%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO503^1 : TPTP v9.3.1. Released v4.1.0.
% 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 : n015.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 08:46:02 AM UTC 2026
% Result : Theorem 3.98s 2.28s
% Output : Refutation 4.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 1
% Syntax : Number of formulae : 40 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 200 ( 31 equ; 0 cnn)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 157 ( 59 ~; 40 |; 6 &; 52 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_decl,type,
a: $o ).
thf(b_decl,type,
b: $o ).
thf(f_decl,type,
f: $o > $o ).
thf(g_decl,type,
g: $o > $o ).
thf(p_decl,type,
p: ( $o > $o ) > $o ).
thf(sk1_decl,type,
sk1: $o ).
thf(1,conjecture,
( ( a = b )
| ~ ( f @ a )
| ~ ( f @ b )
| ~ ( g @ a )
| ~ ( g @ b )
| ~ ( p @ f )
| ( p @ g ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',claim) ).
thf(2,negated_conjecture,
~ ( ( a = b )
| ~ ( f @ a )
| ~ ( f @ b )
| ~ ( g @ a )
| ~ ( g @ b )
| ~ ( p @ f )
| ( p @ g ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( a = b )
| ~ ( f @ a )
| ~ ( f @ b )
| ~ ( g @ a )
| ~ ( g @ b )
| ~ ( p @ f )
| ( p @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( a != b )
& ( f @ a )
& ( f @ b )
& ( g @ a )
& ( g @ b )
& ( p @ f )
& ~ ( p @ g ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
f @ b,
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
g @ b,
inference(cnfConj,[status(thm)],[4]) ).
thf(6,plain,
p @ f,
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
~ ( p @ g ),
inference(cnfConj,[status(thm)],[4]) ).
thf(13,plain,
( ~ $true
| ( ( p @ g )
!= ( p @ f ) ) ),
inference(paramod_ordered,[status(thm)],[6,9]) ).
thf(14,plain,
( ( p @ g )
!= ( p @ f ) ),
inference(simp,[status(thm)],[13]) ).
thf(15,plain,
g != f,
inference(simp,[status(thm)],[14]) ).
thf(18,plain,
( ( g @ sk1 )
!= ( f @ sk1 ) ),
inference(func_ext,[status(esa)],[15]) ).
thf(31,plain,
( ~ ( f @ sk1 )
| ( ( g @ sk1 )
!= ( g @ b ) ) ),
inference(paramod_ordered,[status(thm)],[8,18]) ).
thf(33,plain,
( ~ ( f @ sk1 )
| ( sk1 != b ) ),
inference(simp,[status(thm)],[31]) ).
thf(90,plain,
( ~ $true
| ( sk1 != b )
| ( ( f @ sk1 )
!= ( f @ b ) ) ),
inference(paramod_ordered,[status(thm)],[7,33]) ).
thf(91,plain,
( ( sk1 != b )
| ( ( f @ sk1 )
!= ( f @ b ) ) ),
inference(simp,[status(thm)],[90]) ).
thf(100,plain,
( ( sk1 != b )
| ( sk1 != b ) ),
inference(simp,[status(thm)],[91]) ).
thf(101,plain,
sk1 != b,
inference(simp,[status(thm)],[100]) ).
thf(5,plain,
f @ a,
inference(cnfConj,[status(thm)],[4]) ).
thf(11,plain,
g @ a,
inference(cnfConj,[status(thm)],[4]) ).
thf(30,plain,
( ~ ( f @ sk1 )
| ( ( g @ sk1 )
!= ( g @ a ) ) ),
inference(paramod_ordered,[status(thm)],[11,18]) ).
thf(32,plain,
( ~ ( f @ sk1 )
| ( sk1 != a ) ),
inference(simp,[status(thm)],[30]) ).
thf(56,plain,
( ~ $true
| ( sk1 != a )
| ( ( f @ sk1 )
!= ( f @ a ) ) ),
inference(paramod_ordered,[status(thm)],[5,32]) ).
thf(57,plain,
( ( sk1 != a )
| ( ( f @ sk1 )
!= ( f @ a ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(62,plain,
( ( sk1 != a )
| ( sk1 != a ) ),
inference(simp,[status(thm)],[57]) ).
thf(65,plain,
sk1 != a,
inference(simp,[status(thm)],[62]) ).
thf(10,plain,
a != b,
inference(cnfConj,[status(thm)],[4]) ).
thf(12,plain,
b != a,
inference(lifteq,[status(thm)],[10]) ).
thf(17,plain,
( b
| a ),
inference(bool_ext,[status(thm)],[12]) ).
thf(67,plain,
( sk1
| a ),
inference(bool_ext,[status(thm)],[65]) ).
thf(104,plain,
( a
| ~ b
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[67,101]) ).
thf(105,plain,
( a
| ~ b ),
inference(pattern_uni,[status(thm)],[104:[]]) ).
thf(130,plain,
( a
| a
| ~ $true
| ( b != b ) ),
inference(paramod_ordered,[status(thm)],[17,105]) ).
thf(131,plain,
( a
| ( b != b ) ),
inference(simp,[status(thm)],[130]) ).
thf(132,plain,
a,
inference(pattern_uni,[status(thm)],[131:[]]) ).
thf(134,plain,
~ sk1,
inference(rewrite,[status(thm)],[65,132]) ).
thf(141,plain,
b,
inference(rewrite,[status(thm)],[101,134]) ).
thf(135,plain,
~ b,
inference(rewrite,[status(thm)],[12,132]) ).
thf(152,plain,
$false,
inference(rewrite,[status(thm)],[141,135]) ).
thf(153,plain,
$false,
inference(simp,[status(thm)],[152]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO503^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % 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 : n015.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 17:14:48 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.85/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.16/0.97 % [INFO] Parsing done (171ms).
% 1.16/0.98 % [INFO] Running in sequential loop mode.
% 1.72/1.38 % [INFO] eprover registered as external prover.
% 1.72/1.38 % [INFO] Scanning for conjecture ...
% 1.90/1.47 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.04/1.50 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.04/1.50 % [INFO] Problem is higher-order (TPTP THF).
% 2.04/1.51 % [INFO] Type checking passed.
% 2.04/1.51 % [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 ...
% 3.98/2.27 % [INFO] Killing All external provers ...
% 3.98/2.27 % Time passed: 1918ms (effective reasoning time: 1282ms)
% 3.98/2.27 % 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)>
% 3.98/2.27 % Axioms used in derivation (0):
% 3.98/2.27 % No. of inferences in proof: 40
% 3.98/2.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1918 ms resp. 1282 ms w/o parsing
% 4.41/2.31 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.41/2.31 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------