%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO237^5 : 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 : n010.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 08:45:27 AM UTC 2026
% Result : Theorem 3.40s 2.15s
% Output : Refutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 11 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 57 ( 10 ~; 1 |; 3 &; 34 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
thf(g_decl,type,
g: $i > $i ).
thf(p_decl,type,
p: ( $i > $i ) > $o ).
thf(x_decl,type,
x: $i ).
thf(q_decl,type,
q: $i > $o ).
thf(f_decl,type,
f: $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(1,conjecture,
( ! [A: $i] :
( ( f @ A )
= ( g @ A ) )
=> ( ( p @ f )
=> ( ( q @ x )
=> ( p @ g ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM508) ).
thf(2,negated_conjecture,
~ ( ! [A: $i] :
( ( f @ A )
= ( g @ A ) )
=> ( ( p @ f )
=> ( ( q @ x )
=> ( p @ g ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i] :
( ( f @ A )
= ( g @ A ) )
=> ( ( p @ f )
=> ( ( q @ x )
=> ( p @ g ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: $i] :
( ( ( f @ A )
= ( g @ A ) )
& ( p @ f )
& ( q @ x )
& ~ ( p @ g ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
p @ f,
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
~ ( p @ g ),
inference(cnfConj,[status(thm)],[4]) ).
thf(10,plain,
( ~ $true
| ( ( p @ f )
!= ( p @ g ) ) ),
inference(paramod_ordered,[status(thm)],[6,8]) ).
thf(11,plain,
( ( p @ f )
!= ( p @ g ) ),
inference(simp,[status(thm)],[10]) ).
thf(12,plain,
f != g,
inference(simp,[status(thm)],[11]) ).
thf(13,plain,
( ( f @ sk1 )
!= ( g @ sk1 ) ),
inference(func_ext,[status(esa)],[12]) ).
thf(5,plain,
! [A: $i] :
( ( f @ A )
= ( g @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
! [A: $i] :
( ( f @ A )
= ( g @ A ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(15,plain,
( ( g @ sk1 )
!= ( g @ sk1 ) ),
inference(rewrite,[status(thm)],[13,9]) ).
thf(16,plain,
$false,
inference(simp,[status(thm)],[15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO237^5 : 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 : n010.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 16:40:48 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
% 0.84/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.15/0.97 % [INFO] Parsing done (179ms).
% 1.15/0.98 % [INFO] Running in sequential loop mode.
% 1.71/1.39 % [INFO] eprover registered as external prover.
% 1.71/1.40 % [INFO] Scanning for conjecture ...
% 1.89/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.03/1.52 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.03/1.52 % [INFO] Problem is higher-order (TPTP THF).
% 2.03/1.53 % [INFO] Type checking passed.
% 2.03/1.53 % [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 ...
% 3.40/2.14 % [INFO] Killing All external provers ...
% 3.40/2.15 % Time passed: 1786ms (effective reasoning time: 1154ms)
% 3.40/2.15 % 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)>
% 3.40/2.15 % Axioms used in derivation (0):
% 3.40/2.15 % No. of inferences in proof: 14
% 3.40/2.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1786 ms resp. 1154 ms w/o parsing
% 3.40/2.19 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.40/2.19 % [INFO] Killing All external provers ...
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