%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU445+3 : TPTP v9.3.1. Released v3.4.0.
% 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 : 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 08:39:00 AM UTC 2026
% Result : ContradictoryAxioms 54.96s 21.51s
% Output : Refutation 54.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 21 unt; 0 typ; 1 def)
% Number of atoms : 86 ( 66 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 179 ( 25 ~; 21 |; 7 &; 114 @)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 62 ( 0 ^; 59 !; 2 ?; 62 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(k1_funct_2_decl,type,
k1_funct_2: $i > $i > $i ).
thf(k1_toler_1_decl,type,
k1_toler_1: $i > $i > $i ).
thf(sk16_decl,type,
sk16: $i > $i > $i ).
thf(sk16_def,definition,
( sk16
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ) ) ) ).
thf(145,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
<=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(964,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)],[145]) ).
thf(965,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)],[964]) ).
thf(966,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)],[965]) ).
thf(969,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[966]) ).
thf(973,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[969]) ).
thf(974,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[973]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_zfmisc_1) ).
thf(413,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)],[37]) ).
thf(414,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(cnf,[status(esa)],[413]) ).
thf(415,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(lifteq,[status(thm)],[414]) ).
thf(416,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[415]) ).
thf(417,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk16 ) )
= A ),
inference(cnf,[status(esa)],[416]) ).
thf(5630,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk16 ) )
= A ),
inference(lifteq,[status(thm)],[417]) ).
thf(5635,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
!= ( C @ ( B @ k2_zfmisc_1 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk16 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[974,5630]) ).
thf(5636,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( k1_xboole_0 @ sk16 ) )
= A ),
inference(pattern_uni,[status(thm)],[5635:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(118,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(809,plain,
! [A: $i] :
( ( ( A = k1_xboole_0 )
=> ( A @ v1_xboole_0 ) )
& ( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(810,plain,
( ! [A: $i] :
( ( A = k1_xboole_0 )
=> ( A @ v1_xboole_0 ) )
& ! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[809]) ).
thf(811,plain,
! [B: $i,A: $i] :
( ( ( B @ v1_xboole_0 )
| ( B != k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[810]) ).
thf(813,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[811]) ).
thf(815,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[813]) ).
thf(816,plain,
k1_xboole_0 @ v1_xboole_0,
inference(simp,[status(thm)],[815]) ).
thf(126,axiom,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_2) ).
thf(869,plain,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(870,plain,
~ ? [A: $i] : ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[869]) ).
thf(871,plain,
! [A: $i] :
~ ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 ),
inference(cnf,[status(esa)],[870]) ).
thf(2038,plain,
! [A: $i] :
( ( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[816,871]) ).
thf(2039,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[2038]) ).
thf(2046,plain,
! [A: $i] :
( ( A @ ( A @ k1_funct_2 ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[2039]) ).
thf(5680,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ ( B @ k1_funct_2 ) ) )
| ( ( k1_xboole_0 @ ( k1_xboole_0 @ sk16 ) )
!= k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[5636,2046]) ).
thf(5681,plain,
( ( k1_xboole_0 @ ( k1_xboole_0 @ sk16 ) )
!= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[5680:[bind(A,$thf( D @ ( D @ k1_funct_2 ) )),bind(B,$thf( D ))]]) ).
thf(75,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k1_toler_1 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_triang_1) ).
thf(593,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k1_toler_1 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(594,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k1_toler_1 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[593]) ).
thf(595,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k1_toler_1 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[594]) ).
thf(5669,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ ( k1_xboole_0 @ k1_toler_1 ) ) )
| ( ( k1_xboole_0 @ ( k1_xboole_0 @ sk16 ) )
= k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[5636,595]) ).
thf(5670,plain,
( ( k1_xboole_0 @ ( k1_xboole_0 @ sk16 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[5669:[bind(A,$thf( D @ ( k1_xboole_0 @ k1_toler_1 ) )),bind(B,$thf( D ))]]) ).
thf(6548,plain,
k1_xboole_0 != k1_xboole_0,
inference(rewrite,[status(thm)],[5681,5670]) ).
thf(6549,plain,
$false,
inference(simp,[status(thm)],[6548]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU445+3 : TPTP v9.3.1. Released v3.4.0.
% 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
% 0.12/5.41 % Computer : n016.cluster.edu
% 0.12/5.41 % Model : x86_64 x86_64
% 0.12/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.41 % Memory : 8046.5625MB
% 0.12/5.41 % OS : Linux 6.8.0-71-generic
% 0.12/5.42 % CPULimit : 300
% 0.12/5.42 % WCLimit : 300
% 0.12/5.42 % DateTime : Sat Sep 26 10:03:33 UTC 2026
% 0.12/5.42 % CPUTime :
% 0.12/5.42 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
% 0.18/5.71 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 6.75/7.78 % [INFO] Parsing done (2061ms).
% 6.86/7.81 % [INFO] Running in sequential loop mode.
% 7.34/8.19 % [INFO] eprover registered as external prover.
% 7.34/8.19 % [INFO] Scanning for conjecture ...
% 10.68/9.20 % [INFO] Found a conjecture (or negated_conjecture) and 19127 axioms. Running axiom selection ...
% 13.71/11.14 % [INFO] Axiom selection finished. Selected 253 axioms (removed 18874 axioms).
% 14.33/11.41 % [INFO] Problem is first-order (TPTP FOF).
% 14.33/11.44 % [INFO] Type checking passed.
% 14.33/11.45 % [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 ...
% 66.55/21.49 % [INFO] Killing All external provers ...
% 54.96/21.50 % Time passed: 15984ms (effective reasoning time: 13673ms)
% 54.96/21.50 % Axioms used in derivation (5): t113_zfmisc_1, d5_xboole_0, t115_zfmisc_1, fc2_funct_2, t1_triang_1
% 54.96/21.50 % No. of inferences in proof: 40
% 54.96/21.51 % SZS status ContradictoryAxioms for /export/starexec/sandbox/benchmark/theBenchmark.p : 15984 ms resp. 13673 ms w/o parsing
% 54.96/21.57 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 54.96/21.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------