%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT316+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 : n018.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 07:47:11 AM UTC 2026
% Result : ContradictoryAxioms 77.28s 16.88s
% Output : Refutation 63.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 44 ( 17 unt; 0 typ; 4 def)
% Number of atoms : 183 ( 56 equ; 0 cnn)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 555 ( 70 ~; 33 |; 68 &; 358 @)
% ( 1 <=>; 25 =>; 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 : 136 ( 4 ^; 113 !; 15 ?; 136 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% 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(sk25_decl,type,
sk25: $i > $i ).
thf(sk26_decl,type,
sk26: $i > $i > $i ).
thf(sk158_decl,type,
sk158: $i > $i ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk25_def,definition,
( sk25
= ( ^ [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(sk26_def,definition,
( sk26
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ! [D: $i] :
( ( A @ ( D @ r1_tarski ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( B @ sk25 @ ( C @ r2_hidden ) ) ) ) ) ).
thf(sk158_def,definition,
( sk158
= ( ^ [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(12683,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk7 ) )
= A ),
inference(lifteq,[status(thm)],[694]) ).
thf(12692,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)],[902,12683]) ).
thf(12693,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( k1_xboole_0 @ sk7 ) )
= A ),
inference(pattern_uni,[status(thm)],[12692:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(412,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(2677,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)],[412]) ).
thf(2678,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)],[2677]) ).
thf(2679,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk158 @ ( E @ r2_hidden ) )
| ( A @ sk158 @ ( E @ r2_tarski ) )
| ~ ( A @ sk158 @ ( E @ r1_tarski ) ) )
& ( ( A @ sk158 @ ( D @ k1_zfmisc_1 @ r2_hidden ) )
| ~ ( A @ sk158 @ ( D @ r2_hidden ) ) )
& ( ( A @ sk158 @ ( C @ r2_hidden ) )
| ~ ( B @ ( C @ r1_tarski ) )
| ~ ( A @ sk158 @ ( B @ r2_hidden ) ) )
& ( A @ sk158 @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[2678]) ).
thf(2680,plain,
! [A: $i] : ( A @ sk158 @ ( A @ r2_hidden ) ),
inference(cnfConj,[status(thm)],[2679]) ).
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(1039,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(1040,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)],[1039]) ).
thf(1041,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk25 @ ( F @ r2_hidden ) )
| ( A @ sk25 @ ( F @ r2_tarski ) )
| ~ ( A @ sk25 @ ( F @ r1_tarski ) ) )
& ( ( A @ ( D @ sk26 ) @ ( E @ r2_hidden ) )
| ~ ( D @ ( E @ r1_tarski ) )
| ~ ( A @ sk25 @ ( D @ r2_hidden ) ) )
& ( ( A @ sk25 @ ( A @ ( D @ sk26 ) @ r2_hidden ) )
| ~ ( A @ sk25 @ ( D @ r2_hidden ) ) )
& ( ( A @ sk25 @ ( C @ r2_hidden ) )
| ~ ( B @ ( C @ r1_tarski ) )
| ~ ( A @ sk25 @ ( B @ r2_hidden ) ) )
& ( A @ sk25 @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[1040]) ).
thf(1043,plain,
! [A: $i] : ( A @ sk25 @ ( A @ r2_hidden ) ),
inference(cnfConj,[status(thm)],[1041]) ).
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(1876,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(1877,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ~ ( B @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[1876]) ).
thf(10644,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk25 @ ( A @ r2_hidden ) )
!= ( C @ ( B @ r2_hidden ) ) )
| ~ ( B @ ( C @ r2_hidden ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1043,1877]) ).
thf(10645,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk25 @ ( A @ r2_hidden ) )
!= ( C @ ( B @ r2_hidden ) ) )
| ~ ( B @ ( C @ r2_hidden ) ) ),
inference(simp,[status(thm)],[10644]) ).
thf(10646,plain,
! [A: $i] :
~ ( A @ ( A @ sk25 @ r2_hidden ) ),
inference(pattern_uni,[status(thm)],[10645:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ sk25 ))]]) ).
thf(10672,plain,
! [A: $i] :
~ ( A @ ( A @ sk25 @ r2_hidden ) ),
inference(simp,[status(thm)],[10646]) ).
thf(11692,plain,
! [B: $i,A: $i] :
( ( ( A @ sk158 @ ( A @ r2_hidden ) )
!= ( B @ ( B @ sk25 @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2680,10672]) ).
thf(11693,plain,
! [B: $i,A: $i] :
( ( A @ sk158 @ ( A @ r2_hidden ) )
!= ( B @ ( B @ sk25 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[11692]) ).
thf(11694,plain,
! [B: $i,A: $i] :
( ( ( A @ sk158 )
!= B )
| ( A
!= ( B @ sk25 ) ) ),
inference(simp,[status(thm)],[11693]) ).
thf(11702,plain,
! [A: $i] :
( ( A @ sk25 @ sk158 )
!= A ),
inference(simp,[status(thm)],[11694]) ).
thf(12861,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk25 ) )
| ( ( k1_xboole_0 @ ( k1_xboole_0 @ sk7 ) @ sk158 )
!= B ) ),
inference(paramod_ordered,[status(thm)],[12693,11702]) ).
thf(12862,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( k1_xboole_0 @ sk7 ) @ sk158 )
!= A ),
inference(pattern_uni,[status(thm)],[12861:[bind(A,$thf( C @ sk25 )),bind(B,$thf( C ))]]) ).
thf(13191,plain,
$false,
inference(simp,[status(thm)],[12862]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT316+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
% 0.14/0.42 % Computer : n018.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Fri Sep 25 20:49:51 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 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
% 0.85/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.63/1.76 % [INFO] Parsing done (751ms).
% 3.63/1.78 % [INFO] Running in sequential loop mode.
% 4.89/2.18 % [INFO] eprover registered as external prover.
% 4.89/2.19 % [INFO] Scanning for conjecture ...
% 6.23/2.52 % [INFO] Found a conjecture (or negated_conjecture) and 2984 axioms. Running axiom selection ...
% 8.05/2.98 % [INFO] Axiom selection finished. Selected 620 axioms (removed 2364 axioms).
% 9.64/3.32 % [INFO] Problem is first-order (TPTP FOF).
% 9.64/3.36 % [INFO] Type checking passed.
% 9.64/3.37 % [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 ...
% 77.28/16.87 % [INFO] Killing All external provers ...
% 77.28/16.87 % Time passed: 16312ms (effective reasoning time: 15087ms)
% 77.28/16.88 % Axioms used in derivation (5): t113_zfmisc_1, t115_zfmisc_1, t136_zfmisc_1, t9_tarski, antisymmetry_r2_hidden
% 77.28/16.88 % No. of inferences in proof: 40
% 77.28/16.88 % SZS status ContradictoryAxioms for /export/starexec/sandbox2/benchmark/theBenchmark.p : 16312 ms resp. 15087 ms w/o parsing
% 63.82/16.94 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 63.82/16.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------