%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SWX203+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.gcFvzeAT0o 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 : Tue May 5 07:08:49 PM UTC 2026
% Result : Theorem 3.23s 1.13s
% Output : Refutation 3.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 57
% Number of leaves : 18
% Syntax : Number of formulae : 214 ( 93 unt; 0 typ; 0 def)
% Number of atoms : 605 ( 139 equ; 0 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 3294 ( 272 ~; 335 |; 2 &;2631 @)
% ( 4 <=>; 4 =>; 46 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 3 con; 0-2 aty)
% Number of variables : 423 ( 0 ^; 421 !; 2 ?; 423 :)
% Comments :
%------------------------------------------------------------------------------
thf(nil_type,type,
nil: $i ).
thf(lengthNat_type,type,
lengthNat: $i > $i ).
thf(leqNat_type,type,
leqNat: $i > $i > $o ).
thf(rev_type,type,
rev: $i > $i ).
thf(sorted_type,type,
sorted: $i > $o ).
thf(proj1S_type,type,
proj1S: $i > $i ).
thf(cons_type,type,
cons: $i > $i > $i ).
thf(append_type,type,
append: $i > $i > $i ).
thf(unique_type,type,
unique: $i > $o ).
thf(elemNat_type,type,
elemNat: $i > $i > $o ).
thf(z_type,type,
z: $i ).
thf(s_type,type,
s: $i > $i ).
thf(axiom_006,axiom,
! [Y: $i] : ( leqNat @ z @ Y ) ).
thf(zip_derived_cl5,plain,
! [X0: $i] : ( leqNat @ z @ X0 ),
inference(cnf,[status(esa)],[axiom_006]) ).
thf(axiom_017,axiom,
! [Y: $i,Xs: $i] :
( ( unique @ ( cons @ Y @ Xs ) )
<=> ( ~ ( elemNat @ Y @ Xs )
& ( unique @ Xs ) ) ) ).
thf(zip_derived_cl23,plain,
! [X0: $i,X1: $i] :
( ( unique @ ( cons @ X0 @ X1 ) )
| ~ ( unique @ X1 )
| ( elemNat @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[axiom_017]) ).
thf(axiom_020,axiom,
( ( rev @ nil )
= nil ) ).
thf(zip_derived_cl26,plain,
( ( rev @ nil )
= nil ),
inference(cnf,[status(esa)],[axiom_020]) ).
thf(axiom_021,axiom,
! [Y: $i,Xs: $i] :
( ( rev @ ( cons @ Y @ Xs ) )
= ( append @ ( rev @ Xs ) @ ( cons @ Y @ nil ) ) ) ).
thf(zip_derived_cl27,plain,
! [X0: $i,X1: $i] :
( ( rev @ ( cons @ X1 @ X0 ) )
= ( append @ ( rev @ X0 ) @ ( cons @ X1 @ nil ) ) ),
inference(cnf,[status(esa)],[axiom_021]) ).
thf(zip_derived_cl36,plain,
! [X0: $i] :
( ( rev @ ( cons @ X0 @ nil ) )
= ( append @ nil @ ( cons @ X0 @ nil ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl26,zip_derived_cl27]) ).
thf(axiom_018,axiom,
! [Y: $i] :
( ( append @ nil @ Y )
= Y ) ).
thf(zip_derived_cl24,plain,
! [X0: $i] :
( ( append @ nil @ X0 )
= X0 ),
inference(cnf,[status(esa)],[axiom_018]) ).
thf(zip_derived_cl37,plain,
! [X0: $i] :
( ( rev @ ( cons @ X0 @ nil ) )
= ( cons @ X0 @ nil ) ),
inference(demod,[status(thm)],[zip_derived_cl36,zip_derived_cl24]) ).
thf(zip_derived_cl27_001,plain,
! [X0: $i,X1: $i] :
( ( rev @ ( cons @ X1 @ X0 ) )
= ( append @ ( rev @ X0 ) @ ( cons @ X1 @ nil ) ) ),
inference(cnf,[status(esa)],[axiom_021]) ).
thf(zip_derived_cl40,plain,
! [X0: $i,X1: $i] :
( ( rev @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) )
= ( append @ ( cons @ X0 @ nil ) @ ( cons @ X1 @ nil ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl37,zip_derived_cl27]) ).
thf(axiom_019,axiom,
! [Y: $i,Z: $i,Xs: $i] :
( ( append @ ( cons @ Z @ Xs ) @ Y )
= ( cons @ Z @ ( append @ Xs @ Y ) ) ) ).
thf(zip_derived_cl25,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( append @ ( cons @ X0 @ X1 ) @ X2 )
= ( cons @ X0 @ ( append @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[axiom_019]) ).
thf(zip_derived_cl53,plain,
! [X0: $i,X1: $i] :
( ( rev @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) )
= ( cons @ X0 @ ( append @ nil @ ( cons @ X1 @ nil ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl40,zip_derived_cl25]) ).
thf(zip_derived_cl24_002,plain,
! [X0: $i] :
( ( append @ nil @ X0 )
= X0 ),
inference(cnf,[status(esa)],[axiom_018]) ).
thf(zip_derived_cl54,plain,
! [X0: $i,X1: $i] :
( ( rev @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) )
= ( cons @ X0 @ ( cons @ X1 @ nil ) ) ),
inference(demod,[status(thm)],[zip_derived_cl53,zip_derived_cl24]) ).
thf(axiom_013,axiom,
! [Y: $i,Xs: $i] :
( ( lengthNat @ ( cons @ Y @ Xs ) )
= ( s @ ( lengthNat @ Xs ) ) ) ).
thf(zip_derived_cl15,plain,
! [X0: $i,X1: $i] :
( ( lengthNat @ ( cons @ X1 @ X0 ) )
= ( s @ ( lengthNat @ X0 ) ) ),
inference(cnf,[status(esa)],[axiom_013]) ).
thf(goal_022,conjecture,
? [Xs: $i] :
~ ( ( sorted @ ( rev @ Xs ) )
=> ( ( unique @ Xs )
=> ( leqNat @ ( lengthNat @ Xs ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ? [Xs: $i] :
~ ( ( sorted @ ( rev @ Xs ) )
=> ( ( unique @ Xs )
=> ( leqNat @ ( lengthNat @ Xs ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[goal_022]) ).
thf(zip_derived_cl28,plain,
! [X0: $i] :
( ~ ( unique @ X0 )
| ( leqNat @ ( lengthNat @ X0 ) @ ( s @ ( s @ ( s @ z ) ) ) )
| ~ ( sorted @ ( rev @ X0 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl31,plain,
! [X0: $i,X1: $i] :
( ~ ( unique @ ( cons @ X1 @ X0 ) )
| ( leqNat @ ( s @ ( lengthNat @ X0 ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
| ~ ( sorted @ ( rev @ ( cons @ X1 @ X0 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl15,zip_derived_cl28]) ).
thf(zip_derived_cl57,plain,
! [X0: $i,X1: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ nil ) ) )
| ( leqNat @ ( s @ ( lengthNat @ ( cons @ X1 @ nil ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
| ~ ( sorted @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl54,zip_derived_cl31]) ).
thf(zip_derived_cl15_003,plain,
! [X0: $i,X1: $i] :
( ( lengthNat @ ( cons @ X1 @ X0 ) )
= ( s @ ( lengthNat @ X0 ) ) ),
inference(cnf,[status(esa)],[axiom_013]) ).
thf(axiom_012,axiom,
( ( lengthNat @ nil )
= z ) ).
thf(zip_derived_cl14,plain,
( ( lengthNat @ nil )
= z ),
inference(cnf,[status(esa)],[axiom_012]) ).
thf(zip_derived_cl58,plain,
! [X0: $i,X1: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ nil ) ) )
| ( leqNat @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
| ~ ( sorted @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl57,zip_derived_cl15,zip_derived_cl14]) ).
thf(zip_derived_cl62,plain,
( ( leqNat @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
<= ( leqNat @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
inference(split,[status(esa)],[zip_derived_cl58]) ).
thf(axiom_008,axiom,
! [Z: $i,M: $i] :
( ( leqNat @ ( s @ Z ) @ ( s @ M ) )
<=> ( leqNat @ Z @ M ) ) ).
thf(zip_derived_cl7,plain,
! [X0: $i,X1: $i] :
( ( leqNat @ X0 @ X1 )
| ~ ( leqNat @ ( s @ X0 ) @ ( s @ X1 ) ) ),
inference(cnf,[status(esa)],[axiom_008]) ).
thf(zip_derived_cl72,plain,
( ( leqNat @ ( s @ z ) @ ( s @ ( s @ z ) ) )
<= ( leqNat @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl7]) ).
thf(zip_derived_cl23_004,plain,
! [X0: $i,X1: $i] :
( ( unique @ ( cons @ X0 @ X1 ) )
| ~ ( unique @ X1 )
| ( elemNat @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[axiom_017]) ).
thf(axiom_011,axiom,
! [Y: $i,Y2: $i,Xs: $i] :
( ( sorted @ ( cons @ Y @ ( cons @ Y2 @ Xs ) ) )
<=> ( ( leqNat @ Y @ Y2 )
& ( sorted @ ( cons @ Y2 @ Xs ) ) ) ) ).
thf(zip_derived_cl13,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sorted @ ( cons @ X0 @ ( cons @ X1 @ X2 ) ) )
| ~ ( sorted @ ( cons @ X1 @ X2 ) )
| ~ ( leqNat @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[axiom_011]) ).
thf(zip_derived_cl61,plain,
( ! [X0: $i,X1: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ nil ) ) )
| ~ ( sorted @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) )
<= ! [X0: $i,X1: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ nil ) ) )
| ~ ( sorted @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ),
inference(split,[status(esa)],[zip_derived_cl58]) ).
thf(zip_derived_cl23_005,plain,
! [X0: $i,X1: $i] :
( ( unique @ ( cons @ X0 @ X1 ) )
| ~ ( unique @ X1 )
| ( elemNat @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[axiom_017]) ).
thf(zip_derived_cl63,plain,
( ! [X0: $i,X1: $i] :
( ~ ( sorted @ ( cons @ X0 @ ( cons @ X1 @ nil ) ) )
| ~ ( unique @ ( cons @ X0 @ nil ) )
| ( elemNat @ X1 @ ( cons @ X0 @ nil ) ) )
<= ! [X0: $i,X1: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ nil ) ) )
| ~ ( sorted @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl61,zip_derived_cl23]) ).
thf(zip_derived_cl66,plain,
( ! [X0: $i,X1: $i] :
( ~ ( leqNat @ X1 @ X0 )
| ~ ( sorted @ ( cons @ X0 @ nil ) )
| ~ ( unique @ ( cons @ X1 @ nil ) )
| ( elemNat @ X0 @ ( cons @ X1 @ nil ) ) )
<= ! [X0: $i,X1: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ nil ) ) )
| ~ ( sorted @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl13,zip_derived_cl63]) ).
thf(axiom_010,axiom,
! [Y: $i] : ( sorted @ ( cons @ Y @ nil ) ) ).
thf(zip_derived_cl10,plain,
! [X0: $i] : ( sorted @ ( cons @ X0 @ nil ) ),
inference(cnf,[status(esa)],[axiom_010]) ).
thf(zip_derived_cl67,plain,
( ! [X0: $i,X1: $i] :
( ~ ( leqNat @ X1 @ X0 )
| ~ ( unique @ ( cons @ X1 @ nil ) )
| ( elemNat @ X0 @ ( cons @ X1 @ nil ) ) )
<= ! [X0: $i,X1: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ nil ) ) )
| ~ ( sorted @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl66,zip_derived_cl10]) ).
thf(zip_derived_cl69,plain,
( ! [X0: $i,X1: $i] :
( ( elemNat @ X0 @ nil )
| ~ ( unique @ nil )
| ~ ( leqNat @ X0 @ X1 )
| ( elemNat @ X1 @ ( cons @ X0 @ nil ) ) )
<= ! [X0: $i,X1: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ nil ) ) )
| ~ ( sorted @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl23,zip_derived_cl67]) ).
thf(axiom_014,axiom,
! [X: $i] :
~ ( elemNat @ X @ nil ) ).
thf(zip_derived_cl16,plain,
! [X0: $i] :
~ ( elemNat @ X0 @ nil ),
inference(cnf,[status(esa)],[axiom_014]) ).
thf(axiom_016,axiom,
unique @ nil ).
thf(zip_derived_cl20,plain,
unique @ nil,
inference(cnf,[status(esa)],[axiom_016]) ).
thf(zip_derived_cl70,plain,
( ! [X0: $i,X1: $i] :
( ~ ( leqNat @ X0 @ X1 )
| ( elemNat @ X1 @ ( cons @ X0 @ nil ) ) )
<= ! [X0: $i,X1: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ nil ) ) )
| ~ ( sorted @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl69,zip_derived_cl16,zip_derived_cl20]) ).
thf(axiom_015,axiom,
! [X: $i,Z: $i,Xs: $i] :
( ( elemNat @ X @ ( cons @ Z @ Xs ) )
<=> ( ( X = Z )
| ( elemNat @ X @ Xs ) ) ) ).
thf(zip_derived_cl17,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( elemNat @ X0 @ X1 )
| ( X0 = X2 )
| ~ ( elemNat @ X0 @ ( cons @ X2 @ X1 ) ) ),
inference(cnf,[status(esa)],[axiom_015]) ).
thf(zip_derived_cl71,plain,
( ! [X0: $i,X1: $i] :
( ~ ( leqNat @ X0 @ X1 )
| ( elemNat @ X1 @ nil )
| ( X1 = X0 ) )
<= ! [X0: $i,X1: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ nil ) ) )
| ~ ( sorted @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl70,zip_derived_cl17]) ).
thf(zip_derived_cl16_006,plain,
! [X0: $i] :
~ ( elemNat @ X0 @ nil ),
inference(cnf,[status(esa)],[axiom_014]) ).
thf(zip_derived_cl74,plain,
( ! [X0: $i,X1: $i] :
( ( X1 = X0 )
| ~ ( leqNat @ X0 @ X1 ) )
<= ! [X0: $i,X1: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ nil ) ) )
| ~ ( sorted @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl71,zip_derived_cl16]) ).
thf(zip_derived_cl5_007,plain,
! [X0: $i] : ( leqNat @ z @ X0 ),
inference(cnf,[status(esa)],[axiom_006]) ).
thf(zip_derived_cl79,plain,
( ! [X0: $i] : ( X0 = z )
<= ! [X0: $i,X1: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ nil ) ) )
| ~ ( sorted @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl74,zip_derived_cl5]) ).
thf(axiom_007,axiom,
! [Z: $i] :
~ ( leqNat @ ( s @ Z ) @ z ) ).
thf(zip_derived_cl6,plain,
! [X0: $i] :
~ ( leqNat @ ( s @ X0 ) @ z ),
inference(cnf,[status(esa)],[axiom_007]) ).
thf(zip_derived_cl111,plain,
( ! [X0: $i,X1: $i] :
~ ( leqNat @ ( s @ X1 ) @ X0 )
<= ! [X0: $i,X1: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ nil ) ) )
| ~ ( sorted @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl79,zip_derived_cl6]) ).
thf(zip_derived_cl79_008,plain,
( ! [X0: $i] : ( X0 = z )
<= ! [X0: $i,X1: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ nil ) ) )
| ~ ( sorted @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl74,zip_derived_cl5]) ).
thf(zip_derived_cl5_009,plain,
! [X0: $i] : ( leqNat @ z @ X0 ),
inference(cnf,[status(esa)],[axiom_006]) ).
thf('0',plain,
~ ! [X0: $i,X1: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ nil ) ) )
| ~ ( sorted @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl111,zip_derived_cl79,zip_derived_cl5]) ).
thf('1',plain,
( ( leqNat @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
| ! [X0: $i,X1: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ nil ) ) )
| ~ ( sorted @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ),
inference(split,[status(esa)],[zip_derived_cl58]) ).
thf('2',plain,
leqNat @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ),
inference('sat_resolution*',[status(thm)],['0','1']) ).
thf(zip_derived_cl271,plain,
leqNat @ ( s @ z ) @ ( s @ ( s @ z ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl72,'2']) ).
thf(zip_derived_cl62_010,plain,
( ( leqNat @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
<= ( leqNat @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
inference(split,[status(esa)],[zip_derived_cl58]) ).
thf('3',plain,
leqNat @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ),
inference('sat_resolution*',[status(thm)],['0','1']) ).
thf(zip_derived_cl270,plain,
leqNat @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl62,'3']) ).
thf(zip_derived_cl23_011,plain,
! [X0: $i,X1: $i] :
( ( unique @ ( cons @ X0 @ X1 ) )
| ~ ( unique @ X1 )
| ( elemNat @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[axiom_017]) ).
thf(zip_derived_cl13_012,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sorted @ ( cons @ X0 @ ( cons @ X1 @ X2 ) ) )
| ~ ( sorted @ ( cons @ X1 @ X2 ) )
| ~ ( leqNat @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[axiom_011]) ).
thf(zip_derived_cl13_013,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sorted @ ( cons @ X0 @ ( cons @ X1 @ X2 ) ) )
| ~ ( sorted @ ( cons @ X1 @ X2 ) )
| ~ ( leqNat @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[axiom_011]) ).
thf(zip_derived_cl23_014,plain,
! [X0: $i,X1: $i] :
( ( unique @ ( cons @ X0 @ X1 ) )
| ~ ( unique @ X1 )
| ( elemNat @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[axiom_017]) ).
thf(zip_derived_cl54_015,plain,
! [X0: $i,X1: $i] :
( ( rev @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) )
= ( cons @ X0 @ ( cons @ X1 @ nil ) ) ),
inference(demod,[status(thm)],[zip_derived_cl53,zip_derived_cl24]) ).
thf(zip_derived_cl27_016,plain,
! [X0: $i,X1: $i] :
( ( rev @ ( cons @ X1 @ X0 ) )
= ( append @ ( rev @ X0 ) @ ( cons @ X1 @ nil ) ) ),
inference(cnf,[status(esa)],[axiom_021]) ).
thf(zip_derived_cl56,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( rev @ ( cons @ X2 @ ( cons @ X0 @ ( cons @ X1 @ nil ) ) ) )
= ( append @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) @ ( cons @ X2 @ nil ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl54,zip_derived_cl27]) ).
thf(zip_derived_cl25_017,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( append @ ( cons @ X0 @ X1 ) @ X2 )
= ( cons @ X0 @ ( append @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[axiom_019]) ).
thf(zip_derived_cl105,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( rev @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) )
= ( cons @ X0 @ ( append @ ( cons @ X1 @ nil ) @ ( cons @ X2 @ nil ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl56,zip_derived_cl25]) ).
thf(zip_derived_cl40_018,plain,
! [X0: $i,X1: $i] :
( ( rev @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) )
= ( append @ ( cons @ X0 @ nil ) @ ( cons @ X1 @ nil ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl37,zip_derived_cl27]) ).
thf(zip_derived_cl54_019,plain,
! [X0: $i,X1: $i] :
( ( rev @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) )
= ( cons @ X0 @ ( cons @ X1 @ nil ) ) ),
inference(demod,[status(thm)],[zip_derived_cl53,zip_derived_cl24]) ).
thf(zip_derived_cl55,plain,
! [X0: $i,X1: $i] :
( ( cons @ X0 @ ( cons @ X1 @ nil ) )
= ( append @ ( cons @ X0 @ nil ) @ ( cons @ X1 @ nil ) ) ),
inference(demod,[status(thm)],[zip_derived_cl40,zip_derived_cl54]) ).
thf(zip_derived_cl106,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( rev @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) )
= ( cons @ X0 @ ( cons @ X1 @ ( cons @ X2 @ nil ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl105,zip_derived_cl55]) ).
thf(zip_derived_cl27_020,plain,
! [X0: $i,X1: $i] :
( ( rev @ ( cons @ X1 @ X0 ) )
= ( append @ ( rev @ X0 ) @ ( cons @ X1 @ nil ) ) ),
inference(cnf,[status(esa)],[axiom_021]) ).
thf(zip_derived_cl272,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( rev @ ( cons @ X3 @ ( cons @ X0 @ ( cons @ X1 @ ( cons @ X2 @ nil ) ) ) ) )
= ( append @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) @ ( cons @ X3 @ nil ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl106,zip_derived_cl27]) ).
thf(zip_derived_cl25_021,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( append @ ( cons @ X0 @ X1 ) @ X2 )
= ( cons @ X0 @ ( append @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[axiom_019]) ).
thf(zip_derived_cl289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( rev @ ( cons @ X3 @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) )
= ( cons @ X0 @ ( append @ ( cons @ X1 @ ( cons @ X2 @ nil ) ) @ ( cons @ X3 @ nil ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl272,zip_derived_cl25]) ).
thf(zip_derived_cl25_022,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( append @ ( cons @ X0 @ X1 ) @ X2 )
= ( cons @ X0 @ ( append @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[axiom_019]) ).
thf(zip_derived_cl55_023,plain,
! [X0: $i,X1: $i] :
( ( cons @ X0 @ ( cons @ X1 @ nil ) )
= ( append @ ( cons @ X0 @ nil ) @ ( cons @ X1 @ nil ) ) ),
inference(demod,[status(thm)],[zip_derived_cl40,zip_derived_cl54]) ).
thf(zip_derived_cl290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( rev @ ( cons @ X3 @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) )
= ( cons @ X0 @ ( cons @ X1 @ ( cons @ X2 @ ( cons @ X3 @ nil ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl289,zip_derived_cl25,zip_derived_cl55]) ).
thf(zip_derived_cl31_024,plain,
! [X0: $i,X1: $i] :
( ~ ( unique @ ( cons @ X1 @ X0 ) )
| ( leqNat @ ( s @ ( lengthNat @ X0 ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
| ~ ( sorted @ ( rev @ ( cons @ X1 @ X0 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl15,zip_derived_cl28]) ).
thf(zip_derived_cl293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ ( cons @ X2 @ ( cons @ X3 @ nil ) ) ) ) )
| ( leqNat @ ( s @ ( lengthNat @ ( cons @ X1 @ ( cons @ X2 @ ( cons @ X3 @ nil ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
| ~ ( sorted @ ( cons @ X3 @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl290,zip_derived_cl31]) ).
thf(zip_derived_cl15_025,plain,
! [X0: $i,X1: $i] :
( ( lengthNat @ ( cons @ X1 @ X0 ) )
= ( s @ ( lengthNat @ X0 ) ) ),
inference(cnf,[status(esa)],[axiom_013]) ).
thf(zip_derived_cl15_026,plain,
! [X0: $i,X1: $i] :
( ( lengthNat @ ( cons @ X1 @ X0 ) )
= ( s @ ( lengthNat @ X0 ) ) ),
inference(cnf,[status(esa)],[axiom_013]) ).
thf(zip_derived_cl15_027,plain,
! [X0: $i,X1: $i] :
( ( lengthNat @ ( cons @ X1 @ X0 ) )
= ( s @ ( lengthNat @ X0 ) ) ),
inference(cnf,[status(esa)],[axiom_013]) ).
thf(zip_derived_cl14_028,plain,
( ( lengthNat @ nil )
= z ),
inference(cnf,[status(esa)],[axiom_012]) ).
thf(zip_derived_cl294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ ( cons @ X2 @ ( cons @ X3 @ nil ) ) ) ) )
| ( leqNat @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
| ~ ( sorted @ ( cons @ X3 @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl293,zip_derived_cl15,zip_derived_cl15,zip_derived_cl15,zip_derived_cl14]) ).
thf(zip_derived_cl369,plain,
( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ ( cons @ X2 @ ( cons @ X3 @ nil ) ) ) ) )
| ~ ( sorted @ ( cons @ X3 @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ) )
<= ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ ( cons @ X2 @ ( cons @ X3 @ nil ) ) ) ) )
| ~ ( sorted @ ( cons @ X3 @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ) ) ),
inference(split,[status(esa)],[zip_derived_cl294]) ).
thf(zip_derived_cl23_029,plain,
! [X0: $i,X1: $i] :
( ( unique @ ( cons @ X0 @ X1 ) )
| ~ ( unique @ X1 )
| ( elemNat @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[axiom_017]) ).
thf(zip_derived_cl371,plain,
( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( sorted @ ( cons @ X0 @ ( cons @ X1 @ ( cons @ X2 @ ( cons @ X3 @ nil ) ) ) ) )
| ~ ( unique @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) )
| ( elemNat @ X3 @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) )
<= ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ ( cons @ X2 @ ( cons @ X3 @ nil ) ) ) ) )
| ~ ( sorted @ ( cons @ X3 @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl369,zip_derived_cl23]) ).
thf(zip_derived_cl370,plain,
( ( leqNat @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
<= ( leqNat @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
inference(split,[status(esa)],[zip_derived_cl294]) ).
thf(zip_derived_cl7_030,plain,
! [X0: $i,X1: $i] :
( ( leqNat @ X0 @ X1 )
| ~ ( leqNat @ ( s @ X0 ) @ ( s @ X1 ) ) ),
inference(cnf,[status(esa)],[axiom_008]) ).
thf(zip_derived_cl373,plain,
( ( leqNat @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
<= ( leqNat @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl370,zip_derived_cl7]) ).
thf(zip_derived_cl7_031,plain,
! [X0: $i,X1: $i] :
( ( leqNat @ X0 @ X1 )
| ~ ( leqNat @ ( s @ X0 ) @ ( s @ X1 ) ) ),
inference(cnf,[status(esa)],[axiom_008]) ).
thf(zip_derived_cl374,plain,
( ( leqNat @ ( s @ ( s @ z ) ) @ ( s @ z ) )
<= ( leqNat @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl373,zip_derived_cl7]) ).
thf(zip_derived_cl7_032,plain,
! [X0: $i,X1: $i] :
( ( leqNat @ X0 @ X1 )
| ~ ( leqNat @ ( s @ X0 ) @ ( s @ X1 ) ) ),
inference(cnf,[status(esa)],[axiom_008]) ).
thf(zip_derived_cl375,plain,
( ( leqNat @ ( s @ z ) @ z )
<= ( leqNat @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl374,zip_derived_cl7]) ).
thf(zip_derived_cl6_033,plain,
! [X0: $i] :
~ ( leqNat @ ( s @ X0 ) @ z ),
inference(cnf,[status(esa)],[axiom_007]) ).
thf('4',plain,
~ ( leqNat @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl375,zip_derived_cl6]) ).
thf('5',plain,
( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ ( cons @ X2 @ ( cons @ X3 @ nil ) ) ) ) )
| ~ ( sorted @ ( cons @ X3 @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ) )
| ( leqNat @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
inference(split,[status(esa)],[zip_derived_cl294]) ).
thf('6',plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ ( cons @ X2 @ ( cons @ X3 @ nil ) ) ) ) )
| ~ ( sorted @ ( cons @ X3 @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ) ),
inference('sat_resolution*',[status(thm)],['4','5']) ).
thf(zip_derived_cl381,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( sorted @ ( cons @ X0 @ ( cons @ X1 @ ( cons @ X2 @ ( cons @ X3 @ nil ) ) ) ) )
| ~ ( unique @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) )
| ( elemNat @ X3 @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl371,'6']) ).
thf(zip_derived_cl13_034,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sorted @ ( cons @ X0 @ ( cons @ X1 @ X2 ) ) )
| ~ ( sorted @ ( cons @ X1 @ X2 ) )
| ~ ( leqNat @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[axiom_011]) ).
thf(zip_derived_cl383,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( elemNat @ X0 @ ( cons @ X1 @ ( cons @ X2 @ ( cons @ X3 @ nil ) ) ) )
| ~ ( unique @ ( cons @ X1 @ ( cons @ X2 @ ( cons @ X3 @ nil ) ) ) )
| ~ ( sorted @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) )
| ~ ( leqNat @ X3 @ X2 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl381,zip_derived_cl13]) ).
thf(zip_derived_cl387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( elemNat @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) )
| ~ ( unique @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) )
| ( elemNat @ X3 @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) )
| ~ ( sorted @ ( cons @ X1 @ ( cons @ X2 @ ( cons @ X3 @ nil ) ) ) )
| ~ ( leqNat @ X0 @ X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl23,zip_derived_cl383]) ).
thf(zip_derived_cl17_035,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( elemNat @ X0 @ X1 )
| ( X0 = X2 )
| ~ ( elemNat @ X0 @ ( cons @ X2 @ X1 ) ) ),
inference(cnf,[status(esa)],[axiom_015]) ).
thf(zip_derived_cl411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( leqNat @ X0 @ X1 )
| ~ ( sorted @ ( cons @ X1 @ ( cons @ X2 @ ( cons @ X3 @ nil ) ) ) )
| ~ ( unique @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) )
| ( elemNat @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) )
| ( elemNat @ X3 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) )
| ( X3 = X2 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl387,zip_derived_cl17]) ).
thf(zip_derived_cl412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( leqNat @ X2 @ X1 )
| ~ ( sorted @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) )
| ~ ( leqNat @ X3 @ X2 )
| ~ ( unique @ ( cons @ X2 @ ( cons @ X3 @ nil ) ) )
| ( elemNat @ X1 @ ( cons @ X2 @ ( cons @ X3 @ nil ) ) )
| ( elemNat @ X0 @ ( cons @ X2 @ ( cons @ X3 @ nil ) ) )
| ( X0 = X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl13,zip_derived_cl411]) ).
thf(zip_derived_cl413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( leqNat @ X1 @ X0 )
| ~ ( sorted @ ( cons @ X0 @ nil ) )
| ~ ( leqNat @ X2 @ X1 )
| ~ ( leqNat @ X3 @ X2 )
| ~ ( unique @ ( cons @ X2 @ ( cons @ X3 @ nil ) ) )
| ( elemNat @ X1 @ ( cons @ X2 @ ( cons @ X3 @ nil ) ) )
| ( elemNat @ X0 @ ( cons @ X2 @ ( cons @ X3 @ nil ) ) )
| ( X0 = X1 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl13,zip_derived_cl412]) ).
thf(zip_derived_cl10_036,plain,
! [X0: $i] : ( sorted @ ( cons @ X0 @ nil ) ),
inference(cnf,[status(esa)],[axiom_010]) ).
thf(zip_derived_cl414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( leqNat @ X1 @ X0 )
| ~ ( leqNat @ X2 @ X1 )
| ~ ( leqNat @ X3 @ X2 )
| ~ ( unique @ ( cons @ X2 @ ( cons @ X3 @ nil ) ) )
| ( elemNat @ X1 @ ( cons @ X2 @ ( cons @ X3 @ nil ) ) )
| ( elemNat @ X0 @ ( cons @ X2 @ ( cons @ X3 @ nil ) ) )
| ( X0 = X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl413,zip_derived_cl10]) ).
thf(zip_derived_cl415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( elemNat @ X1 @ ( cons @ X0 @ nil ) )
| ~ ( unique @ ( cons @ X0 @ nil ) )
| ~ ( leqNat @ X3 @ X2 )
| ~ ( leqNat @ X1 @ X3 )
| ~ ( leqNat @ X0 @ X1 )
| ( elemNat @ X3 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) )
| ( elemNat @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) )
| ( X2 = X3 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl23,zip_derived_cl414]) ).
thf(zip_derived_cl417,plain,
! [X0: $i,X1: $i] :
( ( elemNat @ X1 @ ( cons @ X0 @ nil ) )
| ~ ( unique @ ( cons @ X0 @ nil ) )
| ~ ( leqNat @ X1 @ ( s @ ( s @ z ) ) )
| ~ ( leqNat @ X0 @ X1 )
| ( elemNat @ ( s @ ( s @ z ) ) @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) )
| ( elemNat @ ( s @ ( s @ ( s @ z ) ) ) @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) )
| ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ ( s @ z ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl270,zip_derived_cl415]) ).
thf(zip_derived_cl554,plain,
( ! [X0: $i,X1: $i] :
( ~ ( leqNat @ X0 @ X1 )
| ~ ( unique @ ( cons @ X0 @ nil ) )
| ( elemNat @ X1 @ ( cons @ X0 @ nil ) )
| ~ ( leqNat @ X1 @ ( s @ ( s @ z ) ) )
| ( elemNat @ ( s @ ( s @ z ) ) @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) )
| ( elemNat @ ( s @ ( s @ ( s @ z ) ) ) @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) )
<= ! [X0: $i,X1: $i] :
( ~ ( leqNat @ X0 @ X1 )
| ~ ( unique @ ( cons @ X0 @ nil ) )
| ( elemNat @ X1 @ ( cons @ X0 @ nil ) )
| ~ ( leqNat @ X1 @ ( s @ ( s @ z ) ) )
| ( elemNat @ ( s @ ( s @ z ) ) @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) )
| ( elemNat @ ( s @ ( s @ ( s @ z ) ) ) @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ),
inference(split,[status(esa)],[zip_derived_cl417]) ).
thf(zip_derived_cl17_037,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( elemNat @ X0 @ X1 )
| ( X0 = X2 )
| ~ ( elemNat @ X0 @ ( cons @ X2 @ X1 ) ) ),
inference(cnf,[status(esa)],[axiom_015]) ).
thf(zip_derived_cl556,plain,
( ! [X0: $i,X1: $i] :
( ( elemNat @ ( s @ ( s @ z ) ) @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) )
| ~ ( leqNat @ X1 @ ( s @ ( s @ z ) ) )
| ( elemNat @ X1 @ ( cons @ X0 @ nil ) )
| ~ ( unique @ ( cons @ X0 @ nil ) )
| ~ ( leqNat @ X0 @ X1 )
| ( elemNat @ ( s @ ( s @ ( s @ z ) ) ) @ ( cons @ X0 @ nil ) )
| ( ( s @ ( s @ ( s @ z ) ) )
= X1 ) )
<= ! [X0: $i,X1: $i] :
( ~ ( leqNat @ X0 @ X1 )
| ~ ( unique @ ( cons @ X0 @ nil ) )
| ( elemNat @ X1 @ ( cons @ X0 @ nil ) )
| ~ ( leqNat @ X1 @ ( s @ ( s @ z ) ) )
| ( elemNat @ ( s @ ( s @ z ) ) @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) )
| ( elemNat @ ( s @ ( s @ ( s @ z ) ) ) @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl554,zip_derived_cl17]) ).
thf(zip_derived_cl555,plain,
( ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ ( s @ z ) ) )
<= ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ ( s @ z ) ) ) ),
inference(split,[status(esa)],[zip_derived_cl417]) ).
thf(axiom_004,axiom,
! [X: $i] :
( ( proj1S @ ( s @ X ) )
= X ) ).
thf(zip_derived_cl3,plain,
! [X0: $i] :
( ( proj1S @ ( s @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[axiom_004]) ).
thf(zip_derived_cl557,plain,
( ( ( proj1S @ ( s @ ( s @ z ) ) )
= ( s @ ( s @ z ) ) )
<= ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ ( s @ z ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl555,zip_derived_cl3]) ).
thf(zip_derived_cl3_038,plain,
! [X0: $i] :
( ( proj1S @ ( s @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[axiom_004]) ).
thf(zip_derived_cl571,plain,
( ( ( s @ z )
= ( s @ ( s @ z ) ) )
<= ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ ( s @ z ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl557,zip_derived_cl3]) ).
thf(zip_derived_cl3_039,plain,
! [X0: $i] :
( ( proj1S @ ( s @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[axiom_004]) ).
thf(zip_derived_cl575,plain,
( ( ( proj1S @ ( s @ z ) )
= ( s @ z ) )
<= ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ ( s @ z ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl571,zip_derived_cl3]) ).
thf(zip_derived_cl3_040,plain,
! [X0: $i] :
( ( proj1S @ ( s @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[axiom_004]) ).
thf(zip_derived_cl594,plain,
( ( z
= ( s @ z ) )
<= ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ ( s @ z ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl575,zip_derived_cl3]) ).
thf(axiom_005,axiom,
! [X: $i] :
( z
!= ( s @ X ) ) ).
thf(zip_derived_cl4,plain,
! [X0: $i] :
( z
!= ( s @ X0 ) ),
inference(cnf,[status(esa)],[axiom_005]) ).
thf('7',plain,
( ( s @ ( s @ ( s @ z ) ) )
!= ( s @ ( s @ z ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl594,zip_derived_cl4]) ).
thf('8',plain,
( ! [X0: $i,X1: $i] :
( ~ ( leqNat @ X0 @ X1 )
| ~ ( unique @ ( cons @ X0 @ nil ) )
| ( elemNat @ X1 @ ( cons @ X0 @ nil ) )
| ~ ( leqNat @ X1 @ ( s @ ( s @ z ) ) )
| ( elemNat @ ( s @ ( s @ z ) ) @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) )
| ( elemNat @ ( s @ ( s @ ( s @ z ) ) ) @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) )
| ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ ( s @ z ) ) ) ),
inference(split,[status(esa)],[zip_derived_cl417]) ).
thf('9',plain,
! [X0: $i,X1: $i] :
( ~ ( leqNat @ X0 @ X1 )
| ~ ( unique @ ( cons @ X0 @ nil ) )
| ( elemNat @ X1 @ ( cons @ X0 @ nil ) )
| ~ ( leqNat @ X1 @ ( s @ ( s @ z ) ) )
| ( elemNat @ ( s @ ( s @ z ) ) @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) )
| ( elemNat @ ( s @ ( s @ ( s @ z ) ) ) @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ),
inference('sat_resolution*',[status(thm)],['7','8']) ).
thf(zip_derived_cl616,plain,
! [X0: $i,X1: $i] :
( ( elemNat @ ( s @ ( s @ z ) ) @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) )
| ~ ( leqNat @ X1 @ ( s @ ( s @ z ) ) )
| ( elemNat @ X1 @ ( cons @ X0 @ nil ) )
| ~ ( unique @ ( cons @ X0 @ nil ) )
| ~ ( leqNat @ X0 @ X1 )
| ( elemNat @ ( s @ ( s @ ( s @ z ) ) ) @ ( cons @ X0 @ nil ) )
| ( ( s @ ( s @ ( s @ z ) ) )
= X1 ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl556,'9']) ).
thf(zip_derived_cl620,plain,
! [X0: $i] :
( ( elemNat @ ( s @ ( s @ z ) ) @ ( cons @ ( s @ z ) @ ( cons @ X0 @ nil ) ) )
| ( elemNat @ ( s @ z ) @ ( cons @ X0 @ nil ) )
| ~ ( unique @ ( cons @ X0 @ nil ) )
| ~ ( leqNat @ X0 @ ( s @ z ) )
| ( elemNat @ ( s @ ( s @ ( s @ z ) ) ) @ ( cons @ X0 @ nil ) )
| ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ z ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl271,zip_derived_cl616]) ).
thf(zip_derived_cl1564,plain,
( ! [X0: $i] :
( ~ ( unique @ ( cons @ X0 @ nil ) )
| ~ ( leqNat @ X0 @ ( s @ z ) )
| ( elemNat @ ( s @ z ) @ ( cons @ X0 @ nil ) )
| ( elemNat @ ( s @ ( s @ ( s @ z ) ) ) @ ( cons @ X0 @ nil ) )
| ( elemNat @ ( s @ ( s @ z ) ) @ ( cons @ ( s @ z ) @ ( cons @ X0 @ nil ) ) ) )
<= ! [X0: $i] :
( ~ ( unique @ ( cons @ X0 @ nil ) )
| ~ ( leqNat @ X0 @ ( s @ z ) )
| ( elemNat @ ( s @ z ) @ ( cons @ X0 @ nil ) )
| ( elemNat @ ( s @ ( s @ ( s @ z ) ) ) @ ( cons @ X0 @ nil ) )
| ( elemNat @ ( s @ ( s @ z ) ) @ ( cons @ ( s @ z ) @ ( cons @ X0 @ nil ) ) ) ) ),
inference(split,[status(esa)],[zip_derived_cl620]) ).
thf(zip_derived_cl1565,plain,
( ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ z ) )
<= ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ z ) ) ),
inference(split,[status(esa)],[zip_derived_cl620]) ).
thf(zip_derived_cl3_041,plain,
! [X0: $i] :
( ( proj1S @ ( s @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[axiom_004]) ).
thf(zip_derived_cl1568,plain,
( ( ( proj1S @ ( s @ z ) )
= ( s @ ( s @ z ) ) )
<= ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ z ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl1565,zip_derived_cl3]) ).
thf(zip_derived_cl3_042,plain,
! [X0: $i] :
( ( proj1S @ ( s @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[axiom_004]) ).
thf(zip_derived_cl1584,plain,
( ( z
= ( s @ ( s @ z ) ) )
<= ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ z ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1568,zip_derived_cl3]) ).
thf(zip_derived_cl4_043,plain,
! [X0: $i] :
( z
!= ( s @ X0 ) ),
inference(cnf,[status(esa)],[axiom_005]) ).
thf('10',plain,
( ( s @ ( s @ ( s @ z ) ) )
!= ( s @ z ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl1584,zip_derived_cl4]) ).
thf('11',plain,
( ! [X0: $i] :
( ~ ( unique @ ( cons @ X0 @ nil ) )
| ~ ( leqNat @ X0 @ ( s @ z ) )
| ( elemNat @ ( s @ z ) @ ( cons @ X0 @ nil ) )
| ( elemNat @ ( s @ ( s @ ( s @ z ) ) ) @ ( cons @ X0 @ nil ) )
| ( elemNat @ ( s @ ( s @ z ) ) @ ( cons @ ( s @ z ) @ ( cons @ X0 @ nil ) ) ) )
| ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ z ) ) ),
inference(split,[status(esa)],[zip_derived_cl620]) ).
thf('12',plain,
! [X0: $i] :
( ~ ( unique @ ( cons @ X0 @ nil ) )
| ~ ( leqNat @ X0 @ ( s @ z ) )
| ( elemNat @ ( s @ z ) @ ( cons @ X0 @ nil ) )
| ( elemNat @ ( s @ ( s @ ( s @ z ) ) ) @ ( cons @ X0 @ nil ) )
| ( elemNat @ ( s @ ( s @ z ) ) @ ( cons @ ( s @ z ) @ ( cons @ X0 @ nil ) ) ) ),
inference('sat_resolution*',[status(thm)],['10','11']) ).
thf(zip_derived_cl1590,plain,
! [X0: $i] :
( ~ ( unique @ ( cons @ X0 @ nil ) )
| ~ ( leqNat @ X0 @ ( s @ z ) )
| ( elemNat @ ( s @ z ) @ ( cons @ X0 @ nil ) )
| ( elemNat @ ( s @ ( s @ ( s @ z ) ) ) @ ( cons @ X0 @ nil ) )
| ( elemNat @ ( s @ ( s @ z ) ) @ ( cons @ ( s @ z ) @ ( cons @ X0 @ nil ) ) ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl1564,'12']) ).
thf(zip_derived_cl17_044,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( elemNat @ X0 @ X1 )
| ( X0 = X2 )
| ~ ( elemNat @ X0 @ ( cons @ X2 @ X1 ) ) ),
inference(cnf,[status(esa)],[axiom_015]) ).
thf(zip_derived_cl1632,plain,
! [X0: $i] :
( ( elemNat @ ( s @ ( s @ ( s @ z ) ) ) @ ( cons @ X0 @ nil ) )
| ( elemNat @ ( s @ z ) @ ( cons @ X0 @ nil ) )
| ~ ( leqNat @ X0 @ ( s @ z ) )
| ~ ( unique @ ( cons @ X0 @ nil ) )
| ( elemNat @ ( s @ ( s @ z ) ) @ ( cons @ X0 @ nil ) )
| ( ( s @ ( s @ z ) )
= ( s @ z ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1590,zip_derived_cl17]) ).
thf(zip_derived_cl1633,plain,
( ! [X0: $i] :
( ~ ( unique @ ( cons @ X0 @ nil ) )
| ~ ( leqNat @ X0 @ ( s @ z ) )
| ( elemNat @ ( s @ ( s @ z ) ) @ ( cons @ X0 @ nil ) )
| ( elemNat @ ( s @ z ) @ ( cons @ X0 @ nil ) )
| ( elemNat @ ( s @ ( s @ ( s @ z ) ) ) @ ( cons @ X0 @ nil ) ) )
<= ! [X0: $i] :
( ~ ( unique @ ( cons @ X0 @ nil ) )
| ~ ( leqNat @ X0 @ ( s @ z ) )
| ( elemNat @ ( s @ ( s @ z ) ) @ ( cons @ X0 @ nil ) )
| ( elemNat @ ( s @ z ) @ ( cons @ X0 @ nil ) )
| ( elemNat @ ( s @ ( s @ ( s @ z ) ) ) @ ( cons @ X0 @ nil ) ) ) ),
inference(split,[status(esa)],[zip_derived_cl1632]) ).
thf(zip_derived_cl17_045,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( elemNat @ X0 @ X1 )
| ( X0 = X2 )
| ~ ( elemNat @ X0 @ ( cons @ X2 @ X1 ) ) ),
inference(cnf,[status(esa)],[axiom_015]) ).
thf(zip_derived_cl1635,plain,
( ! [X0: $i] :
( ( elemNat @ ( s @ z ) @ ( cons @ X0 @ nil ) )
| ( elemNat @ ( s @ ( s @ z ) ) @ ( cons @ X0 @ nil ) )
| ~ ( leqNat @ X0 @ ( s @ z ) )
| ~ ( unique @ ( cons @ X0 @ nil ) )
| ( elemNat @ ( s @ ( s @ ( s @ z ) ) ) @ nil )
| ( ( s @ ( s @ ( s @ z ) ) )
= X0 ) )
<= ! [X0: $i] :
( ~ ( unique @ ( cons @ X0 @ nil ) )
| ~ ( leqNat @ X0 @ ( s @ z ) )
| ( elemNat @ ( s @ ( s @ z ) ) @ ( cons @ X0 @ nil ) )
| ( elemNat @ ( s @ z ) @ ( cons @ X0 @ nil ) )
| ( elemNat @ ( s @ ( s @ ( s @ z ) ) ) @ ( cons @ X0 @ nil ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1633,zip_derived_cl17]) ).
thf(zip_derived_cl271_046,plain,
leqNat @ ( s @ z ) @ ( s @ ( s @ z ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl72,'2']) ).
thf(zip_derived_cl23_047,plain,
! [X0: $i,X1: $i] :
( ( unique @ ( cons @ X0 @ X1 ) )
| ~ ( unique @ X1 )
| ( elemNat @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[axiom_017]) ).
thf(zip_derived_cl13_048,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sorted @ ( cons @ X0 @ ( cons @ X1 @ X2 ) ) )
| ~ ( sorted @ ( cons @ X1 @ X2 ) )
| ~ ( leqNat @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[axiom_011]) ).
thf(zip_derived_cl23_049,plain,
! [X0: $i,X1: $i] :
( ( unique @ ( cons @ X0 @ X1 ) )
| ~ ( unique @ X1 )
| ( elemNat @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[axiom_017]) ).
thf(zip_derived_cl106_050,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( rev @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) )
= ( cons @ X0 @ ( cons @ X1 @ ( cons @ X2 @ nil ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl105,zip_derived_cl55]) ).
thf(zip_derived_cl31_051,plain,
! [X0: $i,X1: $i] :
( ~ ( unique @ ( cons @ X1 @ X0 ) )
| ( leqNat @ ( s @ ( lengthNat @ X0 ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
| ~ ( sorted @ ( rev @ ( cons @ X1 @ X0 ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl15,zip_derived_cl28]) ).
thf(zip_derived_cl273,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ ( cons @ X2 @ nil ) ) ) )
| ( leqNat @ ( s @ ( lengthNat @ ( cons @ X1 @ ( cons @ X2 @ nil ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
| ~ ( sorted @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl106,zip_derived_cl31]) ).
thf(zip_derived_cl15_052,plain,
! [X0: $i,X1: $i] :
( ( lengthNat @ ( cons @ X1 @ X0 ) )
= ( s @ ( lengthNat @ X0 ) ) ),
inference(cnf,[status(esa)],[axiom_013]) ).
thf(zip_derived_cl15_053,plain,
! [X0: $i,X1: $i] :
( ( lengthNat @ ( cons @ X1 @ X0 ) )
= ( s @ ( lengthNat @ X0 ) ) ),
inference(cnf,[status(esa)],[axiom_013]) ).
thf(zip_derived_cl14_054,plain,
( ( lengthNat @ nil )
= z ),
inference(cnf,[status(esa)],[axiom_012]) ).
thf(zip_derived_cl274,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ ( cons @ X2 @ nil ) ) ) )
| ( leqNat @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
| ~ ( sorted @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl273,zip_derived_cl15,zip_derived_cl15,zip_derived_cl14]) ).
thf(zip_derived_cl279,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ ( cons @ X2 @ nil ) ) ) )
| ~ ( sorted @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) )
<= ! [X0: $i,X1: $i,X2: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ ( cons @ X2 @ nil ) ) ) )
| ~ ( sorted @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ) ),
inference(split,[status(esa)],[zip_derived_cl274]) ).
thf(zip_derived_cl23_055,plain,
! [X0: $i,X1: $i] :
( ( unique @ ( cons @ X0 @ X1 ) )
| ~ ( unique @ X1 )
| ( elemNat @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[axiom_017]) ).
thf(zip_derived_cl281,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ~ ( sorted @ ( cons @ X0 @ ( cons @ X1 @ ( cons @ X2 @ nil ) ) ) )
| ~ ( unique @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) )
| ( elemNat @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) )
<= ! [X0: $i,X1: $i,X2: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ ( cons @ X2 @ nil ) ) ) )
| ~ ( sorted @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl279,zip_derived_cl23]) ).
thf(zip_derived_cl13_056,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sorted @ ( cons @ X0 @ ( cons @ X1 @ X2 ) ) )
| ~ ( sorted @ ( cons @ X1 @ X2 ) )
| ~ ( leqNat @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[axiom_011]) ).
thf(zip_derived_cl286,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( elemNat @ X0 @ ( cons @ X1 @ ( cons @ X2 @ nil ) ) )
| ~ ( unique @ ( cons @ X1 @ ( cons @ X2 @ nil ) ) )
| ~ ( sorted @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) )
| ~ ( leqNat @ X2 @ X1 ) )
<= ! [X0: $i,X1: $i,X2: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ ( cons @ X2 @ nil ) ) ) )
| ~ ( sorted @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl281,zip_derived_cl13]) ).
thf(zip_derived_cl288,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( elemNat @ X1 @ ( cons @ X0 @ nil ) )
| ~ ( unique @ ( cons @ X0 @ nil ) )
| ( elemNat @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) )
| ~ ( sorted @ ( cons @ X1 @ ( cons @ X2 @ nil ) ) )
| ~ ( leqNat @ X0 @ X1 ) )
<= ! [X0: $i,X1: $i,X2: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ ( cons @ X2 @ nil ) ) ) )
| ~ ( sorted @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl23,zip_derived_cl286]) ).
thf(zip_derived_cl17_057,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( elemNat @ X0 @ X1 )
| ( X0 = X2 )
| ~ ( elemNat @ X0 @ ( cons @ X2 @ X1 ) ) ),
inference(cnf,[status(esa)],[axiom_015]) ).
thf(zip_derived_cl295,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ~ ( leqNat @ X0 @ X1 )
| ~ ( sorted @ ( cons @ X1 @ ( cons @ X2 @ nil ) ) )
| ~ ( unique @ ( cons @ X0 @ nil ) )
| ( elemNat @ X1 @ ( cons @ X0 @ nil ) )
| ( elemNat @ X2 @ ( cons @ X0 @ nil ) )
| ( X2 = X1 ) )
<= ! [X0: $i,X1: $i,X2: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ ( cons @ X2 @ nil ) ) ) )
| ~ ( sorted @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl288,zip_derived_cl17]) ).
thf(zip_derived_cl296,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ~ ( leqNat @ X1 @ X0 )
| ~ ( sorted @ ( cons @ X0 @ nil ) )
| ~ ( leqNat @ X2 @ X1 )
| ~ ( unique @ ( cons @ X2 @ nil ) )
| ( elemNat @ X1 @ ( cons @ X2 @ nil ) )
| ( elemNat @ X0 @ ( cons @ X2 @ nil ) )
| ( X0 = X1 ) )
<= ! [X0: $i,X1: $i,X2: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ ( cons @ X2 @ nil ) ) ) )
| ~ ( sorted @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl13,zip_derived_cl295]) ).
thf(zip_derived_cl10_058,plain,
! [X0: $i] : ( sorted @ ( cons @ X0 @ nil ) ),
inference(cnf,[status(esa)],[axiom_010]) ).
thf(zip_derived_cl297,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ~ ( leqNat @ X1 @ X0 )
| ~ ( leqNat @ X2 @ X1 )
| ~ ( unique @ ( cons @ X2 @ nil ) )
| ( elemNat @ X1 @ ( cons @ X2 @ nil ) )
| ( elemNat @ X0 @ ( cons @ X2 @ nil ) )
| ( X0 = X1 ) )
<= ! [X0: $i,X1: $i,X2: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ ( cons @ X2 @ nil ) ) ) )
| ~ ( sorted @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl296,zip_derived_cl10]) ).
thf(zip_derived_cl298,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( elemNat @ X0 @ nil )
| ~ ( unique @ nil )
| ~ ( leqNat @ X2 @ X1 )
| ~ ( leqNat @ X0 @ X2 )
| ( elemNat @ X2 @ ( cons @ X0 @ nil ) )
| ( elemNat @ X1 @ ( cons @ X0 @ nil ) )
| ( X1 = X2 ) )
<= ! [X0: $i,X1: $i,X2: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ ( cons @ X2 @ nil ) ) ) )
| ~ ( sorted @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl23,zip_derived_cl297]) ).
thf(zip_derived_cl16_059,plain,
! [X0: $i] :
~ ( elemNat @ X0 @ nil ),
inference(cnf,[status(esa)],[axiom_014]) ).
thf(zip_derived_cl20_060,plain,
unique @ nil,
inference(cnf,[status(esa)],[axiom_016]) ).
thf(zip_derived_cl299,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ~ ( leqNat @ X2 @ X1 )
| ~ ( leqNat @ X0 @ X2 )
| ( elemNat @ X2 @ ( cons @ X0 @ nil ) )
| ( elemNat @ X1 @ ( cons @ X0 @ nil ) )
| ( X1 = X2 ) )
<= ! [X0: $i,X1: $i,X2: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ ( cons @ X2 @ nil ) ) ) )
| ~ ( sorted @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl298,zip_derived_cl16,zip_derived_cl20]) ).
thf(zip_derived_cl305,plain,
( ! [X0: $i] :
( ~ ( leqNat @ X0 @ ( s @ z ) )
| ( elemNat @ ( s @ z ) @ ( cons @ X0 @ nil ) )
| ( elemNat @ ( s @ ( s @ z ) ) @ ( cons @ X0 @ nil ) )
| ( ( s @ ( s @ z ) )
= ( s @ z ) ) )
<= ! [X0: $i,X1: $i,X2: $i] :
( ~ ( unique @ ( cons @ X0 @ ( cons @ X1 @ ( cons @ X2 @ nil ) ) ) )
| ~ ( sorted @ ( cons @ X2 @ ( cons @ X1 @ ( cons @ X0 @ nil ) ) ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl271,zip_derived_cl299]) ).
thf(zip_derived_cl317,plain,
( ( ( s @ ( s @ z ) )
= ( s @ z ) )
<= ( ( s @ ( s @ z ) )
= ( s @ z ) ) ),
inference(split,[status(esa)],[zip_derived_cl305]) ).
thf(zip_derived_cl3_061,plain,
! [X0: $i] :
( ( proj1S @ ( s @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[axiom_004]) ).
thf(zip_derived_cl319,plain,
( ( ( proj1S @ ( s @ z ) )
= ( s @ z ) )
<= ( ( s @ ( s @ z ) )
= ( s @ z ) ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl317,zip_derived_cl3]) ).
thf(zip_derived_cl3_062,plain,
! [X0: $i] :
( ( proj1S @ ( s @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[axiom_004]) ).
thf(zip_derived_cl336,plain,
( ( z
= ( s @ z ) )
<= ( ( s @ ( s @ z ) )
= ( s @ z ) ) ),
inference(demod,[status(thm)],[zip_derived_cl319,zip_derived_cl3]) ).
thf(zip_derived_cl4_063,plain,
! [X0: $i] :
( z
!= ( s @ X0 ) ),
inference(cnf,[status(esa)],[axiom_005]) ).
thf('13',plain,
( ( s @ ( s @ z ) )
!= ( s @ z ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl336,zip_derived_cl4]) ).
thf('14',plain,
( ! [X0: $i] :
( ~ ( unique @ ( cons @ X0 @ nil ) )
| ~ ( leqNat @ X0 @ ( s @ z ) )
| ( elemNat @ ( s @ ( s @ z ) ) @ ( cons @ X0 @ nil ) )
| ( elemNat @ ( s @ z ) @ ( cons @ X0 @ nil ) )
| ( elemNat @ ( s @ ( s @ ( s @ z ) ) ) @ ( cons @ X0 @ nil ) ) )
| ( ( s @ ( s @ z ) )
= ( s @ z ) ) ),
inference(split,[status(esa)],[zip_derived_cl1632]) ).
thf('15',plain,
! [X0: $i] :
( ~ ( unique @ ( cons @ X0 @ nil ) )
| ~ ( leqNat @ X0 @ ( s @ z ) )
| ( elemNat @ ( s @ ( s @ z ) ) @ ( cons @ X0 @ nil ) )
| ( elemNat @ ( s @ z ) @ ( cons @ X0 @ nil ) )
| ( elemNat @ ( s @ ( s @ ( s @ z ) ) ) @ ( cons @ X0 @ nil ) ) ),
inference('sat_resolution*',[status(thm)],['13','14']) ).
thf(zip_derived_cl1636,plain,
! [X0: $i] :
( ( elemNat @ ( s @ z ) @ ( cons @ X0 @ nil ) )
| ( elemNat @ ( s @ ( s @ z ) ) @ ( cons @ X0 @ nil ) )
| ~ ( leqNat @ X0 @ ( s @ z ) )
| ~ ( unique @ ( cons @ X0 @ nil ) )
| ( elemNat @ ( s @ ( s @ ( s @ z ) ) ) @ nil )
| ( ( s @ ( s @ ( s @ z ) ) )
= X0 ) ),
inference(simpl_trail,[status(thm)],[zip_derived_cl1635,'15']) ).
thf(zip_derived_cl16_064,plain,
! [X0: $i] :
~ ( elemNat @ X0 @ nil ),
inference(cnf,[status(esa)],[axiom_014]) ).
thf(zip_derived_cl1637,plain,
! [X0: $i] :
( ( ( s @ ( s @ ( s @ z ) ) )
= X0 )
| ~ ( unique @ ( cons @ X0 @ nil ) )
| ~ ( leqNat @ X0 @ ( s @ z ) )
| ( elemNat @ ( s @ ( s @ z ) ) @ ( cons @ X0 @ nil ) )
| ( elemNat @ ( s @ z ) @ ( cons @ X0 @ nil ) ) ),
inference(clc,[status(thm)],[zip_derived_cl1636,zip_derived_cl16]) ).
thf(zip_derived_cl17_065,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( elemNat @ X0 @ X1 )
| ( X0 = X2 )
| ~ ( elemNat @ X0 @ ( cons @ X2 @ X1 ) ) ),
inference(cnf,[status(esa)],[axiom_015]) ).
thf(zip_derived_cl1639,plain,
! [X0: $i] :
( ( elemNat @ ( s @ z ) @ ( cons @ X0 @ nil ) )
| ~ ( leqNat @ X0 @ ( s @ z ) )
| ~ ( unique @ ( cons @ X0 @ nil ) )
| ( ( s @ ( s @ ( s @ z ) ) )
= X0 )
| ( elemNat @ ( s @ ( s @ z ) ) @ nil )
| ( ( s @ ( s @ z ) )
= X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1637,zip_derived_cl17]) ).
thf(zip_derived_cl16_066,plain,
! [X0: $i] :
~ ( elemNat @ X0 @ nil ),
inference(cnf,[status(esa)],[axiom_014]) ).
thf(zip_derived_cl1655,plain,
! [X0: $i] :
( ( ( s @ ( s @ z ) )
= X0 )
| ( ( s @ ( s @ ( s @ z ) ) )
= X0 )
| ~ ( unique @ ( cons @ X0 @ nil ) )
| ~ ( leqNat @ X0 @ ( s @ z ) )
| ( elemNat @ ( s @ z ) @ ( cons @ X0 @ nil ) ) ),
inference(clc,[status(thm)],[zip_derived_cl1639,zip_derived_cl16]) ).
thf(zip_derived_cl17_067,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( elemNat @ X0 @ X1 )
| ( X0 = X2 )
| ~ ( elemNat @ X0 @ ( cons @ X2 @ X1 ) ) ),
inference(cnf,[status(esa)],[axiom_015]) ).
thf(zip_derived_cl1656,plain,
! [X0: $i] :
( ~ ( leqNat @ X0 @ ( s @ z ) )
| ~ ( unique @ ( cons @ X0 @ nil ) )
| ( ( s @ ( s @ ( s @ z ) ) )
= X0 )
| ( ( s @ ( s @ z ) )
= X0 )
| ( elemNat @ ( s @ z ) @ nil )
| ( ( s @ z )
= X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1655,zip_derived_cl17]) ).
thf(zip_derived_cl16_068,plain,
! [X0: $i] :
~ ( elemNat @ X0 @ nil ),
inference(cnf,[status(esa)],[axiom_014]) ).
thf(zip_derived_cl1657,plain,
! [X0: $i] :
( ~ ( leqNat @ X0 @ ( s @ z ) )
| ~ ( unique @ ( cons @ X0 @ nil ) )
| ( ( s @ ( s @ ( s @ z ) ) )
= X0 )
| ( ( s @ ( s @ z ) )
= X0 )
| ( ( s @ z )
= X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1656,zip_derived_cl16]) ).
thf(zip_derived_cl1659,plain,
! [X0: $i] :
( ( elemNat @ X0 @ nil )
| ~ ( unique @ nil )
| ~ ( leqNat @ X0 @ ( s @ z ) )
| ( ( s @ ( s @ ( s @ z ) ) )
= X0 )
| ( ( s @ ( s @ z ) )
= X0 )
| ( ( s @ z )
= X0 ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl23,zip_derived_cl1657]) ).
thf(zip_derived_cl16_069,plain,
! [X0: $i] :
~ ( elemNat @ X0 @ nil ),
inference(cnf,[status(esa)],[axiom_014]) ).
thf(zip_derived_cl20_070,plain,
unique @ nil,
inference(cnf,[status(esa)],[axiom_016]) ).
thf(zip_derived_cl1660,plain,
! [X0: $i] :
( ~ ( leqNat @ X0 @ ( s @ z ) )
| ( ( s @ ( s @ ( s @ z ) ) )
= X0 )
| ( ( s @ ( s @ z ) )
= X0 )
| ( ( s @ z )
= X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1659,zip_derived_cl16,zip_derived_cl20]) ).
thf(zip_derived_cl1667,plain,
( ( ( s @ ( s @ ( s @ z ) ) )
= z )
| ( ( s @ ( s @ z ) )
= z )
| ( ( s @ z )
= z ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl5,zip_derived_cl1660]) ).
thf(zip_derived_cl4_071,plain,
! [X0: $i] :
( z
!= ( s @ X0 ) ),
inference(cnf,[status(esa)],[axiom_005]) ).
thf(zip_derived_cl4_072,plain,
! [X0: $i] :
( z
!= ( s @ X0 ) ),
inference(cnf,[status(esa)],[axiom_005]) ).
thf(zip_derived_cl4_073,plain,
! [X0: $i] :
( z
!= ( s @ X0 ) ),
inference(cnf,[status(esa)],[axiom_005]) ).
thf(zip_derived_cl1668,plain,
$false,
inference('simplify_reflect-',[status(thm)],[zip_derived_cl1667,zip_derived_cl4,zip_derived_cl4,zip_derived_cl4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX203+1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.gcFvzeAT0o true
% 0.18/0.34 % Computer : n003.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue May 5 11:26:11 EDT 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 % Running portfolio for 300 s
% 0.18/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.35 % Number of cores: 8
% 0.18/0.35 % Python version: Python 3.6.8
% 0.18/0.35 % Running in FO mode
% 0.53/0.63 % Total configuration time : 435
% 0.53/0.63 % Estimated wc time : 1092
% 0.53/0.63 % Estimated cpu time (7 cpus) : 156.0
% 0.53/0.68 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.54/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.54/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.54/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.54/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.54/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.54/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 3.23/1.13 % Solved by fo/fo1_av.sh.
% 3.23/1.13 % done 426 iterations in 0.385s
% 3.23/1.13 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 3.23/1.13 % SZS output start Refutation
% See solution above
% 3.23/1.13
% 3.23/1.13
% 3.23/1.13 % Terminating...
% 3.96/1.16 % Runner terminated.
% 3.96/1.17 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------