%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO042^2 : TPTP v9.3.1. Released v4.1.0.
% 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 : n008.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 08:45:05 AM UTC 2026
% Result : Theorem 4.77s 2.40s
% Output : Refutation 4.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 28 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 164 ( 33 equ; 9 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 123 ( 53 ~; 11 |; 20 &; 39 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 5 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(g_decl,type,
g: $o > $o ).
thf(p_decl,type,
p: ( $o > $o ) > $o ).
thf(x_decl,type,
x: $o ).
thf(y_decl,type,
y: $o ).
thf(sk1_decl,type,
sk1: $o ).
thf(1,conjecture,
~ ( ( x != y )
& ( ( g @ x )
= y )
& ( ( g @ y )
= x )
& ( p @ g )
& ~ ( p @ (~) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',4) ).
thf(2,negated_conjecture,
~ ~ ( ( x != y )
& ( ( g @ x )
= y )
& ( ( g @ y )
= x )
& ( p @ g )
& ~ ( p @ (~) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ~ ( ( x != y )
& ( ( g @ x )
= y )
& ( ( g @ y )
= x )
& ( p @ g )
& ~ ( p @ (~) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( x != y )
& ( ( g @ x )
= y )
& ( ( g @ y )
= x )
& ( p @ g )
& ~ ( p @ (~) ) ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( x != y )
& ( ( g @ x )
= y )
& ( ( g @ y )
= x )
& ( p @ g )
& ~ ( p @ (~) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(9,plain,
( ( g @ x )
= y ),
inference(cnfConj,[status(thm)],[5]) ).
thf(13,plain,
( ( g @ x )
= y ),
inference(lifteq,[status(thm)],[9]) ).
thf(7,plain,
p @ g,
inference(cnfConj,[status(thm)],[5]) ).
thf(8,plain,
~ ( p @ (~) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(14,plain,
( ~ $true
| ( ( p @ g )
!= ( p @ (~) ) ) ),
inference(paramod_ordered,[status(thm)],[7,8]) ).
thf(15,plain,
( ( p @ g )
!= ( p @ (~) ) ),
inference(simp,[status(thm)],[14]) ).
thf(16,plain,
g != (~),
inference(simp,[status(thm)],[15]) ).
thf(19,plain,
( ( g @ sk1 )
!= ( ~ sk1 ) ),
inference(func_ext,[status(esa)],[16]) ).
thf(39,plain,
( ( ( ~ sk1 ) != y )
| ( ( g @ sk1 )
!= ( g @ x ) ) ),
inference(paramod_ordered,[status(thm)],[13,19]) ).
thf(42,plain,
( ( ( ~ sk1 ) != y )
| ( sk1 != x ) ),
inference(simp,[status(thm)],[39]) ).
thf(20,plain,
( ~ ( g @ sk1 )
| ~ ~ sk1 ),
inference(bool_ext,[status(thm)],[19]) ).
thf(22,plain,
( ~ ( g @ sk1 )
| sk1 ),
inference(cnf,[status(esa)],[20]) ).
thf(6,plain,
x != y,
inference(cnfConj,[status(thm)],[5]) ).
thf(12,plain,
y != x,
inference(lifteq,[status(thm)],[6]) ).
thf(18,plain,
( y
| x ),
inference(bool_ext,[status(thm)],[12]) ).
thf(10,plain,
( ( g @ y )
= x ),
inference(cnfConj,[status(thm)],[5]) ).
thf(11,plain,
( ( g @ y )
= x ),
inference(lifteq,[status(thm)],[10]) ).
thf(21,plain,
( ( g @ sk1 )
| ~ sk1 ),
inference(bool_ext,[status(thm)],[19]) ).
thf(23,plain,
( ( g @ sk1 )
| ~ sk1 ),
inference(cnf,[status(esa)],[21]) ).
thf(33,plain,
( ( ( ~ sk1 ) != x )
| ( ( g @ sk1 )
!= ( g @ y ) ) ),
inference(paramod_ordered,[status(thm)],[11,19]) ).
thf(34,plain,
( ( ( ~ sk1 ) != x )
| ( sk1 != y ) ),
inference(simp,[status(thm)],[33]) ).
thf(17,plain,
( ~ y
| ~ x ),
inference(bool_ext,[status(thm)],[12]) ).
thf(117,plain,
$false,
inference(e,[status(thm)],[42,13,22,12,7,3,18,16,11,23,8,19,34,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO042^2 : TPTP v9.3.1. Released v4.1.0.
% 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
% 0.10/0.22 % Computer : n008.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 16:24:54 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 0.93/0.74 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/0.93 % [INFO] Parsing done (190ms).
% 1.26/0.94 % [INFO] Running in sequential loop mode.
% 1.88/1.35 % [INFO] eprover registered as external prover.
% 1.88/1.36 % [INFO] Scanning for conjecture ...
% 2.08/1.44 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.08/1.47 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.08/1.47 % [INFO] Problem is higher-order (TPTP THF).
% 2.08/1.48 % [INFO] Type checking passed.
% 2.08/1.49 % [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 ...
% 4.37/2.39 % External prover 'e' found a proof!
% 4.37/2.39 % [INFO] Killing All external provers ...
% 4.37/2.40 % Time passed: 2093ms (effective reasoning time: 1445ms)
% 4.37/2.40 % 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)>
% 4.77/2.40 % Axioms used in derivation (0):
% 4.77/2.40 % No. of inferences in proof: 28
% 4.77/2.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2093 ms resp. 1445 ms w/o parsing
% 4.77/2.43 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.77/2.43 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------