%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT304+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 : n007.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 07:47:08 AM UTC 2026
% Result : ContradictoryAxioms 70.19s 23.03s
% Output : Refutation 70.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 15 unt; 0 typ; 3 def)
% Number of atoms : 136 ( 55 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 392 ( 54 ~; 28 |; 41 &; 251 @)
% ( 1 <=>; 17 =>; 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 : 11 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 106 ( 3 ^; 90 !; 10 ?; 106 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(r2_tarski_decl,type,
r2_tarski: $i > $i > $o ).
thf(sk5_decl,type,
sk5: $i > $i > $i ).
thf(sk23_decl,type,
sk23: $i > $i ).
thf(sk24_decl,type,
sk24: $i > $i > $i ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk23_def,definition,
( sk23
= ( ^ [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(sk24_def,definition,
( sk24
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ! [D: $i] :
( ( A @ ( D @ r1_tarski ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( B @ sk23 @ ( C @ r2_hidden ) ) ) ) ) ).
thf(64,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(856,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)],[64]) ).
thf(857,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)],[856]) ).
thf(858,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)],[857]) ).
thf(861,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[858]) ).
thf(865,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[861]) ).
thf(866,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[865]) ).
thf(16,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(654,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)],[16]) ).
thf(655,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(cnf,[status(esa)],[654]) ).
thf(656,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(lifteq,[status(thm)],[655]) ).
thf(657,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[656]) ).
thf(658,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk5 ) )
= A ),
inference(cnf,[status(esa)],[657]) ).
thf(11906,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk5 ) )
= A ),
inference(lifteq,[status(thm)],[658]) ).
thf(11919,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
!= ( C @ ( B @ k2_zfmisc_1 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk5 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[866,11906]) ).
thf(11920,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( k1_xboole_0 @ sk5 ) )
= A ),
inference(pattern_uni,[status(thm)],[11919:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(90,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(1003,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)],[90]) ).
thf(1004,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)],[1003]) ).
thf(1005,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk23 @ ( F @ r2_hidden ) )
| ( A @ sk23 @ ( F @ r2_tarski ) )
| ~ ( A @ sk23 @ ( F @ r1_tarski ) ) )
& ( ( A @ ( D @ sk24 ) @ ( E @ r2_hidden ) )
| ~ ( D @ ( E @ r1_tarski ) )
| ~ ( A @ sk23 @ ( D @ r2_hidden ) ) )
& ( ( A @ sk23 @ ( A @ ( D @ sk24 ) @ r2_hidden ) )
| ~ ( A @ sk23 @ ( D @ r2_hidden ) ) )
& ( ( A @ sk23 @ ( C @ r2_hidden ) )
| ~ ( B @ ( C @ r1_tarski ) )
| ~ ( A @ sk23 @ ( B @ r2_hidden ) ) )
& ( A @ sk23 @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[1004]) ).
thf(1006,plain,
! [A: $i] : ( A @ sk23 @ ( A @ r2_hidden ) ),
inference(cnfConj,[status(thm)],[1005]) ).
thf(248,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(1812,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(1813,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[1812]) ).
thf(8993,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk23 @ ( A @ r2_hidden ) )
!= ( C @ ( B @ r2_hidden ) ) )
| ~ ( B @ ( C @ r2_hidden ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1006,1813]) ).
thf(8994,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk23 @ ( A @ r2_hidden ) )
!= ( C @ ( B @ r2_hidden ) ) )
| ~ ( B @ ( C @ r2_hidden ) ) ),
inference(simp,[status(thm)],[8993]) ).
thf(8995,plain,
! [A: $i] :
~ ( A @ ( A @ sk23 @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[8994:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ sk23 ))]]) ).
thf(9018,plain,
! [A: $i] :
~ ( A @ ( A @ sk23 @ r2_hidden ) ),
inference(simp,[status(thm)],[8995]) ).
thf(11366,plain,
! [B: $i,A: $i] :
( ( ( A @ sk23 @ ( A @ r2_hidden ) )
!= ( B @ ( B @ sk23 @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1006,9018]) ).
thf(11367,plain,
! [B: $i,A: $i] :
( ( A @ sk23 @ ( A @ r2_hidden ) )
!= ( B @ ( B @ sk23 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[11366]) ).
thf(11378,plain,
! [B: $i,A: $i] :
( ( ( A @ sk23 )
!= B )
| ( A
!= ( B @ sk23 ) ) ),
inference(simp,[status(thm)],[11367]) ).
thf(11382,plain,
! [A: $i] :
( ( A @ sk23 @ sk23 )
!= A ),
inference(simp,[status(thm)],[11378]) ).
thf(12018,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk23 @ sk23 ) )
| ( ( k1_xboole_0 @ ( k1_xboole_0 @ sk5 ) )
!= B ) ),
inference(paramod_ordered,[status(thm)],[11920,11382]) ).
thf(12019,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( k1_xboole_0 @ sk5 ) )
!= A ),
inference(pattern_uni,[status(thm)],[12018:[bind(A,$thf( D @ sk23 @ sk23 )),bind(B,$thf( D ))]]) ).
thf(12472,plain,
$false,
inference(simp,[status(thm)],[12019]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT304+2 : 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
% 0.16/5.42 % Computer : n007.cluster.edu
% 0.16/5.42 % Model : x86_64 x86_64
% 0.16/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.42 % Memory : 8046.5625MB
% 0.16/5.42 % OS : Linux 6.8.0-71-generic
% 0.16/5.42 % CPULimit : 300
% 0.16/5.42 % WCLimit : 300
% 0.16/5.42 % DateTime : Fri Sep 25 20:37:29 UTC 2026
% 0.16/5.43 % CPUTime :
% 0.16/5.43 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
% 1.03/6.03 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.45/6.70 % [INFO] Parsing done (661ms).
% 3.45/6.72 % [INFO] Running in sequential loop mode.
% 4.22/7.11 % [INFO] eprover registered as external prover.
% 4.22/7.12 % [INFO] Scanning for conjecture ...
% 5.41/7.43 % [INFO] Found a conjecture (or negated_conjecture) and 2951 axioms. Running axiom selection ...
% 7.12/7.99 % [INFO] Axiom selection finished. Selected 587 axioms (removed 2364 axioms).
% 8.62/8.55 % [INFO] Problem is first-order (TPTP FOF).
% 9.07/8.60 % [INFO] Type checking passed.
% 9.07/8.61 % [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 ...
% 70.19/23.02 % [INFO] Killing All external provers ...
% 70.19/23.03 % Time passed: 17447ms (effective reasoning time: 16302ms)
% 70.19/23.03 % Axioms used in derivation (4): t113_zfmisc_1, t115_zfmisc_1, t9_tarski, antisymmetry_r2_hidden
% 70.19/23.03 % No. of inferences in proof: 35
% 70.19/23.03 % SZS status ContradictoryAxioms for /export/starexec/sandbox2/benchmark/theBenchmark.p : 17447 ms resp. 16302 ms w/o parsing
% 70.72/23.09 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 70.72/23.09 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------