%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT332+2 : 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 : 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 07:47:19 AM UTC 2026
% Result : ContradictoryAxioms 140.77s 55.67s
% Output : Refutation 136.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 14 unt; 0 typ; 2 def)
% Number of atoms : 117 ( 53 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 322 ( 42 ~; 25 |; 31 &; 207 @)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 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 : 89 ( 1 ^; 80 !; 6 ?; 89 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% 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(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(r2_tarski_decl,type,
r2_tarski: $i > $i > $o ).
thf(sk40_decl,type,
sk40: $i > $i > $i ).
thf(sk208_decl,type,
sk208: $i > $i ).
thf(sk40_def,definition,
( sk40
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk208_def,definition,
( sk208
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ? [C: $i] :
( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( C @ k1_zfmisc_1 @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ) ) ) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
<=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(1090,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)],[73]) ).
thf(1091,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)],[1090]) ).
thf(1092,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)],[1091]) ).
thf(1095,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1092]) ).
thf(1099,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1095]) ).
thf(1100,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[1099]) ).
thf(109,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_zfmisc_1) ).
thf(1301,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)],[109]) ).
thf(1302,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(cnf,[status(esa)],[1301]) ).
thf(1303,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(lifteq,[status(thm)],[1302]) ).
thf(1304,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[1303]) ).
thf(1305,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk40 ) )
= A ),
inference(cnf,[status(esa)],[1304]) ).
thf(40058,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk40 ) )
= A ),
inference(lifteq,[status(thm)],[1305]) ).
thf(40071,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
!= ( C @ ( B @ k2_zfmisc_1 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk40 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1100,40058]) ).
thf(40072,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( k1_xboole_0 @ sk40 ) )
= A ),
inference(pattern_uni,[status(thm)],[40071:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(495,axiom,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( C @ k1_zfmisc_1 @ 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/sandbox/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(3481,plain,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( C @ k1_zfmisc_1 @ 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)],[495]) ).
thf(3482,plain,
! [A: $i] :
? [B: $i] :
( ~ ? [C: $i] :
( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( C @ k1_zfmisc_1 @ 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)],[3481]) ).
thf(3483,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk208 @ ( E @ r2_hidden ) )
| ( A @ sk208 @ ( E @ r2_tarski ) )
| ~ ( A @ sk208 @ ( E @ r1_tarski ) ) )
& ( ( A @ sk208 @ ( D @ k1_zfmisc_1 @ r2_hidden ) )
| ~ ( A @ sk208 @ ( D @ r2_hidden ) ) )
& ( ( A @ sk208 @ ( C @ r2_hidden ) )
| ~ ( B @ ( C @ r1_tarski ) )
| ~ ( A @ sk208 @ ( B @ r2_hidden ) ) )
& ( A @ sk208 @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[3482]) ).
thf(3484,plain,
! [A: $i] : ( A @ sk208 @ ( A @ r2_hidden ) ),
inference(cnfConj,[status(thm)],[3483]) ).
thf(315,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(2468,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(2469,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[2468]) ).
thf(7085,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ ( B @ r2_hidden ) )
!= ( B @ ( A @ r2_hidden ) ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(eqfactor_ordered,[status(thm)],[2469]) ).
thf(7086,plain,
! [A: $i] :
~ ( A @ ( A @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[7085:[bind(A,$thf( B ))]]) ).
thf(7087,plain,
! [A: $i] :
~ ( A @ ( A @ r2_hidden ) ),
inference(simp,[status(thm)],[7086]) ).
thf(19567,plain,
! [B: $i,A: $i] :
( ( ( A @ sk208 @ ( A @ r2_hidden ) )
!= ( B @ ( B @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3484,7087]) ).
thf(19568,plain,
! [B: $i,A: $i] :
( ( A @ sk208 @ ( A @ r2_hidden ) )
!= ( B @ ( B @ r2_hidden ) ) ),
inference(simp,[status(thm)],[19567]) ).
thf(19577,plain,
! [B: $i,A: $i] :
( ( ( A @ sk208 )
!= B )
| ( A != B ) ),
inference(simp,[status(thm)],[19568]) ).
thf(19588,plain,
! [A: $i] :
( ( A @ sk208 )
!= A ),
inference(simp,[status(thm)],[19577]) ).
thf(40489,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk208 ) )
| ( ( k1_xboole_0 @ ( k1_xboole_0 @ sk40 ) )
!= B ) ),
inference(paramod_ordered,[status(thm)],[40072,19588]) ).
thf(40490,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( k1_xboole_0 @ sk40 ) )
!= A ),
inference(pattern_uni,[status(thm)],[40489:[bind(A,$thf( C @ sk208 )),bind(B,$thf( C ))]]) ).
thf(41159,plain,
$false,
inference(simp,[status(thm)],[40490]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT332+2 : 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
% 0.13/0.39 % Computer : n002.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Fri Sep 25 21:00:50 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 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
% 0.91/1.21 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 3.72/2.32 % [INFO] Parsing done (1102ms).
% 3.72/2.35 % [INFO] Running in sequential loop mode.
% 4.64/2.90 % [INFO] eprover registered as external prover.
% 4.64/2.90 % [INFO] Scanning for conjecture ...
% 5.61/3.37 % [INFO] Found a conjecture (or negated_conjecture) and 3010 axioms. Running axiom selection ...
% 7.94/4.22 % [INFO] Axiom selection finished. Selected 737 axioms (removed 2273 axioms).
% 10.16/5.20 % [INFO] Problem is first-order (TPTP FOF).
% 10.43/5.29 % [INFO] Type checking passed.
% 10.57/5.30 % [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 ...
% 140.77/55.66 % [INFO] Killing All external provers ...
% 140.77/55.67 % Time passed: 55050ms (effective reasoning time: 53309ms)
% 140.77/55.67 % Axioms used in derivation (4): t113_zfmisc_1, t115_zfmisc_1, t136_zfmisc_1, antisymmetry_r2_hidden
% 140.77/55.67 % No. of inferences in proof: 34
% 140.77/55.67 % SZS status ContradictoryAxioms for /export/starexec/sandbox/benchmark/theBenchmark.p : 55050 ms resp. 53309 ms w/o parsing
% 136.25/55.73 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 136.25/55.73 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------