%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO041^2 : 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 : 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 08:45:05 AM UTC 2026
% Result : Theorem 8.57s 4.06s
% Output : Refutation 8.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 1
% Syntax : Number of formulae : 63 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 480 ( 75 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 349 ( 82 ~; 67 |; 15 &; 185 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(f_decl,type,
f: $o > $o ).
thf(g_decl,type,
g: $o > $o ).
thf(x_decl,type,
x: $o ).
thf(y_decl,type,
y: $o ).
thf(1,conjecture,
~ ( ( x != y )
& ( ( g @ x )
= y )
& ( ( g @ y )
= x )
& ( ( f @ ( f @ ( f @ x ) ) )
= ( g @ ( f @ x ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',3) ).
thf(2,negated_conjecture,
~ ~ ( ( x != y )
& ( ( g @ x )
= y )
& ( ( g @ y )
= x )
& ( ( f @ ( f @ ( f @ x ) ) )
= ( g @ ( f @ x ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ~ ( ( x != y )
& ( ( g @ x )
= y )
& ( ( g @ y )
= x )
& ( ( f @ ( f @ ( f @ x ) ) )
= ( g @ ( f @ x ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( x != y )
& ( ( g @ x )
= y )
& ( ( g @ y )
= x )
& ( ( f @ ( f @ ( f @ x ) ) )
= ( g @ ( f @ x ) ) ) ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( x != y )
& ( ( g @ x )
= y )
& ( ( g @ y )
= x )
& ( ( f @ ( f @ ( f @ x ) ) )
= ( g @ ( f @ x ) ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(8,plain,
( ( g @ y )
= x ),
inference(cnfConj,[status(thm)],[5]) ).
thf(12,plain,
( ( g @ y )
= x ),
inference(lifteq,[status(thm)],[8]) ).
thf(7,plain,
( ( g @ x )
= y ),
inference(cnfConj,[status(thm)],[5]) ).
thf(11,plain,
( ( g @ x )
= y ),
inference(lifteq,[status(thm)],[7]) ).
thf(9,plain,
( ( f @ ( f @ ( f @ x ) ) )
= ( g @ ( f @ x ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(13,plain,
( ( g @ ( f @ x ) )
= ( f @ ( f @ ( f @ x ) ) ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(27,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= y )
| ( ( g @ ( f @ x ) )
!= ( g @ x ) ) ),
inference(paramod_ordered,[status(thm)],[11,13]) ).
thf(32,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= y )
| ( ( f @ x )
!= x ) ),
inference(simp,[status(thm)],[27]) ).
thf(29,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= x )
| ( ( g @ ( f @ x ) )
!= ( g @ y ) ) ),
inference(paramod_ordered,[status(thm)],[12,13]) ).
thf(30,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= x )
| ( ( f @ x )
!= y ) ),
inference(simp,[status(thm)],[29]) ).
thf(140,plain,
( ( ( f @ x )
!= x )
| ( y = x )
| ( ( f @ x )
!= y )
| ( ( f @ ( f @ ( f @ x ) ) )
!= ( f @ ( f @ ( f @ x ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,30]) ).
thf(141,plain,
( ( ( f @ x )
!= x )
| ( y = x )
| ( ( f @ x )
!= y ) ),
inference(pattern_uni,[status(thm)],[140:[]]) ).
thf(6,plain,
x != y,
inference(cnfConj,[status(thm)],[5]) ).
thf(10,plain,
y != x,
inference(lifteq,[status(thm)],[6]) ).
thf(214,plain,
( ( ( f @ x )
!= x )
| ( ( f @ x )
!= y ) ),
inference(simplifyReflect,[status(thm)],[141,10]) ).
thf(220,plain,
( ( ( f @ x )
!= x )
| ( ( f @ x )
!= x )
| ( y != y )
| ( ( f @ ( f @ ( f @ x ) ) )
!= ( f @ x ) ) ),
inference(paramod_ordered,[status(thm)],[32,214]) ).
thf(221,plain,
( ( ( f @ x )
!= x )
| ( ( f @ ( f @ ( f @ x ) ) )
!= ( f @ x ) ) ),
inference(simp,[status(thm)],[220]) ).
thf(225,plain,
( ( ( f @ x )
!= x )
| ( ( f @ ( f @ x ) )
!= x ) ),
inference(simp,[status(thm)],[221]) ).
thf(246,plain,
( ( ( f @ x )
!= x )
| ( ( f @ ( f @ x ) )
!= ( f @ x ) )
| ( x != x ) ),
inference(eqfactor_ordered,[status(thm)],[225]) ).
thf(254,plain,
( ( ( f @ x )
!= x )
| ( ( f @ x )
!= x ) ),
inference(simp,[status(thm)],[246]) ).
thf(259,plain,
( ( f @ x )
!= x ),
inference(simp,[status(thm)],[254]) ).
thf(261,plain,
( ( f @ x )
| x ),
inference(bool_ext,[status(thm)],[259]) ).
thf(15,plain,
( y
| x ),
inference(bool_ext,[status(thm)],[10]) ).
thf(40,plain,
( x
| ( ( g @ $true )
= x )
| ( y != y ) ),
inference(paramod_ordered,[status(thm)],[15,12]) ).
thf(41,plain,
( x
| ( ( g @ $true )
= x ) ),
inference(pattern_uni,[status(thm)],[40:[]]) ).
thf(45,plain,
( x
| ~ ( g @ $true )
| x ),
inference(bool_ext,[status(thm)],[41]) ).
thf(59,plain,
( x
| ~ ( g @ $true ) ),
inference(simp,[status(thm)],[45]) ).
thf(62,plain,
( x
| ~ ( f @ ( f @ ( f @ x ) ) )
| ( ( g @ ( f @ x ) )
!= ( g @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[13,59]) ).
thf(67,plain,
( x
| ~ ( f @ ( f @ ( f @ x ) ) )
| ~ ( f @ x ) ),
inference(simp,[status(thm)],[62]) ).
thf(70,plain,
( x
| ~ ( f @ x )
| ( ( f @ ( f @ ( f @ x ) ) )
!= ( f @ x ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[67]) ).
thf(72,plain,
( x
| ~ ( f @ x )
| ( ( f @ ( f @ x ) )
!= x ) ),
inference(simp,[status(thm)],[70]) ).
thf(74,plain,
( x
| ~ ( f @ x )
| ( f @ ( f @ x ) )
| x ),
inference(bool_ext,[status(thm)],[72]) ).
thf(75,plain,
( x
| ~ ( f @ x )
| ( f @ ( f @ x ) ) ),
inference(simp,[status(thm)],[74]) ).
thf(78,plain,
( x
| ~ ( f @ x )
| x
| ~ ( f @ $true )
| ~ ( f @ x )
| ( ( f @ ( f @ x ) )
!= ( f @ ( f @ x ) ) ) ),
inference(paramod_ordered,[status(thm)],[75,67]) ).
thf(79,plain,
( x
| ~ ( f @ x )
| ~ ( f @ $true )
| ( ( f @ ( f @ x ) )
!= ( f @ ( f @ x ) ) ) ),
inference(simp,[status(thm)],[78]) ).
thf(80,plain,
( x
| ~ ( f @ x )
| ~ ( f @ $true ) ),
inference(pattern_uni,[status(thm)],[79:[]]) ).
thf(107,plain,
( x
| ~ ( f @ x )
| x
| ~ ( f @ x )
| ~ $true
| ( ( f @ ( f @ x ) )
!= ( f @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[75,80]) ).
thf(108,plain,
( x
| ~ ( f @ x )
| ( ( f @ ( f @ x ) )
!= ( f @ $true ) ) ),
inference(simp,[status(thm)],[107]) ).
thf(111,plain,
( x
| ~ ( f @ x )
| ~ ( f @ x ) ),
inference(simp,[status(thm)],[108]) ).
thf(114,plain,
( x
| ~ ( f @ x ) ),
inference(simp,[status(thm)],[111]) ).
thf(276,plain,
( x
| x
| ~ $true
| ( ( f @ x )
!= ( f @ x ) ) ),
inference(paramod_ordered,[status(thm)],[261,114]) ).
thf(277,plain,
( x
| ( ( f @ x )
!= ( f @ x ) ) ),
inference(simp,[status(thm)],[276]) ).
thf(278,plain,
x,
inference(pattern_uni,[status(thm)],[277:[]]) ).
thf(306,plain,
g @ y,
inference(rewrite,[status(thm)],[12,278]) ).
thf(299,plain,
~ y,
inference(rewrite,[status(thm)],[10,278]) ).
thf(312,plain,
g @ $false,
inference(rewrite,[status(thm)],[306,299]) ).
thf(304,plain,
( ( g @ ( f @ $true ) )
= ( f @ ( f @ ( f @ $true ) ) ) ),
inference(rewrite,[status(thm)],[13,278]) ).
thf(260,plain,
( ~ ( f @ x )
| ~ x ),
inference(bool_ext,[status(thm)],[259]) ).
thf(302,plain,
( ~ ( f @ $true )
| ~ $true ),
inference(rewrite,[status(thm)],[260,278]) ).
thf(303,plain,
~ ( f @ $true ),
inference(simp,[status(thm)],[302]) ).
thf(325,plain,
( ( g @ $false )
= ( f @ ( f @ $false ) ) ),
inference(rewrite,[status(thm)],[304,303]) ).
thf(326,plain,
f @ ( f @ $false ),
inference(rewrite,[status(thm)],[312,325]) ).
thf(332,plain,
( ~ $true
| ( ( f @ ( f @ $false ) )
!= ( f @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[326,303]) ).
thf(333,plain,
( ( f @ ( f @ $false ) )
!= ( f @ $true ) ),
inference(simp,[status(thm)],[332]) ).
thf(338,plain,
~ ( f @ $false ),
inference(simp,[status(thm)],[333]) ).
thf(344,plain,
f @ $false,
inference(rewrite,[status(thm)],[326,338]) ).
thf(347,plain,
$false,
inference(rewrite,[status(thm)],[344,338]) ).
thf(348,plain,
$false,
inference(simp,[status(thm)],[347]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYO041^2 : 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
% 0.27/0.32 % Computer : n015.cluster.edu
% 0.27/0.32 % Model : x86_64 x86_64
% 0.27/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.27/0.32 % Memory : 8046.5625MB
% 0.27/0.32 % OS : Linux 6.8.0-71-generic
% 0.27/0.32 % CPULimit : 300
% 0.27/0.32 % WCLimit : 300
% 0.27/0.32 % DateTime : Tue Sep 29 16:27:33 UTC 2026
% 0.27/0.32 % CPUTime :
% 0.27/0.32 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
% 1.44/1.17 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.83/1.43 % [INFO] Parsing done (264ms).
% 1.83/1.46 % [INFO] Running in sequential loop mode.
% 2.82/2.07 % [INFO] eprover registered as external prover.
% 2.82/2.08 % [INFO] Scanning for conjecture ...
% 2.98/2.19 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.04/2.23 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.04/2.24 % [INFO] Problem is higher-order (TPTP THF).
% 3.04/2.25 % [INFO] Type checking passed.
% 3.04/2.26 % [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 ...
% 7.92/4.05 % [INFO] Killing All external provers ...
% 8.57/4.05 % Time passed: 3522ms (effective reasoning time: 2584ms)
% 8.57/4.05 % 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)>
% 8.57/4.06 % Axioms used in derivation (0):
% 8.57/4.06 % No. of inferences in proof: 63
% 8.57/4.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3522 ms resp. 2584 ms w/o parsing
% 8.57/4.11 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.57/4.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------