%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO373^5 : 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 : n007.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 08:45:40 AM UTC 2026
% Result : Theorem 2.86s 1.30s
% Output : Refutation 2.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 8 unt; 0 typ; 1 def)
% Number of atoms : 57 ( 12 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 53 ( 11 ~; 1 |; 2 &; 32 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 10 ( 0 ^; 9 !; 0 ?; 10 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(b_type,type,
b: $tType ).
thf(g_decl,type,
g: b > $o ).
thf(f_decl,type,
f: b > $o ).
thf(sk1_decl,type,
sk1: ( b > $o ) > $o ).
thf(sk2_decl,type,
sk2: b ).
thf(sk1_def,definition,
( sk1
= ( @+[A: ( b > $o ) > $o] :
~ ( ( A @ f )
=> ( A @ g ) ) ) ) ).
thf(1,conjecture,
( ! [A: b] :
( ( f @ A )
= ( g @ A ) )
=> ! [A: ( b > $o ) > $o] :
( ( A @ f )
=> ( A @ g ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEXT_SET) ).
thf(2,negated_conjecture,
~ ( ! [A: b] :
( ( f @ A )
= ( g @ A ) )
=> ! [A: ( b > $o ) > $o] :
( ( A @ f )
=> ( A @ g ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: b] :
( ( f @ A )
= ( g @ A ) )
=> ! [A: ( b > $o ) > $o] :
( ( A @ f )
=> ( A @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: b] :
( ( ( f @ A )
= ( g @ A ) )
& ( sk1 @ f )
& ~ ( sk1 @ g ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
sk1 @ f,
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
~ ( sk1 @ g ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
( ~ $true
| ( ( sk1 @ f )
!= ( sk1 @ g ) ) ),
inference(paramod_ordered,[status(thm)],[6,7]) ).
thf(10,plain,
( ( sk1 @ f )
!= ( sk1 @ g ) ),
inference(simp,[status(thm)],[9]) ).
thf(11,plain,
f != g,
inference(simp,[status(thm)],[10]) ).
thf(12,plain,
( ( f @ sk2 )
!= ( g @ sk2 ) ),
inference(func_ext,[status(esa)],[11]) ).
thf(5,plain,
! [A: b] :
( ( f @ A )
= ( g @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
! [A: b] :
( ( f @ A )
= ( g @ A ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(25,plain,
( ( g @ sk2 )
!= ( g @ sk2 ) ),
inference(rewrite,[status(thm)],[12,8]) ).
thf(26,plain,
$false,
inference(simp,[status(thm)],[25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO373^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.10/0.22 % Computer : n007.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 16:47:40 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 0.68/0.56 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.01/0.65 % [INFO] Parsing done (94ms).
% 1.01/0.66 % [INFO] Running in sequential loop mode.
% 1.29/0.85 % [INFO] eprover registered as external prover.
% 1.29/0.86 % [INFO] Scanning for conjecture ...
% 1.55/0.90 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.55/0.92 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.55/0.92 % [INFO] Problem is higher-order (TPTP THF).
% 1.55/0.92 % [INFO] Type checking passed.
% 1.55/0.92 % [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 ...
% 2.44/1.29 % [INFO] Killing All external provers ...
% 2.86/1.30 % Time passed: 970ms (effective reasoning time: 634ms)
% 2.86/1.30 % 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)>
% 2.86/1.30 % Axioms used in derivation (0):
% 2.86/1.30 % No. of inferences in proof: 14
% 2.86/1.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 970 ms resp. 634 ms w/o parsing
% 2.86/1.32 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.86/1.32 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------