%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO500^1 : 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 : n011.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 08:46:01 AM UTC 2026
% Result : Theorem 4.83s 2.59s
% Output : Refutation 5.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 1
% Syntax : Number of formulae : 35 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 218 ( 23 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 179 ( 42 ~; 41 |; 0 &; 96 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(f_decl,type,
f: $o > $o ).
thf(x_decl,type,
x: $o ).
thf(1,conjecture,
( ( f @ ( f @ ( f @ x ) ) )
= ( f @ x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
( ( f @ ( f @ ( f @ x ) ) )
!= ( f @ x ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( f @ ( f @ ( f @ x ) ) )
!= ( f @ x ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( f @ ( f @ ( f @ x ) ) )
!= ( f @ x ) ),
inference(lifteq,[status(thm)],[3]) ).
thf(5,plain,
( ( f @ ( f @ x ) )
!= x ),
inference(simp,[status(thm)],[4]) ).
thf(9,plain,
( ( f @ ( f @ x ) )
| x ),
inference(bool_ext,[status(thm)],[5]) ).
thf(10,plain,
( x
| ~ ( f @ x )
| ( ( f @ ( f @ ( f @ x ) ) )
!= ( f @ ( f @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,4]) ).
thf(23,plain,
( x
| ~ ( f @ x )
| ( ( f @ ( f @ x ) )
!= ( f @ x ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(110,plain,
( x
| x
| ~ $true
| ( ( f @ ( f @ x ) )
!= ( f @ x ) )
| ( ( f @ ( f @ x ) )
!= ( f @ x ) ) ),
inference(paramod_ordered,[status(thm)],[9,23]) ).
thf(111,plain,
( x
| ( ( f @ ( f @ x ) )
!= ( f @ x ) )
| ( ( f @ ( f @ x ) )
!= ( f @ x ) ) ),
inference(simp,[status(thm)],[110]) ).
thf(130,plain,
( x
| ( ( f @ x )
!= x )
| ( ( f @ x )
!= x ) ),
inference(simp,[status(thm)],[111]) ).
thf(131,plain,
( x
| ( ( f @ x )
!= x ) ),
inference(simp,[status(thm)],[130]) ).
thf(140,plain,
( x
| ( f @ x )
| x ),
inference(bool_ext,[status(thm)],[131]) ).
thf(144,plain,
( x
| ( f @ x ) ),
inference(simp,[status(thm)],[140]) ).
thf(6,plain,
( ~ ( f @ ( f @ ( f @ x ) ) )
| ~ ( f @ x ) ),
inference(bool_ext,[status(thm)],[4]) ).
thf(31,plain,
( x
| ~ ( f @ $true )
| ~ ( f @ x )
| ( ( f @ ( f @ x ) )
!= ( f @ ( f @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,6]) ).
thf(32,plain,
( x
| ~ ( f @ $true )
| ~ ( f @ x ) ),
inference(pattern_uni,[status(thm)],[31:[]]) ).
thf(92,plain,
( x
| x
| ~ $true
| ~ ( f @ x )
| ( ( f @ ( f @ x ) )
!= ( f @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[9,32]) ).
thf(93,plain,
( x
| ~ ( f @ x )
| ( ( f @ ( f @ x ) )
!= ( f @ $true ) ) ),
inference(simp,[status(thm)],[92]) ).
thf(101,plain,
( x
| ~ ( f @ x )
| ~ ( f @ x ) ),
inference(simp,[status(thm)],[93]) ).
thf(106,plain,
( x
| ~ ( f @ x ) ),
inference(simp,[status(thm)],[101]) ).
thf(148,plain,
( x
| x
| ~ $true
| ( ( f @ x )
!= ( f @ x ) ) ),
inference(paramod_ordered,[status(thm)],[144,106]) ).
thf(149,plain,
( x
| ( ( f @ x )
!= ( f @ x ) ) ),
inference(simp,[status(thm)],[148]) ).
thf(150,plain,
x,
inference(pattern_uni,[status(thm)],[149:[]]) ).
thf(186,plain,
~ ( f @ ( f @ $true ) ),
inference(rewrite,[status(thm)],[5,150]) ).
thf(191,plain,
( ( f @ ( f @ ( f @ $true ) ) )
!= ( f @ $true ) ),
inference(rewrite,[status(thm)],[4,150]) ).
thf(196,plain,
( ( f @ $false )
!= ( f @ $true ) ),
inference(rewrite,[status(thm)],[191,186]) ).
thf(199,plain,
( ( f @ $false )
| ( f @ $true ) ),
inference(bool_ext,[status(thm)],[196]) ).
thf(212,plain,
( ( f @ $true )
| ~ $true
| ( ( f @ ( f @ $true ) )
!= ( f @ $false ) ) ),
inference(paramod_ordered,[status(thm)],[199,186]) ).
thf(213,plain,
( ( f @ $true )
| ( ( f @ ( f @ $true ) )
!= ( f @ $false ) ) ),
inference(simp,[status(thm)],[212]) ).
thf(217,plain,
( ( f @ $true )
| ( f @ $true ) ),
inference(simp,[status(thm)],[213]) ).
thf(220,plain,
f @ $true,
inference(simp,[status(thm)],[217]) ).
thf(224,plain,
~ ( f @ $true ),
inference(rewrite,[status(thm)],[186,220]) ).
thf(231,plain,
~ $true,
inference(rewrite,[status(thm)],[224,220]) ).
thf(232,plain,
$false,
inference(simp,[status(thm)],[231]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO500^1 : 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
% 0.10/0.23 % Computer : n011.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Tue Sep 29 17:11:16 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 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
% 1.03/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/0.98 % [INFO] Parsing done (181ms).
% 1.22/1.00 % [INFO] Running in sequential loop mode.
% 2.02/1.41 % [INFO] eprover registered as external prover.
% 2.02/1.42 % [INFO] Scanning for conjecture ...
% 2.02/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.19/1.52 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.19/1.52 % [INFO] Problem is higher-order (TPTP THF).
% 2.19/1.52 % [INFO] Type checking passed.
% 2.19/1.53 % [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 ...
% 4.83/2.58 % [INFO] Killing All external provers ...
% 4.83/2.59 % Time passed: 2215ms (effective reasoning time: 1579ms)
% 4.83/2.59 % 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)>
% 4.83/2.59 % Axioms used in derivation (0):
% 4.83/2.59 % No. of inferences in proof: 35
% 4.83/2.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2215 ms resp. 1579 ms w/o parsing
% 5.22/2.62 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.22/2.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------