%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO310^5 : 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 : 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 08:45:34 AM UTC 2026
% Result : Theorem 2.44s 1.41s
% Output : Refutation 2.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 1
% Syntax : Number of formulae : 5 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 2 equ; 0 cnn)
% Maximal formula atoms : 16 ( 9 avg)
% Number of connectives : 75 ( 19 ~; 4 |; 22 &; 28 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 7 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 3 ( 0 usr; 2 con; 0-2 aty)
% Number of variables : 5 ( 0 ^; 2 !; 3 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
thf(1,conjecture,
( ? [A: $o > $o > $o] :
( ( A @ $true @ $true )
& ( A @ $false @ $false )
& ~ ( A @ $false @ $true )
& ~ ( A @ $true @ $false ) )
& ! [A: $o > $o] :
( ( A @ $true )
= ( A
@ ( $true
=> $true ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cOMEGA_EXAMPLE) ).
thf(2,negated_conjecture,
~ ( ? [A: $o > $o > $o] :
( ( A @ $true @ $true )
& ( A @ $false @ $false )
& ~ ( A @ $false @ $true )
& ~ ( A @ $true @ $false ) )
& ! [A: $o > $o] :
( ( A @ $true )
= ( A
@ ( $true
=> $true ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ? [A: $o > $o > $o] :
( ( A @ $true @ $true )
& ( A @ $false @ $false )
& ~ ( A @ $false @ $true )
& ~ ( A @ $true @ $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(28,plain,
~ ( ( ( ~ $true
& ~ $true )
| ( $true
& $true ) )
& ( ( ~ $false
& ~ $false )
| ( $false
& $false ) )
& ~ ( ( ~ $false
& ~ $true )
| ( $false
& $true ) )
& ~ ( ( ~ $true
& ~ $false )
| ( $true
& $false ) ) ),
inference(instance,[status(thm)],[3]) ).
thf(29,plain,
$false,
inference(simp,[status(thm)],[28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO310^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.11/0.19 % Computer : n014.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Sep 29 16:44:44 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 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
% 0.60/0.51 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.02/0.61 % [INFO] Parsing done (100ms).
% 1.02/0.62 % [INFO] Running in sequential loop mode.
% 1.45/1.02 % [INFO] eprover registered as external prover.
% 1.45/1.03 % [INFO] Scanning for conjecture ...
% 1.72/1.12 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.89/1.16 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.89/1.17 % [INFO] Problem is higher-order (TPTP THF).
% 1.89/1.17 % [INFO] Type checking passed.
% 1.89/1.17 % [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 ...
% 2.44/1.40 % [INFO] Killing All external provers ...
% 2.44/1.41 % Time passed: 1127ms (effective reasoning time: 781ms)
% 2.44/1.41 % 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)>
% 2.44/1.41 % Axioms used in derivation (0):
% 2.44/1.41 % No. of inferences in proof: 5
% 2.44/1.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1127 ms resp. 781 ms w/o parsing
% 2.44/1.45 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.44/1.45 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------