%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT308+2 : 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 : n017.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 07:47:09 AM UTC 2026
% Result : ContradictoryAxioms 158.81s 44.42s
% Output : Refutation 158.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 34 unt; 0 typ; 1 def)
% Number of atoms : 75 ( 55 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 204 ( 20 ~; 11 |; 3 &; 163 @)
% ( 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 : 10 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 64 ( 0 ^; 61 !; 2 ?; 64 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(k2_tarski_decl,type,
k2_tarski: $i > $i > $i ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(k4_xboole_0_decl,type,
k4_xboole_0: $i > $i > $i ).
thf(k1_tarski_decl,type,
k1_tarski: $i > $i ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(sk14_decl,type,
sk14: $i > $i > $i ).
thf(sk14_def,definition,
( sk14
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ) ) ) ).
thf(167,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
= ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_zfmisc_1) ).
thf(1998,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
= ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(1999,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
= ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) ) ),
inference(cnf,[status(esa)],[1998]) ).
thf(2000,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) )
= ( A @ k1_tarski @ k1_zfmisc_1 ) ),
inference(lifteq,[status(thm)],[1999]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_zfmisc_1) ).
thf(1219,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(1220,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1219]) ).
thf(1221,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1220]) ).
thf(45328,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) )
!= ( C @ ( B @ k2_tarski ) ) )
| ( ( A @ k1_tarski @ k1_zfmisc_1 @ ( B @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2000,1221]) ).
thf(45329,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[45328:[bind(A,$thf( D )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( D @ k1_tarski ))]]) ).
thf(45415,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[45329]) ).
thf(39,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(1167,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)],[39]) ).
thf(1168,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(cnf,[status(esa)],[1167]) ).
thf(1169,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(lifteq,[status(thm)],[1168]) ).
thf(1170,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[1169]) ).
thf(1171,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk14 ) )
= A ),
inference(cnf,[status(esa)],[1170]) ).
thf(43765,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk14 ) )
= A ),
inference(lifteq,[status(thm)],[1171]) ).
thf(46514,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ k1_tarski @ k1_zfmisc_1 @ ( k1_xboole_0 @ k1_tarski @ k4_xboole_0 ) )
!= ( C @ ( B @ k4_xboole_0 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk14 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[45415,43765]) ).
thf(46515,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k1_tarski @ k1_zfmisc_1 @ sk14 ) )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(pattern_uni,[status(thm)],[46514:[bind(A,$thf( F )),bind(B,$thf( k1_xboole_0 @ k1_tarski )),bind(C,$thf( F @ k1_tarski @ k1_zfmisc_1 ))]]) ).
thf(46590,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k1_tarski @ k1_zfmisc_1 @ sk14 ) )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(simp,[status(thm)],[46515]) ).
thf(132,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(1837,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(1838,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1837]) ).
thf(1839,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1838]) ).
thf(43784,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
!= ( C @ ( B @ k4_xboole_0 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk14 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1839,43765]) ).
thf(43785,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk14 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[43784:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(46631,plain,
( ( k1_xboole_0 @ k1_tarski )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[46590,43785]) ).
thf(145,axiom,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(1902,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(1903,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(lifteq,[status(thm)],[1902]) ).
thf(322,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(2962,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)],[322]) ).
thf(2963,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)],[2962]) ).
thf(2964,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)],[2963]) ).
thf(2966,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[2964]) ).
thf(2968,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[2966]) ).
thf(2969,plain,
k1_xboole_0 @ v1_xboole_0,
inference(simp,[status(thm)],[2968]) ).
thf(478,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(3785,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(3786,plain,
~ ? [A: $i] : ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[3785]) ).
thf(3787,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(cnf,[status(esa)],[3786]) ).
thf(8051,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2969,3787]) ).
thf(8052,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[8051]) ).
thf(8060,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[8052]) ).
thf(11122,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= ( A @ k1_zfmisc_1 ) )
| ( ( k1_xboole_0 @ k1_tarski )
!= k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1903,8060]) ).
thf(11123,plain,
( ( k1_xboole_0 @ k1_tarski )
!= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[11122:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(46632,plain,
$false,
inference(simplifyReflect,[status(thm)],[46631,11123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT308+2 : 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
% 0.14/0.40 % Computer : n017.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Fri Sep 25 20:37:20 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.84/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 3.23/1.69 % [INFO] Parsing done (710ms).
% 3.65/1.71 % [INFO] Running in sequential loop mode.
% 4.24/2.00 % [INFO] eprover registered as external prover.
% 4.24/2.00 % [INFO] Scanning for conjecture ...
% 5.06/2.19 % [INFO] Found a conjecture (or negated_conjecture) and 2962 axioms. Running axiom selection ...
% 8.09/2.96 % [INFO] Axiom selection finished. Selected 977 axioms (removed 1985 axioms).
% 10.79/3.74 % [INFO] Problem is first-order (TPTP FOF).
% 11.20/3.81 % [INFO] Type checking passed.
% 11.20/3.81 % [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 ...
% 158.81/44.41 % [INFO] Killing All external provers ...
% 158.81/44.42 % Time passed: 43866ms (effective reasoning time: 42697ms)
% 158.81/44.42 % Axioms used in derivation (7): d5_xboole_0, t1_zfmisc_1, fc1_subset_1, t22_zfmisc_1, t30_zfmisc_1, t4_boole, t32_xboole_1
% 158.81/44.42 % No. of inferences in proof: 48
% 158.81/44.42 % SZS status ContradictoryAxioms for /export/starexec/sandbox/benchmark/theBenchmark.p : 43866 ms resp. 42697 ms w/o parsing
% 158.81/44.47 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 158.81/44.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------