%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN983^1 : TPTP v9.3.1. Released v3.6.0.
% 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 : n004.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 08:41:34 AM UTC 2026
% Result : Theorem 3.48s 2.09s
% Output : Refutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 84 ( 7 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 64 ( 13 ~; 6 |; 19 &; 23 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 4 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(p_decl,type,
p: $o > $o ).
thf(1,conjecture,
( ( ( p @ a )
& ( p @ b ) )
=> ( p
@ ( a
& b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ( ( ( p @ a )
& ( p @ b ) )
=> ( p
@ ( a
& b ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ( p @ a )
& ( p @ b ) )
=> ( p
@ ( a
& b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( p @ a )
& ( p @ b )
& ~ ( p
@ ( a
& b ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
p @ b,
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
~ ( p
@ ( a
& b ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(10,plain,
( ~ $true
| ( ( p
@ ( a
& b ) )
!= ( p @ b ) ) ),
inference(paramod_ordered,[status(thm)],[6,7]) ).
thf(11,plain,
( ( p
@ ( a
& b ) )
!= ( p @ b ) ),
inference(simp,[status(thm)],[10]) ).
thf(13,plain,
( ( a
& b )
!= b ),
inference(simp,[status(thm)],[11]) ).
thf(5,plain,
p @ a,
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
( ~ $true
| ( ( p
@ ( a
& b ) )
!= ( p @ a ) ) ),
inference(paramod_ordered,[status(thm)],[5,7]) ).
thf(9,plain,
( ( p
@ ( a
& b ) )
!= ( p @ a ) ),
inference(simp,[status(thm)],[8]) ).
thf(12,plain,
( ( a
& b )
!= a ),
inference(simp,[status(thm)],[9]) ).
thf(15,plain,
( ( a
& b )
| a ),
inference(bool_ext,[status(thm)],[12]) ).
thf(18,plain,
( ( a
| a )
& ( b
| a ) ),
inference(cnf,[status(esa)],[15]) ).
thf(19,plain,
( a
| a ),
inference(cnfConj,[status(thm)],[18]) ).
thf(21,plain,
a,
inference(simp,[status(thm)],[19]) ).
thf(31,plain,
( ( $true
& b )
!= b ),
inference(rewrite,[status(thm)],[13,21]) ).
thf(32,plain,
$false,
inference(simp,[status(thm)],[31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN983^1 : TPTP v9.3.1. Released v3.6.0.
% 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
% 0.10/0.20 % Computer : n004.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 16:19:36 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 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
% 0.88/0.77 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/0.96 % [INFO] Parsing done (180ms).
% 1.22/0.97 % [INFO] Running in sequential loop mode.
% 1.83/1.37 % [INFO] eprover registered as external prover.
% 1.83/1.37 % [INFO] Scanning for conjecture ...
% 2.04/1.44 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.04/1.47 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.04/1.48 % [INFO] Problem is higher-order (TPTP THF).
% 2.04/1.48 % [INFO] Type checking passed.
% 2.04/1.48 % [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 ...
% 3.48/2.08 % [INFO] Killing All external provers ...
% 3.48/2.08 % Time passed: 1745ms (effective reasoning time: 1105ms)
% 3.48/2.08 % 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)>
% 3.48/2.09 % Axioms used in derivation (0):
% 3.48/2.09 % No. of inferences in proof: 19
% 3.48/2.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1745 ms resp. 1105 ms w/o parsing
% 3.48/2.12 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.48/2.12 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------