%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT322+4 : 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 : n016.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 07:47:14 AM UTC 2026
% Result : ContradictoryAxioms 195.11s 69.99s
% Output : Refutation 196.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 52 ( 28 unt; 0 typ; 2 def)
% Number of atoms : 111 ( 50 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 239 ( 34 ~; 19 |; 21 &; 156 @)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 63 ( 0 ^; 58 !; 3 ?; 63 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(v3_struct_0_decl,type,
v3_struct_0: $i > $o ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(l1_pre_topc_decl,type,
l1_pre_topc: $i > $o ).
thf(v2_pre_topc_decl,type,
v2_pre_topc: $i > $o ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $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(v1_pre_topc_decl,type,
v1_pre_topc: $i > $o ).
thf(v3_realset2_decl,type,
v3_realset2: $i > $o ).
thf(k9_tdlat_1_decl,type,
k9_tdlat_1: $i > $i ).
thf(sk210_decl,type,
sk210: $i > $i > $i ).
thf(sk394_decl,type,
sk394: $i ).
thf(sk210_def,definition,
( sk210
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk394_def,definition,
( sk394
= ( @+[A: $i] :
( ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ) ) ) ).
thf(425,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(3540,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)],[425]) ).
thf(3541,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)],[3540]) ).
thf(3542,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)],[3541]) ).
thf(3544,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[3542]) ).
thf(3546,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[3544]) ).
thf(3547,plain,
k1_xboole_0 @ v1_xboole_0,
inference(simp,[status(thm)],[3546]) ).
thf(1332,axiom,
? [A: $i] :
( ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_tex_1) ).
thf(7591,plain,
? [A: $i] :
( ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ( A @ v3_realset2 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1332]) ).
thf(7592,plain,
( ( sk394 @ v2_pre_topc )
& ( sk394 @ v1_pre_topc )
& ( sk394 @ v3_realset2 )
& ~ ( sk394 @ v3_struct_0 )
& ( sk394 @ l1_pre_topc ) ),
inference(cnf,[status(esa)],[7591]) ).
thf(7596,plain,
sk394 @ v2_pre_topc,
inference(cnfConj,[status(thm)],[7592]) ).
thf(620,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ~ ( A @ k9_tdlat_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_tdlat_1) ).
thf(4412,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ~ ( A @ k9_tdlat_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(4413,plain,
! [A: $i] :
( ~ ( A @ k9_tdlat_1 @ v1_xboole_0 )
| ~ ( A @ l1_pre_topc )
| ~ ( A @ v2_pre_topc ) ),
inference(cnf,[status(esa)],[4412]) ).
thf(10518,plain,
! [A: $i] :
( ( ( sk394 @ v2_pre_topc )
!= ( A @ v2_pre_topc ) )
| ~ ( A @ k9_tdlat_1 @ v1_xboole_0 )
| ~ ( A @ l1_pre_topc )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7596,4413]) ).
thf(10519,plain,
! [A: $i] :
( ( ( sk394 @ v2_pre_topc )
!= ( A @ v2_pre_topc ) )
| ~ ( A @ k9_tdlat_1 @ v1_xboole_0 )
| ~ ( A @ l1_pre_topc ) ),
inference(simp,[status(thm)],[10518]) ).
thf(10520,plain,
( ~ ( sk394 @ k9_tdlat_1 @ v1_xboole_0 )
| ~ ( sk394 @ l1_pre_topc ) ),
inference(pattern_uni,[status(thm)],[10519:[bind(A,$thf( sk394 ))]]) ).
thf(7597,plain,
sk394 @ l1_pre_topc,
inference(cnfConj,[status(thm)],[7592]) ).
thf(10689,plain,
( ~ ( sk394 @ k9_tdlat_1 @ v1_xboole_0 )
| ~ $true ),
inference(rewrite,[status(thm)],[10520,7597]) ).
thf(10690,plain,
~ ( sk394 @ k9_tdlat_1 @ v1_xboole_0 ),
inference(simp,[status(thm)],[10689]) ).
thf(10693,plain,
( ( ( sk394 @ k9_tdlat_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3547,10690]) ).
thf(10694,plain,
( ( sk394 @ k9_tdlat_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[10693]) ).
thf(10703,plain,
( ( sk394 @ k9_tdlat_1 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[10694]) ).
thf(340,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(3125,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(3126,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
inference(cnf,[status(esa)],[3125]) ).
thf(3127,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
inference(lifteq,[status(thm)],[3126]) ).
thf(503,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_xboole_1) ).
thf(3862,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)],[503]) ).
thf(3863,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[3862]) ).
thf(3864,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[3863]) ).
thf(17225,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
!= ( C @ ( B @ k2_xboole_0 ) ) )
| ( ( A @ ( B @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[3127,3864]) ).
thf(17226,plain,
! [A: $i] :
( ( A @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[17225:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(678,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(4708,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)],[678]) ).
thf(4709,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(cnf,[status(esa)],[4708]) ).
thf(4710,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(lifteq,[status(thm)],[4709]) ).
thf(4711,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[4710]) ).
thf(4712,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk210 ) )
= A ),
inference(cnf,[status(esa)],[4711]) ).
thf(30139,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk210 ) )
= A ),
inference(lifteq,[status(thm)],[4712]) ).
thf(30140,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ k4_xboole_0 ) )
!= ( C @ ( B @ k4_xboole_0 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk210 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[17226,30139]) ).
thf(30141,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk210 ) )
= A ),
inference(pattern_uni,[status(thm)],[30140:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(540,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(4013,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(4014,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[4013]) ).
thf(4015,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[4014]) ).
thf(30142,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
!= ( C @ ( B @ k4_xboole_0 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk210 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[4015,30139]) ).
thf(30143,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk210 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[30142:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(30453,plain,
! [A: $i] : ( k1_xboole_0 = A ),
inference(rewrite,[status(thm)],[30141,30143]) ).
thf(30462,plain,
$false,
inference(simplifyReflect,[status(thm)],[10703,30453]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT322+4 : 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
% 0.12/5.39 % Computer : n016.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Fri Sep 25 20:57:00 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 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
% 0.17/5.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 9.90/9.76 % [INFO] Parsing done (3772ms).
% 9.90/9.79 % [INFO] Running in sequential loop mode.
% 10.71/10.16 % [INFO] eprover registered as external prover.
% 10.71/10.16 % [INFO] Scanning for conjecture ...
% 15.27/12.32 % [INFO] Found a conjecture (or negated_conjecture) and 34726 axioms. Running axiom selection ...
% 25.59/20.50 % [INFO] Axiom selection finished. Selected 1457 axioms (removed 33269 axioms).
% 28.49/21.46 % [INFO] Problem is first-order (TPTP FOF).
% 28.87/21.54 % [INFO] Type checking passed.
% 28.87/21.54 % [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 ...
% 195.11/69.98 % [INFO] Killing All external provers ...
% 195.11/69.99 % Time passed: 64434ms (effective reasoning time: 60178ms)
% 195.11/69.99 % Axioms used in derivation (7): t1_boole, d5_xboole_0, rc5_tex_1, fc3_tdlat_1, t46_xboole_1, t4_boole, t32_xboole_1
% 195.11/69.99 % No. of inferences in proof: 50
% 195.11/69.99 % SZS status ContradictoryAxioms for /export/starexec/sandbox2/benchmark/theBenchmark.p : 64434 ms resp. 60178 ms w/o parsing
% 196.97/70.07 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 196.97/70.07 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------