%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT334+3 : 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 : n015.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 07:47:20 AM UTC 2026
% Result : ContradictoryAxioms 99.79s 24.15s
% Output : Refutation 79.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of formulae : 67 ( 30 unt; 0 typ; 3 def)
% Number of atoms : 142 ( 77 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 350 ( 48 ~; 35 |; 16 &; 242 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 66 ( 1 ^; 57 !; 5 ?; 66 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
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(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(v1_relat_1_decl,type,
v1_relat_1: $i > $o ).
thf(v1_realset1_decl,type,
v1_realset1: $i > $o ).
thf(k3_tarski_decl,type,
k3_tarski: $i > $i ).
thf(sk9_decl,type,
sk9: $i > $i ).
thf(sk10_decl,type,
sk10: $i > $i > $i ).
thf(sk104_decl,type,
sk104: $i ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk104_def,definition,
( sk104
= ( @+[A: $i] :
( ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(323,axiom,
? [A: $i] :
( ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_realset1) ).
thf(2416,plain,
? [A: $i] :
( ( A @ v1_realset1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(2417,plain,
( ( sk104 @ v1_realset1 )
& ~ ( sk104 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[2416]) ).
thf(2419,plain,
sk104 @ v1_realset1,
inference(cnfConj,[status(thm)],[2417]) ).
thf(24,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( ( A @ v1_realset1 )
& ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_realset1) ).
thf(946,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( ( A @ v1_realset1 )
& ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ~ ( B @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(947,plain,
! [A: $i] :
( ( ~ ( A @ v1_realset1 )
| ( A @ sk9 @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) )
& ( ~ ( A @ v1_realset1 )
| ( A @ ( A @ sk9 @ m1_subset_1 ) )
| ( A @ v1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[946]) ).
thf(949,plain,
! [A: $i] :
( ~ ( A @ v1_realset1 )
| ( A @ sk9 @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[947]) ).
thf(11759,plain,
! [A: $i] :
( ( ( sk104 @ v1_realset1 )
!= ( A @ v1_realset1 ) )
| ~ $true
| ( A @ sk9 @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2419,949]) ).
thf(11760,plain,
! [A: $i] :
( ( ( sk104 @ v1_realset1 )
!= ( A @ v1_realset1 ) )
| ( A @ sk9 @ k1_tarski @ ( A @ k4_xboole_0 ) @ v1_xboole_0 )
| ( A @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[11759]) ).
thf(11761,plain,
( ( sk104 @ sk9 @ k1_tarski @ ( sk104 @ k4_xboole_0 ) @ v1_xboole_0 )
| ( sk104 @ v1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[11760:[bind(A,$thf( sk104 ))]]) ).
thf(2418,plain,
~ ( sk104 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[2417]) ).
thf(12265,plain,
( ( sk104 @ sk9 @ k1_tarski @ ( sk104 @ k4_xboole_0 ) @ v1_xboole_0 )
| $false ),
inference(rewrite,[status(thm)],[11761,2418]) ).
thf(12266,plain,
sk104 @ sk9 @ k1_tarski @ ( sk104 @ k4_xboole_0 ) @ v1_xboole_0,
inference(simp,[status(thm)],[12265]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(874,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(875,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[874]) ).
thf(876,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
| ( A = k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[875]) ).
thf(12362,plain,
! [A: $i] :
( ( ( sk104 @ sk9 @ k1_tarski @ ( sk104 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( A @ v1_xboole_0 ) )
| ~ $true
| ( A = k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[12266,876]) ).
thf(12363,plain,
! [A: $i] :
( ( ( sk104 @ sk9 @ k1_tarski @ ( sk104 @ k4_xboole_0 ) @ v1_xboole_0 )
!= ( A @ v1_xboole_0 ) )
| ( A = k1_xboole_0 ) ),
inference(simp,[status(thm)],[12362]) ).
thf(12364,plain,
( ( sk104 @ sk9 @ k1_tarski @ ( sk104 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[12363:[bind(A,$thf( sk104 @ sk9 @ k1_tarski @ ( sk104 @ k4_xboole_0 ) ))]]) ).
thf(20,axiom,
! [A: $i,B: $i] :
~ ( ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 )
& ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t66_zfmisc_1) ).
thf(926,plain,
! [A: $i,B: $i] :
~ ( ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 )
& ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(927,plain,
~ ? [A: $i,B: $i] :
( ( A
!= ( B @ k1_tarski ) )
& ( A != k1_xboole_0 )
& ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
inference(miniscope,[status(thm)],[926]) ).
thf(928,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 )
| ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
!= k1_xboole_0 ) ),
inference(cnf,[status(esa)],[927]) ).
thf(929,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 )
| ( ( B @ k1_tarski @ ( A @ k4_xboole_0 ) )
!= k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[928]) ).
thf(12628,plain,
! [B: $i,A: $i] :
( ( ( sk104 @ sk9 @ k1_tarski @ ( sk104 @ k4_xboole_0 ) )
!= ( B @ k1_tarski @ ( A @ k4_xboole_0 ) ) )
| ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 )
| ( k1_xboole_0 != k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[12364,929]) ).
thf(12629,plain,
! [B: $i,A: $i] :
( ( ( sk104 @ sk9 @ k1_tarski @ ( sk104 @ k4_xboole_0 ) )
!= ( B @ k1_tarski @ ( A @ k4_xboole_0 ) ) )
| ( A
= ( B @ k1_tarski ) )
| ( A = k1_xboole_0 ) ),
inference(simp,[status(thm)],[12628]) ).
thf(12630,plain,
( ( ( sk104 @ sk9 @ k1_tarski )
= sk104 )
| ( sk104 = k1_xboole_0 ) ),
inference(pattern_uni,[status(thm)],[12629:[bind(A,$thf( sk104 )),bind(B,$thf( sk104 @ sk9 ))]]) ).
thf(64,axiom,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(1149,plain,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(1150,plain,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[1149]) ).
thf(1151,plain,
k1_xboole_0 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[1150]) ).
thf(4689,plain,
( ( ( sk104 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1151,2418]) ).
thf(4690,plain,
( ( sk104 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[4689]) ).
thf(4691,plain,
sk104 != k1_xboole_0,
inference(simp,[status(thm)],[4690]) ).
thf(12667,plain,
( ( sk104 @ sk9 @ k1_tarski )
= sk104 ),
inference(simplifyReflect,[status(thm)],[12630,4691]) ).
thf(192,axiom,
! [A: $i] :
( ( A @ k1_tarski @ k3_tarski )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_zfmisc_1) ).
thf(1742,plain,
! [A: $i] :
( ( A @ k1_tarski @ k3_tarski )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(1743,plain,
! [A: $i] :
( ( A @ k1_tarski @ k3_tarski )
= A ),
inference(cnf,[status(esa)],[1742]) ).
thf(1744,plain,
! [A: $i] :
( ( A @ k1_tarski @ k3_tarski )
= A ),
inference(lifteq,[status(thm)],[1743]) ).
thf(12685,plain,
! [A: $i] :
( ( ( sk104 @ sk9 @ k1_tarski )
!= ( A @ k1_tarski ) )
| ( ( sk104 @ k3_tarski )
= A ) ),
inference(paramod_ordered,[status(thm)],[12667,1744]) ).
thf(12686,plain,
( ( sk104 @ sk9 )
= ( sk104 @ k3_tarski ) ),
inference(pattern_uni,[status(thm)],[12685:[bind(A,$thf( sk104 @ sk9 ))]]) ).
thf(12885,plain,
( ( sk104 @ k3_tarski @ k1_tarski )
= sk104 ),
inference(rewrite,[status(thm)],[12667,12686]) ).
thf(25,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(950,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)],[25]) ).
thf(951,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(cnf,[status(esa)],[950]) ).
thf(952,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(lifteq,[status(thm)],[951]) ).
thf(953,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[952]) ).
thf(954,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk10 ) )
= A ),
inference(cnf,[status(esa)],[953]) ).
thf(12520,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk10 ) )
= A ),
inference(lifteq,[status(thm)],[954]) ).
thf(12631,plain,
! [B: $i,A: $i] :
( ( ( sk104 @ sk9 @ k1_tarski @ ( sk104 @ k4_xboole_0 ) )
!= ( B @ ( A @ k4_xboole_0 ) ) )
| ( ( k1_xboole_0 @ ( B @ sk10 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[12364,12520]) ).
thf(12632,plain,
( ( k1_xboole_0 @ ( sk104 @ sk9 @ k1_tarski @ sk10 ) )
= sk104 ),
inference(pattern_uni,[status(thm)],[12631:[bind(A,$thf( sk104 )),bind(B,$thf( sk104 @ sk9 @ k1_tarski ))]]) ).
thf(13389,plain,
( ( k1_xboole_0 @ ( sk104 @ k3_tarski @ k1_tarski @ sk10 ) )
= sk104 ),
inference(rewrite,[status(thm)],[12632,12686]) ).
thf(13404,plain,
( ( ( sk104 @ k3_tarski @ k1_tarski )
!= ( sk104 @ k3_tarski @ k1_tarski ) )
| ( ( k1_xboole_0 @ ( sk104 @ sk10 ) )
= sk104 ) ),
inference(paramod_ordered,[status(thm)],[12885,13389]) ).
thf(13405,plain,
( ( k1_xboole_0 @ ( sk104 @ sk10 ) )
= sk104 ),
inference(pattern_uni,[status(thm)],[13404:[]]) ).
thf(81,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(1247,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(1248,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[1247]) ).
thf(1249,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[1248]) ).
thf(12525,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
!= ( C @ ( B @ k4_xboole_0 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk10 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1249,12520]) ).
thf(12526,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk10 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[12525:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(19293,plain,
sk104 = k1_xboole_0,
inference(rewrite,[status(thm)],[13405,12526]) ).
thf(20423,plain,
$false,
inference(simplifyReflect,[status(thm)],[19293,4691]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT334+3 : 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
% 0.13/0.40 % Computer : n015.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 21:03:46 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 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
% 0.88/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 6.41/2.68 % [INFO] Parsing done (1675ms).
% 6.58/2.70 % [INFO] Running in sequential loop mode.
% 7.07/3.07 % [INFO] eprover registered as external prover.
% 7.07/3.08 % [INFO] Scanning for conjecture ...
% 10.89/4.05 % [INFO] Found a conjecture (or negated_conjecture) and 13674 axioms. Running axiom selection ...
% 15.08/6.76 % [INFO] Axiom selection finished. Selected 849 axioms (removed 12825 axioms).
% 16.91/7.32 % [INFO] Problem is first-order (TPTP FOF).
% 16.91/7.37 % [INFO] Type checking passed.
% 16.91/7.38 % [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 ...
% 99.79/24.14 % [INFO] Killing All external provers ...
% 99.79/24.15 % Time passed: 23589ms (effective reasoning time: 21438ms)
% 99.79/24.15 % Axioms used in derivation (8): fc4_relat_1, t6_boole, t31_zfmisc_1, rc1_realset1, t4_boole, t32_xboole_1, t6_realset1, t66_zfmisc_1
% 99.79/24.15 % No. of inferences in proof: 64
% 99.79/24.15 % SZS status ContradictoryAxioms for /export/starexec/sandbox/benchmark/theBenchmark.p : 23589 ms resp. 21438 ms w/o parsing
% 79.20/24.20 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 79.20/24.20 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------