%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT319+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 : n003.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 07:47:13 AM UTC 2026
% Result : ContradictoryAxioms 159.86s 48.88s
% Output : Refutation 156.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 28 unt; 0 typ; 1 def)
% Number of atoms : 67 ( 47 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 150 ( 17 ~; 10 |; 3 &; 113 @)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 63 ( 0 ^; 60 !; 2 ?; 63 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(k2_xboole_0_decl,type,
k2_xboole_0: $i > $i > $i ).
thf(k4_xboole_0_decl,type,
k4_xboole_0: $i > $i > $i ).
thf(sk101_decl,type,
sk101: $i > $i > $i ).
thf(sk101_def,definition,
( sk101
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ) ) ) ).
thf(124,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(1355,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)],[124]) ).
thf(1356,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)],[1355]) ).
thf(1357,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)],[1356]) ).
thf(1359,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1357]) ).
thf(1361,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1359]) ).
thf(1362,plain,
k1_xboole_0 @ v1_xboole_0,
inference(simp,[status(thm)],[1361]) ).
thf(227,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(1840,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(1841,plain,
~ ? [A: $i] : ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[1840]) ).
thf(1842,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(cnf,[status(esa)],[1841]) ).
thf(6219,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1362,1842]) ).
thf(6220,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6219]) ).
thf(6233,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[6220]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(859,plain,
! [A: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(860,plain,
! [A: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
inference(cnf,[status(esa)],[859]) ).
thf(861,plain,
! [A: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
inference(lifteq,[status(thm)],[860]) ).
thf(156,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_xboole_1) ).
thf(1496,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(1497,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1496]) ).
thf(1498,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1497]) ).
thf(18241,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ k2_xboole_0 ) )
!= ( C @ ( B @ k2_xboole_0 ) ) )
| ( ( A @ ( B @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[861,1498]) ).
thf(18242,plain,
! [A: $i] :
( ( A @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[18241:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(238,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_xboole_1) ).
thf(1892,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(1893,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(cnf,[status(esa)],[1892]) ).
thf(1894,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(lifteq,[status(thm)],[1893]) ).
thf(1895,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[1894]) ).
thf(1896,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk101 ) )
= A ),
inference(cnf,[status(esa)],[1895]) ).
thf(40647,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk101 ) )
= A ),
inference(lifteq,[status(thm)],[1896]) ).
thf(40674,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ k4_xboole_0 ) )
!= ( C @ ( B @ k4_xboole_0 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk101 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[18242,40647]) ).
thf(40675,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk101 ) )
= A ),
inference(pattern_uni,[status(thm)],[40674:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(164,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(1522,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(1523,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1522]) ).
thf(1524,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1523]) ).
thf(40680,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
!= ( C @ ( B @ k4_xboole_0 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk101 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1524,40647]) ).
thf(40681,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk101 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[40680:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(40816,plain,
! [A: $i] : ( k1_xboole_0 = A ),
inference(rewrite,[status(thm)],[40675,40681]) ).
thf(40829,plain,
$false,
inference(simplifyReflect,[status(thm)],[6233,40816]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT319+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % 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
% 0.14/5.42 % Computer : n003.cluster.edu
% 0.14/5.42 % Model : x86_64 x86_64
% 0.14/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.42 % Memory : 8046.5625MB
% 0.14/5.42 % OS : Linux 6.8.0-71-generic
% 0.14/5.42 % CPULimit : 300
% 0.14/5.42 % WCLimit : 300
% 0.14/5.42 % DateTime : Fri Sep 25 20:51:45 UTC 2026
% 0.14/5.43 % CPUTime :
% 0.14/5.43 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
% 0.18/6.01 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 7.31/7.68 % [INFO] Parsing done (1666ms).
% 7.46/7.71 % [INFO] Running in sequential loop mode.
% 7.98/8.10 % [INFO] eprover registered as external prover.
% 7.98/8.10 % [INFO] Scanning for conjecture ...
% 11.42/9.00 % [INFO] Found a conjecture (or negated_conjecture) and 13645 axioms. Running axiom selection ...
% 15.14/10.86 % [INFO] Axiom selection finished. Selected 733 axioms (removed 12912 axioms).
% 16.85/11.43 % [INFO] Problem is first-order (TPTP FOF).
% 16.85/11.48 % [INFO] Type checking passed.
% 16.85/11.49 % [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 ...
% 159.86/48.87 % [INFO] Killing All external provers ...
% 159.86/48.88 % Time passed: 43303ms (effective reasoning time: 41161ms)
% 159.86/48.88 % Axioms used in derivation (6): d5_xboole_0, fc1_subset_1, t4_boole, t32_xboole_1, idempotence_k2_xboole_0, t46_xboole_1
% 159.86/48.88 % No. of inferences in proof: 41
% 159.86/48.88 % SZS status ContradictoryAxioms for /export/starexec/sandbox/benchmark/theBenchmark.p : 43303 ms resp. 41161 ms w/o parsing
% 156.60/48.92 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 156.60/48.92 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------