%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT313+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 07:47:11 AM UTC 2026
% Result : ContradictoryAxioms 192.21s 49.41s
% Output : Refutation 192.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 18 unt; 0 typ; 4 def)
% Number of atoms : 140 ( 63 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 390 ( 52 ~; 27 |; 42 &; 249 @)
% ( 1 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 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 : 112 ( 4 ^; 93 !; 11 ?; 112 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
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(v3_ordinal1_decl,type,
v3_ordinal1: $i > $o ).
thf(r2_tarski_decl,type,
r2_tarski: $i > $i > $o ).
thf(sk51_decl,type,
sk51: $i > $i ).
thf(sk52_decl,type,
sk52: $i > $i > $i ).
thf(sk56_decl,type,
sk56: $i > $i > $i ).
thf(sk189_decl,type,
sk189: $i > $i ).
thf(sk51_def,definition,
( sk51
= ( ^ [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(sk52_def,definition,
( sk52
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ! [D: $i] :
( ( A @ ( D @ r1_tarski ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( B @ sk51 @ ( C @ r2_hidden ) ) ) ) ) ).
thf(sk56_def,definition,
( sk56
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk189_def,definition,
( sk189
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( B @ v3_ordinal1 )
=> ( A @ ( B @ r2_hidden ) ) ) ) ) ).
thf(95,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(1224,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)],[95]) ).
thf(1225,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)],[1224]) ).
thf(1226,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)],[1225]) ).
thf(1229,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1226]) ).
thf(1233,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1229]) ).
thf(1234,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[1233]) ).
thf(133,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(1434,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)],[133]) ).
thf(1435,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(cnf,[status(esa)],[1434]) ).
thf(1436,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(lifteq,[status(thm)],[1435]) ).
thf(1437,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[1436]) ).
thf(1438,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk56 ) )
= A ),
inference(cnf,[status(esa)],[1437]) ).
thf(38731,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk56 ) )
= A ),
inference(lifteq,[status(thm)],[1438]) ).
thf(38742,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
!= ( C @ ( B @ k2_zfmisc_1 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk56 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1234,38731]) ).
thf(38743,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( k1_xboole_0 @ sk56 ) )
= A ),
inference(pattern_uni,[status(thm)],[38742:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(1228,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1226]) ).
thf(1231,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1228]) ).
thf(1232,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[1231]) ).
thf(38740,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k2_zfmisc_1 ) )
!= ( C @ ( B @ k2_zfmisc_1 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk56 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1232,38731]) ).
thf(38741,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk56 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[38740:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(38868,plain,
! [A: $i] : ( k1_xboole_0 = A ),
inference(rewrite,[status(thm)],[38743,38741]) ).
thf(131,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(1414,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)],[131]) ).
thf(1415,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)],[1414]) ).
thf(1416,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk51 @ ( F @ r2_hidden ) )
| ( A @ sk51 @ ( F @ r2_tarski ) )
| ~ ( A @ sk51 @ ( F @ r1_tarski ) ) )
& ( ( A @ ( D @ sk52 ) @ ( E @ r2_hidden ) )
| ~ ( D @ ( E @ r1_tarski ) )
| ~ ( A @ sk51 @ ( D @ r2_hidden ) ) )
& ( ( A @ sk51 @ ( A @ ( D @ sk52 ) @ r2_hidden ) )
| ~ ( A @ sk51 @ ( D @ r2_hidden ) ) )
& ( ( A @ sk51 @ ( C @ r2_hidden ) )
| ~ ( B @ ( C @ r1_tarski ) )
| ~ ( A @ sk51 @ ( B @ r2_hidden ) ) )
& ( A @ sk51 @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[1415]) ).
thf(1418,plain,
! [A: $i] : ( A @ sk51 @ ( A @ r2_hidden ) ),
inference(cnfConj,[status(thm)],[1416]) ).
thf(353,axiom,
! [A: $i] :
~ ! [B: $i] :
( ( B @ v3_ordinal1 )
=> ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_ordinal1) ).
thf(2665,plain,
! [A: $i] :
~ ! [B: $i] :
( ( B @ v3_ordinal1 )
=> ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(2666,plain,
~ ? [A: $i] :
! [B: $i] :
( ( B @ v3_ordinal1 )
=> ( A @ ( B @ r2_hidden ) ) ),
inference(miniscope,[status(thm)],[2665]) ).
thf(2667,plain,
! [A: $i] :
( ~ ( A @ ( A @ sk189 @ r2_hidden ) )
& ( A @ sk189 @ v3_ordinal1 ) ),
inference(cnf,[status(esa)],[2666]) ).
thf(2669,plain,
! [A: $i] :
~ ( A @ ( A @ sk189 @ r2_hidden ) ),
inference(cnfConj,[status(thm)],[2667]) ).
thf(10907,plain,
! [B: $i,A: $i] :
( ( ( A @ sk51 @ ( A @ r2_hidden ) )
!= ( B @ ( B @ sk189 @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1418,2669]) ).
thf(10908,plain,
! [B: $i,A: $i] :
( ( A @ sk51 @ ( A @ r2_hidden ) )
!= ( B @ ( B @ sk189 @ r2_hidden ) ) ),
inference(simp,[status(thm)],[10907]) ).
thf(10916,plain,
! [B: $i,A: $i] :
( ( ( A @ sk51 )
!= B )
| ( A
!= ( B @ sk189 ) ) ),
inference(simp,[status(thm)],[10908]) ).
thf(10920,plain,
! [A: $i] :
( ( A @ sk189 @ sk51 )
!= A ),
inference(simp,[status(thm)],[10916]) ).
thf(39993,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk189 @ sk51 ) )
| ( k1_xboole_0 != B ) ),
inference(paramod_ordered,[status(thm)],[38868,10920]) ).
thf(39994,plain,
! [A: $i] : ( k1_xboole_0 != A ),
inference(pattern_uni,[status(thm)],[39993:[bind(A,$thf( D @ sk189 @ sk51 )),bind(B,$thf( D ))]]) ).
thf(40647,plain,
$false,
inference(simp,[status(thm)],[39994]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT313+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
% 0.13/0.40 % Computer : n007.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Fri Sep 25 20:42:54 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 1.25/1.18 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 5.53/2.32 % [INFO] Parsing done (1133ms).
% 5.53/2.35 % [INFO] Running in sequential loop mode.
% 7.27/2.95 % [INFO] eprover registered as external prover.
% 7.27/2.96 % [INFO] Scanning for conjecture ...
% 9.06/3.50 % [INFO] Found a conjecture (or negated_conjecture) and 2971 axioms. Running axiom selection ...
% 13.14/4.83 % [INFO] Axiom selection finished. Selected 770 axioms (removed 2201 axioms).
% 16.57/6.05 % [INFO] Problem is first-order (TPTP FOF).
% 17.21/6.15 % [INFO] Type checking passed.
% 17.67/6.16 % [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 ...
% 192.21/49.40 % [INFO] Killing All external provers ...
% 192.21/49.41 % Time passed: 48784ms (effective reasoning time: 47048ms)
% 192.21/49.41 % Axioms used in derivation (4): t113_zfmisc_1, t115_zfmisc_1, t9_tarski, t38_ordinal1
% 192.21/49.41 % No. of inferences in proof: 39
% 192.21/49.41 % SZS status ContradictoryAxioms for /export/starexec/sandbox2/benchmark/theBenchmark.p : 48784 ms resp. 47048 ms w/o parsing
% 192.21/49.47 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 192.21/49.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------