%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU445+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 : n002.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 08:39:00 AM UTC 2026
% Result : ContradictoryAxioms 113.76s 23.08s
% Output : Refutation 84.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% 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 : 210 ( 18 ~; 11 |; 3 &; 171 @)
% ( 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 : 58 ( 0 ^; 55 !; 2 ?; 58 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(k4_xboole_0_decl,type,
k4_xboole_0: $i > $i > $i ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $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(sk4_decl,type,
sk4: $i > $i > $i ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ) ) ) ).
thf(59,axiom,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(682,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= ( k1_xboole_0 @ k1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(683,plain,
( ( k1_xboole_0 @ k1_tarski )
= ( k1_xboole_0 @ k1_zfmisc_1 ) ),
inference(lifteq,[status(thm)],[682]) ).
thf(69,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
= ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_zfmisc_1) ).
thf(732,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)],[69]) ).
thf(733,plain,
! [A: $i] :
( ( A @ k1_tarski @ k1_zfmisc_1 )
= ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) ) ),
inference(cnf,[status(esa)],[732]) ).
thf(734,plain,
! [A: $i] :
( ( A @ k1_tarski @ ( k1_xboole_0 @ k2_tarski ) )
= ( A @ k1_tarski @ k1_zfmisc_1 ) ),
inference(lifteq,[status(thm)],[733]) ).
thf(5942,plain,
! [A: $i] :
( ( ( k1_xboole_0 @ k1_tarski )
!= ( A @ k1_tarski ) )
| ( ( k1_xboole_0 @ k1_zfmisc_1 @ ( k1_xboole_0 @ k2_tarski ) )
= ( A @ k1_tarski @ k1_zfmisc_1 ) ) ),
inference(paramod_ordered,[status(thm)],[683,734]) ).
thf(5943,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 @ ( k1_xboole_0 @ k2_tarski ) )
= ( k1_xboole_0 @ k1_tarski @ k1_zfmisc_1 ) ),
inference(pattern_uni,[status(thm)],[5942:[bind(A,$thf( k1_xboole_0 ))]]) ).
thf(6013,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 @ ( k1_xboole_0 @ k2_tarski ) )
= ( k1_xboole_0 @ k1_zfmisc_1 @ k1_zfmisc_1 ) ),
inference(rewrite,[status(thm)],[5943,683]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_zfmisc_1) ).
thf(454,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)],[18]) ).
thf(455,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[454]) ).
thf(456,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_tarski ) @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[455]) ).
thf(16034,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 @ ( k1_xboole_0 @ k2_tarski ) )
!= ( B @ ( A @ k2_tarski ) ) )
| ( ( k1_xboole_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( A @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[6013,456]) ).
thf(16035,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( k1_xboole_0 @ k1_tarski @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[16034:[bind(A,$thf( k1_xboole_0 )),bind(B,$thf( k1_xboole_0 @ k1_zfmisc_1 ))]]) ).
thf(16122,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( k1_xboole_0 @ k1_zfmisc_1 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[16035,683]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_xboole_1) ).
thf(412,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)],[14]) ).
thf(413,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(cnf,[status(esa)],[412]) ).
thf(414,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(lifteq,[status(thm)],[413]) ).
thf(415,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[414]) ).
thf(416,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk4 ) )
= A ),
inference(cnf,[status(esa)],[415]) ).
thf(3430,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk4 ) )
= A ),
inference(lifteq,[status(thm)],[416]) ).
thf(16255,plain,
! [B: $i,A: $i] :
( ( ( k1_xboole_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( k1_xboole_0 @ k1_zfmisc_1 @ k4_xboole_0 ) )
!= ( B @ ( A @ k4_xboole_0 ) ) )
| ( ( k1_xboole_0 @ ( B @ sk4 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[16122,3430]) ).
thf(16256,plain,
( ( k1_xboole_0 @ ( k1_xboole_0 @ k1_zfmisc_1 @ k1_zfmisc_1 @ sk4 ) )
= ( k1_xboole_0 @ k1_zfmisc_1 ) ),
inference(pattern_uni,[status(thm)],[16255:[bind(A,$thf( k1_xboole_0 @ k1_zfmisc_1 )),bind(B,$thf( k1_xboole_0 @ k1_zfmisc_1 @ k1_zfmisc_1 ))]]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(614,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(615,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[614]) ).
thf(616,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[615]) ).
thf(3439,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
!= ( C @ ( B @ k4_xboole_0 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk4 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[616,3430]) ).
thf(3440,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk4 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[3439:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(16322,plain,
( ( k1_xboole_0 @ k1_zfmisc_1 )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[16256,3440]) ).
thf(204,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(1446,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)],[204]) ).
thf(1447,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)],[1446]) ).
thf(1448,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)],[1447]) ).
thf(1450,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1448]) ).
thf(1452,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1450]) ).
thf(1453,plain,
k1_xboole_0 @ v1_xboole_0,
inference(simp,[status(thm)],[1452]) ).
thf(110,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(916,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(917,plain,
~ ? [A: $i] : ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(miniscope,[status(thm)],[916]) ).
thf(918,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(cnf,[status(esa)],[917]) ).
thf(2379,plain,
! [A: $i] :
( ( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1453,918]) ).
thf(2380,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[2379]) ).
thf(2382,plain,
! [A: $i] :
( ( A @ k1_zfmisc_1 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[2380]) ).
thf(16323,plain,
$false,
inference(simplifyReflect,[status(thm)],[16322,2382]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU445+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.12 % 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
% 0.25/0.50 % Computer : n002.cluster.edu
% 0.25/0.50 % Model : x86_64 x86_64
% 0.25/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.50 % Memory : 8046.5625MB
% 0.25/0.50 % OS : Linux 6.8.0-71-generic
% 0.25/0.50 % CPULimit : 300
% 0.25/0.50 % WCLimit : 300
% 0.25/0.50 % DateTime : Sat Sep 26 10:00:39 UTC 2026
% 0.25/0.51 % CPUTime :
% 0.25/0.51 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
% 1.58/1.41 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 7.38/2.91 % [INFO] Parsing done (1492ms).
% 7.38/2.94 % [INFO] Running in sequential loop mode.
% 8.31/3.43 % [INFO] eprover registered as external prover.
% 8.31/3.43 % [INFO] Scanning for conjecture ...
% 10.18/3.92 % [INFO] Found a conjecture (or negated_conjecture) and 4528 axioms. Running axiom selection ...
% 12.89/4.54 % [INFO] Axiom selection finished. Selected 370 axioms (removed 4158 axioms).
% 14.45/4.93 % [INFO] Problem is first-order (TPTP FOF).
% 14.45/4.97 % [INFO] Type checking passed.
% 14.45/4.98 % [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 ...
% 113.76/23.07 % [INFO] Killing All external provers ...
% 113.76/23.08 % Time passed: 22339ms (effective reasoning time: 20126ms)
% 113.76/23.08 % 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
% 113.76/23.08 % No. of inferences in proof: 48
% 113.76/23.08 % SZS status ContradictoryAxioms for /export/starexec/sandbox2/benchmark/theBenchmark.p : 22339 ms resp. 20126 ms w/o parsing
% 84.80/23.13 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 84.80/23.13 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------