TSTP Solution File: NUM513+3 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM513+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.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 11:40:55 EDT 2023
% Result : Theorem 29.85s 6.43s
% Output : Refutation 29.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 71
% Syntax : Number of formulae : 128 ( 5 unt; 16 typ; 0 def)
% Number of atoms : 603 ( 225 equ; 0 cnn)
% Maximal formula atoms : 22 ( 5 avg)
% Number of connectives : 1636 ( 74 ~; 39 |; 301 &;1071 @)
% ( 5 <=>; 146 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 9 con; 0-2 aty)
% Number of variables : 214 ( 0 ^; 168 !; 46 ?; 214 :)
% 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(xk_type,type,
xk: $i ).
thf(xr_type,type,
xr: $i ).
thf(xn_type,type,
xn: $i ).
thf(xp_type,type,
xp: $i ).
thf(xm_type,type,
xm: $i ).
thf(iLess0_type,type,
iLess0: $i > $i > $o ).
thf(40,axiom,
~ ( ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( ( sdtpldt0 @ xp @ A )
= xn ) )
| ( sdtlseqdt0 @ xp @ xn ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
thf(288,plain,
~ ( ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( ( sdtpldt0 @ xp @ A )
= xn ) )
| ( sdtlseqdt0 @ xp @ xn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(9,axiom,
( ~ ( ( ( aNaturalNumber0 @ ( sdtsldt0 @ xn @ xr ) )
& ( xn
= ( sdtasdt0 @ xr @ ( sdtsldt0 @ xn @ xr ) ) ) )
=> ( ( sdtsldt0 @ xn @ xr )
= xn ) )
& ( aNaturalNumber0 @ ( sdtsldt0 @ xn @ xr ) )
& ( xn
= ( sdtasdt0 @ xr @ ( sdtsldt0 @ xn @ xr ) ) )
& ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( ( sdtpldt0 @ ( sdtsldt0 @ xn @ xr ) @ A )
= xn ) )
& ( sdtlseqdt0 @ ( sdtsldt0 @ xn @ xr ) @ xn ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2504) ).
thf(110,plain,
( ~ ( ( ( aNaturalNumber0 @ ( sdtsldt0 @ xn @ xr ) )
& ( xn
= ( sdtasdt0 @ xr @ ( sdtsldt0 @ xn @ xr ) ) ) )
=> ( ( sdtsldt0 @ xn @ xr )
= xn ) )
& ( aNaturalNumber0 @ ( sdtsldt0 @ xn @ xr ) )
& ( xn
= ( sdtasdt0 @ xr @ ( sdtsldt0 @ xn @ xr ) ) )
& ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( ( sdtpldt0 @ ( sdtsldt0 @ xn @ xr ) @ A )
= xn ) )
& ( sdtlseqdt0 @ ( sdtsldt0 @ xn @ xr ) @ xn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( iLess0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).
thf(169,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(11,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(124,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)],[11]) ).
thf(23,axiom,
( ( xk != sz00 )
& ( xk != sz10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2327) ).
thf(173,plain,
( ( xk != sz00 )
& ( xk != sz10 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(39,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(281,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)],[39]) ).
thf(46,axiom,
( ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( ( sdtpldt0 @ xr @ A )
= xk ) )
& ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( ( sdtasdt0 @ xn @ xm )
= ( sdtasdt0 @ xr @ A ) ) )
& ( doDivides0 @ xr @ ( sdtasdt0 @ xn @ xm ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2362) ).
thf(313,plain,
( ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( ( sdtpldt0 @ xr @ A )
= xk ) )
& ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( ( sdtasdt0 @ xn @ xm )
= ( sdtasdt0 @ xr @ A ) ) )
& ( doDivides0 @ xr @ ( sdtasdt0 @ xn @ xm ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(43,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(303,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)],[43]) ).
thf(15,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(146,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)],[15]) ).
thf(24,axiom,
( ( aNaturalNumber0 @ ( sdtsldt0 @ xn @ xr ) )
& ( xn
= ( sdtasdt0 @ xr @ ( sdtsldt0 @ xn @ xr ) ) )
& ( ( sdtasdt0 @ ( sdtasdt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ) @ xr )
= ( sdtasdt0 @ xn @ xm ) )
& ( aNaturalNumber0 @ ( sdtsldt0 @ ( sdtasdt0 @ xp @ xk ) @ xr ) )
& ( ( sdtasdt0 @ xp @ xk )
= ( sdtasdt0 @ xr @ ( sdtsldt0 @ ( sdtasdt0 @ xp @ xk ) @ xr ) ) )
& ( ( sdtasdt0 @ xn @ xm )
= ( sdtasdt0 @ ( sdtsldt0 @ ( sdtasdt0 @ xp @ xk ) @ xr ) @ xr ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2576) ).
thf(178,plain,
( ( aNaturalNumber0 @ ( sdtsldt0 @ xn @ xr ) )
& ( xn
= ( sdtasdt0 @ xr @ ( sdtsldt0 @ xn @ xr ) ) )
& ( ( sdtasdt0 @ ( sdtasdt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ) @ xr )
= ( sdtasdt0 @ xn @ xm ) )
& ( aNaturalNumber0 @ ( sdtsldt0 @ ( sdtasdt0 @ xp @ xk ) @ xr ) )
& ( ( sdtasdt0 @ xp @ xk )
= ( sdtasdt0 @ xr @ ( sdtsldt0 @ ( sdtasdt0 @ xp @ xk ) @ xr ) ) )
& ( ( sdtasdt0 @ xn @ xm )
= ( sdtasdt0 @ ( sdtsldt0 @ ( sdtasdt0 @ xp @ xk ) @ xr ) @ xr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(29,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
thf(215,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(54,axiom,
( ( ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( xn
= ( sdtasdt0 @ xr @ A ) ) )
& ( doDivides0 @ xr @ xn ) )
| ( ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( xm
= ( sdtasdt0 @ xr @ A ) ) )
& ( doDivides0 @ xr @ xm ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2449) ).
thf(365,plain,
( ( ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( xn
= ( sdtasdt0 @ xr @ A ) ) )
& ( doDivides0 @ xr @ xn ) )
| ( ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( xm
= ( sdtasdt0 @ xr @ A ) ) )
& ( doDivides0 @ xr @ xm ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(31,axiom,
( ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( xn
= ( sdtasdt0 @ xr @ A ) ) )
& ( doDivides0 @ xr @ xn ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2487) ).
thf(234,plain,
( ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( xn
= ( sdtasdt0 @ xr @ A ) ) )
& ( doDivides0 @ xr @ xn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(22,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(170,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)],[22]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
thf(308,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(10,axiom,
( ( aNaturalNumber0 @ sz10 )
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
thf(120,plain,
( ( aNaturalNumber0 @ sz10 )
& ( sz10 != sz00 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(49,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(340,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)],[49]) ).
thf(18,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(153,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)],[18]) ).
thf(25,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(189,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)],[25]) ).
thf(1,conjecture,
( ( ( aNaturalNumber0 @ ( sdtsldt0 @ xk @ xr ) )
& ( xk
= ( sdtasdt0 @ xr @ ( sdtsldt0 @ xk @ xr ) ) ) )
=> ( ( ( aNaturalNumber0 @ ( sdtsldt0 @ xn @ xr ) )
& ( xn
= ( sdtasdt0 @ xr @ ( sdtsldt0 @ xn @ xr ) ) ) )
=> ( ( sdtasdt0 @ xp @ ( sdtsldt0 @ xk @ xr ) )
= ( sdtasdt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ( aNaturalNumber0 @ ( sdtsldt0 @ xk @ xr ) )
& ( xk
= ( sdtasdt0 @ xr @ ( sdtsldt0 @ xk @ xr ) ) ) )
=> ( ( ( aNaturalNumber0 @ ( sdtsldt0 @ xn @ xr ) )
& ( xn
= ( sdtasdt0 @ xr @ ( sdtsldt0 @ xn @ xr ) ) ) )
=> ( ( sdtasdt0 @ xp @ ( sdtsldt0 @ xk @ xr ) )
= ( sdtasdt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(57,plain,
~ ( ( ( aNaturalNumber0 @ ( sdtsldt0 @ xk @ xr ) )
& ( xk
= ( sdtasdt0 @ xr @ ( sdtsldt0 @ xk @ xr ) ) ) )
=> ( ( ( aNaturalNumber0 @ ( sdtsldt0 @ xn @ xr ) )
& ( xn
= ( sdtasdt0 @ xr @ ( sdtsldt0 @ xn @ xr ) ) ) )
=> ( ( sdtasdt0 @ xp @ ( sdtsldt0 @ xk @ xr ) )
= ( sdtasdt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(36,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERefl) ).
thf(261,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
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(164,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(47,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( A = sz00 )
| ( A = sz10 )
| ( ( sz10 != A )
& ( sdtlseqdt0 @ sz10 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLENTr) ).
thf(321,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( A = sz00 )
| ( A = sz10 )
| ( ( sz10 != A )
& ( sdtlseqdt0 @ sz10 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(38,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatSort) ).
thf(280,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(41,axiom,
~ ( ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( ( sdtpldt0 @ xp @ A )
= xm ) )
| ( sdtlseqdt0 @ xp @ xm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2075) ).
thf(293,plain,
~ ( ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( ( sdtpldt0 @ xp @ A )
= xm ) )
| ( sdtlseqdt0 @ xp @ xm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(12,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(133,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)],[12]) ).
thf(34,axiom,
( ( aNaturalNumber0 @ xr )
& ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( xk
= ( sdtasdt0 @ xr @ A ) ) )
& ( doDivides0 @ xr @ xk )
& ( xr != sz00 )
& ( xr != sz10 )
& ! [A: $i] :
( ( ( aNaturalNumber0 @ A )
& ( ? [B: $i] :
( ( aNaturalNumber0 @ B )
& ( xr
= ( sdtasdt0 @ A @ B ) ) )
| ( doDivides0 @ A @ xr ) ) )
=> ( ( A = sz10 )
| ( A = xr ) ) )
& ( isPrime0 @ xr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
thf(243,plain,
( ( aNaturalNumber0 @ xr )
& ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( xk
= ( sdtasdt0 @ xr @ A ) ) )
& ( doDivides0 @ xr @ xk )
& ( xr != sz00 )
& ( xr != sz10 )
& ! [A: $i] :
( ( ( aNaturalNumber0 @ A )
& ( ? [B: $i] :
( ( aNaturalNumber0 @ B )
& ( xr
= ( sdtasdt0 @ A @ B ) ) )
| ( doDivides0 @ A @ xr ) ) )
=> ( ( A = sz10 )
| ( A = xr ) ) )
& ( isPrime0 @ xr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(5,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
thf(74,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( ( ( C != sz00 )
& ( C != sz10 )
& ! [D: $i] :
( ( ( aNaturalNumber0 @ D )
& ? [E: $i] :
( ( aNaturalNumber0 @ E )
& ( C
= ( sdtasdt0 @ D @ E ) ) )
& ( doDivides0 @ D @ C ) )
=> ( ( D = sz10 )
| ( D = C ) ) ) )
| ( isPrime0 @ C ) )
& ( ? [D: $i] :
( ( aNaturalNumber0 @ D )
& ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ C @ D ) ) )
| ( doDivides0 @ C @ ( sdtasdt0 @ A @ B ) ) ) )
=> ( ( iLess0 @ ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C ) @ ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp ) )
=> ( ( ? [D: $i] :
( ( aNaturalNumber0 @ D )
& ( A
= ( sdtasdt0 @ C @ D ) ) )
& ( doDivides0 @ C @ A ) )
| ( ? [D: $i] :
( ( aNaturalNumber0 @ D )
& ( B
= ( sdtasdt0 @ C @ D ) ) )
& ( doDivides0 @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1799) ).
thf(85,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( ( ( C != sz00 )
& ( C != sz10 )
& ! [D: $i] :
( ( ( aNaturalNumber0 @ D )
& ? [E: $i] :
( ( aNaturalNumber0 @ E )
& ( C
= ( sdtasdt0 @ D @ E ) ) )
& ( doDivides0 @ D @ C ) )
=> ( ( D = sz10 )
| ( D = C ) ) ) )
| ( isPrime0 @ C ) )
& ( ? [D: $i] :
( ( aNaturalNumber0 @ D )
& ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ C @ D ) ) )
| ( doDivides0 @ C @ ( sdtasdt0 @ A @ B ) ) ) )
=> ( ( iLess0 @ ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C ) @ ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp ) )
=> ( ( ? [D: $i] :
( ( aNaturalNumber0 @ D )
& ( A
= ( sdtasdt0 @ C @ D ) ) )
& ( doDivides0 @ C @ A ) )
| ( ? [D: $i] :
( ( aNaturalNumber0 @ D )
& ( B
= ( sdtasdt0 @ C @ D ) ) )
& ( doDivides0 @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(30,axiom,
( ( xp != sz00 )
& ( xp != sz10 )
& ! [A: $i] :
( ( ( aNaturalNumber0 @ A )
& ( ? [B: $i] :
( ( aNaturalNumber0 @ B )
& ( xp
= ( sdtasdt0 @ A @ B ) ) )
| ( doDivides0 @ A @ xp ) ) )
=> ( ( A = sz10 )
| ( A = xp ) ) )
& ( isPrime0 @ xp )
& ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( ( sdtasdt0 @ xn @ xm )
= ( sdtasdt0 @ xp @ A ) ) )
& ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xm ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
thf(220,plain,
( ( xp != sz00 )
& ( xp != sz10 )
& ! [A: $i] :
( ( ( aNaturalNumber0 @ A )
& ( ? [B: $i] :
( ( aNaturalNumber0 @ B )
& ( xp
= ( sdtasdt0 @ A @ B ) ) )
| ( doDivides0 @ A @ xp ) ) )
=> ( ( A = sz10 )
| ( A = xp ) ) )
& ( isPrime0 @ xp )
& ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( ( sdtasdt0 @ xn @ xm )
= ( sdtasdt0 @ xp @ A ) ) )
& ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xm ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(4,axiom,
aNaturalNumber0 @ sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
thf(73,plain,
aNaturalNumber0 @ sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(27,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
thf(205,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtpldt0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
thf(311,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtpldt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(42,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(298,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)],[42]) ).
thf(16,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(148,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)],[16]) ).
thf(50,axiom,
( ( aNaturalNumber0 @ xk )
& ( ( sdtasdt0 @ xn @ xm )
= ( sdtasdt0 @ xp @ xk ) )
& ( xk
= ( sdtsldt0 @ ( sdtasdt0 @ xn @ xm ) @ xp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
thf(345,plain,
( ( aNaturalNumber0 @ xk )
& ( ( sdtasdt0 @ xn @ xm )
= ( sdtasdt0 @ xp @ xk ) )
& ( xk
= ( sdtsldt0 @ ( sdtasdt0 @ xn @ xm ) @ xp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(3,axiom,
( ( xk != xp )
& ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( ( sdtpldt0 @ xk @ A )
= xp ) )
& ( sdtlseqdt0 @ xk @ xp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2377) ).
thf(66,plain,
( ( xk != xp )
& ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( ( sdtpldt0 @ xk @ A )
= xp ) )
& ( sdtlseqdt0 @ xk @ xp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtasdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
thf(241,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtasdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(20,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(167,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)],[20]) ).
thf(55,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(374,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)],[55]) ).
thf(52,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(355,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( A != sz00 )
=> ( sdtlseqdt0 @ B @ ( sdtasdt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(26,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(194,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)],[26]) ).
thf(17,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(150,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)],[17]) ).
thf(48,axiom,
( ( xn != xp )
& ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( ( sdtpldt0 @ xn @ A )
= xp ) )
& ( sdtlseqdt0 @ xn @ xp )
& ( xm != xp )
& ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( ( sdtpldt0 @ xm @ A )
= xp ) )
& ( sdtlseqdt0 @ xm @ xp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2287) ).
thf(327,plain,
( ( xn != xp )
& ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( ( sdtpldt0 @ xn @ A )
= xp ) )
& ( sdtlseqdt0 @ xn @ xp )
& ( xm != xp )
& ? [A: $i] :
( ( aNaturalNumber0 @ A )
& ( ( sdtpldt0 @ xm @ A )
= xp ) )
& ( sdtlseqdt0 @ xm @ xp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(37,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(263,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)],[37]) ).
thf(35,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(258,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)],[35]) ).
thf(51,axiom,
( ( aNaturalNumber0 @ xn )
& ( aNaturalNumber0 @ xm )
& ( aNaturalNumber0 @ xp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
thf(351,plain,
( ( aNaturalNumber0 @ xn )
& ( aNaturalNumber0 @ xm )
& ( aNaturalNumber0 @ xp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(14,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(139,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)],[14]) ).
thf(56,axiom,
~ ( ( xk = sz00 )
| ( xk = sz10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2315) ).
thf(383,plain,
~ ( ( xk = sz00 )
| ( xk = sz10 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(7,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(82,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)],[7]) ).
thf(28,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(210,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)],[28]) ).
thf(32,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(239,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)],[32]) ).
thf(13,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(136,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)],[13]) ).
thf(53,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(358,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)],[53]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
thf(79,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14481,plain,
$false,
inference(cvc4,[status(thm)],[288,110,169,124,173,281,313,303,146,178,215,365,234,170,308,120,340,153,189,57,261,164,321,280,293,133,243,74,85,220,73,205,311,298,148,345,66,241,167,374,355,194,150,327,263,258,351,139,383,82,210,239,136,358,79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM513+3 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n014.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 17:16:43 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.92/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/1.01 % [INFO] Parsing done (151ms).
% 1.20/1.01 % [INFO] Running in sequential loop mode.
% 1.88/1.26 % [INFO] eprover registered as external prover.
% 1.88/1.26 % [INFO] cvc4 registered as external prover.
% 1.88/1.27 % [INFO] Scanning for conjecture ...
% 2.06/1.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.06/1.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.06/1.33 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.06/1.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.06/1.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.21/1.37 % [INFO] Found a conjecture and 54 axioms. Running axiom selection ...
% 2.21/1.44 % [INFO] Axiom selection finished. Selected 54 axioms (removed 0 axioms).
% 2.50/1.46 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.50/1.47 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.50/1.48 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.61/1.49 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.61/1.49 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.61/1.50 % [INFO] Problem is first-order (TPTP FOF).
% 2.61/1.51 % [INFO] Type checking passed.
% 2.61/1.51 % [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 ...
% 29.85/6.43 % External prover 'cvc4' found a proof!
% 29.85/6.43 % [INFO] Killing All external provers ...
% 29.85/6.43 % Time passed: 5915ms (effective reasoning time: 5415ms)
% 29.85/6.43 % 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)>
% 29.85/6.43 % Axioms used in derivation (54): mAddComm, mPrimDiv, m_MulZero, mZeroMul, m__2342, mZeroAdd, mMonMul, mIH_03, mDivMin, m__2487, m__2504, m__2075, mAMDistr, mLETotal, mSortsC, m__2287, mLEAsym, mAddCanc, m__2315, mDivSum, mDivTrans, m_MulUnit, m__2377, mDefPrime, mSortsC_01, m__1860, m__1870, m__2449, mMulCanc, mLETran, m__1799, mDefDiff, mDivAsso, m__1837, mMonMul2, mAddAsso, mIH, mMulAsso, mDefDiv, mDefLE, m__2306, mLENTr, mDefQuot, m__2362, m__2576, mSortsB_02, m_AddZero, mSortsB, mNatSort, mMulComm, mDivLE, mLERefl, m__2327, mMonAdd
% 29.85/6.43 % No. of inferences in proof: 112
% 29.85/6.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5915 ms resp. 5415 ms w/o parsing
% 29.85/6.48 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 29.85/6.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------