%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU230+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 08:58:36 AM UTC 2026
% Result : Theorem 83.32s 83.67s
% Output : Proof 83.42s
% 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_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( C = relation_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( D = apply(A,E)
& in(E,B)
& in(E,relation_dom(A)) ) ) ) ),
file('theBenchmark.p',d12_funct_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_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(apply(A,D),B)
& in(D,relation_dom(A)) ) ) ) ),
file('theBenchmark.p',d13_funct_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_enumset1,axiom,
! [A,B,C,D] :
( D = unordered_triple(A,B,C)
<=> ! [E] :
( in(E,D)
<=> ~ ( E != C
& E != B
& E != A ) ) ),
file('theBenchmark.p',d1_enumset1) ).
fof(d1_ordinal1,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('theBenchmark.p',d1_ordinal1) ).
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_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) ) ) ),
file('theBenchmark.p',d5_funct_1) ).
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_enumset1,axiom,
$true,
file('theBenchmark.p',dt_k1_enumset1) ).
fof(dt_k1_funct_1,axiom,
$true,
file('theBenchmark.p',dt_k1_funct_1) ).
fof(dt_k1_ordinal1,axiom,
$true,
file('theBenchmark.p',dt_k1_ordinal1) ).
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_ordinal1,axiom,
! [A] : ~ empty(succ(A)),
file('theBenchmark.p',fc1_ordinal1) ).
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,lemma,
! [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(rc4_funct_1,axiom,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc4_funct_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_ordinal1,conjecture,
! [A] : in(A,succ(A)),
file('theBenchmark.p',t10_ordinal1) ).
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_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> subset(relation_image(B,relation_inverse_image(B,A)),A) ),
file('theBenchmark.p',t145_funct_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_funct_1,lemma,
! [A,B] :
( relation(B)
=> ( subset(A,relation_dom(B))
=> subset(A,relation_inverse_image(B,relation_image(B,A))) ) ),
file('theBenchmark.p',t146_funct_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(t147_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( subset(A,relation_rng(B))
=> relation_image(B,relation_inverse_image(B,A)) = A ) ),
file('theBenchmark.p',t147_funct_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_ordinal1,lemma,
! [A,B,C] :
~ ( in(C,A)
& in(B,C)
& in(A,B) ),
file('theBenchmark.p',t3_ordinal1) ).
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(t72_funct_1,lemma,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,A)
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
file('theBenchmark.p',t72_funct_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_tarski,axiom,
! [A,B] :
~ ( ! [C] :
~ ( ! [D] :
~ ( in(D,C)
& in(D,B) )
& in(C,B) )
& in(A,B) ),
file('theBenchmark.p',t7_tarski) ).
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_image(A,B)
| ? [D] :
( ( ~ in(D,C)
& ? [E] :
( D = apply(A,E)
& in(E,B)
& in(E,relation_dom(A)) ) )
| ( ! [E] :
( D != apply(A,E)
| ~ in(E,B)
| ~ in(E,relation_dom(A)) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ! [E] :
( D != apply(A,E)
| ~ in(E,B)
| ~ in(E,relation_dom(A)) ) )
& ( ? [E] :
( D = apply(A,E)
& in(E,B)
& in(E,relation_dom(A)) )
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d12_funct_1]) ).
fof(f_12_2,plain,
! [U_56] :
( ! [U_55,U_54] :
( ( U_54 = relation_image(U_56,U_55)
| ? [U_53] :
( ( ~ in(U_53,U_54)
& ? [U_52] :
( U_53 = apply(U_56,U_52)
& in(U_52,U_55)
& in(U_52,relation_dom(U_56)) ) )
| ( ! [U_51] :
( U_53 != apply(U_56,U_51)
| ~ in(U_51,U_55)
| ~ in(U_51,relation_dom(U_56)) )
& in(U_53,U_54) ) ) )
& ( ! [U_50] :
( ( in(U_50,U_54)
| ! [U_49] :
( U_50 != apply(U_56,U_49)
| ~ in(U_49,U_55)
| ~ in(U_49,relation_dom(U_56)) ) )
& ( ? [U_48] :
( U_50 = apply(U_56,U_48)
& in(U_48,U_55)
& in(U_48,relation_dom(U_56)) )
| ~ in(U_50,U_54) ) )
| U_54 != relation_image(U_56,U_55) ) )
| ~ function(U_56)
| ~ relation(U_56) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_56] :
( ( ! [U_64,U_62] :
( U_62 = relation_image(U_56,U_64)
| ? [U_60] :
( ~ in(U_60,U_62)
& ? [U_52] :
( U_60 = apply(U_56,U_52)
& in(U_52,U_64)
& in(U_52,relation_dom(U_56)) ) )
| ? [U_59] :
( ! [U_51] :
( U_59 != apply(U_56,U_51)
| ~ in(U_51,U_64)
| ~ in(U_51,relation_dom(U_56)) )
& in(U_59,U_62) ) )
& ! [U_63,U_61] :
( ( ! [U_58] :
( in(U_58,U_61)
| ! [U_49] :
( U_58 != apply(U_56,U_49)
| ~ in(U_49,U_63)
| ~ in(U_49,relation_dom(U_56)) ) )
& ! [U_57] :
( ? [U_48] :
( U_57 = apply(U_56,U_48)
& in(U_48,U_63)
& in(U_48,relation_dom(U_56)) )
| ~ in(U_57,U_61) ) )
| U_61 != relation_image(U_56,U_63) ) )
| ~ function(U_56)
| ~ relation(U_56) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
! [U_56] :
( ( ! [U_64,U_62] :
( U_62 = relation_image(U_56,U_64)
| ? [U_60] :
( ~ in(U_60,U_62)
& ? [U_52] :
( U_60 = apply(U_56,U_52)
& in(U_52,U_64)
& in(U_52,relation_dom(U_56)) ) )
| ? [U_59] :
( ! [U_51] :
( U_59 != apply(U_56,U_51)
| ~ in(U_51,U_64)
| ~ in(U_51,relation_dom(U_56)) )
& in(U_59,U_62) ) )
& ! [U_63,U_61] :
( ( ! [U_58] :
( in(U_58,U_61)
| ! [U_49] :
( U_58 != apply(U_56,U_49)
| ~ in(U_49,U_63)
| ~ in(U_49,relation_dom(U_56)) ) )
& ! [U_57] :
( ( U_57 = apply(U_56,sK9(U_56,U_63,U_61,U_57))
& in(sK9(U_56,U_63,U_61,U_57),U_63)
& in(sK9(U_56,U_63,U_61,U_57),relation_dom(U_56)) )
| ~ in(U_57,U_61) ) )
| U_61 != relation_image(U_56,U_63) ) )
| ~ function(U_56)
| ~ relation(U_56) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_48,sK9(U_56,U_63,U_61,U_57))],[f_12_3]) ).
fof(f_12_5,plain,
! [U_56] :
( ( ! [U_64,U_62] :
( U_62 = relation_image(U_56,U_64)
| ? [U_60] :
( ~ in(U_60,U_62)
& ? [U_52] :
( U_60 = apply(U_56,U_52)
& in(U_52,U_64)
& in(U_52,relation_dom(U_56)) ) )
| ( ! [U_51] :
( sK10(U_56,U_64,U_62) != apply(U_56,U_51)
| ~ in(U_51,U_64)
| ~ in(U_51,relation_dom(U_56)) )
& in(sK10(U_56,U_64,U_62),U_62) ) )
& ! [U_63,U_61] :
( ( ! [U_58] :
( in(U_58,U_61)
| ! [U_49] :
( U_58 != apply(U_56,U_49)
| ~ in(U_49,U_63)
| ~ in(U_49,relation_dom(U_56)) ) )
& ! [U_57] :
( ( U_57 = apply(U_56,sK9(U_56,U_63,U_61,U_57))
& in(sK9(U_56,U_63,U_61,U_57),U_63)
& in(sK9(U_56,U_63,U_61,U_57),relation_dom(U_56)) )
| ~ in(U_57,U_61) ) )
| U_61 != relation_image(U_56,U_63) ) )
| ~ function(U_56)
| ~ relation(U_56) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_59,sK10(U_56,U_64,U_62))],[f_12_4]) ).
fof(f_12_6,plain,
! [U_56] :
( ( ! [U_64,U_62] :
( U_62 = relation_image(U_56,U_64)
| ( ~ in(sK11(U_56,U_64,U_62),U_62)
& ? [U_52] :
( sK11(U_56,U_64,U_62) = apply(U_56,U_52)
& in(U_52,U_64)
& in(U_52,relation_dom(U_56)) ) )
| ( ! [U_51] :
( sK10(U_56,U_64,U_62) != apply(U_56,U_51)
| ~ in(U_51,U_64)
| ~ in(U_51,relation_dom(U_56)) )
& in(sK10(U_56,U_64,U_62),U_62) ) )
& ! [U_63,U_61] :
( ( ! [U_58] :
( in(U_58,U_61)
| ! [U_49] :
( U_58 != apply(U_56,U_49)
| ~ in(U_49,U_63)
| ~ in(U_49,relation_dom(U_56)) ) )
& ! [U_57] :
( ( U_57 = apply(U_56,sK9(U_56,U_63,U_61,U_57))
& in(sK9(U_56,U_63,U_61,U_57),U_63)
& in(sK9(U_56,U_63,U_61,U_57),relation_dom(U_56)) )
| ~ in(U_57,U_61) ) )
| U_61 != relation_image(U_56,U_63) ) )
| ~ function(U_56)
| ~ relation(U_56) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_60,sK11(U_56,U_64,U_62))],[f_12_5]) ).
fof(f_12_7,plain,
! [U_56] :
( ( ! [U_64,U_62] :
( U_62 = relation_image(U_56,U_64)
| ( ~ in(sK11(U_56,U_64,U_62),U_62)
& sK11(U_56,U_64,U_62) = apply(U_56,sK12(U_56,U_64,U_62))
& in(sK12(U_56,U_64,U_62),U_64)
& in(sK12(U_56,U_64,U_62),relation_dom(U_56)) )
| ( ! [U_51] :
( sK10(U_56,U_64,U_62) != apply(U_56,U_51)
| ~ in(U_51,U_64)
| ~ in(U_51,relation_dom(U_56)) )
& in(sK10(U_56,U_64,U_62),U_62) ) )
& ! [U_63,U_61] :
( ( ! [U_58] :
( in(U_58,U_61)
| ! [U_49] :
( U_58 != apply(U_56,U_49)
| ~ in(U_49,U_63)
| ~ in(U_49,relation_dom(U_56)) ) )
& ! [U_57] :
( ( U_57 = apply(U_56,sK9(U_56,U_63,U_61,U_57))
& in(sK9(U_56,U_63,U_61,U_57),U_63)
& in(sK9(U_56,U_63,U_61,U_57),relation_dom(U_56)) )
| ~ in(U_57,U_61) ) )
| U_61 != relation_image(U_56,U_63) ) )
| ~ function(U_56)
| ~ relation(U_56) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_52,sK12(U_56,U_64,U_62))],[f_12_6]) ).
cnf(f_12_8,plain,
( in(sK9(U_56,U_63,U_61,U_57),relation_dom(U_56))
| ~ in(U_57,U_61)
| U_61 != relation_image(U_56,U_63)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_9,plain,
( in(sK9(U_56,U_63,U_61,U_57),U_63)
| ~ in(U_57,U_61)
| U_61 != relation_image(U_56,U_63)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_10,plain,
( U_57 = apply(U_56,sK9(U_56,U_63,U_61,U_57))
| ~ in(U_57,U_61)
| U_61 != relation_image(U_56,U_63)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_11,plain,
( in(U_58,U_61)
| U_58 != apply(U_56,U_49)
| ~ in(U_49,U_63)
| ~ in(U_49,relation_dom(U_56))
| U_61 != relation_image(U_56,U_63)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_12,plain,
( in(sK12(U_56,U_64,U_62),relation_dom(U_56))
| in(sK10(U_56,U_64,U_62),U_62)
| U_62 = relation_image(U_56,U_64)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_13,plain,
( in(sK12(U_56,U_64,U_62),U_64)
| in(sK10(U_56,U_64,U_62),U_62)
| U_62 = relation_image(U_56,U_64)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_14,plain,
( sK11(U_56,U_64,U_62) = apply(U_56,sK12(U_56,U_64,U_62))
| in(sK10(U_56,U_64,U_62),U_62)
| U_62 = relation_image(U_56,U_64)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_15,plain,
( ~ in(sK11(U_56,U_64,U_62),U_62)
| in(sK10(U_56,U_64,U_62),U_62)
| U_62 = relation_image(U_56,U_64)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_16,plain,
( in(sK12(U_56,U_64,U_62),relation_dom(U_56))
| sK10(U_56,U_64,U_62) != apply(U_56,U_51)
| ~ in(U_51,U_64)
| ~ in(U_51,relation_dom(U_56))
| U_62 = relation_image(U_56,U_64)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_17,plain,
( in(sK12(U_56,U_64,U_62),U_64)
| sK10(U_56,U_64,U_62) != apply(U_56,U_51)
| ~ in(U_51,U_64)
| ~ in(U_51,relation_dom(U_56))
| U_62 = relation_image(U_56,U_64)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_18,plain,
( sK11(U_56,U_64,U_62) = apply(U_56,sK12(U_56,U_64,U_62))
| sK10(U_56,U_64,U_62) != apply(U_56,U_51)
| ~ in(U_51,U_64)
| ~ in(U_51,relation_dom(U_56))
| U_62 = relation_image(U_56,U_64)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_12_7]) ).
cnf(f_12_19,plain,
( ~ in(sK11(U_56,U_64,U_62),U_62)
| sK10(U_56,U_64,U_62) != apply(U_56,U_51)
| ~ in(U_51,U_64)
| ~ in(U_51,relation_dom(U_56))
| U_62 = relation_image(U_56,U_64)
| ~ function(U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_12_7]) ).
fof(f_13_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_13_2,plain,
! [U_71,U_70] :
( ! [U_69] :
( ( ( U_69 = relation_rng_restriction(U_71,U_70)
| ? [U_68,U_67] :
( ( ~ in(ordered_pair(U_68,U_67),U_69)
& in(ordered_pair(U_68,U_67),U_70)
& in(U_67,U_71) )
| ( ( ~ in(ordered_pair(U_68,U_67),U_70)
| ~ in(U_67,U_71) )
& in(ordered_pair(U_68,U_67),U_69) ) ) )
& ( ! [U_66,U_65] :
( ( in(ordered_pair(U_66,U_65),U_69)
| ~ in(ordered_pair(U_66,U_65),U_70)
| ~ in(U_65,U_71) )
& ( ( in(ordered_pair(U_66,U_65),U_70)
& in(U_65,U_71) )
| ~ in(ordered_pair(U_66,U_65),U_69) ) )
| U_69 != relation_rng_restriction(U_71,U_70) ) )
| ~ relation(U_69) )
| ~ relation(U_70) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_71,U_70] :
( ! [U_69] :
( ( ( U_69 = relation_rng_restriction(U_71,U_70)
| ? [U_79,U_77] :
( ~ in(ordered_pair(U_79,U_77),U_69)
& in(ordered_pair(U_79,U_77),U_70)
& in(U_77,U_71) )
| ? [U_78,U_76] :
( ( ~ in(ordered_pair(U_78,U_76),U_70)
| ~ in(U_76,U_71) )
& in(ordered_pair(U_78,U_76),U_69) ) )
& ( ( ! [U_75,U_73] :
( in(ordered_pair(U_75,U_73),U_69)
| ~ in(ordered_pair(U_75,U_73),U_70)
| ~ in(U_73,U_71) )
& ! [U_74,U_72] :
( ( in(ordered_pair(U_74,U_72),U_70)
& in(U_72,U_71) )
| ~ in(ordered_pair(U_74,U_72),U_69) ) )
| U_69 != relation_rng_restriction(U_71,U_70) ) )
| ~ relation(U_69) )
| ~ relation(U_70) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
fof(f_13_4,plain,
! [U_71,U_70] :
( ! [U_69] :
( ( ( U_69 = relation_rng_restriction(U_71,U_70)
| ? [U_79,U_77] :
( ~ in(ordered_pair(U_79,U_77),U_69)
& in(ordered_pair(U_79,U_77),U_70)
& in(U_77,U_71) )
| ? [U_76] :
( ( ~ in(ordered_pair(sK13(U_71,U_70,U_69),U_76),U_70)
| ~ in(U_76,U_71) )
& in(ordered_pair(sK13(U_71,U_70,U_69),U_76),U_69) ) )
& ( ( ! [U_75,U_73] :
( in(ordered_pair(U_75,U_73),U_69)
| ~ in(ordered_pair(U_75,U_73),U_70)
| ~ in(U_73,U_71) )
& ! [U_74,U_72] :
( ( in(ordered_pair(U_74,U_72),U_70)
& in(U_72,U_71) )
| ~ in(ordered_pair(U_74,U_72),U_69) ) )
| U_69 != relation_rng_restriction(U_71,U_70) ) )
| ~ relation(U_69) )
| ~ relation(U_70) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_78,sK13(U_71,U_70,U_69))],[f_13_3]) ).
fof(f_13_5,plain,
! [U_71,U_70] :
( ! [U_69] :
( ( ( U_69 = relation_rng_restriction(U_71,U_70)
| ? [U_79,U_77] :
( ~ in(ordered_pair(U_79,U_77),U_69)
& in(ordered_pair(U_79,U_77),U_70)
& in(U_77,U_71) )
| ( ( ~ in(ordered_pair(sK13(U_71,U_70,U_69),sK14(U_71,U_70,U_69)),U_70)
| ~ in(sK14(U_71,U_70,U_69),U_71) )
& in(ordered_pair(sK13(U_71,U_70,U_69),sK14(U_71,U_70,U_69)),U_69) ) )
& ( ( ! [U_75,U_73] :
( in(ordered_pair(U_75,U_73),U_69)
| ~ in(ordered_pair(U_75,U_73),U_70)
| ~ in(U_73,U_71) )
& ! [U_74,U_72] :
( ( in(ordered_pair(U_74,U_72),U_70)
& in(U_72,U_71) )
| ~ in(ordered_pair(U_74,U_72),U_69) ) )
| U_69 != relation_rng_restriction(U_71,U_70) ) )
| ~ relation(U_69) )
| ~ relation(U_70) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_76,sK14(U_71,U_70,U_69))],[f_13_4]) ).
fof(f_13_6,plain,
! [U_71,U_70] :
( ! [U_69] :
( ( ( U_69 = relation_rng_restriction(U_71,U_70)
| ? [U_77] :
( ~ in(ordered_pair(sK15(U_71,U_70,U_69),U_77),U_69)
& in(ordered_pair(sK15(U_71,U_70,U_69),U_77),U_70)
& in(U_77,U_71) )
| ( ( ~ in(ordered_pair(sK13(U_71,U_70,U_69),sK14(U_71,U_70,U_69)),U_70)
| ~ in(sK14(U_71,U_70,U_69),U_71) )
& in(ordered_pair(sK13(U_71,U_70,U_69),sK14(U_71,U_70,U_69)),U_69) ) )
& ( ( ! [U_75,U_73] :
( in(ordered_pair(U_75,U_73),U_69)
| ~ in(ordered_pair(U_75,U_73),U_70)
| ~ in(U_73,U_71) )
& ! [U_74,U_72] :
( ( in(ordered_pair(U_74,U_72),U_70)
& in(U_72,U_71) )
| ~ in(ordered_pair(U_74,U_72),U_69) ) )
| U_69 != relation_rng_restriction(U_71,U_70) ) )
| ~ relation(U_69) )
| ~ relation(U_70) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_79,sK15(U_71,U_70,U_69))],[f_13_5]) ).
fof(f_13_7,plain,
! [U_71,U_70] :
( ! [U_69] :
( ( ( U_69 = relation_rng_restriction(U_71,U_70)
| ( ~ in(ordered_pair(sK15(U_71,U_70,U_69),sK16(U_71,U_70,U_69)),U_69)
& in(ordered_pair(sK15(U_71,U_70,U_69),sK16(U_71,U_70,U_69)),U_70)
& in(sK16(U_71,U_70,U_69),U_71) )
| ( ( ~ in(ordered_pair(sK13(U_71,U_70,U_69),sK14(U_71,U_70,U_69)),U_70)
| ~ in(sK14(U_71,U_70,U_69),U_71) )
& in(ordered_pair(sK13(U_71,U_70,U_69),sK14(U_71,U_70,U_69)),U_69) ) )
& ( ( ! [U_75,U_73] :
( in(ordered_pair(U_75,U_73),U_69)
| ~ in(ordered_pair(U_75,U_73),U_70)
| ~ in(U_73,U_71) )
& ! [U_74,U_72] :
( ( in(ordered_pair(U_74,U_72),U_70)
& in(U_72,U_71) )
| ~ in(ordered_pair(U_74,U_72),U_69) ) )
| U_69 != relation_rng_restriction(U_71,U_70) ) )
| ~ relation(U_69) )
| ~ relation(U_70) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_77,sK16(U_71,U_70,U_69))],[f_13_6]) ).
cnf(f_13_8,plain,
( in(U_72,U_71)
| ~ in(ordered_pair(U_74,U_72),U_69)
| U_69 != relation_rng_restriction(U_71,U_70)
| ~ relation(U_69)
| ~ relation(U_70) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_9,plain,
( in(ordered_pair(U_74,U_72),U_70)
| ~ in(ordered_pair(U_74,U_72),U_69)
| U_69 != relation_rng_restriction(U_71,U_70)
| ~ relation(U_69)
| ~ relation(U_70) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_10,plain,
( in(ordered_pair(U_75,U_73),U_69)
| ~ in(ordered_pair(U_75,U_73),U_70)
| ~ in(U_73,U_71)
| U_69 != relation_rng_restriction(U_71,U_70)
| ~ relation(U_69)
| ~ relation(U_70) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_11,plain,
( in(sK16(U_71,U_70,U_69),U_71)
| in(ordered_pair(sK13(U_71,U_70,U_69),sK14(U_71,U_70,U_69)),U_69)
| U_69 = relation_rng_restriction(U_71,U_70)
| ~ relation(U_69)
| ~ relation(U_70) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_12,plain,
( in(ordered_pair(sK15(U_71,U_70,U_69),sK16(U_71,U_70,U_69)),U_70)
| in(ordered_pair(sK13(U_71,U_70,U_69),sK14(U_71,U_70,U_69)),U_69)
| U_69 = relation_rng_restriction(U_71,U_70)
| ~ relation(U_69)
| ~ relation(U_70) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_13,plain,
( ~ in(ordered_pair(sK15(U_71,U_70,U_69),sK16(U_71,U_70,U_69)),U_69)
| in(ordered_pair(sK13(U_71,U_70,U_69),sK14(U_71,U_70,U_69)),U_69)
| U_69 = relation_rng_restriction(U_71,U_70)
| ~ relation(U_69)
| ~ relation(U_70) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_14,plain,
( in(sK16(U_71,U_70,U_69),U_71)
| ~ in(ordered_pair(sK13(U_71,U_70,U_69),sK14(U_71,U_70,U_69)),U_70)
| ~ in(sK14(U_71,U_70,U_69),U_71)
| U_69 = relation_rng_restriction(U_71,U_70)
| ~ relation(U_69)
| ~ relation(U_70) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_15,plain,
( in(ordered_pair(sK15(U_71,U_70,U_69),sK16(U_71,U_70,U_69)),U_70)
| ~ in(ordered_pair(sK13(U_71,U_70,U_69),sK14(U_71,U_70,U_69)),U_70)
| ~ in(sK14(U_71,U_70,U_69),U_71)
| U_69 = relation_rng_restriction(U_71,U_70)
| ~ relation(U_69)
| ~ relation(U_70) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_16,plain,
( ~ in(ordered_pair(sK15(U_71,U_70,U_69),sK16(U_71,U_70,U_69)),U_69)
| ~ in(ordered_pair(sK13(U_71,U_70,U_69),sK14(U_71,U_70,U_69)),U_70)
| ~ in(sK14(U_71,U_70,U_69),U_71)
| U_69 = relation_rng_restriction(U_71,U_70)
| ~ relation(U_69)
| ~ relation(U_70) ),
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)
& in(apply(A,D),B)
& in(D,relation_dom(A)) )
| ( ( ~ in(apply(A,D),B)
| ~ in(D,relation_dom(A)) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ~ in(apply(A,D),B)
| ~ in(D,relation_dom(A)) )
& ( ( in(apply(A,D),B)
& in(D,relation_dom(A)) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d13_funct_1]) ).
fof(f_14_2,plain,
! [U_84] :
( ! [U_83,U_82] :
( ( U_82 = relation_inverse_image(U_84,U_83)
| ? [U_81] :
( ( ~ in(U_81,U_82)
& in(apply(U_84,U_81),U_83)
& in(U_81,relation_dom(U_84)) )
| ( ( ~ in(apply(U_84,U_81),U_83)
| ~ in(U_81,relation_dom(U_84)) )
& in(U_81,U_82) ) ) )
& ( ! [U_80] :
( ( in(U_80,U_82)
| ~ in(apply(U_84,U_80),U_83)
| ~ in(U_80,relation_dom(U_84)) )
& ( ( in(apply(U_84,U_80),U_83)
& in(U_80,relation_dom(U_84)) )
| ~ in(U_80,U_82) ) )
| U_82 != relation_inverse_image(U_84,U_83) ) )
| ~ function(U_84)
| ~ relation(U_84) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_84] :
( ( ! [U_92,U_90] :
( U_90 = relation_inverse_image(U_84,U_92)
| ? [U_88] :
( ~ in(U_88,U_90)
& in(apply(U_84,U_88),U_92)
& in(U_88,relation_dom(U_84)) )
| ? [U_87] :
( ( ~ in(apply(U_84,U_87),U_92)
| ~ in(U_87,relation_dom(U_84)) )
& in(U_87,U_90) ) )
& ! [U_91,U_89] :
( ( ! [U_86] :
( in(U_86,U_89)
| ~ in(apply(U_84,U_86),U_91)
| ~ in(U_86,relation_dom(U_84)) )
& ! [U_85] :
( ( in(apply(U_84,U_85),U_91)
& in(U_85,relation_dom(U_84)) )
| ~ in(U_85,U_89) ) )
| U_89 != relation_inverse_image(U_84,U_91) ) )
| ~ function(U_84)
| ~ relation(U_84) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
fof(f_14_4,plain,
! [U_84] :
( ( ! [U_92,U_90] :
( U_90 = relation_inverse_image(U_84,U_92)
| ? [U_88] :
( ~ in(U_88,U_90)
& in(apply(U_84,U_88),U_92)
& in(U_88,relation_dom(U_84)) )
| ( ( ~ in(apply(U_84,sK17(U_84,U_92,U_90)),U_92)
| ~ in(sK17(U_84,U_92,U_90),relation_dom(U_84)) )
& in(sK17(U_84,U_92,U_90),U_90) ) )
& ! [U_91,U_89] :
( ( ! [U_86] :
( in(U_86,U_89)
| ~ in(apply(U_84,U_86),U_91)
| ~ in(U_86,relation_dom(U_84)) )
& ! [U_85] :
( ( in(apply(U_84,U_85),U_91)
& in(U_85,relation_dom(U_84)) )
| ~ in(U_85,U_89) ) )
| U_89 != relation_inverse_image(U_84,U_91) ) )
| ~ function(U_84)
| ~ relation(U_84) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_87,sK17(U_84,U_92,U_90))],[f_14_3]) ).
fof(f_14_5,plain,
! [U_84] :
( ( ! [U_92,U_90] :
( U_90 = relation_inverse_image(U_84,U_92)
| ( ~ in(sK18(U_84,U_92,U_90),U_90)
& in(apply(U_84,sK18(U_84,U_92,U_90)),U_92)
& in(sK18(U_84,U_92,U_90),relation_dom(U_84)) )
| ( ( ~ in(apply(U_84,sK17(U_84,U_92,U_90)),U_92)
| ~ in(sK17(U_84,U_92,U_90),relation_dom(U_84)) )
& in(sK17(U_84,U_92,U_90),U_90) ) )
& ! [U_91,U_89] :
( ( ! [U_86] :
( in(U_86,U_89)
| ~ in(apply(U_84,U_86),U_91)
| ~ in(U_86,relation_dom(U_84)) )
& ! [U_85] :
( ( in(apply(U_84,U_85),U_91)
& in(U_85,relation_dom(U_84)) )
| ~ in(U_85,U_89) ) )
| U_89 != relation_inverse_image(U_84,U_91) ) )
| ~ function(U_84)
| ~ relation(U_84) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_88,sK18(U_84,U_92,U_90))],[f_14_4]) ).
cnf(f_14_6,plain,
( in(U_85,relation_dom(U_84))
| ~ in(U_85,U_89)
| U_89 != relation_inverse_image(U_84,U_91)
| ~ function(U_84)
| ~ relation(U_84) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_7,plain,
( in(apply(U_84,U_85),U_91)
| ~ in(U_85,U_89)
| U_89 != relation_inverse_image(U_84,U_91)
| ~ function(U_84)
| ~ relation(U_84) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_8,plain,
( in(U_86,U_89)
| ~ in(apply(U_84,U_86),U_91)
| ~ in(U_86,relation_dom(U_84))
| U_89 != relation_inverse_image(U_84,U_91)
| ~ function(U_84)
| ~ relation(U_84) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_9,plain,
( in(sK18(U_84,U_92,U_90),relation_dom(U_84))
| in(sK17(U_84,U_92,U_90),U_90)
| U_90 = relation_inverse_image(U_84,U_92)
| ~ function(U_84)
| ~ relation(U_84) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_10,plain,
( in(apply(U_84,sK18(U_84,U_92,U_90)),U_92)
| in(sK17(U_84,U_92,U_90),U_90)
| U_90 = relation_inverse_image(U_84,U_92)
| ~ function(U_84)
| ~ relation(U_84) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_11,plain,
( ~ in(sK18(U_84,U_92,U_90),U_90)
| in(sK17(U_84,U_92,U_90),U_90)
| U_90 = relation_inverse_image(U_84,U_92)
| ~ function(U_84)
| ~ relation(U_84) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_12,plain,
( in(sK18(U_84,U_92,U_90),relation_dom(U_84))
| ~ in(apply(U_84,sK17(U_84,U_92,U_90)),U_92)
| ~ in(sK17(U_84,U_92,U_90),relation_dom(U_84))
| U_90 = relation_inverse_image(U_84,U_92)
| ~ function(U_84)
| ~ relation(U_84) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_13,plain,
( in(apply(U_84,sK18(U_84,U_92,U_90)),U_92)
| ~ in(apply(U_84,sK17(U_84,U_92,U_90)),U_92)
| ~ in(sK17(U_84,U_92,U_90),relation_dom(U_84))
| U_90 = relation_inverse_image(U_84,U_92)
| ~ function(U_84)
| ~ relation(U_84) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_14,plain,
( ~ in(sK18(U_84,U_92,U_90),U_90)
| ~ in(apply(U_84,sK17(U_84,U_92,U_90)),U_92)
| ~ in(sK17(U_84,U_92,U_90),relation_dom(U_84))
| U_90 = relation_inverse_image(U_84,U_92)
| ~ function(U_84)
| ~ relation(U_84) ),
inference(clausify,[status(thm)],[f_14_5]) ).
fof(f_15_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_15_2,plain,
! [U_101] :
( ! [U_100,U_99] :
( ( U_99 = relation_image(U_101,U_100)
| ? [U_98] :
( ( ~ in(U_98,U_99)
& ? [U_97] :
( in(U_97,U_100)
& in(ordered_pair(U_97,U_98),U_101) ) )
| ( ! [U_96] :
( ~ in(U_96,U_100)
| ~ in(ordered_pair(U_96,U_98),U_101) )
& in(U_98,U_99) ) ) )
& ( ! [U_95] :
( ( in(U_95,U_99)
| ! [U_94] :
( ~ in(U_94,U_100)
| ~ in(ordered_pair(U_94,U_95),U_101) ) )
& ( ? [U_93] :
( in(U_93,U_100)
& in(ordered_pair(U_93,U_95),U_101) )
| ~ in(U_95,U_99) ) )
| U_99 != relation_image(U_101,U_100) ) )
| ~ relation(U_101) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_101] :
( ( ! [U_109,U_107] :
( U_107 = relation_image(U_101,U_109)
| ? [U_105] :
( ~ in(U_105,U_107)
& ? [U_97] :
( in(U_97,U_109)
& in(ordered_pair(U_97,U_105),U_101) ) )
| ? [U_104] :
( ! [U_96] :
( ~ in(U_96,U_109)
| ~ in(ordered_pair(U_96,U_104),U_101) )
& in(U_104,U_107) ) )
& ! [U_108,U_106] :
( ( ! [U_103] :
( in(U_103,U_106)
| ! [U_94] :
( ~ in(U_94,U_108)
| ~ in(ordered_pair(U_94,U_103),U_101) ) )
& ! [U_102] :
( ? [U_93] :
( in(U_93,U_108)
& in(ordered_pair(U_93,U_102),U_101) )
| ~ in(U_102,U_106) ) )
| U_106 != relation_image(U_101,U_108) ) )
| ~ relation(U_101) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
fof(f_15_4,plain,
! [U_101] :
( ( ! [U_109,U_107] :
( U_107 = relation_image(U_101,U_109)
| ? [U_105] :
( ~ in(U_105,U_107)
& ? [U_97] :
( in(U_97,U_109)
& in(ordered_pair(U_97,U_105),U_101) ) )
| ? [U_104] :
( ! [U_96] :
( ~ in(U_96,U_109)
| ~ in(ordered_pair(U_96,U_104),U_101) )
& in(U_104,U_107) ) )
& ! [U_108,U_106] :
( ( ! [U_103] :
( in(U_103,U_106)
| ! [U_94] :
( ~ in(U_94,U_108)
| ~ in(ordered_pair(U_94,U_103),U_101) ) )
& ! [U_102] :
( ( in(sK19(U_101,U_108,U_106,U_102),U_108)
& in(ordered_pair(sK19(U_101,U_108,U_106,U_102),U_102),U_101) )
| ~ in(U_102,U_106) ) )
| U_106 != relation_image(U_101,U_108) ) )
| ~ relation(U_101) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_93,sK19(U_101,U_108,U_106,U_102))],[f_15_3]) ).
fof(f_15_5,plain,
! [U_101] :
( ( ! [U_109,U_107] :
( U_107 = relation_image(U_101,U_109)
| ? [U_105] :
( ~ in(U_105,U_107)
& ? [U_97] :
( in(U_97,U_109)
& in(ordered_pair(U_97,U_105),U_101) ) )
| ( ! [U_96] :
( ~ in(U_96,U_109)
| ~ in(ordered_pair(U_96,sK20(U_101,U_109,U_107)),U_101) )
& in(sK20(U_101,U_109,U_107),U_107) ) )
& ! [U_108,U_106] :
( ( ! [U_103] :
( in(U_103,U_106)
| ! [U_94] :
( ~ in(U_94,U_108)
| ~ in(ordered_pair(U_94,U_103),U_101) ) )
& ! [U_102] :
( ( in(sK19(U_101,U_108,U_106,U_102),U_108)
& in(ordered_pair(sK19(U_101,U_108,U_106,U_102),U_102),U_101) )
| ~ in(U_102,U_106) ) )
| U_106 != relation_image(U_101,U_108) ) )
| ~ relation(U_101) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_104,sK20(U_101,U_109,U_107))],[f_15_4]) ).
fof(f_15_6,plain,
! [U_101] :
( ( ! [U_109,U_107] :
( U_107 = relation_image(U_101,U_109)
| ( ~ in(sK21(U_101,U_109,U_107),U_107)
& ? [U_97] :
( in(U_97,U_109)
& in(ordered_pair(U_97,sK21(U_101,U_109,U_107)),U_101) ) )
| ( ! [U_96] :
( ~ in(U_96,U_109)
| ~ in(ordered_pair(U_96,sK20(U_101,U_109,U_107)),U_101) )
& in(sK20(U_101,U_109,U_107),U_107) ) )
& ! [U_108,U_106] :
( ( ! [U_103] :
( in(U_103,U_106)
| ! [U_94] :
( ~ in(U_94,U_108)
| ~ in(ordered_pair(U_94,U_103),U_101) ) )
& ! [U_102] :
( ( in(sK19(U_101,U_108,U_106,U_102),U_108)
& in(ordered_pair(sK19(U_101,U_108,U_106,U_102),U_102),U_101) )
| ~ in(U_102,U_106) ) )
| U_106 != relation_image(U_101,U_108) ) )
| ~ relation(U_101) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_105,sK21(U_101,U_109,U_107))],[f_15_5]) ).
fof(f_15_7,plain,
! [U_101] :
( ( ! [U_109,U_107] :
( U_107 = relation_image(U_101,U_109)
| ( ~ in(sK21(U_101,U_109,U_107),U_107)
& in(sK22(U_101,U_109,U_107),U_109)
& in(ordered_pair(sK22(U_101,U_109,U_107),sK21(U_101,U_109,U_107)),U_101) )
| ( ! [U_96] :
( ~ in(U_96,U_109)
| ~ in(ordered_pair(U_96,sK20(U_101,U_109,U_107)),U_101) )
& in(sK20(U_101,U_109,U_107),U_107) ) )
& ! [U_108,U_106] :
( ( ! [U_103] :
( in(U_103,U_106)
| ! [U_94] :
( ~ in(U_94,U_108)
| ~ in(ordered_pair(U_94,U_103),U_101) ) )
& ! [U_102] :
( ( in(sK19(U_101,U_108,U_106,U_102),U_108)
& in(ordered_pair(sK19(U_101,U_108,U_106,U_102),U_102),U_101) )
| ~ in(U_102,U_106) ) )
| U_106 != relation_image(U_101,U_108) ) )
| ~ relation(U_101) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_97,sK22(U_101,U_109,U_107))],[f_15_6]) ).
cnf(f_15_8,plain,
( in(ordered_pair(sK19(U_101,U_108,U_106,U_102),U_102),U_101)
| ~ in(U_102,U_106)
| U_106 != relation_image(U_101,U_108)
| ~ relation(U_101) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_9,plain,
( in(sK19(U_101,U_108,U_106,U_102),U_108)
| ~ in(U_102,U_106)
| U_106 != relation_image(U_101,U_108)
| ~ relation(U_101) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_10,plain,
( in(U_103,U_106)
| ~ in(U_94,U_108)
| ~ in(ordered_pair(U_94,U_103),U_101)
| U_106 != relation_image(U_101,U_108)
| ~ relation(U_101) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_11,plain,
( in(ordered_pair(sK22(U_101,U_109,U_107),sK21(U_101,U_109,U_107)),U_101)
| in(sK20(U_101,U_109,U_107),U_107)
| U_107 = relation_image(U_101,U_109)
| ~ relation(U_101) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_12,plain,
( in(sK22(U_101,U_109,U_107),U_109)
| in(sK20(U_101,U_109,U_107),U_107)
| U_107 = relation_image(U_101,U_109)
| ~ relation(U_101) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_13,plain,
( ~ in(sK21(U_101,U_109,U_107),U_107)
| in(sK20(U_101,U_109,U_107),U_107)
| U_107 = relation_image(U_101,U_109)
| ~ relation(U_101) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_14,plain,
( in(ordered_pair(sK22(U_101,U_109,U_107),sK21(U_101,U_109,U_107)),U_101)
| ~ in(U_96,U_109)
| ~ in(ordered_pair(U_96,sK20(U_101,U_109,U_107)),U_101)
| U_107 = relation_image(U_101,U_109)
| ~ relation(U_101) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_15,plain,
( in(sK22(U_101,U_109,U_107),U_109)
| ~ in(U_96,U_109)
| ~ in(ordered_pair(U_96,sK20(U_101,U_109,U_107)),U_101)
| U_107 = relation_image(U_101,U_109)
| ~ relation(U_101) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_16,plain,
( ~ in(sK21(U_101,U_109,U_107),U_107)
| ~ in(U_96,U_109)
| ~ in(ordered_pair(U_96,sK20(U_101,U_109,U_107)),U_101)
| U_107 = relation_image(U_101,U_109)
| ~ relation(U_101) ),
inference(clausify,[status(thm)],[f_15_7]) ).
fof(f_16_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_16_2,plain,
! [U_118] :
( ! [U_117,U_116] :
( ( U_116 = relation_inverse_image(U_118,U_117)
| ? [U_115] :
( ( ~ in(U_115,U_116)
& ? [U_114] :
( in(U_114,U_117)
& in(ordered_pair(U_115,U_114),U_118) ) )
| ( ! [U_113] :
( ~ in(U_113,U_117)
| ~ in(ordered_pair(U_115,U_113),U_118) )
& in(U_115,U_116) ) ) )
& ( ! [U_112] :
( ( in(U_112,U_116)
| ! [U_111] :
( ~ in(U_111,U_117)
| ~ in(ordered_pair(U_112,U_111),U_118) ) )
& ( ? [U_110] :
( in(U_110,U_117)
& in(ordered_pair(U_112,U_110),U_118) )
| ~ in(U_112,U_116) ) )
| U_116 != relation_inverse_image(U_118,U_117) ) )
| ~ relation(U_118) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_118] :
( ( ! [U_126,U_124] :
( U_124 = relation_inverse_image(U_118,U_126)
| ? [U_122] :
( ~ in(U_122,U_124)
& ? [U_114] :
( in(U_114,U_126)
& in(ordered_pair(U_122,U_114),U_118) ) )
| ? [U_121] :
( ! [U_113] :
( ~ in(U_113,U_126)
| ~ in(ordered_pair(U_121,U_113),U_118) )
& in(U_121,U_124) ) )
& ! [U_125,U_123] :
( ( ! [U_120] :
( in(U_120,U_123)
| ! [U_111] :
( ~ in(U_111,U_125)
| ~ in(ordered_pair(U_120,U_111),U_118) ) )
& ! [U_119] :
( ? [U_110] :
( in(U_110,U_125)
& in(ordered_pair(U_119,U_110),U_118) )
| ~ in(U_119,U_123) ) )
| U_123 != relation_inverse_image(U_118,U_125) ) )
| ~ relation(U_118) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
fof(f_16_4,plain,
! [U_118] :
( ( ! [U_126,U_124] :
( U_124 = relation_inverse_image(U_118,U_126)
| ? [U_122] :
( ~ in(U_122,U_124)
& ? [U_114] :
( in(U_114,U_126)
& in(ordered_pair(U_122,U_114),U_118) ) )
| ? [U_121] :
( ! [U_113] :
( ~ in(U_113,U_126)
| ~ in(ordered_pair(U_121,U_113),U_118) )
& in(U_121,U_124) ) )
& ! [U_125,U_123] :
( ( ! [U_120] :
( in(U_120,U_123)
| ! [U_111] :
( ~ in(U_111,U_125)
| ~ in(ordered_pair(U_120,U_111),U_118) ) )
& ! [U_119] :
( ( in(sK23(U_118,U_125,U_123,U_119),U_125)
& in(ordered_pair(U_119,sK23(U_118,U_125,U_123,U_119)),U_118) )
| ~ in(U_119,U_123) ) )
| U_123 != relation_inverse_image(U_118,U_125) ) )
| ~ relation(U_118) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_110,sK23(U_118,U_125,U_123,U_119))],[f_16_3]) ).
fof(f_16_5,plain,
! [U_118] :
( ( ! [U_126,U_124] :
( U_124 = relation_inverse_image(U_118,U_126)
| ? [U_122] :
( ~ in(U_122,U_124)
& ? [U_114] :
( in(U_114,U_126)
& in(ordered_pair(U_122,U_114),U_118) ) )
| ( ! [U_113] :
( ~ in(U_113,U_126)
| ~ in(ordered_pair(sK24(U_118,U_126,U_124),U_113),U_118) )
& in(sK24(U_118,U_126,U_124),U_124) ) )
& ! [U_125,U_123] :
( ( ! [U_120] :
( in(U_120,U_123)
| ! [U_111] :
( ~ in(U_111,U_125)
| ~ in(ordered_pair(U_120,U_111),U_118) ) )
& ! [U_119] :
( ( in(sK23(U_118,U_125,U_123,U_119),U_125)
& in(ordered_pair(U_119,sK23(U_118,U_125,U_123,U_119)),U_118) )
| ~ in(U_119,U_123) ) )
| U_123 != relation_inverse_image(U_118,U_125) ) )
| ~ relation(U_118) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_121,sK24(U_118,U_126,U_124))],[f_16_4]) ).
fof(f_16_6,plain,
! [U_118] :
( ( ! [U_126,U_124] :
( U_124 = relation_inverse_image(U_118,U_126)
| ( ~ in(sK25(U_118,U_126,U_124),U_124)
& ? [U_114] :
( in(U_114,U_126)
& in(ordered_pair(sK25(U_118,U_126,U_124),U_114),U_118) ) )
| ( ! [U_113] :
( ~ in(U_113,U_126)
| ~ in(ordered_pair(sK24(U_118,U_126,U_124),U_113),U_118) )
& in(sK24(U_118,U_126,U_124),U_124) ) )
& ! [U_125,U_123] :
( ( ! [U_120] :
( in(U_120,U_123)
| ! [U_111] :
( ~ in(U_111,U_125)
| ~ in(ordered_pair(U_120,U_111),U_118) ) )
& ! [U_119] :
( ( in(sK23(U_118,U_125,U_123,U_119),U_125)
& in(ordered_pair(U_119,sK23(U_118,U_125,U_123,U_119)),U_118) )
| ~ in(U_119,U_123) ) )
| U_123 != relation_inverse_image(U_118,U_125) ) )
| ~ relation(U_118) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_122,sK25(U_118,U_126,U_124))],[f_16_5]) ).
fof(f_16_7,plain,
! [U_118] :
( ( ! [U_126,U_124] :
( U_124 = relation_inverse_image(U_118,U_126)
| ( ~ in(sK25(U_118,U_126,U_124),U_124)
& in(sK26(U_118,U_126,U_124),U_126)
& in(ordered_pair(sK25(U_118,U_126,U_124),sK26(U_118,U_126,U_124)),U_118) )
| ( ! [U_113] :
( ~ in(U_113,U_126)
| ~ in(ordered_pair(sK24(U_118,U_126,U_124),U_113),U_118) )
& in(sK24(U_118,U_126,U_124),U_124) ) )
& ! [U_125,U_123] :
( ( ! [U_120] :
( in(U_120,U_123)
| ! [U_111] :
( ~ in(U_111,U_125)
| ~ in(ordered_pair(U_120,U_111),U_118) ) )
& ! [U_119] :
( ( in(sK23(U_118,U_125,U_123,U_119),U_125)
& in(ordered_pair(U_119,sK23(U_118,U_125,U_123,U_119)),U_118) )
| ~ in(U_119,U_123) ) )
| U_123 != relation_inverse_image(U_118,U_125) ) )
| ~ relation(U_118) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_114,sK26(U_118,U_126,U_124))],[f_16_6]) ).
cnf(f_16_8,plain,
( in(ordered_pair(U_119,sK23(U_118,U_125,U_123,U_119)),U_118)
| ~ in(U_119,U_123)
| U_123 != relation_inverse_image(U_118,U_125)
| ~ relation(U_118) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_9,plain,
( in(sK23(U_118,U_125,U_123,U_119),U_125)
| ~ in(U_119,U_123)
| U_123 != relation_inverse_image(U_118,U_125)
| ~ relation(U_118) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_10,plain,
( in(U_120,U_123)
| ~ in(U_111,U_125)
| ~ in(ordered_pair(U_120,U_111),U_118)
| U_123 != relation_inverse_image(U_118,U_125)
| ~ relation(U_118) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_11,plain,
( in(ordered_pair(sK25(U_118,U_126,U_124),sK26(U_118,U_126,U_124)),U_118)
| in(sK24(U_118,U_126,U_124),U_124)
| U_124 = relation_inverse_image(U_118,U_126)
| ~ relation(U_118) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_12,plain,
( in(sK26(U_118,U_126,U_124),U_126)
| in(sK24(U_118,U_126,U_124),U_124)
| U_124 = relation_inverse_image(U_118,U_126)
| ~ relation(U_118) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_13,plain,
( ~ in(sK25(U_118,U_126,U_124),U_124)
| in(sK24(U_118,U_126,U_124),U_124)
| U_124 = relation_inverse_image(U_118,U_126)
| ~ relation(U_118) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_14,plain,
( in(ordered_pair(sK25(U_118,U_126,U_124),sK26(U_118,U_126,U_124)),U_118)
| ~ in(U_113,U_126)
| ~ in(ordered_pair(sK24(U_118,U_126,U_124),U_113),U_118)
| U_124 = relation_inverse_image(U_118,U_126)
| ~ relation(U_118) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_15,plain,
( in(sK26(U_118,U_126,U_124),U_126)
| ~ in(U_113,U_126)
| ~ in(ordered_pair(sK24(U_118,U_126,U_124),U_113),U_118)
| U_124 = relation_inverse_image(U_118,U_126)
| ~ relation(U_118) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_16,plain,
( ~ in(sK25(U_118,U_126,U_124),U_124)
| ~ in(U_113,U_126)
| ~ in(ordered_pair(sK24(U_118,U_126,U_124),U_113),U_118)
| U_124 = relation_inverse_image(U_118,U_126)
| ~ relation(U_118) ),
inference(clausify,[status(thm)],[f_16_7]) ).
fof(f_17_1,plain,
! [A,B,C,D] :
( ( D = unordered_triple(A,B,C)
| ? [E] :
( ( ~ in(E,D)
& ( E = C
| E = B
| E = A ) )
| ( E != C
& E != B
& E != A
& in(E,D) ) ) )
& ( ! [E] :
( ( in(E,D)
| ( E != C
& E != B
& E != A ) )
& ( E = C
| E = B
| E = A
| ~ in(E,D) ) )
| D != unordered_triple(A,B,C) ) ),
inference(fof_nnf,[status(thm)],[d1_enumset1]) ).
fof(f_17_2,plain,
! [U_132,U_131,U_130,U_129] :
( ( U_129 = unordered_triple(U_132,U_131,U_130)
| ? [U_128] :
( ( ~ in(U_128,U_129)
& ( U_128 = U_130
| U_128 = U_131
| U_128 = U_132 ) )
| ( U_128 != U_130
& U_128 != U_131
& U_128 != U_132
& in(U_128,U_129) ) ) )
& ( ! [U_127] :
( ( in(U_127,U_129)
| ( U_127 != U_130
& U_127 != U_131
& U_127 != U_132 ) )
& ( U_127 = U_130
| U_127 = U_131
| U_127 = U_132
| ~ in(U_127,U_129) ) )
| U_129 != unordered_triple(U_132,U_131,U_130) ) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( ! [U_144,U_142,U_140,U_138] :
( U_138 = unordered_triple(U_144,U_142,U_140)
| ? [U_136] :
( ~ in(U_136,U_138)
& ( U_136 = U_140
| U_136 = U_142
| U_136 = U_144 ) )
| ? [U_135] :
( U_135 != U_140
& U_135 != U_142
& U_135 != U_144
& in(U_135,U_138) ) )
& ! [U_143,U_141,U_139,U_137] :
( ( ! [U_134] :
( in(U_134,U_137)
| ( U_134 != U_139
& U_134 != U_141
& U_134 != U_143 ) )
& ! [U_133] :
( U_133 = U_139
| U_133 = U_141
| U_133 = U_143
| ~ in(U_133,U_137) ) )
| U_137 != unordered_triple(U_143,U_141,U_139) ) ),
inference(miniscope,[status(thm)],[f_17_2]) ).
fof(f_17_4,plain,
( ! [U_144,U_142,U_140,U_138] :
( U_138 = unordered_triple(U_144,U_142,U_140)
| ? [U_136] :
( ~ in(U_136,U_138)
& ( U_136 = U_140
| U_136 = U_142
| U_136 = U_144 ) )
| ( sK27(U_144,U_142,U_140,U_138) != U_140
& sK27(U_144,U_142,U_140,U_138) != U_142
& sK27(U_144,U_142,U_140,U_138) != U_144
& in(sK27(U_144,U_142,U_140,U_138),U_138) ) )
& ! [U_143,U_141,U_139,U_137] :
( ( ! [U_134] :
( in(U_134,U_137)
| ( U_134 != U_139
& U_134 != U_141
& U_134 != U_143 ) )
& ! [U_133] :
( U_133 = U_139
| U_133 = U_141
| U_133 = U_143
| ~ in(U_133,U_137) ) )
| U_137 != unordered_triple(U_143,U_141,U_139) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_135,sK27(U_144,U_142,U_140,U_138))],[f_17_3]) ).
fof(f_17_5,plain,
( ! [U_144,U_142,U_140,U_138] :
( U_138 = unordered_triple(U_144,U_142,U_140)
| ( ~ in(sK28(U_144,U_142,U_140,U_138),U_138)
& ( sK28(U_144,U_142,U_140,U_138) = U_140
| sK28(U_144,U_142,U_140,U_138) = U_142
| sK28(U_144,U_142,U_140,U_138) = U_144 ) )
| ( sK27(U_144,U_142,U_140,U_138) != U_140
& sK27(U_144,U_142,U_140,U_138) != U_142
& sK27(U_144,U_142,U_140,U_138) != U_144
& in(sK27(U_144,U_142,U_140,U_138),U_138) ) )
& ! [U_143,U_141,U_139,U_137] :
( ( ! [U_134] :
( in(U_134,U_137)
| ( U_134 != U_139
& U_134 != U_141
& U_134 != U_143 ) )
& ! [U_133] :
( U_133 = U_139
| U_133 = U_141
| U_133 = U_143
| ~ in(U_133,U_137) ) )
| U_137 != unordered_triple(U_143,U_141,U_139) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_136,sK28(U_144,U_142,U_140,U_138))],[f_17_4]) ).
cnf(f_17_6,plain,
( U_133 = U_139
| U_133 = U_141
| U_133 = U_143
| ~ in(U_133,U_137)
| U_137 != unordered_triple(U_143,U_141,U_139) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_7,plain,
( U_134 != U_143
| in(U_134,U_137)
| U_137 != unordered_triple(U_143,U_141,U_139) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_8,plain,
( U_134 != U_141
| in(U_134,U_137)
| U_137 != unordered_triple(U_143,U_141,U_139) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_9,plain,
( U_134 != U_139
| in(U_134,U_137)
| U_137 != unordered_triple(U_143,U_141,U_139) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_10,plain,
( sK28(U_144,U_142,U_140,U_138) = U_140
| sK28(U_144,U_142,U_140,U_138) = U_142
| sK28(U_144,U_142,U_140,U_138) = U_144
| in(sK27(U_144,U_142,U_140,U_138),U_138)
| U_138 = unordered_triple(U_144,U_142,U_140) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_11,plain,
( ~ in(sK28(U_144,U_142,U_140,U_138),U_138)
| in(sK27(U_144,U_142,U_140,U_138),U_138)
| U_138 = unordered_triple(U_144,U_142,U_140) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_12,plain,
( sK27(U_144,U_142,U_140,U_138) != U_144
| sK28(U_144,U_142,U_140,U_138) = U_140
| sK28(U_144,U_142,U_140,U_138) = U_142
| sK28(U_144,U_142,U_140,U_138) = U_144
| U_138 = unordered_triple(U_144,U_142,U_140) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_13,plain,
( sK27(U_144,U_142,U_140,U_138) != U_142
| sK28(U_144,U_142,U_140,U_138) = U_140
| sK28(U_144,U_142,U_140,U_138) = U_142
| sK28(U_144,U_142,U_140,U_138) = U_144
| U_138 = unordered_triple(U_144,U_142,U_140) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_14,plain,
( sK27(U_144,U_142,U_140,U_138) != U_140
| sK28(U_144,U_142,U_140,U_138) = U_140
| sK28(U_144,U_142,U_140,U_138) = U_142
| sK28(U_144,U_142,U_140,U_138) = U_144
| U_138 = unordered_triple(U_144,U_142,U_140) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_15,plain,
( sK27(U_144,U_142,U_140,U_138) != U_144
| ~ in(sK28(U_144,U_142,U_140,U_138),U_138)
| U_138 = unordered_triple(U_144,U_142,U_140) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_16,plain,
( sK27(U_144,U_142,U_140,U_138) != U_142
| ~ in(sK28(U_144,U_142,U_140,U_138),U_138)
| U_138 = unordered_triple(U_144,U_142,U_140) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_17,plain,
( sK27(U_144,U_142,U_140,U_138) != U_140
| ~ in(sK28(U_144,U_142,U_140,U_138),U_138)
| U_138 = unordered_triple(U_144,U_142,U_140) ),
inference(clausify,[status(thm)],[f_17_5]) ).
fof(f_18_1,plain,
! [A] : succ(A) = set_union2(A,singleton(A)),
inference(fof_nnf,[status(thm)],[d1_ordinal1]) ).
fof(f_18_2,plain,
! [U_145] : succ(U_145) = set_union2(U_145,singleton(U_145)),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
succ(U_145) = set_union2(U_145,singleton(U_145)),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_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_19_2,plain,
! [U_152] :
( ( relation(U_152)
| ? [U_151] :
( ! [U_150,U_149] : U_151 != ordered_pair(U_150,U_149)
& in(U_151,U_152) ) )
& ( ! [U_148] :
( ? [U_147,U_146] : U_148 = ordered_pair(U_147,U_146)
| ~ in(U_148,U_152) )
| ~ relation(U_152) ) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( ! [U_154] :
( relation(U_154)
| ? [U_151] :
( ! [U_150,U_149] : U_151 != ordered_pair(U_150,U_149)
& in(U_151,U_154) ) )
& ! [U_153] :
( ! [U_148] :
( ? [U_147,U_146] : U_148 = ordered_pair(U_147,U_146)
| ~ in(U_148,U_153) )
| ~ relation(U_153) ) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
fof(f_19_4,plain,
( ! [U_154] :
( relation(U_154)
| ? [U_151] :
( ! [U_150,U_149] : U_151 != ordered_pair(U_150,U_149)
& in(U_151,U_154) ) )
& ! [U_153] :
( ! [U_148] :
( ? [U_146] : U_148 = ordered_pair(sK29(U_153,U_148),U_146)
| ~ in(U_148,U_153) )
| ~ relation(U_153) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_147,sK29(U_153,U_148))],[f_19_3]) ).
fof(f_19_5,plain,
( ! [U_154] :
( relation(U_154)
| ? [U_151] :
( ! [U_150,U_149] : U_151 != ordered_pair(U_150,U_149)
& in(U_151,U_154) ) )
& ! [U_153] :
( ! [U_148] :
( U_148 = ordered_pair(sK29(U_153,U_148),sK30(U_153,U_148))
| ~ in(U_148,U_153) )
| ~ relation(U_153) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_146,sK30(U_153,U_148))],[f_19_4]) ).
fof(f_19_6,plain,
( ! [U_154] :
( relation(U_154)
| ( ! [U_150,U_149] : sK31(U_154) != ordered_pair(U_150,U_149)
& in(sK31(U_154),U_154) ) )
& ! [U_153] :
( ! [U_148] :
( U_148 = ordered_pair(sK29(U_153,U_148),sK30(U_153,U_148))
| ~ in(U_148,U_153) )
| ~ relation(U_153) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_151,sK31(U_154))],[f_19_5]) ).
cnf(f_19_7,plain,
( U_148 = ordered_pair(sK29(U_153,U_148),sK30(U_153,U_148))
| ~ in(U_148,U_153)
| ~ relation(U_153) ),
inference(clausify,[status(thm)],[f_19_6]) ).
cnf(f_19_8,plain,
( in(sK31(U_154),U_154)
| relation(U_154) ),
inference(clausify,[status(thm)],[f_19_6]) ).
cnf(f_19_9,plain,
( sK31(U_154) != ordered_pair(U_150,U_149)
| relation(U_154) ),
inference(clausify,[status(thm)],[f_19_6]) ).
fof(f_20_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_20_2,plain,
! [U_162,U_161] :
( ( ( ( U_161 = set_meet(U_162)
| U_161 != empty_set )
& ( U_161 = empty_set
| U_161 != set_meet(U_162) ) )
| U_162 != empty_set )
& ( ( ( U_161 = set_meet(U_162)
| ? [U_160] :
( ( ~ in(U_160,U_161)
& ! [U_159] :
( in(U_160,U_159)
| ~ in(U_159,U_162) ) )
| ( ? [U_158] :
( ~ in(U_160,U_158)
& in(U_158,U_162) )
& in(U_160,U_161) ) ) )
& ( ! [U_157] :
( ( in(U_157,U_161)
| ? [U_156] :
( ~ in(U_157,U_156)
& in(U_156,U_162) ) )
& ( ! [U_155] :
( in(U_157,U_155)
| ~ in(U_155,U_162) )
| ~ in(U_157,U_161) ) )
| U_161 != set_meet(U_162) ) )
| U_162 = empty_set ) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( ! [U_174] :
( ( ! [U_172] :
( U_172 = set_meet(U_174)
| U_172 != empty_set )
& ! [U_171] :
( U_171 = empty_set
| U_171 != set_meet(U_174) ) )
| U_174 != empty_set )
& ! [U_173] :
( ( ! [U_170] :
( U_170 = set_meet(U_173)
| ? [U_166] :
( ~ in(U_166,U_170)
& ! [U_159] :
( in(U_166,U_159)
| ~ in(U_159,U_173) ) )
| ? [U_165] :
( ? [U_158] :
( ~ in(U_165,U_158)
& in(U_158,U_173) )
& in(U_165,U_170) ) )
& ! [U_169] :
( ( ! [U_164] :
( in(U_164,U_169)
| ? [U_156] :
( ~ in(U_164,U_156)
& in(U_156,U_173) ) )
& ! [U_163] :
( ! [U_155] :
( in(U_163,U_155)
| ~ in(U_155,U_173) )
| ~ in(U_163,U_169) ) )
| U_169 != set_meet(U_173) ) )
| U_173 = empty_set ) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
fof(f_20_4,plain,
( ! [U_174] :
( ( ! [U_172] :
( U_172 = set_meet(U_174)
| U_172 != empty_set )
& ! [U_171] :
( U_171 = empty_set
| U_171 != set_meet(U_174) ) )
| U_174 != empty_set )
& ! [U_173] :
( ( ! [U_170] :
( U_170 = set_meet(U_173)
| ? [U_166] :
( ~ in(U_166,U_170)
& ! [U_159] :
( in(U_166,U_159)
| ~ in(U_159,U_173) ) )
| ? [U_165] :
( ? [U_158] :
( ~ in(U_165,U_158)
& in(U_158,U_173) )
& in(U_165,U_170) ) )
& ! [U_169] :
( ( ! [U_164] :
( in(U_164,U_169)
| ( ~ in(U_164,sK32(U_173,U_169,U_164))
& in(sK32(U_173,U_169,U_164),U_173) ) )
& ! [U_163] :
( ! [U_155] :
( in(U_163,U_155)
| ~ in(U_155,U_173) )
| ~ in(U_163,U_169) ) )
| U_169 != set_meet(U_173) ) )
| U_173 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_156,sK32(U_173,U_169,U_164))],[f_20_3]) ).
fof(f_20_5,plain,
( ! [U_174] :
( ( ! [U_172] :
( U_172 = set_meet(U_174)
| U_172 != empty_set )
& ! [U_171] :
( U_171 = empty_set
| U_171 != set_meet(U_174) ) )
| U_174 != empty_set )
& ! [U_173] :
( ( ! [U_170] :
( U_170 = set_meet(U_173)
| ? [U_166] :
( ~ in(U_166,U_170)
& ! [U_159] :
( in(U_166,U_159)
| ~ in(U_159,U_173) ) )
| ( ? [U_158] :
( ~ in(sK33(U_173,U_170),U_158)
& in(U_158,U_173) )
& in(sK33(U_173,U_170),U_170) ) )
& ! [U_169] :
( ( ! [U_164] :
( in(U_164,U_169)
| ( ~ in(U_164,sK32(U_173,U_169,U_164))
& in(sK32(U_173,U_169,U_164),U_173) ) )
& ! [U_163] :
( ! [U_155] :
( in(U_163,U_155)
| ~ in(U_155,U_173) )
| ~ in(U_163,U_169) ) )
| U_169 != set_meet(U_173) ) )
| U_173 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_165,sK33(U_173,U_170))],[f_20_4]) ).
fof(f_20_6,plain,
( ! [U_174] :
( ( ! [U_172] :
( U_172 = set_meet(U_174)
| U_172 != empty_set )
& ! [U_171] :
( U_171 = empty_set
| U_171 != set_meet(U_174) ) )
| U_174 != empty_set )
& ! [U_173] :
( ( ! [U_170] :
( U_170 = set_meet(U_173)
| ? [U_166] :
( ~ in(U_166,U_170)
& ! [U_159] :
( in(U_166,U_159)
| ~ in(U_159,U_173) ) )
| ( ~ in(sK33(U_173,U_170),sK34(U_173,U_170))
& in(sK34(U_173,U_170),U_173)
& in(sK33(U_173,U_170),U_170) ) )
& ! [U_169] :
( ( ! [U_164] :
( in(U_164,U_169)
| ( ~ in(U_164,sK32(U_173,U_169,U_164))
& in(sK32(U_173,U_169,U_164),U_173) ) )
& ! [U_163] :
( ! [U_155] :
( in(U_163,U_155)
| ~ in(U_155,U_173) )
| ~ in(U_163,U_169) ) )
| U_169 != set_meet(U_173) ) )
| U_173 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_158,sK34(U_173,U_170))],[f_20_5]) ).
fof(f_20_7,plain,
( ! [U_174] :
( ( ! [U_172] :
( U_172 = set_meet(U_174)
| U_172 != empty_set )
& ! [U_171] :
( U_171 = empty_set
| U_171 != set_meet(U_174) ) )
| U_174 != empty_set )
& ! [U_173] :
( ( ! [U_170] :
( U_170 = set_meet(U_173)
| ( ~ in(sK35(U_173,U_170),U_170)
& ! [U_159] :
( in(sK35(U_173,U_170),U_159)
| ~ in(U_159,U_173) ) )
| ( ~ in(sK33(U_173,U_170),sK34(U_173,U_170))
& in(sK34(U_173,U_170),U_173)
& in(sK33(U_173,U_170),U_170) ) )
& ! [U_169] :
( ( ! [U_164] :
( in(U_164,U_169)
| ( ~ in(U_164,sK32(U_173,U_169,U_164))
& in(sK32(U_173,U_169,U_164),U_173) ) )
& ! [U_163] :
( ! [U_155] :
( in(U_163,U_155)
| ~ in(U_155,U_173) )
| ~ in(U_163,U_169) ) )
| U_169 != set_meet(U_173) ) )
| U_173 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_166,sK35(U_173,U_170))],[f_20_6]) ).
cnf(f_20_8,plain,
( in(U_163,U_155)
| ~ in(U_155,U_173)
| ~ in(U_163,U_169)
| U_169 != set_meet(U_173)
| U_173 = empty_set ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_9,plain,
( in(sK32(U_173,U_169,U_164),U_173)
| in(U_164,U_169)
| U_169 != set_meet(U_173)
| U_173 = empty_set ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_10,plain,
( ~ in(U_164,sK32(U_173,U_169,U_164))
| in(U_164,U_169)
| U_169 != set_meet(U_173)
| U_173 = empty_set ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_11,plain,
( in(sK35(U_173,U_170),U_159)
| ~ in(U_159,U_173)
| in(sK33(U_173,U_170),U_170)
| U_170 = set_meet(U_173)
| U_173 = empty_set ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_12,plain,
( ~ in(sK35(U_173,U_170),U_170)
| in(sK33(U_173,U_170),U_170)
| U_170 = set_meet(U_173)
| U_173 = empty_set ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_13,plain,
( in(sK34(U_173,U_170),U_173)
| in(sK35(U_173,U_170),U_159)
| ~ in(U_159,U_173)
| U_170 = set_meet(U_173)
| U_173 = empty_set ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_14,plain,
( ~ in(sK33(U_173,U_170),sK34(U_173,U_170))
| in(sK35(U_173,U_170),U_159)
| ~ in(U_159,U_173)
| U_170 = set_meet(U_173)
| U_173 = empty_set ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_15,plain,
( in(sK34(U_173,U_170),U_173)
| ~ in(sK35(U_173,U_170),U_170)
| U_170 = set_meet(U_173)
| U_173 = empty_set ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_16,plain,
( ~ in(sK33(U_173,U_170),sK34(U_173,U_170))
| ~ in(sK35(U_173,U_170),U_170)
| U_170 = set_meet(U_173)
| U_173 = empty_set ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_17,plain,
( U_171 = empty_set
| U_171 != set_meet(U_174)
| U_174 != empty_set ),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_18,plain,
( U_172 = set_meet(U_174)
| U_172 != empty_set
| U_174 != empty_set ),
inference(clausify,[status(thm)],[f_20_7]) ).
fof(f_21_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_21_2,plain,
! [U_178,U_177] :
( ( U_177 = singleton(U_178)
| ? [U_176] :
( ( ~ in(U_176,U_177)
& U_176 = U_178 )
| ( U_176 != U_178
& in(U_176,U_177) ) ) )
& ( ! [U_175] :
( ( in(U_175,U_177)
| U_175 != U_178 )
& ( U_175 = U_178
| ~ in(U_175,U_177) ) )
| U_177 != singleton(U_178) ) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( ! [U_186,U_184] :
( U_184 = singleton(U_186)
| ? [U_182] :
( ~ in(U_182,U_184)
& U_182 = U_186 )
| ? [U_181] :
( U_181 != U_186
& in(U_181,U_184) ) )
& ! [U_185,U_183] :
( ( ! [U_180] :
( in(U_180,U_183)
| U_180 != U_185 )
& ! [U_179] :
( U_179 = U_185
| ~ in(U_179,U_183) ) )
| U_183 != singleton(U_185) ) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
fof(f_21_4,plain,
( ! [U_186,U_184] :
( U_184 = singleton(U_186)
| ? [U_182] :
( ~ in(U_182,U_184)
& U_182 = U_186 )
| ( sK36(U_186,U_184) != U_186
& in(sK36(U_186,U_184),U_184) ) )
& ! [U_185,U_183] :
( ( ! [U_180] :
( in(U_180,U_183)
| U_180 != U_185 )
& ! [U_179] :
( U_179 = U_185
| ~ in(U_179,U_183) ) )
| U_183 != singleton(U_185) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_181,sK36(U_186,U_184))],[f_21_3]) ).
fof(f_21_5,plain,
( ! [U_186,U_184] :
( U_184 = singleton(U_186)
| ( ~ in(sK37(U_186,U_184),U_184)
& sK37(U_186,U_184) = U_186 )
| ( sK36(U_186,U_184) != U_186
& in(sK36(U_186,U_184),U_184) ) )
& ! [U_185,U_183] :
( ( ! [U_180] :
( in(U_180,U_183)
| U_180 != U_185 )
& ! [U_179] :
( U_179 = U_185
| ~ in(U_179,U_183) ) )
| U_183 != singleton(U_185) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_182,sK37(U_186,U_184))],[f_21_4]) ).
cnf(f_21_6,plain,
( U_179 = U_185
| ~ in(U_179,U_183)
| U_183 != singleton(U_185) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_7,plain,
( in(U_180,U_183)
| U_180 != U_185
| U_183 != singleton(U_185) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_8,plain,
( sK37(U_186,U_184) = U_186
| in(sK36(U_186,U_184),U_184)
| U_184 = singleton(U_186) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_9,plain,
( ~ in(sK37(U_186,U_184),U_184)
| in(sK36(U_186,U_184),U_184)
| U_184 = singleton(U_186) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_10,plain,
( sK37(U_186,U_184) = U_186
| sK36(U_186,U_184) != U_186
| U_184 = singleton(U_186) ),
inference(clausify,[status(thm)],[f_21_5]) ).
cnf(f_21_11,plain,
( ~ in(sK37(U_186,U_184),U_184)
| sK36(U_186,U_184) != U_186
| U_184 = singleton(U_186) ),
inference(clausify,[status(thm)],[f_21_5]) ).
fof(f_22_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_22_2,plain,
! [U_189] :
( ( U_189 = empty_set
| ? [U_188] : in(U_188,U_189) )
& ( ! [U_187] : ~ in(U_187,U_189)
| U_189 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( ! [U_191] :
( U_191 = empty_set
| ? [U_188] : in(U_188,U_191) )
& ! [U_190] :
( ! [U_187] : ~ in(U_187,U_190)
| U_190 != empty_set ) ),
inference(miniscope,[status(thm)],[f_22_2]) ).
fof(f_22_4,plain,
( ! [U_191] :
( U_191 = empty_set
| in(sK38(U_191),U_191) )
& ! [U_190] :
( ! [U_187] : ~ in(U_187,U_190)
| U_190 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_188,sK38(U_191))],[f_22_3]) ).
cnf(f_22_5,plain,
( ~ in(U_187,U_190)
| U_190 != empty_set ),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_6,plain,
( U_191 = empty_set
| in(sK38(U_191),U_191) ),
inference(clausify,[status(thm)],[f_22_4]) ).
fof(f_23_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_23_2,plain,
! [U_195,U_194] :
( ( U_194 = powerset(U_195)
| ? [U_193] :
( ( ~ in(U_193,U_194)
& subset(U_193,U_195) )
| ( ~ subset(U_193,U_195)
& in(U_193,U_194) ) ) )
& ( ! [U_192] :
( ( in(U_192,U_194)
| ~ subset(U_192,U_195) )
& ( subset(U_192,U_195)
| ~ in(U_192,U_194) ) )
| U_194 != powerset(U_195) ) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( ! [U_203,U_201] :
( U_201 = powerset(U_203)
| ? [U_199] :
( ~ in(U_199,U_201)
& subset(U_199,U_203) )
| ? [U_198] :
( ~ subset(U_198,U_203)
& in(U_198,U_201) ) )
& ! [U_202,U_200] :
( ( ! [U_197] :
( in(U_197,U_200)
| ~ subset(U_197,U_202) )
& ! [U_196] :
( subset(U_196,U_202)
| ~ in(U_196,U_200) ) )
| U_200 != powerset(U_202) ) ),
inference(miniscope,[status(thm)],[f_23_2]) ).
fof(f_23_4,plain,
( ! [U_203,U_201] :
( U_201 = powerset(U_203)
| ? [U_199] :
( ~ in(U_199,U_201)
& subset(U_199,U_203) )
| ( ~ subset(sK39(U_203,U_201),U_203)
& in(sK39(U_203,U_201),U_201) ) )
& ! [U_202,U_200] :
( ( ! [U_197] :
( in(U_197,U_200)
| ~ subset(U_197,U_202) )
& ! [U_196] :
( subset(U_196,U_202)
| ~ in(U_196,U_200) ) )
| U_200 != powerset(U_202) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_198,sK39(U_203,U_201))],[f_23_3]) ).
fof(f_23_5,plain,
( ! [U_203,U_201] :
( U_201 = powerset(U_203)
| ( ~ in(sK40(U_203,U_201),U_201)
& subset(sK40(U_203,U_201),U_203) )
| ( ~ subset(sK39(U_203,U_201),U_203)
& in(sK39(U_203,U_201),U_201) ) )
& ! [U_202,U_200] :
( ( ! [U_197] :
( in(U_197,U_200)
| ~ subset(U_197,U_202) )
& ! [U_196] :
( subset(U_196,U_202)
| ~ in(U_196,U_200) ) )
| U_200 != powerset(U_202) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_199,sK40(U_203,U_201))],[f_23_4]) ).
cnf(f_23_6,plain,
( subset(U_196,U_202)
| ~ in(U_196,U_200)
| U_200 != powerset(U_202) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_7,plain,
( in(U_197,U_200)
| ~ subset(U_197,U_202)
| U_200 != powerset(U_202) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_8,plain,
( subset(sK40(U_203,U_201),U_203)
| in(sK39(U_203,U_201),U_201)
| U_201 = powerset(U_203) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_9,plain,
( ~ in(sK40(U_203,U_201),U_201)
| in(sK39(U_203,U_201),U_201)
| U_201 = powerset(U_203) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_10,plain,
( subset(sK40(U_203,U_201),U_203)
| ~ subset(sK39(U_203,U_201),U_203)
| U_201 = powerset(U_203) ),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_11,plain,
( ~ in(sK40(U_203,U_201),U_201)
| ~ subset(sK39(U_203,U_201),U_203)
| U_201 = powerset(U_203) ),
inference(clausify,[status(thm)],[f_23_5]) ).
fof(f_24_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_24_2,plain,
! [U_209] :
( ! [U_208] :
( ( ( U_209 = U_208
| ? [U_207,U_206] :
( ( ~ in(ordered_pair(U_207,U_206),U_209)
& in(ordered_pair(U_207,U_206),U_208) )
| ( ~ in(ordered_pair(U_207,U_206),U_208)
& in(ordered_pair(U_207,U_206),U_209) ) ) )
& ( ! [U_205,U_204] :
( ( in(ordered_pair(U_205,U_204),U_209)
| ~ in(ordered_pair(U_205,U_204),U_208) )
& ( in(ordered_pair(U_205,U_204),U_208)
| ~ in(ordered_pair(U_205,U_204),U_209) ) )
| U_209 != U_208 ) )
| ~ relation(U_208) )
| ~ relation(U_209) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_209] :
( ! [U_208] :
( ( ( U_209 = U_208
| ? [U_217,U_215] :
( ~ in(ordered_pair(U_217,U_215),U_209)
& in(ordered_pair(U_217,U_215),U_208) )
| ? [U_216,U_214] :
( ~ in(ordered_pair(U_216,U_214),U_208)
& in(ordered_pair(U_216,U_214),U_209) ) )
& ( ( ! [U_213,U_211] :
( in(ordered_pair(U_213,U_211),U_209)
| ~ in(ordered_pair(U_213,U_211),U_208) )
& ! [U_212,U_210] :
( in(ordered_pair(U_212,U_210),U_208)
| ~ in(ordered_pair(U_212,U_210),U_209) ) )
| U_209 != U_208 ) )
| ~ relation(U_208) )
| ~ relation(U_209) ),
inference(miniscope,[status(thm)],[f_24_2]) ).
fof(f_24_4,plain,
! [U_209] :
( ! [U_208] :
( ( ( U_209 = U_208
| ? [U_217,U_215] :
( ~ in(ordered_pair(U_217,U_215),U_209)
& in(ordered_pair(U_217,U_215),U_208) )
| ? [U_214] :
( ~ in(ordered_pair(sK41(U_209,U_208),U_214),U_208)
& in(ordered_pair(sK41(U_209,U_208),U_214),U_209) ) )
& ( ( ! [U_213,U_211] :
( in(ordered_pair(U_213,U_211),U_209)
| ~ in(ordered_pair(U_213,U_211),U_208) )
& ! [U_212,U_210] :
( in(ordered_pair(U_212,U_210),U_208)
| ~ in(ordered_pair(U_212,U_210),U_209) ) )
| U_209 != U_208 ) )
| ~ relation(U_208) )
| ~ relation(U_209) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_216,sK41(U_209,U_208))],[f_24_3]) ).
fof(f_24_5,plain,
! [U_209] :
( ! [U_208] :
( ( ( U_209 = U_208
| ? [U_217,U_215] :
( ~ in(ordered_pair(U_217,U_215),U_209)
& in(ordered_pair(U_217,U_215),U_208) )
| ( ~ in(ordered_pair(sK41(U_209,U_208),sK42(U_209,U_208)),U_208)
& in(ordered_pair(sK41(U_209,U_208),sK42(U_209,U_208)),U_209) ) )
& ( ( ! [U_213,U_211] :
( in(ordered_pair(U_213,U_211),U_209)
| ~ in(ordered_pair(U_213,U_211),U_208) )
& ! [U_212,U_210] :
( in(ordered_pair(U_212,U_210),U_208)
| ~ in(ordered_pair(U_212,U_210),U_209) ) )
| U_209 != U_208 ) )
| ~ relation(U_208) )
| ~ relation(U_209) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_214,sK42(U_209,U_208))],[f_24_4]) ).
fof(f_24_6,plain,
! [U_209] :
( ! [U_208] :
( ( ( U_209 = U_208
| ? [U_215] :
( ~ in(ordered_pair(sK43(U_209,U_208),U_215),U_209)
& in(ordered_pair(sK43(U_209,U_208),U_215),U_208) )
| ( ~ in(ordered_pair(sK41(U_209,U_208),sK42(U_209,U_208)),U_208)
& in(ordered_pair(sK41(U_209,U_208),sK42(U_209,U_208)),U_209) ) )
& ( ( ! [U_213,U_211] :
( in(ordered_pair(U_213,U_211),U_209)
| ~ in(ordered_pair(U_213,U_211),U_208) )
& ! [U_212,U_210] :
( in(ordered_pair(U_212,U_210),U_208)
| ~ in(ordered_pair(U_212,U_210),U_209) ) )
| U_209 != U_208 ) )
| ~ relation(U_208) )
| ~ relation(U_209) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_217,sK43(U_209,U_208))],[f_24_5]) ).
fof(f_24_7,plain,
! [U_209] :
( ! [U_208] :
( ( ( U_209 = U_208
| ( ~ in(ordered_pair(sK43(U_209,U_208),sK44(U_209,U_208)),U_209)
& in(ordered_pair(sK43(U_209,U_208),sK44(U_209,U_208)),U_208) )
| ( ~ in(ordered_pair(sK41(U_209,U_208),sK42(U_209,U_208)),U_208)
& in(ordered_pair(sK41(U_209,U_208),sK42(U_209,U_208)),U_209) ) )
& ( ( ! [U_213,U_211] :
( in(ordered_pair(U_213,U_211),U_209)
| ~ in(ordered_pair(U_213,U_211),U_208) )
& ! [U_212,U_210] :
( in(ordered_pair(U_212,U_210),U_208)
| ~ in(ordered_pair(U_212,U_210),U_209) ) )
| U_209 != U_208 ) )
| ~ relation(U_208) )
| ~ relation(U_209) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_215,sK44(U_209,U_208))],[f_24_6]) ).
cnf(f_24_8,plain,
( in(ordered_pair(U_212,U_210),U_208)
| ~ in(ordered_pair(U_212,U_210),U_209)
| U_209 != U_208
| ~ relation(U_208)
| ~ relation(U_209) ),
inference(clausify,[status(thm)],[f_24_7]) ).
cnf(f_24_9,plain,
( in(ordered_pair(U_213,U_211),U_209)
| ~ in(ordered_pair(U_213,U_211),U_208)
| U_209 != U_208
| ~ relation(U_208)
| ~ relation(U_209) ),
inference(clausify,[status(thm)],[f_24_7]) ).
cnf(f_24_10,plain,
( in(ordered_pair(sK43(U_209,U_208),sK44(U_209,U_208)),U_208)
| in(ordered_pair(sK41(U_209,U_208),sK42(U_209,U_208)),U_209)
| U_209 = U_208
| ~ relation(U_208)
| ~ relation(U_209) ),
inference(clausify,[status(thm)],[f_24_7]) ).
cnf(f_24_11,plain,
( ~ in(ordered_pair(sK43(U_209,U_208),sK44(U_209,U_208)),U_209)
| in(ordered_pair(sK41(U_209,U_208),sK42(U_209,U_208)),U_209)
| U_209 = U_208
| ~ relation(U_208)
| ~ relation(U_209) ),
inference(clausify,[status(thm)],[f_24_7]) ).
cnf(f_24_12,plain,
( in(ordered_pair(sK43(U_209,U_208),sK44(U_209,U_208)),U_208)
| ~ in(ordered_pair(sK41(U_209,U_208),sK42(U_209,U_208)),U_208)
| U_209 = U_208
| ~ relation(U_208)
| ~ relation(U_209) ),
inference(clausify,[status(thm)],[f_24_7]) ).
cnf(f_24_13,plain,
( ~ in(ordered_pair(sK43(U_209,U_208),sK44(U_209,U_208)),U_209)
| ~ in(ordered_pair(sK41(U_209,U_208),sK42(U_209,U_208)),U_208)
| U_209 = U_208
| ~ relation(U_208)
| ~ relation(U_209) ),
inference(clausify,[status(thm)],[f_24_7]) ).
fof(f_25_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_25_2,plain,
! [U_219,U_218] :
( ( ( ( element(U_218,U_219)
| ~ empty(U_218) )
& ( empty(U_218)
| ~ element(U_218,U_219) ) )
| ~ empty(U_219) )
& ( ( ( element(U_218,U_219)
| ~ in(U_218,U_219) )
& ( in(U_218,U_219)
| ~ element(U_218,U_219) ) )
| empty(U_219) ) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( ! [U_227] :
( ( ! [U_225] :
( element(U_225,U_227)
| ~ empty(U_225) )
& ! [U_224] :
( empty(U_224)
| ~ element(U_224,U_227) ) )
| ~ empty(U_227) )
& ! [U_226] :
( ( ! [U_223] :
( element(U_223,U_226)
| ~ in(U_223,U_226) )
& ! [U_222] :
( in(U_222,U_226)
| ~ element(U_222,U_226) ) )
| empty(U_226) ) ),
inference(miniscope,[status(thm)],[f_25_2]) ).
cnf(f_25_4,plain,
( in(U_222,U_226)
| ~ element(U_222,U_226)
| empty(U_226) ),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
( element(U_223,U_226)
| ~ in(U_223,U_226)
| empty(U_226) ),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_6,plain,
( empty(U_224)
| ~ element(U_224,U_227)
| ~ empty(U_227) ),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_7,plain,
( element(U_225,U_227)
| ~ empty(U_225)
| ~ empty(U_227) ),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_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_26_2,plain,
! [U_232,U_231,U_230] :
( ( U_230 = unordered_pair(U_232,U_231)
| ? [U_229] :
( ( ~ in(U_229,U_230)
& ( U_229 = U_231
| U_229 = U_232 ) )
| ( U_229 != U_231
& U_229 != U_232
& in(U_229,U_230) ) ) )
& ( ! [U_228] :
( ( in(U_228,U_230)
| ( U_228 != U_231
& U_228 != U_232 ) )
& ( U_228 = U_231
| U_228 = U_232
| ~ in(U_228,U_230) ) )
| U_230 != unordered_pair(U_232,U_231) ) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( ! [U_242,U_240,U_238] :
( U_238 = unordered_pair(U_242,U_240)
| ? [U_236] :
( ~ in(U_236,U_238)
& ( U_236 = U_240
| U_236 = U_242 ) )
| ? [U_235] :
( U_235 != U_240
& U_235 != U_242
& in(U_235,U_238) ) )
& ! [U_241,U_239,U_237] :
( ( ! [U_234] :
( in(U_234,U_237)
| ( U_234 != U_239
& U_234 != U_241 ) )
& ! [U_233] :
( U_233 = U_239
| U_233 = U_241
| ~ in(U_233,U_237) ) )
| U_237 != unordered_pair(U_241,U_239) ) ),
inference(miniscope,[status(thm)],[f_26_2]) ).
fof(f_26_4,plain,
( ! [U_242,U_240,U_238] :
( U_238 = unordered_pair(U_242,U_240)
| ? [U_236] :
( ~ in(U_236,U_238)
& ( U_236 = U_240
| U_236 = U_242 ) )
| ( sK45(U_242,U_240,U_238) != U_240
& sK45(U_242,U_240,U_238) != U_242
& in(sK45(U_242,U_240,U_238),U_238) ) )
& ! [U_241,U_239,U_237] :
( ( ! [U_234] :
( in(U_234,U_237)
| ( U_234 != U_239
& U_234 != U_241 ) )
& ! [U_233] :
( U_233 = U_239
| U_233 = U_241
| ~ in(U_233,U_237) ) )
| U_237 != unordered_pair(U_241,U_239) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_235,sK45(U_242,U_240,U_238))],[f_26_3]) ).
fof(f_26_5,plain,
( ! [U_242,U_240,U_238] :
( U_238 = unordered_pair(U_242,U_240)
| ( ~ in(sK46(U_242,U_240,U_238),U_238)
& ( sK46(U_242,U_240,U_238) = U_240
| sK46(U_242,U_240,U_238) = U_242 ) )
| ( sK45(U_242,U_240,U_238) != U_240
& sK45(U_242,U_240,U_238) != U_242
& in(sK45(U_242,U_240,U_238),U_238) ) )
& ! [U_241,U_239,U_237] :
( ( ! [U_234] :
( in(U_234,U_237)
| ( U_234 != U_239
& U_234 != U_241 ) )
& ! [U_233] :
( U_233 = U_239
| U_233 = U_241
| ~ in(U_233,U_237) ) )
| U_237 != unordered_pair(U_241,U_239) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_236,sK46(U_242,U_240,U_238))],[f_26_4]) ).
cnf(f_26_6,plain,
( U_233 = U_239
| U_233 = U_241
| ~ in(U_233,U_237)
| U_237 != unordered_pair(U_241,U_239) ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_7,plain,
( U_234 != U_241
| in(U_234,U_237)
| U_237 != unordered_pair(U_241,U_239) ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_8,plain,
( U_234 != U_239
| in(U_234,U_237)
| U_237 != unordered_pair(U_241,U_239) ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_9,plain,
( sK46(U_242,U_240,U_238) = U_240
| sK46(U_242,U_240,U_238) = U_242
| in(sK45(U_242,U_240,U_238),U_238)
| U_238 = unordered_pair(U_242,U_240) ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_10,plain,
( ~ in(sK46(U_242,U_240,U_238),U_238)
| in(sK45(U_242,U_240,U_238),U_238)
| U_238 = unordered_pair(U_242,U_240) ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_11,plain,
( sK45(U_242,U_240,U_238) != U_242
| sK46(U_242,U_240,U_238) = U_240
| sK46(U_242,U_240,U_238) = U_242
| U_238 = unordered_pair(U_242,U_240) ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_12,plain,
( sK45(U_242,U_240,U_238) != U_240
| sK46(U_242,U_240,U_238) = U_240
| sK46(U_242,U_240,U_238) = U_242
| U_238 = unordered_pair(U_242,U_240) ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_13,plain,
( sK45(U_242,U_240,U_238) != U_242
| ~ in(sK46(U_242,U_240,U_238),U_238)
| U_238 = unordered_pair(U_242,U_240) ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_14,plain,
( sK45(U_242,U_240,U_238) != U_240
| ~ in(sK46(U_242,U_240,U_238),U_238)
| U_238 = unordered_pair(U_242,U_240) ),
inference(clausify,[status(thm)],[f_26_5]) ).
fof(f_27_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_27_2,plain,
! [U_247,U_246,U_245] :
( ( U_245 = set_union2(U_247,U_246)
| ? [U_244] :
( ( ~ in(U_244,U_245)
& ( in(U_244,U_246)
| in(U_244,U_247) ) )
| ( ~ in(U_244,U_246)
& ~ in(U_244,U_247)
& in(U_244,U_245) ) ) )
& ( ! [U_243] :
( ( in(U_243,U_245)
| ( ~ in(U_243,U_246)
& ~ in(U_243,U_247) ) )
& ( in(U_243,U_246)
| in(U_243,U_247)
| ~ in(U_243,U_245) ) )
| U_245 != set_union2(U_247,U_246) ) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( ! [U_257,U_255,U_253] :
( U_253 = set_union2(U_257,U_255)
| ? [U_251] :
( ~ in(U_251,U_253)
& ( in(U_251,U_255)
| in(U_251,U_257) ) )
| ? [U_250] :
( ~ in(U_250,U_255)
& ~ in(U_250,U_257)
& in(U_250,U_253) ) )
& ! [U_256,U_254,U_252] :
( ( ! [U_249] :
( in(U_249,U_252)
| ( ~ in(U_249,U_254)
& ~ in(U_249,U_256) ) )
& ! [U_248] :
( in(U_248,U_254)
| in(U_248,U_256)
| ~ in(U_248,U_252) ) )
| U_252 != set_union2(U_256,U_254) ) ),
inference(miniscope,[status(thm)],[f_27_2]) ).
fof(f_27_4,plain,
( ! [U_257,U_255,U_253] :
( U_253 = set_union2(U_257,U_255)
| ? [U_251] :
( ~ in(U_251,U_253)
& ( in(U_251,U_255)
| in(U_251,U_257) ) )
| ( ~ in(sK47(U_257,U_255,U_253),U_255)
& ~ in(sK47(U_257,U_255,U_253),U_257)
& in(sK47(U_257,U_255,U_253),U_253) ) )
& ! [U_256,U_254,U_252] :
( ( ! [U_249] :
( in(U_249,U_252)
| ( ~ in(U_249,U_254)
& ~ in(U_249,U_256) ) )
& ! [U_248] :
( in(U_248,U_254)
| in(U_248,U_256)
| ~ in(U_248,U_252) ) )
| U_252 != set_union2(U_256,U_254) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_250,sK47(U_257,U_255,U_253))],[f_27_3]) ).
fof(f_27_5,plain,
( ! [U_257,U_255,U_253] :
( U_253 = set_union2(U_257,U_255)
| ( ~ in(sK48(U_257,U_255,U_253),U_253)
& ( in(sK48(U_257,U_255,U_253),U_255)
| in(sK48(U_257,U_255,U_253),U_257) ) )
| ( ~ in(sK47(U_257,U_255,U_253),U_255)
& ~ in(sK47(U_257,U_255,U_253),U_257)
& in(sK47(U_257,U_255,U_253),U_253) ) )
& ! [U_256,U_254,U_252] :
( ( ! [U_249] :
( in(U_249,U_252)
| ( ~ in(U_249,U_254)
& ~ in(U_249,U_256) ) )
& ! [U_248] :
( in(U_248,U_254)
| in(U_248,U_256)
| ~ in(U_248,U_252) ) )
| U_252 != set_union2(U_256,U_254) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_251,sK48(U_257,U_255,U_253))],[f_27_4]) ).
cnf(f_27_6,plain,
( in(U_248,U_254)
| in(U_248,U_256)
| ~ in(U_248,U_252)
| U_252 != set_union2(U_256,U_254) ),
inference(clausify,[status(thm)],[f_27_5]) ).
cnf(f_27_7,plain,
( ~ in(U_249,U_256)
| in(U_249,U_252)
| U_252 != set_union2(U_256,U_254) ),
inference(clausify,[status(thm)],[f_27_5]) ).
cnf(f_27_8,plain,
( ~ in(U_249,U_254)
| in(U_249,U_252)
| U_252 != set_union2(U_256,U_254) ),
inference(clausify,[status(thm)],[f_27_5]) ).
cnf(f_27_9,plain,
( in(sK48(U_257,U_255,U_253),U_255)
| in(sK48(U_257,U_255,U_253),U_257)
| in(sK47(U_257,U_255,U_253),U_253)
| U_253 = set_union2(U_257,U_255) ),
inference(clausify,[status(thm)],[f_27_5]) ).
cnf(f_27_10,plain,
( ~ in(sK48(U_257,U_255,U_253),U_253)
| in(sK47(U_257,U_255,U_253),U_253)
| U_253 = set_union2(U_257,U_255) ),
inference(clausify,[status(thm)],[f_27_5]) ).
cnf(f_27_11,plain,
( ~ in(sK47(U_257,U_255,U_253),U_257)
| in(sK48(U_257,U_255,U_253),U_255)
| in(sK48(U_257,U_255,U_253),U_257)
| U_253 = set_union2(U_257,U_255) ),
inference(clausify,[status(thm)],[f_27_5]) ).
cnf(f_27_12,plain,
( ~ in(sK47(U_257,U_255,U_253),U_255)
| in(sK48(U_257,U_255,U_253),U_255)
| in(sK48(U_257,U_255,U_253),U_257)
| U_253 = set_union2(U_257,U_255) ),
inference(clausify,[status(thm)],[f_27_5]) ).
cnf(f_27_13,plain,
( ~ in(sK47(U_257,U_255,U_253),U_257)
| ~ in(sK48(U_257,U_255,U_253),U_253)
| U_253 = set_union2(U_257,U_255) ),
inference(clausify,[status(thm)],[f_27_5]) ).
cnf(f_27_14,plain,
( ~ in(sK47(U_257,U_255,U_253),U_255)
| ~ in(sK48(U_257,U_255,U_253),U_253)
| U_253 = set_union2(U_257,U_255) ),
inference(clausify,[status(thm)],[f_27_5]) ).
fof(f_28_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_28_2,plain,
! [U_270,U_269,U_268] :
( ( U_268 = cartesian_product2(U_270,U_269)
| ? [U_267] :
( ( ~ in(U_267,U_268)
& ? [U_266,U_265] :
( U_267 = ordered_pair(U_266,U_265)
& in(U_265,U_269)
& in(U_266,U_270) ) )
| ( ! [U_264,U_263] :
( U_267 != ordered_pair(U_264,U_263)
| ~ in(U_263,U_269)
| ~ in(U_264,U_270) )
& in(U_267,U_268) ) ) )
& ( ! [U_262] :
( ( in(U_262,U_268)
| ! [U_261,U_260] :
( U_262 != ordered_pair(U_261,U_260)
| ~ in(U_260,U_269)
| ~ in(U_261,U_270) ) )
& ( ? [U_259,U_258] :
( U_262 = ordered_pair(U_259,U_258)
& in(U_258,U_269)
& in(U_259,U_270) )
| ~ in(U_262,U_268) ) )
| U_268 != cartesian_product2(U_270,U_269) ) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( ! [U_280,U_278,U_276] :
( U_276 = cartesian_product2(U_280,U_278)
| ? [U_274] :
( ~ in(U_274,U_276)
& ? [U_266] :
( ? [U_265] :
( U_274 = ordered_pair(U_266,U_265)
& in(U_265,U_278) )
& in(U_266,U_280) ) )
| ? [U_273] :
( ! [U_264] :
( ! [U_263] :
( U_273 != ordered_pair(U_264,U_263)
| ~ in(U_263,U_278) )
| ~ in(U_264,U_280) )
& in(U_273,U_276) ) )
& ! [U_279,U_277,U_275] :
( ( ! [U_272] :
( in(U_272,U_275)
| ! [U_261] :
( ! [U_260] :
( U_272 != ordered_pair(U_261,U_260)
| ~ in(U_260,U_277) )
| ~ in(U_261,U_279) ) )
& ! [U_271] :
( ? [U_259] :
( ? [U_258] :
( U_271 = ordered_pair(U_259,U_258)
& in(U_258,U_277) )
& in(U_259,U_279) )
| ~ in(U_271,U_275) ) )
| U_275 != cartesian_product2(U_279,U_277) ) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
fof(f_28_4,plain,
( ! [U_280,U_278,U_276] :
( U_276 = cartesian_product2(U_280,U_278)
| ? [U_274] :
( ~ in(U_274,U_276)
& ? [U_266] :
( ? [U_265] :
( U_274 = ordered_pair(U_266,U_265)
& in(U_265,U_278) )
& in(U_266,U_280) ) )
| ? [U_273] :
( ! [U_264] :
( ! [U_263] :
( U_273 != ordered_pair(U_264,U_263)
| ~ in(U_263,U_278) )
| ~ in(U_264,U_280) )
& in(U_273,U_276) ) )
& ! [U_279,U_277,U_275] :
( ( ! [U_272] :
( in(U_272,U_275)
| ! [U_261] :
( ! [U_260] :
( U_272 != ordered_pair(U_261,U_260)
| ~ in(U_260,U_277) )
| ~ in(U_261,U_279) ) )
& ! [U_271] :
( ( ? [U_258] :
( U_271 = ordered_pair(sK49(U_279,U_277,U_275,U_271),U_258)
& in(U_258,U_277) )
& in(sK49(U_279,U_277,U_275,U_271),U_279) )
| ~ in(U_271,U_275) ) )
| U_275 != cartesian_product2(U_279,U_277) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_259,sK49(U_279,U_277,U_275,U_271))],[f_28_3]) ).
fof(f_28_5,plain,
( ! [U_280,U_278,U_276] :
( U_276 = cartesian_product2(U_280,U_278)
| ? [U_274] :
( ~ in(U_274,U_276)
& ? [U_266] :
( ? [U_265] :
( U_274 = ordered_pair(U_266,U_265)
& in(U_265,U_278) )
& in(U_266,U_280) ) )
| ? [U_273] :
( ! [U_264] :
( ! [U_263] :
( U_273 != ordered_pair(U_264,U_263)
| ~ in(U_263,U_278) )
| ~ in(U_264,U_280) )
& in(U_273,U_276) ) )
& ! [U_279,U_277,U_275] :
( ( ! [U_272] :
( in(U_272,U_275)
| ! [U_261] :
( ! [U_260] :
( U_272 != ordered_pair(U_261,U_260)
| ~ in(U_260,U_277) )
| ~ in(U_261,U_279) ) )
& ! [U_271] :
( ( U_271 = ordered_pair(sK49(U_279,U_277,U_275,U_271),sK50(U_279,U_277,U_275,U_271))
& in(sK50(U_279,U_277,U_275,U_271),U_277)
& in(sK49(U_279,U_277,U_275,U_271),U_279) )
| ~ in(U_271,U_275) ) )
| U_275 != cartesian_product2(U_279,U_277) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_258,sK50(U_279,U_277,U_275,U_271))],[f_28_4]) ).
fof(f_28_6,plain,
( ! [U_280,U_278,U_276] :
( U_276 = cartesian_product2(U_280,U_278)
| ? [U_274] :
( ~ in(U_274,U_276)
& ? [U_266] :
( ? [U_265] :
( U_274 = ordered_pair(U_266,U_265)
& in(U_265,U_278) )
& in(U_266,U_280) ) )
| ( ! [U_264] :
( ! [U_263] :
( sK51(U_280,U_278,U_276) != ordered_pair(U_264,U_263)
| ~ in(U_263,U_278) )
| ~ in(U_264,U_280) )
& in(sK51(U_280,U_278,U_276),U_276) ) )
& ! [U_279,U_277,U_275] :
( ( ! [U_272] :
( in(U_272,U_275)
| ! [U_261] :
( ! [U_260] :
( U_272 != ordered_pair(U_261,U_260)
| ~ in(U_260,U_277) )
| ~ in(U_261,U_279) ) )
& ! [U_271] :
( ( U_271 = ordered_pair(sK49(U_279,U_277,U_275,U_271),sK50(U_279,U_277,U_275,U_271))
& in(sK50(U_279,U_277,U_275,U_271),U_277)
& in(sK49(U_279,U_277,U_275,U_271),U_279) )
| ~ in(U_271,U_275) ) )
| U_275 != cartesian_product2(U_279,U_277) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_273,sK51(U_280,U_278,U_276))],[f_28_5]) ).
fof(f_28_7,plain,
( ! [U_280,U_278,U_276] :
( U_276 = cartesian_product2(U_280,U_278)
| ( ~ in(sK52(U_280,U_278,U_276),U_276)
& ? [U_266] :
( ? [U_265] :
( sK52(U_280,U_278,U_276) = ordered_pair(U_266,U_265)
& in(U_265,U_278) )
& in(U_266,U_280) ) )
| ( ! [U_264] :
( ! [U_263] :
( sK51(U_280,U_278,U_276) != ordered_pair(U_264,U_263)
| ~ in(U_263,U_278) )
| ~ in(U_264,U_280) )
& in(sK51(U_280,U_278,U_276),U_276) ) )
& ! [U_279,U_277,U_275] :
( ( ! [U_272] :
( in(U_272,U_275)
| ! [U_261] :
( ! [U_260] :
( U_272 != ordered_pair(U_261,U_260)
| ~ in(U_260,U_277) )
| ~ in(U_261,U_279) ) )
& ! [U_271] :
( ( U_271 = ordered_pair(sK49(U_279,U_277,U_275,U_271),sK50(U_279,U_277,U_275,U_271))
& in(sK50(U_279,U_277,U_275,U_271),U_277)
& in(sK49(U_279,U_277,U_275,U_271),U_279) )
| ~ in(U_271,U_275) ) )
| U_275 != cartesian_product2(U_279,U_277) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_274,sK52(U_280,U_278,U_276))],[f_28_6]) ).
fof(f_28_8,plain,
( ! [U_280,U_278,U_276] :
( U_276 = cartesian_product2(U_280,U_278)
| ( ~ in(sK52(U_280,U_278,U_276),U_276)
& ? [U_265] :
( sK52(U_280,U_278,U_276) = ordered_pair(sK53(U_280,U_278,U_276),U_265)
& in(U_265,U_278) )
& in(sK53(U_280,U_278,U_276),U_280) )
| ( ! [U_264] :
( ! [U_263] :
( sK51(U_280,U_278,U_276) != ordered_pair(U_264,U_263)
| ~ in(U_263,U_278) )
| ~ in(U_264,U_280) )
& in(sK51(U_280,U_278,U_276),U_276) ) )
& ! [U_279,U_277,U_275] :
( ( ! [U_272] :
( in(U_272,U_275)
| ! [U_261] :
( ! [U_260] :
( U_272 != ordered_pair(U_261,U_260)
| ~ in(U_260,U_277) )
| ~ in(U_261,U_279) ) )
& ! [U_271] :
( ( U_271 = ordered_pair(sK49(U_279,U_277,U_275,U_271),sK50(U_279,U_277,U_275,U_271))
& in(sK50(U_279,U_277,U_275,U_271),U_277)
& in(sK49(U_279,U_277,U_275,U_271),U_279) )
| ~ in(U_271,U_275) ) )
| U_275 != cartesian_product2(U_279,U_277) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_266,sK53(U_280,U_278,U_276))],[f_28_7]) ).
fof(f_28_9,plain,
( ! [U_280,U_278,U_276] :
( U_276 = cartesian_product2(U_280,U_278)
| ( ~ in(sK52(U_280,U_278,U_276),U_276)
& sK52(U_280,U_278,U_276) = ordered_pair(sK53(U_280,U_278,U_276),sK54(U_280,U_278,U_276))
& in(sK54(U_280,U_278,U_276),U_278)
& in(sK53(U_280,U_278,U_276),U_280) )
| ( ! [U_264] :
( ! [U_263] :
( sK51(U_280,U_278,U_276) != ordered_pair(U_264,U_263)
| ~ in(U_263,U_278) )
| ~ in(U_264,U_280) )
& in(sK51(U_280,U_278,U_276),U_276) ) )
& ! [U_279,U_277,U_275] :
( ( ! [U_272] :
( in(U_272,U_275)
| ! [U_261] :
( ! [U_260] :
( U_272 != ordered_pair(U_261,U_260)
| ~ in(U_260,U_277) )
| ~ in(U_261,U_279) ) )
& ! [U_271] :
( ( U_271 = ordered_pair(sK49(U_279,U_277,U_275,U_271),sK50(U_279,U_277,U_275,U_271))
& in(sK50(U_279,U_277,U_275,U_271),U_277)
& in(sK49(U_279,U_277,U_275,U_271),U_279) )
| ~ in(U_271,U_275) ) )
| U_275 != cartesian_product2(U_279,U_277) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_265,sK54(U_280,U_278,U_276))],[f_28_8]) ).
cnf(f_28_10,plain,
( in(sK49(U_279,U_277,U_275,U_271),U_279)
| ~ in(U_271,U_275)
| U_275 != cartesian_product2(U_279,U_277) ),
inference(clausify,[status(thm)],[f_28_9]) ).
cnf(f_28_11,plain,
( in(sK50(U_279,U_277,U_275,U_271),U_277)
| ~ in(U_271,U_275)
| U_275 != cartesian_product2(U_279,U_277) ),
inference(clausify,[status(thm)],[f_28_9]) ).
cnf(f_28_12,plain,
( U_271 = ordered_pair(sK49(U_279,U_277,U_275,U_271),sK50(U_279,U_277,U_275,U_271))
| ~ in(U_271,U_275)
| U_275 != cartesian_product2(U_279,U_277) ),
inference(clausify,[status(thm)],[f_28_9]) ).
cnf(f_28_13,plain,
( in(U_272,U_275)
| U_272 != ordered_pair(U_261,U_260)
| ~ in(U_260,U_277)
| ~ in(U_261,U_279)
| U_275 != cartesian_product2(U_279,U_277) ),
inference(clausify,[status(thm)],[f_28_9]) ).
cnf(f_28_14,plain,
( in(sK53(U_280,U_278,U_276),U_280)
| in(sK51(U_280,U_278,U_276),U_276)
| U_276 = cartesian_product2(U_280,U_278) ),
inference(clausify,[status(thm)],[f_28_9]) ).
cnf(f_28_15,plain,
( in(sK54(U_280,U_278,U_276),U_278)
| in(sK51(U_280,U_278,U_276),U_276)
| U_276 = cartesian_product2(U_280,U_278) ),
inference(clausify,[status(thm)],[f_28_9]) ).
cnf(f_28_16,plain,
( sK52(U_280,U_278,U_276) = ordered_pair(sK53(U_280,U_278,U_276),sK54(U_280,U_278,U_276))
| in(sK51(U_280,U_278,U_276),U_276)
| U_276 = cartesian_product2(U_280,U_278) ),
inference(clausify,[status(thm)],[f_28_9]) ).
cnf(f_28_17,plain,
( ~ in(sK52(U_280,U_278,U_276),U_276)
| in(sK51(U_280,U_278,U_276),U_276)
| U_276 = cartesian_product2(U_280,U_278) ),
inference(clausify,[status(thm)],[f_28_9]) ).
cnf(f_28_18,plain,
( in(sK53(U_280,U_278,U_276),U_280)
| sK51(U_280,U_278,U_276) != ordered_pair(U_264,U_263)
| ~ in(U_263,U_278)
| ~ in(U_264,U_280)
| U_276 = cartesian_product2(U_280,U_278) ),
inference(clausify,[status(thm)],[f_28_9]) ).
cnf(f_28_19,plain,
( in(sK54(U_280,U_278,U_276),U_278)
| sK51(U_280,U_278,U_276) != ordered_pair(U_264,U_263)
| ~ in(U_263,U_278)
| ~ in(U_264,U_280)
| U_276 = cartesian_product2(U_280,U_278) ),
inference(clausify,[status(thm)],[f_28_9]) ).
cnf(f_28_20,plain,
( sK52(U_280,U_278,U_276) = ordered_pair(sK53(U_280,U_278,U_276),sK54(U_280,U_278,U_276))
| sK51(U_280,U_278,U_276) != ordered_pair(U_264,U_263)
| ~ in(U_263,U_278)
| ~ in(U_264,U_280)
| U_276 = cartesian_product2(U_280,U_278) ),
inference(clausify,[status(thm)],[f_28_9]) ).
cnf(f_28_21,plain,
( ~ in(sK52(U_280,U_278,U_276),U_276)
| sK51(U_280,U_278,U_276) != ordered_pair(U_264,U_263)
| ~ in(U_263,U_278)
| ~ in(U_264,U_280)
| U_276 = cartesian_product2(U_280,U_278) ),
inference(clausify,[status(thm)],[f_28_9]) ).
fof(f_29_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_29_2,plain,
! [U_286] :
( ! [U_285] :
( ( ( subset(U_286,U_285)
| ? [U_284,U_283] :
( ~ in(ordered_pair(U_284,U_283),U_285)
& in(ordered_pair(U_284,U_283),U_286) ) )
& ( ! [U_282,U_281] :
( in(ordered_pair(U_282,U_281),U_285)
| ~ in(ordered_pair(U_282,U_281),U_286) )
| ~ subset(U_286,U_285) ) )
| ~ relation(U_285) )
| ~ relation(U_286) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_286] :
( ! [U_285] :
( ( ( subset(U_286,U_285)
| ? [U_283] :
( ~ in(ordered_pair(sK55(U_286,U_285),U_283),U_285)
& in(ordered_pair(sK55(U_286,U_285),U_283),U_286) ) )
& ( ! [U_282,U_281] :
( in(ordered_pair(U_282,U_281),U_285)
| ~ in(ordered_pair(U_282,U_281),U_286) )
| ~ subset(U_286,U_285) ) )
| ~ relation(U_285) )
| ~ relation(U_286) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_284,sK55(U_286,U_285))],[f_29_2]) ).
fof(f_29_4,plain,
! [U_286] :
( ! [U_285] :
( ( ( subset(U_286,U_285)
| ( ~ in(ordered_pair(sK55(U_286,U_285),sK56(U_286,U_285)),U_285)
& in(ordered_pair(sK55(U_286,U_285),sK56(U_286,U_285)),U_286) ) )
& ( ! [U_282,U_281] :
( in(ordered_pair(U_282,U_281),U_285)
| ~ in(ordered_pair(U_282,U_281),U_286) )
| ~ subset(U_286,U_285) ) )
| ~ relation(U_285) )
| ~ relation(U_286) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_283,sK56(U_286,U_285))],[f_29_3]) ).
cnf(f_29_5,plain,
( in(ordered_pair(U_282,U_281),U_285)
| ~ in(ordered_pair(U_282,U_281),U_286)
| ~ subset(U_286,U_285)
| ~ relation(U_285)
| ~ relation(U_286) ),
inference(clausify,[status(thm)],[f_29_4]) ).
cnf(f_29_6,plain,
( in(ordered_pair(sK55(U_286,U_285),sK56(U_286,U_285)),U_286)
| subset(U_286,U_285)
| ~ relation(U_285)
| ~ relation(U_286) ),
inference(clausify,[status(thm)],[f_29_4]) ).
cnf(f_29_7,plain,
( ~ in(ordered_pair(sK55(U_286,U_285),sK56(U_286,U_285)),U_285)
| subset(U_286,U_285)
| ~ relation(U_285)
| ~ relation(U_286) ),
inference(clausify,[status(thm)],[f_29_4]) ).
fof(f_30_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_30_2,plain,
! [U_290,U_289] :
( ( subset(U_290,U_289)
| ? [U_288] :
( ~ in(U_288,U_289)
& in(U_288,U_290) ) )
& ( ! [U_287] :
( in(U_287,U_289)
| ~ in(U_287,U_290) )
| ~ subset(U_290,U_289) ) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( ! [U_294,U_292] :
( subset(U_294,U_292)
| ? [U_288] :
( ~ in(U_288,U_292)
& in(U_288,U_294) ) )
& ! [U_293,U_291] :
( ! [U_287] :
( in(U_287,U_291)
| ~ in(U_287,U_293) )
| ~ subset(U_293,U_291) ) ),
inference(miniscope,[status(thm)],[f_30_2]) ).
fof(f_30_4,plain,
( ! [U_294,U_292] :
( subset(U_294,U_292)
| ( ~ in(sK57(U_294,U_292),U_292)
& in(sK57(U_294,U_292),U_294) ) )
& ! [U_293,U_291] :
( ! [U_287] :
( in(U_287,U_291)
| ~ in(U_287,U_293) )
| ~ subset(U_293,U_291) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_288,sK57(U_294,U_292))],[f_30_3]) ).
cnf(f_30_5,plain,
( in(U_287,U_291)
| ~ in(U_287,U_293)
| ~ subset(U_293,U_291) ),
inference(clausify,[status(thm)],[f_30_4]) ).
cnf(f_30_6,plain,
( in(sK57(U_294,U_292),U_294)
| subset(U_294,U_292) ),
inference(clausify,[status(thm)],[f_30_4]) ).
cnf(f_30_7,plain,
( ~ in(sK57(U_294,U_292),U_292)
| subset(U_294,U_292) ),
inference(clausify,[status(thm)],[f_30_4]) ).
fof(f_31_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_31_2,plain,
! [U_299,U_298,U_297] :
( ( U_297 = set_intersection2(U_299,U_298)
| ? [U_296] :
( ( ~ in(U_296,U_297)
& in(U_296,U_298)
& in(U_296,U_299) )
| ( ( ~ in(U_296,U_298)
| ~ in(U_296,U_299) )
& in(U_296,U_297) ) ) )
& ( ! [U_295] :
( ( in(U_295,U_297)
| ~ in(U_295,U_298)
| ~ in(U_295,U_299) )
& ( ( in(U_295,U_298)
& in(U_295,U_299) )
| ~ in(U_295,U_297) ) )
| U_297 != set_intersection2(U_299,U_298) ) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( ! [U_309,U_307,U_305] :
( U_305 = set_intersection2(U_309,U_307)
| ? [U_303] :
( ~ in(U_303,U_305)
& in(U_303,U_307)
& in(U_303,U_309) )
| ? [U_302] :
( ( ~ in(U_302,U_307)
| ~ in(U_302,U_309) )
& in(U_302,U_305) ) )
& ! [U_308,U_306,U_304] :
( ( ! [U_301] :
( in(U_301,U_304)
| ~ in(U_301,U_306)
| ~ in(U_301,U_308) )
& ! [U_300] :
( ( in(U_300,U_306)
& in(U_300,U_308) )
| ~ in(U_300,U_304) ) )
| U_304 != set_intersection2(U_308,U_306) ) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
fof(f_31_4,plain,
( ! [U_309,U_307,U_305] :
( U_305 = set_intersection2(U_309,U_307)
| ? [U_303] :
( ~ in(U_303,U_305)
& in(U_303,U_307)
& in(U_303,U_309) )
| ( ( ~ in(sK58(U_309,U_307,U_305),U_307)
| ~ in(sK58(U_309,U_307,U_305),U_309) )
& in(sK58(U_309,U_307,U_305),U_305) ) )
& ! [U_308,U_306,U_304] :
( ( ! [U_301] :
( in(U_301,U_304)
| ~ in(U_301,U_306)
| ~ in(U_301,U_308) )
& ! [U_300] :
( ( in(U_300,U_306)
& in(U_300,U_308) )
| ~ in(U_300,U_304) ) )
| U_304 != set_intersection2(U_308,U_306) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_302,sK58(U_309,U_307,U_305))],[f_31_3]) ).
fof(f_31_5,plain,
( ! [U_309,U_307,U_305] :
( U_305 = set_intersection2(U_309,U_307)
| ( ~ in(sK59(U_309,U_307,U_305),U_305)
& in(sK59(U_309,U_307,U_305),U_307)
& in(sK59(U_309,U_307,U_305),U_309) )
| ( ( ~ in(sK58(U_309,U_307,U_305),U_307)
| ~ in(sK58(U_309,U_307,U_305),U_309) )
& in(sK58(U_309,U_307,U_305),U_305) ) )
& ! [U_308,U_306,U_304] :
( ( ! [U_301] :
( in(U_301,U_304)
| ~ in(U_301,U_306)
| ~ in(U_301,U_308) )
& ! [U_300] :
( ( in(U_300,U_306)
& in(U_300,U_308) )
| ~ in(U_300,U_304) ) )
| U_304 != set_intersection2(U_308,U_306) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_303,sK59(U_309,U_307,U_305))],[f_31_4]) ).
cnf(f_31_6,plain,
( in(U_300,U_308)
| ~ in(U_300,U_304)
| U_304 != set_intersection2(U_308,U_306) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_7,plain,
( in(U_300,U_306)
| ~ in(U_300,U_304)
| U_304 != set_intersection2(U_308,U_306) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_8,plain,
( in(U_301,U_304)
| ~ in(U_301,U_306)
| ~ in(U_301,U_308)
| U_304 != set_intersection2(U_308,U_306) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_9,plain,
( in(sK59(U_309,U_307,U_305),U_309)
| in(sK58(U_309,U_307,U_305),U_305)
| U_305 = set_intersection2(U_309,U_307) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_10,plain,
( in(sK59(U_309,U_307,U_305),U_307)
| in(sK58(U_309,U_307,U_305),U_305)
| U_305 = set_intersection2(U_309,U_307) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_11,plain,
( ~ in(sK59(U_309,U_307,U_305),U_305)
| in(sK58(U_309,U_307,U_305),U_305)
| U_305 = set_intersection2(U_309,U_307) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_12,plain,
( in(sK59(U_309,U_307,U_305),U_309)
| ~ in(sK58(U_309,U_307,U_305),U_307)
| ~ in(sK58(U_309,U_307,U_305),U_309)
| U_305 = set_intersection2(U_309,U_307) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_13,plain,
( in(sK59(U_309,U_307,U_305),U_307)
| ~ in(sK58(U_309,U_307,U_305),U_307)
| ~ in(sK58(U_309,U_307,U_305),U_309)
| U_305 = set_intersection2(U_309,U_307) ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_14,plain,
( ~ in(sK59(U_309,U_307,U_305),U_305)
| ~ in(sK58(U_309,U_307,U_305),U_307)
| ~ in(sK58(U_309,U_307,U_305),U_309)
| U_305 = set_intersection2(U_309,U_307) ),
inference(clausify,[status(thm)],[f_31_5]) ).
fof(f_32_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_32_2,plain,
! [U_312] :
( ! [U_311,U_310] :
( ( ( ( U_310 = apply(U_312,U_311)
| U_310 != empty_set )
& ( U_310 = empty_set
| U_310 != apply(U_312,U_311) ) )
| in(U_311,relation_dom(U_312)) )
& ( ( ( U_310 = apply(U_312,U_311)
| ~ in(ordered_pair(U_311,U_310),U_312) )
& ( in(ordered_pair(U_311,U_310),U_312)
| U_310 != apply(U_312,U_311) ) )
| ~ in(U_311,relation_dom(U_312)) ) )
| ~ function(U_312)
| ~ relation(U_312) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_312] :
( ( ! [U_320] :
( ( ! [U_318] :
( U_318 = apply(U_312,U_320)
| U_318 != empty_set )
& ! [U_317] :
( U_317 = empty_set
| U_317 != apply(U_312,U_320) ) )
| in(U_320,relation_dom(U_312)) )
& ! [U_319] :
( ( ! [U_316] :
( U_316 = apply(U_312,U_319)
| ~ in(ordered_pair(U_319,U_316),U_312) )
& ! [U_315] :
( in(ordered_pair(U_319,U_315),U_312)
| U_315 != apply(U_312,U_319) ) )
| ~ in(U_319,relation_dom(U_312)) ) )
| ~ function(U_312)
| ~ relation(U_312) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
cnf(f_32_4,plain,
( in(ordered_pair(U_319,U_315),U_312)
| U_315 != apply(U_312,U_319)
| ~ in(U_319,relation_dom(U_312))
| ~ function(U_312)
| ~ relation(U_312) ),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_5,plain,
( U_316 = apply(U_312,U_319)
| ~ in(ordered_pair(U_319,U_316),U_312)
| ~ in(U_319,relation_dom(U_312))
| ~ function(U_312)
| ~ relation(U_312) ),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_6,plain,
( U_317 = empty_set
| U_317 != apply(U_312,U_320)
| in(U_320,relation_dom(U_312))
| ~ function(U_312)
| ~ relation(U_312) ),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_7,plain,
( U_318 = apply(U_312,U_320)
| U_318 != empty_set
| in(U_320,relation_dom(U_312))
| ~ function(U_312)
| ~ relation(U_312) ),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_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_33_2,plain,
! [U_328] :
( ! [U_327] :
( ( U_327 = relation_dom(U_328)
| ? [U_326] :
( ( ~ in(U_326,U_327)
& ? [U_325] : in(ordered_pair(U_326,U_325),U_328) )
| ( ! [U_324] : ~ in(ordered_pair(U_326,U_324),U_328)
& in(U_326,U_327) ) ) )
& ( ! [U_323] :
( ( in(U_323,U_327)
| ! [U_322] : ~ in(ordered_pair(U_323,U_322),U_328) )
& ( ? [U_321] : in(ordered_pair(U_323,U_321),U_328)
| ~ in(U_323,U_327) ) )
| U_327 != relation_dom(U_328) ) )
| ~ relation(U_328) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_328] :
( ( ! [U_334] :
( U_334 = relation_dom(U_328)
| ? [U_332] :
( ~ in(U_332,U_334)
& ? [U_325] : in(ordered_pair(U_332,U_325),U_328) )
| ? [U_331] :
( ! [U_324] : ~ in(ordered_pair(U_331,U_324),U_328)
& in(U_331,U_334) ) )
& ! [U_333] :
( ( ! [U_330] :
( in(U_330,U_333)
| ! [U_322] : ~ in(ordered_pair(U_330,U_322),U_328) )
& ! [U_329] :
( ? [U_321] : in(ordered_pair(U_329,U_321),U_328)
| ~ in(U_329,U_333) ) )
| U_333 != relation_dom(U_328) ) )
| ~ relation(U_328) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
fof(f_33_4,plain,
! [U_328] :
( ( ! [U_334] :
( U_334 = relation_dom(U_328)
| ? [U_332] :
( ~ in(U_332,U_334)
& ? [U_325] : in(ordered_pair(U_332,U_325),U_328) )
| ? [U_331] :
( ! [U_324] : ~ in(ordered_pair(U_331,U_324),U_328)
& in(U_331,U_334) ) )
& ! [U_333] :
( ( ! [U_330] :
( in(U_330,U_333)
| ! [U_322] : ~ in(ordered_pair(U_330,U_322),U_328) )
& ! [U_329] :
( in(ordered_pair(U_329,sK60(U_328,U_333,U_329)),U_328)
| ~ in(U_329,U_333) ) )
| U_333 != relation_dom(U_328) ) )
| ~ relation(U_328) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_321,sK60(U_328,U_333,U_329))],[f_33_3]) ).
fof(f_33_5,plain,
! [U_328] :
( ( ! [U_334] :
( U_334 = relation_dom(U_328)
| ? [U_332] :
( ~ in(U_332,U_334)
& ? [U_325] : in(ordered_pair(U_332,U_325),U_328) )
| ( ! [U_324] : ~ in(ordered_pair(sK61(U_328,U_334),U_324),U_328)
& in(sK61(U_328,U_334),U_334) ) )
& ! [U_333] :
( ( ! [U_330] :
( in(U_330,U_333)
| ! [U_322] : ~ in(ordered_pair(U_330,U_322),U_328) )
& ! [U_329] :
( in(ordered_pair(U_329,sK60(U_328,U_333,U_329)),U_328)
| ~ in(U_329,U_333) ) )
| U_333 != relation_dom(U_328) ) )
| ~ relation(U_328) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_331,sK61(U_328,U_334))],[f_33_4]) ).
fof(f_33_6,plain,
! [U_328] :
( ( ! [U_334] :
( U_334 = relation_dom(U_328)
| ( ~ in(sK62(U_328,U_334),U_334)
& ? [U_325] : in(ordered_pair(sK62(U_328,U_334),U_325),U_328) )
| ( ! [U_324] : ~ in(ordered_pair(sK61(U_328,U_334),U_324),U_328)
& in(sK61(U_328,U_334),U_334) ) )
& ! [U_333] :
( ( ! [U_330] :
( in(U_330,U_333)
| ! [U_322] : ~ in(ordered_pair(U_330,U_322),U_328) )
& ! [U_329] :
( in(ordered_pair(U_329,sK60(U_328,U_333,U_329)),U_328)
| ~ in(U_329,U_333) ) )
| U_333 != relation_dom(U_328) ) )
| ~ relation(U_328) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_332,sK62(U_328,U_334))],[f_33_5]) ).
fof(f_33_7,plain,
! [U_328] :
( ( ! [U_334] :
( U_334 = relation_dom(U_328)
| ( ~ in(sK62(U_328,U_334),U_334)
& in(ordered_pair(sK62(U_328,U_334),sK63(U_328,U_334)),U_328) )
| ( ! [U_324] : ~ in(ordered_pair(sK61(U_328,U_334),U_324),U_328)
& in(sK61(U_328,U_334),U_334) ) )
& ! [U_333] :
( ( ! [U_330] :
( in(U_330,U_333)
| ! [U_322] : ~ in(ordered_pair(U_330,U_322),U_328) )
& ! [U_329] :
( in(ordered_pair(U_329,sK60(U_328,U_333,U_329)),U_328)
| ~ in(U_329,U_333) ) )
| U_333 != relation_dom(U_328) ) )
| ~ relation(U_328) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_325,sK63(U_328,U_334))],[f_33_6]) ).
cnf(f_33_8,plain,
( in(ordered_pair(U_329,sK60(U_328,U_333,U_329)),U_328)
| ~ in(U_329,U_333)
| U_333 != relation_dom(U_328)
| ~ relation(U_328) ),
inference(clausify,[status(thm)],[f_33_7]) ).
cnf(f_33_9,plain,
( in(U_330,U_333)
| ~ in(ordered_pair(U_330,U_322),U_328)
| U_333 != relation_dom(U_328)
| ~ relation(U_328) ),
inference(clausify,[status(thm)],[f_33_7]) ).
cnf(f_33_10,plain,
( in(ordered_pair(sK62(U_328,U_334),sK63(U_328,U_334)),U_328)
| in(sK61(U_328,U_334),U_334)
| U_334 = relation_dom(U_328)
| ~ relation(U_328) ),
inference(clausify,[status(thm)],[f_33_7]) ).
cnf(f_33_11,plain,
( ~ in(sK62(U_328,U_334),U_334)
| in(sK61(U_328,U_334),U_334)
| U_334 = relation_dom(U_328)
| ~ relation(U_328) ),
inference(clausify,[status(thm)],[f_33_7]) ).
cnf(f_33_12,plain,
( in(ordered_pair(sK62(U_328,U_334),sK63(U_328,U_334)),U_328)
| ~ in(ordered_pair(sK61(U_328,U_334),U_324),U_328)
| U_334 = relation_dom(U_328)
| ~ relation(U_328) ),
inference(clausify,[status(thm)],[f_33_7]) ).
cnf(f_33_13,plain,
( ~ in(sK62(U_328,U_334),U_334)
| ~ in(ordered_pair(sK61(U_328,U_334),U_324),U_328)
| U_334 = relation_dom(U_328)
| ~ relation(U_328) ),
inference(clausify,[status(thm)],[f_33_7]) ).
fof(f_34_1,plain,
! [A] : cast_to_subset(A) = A,
inference(fof_nnf,[status(thm)],[d4_subset_1]) ).
fof(f_34_2,plain,
! [U_335] : cast_to_subset(U_335) = U_335,
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
cast_to_subset(U_335) = U_335,
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_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_35_2,plain,
! [U_343,U_342] :
( ( U_342 = union(U_343)
| ? [U_341] :
( ( ~ in(U_341,U_342)
& ? [U_340] :
( in(U_340,U_343)
& in(U_341,U_340) ) )
| ( ! [U_339] :
( ~ in(U_339,U_343)
| ~ in(U_341,U_339) )
& in(U_341,U_342) ) ) )
& ( ! [U_338] :
( ( in(U_338,U_342)
| ! [U_337] :
( ~ in(U_337,U_343)
| ~ in(U_338,U_337) ) )
& ( ? [U_336] :
( in(U_336,U_343)
& in(U_338,U_336) )
| ~ in(U_338,U_342) ) )
| U_342 != union(U_343) ) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( ! [U_351,U_349] :
( U_349 = union(U_351)
| ? [U_347] :
( ~ in(U_347,U_349)
& ? [U_340] :
( in(U_340,U_351)
& in(U_347,U_340) ) )
| ? [U_346] :
( ! [U_339] :
( ~ in(U_339,U_351)
| ~ in(U_346,U_339) )
& in(U_346,U_349) ) )
& ! [U_350,U_348] :
( ( ! [U_345] :
( in(U_345,U_348)
| ! [U_337] :
( ~ in(U_337,U_350)
| ~ in(U_345,U_337) ) )
& ! [U_344] :
( ? [U_336] :
( in(U_336,U_350)
& in(U_344,U_336) )
| ~ in(U_344,U_348) ) )
| U_348 != union(U_350) ) ),
inference(miniscope,[status(thm)],[f_35_2]) ).
fof(f_35_4,plain,
( ! [U_351,U_349] :
( U_349 = union(U_351)
| ? [U_347] :
( ~ in(U_347,U_349)
& ? [U_340] :
( in(U_340,U_351)
& in(U_347,U_340) ) )
| ? [U_346] :
( ! [U_339] :
( ~ in(U_339,U_351)
| ~ in(U_346,U_339) )
& in(U_346,U_349) ) )
& ! [U_350,U_348] :
( ( ! [U_345] :
( in(U_345,U_348)
| ! [U_337] :
( ~ in(U_337,U_350)
| ~ in(U_345,U_337) ) )
& ! [U_344] :
( ( in(sK64(U_350,U_348,U_344),U_350)
& in(U_344,sK64(U_350,U_348,U_344)) )
| ~ in(U_344,U_348) ) )
| U_348 != union(U_350) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_336,sK64(U_350,U_348,U_344))],[f_35_3]) ).
fof(f_35_5,plain,
( ! [U_351,U_349] :
( U_349 = union(U_351)
| ? [U_347] :
( ~ in(U_347,U_349)
& ? [U_340] :
( in(U_340,U_351)
& in(U_347,U_340) ) )
| ( ! [U_339] :
( ~ in(U_339,U_351)
| ~ in(sK65(U_351,U_349),U_339) )
& in(sK65(U_351,U_349),U_349) ) )
& ! [U_350,U_348] :
( ( ! [U_345] :
( in(U_345,U_348)
| ! [U_337] :
( ~ in(U_337,U_350)
| ~ in(U_345,U_337) ) )
& ! [U_344] :
( ( in(sK64(U_350,U_348,U_344),U_350)
& in(U_344,sK64(U_350,U_348,U_344)) )
| ~ in(U_344,U_348) ) )
| U_348 != union(U_350) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_346,sK65(U_351,U_349))],[f_35_4]) ).
fof(f_35_6,plain,
( ! [U_351,U_349] :
( U_349 = union(U_351)
| ( ~ in(sK66(U_351,U_349),U_349)
& ? [U_340] :
( in(U_340,U_351)
& in(sK66(U_351,U_349),U_340) ) )
| ( ! [U_339] :
( ~ in(U_339,U_351)
| ~ in(sK65(U_351,U_349),U_339) )
& in(sK65(U_351,U_349),U_349) ) )
& ! [U_350,U_348] :
( ( ! [U_345] :
( in(U_345,U_348)
| ! [U_337] :
( ~ in(U_337,U_350)
| ~ in(U_345,U_337) ) )
& ! [U_344] :
( ( in(sK64(U_350,U_348,U_344),U_350)
& in(U_344,sK64(U_350,U_348,U_344)) )
| ~ in(U_344,U_348) ) )
| U_348 != union(U_350) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_347,sK66(U_351,U_349))],[f_35_5]) ).
fof(f_35_7,plain,
( ! [U_351,U_349] :
( U_349 = union(U_351)
| ( ~ in(sK66(U_351,U_349),U_349)
& in(sK67(U_351,U_349),U_351)
& in(sK66(U_351,U_349),sK67(U_351,U_349)) )
| ( ! [U_339] :
( ~ in(U_339,U_351)
| ~ in(sK65(U_351,U_349),U_339) )
& in(sK65(U_351,U_349),U_349) ) )
& ! [U_350,U_348] :
( ( ! [U_345] :
( in(U_345,U_348)
| ! [U_337] :
( ~ in(U_337,U_350)
| ~ in(U_345,U_337) ) )
& ! [U_344] :
( ( in(sK64(U_350,U_348,U_344),U_350)
& in(U_344,sK64(U_350,U_348,U_344)) )
| ~ in(U_344,U_348) ) )
| U_348 != union(U_350) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_340,sK67(U_351,U_349))],[f_35_6]) ).
cnf(f_35_8,plain,
( in(U_344,sK64(U_350,U_348,U_344))
| ~ in(U_344,U_348)
| U_348 != union(U_350) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_9,plain,
( in(sK64(U_350,U_348,U_344),U_350)
| ~ in(U_344,U_348)
| U_348 != union(U_350) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_10,plain,
( in(U_345,U_348)
| ~ in(U_337,U_350)
| ~ in(U_345,U_337)
| U_348 != union(U_350) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_11,plain,
( in(sK66(U_351,U_349),sK67(U_351,U_349))
| in(sK65(U_351,U_349),U_349)
| U_349 = union(U_351) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_12,plain,
( in(sK67(U_351,U_349),U_351)
| in(sK65(U_351,U_349),U_349)
| U_349 = union(U_351) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_13,plain,
( ~ in(sK66(U_351,U_349),U_349)
| in(sK65(U_351,U_349),U_349)
| U_349 = union(U_351) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_14,plain,
( in(sK66(U_351,U_349),sK67(U_351,U_349))
| ~ in(U_339,U_351)
| ~ in(sK65(U_351,U_349),U_339)
| U_349 = union(U_351) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_15,plain,
( in(sK67(U_351,U_349),U_351)
| ~ in(U_339,U_351)
| ~ in(sK65(U_351,U_349),U_339)
| U_349 = union(U_351) ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_16,plain,
( ~ in(sK66(U_351,U_349),U_349)
| ~ in(U_339,U_351)
| ~ in(sK65(U_351,U_349),U_339)
| U_349 = union(U_351) ),
inference(clausify,[status(thm)],[f_35_7]) ).
fof(f_36_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_36_2,plain,
! [U_356,U_355,U_354] :
( ( U_354 = set_difference(U_356,U_355)
| ? [U_353] :
( ( ~ in(U_353,U_354)
& ~ in(U_353,U_355)
& in(U_353,U_356) )
| ( ( in(U_353,U_355)
| ~ in(U_353,U_356) )
& in(U_353,U_354) ) ) )
& ( ! [U_352] :
( ( in(U_352,U_354)
| in(U_352,U_355)
| ~ in(U_352,U_356) )
& ( ( ~ in(U_352,U_355)
& in(U_352,U_356) )
| ~ in(U_352,U_354) ) )
| U_354 != set_difference(U_356,U_355) ) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
( ! [U_366,U_364,U_362] :
( U_362 = set_difference(U_366,U_364)
| ? [U_360] :
( ~ in(U_360,U_362)
& ~ in(U_360,U_364)
& in(U_360,U_366) )
| ? [U_359] :
( ( in(U_359,U_364)
| ~ in(U_359,U_366) )
& in(U_359,U_362) ) )
& ! [U_365,U_363,U_361] :
( ( ! [U_358] :
( in(U_358,U_361)
| in(U_358,U_363)
| ~ in(U_358,U_365) )
& ! [U_357] :
( ( ~ in(U_357,U_363)
& in(U_357,U_365) )
| ~ in(U_357,U_361) ) )
| U_361 != set_difference(U_365,U_363) ) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
fof(f_36_4,plain,
( ! [U_366,U_364,U_362] :
( U_362 = set_difference(U_366,U_364)
| ? [U_360] :
( ~ in(U_360,U_362)
& ~ in(U_360,U_364)
& in(U_360,U_366) )
| ( ( in(sK68(U_366,U_364,U_362),U_364)
| ~ in(sK68(U_366,U_364,U_362),U_366) )
& in(sK68(U_366,U_364,U_362),U_362) ) )
& ! [U_365,U_363,U_361] :
( ( ! [U_358] :
( in(U_358,U_361)
| in(U_358,U_363)
| ~ in(U_358,U_365) )
& ! [U_357] :
( ( ~ in(U_357,U_363)
& in(U_357,U_365) )
| ~ in(U_357,U_361) ) )
| U_361 != set_difference(U_365,U_363) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_359,sK68(U_366,U_364,U_362))],[f_36_3]) ).
fof(f_36_5,plain,
( ! [U_366,U_364,U_362] :
( U_362 = set_difference(U_366,U_364)
| ( ~ in(sK69(U_366,U_364,U_362),U_362)
& ~ in(sK69(U_366,U_364,U_362),U_364)
& in(sK69(U_366,U_364,U_362),U_366) )
| ( ( in(sK68(U_366,U_364,U_362),U_364)
| ~ in(sK68(U_366,U_364,U_362),U_366) )
& in(sK68(U_366,U_364,U_362),U_362) ) )
& ! [U_365,U_363,U_361] :
( ( ! [U_358] :
( in(U_358,U_361)
| in(U_358,U_363)
| ~ in(U_358,U_365) )
& ! [U_357] :
( ( ~ in(U_357,U_363)
& in(U_357,U_365) )
| ~ in(U_357,U_361) ) )
| U_361 != set_difference(U_365,U_363) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_360,sK69(U_366,U_364,U_362))],[f_36_4]) ).
cnf(f_36_6,plain,
( in(U_357,U_365)
| ~ in(U_357,U_361)
| U_361 != set_difference(U_365,U_363) ),
inference(clausify,[status(thm)],[f_36_5]) ).
cnf(f_36_7,plain,
( ~ in(U_357,U_363)
| ~ in(U_357,U_361)
| U_361 != set_difference(U_365,U_363) ),
inference(clausify,[status(thm)],[f_36_5]) ).
cnf(f_36_8,plain,
( in(U_358,U_361)
| in(U_358,U_363)
| ~ in(U_358,U_365)
| U_361 != set_difference(U_365,U_363) ),
inference(clausify,[status(thm)],[f_36_5]) ).
cnf(f_36_9,plain,
( in(sK69(U_366,U_364,U_362),U_366)
| in(sK68(U_366,U_364,U_362),U_362)
| U_362 = set_difference(U_366,U_364) ),
inference(clausify,[status(thm)],[f_36_5]) ).
cnf(f_36_10,plain,
( ~ in(sK69(U_366,U_364,U_362),U_364)
| in(sK68(U_366,U_364,U_362),U_362)
| U_362 = set_difference(U_366,U_364) ),
inference(clausify,[status(thm)],[f_36_5]) ).
cnf(f_36_11,plain,
( ~ in(sK69(U_366,U_364,U_362),U_362)
| in(sK68(U_366,U_364,U_362),U_362)
| U_362 = set_difference(U_366,U_364) ),
inference(clausify,[status(thm)],[f_36_5]) ).
cnf(f_36_12,plain,
( in(sK69(U_366,U_364,U_362),U_366)
| in(sK68(U_366,U_364,U_362),U_364)
| ~ in(sK68(U_366,U_364,U_362),U_366)
| U_362 = set_difference(U_366,U_364) ),
inference(clausify,[status(thm)],[f_36_5]) ).
cnf(f_36_13,plain,
( ~ in(sK69(U_366,U_364,U_362),U_364)
| in(sK68(U_366,U_364,U_362),U_364)
| ~ in(sK68(U_366,U_364,U_362),U_366)
| U_362 = set_difference(U_366,U_364) ),
inference(clausify,[status(thm)],[f_36_5]) ).
cnf(f_36_14,plain,
( ~ in(sK69(U_366,U_364,U_362),U_362)
| in(sK68(U_366,U_364,U_362),U_364)
| ~ in(sK68(U_366,U_364,U_362),U_366)
| U_362 = set_difference(U_366,U_364) ),
inference(clausify,[status(thm)],[f_36_5]) ).
fof(f_37_1,plain,
! [A] :
( ! [B] :
( ( B = relation_rng(A)
| ? [C] :
( ( ~ in(C,B)
& ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) )
| ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) ) )
& ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d5_funct_1]) ).
fof(f_37_2,plain,
! [U_374] :
( ! [U_373] :
( ( U_373 = relation_rng(U_374)
| ? [U_372] :
( ( ~ in(U_372,U_373)
& ? [U_371] :
( U_372 = apply(U_374,U_371)
& in(U_371,relation_dom(U_374)) ) )
| ( ! [U_370] :
( U_372 != apply(U_374,U_370)
| ~ in(U_370,relation_dom(U_374)) )
& in(U_372,U_373) ) ) )
& ( ! [U_369] :
( ( in(U_369,U_373)
| ! [U_368] :
( U_369 != apply(U_374,U_368)
| ~ in(U_368,relation_dom(U_374)) ) )
& ( ? [U_367] :
( U_369 = apply(U_374,U_367)
& in(U_367,relation_dom(U_374)) )
| ~ in(U_369,U_373) ) )
| U_373 != relation_rng(U_374) ) )
| ~ function(U_374)
| ~ relation(U_374) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_374] :
( ( ! [U_380] :
( U_380 = relation_rng(U_374)
| ? [U_378] :
( ~ in(U_378,U_380)
& ? [U_371] :
( U_378 = apply(U_374,U_371)
& in(U_371,relation_dom(U_374)) ) )
| ? [U_377] :
( ! [U_370] :
( U_377 != apply(U_374,U_370)
| ~ in(U_370,relation_dom(U_374)) )
& in(U_377,U_380) ) )
& ! [U_379] :
( ( ! [U_376] :
( in(U_376,U_379)
| ! [U_368] :
( U_376 != apply(U_374,U_368)
| ~ in(U_368,relation_dom(U_374)) ) )
& ! [U_375] :
( ? [U_367] :
( U_375 = apply(U_374,U_367)
& in(U_367,relation_dom(U_374)) )
| ~ in(U_375,U_379) ) )
| U_379 != relation_rng(U_374) ) )
| ~ function(U_374)
| ~ relation(U_374) ),
inference(miniscope,[status(thm)],[f_37_2]) ).
fof(f_37_4,plain,
! [U_374] :
( ( ! [U_380] :
( U_380 = relation_rng(U_374)
| ? [U_378] :
( ~ in(U_378,U_380)
& ? [U_371] :
( U_378 = apply(U_374,U_371)
& in(U_371,relation_dom(U_374)) ) )
| ? [U_377] :
( ! [U_370] :
( U_377 != apply(U_374,U_370)
| ~ in(U_370,relation_dom(U_374)) )
& in(U_377,U_380) ) )
& ! [U_379] :
( ( ! [U_376] :
( in(U_376,U_379)
| ! [U_368] :
( U_376 != apply(U_374,U_368)
| ~ in(U_368,relation_dom(U_374)) ) )
& ! [U_375] :
( ( U_375 = apply(U_374,sK70(U_374,U_379,U_375))
& in(sK70(U_374,U_379,U_375),relation_dom(U_374)) )
| ~ in(U_375,U_379) ) )
| U_379 != relation_rng(U_374) ) )
| ~ function(U_374)
| ~ relation(U_374) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_367,sK70(U_374,U_379,U_375))],[f_37_3]) ).
fof(f_37_5,plain,
! [U_374] :
( ( ! [U_380] :
( U_380 = relation_rng(U_374)
| ? [U_378] :
( ~ in(U_378,U_380)
& ? [U_371] :
( U_378 = apply(U_374,U_371)
& in(U_371,relation_dom(U_374)) ) )
| ( ! [U_370] :
( sK71(U_374,U_380) != apply(U_374,U_370)
| ~ in(U_370,relation_dom(U_374)) )
& in(sK71(U_374,U_380),U_380) ) )
& ! [U_379] :
( ( ! [U_376] :
( in(U_376,U_379)
| ! [U_368] :
( U_376 != apply(U_374,U_368)
| ~ in(U_368,relation_dom(U_374)) ) )
& ! [U_375] :
( ( U_375 = apply(U_374,sK70(U_374,U_379,U_375))
& in(sK70(U_374,U_379,U_375),relation_dom(U_374)) )
| ~ in(U_375,U_379) ) )
| U_379 != relation_rng(U_374) ) )
| ~ function(U_374)
| ~ relation(U_374) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_377,sK71(U_374,U_380))],[f_37_4]) ).
fof(f_37_6,plain,
! [U_374] :
( ( ! [U_380] :
( U_380 = relation_rng(U_374)
| ( ~ in(sK72(U_374,U_380),U_380)
& ? [U_371] :
( sK72(U_374,U_380) = apply(U_374,U_371)
& in(U_371,relation_dom(U_374)) ) )
| ( ! [U_370] :
( sK71(U_374,U_380) != apply(U_374,U_370)
| ~ in(U_370,relation_dom(U_374)) )
& in(sK71(U_374,U_380),U_380) ) )
& ! [U_379] :
( ( ! [U_376] :
( in(U_376,U_379)
| ! [U_368] :
( U_376 != apply(U_374,U_368)
| ~ in(U_368,relation_dom(U_374)) ) )
& ! [U_375] :
( ( U_375 = apply(U_374,sK70(U_374,U_379,U_375))
& in(sK70(U_374,U_379,U_375),relation_dom(U_374)) )
| ~ in(U_375,U_379) ) )
| U_379 != relation_rng(U_374) ) )
| ~ function(U_374)
| ~ relation(U_374) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_378,sK72(U_374,U_380))],[f_37_5]) ).
fof(f_37_7,plain,
! [U_374] :
( ( ! [U_380] :
( U_380 = relation_rng(U_374)
| ( ~ in(sK72(U_374,U_380),U_380)
& sK72(U_374,U_380) = apply(U_374,sK73(U_374,U_380))
& in(sK73(U_374,U_380),relation_dom(U_374)) )
| ( ! [U_370] :
( sK71(U_374,U_380) != apply(U_374,U_370)
| ~ in(U_370,relation_dom(U_374)) )
& in(sK71(U_374,U_380),U_380) ) )
& ! [U_379] :
( ( ! [U_376] :
( in(U_376,U_379)
| ! [U_368] :
( U_376 != apply(U_374,U_368)
| ~ in(U_368,relation_dom(U_374)) ) )
& ! [U_375] :
( ( U_375 = apply(U_374,sK70(U_374,U_379,U_375))
& in(sK70(U_374,U_379,U_375),relation_dom(U_374)) )
| ~ in(U_375,U_379) ) )
| U_379 != relation_rng(U_374) ) )
| ~ function(U_374)
| ~ relation(U_374) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_371,sK73(U_374,U_380))],[f_37_6]) ).
cnf(f_37_8,plain,
( in(sK70(U_374,U_379,U_375),relation_dom(U_374))
| ~ in(U_375,U_379)
| U_379 != relation_rng(U_374)
| ~ function(U_374)
| ~ relation(U_374) ),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(f_37_9,plain,
( U_375 = apply(U_374,sK70(U_374,U_379,U_375))
| ~ in(U_375,U_379)
| U_379 != relation_rng(U_374)
| ~ function(U_374)
| ~ relation(U_374) ),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(f_37_10,plain,
( in(U_376,U_379)
| U_376 != apply(U_374,U_368)
| ~ in(U_368,relation_dom(U_374))
| U_379 != relation_rng(U_374)
| ~ function(U_374)
| ~ relation(U_374) ),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(f_37_11,plain,
( in(sK73(U_374,U_380),relation_dom(U_374))
| in(sK71(U_374,U_380),U_380)
| U_380 = relation_rng(U_374)
| ~ function(U_374)
| ~ relation(U_374) ),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(f_37_12,plain,
( sK72(U_374,U_380) = apply(U_374,sK73(U_374,U_380))
| in(sK71(U_374,U_380),U_380)
| U_380 = relation_rng(U_374)
| ~ function(U_374)
| ~ relation(U_374) ),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(f_37_13,plain,
( ~ in(sK72(U_374,U_380),U_380)
| in(sK71(U_374,U_380),U_380)
| U_380 = relation_rng(U_374)
| ~ function(U_374)
| ~ relation(U_374) ),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(f_37_14,plain,
( in(sK73(U_374,U_380),relation_dom(U_374))
| sK71(U_374,U_380) != apply(U_374,U_370)
| ~ in(U_370,relation_dom(U_374))
| U_380 = relation_rng(U_374)
| ~ function(U_374)
| ~ relation(U_374) ),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(f_37_15,plain,
( sK72(U_374,U_380) = apply(U_374,sK73(U_374,U_380))
| sK71(U_374,U_380) != apply(U_374,U_370)
| ~ in(U_370,relation_dom(U_374))
| U_380 = relation_rng(U_374)
| ~ function(U_374)
| ~ relation(U_374) ),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(f_37_16,plain,
( ~ in(sK72(U_374,U_380),U_380)
| sK71(U_374,U_380) != apply(U_374,U_370)
| ~ in(U_370,relation_dom(U_374))
| U_380 = relation_rng(U_374)
| ~ function(U_374)
| ~ relation(U_374) ),
inference(clausify,[status(thm)],[f_37_7]) ).
fof(f_38_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_38_2,plain,
! [U_388] :
( ! [U_387] :
( ( U_387 = relation_rng(U_388)
| ? [U_386] :
( ( ~ in(U_386,U_387)
& ? [U_385] : in(ordered_pair(U_385,U_386),U_388) )
| ( ! [U_384] : ~ in(ordered_pair(U_384,U_386),U_388)
& in(U_386,U_387) ) ) )
& ( ! [U_383] :
( ( in(U_383,U_387)
| ! [U_382] : ~ in(ordered_pair(U_382,U_383),U_388) )
& ( ? [U_381] : in(ordered_pair(U_381,U_383),U_388)
| ~ in(U_383,U_387) ) )
| U_387 != relation_rng(U_388) ) )
| ~ relation(U_388) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_388] :
( ( ! [U_394] :
( U_394 = relation_rng(U_388)
| ? [U_392] :
( ~ in(U_392,U_394)
& ? [U_385] : in(ordered_pair(U_385,U_392),U_388) )
| ? [U_391] :
( ! [U_384] : ~ in(ordered_pair(U_384,U_391),U_388)
& in(U_391,U_394) ) )
& ! [U_393] :
( ( ! [U_390] :
( in(U_390,U_393)
| ! [U_382] : ~ in(ordered_pair(U_382,U_390),U_388) )
& ! [U_389] :
( ? [U_381] : in(ordered_pair(U_381,U_389),U_388)
| ~ in(U_389,U_393) ) )
| U_393 != relation_rng(U_388) ) )
| ~ relation(U_388) ),
inference(miniscope,[status(thm)],[f_38_2]) ).
fof(f_38_4,plain,
! [U_388] :
( ( ! [U_394] :
( U_394 = relation_rng(U_388)
| ? [U_392] :
( ~ in(U_392,U_394)
& ? [U_385] : in(ordered_pair(U_385,U_392),U_388) )
| ? [U_391] :
( ! [U_384] : ~ in(ordered_pair(U_384,U_391),U_388)
& in(U_391,U_394) ) )
& ! [U_393] :
( ( ! [U_390] :
( in(U_390,U_393)
| ! [U_382] : ~ in(ordered_pair(U_382,U_390),U_388) )
& ! [U_389] :
( in(ordered_pair(sK74(U_388,U_393,U_389),U_389),U_388)
| ~ in(U_389,U_393) ) )
| U_393 != relation_rng(U_388) ) )
| ~ relation(U_388) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_381,sK74(U_388,U_393,U_389))],[f_38_3]) ).
fof(f_38_5,plain,
! [U_388] :
( ( ! [U_394] :
( U_394 = relation_rng(U_388)
| ? [U_392] :
( ~ in(U_392,U_394)
& ? [U_385] : in(ordered_pair(U_385,U_392),U_388) )
| ( ! [U_384] : ~ in(ordered_pair(U_384,sK75(U_388,U_394)),U_388)
& in(sK75(U_388,U_394),U_394) ) )
& ! [U_393] :
( ( ! [U_390] :
( in(U_390,U_393)
| ! [U_382] : ~ in(ordered_pair(U_382,U_390),U_388) )
& ! [U_389] :
( in(ordered_pair(sK74(U_388,U_393,U_389),U_389),U_388)
| ~ in(U_389,U_393) ) )
| U_393 != relation_rng(U_388) ) )
| ~ relation(U_388) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_391,sK75(U_388,U_394))],[f_38_4]) ).
fof(f_38_6,plain,
! [U_388] :
( ( ! [U_394] :
( U_394 = relation_rng(U_388)
| ( ~ in(sK76(U_388,U_394),U_394)
& ? [U_385] : in(ordered_pair(U_385,sK76(U_388,U_394)),U_388) )
| ( ! [U_384] : ~ in(ordered_pair(U_384,sK75(U_388,U_394)),U_388)
& in(sK75(U_388,U_394),U_394) ) )
& ! [U_393] :
( ( ! [U_390] :
( in(U_390,U_393)
| ! [U_382] : ~ in(ordered_pair(U_382,U_390),U_388) )
& ! [U_389] :
( in(ordered_pair(sK74(U_388,U_393,U_389),U_389),U_388)
| ~ in(U_389,U_393) ) )
| U_393 != relation_rng(U_388) ) )
| ~ relation(U_388) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_392,sK76(U_388,U_394))],[f_38_5]) ).
fof(f_38_7,plain,
! [U_388] :
( ( ! [U_394] :
( U_394 = relation_rng(U_388)
| ( ~ in(sK76(U_388,U_394),U_394)
& in(ordered_pair(sK77(U_388,U_394),sK76(U_388,U_394)),U_388) )
| ( ! [U_384] : ~ in(ordered_pair(U_384,sK75(U_388,U_394)),U_388)
& in(sK75(U_388,U_394),U_394) ) )
& ! [U_393] :
( ( ! [U_390] :
( in(U_390,U_393)
| ! [U_382] : ~ in(ordered_pair(U_382,U_390),U_388) )
& ! [U_389] :
( in(ordered_pair(sK74(U_388,U_393,U_389),U_389),U_388)
| ~ in(U_389,U_393) ) )
| U_393 != relation_rng(U_388) ) )
| ~ relation(U_388) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_385,sK77(U_388,U_394))],[f_38_6]) ).
cnf(f_38_8,plain,
( in(ordered_pair(sK74(U_388,U_393,U_389),U_389),U_388)
| ~ in(U_389,U_393)
| U_393 != relation_rng(U_388)
| ~ relation(U_388) ),
inference(clausify,[status(thm)],[f_38_7]) ).
cnf(f_38_9,plain,
( in(U_390,U_393)
| ~ in(ordered_pair(U_382,U_390),U_388)
| U_393 != relation_rng(U_388)
| ~ relation(U_388) ),
inference(clausify,[status(thm)],[f_38_7]) ).
cnf(f_38_10,plain,
( in(ordered_pair(sK77(U_388,U_394),sK76(U_388,U_394)),U_388)
| in(sK75(U_388,U_394),U_394)
| U_394 = relation_rng(U_388)
| ~ relation(U_388) ),
inference(clausify,[status(thm)],[f_38_7]) ).
cnf(f_38_11,plain,
( ~ in(sK76(U_388,U_394),U_394)
| in(sK75(U_388,U_394),U_394)
| U_394 = relation_rng(U_388)
| ~ relation(U_388) ),
inference(clausify,[status(thm)],[f_38_7]) ).
cnf(f_38_12,plain,
( in(ordered_pair(sK77(U_388,U_394),sK76(U_388,U_394)),U_388)
| ~ in(ordered_pair(U_384,sK75(U_388,U_394)),U_388)
| U_394 = relation_rng(U_388)
| ~ relation(U_388) ),
inference(clausify,[status(thm)],[f_38_7]) ).
cnf(f_38_13,plain,
( ~ in(sK76(U_388,U_394),U_394)
| ~ in(ordered_pair(U_384,sK75(U_388,U_394)),U_388)
| U_394 = relation_rng(U_388)
| ~ relation(U_388) ),
inference(clausify,[status(thm)],[f_38_7]) ).
fof(f_39_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_39_2,plain,
! [U_396,U_395] :
( subset_complement(U_396,U_395) = set_difference(U_396,U_395)
| ~ element(U_395,powerset(U_396)) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
( subset_complement(U_396,U_395) = set_difference(U_396,U_395)
| ~ element(U_395,powerset(U_396)) ),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_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_40_2,plain,
! [U_398,U_397] : ordered_pair(U_398,U_397) = unordered_pair(unordered_pair(U_398,U_397),singleton(U_398)),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
ordered_pair(U_398,U_397) = unordered_pair(unordered_pair(U_398,U_397),singleton(U_398)),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_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_41_2,plain,
! [U_399] :
( relation_field(U_399) = set_union2(relation_dom(U_399),relation_rng(U_399))
| ~ relation(U_399) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
cnf(f_41_3,plain,
( relation_field(U_399) = set_union2(relation_dom(U_399),relation_rng(U_399))
| ~ relation(U_399) ),
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_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_42_2,plain,
! [U_405] :
( ! [U_404] :
( ( ( U_404 = relation_inverse(U_405)
| ? [U_403,U_402] :
( ( ~ in(ordered_pair(U_403,U_402),U_404)
& in(ordered_pair(U_402,U_403),U_405) )
| ( ~ in(ordered_pair(U_402,U_403),U_405)
& in(ordered_pair(U_403,U_402),U_404) ) ) )
& ( ! [U_401,U_400] :
( ( in(ordered_pair(U_401,U_400),U_404)
| ~ in(ordered_pair(U_400,U_401),U_405) )
& ( in(ordered_pair(U_400,U_401),U_405)
| ~ in(ordered_pair(U_401,U_400),U_404) ) )
| U_404 != relation_inverse(U_405) ) )
| ~ relation(U_404) )
| ~ relation(U_405) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_405] :
( ! [U_404] :
( ( ( U_404 = relation_inverse(U_405)
| ? [U_413,U_411] :
( ~ in(ordered_pair(U_413,U_411),U_404)
& in(ordered_pair(U_411,U_413),U_405) )
| ? [U_412,U_410] :
( ~ in(ordered_pair(U_410,U_412),U_405)
& in(ordered_pair(U_412,U_410),U_404) ) )
& ( ( ! [U_409,U_407] :
( in(ordered_pair(U_409,U_407),U_404)
| ~ in(ordered_pair(U_407,U_409),U_405) )
& ! [U_408,U_406] :
( in(ordered_pair(U_406,U_408),U_405)
| ~ in(ordered_pair(U_408,U_406),U_404) ) )
| U_404 != relation_inverse(U_405) ) )
| ~ relation(U_404) )
| ~ relation(U_405) ),
inference(miniscope,[status(thm)],[f_42_2]) ).
fof(f_42_4,plain,
! [U_405] :
( ! [U_404] :
( ( ( U_404 = relation_inverse(U_405)
| ? [U_413,U_411] :
( ~ in(ordered_pair(U_413,U_411),U_404)
& in(ordered_pair(U_411,U_413),U_405) )
| ? [U_410] :
( ~ in(ordered_pair(U_410,sK78(U_405,U_404)),U_405)
& in(ordered_pair(sK78(U_405,U_404),U_410),U_404) ) )
& ( ( ! [U_409,U_407] :
( in(ordered_pair(U_409,U_407),U_404)
| ~ in(ordered_pair(U_407,U_409),U_405) )
& ! [U_408,U_406] :
( in(ordered_pair(U_406,U_408),U_405)
| ~ in(ordered_pair(U_408,U_406),U_404) ) )
| U_404 != relation_inverse(U_405) ) )
| ~ relation(U_404) )
| ~ relation(U_405) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_412,sK78(U_405,U_404))],[f_42_3]) ).
fof(f_42_5,plain,
! [U_405] :
( ! [U_404] :
( ( ( U_404 = relation_inverse(U_405)
| ? [U_413,U_411] :
( ~ in(ordered_pair(U_413,U_411),U_404)
& in(ordered_pair(U_411,U_413),U_405) )
| ( ~ in(ordered_pair(sK79(U_405,U_404),sK78(U_405,U_404)),U_405)
& in(ordered_pair(sK78(U_405,U_404),sK79(U_405,U_404)),U_404) ) )
& ( ( ! [U_409,U_407] :
( in(ordered_pair(U_409,U_407),U_404)
| ~ in(ordered_pair(U_407,U_409),U_405) )
& ! [U_408,U_406] :
( in(ordered_pair(U_406,U_408),U_405)
| ~ in(ordered_pair(U_408,U_406),U_404) ) )
| U_404 != relation_inverse(U_405) ) )
| ~ relation(U_404) )
| ~ relation(U_405) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_410,sK79(U_405,U_404))],[f_42_4]) ).
fof(f_42_6,plain,
! [U_405] :
( ! [U_404] :
( ( ( U_404 = relation_inverse(U_405)
| ? [U_411] :
( ~ in(ordered_pair(sK80(U_405,U_404),U_411),U_404)
& in(ordered_pair(U_411,sK80(U_405,U_404)),U_405) )
| ( ~ in(ordered_pair(sK79(U_405,U_404),sK78(U_405,U_404)),U_405)
& in(ordered_pair(sK78(U_405,U_404),sK79(U_405,U_404)),U_404) ) )
& ( ( ! [U_409,U_407] :
( in(ordered_pair(U_409,U_407),U_404)
| ~ in(ordered_pair(U_407,U_409),U_405) )
& ! [U_408,U_406] :
( in(ordered_pair(U_406,U_408),U_405)
| ~ in(ordered_pair(U_408,U_406),U_404) ) )
| U_404 != relation_inverse(U_405) ) )
| ~ relation(U_404) )
| ~ relation(U_405) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_413,sK80(U_405,U_404))],[f_42_5]) ).
fof(f_42_7,plain,
! [U_405] :
( ! [U_404] :
( ( ( U_404 = relation_inverse(U_405)
| ( ~ in(ordered_pair(sK80(U_405,U_404),sK81(U_405,U_404)),U_404)
& in(ordered_pair(sK81(U_405,U_404),sK80(U_405,U_404)),U_405) )
| ( ~ in(ordered_pair(sK79(U_405,U_404),sK78(U_405,U_404)),U_405)
& in(ordered_pair(sK78(U_405,U_404),sK79(U_405,U_404)),U_404) ) )
& ( ( ! [U_409,U_407] :
( in(ordered_pair(U_409,U_407),U_404)
| ~ in(ordered_pair(U_407,U_409),U_405) )
& ! [U_408,U_406] :
( in(ordered_pair(U_406,U_408),U_405)
| ~ in(ordered_pair(U_408,U_406),U_404) ) )
| U_404 != relation_inverse(U_405) ) )
| ~ relation(U_404) )
| ~ relation(U_405) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_411,sK81(U_405,U_404))],[f_42_6]) ).
cnf(f_42_8,plain,
( in(ordered_pair(U_406,U_408),U_405)
| ~ in(ordered_pair(U_408,U_406),U_404)
| U_404 != relation_inverse(U_405)
| ~ relation(U_404)
| ~ relation(U_405) ),
inference(clausify,[status(thm)],[f_42_7]) ).
cnf(f_42_9,plain,
( in(ordered_pair(U_409,U_407),U_404)
| ~ in(ordered_pair(U_407,U_409),U_405)
| U_404 != relation_inverse(U_405)
| ~ relation(U_404)
| ~ relation(U_405) ),
inference(clausify,[status(thm)],[f_42_7]) ).
cnf(f_42_10,plain,
( in(ordered_pair(sK81(U_405,U_404),sK80(U_405,U_404)),U_405)
| in(ordered_pair(sK78(U_405,U_404),sK79(U_405,U_404)),U_404)
| U_404 = relation_inverse(U_405)
| ~ relation(U_404)
| ~ relation(U_405) ),
inference(clausify,[status(thm)],[f_42_7]) ).
cnf(f_42_11,plain,
( ~ in(ordered_pair(sK80(U_405,U_404),sK81(U_405,U_404)),U_404)
| in(ordered_pair(sK78(U_405,U_404),sK79(U_405,U_404)),U_404)
| U_404 = relation_inverse(U_405)
| ~ relation(U_404)
| ~ relation(U_405) ),
inference(clausify,[status(thm)],[f_42_7]) ).
cnf(f_42_12,plain,
( in(ordered_pair(sK81(U_405,U_404),sK80(U_405,U_404)),U_405)
| ~ in(ordered_pair(sK79(U_405,U_404),sK78(U_405,U_404)),U_405)
| U_404 = relation_inverse(U_405)
| ~ relation(U_404)
| ~ relation(U_405) ),
inference(clausify,[status(thm)],[f_42_7]) ).
cnf(f_42_13,plain,
( ~ in(ordered_pair(sK80(U_405,U_404),sK81(U_405,U_404)),U_404)
| ~ in(ordered_pair(sK79(U_405,U_404),sK78(U_405,U_404)),U_405)
| U_404 = relation_inverse(U_405)
| ~ relation(U_404)
| ~ relation(U_405) ),
inference(clausify,[status(thm)],[f_42_7]) ).
fof(f_43_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_43_2,plain,
! [U_415,U_414] :
( ( disjoint(U_415,U_414)
| set_intersection2(U_415,U_414) != empty_set )
& ( set_intersection2(U_415,U_414) = empty_set
| ~ disjoint(U_415,U_414) ) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
( ! [U_419,U_417] :
( disjoint(U_419,U_417)
| set_intersection2(U_419,U_417) != empty_set )
& ! [U_418,U_416] :
( set_intersection2(U_418,U_416) = empty_set
| ~ disjoint(U_418,U_416) ) ),
inference(miniscope,[status(thm)],[f_43_2]) ).
cnf(f_43_4,plain,
( set_intersection2(U_418,U_416) = empty_set
| ~ disjoint(U_418,U_416) ),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_5,plain,
( disjoint(U_419,U_417)
| set_intersection2(U_419,U_417) != empty_set ),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_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_44_2,plain,
! [U_424] :
( ( ( one_to_one(U_424)
| ? [U_423,U_422] :
( U_423 != U_422
& apply(U_424,U_423) = apply(U_424,U_422)
& in(U_422,relation_dom(U_424))
& in(U_423,relation_dom(U_424)) ) )
& ( ! [U_421,U_420] :
( U_421 = U_420
| apply(U_424,U_421) != apply(U_424,U_420)
| ~ in(U_420,relation_dom(U_424))
| ~ in(U_421,relation_dom(U_424)) )
| ~ one_to_one(U_424) ) )
| ~ function(U_424)
| ~ relation(U_424) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_424] :
( ( ( one_to_one(U_424)
| ? [U_422] :
( sK82(U_424) != U_422
& apply(U_424,sK82(U_424)) = apply(U_424,U_422)
& in(U_422,relation_dom(U_424))
& in(sK82(U_424),relation_dom(U_424)) ) )
& ( ! [U_421,U_420] :
( U_421 = U_420
| apply(U_424,U_421) != apply(U_424,U_420)
| ~ in(U_420,relation_dom(U_424))
| ~ in(U_421,relation_dom(U_424)) )
| ~ one_to_one(U_424) ) )
| ~ function(U_424)
| ~ relation(U_424) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_423,sK82(U_424))],[f_44_2]) ).
fof(f_44_4,plain,
! [U_424] :
( ( ( one_to_one(U_424)
| ( sK82(U_424) != sK83(U_424)
& apply(U_424,sK82(U_424)) = apply(U_424,sK83(U_424))
& in(sK83(U_424),relation_dom(U_424))
& in(sK82(U_424),relation_dom(U_424)) ) )
& ( ! [U_421,U_420] :
( U_421 = U_420
| apply(U_424,U_421) != apply(U_424,U_420)
| ~ in(U_420,relation_dom(U_424))
| ~ in(U_421,relation_dom(U_424)) )
| ~ one_to_one(U_424) ) )
| ~ function(U_424)
| ~ relation(U_424) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_422,sK83(U_424))],[f_44_3]) ).
cnf(f_44_5,plain,
( U_421 = U_420
| apply(U_424,U_421) != apply(U_424,U_420)
| ~ in(U_420,relation_dom(U_424))
| ~ in(U_421,relation_dom(U_424))
| ~ one_to_one(U_424)
| ~ function(U_424)
| ~ relation(U_424) ),
inference(clausify,[status(thm)],[f_44_4]) ).
cnf(f_44_6,plain,
( in(sK82(U_424),relation_dom(U_424))
| one_to_one(U_424)
| ~ function(U_424)
| ~ relation(U_424) ),
inference(clausify,[status(thm)],[f_44_4]) ).
cnf(f_44_7,plain,
( in(sK83(U_424),relation_dom(U_424))
| one_to_one(U_424)
| ~ function(U_424)
| ~ relation(U_424) ),
inference(clausify,[status(thm)],[f_44_4]) ).
cnf(f_44_8,plain,
( apply(U_424,sK82(U_424)) = apply(U_424,sK83(U_424))
| one_to_one(U_424)
| ~ function(U_424)
| ~ relation(U_424) ),
inference(clausify,[status(thm)],[f_44_4]) ).
cnf(f_44_9,plain,
( sK82(U_424) != sK83(U_424)
| one_to_one(U_424)
| ~ function(U_424)
| ~ relation(U_424) ),
inference(clausify,[status(thm)],[f_44_4]) ).
fof(f_45_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_45_2,plain,
! [U_435] :
( ! [U_434] :
( ! [U_433] :
( ( ( U_433 = relation_composition(U_435,U_434)
| ? [U_432,U_431] :
( ( ~ in(ordered_pair(U_432,U_431),U_433)
& ? [U_430] :
( in(ordered_pair(U_430,U_431),U_434)
& in(ordered_pair(U_432,U_430),U_435) ) )
| ( ! [U_429] :
( ~ in(ordered_pair(U_429,U_431),U_434)
| ~ in(ordered_pair(U_432,U_429),U_435) )
& in(ordered_pair(U_432,U_431),U_433) ) ) )
& ( ! [U_428,U_427] :
( ( in(ordered_pair(U_428,U_427),U_433)
| ! [U_426] :
( ~ in(ordered_pair(U_426,U_427),U_434)
| ~ in(ordered_pair(U_428,U_426),U_435) ) )
& ( ? [U_425] :
( in(ordered_pair(U_425,U_427),U_434)
& in(ordered_pair(U_428,U_425),U_435) )
| ~ in(ordered_pair(U_428,U_427),U_433) ) )
| U_433 != relation_composition(U_435,U_434) ) )
| ~ relation(U_433) )
| ~ relation(U_434) )
| ~ relation(U_435) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_435] :
( ! [U_434] :
( ! [U_433] :
( ( ( U_433 = relation_composition(U_435,U_434)
| ? [U_443,U_441] :
( ~ in(ordered_pair(U_443,U_441),U_433)
& ? [U_430] :
( in(ordered_pair(U_430,U_441),U_434)
& in(ordered_pair(U_443,U_430),U_435) ) )
| ? [U_442,U_440] :
( ! [U_429] :
( ~ in(ordered_pair(U_429,U_440),U_434)
| ~ in(ordered_pair(U_442,U_429),U_435) )
& in(ordered_pair(U_442,U_440),U_433) ) )
& ( ( ! [U_439,U_437] :
( in(ordered_pair(U_439,U_437),U_433)
| ! [U_426] :
( ~ in(ordered_pair(U_426,U_437),U_434)
| ~ in(ordered_pair(U_439,U_426),U_435) ) )
& ! [U_438,U_436] :
( ? [U_425] :
( in(ordered_pair(U_425,U_436),U_434)
& in(ordered_pair(U_438,U_425),U_435) )
| ~ in(ordered_pair(U_438,U_436),U_433) ) )
| U_433 != relation_composition(U_435,U_434) ) )
| ~ relation(U_433) )
| ~ relation(U_434) )
| ~ relation(U_435) ),
inference(miniscope,[status(thm)],[f_45_2]) ).
fof(f_45_4,plain,
! [U_435] :
( ! [U_434] :
( ! [U_433] :
( ( ( U_433 = relation_composition(U_435,U_434)
| ? [U_443,U_441] :
( ~ in(ordered_pair(U_443,U_441),U_433)
& ? [U_430] :
( in(ordered_pair(U_430,U_441),U_434)
& in(ordered_pair(U_443,U_430),U_435) ) )
| ? [U_442,U_440] :
( ! [U_429] :
( ~ in(ordered_pair(U_429,U_440),U_434)
| ~ in(ordered_pair(U_442,U_429),U_435) )
& in(ordered_pair(U_442,U_440),U_433) ) )
& ( ( ! [U_439,U_437] :
( in(ordered_pair(U_439,U_437),U_433)
| ! [U_426] :
( ~ in(ordered_pair(U_426,U_437),U_434)
| ~ in(ordered_pair(U_439,U_426),U_435) ) )
& ! [U_438,U_436] :
( ( in(ordered_pair(sK84(U_435,U_434,U_433,U_438,U_436),U_436),U_434)
& in(ordered_pair(U_438,sK84(U_435,U_434,U_433,U_438,U_436)),U_435) )
| ~ in(ordered_pair(U_438,U_436),U_433) ) )
| U_433 != relation_composition(U_435,U_434) ) )
| ~ relation(U_433) )
| ~ relation(U_434) )
| ~ relation(U_435) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_425,sK84(U_435,U_434,U_433,U_438,U_436))],[f_45_3]) ).
fof(f_45_5,plain,
! [U_435] :
( ! [U_434] :
( ! [U_433] :
( ( ( U_433 = relation_composition(U_435,U_434)
| ? [U_443,U_441] :
( ~ in(ordered_pair(U_443,U_441),U_433)
& ? [U_430] :
( in(ordered_pair(U_430,U_441),U_434)
& in(ordered_pair(U_443,U_430),U_435) ) )
| ? [U_440] :
( ! [U_429] :
( ~ in(ordered_pair(U_429,U_440),U_434)
| ~ in(ordered_pair(sK85(U_435,U_434,U_433),U_429),U_435) )
& in(ordered_pair(sK85(U_435,U_434,U_433),U_440),U_433) ) )
& ( ( ! [U_439,U_437] :
( in(ordered_pair(U_439,U_437),U_433)
| ! [U_426] :
( ~ in(ordered_pair(U_426,U_437),U_434)
| ~ in(ordered_pair(U_439,U_426),U_435) ) )
& ! [U_438,U_436] :
( ( in(ordered_pair(sK84(U_435,U_434,U_433,U_438,U_436),U_436),U_434)
& in(ordered_pair(U_438,sK84(U_435,U_434,U_433,U_438,U_436)),U_435) )
| ~ in(ordered_pair(U_438,U_436),U_433) ) )
| U_433 != relation_composition(U_435,U_434) ) )
| ~ relation(U_433) )
| ~ relation(U_434) )
| ~ relation(U_435) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_442,sK85(U_435,U_434,U_433))],[f_45_4]) ).
fof(f_45_6,plain,
! [U_435] :
( ! [U_434] :
( ! [U_433] :
( ( ( U_433 = relation_composition(U_435,U_434)
| ? [U_443,U_441] :
( ~ in(ordered_pair(U_443,U_441),U_433)
& ? [U_430] :
( in(ordered_pair(U_430,U_441),U_434)
& in(ordered_pair(U_443,U_430),U_435) ) )
| ( ! [U_429] :
( ~ in(ordered_pair(U_429,sK86(U_435,U_434,U_433)),U_434)
| ~ in(ordered_pair(sK85(U_435,U_434,U_433),U_429),U_435) )
& in(ordered_pair(sK85(U_435,U_434,U_433),sK86(U_435,U_434,U_433)),U_433) ) )
& ( ( ! [U_439,U_437] :
( in(ordered_pair(U_439,U_437),U_433)
| ! [U_426] :
( ~ in(ordered_pair(U_426,U_437),U_434)
| ~ in(ordered_pair(U_439,U_426),U_435) ) )
& ! [U_438,U_436] :
( ( in(ordered_pair(sK84(U_435,U_434,U_433,U_438,U_436),U_436),U_434)
& in(ordered_pair(U_438,sK84(U_435,U_434,U_433,U_438,U_436)),U_435) )
| ~ in(ordered_pair(U_438,U_436),U_433) ) )
| U_433 != relation_composition(U_435,U_434) ) )
| ~ relation(U_433) )
| ~ relation(U_434) )
| ~ relation(U_435) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_440,sK86(U_435,U_434,U_433))],[f_45_5]) ).
fof(f_45_7,plain,
! [U_435] :
( ! [U_434] :
( ! [U_433] :
( ( ( U_433 = relation_composition(U_435,U_434)
| ? [U_441] :
( ~ in(ordered_pair(sK87(U_435,U_434,U_433),U_441),U_433)
& ? [U_430] :
( in(ordered_pair(U_430,U_441),U_434)
& in(ordered_pair(sK87(U_435,U_434,U_433),U_430),U_435) ) )
| ( ! [U_429] :
( ~ in(ordered_pair(U_429,sK86(U_435,U_434,U_433)),U_434)
| ~ in(ordered_pair(sK85(U_435,U_434,U_433),U_429),U_435) )
& in(ordered_pair(sK85(U_435,U_434,U_433),sK86(U_435,U_434,U_433)),U_433) ) )
& ( ( ! [U_439,U_437] :
( in(ordered_pair(U_439,U_437),U_433)
| ! [U_426] :
( ~ in(ordered_pair(U_426,U_437),U_434)
| ~ in(ordered_pair(U_439,U_426),U_435) ) )
& ! [U_438,U_436] :
( ( in(ordered_pair(sK84(U_435,U_434,U_433,U_438,U_436),U_436),U_434)
& in(ordered_pair(U_438,sK84(U_435,U_434,U_433,U_438,U_436)),U_435) )
| ~ in(ordered_pair(U_438,U_436),U_433) ) )
| U_433 != relation_composition(U_435,U_434) ) )
| ~ relation(U_433) )
| ~ relation(U_434) )
| ~ relation(U_435) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_443,sK87(U_435,U_434,U_433))],[f_45_6]) ).
fof(f_45_8,plain,
! [U_435] :
( ! [U_434] :
( ! [U_433] :
( ( ( U_433 = relation_composition(U_435,U_434)
| ( ~ in(ordered_pair(sK87(U_435,U_434,U_433),sK88(U_435,U_434,U_433)),U_433)
& ? [U_430] :
( in(ordered_pair(U_430,sK88(U_435,U_434,U_433)),U_434)
& in(ordered_pair(sK87(U_435,U_434,U_433),U_430),U_435) ) )
| ( ! [U_429] :
( ~ in(ordered_pair(U_429,sK86(U_435,U_434,U_433)),U_434)
| ~ in(ordered_pair(sK85(U_435,U_434,U_433),U_429),U_435) )
& in(ordered_pair(sK85(U_435,U_434,U_433),sK86(U_435,U_434,U_433)),U_433) ) )
& ( ( ! [U_439,U_437] :
( in(ordered_pair(U_439,U_437),U_433)
| ! [U_426] :
( ~ in(ordered_pair(U_426,U_437),U_434)
| ~ in(ordered_pair(U_439,U_426),U_435) ) )
& ! [U_438,U_436] :
( ( in(ordered_pair(sK84(U_435,U_434,U_433,U_438,U_436),U_436),U_434)
& in(ordered_pair(U_438,sK84(U_435,U_434,U_433,U_438,U_436)),U_435) )
| ~ in(ordered_pair(U_438,U_436),U_433) ) )
| U_433 != relation_composition(U_435,U_434) ) )
| ~ relation(U_433) )
| ~ relation(U_434) )
| ~ relation(U_435) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_441,sK88(U_435,U_434,U_433))],[f_45_7]) ).
fof(f_45_9,plain,
! [U_435] :
( ! [U_434] :
( ! [U_433] :
( ( ( U_433 = relation_composition(U_435,U_434)
| ( ~ in(ordered_pair(sK87(U_435,U_434,U_433),sK88(U_435,U_434,U_433)),U_433)
& in(ordered_pair(sK89(U_435,U_434,U_433),sK88(U_435,U_434,U_433)),U_434)
& in(ordered_pair(sK87(U_435,U_434,U_433),sK89(U_435,U_434,U_433)),U_435) )
| ( ! [U_429] :
( ~ in(ordered_pair(U_429,sK86(U_435,U_434,U_433)),U_434)
| ~ in(ordered_pair(sK85(U_435,U_434,U_433),U_429),U_435) )
& in(ordered_pair(sK85(U_435,U_434,U_433),sK86(U_435,U_434,U_433)),U_433) ) )
& ( ( ! [U_439,U_437] :
( in(ordered_pair(U_439,U_437),U_433)
| ! [U_426] :
( ~ in(ordered_pair(U_426,U_437),U_434)
| ~ in(ordered_pair(U_439,U_426),U_435) ) )
& ! [U_438,U_436] :
( ( in(ordered_pair(sK84(U_435,U_434,U_433,U_438,U_436),U_436),U_434)
& in(ordered_pair(U_438,sK84(U_435,U_434,U_433,U_438,U_436)),U_435) )
| ~ in(ordered_pair(U_438,U_436),U_433) ) )
| U_433 != relation_composition(U_435,U_434) ) )
| ~ relation(U_433) )
| ~ relation(U_434) )
| ~ relation(U_435) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_430,sK89(U_435,U_434,U_433))],[f_45_8]) ).
cnf(f_45_10,plain,
( in(ordered_pair(U_438,sK84(U_435,U_434,U_433,U_438,U_436)),U_435)
| ~ in(ordered_pair(U_438,U_436),U_433)
| U_433 != relation_composition(U_435,U_434)
| ~ relation(U_433)
| ~ relation(U_434)
| ~ relation(U_435) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_11,plain,
( in(ordered_pair(sK84(U_435,U_434,U_433,U_438,U_436),U_436),U_434)
| ~ in(ordered_pair(U_438,U_436),U_433)
| U_433 != relation_composition(U_435,U_434)
| ~ relation(U_433)
| ~ relation(U_434)
| ~ relation(U_435) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_12,plain,
( in(ordered_pair(U_439,U_437),U_433)
| ~ in(ordered_pair(U_426,U_437),U_434)
| ~ in(ordered_pair(U_439,U_426),U_435)
| U_433 != relation_composition(U_435,U_434)
| ~ relation(U_433)
| ~ relation(U_434)
| ~ relation(U_435) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_13,plain,
( in(ordered_pair(sK87(U_435,U_434,U_433),sK89(U_435,U_434,U_433)),U_435)
| in(ordered_pair(sK85(U_435,U_434,U_433),sK86(U_435,U_434,U_433)),U_433)
| U_433 = relation_composition(U_435,U_434)
| ~ relation(U_433)
| ~ relation(U_434)
| ~ relation(U_435) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_14,plain,
( in(ordered_pair(sK89(U_435,U_434,U_433),sK88(U_435,U_434,U_433)),U_434)
| in(ordered_pair(sK85(U_435,U_434,U_433),sK86(U_435,U_434,U_433)),U_433)
| U_433 = relation_composition(U_435,U_434)
| ~ relation(U_433)
| ~ relation(U_434)
| ~ relation(U_435) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_15,plain,
( ~ in(ordered_pair(sK87(U_435,U_434,U_433),sK88(U_435,U_434,U_433)),U_433)
| in(ordered_pair(sK85(U_435,U_434,U_433),sK86(U_435,U_434,U_433)),U_433)
| U_433 = relation_composition(U_435,U_434)
| ~ relation(U_433)
| ~ relation(U_434)
| ~ relation(U_435) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_16,plain,
( in(ordered_pair(sK87(U_435,U_434,U_433),sK89(U_435,U_434,U_433)),U_435)
| ~ in(ordered_pair(U_429,sK86(U_435,U_434,U_433)),U_434)
| ~ in(ordered_pair(sK85(U_435,U_434,U_433),U_429),U_435)
| U_433 = relation_composition(U_435,U_434)
| ~ relation(U_433)
| ~ relation(U_434)
| ~ relation(U_435) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_17,plain,
( in(ordered_pair(sK89(U_435,U_434,U_433),sK88(U_435,U_434,U_433)),U_434)
| ~ in(ordered_pair(U_429,sK86(U_435,U_434,U_433)),U_434)
| ~ in(ordered_pair(sK85(U_435,U_434,U_433),U_429),U_435)
| U_433 = relation_composition(U_435,U_434)
| ~ relation(U_433)
| ~ relation(U_434)
| ~ relation(U_435) ),
inference(clausify,[status(thm)],[f_45_9]) ).
cnf(f_45_18,plain,
( ~ in(ordered_pair(sK87(U_435,U_434,U_433),sK88(U_435,U_434,U_433)),U_433)
| ~ in(ordered_pair(U_429,sK86(U_435,U_434,U_433)),U_434)
| ~ in(ordered_pair(sK85(U_435,U_434,U_433),U_429),U_435)
| U_433 = relation_composition(U_435,U_434)
| ~ relation(U_433)
| ~ relation(U_434)
| ~ relation(U_435) ),
inference(clausify,[status(thm)],[f_45_9]) ).
fof(f_46_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_46_2,plain,
! [U_448,U_447] :
( ! [U_446] :
( ( ( U_446 = complements_of_subsets(U_448,U_447)
| ? [U_445] :
( ( ( ~ in(U_445,U_446)
& in(subset_complement(U_448,U_445),U_447) )
| ( ~ in(subset_complement(U_448,U_445),U_447)
& in(U_445,U_446) ) )
& element(U_445,powerset(U_448)) ) )
& ( ! [U_444] :
( ( ( in(U_444,U_446)
| ~ in(subset_complement(U_448,U_444),U_447) )
& ( in(subset_complement(U_448,U_444),U_447)
| ~ in(U_444,U_446) ) )
| ~ element(U_444,powerset(U_448)) )
| U_446 != complements_of_subsets(U_448,U_447) ) )
| ~ element(U_446,powerset(powerset(U_448))) )
| ~ element(U_447,powerset(powerset(U_448))) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_448,U_447] :
( ! [U_446] :
( ( ( U_446 = complements_of_subsets(U_448,U_447)
| ( ( ( ~ in(sK90(U_448,U_447,U_446),U_446)
& in(subset_complement(U_448,sK90(U_448,U_447,U_446)),U_447) )
| ( ~ in(subset_complement(U_448,sK90(U_448,U_447,U_446)),U_447)
& in(sK90(U_448,U_447,U_446),U_446) ) )
& element(sK90(U_448,U_447,U_446),powerset(U_448)) ) )
& ( ! [U_444] :
( ( ( in(U_444,U_446)
| ~ in(subset_complement(U_448,U_444),U_447) )
& ( in(subset_complement(U_448,U_444),U_447)
| ~ in(U_444,U_446) ) )
| ~ element(U_444,powerset(U_448)) )
| U_446 != complements_of_subsets(U_448,U_447) ) )
| ~ element(U_446,powerset(powerset(U_448))) )
| ~ element(U_447,powerset(powerset(U_448))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_445,sK90(U_448,U_447,U_446))],[f_46_2]) ).
cnf(f_46_4,plain,
( in(subset_complement(U_448,U_444),U_447)
| ~ in(U_444,U_446)
| ~ element(U_444,powerset(U_448))
| U_446 != complements_of_subsets(U_448,U_447)
| ~ element(U_446,powerset(powerset(U_448)))
| ~ element(U_447,powerset(powerset(U_448))) ),
inference(clausify,[status(thm)],[f_46_3]) ).
cnf(f_46_5,plain,
( in(U_444,U_446)
| ~ in(subset_complement(U_448,U_444),U_447)
| ~ element(U_444,powerset(U_448))
| U_446 != complements_of_subsets(U_448,U_447)
| ~ element(U_446,powerset(powerset(U_448)))
| ~ element(U_447,powerset(powerset(U_448))) ),
inference(clausify,[status(thm)],[f_46_3]) ).
cnf(f_46_6,plain,
( element(sK90(U_448,U_447,U_446),powerset(U_448))
| U_446 = complements_of_subsets(U_448,U_447)
| ~ element(U_446,powerset(powerset(U_448)))
| ~ element(U_447,powerset(powerset(U_448))) ),
inference(clausify,[status(thm)],[f_46_3]) ).
cnf(f_46_7,plain,
( in(subset_complement(U_448,sK90(U_448,U_447,U_446)),U_447)
| in(sK90(U_448,U_447,U_446),U_446)
| U_446 = complements_of_subsets(U_448,U_447)
| ~ element(U_446,powerset(powerset(U_448)))
| ~ element(U_447,powerset(powerset(U_448))) ),
inference(clausify,[status(thm)],[f_46_3]) ).
cnf(f_46_8,plain,
( ~ in(sK90(U_448,U_447,U_446),U_446)
| in(sK90(U_448,U_447,U_446),U_446)
| U_446 = complements_of_subsets(U_448,U_447)
| ~ element(U_446,powerset(powerset(U_448)))
| ~ element(U_447,powerset(powerset(U_448))) ),
inference(clausify,[status(thm)],[f_46_3]) ).
cnf(f_46_9,plain,
( in(subset_complement(U_448,sK90(U_448,U_447,U_446)),U_447)
| ~ in(subset_complement(U_448,sK90(U_448,U_447,U_446)),U_447)
| U_446 = complements_of_subsets(U_448,U_447)
| ~ element(U_446,powerset(powerset(U_448)))
| ~ element(U_447,powerset(powerset(U_448))) ),
inference(clausify,[status(thm)],[f_46_3]) ).
cnf(f_46_10,plain,
( ~ in(sK90(U_448,U_447,U_446),U_446)
| ~ in(subset_complement(U_448,sK90(U_448,U_447,U_446)),U_447)
| U_446 = complements_of_subsets(U_448,U_447)
| ~ element(U_446,powerset(powerset(U_448)))
| ~ element(U_447,powerset(powerset(U_448))) ),
inference(clausify,[status(thm)],[f_46_3]) ).
fof(f_47_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_47_2,plain,
! [U_450,U_449] :
( ( proper_subset(U_450,U_449)
| U_450 = U_449
| ~ subset(U_450,U_449) )
& ( ( U_450 != U_449
& subset(U_450,U_449) )
| ~ proper_subset(U_450,U_449) ) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
( ! [U_454,U_452] :
( proper_subset(U_454,U_452)
| U_454 = U_452
| ~ subset(U_454,U_452) )
& ! [U_453,U_451] :
( ( U_453 != U_451
& subset(U_453,U_451) )
| ~ proper_subset(U_453,U_451) ) ),
inference(miniscope,[status(thm)],[f_47_2]) ).
cnf(f_47_4,plain,
( subset(U_453,U_451)
| ~ proper_subset(U_453,U_451) ),
inference(clausify,[status(thm)],[f_47_3]) ).
cnf(f_47_5,plain,
( U_453 != U_451
| ~ proper_subset(U_453,U_451) ),
inference(clausify,[status(thm)],[f_47_3]) ).
cnf(f_47_6,plain,
( proper_subset(U_454,U_452)
| U_454 = U_452
| ~ subset(U_454,U_452) ),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_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_48_2,plain,
! [U_455] :
( function_inverse(U_455) = relation_inverse(U_455)
| ~ one_to_one(U_455)
| ~ function(U_455)
| ~ relation(U_455) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
cnf(f_48_3,plain,
( function_inverse(U_455) = relation_inverse(U_455)
| ~ one_to_one(U_455)
| ~ function(U_455)
| ~ relation(U_455) ),
inference(clausify,[status(thm)],[f_48_2]) ).
fof(f_49_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k10_relat_1]) ).
cnf(f_49_2,plain,
$true,
inference(clausify,[status(thm)],[f_49_1]) ).
fof(f_50_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_enumset1]) ).
cnf(f_50_2,plain,
$true,
inference(clausify,[status(thm)],[f_50_1]) ).
fof(f_51_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_funct_1]) ).
cnf(f_51_2,plain,
$true,
inference(clausify,[status(thm)],[f_51_1]) ).
fof(f_52_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_ordinal1]) ).
cnf(f_52_2,plain,
$true,
inference(clausify,[status(thm)],[f_52_1]) ).
fof(f_53_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
cnf(f_53_2,plain,
$true,
inference(clausify,[status(thm)],[f_53_1]) ).
fof(f_54_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_setfam_1]) ).
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_k1_tarski]) ).
cnf(f_55_2,plain,
$true,
inference(clausify,[status(thm)],[f_55_1]) ).
fof(f_56_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
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_k1_zfmisc_1]) ).
cnf(f_57_2,plain,
$true,
inference(clausify,[status(thm)],[f_57_1]) ).
fof(f_58_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_58_2,plain,
! [U_456] :
( ( function(function_inverse(U_456))
& relation(function_inverse(U_456)) )
| ~ function(U_456)
| ~ relation(U_456) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
cnf(f_58_3,plain,
( relation(function_inverse(U_456))
| ~ function(U_456)
| ~ relation(U_456) ),
inference(clausify,[status(thm)],[f_58_2]) ).
cnf(f_58_4,plain,
( function(function_inverse(U_456))
| ~ function(U_456)
| ~ relation(U_456) ),
inference(clausify,[status(thm)],[f_58_2]) ).
fof(f_59_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_relat_1]) ).
cnf(f_59_2,plain,
$true,
inference(clausify,[status(thm)],[f_59_1]) ).
fof(f_60_1,plain,
! [A] : element(cast_to_subset(A),powerset(A)),
inference(fof_nnf,[status(thm)],[dt_k2_subset_1]) ).
fof(f_60_2,plain,
! [U_457] : element(cast_to_subset(U_457),powerset(U_457)),
inference(variable_rename,[status(thm)],[f_60_1]) ).
cnf(f_60_3,plain,
element(cast_to_subset(U_457),powerset(U_457)),
inference(clausify,[status(thm)],[f_60_2]) ).
fof(f_61_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
cnf(f_61_2,plain,
$true,
inference(clausify,[status(thm)],[f_61_1]) ).
fof(f_62_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
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_k2_zfmisc_1]) ).
cnf(f_63_2,plain,
$true,
inference(clausify,[status(thm)],[f_63_1]) ).
fof(f_64_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_relat_1]) ).
cnf(f_64_2,plain,
$true,
inference(clausify,[status(thm)],[f_64_1]) ).
fof(f_65_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_65_2,plain,
! [U_459,U_458] :
( element(subset_complement(U_459,U_458),powerset(U_459))
| ~ element(U_458,powerset(U_459)) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
cnf(f_65_3,plain,
( element(subset_complement(U_459,U_458),powerset(U_459))
| ~ element(U_458,powerset(U_459)) ),
inference(clausify,[status(thm)],[f_65_2]) ).
fof(f_66_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_tarski]) ).
cnf(f_66_2,plain,
$true,
inference(clausify,[status(thm)],[f_66_1]) ).
fof(f_67_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
cnf(f_67_2,plain,
$true,
inference(clausify,[status(thm)],[f_67_1]) ).
fof(f_68_1,plain,
! [A] :
( relation(relation_inverse(A))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k4_relat_1]) ).
fof(f_68_2,plain,
! [U_460] :
( relation(relation_inverse(U_460))
| ~ relation(U_460) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
cnf(f_68_3,plain,
( relation(relation_inverse(U_460))
| ~ relation(U_460) ),
inference(clausify,[status(thm)],[f_68_2]) ).
fof(f_69_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
cnf(f_69_2,plain,
$true,
inference(clausify,[status(thm)],[f_69_1]) ).
fof(f_70_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
cnf(f_70_2,plain,
$true,
inference(clausify,[status(thm)],[f_70_1]) ).
fof(f_71_1,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_relat_1]) ).
fof(f_71_2,plain,
! [U_462,U_461] :
( relation(relation_composition(U_462,U_461))
| ~ relation(U_461)
| ~ relation(U_462) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
cnf(f_71_3,plain,
( relation(relation_composition(U_462,U_461))
| ~ relation(U_461)
| ~ relation(U_462) ),
inference(clausify,[status(thm)],[f_71_2]) ).
fof(f_72_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_72_2,plain,
! [U_464,U_463] :
( element(union_of_subsets(U_464,U_463),powerset(U_464))
| ~ element(U_463,powerset(powerset(U_464))) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
cnf(f_72_3,plain,
( element(union_of_subsets(U_464,U_463),powerset(U_464))
| ~ element(U_463,powerset(powerset(U_464))) ),
inference(clausify,[status(thm)],[f_72_2]) ).
fof(f_73_1,plain,
! [A] : relation(identity_relation(A)),
inference(fof_nnf,[status(thm)],[dt_k6_relat_1]) ).
fof(f_73_2,plain,
! [U_465] : relation(identity_relation(U_465)),
inference(variable_rename,[status(thm)],[f_73_1]) ).
cnf(f_73_3,plain,
relation(identity_relation(U_465)),
inference(clausify,[status(thm)],[f_73_2]) ).
fof(f_74_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_74_2,plain,
! [U_467,U_466] :
( element(meet_of_subsets(U_467,U_466),powerset(U_467))
| ~ element(U_466,powerset(powerset(U_467))) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
cnf(f_74_3,plain,
( element(meet_of_subsets(U_467,U_466),powerset(U_467))
| ~ element(U_466,powerset(powerset(U_467))) ),
inference(clausify,[status(thm)],[f_74_2]) ).
fof(f_75_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_75_2,plain,
! [U_470,U_469,U_468] :
( element(subset_difference(U_470,U_469,U_468),powerset(U_470))
| ~ element(U_468,powerset(U_470))
| ~ element(U_469,powerset(U_470)) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
cnf(f_75_3,plain,
( element(subset_difference(U_470,U_469,U_468),powerset(U_470))
| ~ element(U_468,powerset(U_470))
| ~ element(U_469,powerset(U_470)) ),
inference(clausify,[status(thm)],[f_75_2]) ).
fof(f_76_1,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k7_relat_1]) ).
fof(f_76_2,plain,
! [U_472,U_471] :
( relation(relation_dom_restriction(U_472,U_471))
| ~ relation(U_472) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
fof(f_76_3,plain,
! [U_472] :
( ! [U_471] : relation(relation_dom_restriction(U_472,U_471))
| ~ relation(U_472) ),
inference(miniscope,[status(thm)],[f_76_2]) ).
cnf(f_76_4,plain,
( relation(relation_dom_restriction(U_472,U_471))
| ~ relation(U_472) ),
inference(clausify,[status(thm)],[f_76_3]) ).
fof(f_77_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_77_2,plain,
! [U_474,U_473] :
( element(complements_of_subsets(U_474,U_473),powerset(powerset(U_474)))
| ~ element(U_473,powerset(powerset(U_474))) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
cnf(f_77_3,plain,
( element(complements_of_subsets(U_474,U_473),powerset(powerset(U_474)))
| ~ element(U_473,powerset(powerset(U_474))) ),
inference(clausify,[status(thm)],[f_77_2]) ).
fof(f_78_1,plain,
! [A,B] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[dt_k8_relat_1]) ).
fof(f_78_2,plain,
! [U_476,U_475] :
( relation(relation_rng_restriction(U_476,U_475))
| ~ relation(U_475) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
cnf(f_78_3,plain,
( relation(relation_rng_restriction(U_476,U_475))
| ~ relation(U_475) ),
inference(clausify,[status(thm)],[f_78_2]) ).
fof(f_79_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k9_relat_1]) ).
cnf(f_79_2,plain,
$true,
inference(clausify,[status(thm)],[f_79_1]) ).
fof(f_80_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_80_2,plain,
$true,
inference(clausify,[status(thm)],[f_80_1]) ).
fof(f_81_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_81_2,plain,
! [U_478] :
? [U_477] : element(U_477,U_478),
inference(variable_rename,[status(thm)],[f_81_1]) ).
fof(f_81_3,plain,
! [U_478] : element(sK91(U_478),U_478),
inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_477,sK91(U_478))],[f_81_2]) ).
cnf(f_81_4,plain,
element(sK91(U_478),U_478),
inference(clausify,[status(thm)],[f_81_3]) ).
fof(f_82_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_82_2,plain,
! [U_480,U_479] :
( ( relation(relation_composition(U_479,U_480))
& empty(relation_composition(U_479,U_480)) )
| ~ relation(U_479)
| ~ empty(U_480) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
cnf(f_82_3,plain,
( empty(relation_composition(U_479,U_480))
| ~ relation(U_479)
| ~ empty(U_480) ),
inference(clausify,[status(thm)],[f_82_2]) ).
cnf(f_82_4,plain,
( relation(relation_composition(U_479,U_480))
| ~ relation(U_479)
| ~ empty(U_480) ),
inference(clausify,[status(thm)],[f_82_2]) ).
fof(f_83_1,plain,
! [A] :
( ( relation(relation_inverse(A))
& empty(relation_inverse(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc11_relat_1]) ).
fof(f_83_2,plain,
! [U_481] :
( ( relation(relation_inverse(U_481))
& empty(relation_inverse(U_481)) )
| ~ empty(U_481) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
cnf(f_83_3,plain,
( empty(relation_inverse(U_481))
| ~ empty(U_481) ),
inference(clausify,[status(thm)],[f_83_2]) ).
cnf(f_83_4,plain,
( relation(relation_inverse(U_481))
| ~ empty(U_481) ),
inference(clausify,[status(thm)],[f_83_2]) ).
fof(f_84_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
cnf(f_84_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_84_1]) ).
cnf(f_84_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_84_1]) ).
cnf(f_84_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_84_1]) ).
fof(f_85_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_85_2,plain,
! [U_483,U_482] :
( ( relation_empty_yielding(relation_dom_restriction(U_483,U_482))
& relation(relation_dom_restriction(U_483,U_482)) )
| ~ relation_empty_yielding(U_483)
| ~ relation(U_483) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
fof(f_85_3,plain,
! [U_483] :
( ( ! [U_485] : relation_empty_yielding(relation_dom_restriction(U_483,U_485))
& ! [U_484] : relation(relation_dom_restriction(U_483,U_484)) )
| ~ relation_empty_yielding(U_483)
| ~ relation(U_483) ),
inference(miniscope,[status(thm)],[f_85_2]) ).
cnf(f_85_4,plain,
( relation(relation_dom_restriction(U_483,U_484))
| ~ relation_empty_yielding(U_483)
| ~ relation(U_483) ),
inference(clausify,[status(thm)],[f_85_3]) ).
cnf(f_85_5,plain,
( relation_empty_yielding(relation_dom_restriction(U_483,U_485))
| ~ relation_empty_yielding(U_483)
| ~ relation(U_483) ),
inference(clausify,[status(thm)],[f_85_3]) ).
fof(f_86_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_86_2,plain,
! [U_487,U_486] :
( ( function(relation_composition(U_487,U_486))
& relation(relation_composition(U_487,U_486)) )
| ~ function(U_486)
| ~ relation(U_486)
| ~ function(U_487)
| ~ relation(U_487) ),
inference(variable_rename,[status(thm)],[f_86_1]) ).
cnf(f_86_3,plain,
( relation(relation_composition(U_487,U_486))
| ~ function(U_486)
| ~ relation(U_486)
| ~ function(U_487)
| ~ relation(U_487) ),
inference(clausify,[status(thm)],[f_86_2]) ).
cnf(f_86_4,plain,
( function(relation_composition(U_487,U_486))
| ~ function(U_486)
| ~ relation(U_486)
| ~ function(U_487)
| ~ relation(U_487) ),
inference(clausify,[status(thm)],[f_86_2]) ).
fof(f_87_1,plain,
! [A] : ~ empty(succ(A)),
inference(fof_nnf,[status(thm)],[fc1_ordinal1]) ).
fof(f_87_2,plain,
! [U_488] : ~ empty(succ(U_488)),
inference(variable_rename,[status(thm)],[f_87_1]) ).
cnf(f_87_3,plain,
~ empty(succ(U_488)),
inference(clausify,[status(thm)],[f_87_2]) ).
fof(f_88_1,plain,
! [A,B] :
( relation(set_intersection2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc1_relat_1]) ).
fof(f_88_2,plain,
! [U_490,U_489] :
( relation(set_intersection2(U_490,U_489))
| ~ relation(U_489)
| ~ relation(U_490) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
cnf(f_88_3,plain,
( relation(set_intersection2(U_490,U_489))
| ~ relation(U_489)
| ~ relation(U_490) ),
inference(clausify,[status(thm)],[f_88_2]) ).
fof(f_89_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_89_2,plain,
! [U_491] : ~ empty(powerset(U_491)),
inference(variable_rename,[status(thm)],[f_89_1]) ).
cnf(f_89_3,plain,
~ empty(powerset(U_491)),
inference(clausify,[status(thm)],[f_89_2]) ).
fof(f_90_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_90_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_90_1]) ).
fof(f_91_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_91_2,plain,
! [U_493,U_492] : ~ empty(ordered_pair(U_493,U_492)),
inference(variable_rename,[status(thm)],[f_91_1]) ).
cnf(f_91_3,plain,
~ empty(ordered_pair(U_493,U_492)),
inference(clausify,[status(thm)],[f_91_2]) ).
fof(f_92_1,plain,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
inference(fof_nnf,[status(thm)],[fc2_funct_1]) ).
fof(f_92_2,plain,
! [U_494] :
( function(identity_relation(U_494))
& relation(identity_relation(U_494)) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
fof(f_92_3,plain,
( ! [U_496] : function(identity_relation(U_496))
& ! [U_495] : relation(identity_relation(U_495)) ),
inference(miniscope,[status(thm)],[f_92_2]) ).
cnf(f_92_4,plain,
relation(identity_relation(U_495)),
inference(clausify,[status(thm)],[f_92_3]) ).
cnf(f_92_5,plain,
function(identity_relation(U_496)),
inference(clausify,[status(thm)],[f_92_3]) ).
fof(f_93_1,plain,
! [A,B] :
( relation(set_union2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc2_relat_1]) ).
fof(f_93_2,plain,
! [U_498,U_497] :
( relation(set_union2(U_498,U_497))
| ~ relation(U_497)
| ~ relation(U_498) ),
inference(variable_rename,[status(thm)],[f_93_1]) ).
cnf(f_93_3,plain,
( relation(set_union2(U_498,U_497))
| ~ relation(U_497)
| ~ relation(U_498) ),
inference(clausify,[status(thm)],[f_93_2]) ).
fof(f_94_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_94_2,plain,
! [U_499] : ~ empty(singleton(U_499)),
inference(variable_rename,[status(thm)],[f_94_1]) ).
cnf(f_94_3,plain,
~ empty(singleton(U_499)),
inference(clausify,[status(thm)],[f_94_2]) ).
fof(f_95_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_95_2,plain,
! [U_501,U_500] :
( ~ empty(set_union2(U_501,U_500))
| empty(U_501) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
fof(f_95_3,plain,
! [U_501] :
( ! [U_500] : ~ empty(set_union2(U_501,U_500))
| empty(U_501) ),
inference(miniscope,[status(thm)],[f_95_2]) ).
cnf(f_95_4,plain,
( ~ empty(set_union2(U_501,U_500))
| empty(U_501) ),
inference(clausify,[status(thm)],[f_95_3]) ).
fof(f_96_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_96_2,plain,
! [U_502] :
( ( function(relation_inverse(U_502))
& relation(relation_inverse(U_502)) )
| ~ one_to_one(U_502)
| ~ function(U_502)
| ~ relation(U_502) ),
inference(variable_rename,[status(thm)],[f_96_1]) ).
cnf(f_96_3,plain,
( relation(relation_inverse(U_502))
| ~ one_to_one(U_502)
| ~ function(U_502)
| ~ relation(U_502) ),
inference(clausify,[status(thm)],[f_96_2]) ).
cnf(f_96_4,plain,
( function(relation_inverse(U_502))
| ~ one_to_one(U_502)
| ~ function(U_502)
| ~ relation(U_502) ),
inference(clausify,[status(thm)],[f_96_2]) ).
fof(f_97_1,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_97_2,plain,
! [U_504,U_503] : ~ empty(unordered_pair(U_504,U_503)),
inference(variable_rename,[status(thm)],[f_97_1]) ).
cnf(f_97_3,plain,
~ empty(unordered_pair(U_504,U_503)),
inference(clausify,[status(thm)],[f_97_2]) ).
fof(f_98_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_98_2,plain,
! [U_506,U_505] :
( ~ empty(set_union2(U_505,U_506))
| empty(U_506) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
fof(f_98_3,plain,
! [U_506] :
( ! [U_505] : ~ empty(set_union2(U_505,U_506))
| empty(U_506) ),
inference(miniscope,[status(thm)],[f_98_2]) ).
cnf(f_98_4,plain,
( ~ empty(set_union2(U_505,U_506))
| empty(U_506) ),
inference(clausify,[status(thm)],[f_98_3]) ).
fof(f_99_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_99_2,plain,
! [U_508,U_507] :
( ( function(relation_dom_restriction(U_508,U_507))
& relation(relation_dom_restriction(U_508,U_507)) )
| ~ function(U_508)
| ~ relation(U_508) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
fof(f_99_3,plain,
! [U_508] :
( ( ! [U_510] : function(relation_dom_restriction(U_508,U_510))
& ! [U_509] : relation(relation_dom_restriction(U_508,U_509)) )
| ~ function(U_508)
| ~ relation(U_508) ),
inference(miniscope,[status(thm)],[f_99_2]) ).
cnf(f_99_4,plain,
( relation(relation_dom_restriction(U_508,U_509))
| ~ function(U_508)
| ~ relation(U_508) ),
inference(clausify,[status(thm)],[f_99_3]) ).
cnf(f_99_5,plain,
( function(relation_dom_restriction(U_508,U_510))
| ~ function(U_508)
| ~ relation(U_508) ),
inference(clausify,[status(thm)],[f_99_3]) ).
fof(f_100_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_100_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_100_1]) ).
cnf(f_100_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_100_1]) ).
fof(f_101_1,plain,
! [A,B] :
( ~ empty(cartesian_product2(A,B))
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc4_subset_1]) ).
fof(f_101_2,plain,
! [U_512,U_511] :
( ~ empty(cartesian_product2(U_512,U_511))
| empty(U_511)
| empty(U_512) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
cnf(f_101_3,plain,
( ~ empty(cartesian_product2(U_512,U_511))
| empty(U_511)
| empty(U_512) ),
inference(clausify,[status(thm)],[f_101_2]) ).
fof(f_102_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_102_2,plain,
! [U_513] :
( ~ empty(relation_dom(U_513))
| ~ relation(U_513)
| empty(U_513) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
cnf(f_102_3,plain,
( ~ empty(relation_dom(U_513))
| ~ relation(U_513)
| empty(U_513) ),
inference(clausify,[status(thm)],[f_102_2]) ).
fof(f_103_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_103_2,plain,
! [U_514] :
( ~ empty(relation_rng(U_514))
| ~ relation(U_514)
| empty(U_514) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
cnf(f_103_3,plain,
( ~ empty(relation_rng(U_514))
| ~ relation(U_514)
| empty(U_514) ),
inference(clausify,[status(thm)],[f_103_2]) ).
fof(f_104_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_104_2,plain,
! [U_515] :
( ( relation(relation_dom(U_515))
& empty(relation_dom(U_515)) )
| ~ empty(U_515) ),
inference(variable_rename,[status(thm)],[f_104_1]) ).
cnf(f_104_3,plain,
( empty(relation_dom(U_515))
| ~ empty(U_515) ),
inference(clausify,[status(thm)],[f_104_2]) ).
cnf(f_104_4,plain,
( relation(relation_dom(U_515))
| ~ empty(U_515) ),
inference(clausify,[status(thm)],[f_104_2]) ).
fof(f_105_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_105_2,plain,
! [U_516] :
( ( relation(relation_rng(U_516))
& empty(relation_rng(U_516)) )
| ~ empty(U_516) ),
inference(variable_rename,[status(thm)],[f_105_1]) ).
cnf(f_105_3,plain,
( empty(relation_rng(U_516))
| ~ empty(U_516) ),
inference(clausify,[status(thm)],[f_105_2]) ).
cnf(f_105_4,plain,
( relation(relation_rng(U_516))
| ~ empty(U_516) ),
inference(clausify,[status(thm)],[f_105_2]) ).
fof(f_106_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_106_2,plain,
! [U_518,U_517] :
( ( relation(relation_composition(U_518,U_517))
& empty(relation_composition(U_518,U_517)) )
| ~ relation(U_517)
| ~ empty(U_518) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
cnf(f_106_3,plain,
( empty(relation_composition(U_518,U_517))
| ~ relation(U_517)
| ~ empty(U_518) ),
inference(clausify,[status(thm)],[f_106_2]) ).
cnf(f_106_4,plain,
( relation(relation_composition(U_518,U_517))
| ~ relation(U_517)
| ~ empty(U_518) ),
inference(clausify,[status(thm)],[f_106_2]) ).
fof(f_107_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_107_2,plain,
! [U_520,U_519] : set_union2(U_520,U_520) = U_520,
inference(variable_rename,[status(thm)],[f_107_1]) ).
fof(f_107_3,plain,
! [U_520] : set_union2(U_520,U_520) = U_520,
inference(miniscope,[status(thm)],[f_107_2]) ).
cnf(f_107_4,plain,
set_union2(U_520,U_520) = U_520,
inference(clausify,[status(thm)],[f_107_3]) ).
fof(f_108_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_108_2,plain,
! [U_522,U_521] : set_intersection2(U_522,U_522) = U_522,
inference(variable_rename,[status(thm)],[f_108_1]) ).
fof(f_108_3,plain,
! [U_522] : set_intersection2(U_522,U_522) = U_522,
inference(miniscope,[status(thm)],[f_108_2]) ).
cnf(f_108_4,plain,
set_intersection2(U_522,U_522) = U_522,
inference(clausify,[status(thm)],[f_108_3]) ).
fof(f_109_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_109_2,plain,
! [U_524,U_523] :
( subset_complement(U_524,subset_complement(U_524,U_523)) = U_523
| ~ element(U_523,powerset(U_524)) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
cnf(f_109_3,plain,
( subset_complement(U_524,subset_complement(U_524,U_523)) = U_523
| ~ element(U_523,powerset(U_524)) ),
inference(clausify,[status(thm)],[f_109_2]) ).
fof(f_110_1,plain,
! [A] :
( relation_inverse(relation_inverse(A)) = A
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[involutiveness_k4_relat_1]) ).
fof(f_110_2,plain,
! [U_525] :
( relation_inverse(relation_inverse(U_525)) = U_525
| ~ relation(U_525) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
cnf(f_110_3,plain,
( relation_inverse(relation_inverse(U_525)) = U_525
| ~ relation(U_525) ),
inference(clausify,[status(thm)],[f_110_2]) ).
fof(f_111_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_111_2,plain,
! [U_527,U_526] :
( complements_of_subsets(U_527,complements_of_subsets(U_527,U_526)) = U_526
| ~ element(U_526,powerset(powerset(U_527))) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
cnf(f_111_3,plain,
( complements_of_subsets(U_527,complements_of_subsets(U_527,U_526)) = U_526
| ~ element(U_526,powerset(powerset(U_527))) ),
inference(clausify,[status(thm)],[f_111_2]) ).
fof(f_112_1,plain,
! [A,B] : ~ proper_subset(A,A),
inference(fof_nnf,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(f_112_2,plain,
! [U_529,U_528] : ~ proper_subset(U_529,U_529),
inference(variable_rename,[status(thm)],[f_112_1]) ).
fof(f_112_3,plain,
! [U_529] : ~ proper_subset(U_529,U_529),
inference(miniscope,[status(thm)],[f_112_2]) ).
cnf(f_112_4,plain,
~ proper_subset(U_529,U_529),
inference(clausify,[status(thm)],[f_112_3]) ).
fof(f_113_1,plain,
! [A] : singleton(A) != empty_set,
inference(fof_nnf,[status(thm)],[l1_zfmisc_1]) ).
fof(f_113_2,plain,
! [U_530] : singleton(U_530) != empty_set,
inference(variable_rename,[status(thm)],[f_113_1]) ).
cnf(f_113_3,plain,
singleton(U_530) != empty_set,
inference(clausify,[status(thm)],[f_113_2]) ).
fof(f_114_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l23_zfmisc_1]) ).
fof(f_114_2,plain,
! [U_532,U_531] :
( set_union2(singleton(U_532),U_531) = U_531
| ~ in(U_532,U_531) ),
inference(variable_rename,[status(thm)],[f_114_1]) ).
cnf(f_114_3,plain,
( set_union2(singleton(U_532),U_531) = U_531
| ~ in(U_532,U_531) ),
inference(clausify,[status(thm)],[f_114_2]) ).
fof(f_115_1,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(fof_nnf,[status(thm)],[l25_zfmisc_1]) ).
fof(f_115_2,plain,
! [U_534,U_533] :
( ~ in(U_534,U_533)
| ~ disjoint(singleton(U_534),U_533) ),
inference(variable_rename,[status(thm)],[f_115_1]) ).
cnf(f_115_3,plain,
( ~ in(U_534,U_533)
| ~ disjoint(singleton(U_534),U_533) ),
inference(clausify,[status(thm)],[f_115_2]) ).
fof(f_116_1,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(fof_nnf,[status(thm)],[l28_zfmisc_1]) ).
fof(f_116_2,plain,
! [U_536,U_535] :
( disjoint(singleton(U_536),U_535)
| in(U_536,U_535) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
cnf(f_116_3,plain,
( disjoint(singleton(U_536),U_535)
| in(U_536,U_535) ),
inference(clausify,[status(thm)],[f_116_2]) ).
fof(f_117_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_117_2,plain,
! [U_538,U_537] :
( ( subset(singleton(U_538),U_537)
| ~ in(U_538,U_537) )
& ( in(U_538,U_537)
| ~ subset(singleton(U_538),U_537) ) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
fof(f_117_3,plain,
( ! [U_542,U_540] :
( subset(singleton(U_542),U_540)
| ~ in(U_542,U_540) )
& ! [U_541,U_539] :
( in(U_541,U_539)
| ~ subset(singleton(U_541),U_539) ) ),
inference(miniscope,[status(thm)],[f_117_2]) ).
cnf(f_117_4,plain,
( in(U_541,U_539)
| ~ subset(singleton(U_541),U_539) ),
inference(clausify,[status(thm)],[f_117_3]) ).
cnf(f_117_5,plain,
( subset(singleton(U_542),U_540)
| ~ in(U_542,U_540) ),
inference(clausify,[status(thm)],[f_117_3]) ).
fof(f_118_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_118_2,plain,
! [U_544,U_543] :
( ( set_difference(U_544,U_543) = empty_set
| ~ subset(U_544,U_543) )
& ( subset(U_544,U_543)
| set_difference(U_544,U_543) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
fof(f_118_3,plain,
( ! [U_548,U_546] :
( set_difference(U_548,U_546) = empty_set
| ~ subset(U_548,U_546) )
& ! [U_547,U_545] :
( subset(U_547,U_545)
| set_difference(U_547,U_545) != empty_set ) ),
inference(miniscope,[status(thm)],[f_118_2]) ).
cnf(f_118_4,plain,
( subset(U_547,U_545)
| set_difference(U_547,U_545) != empty_set ),
inference(clausify,[status(thm)],[f_118_3]) ).
cnf(f_118_5,plain,
( set_difference(U_548,U_546) = empty_set
| ~ subset(U_548,U_546) ),
inference(clausify,[status(thm)],[f_118_3]) ).
fof(f_119_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_119_2,plain,
! [U_551,U_550] :
( ! [U_549] :
( in(U_549,U_551)
| ~ in(U_549,U_550) )
| ~ element(U_550,powerset(U_551)) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
cnf(f_119_3,plain,
( in(U_549,U_551)
| ~ in(U_549,U_550)
| ~ element(U_550,powerset(U_551)) ),
inference(clausify,[status(thm)],[f_119_2]) ).
fof(f_120_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_120_2,plain,
! [U_554,U_553,U_552] :
( subset(U_554,set_difference(U_553,singleton(U_552)))
| in(U_552,U_554)
| ~ subset(U_554,U_553) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
fof(f_120_3,plain,
! [U_554,U_553] :
( ! [U_552] :
( subset(U_554,set_difference(U_553,singleton(U_552)))
| in(U_552,U_554) )
| ~ subset(U_554,U_553) ),
inference(miniscope,[status(thm)],[f_120_2]) ).
cnf(f_120_4,plain,
( subset(U_554,set_difference(U_553,singleton(U_552)))
| in(U_552,U_554)
| ~ subset(U_554,U_553) ),
inference(clausify,[status(thm)],[f_120_3]) ).
fof(f_121_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_121_2,plain,
! [U_556,U_555] :
( ( subset(U_556,singleton(U_555))
| ( U_556 != singleton(U_555)
& U_556 != empty_set ) )
& ( U_556 = singleton(U_555)
| U_556 = empty_set
| ~ subset(U_556,singleton(U_555)) ) ),
inference(variable_rename,[status(thm)],[f_121_1]) ).
fof(f_121_3,plain,
( ! [U_560,U_558] :
( subset(U_560,singleton(U_558))
| ( U_560 != singleton(U_558)
& U_560 != empty_set ) )
& ! [U_559,U_557] :
( U_559 = singleton(U_557)
| U_559 = empty_set
| ~ subset(U_559,singleton(U_557)) ) ),
inference(miniscope,[status(thm)],[f_121_2]) ).
cnf(f_121_4,plain,
( U_559 = singleton(U_557)
| U_559 = empty_set
| ~ subset(U_559,singleton(U_557)) ),
inference(clausify,[status(thm)],[f_121_3]) ).
cnf(f_121_5,plain,
( U_560 != empty_set
| subset(U_560,singleton(U_558)) ),
inference(clausify,[status(thm)],[f_121_3]) ).
cnf(f_121_6,plain,
( U_560 != singleton(U_558)
| subset(U_560,singleton(U_558)) ),
inference(clausify,[status(thm)],[f_121_3]) ).
fof(f_122_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l50_zfmisc_1]) ).
fof(f_122_2,plain,
! [U_562,U_561] :
( subset(U_562,union(U_561))
| ~ in(U_562,U_561) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
cnf(f_122_3,plain,
( subset(U_562,union(U_561))
| ~ in(U_562,U_561) ),
inference(clausify,[status(thm)],[f_122_2]) ).
fof(f_123_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_123_2,plain,
! [U_566,U_565,U_564,U_563] :
( ( in(ordered_pair(U_566,U_565),cartesian_product2(U_564,U_563))
| ~ in(U_565,U_563)
| ~ in(U_566,U_564) )
& ( ( in(U_565,U_563)
& in(U_566,U_564) )
| ~ in(ordered_pair(U_566,U_565),cartesian_product2(U_564,U_563)) ) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
fof(f_123_3,plain,
( ! [U_574,U_572,U_570,U_568] :
( in(ordered_pair(U_574,U_572),cartesian_product2(U_570,U_568))
| ~ in(U_572,U_568)
| ~ in(U_574,U_570) )
& ! [U_573,U_571,U_569,U_567] :
( ( in(U_571,U_567)
& in(U_573,U_569) )
| ~ in(ordered_pair(U_573,U_571),cartesian_product2(U_569,U_567)) ) ),
inference(miniscope,[status(thm)],[f_123_2]) ).
cnf(f_123_4,plain,
( in(U_573,U_569)
| ~ in(ordered_pair(U_573,U_571),cartesian_product2(U_569,U_567)) ),
inference(clausify,[status(thm)],[f_123_3]) ).
cnf(f_123_5,plain,
( in(U_571,U_567)
| ~ in(ordered_pair(U_573,U_571),cartesian_product2(U_569,U_567)) ),
inference(clausify,[status(thm)],[f_123_3]) ).
cnf(f_123_6,plain,
( in(ordered_pair(U_574,U_572),cartesian_product2(U_570,U_568))
| ~ in(U_572,U_568)
| ~ in(U_574,U_570) ),
inference(clausify,[status(thm)],[f_123_3]) ).
fof(f_124_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_124_2,plain,
! [U_577,U_576] :
( element(U_577,powerset(U_576))
| ? [U_575] :
( ~ in(U_575,U_576)
& in(U_575,U_577) ) ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
fof(f_124_3,plain,
! [U_577,U_576] :
( element(U_577,powerset(U_576))
| ( ~ in(sK92(U_577,U_576),U_576)
& in(sK92(U_577,U_576),U_577) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_575,sK92(U_577,U_576))],[f_124_2]) ).
cnf(f_124_4,plain,
( in(sK92(U_577,U_576),U_577)
| element(U_577,powerset(U_576)) ),
inference(clausify,[status(thm)],[f_124_3]) ).
cnf(f_124_5,plain,
( ~ in(sK92(U_577,U_576),U_576)
| element(U_577,powerset(U_576)) ),
inference(clausify,[status(thm)],[f_124_3]) ).
fof(f_125_1,plain,
! [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)],[l82_funct_1]) ).
fof(f_125_2,plain,
! [U_580,U_579,U_578] :
( ( ( in(U_579,relation_dom(relation_dom_restriction(U_578,U_580)))
| ~ in(U_579,U_580)
| ~ in(U_579,relation_dom(U_578)) )
& ( ( in(U_579,U_580)
& in(U_579,relation_dom(U_578)) )
| ~ in(U_579,relation_dom(relation_dom_restriction(U_578,U_580))) ) )
| ~ function(U_578)
| ~ relation(U_578) ),
inference(variable_rename,[status(thm)],[f_125_1]) ).
cnf(f_125_3,plain,
( in(U_579,relation_dom(U_578))
| ~ in(U_579,relation_dom(relation_dom_restriction(U_578,U_580)))
| ~ function(U_578)
| ~ relation(U_578) ),
inference(clausify,[status(thm)],[f_125_2]) ).
cnf(f_125_4,plain,
( in(U_579,U_580)
| ~ in(U_579,relation_dom(relation_dom_restriction(U_578,U_580)))
| ~ function(U_578)
| ~ relation(U_578) ),
inference(clausify,[status(thm)],[f_125_2]) ).
cnf(f_125_5,plain,
( in(U_579,relation_dom(relation_dom_restriction(U_578,U_580)))
| ~ in(U_579,U_580)
| ~ in(U_579,relation_dom(U_578))
| ~ function(U_578)
| ~ relation(U_578) ),
inference(clausify,[status(thm)],[f_125_2]) ).
fof(f_126_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_126_2,plain,
? [U_581] :
( function(U_581)
& relation(U_581) ),
inference(variable_rename,[status(thm)],[f_126_1]) ).
fof(f_126_3,plain,
( function(sK93)
& relation(sK93) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_581,sK93)],[f_126_2]) ).
cnf(f_126_4,plain,
relation(sK93),
inference(clausify,[status(thm)],[f_126_3]) ).
cnf(f_126_5,plain,
function(sK93),
inference(clausify,[status(thm)],[f_126_3]) ).
fof(f_127_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_127_2,plain,
? [U_582] :
( relation(U_582)
& empty(U_582) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
fof(f_127_3,plain,
( relation(sK94)
& empty(sK94) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_582,sK94)],[f_127_2]) ).
cnf(f_127_4,plain,
empty(sK94),
inference(clausify,[status(thm)],[f_127_3]) ).
cnf(f_127_5,plain,
relation(sK94),
inference(clausify,[status(thm)],[f_127_3]) ).
fof(f_128_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_128_2,plain,
! [U_584] :
( ? [U_583] :
( ~ empty(U_583)
& element(U_583,powerset(U_584)) )
| empty(U_584) ),
inference(variable_rename,[status(thm)],[f_128_1]) ).
fof(f_128_3,plain,
! [U_584] :
( ( ~ empty(sK95(U_584))
& element(sK95(U_584),powerset(U_584)) )
| empty(U_584) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_583,sK95(U_584))],[f_128_2]) ).
cnf(f_128_4,plain,
( element(sK95(U_584),powerset(U_584))
| empty(U_584) ),
inference(clausify,[status(thm)],[f_128_3]) ).
cnf(f_128_5,plain,
( ~ empty(sK95(U_584))
| empty(U_584) ),
inference(clausify,[status(thm)],[f_128_3]) ).
fof(f_129_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_129_2,plain,
? [U_585] : empty(U_585),
inference(variable_rename,[status(thm)],[f_129_1]) ).
fof(f_129_3,plain,
empty(sK96),
inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_585,sK96)],[f_129_2]) ).
cnf(f_129_4,plain,
empty(sK96),
inference(clausify,[status(thm)],[f_129_3]) ).
fof(f_130_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_130_2,plain,
? [U_586] :
( function(U_586)
& empty(U_586)
& relation(U_586) ),
inference(variable_rename,[status(thm)],[f_130_1]) ).
fof(f_130_3,plain,
( function(sK97)
& empty(sK97)
& relation(sK97) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_586,sK97)],[f_130_2]) ).
cnf(f_130_4,plain,
relation(sK97),
inference(clausify,[status(thm)],[f_130_3]) ).
cnf(f_130_5,plain,
empty(sK97),
inference(clausify,[status(thm)],[f_130_3]) ).
cnf(f_130_6,plain,
function(sK97),
inference(clausify,[status(thm)],[f_130_3]) ).
fof(f_131_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_131_2,plain,
? [U_587] :
( relation(U_587)
& ~ empty(U_587) ),
inference(variable_rename,[status(thm)],[f_131_1]) ).
fof(f_131_3,plain,
( relation(sK98)
& ~ empty(sK98) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_587,sK98)],[f_131_2]) ).
cnf(f_131_4,plain,
~ empty(sK98),
inference(clausify,[status(thm)],[f_131_3]) ).
cnf(f_131_5,plain,
relation(sK98),
inference(clausify,[status(thm)],[f_131_3]) ).
fof(f_132_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_132_2,plain,
! [U_589] :
? [U_588] :
( empty(U_588)
& element(U_588,powerset(U_589)) ),
inference(variable_rename,[status(thm)],[f_132_1]) ).
fof(f_132_3,plain,
! [U_589] :
( empty(sK99(U_589))
& element(sK99(U_589),powerset(U_589)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_588,sK99(U_589))],[f_132_2]) ).
cnf(f_132_4,plain,
element(sK99(U_589),powerset(U_589)),
inference(clausify,[status(thm)],[f_132_3]) ).
cnf(f_132_5,plain,
empty(sK99(U_589)),
inference(clausify,[status(thm)],[f_132_3]) ).
fof(f_133_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_133_2,plain,
? [U_590] : ~ empty(U_590),
inference(variable_rename,[status(thm)],[f_133_1]) ).
fof(f_133_3,plain,
~ empty(sK100),
inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_590,sK100)],[f_133_2]) ).
cnf(f_133_4,plain,
~ empty(sK100),
inference(clausify,[status(thm)],[f_133_3]) ).
fof(f_134_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_134_2,plain,
? [U_591] :
( one_to_one(U_591)
& function(U_591)
& relation(U_591) ),
inference(variable_rename,[status(thm)],[f_134_1]) ).
fof(f_134_3,plain,
( one_to_one(sK101)
& function(sK101)
& relation(sK101) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_591,sK101)],[f_134_2]) ).
cnf(f_134_4,plain,
relation(sK101),
inference(clausify,[status(thm)],[f_134_3]) ).
cnf(f_134_5,plain,
function(sK101),
inference(clausify,[status(thm)],[f_134_3]) ).
cnf(f_134_6,plain,
one_to_one(sK101),
inference(clausify,[status(thm)],[f_134_3]) ).
fof(f_135_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_135_2,plain,
? [U_592] :
( relation_empty_yielding(U_592)
& relation(U_592) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
fof(f_135_3,plain,
( relation_empty_yielding(sK102)
& relation(sK102) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_592,sK102)],[f_135_2]) ).
cnf(f_135_4,plain,
relation(sK102),
inference(clausify,[status(thm)],[f_135_3]) ).
cnf(f_135_5,plain,
relation_empty_yielding(sK102),
inference(clausify,[status(thm)],[f_135_3]) ).
fof(f_136_1,plain,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc4_funct_1]) ).
fof(f_136_2,plain,
? [U_593] :
( function(U_593)
& relation_empty_yielding(U_593)
& relation(U_593) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
fof(f_136_3,plain,
( function(sK103)
& relation_empty_yielding(sK103)
& relation(sK103) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(U_593,sK103)],[f_136_2]) ).
cnf(f_136_4,plain,
relation(sK103),
inference(clausify,[status(thm)],[f_136_3]) ).
cnf(f_136_5,plain,
relation_empty_yielding(sK103),
inference(clausify,[status(thm)],[f_136_3]) ).
cnf(f_136_6,plain,
function(sK103),
inference(clausify,[status(thm)],[f_136_3]) ).
fof(f_137_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_137_2,plain,
! [U_595,U_594] :
( union_of_subsets(U_595,U_594) = union(U_594)
| ~ element(U_594,powerset(powerset(U_595))) ),
inference(variable_rename,[status(thm)],[f_137_1]) ).
cnf(f_137_3,plain,
( union_of_subsets(U_595,U_594) = union(U_594)
| ~ element(U_594,powerset(powerset(U_595))) ),
inference(clausify,[status(thm)],[f_137_2]) ).
fof(f_138_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_138_2,plain,
! [U_597,U_596] :
( meet_of_subsets(U_597,U_596) = set_meet(U_596)
| ~ element(U_596,powerset(powerset(U_597))) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
cnf(f_138_3,plain,
( meet_of_subsets(U_597,U_596) = set_meet(U_596)
| ~ element(U_596,powerset(powerset(U_597))) ),
inference(clausify,[status(thm)],[f_138_2]) ).
fof(f_139_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_139_2,plain,
! [U_600,U_599,U_598] :
( subset_difference(U_600,U_599,U_598) = set_difference(U_599,U_598)
| ~ element(U_598,powerset(U_600))
| ~ element(U_599,powerset(U_600)) ),
inference(variable_rename,[status(thm)],[f_139_1]) ).
cnf(f_139_3,plain,
( subset_difference(U_600,U_599,U_598) = set_difference(U_599,U_598)
| ~ element(U_598,powerset(U_600))
| ~ element(U_599,powerset(U_600)) ),
inference(clausify,[status(thm)],[f_139_2]) ).
fof(f_140_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_140_2,plain,
! [U_602,U_601] : subset(U_602,U_602),
inference(variable_rename,[status(thm)],[f_140_1]) ).
fof(f_140_3,plain,
! [U_602] : subset(U_602,U_602),
inference(miniscope,[status(thm)],[f_140_2]) ).
cnf(f_140_4,plain,
subset(U_602,U_602),
inference(clausify,[status(thm)],[f_140_3]) ).
fof(f_141_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_141_2,plain,
! [U_604,U_603] :
( disjoint(U_603,U_604)
| ~ disjoint(U_604,U_603) ),
inference(variable_rename,[status(thm)],[f_141_1]) ).
cnf(f_141_3,plain,
( disjoint(U_603,U_604)
| ~ disjoint(U_604,U_603) ),
inference(clausify,[status(thm)],[f_141_2]) ).
fof(f_142_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_142_2,plain,
! [U_608,U_607,U_606,U_605] :
( ( in(ordered_pair(U_608,U_607),cartesian_product2(U_606,U_605))
| ~ in(U_607,U_605)
| ~ in(U_608,U_606) )
& ( ( in(U_607,U_605)
& in(U_608,U_606) )
| ~ in(ordered_pair(U_608,U_607),cartesian_product2(U_606,U_605)) ) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
fof(f_142_3,plain,
( ! [U_616,U_614,U_612,U_610] :
( in(ordered_pair(U_616,U_614),cartesian_product2(U_612,U_610))
| ~ in(U_614,U_610)
| ~ in(U_616,U_612) )
& ! [U_615,U_613,U_611,U_609] :
( ( in(U_613,U_609)
& in(U_615,U_611) )
| ~ in(ordered_pair(U_615,U_613),cartesian_product2(U_611,U_609)) ) ),
inference(miniscope,[status(thm)],[f_142_2]) ).
cnf(f_142_4,plain,
( in(U_615,U_611)
| ~ in(ordered_pair(U_615,U_613),cartesian_product2(U_611,U_609)) ),
inference(clausify,[status(thm)],[f_142_3]) ).
cnf(f_142_5,plain,
( in(U_613,U_609)
| ~ in(ordered_pair(U_615,U_613),cartesian_product2(U_611,U_609)) ),
inference(clausify,[status(thm)],[f_142_3]) ).
cnf(f_142_6,plain,
( in(ordered_pair(U_616,U_614),cartesian_product2(U_612,U_610))
| ~ in(U_614,U_610)
| ~ in(U_616,U_612) ),
inference(clausify,[status(thm)],[f_142_3]) ).
fof(f_143_1,negated_conjecture,
~ ! [A] : in(A,succ(A)),
inference(negate,[status(cth)],[t10_ordinal1]) ).
fof(f_143_2,negated_conjecture,
? [A] : ~ in(A,succ(A)),
inference(fof_nnf,[status(thm)],[f_143_1]) ).
fof(f_143_3,negated_conjecture,
? [U_617] : ~ in(U_617,succ(U_617)),
inference(variable_rename,[status(thm)],[f_143_2]) ).
fof(f_143_4,negated_conjecture,
~ in(sK104,succ(sK104)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK104]),skolemize(U_617,sK104)],[f_143_3]) ).
cnf(f_143_5,negated_conjecture,
~ in(sK104,succ(sK104)),
inference(clausify,[status(thm)],[f_143_4]) ).
fof(f_144_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_144_2,plain,
! [U_621,U_620,U_619,U_618] :
( U_621 = U_618
| U_621 = U_619
| unordered_pair(U_621,U_620) != unordered_pair(U_619,U_618) ),
inference(variable_rename,[status(thm)],[f_144_1]) ).
fof(f_144_3,plain,
! [U_621,U_620,U_619] :
( ! [U_618] :
( U_621 = U_618
| unordered_pair(U_621,U_620) != unordered_pair(U_619,U_618) )
| U_621 = U_619 ),
inference(miniscope,[status(thm)],[f_144_2]) ).
cnf(f_144_4,plain,
( U_621 = U_618
| unordered_pair(U_621,U_620) != unordered_pair(U_619,U_618)
| U_621 = U_619 ),
inference(clausify,[status(thm)],[f_144_3]) ).
fof(f_145_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_145_2,plain,
! [U_624,U_623,U_622] :
( ( ( in(U_624,relation_rng(relation_rng_restriction(U_623,U_622)))
| ~ in(U_624,relation_rng(U_622))
| ~ in(U_624,U_623) )
& ( ( in(U_624,relation_rng(U_622))
& in(U_624,U_623) )
| ~ in(U_624,relation_rng(relation_rng_restriction(U_623,U_622))) ) )
| ~ relation(U_622) ),
inference(variable_rename,[status(thm)],[f_145_1]) ).
cnf(f_145_3,plain,
( in(U_624,U_623)
| ~ in(U_624,relation_rng(relation_rng_restriction(U_623,U_622)))
| ~ relation(U_622) ),
inference(clausify,[status(thm)],[f_145_2]) ).
cnf(f_145_4,plain,
( in(U_624,relation_rng(U_622))
| ~ in(U_624,relation_rng(relation_rng_restriction(U_623,U_622)))
| ~ relation(U_622) ),
inference(clausify,[status(thm)],[f_145_2]) ).
cnf(f_145_5,plain,
( in(U_624,relation_rng(relation_rng_restriction(U_623,U_622)))
| ~ in(U_624,relation_rng(U_622))
| ~ in(U_624,U_623)
| ~ relation(U_622) ),
inference(clausify,[status(thm)],[f_145_2]) ).
fof(f_146_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_146_2,plain,
! [U_626,U_625] :
( subset(relation_rng(relation_rng_restriction(U_626,U_625)),U_626)
| ~ relation(U_625) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
cnf(f_146_3,plain,
( subset(relation_rng(relation_rng_restriction(U_626,U_625)),U_626)
| ~ relation(U_625) ),
inference(clausify,[status(thm)],[f_146_2]) ).
fof(f_147_1,plain,
! [A,B] :
( subset(relation_rng_restriction(A,B),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t117_relat_1]) ).
fof(f_147_2,plain,
! [U_628,U_627] :
( subset(relation_rng_restriction(U_628,U_627),U_627)
| ~ relation(U_627) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
cnf(f_147_3,plain,
( subset(relation_rng_restriction(U_628,U_627),U_627)
| ~ relation(U_627) ),
inference(clausify,[status(thm)],[f_147_2]) ).
fof(f_148_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_148_2,plain,
! [U_630,U_629] :
( subset(relation_rng(relation_rng_restriction(U_630,U_629)),relation_rng(U_629))
| ~ relation(U_629) ),
inference(variable_rename,[status(thm)],[f_148_1]) ).
cnf(f_148_3,plain,
( subset(relation_rng(relation_rng_restriction(U_630,U_629)),relation_rng(U_629))
| ~ relation(U_629) ),
inference(clausify,[status(thm)],[f_148_2]) ).
fof(f_149_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_149_2,plain,
! [U_633,U_632,U_631] :
( ( subset(cartesian_product2(U_631,U_633),cartesian_product2(U_631,U_632))
& subset(cartesian_product2(U_633,U_631),cartesian_product2(U_632,U_631)) )
| ~ subset(U_633,U_632) ),
inference(variable_rename,[status(thm)],[f_149_1]) ).
fof(f_149_3,plain,
! [U_633,U_632] :
( ( ! [U_635] : subset(cartesian_product2(U_635,U_633),cartesian_product2(U_635,U_632))
& ! [U_634] : subset(cartesian_product2(U_633,U_634),cartesian_product2(U_632,U_634)) )
| ~ subset(U_633,U_632) ),
inference(miniscope,[status(thm)],[f_149_2]) ).
cnf(f_149_4,plain,
( subset(cartesian_product2(U_633,U_634),cartesian_product2(U_632,U_634))
| ~ subset(U_633,U_632) ),
inference(clausify,[status(thm)],[f_149_3]) ).
cnf(f_149_5,plain,
( subset(cartesian_product2(U_635,U_633),cartesian_product2(U_635,U_632))
| ~ subset(U_633,U_632) ),
inference(clausify,[status(thm)],[f_149_3]) ).
fof(f_150_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_150_2,plain,
! [U_637,U_636] :
( relation_rng(relation_rng_restriction(U_637,U_636)) = set_intersection2(relation_rng(U_636),U_637)
| ~ relation(U_636) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
cnf(f_150_3,plain,
( relation_rng(relation_rng_restriction(U_637,U_636)) = set_intersection2(relation_rng(U_636),U_637)
| ~ relation(U_636) ),
inference(clausify,[status(thm)],[f_150_2]) ).
fof(f_151_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_151_2,plain,
! [U_641,U_640,U_639,U_638] :
( subset(cartesian_product2(U_641,U_639),cartesian_product2(U_640,U_638))
| ~ subset(U_639,U_638)
| ~ subset(U_641,U_640) ),
inference(variable_rename,[status(thm)],[f_151_1]) ).
cnf(f_151_3,plain,
( subset(cartesian_product2(U_641,U_639),cartesian_product2(U_640,U_638))
| ~ subset(U_639,U_638)
| ~ subset(U_641,U_640) ),
inference(clausify,[status(thm)],[f_151_2]) ).
fof(f_152_1,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t12_xboole_1]) ).
fof(f_152_2,plain,
! [U_643,U_642] :
( set_union2(U_643,U_642) = U_642
| ~ subset(U_643,U_642) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
cnf(f_152_3,plain,
( set_union2(U_643,U_642) = U_642
| ~ subset(U_643,U_642) ),
inference(clausify,[status(thm)],[f_152_2]) ).
fof(f_153_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_153_2,plain,
! [U_649] :
? [U_648] :
( ! [U_647] :
( in(U_647,U_648)
| are_equipotent(U_647,U_648)
| ~ subset(U_647,U_648) )
& ! [U_646] :
( in(powerset(U_646),U_648)
| ~ in(U_646,U_648) )
& ! [U_645,U_644] :
( in(U_644,U_648)
| ~ subset(U_644,U_645)
| ~ in(U_645,U_648) )
& in(U_649,U_648) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
fof(f_153_3,plain,
! [U_649] :
( ! [U_647] :
( in(U_647,sK105(U_649))
| are_equipotent(U_647,sK105(U_649))
| ~ subset(U_647,sK105(U_649)) )
& ! [U_646] :
( in(powerset(U_646),sK105(U_649))
| ~ in(U_646,sK105(U_649)) )
& ! [U_645,U_644] :
( in(U_644,sK105(U_649))
| ~ subset(U_644,U_645)
| ~ in(U_645,sK105(U_649)) )
& in(U_649,sK105(U_649)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK105]),skolemize(U_648,sK105(U_649))],[f_153_2]) ).
cnf(f_153_4,plain,
in(U_649,sK105(U_649)),
inference(clausify,[status(thm)],[f_153_3]) ).
cnf(f_153_5,plain,
( in(U_644,sK105(U_649))
| ~ subset(U_644,U_645)
| ~ in(U_645,sK105(U_649)) ),
inference(clausify,[status(thm)],[f_153_3]) ).
cnf(f_153_6,plain,
( in(powerset(U_646),sK105(U_649))
| ~ in(U_646,sK105(U_649)) ),
inference(clausify,[status(thm)],[f_153_3]) ).
cnf(f_153_7,plain,
( in(U_647,sK105(U_649))
| are_equipotent(U_647,sK105(U_649))
| ~ subset(U_647,sK105(U_649)) ),
inference(clausify,[status(thm)],[f_153_3]) ).
fof(f_154_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_154_2,plain,
! [U_652,U_651,U_650] :
( relation_dom_restriction(relation_rng_restriction(U_652,U_650),U_651) = relation_rng_restriction(U_652,relation_dom_restriction(U_650,U_651))
| ~ relation(U_650) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
cnf(f_154_3,plain,
( relation_dom_restriction(relation_rng_restriction(U_652,U_650),U_651) = relation_rng_restriction(U_652,relation_dom_restriction(U_650,U_651))
| ~ relation(U_650) ),
inference(clausify,[status(thm)],[f_154_2]) ).
fof(f_155_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_155_2,plain,
! [U_657,U_656,U_655] :
( ( ( in(U_657,relation_image(U_655,U_656))
| ! [U_654] :
( ~ in(U_654,U_656)
| ~ in(ordered_pair(U_654,U_657),U_655)
| ~ in(U_654,relation_dom(U_655)) ) )
& ( ? [U_653] :
( in(U_653,U_656)
& in(ordered_pair(U_653,U_657),U_655)
& in(U_653,relation_dom(U_655)) )
| ~ in(U_657,relation_image(U_655,U_656)) ) )
| ~ relation(U_655) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
fof(f_155_3,plain,
! [U_657,U_656,U_655] :
( ( ( in(U_657,relation_image(U_655,U_656))
| ! [U_654] :
( ~ in(U_654,U_656)
| ~ in(ordered_pair(U_654,U_657),U_655)
| ~ in(U_654,relation_dom(U_655)) ) )
& ( ( in(sK106(U_657,U_656,U_655),U_656)
& in(ordered_pair(sK106(U_657,U_656,U_655),U_657),U_655)
& in(sK106(U_657,U_656,U_655),relation_dom(U_655)) )
| ~ in(U_657,relation_image(U_655,U_656)) ) )
| ~ relation(U_655) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK106]),skolemize(U_653,sK106(U_657,U_656,U_655))],[f_155_2]) ).
cnf(f_155_4,plain,
( in(sK106(U_657,U_656,U_655),relation_dom(U_655))
| ~ in(U_657,relation_image(U_655,U_656))
| ~ relation(U_655) ),
inference(clausify,[status(thm)],[f_155_3]) ).
cnf(f_155_5,plain,
( in(ordered_pair(sK106(U_657,U_656,U_655),U_657),U_655)
| ~ in(U_657,relation_image(U_655,U_656))
| ~ relation(U_655) ),
inference(clausify,[status(thm)],[f_155_3]) ).
cnf(f_155_6,plain,
( in(sK106(U_657,U_656,U_655),U_656)
| ~ in(U_657,relation_image(U_655,U_656))
| ~ relation(U_655) ),
inference(clausify,[status(thm)],[f_155_3]) ).
cnf(f_155_7,plain,
( in(U_657,relation_image(U_655,U_656))
| ~ in(U_654,U_656)
| ~ in(ordered_pair(U_654,U_657),U_655)
| ~ in(U_654,relation_dom(U_655))
| ~ relation(U_655) ),
inference(clausify,[status(thm)],[f_155_3]) ).
fof(f_156_1,plain,
! [A,B] :
( subset(relation_image(B,A),relation_rng(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t144_relat_1]) ).
fof(f_156_2,plain,
! [U_659,U_658] :
( subset(relation_image(U_658,U_659),relation_rng(U_658))
| ~ relation(U_658) ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
cnf(f_156_3,plain,
( subset(relation_image(U_658,U_659),relation_rng(U_658))
| ~ relation(U_658) ),
inference(clausify,[status(thm)],[f_156_2]) ).
fof(f_157_1,plain,
! [A,B] :
( subset(relation_image(B,relation_inverse_image(B,A)),A)
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t145_funct_1]) ).
fof(f_157_2,plain,
! [U_661,U_660] :
( subset(relation_image(U_660,relation_inverse_image(U_660,U_661)),U_661)
| ~ function(U_660)
| ~ relation(U_660) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
cnf(f_157_3,plain,
( subset(relation_image(U_660,relation_inverse_image(U_660,U_661)),U_661)
| ~ function(U_660)
| ~ relation(U_660) ),
inference(clausify,[status(thm)],[f_157_2]) ).
fof(f_158_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_158_2,plain,
! [U_663,U_662] :
( relation_image(U_662,U_663) = relation_image(U_662,set_intersection2(relation_dom(U_662),U_663))
| ~ relation(U_662) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
cnf(f_158_3,plain,
( relation_image(U_662,U_663) = relation_image(U_662,set_intersection2(relation_dom(U_662),U_663))
| ~ relation(U_662) ),
inference(clausify,[status(thm)],[f_158_2]) ).
fof(f_159_1,plain,
! [A,B] :
( subset(A,relation_inverse_image(B,relation_image(B,A)))
| ~ subset(A,relation_dom(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t146_funct_1]) ).
fof(f_159_2,plain,
! [U_665,U_664] :
( subset(U_665,relation_inverse_image(U_664,relation_image(U_664,U_665)))
| ~ subset(U_665,relation_dom(U_664))
| ~ relation(U_664) ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
cnf(f_159_3,plain,
( subset(U_665,relation_inverse_image(U_664,relation_image(U_664,U_665)))
| ~ subset(U_665,relation_dom(U_664))
| ~ relation(U_664) ),
inference(clausify,[status(thm)],[f_159_2]) ).
fof(f_160_1,plain,
! [A] :
( relation_image(A,relation_dom(A)) = relation_rng(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t146_relat_1]) ).
fof(f_160_2,plain,
! [U_666] :
( relation_image(U_666,relation_dom(U_666)) = relation_rng(U_666)
| ~ relation(U_666) ),
inference(variable_rename,[status(thm)],[f_160_1]) ).
cnf(f_160_3,plain,
( relation_image(U_666,relation_dom(U_666)) = relation_rng(U_666)
| ~ relation(U_666) ),
inference(clausify,[status(thm)],[f_160_2]) ).
fof(f_161_1,plain,
! [A,B] :
( relation_image(B,relation_inverse_image(B,A)) = A
| ~ subset(A,relation_rng(B))
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t147_funct_1]) ).
fof(f_161_2,plain,
! [U_668,U_667] :
( relation_image(U_667,relation_inverse_image(U_667,U_668)) = U_668
| ~ subset(U_668,relation_rng(U_667))
| ~ function(U_667)
| ~ relation(U_667) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
cnf(f_161_3,plain,
( relation_image(U_667,relation_inverse_image(U_667,U_668)) = U_668
| ~ subset(U_668,relation_rng(U_667))
| ~ function(U_667)
| ~ relation(U_667) ),
inference(clausify,[status(thm)],[f_161_2]) ).
fof(f_162_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_162_2,plain,
! [U_670] :
( ! [U_669] :
( relation_rng(relation_composition(U_670,U_669)) = relation_image(U_669,relation_rng(U_670))
| ~ relation(U_669) )
| ~ relation(U_670) ),
inference(variable_rename,[status(thm)],[f_162_1]) ).
cnf(f_162_3,plain,
( relation_rng(relation_composition(U_670,U_669)) = relation_image(U_669,relation_rng(U_670))
| ~ relation(U_669)
| ~ relation(U_670) ),
inference(clausify,[status(thm)],[f_162_2]) ).
fof(f_163_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_163_2,plain,
! [U_675,U_674,U_673] :
( ( ( in(U_675,relation_inverse_image(U_673,U_674))
| ! [U_672] :
( ~ in(U_672,U_674)
| ~ in(ordered_pair(U_675,U_672),U_673)
| ~ in(U_672,relation_rng(U_673)) ) )
& ( ? [U_671] :
( in(U_671,U_674)
& in(ordered_pair(U_675,U_671),U_673)
& in(U_671,relation_rng(U_673)) )
| ~ in(U_675,relation_inverse_image(U_673,U_674)) ) )
| ~ relation(U_673) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
fof(f_163_3,plain,
! [U_675,U_674,U_673] :
( ( ( in(U_675,relation_inverse_image(U_673,U_674))
| ! [U_672] :
( ~ in(U_672,U_674)
| ~ in(ordered_pair(U_675,U_672),U_673)
| ~ in(U_672,relation_rng(U_673)) ) )
& ( ( in(sK107(U_675,U_674,U_673),U_674)
& in(ordered_pair(U_675,sK107(U_675,U_674,U_673)),U_673)
& in(sK107(U_675,U_674,U_673),relation_rng(U_673)) )
| ~ in(U_675,relation_inverse_image(U_673,U_674)) ) )
| ~ relation(U_673) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(U_671,sK107(U_675,U_674,U_673))],[f_163_2]) ).
cnf(f_163_4,plain,
( in(sK107(U_675,U_674,U_673),relation_rng(U_673))
| ~ in(U_675,relation_inverse_image(U_673,U_674))
| ~ relation(U_673) ),
inference(clausify,[status(thm)],[f_163_3]) ).
cnf(f_163_5,plain,
( in(ordered_pair(U_675,sK107(U_675,U_674,U_673)),U_673)
| ~ in(U_675,relation_inverse_image(U_673,U_674))
| ~ relation(U_673) ),
inference(clausify,[status(thm)],[f_163_3]) ).
cnf(f_163_6,plain,
( in(sK107(U_675,U_674,U_673),U_674)
| ~ in(U_675,relation_inverse_image(U_673,U_674))
| ~ relation(U_673) ),
inference(clausify,[status(thm)],[f_163_3]) ).
cnf(f_163_7,plain,
( in(U_675,relation_inverse_image(U_673,U_674))
| ~ in(U_672,U_674)
| ~ in(ordered_pair(U_675,U_672),U_673)
| ~ in(U_672,relation_rng(U_673))
| ~ relation(U_673) ),
inference(clausify,[status(thm)],[f_163_3]) ).
fof(f_164_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_164_2,plain,
! [U_677,U_676] :
( subset(relation_inverse_image(U_676,U_677),relation_dom(U_676))
| ~ relation(U_676) ),
inference(variable_rename,[status(thm)],[f_164_1]) ).
cnf(f_164_3,plain,
( subset(relation_inverse_image(U_676,U_677),relation_dom(U_676))
| ~ relation(U_676) ),
inference(clausify,[status(thm)],[f_164_2]) ).
fof(f_165_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_165_2,plain,
! [U_679,U_678] :
( relation_inverse_image(U_678,U_679) != empty_set
| ~ subset(U_679,relation_rng(U_678))
| U_679 = empty_set
| ~ relation(U_678) ),
inference(variable_rename,[status(thm)],[f_165_1]) ).
cnf(f_165_3,plain,
( relation_inverse_image(U_678,U_679) != empty_set
| ~ subset(U_679,relation_rng(U_678))
| U_679 = empty_set
| ~ relation(U_678) ),
inference(clausify,[status(thm)],[f_165_2]) ).
fof(f_166_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_166_2,plain,
! [U_682,U_681,U_680] :
( subset(relation_inverse_image(U_680,U_682),relation_inverse_image(U_680,U_681))
| ~ subset(U_682,U_681)
| ~ relation(U_680) ),
inference(variable_rename,[status(thm)],[f_166_1]) ).
cnf(f_166_3,plain,
( subset(relation_inverse_image(U_680,U_682),relation_inverse_image(U_680,U_681))
| ~ subset(U_682,U_681)
| ~ relation(U_680) ),
inference(clausify,[status(thm)],[f_166_2]) ).
fof(f_167_1,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(fof_nnf,[status(thm)],[t17_xboole_1]) ).
fof(f_167_2,plain,
! [U_684,U_683] : subset(set_intersection2(U_684,U_683),U_684),
inference(variable_rename,[status(thm)],[f_167_1]) ).
cnf(f_167_3,plain,
subset(set_intersection2(U_684,U_683),U_684),
inference(clausify,[status(thm)],[f_167_2]) ).
fof(f_168_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_168_2,plain,
! [U_687,U_686,U_685] :
( subset(U_687,set_intersection2(U_686,U_685))
| ~ subset(U_687,U_685)
| ~ subset(U_687,U_686) ),
inference(variable_rename,[status(thm)],[f_168_1]) ).
cnf(f_168_3,plain,
( subset(U_687,set_intersection2(U_686,U_685))
| ~ subset(U_687,U_685)
| ~ subset(U_687,U_686) ),
inference(clausify,[status(thm)],[f_168_2]) ).
fof(f_169_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_169_2,plain,
! [U_688] : set_union2(U_688,empty_set) = U_688,
inference(variable_rename,[status(thm)],[f_169_1]) ).
cnf(f_169_3,plain,
set_union2(U_688,empty_set) = U_688,
inference(clausify,[status(thm)],[f_169_2]) ).
fof(f_170_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_170_2,plain,
! [U_690,U_689] :
( element(U_690,U_689)
| ~ in(U_690,U_689) ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
cnf(f_170_3,plain,
( element(U_690,U_689)
| ~ in(U_690,U_689) ),
inference(clausify,[status(thm)],[f_170_2]) ).
fof(f_171_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_171_2,plain,
! [U_693,U_692,U_691] :
( subset(U_693,U_691)
| ~ subset(U_692,U_691)
| ~ subset(U_693,U_692) ),
inference(variable_rename,[status(thm)],[f_171_1]) ).
cnf(f_171_3,plain,
( subset(U_693,U_691)
| ~ subset(U_692,U_691)
| ~ subset(U_693,U_692) ),
inference(clausify,[status(thm)],[f_171_2]) ).
fof(f_172_1,plain,
powerset(empty_set) = singleton(empty_set),
inference(fof_nnf,[status(thm)],[t1_zfmisc_1]) ).
cnf(f_172_2,plain,
powerset(empty_set) = singleton(empty_set),
inference(clausify,[status(thm)],[f_172_1]) ).
fof(f_173_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_173_2,plain,
! [U_696,U_695,U_694] :
( ( in(U_695,relation_rng(U_694))
& in(U_696,relation_dom(U_694)) )
| ~ in(ordered_pair(U_696,U_695),U_694)
| ~ relation(U_694) ),
inference(variable_rename,[status(thm)],[f_173_1]) ).
cnf(f_173_3,plain,
( in(U_696,relation_dom(U_694))
| ~ in(ordered_pair(U_696,U_695),U_694)
| ~ relation(U_694) ),
inference(clausify,[status(thm)],[f_173_2]) ).
cnf(f_173_4,plain,
( in(U_695,relation_rng(U_694))
| ~ in(ordered_pair(U_696,U_695),U_694)
| ~ relation(U_694) ),
inference(clausify,[status(thm)],[f_173_2]) ).
fof(f_174_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_174_2,plain,
! [U_699,U_698] :
( ! [U_697] :
( ( ( in(U_699,relation_dom(relation_composition(U_697,U_698)))
| ~ in(apply(U_697,U_699),relation_dom(U_698))
| ~ in(U_699,relation_dom(U_697)) )
& ( ( in(apply(U_697,U_699),relation_dom(U_698))
& in(U_699,relation_dom(U_697)) )
| ~ in(U_699,relation_dom(relation_composition(U_697,U_698))) ) )
| ~ function(U_697)
| ~ relation(U_697) )
| ~ function(U_698)
| ~ relation(U_698) ),
inference(variable_rename,[status(thm)],[f_174_1]) ).
cnf(f_174_3,plain,
( in(U_699,relation_dom(U_697))
| ~ in(U_699,relation_dom(relation_composition(U_697,U_698)))
| ~ function(U_697)
| ~ relation(U_697)
| ~ function(U_698)
| ~ relation(U_698) ),
inference(clausify,[status(thm)],[f_174_2]) ).
cnf(f_174_4,plain,
( in(apply(U_697,U_699),relation_dom(U_698))
| ~ in(U_699,relation_dom(relation_composition(U_697,U_698)))
| ~ function(U_697)
| ~ relation(U_697)
| ~ function(U_698)
| ~ relation(U_698) ),
inference(clausify,[status(thm)],[f_174_2]) ).
cnf(f_174_5,plain,
( in(U_699,relation_dom(relation_composition(U_697,U_698)))
| ~ in(apply(U_697,U_699),relation_dom(U_698))
| ~ in(U_699,relation_dom(U_697))
| ~ function(U_697)
| ~ relation(U_697)
| ~ function(U_698)
| ~ relation(U_698) ),
inference(clausify,[status(thm)],[f_174_2]) ).
fof(f_175_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_175_2,plain,
! [U_700] :
( subset(U_700,cartesian_product2(relation_dom(U_700),relation_rng(U_700)))
| ~ relation(U_700) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
cnf(f_175_3,plain,
( subset(U_700,cartesian_product2(relation_dom(U_700),relation_rng(U_700)))
| ~ relation(U_700) ),
inference(clausify,[status(thm)],[f_175_2]) ).
fof(f_176_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_176_2,plain,
! [U_703,U_702] :
( ! [U_701] :
( apply(relation_composition(U_701,U_702),U_703) = apply(U_702,apply(U_701,U_703))
| ~ in(U_703,relation_dom(relation_composition(U_701,U_702)))
| ~ function(U_701)
| ~ relation(U_701) )
| ~ function(U_702)
| ~ relation(U_702) ),
inference(variable_rename,[status(thm)],[f_176_1]) ).
cnf(f_176_3,plain,
( apply(relation_composition(U_701,U_702),U_703) = apply(U_702,apply(U_701,U_703))
| ~ in(U_703,relation_dom(relation_composition(U_701,U_702)))
| ~ function(U_701)
| ~ relation(U_701)
| ~ function(U_702)
| ~ relation(U_702) ),
inference(clausify,[status(thm)],[f_176_2]) ).
fof(f_177_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_177_2,plain,
! [U_706,U_705] :
( ! [U_704] :
( apply(relation_composition(U_705,U_704),U_706) = apply(U_704,apply(U_705,U_706))
| ~ in(U_706,relation_dom(U_705))
| ~ function(U_704)
| ~ relation(U_704) )
| ~ function(U_705)
| ~ relation(U_705) ),
inference(variable_rename,[status(thm)],[f_177_1]) ).
cnf(f_177_3,plain,
( apply(relation_composition(U_705,U_704),U_706) = apply(U_704,apply(U_705,U_706))
| ~ in(U_706,relation_dom(U_705))
| ~ function(U_704)
| ~ relation(U_704)
| ~ function(U_705)
| ~ relation(U_705) ),
inference(clausify,[status(thm)],[f_177_2]) ).
fof(f_178_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_178_2,plain,
! [U_708] :
( ! [U_707] :
( ( subset(relation_rng(U_708),relation_rng(U_707))
& subset(relation_dom(U_708),relation_dom(U_707)) )
| ~ subset(U_708,U_707)
| ~ relation(U_707) )
| ~ relation(U_708) ),
inference(variable_rename,[status(thm)],[f_178_1]) ).
cnf(f_178_3,plain,
( subset(relation_dom(U_708),relation_dom(U_707))
| ~ subset(U_708,U_707)
| ~ relation(U_707)
| ~ relation(U_708) ),
inference(clausify,[status(thm)],[f_178_2]) ).
cnf(f_178_4,plain,
( subset(relation_rng(U_708),relation_rng(U_707))
| ~ subset(U_708,U_707)
| ~ relation(U_707)
| ~ relation(U_708) ),
inference(clausify,[status(thm)],[f_178_2]) ).
fof(f_179_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_179_2,plain,
! [U_711,U_710,U_709] :
( subset(set_intersection2(U_711,U_709),set_intersection2(U_710,U_709))
| ~ subset(U_711,U_710) ),
inference(variable_rename,[status(thm)],[f_179_1]) ).
fof(f_179_3,plain,
! [U_711,U_710] :
( ! [U_709] : subset(set_intersection2(U_711,U_709),set_intersection2(U_710,U_709))
| ~ subset(U_711,U_710) ),
inference(miniscope,[status(thm)],[f_179_2]) ).
cnf(f_179_4,plain,
( subset(set_intersection2(U_711,U_709),set_intersection2(U_710,U_709))
| ~ subset(U_711,U_710) ),
inference(clausify,[status(thm)],[f_179_3]) ).
fof(f_180_1,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t28_xboole_1]) ).
fof(f_180_2,plain,
! [U_713,U_712] :
( set_intersection2(U_713,U_712) = U_713
| ~ subset(U_713,U_712) ),
inference(variable_rename,[status(thm)],[f_180_1]) ).
cnf(f_180_3,plain,
( set_intersection2(U_713,U_712) = U_713
| ~ subset(U_713,U_712) ),
inference(clausify,[status(thm)],[f_180_2]) ).
fof(f_181_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_181_2,plain,
! [U_714] : set_intersection2(U_714,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_181_1]) ).
cnf(f_181_3,plain,
set_intersection2(U_714,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_181_2]) ).
fof(f_182_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_182_2,plain,
! [U_716,U_715] :
( in(U_716,U_715)
| empty(U_715)
| ~ element(U_716,U_715) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
cnf(f_182_3,plain,
( in(U_716,U_715)
| empty(U_715)
| ~ element(U_716,U_715) ),
inference(clausify,[status(thm)],[f_182_2]) ).
fof(f_183_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_183_2,plain,
! [U_719,U_718] :
( U_719 = U_718
| ? [U_717] :
( ( ~ in(U_717,U_719)
& in(U_717,U_718) )
| ( ~ in(U_717,U_718)
& in(U_717,U_719) ) ) ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
fof(f_183_3,plain,
! [U_719,U_718] :
( U_719 = U_718
| ? [U_721] :
( ~ in(U_721,U_719)
& in(U_721,U_718) )
| ? [U_720] :
( ~ in(U_720,U_718)
& in(U_720,U_719) ) ),
inference(miniscope,[status(thm)],[f_183_2]) ).
fof(f_183_4,plain,
! [U_719,U_718] :
( U_719 = U_718
| ? [U_721] :
( ~ in(U_721,U_719)
& in(U_721,U_718) )
| ( ~ in(sK108(U_719,U_718),U_718)
& in(sK108(U_719,U_718),U_719) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK108]),skolemize(U_720,sK108(U_719,U_718))],[f_183_3]) ).
fof(f_183_5,plain,
! [U_719,U_718] :
( U_719 = U_718
| ( ~ in(sK109(U_719,U_718),U_719)
& in(sK109(U_719,U_718),U_718) )
| ( ~ in(sK108(U_719,U_718),U_718)
& in(sK108(U_719,U_718),U_719) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK109]),skolemize(U_721,sK109(U_719,U_718))],[f_183_4]) ).
cnf(f_183_6,plain,
( in(sK109(U_719,U_718),U_718)
| in(sK108(U_719,U_718),U_719)
| U_719 = U_718 ),
inference(clausify,[status(thm)],[f_183_5]) ).
cnf(f_183_7,plain,
( ~ in(sK109(U_719,U_718),U_719)
| in(sK108(U_719,U_718),U_719)
| U_719 = U_718 ),
inference(clausify,[status(thm)],[f_183_5]) ).
cnf(f_183_8,plain,
( in(sK109(U_719,U_718),U_718)
| ~ in(sK108(U_719,U_718),U_718)
| U_719 = U_718 ),
inference(clausify,[status(thm)],[f_183_5]) ).
cnf(f_183_9,plain,
( ~ in(sK109(U_719,U_718),U_719)
| ~ in(sK108(U_719,U_718),U_718)
| U_719 = U_718 ),
inference(clausify,[status(thm)],[f_183_5]) ).
fof(f_184_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_184_2,plain,
! [U_722] : subset(empty_set,U_722),
inference(variable_rename,[status(thm)],[f_184_1]) ).
cnf(f_184_3,plain,
subset(empty_set,U_722),
inference(clausify,[status(thm)],[f_184_2]) ).
fof(f_185_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_185_2,plain,
! [U_725,U_724,U_723] :
( ( in(U_724,relation_field(U_723))
& in(U_725,relation_field(U_723)) )
| ~ in(ordered_pair(U_725,U_724),U_723)
| ~ relation(U_723) ),
inference(variable_rename,[status(thm)],[f_185_1]) ).
cnf(f_185_3,plain,
( in(U_725,relation_field(U_723))
| ~ in(ordered_pair(U_725,U_724),U_723)
| ~ relation(U_723) ),
inference(clausify,[status(thm)],[f_185_2]) ).
cnf(f_185_4,plain,
( in(U_724,relation_field(U_723))
| ~ in(ordered_pair(U_725,U_724),U_723)
| ~ relation(U_723) ),
inference(clausify,[status(thm)],[f_185_2]) ).
fof(f_186_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_186_2,plain,
! [U_728,U_727,U_726] :
( subset(set_difference(U_728,U_726),set_difference(U_727,U_726))
| ~ subset(U_728,U_727) ),
inference(variable_rename,[status(thm)],[f_186_1]) ).
fof(f_186_3,plain,
! [U_728,U_727] :
( ! [U_726] : subset(set_difference(U_728,U_726),set_difference(U_727,U_726))
| ~ subset(U_728,U_727) ),
inference(miniscope,[status(thm)],[f_186_2]) ).
cnf(f_186_4,plain,
( subset(set_difference(U_728,U_726),set_difference(U_727,U_726))
| ~ subset(U_728,U_727) ),
inference(clausify,[status(thm)],[f_186_3]) ).
fof(f_187_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_187_2,plain,
! [U_732,U_731,U_730,U_729] :
( ( U_731 = U_729
& U_732 = U_730 )
| ordered_pair(U_732,U_731) != ordered_pair(U_730,U_729) ),
inference(variable_rename,[status(thm)],[f_187_1]) ).
cnf(f_187_3,plain,
( U_732 = U_730
| ordered_pair(U_732,U_731) != ordered_pair(U_730,U_729) ),
inference(clausify,[status(thm)],[f_187_2]) ).
cnf(f_187_4,plain,
( U_731 = U_729
| ordered_pair(U_732,U_731) != ordered_pair(U_730,U_729) ),
inference(clausify,[status(thm)],[f_187_2]) ).
fof(f_188_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_188_2,plain,
! [U_736,U_735] :
( ( ( U_735 = identity_relation(U_736)
| ? [U_734] :
( apply(U_735,U_734) != U_734
& in(U_734,U_736) )
| relation_dom(U_735) != U_736 )
& ( ( ! [U_733] :
( apply(U_735,U_733) = U_733
| ~ in(U_733,U_736) )
& relation_dom(U_735) = U_736 )
| U_735 != identity_relation(U_736) ) )
| ~ function(U_735)
| ~ relation(U_735) ),
inference(variable_rename,[status(thm)],[f_188_1]) ).
fof(f_188_3,plain,
! [U_736,U_735] :
( ( ( U_735 = identity_relation(U_736)
| ( apply(U_735,sK110(U_736,U_735)) != sK110(U_736,U_735)
& in(sK110(U_736,U_735),U_736) )
| relation_dom(U_735) != U_736 )
& ( ( ! [U_733] :
( apply(U_735,U_733) = U_733
| ~ in(U_733,U_736) )
& relation_dom(U_735) = U_736 )
| U_735 != identity_relation(U_736) ) )
| ~ function(U_735)
| ~ relation(U_735) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK110]),skolemize(U_734,sK110(U_736,U_735))],[f_188_2]) ).
cnf(f_188_4,plain,
( relation_dom(U_735) = U_736
| U_735 != identity_relation(U_736)
| ~ function(U_735)
| ~ relation(U_735) ),
inference(clausify,[status(thm)],[f_188_3]) ).
cnf(f_188_5,plain,
( apply(U_735,U_733) = U_733
| ~ in(U_733,U_736)
| U_735 != identity_relation(U_736)
| ~ function(U_735)
| ~ relation(U_735) ),
inference(clausify,[status(thm)],[f_188_3]) ).
cnf(f_188_6,plain,
( in(sK110(U_736,U_735),U_736)
| relation_dom(U_735) != U_736
| U_735 = identity_relation(U_736)
| ~ function(U_735)
| ~ relation(U_735) ),
inference(clausify,[status(thm)],[f_188_3]) ).
cnf(f_188_7,plain,
( apply(U_735,sK110(U_736,U_735)) != sK110(U_736,U_735)
| relation_dom(U_735) != U_736
| U_735 = identity_relation(U_736)
| ~ function(U_735)
| ~ relation(U_735) ),
inference(clausify,[status(thm)],[f_188_3]) ).
fof(f_189_1,plain,
! [A,B] :
( apply(identity_relation(A),B) = B
| ~ in(B,A) ),
inference(fof_nnf,[status(thm)],[t35_funct_1]) ).
fof(f_189_2,plain,
! [U_738,U_737] :
( apply(identity_relation(U_738),U_737) = U_737
| ~ in(U_737,U_738) ),
inference(variable_rename,[status(thm)],[f_189_1]) ).
cnf(f_189_3,plain,
( apply(identity_relation(U_738),U_737) = U_737
| ~ in(U_737,U_738) ),
inference(clausify,[status(thm)],[f_189_2]) ).
fof(f_190_1,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(fof_nnf,[status(thm)],[t36_xboole_1]) ).
fof(f_190_2,plain,
! [U_740,U_739] : subset(set_difference(U_740,U_739),U_740),
inference(variable_rename,[status(thm)],[f_190_1]) ).
cnf(f_190_3,plain,
subset(set_difference(U_740,U_739),U_740),
inference(clausify,[status(thm)],[f_190_2]) ).
fof(f_191_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_191_2,plain,
! [U_741] :
( ( relation_dom(U_741) = relation_rng(relation_inverse(U_741))
& relation_rng(U_741) = relation_dom(relation_inverse(U_741)) )
| ~ relation(U_741) ),
inference(variable_rename,[status(thm)],[f_191_1]) ).
cnf(f_191_3,plain,
( relation_rng(U_741) = relation_dom(relation_inverse(U_741))
| ~ relation(U_741) ),
inference(clausify,[status(thm)],[f_191_2]) ).
cnf(f_191_4,plain,
( relation_dom(U_741) = relation_rng(relation_inverse(U_741))
| ~ relation(U_741) ),
inference(clausify,[status(thm)],[f_191_2]) ).
fof(f_192_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_192_2,plain,
! [U_743,U_742] :
( ( set_difference(U_743,U_742) = empty_set
| ~ subset(U_743,U_742) )
& ( subset(U_743,U_742)
| set_difference(U_743,U_742) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_192_1]) ).
fof(f_192_3,plain,
( ! [U_747,U_745] :
( set_difference(U_747,U_745) = empty_set
| ~ subset(U_747,U_745) )
& ! [U_746,U_744] :
( subset(U_746,U_744)
| set_difference(U_746,U_744) != empty_set ) ),
inference(miniscope,[status(thm)],[f_192_2]) ).
cnf(f_192_4,plain,
( subset(U_746,U_744)
| set_difference(U_746,U_744) != empty_set ),
inference(clausify,[status(thm)],[f_192_3]) ).
cnf(f_192_5,plain,
( set_difference(U_747,U_745) = empty_set
| ~ subset(U_747,U_745) ),
inference(clausify,[status(thm)],[f_192_3]) ).
fof(f_193_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_193_2,plain,
! [U_749,U_748] :
( ( subset(singleton(U_749),U_748)
| ~ in(U_749,U_748) )
& ( in(U_749,U_748)
| ~ subset(singleton(U_749),U_748) ) ),
inference(variable_rename,[status(thm)],[f_193_1]) ).
fof(f_193_3,plain,
( ! [U_753,U_751] :
( subset(singleton(U_753),U_751)
| ~ in(U_753,U_751) )
& ! [U_752,U_750] :
( in(U_752,U_750)
| ~ subset(singleton(U_752),U_750) ) ),
inference(miniscope,[status(thm)],[f_193_2]) ).
cnf(f_193_4,plain,
( in(U_752,U_750)
| ~ subset(singleton(U_752),U_750) ),
inference(clausify,[status(thm)],[f_193_3]) ).
cnf(f_193_5,plain,
( subset(singleton(U_753),U_751)
| ~ in(U_753,U_751) ),
inference(clausify,[status(thm)],[f_193_3]) ).
fof(f_194_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_194_2,plain,
! [U_756,U_755,U_754] :
( ( subset(unordered_pair(U_756,U_755),U_754)
| ~ in(U_755,U_754)
| ~ in(U_756,U_754) )
& ( ( in(U_755,U_754)
& in(U_756,U_754) )
| ~ subset(unordered_pair(U_756,U_755),U_754) ) ),
inference(variable_rename,[status(thm)],[f_194_1]) ).
fof(f_194_3,plain,
( ! [U_762,U_760,U_758] :
( subset(unordered_pair(U_762,U_760),U_758)
| ~ in(U_760,U_758)
| ~ in(U_762,U_758) )
& ! [U_761,U_759,U_757] :
( ( in(U_759,U_757)
& in(U_761,U_757) )
| ~ subset(unordered_pair(U_761,U_759),U_757) ) ),
inference(miniscope,[status(thm)],[f_194_2]) ).
cnf(f_194_4,plain,
( in(U_761,U_757)
| ~ subset(unordered_pair(U_761,U_759),U_757) ),
inference(clausify,[status(thm)],[f_194_3]) ).
cnf(f_194_5,plain,
( in(U_759,U_757)
| ~ subset(unordered_pair(U_761,U_759),U_757) ),
inference(clausify,[status(thm)],[f_194_3]) ).
cnf(f_194_6,plain,
( subset(unordered_pair(U_762,U_760),U_758)
| ~ in(U_760,U_758)
| ~ in(U_762,U_758) ),
inference(clausify,[status(thm)],[f_194_3]) ).
fof(f_195_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_195_2,plain,
! [U_764,U_763] : set_union2(U_764,set_difference(U_763,U_764)) = set_union2(U_764,U_763),
inference(variable_rename,[status(thm)],[f_195_1]) ).
cnf(f_195_3,plain,
set_union2(U_764,set_difference(U_763,U_764)) = set_union2(U_764,U_763),
inference(clausify,[status(thm)],[f_195_2]) ).
fof(f_196_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_196_2,plain,
! [U_766,U_765] :
( ( subset(U_766,singleton(U_765))
| ( U_766 != singleton(U_765)
& U_766 != empty_set ) )
& ( U_766 = singleton(U_765)
| U_766 = empty_set
| ~ subset(U_766,singleton(U_765)) ) ),
inference(variable_rename,[status(thm)],[f_196_1]) ).
fof(f_196_3,plain,
( ! [U_770,U_768] :
( subset(U_770,singleton(U_768))
| ( U_770 != singleton(U_768)
& U_770 != empty_set ) )
& ! [U_769,U_767] :
( U_769 = singleton(U_767)
| U_769 = empty_set
| ~ subset(U_769,singleton(U_767)) ) ),
inference(miniscope,[status(thm)],[f_196_2]) ).
cnf(f_196_4,plain,
( U_769 = singleton(U_767)
| U_769 = empty_set
| ~ subset(U_769,singleton(U_767)) ),
inference(clausify,[status(thm)],[f_196_3]) ).
cnf(f_196_5,plain,
( U_770 != empty_set
| subset(U_770,singleton(U_768)) ),
inference(clausify,[status(thm)],[f_196_3]) ).
cnf(f_196_6,plain,
( U_770 != singleton(U_768)
| subset(U_770,singleton(U_768)) ),
inference(clausify,[status(thm)],[f_196_3]) ).
fof(f_197_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_197_2,plain,
! [U_771] : set_difference(U_771,empty_set) = U_771,
inference(variable_rename,[status(thm)],[f_197_1]) ).
cnf(f_197_3,plain,
set_difference(U_771,empty_set) = U_771,
inference(clausify,[status(thm)],[f_197_2]) ).
fof(f_198_1,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ in(B,C)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t3_ordinal1]) ).
fof(f_198_2,plain,
! [U_774,U_773,U_772] :
( ~ in(U_772,U_774)
| ~ in(U_773,U_772)
| ~ in(U_774,U_773) ),
inference(variable_rename,[status(thm)],[f_198_1]) ).
fof(f_198_3,plain,
! [U_774,U_773] :
( ! [U_772] :
( ~ in(U_772,U_774)
| ~ in(U_773,U_772) )
| ~ in(U_774,U_773) ),
inference(miniscope,[status(thm)],[f_198_2]) ).
cnf(f_198_4,plain,
( ~ in(U_772,U_774)
| ~ in(U_773,U_772)
| ~ in(U_774,U_773) ),
inference(clausify,[status(thm)],[f_198_3]) ).
fof(f_199_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_199_2,plain,
! [U_776,U_775] :
( ( element(U_776,powerset(U_775))
| ~ subset(U_776,U_775) )
& ( subset(U_776,U_775)
| ~ element(U_776,powerset(U_775)) ) ),
inference(variable_rename,[status(thm)],[f_199_1]) ).
fof(f_199_3,plain,
( ! [U_780,U_778] :
( element(U_780,powerset(U_778))
| ~ subset(U_780,U_778) )
& ! [U_779,U_777] :
( subset(U_779,U_777)
| ~ element(U_779,powerset(U_777)) ) ),
inference(miniscope,[status(thm)],[f_199_2]) ).
cnf(f_199_4,plain,
( subset(U_779,U_777)
| ~ element(U_779,powerset(U_777)) ),
inference(clausify,[status(thm)],[f_199_3]) ).
cnf(f_199_5,plain,
( element(U_780,powerset(U_778))
| ~ subset(U_780,U_778) ),
inference(clausify,[status(thm)],[f_199_3]) ).
fof(f_200_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_200_2,plain,
! [U_784,U_783] :
( ( ~ disjoint(U_784,U_783)
| ! [U_782] :
( ~ in(U_782,U_783)
| ~ in(U_782,U_784) ) )
& ( ? [U_781] :
( in(U_781,U_783)
& in(U_781,U_784) )
| disjoint(U_784,U_783) ) ),
inference(variable_rename,[status(thm)],[f_200_1]) ).
fof(f_200_3,plain,
( ! [U_788,U_786] :
( ~ disjoint(U_788,U_786)
| ! [U_782] :
( ~ in(U_782,U_786)
| ~ in(U_782,U_788) ) )
& ! [U_787,U_785] :
( ? [U_781] :
( in(U_781,U_785)
& in(U_781,U_787) )
| disjoint(U_787,U_785) ) ),
inference(miniscope,[status(thm)],[f_200_2]) ).
fof(f_200_4,plain,
( ! [U_788,U_786] :
( ~ disjoint(U_788,U_786)
| ! [U_782] :
( ~ in(U_782,U_786)
| ~ in(U_782,U_788) ) )
& ! [U_787,U_785] :
( ( in(sK111(U_787,U_785),U_785)
& in(sK111(U_787,U_785),U_787) )
| disjoint(U_787,U_785) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK111]),skolemize(U_781,sK111(U_787,U_785))],[f_200_3]) ).
cnf(f_200_5,plain,
( in(sK111(U_787,U_785),U_787)
| disjoint(U_787,U_785) ),
inference(clausify,[status(thm)],[f_200_4]) ).
cnf(f_200_6,plain,
( in(sK111(U_787,U_785),U_785)
| disjoint(U_787,U_785) ),
inference(clausify,[status(thm)],[f_200_4]) ).
cnf(f_200_7,plain,
( ~ disjoint(U_788,U_786)
| ~ in(U_782,U_786)
| ~ in(U_782,U_788) ),
inference(clausify,[status(thm)],[f_200_4]) ).
fof(f_201_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_201_2,plain,
! [U_789] :
( U_789 = empty_set
| ~ subset(U_789,empty_set) ),
inference(variable_rename,[status(thm)],[f_201_1]) ).
cnf(f_201_3,plain,
( U_789 = empty_set
| ~ subset(U_789,empty_set) ),
inference(clausify,[status(thm)],[f_201_2]) ).
fof(f_202_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_202_2,plain,
! [U_791,U_790] : set_difference(set_union2(U_791,U_790),U_790) = set_difference(U_791,U_790),
inference(variable_rename,[status(thm)],[f_202_1]) ).
cnf(f_202_3,plain,
set_difference(set_union2(U_791,U_790),U_790) = set_difference(U_791,U_790),
inference(clausify,[status(thm)],[f_202_2]) ).
fof(f_203_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_203_2,plain,
! [U_794,U_793] :
( ! [U_792] :
( ( ( disjoint(U_793,U_792)
| ~ subset(U_793,subset_complement(U_794,U_792)) )
& ( subset(U_793,subset_complement(U_794,U_792))
| ~ disjoint(U_793,U_792) ) )
| ~ element(U_792,powerset(U_794)) )
| ~ element(U_793,powerset(U_794)) ),
inference(variable_rename,[status(thm)],[f_203_1]) ).
cnf(f_203_3,plain,
( subset(U_793,subset_complement(U_794,U_792))
| ~ disjoint(U_793,U_792)
| ~ element(U_792,powerset(U_794))
| ~ element(U_793,powerset(U_794)) ),
inference(clausify,[status(thm)],[f_203_2]) ).
cnf(f_203_4,plain,
( disjoint(U_793,U_792)
| ~ subset(U_793,subset_complement(U_794,U_792))
| ~ element(U_792,powerset(U_794))
| ~ element(U_793,powerset(U_794)) ),
inference(clausify,[status(thm)],[f_203_2]) ).
fof(f_204_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_204_2,plain,
! [U_796] :
( ! [U_795] :
( subset(relation_dom(relation_composition(U_796,U_795)),relation_dom(U_796))
| ~ relation(U_795) )
| ~ relation(U_796) ),
inference(variable_rename,[status(thm)],[f_204_1]) ).
cnf(f_204_3,plain,
( subset(relation_dom(relation_composition(U_796,U_795)),relation_dom(U_796))
| ~ relation(U_795)
| ~ relation(U_796) ),
inference(clausify,[status(thm)],[f_204_2]) ).
fof(f_205_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_205_2,plain,
! [U_798] :
( ! [U_797] :
( subset(relation_rng(relation_composition(U_798,U_797)),relation_rng(U_797))
| ~ relation(U_797) )
| ~ relation(U_798) ),
inference(variable_rename,[status(thm)],[f_205_1]) ).
cnf(f_205_3,plain,
( subset(relation_rng(relation_composition(U_798,U_797)),relation_rng(U_797))
| ~ relation(U_797)
| ~ relation(U_798) ),
inference(clausify,[status(thm)],[f_205_2]) ).
fof(f_206_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_206_2,plain,
! [U_800,U_799] :
( U_799 = set_union2(U_800,set_difference(U_799,U_800))
| ~ subset(U_800,U_799) ),
inference(variable_rename,[status(thm)],[f_206_1]) ).
cnf(f_206_3,plain,
( U_799 = set_union2(U_800,set_difference(U_799,U_800))
| ~ subset(U_800,U_799) ),
inference(clausify,[status(thm)],[f_206_2]) ).
fof(f_207_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_207_2,plain,
! [U_802] :
( ! [U_801] :
( relation_dom(relation_composition(U_802,U_801)) = relation_dom(U_802)
| ~ subset(relation_rng(U_802),relation_dom(U_801))
| ~ relation(U_801) )
| ~ relation(U_802) ),
inference(variable_rename,[status(thm)],[f_207_1]) ).
cnf(f_207_3,plain,
( relation_dom(relation_composition(U_802,U_801)) = relation_dom(U_802)
| ~ subset(relation_rng(U_802),relation_dom(U_801))
| ~ relation(U_801)
| ~ relation(U_802) ),
inference(clausify,[status(thm)],[f_207_2]) ).
fof(f_208_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_208_2,plain,
! [U_804,U_803] :
( complements_of_subsets(U_804,U_803) != empty_set
| U_803 = empty_set
| ~ element(U_803,powerset(powerset(U_804))) ),
inference(variable_rename,[status(thm)],[f_208_1]) ).
cnf(f_208_3,plain,
( complements_of_subsets(U_804,U_803) != empty_set
| U_803 = empty_set
| ~ element(U_803,powerset(powerset(U_804))) ),
inference(clausify,[status(thm)],[f_208_2]) ).
fof(f_209_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t46_zfmisc_1]) ).
fof(f_209_2,plain,
! [U_806,U_805] :
( set_union2(singleton(U_806),U_805) = U_805
| ~ in(U_806,U_805) ),
inference(variable_rename,[status(thm)],[f_209_1]) ).
cnf(f_209_3,plain,
( set_union2(singleton(U_806),U_805) = U_805
| ~ in(U_806,U_805) ),
inference(clausify,[status(thm)],[f_209_2]) ).
fof(f_210_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_210_2,plain,
! [U_808] :
( ! [U_807] :
( relation_rng(relation_composition(U_807,U_808)) = relation_rng(U_808)
| ~ subset(relation_dom(U_808),relation_rng(U_807))
| ~ relation(U_807) )
| ~ relation(U_808) ),
inference(variable_rename,[status(thm)],[f_210_1]) ).
cnf(f_210_3,plain,
( relation_rng(relation_composition(U_807,U_808)) = relation_rng(U_808)
| ~ subset(relation_dom(U_808),relation_rng(U_807))
| ~ relation(U_807)
| ~ relation(U_808) ),
inference(clausify,[status(thm)],[f_210_2]) ).
fof(f_211_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_211_2,plain,
! [U_810,U_809] :
( subset_difference(U_810,cast_to_subset(U_810),union_of_subsets(U_810,U_809)) = meet_of_subsets(U_810,complements_of_subsets(U_810,U_809))
| U_809 = empty_set
| ~ element(U_809,powerset(powerset(U_810))) ),
inference(variable_rename,[status(thm)],[f_211_1]) ).
cnf(f_211_3,plain,
( subset_difference(U_810,cast_to_subset(U_810),union_of_subsets(U_810,U_809)) = meet_of_subsets(U_810,complements_of_subsets(U_810,U_809))
| U_809 = empty_set
| ~ element(U_809,powerset(powerset(U_810))) ),
inference(clausify,[status(thm)],[f_211_2]) ).
fof(f_212_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_212_2,plain,
! [U_812,U_811] :
( union_of_subsets(U_812,complements_of_subsets(U_812,U_811)) = subset_difference(U_812,cast_to_subset(U_812),meet_of_subsets(U_812,U_811))
| U_811 = empty_set
| ~ element(U_811,powerset(powerset(U_812))) ),
inference(variable_rename,[status(thm)],[f_212_1]) ).
cnf(f_212_3,plain,
( union_of_subsets(U_812,complements_of_subsets(U_812,U_811)) = subset_difference(U_812,cast_to_subset(U_812),meet_of_subsets(U_812,U_811))
| U_811 = empty_set
| ~ element(U_811,powerset(powerset(U_812))) ),
inference(clausify,[status(thm)],[f_212_2]) ).
fof(f_213_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_213_2,plain,
! [U_814,U_813] : set_difference(U_814,set_difference(U_814,U_813)) = set_intersection2(U_814,U_813),
inference(variable_rename,[status(thm)],[f_213_1]) ).
cnf(f_213_3,plain,
set_difference(U_814,set_difference(U_814,U_813)) = set_intersection2(U_814,U_813),
inference(clausify,[status(thm)],[f_213_2]) ).
fof(f_214_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_214_2,plain,
! [U_815] : set_difference(empty_set,U_815) = empty_set,
inference(variable_rename,[status(thm)],[f_214_1]) ).
cnf(f_214_3,plain,
set_difference(empty_set,U_815) = empty_set,
inference(clausify,[status(thm)],[f_214_2]) ).
fof(f_215_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_215_2,plain,
! [U_818,U_817,U_816] :
( element(U_818,U_816)
| ~ element(U_817,powerset(U_816))
| ~ in(U_818,U_817) ),
inference(variable_rename,[status(thm)],[f_215_1]) ).
cnf(f_215_3,plain,
( element(U_818,U_816)
| ~ element(U_817,powerset(U_816))
| ~ in(U_818,U_817) ),
inference(clausify,[status(thm)],[f_215_2]) ).
fof(f_216_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_216_2,plain,
! [U_822,U_821] :
( ( ~ disjoint(U_822,U_821)
| ! [U_820] : ~ in(U_820,set_intersection2(U_822,U_821)) )
& ( ? [U_819] : in(U_819,set_intersection2(U_822,U_821))
| disjoint(U_822,U_821) ) ),
inference(variable_rename,[status(thm)],[f_216_1]) ).
fof(f_216_3,plain,
( ! [U_826,U_824] :
( ~ disjoint(U_826,U_824)
| ! [U_820] : ~ in(U_820,set_intersection2(U_826,U_824)) )
& ! [U_825,U_823] :
( ? [U_819] : in(U_819,set_intersection2(U_825,U_823))
| disjoint(U_825,U_823) ) ),
inference(miniscope,[status(thm)],[f_216_2]) ).
fof(f_216_4,plain,
( ! [U_826,U_824] :
( ~ disjoint(U_826,U_824)
| ! [U_820] : ~ in(U_820,set_intersection2(U_826,U_824)) )
& ! [U_825,U_823] :
( in(sK112(U_825,U_823),set_intersection2(U_825,U_823))
| disjoint(U_825,U_823) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK112]),skolemize(U_819,sK112(U_825,U_823))],[f_216_3]) ).
cnf(f_216_5,plain,
( in(sK112(U_825,U_823),set_intersection2(U_825,U_823))
| disjoint(U_825,U_823) ),
inference(clausify,[status(thm)],[f_216_4]) ).
cnf(f_216_6,plain,
( ~ disjoint(U_826,U_824)
| ~ in(U_820,set_intersection2(U_826,U_824)) ),
inference(clausify,[status(thm)],[f_216_4]) ).
fof(f_217_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_217_2,plain,
! [U_829] :
( ! [U_828] :
( ! [U_827] :
( in(U_827,subset_complement(U_829,U_828))
| in(U_827,U_828)
| ~ element(U_827,U_829) )
| ~ element(U_828,powerset(U_829)) )
| U_829 = empty_set ),
inference(variable_rename,[status(thm)],[f_217_1]) ).
cnf(f_217_3,plain,
( in(U_827,subset_complement(U_829,U_828))
| in(U_827,U_828)
| ~ element(U_827,U_829)
| ~ element(U_828,powerset(U_829))
| U_829 = empty_set ),
inference(clausify,[status(thm)],[f_217_2]) ).
fof(f_218_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_218_2,plain,
! [U_835] :
( ! [U_834] :
( ( ( U_834 = function_inverse(U_835)
| ? [U_833,U_832] :
( ( ( U_832 != apply(U_834,U_833)
| ~ in(U_833,relation_rng(U_835)) )
& U_833 = apply(U_835,U_832)
& in(U_832,relation_dom(U_835)) )
| ( ( U_833 != apply(U_835,U_832)
| ~ in(U_832,relation_dom(U_835)) )
& U_832 = apply(U_834,U_833)
& in(U_833,relation_rng(U_835)) ) )
| relation_dom(U_834) != relation_rng(U_835) )
& ( ( ! [U_831,U_830] :
( ( ( U_830 = apply(U_834,U_831)
& in(U_831,relation_rng(U_835)) )
| U_831 != apply(U_835,U_830)
| ~ in(U_830,relation_dom(U_835)) )
& ( ( U_831 = apply(U_835,U_830)
& in(U_830,relation_dom(U_835)) )
| U_830 != apply(U_834,U_831)
| ~ in(U_831,relation_rng(U_835)) ) )
& relation_dom(U_834) = relation_rng(U_835) )
| U_834 != function_inverse(U_835) ) )
| ~ function(U_834)
| ~ relation(U_834) )
| ~ one_to_one(U_835)
| ~ function(U_835)
| ~ relation(U_835) ),
inference(variable_rename,[status(thm)],[f_218_1]) ).
fof(f_218_3,plain,
! [U_835] :
( ! [U_834] :
( ( ( U_834 = function_inverse(U_835)
| ? [U_843,U_841] :
( ( U_841 != apply(U_834,U_843)
| ~ in(U_843,relation_rng(U_835)) )
& U_843 = apply(U_835,U_841)
& in(U_841,relation_dom(U_835)) )
| ? [U_842,U_840] :
( ( U_842 != apply(U_835,U_840)
| ~ in(U_840,relation_dom(U_835)) )
& U_840 = apply(U_834,U_842)
& in(U_842,relation_rng(U_835)) )
| relation_dom(U_834) != relation_rng(U_835) )
& ( ( ! [U_839,U_837] :
( ( U_837 = apply(U_834,U_839)
& in(U_839,relation_rng(U_835)) )
| U_839 != apply(U_835,U_837)
| ~ in(U_837,relation_dom(U_835)) )
& ! [U_838,U_836] :
( ( U_838 = apply(U_835,U_836)
& in(U_836,relation_dom(U_835)) )
| U_836 != apply(U_834,U_838)
| ~ in(U_838,relation_rng(U_835)) )
& relation_dom(U_834) = relation_rng(U_835) )
| U_834 != function_inverse(U_835) ) )
| ~ function(U_834)
| ~ relation(U_834) )
| ~ one_to_one(U_835)
| ~ function(U_835)
| ~ relation(U_835) ),
inference(miniscope,[status(thm)],[f_218_2]) ).
fof(f_218_4,plain,
! [U_835] :
( ! [U_834] :
( ( ( U_834 = function_inverse(U_835)
| ? [U_843,U_841] :
( ( U_841 != apply(U_834,U_843)
| ~ in(U_843,relation_rng(U_835)) )
& U_843 = apply(U_835,U_841)
& in(U_841,relation_dom(U_835)) )
| ? [U_840] :
( ( sK113(U_835,U_834) != apply(U_835,U_840)
| ~ in(U_840,relation_dom(U_835)) )
& U_840 = apply(U_834,sK113(U_835,U_834))
& in(sK113(U_835,U_834),relation_rng(U_835)) )
| relation_dom(U_834) != relation_rng(U_835) )
& ( ( ! [U_839,U_837] :
( ( U_837 = apply(U_834,U_839)
& in(U_839,relation_rng(U_835)) )
| U_839 != apply(U_835,U_837)
| ~ in(U_837,relation_dom(U_835)) )
& ! [U_838,U_836] :
( ( U_838 = apply(U_835,U_836)
& in(U_836,relation_dom(U_835)) )
| U_836 != apply(U_834,U_838)
| ~ in(U_838,relation_rng(U_835)) )
& relation_dom(U_834) = relation_rng(U_835) )
| U_834 != function_inverse(U_835) ) )
| ~ function(U_834)
| ~ relation(U_834) )
| ~ one_to_one(U_835)
| ~ function(U_835)
| ~ relation(U_835) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK113]),skolemize(U_842,sK113(U_835,U_834))],[f_218_3]) ).
fof(f_218_5,plain,
! [U_835] :
( ! [U_834] :
( ( ( U_834 = function_inverse(U_835)
| ? [U_843,U_841] :
( ( U_841 != apply(U_834,U_843)
| ~ in(U_843,relation_rng(U_835)) )
& U_843 = apply(U_835,U_841)
& in(U_841,relation_dom(U_835)) )
| ( ( sK113(U_835,U_834) != apply(U_835,sK114(U_835,U_834))
| ~ in(sK114(U_835,U_834),relation_dom(U_835)) )
& sK114(U_835,U_834) = apply(U_834,sK113(U_835,U_834))
& in(sK113(U_835,U_834),relation_rng(U_835)) )
| relation_dom(U_834) != relation_rng(U_835) )
& ( ( ! [U_839,U_837] :
( ( U_837 = apply(U_834,U_839)
& in(U_839,relation_rng(U_835)) )
| U_839 != apply(U_835,U_837)
| ~ in(U_837,relation_dom(U_835)) )
& ! [U_838,U_836] :
( ( U_838 = apply(U_835,U_836)
& in(U_836,relation_dom(U_835)) )
| U_836 != apply(U_834,U_838)
| ~ in(U_838,relation_rng(U_835)) )
& relation_dom(U_834) = relation_rng(U_835) )
| U_834 != function_inverse(U_835) ) )
| ~ function(U_834)
| ~ relation(U_834) )
| ~ one_to_one(U_835)
| ~ function(U_835)
| ~ relation(U_835) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK114]),skolemize(U_840,sK114(U_835,U_834))],[f_218_4]) ).
fof(f_218_6,plain,
! [U_835] :
( ! [U_834] :
( ( ( U_834 = function_inverse(U_835)
| ? [U_841] :
( ( U_841 != apply(U_834,sK115(U_835,U_834))
| ~ in(sK115(U_835,U_834),relation_rng(U_835)) )
& sK115(U_835,U_834) = apply(U_835,U_841)
& in(U_841,relation_dom(U_835)) )
| ( ( sK113(U_835,U_834) != apply(U_835,sK114(U_835,U_834))
| ~ in(sK114(U_835,U_834),relation_dom(U_835)) )
& sK114(U_835,U_834) = apply(U_834,sK113(U_835,U_834))
& in(sK113(U_835,U_834),relation_rng(U_835)) )
| relation_dom(U_834) != relation_rng(U_835) )
& ( ( ! [U_839,U_837] :
( ( U_837 = apply(U_834,U_839)
& in(U_839,relation_rng(U_835)) )
| U_839 != apply(U_835,U_837)
| ~ in(U_837,relation_dom(U_835)) )
& ! [U_838,U_836] :
( ( U_838 = apply(U_835,U_836)
& in(U_836,relation_dom(U_835)) )
| U_836 != apply(U_834,U_838)
| ~ in(U_838,relation_rng(U_835)) )
& relation_dom(U_834) = relation_rng(U_835) )
| U_834 != function_inverse(U_835) ) )
| ~ function(U_834)
| ~ relation(U_834) )
| ~ one_to_one(U_835)
| ~ function(U_835)
| ~ relation(U_835) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK115]),skolemize(U_843,sK115(U_835,U_834))],[f_218_5]) ).
fof(f_218_7,plain,
! [U_835] :
( ! [U_834] :
( ( ( U_834 = function_inverse(U_835)
| ( ( sK116(U_835,U_834) != apply(U_834,sK115(U_835,U_834))
| ~ in(sK115(U_835,U_834),relation_rng(U_835)) )
& sK115(U_835,U_834) = apply(U_835,sK116(U_835,U_834))
& in(sK116(U_835,U_834),relation_dom(U_835)) )
| ( ( sK113(U_835,U_834) != apply(U_835,sK114(U_835,U_834))
| ~ in(sK114(U_835,U_834),relation_dom(U_835)) )
& sK114(U_835,U_834) = apply(U_834,sK113(U_835,U_834))
& in(sK113(U_835,U_834),relation_rng(U_835)) )
| relation_dom(U_834) != relation_rng(U_835) )
& ( ( ! [U_839,U_837] :
( ( U_837 = apply(U_834,U_839)
& in(U_839,relation_rng(U_835)) )
| U_839 != apply(U_835,U_837)
| ~ in(U_837,relation_dom(U_835)) )
& ! [U_838,U_836] :
( ( U_838 = apply(U_835,U_836)
& in(U_836,relation_dom(U_835)) )
| U_836 != apply(U_834,U_838)
| ~ in(U_838,relation_rng(U_835)) )
& relation_dom(U_834) = relation_rng(U_835) )
| U_834 != function_inverse(U_835) ) )
| ~ function(U_834)
| ~ relation(U_834) )
| ~ one_to_one(U_835)
| ~ function(U_835)
| ~ relation(U_835) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK116]),skolemize(U_841,sK116(U_835,U_834))],[f_218_6]) ).
cnf(f_218_8,plain,
( relation_dom(U_834) = relation_rng(U_835)
| U_834 != function_inverse(U_835)
| ~ function(U_834)
| ~ relation(U_834)
| ~ one_to_one(U_835)
| ~ function(U_835)
| ~ relation(U_835) ),
inference(clausify,[status(thm)],[f_218_7]) ).
cnf(f_218_9,plain,
( in(U_836,relation_dom(U_835))
| U_836 != apply(U_834,U_838)
| ~ in(U_838,relation_rng(U_835))
| U_834 != function_inverse(U_835)
| ~ function(U_834)
| ~ relation(U_834)
| ~ one_to_one(U_835)
| ~ function(U_835)
| ~ relation(U_835) ),
inference(clausify,[status(thm)],[f_218_7]) ).
cnf(f_218_10,plain,
( U_838 = apply(U_835,U_836)
| U_836 != apply(U_834,U_838)
| ~ in(U_838,relation_rng(U_835))
| U_834 != function_inverse(U_835)
| ~ function(U_834)
| ~ relation(U_834)
| ~ one_to_one(U_835)
| ~ function(U_835)
| ~ relation(U_835) ),
inference(clausify,[status(thm)],[f_218_7]) ).
cnf(f_218_11,plain,
( in(U_839,relation_rng(U_835))
| U_839 != apply(U_835,U_837)
| ~ in(U_837,relation_dom(U_835))
| U_834 != function_inverse(U_835)
| ~ function(U_834)
| ~ relation(U_834)
| ~ one_to_one(U_835)
| ~ function(U_835)
| ~ relation(U_835) ),
inference(clausify,[status(thm)],[f_218_7]) ).
cnf(f_218_12,plain,
( U_837 = apply(U_834,U_839)
| U_839 != apply(U_835,U_837)
| ~ in(U_837,relation_dom(U_835))
| U_834 != function_inverse(U_835)
| ~ function(U_834)
| ~ relation(U_834)
| ~ one_to_one(U_835)
| ~ function(U_835)
| ~ relation(U_835) ),
inference(clausify,[status(thm)],[f_218_7]) ).
cnf(f_218_13,plain,
( in(sK116(U_835,U_834),relation_dom(U_835))
| in(sK113(U_835,U_834),relation_rng(U_835))
| relation_dom(U_834) != relation_rng(U_835)
| U_834 = function_inverse(U_835)
| ~ function(U_834)
| ~ relation(U_834)
| ~ one_to_one(U_835)
| ~ function(U_835)
| ~ relation(U_835) ),
inference(clausify,[status(thm)],[f_218_7]) ).
cnf(f_218_14,plain,
( sK115(U_835,U_834) = apply(U_835,sK116(U_835,U_834))
| in(sK113(U_835,U_834),relation_rng(U_835))
| relation_dom(U_834) != relation_rng(U_835)
| U_834 = function_inverse(U_835)
| ~ function(U_834)
| ~ relation(U_834)
| ~ one_to_one(U_835)
| ~ function(U_835)
| ~ relation(U_835) ),
inference(clausify,[status(thm)],[f_218_7]) ).
cnf(f_218_15,plain,
( in(sK116(U_835,U_834),relation_dom(U_835))
| sK114(U_835,U_834) = apply(U_834,sK113(U_835,U_834))
| relation_dom(U_834) != relation_rng(U_835)
| U_834 = function_inverse(U_835)
| ~ function(U_834)
| ~ relation(U_834)
| ~ one_to_one(U_835)
| ~ function(U_835)
| ~ relation(U_835) ),
inference(clausify,[status(thm)],[f_218_7]) ).
cnf(f_218_16,plain,
( sK115(U_835,U_834) = apply(U_835,sK116(U_835,U_834))
| sK114(U_835,U_834) = apply(U_834,sK113(U_835,U_834))
| relation_dom(U_834) != relation_rng(U_835)
| U_834 = function_inverse(U_835)
| ~ function(U_834)
| ~ relation(U_834)
| ~ one_to_one(U_835)
| ~ function(U_835)
| ~ relation(U_835) ),
inference(clausify,[status(thm)],[f_218_7]) ).
cnf(f_218_17,plain,
( in(sK113(U_835,U_834),relation_rng(U_835))
| sK116(U_835,U_834) != apply(U_834,sK115(U_835,U_834))
| ~ in(sK115(U_835,U_834),relation_rng(U_835))
| relation_dom(U_834) != relation_rng(U_835)
| U_834 = function_inverse(U_835)
| ~ function(U_834)
| ~ relation(U_834)
| ~ one_to_one(U_835)
| ~ function(U_835)
| ~ relation(U_835) ),
inference(clausify,[status(thm)],[f_218_7]) ).
cnf(f_218_18,plain,
( sK114(U_835,U_834) = apply(U_834,sK113(U_835,U_834))
| sK116(U_835,U_834) != apply(U_834,sK115(U_835,U_834))
| ~ in(sK115(U_835,U_834),relation_rng(U_835))
| relation_dom(U_834) != relation_rng(U_835)
| U_834 = function_inverse(U_835)
| ~ function(U_834)
| ~ relation(U_834)
| ~ one_to_one(U_835)
| ~ function(U_835)
| ~ relation(U_835) ),
inference(clausify,[status(thm)],[f_218_7]) ).
cnf(f_218_19,plain,
( in(sK116(U_835,U_834),relation_dom(U_835))
| sK113(U_835,U_834) != apply(U_835,sK114(U_835,U_834))
| ~ in(sK114(U_835,U_834),relation_dom(U_835))
| relation_dom(U_834) != relation_rng(U_835)
| U_834 = function_inverse(U_835)
| ~ function(U_834)
| ~ relation(U_834)
| ~ one_to_one(U_835)
| ~ function(U_835)
| ~ relation(U_835) ),
inference(clausify,[status(thm)],[f_218_7]) ).
cnf(f_218_20,plain,
( sK115(U_835,U_834) = apply(U_835,sK116(U_835,U_834))
| sK113(U_835,U_834) != apply(U_835,sK114(U_835,U_834))
| ~ in(sK114(U_835,U_834),relation_dom(U_835))
| relation_dom(U_834) != relation_rng(U_835)
| U_834 = function_inverse(U_835)
| ~ function(U_834)
| ~ relation(U_834)
| ~ one_to_one(U_835)
| ~ function(U_835)
| ~ relation(U_835) ),
inference(clausify,[status(thm)],[f_218_7]) ).
cnf(f_218_21,plain,
( sK116(U_835,U_834) != apply(U_834,sK115(U_835,U_834))
| ~ in(sK115(U_835,U_834),relation_rng(U_835))
| sK113(U_835,U_834) != apply(U_835,sK114(U_835,U_834))
| ~ in(sK114(U_835,U_834),relation_dom(U_835))
| relation_dom(U_834) != relation_rng(U_835)
| U_834 = function_inverse(U_835)
| ~ function(U_834)
| ~ relation(U_834)
| ~ one_to_one(U_835)
| ~ function(U_835)
| ~ relation(U_835) ),
inference(clausify,[status(thm)],[f_218_7]) ).
fof(f_219_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_219_2,plain,
! [U_846,U_845,U_844] :
( ~ in(U_845,U_844)
| ~ in(U_845,subset_complement(U_846,U_844))
| ~ element(U_844,powerset(U_846)) ),
inference(variable_rename,[status(thm)],[f_219_1]) ).
cnf(f_219_3,plain,
( ~ in(U_845,U_844)
| ~ in(U_845,subset_complement(U_846,U_844))
| ~ element(U_844,powerset(U_846)) ),
inference(clausify,[status(thm)],[f_219_2]) ).
fof(f_220_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_220_2,plain,
! [U_847] :
( ( relation_dom(U_847) = relation_rng(function_inverse(U_847))
& relation_rng(U_847) = relation_dom(function_inverse(U_847)) )
| ~ one_to_one(U_847)
| ~ function(U_847)
| ~ relation(U_847) ),
inference(variable_rename,[status(thm)],[f_220_1]) ).
cnf(f_220_3,plain,
( relation_rng(U_847) = relation_dom(function_inverse(U_847))
| ~ one_to_one(U_847)
| ~ function(U_847)
| ~ relation(U_847) ),
inference(clausify,[status(thm)],[f_220_2]) ).
cnf(f_220_4,plain,
( relation_dom(U_847) = relation_rng(function_inverse(U_847))
| ~ one_to_one(U_847)
| ~ function(U_847)
| ~ relation(U_847) ),
inference(clausify,[status(thm)],[f_220_2]) ).
fof(f_221_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_221_2,plain,
! [U_850] :
( U_850 = empty_set
| ? [U_849,U_848] : in(ordered_pair(U_849,U_848),U_850)
| ~ relation(U_850) ),
inference(variable_rename,[status(thm)],[f_221_1]) ).
fof(f_221_3,plain,
! [U_850] :
( U_850 = empty_set
| ? [U_848] : in(ordered_pair(sK117(U_850),U_848),U_850)
| ~ relation(U_850) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK117]),skolemize(U_849,sK117(U_850))],[f_221_2]) ).
fof(f_221_4,plain,
! [U_850] :
( U_850 = empty_set
| in(ordered_pair(sK117(U_850),sK118(U_850)),U_850)
| ~ relation(U_850) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK118]),skolemize(U_848,sK118(U_850))],[f_221_3]) ).
cnf(f_221_5,plain,
( U_850 = empty_set
| in(ordered_pair(sK117(U_850),sK118(U_850)),U_850)
| ~ relation(U_850) ),
inference(clausify,[status(thm)],[f_221_4]) ).
fof(f_222_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_222_2,plain,
! [U_852,U_851] :
( ( U_852 = apply(relation_composition(function_inverse(U_851),U_851),U_852)
& U_852 = apply(U_851,apply(function_inverse(U_851),U_852)) )
| ~ in(U_852,relation_rng(U_851))
| ~ one_to_one(U_851)
| ~ function(U_851)
| ~ relation(U_851) ),
inference(variable_rename,[status(thm)],[f_222_1]) ).
cnf(f_222_3,plain,
( U_852 = apply(U_851,apply(function_inverse(U_851),U_852))
| ~ in(U_852,relation_rng(U_851))
| ~ one_to_one(U_851)
| ~ function(U_851)
| ~ relation(U_851) ),
inference(clausify,[status(thm)],[f_222_2]) ).
cnf(f_222_4,plain,
( U_852 = apply(relation_composition(function_inverse(U_851),U_851),U_852)
| ~ in(U_852,relation_rng(U_851))
| ~ one_to_one(U_851)
| ~ function(U_851)
| ~ relation(U_851) ),
inference(clausify,[status(thm)],[f_222_2]) ).
fof(f_223_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_223_2,plain,
! [U_855,U_854,U_853] :
( ~ empty(U_853)
| ~ element(U_854,powerset(U_853))
| ~ in(U_855,U_854) ),
inference(variable_rename,[status(thm)],[f_223_1]) ).
fof(f_223_3,plain,
! [U_855,U_854] :
( ! [U_853] :
( ~ empty(U_853)
| ~ element(U_854,powerset(U_853)) )
| ~ in(U_855,U_854) ),
inference(miniscope,[status(thm)],[f_223_2]) ).
cnf(f_223_4,plain,
( ~ empty(U_853)
| ~ element(U_854,powerset(U_853))
| ~ in(U_855,U_854) ),
inference(clausify,[status(thm)],[f_223_3]) ).
fof(f_224_1,plain,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(fof_nnf,[status(thm)],[t60_relat_1]) ).
cnf(f_224_2,plain,
relation_dom(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_224_1]) ).
cnf(f_224_3,plain,
relation_rng(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_224_1]) ).
fof(f_225_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t60_xboole_1]) ).
fof(f_225_2,plain,
! [U_857,U_856] :
( ~ proper_subset(U_856,U_857)
| ~ subset(U_857,U_856) ),
inference(variable_rename,[status(thm)],[f_225_1]) ).
cnf(f_225_3,plain,
( ~ proper_subset(U_856,U_857)
| ~ subset(U_857,U_856) ),
inference(clausify,[status(thm)],[f_225_2]) ).
fof(f_226_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_226_2,plain,
! [U_858] :
( one_to_one(function_inverse(U_858))
| ~ one_to_one(U_858)
| ~ function(U_858)
| ~ relation(U_858) ),
inference(variable_rename,[status(thm)],[f_226_1]) ).
cnf(f_226_3,plain,
( one_to_one(function_inverse(U_858))
| ~ one_to_one(U_858)
| ~ function(U_858)
| ~ relation(U_858) ),
inference(clausify,[status(thm)],[f_226_2]) ).
fof(f_227_1,plain,
! [A,B,C] :
( disjoint(A,C)
| ~ disjoint(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t63_xboole_1]) ).
fof(f_227_2,plain,
! [U_861,U_860,U_859] :
( disjoint(U_861,U_859)
| ~ disjoint(U_860,U_859)
| ~ subset(U_861,U_860) ),
inference(variable_rename,[status(thm)],[f_227_1]) ).
cnf(f_227_3,plain,
( disjoint(U_861,U_859)
| ~ disjoint(U_860,U_859)
| ~ subset(U_861,U_860) ),
inference(clausify,[status(thm)],[f_227_2]) ).
fof(f_228_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_228_2,plain,
! [U_862] :
( U_862 = empty_set
| ( relation_rng(U_862) != empty_set
& relation_dom(U_862) != empty_set )
| ~ relation(U_862) ),
inference(variable_rename,[status(thm)],[f_228_1]) ).
cnf(f_228_3,plain,
( relation_dom(U_862) != empty_set
| U_862 = empty_set
| ~ relation(U_862) ),
inference(clausify,[status(thm)],[f_228_2]) ).
cnf(f_228_4,plain,
( relation_rng(U_862) != empty_set
| U_862 = empty_set
| ~ relation(U_862) ),
inference(clausify,[status(thm)],[f_228_2]) ).
fof(f_229_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_229_2,plain,
! [U_863] :
( ( ( relation_dom(U_863) = empty_set
| relation_rng(U_863) != empty_set )
& ( relation_rng(U_863) = empty_set
| relation_dom(U_863) != empty_set ) )
| ~ relation(U_863) ),
inference(variable_rename,[status(thm)],[f_229_1]) ).
cnf(f_229_3,plain,
( relation_rng(U_863) = empty_set
| relation_dom(U_863) != empty_set
| ~ relation(U_863) ),
inference(clausify,[status(thm)],[f_229_2]) ).
cnf(f_229_4,plain,
( relation_dom(U_863) = empty_set
| relation_rng(U_863) != empty_set
| ~ relation(U_863) ),
inference(clausify,[status(thm)],[f_229_2]) ).
fof(f_230_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_230_2,plain,
! [U_865,U_864] :
( ( set_difference(U_865,singleton(U_864)) = U_865
| in(U_864,U_865) )
& ( ~ in(U_864,U_865)
| set_difference(U_865,singleton(U_864)) != U_865 ) ),
inference(variable_rename,[status(thm)],[f_230_1]) ).
fof(f_230_3,plain,
( ! [U_869,U_867] :
( set_difference(U_869,singleton(U_867)) = U_869
| in(U_867,U_869) )
& ! [U_868,U_866] :
( ~ in(U_866,U_868)
| set_difference(U_868,singleton(U_866)) != U_868 ) ),
inference(miniscope,[status(thm)],[f_230_2]) ).
cnf(f_230_4,plain,
( ~ in(U_866,U_868)
| set_difference(U_868,singleton(U_866)) != U_868 ),
inference(clausify,[status(thm)],[f_230_3]) ).
cnf(f_230_5,plain,
( set_difference(U_869,singleton(U_867)) = U_869
| in(U_867,U_869) ),
inference(clausify,[status(thm)],[f_230_3]) ).
fof(f_231_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_231_2,plain,
! [U_874,U_873] :
( ! [U_872] :
( ( ( U_873 = relation_dom_restriction(U_872,U_874)
| ? [U_871] :
( apply(U_873,U_871) != apply(U_872,U_871)
& in(U_871,relation_dom(U_873)) )
| relation_dom(U_873) != set_intersection2(relation_dom(U_872),U_874) )
& ( ( ! [U_870] :
( apply(U_873,U_870) = apply(U_872,U_870)
| ~ in(U_870,relation_dom(U_873)) )
& relation_dom(U_873) = set_intersection2(relation_dom(U_872),U_874) )
| U_873 != relation_dom_restriction(U_872,U_874) ) )
| ~ function(U_872)
| ~ relation(U_872) )
| ~ function(U_873)
| ~ relation(U_873) ),
inference(variable_rename,[status(thm)],[f_231_1]) ).
fof(f_231_3,plain,
! [U_874,U_873] :
( ! [U_872] :
( ( ( U_873 = relation_dom_restriction(U_872,U_874)
| ( apply(U_873,sK119(U_874,U_873,U_872)) != apply(U_872,sK119(U_874,U_873,U_872))
& in(sK119(U_874,U_873,U_872),relation_dom(U_873)) )
| relation_dom(U_873) != set_intersection2(relation_dom(U_872),U_874) )
& ( ( ! [U_870] :
( apply(U_873,U_870) = apply(U_872,U_870)
| ~ in(U_870,relation_dom(U_873)) )
& relation_dom(U_873) = set_intersection2(relation_dom(U_872),U_874) )
| U_873 != relation_dom_restriction(U_872,U_874) ) )
| ~ function(U_872)
| ~ relation(U_872) )
| ~ function(U_873)
| ~ relation(U_873) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK119]),skolemize(U_871,sK119(U_874,U_873,U_872))],[f_231_2]) ).
cnf(f_231_4,plain,
( relation_dom(U_873) = set_intersection2(relation_dom(U_872),U_874)
| U_873 != relation_dom_restriction(U_872,U_874)
| ~ function(U_872)
| ~ relation(U_872)
| ~ function(U_873)
| ~ relation(U_873) ),
inference(clausify,[status(thm)],[f_231_3]) ).
cnf(f_231_5,plain,
( apply(U_873,U_870) = apply(U_872,U_870)
| ~ in(U_870,relation_dom(U_873))
| U_873 != relation_dom_restriction(U_872,U_874)
| ~ function(U_872)
| ~ relation(U_872)
| ~ function(U_873)
| ~ relation(U_873) ),
inference(clausify,[status(thm)],[f_231_3]) ).
cnf(f_231_6,plain,
( in(sK119(U_874,U_873,U_872),relation_dom(U_873))
| relation_dom(U_873) != set_intersection2(relation_dom(U_872),U_874)
| U_873 = relation_dom_restriction(U_872,U_874)
| ~ function(U_872)
| ~ relation(U_872)
| ~ function(U_873)
| ~ relation(U_873) ),
inference(clausify,[status(thm)],[f_231_3]) ).
cnf(f_231_7,plain,
( apply(U_873,sK119(U_874,U_873,U_872)) != apply(U_872,sK119(U_874,U_873,U_872))
| relation_dom(U_873) != set_intersection2(relation_dom(U_872),U_874)
| U_873 = relation_dom_restriction(U_872,U_874)
| ~ function(U_872)
| ~ relation(U_872)
| ~ function(U_873)
| ~ relation(U_873) ),
inference(clausify,[status(thm)],[f_231_3]) ).
fof(f_232_1,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(fof_nnf,[status(thm)],[t69_enumset1]) ).
fof(f_232_2,plain,
! [U_875] : unordered_pair(U_875,U_875) = singleton(U_875),
inference(variable_rename,[status(thm)],[f_232_1]) ).
cnf(f_232_3,plain,
unordered_pair(U_875,U_875) = singleton(U_875),
inference(clausify,[status(thm)],[f_232_2]) ).
fof(f_233_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_233_2,plain,
! [U_876] :
( U_876 = empty_set
| ~ empty(U_876) ),
inference(variable_rename,[status(thm)],[f_233_1]) ).
cnf(f_233_3,plain,
( U_876 = empty_set
| ~ empty(U_876) ),
inference(clausify,[status(thm)],[f_233_2]) ).
fof(f_234_1,plain,
! [A,B] :
( A = B
| ~ subset(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t6_zfmisc_1]) ).
fof(f_234_2,plain,
! [U_878,U_877] :
( U_878 = U_877
| ~ subset(singleton(U_878),singleton(U_877)) ),
inference(variable_rename,[status(thm)],[f_234_1]) ).
cnf(f_234_3,plain,
( U_878 = U_877
| ~ subset(singleton(U_878),singleton(U_877)) ),
inference(clausify,[status(thm)],[f_234_2]) ).
fof(f_235_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_235_2,plain,
! [U_881,U_880,U_879] :
( apply(relation_dom_restriction(U_879,U_881),U_880) = apply(U_879,U_880)
| ~ in(U_880,relation_dom(relation_dom_restriction(U_879,U_881)))
| ~ function(U_879)
| ~ relation(U_879) ),
inference(variable_rename,[status(thm)],[f_235_1]) ).
cnf(f_235_3,plain,
( apply(relation_dom_restriction(U_879,U_881),U_880) = apply(U_879,U_880)
| ~ in(U_880,relation_dom(relation_dom_restriction(U_879,U_881)))
| ~ function(U_879)
| ~ relation(U_879) ),
inference(clausify,[status(thm)],[f_235_2]) ).
fof(f_236_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_236_2,plain,
! [U_882] :
( relation_rng(identity_relation(U_882)) = U_882
& relation_dom(identity_relation(U_882)) = U_882 ),
inference(variable_rename,[status(thm)],[f_236_1]) ).
fof(f_236_3,plain,
( ! [U_884] : relation_rng(identity_relation(U_884)) = U_884
& ! [U_883] : relation_dom(identity_relation(U_883)) = U_883 ),
inference(miniscope,[status(thm)],[f_236_2]) ).
cnf(f_236_4,plain,
relation_dom(identity_relation(U_883)) = U_883,
inference(clausify,[status(thm)],[f_236_3]) ).
cnf(f_236_5,plain,
relation_rng(identity_relation(U_884)) = U_884,
inference(clausify,[status(thm)],[f_236_3]) ).
fof(f_237_1,plain,
! [A,B,C] :
( apply(relation_dom_restriction(C,A),B) = apply(C,B)
| ~ in(B,A)
| ~ function(C)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t72_funct_1]) ).
fof(f_237_2,plain,
! [U_887,U_886,U_885] :
( apply(relation_dom_restriction(U_885,U_887),U_886) = apply(U_885,U_886)
| ~ in(U_886,U_887)
| ~ function(U_885)
| ~ relation(U_885) ),
inference(variable_rename,[status(thm)],[f_237_1]) ).
cnf(f_237_3,plain,
( apply(relation_dom_restriction(U_885,U_887),U_886) = apply(U_885,U_886)
| ~ in(U_886,U_887)
| ~ function(U_885)
| ~ relation(U_885) ),
inference(clausify,[status(thm)],[f_237_2]) ).
fof(f_238_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_238_2,plain,
! [U_891,U_890,U_889,U_888] :
( ( ( in(ordered_pair(U_891,U_890),relation_composition(identity_relation(U_889),U_888))
| ~ in(ordered_pair(U_891,U_890),U_888)
| ~ in(U_891,U_889) )
& ( ( in(ordered_pair(U_891,U_890),U_888)
& in(U_891,U_889) )
| ~ in(ordered_pair(U_891,U_890),relation_composition(identity_relation(U_889),U_888)) ) )
| ~ relation(U_888) ),
inference(variable_rename,[status(thm)],[f_238_1]) ).
cnf(f_238_3,plain,
( in(U_891,U_889)
| ~ in(ordered_pair(U_891,U_890),relation_composition(identity_relation(U_889),U_888))
| ~ relation(U_888) ),
inference(clausify,[status(thm)],[f_238_2]) ).
cnf(f_238_4,plain,
( in(ordered_pair(U_891,U_890),U_888)
| ~ in(ordered_pair(U_891,U_890),relation_composition(identity_relation(U_889),U_888))
| ~ relation(U_888) ),
inference(clausify,[status(thm)],[f_238_2]) ).
cnf(f_238_5,plain,
( in(ordered_pair(U_891,U_890),relation_composition(identity_relation(U_889),U_888))
| ~ in(ordered_pair(U_891,U_890),U_888)
| ~ in(U_891,U_889)
| ~ relation(U_888) ),
inference(clausify,[status(thm)],[f_238_2]) ).
fof(f_239_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_239_2,plain,
! [U_893,U_892] :
( ~ empty(U_892)
| ~ in(U_893,U_892) ),
inference(variable_rename,[status(thm)],[f_239_1]) ).
cnf(f_239_3,plain,
( ~ empty(U_892)
| ~ in(U_893,U_892) ),
inference(clausify,[status(thm)],[f_239_2]) ).
fof(f_240_1,plain,
! [A,B] :
( ? [C] :
( ! [D] :
( ~ in(D,C)
| ~ in(D,B) )
& in(C,B) )
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_tarski]) ).
fof(f_240_2,plain,
! [U_897,U_896] :
( ? [U_895] :
( ! [U_894] :
( ~ in(U_894,U_895)
| ~ in(U_894,U_896) )
& in(U_895,U_896) )
| ~ in(U_897,U_896) ),
inference(variable_rename,[status(thm)],[f_240_1]) ).
fof(f_240_3,plain,
! [U_897,U_896] :
( ( ! [U_894] :
( ~ in(U_894,sK120(U_897,U_896))
| ~ in(U_894,U_896) )
& in(sK120(U_897,U_896),U_896) )
| ~ in(U_897,U_896) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK120]),skolemize(U_895,sK120(U_897,U_896))],[f_240_2]) ).
cnf(f_240_4,plain,
( in(sK120(U_897,U_896),U_896)
| ~ in(U_897,U_896) ),
inference(clausify,[status(thm)],[f_240_3]) ).
cnf(f_240_5,plain,
( ~ in(U_894,sK120(U_897,U_896))
| ~ in(U_894,U_896)
| ~ in(U_897,U_896) ),
inference(clausify,[status(thm)],[f_240_3]) ).
fof(f_241_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1]) ).
fof(f_241_2,plain,
! [U_899,U_898] : subset(U_899,set_union2(U_899,U_898)),
inference(variable_rename,[status(thm)],[f_241_1]) ).
cnf(f_241_3,plain,
subset(U_899,set_union2(U_899,U_898)),
inference(clausify,[status(thm)],[f_241_2]) ).
fof(f_242_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_242_2,plain,
! [U_901,U_900] :
( ( disjoint(U_901,U_900)
| set_difference(U_901,U_900) != U_901 )
& ( set_difference(U_901,U_900) = U_901
| ~ disjoint(U_901,U_900) ) ),
inference(variable_rename,[status(thm)],[f_242_1]) ).
fof(f_242_3,plain,
( ! [U_905,U_903] :
( disjoint(U_905,U_903)
| set_difference(U_905,U_903) != U_905 )
& ! [U_904,U_902] :
( set_difference(U_904,U_902) = U_904
| ~ disjoint(U_904,U_902) ) ),
inference(miniscope,[status(thm)],[f_242_2]) ).
cnf(f_242_4,plain,
( set_difference(U_904,U_902) = U_904
| ~ disjoint(U_904,U_902) ),
inference(clausify,[status(thm)],[f_242_3]) ).
cnf(f_242_5,plain,
( disjoint(U_905,U_903)
| set_difference(U_905,U_903) != U_905 ),
inference(clausify,[status(thm)],[f_242_3]) ).
fof(f_243_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_243_2,plain,
! [U_908,U_907,U_906] :
( ( ( in(U_908,relation_dom(relation_dom_restriction(U_906,U_907)))
| ~ in(U_908,relation_dom(U_906))
| ~ in(U_908,U_907) )
& ( ( in(U_908,relation_dom(U_906))
& in(U_908,U_907) )
| ~ in(U_908,relation_dom(relation_dom_restriction(U_906,U_907))) ) )
| ~ relation(U_906) ),
inference(variable_rename,[status(thm)],[f_243_1]) ).
cnf(f_243_3,plain,
( in(U_908,U_907)
| ~ in(U_908,relation_dom(relation_dom_restriction(U_906,U_907)))
| ~ relation(U_906) ),
inference(clausify,[status(thm)],[f_243_2]) ).
cnf(f_243_4,plain,
( in(U_908,relation_dom(U_906))
| ~ in(U_908,relation_dom(relation_dom_restriction(U_906,U_907)))
| ~ relation(U_906) ),
inference(clausify,[status(thm)],[f_243_2]) ).
cnf(f_243_5,plain,
( in(U_908,relation_dom(relation_dom_restriction(U_906,U_907)))
| ~ in(U_908,relation_dom(U_906))
| ~ in(U_908,U_907)
| ~ relation(U_906) ),
inference(clausify,[status(thm)],[f_243_2]) ).
fof(f_244_1,plain,
! [A,B] :
( subset(relation_dom_restriction(B,A),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t88_relat_1]) ).
fof(f_244_2,plain,
! [U_910,U_909] :
( subset(relation_dom_restriction(U_909,U_910),U_909)
| ~ relation(U_909) ),
inference(variable_rename,[status(thm)],[f_244_1]) ).
cnf(f_244_3,plain,
( subset(relation_dom_restriction(U_909,U_910),U_909)
| ~ relation(U_909) ),
inference(clausify,[status(thm)],[f_244_2]) ).
fof(f_245_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_245_2,plain,
! [U_912,U_911] :
( ~ empty(U_911)
| U_912 = U_911
| ~ empty(U_912) ),
inference(variable_rename,[status(thm)],[f_245_1]) ).
fof(f_245_3,plain,
! [U_912] :
( ! [U_911] :
( ~ empty(U_911)
| U_912 = U_911 )
| ~ empty(U_912) ),
inference(miniscope,[status(thm)],[f_245_2]) ).
cnf(f_245_4,plain,
( ~ empty(U_911)
| U_912 = U_911
| ~ empty(U_912) ),
inference(clausify,[status(thm)],[f_245_3]) ).
fof(f_246_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_246_2,plain,
! [U_915,U_914,U_913] :
( ( ( in(ordered_pair(U_915,U_914),U_913)
| U_914 != apply(U_913,U_915)
| ~ in(U_915,relation_dom(U_913)) )
& ( ( U_914 = apply(U_913,U_915)
& in(U_915,relation_dom(U_913)) )
| ~ in(ordered_pair(U_915,U_914),U_913) ) )
| ~ function(U_913)
| ~ relation(U_913) ),
inference(variable_rename,[status(thm)],[f_246_1]) ).
cnf(f_246_3,plain,
( in(U_915,relation_dom(U_913))
| ~ in(ordered_pair(U_915,U_914),U_913)
| ~ function(U_913)
| ~ relation(U_913) ),
inference(clausify,[status(thm)],[f_246_2]) ).
cnf(f_246_4,plain,
( U_914 = apply(U_913,U_915)
| ~ in(ordered_pair(U_915,U_914),U_913)
| ~ function(U_913)
| ~ relation(U_913) ),
inference(clausify,[status(thm)],[f_246_2]) ).
cnf(f_246_5,plain,
( in(ordered_pair(U_915,U_914),U_913)
| U_914 != apply(U_913,U_915)
| ~ in(U_915,relation_dom(U_913))
| ~ function(U_913)
| ~ relation(U_913) ),
inference(clausify,[status(thm)],[f_246_2]) ).
fof(f_247_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_247_2,plain,
! [U_918,U_917,U_916] :
( subset(set_union2(U_918,U_916),U_917)
| ~ subset(U_916,U_917)
| ~ subset(U_918,U_917) ),
inference(variable_rename,[status(thm)],[f_247_1]) ).
cnf(f_247_3,plain,
( subset(set_union2(U_918,U_916),U_917)
| ~ subset(U_916,U_917)
| ~ subset(U_918,U_917) ),
inference(clausify,[status(thm)],[f_247_2]) ).
fof(f_248_1,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t8_zfmisc_1]) ).
fof(f_248_2,plain,
! [U_921,U_920,U_919] :
( U_921 = U_920
| singleton(U_921) != unordered_pair(U_920,U_919) ),
inference(variable_rename,[status(thm)],[f_248_1]) ).
fof(f_248_3,plain,
! [U_921,U_920] :
( ! [U_919] : singleton(U_921) != unordered_pair(U_920,U_919)
| U_921 = U_920 ),
inference(miniscope,[status(thm)],[f_248_2]) ).
cnf(f_248_4,plain,
( singleton(U_921) != unordered_pair(U_920,U_919)
| U_921 = U_920 ),
inference(clausify,[status(thm)],[f_248_3]) ).
fof(f_249_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_249_2,plain,
! [U_923,U_922] :
( relation_dom(relation_dom_restriction(U_922,U_923)) = set_intersection2(relation_dom(U_922),U_923)
| ~ relation(U_922) ),
inference(variable_rename,[status(thm)],[f_249_1]) ).
cnf(f_249_3,plain,
( relation_dom(relation_dom_restriction(U_922,U_923)) = set_intersection2(relation_dom(U_922),U_923)
| ~ relation(U_922) ),
inference(clausify,[status(thm)],[f_249_2]) ).
fof(f_250_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t92_zfmisc_1]) ).
fof(f_250_2,plain,
! [U_925,U_924] :
( subset(U_925,union(U_924))
| ~ in(U_925,U_924) ),
inference(variable_rename,[status(thm)],[f_250_1]) ).
cnf(f_250_3,plain,
( subset(U_925,union(U_924))
| ~ in(U_925,U_924) ),
inference(clausify,[status(thm)],[f_250_2]) ).
fof(f_251_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_251_2,plain,
! [U_927,U_926] :
( relation_dom_restriction(U_926,U_927) = relation_composition(identity_relation(U_927),U_926)
| ~ relation(U_926) ),
inference(variable_rename,[status(thm)],[f_251_1]) ).
cnf(f_251_3,plain,
( relation_dom_restriction(U_926,U_927) = relation_composition(identity_relation(U_927),U_926)
| ~ relation(U_926) ),
inference(clausify,[status(thm)],[f_251_2]) ).
fof(f_252_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_252_2,plain,
! [U_929,U_928] :
( subset(relation_rng(relation_dom_restriction(U_928,U_929)),relation_rng(U_928))
| ~ relation(U_928) ),
inference(variable_rename,[status(thm)],[f_252_1]) ).
cnf(f_252_3,plain,
( subset(relation_rng(relation_dom_restriction(U_928,U_929)),relation_rng(U_928))
| ~ relation(U_928) ),
inference(clausify,[status(thm)],[f_252_2]) ).
fof(f_253_1,plain,
! [A] : union(powerset(A)) = A,
inference(fof_nnf,[status(thm)],[t99_zfmisc_1]) ).
fof(f_253_2,plain,
! [U_930] : union(powerset(U_930)) = U_930,
inference(variable_rename,[status(thm)],[f_253_1]) ).
cnf(f_253_3,plain,
union(powerset(U_930)) = U_930,
inference(clausify,[status(thm)],[f_253_2]) ).
fof(f_254_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_254_2,plain,
! [U_938] :
? [U_937] :
( ! [U_936] :
( in(U_936,U_937)
| are_equipotent(U_936,U_937)
| ~ subset(U_936,U_937) )
& ! [U_935] :
( ? [U_934] :
( ! [U_933] :
( in(U_933,U_934)
| ~ subset(U_933,U_935) )
& in(U_934,U_937) )
| ~ in(U_935,U_937) )
& ! [U_932,U_931] :
( in(U_931,U_937)
| ~ subset(U_931,U_932)
| ~ in(U_932,U_937) )
& in(U_938,U_937) ),
inference(variable_rename,[status(thm)],[f_254_1]) ).
fof(f_254_3,plain,
! [U_938] :
( ! [U_936] :
( in(U_936,sK121(U_938))
| are_equipotent(U_936,sK121(U_938))
| ~ subset(U_936,sK121(U_938)) )
& ! [U_935] :
( ? [U_934] :
( ! [U_933] :
( in(U_933,U_934)
| ~ subset(U_933,U_935) )
& in(U_934,sK121(U_938)) )
| ~ in(U_935,sK121(U_938)) )
& ! [U_932,U_931] :
( in(U_931,sK121(U_938))
| ~ subset(U_931,U_932)
| ~ in(U_932,sK121(U_938)) )
& in(U_938,sK121(U_938)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK121]),skolemize(U_937,sK121(U_938))],[f_254_2]) ).
fof(f_254_4,plain,
! [U_938] :
( ! [U_936] :
( in(U_936,sK121(U_938))
| are_equipotent(U_936,sK121(U_938))
| ~ subset(U_936,sK121(U_938)) )
& ! [U_935] :
( ( ! [U_933] :
( in(U_933,sK122(U_938,U_935))
| ~ subset(U_933,U_935) )
& in(sK122(U_938,U_935),sK121(U_938)) )
| ~ in(U_935,sK121(U_938)) )
& ! [U_932,U_931] :
( in(U_931,sK121(U_938))
| ~ subset(U_931,U_932)
| ~ in(U_932,sK121(U_938)) )
& in(U_938,sK121(U_938)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(U_934,sK122(U_938,U_935))],[f_254_3]) ).
cnf(f_254_5,plain,
in(U_938,sK121(U_938)),
inference(clausify,[status(thm)],[f_254_4]) ).
cnf(f_254_6,plain,
( in(U_931,sK121(U_938))
| ~ subset(U_931,U_932)
| ~ in(U_932,sK121(U_938)) ),
inference(clausify,[status(thm)],[f_254_4]) ).
cnf(f_254_7,plain,
( in(sK122(U_938,U_935),sK121(U_938))
| ~ in(U_935,sK121(U_938)) ),
inference(clausify,[status(thm)],[f_254_4]) ).
cnf(f_254_8,plain,
( in(U_933,sK122(U_938,U_935))
| ~ subset(U_933,U_935)
| ~ in(U_935,sK121(U_938)) ),
inference(clausify,[status(thm)],[f_254_4]) ).
cnf(f_254_9,plain,
( in(U_936,sK121(U_938))
| are_equipotent(U_936,sK121(U_938))
| ~ subset(U_936,sK121(U_938)) ),
inference(clausify,[status(thm)],[f_254_4]) ).
fof(f_255_1,plain,
! [A,B,C] :
( B = C
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t9_zfmisc_1]) ).
fof(f_255_2,plain,
! [U_941,U_940,U_939] :
( U_940 = U_939
| singleton(U_941) != unordered_pair(U_940,U_939) ),
inference(variable_rename,[status(thm)],[f_255_1]) ).
cnf(f_255_3,plain,
( U_940 = U_939
| singleton(U_941) != unordered_pair(U_940,U_939) ),
inference(clausify,[status(thm)],[f_255_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_46_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_46_8]) ).
cnf(f_46_9_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_46_9]) ).
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_51_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_51_2]) ).
cnf(f_52_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_52_2]) ).
cnf(f_53_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_53_2]) ).
cnf(f_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_61_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_61_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_64_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_64_2]) ).
cnf(f_66_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_66_2]) ).
cnf(f_67_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_67_2]) ).
cnf(f_69_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_69_2]) ).
cnf(f_70_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_70_2]) ).
cnf(f_79_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_79_2]) ).
cnf(f_80_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_80_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( unordered_pair(Eq_x_0,Eq_x_1) = unordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( set_union2(Eq_x_0,Eq_x_1) = set_union2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( set_intersection2(Eq_x_0,Eq_x_1) = set_intersection2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( identity_relation(Eq_x_0) = identity_relation(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( ordered_pair(Eq_x_0,Eq_x_1) = ordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( relation_dom_restriction(Eq_x_0,Eq_x_1) = relation_dom_restriction(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( relation_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_11,axiom,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,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_13,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_14,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_15,axiom,
( unordered_triple(Eq_x_0,Eq_x_1,Eq_x_2) = unordered_triple(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_16,axiom,
( succ(Eq_x_0) = succ(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( set_meet(Eq_x_0) = set_meet(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,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_21,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_22,axiom,
( union(Eq_x_0) = union(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,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_24,axiom,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,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_26,axiom,
( relation_field(Eq_x_0) = relation_field(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_27,axiom,
( relation_inverse(Eq_x_0) = relation_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,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_29,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_30,axiom,
( function_inverse(Eq_x_0) = function_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_31,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_32,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_33,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_34,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_35,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_36,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_37,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_38,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_39,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_40,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_41,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_42,axiom,
( sK9(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK9(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_43,axiom,
( 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_44,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_45,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_46,axiom,
( sK13(Eq_x_0,Eq_x_1,Eq_x_2) = sK13(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_47,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_48,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_49,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_50,axiom,
( sK17(Eq_x_0,Eq_x_1,Eq_x_2) = sK17(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,
( 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_52,axiom,
( sK19(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK19(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_53,axiom,
( 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_54,axiom,
( sK21(Eq_x_0,Eq_x_1,Eq_x_2) = sK21(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_55,axiom,
( sK22(Eq_x_0,Eq_x_1,Eq_x_2) = sK22(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_56,axiom,
( sK23(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK23(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_57,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_58,axiom,
( sK25(Eq_x_0,Eq_x_1,Eq_x_2) = sK25(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_59,axiom,
( sK26(Eq_x_0,Eq_x_1,Eq_x_2) = sK26(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_60,axiom,
( sK27(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK27(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_61,axiom,
( sK28(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK28(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_62,axiom,
( 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_63,axiom,
( sK30(Eq_x_0,Eq_x_1) = sK30(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,
( sK31(Eq_x_0) = sK31(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_65,axiom,
( sK32(Eq_x_0,Eq_x_1,Eq_x_2) = sK32(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_66,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_67,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_68,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_69,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_70,axiom,
( sK37(Eq_x_0,Eq_x_1) = sK37(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_71,axiom,
( sK38(Eq_x_0) = sK38(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_72,axiom,
( sK39(Eq_x_0,Eq_x_1) = sK39(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_73,axiom,
( sK40(Eq_x_0,Eq_x_1) = sK40(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_74,axiom,
( sK41(Eq_x_0,Eq_x_1) = sK41(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_75,axiom,
( sK42(Eq_x_0,Eq_x_1) = sK42(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_76,axiom,
( sK43(Eq_x_0,Eq_x_1) = sK43(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_77,axiom,
( sK44(Eq_x_0,Eq_x_1) = sK44(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_78,axiom,
( 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_79,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_80,axiom,
( sK47(Eq_x_0,Eq_x_1,Eq_x_2) = sK47(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_81,axiom,
( sK48(Eq_x_0,Eq_x_1,Eq_x_2) = sK48(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_82,axiom,
( sK49(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK49(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_83,axiom,
( sK50(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK50(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_84,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_85,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_86,axiom,
( sK53(Eq_x_0,Eq_x_1,Eq_x_2) = sK53(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_87,axiom,
( sK54(Eq_x_0,Eq_x_1,Eq_x_2) = sK54(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_88,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_89,axiom,
( sK56(Eq_x_0,Eq_x_1) = sK56(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_90,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_91,axiom,
( sK58(Eq_x_0,Eq_x_1,Eq_x_2) = sK58(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_92,axiom,
( sK59(Eq_x_0,Eq_x_1,Eq_x_2) = sK59(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_93,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_94,axiom,
( sK61(Eq_x_0,Eq_x_1) = sK61(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_95,axiom,
( sK62(Eq_x_0,Eq_x_1) = sK62(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_96,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_97,axiom,
( sK64(Eq_x_0,Eq_x_1,Eq_x_2) = sK64(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_98,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_99,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_100,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_101,axiom,
( sK68(Eq_x_0,Eq_x_1,Eq_x_2) = sK68(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_102,axiom,
( sK69(Eq_x_0,Eq_x_1,Eq_x_2) = sK69(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_103,axiom,
( sK70(Eq_x_0,Eq_x_1,Eq_x_2) = sK70(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_104,axiom,
( sK71(Eq_x_0,Eq_x_1) = sK71(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_105,axiom,
( sK72(Eq_x_0,Eq_x_1) = sK72(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_106,axiom,
( sK73(Eq_x_0,Eq_x_1) = sK73(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_107,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_108,axiom,
( sK75(Eq_x_0,Eq_x_1) = sK75(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_109,axiom,
( sK76(Eq_x_0,Eq_x_1) = sK76(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_110,axiom,
( sK77(Eq_x_0,Eq_x_1) = sK77(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_111,axiom,
( sK78(Eq_x_0,Eq_x_1) = sK78(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_112,axiom,
( sK79(Eq_x_0,Eq_x_1) = sK79(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_113,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_114,axiom,
( sK81(Eq_x_0,Eq_x_1) = sK81(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_115,axiom,
( sK82(Eq_x_0) = sK82(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_116,axiom,
( sK83(Eq_x_0) = sK83(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_117,axiom,
( sK84(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK84(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_118,axiom,
( sK85(Eq_x_0,Eq_x_1,Eq_x_2) = sK85(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_119,axiom,
( sK86(Eq_x_0,Eq_x_1,Eq_x_2) = sK86(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_120,axiom,
( sK87(Eq_x_0,Eq_x_1,Eq_x_2) = sK87(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_121,axiom,
( sK88(Eq_x_0,Eq_x_1,Eq_x_2) = sK88(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_122,axiom,
( sK89(Eq_x_0,Eq_x_1,Eq_x_2) = sK89(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_123,axiom,
( sK90(Eq_x_0,Eq_x_1,Eq_x_2) = sK90(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_124,axiom,
( sK91(Eq_x_0) = sK91(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_125,axiom,
( sK92(Eq_x_0,Eq_x_1) = sK92(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_126,axiom,
( sK95(Eq_x_0) = sK95(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_127,axiom,
( sK99(Eq_x_0) = sK99(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_128,axiom,
( sK105(Eq_x_0) = sK105(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_129,axiom,
( sK106(Eq_x_0,Eq_x_1,Eq_x_2) = sK106(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_130,axiom,
( sK107(Eq_x_0,Eq_x_1,Eq_x_2) = sK107(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_131,axiom,
( sK108(Eq_x_0,Eq_x_1) = sK108(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_132,axiom,
( sK109(Eq_x_0,Eq_x_1) = sK109(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_133,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_134,axiom,
( sK111(Eq_x_0,Eq_x_1) = sK111(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_135,axiom,
( sK112(Eq_x_0,Eq_x_1) = sK112(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_136,axiom,
( sK113(Eq_x_0,Eq_x_1) = sK113(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_137,axiom,
( sK114(Eq_x_0,Eq_x_1) = sK114(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_138,axiom,
( sK115(Eq_x_0,Eq_x_1) = sK115(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_139,axiom,
( sK116(Eq_x_0,Eq_x_1) = sK116(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_140,axiom,
( sK117(Eq_x_0) = sK117(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_141,axiom,
( sK118(Eq_x_0) = sK118(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_142,axiom,
( sK119(Eq_x_0,Eq_x_1,Eq_x_2) = sK119(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_143,axiom,
( sK120(Eq_x_0,Eq_x_1) = sK120(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_144,axiom,
( sK121(Eq_x_0) = sK121(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_145,axiom,
( sK122(Eq_x_0,Eq_x_1) = sK122(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_146,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_147,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_148,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_149,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_150,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_151,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_152,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_153,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_154,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_155,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_156,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 : SEU230+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.39 % Computer : n026.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sat Sep 19 23:39:39 UTC 2026
% 0.10/0.40 % CPUTime :
% 83.32/83.67 % SZS status Theorem for theBenchmark
% 83.32/83.67 % SZS output start Proof for theBenchmark
% See solution above
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