%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO245^5 : 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 : n001.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 08:45:28 AM UTC 2026
% Result : Theorem 5.80s 2.88s
% Output : Refutation 6.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 8 unt; 0 typ; 2 def)
% Number of atoms : 42 ( 30 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 118 ( 23 ~; 5 |; 8 &; 73 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 2 con; 0-2 aty)
% Number of variables : 47 ( 6 ^; 26 !; 13 ?; 47 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(sk1_decl,type,
sk1: ( $i > $o ) > $i ).
thf(sk2_decl,type,
sk2: $i > $i > $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: ( $i > $o ) > $i] :
! [B: $i > $o,C: $i > $o] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $i > $o] :
! [B: $i > $o] :
( ( A @ ( sk1 @ B ) )
= B ) ) ) ).
thf(1,conjecture,
( ! [A: ( $i > $o ) > $i] :
( ? [B: $i > $o] :
( ~ ( B @ ( A @ B ) )
& ( ( A
@ ^ [C: $i] :
? [D: $i > $o] :
( ~ ( D @ ( A @ D ) )
& ( C
= ( A @ D ) ) ) )
= ( A @ B ) ) )
=> ? [B: $i > $o] :
( ~ ( B @ ( A @ B ) )
& ( ( A
@ ^ [C: $i] :
? [D: $i > $o] :
( ~ ( D @ ( A @ D ) )
& ( C
= ( A @ D ) ) ) )
= ( A @ B ) ) ) )
=> ~ ? [A: ( $i > $o ) > $i] :
! [B: $i > $o,C: $i > $o] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM193A) ).
thf(2,negated_conjecture,
~ ( ! [A: ( $i > $o ) > $i] :
( ? [B: $i > $o] :
( ~ ( B @ ( A @ B ) )
& ( ( A
@ ^ [C: $i] :
? [D: $i > $o] :
( ~ ( D @ ( A @ D ) )
& ( C
= ( A @ D ) ) ) )
= ( A @ B ) ) )
=> ? [B: $i > $o] :
( ~ ( B @ ( A @ B ) )
& ( ( A
@ ^ [C: $i] :
? [D: $i > $o] :
( ~ ( D @ ( A @ D ) )
& ( C
= ( A @ D ) ) ) )
= ( A @ B ) ) ) )
=> ~ ? [A: ( $i > $o ) > $i] :
! [B: $i > $o,C: $i > $o] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
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 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
? [A: ( $i > $o ) > $i] :
! [B: $i > $o,C: $i > $o] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
! [B: $i > $o,A: $i > $o] :
( ( ( sk1 @ A )
!= ( sk1 @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(6,plain,
! [B: $i > $o,A: $i > $o] :
( ( ( sk1 @ A )
!= ( sk1 @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(7,plain,
? [A: $i > $i > $o] :
! [B: $i > $o] :
( ( A @ ( sk1 @ B ) )
= B ),
inference(detectInverse,[status(thm)],[6]) ).
thf(8,plain,
! [A: $i > $o] :
( ( sk2 @ ( sk1 @ A ) )
= A ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
! [A: $i > $o] :
( ( sk2 @ ( sk1 @ A ) )
= A ),
inference(lifteq,[status(thm)],[8]) ).
thf(10,plain,
! [B: $i,A: $i > $o] :
( ( sk2 @ ( sk1 @ A ) @ B )
= ( A @ B ) ),
inference(func_ext,[status(esa)],[9]) ).
thf(11,plain,
! [B: $i,A: $i > $o] :
( ~ ( sk2 @ ( sk1 @ A ) @ B )
| ( A @ B ) ),
inference(bool_ext,[status(thm)],[10]) ).
thf(31,plain,
! [B: $i,A: $i > $o] :
( ~ ( sk2 @ ( sk1 @ A ) @ B )
| ( ( A @ B )
!= ( ~ ( sk2 @ ( sk1 @ A ) @ B ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[11]) ).
thf(38,plain,
~ ( sk2
@ ( sk1
@ ^ [A: $i] :
~ ( sk2 @ A @ A ) )
@ ( sk1
@ ^ [A: $i] :
~ ( sk2 @ A @ A ) ) ),
inference(pre_uni,[status(thm)],[31:[bind(A,$thf( ^ [C: $i] : ~ ( sk2 @ C @ C ) )),bind(B,$thf( sk1 @ ^ [C: $i] : ~ ( sk2 @ C @ C ) ))]]) ).
thf(109,plain,
$false,
inference(e,[status(thm)],[10,6,38,9,3,11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO245^5 : 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 : n001.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 16:46:36 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
% 0.90/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/0.99 % [INFO] Parsing done (195ms).
% 1.25/1.01 % [INFO] Running in sequential loop mode.
% 2.02/1.42 % [INFO] eprover registered as external prover.
% 2.02/1.43 % [INFO] Scanning for conjecture ...
% 2.22/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.22/1.56 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.22/1.56 % [INFO] Problem is higher-order (TPTP THF).
% 2.22/1.57 % [INFO] Type checking passed.
% 2.22/1.57 % [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 ...
% 5.80/2.88 % External prover 'e' found a proof!
% 5.80/2.88 % [INFO] Killing All external provers ...
% 5.80/2.88 % Time passed: 2528ms (effective reasoning time: 1863ms)
% 5.80/2.88 % 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)>
% 5.80/2.88 % Axioms used in derivation (0):
% 5.80/2.88 % No. of inferences in proof: 14
% 5.80/2.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2528 ms resp. 1863 ms w/o parsing
% 6.18/2.93 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.18/2.93 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------