%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT304+3 : 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 : n005.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 253.78s 78.13s
% Output : Refutation 238.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 47 ( 31 unt; 0 typ; 2 def)
% Number of atoms : 76 ( 51 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 165 ( 17 ~; 9 |; 7 &; 125 @)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 60 ( 0 ^; 55 !; 3 ?; 60 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(v1_relat_1_decl,type,
v1_relat_1: $i > $o ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(k4_xboole_0_decl,type,
k4_xboole_0: $i > $i > $i ).
thf(k3_xboole_0_decl,type,
k3_xboole_0: $i > $i > $i ).
thf(sk19_decl,type,
sk19: $i > $i > $i ).
thf(sk468_decl,type,
sk468: $i ).
thf(sk19_def,definition,
( sk19
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk468_def,definition,
( sk468
= ( @+[A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(465,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(3640,plain,
! [A: $i] :
( ( ( A = k1_xboole_0 )
=> ( A @ v1_xboole_0 ) )
& ( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(3641,plain,
( ! [A: $i] :
( ( A = k1_xboole_0 )
=> ( A @ v1_xboole_0 ) )
& ! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ) ),
inference(miniscope,[status(thm)],[3640]) ).
thf(3642,plain,
! [B: $i,A: $i] :
( ( ( B @ v1_xboole_0 )
| ( B != k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[3641]) ).
thf(3644,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[3642]) ).
thf(3646,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[3644]) ).
thf(3647,plain,
k1_xboole_0 @ v1_xboole_0,
inference(simp,[status(thm)],[3646]) ).
thf(951,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(6179,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(6180,plain,
( ( sk468 @ v1_relat_1 )
& ~ ( sk468 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[6179]) ).
thf(6181,plain,
~ ( sk468 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[6180]) ).
thf(6961,plain,
( ( ( sk468 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3647,6181]) ).
thf(6962,plain,
( ( sk468 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[6961]) ).
thf(6964,plain,
sk468 != k1_xboole_0,
inference(simp,[status(thm)],[6962]) ).
thf(334,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(2812,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(2813,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[2812]) ).
thf(2814,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[2813]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(1434,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(1435,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) ) ),
inference(cnf,[status(esa)],[1434]) ).
thf(1436,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( B @ ( A @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) ) ),
inference(lifteq,[status(thm)],[1435]) ).
thf(62454,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[2814,1436]) ).
thf(34,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(1296,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(1297,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(cnf,[status(esa)],[1296]) ).
thf(1298,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(lifteq,[status(thm)],[1297]) ).
thf(62482,plain,
! [A: $i] :
( ( A @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[62454,1298]) ).
thf(70,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_xboole_1) ).
thf(1450,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(1451,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(cnf,[status(esa)],[1450]) ).
thf(1452,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(lifteq,[status(thm)],[1451]) ).
thf(1453,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[1452]) ).
thf(1454,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk19 ) )
= A ),
inference(cnf,[status(esa)],[1453]) ).
thf(63997,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk19 ) )
= A ),
inference(lifteq,[status(thm)],[1454]) ).
thf(64012,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ k4_xboole_0 ) )
!= ( C @ ( B @ k4_xboole_0 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk19 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[62482,63997]) ).
thf(64013,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk19 ) )
= A ),
inference(pattern_uni,[status(thm)],[64012:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(197,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(2065,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(2066,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[2065]) ).
thf(2067,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[2066]) ).
thf(63998,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
!= ( C @ ( B @ k4_xboole_0 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk19 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[2067,63997]) ).
thf(63999,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk19 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[63998:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(64064,plain,
! [A: $i] : ( k1_xboole_0 = A ),
inference(rewrite,[status(thm)],[64013,63999]) ).
thf(64070,plain,
$false,
inference(simplifyReflect,[status(thm)],[6964,64064]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT304+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.12 % 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
% 0.21/0.48 % Computer : n005.cluster.edu
% 0.21/0.48 % Model : x86_64 x86_64
% 0.21/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.48 % Memory : 8046.5625MB
% 0.21/0.48 % OS : Linux 6.8.0-71-generic
% 0.21/0.48 % CPULimit : 300
% 0.21/0.48 % WCLimit : 300
% 0.21/0.48 % DateTime : Fri Sep 25 20:39:20 UTC 2026
% 0.21/0.48 % CPUTime :
% 0.21/0.48 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
% 1.44/1.31 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 11.02/4.06 % [INFO] Parsing done (2745ms).
% 11.02/4.08 % [INFO] Running in sequential loop mode.
% 11.58/4.45 % [INFO] eprover registered as external prover.
% 11.58/4.46 % [INFO] Scanning for conjecture ...
% 14.60/5.32 % [INFO] Found a conjecture (or negated_conjecture) and 13610 axioms. Running axiom selection ...
% 19.11/8.22 % [INFO] Axiom selection finished. Selected 1136 axioms (removed 12474 axioms).
% 22.01/9.19 % [INFO] Problem is first-order (TPTP FOF).
% 22.24/9.26 % [INFO] Type checking passed.
% 22.24/9.27 % [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 ...
% 253.78/78.12 % [INFO] Killing All external provers ...
% 253.78/78.13 % Time passed: 77433ms (effective reasoning time: 74028ms)
% 253.78/78.13 % Axioms used in derivation (7): d5_xboole_0, t2_boole, t48_xboole_1, rc2_relat_1, t3_boole, t4_boole, t32_xboole_1
% 253.78/78.13 % No. of inferences in proof: 45
% 253.78/78.13 % SZS status ContradictoryAxioms for /export/starexec/sandbox2/benchmark/theBenchmark.p : 77433 ms resp. 74028 ms w/o parsing
% 238.33/78.17 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 238.33/78.17 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------