%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU224+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 : n005.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 08:58:34 AM UTC 2026
% Result : Theorem 81.55s 81.81s
% Output : Proof 81.55s
% 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_funct_1,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('theBenchmark.p',cc1_funct_1) ).
fof(cc1_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('theBenchmark.p',cc1_relat_1) ).
fof(cc2_funct_1,axiom,
! [A] :
( ( function(A)
& empty(A)
& relation(A) )
=> ( one_to_one(A)
& function(A)
& relation(A) ) ),
file('theBenchmark.p',cc2_funct_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_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( ( ~ in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> C = empty_set ) )
& ( in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) ) ) ) ),
file('theBenchmark.p',d4_funct_1) ).
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_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
<=> ! [B,C] :
( ( apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
=> B = C ) ) ),
file('theBenchmark.p',d8_funct_1) ).
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(d9_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> function_inverse(A) = relation_inverse(A) ) ),
file('theBenchmark.p',d9_funct_1) ).
fof(dt_k10_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k10_relat_1) ).
fof(dt_k1_funct_1,axiom,
$true,
file('theBenchmark.p',dt_k1_funct_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_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( function(function_inverse(A))
& relation(function_inverse(A)) ) ),
file('theBenchmark.p',dt_k2_funct_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(fc11_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_inverse(A))
& empty(relation_inverse(A)) ) ),
file('theBenchmark.p',fc11_relat_1) ).
fof(fc12_relat_1,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc12_relat_1) ).
fof(fc13_relat_1,axiom,
! [A,B] :
( ( relation_empty_yielding(A)
& relation(A) )
=> ( relation_empty_yielding(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) ) ),
file('theBenchmark.p',fc13_relat_1) ).
fof(fc1_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B)
& function(A)
& relation(A) )
=> ( function(relation_composition(A,B))
& relation(relation_composition(A,B)) ) ),
file('theBenchmark.p',fc1_funct_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_funct_1,axiom,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
file('theBenchmark.p',fc2_funct_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_funct_1,axiom,
! [A] :
( ( one_to_one(A)
& function(A)
& relation(A) )
=> ( function(relation_inverse(A))
& relation(relation_inverse(A)) ) ),
file('theBenchmark.p',fc3_funct_1) ).
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_funct_1,axiom,
! [A,B] :
( ( function(A)
& relation(A) )
=> ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) ) ),
file('theBenchmark.p',fc4_funct_1) ).
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(l82_funct_1,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
<=> ( in(B,A)
& in(B,relation_dom(C)) ) ) ),
file('theBenchmark.p',l82_funct_1) ).
fof(rc1_funct_1,axiom,
? [A] :
( function(A)
& relation(A) ),
file('theBenchmark.p',rc1_funct_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_funct_1,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('theBenchmark.p',rc2_funct_1) ).
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(rc3_funct_1,axiom,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc3_funct_1) ).
fof(rc3_relat_1,axiom,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc3_relat_1) ).
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,lemma,
! [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_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(relation_composition(C,B)))
<=> ( in(apply(C,A),relation_dom(B))
& in(A,relation_dom(C)) ) ) ) ),
file('theBenchmark.p',t21_funct_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(t22_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(relation_composition(C,B)))
=> apply(relation_composition(C,B),A) = apply(B,apply(C,A)) ) ) ),
file('theBenchmark.p',t22_funct_1) ).
fof(t23_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(B))
=> apply(relation_composition(B,C),A) = apply(C,apply(B,A)) ) ) ),
file('theBenchmark.p',t23_funct_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(t34_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( B = identity_relation(A)
<=> ( ! [C] :
( in(C,A)
=> apply(B,C) = C )
& relation_dom(B) = A ) ) ),
file('theBenchmark.p',t34_funct_1) ).
fof(t35_funct_1,lemma,
! [A,B] :
( in(B,A)
=> apply(identity_relation(A),B) = B ),
file('theBenchmark.p',t35_funct_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_funct_1,lemma,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( B = function_inverse(A)
<=> ( ! [C,D] :
( ( ( C = apply(A,D)
& in(D,relation_dom(A)) )
=> ( D = apply(B,C)
& in(C,relation_rng(A)) ) )
& ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
=> ( C = apply(A,D)
& in(D,relation_dom(A)) ) ) )
& relation_dom(B) = relation_rng(A) ) ) ) ) ),
file('theBenchmark.p',t54_funct_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(t55_funct_1,lemma,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_dom(A) = relation_rng(function_inverse(A))
& relation_rng(A) = relation_dom(function_inverse(A)) ) ) ),
file('theBenchmark.p',t55_funct_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(t57_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( ( in(A,relation_rng(B))
& one_to_one(B) )
=> ( A = apply(relation_composition(function_inverse(B),B),A)
& A = apply(B,apply(function_inverse(B),A)) ) ) ),
file('theBenchmark.p',t57_funct_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(t62_funct_1,lemma,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> one_to_one(function_inverse(A)) ) ),
file('theBenchmark.p',t62_funct_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(t68_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( B = relation_dom_restriction(C,A)
<=> ( ! [D] :
( in(D,relation_dom(B))
=> apply(B,D) = apply(C,D) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) ) ) ) ),
file('theBenchmark.p',t68_funct_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(t70_funct_1,lemma,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
file('theBenchmark.p',t70_funct_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_funct_1,lemma,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(ordered_pair(A,B),C)
<=> ( B = apply(C,A)
& in(A,relation_dom(C)) ) ) ),
file('theBenchmark.p',t8_funct_1) ).
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] :
( function(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_3_2,plain,
! [U_4] :
( function(U_4)
| ~ empty(U_4) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( function(U_4)
| ~ empty(U_4) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_4_2,plain,
! [U_5] :
( relation(U_5)
| ~ empty(U_5) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( relation(U_5)
| ~ empty(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A] :
( ( one_to_one(A)
& function(A)
& relation(A) )
| ~ function(A)
| ~ empty(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[cc2_funct_1]) ).
fof(f_5_2,plain,
! [U_6] :
( ( one_to_one(U_6)
& function(U_6)
& relation(U_6) )
| ~ function(U_6)
| ~ empty(U_6)
| ~ relation(U_6) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( relation(U_6)
| ~ function(U_6)
| ~ empty(U_6)
| ~ relation(U_6) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( function(U_6)
| ~ function(U_6)
| ~ empty(U_6)
| ~ relation(U_6) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_5,plain,
( one_to_one(U_6)
| ~ function(U_6)
| ~ empty(U_6)
| ~ relation(U_6) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_6_2,plain,
! [U_8,U_7] : unordered_pair(U_8,U_7) = unordered_pair(U_7,U_8),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
unordered_pair(U_8,U_7) = unordered_pair(U_7,U_8),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_7_2,plain,
! [U_10,U_9] : set_union2(U_10,U_9) = set_union2(U_9,U_10),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
set_union2(U_10,U_9) = set_union2(U_9,U_10),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_8_2,plain,
! [U_12,U_11] : set_intersection2(U_12,U_11) = set_intersection2(U_11,U_12),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
set_intersection2(U_12,U_11) = set_intersection2(U_11,U_12),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_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_9_2,plain,
! [U_18,U_17] :
( ( ( U_17 = identity_relation(U_18)
| ? [U_16,U_15] :
( ( ~ in(ordered_pair(U_16,U_15),U_17)
& U_16 = U_15
& in(U_16,U_18) )
| ( ( U_16 != U_15
| ~ in(U_16,U_18) )
& in(ordered_pair(U_16,U_15),U_17) ) ) )
& ( ! [U_14,U_13] :
( ( in(ordered_pair(U_14,U_13),U_17)
| U_14 != U_13
| ~ in(U_14,U_18) )
& ( ( U_14 = U_13
& in(U_14,U_18) )
| ~ in(ordered_pair(U_14,U_13),U_17) ) )
| U_17 != identity_relation(U_18) ) )
| ~ relation(U_17) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_18,U_17] :
( ( ( U_17 = identity_relation(U_18)
| ? [U_26,U_24] :
( ~ in(ordered_pair(U_26,U_24),U_17)
& U_26 = U_24
& in(U_26,U_18) )
| ? [U_25,U_23] :
( ( U_25 != U_23
| ~ in(U_25,U_18) )
& in(ordered_pair(U_25,U_23),U_17) ) )
& ( ( ! [U_22,U_20] :
( in(ordered_pair(U_22,U_20),U_17)
| U_22 != U_20
| ~ in(U_22,U_18) )
& ! [U_21,U_19] :
( ( U_21 = U_19
& in(U_21,U_18) )
| ~ in(ordered_pair(U_21,U_19),U_17) ) )
| U_17 != identity_relation(U_18) ) )
| ~ relation(U_17) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
fof(f_9_4,plain,
! [U_18,U_17] :
( ( ( U_17 = identity_relation(U_18)
| ? [U_26,U_24] :
( ~ in(ordered_pair(U_26,U_24),U_17)
& U_26 = U_24
& in(U_26,U_18) )
| ? [U_23] :
( ( sK1(U_18,U_17) != U_23
| ~ in(sK1(U_18,U_17),U_18) )
& in(ordered_pair(sK1(U_18,U_17),U_23),U_17) ) )
& ( ( ! [U_22,U_20] :
( in(ordered_pair(U_22,U_20),U_17)
| U_22 != U_20
| ~ in(U_22,U_18) )
& ! [U_21,U_19] :
( ( U_21 = U_19
& in(U_21,U_18) )
| ~ in(ordered_pair(U_21,U_19),U_17) ) )
| U_17 != identity_relation(U_18) ) )
| ~ relation(U_17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_25,sK1(U_18,U_17))],[f_9_3]) ).
fof(f_9_5,plain,
! [U_18,U_17] :
( ( ( U_17 = identity_relation(U_18)
| ? [U_26,U_24] :
( ~ in(ordered_pair(U_26,U_24),U_17)
& U_26 = U_24
& in(U_26,U_18) )
| ( ( sK1(U_18,U_17) != sK2(U_18,U_17)
| ~ in(sK1(U_18,U_17),U_18) )
& in(ordered_pair(sK1(U_18,U_17),sK2(U_18,U_17)),U_17) ) )
& ( ( ! [U_22,U_20] :
( in(ordered_pair(U_22,U_20),U_17)
| U_22 != U_20
| ~ in(U_22,U_18) )
& ! [U_21,U_19] :
( ( U_21 = U_19
& in(U_21,U_18) )
| ~ in(ordered_pair(U_21,U_19),U_17) ) )
| U_17 != identity_relation(U_18) ) )
| ~ relation(U_17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_23,sK2(U_18,U_17))],[f_9_4]) ).
fof(f_9_6,plain,
! [U_18,U_17] :
( ( ( U_17 = identity_relation(U_18)
| ? [U_24] :
( ~ in(ordered_pair(sK3(U_18,U_17),U_24),U_17)
& sK3(U_18,U_17) = U_24
& in(sK3(U_18,U_17),U_18) )
| ( ( sK1(U_18,U_17) != sK2(U_18,U_17)
| ~ in(sK1(U_18,U_17),U_18) )
& in(ordered_pair(sK1(U_18,U_17),sK2(U_18,U_17)),U_17) ) )
& ( ( ! [U_22,U_20] :
( in(ordered_pair(U_22,U_20),U_17)
| U_22 != U_20
| ~ in(U_22,U_18) )
& ! [U_21,U_19] :
( ( U_21 = U_19
& in(U_21,U_18) )
| ~ in(ordered_pair(U_21,U_19),U_17) ) )
| U_17 != identity_relation(U_18) ) )
| ~ relation(U_17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_26,sK3(U_18,U_17))],[f_9_5]) ).
fof(f_9_7,plain,
! [U_18,U_17] :
( ( ( U_17 = identity_relation(U_18)
| ( ~ in(ordered_pair(sK3(U_18,U_17),sK4(U_18,U_17)),U_17)
& sK3(U_18,U_17) = sK4(U_18,U_17)
& in(sK3(U_18,U_17),U_18) )
| ( ( sK1(U_18,U_17) != sK2(U_18,U_17)
| ~ in(sK1(U_18,U_17),U_18) )
& in(ordered_pair(sK1(U_18,U_17),sK2(U_18,U_17)),U_17) ) )
& ( ( ! [U_22,U_20] :
( in(ordered_pair(U_22,U_20),U_17)
| U_22 != U_20
| ~ in(U_22,U_18) )
& ! [U_21,U_19] :
( ( U_21 = U_19
& in(U_21,U_18) )
| ~ in(ordered_pair(U_21,U_19),U_17) ) )
| U_17 != identity_relation(U_18) ) )
| ~ relation(U_17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_24,sK4(U_18,U_17))],[f_9_6]) ).
cnf(f_9_8,plain,
( in(U_21,U_18)
| ~ in(ordered_pair(U_21,U_19),U_17)
| U_17 != identity_relation(U_18)
| ~ relation(U_17) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_9,plain,
( U_21 = U_19
| ~ in(ordered_pair(U_21,U_19),U_17)
| U_17 != identity_relation(U_18)
| ~ relation(U_17) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_10,plain,
( in(ordered_pair(U_22,U_20),U_17)
| U_22 != U_20
| ~ in(U_22,U_18)
| U_17 != identity_relation(U_18)
| ~ relation(U_17) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_11,plain,
( in(sK3(U_18,U_17),U_18)
| in(ordered_pair(sK1(U_18,U_17),sK2(U_18,U_17)),U_17)
| U_17 = identity_relation(U_18)
| ~ relation(U_17) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_12,plain,
( sK3(U_18,U_17) = sK4(U_18,U_17)
| in(ordered_pair(sK1(U_18,U_17),sK2(U_18,U_17)),U_17)
| U_17 = identity_relation(U_18)
| ~ relation(U_17) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_13,plain,
( ~ in(ordered_pair(sK3(U_18,U_17),sK4(U_18,U_17)),U_17)
| in(ordered_pair(sK1(U_18,U_17),sK2(U_18,U_17)),U_17)
| U_17 = identity_relation(U_18)
| ~ relation(U_17) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_14,plain,
( in(sK3(U_18,U_17),U_18)
| sK1(U_18,U_17) != sK2(U_18,U_17)
| ~ in(sK1(U_18,U_17),U_18)
| U_17 = identity_relation(U_18)
| ~ relation(U_17) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_15,plain,
( sK3(U_18,U_17) = sK4(U_18,U_17)
| sK1(U_18,U_17) != sK2(U_18,U_17)
| ~ in(sK1(U_18,U_17),U_18)
| U_17 = identity_relation(U_18)
| ~ relation(U_17) ),
inference(clausify,[status(thm)],[f_9_7]) ).
cnf(f_9_16,plain,
( ~ in(ordered_pair(sK3(U_18,U_17),sK4(U_18,U_17)),U_17)
| sK1(U_18,U_17) != sK2(U_18,U_17)
| ~ in(sK1(U_18,U_17),U_18)
| U_17 = identity_relation(U_18)
| ~ relation(U_17) ),
inference(clausify,[status(thm)],[f_9_7]) ).
fof(f_10_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_10_2,plain,
! [U_28,U_27] :
( ( U_28 = U_27
| ~ subset(U_27,U_28)
| ~ subset(U_28,U_27) )
& ( ( subset(U_27,U_28)
& subset(U_28,U_27) )
| U_28 != U_27 ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_32,U_30] :
( U_32 = U_30
| ~ subset(U_30,U_32)
| ~ subset(U_32,U_30) )
& ! [U_31,U_29] :
( ( subset(U_29,U_31)
& subset(U_31,U_29) )
| U_31 != U_29 ) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( subset(U_31,U_29)
| U_31 != U_29 ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_5,plain,
( subset(U_29,U_31)
| U_31 != U_29 ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_6,plain,
( U_32 = U_30
| ~ subset(U_30,U_32)
| ~ subset(U_32,U_30) ),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_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_11_2,plain,
! [U_39] :
( ! [U_38,U_37] :
( ( ( U_37 = relation_dom_restriction(U_39,U_38)
| ? [U_36,U_35] :
( ( ~ in(ordered_pair(U_36,U_35),U_37)
& in(ordered_pair(U_36,U_35),U_39)
& in(U_36,U_38) )
| ( ( ~ in(ordered_pair(U_36,U_35),U_39)
| ~ in(U_36,U_38) )
& in(ordered_pair(U_36,U_35),U_37) ) ) )
& ( ! [U_34,U_33] :
( ( in(ordered_pair(U_34,U_33),U_37)
| ~ in(ordered_pair(U_34,U_33),U_39)
| ~ in(U_34,U_38) )
& ( ( in(ordered_pair(U_34,U_33),U_39)
& in(U_34,U_38) )
| ~ in(ordered_pair(U_34,U_33),U_37) ) )
| U_37 != relation_dom_restriction(U_39,U_38) ) )
| ~ relation(U_37) )
| ~ relation(U_39) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_39] :
( ! [U_38,U_37] :
( ( ( U_37 = relation_dom_restriction(U_39,U_38)
| ? [U_47,U_45] :
( ~ in(ordered_pair(U_47,U_45),U_37)
& in(ordered_pair(U_47,U_45),U_39)
& in(U_47,U_38) )
| ? [U_46,U_44] :
( ( ~ in(ordered_pair(U_46,U_44),U_39)
| ~ in(U_46,U_38) )
& in(ordered_pair(U_46,U_44),U_37) ) )
& ( ( ! [U_43,U_41] :
( in(ordered_pair(U_43,U_41),U_37)
| ~ in(ordered_pair(U_43,U_41),U_39)
| ~ in(U_43,U_38) )
& ! [U_42,U_40] :
( ( in(ordered_pair(U_42,U_40),U_39)
& in(U_42,U_38) )
| ~ in(ordered_pair(U_42,U_40),U_37) ) )
| U_37 != relation_dom_restriction(U_39,U_38) ) )
| ~ relation(U_37) )
| ~ relation(U_39) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
fof(f_11_4,plain,
! [U_39] :
( ! [U_38,U_37] :
( ( ( U_37 = relation_dom_restriction(U_39,U_38)
| ? [U_47,U_45] :
( ~ in(ordered_pair(U_47,U_45),U_37)
& in(ordered_pair(U_47,U_45),U_39)
& in(U_47,U_38) )
| ? [U_44] :
( ( ~ in(ordered_pair(sK5(U_39,U_38,U_37),U_44),U_39)
| ~ in(sK5(U_39,U_38,U_37),U_38) )
& in(ordered_pair(sK5(U_39,U_38,U_37),U_44),U_37) ) )
& ( ( ! [U_43,U_41] :
( in(ordered_pair(U_43,U_41),U_37)
| ~ in(ordered_pair(U_43,U_41),U_39)
| ~ in(U_43,U_38) )
& ! [U_42,U_40] :
( ( in(ordered_pair(U_42,U_40),U_39)
& in(U_42,U_38) )
| ~ in(ordered_pair(U_42,U_40),U_37) ) )
| U_37 != relation_dom_restriction(U_39,U_38) ) )
| ~ relation(U_37) )
| ~ relation(U_39) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_46,sK5(U_39,U_38,U_37))],[f_11_3]) ).
fof(f_11_5,plain,
! [U_39] :
( ! [U_38,U_37] :
( ( ( U_37 = relation_dom_restriction(U_39,U_38)
| ? [U_47,U_45] :
( ~ in(ordered_pair(U_47,U_45),U_37)
& in(ordered_pair(U_47,U_45),U_39)
& in(U_47,U_38) )
| ( ( ~ in(ordered_pair(sK5(U_39,U_38,U_37),sK6(U_39,U_38,U_37)),U_39)
| ~ in(sK5(U_39,U_38,U_37),U_38) )
& in(ordered_pair(sK5(U_39,U_38,U_37),sK6(U_39,U_38,U_37)),U_37) ) )
& ( ( ! [U_43,U_41] :
( in(ordered_pair(U_43,U_41),U_37)
| ~ in(ordered_pair(U_43,U_41),U_39)
| ~ in(U_43,U_38) )
& ! [U_42,U_40] :
( ( in(ordered_pair(U_42,U_40),U_39)
& in(U_42,U_38) )
| ~ in(ordered_pair(U_42,U_40),U_37) ) )
| U_37 != relation_dom_restriction(U_39,U_38) ) )
| ~ relation(U_37) )
| ~ relation(U_39) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_44,sK6(U_39,U_38,U_37))],[f_11_4]) ).
fof(f_11_6,plain,
! [U_39] :
( ! [U_38,U_37] :
( ( ( U_37 = relation_dom_restriction(U_39,U_38)
| ? [U_45] :
( ~ in(ordered_pair(sK7(U_39,U_38,U_37),U_45),U_37)
& in(ordered_pair(sK7(U_39,U_38,U_37),U_45),U_39)
& in(sK7(U_39,U_38,U_37),U_38) )
| ( ( ~ in(ordered_pair(sK5(U_39,U_38,U_37),sK6(U_39,U_38,U_37)),U_39)
| ~ in(sK5(U_39,U_38,U_37),U_38) )
& in(ordered_pair(sK5(U_39,U_38,U_37),sK6(U_39,U_38,U_37)),U_37) ) )
& ( ( ! [U_43,U_41] :
( in(ordered_pair(U_43,U_41),U_37)
| ~ in(ordered_pair(U_43,U_41),U_39)
| ~ in(U_43,U_38) )
& ! [U_42,U_40] :
( ( in(ordered_pair(U_42,U_40),U_39)
& in(U_42,U_38) )
| ~ in(ordered_pair(U_42,U_40),U_37) ) )
| U_37 != relation_dom_restriction(U_39,U_38) ) )
| ~ relation(U_37) )
| ~ relation(U_39) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_47,sK7(U_39,U_38,U_37))],[f_11_5]) ).
fof(f_11_7,plain,
! [U_39] :
( ! [U_38,U_37] :
( ( ( U_37 = relation_dom_restriction(U_39,U_38)
| ( ~ in(ordered_pair(sK7(U_39,U_38,U_37),sK8(U_39,U_38,U_37)),U_37)
& in(ordered_pair(sK7(U_39,U_38,U_37),sK8(U_39,U_38,U_37)),U_39)
& in(sK7(U_39,U_38,U_37),U_38) )
| ( ( ~ in(ordered_pair(sK5(U_39,U_38,U_37),sK6(U_39,U_38,U_37)),U_39)
| ~ in(sK5(U_39,U_38,U_37),U_38) )
& in(ordered_pair(sK5(U_39,U_38,U_37),sK6(U_39,U_38,U_37)),U_37) ) )
& ( ( ! [U_43,U_41] :
( in(ordered_pair(U_43,U_41),U_37)
| ~ in(ordered_pair(U_43,U_41),U_39)
| ~ in(U_43,U_38) )
& ! [U_42,U_40] :
( ( in(ordered_pair(U_42,U_40),U_39)
& in(U_42,U_38) )
| ~ in(ordered_pair(U_42,U_40),U_37) ) )
| U_37 != relation_dom_restriction(U_39,U_38) ) )
| ~ relation(U_37) )
| ~ relation(U_39) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_45,sK8(U_39,U_38,U_37))],[f_11_6]) ).
cnf(f_11_8,plain,
( in(U_42,U_38)
| ~ in(ordered_pair(U_42,U_40),U_37)
| U_37 != relation_dom_restriction(U_39,U_38)
| ~ relation(U_37)
| ~ relation(U_39) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_9,plain,
( in(ordered_pair(U_42,U_40),U_39)
| ~ in(ordered_pair(U_42,U_40),U_37)
| U_37 != relation_dom_restriction(U_39,U_38)
| ~ relation(U_37)
| ~ relation(U_39) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_10,plain,
( in(ordered_pair(U_43,U_41),U_37)
| ~ in(ordered_pair(U_43,U_41),U_39)
| ~ in(U_43,U_38)
| U_37 != relation_dom_restriction(U_39,U_38)
| ~ relation(U_37)
| ~ relation(U_39) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_11,plain,
( in(sK7(U_39,U_38,U_37),U_38)
| in(ordered_pair(sK5(U_39,U_38,U_37),sK6(U_39,U_38,U_37)),U_37)
| U_37 = relation_dom_restriction(U_39,U_38)
| ~ relation(U_37)
| ~ relation(U_39) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_12,plain,
( in(ordered_pair(sK7(U_39,U_38,U_37),sK8(U_39,U_38,U_37)),U_39)
| in(ordered_pair(sK5(U_39,U_38,U_37),sK6(U_39,U_38,U_37)),U_37)
| U_37 = relation_dom_restriction(U_39,U_38)
| ~ relation(U_37)
| ~ relation(U_39) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_13,plain,
( ~ in(ordered_pair(sK7(U_39,U_38,U_37),sK8(U_39,U_38,U_37)),U_37)
| in(ordered_pair(sK5(U_39,U_38,U_37),sK6(U_39,U_38,U_37)),U_37)
| U_37 = relation_dom_restriction(U_39,U_38)
| ~ relation(U_37)
| ~ relation(U_39) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_14,plain,
( in(sK7(U_39,U_38,U_37),U_38)
| ~ in(ordered_pair(sK5(U_39,U_38,U_37),sK6(U_39,U_38,U_37)),U_39)
| ~ in(sK5(U_39,U_38,U_37),U_38)
| U_37 = relation_dom_restriction(U_39,U_38)
| ~ relation(U_37)
| ~ relation(U_39) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_15,plain,
( in(ordered_pair(sK7(U_39,U_38,U_37),sK8(U_39,U_38,U_37)),U_39)
| ~ in(ordered_pair(sK5(U_39,U_38,U_37),sK6(U_39,U_38,U_37)),U_39)
| ~ in(sK5(U_39,U_38,U_37),U_38)
| U_37 = relation_dom_restriction(U_39,U_38)
| ~ relation(U_37)
| ~ relation(U_39) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_16,plain,
( ~ in(ordered_pair(sK7(U_39,U_38,U_37),sK8(U_39,U_38,U_37)),U_37)
| ~ in(ordered_pair(sK5(U_39,U_38,U_37),sK6(U_39,U_38,U_37)),U_39)
| ~ in(sK5(U_39,U_38,U_37),U_38)
| U_37 = relation_dom_restriction(U_39,U_38)
| ~ relation(U_37)
| ~ relation(U_39) ),
inference(clausify,[status(thm)],[f_11_7]) ).
fof(f_12_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_12_2,plain,
! [U_54,U_53] :
( ! [U_52] :
( ( ( U_52 = relation_rng_restriction(U_54,U_53)
| ? [U_51,U_50] :
( ( ~ in(ordered_pair(U_51,U_50),U_52)
& in(ordered_pair(U_51,U_50),U_53)
& in(U_50,U_54) )
| ( ( ~ in(ordered_pair(U_51,U_50),U_53)
| ~ in(U_50,U_54) )
& in(ordered_pair(U_51,U_50),U_52) ) ) )
& ( ! [U_49,U_48] :
( ( in(ordered_pair(U_49,U_48),U_52)
| ~ in(ordered_pair(U_49,U_48),U_53)
| ~ in(U_48,U_54) )
& ( ( in(ordered_pair(U_49,U_48),U_53)
& in(U_48,U_54) )
| ~ in(ordered_pair(U_49,U_48),U_52) ) )
| U_52 != relation_rng_restriction(U_54,U_53) ) )
| ~ relation(U_52) )
| ~ relation(U_53) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_54,U_53] :
( ! [U_52] :
( ( ( U_52 = relation_rng_restriction(U_54,U_53)
| ? [U_62,U_60] :
( ~ in(ordered_pair(U_62,U_60),U_52)
& in(ordered_pair(U_62,U_60),U_53)
& in(U_60,U_54) )
| ? [U_61,U_59] :
( ( ~ in(ordered_pair(U_61,U_59),U_53)
| ~ in(U_59,U_54) )
& in(ordered_pair(U_61,U_59),U_52) ) )
& ( ( ! [U_58,U_56] :
( in(ordered_pair(U_58,U_56),U_52)
| ~ in(ordered_pair(U_58,U_56),U_53)
| ~ in(U_56,U_54) )
& ! [U_57,U_55] :
( ( in(ordered_pair(U_57,U_55),U_53)
& in(U_55,U_54) )
| ~ in(ordered_pair(U_57,U_55),U_52) ) )
| U_52 != relation_rng_restriction(U_54,U_53) ) )
| ~ relation(U_52) )
| ~ relation(U_53) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
! [U_54,U_53] :
( ! [U_52] :
( ( ( U_52 = relation_rng_restriction(U_54,U_53)
| ? [U_62,U_60] :
( ~ in(ordered_pair(U_62,U_60),U_52)
& in(ordered_pair(U_62,U_60),U_53)
& in(U_60,U_54) )
| ? [U_59] :
( ( ~ in(ordered_pair(sK9(U_54,U_53,U_52),U_59),U_53)
| ~ in(U_59,U_54) )
& in(ordered_pair(sK9(U_54,U_53,U_52),U_59),U_52) ) )
& ( ( ! [U_58,U_56] :
( in(ordered_pair(U_58,U_56),U_52)
| ~ in(ordered_pair(U_58,U_56),U_53)
| ~ in(U_56,U_54) )
& ! [U_57,U_55] :
( ( in(ordered_pair(U_57,U_55),U_53)
& in(U_55,U_54) )
| ~ in(ordered_pair(U_57,U_55),U_52) ) )
| U_52 != relation_rng_restriction(U_54,U_53) ) )
| ~ relation(U_52) )
| ~ relation(U_53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_61,sK9(U_54,U_53,U_52))],[f_12_3]) ).
fof(f_12_5,plain,
! [U_54,U_53] :
( ! [U_52] :
( ( ( U_52 = relation_rng_restriction(U_54,U_53)
| ? [U_62,U_60] :
( ~ in(ordered_pair(U_62,U_60),U_52)
& in(ordered_pair(U_62,U_60),U_53)
& in(U_60,U_54) )
| ( ( ~ in(ordered_pair(sK9(U_54,U_53,U_52),sK10(U_54,U_53,U_52)),U_53)
| ~ in(sK10(U_54,U_53,U_52),U_54) )
& in(ordered_pair(sK9(U_54,U_53,U_52),sK10(U_54,U_53,U_52)),U_52) ) )
& ( ( ! [U_58,U_56] :
( in(ordered_pair(U_58,U_56),U_52)
| ~ in(ordered_pair(U_58,U_56),U_53)
| ~ in(U_56,U_54) )
& ! [U_57,U_55] :
( ( in(ordered_pair(U_57,U_55),U_53)
& in(U_55,U_54) )
| ~ in(ordered_pair(U_57,U_55),U_52) ) )
| U_52 != relation_rng_restriction(U_54,U_53) ) )
| ~ relation(U_52) )
| ~ relation(U_53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_59,sK10(U_54,U_53,U_52))],[f_12_4]) ).
fof(f_12_6,plain,
! [U_54,U_53] :
( ! [U_52] :
( ( ( U_52 = relation_rng_restriction(U_54,U_53)
| ? [U_60] :
( ~ in(ordered_pair(sK11(U_54,U_53,U_52),U_60),U_52)
& in(ordered_pair(sK11(U_54,U_53,U_52),U_60),U_53)
& in(U_60,U_54) )
| ( ( ~ in(ordered_pair(sK9(U_54,U_53,U_52),sK10(U_54,U_53,U_52)),U_53)
| ~ in(sK10(U_54,U_53,U_52),U_54) )
& in(ordered_pair(sK9(U_54,U_53,U_52),sK10(U_54,U_53,U_52)),U_52) ) )
& ( ( ! [U_58,U_56] :
( in(ordered_pair(U_58,U_56),U_52)
| ~ in(ordered_pair(U_58,U_56),U_53)
| ~ in(U_56,U_54) )
& ! [U_57,U_55] :
( ( in(ordered_pair(U_57,U_55),U_53)
& in(U_55,U_54) )
| ~ in(ordered_pair(U_57,U_55),U_52) ) )
| U_52 != relation_rng_restriction(U_54,U_53) ) )
| ~ relation(U_52) )
| ~ relation(U_53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_62,sK11(U_54,U_53,U_52))],[f_12_5]) ).
fof(f_12_7,plain,
! [U_54,U_53] :
( ! [U_52] :
( ( ( U_52 = relation_rng_restriction(U_54,U_53)
| ( ~ in(ordered_pair(sK11(U_54,U_53,U_52),sK12(U_54,U_53,U_52)),U_52)
& in(ordered_pair(sK11(U_54,U_53,U_52),sK12(U_54,U_53,U_52)),U_53)
& in(sK12(U_54,U_53,U_52),U_54) )
| ( ( ~ in(ordered_pair(sK9(U_54,U_53,U_52),sK10(U_54,U_53,U_52)),U_53)
| ~ in(sK10(U_54,U_53,U_52),U_54) )
& in(ordered_pair(sK9(U_54,U_53,U_52),sK10(U_54,U_53,U_52)),U_52) ) )
& ( ( ! [U_58,U_56] :
( in(ordered_pair(U_58,U_56),U_52)
| ~ in(ordered_pair(U_58,U_56),U_53)
| ~ in(U_56,U_54) )
& ! [U_57,U_55] :
( ( in(ordered_pair(U_57,U_55),U_53)
& in(U_55,U_54) )
| ~ in(ordered_pair(U_57,U_55),U_52) ) )
| U_52 != relation_rng_restriction(U_54,U_53) ) )
| ~ relation(U_52) )
| ~ relation(U_53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_60,sK12(U_54,U_53,U_52))],[f_12_6]) ).
cnf(f_12_8,plain,
( in(U_55,U_54)
| ~ in(ordered_pair(U_57,U_55),U_52)
| U_52 != relation_rng_restriction(U_54,U_53)
| ~ relation(U_52)
| ~ relation(U_53) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_9,plain,
( in(ordered_pair(U_57,U_55),U_53)
| ~ in(ordered_pair(U_57,U_55),U_52)
| U_52 != relation_rng_restriction(U_54,U_53)
| ~ relation(U_52)
| ~ relation(U_53) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_10,plain,
( in(ordered_pair(U_58,U_56),U_52)
| ~ in(ordered_pair(U_58,U_56),U_53)
| ~ in(U_56,U_54)
| U_52 != relation_rng_restriction(U_54,U_53)
| ~ relation(U_52)
| ~ relation(U_53) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_11,plain,
( in(sK12(U_54,U_53,U_52),U_54)
| in(ordered_pair(sK9(U_54,U_53,U_52),sK10(U_54,U_53,U_52)),U_52)
| U_52 = relation_rng_restriction(U_54,U_53)
| ~ relation(U_52)
| ~ relation(U_53) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_12,plain,
( in(ordered_pair(sK11(U_54,U_53,U_52),sK12(U_54,U_53,U_52)),U_53)
| in(ordered_pair(sK9(U_54,U_53,U_52),sK10(U_54,U_53,U_52)),U_52)
| U_52 = relation_rng_restriction(U_54,U_53)
| ~ relation(U_52)
| ~ relation(U_53) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_13,plain,
( ~ in(ordered_pair(sK11(U_54,U_53,U_52),sK12(U_54,U_53,U_52)),U_52)
| in(ordered_pair(sK9(U_54,U_53,U_52),sK10(U_54,U_53,U_52)),U_52)
| U_52 = relation_rng_restriction(U_54,U_53)
| ~ relation(U_52)
| ~ relation(U_53) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_14,plain,
( in(sK12(U_54,U_53,U_52),U_54)
| ~ in(ordered_pair(sK9(U_54,U_53,U_52),sK10(U_54,U_53,U_52)),U_53)
| ~ in(sK10(U_54,U_53,U_52),U_54)
| U_52 = relation_rng_restriction(U_54,U_53)
| ~ relation(U_52)
| ~ relation(U_53) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_15,plain,
( in(ordered_pair(sK11(U_54,U_53,U_52),sK12(U_54,U_53,U_52)),U_53)
| ~ in(ordered_pair(sK9(U_54,U_53,U_52),sK10(U_54,U_53,U_52)),U_53)
| ~ in(sK10(U_54,U_53,U_52),U_54)
| U_52 = relation_rng_restriction(U_54,U_53)
| ~ relation(U_52)
| ~ relation(U_53) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_16,plain,
( ~ in(ordered_pair(sK11(U_54,U_53,U_52),sK12(U_54,U_53,U_52)),U_52)
| ~ in(ordered_pair(sK9(U_54,U_53,U_52),sK10(U_54,U_53,U_52)),U_53)
| ~ in(sK10(U_54,U_53,U_52),U_54)
| U_52 = relation_rng_restriction(U_54,U_53)
| ~ relation(U_52)
| ~ relation(U_53) ),
inference(clausify,[status(thm)],[f_12_7]) ).
fof(f_13_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_13_2,plain,
! [U_71] :
( ! [U_70,U_69] :
( ( U_69 = relation_image(U_71,U_70)
| ? [U_68] :
( ( ~ in(U_68,U_69)
& ? [U_67] :
( in(U_67,U_70)
& in(ordered_pair(U_67,U_68),U_71) ) )
| ( ! [U_66] :
( ~ in(U_66,U_70)
| ~ in(ordered_pair(U_66,U_68),U_71) )
& in(U_68,U_69) ) ) )
& ( ! [U_65] :
( ( in(U_65,U_69)
| ! [U_64] :
( ~ in(U_64,U_70)
| ~ in(ordered_pair(U_64,U_65),U_71) ) )
& ( ? [U_63] :
( in(U_63,U_70)
& in(ordered_pair(U_63,U_65),U_71) )
| ~ in(U_65,U_69) ) )
| U_69 != relation_image(U_71,U_70) ) )
| ~ relation(U_71) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_71] :
( ( ! [U_79,U_77] :
( U_77 = relation_image(U_71,U_79)
| ? [U_75] :
( ~ in(U_75,U_77)
& ? [U_67] :
( in(U_67,U_79)
& in(ordered_pair(U_67,U_75),U_71) ) )
| ? [U_74] :
( ! [U_66] :
( ~ in(U_66,U_79)
| ~ in(ordered_pair(U_66,U_74),U_71) )
& in(U_74,U_77) ) )
& ! [U_78,U_76] :
( ( ! [U_73] :
( in(U_73,U_76)
| ! [U_64] :
( ~ in(U_64,U_78)
| ~ in(ordered_pair(U_64,U_73),U_71) ) )
& ! [U_72] :
( ? [U_63] :
( in(U_63,U_78)
& in(ordered_pair(U_63,U_72),U_71) )
| ~ in(U_72,U_76) ) )
| U_76 != relation_image(U_71,U_78) ) )
| ~ relation(U_71) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
fof(f_13_4,plain,
! [U_71] :
( ( ! [U_79,U_77] :
( U_77 = relation_image(U_71,U_79)
| ? [U_75] :
( ~ in(U_75,U_77)
& ? [U_67] :
( in(U_67,U_79)
& in(ordered_pair(U_67,U_75),U_71) ) )
| ? [U_74] :
( ! [U_66] :
( ~ in(U_66,U_79)
| ~ in(ordered_pair(U_66,U_74),U_71) )
& in(U_74,U_77) ) )
& ! [U_78,U_76] :
( ( ! [U_73] :
( in(U_73,U_76)
| ! [U_64] :
( ~ in(U_64,U_78)
| ~ in(ordered_pair(U_64,U_73),U_71) ) )
& ! [U_72] :
( ( in(sK13(U_71,U_78,U_76,U_72),U_78)
& in(ordered_pair(sK13(U_71,U_78,U_76,U_72),U_72),U_71) )
| ~ in(U_72,U_76) ) )
| U_76 != relation_image(U_71,U_78) ) )
| ~ relation(U_71) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_63,sK13(U_71,U_78,U_76,U_72))],[f_13_3]) ).
fof(f_13_5,plain,
! [U_71] :
( ( ! [U_79,U_77] :
( U_77 = relation_image(U_71,U_79)
| ? [U_75] :
( ~ in(U_75,U_77)
& ? [U_67] :
( in(U_67,U_79)
& in(ordered_pair(U_67,U_75),U_71) ) )
| ( ! [U_66] :
( ~ in(U_66,U_79)
| ~ in(ordered_pair(U_66,sK14(U_71,U_79,U_77)),U_71) )
& in(sK14(U_71,U_79,U_77),U_77) ) )
& ! [U_78,U_76] :
( ( ! [U_73] :
( in(U_73,U_76)
| ! [U_64] :
( ~ in(U_64,U_78)
| ~ in(ordered_pair(U_64,U_73),U_71) ) )
& ! [U_72] :
( ( in(sK13(U_71,U_78,U_76,U_72),U_78)
& in(ordered_pair(sK13(U_71,U_78,U_76,U_72),U_72),U_71) )
| ~ in(U_72,U_76) ) )
| U_76 != relation_image(U_71,U_78) ) )
| ~ relation(U_71) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_74,sK14(U_71,U_79,U_77))],[f_13_4]) ).
fof(f_13_6,plain,
! [U_71] :
( ( ! [U_79,U_77] :
( U_77 = relation_image(U_71,U_79)
| ( ~ in(sK15(U_71,U_79,U_77),U_77)
& ? [U_67] :
( in(U_67,U_79)
& in(ordered_pair(U_67,sK15(U_71,U_79,U_77)),U_71) ) )
| ( ! [U_66] :
( ~ in(U_66,U_79)
| ~ in(ordered_pair(U_66,sK14(U_71,U_79,U_77)),U_71) )
& in(sK14(U_71,U_79,U_77),U_77) ) )
& ! [U_78,U_76] :
( ( ! [U_73] :
( in(U_73,U_76)
| ! [U_64] :
( ~ in(U_64,U_78)
| ~ in(ordered_pair(U_64,U_73),U_71) ) )
& ! [U_72] :
( ( in(sK13(U_71,U_78,U_76,U_72),U_78)
& in(ordered_pair(sK13(U_71,U_78,U_76,U_72),U_72),U_71) )
| ~ in(U_72,U_76) ) )
| U_76 != relation_image(U_71,U_78) ) )
| ~ relation(U_71) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_75,sK15(U_71,U_79,U_77))],[f_13_5]) ).
fof(f_13_7,plain,
! [U_71] :
( ( ! [U_79,U_77] :
( U_77 = relation_image(U_71,U_79)
| ( ~ in(sK15(U_71,U_79,U_77),U_77)
& in(sK16(U_71,U_79,U_77),U_79)
& in(ordered_pair(sK16(U_71,U_79,U_77),sK15(U_71,U_79,U_77)),U_71) )
| ( ! [U_66] :
( ~ in(U_66,U_79)
| ~ in(ordered_pair(U_66,sK14(U_71,U_79,U_77)),U_71) )
& in(sK14(U_71,U_79,U_77),U_77) ) )
& ! [U_78,U_76] :
( ( ! [U_73] :
( in(U_73,U_76)
| ! [U_64] :
( ~ in(U_64,U_78)
| ~ in(ordered_pair(U_64,U_73),U_71) ) )
& ! [U_72] :
( ( in(sK13(U_71,U_78,U_76,U_72),U_78)
& in(ordered_pair(sK13(U_71,U_78,U_76,U_72),U_72),U_71) )
| ~ in(U_72,U_76) ) )
| U_76 != relation_image(U_71,U_78) ) )
| ~ relation(U_71) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_67,sK16(U_71,U_79,U_77))],[f_13_6]) ).
cnf(f_13_8,plain,
( in(ordered_pair(sK13(U_71,U_78,U_76,U_72),U_72),U_71)
| ~ in(U_72,U_76)
| U_76 != relation_image(U_71,U_78)
| ~ relation(U_71) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_9,plain,
( in(sK13(U_71,U_78,U_76,U_72),U_78)
| ~ in(U_72,U_76)
| U_76 != relation_image(U_71,U_78)
| ~ relation(U_71) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_10,plain,
( in(U_73,U_76)
| ~ in(U_64,U_78)
| ~ in(ordered_pair(U_64,U_73),U_71)
| U_76 != relation_image(U_71,U_78)
| ~ relation(U_71) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_11,plain,
( in(ordered_pair(sK16(U_71,U_79,U_77),sK15(U_71,U_79,U_77)),U_71)
| in(sK14(U_71,U_79,U_77),U_77)
| U_77 = relation_image(U_71,U_79)
| ~ relation(U_71) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_12,plain,
( in(sK16(U_71,U_79,U_77),U_79)
| in(sK14(U_71,U_79,U_77),U_77)
| U_77 = relation_image(U_71,U_79)
| ~ relation(U_71) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_13,plain,
( ~ in(sK15(U_71,U_79,U_77),U_77)
| in(sK14(U_71,U_79,U_77),U_77)
| U_77 = relation_image(U_71,U_79)
| ~ relation(U_71) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_14,plain,
( in(ordered_pair(sK16(U_71,U_79,U_77),sK15(U_71,U_79,U_77)),U_71)
| ~ in(U_66,U_79)
| ~ in(ordered_pair(U_66,sK14(U_71,U_79,U_77)),U_71)
| U_77 = relation_image(U_71,U_79)
| ~ relation(U_71) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_15,plain,
( in(sK16(U_71,U_79,U_77),U_79)
| ~ in(U_66,U_79)
| ~ in(ordered_pair(U_66,sK14(U_71,U_79,U_77)),U_71)
| U_77 = relation_image(U_71,U_79)
| ~ relation(U_71) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_16,plain,
( ~ in(sK15(U_71,U_79,U_77),U_77)
| ~ in(U_66,U_79)
| ~ in(ordered_pair(U_66,sK14(U_71,U_79,U_77)),U_71)
| U_77 = relation_image(U_71,U_79)
| ~ relation(U_71) ),
inference(clausify,[status(thm)],[f_13_7]) ).
fof(f_14_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_14_2,plain,
! [U_88] :
( ! [U_87,U_86] :
( ( U_86 = relation_inverse_image(U_88,U_87)
| ? [U_85] :
( ( ~ in(U_85,U_86)
& ? [U_84] :
( in(U_84,U_87)
& in(ordered_pair(U_85,U_84),U_88) ) )
| ( ! [U_83] :
( ~ in(U_83,U_87)
| ~ in(ordered_pair(U_85,U_83),U_88) )
& in(U_85,U_86) ) ) )
& ( ! [U_82] :
( ( in(U_82,U_86)
| ! [U_81] :
( ~ in(U_81,U_87)
| ~ in(ordered_pair(U_82,U_81),U_88) ) )
& ( ? [U_80] :
( in(U_80,U_87)
& in(ordered_pair(U_82,U_80),U_88) )
| ~ in(U_82,U_86) ) )
| U_86 != relation_inverse_image(U_88,U_87) ) )
| ~ relation(U_88) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_88] :
( ( ! [U_96,U_94] :
( U_94 = relation_inverse_image(U_88,U_96)
| ? [U_92] :
( ~ in(U_92,U_94)
& ? [U_84] :
( in(U_84,U_96)
& in(ordered_pair(U_92,U_84),U_88) ) )
| ? [U_91] :
( ! [U_83] :
( ~ in(U_83,U_96)
| ~ in(ordered_pair(U_91,U_83),U_88) )
& in(U_91,U_94) ) )
& ! [U_95,U_93] :
( ( ! [U_90] :
( in(U_90,U_93)
| ! [U_81] :
( ~ in(U_81,U_95)
| ~ in(ordered_pair(U_90,U_81),U_88) ) )
& ! [U_89] :
( ? [U_80] :
( in(U_80,U_95)
& in(ordered_pair(U_89,U_80),U_88) )
| ~ in(U_89,U_93) ) )
| U_93 != relation_inverse_image(U_88,U_95) ) )
| ~ relation(U_88) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
fof(f_14_4,plain,
! [U_88] :
( ( ! [U_96,U_94] :
( U_94 = relation_inverse_image(U_88,U_96)
| ? [U_92] :
( ~ in(U_92,U_94)
& ? [U_84] :
( in(U_84,U_96)
& in(ordered_pair(U_92,U_84),U_88) ) )
| ? [U_91] :
( ! [U_83] :
( ~ in(U_83,U_96)
| ~ in(ordered_pair(U_91,U_83),U_88) )
& in(U_91,U_94) ) )
& ! [U_95,U_93] :
( ( ! [U_90] :
( in(U_90,U_93)
| ! [U_81] :
( ~ in(U_81,U_95)
| ~ in(ordered_pair(U_90,U_81),U_88) ) )
& ! [U_89] :
( ( in(sK17(U_88,U_95,U_93,U_89),U_95)
& in(ordered_pair(U_89,sK17(U_88,U_95,U_93,U_89)),U_88) )
| ~ in(U_89,U_93) ) )
| U_93 != relation_inverse_image(U_88,U_95) ) )
| ~ relation(U_88) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_80,sK17(U_88,U_95,U_93,U_89))],[f_14_3]) ).
fof(f_14_5,plain,
! [U_88] :
( ( ! [U_96,U_94] :
( U_94 = relation_inverse_image(U_88,U_96)
| ? [U_92] :
( ~ in(U_92,U_94)
& ? [U_84] :
( in(U_84,U_96)
& in(ordered_pair(U_92,U_84),U_88) ) )
| ( ! [U_83] :
( ~ in(U_83,U_96)
| ~ in(ordered_pair(sK18(U_88,U_96,U_94),U_83),U_88) )
& in(sK18(U_88,U_96,U_94),U_94) ) )
& ! [U_95,U_93] :
( ( ! [U_90] :
( in(U_90,U_93)
| ! [U_81] :
( ~ in(U_81,U_95)
| ~ in(ordered_pair(U_90,U_81),U_88) ) )
& ! [U_89] :
( ( in(sK17(U_88,U_95,U_93,U_89),U_95)
& in(ordered_pair(U_89,sK17(U_88,U_95,U_93,U_89)),U_88) )
| ~ in(U_89,U_93) ) )
| U_93 != relation_inverse_image(U_88,U_95) ) )
| ~ relation(U_88) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_91,sK18(U_88,U_96,U_94))],[f_14_4]) ).
fof(f_14_6,plain,
! [U_88] :
( ( ! [U_96,U_94] :
( U_94 = relation_inverse_image(U_88,U_96)
| ( ~ in(sK19(U_88,U_96,U_94),U_94)
& ? [U_84] :
( in(U_84,U_96)
& in(ordered_pair(sK19(U_88,U_96,U_94),U_84),U_88) ) )
| ( ! [U_83] :
( ~ in(U_83,U_96)
| ~ in(ordered_pair(sK18(U_88,U_96,U_94),U_83),U_88) )
& in(sK18(U_88,U_96,U_94),U_94) ) )
& ! [U_95,U_93] :
( ( ! [U_90] :
( in(U_90,U_93)
| ! [U_81] :
( ~ in(U_81,U_95)
| ~ in(ordered_pair(U_90,U_81),U_88) ) )
& ! [U_89] :
( ( in(sK17(U_88,U_95,U_93,U_89),U_95)
& in(ordered_pair(U_89,sK17(U_88,U_95,U_93,U_89)),U_88) )
| ~ in(U_89,U_93) ) )
| U_93 != relation_inverse_image(U_88,U_95) ) )
| ~ relation(U_88) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_92,sK19(U_88,U_96,U_94))],[f_14_5]) ).
fof(f_14_7,plain,
! [U_88] :
( ( ! [U_96,U_94] :
( U_94 = relation_inverse_image(U_88,U_96)
| ( ~ in(sK19(U_88,U_96,U_94),U_94)
& in(sK20(U_88,U_96,U_94),U_96)
& in(ordered_pair(sK19(U_88,U_96,U_94),sK20(U_88,U_96,U_94)),U_88) )
| ( ! [U_83] :
( ~ in(U_83,U_96)
| ~ in(ordered_pair(sK18(U_88,U_96,U_94),U_83),U_88) )
& in(sK18(U_88,U_96,U_94),U_94) ) )
& ! [U_95,U_93] :
( ( ! [U_90] :
( in(U_90,U_93)
| ! [U_81] :
( ~ in(U_81,U_95)
| ~ in(ordered_pair(U_90,U_81),U_88) ) )
& ! [U_89] :
( ( in(sK17(U_88,U_95,U_93,U_89),U_95)
& in(ordered_pair(U_89,sK17(U_88,U_95,U_93,U_89)),U_88) )
| ~ in(U_89,U_93) ) )
| U_93 != relation_inverse_image(U_88,U_95) ) )
| ~ relation(U_88) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_84,sK20(U_88,U_96,U_94))],[f_14_6]) ).
cnf(f_14_8,plain,
( in(ordered_pair(U_89,sK17(U_88,U_95,U_93,U_89)),U_88)
| ~ in(U_89,U_93)
| U_93 != relation_inverse_image(U_88,U_95)
| ~ relation(U_88) ),
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(f_14_9,plain,
( in(sK17(U_88,U_95,U_93,U_89),U_95)
| ~ in(U_89,U_93)
| U_93 != relation_inverse_image(U_88,U_95)
| ~ relation(U_88) ),
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(f_14_10,plain,
( in(U_90,U_93)
| ~ in(U_81,U_95)
| ~ in(ordered_pair(U_90,U_81),U_88)
| U_93 != relation_inverse_image(U_88,U_95)
| ~ relation(U_88) ),
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(f_14_11,plain,
( in(ordered_pair(sK19(U_88,U_96,U_94),sK20(U_88,U_96,U_94)),U_88)
| in(sK18(U_88,U_96,U_94),U_94)
| U_94 = relation_inverse_image(U_88,U_96)
| ~ relation(U_88) ),
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(f_14_12,plain,
( in(sK20(U_88,U_96,U_94),U_96)
| in(sK18(U_88,U_96,U_94),U_94)
| U_94 = relation_inverse_image(U_88,U_96)
| ~ relation(U_88) ),
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(f_14_13,plain,
( ~ in(sK19(U_88,U_96,U_94),U_94)
| in(sK18(U_88,U_96,U_94),U_94)
| U_94 = relation_inverse_image(U_88,U_96)
| ~ relation(U_88) ),
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(f_14_14,plain,
( in(ordered_pair(sK19(U_88,U_96,U_94),sK20(U_88,U_96,U_94)),U_88)
| ~ in(U_83,U_96)
| ~ in(ordered_pair(sK18(U_88,U_96,U_94),U_83),U_88)
| U_94 = relation_inverse_image(U_88,U_96)
| ~ relation(U_88) ),
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(f_14_15,plain,
( in(sK20(U_88,U_96,U_94),U_96)
| ~ in(U_83,U_96)
| ~ in(ordered_pair(sK18(U_88,U_96,U_94),U_83),U_88)
| U_94 = relation_inverse_image(U_88,U_96)
| ~ relation(U_88) ),
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(f_14_16,plain,
( ~ in(sK19(U_88,U_96,U_94),U_94)
| ~ in(U_83,U_96)
| ~ in(ordered_pair(sK18(U_88,U_96,U_94),U_83),U_88)
| U_94 = relation_inverse_image(U_88,U_96)
| ~ relation(U_88) ),
inference(clausify,[status(thm)],[f_14_7]) ).
fof(f_15_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_15_2,plain,
! [U_103] :
( ( relation(U_103)
| ? [U_102] :
( ! [U_101,U_100] : U_102 != ordered_pair(U_101,U_100)
& in(U_102,U_103) ) )
& ( ! [U_99] :
( ? [U_98,U_97] : U_99 = ordered_pair(U_98,U_97)
| ~ in(U_99,U_103) )
| ~ relation(U_103) ) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ! [U_105] :
( relation(U_105)
| ? [U_102] :
( ! [U_101,U_100] : U_102 != ordered_pair(U_101,U_100)
& in(U_102,U_105) ) )
& ! [U_104] :
( ! [U_99] :
( ? [U_98,U_97] : U_99 = ordered_pair(U_98,U_97)
| ~ in(U_99,U_104) )
| ~ relation(U_104) ) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
fof(f_15_4,plain,
( ! [U_105] :
( relation(U_105)
| ? [U_102] :
( ! [U_101,U_100] : U_102 != ordered_pair(U_101,U_100)
& in(U_102,U_105) ) )
& ! [U_104] :
( ! [U_99] :
( ? [U_97] : U_99 = ordered_pair(sK21(U_104,U_99),U_97)
| ~ in(U_99,U_104) )
| ~ relation(U_104) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_98,sK21(U_104,U_99))],[f_15_3]) ).
fof(f_15_5,plain,
( ! [U_105] :
( relation(U_105)
| ? [U_102] :
( ! [U_101,U_100] : U_102 != ordered_pair(U_101,U_100)
& in(U_102,U_105) ) )
& ! [U_104] :
( ! [U_99] :
( U_99 = ordered_pair(sK21(U_104,U_99),sK22(U_104,U_99))
| ~ in(U_99,U_104) )
| ~ relation(U_104) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_97,sK22(U_104,U_99))],[f_15_4]) ).
fof(f_15_6,plain,
( ! [U_105] :
( relation(U_105)
| ( ! [U_101,U_100] : sK23(U_105) != ordered_pair(U_101,U_100)
& in(sK23(U_105),U_105) ) )
& ! [U_104] :
( ! [U_99] :
( U_99 = ordered_pair(sK21(U_104,U_99),sK22(U_104,U_99))
| ~ in(U_99,U_104) )
| ~ relation(U_104) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_102,sK23(U_105))],[f_15_5]) ).
cnf(f_15_7,plain,
( U_99 = ordered_pair(sK21(U_104,U_99),sK22(U_104,U_99))
| ~ in(U_99,U_104)
| ~ relation(U_104) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_8,plain,
( in(sK23(U_105),U_105)
| relation(U_105) ),
inference(clausify,[status(thm)],[f_15_6]) ).
cnf(f_15_9,plain,
( sK23(U_105) != ordered_pair(U_101,U_100)
| relation(U_105) ),
inference(clausify,[status(thm)],[f_15_6]) ).
fof(f_16_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_16_2,plain,
! [U_113,U_112] :
( ( ( ( U_112 = set_meet(U_113)
| U_112 != empty_set )
& ( U_112 = empty_set
| U_112 != set_meet(U_113) ) )
| U_113 != empty_set )
& ( ( ( U_112 = set_meet(U_113)
| ? [U_111] :
( ( ~ in(U_111,U_112)
& ! [U_110] :
( in(U_111,U_110)
| ~ in(U_110,U_113) ) )
| ( ? [U_109] :
( ~ in(U_111,U_109)
& in(U_109,U_113) )
& in(U_111,U_112) ) ) )
& ( ! [U_108] :
( ( in(U_108,U_112)
| ? [U_107] :
( ~ in(U_108,U_107)
& in(U_107,U_113) ) )
& ( ! [U_106] :
( in(U_108,U_106)
| ~ in(U_106,U_113) )
| ~ in(U_108,U_112) ) )
| U_112 != set_meet(U_113) ) )
| U_113 = empty_set ) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( ! [U_125] :
( ( ! [U_123] :
( U_123 = set_meet(U_125)
| U_123 != empty_set )
& ! [U_122] :
( U_122 = empty_set
| U_122 != set_meet(U_125) ) )
| U_125 != empty_set )
& ! [U_124] :
( ( ! [U_121] :
( U_121 = set_meet(U_124)
| ? [U_117] :
( ~ in(U_117,U_121)
& ! [U_110] :
( in(U_117,U_110)
| ~ in(U_110,U_124) ) )
| ? [U_116] :
( ? [U_109] :
( ~ in(U_116,U_109)
& in(U_109,U_124) )
& in(U_116,U_121) ) )
& ! [U_120] :
( ( ! [U_115] :
( in(U_115,U_120)
| ? [U_107] :
( ~ in(U_115,U_107)
& in(U_107,U_124) ) )
& ! [U_114] :
( ! [U_106] :
( in(U_114,U_106)
| ~ in(U_106,U_124) )
| ~ in(U_114,U_120) ) )
| U_120 != set_meet(U_124) ) )
| U_124 = empty_set ) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
fof(f_16_4,plain,
( ! [U_125] :
( ( ! [U_123] :
( U_123 = set_meet(U_125)
| U_123 != empty_set )
& ! [U_122] :
( U_122 = empty_set
| U_122 != set_meet(U_125) ) )
| U_125 != empty_set )
& ! [U_124] :
( ( ! [U_121] :
( U_121 = set_meet(U_124)
| ? [U_117] :
( ~ in(U_117,U_121)
& ! [U_110] :
( in(U_117,U_110)
| ~ in(U_110,U_124) ) )
| ? [U_116] :
( ? [U_109] :
( ~ in(U_116,U_109)
& in(U_109,U_124) )
& in(U_116,U_121) ) )
& ! [U_120] :
( ( ! [U_115] :
( in(U_115,U_120)
| ( ~ in(U_115,sK24(U_124,U_120,U_115))
& in(sK24(U_124,U_120,U_115),U_124) ) )
& ! [U_114] :
( ! [U_106] :
( in(U_114,U_106)
| ~ in(U_106,U_124) )
| ~ in(U_114,U_120) ) )
| U_120 != set_meet(U_124) ) )
| U_124 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_107,sK24(U_124,U_120,U_115))],[f_16_3]) ).
fof(f_16_5,plain,
( ! [U_125] :
( ( ! [U_123] :
( U_123 = set_meet(U_125)
| U_123 != empty_set )
& ! [U_122] :
( U_122 = empty_set
| U_122 != set_meet(U_125) ) )
| U_125 != empty_set )
& ! [U_124] :
( ( ! [U_121] :
( U_121 = set_meet(U_124)
| ? [U_117] :
( ~ in(U_117,U_121)
& ! [U_110] :
( in(U_117,U_110)
| ~ in(U_110,U_124) ) )
| ( ? [U_109] :
( ~ in(sK25(U_124,U_121),U_109)
& in(U_109,U_124) )
& in(sK25(U_124,U_121),U_121) ) )
& ! [U_120] :
( ( ! [U_115] :
( in(U_115,U_120)
| ( ~ in(U_115,sK24(U_124,U_120,U_115))
& in(sK24(U_124,U_120,U_115),U_124) ) )
& ! [U_114] :
( ! [U_106] :
( in(U_114,U_106)
| ~ in(U_106,U_124) )
| ~ in(U_114,U_120) ) )
| U_120 != set_meet(U_124) ) )
| U_124 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_116,sK25(U_124,U_121))],[f_16_4]) ).
fof(f_16_6,plain,
( ! [U_125] :
( ( ! [U_123] :
( U_123 = set_meet(U_125)
| U_123 != empty_set )
& ! [U_122] :
( U_122 = empty_set
| U_122 != set_meet(U_125) ) )
| U_125 != empty_set )
& ! [U_124] :
( ( ! [U_121] :
( U_121 = set_meet(U_124)
| ? [U_117] :
( ~ in(U_117,U_121)
& ! [U_110] :
( in(U_117,U_110)
| ~ in(U_110,U_124) ) )
| ( ~ in(sK25(U_124,U_121),sK26(U_124,U_121))
& in(sK26(U_124,U_121),U_124)
& in(sK25(U_124,U_121),U_121) ) )
& ! [U_120] :
( ( ! [U_115] :
( in(U_115,U_120)
| ( ~ in(U_115,sK24(U_124,U_120,U_115))
& in(sK24(U_124,U_120,U_115),U_124) ) )
& ! [U_114] :
( ! [U_106] :
( in(U_114,U_106)
| ~ in(U_106,U_124) )
| ~ in(U_114,U_120) ) )
| U_120 != set_meet(U_124) ) )
| U_124 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_109,sK26(U_124,U_121))],[f_16_5]) ).
fof(f_16_7,plain,
( ! [U_125] :
( ( ! [U_123] :
( U_123 = set_meet(U_125)
| U_123 != empty_set )
& ! [U_122] :
( U_122 = empty_set
| U_122 != set_meet(U_125) ) )
| U_125 != empty_set )
& ! [U_124] :
( ( ! [U_121] :
( U_121 = set_meet(U_124)
| ( ~ in(sK27(U_124,U_121),U_121)
& ! [U_110] :
( in(sK27(U_124,U_121),U_110)
| ~ in(U_110,U_124) ) )
| ( ~ in(sK25(U_124,U_121),sK26(U_124,U_121))
& in(sK26(U_124,U_121),U_124)
& in(sK25(U_124,U_121),U_121) ) )
& ! [U_120] :
( ( ! [U_115] :
( in(U_115,U_120)
| ( ~ in(U_115,sK24(U_124,U_120,U_115))
& in(sK24(U_124,U_120,U_115),U_124) ) )
& ! [U_114] :
( ! [U_106] :
( in(U_114,U_106)
| ~ in(U_106,U_124) )
| ~ in(U_114,U_120) ) )
| U_120 != set_meet(U_124) ) )
| U_124 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_117,sK27(U_124,U_121))],[f_16_6]) ).
cnf(f_16_8,plain,
( in(U_114,U_106)
| ~ in(U_106,U_124)
| ~ in(U_114,U_120)
| U_120 != set_meet(U_124)
| U_124 = empty_set ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_9,plain,
( in(sK24(U_124,U_120,U_115),U_124)
| in(U_115,U_120)
| U_120 != set_meet(U_124)
| U_124 = empty_set ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_10,plain,
( ~ in(U_115,sK24(U_124,U_120,U_115))
| in(U_115,U_120)
| U_120 != set_meet(U_124)
| U_124 = empty_set ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_11,plain,
( in(sK27(U_124,U_121),U_110)
| ~ in(U_110,U_124)
| in(sK25(U_124,U_121),U_121)
| U_121 = set_meet(U_124)
| U_124 = empty_set ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_12,plain,
( ~ in(sK27(U_124,U_121),U_121)
| in(sK25(U_124,U_121),U_121)
| U_121 = set_meet(U_124)
| U_124 = empty_set ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_13,plain,
( in(sK26(U_124,U_121),U_124)
| in(sK27(U_124,U_121),U_110)
| ~ in(U_110,U_124)
| U_121 = set_meet(U_124)
| U_124 = empty_set ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_14,plain,
( ~ in(sK25(U_124,U_121),sK26(U_124,U_121))
| in(sK27(U_124,U_121),U_110)
| ~ in(U_110,U_124)
| U_121 = set_meet(U_124)
| U_124 = empty_set ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_15,plain,
( in(sK26(U_124,U_121),U_124)
| ~ in(sK27(U_124,U_121),U_121)
| U_121 = set_meet(U_124)
| U_124 = empty_set ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_16,plain,
( ~ in(sK25(U_124,U_121),sK26(U_124,U_121))
| ~ in(sK27(U_124,U_121),U_121)
| U_121 = set_meet(U_124)
| U_124 = empty_set ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_17,plain,
( U_122 = empty_set
| U_122 != set_meet(U_125)
| U_125 != empty_set ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_18,plain,
( U_123 = set_meet(U_125)
| U_123 != empty_set
| U_125 != empty_set ),
inference(clausify,[status(thm)],[f_16_7]) ).
fof(f_17_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_17_2,plain,
! [U_129,U_128] :
( ( U_128 = singleton(U_129)
| ? [U_127] :
( ( ~ in(U_127,U_128)
& U_127 = U_129 )
| ( U_127 != U_129
& in(U_127,U_128) ) ) )
& ( ! [U_126] :
( ( in(U_126,U_128)
| U_126 != U_129 )
& ( U_126 = U_129
| ~ in(U_126,U_128) ) )
| U_128 != singleton(U_129) ) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( ! [U_137,U_135] :
( U_135 = singleton(U_137)
| ? [U_133] :
( ~ in(U_133,U_135)
& U_133 = U_137 )
| ? [U_132] :
( U_132 != U_137
& in(U_132,U_135) ) )
& ! [U_136,U_134] :
( ( ! [U_131] :
( in(U_131,U_134)
| U_131 != U_136 )
& ! [U_130] :
( U_130 = U_136
| ~ in(U_130,U_134) ) )
| U_134 != singleton(U_136) ) ),
inference(miniscope,[status(thm)],[f_17_2]) ).
fof(f_17_4,plain,
( ! [U_137,U_135] :
( U_135 = singleton(U_137)
| ? [U_133] :
( ~ in(U_133,U_135)
& U_133 = U_137 )
| ( sK28(U_137,U_135) != U_137
& in(sK28(U_137,U_135),U_135) ) )
& ! [U_136,U_134] :
( ( ! [U_131] :
( in(U_131,U_134)
| U_131 != U_136 )
& ! [U_130] :
( U_130 = U_136
| ~ in(U_130,U_134) ) )
| U_134 != singleton(U_136) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_132,sK28(U_137,U_135))],[f_17_3]) ).
fof(f_17_5,plain,
( ! [U_137,U_135] :
( U_135 = singleton(U_137)
| ( ~ in(sK29(U_137,U_135),U_135)
& sK29(U_137,U_135) = U_137 )
| ( sK28(U_137,U_135) != U_137
& in(sK28(U_137,U_135),U_135) ) )
& ! [U_136,U_134] :
( ( ! [U_131] :
( in(U_131,U_134)
| U_131 != U_136 )
& ! [U_130] :
( U_130 = U_136
| ~ in(U_130,U_134) ) )
| U_134 != singleton(U_136) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_133,sK29(U_137,U_135))],[f_17_4]) ).
cnf(f_17_6,plain,
( U_130 = U_136
| ~ in(U_130,U_134)
| U_134 != singleton(U_136) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_7,plain,
( in(U_131,U_134)
| U_131 != U_136
| U_134 != singleton(U_136) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_8,plain,
( sK29(U_137,U_135) = U_137
| in(sK28(U_137,U_135),U_135)
| U_135 = singleton(U_137) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_9,plain,
( ~ in(sK29(U_137,U_135),U_135)
| in(sK28(U_137,U_135),U_135)
| U_135 = singleton(U_137) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_10,plain,
( sK29(U_137,U_135) = U_137
| sK28(U_137,U_135) != U_137
| U_135 = singleton(U_137) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_11,plain,
( ~ in(sK29(U_137,U_135),U_135)
| sK28(U_137,U_135) != U_137
| U_135 = singleton(U_137) ),
inference(clausify,[status(thm)],[f_17_5]) ).
fof(f_18_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_18_2,plain,
! [U_140] :
( ( U_140 = empty_set
| ? [U_139] : in(U_139,U_140) )
& ( ! [U_138] : ~ in(U_138,U_140)
| U_140 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( ! [U_142] :
( U_142 = empty_set
| ? [U_139] : in(U_139,U_142) )
& ! [U_141] :
( ! [U_138] : ~ in(U_138,U_141)
| U_141 != empty_set ) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
fof(f_18_4,plain,
( ! [U_142] :
( U_142 = empty_set
| in(sK30(U_142),U_142) )
& ! [U_141] :
( ! [U_138] : ~ in(U_138,U_141)
| U_141 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_139,sK30(U_142))],[f_18_3]) ).
cnf(f_18_5,plain,
( ~ in(U_138,U_141)
| U_141 != empty_set ),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_6,plain,
( U_142 = empty_set
| in(sK30(U_142),U_142) ),
inference(clausify,[status(thm)],[f_18_4]) ).
fof(f_19_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_19_2,plain,
! [U_146,U_145] :
( ( U_145 = powerset(U_146)
| ? [U_144] :
( ( ~ in(U_144,U_145)
& subset(U_144,U_146) )
| ( ~ subset(U_144,U_146)
& in(U_144,U_145) ) ) )
& ( ! [U_143] :
( ( in(U_143,U_145)
| ~ subset(U_143,U_146) )
& ( subset(U_143,U_146)
| ~ in(U_143,U_145) ) )
| U_145 != powerset(U_146) ) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( ! [U_154,U_152] :
( U_152 = powerset(U_154)
| ? [U_150] :
( ~ in(U_150,U_152)
& subset(U_150,U_154) )
| ? [U_149] :
( ~ subset(U_149,U_154)
& in(U_149,U_152) ) )
& ! [U_153,U_151] :
( ( ! [U_148] :
( in(U_148,U_151)
| ~ subset(U_148,U_153) )
& ! [U_147] :
( subset(U_147,U_153)
| ~ in(U_147,U_151) ) )
| U_151 != powerset(U_153) ) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
fof(f_19_4,plain,
( ! [U_154,U_152] :
( U_152 = powerset(U_154)
| ? [U_150] :
( ~ in(U_150,U_152)
& subset(U_150,U_154) )
| ( ~ subset(sK31(U_154,U_152),U_154)
& in(sK31(U_154,U_152),U_152) ) )
& ! [U_153,U_151] :
( ( ! [U_148] :
( in(U_148,U_151)
| ~ subset(U_148,U_153) )
& ! [U_147] :
( subset(U_147,U_153)
| ~ in(U_147,U_151) ) )
| U_151 != powerset(U_153) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_149,sK31(U_154,U_152))],[f_19_3]) ).
fof(f_19_5,plain,
( ! [U_154,U_152] :
( U_152 = powerset(U_154)
| ( ~ in(sK32(U_154,U_152),U_152)
& subset(sK32(U_154,U_152),U_154) )
| ( ~ subset(sK31(U_154,U_152),U_154)
& in(sK31(U_154,U_152),U_152) ) )
& ! [U_153,U_151] :
( ( ! [U_148] :
( in(U_148,U_151)
| ~ subset(U_148,U_153) )
& ! [U_147] :
( subset(U_147,U_153)
| ~ in(U_147,U_151) ) )
| U_151 != powerset(U_153) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_150,sK32(U_154,U_152))],[f_19_4]) ).
cnf(f_19_6,plain,
( subset(U_147,U_153)
| ~ in(U_147,U_151)
| U_151 != powerset(U_153) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_7,plain,
( in(U_148,U_151)
| ~ subset(U_148,U_153)
| U_151 != powerset(U_153) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_8,plain,
( subset(sK32(U_154,U_152),U_154)
| in(sK31(U_154,U_152),U_152)
| U_152 = powerset(U_154) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_9,plain,
( ~ in(sK32(U_154,U_152),U_152)
| in(sK31(U_154,U_152),U_152)
| U_152 = powerset(U_154) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_10,plain,
( subset(sK32(U_154,U_152),U_154)
| ~ subset(sK31(U_154,U_152),U_154)
| U_152 = powerset(U_154) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_11,plain,
( ~ in(sK32(U_154,U_152),U_152)
| ~ subset(sK31(U_154,U_152),U_154)
| U_152 = powerset(U_154) ),
inference(clausify,[status(thm)],[f_19_5]) ).
fof(f_20_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_20_2,plain,
! [U_160] :
( ! [U_159] :
( ( ( U_160 = U_159
| ? [U_158,U_157] :
( ( ~ in(ordered_pair(U_158,U_157),U_160)
& in(ordered_pair(U_158,U_157),U_159) )
| ( ~ in(ordered_pair(U_158,U_157),U_159)
& in(ordered_pair(U_158,U_157),U_160) ) ) )
& ( ! [U_156,U_155] :
( ( in(ordered_pair(U_156,U_155),U_160)
| ~ in(ordered_pair(U_156,U_155),U_159) )
& ( in(ordered_pair(U_156,U_155),U_159)
| ~ in(ordered_pair(U_156,U_155),U_160) ) )
| U_160 != U_159 ) )
| ~ relation(U_159) )
| ~ relation(U_160) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_160] :
( ! [U_159] :
( ( ( U_160 = U_159
| ? [U_168,U_166] :
( ~ in(ordered_pair(U_168,U_166),U_160)
& in(ordered_pair(U_168,U_166),U_159) )
| ? [U_167,U_165] :
( ~ in(ordered_pair(U_167,U_165),U_159)
& in(ordered_pair(U_167,U_165),U_160) ) )
& ( ( ! [U_164,U_162] :
( in(ordered_pair(U_164,U_162),U_160)
| ~ in(ordered_pair(U_164,U_162),U_159) )
& ! [U_163,U_161] :
( in(ordered_pair(U_163,U_161),U_159)
| ~ in(ordered_pair(U_163,U_161),U_160) ) )
| U_160 != U_159 ) )
| ~ relation(U_159) )
| ~ relation(U_160) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
fof(f_20_4,plain,
! [U_160] :
( ! [U_159] :
( ( ( U_160 = U_159
| ? [U_168,U_166] :
( ~ in(ordered_pair(U_168,U_166),U_160)
& in(ordered_pair(U_168,U_166),U_159) )
| ? [U_165] :
( ~ in(ordered_pair(sK33(U_160,U_159),U_165),U_159)
& in(ordered_pair(sK33(U_160,U_159),U_165),U_160) ) )
& ( ( ! [U_164,U_162] :
( in(ordered_pair(U_164,U_162),U_160)
| ~ in(ordered_pair(U_164,U_162),U_159) )
& ! [U_163,U_161] :
( in(ordered_pair(U_163,U_161),U_159)
| ~ in(ordered_pair(U_163,U_161),U_160) ) )
| U_160 != U_159 ) )
| ~ relation(U_159) )
| ~ relation(U_160) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_167,sK33(U_160,U_159))],[f_20_3]) ).
fof(f_20_5,plain,
! [U_160] :
( ! [U_159] :
( ( ( U_160 = U_159
| ? [U_168,U_166] :
( ~ in(ordered_pair(U_168,U_166),U_160)
& in(ordered_pair(U_168,U_166),U_159) )
| ( ~ in(ordered_pair(sK33(U_160,U_159),sK34(U_160,U_159)),U_159)
& in(ordered_pair(sK33(U_160,U_159),sK34(U_160,U_159)),U_160) ) )
& ( ( ! [U_164,U_162] :
( in(ordered_pair(U_164,U_162),U_160)
| ~ in(ordered_pair(U_164,U_162),U_159) )
& ! [U_163,U_161] :
( in(ordered_pair(U_163,U_161),U_159)
| ~ in(ordered_pair(U_163,U_161),U_160) ) )
| U_160 != U_159 ) )
| ~ relation(U_159) )
| ~ relation(U_160) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_165,sK34(U_160,U_159))],[f_20_4]) ).
fof(f_20_6,plain,
! [U_160] :
( ! [U_159] :
( ( ( U_160 = U_159
| ? [U_166] :
( ~ in(ordered_pair(sK35(U_160,U_159),U_166),U_160)
& in(ordered_pair(sK35(U_160,U_159),U_166),U_159) )
| ( ~ in(ordered_pair(sK33(U_160,U_159),sK34(U_160,U_159)),U_159)
& in(ordered_pair(sK33(U_160,U_159),sK34(U_160,U_159)),U_160) ) )
& ( ( ! [U_164,U_162] :
( in(ordered_pair(U_164,U_162),U_160)
| ~ in(ordered_pair(U_164,U_162),U_159) )
& ! [U_163,U_161] :
( in(ordered_pair(U_163,U_161),U_159)
| ~ in(ordered_pair(U_163,U_161),U_160) ) )
| U_160 != U_159 ) )
| ~ relation(U_159) )
| ~ relation(U_160) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_168,sK35(U_160,U_159))],[f_20_5]) ).
fof(f_20_7,plain,
! [U_160] :
( ! [U_159] :
( ( ( U_160 = U_159
| ( ~ in(ordered_pair(sK35(U_160,U_159),sK36(U_160,U_159)),U_160)
& in(ordered_pair(sK35(U_160,U_159),sK36(U_160,U_159)),U_159) )
| ( ~ in(ordered_pair(sK33(U_160,U_159),sK34(U_160,U_159)),U_159)
& in(ordered_pair(sK33(U_160,U_159),sK34(U_160,U_159)),U_160) ) )
& ( ( ! [U_164,U_162] :
( in(ordered_pair(U_164,U_162),U_160)
| ~ in(ordered_pair(U_164,U_162),U_159) )
& ! [U_163,U_161] :
( in(ordered_pair(U_163,U_161),U_159)
| ~ in(ordered_pair(U_163,U_161),U_160) ) )
| U_160 != U_159 ) )
| ~ relation(U_159) )
| ~ relation(U_160) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_166,sK36(U_160,U_159))],[f_20_6]) ).
cnf(f_20_8,plain,
( in(ordered_pair(U_163,U_161),U_159)
| ~ in(ordered_pair(U_163,U_161),U_160)
| U_160 != U_159
| ~ relation(U_159)
| ~ relation(U_160) ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_9,plain,
( in(ordered_pair(U_164,U_162),U_160)
| ~ in(ordered_pair(U_164,U_162),U_159)
| U_160 != U_159
| ~ relation(U_159)
| ~ relation(U_160) ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_10,plain,
( in(ordered_pair(sK35(U_160,U_159),sK36(U_160,U_159)),U_159)
| in(ordered_pair(sK33(U_160,U_159),sK34(U_160,U_159)),U_160)
| U_160 = U_159
| ~ relation(U_159)
| ~ relation(U_160) ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_11,plain,
( ~ in(ordered_pair(sK35(U_160,U_159),sK36(U_160,U_159)),U_160)
| in(ordered_pair(sK33(U_160,U_159),sK34(U_160,U_159)),U_160)
| U_160 = U_159
| ~ relation(U_159)
| ~ relation(U_160) ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_12,plain,
( in(ordered_pair(sK35(U_160,U_159),sK36(U_160,U_159)),U_159)
| ~ in(ordered_pair(sK33(U_160,U_159),sK34(U_160,U_159)),U_159)
| U_160 = U_159
| ~ relation(U_159)
| ~ relation(U_160) ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_13,plain,
( ~ in(ordered_pair(sK35(U_160,U_159),sK36(U_160,U_159)),U_160)
| ~ in(ordered_pair(sK33(U_160,U_159),sK34(U_160,U_159)),U_159)
| U_160 = U_159
| ~ relation(U_159)
| ~ relation(U_160) ),
inference(clausify,[status(thm)],[f_20_7]) ).
fof(f_21_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_21_2,plain,
! [U_170,U_169] :
( ( ( ( element(U_169,U_170)
| ~ empty(U_169) )
& ( empty(U_169)
| ~ element(U_169,U_170) ) )
| ~ empty(U_170) )
& ( ( ( element(U_169,U_170)
| ~ in(U_169,U_170) )
& ( in(U_169,U_170)
| ~ element(U_169,U_170) ) )
| empty(U_170) ) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( ! [U_178] :
( ( ! [U_176] :
( element(U_176,U_178)
| ~ empty(U_176) )
& ! [U_175] :
( empty(U_175)
| ~ element(U_175,U_178) ) )
| ~ empty(U_178) )
& ! [U_177] :
( ( ! [U_174] :
( element(U_174,U_177)
| ~ in(U_174,U_177) )
& ! [U_173] :
( in(U_173,U_177)
| ~ element(U_173,U_177) ) )
| empty(U_177) ) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
( in(U_173,U_177)
| ~ element(U_173,U_177)
| empty(U_177) ),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
( element(U_174,U_177)
| ~ in(U_174,U_177)
| empty(U_177) ),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_6,plain,
( empty(U_175)
| ~ element(U_175,U_178)
| ~ empty(U_178) ),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_7,plain,
( element(U_176,U_178)
| ~ empty(U_176)
| ~ empty(U_178) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_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_22_2,plain,
! [U_183,U_182,U_181] :
( ( U_181 = unordered_pair(U_183,U_182)
| ? [U_180] :
( ( ~ in(U_180,U_181)
& ( U_180 = U_182
| U_180 = U_183 ) )
| ( U_180 != U_182
& U_180 != U_183
& in(U_180,U_181) ) ) )
& ( ! [U_179] :
( ( in(U_179,U_181)
| ( U_179 != U_182
& U_179 != U_183 ) )
& ( U_179 = U_182
| U_179 = U_183
| ~ in(U_179,U_181) ) )
| U_181 != unordered_pair(U_183,U_182) ) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( ! [U_193,U_191,U_189] :
( U_189 = unordered_pair(U_193,U_191)
| ? [U_187] :
( ~ in(U_187,U_189)
& ( U_187 = U_191
| U_187 = U_193 ) )
| ? [U_186] :
( U_186 != U_191
& U_186 != U_193
& in(U_186,U_189) ) )
& ! [U_192,U_190,U_188] :
( ( ! [U_185] :
( in(U_185,U_188)
| ( U_185 != U_190
& U_185 != U_192 ) )
& ! [U_184] :
( U_184 = U_190
| U_184 = U_192
| ~ in(U_184,U_188) ) )
| U_188 != unordered_pair(U_192,U_190) ) ),
inference(miniscope,[status(thm)],[f_22_2]) ).
fof(f_22_4,plain,
( ! [U_193,U_191,U_189] :
( U_189 = unordered_pair(U_193,U_191)
| ? [U_187] :
( ~ in(U_187,U_189)
& ( U_187 = U_191
| U_187 = U_193 ) )
| ( sK37(U_193,U_191,U_189) != U_191
& sK37(U_193,U_191,U_189) != U_193
& in(sK37(U_193,U_191,U_189),U_189) ) )
& ! [U_192,U_190,U_188] :
( ( ! [U_185] :
( in(U_185,U_188)
| ( U_185 != U_190
& U_185 != U_192 ) )
& ! [U_184] :
( U_184 = U_190
| U_184 = U_192
| ~ in(U_184,U_188) ) )
| U_188 != unordered_pair(U_192,U_190) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_186,sK37(U_193,U_191,U_189))],[f_22_3]) ).
fof(f_22_5,plain,
( ! [U_193,U_191,U_189] :
( U_189 = unordered_pair(U_193,U_191)
| ( ~ in(sK38(U_193,U_191,U_189),U_189)
& ( sK38(U_193,U_191,U_189) = U_191
| sK38(U_193,U_191,U_189) = U_193 ) )
| ( sK37(U_193,U_191,U_189) != U_191
& sK37(U_193,U_191,U_189) != U_193
& in(sK37(U_193,U_191,U_189),U_189) ) )
& ! [U_192,U_190,U_188] :
( ( ! [U_185] :
( in(U_185,U_188)
| ( U_185 != U_190
& U_185 != U_192 ) )
& ! [U_184] :
( U_184 = U_190
| U_184 = U_192
| ~ in(U_184,U_188) ) )
| U_188 != unordered_pair(U_192,U_190) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_187,sK38(U_193,U_191,U_189))],[f_22_4]) ).
cnf(f_22_6,plain,
( U_184 = U_190
| U_184 = U_192
| ~ in(U_184,U_188)
| U_188 != unordered_pair(U_192,U_190) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_7,plain,
( U_185 != U_192
| in(U_185,U_188)
| U_188 != unordered_pair(U_192,U_190) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_8,plain,
( U_185 != U_190
| in(U_185,U_188)
| U_188 != unordered_pair(U_192,U_190) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_9,plain,
( sK38(U_193,U_191,U_189) = U_191
| sK38(U_193,U_191,U_189) = U_193
| in(sK37(U_193,U_191,U_189),U_189)
| U_189 = unordered_pair(U_193,U_191) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_10,plain,
( ~ in(sK38(U_193,U_191,U_189),U_189)
| in(sK37(U_193,U_191,U_189),U_189)
| U_189 = unordered_pair(U_193,U_191) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_11,plain,
( sK37(U_193,U_191,U_189) != U_193
| sK38(U_193,U_191,U_189) = U_191
| sK38(U_193,U_191,U_189) = U_193
| U_189 = unordered_pair(U_193,U_191) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_12,plain,
( sK37(U_193,U_191,U_189) != U_191
| sK38(U_193,U_191,U_189) = U_191
| sK38(U_193,U_191,U_189) = U_193
| U_189 = unordered_pair(U_193,U_191) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_13,plain,
( sK37(U_193,U_191,U_189) != U_193
| ~ in(sK38(U_193,U_191,U_189),U_189)
| U_189 = unordered_pair(U_193,U_191) ),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_14,plain,
( sK37(U_193,U_191,U_189) != U_191
| ~ in(sK38(U_193,U_191,U_189),U_189)
| U_189 = unordered_pair(U_193,U_191) ),
inference(clausify,[status(thm)],[f_22_5]) ).
fof(f_23_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_23_2,plain,
! [U_198,U_197,U_196] :
( ( U_196 = set_union2(U_198,U_197)
| ? [U_195] :
( ( ~ in(U_195,U_196)
& ( in(U_195,U_197)
| in(U_195,U_198) ) )
| ( ~ in(U_195,U_197)
& ~ in(U_195,U_198)
& in(U_195,U_196) ) ) )
& ( ! [U_194] :
( ( in(U_194,U_196)
| ( ~ in(U_194,U_197)
& ~ in(U_194,U_198) ) )
& ( in(U_194,U_197)
| in(U_194,U_198)
| ~ in(U_194,U_196) ) )
| U_196 != set_union2(U_198,U_197) ) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( ! [U_208,U_206,U_204] :
( U_204 = set_union2(U_208,U_206)
| ? [U_202] :
( ~ in(U_202,U_204)
& ( in(U_202,U_206)
| in(U_202,U_208) ) )
| ? [U_201] :
( ~ in(U_201,U_206)
& ~ in(U_201,U_208)
& in(U_201,U_204) ) )
& ! [U_207,U_205,U_203] :
( ( ! [U_200] :
( in(U_200,U_203)
| ( ~ in(U_200,U_205)
& ~ in(U_200,U_207) ) )
& ! [U_199] :
( in(U_199,U_205)
| in(U_199,U_207)
| ~ in(U_199,U_203) ) )
| U_203 != set_union2(U_207,U_205) ) ),
inference(miniscope,[status(thm)],[f_23_2]) ).
fof(f_23_4,plain,
( ! [U_208,U_206,U_204] :
( U_204 = set_union2(U_208,U_206)
| ? [U_202] :
( ~ in(U_202,U_204)
& ( in(U_202,U_206)
| in(U_202,U_208) ) )
| ( ~ in(sK39(U_208,U_206,U_204),U_206)
& ~ in(sK39(U_208,U_206,U_204),U_208)
& in(sK39(U_208,U_206,U_204),U_204) ) )
& ! [U_207,U_205,U_203] :
( ( ! [U_200] :
( in(U_200,U_203)
| ( ~ in(U_200,U_205)
& ~ in(U_200,U_207) ) )
& ! [U_199] :
( in(U_199,U_205)
| in(U_199,U_207)
| ~ in(U_199,U_203) ) )
| U_203 != set_union2(U_207,U_205) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_201,sK39(U_208,U_206,U_204))],[f_23_3]) ).
fof(f_23_5,plain,
( ! [U_208,U_206,U_204] :
( U_204 = set_union2(U_208,U_206)
| ( ~ in(sK40(U_208,U_206,U_204),U_204)
& ( in(sK40(U_208,U_206,U_204),U_206)
| in(sK40(U_208,U_206,U_204),U_208) ) )
| ( ~ in(sK39(U_208,U_206,U_204),U_206)
& ~ in(sK39(U_208,U_206,U_204),U_208)
& in(sK39(U_208,U_206,U_204),U_204) ) )
& ! [U_207,U_205,U_203] :
( ( ! [U_200] :
( in(U_200,U_203)
| ( ~ in(U_200,U_205)
& ~ in(U_200,U_207) ) )
& ! [U_199] :
( in(U_199,U_205)
| in(U_199,U_207)
| ~ in(U_199,U_203) ) )
| U_203 != set_union2(U_207,U_205) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_202,sK40(U_208,U_206,U_204))],[f_23_4]) ).
cnf(f_23_6,plain,
( in(U_199,U_205)
| in(U_199,U_207)
| ~ in(U_199,U_203)
| U_203 != set_union2(U_207,U_205) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_7,plain,
( ~ in(U_200,U_207)
| in(U_200,U_203)
| U_203 != set_union2(U_207,U_205) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_8,plain,
( ~ in(U_200,U_205)
| in(U_200,U_203)
| U_203 != set_union2(U_207,U_205) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_9,plain,
( in(sK40(U_208,U_206,U_204),U_206)
| in(sK40(U_208,U_206,U_204),U_208)
| in(sK39(U_208,U_206,U_204),U_204)
| U_204 = set_union2(U_208,U_206) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_10,plain,
( ~ in(sK40(U_208,U_206,U_204),U_204)
| in(sK39(U_208,U_206,U_204),U_204)
| U_204 = set_union2(U_208,U_206) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_11,plain,
( ~ in(sK39(U_208,U_206,U_204),U_208)
| in(sK40(U_208,U_206,U_204),U_206)
| in(sK40(U_208,U_206,U_204),U_208)
| U_204 = set_union2(U_208,U_206) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_12,plain,
( ~ in(sK39(U_208,U_206,U_204),U_206)
| in(sK40(U_208,U_206,U_204),U_206)
| in(sK40(U_208,U_206,U_204),U_208)
| U_204 = set_union2(U_208,U_206) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_13,plain,
( ~ in(sK39(U_208,U_206,U_204),U_208)
| ~ in(sK40(U_208,U_206,U_204),U_204)
| U_204 = set_union2(U_208,U_206) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_14,plain,
( ~ in(sK39(U_208,U_206,U_204),U_206)
| ~ in(sK40(U_208,U_206,U_204),U_204)
| U_204 = set_union2(U_208,U_206) ),
inference(clausify,[status(thm)],[f_23_5]) ).
fof(f_24_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_24_2,plain,
! [U_221,U_220,U_219] :
( ( U_219 = cartesian_product2(U_221,U_220)
| ? [U_218] :
( ( ~ in(U_218,U_219)
& ? [U_217,U_216] :
( U_218 = ordered_pair(U_217,U_216)
& in(U_216,U_220)
& in(U_217,U_221) ) )
| ( ! [U_215,U_214] :
( U_218 != ordered_pair(U_215,U_214)
| ~ in(U_214,U_220)
| ~ in(U_215,U_221) )
& in(U_218,U_219) ) ) )
& ( ! [U_213] :
( ( in(U_213,U_219)
| ! [U_212,U_211] :
( U_213 != ordered_pair(U_212,U_211)
| ~ in(U_211,U_220)
| ~ in(U_212,U_221) ) )
& ( ? [U_210,U_209] :
( U_213 = ordered_pair(U_210,U_209)
& in(U_209,U_220)
& in(U_210,U_221) )
| ~ in(U_213,U_219) ) )
| U_219 != cartesian_product2(U_221,U_220) ) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( ! [U_231,U_229,U_227] :
( U_227 = cartesian_product2(U_231,U_229)
| ? [U_225] :
( ~ in(U_225,U_227)
& ? [U_217] :
( ? [U_216] :
( U_225 = ordered_pair(U_217,U_216)
& in(U_216,U_229) )
& in(U_217,U_231) ) )
| ? [U_224] :
( ! [U_215] :
( ! [U_214] :
( U_224 != ordered_pair(U_215,U_214)
| ~ in(U_214,U_229) )
| ~ in(U_215,U_231) )
& in(U_224,U_227) ) )
& ! [U_230,U_228,U_226] :
( ( ! [U_223] :
( in(U_223,U_226)
| ! [U_212] :
( ! [U_211] :
( U_223 != ordered_pair(U_212,U_211)
| ~ in(U_211,U_228) )
| ~ in(U_212,U_230) ) )
& ! [U_222] :
( ? [U_210] :
( ? [U_209] :
( U_222 = ordered_pair(U_210,U_209)
& in(U_209,U_228) )
& in(U_210,U_230) )
| ~ in(U_222,U_226) ) )
| U_226 != cartesian_product2(U_230,U_228) ) ),
inference(miniscope,[status(thm)],[f_24_2]) ).
fof(f_24_4,plain,
( ! [U_231,U_229,U_227] :
( U_227 = cartesian_product2(U_231,U_229)
| ? [U_225] :
( ~ in(U_225,U_227)
& ? [U_217] :
( ? [U_216] :
( U_225 = ordered_pair(U_217,U_216)
& in(U_216,U_229) )
& in(U_217,U_231) ) )
| ? [U_224] :
( ! [U_215] :
( ! [U_214] :
( U_224 != ordered_pair(U_215,U_214)
| ~ in(U_214,U_229) )
| ~ in(U_215,U_231) )
& in(U_224,U_227) ) )
& ! [U_230,U_228,U_226] :
( ( ! [U_223] :
( in(U_223,U_226)
| ! [U_212] :
( ! [U_211] :
( U_223 != ordered_pair(U_212,U_211)
| ~ in(U_211,U_228) )
| ~ in(U_212,U_230) ) )
& ! [U_222] :
( ( ? [U_209] :
( U_222 = ordered_pair(sK41(U_230,U_228,U_226,U_222),U_209)
& in(U_209,U_228) )
& in(sK41(U_230,U_228,U_226,U_222),U_230) )
| ~ in(U_222,U_226) ) )
| U_226 != cartesian_product2(U_230,U_228) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_210,sK41(U_230,U_228,U_226,U_222))],[f_24_3]) ).
fof(f_24_5,plain,
( ! [U_231,U_229,U_227] :
( U_227 = cartesian_product2(U_231,U_229)
| ? [U_225] :
( ~ in(U_225,U_227)
& ? [U_217] :
( ? [U_216] :
( U_225 = ordered_pair(U_217,U_216)
& in(U_216,U_229) )
& in(U_217,U_231) ) )
| ? [U_224] :
( ! [U_215] :
( ! [U_214] :
( U_224 != ordered_pair(U_215,U_214)
| ~ in(U_214,U_229) )
| ~ in(U_215,U_231) )
& in(U_224,U_227) ) )
& ! [U_230,U_228,U_226] :
( ( ! [U_223] :
( in(U_223,U_226)
| ! [U_212] :
( ! [U_211] :
( U_223 != ordered_pair(U_212,U_211)
| ~ in(U_211,U_228) )
| ~ in(U_212,U_230) ) )
& ! [U_222] :
( ( U_222 = ordered_pair(sK41(U_230,U_228,U_226,U_222),sK42(U_230,U_228,U_226,U_222))
& in(sK42(U_230,U_228,U_226,U_222),U_228)
& in(sK41(U_230,U_228,U_226,U_222),U_230) )
| ~ in(U_222,U_226) ) )
| U_226 != cartesian_product2(U_230,U_228) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_209,sK42(U_230,U_228,U_226,U_222))],[f_24_4]) ).
fof(f_24_6,plain,
( ! [U_231,U_229,U_227] :
( U_227 = cartesian_product2(U_231,U_229)
| ? [U_225] :
( ~ in(U_225,U_227)
& ? [U_217] :
( ? [U_216] :
( U_225 = ordered_pair(U_217,U_216)
& in(U_216,U_229) )
& in(U_217,U_231) ) )
| ( ! [U_215] :
( ! [U_214] :
( sK43(U_231,U_229,U_227) != ordered_pair(U_215,U_214)
| ~ in(U_214,U_229) )
| ~ in(U_215,U_231) )
& in(sK43(U_231,U_229,U_227),U_227) ) )
& ! [U_230,U_228,U_226] :
( ( ! [U_223] :
( in(U_223,U_226)
| ! [U_212] :
( ! [U_211] :
( U_223 != ordered_pair(U_212,U_211)
| ~ in(U_211,U_228) )
| ~ in(U_212,U_230) ) )
& ! [U_222] :
( ( U_222 = ordered_pair(sK41(U_230,U_228,U_226,U_222),sK42(U_230,U_228,U_226,U_222))
& in(sK42(U_230,U_228,U_226,U_222),U_228)
& in(sK41(U_230,U_228,U_226,U_222),U_230) )
| ~ in(U_222,U_226) ) )
| U_226 != cartesian_product2(U_230,U_228) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_224,sK43(U_231,U_229,U_227))],[f_24_5]) ).
fof(f_24_7,plain,
( ! [U_231,U_229,U_227] :
( U_227 = cartesian_product2(U_231,U_229)
| ( ~ in(sK44(U_231,U_229,U_227),U_227)
& ? [U_217] :
( ? [U_216] :
( sK44(U_231,U_229,U_227) = ordered_pair(U_217,U_216)
& in(U_216,U_229) )
& in(U_217,U_231) ) )
| ( ! [U_215] :
( ! [U_214] :
( sK43(U_231,U_229,U_227) != ordered_pair(U_215,U_214)
| ~ in(U_214,U_229) )
| ~ in(U_215,U_231) )
& in(sK43(U_231,U_229,U_227),U_227) ) )
& ! [U_230,U_228,U_226] :
( ( ! [U_223] :
( in(U_223,U_226)
| ! [U_212] :
( ! [U_211] :
( U_223 != ordered_pair(U_212,U_211)
| ~ in(U_211,U_228) )
| ~ in(U_212,U_230) ) )
& ! [U_222] :
( ( U_222 = ordered_pair(sK41(U_230,U_228,U_226,U_222),sK42(U_230,U_228,U_226,U_222))
& in(sK42(U_230,U_228,U_226,U_222),U_228)
& in(sK41(U_230,U_228,U_226,U_222),U_230) )
| ~ in(U_222,U_226) ) )
| U_226 != cartesian_product2(U_230,U_228) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_225,sK44(U_231,U_229,U_227))],[f_24_6]) ).
fof(f_24_8,plain,
( ! [U_231,U_229,U_227] :
( U_227 = cartesian_product2(U_231,U_229)
| ( ~ in(sK44(U_231,U_229,U_227),U_227)
& ? [U_216] :
( sK44(U_231,U_229,U_227) = ordered_pair(sK45(U_231,U_229,U_227),U_216)
& in(U_216,U_229) )
& in(sK45(U_231,U_229,U_227),U_231) )
| ( ! [U_215] :
( ! [U_214] :
( sK43(U_231,U_229,U_227) != ordered_pair(U_215,U_214)
| ~ in(U_214,U_229) )
| ~ in(U_215,U_231) )
& in(sK43(U_231,U_229,U_227),U_227) ) )
& ! [U_230,U_228,U_226] :
( ( ! [U_223] :
( in(U_223,U_226)
| ! [U_212] :
( ! [U_211] :
( U_223 != ordered_pair(U_212,U_211)
| ~ in(U_211,U_228) )
| ~ in(U_212,U_230) ) )
& ! [U_222] :
( ( U_222 = ordered_pair(sK41(U_230,U_228,U_226,U_222),sK42(U_230,U_228,U_226,U_222))
& in(sK42(U_230,U_228,U_226,U_222),U_228)
& in(sK41(U_230,U_228,U_226,U_222),U_230) )
| ~ in(U_222,U_226) ) )
| U_226 != cartesian_product2(U_230,U_228) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_217,sK45(U_231,U_229,U_227))],[f_24_7]) ).
fof(f_24_9,plain,
( ! [U_231,U_229,U_227] :
( U_227 = cartesian_product2(U_231,U_229)
| ( ~ in(sK44(U_231,U_229,U_227),U_227)
& sK44(U_231,U_229,U_227) = ordered_pair(sK45(U_231,U_229,U_227),sK46(U_231,U_229,U_227))
& in(sK46(U_231,U_229,U_227),U_229)
& in(sK45(U_231,U_229,U_227),U_231) )
| ( ! [U_215] :
( ! [U_214] :
( sK43(U_231,U_229,U_227) != ordered_pair(U_215,U_214)
| ~ in(U_214,U_229) )
| ~ in(U_215,U_231) )
& in(sK43(U_231,U_229,U_227),U_227) ) )
& ! [U_230,U_228,U_226] :
( ( ! [U_223] :
( in(U_223,U_226)
| ! [U_212] :
( ! [U_211] :
( U_223 != ordered_pair(U_212,U_211)
| ~ in(U_211,U_228) )
| ~ in(U_212,U_230) ) )
& ! [U_222] :
( ( U_222 = ordered_pair(sK41(U_230,U_228,U_226,U_222),sK42(U_230,U_228,U_226,U_222))
& in(sK42(U_230,U_228,U_226,U_222),U_228)
& in(sK41(U_230,U_228,U_226,U_222),U_230) )
| ~ in(U_222,U_226) ) )
| U_226 != cartesian_product2(U_230,U_228) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_216,sK46(U_231,U_229,U_227))],[f_24_8]) ).
cnf(f_24_10,plain,
( in(sK41(U_230,U_228,U_226,U_222),U_230)
| ~ in(U_222,U_226)
| U_226 != cartesian_product2(U_230,U_228) ),
inference(clausify,[status(thm)],[f_24_9]) ).
cnf(f_24_11,plain,
( in(sK42(U_230,U_228,U_226,U_222),U_228)
| ~ in(U_222,U_226)
| U_226 != cartesian_product2(U_230,U_228) ),
inference(clausify,[status(thm)],[f_24_9]) ).
cnf(f_24_12,plain,
( U_222 = ordered_pair(sK41(U_230,U_228,U_226,U_222),sK42(U_230,U_228,U_226,U_222))
| ~ in(U_222,U_226)
| U_226 != cartesian_product2(U_230,U_228) ),
inference(clausify,[status(thm)],[f_24_9]) ).
cnf(f_24_13,plain,
( in(U_223,U_226)
| U_223 != ordered_pair(U_212,U_211)
| ~ in(U_211,U_228)
| ~ in(U_212,U_230)
| U_226 != cartesian_product2(U_230,U_228) ),
inference(clausify,[status(thm)],[f_24_9]) ).
cnf(f_24_14,plain,
( in(sK45(U_231,U_229,U_227),U_231)
| in(sK43(U_231,U_229,U_227),U_227)
| U_227 = cartesian_product2(U_231,U_229) ),
inference(clausify,[status(thm)],[f_24_9]) ).
cnf(f_24_15,plain,
( in(sK46(U_231,U_229,U_227),U_229)
| in(sK43(U_231,U_229,U_227),U_227)
| U_227 = cartesian_product2(U_231,U_229) ),
inference(clausify,[status(thm)],[f_24_9]) ).
cnf(f_24_16,plain,
( sK44(U_231,U_229,U_227) = ordered_pair(sK45(U_231,U_229,U_227),sK46(U_231,U_229,U_227))
| in(sK43(U_231,U_229,U_227),U_227)
| U_227 = cartesian_product2(U_231,U_229) ),
inference(clausify,[status(thm)],[f_24_9]) ).
cnf(f_24_17,plain,
( ~ in(sK44(U_231,U_229,U_227),U_227)
| in(sK43(U_231,U_229,U_227),U_227)
| U_227 = cartesian_product2(U_231,U_229) ),
inference(clausify,[status(thm)],[f_24_9]) ).
cnf(f_24_18,plain,
( in(sK45(U_231,U_229,U_227),U_231)
| sK43(U_231,U_229,U_227) != ordered_pair(U_215,U_214)
| ~ in(U_214,U_229)
| ~ in(U_215,U_231)
| U_227 = cartesian_product2(U_231,U_229) ),
inference(clausify,[status(thm)],[f_24_9]) ).
cnf(f_24_19,plain,
( in(sK46(U_231,U_229,U_227),U_229)
| sK43(U_231,U_229,U_227) != ordered_pair(U_215,U_214)
| ~ in(U_214,U_229)
| ~ in(U_215,U_231)
| U_227 = cartesian_product2(U_231,U_229) ),
inference(clausify,[status(thm)],[f_24_9]) ).
cnf(f_24_20,plain,
( sK44(U_231,U_229,U_227) = ordered_pair(sK45(U_231,U_229,U_227),sK46(U_231,U_229,U_227))
| sK43(U_231,U_229,U_227) != ordered_pair(U_215,U_214)
| ~ in(U_214,U_229)
| ~ in(U_215,U_231)
| U_227 = cartesian_product2(U_231,U_229) ),
inference(clausify,[status(thm)],[f_24_9]) ).
cnf(f_24_21,plain,
( ~ in(sK44(U_231,U_229,U_227),U_227)
| sK43(U_231,U_229,U_227) != ordered_pair(U_215,U_214)
| ~ in(U_214,U_229)
| ~ in(U_215,U_231)
| U_227 = cartesian_product2(U_231,U_229) ),
inference(clausify,[status(thm)],[f_24_9]) ).
fof(f_25_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_25_2,plain,
! [U_237] :
( ! [U_236] :
( ( ( subset(U_237,U_236)
| ? [U_235,U_234] :
( ~ in(ordered_pair(U_235,U_234),U_236)
& in(ordered_pair(U_235,U_234),U_237) ) )
& ( ! [U_233,U_232] :
( in(ordered_pair(U_233,U_232),U_236)
| ~ in(ordered_pair(U_233,U_232),U_237) )
| ~ subset(U_237,U_236) ) )
| ~ relation(U_236) )
| ~ relation(U_237) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_237] :
( ! [U_236] :
( ( ( subset(U_237,U_236)
| ? [U_234] :
( ~ in(ordered_pair(sK47(U_237,U_236),U_234),U_236)
& in(ordered_pair(sK47(U_237,U_236),U_234),U_237) ) )
& ( ! [U_233,U_232] :
( in(ordered_pair(U_233,U_232),U_236)
| ~ in(ordered_pair(U_233,U_232),U_237) )
| ~ subset(U_237,U_236) ) )
| ~ relation(U_236) )
| ~ relation(U_237) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_235,sK47(U_237,U_236))],[f_25_2]) ).
fof(f_25_4,plain,
! [U_237] :
( ! [U_236] :
( ( ( subset(U_237,U_236)
| ( ~ in(ordered_pair(sK47(U_237,U_236),sK48(U_237,U_236)),U_236)
& in(ordered_pair(sK47(U_237,U_236),sK48(U_237,U_236)),U_237) ) )
& ( ! [U_233,U_232] :
( in(ordered_pair(U_233,U_232),U_236)
| ~ in(ordered_pair(U_233,U_232),U_237) )
| ~ subset(U_237,U_236) ) )
| ~ relation(U_236) )
| ~ relation(U_237) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_234,sK48(U_237,U_236))],[f_25_3]) ).
cnf(f_25_5,plain,
( in(ordered_pair(U_233,U_232),U_236)
| ~ in(ordered_pair(U_233,U_232),U_237)
| ~ subset(U_237,U_236)
| ~ relation(U_236)
| ~ relation(U_237) ),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_6,plain,
( in(ordered_pair(sK47(U_237,U_236),sK48(U_237,U_236)),U_237)
| subset(U_237,U_236)
| ~ relation(U_236)
| ~ relation(U_237) ),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_7,plain,
( ~ in(ordered_pair(sK47(U_237,U_236),sK48(U_237,U_236)),U_236)
| subset(U_237,U_236)
| ~ relation(U_236)
| ~ relation(U_237) ),
inference(clausify,[status(thm)],[f_25_4]) ).
fof(f_26_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_26_2,plain,
! [U_241,U_240] :
( ( subset(U_241,U_240)
| ? [U_239] :
( ~ in(U_239,U_240)
& in(U_239,U_241) ) )
& ( ! [U_238] :
( in(U_238,U_240)
| ~ in(U_238,U_241) )
| ~ subset(U_241,U_240) ) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( ! [U_245,U_243] :
( subset(U_245,U_243)
| ? [U_239] :
( ~ in(U_239,U_243)
& in(U_239,U_245) ) )
& ! [U_244,U_242] :
( ! [U_238] :
( in(U_238,U_242)
| ~ in(U_238,U_244) )
| ~ subset(U_244,U_242) ) ),
inference(miniscope,[status(thm)],[f_26_2]) ).
fof(f_26_4,plain,
( ! [U_245,U_243] :
( subset(U_245,U_243)
| ( ~ in(sK49(U_245,U_243),U_243)
& in(sK49(U_245,U_243),U_245) ) )
& ! [U_244,U_242] :
( ! [U_238] :
( in(U_238,U_242)
| ~ in(U_238,U_244) )
| ~ subset(U_244,U_242) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_239,sK49(U_245,U_243))],[f_26_3]) ).
cnf(f_26_5,plain,
( in(U_238,U_242)
| ~ in(U_238,U_244)
| ~ subset(U_244,U_242) ),
inference(clausify,[status(thm)],[f_26_4]) ).
cnf(f_26_6,plain,
( in(sK49(U_245,U_243),U_245)
| subset(U_245,U_243) ),
inference(clausify,[status(thm)],[f_26_4]) ).
cnf(f_26_7,plain,
( ~ in(sK49(U_245,U_243),U_243)
| subset(U_245,U_243) ),
inference(clausify,[status(thm)],[f_26_4]) ).
fof(f_27_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_27_2,plain,
! [U_250,U_249,U_248] :
( ( U_248 = set_intersection2(U_250,U_249)
| ? [U_247] :
( ( ~ in(U_247,U_248)
& in(U_247,U_249)
& in(U_247,U_250) )
| ( ( ~ in(U_247,U_249)
| ~ in(U_247,U_250) )
& in(U_247,U_248) ) ) )
& ( ! [U_246] :
( ( in(U_246,U_248)
| ~ in(U_246,U_249)
| ~ in(U_246,U_250) )
& ( ( in(U_246,U_249)
& in(U_246,U_250) )
| ~ in(U_246,U_248) ) )
| U_248 != set_intersection2(U_250,U_249) ) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( ! [U_260,U_258,U_256] :
( U_256 = set_intersection2(U_260,U_258)
| ? [U_254] :
( ~ in(U_254,U_256)
& in(U_254,U_258)
& in(U_254,U_260) )
| ? [U_253] :
( ( ~ in(U_253,U_258)
| ~ in(U_253,U_260) )
& in(U_253,U_256) ) )
& ! [U_259,U_257,U_255] :
( ( ! [U_252] :
( in(U_252,U_255)
| ~ in(U_252,U_257)
| ~ in(U_252,U_259) )
& ! [U_251] :
( ( in(U_251,U_257)
& in(U_251,U_259) )
| ~ in(U_251,U_255) ) )
| U_255 != set_intersection2(U_259,U_257) ) ),
inference(miniscope,[status(thm)],[f_27_2]) ).
fof(f_27_4,plain,
( ! [U_260,U_258,U_256] :
( U_256 = set_intersection2(U_260,U_258)
| ? [U_254] :
( ~ in(U_254,U_256)
& in(U_254,U_258)
& in(U_254,U_260) )
| ( ( ~ in(sK50(U_260,U_258,U_256),U_258)
| ~ in(sK50(U_260,U_258,U_256),U_260) )
& in(sK50(U_260,U_258,U_256),U_256) ) )
& ! [U_259,U_257,U_255] :
( ( ! [U_252] :
( in(U_252,U_255)
| ~ in(U_252,U_257)
| ~ in(U_252,U_259) )
& ! [U_251] :
( ( in(U_251,U_257)
& in(U_251,U_259) )
| ~ in(U_251,U_255) ) )
| U_255 != set_intersection2(U_259,U_257) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_253,sK50(U_260,U_258,U_256))],[f_27_3]) ).
fof(f_27_5,plain,
( ! [U_260,U_258,U_256] :
( U_256 = set_intersection2(U_260,U_258)
| ( ~ in(sK51(U_260,U_258,U_256),U_256)
& in(sK51(U_260,U_258,U_256),U_258)
& in(sK51(U_260,U_258,U_256),U_260) )
| ( ( ~ in(sK50(U_260,U_258,U_256),U_258)
| ~ in(sK50(U_260,U_258,U_256),U_260) )
& in(sK50(U_260,U_258,U_256),U_256) ) )
& ! [U_259,U_257,U_255] :
( ( ! [U_252] :
( in(U_252,U_255)
| ~ in(U_252,U_257)
| ~ in(U_252,U_259) )
& ! [U_251] :
( ( in(U_251,U_257)
& in(U_251,U_259) )
| ~ in(U_251,U_255) ) )
| U_255 != set_intersection2(U_259,U_257) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_254,sK51(U_260,U_258,U_256))],[f_27_4]) ).
cnf(f_27_6,plain,
( in(U_251,U_259)
| ~ in(U_251,U_255)
| U_255 != set_intersection2(U_259,U_257) ),
inference(clausify,[status(thm)],[f_27_5]) ).
cnf(f_27_7,plain,
( in(U_251,U_257)
| ~ in(U_251,U_255)
| U_255 != set_intersection2(U_259,U_257) ),
inference(clausify,[status(thm)],[f_27_5]) ).
cnf(f_27_8,plain,
( in(U_252,U_255)
| ~ in(U_252,U_257)
| ~ in(U_252,U_259)
| U_255 != set_intersection2(U_259,U_257) ),
inference(clausify,[status(thm)],[f_27_5]) ).
cnf(f_27_9,plain,
( in(sK51(U_260,U_258,U_256),U_260)
| in(sK50(U_260,U_258,U_256),U_256)
| U_256 = set_intersection2(U_260,U_258) ),
inference(clausify,[status(thm)],[f_27_5]) ).
cnf(f_27_10,plain,
( in(sK51(U_260,U_258,U_256),U_258)
| in(sK50(U_260,U_258,U_256),U_256)
| U_256 = set_intersection2(U_260,U_258) ),
inference(clausify,[status(thm)],[f_27_5]) ).
cnf(f_27_11,plain,
( ~ in(sK51(U_260,U_258,U_256),U_256)
| in(sK50(U_260,U_258,U_256),U_256)
| U_256 = set_intersection2(U_260,U_258) ),
inference(clausify,[status(thm)],[f_27_5]) ).
cnf(f_27_12,plain,
( in(sK51(U_260,U_258,U_256),U_260)
| ~ in(sK50(U_260,U_258,U_256),U_258)
| ~ in(sK50(U_260,U_258,U_256),U_260)
| U_256 = set_intersection2(U_260,U_258) ),
inference(clausify,[status(thm)],[f_27_5]) ).
cnf(f_27_13,plain,
( in(sK51(U_260,U_258,U_256),U_258)
| ~ in(sK50(U_260,U_258,U_256),U_258)
| ~ in(sK50(U_260,U_258,U_256),U_260)
| U_256 = set_intersection2(U_260,U_258) ),
inference(clausify,[status(thm)],[f_27_5]) ).
cnf(f_27_14,plain,
( ~ in(sK51(U_260,U_258,U_256),U_256)
| ~ in(sK50(U_260,U_258,U_256),U_258)
| ~ in(sK50(U_260,U_258,U_256),U_260)
| U_256 = set_intersection2(U_260,U_258) ),
inference(clausify,[status(thm)],[f_27_5]) ).
fof(f_28_1,plain,
! [A] :
( ! [B,C] :
( ( ( ( C = apply(A,B)
| C != empty_set )
& ( C = empty_set
| C != apply(A,B) ) )
| in(B,relation_dom(A)) )
& ( ( ( C = apply(A,B)
| ~ in(ordered_pair(B,C),A) )
& ( in(ordered_pair(B,C),A)
| C != apply(A,B) ) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d4_funct_1]) ).
fof(f_28_2,plain,
! [U_263] :
( ! [U_262,U_261] :
( ( ( ( U_261 = apply(U_263,U_262)
| U_261 != empty_set )
& ( U_261 = empty_set
| U_261 != apply(U_263,U_262) ) )
| in(U_262,relation_dom(U_263)) )
& ( ( ( U_261 = apply(U_263,U_262)
| ~ in(ordered_pair(U_262,U_261),U_263) )
& ( in(ordered_pair(U_262,U_261),U_263)
| U_261 != apply(U_263,U_262) ) )
| ~ in(U_262,relation_dom(U_263)) ) )
| ~ function(U_263)
| ~ relation(U_263) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_263] :
( ( ! [U_271] :
( ( ! [U_269] :
( U_269 = apply(U_263,U_271)
| U_269 != empty_set )
& ! [U_268] :
( U_268 = empty_set
| U_268 != apply(U_263,U_271) ) )
| in(U_271,relation_dom(U_263)) )
& ! [U_270] :
( ( ! [U_267] :
( U_267 = apply(U_263,U_270)
| ~ in(ordered_pair(U_270,U_267),U_263) )
& ! [U_266] :
( in(ordered_pair(U_270,U_266),U_263)
| U_266 != apply(U_263,U_270) ) )
| ~ in(U_270,relation_dom(U_263)) ) )
| ~ function(U_263)
| ~ relation(U_263) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
cnf(f_28_4,plain,
( in(ordered_pair(U_270,U_266),U_263)
| U_266 != apply(U_263,U_270)
| ~ in(U_270,relation_dom(U_263))
| ~ function(U_263)
| ~ relation(U_263) ),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_5,plain,
( U_267 = apply(U_263,U_270)
| ~ in(ordered_pair(U_270,U_267),U_263)
| ~ in(U_270,relation_dom(U_263))
| ~ function(U_263)
| ~ relation(U_263) ),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_6,plain,
( U_268 = empty_set
| U_268 != apply(U_263,U_271)
| in(U_271,relation_dom(U_263))
| ~ function(U_263)
| ~ relation(U_263) ),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_7,plain,
( U_269 = apply(U_263,U_271)
| U_269 != empty_set
| in(U_271,relation_dom(U_263))
| ~ function(U_263)
| ~ relation(U_263) ),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_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_29_2,plain,
! [U_279] :
( ! [U_278] :
( ( U_278 = relation_dom(U_279)
| ? [U_277] :
( ( ~ in(U_277,U_278)
& ? [U_276] : in(ordered_pair(U_277,U_276),U_279) )
| ( ! [U_275] : ~ in(ordered_pair(U_277,U_275),U_279)
& in(U_277,U_278) ) ) )
& ( ! [U_274] :
( ( in(U_274,U_278)
| ! [U_273] : ~ in(ordered_pair(U_274,U_273),U_279) )
& ( ? [U_272] : in(ordered_pair(U_274,U_272),U_279)
| ~ in(U_274,U_278) ) )
| U_278 != relation_dom(U_279) ) )
| ~ relation(U_279) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_279] :
( ( ! [U_285] :
( U_285 = relation_dom(U_279)
| ? [U_283] :
( ~ in(U_283,U_285)
& ? [U_276] : in(ordered_pair(U_283,U_276),U_279) )
| ? [U_282] :
( ! [U_275] : ~ in(ordered_pair(U_282,U_275),U_279)
& in(U_282,U_285) ) )
& ! [U_284] :
( ( ! [U_281] :
( in(U_281,U_284)
| ! [U_273] : ~ in(ordered_pair(U_281,U_273),U_279) )
& ! [U_280] :
( ? [U_272] : in(ordered_pair(U_280,U_272),U_279)
| ~ in(U_280,U_284) ) )
| U_284 != relation_dom(U_279) ) )
| ~ relation(U_279) ),
inference(miniscope,[status(thm)],[f_29_2]) ).
fof(f_29_4,plain,
! [U_279] :
( ( ! [U_285] :
( U_285 = relation_dom(U_279)
| ? [U_283] :
( ~ in(U_283,U_285)
& ? [U_276] : in(ordered_pair(U_283,U_276),U_279) )
| ? [U_282] :
( ! [U_275] : ~ in(ordered_pair(U_282,U_275),U_279)
& in(U_282,U_285) ) )
& ! [U_284] :
( ( ! [U_281] :
( in(U_281,U_284)
| ! [U_273] : ~ in(ordered_pair(U_281,U_273),U_279) )
& ! [U_280] :
( in(ordered_pair(U_280,sK52(U_279,U_284,U_280)),U_279)
| ~ in(U_280,U_284) ) )
| U_284 != relation_dom(U_279) ) )
| ~ relation(U_279) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_272,sK52(U_279,U_284,U_280))],[f_29_3]) ).
fof(f_29_5,plain,
! [U_279] :
( ( ! [U_285] :
( U_285 = relation_dom(U_279)
| ? [U_283] :
( ~ in(U_283,U_285)
& ? [U_276] : in(ordered_pair(U_283,U_276),U_279) )
| ( ! [U_275] : ~ in(ordered_pair(sK53(U_279,U_285),U_275),U_279)
& in(sK53(U_279,U_285),U_285) ) )
& ! [U_284] :
( ( ! [U_281] :
( in(U_281,U_284)
| ! [U_273] : ~ in(ordered_pair(U_281,U_273),U_279) )
& ! [U_280] :
( in(ordered_pair(U_280,sK52(U_279,U_284,U_280)),U_279)
| ~ in(U_280,U_284) ) )
| U_284 != relation_dom(U_279) ) )
| ~ relation(U_279) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_282,sK53(U_279,U_285))],[f_29_4]) ).
fof(f_29_6,plain,
! [U_279] :
( ( ! [U_285] :
( U_285 = relation_dom(U_279)
| ( ~ in(sK54(U_279,U_285),U_285)
& ? [U_276] : in(ordered_pair(sK54(U_279,U_285),U_276),U_279) )
| ( ! [U_275] : ~ in(ordered_pair(sK53(U_279,U_285),U_275),U_279)
& in(sK53(U_279,U_285),U_285) ) )
& ! [U_284] :
( ( ! [U_281] :
( in(U_281,U_284)
| ! [U_273] : ~ in(ordered_pair(U_281,U_273),U_279) )
& ! [U_280] :
( in(ordered_pair(U_280,sK52(U_279,U_284,U_280)),U_279)
| ~ in(U_280,U_284) ) )
| U_284 != relation_dom(U_279) ) )
| ~ relation(U_279) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_283,sK54(U_279,U_285))],[f_29_5]) ).
fof(f_29_7,plain,
! [U_279] :
( ( ! [U_285] :
( U_285 = relation_dom(U_279)
| ( ~ in(sK54(U_279,U_285),U_285)
& in(ordered_pair(sK54(U_279,U_285),sK55(U_279,U_285)),U_279) )
| ( ! [U_275] : ~ in(ordered_pair(sK53(U_279,U_285),U_275),U_279)
& in(sK53(U_279,U_285),U_285) ) )
& ! [U_284] :
( ( ! [U_281] :
( in(U_281,U_284)
| ! [U_273] : ~ in(ordered_pair(U_281,U_273),U_279) )
& ! [U_280] :
( in(ordered_pair(U_280,sK52(U_279,U_284,U_280)),U_279)
| ~ in(U_280,U_284) ) )
| U_284 != relation_dom(U_279) ) )
| ~ relation(U_279) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_276,sK55(U_279,U_285))],[f_29_6]) ).
cnf(f_29_8,plain,
( in(ordered_pair(U_280,sK52(U_279,U_284,U_280)),U_279)
| ~ in(U_280,U_284)
| U_284 != relation_dom(U_279)
| ~ relation(U_279) ),
inference(clausify,[status(thm)],[f_29_7]) ).
cnf(f_29_9,plain,
( in(U_281,U_284)
| ~ in(ordered_pair(U_281,U_273),U_279)
| U_284 != relation_dom(U_279)
| ~ relation(U_279) ),
inference(clausify,[status(thm)],[f_29_7]) ).
cnf(f_29_10,plain,
( in(ordered_pair(sK54(U_279,U_285),sK55(U_279,U_285)),U_279)
| in(sK53(U_279,U_285),U_285)
| U_285 = relation_dom(U_279)
| ~ relation(U_279) ),
inference(clausify,[status(thm)],[f_29_7]) ).
cnf(f_29_11,plain,
( ~ in(sK54(U_279,U_285),U_285)
| in(sK53(U_279,U_285),U_285)
| U_285 = relation_dom(U_279)
| ~ relation(U_279) ),
inference(clausify,[status(thm)],[f_29_7]) ).
cnf(f_29_12,plain,
( in(ordered_pair(sK54(U_279,U_285),sK55(U_279,U_285)),U_279)
| ~ in(ordered_pair(sK53(U_279,U_285),U_275),U_279)
| U_285 = relation_dom(U_279)
| ~ relation(U_279) ),
inference(clausify,[status(thm)],[f_29_7]) ).
cnf(f_29_13,plain,
( ~ in(sK54(U_279,U_285),U_285)
| ~ in(ordered_pair(sK53(U_279,U_285),U_275),U_279)
| U_285 = relation_dom(U_279)
| ~ relation(U_279) ),
inference(clausify,[status(thm)],[f_29_7]) ).
fof(f_30_1,plain,
! [A] : cast_to_subset(A) = A,
inference(fof_nnf,[status(thm)],[d4_subset_1]) ).
fof(f_30_2,plain,
! [U_286] : cast_to_subset(U_286) = U_286,
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
cast_to_subset(U_286) = U_286,
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_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_31_2,plain,
! [U_294,U_293] :
( ( U_293 = union(U_294)
| ? [U_292] :
( ( ~ in(U_292,U_293)
& ? [U_291] :
( in(U_291,U_294)
& in(U_292,U_291) ) )
| ( ! [U_290] :
( ~ in(U_290,U_294)
| ~ in(U_292,U_290) )
& in(U_292,U_293) ) ) )
& ( ! [U_289] :
( ( in(U_289,U_293)
| ! [U_288] :
( ~ in(U_288,U_294)
| ~ in(U_289,U_288) ) )
& ( ? [U_287] :
( in(U_287,U_294)
& in(U_289,U_287) )
| ~ in(U_289,U_293) ) )
| U_293 != union(U_294) ) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( ! [U_302,U_300] :
( U_300 = union(U_302)
| ? [U_298] :
( ~ in(U_298,U_300)
& ? [U_291] :
( in(U_291,U_302)
& in(U_298,U_291) ) )
| ? [U_297] :
( ! [U_290] :
( ~ in(U_290,U_302)
| ~ in(U_297,U_290) )
& in(U_297,U_300) ) )
& ! [U_301,U_299] :
( ( ! [U_296] :
( in(U_296,U_299)
| ! [U_288] :
( ~ in(U_288,U_301)
| ~ in(U_296,U_288) ) )
& ! [U_295] :
( ? [U_287] :
( in(U_287,U_301)
& in(U_295,U_287) )
| ~ in(U_295,U_299) ) )
| U_299 != union(U_301) ) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
fof(f_31_4,plain,
( ! [U_302,U_300] :
( U_300 = union(U_302)
| ? [U_298] :
( ~ in(U_298,U_300)
& ? [U_291] :
( in(U_291,U_302)
& in(U_298,U_291) ) )
| ? [U_297] :
( ! [U_290] :
( ~ in(U_290,U_302)
| ~ in(U_297,U_290) )
& in(U_297,U_300) ) )
& ! [U_301,U_299] :
( ( ! [U_296] :
( in(U_296,U_299)
| ! [U_288] :
( ~ in(U_288,U_301)
| ~ in(U_296,U_288) ) )
& ! [U_295] :
( ( in(sK56(U_301,U_299,U_295),U_301)
& in(U_295,sK56(U_301,U_299,U_295)) )
| ~ in(U_295,U_299) ) )
| U_299 != union(U_301) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_287,sK56(U_301,U_299,U_295))],[f_31_3]) ).
fof(f_31_5,plain,
( ! [U_302,U_300] :
( U_300 = union(U_302)
| ? [U_298] :
( ~ in(U_298,U_300)
& ? [U_291] :
( in(U_291,U_302)
& in(U_298,U_291) ) )
| ( ! [U_290] :
( ~ in(U_290,U_302)
| ~ in(sK57(U_302,U_300),U_290) )
& in(sK57(U_302,U_300),U_300) ) )
& ! [U_301,U_299] :
( ( ! [U_296] :
( in(U_296,U_299)
| ! [U_288] :
( ~ in(U_288,U_301)
| ~ in(U_296,U_288) ) )
& ! [U_295] :
( ( in(sK56(U_301,U_299,U_295),U_301)
& in(U_295,sK56(U_301,U_299,U_295)) )
| ~ in(U_295,U_299) ) )
| U_299 != union(U_301) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_297,sK57(U_302,U_300))],[f_31_4]) ).
fof(f_31_6,plain,
( ! [U_302,U_300] :
( U_300 = union(U_302)
| ( ~ in(sK58(U_302,U_300),U_300)
& ? [U_291] :
( in(U_291,U_302)
& in(sK58(U_302,U_300),U_291) ) )
| ( ! [U_290] :
( ~ in(U_290,U_302)
| ~ in(sK57(U_302,U_300),U_290) )
& in(sK57(U_302,U_300),U_300) ) )
& ! [U_301,U_299] :
( ( ! [U_296] :
( in(U_296,U_299)
| ! [U_288] :
( ~ in(U_288,U_301)
| ~ in(U_296,U_288) ) )
& ! [U_295] :
( ( in(sK56(U_301,U_299,U_295),U_301)
& in(U_295,sK56(U_301,U_299,U_295)) )
| ~ in(U_295,U_299) ) )
| U_299 != union(U_301) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_298,sK58(U_302,U_300))],[f_31_5]) ).
fof(f_31_7,plain,
( ! [U_302,U_300] :
( U_300 = union(U_302)
| ( ~ in(sK58(U_302,U_300),U_300)
& in(sK59(U_302,U_300),U_302)
& in(sK58(U_302,U_300),sK59(U_302,U_300)) )
| ( ! [U_290] :
( ~ in(U_290,U_302)
| ~ in(sK57(U_302,U_300),U_290) )
& in(sK57(U_302,U_300),U_300) ) )
& ! [U_301,U_299] :
( ( ! [U_296] :
( in(U_296,U_299)
| ! [U_288] :
( ~ in(U_288,U_301)
| ~ in(U_296,U_288) ) )
& ! [U_295] :
( ( in(sK56(U_301,U_299,U_295),U_301)
& in(U_295,sK56(U_301,U_299,U_295)) )
| ~ in(U_295,U_299) ) )
| U_299 != union(U_301) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_291,sK59(U_302,U_300))],[f_31_6]) ).
cnf(f_31_8,plain,
( in(U_295,sK56(U_301,U_299,U_295))
| ~ in(U_295,U_299)
| U_299 != union(U_301) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_9,plain,
( in(sK56(U_301,U_299,U_295),U_301)
| ~ in(U_295,U_299)
| U_299 != union(U_301) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_10,plain,
( in(U_296,U_299)
| ~ in(U_288,U_301)
| ~ in(U_296,U_288)
| U_299 != union(U_301) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_11,plain,
( in(sK58(U_302,U_300),sK59(U_302,U_300))
| in(sK57(U_302,U_300),U_300)
| U_300 = union(U_302) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_12,plain,
( in(sK59(U_302,U_300),U_302)
| in(sK57(U_302,U_300),U_300)
| U_300 = union(U_302) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_13,plain,
( ~ in(sK58(U_302,U_300),U_300)
| in(sK57(U_302,U_300),U_300)
| U_300 = union(U_302) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_14,plain,
( in(sK58(U_302,U_300),sK59(U_302,U_300))
| ~ in(U_290,U_302)
| ~ in(sK57(U_302,U_300),U_290)
| U_300 = union(U_302) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_15,plain,
( in(sK59(U_302,U_300),U_302)
| ~ in(U_290,U_302)
| ~ in(sK57(U_302,U_300),U_290)
| U_300 = union(U_302) ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_16,plain,
( ~ in(sK58(U_302,U_300),U_300)
| ~ in(U_290,U_302)
| ~ in(sK57(U_302,U_300),U_290)
| U_300 = union(U_302) ),
inference(clausify,[status(thm)],[f_31_7]) ).
fof(f_32_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_32_2,plain,
! [U_307,U_306,U_305] :
( ( U_305 = set_difference(U_307,U_306)
| ? [U_304] :
( ( ~ in(U_304,U_305)
& ~ in(U_304,U_306)
& in(U_304,U_307) )
| ( ( in(U_304,U_306)
| ~ in(U_304,U_307) )
& in(U_304,U_305) ) ) )
& ( ! [U_303] :
( ( in(U_303,U_305)
| in(U_303,U_306)
| ~ in(U_303,U_307) )
& ( ( ~ in(U_303,U_306)
& in(U_303,U_307) )
| ~ in(U_303,U_305) ) )
| U_305 != set_difference(U_307,U_306) ) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
( ! [U_317,U_315,U_313] :
( U_313 = set_difference(U_317,U_315)
| ? [U_311] :
( ~ in(U_311,U_313)
& ~ in(U_311,U_315)
& in(U_311,U_317) )
| ? [U_310] :
( ( in(U_310,U_315)
| ~ in(U_310,U_317) )
& in(U_310,U_313) ) )
& ! [U_316,U_314,U_312] :
( ( ! [U_309] :
( in(U_309,U_312)
| in(U_309,U_314)
| ~ in(U_309,U_316) )
& ! [U_308] :
( ( ~ in(U_308,U_314)
& in(U_308,U_316) )
| ~ in(U_308,U_312) ) )
| U_312 != set_difference(U_316,U_314) ) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
fof(f_32_4,plain,
( ! [U_317,U_315,U_313] :
( U_313 = set_difference(U_317,U_315)
| ? [U_311] :
( ~ in(U_311,U_313)
& ~ in(U_311,U_315)
& in(U_311,U_317) )
| ( ( in(sK60(U_317,U_315,U_313),U_315)
| ~ in(sK60(U_317,U_315,U_313),U_317) )
& in(sK60(U_317,U_315,U_313),U_313) ) )
& ! [U_316,U_314,U_312] :
( ( ! [U_309] :
( in(U_309,U_312)
| in(U_309,U_314)
| ~ in(U_309,U_316) )
& ! [U_308] :
( ( ~ in(U_308,U_314)
& in(U_308,U_316) )
| ~ in(U_308,U_312) ) )
| U_312 != set_difference(U_316,U_314) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_310,sK60(U_317,U_315,U_313))],[f_32_3]) ).
fof(f_32_5,plain,
( ! [U_317,U_315,U_313] :
( U_313 = set_difference(U_317,U_315)
| ( ~ in(sK61(U_317,U_315,U_313),U_313)
& ~ in(sK61(U_317,U_315,U_313),U_315)
& in(sK61(U_317,U_315,U_313),U_317) )
| ( ( in(sK60(U_317,U_315,U_313),U_315)
| ~ in(sK60(U_317,U_315,U_313),U_317) )
& in(sK60(U_317,U_315,U_313),U_313) ) )
& ! [U_316,U_314,U_312] :
( ( ! [U_309] :
( in(U_309,U_312)
| in(U_309,U_314)
| ~ in(U_309,U_316) )
& ! [U_308] :
( ( ~ in(U_308,U_314)
& in(U_308,U_316) )
| ~ in(U_308,U_312) ) )
| U_312 != set_difference(U_316,U_314) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_311,sK61(U_317,U_315,U_313))],[f_32_4]) ).
cnf(f_32_6,plain,
( in(U_308,U_316)
| ~ in(U_308,U_312)
| U_312 != set_difference(U_316,U_314) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_7,plain,
( ~ in(U_308,U_314)
| ~ in(U_308,U_312)
| U_312 != set_difference(U_316,U_314) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_8,plain,
( in(U_309,U_312)
| in(U_309,U_314)
| ~ in(U_309,U_316)
| U_312 != set_difference(U_316,U_314) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_9,plain,
( in(sK61(U_317,U_315,U_313),U_317)
| in(sK60(U_317,U_315,U_313),U_313)
| U_313 = set_difference(U_317,U_315) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_10,plain,
( ~ in(sK61(U_317,U_315,U_313),U_315)
| in(sK60(U_317,U_315,U_313),U_313)
| U_313 = set_difference(U_317,U_315) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_11,plain,
( ~ in(sK61(U_317,U_315,U_313),U_313)
| in(sK60(U_317,U_315,U_313),U_313)
| U_313 = set_difference(U_317,U_315) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_12,plain,
( in(sK61(U_317,U_315,U_313),U_317)
| in(sK60(U_317,U_315,U_313),U_315)
| ~ in(sK60(U_317,U_315,U_313),U_317)
| U_313 = set_difference(U_317,U_315) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_13,plain,
( ~ in(sK61(U_317,U_315,U_313),U_315)
| in(sK60(U_317,U_315,U_313),U_315)
| ~ in(sK60(U_317,U_315,U_313),U_317)
| U_313 = set_difference(U_317,U_315) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_14,plain,
( ~ in(sK61(U_317,U_315,U_313),U_313)
| in(sK60(U_317,U_315,U_313),U_315)
| ~ in(sK60(U_317,U_315,U_313),U_317)
| U_313 = set_difference(U_317,U_315) ),
inference(clausify,[status(thm)],[f_32_5]) ).
fof(f_33_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_33_2,plain,
! [U_325] :
( ! [U_324] :
( ( U_324 = relation_rng(U_325)
| ? [U_323] :
( ( ~ in(U_323,U_324)
& ? [U_322] : in(ordered_pair(U_322,U_323),U_325) )
| ( ! [U_321] : ~ in(ordered_pair(U_321,U_323),U_325)
& in(U_323,U_324) ) ) )
& ( ! [U_320] :
( ( in(U_320,U_324)
| ! [U_319] : ~ in(ordered_pair(U_319,U_320),U_325) )
& ( ? [U_318] : in(ordered_pair(U_318,U_320),U_325)
| ~ in(U_320,U_324) ) )
| U_324 != relation_rng(U_325) ) )
| ~ relation(U_325) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_325] :
( ( ! [U_331] :
( U_331 = relation_rng(U_325)
| ? [U_329] :
( ~ in(U_329,U_331)
& ? [U_322] : in(ordered_pair(U_322,U_329),U_325) )
| ? [U_328] :
( ! [U_321] : ~ in(ordered_pair(U_321,U_328),U_325)
& in(U_328,U_331) ) )
& ! [U_330] :
( ( ! [U_327] :
( in(U_327,U_330)
| ! [U_319] : ~ in(ordered_pair(U_319,U_327),U_325) )
& ! [U_326] :
( ? [U_318] : in(ordered_pair(U_318,U_326),U_325)
| ~ in(U_326,U_330) ) )
| U_330 != relation_rng(U_325) ) )
| ~ relation(U_325) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
fof(f_33_4,plain,
! [U_325] :
( ( ! [U_331] :
( U_331 = relation_rng(U_325)
| ? [U_329] :
( ~ in(U_329,U_331)
& ? [U_322] : in(ordered_pair(U_322,U_329),U_325) )
| ? [U_328] :
( ! [U_321] : ~ in(ordered_pair(U_321,U_328),U_325)
& in(U_328,U_331) ) )
& ! [U_330] :
( ( ! [U_327] :
( in(U_327,U_330)
| ! [U_319] : ~ in(ordered_pair(U_319,U_327),U_325) )
& ! [U_326] :
( in(ordered_pair(sK62(U_325,U_330,U_326),U_326),U_325)
| ~ in(U_326,U_330) ) )
| U_330 != relation_rng(U_325) ) )
| ~ relation(U_325) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_318,sK62(U_325,U_330,U_326))],[f_33_3]) ).
fof(f_33_5,plain,
! [U_325] :
( ( ! [U_331] :
( U_331 = relation_rng(U_325)
| ? [U_329] :
( ~ in(U_329,U_331)
& ? [U_322] : in(ordered_pair(U_322,U_329),U_325) )
| ( ! [U_321] : ~ in(ordered_pair(U_321,sK63(U_325,U_331)),U_325)
& in(sK63(U_325,U_331),U_331) ) )
& ! [U_330] :
( ( ! [U_327] :
( in(U_327,U_330)
| ! [U_319] : ~ in(ordered_pair(U_319,U_327),U_325) )
& ! [U_326] :
( in(ordered_pair(sK62(U_325,U_330,U_326),U_326),U_325)
| ~ in(U_326,U_330) ) )
| U_330 != relation_rng(U_325) ) )
| ~ relation(U_325) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_328,sK63(U_325,U_331))],[f_33_4]) ).
fof(f_33_6,plain,
! [U_325] :
( ( ! [U_331] :
( U_331 = relation_rng(U_325)
| ( ~ in(sK64(U_325,U_331),U_331)
& ? [U_322] : in(ordered_pair(U_322,sK64(U_325,U_331)),U_325) )
| ( ! [U_321] : ~ in(ordered_pair(U_321,sK63(U_325,U_331)),U_325)
& in(sK63(U_325,U_331),U_331) ) )
& ! [U_330] :
( ( ! [U_327] :
( in(U_327,U_330)
| ! [U_319] : ~ in(ordered_pair(U_319,U_327),U_325) )
& ! [U_326] :
( in(ordered_pair(sK62(U_325,U_330,U_326),U_326),U_325)
| ~ in(U_326,U_330) ) )
| U_330 != relation_rng(U_325) ) )
| ~ relation(U_325) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_329,sK64(U_325,U_331))],[f_33_5]) ).
fof(f_33_7,plain,
! [U_325] :
( ( ! [U_331] :
( U_331 = relation_rng(U_325)
| ( ~ in(sK64(U_325,U_331),U_331)
& in(ordered_pair(sK65(U_325,U_331),sK64(U_325,U_331)),U_325) )
| ( ! [U_321] : ~ in(ordered_pair(U_321,sK63(U_325,U_331)),U_325)
& in(sK63(U_325,U_331),U_331) ) )
& ! [U_330] :
( ( ! [U_327] :
( in(U_327,U_330)
| ! [U_319] : ~ in(ordered_pair(U_319,U_327),U_325) )
& ! [U_326] :
( in(ordered_pair(sK62(U_325,U_330,U_326),U_326),U_325)
| ~ in(U_326,U_330) ) )
| U_330 != relation_rng(U_325) ) )
| ~ relation(U_325) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_322,sK65(U_325,U_331))],[f_33_6]) ).
cnf(f_33_8,plain,
( in(ordered_pair(sK62(U_325,U_330,U_326),U_326),U_325)
| ~ in(U_326,U_330)
| U_330 != relation_rng(U_325)
| ~ relation(U_325) ),
inference(clausify,[status(thm)],[f_33_7]) ).
cnf(f_33_9,plain,
( in(U_327,U_330)
| ~ in(ordered_pair(U_319,U_327),U_325)
| U_330 != relation_rng(U_325)
| ~ relation(U_325) ),
inference(clausify,[status(thm)],[f_33_7]) ).
cnf(f_33_10,plain,
( in(ordered_pair(sK65(U_325,U_331),sK64(U_325,U_331)),U_325)
| in(sK63(U_325,U_331),U_331)
| U_331 = relation_rng(U_325)
| ~ relation(U_325) ),
inference(clausify,[status(thm)],[f_33_7]) ).
cnf(f_33_11,plain,
( ~ in(sK64(U_325,U_331),U_331)
| in(sK63(U_325,U_331),U_331)
| U_331 = relation_rng(U_325)
| ~ relation(U_325) ),
inference(clausify,[status(thm)],[f_33_7]) ).
cnf(f_33_12,plain,
( in(ordered_pair(sK65(U_325,U_331),sK64(U_325,U_331)),U_325)
| ~ in(ordered_pair(U_321,sK63(U_325,U_331)),U_325)
| U_331 = relation_rng(U_325)
| ~ relation(U_325) ),
inference(clausify,[status(thm)],[f_33_7]) ).
cnf(f_33_13,plain,
( ~ in(sK64(U_325,U_331),U_331)
| ~ in(ordered_pair(U_321,sK63(U_325,U_331)),U_325)
| U_331 = relation_rng(U_325)
| ~ relation(U_325) ),
inference(clausify,[status(thm)],[f_33_7]) ).
fof(f_34_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_34_2,plain,
! [U_333,U_332] :
( subset_complement(U_333,U_332) = set_difference(U_333,U_332)
| ~ element(U_332,powerset(U_333)) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( subset_complement(U_333,U_332) = set_difference(U_333,U_332)
| ~ element(U_332,powerset(U_333)) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_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_35_2,plain,
! [U_335,U_334] : ordered_pair(U_335,U_334) = unordered_pair(unordered_pair(U_335,U_334),singleton(U_335)),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
ordered_pair(U_335,U_334) = unordered_pair(unordered_pair(U_335,U_334),singleton(U_335)),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_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_36_2,plain,
! [U_336] :
( relation_field(U_336) = set_union2(relation_dom(U_336),relation_rng(U_336))
| ~ relation(U_336) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
( relation_field(U_336) = set_union2(relation_dom(U_336),relation_rng(U_336))
| ~ relation(U_336) ),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_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_37_2,plain,
! [U_342] :
( ! [U_341] :
( ( ( U_341 = relation_inverse(U_342)
| ? [U_340,U_339] :
( ( ~ in(ordered_pair(U_340,U_339),U_341)
& in(ordered_pair(U_339,U_340),U_342) )
| ( ~ in(ordered_pair(U_339,U_340),U_342)
& in(ordered_pair(U_340,U_339),U_341) ) ) )
& ( ! [U_338,U_337] :
( ( in(ordered_pair(U_338,U_337),U_341)
| ~ in(ordered_pair(U_337,U_338),U_342) )
& ( in(ordered_pair(U_337,U_338),U_342)
| ~ in(ordered_pair(U_338,U_337),U_341) ) )
| U_341 != relation_inverse(U_342) ) )
| ~ relation(U_341) )
| ~ relation(U_342) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_342] :
( ! [U_341] :
( ( ( U_341 = relation_inverse(U_342)
| ? [U_350,U_348] :
( ~ in(ordered_pair(U_350,U_348),U_341)
& in(ordered_pair(U_348,U_350),U_342) )
| ? [U_349,U_347] :
( ~ in(ordered_pair(U_347,U_349),U_342)
& in(ordered_pair(U_349,U_347),U_341) ) )
& ( ( ! [U_346,U_344] :
( in(ordered_pair(U_346,U_344),U_341)
| ~ in(ordered_pair(U_344,U_346),U_342) )
& ! [U_345,U_343] :
( in(ordered_pair(U_343,U_345),U_342)
| ~ in(ordered_pair(U_345,U_343),U_341) ) )
| U_341 != relation_inverse(U_342) ) )
| ~ relation(U_341) )
| ~ relation(U_342) ),
inference(miniscope,[status(thm)],[f_37_2]) ).
fof(f_37_4,plain,
! [U_342] :
( ! [U_341] :
( ( ( U_341 = relation_inverse(U_342)
| ? [U_350,U_348] :
( ~ in(ordered_pair(U_350,U_348),U_341)
& in(ordered_pair(U_348,U_350),U_342) )
| ? [U_347] :
( ~ in(ordered_pair(U_347,sK66(U_342,U_341)),U_342)
& in(ordered_pair(sK66(U_342,U_341),U_347),U_341) ) )
& ( ( ! [U_346,U_344] :
( in(ordered_pair(U_346,U_344),U_341)
| ~ in(ordered_pair(U_344,U_346),U_342) )
& ! [U_345,U_343] :
( in(ordered_pair(U_343,U_345),U_342)
| ~ in(ordered_pair(U_345,U_343),U_341) ) )
| U_341 != relation_inverse(U_342) ) )
| ~ relation(U_341) )
| ~ relation(U_342) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_349,sK66(U_342,U_341))],[f_37_3]) ).
fof(f_37_5,plain,
! [U_342] :
( ! [U_341] :
( ( ( U_341 = relation_inverse(U_342)
| ? [U_350,U_348] :
( ~ in(ordered_pair(U_350,U_348),U_341)
& in(ordered_pair(U_348,U_350),U_342) )
| ( ~ in(ordered_pair(sK67(U_342,U_341),sK66(U_342,U_341)),U_342)
& in(ordered_pair(sK66(U_342,U_341),sK67(U_342,U_341)),U_341) ) )
& ( ( ! [U_346,U_344] :
( in(ordered_pair(U_346,U_344),U_341)
| ~ in(ordered_pair(U_344,U_346),U_342) )
& ! [U_345,U_343] :
( in(ordered_pair(U_343,U_345),U_342)
| ~ in(ordered_pair(U_345,U_343),U_341) ) )
| U_341 != relation_inverse(U_342) ) )
| ~ relation(U_341) )
| ~ relation(U_342) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_347,sK67(U_342,U_341))],[f_37_4]) ).
fof(f_37_6,plain,
! [U_342] :
( ! [U_341] :
( ( ( U_341 = relation_inverse(U_342)
| ? [U_348] :
( ~ in(ordered_pair(sK68(U_342,U_341),U_348),U_341)
& in(ordered_pair(U_348,sK68(U_342,U_341)),U_342) )
| ( ~ in(ordered_pair(sK67(U_342,U_341),sK66(U_342,U_341)),U_342)
& in(ordered_pair(sK66(U_342,U_341),sK67(U_342,U_341)),U_341) ) )
& ( ( ! [U_346,U_344] :
( in(ordered_pair(U_346,U_344),U_341)
| ~ in(ordered_pair(U_344,U_346),U_342) )
& ! [U_345,U_343] :
( in(ordered_pair(U_343,U_345),U_342)
| ~ in(ordered_pair(U_345,U_343),U_341) ) )
| U_341 != relation_inverse(U_342) ) )
| ~ relation(U_341) )
| ~ relation(U_342) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_350,sK68(U_342,U_341))],[f_37_5]) ).
fof(f_37_7,plain,
! [U_342] :
( ! [U_341] :
( ( ( U_341 = relation_inverse(U_342)
| ( ~ in(ordered_pair(sK68(U_342,U_341),sK69(U_342,U_341)),U_341)
& in(ordered_pair(sK69(U_342,U_341),sK68(U_342,U_341)),U_342) )
| ( ~ in(ordered_pair(sK67(U_342,U_341),sK66(U_342,U_341)),U_342)
& in(ordered_pair(sK66(U_342,U_341),sK67(U_342,U_341)),U_341) ) )
& ( ( ! [U_346,U_344] :
( in(ordered_pair(U_346,U_344),U_341)
| ~ in(ordered_pair(U_344,U_346),U_342) )
& ! [U_345,U_343] :
( in(ordered_pair(U_343,U_345),U_342)
| ~ in(ordered_pair(U_345,U_343),U_341) ) )
| U_341 != relation_inverse(U_342) ) )
| ~ relation(U_341) )
| ~ relation(U_342) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_348,sK69(U_342,U_341))],[f_37_6]) ).
cnf(f_37_8,plain,
( in(ordered_pair(U_343,U_345),U_342)
| ~ in(ordered_pair(U_345,U_343),U_341)
| U_341 != relation_inverse(U_342)
| ~ relation(U_341)
| ~ relation(U_342) ),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(f_37_9,plain,
( in(ordered_pair(U_346,U_344),U_341)
| ~ in(ordered_pair(U_344,U_346),U_342)
| U_341 != relation_inverse(U_342)
| ~ relation(U_341)
| ~ relation(U_342) ),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(f_37_10,plain,
( in(ordered_pair(sK69(U_342,U_341),sK68(U_342,U_341)),U_342)
| in(ordered_pair(sK66(U_342,U_341),sK67(U_342,U_341)),U_341)
| U_341 = relation_inverse(U_342)
| ~ relation(U_341)
| ~ relation(U_342) ),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(f_37_11,plain,
( ~ in(ordered_pair(sK68(U_342,U_341),sK69(U_342,U_341)),U_341)
| in(ordered_pair(sK66(U_342,U_341),sK67(U_342,U_341)),U_341)
| U_341 = relation_inverse(U_342)
| ~ relation(U_341)
| ~ relation(U_342) ),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(f_37_12,plain,
( in(ordered_pair(sK69(U_342,U_341),sK68(U_342,U_341)),U_342)
| ~ in(ordered_pair(sK67(U_342,U_341),sK66(U_342,U_341)),U_342)
| U_341 = relation_inverse(U_342)
| ~ relation(U_341)
| ~ relation(U_342) ),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(f_37_13,plain,
( ~ in(ordered_pair(sK68(U_342,U_341),sK69(U_342,U_341)),U_341)
| ~ in(ordered_pair(sK67(U_342,U_341),sK66(U_342,U_341)),U_342)
| U_341 = relation_inverse(U_342)
| ~ relation(U_341)
| ~ relation(U_342) ),
inference(clausify,[status(thm)],[f_37_7]) ).
fof(f_38_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_38_2,plain,
! [U_352,U_351] :
( ( disjoint(U_352,U_351)
| set_intersection2(U_352,U_351) != empty_set )
& ( set_intersection2(U_352,U_351) = empty_set
| ~ disjoint(U_352,U_351) ) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
( ! [U_356,U_354] :
( disjoint(U_356,U_354)
| set_intersection2(U_356,U_354) != empty_set )
& ! [U_355,U_353] :
( set_intersection2(U_355,U_353) = empty_set
| ~ disjoint(U_355,U_353) ) ),
inference(miniscope,[status(thm)],[f_38_2]) ).
cnf(f_38_4,plain,
( set_intersection2(U_355,U_353) = empty_set
| ~ disjoint(U_355,U_353) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_5,plain,
( disjoint(U_356,U_354)
| set_intersection2(U_356,U_354) != empty_set ),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
! [A] :
( ( ( one_to_one(A)
| ? [B,C] :
( B != C
& apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) ) )
& ( ! [B,C] :
( B = C
| apply(A,B) != apply(A,C)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d8_funct_1]) ).
fof(f_39_2,plain,
! [U_361] :
( ( ( one_to_one(U_361)
| ? [U_360,U_359] :
( U_360 != U_359
& apply(U_361,U_360) = apply(U_361,U_359)
& in(U_359,relation_dom(U_361))
& in(U_360,relation_dom(U_361)) ) )
& ( ! [U_358,U_357] :
( U_358 = U_357
| apply(U_361,U_358) != apply(U_361,U_357)
| ~ in(U_357,relation_dom(U_361))
| ~ in(U_358,relation_dom(U_361)) )
| ~ one_to_one(U_361) ) )
| ~ function(U_361)
| ~ relation(U_361) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_361] :
( ( ( one_to_one(U_361)
| ? [U_359] :
( sK70(U_361) != U_359
& apply(U_361,sK70(U_361)) = apply(U_361,U_359)
& in(U_359,relation_dom(U_361))
& in(sK70(U_361),relation_dom(U_361)) ) )
& ( ! [U_358,U_357] :
( U_358 = U_357
| apply(U_361,U_358) != apply(U_361,U_357)
| ~ in(U_357,relation_dom(U_361))
| ~ in(U_358,relation_dom(U_361)) )
| ~ one_to_one(U_361) ) )
| ~ function(U_361)
| ~ relation(U_361) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_360,sK70(U_361))],[f_39_2]) ).
fof(f_39_4,plain,
! [U_361] :
( ( ( one_to_one(U_361)
| ( sK70(U_361) != sK71(U_361)
& apply(U_361,sK70(U_361)) = apply(U_361,sK71(U_361))
& in(sK71(U_361),relation_dom(U_361))
& in(sK70(U_361),relation_dom(U_361)) ) )
& ( ! [U_358,U_357] :
( U_358 = U_357
| apply(U_361,U_358) != apply(U_361,U_357)
| ~ in(U_357,relation_dom(U_361))
| ~ in(U_358,relation_dom(U_361)) )
| ~ one_to_one(U_361) ) )
| ~ function(U_361)
| ~ relation(U_361) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_359,sK71(U_361))],[f_39_3]) ).
cnf(f_39_5,plain,
( U_358 = U_357
| apply(U_361,U_358) != apply(U_361,U_357)
| ~ in(U_357,relation_dom(U_361))
| ~ in(U_358,relation_dom(U_361))
| ~ one_to_one(U_361)
| ~ function(U_361)
| ~ relation(U_361) ),
inference(clausify,[status(thm)],[f_39_4]) ).
cnf(f_39_6,plain,
( in(sK70(U_361),relation_dom(U_361))
| one_to_one(U_361)
| ~ function(U_361)
| ~ relation(U_361) ),
inference(clausify,[status(thm)],[f_39_4]) ).
cnf(f_39_7,plain,
( in(sK71(U_361),relation_dom(U_361))
| one_to_one(U_361)
| ~ function(U_361)
| ~ relation(U_361) ),
inference(clausify,[status(thm)],[f_39_4]) ).
cnf(f_39_8,plain,
( apply(U_361,sK70(U_361)) = apply(U_361,sK71(U_361))
| one_to_one(U_361)
| ~ function(U_361)
| ~ relation(U_361) ),
inference(clausify,[status(thm)],[f_39_4]) ).
cnf(f_39_9,plain,
( sK70(U_361) != sK71(U_361)
| one_to_one(U_361)
| ~ function(U_361)
| ~ relation(U_361) ),
inference(clausify,[status(thm)],[f_39_4]) ).
fof(f_40_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_40_2,plain,
! [U_372] :
( ! [U_371] :
( ! [U_370] :
( ( ( U_370 = relation_composition(U_372,U_371)
| ? [U_369,U_368] :
( ( ~ in(ordered_pair(U_369,U_368),U_370)
& ? [U_367] :
( in(ordered_pair(U_367,U_368),U_371)
& in(ordered_pair(U_369,U_367),U_372) ) )
| ( ! [U_366] :
( ~ in(ordered_pair(U_366,U_368),U_371)
| ~ in(ordered_pair(U_369,U_366),U_372) )
& in(ordered_pair(U_369,U_368),U_370) ) ) )
& ( ! [U_365,U_364] :
( ( in(ordered_pair(U_365,U_364),U_370)
| ! [U_363] :
( ~ in(ordered_pair(U_363,U_364),U_371)
| ~ in(ordered_pair(U_365,U_363),U_372) ) )
& ( ? [U_362] :
( in(ordered_pair(U_362,U_364),U_371)
& in(ordered_pair(U_365,U_362),U_372) )
| ~ in(ordered_pair(U_365,U_364),U_370) ) )
| U_370 != relation_composition(U_372,U_371) ) )
| ~ relation(U_370) )
| ~ relation(U_371) )
| ~ relation(U_372) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_372] :
( ! [U_371] :
( ! [U_370] :
( ( ( U_370 = relation_composition(U_372,U_371)
| ? [U_380,U_378] :
( ~ in(ordered_pair(U_380,U_378),U_370)
& ? [U_367] :
( in(ordered_pair(U_367,U_378),U_371)
& in(ordered_pair(U_380,U_367),U_372) ) )
| ? [U_379,U_377] :
( ! [U_366] :
( ~ in(ordered_pair(U_366,U_377),U_371)
| ~ in(ordered_pair(U_379,U_366),U_372) )
& in(ordered_pair(U_379,U_377),U_370) ) )
& ( ( ! [U_376,U_374] :
( in(ordered_pair(U_376,U_374),U_370)
| ! [U_363] :
( ~ in(ordered_pair(U_363,U_374),U_371)
| ~ in(ordered_pair(U_376,U_363),U_372) ) )
& ! [U_375,U_373] :
( ? [U_362] :
( in(ordered_pair(U_362,U_373),U_371)
& in(ordered_pair(U_375,U_362),U_372) )
| ~ in(ordered_pair(U_375,U_373),U_370) ) )
| U_370 != relation_composition(U_372,U_371) ) )
| ~ relation(U_370) )
| ~ relation(U_371) )
| ~ relation(U_372) ),
inference(miniscope,[status(thm)],[f_40_2]) ).
fof(f_40_4,plain,
! [U_372] :
( ! [U_371] :
( ! [U_370] :
( ( ( U_370 = relation_composition(U_372,U_371)
| ? [U_380,U_378] :
( ~ in(ordered_pair(U_380,U_378),U_370)
& ? [U_367] :
( in(ordered_pair(U_367,U_378),U_371)
& in(ordered_pair(U_380,U_367),U_372) ) )
| ? [U_379,U_377] :
( ! [U_366] :
( ~ in(ordered_pair(U_366,U_377),U_371)
| ~ in(ordered_pair(U_379,U_366),U_372) )
& in(ordered_pair(U_379,U_377),U_370) ) )
& ( ( ! [U_376,U_374] :
( in(ordered_pair(U_376,U_374),U_370)
| ! [U_363] :
( ~ in(ordered_pair(U_363,U_374),U_371)
| ~ in(ordered_pair(U_376,U_363),U_372) ) )
& ! [U_375,U_373] :
( ( in(ordered_pair(sK72(U_372,U_371,U_370,U_375,U_373),U_373),U_371)
& in(ordered_pair(U_375,sK72(U_372,U_371,U_370,U_375,U_373)),U_372) )
| ~ in(ordered_pair(U_375,U_373),U_370) ) )
| U_370 != relation_composition(U_372,U_371) ) )
| ~ relation(U_370) )
| ~ relation(U_371) )
| ~ relation(U_372) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_362,sK72(U_372,U_371,U_370,U_375,U_373))],[f_40_3]) ).
fof(f_40_5,plain,
! [U_372] :
( ! [U_371] :
( ! [U_370] :
( ( ( U_370 = relation_composition(U_372,U_371)
| ? [U_380,U_378] :
( ~ in(ordered_pair(U_380,U_378),U_370)
& ? [U_367] :
( in(ordered_pair(U_367,U_378),U_371)
& in(ordered_pair(U_380,U_367),U_372) ) )
| ? [U_377] :
( ! [U_366] :
( ~ in(ordered_pair(U_366,U_377),U_371)
| ~ in(ordered_pair(sK73(U_372,U_371,U_370),U_366),U_372) )
& in(ordered_pair(sK73(U_372,U_371,U_370),U_377),U_370) ) )
& ( ( ! [U_376,U_374] :
( in(ordered_pair(U_376,U_374),U_370)
| ! [U_363] :
( ~ in(ordered_pair(U_363,U_374),U_371)
| ~ in(ordered_pair(U_376,U_363),U_372) ) )
& ! [U_375,U_373] :
( ( in(ordered_pair(sK72(U_372,U_371,U_370,U_375,U_373),U_373),U_371)
& in(ordered_pair(U_375,sK72(U_372,U_371,U_370,U_375,U_373)),U_372) )
| ~ in(ordered_pair(U_375,U_373),U_370) ) )
| U_370 != relation_composition(U_372,U_371) ) )
| ~ relation(U_370) )
| ~ relation(U_371) )
| ~ relation(U_372) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_379,sK73(U_372,U_371,U_370))],[f_40_4]) ).
fof(f_40_6,plain,
! [U_372] :
( ! [U_371] :
( ! [U_370] :
( ( ( U_370 = relation_composition(U_372,U_371)
| ? [U_380,U_378] :
( ~ in(ordered_pair(U_380,U_378),U_370)
& ? [U_367] :
( in(ordered_pair(U_367,U_378),U_371)
& in(ordered_pair(U_380,U_367),U_372) ) )
| ( ! [U_366] :
( ~ in(ordered_pair(U_366,sK74(U_372,U_371,U_370)),U_371)
| ~ in(ordered_pair(sK73(U_372,U_371,U_370),U_366),U_372) )
& in(ordered_pair(sK73(U_372,U_371,U_370),sK74(U_372,U_371,U_370)),U_370) ) )
& ( ( ! [U_376,U_374] :
( in(ordered_pair(U_376,U_374),U_370)
| ! [U_363] :
( ~ in(ordered_pair(U_363,U_374),U_371)
| ~ in(ordered_pair(U_376,U_363),U_372) ) )
& ! [U_375,U_373] :
( ( in(ordered_pair(sK72(U_372,U_371,U_370,U_375,U_373),U_373),U_371)
& in(ordered_pair(U_375,sK72(U_372,U_371,U_370,U_375,U_373)),U_372) )
| ~ in(ordered_pair(U_375,U_373),U_370) ) )
| U_370 != relation_composition(U_372,U_371) ) )
| ~ relation(U_370) )
| ~ relation(U_371) )
| ~ relation(U_372) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_377,sK74(U_372,U_371,U_370))],[f_40_5]) ).
fof(f_40_7,plain,
! [U_372] :
( ! [U_371] :
( ! [U_370] :
( ( ( U_370 = relation_composition(U_372,U_371)
| ? [U_378] :
( ~ in(ordered_pair(sK75(U_372,U_371,U_370),U_378),U_370)
& ? [U_367] :
( in(ordered_pair(U_367,U_378),U_371)
& in(ordered_pair(sK75(U_372,U_371,U_370),U_367),U_372) ) )
| ( ! [U_366] :
( ~ in(ordered_pair(U_366,sK74(U_372,U_371,U_370)),U_371)
| ~ in(ordered_pair(sK73(U_372,U_371,U_370),U_366),U_372) )
& in(ordered_pair(sK73(U_372,U_371,U_370),sK74(U_372,U_371,U_370)),U_370) ) )
& ( ( ! [U_376,U_374] :
( in(ordered_pair(U_376,U_374),U_370)
| ! [U_363] :
( ~ in(ordered_pair(U_363,U_374),U_371)
| ~ in(ordered_pair(U_376,U_363),U_372) ) )
& ! [U_375,U_373] :
( ( in(ordered_pair(sK72(U_372,U_371,U_370,U_375,U_373),U_373),U_371)
& in(ordered_pair(U_375,sK72(U_372,U_371,U_370,U_375,U_373)),U_372) )
| ~ in(ordered_pair(U_375,U_373),U_370) ) )
| U_370 != relation_composition(U_372,U_371) ) )
| ~ relation(U_370) )
| ~ relation(U_371) )
| ~ relation(U_372) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_380,sK75(U_372,U_371,U_370))],[f_40_6]) ).
fof(f_40_8,plain,
! [U_372] :
( ! [U_371] :
( ! [U_370] :
( ( ( U_370 = relation_composition(U_372,U_371)
| ( ~ in(ordered_pair(sK75(U_372,U_371,U_370),sK76(U_372,U_371,U_370)),U_370)
& ? [U_367] :
( in(ordered_pair(U_367,sK76(U_372,U_371,U_370)),U_371)
& in(ordered_pair(sK75(U_372,U_371,U_370),U_367),U_372) ) )
| ( ! [U_366] :
( ~ in(ordered_pair(U_366,sK74(U_372,U_371,U_370)),U_371)
| ~ in(ordered_pair(sK73(U_372,U_371,U_370),U_366),U_372) )
& in(ordered_pair(sK73(U_372,U_371,U_370),sK74(U_372,U_371,U_370)),U_370) ) )
& ( ( ! [U_376,U_374] :
( in(ordered_pair(U_376,U_374),U_370)
| ! [U_363] :
( ~ in(ordered_pair(U_363,U_374),U_371)
| ~ in(ordered_pair(U_376,U_363),U_372) ) )
& ! [U_375,U_373] :
( ( in(ordered_pair(sK72(U_372,U_371,U_370,U_375,U_373),U_373),U_371)
& in(ordered_pair(U_375,sK72(U_372,U_371,U_370,U_375,U_373)),U_372) )
| ~ in(ordered_pair(U_375,U_373),U_370) ) )
| U_370 != relation_composition(U_372,U_371) ) )
| ~ relation(U_370) )
| ~ relation(U_371) )
| ~ relation(U_372) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_378,sK76(U_372,U_371,U_370))],[f_40_7]) ).
fof(f_40_9,plain,
! [U_372] :
( ! [U_371] :
( ! [U_370] :
( ( ( U_370 = relation_composition(U_372,U_371)
| ( ~ in(ordered_pair(sK75(U_372,U_371,U_370),sK76(U_372,U_371,U_370)),U_370)
& in(ordered_pair(sK77(U_372,U_371,U_370),sK76(U_372,U_371,U_370)),U_371)
& in(ordered_pair(sK75(U_372,U_371,U_370),sK77(U_372,U_371,U_370)),U_372) )
| ( ! [U_366] :
( ~ in(ordered_pair(U_366,sK74(U_372,U_371,U_370)),U_371)
| ~ in(ordered_pair(sK73(U_372,U_371,U_370),U_366),U_372) )
& in(ordered_pair(sK73(U_372,U_371,U_370),sK74(U_372,U_371,U_370)),U_370) ) )
& ( ( ! [U_376,U_374] :
( in(ordered_pair(U_376,U_374),U_370)
| ! [U_363] :
( ~ in(ordered_pair(U_363,U_374),U_371)
| ~ in(ordered_pair(U_376,U_363),U_372) ) )
& ! [U_375,U_373] :
( ( in(ordered_pair(sK72(U_372,U_371,U_370,U_375,U_373),U_373),U_371)
& in(ordered_pair(U_375,sK72(U_372,U_371,U_370,U_375,U_373)),U_372) )
| ~ in(ordered_pair(U_375,U_373),U_370) ) )
| U_370 != relation_composition(U_372,U_371) ) )
| ~ relation(U_370) )
| ~ relation(U_371) )
| ~ relation(U_372) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_367,sK77(U_372,U_371,U_370))],[f_40_8]) ).
cnf(f_40_10,plain,
( in(ordered_pair(U_375,sK72(U_372,U_371,U_370,U_375,U_373)),U_372)
| ~ in(ordered_pair(U_375,U_373),U_370)
| U_370 != relation_composition(U_372,U_371)
| ~ relation(U_370)
| ~ relation(U_371)
| ~ relation(U_372) ),
inference(clausify,[status(thm)],[f_40_9]) ).
cnf(f_40_11,plain,
( in(ordered_pair(sK72(U_372,U_371,U_370,U_375,U_373),U_373),U_371)
| ~ in(ordered_pair(U_375,U_373),U_370)
| U_370 != relation_composition(U_372,U_371)
| ~ relation(U_370)
| ~ relation(U_371)
| ~ relation(U_372) ),
inference(clausify,[status(thm)],[f_40_9]) ).
cnf(f_40_12,plain,
( in(ordered_pair(U_376,U_374),U_370)
| ~ in(ordered_pair(U_363,U_374),U_371)
| ~ in(ordered_pair(U_376,U_363),U_372)
| U_370 != relation_composition(U_372,U_371)
| ~ relation(U_370)
| ~ relation(U_371)
| ~ relation(U_372) ),
inference(clausify,[status(thm)],[f_40_9]) ).
cnf(f_40_13,plain,
( in(ordered_pair(sK75(U_372,U_371,U_370),sK77(U_372,U_371,U_370)),U_372)
| in(ordered_pair(sK73(U_372,U_371,U_370),sK74(U_372,U_371,U_370)),U_370)
| U_370 = relation_composition(U_372,U_371)
| ~ relation(U_370)
| ~ relation(U_371)
| ~ relation(U_372) ),
inference(clausify,[status(thm)],[f_40_9]) ).
cnf(f_40_14,plain,
( in(ordered_pair(sK77(U_372,U_371,U_370),sK76(U_372,U_371,U_370)),U_371)
| in(ordered_pair(sK73(U_372,U_371,U_370),sK74(U_372,U_371,U_370)),U_370)
| U_370 = relation_composition(U_372,U_371)
| ~ relation(U_370)
| ~ relation(U_371)
| ~ relation(U_372) ),
inference(clausify,[status(thm)],[f_40_9]) ).
cnf(f_40_15,plain,
( ~ in(ordered_pair(sK75(U_372,U_371,U_370),sK76(U_372,U_371,U_370)),U_370)
| in(ordered_pair(sK73(U_372,U_371,U_370),sK74(U_372,U_371,U_370)),U_370)
| U_370 = relation_composition(U_372,U_371)
| ~ relation(U_370)
| ~ relation(U_371)
| ~ relation(U_372) ),
inference(clausify,[status(thm)],[f_40_9]) ).
cnf(f_40_16,plain,
( in(ordered_pair(sK75(U_372,U_371,U_370),sK77(U_372,U_371,U_370)),U_372)
| ~ in(ordered_pair(U_366,sK74(U_372,U_371,U_370)),U_371)
| ~ in(ordered_pair(sK73(U_372,U_371,U_370),U_366),U_372)
| U_370 = relation_composition(U_372,U_371)
| ~ relation(U_370)
| ~ relation(U_371)
| ~ relation(U_372) ),
inference(clausify,[status(thm)],[f_40_9]) ).
cnf(f_40_17,plain,
( in(ordered_pair(sK77(U_372,U_371,U_370),sK76(U_372,U_371,U_370)),U_371)
| ~ in(ordered_pair(U_366,sK74(U_372,U_371,U_370)),U_371)
| ~ in(ordered_pair(sK73(U_372,U_371,U_370),U_366),U_372)
| U_370 = relation_composition(U_372,U_371)
| ~ relation(U_370)
| ~ relation(U_371)
| ~ relation(U_372) ),
inference(clausify,[status(thm)],[f_40_9]) ).
cnf(f_40_18,plain,
( ~ in(ordered_pair(sK75(U_372,U_371,U_370),sK76(U_372,U_371,U_370)),U_370)
| ~ in(ordered_pair(U_366,sK74(U_372,U_371,U_370)),U_371)
| ~ in(ordered_pair(sK73(U_372,U_371,U_370),U_366),U_372)
| U_370 = relation_composition(U_372,U_371)
| ~ relation(U_370)
| ~ relation(U_371)
| ~ relation(U_372) ),
inference(clausify,[status(thm)],[f_40_9]) ).
fof(f_41_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_41_2,plain,
! [U_385,U_384] :
( ! [U_383] :
( ( ( U_383 = complements_of_subsets(U_385,U_384)
| ? [U_382] :
( ( ( ~ in(U_382,U_383)
& in(subset_complement(U_385,U_382),U_384) )
| ( ~ in(subset_complement(U_385,U_382),U_384)
& in(U_382,U_383) ) )
& element(U_382,powerset(U_385)) ) )
& ( ! [U_381] :
( ( ( in(U_381,U_383)
| ~ in(subset_complement(U_385,U_381),U_384) )
& ( in(subset_complement(U_385,U_381),U_384)
| ~ in(U_381,U_383) ) )
| ~ element(U_381,powerset(U_385)) )
| U_383 != complements_of_subsets(U_385,U_384) ) )
| ~ element(U_383,powerset(powerset(U_385))) )
| ~ element(U_384,powerset(powerset(U_385))) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_385,U_384] :
( ! [U_383] :
( ( ( U_383 = complements_of_subsets(U_385,U_384)
| ( ( ( ~ in(sK78(U_385,U_384,U_383),U_383)
& in(subset_complement(U_385,sK78(U_385,U_384,U_383)),U_384) )
| ( ~ in(subset_complement(U_385,sK78(U_385,U_384,U_383)),U_384)
& in(sK78(U_385,U_384,U_383),U_383) ) )
& element(sK78(U_385,U_384,U_383),powerset(U_385)) ) )
& ( ! [U_381] :
( ( ( in(U_381,U_383)
| ~ in(subset_complement(U_385,U_381),U_384) )
& ( in(subset_complement(U_385,U_381),U_384)
| ~ in(U_381,U_383) ) )
| ~ element(U_381,powerset(U_385)) )
| U_383 != complements_of_subsets(U_385,U_384) ) )
| ~ element(U_383,powerset(powerset(U_385))) )
| ~ element(U_384,powerset(powerset(U_385))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_382,sK78(U_385,U_384,U_383))],[f_41_2]) ).
cnf(f_41_4,plain,
( in(subset_complement(U_385,U_381),U_384)
| ~ in(U_381,U_383)
| ~ element(U_381,powerset(U_385))
| U_383 != complements_of_subsets(U_385,U_384)
| ~ element(U_383,powerset(powerset(U_385)))
| ~ element(U_384,powerset(powerset(U_385))) ),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_5,plain,
( in(U_381,U_383)
| ~ in(subset_complement(U_385,U_381),U_384)
| ~ element(U_381,powerset(U_385))
| U_383 != complements_of_subsets(U_385,U_384)
| ~ element(U_383,powerset(powerset(U_385)))
| ~ element(U_384,powerset(powerset(U_385))) ),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_6,plain,
( element(sK78(U_385,U_384,U_383),powerset(U_385))
| U_383 = complements_of_subsets(U_385,U_384)
| ~ element(U_383,powerset(powerset(U_385)))
| ~ element(U_384,powerset(powerset(U_385))) ),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_7,plain,
( in(subset_complement(U_385,sK78(U_385,U_384,U_383)),U_384)
| in(sK78(U_385,U_384,U_383),U_383)
| U_383 = complements_of_subsets(U_385,U_384)
| ~ element(U_383,powerset(powerset(U_385)))
| ~ element(U_384,powerset(powerset(U_385))) ),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_8,plain,
( ~ in(sK78(U_385,U_384,U_383),U_383)
| in(sK78(U_385,U_384,U_383),U_383)
| U_383 = complements_of_subsets(U_385,U_384)
| ~ element(U_383,powerset(powerset(U_385)))
| ~ element(U_384,powerset(powerset(U_385))) ),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_9,plain,
( in(subset_complement(U_385,sK78(U_385,U_384,U_383)),U_384)
| ~ in(subset_complement(U_385,sK78(U_385,U_384,U_383)),U_384)
| U_383 = complements_of_subsets(U_385,U_384)
| ~ element(U_383,powerset(powerset(U_385)))
| ~ element(U_384,powerset(powerset(U_385))) ),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_10,plain,
( ~ in(sK78(U_385,U_384,U_383),U_383)
| ~ in(subset_complement(U_385,sK78(U_385,U_384,U_383)),U_384)
| U_383 = complements_of_subsets(U_385,U_384)
| ~ element(U_383,powerset(powerset(U_385)))
| ~ element(U_384,powerset(powerset(U_385))) ),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_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_42_2,plain,
! [U_387,U_386] :
( ( proper_subset(U_387,U_386)
| U_387 = U_386
| ~ subset(U_387,U_386) )
& ( ( U_387 != U_386
& subset(U_387,U_386) )
| ~ proper_subset(U_387,U_386) ) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
( ! [U_391,U_389] :
( proper_subset(U_391,U_389)
| U_391 = U_389
| ~ subset(U_391,U_389) )
& ! [U_390,U_388] :
( ( U_390 != U_388
& subset(U_390,U_388) )
| ~ proper_subset(U_390,U_388) ) ),
inference(miniscope,[status(thm)],[f_42_2]) ).
cnf(f_42_4,plain,
( subset(U_390,U_388)
| ~ proper_subset(U_390,U_388) ),
inference(clausify,[status(thm)],[f_42_3]) ).
cnf(f_42_5,plain,
( U_390 != U_388
| ~ proper_subset(U_390,U_388) ),
inference(clausify,[status(thm)],[f_42_3]) ).
cnf(f_42_6,plain,
( proper_subset(U_391,U_389)
| U_391 = U_389
| ~ subset(U_391,U_389) ),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_1,plain,
! [A] :
( function_inverse(A) = relation_inverse(A)
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d9_funct_1]) ).
fof(f_43_2,plain,
! [U_392] :
( function_inverse(U_392) = relation_inverse(U_392)
| ~ one_to_one(U_392)
| ~ function(U_392)
| ~ relation(U_392) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
cnf(f_43_3,plain,
( function_inverse(U_392) = relation_inverse(U_392)
| ~ one_to_one(U_392)
| ~ function(U_392)
| ~ relation(U_392) ),
inference(clausify,[status(thm)],[f_43_2]) ).
fof(f_44_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k10_relat_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_k1_funct_1]) ).
cnf(f_45_2,plain,
$true,
inference(clausify,[status(thm)],[f_45_1]) ).
fof(f_46_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
cnf(f_46_2,plain,
$true,
inference(clausify,[status(thm)],[f_46_1]) ).
fof(f_47_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_setfam_1]) ).
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_k1_tarski]) ).
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_k1_xboole_0]) ).
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_k1_zfmisc_1]) ).
cnf(f_50_2,plain,
$true,
inference(clausify,[status(thm)],[f_50_1]) ).
fof(f_51_1,plain,
! [A] :
( ( function(function_inverse(A))
& relation(function_inverse(A)) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_funct_1]) ).
fof(f_51_2,plain,
! [U_393] :
( ( function(function_inverse(U_393))
& relation(function_inverse(U_393)) )
| ~ function(U_393)
| ~ relation(U_393) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
cnf(f_51_3,plain,
( relation(function_inverse(U_393))
| ~ function(U_393)
| ~ relation(U_393) ),
inference(clausify,[status(thm)],[f_51_2]) ).
cnf(f_51_4,plain,
( function(function_inverse(U_393))
| ~ function(U_393)
| ~ relation(U_393) ),
inference(clausify,[status(thm)],[f_51_2]) ).
fof(f_52_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_relat_1]) ).
cnf(f_52_2,plain,
$true,
inference(clausify,[status(thm)],[f_52_1]) ).
fof(f_53_1,plain,
! [A] : element(cast_to_subset(A),powerset(A)),
inference(fof_nnf,[status(thm)],[dt_k2_subset_1]) ).
fof(f_53_2,plain,
! [U_394] : element(cast_to_subset(U_394),powerset(U_394)),
inference(variable_rename,[status(thm)],[f_53_1]) ).
cnf(f_53_3,plain,
element(cast_to_subset(U_394),powerset(U_394)),
inference(clausify,[status(thm)],[f_53_2]) ).
fof(f_54_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
cnf(f_54_2,plain,
$true,
inference(clausify,[status(thm)],[f_54_1]) ).
fof(f_55_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
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_k2_zfmisc_1]) ).
cnf(f_56_2,plain,
$true,
inference(clausify,[status(thm)],[f_56_1]) ).
fof(f_57_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_relat_1]) ).
cnf(f_57_2,plain,
$true,
inference(clausify,[status(thm)],[f_57_1]) ).
fof(f_58_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_58_2,plain,
! [U_396,U_395] :
( element(subset_complement(U_396,U_395),powerset(U_396))
| ~ element(U_395,powerset(U_396)) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
cnf(f_58_3,plain,
( element(subset_complement(U_396,U_395),powerset(U_396))
| ~ element(U_395,powerset(U_396)) ),
inference(clausify,[status(thm)],[f_58_2]) ).
fof(f_59_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_tarski]) ).
cnf(f_59_2,plain,
$true,
inference(clausify,[status(thm)],[f_59_1]) ).
fof(f_60_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
cnf(f_60_2,plain,
$true,
inference(clausify,[status(thm)],[f_60_1]) ).
fof(f_61_1,plain,
! [A] :
( relation(relation_inverse(A))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k4_relat_1]) ).
fof(f_61_2,plain,
! [U_397] :
( relation(relation_inverse(U_397))
| ~ relation(U_397) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
cnf(f_61_3,plain,
( relation(relation_inverse(U_397))
| ~ relation(U_397) ),
inference(clausify,[status(thm)],[f_61_2]) ).
fof(f_62_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
cnf(f_62_2,plain,
$true,
inference(clausify,[status(thm)],[f_62_1]) ).
fof(f_63_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
cnf(f_63_2,plain,
$true,
inference(clausify,[status(thm)],[f_63_1]) ).
fof(f_64_1,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_relat_1]) ).
fof(f_64_2,plain,
! [U_399,U_398] :
( relation(relation_composition(U_399,U_398))
| ~ relation(U_398)
| ~ relation(U_399) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
cnf(f_64_3,plain,
( relation(relation_composition(U_399,U_398))
| ~ relation(U_398)
| ~ relation(U_399) ),
inference(clausify,[status(thm)],[f_64_2]) ).
fof(f_65_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_65_2,plain,
! [U_401,U_400] :
( element(union_of_subsets(U_401,U_400),powerset(U_401))
| ~ element(U_400,powerset(powerset(U_401))) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
cnf(f_65_3,plain,
( element(union_of_subsets(U_401,U_400),powerset(U_401))
| ~ element(U_400,powerset(powerset(U_401))) ),
inference(clausify,[status(thm)],[f_65_2]) ).
fof(f_66_1,plain,
! [A] : relation(identity_relation(A)),
inference(fof_nnf,[status(thm)],[dt_k6_relat_1]) ).
fof(f_66_2,plain,
! [U_402] : relation(identity_relation(U_402)),
inference(variable_rename,[status(thm)],[f_66_1]) ).
cnf(f_66_3,plain,
relation(identity_relation(U_402)),
inference(clausify,[status(thm)],[f_66_2]) ).
fof(f_67_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_67_2,plain,
! [U_404,U_403] :
( element(meet_of_subsets(U_404,U_403),powerset(U_404))
| ~ element(U_403,powerset(powerset(U_404))) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
cnf(f_67_3,plain,
( element(meet_of_subsets(U_404,U_403),powerset(U_404))
| ~ element(U_403,powerset(powerset(U_404))) ),
inference(clausify,[status(thm)],[f_67_2]) ).
fof(f_68_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_68_2,plain,
! [U_407,U_406,U_405] :
( element(subset_difference(U_407,U_406,U_405),powerset(U_407))
| ~ element(U_405,powerset(U_407))
| ~ element(U_406,powerset(U_407)) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
cnf(f_68_3,plain,
( element(subset_difference(U_407,U_406,U_405),powerset(U_407))
| ~ element(U_405,powerset(U_407))
| ~ element(U_406,powerset(U_407)) ),
inference(clausify,[status(thm)],[f_68_2]) ).
fof(f_69_1,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k7_relat_1]) ).
fof(f_69_2,plain,
! [U_409,U_408] :
( relation(relation_dom_restriction(U_409,U_408))
| ~ relation(U_409) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
fof(f_69_3,plain,
! [U_409] :
( ! [U_408] : relation(relation_dom_restriction(U_409,U_408))
| ~ relation(U_409) ),
inference(miniscope,[status(thm)],[f_69_2]) ).
cnf(f_69_4,plain,
( relation(relation_dom_restriction(U_409,U_408))
| ~ relation(U_409) ),
inference(clausify,[status(thm)],[f_69_3]) ).
fof(f_70_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_70_2,plain,
! [U_411,U_410] :
( element(complements_of_subsets(U_411,U_410),powerset(powerset(U_411)))
| ~ element(U_410,powerset(powerset(U_411))) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
cnf(f_70_3,plain,
( element(complements_of_subsets(U_411,U_410),powerset(powerset(U_411)))
| ~ element(U_410,powerset(powerset(U_411))) ),
inference(clausify,[status(thm)],[f_70_2]) ).
fof(f_71_1,plain,
! [A,B] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[dt_k8_relat_1]) ).
fof(f_71_2,plain,
! [U_413,U_412] :
( relation(relation_rng_restriction(U_413,U_412))
| ~ relation(U_412) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
cnf(f_71_3,plain,
( relation(relation_rng_restriction(U_413,U_412))
| ~ relation(U_412) ),
inference(clausify,[status(thm)],[f_71_2]) ).
fof(f_72_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k9_relat_1]) ).
cnf(f_72_2,plain,
$true,
inference(clausify,[status(thm)],[f_72_1]) ).
fof(f_73_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_73_2,plain,
$true,
inference(clausify,[status(thm)],[f_73_1]) ).
fof(f_74_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_74_2,plain,
! [U_415] :
? [U_414] : element(U_414,U_415),
inference(variable_rename,[status(thm)],[f_74_1]) ).
fof(f_74_3,plain,
! [U_415] : element(sK79(U_415),U_415),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_414,sK79(U_415))],[f_74_2]) ).
cnf(f_74_4,plain,
element(sK79(U_415),U_415),
inference(clausify,[status(thm)],[f_74_3]) ).
fof(f_75_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_75_2,plain,
! [U_417,U_416] :
( ( relation(relation_composition(U_416,U_417))
& empty(relation_composition(U_416,U_417)) )
| ~ relation(U_416)
| ~ empty(U_417) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
cnf(f_75_3,plain,
( empty(relation_composition(U_416,U_417))
| ~ relation(U_416)
| ~ empty(U_417) ),
inference(clausify,[status(thm)],[f_75_2]) ).
cnf(f_75_4,plain,
( relation(relation_composition(U_416,U_417))
| ~ relation(U_416)
| ~ empty(U_417) ),
inference(clausify,[status(thm)],[f_75_2]) ).
fof(f_76_1,plain,
! [A] :
( ( relation(relation_inverse(A))
& empty(relation_inverse(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc11_relat_1]) ).
fof(f_76_2,plain,
! [U_418] :
( ( relation(relation_inverse(U_418))
& empty(relation_inverse(U_418)) )
| ~ empty(U_418) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
cnf(f_76_3,plain,
( empty(relation_inverse(U_418))
| ~ empty(U_418) ),
inference(clausify,[status(thm)],[f_76_2]) ).
cnf(f_76_4,plain,
( relation(relation_inverse(U_418))
| ~ empty(U_418) ),
inference(clausify,[status(thm)],[f_76_2]) ).
fof(f_77_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
cnf(f_77_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_77_1]) ).
cnf(f_77_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_77_1]) ).
cnf(f_77_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_77_1]) ).
fof(f_78_1,plain,
! [A,B] :
( ( relation_empty_yielding(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) )
| ~ relation_empty_yielding(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc13_relat_1]) ).
fof(f_78_2,plain,
! [U_420,U_419] :
( ( relation_empty_yielding(relation_dom_restriction(U_420,U_419))
& relation(relation_dom_restriction(U_420,U_419)) )
| ~ relation_empty_yielding(U_420)
| ~ relation(U_420) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
fof(f_78_3,plain,
! [U_420] :
( ( ! [U_422] : relation_empty_yielding(relation_dom_restriction(U_420,U_422))
& ! [U_421] : relation(relation_dom_restriction(U_420,U_421)) )
| ~ relation_empty_yielding(U_420)
| ~ relation(U_420) ),
inference(miniscope,[status(thm)],[f_78_2]) ).
cnf(f_78_4,plain,
( relation(relation_dom_restriction(U_420,U_421))
| ~ relation_empty_yielding(U_420)
| ~ relation(U_420) ),
inference(clausify,[status(thm)],[f_78_3]) ).
cnf(f_78_5,plain,
( relation_empty_yielding(relation_dom_restriction(U_420,U_422))
| ~ relation_empty_yielding(U_420)
| ~ relation(U_420) ),
inference(clausify,[status(thm)],[f_78_3]) ).
fof(f_79_1,plain,
! [A,B] :
( ( function(relation_composition(A,B))
& relation(relation_composition(A,B)) )
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc1_funct_1]) ).
fof(f_79_2,plain,
! [U_424,U_423] :
( ( function(relation_composition(U_424,U_423))
& relation(relation_composition(U_424,U_423)) )
| ~ function(U_423)
| ~ relation(U_423)
| ~ function(U_424)
| ~ relation(U_424) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
cnf(f_79_3,plain,
( relation(relation_composition(U_424,U_423))
| ~ function(U_423)
| ~ relation(U_423)
| ~ function(U_424)
| ~ relation(U_424) ),
inference(clausify,[status(thm)],[f_79_2]) ).
cnf(f_79_4,plain,
( function(relation_composition(U_424,U_423))
| ~ function(U_423)
| ~ relation(U_423)
| ~ function(U_424)
| ~ relation(U_424) ),
inference(clausify,[status(thm)],[f_79_2]) ).
fof(f_80_1,plain,
! [A,B] :
( relation(set_intersection2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc1_relat_1]) ).
fof(f_80_2,plain,
! [U_426,U_425] :
( relation(set_intersection2(U_426,U_425))
| ~ relation(U_425)
| ~ relation(U_426) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
cnf(f_80_3,plain,
( relation(set_intersection2(U_426,U_425))
| ~ relation(U_425)
| ~ relation(U_426) ),
inference(clausify,[status(thm)],[f_80_2]) ).
fof(f_81_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_81_2,plain,
! [U_427] : ~ empty(powerset(U_427)),
inference(variable_rename,[status(thm)],[f_81_1]) ).
cnf(f_81_3,plain,
~ empty(powerset(U_427)),
inference(clausify,[status(thm)],[f_81_2]) ).
fof(f_82_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_82_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_82_1]) ).
fof(f_83_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_83_2,plain,
! [U_429,U_428] : ~ empty(ordered_pair(U_429,U_428)),
inference(variable_rename,[status(thm)],[f_83_1]) ).
cnf(f_83_3,plain,
~ empty(ordered_pair(U_429,U_428)),
inference(clausify,[status(thm)],[f_83_2]) ).
fof(f_84_1,plain,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
inference(fof_nnf,[status(thm)],[fc2_funct_1]) ).
fof(f_84_2,plain,
! [U_430] :
( function(identity_relation(U_430))
& relation(identity_relation(U_430)) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
fof(f_84_3,plain,
( ! [U_432] : function(identity_relation(U_432))
& ! [U_431] : relation(identity_relation(U_431)) ),
inference(miniscope,[status(thm)],[f_84_2]) ).
cnf(f_84_4,plain,
relation(identity_relation(U_431)),
inference(clausify,[status(thm)],[f_84_3]) ).
cnf(f_84_5,plain,
function(identity_relation(U_432)),
inference(clausify,[status(thm)],[f_84_3]) ).
fof(f_85_1,plain,
! [A,B] :
( relation(set_union2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc2_relat_1]) ).
fof(f_85_2,plain,
! [U_434,U_433] :
( relation(set_union2(U_434,U_433))
| ~ relation(U_433)
| ~ relation(U_434) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
cnf(f_85_3,plain,
( relation(set_union2(U_434,U_433))
| ~ relation(U_433)
| ~ relation(U_434) ),
inference(clausify,[status(thm)],[f_85_2]) ).
fof(f_86_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_86_2,plain,
! [U_435] : ~ empty(singleton(U_435)),
inference(variable_rename,[status(thm)],[f_86_1]) ).
cnf(f_86_3,plain,
~ empty(singleton(U_435)),
inference(clausify,[status(thm)],[f_86_2]) ).
fof(f_87_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_87_2,plain,
! [U_437,U_436] :
( ~ empty(set_union2(U_437,U_436))
| empty(U_437) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
fof(f_87_3,plain,
! [U_437] :
( ! [U_436] : ~ empty(set_union2(U_437,U_436))
| empty(U_437) ),
inference(miniscope,[status(thm)],[f_87_2]) ).
cnf(f_87_4,plain,
( ~ empty(set_union2(U_437,U_436))
| empty(U_437) ),
inference(clausify,[status(thm)],[f_87_3]) ).
fof(f_88_1,plain,
! [A] :
( ( function(relation_inverse(A))
& relation(relation_inverse(A)) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc3_funct_1]) ).
fof(f_88_2,plain,
! [U_438] :
( ( function(relation_inverse(U_438))
& relation(relation_inverse(U_438)) )
| ~ one_to_one(U_438)
| ~ function(U_438)
| ~ relation(U_438) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
cnf(f_88_3,plain,
( relation(relation_inverse(U_438))
| ~ one_to_one(U_438)
| ~ function(U_438)
| ~ relation(U_438) ),
inference(clausify,[status(thm)],[f_88_2]) ).
cnf(f_88_4,plain,
( function(relation_inverse(U_438))
| ~ one_to_one(U_438)
| ~ function(U_438)
| ~ relation(U_438) ),
inference(clausify,[status(thm)],[f_88_2]) ).
fof(f_89_1,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_89_2,plain,
! [U_440,U_439] : ~ empty(unordered_pair(U_440,U_439)),
inference(variable_rename,[status(thm)],[f_89_1]) ).
cnf(f_89_3,plain,
~ empty(unordered_pair(U_440,U_439)),
inference(clausify,[status(thm)],[f_89_2]) ).
fof(f_90_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_90_2,plain,
! [U_442,U_441] :
( ~ empty(set_union2(U_441,U_442))
| empty(U_442) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
fof(f_90_3,plain,
! [U_442] :
( ! [U_441] : ~ empty(set_union2(U_441,U_442))
| empty(U_442) ),
inference(miniscope,[status(thm)],[f_90_2]) ).
cnf(f_90_4,plain,
( ~ empty(set_union2(U_441,U_442))
| empty(U_442) ),
inference(clausify,[status(thm)],[f_90_3]) ).
fof(f_91_1,plain,
! [A,B] :
( ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc4_funct_1]) ).
fof(f_91_2,plain,
! [U_444,U_443] :
( ( function(relation_dom_restriction(U_444,U_443))
& relation(relation_dom_restriction(U_444,U_443)) )
| ~ function(U_444)
| ~ relation(U_444) ),
inference(variable_rename,[status(thm)],[f_91_1]) ).
fof(f_91_3,plain,
! [U_444] :
( ( ! [U_446] : function(relation_dom_restriction(U_444,U_446))
& ! [U_445] : relation(relation_dom_restriction(U_444,U_445)) )
| ~ function(U_444)
| ~ relation(U_444) ),
inference(miniscope,[status(thm)],[f_91_2]) ).
cnf(f_91_4,plain,
( relation(relation_dom_restriction(U_444,U_445))
| ~ function(U_444)
| ~ relation(U_444) ),
inference(clausify,[status(thm)],[f_91_3]) ).
cnf(f_91_5,plain,
( function(relation_dom_restriction(U_444,U_446))
| ~ function(U_444)
| ~ relation(U_444) ),
inference(clausify,[status(thm)],[f_91_3]) ).
fof(f_92_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_92_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_92_1]) ).
cnf(f_92_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_92_1]) ).
fof(f_93_1,plain,
! [A,B] :
( ~ empty(cartesian_product2(A,B))
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc4_subset_1]) ).
fof(f_93_2,plain,
! [U_448,U_447] :
( ~ empty(cartesian_product2(U_448,U_447))
| empty(U_447)
| empty(U_448) ),
inference(variable_rename,[status(thm)],[f_93_1]) ).
cnf(f_93_3,plain,
( ~ empty(cartesian_product2(U_448,U_447))
| empty(U_447)
| empty(U_448) ),
inference(clausify,[status(thm)],[f_93_2]) ).
fof(f_94_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_94_2,plain,
! [U_449] :
( ~ empty(relation_dom(U_449))
| ~ relation(U_449)
| empty(U_449) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
cnf(f_94_3,plain,
( ~ empty(relation_dom(U_449))
| ~ relation(U_449)
| empty(U_449) ),
inference(clausify,[status(thm)],[f_94_2]) ).
fof(f_95_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_95_2,plain,
! [U_450] :
( ~ empty(relation_rng(U_450))
| ~ relation(U_450)
| empty(U_450) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
cnf(f_95_3,plain,
( ~ empty(relation_rng(U_450))
| ~ relation(U_450)
| empty(U_450) ),
inference(clausify,[status(thm)],[f_95_2]) ).
fof(f_96_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_96_2,plain,
! [U_451] :
( ( relation(relation_dom(U_451))
& empty(relation_dom(U_451)) )
| ~ empty(U_451) ),
inference(variable_rename,[status(thm)],[f_96_1]) ).
cnf(f_96_3,plain,
( empty(relation_dom(U_451))
| ~ empty(U_451) ),
inference(clausify,[status(thm)],[f_96_2]) ).
cnf(f_96_4,plain,
( relation(relation_dom(U_451))
| ~ empty(U_451) ),
inference(clausify,[status(thm)],[f_96_2]) ).
fof(f_97_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_97_2,plain,
! [U_452] :
( ( relation(relation_rng(U_452))
& empty(relation_rng(U_452)) )
| ~ empty(U_452) ),
inference(variable_rename,[status(thm)],[f_97_1]) ).
cnf(f_97_3,plain,
( empty(relation_rng(U_452))
| ~ empty(U_452) ),
inference(clausify,[status(thm)],[f_97_2]) ).
cnf(f_97_4,plain,
( relation(relation_rng(U_452))
| ~ empty(U_452) ),
inference(clausify,[status(thm)],[f_97_2]) ).
fof(f_98_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_98_2,plain,
! [U_454,U_453] :
( ( relation(relation_composition(U_454,U_453))
& empty(relation_composition(U_454,U_453)) )
| ~ relation(U_453)
| ~ empty(U_454) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
cnf(f_98_3,plain,
( empty(relation_composition(U_454,U_453))
| ~ relation(U_453)
| ~ empty(U_454) ),
inference(clausify,[status(thm)],[f_98_2]) ).
cnf(f_98_4,plain,
( relation(relation_composition(U_454,U_453))
| ~ relation(U_453)
| ~ empty(U_454) ),
inference(clausify,[status(thm)],[f_98_2]) ).
fof(f_99_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_99_2,plain,
! [U_456,U_455] : set_union2(U_456,U_456) = U_456,
inference(variable_rename,[status(thm)],[f_99_1]) ).
fof(f_99_3,plain,
! [U_456] : set_union2(U_456,U_456) = U_456,
inference(miniscope,[status(thm)],[f_99_2]) ).
cnf(f_99_4,plain,
set_union2(U_456,U_456) = U_456,
inference(clausify,[status(thm)],[f_99_3]) ).
fof(f_100_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_100_2,plain,
! [U_458,U_457] : set_intersection2(U_458,U_458) = U_458,
inference(variable_rename,[status(thm)],[f_100_1]) ).
fof(f_100_3,plain,
! [U_458] : set_intersection2(U_458,U_458) = U_458,
inference(miniscope,[status(thm)],[f_100_2]) ).
cnf(f_100_4,plain,
set_intersection2(U_458,U_458) = U_458,
inference(clausify,[status(thm)],[f_100_3]) ).
fof(f_101_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_101_2,plain,
! [U_460,U_459] :
( subset_complement(U_460,subset_complement(U_460,U_459)) = U_459
| ~ element(U_459,powerset(U_460)) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
cnf(f_101_3,plain,
( subset_complement(U_460,subset_complement(U_460,U_459)) = U_459
| ~ element(U_459,powerset(U_460)) ),
inference(clausify,[status(thm)],[f_101_2]) ).
fof(f_102_1,plain,
! [A] :
( relation_inverse(relation_inverse(A)) = A
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[involutiveness_k4_relat_1]) ).
fof(f_102_2,plain,
! [U_461] :
( relation_inverse(relation_inverse(U_461)) = U_461
| ~ relation(U_461) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
cnf(f_102_3,plain,
( relation_inverse(relation_inverse(U_461)) = U_461
| ~ relation(U_461) ),
inference(clausify,[status(thm)],[f_102_2]) ).
fof(f_103_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_103_2,plain,
! [U_463,U_462] :
( complements_of_subsets(U_463,complements_of_subsets(U_463,U_462)) = U_462
| ~ element(U_462,powerset(powerset(U_463))) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
cnf(f_103_3,plain,
( complements_of_subsets(U_463,complements_of_subsets(U_463,U_462)) = U_462
| ~ element(U_462,powerset(powerset(U_463))) ),
inference(clausify,[status(thm)],[f_103_2]) ).
fof(f_104_1,plain,
! [A,B] : ~ proper_subset(A,A),
inference(fof_nnf,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(f_104_2,plain,
! [U_465,U_464] : ~ proper_subset(U_465,U_465),
inference(variable_rename,[status(thm)],[f_104_1]) ).
fof(f_104_3,plain,
! [U_465] : ~ proper_subset(U_465,U_465),
inference(miniscope,[status(thm)],[f_104_2]) ).
cnf(f_104_4,plain,
~ proper_subset(U_465,U_465),
inference(clausify,[status(thm)],[f_104_3]) ).
fof(f_105_1,plain,
! [A] : singleton(A) != empty_set,
inference(fof_nnf,[status(thm)],[l1_zfmisc_1]) ).
fof(f_105_2,plain,
! [U_466] : singleton(U_466) != empty_set,
inference(variable_rename,[status(thm)],[f_105_1]) ).
cnf(f_105_3,plain,
singleton(U_466) != empty_set,
inference(clausify,[status(thm)],[f_105_2]) ).
fof(f_106_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l23_zfmisc_1]) ).
fof(f_106_2,plain,
! [U_468,U_467] :
( set_union2(singleton(U_468),U_467) = U_467
| ~ in(U_468,U_467) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
cnf(f_106_3,plain,
( set_union2(singleton(U_468),U_467) = U_467
| ~ in(U_468,U_467) ),
inference(clausify,[status(thm)],[f_106_2]) ).
fof(f_107_1,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(fof_nnf,[status(thm)],[l25_zfmisc_1]) ).
fof(f_107_2,plain,
! [U_470,U_469] :
( ~ in(U_470,U_469)
| ~ disjoint(singleton(U_470),U_469) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
cnf(f_107_3,plain,
( ~ in(U_470,U_469)
| ~ disjoint(singleton(U_470),U_469) ),
inference(clausify,[status(thm)],[f_107_2]) ).
fof(f_108_1,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(fof_nnf,[status(thm)],[l28_zfmisc_1]) ).
fof(f_108_2,plain,
! [U_472,U_471] :
( disjoint(singleton(U_472),U_471)
| in(U_472,U_471) ),
inference(variable_rename,[status(thm)],[f_108_1]) ).
cnf(f_108_3,plain,
( disjoint(singleton(U_472),U_471)
| in(U_472,U_471) ),
inference(clausify,[status(thm)],[f_108_2]) ).
fof(f_109_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_109_2,plain,
! [U_474,U_473] :
( ( subset(singleton(U_474),U_473)
| ~ in(U_474,U_473) )
& ( in(U_474,U_473)
| ~ subset(singleton(U_474),U_473) ) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
fof(f_109_3,plain,
( ! [U_478,U_476] :
( subset(singleton(U_478),U_476)
| ~ in(U_478,U_476) )
& ! [U_477,U_475] :
( in(U_477,U_475)
| ~ subset(singleton(U_477),U_475) ) ),
inference(miniscope,[status(thm)],[f_109_2]) ).
cnf(f_109_4,plain,
( in(U_477,U_475)
| ~ subset(singleton(U_477),U_475) ),
inference(clausify,[status(thm)],[f_109_3]) ).
cnf(f_109_5,plain,
( subset(singleton(U_478),U_476)
| ~ in(U_478,U_476) ),
inference(clausify,[status(thm)],[f_109_3]) ).
fof(f_110_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_110_2,plain,
! [U_480,U_479] :
( ( set_difference(U_480,U_479) = empty_set
| ~ subset(U_480,U_479) )
& ( subset(U_480,U_479)
| set_difference(U_480,U_479) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
fof(f_110_3,plain,
( ! [U_484,U_482] :
( set_difference(U_484,U_482) = empty_set
| ~ subset(U_484,U_482) )
& ! [U_483,U_481] :
( subset(U_483,U_481)
| set_difference(U_483,U_481) != empty_set ) ),
inference(miniscope,[status(thm)],[f_110_2]) ).
cnf(f_110_4,plain,
( subset(U_483,U_481)
| set_difference(U_483,U_481) != empty_set ),
inference(clausify,[status(thm)],[f_110_3]) ).
cnf(f_110_5,plain,
( set_difference(U_484,U_482) = empty_set
| ~ subset(U_484,U_482) ),
inference(clausify,[status(thm)],[f_110_3]) ).
fof(f_111_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_111_2,plain,
! [U_487,U_486] :
( ! [U_485] :
( in(U_485,U_487)
| ~ in(U_485,U_486) )
| ~ element(U_486,powerset(U_487)) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
cnf(f_111_3,plain,
( in(U_485,U_487)
| ~ in(U_485,U_486)
| ~ element(U_486,powerset(U_487)) ),
inference(clausify,[status(thm)],[f_111_2]) ).
fof(f_112_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_112_2,plain,
! [U_490,U_489,U_488] :
( subset(U_490,set_difference(U_489,singleton(U_488)))
| in(U_488,U_490)
| ~ subset(U_490,U_489) ),
inference(variable_rename,[status(thm)],[f_112_1]) ).
fof(f_112_3,plain,
! [U_490,U_489] :
( ! [U_488] :
( subset(U_490,set_difference(U_489,singleton(U_488)))
| in(U_488,U_490) )
| ~ subset(U_490,U_489) ),
inference(miniscope,[status(thm)],[f_112_2]) ).
cnf(f_112_4,plain,
( subset(U_490,set_difference(U_489,singleton(U_488)))
| in(U_488,U_490)
| ~ subset(U_490,U_489) ),
inference(clausify,[status(thm)],[f_112_3]) ).
fof(f_113_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_113_2,plain,
! [U_492,U_491] :
( ( subset(U_492,singleton(U_491))
| ( U_492 != singleton(U_491)
& U_492 != empty_set ) )
& ( U_492 = singleton(U_491)
| U_492 = empty_set
| ~ subset(U_492,singleton(U_491)) ) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
fof(f_113_3,plain,
( ! [U_496,U_494] :
( subset(U_496,singleton(U_494))
| ( U_496 != singleton(U_494)
& U_496 != empty_set ) )
& ! [U_495,U_493] :
( U_495 = singleton(U_493)
| U_495 = empty_set
| ~ subset(U_495,singleton(U_493)) ) ),
inference(miniscope,[status(thm)],[f_113_2]) ).
cnf(f_113_4,plain,
( U_495 = singleton(U_493)
| U_495 = empty_set
| ~ subset(U_495,singleton(U_493)) ),
inference(clausify,[status(thm)],[f_113_3]) ).
cnf(f_113_5,plain,
( U_496 != empty_set
| subset(U_496,singleton(U_494)) ),
inference(clausify,[status(thm)],[f_113_3]) ).
cnf(f_113_6,plain,
( U_496 != singleton(U_494)
| subset(U_496,singleton(U_494)) ),
inference(clausify,[status(thm)],[f_113_3]) ).
fof(f_114_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l50_zfmisc_1]) ).
fof(f_114_2,plain,
! [U_498,U_497] :
( subset(U_498,union(U_497))
| ~ in(U_498,U_497) ),
inference(variable_rename,[status(thm)],[f_114_1]) ).
cnf(f_114_3,plain,
( subset(U_498,union(U_497))
| ~ in(U_498,U_497) ),
inference(clausify,[status(thm)],[f_114_2]) ).
fof(f_115_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_115_2,plain,
! [U_502,U_501,U_500,U_499] :
( ( in(ordered_pair(U_502,U_501),cartesian_product2(U_500,U_499))
| ~ in(U_501,U_499)
| ~ in(U_502,U_500) )
& ( ( in(U_501,U_499)
& in(U_502,U_500) )
| ~ in(ordered_pair(U_502,U_501),cartesian_product2(U_500,U_499)) ) ),
inference(variable_rename,[status(thm)],[f_115_1]) ).
fof(f_115_3,plain,
( ! [U_510,U_508,U_506,U_504] :
( in(ordered_pair(U_510,U_508),cartesian_product2(U_506,U_504))
| ~ in(U_508,U_504)
| ~ in(U_510,U_506) )
& ! [U_509,U_507,U_505,U_503] :
( ( in(U_507,U_503)
& in(U_509,U_505) )
| ~ in(ordered_pair(U_509,U_507),cartesian_product2(U_505,U_503)) ) ),
inference(miniscope,[status(thm)],[f_115_2]) ).
cnf(f_115_4,plain,
( in(U_509,U_505)
| ~ in(ordered_pair(U_509,U_507),cartesian_product2(U_505,U_503)) ),
inference(clausify,[status(thm)],[f_115_3]) ).
cnf(f_115_5,plain,
( in(U_507,U_503)
| ~ in(ordered_pair(U_509,U_507),cartesian_product2(U_505,U_503)) ),
inference(clausify,[status(thm)],[f_115_3]) ).
cnf(f_115_6,plain,
( in(ordered_pair(U_510,U_508),cartesian_product2(U_506,U_504))
| ~ in(U_508,U_504)
| ~ in(U_510,U_506) ),
inference(clausify,[status(thm)],[f_115_3]) ).
fof(f_116_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_116_2,plain,
! [U_513,U_512] :
( element(U_513,powerset(U_512))
| ? [U_511] :
( ~ in(U_511,U_512)
& in(U_511,U_513) ) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
fof(f_116_3,plain,
! [U_513,U_512] :
( element(U_513,powerset(U_512))
| ( ~ in(sK80(U_513,U_512),U_512)
& in(sK80(U_513,U_512),U_513) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_511,sK80(U_513,U_512))],[f_116_2]) ).
cnf(f_116_4,plain,
( in(sK80(U_513,U_512),U_513)
| element(U_513,powerset(U_512)) ),
inference(clausify,[status(thm)],[f_116_3]) ).
cnf(f_116_5,plain,
( ~ in(sK80(U_513,U_512),U_512)
| element(U_513,powerset(U_512)) ),
inference(clausify,[status(thm)],[f_116_3]) ).
fof(f_117_1,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
<=> ( in(B,A)
& in(B,relation_dom(C)) ) ) ),
inference(negate,[status(cth)],[l82_funct_1]) ).
fof(f_117_2,negated_conjecture,
? [A,B,C] :
( ( ( ~ in(B,relation_dom(relation_dom_restriction(C,A)))
& in(B,A)
& in(B,relation_dom(C)) )
| ( ( ~ in(B,A)
| ~ in(B,relation_dom(C)) )
& in(B,relation_dom(relation_dom_restriction(C,A))) ) )
& function(C)
& relation(C) ),
inference(fof_nnf,[status(thm)],[f_117_1]) ).
fof(f_117_3,negated_conjecture,
? [U_516,U_515,U_514] :
( ( ( ~ in(U_515,relation_dom(relation_dom_restriction(U_514,U_516)))
& in(U_515,U_516)
& in(U_515,relation_dom(U_514)) )
| ( ( ~ in(U_515,U_516)
| ~ in(U_515,relation_dom(U_514)) )
& in(U_515,relation_dom(relation_dom_restriction(U_514,U_516))) ) )
& function(U_514)
& relation(U_514) ),
inference(variable_rename,[status(thm)],[f_117_2]) ).
fof(f_117_4,negated_conjecture,
? [U_515,U_514] :
( ( ( ~ in(U_515,relation_dom(relation_dom_restriction(U_514,sK81)))
& in(U_515,sK81)
& in(U_515,relation_dom(U_514)) )
| ( ( ~ in(U_515,sK81)
| ~ in(U_515,relation_dom(U_514)) )
& in(U_515,relation_dom(relation_dom_restriction(U_514,sK81))) ) )
& function(U_514)
& relation(U_514) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_516,sK81)],[f_117_3]) ).
fof(f_117_5,negated_conjecture,
? [U_514] :
( ( ( ~ in(sK82,relation_dom(relation_dom_restriction(U_514,sK81)))
& in(sK82,sK81)
& in(sK82,relation_dom(U_514)) )
| ( ( ~ in(sK82,sK81)
| ~ in(sK82,relation_dom(U_514)) )
& in(sK82,relation_dom(relation_dom_restriction(U_514,sK81))) ) )
& function(U_514)
& relation(U_514) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_515,sK82)],[f_117_4]) ).
fof(f_117_6,negated_conjecture,
( ( ( ~ in(sK82,relation_dom(relation_dom_restriction(sK83,sK81)))
& in(sK82,sK81)
& in(sK82,relation_dom(sK83)) )
| ( ( ~ in(sK82,sK81)
| ~ in(sK82,relation_dom(sK83)) )
& in(sK82,relation_dom(relation_dom_restriction(sK83,sK81))) ) )
& function(sK83)
& relation(sK83) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_514,sK83)],[f_117_5]) ).
cnf(f_117_7,negated_conjecture,
relation(sK83),
inference(clausify,[status(thm)],[f_117_6]) ).
cnf(f_117_8,negated_conjecture,
function(sK83),
inference(clausify,[status(thm)],[f_117_6]) ).
cnf(f_117_9,negated_conjecture,
( in(sK82,relation_dom(sK83))
| in(sK82,relation_dom(relation_dom_restriction(sK83,sK81))) ),
inference(clausify,[status(thm)],[f_117_6]) ).
cnf(f_117_10,negated_conjecture,
( in(sK82,sK81)
| in(sK82,relation_dom(relation_dom_restriction(sK83,sK81))) ),
inference(clausify,[status(thm)],[f_117_6]) ).
cnf(f_117_11,negated_conjecture,
( ~ in(sK82,relation_dom(relation_dom_restriction(sK83,sK81)))
| in(sK82,relation_dom(relation_dom_restriction(sK83,sK81))) ),
inference(clausify,[status(thm)],[f_117_6]) ).
cnf(f_117_12,negated_conjecture,
( in(sK82,relation_dom(sK83))
| ~ in(sK82,sK81)
| ~ in(sK82,relation_dom(sK83)) ),
inference(clausify,[status(thm)],[f_117_6]) ).
cnf(f_117_13,negated_conjecture,
( in(sK82,sK81)
| ~ in(sK82,sK81)
| ~ in(sK82,relation_dom(sK83)) ),
inference(clausify,[status(thm)],[f_117_6]) ).
cnf(f_117_14,negated_conjecture,
( ~ in(sK82,relation_dom(relation_dom_restriction(sK83,sK81)))
| ~ in(sK82,sK81)
| ~ in(sK82,relation_dom(sK83)) ),
inference(clausify,[status(thm)],[f_117_6]) ).
fof(f_118_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_118_2,plain,
? [U_517] :
( function(U_517)
& relation(U_517) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
fof(f_118_3,plain,
( function(sK84)
& relation(sK84) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_517,sK84)],[f_118_2]) ).
cnf(f_118_4,plain,
relation(sK84),
inference(clausify,[status(thm)],[f_118_3]) ).
cnf(f_118_5,plain,
function(sK84),
inference(clausify,[status(thm)],[f_118_3]) ).
fof(f_119_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_119_2,plain,
? [U_518] :
( relation(U_518)
& empty(U_518) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
fof(f_119_3,plain,
( relation(sK85)
& empty(sK85) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_518,sK85)],[f_119_2]) ).
cnf(f_119_4,plain,
empty(sK85),
inference(clausify,[status(thm)],[f_119_3]) ).
cnf(f_119_5,plain,
relation(sK85),
inference(clausify,[status(thm)],[f_119_3]) ).
fof(f_120_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_120_2,plain,
! [U_520] :
( ? [U_519] :
( ~ empty(U_519)
& element(U_519,powerset(U_520)) )
| empty(U_520) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
fof(f_120_3,plain,
! [U_520] :
( ( ~ empty(sK86(U_520))
& element(sK86(U_520),powerset(U_520)) )
| empty(U_520) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_519,sK86(U_520))],[f_120_2]) ).
cnf(f_120_4,plain,
( element(sK86(U_520),powerset(U_520))
| empty(U_520) ),
inference(clausify,[status(thm)],[f_120_3]) ).
cnf(f_120_5,plain,
( ~ empty(sK86(U_520))
| empty(U_520) ),
inference(clausify,[status(thm)],[f_120_3]) ).
fof(f_121_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_121_2,plain,
? [U_521] : empty(U_521),
inference(variable_rename,[status(thm)],[f_121_1]) ).
fof(f_121_3,plain,
empty(sK87),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_521,sK87)],[f_121_2]) ).
cnf(f_121_4,plain,
empty(sK87),
inference(clausify,[status(thm)],[f_121_3]) ).
fof(f_122_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_122_2,plain,
? [U_522] :
( function(U_522)
& empty(U_522)
& relation(U_522) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
fof(f_122_3,plain,
( function(sK88)
& empty(sK88)
& relation(sK88) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_522,sK88)],[f_122_2]) ).
cnf(f_122_4,plain,
relation(sK88),
inference(clausify,[status(thm)],[f_122_3]) ).
cnf(f_122_5,plain,
empty(sK88),
inference(clausify,[status(thm)],[f_122_3]) ).
cnf(f_122_6,plain,
function(sK88),
inference(clausify,[status(thm)],[f_122_3]) ).
fof(f_123_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_123_2,plain,
? [U_523] :
( relation(U_523)
& ~ empty(U_523) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
fof(f_123_3,plain,
( relation(sK89)
& ~ empty(sK89) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_523,sK89)],[f_123_2]) ).
cnf(f_123_4,plain,
~ empty(sK89),
inference(clausify,[status(thm)],[f_123_3]) ).
cnf(f_123_5,plain,
relation(sK89),
inference(clausify,[status(thm)],[f_123_3]) ).
fof(f_124_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_124_2,plain,
! [U_525] :
? [U_524] :
( empty(U_524)
& element(U_524,powerset(U_525)) ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
fof(f_124_3,plain,
! [U_525] :
( empty(sK90(U_525))
& element(sK90(U_525),powerset(U_525)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_524,sK90(U_525))],[f_124_2]) ).
cnf(f_124_4,plain,
element(sK90(U_525),powerset(U_525)),
inference(clausify,[status(thm)],[f_124_3]) ).
cnf(f_124_5,plain,
empty(sK90(U_525)),
inference(clausify,[status(thm)],[f_124_3]) ).
fof(f_125_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_125_2,plain,
? [U_526] : ~ empty(U_526),
inference(variable_rename,[status(thm)],[f_125_1]) ).
fof(f_125_3,plain,
~ empty(sK91),
inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_526,sK91)],[f_125_2]) ).
cnf(f_125_4,plain,
~ empty(sK91),
inference(clausify,[status(thm)],[f_125_3]) ).
fof(f_126_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_126_2,plain,
? [U_527] :
( one_to_one(U_527)
& function(U_527)
& relation(U_527) ),
inference(variable_rename,[status(thm)],[f_126_1]) ).
fof(f_126_3,plain,
( one_to_one(sK92)
& function(sK92)
& relation(sK92) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_527,sK92)],[f_126_2]) ).
cnf(f_126_4,plain,
relation(sK92),
inference(clausify,[status(thm)],[f_126_3]) ).
cnf(f_126_5,plain,
function(sK92),
inference(clausify,[status(thm)],[f_126_3]) ).
cnf(f_126_6,plain,
one_to_one(sK92),
inference(clausify,[status(thm)],[f_126_3]) ).
fof(f_127_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_127_2,plain,
? [U_528] :
( relation_empty_yielding(U_528)
& relation(U_528) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
fof(f_127_3,plain,
( relation_empty_yielding(sK93)
& relation(sK93) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_528,sK93)],[f_127_2]) ).
cnf(f_127_4,plain,
relation(sK93),
inference(clausify,[status(thm)],[f_127_3]) ).
cnf(f_127_5,plain,
relation_empty_yielding(sK93),
inference(clausify,[status(thm)],[f_127_3]) ).
fof(f_128_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_128_2,plain,
! [U_530,U_529] :
( union_of_subsets(U_530,U_529) = union(U_529)
| ~ element(U_529,powerset(powerset(U_530))) ),
inference(variable_rename,[status(thm)],[f_128_1]) ).
cnf(f_128_3,plain,
( union_of_subsets(U_530,U_529) = union(U_529)
| ~ element(U_529,powerset(powerset(U_530))) ),
inference(clausify,[status(thm)],[f_128_2]) ).
fof(f_129_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_129_2,plain,
! [U_532,U_531] :
( meet_of_subsets(U_532,U_531) = set_meet(U_531)
| ~ element(U_531,powerset(powerset(U_532))) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
cnf(f_129_3,plain,
( meet_of_subsets(U_532,U_531) = set_meet(U_531)
| ~ element(U_531,powerset(powerset(U_532))) ),
inference(clausify,[status(thm)],[f_129_2]) ).
fof(f_130_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_130_2,plain,
! [U_535,U_534,U_533] :
( subset_difference(U_535,U_534,U_533) = set_difference(U_534,U_533)
| ~ element(U_533,powerset(U_535))
| ~ element(U_534,powerset(U_535)) ),
inference(variable_rename,[status(thm)],[f_130_1]) ).
cnf(f_130_3,plain,
( subset_difference(U_535,U_534,U_533) = set_difference(U_534,U_533)
| ~ element(U_533,powerset(U_535))
| ~ element(U_534,powerset(U_535)) ),
inference(clausify,[status(thm)],[f_130_2]) ).
fof(f_131_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_131_2,plain,
! [U_537,U_536] : subset(U_537,U_537),
inference(variable_rename,[status(thm)],[f_131_1]) ).
fof(f_131_3,plain,
! [U_537] : subset(U_537,U_537),
inference(miniscope,[status(thm)],[f_131_2]) ).
cnf(f_131_4,plain,
subset(U_537,U_537),
inference(clausify,[status(thm)],[f_131_3]) ).
fof(f_132_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_132_2,plain,
! [U_539,U_538] :
( disjoint(U_538,U_539)
| ~ disjoint(U_539,U_538) ),
inference(variable_rename,[status(thm)],[f_132_1]) ).
cnf(f_132_3,plain,
( disjoint(U_538,U_539)
| ~ disjoint(U_539,U_538) ),
inference(clausify,[status(thm)],[f_132_2]) ).
fof(f_133_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_133_2,plain,
! [U_543,U_542,U_541,U_540] :
( ( in(ordered_pair(U_543,U_542),cartesian_product2(U_541,U_540))
| ~ in(U_542,U_540)
| ~ in(U_543,U_541) )
& ( ( in(U_542,U_540)
& in(U_543,U_541) )
| ~ in(ordered_pair(U_543,U_542),cartesian_product2(U_541,U_540)) ) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
fof(f_133_3,plain,
( ! [U_551,U_549,U_547,U_545] :
( in(ordered_pair(U_551,U_549),cartesian_product2(U_547,U_545))
| ~ in(U_549,U_545)
| ~ in(U_551,U_547) )
& ! [U_550,U_548,U_546,U_544] :
( ( in(U_548,U_544)
& in(U_550,U_546) )
| ~ in(ordered_pair(U_550,U_548),cartesian_product2(U_546,U_544)) ) ),
inference(miniscope,[status(thm)],[f_133_2]) ).
cnf(f_133_4,plain,
( in(U_550,U_546)
| ~ in(ordered_pair(U_550,U_548),cartesian_product2(U_546,U_544)) ),
inference(clausify,[status(thm)],[f_133_3]) ).
cnf(f_133_5,plain,
( in(U_548,U_544)
| ~ in(ordered_pair(U_550,U_548),cartesian_product2(U_546,U_544)) ),
inference(clausify,[status(thm)],[f_133_3]) ).
cnf(f_133_6,plain,
( in(ordered_pair(U_551,U_549),cartesian_product2(U_547,U_545))
| ~ in(U_549,U_545)
| ~ in(U_551,U_547) ),
inference(clausify,[status(thm)],[f_133_3]) ).
fof(f_134_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_134_2,plain,
! [U_555,U_554,U_553,U_552] :
( U_555 = U_552
| U_555 = U_553
| unordered_pair(U_555,U_554) != unordered_pair(U_553,U_552) ),
inference(variable_rename,[status(thm)],[f_134_1]) ).
fof(f_134_3,plain,
! [U_555,U_554,U_553] :
( ! [U_552] :
( U_555 = U_552
| unordered_pair(U_555,U_554) != unordered_pair(U_553,U_552) )
| U_555 = U_553 ),
inference(miniscope,[status(thm)],[f_134_2]) ).
cnf(f_134_4,plain,
( U_555 = U_552
| unordered_pair(U_555,U_554) != unordered_pair(U_553,U_552)
| U_555 = U_553 ),
inference(clausify,[status(thm)],[f_134_3]) ).
fof(f_135_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_135_2,plain,
! [U_558,U_557,U_556] :
( ( ( in(U_558,relation_rng(relation_rng_restriction(U_557,U_556)))
| ~ in(U_558,relation_rng(U_556))
| ~ in(U_558,U_557) )
& ( ( in(U_558,relation_rng(U_556))
& in(U_558,U_557) )
| ~ in(U_558,relation_rng(relation_rng_restriction(U_557,U_556))) ) )
| ~ relation(U_556) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
cnf(f_135_3,plain,
( in(U_558,U_557)
| ~ in(U_558,relation_rng(relation_rng_restriction(U_557,U_556)))
| ~ relation(U_556) ),
inference(clausify,[status(thm)],[f_135_2]) ).
cnf(f_135_4,plain,
( in(U_558,relation_rng(U_556))
| ~ in(U_558,relation_rng(relation_rng_restriction(U_557,U_556)))
| ~ relation(U_556) ),
inference(clausify,[status(thm)],[f_135_2]) ).
cnf(f_135_5,plain,
( in(U_558,relation_rng(relation_rng_restriction(U_557,U_556)))
| ~ in(U_558,relation_rng(U_556))
| ~ in(U_558,U_557)
| ~ relation(U_556) ),
inference(clausify,[status(thm)],[f_135_2]) ).
fof(f_136_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_136_2,plain,
! [U_560,U_559] :
( subset(relation_rng(relation_rng_restriction(U_560,U_559)),U_560)
| ~ relation(U_559) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
cnf(f_136_3,plain,
( subset(relation_rng(relation_rng_restriction(U_560,U_559)),U_560)
| ~ relation(U_559) ),
inference(clausify,[status(thm)],[f_136_2]) ).
fof(f_137_1,plain,
! [A,B] :
( subset(relation_rng_restriction(A,B),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t117_relat_1]) ).
fof(f_137_2,plain,
! [U_562,U_561] :
( subset(relation_rng_restriction(U_562,U_561),U_561)
| ~ relation(U_561) ),
inference(variable_rename,[status(thm)],[f_137_1]) ).
cnf(f_137_3,plain,
( subset(relation_rng_restriction(U_562,U_561),U_561)
| ~ relation(U_561) ),
inference(clausify,[status(thm)],[f_137_2]) ).
fof(f_138_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_138_2,plain,
! [U_564,U_563] :
( subset(relation_rng(relation_rng_restriction(U_564,U_563)),relation_rng(U_563))
| ~ relation(U_563) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
cnf(f_138_3,plain,
( subset(relation_rng(relation_rng_restriction(U_564,U_563)),relation_rng(U_563))
| ~ relation(U_563) ),
inference(clausify,[status(thm)],[f_138_2]) ).
fof(f_139_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_139_2,plain,
! [U_567,U_566,U_565] :
( ( subset(cartesian_product2(U_565,U_567),cartesian_product2(U_565,U_566))
& subset(cartesian_product2(U_567,U_565),cartesian_product2(U_566,U_565)) )
| ~ subset(U_567,U_566) ),
inference(variable_rename,[status(thm)],[f_139_1]) ).
fof(f_139_3,plain,
! [U_567,U_566] :
( ( ! [U_569] : subset(cartesian_product2(U_569,U_567),cartesian_product2(U_569,U_566))
& ! [U_568] : subset(cartesian_product2(U_567,U_568),cartesian_product2(U_566,U_568)) )
| ~ subset(U_567,U_566) ),
inference(miniscope,[status(thm)],[f_139_2]) ).
cnf(f_139_4,plain,
( subset(cartesian_product2(U_567,U_568),cartesian_product2(U_566,U_568))
| ~ subset(U_567,U_566) ),
inference(clausify,[status(thm)],[f_139_3]) ).
cnf(f_139_5,plain,
( subset(cartesian_product2(U_569,U_567),cartesian_product2(U_569,U_566))
| ~ subset(U_567,U_566) ),
inference(clausify,[status(thm)],[f_139_3]) ).
fof(f_140_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_140_2,plain,
! [U_571,U_570] :
( relation_rng(relation_rng_restriction(U_571,U_570)) = set_intersection2(relation_rng(U_570),U_571)
| ~ relation(U_570) ),
inference(variable_rename,[status(thm)],[f_140_1]) ).
cnf(f_140_3,plain,
( relation_rng(relation_rng_restriction(U_571,U_570)) = set_intersection2(relation_rng(U_570),U_571)
| ~ relation(U_570) ),
inference(clausify,[status(thm)],[f_140_2]) ).
fof(f_141_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_141_2,plain,
! [U_575,U_574,U_573,U_572] :
( subset(cartesian_product2(U_575,U_573),cartesian_product2(U_574,U_572))
| ~ subset(U_573,U_572)
| ~ subset(U_575,U_574) ),
inference(variable_rename,[status(thm)],[f_141_1]) ).
cnf(f_141_3,plain,
( subset(cartesian_product2(U_575,U_573),cartesian_product2(U_574,U_572))
| ~ subset(U_573,U_572)
| ~ subset(U_575,U_574) ),
inference(clausify,[status(thm)],[f_141_2]) ).
fof(f_142_1,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t12_xboole_1]) ).
fof(f_142_2,plain,
! [U_577,U_576] :
( set_union2(U_577,U_576) = U_576
| ~ subset(U_577,U_576) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
cnf(f_142_3,plain,
( set_union2(U_577,U_576) = U_576
| ~ subset(U_577,U_576) ),
inference(clausify,[status(thm)],[f_142_2]) ).
fof(f_143_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_143_2,plain,
! [U_583] :
? [U_582] :
( ! [U_581] :
( in(U_581,U_582)
| are_equipotent(U_581,U_582)
| ~ subset(U_581,U_582) )
& ! [U_580] :
( in(powerset(U_580),U_582)
| ~ in(U_580,U_582) )
& ! [U_579,U_578] :
( in(U_578,U_582)
| ~ subset(U_578,U_579)
| ~ in(U_579,U_582) )
& in(U_583,U_582) ),
inference(variable_rename,[status(thm)],[f_143_1]) ).
fof(f_143_3,plain,
! [U_583] :
( ! [U_581] :
( in(U_581,sK94(U_583))
| are_equipotent(U_581,sK94(U_583))
| ~ subset(U_581,sK94(U_583)) )
& ! [U_580] :
( in(powerset(U_580),sK94(U_583))
| ~ in(U_580,sK94(U_583)) )
& ! [U_579,U_578] :
( in(U_578,sK94(U_583))
| ~ subset(U_578,U_579)
| ~ in(U_579,sK94(U_583)) )
& in(U_583,sK94(U_583)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_582,sK94(U_583))],[f_143_2]) ).
cnf(f_143_4,plain,
in(U_583,sK94(U_583)),
inference(clausify,[status(thm)],[f_143_3]) ).
cnf(f_143_5,plain,
( in(U_578,sK94(U_583))
| ~ subset(U_578,U_579)
| ~ in(U_579,sK94(U_583)) ),
inference(clausify,[status(thm)],[f_143_3]) ).
cnf(f_143_6,plain,
( in(powerset(U_580),sK94(U_583))
| ~ in(U_580,sK94(U_583)) ),
inference(clausify,[status(thm)],[f_143_3]) ).
cnf(f_143_7,plain,
( in(U_581,sK94(U_583))
| are_equipotent(U_581,sK94(U_583))
| ~ subset(U_581,sK94(U_583)) ),
inference(clausify,[status(thm)],[f_143_3]) ).
fof(f_144_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_144_2,plain,
! [U_586,U_585,U_584] :
( relation_dom_restriction(relation_rng_restriction(U_586,U_584),U_585) = relation_rng_restriction(U_586,relation_dom_restriction(U_584,U_585))
| ~ relation(U_584) ),
inference(variable_rename,[status(thm)],[f_144_1]) ).
cnf(f_144_3,plain,
( relation_dom_restriction(relation_rng_restriction(U_586,U_584),U_585) = relation_rng_restriction(U_586,relation_dom_restriction(U_584,U_585))
| ~ relation(U_584) ),
inference(clausify,[status(thm)],[f_144_2]) ).
fof(f_145_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_145_2,plain,
! [U_591,U_590,U_589] :
( ( ( in(U_591,relation_image(U_589,U_590))
| ! [U_588] :
( ~ in(U_588,U_590)
| ~ in(ordered_pair(U_588,U_591),U_589)
| ~ in(U_588,relation_dom(U_589)) ) )
& ( ? [U_587] :
( in(U_587,U_590)
& in(ordered_pair(U_587,U_591),U_589)
& in(U_587,relation_dom(U_589)) )
| ~ in(U_591,relation_image(U_589,U_590)) ) )
| ~ relation(U_589) ),
inference(variable_rename,[status(thm)],[f_145_1]) ).
fof(f_145_3,plain,
! [U_591,U_590,U_589] :
( ( ( in(U_591,relation_image(U_589,U_590))
| ! [U_588] :
( ~ in(U_588,U_590)
| ~ in(ordered_pair(U_588,U_591),U_589)
| ~ in(U_588,relation_dom(U_589)) ) )
& ( ( in(sK95(U_591,U_590,U_589),U_590)
& in(ordered_pair(sK95(U_591,U_590,U_589),U_591),U_589)
& in(sK95(U_591,U_590,U_589),relation_dom(U_589)) )
| ~ in(U_591,relation_image(U_589,U_590)) ) )
| ~ relation(U_589) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_587,sK95(U_591,U_590,U_589))],[f_145_2]) ).
cnf(f_145_4,plain,
( in(sK95(U_591,U_590,U_589),relation_dom(U_589))
| ~ in(U_591,relation_image(U_589,U_590))
| ~ relation(U_589) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_5,plain,
( in(ordered_pair(sK95(U_591,U_590,U_589),U_591),U_589)
| ~ in(U_591,relation_image(U_589,U_590))
| ~ relation(U_589) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_6,plain,
( in(sK95(U_591,U_590,U_589),U_590)
| ~ in(U_591,relation_image(U_589,U_590))
| ~ relation(U_589) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_7,plain,
( in(U_591,relation_image(U_589,U_590))
| ~ in(U_588,U_590)
| ~ in(ordered_pair(U_588,U_591),U_589)
| ~ in(U_588,relation_dom(U_589))
| ~ relation(U_589) ),
inference(clausify,[status(thm)],[f_145_3]) ).
fof(f_146_1,plain,
! [A,B] :
( subset(relation_image(B,A),relation_rng(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t144_relat_1]) ).
fof(f_146_2,plain,
! [U_593,U_592] :
( subset(relation_image(U_592,U_593),relation_rng(U_592))
| ~ relation(U_592) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
cnf(f_146_3,plain,
( subset(relation_image(U_592,U_593),relation_rng(U_592))
| ~ relation(U_592) ),
inference(clausify,[status(thm)],[f_146_2]) ).
fof(f_147_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_147_2,plain,
! [U_595,U_594] :
( relation_image(U_594,U_595) = relation_image(U_594,set_intersection2(relation_dom(U_594),U_595))
| ~ relation(U_594) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
cnf(f_147_3,plain,
( relation_image(U_594,U_595) = relation_image(U_594,set_intersection2(relation_dom(U_594),U_595))
| ~ relation(U_594) ),
inference(clausify,[status(thm)],[f_147_2]) ).
fof(f_148_1,plain,
! [A] :
( relation_image(A,relation_dom(A)) = relation_rng(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t146_relat_1]) ).
fof(f_148_2,plain,
! [U_596] :
( relation_image(U_596,relation_dom(U_596)) = relation_rng(U_596)
| ~ relation(U_596) ),
inference(variable_rename,[status(thm)],[f_148_1]) ).
cnf(f_148_3,plain,
( relation_image(U_596,relation_dom(U_596)) = relation_rng(U_596)
| ~ relation(U_596) ),
inference(clausify,[status(thm)],[f_148_2]) ).
fof(f_149_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_149_2,plain,
! [U_598] :
( ! [U_597] :
( relation_rng(relation_composition(U_598,U_597)) = relation_image(U_597,relation_rng(U_598))
| ~ relation(U_597) )
| ~ relation(U_598) ),
inference(variable_rename,[status(thm)],[f_149_1]) ).
cnf(f_149_3,plain,
( relation_rng(relation_composition(U_598,U_597)) = relation_image(U_597,relation_rng(U_598))
| ~ relation(U_597)
| ~ relation(U_598) ),
inference(clausify,[status(thm)],[f_149_2]) ).
fof(f_150_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_150_2,plain,
! [U_603,U_602,U_601] :
( ( ( in(U_603,relation_inverse_image(U_601,U_602))
| ! [U_600] :
( ~ in(U_600,U_602)
| ~ in(ordered_pair(U_603,U_600),U_601)
| ~ in(U_600,relation_rng(U_601)) ) )
& ( ? [U_599] :
( in(U_599,U_602)
& in(ordered_pair(U_603,U_599),U_601)
& in(U_599,relation_rng(U_601)) )
| ~ in(U_603,relation_inverse_image(U_601,U_602)) ) )
| ~ relation(U_601) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
fof(f_150_3,plain,
! [U_603,U_602,U_601] :
( ( ( in(U_603,relation_inverse_image(U_601,U_602))
| ! [U_600] :
( ~ in(U_600,U_602)
| ~ in(ordered_pair(U_603,U_600),U_601)
| ~ in(U_600,relation_rng(U_601)) ) )
& ( ( in(sK96(U_603,U_602,U_601),U_602)
& in(ordered_pair(U_603,sK96(U_603,U_602,U_601)),U_601)
& in(sK96(U_603,U_602,U_601),relation_rng(U_601)) )
| ~ in(U_603,relation_inverse_image(U_601,U_602)) ) )
| ~ relation(U_601) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_599,sK96(U_603,U_602,U_601))],[f_150_2]) ).
cnf(f_150_4,plain,
( in(sK96(U_603,U_602,U_601),relation_rng(U_601))
| ~ in(U_603,relation_inverse_image(U_601,U_602))
| ~ relation(U_601) ),
inference(clausify,[status(thm)],[f_150_3]) ).
cnf(f_150_5,plain,
( in(ordered_pair(U_603,sK96(U_603,U_602,U_601)),U_601)
| ~ in(U_603,relation_inverse_image(U_601,U_602))
| ~ relation(U_601) ),
inference(clausify,[status(thm)],[f_150_3]) ).
cnf(f_150_6,plain,
( in(sK96(U_603,U_602,U_601),U_602)
| ~ in(U_603,relation_inverse_image(U_601,U_602))
| ~ relation(U_601) ),
inference(clausify,[status(thm)],[f_150_3]) ).
cnf(f_150_7,plain,
( in(U_603,relation_inverse_image(U_601,U_602))
| ~ in(U_600,U_602)
| ~ in(ordered_pair(U_603,U_600),U_601)
| ~ in(U_600,relation_rng(U_601))
| ~ relation(U_601) ),
inference(clausify,[status(thm)],[f_150_3]) ).
fof(f_151_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_151_2,plain,
! [U_605,U_604] :
( subset(relation_inverse_image(U_604,U_605),relation_dom(U_604))
| ~ relation(U_604) ),
inference(variable_rename,[status(thm)],[f_151_1]) ).
cnf(f_151_3,plain,
( subset(relation_inverse_image(U_604,U_605),relation_dom(U_604))
| ~ relation(U_604) ),
inference(clausify,[status(thm)],[f_151_2]) ).
fof(f_152_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_152_2,plain,
! [U_607,U_606] :
( relation_inverse_image(U_606,U_607) != empty_set
| ~ subset(U_607,relation_rng(U_606))
| U_607 = empty_set
| ~ relation(U_606) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
cnf(f_152_3,plain,
( relation_inverse_image(U_606,U_607) != empty_set
| ~ subset(U_607,relation_rng(U_606))
| U_607 = empty_set
| ~ relation(U_606) ),
inference(clausify,[status(thm)],[f_152_2]) ).
fof(f_153_1,plain,
! [A,B,C] :
( subset(relation_inverse_image(C,A),relation_inverse_image(C,B))
| ~ subset(A,B)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t178_relat_1]) ).
fof(f_153_2,plain,
! [U_610,U_609,U_608] :
( subset(relation_inverse_image(U_608,U_610),relation_inverse_image(U_608,U_609))
| ~ subset(U_610,U_609)
| ~ relation(U_608) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
cnf(f_153_3,plain,
( subset(relation_inverse_image(U_608,U_610),relation_inverse_image(U_608,U_609))
| ~ subset(U_610,U_609)
| ~ relation(U_608) ),
inference(clausify,[status(thm)],[f_153_2]) ).
fof(f_154_1,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(fof_nnf,[status(thm)],[t17_xboole_1]) ).
fof(f_154_2,plain,
! [U_612,U_611] : subset(set_intersection2(U_612,U_611),U_612),
inference(variable_rename,[status(thm)],[f_154_1]) ).
cnf(f_154_3,plain,
subset(set_intersection2(U_612,U_611),U_612),
inference(clausify,[status(thm)],[f_154_2]) ).
fof(f_155_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_155_2,plain,
! [U_615,U_614,U_613] :
( subset(U_615,set_intersection2(U_614,U_613))
| ~ subset(U_615,U_613)
| ~ subset(U_615,U_614) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
cnf(f_155_3,plain,
( subset(U_615,set_intersection2(U_614,U_613))
| ~ subset(U_615,U_613)
| ~ subset(U_615,U_614) ),
inference(clausify,[status(thm)],[f_155_2]) ).
fof(f_156_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_156_2,plain,
! [U_616] : set_union2(U_616,empty_set) = U_616,
inference(variable_rename,[status(thm)],[f_156_1]) ).
cnf(f_156_3,plain,
set_union2(U_616,empty_set) = U_616,
inference(clausify,[status(thm)],[f_156_2]) ).
fof(f_157_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_157_2,plain,
! [U_618,U_617] :
( element(U_618,U_617)
| ~ in(U_618,U_617) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
cnf(f_157_3,plain,
( element(U_618,U_617)
| ~ in(U_618,U_617) ),
inference(clausify,[status(thm)],[f_157_2]) ).
fof(f_158_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_158_2,plain,
! [U_621,U_620,U_619] :
( subset(U_621,U_619)
| ~ subset(U_620,U_619)
| ~ subset(U_621,U_620) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
cnf(f_158_3,plain,
( subset(U_621,U_619)
| ~ subset(U_620,U_619)
| ~ subset(U_621,U_620) ),
inference(clausify,[status(thm)],[f_158_2]) ).
fof(f_159_1,plain,
powerset(empty_set) = singleton(empty_set),
inference(fof_nnf,[status(thm)],[t1_zfmisc_1]) ).
cnf(f_159_2,plain,
powerset(empty_set) = singleton(empty_set),
inference(clausify,[status(thm)],[f_159_1]) ).
fof(f_160_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_160_2,plain,
! [U_624,U_623,U_622] :
( ( in(U_623,relation_rng(U_622))
& in(U_624,relation_dom(U_622)) )
| ~ in(ordered_pair(U_624,U_623),U_622)
| ~ relation(U_622) ),
inference(variable_rename,[status(thm)],[f_160_1]) ).
cnf(f_160_3,plain,
( in(U_624,relation_dom(U_622))
| ~ in(ordered_pair(U_624,U_623),U_622)
| ~ relation(U_622) ),
inference(clausify,[status(thm)],[f_160_2]) ).
cnf(f_160_4,plain,
( in(U_623,relation_rng(U_622))
| ~ in(ordered_pair(U_624,U_623),U_622)
| ~ relation(U_622) ),
inference(clausify,[status(thm)],[f_160_2]) ).
fof(f_161_1,plain,
! [A,B] :
( ! [C] :
( ( ( in(A,relation_dom(relation_composition(C,B)))
| ~ in(apply(C,A),relation_dom(B))
| ~ in(A,relation_dom(C)) )
& ( ( in(apply(C,A),relation_dom(B))
& in(A,relation_dom(C)) )
| ~ in(A,relation_dom(relation_composition(C,B))) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t21_funct_1]) ).
fof(f_161_2,plain,
! [U_627,U_626] :
( ! [U_625] :
( ( ( in(U_627,relation_dom(relation_composition(U_625,U_626)))
| ~ in(apply(U_625,U_627),relation_dom(U_626))
| ~ in(U_627,relation_dom(U_625)) )
& ( ( in(apply(U_625,U_627),relation_dom(U_626))
& in(U_627,relation_dom(U_625)) )
| ~ in(U_627,relation_dom(relation_composition(U_625,U_626))) ) )
| ~ function(U_625)
| ~ relation(U_625) )
| ~ function(U_626)
| ~ relation(U_626) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
cnf(f_161_3,plain,
( in(U_627,relation_dom(U_625))
| ~ in(U_627,relation_dom(relation_composition(U_625,U_626)))
| ~ function(U_625)
| ~ relation(U_625)
| ~ function(U_626)
| ~ relation(U_626) ),
inference(clausify,[status(thm)],[f_161_2]) ).
cnf(f_161_4,plain,
( in(apply(U_625,U_627),relation_dom(U_626))
| ~ in(U_627,relation_dom(relation_composition(U_625,U_626)))
| ~ function(U_625)
| ~ relation(U_625)
| ~ function(U_626)
| ~ relation(U_626) ),
inference(clausify,[status(thm)],[f_161_2]) ).
cnf(f_161_5,plain,
( in(U_627,relation_dom(relation_composition(U_625,U_626)))
| ~ in(apply(U_625,U_627),relation_dom(U_626))
| ~ in(U_627,relation_dom(U_625))
| ~ function(U_625)
| ~ relation(U_625)
| ~ function(U_626)
| ~ relation(U_626) ),
inference(clausify,[status(thm)],[f_161_2]) ).
fof(f_162_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_162_2,plain,
! [U_628] :
( subset(U_628,cartesian_product2(relation_dom(U_628),relation_rng(U_628)))
| ~ relation(U_628) ),
inference(variable_rename,[status(thm)],[f_162_1]) ).
cnf(f_162_3,plain,
( subset(U_628,cartesian_product2(relation_dom(U_628),relation_rng(U_628)))
| ~ relation(U_628) ),
inference(clausify,[status(thm)],[f_162_2]) ).
fof(f_163_1,plain,
! [A,B] :
( ! [C] :
( apply(relation_composition(C,B),A) = apply(B,apply(C,A))
| ~ in(A,relation_dom(relation_composition(C,B)))
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t22_funct_1]) ).
fof(f_163_2,plain,
! [U_631,U_630] :
( ! [U_629] :
( apply(relation_composition(U_629,U_630),U_631) = apply(U_630,apply(U_629,U_631))
| ~ in(U_631,relation_dom(relation_composition(U_629,U_630)))
| ~ function(U_629)
| ~ relation(U_629) )
| ~ function(U_630)
| ~ relation(U_630) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
cnf(f_163_3,plain,
( apply(relation_composition(U_629,U_630),U_631) = apply(U_630,apply(U_629,U_631))
| ~ in(U_631,relation_dom(relation_composition(U_629,U_630)))
| ~ function(U_629)
| ~ relation(U_629)
| ~ function(U_630)
| ~ relation(U_630) ),
inference(clausify,[status(thm)],[f_163_2]) ).
fof(f_164_1,plain,
! [A,B] :
( ! [C] :
( apply(relation_composition(B,C),A) = apply(C,apply(B,A))
| ~ in(A,relation_dom(B))
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t23_funct_1]) ).
fof(f_164_2,plain,
! [U_634,U_633] :
( ! [U_632] :
( apply(relation_composition(U_633,U_632),U_634) = apply(U_632,apply(U_633,U_634))
| ~ in(U_634,relation_dom(U_633))
| ~ function(U_632)
| ~ relation(U_632) )
| ~ function(U_633)
| ~ relation(U_633) ),
inference(variable_rename,[status(thm)],[f_164_1]) ).
cnf(f_164_3,plain,
( apply(relation_composition(U_633,U_632),U_634) = apply(U_632,apply(U_633,U_634))
| ~ in(U_634,relation_dom(U_633))
| ~ function(U_632)
| ~ relation(U_632)
| ~ function(U_633)
| ~ relation(U_633) ),
inference(clausify,[status(thm)],[f_164_2]) ).
fof(f_165_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_165_2,plain,
! [U_636] :
( ! [U_635] :
( ( subset(relation_rng(U_636),relation_rng(U_635))
& subset(relation_dom(U_636),relation_dom(U_635)) )
| ~ subset(U_636,U_635)
| ~ relation(U_635) )
| ~ relation(U_636) ),
inference(variable_rename,[status(thm)],[f_165_1]) ).
cnf(f_165_3,plain,
( subset(relation_dom(U_636),relation_dom(U_635))
| ~ subset(U_636,U_635)
| ~ relation(U_635)
| ~ relation(U_636) ),
inference(clausify,[status(thm)],[f_165_2]) ).
cnf(f_165_4,plain,
( subset(relation_rng(U_636),relation_rng(U_635))
| ~ subset(U_636,U_635)
| ~ relation(U_635)
| ~ relation(U_636) ),
inference(clausify,[status(thm)],[f_165_2]) ).
fof(f_166_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_166_2,plain,
! [U_639,U_638,U_637] :
( subset(set_intersection2(U_639,U_637),set_intersection2(U_638,U_637))
| ~ subset(U_639,U_638) ),
inference(variable_rename,[status(thm)],[f_166_1]) ).
fof(f_166_3,plain,
! [U_639,U_638] :
( ! [U_637] : subset(set_intersection2(U_639,U_637),set_intersection2(U_638,U_637))
| ~ subset(U_639,U_638) ),
inference(miniscope,[status(thm)],[f_166_2]) ).
cnf(f_166_4,plain,
( subset(set_intersection2(U_639,U_637),set_intersection2(U_638,U_637))
| ~ subset(U_639,U_638) ),
inference(clausify,[status(thm)],[f_166_3]) ).
fof(f_167_1,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t28_xboole_1]) ).
fof(f_167_2,plain,
! [U_641,U_640] :
( set_intersection2(U_641,U_640) = U_641
| ~ subset(U_641,U_640) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
cnf(f_167_3,plain,
( set_intersection2(U_641,U_640) = U_641
| ~ subset(U_641,U_640) ),
inference(clausify,[status(thm)],[f_167_2]) ).
fof(f_168_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_168_2,plain,
! [U_642] : set_intersection2(U_642,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_168_1]) ).
cnf(f_168_3,plain,
set_intersection2(U_642,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_168_2]) ).
fof(f_169_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_169_2,plain,
! [U_644,U_643] :
( in(U_644,U_643)
| empty(U_643)
| ~ element(U_644,U_643) ),
inference(variable_rename,[status(thm)],[f_169_1]) ).
cnf(f_169_3,plain,
( in(U_644,U_643)
| empty(U_643)
| ~ element(U_644,U_643) ),
inference(clausify,[status(thm)],[f_169_2]) ).
fof(f_170_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_170_2,plain,
! [U_647,U_646] :
( U_647 = U_646
| ? [U_645] :
( ( ~ in(U_645,U_647)
& in(U_645,U_646) )
| ( ~ in(U_645,U_646)
& in(U_645,U_647) ) ) ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
fof(f_170_3,plain,
! [U_647,U_646] :
( U_647 = U_646
| ? [U_649] :
( ~ in(U_649,U_647)
& in(U_649,U_646) )
| ? [U_648] :
( ~ in(U_648,U_646)
& in(U_648,U_647) ) ),
inference(miniscope,[status(thm)],[f_170_2]) ).
fof(f_170_4,plain,
! [U_647,U_646] :
( U_647 = U_646
| ? [U_649] :
( ~ in(U_649,U_647)
& in(U_649,U_646) )
| ( ~ in(sK97(U_647,U_646),U_646)
& in(sK97(U_647,U_646),U_647) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_648,sK97(U_647,U_646))],[f_170_3]) ).
fof(f_170_5,plain,
! [U_647,U_646] :
( U_647 = U_646
| ( ~ in(sK98(U_647,U_646),U_647)
& in(sK98(U_647,U_646),U_646) )
| ( ~ in(sK97(U_647,U_646),U_646)
& in(sK97(U_647,U_646),U_647) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_649,sK98(U_647,U_646))],[f_170_4]) ).
cnf(f_170_6,plain,
( in(sK98(U_647,U_646),U_646)
| in(sK97(U_647,U_646),U_647)
| U_647 = U_646 ),
inference(clausify,[status(thm)],[f_170_5]) ).
cnf(f_170_7,plain,
( ~ in(sK98(U_647,U_646),U_647)
| in(sK97(U_647,U_646),U_647)
| U_647 = U_646 ),
inference(clausify,[status(thm)],[f_170_5]) ).
cnf(f_170_8,plain,
( in(sK98(U_647,U_646),U_646)
| ~ in(sK97(U_647,U_646),U_646)
| U_647 = U_646 ),
inference(clausify,[status(thm)],[f_170_5]) ).
cnf(f_170_9,plain,
( ~ in(sK98(U_647,U_646),U_647)
| ~ in(sK97(U_647,U_646),U_646)
| U_647 = U_646 ),
inference(clausify,[status(thm)],[f_170_5]) ).
fof(f_171_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_171_2,plain,
! [U_650] : subset(empty_set,U_650),
inference(variable_rename,[status(thm)],[f_171_1]) ).
cnf(f_171_3,plain,
subset(empty_set,U_650),
inference(clausify,[status(thm)],[f_171_2]) ).
fof(f_172_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_172_2,plain,
! [U_653,U_652,U_651] :
( ( in(U_652,relation_field(U_651))
& in(U_653,relation_field(U_651)) )
| ~ in(ordered_pair(U_653,U_652),U_651)
| ~ relation(U_651) ),
inference(variable_rename,[status(thm)],[f_172_1]) ).
cnf(f_172_3,plain,
( in(U_653,relation_field(U_651))
| ~ in(ordered_pair(U_653,U_652),U_651)
| ~ relation(U_651) ),
inference(clausify,[status(thm)],[f_172_2]) ).
cnf(f_172_4,plain,
( in(U_652,relation_field(U_651))
| ~ in(ordered_pair(U_653,U_652),U_651)
| ~ relation(U_651) ),
inference(clausify,[status(thm)],[f_172_2]) ).
fof(f_173_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_173_2,plain,
! [U_656,U_655,U_654] :
( subset(set_difference(U_656,U_654),set_difference(U_655,U_654))
| ~ subset(U_656,U_655) ),
inference(variable_rename,[status(thm)],[f_173_1]) ).
fof(f_173_3,plain,
! [U_656,U_655] :
( ! [U_654] : subset(set_difference(U_656,U_654),set_difference(U_655,U_654))
| ~ subset(U_656,U_655) ),
inference(miniscope,[status(thm)],[f_173_2]) ).
cnf(f_173_4,plain,
( subset(set_difference(U_656,U_654),set_difference(U_655,U_654))
| ~ subset(U_656,U_655) ),
inference(clausify,[status(thm)],[f_173_3]) ).
fof(f_174_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_174_2,plain,
! [U_660,U_659,U_658,U_657] :
( ( U_659 = U_657
& U_660 = U_658 )
| ordered_pair(U_660,U_659) != ordered_pair(U_658,U_657) ),
inference(variable_rename,[status(thm)],[f_174_1]) ).
cnf(f_174_3,plain,
( U_660 = U_658
| ordered_pair(U_660,U_659) != ordered_pair(U_658,U_657) ),
inference(clausify,[status(thm)],[f_174_2]) ).
cnf(f_174_4,plain,
( U_659 = U_657
| ordered_pair(U_660,U_659) != ordered_pair(U_658,U_657) ),
inference(clausify,[status(thm)],[f_174_2]) ).
fof(f_175_1,plain,
! [A,B] :
( ( ( B = identity_relation(A)
| ? [C] :
( apply(B,C) != C
& in(C,A) )
| relation_dom(B) != A )
& ( ( ! [C] :
( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A )
| B != identity_relation(A) ) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t34_funct_1]) ).
fof(f_175_2,plain,
! [U_664,U_663] :
( ( ( U_663 = identity_relation(U_664)
| ? [U_662] :
( apply(U_663,U_662) != U_662
& in(U_662,U_664) )
| relation_dom(U_663) != U_664 )
& ( ( ! [U_661] :
( apply(U_663,U_661) = U_661
| ~ in(U_661,U_664) )
& relation_dom(U_663) = U_664 )
| U_663 != identity_relation(U_664) ) )
| ~ function(U_663)
| ~ relation(U_663) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
fof(f_175_3,plain,
! [U_664,U_663] :
( ( ( U_663 = identity_relation(U_664)
| ( apply(U_663,sK99(U_664,U_663)) != sK99(U_664,U_663)
& in(sK99(U_664,U_663),U_664) )
| relation_dom(U_663) != U_664 )
& ( ( ! [U_661] :
( apply(U_663,U_661) = U_661
| ~ in(U_661,U_664) )
& relation_dom(U_663) = U_664 )
| U_663 != identity_relation(U_664) ) )
| ~ function(U_663)
| ~ relation(U_663) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_662,sK99(U_664,U_663))],[f_175_2]) ).
cnf(f_175_4,plain,
( relation_dom(U_663) = U_664
| U_663 != identity_relation(U_664)
| ~ function(U_663)
| ~ relation(U_663) ),
inference(clausify,[status(thm)],[f_175_3]) ).
cnf(f_175_5,plain,
( apply(U_663,U_661) = U_661
| ~ in(U_661,U_664)
| U_663 != identity_relation(U_664)
| ~ function(U_663)
| ~ relation(U_663) ),
inference(clausify,[status(thm)],[f_175_3]) ).
cnf(f_175_6,plain,
( in(sK99(U_664,U_663),U_664)
| relation_dom(U_663) != U_664
| U_663 = identity_relation(U_664)
| ~ function(U_663)
| ~ relation(U_663) ),
inference(clausify,[status(thm)],[f_175_3]) ).
cnf(f_175_7,plain,
( apply(U_663,sK99(U_664,U_663)) != sK99(U_664,U_663)
| relation_dom(U_663) != U_664
| U_663 = identity_relation(U_664)
| ~ function(U_663)
| ~ relation(U_663) ),
inference(clausify,[status(thm)],[f_175_3]) ).
fof(f_176_1,plain,
! [A,B] :
( apply(identity_relation(A),B) = B
| ~ in(B,A) ),
inference(fof_nnf,[status(thm)],[t35_funct_1]) ).
fof(f_176_2,plain,
! [U_666,U_665] :
( apply(identity_relation(U_666),U_665) = U_665
| ~ in(U_665,U_666) ),
inference(variable_rename,[status(thm)],[f_176_1]) ).
cnf(f_176_3,plain,
( apply(identity_relation(U_666),U_665) = U_665
| ~ in(U_665,U_666) ),
inference(clausify,[status(thm)],[f_176_2]) ).
fof(f_177_1,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(fof_nnf,[status(thm)],[t36_xboole_1]) ).
fof(f_177_2,plain,
! [U_668,U_667] : subset(set_difference(U_668,U_667),U_668),
inference(variable_rename,[status(thm)],[f_177_1]) ).
cnf(f_177_3,plain,
subset(set_difference(U_668,U_667),U_668),
inference(clausify,[status(thm)],[f_177_2]) ).
fof(f_178_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_178_2,plain,
! [U_669] :
( ( relation_dom(U_669) = relation_rng(relation_inverse(U_669))
& relation_rng(U_669) = relation_dom(relation_inverse(U_669)) )
| ~ relation(U_669) ),
inference(variable_rename,[status(thm)],[f_178_1]) ).
cnf(f_178_3,plain,
( relation_rng(U_669) = relation_dom(relation_inverse(U_669))
| ~ relation(U_669) ),
inference(clausify,[status(thm)],[f_178_2]) ).
cnf(f_178_4,plain,
( relation_dom(U_669) = relation_rng(relation_inverse(U_669))
| ~ relation(U_669) ),
inference(clausify,[status(thm)],[f_178_2]) ).
fof(f_179_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_179_2,plain,
! [U_671,U_670] :
( ( set_difference(U_671,U_670) = empty_set
| ~ subset(U_671,U_670) )
& ( subset(U_671,U_670)
| set_difference(U_671,U_670) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_179_1]) ).
fof(f_179_3,plain,
( ! [U_675,U_673] :
( set_difference(U_675,U_673) = empty_set
| ~ subset(U_675,U_673) )
& ! [U_674,U_672] :
( subset(U_674,U_672)
| set_difference(U_674,U_672) != empty_set ) ),
inference(miniscope,[status(thm)],[f_179_2]) ).
cnf(f_179_4,plain,
( subset(U_674,U_672)
| set_difference(U_674,U_672) != empty_set ),
inference(clausify,[status(thm)],[f_179_3]) ).
cnf(f_179_5,plain,
( set_difference(U_675,U_673) = empty_set
| ~ subset(U_675,U_673) ),
inference(clausify,[status(thm)],[f_179_3]) ).
fof(f_180_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_180_2,plain,
! [U_677,U_676] :
( ( subset(singleton(U_677),U_676)
| ~ in(U_677,U_676) )
& ( in(U_677,U_676)
| ~ subset(singleton(U_677),U_676) ) ),
inference(variable_rename,[status(thm)],[f_180_1]) ).
fof(f_180_3,plain,
( ! [U_681,U_679] :
( subset(singleton(U_681),U_679)
| ~ in(U_681,U_679) )
& ! [U_680,U_678] :
( in(U_680,U_678)
| ~ subset(singleton(U_680),U_678) ) ),
inference(miniscope,[status(thm)],[f_180_2]) ).
cnf(f_180_4,plain,
( in(U_680,U_678)
| ~ subset(singleton(U_680),U_678) ),
inference(clausify,[status(thm)],[f_180_3]) ).
cnf(f_180_5,plain,
( subset(singleton(U_681),U_679)
| ~ in(U_681,U_679) ),
inference(clausify,[status(thm)],[f_180_3]) ).
fof(f_181_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_181_2,plain,
! [U_684,U_683,U_682] :
( ( subset(unordered_pair(U_684,U_683),U_682)
| ~ in(U_683,U_682)
| ~ in(U_684,U_682) )
& ( ( in(U_683,U_682)
& in(U_684,U_682) )
| ~ subset(unordered_pair(U_684,U_683),U_682) ) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
fof(f_181_3,plain,
( ! [U_690,U_688,U_686] :
( subset(unordered_pair(U_690,U_688),U_686)
| ~ in(U_688,U_686)
| ~ in(U_690,U_686) )
& ! [U_689,U_687,U_685] :
( ( in(U_687,U_685)
& in(U_689,U_685) )
| ~ subset(unordered_pair(U_689,U_687),U_685) ) ),
inference(miniscope,[status(thm)],[f_181_2]) ).
cnf(f_181_4,plain,
( in(U_689,U_685)
| ~ subset(unordered_pair(U_689,U_687),U_685) ),
inference(clausify,[status(thm)],[f_181_3]) ).
cnf(f_181_5,plain,
( in(U_687,U_685)
| ~ subset(unordered_pair(U_689,U_687),U_685) ),
inference(clausify,[status(thm)],[f_181_3]) ).
cnf(f_181_6,plain,
( subset(unordered_pair(U_690,U_688),U_686)
| ~ in(U_688,U_686)
| ~ in(U_690,U_686) ),
inference(clausify,[status(thm)],[f_181_3]) ).
fof(f_182_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_182_2,plain,
! [U_692,U_691] : set_union2(U_692,set_difference(U_691,U_692)) = set_union2(U_692,U_691),
inference(variable_rename,[status(thm)],[f_182_1]) ).
cnf(f_182_3,plain,
set_union2(U_692,set_difference(U_691,U_692)) = set_union2(U_692,U_691),
inference(clausify,[status(thm)],[f_182_2]) ).
fof(f_183_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_183_2,plain,
! [U_694,U_693] :
( ( subset(U_694,singleton(U_693))
| ( U_694 != singleton(U_693)
& U_694 != empty_set ) )
& ( U_694 = singleton(U_693)
| U_694 = empty_set
| ~ subset(U_694,singleton(U_693)) ) ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
fof(f_183_3,plain,
( ! [U_698,U_696] :
( subset(U_698,singleton(U_696))
| ( U_698 != singleton(U_696)
& U_698 != empty_set ) )
& ! [U_697,U_695] :
( U_697 = singleton(U_695)
| U_697 = empty_set
| ~ subset(U_697,singleton(U_695)) ) ),
inference(miniscope,[status(thm)],[f_183_2]) ).
cnf(f_183_4,plain,
( U_697 = singleton(U_695)
| U_697 = empty_set
| ~ subset(U_697,singleton(U_695)) ),
inference(clausify,[status(thm)],[f_183_3]) ).
cnf(f_183_5,plain,
( U_698 != empty_set
| subset(U_698,singleton(U_696)) ),
inference(clausify,[status(thm)],[f_183_3]) ).
cnf(f_183_6,plain,
( U_698 != singleton(U_696)
| subset(U_698,singleton(U_696)) ),
inference(clausify,[status(thm)],[f_183_3]) ).
fof(f_184_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_184_2,plain,
! [U_699] : set_difference(U_699,empty_set) = U_699,
inference(variable_rename,[status(thm)],[f_184_1]) ).
cnf(f_184_3,plain,
set_difference(U_699,empty_set) = U_699,
inference(clausify,[status(thm)],[f_184_2]) ).
fof(f_185_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_185_2,plain,
! [U_701,U_700] :
( ( element(U_701,powerset(U_700))
| ~ subset(U_701,U_700) )
& ( subset(U_701,U_700)
| ~ element(U_701,powerset(U_700)) ) ),
inference(variable_rename,[status(thm)],[f_185_1]) ).
fof(f_185_3,plain,
( ! [U_705,U_703] :
( element(U_705,powerset(U_703))
| ~ subset(U_705,U_703) )
& ! [U_704,U_702] :
( subset(U_704,U_702)
| ~ element(U_704,powerset(U_702)) ) ),
inference(miniscope,[status(thm)],[f_185_2]) ).
cnf(f_185_4,plain,
( subset(U_704,U_702)
| ~ element(U_704,powerset(U_702)) ),
inference(clausify,[status(thm)],[f_185_3]) ).
cnf(f_185_5,plain,
( element(U_705,powerset(U_703))
| ~ subset(U_705,U_703) ),
inference(clausify,[status(thm)],[f_185_3]) ).
fof(f_186_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_186_2,plain,
! [U_709,U_708] :
( ( ~ disjoint(U_709,U_708)
| ! [U_707] :
( ~ in(U_707,U_708)
| ~ in(U_707,U_709) ) )
& ( ? [U_706] :
( in(U_706,U_708)
& in(U_706,U_709) )
| disjoint(U_709,U_708) ) ),
inference(variable_rename,[status(thm)],[f_186_1]) ).
fof(f_186_3,plain,
( ! [U_713,U_711] :
( ~ disjoint(U_713,U_711)
| ! [U_707] :
( ~ in(U_707,U_711)
| ~ in(U_707,U_713) ) )
& ! [U_712,U_710] :
( ? [U_706] :
( in(U_706,U_710)
& in(U_706,U_712) )
| disjoint(U_712,U_710) ) ),
inference(miniscope,[status(thm)],[f_186_2]) ).
fof(f_186_4,plain,
( ! [U_713,U_711] :
( ~ disjoint(U_713,U_711)
| ! [U_707] :
( ~ in(U_707,U_711)
| ~ in(U_707,U_713) ) )
& ! [U_712,U_710] :
( ( in(sK100(U_712,U_710),U_710)
& in(sK100(U_712,U_710),U_712) )
| disjoint(U_712,U_710) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_706,sK100(U_712,U_710))],[f_186_3]) ).
cnf(f_186_5,plain,
( in(sK100(U_712,U_710),U_712)
| disjoint(U_712,U_710) ),
inference(clausify,[status(thm)],[f_186_4]) ).
cnf(f_186_6,plain,
( in(sK100(U_712,U_710),U_710)
| disjoint(U_712,U_710) ),
inference(clausify,[status(thm)],[f_186_4]) ).
cnf(f_186_7,plain,
( ~ disjoint(U_713,U_711)
| ~ in(U_707,U_711)
| ~ in(U_707,U_713) ),
inference(clausify,[status(thm)],[f_186_4]) ).
fof(f_187_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_187_2,plain,
! [U_714] :
( U_714 = empty_set
| ~ subset(U_714,empty_set) ),
inference(variable_rename,[status(thm)],[f_187_1]) ).
cnf(f_187_3,plain,
( U_714 = empty_set
| ~ subset(U_714,empty_set) ),
inference(clausify,[status(thm)],[f_187_2]) ).
fof(f_188_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_188_2,plain,
! [U_716,U_715] : set_difference(set_union2(U_716,U_715),U_715) = set_difference(U_716,U_715),
inference(variable_rename,[status(thm)],[f_188_1]) ).
cnf(f_188_3,plain,
set_difference(set_union2(U_716,U_715),U_715) = set_difference(U_716,U_715),
inference(clausify,[status(thm)],[f_188_2]) ).
fof(f_189_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_189_2,plain,
! [U_719,U_718] :
( ! [U_717] :
( ( ( disjoint(U_718,U_717)
| ~ subset(U_718,subset_complement(U_719,U_717)) )
& ( subset(U_718,subset_complement(U_719,U_717))
| ~ disjoint(U_718,U_717) ) )
| ~ element(U_717,powerset(U_719)) )
| ~ element(U_718,powerset(U_719)) ),
inference(variable_rename,[status(thm)],[f_189_1]) ).
cnf(f_189_3,plain,
( subset(U_718,subset_complement(U_719,U_717))
| ~ disjoint(U_718,U_717)
| ~ element(U_717,powerset(U_719))
| ~ element(U_718,powerset(U_719)) ),
inference(clausify,[status(thm)],[f_189_2]) ).
cnf(f_189_4,plain,
( disjoint(U_718,U_717)
| ~ subset(U_718,subset_complement(U_719,U_717))
| ~ element(U_717,powerset(U_719))
| ~ element(U_718,powerset(U_719)) ),
inference(clausify,[status(thm)],[f_189_2]) ).
fof(f_190_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_190_2,plain,
! [U_721] :
( ! [U_720] :
( subset(relation_dom(relation_composition(U_721,U_720)),relation_dom(U_721))
| ~ relation(U_720) )
| ~ relation(U_721) ),
inference(variable_rename,[status(thm)],[f_190_1]) ).
cnf(f_190_3,plain,
( subset(relation_dom(relation_composition(U_721,U_720)),relation_dom(U_721))
| ~ relation(U_720)
| ~ relation(U_721) ),
inference(clausify,[status(thm)],[f_190_2]) ).
fof(f_191_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_191_2,plain,
! [U_723] :
( ! [U_722] :
( subset(relation_rng(relation_composition(U_723,U_722)),relation_rng(U_722))
| ~ relation(U_722) )
| ~ relation(U_723) ),
inference(variable_rename,[status(thm)],[f_191_1]) ).
cnf(f_191_3,plain,
( subset(relation_rng(relation_composition(U_723,U_722)),relation_rng(U_722))
| ~ relation(U_722)
| ~ relation(U_723) ),
inference(clausify,[status(thm)],[f_191_2]) ).
fof(f_192_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_192_2,plain,
! [U_725,U_724] :
( U_724 = set_union2(U_725,set_difference(U_724,U_725))
| ~ subset(U_725,U_724) ),
inference(variable_rename,[status(thm)],[f_192_1]) ).
cnf(f_192_3,plain,
( U_724 = set_union2(U_725,set_difference(U_724,U_725))
| ~ subset(U_725,U_724) ),
inference(clausify,[status(thm)],[f_192_2]) ).
fof(f_193_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_193_2,plain,
! [U_727] :
( ! [U_726] :
( relation_dom(relation_composition(U_727,U_726)) = relation_dom(U_727)
| ~ subset(relation_rng(U_727),relation_dom(U_726))
| ~ relation(U_726) )
| ~ relation(U_727) ),
inference(variable_rename,[status(thm)],[f_193_1]) ).
cnf(f_193_3,plain,
( relation_dom(relation_composition(U_727,U_726)) = relation_dom(U_727)
| ~ subset(relation_rng(U_727),relation_dom(U_726))
| ~ relation(U_726)
| ~ relation(U_727) ),
inference(clausify,[status(thm)],[f_193_2]) ).
fof(f_194_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_194_2,plain,
! [U_729,U_728] :
( complements_of_subsets(U_729,U_728) != empty_set
| U_728 = empty_set
| ~ element(U_728,powerset(powerset(U_729))) ),
inference(variable_rename,[status(thm)],[f_194_1]) ).
cnf(f_194_3,plain,
( complements_of_subsets(U_729,U_728) != empty_set
| U_728 = empty_set
| ~ element(U_728,powerset(powerset(U_729))) ),
inference(clausify,[status(thm)],[f_194_2]) ).
fof(f_195_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t46_zfmisc_1]) ).
fof(f_195_2,plain,
! [U_731,U_730] :
( set_union2(singleton(U_731),U_730) = U_730
| ~ in(U_731,U_730) ),
inference(variable_rename,[status(thm)],[f_195_1]) ).
cnf(f_195_3,plain,
( set_union2(singleton(U_731),U_730) = U_730
| ~ in(U_731,U_730) ),
inference(clausify,[status(thm)],[f_195_2]) ).
fof(f_196_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_196_2,plain,
! [U_733] :
( ! [U_732] :
( relation_rng(relation_composition(U_732,U_733)) = relation_rng(U_733)
| ~ subset(relation_dom(U_733),relation_rng(U_732))
| ~ relation(U_732) )
| ~ relation(U_733) ),
inference(variable_rename,[status(thm)],[f_196_1]) ).
cnf(f_196_3,plain,
( relation_rng(relation_composition(U_732,U_733)) = relation_rng(U_733)
| ~ subset(relation_dom(U_733),relation_rng(U_732))
| ~ relation(U_732)
| ~ relation(U_733) ),
inference(clausify,[status(thm)],[f_196_2]) ).
fof(f_197_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_197_2,plain,
! [U_735,U_734] :
( subset_difference(U_735,cast_to_subset(U_735),union_of_subsets(U_735,U_734)) = meet_of_subsets(U_735,complements_of_subsets(U_735,U_734))
| U_734 = empty_set
| ~ element(U_734,powerset(powerset(U_735))) ),
inference(variable_rename,[status(thm)],[f_197_1]) ).
cnf(f_197_3,plain,
( subset_difference(U_735,cast_to_subset(U_735),union_of_subsets(U_735,U_734)) = meet_of_subsets(U_735,complements_of_subsets(U_735,U_734))
| U_734 = empty_set
| ~ element(U_734,powerset(powerset(U_735))) ),
inference(clausify,[status(thm)],[f_197_2]) ).
fof(f_198_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_198_2,plain,
! [U_737,U_736] :
( union_of_subsets(U_737,complements_of_subsets(U_737,U_736)) = subset_difference(U_737,cast_to_subset(U_737),meet_of_subsets(U_737,U_736))
| U_736 = empty_set
| ~ element(U_736,powerset(powerset(U_737))) ),
inference(variable_rename,[status(thm)],[f_198_1]) ).
cnf(f_198_3,plain,
( union_of_subsets(U_737,complements_of_subsets(U_737,U_736)) = subset_difference(U_737,cast_to_subset(U_737),meet_of_subsets(U_737,U_736))
| U_736 = empty_set
| ~ element(U_736,powerset(powerset(U_737))) ),
inference(clausify,[status(thm)],[f_198_2]) ).
fof(f_199_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_199_2,plain,
! [U_739,U_738] : set_difference(U_739,set_difference(U_739,U_738)) = set_intersection2(U_739,U_738),
inference(variable_rename,[status(thm)],[f_199_1]) ).
cnf(f_199_3,plain,
set_difference(U_739,set_difference(U_739,U_738)) = set_intersection2(U_739,U_738),
inference(clausify,[status(thm)],[f_199_2]) ).
fof(f_200_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_200_2,plain,
! [U_740] : set_difference(empty_set,U_740) = empty_set,
inference(variable_rename,[status(thm)],[f_200_1]) ).
cnf(f_200_3,plain,
set_difference(empty_set,U_740) = empty_set,
inference(clausify,[status(thm)],[f_200_2]) ).
fof(f_201_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_201_2,plain,
! [U_743,U_742,U_741] :
( element(U_743,U_741)
| ~ element(U_742,powerset(U_741))
| ~ in(U_743,U_742) ),
inference(variable_rename,[status(thm)],[f_201_1]) ).
cnf(f_201_3,plain,
( element(U_743,U_741)
| ~ element(U_742,powerset(U_741))
| ~ in(U_743,U_742) ),
inference(clausify,[status(thm)],[f_201_2]) ).
fof(f_202_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_202_2,plain,
! [U_747,U_746] :
( ( ~ disjoint(U_747,U_746)
| ! [U_745] : ~ in(U_745,set_intersection2(U_747,U_746)) )
& ( ? [U_744] : in(U_744,set_intersection2(U_747,U_746))
| disjoint(U_747,U_746) ) ),
inference(variable_rename,[status(thm)],[f_202_1]) ).
fof(f_202_3,plain,
( ! [U_751,U_749] :
( ~ disjoint(U_751,U_749)
| ! [U_745] : ~ in(U_745,set_intersection2(U_751,U_749)) )
& ! [U_750,U_748] :
( ? [U_744] : in(U_744,set_intersection2(U_750,U_748))
| disjoint(U_750,U_748) ) ),
inference(miniscope,[status(thm)],[f_202_2]) ).
fof(f_202_4,plain,
( ! [U_751,U_749] :
( ~ disjoint(U_751,U_749)
| ! [U_745] : ~ in(U_745,set_intersection2(U_751,U_749)) )
& ! [U_750,U_748] :
( in(sK101(U_750,U_748),set_intersection2(U_750,U_748))
| disjoint(U_750,U_748) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_744,sK101(U_750,U_748))],[f_202_3]) ).
cnf(f_202_5,plain,
( in(sK101(U_750,U_748),set_intersection2(U_750,U_748))
| disjoint(U_750,U_748) ),
inference(clausify,[status(thm)],[f_202_4]) ).
cnf(f_202_6,plain,
( ~ disjoint(U_751,U_749)
| ~ in(U_745,set_intersection2(U_751,U_749)) ),
inference(clausify,[status(thm)],[f_202_4]) ).
fof(f_203_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_203_2,plain,
! [U_754] :
( ! [U_753] :
( ! [U_752] :
( in(U_752,subset_complement(U_754,U_753))
| in(U_752,U_753)
| ~ element(U_752,U_754) )
| ~ element(U_753,powerset(U_754)) )
| U_754 = empty_set ),
inference(variable_rename,[status(thm)],[f_203_1]) ).
cnf(f_203_3,plain,
( in(U_752,subset_complement(U_754,U_753))
| in(U_752,U_753)
| ~ element(U_752,U_754)
| ~ element(U_753,powerset(U_754))
| U_754 = empty_set ),
inference(clausify,[status(thm)],[f_203_2]) ).
fof(f_204_1,plain,
! [A] :
( ! [B] :
( ( ( B = function_inverse(A)
| ? [C,D] :
( ( ( D != apply(B,C)
| ~ in(C,relation_rng(A)) )
& C = apply(A,D)
& in(D,relation_dom(A)) )
| ( ( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& D = apply(B,C)
& in(C,relation_rng(A)) ) )
| relation_dom(B) != relation_rng(A) )
& ( ( ! [C,D] :
( ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
| C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& ( ( C = apply(A,D)
& in(D,relation_dom(A)) )
| D != apply(B,C)
| ~ in(C,relation_rng(A)) ) )
& relation_dom(B) = relation_rng(A) )
| B != function_inverse(A) ) )
| ~ function(B)
| ~ relation(B) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t54_funct_1]) ).
fof(f_204_2,plain,
! [U_760] :
( ! [U_759] :
( ( ( U_759 = function_inverse(U_760)
| ? [U_758,U_757] :
( ( ( U_757 != apply(U_759,U_758)
| ~ in(U_758,relation_rng(U_760)) )
& U_758 = apply(U_760,U_757)
& in(U_757,relation_dom(U_760)) )
| ( ( U_758 != apply(U_760,U_757)
| ~ in(U_757,relation_dom(U_760)) )
& U_757 = apply(U_759,U_758)
& in(U_758,relation_rng(U_760)) ) )
| relation_dom(U_759) != relation_rng(U_760) )
& ( ( ! [U_756,U_755] :
( ( ( U_755 = apply(U_759,U_756)
& in(U_756,relation_rng(U_760)) )
| U_756 != apply(U_760,U_755)
| ~ in(U_755,relation_dom(U_760)) )
& ( ( U_756 = apply(U_760,U_755)
& in(U_755,relation_dom(U_760)) )
| U_755 != apply(U_759,U_756)
| ~ in(U_756,relation_rng(U_760)) ) )
& relation_dom(U_759) = relation_rng(U_760) )
| U_759 != function_inverse(U_760) ) )
| ~ function(U_759)
| ~ relation(U_759) )
| ~ one_to_one(U_760)
| ~ function(U_760)
| ~ relation(U_760) ),
inference(variable_rename,[status(thm)],[f_204_1]) ).
fof(f_204_3,plain,
! [U_760] :
( ! [U_759] :
( ( ( U_759 = function_inverse(U_760)
| ? [U_768,U_766] :
( ( U_766 != apply(U_759,U_768)
| ~ in(U_768,relation_rng(U_760)) )
& U_768 = apply(U_760,U_766)
& in(U_766,relation_dom(U_760)) )
| ? [U_767,U_765] :
( ( U_767 != apply(U_760,U_765)
| ~ in(U_765,relation_dom(U_760)) )
& U_765 = apply(U_759,U_767)
& in(U_767,relation_rng(U_760)) )
| relation_dom(U_759) != relation_rng(U_760) )
& ( ( ! [U_764,U_762] :
( ( U_762 = apply(U_759,U_764)
& in(U_764,relation_rng(U_760)) )
| U_764 != apply(U_760,U_762)
| ~ in(U_762,relation_dom(U_760)) )
& ! [U_763,U_761] :
( ( U_763 = apply(U_760,U_761)
& in(U_761,relation_dom(U_760)) )
| U_761 != apply(U_759,U_763)
| ~ in(U_763,relation_rng(U_760)) )
& relation_dom(U_759) = relation_rng(U_760) )
| U_759 != function_inverse(U_760) ) )
| ~ function(U_759)
| ~ relation(U_759) )
| ~ one_to_one(U_760)
| ~ function(U_760)
| ~ relation(U_760) ),
inference(miniscope,[status(thm)],[f_204_2]) ).
fof(f_204_4,plain,
! [U_760] :
( ! [U_759] :
( ( ( U_759 = function_inverse(U_760)
| ? [U_768,U_766] :
( ( U_766 != apply(U_759,U_768)
| ~ in(U_768,relation_rng(U_760)) )
& U_768 = apply(U_760,U_766)
& in(U_766,relation_dom(U_760)) )
| ? [U_765] :
( ( sK102(U_760,U_759) != apply(U_760,U_765)
| ~ in(U_765,relation_dom(U_760)) )
& U_765 = apply(U_759,sK102(U_760,U_759))
& in(sK102(U_760,U_759),relation_rng(U_760)) )
| relation_dom(U_759) != relation_rng(U_760) )
& ( ( ! [U_764,U_762] :
( ( U_762 = apply(U_759,U_764)
& in(U_764,relation_rng(U_760)) )
| U_764 != apply(U_760,U_762)
| ~ in(U_762,relation_dom(U_760)) )
& ! [U_763,U_761] :
( ( U_763 = apply(U_760,U_761)
& in(U_761,relation_dom(U_760)) )
| U_761 != apply(U_759,U_763)
| ~ in(U_763,relation_rng(U_760)) )
& relation_dom(U_759) = relation_rng(U_760) )
| U_759 != function_inverse(U_760) ) )
| ~ function(U_759)
| ~ relation(U_759) )
| ~ one_to_one(U_760)
| ~ function(U_760)
| ~ relation(U_760) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_767,sK102(U_760,U_759))],[f_204_3]) ).
fof(f_204_5,plain,
! [U_760] :
( ! [U_759] :
( ( ( U_759 = function_inverse(U_760)
| ? [U_768,U_766] :
( ( U_766 != apply(U_759,U_768)
| ~ in(U_768,relation_rng(U_760)) )
& U_768 = apply(U_760,U_766)
& in(U_766,relation_dom(U_760)) )
| ( ( sK102(U_760,U_759) != apply(U_760,sK103(U_760,U_759))
| ~ in(sK103(U_760,U_759),relation_dom(U_760)) )
& sK103(U_760,U_759) = apply(U_759,sK102(U_760,U_759))
& in(sK102(U_760,U_759),relation_rng(U_760)) )
| relation_dom(U_759) != relation_rng(U_760) )
& ( ( ! [U_764,U_762] :
( ( U_762 = apply(U_759,U_764)
& in(U_764,relation_rng(U_760)) )
| U_764 != apply(U_760,U_762)
| ~ in(U_762,relation_dom(U_760)) )
& ! [U_763,U_761] :
( ( U_763 = apply(U_760,U_761)
& in(U_761,relation_dom(U_760)) )
| U_761 != apply(U_759,U_763)
| ~ in(U_763,relation_rng(U_760)) )
& relation_dom(U_759) = relation_rng(U_760) )
| U_759 != function_inverse(U_760) ) )
| ~ function(U_759)
| ~ relation(U_759) )
| ~ one_to_one(U_760)
| ~ function(U_760)
| ~ relation(U_760) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(U_765,sK103(U_760,U_759))],[f_204_4]) ).
fof(f_204_6,plain,
! [U_760] :
( ! [U_759] :
( ( ( U_759 = function_inverse(U_760)
| ? [U_766] :
( ( U_766 != apply(U_759,sK104(U_760,U_759))
| ~ in(sK104(U_760,U_759),relation_rng(U_760)) )
& sK104(U_760,U_759) = apply(U_760,U_766)
& in(U_766,relation_dom(U_760)) )
| ( ( sK102(U_760,U_759) != apply(U_760,sK103(U_760,U_759))
| ~ in(sK103(U_760,U_759),relation_dom(U_760)) )
& sK103(U_760,U_759) = apply(U_759,sK102(U_760,U_759))
& in(sK102(U_760,U_759),relation_rng(U_760)) )
| relation_dom(U_759) != relation_rng(U_760) )
& ( ( ! [U_764,U_762] :
( ( U_762 = apply(U_759,U_764)
& in(U_764,relation_rng(U_760)) )
| U_764 != apply(U_760,U_762)
| ~ in(U_762,relation_dom(U_760)) )
& ! [U_763,U_761] :
( ( U_763 = apply(U_760,U_761)
& in(U_761,relation_dom(U_760)) )
| U_761 != apply(U_759,U_763)
| ~ in(U_763,relation_rng(U_760)) )
& relation_dom(U_759) = relation_rng(U_760) )
| U_759 != function_inverse(U_760) ) )
| ~ function(U_759)
| ~ relation(U_759) )
| ~ one_to_one(U_760)
| ~ function(U_760)
| ~ relation(U_760) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK104]),skolemize(U_768,sK104(U_760,U_759))],[f_204_5]) ).
fof(f_204_7,plain,
! [U_760] :
( ! [U_759] :
( ( ( U_759 = function_inverse(U_760)
| ( ( sK105(U_760,U_759) != apply(U_759,sK104(U_760,U_759))
| ~ in(sK104(U_760,U_759),relation_rng(U_760)) )
& sK104(U_760,U_759) = apply(U_760,sK105(U_760,U_759))
& in(sK105(U_760,U_759),relation_dom(U_760)) )
| ( ( sK102(U_760,U_759) != apply(U_760,sK103(U_760,U_759))
| ~ in(sK103(U_760,U_759),relation_dom(U_760)) )
& sK103(U_760,U_759) = apply(U_759,sK102(U_760,U_759))
& in(sK102(U_760,U_759),relation_rng(U_760)) )
| relation_dom(U_759) != relation_rng(U_760) )
& ( ( ! [U_764,U_762] :
( ( U_762 = apply(U_759,U_764)
& in(U_764,relation_rng(U_760)) )
| U_764 != apply(U_760,U_762)
| ~ in(U_762,relation_dom(U_760)) )
& ! [U_763,U_761] :
( ( U_763 = apply(U_760,U_761)
& in(U_761,relation_dom(U_760)) )
| U_761 != apply(U_759,U_763)
| ~ in(U_763,relation_rng(U_760)) )
& relation_dom(U_759) = relation_rng(U_760) )
| U_759 != function_inverse(U_760) ) )
| ~ function(U_759)
| ~ relation(U_759) )
| ~ one_to_one(U_760)
| ~ function(U_760)
| ~ relation(U_760) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK105]),skolemize(U_766,sK105(U_760,U_759))],[f_204_6]) ).
cnf(f_204_8,plain,
( relation_dom(U_759) = relation_rng(U_760)
| U_759 != function_inverse(U_760)
| ~ function(U_759)
| ~ relation(U_759)
| ~ one_to_one(U_760)
| ~ function(U_760)
| ~ relation(U_760) ),
inference(clausify,[status(thm)],[f_204_7]) ).
cnf(f_204_9,plain,
( in(U_761,relation_dom(U_760))
| U_761 != apply(U_759,U_763)
| ~ in(U_763,relation_rng(U_760))
| U_759 != function_inverse(U_760)
| ~ function(U_759)
| ~ relation(U_759)
| ~ one_to_one(U_760)
| ~ function(U_760)
| ~ relation(U_760) ),
inference(clausify,[status(thm)],[f_204_7]) ).
cnf(f_204_10,plain,
( U_763 = apply(U_760,U_761)
| U_761 != apply(U_759,U_763)
| ~ in(U_763,relation_rng(U_760))
| U_759 != function_inverse(U_760)
| ~ function(U_759)
| ~ relation(U_759)
| ~ one_to_one(U_760)
| ~ function(U_760)
| ~ relation(U_760) ),
inference(clausify,[status(thm)],[f_204_7]) ).
cnf(f_204_11,plain,
( in(U_764,relation_rng(U_760))
| U_764 != apply(U_760,U_762)
| ~ in(U_762,relation_dom(U_760))
| U_759 != function_inverse(U_760)
| ~ function(U_759)
| ~ relation(U_759)
| ~ one_to_one(U_760)
| ~ function(U_760)
| ~ relation(U_760) ),
inference(clausify,[status(thm)],[f_204_7]) ).
cnf(f_204_12,plain,
( U_762 = apply(U_759,U_764)
| U_764 != apply(U_760,U_762)
| ~ in(U_762,relation_dom(U_760))
| U_759 != function_inverse(U_760)
| ~ function(U_759)
| ~ relation(U_759)
| ~ one_to_one(U_760)
| ~ function(U_760)
| ~ relation(U_760) ),
inference(clausify,[status(thm)],[f_204_7]) ).
cnf(f_204_13,plain,
( in(sK105(U_760,U_759),relation_dom(U_760))
| in(sK102(U_760,U_759),relation_rng(U_760))
| relation_dom(U_759) != relation_rng(U_760)
| U_759 = function_inverse(U_760)
| ~ function(U_759)
| ~ relation(U_759)
| ~ one_to_one(U_760)
| ~ function(U_760)
| ~ relation(U_760) ),
inference(clausify,[status(thm)],[f_204_7]) ).
cnf(f_204_14,plain,
( sK104(U_760,U_759) = apply(U_760,sK105(U_760,U_759))
| in(sK102(U_760,U_759),relation_rng(U_760))
| relation_dom(U_759) != relation_rng(U_760)
| U_759 = function_inverse(U_760)
| ~ function(U_759)
| ~ relation(U_759)
| ~ one_to_one(U_760)
| ~ function(U_760)
| ~ relation(U_760) ),
inference(clausify,[status(thm)],[f_204_7]) ).
cnf(f_204_15,plain,
( in(sK105(U_760,U_759),relation_dom(U_760))
| sK103(U_760,U_759) = apply(U_759,sK102(U_760,U_759))
| relation_dom(U_759) != relation_rng(U_760)
| U_759 = function_inverse(U_760)
| ~ function(U_759)
| ~ relation(U_759)
| ~ one_to_one(U_760)
| ~ function(U_760)
| ~ relation(U_760) ),
inference(clausify,[status(thm)],[f_204_7]) ).
cnf(f_204_16,plain,
( sK104(U_760,U_759) = apply(U_760,sK105(U_760,U_759))
| sK103(U_760,U_759) = apply(U_759,sK102(U_760,U_759))
| relation_dom(U_759) != relation_rng(U_760)
| U_759 = function_inverse(U_760)
| ~ function(U_759)
| ~ relation(U_759)
| ~ one_to_one(U_760)
| ~ function(U_760)
| ~ relation(U_760) ),
inference(clausify,[status(thm)],[f_204_7]) ).
cnf(f_204_17,plain,
( in(sK102(U_760,U_759),relation_rng(U_760))
| sK105(U_760,U_759) != apply(U_759,sK104(U_760,U_759))
| ~ in(sK104(U_760,U_759),relation_rng(U_760))
| relation_dom(U_759) != relation_rng(U_760)
| U_759 = function_inverse(U_760)
| ~ function(U_759)
| ~ relation(U_759)
| ~ one_to_one(U_760)
| ~ function(U_760)
| ~ relation(U_760) ),
inference(clausify,[status(thm)],[f_204_7]) ).
cnf(f_204_18,plain,
( sK103(U_760,U_759) = apply(U_759,sK102(U_760,U_759))
| sK105(U_760,U_759) != apply(U_759,sK104(U_760,U_759))
| ~ in(sK104(U_760,U_759),relation_rng(U_760))
| relation_dom(U_759) != relation_rng(U_760)
| U_759 = function_inverse(U_760)
| ~ function(U_759)
| ~ relation(U_759)
| ~ one_to_one(U_760)
| ~ function(U_760)
| ~ relation(U_760) ),
inference(clausify,[status(thm)],[f_204_7]) ).
cnf(f_204_19,plain,
( in(sK105(U_760,U_759),relation_dom(U_760))
| sK102(U_760,U_759) != apply(U_760,sK103(U_760,U_759))
| ~ in(sK103(U_760,U_759),relation_dom(U_760))
| relation_dom(U_759) != relation_rng(U_760)
| U_759 = function_inverse(U_760)
| ~ function(U_759)
| ~ relation(U_759)
| ~ one_to_one(U_760)
| ~ function(U_760)
| ~ relation(U_760) ),
inference(clausify,[status(thm)],[f_204_7]) ).
cnf(f_204_20,plain,
( sK104(U_760,U_759) = apply(U_760,sK105(U_760,U_759))
| sK102(U_760,U_759) != apply(U_760,sK103(U_760,U_759))
| ~ in(sK103(U_760,U_759),relation_dom(U_760))
| relation_dom(U_759) != relation_rng(U_760)
| U_759 = function_inverse(U_760)
| ~ function(U_759)
| ~ relation(U_759)
| ~ one_to_one(U_760)
| ~ function(U_760)
| ~ relation(U_760) ),
inference(clausify,[status(thm)],[f_204_7]) ).
cnf(f_204_21,plain,
( sK105(U_760,U_759) != apply(U_759,sK104(U_760,U_759))
| ~ in(sK104(U_760,U_759),relation_rng(U_760))
| sK102(U_760,U_759) != apply(U_760,sK103(U_760,U_759))
| ~ in(sK103(U_760,U_759),relation_dom(U_760))
| relation_dom(U_759) != relation_rng(U_760)
| U_759 = function_inverse(U_760)
| ~ function(U_759)
| ~ relation(U_759)
| ~ one_to_one(U_760)
| ~ function(U_760)
| ~ relation(U_760) ),
inference(clausify,[status(thm)],[f_204_7]) ).
fof(f_205_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_205_2,plain,
! [U_771,U_770,U_769] :
( ~ in(U_770,U_769)
| ~ in(U_770,subset_complement(U_771,U_769))
| ~ element(U_769,powerset(U_771)) ),
inference(variable_rename,[status(thm)],[f_205_1]) ).
cnf(f_205_3,plain,
( ~ in(U_770,U_769)
| ~ in(U_770,subset_complement(U_771,U_769))
| ~ element(U_769,powerset(U_771)) ),
inference(clausify,[status(thm)],[f_205_2]) ).
fof(f_206_1,plain,
! [A] :
( ( relation_dom(A) = relation_rng(function_inverse(A))
& relation_rng(A) = relation_dom(function_inverse(A)) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t55_funct_1]) ).
fof(f_206_2,plain,
! [U_772] :
( ( relation_dom(U_772) = relation_rng(function_inverse(U_772))
& relation_rng(U_772) = relation_dom(function_inverse(U_772)) )
| ~ one_to_one(U_772)
| ~ function(U_772)
| ~ relation(U_772) ),
inference(variable_rename,[status(thm)],[f_206_1]) ).
cnf(f_206_3,plain,
( relation_rng(U_772) = relation_dom(function_inverse(U_772))
| ~ one_to_one(U_772)
| ~ function(U_772)
| ~ relation(U_772) ),
inference(clausify,[status(thm)],[f_206_2]) ).
cnf(f_206_4,plain,
( relation_dom(U_772) = relation_rng(function_inverse(U_772))
| ~ one_to_one(U_772)
| ~ function(U_772)
| ~ relation(U_772) ),
inference(clausify,[status(thm)],[f_206_2]) ).
fof(f_207_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_207_2,plain,
! [U_775] :
( U_775 = empty_set
| ? [U_774,U_773] : in(ordered_pair(U_774,U_773),U_775)
| ~ relation(U_775) ),
inference(variable_rename,[status(thm)],[f_207_1]) ).
fof(f_207_3,plain,
! [U_775] :
( U_775 = empty_set
| ? [U_773] : in(ordered_pair(sK106(U_775),U_773),U_775)
| ~ relation(U_775) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK106]),skolemize(U_774,sK106(U_775))],[f_207_2]) ).
fof(f_207_4,plain,
! [U_775] :
( U_775 = empty_set
| in(ordered_pair(sK106(U_775),sK107(U_775)),U_775)
| ~ relation(U_775) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(U_773,sK107(U_775))],[f_207_3]) ).
cnf(f_207_5,plain,
( U_775 = empty_set
| in(ordered_pair(sK106(U_775),sK107(U_775)),U_775)
| ~ relation(U_775) ),
inference(clausify,[status(thm)],[f_207_4]) ).
fof(f_208_1,plain,
! [A,B] :
( ( A = apply(relation_composition(function_inverse(B),B),A)
& A = apply(B,apply(function_inverse(B),A)) )
| ~ in(A,relation_rng(B))
| ~ one_to_one(B)
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t57_funct_1]) ).
fof(f_208_2,plain,
! [U_777,U_776] :
( ( U_777 = apply(relation_composition(function_inverse(U_776),U_776),U_777)
& U_777 = apply(U_776,apply(function_inverse(U_776),U_777)) )
| ~ in(U_777,relation_rng(U_776))
| ~ one_to_one(U_776)
| ~ function(U_776)
| ~ relation(U_776) ),
inference(variable_rename,[status(thm)],[f_208_1]) ).
cnf(f_208_3,plain,
( U_777 = apply(U_776,apply(function_inverse(U_776),U_777))
| ~ in(U_777,relation_rng(U_776))
| ~ one_to_one(U_776)
| ~ function(U_776)
| ~ relation(U_776) ),
inference(clausify,[status(thm)],[f_208_2]) ).
cnf(f_208_4,plain,
( U_777 = apply(relation_composition(function_inverse(U_776),U_776),U_777)
| ~ in(U_777,relation_rng(U_776))
| ~ one_to_one(U_776)
| ~ function(U_776)
| ~ relation(U_776) ),
inference(clausify,[status(thm)],[f_208_2]) ).
fof(f_209_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_209_2,plain,
! [U_780,U_779,U_778] :
( ~ empty(U_778)
| ~ element(U_779,powerset(U_778))
| ~ in(U_780,U_779) ),
inference(variable_rename,[status(thm)],[f_209_1]) ).
fof(f_209_3,plain,
! [U_780,U_779] :
( ! [U_778] :
( ~ empty(U_778)
| ~ element(U_779,powerset(U_778)) )
| ~ in(U_780,U_779) ),
inference(miniscope,[status(thm)],[f_209_2]) ).
cnf(f_209_4,plain,
( ~ empty(U_778)
| ~ element(U_779,powerset(U_778))
| ~ in(U_780,U_779) ),
inference(clausify,[status(thm)],[f_209_3]) ).
fof(f_210_1,plain,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(fof_nnf,[status(thm)],[t60_relat_1]) ).
cnf(f_210_2,plain,
relation_dom(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_210_1]) ).
cnf(f_210_3,plain,
relation_rng(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_210_1]) ).
fof(f_211_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t60_xboole_1]) ).
fof(f_211_2,plain,
! [U_782,U_781] :
( ~ proper_subset(U_781,U_782)
| ~ subset(U_782,U_781) ),
inference(variable_rename,[status(thm)],[f_211_1]) ).
cnf(f_211_3,plain,
( ~ proper_subset(U_781,U_782)
| ~ subset(U_782,U_781) ),
inference(clausify,[status(thm)],[f_211_2]) ).
fof(f_212_1,plain,
! [A] :
( one_to_one(function_inverse(A))
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t62_funct_1]) ).
fof(f_212_2,plain,
! [U_783] :
( one_to_one(function_inverse(U_783))
| ~ one_to_one(U_783)
| ~ function(U_783)
| ~ relation(U_783) ),
inference(variable_rename,[status(thm)],[f_212_1]) ).
cnf(f_212_3,plain,
( one_to_one(function_inverse(U_783))
| ~ one_to_one(U_783)
| ~ function(U_783)
| ~ relation(U_783) ),
inference(clausify,[status(thm)],[f_212_2]) ).
fof(f_213_1,plain,
! [A,B,C] :
( disjoint(A,C)
| ~ disjoint(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t63_xboole_1]) ).
fof(f_213_2,plain,
! [U_786,U_785,U_784] :
( disjoint(U_786,U_784)
| ~ disjoint(U_785,U_784)
| ~ subset(U_786,U_785) ),
inference(variable_rename,[status(thm)],[f_213_1]) ).
cnf(f_213_3,plain,
( disjoint(U_786,U_784)
| ~ disjoint(U_785,U_784)
| ~ subset(U_786,U_785) ),
inference(clausify,[status(thm)],[f_213_2]) ).
fof(f_214_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_214_2,plain,
! [U_787] :
( U_787 = empty_set
| ( relation_rng(U_787) != empty_set
& relation_dom(U_787) != empty_set )
| ~ relation(U_787) ),
inference(variable_rename,[status(thm)],[f_214_1]) ).
cnf(f_214_3,plain,
( relation_dom(U_787) != empty_set
| U_787 = empty_set
| ~ relation(U_787) ),
inference(clausify,[status(thm)],[f_214_2]) ).
cnf(f_214_4,plain,
( relation_rng(U_787) != empty_set
| U_787 = empty_set
| ~ relation(U_787) ),
inference(clausify,[status(thm)],[f_214_2]) ).
fof(f_215_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_215_2,plain,
! [U_788] :
( ( ( relation_dom(U_788) = empty_set
| relation_rng(U_788) != empty_set )
& ( relation_rng(U_788) = empty_set
| relation_dom(U_788) != empty_set ) )
| ~ relation(U_788) ),
inference(variable_rename,[status(thm)],[f_215_1]) ).
cnf(f_215_3,plain,
( relation_rng(U_788) = empty_set
| relation_dom(U_788) != empty_set
| ~ relation(U_788) ),
inference(clausify,[status(thm)],[f_215_2]) ).
cnf(f_215_4,plain,
( relation_dom(U_788) = empty_set
| relation_rng(U_788) != empty_set
| ~ relation(U_788) ),
inference(clausify,[status(thm)],[f_215_2]) ).
fof(f_216_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_216_2,plain,
! [U_790,U_789] :
( ( set_difference(U_790,singleton(U_789)) = U_790
| in(U_789,U_790) )
& ( ~ in(U_789,U_790)
| set_difference(U_790,singleton(U_789)) != U_790 ) ),
inference(variable_rename,[status(thm)],[f_216_1]) ).
fof(f_216_3,plain,
( ! [U_794,U_792] :
( set_difference(U_794,singleton(U_792)) = U_794
| in(U_792,U_794) )
& ! [U_793,U_791] :
( ~ in(U_791,U_793)
| set_difference(U_793,singleton(U_791)) != U_793 ) ),
inference(miniscope,[status(thm)],[f_216_2]) ).
cnf(f_216_4,plain,
( ~ in(U_791,U_793)
| set_difference(U_793,singleton(U_791)) != U_793 ),
inference(clausify,[status(thm)],[f_216_3]) ).
cnf(f_216_5,plain,
( set_difference(U_794,singleton(U_792)) = U_794
| in(U_792,U_794) ),
inference(clausify,[status(thm)],[f_216_3]) ).
fof(f_217_1,plain,
! [A,B] :
( ! [C] :
( ( ( B = relation_dom_restriction(C,A)
| ? [D] :
( apply(B,D) != apply(C,D)
& in(D,relation_dom(B)) )
| relation_dom(B) != set_intersection2(relation_dom(C),A) )
& ( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) )
| B != relation_dom_restriction(C,A) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t68_funct_1]) ).
fof(f_217_2,plain,
! [U_799,U_798] :
( ! [U_797] :
( ( ( U_798 = relation_dom_restriction(U_797,U_799)
| ? [U_796] :
( apply(U_798,U_796) != apply(U_797,U_796)
& in(U_796,relation_dom(U_798)) )
| relation_dom(U_798) != set_intersection2(relation_dom(U_797),U_799) )
& ( ( ! [U_795] :
( apply(U_798,U_795) = apply(U_797,U_795)
| ~ in(U_795,relation_dom(U_798)) )
& relation_dom(U_798) = set_intersection2(relation_dom(U_797),U_799) )
| U_798 != relation_dom_restriction(U_797,U_799) ) )
| ~ function(U_797)
| ~ relation(U_797) )
| ~ function(U_798)
| ~ relation(U_798) ),
inference(variable_rename,[status(thm)],[f_217_1]) ).
fof(f_217_3,plain,
! [U_799,U_798] :
( ! [U_797] :
( ( ( U_798 = relation_dom_restriction(U_797,U_799)
| ( apply(U_798,sK108(U_799,U_798,U_797)) != apply(U_797,sK108(U_799,U_798,U_797))
& in(sK108(U_799,U_798,U_797),relation_dom(U_798)) )
| relation_dom(U_798) != set_intersection2(relation_dom(U_797),U_799) )
& ( ( ! [U_795] :
( apply(U_798,U_795) = apply(U_797,U_795)
| ~ in(U_795,relation_dom(U_798)) )
& relation_dom(U_798) = set_intersection2(relation_dom(U_797),U_799) )
| U_798 != relation_dom_restriction(U_797,U_799) ) )
| ~ function(U_797)
| ~ relation(U_797) )
| ~ function(U_798)
| ~ relation(U_798) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK108]),skolemize(U_796,sK108(U_799,U_798,U_797))],[f_217_2]) ).
cnf(f_217_4,plain,
( relation_dom(U_798) = set_intersection2(relation_dom(U_797),U_799)
| U_798 != relation_dom_restriction(U_797,U_799)
| ~ function(U_797)
| ~ relation(U_797)
| ~ function(U_798)
| ~ relation(U_798) ),
inference(clausify,[status(thm)],[f_217_3]) ).
cnf(f_217_5,plain,
( apply(U_798,U_795) = apply(U_797,U_795)
| ~ in(U_795,relation_dom(U_798))
| U_798 != relation_dom_restriction(U_797,U_799)
| ~ function(U_797)
| ~ relation(U_797)
| ~ function(U_798)
| ~ relation(U_798) ),
inference(clausify,[status(thm)],[f_217_3]) ).
cnf(f_217_6,plain,
( in(sK108(U_799,U_798,U_797),relation_dom(U_798))
| relation_dom(U_798) != set_intersection2(relation_dom(U_797),U_799)
| U_798 = relation_dom_restriction(U_797,U_799)
| ~ function(U_797)
| ~ relation(U_797)
| ~ function(U_798)
| ~ relation(U_798) ),
inference(clausify,[status(thm)],[f_217_3]) ).
cnf(f_217_7,plain,
( apply(U_798,sK108(U_799,U_798,U_797)) != apply(U_797,sK108(U_799,U_798,U_797))
| relation_dom(U_798) != set_intersection2(relation_dom(U_797),U_799)
| U_798 = relation_dom_restriction(U_797,U_799)
| ~ function(U_797)
| ~ relation(U_797)
| ~ function(U_798)
| ~ relation(U_798) ),
inference(clausify,[status(thm)],[f_217_3]) ).
fof(f_218_1,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(fof_nnf,[status(thm)],[t69_enumset1]) ).
fof(f_218_2,plain,
! [U_800] : unordered_pair(U_800,U_800) = singleton(U_800),
inference(variable_rename,[status(thm)],[f_218_1]) ).
cnf(f_218_3,plain,
unordered_pair(U_800,U_800) = singleton(U_800),
inference(clausify,[status(thm)],[f_218_2]) ).
fof(f_219_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_219_2,plain,
! [U_801] :
( U_801 = empty_set
| ~ empty(U_801) ),
inference(variable_rename,[status(thm)],[f_219_1]) ).
cnf(f_219_3,plain,
( U_801 = empty_set
| ~ empty(U_801) ),
inference(clausify,[status(thm)],[f_219_2]) ).
fof(f_220_1,plain,
! [A,B] :
( A = B
| ~ subset(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t6_zfmisc_1]) ).
fof(f_220_2,plain,
! [U_803,U_802] :
( U_803 = U_802
| ~ subset(singleton(U_803),singleton(U_802)) ),
inference(variable_rename,[status(thm)],[f_220_1]) ).
cnf(f_220_3,plain,
( U_803 = U_802
| ~ subset(singleton(U_803),singleton(U_802)) ),
inference(clausify,[status(thm)],[f_220_2]) ).
fof(f_221_1,plain,
! [A,B,C] :
( apply(relation_dom_restriction(C,A),B) = apply(C,B)
| ~ in(B,relation_dom(relation_dom_restriction(C,A)))
| ~ function(C)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t70_funct_1]) ).
fof(f_221_2,plain,
! [U_806,U_805,U_804] :
( apply(relation_dom_restriction(U_804,U_806),U_805) = apply(U_804,U_805)
| ~ in(U_805,relation_dom(relation_dom_restriction(U_804,U_806)))
| ~ function(U_804)
| ~ relation(U_804) ),
inference(variable_rename,[status(thm)],[f_221_1]) ).
cnf(f_221_3,plain,
( apply(relation_dom_restriction(U_804,U_806),U_805) = apply(U_804,U_805)
| ~ in(U_805,relation_dom(relation_dom_restriction(U_804,U_806)))
| ~ function(U_804)
| ~ relation(U_804) ),
inference(clausify,[status(thm)],[f_221_2]) ).
fof(f_222_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_222_2,plain,
! [U_807] :
( relation_rng(identity_relation(U_807)) = U_807
& relation_dom(identity_relation(U_807)) = U_807 ),
inference(variable_rename,[status(thm)],[f_222_1]) ).
fof(f_222_3,plain,
( ! [U_809] : relation_rng(identity_relation(U_809)) = U_809
& ! [U_808] : relation_dom(identity_relation(U_808)) = U_808 ),
inference(miniscope,[status(thm)],[f_222_2]) ).
cnf(f_222_4,plain,
relation_dom(identity_relation(U_808)) = U_808,
inference(clausify,[status(thm)],[f_222_3]) ).
cnf(f_222_5,plain,
relation_rng(identity_relation(U_809)) = U_809,
inference(clausify,[status(thm)],[f_222_3]) ).
fof(f_223_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_223_2,plain,
! [U_813,U_812,U_811,U_810] :
( ( ( in(ordered_pair(U_813,U_812),relation_composition(identity_relation(U_811),U_810))
| ~ in(ordered_pair(U_813,U_812),U_810)
| ~ in(U_813,U_811) )
& ( ( in(ordered_pair(U_813,U_812),U_810)
& in(U_813,U_811) )
| ~ in(ordered_pair(U_813,U_812),relation_composition(identity_relation(U_811),U_810)) ) )
| ~ relation(U_810) ),
inference(variable_rename,[status(thm)],[f_223_1]) ).
cnf(f_223_3,plain,
( in(U_813,U_811)
| ~ in(ordered_pair(U_813,U_812),relation_composition(identity_relation(U_811),U_810))
| ~ relation(U_810) ),
inference(clausify,[status(thm)],[f_223_2]) ).
cnf(f_223_4,plain,
( in(ordered_pair(U_813,U_812),U_810)
| ~ in(ordered_pair(U_813,U_812),relation_composition(identity_relation(U_811),U_810))
| ~ relation(U_810) ),
inference(clausify,[status(thm)],[f_223_2]) ).
cnf(f_223_5,plain,
( in(ordered_pair(U_813,U_812),relation_composition(identity_relation(U_811),U_810))
| ~ in(ordered_pair(U_813,U_812),U_810)
| ~ in(U_813,U_811)
| ~ relation(U_810) ),
inference(clausify,[status(thm)],[f_223_2]) ).
fof(f_224_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_224_2,plain,
! [U_815,U_814] :
( ~ empty(U_814)
| ~ in(U_815,U_814) ),
inference(variable_rename,[status(thm)],[f_224_1]) ).
cnf(f_224_3,plain,
( ~ empty(U_814)
| ~ in(U_815,U_814) ),
inference(clausify,[status(thm)],[f_224_2]) ).
fof(f_225_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1]) ).
fof(f_225_2,plain,
! [U_817,U_816] : subset(U_817,set_union2(U_817,U_816)),
inference(variable_rename,[status(thm)],[f_225_1]) ).
cnf(f_225_3,plain,
subset(U_817,set_union2(U_817,U_816)),
inference(clausify,[status(thm)],[f_225_2]) ).
fof(f_226_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_226_2,plain,
! [U_819,U_818] :
( ( disjoint(U_819,U_818)
| set_difference(U_819,U_818) != U_819 )
& ( set_difference(U_819,U_818) = U_819
| ~ disjoint(U_819,U_818) ) ),
inference(variable_rename,[status(thm)],[f_226_1]) ).
fof(f_226_3,plain,
( ! [U_823,U_821] :
( disjoint(U_823,U_821)
| set_difference(U_823,U_821) != U_823 )
& ! [U_822,U_820] :
( set_difference(U_822,U_820) = U_822
| ~ disjoint(U_822,U_820) ) ),
inference(miniscope,[status(thm)],[f_226_2]) ).
cnf(f_226_4,plain,
( set_difference(U_822,U_820) = U_822
| ~ disjoint(U_822,U_820) ),
inference(clausify,[status(thm)],[f_226_3]) ).
cnf(f_226_5,plain,
( disjoint(U_823,U_821)
| set_difference(U_823,U_821) != U_823 ),
inference(clausify,[status(thm)],[f_226_3]) ).
fof(f_227_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_227_2,plain,
! [U_826,U_825,U_824] :
( ( ( in(U_826,relation_dom(relation_dom_restriction(U_824,U_825)))
| ~ in(U_826,relation_dom(U_824))
| ~ in(U_826,U_825) )
& ( ( in(U_826,relation_dom(U_824))
& in(U_826,U_825) )
| ~ in(U_826,relation_dom(relation_dom_restriction(U_824,U_825))) ) )
| ~ relation(U_824) ),
inference(variable_rename,[status(thm)],[f_227_1]) ).
cnf(f_227_3,plain,
( in(U_826,U_825)
| ~ in(U_826,relation_dom(relation_dom_restriction(U_824,U_825)))
| ~ relation(U_824) ),
inference(clausify,[status(thm)],[f_227_2]) ).
cnf(f_227_4,plain,
( in(U_826,relation_dom(U_824))
| ~ in(U_826,relation_dom(relation_dom_restriction(U_824,U_825)))
| ~ relation(U_824) ),
inference(clausify,[status(thm)],[f_227_2]) ).
cnf(f_227_5,plain,
( in(U_826,relation_dom(relation_dom_restriction(U_824,U_825)))
| ~ in(U_826,relation_dom(U_824))
| ~ in(U_826,U_825)
| ~ relation(U_824) ),
inference(clausify,[status(thm)],[f_227_2]) ).
fof(f_228_1,plain,
! [A,B] :
( subset(relation_dom_restriction(B,A),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t88_relat_1]) ).
fof(f_228_2,plain,
! [U_828,U_827] :
( subset(relation_dom_restriction(U_827,U_828),U_827)
| ~ relation(U_827) ),
inference(variable_rename,[status(thm)],[f_228_1]) ).
cnf(f_228_3,plain,
( subset(relation_dom_restriction(U_827,U_828),U_827)
| ~ relation(U_827) ),
inference(clausify,[status(thm)],[f_228_2]) ).
fof(f_229_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_229_2,plain,
! [U_830,U_829] :
( ~ empty(U_829)
| U_830 = U_829
| ~ empty(U_830) ),
inference(variable_rename,[status(thm)],[f_229_1]) ).
fof(f_229_3,plain,
! [U_830] :
( ! [U_829] :
( ~ empty(U_829)
| U_830 = U_829 )
| ~ empty(U_830) ),
inference(miniscope,[status(thm)],[f_229_2]) ).
cnf(f_229_4,plain,
( ~ empty(U_829)
| U_830 = U_829
| ~ empty(U_830) ),
inference(clausify,[status(thm)],[f_229_3]) ).
fof(f_230_1,plain,
! [A,B,C] :
( ( ( in(ordered_pair(A,B),C)
| B != apply(C,A)
| ~ in(A,relation_dom(C)) )
& ( ( B = apply(C,A)
& in(A,relation_dom(C)) )
| ~ in(ordered_pair(A,B),C) ) )
| ~ function(C)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t8_funct_1]) ).
fof(f_230_2,plain,
! [U_833,U_832,U_831] :
( ( ( in(ordered_pair(U_833,U_832),U_831)
| U_832 != apply(U_831,U_833)
| ~ in(U_833,relation_dom(U_831)) )
& ( ( U_832 = apply(U_831,U_833)
& in(U_833,relation_dom(U_831)) )
| ~ in(ordered_pair(U_833,U_832),U_831) ) )
| ~ function(U_831)
| ~ relation(U_831) ),
inference(variable_rename,[status(thm)],[f_230_1]) ).
cnf(f_230_3,plain,
( in(U_833,relation_dom(U_831))
| ~ in(ordered_pair(U_833,U_832),U_831)
| ~ function(U_831)
| ~ relation(U_831) ),
inference(clausify,[status(thm)],[f_230_2]) ).
cnf(f_230_4,plain,
( U_832 = apply(U_831,U_833)
| ~ in(ordered_pair(U_833,U_832),U_831)
| ~ function(U_831)
| ~ relation(U_831) ),
inference(clausify,[status(thm)],[f_230_2]) ).
cnf(f_230_5,plain,
( in(ordered_pair(U_833,U_832),U_831)
| U_832 != apply(U_831,U_833)
| ~ in(U_833,relation_dom(U_831))
| ~ function(U_831)
| ~ relation(U_831) ),
inference(clausify,[status(thm)],[f_230_2]) ).
fof(f_231_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_231_2,plain,
! [U_836,U_835,U_834] :
( subset(set_union2(U_836,U_834),U_835)
| ~ subset(U_834,U_835)
| ~ subset(U_836,U_835) ),
inference(variable_rename,[status(thm)],[f_231_1]) ).
cnf(f_231_3,plain,
( subset(set_union2(U_836,U_834),U_835)
| ~ subset(U_834,U_835)
| ~ subset(U_836,U_835) ),
inference(clausify,[status(thm)],[f_231_2]) ).
fof(f_232_1,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t8_zfmisc_1]) ).
fof(f_232_2,plain,
! [U_839,U_838,U_837] :
( U_839 = U_838
| singleton(U_839) != unordered_pair(U_838,U_837) ),
inference(variable_rename,[status(thm)],[f_232_1]) ).
fof(f_232_3,plain,
! [U_839,U_838] :
( ! [U_837] : singleton(U_839) != unordered_pair(U_838,U_837)
| U_839 = U_838 ),
inference(miniscope,[status(thm)],[f_232_2]) ).
cnf(f_232_4,plain,
( singleton(U_839) != unordered_pair(U_838,U_837)
| U_839 = U_838 ),
inference(clausify,[status(thm)],[f_232_3]) ).
fof(f_233_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_233_2,plain,
! [U_841,U_840] :
( relation_dom(relation_dom_restriction(U_840,U_841)) = set_intersection2(relation_dom(U_840),U_841)
| ~ relation(U_840) ),
inference(variable_rename,[status(thm)],[f_233_1]) ).
cnf(f_233_3,plain,
( relation_dom(relation_dom_restriction(U_840,U_841)) = set_intersection2(relation_dom(U_840),U_841)
| ~ relation(U_840) ),
inference(clausify,[status(thm)],[f_233_2]) ).
fof(f_234_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t92_zfmisc_1]) ).
fof(f_234_2,plain,
! [U_843,U_842] :
( subset(U_843,union(U_842))
| ~ in(U_843,U_842) ),
inference(variable_rename,[status(thm)],[f_234_1]) ).
cnf(f_234_3,plain,
( subset(U_843,union(U_842))
| ~ in(U_843,U_842) ),
inference(clausify,[status(thm)],[f_234_2]) ).
fof(f_235_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_235_2,plain,
! [U_845,U_844] :
( relation_dom_restriction(U_844,U_845) = relation_composition(identity_relation(U_845),U_844)
| ~ relation(U_844) ),
inference(variable_rename,[status(thm)],[f_235_1]) ).
cnf(f_235_3,plain,
( relation_dom_restriction(U_844,U_845) = relation_composition(identity_relation(U_845),U_844)
| ~ relation(U_844) ),
inference(clausify,[status(thm)],[f_235_2]) ).
fof(f_236_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_236_2,plain,
! [U_847,U_846] :
( subset(relation_rng(relation_dom_restriction(U_846,U_847)),relation_rng(U_846))
| ~ relation(U_846) ),
inference(variable_rename,[status(thm)],[f_236_1]) ).
cnf(f_236_3,plain,
( subset(relation_rng(relation_dom_restriction(U_846,U_847)),relation_rng(U_846))
| ~ relation(U_846) ),
inference(clausify,[status(thm)],[f_236_2]) ).
fof(f_237_1,plain,
! [A] : union(powerset(A)) = A,
inference(fof_nnf,[status(thm)],[t99_zfmisc_1]) ).
fof(f_237_2,plain,
! [U_848] : union(powerset(U_848)) = U_848,
inference(variable_rename,[status(thm)],[f_237_1]) ).
cnf(f_237_3,plain,
union(powerset(U_848)) = U_848,
inference(clausify,[status(thm)],[f_237_2]) ).
fof(f_238_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_238_2,plain,
! [U_856] :
? [U_855] :
( ! [U_854] :
( in(U_854,U_855)
| are_equipotent(U_854,U_855)
| ~ subset(U_854,U_855) )
& ! [U_853] :
( ? [U_852] :
( ! [U_851] :
( in(U_851,U_852)
| ~ subset(U_851,U_853) )
& in(U_852,U_855) )
| ~ in(U_853,U_855) )
& ! [U_850,U_849] :
( in(U_849,U_855)
| ~ subset(U_849,U_850)
| ~ in(U_850,U_855) )
& in(U_856,U_855) ),
inference(variable_rename,[status(thm)],[f_238_1]) ).
fof(f_238_3,plain,
! [U_856] :
( ! [U_854] :
( in(U_854,sK109(U_856))
| are_equipotent(U_854,sK109(U_856))
| ~ subset(U_854,sK109(U_856)) )
& ! [U_853] :
( ? [U_852] :
( ! [U_851] :
( in(U_851,U_852)
| ~ subset(U_851,U_853) )
& in(U_852,sK109(U_856)) )
| ~ in(U_853,sK109(U_856)) )
& ! [U_850,U_849] :
( in(U_849,sK109(U_856))
| ~ subset(U_849,U_850)
| ~ in(U_850,sK109(U_856)) )
& in(U_856,sK109(U_856)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK109]),skolemize(U_855,sK109(U_856))],[f_238_2]) ).
fof(f_238_4,plain,
! [U_856] :
( ! [U_854] :
( in(U_854,sK109(U_856))
| are_equipotent(U_854,sK109(U_856))
| ~ subset(U_854,sK109(U_856)) )
& ! [U_853] :
( ( ! [U_851] :
( in(U_851,sK110(U_856,U_853))
| ~ subset(U_851,U_853) )
& in(sK110(U_856,U_853),sK109(U_856)) )
| ~ in(U_853,sK109(U_856)) )
& ! [U_850,U_849] :
( in(U_849,sK109(U_856))
| ~ subset(U_849,U_850)
| ~ in(U_850,sK109(U_856)) )
& in(U_856,sK109(U_856)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK110]),skolemize(U_852,sK110(U_856,U_853))],[f_238_3]) ).
cnf(f_238_5,plain,
in(U_856,sK109(U_856)),
inference(clausify,[status(thm)],[f_238_4]) ).
cnf(f_238_6,plain,
( in(U_849,sK109(U_856))
| ~ subset(U_849,U_850)
| ~ in(U_850,sK109(U_856)) ),
inference(clausify,[status(thm)],[f_238_4]) ).
cnf(f_238_7,plain,
( in(sK110(U_856,U_853),sK109(U_856))
| ~ in(U_853,sK109(U_856)) ),
inference(clausify,[status(thm)],[f_238_4]) ).
cnf(f_238_8,plain,
( in(U_851,sK110(U_856,U_853))
| ~ subset(U_851,U_853)
| ~ in(U_853,sK109(U_856)) ),
inference(clausify,[status(thm)],[f_238_4]) ).
cnf(f_238_9,plain,
( in(U_854,sK109(U_856))
| are_equipotent(U_854,sK109(U_856))
| ~ subset(U_854,sK109(U_856)) ),
inference(clausify,[status(thm)],[f_238_4]) ).
fof(f_239_1,plain,
! [A,B,C] :
( B = C
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t9_zfmisc_1]) ).
fof(f_239_2,plain,
! [U_859,U_858,U_857] :
( U_858 = U_857
| singleton(U_859) != unordered_pair(U_858,U_857) ),
inference(variable_rename,[status(thm)],[f_239_1]) ).
cnf(f_239_3,plain,
( U_858 = U_857
| singleton(U_859) != unordered_pair(U_858,U_857) ),
inference(clausify,[status(thm)],[f_239_2]) ).
cnf(f_5_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_3]) ).
cnf(f_5_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_4]) ).
cnf(f_41_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_41_8]) ).
cnf(f_41_9_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_41_9]) ).
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_46_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_46_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_54_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_54_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_57_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_57_2]) ).
cnf(f_59_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_59_2]) ).
cnf(f_60_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_60_2]) ).
cnf(f_62_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_62_2]) ).
cnf(f_63_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_63_2]) ).
cnf(f_72_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_72_2]) ).
cnf(f_73_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_73_2]) ).
cnf(f_117_11_true,negated_conjecture,
$true,
inference(clause_is_true,[status(thm)],[f_117_11]) ).
cnf(f_117_12_true,negated_conjecture,
$true,
inference(clause_is_true,[status(thm)],[f_117_12]) ).
cnf(f_117_13_true,negated_conjecture,
$true,
inference(clause_is_true,[status(thm)],[f_117_13]) ).
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,
( apply(Eq_x_0,Eq_x_1) = apply(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( cast_to_subset(Eq_x_0) = cast_to_subset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( union(Eq_x_0) = union(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,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_22,axiom,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,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_24,axiom,
( relation_field(Eq_x_0) = relation_field(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( relation_inverse(Eq_x_0) = relation_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,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_27,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_28,axiom,
( function_inverse(Eq_x_0) = function_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_29,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_30,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_31,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_32,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_33,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_34,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_35,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_36,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_37,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_38,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_39,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_40,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_41,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_42,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_43,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_44,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_45,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_46,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_47,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_48,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_49,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_50,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_51,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_52,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_53,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_54,axiom,
( sK23(Eq_x_0) = sK23(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_55,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_56,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_57,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_58,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_59,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_60,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_61,axiom,
( sK30(Eq_x_0) = sK30(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_62,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_63,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_64,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_65,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_66,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_67,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_68,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_69,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_70,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_71,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_72,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_73,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_74,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_75,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_76,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_77,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_78,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_79,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_80,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_81,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_82,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_83,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_84,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_85,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_86,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_87,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_88,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_89,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_90,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_91,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_92,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_93,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_94,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_95,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_96,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_97,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_98,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_99,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_100,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_101,axiom,
( sK70(Eq_x_0) = sK70(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_102,axiom,
( sK71(Eq_x_0) = sK71(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_103,axiom,
( sK72(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK72(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_104,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_105,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_106,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_107,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_108,axiom,
( sK77(Eq_x_0,Eq_x_1,Eq_x_2) = sK77(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_109,axiom,
( sK78(Eq_x_0,Eq_x_1,Eq_x_2) = sK78(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_110,axiom,
( sK79(Eq_x_0) = sK79(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_111,axiom,
( sK80(Eq_x_0,Eq_x_1) = sK80(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_112,axiom,
( sK86(Eq_x_0) = sK86(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_113,axiom,
( sK90(Eq_x_0) = sK90(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_114,axiom,
( sK94(Eq_x_0) = sK94(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_115,axiom,
( sK95(Eq_x_0,Eq_x_1,Eq_x_2) = sK95(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_116,axiom,
( sK96(Eq_x_0,Eq_x_1,Eq_x_2) = sK96(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_117,axiom,
( sK97(Eq_x_0,Eq_x_1) = sK97(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_118,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_119,axiom,
( sK99(Eq_x_0,Eq_x_1) = sK99(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_120,axiom,
( sK100(Eq_x_0,Eq_x_1) = sK100(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,
( sK101(Eq_x_0,Eq_x_1) = sK101(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_122,axiom,
( sK102(Eq_x_0,Eq_x_1) = sK102(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_123,axiom,
( sK103(Eq_x_0,Eq_x_1) = sK103(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_124,axiom,
( sK104(Eq_x_0,Eq_x_1) = sK104(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_125,axiom,
( sK105(Eq_x_0,Eq_x_1) = sK105(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_126,axiom,
( sK106(Eq_x_0) = sK106(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_127,axiom,
( sK107(Eq_x_0) = sK107(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_128,axiom,
( sK108(Eq_x_0,Eq_x_1,Eq_x_2) = sK108(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_129,axiom,
( sK109(Eq_x_0) = sK109(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_130,axiom,
( sK110(Eq_x_0,Eq_x_1) = sK110(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_131,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_132,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_133,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_134,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_135,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_136,axiom,
( one_to_one(Eq_y_0)
| ~ one_to_one(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_137,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_138,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_139,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_140,axiom,
( relation_empty_yielding(Eq_y_0)
| ~ relation_empty_yielding(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_141,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 : SEU224+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 23:35:05 UTC 2026
% 0.10/0.37 % CPUTime :
% 81.55/81.81 % SZS status Theorem for theBenchmark
% 81.55/81.81 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------