%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO360^5 : 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 : n002.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 3.62s 2.20s
% Output : Refutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 22 ( 21 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 69 ( 7 ~; 0 |; 5 &; 54 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 19 ( 0 ^; 19 !; 0 ?; 19 :)
% 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(1,conjecture,
( ( ! [A: a > a,B: a] :
( ( f @ A @ B )
= ( g @ A @ B ) )
& ! [A: a] :
( ( h @ A )
= ( j @ A ) ) )
=> ( ( f @ h )
= ( g @ j ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEDEC1) ).
thf(2,negated_conjecture,
~ ( ( ! [A: a > a,B: a] :
( ( f @ A @ B )
= ( g @ A @ B ) )
& ! [A: a] :
( ( h @ A )
= ( j @ A ) ) )
=> ( ( f @ h )
= ( 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 ) ) )
=> ( ( f @ h )
= ( 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 ) )
& ( ( f @ h )
!= ( g @ j ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
( ( f @ h )
!= ( g @ j ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(11,plain,
( ( f @ h )
!= ( g @ j ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(6,plain,
! [A: a] :
( ( h @ A )
= ( j @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
! [A: a] :
( ( h @ A )
= ( j @ A ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(10,plain,
! [A: a] :
( ( h @ A )
= ( j @ A ) ),
inference(simp,[status(thm)],[9]) ).
thf(13,plain,
( ( f @ j )
!= ( g @ j ) ),
inference(rewrite,[status(thm)],[11,10]) ).
thf(5,plain,
! [B: a,A: a > a] :
( ( f @ A @ B )
= ( g @ A @ B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
! [B: a,A: a > a] :
( ( f @ A @ B )
= ( g @ A @ B ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(16,plain,
( ( g @ j )
!= ( g @ j ) ),
inference(rewrite,[status(thm)],[13,8]) ).
thf(17,plain,
$false,
inference(simp,[status(thm)],[16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO360^5 : 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
% 0.10/0.21 % Computer : n002.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 16:51:22 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
% 0.84/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.15/0.97 % [INFO] Parsing done (181ms).
% 1.15/0.98 % [INFO] Running in sequential loop mode.
% 1.70/1.38 % [INFO] eprover registered as external prover.
% 1.70/1.39 % [INFO] Scanning for conjecture ...
% 1.88/1.48 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.03/1.51 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.03/1.52 % [INFO] Problem is higher-order (TPTP THF).
% 2.03/1.52 % [INFO] Type checking passed.
% 2.03/1.52 % [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 ...
% 3.62/2.20 % [INFO] Killing All external provers ...
% 3.62/2.20 % Time passed: 1840ms (effective reasoning time: 1208ms)
% 3.62/2.20 % 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)>
% 3.62/2.20 % Axioms used in derivation (0):
% 3.62/2.20 % No. of inferences in proof: 14
% 3.62/2.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1840 ms resp. 1208 ms w/o parsing
% 3.62/2.25 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.62/2.25 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------