%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU156+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n014.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 : Sun Sep 27 08:37:48 AM UTC 2026
% Result : Theorem 11.29s 9.13s
% Output : Refutation 11.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 69
% Syntax : Number of formulae : 206 ( 94 unt; 0 typ; 15 def)
% Number of atoms : 608 ( 286 equ; 0 cnn)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 1552 ( 163 ~; 122 |; 101 &;1022 @)
% ( 20 <=>; 124 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 28 usr; 9 con; 0-3 aty)
% Number of variables : 448 ( 20 ^; 393 !; 20 ?; 448 :)
% ( 0 !>; 0 ?*; 0 @-; 15 @+)
% Comments :
%------------------------------------------------------------------------------
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(set_difference_decl,type,
set_difference: $i > $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(union_decl,type,
union: $i > $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(set_union2_decl,type,
set_union2: $i > $i > $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i > $o ).
thf(sk7_decl,type,
sk7: $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i > $i ).
thf(sk9_decl,type,
sk9: $i > $i > $i ).
thf(sk13_decl,type,
sk13: $i > $i ).
thf(sk22_decl,type,
sk22: $i ).
thf(sk23_decl,type,
sk23: $i ).
thf(sk24_decl,type,
sk24: $i > $i > $i > $o ).
thf(sk25_decl,type,
sk25: $i > $i > $i > $i ).
thf(sk26_decl,type,
sk26: $i > $i > $i > $i ).
thf(sk27_decl,type,
sk27: $i > $i > $i ).
thf(sk28_decl,type,
sk28: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ordered_pair ) )
= ( D @ ( C @ ordered_pair ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( A @ ( sk1 @ ordered_pair ) )
= ( C @ ( B @ ordered_pair ) ) )
=> ( ( A = C )
& ( sk1 = B ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk2 @ ( sk1 @ ordered_pair ) )
= ( B @ ( A @ ordered_pair ) ) )
=> ( ( sk2 = B )
& ( sk1 = A ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( ( sk2 @ ( sk1 @ ordered_pair ) )
= ( A @ ( sk3 @ ordered_pair ) ) )
=> ( ( sk2 = A )
& ( sk1 = sk3 ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
( ( C @ ( D @ in ) )
& ( D @ ( A @ in ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ in ) )
=> ? [D: $i] :
( ( B @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ? [D: $i] :
( ( B @ ( D @ in ) )
& ( D @ ( C @ in ) ) )
=> ( A @ ( C @ in ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( B @ ( C @ in ) )
& ( C @ ( B @ ( A @ sk8 ) @ in ) ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ in ) ) ) ) ).
thf(sk22_def,definition,
( sk22
= ( @+[A: $i] : ( A @ empty ) ) ) ).
thf(sk23_def,definition,
( sk23
= ( @+[A: $i] :
~ ( A @ empty ) ) ) ).
thf(sk25_def,definition,
( sk25
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( A @ ( D @ in ) )
=> ( ( D = B )
| ( D = C ) ) ) ) ) ).
thf(sk26_def,definition,
( sk26
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( ( D = B )
| ( D = C ) )
=> ( A @ ( D @ in ) ) ) ) ) ).
thf(sk27_def,definition,
( sk27
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ in ) )
=> ( C = B ) ) ) ) ).
thf(sk28_def,definition,
( sk28
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( C = B )
=> ( A @ ( C @ in ) ) ) ) ) ).
thf(39,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(301,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(33,axiom,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(285,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(55,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(391,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(392,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ ordered_pair ) @ empty ),
inference(miniscope,[status(thm)],[391]) ).
thf(393,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
inference(cnf,[status(esa)],[392]) ).
thf(15,axiom,
! [A: $i] :
( ( empty_set @ ( A @ subset ) )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(155,plain,
! [A: $i] :
( ( empty_set @ ( A @ subset ) )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(40,axiom,
empty_set @ empty,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(304,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(302,plain,
~ ! [A: $i] : ( A @ empty ),
inference(miniscope,[status(thm)],[301]) ).
thf(303,plain,
~ ( sk23 @ empty ),
inference(cnf,[status(esa)],[302]) ).
thf(397,plain,
( ( ( sk23 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[304,303]) ).
thf(398,plain,
( ( sk23 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[397]) ).
thf(399,plain,
sk23 != empty_set,
inference(simp,[status(thm)],[398]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(340,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(341,plain,
! [A: $i] :
( ( A = empty_set )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[340]) ).
thf(342,plain,
! [A: $i] :
( ~ ( A @ empty )
| ( A = empty_set ) ),
inference(lifteq,[status(thm)],[341]) ).
thf(51,axiom,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(379,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(380,plain,
~ ? [A: $i] :
( ( A @ singleton )
= empty_set ),
inference(miniscope,[status(thm)],[379]) ).
thf(381,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(cnf,[status(esa)],[380]) ).
thf(382,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(lifteq,[status(thm)],[381]) ).
thf(513,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ singleton ) )
| ( empty_set != empty_set )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[342,382]) ).
thf(514,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ singleton ) )
| ~ ( A @ empty ) ),
inference(simp,[status(thm)],[513]) ).
thf(515,plain,
! [A: $i] :
~ ( A @ singleton @ empty ),
inference(pattern_uni,[status(thm)],[514:[bind(A,$thf( C @ singleton )),bind(B,$thf( C ))]]) ).
thf(556,plain,
! [A: $i] :
~ ( A @ singleton @ empty ),
inference(simp,[status(thm)],[515]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ set_difference ) )
= empty_set )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(62,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_difference ) )
= empty_set ) )
& ( ( ( B @ ( A @ set_difference ) )
= empty_set )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(63,plain,
( ! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_difference ) )
= empty_set ) )
& ! [A: $i,B: $i] :
( ( ( B @ ( A @ set_difference ) )
= empty_set )
=> ( B @ ( A @ subset ) ) ) ),
inference(miniscope,[status(thm)],[62]) ).
thf(64,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ( D @ ( C @ set_difference ) )
= empty_set )
| ~ ( D @ ( C @ subset ) ) )
& ( ( B @ ( A @ subset ) )
| ( ( B @ ( A @ set_difference ) )
!= empty_set ) ) ),
inference(cnf,[status(esa)],[63]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ set_difference ) )
= empty_set )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[64]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ subset ) )
| ( ( B @ ( A @ set_difference ) )
= empty_set ) ),
inference(lifteq,[status(thm)],[66]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ subset ) )
| ( ( B @ ( A @ set_difference ) )
= empty_set ) ),
inference(simp,[status(thm)],[68]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ singleton ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(355,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( C = A ) ) )
=> ( B
= ( A @ singleton ) ) )
& ( ( B
= ( A @ singleton ) )
=> ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(356,plain,
( ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C = A )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( C = A ) ) )
=> ( B
= ( A @ singleton ) ) )
& ! [A: $i,B: $i] :
( ( B
= ( A @ singleton ) )
=> ( ! [C: $i] :
( ( C = A )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( C = A ) ) ) ) ),
inference(miniscope,[status(thm)],[355]) ).
thf(357,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F
= ( E @ singleton ) )
| ~ ( F @ ( E @ ( F @ sk28 ) @ in ) )
| ( ( E @ ( F @ sk27 ) )
!= E ) )
& ( ( F
= ( E @ singleton ) )
| ( ( E @ ( F @ sk28 ) )
= E )
| ( ( E @ ( F @ sk27 ) )
!= E ) )
& ( ( F
= ( E @ singleton ) )
| ~ ( F @ ( E @ ( F @ sk28 ) @ in ) )
| ( F @ ( E @ ( F @ sk27 ) @ in ) ) )
& ( ( F
= ( E @ singleton ) )
| ( ( E @ ( F @ sk28 ) )
= E )
| ( F @ ( E @ ( F @ sk27 ) @ in ) ) )
& ( ( B @ ( D @ in ) )
| ( D != A )
| ( B
!= ( A @ singleton ) ) )
& ( ( C = A )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ singleton ) ) ) ),
inference(cnf,[status(esa)],[356]) ).
thf(361,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ( C != A )
| ( B
!= ( A @ singleton ) ) ),
inference(cnfConj,[status(thm)],[357]) ).
thf(364,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ( C != A )
| ( B
!= ( A @ singleton ) ) ),
inference(lifteq,[status(thm)],[361]) ).
thf(365,plain,
! [A: $i] : ( A @ singleton @ ( A @ in ) ),
inference(simp,[status(thm)],[364]) ).
thf(48,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(352,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( B @ ( C @ ( A @ set_union2 ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(269,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( B @ ( C @ ( A @ set_union2 ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(53,axiom,
! [A: $i] :
( ( A @ ( A @ unordered_pair ) )
= ( A @ singleton ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
thf(385,plain,
! [A: $i] :
( ( A @ ( A @ unordered_pair ) )
= ( A @ singleton ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(52,axiom,
( ( empty_set @ powerset )
= ( empty_set @ singleton ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(383,plain,
( ( empty_set @ powerset )
= ( empty_set @ singleton ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(384,plain,
( ( empty_set @ powerset )
= ( empty_set @ singleton ) ),
inference(lifteq,[status(thm)],[383]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ordered_pair ) )
= ( D @ ( C @ ordered_pair ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ordered_pair ) )
= ( D @ ( C @ ordered_pair ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(56,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ordered_pair ) )
= ( D @ ( C @ ordered_pair ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(110,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ set_difference ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ~ ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(125,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ~ ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ~ ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ set_difference ) ) ) )
& ( ( C
= ( B @ ( A @ set_difference ) ) )
=> ! [D: $i] :
( ( ( ~ ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ~ ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(14,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(152,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(289,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ union ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
thf(78,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) )
=> ( B
= ( A @ union ) ) )
& ( ( B
= ( A @ union ) )
=> ! [C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(261,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ ( A @ subset ) ) )
& ( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(37,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(296,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(297,plain,
sk22 @ empty,
inference(cnf,[status(esa)],[296]) ).
thf(490,plain,
! [A: $i] :
( ( ( sk22 @ empty )
!= ( A @ empty ) )
| ~ $true
| ( A = empty_set ) ),
inference(paramod_ordered,[status(thm)],[297,342]) ).
thf(491,plain,
! [A: $i] :
( ( ( sk22 @ empty )
!= ( A @ empty ) )
| ( A = empty_set ) ),
inference(simp,[status(thm)],[490]) ).
thf(492,plain,
sk22 = empty_set,
inference(pattern_uni,[status(thm)],[491:[bind(A,$thf( sk22 ))]]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ singleton @ subset ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(376,plain,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ singleton @ subset ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(6,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ set_difference ) @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(105,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ set_difference ) @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(106,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ set_difference ) @ subset ) ),
inference(cnf,[status(esa)],[105]) ).
thf(57,plain,
( ( ( sk2 != sk4 )
| ( sk1 != sk3 ) )
& ( ( sk2 @ ( sk1 @ ordered_pair ) )
= ( sk4 @ ( sk3 @ ordered_pair ) ) ) ),
inference(cnf,[status(esa)],[56]) ).
thf(59,plain,
( ( sk2 != sk4 )
| ( sk1 != sk3 ) ),
inference(cnfConj,[status(thm)],[57]) ).
thf(61,plain,
( ( sk4 != sk2 )
| ( sk3 != sk1 ) ),
inference(lifteq,[status(thm)],[59]) ).
thf(408,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ordered_pair ) @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[304,393]) ).
thf(409,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered_pair ) @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[408]) ).
thf(411,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered_pair ) )
!= empty_set ),
inference(simp,[status(thm)],[409]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( C @ ( B @ set_difference ) @ ( C @ ( A @ set_difference ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(116,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( C @ ( B @ set_difference ) @ ( C @ ( A @ set_difference ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(36,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(292,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(233,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(58,plain,
( ( sk2 @ ( sk1 @ ordered_pair ) )
= ( sk4 @ ( sk3 @ ordered_pair ) ) ),
inference(cnfConj,[status(thm)],[57]) ).
thf(60,plain,
( ( sk4 @ ( sk3 @ ordered_pair ) )
= ( sk2 @ ( sk1 @ ordered_pair ) ) ),
inference(lifteq,[status(thm)],[58]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ singleton @ subset ) )
<=> ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(201,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ in ) )
=> ( B @ ( A @ singleton @ subset ) ) )
& ( ( B @ ( A @ singleton @ subset ) )
=> ( B @ ( A @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(349,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(160,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ set_difference ) )
= empty_set )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
thf(70,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_difference ) )
= empty_set ) )
& ( ( ( B @ ( A @ set_difference ) )
= empty_set )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
thf(388,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(18,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(163,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( A @ ( B @ in ) )
=> ( A = empty_set ) )
& ( ( A = empty_set )
=> ! [B: $i] :
~ ( A @ ( B @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(164,plain,
( ! [A: $i] :
( ~ ? [B: $i] : ( A @ ( B @ in ) )
=> ( A = empty_set ) )
& ! [A: $i] :
( ( A = empty_set )
=> ~ ? [B: $i] : ( A @ ( B @ in ) ) ) ),
inference(miniscope,[status(thm)],[163]) ).
thf(165,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C = empty_set )
| ( C @ ( C @ sk13 @ in ) ) )
& ( ~ ( A @ ( B @ in ) )
| ( A != empty_set ) ) ),
inference(cnf,[status(esa)],[164]) ).
thf(166,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ in ) )
| ( A != empty_set ) ),
inference(cnfConj,[status(thm)],[165]) ).
thf(168,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ in ) )
| ( A != empty_set ) ),
inference(lifteq,[status(thm)],[166]) ).
thf(169,plain,
! [A: $i] :
~ ( empty_set @ ( A @ in ) ),
inference(simp,[status(thm)],[168]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(256,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(122,plain,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(123,plain,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
inference(cnf,[status(esa)],[122]) ).
thf(124,plain,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
inference(lifteq,[status(thm)],[123]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(343,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(298,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(22,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(207,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(208,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(cnf,[status(esa)],[207]) ).
thf(428,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ~ $true
| ( ( C @ ( B @ set_difference ) )
= empty_set ) ),
inference(paramod_ordered,[status(thm)],[208,69]) ).
thf(429,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( C @ ( B @ subset ) ) )
| ( ( C @ ( B @ set_difference ) )
= empty_set ) ),
inference(simp,[status(thm)],[428]) ).
thf(430,plain,
! [A: $i] :
( ( A @ ( A @ set_difference ) )
= empty_set ),
inference(pattern_uni,[status(thm)],[429:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(286,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(cnf,[status(esa)],[285]) ).
thf(544,plain,
! [A: $i] :
( ( A != sk4 )
| ( sk2 != empty_set )
| ( sk3 != sk1 )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[342,61]) ).
thf(545,plain,
( ( sk2 != empty_set )
| ( sk3 != sk1 )
| ~ ( sk4 @ empty ) ),
inference(pattern_uni,[status(thm)],[544:[bind(A,$thf( sk4 ))]]) ).
thf(16,axiom,
! [A: $i,B: $i] : ( B @ ( A @ set_union2 ) @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(158,plain,
! [A: $i,B: $i] : ( B @ ( A @ set_union2 ) @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(159,plain,
! [B: $i,A: $i] : ( B @ ( A @ set_union2 ) @ ( A @ subset ) ),
inference(cnf,[status(esa)],[158]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ set_union2 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(172,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ set_union2 ) ) ) )
& ( ( C
= ( B @ ( A @ set_union2 ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ set_union2 ) @ set_difference ) )
= ( B @ ( A @ set_difference ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(113,plain,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ set_union2 ) @ set_difference ) )
= ( B @ ( A @ set_difference ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( ( B @ ( A @ singleton @ set_union2 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l23_zfmisc_1) ).
thf(230,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( ( B @ ( A @ singleton @ set_union2 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
<=> ( B @ ( C @ in ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(245,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) )
& ( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ subset ) )
<=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
thf(271,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) )
=> ( B @ singleton @ ( A @ subset ) ) )
& ( ( B @ singleton @ ( A @ subset ) )
=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(161,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(cnf,[status(esa)],[160]) ).
thf(162,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(lifteq,[status(thm)],[161]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ powerset ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( A @ ( C @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(209,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( A @ ( C @ subset ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( A @ ( C @ subset ) ) ) )
=> ( B
= ( A @ powerset ) ) )
& ( ( B
= ( A @ powerset ) )
=> ! [C: $i] :
( ( ( A @ ( C @ subset ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( A @ ( C @ subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(111,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
inference(cnf,[status(esa)],[110]) ).
thf(112,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
inference(lifteq,[status(thm)],[111]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_union2 ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(282,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_union2 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( D = B )
| ( D = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
thf(305,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) )
=> ( C
= ( B @ ( A @ unordered_pair ) ) ) )
& ( ( C
= ( B @ ( A @ unordered_pair ) ) )
=> ! [D: $i] :
( ( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(306,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ! [D: $i] :
( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) )
=> ( C
= ( B @ ( A @ unordered_pair ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
=> ( ! [D: $i] :
( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ! [D: $i] :
( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) ) ) ),
inference(miniscope,[status(thm)],[305]) ).
thf(307,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( F @ ( G @ ( H @ sk26 ) ) @ in ) )
| ( H @ ( G @ ( F @ sk24 ) ) ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ( ( F @ ( G @ ( H @ sk26 ) ) )
= G )
| ( ( F @ ( G @ ( H @ sk26 ) ) )
= F )
| ( H @ ( G @ ( F @ sk24 ) ) ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( G @ ( F @ sk24 ) ) )
| ( ( F @ ( G @ ( H @ sk25 ) ) )
!= G ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( G @ ( F @ sk24 ) ) )
| ( ( F @ ( G @ ( H @ sk25 ) ) )
!= F ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( G @ ( F @ sk24 ) ) )
| ( H @ ( F @ ( G @ ( H @ sk25 ) ) @ in ) ) )
& ( ( C @ ( E @ in ) )
| ( E != B )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) )
& ( ( C @ ( E @ in ) )
| ( E != A )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) )
& ( ( D = B )
| ( D = A )
| ~ ( C @ ( D @ in ) )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ) ),
inference(cnf,[status(esa)],[306]) ).
thf(314,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ( D != A )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(cnfConj,[status(thm)],[307]) ).
thf(326,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ( D != A )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[314]) ).
thf(327,plain,
! [B: $i,A: $i] : ( B @ ( A @ unordered_pair ) @ ( A @ in ) ),
inference(simp,[status(thm)],[326]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( ( B @ ( A @ set_difference ) )
!= empty_set ) ),
inference(cnfConj,[status(thm)],[64]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( ( B @ ( A @ set_difference ) )
!= empty_set ) ),
inference(lifteq,[status(thm)],[65]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(199,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( ( B @ ( A @ unordered_pair ) )
= ( D @ ( C @ unordered_pair ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(336,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( ( B @ ( A @ unordered_pair ) )
= ( D @ ( C @ unordered_pair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(153,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
inference(cnf,[status(esa)],[152]) ).
thf(154,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
inference(lifteq,[status(thm)],[153]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( ( C @ singleton @ ( B @ set_difference ) @ ( A @ subset ) )
| ( A @ ( C @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_zfmisc_1) ).
thf(258,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( ( C @ singleton @ ( B @ set_difference ) @ ( A @ subset ) )
| ( A @ ( C @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(406,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ordered_pair ) @ empty )
!= ( sk22 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[297,393]) ).
thf(407,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered_pair ) @ empty )
!= ( sk22 @ empty ) ),
inference(simp,[status(thm)],[406]) ).
thf(410,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered_pair ) )
!= sk22 ),
inference(simp,[status(thm)],[407]) ).
thf(447,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ ordered_pair ) )
!= ( B @ ( A @ ordered_pair ) ) )
| ( ( sk2 @ ( sk1 @ ordered_pair ) )
!= sk22 ) ),
inference(paramod_ordered,[status(thm)],[60,410]) ).
thf(448,plain,
( ( sk2 @ ( sk1 @ ordered_pair ) )
!= sk22 ),
inference(pattern_uni,[status(thm)],[447:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(568,plain,
( ( sk2 @ ( sk1 @ ordered_pair ) )
!= empty_set ),
inference(rewrite,[status(thm)],[448,492]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ set_difference ) @ ( A @ set_union2 ) )
= ( B @ ( A @ set_union2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(119,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ set_difference ) @ ( A @ set_union2 ) )
= ( B @ ( A @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(346,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(287,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( B
= ( A @ ( B @ set_difference ) @ ( A @ set_union2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(107,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( B
= ( A @ ( B @ set_difference ) @ ( A @ set_union2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(332,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(79,plain,
( ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) )
=> ( B
= ( A @ union ) ) )
& ! [A: $i,B: $i] :
( ( B
= ( A @ union ) )
=> ( ! [C: $i] :
( ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[78]) ).
thf(80,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G
= ( F @ union ) )
| ~ ( G @ ( F @ ( G @ sk8 ) @ in ) )
| ( G @ ( F @ sk6 ) ) )
& ( ( G
= ( F @ union ) )
| ( F @ ( F @ ( G @ sk9 ) @ in ) )
| ( G @ ( F @ sk6 ) ) )
& ( ( G
= ( F @ union ) )
| ( F @ ( G @ sk9 ) @ ( F @ ( G @ sk8 ) @ in ) )
| ( G @ ( F @ sk6 ) ) )
& ( ( G
= ( F @ union ) )
| ~ ( G @ ( F @ sk6 ) )
| ~ ( F @ ( H @ in ) )
| ~ ( H @ ( F @ ( G @ sk7 ) @ in ) ) )
& ( ( G
= ( F @ union ) )
| ~ ( G @ ( F @ sk6 ) )
| ( G @ ( F @ ( G @ sk7 ) @ in ) ) )
& ( ( B @ ( D @ in ) )
| ~ ( A @ ( E @ in ) )
| ~ ( E @ ( D @ in ) )
| ( B
!= ( A @ union ) ) )
& ( ( A @ ( A @ ( B @ ( C @ sk5 ) ) @ in ) )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ union ) ) )
& ( ( A @ ( B @ ( C @ sk5 ) ) @ ( C @ in ) )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ union ) ) ) ),
inference(cnf,[status(esa)],[79]) ).
thf(88,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ union ) )
| ( A @ ( A @ ( B @ sk9 ) @ in ) )
| ( B @ ( A @ sk6 ) ) ),
inference(cnfConj,[status(thm)],[80]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk9 ) @ in ) )
| ( B @ ( A @ sk6 ) )
| ( B
= ( A @ union ) ) ),
inference(lifteq,[status(thm)],[88]) ).
thf(90,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ sk9 ) @ in ) )
| ( B @ ( A @ sk6 ) )
| ( B
= ( A @ union ) ) ),
inference(simp,[status(thm)],[89]) ).
thf(542,plain,
! [A: $i] :
( ( A != sk3 )
| ( sk4 != sk2 )
| ( sk1 != empty_set )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[342,61]) ).
thf(543,plain,
( ( sk4 != sk2 )
| ( sk1 != empty_set )
| ~ ( sk3 @ empty ) ),
inference(pattern_uni,[status(thm)],[542:[bind(A,$thf( sk3 ))]]) ).
thf(1250,plain,
$false,
inference(e,[status(thm)],[301,285,393,155,399,556,69,365,352,379,269,385,340,384,56,110,125,152,289,78,261,492,376,106,61,411,116,292,233,60,201,349,160,70,388,169,256,124,343,105,298,430,296,286,545,391,382,159,172,113,230,245,303,271,208,162,209,112,342,355,282,327,67,199,336,154,304,258,158,568,119,207,383,346,287,305,107,332,163,62,90,122,543]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU156+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.16/5.42 % Computer : n014.cluster.edu
% 0.16/5.42 % Model : x86_64 x86_64
% 0.16/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.42 % Memory : 8046.5625MB
% 0.16/5.42 % OS : Linux 6.8.0-71-generic
% 0.16/5.42 % CPULimit : 300
% 0.16/5.42 % WCLimit : 300
% 0.16/5.42 % DateTime : Sat Sep 26 08:41:52 UTC 2026
% 0.16/5.42 % CPUTime :
% 0.16/5.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.19/6.01 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.36/6.24 % [INFO] Parsing done (229ms).
% 1.36/6.25 % [INFO] Running in sequential loop mode.
% 2.34/6.64 % [INFO] eprover registered as external prover.
% 2.34/6.64 % [INFO] Scanning for conjecture ...
% 2.54/6.75 % [INFO] Found a conjecture (or negated_conjecture) and 83 axioms. Running axiom selection ...
% 2.68/6.84 % [INFO] Axiom selection finished. Selected 53 axioms (removed 30 axioms).
% 2.90/6.91 % [INFO] Problem is first-order (TPTP FOF).
% 2.90/6.92 % [INFO] Type checking passed.
% 2.90/6.92 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 11.29/9.12 % External prover 'e' found a proof!
% 11.29/9.12 % [INFO] Killing All external provers ...
% 11.29/9.13 % Time passed: 3565ms (effective reasoning time: 2867ms)
% 11.29/9.13 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 11.29/9.13 % Axioms used in derivation (53): t37_xboole_1, t6_boole, t1_zfmisc_1, t9_zfmisc_1, t7_boole, l2_zfmisc_1, t3_boole, fc1_zfmisc_1, d1_tarski, t1_boole, t3_xboole_1, fc1_xboole_0, d5_tarski, d2_tarski, fc2_xboole_0, d1_xboole_0, l50_zfmisc_1, t1_xboole_1, commutativity_k2_xboole_0, t2_tarski, t33_xboole_1, l32_xboole_1, t8_zfmisc_1, t4_boole, fc3_xboole_0, d2_xboole_0, d4_tarski, l4_zfmisc_1, l3_zfmisc_1, commutativity_k2_tarski, d1_zfmisc_1, t69_enumset1, t8_xboole_1, d3_tarski, reflexivity_r1_tarski, t6_zfmisc_1, t2_xboole_1, d4_xboole_0, t36_xboole_1, l23_zfmisc_1, t8_boole, rc1_xboole_0, t12_xboole_1, t10_zfmisc_1, idempotence_k2_xboole_0, d10_xboole_0, t7_xboole_1, rc2_xboole_0, t45_xboole_1, t40_xboole_1, l1_zfmisc_1, t39_xboole_1, antisymmetry_r2_hidden
% 11.29/9.13 % No. of inferences in proof: 191
% 11.29/9.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3565 ms resp. 2867 ms w/o parsing
% 11.26/9.27 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.26/9.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------