%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM024^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n006.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 07:46:17 AM UTC 2026
% Result : Theorem 6.77s 2.42s
% Output : Refutation 6.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 11 unt; 0 typ; 1 def)
% Number of atoms : 24 ( 23 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 74 ( 14 ~; 2 |; 1 &; 54 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 35 ( 7 ^; 23 !; 4 ?; 35 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(cTM_decl,type,
cTM: $i > $i > $i ).
thf(cTH_decl,type,
cTH: ( $i > $i ) > $i ).
thf(sk1_decl,type,
sk1: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $i] :
~ ? [B: $i] :
( ( cTM @ ( A @ B ) )
= ( cTM @ B ) ) ) ) ).
thf(1,conjecture,
( ! [A: $i > $i] :
( ( cTM @ ( cTH @ A ) )
= A )
=> ! [A: $i > $i] :
? [B: $i] :
( ( cTM @ ( A @ B ) )
= ( cTM @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM9) ).
thf(2,negated_conjecture,
~ ( ! [A: $i > $i] :
( ( cTM @ ( cTH @ A ) )
= A )
=> ! [A: $i > $i] :
? [B: $i] :
( ( cTM @ ( A @ B ) )
= ( cTM @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i > $i] :
( ( cTM @ ( cTH @ A ) )
= A )
=> ! [A: $i > $i] :
? [B: $i] :
( ( cTM @ ( A @ B ) )
= ( cTM @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: $i,A: $i > $i] :
( ( ( cTM @ ( cTH @ A ) )
= A )
& ( ( cTM @ ( sk1 @ B ) )
!= ( cTM @ B ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [A: $i > $i] :
( ( cTM @ ( cTH @ A ) )
= A ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
! [A: $i > $i] :
( ( cTM @ ( cTH @ A ) )
= A ),
inference(lifteq,[status(thm)],[5]) ).
thf(10,plain,
! [B: $i,A: $i > $i] :
( ( cTM @ ( cTH @ A ) @ B )
= ( A @ B ) ),
inference(func_ext,[status(esa)],[7]) ).
thf(6,plain,
! [A: $i] :
( ( cTM @ ( sk1 @ A ) )
!= ( cTM @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
! [A: $i] :
( ( cTM @ ( sk1 @ A ) )
!= ( cTM @ A ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(9,plain,
! [A: $i] :
( ( cTM @ ( sk1 @ A ) )
!= ( cTM @ A ) ),
inference(simp,[status(thm)],[8]) ).
thf(11,plain,
! [A: $i] :
( ( ( ^ [B: $i] : ( sk1 @ A ) )
!= ( ^ [B: $i] : A ) )
| ( ( ^ [B: $i] : B )
!= ( ^ [B: $i] : B ) ) ),
inference(simp,[status(thm)],[9]) ).
thf(20,plain,
! [A: $i] :
( ( ^ [B: $i] : ( sk1 @ A ) )
!= ( ^ [B: $i] : A ) ),
inference(simp,[status(thm)],[11]) ).
thf(22,plain,
! [A: $i] :
( ( sk1 @ A )
!= A ),
inference(func_ext,[status(esa)],[20]) ).
thf(60,plain,
! [C: $i,B: $i,A: $i > $i] :
( ( ( cTM @ ( cTH @ A ) @ B )
!= C )
| ( ( A @ B )
!= ( sk1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[10,22]) ).
thf(71,plain,
! [B: $i > $i,A: $i] :
( ( cTM
@ ( cTH
@ ^ [C: $i] : ( sk1 @ ( B @ C ) ) )
@ A )
!= ( B @ A ) ),
inference(pre_uni,[status(thm)],[60:[bind(A,$thf( ^ [E: $i] : ( sk1 @ ( D @ E ) ) )),bind(B,$thf( B )),bind(C,$thf( D @ B ))]]) ).
thf(73,plain,
$false,
inference(pre_uni,[status(thm)],[71:[bind(A,$thf( cTH @ ^ [C: $i] : ( sk1 @ ( cTM @ C @ C ) ) )),bind(B,$thf( ^ [C: $i] : ( cTM @ C @ C ) ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM024^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.09/0.22 % Computer : n006.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 17:45:54 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 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
% 0.68/0.57 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.17/0.71 % [INFO] Parsing done (136ms).
% 1.17/0.72 % [INFO] Running in sequential loop mode.
% 1.51/0.99 % [INFO] eprover registered as external prover.
% 1.51/0.99 % [INFO] Scanning for conjecture ...
% 1.51/1.04 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.84/1.06 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.84/1.06 % [INFO] Problem is higher-order (TPTP THF).
% 1.84/1.06 % [INFO] Type checking passed.
% 1.84/1.07 % [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 ...
% 6.77/2.41 % [INFO] Killing All external provers ...
% 6.77/2.41 % Time passed: 2092ms (effective reasoning time: 1686ms)
% 6.77/2.41 % 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)>
% 6.77/2.41 % Axioms used in derivation (0):
% 6.77/2.41 % No. of inferences in proof: 16
% 6.77/2.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2092 ms resp. 1686 ms w/o parsing
% 6.77/2.49 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.77/2.49 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------