%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU211+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 : n019.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 08:58:30 AM UTC 2026
% Result : Theorem 165.16s 165.47s
% Output : Proof 165.36s
% 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(d13_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = relation_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) ) ) ) ),
file('theBenchmark.p',d13_relat_1) ).
fof(d14_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) ) ) ) ),
file('theBenchmark.p',d14_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_k10_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k10_relat_1) ).
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_k9_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k9_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,lemma,
! [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_relat_1,lemma,
! [A,B] :
( relation(B)
=> relation_rng(relation_rng_restriction(A,B)) = set_intersection2(relation_rng(B),A) ),
file('theBenchmark.p',t119_relat_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(t140_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> relation_dom_restriction(relation_rng_restriction(A,C),B) = relation_rng_restriction(A,relation_dom_restriction(C,B)) ),
file('theBenchmark.p',t140_relat_1) ).
fof(t143_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_image(C,B))
<=> ? [D] :
( in(D,B)
& in(ordered_pair(D,A),C)
& in(D,relation_dom(C)) ) ) ),
file('theBenchmark.p',t143_relat_1) ).
fof(t144_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_image(B,A),relation_rng(B)) ),
file('theBenchmark.p',t144_relat_1) ).
fof(t145_relat_1,lemma,
! [A,B] :
( relation(B)
=> relation_image(B,A) = relation_image(B,set_intersection2(relation_dom(B),A)) ),
file('theBenchmark.p',t145_relat_1) ).
fof(t146_relat_1,lemma,
! [A] :
( relation(A)
=> relation_image(A,relation_dom(A)) = relation_rng(A) ),
file('theBenchmark.p',t146_relat_1) ).
fof(t160_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> relation_rng(relation_composition(A,B)) = relation_image(B,relation_rng(A)) ) ),
file('theBenchmark.p',t160_relat_1) ).
fof(t166_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_inverse_image(C,B))
<=> ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) ) ) ),
file('theBenchmark.p',t166_relat_1) ).
fof(t167_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_inverse_image(B,A),relation_dom(B)) ),
file('theBenchmark.p',t167_relat_1) ).
fof(t174_relat_1,lemma,
! [A,B] :
( relation(B)
=> ~ ( relation_inverse_image(B,A) = empty_set
& subset(A,relation_rng(B))
& A != empty_set ) ),
file('theBenchmark.p',t174_relat_1) ).
fof(t178_relat_1,conjecture,
! [A,B,C] :
( relation(C)
=> ( subset(A,B)
=> subset(relation_inverse_image(C,A),relation_inverse_image(C,B)) ) ),
file('theBenchmark.p',t178_relat_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]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ proper_subset(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(f_2_2,plain,
! [U_3,U_2] :
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_3_2,plain,
! [U_4] :
( relation(U_4)
| ~ empty(U_4) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( relation(U_4)
| ~ empty(U_4) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_4_2,plain,
! [U_6,U_5] : unordered_pair(U_6,U_5) = unordered_pair(U_5,U_6),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
unordered_pair(U_6,U_5) = unordered_pair(U_5,U_6),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_5_2,plain,
! [U_8,U_7] : set_union2(U_8,U_7) = set_union2(U_7,U_8),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
set_union2(U_8,U_7) = set_union2(U_7,U_8),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_6_2,plain,
! [U_10,U_9] : set_intersection2(U_10,U_9) = set_intersection2(U_9,U_10),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
set_intersection2(U_10,U_9) = set_intersection2(U_9,U_10),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A,B] :
( ( ( B = identity_relation(A)
| ? [C,D] :
( ( ~ in(ordered_pair(C,D),B)
& C = D
& in(C,A) )
| ( ( C != D
| ~ in(C,A) )
& in(ordered_pair(C,D),B) ) ) )
& ( ! [C,D] :
( ( in(ordered_pair(C,D),B)
| C != D
| ~ in(C,A) )
& ( ( C = D
& in(C,A) )
| ~ in(ordered_pair(C,D),B) ) )
| B != identity_relation(A) ) )
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[d10_relat_1]) ).
fof(f_7_2,plain,
! [U_16,U_15] :
( ( ( U_15 = identity_relation(U_16)
| ? [U_14,U_13] :
( ( ~ in(ordered_pair(U_14,U_13),U_15)
& U_14 = U_13
& in(U_14,U_16) )
| ( ( U_14 != U_13
| ~ in(U_14,U_16) )
& in(ordered_pair(U_14,U_13),U_15) ) ) )
& ( ! [U_12,U_11] :
( ( in(ordered_pair(U_12,U_11),U_15)
| U_12 != U_11
| ~ in(U_12,U_16) )
& ( ( U_12 = U_11
& in(U_12,U_16) )
| ~ in(ordered_pair(U_12,U_11),U_15) ) )
| U_15 != identity_relation(U_16) ) )
| ~ relation(U_15) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_16,U_15] :
( ( ( U_15 = identity_relation(U_16)
| ? [U_24,U_22] :
( ~ in(ordered_pair(U_24,U_22),U_15)
& U_24 = U_22
& in(U_24,U_16) )
| ? [U_23,U_21] :
( ( U_23 != U_21
| ~ in(U_23,U_16) )
& in(ordered_pair(U_23,U_21),U_15) ) )
& ( ( ! [U_20,U_18] :
( in(ordered_pair(U_20,U_18),U_15)
| U_20 != U_18
| ~ in(U_20,U_16) )
& ! [U_19,U_17] :
( ( U_19 = U_17
& in(U_19,U_16) )
| ~ in(ordered_pair(U_19,U_17),U_15) ) )
| U_15 != identity_relation(U_16) ) )
| ~ relation(U_15) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
! [U_16,U_15] :
( ( ( U_15 = identity_relation(U_16)
| ? [U_24,U_22] :
( ~ in(ordered_pair(U_24,U_22),U_15)
& U_24 = U_22
& in(U_24,U_16) )
| ? [U_21] :
( ( sK1(U_16,U_15) != U_21
| ~ in(sK1(U_16,U_15),U_16) )
& in(ordered_pair(sK1(U_16,U_15),U_21),U_15) ) )
& ( ( ! [U_20,U_18] :
( in(ordered_pair(U_20,U_18),U_15)
| U_20 != U_18
| ~ in(U_20,U_16) )
& ! [U_19,U_17] :
( ( U_19 = U_17
& in(U_19,U_16) )
| ~ in(ordered_pair(U_19,U_17),U_15) ) )
| U_15 != identity_relation(U_16) ) )
| ~ relation(U_15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_23,sK1(U_16,U_15))],[f_7_3]) ).
fof(f_7_5,plain,
! [U_16,U_15] :
( ( ( U_15 = identity_relation(U_16)
| ? [U_24,U_22] :
( ~ in(ordered_pair(U_24,U_22),U_15)
& U_24 = U_22
& in(U_24,U_16) )
| ( ( sK1(U_16,U_15) != sK2(U_16,U_15)
| ~ in(sK1(U_16,U_15),U_16) )
& in(ordered_pair(sK1(U_16,U_15),sK2(U_16,U_15)),U_15) ) )
& ( ( ! [U_20,U_18] :
( in(ordered_pair(U_20,U_18),U_15)
| U_20 != U_18
| ~ in(U_20,U_16) )
& ! [U_19,U_17] :
( ( U_19 = U_17
& in(U_19,U_16) )
| ~ in(ordered_pair(U_19,U_17),U_15) ) )
| U_15 != identity_relation(U_16) ) )
| ~ relation(U_15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_21,sK2(U_16,U_15))],[f_7_4]) ).
fof(f_7_6,plain,
! [U_16,U_15] :
( ( ( U_15 = identity_relation(U_16)
| ? [U_22] :
( ~ in(ordered_pair(sK3(U_16,U_15),U_22),U_15)
& sK3(U_16,U_15) = U_22
& in(sK3(U_16,U_15),U_16) )
| ( ( sK1(U_16,U_15) != sK2(U_16,U_15)
| ~ in(sK1(U_16,U_15),U_16) )
& in(ordered_pair(sK1(U_16,U_15),sK2(U_16,U_15)),U_15) ) )
& ( ( ! [U_20,U_18] :
( in(ordered_pair(U_20,U_18),U_15)
| U_20 != U_18
| ~ in(U_20,U_16) )
& ! [U_19,U_17] :
( ( U_19 = U_17
& in(U_19,U_16) )
| ~ in(ordered_pair(U_19,U_17),U_15) ) )
| U_15 != identity_relation(U_16) ) )
| ~ relation(U_15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_24,sK3(U_16,U_15))],[f_7_5]) ).
fof(f_7_7,plain,
! [U_16,U_15] :
( ( ( U_15 = identity_relation(U_16)
| ( ~ in(ordered_pair(sK3(U_16,U_15),sK4(U_16,U_15)),U_15)
& sK3(U_16,U_15) = sK4(U_16,U_15)
& in(sK3(U_16,U_15),U_16) )
| ( ( sK1(U_16,U_15) != sK2(U_16,U_15)
| ~ in(sK1(U_16,U_15),U_16) )
& in(ordered_pair(sK1(U_16,U_15),sK2(U_16,U_15)),U_15) ) )
& ( ( ! [U_20,U_18] :
( in(ordered_pair(U_20,U_18),U_15)
| U_20 != U_18
| ~ in(U_20,U_16) )
& ! [U_19,U_17] :
( ( U_19 = U_17
& in(U_19,U_16) )
| ~ in(ordered_pair(U_19,U_17),U_15) ) )
| U_15 != identity_relation(U_16) ) )
| ~ relation(U_15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_22,sK4(U_16,U_15))],[f_7_6]) ).
cnf(f_7_8,plain,
( in(U_19,U_16)
| ~ in(ordered_pair(U_19,U_17),U_15)
| U_15 != identity_relation(U_16)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_9,plain,
( U_19 = U_17
| ~ in(ordered_pair(U_19,U_17),U_15)
| U_15 != identity_relation(U_16)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_10,plain,
( in(ordered_pair(U_20,U_18),U_15)
| U_20 != U_18
| ~ in(U_20,U_16)
| U_15 != identity_relation(U_16)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_11,plain,
( in(sK3(U_16,U_15),U_16)
| in(ordered_pair(sK1(U_16,U_15),sK2(U_16,U_15)),U_15)
| U_15 = identity_relation(U_16)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_12,plain,
( sK3(U_16,U_15) = sK4(U_16,U_15)
| in(ordered_pair(sK1(U_16,U_15),sK2(U_16,U_15)),U_15)
| U_15 = identity_relation(U_16)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_13,plain,
( ~ in(ordered_pair(sK3(U_16,U_15),sK4(U_16,U_15)),U_15)
| in(ordered_pair(sK1(U_16,U_15),sK2(U_16,U_15)),U_15)
| U_15 = identity_relation(U_16)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_14,plain,
( in(sK3(U_16,U_15),U_16)
| sK1(U_16,U_15) != sK2(U_16,U_15)
| ~ in(sK1(U_16,U_15),U_16)
| U_15 = identity_relation(U_16)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_15,plain,
( sK3(U_16,U_15) = sK4(U_16,U_15)
| sK1(U_16,U_15) != sK2(U_16,U_15)
| ~ in(sK1(U_16,U_15),U_16)
| U_15 = identity_relation(U_16)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_16,plain,
( ~ in(ordered_pair(sK3(U_16,U_15),sK4(U_16,U_15)),U_15)
| sK1(U_16,U_15) != sK2(U_16,U_15)
| ~ in(sK1(U_16,U_15),U_16)
| U_15 = identity_relation(U_16)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_7_7]) ).
fof(f_8_1,plain,
! [A,B] :
( ( A = B
| ~ subset(B,A)
| ~ subset(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(fof_nnf,[status(thm)],[d10_xboole_0]) ).
fof(f_8_2,plain,
! [U_26,U_25] :
( ( U_26 = U_25
| ~ subset(U_25,U_26)
| ~ subset(U_26,U_25) )
& ( ( subset(U_25,U_26)
& subset(U_26,U_25) )
| U_26 != U_25 ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_30,U_28] :
( U_30 = U_28
| ~ subset(U_28,U_30)
| ~ subset(U_30,U_28) )
& ! [U_29,U_27] :
( ( subset(U_27,U_29)
& subset(U_29,U_27) )
| U_29 != U_27 ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( subset(U_29,U_27)
| U_29 != U_27 ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( subset(U_27,U_29)
| U_29 != U_27 ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_6,plain,
( U_30 = U_28
| ~ subset(U_28,U_30)
| ~ subset(U_30,U_28) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [A] :
( ! [B,C] :
( ( ( C = relation_dom_restriction(A,B)
| ? [D,E] :
( ( ~ in(ordered_pair(D,E),C)
& in(ordered_pair(D,E),A)
& in(D,B) )
| ( ( ~ in(ordered_pair(D,E),A)
| ~ in(D,B) )
& in(ordered_pair(D,E),C) ) ) )
& ( ! [D,E] :
( ( in(ordered_pair(D,E),C)
| ~ in(ordered_pair(D,E),A)
| ~ in(D,B) )
& ( ( in(ordered_pair(D,E),A)
& in(D,B) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_dom_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d11_relat_1]) ).
fof(f_9_2,plain,
! [U_37] :
( ! [U_36,U_35] :
( ( ( U_35 = relation_dom_restriction(U_37,U_36)
| ? [U_34,U_33] :
( ( ~ in(ordered_pair(U_34,U_33),U_35)
& in(ordered_pair(U_34,U_33),U_37)
& in(U_34,U_36) )
| ( ( ~ in(ordered_pair(U_34,U_33),U_37)
| ~ in(U_34,U_36) )
& in(ordered_pair(U_34,U_33),U_35) ) ) )
& ( ! [U_32,U_31] :
( ( in(ordered_pair(U_32,U_31),U_35)
| ~ in(ordered_pair(U_32,U_31),U_37)
| ~ in(U_32,U_36) )
& ( ( in(ordered_pair(U_32,U_31),U_37)
& in(U_32,U_36) )
| ~ in(ordered_pair(U_32,U_31),U_35) ) )
| U_35 != relation_dom_restriction(U_37,U_36) ) )
| ~ relation(U_35) )
| ~ relation(U_37) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_37] :
( ! [U_36,U_35] :
( ( ( U_35 = relation_dom_restriction(U_37,U_36)
| ? [U_45,U_43] :
( ~ in(ordered_pair(U_45,U_43),U_35)
& in(ordered_pair(U_45,U_43),U_37)
& in(U_45,U_36) )
| ? [U_44,U_42] :
( ( ~ in(ordered_pair(U_44,U_42),U_37)
| ~ in(U_44,U_36) )
& in(ordered_pair(U_44,U_42),U_35) ) )
& ( ( ! [U_41,U_39] :
( in(ordered_pair(U_41,U_39),U_35)
| ~ in(ordered_pair(U_41,U_39),U_37)
| ~ in(U_41,U_36) )
& ! [U_40,U_38] :
( ( in(ordered_pair(U_40,U_38),U_37)
& in(U_40,U_36) )
| ~ in(ordered_pair(U_40,U_38),U_35) ) )
| U_35 != relation_dom_restriction(U_37,U_36) ) )
| ~ relation(U_35) )
| ~ relation(U_37) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
fof(f_9_4,plain,
! [U_37] :
( ! [U_36,U_35] :
( ( ( U_35 = relation_dom_restriction(U_37,U_36)
| ? [U_45,U_43] :
( ~ in(ordered_pair(U_45,U_43),U_35)
& in(ordered_pair(U_45,U_43),U_37)
& in(U_45,U_36) )
| ? [U_42] :
( ( ~ in(ordered_pair(sK5(U_37,U_36,U_35),U_42),U_37)
| ~ in(sK5(U_37,U_36,U_35),U_36) )
& in(ordered_pair(sK5(U_37,U_36,U_35),U_42),U_35) ) )
& ( ( ! [U_41,U_39] :
( in(ordered_pair(U_41,U_39),U_35)
| ~ in(ordered_pair(U_41,U_39),U_37)
| ~ in(U_41,U_36) )
& ! [U_40,U_38] :
( ( in(ordered_pair(U_40,U_38),U_37)
& in(U_40,U_36) )
| ~ in(ordered_pair(U_40,U_38),U_35) ) )
| U_35 != relation_dom_restriction(U_37,U_36) ) )
| ~ relation(U_35) )
| ~ relation(U_37) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_44,sK5(U_37,U_36,U_35))],[f_9_3]) ).
fof(f_9_5,plain,
! [U_37] :
( ! [U_36,U_35] :
( ( ( U_35 = relation_dom_restriction(U_37,U_36)
| ? [U_45,U_43] :
( ~ in(ordered_pair(U_45,U_43),U_35)
& in(ordered_pair(U_45,U_43),U_37)
& in(U_45,U_36) )
| ( ( ~ in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_37)
| ~ in(sK5(U_37,U_36,U_35),U_36) )
& in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_35) ) )
& ( ( ! [U_41,U_39] :
( in(ordered_pair(U_41,U_39),U_35)
| ~ in(ordered_pair(U_41,U_39),U_37)
| ~ in(U_41,U_36) )
& ! [U_40,U_38] :
( ( in(ordered_pair(U_40,U_38),U_37)
& in(U_40,U_36) )
| ~ in(ordered_pair(U_40,U_38),U_35) ) )
| U_35 != relation_dom_restriction(U_37,U_36) ) )
| ~ relation(U_35) )
| ~ relation(U_37) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_42,sK6(U_37,U_36,U_35))],[f_9_4]) ).
fof(f_9_6,plain,
! [U_37] :
( ! [U_36,U_35] :
( ( ( U_35 = relation_dom_restriction(U_37,U_36)
| ? [U_43] :
( ~ in(ordered_pair(sK7(U_37,U_36,U_35),U_43),U_35)
& in(ordered_pair(sK7(U_37,U_36,U_35),U_43),U_37)
& in(sK7(U_37,U_36,U_35),U_36) )
| ( ( ~ in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_37)
| ~ in(sK5(U_37,U_36,U_35),U_36) )
& in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_35) ) )
& ( ( ! [U_41,U_39] :
( in(ordered_pair(U_41,U_39),U_35)
| ~ in(ordered_pair(U_41,U_39),U_37)
| ~ in(U_41,U_36) )
& ! [U_40,U_38] :
( ( in(ordered_pair(U_40,U_38),U_37)
& in(U_40,U_36) )
| ~ in(ordered_pair(U_40,U_38),U_35) ) )
| U_35 != relation_dom_restriction(U_37,U_36) ) )
| ~ relation(U_35) )
| ~ relation(U_37) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_45,sK7(U_37,U_36,U_35))],[f_9_5]) ).
fof(f_9_7,plain,
! [U_37] :
( ! [U_36,U_35] :
( ( ( U_35 = relation_dom_restriction(U_37,U_36)
| ( ~ in(ordered_pair(sK7(U_37,U_36,U_35),sK8(U_37,U_36,U_35)),U_35)
& in(ordered_pair(sK7(U_37,U_36,U_35),sK8(U_37,U_36,U_35)),U_37)
& in(sK7(U_37,U_36,U_35),U_36) )
| ( ( ~ in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_37)
| ~ in(sK5(U_37,U_36,U_35),U_36) )
& in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_35) ) )
& ( ( ! [U_41,U_39] :
( in(ordered_pair(U_41,U_39),U_35)
| ~ in(ordered_pair(U_41,U_39),U_37)
| ~ in(U_41,U_36) )
& ! [U_40,U_38] :
( ( in(ordered_pair(U_40,U_38),U_37)
& in(U_40,U_36) )
| ~ in(ordered_pair(U_40,U_38),U_35) ) )
| U_35 != relation_dom_restriction(U_37,U_36) ) )
| ~ relation(U_35) )
| ~ relation(U_37) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_43,sK8(U_37,U_36,U_35))],[f_9_6]) ).
cnf(f_9_8,plain,
( in(U_40,U_36)
| ~ in(ordered_pair(U_40,U_38),U_35)
| U_35 != relation_dom_restriction(U_37,U_36)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_9,plain,
( in(ordered_pair(U_40,U_38),U_37)
| ~ in(ordered_pair(U_40,U_38),U_35)
| U_35 != relation_dom_restriction(U_37,U_36)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_10,plain,
( in(ordered_pair(U_41,U_39),U_35)
| ~ in(ordered_pair(U_41,U_39),U_37)
| ~ in(U_41,U_36)
| U_35 != relation_dom_restriction(U_37,U_36)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_11,plain,
( in(sK7(U_37,U_36,U_35),U_36)
| in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_35)
| U_35 = relation_dom_restriction(U_37,U_36)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_12,plain,
( in(ordered_pair(sK7(U_37,U_36,U_35),sK8(U_37,U_36,U_35)),U_37)
| in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_35)
| U_35 = relation_dom_restriction(U_37,U_36)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_13,plain,
( ~ in(ordered_pair(sK7(U_37,U_36,U_35),sK8(U_37,U_36,U_35)),U_35)
| in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_35)
| U_35 = relation_dom_restriction(U_37,U_36)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_14,plain,
( in(sK7(U_37,U_36,U_35),U_36)
| ~ in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_37)
| ~ in(sK5(U_37,U_36,U_35),U_36)
| U_35 = relation_dom_restriction(U_37,U_36)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_15,plain,
( in(ordered_pair(sK7(U_37,U_36,U_35),sK8(U_37,U_36,U_35)),U_37)
| ~ in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_37)
| ~ in(sK5(U_37,U_36,U_35),U_36)
| U_35 = relation_dom_restriction(U_37,U_36)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_16,plain,
( ~ in(ordered_pair(sK7(U_37,U_36,U_35),sK8(U_37,U_36,U_35)),U_35)
| ~ in(ordered_pair(sK5(U_37,U_36,U_35),sK6(U_37,U_36,U_35)),U_37)
| ~ in(sK5(U_37,U_36,U_35),U_36)
| U_35 = relation_dom_restriction(U_37,U_36)
| ~ relation(U_35)
| ~ relation(U_37) ),
inference(clausify,[status(thm)],[f_9_7]) ).
fof(f_10_1,plain,
! [A,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]) ).
cnf(f_10_8,plain,
( 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(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_9,plain,
( in(ordered_pair(U_55,U_53),U_51)
| ~ 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(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_10,plain,
( in(ordered_pair(U_56,U_54),U_50)
| ~ in(ordered_pair(U_56,U_54),U_51)
| ~ in(U_54,U_52)
| U_50 != relation_rng_restriction(U_52,U_51)
| ~ relation(U_50)
| ~ relation(U_51) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_11,plain,
( 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_50)
| U_50 = relation_rng_restriction(U_52,U_51)
| ~ relation(U_50)
| ~ relation(U_51) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_12,plain,
( in(ordered_pair(sK11(U_52,U_51,U_50),sK12(U_52,U_51,U_50)),U_51)
| in(ordered_pair(sK9(U_52,U_51,U_50),sK10(U_52,U_51,U_50)),U_50)
| U_50 = relation_rng_restriction(U_52,U_51)
| ~ relation(U_50)
| ~ relation(U_51) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_13,plain,
( ~ in(ordered_pair(sK11(U_52,U_51,U_50),sK12(U_52,U_51,U_50)),U_50)
| in(ordered_pair(sK9(U_52,U_51,U_50),sK10(U_52,U_51,U_50)),U_50)
| U_50 = relation_rng_restriction(U_52,U_51)
| ~ relation(U_50)
| ~ relation(U_51) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_14,plain,
( 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)
| U_50 = relation_rng_restriction(U_52,U_51)
| ~ relation(U_50)
| ~ relation(U_51) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_15,plain,
( in(ordered_pair(sK11(U_52,U_51,U_50),sK12(U_52,U_51,U_50)),U_51)
| ~ 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)
| U_50 = relation_rng_restriction(U_52,U_51)
| ~ relation(U_50)
| ~ relation(U_51) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_16,plain,
( ~ in(ordered_pair(sK11(U_52,U_51,U_50),sK12(U_52,U_51,U_50)),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)
| U_50 = relation_rng_restriction(U_52,U_51)
| ~ relation(U_50)
| ~ relation(U_51) ),
inference(clausify,[status(thm)],[f_10_7]) ).
fof(f_11_1,plain,
! [A] :
( ! [B,C] :
( ( C = relation_image(A,B)
| ? [D] :
( ( ~ in(D,C)
& ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) ) )
| ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) ) )
& ( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d13_relat_1]) ).
fof(f_11_2,plain,
! [U_69] :
( ! [U_68,U_67] :
( ( U_67 = relation_image(U_69,U_68)
| ? [U_66] :
( ( ~ in(U_66,U_67)
& ? [U_65] :
( in(U_65,U_68)
& in(ordered_pair(U_65,U_66),U_69) ) )
| ( ! [U_64] :
( ~ in(U_64,U_68)
| ~ in(ordered_pair(U_64,U_66),U_69) )
& in(U_66,U_67) ) ) )
& ( ! [U_63] :
( ( in(U_63,U_67)
| ! [U_62] :
( ~ in(U_62,U_68)
| ~ in(ordered_pair(U_62,U_63),U_69) ) )
& ( ? [U_61] :
( in(U_61,U_68)
& in(ordered_pair(U_61,U_63),U_69) )
| ~ in(U_63,U_67) ) )
| U_67 != relation_image(U_69,U_68) ) )
| ~ relation(U_69) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_69] :
( ( ! [U_77,U_75] :
( U_75 = relation_image(U_69,U_77)
| ? [U_73] :
( ~ in(U_73,U_75)
& ? [U_65] :
( in(U_65,U_77)
& in(ordered_pair(U_65,U_73),U_69) ) )
| ? [U_72] :
( ! [U_64] :
( ~ in(U_64,U_77)
| ~ in(ordered_pair(U_64,U_72),U_69) )
& in(U_72,U_75) ) )
& ! [U_76,U_74] :
( ( ! [U_71] :
( in(U_71,U_74)
| ! [U_62] :
( ~ in(U_62,U_76)
| ~ in(ordered_pair(U_62,U_71),U_69) ) )
& ! [U_70] :
( ? [U_61] :
( in(U_61,U_76)
& in(ordered_pair(U_61,U_70),U_69) )
| ~ in(U_70,U_74) ) )
| U_74 != relation_image(U_69,U_76) ) )
| ~ relation(U_69) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
fof(f_11_4,plain,
! [U_69] :
( ( ! [U_77,U_75] :
( U_75 = relation_image(U_69,U_77)
| ? [U_73] :
( ~ in(U_73,U_75)
& ? [U_65] :
( in(U_65,U_77)
& in(ordered_pair(U_65,U_73),U_69) ) )
| ? [U_72] :
( ! [U_64] :
( ~ in(U_64,U_77)
| ~ in(ordered_pair(U_64,U_72),U_69) )
& in(U_72,U_75) ) )
& ! [U_76,U_74] :
( ( ! [U_71] :
( in(U_71,U_74)
| ! [U_62] :
( ~ in(U_62,U_76)
| ~ in(ordered_pair(U_62,U_71),U_69) ) )
& ! [U_70] :
( ( in(sK13(U_69,U_76,U_74,U_70),U_76)
& in(ordered_pair(sK13(U_69,U_76,U_74,U_70),U_70),U_69) )
| ~ in(U_70,U_74) ) )
| U_74 != relation_image(U_69,U_76) ) )
| ~ relation(U_69) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_61,sK13(U_69,U_76,U_74,U_70))],[f_11_3]) ).
fof(f_11_5,plain,
! [U_69] :
( ( ! [U_77,U_75] :
( U_75 = relation_image(U_69,U_77)
| ? [U_73] :
( ~ in(U_73,U_75)
& ? [U_65] :
( in(U_65,U_77)
& in(ordered_pair(U_65,U_73),U_69) ) )
| ( ! [U_64] :
( ~ in(U_64,U_77)
| ~ in(ordered_pair(U_64,sK14(U_69,U_77,U_75)),U_69) )
& in(sK14(U_69,U_77,U_75),U_75) ) )
& ! [U_76,U_74] :
( ( ! [U_71] :
( in(U_71,U_74)
| ! [U_62] :
( ~ in(U_62,U_76)
| ~ in(ordered_pair(U_62,U_71),U_69) ) )
& ! [U_70] :
( ( in(sK13(U_69,U_76,U_74,U_70),U_76)
& in(ordered_pair(sK13(U_69,U_76,U_74,U_70),U_70),U_69) )
| ~ in(U_70,U_74) ) )
| U_74 != relation_image(U_69,U_76) ) )
| ~ relation(U_69) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_72,sK14(U_69,U_77,U_75))],[f_11_4]) ).
fof(f_11_6,plain,
! [U_69] :
( ( ! [U_77,U_75] :
( U_75 = relation_image(U_69,U_77)
| ( ~ in(sK15(U_69,U_77,U_75),U_75)
& ? [U_65] :
( in(U_65,U_77)
& in(ordered_pair(U_65,sK15(U_69,U_77,U_75)),U_69) ) )
| ( ! [U_64] :
( ~ in(U_64,U_77)
| ~ in(ordered_pair(U_64,sK14(U_69,U_77,U_75)),U_69) )
& in(sK14(U_69,U_77,U_75),U_75) ) )
& ! [U_76,U_74] :
( ( ! [U_71] :
( in(U_71,U_74)
| ! [U_62] :
( ~ in(U_62,U_76)
| ~ in(ordered_pair(U_62,U_71),U_69) ) )
& ! [U_70] :
( ( in(sK13(U_69,U_76,U_74,U_70),U_76)
& in(ordered_pair(sK13(U_69,U_76,U_74,U_70),U_70),U_69) )
| ~ in(U_70,U_74) ) )
| U_74 != relation_image(U_69,U_76) ) )
| ~ relation(U_69) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_73,sK15(U_69,U_77,U_75))],[f_11_5]) ).
fof(f_11_7,plain,
! [U_69] :
( ( ! [U_77,U_75] :
( U_75 = relation_image(U_69,U_77)
| ( ~ in(sK15(U_69,U_77,U_75),U_75)
& in(sK16(U_69,U_77,U_75),U_77)
& in(ordered_pair(sK16(U_69,U_77,U_75),sK15(U_69,U_77,U_75)),U_69) )
| ( ! [U_64] :
( ~ in(U_64,U_77)
| ~ in(ordered_pair(U_64,sK14(U_69,U_77,U_75)),U_69) )
& in(sK14(U_69,U_77,U_75),U_75) ) )
& ! [U_76,U_74] :
( ( ! [U_71] :
( in(U_71,U_74)
| ! [U_62] :
( ~ in(U_62,U_76)
| ~ in(ordered_pair(U_62,U_71),U_69) ) )
& ! [U_70] :
( ( in(sK13(U_69,U_76,U_74,U_70),U_76)
& in(ordered_pair(sK13(U_69,U_76,U_74,U_70),U_70),U_69) )
| ~ in(U_70,U_74) ) )
| U_74 != relation_image(U_69,U_76) ) )
| ~ relation(U_69) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_65,sK16(U_69,U_77,U_75))],[f_11_6]) ).
cnf(f_11_8,plain,
( in(ordered_pair(sK13(U_69,U_76,U_74,U_70),U_70),U_69)
| ~ in(U_70,U_74)
| U_74 != relation_image(U_69,U_76)
| ~ relation(U_69) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_9,plain,
( in(sK13(U_69,U_76,U_74,U_70),U_76)
| ~ in(U_70,U_74)
| U_74 != relation_image(U_69,U_76)
| ~ relation(U_69) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_10,plain,
( in(U_71,U_74)
| ~ in(U_62,U_76)
| ~ in(ordered_pair(U_62,U_71),U_69)
| U_74 != relation_image(U_69,U_76)
| ~ relation(U_69) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_11,plain,
( in(ordered_pair(sK16(U_69,U_77,U_75),sK15(U_69,U_77,U_75)),U_69)
| in(sK14(U_69,U_77,U_75),U_75)
| U_75 = relation_image(U_69,U_77)
| ~ relation(U_69) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_12,plain,
( in(sK16(U_69,U_77,U_75),U_77)
| in(sK14(U_69,U_77,U_75),U_75)
| U_75 = relation_image(U_69,U_77)
| ~ relation(U_69) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_13,plain,
( ~ in(sK15(U_69,U_77,U_75),U_75)
| in(sK14(U_69,U_77,U_75),U_75)
| U_75 = relation_image(U_69,U_77)
| ~ relation(U_69) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_14,plain,
( in(ordered_pair(sK16(U_69,U_77,U_75),sK15(U_69,U_77,U_75)),U_69)
| ~ in(U_64,U_77)
| ~ in(ordered_pair(U_64,sK14(U_69,U_77,U_75)),U_69)
| U_75 = relation_image(U_69,U_77)
| ~ relation(U_69) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_15,plain,
( in(sK16(U_69,U_77,U_75),U_77)
| ~ in(U_64,U_77)
| ~ in(ordered_pair(U_64,sK14(U_69,U_77,U_75)),U_69)
| U_75 = relation_image(U_69,U_77)
| ~ relation(U_69) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_16,plain,
( ~ in(sK15(U_69,U_77,U_75),U_75)
| ~ in(U_64,U_77)
| ~ in(ordered_pair(U_64,sK14(U_69,U_77,U_75)),U_69)
| U_75 = relation_image(U_69,U_77)
| ~ relation(U_69) ),
inference(clausify,[status(thm)],[f_11_7]) ).
fof(f_12_1,plain,
! [A] :
( ! [B,C] :
( ( C = relation_inverse_image(A,B)
| ? [D] :
( ( ~ in(D,C)
& ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) ) )
| ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) ) )
& ( ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d14_relat_1]) ).
fof(f_12_2,plain,
! [U_86] :
( ! [U_85,U_84] :
( ( U_84 = relation_inverse_image(U_86,U_85)
| ? [U_83] :
( ( ~ in(U_83,U_84)
& ? [U_82] :
( in(U_82,U_85)
& in(ordered_pair(U_83,U_82),U_86) ) )
| ( ! [U_81] :
( ~ in(U_81,U_85)
| ~ in(ordered_pair(U_83,U_81),U_86) )
& in(U_83,U_84) ) ) )
& ( ! [U_80] :
( ( in(U_80,U_84)
| ! [U_79] :
( ~ in(U_79,U_85)
| ~ in(ordered_pair(U_80,U_79),U_86) ) )
& ( ? [U_78] :
( in(U_78,U_85)
& in(ordered_pair(U_80,U_78),U_86) )
| ~ in(U_80,U_84) ) )
| U_84 != relation_inverse_image(U_86,U_85) ) )
| ~ relation(U_86) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_86] :
( ( ! [U_94,U_92] :
( U_92 = relation_inverse_image(U_86,U_94)
| ? [U_90] :
( ~ in(U_90,U_92)
& ? [U_82] :
( in(U_82,U_94)
& in(ordered_pair(U_90,U_82),U_86) ) )
| ? [U_89] :
( ! [U_81] :
( ~ in(U_81,U_94)
| ~ in(ordered_pair(U_89,U_81),U_86) )
& in(U_89,U_92) ) )
& ! [U_93,U_91] :
( ( ! [U_88] :
( in(U_88,U_91)
| ! [U_79] :
( ~ in(U_79,U_93)
| ~ in(ordered_pair(U_88,U_79),U_86) ) )
& ! [U_87] :
( ? [U_78] :
( in(U_78,U_93)
& in(ordered_pair(U_87,U_78),U_86) )
| ~ in(U_87,U_91) ) )
| U_91 != relation_inverse_image(U_86,U_93) ) )
| ~ relation(U_86) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
! [U_86] :
( ( ! [U_94,U_92] :
( U_92 = relation_inverse_image(U_86,U_94)
| ? [U_90] :
( ~ in(U_90,U_92)
& ? [U_82] :
( in(U_82,U_94)
& in(ordered_pair(U_90,U_82),U_86) ) )
| ? [U_89] :
( ! [U_81] :
( ~ in(U_81,U_94)
| ~ in(ordered_pair(U_89,U_81),U_86) )
& in(U_89,U_92) ) )
& ! [U_93,U_91] :
( ( ! [U_88] :
( in(U_88,U_91)
| ! [U_79] :
( ~ in(U_79,U_93)
| ~ in(ordered_pair(U_88,U_79),U_86) ) )
& ! [U_87] :
( ( in(sK17(U_86,U_93,U_91,U_87),U_93)
& in(ordered_pair(U_87,sK17(U_86,U_93,U_91,U_87)),U_86) )
| ~ in(U_87,U_91) ) )
| U_91 != relation_inverse_image(U_86,U_93) ) )
| ~ relation(U_86) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_78,sK17(U_86,U_93,U_91,U_87))],[f_12_3]) ).
fof(f_12_5,plain,
! [U_86] :
( ( ! [U_94,U_92] :
( U_92 = relation_inverse_image(U_86,U_94)
| ? [U_90] :
( ~ in(U_90,U_92)
& ? [U_82] :
( in(U_82,U_94)
& in(ordered_pair(U_90,U_82),U_86) ) )
| ( ! [U_81] :
( ~ in(U_81,U_94)
| ~ in(ordered_pair(sK18(U_86,U_94,U_92),U_81),U_86) )
& in(sK18(U_86,U_94,U_92),U_92) ) )
& ! [U_93,U_91] :
( ( ! [U_88] :
( in(U_88,U_91)
| ! [U_79] :
( ~ in(U_79,U_93)
| ~ in(ordered_pair(U_88,U_79),U_86) ) )
& ! [U_87] :
( ( in(sK17(U_86,U_93,U_91,U_87),U_93)
& in(ordered_pair(U_87,sK17(U_86,U_93,U_91,U_87)),U_86) )
| ~ in(U_87,U_91) ) )
| U_91 != relation_inverse_image(U_86,U_93) ) )
| ~ relation(U_86) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_89,sK18(U_86,U_94,U_92))],[f_12_4]) ).
fof(f_12_6,plain,
! [U_86] :
( ( ! [U_94,U_92] :
( U_92 = relation_inverse_image(U_86,U_94)
| ( ~ in(sK19(U_86,U_94,U_92),U_92)
& ? [U_82] :
( in(U_82,U_94)
& in(ordered_pair(sK19(U_86,U_94,U_92),U_82),U_86) ) )
| ( ! [U_81] :
( ~ in(U_81,U_94)
| ~ in(ordered_pair(sK18(U_86,U_94,U_92),U_81),U_86) )
& in(sK18(U_86,U_94,U_92),U_92) ) )
& ! [U_93,U_91] :
( ( ! [U_88] :
( in(U_88,U_91)
| ! [U_79] :
( ~ in(U_79,U_93)
| ~ in(ordered_pair(U_88,U_79),U_86) ) )
& ! [U_87] :
( ( in(sK17(U_86,U_93,U_91,U_87),U_93)
& in(ordered_pair(U_87,sK17(U_86,U_93,U_91,U_87)),U_86) )
| ~ in(U_87,U_91) ) )
| U_91 != relation_inverse_image(U_86,U_93) ) )
| ~ relation(U_86) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_90,sK19(U_86,U_94,U_92))],[f_12_5]) ).
fof(f_12_7,plain,
! [U_86] :
( ( ! [U_94,U_92] :
( U_92 = relation_inverse_image(U_86,U_94)
| ( ~ in(sK19(U_86,U_94,U_92),U_92)
& in(sK20(U_86,U_94,U_92),U_94)
& in(ordered_pair(sK19(U_86,U_94,U_92),sK20(U_86,U_94,U_92)),U_86) )
| ( ! [U_81] :
( ~ in(U_81,U_94)
| ~ in(ordered_pair(sK18(U_86,U_94,U_92),U_81),U_86) )
& in(sK18(U_86,U_94,U_92),U_92) ) )
& ! [U_93,U_91] :
( ( ! [U_88] :
( in(U_88,U_91)
| ! [U_79] :
( ~ in(U_79,U_93)
| ~ in(ordered_pair(U_88,U_79),U_86) ) )
& ! [U_87] :
( ( in(sK17(U_86,U_93,U_91,U_87),U_93)
& in(ordered_pair(U_87,sK17(U_86,U_93,U_91,U_87)),U_86) )
| ~ in(U_87,U_91) ) )
| U_91 != relation_inverse_image(U_86,U_93) ) )
| ~ relation(U_86) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_82,sK20(U_86,U_94,U_92))],[f_12_6]) ).
cnf(f_12_8,plain,
( in(ordered_pair(U_87,sK17(U_86,U_93,U_91,U_87)),U_86)
| ~ in(U_87,U_91)
| U_91 != relation_inverse_image(U_86,U_93)
| ~ relation(U_86) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_9,plain,
( in(sK17(U_86,U_93,U_91,U_87),U_93)
| ~ in(U_87,U_91)
| U_91 != relation_inverse_image(U_86,U_93)
| ~ relation(U_86) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_10,plain,
( in(U_88,U_91)
| ~ in(U_79,U_93)
| ~ in(ordered_pair(U_88,U_79),U_86)
| U_91 != relation_inverse_image(U_86,U_93)
| ~ relation(U_86) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_11,plain,
( in(ordered_pair(sK19(U_86,U_94,U_92),sK20(U_86,U_94,U_92)),U_86)
| in(sK18(U_86,U_94,U_92),U_92)
| U_92 = relation_inverse_image(U_86,U_94)
| ~ relation(U_86) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_12,plain,
( in(sK20(U_86,U_94,U_92),U_94)
| in(sK18(U_86,U_94,U_92),U_92)
| U_92 = relation_inverse_image(U_86,U_94)
| ~ relation(U_86) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_13,plain,
( ~ in(sK19(U_86,U_94,U_92),U_92)
| in(sK18(U_86,U_94,U_92),U_92)
| U_92 = relation_inverse_image(U_86,U_94)
| ~ relation(U_86) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_14,plain,
( in(ordered_pair(sK19(U_86,U_94,U_92),sK20(U_86,U_94,U_92)),U_86)
| ~ in(U_81,U_94)
| ~ in(ordered_pair(sK18(U_86,U_94,U_92),U_81),U_86)
| U_92 = relation_inverse_image(U_86,U_94)
| ~ relation(U_86) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_15,plain,
( in(sK20(U_86,U_94,U_92),U_94)
| ~ in(U_81,U_94)
| ~ in(ordered_pair(sK18(U_86,U_94,U_92),U_81),U_86)
| U_92 = relation_inverse_image(U_86,U_94)
| ~ relation(U_86) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_16,plain,
( ~ in(sK19(U_86,U_94,U_92),U_92)
| ~ in(U_81,U_94)
| ~ in(ordered_pair(sK18(U_86,U_94,U_92),U_81),U_86)
| U_92 = relation_inverse_image(U_86,U_94)
| ~ relation(U_86) ),
inference(clausify,[status(thm)],[f_12_7]) ).
fof(f_13_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_13_2,plain,
! [U_101] :
( ( relation(U_101)
| ? [U_100] :
( ! [U_99,U_98] : U_100 != ordered_pair(U_99,U_98)
& in(U_100,U_101) ) )
& ( ! [U_97] :
( ? [U_96,U_95] : U_97 = ordered_pair(U_96,U_95)
| ~ in(U_97,U_101) )
| ~ relation(U_101) ) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_103] :
( relation(U_103)
| ? [U_100] :
( ! [U_99,U_98] : U_100 != ordered_pair(U_99,U_98)
& in(U_100,U_103) ) )
& ! [U_102] :
( ! [U_97] :
( ? [U_96,U_95] : U_97 = ordered_pair(U_96,U_95)
| ~ in(U_97,U_102) )
| ~ relation(U_102) ) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
fof(f_13_4,plain,
( ! [U_103] :
( relation(U_103)
| ? [U_100] :
( ! [U_99,U_98] : U_100 != ordered_pair(U_99,U_98)
& in(U_100,U_103) ) )
& ! [U_102] :
( ! [U_97] :
( ? [U_95] : U_97 = ordered_pair(sK21(U_102,U_97),U_95)
| ~ in(U_97,U_102) )
| ~ relation(U_102) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_96,sK21(U_102,U_97))],[f_13_3]) ).
fof(f_13_5,plain,
( ! [U_103] :
( relation(U_103)
| ? [U_100] :
( ! [U_99,U_98] : U_100 != ordered_pair(U_99,U_98)
& in(U_100,U_103) ) )
& ! [U_102] :
( ! [U_97] :
( U_97 = ordered_pair(sK21(U_102,U_97),sK22(U_102,U_97))
| ~ in(U_97,U_102) )
| ~ relation(U_102) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_95,sK22(U_102,U_97))],[f_13_4]) ).
fof(f_13_6,plain,
( ! [U_103] :
( relation(U_103)
| ( ! [U_99,U_98] : sK23(U_103) != ordered_pair(U_99,U_98)
& in(sK23(U_103),U_103) ) )
& ! [U_102] :
( ! [U_97] :
( U_97 = ordered_pair(sK21(U_102,U_97),sK22(U_102,U_97))
| ~ in(U_97,U_102) )
| ~ relation(U_102) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_100,sK23(U_103))],[f_13_5]) ).
cnf(f_13_7,plain,
( U_97 = ordered_pair(sK21(U_102,U_97),sK22(U_102,U_97))
| ~ in(U_97,U_102)
| ~ relation(U_102) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_8,plain,
( in(sK23(U_103),U_103)
| relation(U_103) ),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_9,plain,
( sK23(U_103) != ordered_pair(U_99,U_98)
| relation(U_103) ),
inference(clausify,[status(thm)],[f_13_6]) ).
fof(f_14_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_14_2,plain,
! [U_111,U_110] :
( ( ( ( U_110 = set_meet(U_111)
| U_110 != empty_set )
& ( U_110 = empty_set
| U_110 != set_meet(U_111) ) )
| U_111 != empty_set )
& ( ( ( U_110 = set_meet(U_111)
| ? [U_109] :
( ( ~ in(U_109,U_110)
& ! [U_108] :
( in(U_109,U_108)
| ~ in(U_108,U_111) ) )
| ( ? [U_107] :
( ~ in(U_109,U_107)
& in(U_107,U_111) )
& in(U_109,U_110) ) ) )
& ( ! [U_106] :
( ( in(U_106,U_110)
| ? [U_105] :
( ~ in(U_106,U_105)
& in(U_105,U_111) ) )
& ( ! [U_104] :
( in(U_106,U_104)
| ~ in(U_104,U_111) )
| ~ in(U_106,U_110) ) )
| U_110 != set_meet(U_111) ) )
| U_111 = empty_set ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_123] :
( ( ! [U_121] :
( U_121 = set_meet(U_123)
| U_121 != empty_set )
& ! [U_120] :
( U_120 = empty_set
| U_120 != set_meet(U_123) ) )
| U_123 != empty_set )
& ! [U_122] :
( ( ! [U_119] :
( U_119 = set_meet(U_122)
| ? [U_115] :
( ~ in(U_115,U_119)
& ! [U_108] :
( in(U_115,U_108)
| ~ in(U_108,U_122) ) )
| ? [U_114] :
( ? [U_107] :
( ~ in(U_114,U_107)
& in(U_107,U_122) )
& in(U_114,U_119) ) )
& ! [U_118] :
( ( ! [U_113] :
( in(U_113,U_118)
| ? [U_105] :
( ~ in(U_113,U_105)
& in(U_105,U_122) ) )
& ! [U_112] :
( ! [U_104] :
( in(U_112,U_104)
| ~ in(U_104,U_122) )
| ~ in(U_112,U_118) ) )
| U_118 != set_meet(U_122) ) )
| U_122 = empty_set ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
fof(f_14_4,plain,
( ! [U_123] :
( ( ! [U_121] :
( U_121 = set_meet(U_123)
| U_121 != empty_set )
& ! [U_120] :
( U_120 = empty_set
| U_120 != set_meet(U_123) ) )
| U_123 != empty_set )
& ! [U_122] :
( ( ! [U_119] :
( U_119 = set_meet(U_122)
| ? [U_115] :
( ~ in(U_115,U_119)
& ! [U_108] :
( in(U_115,U_108)
| ~ in(U_108,U_122) ) )
| ? [U_114] :
( ? [U_107] :
( ~ in(U_114,U_107)
& in(U_107,U_122) )
& in(U_114,U_119) ) )
& ! [U_118] :
( ( ! [U_113] :
( in(U_113,U_118)
| ( ~ in(U_113,sK24(U_122,U_118,U_113))
& in(sK24(U_122,U_118,U_113),U_122) ) )
& ! [U_112] :
( ! [U_104] :
( in(U_112,U_104)
| ~ in(U_104,U_122) )
| ~ in(U_112,U_118) ) )
| U_118 != set_meet(U_122) ) )
| U_122 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_105,sK24(U_122,U_118,U_113))],[f_14_3]) ).
fof(f_14_5,plain,
( ! [U_123] :
( ( ! [U_121] :
( U_121 = set_meet(U_123)
| U_121 != empty_set )
& ! [U_120] :
( U_120 = empty_set
| U_120 != set_meet(U_123) ) )
| U_123 != empty_set )
& ! [U_122] :
( ( ! [U_119] :
( U_119 = set_meet(U_122)
| ? [U_115] :
( ~ in(U_115,U_119)
& ! [U_108] :
( in(U_115,U_108)
| ~ in(U_108,U_122) ) )
| ( ? [U_107] :
( ~ in(sK25(U_122,U_119),U_107)
& in(U_107,U_122) )
& in(sK25(U_122,U_119),U_119) ) )
& ! [U_118] :
( ( ! [U_113] :
( in(U_113,U_118)
| ( ~ in(U_113,sK24(U_122,U_118,U_113))
& in(sK24(U_122,U_118,U_113),U_122) ) )
& ! [U_112] :
( ! [U_104] :
( in(U_112,U_104)
| ~ in(U_104,U_122) )
| ~ in(U_112,U_118) ) )
| U_118 != set_meet(U_122) ) )
| U_122 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_114,sK25(U_122,U_119))],[f_14_4]) ).
fof(f_14_6,plain,
( ! [U_123] :
( ( ! [U_121] :
( U_121 = set_meet(U_123)
| U_121 != empty_set )
& ! [U_120] :
( U_120 = empty_set
| U_120 != set_meet(U_123) ) )
| U_123 != empty_set )
& ! [U_122] :
( ( ! [U_119] :
( U_119 = set_meet(U_122)
| ? [U_115] :
( ~ in(U_115,U_119)
& ! [U_108] :
( in(U_115,U_108)
| ~ in(U_108,U_122) ) )
| ( ~ in(sK25(U_122,U_119),sK26(U_122,U_119))
& in(sK26(U_122,U_119),U_122)
& in(sK25(U_122,U_119),U_119) ) )
& ! [U_118] :
( ( ! [U_113] :
( in(U_113,U_118)
| ( ~ in(U_113,sK24(U_122,U_118,U_113))
& in(sK24(U_122,U_118,U_113),U_122) ) )
& ! [U_112] :
( ! [U_104] :
( in(U_112,U_104)
| ~ in(U_104,U_122) )
| ~ in(U_112,U_118) ) )
| U_118 != set_meet(U_122) ) )
| U_122 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_107,sK26(U_122,U_119))],[f_14_5]) ).
fof(f_14_7,plain,
( ! [U_123] :
( ( ! [U_121] :
( U_121 = set_meet(U_123)
| U_121 != empty_set )
& ! [U_120] :
( U_120 = empty_set
| U_120 != set_meet(U_123) ) )
| U_123 != empty_set )
& ! [U_122] :
( ( ! [U_119] :
( U_119 = set_meet(U_122)
| ( ~ in(sK27(U_122,U_119),U_119)
& ! [U_108] :
( in(sK27(U_122,U_119),U_108)
| ~ in(U_108,U_122) ) )
| ( ~ in(sK25(U_122,U_119),sK26(U_122,U_119))
& in(sK26(U_122,U_119),U_122)
& in(sK25(U_122,U_119),U_119) ) )
& ! [U_118] :
( ( ! [U_113] :
( in(U_113,U_118)
| ( ~ in(U_113,sK24(U_122,U_118,U_113))
& in(sK24(U_122,U_118,U_113),U_122) ) )
& ! [U_112] :
( ! [U_104] :
( in(U_112,U_104)
| ~ in(U_104,U_122) )
| ~ in(U_112,U_118) ) )
| U_118 != set_meet(U_122) ) )
| U_122 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_115,sK27(U_122,U_119))],[f_14_6]) ).
cnf(f_14_8,plain,
( in(U_112,U_104)
| ~ in(U_104,U_122)
| ~ in(U_112,U_118)
| U_118 != set_meet(U_122)
| U_122 = empty_set ),
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(f_14_9,plain,
( in(sK24(U_122,U_118,U_113),U_122)
| in(U_113,U_118)
| U_118 != set_meet(U_122)
| U_122 = empty_set ),
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(f_14_10,plain,
( ~ in(U_113,sK24(U_122,U_118,U_113))
| in(U_113,U_118)
| U_118 != set_meet(U_122)
| U_122 = empty_set ),
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(f_14_11,plain,
( in(sK27(U_122,U_119),U_108)
| ~ in(U_108,U_122)
| in(sK25(U_122,U_119),U_119)
| U_119 = set_meet(U_122)
| U_122 = empty_set ),
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(f_14_12,plain,
( ~ in(sK27(U_122,U_119),U_119)
| in(sK25(U_122,U_119),U_119)
| U_119 = set_meet(U_122)
| U_122 = empty_set ),
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(f_14_13,plain,
( in(sK26(U_122,U_119),U_122)
| in(sK27(U_122,U_119),U_108)
| ~ in(U_108,U_122)
| U_119 = set_meet(U_122)
| U_122 = empty_set ),
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(f_14_14,plain,
( ~ in(sK25(U_122,U_119),sK26(U_122,U_119))
| in(sK27(U_122,U_119),U_108)
| ~ in(U_108,U_122)
| U_119 = set_meet(U_122)
| U_122 = empty_set ),
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(f_14_15,plain,
( in(sK26(U_122,U_119),U_122)
| ~ in(sK27(U_122,U_119),U_119)
| U_119 = set_meet(U_122)
| U_122 = empty_set ),
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(f_14_16,plain,
( ~ in(sK25(U_122,U_119),sK26(U_122,U_119))
| ~ in(sK27(U_122,U_119),U_119)
| U_119 = set_meet(U_122)
| U_122 = empty_set ),
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(f_14_17,plain,
( U_120 = empty_set
| U_120 != set_meet(U_123)
| U_123 != empty_set ),
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(f_14_18,plain,
( U_121 = set_meet(U_123)
| U_121 != empty_set
| U_123 != empty_set ),
inference(clausify,[status(thm)],[f_14_7]) ).
fof(f_15_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_15_2,plain,
! [U_127,U_126] :
( ( U_126 = singleton(U_127)
| ? [U_125] :
( ( ~ in(U_125,U_126)
& U_125 = U_127 )
| ( U_125 != U_127
& in(U_125,U_126) ) ) )
& ( ! [U_124] :
( ( in(U_124,U_126)
| U_124 != U_127 )
& ( U_124 = U_127
| ~ in(U_124,U_126) ) )
| U_126 != singleton(U_127) ) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ! [U_135,U_133] :
( U_133 = singleton(U_135)
| ? [U_131] :
( ~ in(U_131,U_133)
& U_131 = U_135 )
| ? [U_130] :
( U_130 != U_135
& in(U_130,U_133) ) )
& ! [U_134,U_132] :
( ( ! [U_129] :
( in(U_129,U_132)
| U_129 != U_134 )
& ! [U_128] :
( U_128 = U_134
| ~ in(U_128,U_132) ) )
| U_132 != singleton(U_134) ) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
fof(f_15_4,plain,
( ! [U_135,U_133] :
( U_133 = singleton(U_135)
| ? [U_131] :
( ~ in(U_131,U_133)
& U_131 = U_135 )
| ( sK28(U_135,U_133) != U_135
& in(sK28(U_135,U_133),U_133) ) )
& ! [U_134,U_132] :
( ( ! [U_129] :
( in(U_129,U_132)
| U_129 != U_134 )
& ! [U_128] :
( U_128 = U_134
| ~ in(U_128,U_132) ) )
| U_132 != singleton(U_134) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_130,sK28(U_135,U_133))],[f_15_3]) ).
fof(f_15_5,plain,
( ! [U_135,U_133] :
( U_133 = singleton(U_135)
| ( ~ in(sK29(U_135,U_133),U_133)
& sK29(U_135,U_133) = U_135 )
| ( sK28(U_135,U_133) != U_135
& in(sK28(U_135,U_133),U_133) ) )
& ! [U_134,U_132] :
( ( ! [U_129] :
( in(U_129,U_132)
| U_129 != U_134 )
& ! [U_128] :
( U_128 = U_134
| ~ in(U_128,U_132) ) )
| U_132 != singleton(U_134) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_131,sK29(U_135,U_133))],[f_15_4]) ).
cnf(f_15_6,plain,
( U_128 = U_134
| ~ in(U_128,U_132)
| U_132 != singleton(U_134) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_7,plain,
( in(U_129,U_132)
| U_129 != U_134
| U_132 != singleton(U_134) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_8,plain,
( sK29(U_135,U_133) = U_135
| in(sK28(U_135,U_133),U_133)
| U_133 = singleton(U_135) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_9,plain,
( ~ in(sK29(U_135,U_133),U_133)
| in(sK28(U_135,U_133),U_133)
| U_133 = singleton(U_135) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_10,plain,
( sK29(U_135,U_133) = U_135
| sK28(U_135,U_133) != U_135
| U_133 = singleton(U_135) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_11,plain,
( ~ in(sK29(U_135,U_133),U_133)
| sK28(U_135,U_133) != U_135
| U_133 = singleton(U_135) ),
inference(clausify,[status(thm)],[f_15_5]) ).
fof(f_16_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_16_2,plain,
! [U_138] :
( ( U_138 = empty_set
| ? [U_137] : in(U_137,U_138) )
& ( ! [U_136] : ~ in(U_136,U_138)
| U_138 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( ! [U_140] :
( U_140 = empty_set
| ? [U_137] : in(U_137,U_140) )
& ! [U_139] :
( ! [U_136] : ~ in(U_136,U_139)
| U_139 != empty_set ) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
fof(f_16_4,plain,
( ! [U_140] :
( U_140 = empty_set
| in(sK30(U_140),U_140) )
& ! [U_139] :
( ! [U_136] : ~ in(U_136,U_139)
| U_139 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_137,sK30(U_140))],[f_16_3]) ).
cnf(f_16_5,plain,
( ~ in(U_136,U_139)
| U_139 != empty_set ),
inference(clausify,[status(thm)],[f_16_4]) ).
cnf(f_16_6,plain,
( U_140 = empty_set
| in(sK30(U_140),U_140) ),
inference(clausify,[status(thm)],[f_16_4]) ).
fof(f_17_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_17_2,plain,
! [U_144,U_143] :
( ( U_143 = powerset(U_144)
| ? [U_142] :
( ( ~ in(U_142,U_143)
& subset(U_142,U_144) )
| ( ~ subset(U_142,U_144)
& in(U_142,U_143) ) ) )
& ( ! [U_141] :
( ( in(U_141,U_143)
| ~ subset(U_141,U_144) )
& ( subset(U_141,U_144)
| ~ in(U_141,U_143) ) )
| U_143 != powerset(U_144) ) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( ! [U_152,U_150] :
( U_150 = powerset(U_152)
| ? [U_148] :
( ~ in(U_148,U_150)
& subset(U_148,U_152) )
| ? [U_147] :
( ~ subset(U_147,U_152)
& in(U_147,U_150) ) )
& ! [U_151,U_149] :
( ( ! [U_146] :
( in(U_146,U_149)
| ~ subset(U_146,U_151) )
& ! [U_145] :
( subset(U_145,U_151)
| ~ in(U_145,U_149) ) )
| U_149 != powerset(U_151) ) ),
inference(miniscope,[status(thm)],[f_17_2]) ).
fof(f_17_4,plain,
( ! [U_152,U_150] :
( U_150 = powerset(U_152)
| ? [U_148] :
( ~ in(U_148,U_150)
& subset(U_148,U_152) )
| ( ~ subset(sK31(U_152,U_150),U_152)
& in(sK31(U_152,U_150),U_150) ) )
& ! [U_151,U_149] :
( ( ! [U_146] :
( in(U_146,U_149)
| ~ subset(U_146,U_151) )
& ! [U_145] :
( subset(U_145,U_151)
| ~ in(U_145,U_149) ) )
| U_149 != powerset(U_151) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_147,sK31(U_152,U_150))],[f_17_3]) ).
fof(f_17_5,plain,
( ! [U_152,U_150] :
( U_150 = powerset(U_152)
| ( ~ in(sK32(U_152,U_150),U_150)
& subset(sK32(U_152,U_150),U_152) )
| ( ~ subset(sK31(U_152,U_150),U_152)
& in(sK31(U_152,U_150),U_150) ) )
& ! [U_151,U_149] :
( ( ! [U_146] :
( in(U_146,U_149)
| ~ subset(U_146,U_151) )
& ! [U_145] :
( subset(U_145,U_151)
| ~ in(U_145,U_149) ) )
| U_149 != powerset(U_151) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_148,sK32(U_152,U_150))],[f_17_4]) ).
cnf(f_17_6,plain,
( subset(U_145,U_151)
| ~ in(U_145,U_149)
| U_149 != powerset(U_151) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_7,plain,
( in(U_146,U_149)
| ~ subset(U_146,U_151)
| U_149 != powerset(U_151) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_8,plain,
( subset(sK32(U_152,U_150),U_152)
| in(sK31(U_152,U_150),U_150)
| U_150 = powerset(U_152) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_9,plain,
( ~ in(sK32(U_152,U_150),U_150)
| in(sK31(U_152,U_150),U_150)
| U_150 = powerset(U_152) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_10,plain,
( subset(sK32(U_152,U_150),U_152)
| ~ subset(sK31(U_152,U_150),U_152)
| U_150 = powerset(U_152) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_11,plain,
( ~ in(sK32(U_152,U_150),U_150)
| ~ subset(sK31(U_152,U_150),U_152)
| U_150 = powerset(U_152) ),
inference(clausify,[status(thm)],[f_17_5]) ).
fof(f_18_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_18_2,plain,
! [U_158] :
( ! [U_157] :
( ( ( U_158 = U_157
| ? [U_156,U_155] :
( ( ~ in(ordered_pair(U_156,U_155),U_158)
& in(ordered_pair(U_156,U_155),U_157) )
| ( ~ in(ordered_pair(U_156,U_155),U_157)
& in(ordered_pair(U_156,U_155),U_158) ) ) )
& ( ! [U_154,U_153] :
( ( in(ordered_pair(U_154,U_153),U_158)
| ~ in(ordered_pair(U_154,U_153),U_157) )
& ( in(ordered_pair(U_154,U_153),U_157)
| ~ in(ordered_pair(U_154,U_153),U_158) ) )
| U_158 != U_157 ) )
| ~ relation(U_157) )
| ~ relation(U_158) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_158] :
( ! [U_157] :
( ( ( U_158 = U_157
| ? [U_166,U_164] :
( ~ in(ordered_pair(U_166,U_164),U_158)
& in(ordered_pair(U_166,U_164),U_157) )
| ? [U_165,U_163] :
( ~ in(ordered_pair(U_165,U_163),U_157)
& in(ordered_pair(U_165,U_163),U_158) ) )
& ( ( ! [U_162,U_160] :
( in(ordered_pair(U_162,U_160),U_158)
| ~ in(ordered_pair(U_162,U_160),U_157) )
& ! [U_161,U_159] :
( in(ordered_pair(U_161,U_159),U_157)
| ~ in(ordered_pair(U_161,U_159),U_158) ) )
| U_158 != U_157 ) )
| ~ relation(U_157) )
| ~ relation(U_158) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
fof(f_18_4,plain,
! [U_158] :
( ! [U_157] :
( ( ( U_158 = U_157
| ? [U_166,U_164] :
( ~ in(ordered_pair(U_166,U_164),U_158)
& in(ordered_pair(U_166,U_164),U_157) )
| ? [U_163] :
( ~ in(ordered_pair(sK33(U_158,U_157),U_163),U_157)
& in(ordered_pair(sK33(U_158,U_157),U_163),U_158) ) )
& ( ( ! [U_162,U_160] :
( in(ordered_pair(U_162,U_160),U_158)
| ~ in(ordered_pair(U_162,U_160),U_157) )
& ! [U_161,U_159] :
( in(ordered_pair(U_161,U_159),U_157)
| ~ in(ordered_pair(U_161,U_159),U_158) ) )
| U_158 != U_157 ) )
| ~ relation(U_157) )
| ~ relation(U_158) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_165,sK33(U_158,U_157))],[f_18_3]) ).
fof(f_18_5,plain,
! [U_158] :
( ! [U_157] :
( ( ( U_158 = U_157
| ? [U_166,U_164] :
( ~ in(ordered_pair(U_166,U_164),U_158)
& in(ordered_pair(U_166,U_164),U_157) )
| ( ~ in(ordered_pair(sK33(U_158,U_157),sK34(U_158,U_157)),U_157)
& in(ordered_pair(sK33(U_158,U_157),sK34(U_158,U_157)),U_158) ) )
& ( ( ! [U_162,U_160] :
( in(ordered_pair(U_162,U_160),U_158)
| ~ in(ordered_pair(U_162,U_160),U_157) )
& ! [U_161,U_159] :
( in(ordered_pair(U_161,U_159),U_157)
| ~ in(ordered_pair(U_161,U_159),U_158) ) )
| U_158 != U_157 ) )
| ~ relation(U_157) )
| ~ relation(U_158) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_163,sK34(U_158,U_157))],[f_18_4]) ).
fof(f_18_6,plain,
! [U_158] :
( ! [U_157] :
( ( ( U_158 = U_157
| ? [U_164] :
( ~ in(ordered_pair(sK35(U_158,U_157),U_164),U_158)
& in(ordered_pair(sK35(U_158,U_157),U_164),U_157) )
| ( ~ in(ordered_pair(sK33(U_158,U_157),sK34(U_158,U_157)),U_157)
& in(ordered_pair(sK33(U_158,U_157),sK34(U_158,U_157)),U_158) ) )
& ( ( ! [U_162,U_160] :
( in(ordered_pair(U_162,U_160),U_158)
| ~ in(ordered_pair(U_162,U_160),U_157) )
& ! [U_161,U_159] :
( in(ordered_pair(U_161,U_159),U_157)
| ~ in(ordered_pair(U_161,U_159),U_158) ) )
| U_158 != U_157 ) )
| ~ relation(U_157) )
| ~ relation(U_158) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_166,sK35(U_158,U_157))],[f_18_5]) ).
fof(f_18_7,plain,
! [U_158] :
( ! [U_157] :
( ( ( U_158 = U_157
| ( ~ in(ordered_pair(sK35(U_158,U_157),sK36(U_158,U_157)),U_158)
& in(ordered_pair(sK35(U_158,U_157),sK36(U_158,U_157)),U_157) )
| ( ~ in(ordered_pair(sK33(U_158,U_157),sK34(U_158,U_157)),U_157)
& in(ordered_pair(sK33(U_158,U_157),sK34(U_158,U_157)),U_158) ) )
& ( ( ! [U_162,U_160] :
( in(ordered_pair(U_162,U_160),U_158)
| ~ in(ordered_pair(U_162,U_160),U_157) )
& ! [U_161,U_159] :
( in(ordered_pair(U_161,U_159),U_157)
| ~ in(ordered_pair(U_161,U_159),U_158) ) )
| U_158 != U_157 ) )
| ~ relation(U_157) )
| ~ relation(U_158) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_164,sK36(U_158,U_157))],[f_18_6]) ).
cnf(f_18_8,plain,
( in(ordered_pair(U_161,U_159),U_157)
| ~ in(ordered_pair(U_161,U_159),U_158)
| U_158 != U_157
| ~ relation(U_157)
| ~ relation(U_158) ),
inference(clausify,[status(thm)],[f_18_7]) ).
cnf(f_18_9,plain,
( in(ordered_pair(U_162,U_160),U_158)
| ~ in(ordered_pair(U_162,U_160),U_157)
| U_158 != U_157
| ~ relation(U_157)
| ~ relation(U_158) ),
inference(clausify,[status(thm)],[f_18_7]) ).
cnf(f_18_10,plain,
( in(ordered_pair(sK35(U_158,U_157),sK36(U_158,U_157)),U_157)
| in(ordered_pair(sK33(U_158,U_157),sK34(U_158,U_157)),U_158)
| U_158 = U_157
| ~ relation(U_157)
| ~ relation(U_158) ),
inference(clausify,[status(thm)],[f_18_7]) ).
cnf(f_18_11,plain,
( ~ in(ordered_pair(sK35(U_158,U_157),sK36(U_158,U_157)),U_158)
| in(ordered_pair(sK33(U_158,U_157),sK34(U_158,U_157)),U_158)
| U_158 = U_157
| ~ relation(U_157)
| ~ relation(U_158) ),
inference(clausify,[status(thm)],[f_18_7]) ).
cnf(f_18_12,plain,
( in(ordered_pair(sK35(U_158,U_157),sK36(U_158,U_157)),U_157)
| ~ in(ordered_pair(sK33(U_158,U_157),sK34(U_158,U_157)),U_157)
| U_158 = U_157
| ~ relation(U_157)
| ~ relation(U_158) ),
inference(clausify,[status(thm)],[f_18_7]) ).
cnf(f_18_13,plain,
( ~ in(ordered_pair(sK35(U_158,U_157),sK36(U_158,U_157)),U_158)
| ~ in(ordered_pair(sK33(U_158,U_157),sK34(U_158,U_157)),U_157)
| U_158 = U_157
| ~ relation(U_157)
| ~ relation(U_158) ),
inference(clausify,[status(thm)],[f_18_7]) ).
fof(f_19_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_19_2,plain,
! [U_168,U_167] :
( ( ( ( element(U_167,U_168)
| ~ empty(U_167) )
& ( empty(U_167)
| ~ element(U_167,U_168) ) )
| ~ empty(U_168) )
& ( ( ( element(U_167,U_168)
| ~ in(U_167,U_168) )
& ( in(U_167,U_168)
| ~ element(U_167,U_168) ) )
| empty(U_168) ) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( ! [U_176] :
( ( ! [U_174] :
( element(U_174,U_176)
| ~ empty(U_174) )
& ! [U_173] :
( empty(U_173)
| ~ element(U_173,U_176) ) )
| ~ empty(U_176) )
& ! [U_175] :
( ( ! [U_172] :
( element(U_172,U_175)
| ~ in(U_172,U_175) )
& ! [U_171] :
( in(U_171,U_175)
| ~ element(U_171,U_175) ) )
| empty(U_175) ) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
cnf(f_19_4,plain,
( in(U_171,U_175)
| ~ element(U_171,U_175)
| empty(U_175) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_5,plain,
( element(U_172,U_175)
| ~ in(U_172,U_175)
| empty(U_175) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_6,plain,
( empty(U_173)
| ~ element(U_173,U_176)
| ~ empty(U_176) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_7,plain,
( element(U_174,U_176)
| ~ empty(U_174)
| ~ empty(U_176) ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_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_20_2,plain,
! [U_181,U_180,U_179] :
( ( U_179 = unordered_pair(U_181,U_180)
| ? [U_178] :
( ( ~ in(U_178,U_179)
& ( U_178 = U_180
| U_178 = U_181 ) )
| ( U_178 != U_180
& U_178 != U_181
& in(U_178,U_179) ) ) )
& ( ! [U_177] :
( ( in(U_177,U_179)
| ( U_177 != U_180
& U_177 != U_181 ) )
& ( U_177 = U_180
| U_177 = U_181
| ~ in(U_177,U_179) ) )
| U_179 != unordered_pair(U_181,U_180) ) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( ! [U_191,U_189,U_187] :
( U_187 = unordered_pair(U_191,U_189)
| ? [U_185] :
( ~ in(U_185,U_187)
& ( U_185 = U_189
| U_185 = U_191 ) )
| ? [U_184] :
( U_184 != U_189
& U_184 != U_191
& in(U_184,U_187) ) )
& ! [U_190,U_188,U_186] :
( ( ! [U_183] :
( in(U_183,U_186)
| ( U_183 != U_188
& U_183 != U_190 ) )
& ! [U_182] :
( U_182 = U_188
| U_182 = U_190
| ~ in(U_182,U_186) ) )
| U_186 != unordered_pair(U_190,U_188) ) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
fof(f_20_4,plain,
( ! [U_191,U_189,U_187] :
( U_187 = unordered_pair(U_191,U_189)
| ? [U_185] :
( ~ in(U_185,U_187)
& ( U_185 = U_189
| U_185 = U_191 ) )
| ( sK37(U_191,U_189,U_187) != U_189
& sK37(U_191,U_189,U_187) != U_191
& in(sK37(U_191,U_189,U_187),U_187) ) )
& ! [U_190,U_188,U_186] :
( ( ! [U_183] :
( in(U_183,U_186)
| ( U_183 != U_188
& U_183 != U_190 ) )
& ! [U_182] :
( U_182 = U_188
| U_182 = U_190
| ~ in(U_182,U_186) ) )
| U_186 != unordered_pair(U_190,U_188) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_184,sK37(U_191,U_189,U_187))],[f_20_3]) ).
fof(f_20_5,plain,
( ! [U_191,U_189,U_187] :
( U_187 = unordered_pair(U_191,U_189)
| ( ~ in(sK38(U_191,U_189,U_187),U_187)
& ( sK38(U_191,U_189,U_187) = U_189
| sK38(U_191,U_189,U_187) = U_191 ) )
| ( sK37(U_191,U_189,U_187) != U_189
& sK37(U_191,U_189,U_187) != U_191
& in(sK37(U_191,U_189,U_187),U_187) ) )
& ! [U_190,U_188,U_186] :
( ( ! [U_183] :
( in(U_183,U_186)
| ( U_183 != U_188
& U_183 != U_190 ) )
& ! [U_182] :
( U_182 = U_188
| U_182 = U_190
| ~ in(U_182,U_186) ) )
| U_186 != unordered_pair(U_190,U_188) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_185,sK38(U_191,U_189,U_187))],[f_20_4]) ).
cnf(f_20_6,plain,
( U_182 = U_188
| U_182 = U_190
| ~ in(U_182,U_186)
| U_186 != unordered_pair(U_190,U_188) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_7,plain,
( U_183 != U_190
| in(U_183,U_186)
| U_186 != unordered_pair(U_190,U_188) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_8,plain,
( U_183 != U_188
| in(U_183,U_186)
| U_186 != unordered_pair(U_190,U_188) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_9,plain,
( sK38(U_191,U_189,U_187) = U_189
| sK38(U_191,U_189,U_187) = U_191
| in(sK37(U_191,U_189,U_187),U_187)
| U_187 = unordered_pair(U_191,U_189) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_10,plain,
( ~ in(sK38(U_191,U_189,U_187),U_187)
| in(sK37(U_191,U_189,U_187),U_187)
| U_187 = unordered_pair(U_191,U_189) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_11,plain,
( sK37(U_191,U_189,U_187) != U_191
| sK38(U_191,U_189,U_187) = U_189
| sK38(U_191,U_189,U_187) = U_191
| U_187 = unordered_pair(U_191,U_189) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_12,plain,
( sK37(U_191,U_189,U_187) != U_189
| sK38(U_191,U_189,U_187) = U_189
| sK38(U_191,U_189,U_187) = U_191
| U_187 = unordered_pair(U_191,U_189) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_13,plain,
( sK37(U_191,U_189,U_187) != U_191
| ~ in(sK38(U_191,U_189,U_187),U_187)
| U_187 = unordered_pair(U_191,U_189) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_14,plain,
( sK37(U_191,U_189,U_187) != U_189
| ~ in(sK38(U_191,U_189,U_187),U_187)
| U_187 = unordered_pair(U_191,U_189) ),
inference(clausify,[status(thm)],[f_20_5]) ).
fof(f_21_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_21_2,plain,
! [U_196,U_195,U_194] :
( ( U_194 = set_union2(U_196,U_195)
| ? [U_193] :
( ( ~ in(U_193,U_194)
& ( in(U_193,U_195)
| in(U_193,U_196) ) )
| ( ~ in(U_193,U_195)
& ~ in(U_193,U_196)
& in(U_193,U_194) ) ) )
& ( ! [U_192] :
( ( in(U_192,U_194)
| ( ~ in(U_192,U_195)
& ~ in(U_192,U_196) ) )
& ( in(U_192,U_195)
| in(U_192,U_196)
| ~ in(U_192,U_194) ) )
| U_194 != set_union2(U_196,U_195) ) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( ! [U_206,U_204,U_202] :
( U_202 = set_union2(U_206,U_204)
| ? [U_200] :
( ~ in(U_200,U_202)
& ( in(U_200,U_204)
| in(U_200,U_206) ) )
| ? [U_199] :
( ~ in(U_199,U_204)
& ~ in(U_199,U_206)
& in(U_199,U_202) ) )
& ! [U_205,U_203,U_201] :
( ( ! [U_198] :
( in(U_198,U_201)
| ( ~ in(U_198,U_203)
& ~ in(U_198,U_205) ) )
& ! [U_197] :
( in(U_197,U_203)
| in(U_197,U_205)
| ~ in(U_197,U_201) ) )
| U_201 != set_union2(U_205,U_203) ) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
fof(f_21_4,plain,
( ! [U_206,U_204,U_202] :
( U_202 = set_union2(U_206,U_204)
| ? [U_200] :
( ~ in(U_200,U_202)
& ( in(U_200,U_204)
| in(U_200,U_206) ) )
| ( ~ in(sK39(U_206,U_204,U_202),U_204)
& ~ in(sK39(U_206,U_204,U_202),U_206)
& in(sK39(U_206,U_204,U_202),U_202) ) )
& ! [U_205,U_203,U_201] :
( ( ! [U_198] :
( in(U_198,U_201)
| ( ~ in(U_198,U_203)
& ~ in(U_198,U_205) ) )
& ! [U_197] :
( in(U_197,U_203)
| in(U_197,U_205)
| ~ in(U_197,U_201) ) )
| U_201 != set_union2(U_205,U_203) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_199,sK39(U_206,U_204,U_202))],[f_21_3]) ).
fof(f_21_5,plain,
( ! [U_206,U_204,U_202] :
( U_202 = set_union2(U_206,U_204)
| ( ~ in(sK40(U_206,U_204,U_202),U_202)
& ( in(sK40(U_206,U_204,U_202),U_204)
| in(sK40(U_206,U_204,U_202),U_206) ) )
| ( ~ in(sK39(U_206,U_204,U_202),U_204)
& ~ in(sK39(U_206,U_204,U_202),U_206)
& in(sK39(U_206,U_204,U_202),U_202) ) )
& ! [U_205,U_203,U_201] :
( ( ! [U_198] :
( in(U_198,U_201)
| ( ~ in(U_198,U_203)
& ~ in(U_198,U_205) ) )
& ! [U_197] :
( in(U_197,U_203)
| in(U_197,U_205)
| ~ in(U_197,U_201) ) )
| U_201 != set_union2(U_205,U_203) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_200,sK40(U_206,U_204,U_202))],[f_21_4]) ).
cnf(f_21_6,plain,
( in(U_197,U_203)
| in(U_197,U_205)
| ~ in(U_197,U_201)
| U_201 != set_union2(U_205,U_203) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_7,plain,
( ~ in(U_198,U_205)
| in(U_198,U_201)
| U_201 != set_union2(U_205,U_203) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_8,plain,
( ~ in(U_198,U_203)
| in(U_198,U_201)
| U_201 != set_union2(U_205,U_203) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_9,plain,
( in(sK40(U_206,U_204,U_202),U_204)
| in(sK40(U_206,U_204,U_202),U_206)
| in(sK39(U_206,U_204,U_202),U_202)
| U_202 = set_union2(U_206,U_204) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_10,plain,
( ~ in(sK40(U_206,U_204,U_202),U_202)
| in(sK39(U_206,U_204,U_202),U_202)
| U_202 = set_union2(U_206,U_204) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_11,plain,
( ~ in(sK39(U_206,U_204,U_202),U_206)
| in(sK40(U_206,U_204,U_202),U_204)
| in(sK40(U_206,U_204,U_202),U_206)
| U_202 = set_union2(U_206,U_204) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_12,plain,
( ~ in(sK39(U_206,U_204,U_202),U_204)
| in(sK40(U_206,U_204,U_202),U_204)
| in(sK40(U_206,U_204,U_202),U_206)
| U_202 = set_union2(U_206,U_204) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_13,plain,
( ~ in(sK39(U_206,U_204,U_202),U_206)
| ~ in(sK40(U_206,U_204,U_202),U_202)
| U_202 = set_union2(U_206,U_204) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_14,plain,
( ~ in(sK39(U_206,U_204,U_202),U_204)
| ~ in(sK40(U_206,U_204,U_202),U_202)
| U_202 = set_union2(U_206,U_204) ),
inference(clausify,[status(thm)],[f_21_5]) ).
fof(f_22_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_22_2,plain,
! [U_219,U_218,U_217] :
( ( U_217 = cartesian_product2(U_219,U_218)
| ? [U_216] :
( ( ~ in(U_216,U_217)
& ? [U_215,U_214] :
( U_216 = ordered_pair(U_215,U_214)
& in(U_214,U_218)
& in(U_215,U_219) ) )
| ( ! [U_213,U_212] :
( U_216 != ordered_pair(U_213,U_212)
| ~ in(U_212,U_218)
| ~ in(U_213,U_219) )
& in(U_216,U_217) ) ) )
& ( ! [U_211] :
( ( in(U_211,U_217)
| ! [U_210,U_209] :
( U_211 != ordered_pair(U_210,U_209)
| ~ in(U_209,U_218)
| ~ in(U_210,U_219) ) )
& ( ? [U_208,U_207] :
( U_211 = ordered_pair(U_208,U_207)
& in(U_207,U_218)
& in(U_208,U_219) )
| ~ in(U_211,U_217) ) )
| U_217 != cartesian_product2(U_219,U_218) ) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( ! [U_229,U_227,U_225] :
( U_225 = cartesian_product2(U_229,U_227)
| ? [U_223] :
( ~ in(U_223,U_225)
& ? [U_215] :
( ? [U_214] :
( U_223 = ordered_pair(U_215,U_214)
& in(U_214,U_227) )
& in(U_215,U_229) ) )
| ? [U_222] :
( ! [U_213] :
( ! [U_212] :
( U_222 != ordered_pair(U_213,U_212)
| ~ in(U_212,U_227) )
| ~ in(U_213,U_229) )
& in(U_222,U_225) ) )
& ! [U_228,U_226,U_224] :
( ( ! [U_221] :
( in(U_221,U_224)
| ! [U_210] :
( ! [U_209] :
( U_221 != ordered_pair(U_210,U_209)
| ~ in(U_209,U_226) )
| ~ in(U_210,U_228) ) )
& ! [U_220] :
( ? [U_208] :
( ? [U_207] :
( U_220 = ordered_pair(U_208,U_207)
& in(U_207,U_226) )
& in(U_208,U_228) )
| ~ in(U_220,U_224) ) )
| U_224 != cartesian_product2(U_228,U_226) ) ),
inference(miniscope,[status(thm)],[f_22_2]) ).
fof(f_22_4,plain,
( ! [U_229,U_227,U_225] :
( U_225 = cartesian_product2(U_229,U_227)
| ? [U_223] :
( ~ in(U_223,U_225)
& ? [U_215] :
( ? [U_214] :
( U_223 = ordered_pair(U_215,U_214)
& in(U_214,U_227) )
& in(U_215,U_229) ) )
| ? [U_222] :
( ! [U_213] :
( ! [U_212] :
( U_222 != ordered_pair(U_213,U_212)
| ~ in(U_212,U_227) )
| ~ in(U_213,U_229) )
& in(U_222,U_225) ) )
& ! [U_228,U_226,U_224] :
( ( ! [U_221] :
( in(U_221,U_224)
| ! [U_210] :
( ! [U_209] :
( U_221 != ordered_pair(U_210,U_209)
| ~ in(U_209,U_226) )
| ~ in(U_210,U_228) ) )
& ! [U_220] :
( ( ? [U_207] :
( U_220 = ordered_pair(sK41(U_228,U_226,U_224,U_220),U_207)
& in(U_207,U_226) )
& in(sK41(U_228,U_226,U_224,U_220),U_228) )
| ~ in(U_220,U_224) ) )
| U_224 != cartesian_product2(U_228,U_226) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_208,sK41(U_228,U_226,U_224,U_220))],[f_22_3]) ).
fof(f_22_5,plain,
( ! [U_229,U_227,U_225] :
( U_225 = cartesian_product2(U_229,U_227)
| ? [U_223] :
( ~ in(U_223,U_225)
& ? [U_215] :
( ? [U_214] :
( U_223 = ordered_pair(U_215,U_214)
& in(U_214,U_227) )
& in(U_215,U_229) ) )
| ? [U_222] :
( ! [U_213] :
( ! [U_212] :
( U_222 != ordered_pair(U_213,U_212)
| ~ in(U_212,U_227) )
| ~ in(U_213,U_229) )
& in(U_222,U_225) ) )
& ! [U_228,U_226,U_224] :
( ( ! [U_221] :
( in(U_221,U_224)
| ! [U_210] :
( ! [U_209] :
( U_221 != ordered_pair(U_210,U_209)
| ~ in(U_209,U_226) )
| ~ in(U_210,U_228) ) )
& ! [U_220] :
( ( U_220 = ordered_pair(sK41(U_228,U_226,U_224,U_220),sK42(U_228,U_226,U_224,U_220))
& in(sK42(U_228,U_226,U_224,U_220),U_226)
& in(sK41(U_228,U_226,U_224,U_220),U_228) )
| ~ in(U_220,U_224) ) )
| U_224 != cartesian_product2(U_228,U_226) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_207,sK42(U_228,U_226,U_224,U_220))],[f_22_4]) ).
fof(f_22_6,plain,
( ! [U_229,U_227,U_225] :
( U_225 = cartesian_product2(U_229,U_227)
| ? [U_223] :
( ~ in(U_223,U_225)
& ? [U_215] :
( ? [U_214] :
( U_223 = ordered_pair(U_215,U_214)
& in(U_214,U_227) )
& in(U_215,U_229) ) )
| ( ! [U_213] :
( ! [U_212] :
( sK43(U_229,U_227,U_225) != ordered_pair(U_213,U_212)
| ~ in(U_212,U_227) )
| ~ in(U_213,U_229) )
& in(sK43(U_229,U_227,U_225),U_225) ) )
& ! [U_228,U_226,U_224] :
( ( ! [U_221] :
( in(U_221,U_224)
| ! [U_210] :
( ! [U_209] :
( U_221 != ordered_pair(U_210,U_209)
| ~ in(U_209,U_226) )
| ~ in(U_210,U_228) ) )
& ! [U_220] :
( ( U_220 = ordered_pair(sK41(U_228,U_226,U_224,U_220),sK42(U_228,U_226,U_224,U_220))
& in(sK42(U_228,U_226,U_224,U_220),U_226)
& in(sK41(U_228,U_226,U_224,U_220),U_228) )
| ~ in(U_220,U_224) ) )
| U_224 != cartesian_product2(U_228,U_226) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_222,sK43(U_229,U_227,U_225))],[f_22_5]) ).
fof(f_22_7,plain,
( ! [U_229,U_227,U_225] :
( U_225 = cartesian_product2(U_229,U_227)
| ( ~ in(sK44(U_229,U_227,U_225),U_225)
& ? [U_215] :
( ? [U_214] :
( sK44(U_229,U_227,U_225) = ordered_pair(U_215,U_214)
& in(U_214,U_227) )
& in(U_215,U_229) ) )
| ( ! [U_213] :
( ! [U_212] :
( sK43(U_229,U_227,U_225) != ordered_pair(U_213,U_212)
| ~ in(U_212,U_227) )
| ~ in(U_213,U_229) )
& in(sK43(U_229,U_227,U_225),U_225) ) )
& ! [U_228,U_226,U_224] :
( ( ! [U_221] :
( in(U_221,U_224)
| ! [U_210] :
( ! [U_209] :
( U_221 != ordered_pair(U_210,U_209)
| ~ in(U_209,U_226) )
| ~ in(U_210,U_228) ) )
& ! [U_220] :
( ( U_220 = ordered_pair(sK41(U_228,U_226,U_224,U_220),sK42(U_228,U_226,U_224,U_220))
& in(sK42(U_228,U_226,U_224,U_220),U_226)
& in(sK41(U_228,U_226,U_224,U_220),U_228) )
| ~ in(U_220,U_224) ) )
| U_224 != cartesian_product2(U_228,U_226) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_223,sK44(U_229,U_227,U_225))],[f_22_6]) ).
fof(f_22_8,plain,
( ! [U_229,U_227,U_225] :
( U_225 = cartesian_product2(U_229,U_227)
| ( ~ in(sK44(U_229,U_227,U_225),U_225)
& ? [U_214] :
( sK44(U_229,U_227,U_225) = ordered_pair(sK45(U_229,U_227,U_225),U_214)
& in(U_214,U_227) )
& in(sK45(U_229,U_227,U_225),U_229) )
| ( ! [U_213] :
( ! [U_212] :
( sK43(U_229,U_227,U_225) != ordered_pair(U_213,U_212)
| ~ in(U_212,U_227) )
| ~ in(U_213,U_229) )
& in(sK43(U_229,U_227,U_225),U_225) ) )
& ! [U_228,U_226,U_224] :
( ( ! [U_221] :
( in(U_221,U_224)
| ! [U_210] :
( ! [U_209] :
( U_221 != ordered_pair(U_210,U_209)
| ~ in(U_209,U_226) )
| ~ in(U_210,U_228) ) )
& ! [U_220] :
( ( U_220 = ordered_pair(sK41(U_228,U_226,U_224,U_220),sK42(U_228,U_226,U_224,U_220))
& in(sK42(U_228,U_226,U_224,U_220),U_226)
& in(sK41(U_228,U_226,U_224,U_220),U_228) )
| ~ in(U_220,U_224) ) )
| U_224 != cartesian_product2(U_228,U_226) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_215,sK45(U_229,U_227,U_225))],[f_22_7]) ).
fof(f_22_9,plain,
( ! [U_229,U_227,U_225] :
( U_225 = cartesian_product2(U_229,U_227)
| ( ~ in(sK44(U_229,U_227,U_225),U_225)
& sK44(U_229,U_227,U_225) = ordered_pair(sK45(U_229,U_227,U_225),sK46(U_229,U_227,U_225))
& in(sK46(U_229,U_227,U_225),U_227)
& in(sK45(U_229,U_227,U_225),U_229) )
| ( ! [U_213] :
( ! [U_212] :
( sK43(U_229,U_227,U_225) != ordered_pair(U_213,U_212)
| ~ in(U_212,U_227) )
| ~ in(U_213,U_229) )
& in(sK43(U_229,U_227,U_225),U_225) ) )
& ! [U_228,U_226,U_224] :
( ( ! [U_221] :
( in(U_221,U_224)
| ! [U_210] :
( ! [U_209] :
( U_221 != ordered_pair(U_210,U_209)
| ~ in(U_209,U_226) )
| ~ in(U_210,U_228) ) )
& ! [U_220] :
( ( U_220 = ordered_pair(sK41(U_228,U_226,U_224,U_220),sK42(U_228,U_226,U_224,U_220))
& in(sK42(U_228,U_226,U_224,U_220),U_226)
& in(sK41(U_228,U_226,U_224,U_220),U_228) )
| ~ in(U_220,U_224) ) )
| U_224 != cartesian_product2(U_228,U_226) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_214,sK46(U_229,U_227,U_225))],[f_22_8]) ).
cnf(f_22_10,plain,
( in(sK41(U_228,U_226,U_224,U_220),U_228)
| ~ in(U_220,U_224)
| U_224 != cartesian_product2(U_228,U_226) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_11,plain,
( in(sK42(U_228,U_226,U_224,U_220),U_226)
| ~ in(U_220,U_224)
| U_224 != cartesian_product2(U_228,U_226) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_12,plain,
( U_220 = ordered_pair(sK41(U_228,U_226,U_224,U_220),sK42(U_228,U_226,U_224,U_220))
| ~ in(U_220,U_224)
| U_224 != cartesian_product2(U_228,U_226) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_13,plain,
( in(U_221,U_224)
| U_221 != ordered_pair(U_210,U_209)
| ~ in(U_209,U_226)
| ~ in(U_210,U_228)
| U_224 != cartesian_product2(U_228,U_226) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_14,plain,
( in(sK45(U_229,U_227,U_225),U_229)
| in(sK43(U_229,U_227,U_225),U_225)
| U_225 = cartesian_product2(U_229,U_227) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_15,plain,
( in(sK46(U_229,U_227,U_225),U_227)
| in(sK43(U_229,U_227,U_225),U_225)
| U_225 = cartesian_product2(U_229,U_227) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_16,plain,
( sK44(U_229,U_227,U_225) = ordered_pair(sK45(U_229,U_227,U_225),sK46(U_229,U_227,U_225))
| in(sK43(U_229,U_227,U_225),U_225)
| U_225 = cartesian_product2(U_229,U_227) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_17,plain,
( ~ in(sK44(U_229,U_227,U_225),U_225)
| in(sK43(U_229,U_227,U_225),U_225)
| U_225 = cartesian_product2(U_229,U_227) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_18,plain,
( in(sK45(U_229,U_227,U_225),U_229)
| sK43(U_229,U_227,U_225) != ordered_pair(U_213,U_212)
| ~ in(U_212,U_227)
| ~ in(U_213,U_229)
| U_225 = cartesian_product2(U_229,U_227) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_19,plain,
( in(sK46(U_229,U_227,U_225),U_227)
| sK43(U_229,U_227,U_225) != ordered_pair(U_213,U_212)
| ~ in(U_212,U_227)
| ~ in(U_213,U_229)
| U_225 = cartesian_product2(U_229,U_227) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_20,plain,
( sK44(U_229,U_227,U_225) = ordered_pair(sK45(U_229,U_227,U_225),sK46(U_229,U_227,U_225))
| sK43(U_229,U_227,U_225) != ordered_pair(U_213,U_212)
| ~ in(U_212,U_227)
| ~ in(U_213,U_229)
| U_225 = cartesian_product2(U_229,U_227) ),
inference(clausify,[status(thm)],[f_22_9]) ).
cnf(f_22_21,plain,
( ~ in(sK44(U_229,U_227,U_225),U_225)
| sK43(U_229,U_227,U_225) != ordered_pair(U_213,U_212)
| ~ in(U_212,U_227)
| ~ in(U_213,U_229)
| U_225 = cartesian_product2(U_229,U_227) ),
inference(clausify,[status(thm)],[f_22_9]) ).
fof(f_23_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_23_2,plain,
! [U_235] :
( ! [U_234] :
( ( ( subset(U_235,U_234)
| ? [U_233,U_232] :
( ~ in(ordered_pair(U_233,U_232),U_234)
& in(ordered_pair(U_233,U_232),U_235) ) )
& ( ! [U_231,U_230] :
( in(ordered_pair(U_231,U_230),U_234)
| ~ in(ordered_pair(U_231,U_230),U_235) )
| ~ subset(U_235,U_234) ) )
| ~ relation(U_234) )
| ~ relation(U_235) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_235] :
( ! [U_234] :
( ( ( subset(U_235,U_234)
| ? [U_232] :
( ~ in(ordered_pair(sK47(U_235,U_234),U_232),U_234)
& in(ordered_pair(sK47(U_235,U_234),U_232),U_235) ) )
& ( ! [U_231,U_230] :
( in(ordered_pair(U_231,U_230),U_234)
| ~ in(ordered_pair(U_231,U_230),U_235) )
| ~ subset(U_235,U_234) ) )
| ~ relation(U_234) )
| ~ relation(U_235) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_233,sK47(U_235,U_234))],[f_23_2]) ).
fof(f_23_4,plain,
! [U_235] :
( ! [U_234] :
( ( ( subset(U_235,U_234)
| ( ~ in(ordered_pair(sK47(U_235,U_234),sK48(U_235,U_234)),U_234)
& in(ordered_pair(sK47(U_235,U_234),sK48(U_235,U_234)),U_235) ) )
& ( ! [U_231,U_230] :
( in(ordered_pair(U_231,U_230),U_234)
| ~ in(ordered_pair(U_231,U_230),U_235) )
| ~ subset(U_235,U_234) ) )
| ~ relation(U_234) )
| ~ relation(U_235) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_232,sK48(U_235,U_234))],[f_23_3]) ).
cnf(f_23_5,plain,
( in(ordered_pair(U_231,U_230),U_234)
| ~ in(ordered_pair(U_231,U_230),U_235)
| ~ subset(U_235,U_234)
| ~ relation(U_234)
| ~ relation(U_235) ),
inference(clausify,[status(thm)],[f_23_4]) ).
cnf(f_23_6,plain,
( in(ordered_pair(sK47(U_235,U_234),sK48(U_235,U_234)),U_235)
| subset(U_235,U_234)
| ~ relation(U_234)
| ~ relation(U_235) ),
inference(clausify,[status(thm)],[f_23_4]) ).
cnf(f_23_7,plain,
( ~ in(ordered_pair(sK47(U_235,U_234),sK48(U_235,U_234)),U_234)
| subset(U_235,U_234)
| ~ relation(U_234)
| ~ relation(U_235) ),
inference(clausify,[status(thm)],[f_23_4]) ).
fof(f_24_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_24_2,plain,
! [U_239,U_238] :
( ( subset(U_239,U_238)
| ? [U_237] :
( ~ in(U_237,U_238)
& in(U_237,U_239) ) )
& ( ! [U_236] :
( in(U_236,U_238)
| ~ in(U_236,U_239) )
| ~ subset(U_239,U_238) ) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( ! [U_243,U_241] :
( subset(U_243,U_241)
| ? [U_237] :
( ~ in(U_237,U_241)
& in(U_237,U_243) ) )
& ! [U_242,U_240] :
( ! [U_236] :
( in(U_236,U_240)
| ~ in(U_236,U_242) )
| ~ subset(U_242,U_240) ) ),
inference(miniscope,[status(thm)],[f_24_2]) ).
fof(f_24_4,plain,
( ! [U_243,U_241] :
( subset(U_243,U_241)
| ( ~ in(sK49(U_243,U_241),U_241)
& in(sK49(U_243,U_241),U_243) ) )
& ! [U_242,U_240] :
( ! [U_236] :
( in(U_236,U_240)
| ~ in(U_236,U_242) )
| ~ subset(U_242,U_240) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_237,sK49(U_243,U_241))],[f_24_3]) ).
cnf(f_24_5,plain,
( in(U_236,U_240)
| ~ in(U_236,U_242)
| ~ subset(U_242,U_240) ),
inference(clausify,[status(thm)],[f_24_4]) ).
cnf(f_24_6,plain,
( in(sK49(U_243,U_241),U_243)
| subset(U_243,U_241) ),
inference(clausify,[status(thm)],[f_24_4]) ).
cnf(f_24_7,plain,
( ~ in(sK49(U_243,U_241),U_241)
| subset(U_243,U_241) ),
inference(clausify,[status(thm)],[f_24_4]) ).
fof(f_25_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_25_2,plain,
! [U_248,U_247,U_246] :
( ( U_246 = set_intersection2(U_248,U_247)
| ? [U_245] :
( ( ~ in(U_245,U_246)
& in(U_245,U_247)
& in(U_245,U_248) )
| ( ( ~ in(U_245,U_247)
| ~ in(U_245,U_248) )
& in(U_245,U_246) ) ) )
& ( ! [U_244] :
( ( in(U_244,U_246)
| ~ in(U_244,U_247)
| ~ in(U_244,U_248) )
& ( ( in(U_244,U_247)
& in(U_244,U_248) )
| ~ in(U_244,U_246) ) )
| U_246 != set_intersection2(U_248,U_247) ) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( ! [U_258,U_256,U_254] :
( U_254 = set_intersection2(U_258,U_256)
| ? [U_252] :
( ~ in(U_252,U_254)
& in(U_252,U_256)
& in(U_252,U_258) )
| ? [U_251] :
( ( ~ in(U_251,U_256)
| ~ in(U_251,U_258) )
& in(U_251,U_254) ) )
& ! [U_257,U_255,U_253] :
( ( ! [U_250] :
( in(U_250,U_253)
| ~ in(U_250,U_255)
| ~ in(U_250,U_257) )
& ! [U_249] :
( ( in(U_249,U_255)
& in(U_249,U_257) )
| ~ in(U_249,U_253) ) )
| U_253 != set_intersection2(U_257,U_255) ) ),
inference(miniscope,[status(thm)],[f_25_2]) ).
fof(f_25_4,plain,
( ! [U_258,U_256,U_254] :
( U_254 = set_intersection2(U_258,U_256)
| ? [U_252] :
( ~ in(U_252,U_254)
& in(U_252,U_256)
& in(U_252,U_258) )
| ( ( ~ in(sK50(U_258,U_256,U_254),U_256)
| ~ in(sK50(U_258,U_256,U_254),U_258) )
& in(sK50(U_258,U_256,U_254),U_254) ) )
& ! [U_257,U_255,U_253] :
( ( ! [U_250] :
( in(U_250,U_253)
| ~ in(U_250,U_255)
| ~ in(U_250,U_257) )
& ! [U_249] :
( ( in(U_249,U_255)
& in(U_249,U_257) )
| ~ in(U_249,U_253) ) )
| U_253 != set_intersection2(U_257,U_255) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_251,sK50(U_258,U_256,U_254))],[f_25_3]) ).
fof(f_25_5,plain,
( ! [U_258,U_256,U_254] :
( U_254 = set_intersection2(U_258,U_256)
| ( ~ in(sK51(U_258,U_256,U_254),U_254)
& in(sK51(U_258,U_256,U_254),U_256)
& in(sK51(U_258,U_256,U_254),U_258) )
| ( ( ~ in(sK50(U_258,U_256,U_254),U_256)
| ~ in(sK50(U_258,U_256,U_254),U_258) )
& in(sK50(U_258,U_256,U_254),U_254) ) )
& ! [U_257,U_255,U_253] :
( ( ! [U_250] :
( in(U_250,U_253)
| ~ in(U_250,U_255)
| ~ in(U_250,U_257) )
& ! [U_249] :
( ( in(U_249,U_255)
& in(U_249,U_257) )
| ~ in(U_249,U_253) ) )
| U_253 != set_intersection2(U_257,U_255) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_252,sK51(U_258,U_256,U_254))],[f_25_4]) ).
cnf(f_25_6,plain,
( in(U_249,U_257)
| ~ in(U_249,U_253)
| U_253 != set_intersection2(U_257,U_255) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_7,plain,
( in(U_249,U_255)
| ~ in(U_249,U_253)
| U_253 != set_intersection2(U_257,U_255) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_8,plain,
( in(U_250,U_253)
| ~ in(U_250,U_255)
| ~ in(U_250,U_257)
| U_253 != set_intersection2(U_257,U_255) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_9,plain,
( in(sK51(U_258,U_256,U_254),U_258)
| in(sK50(U_258,U_256,U_254),U_254)
| U_254 = set_intersection2(U_258,U_256) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_10,plain,
( in(sK51(U_258,U_256,U_254),U_256)
| in(sK50(U_258,U_256,U_254),U_254)
| U_254 = set_intersection2(U_258,U_256) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_11,plain,
( ~ in(sK51(U_258,U_256,U_254),U_254)
| in(sK50(U_258,U_256,U_254),U_254)
| U_254 = set_intersection2(U_258,U_256) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_12,plain,
( in(sK51(U_258,U_256,U_254),U_258)
| ~ in(sK50(U_258,U_256,U_254),U_256)
| ~ in(sK50(U_258,U_256,U_254),U_258)
| U_254 = set_intersection2(U_258,U_256) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_13,plain,
( in(sK51(U_258,U_256,U_254),U_256)
| ~ in(sK50(U_258,U_256,U_254),U_256)
| ~ in(sK50(U_258,U_256,U_254),U_258)
| U_254 = set_intersection2(U_258,U_256) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_14,plain,
( ~ in(sK51(U_258,U_256,U_254),U_254)
| ~ in(sK50(U_258,U_256,U_254),U_256)
| ~ in(sK50(U_258,U_256,U_254),U_258)
| U_254 = set_intersection2(U_258,U_256) ),
inference(clausify,[status(thm)],[f_25_5]) ).
fof(f_26_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_26_2,plain,
! [U_266] :
( ! [U_265] :
( ( U_265 = relation_dom(U_266)
| ? [U_264] :
( ( ~ in(U_264,U_265)
& ? [U_263] : in(ordered_pair(U_264,U_263),U_266) )
| ( ! [U_262] : ~ in(ordered_pair(U_264,U_262),U_266)
& in(U_264,U_265) ) ) )
& ( ! [U_261] :
( ( in(U_261,U_265)
| ! [U_260] : ~ in(ordered_pair(U_261,U_260),U_266) )
& ( ? [U_259] : in(ordered_pair(U_261,U_259),U_266)
| ~ in(U_261,U_265) ) )
| U_265 != relation_dom(U_266) ) )
| ~ relation(U_266) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_266] :
( ( ! [U_272] :
( U_272 = relation_dom(U_266)
| ? [U_270] :
( ~ in(U_270,U_272)
& ? [U_263] : in(ordered_pair(U_270,U_263),U_266) )
| ? [U_269] :
( ! [U_262] : ~ in(ordered_pair(U_269,U_262),U_266)
& in(U_269,U_272) ) )
& ! [U_271] :
( ( ! [U_268] :
( in(U_268,U_271)
| ! [U_260] : ~ in(ordered_pair(U_268,U_260),U_266) )
& ! [U_267] :
( ? [U_259] : in(ordered_pair(U_267,U_259),U_266)
| ~ in(U_267,U_271) ) )
| U_271 != relation_dom(U_266) ) )
| ~ relation(U_266) ),
inference(miniscope,[status(thm)],[f_26_2]) ).
fof(f_26_4,plain,
! [U_266] :
( ( ! [U_272] :
( U_272 = relation_dom(U_266)
| ? [U_270] :
( ~ in(U_270,U_272)
& ? [U_263] : in(ordered_pair(U_270,U_263),U_266) )
| ? [U_269] :
( ! [U_262] : ~ in(ordered_pair(U_269,U_262),U_266)
& in(U_269,U_272) ) )
& ! [U_271] :
( ( ! [U_268] :
( in(U_268,U_271)
| ! [U_260] : ~ in(ordered_pair(U_268,U_260),U_266) )
& ! [U_267] :
( in(ordered_pair(U_267,sK52(U_266,U_271,U_267)),U_266)
| ~ in(U_267,U_271) ) )
| U_271 != relation_dom(U_266) ) )
| ~ relation(U_266) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_259,sK52(U_266,U_271,U_267))],[f_26_3]) ).
fof(f_26_5,plain,
! [U_266] :
( ( ! [U_272] :
( U_272 = relation_dom(U_266)
| ? [U_270] :
( ~ in(U_270,U_272)
& ? [U_263] : in(ordered_pair(U_270,U_263),U_266) )
| ( ! [U_262] : ~ in(ordered_pair(sK53(U_266,U_272),U_262),U_266)
& in(sK53(U_266,U_272),U_272) ) )
& ! [U_271] :
( ( ! [U_268] :
( in(U_268,U_271)
| ! [U_260] : ~ in(ordered_pair(U_268,U_260),U_266) )
& ! [U_267] :
( in(ordered_pair(U_267,sK52(U_266,U_271,U_267)),U_266)
| ~ in(U_267,U_271) ) )
| U_271 != relation_dom(U_266) ) )
| ~ relation(U_266) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_269,sK53(U_266,U_272))],[f_26_4]) ).
fof(f_26_6,plain,
! [U_266] :
( ( ! [U_272] :
( U_272 = relation_dom(U_266)
| ( ~ in(sK54(U_266,U_272),U_272)
& ? [U_263] : in(ordered_pair(sK54(U_266,U_272),U_263),U_266) )
| ( ! [U_262] : ~ in(ordered_pair(sK53(U_266,U_272),U_262),U_266)
& in(sK53(U_266,U_272),U_272) ) )
& ! [U_271] :
( ( ! [U_268] :
( in(U_268,U_271)
| ! [U_260] : ~ in(ordered_pair(U_268,U_260),U_266) )
& ! [U_267] :
( in(ordered_pair(U_267,sK52(U_266,U_271,U_267)),U_266)
| ~ in(U_267,U_271) ) )
| U_271 != relation_dom(U_266) ) )
| ~ relation(U_266) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_270,sK54(U_266,U_272))],[f_26_5]) ).
fof(f_26_7,plain,
! [U_266] :
( ( ! [U_272] :
( U_272 = relation_dom(U_266)
| ( ~ in(sK54(U_266,U_272),U_272)
& in(ordered_pair(sK54(U_266,U_272),sK55(U_266,U_272)),U_266) )
| ( ! [U_262] : ~ in(ordered_pair(sK53(U_266,U_272),U_262),U_266)
& in(sK53(U_266,U_272),U_272) ) )
& ! [U_271] :
( ( ! [U_268] :
( in(U_268,U_271)
| ! [U_260] : ~ in(ordered_pair(U_268,U_260),U_266) )
& ! [U_267] :
( in(ordered_pair(U_267,sK52(U_266,U_271,U_267)),U_266)
| ~ in(U_267,U_271) ) )
| U_271 != relation_dom(U_266) ) )
| ~ relation(U_266) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_263,sK55(U_266,U_272))],[f_26_6]) ).
cnf(f_26_8,plain,
( in(ordered_pair(U_267,sK52(U_266,U_271,U_267)),U_266)
| ~ in(U_267,U_271)
| U_271 != relation_dom(U_266)
| ~ relation(U_266) ),
inference(clausify,[status(thm)],[f_26_7]) ).
cnf(f_26_9,plain,
( in(U_268,U_271)
| ~ in(ordered_pair(U_268,U_260),U_266)
| U_271 != relation_dom(U_266)
| ~ relation(U_266) ),
inference(clausify,[status(thm)],[f_26_7]) ).
cnf(f_26_10,plain,
( in(ordered_pair(sK54(U_266,U_272),sK55(U_266,U_272)),U_266)
| in(sK53(U_266,U_272),U_272)
| U_272 = relation_dom(U_266)
| ~ relation(U_266) ),
inference(clausify,[status(thm)],[f_26_7]) ).
cnf(f_26_11,plain,
( ~ in(sK54(U_266,U_272),U_272)
| in(sK53(U_266,U_272),U_272)
| U_272 = relation_dom(U_266)
| ~ relation(U_266) ),
inference(clausify,[status(thm)],[f_26_7]) ).
cnf(f_26_12,plain,
( in(ordered_pair(sK54(U_266,U_272),sK55(U_266,U_272)),U_266)
| ~ in(ordered_pair(sK53(U_266,U_272),U_262),U_266)
| U_272 = relation_dom(U_266)
| ~ relation(U_266) ),
inference(clausify,[status(thm)],[f_26_7]) ).
cnf(f_26_13,plain,
( ~ in(sK54(U_266,U_272),U_272)
| ~ in(ordered_pair(sK53(U_266,U_272),U_262),U_266)
| U_272 = relation_dom(U_266)
| ~ relation(U_266) ),
inference(clausify,[status(thm)],[f_26_7]) ).
fof(f_27_1,plain,
! [A] : cast_to_subset(A) = A,
inference(fof_nnf,[status(thm)],[d4_subset_1]) ).
fof(f_27_2,plain,
! [U_273] : cast_to_subset(U_273) = U_273,
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
cast_to_subset(U_273) = U_273,
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_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_28_2,plain,
! [U_281,U_280] :
( ( U_280 = union(U_281)
| ? [U_279] :
( ( ~ in(U_279,U_280)
& ? [U_278] :
( in(U_278,U_281)
& in(U_279,U_278) ) )
| ( ! [U_277] :
( ~ in(U_277,U_281)
| ~ in(U_279,U_277) )
& in(U_279,U_280) ) ) )
& ( ! [U_276] :
( ( in(U_276,U_280)
| ! [U_275] :
( ~ in(U_275,U_281)
| ~ in(U_276,U_275) ) )
& ( ? [U_274] :
( in(U_274,U_281)
& in(U_276,U_274) )
| ~ in(U_276,U_280) ) )
| U_280 != union(U_281) ) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( ! [U_289,U_287] :
( U_287 = union(U_289)
| ? [U_285] :
( ~ in(U_285,U_287)
& ? [U_278] :
( in(U_278,U_289)
& in(U_285,U_278) ) )
| ? [U_284] :
( ! [U_277] :
( ~ in(U_277,U_289)
| ~ in(U_284,U_277) )
& in(U_284,U_287) ) )
& ! [U_288,U_286] :
( ( ! [U_283] :
( in(U_283,U_286)
| ! [U_275] :
( ~ in(U_275,U_288)
| ~ in(U_283,U_275) ) )
& ! [U_282] :
( ? [U_274] :
( in(U_274,U_288)
& in(U_282,U_274) )
| ~ in(U_282,U_286) ) )
| U_286 != union(U_288) ) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
fof(f_28_4,plain,
( ! [U_289,U_287] :
( U_287 = union(U_289)
| ? [U_285] :
( ~ in(U_285,U_287)
& ? [U_278] :
( in(U_278,U_289)
& in(U_285,U_278) ) )
| ? [U_284] :
( ! [U_277] :
( ~ in(U_277,U_289)
| ~ in(U_284,U_277) )
& in(U_284,U_287) ) )
& ! [U_288,U_286] :
( ( ! [U_283] :
( in(U_283,U_286)
| ! [U_275] :
( ~ in(U_275,U_288)
| ~ in(U_283,U_275) ) )
& ! [U_282] :
( ( in(sK56(U_288,U_286,U_282),U_288)
& in(U_282,sK56(U_288,U_286,U_282)) )
| ~ in(U_282,U_286) ) )
| U_286 != union(U_288) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_274,sK56(U_288,U_286,U_282))],[f_28_3]) ).
fof(f_28_5,plain,
( ! [U_289,U_287] :
( U_287 = union(U_289)
| ? [U_285] :
( ~ in(U_285,U_287)
& ? [U_278] :
( in(U_278,U_289)
& in(U_285,U_278) ) )
| ( ! [U_277] :
( ~ in(U_277,U_289)
| ~ in(sK57(U_289,U_287),U_277) )
& in(sK57(U_289,U_287),U_287) ) )
& ! [U_288,U_286] :
( ( ! [U_283] :
( in(U_283,U_286)
| ! [U_275] :
( ~ in(U_275,U_288)
| ~ in(U_283,U_275) ) )
& ! [U_282] :
( ( in(sK56(U_288,U_286,U_282),U_288)
& in(U_282,sK56(U_288,U_286,U_282)) )
| ~ in(U_282,U_286) ) )
| U_286 != union(U_288) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_284,sK57(U_289,U_287))],[f_28_4]) ).
fof(f_28_6,plain,
( ! [U_289,U_287] :
( U_287 = union(U_289)
| ( ~ in(sK58(U_289,U_287),U_287)
& ? [U_278] :
( in(U_278,U_289)
& in(sK58(U_289,U_287),U_278) ) )
| ( ! [U_277] :
( ~ in(U_277,U_289)
| ~ in(sK57(U_289,U_287),U_277) )
& in(sK57(U_289,U_287),U_287) ) )
& ! [U_288,U_286] :
( ( ! [U_283] :
( in(U_283,U_286)
| ! [U_275] :
( ~ in(U_275,U_288)
| ~ in(U_283,U_275) ) )
& ! [U_282] :
( ( in(sK56(U_288,U_286,U_282),U_288)
& in(U_282,sK56(U_288,U_286,U_282)) )
| ~ in(U_282,U_286) ) )
| U_286 != union(U_288) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_285,sK58(U_289,U_287))],[f_28_5]) ).
fof(f_28_7,plain,
( ! [U_289,U_287] :
( U_287 = union(U_289)
| ( ~ in(sK58(U_289,U_287),U_287)
& in(sK59(U_289,U_287),U_289)
& in(sK58(U_289,U_287),sK59(U_289,U_287)) )
| ( ! [U_277] :
( ~ in(U_277,U_289)
| ~ in(sK57(U_289,U_287),U_277) )
& in(sK57(U_289,U_287),U_287) ) )
& ! [U_288,U_286] :
( ( ! [U_283] :
( in(U_283,U_286)
| ! [U_275] :
( ~ in(U_275,U_288)
| ~ in(U_283,U_275) ) )
& ! [U_282] :
( ( in(sK56(U_288,U_286,U_282),U_288)
& in(U_282,sK56(U_288,U_286,U_282)) )
| ~ in(U_282,U_286) ) )
| U_286 != union(U_288) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_278,sK59(U_289,U_287))],[f_28_6]) ).
cnf(f_28_8,plain,
( in(U_282,sK56(U_288,U_286,U_282))
| ~ in(U_282,U_286)
| U_286 != union(U_288) ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_9,plain,
( in(sK56(U_288,U_286,U_282),U_288)
| ~ in(U_282,U_286)
| U_286 != union(U_288) ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_10,plain,
( in(U_283,U_286)
| ~ in(U_275,U_288)
| ~ in(U_283,U_275)
| U_286 != union(U_288) ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_11,plain,
( in(sK58(U_289,U_287),sK59(U_289,U_287))
| in(sK57(U_289,U_287),U_287)
| U_287 = union(U_289) ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_12,plain,
( in(sK59(U_289,U_287),U_289)
| in(sK57(U_289,U_287),U_287)
| U_287 = union(U_289) ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_13,plain,
( ~ in(sK58(U_289,U_287),U_287)
| in(sK57(U_289,U_287),U_287)
| U_287 = union(U_289) ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_14,plain,
( in(sK58(U_289,U_287),sK59(U_289,U_287))
| ~ in(U_277,U_289)
| ~ in(sK57(U_289,U_287),U_277)
| U_287 = union(U_289) ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_15,plain,
( in(sK59(U_289,U_287),U_289)
| ~ in(U_277,U_289)
| ~ in(sK57(U_289,U_287),U_277)
| U_287 = union(U_289) ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_16,plain,
( ~ in(sK58(U_289,U_287),U_287)
| ~ in(U_277,U_289)
| ~ in(sK57(U_289,U_287),U_277)
| U_287 = union(U_289) ),
inference(clausify,[status(thm)],[f_28_7]) ).
fof(f_29_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_29_2,plain,
! [U_294,U_293,U_292] :
( ( U_292 = set_difference(U_294,U_293)
| ? [U_291] :
( ( ~ in(U_291,U_292)
& ~ in(U_291,U_293)
& in(U_291,U_294) )
| ( ( in(U_291,U_293)
| ~ in(U_291,U_294) )
& in(U_291,U_292) ) ) )
& ( ! [U_290] :
( ( in(U_290,U_292)
| in(U_290,U_293)
| ~ in(U_290,U_294) )
& ( ( ~ in(U_290,U_293)
& in(U_290,U_294) )
| ~ in(U_290,U_292) ) )
| U_292 != set_difference(U_294,U_293) ) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
( ! [U_304,U_302,U_300] :
( U_300 = set_difference(U_304,U_302)
| ? [U_298] :
( ~ in(U_298,U_300)
& ~ in(U_298,U_302)
& in(U_298,U_304) )
| ? [U_297] :
( ( in(U_297,U_302)
| ~ in(U_297,U_304) )
& in(U_297,U_300) ) )
& ! [U_303,U_301,U_299] :
( ( ! [U_296] :
( in(U_296,U_299)
| in(U_296,U_301)
| ~ in(U_296,U_303) )
& ! [U_295] :
( ( ~ in(U_295,U_301)
& in(U_295,U_303) )
| ~ in(U_295,U_299) ) )
| U_299 != set_difference(U_303,U_301) ) ),
inference(miniscope,[status(thm)],[f_29_2]) ).
fof(f_29_4,plain,
( ! [U_304,U_302,U_300] :
( U_300 = set_difference(U_304,U_302)
| ? [U_298] :
( ~ in(U_298,U_300)
& ~ in(U_298,U_302)
& in(U_298,U_304) )
| ( ( in(sK60(U_304,U_302,U_300),U_302)
| ~ in(sK60(U_304,U_302,U_300),U_304) )
& in(sK60(U_304,U_302,U_300),U_300) ) )
& ! [U_303,U_301,U_299] :
( ( ! [U_296] :
( in(U_296,U_299)
| in(U_296,U_301)
| ~ in(U_296,U_303) )
& ! [U_295] :
( ( ~ in(U_295,U_301)
& in(U_295,U_303) )
| ~ in(U_295,U_299) ) )
| U_299 != set_difference(U_303,U_301) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_297,sK60(U_304,U_302,U_300))],[f_29_3]) ).
fof(f_29_5,plain,
( ! [U_304,U_302,U_300] :
( U_300 = set_difference(U_304,U_302)
| ( ~ in(sK61(U_304,U_302,U_300),U_300)
& ~ in(sK61(U_304,U_302,U_300),U_302)
& in(sK61(U_304,U_302,U_300),U_304) )
| ( ( in(sK60(U_304,U_302,U_300),U_302)
| ~ in(sK60(U_304,U_302,U_300),U_304) )
& in(sK60(U_304,U_302,U_300),U_300) ) )
& ! [U_303,U_301,U_299] :
( ( ! [U_296] :
( in(U_296,U_299)
| in(U_296,U_301)
| ~ in(U_296,U_303) )
& ! [U_295] :
( ( ~ in(U_295,U_301)
& in(U_295,U_303) )
| ~ in(U_295,U_299) ) )
| U_299 != set_difference(U_303,U_301) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_298,sK61(U_304,U_302,U_300))],[f_29_4]) ).
cnf(f_29_6,plain,
( in(U_295,U_303)
| ~ in(U_295,U_299)
| U_299 != set_difference(U_303,U_301) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_7,plain,
( ~ in(U_295,U_301)
| ~ in(U_295,U_299)
| U_299 != set_difference(U_303,U_301) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_8,plain,
( in(U_296,U_299)
| in(U_296,U_301)
| ~ in(U_296,U_303)
| U_299 != set_difference(U_303,U_301) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_9,plain,
( in(sK61(U_304,U_302,U_300),U_304)
| in(sK60(U_304,U_302,U_300),U_300)
| U_300 = set_difference(U_304,U_302) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_10,plain,
( ~ in(sK61(U_304,U_302,U_300),U_302)
| in(sK60(U_304,U_302,U_300),U_300)
| U_300 = set_difference(U_304,U_302) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_11,plain,
( ~ in(sK61(U_304,U_302,U_300),U_300)
| in(sK60(U_304,U_302,U_300),U_300)
| U_300 = set_difference(U_304,U_302) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_12,plain,
( in(sK61(U_304,U_302,U_300),U_304)
| in(sK60(U_304,U_302,U_300),U_302)
| ~ in(sK60(U_304,U_302,U_300),U_304)
| U_300 = set_difference(U_304,U_302) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_13,plain,
( ~ in(sK61(U_304,U_302,U_300),U_302)
| in(sK60(U_304,U_302,U_300),U_302)
| ~ in(sK60(U_304,U_302,U_300),U_304)
| U_300 = set_difference(U_304,U_302) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_14,plain,
( ~ in(sK61(U_304,U_302,U_300),U_300)
| in(sK60(U_304,U_302,U_300),U_302)
| ~ in(sK60(U_304,U_302,U_300),U_304)
| U_300 = set_difference(U_304,U_302) ),
inference(clausify,[status(thm)],[f_29_5]) ).
fof(f_30_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_30_2,plain,
! [U_312] :
( ! [U_311] :
( ( U_311 = relation_rng(U_312)
| ? [U_310] :
( ( ~ in(U_310,U_311)
& ? [U_309] : in(ordered_pair(U_309,U_310),U_312) )
| ( ! [U_308] : ~ in(ordered_pair(U_308,U_310),U_312)
& in(U_310,U_311) ) ) )
& ( ! [U_307] :
( ( in(U_307,U_311)
| ! [U_306] : ~ in(ordered_pair(U_306,U_307),U_312) )
& ( ? [U_305] : in(ordered_pair(U_305,U_307),U_312)
| ~ in(U_307,U_311) ) )
| U_311 != relation_rng(U_312) ) )
| ~ relation(U_312) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_312] :
( ( ! [U_318] :
( U_318 = relation_rng(U_312)
| ? [U_316] :
( ~ in(U_316,U_318)
& ? [U_309] : in(ordered_pair(U_309,U_316),U_312) )
| ? [U_315] :
( ! [U_308] : ~ in(ordered_pair(U_308,U_315),U_312)
& in(U_315,U_318) ) )
& ! [U_317] :
( ( ! [U_314] :
( in(U_314,U_317)
| ! [U_306] : ~ in(ordered_pair(U_306,U_314),U_312) )
& ! [U_313] :
( ? [U_305] : in(ordered_pair(U_305,U_313),U_312)
| ~ in(U_313,U_317) ) )
| U_317 != relation_rng(U_312) ) )
| ~ relation(U_312) ),
inference(miniscope,[status(thm)],[f_30_2]) ).
fof(f_30_4,plain,
! [U_312] :
( ( ! [U_318] :
( U_318 = relation_rng(U_312)
| ? [U_316] :
( ~ in(U_316,U_318)
& ? [U_309] : in(ordered_pair(U_309,U_316),U_312) )
| ? [U_315] :
( ! [U_308] : ~ in(ordered_pair(U_308,U_315),U_312)
& in(U_315,U_318) ) )
& ! [U_317] :
( ( ! [U_314] :
( in(U_314,U_317)
| ! [U_306] : ~ in(ordered_pair(U_306,U_314),U_312) )
& ! [U_313] :
( in(ordered_pair(sK62(U_312,U_317,U_313),U_313),U_312)
| ~ in(U_313,U_317) ) )
| U_317 != relation_rng(U_312) ) )
| ~ relation(U_312) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_305,sK62(U_312,U_317,U_313))],[f_30_3]) ).
fof(f_30_5,plain,
! [U_312] :
( ( ! [U_318] :
( U_318 = relation_rng(U_312)
| ? [U_316] :
( ~ in(U_316,U_318)
& ? [U_309] : in(ordered_pair(U_309,U_316),U_312) )
| ( ! [U_308] : ~ in(ordered_pair(U_308,sK63(U_312,U_318)),U_312)
& in(sK63(U_312,U_318),U_318) ) )
& ! [U_317] :
( ( ! [U_314] :
( in(U_314,U_317)
| ! [U_306] : ~ in(ordered_pair(U_306,U_314),U_312) )
& ! [U_313] :
( in(ordered_pair(sK62(U_312,U_317,U_313),U_313),U_312)
| ~ in(U_313,U_317) ) )
| U_317 != relation_rng(U_312) ) )
| ~ relation(U_312) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_315,sK63(U_312,U_318))],[f_30_4]) ).
fof(f_30_6,plain,
! [U_312] :
( ( ! [U_318] :
( U_318 = relation_rng(U_312)
| ( ~ in(sK64(U_312,U_318),U_318)
& ? [U_309] : in(ordered_pair(U_309,sK64(U_312,U_318)),U_312) )
| ( ! [U_308] : ~ in(ordered_pair(U_308,sK63(U_312,U_318)),U_312)
& in(sK63(U_312,U_318),U_318) ) )
& ! [U_317] :
( ( ! [U_314] :
( in(U_314,U_317)
| ! [U_306] : ~ in(ordered_pair(U_306,U_314),U_312) )
& ! [U_313] :
( in(ordered_pair(sK62(U_312,U_317,U_313),U_313),U_312)
| ~ in(U_313,U_317) ) )
| U_317 != relation_rng(U_312) ) )
| ~ relation(U_312) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_316,sK64(U_312,U_318))],[f_30_5]) ).
fof(f_30_7,plain,
! [U_312] :
( ( ! [U_318] :
( U_318 = relation_rng(U_312)
| ( ~ in(sK64(U_312,U_318),U_318)
& in(ordered_pair(sK65(U_312,U_318),sK64(U_312,U_318)),U_312) )
| ( ! [U_308] : ~ in(ordered_pair(U_308,sK63(U_312,U_318)),U_312)
& in(sK63(U_312,U_318),U_318) ) )
& ! [U_317] :
( ( ! [U_314] :
( in(U_314,U_317)
| ! [U_306] : ~ in(ordered_pair(U_306,U_314),U_312) )
& ! [U_313] :
( in(ordered_pair(sK62(U_312,U_317,U_313),U_313),U_312)
| ~ in(U_313,U_317) ) )
| U_317 != relation_rng(U_312) ) )
| ~ relation(U_312) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_309,sK65(U_312,U_318))],[f_30_6]) ).
cnf(f_30_8,plain,
( in(ordered_pair(sK62(U_312,U_317,U_313),U_313),U_312)
| ~ in(U_313,U_317)
| U_317 != relation_rng(U_312)
| ~ relation(U_312) ),
inference(clausify,[status(thm)],[f_30_7]) ).
cnf(f_30_9,plain,
( in(U_314,U_317)
| ~ in(ordered_pair(U_306,U_314),U_312)
| U_317 != relation_rng(U_312)
| ~ relation(U_312) ),
inference(clausify,[status(thm)],[f_30_7]) ).
cnf(f_30_10,plain,
( in(ordered_pair(sK65(U_312,U_318),sK64(U_312,U_318)),U_312)
| in(sK63(U_312,U_318),U_318)
| U_318 = relation_rng(U_312)
| ~ relation(U_312) ),
inference(clausify,[status(thm)],[f_30_7]) ).
cnf(f_30_11,plain,
( ~ in(sK64(U_312,U_318),U_318)
| in(sK63(U_312,U_318),U_318)
| U_318 = relation_rng(U_312)
| ~ relation(U_312) ),
inference(clausify,[status(thm)],[f_30_7]) ).
cnf(f_30_12,plain,
( in(ordered_pair(sK65(U_312,U_318),sK64(U_312,U_318)),U_312)
| ~ in(ordered_pair(U_308,sK63(U_312,U_318)),U_312)
| U_318 = relation_rng(U_312)
| ~ relation(U_312) ),
inference(clausify,[status(thm)],[f_30_7]) ).
cnf(f_30_13,plain,
( ~ in(sK64(U_312,U_318),U_318)
| ~ in(ordered_pair(U_308,sK63(U_312,U_318)),U_312)
| U_318 = relation_rng(U_312)
| ~ relation(U_312) ),
inference(clausify,[status(thm)],[f_30_7]) ).
fof(f_31_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_31_2,plain,
! [U_320,U_319] :
( subset_complement(U_320,U_319) = set_difference(U_320,U_319)
| ~ element(U_319,powerset(U_320)) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( subset_complement(U_320,U_319) = set_difference(U_320,U_319)
| ~ element(U_319,powerset(U_320)) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_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_32_2,plain,
! [U_322,U_321] : ordered_pair(U_322,U_321) = unordered_pair(unordered_pair(U_322,U_321),singleton(U_322)),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
ordered_pair(U_322,U_321) = unordered_pair(unordered_pair(U_322,U_321),singleton(U_322)),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_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_33_2,plain,
! [U_323] :
( relation_field(U_323) = set_union2(relation_dom(U_323),relation_rng(U_323))
| ~ relation(U_323) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( relation_field(U_323) = set_union2(relation_dom(U_323),relation_rng(U_323))
| ~ relation(U_323) ),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_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_34_2,plain,
! [U_329] :
( ! [U_328] :
( ( ( U_328 = relation_inverse(U_329)
| ? [U_327,U_326] :
( ( ~ in(ordered_pair(U_327,U_326),U_328)
& in(ordered_pair(U_326,U_327),U_329) )
| ( ~ in(ordered_pair(U_326,U_327),U_329)
& in(ordered_pair(U_327,U_326),U_328) ) ) )
& ( ! [U_325,U_324] :
( ( in(ordered_pair(U_325,U_324),U_328)
| ~ in(ordered_pair(U_324,U_325),U_329) )
& ( in(ordered_pair(U_324,U_325),U_329)
| ~ in(ordered_pair(U_325,U_324),U_328) ) )
| U_328 != relation_inverse(U_329) ) )
| ~ relation(U_328) )
| ~ relation(U_329) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_329] :
( ! [U_328] :
( ( ( U_328 = relation_inverse(U_329)
| ? [U_337,U_335] :
( ~ in(ordered_pair(U_337,U_335),U_328)
& in(ordered_pair(U_335,U_337),U_329) )
| ? [U_336,U_334] :
( ~ in(ordered_pair(U_334,U_336),U_329)
& in(ordered_pair(U_336,U_334),U_328) ) )
& ( ( ! [U_333,U_331] :
( in(ordered_pair(U_333,U_331),U_328)
| ~ in(ordered_pair(U_331,U_333),U_329) )
& ! [U_332,U_330] :
( in(ordered_pair(U_330,U_332),U_329)
| ~ in(ordered_pair(U_332,U_330),U_328) ) )
| U_328 != relation_inverse(U_329) ) )
| ~ relation(U_328) )
| ~ relation(U_329) ),
inference(miniscope,[status(thm)],[f_34_2]) ).
fof(f_34_4,plain,
! [U_329] :
( ! [U_328] :
( ( ( U_328 = relation_inverse(U_329)
| ? [U_337,U_335] :
( ~ in(ordered_pair(U_337,U_335),U_328)
& in(ordered_pair(U_335,U_337),U_329) )
| ? [U_334] :
( ~ in(ordered_pair(U_334,sK66(U_329,U_328)),U_329)
& in(ordered_pair(sK66(U_329,U_328),U_334),U_328) ) )
& ( ( ! [U_333,U_331] :
( in(ordered_pair(U_333,U_331),U_328)
| ~ in(ordered_pair(U_331,U_333),U_329) )
& ! [U_332,U_330] :
( in(ordered_pair(U_330,U_332),U_329)
| ~ in(ordered_pair(U_332,U_330),U_328) ) )
| U_328 != relation_inverse(U_329) ) )
| ~ relation(U_328) )
| ~ relation(U_329) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_336,sK66(U_329,U_328))],[f_34_3]) ).
fof(f_34_5,plain,
! [U_329] :
( ! [U_328] :
( ( ( U_328 = relation_inverse(U_329)
| ? [U_337,U_335] :
( ~ in(ordered_pair(U_337,U_335),U_328)
& in(ordered_pair(U_335,U_337),U_329) )
| ( ~ in(ordered_pair(sK67(U_329,U_328),sK66(U_329,U_328)),U_329)
& in(ordered_pair(sK66(U_329,U_328),sK67(U_329,U_328)),U_328) ) )
& ( ( ! [U_333,U_331] :
( in(ordered_pair(U_333,U_331),U_328)
| ~ in(ordered_pair(U_331,U_333),U_329) )
& ! [U_332,U_330] :
( in(ordered_pair(U_330,U_332),U_329)
| ~ in(ordered_pair(U_332,U_330),U_328) ) )
| U_328 != relation_inverse(U_329) ) )
| ~ relation(U_328) )
| ~ relation(U_329) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_334,sK67(U_329,U_328))],[f_34_4]) ).
fof(f_34_6,plain,
! [U_329] :
( ! [U_328] :
( ( ( U_328 = relation_inverse(U_329)
| ? [U_335] :
( ~ in(ordered_pair(sK68(U_329,U_328),U_335),U_328)
& in(ordered_pair(U_335,sK68(U_329,U_328)),U_329) )
| ( ~ in(ordered_pair(sK67(U_329,U_328),sK66(U_329,U_328)),U_329)
& in(ordered_pair(sK66(U_329,U_328),sK67(U_329,U_328)),U_328) ) )
& ( ( ! [U_333,U_331] :
( in(ordered_pair(U_333,U_331),U_328)
| ~ in(ordered_pair(U_331,U_333),U_329) )
& ! [U_332,U_330] :
( in(ordered_pair(U_330,U_332),U_329)
| ~ in(ordered_pair(U_332,U_330),U_328) ) )
| U_328 != relation_inverse(U_329) ) )
| ~ relation(U_328) )
| ~ relation(U_329) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_337,sK68(U_329,U_328))],[f_34_5]) ).
fof(f_34_7,plain,
! [U_329] :
( ! [U_328] :
( ( ( U_328 = relation_inverse(U_329)
| ( ~ in(ordered_pair(sK68(U_329,U_328),sK69(U_329,U_328)),U_328)
& in(ordered_pair(sK69(U_329,U_328),sK68(U_329,U_328)),U_329) )
| ( ~ in(ordered_pair(sK67(U_329,U_328),sK66(U_329,U_328)),U_329)
& in(ordered_pair(sK66(U_329,U_328),sK67(U_329,U_328)),U_328) ) )
& ( ( ! [U_333,U_331] :
( in(ordered_pair(U_333,U_331),U_328)
| ~ in(ordered_pair(U_331,U_333),U_329) )
& ! [U_332,U_330] :
( in(ordered_pair(U_330,U_332),U_329)
| ~ in(ordered_pair(U_332,U_330),U_328) ) )
| U_328 != relation_inverse(U_329) ) )
| ~ relation(U_328) )
| ~ relation(U_329) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_335,sK69(U_329,U_328))],[f_34_6]) ).
cnf(f_34_8,plain,
( in(ordered_pair(U_330,U_332),U_329)
| ~ in(ordered_pair(U_332,U_330),U_328)
| U_328 != relation_inverse(U_329)
| ~ relation(U_328)
| ~ relation(U_329) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_9,plain,
( in(ordered_pair(U_333,U_331),U_328)
| ~ in(ordered_pair(U_331,U_333),U_329)
| U_328 != relation_inverse(U_329)
| ~ relation(U_328)
| ~ relation(U_329) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_10,plain,
( in(ordered_pair(sK69(U_329,U_328),sK68(U_329,U_328)),U_329)
| in(ordered_pair(sK66(U_329,U_328),sK67(U_329,U_328)),U_328)
| U_328 = relation_inverse(U_329)
| ~ relation(U_328)
| ~ relation(U_329) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_11,plain,
( ~ in(ordered_pair(sK68(U_329,U_328),sK69(U_329,U_328)),U_328)
| in(ordered_pair(sK66(U_329,U_328),sK67(U_329,U_328)),U_328)
| U_328 = relation_inverse(U_329)
| ~ relation(U_328)
| ~ relation(U_329) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_12,plain,
( in(ordered_pair(sK69(U_329,U_328),sK68(U_329,U_328)),U_329)
| ~ in(ordered_pair(sK67(U_329,U_328),sK66(U_329,U_328)),U_329)
| U_328 = relation_inverse(U_329)
| ~ relation(U_328)
| ~ relation(U_329) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_13,plain,
( ~ in(ordered_pair(sK68(U_329,U_328),sK69(U_329,U_328)),U_328)
| ~ in(ordered_pair(sK67(U_329,U_328),sK66(U_329,U_328)),U_329)
| U_328 = relation_inverse(U_329)
| ~ relation(U_328)
| ~ relation(U_329) ),
inference(clausify,[status(thm)],[f_34_7]) ).
fof(f_35_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_35_2,plain,
! [U_339,U_338] :
( ( disjoint(U_339,U_338)
| set_intersection2(U_339,U_338) != empty_set )
& ( set_intersection2(U_339,U_338) = empty_set
| ~ disjoint(U_339,U_338) ) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( ! [U_343,U_341] :
( disjoint(U_343,U_341)
| set_intersection2(U_343,U_341) != empty_set )
& ! [U_342,U_340] :
( set_intersection2(U_342,U_340) = empty_set
| ~ disjoint(U_342,U_340) ) ),
inference(miniscope,[status(thm)],[f_35_2]) ).
cnf(f_35_4,plain,
( set_intersection2(U_342,U_340) = empty_set
| ~ disjoint(U_342,U_340) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_5,plain,
( disjoint(U_343,U_341)
| set_intersection2(U_343,U_341) != empty_set ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_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_36_2,plain,
! [U_354] :
( ! [U_353] :
( ! [U_352] :
( ( ( U_352 = relation_composition(U_354,U_353)
| ? [U_351,U_350] :
( ( ~ in(ordered_pair(U_351,U_350),U_352)
& ? [U_349] :
( in(ordered_pair(U_349,U_350),U_353)
& in(ordered_pair(U_351,U_349),U_354) ) )
| ( ! [U_348] :
( ~ in(ordered_pair(U_348,U_350),U_353)
| ~ in(ordered_pair(U_351,U_348),U_354) )
& in(ordered_pair(U_351,U_350),U_352) ) ) )
& ( ! [U_347,U_346] :
( ( in(ordered_pair(U_347,U_346),U_352)
| ! [U_345] :
( ~ in(ordered_pair(U_345,U_346),U_353)
| ~ in(ordered_pair(U_347,U_345),U_354) ) )
& ( ? [U_344] :
( in(ordered_pair(U_344,U_346),U_353)
& in(ordered_pair(U_347,U_344),U_354) )
| ~ in(ordered_pair(U_347,U_346),U_352) ) )
| U_352 != relation_composition(U_354,U_353) ) )
| ~ relation(U_352) )
| ~ relation(U_353) )
| ~ relation(U_354) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_354] :
( ! [U_353] :
( ! [U_352] :
( ( ( U_352 = relation_composition(U_354,U_353)
| ? [U_362,U_360] :
( ~ in(ordered_pair(U_362,U_360),U_352)
& ? [U_349] :
( in(ordered_pair(U_349,U_360),U_353)
& in(ordered_pair(U_362,U_349),U_354) ) )
| ? [U_361,U_359] :
( ! [U_348] :
( ~ in(ordered_pair(U_348,U_359),U_353)
| ~ in(ordered_pair(U_361,U_348),U_354) )
& in(ordered_pair(U_361,U_359),U_352) ) )
& ( ( ! [U_358,U_356] :
( in(ordered_pair(U_358,U_356),U_352)
| ! [U_345] :
( ~ in(ordered_pair(U_345,U_356),U_353)
| ~ in(ordered_pair(U_358,U_345),U_354) ) )
& ! [U_357,U_355] :
( ? [U_344] :
( in(ordered_pair(U_344,U_355),U_353)
& in(ordered_pair(U_357,U_344),U_354) )
| ~ in(ordered_pair(U_357,U_355),U_352) ) )
| U_352 != relation_composition(U_354,U_353) ) )
| ~ relation(U_352) )
| ~ relation(U_353) )
| ~ relation(U_354) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
fof(f_36_4,plain,
! [U_354] :
( ! [U_353] :
( ! [U_352] :
( ( ( U_352 = relation_composition(U_354,U_353)
| ? [U_362,U_360] :
( ~ in(ordered_pair(U_362,U_360),U_352)
& ? [U_349] :
( in(ordered_pair(U_349,U_360),U_353)
& in(ordered_pair(U_362,U_349),U_354) ) )
| ? [U_361,U_359] :
( ! [U_348] :
( ~ in(ordered_pair(U_348,U_359),U_353)
| ~ in(ordered_pair(U_361,U_348),U_354) )
& in(ordered_pair(U_361,U_359),U_352) ) )
& ( ( ! [U_358,U_356] :
( in(ordered_pair(U_358,U_356),U_352)
| ! [U_345] :
( ~ in(ordered_pair(U_345,U_356),U_353)
| ~ in(ordered_pair(U_358,U_345),U_354) ) )
& ! [U_357,U_355] :
( ( in(ordered_pair(sK70(U_354,U_353,U_352,U_357,U_355),U_355),U_353)
& in(ordered_pair(U_357,sK70(U_354,U_353,U_352,U_357,U_355)),U_354) )
| ~ in(ordered_pair(U_357,U_355),U_352) ) )
| U_352 != relation_composition(U_354,U_353) ) )
| ~ relation(U_352) )
| ~ relation(U_353) )
| ~ relation(U_354) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_344,sK70(U_354,U_353,U_352,U_357,U_355))],[f_36_3]) ).
fof(f_36_5,plain,
! [U_354] :
( ! [U_353] :
( ! [U_352] :
( ( ( U_352 = relation_composition(U_354,U_353)
| ? [U_362,U_360] :
( ~ in(ordered_pair(U_362,U_360),U_352)
& ? [U_349] :
( in(ordered_pair(U_349,U_360),U_353)
& in(ordered_pair(U_362,U_349),U_354) ) )
| ? [U_359] :
( ! [U_348] :
( ~ in(ordered_pair(U_348,U_359),U_353)
| ~ in(ordered_pair(sK71(U_354,U_353,U_352),U_348),U_354) )
& in(ordered_pair(sK71(U_354,U_353,U_352),U_359),U_352) ) )
& ( ( ! [U_358,U_356] :
( in(ordered_pair(U_358,U_356),U_352)
| ! [U_345] :
( ~ in(ordered_pair(U_345,U_356),U_353)
| ~ in(ordered_pair(U_358,U_345),U_354) ) )
& ! [U_357,U_355] :
( ( in(ordered_pair(sK70(U_354,U_353,U_352,U_357,U_355),U_355),U_353)
& in(ordered_pair(U_357,sK70(U_354,U_353,U_352,U_357,U_355)),U_354) )
| ~ in(ordered_pair(U_357,U_355),U_352) ) )
| U_352 != relation_composition(U_354,U_353) ) )
| ~ relation(U_352) )
| ~ relation(U_353) )
| ~ relation(U_354) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_361,sK71(U_354,U_353,U_352))],[f_36_4]) ).
fof(f_36_6,plain,
! [U_354] :
( ! [U_353] :
( ! [U_352] :
( ( ( U_352 = relation_composition(U_354,U_353)
| ? [U_362,U_360] :
( ~ in(ordered_pair(U_362,U_360),U_352)
& ? [U_349] :
( in(ordered_pair(U_349,U_360),U_353)
& in(ordered_pair(U_362,U_349),U_354) ) )
| ( ! [U_348] :
( ~ in(ordered_pair(U_348,sK72(U_354,U_353,U_352)),U_353)
| ~ in(ordered_pair(sK71(U_354,U_353,U_352),U_348),U_354) )
& in(ordered_pair(sK71(U_354,U_353,U_352),sK72(U_354,U_353,U_352)),U_352) ) )
& ( ( ! [U_358,U_356] :
( in(ordered_pair(U_358,U_356),U_352)
| ! [U_345] :
( ~ in(ordered_pair(U_345,U_356),U_353)
| ~ in(ordered_pair(U_358,U_345),U_354) ) )
& ! [U_357,U_355] :
( ( in(ordered_pair(sK70(U_354,U_353,U_352,U_357,U_355),U_355),U_353)
& in(ordered_pair(U_357,sK70(U_354,U_353,U_352,U_357,U_355)),U_354) )
| ~ in(ordered_pair(U_357,U_355),U_352) ) )
| U_352 != relation_composition(U_354,U_353) ) )
| ~ relation(U_352) )
| ~ relation(U_353) )
| ~ relation(U_354) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_359,sK72(U_354,U_353,U_352))],[f_36_5]) ).
fof(f_36_7,plain,
! [U_354] :
( ! [U_353] :
( ! [U_352] :
( ( ( U_352 = relation_composition(U_354,U_353)
| ? [U_360] :
( ~ in(ordered_pair(sK73(U_354,U_353,U_352),U_360),U_352)
& ? [U_349] :
( in(ordered_pair(U_349,U_360),U_353)
& in(ordered_pair(sK73(U_354,U_353,U_352),U_349),U_354) ) )
| ( ! [U_348] :
( ~ in(ordered_pair(U_348,sK72(U_354,U_353,U_352)),U_353)
| ~ in(ordered_pair(sK71(U_354,U_353,U_352),U_348),U_354) )
& in(ordered_pair(sK71(U_354,U_353,U_352),sK72(U_354,U_353,U_352)),U_352) ) )
& ( ( ! [U_358,U_356] :
( in(ordered_pair(U_358,U_356),U_352)
| ! [U_345] :
( ~ in(ordered_pair(U_345,U_356),U_353)
| ~ in(ordered_pair(U_358,U_345),U_354) ) )
& ! [U_357,U_355] :
( ( in(ordered_pair(sK70(U_354,U_353,U_352,U_357,U_355),U_355),U_353)
& in(ordered_pair(U_357,sK70(U_354,U_353,U_352,U_357,U_355)),U_354) )
| ~ in(ordered_pair(U_357,U_355),U_352) ) )
| U_352 != relation_composition(U_354,U_353) ) )
| ~ relation(U_352) )
| ~ relation(U_353) )
| ~ relation(U_354) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_362,sK73(U_354,U_353,U_352))],[f_36_6]) ).
fof(f_36_8,plain,
! [U_354] :
( ! [U_353] :
( ! [U_352] :
( ( ( U_352 = relation_composition(U_354,U_353)
| ( ~ in(ordered_pair(sK73(U_354,U_353,U_352),sK74(U_354,U_353,U_352)),U_352)
& ? [U_349] :
( in(ordered_pair(U_349,sK74(U_354,U_353,U_352)),U_353)
& in(ordered_pair(sK73(U_354,U_353,U_352),U_349),U_354) ) )
| ( ! [U_348] :
( ~ in(ordered_pair(U_348,sK72(U_354,U_353,U_352)),U_353)
| ~ in(ordered_pair(sK71(U_354,U_353,U_352),U_348),U_354) )
& in(ordered_pair(sK71(U_354,U_353,U_352),sK72(U_354,U_353,U_352)),U_352) ) )
& ( ( ! [U_358,U_356] :
( in(ordered_pair(U_358,U_356),U_352)
| ! [U_345] :
( ~ in(ordered_pair(U_345,U_356),U_353)
| ~ in(ordered_pair(U_358,U_345),U_354) ) )
& ! [U_357,U_355] :
( ( in(ordered_pair(sK70(U_354,U_353,U_352,U_357,U_355),U_355),U_353)
& in(ordered_pair(U_357,sK70(U_354,U_353,U_352,U_357,U_355)),U_354) )
| ~ in(ordered_pair(U_357,U_355),U_352) ) )
| U_352 != relation_composition(U_354,U_353) ) )
| ~ relation(U_352) )
| ~ relation(U_353) )
| ~ relation(U_354) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_360,sK74(U_354,U_353,U_352))],[f_36_7]) ).
fof(f_36_9,plain,
! [U_354] :
( ! [U_353] :
( ! [U_352] :
( ( ( U_352 = relation_composition(U_354,U_353)
| ( ~ in(ordered_pair(sK73(U_354,U_353,U_352),sK74(U_354,U_353,U_352)),U_352)
& in(ordered_pair(sK75(U_354,U_353,U_352),sK74(U_354,U_353,U_352)),U_353)
& in(ordered_pair(sK73(U_354,U_353,U_352),sK75(U_354,U_353,U_352)),U_354) )
| ( ! [U_348] :
( ~ in(ordered_pair(U_348,sK72(U_354,U_353,U_352)),U_353)
| ~ in(ordered_pair(sK71(U_354,U_353,U_352),U_348),U_354) )
& in(ordered_pair(sK71(U_354,U_353,U_352),sK72(U_354,U_353,U_352)),U_352) ) )
& ( ( ! [U_358,U_356] :
( in(ordered_pair(U_358,U_356),U_352)
| ! [U_345] :
( ~ in(ordered_pair(U_345,U_356),U_353)
| ~ in(ordered_pair(U_358,U_345),U_354) ) )
& ! [U_357,U_355] :
( ( in(ordered_pair(sK70(U_354,U_353,U_352,U_357,U_355),U_355),U_353)
& in(ordered_pair(U_357,sK70(U_354,U_353,U_352,U_357,U_355)),U_354) )
| ~ in(ordered_pair(U_357,U_355),U_352) ) )
| U_352 != relation_composition(U_354,U_353) ) )
| ~ relation(U_352) )
| ~ relation(U_353) )
| ~ relation(U_354) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_349,sK75(U_354,U_353,U_352))],[f_36_8]) ).
cnf(f_36_10,plain,
( in(ordered_pair(U_357,sK70(U_354,U_353,U_352,U_357,U_355)),U_354)
| ~ in(ordered_pair(U_357,U_355),U_352)
| U_352 != relation_composition(U_354,U_353)
| ~ relation(U_352)
| ~ relation(U_353)
| ~ relation(U_354) ),
inference(clausify,[status(thm)],[f_36_9]) ).
cnf(f_36_11,plain,
( in(ordered_pair(sK70(U_354,U_353,U_352,U_357,U_355),U_355),U_353)
| ~ in(ordered_pair(U_357,U_355),U_352)
| U_352 != relation_composition(U_354,U_353)
| ~ relation(U_352)
| ~ relation(U_353)
| ~ relation(U_354) ),
inference(clausify,[status(thm)],[f_36_9]) ).
cnf(f_36_12,plain,
( in(ordered_pair(U_358,U_356),U_352)
| ~ in(ordered_pair(U_345,U_356),U_353)
| ~ in(ordered_pair(U_358,U_345),U_354)
| U_352 != relation_composition(U_354,U_353)
| ~ relation(U_352)
| ~ relation(U_353)
| ~ relation(U_354) ),
inference(clausify,[status(thm)],[f_36_9]) ).
cnf(f_36_13,plain,
( in(ordered_pair(sK73(U_354,U_353,U_352),sK75(U_354,U_353,U_352)),U_354)
| in(ordered_pair(sK71(U_354,U_353,U_352),sK72(U_354,U_353,U_352)),U_352)
| U_352 = relation_composition(U_354,U_353)
| ~ relation(U_352)
| ~ relation(U_353)
| ~ relation(U_354) ),
inference(clausify,[status(thm)],[f_36_9]) ).
cnf(f_36_14,plain,
( in(ordered_pair(sK75(U_354,U_353,U_352),sK74(U_354,U_353,U_352)),U_353)
| in(ordered_pair(sK71(U_354,U_353,U_352),sK72(U_354,U_353,U_352)),U_352)
| U_352 = relation_composition(U_354,U_353)
| ~ relation(U_352)
| ~ relation(U_353)
| ~ relation(U_354) ),
inference(clausify,[status(thm)],[f_36_9]) ).
cnf(f_36_15,plain,
( ~ in(ordered_pair(sK73(U_354,U_353,U_352),sK74(U_354,U_353,U_352)),U_352)
| in(ordered_pair(sK71(U_354,U_353,U_352),sK72(U_354,U_353,U_352)),U_352)
| U_352 = relation_composition(U_354,U_353)
| ~ relation(U_352)
| ~ relation(U_353)
| ~ relation(U_354) ),
inference(clausify,[status(thm)],[f_36_9]) ).
cnf(f_36_16,plain,
( in(ordered_pair(sK73(U_354,U_353,U_352),sK75(U_354,U_353,U_352)),U_354)
| ~ in(ordered_pair(U_348,sK72(U_354,U_353,U_352)),U_353)
| ~ in(ordered_pair(sK71(U_354,U_353,U_352),U_348),U_354)
| U_352 = relation_composition(U_354,U_353)
| ~ relation(U_352)
| ~ relation(U_353)
| ~ relation(U_354) ),
inference(clausify,[status(thm)],[f_36_9]) ).
cnf(f_36_17,plain,
( in(ordered_pair(sK75(U_354,U_353,U_352),sK74(U_354,U_353,U_352)),U_353)
| ~ in(ordered_pair(U_348,sK72(U_354,U_353,U_352)),U_353)
| ~ in(ordered_pair(sK71(U_354,U_353,U_352),U_348),U_354)
| U_352 = relation_composition(U_354,U_353)
| ~ relation(U_352)
| ~ relation(U_353)
| ~ relation(U_354) ),
inference(clausify,[status(thm)],[f_36_9]) ).
cnf(f_36_18,plain,
( ~ in(ordered_pair(sK73(U_354,U_353,U_352),sK74(U_354,U_353,U_352)),U_352)
| ~ in(ordered_pair(U_348,sK72(U_354,U_353,U_352)),U_353)
| ~ in(ordered_pair(sK71(U_354,U_353,U_352),U_348),U_354)
| U_352 = relation_composition(U_354,U_353)
| ~ relation(U_352)
| ~ relation(U_353)
| ~ relation(U_354) ),
inference(clausify,[status(thm)],[f_36_9]) ).
fof(f_37_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_37_2,plain,
! [U_367,U_366] :
( ! [U_365] :
( ( ( U_365 = complements_of_subsets(U_367,U_366)
| ? [U_364] :
( ( ( ~ in(U_364,U_365)
& in(subset_complement(U_367,U_364),U_366) )
| ( ~ in(subset_complement(U_367,U_364),U_366)
& in(U_364,U_365) ) )
& element(U_364,powerset(U_367)) ) )
& ( ! [U_363] :
( ( ( in(U_363,U_365)
| ~ in(subset_complement(U_367,U_363),U_366) )
& ( in(subset_complement(U_367,U_363),U_366)
| ~ in(U_363,U_365) ) )
| ~ element(U_363,powerset(U_367)) )
| U_365 != complements_of_subsets(U_367,U_366) ) )
| ~ element(U_365,powerset(powerset(U_367))) )
| ~ element(U_366,powerset(powerset(U_367))) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_367,U_366] :
( ! [U_365] :
( ( ( U_365 = complements_of_subsets(U_367,U_366)
| ( ( ( ~ in(sK76(U_367,U_366,U_365),U_365)
& in(subset_complement(U_367,sK76(U_367,U_366,U_365)),U_366) )
| ( ~ in(subset_complement(U_367,sK76(U_367,U_366,U_365)),U_366)
& in(sK76(U_367,U_366,U_365),U_365) ) )
& element(sK76(U_367,U_366,U_365),powerset(U_367)) ) )
& ( ! [U_363] :
( ( ( in(U_363,U_365)
| ~ in(subset_complement(U_367,U_363),U_366) )
& ( in(subset_complement(U_367,U_363),U_366)
| ~ in(U_363,U_365) ) )
| ~ element(U_363,powerset(U_367)) )
| U_365 != complements_of_subsets(U_367,U_366) ) )
| ~ element(U_365,powerset(powerset(U_367))) )
| ~ element(U_366,powerset(powerset(U_367))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_364,sK76(U_367,U_366,U_365))],[f_37_2]) ).
cnf(f_37_4,plain,
( in(subset_complement(U_367,U_363),U_366)
| ~ in(U_363,U_365)
| ~ element(U_363,powerset(U_367))
| U_365 != complements_of_subsets(U_367,U_366)
| ~ element(U_365,powerset(powerset(U_367)))
| ~ element(U_366,powerset(powerset(U_367))) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_5,plain,
( in(U_363,U_365)
| ~ in(subset_complement(U_367,U_363),U_366)
| ~ element(U_363,powerset(U_367))
| U_365 != complements_of_subsets(U_367,U_366)
| ~ element(U_365,powerset(powerset(U_367)))
| ~ element(U_366,powerset(powerset(U_367))) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_6,plain,
( element(sK76(U_367,U_366,U_365),powerset(U_367))
| U_365 = complements_of_subsets(U_367,U_366)
| ~ element(U_365,powerset(powerset(U_367)))
| ~ element(U_366,powerset(powerset(U_367))) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_7,plain,
( in(subset_complement(U_367,sK76(U_367,U_366,U_365)),U_366)
| in(sK76(U_367,U_366,U_365),U_365)
| U_365 = complements_of_subsets(U_367,U_366)
| ~ element(U_365,powerset(powerset(U_367)))
| ~ element(U_366,powerset(powerset(U_367))) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_8,plain,
( ~ in(sK76(U_367,U_366,U_365),U_365)
| in(sK76(U_367,U_366,U_365),U_365)
| U_365 = complements_of_subsets(U_367,U_366)
| ~ element(U_365,powerset(powerset(U_367)))
| ~ element(U_366,powerset(powerset(U_367))) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_9,plain,
( in(subset_complement(U_367,sK76(U_367,U_366,U_365)),U_366)
| ~ in(subset_complement(U_367,sK76(U_367,U_366,U_365)),U_366)
| U_365 = complements_of_subsets(U_367,U_366)
| ~ element(U_365,powerset(powerset(U_367)))
| ~ element(U_366,powerset(powerset(U_367))) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_10,plain,
( ~ in(sK76(U_367,U_366,U_365),U_365)
| ~ in(subset_complement(U_367,sK76(U_367,U_366,U_365)),U_366)
| U_365 = complements_of_subsets(U_367,U_366)
| ~ element(U_365,powerset(powerset(U_367)))
| ~ element(U_366,powerset(powerset(U_367))) ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_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_38_2,plain,
! [U_369,U_368] :
( ( proper_subset(U_369,U_368)
| U_369 = U_368
| ~ subset(U_369,U_368) )
& ( ( U_369 != U_368
& subset(U_369,U_368) )
| ~ proper_subset(U_369,U_368) ) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
( ! [U_373,U_371] :
( proper_subset(U_373,U_371)
| U_373 = U_371
| ~ subset(U_373,U_371) )
& ! [U_372,U_370] :
( ( U_372 != U_370
& subset(U_372,U_370) )
| ~ proper_subset(U_372,U_370) ) ),
inference(miniscope,[status(thm)],[f_38_2]) ).
cnf(f_38_4,plain,
( subset(U_372,U_370)
| ~ proper_subset(U_372,U_370) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_5,plain,
( U_372 != U_370
| ~ proper_subset(U_372,U_370) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_6,plain,
( proper_subset(U_373,U_371)
| U_373 = U_371
| ~ subset(U_373,U_371) ),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k10_relat_1]) ).
cnf(f_39_2,plain,
$true,
inference(clausify,[status(thm)],[f_39_1]) ).
fof(f_40_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
cnf(f_40_2,plain,
$true,
inference(clausify,[status(thm)],[f_40_1]) ).
fof(f_41_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_setfam_1]) ).
cnf(f_41_2,plain,
$true,
inference(clausify,[status(thm)],[f_41_1]) ).
fof(f_42_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
cnf(f_42_2,plain,
$true,
inference(clausify,[status(thm)],[f_42_1]) ).
fof(f_43_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_43_2,plain,
$true,
inference(clausify,[status(thm)],[f_43_1]) ).
fof(f_44_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_44_2,plain,
$true,
inference(clausify,[status(thm)],[f_44_1]) ).
fof(f_45_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_relat_1]) ).
cnf(f_45_2,plain,
$true,
inference(clausify,[status(thm)],[f_45_1]) ).
fof(f_46_1,plain,
! [A] : element(cast_to_subset(A),powerset(A)),
inference(fof_nnf,[status(thm)],[dt_k2_subset_1]) ).
fof(f_46_2,plain,
! [U_374] : element(cast_to_subset(U_374),powerset(U_374)),
inference(variable_rename,[status(thm)],[f_46_1]) ).
cnf(f_46_3,plain,
element(cast_to_subset(U_374),powerset(U_374)),
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
cnf(f_47_2,plain,
$true,
inference(clausify,[status(thm)],[f_47_1]) ).
fof(f_48_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
cnf(f_48_2,plain,
$true,
inference(clausify,[status(thm)],[f_48_1]) ).
fof(f_49_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
cnf(f_49_2,plain,
$true,
inference(clausify,[status(thm)],[f_49_1]) ).
fof(f_50_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_relat_1]) ).
cnf(f_50_2,plain,
$true,
inference(clausify,[status(thm)],[f_50_1]) ).
fof(f_51_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_51_2,plain,
! [U_376,U_375] :
( element(subset_complement(U_376,U_375),powerset(U_376))
| ~ element(U_375,powerset(U_376)) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
cnf(f_51_3,plain,
( element(subset_complement(U_376,U_375),powerset(U_376))
| ~ element(U_375,powerset(U_376)) ),
inference(clausify,[status(thm)],[f_51_2]) ).
fof(f_52_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_tarski]) ).
cnf(f_52_2,plain,
$true,
inference(clausify,[status(thm)],[f_52_1]) ).
fof(f_53_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
cnf(f_53_2,plain,
$true,
inference(clausify,[status(thm)],[f_53_1]) ).
fof(f_54_1,plain,
! [A] :
( relation(relation_inverse(A))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k4_relat_1]) ).
fof(f_54_2,plain,
! [U_377] :
( relation(relation_inverse(U_377))
| ~ relation(U_377) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
cnf(f_54_3,plain,
( relation(relation_inverse(U_377))
| ~ relation(U_377) ),
inference(clausify,[status(thm)],[f_54_2]) ).
fof(f_55_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
cnf(f_55_2,plain,
$true,
inference(clausify,[status(thm)],[f_55_1]) ).
fof(f_56_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
cnf(f_56_2,plain,
$true,
inference(clausify,[status(thm)],[f_56_1]) ).
fof(f_57_1,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_relat_1]) ).
fof(f_57_2,plain,
! [U_379,U_378] :
( relation(relation_composition(U_379,U_378))
| ~ relation(U_378)
| ~ relation(U_379) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
cnf(f_57_3,plain,
( relation(relation_composition(U_379,U_378))
| ~ relation(U_378)
| ~ relation(U_379) ),
inference(clausify,[status(thm)],[f_57_2]) ).
fof(f_58_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_58_2,plain,
! [U_381,U_380] :
( element(union_of_subsets(U_381,U_380),powerset(U_381))
| ~ element(U_380,powerset(powerset(U_381))) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
cnf(f_58_3,plain,
( element(union_of_subsets(U_381,U_380),powerset(U_381))
| ~ element(U_380,powerset(powerset(U_381))) ),
inference(clausify,[status(thm)],[f_58_2]) ).
fof(f_59_1,plain,
! [A] : relation(identity_relation(A)),
inference(fof_nnf,[status(thm)],[dt_k6_relat_1]) ).
fof(f_59_2,plain,
! [U_382] : relation(identity_relation(U_382)),
inference(variable_rename,[status(thm)],[f_59_1]) ).
cnf(f_59_3,plain,
relation(identity_relation(U_382)),
inference(clausify,[status(thm)],[f_59_2]) ).
fof(f_60_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_60_2,plain,
! [U_384,U_383] :
( element(meet_of_subsets(U_384,U_383),powerset(U_384))
| ~ element(U_383,powerset(powerset(U_384))) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
cnf(f_60_3,plain,
( element(meet_of_subsets(U_384,U_383),powerset(U_384))
| ~ element(U_383,powerset(powerset(U_384))) ),
inference(clausify,[status(thm)],[f_60_2]) ).
fof(f_61_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_61_2,plain,
! [U_387,U_386,U_385] :
( element(subset_difference(U_387,U_386,U_385),powerset(U_387))
| ~ element(U_385,powerset(U_387))
| ~ element(U_386,powerset(U_387)) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
cnf(f_61_3,plain,
( element(subset_difference(U_387,U_386,U_385),powerset(U_387))
| ~ element(U_385,powerset(U_387))
| ~ element(U_386,powerset(U_387)) ),
inference(clausify,[status(thm)],[f_61_2]) ).
fof(f_62_1,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k7_relat_1]) ).
fof(f_62_2,plain,
! [U_389,U_388] :
( relation(relation_dom_restriction(U_389,U_388))
| ~ relation(U_389) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
! [U_389] :
( ! [U_388] : relation(relation_dom_restriction(U_389,U_388))
| ~ relation(U_389) ),
inference(miniscope,[status(thm)],[f_62_2]) ).
cnf(f_62_4,plain,
( relation(relation_dom_restriction(U_389,U_388))
| ~ relation(U_389) ),
inference(clausify,[status(thm)],[f_62_3]) ).
fof(f_63_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_63_2,plain,
! [U_391,U_390] :
( element(complements_of_subsets(U_391,U_390),powerset(powerset(U_391)))
| ~ element(U_390,powerset(powerset(U_391))) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
cnf(f_63_3,plain,
( element(complements_of_subsets(U_391,U_390),powerset(powerset(U_391)))
| ~ element(U_390,powerset(powerset(U_391))) ),
inference(clausify,[status(thm)],[f_63_2]) ).
fof(f_64_1,plain,
! [A,B] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[dt_k8_relat_1]) ).
fof(f_64_2,plain,
! [U_393,U_392] :
( relation(relation_rng_restriction(U_393,U_392))
| ~ relation(U_392) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
cnf(f_64_3,plain,
( relation(relation_rng_restriction(U_393,U_392))
| ~ relation(U_392) ),
inference(clausify,[status(thm)],[f_64_2]) ).
fof(f_65_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k9_relat_1]) ).
cnf(f_65_2,plain,
$true,
inference(clausify,[status(thm)],[f_65_1]) ).
fof(f_66_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_66_2,plain,
$true,
inference(clausify,[status(thm)],[f_66_1]) ).
fof(f_67_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_67_2,plain,
! [U_395] :
? [U_394] : element(U_394,U_395),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
! [U_395] : element(sK77(U_395),U_395),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_394,sK77(U_395))],[f_67_2]) ).
cnf(f_67_4,plain,
element(sK77(U_395),U_395),
inference(clausify,[status(thm)],[f_67_3]) ).
fof(f_68_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_68_2,plain,
! [U_397,U_396] :
( ( relation(relation_composition(U_396,U_397))
& empty(relation_composition(U_396,U_397)) )
| ~ relation(U_396)
| ~ empty(U_397) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
cnf(f_68_3,plain,
( empty(relation_composition(U_396,U_397))
| ~ relation(U_396)
| ~ empty(U_397) ),
inference(clausify,[status(thm)],[f_68_2]) ).
cnf(f_68_4,plain,
( relation(relation_composition(U_396,U_397))
| ~ relation(U_396)
| ~ empty(U_397) ),
inference(clausify,[status(thm)],[f_68_2]) ).
fof(f_69_1,plain,
! [A,B] :
( relation(set_intersection2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc1_relat_1]) ).
fof(f_69_2,plain,
! [U_399,U_398] :
( relation(set_intersection2(U_399,U_398))
| ~ relation(U_398)
| ~ relation(U_399) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
cnf(f_69_3,plain,
( relation(set_intersection2(U_399,U_398))
| ~ relation(U_398)
| ~ relation(U_399) ),
inference(clausify,[status(thm)],[f_69_2]) ).
fof(f_70_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_70_2,plain,
! [U_400] : ~ empty(powerset(U_400)),
inference(variable_rename,[status(thm)],[f_70_1]) ).
cnf(f_70_3,plain,
~ empty(powerset(U_400)),
inference(clausify,[status(thm)],[f_70_2]) ).
fof(f_71_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_71_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_71_1]) ).
fof(f_72_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_72_2,plain,
! [U_402,U_401] : ~ empty(ordered_pair(U_402,U_401)),
inference(variable_rename,[status(thm)],[f_72_1]) ).
cnf(f_72_3,plain,
~ empty(ordered_pair(U_402,U_401)),
inference(clausify,[status(thm)],[f_72_2]) ).
fof(f_73_1,plain,
! [A,B] :
( relation(set_union2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc2_relat_1]) ).
fof(f_73_2,plain,
! [U_404,U_403] :
( relation(set_union2(U_404,U_403))
| ~ relation(U_403)
| ~ relation(U_404) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
cnf(f_73_3,plain,
( relation(set_union2(U_404,U_403))
| ~ relation(U_403)
| ~ relation(U_404) ),
inference(clausify,[status(thm)],[f_73_2]) ).
fof(f_74_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_74_2,plain,
! [U_405] : ~ empty(singleton(U_405)),
inference(variable_rename,[status(thm)],[f_74_1]) ).
cnf(f_74_3,plain,
~ empty(singleton(U_405)),
inference(clausify,[status(thm)],[f_74_2]) ).
fof(f_75_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_75_2,plain,
! [U_407,U_406] :
( ~ empty(set_union2(U_407,U_406))
| empty(U_407) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
fof(f_75_3,plain,
! [U_407] :
( ! [U_406] : ~ empty(set_union2(U_407,U_406))
| empty(U_407) ),
inference(miniscope,[status(thm)],[f_75_2]) ).
cnf(f_75_4,plain,
( ~ empty(set_union2(U_407,U_406))
| empty(U_407) ),
inference(clausify,[status(thm)],[f_75_3]) ).
fof(f_76_1,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_76_2,plain,
! [U_409,U_408] : ~ empty(unordered_pair(U_409,U_408)),
inference(variable_rename,[status(thm)],[f_76_1]) ).
cnf(f_76_3,plain,
~ empty(unordered_pair(U_409,U_408)),
inference(clausify,[status(thm)],[f_76_2]) ).
fof(f_77_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_77_2,plain,
! [U_411,U_410] :
( ~ empty(set_union2(U_410,U_411))
| empty(U_411) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
fof(f_77_3,plain,
! [U_411] :
( ! [U_410] : ~ empty(set_union2(U_410,U_411))
| empty(U_411) ),
inference(miniscope,[status(thm)],[f_77_2]) ).
cnf(f_77_4,plain,
( ~ empty(set_union2(U_410,U_411))
| empty(U_411) ),
inference(clausify,[status(thm)],[f_77_3]) ).
fof(f_78_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_78_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_78_1]) ).
cnf(f_78_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_78_1]) ).
fof(f_79_1,plain,
! [A,B] :
( ~ empty(cartesian_product2(A,B))
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc4_subset_1]) ).
fof(f_79_2,plain,
! [U_413,U_412] :
( ~ empty(cartesian_product2(U_413,U_412))
| empty(U_412)
| empty(U_413) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
cnf(f_79_3,plain,
( ~ empty(cartesian_product2(U_413,U_412))
| empty(U_412)
| empty(U_413) ),
inference(clausify,[status(thm)],[f_79_2]) ).
fof(f_80_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_80_2,plain,
! [U_414] :
( ~ empty(relation_dom(U_414))
| ~ relation(U_414)
| empty(U_414) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
cnf(f_80_3,plain,
( ~ empty(relation_dom(U_414))
| ~ relation(U_414)
| empty(U_414) ),
inference(clausify,[status(thm)],[f_80_2]) ).
fof(f_81_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_81_2,plain,
! [U_415] :
( ~ empty(relation_rng(U_415))
| ~ relation(U_415)
| empty(U_415) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
cnf(f_81_3,plain,
( ~ empty(relation_rng(U_415))
| ~ relation(U_415)
| empty(U_415) ),
inference(clausify,[status(thm)],[f_81_2]) ).
fof(f_82_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_82_2,plain,
! [U_416] :
( ( relation(relation_dom(U_416))
& empty(relation_dom(U_416)) )
| ~ empty(U_416) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
cnf(f_82_3,plain,
( empty(relation_dom(U_416))
| ~ empty(U_416) ),
inference(clausify,[status(thm)],[f_82_2]) ).
cnf(f_82_4,plain,
( relation(relation_dom(U_416))
| ~ empty(U_416) ),
inference(clausify,[status(thm)],[f_82_2]) ).
fof(f_83_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_83_2,plain,
! [U_417] :
( ( relation(relation_rng(U_417))
& empty(relation_rng(U_417)) )
| ~ empty(U_417) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
cnf(f_83_3,plain,
( empty(relation_rng(U_417))
| ~ empty(U_417) ),
inference(clausify,[status(thm)],[f_83_2]) ).
cnf(f_83_4,plain,
( relation(relation_rng(U_417))
| ~ empty(U_417) ),
inference(clausify,[status(thm)],[f_83_2]) ).
fof(f_84_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_84_2,plain,
! [U_419,U_418] :
( ( relation(relation_composition(U_419,U_418))
& empty(relation_composition(U_419,U_418)) )
| ~ relation(U_418)
| ~ empty(U_419) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
cnf(f_84_3,plain,
( empty(relation_composition(U_419,U_418))
| ~ relation(U_418)
| ~ empty(U_419) ),
inference(clausify,[status(thm)],[f_84_2]) ).
cnf(f_84_4,plain,
( relation(relation_composition(U_419,U_418))
| ~ relation(U_418)
| ~ empty(U_419) ),
inference(clausify,[status(thm)],[f_84_2]) ).
fof(f_85_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_85_2,plain,
! [U_421,U_420] : set_union2(U_421,U_421) = U_421,
inference(variable_rename,[status(thm)],[f_85_1]) ).
fof(f_85_3,plain,
! [U_421] : set_union2(U_421,U_421) = U_421,
inference(miniscope,[status(thm)],[f_85_2]) ).
cnf(f_85_4,plain,
set_union2(U_421,U_421) = U_421,
inference(clausify,[status(thm)],[f_85_3]) ).
fof(f_86_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_86_2,plain,
! [U_423,U_422] : set_intersection2(U_423,U_423) = U_423,
inference(variable_rename,[status(thm)],[f_86_1]) ).
fof(f_86_3,plain,
! [U_423] : set_intersection2(U_423,U_423) = U_423,
inference(miniscope,[status(thm)],[f_86_2]) ).
cnf(f_86_4,plain,
set_intersection2(U_423,U_423) = U_423,
inference(clausify,[status(thm)],[f_86_3]) ).
fof(f_87_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_87_2,plain,
! [U_425,U_424] :
( subset_complement(U_425,subset_complement(U_425,U_424)) = U_424
| ~ element(U_424,powerset(U_425)) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
cnf(f_87_3,plain,
( subset_complement(U_425,subset_complement(U_425,U_424)) = U_424
| ~ element(U_424,powerset(U_425)) ),
inference(clausify,[status(thm)],[f_87_2]) ).
fof(f_88_1,plain,
! [A] :
( relation_inverse(relation_inverse(A)) = A
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[involutiveness_k4_relat_1]) ).
fof(f_88_2,plain,
! [U_426] :
( relation_inverse(relation_inverse(U_426)) = U_426
| ~ relation(U_426) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
cnf(f_88_3,plain,
( relation_inverse(relation_inverse(U_426)) = U_426
| ~ relation(U_426) ),
inference(clausify,[status(thm)],[f_88_2]) ).
fof(f_89_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_89_2,plain,
! [U_428,U_427] :
( complements_of_subsets(U_428,complements_of_subsets(U_428,U_427)) = U_427
| ~ element(U_427,powerset(powerset(U_428))) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
cnf(f_89_3,plain,
( complements_of_subsets(U_428,complements_of_subsets(U_428,U_427)) = U_427
| ~ element(U_427,powerset(powerset(U_428))) ),
inference(clausify,[status(thm)],[f_89_2]) ).
fof(f_90_1,plain,
! [A,B] : ~ proper_subset(A,A),
inference(fof_nnf,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(f_90_2,plain,
! [U_430,U_429] : ~ proper_subset(U_430,U_430),
inference(variable_rename,[status(thm)],[f_90_1]) ).
fof(f_90_3,plain,
! [U_430] : ~ proper_subset(U_430,U_430),
inference(miniscope,[status(thm)],[f_90_2]) ).
cnf(f_90_4,plain,
~ proper_subset(U_430,U_430),
inference(clausify,[status(thm)],[f_90_3]) ).
fof(f_91_1,plain,
! [A] : singleton(A) != empty_set,
inference(fof_nnf,[status(thm)],[l1_zfmisc_1]) ).
fof(f_91_2,plain,
! [U_431] : singleton(U_431) != empty_set,
inference(variable_rename,[status(thm)],[f_91_1]) ).
cnf(f_91_3,plain,
singleton(U_431) != empty_set,
inference(clausify,[status(thm)],[f_91_2]) ).
fof(f_92_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l23_zfmisc_1]) ).
fof(f_92_2,plain,
! [U_433,U_432] :
( set_union2(singleton(U_433),U_432) = U_432
| ~ in(U_433,U_432) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
cnf(f_92_3,plain,
( set_union2(singleton(U_433),U_432) = U_432
| ~ in(U_433,U_432) ),
inference(clausify,[status(thm)],[f_92_2]) ).
fof(f_93_1,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(fof_nnf,[status(thm)],[l25_zfmisc_1]) ).
fof(f_93_2,plain,
! [U_435,U_434] :
( ~ in(U_435,U_434)
| ~ disjoint(singleton(U_435),U_434) ),
inference(variable_rename,[status(thm)],[f_93_1]) ).
cnf(f_93_3,plain,
( ~ in(U_435,U_434)
| ~ disjoint(singleton(U_435),U_434) ),
inference(clausify,[status(thm)],[f_93_2]) ).
fof(f_94_1,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(fof_nnf,[status(thm)],[l28_zfmisc_1]) ).
fof(f_94_2,plain,
! [U_437,U_436] :
( disjoint(singleton(U_437),U_436)
| in(U_437,U_436) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
cnf(f_94_3,plain,
( disjoint(singleton(U_437),U_436)
| in(U_437,U_436) ),
inference(clausify,[status(thm)],[f_94_2]) ).
fof(f_95_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_95_2,plain,
! [U_439,U_438] :
( ( subset(singleton(U_439),U_438)
| ~ in(U_439,U_438) )
& ( in(U_439,U_438)
| ~ subset(singleton(U_439),U_438) ) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
fof(f_95_3,plain,
( ! [U_443,U_441] :
( subset(singleton(U_443),U_441)
| ~ in(U_443,U_441) )
& ! [U_442,U_440] :
( in(U_442,U_440)
| ~ subset(singleton(U_442),U_440) ) ),
inference(miniscope,[status(thm)],[f_95_2]) ).
cnf(f_95_4,plain,
( in(U_442,U_440)
| ~ subset(singleton(U_442),U_440) ),
inference(clausify,[status(thm)],[f_95_3]) ).
cnf(f_95_5,plain,
( subset(singleton(U_443),U_441)
| ~ in(U_443,U_441) ),
inference(clausify,[status(thm)],[f_95_3]) ).
fof(f_96_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_96_2,plain,
! [U_445,U_444] :
( ( set_difference(U_445,U_444) = empty_set
| ~ subset(U_445,U_444) )
& ( subset(U_445,U_444)
| set_difference(U_445,U_444) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_96_1]) ).
fof(f_96_3,plain,
( ! [U_449,U_447] :
( set_difference(U_449,U_447) = empty_set
| ~ subset(U_449,U_447) )
& ! [U_448,U_446] :
( subset(U_448,U_446)
| set_difference(U_448,U_446) != empty_set ) ),
inference(miniscope,[status(thm)],[f_96_2]) ).
cnf(f_96_4,plain,
( subset(U_448,U_446)
| set_difference(U_448,U_446) != empty_set ),
inference(clausify,[status(thm)],[f_96_3]) ).
cnf(f_96_5,plain,
( set_difference(U_449,U_447) = empty_set
| ~ subset(U_449,U_447) ),
inference(clausify,[status(thm)],[f_96_3]) ).
fof(f_97_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_97_2,plain,
! [U_452,U_451] :
( ! [U_450] :
( in(U_450,U_452)
| ~ in(U_450,U_451) )
| ~ element(U_451,powerset(U_452)) ),
inference(variable_rename,[status(thm)],[f_97_1]) ).
cnf(f_97_3,plain,
( in(U_450,U_452)
| ~ in(U_450,U_451)
| ~ element(U_451,powerset(U_452)) ),
inference(clausify,[status(thm)],[f_97_2]) ).
fof(f_98_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_98_2,plain,
! [U_455,U_454,U_453] :
( subset(U_455,set_difference(U_454,singleton(U_453)))
| in(U_453,U_455)
| ~ subset(U_455,U_454) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
fof(f_98_3,plain,
! [U_455,U_454] :
( ! [U_453] :
( subset(U_455,set_difference(U_454,singleton(U_453)))
| in(U_453,U_455) )
| ~ subset(U_455,U_454) ),
inference(miniscope,[status(thm)],[f_98_2]) ).
cnf(f_98_4,plain,
( subset(U_455,set_difference(U_454,singleton(U_453)))
| in(U_453,U_455)
| ~ subset(U_455,U_454) ),
inference(clausify,[status(thm)],[f_98_3]) ).
fof(f_99_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_99_2,plain,
! [U_457,U_456] :
( ( subset(U_457,singleton(U_456))
| ( U_457 != singleton(U_456)
& U_457 != empty_set ) )
& ( U_457 = singleton(U_456)
| U_457 = empty_set
| ~ subset(U_457,singleton(U_456)) ) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
fof(f_99_3,plain,
( ! [U_461,U_459] :
( subset(U_461,singleton(U_459))
| ( U_461 != singleton(U_459)
& U_461 != empty_set ) )
& ! [U_460,U_458] :
( U_460 = singleton(U_458)
| U_460 = empty_set
| ~ subset(U_460,singleton(U_458)) ) ),
inference(miniscope,[status(thm)],[f_99_2]) ).
cnf(f_99_4,plain,
( U_460 = singleton(U_458)
| U_460 = empty_set
| ~ subset(U_460,singleton(U_458)) ),
inference(clausify,[status(thm)],[f_99_3]) ).
cnf(f_99_5,plain,
( U_461 != empty_set
| subset(U_461,singleton(U_459)) ),
inference(clausify,[status(thm)],[f_99_3]) ).
cnf(f_99_6,plain,
( U_461 != singleton(U_459)
| subset(U_461,singleton(U_459)) ),
inference(clausify,[status(thm)],[f_99_3]) ).
fof(f_100_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l50_zfmisc_1]) ).
fof(f_100_2,plain,
! [U_463,U_462] :
( subset(U_463,union(U_462))
| ~ in(U_463,U_462) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
cnf(f_100_3,plain,
( subset(U_463,union(U_462))
| ~ in(U_463,U_462) ),
inference(clausify,[status(thm)],[f_100_2]) ).
fof(f_101_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_101_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_101_1]) ).
fof(f_101_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_101_2]) ).
cnf(f_101_4,plain,
( in(U_474,U_470)
| ~ in(ordered_pair(U_474,U_472),cartesian_product2(U_470,U_468)) ),
inference(clausify,[status(thm)],[f_101_3]) ).
cnf(f_101_5,plain,
( in(U_472,U_468)
| ~ in(ordered_pair(U_474,U_472),cartesian_product2(U_470,U_468)) ),
inference(clausify,[status(thm)],[f_101_3]) ).
cnf(f_101_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_101_3]) ).
fof(f_102_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_102_2,plain,
! [U_478,U_477] :
( element(U_478,powerset(U_477))
| ? [U_476] :
( ~ in(U_476,U_477)
& in(U_476,U_478) ) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
fof(f_102_3,plain,
! [U_478,U_477] :
( element(U_478,powerset(U_477))
| ( ~ in(sK78(U_478,U_477),U_477)
& in(sK78(U_478,U_477),U_478) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_476,sK78(U_478,U_477))],[f_102_2]) ).
cnf(f_102_4,plain,
( in(sK78(U_478,U_477),U_478)
| element(U_478,powerset(U_477)) ),
inference(clausify,[status(thm)],[f_102_3]) ).
cnf(f_102_5,plain,
( ~ in(sK78(U_478,U_477),U_477)
| element(U_478,powerset(U_477)) ),
inference(clausify,[status(thm)],[f_102_3]) ).
fof(f_103_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_103_2,plain,
? [U_479] :
( relation(U_479)
& empty(U_479) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
fof(f_103_3,plain,
( relation(sK79)
& empty(sK79) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_479,sK79)],[f_103_2]) ).
cnf(f_103_4,plain,
empty(sK79),
inference(clausify,[status(thm)],[f_103_3]) ).
cnf(f_103_5,plain,
relation(sK79),
inference(clausify,[status(thm)],[f_103_3]) ).
fof(f_104_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_104_2,plain,
! [U_481] :
( ? [U_480] :
( ~ empty(U_480)
& element(U_480,powerset(U_481)) )
| empty(U_481) ),
inference(variable_rename,[status(thm)],[f_104_1]) ).
fof(f_104_3,plain,
! [U_481] :
( ( ~ empty(sK80(U_481))
& element(sK80(U_481),powerset(U_481)) )
| empty(U_481) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_480,sK80(U_481))],[f_104_2]) ).
cnf(f_104_4,plain,
( element(sK80(U_481),powerset(U_481))
| empty(U_481) ),
inference(clausify,[status(thm)],[f_104_3]) ).
cnf(f_104_5,plain,
( ~ empty(sK80(U_481))
| empty(U_481) ),
inference(clausify,[status(thm)],[f_104_3]) ).
fof(f_105_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_105_2,plain,
? [U_482] : empty(U_482),
inference(variable_rename,[status(thm)],[f_105_1]) ).
fof(f_105_3,plain,
empty(sK81),
inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_482,sK81)],[f_105_2]) ).
cnf(f_105_4,plain,
empty(sK81),
inference(clausify,[status(thm)],[f_105_3]) ).
fof(f_106_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_106_2,plain,
? [U_483] :
( relation(U_483)
& ~ empty(U_483) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
fof(f_106_3,plain,
( relation(sK82)
& ~ empty(sK82) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_483,sK82)],[f_106_2]) ).
cnf(f_106_4,plain,
~ empty(sK82),
inference(clausify,[status(thm)],[f_106_3]) ).
cnf(f_106_5,plain,
relation(sK82),
inference(clausify,[status(thm)],[f_106_3]) ).
fof(f_107_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_107_2,plain,
! [U_485] :
? [U_484] :
( empty(U_484)
& element(U_484,powerset(U_485)) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
fof(f_107_3,plain,
! [U_485] :
( empty(sK83(U_485))
& element(sK83(U_485),powerset(U_485)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_484,sK83(U_485))],[f_107_2]) ).
cnf(f_107_4,plain,
element(sK83(U_485),powerset(U_485)),
inference(clausify,[status(thm)],[f_107_3]) ).
cnf(f_107_5,plain,
empty(sK83(U_485)),
inference(clausify,[status(thm)],[f_107_3]) ).
fof(f_108_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_108_2,plain,
? [U_486] : ~ empty(U_486),
inference(variable_rename,[status(thm)],[f_108_1]) ).
fof(f_108_3,plain,
~ empty(sK84),
inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_486,sK84)],[f_108_2]) ).
cnf(f_108_4,plain,
~ empty(sK84),
inference(clausify,[status(thm)],[f_108_3]) ).
fof(f_109_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_109_2,plain,
! [U_488,U_487] :
( union_of_subsets(U_488,U_487) = union(U_487)
| ~ element(U_487,powerset(powerset(U_488))) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
cnf(f_109_3,plain,
( union_of_subsets(U_488,U_487) = union(U_487)
| ~ element(U_487,powerset(powerset(U_488))) ),
inference(clausify,[status(thm)],[f_109_2]) ).
fof(f_110_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_110_2,plain,
! [U_490,U_489] :
( meet_of_subsets(U_490,U_489) = set_meet(U_489)
| ~ element(U_489,powerset(powerset(U_490))) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
cnf(f_110_3,plain,
( meet_of_subsets(U_490,U_489) = set_meet(U_489)
| ~ element(U_489,powerset(powerset(U_490))) ),
inference(clausify,[status(thm)],[f_110_2]) ).
fof(f_111_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_111_2,plain,
! [U_493,U_492,U_491] :
( subset_difference(U_493,U_492,U_491) = set_difference(U_492,U_491)
| ~ element(U_491,powerset(U_493))
| ~ element(U_492,powerset(U_493)) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
cnf(f_111_3,plain,
( subset_difference(U_493,U_492,U_491) = set_difference(U_492,U_491)
| ~ element(U_491,powerset(U_493))
| ~ element(U_492,powerset(U_493)) ),
inference(clausify,[status(thm)],[f_111_2]) ).
fof(f_112_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_112_2,plain,
! [U_495,U_494] : subset(U_495,U_495),
inference(variable_rename,[status(thm)],[f_112_1]) ).
fof(f_112_3,plain,
! [U_495] : subset(U_495,U_495),
inference(miniscope,[status(thm)],[f_112_2]) ).
cnf(f_112_4,plain,
subset(U_495,U_495),
inference(clausify,[status(thm)],[f_112_3]) ).
fof(f_113_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_113_2,plain,
! [U_497,U_496] :
( disjoint(U_496,U_497)
| ~ disjoint(U_497,U_496) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
cnf(f_113_3,plain,
( disjoint(U_496,U_497)
| ~ disjoint(U_497,U_496) ),
inference(clausify,[status(thm)],[f_113_2]) ).
fof(f_114_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_114_2,plain,
! [U_501,U_500,U_499,U_498] :
( ( in(ordered_pair(U_501,U_500),cartesian_product2(U_499,U_498))
| ~ in(U_500,U_498)
| ~ in(U_501,U_499) )
& ( ( in(U_500,U_498)
& in(U_501,U_499) )
| ~ in(ordered_pair(U_501,U_500),cartesian_product2(U_499,U_498)) ) ),
inference(variable_rename,[status(thm)],[f_114_1]) ).
fof(f_114_3,plain,
( ! [U_509,U_507,U_505,U_503] :
( in(ordered_pair(U_509,U_507),cartesian_product2(U_505,U_503))
| ~ in(U_507,U_503)
| ~ in(U_509,U_505) )
& ! [U_508,U_506,U_504,U_502] :
( ( in(U_506,U_502)
& in(U_508,U_504) )
| ~ in(ordered_pair(U_508,U_506),cartesian_product2(U_504,U_502)) ) ),
inference(miniscope,[status(thm)],[f_114_2]) ).
cnf(f_114_4,plain,
( in(U_508,U_504)
| ~ in(ordered_pair(U_508,U_506),cartesian_product2(U_504,U_502)) ),
inference(clausify,[status(thm)],[f_114_3]) ).
cnf(f_114_5,plain,
( in(U_506,U_502)
| ~ in(ordered_pair(U_508,U_506),cartesian_product2(U_504,U_502)) ),
inference(clausify,[status(thm)],[f_114_3]) ).
cnf(f_114_6,plain,
( in(ordered_pair(U_509,U_507),cartesian_product2(U_505,U_503))
| ~ in(U_507,U_503)
| ~ in(U_509,U_505) ),
inference(clausify,[status(thm)],[f_114_3]) ).
fof(f_115_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_115_2,plain,
! [U_513,U_512,U_511,U_510] :
( U_513 = U_510
| U_513 = U_511
| unordered_pair(U_513,U_512) != unordered_pair(U_511,U_510) ),
inference(variable_rename,[status(thm)],[f_115_1]) ).
fof(f_115_3,plain,
! [U_513,U_512,U_511] :
( ! [U_510] :
( U_513 = U_510
| unordered_pair(U_513,U_512) != unordered_pair(U_511,U_510) )
| U_513 = U_511 ),
inference(miniscope,[status(thm)],[f_115_2]) ).
cnf(f_115_4,plain,
( U_513 = U_510
| unordered_pair(U_513,U_512) != unordered_pair(U_511,U_510)
| U_513 = U_511 ),
inference(clausify,[status(thm)],[f_115_3]) ).
fof(f_116_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_116_2,plain,
! [U_516,U_515,U_514] :
( ( ( in(U_516,relation_rng(relation_rng_restriction(U_515,U_514)))
| ~ in(U_516,relation_rng(U_514))
| ~ in(U_516,U_515) )
& ( ( in(U_516,relation_rng(U_514))
& in(U_516,U_515) )
| ~ in(U_516,relation_rng(relation_rng_restriction(U_515,U_514))) ) )
| ~ relation(U_514) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
cnf(f_116_3,plain,
( in(U_516,U_515)
| ~ in(U_516,relation_rng(relation_rng_restriction(U_515,U_514)))
| ~ relation(U_514) ),
inference(clausify,[status(thm)],[f_116_2]) ).
cnf(f_116_4,plain,
( in(U_516,relation_rng(U_514))
| ~ in(U_516,relation_rng(relation_rng_restriction(U_515,U_514)))
| ~ relation(U_514) ),
inference(clausify,[status(thm)],[f_116_2]) ).
cnf(f_116_5,plain,
( in(U_516,relation_rng(relation_rng_restriction(U_515,U_514)))
| ~ in(U_516,relation_rng(U_514))
| ~ in(U_516,U_515)
| ~ relation(U_514) ),
inference(clausify,[status(thm)],[f_116_2]) ).
fof(f_117_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_117_2,plain,
! [U_518,U_517] :
( subset(relation_rng(relation_rng_restriction(U_518,U_517)),U_518)
| ~ relation(U_517) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
cnf(f_117_3,plain,
( subset(relation_rng(relation_rng_restriction(U_518,U_517)),U_518)
| ~ relation(U_517) ),
inference(clausify,[status(thm)],[f_117_2]) ).
fof(f_118_1,plain,
! [A,B] :
( subset(relation_rng_restriction(A,B),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t117_relat_1]) ).
fof(f_118_2,plain,
! [U_520,U_519] :
( subset(relation_rng_restriction(U_520,U_519),U_519)
| ~ relation(U_519) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
cnf(f_118_3,plain,
( subset(relation_rng_restriction(U_520,U_519),U_519)
| ~ relation(U_519) ),
inference(clausify,[status(thm)],[f_118_2]) ).
fof(f_119_1,plain,
! [A,B] :
( subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t118_relat_1]) ).
fof(f_119_2,plain,
! [U_522,U_521] :
( subset(relation_rng(relation_rng_restriction(U_522,U_521)),relation_rng(U_521))
| ~ relation(U_521) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
cnf(f_119_3,plain,
( subset(relation_rng(relation_rng_restriction(U_522,U_521)),relation_rng(U_521))
| ~ relation(U_521) ),
inference(clausify,[status(thm)],[f_119_2]) ).
fof(f_120_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_120_2,plain,
! [U_525,U_524,U_523] :
( ( subset(cartesian_product2(U_523,U_525),cartesian_product2(U_523,U_524))
& subset(cartesian_product2(U_525,U_523),cartesian_product2(U_524,U_523)) )
| ~ subset(U_525,U_524) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
fof(f_120_3,plain,
! [U_525,U_524] :
( ( ! [U_527] : subset(cartesian_product2(U_527,U_525),cartesian_product2(U_527,U_524))
& ! [U_526] : subset(cartesian_product2(U_525,U_526),cartesian_product2(U_524,U_526)) )
| ~ subset(U_525,U_524) ),
inference(miniscope,[status(thm)],[f_120_2]) ).
cnf(f_120_4,plain,
( subset(cartesian_product2(U_525,U_526),cartesian_product2(U_524,U_526))
| ~ subset(U_525,U_524) ),
inference(clausify,[status(thm)],[f_120_3]) ).
cnf(f_120_5,plain,
( subset(cartesian_product2(U_527,U_525),cartesian_product2(U_527,U_524))
| ~ subset(U_525,U_524) ),
inference(clausify,[status(thm)],[f_120_3]) ).
fof(f_121_1,plain,
! [A,B] :
( relation_rng(relation_rng_restriction(A,B)) = set_intersection2(relation_rng(B),A)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t119_relat_1]) ).
fof(f_121_2,plain,
! [U_529,U_528] :
( relation_rng(relation_rng_restriction(U_529,U_528)) = set_intersection2(relation_rng(U_528),U_529)
| ~ relation(U_528) ),
inference(variable_rename,[status(thm)],[f_121_1]) ).
cnf(f_121_3,plain,
( relation_rng(relation_rng_restriction(U_529,U_528)) = set_intersection2(relation_rng(U_528),U_529)
| ~ relation(U_528) ),
inference(clausify,[status(thm)],[f_121_2]) ).
fof(f_122_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_122_2,plain,
! [U_533,U_532,U_531,U_530] :
( subset(cartesian_product2(U_533,U_531),cartesian_product2(U_532,U_530))
| ~ subset(U_531,U_530)
| ~ subset(U_533,U_532) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
cnf(f_122_3,plain,
( subset(cartesian_product2(U_533,U_531),cartesian_product2(U_532,U_530))
| ~ subset(U_531,U_530)
| ~ subset(U_533,U_532) ),
inference(clausify,[status(thm)],[f_122_2]) ).
fof(f_123_1,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t12_xboole_1]) ).
fof(f_123_2,plain,
! [U_535,U_534] :
( set_union2(U_535,U_534) = U_534
| ~ subset(U_535,U_534) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
cnf(f_123_3,plain,
( set_union2(U_535,U_534) = U_534
| ~ subset(U_535,U_534) ),
inference(clausify,[status(thm)],[f_123_2]) ).
fof(f_124_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_124_2,plain,
! [U_541] :
? [U_540] :
( ! [U_539] :
( in(U_539,U_540)
| are_equipotent(U_539,U_540)
| ~ subset(U_539,U_540) )
& ! [U_538] :
( in(powerset(U_538),U_540)
| ~ in(U_538,U_540) )
& ! [U_537,U_536] :
( in(U_536,U_540)
| ~ subset(U_536,U_537)
| ~ in(U_537,U_540) )
& in(U_541,U_540) ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
fof(f_124_3,plain,
! [U_541] :
( ! [U_539] :
( in(U_539,sK85(U_541))
| are_equipotent(U_539,sK85(U_541))
| ~ subset(U_539,sK85(U_541)) )
& ! [U_538] :
( in(powerset(U_538),sK85(U_541))
| ~ in(U_538,sK85(U_541)) )
& ! [U_537,U_536] :
( in(U_536,sK85(U_541))
| ~ subset(U_536,U_537)
| ~ in(U_537,sK85(U_541)) )
& in(U_541,sK85(U_541)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_540,sK85(U_541))],[f_124_2]) ).
cnf(f_124_4,plain,
in(U_541,sK85(U_541)),
inference(clausify,[status(thm)],[f_124_3]) ).
cnf(f_124_5,plain,
( in(U_536,sK85(U_541))
| ~ subset(U_536,U_537)
| ~ in(U_537,sK85(U_541)) ),
inference(clausify,[status(thm)],[f_124_3]) ).
cnf(f_124_6,plain,
( in(powerset(U_538),sK85(U_541))
| ~ in(U_538,sK85(U_541)) ),
inference(clausify,[status(thm)],[f_124_3]) ).
cnf(f_124_7,plain,
( in(U_539,sK85(U_541))
| are_equipotent(U_539,sK85(U_541))
| ~ subset(U_539,sK85(U_541)) ),
inference(clausify,[status(thm)],[f_124_3]) ).
fof(f_125_1,plain,
! [A,B,C] :
( relation_dom_restriction(relation_rng_restriction(A,C),B) = relation_rng_restriction(A,relation_dom_restriction(C,B))
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t140_relat_1]) ).
fof(f_125_2,plain,
! [U_544,U_543,U_542] :
( relation_dom_restriction(relation_rng_restriction(U_544,U_542),U_543) = relation_rng_restriction(U_544,relation_dom_restriction(U_542,U_543))
| ~ relation(U_542) ),
inference(variable_rename,[status(thm)],[f_125_1]) ).
cnf(f_125_3,plain,
( relation_dom_restriction(relation_rng_restriction(U_544,U_542),U_543) = relation_rng_restriction(U_544,relation_dom_restriction(U_542,U_543))
| ~ relation(U_542) ),
inference(clausify,[status(thm)],[f_125_2]) ).
fof(f_126_1,plain,
! [A,B,C] :
( ( ( in(A,relation_image(C,B))
| ! [D] :
( ~ in(D,B)
| ~ in(ordered_pair(D,A),C)
| ~ in(D,relation_dom(C)) ) )
& ( ? [D] :
( in(D,B)
& in(ordered_pair(D,A),C)
& in(D,relation_dom(C)) )
| ~ in(A,relation_image(C,B)) ) )
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t143_relat_1]) ).
fof(f_126_2,plain,
! [U_549,U_548,U_547] :
( ( ( in(U_549,relation_image(U_547,U_548))
| ! [U_546] :
( ~ in(U_546,U_548)
| ~ in(ordered_pair(U_546,U_549),U_547)
| ~ in(U_546,relation_dom(U_547)) ) )
& ( ? [U_545] :
( in(U_545,U_548)
& in(ordered_pair(U_545,U_549),U_547)
& in(U_545,relation_dom(U_547)) )
| ~ in(U_549,relation_image(U_547,U_548)) ) )
| ~ relation(U_547) ),
inference(variable_rename,[status(thm)],[f_126_1]) ).
fof(f_126_3,plain,
! [U_549,U_548,U_547] :
( ( ( in(U_549,relation_image(U_547,U_548))
| ! [U_546] :
( ~ in(U_546,U_548)
| ~ in(ordered_pair(U_546,U_549),U_547)
| ~ in(U_546,relation_dom(U_547)) ) )
& ( ( in(sK86(U_549,U_548,U_547),U_548)
& in(ordered_pair(sK86(U_549,U_548,U_547),U_549),U_547)
& in(sK86(U_549,U_548,U_547),relation_dom(U_547)) )
| ~ in(U_549,relation_image(U_547,U_548)) ) )
| ~ relation(U_547) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_545,sK86(U_549,U_548,U_547))],[f_126_2]) ).
cnf(f_126_4,plain,
( in(sK86(U_549,U_548,U_547),relation_dom(U_547))
| ~ in(U_549,relation_image(U_547,U_548))
| ~ relation(U_547) ),
inference(clausify,[status(thm)],[f_126_3]) ).
cnf(f_126_5,plain,
( in(ordered_pair(sK86(U_549,U_548,U_547),U_549),U_547)
| ~ in(U_549,relation_image(U_547,U_548))
| ~ relation(U_547) ),
inference(clausify,[status(thm)],[f_126_3]) ).
cnf(f_126_6,plain,
( in(sK86(U_549,U_548,U_547),U_548)
| ~ in(U_549,relation_image(U_547,U_548))
| ~ relation(U_547) ),
inference(clausify,[status(thm)],[f_126_3]) ).
cnf(f_126_7,plain,
( in(U_549,relation_image(U_547,U_548))
| ~ in(U_546,U_548)
| ~ in(ordered_pair(U_546,U_549),U_547)
| ~ in(U_546,relation_dom(U_547))
| ~ relation(U_547) ),
inference(clausify,[status(thm)],[f_126_3]) ).
fof(f_127_1,plain,
! [A,B] :
( subset(relation_image(B,A),relation_rng(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t144_relat_1]) ).
fof(f_127_2,plain,
! [U_551,U_550] :
( subset(relation_image(U_550,U_551),relation_rng(U_550))
| ~ relation(U_550) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
cnf(f_127_3,plain,
( subset(relation_image(U_550,U_551),relation_rng(U_550))
| ~ relation(U_550) ),
inference(clausify,[status(thm)],[f_127_2]) ).
fof(f_128_1,plain,
! [A,B] :
( relation_image(B,A) = relation_image(B,set_intersection2(relation_dom(B),A))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t145_relat_1]) ).
fof(f_128_2,plain,
! [U_553,U_552] :
( relation_image(U_552,U_553) = relation_image(U_552,set_intersection2(relation_dom(U_552),U_553))
| ~ relation(U_552) ),
inference(variable_rename,[status(thm)],[f_128_1]) ).
cnf(f_128_3,plain,
( relation_image(U_552,U_553) = relation_image(U_552,set_intersection2(relation_dom(U_552),U_553))
| ~ relation(U_552) ),
inference(clausify,[status(thm)],[f_128_2]) ).
fof(f_129_1,plain,
! [A] :
( relation_image(A,relation_dom(A)) = relation_rng(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t146_relat_1]) ).
fof(f_129_2,plain,
! [U_554] :
( relation_image(U_554,relation_dom(U_554)) = relation_rng(U_554)
| ~ relation(U_554) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
cnf(f_129_3,plain,
( relation_image(U_554,relation_dom(U_554)) = relation_rng(U_554)
| ~ relation(U_554) ),
inference(clausify,[status(thm)],[f_129_2]) ).
fof(f_130_1,plain,
! [A] :
( ! [B] :
( relation_rng(relation_composition(A,B)) = relation_image(B,relation_rng(A))
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t160_relat_1]) ).
fof(f_130_2,plain,
! [U_556] :
( ! [U_555] :
( relation_rng(relation_composition(U_556,U_555)) = relation_image(U_555,relation_rng(U_556))
| ~ relation(U_555) )
| ~ relation(U_556) ),
inference(variable_rename,[status(thm)],[f_130_1]) ).
cnf(f_130_3,plain,
( relation_rng(relation_composition(U_556,U_555)) = relation_image(U_555,relation_rng(U_556))
| ~ relation(U_555)
| ~ relation(U_556) ),
inference(clausify,[status(thm)],[f_130_2]) ).
fof(f_131_1,plain,
! [A,B,C] :
( ( ( in(A,relation_inverse_image(C,B))
| ! [D] :
( ~ in(D,B)
| ~ in(ordered_pair(A,D),C)
| ~ in(D,relation_rng(C)) ) )
& ( ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) )
| ~ in(A,relation_inverse_image(C,B)) ) )
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t166_relat_1]) ).
fof(f_131_2,plain,
! [U_561,U_560,U_559] :
( ( ( in(U_561,relation_inverse_image(U_559,U_560))
| ! [U_558] :
( ~ in(U_558,U_560)
| ~ in(ordered_pair(U_561,U_558),U_559)
| ~ in(U_558,relation_rng(U_559)) ) )
& ( ? [U_557] :
( in(U_557,U_560)
& in(ordered_pair(U_561,U_557),U_559)
& in(U_557,relation_rng(U_559)) )
| ~ in(U_561,relation_inverse_image(U_559,U_560)) ) )
| ~ relation(U_559) ),
inference(variable_rename,[status(thm)],[f_131_1]) ).
fof(f_131_3,plain,
! [U_561,U_560,U_559] :
( ( ( in(U_561,relation_inverse_image(U_559,U_560))
| ! [U_558] :
( ~ in(U_558,U_560)
| ~ in(ordered_pair(U_561,U_558),U_559)
| ~ in(U_558,relation_rng(U_559)) ) )
& ( ( in(sK87(U_561,U_560,U_559),U_560)
& in(ordered_pair(U_561,sK87(U_561,U_560,U_559)),U_559)
& in(sK87(U_561,U_560,U_559),relation_rng(U_559)) )
| ~ in(U_561,relation_inverse_image(U_559,U_560)) ) )
| ~ relation(U_559) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_557,sK87(U_561,U_560,U_559))],[f_131_2]) ).
cnf(f_131_4,plain,
( in(sK87(U_561,U_560,U_559),relation_rng(U_559))
| ~ in(U_561,relation_inverse_image(U_559,U_560))
| ~ relation(U_559) ),
inference(clausify,[status(thm)],[f_131_3]) ).
cnf(f_131_5,plain,
( in(ordered_pair(U_561,sK87(U_561,U_560,U_559)),U_559)
| ~ in(U_561,relation_inverse_image(U_559,U_560))
| ~ relation(U_559) ),
inference(clausify,[status(thm)],[f_131_3]) ).
cnf(f_131_6,plain,
( in(sK87(U_561,U_560,U_559),U_560)
| ~ in(U_561,relation_inverse_image(U_559,U_560))
| ~ relation(U_559) ),
inference(clausify,[status(thm)],[f_131_3]) ).
cnf(f_131_7,plain,
( in(U_561,relation_inverse_image(U_559,U_560))
| ~ in(U_558,U_560)
| ~ in(ordered_pair(U_561,U_558),U_559)
| ~ in(U_558,relation_rng(U_559))
| ~ relation(U_559) ),
inference(clausify,[status(thm)],[f_131_3]) ).
fof(f_132_1,plain,
! [A,B] :
( subset(relation_inverse_image(B,A),relation_dom(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t167_relat_1]) ).
fof(f_132_2,plain,
! [U_563,U_562] :
( subset(relation_inverse_image(U_562,U_563),relation_dom(U_562))
| ~ relation(U_562) ),
inference(variable_rename,[status(thm)],[f_132_1]) ).
cnf(f_132_3,plain,
( subset(relation_inverse_image(U_562,U_563),relation_dom(U_562))
| ~ relation(U_562) ),
inference(clausify,[status(thm)],[f_132_2]) ).
fof(f_133_1,plain,
! [A,B] :
( relation_inverse_image(B,A) != empty_set
| ~ subset(A,relation_rng(B))
| A = empty_set
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t174_relat_1]) ).
fof(f_133_2,plain,
! [U_565,U_564] :
( relation_inverse_image(U_564,U_565) != empty_set
| ~ subset(U_565,relation_rng(U_564))
| U_565 = empty_set
| ~ relation(U_564) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
cnf(f_133_3,plain,
( relation_inverse_image(U_564,U_565) != empty_set
| ~ subset(U_565,relation_rng(U_564))
| U_565 = empty_set
| ~ relation(U_564) ),
inference(clausify,[status(thm)],[f_133_2]) ).
fof(f_134_1,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> ( subset(A,B)
=> subset(relation_inverse_image(C,A),relation_inverse_image(C,B)) ) ),
inference(negate,[status(cth)],[t178_relat_1]) ).
fof(f_134_2,negated_conjecture,
? [A,B,C] :
( ~ subset(relation_inverse_image(C,A),relation_inverse_image(C,B))
& subset(A,B)
& relation(C) ),
inference(fof_nnf,[status(thm)],[f_134_1]) ).
fof(f_134_3,negated_conjecture,
? [U_568,U_567,U_566] :
( ~ subset(relation_inverse_image(U_566,U_568),relation_inverse_image(U_566,U_567))
& subset(U_568,U_567)
& relation(U_566) ),
inference(variable_rename,[status(thm)],[f_134_2]) ).
fof(f_134_4,negated_conjecture,
? [U_567,U_566] :
( ~ subset(relation_inverse_image(U_566,sK88),relation_inverse_image(U_566,U_567))
& subset(sK88,U_567)
& relation(U_566) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_568,sK88)],[f_134_3]) ).
fof(f_134_5,negated_conjecture,
? [U_566] :
( ~ subset(relation_inverse_image(U_566,sK88),relation_inverse_image(U_566,sK89))
& subset(sK88,sK89)
& relation(U_566) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_567,sK89)],[f_134_4]) ).
fof(f_134_6,negated_conjecture,
( ~ subset(relation_inverse_image(sK90,sK88),relation_inverse_image(sK90,sK89))
& subset(sK88,sK89)
& relation(sK90) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_566,sK90)],[f_134_5]) ).
cnf(f_134_7,negated_conjecture,
relation(sK90),
inference(clausify,[status(thm)],[f_134_6]) ).
cnf(f_134_8,negated_conjecture,
subset(sK88,sK89),
inference(clausify,[status(thm)],[f_134_6]) ).
cnf(f_134_9,negated_conjecture,
~ subset(relation_inverse_image(sK90,sK88),relation_inverse_image(sK90,sK89)),
inference(clausify,[status(thm)],[f_134_6]) ).
fof(f_135_1,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(fof_nnf,[status(thm)],[t17_xboole_1]) ).
fof(f_135_2,plain,
! [U_570,U_569] : subset(set_intersection2(U_570,U_569),U_570),
inference(variable_rename,[status(thm)],[f_135_1]) ).
cnf(f_135_3,plain,
subset(set_intersection2(U_570,U_569),U_570),
inference(clausify,[status(thm)],[f_135_2]) ).
fof(f_136_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_136_2,plain,
! [U_573,U_572,U_571] :
( subset(U_573,set_intersection2(U_572,U_571))
| ~ subset(U_573,U_571)
| ~ subset(U_573,U_572) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
cnf(f_136_3,plain,
( subset(U_573,set_intersection2(U_572,U_571))
| ~ subset(U_573,U_571)
| ~ subset(U_573,U_572) ),
inference(clausify,[status(thm)],[f_136_2]) ).
fof(f_137_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_137_2,plain,
! [U_574] : set_union2(U_574,empty_set) = U_574,
inference(variable_rename,[status(thm)],[f_137_1]) ).
cnf(f_137_3,plain,
set_union2(U_574,empty_set) = U_574,
inference(clausify,[status(thm)],[f_137_2]) ).
fof(f_138_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_138_2,plain,
! [U_576,U_575] :
( element(U_576,U_575)
| ~ in(U_576,U_575) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
cnf(f_138_3,plain,
( element(U_576,U_575)
| ~ in(U_576,U_575) ),
inference(clausify,[status(thm)],[f_138_2]) ).
fof(f_139_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_139_2,plain,
! [U_579,U_578,U_577] :
( subset(U_579,U_577)
| ~ subset(U_578,U_577)
| ~ subset(U_579,U_578) ),
inference(variable_rename,[status(thm)],[f_139_1]) ).
cnf(f_139_3,plain,
( subset(U_579,U_577)
| ~ subset(U_578,U_577)
| ~ subset(U_579,U_578) ),
inference(clausify,[status(thm)],[f_139_2]) ).
fof(f_140_1,plain,
powerset(empty_set) = singleton(empty_set),
inference(fof_nnf,[status(thm)],[t1_zfmisc_1]) ).
cnf(f_140_2,plain,
powerset(empty_set) = singleton(empty_set),
inference(clausify,[status(thm)],[f_140_1]) ).
fof(f_141_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_141_2,plain,
! [U_582,U_581,U_580] :
( ( in(U_581,relation_rng(U_580))
& in(U_582,relation_dom(U_580)) )
| ~ in(ordered_pair(U_582,U_581),U_580)
| ~ relation(U_580) ),
inference(variable_rename,[status(thm)],[f_141_1]) ).
cnf(f_141_3,plain,
( in(U_582,relation_dom(U_580))
| ~ in(ordered_pair(U_582,U_581),U_580)
| ~ relation(U_580) ),
inference(clausify,[status(thm)],[f_141_2]) ).
cnf(f_141_4,plain,
( in(U_581,relation_rng(U_580))
| ~ in(ordered_pair(U_582,U_581),U_580)
| ~ relation(U_580) ),
inference(clausify,[status(thm)],[f_141_2]) ).
fof(f_142_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_142_2,plain,
! [U_583] :
( subset(U_583,cartesian_product2(relation_dom(U_583),relation_rng(U_583)))
| ~ relation(U_583) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
cnf(f_142_3,plain,
( subset(U_583,cartesian_product2(relation_dom(U_583),relation_rng(U_583)))
| ~ relation(U_583) ),
inference(clausify,[status(thm)],[f_142_2]) ).
fof(f_143_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_143_2,plain,
! [U_585] :
( ! [U_584] :
( ( subset(relation_rng(U_585),relation_rng(U_584))
& subset(relation_dom(U_585),relation_dom(U_584)) )
| ~ subset(U_585,U_584)
| ~ relation(U_584) )
| ~ relation(U_585) ),
inference(variable_rename,[status(thm)],[f_143_1]) ).
cnf(f_143_3,plain,
( subset(relation_dom(U_585),relation_dom(U_584))
| ~ subset(U_585,U_584)
| ~ relation(U_584)
| ~ relation(U_585) ),
inference(clausify,[status(thm)],[f_143_2]) ).
cnf(f_143_4,plain,
( subset(relation_rng(U_585),relation_rng(U_584))
| ~ subset(U_585,U_584)
| ~ relation(U_584)
| ~ relation(U_585) ),
inference(clausify,[status(thm)],[f_143_2]) ).
fof(f_144_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_144_2,plain,
! [U_588,U_587,U_586] :
( subset(set_intersection2(U_588,U_586),set_intersection2(U_587,U_586))
| ~ subset(U_588,U_587) ),
inference(variable_rename,[status(thm)],[f_144_1]) ).
fof(f_144_3,plain,
! [U_588,U_587] :
( ! [U_586] : subset(set_intersection2(U_588,U_586),set_intersection2(U_587,U_586))
| ~ subset(U_588,U_587) ),
inference(miniscope,[status(thm)],[f_144_2]) ).
cnf(f_144_4,plain,
( subset(set_intersection2(U_588,U_586),set_intersection2(U_587,U_586))
| ~ subset(U_588,U_587) ),
inference(clausify,[status(thm)],[f_144_3]) ).
fof(f_145_1,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t28_xboole_1]) ).
fof(f_145_2,plain,
! [U_590,U_589] :
( set_intersection2(U_590,U_589) = U_590
| ~ subset(U_590,U_589) ),
inference(variable_rename,[status(thm)],[f_145_1]) ).
cnf(f_145_3,plain,
( set_intersection2(U_590,U_589) = U_590
| ~ subset(U_590,U_589) ),
inference(clausify,[status(thm)],[f_145_2]) ).
fof(f_146_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_146_2,plain,
! [U_591] : set_intersection2(U_591,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_146_1]) ).
cnf(f_146_3,plain,
set_intersection2(U_591,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_146_2]) ).
fof(f_147_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_147_2,plain,
! [U_593,U_592] :
( in(U_593,U_592)
| empty(U_592)
| ~ element(U_593,U_592) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
cnf(f_147_3,plain,
( in(U_593,U_592)
| empty(U_592)
| ~ element(U_593,U_592) ),
inference(clausify,[status(thm)],[f_147_2]) ).
fof(f_148_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_148_2,plain,
! [U_596,U_595] :
( U_596 = U_595
| ? [U_594] :
( ( ~ in(U_594,U_596)
& in(U_594,U_595) )
| ( ~ in(U_594,U_595)
& in(U_594,U_596) ) ) ),
inference(variable_rename,[status(thm)],[f_148_1]) ).
fof(f_148_3,plain,
! [U_596,U_595] :
( U_596 = U_595
| ? [U_598] :
( ~ in(U_598,U_596)
& in(U_598,U_595) )
| ? [U_597] :
( ~ in(U_597,U_595)
& in(U_597,U_596) ) ),
inference(miniscope,[status(thm)],[f_148_2]) ).
fof(f_148_4,plain,
! [U_596,U_595] :
( U_596 = U_595
| ? [U_598] :
( ~ in(U_598,U_596)
& in(U_598,U_595) )
| ( ~ in(sK91(U_596,U_595),U_595)
& in(sK91(U_596,U_595),U_596) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_597,sK91(U_596,U_595))],[f_148_3]) ).
fof(f_148_5,plain,
! [U_596,U_595] :
( U_596 = U_595
| ( ~ in(sK92(U_596,U_595),U_596)
& in(sK92(U_596,U_595),U_595) )
| ( ~ in(sK91(U_596,U_595),U_595)
& in(sK91(U_596,U_595),U_596) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_598,sK92(U_596,U_595))],[f_148_4]) ).
cnf(f_148_6,plain,
( in(sK92(U_596,U_595),U_595)
| in(sK91(U_596,U_595),U_596)
| U_596 = U_595 ),
inference(clausify,[status(thm)],[f_148_5]) ).
cnf(f_148_7,plain,
( ~ in(sK92(U_596,U_595),U_596)
| in(sK91(U_596,U_595),U_596)
| U_596 = U_595 ),
inference(clausify,[status(thm)],[f_148_5]) ).
cnf(f_148_8,plain,
( in(sK92(U_596,U_595),U_595)
| ~ in(sK91(U_596,U_595),U_595)
| U_596 = U_595 ),
inference(clausify,[status(thm)],[f_148_5]) ).
cnf(f_148_9,plain,
( ~ in(sK92(U_596,U_595),U_596)
| ~ in(sK91(U_596,U_595),U_595)
| U_596 = U_595 ),
inference(clausify,[status(thm)],[f_148_5]) ).
fof(f_149_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_149_2,plain,
! [U_599] : subset(empty_set,U_599),
inference(variable_rename,[status(thm)],[f_149_1]) ).
cnf(f_149_3,plain,
subset(empty_set,U_599),
inference(clausify,[status(thm)],[f_149_2]) ).
fof(f_150_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_150_2,plain,
! [U_602,U_601,U_600] :
( ( in(U_601,relation_field(U_600))
& in(U_602,relation_field(U_600)) )
| ~ in(ordered_pair(U_602,U_601),U_600)
| ~ relation(U_600) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
cnf(f_150_3,plain,
( in(U_602,relation_field(U_600))
| ~ in(ordered_pair(U_602,U_601),U_600)
| ~ relation(U_600) ),
inference(clausify,[status(thm)],[f_150_2]) ).
cnf(f_150_4,plain,
( in(U_601,relation_field(U_600))
| ~ in(ordered_pair(U_602,U_601),U_600)
| ~ relation(U_600) ),
inference(clausify,[status(thm)],[f_150_2]) ).
fof(f_151_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_151_2,plain,
! [U_605,U_604,U_603] :
( subset(set_difference(U_605,U_603),set_difference(U_604,U_603))
| ~ subset(U_605,U_604) ),
inference(variable_rename,[status(thm)],[f_151_1]) ).
fof(f_151_3,plain,
! [U_605,U_604] :
( ! [U_603] : subset(set_difference(U_605,U_603),set_difference(U_604,U_603))
| ~ subset(U_605,U_604) ),
inference(miniscope,[status(thm)],[f_151_2]) ).
cnf(f_151_4,plain,
( subset(set_difference(U_605,U_603),set_difference(U_604,U_603))
| ~ subset(U_605,U_604) ),
inference(clausify,[status(thm)],[f_151_3]) ).
fof(f_152_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_152_2,plain,
! [U_609,U_608,U_607,U_606] :
( ( U_608 = U_606
& U_609 = U_607 )
| ordered_pair(U_609,U_608) != ordered_pair(U_607,U_606) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
cnf(f_152_3,plain,
( U_609 = U_607
| ordered_pair(U_609,U_608) != ordered_pair(U_607,U_606) ),
inference(clausify,[status(thm)],[f_152_2]) ).
cnf(f_152_4,plain,
( U_608 = U_606
| ordered_pair(U_609,U_608) != ordered_pair(U_607,U_606) ),
inference(clausify,[status(thm)],[f_152_2]) ).
fof(f_153_1,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(fof_nnf,[status(thm)],[t36_xboole_1]) ).
fof(f_153_2,plain,
! [U_611,U_610] : subset(set_difference(U_611,U_610),U_611),
inference(variable_rename,[status(thm)],[f_153_1]) ).
cnf(f_153_3,plain,
subset(set_difference(U_611,U_610),U_611),
inference(clausify,[status(thm)],[f_153_2]) ).
fof(f_154_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_154_2,plain,
! [U_612] :
( ( relation_dom(U_612) = relation_rng(relation_inverse(U_612))
& relation_rng(U_612) = relation_dom(relation_inverse(U_612)) )
| ~ relation(U_612) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
cnf(f_154_3,plain,
( relation_rng(U_612) = relation_dom(relation_inverse(U_612))
| ~ relation(U_612) ),
inference(clausify,[status(thm)],[f_154_2]) ).
cnf(f_154_4,plain,
( relation_dom(U_612) = relation_rng(relation_inverse(U_612))
| ~ relation(U_612) ),
inference(clausify,[status(thm)],[f_154_2]) ).
fof(f_155_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_155_2,plain,
! [U_614,U_613] :
( ( set_difference(U_614,U_613) = empty_set
| ~ subset(U_614,U_613) )
& ( subset(U_614,U_613)
| set_difference(U_614,U_613) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
fof(f_155_3,plain,
( ! [U_618,U_616] :
( set_difference(U_618,U_616) = empty_set
| ~ subset(U_618,U_616) )
& ! [U_617,U_615] :
( subset(U_617,U_615)
| set_difference(U_617,U_615) != empty_set ) ),
inference(miniscope,[status(thm)],[f_155_2]) ).
cnf(f_155_4,plain,
( subset(U_617,U_615)
| set_difference(U_617,U_615) != empty_set ),
inference(clausify,[status(thm)],[f_155_3]) ).
cnf(f_155_5,plain,
( set_difference(U_618,U_616) = empty_set
| ~ subset(U_618,U_616) ),
inference(clausify,[status(thm)],[f_155_3]) ).
fof(f_156_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_156_2,plain,
! [U_620,U_619] :
( ( subset(singleton(U_620),U_619)
| ~ in(U_620,U_619) )
& ( in(U_620,U_619)
| ~ subset(singleton(U_620),U_619) ) ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
fof(f_156_3,plain,
( ! [U_624,U_622] :
( subset(singleton(U_624),U_622)
| ~ in(U_624,U_622) )
& ! [U_623,U_621] :
( in(U_623,U_621)
| ~ subset(singleton(U_623),U_621) ) ),
inference(miniscope,[status(thm)],[f_156_2]) ).
cnf(f_156_4,plain,
( in(U_623,U_621)
| ~ subset(singleton(U_623),U_621) ),
inference(clausify,[status(thm)],[f_156_3]) ).
cnf(f_156_5,plain,
( subset(singleton(U_624),U_622)
| ~ in(U_624,U_622) ),
inference(clausify,[status(thm)],[f_156_3]) ).
fof(f_157_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_157_2,plain,
! [U_627,U_626,U_625] :
( ( subset(unordered_pair(U_627,U_626),U_625)
| ~ in(U_626,U_625)
| ~ in(U_627,U_625) )
& ( ( in(U_626,U_625)
& in(U_627,U_625) )
| ~ subset(unordered_pair(U_627,U_626),U_625) ) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
fof(f_157_3,plain,
( ! [U_633,U_631,U_629] :
( subset(unordered_pair(U_633,U_631),U_629)
| ~ in(U_631,U_629)
| ~ in(U_633,U_629) )
& ! [U_632,U_630,U_628] :
( ( in(U_630,U_628)
& in(U_632,U_628) )
| ~ subset(unordered_pair(U_632,U_630),U_628) ) ),
inference(miniscope,[status(thm)],[f_157_2]) ).
cnf(f_157_4,plain,
( in(U_632,U_628)
| ~ subset(unordered_pair(U_632,U_630),U_628) ),
inference(clausify,[status(thm)],[f_157_3]) ).
cnf(f_157_5,plain,
( in(U_630,U_628)
| ~ subset(unordered_pair(U_632,U_630),U_628) ),
inference(clausify,[status(thm)],[f_157_3]) ).
cnf(f_157_6,plain,
( subset(unordered_pair(U_633,U_631),U_629)
| ~ in(U_631,U_629)
| ~ in(U_633,U_629) ),
inference(clausify,[status(thm)],[f_157_3]) ).
fof(f_158_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_158_2,plain,
! [U_635,U_634] : set_union2(U_635,set_difference(U_634,U_635)) = set_union2(U_635,U_634),
inference(variable_rename,[status(thm)],[f_158_1]) ).
cnf(f_158_3,plain,
set_union2(U_635,set_difference(U_634,U_635)) = set_union2(U_635,U_634),
inference(clausify,[status(thm)],[f_158_2]) ).
fof(f_159_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_159_2,plain,
! [U_637,U_636] :
( ( subset(U_637,singleton(U_636))
| ( U_637 != singleton(U_636)
& U_637 != empty_set ) )
& ( U_637 = singleton(U_636)
| U_637 = empty_set
| ~ subset(U_637,singleton(U_636)) ) ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
fof(f_159_3,plain,
( ! [U_641,U_639] :
( subset(U_641,singleton(U_639))
| ( U_641 != singleton(U_639)
& U_641 != empty_set ) )
& ! [U_640,U_638] :
( U_640 = singleton(U_638)
| U_640 = empty_set
| ~ subset(U_640,singleton(U_638)) ) ),
inference(miniscope,[status(thm)],[f_159_2]) ).
cnf(f_159_4,plain,
( U_640 = singleton(U_638)
| U_640 = empty_set
| ~ subset(U_640,singleton(U_638)) ),
inference(clausify,[status(thm)],[f_159_3]) ).
cnf(f_159_5,plain,
( U_641 != empty_set
| subset(U_641,singleton(U_639)) ),
inference(clausify,[status(thm)],[f_159_3]) ).
cnf(f_159_6,plain,
( U_641 != singleton(U_639)
| subset(U_641,singleton(U_639)) ),
inference(clausify,[status(thm)],[f_159_3]) ).
fof(f_160_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_160_2,plain,
! [U_642] : set_difference(U_642,empty_set) = U_642,
inference(variable_rename,[status(thm)],[f_160_1]) ).
cnf(f_160_3,plain,
set_difference(U_642,empty_set) = U_642,
inference(clausify,[status(thm)],[f_160_2]) ).
fof(f_161_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_161_2,plain,
! [U_644,U_643] :
( ( element(U_644,powerset(U_643))
| ~ subset(U_644,U_643) )
& ( subset(U_644,U_643)
| ~ element(U_644,powerset(U_643)) ) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
fof(f_161_3,plain,
( ! [U_648,U_646] :
( element(U_648,powerset(U_646))
| ~ subset(U_648,U_646) )
& ! [U_647,U_645] :
( subset(U_647,U_645)
| ~ element(U_647,powerset(U_645)) ) ),
inference(miniscope,[status(thm)],[f_161_2]) ).
cnf(f_161_4,plain,
( subset(U_647,U_645)
| ~ element(U_647,powerset(U_645)) ),
inference(clausify,[status(thm)],[f_161_3]) ).
cnf(f_161_5,plain,
( element(U_648,powerset(U_646))
| ~ subset(U_648,U_646) ),
inference(clausify,[status(thm)],[f_161_3]) ).
fof(f_162_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_162_2,plain,
! [U_652,U_651] :
( ( ~ disjoint(U_652,U_651)
| ! [U_650] :
( ~ in(U_650,U_651)
| ~ in(U_650,U_652) ) )
& ( ? [U_649] :
( in(U_649,U_651)
& in(U_649,U_652) )
| disjoint(U_652,U_651) ) ),
inference(variable_rename,[status(thm)],[f_162_1]) ).
fof(f_162_3,plain,
( ! [U_656,U_654] :
( ~ disjoint(U_656,U_654)
| ! [U_650] :
( ~ in(U_650,U_654)
| ~ in(U_650,U_656) ) )
& ! [U_655,U_653] :
( ? [U_649] :
( in(U_649,U_653)
& in(U_649,U_655) )
| disjoint(U_655,U_653) ) ),
inference(miniscope,[status(thm)],[f_162_2]) ).
fof(f_162_4,plain,
( ! [U_656,U_654] :
( ~ disjoint(U_656,U_654)
| ! [U_650] :
( ~ in(U_650,U_654)
| ~ in(U_650,U_656) ) )
& ! [U_655,U_653] :
( ( in(sK93(U_655,U_653),U_653)
& in(sK93(U_655,U_653),U_655) )
| disjoint(U_655,U_653) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_649,sK93(U_655,U_653))],[f_162_3]) ).
cnf(f_162_5,plain,
( in(sK93(U_655,U_653),U_655)
| disjoint(U_655,U_653) ),
inference(clausify,[status(thm)],[f_162_4]) ).
cnf(f_162_6,plain,
( in(sK93(U_655,U_653),U_653)
| disjoint(U_655,U_653) ),
inference(clausify,[status(thm)],[f_162_4]) ).
cnf(f_162_7,plain,
( ~ disjoint(U_656,U_654)
| ~ in(U_650,U_654)
| ~ in(U_650,U_656) ),
inference(clausify,[status(thm)],[f_162_4]) ).
fof(f_163_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_163_2,plain,
! [U_657] :
( U_657 = empty_set
| ~ subset(U_657,empty_set) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
cnf(f_163_3,plain,
( U_657 = empty_set
| ~ subset(U_657,empty_set) ),
inference(clausify,[status(thm)],[f_163_2]) ).
fof(f_164_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_164_2,plain,
! [U_659,U_658] : set_difference(set_union2(U_659,U_658),U_658) = set_difference(U_659,U_658),
inference(variable_rename,[status(thm)],[f_164_1]) ).
cnf(f_164_3,plain,
set_difference(set_union2(U_659,U_658),U_658) = set_difference(U_659,U_658),
inference(clausify,[status(thm)],[f_164_2]) ).
fof(f_165_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_165_2,plain,
! [U_662,U_661] :
( ! [U_660] :
( ( ( disjoint(U_661,U_660)
| ~ subset(U_661,subset_complement(U_662,U_660)) )
& ( subset(U_661,subset_complement(U_662,U_660))
| ~ disjoint(U_661,U_660) ) )
| ~ element(U_660,powerset(U_662)) )
| ~ element(U_661,powerset(U_662)) ),
inference(variable_rename,[status(thm)],[f_165_1]) ).
cnf(f_165_3,plain,
( subset(U_661,subset_complement(U_662,U_660))
| ~ disjoint(U_661,U_660)
| ~ element(U_660,powerset(U_662))
| ~ element(U_661,powerset(U_662)) ),
inference(clausify,[status(thm)],[f_165_2]) ).
cnf(f_165_4,plain,
( disjoint(U_661,U_660)
| ~ subset(U_661,subset_complement(U_662,U_660))
| ~ element(U_660,powerset(U_662))
| ~ element(U_661,powerset(U_662)) ),
inference(clausify,[status(thm)],[f_165_2]) ).
fof(f_166_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_166_2,plain,
! [U_664] :
( ! [U_663] :
( subset(relation_dom(relation_composition(U_664,U_663)),relation_dom(U_664))
| ~ relation(U_663) )
| ~ relation(U_664) ),
inference(variable_rename,[status(thm)],[f_166_1]) ).
cnf(f_166_3,plain,
( subset(relation_dom(relation_composition(U_664,U_663)),relation_dom(U_664))
| ~ relation(U_663)
| ~ relation(U_664) ),
inference(clausify,[status(thm)],[f_166_2]) ).
fof(f_167_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_167_2,plain,
! [U_666] :
( ! [U_665] :
( subset(relation_rng(relation_composition(U_666,U_665)),relation_rng(U_665))
| ~ relation(U_665) )
| ~ relation(U_666) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
cnf(f_167_3,plain,
( subset(relation_rng(relation_composition(U_666,U_665)),relation_rng(U_665))
| ~ relation(U_665)
| ~ relation(U_666) ),
inference(clausify,[status(thm)],[f_167_2]) ).
fof(f_168_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_168_2,plain,
! [U_668,U_667] :
( U_667 = set_union2(U_668,set_difference(U_667,U_668))
| ~ subset(U_668,U_667) ),
inference(variable_rename,[status(thm)],[f_168_1]) ).
cnf(f_168_3,plain,
( U_667 = set_union2(U_668,set_difference(U_667,U_668))
| ~ subset(U_668,U_667) ),
inference(clausify,[status(thm)],[f_168_2]) ).
fof(f_169_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_169_2,plain,
! [U_670] :
( ! [U_669] :
( relation_dom(relation_composition(U_670,U_669)) = relation_dom(U_670)
| ~ subset(relation_rng(U_670),relation_dom(U_669))
| ~ relation(U_669) )
| ~ relation(U_670) ),
inference(variable_rename,[status(thm)],[f_169_1]) ).
cnf(f_169_3,plain,
( relation_dom(relation_composition(U_670,U_669)) = relation_dom(U_670)
| ~ subset(relation_rng(U_670),relation_dom(U_669))
| ~ relation(U_669)
| ~ relation(U_670) ),
inference(clausify,[status(thm)],[f_169_2]) ).
fof(f_170_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_170_2,plain,
! [U_672,U_671] :
( complements_of_subsets(U_672,U_671) != empty_set
| U_671 = empty_set
| ~ element(U_671,powerset(powerset(U_672))) ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
cnf(f_170_3,plain,
( complements_of_subsets(U_672,U_671) != empty_set
| U_671 = empty_set
| ~ element(U_671,powerset(powerset(U_672))) ),
inference(clausify,[status(thm)],[f_170_2]) ).
fof(f_171_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t46_zfmisc_1]) ).
fof(f_171_2,plain,
! [U_674,U_673] :
( set_union2(singleton(U_674),U_673) = U_673
| ~ in(U_674,U_673) ),
inference(variable_rename,[status(thm)],[f_171_1]) ).
cnf(f_171_3,plain,
( set_union2(singleton(U_674),U_673) = U_673
| ~ in(U_674,U_673) ),
inference(clausify,[status(thm)],[f_171_2]) ).
fof(f_172_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_172_2,plain,
! [U_676] :
( ! [U_675] :
( relation_rng(relation_composition(U_675,U_676)) = relation_rng(U_676)
| ~ subset(relation_dom(U_676),relation_rng(U_675))
| ~ relation(U_675) )
| ~ relation(U_676) ),
inference(variable_rename,[status(thm)],[f_172_1]) ).
cnf(f_172_3,plain,
( relation_rng(relation_composition(U_675,U_676)) = relation_rng(U_676)
| ~ subset(relation_dom(U_676),relation_rng(U_675))
| ~ relation(U_675)
| ~ relation(U_676) ),
inference(clausify,[status(thm)],[f_172_2]) ).
fof(f_173_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_173_2,plain,
! [U_678,U_677] :
( subset_difference(U_678,cast_to_subset(U_678),union_of_subsets(U_678,U_677)) = meet_of_subsets(U_678,complements_of_subsets(U_678,U_677))
| U_677 = empty_set
| ~ element(U_677,powerset(powerset(U_678))) ),
inference(variable_rename,[status(thm)],[f_173_1]) ).
cnf(f_173_3,plain,
( subset_difference(U_678,cast_to_subset(U_678),union_of_subsets(U_678,U_677)) = meet_of_subsets(U_678,complements_of_subsets(U_678,U_677))
| U_677 = empty_set
| ~ element(U_677,powerset(powerset(U_678))) ),
inference(clausify,[status(thm)],[f_173_2]) ).
fof(f_174_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_174_2,plain,
! [U_680,U_679] :
( union_of_subsets(U_680,complements_of_subsets(U_680,U_679)) = subset_difference(U_680,cast_to_subset(U_680),meet_of_subsets(U_680,U_679))
| U_679 = empty_set
| ~ element(U_679,powerset(powerset(U_680))) ),
inference(variable_rename,[status(thm)],[f_174_1]) ).
cnf(f_174_3,plain,
( union_of_subsets(U_680,complements_of_subsets(U_680,U_679)) = subset_difference(U_680,cast_to_subset(U_680),meet_of_subsets(U_680,U_679))
| U_679 = empty_set
| ~ element(U_679,powerset(powerset(U_680))) ),
inference(clausify,[status(thm)],[f_174_2]) ).
fof(f_175_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_175_2,plain,
! [U_682,U_681] : set_difference(U_682,set_difference(U_682,U_681)) = set_intersection2(U_682,U_681),
inference(variable_rename,[status(thm)],[f_175_1]) ).
cnf(f_175_3,plain,
set_difference(U_682,set_difference(U_682,U_681)) = set_intersection2(U_682,U_681),
inference(clausify,[status(thm)],[f_175_2]) ).
fof(f_176_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_176_2,plain,
! [U_683] : set_difference(empty_set,U_683) = empty_set,
inference(variable_rename,[status(thm)],[f_176_1]) ).
cnf(f_176_3,plain,
set_difference(empty_set,U_683) = empty_set,
inference(clausify,[status(thm)],[f_176_2]) ).
fof(f_177_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_177_2,plain,
! [U_686,U_685,U_684] :
( element(U_686,U_684)
| ~ element(U_685,powerset(U_684))
| ~ in(U_686,U_685) ),
inference(variable_rename,[status(thm)],[f_177_1]) ).
cnf(f_177_3,plain,
( element(U_686,U_684)
| ~ element(U_685,powerset(U_684))
| ~ in(U_686,U_685) ),
inference(clausify,[status(thm)],[f_177_2]) ).
fof(f_178_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_178_2,plain,
! [U_690,U_689] :
( ( ~ disjoint(U_690,U_689)
| ! [U_688] : ~ in(U_688,set_intersection2(U_690,U_689)) )
& ( ? [U_687] : in(U_687,set_intersection2(U_690,U_689))
| disjoint(U_690,U_689) ) ),
inference(variable_rename,[status(thm)],[f_178_1]) ).
fof(f_178_3,plain,
( ! [U_694,U_692] :
( ~ disjoint(U_694,U_692)
| ! [U_688] : ~ in(U_688,set_intersection2(U_694,U_692)) )
& ! [U_693,U_691] :
( ? [U_687] : in(U_687,set_intersection2(U_693,U_691))
| disjoint(U_693,U_691) ) ),
inference(miniscope,[status(thm)],[f_178_2]) ).
fof(f_178_4,plain,
( ! [U_694,U_692] :
( ~ disjoint(U_694,U_692)
| ! [U_688] : ~ in(U_688,set_intersection2(U_694,U_692)) )
& ! [U_693,U_691] :
( in(sK94(U_693,U_691),set_intersection2(U_693,U_691))
| disjoint(U_693,U_691) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_687,sK94(U_693,U_691))],[f_178_3]) ).
cnf(f_178_5,plain,
( in(sK94(U_693,U_691),set_intersection2(U_693,U_691))
| disjoint(U_693,U_691) ),
inference(clausify,[status(thm)],[f_178_4]) ).
cnf(f_178_6,plain,
( ~ disjoint(U_694,U_692)
| ~ in(U_688,set_intersection2(U_694,U_692)) ),
inference(clausify,[status(thm)],[f_178_4]) ).
fof(f_179_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_179_2,plain,
! [U_697] :
( ! [U_696] :
( ! [U_695] :
( in(U_695,subset_complement(U_697,U_696))
| in(U_695,U_696)
| ~ element(U_695,U_697) )
| ~ element(U_696,powerset(U_697)) )
| U_697 = empty_set ),
inference(variable_rename,[status(thm)],[f_179_1]) ).
cnf(f_179_3,plain,
( in(U_695,subset_complement(U_697,U_696))
| in(U_695,U_696)
| ~ element(U_695,U_697)
| ~ element(U_696,powerset(U_697))
| U_697 = empty_set ),
inference(clausify,[status(thm)],[f_179_2]) ).
fof(f_180_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_180_2,plain,
! [U_700,U_699,U_698] :
( ~ in(U_699,U_698)
| ~ in(U_699,subset_complement(U_700,U_698))
| ~ element(U_698,powerset(U_700)) ),
inference(variable_rename,[status(thm)],[f_180_1]) ).
cnf(f_180_3,plain,
( ~ in(U_699,U_698)
| ~ in(U_699,subset_complement(U_700,U_698))
| ~ element(U_698,powerset(U_700)) ),
inference(clausify,[status(thm)],[f_180_2]) ).
fof(f_181_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_181_2,plain,
! [U_703] :
( U_703 = empty_set
| ? [U_702,U_701] : in(ordered_pair(U_702,U_701),U_703)
| ~ relation(U_703) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
fof(f_181_3,plain,
! [U_703] :
( U_703 = empty_set
| ? [U_701] : in(ordered_pair(sK95(U_703),U_701),U_703)
| ~ relation(U_703) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_702,sK95(U_703))],[f_181_2]) ).
fof(f_181_4,plain,
! [U_703] :
( U_703 = empty_set
| in(ordered_pair(sK95(U_703),sK96(U_703)),U_703)
| ~ relation(U_703) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_701,sK96(U_703))],[f_181_3]) ).
cnf(f_181_5,plain,
( U_703 = empty_set
| in(ordered_pair(sK95(U_703),sK96(U_703)),U_703)
| ~ relation(U_703) ),
inference(clausify,[status(thm)],[f_181_4]) ).
fof(f_182_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_182_2,plain,
! [U_706,U_705,U_704] :
( ~ empty(U_704)
| ~ element(U_705,powerset(U_704))
| ~ in(U_706,U_705) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
fof(f_182_3,plain,
! [U_706,U_705] :
( ! [U_704] :
( ~ empty(U_704)
| ~ element(U_705,powerset(U_704)) )
| ~ in(U_706,U_705) ),
inference(miniscope,[status(thm)],[f_182_2]) ).
cnf(f_182_4,plain,
( ~ empty(U_704)
| ~ element(U_705,powerset(U_704))
| ~ in(U_706,U_705) ),
inference(clausify,[status(thm)],[f_182_3]) ).
fof(f_183_1,plain,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(fof_nnf,[status(thm)],[t60_relat_1]) ).
cnf(f_183_2,plain,
relation_dom(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_183_1]) ).
cnf(f_183_3,plain,
relation_rng(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_183_1]) ).
fof(f_184_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t60_xboole_1]) ).
fof(f_184_2,plain,
! [U_708,U_707] :
( ~ proper_subset(U_707,U_708)
| ~ subset(U_708,U_707) ),
inference(variable_rename,[status(thm)],[f_184_1]) ).
cnf(f_184_3,plain,
( ~ proper_subset(U_707,U_708)
| ~ subset(U_708,U_707) ),
inference(clausify,[status(thm)],[f_184_2]) ).
fof(f_185_1,plain,
! [A,B,C] :
( disjoint(A,C)
| ~ disjoint(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t63_xboole_1]) ).
fof(f_185_2,plain,
! [U_711,U_710,U_709] :
( disjoint(U_711,U_709)
| ~ disjoint(U_710,U_709)
| ~ subset(U_711,U_710) ),
inference(variable_rename,[status(thm)],[f_185_1]) ).
cnf(f_185_3,plain,
( disjoint(U_711,U_709)
| ~ disjoint(U_710,U_709)
| ~ subset(U_711,U_710) ),
inference(clausify,[status(thm)],[f_185_2]) ).
fof(f_186_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_186_2,plain,
! [U_712] :
( U_712 = empty_set
| ( relation_rng(U_712) != empty_set
& relation_dom(U_712) != empty_set )
| ~ relation(U_712) ),
inference(variable_rename,[status(thm)],[f_186_1]) ).
cnf(f_186_3,plain,
( relation_dom(U_712) != empty_set
| U_712 = empty_set
| ~ relation(U_712) ),
inference(clausify,[status(thm)],[f_186_2]) ).
cnf(f_186_4,plain,
( relation_rng(U_712) != empty_set
| U_712 = empty_set
| ~ relation(U_712) ),
inference(clausify,[status(thm)],[f_186_2]) ).
fof(f_187_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_187_2,plain,
! [U_713] :
( ( ( relation_dom(U_713) = empty_set
| relation_rng(U_713) != empty_set )
& ( relation_rng(U_713) = empty_set
| relation_dom(U_713) != empty_set ) )
| ~ relation(U_713) ),
inference(variable_rename,[status(thm)],[f_187_1]) ).
cnf(f_187_3,plain,
( relation_rng(U_713) = empty_set
| relation_dom(U_713) != empty_set
| ~ relation(U_713) ),
inference(clausify,[status(thm)],[f_187_2]) ).
cnf(f_187_4,plain,
( relation_dom(U_713) = empty_set
| relation_rng(U_713) != empty_set
| ~ relation(U_713) ),
inference(clausify,[status(thm)],[f_187_2]) ).
fof(f_188_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_188_2,plain,
! [U_715,U_714] :
( ( set_difference(U_715,singleton(U_714)) = U_715
| in(U_714,U_715) )
& ( ~ in(U_714,U_715)
| set_difference(U_715,singleton(U_714)) != U_715 ) ),
inference(variable_rename,[status(thm)],[f_188_1]) ).
fof(f_188_3,plain,
( ! [U_719,U_717] :
( set_difference(U_719,singleton(U_717)) = U_719
| in(U_717,U_719) )
& ! [U_718,U_716] :
( ~ in(U_716,U_718)
| set_difference(U_718,singleton(U_716)) != U_718 ) ),
inference(miniscope,[status(thm)],[f_188_2]) ).
cnf(f_188_4,plain,
( ~ in(U_716,U_718)
| set_difference(U_718,singleton(U_716)) != U_718 ),
inference(clausify,[status(thm)],[f_188_3]) ).
cnf(f_188_5,plain,
( set_difference(U_719,singleton(U_717)) = U_719
| in(U_717,U_719) ),
inference(clausify,[status(thm)],[f_188_3]) ).
fof(f_189_1,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(fof_nnf,[status(thm)],[t69_enumset1]) ).
fof(f_189_2,plain,
! [U_720] : unordered_pair(U_720,U_720) = singleton(U_720),
inference(variable_rename,[status(thm)],[f_189_1]) ).
cnf(f_189_3,plain,
unordered_pair(U_720,U_720) = singleton(U_720),
inference(clausify,[status(thm)],[f_189_2]) ).
fof(f_190_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_190_2,plain,
! [U_721] :
( U_721 = empty_set
| ~ empty(U_721) ),
inference(variable_rename,[status(thm)],[f_190_1]) ).
cnf(f_190_3,plain,
( U_721 = empty_set
| ~ empty(U_721) ),
inference(clausify,[status(thm)],[f_190_2]) ).
fof(f_191_1,plain,
! [A,B] :
( A = B
| ~ subset(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t6_zfmisc_1]) ).
fof(f_191_2,plain,
! [U_723,U_722] :
( U_723 = U_722
| ~ subset(singleton(U_723),singleton(U_722)) ),
inference(variable_rename,[status(thm)],[f_191_1]) ).
cnf(f_191_3,plain,
( U_723 = U_722
| ~ subset(singleton(U_723),singleton(U_722)) ),
inference(clausify,[status(thm)],[f_191_2]) ).
fof(f_192_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_192_2,plain,
! [U_724] :
( relation_rng(identity_relation(U_724)) = U_724
& relation_dom(identity_relation(U_724)) = U_724 ),
inference(variable_rename,[status(thm)],[f_192_1]) ).
fof(f_192_3,plain,
( ! [U_726] : relation_rng(identity_relation(U_726)) = U_726
& ! [U_725] : relation_dom(identity_relation(U_725)) = U_725 ),
inference(miniscope,[status(thm)],[f_192_2]) ).
cnf(f_192_4,plain,
relation_dom(identity_relation(U_725)) = U_725,
inference(clausify,[status(thm)],[f_192_3]) ).
cnf(f_192_5,plain,
relation_rng(identity_relation(U_726)) = U_726,
inference(clausify,[status(thm)],[f_192_3]) ).
fof(f_193_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_193_2,plain,
! [U_730,U_729,U_728,U_727] :
( ( ( in(ordered_pair(U_730,U_729),relation_composition(identity_relation(U_728),U_727))
| ~ in(ordered_pair(U_730,U_729),U_727)
| ~ in(U_730,U_728) )
& ( ( in(ordered_pair(U_730,U_729),U_727)
& in(U_730,U_728) )
| ~ in(ordered_pair(U_730,U_729),relation_composition(identity_relation(U_728),U_727)) ) )
| ~ relation(U_727) ),
inference(variable_rename,[status(thm)],[f_193_1]) ).
cnf(f_193_3,plain,
( in(U_730,U_728)
| ~ in(ordered_pair(U_730,U_729),relation_composition(identity_relation(U_728),U_727))
| ~ relation(U_727) ),
inference(clausify,[status(thm)],[f_193_2]) ).
cnf(f_193_4,plain,
( in(ordered_pair(U_730,U_729),U_727)
| ~ in(ordered_pair(U_730,U_729),relation_composition(identity_relation(U_728),U_727))
| ~ relation(U_727) ),
inference(clausify,[status(thm)],[f_193_2]) ).
cnf(f_193_5,plain,
( in(ordered_pair(U_730,U_729),relation_composition(identity_relation(U_728),U_727))
| ~ in(ordered_pair(U_730,U_729),U_727)
| ~ in(U_730,U_728)
| ~ relation(U_727) ),
inference(clausify,[status(thm)],[f_193_2]) ).
fof(f_194_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_194_2,plain,
! [U_732,U_731] :
( ~ empty(U_731)
| ~ in(U_732,U_731) ),
inference(variable_rename,[status(thm)],[f_194_1]) ).
cnf(f_194_3,plain,
( ~ empty(U_731)
| ~ in(U_732,U_731) ),
inference(clausify,[status(thm)],[f_194_2]) ).
fof(f_195_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1]) ).
fof(f_195_2,plain,
! [U_734,U_733] : subset(U_734,set_union2(U_734,U_733)),
inference(variable_rename,[status(thm)],[f_195_1]) ).
cnf(f_195_3,plain,
subset(U_734,set_union2(U_734,U_733)),
inference(clausify,[status(thm)],[f_195_2]) ).
fof(f_196_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_196_2,plain,
! [U_736,U_735] :
( ( disjoint(U_736,U_735)
| set_difference(U_736,U_735) != U_736 )
& ( set_difference(U_736,U_735) = U_736
| ~ disjoint(U_736,U_735) ) ),
inference(variable_rename,[status(thm)],[f_196_1]) ).
fof(f_196_3,plain,
( ! [U_740,U_738] :
( disjoint(U_740,U_738)
| set_difference(U_740,U_738) != U_740 )
& ! [U_739,U_737] :
( set_difference(U_739,U_737) = U_739
| ~ disjoint(U_739,U_737) ) ),
inference(miniscope,[status(thm)],[f_196_2]) ).
cnf(f_196_4,plain,
( set_difference(U_739,U_737) = U_739
| ~ disjoint(U_739,U_737) ),
inference(clausify,[status(thm)],[f_196_3]) ).
cnf(f_196_5,plain,
( disjoint(U_740,U_738)
| set_difference(U_740,U_738) != U_740 ),
inference(clausify,[status(thm)],[f_196_3]) ).
fof(f_197_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_197_2,plain,
! [U_743,U_742,U_741] :
( ( ( in(U_743,relation_dom(relation_dom_restriction(U_741,U_742)))
| ~ in(U_743,relation_dom(U_741))
| ~ in(U_743,U_742) )
& ( ( in(U_743,relation_dom(U_741))
& in(U_743,U_742) )
| ~ in(U_743,relation_dom(relation_dom_restriction(U_741,U_742))) ) )
| ~ relation(U_741) ),
inference(variable_rename,[status(thm)],[f_197_1]) ).
cnf(f_197_3,plain,
( in(U_743,U_742)
| ~ in(U_743,relation_dom(relation_dom_restriction(U_741,U_742)))
| ~ relation(U_741) ),
inference(clausify,[status(thm)],[f_197_2]) ).
cnf(f_197_4,plain,
( in(U_743,relation_dom(U_741))
| ~ in(U_743,relation_dom(relation_dom_restriction(U_741,U_742)))
| ~ relation(U_741) ),
inference(clausify,[status(thm)],[f_197_2]) ).
cnf(f_197_5,plain,
( in(U_743,relation_dom(relation_dom_restriction(U_741,U_742)))
| ~ in(U_743,relation_dom(U_741))
| ~ in(U_743,U_742)
| ~ relation(U_741) ),
inference(clausify,[status(thm)],[f_197_2]) ).
fof(f_198_1,plain,
! [A,B] :
( subset(relation_dom_restriction(B,A),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t88_relat_1]) ).
fof(f_198_2,plain,
! [U_745,U_744] :
( subset(relation_dom_restriction(U_744,U_745),U_744)
| ~ relation(U_744) ),
inference(variable_rename,[status(thm)],[f_198_1]) ).
cnf(f_198_3,plain,
( subset(relation_dom_restriction(U_744,U_745),U_744)
| ~ relation(U_744) ),
inference(clausify,[status(thm)],[f_198_2]) ).
fof(f_199_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_199_2,plain,
! [U_747,U_746] :
( ~ empty(U_746)
| U_747 = U_746
| ~ empty(U_747) ),
inference(variable_rename,[status(thm)],[f_199_1]) ).
fof(f_199_3,plain,
! [U_747] :
( ! [U_746] :
( ~ empty(U_746)
| U_747 = U_746 )
| ~ empty(U_747) ),
inference(miniscope,[status(thm)],[f_199_2]) ).
cnf(f_199_4,plain,
( ~ empty(U_746)
| U_747 = U_746
| ~ empty(U_747) ),
inference(clausify,[status(thm)],[f_199_3]) ).
fof(f_200_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_200_2,plain,
! [U_750,U_749,U_748] :
( subset(set_union2(U_750,U_748),U_749)
| ~ subset(U_748,U_749)
| ~ subset(U_750,U_749) ),
inference(variable_rename,[status(thm)],[f_200_1]) ).
cnf(f_200_3,plain,
( subset(set_union2(U_750,U_748),U_749)
| ~ subset(U_748,U_749)
| ~ subset(U_750,U_749) ),
inference(clausify,[status(thm)],[f_200_2]) ).
fof(f_201_1,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t8_zfmisc_1]) ).
fof(f_201_2,plain,
! [U_753,U_752,U_751] :
( U_753 = U_752
| singleton(U_753) != unordered_pair(U_752,U_751) ),
inference(variable_rename,[status(thm)],[f_201_1]) ).
fof(f_201_3,plain,
! [U_753,U_752] :
( ! [U_751] : singleton(U_753) != unordered_pair(U_752,U_751)
| U_753 = U_752 ),
inference(miniscope,[status(thm)],[f_201_2]) ).
cnf(f_201_4,plain,
( singleton(U_753) != unordered_pair(U_752,U_751)
| U_753 = U_752 ),
inference(clausify,[status(thm)],[f_201_3]) ).
fof(f_202_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_202_2,plain,
! [U_755,U_754] :
( relation_dom(relation_dom_restriction(U_754,U_755)) = set_intersection2(relation_dom(U_754),U_755)
| ~ relation(U_754) ),
inference(variable_rename,[status(thm)],[f_202_1]) ).
cnf(f_202_3,plain,
( relation_dom(relation_dom_restriction(U_754,U_755)) = set_intersection2(relation_dom(U_754),U_755)
| ~ relation(U_754) ),
inference(clausify,[status(thm)],[f_202_2]) ).
fof(f_203_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t92_zfmisc_1]) ).
fof(f_203_2,plain,
! [U_757,U_756] :
( subset(U_757,union(U_756))
| ~ in(U_757,U_756) ),
inference(variable_rename,[status(thm)],[f_203_1]) ).
cnf(f_203_3,plain,
( subset(U_757,union(U_756))
| ~ in(U_757,U_756) ),
inference(clausify,[status(thm)],[f_203_2]) ).
fof(f_204_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_204_2,plain,
! [U_759,U_758] :
( relation_dom_restriction(U_758,U_759) = relation_composition(identity_relation(U_759),U_758)
| ~ relation(U_758) ),
inference(variable_rename,[status(thm)],[f_204_1]) ).
cnf(f_204_3,plain,
( relation_dom_restriction(U_758,U_759) = relation_composition(identity_relation(U_759),U_758)
| ~ relation(U_758) ),
inference(clausify,[status(thm)],[f_204_2]) ).
fof(f_205_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_205_2,plain,
! [U_761,U_760] :
( subset(relation_rng(relation_dom_restriction(U_760,U_761)),relation_rng(U_760))
| ~ relation(U_760) ),
inference(variable_rename,[status(thm)],[f_205_1]) ).
cnf(f_205_3,plain,
( subset(relation_rng(relation_dom_restriction(U_760,U_761)),relation_rng(U_760))
| ~ relation(U_760) ),
inference(clausify,[status(thm)],[f_205_2]) ).
fof(f_206_1,plain,
! [A] : union(powerset(A)) = A,
inference(fof_nnf,[status(thm)],[t99_zfmisc_1]) ).
fof(f_206_2,plain,
! [U_762] : union(powerset(U_762)) = U_762,
inference(variable_rename,[status(thm)],[f_206_1]) ).
cnf(f_206_3,plain,
union(powerset(U_762)) = U_762,
inference(clausify,[status(thm)],[f_206_2]) ).
fof(f_207_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_207_2,plain,
! [U_770] :
? [U_769] :
( ! [U_768] :
( in(U_768,U_769)
| are_equipotent(U_768,U_769)
| ~ subset(U_768,U_769) )
& ! [U_767] :
( ? [U_766] :
( ! [U_765] :
( in(U_765,U_766)
| ~ subset(U_765,U_767) )
& in(U_766,U_769) )
| ~ in(U_767,U_769) )
& ! [U_764,U_763] :
( in(U_763,U_769)
| ~ subset(U_763,U_764)
| ~ in(U_764,U_769) )
& in(U_770,U_769) ),
inference(variable_rename,[status(thm)],[f_207_1]) ).
fof(f_207_3,plain,
! [U_770] :
( ! [U_768] :
( in(U_768,sK97(U_770))
| are_equipotent(U_768,sK97(U_770))
| ~ subset(U_768,sK97(U_770)) )
& ! [U_767] :
( ? [U_766] :
( ! [U_765] :
( in(U_765,U_766)
| ~ subset(U_765,U_767) )
& in(U_766,sK97(U_770)) )
| ~ in(U_767,sK97(U_770)) )
& ! [U_764,U_763] :
( in(U_763,sK97(U_770))
| ~ subset(U_763,U_764)
| ~ in(U_764,sK97(U_770)) )
& in(U_770,sK97(U_770)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_769,sK97(U_770))],[f_207_2]) ).
fof(f_207_4,plain,
! [U_770] :
( ! [U_768] :
( in(U_768,sK97(U_770))
| are_equipotent(U_768,sK97(U_770))
| ~ subset(U_768,sK97(U_770)) )
& ! [U_767] :
( ( ! [U_765] :
( in(U_765,sK98(U_770,U_767))
| ~ subset(U_765,U_767) )
& in(sK98(U_770,U_767),sK97(U_770)) )
| ~ in(U_767,sK97(U_770)) )
& ! [U_764,U_763] :
( in(U_763,sK97(U_770))
| ~ subset(U_763,U_764)
| ~ in(U_764,sK97(U_770)) )
& in(U_770,sK97(U_770)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_766,sK98(U_770,U_767))],[f_207_3]) ).
cnf(f_207_5,plain,
in(U_770,sK97(U_770)),
inference(clausify,[status(thm)],[f_207_4]) ).
cnf(f_207_6,plain,
( in(U_763,sK97(U_770))
| ~ subset(U_763,U_764)
| ~ in(U_764,sK97(U_770)) ),
inference(clausify,[status(thm)],[f_207_4]) ).
cnf(f_207_7,plain,
( in(sK98(U_770,U_767),sK97(U_770))
| ~ in(U_767,sK97(U_770)) ),
inference(clausify,[status(thm)],[f_207_4]) ).
cnf(f_207_8,plain,
( in(U_765,sK98(U_770,U_767))
| ~ subset(U_765,U_767)
| ~ in(U_767,sK97(U_770)) ),
inference(clausify,[status(thm)],[f_207_4]) ).
cnf(f_207_9,plain,
( in(U_768,sK97(U_770))
| are_equipotent(U_768,sK97(U_770))
| ~ subset(U_768,sK97(U_770)) ),
inference(clausify,[status(thm)],[f_207_4]) ).
fof(f_208_1,plain,
! [A,B,C] :
( B = C
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t9_zfmisc_1]) ).
fof(f_208_2,plain,
! [U_773,U_772,U_771] :
( U_772 = U_771
| singleton(U_773) != unordered_pair(U_772,U_771) ),
inference(variable_rename,[status(thm)],[f_208_1]) ).
cnf(f_208_3,plain,
( U_772 = U_771
| singleton(U_773) != unordered_pair(U_772,U_771) ),
inference(clausify,[status(thm)],[f_208_2]) ).
cnf(f_37_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_37_8]) ).
cnf(f_37_9_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_37_9]) ).
cnf(f_39_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_39_2]) ).
cnf(f_40_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_40_2]) ).
cnf(f_41_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_41_2]) ).
cnf(f_42_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_42_2]) ).
cnf(f_43_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_43_2]) ).
cnf(f_44_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_44_2]) ).
cnf(f_45_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_45_2]) ).
cnf(f_47_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_47_2]) ).
cnf(f_48_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_48_2]) ).
cnf(f_49_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_49_2]) ).
cnf(f_50_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_50_2]) ).
cnf(f_52_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_52_2]) ).
cnf(f_53_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_53_2]) ).
cnf(f_55_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_55_2]) ).
cnf(f_56_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_56_2]) ).
cnf(f_65_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_65_2]) ).
cnf(f_66_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_66_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( unordered_pair(Eq_x_0,Eq_x_1) = unordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( set_union2(Eq_x_0,Eq_x_1) = set_union2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( set_intersection2(Eq_x_0,Eq_x_1) = set_intersection2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( identity_relation(Eq_x_0) = identity_relation(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( ordered_pair(Eq_x_0,Eq_x_1) = ordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( relation_dom_restriction(Eq_x_0,Eq_x_1) = relation_dom_restriction(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( 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,
( relation_image(Eq_x_0,Eq_x_1) = relation_image(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( relation_inverse_image(Eq_x_0,Eq_x_1) = relation_inverse_image(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( set_meet(Eq_x_0) = set_meet(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,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_17,axiom,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,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_19,axiom,
( union(Eq_x_0) = union(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,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_21,axiom,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,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_23,axiom,
( relation_field(Eq_x_0) = relation_field(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,axiom,
( relation_inverse(Eq_x_0) = relation_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,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_26,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_27,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_28,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_29,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_30,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_31,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_32,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_33,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_34,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_35,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_36,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_37,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_38,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_39,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_40,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_41,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_42,axiom,
( sK13(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK13(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_43,axiom,
( sK14(Eq_x_0,Eq_x_1,Eq_x_2) = sK14(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_44,axiom,
( sK15(Eq_x_0,Eq_x_1,Eq_x_2) = sK15(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_45,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_46,axiom,
( sK17(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK17(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_47,axiom,
( sK18(Eq_x_0,Eq_x_1,Eq_x_2) = sK18(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_48,axiom,
( sK19(Eq_x_0,Eq_x_1,Eq_x_2) = sK19(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_49,axiom,
( sK20(Eq_x_0,Eq_x_1,Eq_x_2) = sK20(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_50,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_51,axiom,
( sK22(Eq_x_0,Eq_x_1) = sK22(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_52,axiom,
( sK23(Eq_x_0) = sK23(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_53,axiom,
( sK24(Eq_x_0,Eq_x_1,Eq_x_2) = sK24(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_54,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_55,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_56,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_57,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_58,axiom,
( sK29(Eq_x_0,Eq_x_1) = sK29(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_59,axiom,
( sK30(Eq_x_0) = sK30(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_60,axiom,
( sK31(Eq_x_0,Eq_x_1) = sK31(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_61,axiom,
( sK32(Eq_x_0,Eq_x_1) = sK32(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_62,axiom,
( sK33(Eq_x_0,Eq_x_1) = sK33(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_63,axiom,
( sK34(Eq_x_0,Eq_x_1) = sK34(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_64,axiom,
( sK35(Eq_x_0,Eq_x_1) = sK35(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_65,axiom,
( sK36(Eq_x_0,Eq_x_1) = sK36(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_66,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_67,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_68,axiom,
( sK39(Eq_x_0,Eq_x_1,Eq_x_2) = sK39(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_69,axiom,
( sK40(Eq_x_0,Eq_x_1,Eq_x_2) = sK40(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_70,axiom,
( sK41(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK41(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_71,axiom,
( sK42(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK42(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_72,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_73,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_74,axiom,
( sK45(Eq_x_0,Eq_x_1,Eq_x_2) = sK45(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_75,axiom,
( sK46(Eq_x_0,Eq_x_1,Eq_x_2) = sK46(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_76,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_77,axiom,
( sK48(Eq_x_0,Eq_x_1) = sK48(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_78,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_79,axiom,
( sK50(Eq_x_0,Eq_x_1,Eq_x_2) = sK50(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_80,axiom,
( sK51(Eq_x_0,Eq_x_1,Eq_x_2) = sK51(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,
( 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_82,axiom,
( sK53(Eq_x_0,Eq_x_1) = sK53(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_83,axiom,
( sK54(Eq_x_0,Eq_x_1) = sK54(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_84,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_85,axiom,
( sK56(Eq_x_0,Eq_x_1,Eq_x_2) = sK56(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_86,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_87,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_88,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_89,axiom,
( sK60(Eq_x_0,Eq_x_1,Eq_x_2) = sK60(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_90,axiom,
( sK61(Eq_x_0,Eq_x_1,Eq_x_2) = sK61(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_91,axiom,
( sK62(Eq_x_0,Eq_x_1,Eq_x_2) = sK62(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_92,axiom,
( sK63(Eq_x_0,Eq_x_1) = sK63(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_93,axiom,
( sK64(Eq_x_0,Eq_x_1) = sK64(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_94,axiom,
( sK65(Eq_x_0,Eq_x_1) = sK65(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_95,axiom,
( sK66(Eq_x_0,Eq_x_1) = sK66(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_96,axiom,
( sK67(Eq_x_0,Eq_x_1) = sK67(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_97,axiom,
( sK68(Eq_x_0,Eq_x_1) = sK68(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,
( sK69(Eq_x_0,Eq_x_1) = sK69(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_99,axiom,
( sK70(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK70(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_100,axiom,
( sK71(Eq_x_0,Eq_x_1,Eq_x_2) = sK71(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_101,axiom,
( sK72(Eq_x_0,Eq_x_1,Eq_x_2) = sK72(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_102,axiom,
( sK73(Eq_x_0,Eq_x_1,Eq_x_2) = sK73(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_103,axiom,
( sK74(Eq_x_0,Eq_x_1,Eq_x_2) = sK74(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_104,axiom,
( sK75(Eq_x_0,Eq_x_1,Eq_x_2) = sK75(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_105,axiom,
( sK76(Eq_x_0,Eq_x_1,Eq_x_2) = sK76(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_106,axiom,
( sK77(Eq_x_0) = sK77(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_107,axiom,
( sK78(Eq_x_0,Eq_x_1) = sK78(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_108,axiom,
( sK80(Eq_x_0) = sK80(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_109,axiom,
( sK83(Eq_x_0) = sK83(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_110,axiom,
( sK85(Eq_x_0) = sK85(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_111,axiom,
( sK86(Eq_x_0,Eq_x_1,Eq_x_2) = sK86(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_112,axiom,
( sK87(Eq_x_0,Eq_x_1,Eq_x_2) = sK87(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_113,axiom,
( sK91(Eq_x_0,Eq_x_1) = sK91(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_114,axiom,
( sK92(Eq_x_0,Eq_x_1) = sK92(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_115,axiom,
( sK93(Eq_x_0,Eq_x_1) = sK93(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_116,axiom,
( sK94(Eq_x_0,Eq_x_1) = sK94(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_117,axiom,
( sK95(Eq_x_0) = sK95(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_118,axiom,
( sK96(Eq_x_0) = sK96(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_119,axiom,
( sK97(Eq_x_0) = sK97(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_120,axiom,
( sK98(Eq_x_0,Eq_x_1) = sK98(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_121,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_122,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_123,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_124,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_125,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_126,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_127,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_128,axiom,
( are_equipotent(Eq_y_0,Eq_y_1)
| ~ are_equipotent(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU211+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n019.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 19 23:32:06 UTC 2026
% 0.09/0.37 % CPUTime :
% 165.16/165.47 % SZS status Theorem for theBenchmark
% 165.16/165.47 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------