%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT319+4 : 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 : n009.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 07:47:13 AM UTC 2026
% Result : ContradictoryAxioms 214.08s 67.07s
% Output : Refutation 214.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 52 ( 28 unt; 0 typ; 2 def)
% Number of atoms : 107 ( 50 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 231 ( 34 ~; 19 |; 17 &; 152 @)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 63 ( 0 ^; 58 !; 3 ?; 63 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(v3_struct_0_decl,type,
v3_struct_0: $i > $o ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(l1_pre_topc_decl,type,
l1_pre_topc: $i > $o ).
thf(v2_pre_topc_decl,type,
v2_pre_topc: $i > $o ).
thf(k2_xboole_0_decl,type,
k2_xboole_0: $i > $i > $i ).
thf(k4_xboole_0_decl,type,
k4_xboole_0: $i > $i > $i ).
thf(v1_pre_topc_decl,type,
v1_pre_topc: $i > $o ).
thf(k9_tdlat_1_decl,type,
k9_tdlat_1: $i > $i ).
thf(sk202_decl,type,
sk202: $i > $i > $i ).
thf(sk257_decl,type,
sk257: $i ).
thf(sk202_def,definition,
( sk202
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk257_def,definition,
( sk257
= ( @+[A: $i] :
( ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ) ) ) ).
thf(399,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
<=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_xboole_0) ).
thf(3281,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)],[399]) ).
thf(3282,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)],[3281]) ).
thf(3283,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)],[3282]) ).
thf(3285,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[3283]) ).
thf(3287,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[3285]) ).
thf(3288,plain,
k1_xboole_0 @ v1_xboole_0,
inference(simp,[status(thm)],[3287]) ).
thf(813,axiom,
? [A: $i] :
( ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_pre_topc) ).
thf(5193,plain,
? [A: $i] :
( ( A @ v2_pre_topc )
& ( A @ v1_pre_topc )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_pre_topc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(5194,plain,
( ( sk257 @ v2_pre_topc )
& ( sk257 @ v1_pre_topc )
& ~ ( sk257 @ v3_struct_0 )
& ( sk257 @ l1_pre_topc ) ),
inference(cnf,[status(esa)],[5193]) ).
thf(5198,plain,
sk257 @ v2_pre_topc,
inference(cnfConj,[status(thm)],[5194]) ).
thf(593,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ~ ( A @ k9_tdlat_1 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_tdlat_1) ).
thf(4143,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ~ ( A @ k9_tdlat_1 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(4144,plain,
! [A: $i] :
( ~ ( A @ k9_tdlat_1 @ v1_xboole_0 )
| ~ ( A @ l1_pre_topc )
| ~ ( A @ v2_pre_topc ) ),
inference(cnf,[status(esa)],[4143]) ).
thf(19468,plain,
! [A: $i] :
( ( ( sk257 @ v2_pre_topc )
!= ( A @ v2_pre_topc ) )
| ~ ( A @ k9_tdlat_1 @ v1_xboole_0 )
| ~ ( A @ l1_pre_topc )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5198,4144]) ).
thf(19469,plain,
! [A: $i] :
( ( ( sk257 @ v2_pre_topc )
!= ( A @ v2_pre_topc ) )
| ~ ( A @ k9_tdlat_1 @ v1_xboole_0 )
| ~ ( A @ l1_pre_topc ) ),
inference(simp,[status(thm)],[19468]) ).
thf(19470,plain,
( ~ ( sk257 @ k9_tdlat_1 @ v1_xboole_0 )
| ~ ( sk257 @ l1_pre_topc ) ),
inference(pattern_uni,[status(thm)],[19469:[bind(A,$thf( sk257 ))]]) ).
thf(5195,plain,
sk257 @ l1_pre_topc,
inference(cnfConj,[status(thm)],[5194]) ).
thf(20376,plain,
( ~ ( sk257 @ k9_tdlat_1 @ v1_xboole_0 )
| ~ $true ),
inference(rewrite,[status(thm)],[19470,5195]) ).
thf(20377,plain,
~ ( sk257 @ k9_tdlat_1 @ v1_xboole_0 ),
inference(simp,[status(thm)],[20376]) ).
thf(20412,plain,
( ( ( sk257 @ k9_tdlat_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3288,20377]) ).
thf(20413,plain,
( ( sk257 @ k9_tdlat_1 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[20412]) ).
thf(20421,plain,
( ( sk257 @ k9_tdlat_1 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[20413]) ).
thf(318,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(2884,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(2885,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
inference(cnf,[status(esa)],[2884]) ).
thf(2886,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
inference(lifteq,[status(thm)],[2885]) ).
thf(472,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_xboole_1) ).
thf(3598,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(3599,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[3598]) ).
thf(3600,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[3599]) ).
thf(29266,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
!= ( C @ ( B @ k2_xboole_0 ) ) )
| ( ( A @ ( B @ k4_xboole_0 ) )
= k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[2886,3600]) ).
thf(29267,plain,
! [A: $i] :
( ( A @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[29266:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(653,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k4_xboole_0 ) )
= ( A @ ( B @ k4_xboole_0 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_xboole_1) ).
thf(4471,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)],[653]) ).
thf(4472,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(cnf,[status(esa)],[4471]) ).
thf(4473,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(lifteq,[status(thm)],[4472]) ).
thf(4474,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[4473]) ).
thf(4475,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk202 ) )
= A ),
inference(cnf,[status(esa)],[4474]) ).
thf(45272,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk202 ) )
= A ),
inference(lifteq,[status(thm)],[4475]) ).
thf(45275,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ k4_xboole_0 ) )
!= ( C @ ( B @ k4_xboole_0 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk202 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[29267,45272]) ).
thf(45276,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk202 ) )
= A ),
inference(pattern_uni,[status(thm)],[45275:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(508,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(3744,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(3745,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[3744]) ).
thf(3746,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[3745]) ).
thf(45299,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
!= ( C @ ( B @ k4_xboole_0 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk202 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[3746,45272]) ).
thf(45300,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk202 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[45299:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(46151,plain,
! [A: $i] : ( k1_xboole_0 = A ),
inference(rewrite,[status(thm)],[45276,45300]) ).
thf(46166,plain,
$false,
inference(simplifyReflect,[status(thm)],[20421,46151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT319+4 : 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 : n009.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 20:50:06 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
% 0.71/0.70 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 8.85/3.40 % [INFO] Parsing done (2695ms).
% 8.85/3.43 % [INFO] Running in sequential loop mode.
% 9.75/3.86 % [INFO] eprover registered as external prover.
% 9.75/3.87 % [INFO] Scanning for conjecture ...
% 15.28/6.24 % [INFO] Found a conjecture (or negated_conjecture) and 34720 axioms. Running axiom selection ...
% 25.01/13.75 % [INFO] Axiom selection finished. Selected 1385 axioms (removed 33335 axioms).
% 28.13/14.74 % [INFO] Problem is first-order (TPTP FOF).
% 28.41/14.81 % [INFO] Type checking passed.
% 28.41/14.81 % [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 ...
% 214.08/67.06 % [INFO] Killing All external provers ...
% 214.08/67.06 % Time passed: 66568ms (effective reasoning time: 63618ms)
% 214.08/67.07 % Axioms used in derivation (7): t1_boole, d5_xboole_0, fc3_tdlat_1, t4_boole, t32_xboole_1, rc2_pre_topc, t46_xboole_1
% 214.08/67.07 % No. of inferences in proof: 50
% 214.08/67.07 % SZS status ContradictoryAxioms for /export/starexec/sandbox/benchmark/theBenchmark.p : 66568 ms resp. 63618 ms w/o parsing
% 214.08/67.11 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 214.08/67.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------