%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM476+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 : 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 08:08:56 AM UTC 2026
% Result : Theorem 46.46s 12.56s
% Output : Refutation 46.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 73 ( 28 unt; 0 typ; 6 def)
% Number of atoms : 289 ( 172 equ; 0 cnn)
% Maximal formula atoms : 31 ( 3 avg)
% Number of connectives : 712 ( 56 ~; 62 |; 114 &; 470 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 12 con; 0-2 aty)
% Number of variables : 57 ( 0 ^; 27 !; 24 ?; 57 :)
% ( 0 !>; 0 ?*; 0 @-; 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(sdtmndt0_decl,type,
sdtmndt0: $i > $i > $i ).
thf(doDivides0_decl,type,
doDivides0: $i > $i > $o ).
thf(sdtasdt0_decl,type,
sdtasdt0: $i > $i > $i ).
thf(sz00_decl,type,
sz00: $i ).
thf(sdtsldt0_decl,type,
sdtsldt0: $i > $i > $i ).
thf(xl_decl,type,
xl: $i ).
thf(xm_decl,type,
xm: $i ).
thf(xn_decl,type,
xn: $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
( ? [B: $i] :
( ? [C: $i] :
( ( xn
= ( C @ ( xl @ sdtasdt0 ) ) )
& ( ( C @ ( xl @ sdtasdt0 ) @ ( A @ ( xl @ sdtasdt0 ) @ sdtpldt0 ) )
= ( xn @ ( A @ ( xl @ sdtasdt0 ) @ sdtpldt0 ) ) )
& ( C
= ( A @ ( B @ sdtmndt0 ) ) )
& ( ( C @ ( A @ sdtpldt0 ) )
= B )
& ( C @ aNaturalNumber0 ) )
& ( B @ ( A @ sdtlseqdt0 ) )
& ? [C: $i] :
( ( ( C @ ( A @ sdtpldt0 ) )
= B )
& ( C @ aNaturalNumber0 ) )
& ( B
= ( xl @ ( xn @ ( xm @ sdtpldt0 ) @ sdtsldt0 ) ) )
& ( ( xn @ ( xm @ sdtpldt0 ) )
= ( B @ ( xl @ sdtasdt0 ) ) )
& ( B @ aNaturalNumber0 ) )
& ( A
= ( xl @ ( xm @ sdtsldt0 ) ) )
& ( xm
= ( A @ ( xl @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
( ? [B: $i] :
( ( xn
= ( B @ ( xl @ sdtasdt0 ) ) )
& ( ( B @ ( xl @ sdtasdt0 ) @ ( sk1 @ ( xl @ sdtasdt0 ) @ sdtpldt0 ) )
= ( xn @ ( sk1 @ ( xl @ sdtasdt0 ) @ sdtpldt0 ) ) )
& ( B
= ( sk1 @ ( A @ sdtmndt0 ) ) )
& ( ( B @ ( sk1 @ sdtpldt0 ) )
= A )
& ( B @ aNaturalNumber0 ) )
& ( A @ ( sk1 @ sdtlseqdt0 ) )
& ? [B: $i] :
( ( ( B @ ( sk1 @ sdtpldt0 ) )
= A )
& ( B @ aNaturalNumber0 ) )
& ( A
= ( xl @ ( xn @ ( xm @ sdtpldt0 ) @ sdtsldt0 ) ) )
& ( ( xn @ ( xm @ sdtpldt0 ) )
= ( A @ ( xl @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
( ( ( A @ ( sk1 @ sdtpldt0 ) )
= sk2 )
& ( A @ aNaturalNumber0 ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
( ( xn
= ( A @ ( xl @ sdtasdt0 ) ) )
& ( ( A @ ( xl @ sdtasdt0 ) @ ( sk1 @ ( xl @ sdtasdt0 ) @ sdtpldt0 ) )
= ( xn @ ( sk1 @ ( xl @ sdtasdt0 ) @ sdtpldt0 ) ) )
& ( A
= ( sk1 @ ( sk2 @ sdtmndt0 ) ) )
& ( ( A @ ( sk1 @ sdtpldt0 ) )
= sk2 )
& ( A @ aNaturalNumber0 ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
( ( xm
= ( A @ ( xl @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
( ( ( xn @ ( xm @ sdtpldt0 ) )
= ( A @ ( xl @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ) ) ).
thf(27,axiom,
( ( xn @ aNaturalNumber0 )
& ( xm @ aNaturalNumber0 )
& ( xl @ aNaturalNumber0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324) ).
thf(188,plain,
( ( xn @ aNaturalNumber0 )
& ( xm @ aNaturalNumber0 )
& ( xl @ aNaturalNumber0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(189,plain,
( ( xn @ aNaturalNumber0 )
& ( xm @ aNaturalNumber0 )
& ( xl @ aNaturalNumber0 ) ),
inference(cnf,[status(esa)],[188]) ).
thf(192,plain,
xn @ aNaturalNumber0,
inference(cnfConj,[status(thm)],[189]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ aNaturalNumber0 )
=> ( ( A
= ( A @ ( sz00 @ sdtpldt0 ) ) )
& ( ( sz00 @ ( A @ sdtpldt0 ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
thf(143,plain,
! [A: $i] :
( ( A @ aNaturalNumber0 )
=> ( ( A
= ( A @ ( sz00 @ sdtpldt0 ) ) )
& ( ( sz00 @ ( A @ sdtpldt0 ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(144,plain,
! [A: $i] :
( ( ( A
= ( A @ ( sz00 @ sdtpldt0 ) ) )
| ~ ( A @ aNaturalNumber0 ) )
& ( ( ( sz00 @ ( A @ sdtpldt0 ) )
= A )
| ~ ( A @ aNaturalNumber0 ) ) ),
inference(cnf,[status(esa)],[143]) ).
thf(146,plain,
! [A: $i] :
( ( A
= ( A @ ( sz00 @ sdtpldt0 ) ) )
| ~ ( A @ aNaturalNumber0 ) ),
inference(cnfConj,[status(thm)],[144]) ).
thf(148,plain,
! [A: $i] :
( ~ ( A @ aNaturalNumber0 )
| ( ( A @ ( sz00 @ sdtpldt0 ) )
= A ) ),
inference(lifteq,[status(thm)],[146]) ).
thf(9984,plain,
! [A: $i] :
( ( ( xn @ aNaturalNumber0 )
!= ( A @ aNaturalNumber0 ) )
| ~ $true
| ( ( A @ ( sz00 @ sdtpldt0 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[192,148]) ).
thf(9985,plain,
! [A: $i] :
( ( ( xn @ aNaturalNumber0 )
!= ( A @ aNaturalNumber0 ) )
| ( ( A @ ( sz00 @ sdtpldt0 ) )
= A ) ),
inference(simp,[status(thm)],[9984]) ).
thf(9986,plain,
( ( xn @ ( sz00 @ sdtpldt0 ) )
= xn ),
inference(pattern_uni,[status(thm)],[9985:[bind(A,$thf( xn ))]]) ).
thf(31,axiom,
( ( xn @ ( xm @ sdtpldt0 ) @ ( xl @ doDivides0 ) )
& ? [A: $i] :
( ( ( xn @ ( xm @ sdtpldt0 ) )
= ( A @ ( xl @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) )
& ( xm @ ( xl @ doDivides0 ) )
& ? [A: $i] :
( ( xm
= ( A @ ( xl @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324_04) ).
thf(207,plain,
( ( xn @ ( xm @ sdtpldt0 ) @ ( xl @ doDivides0 ) )
& ? [A: $i] :
( ( ( xn @ ( xm @ sdtpldt0 ) )
= ( A @ ( xl @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) )
& ( xm @ ( xl @ doDivides0 ) )
& ? [A: $i] :
( ( xm
= ( A @ ( xl @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(208,plain,
( ( xn @ ( xm @ sdtpldt0 ) @ ( xl @ doDivides0 ) )
& ( ( xn @ ( xm @ sdtpldt0 ) )
= ( sk8 @ ( xl @ sdtasdt0 ) ) )
& ( sk8 @ aNaturalNumber0 )
& ( xm @ ( xl @ doDivides0 ) )
& ( xm
= ( sk7 @ ( xl @ sdtasdt0 ) ) )
& ( sk7 @ aNaturalNumber0 ) ),
inference(cnf,[status(esa)],[207]) ).
thf(213,plain,
( ( xn @ ( xm @ sdtpldt0 ) )
= ( sk8 @ ( xl @ sdtasdt0 ) ) ),
inference(cnfConj,[status(thm)],[208]) ).
thf(215,plain,
( ( sk8 @ ( xl @ sdtasdt0 ) )
= ( xn @ ( xm @ sdtpldt0 ) ) ),
inference(lifteq,[status(thm)],[213]) ).
thf(1,conjecture,
( ( ( xl != sz00 )
=> ? [A: $i] :
( ? [B: $i] :
( ? [C: $i] :
( ( xn
= ( C @ ( xl @ sdtasdt0 ) ) )
& ( ( C @ ( xl @ sdtasdt0 ) @ ( A @ ( xl @ sdtasdt0 ) @ sdtpldt0 ) )
= ( xn @ ( A @ ( xl @ sdtasdt0 ) @ sdtpldt0 ) ) )
& ( C
= ( A @ ( B @ sdtmndt0 ) ) )
& ( ( C @ ( A @ sdtpldt0 ) )
= B )
& ( C @ aNaturalNumber0 ) )
& ( B @ ( A @ sdtlseqdt0 ) )
& ? [C: $i] :
( ( ( C @ ( A @ sdtpldt0 ) )
= B )
& ( C @ aNaturalNumber0 ) )
& ( B
= ( xl @ ( xn @ ( xm @ sdtpldt0 ) @ sdtsldt0 ) ) )
& ( ( xn @ ( xm @ sdtpldt0 ) )
= ( B @ ( xl @ sdtasdt0 ) ) )
& ( B @ aNaturalNumber0 ) )
& ( A
= ( xl @ ( xm @ sdtsldt0 ) ) )
& ( xm
= ( A @ ( xl @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) )
=> ( ( xn @ ( xl @ doDivides0 ) )
| ? [A: $i] :
( ( xn
= ( A @ ( xl @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ( xl != sz00 )
=> ? [A: $i] :
( ? [B: $i] :
( ? [C: $i] :
( ( xn
= ( C @ ( xl @ sdtasdt0 ) ) )
& ( ( C @ ( xl @ sdtasdt0 ) @ ( A @ ( xl @ sdtasdt0 ) @ sdtpldt0 ) )
= ( xn @ ( A @ ( xl @ sdtasdt0 ) @ sdtpldt0 ) ) )
& ( C
= ( A @ ( B @ sdtmndt0 ) ) )
& ( ( C @ ( A @ sdtpldt0 ) )
= B )
& ( C @ aNaturalNumber0 ) )
& ( B @ ( A @ sdtlseqdt0 ) )
& ? [C: $i] :
( ( ( C @ ( A @ sdtpldt0 ) )
= B )
& ( C @ aNaturalNumber0 ) )
& ( B
= ( xl @ ( xn @ ( xm @ sdtpldt0 ) @ sdtsldt0 ) ) )
& ( ( xn @ ( xm @ sdtpldt0 ) )
= ( B @ ( xl @ sdtasdt0 ) ) )
& ( B @ aNaturalNumber0 ) )
& ( A
= ( xl @ ( xm @ sdtsldt0 ) ) )
& ( xm
= ( A @ ( xl @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) )
=> ( ( xn @ ( xl @ doDivides0 ) )
| ? [A: $i] :
( ( xn
= ( A @ ( xl @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(38,plain,
~ ( ( ( xl != sz00 )
=> ? [A: $i] :
( ? [B: $i] :
( ? [C: $i] :
( ( xn
= ( C @ ( xl @ sdtasdt0 ) ) )
& ( ( C @ ( xl @ sdtasdt0 ) @ ( A @ ( xl @ sdtasdt0 ) @ sdtpldt0 ) )
= ( xn @ ( A @ ( xl @ sdtasdt0 ) @ sdtpldt0 ) ) )
& ( C
= ( A @ ( B @ sdtmndt0 ) ) )
& ( ( C @ ( A @ sdtpldt0 ) )
= B )
& ( C @ aNaturalNumber0 ) )
& ( B @ ( A @ sdtlseqdt0 ) )
& ? [C: $i] :
( ( ( C @ ( A @ sdtpldt0 ) )
= B )
& ( C @ aNaturalNumber0 ) )
& ( B
= ( xl @ ( xn @ ( xm @ sdtpldt0 ) @ sdtsldt0 ) ) )
& ( ( xn @ ( xm @ sdtpldt0 ) )
= ( B @ ( xl @ sdtasdt0 ) ) )
& ( B @ aNaturalNumber0 ) )
& ( A
= ( xl @ ( xm @ sdtsldt0 ) ) )
& ( xm
= ( A @ ( xl @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) )
=> ( ( xn @ ( xl @ doDivides0 ) )
| ? [A: $i] :
( ( xn
= ( A @ ( xl @ sdtasdt0 ) ) )
& ( A @ aNaturalNumber0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(39,plain,
! [A: $i] :
( ~ ( xn @ ( xl @ doDivides0 ) )
& ( ( xn
!= ( A @ ( xl @ sdtasdt0 ) ) )
| ~ ( A @ aNaturalNumber0 ) )
& ( ( xn
= ( sk4 @ ( xl @ sdtasdt0 ) ) )
| ( xl = sz00 ) )
& ( ( ( sk4 @ ( xl @ sdtasdt0 ) @ ( sk1 @ ( xl @ sdtasdt0 ) @ sdtpldt0 ) )
= ( xn @ ( sk1 @ ( xl @ sdtasdt0 ) @ sdtpldt0 ) ) )
| ( xl = sz00 ) )
& ( ( sk4
= ( sk1 @ ( sk2 @ sdtmndt0 ) ) )
| ( xl = sz00 ) )
& ( ( ( sk4 @ ( sk1 @ sdtpldt0 ) )
= sk2 )
| ( xl = sz00 ) )
& ( ( sk4 @ aNaturalNumber0 )
| ( xl = sz00 ) )
& ( ( sk2 @ ( sk1 @ sdtlseqdt0 ) )
| ( xl = sz00 ) )
& ( ( ( sk3 @ ( sk1 @ sdtpldt0 ) )
= sk2 )
| ( xl = sz00 ) )
& ( ( sk3 @ aNaturalNumber0 )
| ( xl = sz00 ) )
& ( ( sk2
= ( xl @ ( xn @ ( xm @ sdtpldt0 ) @ sdtsldt0 ) ) )
| ( xl = sz00 ) )
& ( ( ( xn @ ( xm @ sdtpldt0 ) )
= ( sk2 @ ( xl @ sdtasdt0 ) ) )
| ( xl = sz00 ) )
& ( ( sk2 @ aNaturalNumber0 )
| ( xl = sz00 ) )
& ( ( sk1
= ( xl @ ( xm @ sdtsldt0 ) ) )
| ( xl = sz00 ) )
& ( ( xm
= ( sk1 @ ( xl @ sdtasdt0 ) ) )
| ( xl = sz00 ) )
& ( ( sk1 @ aNaturalNumber0 )
| ( xl = sz00 ) ) ),
inference(cnf,[status(esa)],[38]) ).
thf(49,plain,
( ( sk4 @ aNaturalNumber0 )
| ( xl = sz00 ) ),
inference(cnfConj,[status(thm)],[39]) ).
thf(68,plain,
( ( sk4 @ aNaturalNumber0 )
| ( xl = sz00 ) ),
inference(lifteq,[status(thm)],[49]) ).
thf(42,plain,
( ( xn
= ( sk4 @ ( xl @ sdtasdt0 ) ) )
| ( xl = sz00 ) ),
inference(cnfConj,[status(thm)],[39]) ).
thf(56,plain,
( ( ( sk4 @ ( xl @ sdtasdt0 ) )
= xn )
| ( xl = sz00 ) ),
inference(lifteq,[status(thm)],[42]) ).
thf(52,plain,
! [A: $i] :
( ( xn
!= ( A @ ( xl @ sdtasdt0 ) ) )
| ~ ( A @ aNaturalNumber0 ) ),
inference(cnfConj,[status(thm)],[39]) ).
thf(57,plain,
! [A: $i] :
( ~ ( A @ aNaturalNumber0 )
| ( ( A @ ( xl @ sdtasdt0 ) )
!= xn ) ),
inference(lifteq,[status(thm)],[52]) ).
thf(281,plain,
! [A: $i] :
( ( ( sk4 @ ( xl @ sdtasdt0 ) )
!= ( A @ ( xl @ sdtasdt0 ) ) )
| ~ ( A @ aNaturalNumber0 )
| ( xn != xn )
| ( xl = sz00 ) ),
inference(paramod_ordered,[status(thm)],[56,57]) ).
thf(282,plain,
! [A: $i] :
( ( ( sk4 @ ( xl @ sdtasdt0 ) )
!= ( A @ ( xl @ sdtasdt0 ) ) )
| ~ ( A @ aNaturalNumber0 )
| ( xl = sz00 ) ),
inference(simp,[status(thm)],[281]) ).
thf(283,plain,
( ~ ( sk4 @ aNaturalNumber0 )
| ( xl = sz00 ) ),
inference(pattern_uni,[status(thm)],[282:[bind(A,$thf( sk4 ))]]) ).
thf(562,plain,
( ( ( sk4 @ aNaturalNumber0 )
!= ( sk4 @ aNaturalNumber0 ) )
| ~ $true
| ( xl = sz00 )
| ( xl = sz00 ) ),
inference(paramod_ordered,[status(thm)],[68,283]) ).
thf(563,plain,
( ( ( sk4 @ aNaturalNumber0 )
!= ( sk4 @ aNaturalNumber0 ) )
| ( xl = sz00 ) ),
inference(simp,[status(thm)],[562]) ).
thf(564,plain,
xl = sz00,
inference(pattern_uni,[status(thm)],[563:[]]) ).
thf(665,plain,
( ( sk8 @ ( sz00 @ sdtasdt0 ) )
= ( xn @ ( xm @ sdtpldt0 ) ) ),
inference(rewrite,[status(thm)],[215,564]) ).
thf(209,plain,
sk7 @ aNaturalNumber0,
inference(cnfConj,[status(thm)],[208]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ aNaturalNumber0 )
=> ( ( sz00
= ( A @ ( sz00 @ sdtasdt0 ) ) )
& ( ( sz00 @ ( A @ sdtasdt0 ) )
= sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
thf(71,plain,
! [A: $i] :
( ( A @ aNaturalNumber0 )
=> ( ( sz00
= ( A @ ( sz00 @ sdtasdt0 ) ) )
& ( ( sz00 @ ( A @ sdtasdt0 ) )
= sz00 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(72,plain,
! [A: $i] :
( ( ( sz00
= ( A @ ( sz00 @ sdtasdt0 ) ) )
| ~ ( A @ aNaturalNumber0 ) )
& ( ( ( sz00 @ ( A @ sdtasdt0 ) )
= sz00 )
| ~ ( A @ aNaturalNumber0 ) ) ),
inference(cnf,[status(esa)],[71]) ).
thf(74,plain,
! [A: $i] :
( ( sz00
= ( A @ ( sz00 @ sdtasdt0 ) ) )
| ~ ( A @ aNaturalNumber0 ) ),
inference(cnfConj,[status(thm)],[72]) ).
thf(76,plain,
! [A: $i] :
( ~ ( A @ aNaturalNumber0 )
| ( ( A @ ( sz00 @ sdtasdt0 ) )
= sz00 ) ),
inference(lifteq,[status(thm)],[74]) ).
thf(886,plain,
! [A: $i] :
( ( ( sk7 @ aNaturalNumber0 )
!= ( A @ aNaturalNumber0 ) )
| ~ $true
| ( ( A @ ( sz00 @ sdtasdt0 ) )
= sz00 ) ),
inference(paramod_ordered,[status(thm)],[209,76]) ).
thf(887,plain,
! [A: $i] :
( ( ( sk7 @ aNaturalNumber0 )
!= ( A @ aNaturalNumber0 ) )
| ( ( A @ ( sz00 @ sdtasdt0 ) )
= sz00 ) ),
inference(simp,[status(thm)],[886]) ).
thf(888,plain,
( ( sk7 @ ( sz00 @ sdtasdt0 ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[887:[bind(A,$thf( sk7 ))]]) ).
thf(210,plain,
( xm
= ( sk7 @ ( xl @ sdtasdt0 ) ) ),
inference(cnfConj,[status(thm)],[208]) ).
thf(216,plain,
( ( sk7 @ ( xl @ sdtasdt0 ) )
= xm ),
inference(lifteq,[status(thm)],[210]) ).
thf(621,plain,
( ( sk7 @ ( sz00 @ sdtasdt0 ) )
= xm ),
inference(rewrite,[status(thm)],[216,564]) ).
thf(1303,plain,
xm = sz00,
inference(rewrite,[status(thm)],[888,621]) ).
thf(1306,plain,
( ( sk8 @ ( sz00 @ sdtasdt0 ) )
= ( xn @ ( sz00 @ sdtpldt0 ) ) ),
inference(rewrite,[status(thm)],[665,1303]) ).
thf(214,plain,
sk8 @ aNaturalNumber0,
inference(cnfConj,[status(thm)],[208]) ).
thf(921,plain,
! [A: $i] :
( ( ( sk8 @ aNaturalNumber0 )
!= ( A @ aNaturalNumber0 ) )
| ~ $true
| ( ( A @ ( sz00 @ sdtasdt0 ) )
= sz00 ) ),
inference(paramod_ordered,[status(thm)],[214,76]) ).
thf(922,plain,
! [A: $i] :
( ( ( sk8 @ aNaturalNumber0 )
!= ( A @ aNaturalNumber0 ) )
| ( ( A @ ( sz00 @ sdtasdt0 ) )
= sz00 ) ),
inference(simp,[status(thm)],[921]) ).
thf(923,plain,
( ( sk8 @ ( sz00 @ sdtasdt0 ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[922:[bind(A,$thf( sk8 ))]]) ).
thf(1516,plain,
( ( xn @ ( sz00 @ sdtpldt0 ) )
= sz00 ),
inference(rewrite,[status(thm)],[1306,923]) ).
thf(10123,plain,
xn = sz00,
inference(rewrite,[status(thm)],[9986,1516]) ).
thf(73,plain,
! [A: $i] :
( ( ( sz00 @ ( A @ sdtasdt0 ) )
= sz00 )
| ~ ( A @ aNaturalNumber0 ) ),
inference(cnfConj,[status(thm)],[72]) ).
thf(75,plain,
! [A: $i] :
( ~ ( A @ aNaturalNumber0 )
| ( ( sz00 @ ( A @ sdtasdt0 ) )
= sz00 ) ),
inference(lifteq,[status(thm)],[73]) ).
thf(740,plain,
! [A: $i] :
( ( ( xn @ aNaturalNumber0 )
!= ( A @ aNaturalNumber0 ) )
| ~ $true
| ( ( sz00 @ ( A @ sdtasdt0 ) )
= sz00 ) ),
inference(paramod_ordered,[status(thm)],[192,75]) ).
thf(741,plain,
! [A: $i] :
( ( ( xn @ aNaturalNumber0 )
!= ( A @ aNaturalNumber0 ) )
| ( ( sz00 @ ( A @ sdtasdt0 ) )
= sz00 ) ),
inference(simp,[status(thm)],[740]) ).
thf(742,plain,
( ( sz00 @ ( xn @ sdtasdt0 ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[741:[bind(A,$thf( xn ))]]) ).
thf(254,plain,
! [A: $i] :
( ( ( xn @ aNaturalNumber0 )
!= ( A @ aNaturalNumber0 ) )
| ~ $true
| ( ( A @ ( xl @ sdtasdt0 ) )
!= xn ) ),
inference(paramod_ordered,[status(thm)],[192,57]) ).
thf(255,plain,
! [A: $i] :
( ( ( xn @ aNaturalNumber0 )
!= ( A @ aNaturalNumber0 ) )
| ( ( A @ ( xl @ sdtasdt0 ) )
!= xn ) ),
inference(simp,[status(thm)],[254]) ).
thf(256,plain,
( ( xn @ ( xl @ sdtasdt0 ) )
!= xn ),
inference(pattern_uni,[status(thm)],[255:[bind(A,$thf( xn ))]]) ).
thf(623,plain,
( ( xn @ ( sz00 @ sdtasdt0 ) )
!= xn ),
inference(rewrite,[status(thm)],[256,564]) ).
thf(786,plain,
( ( ( sz00 @ ( xn @ sdtasdt0 ) )
!= ( xn @ ( sz00 @ sdtasdt0 ) ) )
| ( xn != sz00 ) ),
inference(paramod_ordered,[status(thm)],[742,623]) ).
thf(800,plain,
( ( xn != sz00 )
| ( xn != sz00 )
| ( xn != sz00 ) ),
inference(simp,[status(thm)],[786]) ).
thf(802,plain,
xn != sz00,
inference(simp,[status(thm)],[800]) ).
thf(10124,plain,
$false,
inference(simplifyReflect,[status(thm)],[10123,802]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM476+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.22/0.48 % Computer : n014.cluster.edu
% 0.22/0.48 % Model : x86_64 x86_64
% 0.22/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.48 % Memory : 8046.5625MB
% 0.22/0.48 % OS : Linux 6.8.0-71-generic
% 0.22/0.48 % CPULimit : 300
% 0.22/0.48 % WCLimit : 300
% 0.22/0.48 % DateTime : Sat Sep 26 02:54:32 UTC 2026
% 0.22/0.48 % CPUTime :
% 0.22/0.48 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
% 1.32/1.22 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.88/1.54 % [INFO] Parsing done (314ms).
% 1.88/1.57 % [INFO] Running in sequential loop mode.
% 3.19/2.16 % [INFO] eprover registered as external prover.
% 3.19/2.17 % [INFO] Scanning for conjecture ...
% 3.28/2.29 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.46/2.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.46/2.31 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.46/2.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.46/2.39 % [INFO] Found a conjecture (or negated_conjecture) and 35 axioms. Running axiom selection ...
% 3.93/2.52 % [INFO] Axiom selection finished. Selected 35 axioms (removed 0 axioms).
% 3.93/2.54 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.93/2.55 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.93/2.56 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.93/2.57 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.14/2.60 % [INFO] Problem is first-order (TPTP FOF).
% 4.14/2.62 % [INFO] Type checking passed.
% 4.14/2.63 % [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 ...
% 46.46/12.55 % [INFO] Killing All external provers ...
% 46.46/12.56 % Time passed: 11870ms (effective reasoning time: 10976ms)
% 46.46/12.56 % 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)>
% 46.46/12.56 % Axioms used in derivation (4): m__1324, m_AddZero, m__1324_04, m_MulZero
% 46.46/12.56 % No. of inferences in proof: 67
% 46.46/12.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 11870 ms resp. 10976 ms w/o parsing
% 46.92/12.64 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 46.92/12.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------