TSTP Solution File: NUM516+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM516+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n007.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 11:40:56 EDT 2023
% Result : Theorem 12.17s 3.54s
% Output : Refutation 12.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 71
% Syntax : Number of formulae : 184 ( 48 unt; 16 typ; 0 def)
% Number of atoms : 566 ( 188 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1596 ( 131 ~; 57 |; 192 &;1079 @)
% ( 5 <=>; 132 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 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 : 185 ( 0 ^; 177 !; 8 ?; 185 :)
% 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(xn_type,type,
xn: $i ).
thf(xr_type,type,
xr: $i ).
thf(xm_type,type,
xm: $i ).
thf(xp_type,type,
xp: $i ).
thf(xk_type,type,
xk: $i ).
thf(iLess0_type,type,
iLess0: $i > $i > $o ).
thf(23,axiom,
( ( sdtlseqdt0 @ xr @ xk )
& ( doDivides0 @ xr @ ( sdtasdt0 @ xn @ xm ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2362) ).
thf(148,plain,
( ( sdtlseqdt0 @ xr @ xk )
& ( doDivides0 @ xr @ ( sdtasdt0 @ xn @ xm ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(150,plain,
sdtlseqdt0 @ xr @ xk,
inference(cnf,[status(esa)],[148]) ).
thf(1,conjecture,
( ( ( sdtpldt0 @ ( sdtpldt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ) @ xp )
!= ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp ) )
& ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ) @ xp ) @ ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ( sdtpldt0 @ ( sdtpldt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ) @ xp )
!= ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp ) )
& ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ) @ xp ) @ ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(57,plain,
~ ( ( ( sdtpldt0 @ ( sdtpldt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ) @ xp )
!= ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp ) )
& ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ) @ xp ) @ ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(58,plain,
( ( ( sdtpldt0 @ ( sdtpldt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ) @ xp )
= ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ) @ xp ) @ ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp ) ) ),
inference(cnf,[status(esa)],[57]) ).
thf(59,plain,
( ( ( sdtpldt0 @ ( sdtpldt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ) @ xp )
= ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp ) )
| ~ ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ) @ xp ) @ ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp ) ) ),
inference(lifteq,[status(thm)],[58]) ).
thf(338,plain,
( ( ( sdtpldt0 @ ( sdtpldt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ) @ xp )
= ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp ) )
| ( ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ) @ xp ) @ ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp ) )
!= ( sdtlseqdt0 @ xr @ xk ) ) ),
inference(paramod_ordered,[status(thm)],[150,59]) ).
thf(340,plain,
( ( ( sdtpldt0 @ ( sdtpldt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ) @ xp )
= ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp ) )
| ( ( sdtpldt0 @ ( sdtpldt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ) @ xp )
!= xr )
| ( ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp )
!= xk ) ),
inference(simp,[status(thm)],[338]) ).
thf(48,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(257,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)],[48]) ).
thf(34,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(196,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)],[34]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtasdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
thf(129,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtasdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
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(65,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(66,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ),
inference(cnf,[status(esa)],[65]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(lifteq,[status(thm)],[66]) ).
thf(21,axiom,
~ ( sdtlseqdt0 @ xp @ xm ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2075) ).
thf(143,plain,
~ ( sdtlseqdt0 @ xp @ xm ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(30,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(186,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)],[30]) ).
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(68,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(69,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)],[68]) ).
thf(46,axiom,
( ( xn != xp )
& ( sdtlseqdt0 @ xn @ xp )
& ( xm != xp )
& ( sdtlseqdt0 @ xm @ xp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2287) ).
thf(246,plain,
( ( xn != xp )
& ( sdtlseqdt0 @ xn @ xp )
& ( xm != xp )
& ( sdtlseqdt0 @ xm @ xp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(249,plain,
sdtlseqdt0 @ xn @ xp,
inference(cnf,[status(esa)],[246]) ).
thf(41,axiom,
~ ( sdtlseqdt0 @ xp @ xn ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
thf(234,plain,
~ ( sdtlseqdt0 @ xp @ xn ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(15,axiom,
( ( aNaturalNumber0 @ sz10 )
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
thf(113,plain,
( ( aNaturalNumber0 @ sz10 )
& ( sz10 != sz00 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(115,plain,
aNaturalNumber0 @ sz10,
inference(cnf,[status(esa)],[113]) ).
thf(55,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERefl) ).
thf(276,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(247,plain,
sdtlseqdt0 @ xm @ xp,
inference(cnf,[status(esa)],[246]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( isPrime0 @ C )
& ( doDivides0 @ C @ ( sdtasdt0 @ A @ B ) ) )
=> ( ( iLess0 @ ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C ) @ ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp ) )
=> ( ( doDivides0 @ C @ A )
| ( doDivides0 @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1799) ).
thf(269,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B )
& ( aNaturalNumber0 @ C ) )
=> ( ( ( isPrime0 @ C )
& ( doDivides0 @ C @ ( sdtasdt0 @ A @ B ) ) )
=> ( ( iLess0 @ ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C ) @ ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp ) )
=> ( ( doDivides0 @ C @ A )
| ( doDivides0 @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(31,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(189,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)],[31]) ).
thf(418,plain,
( ( ( sdtpldt0 @ ( sdtpldt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ) @ xp )
= ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp ) )
| ( ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ) @ xp ) @ ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp ) )
!= ( sdtlseqdt0 @ xn @ xp ) ) ),
inference(paramod_ordered,[status(thm)],[249,59]) ).
thf(421,plain,
( ( ( sdtpldt0 @ ( sdtpldt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ) @ xp )
= ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp ) )
| ( ( sdtpldt0 @ ( sdtpldt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ) @ xp )
!= xn )
| ( ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp )
!= xp ) ),
inference(simp,[status(thm)],[418]) ).
thf(37,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(216,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)],[37]) ).
thf(47,axiom,
( ( aNaturalNumber0 @ xn )
& ( aNaturalNumber0 @ xm )
& ( aNaturalNumber0 @ xp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
thf(253,plain,
( ( aNaturalNumber0 @ xn )
& ( aNaturalNumber0 @ xm )
& ( aNaturalNumber0 @ xp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(43,axiom,
( ( aNaturalNumber0 @ xr )
& ( doDivides0 @ xr @ xk )
& ( isPrime0 @ xr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
thf(238,plain,
( ( aNaturalNumber0 @ xr )
& ( doDivides0 @ xr @ xk )
& ( isPrime0 @ xr ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(22,axiom,
( ( isPrime0 @ xp )
& ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xm ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
thf(145,plain,
( ( isPrime0 @ xp )
& ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xm ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(147,plain,
isPrime0 @ xp,
inference(cnf,[status(esa)],[145]) ).
thf(10,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(82,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)],[10]) ).
thf(89,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( isPrime0 @ A )
| ( A != sz10 ) ),
inference(cnf,[status(esa)],[82]) ).
thf(92,plain,
! [A: $i] :
( ( A != sz10 )
| ~ ( aNaturalNumber0 @ A )
| ~ ( isPrime0 @ A ) ),
inference(lifteq,[status(thm)],[89]) ).
thf(93,plain,
( ~ ( aNaturalNumber0 @ sz10 )
| ~ ( isPrime0 @ sz10 ) ),
inference(simp,[status(thm)],[92]) ).
thf(344,plain,
( ~ $true
| ~ ( isPrime0 @ sz10 ) ),
inference(rewrite,[status(thm)],[93,115]) ).
thf(345,plain,
~ ( isPrime0 @ sz10 ),
inference(simp,[status(thm)],[344]) ).
thf(346,plain,
( ( isPrime0 @ xp )
!= ( isPrime0 @ sz10 ) ),
inference(paramod_ordered,[status(thm)],[147,345]) ).
thf(348,plain,
xp != sz10,
inference(simp,[status(thm)],[346]) ).
thf(38,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(221,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)],[38]) ).
thf(114,plain,
sz10 != sz00,
inference(cnf,[status(esa)],[113]) ).
thf(116,plain,
sz10 != sz00,
inference(lifteq,[status(thm)],[114]) ).
thf(45,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(243,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)],[45]) ).
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(60,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,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(117,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)],[16]) ).
thf(239,plain,
isPrime0 @ xr,
inference(cnf,[status(esa)],[238]) ).
thf(347,plain,
( ( isPrime0 @ xr )
!= ( isPrime0 @ sz10 ) ),
inference(paramod_ordered,[status(thm)],[239,345]) ).
thf(349,plain,
xr != sz10,
inference(simp,[status(thm)],[347]) ).
thf(25,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(160,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)],[25]) ).
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(70,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(85,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( isPrime0 @ A )
| ( A != sz00 ) ),
inference(cnf,[status(esa)],[82]) ).
thf(94,plain,
! [A: $i] :
( ( A != sz00 )
| ~ ( aNaturalNumber0 @ A )
| ~ ( isPrime0 @ A ) ),
inference(lifteq,[status(thm)],[85]) ).
thf(95,plain,
( ~ ( aNaturalNumber0 @ sz00 )
| ~ ( isPrime0 @ sz00 ) ),
inference(simp,[status(thm)],[94]) ).
thf(13,axiom,
aNaturalNumber0 @ sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
thf(107,plain,
aNaturalNumber0 @ sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(425,plain,
( ~ $true
| ~ ( isPrime0 @ sz00 ) ),
inference(rewrite,[status(thm)],[95,107]) ).
thf(426,plain,
~ ( isPrime0 @ sz00 ),
inference(simp,[status(thm)],[425]) ).
thf(427,plain,
( ( isPrime0 @ xp )
!= ( isPrime0 @ sz00 ) ),
inference(paramod_ordered,[status(thm)],[147,426]) ).
thf(429,plain,
xp != sz00,
inference(simp,[status(thm)],[427]) ).
thf(20,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( A = sz00 )
| ( A = sz10 )
| ( ( sz10 != A )
& ( sdtlseqdt0 @ sz10 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLENTr) ).
thf(137,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( A = sz00 )
| ( A = sz10 )
| ( ( sz10 != A )
& ( sdtlseqdt0 @ sz10 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(27,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(165,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)],[27]) ).
thf(250,plain,
xn != xp,
inference(cnf,[status(esa)],[246]) ).
thf(252,plain,
xp != xn,
inference(lifteq,[status(thm)],[250]) ).
thf(256,plain,
aNaturalNumber0 @ xn,
inference(cnf,[status(esa)],[253]) ).
thf(17,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
thf(124,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtasdt0 @ A @ sz10 )
= A )
& ( A
= ( sdtasdt0 @ sz10 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(36,axiom,
( ( ( sdtsldt0 @ xn @ xr )
!= xn )
& ( sdtlseqdt0 @ ( sdtsldt0 @ xn @ xr ) @ xn ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2504) ).
thf(212,plain,
( ( ( sdtsldt0 @ xn @ xr )
!= xn )
& ( sdtlseqdt0 @ ( sdtsldt0 @ xn @ xr ) @ xn ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
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(73,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(50,axiom,
( ( xk != xp )
& ( sdtlseqdt0 @ xk @ xp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2377) ).
thf(263,plain,
( ( xk != xp )
& ( sdtlseqdt0 @ xk @ xp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(265,plain,
xk != xp,
inference(cnf,[status(esa)],[263]) ).
thf(266,plain,
xk != xp,
inference(lifteq,[status(thm)],[265]) ).
thf(62,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( sz00
= ( sdtasdt0 @ sz00 @ A ) ) ),
inference(cnf,[status(esa)],[60]) ).
thf(64,plain,
! [A: $i] :
( ( ( sdtasdt0 @ sz00 @ A )
= sz00 )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[62]) ).
thf(32,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(191,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( A != sz00 )
=> ( sdtlseqdt0 @ B @ ( sdtasdt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(144,plain,
~ ( sdtlseqdt0 @ xp @ xm ),
inference(polarity_switch,[status(thm)],[143]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtpldt0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
thf(236,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aNaturalNumber0 @ ( sdtpldt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(28,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(172,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)],[28]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( iLess0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).
thf(81,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(8,axiom,
( ( xk != sz00 )
& ( xk != sz10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2327) ).
thf(76,plain,
( ( xk != sz00 )
& ( xk != sz10 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(53,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(271,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)],[53]) ).
thf(14,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(108,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)],[14]) ).
thf(240,plain,
doDivides0 @ xr @ xk,
inference(cnf,[status(esa)],[238]) ).
thf(248,plain,
xm != xp,
inference(cnf,[status(esa)],[246]) ).
thf(251,plain,
xp != xm,
inference(lifteq,[status(thm)],[248]) ).
thf(56,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(278,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)],[56]) ).
thf(39,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(226,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)],[39]) ).
thf(51,axiom,
( xk
= ( sdtsldt0 @ ( sdtasdt0 @ xn @ xm ) @ xp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
thf(267,plain,
( xk
= ( sdtsldt0 @ ( sdtasdt0 @ xn @ xm ) @ xp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(241,plain,
aNaturalNumber0 @ xr,
inference(cnf,[status(esa)],[238]) ).
thf(78,plain,
xk != sz00,
inference(cnf,[status(esa)],[76]) ).
thf(80,plain,
xk != sz00,
inference(lifteq,[status(thm)],[78]) ).
thf(255,plain,
aNaturalNumber0 @ xm,
inference(cnf,[status(esa)],[253]) ).
thf(33,axiom,
( ( doDivides0 @ xr @ xn )
| ( doDivides0 @ xr @ xm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2449) ).
thf(194,plain,
( ( doDivides0 @ xr @ xn )
| ( doDivides0 @ xr @ xm ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(61,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( sdtasdt0 @ A @ sz00 )
= sz00 ) ),
inference(cnf,[status(esa)],[60]) ).
thf(63,plain,
! [A: $i] :
( ( ( sdtasdt0 @ A @ sz00 )
= sz00 )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[61]) ).
thf(411,plain,
( ( ( sdtpldt0 @ ( sdtpldt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ) @ xp )
= ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp ) )
| ( ( sdtlseqdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ) @ xp ) @ ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp ) )
!= ( sdtlseqdt0 @ xm @ xp ) ) ),
inference(paramod_ordered,[status(thm)],[247,59]) ).
thf(414,plain,
( ( ( sdtpldt0 @ ( sdtpldt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ) @ xp )
= ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp ) )
| ( ( sdtpldt0 @ ( sdtpldt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ) @ xp )
!= xm )
| ( ( sdtpldt0 @ ( sdtpldt0 @ xn @ xm ) @ xp )
!= xp ) ),
inference(simp,[status(thm)],[411]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
thf(231,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(11,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatSort) ).
thf(99,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(35,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
thf(207,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz00 )
= A )
& ( A
= ( sdtpldt0 @ sz00 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(235,plain,
~ ( sdtlseqdt0 @ xp @ xn ),
inference(polarity_switch,[status(thm)],[234]) ).
thf(24,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(151,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)],[24]) ).
thf(49,axiom,
doDivides0 @ xr @ xn,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2487) ).
thf(262,plain,
doDivides0 @ xr @ xn,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(29,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(183,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)],[29]) ).
thf(54,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(273,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)],[54]) ).
thf(77,plain,
xk != sz10,
inference(cnf,[status(esa)],[76]) ).
thf(79,plain,
xk != sz10,
inference(lifteq,[status(thm)],[77]) ).
thf(44,axiom,
doDivides0 @ xp @ ( sdtasdt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2529) ).
thf(242,plain,
doDivides0 @ xp @ ( sdtasdt0 @ ( sdtsldt0 @ xn @ xr ) @ xm ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(19,axiom,
~ ( ( xk = sz00 )
| ( xk = sz10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2315) ).
thf(131,plain,
~ ( ( xk = sz00 )
| ( xk = sz10 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(26,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(163,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)],[26]) ).
thf(254,plain,
aNaturalNumber0 @ xp,
inference(cnf,[status(esa)],[253]) ).
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(100,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(1832,plain,
$false,
inference(cvc4,[status(thm)],[340,257,196,129,67,143,186,69,249,234,115,276,247,269,189,421,57,216,253,238,348,147,221,116,243,60,117,349,160,70,429,137,165,252,65,256,124,212,73,266,148,64,191,59,144,236,172,113,81,76,271,345,108,240,251,278,226,267,241,80,426,255,194,145,63,150,414,263,231,99,207,82,235,246,151,262,183,273,107,79,239,242,131,163,68,254,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : NUM516+1 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.14 % Command : run_Leo-III %s %d
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 17:27:24 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.81/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/0.95 % [INFO] Parsing done (170ms).
% 1.23/0.96 % [INFO] Running in sequential loop mode.
% 1.68/1.20 % [INFO] eprover registered as external prover.
% 1.68/1.20 % [INFO] cvc4 registered as external prover.
% 1.68/1.21 % [INFO] Scanning for conjecture ...
% 1.83/1.26 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.83/1.26 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.83/1.27 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.83/1.27 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.83/1.28 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.83/1.30 % [INFO] Found a conjecture and 54 axioms. Running axiom selection ...
% 2.14/1.36 % [INFO] Axiom selection finished. Selected 54 axioms (removed 0 axioms).
% 2.14/1.37 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.14/1.37 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.14/1.39 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.14/1.39 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.14/1.39 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.14/1.41 % [INFO] Problem is first-order (TPTP FOF).
% 2.14/1.43 % [INFO] Type checking passed.
% 2.14/1.43 % [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 ...
% 12.17/3.54 % External prover 'cvc4' found a proof!
% 12.17/3.54 % [INFO] Killing All external provers ...
% 12.17/3.54 % Time passed: 3078ms (effective reasoning time: 2571ms)
% 12.17/3.54 % 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)>
% 12.17/3.54 % Axioms used in derivation (54): mAddComm, mPrimDiv, m_MulZero, mZeroMul, m__2342, mZeroAdd, mMonMul, mIH_03, mDivMin, m__2487, m__2504, m__2075, 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, mSortsB_02, m_AddZero, mAMDistr, m__2529, mSortsB, mNatSort, mMulComm, mDivLE, mLERefl, m__2327, mMonAdd
% 12.17/3.54 % No. of inferences in proof: 168
% 12.17/3.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3078 ms resp. 2571 ms w/o parsing
% 12.27/3.61 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.27/3.61 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------