%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT298+2 : 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 : n018.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 07:47:05 AM UTC 2026
% Result : ContradictoryAxioms 159.96s 40.45s
% Output : Refutation 159.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 15 unt; 0 typ; 2 def)
% Number of atoms : 90 ( 65 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 168 ( 24 ~; 22 |; 11 &; 99 @)
% ( 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; 4 con; 0-2 aty)
% Number of variables : 60 ( 0 ^; 55 !; 3 ?; 60 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(v1_relat_1_decl,type,
v1_relat_1: $i > $o ).
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_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(sk43_decl,type,
sk43: $i > $i > $i ).
thf(sk78_decl,type,
sk78: $i ).
thf(sk43_def,definition,
( sk43
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk78_def,definition,
( sk78
= ( @+[A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(61,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(961,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)],[61]) ).
thf(962,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)],[961]) ).
thf(963,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)],[962]) ).
thf(965,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[963]) ).
thf(967,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[965]) ).
thf(968,plain,
k1_xboole_0 @ v1_xboole_0,
inference(simp,[status(thm)],[967]) ).
thf(190,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(1571,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(1572,plain,
( ( sk78 @ v1_relat_1 )
& ~ ( sk78 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[1571]) ).
thf(1573,plain,
~ ( sk78 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[1572]) ).
thf(4018,plain,
( ( ( sk78 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[968,1573]) ).
thf(4019,plain,
( ( sk78 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[4018]) ).
thf(4020,plain,
sk78 != k1_xboole_0,
inference(simp,[status(thm)],[4019]) ).
thf(73,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(1024,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)],[73]) ).
thf(1025,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)],[1024]) ).
thf(1026,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)],[1025]) ).
thf(1029,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1026]) ).
thf(1033,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1029]) ).
thf(1034,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[1033]) ).
thf(105,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(1183,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)],[105]) ).
thf(1184,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(cnf,[status(esa)],[1183]) ).
thf(1185,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(lifteq,[status(thm)],[1184]) ).
thf(1186,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[1185]) ).
thf(1187,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk43 ) )
= A ),
inference(cnf,[status(esa)],[1186]) ).
thf(40939,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk43 ) )
= A ),
inference(lifteq,[status(thm)],[1187]) ).
thf(40982,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
!= ( C @ ( B @ k2_zfmisc_1 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk43 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1034,40939]) ).
thf(40983,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( k1_xboole_0 @ sk43 ) )
= A ),
inference(pattern_uni,[status(thm)],[40982:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(1028,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1026]) ).
thf(1031,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1028]) ).
thf(1032,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[1031]) ).
thf(40952,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k2_zfmisc_1 ) )
!= ( C @ ( B @ k2_zfmisc_1 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk43 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1032,40939]) ).
thf(40953,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk43 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[40952:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(41507,plain,
! [A: $i] : ( k1_xboole_0 = A ),
inference(rewrite,[status(thm)],[40983,40953]) ).
thf(41527,plain,
$false,
inference(simplifyReflect,[status(thm)],[4020,41507]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT298+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.13 % 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
% 0.24/0.50 % Computer : n018.cluster.edu
% 0.24/0.50 % Model : x86_64 x86_64
% 0.24/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.50 % Memory : 8046.5625MB
% 0.24/0.50 % OS : Linux 6.8.0-71-generic
% 0.24/0.50 % CPULimit : 300
% 0.24/0.50 % WCLimit : 300
% 0.24/0.50 % DateTime : Fri Sep 25 20:37:52 UTC 2026
% 0.24/0.50 % CPUTime :
% 0.24/0.50 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
% 1.43/1.36 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 5.77/2.52 % [INFO] Parsing done (1148ms).
% 5.77/2.55 % [INFO] Running in sequential loop mode.
% 7.33/3.15 % [INFO] eprover registered as external prover.
% 7.52/3.16 % [INFO] Scanning for conjecture ...
% 9.12/3.68 % [INFO] Found a conjecture (or negated_conjecture) and 2933 axioms. Running axiom selection ...
% 12.52/4.68 % [INFO] Axiom selection finished. Selected 666 axioms (removed 2267 axioms).
% 15.36/5.72 % [INFO] Problem is first-order (TPTP FOF).
% 15.79/5.80 % [INFO] Type checking passed.
% 15.79/5.81 % [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 ...
% 159.96/40.44 % [INFO] Killing All external provers ...
% 159.96/40.44 % Time passed: 39727ms (effective reasoning time: 37884ms)
% 159.96/40.45 % Axioms used in derivation (4): d5_xboole_0, rc2_relat_1, t113_zfmisc_1, t115_zfmisc_1
% 159.96/40.45 % No. of inferences in proof: 37
% 159.96/40.45 % SZS status ContradictoryAxioms for /export/starexec/sandbox2/benchmark/theBenchmark.p : 39727 ms resp. 37884 ms w/o parsing
% 159.96/40.49 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 159.96/40.49 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------