TSTP Solution File: NUM454+6 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM454+6 : TPTP v8.1.2. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.h7rn5ww7H8 true
% Computer : n003.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 Aug 31 12:41:33 EDT 2023
% Result : Theorem 6.26s 1.51s
% Output : Refutation 6.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 39
% Syntax : Number of formulae : 359 ( 190 unt; 19 typ; 0 def)
% Number of atoms : 673 ( 258 equ; 0 cnn)
% Maximal formula atoms : 26 ( 1 avg)
% Number of connectives : 2663 ( 252 ~; 256 |; 53 &;2078 @)
% ( 6 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 19 usr; 8 con; 0-3 aty)
% Number of variables : 176 ( 0 ^; 170 !; 6 ?; 176 :)
% Comments :
%------------------------------------------------------------------------------
thf(smndt0_type,type,
smndt0: $i > $i ).
thf(sdtasdt0_type,type,
sdtasdt0: $i > $i > $i ).
thf(aInteger0_type,type,
aInteger0: $i > $o ).
thf(sz10_type,type,
sz10: $i ).
thf(xS_type,type,
xS: $i ).
thf(xp_type,type,
xp: $i ).
thf(sk__26_type,type,
sk__26: $i ).
thf(cS2076_type,type,
cS2076: $i ).
thf(sz00_type,type,
sz00: $i ).
thf(sdtpldt0_type,type,
sdtpldt0: $i > $i > $i ).
thf(sbsmnsldt0_type,type,
sbsmnsldt0: $i > $i ).
thf(szAzrzSzezqlpdtcmdtrp0_type,type,
szAzrzSzezqlpdtcmdtrp0: $i > $i > $i ).
thf(stldt0_type,type,
stldt0: $i > $i ).
thf(aSubsetOf0_type,type,
aSubsetOf0: $i > $i > $o ).
thf(aElementOf0_type,type,
aElementOf0: $i > $i > $o ).
thf(aDivisorOf0_type,type,
aDivisorOf0: $i > $i > $o ).
thf(sdteqdtlpzmzozddtrp0_type,type,
sdteqdtlpzmzozddtrp0: $i > $i > $i > $o ).
thf(sk__27_type,type,
sk__27: $i ).
thf(aSet0_type,type,
aSet0: $i > $o ).
thf(mAddZero,axiom,
! [W0: $i] :
( ( aInteger0 @ W0 )
=> ( ( ( sdtpldt0 @ W0 @ sz00 )
= W0 )
& ( W0
= ( sdtpldt0 @ sz00 @ W0 ) ) ) ) ).
thf(zip_derived_cl9,plain,
! [X0: $i] :
( ( X0
= ( sdtpldt0 @ sz00 @ X0 ) )
| ~ ( aInteger0 @ X0 ) ),
inference(cnf,[status(esa)],[mAddZero]) ).
thf(mMulOne,axiom,
! [W0: $i] :
( ( aInteger0 @ W0 )
=> ( ( ( sdtasdt0 @ W0 @ sz10 )
= W0 )
& ( W0
= ( sdtasdt0 @ sz10 @ W0 ) ) ) ) ).
thf(zip_derived_cl14,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ X0 @ sz10 )
= X0 )
| ~ ( aInteger0 @ X0 ) ),
inference(cnf,[status(esa)],[mMulOne]) ).
thf(m__2232,axiom,
( ( aElementOf0 @ ( sdtpldt0 @ sz10 @ ( smndt0 @ xp ) ) @ ( szAzrzSzezqlpdtcmdtrp0 @ sz10 @ xp ) )
& ( sdteqdtlpzmzozddtrp0 @ ( sdtpldt0 @ sz10 @ ( smndt0 @ xp ) ) @ sz10 @ xp )
& ( aDivisorOf0 @ xp @ ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ ( smndt0 @ xp ) ) @ ( smndt0 @ sz10 ) ) )
& ? [W0: $i] :
( ( ( sdtasdt0 @ xp @ W0 )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ ( smndt0 @ xp ) ) @ ( smndt0 @ sz10 ) ) )
& ( aInteger0 @ W0 ) )
& ( aElementOf0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( szAzrzSzezqlpdtcmdtrp0 @ sz10 @ xp ) )
& ( sdteqdtlpzmzozddtrp0 @ ( sdtpldt0 @ sz10 @ xp ) @ sz10 @ xp )
& ( aDivisorOf0 @ xp @ ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( smndt0 @ sz10 ) ) )
& ? [W0: $i] :
( ( ( sdtasdt0 @ xp @ W0 )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( smndt0 @ sz10 ) ) )
& ( aInteger0 @ W0 ) ) ) ).
thf(zip_derived_cl218,plain,
( ( sdtasdt0 @ xp @ sk__26 )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ ( smndt0 @ xp ) ) @ ( smndt0 @ sz10 ) ) ),
inference(cnf,[status(esa)],[m__2232]) ).
thf(m__,conjecture,
( ( ( sdtpldt0 @ sz10 @ xp )
!= ( smndt0 @ sz10 ) )
| ( ( sdtpldt0 @ sz10 @ ( smndt0 @ xp ) )
!= ( smndt0 @ sz10 ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ( ( ( sdtpldt0 @ sz10 @ xp )
!= ( smndt0 @ sz10 ) )
| ( ( sdtpldt0 @ sz10 @ ( smndt0 @ xp ) )
!= ( smndt0 @ sz10 ) ) ),
inference('cnf.neg',[status(esa)],[m__]) ).
thf(zip_derived_cl225,plain,
( ( sdtpldt0 @ sz10 @ ( smndt0 @ xp ) )
= ( smndt0 @ sz10 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl226,plain,
( ( sdtpldt0 @ sz10 @ xp )
= ( smndt0 @ sz10 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1844,plain,
( ( sdtpldt0 @ sz10 @ ( smndt0 @ xp ) )
= ( sdtpldt0 @ sz10 @ xp ) ),
inference(demod,[status(thm)],[zip_derived_cl225,zip_derived_cl226]) ).
thf(zip_derived_cl226_001,plain,
( ( sdtpldt0 @ sz10 @ xp )
= ( smndt0 @ sz10 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl213,plain,
( ( sdtasdt0 @ xp @ sk__27 )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( smndt0 @ sz10 ) ) ),
inference(cnf,[status(esa)],[m__2232]) ).
thf(zip_derived_cl226_002,plain,
( ( sdtpldt0 @ sz10 @ xp )
= ( smndt0 @ sz10 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1848,plain,
( ( sdtasdt0 @ xp @ sk__27 )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( sdtpldt0 @ sz10 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl213,zip_derived_cl226]) ).
thf(zip_derived_cl1851,plain,
( ( sdtasdt0 @ xp @ sk__26 )
= ( sdtasdt0 @ xp @ sk__27 ) ),
inference(demod,[status(thm)],[zip_derived_cl218,zip_derived_cl1844,zip_derived_cl226,zip_derived_cl1848]) ).
thf(mMulAsso,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aInteger0 @ W0 )
& ( aInteger0 @ W1 )
& ( aInteger0 @ W2 ) )
=> ( ( sdtasdt0 @ W0 @ ( sdtasdt0 @ W1 @ W2 ) )
= ( sdtasdt0 @ ( sdtasdt0 @ W0 @ W1 ) @ W2 ) ) ) ).
thf(zip_derived_cl12,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X1 )
| ~ ( aInteger0 @ X2 )
| ( ( sdtasdt0 @ X1 @ ( sdtasdt0 @ X0 @ X2 ) )
= ( sdtasdt0 @ ( sdtasdt0 @ X1 @ X0 ) @ X2 ) ) ),
inference(cnf,[status(esa)],[mMulAsso]) ).
thf(zip_derived_cl2002,plain,
! [X0: $i] :
( ~ ( aInteger0 @ sk__27 )
| ~ ( aInteger0 @ xp )
| ~ ( aInteger0 @ X0 )
| ( ( sdtasdt0 @ xp @ ( sdtasdt0 @ sk__27 @ X0 ) )
= ( sdtasdt0 @ ( sdtasdt0 @ xp @ sk__26 ) @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1851,zip_derived_cl12]) ).
thf(zip_derived_cl214,plain,
aInteger0 @ sk__27,
inference(cnf,[status(esa)],[m__2232]) ).
thf(m__2171,axiom,
( ( aSubsetOf0 @ ( szAzrzSzezqlpdtcmdtrp0 @ sz10 @ xp ) @ ( stldt0 @ ( sbsmnsldt0 @ xS ) ) )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ ( szAzrzSzezqlpdtcmdtrp0 @ sz10 @ xp ) )
=> ( aElementOf0 @ W0 @ ( stldt0 @ ( sbsmnsldt0 @ xS ) ) ) )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ ( stldt0 @ ( sbsmnsldt0 @ xS ) ) )
<=> ( ( aInteger0 @ W0 )
& ~ ( aElementOf0 @ W0 @ ( sbsmnsldt0 @ xS ) ) ) )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ ( sbsmnsldt0 @ xS ) )
<=> ( ( aInteger0 @ W0 )
& ? [W1: $i] :
( ( aElementOf0 @ W0 @ W1 )
& ( aElementOf0 @ W1 @ xS ) ) ) )
& ( aSet0 @ ( sbsmnsldt0 @ xS ) )
& ! [W0: $i] :
( ( ( ( aInteger0 @ W0 )
& ( ? [W1: $i] :
( ( ( sdtasdt0 @ xp @ W1 )
= ( sdtpldt0 @ W0 @ ( smndt0 @ sz10 ) ) )
& ( aInteger0 @ W1 ) )
| ( aDivisorOf0 @ xp @ ( sdtpldt0 @ W0 @ ( smndt0 @ sz10 ) ) )
| ( sdteqdtlpzmzozddtrp0 @ W0 @ sz10 @ xp ) ) )
=> ( aElementOf0 @ W0 @ ( szAzrzSzezqlpdtcmdtrp0 @ sz10 @ xp ) ) )
& ( ( aElementOf0 @ W0 @ ( szAzrzSzezqlpdtcmdtrp0 @ sz10 @ xp ) )
=> ( ( aInteger0 @ W0 )
& ? [W1: $i] :
( ( ( sdtasdt0 @ xp @ W1 )
= ( sdtpldt0 @ W0 @ ( smndt0 @ sz10 ) ) )
& ( aInteger0 @ W1 ) )
& ( aDivisorOf0 @ xp @ ( sdtpldt0 @ W0 @ ( smndt0 @ sz10 ) ) )
& ( sdteqdtlpzmzozddtrp0 @ W0 @ sz10 @ xp ) ) ) )
& ( aSet0 @ ( szAzrzSzezqlpdtcmdtrp0 @ sz10 @ xp ) )
& ( xp != sz00 )
& ( aInteger0 @ xp ) ) ).
thf(zip_derived_cl192,plain,
aInteger0 @ xp,
inference(cnf,[status(esa)],[m__2171]) ).
thf(zip_derived_cl2004,plain,
! [X0: $i] :
( ~ ( aInteger0 @ X0 )
| ( ( sdtasdt0 @ xp @ ( sdtasdt0 @ sk__27 @ X0 ) )
= ( sdtasdt0 @ ( sdtasdt0 @ xp @ sk__26 ) @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2002,zip_derived_cl214,zip_derived_cl192]) ).
thf(zip_derived_cl8,plain,
! [X0: $i] :
( ( ( sdtpldt0 @ X0 @ sz00 )
= X0 )
| ~ ( aInteger0 @ X0 ) ),
inference(cnf,[status(esa)],[mAddZero]) ).
thf(zip_derived_cl1848_003,plain,
( ( sdtasdt0 @ xp @ sk__27 )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( sdtpldt0 @ sz10 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl213,zip_derived_cl226]) ).
thf(zip_derived_cl1851_004,plain,
( ( sdtasdt0 @ xp @ sk__26 )
= ( sdtasdt0 @ xp @ sk__27 ) ),
inference(demod,[status(thm)],[zip_derived_cl218,zip_derived_cl1844,zip_derived_cl226,zip_derived_cl1848]) ).
thf(zip_derived_cl1852,plain,
( ( sdtasdt0 @ xp @ sk__26 )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( sdtpldt0 @ sz10 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1848,zip_derived_cl1851]) ).
thf(mAddAsso,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aInteger0 @ W0 )
& ( aInteger0 @ W1 )
& ( aInteger0 @ W2 ) )
=> ( ( sdtpldt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 ) ) ) ).
thf(zip_derived_cl6,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X1 )
| ~ ( aInteger0 @ X2 )
| ( ( sdtpldt0 @ X1 @ ( sdtpldt0 @ X0 @ X2 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ X1 @ X0 ) @ X2 ) ) ),
inference(cnf,[status(esa)],[mAddAsso]) ).
thf(zip_derived_cl1859,plain,
( ~ ( aInteger0 @ xp )
| ~ ( aInteger0 @ sz10 )
| ~ ( aInteger0 @ ( sdtpldt0 @ sz10 @ xp ) )
| ( ( sdtpldt0 @ sz10 @ ( sdtpldt0 @ xp @ ( sdtpldt0 @ sz10 @ xp ) ) )
= ( sdtasdt0 @ xp @ sk__26 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1852,zip_derived_cl6]) ).
thf(zip_derived_cl192_005,plain,
aInteger0 @ xp,
inference(cnf,[status(esa)],[m__2171]) ).
thf(mIntOne,axiom,
aInteger0 @ sz10 ).
thf(zip_derived_cl2,plain,
aInteger0 @ sz10,
inference(cnf,[status(esa)],[mIntOne]) ).
thf(zip_derived_cl226_006,plain,
( ( sdtpldt0 @ sz10 @ xp )
= ( smndt0 @ sz10 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(mIntNeg,axiom,
! [W0: $i] :
( ( aInteger0 @ W0 )
=> ( aInteger0 @ ( smndt0 @ W0 ) ) ) ).
thf(zip_derived_cl3,plain,
! [X0: $i] :
( ( aInteger0 @ ( smndt0 @ X0 ) )
| ~ ( aInteger0 @ X0 ) ),
inference(cnf,[status(esa)],[mIntNeg]) ).
thf(zip_derived_cl1842,plain,
( ( aInteger0 @ ( sdtpldt0 @ sz10 @ xp ) )
| ~ ( aInteger0 @ sz10 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl226,zip_derived_cl3]) ).
thf(zip_derived_cl2_007,plain,
aInteger0 @ sz10,
inference(cnf,[status(esa)],[mIntOne]) ).
thf(zip_derived_cl1843,plain,
aInteger0 @ ( sdtpldt0 @ sz10 @ xp ),
inference(demod,[status(thm)],[zip_derived_cl1842,zip_derived_cl2]) ).
thf(zip_derived_cl1863,plain,
( ( sdtpldt0 @ sz10 @ ( sdtpldt0 @ xp @ ( sdtpldt0 @ sz10 @ xp ) ) )
= ( sdtasdt0 @ xp @ sk__26 ) ),
inference(demod,[status(thm)],[zip_derived_cl1859,zip_derived_cl192,zip_derived_cl2,zip_derived_cl1843]) ).
thf(mAddNeg,axiom,
! [W0: $i] :
( ( aInteger0 @ W0 )
=> ( ( ( sdtpldt0 @ W0 @ ( smndt0 @ W0 ) )
= sz00 )
& ( sz00
= ( sdtpldt0 @ ( smndt0 @ W0 ) @ W0 ) ) ) ) ).
thf(zip_derived_cl11,plain,
! [X0: $i] :
( ( sz00
= ( sdtpldt0 @ ( smndt0 @ X0 ) @ X0 ) )
| ~ ( aInteger0 @ X0 ) ),
inference(cnf,[status(esa)],[mAddNeg]) ).
thf(zip_derived_cl3_008,plain,
! [X0: $i] :
( ( aInteger0 @ ( smndt0 @ X0 ) )
| ~ ( aInteger0 @ X0 ) ),
inference(cnf,[status(esa)],[mIntNeg]) ).
thf(zip_derived_cl1844_009,plain,
( ( sdtpldt0 @ sz10 @ ( smndt0 @ xp ) )
= ( sdtpldt0 @ sz10 @ xp ) ),
inference(demod,[status(thm)],[zip_derived_cl225,zip_derived_cl226]) ).
thf(zip_derived_cl6_010,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X1 )
| ~ ( aInteger0 @ X2 )
| ( ( sdtpldt0 @ X1 @ ( sdtpldt0 @ X0 @ X2 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ X1 @ X0 ) @ X2 ) ) ),
inference(cnf,[status(esa)],[mAddAsso]) ).
thf(zip_derived_cl1860,plain,
! [X0: $i] :
( ~ ( aInteger0 @ ( smndt0 @ xp ) )
| ~ ( aInteger0 @ sz10 )
| ~ ( aInteger0 @ X0 )
| ( ( sdtpldt0 @ sz10 @ ( sdtpldt0 @ ( smndt0 @ xp ) @ X0 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1844,zip_derived_cl6]) ).
thf(zip_derived_cl2_011,plain,
aInteger0 @ sz10,
inference(cnf,[status(esa)],[mIntOne]) ).
thf(zip_derived_cl1864,plain,
! [X0: $i] :
( ~ ( aInteger0 @ ( smndt0 @ xp ) )
| ~ ( aInteger0 @ X0 )
| ( ( sdtpldt0 @ sz10 @ ( sdtpldt0 @ ( smndt0 @ xp ) @ X0 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1860,zip_derived_cl2]) ).
thf(zip_derived_cl2265,plain,
! [X0: $i] :
( ~ ( aInteger0 @ xp )
| ~ ( aInteger0 @ X0 )
| ( ( sdtpldt0 @ sz10 @ ( sdtpldt0 @ ( smndt0 @ xp ) @ X0 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ X0 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl3,zip_derived_cl1864]) ).
thf(zip_derived_cl192_012,plain,
aInteger0 @ xp,
inference(cnf,[status(esa)],[m__2171]) ).
thf(zip_derived_cl2266,plain,
! [X0: $i] :
( ~ ( aInteger0 @ X0 )
| ( ( sdtpldt0 @ sz10 @ ( sdtpldt0 @ ( smndt0 @ xp ) @ X0 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2265,zip_derived_cl192]) ).
thf(zip_derived_cl2332,plain,
( ~ ( aInteger0 @ xp )
| ~ ( aInteger0 @ xp )
| ( ( sdtpldt0 @ sz10 @ sz00 )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ xp ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl2266]) ).
thf(zip_derived_cl192_013,plain,
aInteger0 @ xp,
inference(cnf,[status(esa)],[m__2171]) ).
thf(zip_derived_cl192_014,plain,
aInteger0 @ xp,
inference(cnf,[status(esa)],[m__2171]) ).
thf(zip_derived_cl2336,plain,
( ( sdtpldt0 @ sz10 @ sz00 )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ xp ) ),
inference(demod,[status(thm)],[zip_derived_cl2332,zip_derived_cl192,zip_derived_cl192]) ).
thf(mAddComm,axiom,
! [W0: $i,W1: $i] :
( ( ( aInteger0 @ W0 )
& ( aInteger0 @ W1 ) )
=> ( ( sdtpldt0 @ W0 @ W1 )
= ( sdtpldt0 @ W1 @ W0 ) ) ) ).
thf(zip_derived_cl7,plain,
! [X0: $i,X1: $i] :
( ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X1 )
| ( ( sdtpldt0 @ X0 @ X1 )
= ( sdtpldt0 @ X1 @ X0 ) ) ),
inference(cnf,[status(esa)],[mAddComm]) ).
thf(zip_derived_cl2343,plain,
( ~ ( aInteger0 @ ( sdtpldt0 @ sz10 @ xp ) )
| ~ ( aInteger0 @ xp )
| ( ( sdtpldt0 @ sz10 @ sz00 )
= ( sdtpldt0 @ xp @ ( sdtpldt0 @ sz10 @ xp ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2336,zip_derived_cl7]) ).
thf(zip_derived_cl1843_015,plain,
aInteger0 @ ( sdtpldt0 @ sz10 @ xp ),
inference(demod,[status(thm)],[zip_derived_cl1842,zip_derived_cl2]) ).
thf(zip_derived_cl192_016,plain,
aInteger0 @ xp,
inference(cnf,[status(esa)],[m__2171]) ).
thf(zip_derived_cl2349,plain,
( ( sdtpldt0 @ sz10 @ sz00 )
= ( sdtpldt0 @ xp @ ( sdtpldt0 @ sz10 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2343,zip_derived_cl1843,zip_derived_cl192]) ).
thf(zip_derived_cl2354,plain,
( ( sdtpldt0 @ sz10 @ ( sdtpldt0 @ sz10 @ sz00 ) )
= ( sdtasdt0 @ xp @ sk__26 ) ),
inference(demod,[status(thm)],[zip_derived_cl1863,zip_derived_cl2349]) ).
thf(zip_derived_cl2511,plain,
( ~ ( aInteger0 @ sz10 )
| ( ( sdtpldt0 @ sz10 @ sz10 )
= ( sdtasdt0 @ xp @ sk__26 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl8,zip_derived_cl2354]) ).
thf(zip_derived_cl2_017,plain,
aInteger0 @ sz10,
inference(cnf,[status(esa)],[mIntOne]) ).
thf(zip_derived_cl2514,plain,
( ( sdtpldt0 @ sz10 @ sz10 )
= ( sdtasdt0 @ xp @ sk__26 ) ),
inference(demod,[status(thm)],[zip_derived_cl2511,zip_derived_cl2]) ).
thf(zip_derived_cl4801,plain,
! [X0: $i] :
( ~ ( aInteger0 @ X0 )
| ( ( sdtasdt0 @ xp @ ( sdtasdt0 @ sk__27 @ X0 ) )
= ( sdtasdt0 @ ( sdtpldt0 @ sz10 @ sz10 ) @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2004,zip_derived_cl2514]) ).
thf(zip_derived_cl4817,plain,
( ~ ( aInteger0 @ sk__27 )
| ~ ( aInteger0 @ sz10 )
| ( ( sdtasdt0 @ xp @ sk__27 )
= ( sdtasdt0 @ ( sdtpldt0 @ sz10 @ sz10 ) @ sz10 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl14,zip_derived_cl4801]) ).
thf(zip_derived_cl214_018,plain,
aInteger0 @ sk__27,
inference(cnf,[status(esa)],[m__2232]) ).
thf(zip_derived_cl2_019,plain,
aInteger0 @ sz10,
inference(cnf,[status(esa)],[mIntOne]) ).
thf(zip_derived_cl1851_020,plain,
( ( sdtasdt0 @ xp @ sk__26 )
= ( sdtasdt0 @ xp @ sk__27 ) ),
inference(demod,[status(thm)],[zip_derived_cl218,zip_derived_cl1844,zip_derived_cl226,zip_derived_cl1848]) ).
thf(zip_derived_cl2514_021,plain,
( ( sdtpldt0 @ sz10 @ sz10 )
= ( sdtasdt0 @ xp @ sk__26 ) ),
inference(demod,[status(thm)],[zip_derived_cl2511,zip_derived_cl2]) ).
thf(zip_derived_cl2549,plain,
( ( sdtpldt0 @ sz10 @ sz10 )
= ( sdtasdt0 @ xp @ sk__27 ) ),
inference(demod,[status(thm)],[zip_derived_cl1851,zip_derived_cl2514]) ).
thf(zip_derived_cl4825,plain,
( ( sdtpldt0 @ sz10 @ sz10 )
= ( sdtasdt0 @ ( sdtpldt0 @ sz10 @ sz10 ) @ sz10 ) ),
inference(demod,[status(thm)],[zip_derived_cl4817,zip_derived_cl214,zip_derived_cl2,zip_derived_cl2549]) ).
thf(zip_derived_cl1852_022,plain,
( ( sdtasdt0 @ xp @ sk__26 )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( sdtpldt0 @ sz10 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1848,zip_derived_cl1851]) ).
thf(zip_derived_cl2514_023,plain,
( ( sdtpldt0 @ sz10 @ sz10 )
= ( sdtasdt0 @ xp @ sk__26 ) ),
inference(demod,[status(thm)],[zip_derived_cl2511,zip_derived_cl2]) ).
thf(zip_derived_cl2550,plain,
( ( sdtpldt0 @ sz10 @ sz10 )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( sdtpldt0 @ sz10 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1852,zip_derived_cl2514]) ).
thf(zip_derived_cl226_024,plain,
( ( sdtpldt0 @ sz10 @ xp )
= ( smndt0 @ sz10 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl11_025,plain,
! [X0: $i] :
( ( sz00
= ( sdtpldt0 @ ( smndt0 @ X0 ) @ X0 ) )
| ~ ( aInteger0 @ X0 ) ),
inference(cnf,[status(esa)],[mAddNeg]) ).
thf(zip_derived_cl1969,plain,
( ( sz00
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ sz10 ) )
| ~ ( aInteger0 @ sz10 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl226,zip_derived_cl11]) ).
thf(zip_derived_cl2_026,plain,
aInteger0 @ sz10,
inference(cnf,[status(esa)],[mIntOne]) ).
thf(zip_derived_cl1970,plain,
( sz00
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ sz10 ) ),
inference(demod,[status(thm)],[zip_derived_cl1969,zip_derived_cl2]) ).
thf(zip_derived_cl6_027,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X1 )
| ~ ( aInteger0 @ X2 )
| ( ( sdtpldt0 @ X1 @ ( sdtpldt0 @ X0 @ X2 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ X1 @ X0 ) @ X2 ) ) ),
inference(cnf,[status(esa)],[mAddAsso]) ).
thf(zip_derived_cl1989,plain,
! [X0: $i] :
( ~ ( aInteger0 @ sz10 )
| ~ ( aInteger0 @ ( sdtpldt0 @ sz10 @ xp ) )
| ~ ( aInteger0 @ X0 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( sdtpldt0 @ sz10 @ X0 ) )
= ( sdtpldt0 @ sz00 @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1970,zip_derived_cl6]) ).
thf(zip_derived_cl2_028,plain,
aInteger0 @ sz10,
inference(cnf,[status(esa)],[mIntOne]) ).
thf(zip_derived_cl1843_029,plain,
aInteger0 @ ( sdtpldt0 @ sz10 @ xp ),
inference(demod,[status(thm)],[zip_derived_cl1842,zip_derived_cl2]) ).
thf(zip_derived_cl1995,plain,
! [X0: $i] :
( ~ ( aInteger0 @ X0 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( sdtpldt0 @ sz10 @ X0 ) )
= ( sdtpldt0 @ sz00 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1989,zip_derived_cl2,zip_derived_cl1843]) ).
thf(zip_derived_cl4758,plain,
( ~ ( aInteger0 @ xp )
| ( ( sdtpldt0 @ sz10 @ sz10 )
= ( sdtpldt0 @ sz00 @ xp ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2550,zip_derived_cl1995]) ).
thf(zip_derived_cl192_030,plain,
aInteger0 @ xp,
inference(cnf,[status(esa)],[m__2171]) ).
thf(zip_derived_cl4773,plain,
( ( sdtpldt0 @ sz10 @ sz10 )
= ( sdtpldt0 @ sz00 @ xp ) ),
inference(demod,[status(thm)],[zip_derived_cl4758,zip_derived_cl192]) ).
thf(zip_derived_cl4773_031,plain,
( ( sdtpldt0 @ sz10 @ sz10 )
= ( sdtpldt0 @ sz00 @ xp ) ),
inference(demod,[status(thm)],[zip_derived_cl4758,zip_derived_cl192]) ).
thf(zip_derived_cl5287,plain,
( ( sdtpldt0 @ sz00 @ xp )
= ( sdtasdt0 @ ( sdtpldt0 @ sz00 @ xp ) @ sz10 ) ),
inference(demod,[status(thm)],[zip_derived_cl4825,zip_derived_cl4773,zip_derived_cl4773]) ).
thf(zip_derived_cl5303,plain,
( ~ ( aInteger0 @ xp )
| ( xp
= ( sdtasdt0 @ xp @ sz10 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl9,zip_derived_cl5287]) ).
thf(zip_derived_cl192_032,plain,
aInteger0 @ xp,
inference(cnf,[status(esa)],[m__2171]) ).
thf(zip_derived_cl5304,plain,
( xp
= ( sdtasdt0 @ xp @ sz10 ) ),
inference(demod,[status(thm)],[zip_derived_cl5303,zip_derived_cl192]) ).
thf(mMulMinOne,axiom,
! [W0: $i] :
( ( aInteger0 @ W0 )
=> ( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ W0 )
= ( smndt0 @ W0 ) )
& ( ( smndt0 @ W0 )
= ( sdtasdt0 @ W0 @ ( smndt0 @ sz10 ) ) ) ) ) ).
thf(zip_derived_cl20,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ ( smndt0 @ sz10 ) @ X0 )
= ( smndt0 @ X0 ) )
| ~ ( aInteger0 @ X0 ) ),
inference(cnf,[status(esa)],[mMulMinOne]) ).
thf(zip_derived_cl226_033,plain,
( ( sdtpldt0 @ sz10 @ xp )
= ( smndt0 @ sz10 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2201,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ ( sdtpldt0 @ sz10 @ xp ) @ X0 )
= ( smndt0 @ X0 ) )
| ~ ( aInteger0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl20,zip_derived_cl226]) ).
thf(mDistrib,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aInteger0 @ W0 )
& ( aInteger0 @ W1 )
& ( aInteger0 @ W2 ) )
=> ( ( ( sdtasdt0 @ W0 @ ( sdtpldt0 @ W1 @ W2 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W1 ) @ ( sdtasdt0 @ W0 @ W2 ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ W0 @ W1 ) @ W2 )
= ( sdtpldt0 @ ( sdtasdt0 @ W0 @ W2 ) @ ( sdtasdt0 @ W1 @ W2 ) ) ) ) ) ).
thf(zip_derived_cl17,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X1 )
| ~ ( aInteger0 @ X2 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ X1 @ X0 ) @ X2 )
= ( sdtpldt0 @ ( sdtasdt0 @ X1 @ X2 ) @ ( sdtasdt0 @ X0 @ X2 ) ) ) ),
inference(cnf,[status(esa)],[mDistrib]) ).
thf(zip_derived_cl2207,plain,
! [X0: $i,X1: $i] :
( ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ ( sdtpldt0 @ sz10 @ xp ) )
| ~ ( aInteger0 @ X1 )
| ~ ( aInteger0 @ X0 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ X1 @ ( sdtpldt0 @ sz10 @ xp ) ) @ X0 )
= ( sdtpldt0 @ ( sdtasdt0 @ X1 @ X0 ) @ ( smndt0 @ X0 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2201,zip_derived_cl17]) ).
thf(zip_derived_cl1843_034,plain,
aInteger0 @ ( sdtpldt0 @ sz10 @ xp ),
inference(demod,[status(thm)],[zip_derived_cl1842,zip_derived_cl2]) ).
thf(zip_derived_cl2222,plain,
! [X0: $i,X1: $i] :
( ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X1 )
| ~ ( aInteger0 @ X0 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ X1 @ ( sdtpldt0 @ sz10 @ xp ) ) @ X0 )
= ( sdtpldt0 @ ( sdtasdt0 @ X1 @ X0 ) @ ( smndt0 @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2207,zip_derived_cl1843]) ).
thf(zip_derived_cl2223,plain,
! [X0: $i,X1: $i] :
( ( ( sdtasdt0 @ ( sdtpldt0 @ X1 @ ( sdtpldt0 @ sz10 @ xp ) ) @ X0 )
= ( sdtpldt0 @ ( sdtasdt0 @ X1 @ X0 ) @ ( smndt0 @ X0 ) ) )
| ~ ( aInteger0 @ X1 )
| ~ ( aInteger0 @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl2222]) ).
thf(zip_derived_cl5366,plain,
( ( ( sdtasdt0 @ ( sdtpldt0 @ xp @ ( sdtpldt0 @ sz10 @ xp ) ) @ sz10 )
= ( sdtpldt0 @ xp @ ( smndt0 @ sz10 ) ) )
| ~ ( aInteger0 @ xp )
| ~ ( aInteger0 @ sz10 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl5304,zip_derived_cl2223]) ).
thf(zip_derived_cl2349_035,plain,
( ( sdtpldt0 @ sz10 @ sz00 )
= ( sdtpldt0 @ xp @ ( sdtpldt0 @ sz10 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2343,zip_derived_cl1843,zip_derived_cl192]) ).
thf(zip_derived_cl1970_036,plain,
( sz00
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ sz10 ) ),
inference(demod,[status(thm)],[zip_derived_cl1969,zip_derived_cl2]) ).
thf(zip_derived_cl226_037,plain,
( ( sdtpldt0 @ sz10 @ xp )
= ( smndt0 @ sz10 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl10,plain,
! [X0: $i] :
( ( ( sdtpldt0 @ X0 @ ( smndt0 @ X0 ) )
= sz00 )
| ~ ( aInteger0 @ X0 ) ),
inference(cnf,[status(esa)],[mAddNeg]) ).
thf(zip_derived_cl1955,plain,
( ( ( sdtpldt0 @ sz10 @ ( sdtpldt0 @ sz10 @ xp ) )
= sz00 )
| ~ ( aInteger0 @ sz10 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl226,zip_derived_cl10]) ).
thf(zip_derived_cl2_038,plain,
aInteger0 @ sz10,
inference(cnf,[status(esa)],[mIntOne]) ).
thf(zip_derived_cl1956,plain,
( ( sdtpldt0 @ sz10 @ ( sdtpldt0 @ sz10 @ xp ) )
= sz00 ),
inference(demod,[status(thm)],[zip_derived_cl1955,zip_derived_cl2]) ).
thf(zip_derived_cl6_039,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X1 )
| ~ ( aInteger0 @ X2 )
| ( ( sdtpldt0 @ X1 @ ( sdtpldt0 @ X0 @ X2 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ X1 @ X0 ) @ X2 ) ) ),
inference(cnf,[status(esa)],[mAddAsso]) ).
thf(zip_derived_cl1980,plain,
! [X0: $i] :
( ~ ( aInteger0 @ ( sdtpldt0 @ sz10 @ xp ) )
| ~ ( aInteger0 @ sz10 )
| ~ ( aInteger0 @ X0 )
| ( ( sdtpldt0 @ sz10 @ ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ X0 ) )
= ( sdtpldt0 @ sz00 @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1956,zip_derived_cl6]) ).
thf(zip_derived_cl1843_040,plain,
aInteger0 @ ( sdtpldt0 @ sz10 @ xp ),
inference(demod,[status(thm)],[zip_derived_cl1842,zip_derived_cl2]) ).
thf(zip_derived_cl2_041,plain,
aInteger0 @ sz10,
inference(cnf,[status(esa)],[mIntOne]) ).
thf(zip_derived_cl1984,plain,
! [X0: $i] :
( ~ ( aInteger0 @ X0 )
| ( ( sdtpldt0 @ sz10 @ ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ X0 ) )
= ( sdtpldt0 @ sz00 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1980,zip_derived_cl1843,zip_derived_cl2]) ).
thf(zip_derived_cl4655,plain,
( ~ ( aInteger0 @ sz10 )
| ( ( sdtpldt0 @ sz10 @ sz00 )
= ( sdtpldt0 @ sz00 @ sz10 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1970,zip_derived_cl1984]) ).
thf(zip_derived_cl2_042,plain,
aInteger0 @ sz10,
inference(cnf,[status(esa)],[mIntOne]) ).
thf(zip_derived_cl8_043,plain,
! [X0: $i] :
( ( ( sdtpldt0 @ X0 @ sz00 )
= X0 )
| ~ ( aInteger0 @ X0 ) ),
inference(cnf,[status(esa)],[mAddZero]) ).
thf(zip_derived_cl2550_044,plain,
( ( sdtpldt0 @ sz10 @ sz10 )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( sdtpldt0 @ sz10 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1852,zip_derived_cl2514]) ).
thf(zip_derived_cl2550_045,plain,
( ( sdtpldt0 @ sz10 @ sz10 )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( sdtpldt0 @ sz10 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1852,zip_derived_cl2514]) ).
thf(zip_derived_cl6_046,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X1 )
| ~ ( aInteger0 @ X2 )
| ( ( sdtpldt0 @ X1 @ ( sdtpldt0 @ X0 @ X2 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ X1 @ X0 ) @ X2 ) ) ),
inference(cnf,[status(esa)],[mAddAsso]) ).
thf(zip_derived_cl2608,plain,
! [X0: $i] :
( ~ ( aInteger0 @ ( sdtpldt0 @ sz10 @ xp ) )
| ~ ( aInteger0 @ ( sdtpldt0 @ sz10 @ xp ) )
| ~ ( aInteger0 @ X0 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ X0 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ sz10 ) @ X0 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2550,zip_derived_cl6]) ).
thf(zip_derived_cl1843_047,plain,
aInteger0 @ ( sdtpldt0 @ sz10 @ xp ),
inference(demod,[status(thm)],[zip_derived_cl1842,zip_derived_cl2]) ).
thf(zip_derived_cl1843_048,plain,
aInteger0 @ ( sdtpldt0 @ sz10 @ xp ),
inference(demod,[status(thm)],[zip_derived_cl1842,zip_derived_cl2]) ).
thf(zip_derived_cl2615,plain,
! [X0: $i] :
( ~ ( aInteger0 @ X0 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ X0 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ sz10 ) @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2608,zip_derived_cl1843,zip_derived_cl1843]) ).
thf(zip_derived_cl2791,plain,
( ~ ( aInteger0 @ ( sdtpldt0 @ sz10 @ xp ) )
| ( ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( sdtpldt0 @ sz10 @ sz10 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ sz10 ) @ ( sdtpldt0 @ sz10 @ xp ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2550,zip_derived_cl2615]) ).
thf(zip_derived_cl1843_049,plain,
aInteger0 @ ( sdtpldt0 @ sz10 @ xp ),
inference(demod,[status(thm)],[zip_derived_cl1842,zip_derived_cl2]) ).
thf(zip_derived_cl2804,plain,
( ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( sdtpldt0 @ sz10 @ sz10 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ sz10 ) @ ( sdtpldt0 @ sz10 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2791,zip_derived_cl1843]) ).
thf(zip_derived_cl6_050,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X1 )
| ~ ( aInteger0 @ X2 )
| ( ( sdtpldt0 @ X1 @ ( sdtpldt0 @ X0 @ X2 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ X1 @ X0 ) @ X2 ) ) ),
inference(cnf,[status(esa)],[mAddAsso]) ).
thf(zip_derived_cl2849,plain,
( ~ ( aInteger0 @ xp )
| ~ ( aInteger0 @ sz10 )
| ~ ( aInteger0 @ ( sdtpldt0 @ sz10 @ sz10 ) )
| ( ( sdtpldt0 @ sz10 @ ( sdtpldt0 @ xp @ ( sdtpldt0 @ sz10 @ sz10 ) ) )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ sz10 ) @ ( sdtpldt0 @ sz10 @ xp ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2804,zip_derived_cl6]) ).
thf(zip_derived_cl192_051,plain,
aInteger0 @ xp,
inference(cnf,[status(esa)],[m__2171]) ).
thf(zip_derived_cl2_052,plain,
aInteger0 @ sz10,
inference(cnf,[status(esa)],[mIntOne]) ).
thf(zip_derived_cl1848_053,plain,
( ( sdtasdt0 @ xp @ sk__27 )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( sdtpldt0 @ sz10 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl213,zip_derived_cl226]) ).
thf(mIntPlus,axiom,
! [W0: $i,W1: $i] :
( ( ( aInteger0 @ W0 )
& ( aInteger0 @ W1 ) )
=> ( aInteger0 @ ( sdtpldt0 @ W0 @ W1 ) ) ) ).
thf(zip_derived_cl4,plain,
! [X0: $i,X1: $i] :
( ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X1 )
| ( aInteger0 @ ( sdtpldt0 @ X0 @ X1 ) ) ),
inference(cnf,[status(esa)],[mIntPlus]) ).
thf(zip_derived_cl1849,plain,
( ~ ( aInteger0 @ ( sdtpldt0 @ sz10 @ xp ) )
| ~ ( aInteger0 @ ( sdtpldt0 @ sz10 @ xp ) )
| ( aInteger0 @ ( sdtasdt0 @ xp @ sk__27 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1848,zip_derived_cl4]) ).
thf(zip_derived_cl1843_054,plain,
aInteger0 @ ( sdtpldt0 @ sz10 @ xp ),
inference(demod,[status(thm)],[zip_derived_cl1842,zip_derived_cl2]) ).
thf(zip_derived_cl1843_055,plain,
aInteger0 @ ( sdtpldt0 @ sz10 @ xp ),
inference(demod,[status(thm)],[zip_derived_cl1842,zip_derived_cl2]) ).
thf(zip_derived_cl1850,plain,
aInteger0 @ ( sdtasdt0 @ xp @ sk__27 ),
inference(demod,[status(thm)],[zip_derived_cl1849,zip_derived_cl1843,zip_derived_cl1843]) ).
thf(zip_derived_cl1851_056,plain,
( ( sdtasdt0 @ xp @ sk__26 )
= ( sdtasdt0 @ xp @ sk__27 ) ),
inference(demod,[status(thm)],[zip_derived_cl218,zip_derived_cl1844,zip_derived_cl226,zip_derived_cl1848]) ).
thf(zip_derived_cl2079,plain,
aInteger0 @ ( sdtasdt0 @ xp @ sk__26 ),
inference(demod,[status(thm)],[zip_derived_cl1850,zip_derived_cl1851]) ).
thf(zip_derived_cl2514_057,plain,
( ( sdtpldt0 @ sz10 @ sz10 )
= ( sdtasdt0 @ xp @ sk__26 ) ),
inference(demod,[status(thm)],[zip_derived_cl2511,zip_derived_cl2]) ).
thf(zip_derived_cl2552,plain,
aInteger0 @ ( sdtpldt0 @ sz10 @ sz10 ),
inference(demod,[status(thm)],[zip_derived_cl2079,zip_derived_cl2514]) ).
thf(zip_derived_cl2859,plain,
( ( sdtpldt0 @ sz10 @ ( sdtpldt0 @ xp @ ( sdtpldt0 @ sz10 @ sz10 ) ) )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ sz10 ) @ ( sdtpldt0 @ sz10 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2849,zip_derived_cl192,zip_derived_cl2,zip_derived_cl2552]) ).
thf(zip_derived_cl2859_058,plain,
( ( sdtpldt0 @ sz10 @ ( sdtpldt0 @ xp @ ( sdtpldt0 @ sz10 @ sz10 ) ) )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ sz10 ) @ ( sdtpldt0 @ sz10 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2849,zip_derived_cl192,zip_derived_cl2,zip_derived_cl2552]) ).
thf(zip_derived_cl6_059,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X1 )
| ~ ( aInteger0 @ X2 )
| ( ( sdtpldt0 @ X1 @ ( sdtpldt0 @ X0 @ X2 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ X1 @ X0 ) @ X2 ) ) ),
inference(cnf,[status(esa)],[mAddAsso]) ).
thf(zip_derived_cl2870,plain,
( ~ ( aInteger0 @ sz10 )
| ~ ( aInteger0 @ sz10 )
| ~ ( aInteger0 @ ( sdtpldt0 @ sz10 @ xp ) )
| ( ( sdtpldt0 @ sz10 @ ( sdtpldt0 @ sz10 @ ( sdtpldt0 @ sz10 @ xp ) ) )
= ( sdtpldt0 @ sz10 @ ( sdtpldt0 @ xp @ ( sdtpldt0 @ sz10 @ sz10 ) ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2859,zip_derived_cl6]) ).
thf(zip_derived_cl2_060,plain,
aInteger0 @ sz10,
inference(cnf,[status(esa)],[mIntOne]) ).
thf(zip_derived_cl2_061,plain,
aInteger0 @ sz10,
inference(cnf,[status(esa)],[mIntOne]) ).
thf(zip_derived_cl1843_062,plain,
aInteger0 @ ( sdtpldt0 @ sz10 @ xp ),
inference(demod,[status(thm)],[zip_derived_cl1842,zip_derived_cl2]) ).
thf(zip_derived_cl1956_063,plain,
( ( sdtpldt0 @ sz10 @ ( sdtpldt0 @ sz10 @ xp ) )
= sz00 ),
inference(demod,[status(thm)],[zip_derived_cl1955,zip_derived_cl2]) ).
thf(zip_derived_cl2879,plain,
( ( sdtpldt0 @ sz10 @ sz00 )
= ( sdtpldt0 @ sz10 @ ( sdtpldt0 @ xp @ ( sdtpldt0 @ sz10 @ sz10 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2870,zip_derived_cl2,zip_derived_cl2,zip_derived_cl1843,zip_derived_cl1956]) ).
thf(zip_derived_cl2936,plain,
( ( sdtpldt0 @ sz10 @ sz00 )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ sz10 ) @ ( sdtpldt0 @ sz10 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2859,zip_derived_cl2879]) ).
thf(zip_derived_cl9_064,plain,
! [X0: $i] :
( ( X0
= ( sdtpldt0 @ sz00 @ X0 ) )
| ~ ( aInteger0 @ X0 ) ),
inference(cnf,[status(esa)],[mAddZero]) ).
thf(zip_derived_cl6_065,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X1 )
| ~ ( aInteger0 @ X2 )
| ( ( sdtpldt0 @ X1 @ ( sdtpldt0 @ X0 @ X2 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ X1 @ X0 ) @ X2 ) ) ),
inference(cnf,[status(esa)],[mAddAsso]) ).
thf(zip_derived_cl1934,plain,
! [X0: $i,X1: $i] :
( ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ sz00 )
| ~ ( aInteger0 @ X1 )
| ( ( sdtpldt0 @ sz00 @ ( sdtpldt0 @ X0 @ X1 ) )
= ( sdtpldt0 @ X0 @ X1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl9,zip_derived_cl6]) ).
thf(mIntZero,axiom,
aInteger0 @ sz00 ).
thf(zip_derived_cl1,plain,
aInteger0 @ sz00,
inference(cnf,[status(esa)],[mIntZero]) ).
thf(zip_derived_cl1942,plain,
! [X0: $i,X1: $i] :
( ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X1 )
| ( ( sdtpldt0 @ sz00 @ ( sdtpldt0 @ X0 @ X1 ) )
= ( sdtpldt0 @ X0 @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1934,zip_derived_cl1]) ).
thf(zip_derived_cl1943,plain,
! [X0: $i,X1: $i] :
( ( ( sdtpldt0 @ sz00 @ ( sdtpldt0 @ X0 @ X1 ) )
= ( sdtpldt0 @ X0 @ X1 ) )
| ~ ( aInteger0 @ X1 )
| ~ ( aInteger0 @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl1942]) ).
thf(zip_derived_cl3039,plain,
( ( ( sdtpldt0 @ sz00 @ ( sdtpldt0 @ sz10 @ sz00 ) )
= ( sdtpldt0 @ sz10 @ sz00 ) )
| ~ ( aInteger0 @ ( sdtpldt0 @ sz10 @ xp ) )
| ~ ( aInteger0 @ ( sdtpldt0 @ sz10 @ sz10 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2936,zip_derived_cl1943]) ).
thf(zip_derived_cl1843_066,plain,
aInteger0 @ ( sdtpldt0 @ sz10 @ xp ),
inference(demod,[status(thm)],[zip_derived_cl1842,zip_derived_cl2]) ).
thf(zip_derived_cl2552_067,plain,
aInteger0 @ ( sdtpldt0 @ sz10 @ sz10 ),
inference(demod,[status(thm)],[zip_derived_cl2079,zip_derived_cl2514]) ).
thf(zip_derived_cl3078,plain,
( ( sdtpldt0 @ sz00 @ ( sdtpldt0 @ sz10 @ sz00 ) )
= ( sdtpldt0 @ sz10 @ sz00 ) ),
inference(demod,[status(thm)],[zip_derived_cl3039,zip_derived_cl1843,zip_derived_cl2552]) ).
thf(zip_derived_cl3743,plain,
( ~ ( aInteger0 @ sz10 )
| ( ( sdtpldt0 @ sz00 @ sz10 )
= sz10 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl8,zip_derived_cl3078]) ).
thf(zip_derived_cl2_068,plain,
aInteger0 @ sz10,
inference(cnf,[status(esa)],[mIntOne]) ).
thf(zip_derived_cl3746,plain,
( ( sdtpldt0 @ sz00 @ sz10 )
= sz10 ),
inference(demod,[status(thm)],[zip_derived_cl3743,zip_derived_cl2]) ).
thf(zip_derived_cl4672,plain,
( ( sdtpldt0 @ sz10 @ sz00 )
= sz10 ),
inference(demod,[status(thm)],[zip_derived_cl4655,zip_derived_cl2,zip_derived_cl3746]) ).
thf(zip_derived_cl4687,plain,
( sz10
= ( sdtpldt0 @ xp @ ( sdtpldt0 @ sz10 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2349,zip_derived_cl4672]) ).
thf(zip_derived_cl226_069,plain,
( ( sdtpldt0 @ sz10 @ xp )
= ( smndt0 @ sz10 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl4687_070,plain,
( sz10
= ( sdtpldt0 @ xp @ ( sdtpldt0 @ sz10 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2349,zip_derived_cl4672]) ).
thf(zip_derived_cl192_071,plain,
aInteger0 @ xp,
inference(cnf,[status(esa)],[m__2171]) ).
thf(zip_derived_cl2_072,plain,
aInteger0 @ sz10,
inference(cnf,[status(esa)],[mIntOne]) ).
thf(zip_derived_cl5384,plain,
( ( sdtasdt0 @ sz10 @ sz10 )
= sz10 ),
inference(demod,[status(thm)],[zip_derived_cl5366,zip_derived_cl4687,zip_derived_cl226,zip_derived_cl4687,zip_derived_cl192,zip_derived_cl2]) ).
thf(zip_derived_cl2223_073,plain,
! [X0: $i,X1: $i] :
( ( ( sdtasdt0 @ ( sdtpldt0 @ X1 @ ( sdtpldt0 @ sz10 @ xp ) ) @ X0 )
= ( sdtpldt0 @ ( sdtasdt0 @ X1 @ X0 ) @ ( smndt0 @ X0 ) ) )
| ~ ( aInteger0 @ X1 )
| ~ ( aInteger0 @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl2222]) ).
thf(zip_derived_cl5491,plain,
( ( ( sdtasdt0 @ ( sdtpldt0 @ sz10 @ ( sdtpldt0 @ sz10 @ xp ) ) @ sz10 )
= ( sdtpldt0 @ sz10 @ ( smndt0 @ sz10 ) ) )
| ~ ( aInteger0 @ sz10 )
| ~ ( aInteger0 @ sz10 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl5384,zip_derived_cl2223]) ).
thf(zip_derived_cl1956_074,plain,
( ( sdtpldt0 @ sz10 @ ( sdtpldt0 @ sz10 @ xp ) )
= sz00 ),
inference(demod,[status(thm)],[zip_derived_cl1955,zip_derived_cl2]) ).
thf(zip_derived_cl226_075,plain,
( ( sdtpldt0 @ sz10 @ xp )
= ( smndt0 @ sz10 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1956_076,plain,
( ( sdtpldt0 @ sz10 @ ( sdtpldt0 @ sz10 @ xp ) )
= sz00 ),
inference(demod,[status(thm)],[zip_derived_cl1955,zip_derived_cl2]) ).
thf(zip_derived_cl2_077,plain,
aInteger0 @ sz10,
inference(cnf,[status(esa)],[mIntOne]) ).
thf(zip_derived_cl2_078,plain,
aInteger0 @ sz10,
inference(cnf,[status(esa)],[mIntOne]) ).
thf(zip_derived_cl5508,plain,
( ( sdtasdt0 @ sz00 @ sz10 )
= sz00 ),
inference(demod,[status(thm)],[zip_derived_cl5491,zip_derived_cl1956,zip_derived_cl226,zip_derived_cl1956,zip_derived_cl2,zip_derived_cl2]) ).
thf(zip_derived_cl2223_079,plain,
! [X0: $i,X1: $i] :
( ( ( sdtasdt0 @ ( sdtpldt0 @ X1 @ ( sdtpldt0 @ sz10 @ xp ) ) @ X0 )
= ( sdtpldt0 @ ( sdtasdt0 @ X1 @ X0 ) @ ( smndt0 @ X0 ) ) )
| ~ ( aInteger0 @ X1 )
| ~ ( aInteger0 @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl2222]) ).
thf(zip_derived_cl5760,plain,
( ( ( sdtasdt0 @ ( sdtpldt0 @ sz00 @ ( sdtpldt0 @ sz10 @ xp ) ) @ sz10 )
= ( sdtpldt0 @ sz00 @ ( smndt0 @ sz10 ) ) )
| ~ ( aInteger0 @ sz00 )
| ~ ( aInteger0 @ sz10 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl5508,zip_derived_cl2223]) ).
thf(zip_derived_cl3_080,plain,
! [X0: $i] :
( ( aInteger0 @ ( smndt0 @ X0 ) )
| ~ ( aInteger0 @ X0 ) ),
inference(cnf,[status(esa)],[mIntNeg]) ).
thf(zip_derived_cl8_081,plain,
! [X0: $i] :
( ( ( sdtpldt0 @ X0 @ sz00 )
= X0 )
| ~ ( aInteger0 @ X0 ) ),
inference(cnf,[status(esa)],[mAddZero]) ).
thf(zip_derived_cl2266_082,plain,
! [X0: $i] :
( ~ ( aInteger0 @ X0 )
| ( ( sdtpldt0 @ sz10 @ ( sdtpldt0 @ ( smndt0 @ xp ) @ X0 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2265,zip_derived_cl192]) ).
thf(zip_derived_cl2330,plain,
( ~ ( aInteger0 @ ( smndt0 @ xp ) )
| ~ ( aInteger0 @ sz00 )
| ( ( sdtpldt0 @ sz10 @ ( smndt0 @ xp ) )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ sz00 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl8,zip_derived_cl2266]) ).
thf(zip_derived_cl1_083,plain,
aInteger0 @ sz00,
inference(cnf,[status(esa)],[mIntZero]) ).
thf(zip_derived_cl1844_084,plain,
( ( sdtpldt0 @ sz10 @ ( smndt0 @ xp ) )
= ( sdtpldt0 @ sz10 @ xp ) ),
inference(demod,[status(thm)],[zip_derived_cl225,zip_derived_cl226]) ).
thf(zip_derived_cl2335,plain,
( ~ ( aInteger0 @ ( smndt0 @ xp ) )
| ( ( sdtpldt0 @ sz10 @ xp )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ sz00 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2330,zip_derived_cl1,zip_derived_cl1844]) ).
thf(zip_derived_cl2394,plain,
( ~ ( aInteger0 @ xp )
| ( ( sdtpldt0 @ sz10 @ xp )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ sz00 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl3,zip_derived_cl2335]) ).
thf(zip_derived_cl192_085,plain,
aInteger0 @ xp,
inference(cnf,[status(esa)],[m__2171]) ).
thf(zip_derived_cl2395,plain,
( ( sdtpldt0 @ sz10 @ xp )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ sz00 ) ),
inference(demod,[status(thm)],[zip_derived_cl2394,zip_derived_cl192]) ).
thf(zip_derived_cl7_086,plain,
! [X0: $i,X1: $i] :
( ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X1 )
| ( ( sdtpldt0 @ X0 @ X1 )
= ( sdtpldt0 @ X1 @ X0 ) ) ),
inference(cnf,[status(esa)],[mAddComm]) ).
thf(zip_derived_cl2419,plain,
( ~ ( aInteger0 @ ( sdtpldt0 @ sz10 @ xp ) )
| ~ ( aInteger0 @ sz00 )
| ( ( sdtpldt0 @ sz10 @ xp )
= ( sdtpldt0 @ sz00 @ ( sdtpldt0 @ sz10 @ xp ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2395,zip_derived_cl7]) ).
thf(zip_derived_cl1843_087,plain,
aInteger0 @ ( sdtpldt0 @ sz10 @ xp ),
inference(demod,[status(thm)],[zip_derived_cl1842,zip_derived_cl2]) ).
thf(zip_derived_cl1_088,plain,
aInteger0 @ sz00,
inference(cnf,[status(esa)],[mIntZero]) ).
thf(zip_derived_cl2425,plain,
( ( sdtpldt0 @ sz10 @ xp )
= ( sdtpldt0 @ sz00 @ ( sdtpldt0 @ sz10 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2419,zip_derived_cl1843,zip_derived_cl1]) ).
thf(zip_derived_cl226_089,plain,
( ( sdtpldt0 @ sz10 @ xp )
= ( smndt0 @ sz10 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2425_090,plain,
( ( sdtpldt0 @ sz10 @ xp )
= ( sdtpldt0 @ sz00 @ ( sdtpldt0 @ sz10 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2419,zip_derived_cl1843,zip_derived_cl1]) ).
thf(zip_derived_cl1_091,plain,
aInteger0 @ sz00,
inference(cnf,[status(esa)],[mIntZero]) ).
thf(zip_derived_cl2_092,plain,
aInteger0 @ sz10,
inference(cnf,[status(esa)],[mIntOne]) ).
thf(zip_derived_cl5775,plain,
( ( sdtasdt0 @ ( sdtpldt0 @ sz10 @ xp ) @ sz10 )
= ( sdtpldt0 @ sz10 @ xp ) ),
inference(demod,[status(thm)],[zip_derived_cl5760,zip_derived_cl2425,zip_derived_cl226,zip_derived_cl2425,zip_derived_cl1,zip_derived_cl2]) ).
thf(zip_derived_cl2201_093,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ ( sdtpldt0 @ sz10 @ xp ) @ X0 )
= ( smndt0 @ X0 ) )
| ~ ( aInteger0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl20,zip_derived_cl226]) ).
thf(zip_derived_cl12_094,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X1 )
| ~ ( aInteger0 @ X2 )
| ( ( sdtasdt0 @ X1 @ ( sdtasdt0 @ X0 @ X2 ) )
= ( sdtasdt0 @ ( sdtasdt0 @ X1 @ X0 ) @ X2 ) ) ),
inference(cnf,[status(esa)],[mMulAsso]) ).
thf(zip_derived_cl2204,plain,
! [X0: $i,X1: $i] :
( ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ ( sdtpldt0 @ sz10 @ xp ) )
| ~ ( aInteger0 @ X1 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( sdtasdt0 @ X0 @ X1 ) )
= ( sdtasdt0 @ ( smndt0 @ X0 ) @ X1 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2201,zip_derived_cl12]) ).
thf(zip_derived_cl1843_095,plain,
aInteger0 @ ( sdtpldt0 @ sz10 @ xp ),
inference(demod,[status(thm)],[zip_derived_cl1842,zip_derived_cl2]) ).
thf(zip_derived_cl2216,plain,
! [X0: $i,X1: $i] :
( ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X1 )
| ( ( sdtasdt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( sdtasdt0 @ X0 @ X1 ) )
= ( sdtasdt0 @ ( smndt0 @ X0 ) @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2204,zip_derived_cl1843]) ).
thf(zip_derived_cl2217,plain,
! [X0: $i,X1: $i] :
( ( ( sdtasdt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( sdtasdt0 @ X0 @ X1 ) )
= ( sdtasdt0 @ ( smndt0 @ X0 ) @ X1 ) )
| ~ ( aInteger0 @ X1 )
| ~ ( aInteger0 @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl2216]) ).
thf(zip_derived_cl5847,plain,
( ( ( sdtasdt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( sdtpldt0 @ sz10 @ xp ) )
= ( sdtasdt0 @ ( smndt0 @ ( sdtpldt0 @ sz10 @ xp ) ) @ sz10 ) )
| ~ ( aInteger0 @ sz10 )
| ~ ( aInteger0 @ ( sdtpldt0 @ sz10 @ xp ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl5775,zip_derived_cl2217]) ).
thf(zip_derived_cl3_096,plain,
! [X0: $i] :
( ( aInteger0 @ ( smndt0 @ X0 ) )
| ~ ( aInteger0 @ X0 ) ),
inference(cnf,[status(esa)],[mIntNeg]) ).
thf(zip_derived_cl11_097,plain,
! [X0: $i] :
( ( sz00
= ( sdtpldt0 @ ( smndt0 @ X0 ) @ X0 ) )
| ~ ( aInteger0 @ X0 ) ),
inference(cnf,[status(esa)],[mAddNeg]) ).
thf(zip_derived_cl196,plain,
! [X0: $i] :
( ( aElementOf0 @ X0 @ ( szAzrzSzezqlpdtcmdtrp0 @ sz10 @ xp ) )
| ~ ( aDivisorOf0 @ xp @ ( sdtpldt0 @ X0 @ ( smndt0 @ sz10 ) ) )
| ~ ( aInteger0 @ X0 ) ),
inference(cnf,[status(esa)],[m__2171]) ).
thf(zip_derived_cl226_098,plain,
( ( sdtpldt0 @ sz10 @ xp )
= ( smndt0 @ sz10 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3992,plain,
! [X0: $i] :
( ( aElementOf0 @ X0 @ ( szAzrzSzezqlpdtcmdtrp0 @ sz10 @ xp ) )
| ~ ( aDivisorOf0 @ xp @ ( sdtpldt0 @ X0 @ ( sdtpldt0 @ sz10 @ xp ) ) )
| ~ ( aInteger0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl196,zip_derived_cl226]) ).
thf(zip_derived_cl4000,plain,
( ~ ( aInteger0 @ ( sdtpldt0 @ sz10 @ xp ) )
| ( aElementOf0 @ ( smndt0 @ ( sdtpldt0 @ sz10 @ xp ) ) @ ( szAzrzSzezqlpdtcmdtrp0 @ sz10 @ xp ) )
| ~ ( aDivisorOf0 @ xp @ sz00 )
| ~ ( aInteger0 @ ( smndt0 @ ( sdtpldt0 @ sz10 @ xp ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl3992]) ).
thf(zip_derived_cl1843_099,plain,
aInteger0 @ ( sdtpldt0 @ sz10 @ xp ),
inference(demod,[status(thm)],[zip_derived_cl1842,zip_derived_cl2]) ).
thf(zip_derived_cl1956_100,plain,
( ( sdtpldt0 @ sz10 @ ( sdtpldt0 @ sz10 @ xp ) )
= sz00 ),
inference(demod,[status(thm)],[zip_derived_cl1955,zip_derived_cl2]) ).
thf(zip_derived_cl201,plain,
! [X0: $i] :
( ( aDivisorOf0 @ xp @ ( sdtpldt0 @ X0 @ ( smndt0 @ sz10 ) ) )
| ~ ( aElementOf0 @ X0 @ ( szAzrzSzezqlpdtcmdtrp0 @ sz10 @ xp ) ) ),
inference(cnf,[status(esa)],[m__2171]) ).
thf(zip_derived_cl226_101,plain,
( ( sdtpldt0 @ sz10 @ xp )
= ( smndt0 @ sz10 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3963,plain,
! [X0: $i] :
( ( aDivisorOf0 @ xp @ ( sdtpldt0 @ X0 @ ( sdtpldt0 @ sz10 @ xp ) ) )
| ~ ( aElementOf0 @ X0 @ ( szAzrzSzezqlpdtcmdtrp0 @ sz10 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl201,zip_derived_cl226]) ).
thf(zip_derived_cl3970,plain,
( ( aDivisorOf0 @ xp @ sz00 )
| ~ ( aElementOf0 @ sz10 @ ( szAzrzSzezqlpdtcmdtrp0 @ sz10 @ xp ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1956,zip_derived_cl3963]) ).
thf(mEquModRef,axiom,
! [W0: $i,W1: $i] :
( ( ( aInteger0 @ W0 )
& ( aInteger0 @ W1 )
& ( W1 != sz00 ) )
=> ( sdteqdtlpzmzozddtrp0 @ W0 @ W0 @ W1 ) ) ).
thf(zip_derived_cl30,plain,
! [X0: $i,X1: $i] :
( ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X1 )
| ( X1 = sz00 )
| ( sdteqdtlpzmzozddtrp0 @ X0 @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[mEquModRef]) ).
thf(zip_derived_cl195,plain,
! [X0: $i] :
( ( aElementOf0 @ X0 @ ( szAzrzSzezqlpdtcmdtrp0 @ sz10 @ xp ) )
| ~ ( sdteqdtlpzmzozddtrp0 @ X0 @ sz10 @ xp )
| ~ ( aInteger0 @ X0 ) ),
inference(cnf,[status(esa)],[m__2171]) ).
thf(zip_derived_cl3919,plain,
( ( xp = sz00 )
| ~ ( aInteger0 @ xp )
| ~ ( aInteger0 @ sz10 )
| ( aElementOf0 @ sz10 @ ( szAzrzSzezqlpdtcmdtrp0 @ sz10 @ xp ) )
| ~ ( aInteger0 @ sz10 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl195]) ).
thf(zip_derived_cl192_102,plain,
aInteger0 @ xp,
inference(cnf,[status(esa)],[m__2171]) ).
thf(zip_derived_cl2_103,plain,
aInteger0 @ sz10,
inference(cnf,[status(esa)],[mIntOne]) ).
thf(zip_derived_cl2_104,plain,
aInteger0 @ sz10,
inference(cnf,[status(esa)],[mIntOne]) ).
thf(zip_derived_cl3923,plain,
( ( xp = sz00 )
| ( aElementOf0 @ sz10 @ ( szAzrzSzezqlpdtcmdtrp0 @ sz10 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3919,zip_derived_cl192,zip_derived_cl2,zip_derived_cl2]) ).
thf(zip_derived_cl193,plain,
xp != sz00,
inference(cnf,[status(esa)],[m__2171]) ).
thf(zip_derived_cl3924,plain,
aElementOf0 @ sz10 @ ( szAzrzSzezqlpdtcmdtrp0 @ sz10 @ xp ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl3923,zip_derived_cl193]) ).
thf(zip_derived_cl3981,plain,
aDivisorOf0 @ xp @ sz00,
inference(demod,[status(thm)],[zip_derived_cl3970,zip_derived_cl3924]) ).
thf(zip_derived_cl4014,plain,
( ( aElementOf0 @ ( smndt0 @ ( sdtpldt0 @ sz10 @ xp ) ) @ ( szAzrzSzezqlpdtcmdtrp0 @ sz10 @ xp ) )
| ~ ( aInteger0 @ ( smndt0 @ ( sdtpldt0 @ sz10 @ xp ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4000,zip_derived_cl1843,zip_derived_cl3981]) ).
thf(zip_derived_cl4373,plain,
( ~ ( aInteger0 @ ( sdtpldt0 @ sz10 @ xp ) )
| ( aElementOf0 @ ( smndt0 @ ( sdtpldt0 @ sz10 @ xp ) ) @ ( szAzrzSzezqlpdtcmdtrp0 @ sz10 @ xp ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl3,zip_derived_cl4014]) ).
thf(zip_derived_cl1843_105,plain,
aInteger0 @ ( sdtpldt0 @ sz10 @ xp ),
inference(demod,[status(thm)],[zip_derived_cl1842,zip_derived_cl2]) ).
thf(zip_derived_cl4374,plain,
aElementOf0 @ ( smndt0 @ ( sdtpldt0 @ sz10 @ xp ) ) @ ( szAzrzSzezqlpdtcmdtrp0 @ sz10 @ xp ),
inference(demod,[status(thm)],[zip_derived_cl4373,zip_derived_cl1843]) ).
thf(zip_derived_cl212,plain,
aSubsetOf0 @ ( szAzrzSzezqlpdtcmdtrp0 @ sz10 @ xp ) @ ( stldt0 @ ( sbsmnsldt0 @ xS ) ),
inference(cnf,[status(esa)],[m__2171]) ).
thf(m__2079,axiom,
( ( ( stldt0 @ ( sbsmnsldt0 @ xS ) )
= cS2076 )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ ( stldt0 @ ( sbsmnsldt0 @ xS ) ) )
<=> ( ( W0 = sz10 )
| ( W0
= ( smndt0 @ sz10 ) ) ) )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ ( stldt0 @ ( sbsmnsldt0 @ xS ) ) )
<=> ( ( aInteger0 @ W0 )
& ~ ( aElementOf0 @ W0 @ ( sbsmnsldt0 @ xS ) ) ) )
& ( aSet0 @ ( stldt0 @ ( sbsmnsldt0 @ xS ) ) )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ ( sbsmnsldt0 @ xS ) )
<=> ( ( aInteger0 @ W0 )
& ? [W1: $i] :
( ( aElementOf0 @ W0 @ W1 )
& ( aElementOf0 @ W1 @ xS ) ) ) )
& ( aSet0 @ ( sbsmnsldt0 @ xS ) ) ) ).
thf(zip_derived_cl147,plain,
( ( stldt0 @ ( sbsmnsldt0 @ xS ) )
= cS2076 ),
inference(cnf,[status(esa)],[m__2079]) ).
thf(zip_derived_cl2772,plain,
aSubsetOf0 @ ( szAzrzSzezqlpdtcmdtrp0 @ sz10 @ xp ) @ cS2076,
inference(demod,[status(thm)],[zip_derived_cl212,zip_derived_cl147]) ).
thf(mSubset,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aSubsetOf0 @ W1 @ W0 )
<=> ( ( aSet0 @ W1 )
& ! [W2: $i] :
( ( aElementOf0 @ W2 @ W1 )
=> ( aElementOf0 @ W2 @ W0 ) ) ) ) ) ).
thf(zip_derived_cl44,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( aSubsetOf0 @ X0 @ X1 )
| ( aElementOf0 @ X2 @ X1 )
| ~ ( aElementOf0 @ X2 @ X0 )
| ~ ( aSet0 @ X1 ) ),
inference(cnf,[status(esa)],[mSubset]) ).
thf(zip_derived_cl2773,plain,
! [X0: $i] :
( ( aElementOf0 @ X0 @ cS2076 )
| ~ ( aElementOf0 @ X0 @ ( szAzrzSzezqlpdtcmdtrp0 @ sz10 @ xp ) )
| ~ ( aSet0 @ cS2076 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl2772,zip_derived_cl44]) ).
thf(zip_derived_cl140,plain,
aSet0 @ ( stldt0 @ ( sbsmnsldt0 @ xS ) ),
inference(cnf,[status(esa)],[m__2079]) ).
thf(zip_derived_cl147_106,plain,
( ( stldt0 @ ( sbsmnsldt0 @ xS ) )
= cS2076 ),
inference(cnf,[status(esa)],[m__2079]) ).
thf(zip_derived_cl2008,plain,
aSet0 @ cS2076,
inference(demod,[status(thm)],[zip_derived_cl140,zip_derived_cl147]) ).
thf(zip_derived_cl2775,plain,
! [X0: $i] :
( ( aElementOf0 @ X0 @ cS2076 )
| ~ ( aElementOf0 @ X0 @ ( szAzrzSzezqlpdtcmdtrp0 @ sz10 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2773,zip_derived_cl2008]) ).
thf(zip_derived_cl4376,plain,
aElementOf0 @ ( smndt0 @ ( sdtpldt0 @ sz10 @ xp ) ) @ cS2076,
inference('s_sup-',[status(thm)],[zip_derived_cl4374,zip_derived_cl2775]) ).
thf(zip_derived_cl146,plain,
! [X0: $i] :
( ( X0
= ( smndt0 @ sz10 ) )
| ( X0 = sz10 )
| ~ ( aElementOf0 @ X0 @ ( stldt0 @ ( sbsmnsldt0 @ xS ) ) ) ),
inference(cnf,[status(esa)],[m__2079]) ).
thf(zip_derived_cl226_107,plain,
( ( sdtpldt0 @ sz10 @ xp )
= ( smndt0 @ sz10 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl147_108,plain,
( ( stldt0 @ ( sbsmnsldt0 @ xS ) )
= cS2076 ),
inference(cnf,[status(esa)],[m__2079]) ).
thf(zip_derived_cl3774,plain,
! [X0: $i] :
( ( X0
= ( sdtpldt0 @ sz10 @ xp ) )
| ( X0 = sz10 )
| ~ ( aElementOf0 @ X0 @ cS2076 ) ),
inference(demod,[status(thm)],[zip_derived_cl146,zip_derived_cl226,zip_derived_cl147]) ).
thf(zip_derived_cl4415,plain,
( ( ( smndt0 @ ( sdtpldt0 @ sz10 @ xp ) )
= ( sdtpldt0 @ sz10 @ xp ) )
| ( ( smndt0 @ ( sdtpldt0 @ sz10 @ xp ) )
= sz10 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl4376,zip_derived_cl3774]) ).
thf(zip_derived_cl3_109,plain,
! [X0: $i] :
( ( aInteger0 @ ( smndt0 @ X0 ) )
| ~ ( aInteger0 @ X0 ) ),
inference(cnf,[status(esa)],[mIntNeg]) ).
thf(zip_derived_cl10_110,plain,
! [X0: $i] :
( ( ( sdtpldt0 @ X0 @ ( smndt0 @ X0 ) )
= sz00 )
| ~ ( aInteger0 @ X0 ) ),
inference(cnf,[status(esa)],[mAddNeg]) ).
thf(zip_derived_cl2615_111,plain,
! [X0: $i] :
( ~ ( aInteger0 @ X0 )
| ( ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ X0 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ sz10 ) @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2608,zip_derived_cl1843,zip_derived_cl1843]) ).
thf(zip_derived_cl2786,plain,
( ~ ( aInteger0 @ ( sdtpldt0 @ sz10 @ xp ) )
| ~ ( aInteger0 @ ( smndt0 @ ( sdtpldt0 @ sz10 @ xp ) ) )
| ( ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ sz00 )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ sz10 ) @ ( smndt0 @ ( sdtpldt0 @ sz10 @ xp ) ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl10,zip_derived_cl2615]) ).
thf(zip_derived_cl1843_112,plain,
aInteger0 @ ( sdtpldt0 @ sz10 @ xp ),
inference(demod,[status(thm)],[zip_derived_cl1842,zip_derived_cl2]) ).
thf(zip_derived_cl2395_113,plain,
( ( sdtpldt0 @ sz10 @ xp )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ sz00 ) ),
inference(demod,[status(thm)],[zip_derived_cl2394,zip_derived_cl192]) ).
thf(zip_derived_cl2799,plain,
( ~ ( aInteger0 @ ( smndt0 @ ( sdtpldt0 @ sz10 @ xp ) ) )
| ( ( sdtpldt0 @ sz10 @ xp )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ sz10 ) @ ( smndt0 @ ( sdtpldt0 @ sz10 @ xp ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2786,zip_derived_cl1843,zip_derived_cl2395]) ).
thf(zip_derived_cl3687,plain,
( ~ ( aInteger0 @ ( sdtpldt0 @ sz10 @ xp ) )
| ( ( sdtpldt0 @ sz10 @ xp )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ sz10 ) @ ( smndt0 @ ( sdtpldt0 @ sz10 @ xp ) ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl3,zip_derived_cl2799]) ).
thf(zip_derived_cl1843_114,plain,
aInteger0 @ ( sdtpldt0 @ sz10 @ xp ),
inference(demod,[status(thm)],[zip_derived_cl1842,zip_derived_cl2]) ).
thf(zip_derived_cl3688,plain,
( ( sdtpldt0 @ sz10 @ xp )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ sz10 ) @ ( smndt0 @ ( sdtpldt0 @ sz10 @ xp ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3687,zip_derived_cl1843]) ).
thf(zip_derived_cl4437,plain,
( ( ( smndt0 @ ( sdtpldt0 @ sz10 @ xp ) )
= sz10 )
| ( ( sdtpldt0 @ sz10 @ xp )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ sz10 ) @ ( sdtpldt0 @ sz10 @ xp ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4415,zip_derived_cl3688]) ).
thf(zip_derived_cl2936_115,plain,
( ( sdtpldt0 @ sz10 @ sz00 )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ sz10 ) @ ( sdtpldt0 @ sz10 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2859,zip_derived_cl2879]) ).
thf(zip_derived_cl4452,plain,
( ( ( smndt0 @ ( sdtpldt0 @ sz10 @ xp ) )
= sz10 )
| ( ( sdtpldt0 @ sz10 @ xp )
= ( sdtpldt0 @ sz10 @ sz00 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4437,zip_derived_cl2936]) ).
thf(zip_derived_cl4672_116,plain,
( ( sdtpldt0 @ sz10 @ sz00 )
= sz10 ),
inference(demod,[status(thm)],[zip_derived_cl4655,zip_derived_cl2,zip_derived_cl3746]) ).
thf(zip_derived_cl4699,plain,
( ( ( smndt0 @ ( sdtpldt0 @ sz10 @ xp ) )
= sz10 )
| ( ( sdtpldt0 @ sz10 @ xp )
= sz10 ) ),
inference(demod,[status(thm)],[zip_derived_cl4452,zip_derived_cl4672]) ).
thf(m__2258,axiom,
( ( ( sdtpldt0 @ sz10 @ ( smndt0 @ xp ) )
!= sz10 )
& ( ( sdtpldt0 @ sz10 @ xp )
!= sz10 ) ) ).
thf(zip_derived_cl224,plain,
( ( sdtpldt0 @ sz10 @ xp )
!= sz10 ),
inference(cnf,[status(esa)],[m__2258]) ).
thf(zip_derived_cl4700,plain,
( ( smndt0 @ ( sdtpldt0 @ sz10 @ xp ) )
= sz10 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl4699,zip_derived_cl224]) ).
thf(zip_derived_cl5384_117,plain,
( ( sdtasdt0 @ sz10 @ sz10 )
= sz10 ),
inference(demod,[status(thm)],[zip_derived_cl5366,zip_derived_cl4687,zip_derived_cl226,zip_derived_cl4687,zip_derived_cl192,zip_derived_cl2]) ).
thf(zip_derived_cl2_118,plain,
aInteger0 @ sz10,
inference(cnf,[status(esa)],[mIntOne]) ).
thf(zip_derived_cl1843_119,plain,
aInteger0 @ ( sdtpldt0 @ sz10 @ xp ),
inference(demod,[status(thm)],[zip_derived_cl1842,zip_derived_cl2]) ).
thf(zip_derived_cl5868,plain,
( ( sdtasdt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( sdtpldt0 @ sz10 @ xp ) )
= sz10 ),
inference(demod,[status(thm)],[zip_derived_cl5847,zip_derived_cl4700,zip_derived_cl5384,zip_derived_cl2,zip_derived_cl1843]) ).
thf(zip_derived_cl21,plain,
! [X0: $i] :
( ( ( smndt0 @ X0 )
= ( sdtasdt0 @ X0 @ ( smndt0 @ sz10 ) ) )
| ~ ( aInteger0 @ X0 ) ),
inference(cnf,[status(esa)],[mMulMinOne]) ).
thf(zip_derived_cl226_120,plain,
( ( sdtpldt0 @ sz10 @ xp )
= ( smndt0 @ sz10 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2233,plain,
! [X0: $i] :
( ( ( smndt0 @ X0 )
= ( sdtasdt0 @ X0 @ ( sdtpldt0 @ sz10 @ xp ) ) )
| ~ ( aInteger0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl21,zip_derived_cl226]) ).
thf(zip_derived_cl16,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X1 )
| ~ ( aInteger0 @ X2 )
| ( ( sdtasdt0 @ X1 @ ( sdtpldt0 @ X0 @ X2 ) )
= ( sdtpldt0 @ ( sdtasdt0 @ X1 @ X0 ) @ ( sdtasdt0 @ X1 @ X2 ) ) ) ),
inference(cnf,[status(esa)],[mDistrib]) ).
thf(zip_derived_cl2238,plain,
! [X0: $i,X1: $i] :
( ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ ( sdtpldt0 @ sz10 @ xp ) )
| ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X1 )
| ( ( sdtasdt0 @ X0 @ ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ X1 ) )
= ( sdtpldt0 @ ( smndt0 @ X0 ) @ ( sdtasdt0 @ X0 @ X1 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl2233,zip_derived_cl16]) ).
thf(zip_derived_cl1843_121,plain,
aInteger0 @ ( sdtpldt0 @ sz10 @ xp ),
inference(demod,[status(thm)],[zip_derived_cl1842,zip_derived_cl2]) ).
thf(zip_derived_cl2253,plain,
! [X0: $i,X1: $i] :
( ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X1 )
| ( ( sdtasdt0 @ X0 @ ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ X1 ) )
= ( sdtpldt0 @ ( smndt0 @ X0 ) @ ( sdtasdt0 @ X0 @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2238,zip_derived_cl1843]) ).
thf(zip_derived_cl2254,plain,
! [X0: $i,X1: $i] :
( ( ( sdtasdt0 @ X0 @ ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ X1 ) )
= ( sdtpldt0 @ ( smndt0 @ X0 ) @ ( sdtasdt0 @ X0 @ X1 ) ) )
| ~ ( aInteger0 @ X1 )
| ~ ( aInteger0 @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl2253]) ).
thf(zip_derived_cl6790,plain,
( ( ( sdtasdt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( sdtpldt0 @ sz10 @ xp ) ) )
= ( sdtpldt0 @ ( smndt0 @ ( sdtpldt0 @ sz10 @ xp ) ) @ sz10 ) )
| ~ ( aInteger0 @ ( sdtpldt0 @ sz10 @ xp ) )
| ~ ( aInteger0 @ ( sdtpldt0 @ sz10 @ xp ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl5868,zip_derived_cl2254]) ).
thf(zip_derived_cl2550_122,plain,
( ( sdtpldt0 @ sz10 @ sz10 )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( sdtpldt0 @ sz10 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1852,zip_derived_cl2514]) ).
thf(zip_derived_cl4773_123,plain,
( ( sdtpldt0 @ sz10 @ sz10 )
= ( sdtpldt0 @ sz00 @ xp ) ),
inference(demod,[status(thm)],[zip_derived_cl4758,zip_derived_cl192]) ).
thf(zip_derived_cl4845,plain,
( ( sdtpldt0 @ sz00 @ xp )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( sdtpldt0 @ sz10 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2550,zip_derived_cl4773]) ).
thf(zip_derived_cl4845_124,plain,
( ( sdtpldt0 @ sz00 @ xp )
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( sdtpldt0 @ sz10 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2550,zip_derived_cl4773]) ).
thf(zip_derived_cl7_125,plain,
! [X0: $i,X1: $i] :
( ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X1 )
| ( ( sdtpldt0 @ X0 @ X1 )
= ( sdtpldt0 @ X1 @ X0 ) ) ),
inference(cnf,[status(esa)],[mAddComm]) ).
thf(zip_derived_cl6_126,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X1 )
| ~ ( aInteger0 @ X2 )
| ( ( sdtpldt0 @ X1 @ ( sdtpldt0 @ X0 @ X2 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ X1 @ X0 ) @ X2 ) ) ),
inference(cnf,[status(esa)],[mAddAsso]) ).
thf(zip_derived_cl1880,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X1 )
| ~ ( aInteger0 @ X1 )
| ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X2 )
| ( ( sdtpldt0 @ X0 @ ( sdtpldt0 @ X1 @ X2 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ X1 @ X0 ) @ X2 ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl6]) ).
thf(zip_derived_cl1894,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( sdtpldt0 @ X0 @ ( sdtpldt0 @ X1 @ X2 ) )
= ( sdtpldt0 @ ( sdtpldt0 @ X1 @ X0 ) @ X2 ) )
| ~ ( aInteger0 @ X2 )
| ~ ( aInteger0 @ X1 )
| ~ ( aInteger0 @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl1880]) ).
thf(zip_derived_cl5644,plain,
( ( ( sdtpldt0 @ xp @ ( sdtpldt0 @ sz10 @ ( sdtpldt0 @ sz10 @ xp ) ) )
= ( sdtpldt0 @ sz00 @ xp ) )
| ~ ( aInteger0 @ ( sdtpldt0 @ sz10 @ xp ) )
| ~ ( aInteger0 @ sz10 )
| ~ ( aInteger0 @ xp ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl4845,zip_derived_cl1894]) ).
thf(zip_derived_cl1956_127,plain,
( ( sdtpldt0 @ sz10 @ ( sdtpldt0 @ sz10 @ xp ) )
= sz00 ),
inference(demod,[status(thm)],[zip_derived_cl1955,zip_derived_cl2]) ).
thf(zip_derived_cl1843_128,plain,
aInteger0 @ ( sdtpldt0 @ sz10 @ xp ),
inference(demod,[status(thm)],[zip_derived_cl1842,zip_derived_cl2]) ).
thf(zip_derived_cl2_129,plain,
aInteger0 @ sz10,
inference(cnf,[status(esa)],[mIntOne]) ).
thf(zip_derived_cl192_130,plain,
aInteger0 @ xp,
inference(cnf,[status(esa)],[m__2171]) ).
thf(zip_derived_cl5697,plain,
( ( sdtpldt0 @ xp @ sz00 )
= ( sdtpldt0 @ sz00 @ xp ) ),
inference(demod,[status(thm)],[zip_derived_cl5644,zip_derived_cl1956,zip_derived_cl1843,zip_derived_cl2,zip_derived_cl192]) ).
thf(zip_derived_cl8_131,plain,
! [X0: $i] :
( ( ( sdtpldt0 @ X0 @ sz00 )
= X0 )
| ~ ( aInteger0 @ X0 ) ),
inference(cnf,[status(esa)],[mAddZero]) ).
thf(zip_derived_cl6079,plain,
( ( ( sdtpldt0 @ sz00 @ xp )
= xp )
| ~ ( aInteger0 @ xp ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl5697,zip_derived_cl8]) ).
thf(zip_derived_cl192_132,plain,
aInteger0 @ xp,
inference(cnf,[status(esa)],[m__2171]) ).
thf(zip_derived_cl6088,plain,
( ( sdtpldt0 @ sz00 @ xp )
= xp ),
inference(demod,[status(thm)],[zip_derived_cl6079,zip_derived_cl192]) ).
thf(zip_derived_cl6173,plain,
( xp
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( sdtpldt0 @ sz10 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4845,zip_derived_cl6088]) ).
thf(zip_derived_cl4700_133,plain,
( ( smndt0 @ ( sdtpldt0 @ sz10 @ xp ) )
= sz10 ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl4699,zip_derived_cl224]) ).
thf(zip_derived_cl4773_134,plain,
( ( sdtpldt0 @ sz10 @ sz10 )
= ( sdtpldt0 @ sz00 @ xp ) ),
inference(demod,[status(thm)],[zip_derived_cl4758,zip_derived_cl192]) ).
thf(zip_derived_cl6088_135,plain,
( ( sdtpldt0 @ sz00 @ xp )
= xp ),
inference(demod,[status(thm)],[zip_derived_cl6079,zip_derived_cl192]) ).
thf(zip_derived_cl6172,plain,
( ( sdtpldt0 @ sz10 @ sz10 )
= xp ),
inference(demod,[status(thm)],[zip_derived_cl4773,zip_derived_cl6088]) ).
thf(zip_derived_cl1843_136,plain,
aInteger0 @ ( sdtpldt0 @ sz10 @ xp ),
inference(demod,[status(thm)],[zip_derived_cl1842,zip_derived_cl2]) ).
thf(zip_derived_cl1843_137,plain,
aInteger0 @ ( sdtpldt0 @ sz10 @ xp ),
inference(demod,[status(thm)],[zip_derived_cl1842,zip_derived_cl2]) ).
thf(zip_derived_cl6817,plain,
( ( sdtasdt0 @ ( sdtpldt0 @ sz10 @ xp ) @ xp )
= xp ),
inference(demod,[status(thm)],[zip_derived_cl6790,zip_derived_cl6173,zip_derived_cl4700,zip_derived_cl6172,zip_derived_cl1843,zip_derived_cl1843]) ).
thf(zip_derived_cl2223_138,plain,
! [X0: $i,X1: $i] :
( ( ( sdtasdt0 @ ( sdtpldt0 @ X1 @ ( sdtpldt0 @ sz10 @ xp ) ) @ X0 )
= ( sdtpldt0 @ ( sdtasdt0 @ X1 @ X0 ) @ ( smndt0 @ X0 ) ) )
| ~ ( aInteger0 @ X1 )
| ~ ( aInteger0 @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl2222]) ).
thf(zip_derived_cl6904,plain,
( ( ( sdtasdt0 @ ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( sdtpldt0 @ sz10 @ xp ) ) @ xp )
= ( sdtpldt0 @ xp @ ( smndt0 @ xp ) ) )
| ~ ( aInteger0 @ ( sdtpldt0 @ sz10 @ xp ) )
| ~ ( aInteger0 @ xp ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl6817,zip_derived_cl2223]) ).
thf(zip_derived_cl6173_139,plain,
( xp
= ( sdtpldt0 @ ( sdtpldt0 @ sz10 @ xp ) @ ( sdtpldt0 @ sz10 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4845,zip_derived_cl6088]) ).
thf(zip_derived_cl1843_140,plain,
aInteger0 @ ( sdtpldt0 @ sz10 @ xp ),
inference(demod,[status(thm)],[zip_derived_cl1842,zip_derived_cl2]) ).
thf(zip_derived_cl192_141,plain,
aInteger0 @ xp,
inference(cnf,[status(esa)],[m__2171]) ).
thf(zip_derived_cl6927,plain,
( ( sdtasdt0 @ xp @ xp )
= ( sdtpldt0 @ xp @ ( smndt0 @ xp ) ) ),
inference(demod,[status(thm)],[zip_derived_cl6904,zip_derived_cl6173,zip_derived_cl1843,zip_derived_cl192]) ).
thf(zip_derived_cl6817_142,plain,
( ( sdtasdt0 @ ( sdtpldt0 @ sz10 @ xp ) @ xp )
= xp ),
inference(demod,[status(thm)],[zip_derived_cl6790,zip_derived_cl6173,zip_derived_cl4700,zip_derived_cl6172,zip_derived_cl1843,zip_derived_cl1843]) ).
thf(zip_derived_cl2201_143,plain,
! [X0: $i] :
( ( ( sdtasdt0 @ ( sdtpldt0 @ sz10 @ xp ) @ X0 )
= ( smndt0 @ X0 ) )
| ~ ( aInteger0 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl20,zip_derived_cl226]) ).
thf(zip_derived_cl6913,plain,
( ( xp
= ( smndt0 @ xp ) )
| ~ ( aInteger0 @ xp ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl6817,zip_derived_cl2201]) ).
thf(zip_derived_cl192_144,plain,
aInteger0 @ xp,
inference(cnf,[status(esa)],[m__2171]) ).
thf(zip_derived_cl6938,plain,
( xp
= ( smndt0 @ xp ) ),
inference(demod,[status(thm)],[zip_derived_cl6913,zip_derived_cl192]) ).
thf(zip_derived_cl6938_145,plain,
( xp
= ( smndt0 @ xp ) ),
inference(demod,[status(thm)],[zip_derived_cl6913,zip_derived_cl192]) ).
thf(zip_derived_cl10_146,plain,
! [X0: $i] :
( ( ( sdtpldt0 @ X0 @ ( smndt0 @ X0 ) )
= sz00 )
| ~ ( aInteger0 @ X0 ) ),
inference(cnf,[status(esa)],[mAddNeg]) ).
thf(zip_derived_cl6953,plain,
( ( ( sdtpldt0 @ xp @ xp )
= sz00 )
| ~ ( aInteger0 @ xp ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl6938,zip_derived_cl10]) ).
thf(zip_derived_cl192_147,plain,
aInteger0 @ xp,
inference(cnf,[status(esa)],[m__2171]) ).
thf(zip_derived_cl6970,plain,
( ( sdtpldt0 @ xp @ xp )
= sz00 ),
inference(demod,[status(thm)],[zip_derived_cl6953,zip_derived_cl192]) ).
thf(zip_derived_cl7147,plain,
( ( sdtasdt0 @ xp @ xp )
= sz00 ),
inference(demod,[status(thm)],[zip_derived_cl6927,zip_derived_cl6938,zip_derived_cl6970]) ).
thf(mZeroDiv,axiom,
! [W0: $i,W1: $i] :
( ( ( aInteger0 @ W0 )
& ( aInteger0 @ W1 ) )
=> ( ( ( sdtasdt0 @ W0 @ W1 )
= sz00 )
=> ( ( W0 = sz00 )
| ( W1 = sz00 ) ) ) ) ).
thf(zip_derived_cl22,plain,
! [X0: $i,X1: $i] :
( ( X0 = sz00 )
| ~ ( aInteger0 @ X0 )
| ~ ( aInteger0 @ X1 )
| ( X1 = sz00 )
| ( ( sdtasdt0 @ X0 @ X1 )
!= sz00 ) ),
inference(cnf,[status(esa)],[mZeroDiv]) ).
thf(zip_derived_cl7150,plain,
( ( xp = sz00 )
| ~ ( aInteger0 @ xp )
| ~ ( aInteger0 @ xp )
| ( xp = sz00 )
| ( sz00 != sz00 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl7147,zip_derived_cl22]) ).
thf(zip_derived_cl192_148,plain,
aInteger0 @ xp,
inference(cnf,[status(esa)],[m__2171]) ).
thf(zip_derived_cl192_149,plain,
aInteger0 @ xp,
inference(cnf,[status(esa)],[m__2171]) ).
thf(zip_derived_cl7170,plain,
( ( xp = sz00 )
| ( xp = sz00 )
| ( sz00 != sz00 ) ),
inference(demod,[status(thm)],[zip_derived_cl7150,zip_derived_cl192,zip_derived_cl192]) ).
thf(zip_derived_cl7171,plain,
xp = sz00,
inference(simplify,[status(thm)],[zip_derived_cl7170]) ).
thf(zip_derived_cl193_150,plain,
xp != sz00,
inference(cnf,[status(esa)],[m__2171]) ).
thf(zip_derived_cl7172,plain,
$false,
inference('simplify_reflect-',[status(thm)],[zip_derived_cl7171,zip_derived_cl193]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM454+6 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.h7rn5ww7H8 true
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 08:47:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.34 % Number of cores: 8
% 0.19/0.35 % Python version: Python 3.6.8
% 0.19/0.35 % Running in FO mode
% 0.21/0.63 % Total configuration time : 435
% 0.21/0.63 % Estimated wc time : 1092
% 0.21/0.63 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 6.26/1.51 % Solved by fo/fo6_bce.sh.
% 6.26/1.51 % BCE start: 227
% 6.26/1.51 % BCE eliminated: 1
% 6.26/1.51 % PE start: 226
% 6.26/1.51 logic: eq
% 6.26/1.51 % PE eliminated: 6
% 6.26/1.51 % done 781 iterations in 0.778s
% 6.26/1.51 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 6.26/1.51 % SZS output start Refutation
% See solution above
% 6.26/1.51
% 6.26/1.51
% 6.26/1.51 % Terminating...
% 6.78/1.57 % Runner terminated.
% 6.78/1.59 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------