%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM489+3 : 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 : n005.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 : Sun Sep 27 08:08:58 AM UTC 2026
% Result : Theorem 8.22s 3.64s
% Output : Refutation 8.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 16 ( 12 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 3 ~; 0 |; 6 &; 27 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(aNaturalNumber0_decl,type,
aNaturalNumber0: $i > $o ).
thf(sdtpldt0_decl,type,
sdtpldt0: $i > $i > $i ).
thf(sdtmndt0_decl,type,
sdtmndt0: $i > $i > $i ).
thf(xn_decl,type,
xn: $i ).
thf(xp_decl,type,
xp: $i ).
thf(xr_decl,type,
xr: $i ).
thf(29,axiom,
( ( xr
= ( xp @ ( xn @ sdtmndt0 ) ) )
& ( ( xr @ ( xp @ sdtpldt0 ) )
= xn )
& ( xr @ aNaturalNumber0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1883) ).
thf(176,plain,
( ( xr
= ( xp @ ( xn @ sdtmndt0 ) ) )
& ( ( xr @ ( xp @ sdtpldt0 ) )
= xn )
& ( xr @ aNaturalNumber0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(177,plain,
( ( xr
= ( xp @ ( xn @ sdtmndt0 ) ) )
& ( ( xr @ ( xp @ sdtpldt0 ) )
= xn )
& ( xr @ aNaturalNumber0 ) ),
inference(cnf,[status(esa)],[176]) ).
thf(179,plain,
( ( xr @ ( xp @ sdtpldt0 ) )
= xn ),
inference(cnfConj,[status(thm)],[177]) ).
thf(181,plain,
( ( xr @ ( xp @ sdtpldt0 ) )
= xn ),
inference(lifteq,[status(thm)],[179]) ).
thf(1,conjecture,
( xn
= ( xr @ ( xp @ sdtpldt0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
( xn
!= ( xr @ ( xp @ sdtpldt0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(47,plain,
( xn
!= ( xr @ ( xp @ sdtpldt0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(48,plain,
( ( xr @ ( xp @ sdtpldt0 ) )
!= xn ),
inference(lifteq,[status(thm)],[47]) ).
thf(374,plain,
$false,
inference(simplifyReflect,[status(thm)],[181,48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM489+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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
% 0.14/0.41 % Computer : n005.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 02:57:47 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.87/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.41/1.24 % [INFO] Parsing done (243ms).
% 1.41/1.26 % [INFO] Running in sequential loop mode.
% 2.22/1.67 % [INFO] eprover registered as external prover.
% 2.22/1.68 % [INFO] Scanning for conjecture ...
% 2.45/1.76 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.45/1.77 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.45/1.78 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.45/1.78 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.45/1.79 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.66/1.82 % [INFO] Found a conjecture (or negated_conjecture) and 44 axioms. Running axiom selection ...
% 2.89/1.90 % [INFO] Axiom selection finished. Selected 44 axioms (removed 0 axioms).
% 2.89/1.94 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.89/1.94 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.89/1.95 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.89/1.96 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.89/1.96 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.89/2.00 % [INFO] Problem is first-order (TPTP FOF).
% 2.89/2.01 % [INFO] Type checking passed.
% 2.89/2.01 % [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 ...
% 8.22/3.63 % [INFO] Killing All external provers ...
% 8.22/3.64 % Time passed: 3077ms (effective reasoning time: 2366ms)
% 8.22/3.64 % 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)>
% 8.22/3.64 % Axioms used in derivation (1): m__1883
% 8.22/3.64 % No. of inferences in proof: 10
% 8.22/3.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3077 ms resp. 2366 ms w/o parsing
% 8.22/3.66 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.22/3.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------