%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO363^5 : 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 : n020.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 08:45:39 AM UTC 2026
% Result : Theorem 3.92s 2.29s
% Output : Refutation 4.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 18 ( 13 unt; 0 typ; 1 def)
% Number of atoms : 30 ( 19 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 101 ( 11 ~; 1 |; 6 &; 76 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 23 ( 0 ^; 22 !; 0 ?; 23 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(j_decl,type,
j: a > a ).
thf(g_decl,type,
g: ( a > a ) > a > a ).
thf(h_decl,type,
h: a > a ).
thf(f_decl,type,
f: ( a > a ) > a > a ).
thf(sk1_decl,type,
sk1: ( a > a ) > $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: ( a > a ) > $o] :
~ ( ( A @ ( f @ h ) )
=> ( A @ ( g @ j ) ) ) ) ) ).
thf(1,conjecture,
( ( ! [A: a > a,B: a] :
( ( f @ A @ B )
= ( g @ A @ B ) )
& ! [A: a] :
( ( h @ A )
= ( j @ A ) ) )
=> ! [A: ( a > a ) > $o] :
( ( A @ ( f @ h ) )
=> ( A @ ( g @ j ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEDEC2_pme) ).
thf(2,negated_conjecture,
~ ( ( ! [A: a > a,B: a] :
( ( f @ A @ B )
= ( g @ A @ B ) )
& ! [A: a] :
( ( h @ A )
= ( j @ A ) ) )
=> ! [A: ( a > a ) > $o] :
( ( A @ ( f @ h ) )
=> ( A @ ( g @ j ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ! [A: a > a,B: a] :
( ( f @ A @ B )
= ( g @ A @ B ) )
& ! [A: a] :
( ( h @ A )
= ( j @ A ) ) )
=> ! [A: ( a > a ) > $o] :
( ( A @ ( f @ h ) )
=> ( A @ ( g @ j ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [C: a,B: a,A: a > a] :
( ( ( f @ A @ B )
= ( g @ A @ B ) )
& ( ( h @ C )
= ( j @ C ) )
& ( sk1 @ ( f @ h ) )
& ~ ( sk1 @ ( g @ j ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
sk1 @ ( f @ h ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
~ ( sk1 @ ( g @ j ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(12,plain,
( ~ $true
| ( ( sk1 @ ( f @ h ) )
!= ( sk1 @ ( g @ j ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,8]) ).
thf(13,plain,
( ( sk1 @ ( f @ h ) )
!= ( sk1 @ ( g @ j ) ) ),
inference(simp,[status(thm)],[12]) ).
thf(14,plain,
( ( f @ h )
!= ( g @ j ) ),
inference(simp,[status(thm)],[13]) ).
thf(6,plain,
! [A: a] :
( ( h @ A )
= ( j @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(10,plain,
! [A: a] :
( ( h @ A )
= ( j @ A ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(11,plain,
! [A: a] :
( ( h @ A )
= ( j @ A ) ),
inference(simp,[status(thm)],[10]) ).
thf(17,plain,
( ( f @ j )
!= ( g @ j ) ),
inference(rewrite,[status(thm)],[14,11]) ).
thf(5,plain,
! [B: a,A: a > a] :
( ( f @ A @ B )
= ( g @ A @ B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
! [B: a,A: a > a] :
( ( f @ A @ B )
= ( g @ A @ B ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(23,plain,
( ( g @ j )
!= ( g @ j ) ),
inference(rewrite,[status(thm)],[17,9]) ).
thf(24,plain,
$false,
inference(simp,[status(thm)],[23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO363^5 : 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
% 0.08/0.21 % Computer : n020.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.22 % CPULimit : 300
% 0.08/0.22 % WCLimit : 300
% 0.08/0.22 % DateTime : Tue Sep 29 16:49:49 UTC 2026
% 0.08/0.22 % CPUTime :
% 0.08/0.22 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
% 0.89/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/0.97 % [INFO] Parsing done (183ms).
% 1.24/0.98 % [INFO] Running in sequential loop mode.
% 1.85/1.38 % [INFO] eprover registered as external prover.
% 1.85/1.39 % [INFO] Scanning for conjecture ...
% 2.05/1.48 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.22/1.52 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.22/1.52 % [INFO] Problem is higher-order (TPTP THF).
% 2.22/1.52 % [INFO] Type checking passed.
% 2.22/1.53 % [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 ...
% 3.92/2.28 % [INFO] Killing All external provers ...
% 3.92/2.28 % Time passed: 1926ms (effective reasoning time: 1292ms)
% 3.92/2.28 % 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)>
% 3.92/2.29 % Axioms used in derivation (0):
% 3.92/2.29 % No. of inferences in proof: 17
% 3.92/2.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1926 ms resp. 1292 ms w/o parsing
% 4.22/2.34 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.22/2.34 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------