%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT338+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 : n006.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 07:47:23 AM UTC 2026
% Result : ContradictoryAxioms 173.23s 49.89s
% Output : Refutation 145.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 17 unt; 0 typ; 1 def)
% Number of atoms : 72 ( 55 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 156 ( 19 ~; 18 |; 7 &; 105 @)
% ( 1 <=>; 6 =>; 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 : 63 ( 0 ^; 59 !; 3 ?; 63 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(v1_relat_1_decl,type,
v1_relat_1: $i > $o ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(k4_tarski_decl,type,
k4_tarski: $i > $i > $i ).
thf(sk420_decl,type,
sk420: $i > $i > $i ).
thf(sk420_def,definition,
( sk420
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ) ) ) ).
thf(683,axiom,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(5188,plain,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(5189,plain,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[5188]) ).
thf(5190,plain,
k1_xboole_0 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[5189]) ).
thf(417,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(3635,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(3636,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[3635]) ).
thf(3637,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ k4_tarski ) @ v1_xboole_0 ),
inference(cnf,[status(esa)],[3636]) ).
thf(16256,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5190,3637]) ).
thf(16257,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[16256]) ).
thf(16267,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_tarski ) )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[16257]) ).
thf(1226,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(8244,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)],[1226]) ).
thf(8245,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)],[8244]) ).
thf(8246,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)],[8245]) ).
thf(8249,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[8246]) ).
thf(8253,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[8249]) ).
thf(8254,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[8253]) ).
thf(857,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(6125,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)],[857]) ).
thf(6126,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(cnf,[status(esa)],[6125]) ).
thf(6127,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(lifteq,[status(thm)],[6126]) ).
thf(6128,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[6127]) ).
thf(6129,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk420 ) )
= A ),
inference(cnf,[status(esa)],[6128]) ).
thf(39437,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk420 ) )
= A ),
inference(lifteq,[status(thm)],[6129]) ).
thf(39444,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
!= ( C @ ( B @ k2_zfmisc_1 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk420 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[8254,39437]) ).
thf(39445,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( k1_xboole_0 @ sk420 ) )
= A ),
inference(pattern_uni,[status(thm)],[39444:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(8248,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[8246]) ).
thf(8251,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[8248]) ).
thf(8252,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[8251]) ).
thf(39442,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k2_zfmisc_1 ) )
!= ( C @ ( B @ k2_zfmisc_1 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk420 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[8252,39437]) ).
thf(39443,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk420 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[39442:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(39472,plain,
! [A: $i] : ( k1_xboole_0 = A ),
inference(rewrite,[status(thm)],[39445,39443]) ).
thf(39515,plain,
$false,
inference(simplifyReflect,[status(thm)],[16267,39472]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT338+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % 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
% 0.13/0.40 % Computer : n006.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Fri Sep 25 21:02:02 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.87/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.94/1.90 % [INFO] Parsing done (904ms).
% 4.33/1.91 % [INFO] Running in sequential loop mode.
% 5.01/2.28 % [INFO] eprover registered as external prover.
% 5.01/2.28 % [INFO] Scanning for conjecture ...
% 6.72/2.77 % [INFO] Found a conjecture (or negated_conjecture) and 5469 axioms. Running axiom selection ...
% 11.03/4.83 % [INFO] Axiom selection finished. Selected 1447 axioms (removed 4022 axioms).
% 14.22/5.91 % [INFO] Problem is first-order (TPTP FOF).
% 14.22/6.00 % [INFO] Type checking passed.
% 14.22/6.01 % [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 ...
% 173.23/49.88 % [INFO] Killing All external provers ...
% 173.23/49.88 % Time passed: 49334ms (effective reasoning time: 47959ms)
% 173.23/49.88 % Axioms used in derivation (4): fc4_relat_1, fc1_zfmisc_1, t113_zfmisc_1, t115_zfmisc_1
% 173.23/49.88 % No. of inferences in proof: 34
% 173.23/49.89 % SZS status ContradictoryAxioms for /export/starexec/sandbox2/benchmark/theBenchmark.p : 49334 ms resp. 47959 ms w/o parsing
% 145.53/49.93 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 145.53/49.93 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------