%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM464+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 : n014.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 08:08:54 AM UTC 2026
% Result : Theorem 13.47s 9.77s
% Output : Refutation 13.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 6
% Syntax : Number of formulae : 50 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 173 ( 52 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 375 ( 92 ~; 78 |; 20 &; 174 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 37 ( 0 ^; 34 !; 3 ?; 37 :)
% 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(sz10_decl,type,
sz10: $i ).
thf(xn_decl,type,
xn: $i ).
thf(16,axiom,
! [A: $i] :
( ( A @ aNaturalNumber0 )
=> ( A @ ( A @ sdtlseqdt0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERefl) ).
thf(107,plain,
! [A: $i] :
( ( A @ aNaturalNumber0 )
=> ( A @ ( A @ sdtlseqdt0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(108,plain,
! [A: $i] :
( ( A @ ( A @ sdtlseqdt0 ) )
| ~ ( A @ aNaturalNumber0 ) ),
inference(cnf,[status(esa)],[107]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ aNaturalNumber0 )
& ( B @ aNaturalNumber0 )
& ( A @ aNaturalNumber0 ) )
=> ( ( ( C @ ( B @ sdtlseqdt0 ) )
& ( B @ ( A @ sdtlseqdt0 ) ) )
=> ( C @ ( A @ sdtlseqdt0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).
thf(75,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ aNaturalNumber0 )
& ( B @ aNaturalNumber0 )
& ( A @ aNaturalNumber0 ) )
=> ( ( ( C @ ( B @ sdtlseqdt0 ) )
& ( B @ ( A @ sdtlseqdt0 ) ) )
=> ( C @ ( A @ sdtlseqdt0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(76,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ sdtlseqdt0 ) )
| ~ ( C @ ( B @ sdtlseqdt0 ) )
| ~ ( B @ ( A @ sdtlseqdt0 ) )
| ~ ( C @ aNaturalNumber0 )
| ~ ( B @ aNaturalNumber0 )
| ~ ( A @ aNaturalNumber0 ) ),
inference(cnf,[status(esa)],[75]) ).
thf(1,conjecture,
( ( xm != sz00 )
=> ( ( xm @ ( sz10 @ sdtlseqdt0 ) )
| ? [A: $i] :
( ( ( A @ ( sz10 @ sdtpldt0 ) )
= xm )
& ( A @ aNaturalNumber0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( xm != sz00 )
=> ( ( xm @ ( sz10 @ sdtlseqdt0 ) )
| ? [A: $i] :
( ( ( A @ ( sz10 @ sdtpldt0 ) )
= xm )
& ( A @ aNaturalNumber0 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(30,plain,
~ ( ( xm != sz00 )
=> ( ( xm @ ( sz10 @ sdtlseqdt0 ) )
| ? [A: $i] :
( ( ( A @ ( sz10 @ sdtpldt0 ) )
= xm )
& ( A @ aNaturalNumber0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(31,plain,
! [A: $i] :
( ~ ( xm @ ( sz10 @ sdtlseqdt0 ) )
& ( ( ( A @ ( sz10 @ sdtpldt0 ) )
!= xm )
| ~ ( A @ aNaturalNumber0 ) )
& ( xm != sz00 ) ),
inference(cnf,[status(esa)],[30]) ).
thf(34,plain,
~ ( xm @ ( sz10 @ sdtlseqdt0 ) ),
inference(cnfConj,[status(thm)],[31]) ).
thf(251,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ sdtlseqdt0 ) )
!= ( xm @ ( sz10 @ sdtlseqdt0 ) ) )
| ~ $true
| ~ ( C @ ( B @ sdtlseqdt0 ) )
| ~ ( B @ ( A @ sdtlseqdt0 ) )
| ~ ( C @ aNaturalNumber0 )
| ~ ( B @ aNaturalNumber0 )
| ~ ( A @ aNaturalNumber0 ) ),
inference(paramod_ordered,[status(thm)],[76,34]) ).
thf(252,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ sdtlseqdt0 ) )
!= ( xm @ ( sz10 @ sdtlseqdt0 ) ) )
| ~ ( C @ ( B @ sdtlseqdt0 ) )
| ~ ( B @ ( A @ sdtlseqdt0 ) )
| ~ ( C @ aNaturalNumber0 )
| ~ ( B @ aNaturalNumber0 )
| ~ ( A @ aNaturalNumber0 ) ),
inference(simp,[status(thm)],[251]) ).
thf(253,plain,
! [A: $i] :
( ~ ( xm @ ( A @ sdtlseqdt0 ) )
| ~ ( A @ ( sz10 @ sdtlseqdt0 ) )
| ~ ( xm @ aNaturalNumber0 )
| ~ ( A @ aNaturalNumber0 )
| ~ ( sz10 @ aNaturalNumber0 ) ),
inference(pattern_uni,[status(thm)],[252:[bind(A,$thf( sz10 )),bind(B,$thf( B )),bind(C,$thf( xm ))]]) ).
thf(265,plain,
! [A: $i] :
( ~ ( xm @ ( A @ sdtlseqdt0 ) )
| ~ ( A @ ( sz10 @ sdtlseqdt0 ) )
| ~ ( xm @ aNaturalNumber0 )
| ~ ( A @ aNaturalNumber0 )
| ~ ( sz10 @ aNaturalNumber0 ) ),
inference(simp,[status(thm)],[253]) ).
thf(5,axiom,
( ( sz10 != sz00 )
& ( sz10 @ aNaturalNumber0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
thf(46,plain,
( ( sz10 != sz00 )
& ( sz10 @ aNaturalNumber0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(47,plain,
( ( sz10 != sz00 )
& ( sz10 @ aNaturalNumber0 ) ),
inference(cnf,[status(esa)],[46]) ).
thf(48,plain,
sz10 @ aNaturalNumber0,
inference(cnfConj,[status(thm)],[47]) ).
thf(19,axiom,
( ( xn @ aNaturalNumber0 )
& ( xm @ aNaturalNumber0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__987) ).
thf(120,plain,
( ( xn @ aNaturalNumber0 )
& ( xm @ aNaturalNumber0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(121,plain,
( ( xn @ aNaturalNumber0 )
& ( xm @ aNaturalNumber0 ) ),
inference(cnf,[status(esa)],[120]) ).
thf(122,plain,
xm @ aNaturalNumber0,
inference(cnfConj,[status(thm)],[121]) ).
thf(282,plain,
! [A: $i] :
( ~ ( xm @ ( A @ sdtlseqdt0 ) )
| ~ ( A @ ( sz10 @ sdtlseqdt0 ) )
| ~ $true
| ~ ( A @ aNaturalNumber0 )
| ~ $true ),
inference(rewrite,[status(thm)],[265,48,122]) ).
thf(283,plain,
! [A: $i] :
( ~ ( xm @ ( A @ sdtlseqdt0 ) )
| ~ ( A @ ( sz10 @ sdtlseqdt0 ) )
| ~ ( A @ aNaturalNumber0 ) ),
inference(simp,[status(thm)],[282]) ).
thf(302,plain,
! [A: $i] :
( ~ $true
| ( ( xm @ ( A @ sdtlseqdt0 ) )
!= ( A @ ( sz10 @ sdtlseqdt0 ) ) )
| ~ ( A @ ( sz10 @ sdtlseqdt0 ) )
| ~ ( A @ aNaturalNumber0 ) ),
inference(eqfactor_ordered,[status(thm)],[283]) ).
thf(304,plain,
! [A: $i] :
( ( xm != A )
| ( A != sz10 )
| ~ ( A @ ( sz10 @ sdtlseqdt0 ) )
| ~ ( A @ aNaturalNumber0 ) ),
inference(simp,[status(thm)],[302]) ).
thf(305,plain,
( ( sz10 != xm )
| ~ ( sz10 @ ( sz10 @ sdtlseqdt0 ) )
| ~ ( sz10 @ aNaturalNumber0 ) ),
inference(simp,[status(thm)],[304]) ).
thf(478,plain,
( ( sz10 != xm )
| ~ ( sz10 @ ( sz10 @ sdtlseqdt0 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[305,48]) ).
thf(479,plain,
( ( sz10 != xm )
| ~ ( sz10 @ ( sz10 @ sdtlseqdt0 ) ) ),
inference(simp,[status(thm)],[478]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ aNaturalNumber0 )
=> ( ( ( A @ ( sz10 @ sdtlseqdt0 ) )
& ( sz10 != A ) )
| ( A = sz10 )
| ( A = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLENTr) ).
thf(142,plain,
! [A: $i] :
( ( A @ aNaturalNumber0 )
=> ( ( ( A @ ( sz10 @ sdtlseqdt0 ) )
& ( sz10 != A ) )
| ( A = sz10 )
| ( A = sz00 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(143,plain,
! [A: $i] :
( ( ( A @ ( sz10 @ sdtlseqdt0 ) )
| ( A = sz10 )
| ( A = sz00 )
| ~ ( A @ aNaturalNumber0 ) )
& ( ( sz10 != A )
| ( A = sz10 )
| ( A = sz00 )
| ~ ( A @ aNaturalNumber0 ) ) ),
inference(cnf,[status(esa)],[142]) ).
thf(145,plain,
! [A: $i] :
( ( A @ ( sz10 @ sdtlseqdt0 ) )
| ( A = sz10 )
| ( A = sz00 )
| ~ ( A @ aNaturalNumber0 ) ),
inference(cnfConj,[status(thm)],[143]) ).
thf(148,plain,
! [A: $i] :
( ( A @ ( sz10 @ sdtlseqdt0 ) )
| ~ ( A @ aNaturalNumber0 )
| ( A = sz10 )
| ( A = sz00 ) ),
inference(lifteq,[status(thm)],[145]) ).
thf(719,plain,
! [A: $i] :
( ( ( A @ ( sz10 @ sdtlseqdt0 ) )
!= ( xm @ ( sz10 @ sdtlseqdt0 ) ) )
| ~ $true
| ~ ( A @ aNaturalNumber0 )
| ( A = sz10 )
| ( A = sz00 ) ),
inference(paramod_ordered,[status(thm)],[148,34]) ).
thf(720,plain,
! [A: $i] :
( ( ( A @ ( sz10 @ sdtlseqdt0 ) )
!= ( xm @ ( sz10 @ sdtlseqdt0 ) ) )
| ~ ( A @ aNaturalNumber0 )
| ( A = sz10 )
| ( A = sz00 ) ),
inference(simp,[status(thm)],[719]) ).
thf(721,plain,
( ~ ( xm @ aNaturalNumber0 )
| ( sz10 = xm )
| ( sz00 = xm ) ),
inference(pattern_uni,[status(thm)],[720:[bind(A,$thf( xm ))]]) ).
thf(812,plain,
( ~ $true
| ( sz10 = xm )
| ( sz00 = xm ) ),
inference(rewrite,[status(thm)],[721,122]) ).
thf(813,plain,
( ( sz10 = xm )
| ( sz00 = xm ) ),
inference(simp,[status(thm)],[812]) ).
thf(32,plain,
xm != sz00,
inference(cnfConj,[status(thm)],[31]) ).
thf(35,plain,
sz00 != xm,
inference(lifteq,[status(thm)],[32]) ).
thf(814,plain,
sz10 = xm,
inference(simplifyReflect,[status(thm)],[813,35]) ).
thf(820,plain,
( ( xm != xm )
| ~ ( xm @ ( xm @ sdtlseqdt0 ) ) ),
inference(rewrite,[status(thm)],[479,814]) ).
thf(821,plain,
~ ( xm @ ( xm @ sdtlseqdt0 ) ),
inference(simp,[status(thm)],[820]) ).
thf(1681,plain,
! [A: $i] :
( ( ( A @ ( A @ sdtlseqdt0 ) )
!= ( xm @ ( xm @ sdtlseqdt0 ) ) )
| ~ $true
| ~ ( A @ aNaturalNumber0 ) ),
inference(paramod_ordered,[status(thm)],[108,821]) ).
thf(1682,plain,
! [A: $i] :
( ( ( A @ ( A @ sdtlseqdt0 ) )
!= ( xm @ ( xm @ sdtlseqdt0 ) ) )
| ~ ( A @ aNaturalNumber0 ) ),
inference(simp,[status(thm)],[1681]) ).
thf(1683,plain,
~ ( xm @ aNaturalNumber0 ),
inference(pattern_uni,[status(thm)],[1682:[bind(A,$thf( xm ))]]) ).
thf(1763,plain,
~ $true,
inference(rewrite,[status(thm)],[1683,122]) ).
thf(1764,plain,
$false,
inference(simp,[status(thm)],[1763]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM464+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
% 0.18/5.43 % Computer : n014.cluster.edu
% 0.18/5.43 % Model : x86_64 x86_64
% 0.18/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.43 % Memory : 8046.5625MB
% 0.18/5.43 % OS : Linux 6.8.0-71-generic
% 0.18/5.44 % CPULimit : 300
% 0.18/5.44 % WCLimit : 300
% 0.18/5.44 % DateTime : Sat Sep 26 02:51:24 UTC 2026
% 0.18/5.44 % CPUTime :
% 0.18/5.44 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
% 0.21/6.02 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.38/6.23 % [INFO] Parsing done (206ms).
% 1.38/6.24 % [INFO] Running in sequential loop mode.
% 2.12/6.65 % [INFO] eprover registered as external prover.
% 2.12/6.66 % [INFO] Scanning for conjecture ...
% 2.35/6.75 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.35/6.76 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.35/6.79 % [INFO] Found a conjecture (or negated_conjecture) and 27 axioms. Running axiom selection ...
% 2.56/6.87 % [INFO] Axiom selection finished. Selected 27 axioms (removed 0 axioms).
% 2.56/6.89 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.77/6.90 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.77/6.93 % [INFO] Problem is first-order (TPTP FOF).
% 2.77/6.94 % [INFO] Type checking passed.
% 2.77/6.95 % [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 ...
% 13.47/9.76 % [INFO] Killing All external provers ...
% 13.47/9.77 % Time passed: 4185ms (effective reasoning time: 3515ms)
% 13.47/9.77 % 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)>
% 13.47/9.77 % Axioms used in derivation (5): m__987, mSortsC_01, mLETran, mLENTr, mLERefl
% 13.47/9.77 % No. of inferences in proof: 50
% 13.47/9.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4185 ms resp. 3515 ms w/o parsing
% 13.97/9.81 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.97/9.81 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------