%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM472+2 : 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 : Sun Sep 27 08:08:55 AM UTC 2026
% Result : Theorem 6.50s 8.19s
% Output : Refutation 6.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 6 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 83 ( 10 ~; 6 |; 10 &; 57 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 6 ( 0 ^; 3 !; 3 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
thf(aNaturalNumber0_decl,type,
aNaturalNumber0: $i > $o ).
thf(sdtlseqdt0_decl,type,
sdtlseqdt0: $i > $i > $o ).
thf(sdtpldt0_decl,type,
sdtpldt0: $i > $i > $i ).
thf(xm_decl,type,
xm: $i ).
thf(xn_decl,type,
xn: $i ).
thf(xl_decl,type,
xl: $i ).
thf(28,axiom,
( ( xn @ aNaturalNumber0 )
& ( xm @ aNaturalNumber0 )
& ( xl @ aNaturalNumber0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324) ).
thf(166,plain,
( ( xn @ aNaturalNumber0 )
& ( xm @ aNaturalNumber0 )
& ( xl @ aNaturalNumber0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(167,plain,
( ( xn @ aNaturalNumber0 )
& ( xm @ aNaturalNumber0 )
& ( xl @ aNaturalNumber0 ) ),
inference(cnf,[status(esa)],[166]) ).
thf(170,plain,
xn @ aNaturalNumber0,
inference(cnfConj,[status(thm)],[167]) ).
thf(1,conjecture,
( ( xn @ ( xm @ sdtpldt0 ) @ ( xm @ sdtlseqdt0 ) )
| ? [A: $i] :
( ( ( A @ ( xm @ sdtpldt0 ) )
= ( xn @ ( xm @ sdtpldt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( xn @ ( xm @ sdtpldt0 ) @ ( xm @ sdtlseqdt0 ) )
| ? [A: $i] :
( ( ( A @ ( xm @ sdtpldt0 ) )
= ( xn @ ( xm @ sdtpldt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(41,plain,
~ ( ( xn @ ( xm @ sdtpldt0 ) @ ( xm @ sdtlseqdt0 ) )
| ? [A: $i] :
( ( ( A @ ( xm @ sdtpldt0 ) )
= ( xn @ ( xm @ sdtpldt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(42,plain,
! [A: $i] :
( ~ ( xn @ ( xm @ sdtpldt0 ) @ ( xm @ sdtlseqdt0 ) )
& ( ( ( A @ ( xm @ sdtpldt0 ) )
!= ( xn @ ( xm @ sdtpldt0 ) ) )
| ~ ( A @ aNaturalNumber0 ) ) ),
inference(cnf,[status(esa)],[41]) ).
thf(43,plain,
! [A: $i] :
( ( ( A @ ( xm @ sdtpldt0 ) )
!= ( xn @ ( xm @ sdtpldt0 ) ) )
| ~ ( A @ aNaturalNumber0 ) ),
inference(cnfConj,[status(thm)],[42]) ).
thf(45,plain,
! [A: $i] :
( ~ ( A @ aNaturalNumber0 )
| ( ( A @ ( xm @ sdtpldt0 ) )
!= ( xn @ ( xm @ sdtpldt0 ) ) ) ),
inference(lifteq,[status(thm)],[43]) ).
thf(238,plain,
~ ( xn @ aNaturalNumber0 ),
inference(pattern_uni,[status(thm)],[45:[bind(A,$thf( xn ))]]) ).
thf(268,plain,
$false,
inference(rewrite,[status(thm)],[170,238]) ).
thf(269,plain,
$false,
inference(simp,[status(thm)],[268]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM472+2 : 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
% 0.14/5.41 % Computer : n011.cluster.edu
% 0.14/5.41 % Model : x86_64 x86_64
% 0.14/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.41 % Memory : 8046.5625MB
% 0.14/5.41 % OS : Linux 6.8.0-71-generic
% 0.14/5.41 % CPULimit : 300
% 0.14/5.41 % WCLimit : 300
% 0.14/5.41 % DateTime : Sat Sep 26 02:53:49 UTC 2026
% 0.14/5.41 % CPUTime :
% 0.14/5.41 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
% 0.19/6.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.39/6.23 % [INFO] Parsing done (229ms).
% 1.39/6.25 % [INFO] Running in sequential loop mode.
% 2.10/6.66 % [INFO] eprover registered as external prover.
% 2.10/6.66 % [INFO] Scanning for conjecture ...
% 2.33/6.75 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.33/6.76 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.33/6.77 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.33/6.77 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.54/6.81 % [INFO] Found a conjecture (or negated_conjecture) and 38 axioms. Running axiom selection ...
% 2.54/6.89 % [INFO] Axiom selection finished. Selected 38 axioms (removed 0 axioms).
% 2.75/6.91 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/6.92 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/6.93 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/6.94 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.75/6.97 % [INFO] Problem is first-order (TPTP FOF).
% 2.75/6.98 % [INFO] Type checking passed.
% 2.75/6.99 % [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 ...
% 6.50/8.18 % [INFO] Killing All external provers ...
% 6.50/8.19 % Time passed: 2631ms (effective reasoning time: 1932ms)
% 6.50/8.19 % 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)>
% 6.50/8.19 % Axioms used in derivation (1): m__1324
% 6.50/8.19 % No. of inferences in proof: 13
% 6.50/8.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2631 ms resp. 1932 ms w/o parsing
% 6.79/8.22 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.79/8.22 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------