%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU450+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 : 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 08:39:01 AM UTC 2026
% Result : ContradictoryAxioms 66.49s 20.75s
% Output : Refutation 66.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 27 unt; 0 typ; 1 def)
% Number of atoms : 76 ( 51 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 196 ( 21 ~; 11 |; 7 &; 150 @)
% ( 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 : 11 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 62 ( 0 ^; 59 !; 2 ?; 62 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(k4_xboole_0_decl,type,
k4_xboole_0: $i > $i > $i ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(k1_tarski_decl,type,
k1_tarski: $i > $i ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(k2_tarski_decl,type,
k2_tarski: $i > $i > $i ).
thf(v1_finset_1_decl,type,
v1_finset_1: $i > $o ).
thf(sk6_decl,type,
sk6: $i > $i > $i ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ) ) ) ).
thf(79,axiom,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(1272,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(1273,plain,
( ( k1_xboole_0 @ k1_tarski )
= ( k1_xboole_0 @ k1_zfmisc_1 ) ),
inference(lifteq,[status(thm)],[1272]) ).
thf(23,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(987,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)],[23]) ).
thf(988,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[987]) ).
thf(989,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[988]) ).
thf(11397,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_tarski )
!= ( A @ k1_tarski ) )
| ( ( B @ ( A @ k2_tarski ) @ ( k1_xboole_0 @ k1_zfmisc_1 @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1273,989]) ).
thf(11398,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k2_tarski ) @ ( k1_xboole_0 @ k1_zfmisc_1 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[11397:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(11472,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k2_tarski ) @ ( k1_xboole_0 @ k1_zfmisc_1 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[11398]) ).
thf(18,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(962,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)],[18]) ).
thf(963,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(cnf,[status(esa)],[962]) ).
thf(964,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(lifteq,[status(thm)],[963]) ).
thf(965,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[964]) ).
thf(966,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk6 ) )
= A ),
inference(cnf,[status(esa)],[965]) ).
thf(7187,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk6 ) )
= A ),
inference(lifteq,[status(thm)],[966]) ).
thf(11758,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k2_tarski ) @ ( k1_xboole_0 @ k1_zfmisc_1 @ k4_xboole_0 ) )
!= ( C @ ( B @ k4_xboole_0 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk6 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[11472,7187]) ).
thf(11759,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ ( k1_xboole_0 @ k2_tarski ) @ sk6 ) )
= ( k1_xboole_0 @ k1_zfmisc_1 ) ),
inference(pattern_uni,[status(thm)],[11758:[bind(A,$thf( F )),bind(B,$thf( k1_xboole_0 @ k1_zfmisc_1 )),bind(C,$thf( F @ ( k1_xboole_0 @ k2_tarski ) ))]]) ).
thf(11828,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ ( k1_xboole_0 @ k2_tarski ) @ sk6 ) )
= ( k1_xboole_0 @ k1_zfmisc_1 ) ),
inference(simp,[status(thm)],[11759]) ).
thf(58,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(1178,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(1179,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1178]) ).
thf(1180,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1179]) ).
thf(7200,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
!= ( C @ ( B @ k4_xboole_0 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk6 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1180,7187]) ).
thf(7201,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk6 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[7200:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(12792,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[11828,7201]) ).
thf(670,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(4473,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)],[670]) ).
thf(4474,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)],[4473]) ).
thf(4475,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)],[4474]) ).
thf(4477,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[4475]) ).
thf(4479,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[4477]) ).
thf(4480,plain,
k1_xboole_0 @ v1_xboole_0,
inference(simp,[status(thm)],[4479]) ).
thf(243,axiom,
! [A: $i] :
( ( A @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_finset_1) ).
thf(2174,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(2175,plain,
( ! [A: $i] : ( A @ k1_tarski @ v1_finset_1 )
& ~ ? [A: $i] : ( A @ k1_tarski @ v1_xboole_0 ) ),
inference(miniscope,[status(thm)],[2174]) ).
thf(2176,plain,
! [B: $i,A: $i] :
( ( B @ k1_tarski @ v1_finset_1 )
& ~ ( A @ k1_tarski @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[2175]) ).
thf(2177,plain,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[2176]) ).
thf(5645,plain,
! [A: $i] :
( ( ( A @ k1_tarski @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4480,2177]) ).
thf(5646,plain,
! [A: $i] :
( ( A @ k1_tarski @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[5645]) ).
thf(5648,plain,
! [A: $i] :
( ( A @ k1_tarski )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[5646]) ).
thf(5711,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski )
!= ( A @ k1_tarski ) )
| ( ( k1_xboole_0 @ k1_zfmisc_1 )
!= k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1273,5648]) ).
thf(5712,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
!= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[5711:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(12793,plain,
$false,
inference(simplifyReflect,[status(thm)],[12792,5712]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU450+2 : 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
% 0.15/5.97 % Computer : n003.cluster.edu
% 0.15/5.97 % Model : x86_64 x86_64
% 0.15/5.97 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.97 % Memory : 8046.5625MB
% 0.15/5.97 % OS : Linux 6.8.0-71-generic
% 0.15/5.97 % CPULimit : 300
% 0.15/5.97 % WCLimit : 300
% 0.15/5.97 % DateTime : Sat Sep 26 10:03:31 UTC 2026
% 0.15/5.97 % CPUTime :
% 0.15/5.97 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
% 0.58/6.28 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 3.36/6.91 % [INFO] Parsing done (626ms).
% 3.36/6.93 % [INFO] Running in sequential loop mode.
% 4.11/7.16 % [INFO] eprover registered as external prover.
% 4.11/7.17 % [INFO] Scanning for conjecture ...
% 5.19/7.42 % [INFO] Found a conjecture (or negated_conjecture) and 4535 axioms. Running axiom selection ...
% 7.38/7.96 % [INFO] Axiom selection finished. Selected 901 axioms (removed 3634 axioms).
% 9.52/8.41 % [INFO] Problem is first-order (TPTP FOF).
% 9.52/8.48 % [INFO] Type checking passed.
% 9.52/8.49 % [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 ...
% 66.49/20.74 % [INFO] Killing All external provers ...
% 66.49/20.74 % Time passed: 14665ms (effective reasoning time: 13807ms)
% 66.49/20.75 % Axioms used in derivation (6): d5_xboole_0, t1_zfmisc_1, fc1_finset_1, t22_zfmisc_1, t4_boole, t32_xboole_1
% 66.49/20.75 % No. of inferences in proof: 45
% 66.49/20.75 % SZS status ContradictoryAxioms for /export/starexec/sandbox/benchmark/theBenchmark.p : 14665 ms resp. 13807 ms w/o parsing
% 66.49/20.79 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 66.49/20.79 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------