%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO359^5 : 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 : n019.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 08:45:38 AM UTC 2026
% Result : Theorem 3.31s 2.16s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 10 unt; 0 typ; 1 def)
% Number of atoms : 73 ( 22 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 75 ( 11 ~; 2 |; 2 &; 48 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 0 ^; 14 !; 0 ?; 15 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(b_type,type,
b: $tType ).
thf(gtype_type,type,
gtype: $tType ).
thf(g_decl,type,
g: b > $o ).
thf(h_decl,type,
h: ( b > $o ) > gtype ).
thf(f_decl,type,
f: b > $o ).
thf(sk1_decl,type,
sk1: b ).
thf(sk2_decl,type,
sk2: b ).
thf(sk1_def,definition,
( sk1
= ( @+[A: b] :
( ( f @ A )
!= ( g @ A ) ) ) ) ).
thf(1,conjecture,
( ( ! [A: b] :
( ( f @ A )
= ( g @ A ) )
=> ! [A: ( b > $o ) > $o] :
( ( A @ f )
=> ( A @ g ) ) )
=> ( ! [A: b] :
( ( f @ A )
= ( g @ A ) )
=> ( ( h @ f )
= ( h @ g ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEXT1) ).
thf(2,negated_conjecture,
~ ( ( ! [A: b] :
( ( f @ A )
= ( g @ A ) )
=> ! [A: ( b > $o ) > $o] :
( ( A @ f )
=> ( A @ g ) ) )
=> ( ! [A: b] :
( ( f @ A )
= ( g @ A ) )
=> ( ( h @ f )
= ( h @ g ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ! [A: b] :
( ( f @ A )
= ( g @ A ) )
=> ! [A: ( b > $o ) > $o] :
( ( A @ f )
=> ( A @ g ) ) )
=> ( ! [A: b] :
( ( f @ A )
= ( g @ A ) )
=> ( ( h @ f )
= ( h @ g ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: b,A: ( b > $o ) > $o] :
( ( ( ( f @ sk1 )
!= ( g @ sk1 ) )
| ~ ( A @ f )
| ( A @ g ) )
& ( ( f @ B )
= ( g @ B ) )
& ( ( h @ f )
!= ( h @ g ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
( ( h @ f )
!= ( h @ g ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(12,plain,
( ( h @ f )
!= ( h @ g ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(15,plain,
f != g,
inference(simp,[status(thm)],[12]) ).
thf(16,plain,
( ( f @ sk2 )
!= ( g @ sk2 ) ),
inference(func_ext,[status(esa)],[15]) ).
thf(6,plain,
! [A: b] :
( ( f @ A )
= ( g @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(10,plain,
! [A: b] :
( ( f @ A )
= ( g @ A ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(11,plain,
! [A: b] :
( ( f @ A )
= ( g @ A ) ),
inference(simp,[status(thm)],[10]) ).
thf(19,plain,
( ( g @ sk2 )
!= ( g @ sk2 ) ),
inference(rewrite,[status(thm)],[16,11]) ).
thf(20,plain,
$false,
inference(simp,[status(thm)],[19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO359^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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
% 0.11/0.20 % Computer : n019.cluster.edu
% 0.11/0.20 % Model : x86_64 x86_64
% 0.11/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.20 % Memory : 8046.5625MB
% 0.11/0.20 % OS : Linux 6.8.0-71-generic
% 0.11/0.20 % CPULimit : 300
% 0.11/0.20 % WCLimit : 300
% 0.11/0.20 % DateTime : Tue Sep 29 16:48:47 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.21 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
% 0.87/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.17/0.97 % [INFO] Parsing done (185ms).
% 1.17/0.99 % [INFO] Running in sequential loop mode.
% 1.74/1.39 % [INFO] eprover registered as external prover.
% 1.91/1.40 % [INFO] Scanning for conjecture ...
% 1.91/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.08/1.52 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.08/1.52 % [INFO] Problem is higher-order (TPTP THF).
% 2.08/1.53 % [INFO] Type checking passed.
% 2.08/1.53 % [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 ...
% 3.31/2.16 % [INFO] Killing All external provers ...
% 3.31/2.16 % Time passed: 1805ms (effective reasoning time: 1164ms)
% 3.31/2.16 % 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)>
% 3.31/2.16 % Axioms used in derivation (0):
% 3.31/2.16 % No. of inferences in proof: 13
% 3.31/2.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1805 ms resp. 1164 ms w/o parsing
% 3.51/2.21 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.51/2.21 % [INFO] Killing All external provers ...
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