%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT290+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 : n005.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 07:47:00 AM UTC 2026
% Result : ContradictoryAxioms 138.14s 37.04s
% Output : Refutation 138.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 21 unt; 0 typ; 3 def)
% Number of atoms : 150 ( 64 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 433 ( 58 ~; 31 |; 44 &; 284 @)
% ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 121 ( 3 ^; 103 !; 12 ?; 121 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(k3_tarski_decl,type,
k3_tarski: $i > $i ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(r2_tarski_decl,type,
r2_tarski: $i > $i > $o ).
thf(sk6_decl,type,
sk6: $i > $i > $i ).
thf(sk52_decl,type,
sk52: $i > $i ).
thf(sk53_decl,type,
sk53: $i > $i > $i ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk52_def,definition,
( sk52
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ? [C: $i] :
( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ~ ? [C: $i] :
( ~ ? [D: $i] :
( ! [E: $i] :
( ( C @ ( E @ r1_tarski ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ) ) ) ).
thf(sk53_def,definition,
( sk53
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ! [D: $i] :
( ( A @ ( D @ r1_tarski ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( B @ sk52 @ ( C @ r2_hidden ) ) ) ) ) ).
thf(200,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(2019,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)],[200]) ).
thf(2020,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)],[2019]) ).
thf(2021,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)],[2020]) ).
thf(2024,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[2021]) ).
thf(2028,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[2024]) ).
thf(2029,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[2028]) ).
thf(28,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(1339,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)],[28]) ).
thf(1340,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(cnf,[status(esa)],[1339]) ).
thf(1341,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(lifteq,[status(thm)],[1340]) ).
thf(1342,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[1341]) ).
thf(1343,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk6 ) )
= A ),
inference(cnf,[status(esa)],[1342]) ).
thf(27783,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk6 ) )
= A ),
inference(lifteq,[status(thm)],[1343]) ).
thf(27798,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
!= ( C @ ( B @ k2_zfmisc_1 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk6 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[2029,27783]) ).
thf(27799,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( k1_xboole_0 @ sk6 ) )
= A ),
inference(pattern_uni,[status(thm)],[27798:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(2023,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[2021]) ).
thf(2026,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[2023]) ).
thf(2027,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[2026]) ).
thf(27788,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k2_zfmisc_1 ) )
!= ( C @ ( B @ k2_zfmisc_1 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk6 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[2027,27783]) ).
thf(27789,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk6 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[27788:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(27848,plain,
! [A: $i] : ( k1_xboole_0 = A ),
inference(rewrite,[status(thm)],[27799,27789]) ).
thf(988,axiom,
! [A: $i] : ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_zfmisc_1) ).
thf(5572,plain,
! [A: $i] : ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(5573,plain,
! [A: $i] : ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) ),
inference(cnf,[status(esa)],[5572]) ).
thf(302,axiom,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
~ ( ! [D: $i] :
~ ( ! [E: $i] :
( ( C @ ( E @ r1_tarski ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tarski) ).
thf(2448,plain,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
~ ( ! [D: $i] :
~ ( ! [E: $i] :
( ( C @ ( E @ r1_tarski ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(2449,plain,
! [A: $i] :
? [B: $i] :
( ~ ? [C: $i] :
( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ~ ? [C: $i] :
( ~ ? [D: $i] :
( ! [E: $i] :
( ( C @ ( E @ r1_tarski ) )
=> ( D @ ( E @ r2_hidden ) ) )
& ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( C @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(miniscope,[status(thm)],[2448]) ).
thf(2450,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk52 @ ( F @ r2_hidden ) )
| ( A @ sk52 @ ( F @ r2_tarski ) )
| ~ ( A @ sk52 @ ( F @ r1_tarski ) ) )
& ( ( A @ ( D @ sk53 ) @ ( E @ r2_hidden ) )
| ~ ( D @ ( E @ r1_tarski ) )
| ~ ( A @ sk52 @ ( D @ r2_hidden ) ) )
& ( ( A @ sk52 @ ( A @ ( D @ sk53 ) @ r2_hidden ) )
| ~ ( A @ sk52 @ ( D @ r2_hidden ) ) )
& ( ( A @ sk52 @ ( C @ r2_hidden ) )
| ~ ( B @ ( C @ r1_tarski ) )
| ~ ( A @ sk52 @ ( B @ r2_hidden ) ) )
& ( A @ sk52 @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[2449]) ).
thf(2455,plain,
! [A: $i] : ( A @ sk52 @ ( A @ r2_hidden ) ),
inference(cnfConj,[status(thm)],[2450]) ).
thf(864,axiom,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(4909,plain,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(4910,plain,
~ ? [A: $i,B: $i] :
( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(miniscope,[status(thm)],[4909]) ).
thf(4911,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r1_tarski ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[4910]) ).
thf(8865,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk52 @ ( A @ r2_hidden ) )
!= ( C @ ( B @ r2_hidden ) ) )
| ~ ( B @ ( C @ r1_tarski ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2455,4911]) ).
thf(8866,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk52 @ ( A @ r2_hidden ) )
!= ( C @ ( B @ r2_hidden ) ) )
| ~ ( B @ ( C @ r1_tarski ) ) ),
inference(simp,[status(thm)],[8865]) ).
thf(8867,plain,
! [A: $i] :
~ ( A @ ( A @ sk52 @ r1_tarski ) ),
inference(pattern_uni,[status(thm)],[8866:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ sk52 ))]]) ).
thf(8889,plain,
! [A: $i] :
~ ( A @ ( A @ sk52 @ r1_tarski ) ),
inference(simp,[status(thm)],[8867]) ).
thf(16947,plain,
! [B: $i,A: $i] :
( ( ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
!= ( B @ ( B @ sk52 @ r1_tarski ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5573,8889]) ).
thf(16948,plain,
! [B: $i,A: $i] :
( ( A @ k3_tarski @ k1_zfmisc_1 @ ( A @ r1_tarski ) )
!= ( B @ ( B @ sk52 @ r1_tarski ) ) ),
inference(simp,[status(thm)],[16947]) ).
thf(16949,plain,
! [B: $i,A: $i] :
( ( ( A @ k3_tarski @ k1_zfmisc_1 )
!= B )
| ( A
!= ( B @ sk52 ) ) ),
inference(simp,[status(thm)],[16948]) ).
thf(16956,plain,
! [A: $i] :
( ( A @ sk52 @ k3_tarski @ k1_zfmisc_1 )
!= A ),
inference(simp,[status(thm)],[16949]) ).
thf(29361,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk52 ) )
| ( ( k1_xboole_0 @ k3_tarski @ k1_zfmisc_1 )
!= B ) ),
inference(paramod_ordered,[status(thm)],[27848,16956]) ).
thf(29362,plain,
! [A: $i] :
( ( k1_xboole_0 @ k3_tarski @ k1_zfmisc_1 )
!= A ),
inference(pattern_uni,[status(thm)],[29361:[bind(A,$thf( C @ sk52 )),bind(B,$thf( C ))]]) ).
thf(29920,plain,
$false,
inference(simp,[status(thm)],[29362]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT290+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % 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
% 0.14/0.40 % Computer : n005.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Fri Sep 25 20:30:18 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.83/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 4.75/2.04 % [INFO] Parsing done (1056ms).
% 4.75/2.06 % [INFO] Running in sequential loop mode.
% 5.42/2.43 % [INFO] eprover registered as external prover.
% 5.42/2.44 % [INFO] Scanning for conjecture ...
% 7.81/3.07 % [INFO] Found a conjecture (or negated_conjecture) and 6453 axioms. Running axiom selection ...
% 10.98/4.36 % [INFO] Axiom selection finished. Selected 1217 axioms (removed 5236 axioms).
% 14.24/5.23 % [INFO] Problem is first-order (TPTP FOF).
% 14.66/5.34 % [INFO] Type checking passed.
% 14.66/5.35 % [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 ...
% 136.80/37.03 % [INFO] Killing All external provers ...
% 138.14/37.04 % Time passed: 36483ms (effective reasoning time: 34969ms)
% 138.14/37.04 % Axioms used in derivation (5): t113_zfmisc_1, t115_zfmisc_1, t7_ordinal1, t100_zfmisc_1, t9_tarski
% 138.14/37.04 % No. of inferences in proof: 45
% 138.14/37.04 % SZS status ContradictoryAxioms for /export/starexec/sandbox2/benchmark/theBenchmark.p : 36483 ms resp. 34969 ms w/o parsing
% 138.14/37.10 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 138.14/37.10 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------