%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO022^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n014.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 08:45:02 AM UTC 2026
% Result : Theorem 4.27s 2.31s
% Output : Refutation 4.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 10 unt; 0 typ; 2 def)
% Number of atoms : 53 ( 7 equ; 9 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 103 ( 47 ~; 19 |; 16 &; 18 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 23 ( 20 ^; 2 !; 0 ?; 23 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(leibeq_decl,type,
leibeq: ( $o > $o > $o ) > ( $o > $o > $o ) > $o ).
thf(sk1_decl,type,
sk1: ( $o > $o > $o ) > $o ).
thf(sk2_decl,type,
sk2: $o ).
thf(sk3_decl,type,
sk3: $o ).
thf(leibeq_def,definition,
( leibeq
= ( ^ [A: $o > $o > $o,B: $o > $o > $o] :
! [C: ( $o > $o > $o ) > $o] :
( ( C @ A )
=> ( C @ B ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: ( $o > $o > $o ) > $o] :
~ ( ( A @ (&) )
=> ( A
@ ^ [B: $o,C: $o] :
~ ( ~ B
| ~ C ) ) ) ) ) ).
thf(1,conjecture,
( leibeq @ (&)
@ ^ [A: $o,B: $o] :
~ ( ~ A
| ~ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ( leibeq @ (&)
@ ^ [A: $o,B: $o] :
~ ( ~ A
| ~ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: ( $o > $o > $o ) > $o] :
( ( A @ (&) )
=> ( A
@ ^ [B: $o,C: $o] :
~ ( ~ B
| ~ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( sk1 @ (&) )
& ~ ( sk1
@ ^ [A: $o,B: $o] :
~ ( ~ A
| ~ B ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
sk1 @ (&),
inference(cnfConj,[status(thm)],[4]) ).
thf(6,plain,
~ ( sk1
@ ^ [A: $o,B: $o] :
~ ( ~ A
| ~ B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
( ~ $true
| ( ( sk1 @ (&) )
!= ( sk1
@ ^ [A: $o,B: $o] :
~ ( ~ A
| ~ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[5,6]) ).
thf(8,plain,
( ( sk1 @ (&) )
!= ( sk1
@ ^ [A: $o,B: $o] :
~ ( ~ A
| ~ B ) ) ),
inference(simp,[status(thm)],[7]) ).
thf(9,plain,
( (&)
!= ( ^ [A: $o,B: $o] :
~ ( ~ A
| ~ B ) ) ),
inference(simp,[status(thm)],[8]) ).
thf(10,plain,
( ( sk2
& sk3 )
!= ( ~ ( ~ sk2
| ~ sk3 ) ) ),
inference(func_ext,[status(esa)],[9]) ).
thf(12,plain,
( ( sk2
& sk3 )
| ~ ( ~ sk2
| ~ sk3 ) ),
inference(bool_ext,[status(thm)],[10]) ).
thf(15,plain,
( ( sk2
| sk2 )
& ( sk2
| sk3 )
& ( sk3
| sk2 )
& ( sk3
| sk3 ) ),
inference(cnf,[status(esa)],[12]) ).
thf(16,plain,
( sk2
| sk2 ),
inference(cnfConj,[status(thm)],[15]) ).
thf(19,plain,
sk2,
inference(simp,[status(thm)],[16]) ).
thf(21,plain,
( ( $true
& sk3 )
!= ( ~ ( ~ $true
| ~ sk3 ) ) ),
inference(rewrite,[status(thm)],[10,19]) ).
thf(22,plain,
$false,
inference(simp,[status(thm)],[21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO022^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % 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
% 0.11/0.21 % Computer : n014.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 16:23:08 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 0.90/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/0.97 % [INFO] Parsing done (190ms).
% 1.25/0.99 % [INFO] Running in sequential loop mode.
% 1.87/1.38 % [INFO] eprover registered as external prover.
% 1.87/1.39 % [INFO] Scanning for conjecture ...
% 2.07/1.48 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.24/1.52 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.24/1.52 % [INFO] Problem is higher-order (TPTP THF).
% 2.24/1.52 % [INFO] Type checking passed.
% 2.24/1.53 % [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 ...
% 4.27/2.31 % [INFO] Killing All external provers ...
% 4.27/2.31 % Time passed: 1961ms (effective reasoning time: 1316ms)
% 4.27/2.31 % 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)>
% 4.27/2.31 % Axioms used in derivation (0):
% 4.27/2.31 % No. of inferences in proof: 16
% 4.27/2.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1961 ms resp. 1316 ms w/o parsing
% 4.27/2.36 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.27/2.36 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------