,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_114,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_115,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_116,axiom,
( are_equipotent(Eq_y_0,Eq_y_1)
| ~ are_equipotent(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_117,axiom,
( sP0(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP0(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_118,axiom,
( sP1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_119,axiom,
( sP2(Eq_y_0,Eq_y_1)
| ~ sP2(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_120,axiom,
( sP3(Eq_y_0,Eq_y_1)
| ~ sP3(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_121,axiom,
( sP4(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP4(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_122,axiom,
( sP5(Eq_y_0,Eq_y_1)
| ~ sP5(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_123,axiom,
( sP6(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP6(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_124,axiom,
( sP7(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP7(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_125,axiom,
( sP8(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP8(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_126,axiom,
( sP9(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP9(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_127,axiom,
( sP10(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP10(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_128,axiom,
( sP11(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP11(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_129,axiom,
( sP12(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP12(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_130,axiom,
( sP13(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP13(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_131,axiom,
( sP14(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP14(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_132,axiom,
( sP15(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP15(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_133,axiom,
( sP16(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP16(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_134,axiom,
( sP17(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP17(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_135,axiom,
( sP18(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP18(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_136,axiom,
( sP19(Eq_y_0,Eq_y_1)
| ~ sP19(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_137,axiom,
( sP20(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP20(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_138,axiom,
( sP21(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP21(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_139,axiom,
( sP22(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP22(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_140,axiom,
( sP23(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP23(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_141,axiom,
( sP24(Eq_y_0,Eq_y_1)
| ~ sP24(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_142,axiom,
( sP25(Eq_y_0,Eq_y_1)
| ~ sP25(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_143,axiom,
( sP26(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP26(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_144,axiom,
( sP27(Eq_y_0,Eq_y_1)
| ~ sP27(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_145,axiom,
( sP28(Eq_y_0,Eq_y_1)
| ~ sP28(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_146,axiom,
( sP29(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP29(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_147,axiom,
( sP30(Eq_y_0,Eq_y_1)
| ~ sP30(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_148,axiom,
( sP31(Eq_y_0,Eq_y_1)
| ~ sP31(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_149,axiom,
( sP32(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP32(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_150,axiom,
( sP33(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP33(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_151,axiom,
( sP34(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP34(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_152,axiom,
( sP35(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP35(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_153,axiom,
( sP36(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP36(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_154,axiom,
( sP37(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP37(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_155,axiom,
( sP38(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP38(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_156,axiom,
( sP39(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP39(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_157,axiom,
( sP40(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP40(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_158,axiom,
( sP41(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP41(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_159,axiom,
( sP42(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP42(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_160,axiom,
( sP43(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP43(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_161,axiom,
( sP44(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP44(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_162,axiom,
( sP45(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP45(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_163,axiom,
( sP46(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP46(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_164,axiom,
( sP47(Eq_y_0,Eq_y_1)
| ~ sP47(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_165,axiom,
( sP48(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP48(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_166,axiom,
( sP49(Eq_y_0,Eq_y_1)
| ~ sP49(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_167,axiom,
( sP50(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP50(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_168,axiom,
( sP51(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP51(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_169,axiom,
( sP52(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP52(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_170,axiom,
( sP53(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP53(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_171,axiom,
( sP54(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP54(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_172,axiom,
( sP55(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP55(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_173,axiom,
( sP56(Eq_y_0,Eq_y_1)
| ~ sP56(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_174,axiom,
( sP57(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP57(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_175,axiom,
( sP58(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP58(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_176,axiom,
( sP59(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP59(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_177,axiom,
( sP60(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP60(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_178,axiom,
( sP61(Eq_y_0,Eq_y_1)
| ~ sP61(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_179,axiom,
( sP62(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP62(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_180,axiom,
( sP63(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP63(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_181,axiom,
( sP64(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP64(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_182,axiom,
( sP65(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP65(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_183,axiom,
( sP66(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP66(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_184,axiom,
( sP67(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP67(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_185,axiom,
( sP68(Eq_y_0,Eq_y_1)
| ~ sP68(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_186,axiom,
( sP69(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP69(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_187,axiom,
( sP70(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP70(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_188,axiom,
( sP71(Eq_y_0,Eq_y_1)
| ~ sP71(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_189,axiom,
( sP72(Eq_y_0,Eq_y_1)
| ~ sP72(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_190,axiom,
( sP73(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP73(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_191,axiom,
( sP74(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP74(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_192,axiom,
( sP75(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| ~ sP75(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7)
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_193,axiom,
( sP76(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP76(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_194,axiom,
( sP77(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP77(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_195,axiom,
( sP78(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8)
| ~ sP78(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8)
| Eq_x_8 != Eq_y_8
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_196,axiom,
( sP79(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP79(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_197,axiom,
( sP80(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP80(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_198,axiom,
( sP81(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP81(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_199,axiom,
( sP82(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP82(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_200,axiom,
( sP83(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP83(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_201,axiom,
( sP84(Eq_y_0,Eq_y_1)
| ~ sP84(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_202,axiom,
( sP85(Eq_y_0,Eq_y_1)
| ~ sP85(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_203,axiom,
( sP86(Eq_y_0)
| ~ sP86(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_204,axiom,
( sP87(Eq_y_0)
| ~ sP87(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_205,axiom,
( sP88(Eq_y_0,Eq_y_1)
| ~ sP88(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_206,axiom,
( sP89(Eq_y_0,Eq_y_1)
| ~ sP89(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_207,axiom,
( sP90(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP90(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_208,axiom,
( sP91(Eq_y_0,Eq_y_1)
| ~ sP91(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_209,axiom,
( sP92(Eq_y_0)
| ~ sP92(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_210,axiom,
( sP93(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP93(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_211,axiom,
( sP94(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP94(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_212,axiom,
( sP95(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP95(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_213,axiom,
( sP96(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP96(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_214,axiom,
( sP97(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP97(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_215,axiom,
( sP98(Eq_y_0,Eq_y_1)
| ~ sP98(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_216,axiom,
( sP99(Eq_y_0,Eq_y_1)
| ~ sP99(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_217,axiom,
( sP100(Eq_y_0,Eq_y_1)
| ~ sP100(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_218,axiom,
( sP101(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP101(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_219,axiom,
( sP102(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP102(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_220,axiom,
( sP103(Eq_y_0)
| ~ sP103(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_221,axiom,
( sP104(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP104(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_222,axiom,
( sP105(Eq_y_0,Eq_y_1)
| ~ sP105(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_223,axiom,
( sP106(Eq_y_0,Eq_y_1)
| ~ sP106(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_224,axiom,
( sP107(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP107(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_225,axiom,
( sP108(Eq_y_0)
| ~ sP108(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_226,axiom,
( sP109(Eq_y_0)
| ~ sP109(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_227,axiom,
( sP110(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP110(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_228,axiom,
( sP111(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP111(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_229,axiom,
( sP112(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP112(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_230,axiom,
( sP113(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP113(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_231,axiom,
( sP114(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP114(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU200+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
% 0.07/0.34 % Computer : n009.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 19 23:30:11 UTC 2026
% 0.07/0.35 % CPUTime :
% 45.55/45.81 % SZS status Theorem for theBenchmark
% 45.55/45.81 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------