%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO219^5 : 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 : n008.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 08:45:25 AM UTC 2026
% Result : Theorem 4.09s 2.38s
% Output : Refutation 4.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 10 unt; 0 typ; 2 def)
% Number of atoms : 24 ( 23 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 59 ( 17 ~; 1 |; 1 &; 36 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 36 ( 2 ^; 22 !; 10 ?; 36 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(cS_decl,type,
cS: $i > $i ).
thf(sk1_decl,type,
sk1: $i > $i > $i ).
thf(sk2_decl,type,
sk2: ( $i > $i ) > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $i > $i] :
! [B: $i > $i] :
? [C: $i] :
( ( A @ C )
= B ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i > $i] :
@+[B: $i] :
( ( sk1 @ B )
= A ) ) ) ).
thf(1,conjecture,
( ! [A: $i] :
( ( cS @ A )
!= A )
=> ~ ? [A: $i > $i > $i] :
! [B: $i > $i] :
? [C: $i] :
( ( A @ C )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM6) ).
thf(2,negated_conjecture,
~ ( ! [A: $i] :
( ( cS @ A )
!= A )
=> ~ ? [A: $i > $i > $i] :
! [B: $i > $i] :
? [C: $i] :
( ( A @ C )
= B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i] :
( ( cS @ A )
!= A )
=> ~ ? [A: $i > $i > $i] :
! [B: $i > $i] :
? [C: $i] :
( ( A @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ~ ? [A: $i] :
( ( cS @ A )
= A )
=> ~ ? [A: $i > $i > $i] :
! [B: $i > $i] :
? [C: $i] :
( ( A @ C )
= B ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [B: $i > $i,A: $i] :
( ( ( cS @ A )
!= A )
& ( ( sk1 @ ( sk2 @ B ) )
= B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(7,plain,
! [A: $i > $i] :
( ( sk1 @ ( sk2 @ A ) )
= A ),
inference(cnfConj,[status(thm)],[5]) ).
thf(9,plain,
! [A: $i > $i] :
( ( sk1 @ ( sk2 @ A ) )
= A ),
inference(lifteq,[status(thm)],[7]) ).
thf(10,plain,
! [A: $i > $i] :
( ( sk1 @ ( sk2 @ A ) )
= A ),
inference(simp,[status(thm)],[9]) ).
thf(11,plain,
! [B: $i,A: $i > $i] :
( ( sk1 @ ( sk2 @ A ) @ B )
= ( A @ B ) ),
inference(func_ext,[status(esa)],[10]) ).
thf(6,plain,
! [A: $i] :
( ( cS @ A )
!= A ),
inference(cnfConj,[status(thm)],[5]) ).
thf(8,plain,
! [A: $i] :
( ( cS @ A )
!= A ),
inference(lifteq,[status(thm)],[6]) ).
thf(12,plain,
! [C: $i,B: $i,A: $i > $i] :
( ( ( sk1 @ ( sk2 @ A ) @ B )
!= C )
| ( ( A @ B )
!= ( cS @ C ) ) ),
inference(paramod_ordered,[status(thm)],[11,8]) ).
thf(15,plain,
! [B: $i > $i,A: $i] :
( ( sk1
@ ( sk2
@ ^ [C: $i] : ( cS @ ( B @ C ) ) )
@ A )
!= ( B @ A ) ),
inference(pre_uni,[status(thm)],[12:[bind(A,$thf( ^ [E: $i] : ( cS @ ( D @ E ) ) )),bind(B,$thf( B )),bind(C,$thf( D @ B ))]]) ).
thf(17,plain,
$false,
inference(pre_uni,[status(thm)],[15:[bind(A,$thf( sk2 @ ^ [C: $i] : ( cS @ ( sk1 @ C @ C ) ) )),bind(B,$thf( ^ [C: $i] : ( sk1 @ C @ C ) ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO219^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % 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
% 0.10/0.22 % Computer : n008.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Tue Sep 29 16:40:24 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 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
% 1.04/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/1.00 % [INFO] Parsing done (188ms).
% 1.21/1.01 % [INFO] Running in sequential loop mode.
% 2.01/1.42 % [INFO] eprover registered as external prover.
% 2.01/1.43 % [INFO] Scanning for conjecture ...
% 2.21/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.21/1.55 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.21/1.55 % [INFO] Problem is higher-order (TPTP THF).
% 2.21/1.56 % [INFO] Type checking passed.
% 2.21/1.56 % [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 ...
% 4.09/2.38 % [INFO] Killing All external provers ...
% 4.09/2.38 % Time passed: 2011ms (effective reasoning time: 1361ms)
% 4.09/2.38 % 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)>
% 4.09/2.38 % Axioms used in derivation (0):
% 4.09/2.38 % No. of inferences in proof: 14
% 4.09/2.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2011 ms resp. 1361 ms w/o parsing
% 4.44/2.44 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.44/2.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------