TSTP Solution File: NUM528+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM528+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.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 11:40:59 EDT 2023
% Result : Theorem 40.80s 13.99s
% Output : Refutation 40.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 63
% Syntax : Number of formulae : 113 ( 13 unt; 15 typ; 0 def)
% Number of atoms : 448 ( 145 equ; 0 cnn)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 1148 ( 61 ~; 17 |; 190 &; 737 @)
% ( 5 <=>; 138 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 8 con; 0-2 aty)
% Number of variables : 176 ( 0 ^; 168 !; 8 ?; 176 :)
% 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(isPrime0_type,type,
isPrime0: $i > $o ).
thf(sz10_type,type,
sz10: $i ).
thf(xm_type,type,
xm: $i ).
thf(xn_type,type,
xn: $i ).
thf(iLess0_type,type,
iLess0: $i > $i > $o ).
thf(xp_type,type,
xp: $i ).
thf(xq_type,type,
xq: $i ).
thf(8,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(69,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)],[8]) ).
thf(37,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(202,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)],[37]) ).
thf(27,axiom,
! [A: $i] :
( ( ( aNaturalNumber0 @ A )
& ( A != sz00 )
& ( A != sz10 ) )
=> ? [B: $i] :
( ( aNaturalNumber0 @ B )
& ( doDivides0 @ B @ A )
& ( isPrime0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPrimDiv) ).
thf(152,plain,
! [A: $i] :
( ( ( aNaturalNumber0 @ A )
& ( A != sz00 )
& ( A != sz10 ) )
=> ? [B: $i] :
( ( aNaturalNumber0 @ B )
& ( doDivides0 @ B @ A )
& ( isPrime0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(47,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(248,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)],[47]) ).
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(53,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(35,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(193,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)],[35]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
thf(129,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(22,axiom,
aNaturalNumber0 @ sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
thf(134,plain,
aNaturalNumber0 @ sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(12,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(76,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)],[12]) ).
thf(23,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(135,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)],[23]) ).
thf(1,conjecture,
( ( xm != xn )
& ( sdtlseqdt0 @ xm @ xn ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( xm != xn )
& ( sdtlseqdt0 @ xm @ xn ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(50,plain,
~ ( ( xm != xn )
& ( sdtlseqdt0 @ xm @ xn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( doDivides0 @ A @ B )
& ( doDivides0 @ A @ ( sdtpldt0 @ B @ C ) ) )
=> ( doDivides0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivMin) ).
thf(72,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( doDivides0 @ A @ B )
& ( doDivides0 @ A @ ( sdtpldt0 @ B @ C ) ) )
=> ( doDivides0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(36,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(195,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)],[36]) ).
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(216,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(18,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatSort) ).
thf(121,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C )
& ( A != sz00 )
& ( B != sz00 )
& ( C != sz00 ) )
=> ( ( ( sdtasdt0 @ C @ ( sdtasdt0 @ B @ B ) )
= ( sdtasdt0 @ A @ A ) )
=> ( ( iLess0 @ A @ xn )
=> ~ ( isPrime0 @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2963) ).
thf(211,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C )
& ( A != sz00 )
& ( B != sz00 )
& ( C != sz00 ) )
=> ( ( ( sdtasdt0 @ C @ ( sdtasdt0 @ B @ B ) )
= ( sdtasdt0 @ A @ A ) )
=> ( ( iLess0 @ A @ xn )
=> ~ ( isPrime0 @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(49,axiom,
( ( sdtasdt0 @ xp @ ( sdtasdt0 @ xm @ xm ) )
= ( sdtasdt0 @ xn @ xn ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).
thf(253,plain,
( ( sdtasdt0 @ xp @ ( sdtasdt0 @ xm @ xm ) )
= ( sdtasdt0 @ xn @ xn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(26,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(147,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)],[26]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( A != sz00 )
& ( doDivides0 @ A @ B ) )
=> ! [C: $i] :
( ( aNaturalNumber0 @ C )
=> ( ( sdtasdt0 @ C @ ( sdtsldt0 @ B @ A ) )
= ( sdtsldt0 @ ( sdtasdt0 @ C @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivAsso) ).
thf(61,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( A != sz00 )
& ( doDivides0 @ A @ B ) )
=> ! [C: $i] :
( ( aNaturalNumber0 @ C )
=> ( ( sdtasdt0 @ C @ ( sdtsldt0 @ B @ A ) )
= ( sdtsldt0 @ ( sdtasdt0 @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(41,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( A = sz00 )
| ( A = sz10 )
| ( ( sz10 != A )
& ( sdtlseqdt0 @ sz10 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLENTr) ).
thf(221,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( A = sz00 )
| ( A = sz10 )
| ( ( sz10 != A )
& ( sdtlseqdt0 @ sz10 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtpldt0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
thf(132,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtpldt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(45,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(243,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( A != sz00 )
=> ( sdtlseqdt0 @ B @ ( sdtasdt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( iLess0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).
thf(74,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(14,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(92,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)],[14]) ).
thf(43,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(229,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)],[43]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( isPrime0 @ C )
& ( doDivides0 @ C @ ( sdtasdt0 @ A @ B ) ) )
=> ( ( doDivides0 @ C @ A )
| ( doDivides0 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPDP) ).
thf(97,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( isPrime0 @ C )
& ( doDivides0 @ C @ ( sdtasdt0 @ A @ B ) ) )
=> ( ( doDivides0 @ C @ A )
| ( doDivides0 @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtasdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
thf(161,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtasdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(6,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(64,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)],[6]) ).
thf(25,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(144,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)],[25]) ).
thf(33,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(181,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)],[33]) ).
thf(28,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(159,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)],[28]) ).
thf(24,axiom,
( ( aNaturalNumber0 @ sz10 )
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
thf(140,plain,
( ( aNaturalNumber0 @ sz10 )
& ( sz10 != sz00 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(7,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(66,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)],[7]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( doDivides0 @ A @ B )
& ( B != sz00 ) )
=> ( sdtlseqdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivLE) ).
thf(240,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( doDivides0 @ A @ B )
& ( B != sz00 ) )
=> ( sdtlseqdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(48,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERefl) ).
thf(251,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(16,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
thf(99,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
thf(87,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(17,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( isPrime0 @ A )
<=> ( ( A != sz00 )
& ( A != sz10 )
& ! [B: $i] :
( ( ( aNaturalNumber0 @ B )
& ( doDivides0 @ B @ A ) )
=> ( ( B = sz10 )
| ( B = A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
thf(104,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( isPrime0 @ A )
=> ( ( A != sz00 )
& ( A != sz10 )
& ! [B: $i] :
( ( ( aNaturalNumber0 @ B )
& ( doDivides0 @ B @ A ) )
=> ( ( B = sz10 )
| ( B = A ) ) ) ) )
& ( ( ( A != sz00 )
& ( A != sz10 )
& ! [B: $i] :
( ( ( aNaturalNumber0 @ B )
& ( doDivides0 @ B @ A ) )
=> ( ( B = sz10 )
| ( B = A ) ) ) )
=> ( isPrime0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(11,axiom,
isPrime0 @ xp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3025) ).
thf(75,plain,
isPrime0 @ xp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
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(58,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(46,axiom,
( ( sdtasdt0 @ xm @ xm )
= ( sdtasdt0 @ xp @ ( sdtasdt0 @ xq @ xq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3082) ).
thf(246,plain,
( ( sdtasdt0 @ xm @ xm )
= ( sdtasdt0 @ xp @ ( sdtasdt0 @ xq @ xq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(39,axiom,
( ( sdtlseqdt0 @ xn @ xm )
=> ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xn ) @ ( sdtasdt0 @ xm @ xm ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3152) ).
thf(214,plain,
( ( sdtlseqdt0 @ xn @ xm )
=> ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xn ) @ ( sdtasdt0 @ xm @ xm ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(31,axiom,
( ( aNaturalNumber0 @ xn )
& ( aNaturalNumber0 @ xm )
& ( aNaturalNumber0 @ xp )
& ( xn != sz00 )
& ( xm != sz00 )
& ( xp != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2987) ).
thf(168,plain,
( ( aNaturalNumber0 @ xn )
& ( aNaturalNumber0 @ xm )
& ( aNaturalNumber0 @ xp )
& ( xn != sz00 )
& ( xm != sz00 )
& ( xp != sz00 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(34,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(190,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)],[34]) ).
thf(30,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(163,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)],[30]) ).
thf(32,axiom,
( ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) )
& ( doDivides0 @ xp @ xn ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3046) ).
thf(178,plain,
( ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xn ) )
& ( doDivides0 @ xp @ xn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(42,axiom,
( xq
= ( sdtsldt0 @ xn @ xp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3059) ).
thf(227,plain,
( xq
= ( sdtsldt0 @ xn @ xp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(19,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(122,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)],[19]) ).
thf(2898,plain,
$false,
inference(cvc4,[status(thm)],[69,202,152,248,53,193,129,134,76,135,50,72,195,216,121,211,253,147,61,221,132,243,74,92,229,97,161,64,144,181,159,140,66,240,251,99,87,104,75,58,246,214,168,190,163,178,227,122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM528+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n005.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 17:02:54 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.91/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/0.98 % [INFO] Parsing done (142ms).
% 1.43/0.99 % [INFO] Running in sequential loop mode.
% 1.80/1.19 % [INFO] eprover registered as external prover.
% 1.80/1.19 % [INFO] cvc4 registered as external prover.
% 1.80/1.19 % [INFO] Scanning for conjecture ...
% 1.98/1.24 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.98/1.25 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.98/1.25 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.98/1.26 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.98/1.26 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.09/1.28 % [INFO] Found a conjecture and 47 axioms. Running axiom selection ...
% 2.09/1.33 % [INFO] Axiom selection finished. Selected 47 axioms (removed 0 axioms).
% 2.28/1.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.28/1.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.28/1.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.40/1.37 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.40/1.38 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.40/1.38 % [INFO] Problem is first-order (TPTP FOF).
% 2.40/1.39 % [INFO] Type checking passed.
% 2.40/1.39 % [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 ...
% 40.80/13.98 % External prover 'cvc4' found a proof!
% 40.80/13.98 % [INFO] Killing All external provers ...
% 40.80/13.98 % Time passed: 13471ms (effective reasoning time: 12991ms)
% 40.80/13.98 % 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)>
% 40.80/13.99 % Axioms used in derivation (47): mSortsC, mAddComm, mPrimDiv, m_MulZero, mZeroMul, mZeroAdd, mDivAsso, mLENTr, mMonMul, mIH_03, mDivMin, mAMDistr, mLETotal, mMonAdd, m__2963, mLEAsym, mAddCanc, m__3059, m__3152, mDivSum, mDivTrans, m_MulUnit, mDefPrime, mSortsC_01, mMulCanc, mLETran, m__2987, mDefDiff, mMonMul2, mAddAsso, mIH, mMulAsso, mDefDiv, mDefLE, mDefQuot, m__3046, mPDP, mSortsB_02, m__3025, m_AddZero, m__3014, mSortsB, mNatSort, mMulComm, m__3082, mDivLE, mLERefl
% 40.80/13.99 % No. of inferences in proof: 98
% 40.80/13.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 13471 ms resp. 12991 ms w/o parsing
% 40.93/14.06 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 40.93/14.06 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------