%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU902^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n020.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 : Wed Sep 30 08:29:33 AM UTC 2026
% Result : Theorem 11.97s 3.15s
% Output : Refutation 11.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 18 unt; 0 typ; 3 def)
% Number of atoms : 122 ( 53 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 189 ( 34 ~; 8 |; 18 &; 121 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 46 ( 46 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 7 ^; 31 !; 11 ?; 52 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(d_decl,type,
d: $i > $o ).
thf(sk1_decl,type,
sk1: ( $i > $o ) > $i ).
thf(sk2_decl,type,
sk2: $i > $i > $o ).
thf(sk8_decl,type,
sk8: $i > $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: ( $i > $o ) > $i] :
~ ( ( ! [B: $i > $o,C: $i > $o] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
& ( d
= ( ^ [B: $i] :
? [C: $i > $o] :
( ~ ( C @ ( A @ C ) )
& ( B
= ( A @ C ) ) ) ) ) )
=> ~ ( d @ ( A @ d ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $i > $o] :
! [B: $i > $o] :
( ( A @ ( sk1 @ B ) )
= B ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i > $o] :
( ~ ( A @ ( sk1 @ A ) )
& ( ( sk1 @ d )
= ( sk1 @ A ) ) ) ) ) ).
thf(1,conjecture,
! [A: ( $i > $o ) > $i] :
( ( ! [B: $i > $o,C: $i > $o] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
& ( d
= ( ^ [B: $i] :
? [C: $i > $o] :
( ~ ( C @ ( A @ C ) )
& ( B
= ( A @ C ) ) ) ) ) )
=> ~ ( d @ ( A @ d ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM143_pme) ).
thf(2,negated_conjecture,
~ ! [A: ( $i > $o ) > $i] :
( ( ! [B: $i > $o,C: $i > $o] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
& ( d
= ( ^ [B: $i] :
? [C: $i > $o] :
( ~ ( C @ ( A @ C ) )
& ( B
= ( A @ C ) ) ) ) ) )
=> ~ ( d @ ( A @ d ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: ( $i > $o ) > $i] :
( ( ! [B: $i > $o,C: $i > $o] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
& ( d
= ( ^ [B: $i] :
? [C: $i > $o] :
( ~ ( C @ ( A @ C ) )
& ( B
= ( A @ C ) ) ) ) ) )
=> ~ ( d @ ( A @ d ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: $i > $o,A: $i > $o] :
( ( ( ( sk1 @ A )
!= ( sk1 @ B ) )
| ( A = B ) )
& ( d
= ( ^ [C: $i] :
? [D: $i > $o] :
( ~ ( D @ ( sk1 @ D ) )
& ( C
= ( sk1 @ D ) ) ) ) )
& ( d @ ( sk1 @ d ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [B: $i > $o,A: $i > $o] :
( ( ( sk1 @ A )
!= ( sk1 @ B ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
! [B: $i > $o,A: $i > $o] :
( ( ( sk1 @ A )
!= ( sk1 @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(9,plain,
? [A: $i > $i > $o] :
! [B: $i > $o] :
( ( A @ ( sk1 @ B ) )
= B ),
inference(detectInverse,[status(thm)],[8]) ).
thf(10,plain,
! [A: $i > $o] :
( ( sk2 @ ( sk1 @ A ) )
= A ),
inference(cnf,[status(esa)],[9]) ).
thf(17,plain,
! [A: $i > $o] :
( ( sk2 @ ( sk1 @ A ) )
= A ),
inference(lifteq,[status(thm)],[10]) ).
thf(18,plain,
! [B: $i,A: $i > $o] :
( ( sk2 @ ( sk1 @ A ) @ B )
= ( A @ B ) ),
inference(func_ext,[status(esa)],[17]) ).
thf(6,plain,
( d
= ( ^ [A: $i] :
? [B: $i > $o] :
( ~ ( B @ ( sk1 @ B ) )
& ( A
= ( sk1 @ B ) ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(11,plain,
( d
= ( ^ [A: $i] :
? [B: $i > $o] :
( ~ ( B @ ( sk1 @ B ) )
& ( A
= ( sk1 @ B ) ) ) ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(12,plain,
! [A: $i] :
( ( d @ A )
= ( ? [B: $i > $o] :
( ~ ( B @ ( sk1 @ B ) )
& ( A
= ( sk1 @ B ) ) ) ) ),
inference(func_ext,[status(esa)],[11]) ).
thf(7,plain,
d @ ( sk1 @ d ),
inference(cnfConj,[status(thm)],[4]) ).
thf(74,plain,
! [A: $i] :
( ? [B: $i > $o] :
( ~ ( B @ ( sk1 @ B ) )
& ( A
= ( sk1 @ B ) ) )
| ( ( d @ A )
!= ( d @ ( sk1 @ d ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,7]) ).
thf(75,plain,
? [A: $i > $o] :
( ~ ( A @ ( sk1 @ A ) )
& ( ( sk1 @ d )
= ( sk1 @ A ) ) ),
inference(pattern_uni,[status(thm)],[74:[bind(A,$thf( sk1 @ d ))]]) ).
thf(105,plain,
( ~ ( sk8 @ ( sk1 @ sk8 ) )
& ( ( sk1 @ d )
= ( sk1 @ sk8 ) ) ),
inference(cnf,[status(esa)],[75]) ).
thf(106,plain,
~ ( sk8 @ ( sk1 @ sk8 ) ),
inference(cnfConj,[status(thm)],[105]) ).
thf(168,plain,
! [B: $i,A: $i > $o] :
( ~ ( sk2 @ ( sk1 @ A ) @ B )
| ( ( A @ B )
!= ( sk8 @ ( sk1 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,106]) ).
thf(173,plain,
~ ( sk2 @ ( sk1 @ sk8 ) @ ( sk1 @ sk8 ) ),
inference(pre_uni,[status(thm)],[168:[bind(A,$thf( sk8 )),bind(B,$thf( sk1 @ sk8 ))]]) ).
thf(107,plain,
( ( sk1 @ d )
= ( sk1 @ sk8 ) ),
inference(cnfConj,[status(thm)],[105]) ).
thf(108,plain,
( ( sk1 @ sk8 )
= ( sk1 @ d ) ),
inference(lifteq,[status(thm)],[107]) ).
thf(195,plain,
! [A: $i > $o] :
( ( ( sk2 @ ( sk1 @ d ) )
= A )
| ( ( sk1 @ sk8 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[108,17]) ).
thf(196,plain,
( ( sk2 @ ( sk1 @ d ) )
= sk8 ),
inference(pattern_uni,[status(thm)],[195:[bind(A,$thf( sk8 ))]]) ).
thf(585,plain,
! [A: $i > $o] :
( ( sk8 = A )
| ( ( sk2 @ ( sk1 @ d ) )
!= ( sk2 @ ( sk1 @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[196,17]) ).
thf(586,plain,
sk8 = d,
inference(pattern_uni,[status(thm)],[585:[bind(A,$thf( d ))]]) ).
thf(607,plain,
~ ( sk2 @ ( sk1 @ d ) @ ( sk1 @ d ) ),
inference(rewrite,[status(thm)],[173,586]) ).
thf(610,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ B )
| ( ( sk2 @ ( sk1 @ A ) @ B )
!= ( sk2 @ ( sk1 @ d ) @ ( sk1 @ d ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,607]) ).
thf(611,plain,
~ ( d @ ( sk1 @ d ) ),
inference(pattern_uni,[status(thm)],[610:[bind(A,$thf( d )),bind(B,$thf( sk1 @ d ))]]) ).
thf(654,plain,
~ $true,
inference(rewrite,[status(thm)],[611,7]) ).
thf(655,plain,
$false,
inference(simp,[status(thm)],[654]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU902^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.10/0.21 % Computer : n020.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 14:45:19 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.67/0.55 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.99/0.64 % [INFO] Parsing done (94ms).
% 0.99/0.65 % [INFO] Running in sequential loop mode.
% 1.29/0.84 % [INFO] eprover registered as external prover.
% 1.29/0.85 % [INFO] Scanning for conjecture ...
% 1.29/0.89 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.55/0.91 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.55/0.91 % [INFO] Problem is higher-order (TPTP THF).
% 1.55/0.91 % [INFO] Type checking passed.
% 1.55/0.91 % [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 ...
% 11.97/3.15 % [INFO] Killing All external provers ...
% 11.97/3.15 % Time passed: 2827ms (effective reasoning time: 2497ms)
% 11.97/3.15 % Solved by 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)>
% 11.97/3.15 % Axioms used in derivation (0):
% 11.97/3.15 % No. of inferences in proof: 31
% 11.97/3.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2827 ms resp. 2497 ms w/o parsing
% 11.97/3.18 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.97/3.18 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------