%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM492+3 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.TkzemE2Lah true
% 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 : Thu Oct 2 04:47:11 PM UTC 2025
% Result : Theorem 119.35s 19.71s
% Output : Refutation 119.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 26
% Syntax : Number of formulae : 313 ( 132 unt; 0 typ; 0 def)
% Number of atoms : 817 ( 265 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 2554 ( 426 ~; 415 |; 58 &;1624 @)
% ( 3 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 236 ( 0 ^; 227 !; 9 ?; 236 :)
% Comments :
%------------------------------------------------------------------------------
thf(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
thf(xp_type,type,
xp: $i ).
thf(sz10_type,type,
sz10: $i ).
thf(sdtpldt0_type,type,
sdtpldt0: $i > $i > $i ).
thf(sdtasdt0_type,type,
sdtasdt0: $i > $i > $i ).
thf(isPrime0_type,type,
isPrime0: $i > $o ).
thf(sz00_type,type,
sz00: $i ).
thf(sk__1_type,type,
sk__1: $i > $i > $i ).
thf(xr_type,type,
xr: $i ).
thf(doDivides0_type,type,
doDivides0: $i > $i > $o ).
thf(sdtmndt0_type,type,
sdtmndt0: $i > $i > $i ).
thf(xn_type,type,
xn: $i ).
thf(sdtlseqdt0_type,type,
sdtlseqdt0: $i > $i > $o ).
thf(sk__8_type,type,
sk__8: $i ).
thf(xm_type,type,
xm: $i ).
thf(sk__11_type,type,
sk__11: $i ).
thf(sk__type,type,
sk_: $i > $i > $i ).
thf(mDefDiv,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( doDivides0 @ W0 @ W1 )
<=> ? [W2: $i] :
( ( W1
= ( sdtasdt0 @ W0 @ W2 ) )
& ( aNaturalNumber0 @ W2 ) ) ) ) ).
thf(zip_derived_cl50,plain,
! [X0: $i,X1: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( aNaturalNumber0 @ ( sk__1 @ X1 @ X0 ) )
| ~ ( doDivides0 @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[mDefDiv]) ).
thf(zip_derived_cl49,plain,
! [X0: $i,X1: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( X1
= ( sdtasdt0 @ X0 @ ( sk__1 @ X1 @ X0 ) ) )
| ~ ( doDivides0 @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[mDefDiv]) ).
thf(m__,conjecture,
( ( doDivides0 @ xp @ ( sdtasdt0 @ xr @ xm ) )
| ? [W0: $i] :
( ( ( sdtasdt0 @ xr @ xm )
= ( sdtasdt0 @ xp @ W0 ) )
& ( aNaturalNumber0 @ W0 ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ( ( doDivides0 @ xp @ ( sdtasdt0 @ xr @ xm ) )
| ? [W0: $i] :
( ( ( sdtasdt0 @ xr @ xm )
= ( sdtasdt0 @ xp @ W0 ) )
& ( aNaturalNumber0 @ W0 ) ) ),
inference('cnf.neg',[status(esa)],[m__]) ).
thf(zip_derived_cl122,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ xr @ xm )
!= ( sdtasdt0 @ xp @ X0 ) )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2757,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ xr @ xm )
!= X0 )
| ~ ( doDivides0 @ xp @ X0 )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ xp )
| ~ ( aNaturalNumber0 @ ( sk__1 @ X0 @ xp ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl49,zip_derived_cl122]) ).
thf(m__1837,axiom,
( ( aNaturalNumber0 @ xp )
& ( aNaturalNumber0 @ xm )
& ( aNaturalNumber0 @ xn ) ) ).
thf(zip_derived_cl70,plain,
aNaturalNumber0 @ xp,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl2782,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ xr @ xm )
!= X0 )
| ~ ( doDivides0 @ xp @ X0 )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ ( sk__1 @ X0 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2757,zip_derived_cl70]) ).
thf(zip_derived_cl2853,plain,
! [X0: $i] :
( ~ ( doDivides0 @ xp @ X0 )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ xp )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( doDivides0 @ xp @ X0 )
| ( ( sdtasdt0 @ xr @ xm )
!= X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl50,zip_derived_cl2782]) ).
thf(zip_derived_cl70_001,plain,
aNaturalNumber0 @ xp,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl2854,plain,
! [X0: $i] :
( ~ ( doDivides0 @ xp @ X0 )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( doDivides0 @ xp @ X0 )
| ( ( sdtasdt0 @ xr @ xm )
!= X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2853,zip_derived_cl70]) ).
thf(zip_derived_cl2855,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ xr @ xm )
!= X0 )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( doDivides0 @ xp @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl2854]) ).
thf(m__1883,axiom,
( ( xr
= ( sdtmndt0 @ xn @ xp ) )
& ( ( sdtpldt0 @ xp @ xr )
= xn )
& ( aNaturalNumber0 @ xr ) ) ).
thf(zip_derived_cl107,plain,
( ( sdtpldt0 @ xp @ xr )
= xn ),
inference(cnf,[status(esa)],[m__1883]) ).
thf(mAMDistr,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ W1 @ W2 ) @ W0 )
= ( sdtpldt0 @ ( sdtasdt0 @ W1 @ W0 ) @ ( sdtasdt0 @ W2 @ W0 ) ) ) ) ) ).
thf(zip_derived_cl16,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ~ ( aNaturalNumber0 @ X2 )
| ( ( sdtasdt0 @ X1 @ ( sdtpldt0 @ X0 @ X2 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ X1 @ X0 ) @ ( sdtasdt0 @ X1 @ X2 ) ) ) ),
inference(cnf,[status(esa)],[mAMDistr]) ).
thf(zip_derived_cl1350,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ X0 @ xn )
= ( sdtpldt0 @ ( sdtasdt0 @ X0 @ xp ) @ ( sdtasdt0 @ X0 @ xr ) ) )
| ~ ( aNaturalNumber0 @ xr )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ xp ) ),
inference('sup+',[status(thm)],[zip_derived_cl107,zip_derived_cl16]) ).
thf(zip_derived_cl108,plain,
aNaturalNumber0 @ xr,
inference(cnf,[status(esa)],[m__1883]) ).
thf(zip_derived_cl70_002,plain,
aNaturalNumber0 @ xp,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl1361,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ X0 @ xn )
= ( sdtpldt0 @ ( sdtasdt0 @ X0 @ xp ) @ ( sdtasdt0 @ X0 @ xr ) ) )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1350,zip_derived_cl108,zip_derived_cl70]) ).
thf(mMulComm,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W1 @ W0 ) ) ) ).
thf(zip_derived_cl10,plain,
! [X0: $i,X1: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( ( sdtasdt0 @ X0 @ X1 )
= ( sdtasdt0 @ X1 @ X0 ) ) ),
inference(cnf,[status(esa)],[mMulComm]) ).
thf(m__1951,axiom,
( ( sdtasdt0 @ xn @ xm )
= ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xr @ xm ) ) ) ).
thf(zip_derived_cl114,plain,
( ( sdtasdt0 @ xn @ xm )
= ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xr @ xm ) ) ),
inference(cnf,[status(esa)],[m__1951]) ).
thf(zip_derived_cl1200,plain,
( ( ( sdtasdt0 @ xn @ xm )
= ( sdtpldt0 @ ( sdtasdt0 @ xm @ xp ) @ ( sdtasdt0 @ xr @ xm ) ) )
| ~ ( aNaturalNumber0 @ xp )
| ~ ( aNaturalNumber0 @ xm ) ),
inference('sup+',[status(thm)],[zip_derived_cl10,zip_derived_cl114]) ).
thf(zip_derived_cl70_003,plain,
aNaturalNumber0 @ xp,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl71,plain,
aNaturalNumber0 @ xm,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl1243,plain,
( ( sdtasdt0 @ xn @ xm )
= ( sdtpldt0 @ ( sdtasdt0 @ xm @ xp ) @ ( sdtasdt0 @ xr @ xm ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1200,zip_derived_cl70,zip_derived_cl71]) ).
thf(mAddCanc,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W0 @ W2 ) )
| ( ( sdtpldt0 @ W1 @ W0 )
= ( sdtpldt0 @ W2 @ W0 ) ) )
=> ( W1 = W2 ) ) ) ).
thf(zip_derived_cl19,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ~ ( aNaturalNumber0 @ X2 )
| ( X0 = X2 )
| ( ( sdtpldt0 @ X1 @ X0 )
!= ( sdtpldt0 @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[mAddCanc]) ).
thf(zip_derived_cl2704,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ xn @ xm )
!= ( sdtpldt0 @ ( sdtasdt0 @ xm @ xp ) @ X0 ) )
| ( ( sdtasdt0 @ xr @ xm )
= X0 )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xm @ xp ) )
| ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xr @ xm ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1243,zip_derived_cl19]) ).
thf(zip_derived_cl10_004,plain,
! [X0: $i,X1: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( ( sdtasdt0 @ X0 @ X1 )
= ( sdtasdt0 @ X1 @ X0 ) ) ),
inference(cnf,[status(esa)],[mMulComm]) ).
thf(m__2001,axiom,
( ( doDivides0 @ xp @ ( sdtasdt0 @ xp @ xm ) )
& ? [W0: $i] :
( ( ( sdtasdt0 @ xp @ xm )
= ( sdtasdt0 @ xp @ W0 ) )
& ( aNaturalNumber0 @ W0 ) )
& ? [W0: $i] :
( ( ( sdtasdt0 @ xn @ xm )
= ( sdtasdt0 @ xp @ W0 ) )
& ( aNaturalNumber0 @ W0 ) ) ) ).
thf(zip_derived_cl119,plain,
( ( sdtasdt0 @ xp @ xm )
= ( sdtasdt0 @ xp @ sk__11 ) ),
inference(cnf,[status(esa)],[m__2001]) ).
thf(mSortsB_02,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( aNaturalNumber0 @ ( sdtasdt0 @ W0 @ W1 ) ) ) ).
thf(zip_derived_cl5,plain,
! [X0: $i,X1: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( aNaturalNumber0 @ ( sdtasdt0 @ X0 @ X1 ) ) ),
inference(cnf,[status(esa)],[mSortsB_02]) ).
thf(zip_derived_cl1080,plain,
( ( aNaturalNumber0 @ ( sdtasdt0 @ xp @ xm ) )
| ~ ( aNaturalNumber0 @ sk__11 )
| ~ ( aNaturalNumber0 @ xp ) ),
inference('sup+',[status(thm)],[zip_derived_cl119,zip_derived_cl5]) ).
thf(zip_derived_cl120,plain,
aNaturalNumber0 @ sk__11,
inference(cnf,[status(esa)],[m__2001]) ).
thf(zip_derived_cl70_005,plain,
aNaturalNumber0 @ xp,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl1081,plain,
aNaturalNumber0 @ ( sdtasdt0 @ xp @ xm ),
inference(demod,[status(thm)],[zip_derived_cl1080,zip_derived_cl120,zip_derived_cl70]) ).
thf(zip_derived_cl1203,plain,
( ( aNaturalNumber0 @ ( sdtasdt0 @ xm @ xp ) )
| ~ ( aNaturalNumber0 @ xp )
| ~ ( aNaturalNumber0 @ xm ) ),
inference('sup+',[status(thm)],[zip_derived_cl10,zip_derived_cl1081]) ).
thf(zip_derived_cl70_006,plain,
aNaturalNumber0 @ xp,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl71_007,plain,
aNaturalNumber0 @ xm,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl1246,plain,
aNaturalNumber0 @ ( sdtasdt0 @ xm @ xp ),
inference(demod,[status(thm)],[zip_derived_cl1203,zip_derived_cl70,zip_derived_cl71]) ).
thf(zip_derived_cl2724,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ xn @ xm )
!= ( sdtpldt0 @ ( sdtasdt0 @ xm @ xp ) @ X0 ) )
| ( ( sdtasdt0 @ xr @ xm )
= X0 )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xr @ xm ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2704,zip_derived_cl1246]) ).
thf(zip_derived_cl10_008,plain,
! [X0: $i,X1: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( ( sdtasdt0 @ X0 @ X1 )
= ( sdtasdt0 @ X1 @ X0 ) ) ),
inference(cnf,[status(esa)],[mMulComm]) ).
thf(mMonMul,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( W0 != sz00 )
& ( W1 != W2 )
& ( sdtlseqdt0 @ W1 @ W2 ) )
=> ( ( ( sdtasdt0 @ W0 @ W1 )
!= ( sdtasdt0 @ W0 @ W2 ) )
& ( sdtlseqdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) )
& ( ( sdtasdt0 @ W1 @ W0 )
!= ( sdtasdt0 @ W2 @ W0 ) )
& ( sdtlseqdt0 @ ( sdtasdt0 @ W1 @ W0 ) @ ( sdtasdt0 @ W2 @ W0 ) ) ) ) ) ).
thf(zip_derived_cl41,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = sz00 )
| ~ ( aNaturalNumber0 @ X1 )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X2 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ X0 @ X1 ) @ ( sdtasdt0 @ X0 @ X2 ) )
| ~ ( sdtlseqdt0 @ X1 @ X2 )
| ( X1 = X2 ) ),
inference(cnf,[status(esa)],[mMonMul]) ).
thf(zip_derived_cl2433,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtlseqdt0 @ ( sdtasdt0 @ X0 @ X2 ) @ ( sdtasdt0 @ X1 @ X0 ) )
| ~ ( aNaturalNumber0 @ X1 )
| ~ ( aNaturalNumber0 @ X0 )
| ( X2 = X1 )
| ~ ( sdtlseqdt0 @ X2 @ X1 )
| ~ ( aNaturalNumber0 @ X1 )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X2 )
| ( X0 = sz00 ) ),
inference('sup+',[status(thm)],[zip_derived_cl10,zip_derived_cl41]) ).
thf(zip_derived_cl2457,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = sz00 )
| ~ ( aNaturalNumber0 @ X2 )
| ~ ( sdtlseqdt0 @ X2 @ X1 )
| ( X2 = X1 )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( sdtlseqdt0 @ ( sdtasdt0 @ X0 @ X2 ) @ ( sdtasdt0 @ X1 @ X0 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl2433]) ).
thf(m__1978,axiom,
( ( ( sdtasdt0 @ xr @ xm )
= ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) ) )
& ( ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xr @ xm ) )
= ( sdtasdt0 @ xn @ xm ) ) ) ).
thf(zip_derived_cl115,plain,
( ( sdtasdt0 @ xr @ xm )
= ( sdtmndt0 @ ( sdtasdt0 @ xn @ xm ) @ ( sdtasdt0 @ xp @ xm ) ) ),
inference(cnf,[status(esa)],[m__1978]) ).
thf(mDefDiff,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
=> ! [W2: $i] :
( ( W2
= ( sdtmndt0 @ W1 @ W0 ) )
<=> ( ( aNaturalNumber0 @ W2 )
& ( ( sdtpldt0 @ W0 @ W2 )
= W1 ) ) ) ) ) ).
thf(zip_derived_cl30,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( X2
!= ( sdtmndt0 @ X1 @ X0 ) )
| ( aNaturalNumber0 @ X2 )
| ~ ( sdtlseqdt0 @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[mDefDiff]) ).
thf(zip_derived_cl1589,plain,
! [X0: $i] :
( ( X0
!= ( sdtasdt0 @ xr @ xm ) )
| ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xn @ xm ) )
| ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) )
| ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xp @ xm ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl115,zip_derived_cl30]) ).
thf(m__1860,axiom,
( ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xm ) )
& ? [W0: $i] :
( ( ( sdtasdt0 @ xn @ xm )
= ( sdtasdt0 @ xp @ W0 ) )
& ( aNaturalNumber0 @ W0 ) )
& ( isPrime0 @ xp )
& ! [W0: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( ? [W1: $i] :
( ( xp
= ( sdtasdt0 @ W0 @ W1 ) )
& ( aNaturalNumber0 @ W1 ) )
| ( doDivides0 @ W0 @ xp ) ) )
=> ( ( W0 = sz10 )
| ( W0 = xp ) ) )
& ( xp != sz10 )
& ( xp != sz00 ) ) ).
thf(zip_derived_cl100,plain,
( ( sdtasdt0 @ xn @ xm )
= ( sdtasdt0 @ xp @ sk__8 ) ),
inference(cnf,[status(esa)],[m__1860]) ).
thf(zip_derived_cl5_009,plain,
! [X0: $i,X1: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( aNaturalNumber0 @ ( sdtasdt0 @ X0 @ X1 ) ) ),
inference(cnf,[status(esa)],[mSortsB_02]) ).
thf(zip_derived_cl1084,plain,
( ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) )
| ~ ( aNaturalNumber0 @ sk__8 )
| ~ ( aNaturalNumber0 @ xp ) ),
inference('sup+',[status(thm)],[zip_derived_cl100,zip_derived_cl5]) ).
thf(zip_derived_cl101,plain,
aNaturalNumber0 @ sk__8,
inference(cnf,[status(esa)],[m__1860]) ).
thf(zip_derived_cl70_010,plain,
aNaturalNumber0 @ xp,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl1085,plain,
aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ),
inference(demod,[status(thm)],[zip_derived_cl1084,zip_derived_cl101,zip_derived_cl70]) ).
thf(zip_derived_cl1081_011,plain,
aNaturalNumber0 @ ( sdtasdt0 @ xp @ xm ),
inference(demod,[status(thm)],[zip_derived_cl1080,zip_derived_cl120,zip_derived_cl70]) ).
thf(zip_derived_cl1592,plain,
! [X0: $i] :
( ( X0
!= ( sdtasdt0 @ xr @ xm ) )
| ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xn @ xm ) )
| ( aNaturalNumber0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1589,zip_derived_cl1085,zip_derived_cl1081]) ).
thf(zip_derived_cl5_012,plain,
! [X0: $i,X1: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( aNaturalNumber0 @ ( sdtasdt0 @ X0 @ X1 ) ) ),
inference(cnf,[status(esa)],[mSortsB_02]) ).
thf(zip_derived_cl1243_013,plain,
( ( sdtasdt0 @ xn @ xm )
= ( sdtpldt0 @ ( sdtasdt0 @ xm @ xp ) @ ( sdtasdt0 @ xr @ xm ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1200,zip_derived_cl70,zip_derived_cl71]) ).
thf(zip_derived_cl114_014,plain,
( ( sdtasdt0 @ xn @ xm )
= ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xr @ xm ) ) ),
inference(cnf,[status(esa)],[m__1951]) ).
thf(zip_derived_cl18,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ~ ( aNaturalNumber0 @ X2 )
| ( X0 = X2 )
| ( ( sdtpldt0 @ X0 @ X1 )
!= ( sdtpldt0 @ X2 @ X1 ) ) ),
inference(cnf,[status(esa)],[mAddCanc]) ).
thf(zip_derived_cl1463,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ xn @ xm )
!= ( sdtpldt0 @ X0 @ ( sdtasdt0 @ xr @ xm ) ) )
| ( ( sdtasdt0 @ xp @ xm )
= X0 )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xr @ xm ) )
| ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xp @ xm ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl114,zip_derived_cl18]) ).
thf(zip_derived_cl1081_015,plain,
aNaturalNumber0 @ ( sdtasdt0 @ xp @ xm ),
inference(demod,[status(thm)],[zip_derived_cl1080,zip_derived_cl120,zip_derived_cl70]) ).
thf(zip_derived_cl1485,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ xn @ xm )
!= ( sdtpldt0 @ X0 @ ( sdtasdt0 @ xr @ xm ) ) )
| ( ( sdtasdt0 @ xp @ xm )
= X0 )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xr @ xm ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1463,zip_derived_cl1081]) ).
thf(zip_derived_cl22029,plain,
( ( ( sdtasdt0 @ xn @ xm )
!= ( sdtasdt0 @ xn @ xm ) )
| ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xr @ xm ) )
| ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xm @ xp ) )
| ( ( sdtasdt0 @ xp @ xm )
= ( sdtasdt0 @ xm @ xp ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1243,zip_derived_cl1485]) ).
thf(zip_derived_cl1246_016,plain,
aNaturalNumber0 @ ( sdtasdt0 @ xm @ xp ),
inference(demod,[status(thm)],[zip_derived_cl1203,zip_derived_cl70,zip_derived_cl71]) ).
thf(zip_derived_cl22048,plain,
( ( ( sdtasdt0 @ xn @ xm )
!= ( sdtasdt0 @ xn @ xm ) )
| ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xr @ xm ) )
| ( ( sdtasdt0 @ xp @ xm )
= ( sdtasdt0 @ xm @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl22029,zip_derived_cl1246]) ).
thf(zip_derived_cl22049,plain,
( ( ( sdtasdt0 @ xp @ xm )
= ( sdtasdt0 @ xm @ xp ) )
| ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xr @ xm ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl22048]) ).
thf(zip_derived_cl22117,plain,
( ~ ( aNaturalNumber0 @ xm )
| ~ ( aNaturalNumber0 @ xr )
| ( ( sdtasdt0 @ xp @ xm )
= ( sdtasdt0 @ xm @ xp ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl5,zip_derived_cl22049]) ).
thf(zip_derived_cl71_017,plain,
aNaturalNumber0 @ xm,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl108_018,plain,
aNaturalNumber0 @ xr,
inference(cnf,[status(esa)],[m__1883]) ).
thf(zip_derived_cl22120,plain,
( ( sdtasdt0 @ xp @ xm )
= ( sdtasdt0 @ xm @ xp ) ),
inference(demod,[status(thm)],[zip_derived_cl22117,zip_derived_cl71,zip_derived_cl108]) ).
thf(zip_derived_cl24823,plain,
! [X0: $i] :
( ( X0
!= ( sdtasdt0 @ xr @ xm ) )
| ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xm @ xp ) @ ( sdtasdt0 @ xn @ xm ) )
| ( aNaturalNumber0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1592,zip_derived_cl22120]) ).
thf(zip_derived_cl52002,plain,
! [X0: $i] :
( ~ ( aNaturalNumber0 @ xn )
| ~ ( aNaturalNumber0 @ xm )
| ( xp = xn )
| ~ ( sdtlseqdt0 @ xp @ xn )
| ~ ( aNaturalNumber0 @ xp )
| ( xm = sz00 )
| ( aNaturalNumber0 @ X0 )
| ( X0
!= ( sdtasdt0 @ xr @ xm ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2457,zip_derived_cl24823]) ).
thf(zip_derived_cl72,plain,
aNaturalNumber0 @ xn,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl71_019,plain,
aNaturalNumber0 @ xm,
inference(cnf,[status(esa)],[m__1837]) ).
thf(m__1870,axiom,
( ( sdtlseqdt0 @ xp @ xn )
& ? [W0: $i] :
( ( ( sdtpldt0 @ xp @ W0 )
= xn )
& ( aNaturalNumber0 @ W0 ) ) ) ).
thf(zip_derived_cl105,plain,
sdtlseqdt0 @ xp @ xn,
inference(cnf,[status(esa)],[m__1870]) ).
thf(zip_derived_cl70_020,plain,
aNaturalNumber0 @ xp,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl52338,plain,
! [X0: $i] :
( ( xp = xn )
| ( xm = sz00 )
| ( aNaturalNumber0 @ X0 )
| ( X0
!= ( sdtasdt0 @ xr @ xm ) ) ),
inference(demod,[status(thm)],[zip_derived_cl52002,zip_derived_cl72,zip_derived_cl71,zip_derived_cl105,zip_derived_cl70]) ).
thf(zip_derived_cl71_021,plain,
aNaturalNumber0 @ xm,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl71_022,plain,
aNaturalNumber0 @ xm,
inference(cnf,[status(esa)],[m__1837]) ).
thf(mLETotal,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
| ( ( W1 != W0 )
& ( sdtlseqdt0 @ W1 @ W0 ) ) ) ) ).
thf(zip_derived_cl35,plain,
! [X0: $i,X1: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( sdtlseqdt0 @ X0 @ X1 )
| ( sdtlseqdt0 @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[mLETotal]) ).
thf(zip_derived_cl1522,plain,
! [X0: $i] :
( ( sdtlseqdt0 @ X0 @ xm )
| ( sdtlseqdt0 @ xm @ X0 )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl71,zip_derived_cl35]) ).
thf(zip_derived_cl22958,plain,
( ( sdtlseqdt0 @ xm @ xm )
| ( sdtlseqdt0 @ xm @ xm ) ),
inference('sup-',[status(thm)],[zip_derived_cl71,zip_derived_cl1522]) ).
thf(zip_derived_cl22970,plain,
sdtlseqdt0 @ xm @ xm,
inference(simplify,[status(thm)],[zip_derived_cl22958]) ).
thf(zip_derived_cl34,plain,
! [X0: $i,X1: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( sdtlseqdt0 @ X0 @ X1 )
| ( X1 != X0 ) ),
inference(cnf,[status(esa)],[mLETotal]) ).
thf(zip_derived_cl102,plain,
doDivides0 @ xp @ ( sdtasdt0 @ xn @ xm ),
inference(cnf,[status(esa)],[m__1860]) ).
thf(mDivLE,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( ( doDivides0 @ W0 @ W1 )
& ( W1 != sz00 ) )
=> ( sdtlseqdt0 @ W0 @ W1 ) ) ) ).
thf(zip_derived_cl58,plain,
! [X0: $i,X1: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( sdtlseqdt0 @ X0 @ X1 )
| ( X1 = sz00 )
| ~ ( doDivides0 @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[mDivLE]) ).
thf(zip_derived_cl1855,plain,
( ( ( sdtasdt0 @ xn @ xm )
= sz00 )
| ( sdtlseqdt0 @ xp @ ( sdtasdt0 @ xn @ xm ) )
| ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) )
| ~ ( aNaturalNumber0 @ xp ) ),
inference('sup-',[status(thm)],[zip_derived_cl102,zip_derived_cl58]) ).
thf(zip_derived_cl1085_023,plain,
aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ),
inference(demod,[status(thm)],[zip_derived_cl1084,zip_derived_cl101,zip_derived_cl70]) ).
thf(zip_derived_cl70_024,plain,
aNaturalNumber0 @ xp,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl1858,plain,
( ( ( sdtasdt0 @ xn @ xm )
= sz00 )
| ( sdtlseqdt0 @ xp @ ( sdtasdt0 @ xn @ xm ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1855,zip_derived_cl1085,zip_derived_cl70]) ).
thf(zip_derived_cl5_025,plain,
! [X0: $i,X1: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( aNaturalNumber0 @ ( sdtasdt0 @ X0 @ X1 ) ) ),
inference(cnf,[status(esa)],[mSortsB_02]) ).
thf(zip_derived_cl114_026,plain,
( ( sdtasdt0 @ xn @ xm )
= ( sdtpldt0 @ ( sdtasdt0 @ xp @ xm ) @ ( sdtasdt0 @ xr @ xm ) ) ),
inference(cnf,[status(esa)],[m__1951]) ).
thf(mZeroAdd,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( ( sdtpldt0 @ W0 @ W1 )
= sz00 )
=> ( ( W0 = sz00 )
& ( W1 = sz00 ) ) ) ) ).
thf(zip_derived_cl23,plain,
! [X0: $i,X1: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( X1 = sz00 )
| ( ( sdtpldt0 @ X0 @ X1 )
!= sz00 ) ),
inference(cnf,[status(esa)],[mZeroAdd]) ).
thf(zip_derived_cl1183,plain,
( ( ( sdtasdt0 @ xn @ xm )
!= sz00 )
| ( ( sdtasdt0 @ xr @ xm )
= sz00 )
| ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xr @ xm ) )
| ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xp @ xm ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl114,zip_derived_cl23]) ).
thf(zip_derived_cl1081_027,plain,
aNaturalNumber0 @ ( sdtasdt0 @ xp @ xm ),
inference(demod,[status(thm)],[zip_derived_cl1080,zip_derived_cl120,zip_derived_cl70]) ).
thf(zip_derived_cl1194,plain,
( ( ( sdtasdt0 @ xn @ xm )
!= sz00 )
| ( ( sdtasdt0 @ xr @ xm )
= sz00 )
| ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xr @ xm ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1183,zip_derived_cl1081]) ).
thf(zip_derived_cl1653,plain,
( ~ ( aNaturalNumber0 @ xm )
| ~ ( aNaturalNumber0 @ xr )
| ( ( sdtasdt0 @ xr @ xm )
= sz00 )
| ( ( sdtasdt0 @ xn @ xm )
!= sz00 ) ),
inference('sup-',[status(thm)],[zip_derived_cl5,zip_derived_cl1194]) ).
thf(zip_derived_cl71_028,plain,
aNaturalNumber0 @ xm,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl108_029,plain,
aNaturalNumber0 @ xr,
inference(cnf,[status(esa)],[m__1883]) ).
thf(zip_derived_cl1657,plain,
( ( ( sdtasdt0 @ xr @ xm )
= sz00 )
| ( ( sdtasdt0 @ xn @ xm )
!= sz00 ) ),
inference(demod,[status(thm)],[zip_derived_cl1653,zip_derived_cl71,zip_derived_cl108]) ).
thf(zip_derived_cl10_030,plain,
! [X0: $i,X1: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( ( sdtasdt0 @ X0 @ X1 )
= ( sdtasdt0 @ X1 @ X0 ) ) ),
inference(cnf,[status(esa)],[mMulComm]) ).
thf(zip_derived_cl1733,plain,
( ( sz00
= ( sdtasdt0 @ xm @ xr ) )
| ( ( sdtasdt0 @ xn @ xm )
!= sz00 )
| ~ ( aNaturalNumber0 @ xm )
| ~ ( aNaturalNumber0 @ xr ) ),
inference('sup+',[status(thm)],[zip_derived_cl1657,zip_derived_cl10]) ).
thf(zip_derived_cl71_031,plain,
aNaturalNumber0 @ xm,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl108_032,plain,
aNaturalNumber0 @ xr,
inference(cnf,[status(esa)],[m__1883]) ).
thf(zip_derived_cl1744,plain,
( ( sz00
= ( sdtasdt0 @ xm @ xr ) )
| ( ( sdtasdt0 @ xn @ xm )
!= sz00 ) ),
inference(demod,[status(thm)],[zip_derived_cl1733,zip_derived_cl71,zip_derived_cl108]) ).
thf(m_MulZero,axiom,
! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( ( sdtasdt0 @ W0 @ sz00 )
= sz00 )
& ( sz00
= ( sdtasdt0 @ sz00 @ W0 ) ) ) ) ).
thf(zip_derived_cl14,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ X0 @ sz00 )
= sz00 )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference(cnf,[status(esa)],[m_MulZero]) ).
thf(zip_derived_cl10_033,plain,
! [X0: $i,X1: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( ( sdtasdt0 @ X0 @ X1 )
= ( sdtasdt0 @ X1 @ X0 ) ) ),
inference(cnf,[status(esa)],[mMulComm]) ).
thf(zip_derived_cl122_034,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ xr @ xm )
!= ( sdtasdt0 @ xp @ X0 ) )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1205,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ xm @ xr )
!= ( sdtasdt0 @ xp @ X0 ) )
| ~ ( aNaturalNumber0 @ xr )
| ~ ( aNaturalNumber0 @ xm )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl122]) ).
thf(zip_derived_cl108_035,plain,
aNaturalNumber0 @ xr,
inference(cnf,[status(esa)],[m__1883]) ).
thf(zip_derived_cl71_036,plain,
aNaturalNumber0 @ xm,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl1248,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ xm @ xr )
!= ( sdtasdt0 @ xp @ X0 ) )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1205,zip_derived_cl108,zip_derived_cl71]) ).
thf(zip_derived_cl1312,plain,
( ( ( sdtasdt0 @ xm @ xr )
!= sz00 )
| ~ ( aNaturalNumber0 @ xp )
| ~ ( aNaturalNumber0 @ sz00 ) ),
inference('sup-',[status(thm)],[zip_derived_cl14,zip_derived_cl1248]) ).
thf(zip_derived_cl70_037,plain,
aNaturalNumber0 @ xp,
inference(cnf,[status(esa)],[m__1837]) ).
thf(mSortsC,axiom,
aNaturalNumber0 @ sz00 ).
thf(zip_derived_cl1,plain,
aNaturalNumber0 @ sz00,
inference(cnf,[status(esa)],[mSortsC]) ).
thf(zip_derived_cl1321,plain,
( ( sdtasdt0 @ xm @ xr )
!= sz00 ),
inference(demod,[status(thm)],[zip_derived_cl1312,zip_derived_cl70,zip_derived_cl1]) ).
thf(zip_derived_cl1745,plain,
( ( sdtasdt0 @ xn @ xm )
!= sz00 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl1744,zip_derived_cl1321]) ).
thf(zip_derived_cl1859,plain,
sdtlseqdt0 @ xp @ ( sdtasdt0 @ xn @ xm ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl1858,zip_derived_cl1745]) ).
thf(mLETran,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W2 ) )
=> ( sdtlseqdt0 @ W0 @ W2 ) ) ) ).
thf(zip_derived_cl33,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( sdtlseqdt0 @ X0 @ X1 )
| ~ ( aNaturalNumber0 @ X1 )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X2 )
| ( sdtlseqdt0 @ X0 @ X2 )
| ~ ( sdtlseqdt0 @ X1 @ X2 ) ),
inference(cnf,[status(esa)],[mLETran]) ).
thf(zip_derived_cl1866,plain,
! [X0: $i] :
( ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ X0 )
| ( sdtlseqdt0 @ xp @ X0 )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ xp )
| ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1859,zip_derived_cl33]) ).
thf(zip_derived_cl70_038,plain,
aNaturalNumber0 @ xp,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl1085_039,plain,
aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ),
inference(demod,[status(thm)],[zip_derived_cl1084,zip_derived_cl101,zip_derived_cl70]) ).
thf(zip_derived_cl1868,plain,
! [X0: $i] :
( ~ ( sdtlseqdt0 @ ( sdtasdt0 @ xn @ xm ) @ X0 )
| ( sdtlseqdt0 @ xp @ X0 )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1866,zip_derived_cl70,zip_derived_cl1085]) ).
thf(zip_derived_cl1934,plain,
! [X0: $i] :
( ( X0
!= ( sdtasdt0 @ xn @ xm ) )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ) )
| ~ ( aNaturalNumber0 @ X0 )
| ( sdtlseqdt0 @ xp @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl34,zip_derived_cl1868]) ).
thf(zip_derived_cl1085_040,plain,
aNaturalNumber0 @ ( sdtasdt0 @ xn @ xm ),
inference(demod,[status(thm)],[zip_derived_cl1084,zip_derived_cl101,zip_derived_cl70]) ).
thf(zip_derived_cl1936,plain,
! [X0: $i] :
( ( X0
!= ( sdtasdt0 @ xn @ xm ) )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X0 )
| ( sdtlseqdt0 @ xp @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1934,zip_derived_cl1085]) ).
thf(zip_derived_cl1937,plain,
! [X0: $i] :
( ( sdtlseqdt0 @ xp @ X0 )
| ~ ( aNaturalNumber0 @ X0 )
| ( X0
!= ( sdtasdt0 @ xn @ xm ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl1936]) ).
thf(zip_derived_cl33_041,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( sdtlseqdt0 @ X0 @ X1 )
| ~ ( aNaturalNumber0 @ X1 )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X2 )
| ( sdtlseqdt0 @ X0 @ X2 )
| ~ ( sdtlseqdt0 @ X1 @ X2 ) ),
inference(cnf,[status(esa)],[mLETran]) ).
thf(zip_derived_cl1942,plain,
! [X0: $i,X1: $i] :
( ( X0
!= ( sdtasdt0 @ xn @ xm ) )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( sdtlseqdt0 @ X0 @ X1 )
| ( sdtlseqdt0 @ xp @ X1 )
| ~ ( aNaturalNumber0 @ X1 )
| ~ ( aNaturalNumber0 @ xp )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl1937,zip_derived_cl33]) ).
thf(zip_derived_cl70_042,plain,
aNaturalNumber0 @ xp,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl1944,plain,
! [X0: $i,X1: $i] :
( ( X0
!= ( sdtasdt0 @ xn @ xm ) )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( sdtlseqdt0 @ X0 @ X1 )
| ( sdtlseqdt0 @ xp @ X1 )
| ~ ( aNaturalNumber0 @ X1 )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1942,zip_derived_cl70]) ).
thf(zip_derived_cl1945,plain,
! [X0: $i,X1: $i] :
( ~ ( aNaturalNumber0 @ X1 )
| ( sdtlseqdt0 @ xp @ X1 )
| ~ ( sdtlseqdt0 @ X0 @ X1 )
| ~ ( aNaturalNumber0 @ X0 )
| ( X0
!= ( sdtasdt0 @ xn @ xm ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl1944]) ).
thf(zip_derived_cl22972,plain,
( ( xm
!= ( sdtasdt0 @ xn @ xm ) )
| ~ ( aNaturalNumber0 @ xm )
| ( sdtlseqdt0 @ xp @ xm )
| ~ ( aNaturalNumber0 @ xm ) ),
inference('sup-',[status(thm)],[zip_derived_cl22970,zip_derived_cl1945]) ).
thf(zip_derived_cl71_043,plain,
aNaturalNumber0 @ xm,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl71_044,plain,
aNaturalNumber0 @ xm,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl22975,plain,
( ( xm
!= ( sdtasdt0 @ xn @ xm ) )
| ( sdtlseqdt0 @ xp @ xm ) ),
inference(demod,[status(thm)],[zip_derived_cl22972,zip_derived_cl71,zip_derived_cl71]) ).
thf(mDefLE,axiom,
! [W0: $i,W1: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
<=> ? [W2: $i] :
( ( ( sdtpldt0 @ W0 @ W2 )
= W1 )
& ( aNaturalNumber0 @ W2 ) ) ) ) ).
thf(zip_derived_cl25,plain,
! [X0: $i,X1: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( ( sdtpldt0 @ X0 @ ( sk_ @ X1 @ X0 ) )
= X1 )
| ~ ( sdtlseqdt0 @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[mDefLE]) ).
thf(zip_derived_cl22,plain,
! [X0: $i,X1: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( X0 = sz00 )
| ( ( sdtpldt0 @ X0 @ X1 )
!= sz00 ) ),
inference(cnf,[status(esa)],[mZeroAdd]) ).
thf(zip_derived_cl1971,plain,
! [X0: $i,X1: $i] :
( ( X0 != sz00 )
| ~ ( sdtlseqdt0 @ X1 @ X0 )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( X1 = sz00 )
| ~ ( aNaturalNumber0 @ ( sk_ @ X0 @ X1 ) )
| ~ ( aNaturalNumber0 @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl25,zip_derived_cl22]) ).
thf(zip_derived_cl1984,plain,
! [X0: $i,X1: $i] :
( ~ ( aNaturalNumber0 @ ( sk_ @ X0 @ X1 ) )
| ( X1 = sz00 )
| ~ ( aNaturalNumber0 @ X1 )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( sdtlseqdt0 @ X1 @ X0 )
| ( X0 != sz00 ) ),
inference(simplify,[status(thm)],[zip_derived_cl1971]) ).
thf(zip_derived_cl26,plain,
! [X0: $i,X1: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( aNaturalNumber0 @ ( sk_ @ X1 @ X0 ) )
| ~ ( sdtlseqdt0 @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[mDefLE]) ).
thf(zip_derived_cl35156,plain,
! [X0: $i,X1: $i] :
( ( X0 != sz00 )
| ~ ( sdtlseqdt0 @ X1 @ X0 )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( X1 = sz00 ) ),
inference(clc,[status(thm)],[zip_derived_cl1984,zip_derived_cl26]) ).
thf(zip_derived_cl35218,plain,
( ( xm
!= ( sdtasdt0 @ xn @ xm ) )
| ( xp = sz00 )
| ~ ( aNaturalNumber0 @ xp )
| ~ ( aNaturalNumber0 @ xm )
| ( xm != sz00 ) ),
inference('sup-',[status(thm)],[zip_derived_cl22975,zip_derived_cl35156]) ).
thf(zip_derived_cl70_045,plain,
aNaturalNumber0 @ xp,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl71_046,plain,
aNaturalNumber0 @ xm,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl35278,plain,
( ( xm
!= ( sdtasdt0 @ xn @ xm ) )
| ( xp = sz00 )
| ( xm != sz00 ) ),
inference(demod,[status(thm)],[zip_derived_cl35218,zip_derived_cl70,zip_derived_cl71]) ).
thf(zip_derived_cl95,plain,
xp != sz00,
inference(cnf,[status(esa)],[m__1860]) ).
thf(zip_derived_cl35279,plain,
( ( xm
!= ( sdtasdt0 @ xn @ xm ) )
| ( xm != sz00 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl35278,zip_derived_cl95]) ).
thf(zip_derived_cl35280,plain,
( ( sz00
!= ( sdtasdt0 @ xn @ sz00 ) )
| ( xm != sz00 ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl35279]) ).
thf(zip_derived_cl14_047,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ X0 @ sz00 )
= sz00 )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference(cnf,[status(esa)],[m_MulZero]) ).
thf(zip_derived_cl107_048,plain,
( ( sdtpldt0 @ xp @ xr )
= xn ),
inference(cnf,[status(esa)],[m__1883]) ).
thf(zip_derived_cl17,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ~ ( aNaturalNumber0 @ X2 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ X0 @ X2 ) @ X1 )
= ( sdtpldt0 @ ( sdtasdt0 @ X0 @ X1 ) @ ( sdtasdt0 @ X2 @ X1 ) ) ) ),
inference(cnf,[status(esa)],[mAMDistr]) ).
thf(zip_derived_cl1409,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ xn @ X0 )
= ( sdtpldt0 @ ( sdtasdt0 @ xp @ X0 ) @ ( sdtasdt0 @ xr @ X0 ) ) )
| ~ ( aNaturalNumber0 @ xr )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ xp ) ),
inference('sup+',[status(thm)],[zip_derived_cl107,zip_derived_cl17]) ).
thf(zip_derived_cl108_049,plain,
aNaturalNumber0 @ xr,
inference(cnf,[status(esa)],[m__1883]) ).
thf(zip_derived_cl70_050,plain,
aNaturalNumber0 @ xp,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl1420,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ xn @ X0 )
= ( sdtpldt0 @ ( sdtasdt0 @ xp @ X0 ) @ ( sdtasdt0 @ xr @ X0 ) ) )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1409,zip_derived_cl108,zip_derived_cl70]) ).
thf(zip_derived_cl18449,plain,
( ( ( sdtasdt0 @ xn @ sz00 )
= ( sdtpldt0 @ ( sdtasdt0 @ xp @ sz00 ) @ sz00 ) )
| ~ ( aNaturalNumber0 @ xr )
| ~ ( aNaturalNumber0 @ sz00 ) ),
inference('sup+',[status(thm)],[zip_derived_cl14,zip_derived_cl1420]) ).
thf(zip_derived_cl14_051,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ X0 @ sz00 )
= sz00 )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference(cnf,[status(esa)],[m_MulZero]) ).
thf(zip_derived_cl119_052,plain,
( ( sdtasdt0 @ xp @ xm )
= ( sdtasdt0 @ xp @ sk__11 ) ),
inference(cnf,[status(esa)],[m__2001]) ).
thf(mMulAsso,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 )
= ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) ).
thf(zip_derived_cl11,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ~ ( aNaturalNumber0 @ X2 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ X1 @ X0 ) @ X2 )
= ( sdtasdt0 @ X1 @ ( sdtasdt0 @ X0 @ X2 ) ) ) ),
inference(cnf,[status(esa)],[mMulAsso]) ).
thf(zip_derived_cl1274,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ ( sdtasdt0 @ xp @ xm ) @ X0 )
= ( sdtasdt0 @ xp @ ( sdtasdt0 @ sk__11 @ X0 ) ) )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ xp )
| ~ ( aNaturalNumber0 @ sk__11 ) ),
inference('sup+',[status(thm)],[zip_derived_cl119,zip_derived_cl11]) ).
thf(zip_derived_cl70_053,plain,
aNaturalNumber0 @ xp,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl120_054,plain,
aNaturalNumber0 @ sk__11,
inference(cnf,[status(esa)],[m__2001]) ).
thf(zip_derived_cl1290,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ ( sdtasdt0 @ xp @ xm ) @ X0 )
= ( sdtasdt0 @ xp @ ( sdtasdt0 @ sk__11 @ X0 ) ) )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1274,zip_derived_cl70,zip_derived_cl120]) ).
thf(zip_derived_cl119_055,plain,
( ( sdtasdt0 @ xp @ xm )
= ( sdtasdt0 @ xp @ sk__11 ) ),
inference(cnf,[status(esa)],[m__2001]) ).
thf(mMulCanc,axiom,
! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( W0 != sz00 )
=> ! [W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( ( sdtasdt0 @ W0 @ W1 )
= ( sdtasdt0 @ W0 @ W2 ) )
| ( ( sdtasdt0 @ W1 @ W0 )
= ( sdtasdt0 @ W2 @ W0 ) ) )
=> ( W1 = W2 ) ) ) ) ) ).
thf(zip_derived_cl21,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = sz00 )
| ( ( sdtasdt0 @ X0 @ X2 )
!= ( sdtasdt0 @ X0 @ X1 ) )
| ( X2 = X1 )
| ~ ( aNaturalNumber0 @ X1 )
| ~ ( aNaturalNumber0 @ X2 )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference(cnf,[status(esa)],[mMulCanc]) ).
thf(zip_derived_cl1784,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ xp @ xm )
!= ( sdtasdt0 @ xp @ X0 ) )
| ~ ( aNaturalNumber0 @ xp )
| ~ ( aNaturalNumber0 @ sk__11 )
| ~ ( aNaturalNumber0 @ X0 )
| ( sk__11 = X0 )
| ( xp = sz00 ) ),
inference('sup-',[status(thm)],[zip_derived_cl119,zip_derived_cl21]) ).
thf(zip_derived_cl70_056,plain,
aNaturalNumber0 @ xp,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl120_057,plain,
aNaturalNumber0 @ sk__11,
inference(cnf,[status(esa)],[m__2001]) ).
thf(zip_derived_cl1816,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ xp @ xm )
!= ( sdtasdt0 @ xp @ X0 ) )
| ~ ( aNaturalNumber0 @ X0 )
| ( sk__11 = X0 )
| ( xp = sz00 ) ),
inference(demod,[status(thm)],[zip_derived_cl1784,zip_derived_cl70,zip_derived_cl120]) ).
thf(zip_derived_cl95_058,plain,
xp != sz00,
inference(cnf,[status(esa)],[m__1860]) ).
thf(zip_derived_cl1817,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ xp @ xm )
!= ( sdtasdt0 @ xp @ X0 ) )
| ~ ( aNaturalNumber0 @ X0 )
| ( sk__11 = X0 ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl1816,zip_derived_cl95]) ).
thf(zip_derived_cl1884,plain,
( ( sk__11 = xm )
| ~ ( aNaturalNumber0 @ xm ) ),
inference(eq_res,[status(thm)],[zip_derived_cl1817]) ).
thf(zip_derived_cl71_059,plain,
aNaturalNumber0 @ xm,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl1885,plain,
sk__11 = xm,
inference(demod,[status(thm)],[zip_derived_cl1884,zip_derived_cl71]) ).
thf(zip_derived_cl10459,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ ( sdtasdt0 @ xp @ xm ) @ X0 )
= ( sdtasdt0 @ xp @ ( sdtasdt0 @ xm @ X0 ) ) )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1290,zip_derived_cl1885]) ).
thf(zip_derived_cl14_060,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ X0 @ sz00 )
= sz00 )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference(cnf,[status(esa)],[m_MulZero]) ).
thf(zip_derived_cl10493,plain,
( ( ( sdtasdt0 @ xp @ ( sdtasdt0 @ xm @ sz00 ) )
= sz00 )
| ~ ( aNaturalNumber0 @ sz00 )
| ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xp @ xm ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl10459,zip_derived_cl14]) ).
thf(zip_derived_cl1_061,plain,
aNaturalNumber0 @ sz00,
inference(cnf,[status(esa)],[mSortsC]) ).
thf(zip_derived_cl1081_062,plain,
aNaturalNumber0 @ ( sdtasdt0 @ xp @ xm ),
inference(demod,[status(thm)],[zip_derived_cl1080,zip_derived_cl120,zip_derived_cl70]) ).
thf(zip_derived_cl10611,plain,
( ( sdtasdt0 @ xp @ ( sdtasdt0 @ xm @ sz00 ) )
= sz00 ),
inference(demod,[status(thm)],[zip_derived_cl10493,zip_derived_cl1,zip_derived_cl1081]) ).
thf(zip_derived_cl11098,plain,
( ( ( sdtasdt0 @ xp @ sz00 )
= sz00 )
| ~ ( aNaturalNumber0 @ xm ) ),
inference('sup+',[status(thm)],[zip_derived_cl14,zip_derived_cl10611]) ).
thf(zip_derived_cl71_063,plain,
aNaturalNumber0 @ xm,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl11101,plain,
( ( sdtasdt0 @ xp @ sz00 )
= sz00 ),
inference(demod,[status(thm)],[zip_derived_cl11098,zip_derived_cl71]) ).
thf(zip_derived_cl1_064,plain,
aNaturalNumber0 @ sz00,
inference(cnf,[status(esa)],[mSortsC]) ).
thf(zip_derived_cl14_065,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ X0 @ sz00 )
= sz00 )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference(cnf,[status(esa)],[m_MulZero]) ).
thf(zip_derived_cl11_066,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ~ ( aNaturalNumber0 @ X2 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ X1 @ X0 ) @ X2 )
= ( sdtasdt0 @ X1 @ ( sdtasdt0 @ X0 @ X2 ) ) ) ),
inference(cnf,[status(esa)],[mMulAsso]) ).
thf(zip_derived_cl1264,plain,
! [X0: $i,X1: $i] :
( ( sz00
= ( sdtasdt0 @ X1 @ ( sdtasdt0 @ X0 @ sz00 ) ) )
| ~ ( aNaturalNumber0 @ ( sdtasdt0 @ X1 @ X0 ) )
| ~ ( aNaturalNumber0 @ sz00 )
| ~ ( aNaturalNumber0 @ X1 )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl14,zip_derived_cl11]) ).
thf(zip_derived_cl1_067,plain,
aNaturalNumber0 @ sz00,
inference(cnf,[status(esa)],[mSortsC]) ).
thf(zip_derived_cl1276,plain,
! [X0: $i,X1: $i] :
( ( sz00
= ( sdtasdt0 @ X1 @ ( sdtasdt0 @ X0 @ sz00 ) ) )
| ~ ( aNaturalNumber0 @ ( sdtasdt0 @ X1 @ X0 ) )
| ~ ( aNaturalNumber0 @ X1 )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1264,zip_derived_cl1]) ).
thf(zip_derived_cl5_068,plain,
! [X0: $i,X1: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( aNaturalNumber0 @ ( sdtasdt0 @ X0 @ X1 ) ) ),
inference(cnf,[status(esa)],[mSortsB_02]) ).
thf(zip_derived_cl8615,plain,
! [X0: $i,X1: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( sz00
= ( sdtasdt0 @ X1 @ ( sdtasdt0 @ X0 @ sz00 ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl1276,zip_derived_cl5]) ).
thf(zip_derived_cl14_069,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ X0 @ sz00 )
= sz00 )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference(cnf,[status(esa)],[m_MulZero]) ).
thf(zip_derived_cl11_070,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ~ ( aNaturalNumber0 @ X2 )
| ( ( sdtasdt0 @ ( sdtasdt0 @ X1 @ X0 ) @ X2 )
= ( sdtasdt0 @ X1 @ ( sdtasdt0 @ X0 @ X2 ) ) ) ),
inference(cnf,[status(esa)],[mMulAsso]) ).
thf(zip_derived_cl1268,plain,
! [X0: $i,X1: $i] :
( ( ( sdtasdt0 @ sz00 @ X0 )
= ( sdtasdt0 @ X1 @ ( sdtasdt0 @ sz00 @ X0 ) ) )
| ~ ( aNaturalNumber0 @ X1 )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ~ ( aNaturalNumber0 @ sz00 ) ),
inference('sup+',[status(thm)],[zip_derived_cl14,zip_derived_cl11]) ).
thf(zip_derived_cl1_071,plain,
aNaturalNumber0 @ sz00,
inference(cnf,[status(esa)],[mSortsC]) ).
thf(zip_derived_cl1280,plain,
! [X0: $i,X1: $i] :
( ( ( sdtasdt0 @ sz00 @ X0 )
= ( sdtasdt0 @ X1 @ ( sdtasdt0 @ sz00 @ X0 ) ) )
| ~ ( aNaturalNumber0 @ X1 )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl1268,zip_derived_cl1]) ).
thf(zip_derived_cl1281,plain,
! [X0: $i,X1: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( ( sdtasdt0 @ sz00 @ X0 )
= ( sdtasdt0 @ X1 @ ( sdtasdt0 @ sz00 @ X0 ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl1280]) ).
thf(zip_derived_cl9179,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ sz00 @ sz00 )
= sz00 )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ sz00 )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ sz00 ) ),
inference('sup+',[status(thm)],[zip_derived_cl8615,zip_derived_cl1281]) ).
thf(zip_derived_cl1_072,plain,
aNaturalNumber0 @ sz00,
inference(cnf,[status(esa)],[mSortsC]) ).
thf(zip_derived_cl1_073,plain,
aNaturalNumber0 @ sz00,
inference(cnf,[status(esa)],[mSortsC]) ).
thf(zip_derived_cl9189,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ sz00 @ sz00 )
= sz00 )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl9179,zip_derived_cl1,zip_derived_cl1]) ).
thf(zip_derived_cl9190,plain,
! [X0: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ( ( sdtasdt0 @ sz00 @ sz00 )
= sz00 ) ),
inference(simplify,[status(thm)],[zip_derived_cl9189]) ).
thf(zip_derived_cl9279,plain,
( ( sdtasdt0 @ sz00 @ sz00 )
= sz00 ),
inference('sup-',[status(thm)],[zip_derived_cl1,zip_derived_cl9190]) ).
thf(m_AddZero,axiom,
! [W0: $i] :
( ( aNaturalNumber0 @ W0 )
=> ( ( ( sdtpldt0 @ W0 @ sz00 )
= W0 )
& ( W0
= ( sdtpldt0 @ sz00 @ W0 ) ) ) ) ).
thf(zip_derived_cl8,plain,
! [X0: $i] :
( ( ( sdtpldt0 @ X0 @ sz00 )
= X0 )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference(cnf,[status(esa)],[m_AddZero]) ).
thf(zip_derived_cl16_074,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ~ ( aNaturalNumber0 @ X2 )
| ( ( sdtasdt0 @ X1 @ ( sdtpldt0 @ X0 @ X2 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ X1 @ X0 ) @ ( sdtasdt0 @ X1 @ X2 ) ) ) ),
inference(cnf,[status(esa)],[mAMDistr]) ).
thf(zip_derived_cl1346,plain,
! [X0: $i,X1: $i] :
( ( ( sdtasdt0 @ X1 @ X0 )
= ( sdtpldt0 @ ( sdtasdt0 @ X1 @ X0 ) @ ( sdtasdt0 @ X1 @ sz00 ) ) )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ sz00 )
| ~ ( aNaturalNumber0 @ X1 )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl8,zip_derived_cl16]) ).
thf(zip_derived_cl1_075,plain,
aNaturalNumber0 @ sz00,
inference(cnf,[status(esa)],[mSortsC]) ).
thf(zip_derived_cl1355,plain,
! [X0: $i,X1: $i] :
( ( ( sdtasdt0 @ X1 @ X0 )
= ( sdtpldt0 @ ( sdtasdt0 @ X1 @ X0 ) @ ( sdtasdt0 @ X1 @ sz00 ) ) )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1346,zip_derived_cl1]) ).
thf(zip_derived_cl1356,plain,
! [X0: $i,X1: $i] :
( ~ ( aNaturalNumber0 @ X1 )
| ~ ( aNaturalNumber0 @ X0 )
| ( ( sdtasdt0 @ X1 @ X0 )
= ( sdtpldt0 @ ( sdtasdt0 @ X1 @ X0 ) @ ( sdtasdt0 @ X1 @ sz00 ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl1355]) ).
thf(zip_derived_cl13103,plain,
( ( ( sdtasdt0 @ sz00 @ sz00 )
= ( sdtpldt0 @ sz00 @ ( sdtasdt0 @ sz00 @ sz00 ) ) )
| ~ ( aNaturalNumber0 @ sz00 )
| ~ ( aNaturalNumber0 @ sz00 ) ),
inference('sup+',[status(thm)],[zip_derived_cl9279,zip_derived_cl1356]) ).
thf(zip_derived_cl9279_076,plain,
( ( sdtasdt0 @ sz00 @ sz00 )
= sz00 ),
inference('sup-',[status(thm)],[zip_derived_cl1,zip_derived_cl9190]) ).
thf(zip_derived_cl9279_077,plain,
( ( sdtasdt0 @ sz00 @ sz00 )
= sz00 ),
inference('sup-',[status(thm)],[zip_derived_cl1,zip_derived_cl9190]) ).
thf(zip_derived_cl1_078,plain,
aNaturalNumber0 @ sz00,
inference(cnf,[status(esa)],[mSortsC]) ).
thf(zip_derived_cl1_079,plain,
aNaturalNumber0 @ sz00,
inference(cnf,[status(esa)],[mSortsC]) ).
thf(zip_derived_cl13168,plain,
( sz00
= ( sdtpldt0 @ sz00 @ sz00 ) ),
inference(demod,[status(thm)],[zip_derived_cl13103,zip_derived_cl9279,zip_derived_cl9279,zip_derived_cl1,zip_derived_cl1]) ).
thf(zip_derived_cl108_080,plain,
aNaturalNumber0 @ xr,
inference(cnf,[status(esa)],[m__1883]) ).
thf(zip_derived_cl1_081,plain,
aNaturalNumber0 @ sz00,
inference(cnf,[status(esa)],[mSortsC]) ).
thf(zip_derived_cl18489,plain,
( ( sdtasdt0 @ xn @ sz00 )
= sz00 ),
inference(demod,[status(thm)],[zip_derived_cl18449,zip_derived_cl11101,zip_derived_cl13168,zip_derived_cl108,zip_derived_cl1]) ).
thf(zip_derived_cl35391,plain,
( ( sz00 != sz00 )
| ( xm != sz00 ) ),
inference(demod,[status(thm)],[zip_derived_cl35280,zip_derived_cl18489]) ).
thf(zip_derived_cl35392,plain,
xm != sz00,
inference(simplify,[status(thm)],[zip_derived_cl35391]) ).
thf(zip_derived_cl14_082,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ X0 @ sz00 )
= sz00 )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference(cnf,[status(esa)],[m_MulZero]) ).
thf(zip_derived_cl8_083,plain,
! [X0: $i] :
( ( ( sdtpldt0 @ X0 @ sz00 )
= X0 )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference(cnf,[status(esa)],[m_AddZero]) ).
thf(zip_derived_cl107_084,plain,
( ( sdtpldt0 @ xp @ xr )
= xn ),
inference(cnf,[status(esa)],[m__1883]) ).
thf(zip_derived_cl19_085,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ~ ( aNaturalNumber0 @ X2 )
| ( X0 = X2 )
| ( ( sdtpldt0 @ X1 @ X0 )
!= ( sdtpldt0 @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[mAddCanc]) ).
thf(zip_derived_cl1547,plain,
! [X0: $i] :
( ( xn
!= ( sdtpldt0 @ xp @ X0 ) )
| ( xr = X0 )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ xp )
| ~ ( aNaturalNumber0 @ xr ) ),
inference('sup-',[status(thm)],[zip_derived_cl107,zip_derived_cl19]) ).
thf(zip_derived_cl70_086,plain,
aNaturalNumber0 @ xp,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl108_087,plain,
aNaturalNumber0 @ xr,
inference(cnf,[status(esa)],[m__1883]) ).
thf(zip_derived_cl1569,plain,
! [X0: $i] :
( ( xn
!= ( sdtpldt0 @ xp @ X0 ) )
| ( xr = X0 )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1547,zip_derived_cl70,zip_derived_cl108]) ).
thf(zip_derived_cl5218,plain,
( ( xn != xp )
| ~ ( aNaturalNumber0 @ xp )
| ~ ( aNaturalNumber0 @ sz00 )
| ( xr = sz00 ) ),
inference('sup-',[status(thm)],[zip_derived_cl8,zip_derived_cl1569]) ).
thf(zip_derived_cl70_088,plain,
aNaturalNumber0 @ xp,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl1_089,plain,
aNaturalNumber0 @ sz00,
inference(cnf,[status(esa)],[mSortsC]) ).
thf(zip_derived_cl5227,plain,
( ( xn != xp )
| ( xr = sz00 ) ),
inference(demod,[status(thm)],[zip_derived_cl5218,zip_derived_cl70,zip_derived_cl1]) ).
thf(zip_derived_cl1321_090,plain,
( ( sdtasdt0 @ xm @ xr )
!= sz00 ),
inference(demod,[status(thm)],[zip_derived_cl1312,zip_derived_cl70,zip_derived_cl1]) ).
thf(zip_derived_cl5258,plain,
( ( ( sdtasdt0 @ xm @ sz00 )
!= sz00 )
| ( xn != xp ) ),
inference('sup-',[status(thm)],[zip_derived_cl5227,zip_derived_cl1321]) ).
thf(zip_derived_cl5364,plain,
( ( sz00 != sz00 )
| ~ ( aNaturalNumber0 @ xm )
| ( xn != xp ) ),
inference('sup-',[status(thm)],[zip_derived_cl14,zip_derived_cl5258]) ).
thf(zip_derived_cl71_091,plain,
aNaturalNumber0 @ xm,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl5367,plain,
( ( sz00 != sz00 )
| ( xn != xp ) ),
inference(demod,[status(thm)],[zip_derived_cl5364,zip_derived_cl71]) ).
thf(zip_derived_cl5368,plain,
xn != xp,
inference(simplify,[status(thm)],[zip_derived_cl5367]) ).
thf(zip_derived_cl52339,plain,
! [X0: $i] :
( ( aNaturalNumber0 @ X0 )
| ( X0
!= ( sdtasdt0 @ xr @ xm ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl52338,zip_derived_cl35392,zip_derived_cl5368]) ).
thf(zip_derived_cl52344,plain,
aNaturalNumber0 @ ( sdtasdt0 @ xr @ xm ),
inference(eq_res,[status(thm)],[zip_derived_cl52339]) ).
thf(zip_derived_cl68964,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ xn @ xm )
!= ( sdtpldt0 @ ( sdtasdt0 @ xm @ xp ) @ X0 ) )
| ( ( sdtasdt0 @ xr @ xm )
= X0 )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2724,zip_derived_cl52344]) ).
thf(zip_derived_cl68982,plain,
( ( ( sdtasdt0 @ xn @ xm )
!= ( sdtasdt0 @ xm @ xn ) )
| ~ ( aNaturalNumber0 @ xm )
| ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xm @ xr ) )
| ( ( sdtasdt0 @ xr @ xm )
= ( sdtasdt0 @ xm @ xr ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1361,zip_derived_cl68964]) ).
thf(zip_derived_cl10_092,plain,
! [X0: $i,X1: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( ( sdtasdt0 @ X0 @ X1 )
= ( sdtasdt0 @ X1 @ X0 ) ) ),
inference(cnf,[status(esa)],[mMulComm]) ).
thf(zip_derived_cl1243_093,plain,
( ( sdtasdt0 @ xn @ xm )
= ( sdtpldt0 @ ( sdtasdt0 @ xm @ xp ) @ ( sdtasdt0 @ xr @ xm ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1200,zip_derived_cl70,zip_derived_cl71]) ).
thf(zip_derived_cl2715,plain,
( ( ( sdtasdt0 @ xn @ xm )
= ( sdtpldt0 @ ( sdtasdt0 @ xm @ xp ) @ ( sdtasdt0 @ xm @ xr ) ) )
| ~ ( aNaturalNumber0 @ xm )
| ~ ( aNaturalNumber0 @ xr ) ),
inference('sup+',[status(thm)],[zip_derived_cl10,zip_derived_cl1243]) ).
thf(zip_derived_cl71_094,plain,
aNaturalNumber0 @ xm,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl108_095,plain,
aNaturalNumber0 @ xr,
inference(cnf,[status(esa)],[m__1883]) ).
thf(zip_derived_cl2717,plain,
( ( sdtasdt0 @ xn @ xm )
= ( sdtpldt0 @ ( sdtasdt0 @ xm @ xp ) @ ( sdtasdt0 @ xm @ xr ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2715,zip_derived_cl71,zip_derived_cl108]) ).
thf(zip_derived_cl1361_096,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ X0 @ xn )
= ( sdtpldt0 @ ( sdtasdt0 @ X0 @ xp ) @ ( sdtasdt0 @ X0 @ xr ) ) )
| ~ ( aNaturalNumber0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1350,zip_derived_cl108,zip_derived_cl70]) ).
thf(zip_derived_cl13953,plain,
( ( ( sdtasdt0 @ xm @ xn )
= ( sdtasdt0 @ xn @ xm ) )
| ~ ( aNaturalNumber0 @ xm ) ),
inference('sup+',[status(thm)],[zip_derived_cl2717,zip_derived_cl1361]) ).
thf(zip_derived_cl71_097,plain,
aNaturalNumber0 @ xm,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl13979,plain,
( ( sdtasdt0 @ xm @ xn )
= ( sdtasdt0 @ xn @ xm ) ),
inference(demod,[status(thm)],[zip_derived_cl13953,zip_derived_cl71]) ).
thf(zip_derived_cl71_098,plain,
aNaturalNumber0 @ xm,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl10_099,plain,
! [X0: $i,X1: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( ( sdtasdt0 @ X0 @ X1 )
= ( sdtasdt0 @ X1 @ X0 ) ) ),
inference(cnf,[status(esa)],[mMulComm]) ).
thf(zip_derived_cl52344_100,plain,
aNaturalNumber0 @ ( sdtasdt0 @ xr @ xm ),
inference(eq_res,[status(thm)],[zip_derived_cl52339]) ).
thf(zip_derived_cl52377,plain,
( ( aNaturalNumber0 @ ( sdtasdt0 @ xm @ xr ) )
| ~ ( aNaturalNumber0 @ xm )
| ~ ( aNaturalNumber0 @ xr ) ),
inference('sup+',[status(thm)],[zip_derived_cl10,zip_derived_cl52344]) ).
thf(zip_derived_cl71_101,plain,
aNaturalNumber0 @ xm,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl108_102,plain,
aNaturalNumber0 @ xr,
inference(cnf,[status(esa)],[m__1883]) ).
thf(zip_derived_cl52379,plain,
aNaturalNumber0 @ ( sdtasdt0 @ xm @ xr ),
inference(demod,[status(thm)],[zip_derived_cl52377,zip_derived_cl71,zip_derived_cl108]) ).
thf(zip_derived_cl69009,plain,
( ( ( sdtasdt0 @ xn @ xm )
!= ( sdtasdt0 @ xn @ xm ) )
| ( ( sdtasdt0 @ xr @ xm )
= ( sdtasdt0 @ xm @ xr ) ) ),
inference(demod,[status(thm)],[zip_derived_cl68982,zip_derived_cl13979,zip_derived_cl71,zip_derived_cl52379]) ).
thf(zip_derived_cl69010,plain,
( ( sdtasdt0 @ xr @ xm )
= ( sdtasdt0 @ xm @ xr ) ),
inference(simplify,[status(thm)],[zip_derived_cl69009]) ).
thf(zip_derived_cl69028,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ xm @ xr )
!= X0 )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( doDivides0 @ xp @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl2855,zip_derived_cl69010]) ).
thf(zip_derived_cl10_103,plain,
! [X0: $i,X1: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( ( sdtasdt0 @ X0 @ X1 )
= ( sdtasdt0 @ X1 @ X0 ) ) ),
inference(cnf,[status(esa)],[mMulComm]) ).
thf(zip_derived_cl52339_104,plain,
! [X0: $i] :
( ( aNaturalNumber0 @ X0 )
| ( X0
!= ( sdtasdt0 @ xr @ xm ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl52338,zip_derived_cl35392,zip_derived_cl5368]) ).
thf(zip_derived_cl52342,plain,
! [X0: $i] :
( ( X0
!= ( sdtasdt0 @ xm @ xr ) )
| ~ ( aNaturalNumber0 @ xm )
| ~ ( aNaturalNumber0 @ xr )
| ( aNaturalNumber0 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl52339]) ).
thf(zip_derived_cl71_105,plain,
aNaturalNumber0 @ xm,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl108_106,plain,
aNaturalNumber0 @ xr,
inference(cnf,[status(esa)],[m__1883]) ).
thf(zip_derived_cl52345,plain,
! [X0: $i] :
( ( X0
!= ( sdtasdt0 @ xm @ xr ) )
| ( aNaturalNumber0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl52342,zip_derived_cl71,zip_derived_cl108]) ).
thf(zip_derived_cl72942,plain,
! [X0: $i] :
( ~ ( doDivides0 @ xp @ X0 )
| ( ( sdtasdt0 @ xm @ xr )
!= X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl69028,zip_derived_cl52345]) ).
thf(zip_derived_cl1243_107,plain,
( ( sdtasdt0 @ xn @ xm )
= ( sdtpldt0 @ ( sdtasdt0 @ xm @ xp ) @ ( sdtasdt0 @ xr @ xm ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1200,zip_derived_cl70,zip_derived_cl71]) ).
thf(mDivMin,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aNaturalNumber0 @ W0 )
& ( aNaturalNumber0 @ W1 )
& ( aNaturalNumber0 @ W2 ) )
=> ( ( ( doDivides0 @ W0 @ W1 )
& ( doDivides0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) ) )
=> ( doDivides0 @ W0 @ W2 ) ) ) ).
thf(zip_derived_cl57,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( doDivides0 @ X0 @ X1 )
| ~ ( aNaturalNumber0 @ X1 )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X2 )
| ( doDivides0 @ X0 @ X2 )
| ~ ( doDivides0 @ X0 @ ( sdtpldt0 @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[mDivMin]) ).
thf(zip_derived_cl3046,plain,
! [X0: $i] :
( ~ ( doDivides0 @ X0 @ ( sdtasdt0 @ xn @ xm ) )
| ( doDivides0 @ X0 @ ( sdtasdt0 @ xr @ xm ) )
| ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xr @ xm ) )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xm @ xp ) )
| ~ ( doDivides0 @ X0 @ ( sdtasdt0 @ xm @ xp ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1243,zip_derived_cl57]) ).
thf(zip_derived_cl1246_108,plain,
aNaturalNumber0 @ ( sdtasdt0 @ xm @ xp ),
inference(demod,[status(thm)],[zip_derived_cl1203,zip_derived_cl70,zip_derived_cl71]) ).
thf(zip_derived_cl3062,plain,
! [X0: $i] :
( ~ ( doDivides0 @ X0 @ ( sdtasdt0 @ xn @ xm ) )
| ( doDivides0 @ X0 @ ( sdtasdt0 @ xr @ xm ) )
| ~ ( aNaturalNumber0 @ ( sdtasdt0 @ xr @ xm ) )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( doDivides0 @ X0 @ ( sdtasdt0 @ xm @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3046,zip_derived_cl1246]) ).
thf(zip_derived_cl69010_109,plain,
( ( sdtasdt0 @ xr @ xm )
= ( sdtasdt0 @ xm @ xr ) ),
inference(simplify,[status(thm)],[zip_derived_cl69009]) ).
thf(zip_derived_cl69010_110,plain,
( ( sdtasdt0 @ xr @ xm )
= ( sdtasdt0 @ xm @ xr ) ),
inference(simplify,[status(thm)],[zip_derived_cl69009]) ).
thf(zip_derived_cl52379_111,plain,
aNaturalNumber0 @ ( sdtasdt0 @ xm @ xr ),
inference(demod,[status(thm)],[zip_derived_cl52377,zip_derived_cl71,zip_derived_cl108]) ).
thf(zip_derived_cl85280,plain,
! [X0: $i] :
( ~ ( doDivides0 @ X0 @ ( sdtasdt0 @ xn @ xm ) )
| ( doDivides0 @ X0 @ ( sdtasdt0 @ xm @ xr ) )
| ~ ( aNaturalNumber0 @ X0 )
| ~ ( doDivides0 @ X0 @ ( sdtasdt0 @ xm @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3062,zip_derived_cl69010,zip_derived_cl69010,zip_derived_cl52379]) ).
thf(zip_derived_cl85326,plain,
( ( ( sdtasdt0 @ xm @ xr )
!= ( sdtasdt0 @ xm @ xr ) )
| ~ ( doDivides0 @ xp @ ( sdtasdt0 @ xm @ xp ) )
| ~ ( aNaturalNumber0 @ xp )
| ~ ( doDivides0 @ xp @ ( sdtasdt0 @ xn @ xm ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl72942,zip_derived_cl85280]) ).
thf(zip_derived_cl10_112,plain,
! [X0: $i,X1: $i] :
( ~ ( aNaturalNumber0 @ X0 )
| ~ ( aNaturalNumber0 @ X1 )
| ( ( sdtasdt0 @ X0 @ X1 )
= ( sdtasdt0 @ X1 @ X0 ) ) ),
inference(cnf,[status(esa)],[mMulComm]) ).
thf(zip_derived_cl121,plain,
doDivides0 @ xp @ ( sdtasdt0 @ xp @ xm ),
inference(cnf,[status(esa)],[m__2001]) ).
thf(zip_derived_cl1202,plain,
( ( doDivides0 @ xp @ ( sdtasdt0 @ xm @ xp ) )
| ~ ( aNaturalNumber0 @ xp )
| ~ ( aNaturalNumber0 @ xm ) ),
inference('sup+',[status(thm)],[zip_derived_cl10,zip_derived_cl121]) ).
thf(zip_derived_cl70_113,plain,
aNaturalNumber0 @ xp,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl71_114,plain,
aNaturalNumber0 @ xm,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl1245,plain,
doDivides0 @ xp @ ( sdtasdt0 @ xm @ xp ),
inference(demod,[status(thm)],[zip_derived_cl1202,zip_derived_cl70,zip_derived_cl71]) ).
thf(zip_derived_cl70_115,plain,
aNaturalNumber0 @ xp,
inference(cnf,[status(esa)],[m__1837]) ).
thf(zip_derived_cl102_116,plain,
doDivides0 @ xp @ ( sdtasdt0 @ xn @ xm ),
inference(cnf,[status(esa)],[m__1860]) ).
thf(zip_derived_cl85354,plain,
( ( sdtasdt0 @ xm @ xr )
!= ( sdtasdt0 @ xm @ xr ) ),
inference(demod,[status(thm)],[zip_derived_cl85326,zip_derived_cl1245,zip_derived_cl70,zip_derived_cl102]) ).
thf(zip_derived_cl85355,plain,
$false,
inference(simplify,[status(thm)],[zip_derived_cl85354]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : NUM492+3 : TPTP v9.2.0. Released v4.0.0.
% 0.04/0.10 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.TkzemE2Lah true
% 0.07/0.31 % Computer : n005.cluster.edu
% 0.07/0.31 % Model : x86_64 x86_64
% 0.07/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.31 % Memory : 8042.1875MB
% 0.07/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.31 % CPULimit : 300
% 0.07/0.31 % WCLimit : 300
% 0.07/0.31 % DateTime : Wed Oct 1 16:28:38 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.12/0.32 % Running portfolio for 300 s
% 0.12/0.32 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.32 % Number of cores: 8
% 0.12/0.34 % Python version: Python 3.6.8
% 0.12/0.35 % Running in FO mode
% 0.45/0.71 % Total configuration time : 435
% 0.45/0.71 % Estimated wc time : 1092
% 0.45/0.71 % Estimated cpu time (7 cpus) : 156.0
% 0.45/0.80 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.45/0.80 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.45/0.80 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.45/0.80 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.45/0.80 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.45/0.80 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.45/0.81 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 119.35/19.71 % Solved by fo/fo3_bce.sh.
% 119.35/19.71 % BCE start: 124
% 119.35/19.71 % BCE eliminated: 1
% 119.35/19.71 % PE start: 123
% 119.35/19.71 logic: eq
% 119.35/19.71 % PE eliminated: -8
% 119.35/19.71 % done 6099 iterations in 18.859s
% 119.35/19.71 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 119.35/19.71 % SZS output start Refutation
% See solution above
% 119.35/19.71
% 119.35/19.71
% 119.35/19.71 % Terminating...
% 120.23/19.85 % Runner terminated.
% 120.23/19.86 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------