%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM458+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/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 : Sun Sep 27 08:08:53 AM UTC 2026
% Result : Theorem 6.92s 13.34s
% Output : Refutation 6.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 52 ( 22 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 120 ( 26 ~; 16 |; 7 &; 69 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 14 ( 0 ^; 11 !; 3 ?; 14 :)
% 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(sz00_decl,type,
sz00: $i ).
thf(10,axiom,
! [A: $i] :
( ( A @ aNaturalNumber0 )
=> ( ( A
= ( A @ ( sz00 @ sdtpldt0 ) ) )
& ( ( sz00 @ ( A @ sdtpldt0 ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
thf(66,plain,
! [A: $i] :
( ( A @ aNaturalNumber0 )
=> ( ( A
= ( A @ ( sz00 @ sdtpldt0 ) ) )
& ( ( sz00 @ ( A @ sdtpldt0 ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(67,plain,
! [A: $i] :
( ( ( A
= ( A @ ( sz00 @ sdtpldt0 ) ) )
| ~ ( A @ aNaturalNumber0 ) )
& ( ( ( sz00 @ ( A @ sdtpldt0 ) )
= A )
| ~ ( A @ aNaturalNumber0 ) ) ),
inference(cnf,[status(esa)],[66]) ).
thf(68,plain,
! [A: $i] :
( ( ( sz00 @ ( A @ sdtpldt0 ) )
= A )
| ~ ( A @ aNaturalNumber0 ) ),
inference(cnfConj,[status(thm)],[67]) ).
thf(70,plain,
! [A: $i] :
( ~ ( A @ aNaturalNumber0 )
| ( ( sz00 @ ( A @ sdtpldt0 ) )
= A ) ),
inference(lifteq,[status(thm)],[68]) ).
thf(14,axiom,
sz00 @ aNaturalNumber0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
thf(83,plain,
sz00 @ aNaturalNumber0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(1,conjecture,
( ( xm @ ( xm @ sdtlseqdt0 ) )
| ? [A: $i] :
( ( ( A @ ( xm @ sdtpldt0 ) )
= xm )
& ( A @ aNaturalNumber0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( xm @ ( xm @ sdtlseqdt0 ) )
| ? [A: $i] :
( ( ( A @ ( xm @ sdtpldt0 ) )
= xm )
& ( A @ aNaturalNumber0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(23,plain,
~ ( ( xm @ ( xm @ sdtlseqdt0 ) )
| ? [A: $i] :
( ( ( A @ ( xm @ sdtpldt0 ) )
= xm )
& ( A @ aNaturalNumber0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(24,plain,
! [A: $i] :
( ~ ( xm @ ( xm @ sdtlseqdt0 ) )
& ( ( ( A @ ( xm @ sdtpldt0 ) )
!= xm )
| ~ ( A @ aNaturalNumber0 ) ) ),
inference(cnf,[status(esa)],[23]) ).
thf(25,plain,
! [A: $i] :
( ( ( A @ ( xm @ sdtpldt0 ) )
!= xm )
| ~ ( A @ aNaturalNumber0 ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(27,plain,
! [A: $i] :
( ~ ( A @ aNaturalNumber0 )
| ( ( A @ ( xm @ sdtpldt0 ) )
!= xm ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(123,plain,
! [A: $i] :
( ( ( sz00 @ aNaturalNumber0 )
!= ( A @ aNaturalNumber0 ) )
| ~ $true
| ( ( A @ ( xm @ sdtpldt0 ) )
!= xm ) ),
inference(paramod_ordered,[status(thm)],[83,27]) ).
thf(124,plain,
! [A: $i] :
( ( ( sz00 @ aNaturalNumber0 )
!= ( A @ aNaturalNumber0 ) )
| ( ( A @ ( xm @ sdtpldt0 ) )
!= xm ) ),
inference(simp,[status(thm)],[123]) ).
thf(125,plain,
( ( sz00 @ ( xm @ sdtpldt0 ) )
!= xm ),
inference(pattern_uni,[status(thm)],[124:[bind(A,$thf( sz00 ))]]) ).
thf(466,plain,
! [A: $i] :
( ( ( sz00 @ ( A @ sdtpldt0 ) )
!= ( sz00 @ ( xm @ sdtpldt0 ) ) )
| ( A != xm )
| ~ ( A @ aNaturalNumber0 ) ),
inference(paramod_ordered,[status(thm)],[70,125]) ).
thf(467,plain,
( ( xm != xm )
| ~ ( xm @ aNaturalNumber0 ) ),
inference(pattern_uni,[status(thm)],[466:[bind(A,$thf( xm ))]]) ).
thf(510,plain,
~ ( xm @ aNaturalNumber0 ),
inference(simp,[status(thm)],[467]) ).
thf(15,axiom,
xm @ aNaturalNumber0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__718) ).
thf(84,plain,
xm @ aNaturalNumber0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(516,plain,
~ $true,
inference(rewrite,[status(thm)],[510,84]) ).
thf(517,plain,
$false,
inference(simp,[status(thm)],[516]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM458+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/10.42 % Computer : n015.cluster.edu
% 0.14/10.42 % Model : x86_64 x86_64
% 0.14/10.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/10.42 % Memory : 8046.5625MB
% 0.14/10.42 % OS : Linux 6.8.0-71-generic
% 0.14/10.42 % CPULimit : 300
% 0.14/10.42 % WCLimit : 300
% 0.14/10.42 % DateTime : Sat Sep 26 02:53:23 UTC 2026
% 0.14/10.42 % CPUTime :
% 0.14/10.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.18/11.02 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.31/11.24 % [INFO] Parsing done (209ms).
% 1.31/11.25 % [INFO] Running in sequential loop mode.
% 1.99/11.64 % [INFO] eprover registered as external prover.
% 1.99/11.65 % [INFO] Scanning for conjecture ...
% 2.18/11.73 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.18/11.74 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.18/11.76 % [INFO] Found a conjecture (or negated_conjecture) and 20 axioms. Running axiom selection ...
% 2.34/11.83 % [INFO] Axiom selection finished. Selected 20 axioms (removed 0 axioms).
% 2.34/11.84 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.34/11.85 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.34/11.87 % [INFO] Problem is first-order (TPTP FOF).
% 2.34/11.88 % [INFO] Type checking passed.
% 2.34/11.89 % [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 ...
% 6.92/13.34 % [INFO] Killing All external provers ...
% 6.92/13.34 % Time passed: 2768ms (effective reasoning time: 2082ms)
% 6.92/13.34 % 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)>
% 6.92/13.34 % Axioms used in derivation (3): m_AddZero, mSortsC, m__718
% 6.92/13.34 % No. of inferences in proof: 23
% 6.92/13.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2768 ms resp. 2082 ms w/o parsing
% 6.92/13.38 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.92/13.38 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------