%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO020^1 : 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 : n005.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 2.90s 1.75s
% Output : Refutation 3.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 11 unt; 0 typ; 4 def)
% Number of atoms : 69 ( 8 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 115 ( 51 ~; 20 |; 17 &; 22 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 16 ( 2 ^; 11 !; 0 ?; 16 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(leibeq_decl,type,
leibeq: $o > $o > $o ).
thf(sk1_decl,type,
sk1: $o ).
thf(sk2_decl,type,
sk2: $o ).
thf(sk3_decl,type,
sk3: $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] :
~ ! [B: $o,C: $o > $o] :
( ( C
@ ( A
& B ) )
=> ( C
@ ~ ( ~ A
| ~ B ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $o] :
~ ! [B: $o > $o] :
( ( B
@ ( sk1
& A ) )
=> ( B
@ ~ ( ~ sk1
| ~ A ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $o > $o] :
~ ( ( A
@ ( sk1
& sk2 ) )
=> ( A
@ ~ ( ~ sk1
| ~ sk2 ) ) ) ) ) ).
thf(1,conjecture,
! [A: $o,B: $o] :
( leibeq
@ ( A
& B )
@ ~ ( ~ A
| ~ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $o,B: $o] :
( leibeq
@ ( A
& B )
@ ~ ( ~ A
| ~ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $o,B: $o,C: $o > $o] :
( ( C
@ ( A
& B ) )
=> ( C
@ ~ ( ~ A
| ~ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( sk3
@ ( sk1
& sk2 ) )
& ~ ( sk3
@ ~ ( ~ sk1
| ~ sk2 ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( sk3
@ ( sk1
& sk2 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(6,plain,
~ ( sk3
@ ~ ( ~ sk1
| ~ sk2 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
( ~ $true
| ( ( sk3
@ ( sk1
& sk2 ) )
!= ( sk3
@ ~ ( ~ sk1
| ~ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[5,6]) ).
thf(8,plain,
( ( sk3
@ ( sk1
& sk2 ) )
!= ( sk3
@ ~ ( ~ sk1
| ~ sk2 ) ) ),
inference(simp,[status(thm)],[7]) ).
thf(9,plain,
( ( sk1
& sk2 )
!= ( ~ ( ~ sk1
| ~ sk2 ) ) ),
inference(simp,[status(thm)],[8]) ).
thf(11,plain,
( ( sk1
& sk2 )
| ~ ( ~ sk1
| ~ sk2 ) ),
inference(bool_ext,[status(thm)],[9]) ).
thf(14,plain,
( ( sk1
| sk1 )
& ( sk1
| sk2 )
& ( sk2
| sk1 )
& ( sk2
| sk2 ) ),
inference(cnf,[status(esa)],[11]) ).
thf(15,plain,
( sk1
| sk1 ),
inference(cnfConj,[status(thm)],[14]) ).
thf(18,plain,
sk1,
inference(simp,[status(thm)],[15]) ).
thf(24,plain,
( ( $true
& sk2 )
!= ( ~ ( ~ $true
| ~ sk2 ) ) ),
inference(rewrite,[status(thm)],[9,18]) ).
thf(25,plain,
$false,
inference(simp,[status(thm)],[24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO020^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % 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
% 0.11/0.20 % Computer : n005.cluster.edu
% 0.11/0.20 % Model : x86_64 x86_64
% 0.11/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.20 % Memory : 8046.5625MB
% 0.11/0.20 % OS : Linux 6.8.0-71-generic
% 0.11/0.20 % CPULimit : 300
% 0.11/0.20 % WCLimit : 300
% 0.11/0.20 % DateTime : Tue Sep 29 16:23:09 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 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
% 0.64/0.51 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.89/0.62 % [INFO] Parsing done (109ms).
% 1.02/0.63 % [INFO] Running in sequential loop mode.
% 1.59/1.04 % [INFO] eprover registered as external prover.
% 1.59/1.05 % [INFO] Scanning for conjecture ...
% 1.73/1.14 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.73/1.17 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.73/1.17 % [INFO] Problem is higher-order (TPTP THF).
% 1.73/1.17 % [INFO] Type checking passed.
% 1.73/1.18 % [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 ...
% 2.90/1.75 % [INFO] Killing All external provers ...
% 2.90/1.75 % Time passed: 1460ms (effective reasoning time: 1108ms)
% 2.90/1.75 % 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)>
% 2.90/1.75 % Axioms used in derivation (0):
% 2.90/1.75 % No. of inferences in proof: 15
% 2.90/1.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1460 ms resp. 1108 ms w/o parsing
% 3.16/1.80 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.16/1.80 % [INFO] Killing All external provers ...
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