%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO040^2 : 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 : n013.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 08:45:04 AM UTC 2026
% Result : Theorem 7.15s 3.74s
% Output : Refutation 7.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 1
% Syntax : Number of formulae : 33 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 184 ( 18 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 158 ( 35 ~; 33 |; 0 &; 90 @)
% ( 0 <=>; 0 =>; 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 : 6 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(f_decl,type,
f: $o > $o ).
thf(h_decl,type,
h: $o > $i ).
thf(x_decl,type,
x: $o ).
thf(1,conjecture,
( ( h @ ( f @ ( f @ ( f @ x ) ) ) )
= ( h @ ( f @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',2) ).
thf(2,negated_conjecture,
( ( h @ ( f @ ( f @ ( f @ x ) ) ) )
!= ( h @ ( f @ x ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( h @ ( f @ ( f @ ( f @ x ) ) ) )
!= ( h @ ( f @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( h @ ( f @ ( f @ ( f @ x ) ) ) )
!= ( h @ ( f @ x ) ) ),
inference(lifteq,[status(thm)],[3]) ).
thf(5,plain,
( ( f @ ( f @ ( f @ x ) ) )
!= ( f @ x ) ),
inference(simp,[status(thm)],[4]) ).
thf(6,plain,
( ( f @ ( f @ x ) )
!= x ),
inference(simp,[status(thm)],[5]) ).
thf(10,plain,
( ( f @ ( f @ x ) )
| x ),
inference(bool_ext,[status(thm)],[6]) ).
thf(7,plain,
( ~ ( f @ ( f @ ( f @ x ) ) )
| ~ ( f @ x ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(29,plain,
( x
| ~ ( f @ $true )
| ~ ( f @ x )
| ( ( f @ ( f @ x ) )
!= ( f @ ( f @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[10,7]) ).
thf(30,plain,
( x
| ~ ( f @ $true )
| ~ ( f @ x ) ),
inference(pattern_uni,[status(thm)],[29:[]]) ).
thf(59,plain,
( x
| x
| ~ $true
| ~ ( f @ x )
| ( ( f @ ( f @ x ) )
!= ( f @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[10,30]) ).
thf(60,plain,
( x
| ~ ( f @ x )
| ( ( f @ ( f @ x ) )
!= ( f @ $true ) ) ),
inference(simp,[status(thm)],[59]) ).
thf(64,plain,
( x
| ~ ( f @ x )
| ~ ( f @ x ) ),
inference(simp,[status(thm)],[60]) ).
thf(68,plain,
( x
| ~ ( f @ x ) ),
inference(simp,[status(thm)],[64]) ).
thf(128,plain,
( x
| x
| ~ $true
| ( ( f @ ( f @ x ) )
!= ( f @ x ) ) ),
inference(paramod_ordered,[status(thm)],[10,68]) ).
thf(129,plain,
( x
| ( ( f @ ( f @ x ) )
!= ( f @ x ) ) ),
inference(simp,[status(thm)],[128]) ).
thf(132,plain,
( x
| ( ( f @ x )
!= x ) ),
inference(simp,[status(thm)],[129]) ).
thf(135,plain,
( x
| ( f @ x )
| x ),
inference(bool_ext,[status(thm)],[132]) ).
thf(139,plain,
( x
| ( f @ x ) ),
inference(simp,[status(thm)],[135]) ).
thf(175,plain,
( x
| x
| ~ $true
| ( ( f @ x )
!= ( f @ x ) ) ),
inference(paramod_ordered,[status(thm)],[139,68]) ).
thf(176,plain,
( x
| ( ( f @ x )
!= ( f @ x ) ) ),
inference(simp,[status(thm)],[175]) ).
thf(177,plain,
x,
inference(pattern_uni,[status(thm)],[176:[]]) ).
thf(192,plain,
~ ( f @ ( f @ $true ) ),
inference(rewrite,[status(thm)],[6,177]) ).
thf(191,plain,
( ( f @ ( f @ ( f @ $true ) ) )
!= ( f @ $true ) ),
inference(rewrite,[status(thm)],[5,177]) ).
thf(204,plain,
( ( f @ $false )
!= ( f @ $true ) ),
inference(rewrite,[status(thm)],[191,192]) ).
thf(207,plain,
( ( f @ $false )
| ( f @ $true ) ),
inference(bool_ext,[status(thm)],[204]) ).
thf(225,plain,
( ( f @ $true )
| ~ $true
| ( ( f @ ( f @ $true ) )
!= ( f @ $false ) ) ),
inference(paramod_ordered,[status(thm)],[207,192]) ).
thf(226,plain,
( ( f @ $true )
| ( ( f @ ( f @ $true ) )
!= ( f @ $false ) ) ),
inference(simp,[status(thm)],[225]) ).
thf(234,plain,
( ( f @ $true )
| ( f @ $true ) ),
inference(simp,[status(thm)],[226]) ).
thf(240,plain,
f @ $true,
inference(simp,[status(thm)],[234]) ).
thf(247,plain,
~ ( f @ $true ),
inference(rewrite,[status(thm)],[192,240]) ).
thf(253,plain,
~ $true,
inference(rewrite,[status(thm)],[247,240]) ).
thf(254,plain,
$false,
inference(simp,[status(thm)],[253]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYO040^2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.12 % 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
% 0.29/0.33 % Computer : n013.cluster.edu
% 0.29/0.33 % Model : x86_64 x86_64
% 0.29/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.29/0.33 % Memory : 8046.5625MB
% 0.29/0.33 % OS : Linux 6.8.0-71-generic
% 0.29/0.33 % CPULimit : 300
% 0.29/0.33 % WCLimit : 300
% 0.29/0.33 % DateTime : Tue Sep 29 16:23:30 UTC 2026
% 0.29/0.33 % CPUTime :
% 0.29/0.33 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
% 1.45/1.16 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.85/1.42 % [INFO] Parsing done (250ms).
% 1.85/1.44 % [INFO] Running in sequential loop mode.
% 2.55/2.04 % [INFO] eprover registered as external prover.
% 2.55/2.05 % [INFO] Scanning for conjecture ...
% 2.97/2.15 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.97/2.19 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.97/2.19 % [INFO] Problem is higher-order (TPTP THF).
% 3.04/2.20 % [INFO] Type checking passed.
% 3.04/2.21 % [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 ...
% 7.15/3.73 % [INFO] Killing All external provers ...
% 7.15/3.74 % Time passed: 3199ms (effective reasoning time: 2288ms)
% 7.15/3.74 % 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)>
% 7.15/3.74 % Axioms used in derivation (0):
% 7.15/3.74 % No. of inferences in proof: 33
% 7.15/3.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3199 ms resp. 2288 ms w/o parsing
% 7.15/3.79 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.15/3.79 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------