%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU921^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : 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 08:29:35 AM UTC 2026
% Result : Theorem 3.63s 2.15s
% Output : Refutation 3.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 20 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 52 ( 9 ~; 3 |; 1 &; 33 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 19 ( 6 ^; 13 !; 0 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
thf(f_decl,type,
f: $i > $i ).
thf(g_decl,type,
g: $i > $i ).
thf(h_decl,type,
h: $i > $i ).
thf(1,conjecture,
( ! [A: $i,B: $i] :
( ( ( g @ A )
= B )
=> ( ( h @ B )
= ( f @ A ) ) )
=> ( ( ^ [A: $i] : ( h @ ( g @ A ) ) )
= f ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM588LEM2_pme) ).
thf(2,negated_conjecture,
~ ( ! [A: $i,B: $i] :
( ( ( g @ A )
= B )
=> ( ( h @ B )
= ( f @ A ) ) )
=> ( ( ^ [A: $i] : ( h @ ( g @ A ) ) )
= f ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ( ( g @ A )
= B )
=> ( ( h @ B )
= ( f @ A ) ) )
=> ( ( ^ [A: $i] : ( h @ ( g @ A ) ) )
= f ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: $i,A: $i] :
( ( ( ( g @ A )
!= B )
| ( ( h @ B )
= ( f @ A ) ) )
& ( ( ^ [C: $i] : ( h @ ( g @ C ) ) )
!= f ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
( ( ^ [A: $i] : ( h @ ( g @ A ) ) )
!= f ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
( ( ^ [A: $i] : ( h @ ( g @ A ) ) )
!= f ),
inference(lifteq,[status(thm)],[6]) ).
thf(5,plain,
! [B: $i,A: $i] :
( ( ( g @ A )
!= B )
| ( ( h @ B )
= ( f @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
! [B: $i,A: $i] :
( ( ( g @ A )
!= B )
| ( ( h @ B )
= ( f @ A ) ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(8,plain,
! [A: $i] :
( ( h @ ( g @ A ) )
= ( f @ A ) ),
inference(simp,[status(thm)],[7]) ).
thf(11,plain,
f != f,
inference(rewrite,[status(thm)],[9,8]) ).
thf(12,plain,
$false,
inference(simp,[status(thm)],[11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU921^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.11/0.22 % Computer : n014.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 14:46:15 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 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
% 0.90/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/0.98 % [INFO] Parsing done (181ms).
% 1.25/0.99 % [INFO] Running in sequential loop mode.
% 2.03/1.40 % [INFO] eprover registered as external prover.
% 2.03/1.41 % [INFO] Scanning for conjecture ...
% 2.21/1.50 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.21/1.53 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.21/1.54 % [INFO] Problem is higher-order (TPTP THF).
% 2.21/1.54 % [INFO] Type checking passed.
% 2.21/1.54 % [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 ...
% 3.63/2.15 % [INFO] Killing All external provers ...
% 3.63/2.15 % Time passed: 1780ms (effective reasoning time: 1147ms)
% 3.63/2.15 % 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)>
% 3.63/2.15 % Axioms used in derivation (0):
% 3.63/2.15 % No. of inferences in proof: 11
% 3.63/2.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1780 ms resp. 1147 ms w/o parsing
% 3.90/2.20 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.90/2.20 % [INFO] Killing All external provers ...
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