TSTP Solution File: NUM471+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM471+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:40:43 EDT 2023
% Result : Theorem 167.36s 115.93s
% Output : Refutation 167.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 54
% Syntax : Number of formulae : 144 ( 35 unt; 15 typ; 0 def)
% Number of atoms : 557 ( 155 equ; 0 cnn)
% Maximal formula atoms : 23 ( 4 avg)
% Number of connectives : 1480 ( 188 ~; 164 |; 133 &; 888 @)
% ( 4 <=>; 103 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 9 con; 0-2 aty)
% Number of variables : 225 ( 0 ^; 219 !; 6 ?; 225 :)
% Comments :
%------------------------------------------------------------------------------
thf(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
thf(sdtlseqdt0_type,type,
sdtlseqdt0: $i > $i > $o ).
thf(sdtpldt0_type,type,
sdtpldt0: $i > $i > $i ).
thf(sdtmndt0_type,type,
sdtmndt0: $i > $i > $i ).
thf(doDivides0_type,type,
doDivides0: $i > $i > $o ).
thf(sdtasdt0_type,type,
sdtasdt0: $i > $i > $i ).
thf(sz00_type,type,
sz00: $i ).
thf(sdtsldt0_type,type,
sdtsldt0: $i > $i > $i ).
thf(xp_type,type,
xp: $i ).
thf(xq_type,type,
xq: $i ).
thf(xl_type,type,
xl: $i ).
thf(xm_type,type,
xm: $i ).
thf(xn_type,type,
xn: $i ).
thf(sz10_type,type,
sz10: $i ).
thf(iLess0_type,type,
iLess0: $i > $i > $o ).
thf(9,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
thf(69,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(36,axiom,
( xq
= ( sdtsldt0 @ ( sdtpldt0 @ xm @ xn ) @ xl ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1379) ).
thf(178,plain,
( xq
= ( sdtsldt0 @ ( sdtpldt0 @ xm @ xn ) @ xl ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(179,plain,
( ( sdtsldt0 @ ( sdtpldt0 @ xm @ xn ) @ xl )
= xq ),
inference(lifteq,[status(thm)],[178]) ).
thf(32,axiom,
( xp
= ( sdtsldt0 @ xm @ xl ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1360) ).
thf(156,plain,
( xp
= ( sdtsldt0 @ xm @ xl ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(157,plain,
( ( sdtsldt0 @ xm @ xl )
= xp ),
inference(lifteq,[status(thm)],[156]) ).
thf(1160,plain,
( ( xq = xp )
| ( ( sdtsldt0 @ ( sdtpldt0 @ xm @ xn ) @ xl )
!= ( sdtsldt0 @ xm @ xl ) ) ),
inference(paramod_ordered,[status(thm)],[179,157]) ).
thf(1162,plain,
( ( xq = xp )
| ( ( sdtpldt0 @ xm @ xn )
!= xm )
| ( xl != xl ) ),
inference(simp,[status(thm)],[1160]) ).
thf(1164,plain,
( ( xq = xp )
| ( ( sdtpldt0 @ xm @ xn )
!= xm ) ),
inference(simp,[status(thm)],[1162]) ).
thf(18,axiom,
( ( aNaturalNumber0 @ sz10 )
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
thf(102,plain,
( ( aNaturalNumber0 @ sz10 )
& ( sz10 != sz00 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(104,plain,
aNaturalNumber0 @ sz10,
inference(cnf,[status(esa)],[102]) ).
thf(3,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
thf(42,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(44,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ),
inference(cnf,[status(esa)],[42]) ).
thf(46,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[44]) ).
thf(428,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ sz10 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[104,46]) ).
thf(429,plain,
( ( sdtasdt0 @ sz00 @ sz10 )
= sz00 ),
inference(pattern_uni,[status(thm)],[428:[bind(A,$thf( sz10 ))]]) ).
thf(103,plain,
sz10 != sz00,
inference(cnf,[status(esa)],[102]) ).
thf(105,plain,
sz10 != sz00,
inference(lifteq,[status(thm)],[103]) ).
thf(15,axiom,
( ( aNaturalNumber0 @ xl )
& ( aNaturalNumber0 @ xm )
& ( aNaturalNumber0 @ xn ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324) ).
thf(92,plain,
( ( aNaturalNumber0 @ xl )
& ( aNaturalNumber0 @ xm )
& ( aNaturalNumber0 @ xn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(94,plain,
aNaturalNumber0 @ xm,
inference(cnf,[status(esa)],[92]) ).
thf(43,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( sdtasdt0 @ A @ sz00 )
= sz00 ) ),
inference(cnf,[status(esa)],[42]) ).
thf(45,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[43]) ).
thf(207,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ xm )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[94,45]) ).
thf(208,plain,
( ( sdtasdt0 @ xm @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[207:[bind(A,$thf( xm ))]]) ).
thf(95,plain,
aNaturalNumber0 @ xl,
inference(cnf,[status(esa)],[92]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( A != sz00 )
=> ( sdtlseqdt0 @ B @ ( sdtasdt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
thf(175,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( A != sz00 )
=> ( sdtlseqdt0 @ B @ ( sdtasdt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( A != sz00 )
& ( doDivides0 @ A @ B ) )
=> ! [C: $i] :
( ( C
= ( sdtsldt0 @ B @ A ) )
<=> ( ( aNaturalNumber0 @ C )
& ( B
= ( sdtasdt0 @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
thf(58,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( A != sz00 )
& ( doDivides0 @ A @ B ) )
=> ! [C: $i] :
( ( ( C
= ( sdtsldt0 @ B @ A ) )
=> ( ( aNaturalNumber0 @ C )
& ( B
= ( sdtasdt0 @ A @ C ) ) ) )
& ( ( ( aNaturalNumber0 @ C )
& ( B
= ( sdtasdt0 @ A @ C ) ) )
=> ( C
= ( sdtsldt0 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtpldt0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
thf(90,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtpldt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(22,axiom,
( ( doDivides0 @ xl @ xm )
& ( doDivides0 @ xl @ ( sdtpldt0 @ xm @ xn ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324_04) ).
thf(115,plain,
( ( doDivides0 @ xl @ xm )
& ( doDivides0 @ xl @ ( sdtpldt0 @ xm @ xn ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(16,axiom,
aNaturalNumber0 @ sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
thf(96,plain,
aNaturalNumber0 @ sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(201,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ sz00 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[96,45]) ).
thf(202,plain,
( ( sdtasdt0 @ sz00 @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[201:[bind(A,$thf( sz00 ))]]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( A != sz00 )
& ( B != C )
& ( sdtlseqdt0 @ B @ C ) )
=> ( ( ( sdtasdt0 @ A @ B )
!= ( sdtasdt0 @ A @ C ) )
& ( sdtlseqdt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) )
& ( ( sdtasdt0 @ B @ A )
!= ( sdtasdt0 @ C @ A ) )
& ( sdtlseqdt0 @ ( sdtasdt0 @ B @ A ) @ ( sdtasdt0 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul) ).
thf(185,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( A != sz00 )
& ( B != C )
& ( sdtlseqdt0 @ B @ C ) )
=> ( ( ( sdtasdt0 @ A @ B )
!= ( sdtasdt0 @ A @ C ) )
& ( sdtlseqdt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) )
& ( ( sdtasdt0 @ B @ A )
!= ( sdtasdt0 @ C @ A ) )
& ( sdtlseqdt0 @ ( sdtasdt0 @ B @ A ) @ ( sdtasdt0 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C )
= ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
thf(52,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C )
= ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ A @ C ) )
| ( ( sdtpldt0 @ B @ A )
= ( sdtpldt0 @ C @ A ) ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddCanc) ).
thf(110,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ A @ C ) )
| ( ( sdtpldt0 @ B @ A )
= ( sdtpldt0 @ C @ A ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtasdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
thf(125,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtasdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(93,plain,
aNaturalNumber0 @ xn,
inference(cnf,[status(esa)],[92]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
=> ! [C: $i] :
( ( C
= ( sdtmndt0 @ B @ A ) )
<=> ( ( aNaturalNumber0 @ C )
& ( ( sdtpldt0 @ A @ C )
= B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
thf(164,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
=> ! [C: $i] :
( ( ( C
= ( sdtmndt0 @ B @ A ) )
=> ( ( aNaturalNumber0 @ C )
& ( ( sdtpldt0 @ A @ C )
= B ) ) )
& ( ( ( aNaturalNumber0 @ C )
& ( ( sdtpldt0 @ A @ C )
= B ) )
=> ( C
= ( sdtmndt0 @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
thf(106,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ C ) )
=> ( sdtlseqdt0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).
thf(147,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ C ) )
=> ( sdtlseqdt0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(116,plain,
doDivides0 @ xl @ ( sdtpldt0 @ xm @ xn ),
inference(cnf,[status(esa)],[115]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ B @ C ) @ A )
= ( sdtpldt0 @ ( sdtasdt0 @ B @ A ) @ ( sdtasdt0 @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
thf(74,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ B @ C ) @ A )
= ( sdtpldt0 @ ( sdtasdt0 @ B @ A ) @ ( sdtasdt0 @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(205,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ sz10 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[104,45]) ).
thf(206,plain,
( ( sdtasdt0 @ sz10 @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[205:[bind(A,$thf( sz10 ))]]) ).
thf(117,plain,
doDivides0 @ xl @ xm,
inference(cnf,[status(esa)],[115]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( doDivides0 @ A @ B )
& ( doDivides0 @ B @ C ) )
=> ( doDivides0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivTrans) ).
thf(50,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( doDivides0 @ A @ B )
& ( doDivides0 @ B @ C ) )
=> ( doDivides0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ~ ( doDivides0 @ A @ B )
| ~ ( doDivides0 @ B @ C )
| ( doDivides0 @ A @ C ) ),
inference(cnf,[status(esa)],[50]) ).
thf(255,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ~ ( doDivides0 @ A @ B )
| ~ ( doDivides0 @ B @ C )
| ~ ( aNaturalNumber0 @ D )
| ~ ( aNaturalNumber0 @ E )
| ~ ( aNaturalNumber0 @ F )
| ~ ( doDivides0 @ E @ F )
| ( doDivides0 @ D @ F )
| ( ( doDivides0 @ A @ C )
!= ( doDivides0 @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[51,51]) ).
thf(256,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ~ ( doDivides0 @ A @ B )
| ~ ( doDivides0 @ B @ C )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ C )
| ~ ( aNaturalNumber0 @ D )
| ~ ( doDivides0 @ C @ D )
| ( doDivides0 @ A @ D ) ),
inference(pattern_uni,[status(thm)],[255:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(267,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ~ ( doDivides0 @ A @ B )
| ~ ( doDivides0 @ B @ C )
| ~ ( aNaturalNumber0 @ D )
| ~ ( doDivides0 @ C @ D )
| ( doDivides0 @ A @ D ) ),
inference(simp,[status(thm)],[256]) ).
thf(303,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ~ ( doDivides0 @ A @ B )
| ~ ( doDivides0 @ B @ C )
| ~ ( aNaturalNumber0 @ D )
| ~ ( doDivides0 @ C @ D )
| ~ ( aNaturalNumber0 @ E )
| ~ ( aNaturalNumber0 @ F )
| ~ ( aNaturalNumber0 @ G )
| ~ ( doDivides0 @ F @ G )
| ~ ( aNaturalNumber0 @ H )
| ~ ( doDivides0 @ G @ H )
| ( doDivides0 @ E @ H )
| ( ( doDivides0 @ A @ D )
!= ( doDivides0 @ E @ F ) ) ),
inference(paramod_ordered,[status(thm)],[267,267]) ).
thf(304,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ~ ( doDivides0 @ A @ B )
| ~ ( doDivides0 @ B @ C )
| ~ ( aNaturalNumber0 @ D )
| ~ ( doDivides0 @ C @ D )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ D )
| ~ ( aNaturalNumber0 @ E )
| ~ ( doDivides0 @ D @ E )
| ~ ( aNaturalNumber0 @ F )
| ~ ( doDivides0 @ E @ F )
| ( doDivides0 @ A @ F ) ),
inference(pattern_uni,[status(thm)],[303:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( D ))]]) ).
thf(370,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ~ ( doDivides0 @ A @ B )
| ~ ( doDivides0 @ B @ C )
| ~ ( aNaturalNumber0 @ D )
| ~ ( doDivides0 @ C @ D )
| ~ ( aNaturalNumber0 @ E )
| ~ ( doDivides0 @ D @ E )
| ~ ( aNaturalNumber0 @ F )
| ~ ( doDivides0 @ E @ F )
| ( doDivides0 @ A @ F ) ),
inference(simp,[status(thm)],[304]) ).
thf(548,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ~ ( doDivides0 @ A @ B )
| ~ ( doDivides0 @ B @ C )
| ~ ( aNaturalNumber0 @ D )
| ~ ( doDivides0 @ C @ D )
| ~ ( aNaturalNumber0 @ E )
| ~ ( doDivides0 @ D @ E )
| ~ ( aNaturalNumber0 @ F )
| ~ ( doDivides0 @ E @ F )
| ~ ( aNaturalNumber0 @ G )
| ~ ( aNaturalNumber0 @ H )
| ~ ( aNaturalNumber0 @ I )
| ~ ( doDivides0 @ H @ I )
| ~ ( aNaturalNumber0 @ J )
| ~ ( doDivides0 @ I @ J )
| ~ ( aNaturalNumber0 @ K )
| ~ ( doDivides0 @ J @ K )
| ~ ( aNaturalNumber0 @ L )
| ~ ( doDivides0 @ K @ L )
| ( doDivides0 @ G @ L )
| ( ( doDivides0 @ A @ F )
!= ( doDivides0 @ G @ H ) ) ),
inference(paramod_ordered,[status(thm)],[370,370]) ).
thf(549,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ~ ( doDivides0 @ A @ B )
| ~ ( doDivides0 @ B @ C )
| ~ ( aNaturalNumber0 @ D )
| ~ ( doDivides0 @ C @ D )
| ~ ( aNaturalNumber0 @ E )
| ~ ( doDivides0 @ D @ E )
| ~ ( aNaturalNumber0 @ F )
| ~ ( doDivides0 @ E @ F )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ F )
| ~ ( aNaturalNumber0 @ G )
| ~ ( doDivides0 @ F @ G )
| ~ ( aNaturalNumber0 @ H )
| ~ ( doDivides0 @ G @ H )
| ~ ( aNaturalNumber0 @ I )
| ~ ( doDivides0 @ H @ I )
| ~ ( aNaturalNumber0 @ J )
| ~ ( doDivides0 @ I @ J )
| ( doDivides0 @ A @ J ) ),
inference(pattern_uni,[status(thm)],[548:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( A )),bind(H,$thf( F ))]]) ).
thf(678,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ~ ( aNaturalNumber0 @ C )
| ~ ( doDivides0 @ A @ B )
| ~ ( doDivides0 @ B @ C )
| ~ ( aNaturalNumber0 @ D )
| ~ ( doDivides0 @ C @ D )
| ~ ( aNaturalNumber0 @ E )
| ~ ( doDivides0 @ D @ E )
| ~ ( aNaturalNumber0 @ F )
| ~ ( doDivides0 @ E @ F )
| ~ ( aNaturalNumber0 @ G )
| ~ ( doDivides0 @ F @ G )
| ~ ( aNaturalNumber0 @ H )
| ~ ( doDivides0 @ G @ H )
| ~ ( aNaturalNumber0 @ I )
| ~ ( doDivides0 @ H @ I )
| ~ ( aNaturalNumber0 @ J )
| ~ ( doDivides0 @ I @ J )
| ( doDivides0 @ A @ J ) ),
inference(simp,[status(thm)],[549]) ).
thf(434,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ xn )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[93,46]) ).
thf(435,plain,
( ( sdtasdt0 @ sz00 @ xn )
= sz00 ),
inference(pattern_uni,[status(thm)],[434:[bind(A,$thf( xn ))]]) ).
thf(17,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( A != sz00 )
=> ! [B: $i,C: $i] :
( ( ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ A @ C ) )
| ( ( sdtasdt0 @ B @ A )
= ( sdtasdt0 @ C @ A ) ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
thf(97,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( A != sz00 )
=> ! [B: $i,C: $i] :
( ( ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ A @ C ) )
| ( ( sdtasdt0 @ B @ A )
= ( sdtasdt0 @ C @ A ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( iLess0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).
thf(109,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(26,axiom,
xl != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1347) ).
thf(127,plain,
xl != sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(128,plain,
xl != sz00,
inference(polarity_switch,[status(thm)],[127]) ).
thf(129,plain,
xl != sz00,
inference(lifteq,[status(thm)],[128]) ).
thf(1,conjecture,
sdtlseqdt0 @ xp @ xq,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( sdtlseqdt0 @ xp @ xq ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(41,plain,
~ ( sdtlseqdt0 @ xp @ xq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( A != B )
& ( sdtlseqdt0 @ A @ B ) )
=> ( iLess0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH_03) ).
thf(180,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( A != B )
& ( sdtlseqdt0 @ A @ B ) )
=> ( iLess0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
<=> ? [C: $i] :
( ( aNaturalNumber0 @ C )
& ( ( sdtpldt0 @ A @ C )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
thf(149,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
=> ? [C: $i] :
( ( aNaturalNumber0 @ C )
& ( ( sdtpldt0 @ A @ C )
= B ) ) )
& ( ? [C: $i] :
( ( aNaturalNumber0 @ C )
& ( ( sdtpldt0 @ A @ C )
= B ) )
=> ( sdtlseqdt0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(23,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
thf(118,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(203,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ xl )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[95,45]) ).
thf(204,plain,
( ( sdtasdt0 @ xl @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[203:[bind(A,$thf( xl ))]]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
thf(144,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
thf(47,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
inference(cnf,[status(esa)],[47]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(lifteq,[status(thm)],[48]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( sdtpldt0 @ A @ B )
= sz00 )
=> ( ( A = sz00 )
& ( B = sz00 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroAdd) ).
thf(130,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( sdtpldt0 @ A @ B )
= sz00 )
=> ( ( A = sz00 )
& ( B = sz00 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( A != B )
& ( sdtlseqdt0 @ A @ B ) )
=> ! [C: $i] :
( ( aNaturalNumber0 @ C )
=> ( ( ( sdtpldt0 @ C @ A )
!= ( sdtpldt0 @ C @ B ) )
& ( sdtlseqdt0 @ ( sdtpldt0 @ C @ A ) @ ( sdtpldt0 @ C @ B ) )
& ( ( sdtpldt0 @ A @ C )
!= ( sdtpldt0 @ B @ C ) )
& ( sdtlseqdt0 @ ( sdtpldt0 @ A @ C ) @ ( sdtpldt0 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonAdd) ).
thf(135,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( A != B )
& ( sdtlseqdt0 @ A @ B ) )
=> ! [C: $i] :
( ( aNaturalNumber0 @ C )
=> ( ( ( sdtpldt0 @ C @ A )
!= ( sdtpldt0 @ C @ B ) )
& ( sdtlseqdt0 @ ( sdtpldt0 @ C @ A ) @ ( sdtpldt0 @ C @ B ) )
& ( ( sdtpldt0 @ A @ C )
!= ( sdtpldt0 @ B @ C ) )
& ( sdtlseqdt0 @ ( sdtpldt0 @ A @ C ) @ ( sdtpldt0 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(430,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ xm )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[94,46]) ).
thf(431,plain,
( ( sdtasdt0 @ sz00 @ xm )
= sz00 ),
inference(pattern_uni,[status(thm)],[430:[bind(A,$thf( xm ))]]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( doDivides0 @ A @ B )
<=> ? [C: $i] :
( ( aNaturalNumber0 @ C )
& ( B
= ( sdtasdt0 @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
thf(80,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( doDivides0 @ A @ B )
=> ? [C: $i] :
( ( aNaturalNumber0 @ C )
& ( B
= ( sdtasdt0 @ A @ C ) ) ) )
& ( ? [C: $i] :
( ( aNaturalNumber0 @ C )
& ( B
= ( sdtasdt0 @ A @ C ) ) )
=> ( doDivides0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( doDivides0 @ A @ B )
& ( doDivides0 @ A @ C ) )
=> ( doDivides0 @ A @ ( sdtpldt0 @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivSum) ).
thf(123,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( doDivides0 @ A @ B )
& ( doDivides0 @ A @ C ) )
=> ( doDivides0 @ A @ ( sdtpldt0 @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
| ( ( B != A )
& ( sdtlseqdt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
thf(194,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
| ( ( B != A )
& ( sdtlseqdt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
thf(87,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(33,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( A = sz00 )
| ( A = sz10 )
| ( ( sz10 != A )
& ( sdtlseqdt0 @ sz10 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLENTr) ).
thf(158,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( A = sz00 )
| ( A = sz10 )
| ( ( sz10 != A )
& ( sdtlseqdt0 @ sz10 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( sdtasdt0 @ A @ B )
= sz00 )
=> ( ( A = sz00 )
| ( B = sz00 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroMul) ).
thf(55,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( sdtasdt0 @ A @ B )
= sz00 )
=> ( ( A = sz00 )
| ( B = sz00 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(38,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERefl) ).
thf(183,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(11,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatSort) ).
thf(79,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(426,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ( ( aNaturalNumber0 @ xl )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[95,46]) ).
thf(427,plain,
( ( sdtasdt0 @ sz00 @ xl )
= sz00 ),
inference(pattern_uni,[status(thm)],[426:[bind(A,$thf( xl ))]]) ).
thf(199,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ( ( aNaturalNumber0 @ xn )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[93,45]) ).
thf(200,plain,
( ( sdtasdt0 @ xn @ sz00 )
= sz00 ),
inference(pattern_uni,[status(thm)],[199:[bind(A,$thf( xn ))]]) ).
thf(5363,plain,
$false,
inference(cvc4,[status(thm)],[69,1164,429,156,105,208,95,175,58,90,115,202,185,42,52,110,125,157,46,93,164,179,106,147,116,74,206,117,678,102,92,435,97,109,96,129,41,45,180,149,118,204,144,49,130,135,267,431,80,123,194,50,370,127,87,104,158,55,51,183,79,94,427,47,200,178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM471+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n015.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 17:09:08 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.99/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.36/1.01 % [INFO] Parsing done (143ms).
% 1.36/1.02 % [INFO] Running in sequential loop mode.
% 1.79/1.23 % [INFO] eprover registered as external prover.
% 1.79/1.23 % [INFO] cvc4 registered as external prover.
% 1.95/1.23 % [INFO] Scanning for conjecture ...
% 2.04/1.28 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.29 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.29 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.31 % [INFO] Found a conjecture and 38 axioms. Running axiom selection ...
% 2.38/1.36 % [INFO] Axiom selection finished. Selected 38 axioms (removed 0 axioms).
% 2.38/1.37 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.38/1.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.38/1.40 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.38/1.41 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.38/1.41 % [INFO] Problem is first-order (TPTP FOF).
% 2.38/1.42 % [INFO] Type checking passed.
% 2.38/1.42 % [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 ...
% 167.36/115.93 % External prover 'cvc4' found a proof!
% 167.36/115.93 % [INFO] Killing All external provers ...
% 167.36/115.93 % Time passed: 115395ms (effective reasoning time: 114913ms)
% 167.36/115.93 % 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)>
% 167.36/115.93 % Axioms used in derivation (38): mSortsC, mAddComm, m_MulUnit, m_MulZero, mZeroMul, mZeroAdd, mLENTr, mMonMul, mIH_03, mDefQuot, m__1360, mAMDistr, mLETotal, mLEAsym, mAddCanc, m__1324_04, m__1347, mDivSum, mDivTrans, mSortsC_01, mMulCanc, mLETran, mDefDiff, mMonMul2, mAddAsso, mIH, mMulAsso, mDefDiv, mDefLE, mSortsB_02, m_AddZero, mSortsB, mNatSort, mMulComm, m__1379, mLERefl, mMonAdd, m__1324
% 167.36/115.93 % No. of inferences in proof: 129
% 167.36/115.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 115395 ms resp. 114913 ms w/o parsing
% 167.71/115.98 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 167.71/115.98 % [INFO] Killing All external provers ...
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