%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO212^5 : 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 08:45:24 AM UTC 2026
% Result : Theorem 3.25s 2.08s
% Output : Refutation 3.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 8 unt; 0 typ; 1 def)
% Number of atoms : 81 ( 8 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 71 ( 14 ~; 6 |; 21 &; 26 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 4 con; 0-2 aty)
% Number of variables : 4 ( 0 ^; 3 !; 0 ?; 4 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(b_decl,type,
b: $o ).
thf(a_decl,type,
a: $o ).
thf(sk1_decl,type,
sk1: $o > $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $o > $o] :
~ ( ( ( A @ a )
& ( A @ b ) )
=> ( A
@ ( a
& b ) ) ) ) ) ).
thf(1,conjecture,
! [A: $o > $o] :
( ( ( A @ a )
& ( A @ b ) )
=> ( A
@ ( a
& b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEMB2) ).
thf(2,negated_conjecture,
~ ! [A: $o > $o] :
( ( ( A @ a )
& ( A @ b ) )
=> ( A
@ ( a
& b ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $o > $o] :
( ( ( A @ a )
& ( A @ b ) )
=> ( A
@ ( a
& b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( sk1 @ a )
& ( sk1 @ b )
& ~ ( sk1
@ ( a
& b ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
sk1 @ b,
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
~ ( sk1
@ ( a
& b ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(10,plain,
( ~ $true
| ( ( sk1
@ ( a
& b ) )
!= ( sk1 @ b ) ) ),
inference(paramod_ordered,[status(thm)],[6,7]) ).
thf(11,plain,
( ( sk1
@ ( a
& b ) )
!= ( sk1 @ b ) ),
inference(simp,[status(thm)],[10]) ).
thf(13,plain,
( ( a
& b )
!= b ),
inference(simp,[status(thm)],[11]) ).
thf(5,plain,
sk1 @ a,
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
( ~ $true
| ( ( sk1
@ ( a
& b ) )
!= ( sk1 @ a ) ) ),
inference(paramod_ordered,[status(thm)],[5,7]) ).
thf(9,plain,
( ( sk1
@ ( a
& b ) )
!= ( sk1 @ 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
% 0.00/0.02 % Problem : SYO212^5 : 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
% 0.07/0.19 % Computer : n014.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 16:39:14 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 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
% 0.85/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/0.95 % [INFO] Parsing done (179ms).
% 1.17/0.96 % [INFO] Running in sequential loop mode.
% 1.73/1.36 % [INFO] eprover registered as external prover.
% 1.73/1.37 % [INFO] Scanning for conjecture ...
% 1.91/1.45 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.91/1.48 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.91/1.48 % [INFO] Problem is higher-order (TPTP THF).
% 1.91/1.49 % [INFO] Type checking passed.
% 1.91/1.49 % [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 ...
% 3.25/2.07 % [INFO] Killing All external provers ...
% 3.25/2.07 % Time passed: 1742ms (effective reasoning time: 1103ms)
% 3.25/2.07 % 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)>
% 3.25/2.08 % Axioms used in derivation (0):
% 3.25/2.08 % No. of inferences in proof: 19
% 3.25/2.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1742 ms resp. 1103 ms w/o parsing
% 3.25/2.12 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.25/2.12 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------