%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM458+1 : 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 : n017.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 43.58s 11.57s
% Output : Refutation 43.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 12 unt; 0 typ; 1 def)
% Number of atoms : 117 ( 32 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 319 ( 67 ~; 54 |; 12 &; 179 @)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 39 ( 2 ^; 33 !; 3 ?; 39 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% 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(sk1_decl,type,
sk1: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( ( C @ ( B @ sdtpldt0 ) )
= A )
& ( C @ aNaturalNumber0 ) ) ) ) ).
thf(22,axiom,
xm @ aNaturalNumber0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__718) ).
thf(112,plain,
xm @ aNaturalNumber0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ aNaturalNumber0 )
=> ( ( A
= ( A @ ( sz00 @ sdtpldt0 ) ) )
& ( ( sz00 @ ( A @ sdtpldt0 ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
thf(39,plain,
! [A: $i] :
( ( A @ aNaturalNumber0 )
=> ( ( A
= ( A @ ( sz00 @ sdtpldt0 ) ) )
& ( ( sz00 @ ( A @ sdtpldt0 ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(40,plain,
! [A: $i] :
( ( ( A
= ( A @ ( sz00 @ sdtpldt0 ) ) )
| ~ ( A @ aNaturalNumber0 ) )
& ( ( ( sz00 @ ( A @ sdtpldt0 ) )
= A )
| ~ ( A @ aNaturalNumber0 ) ) ),
inference(cnf,[status(esa)],[39]) ).
thf(41,plain,
! [A: $i] :
( ( ( sz00 @ ( A @ sdtpldt0 ) )
= A )
| ~ ( A @ aNaturalNumber0 ) ),
inference(cnfConj,[status(thm)],[40]) ).
thf(43,plain,
! [A: $i] :
( ~ ( A @ aNaturalNumber0 )
| ( ( sz00 @ ( A @ sdtpldt0 ) )
= A ) ),
inference(lifteq,[status(thm)],[41]) ).
thf(264,plain,
! [A: $i] :
( ( ( xm @ aNaturalNumber0 )
!= ( A @ aNaturalNumber0 ) )
| ~ $true
| ( ( sz00 @ ( A @ sdtpldt0 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[112,43]) ).
thf(265,plain,
! [A: $i] :
( ( ( xm @ aNaturalNumber0 )
!= ( A @ aNaturalNumber0 ) )
| ( ( sz00 @ ( A @ sdtpldt0 ) )
= A ) ),
inference(simp,[status(thm)],[264]) ).
thf(266,plain,
( ( sz00 @ ( xm @ sdtpldt0 ) )
= xm ),
inference(pattern_uni,[status(thm)],[265:[bind(A,$thf( xm ))]]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ( B @ aNaturalNumber0 )
& ( A @ aNaturalNumber0 ) )
=> ( ( B @ ( A @ sdtlseqdt0 ) )
<=> ? [C: $i] :
( ( ( C @ ( A @ sdtpldt0 ) )
= B )
& ( C @ aNaturalNumber0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
thf(92,plain,
! [A: $i,B: $i] :
( ( ( B @ aNaturalNumber0 )
& ( A @ aNaturalNumber0 ) )
=> ( ( ? [C: $i] :
( ( ( C @ ( A @ sdtpldt0 ) )
= B )
& ( C @ aNaturalNumber0 ) )
=> ( B @ ( A @ sdtlseqdt0 ) ) )
& ( ( B @ ( A @ sdtlseqdt0 ) )
=> ? [C: $i] :
( ( ( C @ ( A @ sdtpldt0 ) )
= B )
& ( C @ aNaturalNumber0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(93,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sdtlseqdt0 ) )
| ( ( C @ ( A @ sdtpldt0 ) )
!= B )
| ~ ( C @ aNaturalNumber0 )
| ~ ( B @ aNaturalNumber0 )
| ~ ( A @ aNaturalNumber0 ) )
& ( ( ( A @ ( B @ sk1 ) @ ( A @ sdtpldt0 ) )
= B )
| ~ ( B @ ( A @ sdtlseqdt0 ) )
| ~ ( B @ aNaturalNumber0 )
| ~ ( A @ aNaturalNumber0 ) )
& ( ( A @ ( B @ sk1 ) @ aNaturalNumber0 )
| ~ ( B @ ( A @ sdtlseqdt0 ) )
| ~ ( B @ aNaturalNumber0 )
| ~ ( A @ aNaturalNumber0 ) ) ),
inference(cnf,[status(esa)],[92]) ).
thf(96,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ sdtlseqdt0 ) )
| ( ( C @ ( A @ sdtpldt0 ) )
!= B )
| ~ ( C @ aNaturalNumber0 )
| ~ ( B @ aNaturalNumber0 )
| ~ ( A @ aNaturalNumber0 ) ),
inference(cnfConj,[status(thm)],[93]) ).
thf(98,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ sdtlseqdt0 ) )
| ~ ( C @ aNaturalNumber0 )
| ~ ( B @ aNaturalNumber0 )
| ~ ( A @ aNaturalNumber0 )
| ( ( C @ ( A @ sdtpldt0 ) )
!= B ) ),
inference(lifteq,[status(thm)],[96]) ).
thf(99,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sdtpldt0 ) @ ( A @ sdtlseqdt0 ) )
| ~ ( B @ aNaturalNumber0 )
| ~ ( B @ ( A @ sdtpldt0 ) @ aNaturalNumber0 )
| ~ ( A @ aNaturalNumber0 ) ),
inference(simp,[status(thm)],[98]) ).
thf(1,conjecture,
xm @ ( xm @ sdtlseqdt0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( xm @ ( xm @ sdtlseqdt0 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(23,plain,
~ ( xm @ ( xm @ sdtlseqdt0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20658,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sdtpldt0 ) @ ( A @ sdtlseqdt0 ) )
!= ( xm @ ( xm @ sdtlseqdt0 ) ) )
| ~ $true
| ~ ( B @ aNaturalNumber0 )
| ~ ( B @ ( A @ sdtpldt0 ) @ aNaturalNumber0 )
| ~ ( A @ aNaturalNumber0 ) ),
inference(paramod_ordered,[status(thm)],[99,23]) ).
thf(20659,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sdtpldt0 ) @ ( A @ sdtlseqdt0 ) )
!= ( xm @ ( xm @ sdtlseqdt0 ) ) )
| ~ ( B @ aNaturalNumber0 )
| ~ ( B @ ( A @ sdtpldt0 ) @ aNaturalNumber0 )
| ~ ( A @ aNaturalNumber0 ) ),
inference(simp,[status(thm)],[20658]) ).
thf(20697,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sdtpldt0 ) )
!= xm )
| ( A != xm )
| ~ ( B @ aNaturalNumber0 )
| ~ ( B @ ( A @ sdtpldt0 ) @ aNaturalNumber0 )
| ~ ( A @ aNaturalNumber0 ) ),
inference(simp,[status(thm)],[20659]) ).
thf(20746,plain,
! [A: $i] :
( ( ( A @ ( xm @ sdtpldt0 ) )
!= xm )
| ~ ( A @ aNaturalNumber0 )
| ~ ( A @ ( xm @ sdtpldt0 ) @ aNaturalNumber0 )
| ~ ( xm @ aNaturalNumber0 ) ),
inference(simp,[status(thm)],[20697]) ).
thf(23333,plain,
! [A: $i] :
( ( ( A @ ( xm @ sdtpldt0 ) )
!= xm )
| ~ ( A @ aNaturalNumber0 )
| ~ ( A @ ( xm @ sdtpldt0 ) @ aNaturalNumber0 )
| ~ $true ),
inference(rewrite,[status(thm)],[20746,112]) ).
thf(23334,plain,
! [A: $i] :
( ( ( A @ ( xm @ sdtpldt0 ) )
!= xm )
| ~ ( A @ aNaturalNumber0 )
| ~ ( A @ ( xm @ sdtpldt0 ) @ aNaturalNumber0 ) ),
inference(simp,[status(thm)],[23333]) ).
thf(23438,plain,
! [A: $i] :
( ( ( sz00 @ ( xm @ sdtpldt0 ) )
!= ( A @ ( xm @ sdtpldt0 ) ) )
| ( xm != xm )
| ~ ( A @ aNaturalNumber0 )
| ~ ( A @ ( xm @ sdtpldt0 ) @ aNaturalNumber0 ) ),
inference(paramod_ordered,[status(thm)],[266,23334]) ).
thf(23439,plain,
! [A: $i] :
( ( ( sz00 @ ( xm @ sdtpldt0 ) )
!= ( A @ ( xm @ sdtpldt0 ) ) )
| ~ ( A @ aNaturalNumber0 )
| ~ ( A @ ( xm @ sdtpldt0 ) @ aNaturalNumber0 ) ),
inference(simp,[status(thm)],[23438]) ).
thf(23440,plain,
( ~ ( sz00 @ aNaturalNumber0 )
| ~ ( sz00 @ ( xm @ sdtpldt0 ) @ aNaturalNumber0 ) ),
inference(pattern_uni,[status(thm)],[23439:[bind(A,$thf( sz00 ))]]) ).
thf(10,axiom,
sz00 @ aNaturalNumber0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
thf(56,plain,
sz00 @ aNaturalNumber0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(23600,plain,
( ~ $true
| ~ ( xm @ aNaturalNumber0 ) ),
inference(rewrite,[status(thm)],[23440,56,266]) ).
thf(23601,plain,
~ ( xm @ aNaturalNumber0 ),
inference(simp,[status(thm)],[23600]) ).
thf(23602,plain,
$false,
inference(rewrite,[status(thm)],[112,23601]) ).
thf(23603,plain,
$false,
inference(simp,[status(thm)],[23602]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM458+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.13 % 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
% 0.25/0.49 % Computer : n017.cluster.edu
% 0.25/0.49 % Model : x86_64 x86_64
% 0.25/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.49 % Memory : 8046.5625MB
% 0.25/0.49 % OS : Linux 6.8.0-71-generic
% 0.25/0.50 % CPULimit : 300
% 0.25/0.50 % WCLimit : 300
% 0.25/0.50 % DateTime : Sat Sep 26 02:45:02 UTC 2026
% 0.25/0.50 % CPUTime :
% 0.25/0.50 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
% 1.31/1.20 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.69/1.41 % [INFO] Parsing done (200ms).
% 1.69/1.42 % [INFO] Running in sequential loop mode.
% 2.43/1.83 % [INFO] eprover registered as external prover.
% 2.43/1.84 % [INFO] Scanning for conjecture ...
% 2.63/1.93 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.63/1.93 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.63/1.96 % [INFO] Found a conjecture (or negated_conjecture) and 20 axioms. Running axiom selection ...
% 2.63/2.02 % [INFO] Axiom selection finished. Selected 20 axioms (removed 0 axioms).
% 2.88/2.06 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.88/2.07 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.88/2.07 % [INFO] Problem is first-order (TPTP FOF).
% 2.88/2.08 % [INFO] Type checking passed.
% 2.88/2.08 % [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 ...
% 43.58/11.56 % [INFO] Killing All external provers ...
% 43.58/11.56 % Time passed: 10851ms (effective reasoning time: 10135ms)
% 43.58/11.56 % 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)>
% 43.58/11.56 % Axioms used in derivation (4): m__718, m_AddZero, mDefLE, mSortsC
% 43.58/11.56 % No. of inferences in proof: 34
% 43.58/11.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10851 ms resp. 10135 ms w/o parsing
% 43.58/11.59 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 43.58/11.59 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------