%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO504^1 : TPTP v9.3.1. Released v4.1.0.
% 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 : n015.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 08:46:02 AM UTC 2026
% Result : Theorem 3.75s 2.16s
% Output : Refutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1
% Syntax : Number of formulae : 4 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 70 ( 9 equ; 0 cnn)
% Maximal formula atoms : 8 ( 17 avg)
% Number of connectives : 50 ( 2 ~; 3 |; 12 &; 30 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 5 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_decl,type,
a: $o ).
thf(b_decl,type,
b: $o ).
thf(h_decl,type,
h: $o > $o > $o ).
thf(i_decl,type,
i: $o > $o > $o ).
thf(g_decl,type,
g: ( $o > $o > $o ) > $o ).
thf(f_decl,type,
f: ( ( $o > $o > $o ) > $o ) > $o ).
thf(1,conjecture,
( ( ( ( h @ a @ b )
= ( a
& b ) )
& ( ( i @ a @ b )
= ( a
| b ) )
& ( ( f @ g )
= ( i @ a @ b ) )
& ( h @ a @ b ) )
=> ( f @ g ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',claim) ).
thf(2,negated_conjecture,
~ ( ( ( ( h @ a @ b )
= ( a
& b ) )
& ( ( i @ a @ b )
= ( a
| b ) )
& ( ( f @ g )
= ( i @ a @ b ) )
& ( h @ a @ b ) )
=> ( f @ g ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ( ( h @ a @ b )
= ( a
& b ) )
& ( ( i @ a @ b )
= ( a
| b ) )
& ( ( f @ g )
= ( i @ a @ b ) )
& ( h @ a @ b ) )
=> ( f @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO504^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % 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
% 0.11/0.22 % Computer : n015.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 17:14:48 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 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
% 1.04/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/0.98 % [INFO] Parsing done (176ms).
% 1.24/1.00 % [INFO] Running in sequential loop mode.
% 2.03/1.41 % [INFO] eprover registered as external prover.
% 2.03/1.41 % [INFO] Scanning for conjecture ...
% 2.22/1.50 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.22/1.53 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.22/1.54 % [INFO] Problem is higher-order (TPTP THF).
% 2.22/1.54 % [INFO] Type checking passed.
% 2.22/1.55 % [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 ...
% 3.75/2.15 % External prover 'e' found a proof!
% 3.75/2.15 % [INFO] Killing All external provers ...
% 3.75/2.16 % Time passed: 1786ms (effective reasoning time: 1152ms)
% 3.75/2.16 % 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)>
% 3.75/2.16 % Axioms used in derivation (0):
% 3.75/2.16 % No. of inferences in proof: 4
% 3.75/2.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1786 ms resp. 1152 ms w/o parsing
% 3.84/2.20 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.84/2.20 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------