%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO016^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n002.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 08:45:01 AM UTC 2026
% Result : Theorem 8.13s 3.29s
% Output : Refutation 7.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 9 unt; 0 typ; 3 def)
% Number of atoms : 184 ( 13 equ; 0 cnn)
% Maximal formula atoms : 9 ( 6 avg)
% Number of connectives : 204 ( 31 ~; 9 |; 2 &; 146 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 23 ( 2 ^; 19 !; 0 ?; 23 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(leibeq_decl,type,
leibeq: $o > $o > $o ).
thf(h_decl,type,
h: $o > $o ).
thf(sk1_decl,type,
sk1: $o > $o ).
thf(sk15_decl,type,
sk15: $o > $o ).
thf(leibeq_def,definition,
( leibeq
= ( ^ [A: $o,B: $o] :
! [C: $o > $o] :
( ( C @ A )
=> ( C @ B ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $o > $o] :
~ ( ( A
@ ( h
@ ! [B: $o > $o] :
( ( B @ ( h @ $true ) )
=> ( B @ ( h @ $false ) ) ) ) )
=> ( A @ ( h @ $false ) ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( @+[A: $o > $o] :
~ ( ( A @ ( h @ $true ) )
=> ( A @ ( h @ $false ) ) ) ) ) ).
thf(1,conjecture,
leibeq @ ( h @ ( leibeq @ ( h @ $true ) @ ( h @ $false ) ) ) @ ( h @ $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ( leibeq @ ( h @ ( leibeq @ ( h @ $true ) @ ( h @ $false ) ) ) @ ( h @ $false ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $o > $o] :
( ( A
@ ( h
@ ! [B: $o > $o] :
( ( B @ ( h @ $true ) )
=> ( B @ ( h @ $false ) ) ) ) )
=> ( A @ ( h @ $false ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( sk1
@ ( h
@ ! [A: $o > $o] :
( ( A @ ( h @ $true ) )
=> ( A @ ( h @ $false ) ) ) ) )
& ~ ( sk1 @ ( h @ $false ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( sk1
@ ( h
@ ! [A: $o > $o] :
( ( A @ ( h @ $true ) )
=> ( A @ ( h @ $false ) ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(6,plain,
~ ( sk1 @ ( h @ $false ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
( ~ $true
| ( ( sk1
@ ( h
@ ! [A: $o > $o] :
( ( A @ ( h @ $true ) )
=> ( A @ ( h @ $false ) ) ) ) )
!= ( sk1 @ ( h @ $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[5,6]) ).
thf(8,plain,
( ( sk1
@ ( h
@ ! [A: $o > $o] :
( ( A @ ( h @ $true ) )
=> ( A @ ( h @ $false ) ) ) ) )
!= ( sk1 @ ( h @ $false ) ) ),
inference(simp,[status(thm)],[7]) ).
thf(9,plain,
( ( h
@ ! [A: $o > $o] :
( ( A @ ( h @ $true ) )
=> ( A @ ( h @ $false ) ) ) )
!= ( h @ $false ) ),
inference(simp,[status(thm)],[8]) ).
thf(10,plain,
! [A: $o > $o] :
( ( A @ ( h @ $true ) )
=> ( A @ ( h @ $false ) ) ),
inference(simp,[status(thm)],[9]) ).
thf(13,plain,
! [A: $o > $o] :
( ~ ( A @ ( h @ $true ) )
| ( A @ ( h @ $false ) ) ),
inference(cnf,[status(esa)],[10]) ).
thf(306,plain,
! [A: $o > $o] :
( ~ ( A @ ( h @ $true ) )
| ~ $true
| ( ( A @ ( h @ $false ) )
!= ( sk1 @ ( h @ $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,6]) ).
thf(307,plain,
! [A: $o > $o] :
( ~ ( A @ ( h @ $true ) )
| ( ( A @ ( h @ $false ) )
!= ( sk1 @ ( h @ $false ) ) ) ),
inference(simp,[status(thm)],[306]) ).
thf(444,plain,
~ ( sk1 @ ( h @ $true ) ),
inference(pre_uni,[status(thm)],[307:[bind(A,$thf( sk1 ))]]) ).
thf(556,plain,
( ~ $true
| ( ( sk1
@ ( h
@ ! [A: $o > $o] :
( ( A @ ( h @ $true ) )
=> ( A @ ( h @ $false ) ) ) ) )
!= ( sk1 @ ( h @ $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[5,444]) ).
thf(557,plain,
( ( sk1
@ ( h
@ ! [A: $o > $o] :
( ( A @ ( h @ $true ) )
=> ( A @ ( h @ $false ) ) ) ) )
!= ( sk1 @ ( h @ $true ) ) ),
inference(simp,[status(thm)],[556]) ).
thf(572,plain,
( ( h
@ ! [A: $o > $o] :
( ( A @ ( h @ $true ) )
=> ( A @ ( h @ $false ) ) ) )
!= ( h @ $true ) ),
inference(simp,[status(thm)],[557]) ).
thf(580,plain,
~ ! [A: $o > $o] :
( ( A @ ( h @ $true ) )
=> ( A @ ( h @ $false ) ) ),
inference(simp,[status(thm)],[572]) ).
thf(627,plain,
( ( sk15 @ ( h @ $true ) )
& ~ ( sk15 @ ( h @ $false ) ) ),
inference(cnf,[status(esa)],[580]) ).
thf(629,plain,
~ ( sk15 @ ( h @ $false ) ),
inference(cnfConj,[status(thm)],[627]) ).
thf(680,plain,
! [A: $o > $o] :
( ~ ( A @ ( h @ $true ) )
| ~ $true
| ( ( A @ ( h @ $false ) )
!= ( sk15 @ ( h @ $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,629]) ).
thf(681,plain,
! [A: $o > $o] :
( ~ ( A @ ( h @ $true ) )
| ( ( A @ ( h @ $false ) )
!= ( sk15 @ ( h @ $false ) ) ) ),
inference(simp,[status(thm)],[680]) ).
thf(703,plain,
~ ( sk15 @ ( h @ $true ) ),
inference(pre_uni,[status(thm)],[681:[bind(A,$thf( sk15 ))]]) ).
thf(628,plain,
sk15 @ ( h @ $true ),
inference(cnfConj,[status(thm)],[627]) ).
thf(732,plain,
~ $true,
inference(rewrite,[status(thm)],[703,628]) ).
thf(733,plain,
$false,
inference(simp,[status(thm)],[732]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO016^1 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.09/0.22 % Computer : n002.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 16:24:07 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 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
% 1.03/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/0.99 % [INFO] Parsing done (174ms).
% 1.21/1.01 % [INFO] Running in sequential loop mode.
% 2.00/1.42 % [INFO] eprover registered as external prover.
% 2.00/1.42 % [INFO] Scanning for conjecture ...
% 2.19/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.19/1.55 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.19/1.55 % [INFO] Problem is higher-order (TPTP THF).
% 2.19/1.55 % [INFO] Type checking passed.
% 2.19/1.56 % [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 ...
% 8.13/3.29 % [INFO] Killing All external provers ...
% 8.13/3.29 % Time passed: 2918ms (effective reasoning time: 2278ms)
% 8.13/3.29 % 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)>
% 8.13/3.29 % Axioms used in derivation (0):
% 8.13/3.29 % No. of inferences in proof: 26
% 8.13/3.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2918 ms resp. 2278 ms w/o parsing
% 7.37/3.35 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.37/3.35 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------