%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU435+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 : n016.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 08:38:55 AM UTC 2026
% Result : ContradictoryAxioms 109.68s 27.90s
% Output : Refutation 109.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 44 ( 31 unt; 0 typ; 2 def)
% Number of atoms : 67 ( 42 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 155 ( 13 ~; 5 |; 10 &; 125 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 0 ^; 47 !; 3 ?; 52 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(k4_xboole_0_decl,type,
k4_xboole_0: $i > $i > $i ).
thf(v1_relat_1_decl,type,
v1_relat_1: $i > $o ).
thf(k3_xboole_0_decl,type,
k3_xboole_0: $i > $i > $i ).
thf(v3_relat_1_decl,type,
v3_relat_1: $i > $o ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(sk9_decl,type,
sk9: $i > $i > $i ).
thf(sk476_decl,type,
sk476: $i ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk476_def,definition,
( sk476
= ( @+[A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ) ) ) ).
thf(121,axiom,
( ( k1_xboole_0 @ v3_relat_1 )
& ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(1735,plain,
( ( k1_xboole_0 @ v3_relat_1 )
& ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(1736,plain,
( ( k1_xboole_0 @ v3_relat_1 )
& ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[1735]) ).
thf(1737,plain,
k1_xboole_0 @ v1_xboole_0,
inference(cnfConj,[status(thm)],[1736]) ).
thf(1072,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(7014,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(7015,plain,
( ( sk476 @ v1_relat_1 )
& ~ ( sk476 @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[7014]) ).
thf(7016,plain,
~ ( sk476 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[7015]) ).
thf(7668,plain,
( ( ( sk476 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1737,7016]) ).
thf(7669,plain,
( ( sk476 @ v1_xboole_0 )
!= ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(simp,[status(thm)],[7668]) ).
thf(7670,plain,
sk476 != k1_xboole_0,
inference(simp,[status(thm)],[7669]) ).
thf(836,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(5692,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(5693,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[5692]) ).
thf(5694,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[5693]) ).
thf(36,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(1357,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)],[36]) ).
thf(1358,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= ( B @ ( A @ k3_xboole_0 ) ) ),
inference(cnf,[status(esa)],[1357]) ).
thf(1359,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( B @ ( A @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) ) ),
inference(lifteq,[status(thm)],[1358]) ).
thf(21348,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[5694,1359]) ).
thf(19,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(1293,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1294,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(cnf,[status(esa)],[1293]) ).
thf(1295,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(lifteq,[status(thm)],[1294]) ).
thf(30919,plain,
! [A: $i] :
( ( A @ ( A @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(rewrite,[status(thm)],[21348,1295]) ).
thf(40,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(1375,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)],[40]) ).
thf(1376,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(cnf,[status(esa)],[1375]) ).
thf(1377,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ k4_xboole_0 ) )
!= ( A @ ( B @ k4_xboole_0 ) ) ) ),
inference(lifteq,[status(thm)],[1376]) ).
thf(1378,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k4_xboole_0 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[1377]) ).
thf(1379,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk9 ) )
= A ),
inference(cnf,[status(esa)],[1378]) ).
thf(28912,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k4_xboole_0 ) @ ( B @ sk9 ) )
= A ),
inference(lifteq,[status(thm)],[1379]) ).
thf(30957,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ k4_xboole_0 ) )
!= ( C @ ( B @ k4_xboole_0 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk9 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[30919,28912]) ).
thf(30958,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk9 ) )
= A ),
inference(pattern_uni,[status(thm)],[30957:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(169,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(2001,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(2002,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(cnf,[status(esa)],[2001]) ).
thf(2003,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(lifteq,[status(thm)],[2002]) ).
thf(28939,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
!= ( C @ ( B @ k4_xboole_0 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk9 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[2003,28912]) ).
thf(28940,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ sk9 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[28939:[bind(A,$thf( A )),bind(B,$thf( k1_xboole_0 )),bind(C,$thf( A ))]]) ).
thf(31860,plain,
! [A: $i] : ( k1_xboole_0 = A ),
inference(rewrite,[status(thm)],[30958,28940]) ).
thf(31902,plain,
$false,
inference(simplifyReflect,[status(thm)],[7670,31860]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU435+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % 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
% 0.13/0.82 % Computer : n016.cluster.edu
% 0.13/0.82 % Model : x86_64 x86_64
% 0.13/0.82 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.82 % Memory : 8046.5625MB
% 0.13/0.82 % OS : Linux 6.8.0-71-generic
% 0.13/0.83 % CPULimit : 300
% 0.13/0.83 % WCLimit : 300
% 0.13/0.83 % DateTime : Sat Sep 26 09:55:33 UTC 2026
% 0.13/0.83 % CPUTime :
% 0.13/0.83 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
% 0.99/1.41 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 4.05/2.29 % [INFO] Parsing done (874ms).
% 4.45/2.31 % [INFO] Running in sequential loop mode.
% 5.07/2.69 % [INFO] eprover registered as external prover.
% 5.07/2.69 % [INFO] Scanning for conjecture ...
% 6.53/3.12 % [INFO] Found a conjecture (or negated_conjecture) and 4509 axioms. Running axiom selection ...
% 9.89/4.04 % [INFO] Axiom selection finished. Selected 1229 axioms (removed 3280 axioms).
% 11.86/4.78 % [INFO] Problem is first-order (TPTP FOF).
% 12.20/4.85 % [INFO] Type checking passed.
% 12.20/4.85 % [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 ...
% 111.07/27.89 % [INFO] Killing All external provers ...
% 111.07/27.90 % Time passed: 26922ms (effective reasoning time: 25579ms)
% 111.07/27.90 % Axioms used in derivation (7): t2_boole, t48_xboole_1, rc2_relat_1, fc12_relat_1, t3_boole, t4_boole, t32_xboole_1
% 109.68/27.90 % No. of inferences in proof: 42
% 109.68/27.90 % SZS status ContradictoryAxioms for /export/starexec/sandbox2/benchmark/theBenchmark.p : 26922 ms resp. 25579 ms w/o parsing
% 109.68/27.92 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 109.68/27.92 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------