%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU173+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 08:58:21 AM UTC 2026
% Result : Theorem 172.15s 172.41s
% Output : Proof 172.43s
% 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(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_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
fof(d1_zfmisc_1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('theBenchmark.p',d1_zfmisc_1) ).
fof(d2_subset_1,axiom,
! [A,B] :
( ( empty(A)
=> ( element(B,A)
<=> empty(B) ) )
& ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) ) ),
file('theBenchmark.p',d2_subset_1) ).
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('theBenchmark.p',d2_tarski) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('theBenchmark.p',d2_xboole_0) ).
fof(d2_zfmisc_1,axiom,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) ) ) ),
file('theBenchmark.p',d2_zfmisc_1) ).
fof(d3_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_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_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(d7_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('theBenchmark.p',d7_xboole_0) ).
fof(d8_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('theBenchmark.p',d8_xboole_0) ).
fof(dt_k1_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_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_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_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_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(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_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(A,B)) ),
file('theBenchmark.p',fc2_xboole_0) ).
fof(fc3_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(B,A)) ),
file('theBenchmark.p',fc3_xboole_0) ).
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(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,conjecture,
! [A,B] :
( ! [C] :
( in(C,A)
=> in(C,B) )
=> element(A,powerset(B)) ),
file('theBenchmark.p',l71_subset_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_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(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t106_zfmisc_1,lemma,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('theBenchmark.p',t106_zfmisc_1) ).
fof(t10_zfmisc_1,lemma,
! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
file('theBenchmark.p',t10_zfmisc_1) ).
fof(t118_zfmisc_1,lemma,
! [A,B,C] :
( subset(A,B)
=> ( subset(cartesian_product2(C,A),cartesian_product2(C,B))
& subset(cartesian_product2(A,C),cartesian_product2(B,C)) ) ),
file('theBenchmark.p',t118_zfmisc_1) ).
fof(t119_zfmisc_1,lemma,
! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('theBenchmark.p',t119_zfmisc_1) ).
fof(t12_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
file('theBenchmark.p',t12_xboole_1) ).
fof(t136_zfmisc_1,lemma,
! [A] :
? [B] :
( ! [C] :
~ ( ~ in(C,B)
& ~ are_equipotent(C,B)
& subset(C,B) )
& ! [C] :
( in(C,B)
=> in(powerset(C),B) )
& ! [C,D] :
( ( subset(D,C)
& in(C,B) )
=> in(D,B) )
& in(A,B) ),
file('theBenchmark.p',t136_zfmisc_1) ).
fof(t17_xboole_1,lemma,
! [A,B] : subset(set_intersection2(A,B),A),
file('theBenchmark.p',t17_xboole_1) ).
fof(t19_xboole_1,lemma,
! [A,B,C] :
( ( subset(A,C)
& subset(A,B) )
=> subset(A,set_intersection2(B,C)) ),
file('theBenchmark.p',t19_xboole_1) ).
fof(t1_boole,axiom,
! [A] : set_union2(A,empty_set) = A,
file('theBenchmark.p',t1_boole) ).
fof(t1_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(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_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(t33_xboole_1,lemma,
! [A,B,C] :
( subset(A,B)
=> subset(set_difference(A,C),set_difference(B,C)) ),
file('theBenchmark.p',t33_xboole_1) ).
fof(t33_zfmisc_1,lemma,
! [A,B,C,D] :
( ordered_pair(A,B) = ordered_pair(C,D)
=> ( B = D
& A = C ) ),
file('theBenchmark.p',t33_zfmisc_1) ).
fof(t36_xboole_1,lemma,
! [A,B] : subset(set_difference(A,B),A),
file('theBenchmark.p',t36_xboole_1) ).
fof(t37_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_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(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_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('theBenchmark.p',t46_zfmisc_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_xboole_0,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t4_xboole_0) ).
fof(t50_subset_1,lemma,
! [A] :
( A != empty_set
=> ! [B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,A)
=> ( ~ in(C,B)
=> in(C,subset_complement(A,B)) ) ) ) ),
file('theBenchmark.p',t50_subset_1) ).
fof(t54_subset_1,lemma,
! [A,B,C] :
( element(C,powerset(A))
=> ~ ( in(B,C)
& in(B,subset_complement(A,C)) ) ),
file('theBenchmark.p',t54_subset_1) ).
fof(t60_xboole_1,lemma,
! [A,B] :
~ ( proper_subset(B,A)
& subset(A,B) ),
file('theBenchmark.p',t60_xboole_1) ).
fof(t63_xboole_1,lemma,
! [A,B,C] :
( ( disjoint(B,C)
& subset(A,B) )
=> disjoint(A,C) ),
file('theBenchmark.p',t63_xboole_1) ).
fof(t65_zfmisc_1,lemma,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('theBenchmark.p',t65_zfmisc_1) ).
fof(t69_enumset1,lemma,
! [A] : unordered_pair(A,A) = singleton(A),
file('theBenchmark.p',t69_enumset1) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t6_zfmisc_1,lemma,
! [A,B] :
( subset(singleton(A),singleton(B))
=> A = B ),
file('theBenchmark.p',t6_zfmisc_1) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t7_xboole_1,lemma,
! [A,B] : subset(A,set_union2(A,B)),
file('theBenchmark.p',t7_xboole_1) ).
fof(t83_xboole_1,lemma,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('theBenchmark.p',t83_xboole_1) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(t8_xboole_1,lemma,
! [A,B,C] :
( ( subset(C,B)
& subset(A,B) )
=> subset(set_union2(A,C),B) ),
file('theBenchmark.p',t8_xboole_1) ).
fof(t8_zfmisc_1,lemma,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ),
file('theBenchmark.p',t8_zfmisc_1) ).
fof(t92_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
file('theBenchmark.p',t92_zfmisc_1) ).
fof(t99_zfmisc_1,lemma,
! [A] : union(powerset(A)) = A,
file('theBenchmark.p',t99_zfmisc_1) ).
fof(t9_tarski,axiom,
! [A] :
? [B] :
( ! [C] :
~ ( ~ in(C,B)
& ~ are_equipotent(C,B)
& subset(C,B) )
& ! [C] :
~ ( ! [D] :
~ ( ! [E] :
( subset(E,C)
=> in(E,D) )
& in(D,B) )
& in(C,B) )
& ! [C,D] :
( ( subset(D,C)
& in(C,B) )
=> in(D,B) )
& in(A,B) ),
file('theBenchmark.p',t9_tarski) ).
fof(t9_zfmisc_1,lemma,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> B = C ),
file('theBenchmark.p',t9_zfmisc_1) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ proper_subset(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(f_2_2,plain,
! [U_3,U_2] :
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_3_2,plain,
! [U_5,U_4] : unordered_pair(U_5,U_4) = unordered_pair(U_4,U_5),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
unordered_pair(U_5,U_4) = unordered_pair(U_4,U_5),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_4_2,plain,
! [U_7,U_6] : set_union2(U_7,U_6) = set_union2(U_6,U_7),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
set_union2(U_7,U_6) = set_union2(U_6,U_7),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_5_2,plain,
! [U_9,U_8] : set_intersection2(U_9,U_8) = set_intersection2(U_8,U_9),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
set_intersection2(U_9,U_8) = set_intersection2(U_8,U_9),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_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_6_2,plain,
! [U_11,U_10] :
( ( U_11 = U_10
| ~ subset(U_10,U_11)
| ~ subset(U_11,U_10) )
& ( ( subset(U_10,U_11)
& subset(U_11,U_10) )
| U_11 != U_10 ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_15,U_13] :
( U_15 = U_13
| ~ subset(U_13,U_15)
| ~ subset(U_15,U_13) )
& ! [U_14,U_12] :
( ( subset(U_12,U_14)
& subset(U_14,U_12) )
| U_14 != U_12 ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( subset(U_14,U_12)
| U_14 != U_12 ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( subset(U_12,U_14)
| U_14 != U_12 ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
( U_15 = U_13
| ~ subset(U_13,U_15)
| ~ subset(U_15,U_13) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_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_7_2,plain,
! [U_19,U_18] :
( ( U_18 = singleton(U_19)
| ? [U_17] :
( ( ~ in(U_17,U_18)
& U_17 = U_19 )
| ( U_17 != U_19
& in(U_17,U_18) ) ) )
& ( ! [U_16] :
( ( in(U_16,U_18)
| U_16 != U_19 )
& ( U_16 = U_19
| ~ in(U_16,U_18) ) )
| U_18 != singleton(U_19) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_27,U_25] :
( U_25 = singleton(U_27)
| ? [U_23] :
( ~ in(U_23,U_25)
& U_23 = U_27 )
| ? [U_22] :
( U_22 != U_27
& in(U_22,U_25) ) )
& ! [U_26,U_24] :
( ( ! [U_21] :
( in(U_21,U_24)
| U_21 != U_26 )
& ! [U_20] :
( U_20 = U_26
| ~ in(U_20,U_24) ) )
| U_24 != singleton(U_26) ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
( ! [U_27,U_25] :
( U_25 = singleton(U_27)
| ? [U_23] :
( ~ in(U_23,U_25)
& U_23 = U_27 )
| ( sK1(U_27,U_25) != U_27
& in(sK1(U_27,U_25),U_25) ) )
& ! [U_26,U_24] :
( ( ! [U_21] :
( in(U_21,U_24)
| U_21 != U_26 )
& ! [U_20] :
( U_20 = U_26
| ~ in(U_20,U_24) ) )
| U_24 != singleton(U_26) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_22,sK1(U_27,U_25))],[f_7_3]) ).
fof(f_7_5,plain,
( ! [U_27,U_25] :
( U_25 = singleton(U_27)
| ( ~ in(sK2(U_27,U_25),U_25)
& sK2(U_27,U_25) = U_27 )
| ( sK1(U_27,U_25) != U_27
& in(sK1(U_27,U_25),U_25) ) )
& ! [U_26,U_24] :
( ( ! [U_21] :
( in(U_21,U_24)
| U_21 != U_26 )
& ! [U_20] :
( U_20 = U_26
| ~ in(U_20,U_24) ) )
| U_24 != singleton(U_26) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_23,sK2(U_27,U_25))],[f_7_4]) ).
cnf(f_7_6,plain,
( U_20 = U_26
| ~ in(U_20,U_24)
| U_24 != singleton(U_26) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_7,plain,
( in(U_21,U_24)
| U_21 != U_26
| U_24 != singleton(U_26) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_8,plain,
( sK2(U_27,U_25) = U_27
| in(sK1(U_27,U_25),U_25)
| U_25 = singleton(U_27) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_9,plain,
( ~ in(sK2(U_27,U_25),U_25)
| in(sK1(U_27,U_25),U_25)
| U_25 = singleton(U_27) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_10,plain,
( sK2(U_27,U_25) = U_27
| sK1(U_27,U_25) != U_27
| U_25 = singleton(U_27) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_11,plain,
( ~ in(sK2(U_27,U_25),U_25)
| sK1(U_27,U_25) != U_27
| U_25 = singleton(U_27) ),
inference(clausify,[status(thm)],[f_7_5]) ).
fof(f_8_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_8_2,plain,
! [U_30] :
( ( U_30 = empty_set
| ? [U_29] : in(U_29,U_30) )
& ( ! [U_28] : ~ in(U_28,U_30)
| U_30 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_32] :
( U_32 = empty_set
| ? [U_29] : in(U_29,U_32) )
& ! [U_31] :
( ! [U_28] : ~ in(U_28,U_31)
| U_31 != empty_set ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
( ! [U_32] :
( U_32 = empty_set
| in(sK3(U_32),U_32) )
& ! [U_31] :
( ! [U_28] : ~ in(U_28,U_31)
| U_31 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_29,sK3(U_32))],[f_8_3]) ).
cnf(f_8_5,plain,
( ~ in(U_28,U_31)
| U_31 != empty_set ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_6,plain,
( U_32 = empty_set
| in(sK3(U_32),U_32) ),
inference(clausify,[status(thm)],[f_8_4]) ).
fof(f_9_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_9_2,plain,
! [U_36,U_35] :
( ( U_35 = powerset(U_36)
| ? [U_34] :
( ( ~ in(U_34,U_35)
& subset(U_34,U_36) )
| ( ~ subset(U_34,U_36)
& in(U_34,U_35) ) ) )
& ( ! [U_33] :
( ( in(U_33,U_35)
| ~ subset(U_33,U_36) )
& ( subset(U_33,U_36)
| ~ in(U_33,U_35) ) )
| U_35 != powerset(U_36) ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_44,U_42] :
( U_42 = powerset(U_44)
| ? [U_40] :
( ~ in(U_40,U_42)
& subset(U_40,U_44) )
| ? [U_39] :
( ~ subset(U_39,U_44)
& in(U_39,U_42) ) )
& ! [U_43,U_41] :
( ( ! [U_38] :
( in(U_38,U_41)
| ~ subset(U_38,U_43) )
& ! [U_37] :
( subset(U_37,U_43)
| ~ in(U_37,U_41) ) )
| U_41 != powerset(U_43) ) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
fof(f_9_4,plain,
( ! [U_44,U_42] :
( U_42 = powerset(U_44)
| ? [U_40] :
( ~ in(U_40,U_42)
& subset(U_40,U_44) )
| ( ~ subset(sK4(U_44,U_42),U_44)
& in(sK4(U_44,U_42),U_42) ) )
& ! [U_43,U_41] :
( ( ! [U_38] :
( in(U_38,U_41)
| ~ subset(U_38,U_43) )
& ! [U_37] :
( subset(U_37,U_43)
| ~ in(U_37,U_41) ) )
| U_41 != powerset(U_43) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_39,sK4(U_44,U_42))],[f_9_3]) ).
fof(f_9_5,plain,
( ! [U_44,U_42] :
( U_42 = powerset(U_44)
| ( ~ in(sK5(U_44,U_42),U_42)
& subset(sK5(U_44,U_42),U_44) )
| ( ~ subset(sK4(U_44,U_42),U_44)
& in(sK4(U_44,U_42),U_42) ) )
& ! [U_43,U_41] :
( ( ! [U_38] :
( in(U_38,U_41)
| ~ subset(U_38,U_43) )
& ! [U_37] :
( subset(U_37,U_43)
| ~ in(U_37,U_41) ) )
| U_41 != powerset(U_43) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_40,sK5(U_44,U_42))],[f_9_4]) ).
cnf(f_9_6,plain,
( subset(U_37,U_43)
| ~ in(U_37,U_41)
| U_41 != powerset(U_43) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_7,plain,
( in(U_38,U_41)
| ~ subset(U_38,U_43)
| U_41 != powerset(U_43) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_8,plain,
( subset(sK5(U_44,U_42),U_44)
| in(sK4(U_44,U_42),U_42)
| U_42 = powerset(U_44) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_9,plain,
( ~ in(sK5(U_44,U_42),U_42)
| in(sK4(U_44,U_42),U_42)
| U_42 = powerset(U_44) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_10,plain,
( subset(sK5(U_44,U_42),U_44)
| ~ subset(sK4(U_44,U_42),U_44)
| U_42 = powerset(U_44) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_11,plain,
( ~ in(sK5(U_44,U_42),U_42)
| ~ subset(sK4(U_44,U_42),U_44)
| U_42 = powerset(U_44) ),
inference(clausify,[status(thm)],[f_9_5]) ).
fof(f_10_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_10_2,plain,
! [U_46,U_45] :
( ( ( ( element(U_45,U_46)
| ~ empty(U_45) )
& ( empty(U_45)
| ~ element(U_45,U_46) ) )
| ~ empty(U_46) )
& ( ( ( element(U_45,U_46)
| ~ in(U_45,U_46) )
& ( in(U_45,U_46)
| ~ element(U_45,U_46) ) )
| empty(U_46) ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_54] :
( ( ! [U_52] :
( element(U_52,U_54)
| ~ empty(U_52) )
& ! [U_51] :
( empty(U_51)
| ~ element(U_51,U_54) ) )
| ~ empty(U_54) )
& ! [U_53] :
( ( ! [U_50] :
( element(U_50,U_53)
| ~ in(U_50,U_53) )
& ! [U_49] :
( in(U_49,U_53)
| ~ element(U_49,U_53) ) )
| empty(U_53) ) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( in(U_49,U_53)
| ~ element(U_49,U_53)
| empty(U_53) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_5,plain,
( element(U_50,U_53)
| ~ in(U_50,U_53)
| empty(U_53) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_6,plain,
( empty(U_51)
| ~ element(U_51,U_54)
| ~ empty(U_54) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_7,plain,
( element(U_52,U_54)
| ~ empty(U_52)
| ~ empty(U_54) ),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_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_11_2,plain,
! [U_59,U_58,U_57] :
( ( U_57 = unordered_pair(U_59,U_58)
| ? [U_56] :
( ( ~ in(U_56,U_57)
& ( U_56 = U_58
| U_56 = U_59 ) )
| ( U_56 != U_58
& U_56 != U_59
& in(U_56,U_57) ) ) )
& ( ! [U_55] :
( ( in(U_55,U_57)
| ( U_55 != U_58
& U_55 != U_59 ) )
& ( U_55 = U_58
| U_55 = U_59
| ~ in(U_55,U_57) ) )
| U_57 != unordered_pair(U_59,U_58) ) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
( ! [U_69,U_67,U_65] :
( U_65 = unordered_pair(U_69,U_67)
| ? [U_63] :
( ~ in(U_63,U_65)
& ( U_63 = U_67
| U_63 = U_69 ) )
| ? [U_62] :
( U_62 != U_67
& U_62 != U_69
& in(U_62,U_65) ) )
& ! [U_68,U_66,U_64] :
( ( ! [U_61] :
( in(U_61,U_64)
| ( U_61 != U_66
& U_61 != U_68 ) )
& ! [U_60] :
( U_60 = U_66
| U_60 = U_68
| ~ in(U_60,U_64) ) )
| U_64 != unordered_pair(U_68,U_66) ) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
fof(f_11_4,plain,
( ! [U_69,U_67,U_65] :
( U_65 = unordered_pair(U_69,U_67)
| ? [U_63] :
( ~ in(U_63,U_65)
& ( U_63 = U_67
| U_63 = U_69 ) )
| ( sK6(U_69,U_67,U_65) != U_67
& sK6(U_69,U_67,U_65) != U_69
& in(sK6(U_69,U_67,U_65),U_65) ) )
& ! [U_68,U_66,U_64] :
( ( ! [U_61] :
( in(U_61,U_64)
| ( U_61 != U_66
& U_61 != U_68 ) )
& ! [U_60] :
( U_60 = U_66
| U_60 = U_68
| ~ in(U_60,U_64) ) )
| U_64 != unordered_pair(U_68,U_66) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_62,sK6(U_69,U_67,U_65))],[f_11_3]) ).
fof(f_11_5,plain,
( ! [U_69,U_67,U_65] :
( U_65 = unordered_pair(U_69,U_67)
| ( ~ in(sK7(U_69,U_67,U_65),U_65)
& ( sK7(U_69,U_67,U_65) = U_67
| sK7(U_69,U_67,U_65) = U_69 ) )
| ( sK6(U_69,U_67,U_65) != U_67
& sK6(U_69,U_67,U_65) != U_69
& in(sK6(U_69,U_67,U_65),U_65) ) )
& ! [U_68,U_66,U_64] :
( ( ! [U_61] :
( in(U_61,U_64)
| ( U_61 != U_66
& U_61 != U_68 ) )
& ! [U_60] :
( U_60 = U_66
| U_60 = U_68
| ~ in(U_60,U_64) ) )
| U_64 != unordered_pair(U_68,U_66) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_63,sK7(U_69,U_67,U_65))],[f_11_4]) ).
cnf(f_11_6,plain,
( U_60 = U_66
| U_60 = U_68
| ~ in(U_60,U_64)
| U_64 != unordered_pair(U_68,U_66) ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_7,plain,
( U_61 != U_68
| in(U_61,U_64)
| U_64 != unordered_pair(U_68,U_66) ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_8,plain,
( U_61 != U_66
| in(U_61,U_64)
| U_64 != unordered_pair(U_68,U_66) ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_9,plain,
( sK7(U_69,U_67,U_65) = U_67
| sK7(U_69,U_67,U_65) = U_69
| in(sK6(U_69,U_67,U_65),U_65)
| U_65 = unordered_pair(U_69,U_67) ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_10,plain,
( ~ in(sK7(U_69,U_67,U_65),U_65)
| in(sK6(U_69,U_67,U_65),U_65)
| U_65 = unordered_pair(U_69,U_67) ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_11,plain,
( sK6(U_69,U_67,U_65) != U_69
| sK7(U_69,U_67,U_65) = U_67
| sK7(U_69,U_67,U_65) = U_69
| U_65 = unordered_pair(U_69,U_67) ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_12,plain,
( sK6(U_69,U_67,U_65) != U_67
| sK7(U_69,U_67,U_65) = U_67
| sK7(U_69,U_67,U_65) = U_69
| U_65 = unordered_pair(U_69,U_67) ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_13,plain,
( sK6(U_69,U_67,U_65) != U_69
| ~ in(sK7(U_69,U_67,U_65),U_65)
| U_65 = unordered_pair(U_69,U_67) ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_14,plain,
( sK6(U_69,U_67,U_65) != U_67
| ~ in(sK7(U_69,U_67,U_65),U_65)
| U_65 = unordered_pair(U_69,U_67) ),
inference(clausify,[status(thm)],[f_11_5]) ).
fof(f_12_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_12_2,plain,
! [U_74,U_73,U_72] :
( ( U_72 = set_union2(U_74,U_73)
| ? [U_71] :
( ( ~ in(U_71,U_72)
& ( in(U_71,U_73)
| in(U_71,U_74) ) )
| ( ~ in(U_71,U_73)
& ~ in(U_71,U_74)
& in(U_71,U_72) ) ) )
& ( ! [U_70] :
( ( in(U_70,U_72)
| ( ~ in(U_70,U_73)
& ~ in(U_70,U_74) ) )
& ( in(U_70,U_73)
| in(U_70,U_74)
| ~ in(U_70,U_72) ) )
| U_72 != set_union2(U_74,U_73) ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_84,U_82,U_80] :
( U_80 = set_union2(U_84,U_82)
| ? [U_78] :
( ~ in(U_78,U_80)
& ( in(U_78,U_82)
| in(U_78,U_84) ) )
| ? [U_77] :
( ~ in(U_77,U_82)
& ~ in(U_77,U_84)
& in(U_77,U_80) ) )
& ! [U_83,U_81,U_79] :
( ( ! [U_76] :
( in(U_76,U_79)
| ( ~ in(U_76,U_81)
& ~ in(U_76,U_83) ) )
& ! [U_75] :
( in(U_75,U_81)
| in(U_75,U_83)
| ~ in(U_75,U_79) ) )
| U_79 != set_union2(U_83,U_81) ) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
( ! [U_84,U_82,U_80] :
( U_80 = set_union2(U_84,U_82)
| ? [U_78] :
( ~ in(U_78,U_80)
& ( in(U_78,U_82)
| in(U_78,U_84) ) )
| ( ~ in(sK8(U_84,U_82,U_80),U_82)
& ~ in(sK8(U_84,U_82,U_80),U_84)
& in(sK8(U_84,U_82,U_80),U_80) ) )
& ! [U_83,U_81,U_79] :
( ( ! [U_76] :
( in(U_76,U_79)
| ( ~ in(U_76,U_81)
& ~ in(U_76,U_83) ) )
& ! [U_75] :
( in(U_75,U_81)
| in(U_75,U_83)
| ~ in(U_75,U_79) ) )
| U_79 != set_union2(U_83,U_81) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_77,sK8(U_84,U_82,U_80))],[f_12_3]) ).
fof(f_12_5,plain,
( ! [U_84,U_82,U_80] :
( U_80 = set_union2(U_84,U_82)
| ( ~ in(sK9(U_84,U_82,U_80),U_80)
& ( in(sK9(U_84,U_82,U_80),U_82)
| in(sK9(U_84,U_82,U_80),U_84) ) )
| ( ~ in(sK8(U_84,U_82,U_80),U_82)
& ~ in(sK8(U_84,U_82,U_80),U_84)
& in(sK8(U_84,U_82,U_80),U_80) ) )
& ! [U_83,U_81,U_79] :
( ( ! [U_76] :
( in(U_76,U_79)
| ( ~ in(U_76,U_81)
& ~ in(U_76,U_83) ) )
& ! [U_75] :
( in(U_75,U_81)
| in(U_75,U_83)
| ~ in(U_75,U_79) ) )
| U_79 != set_union2(U_83,U_81) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_78,sK9(U_84,U_82,U_80))],[f_12_4]) ).
cnf(f_12_6,plain,
( in(U_75,U_81)
| in(U_75,U_83)
| ~ in(U_75,U_79)
| U_79 != set_union2(U_83,U_81) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_7,plain,
( ~ in(U_76,U_83)
| in(U_76,U_79)
| U_79 != set_union2(U_83,U_81) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_8,plain,
( ~ in(U_76,U_81)
| in(U_76,U_79)
| U_79 != set_union2(U_83,U_81) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_9,plain,
( in(sK9(U_84,U_82,U_80),U_82)
| in(sK9(U_84,U_82,U_80),U_84)
| in(sK8(U_84,U_82,U_80),U_80)
| U_80 = set_union2(U_84,U_82) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_10,plain,
( ~ in(sK9(U_84,U_82,U_80),U_80)
| in(sK8(U_84,U_82,U_80),U_80)
| U_80 = set_union2(U_84,U_82) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_11,plain,
( ~ in(sK8(U_84,U_82,U_80),U_84)
| in(sK9(U_84,U_82,U_80),U_82)
| in(sK9(U_84,U_82,U_80),U_84)
| U_80 = set_union2(U_84,U_82) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_12,plain,
( ~ in(sK8(U_84,U_82,U_80),U_82)
| in(sK9(U_84,U_82,U_80),U_82)
| in(sK9(U_84,U_82,U_80),U_84)
| U_80 = set_union2(U_84,U_82) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_13,plain,
( ~ in(sK8(U_84,U_82,U_80),U_84)
| ~ in(sK9(U_84,U_82,U_80),U_80)
| U_80 = set_union2(U_84,U_82) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_14,plain,
( ~ in(sK8(U_84,U_82,U_80),U_82)
| ~ in(sK9(U_84,U_82,U_80),U_80)
| U_80 = set_union2(U_84,U_82) ),
inference(clausify,[status(thm)],[f_12_5]) ).
fof(f_13_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_13_2,plain,
! [U_97,U_96,U_95] :
( ( U_95 = cartesian_product2(U_97,U_96)
| ? [U_94] :
( ( ~ in(U_94,U_95)
& ? [U_93,U_92] :
( U_94 = ordered_pair(U_93,U_92)
& in(U_92,U_96)
& in(U_93,U_97) ) )
| ( ! [U_91,U_90] :
( U_94 != ordered_pair(U_91,U_90)
| ~ in(U_90,U_96)
| ~ in(U_91,U_97) )
& in(U_94,U_95) ) ) )
& ( ! [U_89] :
( ( in(U_89,U_95)
| ! [U_88,U_87] :
( U_89 != ordered_pair(U_88,U_87)
| ~ in(U_87,U_96)
| ~ in(U_88,U_97) ) )
& ( ? [U_86,U_85] :
( U_89 = ordered_pair(U_86,U_85)
& in(U_85,U_96)
& in(U_86,U_97) )
| ~ in(U_89,U_95) ) )
| U_95 != cartesian_product2(U_97,U_96) ) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_107,U_105,U_103] :
( U_103 = cartesian_product2(U_107,U_105)
| ? [U_101] :
( ~ in(U_101,U_103)
& ? [U_93] :
( ? [U_92] :
( U_101 = ordered_pair(U_93,U_92)
& in(U_92,U_105) )
& in(U_93,U_107) ) )
| ? [U_100] :
( ! [U_91] :
( ! [U_90] :
( U_100 != ordered_pair(U_91,U_90)
| ~ in(U_90,U_105) )
| ~ in(U_91,U_107) )
& in(U_100,U_103) ) )
& ! [U_106,U_104,U_102] :
( ( ! [U_99] :
( in(U_99,U_102)
| ! [U_88] :
( ! [U_87] :
( U_99 != ordered_pair(U_88,U_87)
| ~ in(U_87,U_104) )
| ~ in(U_88,U_106) ) )
& ! [U_98] :
( ? [U_86] :
( ? [U_85] :
( U_98 = ordered_pair(U_86,U_85)
& in(U_85,U_104) )
& in(U_86,U_106) )
| ~ in(U_98,U_102) ) )
| U_102 != cartesian_product2(U_106,U_104) ) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
fof(f_13_4,plain,
( ! [U_107,U_105,U_103] :
( U_103 = cartesian_product2(U_107,U_105)
| ? [U_101] :
( ~ in(U_101,U_103)
& ? [U_93] :
( ? [U_92] :
( U_101 = ordered_pair(U_93,U_92)
& in(U_92,U_105) )
& in(U_93,U_107) ) )
| ? [U_100] :
( ! [U_91] :
( ! [U_90] :
( U_100 != ordered_pair(U_91,U_90)
| ~ in(U_90,U_105) )
| ~ in(U_91,U_107) )
& in(U_100,U_103) ) )
& ! [U_106,U_104,U_102] :
( ( ! [U_99] :
( in(U_99,U_102)
| ! [U_88] :
( ! [U_87] :
( U_99 != ordered_pair(U_88,U_87)
| ~ in(U_87,U_104) )
| ~ in(U_88,U_106) ) )
& ! [U_98] :
( ( ? [U_85] :
( U_98 = ordered_pair(sK10(U_106,U_104,U_102,U_98),U_85)
& in(U_85,U_104) )
& in(sK10(U_106,U_104,U_102,U_98),U_106) )
| ~ in(U_98,U_102) ) )
| U_102 != cartesian_product2(U_106,U_104) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_86,sK10(U_106,U_104,U_102,U_98))],[f_13_3]) ).
fof(f_13_5,plain,
( ! [U_107,U_105,U_103] :
( U_103 = cartesian_product2(U_107,U_105)
| ? [U_101] :
( ~ in(U_101,U_103)
& ? [U_93] :
( ? [U_92] :
( U_101 = ordered_pair(U_93,U_92)
& in(U_92,U_105) )
& in(U_93,U_107) ) )
| ? [U_100] :
( ! [U_91] :
( ! [U_90] :
( U_100 != ordered_pair(U_91,U_90)
| ~ in(U_90,U_105) )
| ~ in(U_91,U_107) )
& in(U_100,U_103) ) )
& ! [U_106,U_104,U_102] :
( ( ! [U_99] :
( in(U_99,U_102)
| ! [U_88] :
( ! [U_87] :
( U_99 != ordered_pair(U_88,U_87)
| ~ in(U_87,U_104) )
| ~ in(U_88,U_106) ) )
& ! [U_98] :
( ( U_98 = ordered_pair(sK10(U_106,U_104,U_102,U_98),sK11(U_106,U_104,U_102,U_98))
& in(sK11(U_106,U_104,U_102,U_98),U_104)
& in(sK10(U_106,U_104,U_102,U_98),U_106) )
| ~ in(U_98,U_102) ) )
| U_102 != cartesian_product2(U_106,U_104) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_85,sK11(U_106,U_104,U_102,U_98))],[f_13_4]) ).
fof(f_13_6,plain,
( ! [U_107,U_105,U_103] :
( U_103 = cartesian_product2(U_107,U_105)
| ? [U_101] :
( ~ in(U_101,U_103)
& ? [U_93] :
( ? [U_92] :
( U_101 = ordered_pair(U_93,U_92)
& in(U_92,U_105) )
& in(U_93,U_107) ) )
| ( ! [U_91] :
( ! [U_90] :
( sK12(U_107,U_105,U_103) != ordered_pair(U_91,U_90)
| ~ in(U_90,U_105) )
| ~ in(U_91,U_107) )
& in(sK12(U_107,U_105,U_103),U_103) ) )
& ! [U_106,U_104,U_102] :
( ( ! [U_99] :
( in(U_99,U_102)
| ! [U_88] :
( ! [U_87] :
( U_99 != ordered_pair(U_88,U_87)
| ~ in(U_87,U_104) )
| ~ in(U_88,U_106) ) )
& ! [U_98] :
( ( U_98 = ordered_pair(sK10(U_106,U_104,U_102,U_98),sK11(U_106,U_104,U_102,U_98))
& in(sK11(U_106,U_104,U_102,U_98),U_104)
& in(sK10(U_106,U_104,U_102,U_98),U_106) )
| ~ in(U_98,U_102) ) )
| U_102 != cartesian_product2(U_106,U_104) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_100,sK12(U_107,U_105,U_103))],[f_13_5]) ).
fof(f_13_7,plain,
( ! [U_107,U_105,U_103] :
( U_103 = cartesian_product2(U_107,U_105)
| ( ~ in(sK13(U_107,U_105,U_103),U_103)
& ? [U_93] :
( ? [U_92] :
( sK13(U_107,U_105,U_103) = ordered_pair(U_93,U_92)
& in(U_92,U_105) )
& in(U_93,U_107) ) )
| ( ! [U_91] :
( ! [U_90] :
( sK12(U_107,U_105,U_103) != ordered_pair(U_91,U_90)
| ~ in(U_90,U_105) )
| ~ in(U_91,U_107) )
& in(sK12(U_107,U_105,U_103),U_103) ) )
& ! [U_106,U_104,U_102] :
( ( ! [U_99] :
( in(U_99,U_102)
| ! [U_88] :
( ! [U_87] :
( U_99 != ordered_pair(U_88,U_87)
| ~ in(U_87,U_104) )
| ~ in(U_88,U_106) ) )
& ! [U_98] :
( ( U_98 = ordered_pair(sK10(U_106,U_104,U_102,U_98),sK11(U_106,U_104,U_102,U_98))
& in(sK11(U_106,U_104,U_102,U_98),U_104)
& in(sK10(U_106,U_104,U_102,U_98),U_106) )
| ~ in(U_98,U_102) ) )
| U_102 != cartesian_product2(U_106,U_104) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_101,sK13(U_107,U_105,U_103))],[f_13_6]) ).
fof(f_13_8,plain,
( ! [U_107,U_105,U_103] :
( U_103 = cartesian_product2(U_107,U_105)
| ( ~ in(sK13(U_107,U_105,U_103),U_103)
& ? [U_92] :
( sK13(U_107,U_105,U_103) = ordered_pair(sK14(U_107,U_105,U_103),U_92)
& in(U_92,U_105) )
& in(sK14(U_107,U_105,U_103),U_107) )
| ( ! [U_91] :
( ! [U_90] :
( sK12(U_107,U_105,U_103) != ordered_pair(U_91,U_90)
| ~ in(U_90,U_105) )
| ~ in(U_91,U_107) )
& in(sK12(U_107,U_105,U_103),U_103) ) )
& ! [U_106,U_104,U_102] :
( ( ! [U_99] :
( in(U_99,U_102)
| ! [U_88] :
( ! [U_87] :
( U_99 != ordered_pair(U_88,U_87)
| ~ in(U_87,U_104) )
| ~ in(U_88,U_106) ) )
& ! [U_98] :
( ( U_98 = ordered_pair(sK10(U_106,U_104,U_102,U_98),sK11(U_106,U_104,U_102,U_98))
& in(sK11(U_106,U_104,U_102,U_98),U_104)
& in(sK10(U_106,U_104,U_102,U_98),U_106) )
| ~ in(U_98,U_102) ) )
| U_102 != cartesian_product2(U_106,U_104) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_93,sK14(U_107,U_105,U_103))],[f_13_7]) ).
fof(f_13_9,plain,
( ! [U_107,U_105,U_103] :
( U_103 = cartesian_product2(U_107,U_105)
| ( ~ in(sK13(U_107,U_105,U_103),U_103)
& sK13(U_107,U_105,U_103) = ordered_pair(sK14(U_107,U_105,U_103),sK15(U_107,U_105,U_103))
& in(sK15(U_107,U_105,U_103),U_105)
& in(sK14(U_107,U_105,U_103),U_107) )
| ( ! [U_91] :
( ! [U_90] :
( sK12(U_107,U_105,U_103) != ordered_pair(U_91,U_90)
| ~ in(U_90,U_105) )
| ~ in(U_91,U_107) )
& in(sK12(U_107,U_105,U_103),U_103) ) )
& ! [U_106,U_104,U_102] :
( ( ! [U_99] :
( in(U_99,U_102)
| ! [U_88] :
( ! [U_87] :
( U_99 != ordered_pair(U_88,U_87)
| ~ in(U_87,U_104) )
| ~ in(U_88,U_106) ) )
& ! [U_98] :
( ( U_98 = ordered_pair(sK10(U_106,U_104,U_102,U_98),sK11(U_106,U_104,U_102,U_98))
& in(sK11(U_106,U_104,U_102,U_98),U_104)
& in(sK10(U_106,U_104,U_102,U_98),U_106) )
| ~ in(U_98,U_102) ) )
| U_102 != cartesian_product2(U_106,U_104) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_92,sK15(U_107,U_105,U_103))],[f_13_8]) ).
cnf(f_13_10,plain,
( in(sK10(U_106,U_104,U_102,U_98),U_106)
| ~ in(U_98,U_102)
| U_102 != cartesian_product2(U_106,U_104) ),
inference(clausify,[status(thm)],[f_13_9]) ).
cnf(f_13_11,plain,
( in(sK11(U_106,U_104,U_102,U_98),U_104)
| ~ in(U_98,U_102)
| U_102 != cartesian_product2(U_106,U_104) ),
inference(clausify,[status(thm)],[f_13_9]) ).
cnf(f_13_12,plain,
( U_98 = ordered_pair(sK10(U_106,U_104,U_102,U_98),sK11(U_106,U_104,U_102,U_98))
| ~ in(U_98,U_102)
| U_102 != cartesian_product2(U_106,U_104) ),
inference(clausify,[status(thm)],[f_13_9]) ).
cnf(f_13_13,plain,
( in(U_99,U_102)
| U_99 != ordered_pair(U_88,U_87)
| ~ in(U_87,U_104)
| ~ in(U_88,U_106)
| U_102 != cartesian_product2(U_106,U_104) ),
inference(clausify,[status(thm)],[f_13_9]) ).
cnf(f_13_14,plain,
( in(sK14(U_107,U_105,U_103),U_107)
| in(sK12(U_107,U_105,U_103),U_103)
| U_103 = cartesian_product2(U_107,U_105) ),
inference(clausify,[status(thm)],[f_13_9]) ).
cnf(f_13_15,plain,
( in(sK15(U_107,U_105,U_103),U_105)
| in(sK12(U_107,U_105,U_103),U_103)
| U_103 = cartesian_product2(U_107,U_105) ),
inference(clausify,[status(thm)],[f_13_9]) ).
cnf(f_13_16,plain,
( sK13(U_107,U_105,U_103) = ordered_pair(sK14(U_107,U_105,U_103),sK15(U_107,U_105,U_103))
| in(sK12(U_107,U_105,U_103),U_103)
| U_103 = cartesian_product2(U_107,U_105) ),
inference(clausify,[status(thm)],[f_13_9]) ).
cnf(f_13_17,plain,
( ~ in(sK13(U_107,U_105,U_103),U_103)
| in(sK12(U_107,U_105,U_103),U_103)
| U_103 = cartesian_product2(U_107,U_105) ),
inference(clausify,[status(thm)],[f_13_9]) ).
cnf(f_13_18,plain,
( in(sK14(U_107,U_105,U_103),U_107)
| sK12(U_107,U_105,U_103) != ordered_pair(U_91,U_90)
| ~ in(U_90,U_105)
| ~ in(U_91,U_107)
| U_103 = cartesian_product2(U_107,U_105) ),
inference(clausify,[status(thm)],[f_13_9]) ).
cnf(f_13_19,plain,
( in(sK15(U_107,U_105,U_103),U_105)
| sK12(U_107,U_105,U_103) != ordered_pair(U_91,U_90)
| ~ in(U_90,U_105)
| ~ in(U_91,U_107)
| U_103 = cartesian_product2(U_107,U_105) ),
inference(clausify,[status(thm)],[f_13_9]) ).
cnf(f_13_20,plain,
( sK13(U_107,U_105,U_103) = ordered_pair(sK14(U_107,U_105,U_103),sK15(U_107,U_105,U_103))
| sK12(U_107,U_105,U_103) != ordered_pair(U_91,U_90)
| ~ in(U_90,U_105)
| ~ in(U_91,U_107)
| U_103 = cartesian_product2(U_107,U_105) ),
inference(clausify,[status(thm)],[f_13_9]) ).
cnf(f_13_21,plain,
( ~ in(sK13(U_107,U_105,U_103),U_103)
| sK12(U_107,U_105,U_103) != ordered_pair(U_91,U_90)
| ~ in(U_90,U_105)
| ~ in(U_91,U_107)
| U_103 = cartesian_product2(U_107,U_105) ),
inference(clausify,[status(thm)],[f_13_9]) ).
fof(f_14_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_14_2,plain,
! [U_111,U_110] :
( ( subset(U_111,U_110)
| ? [U_109] :
( ~ in(U_109,U_110)
& in(U_109,U_111) ) )
& ( ! [U_108] :
( in(U_108,U_110)
| ~ in(U_108,U_111) )
| ~ subset(U_111,U_110) ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_115,U_113] :
( subset(U_115,U_113)
| ? [U_109] :
( ~ in(U_109,U_113)
& in(U_109,U_115) ) )
& ! [U_114,U_112] :
( ! [U_108] :
( in(U_108,U_112)
| ~ in(U_108,U_114) )
| ~ subset(U_114,U_112) ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
fof(f_14_4,plain,
( ! [U_115,U_113] :
( subset(U_115,U_113)
| ( ~ in(sK16(U_115,U_113),U_113)
& in(sK16(U_115,U_113),U_115) ) )
& ! [U_114,U_112] :
( ! [U_108] :
( in(U_108,U_112)
| ~ in(U_108,U_114) )
| ~ subset(U_114,U_112) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_109,sK16(U_115,U_113))],[f_14_3]) ).
cnf(f_14_5,plain,
( in(U_108,U_112)
| ~ in(U_108,U_114)
| ~ subset(U_114,U_112) ),
inference(clausify,[status(thm)],[f_14_4]) ).
cnf(f_14_6,plain,
( in(sK16(U_115,U_113),U_115)
| subset(U_115,U_113) ),
inference(clausify,[status(thm)],[f_14_4]) ).
cnf(f_14_7,plain,
( ~ in(sK16(U_115,U_113),U_113)
| subset(U_115,U_113) ),
inference(clausify,[status(thm)],[f_14_4]) ).
fof(f_15_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_15_2,plain,
! [U_120,U_119,U_118] :
( ( U_118 = set_intersection2(U_120,U_119)
| ? [U_117] :
( ( ~ in(U_117,U_118)
& in(U_117,U_119)
& in(U_117,U_120) )
| ( ( ~ in(U_117,U_119)
| ~ in(U_117,U_120) )
& in(U_117,U_118) ) ) )
& ( ! [U_116] :
( ( in(U_116,U_118)
| ~ in(U_116,U_119)
| ~ in(U_116,U_120) )
& ( ( in(U_116,U_119)
& in(U_116,U_120) )
| ~ in(U_116,U_118) ) )
| U_118 != set_intersection2(U_120,U_119) ) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ! [U_130,U_128,U_126] :
( U_126 = set_intersection2(U_130,U_128)
| ? [U_124] :
( ~ in(U_124,U_126)
& in(U_124,U_128)
& in(U_124,U_130) )
| ? [U_123] :
( ( ~ in(U_123,U_128)
| ~ in(U_123,U_130) )
& in(U_123,U_126) ) )
& ! [U_129,U_127,U_125] :
( ( ! [U_122] :
( in(U_122,U_125)
| ~ in(U_122,U_127)
| ~ in(U_122,U_129) )
& ! [U_121] :
( ( in(U_121,U_127)
& in(U_121,U_129) )
| ~ in(U_121,U_125) ) )
| U_125 != set_intersection2(U_129,U_127) ) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
fof(f_15_4,plain,
( ! [U_130,U_128,U_126] :
( U_126 = set_intersection2(U_130,U_128)
| ? [U_124] :
( ~ in(U_124,U_126)
& in(U_124,U_128)
& in(U_124,U_130) )
| ( ( ~ in(sK17(U_130,U_128,U_126),U_128)
| ~ in(sK17(U_130,U_128,U_126),U_130) )
& in(sK17(U_130,U_128,U_126),U_126) ) )
& ! [U_129,U_127,U_125] :
( ( ! [U_122] :
( in(U_122,U_125)
| ~ in(U_122,U_127)
| ~ in(U_122,U_129) )
& ! [U_121] :
( ( in(U_121,U_127)
& in(U_121,U_129) )
| ~ in(U_121,U_125) ) )
| U_125 != set_intersection2(U_129,U_127) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_123,sK17(U_130,U_128,U_126))],[f_15_3]) ).
fof(f_15_5,plain,
( ! [U_130,U_128,U_126] :
( U_126 = set_intersection2(U_130,U_128)
| ( ~ in(sK18(U_130,U_128,U_126),U_126)
& in(sK18(U_130,U_128,U_126),U_128)
& in(sK18(U_130,U_128,U_126),U_130) )
| ( ( ~ in(sK17(U_130,U_128,U_126),U_128)
| ~ in(sK17(U_130,U_128,U_126),U_130) )
& in(sK17(U_130,U_128,U_126),U_126) ) )
& ! [U_129,U_127,U_125] :
( ( ! [U_122] :
( in(U_122,U_125)
| ~ in(U_122,U_127)
| ~ in(U_122,U_129) )
& ! [U_121] :
( ( in(U_121,U_127)
& in(U_121,U_129) )
| ~ in(U_121,U_125) ) )
| U_125 != set_intersection2(U_129,U_127) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_124,sK18(U_130,U_128,U_126))],[f_15_4]) ).
cnf(f_15_6,plain,
( in(U_121,U_129)
| ~ in(U_121,U_125)
| U_125 != set_intersection2(U_129,U_127) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_7,plain,
( in(U_121,U_127)
| ~ in(U_121,U_125)
| U_125 != set_intersection2(U_129,U_127) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_8,plain,
( in(U_122,U_125)
| ~ in(U_122,U_127)
| ~ in(U_122,U_129)
| U_125 != set_intersection2(U_129,U_127) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_9,plain,
( in(sK18(U_130,U_128,U_126),U_130)
| in(sK17(U_130,U_128,U_126),U_126)
| U_126 = set_intersection2(U_130,U_128) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_10,plain,
( in(sK18(U_130,U_128,U_126),U_128)
| in(sK17(U_130,U_128,U_126),U_126)
| U_126 = set_intersection2(U_130,U_128) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_11,plain,
( ~ in(sK18(U_130,U_128,U_126),U_126)
| in(sK17(U_130,U_128,U_126),U_126)
| U_126 = set_intersection2(U_130,U_128) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_12,plain,
( in(sK18(U_130,U_128,U_126),U_130)
| ~ in(sK17(U_130,U_128,U_126),U_128)
| ~ in(sK17(U_130,U_128,U_126),U_130)
| U_126 = set_intersection2(U_130,U_128) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_13,plain,
( in(sK18(U_130,U_128,U_126),U_128)
| ~ in(sK17(U_130,U_128,U_126),U_128)
| ~ in(sK17(U_130,U_128,U_126),U_130)
| U_126 = set_intersection2(U_130,U_128) ),
inference(clausify,[status(thm)],[f_15_5]) ).
cnf(f_15_14,plain,
( ~ in(sK18(U_130,U_128,U_126),U_126)
| ~ in(sK17(U_130,U_128,U_126),U_128)
| ~ in(sK17(U_130,U_128,U_126),U_130)
| U_126 = set_intersection2(U_130,U_128) ),
inference(clausify,[status(thm)],[f_15_5]) ).
fof(f_16_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_16_2,plain,
! [U_138,U_137] :
( ( U_137 = union(U_138)
| ? [U_136] :
( ( ~ in(U_136,U_137)
& ? [U_135] :
( in(U_135,U_138)
& in(U_136,U_135) ) )
| ( ! [U_134] :
( ~ in(U_134,U_138)
| ~ in(U_136,U_134) )
& in(U_136,U_137) ) ) )
& ( ! [U_133] :
( ( in(U_133,U_137)
| ! [U_132] :
( ~ in(U_132,U_138)
| ~ in(U_133,U_132) ) )
& ( ? [U_131] :
( in(U_131,U_138)
& in(U_133,U_131) )
| ~ in(U_133,U_137) ) )
| U_137 != union(U_138) ) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( ! [U_146,U_144] :
( U_144 = union(U_146)
| ? [U_142] :
( ~ in(U_142,U_144)
& ? [U_135] :
( in(U_135,U_146)
& in(U_142,U_135) ) )
| ? [U_141] :
( ! [U_134] :
( ~ in(U_134,U_146)
| ~ in(U_141,U_134) )
& in(U_141,U_144) ) )
& ! [U_145,U_143] :
( ( ! [U_140] :
( in(U_140,U_143)
| ! [U_132] :
( ~ in(U_132,U_145)
| ~ in(U_140,U_132) ) )
& ! [U_139] :
( ? [U_131] :
( in(U_131,U_145)
& in(U_139,U_131) )
| ~ in(U_139,U_143) ) )
| U_143 != union(U_145) ) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
fof(f_16_4,plain,
( ! [U_146,U_144] :
( U_144 = union(U_146)
| ? [U_142] :
( ~ in(U_142,U_144)
& ? [U_135] :
( in(U_135,U_146)
& in(U_142,U_135) ) )
| ? [U_141] :
( ! [U_134] :
( ~ in(U_134,U_146)
| ~ in(U_141,U_134) )
& in(U_141,U_144) ) )
& ! [U_145,U_143] :
( ( ! [U_140] :
( in(U_140,U_143)
| ! [U_132] :
( ~ in(U_132,U_145)
| ~ in(U_140,U_132) ) )
& ! [U_139] :
( ( in(sK19(U_145,U_143,U_139),U_145)
& in(U_139,sK19(U_145,U_143,U_139)) )
| ~ in(U_139,U_143) ) )
| U_143 != union(U_145) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_131,sK19(U_145,U_143,U_139))],[f_16_3]) ).
fof(f_16_5,plain,
( ! [U_146,U_144] :
( U_144 = union(U_146)
| ? [U_142] :
( ~ in(U_142,U_144)
& ? [U_135] :
( in(U_135,U_146)
& in(U_142,U_135) ) )
| ( ! [U_134] :
( ~ in(U_134,U_146)
| ~ in(sK20(U_146,U_144),U_134) )
& in(sK20(U_146,U_144),U_144) ) )
& ! [U_145,U_143] :
( ( ! [U_140] :
( in(U_140,U_143)
| ! [U_132] :
( ~ in(U_132,U_145)
| ~ in(U_140,U_132) ) )
& ! [U_139] :
( ( in(sK19(U_145,U_143,U_139),U_145)
& in(U_139,sK19(U_145,U_143,U_139)) )
| ~ in(U_139,U_143) ) )
| U_143 != union(U_145) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_141,sK20(U_146,U_144))],[f_16_4]) ).
fof(f_16_6,plain,
( ! [U_146,U_144] :
( U_144 = union(U_146)
| ( ~ in(sK21(U_146,U_144),U_144)
& ? [U_135] :
( in(U_135,U_146)
& in(sK21(U_146,U_144),U_135) ) )
| ( ! [U_134] :
( ~ in(U_134,U_146)
| ~ in(sK20(U_146,U_144),U_134) )
& in(sK20(U_146,U_144),U_144) ) )
& ! [U_145,U_143] :
( ( ! [U_140] :
( in(U_140,U_143)
| ! [U_132] :
( ~ in(U_132,U_145)
| ~ in(U_140,U_132) ) )
& ! [U_139] :
( ( in(sK19(U_145,U_143,U_139),U_145)
& in(U_139,sK19(U_145,U_143,U_139)) )
| ~ in(U_139,U_143) ) )
| U_143 != union(U_145) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_142,sK21(U_146,U_144))],[f_16_5]) ).
fof(f_16_7,plain,
( ! [U_146,U_144] :
( U_144 = union(U_146)
| ( ~ in(sK21(U_146,U_144),U_144)
& in(sK22(U_146,U_144),U_146)
& in(sK21(U_146,U_144),sK22(U_146,U_144)) )
| ( ! [U_134] :
( ~ in(U_134,U_146)
| ~ in(sK20(U_146,U_144),U_134) )
& in(sK20(U_146,U_144),U_144) ) )
& ! [U_145,U_143] :
( ( ! [U_140] :
( in(U_140,U_143)
| ! [U_132] :
( ~ in(U_132,U_145)
| ~ in(U_140,U_132) ) )
& ! [U_139] :
( ( in(sK19(U_145,U_143,U_139),U_145)
& in(U_139,sK19(U_145,U_143,U_139)) )
| ~ in(U_139,U_143) ) )
| U_143 != union(U_145) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_135,sK22(U_146,U_144))],[f_16_6]) ).
cnf(f_16_8,plain,
( in(U_139,sK19(U_145,U_143,U_139))
| ~ in(U_139,U_143)
| U_143 != union(U_145) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_9,plain,
( in(sK19(U_145,U_143,U_139),U_145)
| ~ in(U_139,U_143)
| U_143 != union(U_145) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_10,plain,
( in(U_140,U_143)
| ~ in(U_132,U_145)
| ~ in(U_140,U_132)
| U_143 != union(U_145) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_11,plain,
( in(sK21(U_146,U_144),sK22(U_146,U_144))
| in(sK20(U_146,U_144),U_144)
| U_144 = union(U_146) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_12,plain,
( in(sK22(U_146,U_144),U_146)
| in(sK20(U_146,U_144),U_144)
| U_144 = union(U_146) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_13,plain,
( ~ in(sK21(U_146,U_144),U_144)
| in(sK20(U_146,U_144),U_144)
| U_144 = union(U_146) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_14,plain,
( in(sK21(U_146,U_144),sK22(U_146,U_144))
| ~ in(U_134,U_146)
| ~ in(sK20(U_146,U_144),U_134)
| U_144 = union(U_146) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_15,plain,
( in(sK22(U_146,U_144),U_146)
| ~ in(U_134,U_146)
| ~ in(sK20(U_146,U_144),U_134)
| U_144 = union(U_146) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_16,plain,
( ~ in(sK21(U_146,U_144),U_144)
| ~ in(U_134,U_146)
| ~ in(sK20(U_146,U_144),U_134)
| U_144 = union(U_146) ),
inference(clausify,[status(thm)],[f_16_7]) ).
fof(f_17_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_17_2,plain,
! [U_151,U_150,U_149] :
( ( U_149 = set_difference(U_151,U_150)
| ? [U_148] :
( ( ~ in(U_148,U_149)
& ~ in(U_148,U_150)
& in(U_148,U_151) )
| ( ( in(U_148,U_150)
| ~ in(U_148,U_151) )
& in(U_148,U_149) ) ) )
& ( ! [U_147] :
( ( in(U_147,U_149)
| in(U_147,U_150)
| ~ in(U_147,U_151) )
& ( ( ~ in(U_147,U_150)
& in(U_147,U_151) )
| ~ in(U_147,U_149) ) )
| U_149 != set_difference(U_151,U_150) ) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( ! [U_161,U_159,U_157] :
( U_157 = set_difference(U_161,U_159)
| ? [U_155] :
( ~ in(U_155,U_157)
& ~ in(U_155,U_159)
& in(U_155,U_161) )
| ? [U_154] :
( ( in(U_154,U_159)
| ~ in(U_154,U_161) )
& in(U_154,U_157) ) )
& ! [U_160,U_158,U_156] :
( ( ! [U_153] :
( in(U_153,U_156)
| in(U_153,U_158)
| ~ in(U_153,U_160) )
& ! [U_152] :
( ( ~ in(U_152,U_158)
& in(U_152,U_160) )
| ~ in(U_152,U_156) ) )
| U_156 != set_difference(U_160,U_158) ) ),
inference(miniscope,[status(thm)],[f_17_2]) ).
fof(f_17_4,plain,
( ! [U_161,U_159,U_157] :
( U_157 = set_difference(U_161,U_159)
| ? [U_155] :
( ~ in(U_155,U_157)
& ~ in(U_155,U_159)
& in(U_155,U_161) )
| ( ( in(sK23(U_161,U_159,U_157),U_159)
| ~ in(sK23(U_161,U_159,U_157),U_161) )
& in(sK23(U_161,U_159,U_157),U_157) ) )
& ! [U_160,U_158,U_156] :
( ( ! [U_153] :
( in(U_153,U_156)
| in(U_153,U_158)
| ~ in(U_153,U_160) )
& ! [U_152] :
( ( ~ in(U_152,U_158)
& in(U_152,U_160) )
| ~ in(U_152,U_156) ) )
| U_156 != set_difference(U_160,U_158) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_154,sK23(U_161,U_159,U_157))],[f_17_3]) ).
fof(f_17_5,plain,
( ! [U_161,U_159,U_157] :
( U_157 = set_difference(U_161,U_159)
| ( ~ in(sK24(U_161,U_159,U_157),U_157)
& ~ in(sK24(U_161,U_159,U_157),U_159)
& in(sK24(U_161,U_159,U_157),U_161) )
| ( ( in(sK23(U_161,U_159,U_157),U_159)
| ~ in(sK23(U_161,U_159,U_157),U_161) )
& in(sK23(U_161,U_159,U_157),U_157) ) )
& ! [U_160,U_158,U_156] :
( ( ! [U_153] :
( in(U_153,U_156)
| in(U_153,U_158)
| ~ in(U_153,U_160) )
& ! [U_152] :
( ( ~ in(U_152,U_158)
& in(U_152,U_160) )
| ~ in(U_152,U_156) ) )
| U_156 != set_difference(U_160,U_158) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_155,sK24(U_161,U_159,U_157))],[f_17_4]) ).
cnf(f_17_6,plain,
( in(U_152,U_160)
| ~ in(U_152,U_156)
| U_156 != set_difference(U_160,U_158) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_7,plain,
( ~ in(U_152,U_158)
| ~ in(U_152,U_156)
| U_156 != set_difference(U_160,U_158) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_8,plain,
( in(U_153,U_156)
| in(U_153,U_158)
| ~ in(U_153,U_160)
| U_156 != set_difference(U_160,U_158) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_9,plain,
( in(sK24(U_161,U_159,U_157),U_161)
| in(sK23(U_161,U_159,U_157),U_157)
| U_157 = set_difference(U_161,U_159) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_10,plain,
( ~ in(sK24(U_161,U_159,U_157),U_159)
| in(sK23(U_161,U_159,U_157),U_157)
| U_157 = set_difference(U_161,U_159) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_11,plain,
( ~ in(sK24(U_161,U_159,U_157),U_157)
| in(sK23(U_161,U_159,U_157),U_157)
| U_157 = set_difference(U_161,U_159) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_12,plain,
( in(sK24(U_161,U_159,U_157),U_161)
| in(sK23(U_161,U_159,U_157),U_159)
| ~ in(sK23(U_161,U_159,U_157),U_161)
| U_157 = set_difference(U_161,U_159) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_13,plain,
( ~ in(sK24(U_161,U_159,U_157),U_159)
| in(sK23(U_161,U_159,U_157),U_159)
| ~ in(sK23(U_161,U_159,U_157),U_161)
| U_157 = set_difference(U_161,U_159) ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_14,plain,
( ~ in(sK24(U_161,U_159,U_157),U_157)
| in(sK23(U_161,U_159,U_157),U_159)
| ~ in(sK23(U_161,U_159,U_157),U_161)
| U_157 = set_difference(U_161,U_159) ),
inference(clausify,[status(thm)],[f_17_5]) ).
fof(f_18_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_18_2,plain,
! [U_163,U_162] :
( subset_complement(U_163,U_162) = set_difference(U_163,U_162)
| ~ element(U_162,powerset(U_163)) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( subset_complement(U_163,U_162) = set_difference(U_163,U_162)
| ~ element(U_162,powerset(U_163)) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_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_19_2,plain,
! [U_165,U_164] : ordered_pair(U_165,U_164) = unordered_pair(unordered_pair(U_165,U_164),singleton(U_165)),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
ordered_pair(U_165,U_164) = unordered_pair(unordered_pair(U_165,U_164),singleton(U_165)),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_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_20_2,plain,
! [U_167,U_166] :
( ( disjoint(U_167,U_166)
| set_intersection2(U_167,U_166) != empty_set )
& ( set_intersection2(U_167,U_166) = empty_set
| ~ disjoint(U_167,U_166) ) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( ! [U_171,U_169] :
( disjoint(U_171,U_169)
| set_intersection2(U_171,U_169) != empty_set )
& ! [U_170,U_168] :
( set_intersection2(U_170,U_168) = empty_set
| ~ disjoint(U_170,U_168) ) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
cnf(f_20_4,plain,
( set_intersection2(U_170,U_168) = empty_set
| ~ disjoint(U_170,U_168) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_5,plain,
( disjoint(U_171,U_169)
| set_intersection2(U_171,U_169) != empty_set ),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_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_21_2,plain,
! [U_173,U_172] :
( ( proper_subset(U_173,U_172)
| U_173 = U_172
| ~ subset(U_173,U_172) )
& ( ( U_173 != U_172
& subset(U_173,U_172) )
| ~ proper_subset(U_173,U_172) ) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( ! [U_177,U_175] :
( proper_subset(U_177,U_175)
| U_177 = U_175
| ~ subset(U_177,U_175) )
& ! [U_176,U_174] :
( ( U_176 != U_174
& subset(U_176,U_174) )
| ~ proper_subset(U_176,U_174) ) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
( subset(U_176,U_174)
| ~ proper_subset(U_176,U_174) ),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
( U_176 != U_174
| ~ proper_subset(U_176,U_174) ),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_6,plain,
( proper_subset(U_177,U_175)
| U_177 = U_175
| ~ subset(U_177,U_175) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
cnf(f_22_2,plain,
$true,
inference(clausify,[status(thm)],[f_22_1]) ).
fof(f_23_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_23_2,plain,
$true,
inference(clausify,[status(thm)],[f_23_1]) ).
fof(f_24_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_24_2,plain,
$true,
inference(clausify,[status(thm)],[f_24_1]) ).
fof(f_25_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
cnf(f_25_2,plain,
$true,
inference(clausify,[status(thm)],[f_25_1]) ).
fof(f_26_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
cnf(f_26_2,plain,
$true,
inference(clausify,[status(thm)],[f_26_1]) ).
fof(f_27_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
cnf(f_27_2,plain,
$true,
inference(clausify,[status(thm)],[f_27_1]) ).
fof(f_28_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_28_2,plain,
! [U_179,U_178] :
( element(subset_complement(U_179,U_178),powerset(U_179))
| ~ element(U_178,powerset(U_179)) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( element(subset_complement(U_179,U_178),powerset(U_179))
| ~ element(U_178,powerset(U_179)) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_tarski]) ).
cnf(f_29_2,plain,
$true,
inference(clausify,[status(thm)],[f_29_1]) ).
fof(f_30_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
cnf(f_30_2,plain,
$true,
inference(clausify,[status(thm)],[f_30_1]) ).
fof(f_31_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
cnf(f_31_2,plain,
$true,
inference(clausify,[status(thm)],[f_31_1]) ).
fof(f_32_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
cnf(f_32_2,plain,
$true,
inference(clausify,[status(thm)],[f_32_1]) ).
fof(f_33_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_33_2,plain,
$true,
inference(clausify,[status(thm)],[f_33_1]) ).
fof(f_34_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_34_2,plain,
! [U_181] :
? [U_180] : element(U_180,U_181),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_181] : element(sK25(U_181),U_181),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_180,sK25(U_181))],[f_34_2]) ).
cnf(f_34_4,plain,
element(sK25(U_181),U_181),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_35_2,plain,
! [U_182] : ~ empty(powerset(U_182)),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
~ empty(powerset(U_182)),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_36_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_36_1]) ).
fof(f_37_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_37_2,plain,
! [U_184,U_183] : ~ empty(ordered_pair(U_184,U_183)),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
~ empty(ordered_pair(U_184,U_183)),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_38_2,plain,
! [U_186,U_185] :
( ~ empty(set_union2(U_186,U_185))
| empty(U_186) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_186] :
( ! [U_185] : ~ empty(set_union2(U_186,U_185))
| empty(U_186) ),
inference(miniscope,[status(thm)],[f_38_2]) ).
cnf(f_38_4,plain,
( ~ empty(set_union2(U_186,U_185))
| empty(U_186) ),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_39_2,plain,
! [U_188,U_187] :
( ~ empty(set_union2(U_187,U_188))
| empty(U_188) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_188] :
( ! [U_187] : ~ empty(set_union2(U_187,U_188))
| empty(U_188) ),
inference(miniscope,[status(thm)],[f_39_2]) ).
cnf(f_39_4,plain,
( ~ empty(set_union2(U_187,U_188))
| empty(U_188) ),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_40_2,plain,
! [U_190,U_189] : set_union2(U_190,U_190) = U_190,
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_190] : set_union2(U_190,U_190) = U_190,
inference(miniscope,[status(thm)],[f_40_2]) ).
cnf(f_40_4,plain,
set_union2(U_190,U_190) = U_190,
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_41_2,plain,
! [U_192,U_191] : set_intersection2(U_192,U_192) = U_192,
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_192] : set_intersection2(U_192,U_192) = U_192,
inference(miniscope,[status(thm)],[f_41_2]) ).
cnf(f_41_4,plain,
set_intersection2(U_192,U_192) = U_192,
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_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_42_2,plain,
! [U_194,U_193] :
( subset_complement(U_194,subset_complement(U_194,U_193)) = U_193
| ~ element(U_193,powerset(U_194)) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,plain,
( subset_complement(U_194,subset_complement(U_194,U_193)) = U_193
| ~ element(U_193,powerset(U_194)) ),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_1,plain,
! [A,B] : ~ proper_subset(A,A),
inference(fof_nnf,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(f_43_2,plain,
! [U_196,U_195] : ~ proper_subset(U_196,U_196),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_196] : ~ proper_subset(U_196,U_196),
inference(miniscope,[status(thm)],[f_43_2]) ).
cnf(f_43_4,plain,
~ proper_subset(U_196,U_196),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
! [A] : singleton(A) != empty_set,
inference(fof_nnf,[status(thm)],[l1_zfmisc_1]) ).
fof(f_44_2,plain,
! [U_197] : singleton(U_197) != empty_set,
inference(variable_rename,[status(thm)],[f_44_1]) ).
cnf(f_44_3,plain,
singleton(U_197) != empty_set,
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l23_zfmisc_1]) ).
fof(f_45_2,plain,
! [U_199,U_198] :
( set_union2(singleton(U_199),U_198) = U_198
| ~ in(U_199,U_198) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
cnf(f_45_3,plain,
( set_union2(singleton(U_199),U_198) = U_198
| ~ in(U_199,U_198) ),
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_1,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(fof_nnf,[status(thm)],[l25_zfmisc_1]) ).
fof(f_46_2,plain,
! [U_201,U_200] :
( ~ in(U_201,U_200)
| ~ disjoint(singleton(U_201),U_200) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
cnf(f_46_3,plain,
( ~ in(U_201,U_200)
| ~ disjoint(singleton(U_201),U_200) ),
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_1,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(fof_nnf,[status(thm)],[l28_zfmisc_1]) ).
fof(f_47_2,plain,
! [U_203,U_202] :
( disjoint(singleton(U_203),U_202)
| in(U_203,U_202) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
cnf(f_47_3,plain,
( disjoint(singleton(U_203),U_202)
| in(U_203,U_202) ),
inference(clausify,[status(thm)],[f_47_2]) ).
fof(f_48_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_48_2,plain,
! [U_205,U_204] :
( ( subset(singleton(U_205),U_204)
| ~ in(U_205,U_204) )
& ( in(U_205,U_204)
| ~ subset(singleton(U_205),U_204) ) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
( ! [U_209,U_207] :
( subset(singleton(U_209),U_207)
| ~ in(U_209,U_207) )
& ! [U_208,U_206] :
( in(U_208,U_206)
| ~ subset(singleton(U_208),U_206) ) ),
inference(miniscope,[status(thm)],[f_48_2]) ).
cnf(f_48_4,plain,
( in(U_208,U_206)
| ~ subset(singleton(U_208),U_206) ),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_5,plain,
( subset(singleton(U_209),U_207)
| ~ in(U_209,U_207) ),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_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_49_2,plain,
! [U_211,U_210] :
( ( set_difference(U_211,U_210) = empty_set
| ~ subset(U_211,U_210) )
& ( subset(U_211,U_210)
| set_difference(U_211,U_210) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
( ! [U_215,U_213] :
( set_difference(U_215,U_213) = empty_set
| ~ subset(U_215,U_213) )
& ! [U_214,U_212] :
( subset(U_214,U_212)
| set_difference(U_214,U_212) != empty_set ) ),
inference(miniscope,[status(thm)],[f_49_2]) ).
cnf(f_49_4,plain,
( subset(U_214,U_212)
| set_difference(U_214,U_212) != empty_set ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_5,plain,
( set_difference(U_215,U_213) = empty_set
| ~ subset(U_215,U_213) ),
inference(clausify,[status(thm)],[f_49_3]) ).
fof(f_50_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_50_2,plain,
! [U_218,U_217] :
( ! [U_216] :
( in(U_216,U_218)
| ~ in(U_216,U_217) )
| ~ element(U_217,powerset(U_218)) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
cnf(f_50_3,plain,
( in(U_216,U_218)
| ~ in(U_216,U_217)
| ~ element(U_217,powerset(U_218)) ),
inference(clausify,[status(thm)],[f_50_2]) ).
fof(f_51_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_51_2,plain,
! [U_221,U_220,U_219] :
( subset(U_221,set_difference(U_220,singleton(U_219)))
| in(U_219,U_221)
| ~ subset(U_221,U_220) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
! [U_221,U_220] :
( ! [U_219] :
( subset(U_221,set_difference(U_220,singleton(U_219)))
| in(U_219,U_221) )
| ~ subset(U_221,U_220) ),
inference(miniscope,[status(thm)],[f_51_2]) ).
cnf(f_51_4,plain,
( subset(U_221,set_difference(U_220,singleton(U_219)))
| in(U_219,U_221)
| ~ subset(U_221,U_220) ),
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_52_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_52_2,plain,
! [U_223,U_222] :
( ( subset(U_223,singleton(U_222))
| ( U_223 != singleton(U_222)
& U_223 != empty_set ) )
& ( U_223 = singleton(U_222)
| U_223 = empty_set
| ~ subset(U_223,singleton(U_222)) ) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
( ! [U_227,U_225] :
( subset(U_227,singleton(U_225))
| ( U_227 != singleton(U_225)
& U_227 != empty_set ) )
& ! [U_226,U_224] :
( U_226 = singleton(U_224)
| U_226 = empty_set
| ~ subset(U_226,singleton(U_224)) ) ),
inference(miniscope,[status(thm)],[f_52_2]) ).
cnf(f_52_4,plain,
( U_226 = singleton(U_224)
| U_226 = empty_set
| ~ subset(U_226,singleton(U_224)) ),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_5,plain,
( U_227 != empty_set
| subset(U_227,singleton(U_225)) ),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_6,plain,
( U_227 != singleton(U_225)
| subset(U_227,singleton(U_225)) ),
inference(clausify,[status(thm)],[f_52_3]) ).
fof(f_53_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l50_zfmisc_1]) ).
fof(f_53_2,plain,
! [U_229,U_228] :
( subset(U_229,union(U_228))
| ~ in(U_229,U_228) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
cnf(f_53_3,plain,
( subset(U_229,union(U_228))
| ~ in(U_229,U_228) ),
inference(clausify,[status(thm)],[f_53_2]) ).
fof(f_54_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_54_2,plain,
! [U_233,U_232,U_231,U_230] :
( ( in(ordered_pair(U_233,U_232),cartesian_product2(U_231,U_230))
| ~ in(U_232,U_230)
| ~ in(U_233,U_231) )
& ( ( in(U_232,U_230)
& in(U_233,U_231) )
| ~ in(ordered_pair(U_233,U_232),cartesian_product2(U_231,U_230)) ) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
( ! [U_241,U_239,U_237,U_235] :
( in(ordered_pair(U_241,U_239),cartesian_product2(U_237,U_235))
| ~ in(U_239,U_235)
| ~ in(U_241,U_237) )
& ! [U_240,U_238,U_236,U_234] :
( ( in(U_238,U_234)
& in(U_240,U_236) )
| ~ in(ordered_pair(U_240,U_238),cartesian_product2(U_236,U_234)) ) ),
inference(miniscope,[status(thm)],[f_54_2]) ).
cnf(f_54_4,plain,
( in(U_240,U_236)
| ~ in(ordered_pair(U_240,U_238),cartesian_product2(U_236,U_234)) ),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_5,plain,
( in(U_238,U_234)
| ~ in(ordered_pair(U_240,U_238),cartesian_product2(U_236,U_234)) ),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_54_6,plain,
( in(ordered_pair(U_241,U_239),cartesian_product2(U_237,U_235))
| ~ in(U_239,U_235)
| ~ in(U_241,U_237) ),
inference(clausify,[status(thm)],[f_54_3]) ).
fof(f_55_1,negated_conjecture,
~ ! [A,B] :
( ! [C] :
( in(C,A)
=> in(C,B) )
=> element(A,powerset(B)) ),
inference(negate,[status(cth)],[l71_subset_1]) ).
fof(f_55_2,negated_conjecture,
? [A,B] :
( ~ element(A,powerset(B))
& ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(fof_nnf,[status(thm)],[f_55_1]) ).
fof(f_55_3,negated_conjecture,
? [U_244,U_243] :
( ~ element(U_244,powerset(U_243))
& ! [U_242] :
( in(U_242,U_243)
| ~ in(U_242,U_244) ) ),
inference(variable_rename,[status(thm)],[f_55_2]) ).
fof(f_55_4,negated_conjecture,
? [U_243] :
( ~ element(sK26,powerset(U_243))
& ! [U_242] :
( in(U_242,U_243)
| ~ in(U_242,sK26) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_244,sK26)],[f_55_3]) ).
fof(f_55_5,negated_conjecture,
( ~ element(sK26,powerset(sK27))
& ! [U_242] :
( in(U_242,sK27)
| ~ in(U_242,sK26) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_243,sK27)],[f_55_4]) ).
cnf(f_55_6,negated_conjecture,
( in(U_242,sK27)
| ~ in(U_242,sK26) ),
inference(clausify,[status(thm)],[f_55_5]) ).
cnf(f_55_7,negated_conjecture,
~ element(sK26,powerset(sK27)),
inference(clausify,[status(thm)],[f_55_5]) ).
fof(f_56_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_56_2,plain,
! [U_246] :
( ? [U_245] :
( ~ empty(U_245)
& element(U_245,powerset(U_246)) )
| empty(U_246) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
! [U_246] :
( ( ~ empty(sK28(U_246))
& element(sK28(U_246),powerset(U_246)) )
| empty(U_246) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_245,sK28(U_246))],[f_56_2]) ).
cnf(f_56_4,plain,
( element(sK28(U_246),powerset(U_246))
| empty(U_246) ),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_5,plain,
( ~ empty(sK28(U_246))
| empty(U_246) ),
inference(clausify,[status(thm)],[f_56_3]) ).
fof(f_57_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_57_2,plain,
? [U_247] : empty(U_247),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
empty(sK29),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_247,sK29)],[f_57_2]) ).
cnf(f_57_4,plain,
empty(sK29),
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_58_2,plain,
! [U_249] :
? [U_248] :
( empty(U_248)
& element(U_248,powerset(U_249)) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
! [U_249] :
( empty(sK30(U_249))
& element(sK30(U_249),powerset(U_249)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_248,sK30(U_249))],[f_58_2]) ).
cnf(f_58_4,plain,
element(sK30(U_249),powerset(U_249)),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_5,plain,
empty(sK30(U_249)),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_59_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_59_2,plain,
? [U_250] : ~ empty(U_250),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
~ empty(sK31),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_250,sK31)],[f_59_2]) ).
cnf(f_59_4,plain,
~ empty(sK31),
inference(clausify,[status(thm)],[f_59_3]) ).
fof(f_60_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_60_2,plain,
! [U_252,U_251] : subset(U_252,U_252),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
! [U_252] : subset(U_252,U_252),
inference(miniscope,[status(thm)],[f_60_2]) ).
cnf(f_60_4,plain,
subset(U_252,U_252),
inference(clausify,[status(thm)],[f_60_3]) ).
fof(f_61_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_61_2,plain,
! [U_254,U_253] :
( disjoint(U_253,U_254)
| ~ disjoint(U_254,U_253) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
cnf(f_61_3,plain,
( disjoint(U_253,U_254)
| ~ disjoint(U_254,U_253) ),
inference(clausify,[status(thm)],[f_61_2]) ).
fof(f_62_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_62_2,plain,
! [U_258,U_257,U_256,U_255] :
( ( in(ordered_pair(U_258,U_257),cartesian_product2(U_256,U_255))
| ~ in(U_257,U_255)
| ~ in(U_258,U_256) )
& ( ( in(U_257,U_255)
& in(U_258,U_256) )
| ~ in(ordered_pair(U_258,U_257),cartesian_product2(U_256,U_255)) ) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
( ! [U_266,U_264,U_262,U_260] :
( in(ordered_pair(U_266,U_264),cartesian_product2(U_262,U_260))
| ~ in(U_264,U_260)
| ~ in(U_266,U_262) )
& ! [U_265,U_263,U_261,U_259] :
( ( in(U_263,U_259)
& in(U_265,U_261) )
| ~ in(ordered_pair(U_265,U_263),cartesian_product2(U_261,U_259)) ) ),
inference(miniscope,[status(thm)],[f_62_2]) ).
cnf(f_62_4,plain,
( in(U_265,U_261)
| ~ in(ordered_pair(U_265,U_263),cartesian_product2(U_261,U_259)) ),
inference(clausify,[status(thm)],[f_62_3]) ).
cnf(f_62_5,plain,
( in(U_263,U_259)
| ~ in(ordered_pair(U_265,U_263),cartesian_product2(U_261,U_259)) ),
inference(clausify,[status(thm)],[f_62_3]) ).
cnf(f_62_6,plain,
( in(ordered_pair(U_266,U_264),cartesian_product2(U_262,U_260))
| ~ in(U_264,U_260)
| ~ in(U_266,U_262) ),
inference(clausify,[status(thm)],[f_62_3]) ).
fof(f_63_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_63_2,plain,
! [U_270,U_269,U_268,U_267] :
( U_270 = U_267
| U_270 = U_268
| unordered_pair(U_270,U_269) != unordered_pair(U_268,U_267) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
! [U_270,U_269,U_268] :
( ! [U_267] :
( U_270 = U_267
| unordered_pair(U_270,U_269) != unordered_pair(U_268,U_267) )
| U_270 = U_268 ),
inference(miniscope,[status(thm)],[f_63_2]) ).
cnf(f_63_4,plain,
( U_270 = U_267
| unordered_pair(U_270,U_269) != unordered_pair(U_268,U_267)
| U_270 = U_268 ),
inference(clausify,[status(thm)],[f_63_3]) ).
fof(f_64_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_64_2,plain,
! [U_273,U_272,U_271] :
( ( subset(cartesian_product2(U_271,U_273),cartesian_product2(U_271,U_272))
& subset(cartesian_product2(U_273,U_271),cartesian_product2(U_272,U_271)) )
| ~ subset(U_273,U_272) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
! [U_273,U_272] :
( ( ! [U_275] : subset(cartesian_product2(U_275,U_273),cartesian_product2(U_275,U_272))
& ! [U_274] : subset(cartesian_product2(U_273,U_274),cartesian_product2(U_272,U_274)) )
| ~ subset(U_273,U_272) ),
inference(miniscope,[status(thm)],[f_64_2]) ).
cnf(f_64_4,plain,
( subset(cartesian_product2(U_273,U_274),cartesian_product2(U_272,U_274))
| ~ subset(U_273,U_272) ),
inference(clausify,[status(thm)],[f_64_3]) ).
cnf(f_64_5,plain,
( subset(cartesian_product2(U_275,U_273),cartesian_product2(U_275,U_272))
| ~ subset(U_273,U_272) ),
inference(clausify,[status(thm)],[f_64_3]) ).
fof(f_65_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_65_2,plain,
! [U_279,U_278,U_277,U_276] :
( subset(cartesian_product2(U_279,U_277),cartesian_product2(U_278,U_276))
| ~ subset(U_277,U_276)
| ~ subset(U_279,U_278) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
cnf(f_65_3,plain,
( subset(cartesian_product2(U_279,U_277),cartesian_product2(U_278,U_276))
| ~ subset(U_277,U_276)
| ~ subset(U_279,U_278) ),
inference(clausify,[status(thm)],[f_65_2]) ).
fof(f_66_1,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t12_xboole_1]) ).
fof(f_66_2,plain,
! [U_281,U_280] :
( set_union2(U_281,U_280) = U_280
| ~ subset(U_281,U_280) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
cnf(f_66_3,plain,
( set_union2(U_281,U_280) = U_280
| ~ subset(U_281,U_280) ),
inference(clausify,[status(thm)],[f_66_2]) ).
fof(f_67_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_67_2,plain,
! [U_287] :
? [U_286] :
( ! [U_285] :
( in(U_285,U_286)
| are_equipotent(U_285,U_286)
| ~ subset(U_285,U_286) )
& ! [U_284] :
( in(powerset(U_284),U_286)
| ~ in(U_284,U_286) )
& ! [U_283,U_282] :
( in(U_282,U_286)
| ~ subset(U_282,U_283)
| ~ in(U_283,U_286) )
& in(U_287,U_286) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
! [U_287] :
( ! [U_285] :
( in(U_285,sK32(U_287))
| are_equipotent(U_285,sK32(U_287))
| ~ subset(U_285,sK32(U_287)) )
& ! [U_284] :
( in(powerset(U_284),sK32(U_287))
| ~ in(U_284,sK32(U_287)) )
& ! [U_283,U_282] :
( in(U_282,sK32(U_287))
| ~ subset(U_282,U_283)
| ~ in(U_283,sK32(U_287)) )
& in(U_287,sK32(U_287)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_286,sK32(U_287))],[f_67_2]) ).
cnf(f_67_4,plain,
in(U_287,sK32(U_287)),
inference(clausify,[status(thm)],[f_67_3]) ).
cnf(f_67_5,plain,
( in(U_282,sK32(U_287))
| ~ subset(U_282,U_283)
| ~ in(U_283,sK32(U_287)) ),
inference(clausify,[status(thm)],[f_67_3]) ).
cnf(f_67_6,plain,
( in(powerset(U_284),sK32(U_287))
| ~ in(U_284,sK32(U_287)) ),
inference(clausify,[status(thm)],[f_67_3]) ).
cnf(f_67_7,plain,
( in(U_285,sK32(U_287))
| are_equipotent(U_285,sK32(U_287))
| ~ subset(U_285,sK32(U_287)) ),
inference(clausify,[status(thm)],[f_67_3]) ).
fof(f_68_1,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(fof_nnf,[status(thm)],[t17_xboole_1]) ).
fof(f_68_2,plain,
! [U_289,U_288] : subset(set_intersection2(U_289,U_288),U_289),
inference(variable_rename,[status(thm)],[f_68_1]) ).
cnf(f_68_3,plain,
subset(set_intersection2(U_289,U_288),U_289),
inference(clausify,[status(thm)],[f_68_2]) ).
fof(f_69_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_69_2,plain,
! [U_292,U_291,U_290] :
( subset(U_292,set_intersection2(U_291,U_290))
| ~ subset(U_292,U_290)
| ~ subset(U_292,U_291) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
cnf(f_69_3,plain,
( subset(U_292,set_intersection2(U_291,U_290))
| ~ subset(U_292,U_290)
| ~ subset(U_292,U_291) ),
inference(clausify,[status(thm)],[f_69_2]) ).
fof(f_70_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_70_2,plain,
! [U_293] : set_union2(U_293,empty_set) = U_293,
inference(variable_rename,[status(thm)],[f_70_1]) ).
cnf(f_70_3,plain,
set_union2(U_293,empty_set) = U_293,
inference(clausify,[status(thm)],[f_70_2]) ).
fof(f_71_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_71_2,plain,
! [U_296,U_295,U_294] :
( subset(U_296,U_294)
| ~ subset(U_295,U_294)
| ~ subset(U_296,U_295) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
cnf(f_71_3,plain,
( subset(U_296,U_294)
| ~ subset(U_295,U_294)
| ~ subset(U_296,U_295) ),
inference(clausify,[status(thm)],[f_71_2]) ).
fof(f_72_1,plain,
powerset(empty_set) = singleton(empty_set),
inference(fof_nnf,[status(thm)],[t1_zfmisc_1]) ).
cnf(f_72_2,plain,
powerset(empty_set) = singleton(empty_set),
inference(clausify,[status(thm)],[f_72_1]) ).
fof(f_73_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_73_2,plain,
! [U_299,U_298,U_297] :
( subset(set_intersection2(U_299,U_297),set_intersection2(U_298,U_297))
| ~ subset(U_299,U_298) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
fof(f_73_3,plain,
! [U_299,U_298] :
( ! [U_297] : subset(set_intersection2(U_299,U_297),set_intersection2(U_298,U_297))
| ~ subset(U_299,U_298) ),
inference(miniscope,[status(thm)],[f_73_2]) ).
cnf(f_73_4,plain,
( subset(set_intersection2(U_299,U_297),set_intersection2(U_298,U_297))
| ~ subset(U_299,U_298) ),
inference(clausify,[status(thm)],[f_73_3]) ).
fof(f_74_1,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t28_xboole_1]) ).
fof(f_74_2,plain,
! [U_301,U_300] :
( set_intersection2(U_301,U_300) = U_301
| ~ subset(U_301,U_300) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
cnf(f_74_3,plain,
( set_intersection2(U_301,U_300) = U_301
| ~ subset(U_301,U_300) ),
inference(clausify,[status(thm)],[f_74_2]) ).
fof(f_75_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_75_2,plain,
! [U_302] : set_intersection2(U_302,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_75_1]) ).
cnf(f_75_3,plain,
set_intersection2(U_302,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_75_2]) ).
fof(f_76_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_76_2,plain,
! [U_305,U_304] :
( U_305 = U_304
| ? [U_303] :
( ( ~ in(U_303,U_305)
& in(U_303,U_304) )
| ( ~ in(U_303,U_304)
& in(U_303,U_305) ) ) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
fof(f_76_3,plain,
! [U_305,U_304] :
( U_305 = U_304
| ? [U_307] :
( ~ in(U_307,U_305)
& in(U_307,U_304) )
| ? [U_306] :
( ~ in(U_306,U_304)
& in(U_306,U_305) ) ),
inference(miniscope,[status(thm)],[f_76_2]) ).
fof(f_76_4,plain,
! [U_305,U_304] :
( U_305 = U_304
| ? [U_307] :
( ~ in(U_307,U_305)
& in(U_307,U_304) )
| ( ~ in(sK33(U_305,U_304),U_304)
& in(sK33(U_305,U_304),U_305) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_306,sK33(U_305,U_304))],[f_76_3]) ).
fof(f_76_5,plain,
! [U_305,U_304] :
( U_305 = U_304
| ( ~ in(sK34(U_305,U_304),U_305)
& in(sK34(U_305,U_304),U_304) )
| ( ~ in(sK33(U_305,U_304),U_304)
& in(sK33(U_305,U_304),U_305) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_307,sK34(U_305,U_304))],[f_76_4]) ).
cnf(f_76_6,plain,
( in(sK34(U_305,U_304),U_304)
| in(sK33(U_305,U_304),U_305)
| U_305 = U_304 ),
inference(clausify,[status(thm)],[f_76_5]) ).
cnf(f_76_7,plain,
( ~ in(sK34(U_305,U_304),U_305)
| in(sK33(U_305,U_304),U_305)
| U_305 = U_304 ),
inference(clausify,[status(thm)],[f_76_5]) ).
cnf(f_76_8,plain,
( in(sK34(U_305,U_304),U_304)
| ~ in(sK33(U_305,U_304),U_304)
| U_305 = U_304 ),
inference(clausify,[status(thm)],[f_76_5]) ).
cnf(f_76_9,plain,
( ~ in(sK34(U_305,U_304),U_305)
| ~ in(sK33(U_305,U_304),U_304)
| U_305 = U_304 ),
inference(clausify,[status(thm)],[f_76_5]) ).
fof(f_77_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_77_2,plain,
! [U_308] : subset(empty_set,U_308),
inference(variable_rename,[status(thm)],[f_77_1]) ).
cnf(f_77_3,plain,
subset(empty_set,U_308),
inference(clausify,[status(thm)],[f_77_2]) ).
fof(f_78_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_78_2,plain,
! [U_311,U_310,U_309] :
( subset(set_difference(U_311,U_309),set_difference(U_310,U_309))
| ~ subset(U_311,U_310) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
fof(f_78_3,plain,
! [U_311,U_310] :
( ! [U_309] : subset(set_difference(U_311,U_309),set_difference(U_310,U_309))
| ~ subset(U_311,U_310) ),
inference(miniscope,[status(thm)],[f_78_2]) ).
cnf(f_78_4,plain,
( subset(set_difference(U_311,U_309),set_difference(U_310,U_309))
| ~ subset(U_311,U_310) ),
inference(clausify,[status(thm)],[f_78_3]) ).
fof(f_79_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_79_2,plain,
! [U_315,U_314,U_313,U_312] :
( ( U_314 = U_312
& U_315 = U_313 )
| ordered_pair(U_315,U_314) != ordered_pair(U_313,U_312) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
cnf(f_79_3,plain,
( U_315 = U_313
| ordered_pair(U_315,U_314) != ordered_pair(U_313,U_312) ),
inference(clausify,[status(thm)],[f_79_2]) ).
cnf(f_79_4,plain,
( U_314 = U_312
| ordered_pair(U_315,U_314) != ordered_pair(U_313,U_312) ),
inference(clausify,[status(thm)],[f_79_2]) ).
fof(f_80_1,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(fof_nnf,[status(thm)],[t36_xboole_1]) ).
fof(f_80_2,plain,
! [U_317,U_316] : subset(set_difference(U_317,U_316),U_317),
inference(variable_rename,[status(thm)],[f_80_1]) ).
cnf(f_80_3,plain,
subset(set_difference(U_317,U_316),U_317),
inference(clausify,[status(thm)],[f_80_2]) ).
fof(f_81_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_81_2,plain,
! [U_319,U_318] :
( ( set_difference(U_319,U_318) = empty_set
| ~ subset(U_319,U_318) )
& ( subset(U_319,U_318)
| set_difference(U_319,U_318) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
fof(f_81_3,plain,
( ! [U_323,U_321] :
( set_difference(U_323,U_321) = empty_set
| ~ subset(U_323,U_321) )
& ! [U_322,U_320] :
( subset(U_322,U_320)
| set_difference(U_322,U_320) != empty_set ) ),
inference(miniscope,[status(thm)],[f_81_2]) ).
cnf(f_81_4,plain,
( subset(U_322,U_320)
| set_difference(U_322,U_320) != empty_set ),
inference(clausify,[status(thm)],[f_81_3]) ).
cnf(f_81_5,plain,
( set_difference(U_323,U_321) = empty_set
| ~ subset(U_323,U_321) ),
inference(clausify,[status(thm)],[f_81_3]) ).
fof(f_82_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_82_2,plain,
! [U_325,U_324] :
( ( subset(singleton(U_325),U_324)
| ~ in(U_325,U_324) )
& ( in(U_325,U_324)
| ~ subset(singleton(U_325),U_324) ) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
fof(f_82_3,plain,
( ! [U_329,U_327] :
( subset(singleton(U_329),U_327)
| ~ in(U_329,U_327) )
& ! [U_328,U_326] :
( in(U_328,U_326)
| ~ subset(singleton(U_328),U_326) ) ),
inference(miniscope,[status(thm)],[f_82_2]) ).
cnf(f_82_4,plain,
( in(U_328,U_326)
| ~ subset(singleton(U_328),U_326) ),
inference(clausify,[status(thm)],[f_82_3]) ).
cnf(f_82_5,plain,
( subset(singleton(U_329),U_327)
| ~ in(U_329,U_327) ),
inference(clausify,[status(thm)],[f_82_3]) ).
fof(f_83_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_83_2,plain,
! [U_332,U_331,U_330] :
( ( subset(unordered_pair(U_332,U_331),U_330)
| ~ in(U_331,U_330)
| ~ in(U_332,U_330) )
& ( ( in(U_331,U_330)
& in(U_332,U_330) )
| ~ subset(unordered_pair(U_332,U_331),U_330) ) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
fof(f_83_3,plain,
( ! [U_338,U_336,U_334] :
( subset(unordered_pair(U_338,U_336),U_334)
| ~ in(U_336,U_334)
| ~ in(U_338,U_334) )
& ! [U_337,U_335,U_333] :
( ( in(U_335,U_333)
& in(U_337,U_333) )
| ~ subset(unordered_pair(U_337,U_335),U_333) ) ),
inference(miniscope,[status(thm)],[f_83_2]) ).
cnf(f_83_4,plain,
( in(U_337,U_333)
| ~ subset(unordered_pair(U_337,U_335),U_333) ),
inference(clausify,[status(thm)],[f_83_3]) ).
cnf(f_83_5,plain,
( in(U_335,U_333)
| ~ subset(unordered_pair(U_337,U_335),U_333) ),
inference(clausify,[status(thm)],[f_83_3]) ).
cnf(f_83_6,plain,
( subset(unordered_pair(U_338,U_336),U_334)
| ~ in(U_336,U_334)
| ~ in(U_338,U_334) ),
inference(clausify,[status(thm)],[f_83_3]) ).
fof(f_84_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_84_2,plain,
! [U_340,U_339] : set_union2(U_340,set_difference(U_339,U_340)) = set_union2(U_340,U_339),
inference(variable_rename,[status(thm)],[f_84_1]) ).
cnf(f_84_3,plain,
set_union2(U_340,set_difference(U_339,U_340)) = set_union2(U_340,U_339),
inference(clausify,[status(thm)],[f_84_2]) ).
fof(f_85_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_85_2,plain,
! [U_342,U_341] :
( ( subset(U_342,singleton(U_341))
| ( U_342 != singleton(U_341)
& U_342 != empty_set ) )
& ( U_342 = singleton(U_341)
| U_342 = empty_set
| ~ subset(U_342,singleton(U_341)) ) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
fof(f_85_3,plain,
( ! [U_346,U_344] :
( subset(U_346,singleton(U_344))
| ( U_346 != singleton(U_344)
& U_346 != empty_set ) )
& ! [U_345,U_343] :
( U_345 = singleton(U_343)
| U_345 = empty_set
| ~ subset(U_345,singleton(U_343)) ) ),
inference(miniscope,[status(thm)],[f_85_2]) ).
cnf(f_85_4,plain,
( U_345 = singleton(U_343)
| U_345 = empty_set
| ~ subset(U_345,singleton(U_343)) ),
inference(clausify,[status(thm)],[f_85_3]) ).
cnf(f_85_5,plain,
( U_346 != empty_set
| subset(U_346,singleton(U_344)) ),
inference(clausify,[status(thm)],[f_85_3]) ).
cnf(f_85_6,plain,
( U_346 != singleton(U_344)
| subset(U_346,singleton(U_344)) ),
inference(clausify,[status(thm)],[f_85_3]) ).
fof(f_86_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_86_2,plain,
! [U_347] : set_difference(U_347,empty_set) = U_347,
inference(variable_rename,[status(thm)],[f_86_1]) ).
cnf(f_86_3,plain,
set_difference(U_347,empty_set) = U_347,
inference(clausify,[status(thm)],[f_86_2]) ).
fof(f_87_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_87_2,plain,
! [U_351,U_350] :
( ( ~ disjoint(U_351,U_350)
| ! [U_349] :
( ~ in(U_349,U_350)
| ~ in(U_349,U_351) ) )
& ( ? [U_348] :
( in(U_348,U_350)
& in(U_348,U_351) )
| disjoint(U_351,U_350) ) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
fof(f_87_3,plain,
( ! [U_355,U_353] :
( ~ disjoint(U_355,U_353)
| ! [U_349] :
( ~ in(U_349,U_353)
| ~ in(U_349,U_355) ) )
& ! [U_354,U_352] :
( ? [U_348] :
( in(U_348,U_352)
& in(U_348,U_354) )
| disjoint(U_354,U_352) ) ),
inference(miniscope,[status(thm)],[f_87_2]) ).
fof(f_87_4,plain,
( ! [U_355,U_353] :
( ~ disjoint(U_355,U_353)
| ! [U_349] :
( ~ in(U_349,U_353)
| ~ in(U_349,U_355) ) )
& ! [U_354,U_352] :
( ( in(sK35(U_354,U_352),U_352)
& in(sK35(U_354,U_352),U_354) )
| disjoint(U_354,U_352) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_348,sK35(U_354,U_352))],[f_87_3]) ).
cnf(f_87_5,plain,
( in(sK35(U_354,U_352),U_354)
| disjoint(U_354,U_352) ),
inference(clausify,[status(thm)],[f_87_4]) ).
cnf(f_87_6,plain,
( in(sK35(U_354,U_352),U_352)
| disjoint(U_354,U_352) ),
inference(clausify,[status(thm)],[f_87_4]) ).
cnf(f_87_7,plain,
( ~ disjoint(U_355,U_353)
| ~ in(U_349,U_353)
| ~ in(U_349,U_355) ),
inference(clausify,[status(thm)],[f_87_4]) ).
fof(f_88_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_88_2,plain,
! [U_356] :
( U_356 = empty_set
| ~ subset(U_356,empty_set) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
cnf(f_88_3,plain,
( U_356 = empty_set
| ~ subset(U_356,empty_set) ),
inference(clausify,[status(thm)],[f_88_2]) ).
fof(f_89_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_89_2,plain,
! [U_358,U_357] : set_difference(set_union2(U_358,U_357),U_357) = set_difference(U_358,U_357),
inference(variable_rename,[status(thm)],[f_89_1]) ).
cnf(f_89_3,plain,
set_difference(set_union2(U_358,U_357),U_357) = set_difference(U_358,U_357),
inference(clausify,[status(thm)],[f_89_2]) ).
fof(f_90_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_90_2,plain,
! [U_361,U_360] :
( ! [U_359] :
( ( ( disjoint(U_360,U_359)
| ~ subset(U_360,subset_complement(U_361,U_359)) )
& ( subset(U_360,subset_complement(U_361,U_359))
| ~ disjoint(U_360,U_359) ) )
| ~ element(U_359,powerset(U_361)) )
| ~ element(U_360,powerset(U_361)) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
cnf(f_90_3,plain,
( subset(U_360,subset_complement(U_361,U_359))
| ~ disjoint(U_360,U_359)
| ~ element(U_359,powerset(U_361))
| ~ element(U_360,powerset(U_361)) ),
inference(clausify,[status(thm)],[f_90_2]) ).
cnf(f_90_4,plain,
( disjoint(U_360,U_359)
| ~ subset(U_360,subset_complement(U_361,U_359))
| ~ element(U_359,powerset(U_361))
| ~ element(U_360,powerset(U_361)) ),
inference(clausify,[status(thm)],[f_90_2]) ).
fof(f_91_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_91_2,plain,
! [U_363,U_362] :
( U_362 = set_union2(U_363,set_difference(U_362,U_363))
| ~ subset(U_363,U_362) ),
inference(variable_rename,[status(thm)],[f_91_1]) ).
cnf(f_91_3,plain,
( U_362 = set_union2(U_363,set_difference(U_362,U_363))
| ~ subset(U_363,U_362) ),
inference(clausify,[status(thm)],[f_91_2]) ).
fof(f_92_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t46_zfmisc_1]) ).
fof(f_92_2,plain,
! [U_365,U_364] :
( set_union2(singleton(U_365),U_364) = U_364
| ~ in(U_365,U_364) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
cnf(f_92_3,plain,
( set_union2(singleton(U_365),U_364) = U_364
| ~ in(U_365,U_364) ),
inference(clausify,[status(thm)],[f_92_2]) ).
fof(f_93_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_93_2,plain,
! [U_367,U_366] : set_difference(U_367,set_difference(U_367,U_366)) = set_intersection2(U_367,U_366),
inference(variable_rename,[status(thm)],[f_93_1]) ).
cnf(f_93_3,plain,
set_difference(U_367,set_difference(U_367,U_366)) = set_intersection2(U_367,U_366),
inference(clausify,[status(thm)],[f_93_2]) ).
fof(f_94_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_94_2,plain,
! [U_368] : set_difference(empty_set,U_368) = empty_set,
inference(variable_rename,[status(thm)],[f_94_1]) ).
cnf(f_94_3,plain,
set_difference(empty_set,U_368) = empty_set,
inference(clausify,[status(thm)],[f_94_2]) ).
fof(f_95_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_95_2,plain,
! [U_372,U_371] :
( ( ~ disjoint(U_372,U_371)
| ! [U_370] : ~ in(U_370,set_intersection2(U_372,U_371)) )
& ( ? [U_369] : in(U_369,set_intersection2(U_372,U_371))
| disjoint(U_372,U_371) ) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
fof(f_95_3,plain,
( ! [U_376,U_374] :
( ~ disjoint(U_376,U_374)
| ! [U_370] : ~ in(U_370,set_intersection2(U_376,U_374)) )
& ! [U_375,U_373] :
( ? [U_369] : in(U_369,set_intersection2(U_375,U_373))
| disjoint(U_375,U_373) ) ),
inference(miniscope,[status(thm)],[f_95_2]) ).
fof(f_95_4,plain,
( ! [U_376,U_374] :
( ~ disjoint(U_376,U_374)
| ! [U_370] : ~ in(U_370,set_intersection2(U_376,U_374)) )
& ! [U_375,U_373] :
( in(sK36(U_375,U_373),set_intersection2(U_375,U_373))
| disjoint(U_375,U_373) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_369,sK36(U_375,U_373))],[f_95_3]) ).
cnf(f_95_5,plain,
( in(sK36(U_375,U_373),set_intersection2(U_375,U_373))
| disjoint(U_375,U_373) ),
inference(clausify,[status(thm)],[f_95_4]) ).
cnf(f_95_6,plain,
( ~ disjoint(U_376,U_374)
| ~ in(U_370,set_intersection2(U_376,U_374)) ),
inference(clausify,[status(thm)],[f_95_4]) ).
fof(f_96_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_96_2,plain,
! [U_379] :
( ! [U_378] :
( ! [U_377] :
( in(U_377,subset_complement(U_379,U_378))
| in(U_377,U_378)
| ~ element(U_377,U_379) )
| ~ element(U_378,powerset(U_379)) )
| U_379 = empty_set ),
inference(variable_rename,[status(thm)],[f_96_1]) ).
cnf(f_96_3,plain,
( in(U_377,subset_complement(U_379,U_378))
| in(U_377,U_378)
| ~ element(U_377,U_379)
| ~ element(U_378,powerset(U_379))
| U_379 = empty_set ),
inference(clausify,[status(thm)],[f_96_2]) ).
fof(f_97_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_97_2,plain,
! [U_382,U_381,U_380] :
( ~ in(U_381,U_380)
| ~ in(U_381,subset_complement(U_382,U_380))
| ~ element(U_380,powerset(U_382)) ),
inference(variable_rename,[status(thm)],[f_97_1]) ).
cnf(f_97_3,plain,
( ~ in(U_381,U_380)
| ~ in(U_381,subset_complement(U_382,U_380))
| ~ element(U_380,powerset(U_382)) ),
inference(clausify,[status(thm)],[f_97_2]) ).
fof(f_98_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t60_xboole_1]) ).
fof(f_98_2,plain,
! [U_384,U_383] :
( ~ proper_subset(U_383,U_384)
| ~ subset(U_384,U_383) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
cnf(f_98_3,plain,
( ~ proper_subset(U_383,U_384)
| ~ subset(U_384,U_383) ),
inference(clausify,[status(thm)],[f_98_2]) ).
fof(f_99_1,plain,
! [A,B,C] :
( disjoint(A,C)
| ~ disjoint(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t63_xboole_1]) ).
fof(f_99_2,plain,
! [U_387,U_386,U_385] :
( disjoint(U_387,U_385)
| ~ disjoint(U_386,U_385)
| ~ subset(U_387,U_386) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
cnf(f_99_3,plain,
( disjoint(U_387,U_385)
| ~ disjoint(U_386,U_385)
| ~ subset(U_387,U_386) ),
inference(clausify,[status(thm)],[f_99_2]) ).
fof(f_100_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_100_2,plain,
! [U_389,U_388] :
( ( set_difference(U_389,singleton(U_388)) = U_389
| in(U_388,U_389) )
& ( ~ in(U_388,U_389)
| set_difference(U_389,singleton(U_388)) != U_389 ) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
fof(f_100_3,plain,
( ! [U_393,U_391] :
( set_difference(U_393,singleton(U_391)) = U_393
| in(U_391,U_393) )
& ! [U_392,U_390] :
( ~ in(U_390,U_392)
| set_difference(U_392,singleton(U_390)) != U_392 ) ),
inference(miniscope,[status(thm)],[f_100_2]) ).
cnf(f_100_4,plain,
( ~ in(U_390,U_392)
| set_difference(U_392,singleton(U_390)) != U_392 ),
inference(clausify,[status(thm)],[f_100_3]) ).
cnf(f_100_5,plain,
( set_difference(U_393,singleton(U_391)) = U_393
| in(U_391,U_393) ),
inference(clausify,[status(thm)],[f_100_3]) ).
fof(f_101_1,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(fof_nnf,[status(thm)],[t69_enumset1]) ).
fof(f_101_2,plain,
! [U_394] : unordered_pair(U_394,U_394) = singleton(U_394),
inference(variable_rename,[status(thm)],[f_101_1]) ).
cnf(f_101_3,plain,
unordered_pair(U_394,U_394) = singleton(U_394),
inference(clausify,[status(thm)],[f_101_2]) ).
fof(f_102_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_102_2,plain,
! [U_395] :
( U_395 = empty_set
| ~ empty(U_395) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
cnf(f_102_3,plain,
( U_395 = empty_set
| ~ empty(U_395) ),
inference(clausify,[status(thm)],[f_102_2]) ).
fof(f_103_1,plain,
! [A,B] :
( A = B
| ~ subset(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t6_zfmisc_1]) ).
fof(f_103_2,plain,
! [U_397,U_396] :
( U_397 = U_396
| ~ subset(singleton(U_397),singleton(U_396)) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
cnf(f_103_3,plain,
( U_397 = U_396
| ~ subset(singleton(U_397),singleton(U_396)) ),
inference(clausify,[status(thm)],[f_103_2]) ).
fof(f_104_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_104_2,plain,
! [U_399,U_398] :
( ~ empty(U_398)
| ~ in(U_399,U_398) ),
inference(variable_rename,[status(thm)],[f_104_1]) ).
cnf(f_104_3,plain,
( ~ empty(U_398)
| ~ in(U_399,U_398) ),
inference(clausify,[status(thm)],[f_104_2]) ).
fof(f_105_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1]) ).
fof(f_105_2,plain,
! [U_401,U_400] : subset(U_401,set_union2(U_401,U_400)),
inference(variable_rename,[status(thm)],[f_105_1]) ).
cnf(f_105_3,plain,
subset(U_401,set_union2(U_401,U_400)),
inference(clausify,[status(thm)],[f_105_2]) ).
fof(f_106_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_106_2,plain,
! [U_403,U_402] :
( ( disjoint(U_403,U_402)
| set_difference(U_403,U_402) != U_403 )
& ( set_difference(U_403,U_402) = U_403
| ~ disjoint(U_403,U_402) ) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
fof(f_106_3,plain,
( ! [U_407,U_405] :
( disjoint(U_407,U_405)
| set_difference(U_407,U_405) != U_407 )
& ! [U_406,U_404] :
( set_difference(U_406,U_404) = U_406
| ~ disjoint(U_406,U_404) ) ),
inference(miniscope,[status(thm)],[f_106_2]) ).
cnf(f_106_4,plain,
( set_difference(U_406,U_404) = U_406
| ~ disjoint(U_406,U_404) ),
inference(clausify,[status(thm)],[f_106_3]) ).
cnf(f_106_5,plain,
( disjoint(U_407,U_405)
| set_difference(U_407,U_405) != U_407 ),
inference(clausify,[status(thm)],[f_106_3]) ).
fof(f_107_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_107_2,plain,
! [U_409,U_408] :
( ~ empty(U_408)
| U_409 = U_408
| ~ empty(U_409) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
fof(f_107_3,plain,
! [U_409] :
( ! [U_408] :
( ~ empty(U_408)
| U_409 = U_408 )
| ~ empty(U_409) ),
inference(miniscope,[status(thm)],[f_107_2]) ).
cnf(f_107_4,plain,
( ~ empty(U_408)
| U_409 = U_408
| ~ empty(U_409) ),
inference(clausify,[status(thm)],[f_107_3]) ).
fof(f_108_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_108_2,plain,
! [U_412,U_411,U_410] :
( subset(set_union2(U_412,U_410),U_411)
| ~ subset(U_410,U_411)
| ~ subset(U_412,U_411) ),
inference(variable_rename,[status(thm)],[f_108_1]) ).
cnf(f_108_3,plain,
( subset(set_union2(U_412,U_410),U_411)
| ~ subset(U_410,U_411)
| ~ subset(U_412,U_411) ),
inference(clausify,[status(thm)],[f_108_2]) ).
fof(f_109_1,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t8_zfmisc_1]) ).
fof(f_109_2,plain,
! [U_415,U_414,U_413] :
( U_415 = U_414
| singleton(U_415) != unordered_pair(U_414,U_413) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
fof(f_109_3,plain,
! [U_415,U_414] :
( ! [U_413] : singleton(U_415) != unordered_pair(U_414,U_413)
| U_415 = U_414 ),
inference(miniscope,[status(thm)],[f_109_2]) ).
cnf(f_109_4,plain,
( singleton(U_415) != unordered_pair(U_414,U_413)
| U_415 = U_414 ),
inference(clausify,[status(thm)],[f_109_3]) ).
fof(f_110_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t92_zfmisc_1]) ).
fof(f_110_2,plain,
! [U_417,U_416] :
( subset(U_417,union(U_416))
| ~ in(U_417,U_416) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
cnf(f_110_3,plain,
( subset(U_417,union(U_416))
| ~ in(U_417,U_416) ),
inference(clausify,[status(thm)],[f_110_2]) ).
fof(f_111_1,plain,
! [A] : union(powerset(A)) = A,
inference(fof_nnf,[status(thm)],[t99_zfmisc_1]) ).
fof(f_111_2,plain,
! [U_418] : union(powerset(U_418)) = U_418,
inference(variable_rename,[status(thm)],[f_111_1]) ).
cnf(f_111_3,plain,
union(powerset(U_418)) = U_418,
inference(clausify,[status(thm)],[f_111_2]) ).
fof(f_112_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_112_2,plain,
! [U_426] :
? [U_425] :
( ! [U_424] :
( in(U_424,U_425)
| are_equipotent(U_424,U_425)
| ~ subset(U_424,U_425) )
& ! [U_423] :
( ? [U_422] :
( ! [U_421] :
( in(U_421,U_422)
| ~ subset(U_421,U_423) )
& in(U_422,U_425) )
| ~ in(U_423,U_425) )
& ! [U_420,U_419] :
( in(U_419,U_425)
| ~ subset(U_419,U_420)
| ~ in(U_420,U_425) )
& in(U_426,U_425) ),
inference(variable_rename,[status(thm)],[f_112_1]) ).
fof(f_112_3,plain,
! [U_426] :
( ! [U_424] :
( in(U_424,sK37(U_426))
| are_equipotent(U_424,sK37(U_426))
| ~ subset(U_424,sK37(U_426)) )
& ! [U_423] :
( ? [U_422] :
( ! [U_421] :
( in(U_421,U_422)
| ~ subset(U_421,U_423) )
& in(U_422,sK37(U_426)) )
| ~ in(U_423,sK37(U_426)) )
& ! [U_420,U_419] :
( in(U_419,sK37(U_426))
| ~ subset(U_419,U_420)
| ~ in(U_420,sK37(U_426)) )
& in(U_426,sK37(U_426)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_425,sK37(U_426))],[f_112_2]) ).
fof(f_112_4,plain,
! [U_426] :
( ! [U_424] :
( in(U_424,sK37(U_426))
| are_equipotent(U_424,sK37(U_426))
| ~ subset(U_424,sK37(U_426)) )
& ! [U_423] :
( ( ! [U_421] :
( in(U_421,sK38(U_426,U_423))
| ~ subset(U_421,U_423) )
& in(sK38(U_426,U_423),sK37(U_426)) )
| ~ in(U_423,sK37(U_426)) )
& ! [U_420,U_419] :
( in(U_419,sK37(U_426))
| ~ subset(U_419,U_420)
| ~ in(U_420,sK37(U_426)) )
& in(U_426,sK37(U_426)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_422,sK38(U_426,U_423))],[f_112_3]) ).
cnf(f_112_5,plain,
in(U_426,sK37(U_426)),
inference(clausify,[status(thm)],[f_112_4]) ).
cnf(f_112_6,plain,
( in(U_419,sK37(U_426))
| ~ subset(U_419,U_420)
| ~ in(U_420,sK37(U_426)) ),
inference(clausify,[status(thm)],[f_112_4]) ).
cnf(f_112_7,plain,
( in(sK38(U_426,U_423),sK37(U_426))
| ~ in(U_423,sK37(U_426)) ),
inference(clausify,[status(thm)],[f_112_4]) ).
cnf(f_112_8,plain,
( in(U_421,sK38(U_426,U_423))
| ~ subset(U_421,U_423)
| ~ in(U_423,sK37(U_426)) ),
inference(clausify,[status(thm)],[f_112_4]) ).
cnf(f_112_9,plain,
( in(U_424,sK37(U_426))
| are_equipotent(U_424,sK37(U_426))
| ~ subset(U_424,sK37(U_426)) ),
inference(clausify,[status(thm)],[f_112_4]) ).
fof(f_113_1,plain,
! [A,B,C] :
( B = C
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t9_zfmisc_1]) ).
fof(f_113_2,plain,
! [U_429,U_428,U_427] :
( U_428 = U_427
| singleton(U_429) != unordered_pair(U_428,U_427) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
cnf(f_113_3,plain,
( U_428 = U_427
| singleton(U_429) != unordered_pair(U_428,U_427) ),
inference(clausify,[status(thm)],[f_113_2]) ).
cnf(f_22_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_22_2]) ).
cnf(f_23_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_23_2]) ).
cnf(f_24_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_24_2]) ).
cnf(f_25_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_25_2]) ).
cnf(f_26_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_26_2]) ).
cnf(f_27_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_27_2]) ).
cnf(f_29_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_29_2]) ).
cnf(f_30_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_30_2]) ).
cnf(f_31_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_31_2]) ).
cnf(f_32_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_32_2]) ).
cnf(f_33_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_33_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,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,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_10,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_11,axiom,
( union(Eq_x_0) = union(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,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_13,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_14,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_15,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_16,axiom,
( sK3(Eq_x_0) = sK3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,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_18,axiom,
( sK5(Eq_x_0,Eq_x_1) = sK5(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( 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_20,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_21,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_22,axiom,
( sK9(Eq_x_0,Eq_x_1,Eq_x_2) = sK9(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( sK10(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK10(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_24,axiom,
( sK11(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK11(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_25,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_26,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_27,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_28,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_29,axiom,
( sK16(Eq_x_0,Eq_x_1) = sK16(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_30,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_31,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_32,axiom,
( sK19(Eq_x_0,Eq_x_1,Eq_x_2) = sK19(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,axiom,
( sK20(Eq_x_0,Eq_x_1) = sK20(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_34,axiom,
( sK21(Eq_x_0,Eq_x_1) = sK21(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_35,axiom,
( sK22(Eq_x_0,Eq_x_1) = sK22(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_36,axiom,
( sK23(Eq_x_0,Eq_x_1,Eq_x_2) = sK23(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_37,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_38,axiom,
( sK25(Eq_x_0) = sK25(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,axiom,
( sK28(Eq_x_0) = sK28(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_40,axiom,
( sK30(Eq_x_0) = sK30(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_41,axiom,
( sK32(Eq_x_0) = sK32(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_42,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_43,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_44,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_45,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_46,axiom,
( sK37(Eq_x_0) = sK37(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_47,axiom,
( sK38(Eq_x_0,Eq_x_1) = sK38(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_48,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_49,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_50,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_51,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_52,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_53,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_54,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
% 0.00/0.02 % Problem : SEU173+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 23:23:19 UTC 2026
% 0.12/0.36 % CPUTime :
% 172.15/172.41 % SZS status Theorem for theBenchmark
% 172.15/172.41 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------