%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU451+4 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n016.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 08:39:02 AM UTC 2026
% Result : ContradictoryAxioms 155.66s 54.38s
% Output : Refutation 139.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 10
% Syntax : Number of formulae : 76 ( 40 unt; 0 typ; 3 def)
% Number of atoms : 145 ( 107 equ; 0 cnn)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 521 ( 43 ~; 35 |; 10 &; 416 @)
% ( 3 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 138 ( 2 ^; 124 !; 9 ?; 138 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(k6_partfun1_decl,type,
k6_partfun1: $i > $i ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(k1_tarski_decl,type,
k1_tarski: $i > $i ).
thf(k1_card_1_decl,type,
k1_card_1: $i > $i ).
thf(sk31_decl,type,
sk31: $i > $i > $i ).
thf(sk77_decl,type,
sk77: $i > $i ).
thf(sk94_decl,type,
sk94: $i > $i ).
thf(sk31_def,definition,
( sk31
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk77_def,definition,
( sk77
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ r2_hidden ) ) ) ) ).
thf(sk94_def,definition,
( sk94
= ( ^ [A: $i] :
@+[B: $i] :
( A
= ( B @ k1_tarski ) ) ) ) ).
thf(53,axiom,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(592,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(593,plain,
( ( k1_xboole_0 @ k1_tarski )
= ( k1_xboole_0 @ k1_zfmisc_1 ) ),
inference(lifteq,[status(thm)],[592]) ).
thf(198,axiom,
! [A: $i,B: $i] :
( ( ( A @ k1_card_1 )
= ( B @ k1_tarski @ k1_card_1 ) )
<=> ? [C: $i] :
( A
= ( C @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_card_1) ).
thf(1455,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ k1_tarski ) )
=> ( ( A @ k1_card_1 )
= ( B @ k1_tarski @ k1_card_1 ) ) )
& ( ( ( A @ k1_card_1 )
= ( B @ k1_tarski @ k1_card_1 ) )
=> ? [C: $i] :
( A
= ( C @ k1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(1456,plain,
( ! [A: $i] :
( ? [B: $i] :
( A
= ( B @ k1_tarski ) )
=> ! [B: $i] :
( ( A @ k1_card_1 )
= ( B @ k1_tarski @ k1_card_1 ) ) )
& ! [A: $i] :
( ? [B: $i] :
( ( A @ k1_card_1 )
= ( B @ k1_tarski @ k1_card_1 ) )
=> ? [B: $i] :
( A
= ( B @ k1_tarski ) ) ) ),
inference(miniscope,[status(thm)],[1455]) ).
thf(1457,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ( C @ k1_card_1 )
= ( E @ k1_tarski @ k1_card_1 ) )
| ( C
!= ( D @ k1_tarski ) ) )
& ( ( A
= ( A @ sk94 @ k1_tarski ) )
| ( ( A @ k1_card_1 )
!= ( B @ k1_tarski @ k1_card_1 ) ) ) ),
inference(cnf,[status(esa)],[1456]) ).
thf(1459,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k1_card_1 )
= ( C @ k1_tarski @ k1_card_1 ) )
| ( A
!= ( B @ k1_tarski ) ) ),
inference(cnfConj,[status(thm)],[1457]) ).
thf(1461,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k1_card_1 )
= ( C @ k1_tarski @ k1_card_1 ) )
| ( A
!= ( B @ k1_tarski ) ) ),
inference(lifteq,[status(thm)],[1459]) ).
thf(1462,plain,
! [B: $i,A: $i] :
( ( A @ k1_tarski @ k1_card_1 )
= ( B @ k1_tarski @ k1_card_1 ) ),
inference(simp,[status(thm)],[1461]) ).
thf(4585,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_tarski )
!= ( B @ k1_tarski ) )
| ( ( A @ k1_tarski @ k1_card_1 )
= ( k1_xboole_0 @ k1_zfmisc_1 @ k1_card_1 ) ) ),
inference(paramod_ordered,[status(thm)],[593,1462]) ).
thf(4586,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_card_1 )
= ( k1_xboole_0 @ k1_zfmisc_1 @ k1_card_1 ) ),
inference(pattern_uni,[status(thm)],[4585:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 ))]]) ).
thf(64,axiom,
! [A: $i] :
( ( A @ k6_partfun1 @ k1_card_1 )
= ( A @ k1_card_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_necklace) ).
thf(642,plain,
! [A: $i] :
( ( A @ k6_partfun1 @ k1_card_1 )
= ( A @ k1_card_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(643,plain,
! [A: $i] :
( ( A @ k6_partfun1 @ k1_card_1 )
= ( A @ k1_card_1 ) ),
inference(cnf,[status(esa)],[642]) ).
thf(644,plain,
! [A: $i] :
( ( A @ k6_partfun1 @ k1_card_1 )
= ( A @ k1_card_1 ) ),
inference(lifteq,[status(thm)],[643]) ).
thf(149,axiom,
! [A: $i] : ( A @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_card_1) ).
thf(1120,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(1121,plain,
! [A: $i] : ( A @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ),
inference(cnf,[status(esa)],[1120]) ).
thf(3881,plain,
! [B: $i,A: $i] :
( ( ( A @ k6_partfun1 @ k1_card_1 )
!= ( B @ k1_card_1 ) )
| ( B @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[644,1121]) ).
thf(3882,plain,
! [A: $i] : ( A @ k6_partfun1 @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[3881:[bind(A,$thf( C )),bind(B,$thf( C @ k6_partfun1 ))]]) ).
thf(3895,plain,
! [A: $i] : ( A @ k6_partfun1 @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ),
inference(simp,[status(thm)],[3882]) ).
thf(6750,plain,
! [B: $i,A: $i] :
( ( ( A @ k6_partfun1 @ k1_card_1 )
!= ( B @ k1_card_1 ) )
| ( B @ k6_partfun1 @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[644,3895]) ).
thf(6751,plain,
! [A: $i] : ( A @ k6_partfun1 @ k6_partfun1 @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[6750:[bind(A,$thf( C )),bind(B,$thf( C @ k6_partfun1 ))]]) ).
thf(6775,plain,
! [A: $i] : ( A @ k6_partfun1 @ k6_partfun1 @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ),
inference(simp,[status(thm)],[6751]) ).
thf(8067,plain,
! [B: $i,A: $i] :
( ( ( A @ k6_partfun1 @ k1_card_1 )
!= ( B @ k1_card_1 ) )
| ( B @ k6_partfun1 @ k6_partfun1 @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[644,6775]) ).
thf(8068,plain,
! [A: $i] : ( A @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[8067:[bind(A,$thf( C )),bind(B,$thf( C @ k6_partfun1 ))]]) ).
thf(8086,plain,
! [A: $i] : ( A @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ),
inference(simp,[status(thm)],[8068]) ).
thf(10614,plain,
! [B: $i,A: $i] :
( ( ( A @ k6_partfun1 @ k1_card_1 )
!= ( B @ k1_card_1 ) )
| ( B @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[644,8086]) ).
thf(10615,plain,
! [A: $i] : ( A @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[10614:[bind(A,$thf( C )),bind(B,$thf( C @ k6_partfun1 ))]]) ).
thf(10649,plain,
! [A: $i] : ( A @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ),
inference(simp,[status(thm)],[10615]) ).
thf(13017,plain,
! [B: $i,A: $i] :
( ( ( A @ k6_partfun1 @ k1_card_1 )
!= ( B @ k1_card_1 ) )
| ( B @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[644,10649]) ).
thf(13018,plain,
! [A: $i] : ( A @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[13017:[bind(A,$thf( C )),bind(B,$thf( C @ k6_partfun1 ))]]) ).
thf(13053,plain,
! [A: $i] : ( A @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k1_zfmisc_1 @ k1_card_1 @ ( A @ k1_card_1 @ r2_hidden ) ),
inference(simp,[status(thm)],[13018]) ).
thf(24136,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_tarski @ k1_card_1 )
!= ( B @ k1_card_1 ) )
| ( B @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k1_zfmisc_1 @ k1_card_1 @ ( k1_xboole_0 @ k1_zfmisc_1 @ k1_card_1 @ r2_hidden ) ) ),
inference(paramod_ordered,[status(thm)],[4586,13053]) ).
thf(24137,plain,
! [A: $i] : ( A @ k1_tarski @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k1_zfmisc_1 @ k1_card_1 @ ( k1_xboole_0 @ k1_zfmisc_1 @ k1_card_1 @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[24136:[bind(A,$thf( C )),bind(B,$thf( C @ k1_tarski ))]]) ).
thf(24209,plain,
! [A: $i] : ( A @ k1_tarski @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k1_zfmisc_1 @ k1_card_1 @ ( k1_xboole_0 @ k1_zfmisc_1 @ k1_card_1 @ r2_hidden ) ),
inference(simp,[status(thm)],[24137]) ).
thf(163,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(1218,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) )
=> ( A = k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
=> ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(1219,plain,
( ! [A: $i] :
( ~ ? [B: $i] : ( A @ ( B @ r2_hidden ) )
=> ( A = k1_xboole_0 ) )
& ! [A: $i] :
( ( A = k1_xboole_0 )
=> ~ ? [B: $i] : ( A @ ( B @ r2_hidden ) ) ) ),
inference(miniscope,[status(thm)],[1218]) ).
thf(1220,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C = k1_xboole_0 )
| ( C @ ( C @ sk77 @ r2_hidden ) ) )
& ( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[1219]) ).
thf(1221,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1220]) ).
thf(1223,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1221]) ).
thf(1224,plain,
! [A: $i] :
~ ( k1_xboole_0 @ ( A @ r2_hidden ) ),
inference(simp,[status(thm)],[1223]) ).
thf(30133,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_tarski @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k1_zfmisc_1 @ k1_card_1 @ ( k1_xboole_0 @ k1_zfmisc_1 @ k1_card_1 @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24209,1224]) ).
thf(30134,plain,
! [B: $i,A: $i] :
( ( A @ k1_tarski @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k1_zfmisc_1 @ k1_card_1 @ ( k1_xboole_0 @ k1_zfmisc_1 @ k1_card_1 @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) ),
inference(simp,[status(thm)],[30133]) ).
thf(30202,plain,
! [B: $i,A: $i] :
( ( ( A @ k1_tarski @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k1_zfmisc_1 @ k1_card_1 )
!= k1_xboole_0 )
| ( ( k1_xboole_0 @ k1_zfmisc_1 @ k1_card_1 )
!= B ) ),
inference(simp,[status(thm)],[30134]) ).
thf(30271,plain,
! [A: $i] :
( ( A @ k1_tarski @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k1_zfmisc_1 @ k1_card_1 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[30202]) ).
thf(33032,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski )
!= ( A @ k1_tarski ) )
| ( ( k1_xboole_0 @ k1_zfmisc_1 @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k1_zfmisc_1 @ k1_card_1 )
!= k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[593,30271]) ).
thf(33033,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k6_partfun1 @ k1_zfmisc_1 @ k1_card_1 )
!= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[33032:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(195,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
<=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(1429,plain,
! [A: $i,B: $i] :
( ( ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) )
& ( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(1430,plain,
( ! [A: $i,B: $i] :
( ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) )
& ! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(miniscope,[status(thm)],[1429]) ).
thf(1431,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ( D @ ( C @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( D != k1_xboole_0 ) )
& ( ( ( D @ ( C @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( C != k1_xboole_0 ) )
& ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 )
| ( ( B @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[1430]) ).
thf(1434,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1431]) ).
thf(1438,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1434]) ).
thf(1439,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[1438]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_zfmisc_1) ).
thf(692,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(693,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(cnf,[status(esa)],[692]) ).
thf(694,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(lifteq,[status(thm)],[693]) ).
thf(695,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[694]) ).
thf(696,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk31 ) )
= A ),
inference(cnf,[status(esa)],[695]) ).
thf(35947,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk31 ) )
= A ),
inference(lifteq,[status(thm)],[696]) ).
thf(35966,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
!= ( C @ ( B @ k2_zfmisc_1 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk31 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1439,35947]) ).
thf(35967,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( k1_xboole_0 @ sk31 ) )
= A ),
inference(pattern_uni,[status(thm)],[35966:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(1433,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1431]) ).
thf(1436,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1433]) ).
thf(1437,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[1436]) ).
thf(35948,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k2_zfmisc_1 ) )
!= ( C @ ( B @ k2_zfmisc_1 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk31 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1437,35947]) ).
thf(35949,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk31 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[35948:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(36018,plain,
! [A: $i] : ( k1_xboole_0 = A ),
inference(rewrite,[status(thm)],[35967,35949]) ).
thf(36066,plain,
$false,
inference(simplifyReflect,[status(thm)],[33033,36018]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU451+4 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.38 % Computer : n016.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sat Sep 26 10:08:11 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.88/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 16.08/9.36 % [INFO] Parsing done (8383ms).
% 16.23/9.49 % [INFO] Running in sequential loop mode.
% 16.79/9.88 % [INFO] eprover registered as external prover.
% 16.79/9.89 % [INFO] Scanning for conjecture ...
% 25.50/14.89 % [INFO] Found a conjecture (or negated_conjecture) and 71146 axioms. Running axiom selection ...
% 39.54/25.84 % [INFO] Axiom selection finished. Selected 303 axioms (removed 70843 axioms).
% 40.55/26.22 % [INFO] Problem is first-order (TPTP FOF).
% 40.55/26.25 % [INFO] Type checking passed.
% 40.55/26.26 % [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 ...
% 155.66/54.37 % [INFO] Killing All external provers ...
% 155.66/54.37 % Time passed: 53844ms (effective reasoning time: 44869ms)
% 155.66/54.38 % Axioms used in derivation (7): t113_zfmisc_1, t30_card_1, t115_zfmisc_1, d1_xboole_0, t49_card_1, t1_zfmisc_1, t6_necklace
% 155.66/54.38 % No. of inferences in proof: 73
% 155.66/54.38 % SZS status ContradictoryAxioms for /export/starexec/sandbox2/benchmark/theBenchmark.p : 53844 ms resp. 44869 ms w/o parsing
% 139.90/54.44 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 139.90/54.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------