%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT318+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 : n001.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 07:47:12 AM UTC 2026
% Result : ContradictoryAxioms 90.90s 19.94s
% Output : Refutation 90.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 14 unt; 0 typ; 2 def)
% Number of atoms : 121 ( 54 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 341 ( 44 ~; 26 |; 31 &; 223 @)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 93 ( 1 ^; 84 !; 6 ?; 93 :)
% ( 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(sk7_decl,type,
sk7: $i > $i > $i ).
thf(sk157_decl,type,
sk157: $i > $i ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk157_def,definition,
( sk157
= ( ^ [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(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(892,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(893,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)],[892]) ).
thf(894,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)],[893]) ).
thf(897,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[894]) ).
thf(901,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[897]) ).
thf(902,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[901]) ).
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(690,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(691,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(cnf,[status(esa)],[690]) ).
thf(692,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(lifteq,[status(thm)],[691]) ).
thf(693,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[692]) ).
thf(694,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk7 ) )
= A ),
inference(cnf,[status(esa)],[693]) ).
thf(12404,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk7 ) )
= A ),
inference(lifteq,[status(thm)],[694]) ).
thf(12405,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
!= ( C @ ( B @ k2_zfmisc_1 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk7 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[902,12404]) ).
thf(12406,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( k1_xboole_0 @ sk7 ) )
= A ),
inference(pattern_uni,[status(thm)],[12405:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(409,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/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(2670,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)],[409]) ).
thf(2671,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)],[2670]) ).
thf(2672,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk157 @ ( E @ r2_hidden ) )
| ( A @ sk157 @ ( E @ r2_tarski ) )
| ~ ( A @ sk157 @ ( E @ r1_tarski ) ) )
& ( ( A @ sk157 @ ( D @ k1_zfmisc_1 @ r2_hidden ) )
| ~ ( A @ sk157 @ ( D @ r2_hidden ) ) )
& ( ( A @ sk157 @ ( C @ r2_hidden ) )
| ~ ( B @ ( C @ r1_tarski ) )
| ~ ( A @ sk157 @ ( B @ r2_hidden ) ) )
& ( A @ sk157 @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[2671]) ).
thf(2673,plain,
! [A: $i] : ( A @ sk157 @ ( A @ r2_hidden ) ),
inference(cnfConj,[status(thm)],[2672]) ).
thf(251,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(1875,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(1876,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[1875]) ).
thf(10681,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk157 @ ( A @ r2_hidden ) )
!= ( C @ ( B @ r2_hidden ) ) )
| ~ ( B @ ( C @ r2_hidden ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2673,1876]) ).
thf(10682,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk157 @ ( A @ r2_hidden ) )
!= ( C @ ( B @ r2_hidden ) ) )
| ~ ( B @ ( C @ r2_hidden ) ) ),
inference(simp,[status(thm)],[10681]) ).
thf(10683,plain,
! [A: $i] :
~ ( A @ ( A @ sk157 @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[10682:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ sk157 ))]]) ).
thf(10700,plain,
! [A: $i] :
~ ( A @ ( A @ sk157 @ r2_hidden ) ),
inference(simp,[status(thm)],[10683]) ).
thf(11636,plain,
! [B: $i,A: $i] :
( ( ( A @ sk157 @ ( A @ r2_hidden ) )
!= ( B @ ( B @ sk157 @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2673,10700]) ).
thf(11637,plain,
! [B: $i,A: $i] :
( ( A @ sk157 @ ( A @ r2_hidden ) )
!= ( B @ ( B @ sk157 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[11636]) ).
thf(11655,plain,
! [B: $i,A: $i] :
( ( ( A @ sk157 )
!= B )
| ( A
!= ( B @ sk157 ) ) ),
inference(simp,[status(thm)],[11637]) ).
thf(11661,plain,
! [A: $i] :
( ( A @ sk157 @ sk157 )
!= A ),
inference(simp,[status(thm)],[11655]) ).
thf(12810,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk157 ) )
| ( ( k1_xboole_0 @ ( k1_xboole_0 @ sk7 ) @ sk157 )
!= B ) ),
inference(paramod_ordered,[status(thm)],[12406,11661]) ).
thf(12811,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( k1_xboole_0 @ sk7 ) @ sk157 )
!= A ),
inference(pattern_uni,[status(thm)],[12810:[bind(A,$thf( C @ sk157 )),bind(B,$thf( C ))]]) ).
thf(12896,plain,
$false,
inference(simp,[status(thm)],[12811]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT318+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
% 0.14/0.39 % Computer : n001.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Fri Sep 25 20:54:26 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 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
% 0.89/0.96 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.75/1.70 % [INFO] Parsing done (744ms).
% 3.75/1.73 % [INFO] Running in sequential loop mode.
% 5.02/2.14 % [INFO] eprover registered as external prover.
% 5.02/2.15 % [INFO] Scanning for conjecture ...
% 6.03/2.45 % [INFO] Found a conjecture (or negated_conjecture) and 2985 axioms. Running axiom selection ...
% 8.91/3.18 % [INFO] Axiom selection finished. Selected 621 axioms (removed 2364 axioms).
% 11.16/3.83 % [INFO] Problem is first-order (TPTP FOF).
% 11.16/3.89 % [INFO] Type checking passed.
% 11.16/3.89 % [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 ...
% 90.90/19.93 % [INFO] Killing All external provers ...
% 90.90/19.94 % Time passed: 19402ms (effective reasoning time: 18195ms)
% 90.90/19.94 % Axioms used in derivation (4): t113_zfmisc_1, t115_zfmisc_1, t136_zfmisc_1, antisymmetry_r2_hidden
% 90.90/19.94 % No. of inferences in proof: 35
% 90.90/19.94 % SZS status ContradictoryAxioms for /export/starexec/sandbox2/benchmark/theBenchmark.p : 19402 ms resp. 18195 ms w/o parsing
% 90.90/19.99 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 90.90/20.00 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------