%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU165+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 : n020.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 08:58:18 AM UTC 2026
% Result : Theorem 1.33s 6.84s
% Output : Proof 1.33s
% 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_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_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_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(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(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_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(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
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,conjecture,
! [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(t12_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
file('theBenchmark.p',t12_xboole_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(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(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_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,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_10_2,plain,
! [U_49,U_48,U_47] :
( ( U_47 = unordered_pair(U_49,U_48)
| ? [U_46] :
( ( ~ in(U_46,U_47)
& ( U_46 = U_48
| U_46 = U_49 ) )
| ( U_46 != U_48
& U_46 != U_49
& in(U_46,U_47) ) ) )
& ( ! [U_45] :
( ( in(U_45,U_47)
| ( U_45 != U_48
& U_45 != U_49 ) )
& ( U_45 = U_48
| U_45 = U_49
| ~ in(U_45,U_47) ) )
| U_47 != unordered_pair(U_49,U_48) ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_59,U_57,U_55] :
( U_55 = unordered_pair(U_59,U_57)
| ? [U_53] :
( ~ in(U_53,U_55)
& ( U_53 = U_57
| U_53 = U_59 ) )
| ? [U_52] :
( U_52 != U_57
& U_52 != U_59
& in(U_52,U_55) ) )
& ! [U_58,U_56,U_54] :
( ( ! [U_51] :
( in(U_51,U_54)
| ( U_51 != U_56
& U_51 != U_58 ) )
& ! [U_50] :
( U_50 = U_56
| U_50 = U_58
| ~ in(U_50,U_54) ) )
| U_54 != unordered_pair(U_58,U_56) ) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
fof(f_10_4,plain,
( ! [U_59,U_57,U_55] :
( U_55 = unordered_pair(U_59,U_57)
| ? [U_53] :
( ~ in(U_53,U_55)
& ( U_53 = U_57
| U_53 = U_59 ) )
| ( sK6(U_59,U_57,U_55) != U_57
& sK6(U_59,U_57,U_55) != U_59
& in(sK6(U_59,U_57,U_55),U_55) ) )
& ! [U_58,U_56,U_54] :
( ( ! [U_51] :
( in(U_51,U_54)
| ( U_51 != U_56
& U_51 != U_58 ) )
& ! [U_50] :
( U_50 = U_56
| U_50 = U_58
| ~ in(U_50,U_54) ) )
| U_54 != unordered_pair(U_58,U_56) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_52,sK6(U_59,U_57,U_55))],[f_10_3]) ).
fof(f_10_5,plain,
( ! [U_59,U_57,U_55] :
( U_55 = unordered_pair(U_59,U_57)
| ( ~ in(sK7(U_59,U_57,U_55),U_55)
& ( sK7(U_59,U_57,U_55) = U_57
| sK7(U_59,U_57,U_55) = U_59 ) )
| ( sK6(U_59,U_57,U_55) != U_57
& sK6(U_59,U_57,U_55) != U_59
& in(sK6(U_59,U_57,U_55),U_55) ) )
& ! [U_58,U_56,U_54] :
( ( ! [U_51] :
( in(U_51,U_54)
| ( U_51 != U_56
& U_51 != U_58 ) )
& ! [U_50] :
( U_50 = U_56
| U_50 = U_58
| ~ in(U_50,U_54) ) )
| U_54 != unordered_pair(U_58,U_56) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_53,sK7(U_59,U_57,U_55))],[f_10_4]) ).
cnf(f_10_6,plain,
( U_50 = U_56
| U_50 = U_58
| ~ in(U_50,U_54)
| U_54 != unordered_pair(U_58,U_56) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_7,plain,
( U_51 != U_58
| in(U_51,U_54)
| U_54 != unordered_pair(U_58,U_56) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_8,plain,
( U_51 != U_56
| in(U_51,U_54)
| U_54 != unordered_pair(U_58,U_56) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_9,plain,
( sK7(U_59,U_57,U_55) = U_57
| sK7(U_59,U_57,U_55) = U_59
| in(sK6(U_59,U_57,U_55),U_55)
| U_55 = unordered_pair(U_59,U_57) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_10,plain,
( ~ in(sK7(U_59,U_57,U_55),U_55)
| in(sK6(U_59,U_57,U_55),U_55)
| U_55 = unordered_pair(U_59,U_57) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_11,plain,
( sK6(U_59,U_57,U_55) != U_59
| sK7(U_59,U_57,U_55) = U_57
| sK7(U_59,U_57,U_55) = U_59
| U_55 = unordered_pair(U_59,U_57) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_12,plain,
( sK6(U_59,U_57,U_55) != U_57
| sK7(U_59,U_57,U_55) = U_57
| sK7(U_59,U_57,U_55) = U_59
| U_55 = unordered_pair(U_59,U_57) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_13,plain,
( sK6(U_59,U_57,U_55) != U_59
| ~ in(sK7(U_59,U_57,U_55),U_55)
| U_55 = unordered_pair(U_59,U_57) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_14,plain,
( sK6(U_59,U_57,U_55) != U_57
| ~ in(sK7(U_59,U_57,U_55),U_55)
| U_55 = unordered_pair(U_59,U_57) ),
inference(clausify,[status(thm)],[f_10_5]) ).
fof(f_11_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_11_2,plain,
! [U_64,U_63,U_62] :
( ( U_62 = set_union2(U_64,U_63)
| ? [U_61] :
( ( ~ in(U_61,U_62)
& ( in(U_61,U_63)
| in(U_61,U_64) ) )
| ( ~ in(U_61,U_63)
& ~ in(U_61,U_64)
& in(U_61,U_62) ) ) )
& ( ! [U_60] :
( ( in(U_60,U_62)
| ( ~ in(U_60,U_63)
& ~ in(U_60,U_64) ) )
& ( in(U_60,U_63)
| in(U_60,U_64)
| ~ in(U_60,U_62) ) )
| U_62 != set_union2(U_64,U_63) ) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
( ! [U_74,U_72,U_70] :
( U_70 = set_union2(U_74,U_72)
| ? [U_68] :
( ~ in(U_68,U_70)
& ( in(U_68,U_72)
| in(U_68,U_74) ) )
| ? [U_67] :
( ~ in(U_67,U_72)
& ~ in(U_67,U_74)
& in(U_67,U_70) ) )
& ! [U_73,U_71,U_69] :
( ( ! [U_66] :
( in(U_66,U_69)
| ( ~ in(U_66,U_71)
& ~ in(U_66,U_73) ) )
& ! [U_65] :
( in(U_65,U_71)
| in(U_65,U_73)
| ~ in(U_65,U_69) ) )
| U_69 != set_union2(U_73,U_71) ) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
fof(f_11_4,plain,
( ! [U_74,U_72,U_70] :
( U_70 = set_union2(U_74,U_72)
| ? [U_68] :
( ~ in(U_68,U_70)
& ( in(U_68,U_72)
| in(U_68,U_74) ) )
| ( ~ in(sK8(U_74,U_72,U_70),U_72)
& ~ in(sK8(U_74,U_72,U_70),U_74)
& in(sK8(U_74,U_72,U_70),U_70) ) )
& ! [U_73,U_71,U_69] :
( ( ! [U_66] :
( in(U_66,U_69)
| ( ~ in(U_66,U_71)
& ~ in(U_66,U_73) ) )
& ! [U_65] :
( in(U_65,U_71)
| in(U_65,U_73)
| ~ in(U_65,U_69) ) )
| U_69 != set_union2(U_73,U_71) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_67,sK8(U_74,U_72,U_70))],[f_11_3]) ).
fof(f_11_5,plain,
( ! [U_74,U_72,U_70] :
( U_70 = set_union2(U_74,U_72)
| ( ~ in(sK9(U_74,U_72,U_70),U_70)
& ( in(sK9(U_74,U_72,U_70),U_72)
| in(sK9(U_74,U_72,U_70),U_74) ) )
| ( ~ in(sK8(U_74,U_72,U_70),U_72)
& ~ in(sK8(U_74,U_72,U_70),U_74)
& in(sK8(U_74,U_72,U_70),U_70) ) )
& ! [U_73,U_71,U_69] :
( ( ! [U_66] :
( in(U_66,U_69)
| ( ~ in(U_66,U_71)
& ~ in(U_66,U_73) ) )
& ! [U_65] :
( in(U_65,U_71)
| in(U_65,U_73)
| ~ in(U_65,U_69) ) )
| U_69 != set_union2(U_73,U_71) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_68,sK9(U_74,U_72,U_70))],[f_11_4]) ).
cnf(f_11_6,plain,
( in(U_65,U_71)
| in(U_65,U_73)
| ~ in(U_65,U_69)
| U_69 != set_union2(U_73,U_71) ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_7,plain,
( ~ in(U_66,U_73)
| in(U_66,U_69)
| U_69 != set_union2(U_73,U_71) ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_8,plain,
( ~ in(U_66,U_71)
| in(U_66,U_69)
| U_69 != set_union2(U_73,U_71) ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_9,plain,
( in(sK9(U_74,U_72,U_70),U_72)
| in(sK9(U_74,U_72,U_70),U_74)
| in(sK8(U_74,U_72,U_70),U_70)
| U_70 = set_union2(U_74,U_72) ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_10,plain,
( ~ in(sK9(U_74,U_72,U_70),U_70)
| in(sK8(U_74,U_72,U_70),U_70)
| U_70 = set_union2(U_74,U_72) ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_11,plain,
( ~ in(sK8(U_74,U_72,U_70),U_74)
| in(sK9(U_74,U_72,U_70),U_72)
| in(sK9(U_74,U_72,U_70),U_74)
| U_70 = set_union2(U_74,U_72) ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_12,plain,
( ~ in(sK8(U_74,U_72,U_70),U_72)
| in(sK9(U_74,U_72,U_70),U_72)
| in(sK9(U_74,U_72,U_70),U_74)
| U_70 = set_union2(U_74,U_72) ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_13,plain,
( ~ in(sK8(U_74,U_72,U_70),U_74)
| ~ in(sK9(U_74,U_72,U_70),U_70)
| U_70 = set_union2(U_74,U_72) ),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(f_11_14,plain,
( ~ in(sK8(U_74,U_72,U_70),U_72)
| ~ in(sK9(U_74,U_72,U_70),U_70)
| U_70 = set_union2(U_74,U_72) ),
inference(clausify,[status(thm)],[f_11_5]) ).
fof(f_12_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_12_2,plain,
! [U_87,U_86,U_85] :
( ( U_85 = cartesian_product2(U_87,U_86)
| ? [U_84] :
( ( ~ in(U_84,U_85)
& ? [U_83,U_82] :
( U_84 = ordered_pair(U_83,U_82)
& in(U_82,U_86)
& in(U_83,U_87) ) )
| ( ! [U_81,U_80] :
( U_84 != ordered_pair(U_81,U_80)
| ~ in(U_80,U_86)
| ~ in(U_81,U_87) )
& in(U_84,U_85) ) ) )
& ( ! [U_79] :
( ( in(U_79,U_85)
| ! [U_78,U_77] :
( U_79 != ordered_pair(U_78,U_77)
| ~ in(U_77,U_86)
| ~ in(U_78,U_87) ) )
& ( ? [U_76,U_75] :
( U_79 = ordered_pair(U_76,U_75)
& in(U_75,U_86)
& in(U_76,U_87) )
| ~ in(U_79,U_85) ) )
| U_85 != cartesian_product2(U_87,U_86) ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_97,U_95,U_93] :
( U_93 = cartesian_product2(U_97,U_95)
| ? [U_91] :
( ~ in(U_91,U_93)
& ? [U_83] :
( ? [U_82] :
( U_91 = ordered_pair(U_83,U_82)
& in(U_82,U_95) )
& in(U_83,U_97) ) )
| ? [U_90] :
( ! [U_81] :
( ! [U_80] :
( U_90 != ordered_pair(U_81,U_80)
| ~ in(U_80,U_95) )
| ~ in(U_81,U_97) )
& in(U_90,U_93) ) )
& ! [U_96,U_94,U_92] :
( ( ! [U_89] :
( in(U_89,U_92)
| ! [U_78] :
( ! [U_77] :
( U_89 != ordered_pair(U_78,U_77)
| ~ in(U_77,U_94) )
| ~ in(U_78,U_96) ) )
& ! [U_88] :
( ? [U_76] :
( ? [U_75] :
( U_88 = ordered_pair(U_76,U_75)
& in(U_75,U_94) )
& in(U_76,U_96) )
| ~ in(U_88,U_92) ) )
| U_92 != cartesian_product2(U_96,U_94) ) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
( ! [U_97,U_95,U_93] :
( U_93 = cartesian_product2(U_97,U_95)
| ? [U_91] :
( ~ in(U_91,U_93)
& ? [U_83] :
( ? [U_82] :
( U_91 = ordered_pair(U_83,U_82)
& in(U_82,U_95) )
& in(U_83,U_97) ) )
| ? [U_90] :
( ! [U_81] :
( ! [U_80] :
( U_90 != ordered_pair(U_81,U_80)
| ~ in(U_80,U_95) )
| ~ in(U_81,U_97) )
& in(U_90,U_93) ) )
& ! [U_96,U_94,U_92] :
( ( ! [U_89] :
( in(U_89,U_92)
| ! [U_78] :
( ! [U_77] :
( U_89 != ordered_pair(U_78,U_77)
| ~ in(U_77,U_94) )
| ~ in(U_78,U_96) ) )
& ! [U_88] :
( ( ? [U_75] :
( U_88 = ordered_pair(sK10(U_96,U_94,U_92,U_88),U_75)
& in(U_75,U_94) )
& in(sK10(U_96,U_94,U_92,U_88),U_96) )
| ~ in(U_88,U_92) ) )
| U_92 != cartesian_product2(U_96,U_94) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_76,sK10(U_96,U_94,U_92,U_88))],[f_12_3]) ).
fof(f_12_5,plain,
( ! [U_97,U_95,U_93] :
( U_93 = cartesian_product2(U_97,U_95)
| ? [U_91] :
( ~ in(U_91,U_93)
& ? [U_83] :
( ? [U_82] :
( U_91 = ordered_pair(U_83,U_82)
& in(U_82,U_95) )
& in(U_83,U_97) ) )
| ? [U_90] :
( ! [U_81] :
( ! [U_80] :
( U_90 != ordered_pair(U_81,U_80)
| ~ in(U_80,U_95) )
| ~ in(U_81,U_97) )
& in(U_90,U_93) ) )
& ! [U_96,U_94,U_92] :
( ( ! [U_89] :
( in(U_89,U_92)
| ! [U_78] :
( ! [U_77] :
( U_89 != ordered_pair(U_78,U_77)
| ~ in(U_77,U_94) )
| ~ in(U_78,U_96) ) )
& ! [U_88] :
( ( U_88 = ordered_pair(sK10(U_96,U_94,U_92,U_88),sK11(U_96,U_94,U_92,U_88))
& in(sK11(U_96,U_94,U_92,U_88),U_94)
& in(sK10(U_96,U_94,U_92,U_88),U_96) )
| ~ in(U_88,U_92) ) )
| U_92 != cartesian_product2(U_96,U_94) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_75,sK11(U_96,U_94,U_92,U_88))],[f_12_4]) ).
fof(f_12_6,plain,
( ! [U_97,U_95,U_93] :
( U_93 = cartesian_product2(U_97,U_95)
| ? [U_91] :
( ~ in(U_91,U_93)
& ? [U_83] :
( ? [U_82] :
( U_91 = ordered_pair(U_83,U_82)
& in(U_82,U_95) )
& in(U_83,U_97) ) )
| ( ! [U_81] :
( ! [U_80] :
( sK12(U_97,U_95,U_93) != ordered_pair(U_81,U_80)
| ~ in(U_80,U_95) )
| ~ in(U_81,U_97) )
& in(sK12(U_97,U_95,U_93),U_93) ) )
& ! [U_96,U_94,U_92] :
( ( ! [U_89] :
( in(U_89,U_92)
| ! [U_78] :
( ! [U_77] :
( U_89 != ordered_pair(U_78,U_77)
| ~ in(U_77,U_94) )
| ~ in(U_78,U_96) ) )
& ! [U_88] :
( ( U_88 = ordered_pair(sK10(U_96,U_94,U_92,U_88),sK11(U_96,U_94,U_92,U_88))
& in(sK11(U_96,U_94,U_92,U_88),U_94)
& in(sK10(U_96,U_94,U_92,U_88),U_96) )
| ~ in(U_88,U_92) ) )
| U_92 != cartesian_product2(U_96,U_94) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_90,sK12(U_97,U_95,U_93))],[f_12_5]) ).
fof(f_12_7,plain,
( ! [U_97,U_95,U_93] :
( U_93 = cartesian_product2(U_97,U_95)
| ( ~ in(sK13(U_97,U_95,U_93),U_93)
& ? [U_83] :
( ? [U_82] :
( sK13(U_97,U_95,U_93) = ordered_pair(U_83,U_82)
& in(U_82,U_95) )
& in(U_83,U_97) ) )
| ( ! [U_81] :
( ! [U_80] :
( sK12(U_97,U_95,U_93) != ordered_pair(U_81,U_80)
| ~ in(U_80,U_95) )
| ~ in(U_81,U_97) )
& in(sK12(U_97,U_95,U_93),U_93) ) )
& ! [U_96,U_94,U_92] :
( ( ! [U_89] :
( in(U_89,U_92)
| ! [U_78] :
( ! [U_77] :
( U_89 != ordered_pair(U_78,U_77)
| ~ in(U_77,U_94) )
| ~ in(U_78,U_96) ) )
& ! [U_88] :
( ( U_88 = ordered_pair(sK10(U_96,U_94,U_92,U_88),sK11(U_96,U_94,U_92,U_88))
& in(sK11(U_96,U_94,U_92,U_88),U_94)
& in(sK10(U_96,U_94,U_92,U_88),U_96) )
| ~ in(U_88,U_92) ) )
| U_92 != cartesian_product2(U_96,U_94) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_91,sK13(U_97,U_95,U_93))],[f_12_6]) ).
fof(f_12_8,plain,
( ! [U_97,U_95,U_93] :
( U_93 = cartesian_product2(U_97,U_95)
| ( ~ in(sK13(U_97,U_95,U_93),U_93)
& ? [U_82] :
( sK13(U_97,U_95,U_93) = ordered_pair(sK14(U_97,U_95,U_93),U_82)
& in(U_82,U_95) )
& in(sK14(U_97,U_95,U_93),U_97) )
| ( ! [U_81] :
( ! [U_80] :
( sK12(U_97,U_95,U_93) != ordered_pair(U_81,U_80)
| ~ in(U_80,U_95) )
| ~ in(U_81,U_97) )
& in(sK12(U_97,U_95,U_93),U_93) ) )
& ! [U_96,U_94,U_92] :
( ( ! [U_89] :
( in(U_89,U_92)
| ! [U_78] :
( ! [U_77] :
( U_89 != ordered_pair(U_78,U_77)
| ~ in(U_77,U_94) )
| ~ in(U_78,U_96) ) )
& ! [U_88] :
( ( U_88 = ordered_pair(sK10(U_96,U_94,U_92,U_88),sK11(U_96,U_94,U_92,U_88))
& in(sK11(U_96,U_94,U_92,U_88),U_94)
& in(sK10(U_96,U_94,U_92,U_88),U_96) )
| ~ in(U_88,U_92) ) )
| U_92 != cartesian_product2(U_96,U_94) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_83,sK14(U_97,U_95,U_93))],[f_12_7]) ).
fof(f_12_9,plain,
( ! [U_97,U_95,U_93] :
( U_93 = cartesian_product2(U_97,U_95)
| ( ~ in(sK13(U_97,U_95,U_93),U_93)
& sK13(U_97,U_95,U_93) = ordered_pair(sK14(U_97,U_95,U_93),sK15(U_97,U_95,U_93))
& in(sK15(U_97,U_95,U_93),U_95)
& in(sK14(U_97,U_95,U_93),U_97) )
| ( ! [U_81] :
( ! [U_80] :
( sK12(U_97,U_95,U_93) != ordered_pair(U_81,U_80)
| ~ in(U_80,U_95) )
| ~ in(U_81,U_97) )
& in(sK12(U_97,U_95,U_93),U_93) ) )
& ! [U_96,U_94,U_92] :
( ( ! [U_89] :
( in(U_89,U_92)
| ! [U_78] :
( ! [U_77] :
( U_89 != ordered_pair(U_78,U_77)
| ~ in(U_77,U_94) )
| ~ in(U_78,U_96) ) )
& ! [U_88] :
( ( U_88 = ordered_pair(sK10(U_96,U_94,U_92,U_88),sK11(U_96,U_94,U_92,U_88))
& in(sK11(U_96,U_94,U_92,U_88),U_94)
& in(sK10(U_96,U_94,U_92,U_88),U_96) )
| ~ in(U_88,U_92) ) )
| U_92 != cartesian_product2(U_96,U_94) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_82,sK15(U_97,U_95,U_93))],[f_12_8]) ).
cnf(f_12_10,plain,
( in(sK10(U_96,U_94,U_92,U_88),U_96)
| ~ in(U_88,U_92)
| U_92 != cartesian_product2(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_11,plain,
( in(sK11(U_96,U_94,U_92,U_88),U_94)
| ~ in(U_88,U_92)
| U_92 != cartesian_product2(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_12,plain,
( U_88 = ordered_pair(sK10(U_96,U_94,U_92,U_88),sK11(U_96,U_94,U_92,U_88))
| ~ in(U_88,U_92)
| U_92 != cartesian_product2(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_13,plain,
( in(U_89,U_92)
| U_89 != ordered_pair(U_78,U_77)
| ~ in(U_77,U_94)
| ~ in(U_78,U_96)
| U_92 != cartesian_product2(U_96,U_94) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_14,plain,
( in(sK14(U_97,U_95,U_93),U_97)
| in(sK12(U_97,U_95,U_93),U_93)
| U_93 = cartesian_product2(U_97,U_95) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_15,plain,
( in(sK15(U_97,U_95,U_93),U_95)
| in(sK12(U_97,U_95,U_93),U_93)
| U_93 = cartesian_product2(U_97,U_95) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_16,plain,
( sK13(U_97,U_95,U_93) = ordered_pair(sK14(U_97,U_95,U_93),sK15(U_97,U_95,U_93))
| in(sK12(U_97,U_95,U_93),U_93)
| U_93 = cartesian_product2(U_97,U_95) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_17,plain,
( ~ in(sK13(U_97,U_95,U_93),U_93)
| in(sK12(U_97,U_95,U_93),U_93)
| U_93 = cartesian_product2(U_97,U_95) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_18,plain,
( in(sK14(U_97,U_95,U_93),U_97)
| sK12(U_97,U_95,U_93) != ordered_pair(U_81,U_80)
| ~ in(U_80,U_95)
| ~ in(U_81,U_97)
| U_93 = cartesian_product2(U_97,U_95) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_19,plain,
( in(sK15(U_97,U_95,U_93),U_95)
| sK12(U_97,U_95,U_93) != ordered_pair(U_81,U_80)
| ~ in(U_80,U_95)
| ~ in(U_81,U_97)
| U_93 = cartesian_product2(U_97,U_95) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_20,plain,
( sK13(U_97,U_95,U_93) = ordered_pair(sK14(U_97,U_95,U_93),sK15(U_97,U_95,U_93))
| sK12(U_97,U_95,U_93) != ordered_pair(U_81,U_80)
| ~ in(U_80,U_95)
| ~ in(U_81,U_97)
| U_93 = cartesian_product2(U_97,U_95) ),
inference(clausify,[status(thm)],[f_12_9]) ).
cnf(f_12_21,plain,
( ~ in(sK13(U_97,U_95,U_93),U_93)
| sK12(U_97,U_95,U_93) != ordered_pair(U_81,U_80)
| ~ in(U_80,U_95)
| ~ in(U_81,U_97)
| U_93 = cartesian_product2(U_97,U_95) ),
inference(clausify,[status(thm)],[f_12_9]) ).
fof(f_13_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_13_2,plain,
! [U_101,U_100] :
( ( subset(U_101,U_100)
| ? [U_99] :
( ~ in(U_99,U_100)
& in(U_99,U_101) ) )
& ( ! [U_98] :
( in(U_98,U_100)
| ~ in(U_98,U_101) )
| ~ subset(U_101,U_100) ) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_105,U_103] :
( subset(U_105,U_103)
| ? [U_99] :
( ~ in(U_99,U_103)
& in(U_99,U_105) ) )
& ! [U_104,U_102] :
( ! [U_98] :
( in(U_98,U_102)
| ~ in(U_98,U_104) )
| ~ subset(U_104,U_102) ) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
fof(f_13_4,plain,
( ! [U_105,U_103] :
( subset(U_105,U_103)
| ( ~ in(sK16(U_105,U_103),U_103)
& in(sK16(U_105,U_103),U_105) ) )
& ! [U_104,U_102] :
( ! [U_98] :
( in(U_98,U_102)
| ~ in(U_98,U_104) )
| ~ subset(U_104,U_102) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_99,sK16(U_105,U_103))],[f_13_3]) ).
cnf(f_13_5,plain,
( in(U_98,U_102)
| ~ in(U_98,U_104)
| ~ subset(U_104,U_102) ),
inference(clausify,[status(thm)],[f_13_4]) ).
cnf(f_13_6,plain,
( in(sK16(U_105,U_103),U_105)
| subset(U_105,U_103) ),
inference(clausify,[status(thm)],[f_13_4]) ).
cnf(f_13_7,plain,
( ~ in(sK16(U_105,U_103),U_103)
| subset(U_105,U_103) ),
inference(clausify,[status(thm)],[f_13_4]) ).
fof(f_14_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_14_2,plain,
! [U_110,U_109,U_108] :
( ( U_108 = set_intersection2(U_110,U_109)
| ? [U_107] :
( ( ~ in(U_107,U_108)
& in(U_107,U_109)
& in(U_107,U_110) )
| ( ( ~ in(U_107,U_109)
| ~ in(U_107,U_110) )
& in(U_107,U_108) ) ) )
& ( ! [U_106] :
( ( in(U_106,U_108)
| ~ in(U_106,U_109)
| ~ in(U_106,U_110) )
& ( ( in(U_106,U_109)
& in(U_106,U_110) )
| ~ in(U_106,U_108) ) )
| U_108 != set_intersection2(U_110,U_109) ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_120,U_118,U_116] :
( U_116 = set_intersection2(U_120,U_118)
| ? [U_114] :
( ~ in(U_114,U_116)
& in(U_114,U_118)
& in(U_114,U_120) )
| ? [U_113] :
( ( ~ in(U_113,U_118)
| ~ in(U_113,U_120) )
& in(U_113,U_116) ) )
& ! [U_119,U_117,U_115] :
( ( ! [U_112] :
( in(U_112,U_115)
| ~ in(U_112,U_117)
| ~ in(U_112,U_119) )
& ! [U_111] :
( ( in(U_111,U_117)
& in(U_111,U_119) )
| ~ in(U_111,U_115) ) )
| U_115 != set_intersection2(U_119,U_117) ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
fof(f_14_4,plain,
( ! [U_120,U_118,U_116] :
( U_116 = set_intersection2(U_120,U_118)
| ? [U_114] :
( ~ in(U_114,U_116)
& in(U_114,U_118)
& in(U_114,U_120) )
| ( ( ~ in(sK17(U_120,U_118,U_116),U_118)
| ~ in(sK17(U_120,U_118,U_116),U_120) )
& in(sK17(U_120,U_118,U_116),U_116) ) )
& ! [U_119,U_117,U_115] :
( ( ! [U_112] :
( in(U_112,U_115)
| ~ in(U_112,U_117)
| ~ in(U_112,U_119) )
& ! [U_111] :
( ( in(U_111,U_117)
& in(U_111,U_119) )
| ~ in(U_111,U_115) ) )
| U_115 != set_intersection2(U_119,U_117) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_113,sK17(U_120,U_118,U_116))],[f_14_3]) ).
fof(f_14_5,plain,
( ! [U_120,U_118,U_116] :
( U_116 = set_intersection2(U_120,U_118)
| ( ~ in(sK18(U_120,U_118,U_116),U_116)
& in(sK18(U_120,U_118,U_116),U_118)
& in(sK18(U_120,U_118,U_116),U_120) )
| ( ( ~ in(sK17(U_120,U_118,U_116),U_118)
| ~ in(sK17(U_120,U_118,U_116),U_120) )
& in(sK17(U_120,U_118,U_116),U_116) ) )
& ! [U_119,U_117,U_115] :
( ( ! [U_112] :
( in(U_112,U_115)
| ~ in(U_112,U_117)
| ~ in(U_112,U_119) )
& ! [U_111] :
( ( in(U_111,U_117)
& in(U_111,U_119) )
| ~ in(U_111,U_115) ) )
| U_115 != set_intersection2(U_119,U_117) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_114,sK18(U_120,U_118,U_116))],[f_14_4]) ).
cnf(f_14_6,plain,
( in(U_111,U_119)
| ~ in(U_111,U_115)
| U_115 != set_intersection2(U_119,U_117) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_7,plain,
( in(U_111,U_117)
| ~ in(U_111,U_115)
| U_115 != set_intersection2(U_119,U_117) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_8,plain,
( in(U_112,U_115)
| ~ in(U_112,U_117)
| ~ in(U_112,U_119)
| U_115 != set_intersection2(U_119,U_117) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_9,plain,
( in(sK18(U_120,U_118,U_116),U_120)
| in(sK17(U_120,U_118,U_116),U_116)
| U_116 = set_intersection2(U_120,U_118) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_10,plain,
( in(sK18(U_120,U_118,U_116),U_118)
| in(sK17(U_120,U_118,U_116),U_116)
| U_116 = set_intersection2(U_120,U_118) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_11,plain,
( ~ in(sK18(U_120,U_118,U_116),U_116)
| in(sK17(U_120,U_118,U_116),U_116)
| U_116 = set_intersection2(U_120,U_118) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_12,plain,
( in(sK18(U_120,U_118,U_116),U_120)
| ~ in(sK17(U_120,U_118,U_116),U_118)
| ~ in(sK17(U_120,U_118,U_116),U_120)
| U_116 = set_intersection2(U_120,U_118) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_13,plain,
( in(sK18(U_120,U_118,U_116),U_118)
| ~ in(sK17(U_120,U_118,U_116),U_118)
| ~ in(sK17(U_120,U_118,U_116),U_120)
| U_116 = set_intersection2(U_120,U_118) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_14,plain,
( ~ in(sK18(U_120,U_118,U_116),U_116)
| ~ in(sK17(U_120,U_118,U_116),U_118)
| ~ in(sK17(U_120,U_118,U_116),U_120)
| U_116 = set_intersection2(U_120,U_118) ),
inference(clausify,[status(thm)],[f_14_5]) ).
fof(f_15_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_15_2,plain,
! [U_128,U_127] :
( ( U_127 = union(U_128)
| ? [U_126] :
( ( ~ in(U_126,U_127)
& ? [U_125] :
( in(U_125,U_128)
& in(U_126,U_125) ) )
| ( ! [U_124] :
( ~ in(U_124,U_128)
| ~ in(U_126,U_124) )
& in(U_126,U_127) ) ) )
& ( ! [U_123] :
( ( in(U_123,U_127)
| ! [U_122] :
( ~ in(U_122,U_128)
| ~ in(U_123,U_122) ) )
& ( ? [U_121] :
( in(U_121,U_128)
& in(U_123,U_121) )
| ~ in(U_123,U_127) ) )
| U_127 != union(U_128) ) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ! [U_136,U_134] :
( U_134 = union(U_136)
| ? [U_132] :
( ~ in(U_132,U_134)
& ? [U_125] :
( in(U_125,U_136)
& in(U_132,U_125) ) )
| ? [U_131] :
( ! [U_124] :
( ~ in(U_124,U_136)
| ~ in(U_131,U_124) )
& in(U_131,U_134) ) )
& ! [U_135,U_133] :
( ( ! [U_130] :
( in(U_130,U_133)
| ! [U_122] :
( ~ in(U_122,U_135)
| ~ in(U_130,U_122) ) )
& ! [U_129] :
( ? [U_121] :
( in(U_121,U_135)
& in(U_129,U_121) )
| ~ in(U_129,U_133) ) )
| U_133 != union(U_135) ) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
fof(f_15_4,plain,
( ! [U_136,U_134] :
( U_134 = union(U_136)
| ? [U_132] :
( ~ in(U_132,U_134)
& ? [U_125] :
( in(U_125,U_136)
& in(U_132,U_125) ) )
| ? [U_131] :
( ! [U_124] :
( ~ in(U_124,U_136)
| ~ in(U_131,U_124) )
& in(U_131,U_134) ) )
& ! [U_135,U_133] :
( ( ! [U_130] :
( in(U_130,U_133)
| ! [U_122] :
( ~ in(U_122,U_135)
| ~ in(U_130,U_122) ) )
& ! [U_129] :
( ( in(sK19(U_135,U_133,U_129),U_135)
& in(U_129,sK19(U_135,U_133,U_129)) )
| ~ in(U_129,U_133) ) )
| U_133 != union(U_135) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_121,sK19(U_135,U_133,U_129))],[f_15_3]) ).
fof(f_15_5,plain,
( ! [U_136,U_134] :
( U_134 = union(U_136)
| ? [U_132] :
( ~ in(U_132,U_134)
& ? [U_125] :
( in(U_125,U_136)
& in(U_132,U_125) ) )
| ( ! [U_124] :
( ~ in(U_124,U_136)
| ~ in(sK20(U_136,U_134),U_124) )
& in(sK20(U_136,U_134),U_134) ) )
& ! [U_135,U_133] :
( ( ! [U_130] :
( in(U_130,U_133)
| ! [U_122] :
( ~ in(U_122,U_135)
| ~ in(U_130,U_122) ) )
& ! [U_129] :
( ( in(sK19(U_135,U_133,U_129),U_135)
& in(U_129,sK19(U_135,U_133,U_129)) )
| ~ in(U_129,U_133) ) )
| U_133 != union(U_135) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_131,sK20(U_136,U_134))],[f_15_4]) ).
fof(f_15_6,plain,
( ! [U_136,U_134] :
( U_134 = union(U_136)
| ( ~ in(sK21(U_136,U_134),U_134)
& ? [U_125] :
( in(U_125,U_136)
& in(sK21(U_136,U_134),U_125) ) )
| ( ! [U_124] :
( ~ in(U_124,U_136)
| ~ in(sK20(U_136,U_134),U_124) )
& in(sK20(U_136,U_134),U_134) ) )
& ! [U_135,U_133] :
( ( ! [U_130] :
( in(U_130,U_133)
| ! [U_122] :
( ~ in(U_122,U_135)
| ~ in(U_130,U_122) ) )
& ! [U_129] :
( ( in(sK19(U_135,U_133,U_129),U_135)
& in(U_129,sK19(U_135,U_133,U_129)) )
| ~ in(U_129,U_133) ) )
| U_133 != union(U_135) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_132,sK21(U_136,U_134))],[f_15_5]) ).
fof(f_15_7,plain,
( ! [U_136,U_134] :
( U_134 = union(U_136)
| ( ~ in(sK21(U_136,U_134),U_134)
& in(sK22(U_136,U_134),U_136)
& in(sK21(U_136,U_134),sK22(U_136,U_134)) )
| ( ! [U_124] :
( ~ in(U_124,U_136)
| ~ in(sK20(U_136,U_134),U_124) )
& in(sK20(U_136,U_134),U_134) ) )
& ! [U_135,U_133] :
( ( ! [U_130] :
( in(U_130,U_133)
| ! [U_122] :
( ~ in(U_122,U_135)
| ~ in(U_130,U_122) ) )
& ! [U_129] :
( ( in(sK19(U_135,U_133,U_129),U_135)
& in(U_129,sK19(U_135,U_133,U_129)) )
| ~ in(U_129,U_133) ) )
| U_133 != union(U_135) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_125,sK22(U_136,U_134))],[f_15_6]) ).
cnf(f_15_8,plain,
( in(U_129,sK19(U_135,U_133,U_129))
| ~ in(U_129,U_133)
| U_133 != union(U_135) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_9,plain,
( in(sK19(U_135,U_133,U_129),U_135)
| ~ in(U_129,U_133)
| U_133 != union(U_135) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_10,plain,
( in(U_130,U_133)
| ~ in(U_122,U_135)
| ~ in(U_130,U_122)
| U_133 != union(U_135) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_11,plain,
( in(sK21(U_136,U_134),sK22(U_136,U_134))
| in(sK20(U_136,U_134),U_134)
| U_134 = union(U_136) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_12,plain,
( in(sK22(U_136,U_134),U_136)
| in(sK20(U_136,U_134),U_134)
| U_134 = union(U_136) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_13,plain,
( ~ in(sK21(U_136,U_134),U_134)
| in(sK20(U_136,U_134),U_134)
| U_134 = union(U_136) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_14,plain,
( in(sK21(U_136,U_134),sK22(U_136,U_134))
| ~ in(U_124,U_136)
| ~ in(sK20(U_136,U_134),U_124)
| U_134 = union(U_136) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_15,plain,
( in(sK22(U_136,U_134),U_136)
| ~ in(U_124,U_136)
| ~ in(sK20(U_136,U_134),U_124)
| U_134 = union(U_136) ),
inference(clausify,[status(thm)],[f_15_7]) ).
cnf(f_15_16,plain,
( ~ in(sK21(U_136,U_134),U_134)
| ~ in(U_124,U_136)
| ~ in(sK20(U_136,U_134),U_124)
| U_134 = union(U_136) ),
inference(clausify,[status(thm)],[f_15_7]) ).
fof(f_16_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_16_2,plain,
! [U_141,U_140,U_139] :
( ( U_139 = set_difference(U_141,U_140)
| ? [U_138] :
( ( ~ in(U_138,U_139)
& ~ in(U_138,U_140)
& in(U_138,U_141) )
| ( ( in(U_138,U_140)
| ~ in(U_138,U_141) )
& in(U_138,U_139) ) ) )
& ( ! [U_137] :
( ( in(U_137,U_139)
| in(U_137,U_140)
| ~ in(U_137,U_141) )
& ( ( ~ in(U_137,U_140)
& in(U_137,U_141) )
| ~ in(U_137,U_139) ) )
| U_139 != set_difference(U_141,U_140) ) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( ! [U_151,U_149,U_147] :
( U_147 = set_difference(U_151,U_149)
| ? [U_145] :
( ~ in(U_145,U_147)
& ~ in(U_145,U_149)
& in(U_145,U_151) )
| ? [U_144] :
( ( in(U_144,U_149)
| ~ in(U_144,U_151) )
& in(U_144,U_147) ) )
& ! [U_150,U_148,U_146] :
( ( ! [U_143] :
( in(U_143,U_146)
| in(U_143,U_148)
| ~ in(U_143,U_150) )
& ! [U_142] :
( ( ~ in(U_142,U_148)
& in(U_142,U_150) )
| ~ in(U_142,U_146) ) )
| U_146 != set_difference(U_150,U_148) ) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
fof(f_16_4,plain,
( ! [U_151,U_149,U_147] :
( U_147 = set_difference(U_151,U_149)
| ? [U_145] :
( ~ in(U_145,U_147)
& ~ in(U_145,U_149)
& in(U_145,U_151) )
| ( ( in(sK23(U_151,U_149,U_147),U_149)
| ~ in(sK23(U_151,U_149,U_147),U_151) )
& in(sK23(U_151,U_149,U_147),U_147) ) )
& ! [U_150,U_148,U_146] :
( ( ! [U_143] :
( in(U_143,U_146)
| in(U_143,U_148)
| ~ in(U_143,U_150) )
& ! [U_142] :
( ( ~ in(U_142,U_148)
& in(U_142,U_150) )
| ~ in(U_142,U_146) ) )
| U_146 != set_difference(U_150,U_148) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_144,sK23(U_151,U_149,U_147))],[f_16_3]) ).
fof(f_16_5,plain,
( ! [U_151,U_149,U_147] :
( U_147 = set_difference(U_151,U_149)
| ( ~ in(sK24(U_151,U_149,U_147),U_147)
& ~ in(sK24(U_151,U_149,U_147),U_149)
& in(sK24(U_151,U_149,U_147),U_151) )
| ( ( in(sK23(U_151,U_149,U_147),U_149)
| ~ in(sK23(U_151,U_149,U_147),U_151) )
& in(sK23(U_151,U_149,U_147),U_147) ) )
& ! [U_150,U_148,U_146] :
( ( ! [U_143] :
( in(U_143,U_146)
| in(U_143,U_148)
| ~ in(U_143,U_150) )
& ! [U_142] :
( ( ~ in(U_142,U_148)
& in(U_142,U_150) )
| ~ in(U_142,U_146) ) )
| U_146 != set_difference(U_150,U_148) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_145,sK24(U_151,U_149,U_147))],[f_16_4]) ).
cnf(f_16_6,plain,
( in(U_142,U_150)
| ~ in(U_142,U_146)
| U_146 != set_difference(U_150,U_148) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_7,plain,
( ~ in(U_142,U_148)
| ~ in(U_142,U_146)
| U_146 != set_difference(U_150,U_148) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_8,plain,
( in(U_143,U_146)
| in(U_143,U_148)
| ~ in(U_143,U_150)
| U_146 != set_difference(U_150,U_148) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_9,plain,
( in(sK24(U_151,U_149,U_147),U_151)
| in(sK23(U_151,U_149,U_147),U_147)
| U_147 = set_difference(U_151,U_149) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_10,plain,
( ~ in(sK24(U_151,U_149,U_147),U_149)
| in(sK23(U_151,U_149,U_147),U_147)
| U_147 = set_difference(U_151,U_149) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_11,plain,
( ~ in(sK24(U_151,U_149,U_147),U_147)
| in(sK23(U_151,U_149,U_147),U_147)
| U_147 = set_difference(U_151,U_149) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_12,plain,
( in(sK24(U_151,U_149,U_147),U_151)
| in(sK23(U_151,U_149,U_147),U_149)
| ~ in(sK23(U_151,U_149,U_147),U_151)
| U_147 = set_difference(U_151,U_149) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_13,plain,
( ~ in(sK24(U_151,U_149,U_147),U_149)
| in(sK23(U_151,U_149,U_147),U_149)
| ~ in(sK23(U_151,U_149,U_147),U_151)
| U_147 = set_difference(U_151,U_149) ),
inference(clausify,[status(thm)],[f_16_5]) ).
cnf(f_16_14,plain,
( ~ in(sK24(U_151,U_149,U_147),U_147)
| in(sK23(U_151,U_149,U_147),U_149)
| ~ in(sK23(U_151,U_149,U_147),U_151)
| U_147 = set_difference(U_151,U_149) ),
inference(clausify,[status(thm)],[f_16_5]) ).
fof(f_17_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_17_2,plain,
! [U_153,U_152] : ordered_pair(U_153,U_152) = unordered_pair(unordered_pair(U_153,U_152),singleton(U_153)),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
ordered_pair(U_153,U_152) = unordered_pair(unordered_pair(U_153,U_152),singleton(U_153)),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_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_18_2,plain,
! [U_155,U_154] :
( ( disjoint(U_155,U_154)
| set_intersection2(U_155,U_154) != empty_set )
& ( set_intersection2(U_155,U_154) = empty_set
| ~ disjoint(U_155,U_154) ) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( ! [U_159,U_157] :
( disjoint(U_159,U_157)
| set_intersection2(U_159,U_157) != empty_set )
& ! [U_158,U_156] :
( set_intersection2(U_158,U_156) = empty_set
| ~ disjoint(U_158,U_156) ) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
cnf(f_18_4,plain,
( set_intersection2(U_158,U_156) = empty_set
| ~ disjoint(U_158,U_156) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_5,plain,
( disjoint(U_159,U_157)
| set_intersection2(U_159,U_157) != empty_set ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_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_19_2,plain,
! [U_161,U_160] :
( ( proper_subset(U_161,U_160)
| U_161 = U_160
| ~ subset(U_161,U_160) )
& ( ( U_161 != U_160
& subset(U_161,U_160) )
| ~ proper_subset(U_161,U_160) ) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( ! [U_165,U_163] :
( proper_subset(U_165,U_163)
| U_165 = U_163
| ~ subset(U_165,U_163) )
& ! [U_164,U_162] :
( ( U_164 != U_162
& subset(U_164,U_162) )
| ~ proper_subset(U_164,U_162) ) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
cnf(f_19_4,plain,
( subset(U_164,U_162)
| ~ proper_subset(U_164,U_162) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_5,plain,
( U_164 != U_162
| ~ proper_subset(U_164,U_162) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_6,plain,
( proper_subset(U_165,U_163)
| U_165 = U_163
| ~ subset(U_165,U_163) ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
cnf(f_20_2,plain,
$true,
inference(clausify,[status(thm)],[f_20_1]) ).
fof(f_21_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_21_2,plain,
$true,
inference(clausify,[status(thm)],[f_21_1]) ).
fof(f_22_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
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_k2_tarski]) ).
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_k2_xboole_0]) ).
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_zfmisc_1]) ).
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_k3_tarski]) ).
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_k3_xboole_0]) ).
cnf(f_27_2,plain,
$true,
inference(clausify,[status(thm)],[f_27_1]) ).
fof(f_28_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
cnf(f_28_2,plain,
$true,
inference(clausify,[status(thm)],[f_28_1]) ).
fof(f_29_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
cnf(f_29_2,plain,
$true,
inference(clausify,[status(thm)],[f_29_1]) ).
fof(f_30_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_30_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_30_1]) ).
fof(f_31_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_31_2,plain,
! [U_167,U_166] : ~ empty(ordered_pair(U_167,U_166)),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
~ empty(ordered_pair(U_167,U_166)),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_32_2,plain,
! [U_169,U_168] :
( ~ empty(set_union2(U_169,U_168))
| empty(U_169) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_169] :
( ! [U_168] : ~ empty(set_union2(U_169,U_168))
| empty(U_169) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
cnf(f_32_4,plain,
( ~ empty(set_union2(U_169,U_168))
| empty(U_169) ),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_33_2,plain,
! [U_171,U_170] :
( ~ empty(set_union2(U_170,U_171))
| empty(U_171) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_171] :
( ! [U_170] : ~ empty(set_union2(U_170,U_171))
| empty(U_171) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
cnf(f_33_4,plain,
( ~ empty(set_union2(U_170,U_171))
| empty(U_171) ),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_34_2,plain,
! [U_173,U_172] : set_union2(U_173,U_173) = U_173,
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_173] : set_union2(U_173,U_173) = U_173,
inference(miniscope,[status(thm)],[f_34_2]) ).
cnf(f_34_4,plain,
set_union2(U_173,U_173) = U_173,
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_35_2,plain,
! [U_175,U_174] : set_intersection2(U_175,U_175) = U_175,
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_175] : set_intersection2(U_175,U_175) = U_175,
inference(miniscope,[status(thm)],[f_35_2]) ).
cnf(f_35_4,plain,
set_intersection2(U_175,U_175) = U_175,
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
! [A,B] : ~ proper_subset(A,A),
inference(fof_nnf,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(f_36_2,plain,
! [U_177,U_176] : ~ proper_subset(U_177,U_177),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_177] : ~ proper_subset(U_177,U_177),
inference(miniscope,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
~ proper_subset(U_177,U_177),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
! [A] : singleton(A) != empty_set,
inference(fof_nnf,[status(thm)],[l1_zfmisc_1]) ).
fof(f_37_2,plain,
! [U_178] : singleton(U_178) != empty_set,
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
singleton(U_178) != empty_set,
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l23_zfmisc_1]) ).
fof(f_38_2,plain,
! [U_180,U_179] :
( set_union2(singleton(U_180),U_179) = U_179
| ~ in(U_180,U_179) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
cnf(f_38_3,plain,
( set_union2(singleton(U_180),U_179) = U_179
| ~ in(U_180,U_179) ),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_1,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(fof_nnf,[status(thm)],[l25_zfmisc_1]) ).
fof(f_39_2,plain,
! [U_182,U_181] :
( ~ in(U_182,U_181)
| ~ disjoint(singleton(U_182),U_181) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
( ~ in(U_182,U_181)
| ~ disjoint(singleton(U_182),U_181) ),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_1,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(fof_nnf,[status(thm)],[l28_zfmisc_1]) ).
fof(f_40_2,plain,
! [U_184,U_183] :
( disjoint(singleton(U_184),U_183)
| in(U_184,U_183) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
( disjoint(singleton(U_184),U_183)
| in(U_184,U_183) ),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_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_41_2,plain,
! [U_186,U_185] :
( ( subset(singleton(U_186),U_185)
| ~ in(U_186,U_185) )
& ( in(U_186,U_185)
| ~ subset(singleton(U_186),U_185) ) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
( ! [U_190,U_188] :
( subset(singleton(U_190),U_188)
| ~ in(U_190,U_188) )
& ! [U_189,U_187] :
( in(U_189,U_187)
| ~ subset(singleton(U_189),U_187) ) ),
inference(miniscope,[status(thm)],[f_41_2]) ).
cnf(f_41_4,plain,
( in(U_189,U_187)
| ~ subset(singleton(U_189),U_187) ),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_5,plain,
( subset(singleton(U_190),U_188)
| ~ in(U_190,U_188) ),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_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_42_2,plain,
! [U_192,U_191] :
( ( set_difference(U_192,U_191) = empty_set
| ~ subset(U_192,U_191) )
& ( subset(U_192,U_191)
| set_difference(U_192,U_191) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
( ! [U_196,U_194] :
( set_difference(U_196,U_194) = empty_set
| ~ subset(U_196,U_194) )
& ! [U_195,U_193] :
( subset(U_195,U_193)
| set_difference(U_195,U_193) != empty_set ) ),
inference(miniscope,[status(thm)],[f_42_2]) ).
cnf(f_42_4,plain,
( subset(U_195,U_193)
| set_difference(U_195,U_193) != empty_set ),
inference(clausify,[status(thm)],[f_42_3]) ).
cnf(f_42_5,plain,
( set_difference(U_196,U_194) = empty_set
| ~ subset(U_196,U_194) ),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_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_43_2,plain,
! [U_199,U_198,U_197] :
( subset(U_199,set_difference(U_198,singleton(U_197)))
| in(U_197,U_199)
| ~ subset(U_199,U_198) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_199,U_198] :
( ! [U_197] :
( subset(U_199,set_difference(U_198,singleton(U_197)))
| in(U_197,U_199) )
| ~ subset(U_199,U_198) ),
inference(miniscope,[status(thm)],[f_43_2]) ).
cnf(f_43_4,plain,
( subset(U_199,set_difference(U_198,singleton(U_197)))
| in(U_197,U_199)
| ~ subset(U_199,U_198) ),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_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_44_2,plain,
! [U_201,U_200] :
( ( subset(U_201,singleton(U_200))
| ( U_201 != singleton(U_200)
& U_201 != empty_set ) )
& ( U_201 = singleton(U_200)
| U_201 = empty_set
| ~ subset(U_201,singleton(U_200)) ) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
( ! [U_205,U_203] :
( subset(U_205,singleton(U_203))
| ( U_205 != singleton(U_203)
& U_205 != empty_set ) )
& ! [U_204,U_202] :
( U_204 = singleton(U_202)
| U_204 = empty_set
| ~ subset(U_204,singleton(U_202)) ) ),
inference(miniscope,[status(thm)],[f_44_2]) ).
cnf(f_44_4,plain,
( U_204 = singleton(U_202)
| U_204 = empty_set
| ~ subset(U_204,singleton(U_202)) ),
inference(clausify,[status(thm)],[f_44_3]) ).
cnf(f_44_5,plain,
( U_205 != empty_set
| subset(U_205,singleton(U_203)) ),
inference(clausify,[status(thm)],[f_44_3]) ).
cnf(f_44_6,plain,
( U_205 != singleton(U_203)
| subset(U_205,singleton(U_203)) ),
inference(clausify,[status(thm)],[f_44_3]) ).
fof(f_45_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l50_zfmisc_1]) ).
fof(f_45_2,plain,
! [U_207,U_206] :
( subset(U_207,union(U_206))
| ~ in(U_207,U_206) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
cnf(f_45_3,plain,
( subset(U_207,union(U_206))
| ~ in(U_207,U_206) ),
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_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_46_2,plain,
! [U_211,U_210,U_209,U_208] :
( ( in(ordered_pair(U_211,U_210),cartesian_product2(U_209,U_208))
| ~ in(U_210,U_208)
| ~ in(U_211,U_209) )
& ( ( in(U_210,U_208)
& in(U_211,U_209) )
| ~ in(ordered_pair(U_211,U_210),cartesian_product2(U_209,U_208)) ) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
( ! [U_219,U_217,U_215,U_213] :
( in(ordered_pair(U_219,U_217),cartesian_product2(U_215,U_213))
| ~ in(U_217,U_213)
| ~ in(U_219,U_215) )
& ! [U_218,U_216,U_214,U_212] :
( ( in(U_216,U_212)
& in(U_218,U_214) )
| ~ in(ordered_pair(U_218,U_216),cartesian_product2(U_214,U_212)) ) ),
inference(miniscope,[status(thm)],[f_46_2]) ).
cnf(f_46_4,plain,
( in(U_218,U_214)
| ~ in(ordered_pair(U_218,U_216),cartesian_product2(U_214,U_212)) ),
inference(clausify,[status(thm)],[f_46_3]) ).
cnf(f_46_5,plain,
( in(U_216,U_212)
| ~ in(ordered_pair(U_218,U_216),cartesian_product2(U_214,U_212)) ),
inference(clausify,[status(thm)],[f_46_3]) ).
cnf(f_46_6,plain,
( in(ordered_pair(U_219,U_217),cartesian_product2(U_215,U_213))
| ~ in(U_217,U_213)
| ~ in(U_219,U_215) ),
inference(clausify,[status(thm)],[f_46_3]) ).
fof(f_47_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_47_2,plain,
? [U_220] : empty(U_220),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
empty(sK25),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_220,sK25)],[f_47_2]) ).
cnf(f_47_4,plain,
empty(sK25),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_48_2,plain,
? [U_221] : ~ empty(U_221),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
~ empty(sK26),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_221,sK26)],[f_48_2]) ).
cnf(f_48_4,plain,
~ empty(sK26),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_49_2,plain,
! [U_223,U_222] : subset(U_223,U_223),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
! [U_223] : subset(U_223,U_223),
inference(miniscope,[status(thm)],[f_49_2]) ).
cnf(f_49_4,plain,
subset(U_223,U_223),
inference(clausify,[status(thm)],[f_49_3]) ).
fof(f_50_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_50_2,plain,
! [U_225,U_224] :
( disjoint(U_224,U_225)
| ~ disjoint(U_225,U_224) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
cnf(f_50_3,plain,
( disjoint(U_224,U_225)
| ~ disjoint(U_225,U_224) ),
inference(clausify,[status(thm)],[f_50_2]) ).
fof(f_51_1,negated_conjecture,
~ ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
inference(negate,[status(cth)],[t106_zfmisc_1]) ).
fof(f_51_2,negated_conjecture,
? [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)],[f_51_1]) ).
fof(f_51_3,negated_conjecture,
? [U_229,U_228,U_227,U_226] :
( ( ~ in(ordered_pair(U_229,U_228),cartesian_product2(U_227,U_226))
& in(U_228,U_226)
& in(U_229,U_227) )
| ( ( ~ in(U_228,U_226)
| ~ in(U_229,U_227) )
& in(ordered_pair(U_229,U_228),cartesian_product2(U_227,U_226)) ) ),
inference(variable_rename,[status(thm)],[f_51_2]) ).
fof(f_51_4,negated_conjecture,
( ? [U_237,U_235,U_233,U_231] :
( ~ in(ordered_pair(U_237,U_235),cartesian_product2(U_233,U_231))
& in(U_235,U_231)
& in(U_237,U_233) )
| ? [U_236,U_234,U_232,U_230] :
( ( ~ in(U_234,U_230)
| ~ in(U_236,U_232) )
& in(ordered_pair(U_236,U_234),cartesian_product2(U_232,U_230)) ) ),
inference(miniscope,[status(thm)],[f_51_3]) ).
fof(f_51_5,negated_conjecture,
( ? [U_237,U_235,U_233,U_231] :
( ~ in(ordered_pair(U_237,U_235),cartesian_product2(U_233,U_231))
& in(U_235,U_231)
& in(U_237,U_233) )
| ? [U_234,U_232,U_230] :
( ( ~ in(U_234,U_230)
| ~ in(sK27,U_232) )
& in(ordered_pair(sK27,U_234),cartesian_product2(U_232,U_230)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_236,sK27)],[f_51_4]) ).
fof(f_51_6,negated_conjecture,
( ? [U_237,U_235,U_233,U_231] :
( ~ in(ordered_pair(U_237,U_235),cartesian_product2(U_233,U_231))
& in(U_235,U_231)
& in(U_237,U_233) )
| ? [U_232,U_230] :
( ( ~ in(sK28,U_230)
| ~ in(sK27,U_232) )
& in(ordered_pair(sK27,sK28),cartesian_product2(U_232,U_230)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_234,sK28)],[f_51_5]) ).
fof(f_51_7,negated_conjecture,
( ? [U_237,U_235,U_233,U_231] :
( ~ in(ordered_pair(U_237,U_235),cartesian_product2(U_233,U_231))
& in(U_235,U_231)
& in(U_237,U_233) )
| ? [U_230] :
( ( ~ in(sK28,U_230)
| ~ in(sK27,sK29) )
& in(ordered_pair(sK27,sK28),cartesian_product2(sK29,U_230)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_232,sK29)],[f_51_6]) ).
fof(f_51_8,negated_conjecture,
( ? [U_237,U_235,U_233,U_231] :
( ~ in(ordered_pair(U_237,U_235),cartesian_product2(U_233,U_231))
& in(U_235,U_231)
& in(U_237,U_233) )
| ( ( ~ in(sK28,sK30)
| ~ in(sK27,sK29) )
& in(ordered_pair(sK27,sK28),cartesian_product2(sK29,sK30)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_230,sK30)],[f_51_7]) ).
fof(f_51_9,negated_conjecture,
( ? [U_235,U_233,U_231] :
( ~ in(ordered_pair(sK31,U_235),cartesian_product2(U_233,U_231))
& in(U_235,U_231)
& in(sK31,U_233) )
| ( ( ~ in(sK28,sK30)
| ~ in(sK27,sK29) )
& in(ordered_pair(sK27,sK28),cartesian_product2(sK29,sK30)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_237,sK31)],[f_51_8]) ).
fof(f_51_10,negated_conjecture,
( ? [U_233,U_231] :
( ~ in(ordered_pair(sK31,sK32),cartesian_product2(U_233,U_231))
& in(sK32,U_231)
& in(sK31,U_233) )
| ( ( ~ in(sK28,sK30)
| ~ in(sK27,sK29) )
& in(ordered_pair(sK27,sK28),cartesian_product2(sK29,sK30)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_235,sK32)],[f_51_9]) ).
fof(f_51_11,negated_conjecture,
( ? [U_231] :
( ~ in(ordered_pair(sK31,sK32),cartesian_product2(sK33,U_231))
& in(sK32,U_231)
& in(sK31,sK33) )
| ( ( ~ in(sK28,sK30)
| ~ in(sK27,sK29) )
& in(ordered_pair(sK27,sK28),cartesian_product2(sK29,sK30)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_233,sK33)],[f_51_10]) ).
fof(f_51_12,negated_conjecture,
( ( ~ in(ordered_pair(sK31,sK32),cartesian_product2(sK33,sK34))
& in(sK32,sK34)
& in(sK31,sK33) )
| ( ( ~ in(sK28,sK30)
| ~ in(sK27,sK29) )
& in(ordered_pair(sK27,sK28),cartesian_product2(sK29,sK30)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_231,sK34)],[f_51_11]) ).
fof(f_51_13,negated_conjecture,
( ( ~ in(ordered_pair(sK31,sK32),cartesian_product2(sK33,sK34))
| ~ sP1 )
& ( in(sK32,sK34)
| ~ sP1 )
& ( in(sK31,sK33)
| ~ sP1 )
& ( ~ in(sK28,sK30)
| ~ in(sK27,sK29)
| ~ sP0 )
& ( in(ordered_pair(sK27,sK28),cartesian_product2(sK29,sK30))
| ~ sP0 )
& ( sP1
| sP0 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_51_12]) ).
cnf(f_51_14,negated_conjecture,
( sP1
| sP0 ),
inference(clausify,[status(thm)],[f_51_13]) ).
cnf(f_51_15,negated_conjecture,
( in(ordered_pair(sK27,sK28),cartesian_product2(sK29,sK30))
| ~ sP0 ),
inference(clausify,[status(thm)],[f_51_13]) ).
cnf(f_51_16,negated_conjecture,
( ~ in(sK28,sK30)
| ~ in(sK27,sK29)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_51_13]) ).
cnf(f_51_17,negated_conjecture,
( in(sK31,sK33)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_51_13]) ).
cnf(f_51_18,negated_conjecture,
( in(sK32,sK34)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_51_13]) ).
cnf(f_51_19,negated_conjecture,
( ~ in(ordered_pair(sK31,sK32),cartesian_product2(sK33,sK34))
| ~ sP1 ),
inference(clausify,[status(thm)],[f_51_13]) ).
fof(f_52_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_52_2,plain,
! [U_241,U_240,U_239,U_238] :
( U_241 = U_238
| U_241 = U_239
| unordered_pair(U_241,U_240) != unordered_pair(U_239,U_238) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
! [U_241,U_240,U_239] :
( ! [U_238] :
( U_241 = U_238
| unordered_pair(U_241,U_240) != unordered_pair(U_239,U_238) )
| U_241 = U_239 ),
inference(miniscope,[status(thm)],[f_52_2]) ).
cnf(f_52_4,plain,
( U_241 = U_238
| unordered_pair(U_241,U_240) != unordered_pair(U_239,U_238)
| U_241 = U_239 ),
inference(clausify,[status(thm)],[f_52_3]) ).
fof(f_53_1,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t12_xboole_1]) ).
fof(f_53_2,plain,
! [U_243,U_242] :
( set_union2(U_243,U_242) = U_242
| ~ subset(U_243,U_242) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
cnf(f_53_3,plain,
( set_union2(U_243,U_242) = U_242
| ~ subset(U_243,U_242) ),
inference(clausify,[status(thm)],[f_53_2]) ).
fof(f_54_1,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(fof_nnf,[status(thm)],[t17_xboole_1]) ).
fof(f_54_2,plain,
! [U_245,U_244] : subset(set_intersection2(U_245,U_244),U_245),
inference(variable_rename,[status(thm)],[f_54_1]) ).
cnf(f_54_3,plain,
subset(set_intersection2(U_245,U_244),U_245),
inference(clausify,[status(thm)],[f_54_2]) ).
fof(f_55_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_55_2,plain,
! [U_248,U_247,U_246] :
( subset(U_248,set_intersection2(U_247,U_246))
| ~ subset(U_248,U_246)
| ~ subset(U_248,U_247) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
cnf(f_55_3,plain,
( subset(U_248,set_intersection2(U_247,U_246))
| ~ subset(U_248,U_246)
| ~ subset(U_248,U_247) ),
inference(clausify,[status(thm)],[f_55_2]) ).
fof(f_56_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_56_2,plain,
! [U_249] : set_union2(U_249,empty_set) = U_249,
inference(variable_rename,[status(thm)],[f_56_1]) ).
cnf(f_56_3,plain,
set_union2(U_249,empty_set) = U_249,
inference(clausify,[status(thm)],[f_56_2]) ).
fof(f_57_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_57_2,plain,
! [U_252,U_251,U_250] :
( subset(U_252,U_250)
| ~ subset(U_251,U_250)
| ~ subset(U_252,U_251) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
cnf(f_57_3,plain,
( subset(U_252,U_250)
| ~ subset(U_251,U_250)
| ~ subset(U_252,U_251) ),
inference(clausify,[status(thm)],[f_57_2]) ).
fof(f_58_1,plain,
powerset(empty_set) = singleton(empty_set),
inference(fof_nnf,[status(thm)],[t1_zfmisc_1]) ).
cnf(f_58_2,plain,
powerset(empty_set) = singleton(empty_set),
inference(clausify,[status(thm)],[f_58_1]) ).
fof(f_59_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_59_2,plain,
! [U_255,U_254,U_253] :
( subset(set_intersection2(U_255,U_253),set_intersection2(U_254,U_253))
| ~ subset(U_255,U_254) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
! [U_255,U_254] :
( ! [U_253] : subset(set_intersection2(U_255,U_253),set_intersection2(U_254,U_253))
| ~ subset(U_255,U_254) ),
inference(miniscope,[status(thm)],[f_59_2]) ).
cnf(f_59_4,plain,
( subset(set_intersection2(U_255,U_253),set_intersection2(U_254,U_253))
| ~ subset(U_255,U_254) ),
inference(clausify,[status(thm)],[f_59_3]) ).
fof(f_60_1,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t28_xboole_1]) ).
fof(f_60_2,plain,
! [U_257,U_256] :
( set_intersection2(U_257,U_256) = U_257
| ~ subset(U_257,U_256) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
cnf(f_60_3,plain,
( set_intersection2(U_257,U_256) = U_257
| ~ subset(U_257,U_256) ),
inference(clausify,[status(thm)],[f_60_2]) ).
fof(f_61_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_61_2,plain,
! [U_258] : set_intersection2(U_258,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_61_1]) ).
cnf(f_61_3,plain,
set_intersection2(U_258,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_61_2]) ).
fof(f_62_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_62_2,plain,
! [U_261,U_260] :
( U_261 = U_260
| ? [U_259] :
( ( ~ in(U_259,U_261)
& in(U_259,U_260) )
| ( ~ in(U_259,U_260)
& in(U_259,U_261) ) ) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
! [U_261,U_260] :
( U_261 = U_260
| ? [U_263] :
( ~ in(U_263,U_261)
& in(U_263,U_260) )
| ? [U_262] :
( ~ in(U_262,U_260)
& in(U_262,U_261) ) ),
inference(miniscope,[status(thm)],[f_62_2]) ).
fof(f_62_4,plain,
! [U_261,U_260] :
( U_261 = U_260
| ? [U_263] :
( ~ in(U_263,U_261)
& in(U_263,U_260) )
| ( ~ in(sK35(U_261,U_260),U_260)
& in(sK35(U_261,U_260),U_261) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_262,sK35(U_261,U_260))],[f_62_3]) ).
fof(f_62_5,plain,
! [U_261,U_260] :
( U_261 = U_260
| ( ~ in(sK36(U_261,U_260),U_261)
& in(sK36(U_261,U_260),U_260) )
| ( ~ in(sK35(U_261,U_260),U_260)
& in(sK35(U_261,U_260),U_261) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_263,sK36(U_261,U_260))],[f_62_4]) ).
cnf(f_62_6,plain,
( in(sK36(U_261,U_260),U_260)
| in(sK35(U_261,U_260),U_261)
| U_261 = U_260 ),
inference(clausify,[status(thm)],[f_62_5]) ).
cnf(f_62_7,plain,
( ~ in(sK36(U_261,U_260),U_261)
| in(sK35(U_261,U_260),U_261)
| U_261 = U_260 ),
inference(clausify,[status(thm)],[f_62_5]) ).
cnf(f_62_8,plain,
( in(sK36(U_261,U_260),U_260)
| ~ in(sK35(U_261,U_260),U_260)
| U_261 = U_260 ),
inference(clausify,[status(thm)],[f_62_5]) ).
cnf(f_62_9,plain,
( ~ in(sK36(U_261,U_260),U_261)
| ~ in(sK35(U_261,U_260),U_260)
| U_261 = U_260 ),
inference(clausify,[status(thm)],[f_62_5]) ).
fof(f_63_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_63_2,plain,
! [U_264] : subset(empty_set,U_264),
inference(variable_rename,[status(thm)],[f_63_1]) ).
cnf(f_63_3,plain,
subset(empty_set,U_264),
inference(clausify,[status(thm)],[f_63_2]) ).
fof(f_64_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_64_2,plain,
! [U_267,U_266,U_265] :
( subset(set_difference(U_267,U_265),set_difference(U_266,U_265))
| ~ subset(U_267,U_266) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
! [U_267,U_266] :
( ! [U_265] : subset(set_difference(U_267,U_265),set_difference(U_266,U_265))
| ~ subset(U_267,U_266) ),
inference(miniscope,[status(thm)],[f_64_2]) ).
cnf(f_64_4,plain,
( subset(set_difference(U_267,U_265),set_difference(U_266,U_265))
| ~ subset(U_267,U_266) ),
inference(clausify,[status(thm)],[f_64_3]) ).
fof(f_65_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_65_2,plain,
! [U_271,U_270,U_269,U_268] :
( ( U_270 = U_268
& U_271 = U_269 )
| ordered_pair(U_271,U_270) != ordered_pair(U_269,U_268) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
cnf(f_65_3,plain,
( U_271 = U_269
| ordered_pair(U_271,U_270) != ordered_pair(U_269,U_268) ),
inference(clausify,[status(thm)],[f_65_2]) ).
cnf(f_65_4,plain,
( U_270 = U_268
| ordered_pair(U_271,U_270) != ordered_pair(U_269,U_268) ),
inference(clausify,[status(thm)],[f_65_2]) ).
fof(f_66_1,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(fof_nnf,[status(thm)],[t36_xboole_1]) ).
fof(f_66_2,plain,
! [U_273,U_272] : subset(set_difference(U_273,U_272),U_273),
inference(variable_rename,[status(thm)],[f_66_1]) ).
cnf(f_66_3,plain,
subset(set_difference(U_273,U_272),U_273),
inference(clausify,[status(thm)],[f_66_2]) ).
fof(f_67_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_67_2,plain,
! [U_275,U_274] :
( ( set_difference(U_275,U_274) = empty_set
| ~ subset(U_275,U_274) )
& ( subset(U_275,U_274)
| set_difference(U_275,U_274) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
( ! [U_279,U_277] :
( set_difference(U_279,U_277) = empty_set
| ~ subset(U_279,U_277) )
& ! [U_278,U_276] :
( subset(U_278,U_276)
| set_difference(U_278,U_276) != empty_set ) ),
inference(miniscope,[status(thm)],[f_67_2]) ).
cnf(f_67_4,plain,
( subset(U_278,U_276)
| set_difference(U_278,U_276) != empty_set ),
inference(clausify,[status(thm)],[f_67_3]) ).
cnf(f_67_5,plain,
( set_difference(U_279,U_277) = empty_set
| ~ subset(U_279,U_277) ),
inference(clausify,[status(thm)],[f_67_3]) ).
fof(f_68_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_68_2,plain,
! [U_281,U_280] :
( ( subset(singleton(U_281),U_280)
| ~ in(U_281,U_280) )
& ( in(U_281,U_280)
| ~ subset(singleton(U_281),U_280) ) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
fof(f_68_3,plain,
( ! [U_285,U_283] :
( subset(singleton(U_285),U_283)
| ~ in(U_285,U_283) )
& ! [U_284,U_282] :
( in(U_284,U_282)
| ~ subset(singleton(U_284),U_282) ) ),
inference(miniscope,[status(thm)],[f_68_2]) ).
cnf(f_68_4,plain,
( in(U_284,U_282)
| ~ subset(singleton(U_284),U_282) ),
inference(clausify,[status(thm)],[f_68_3]) ).
cnf(f_68_5,plain,
( subset(singleton(U_285),U_283)
| ~ in(U_285,U_283) ),
inference(clausify,[status(thm)],[f_68_3]) ).
fof(f_69_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_69_2,plain,
! [U_288,U_287,U_286] :
( ( subset(unordered_pair(U_288,U_287),U_286)
| ~ in(U_287,U_286)
| ~ in(U_288,U_286) )
& ( ( in(U_287,U_286)
& in(U_288,U_286) )
| ~ subset(unordered_pair(U_288,U_287),U_286) ) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
fof(f_69_3,plain,
( ! [U_294,U_292,U_290] :
( subset(unordered_pair(U_294,U_292),U_290)
| ~ in(U_292,U_290)
| ~ in(U_294,U_290) )
& ! [U_293,U_291,U_289] :
( ( in(U_291,U_289)
& in(U_293,U_289) )
| ~ subset(unordered_pair(U_293,U_291),U_289) ) ),
inference(miniscope,[status(thm)],[f_69_2]) ).
cnf(f_69_4,plain,
( in(U_293,U_289)
| ~ subset(unordered_pair(U_293,U_291),U_289) ),
inference(clausify,[status(thm)],[f_69_3]) ).
cnf(f_69_5,plain,
( in(U_291,U_289)
| ~ subset(unordered_pair(U_293,U_291),U_289) ),
inference(clausify,[status(thm)],[f_69_3]) ).
cnf(f_69_6,plain,
( subset(unordered_pair(U_294,U_292),U_290)
| ~ in(U_292,U_290)
| ~ in(U_294,U_290) ),
inference(clausify,[status(thm)],[f_69_3]) ).
fof(f_70_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_70_2,plain,
! [U_296,U_295] : set_union2(U_296,set_difference(U_295,U_296)) = set_union2(U_296,U_295),
inference(variable_rename,[status(thm)],[f_70_1]) ).
cnf(f_70_3,plain,
set_union2(U_296,set_difference(U_295,U_296)) = set_union2(U_296,U_295),
inference(clausify,[status(thm)],[f_70_2]) ).
fof(f_71_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_71_2,plain,
! [U_298,U_297] :
( ( subset(U_298,singleton(U_297))
| ( U_298 != singleton(U_297)
& U_298 != empty_set ) )
& ( U_298 = singleton(U_297)
| U_298 = empty_set
| ~ subset(U_298,singleton(U_297)) ) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
fof(f_71_3,plain,
( ! [U_302,U_300] :
( subset(U_302,singleton(U_300))
| ( U_302 != singleton(U_300)
& U_302 != empty_set ) )
& ! [U_301,U_299] :
( U_301 = singleton(U_299)
| U_301 = empty_set
| ~ subset(U_301,singleton(U_299)) ) ),
inference(miniscope,[status(thm)],[f_71_2]) ).
cnf(f_71_4,plain,
( U_301 = singleton(U_299)
| U_301 = empty_set
| ~ subset(U_301,singleton(U_299)) ),
inference(clausify,[status(thm)],[f_71_3]) ).
cnf(f_71_5,plain,
( U_302 != empty_set
| subset(U_302,singleton(U_300)) ),
inference(clausify,[status(thm)],[f_71_3]) ).
cnf(f_71_6,plain,
( U_302 != singleton(U_300)
| subset(U_302,singleton(U_300)) ),
inference(clausify,[status(thm)],[f_71_3]) ).
fof(f_72_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_72_2,plain,
! [U_303] : set_difference(U_303,empty_set) = U_303,
inference(variable_rename,[status(thm)],[f_72_1]) ).
cnf(f_72_3,plain,
set_difference(U_303,empty_set) = U_303,
inference(clausify,[status(thm)],[f_72_2]) ).
fof(f_73_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_73_2,plain,
! [U_307,U_306] :
( ( ~ disjoint(U_307,U_306)
| ! [U_305] :
( ~ in(U_305,U_306)
| ~ in(U_305,U_307) ) )
& ( ? [U_304] :
( in(U_304,U_306)
& in(U_304,U_307) )
| disjoint(U_307,U_306) ) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
fof(f_73_3,plain,
( ! [U_311,U_309] :
( ~ disjoint(U_311,U_309)
| ! [U_305] :
( ~ in(U_305,U_309)
| ~ in(U_305,U_311) ) )
& ! [U_310,U_308] :
( ? [U_304] :
( in(U_304,U_308)
& in(U_304,U_310) )
| disjoint(U_310,U_308) ) ),
inference(miniscope,[status(thm)],[f_73_2]) ).
fof(f_73_4,plain,
( ! [U_311,U_309] :
( ~ disjoint(U_311,U_309)
| ! [U_305] :
( ~ in(U_305,U_309)
| ~ in(U_305,U_311) ) )
& ! [U_310,U_308] :
( ( in(sK37(U_310,U_308),U_308)
& in(sK37(U_310,U_308),U_310) )
| disjoint(U_310,U_308) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_304,sK37(U_310,U_308))],[f_73_3]) ).
cnf(f_73_5,plain,
( in(sK37(U_310,U_308),U_310)
| disjoint(U_310,U_308) ),
inference(clausify,[status(thm)],[f_73_4]) ).
cnf(f_73_6,plain,
( in(sK37(U_310,U_308),U_308)
| disjoint(U_310,U_308) ),
inference(clausify,[status(thm)],[f_73_4]) ).
cnf(f_73_7,plain,
( ~ disjoint(U_311,U_309)
| ~ in(U_305,U_309)
| ~ in(U_305,U_311) ),
inference(clausify,[status(thm)],[f_73_4]) ).
fof(f_74_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_74_2,plain,
! [U_312] :
( U_312 = empty_set
| ~ subset(U_312,empty_set) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
cnf(f_74_3,plain,
( U_312 = empty_set
| ~ subset(U_312,empty_set) ),
inference(clausify,[status(thm)],[f_74_2]) ).
fof(f_75_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_75_2,plain,
! [U_314,U_313] : set_difference(set_union2(U_314,U_313),U_313) = set_difference(U_314,U_313),
inference(variable_rename,[status(thm)],[f_75_1]) ).
cnf(f_75_3,plain,
set_difference(set_union2(U_314,U_313),U_313) = set_difference(U_314,U_313),
inference(clausify,[status(thm)],[f_75_2]) ).
fof(f_76_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_76_2,plain,
! [U_316,U_315] :
( U_315 = set_union2(U_316,set_difference(U_315,U_316))
| ~ subset(U_316,U_315) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
cnf(f_76_3,plain,
( U_315 = set_union2(U_316,set_difference(U_315,U_316))
| ~ subset(U_316,U_315) ),
inference(clausify,[status(thm)],[f_76_2]) ).
fof(f_77_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t46_zfmisc_1]) ).
fof(f_77_2,plain,
! [U_318,U_317] :
( set_union2(singleton(U_318),U_317) = U_317
| ~ in(U_318,U_317) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
cnf(f_77_3,plain,
( set_union2(singleton(U_318),U_317) = U_317
| ~ in(U_318,U_317) ),
inference(clausify,[status(thm)],[f_77_2]) ).
fof(f_78_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_78_2,plain,
! [U_320,U_319] : set_difference(U_320,set_difference(U_320,U_319)) = set_intersection2(U_320,U_319),
inference(variable_rename,[status(thm)],[f_78_1]) ).
cnf(f_78_3,plain,
set_difference(U_320,set_difference(U_320,U_319)) = set_intersection2(U_320,U_319),
inference(clausify,[status(thm)],[f_78_2]) ).
fof(f_79_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_79_2,plain,
! [U_321] : set_difference(empty_set,U_321) = empty_set,
inference(variable_rename,[status(thm)],[f_79_1]) ).
cnf(f_79_3,plain,
set_difference(empty_set,U_321) = empty_set,
inference(clausify,[status(thm)],[f_79_2]) ).
fof(f_80_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_80_2,plain,
! [U_325,U_324] :
( ( ~ disjoint(U_325,U_324)
| ! [U_323] : ~ in(U_323,set_intersection2(U_325,U_324)) )
& ( ? [U_322] : in(U_322,set_intersection2(U_325,U_324))
| disjoint(U_325,U_324) ) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
fof(f_80_3,plain,
( ! [U_329,U_327] :
( ~ disjoint(U_329,U_327)
| ! [U_323] : ~ in(U_323,set_intersection2(U_329,U_327)) )
& ! [U_328,U_326] :
( ? [U_322] : in(U_322,set_intersection2(U_328,U_326))
| disjoint(U_328,U_326) ) ),
inference(miniscope,[status(thm)],[f_80_2]) ).
fof(f_80_4,plain,
( ! [U_329,U_327] :
( ~ disjoint(U_329,U_327)
| ! [U_323] : ~ in(U_323,set_intersection2(U_329,U_327)) )
& ! [U_328,U_326] :
( in(sK38(U_328,U_326),set_intersection2(U_328,U_326))
| disjoint(U_328,U_326) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_322,sK38(U_328,U_326))],[f_80_3]) ).
cnf(f_80_5,plain,
( in(sK38(U_328,U_326),set_intersection2(U_328,U_326))
| disjoint(U_328,U_326) ),
inference(clausify,[status(thm)],[f_80_4]) ).
cnf(f_80_6,plain,
( ~ disjoint(U_329,U_327)
| ~ in(U_323,set_intersection2(U_329,U_327)) ),
inference(clausify,[status(thm)],[f_80_4]) ).
fof(f_81_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t60_xboole_1]) ).
fof(f_81_2,plain,
! [U_331,U_330] :
( ~ proper_subset(U_330,U_331)
| ~ subset(U_331,U_330) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
cnf(f_81_3,plain,
( ~ proper_subset(U_330,U_331)
| ~ subset(U_331,U_330) ),
inference(clausify,[status(thm)],[f_81_2]) ).
fof(f_82_1,plain,
! [A,B,C] :
( disjoint(A,C)
| ~ disjoint(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t63_xboole_1]) ).
fof(f_82_2,plain,
! [U_334,U_333,U_332] :
( disjoint(U_334,U_332)
| ~ disjoint(U_333,U_332)
| ~ subset(U_334,U_333) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
cnf(f_82_3,plain,
( disjoint(U_334,U_332)
| ~ disjoint(U_333,U_332)
| ~ subset(U_334,U_333) ),
inference(clausify,[status(thm)],[f_82_2]) ).
fof(f_83_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_83_2,plain,
! [U_336,U_335] :
( ( set_difference(U_336,singleton(U_335)) = U_336
| in(U_335,U_336) )
& ( ~ in(U_335,U_336)
| set_difference(U_336,singleton(U_335)) != U_336 ) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
fof(f_83_3,plain,
( ! [U_340,U_338] :
( set_difference(U_340,singleton(U_338)) = U_340
| in(U_338,U_340) )
& ! [U_339,U_337] :
( ~ in(U_337,U_339)
| set_difference(U_339,singleton(U_337)) != U_339 ) ),
inference(miniscope,[status(thm)],[f_83_2]) ).
cnf(f_83_4,plain,
( ~ in(U_337,U_339)
| set_difference(U_339,singleton(U_337)) != U_339 ),
inference(clausify,[status(thm)],[f_83_3]) ).
cnf(f_83_5,plain,
( set_difference(U_340,singleton(U_338)) = U_340
| in(U_338,U_340) ),
inference(clausify,[status(thm)],[f_83_3]) ).
fof(f_84_1,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(fof_nnf,[status(thm)],[t69_enumset1]) ).
fof(f_84_2,plain,
! [U_341] : unordered_pair(U_341,U_341) = singleton(U_341),
inference(variable_rename,[status(thm)],[f_84_1]) ).
cnf(f_84_3,plain,
unordered_pair(U_341,U_341) = singleton(U_341),
inference(clausify,[status(thm)],[f_84_2]) ).
fof(f_85_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_85_2,plain,
! [U_342] :
( U_342 = empty_set
| ~ empty(U_342) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
cnf(f_85_3,plain,
( U_342 = empty_set
| ~ empty(U_342) ),
inference(clausify,[status(thm)],[f_85_2]) ).
fof(f_86_1,plain,
! [A,B] :
( A = B
| ~ subset(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t6_zfmisc_1]) ).
fof(f_86_2,plain,
! [U_344,U_343] :
( U_344 = U_343
| ~ subset(singleton(U_344),singleton(U_343)) ),
inference(variable_rename,[status(thm)],[f_86_1]) ).
cnf(f_86_3,plain,
( U_344 = U_343
| ~ subset(singleton(U_344),singleton(U_343)) ),
inference(clausify,[status(thm)],[f_86_2]) ).
fof(f_87_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_87_2,plain,
! [U_346,U_345] :
( ~ empty(U_345)
| ~ in(U_346,U_345) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
cnf(f_87_3,plain,
( ~ empty(U_345)
| ~ in(U_346,U_345) ),
inference(clausify,[status(thm)],[f_87_2]) ).
fof(f_88_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1]) ).
fof(f_88_2,plain,
! [U_348,U_347] : subset(U_348,set_union2(U_348,U_347)),
inference(variable_rename,[status(thm)],[f_88_1]) ).
cnf(f_88_3,plain,
subset(U_348,set_union2(U_348,U_347)),
inference(clausify,[status(thm)],[f_88_2]) ).
fof(f_89_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_89_2,plain,
! [U_350,U_349] :
( ( disjoint(U_350,U_349)
| set_difference(U_350,U_349) != U_350 )
& ( set_difference(U_350,U_349) = U_350
| ~ disjoint(U_350,U_349) ) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
fof(f_89_3,plain,
( ! [U_354,U_352] :
( disjoint(U_354,U_352)
| set_difference(U_354,U_352) != U_354 )
& ! [U_353,U_351] :
( set_difference(U_353,U_351) = U_353
| ~ disjoint(U_353,U_351) ) ),
inference(miniscope,[status(thm)],[f_89_2]) ).
cnf(f_89_4,plain,
( set_difference(U_353,U_351) = U_353
| ~ disjoint(U_353,U_351) ),
inference(clausify,[status(thm)],[f_89_3]) ).
cnf(f_89_5,plain,
( disjoint(U_354,U_352)
| set_difference(U_354,U_352) != U_354 ),
inference(clausify,[status(thm)],[f_89_3]) ).
fof(f_90_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_90_2,plain,
! [U_356,U_355] :
( ~ empty(U_355)
| U_356 = U_355
| ~ empty(U_356) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
fof(f_90_3,plain,
! [U_356] :
( ! [U_355] :
( ~ empty(U_355)
| U_356 = U_355 )
| ~ empty(U_356) ),
inference(miniscope,[status(thm)],[f_90_2]) ).
cnf(f_90_4,plain,
( ~ empty(U_355)
| U_356 = U_355
| ~ empty(U_356) ),
inference(clausify,[status(thm)],[f_90_3]) ).
fof(f_91_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_91_2,plain,
! [U_359,U_358,U_357] :
( subset(set_union2(U_359,U_357),U_358)
| ~ subset(U_357,U_358)
| ~ subset(U_359,U_358) ),
inference(variable_rename,[status(thm)],[f_91_1]) ).
cnf(f_91_3,plain,
( subset(set_union2(U_359,U_357),U_358)
| ~ subset(U_357,U_358)
| ~ subset(U_359,U_358) ),
inference(clausify,[status(thm)],[f_91_2]) ).
fof(f_92_1,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t8_zfmisc_1]) ).
fof(f_92_2,plain,
! [U_362,U_361,U_360] :
( U_362 = U_361
| singleton(U_362) != unordered_pair(U_361,U_360) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
fof(f_92_3,plain,
! [U_362,U_361] :
( ! [U_360] : singleton(U_362) != unordered_pair(U_361,U_360)
| U_362 = U_361 ),
inference(miniscope,[status(thm)],[f_92_2]) ).
cnf(f_92_4,plain,
( singleton(U_362) != unordered_pair(U_361,U_360)
| U_362 = U_361 ),
inference(clausify,[status(thm)],[f_92_3]) ).
fof(f_93_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t92_zfmisc_1]) ).
fof(f_93_2,plain,
! [U_364,U_363] :
( subset(U_364,union(U_363))
| ~ in(U_364,U_363) ),
inference(variable_rename,[status(thm)],[f_93_1]) ).
cnf(f_93_3,plain,
( subset(U_364,union(U_363))
| ~ in(U_364,U_363) ),
inference(clausify,[status(thm)],[f_93_2]) ).
fof(f_94_1,plain,
! [A] : union(powerset(A)) = A,
inference(fof_nnf,[status(thm)],[t99_zfmisc_1]) ).
fof(f_94_2,plain,
! [U_365] : union(powerset(U_365)) = U_365,
inference(variable_rename,[status(thm)],[f_94_1]) ).
cnf(f_94_3,plain,
union(powerset(U_365)) = U_365,
inference(clausify,[status(thm)],[f_94_2]) ).
fof(f_95_1,plain,
! [A,B,C] :
( B = C
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t9_zfmisc_1]) ).
fof(f_95_2,plain,
! [U_368,U_367,U_366] :
( U_367 = U_366
| singleton(U_368) != unordered_pair(U_367,U_366) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
cnf(f_95_3,plain,
( U_367 = U_366
| singleton(U_368) != unordered_pair(U_367,U_366) ),
inference(clausify,[status(thm)],[f_95_2]) ).
cnf(f_20_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_20_2]) ).
cnf(f_21_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_21_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_28_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_28_2]) ).
cnf(f_29_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_29_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,
( 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_14,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_15,axiom,
( sK3(Eq_x_0) = sK3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,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_17,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_18,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_19,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_20,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_21,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_22,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_23,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_24,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_25,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_26,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_27,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_28,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_29,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_30,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_31,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_32,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_33,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_34,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_35,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_36,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_37,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_38,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_39,axiom,
( sK37(Eq_x_0,Eq_x_1) = sK37(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_40,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_41,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_42,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_43,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_44,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_45,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU165+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/5.60 % Computer : n020.cluster.edu
% 0.02/5.60 % Model : x86_64 x86_64
% 0.02/5.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/5.60 % Memory : 8046.5625MB
% 0.02/5.60 % OS : Linux 6.8.0-71-generic
% 0.02/5.60 % CPULimit : 300
% 0.02/5.60 % WCLimit : 300
% 0.02/5.60 % DateTime : Sat Sep 19 23:25:53 UTC 2026
% 0.02/5.60 % CPUTime :
% 1.33/6.84 % SZS status Theorem for theBenchmark
% 1.33/6.84 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------