%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYO225^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.RMeJwo7gPb true
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 05:50:22 EDT 2023
% Result : Theorem 1.42s 0.94s
% Output : Refutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 34
% Syntax : Number of formulae : 152 ( 17 unt; 21 typ; 0 def)
% Number of atoms : 1085 ( 89 equ; 0 cnn)
% Maximal formula atoms : 45 ( 8 avg)
% Number of connectives : 3849 ( 161 ~; 130 |; 362 &;2388 @)
% ( 0 <=>; 290 =>; 0 <=; 0 <~>)
% Maximal formula depth : 46 ( 10 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 219 ( 219 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 12 con; 0-2 aty)
% ( 518 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 622 ( 518 ^; 104 !; 0 ?; 622 :)
% Comments :
%------------------------------------------------------------------------------
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(g_type,type,
g: $tType ).
thf('#sk18_type',type,
'#sk18': g ).
thf('#form19_type',type,
'#form19': $o ).
thf('#form22_type',type,
'#form22': $o ).
thf('#sk12_type',type,
'#sk12': b > b > b ).
thf('#sk11_type',type,
'#sk11': b > $o ).
thf('#sk20_type',type,
'#sk20': g ).
thf('#sk10_type',type,
'#sk10': g > g > g ).
thf('#sk21_type',type,
'#sk21': g ).
thf('#sk15_type',type,
'#sk15': g ).
thf('#sk24_type',type,
'#sk24': a ).
thf('#form17_type',type,
'#form17': $o ).
thf('#sk14_type',type,
'#sk14': a > a > a ).
thf('#sk9_type',type,
'#sk9': g > $o ).
thf('#sk13_type',type,
'#sk13': a > $o ).
thf('#sk7_type',type,
'#sk7': g > b ).
thf('#sk23_type',type,
'#sk23': a ).
thf('#sk8_type',type,
'#sk8': b > a ).
thf('#sk16_type',type,
'#sk16': g ).
thf(cTHM126_CORRECTED_pme,conjecture,
! [Xh1: g > b,Xh2: b > a,Xs1: g > $o,Xf1: g > g > g,Xs2: b > $o,Xf2: b > b > b,Xh10: g > b,Xh20: b > a,Xs10: g > $o,Xf10: g > g > g,Xs20: b > $o,Xf20: b > b > b,Xs3: a > $o,Xf3: a > a > a] :
( ( ! [Xx: b,Xy: b] :
( ( ( Xs20 @ Xy )
& ( Xs20 @ Xx ) )
=> ( ( Xh20 @ ( Xf20 @ Xx @ Xy ) )
= ( Xf3 @ ( Xh20 @ Xx ) @ ( Xh20 @ Xy ) ) ) )
& ! [Xx: b] :
( ( Xs20 @ Xx )
=> ( Xs3 @ ( Xh20 @ Xx ) ) )
& ! [Xx: a,Xy: a] :
( ( ( Xs3 @ Xy )
& ( Xs3 @ Xx ) )
=> ( Xs3 @ ( Xf3 @ Xx @ Xy ) ) )
& ! [Xx: g,Xy: g] :
( ( ( Xs10 @ Xy )
& ( Xs10 @ Xx ) )
=> ( ( Xh10 @ ( Xf10 @ Xx @ Xy ) )
= ( Xf20 @ ( Xh10 @ Xx ) @ ( Xh10 @ Xy ) ) ) )
& ! [Xx: g] :
( ( Xs10 @ Xx )
=> ( Xs20 @ ( Xh10 @ Xx ) ) )
& ! [Xx: g] :
( ( Xs10 @ Xx )
=> ( Xs20 @ ( Xh10 @ Xx ) ) )
& ! [Xx: g] :
( ( Xs10 @ Xx )
=> ( Xs20 @ ( Xh10 @ Xx ) ) )
& ! [Xx: g,Xy: g] :
( ( ( Xs10 @ Xy )
& ( Xs10 @ Xx ) )
=> ( Xs10 @ ( Xf10 @ Xx @ Xy ) ) ) )
=> ( ! [Xx: g,Xy: g] :
( ( ( Xs10 @ Xy )
& ( Xs10 @ Xx )
& ( Xs10 @ Xy )
& ( Xs10 @ Xx ) )
=> ( ( Xh20 @ ( Xh10 @ ( Xf10 @ Xx @ Xy ) ) )
= ( Xf3 @ ( Xh20 @ ( Xh10 @ Xx ) ) @ ( Xh20 @ ( Xh10 @ Xy ) ) ) ) )
& ! [Xx: g] :
( ( Xs10 @ Xx )
=> ( Xs3 @ ( Xh20 @ ( Xh10 @ Xx ) ) ) )
& ! [Xx: a,Xy: a] :
( ( ( Xs3 @ Xy )
& ( Xs3 @ Xx ) )
=> ( Xs3 @ ( Xf3 @ Xx @ Xy ) ) )
& ! [Xx: g,Xy: g] :
( ( ( Xs10 @ Xy )
& ( Xs10 @ Xx ) )
=> ( Xs10 @ ( Xf10 @ Xx @ Xy ) ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [Xh1: g > b,Xh2: b > a,Xs1: g > $o,Xf1: g > g > g,Xs2: b > $o,Xf2: b > b > b,Xh10: g > b,Xh20: b > a,Xs10: g > $o,Xf10: g > g > g,Xs20: b > $o,Xf20: b > b > b,Xs3: a > $o,Xf3: a > a > a] :
( ( ! [Xx: b,Xy: b] :
( ( ( Xs20 @ Xy )
& ( Xs20 @ Xx ) )
=> ( ( Xh20 @ ( Xf20 @ Xx @ Xy ) )
= ( Xf3 @ ( Xh20 @ Xx ) @ ( Xh20 @ Xy ) ) ) )
& ! [Xx: b] :
( ( Xs20 @ Xx )
=> ( Xs3 @ ( Xh20 @ Xx ) ) )
& ! [Xx: a,Xy: a] :
( ( ( Xs3 @ Xy )
& ( Xs3 @ Xx ) )
=> ( Xs3 @ ( Xf3 @ Xx @ Xy ) ) )
& ! [Xx: g,Xy: g] :
( ( ( Xs10 @ Xy )
& ( Xs10 @ Xx ) )
=> ( ( Xh10 @ ( Xf10 @ Xx @ Xy ) )
= ( Xf20 @ ( Xh10 @ Xx ) @ ( Xh10 @ Xy ) ) ) )
& ! [Xx: g] :
( ( Xs10 @ Xx )
=> ( Xs20 @ ( Xh10 @ Xx ) ) )
& ! [Xx: g] :
( ( Xs10 @ Xx )
=> ( Xs20 @ ( Xh10 @ Xx ) ) )
& ! [Xx: g] :
( ( Xs10 @ Xx )
=> ( Xs20 @ ( Xh10 @ Xx ) ) )
& ! [Xx: g,Xy: g] :
( ( ( Xs10 @ Xy )
& ( Xs10 @ Xx ) )
=> ( Xs10 @ ( Xf10 @ Xx @ Xy ) ) ) )
=> ( ! [Xx: g,Xy: g] :
( ( ( Xs10 @ Xy )
& ( Xs10 @ Xx )
& ( Xs10 @ Xy )
& ( Xs10 @ Xx ) )
=> ( ( Xh20 @ ( Xh10 @ ( Xf10 @ Xx @ Xy ) ) )
= ( Xf3 @ ( Xh20 @ ( Xh10 @ Xx ) ) @ ( Xh20 @ ( Xh10 @ Xy ) ) ) ) )
& ! [Xx: g] :
( ( Xs10 @ Xx )
=> ( Xs3 @ ( Xh20 @ ( Xh10 @ Xx ) ) ) )
& ! [Xx: a,Xy: a] :
( ( ( Xs3 @ Xy )
& ( Xs3 @ Xx ) )
=> ( Xs3 @ ( Xf3 @ Xx @ Xy ) ) )
& ! [Xx: g,Xy: g] :
( ( ( Xs10 @ Xy )
& ( Xs10 @ Xx ) )
=> ( Xs10 @ ( Xf10 @ Xx @ Xy ) ) ) ) ),
inference('cnf.neg',[status(esa)],[cTHM126_CORRECTED_pme]) ).
thf(zip_derived_cl0,plain,
~ ( !!
@ ^ [Y0: g > b] :
( !!
@ ^ [Y1: b > a] :
( !!
@ ^ [Y2: g > $o] :
( !!
@ ^ [Y3: g > g > g] :
( !!
@ ^ [Y4: b > $o] :
( !!
@ ^ [Y5: b > b > b] :
( !!
@ ^ [Y6: g > b] :
( !!
@ ^ [Y7: b > a] :
( !!
@ ^ [Y8: g > $o] :
( !!
@ ^ [Y9: g > g > g] :
( !!
@ ^ [Y10: b > $o] :
( !!
@ ^ [Y11: b > b > b] :
( !!
@ ^ [Y12: a > $o] :
( !!
@ ^ [Y13: a > a > a] :
( ( ( !!
@ ^ [Y14: b] :
( !!
@ ^ [Y15: b] :
( ( ( Y10 @ Y15 )
& ( Y10 @ Y14 ) )
=> ( ( Y7 @ ( Y11 @ Y14 @ Y15 ) )
= ( Y13 @ ( Y7 @ Y14 ) @ ( Y7 @ Y15 ) ) ) ) ) )
& ( !!
@ ^ [Y14: b] :
( ( Y10 @ Y14 )
=> ( Y12 @ ( Y7 @ Y14 ) ) ) )
& ( !!
@ ^ [Y14: a] :
( !!
@ ^ [Y15: a] :
( ( ( Y12 @ Y15 )
& ( Y12 @ Y14 ) )
=> ( Y12 @ ( Y13 @ Y14 @ Y15 ) ) ) ) )
& ( !!
@ ^ [Y14: g] :
( !!
@ ^ [Y15: g] :
( ( ( Y8 @ Y15 )
& ( Y8 @ Y14 ) )
=> ( ( Y6 @ ( Y9 @ Y14 @ Y15 ) )
= ( Y11 @ ( Y6 @ Y14 ) @ ( Y6 @ Y15 ) ) ) ) ) )
& ( !!
@ ^ [Y14: g] :
( ( Y8 @ Y14 )
=> ( Y10 @ ( Y6 @ Y14 ) ) ) )
& ( !!
@ ^ [Y14: g] :
( ( Y8 @ Y14 )
=> ( Y10 @ ( Y6 @ Y14 ) ) ) )
& ( !!
@ ^ [Y14: g] :
( ( Y8 @ Y14 )
=> ( Y10 @ ( Y6 @ Y14 ) ) ) )
& ( !!
@ ^ [Y14: g] :
( !!
@ ^ [Y15: g] :
( ( ( Y8 @ Y15 )
& ( Y8 @ Y14 ) )
=> ( Y8 @ ( Y9 @ Y14 @ Y15 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y14: g] :
( !!
@ ^ [Y15: g] :
( ( ( Y8 @ Y15 )
& ( Y8 @ Y14 )
& ( Y8 @ Y15 )
& ( Y8 @ Y14 ) )
=> ( ( Y7 @ ( Y6 @ ( Y9 @ Y14 @ Y15 ) ) )
= ( Y13 @ ( Y7 @ ( Y6 @ Y14 ) ) @ ( Y7 @ ( Y6 @ Y15 ) ) ) ) ) ) )
& ( !!
@ ^ [Y14: g] :
( ( Y8 @ Y14 )
=> ( Y12 @ ( Y7 @ ( Y6 @ Y14 ) ) ) ) )
& ( !!
@ ^ [Y14: a] :
( !!
@ ^ [Y15: a] :
( ( ( Y12 @ Y15 )
& ( Y12 @ Y14 ) )
=> ( Y12 @ ( Y13 @ Y14 @ Y15 ) ) ) ) )
& ( !!
@ ^ [Y14: g] :
( !!
@ ^ [Y15: g] :
( ( ( Y8 @ Y15 )
& ( Y8 @ Y14 ) )
=> ( Y8 @ ( Y9 @ Y14 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1,plain,
~ ( !!
@ ^ [Y0: g > b] :
( !!
@ ^ [Y1: b > a] :
( !!
@ ^ [Y2: g > $o] :
( !!
@ ^ [Y3: g > g > g] :
( !!
@ ^ [Y4: b > $o] :
( !!
@ ^ [Y5: b > b > b] :
( !!
@ ^ [Y6: g > b] :
( !!
@ ^ [Y7: b > a] :
( !!
@ ^ [Y8: g > $o] :
( !!
@ ^ [Y9: g > g > g] :
( !!
@ ^ [Y10: b > $o] :
( !!
@ ^ [Y11: b > b > b] :
( !!
@ ^ [Y12: a > $o] :
( !!
@ ^ [Y13: a > a > a] :
( ( ( !!
@ ^ [Y14: g] :
( ( Y8 @ Y14 )
=> ( Y10 @ ( Y6 @ Y14 ) ) ) )
& ( !!
@ ^ [Y14: b] :
( ( Y10 @ Y14 )
=> ( Y12 @ ( Y7 @ Y14 ) ) ) )
& ( !!
@ ^ [Y14: b] :
( !!
@ ^ [Y15: b] :
( ( ( Y10 @ Y15 )
& ( Y10 @ Y14 ) )
=> ( ( Y7 @ ( Y11 @ Y14 @ Y15 ) )
= ( Y13 @ ( Y7 @ Y14 ) @ ( Y7 @ Y15 ) ) ) ) ) )
& ( !!
@ ^ [Y14: a] :
( !!
@ ^ [Y15: a] :
( ( ( Y12 @ Y15 )
& ( Y12 @ Y14 ) )
=> ( Y12 @ ( Y13 @ Y14 @ Y15 ) ) ) ) )
& ( !!
@ ^ [Y14: g] :
( !!
@ ^ [Y15: g] :
( ( ( Y8 @ Y15 )
& ( Y8 @ Y14 ) )
=> ( ( Y6 @ ( Y9 @ Y14 @ Y15 ) )
= ( Y11 @ ( Y6 @ Y14 ) @ ( Y6 @ Y15 ) ) ) ) ) )
& ( !!
@ ^ [Y14: g] :
( !!
@ ^ [Y15: g] :
( ( ( Y8 @ Y15 )
& ( Y8 @ Y14 ) )
=> ( Y8 @ ( Y9 @ Y14 @ Y15 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y14: g] :
( !!
@ ^ [Y15: g] :
( ( ( Y8 @ Y14 )
& ( Y8 @ Y15 ) )
=> ( ( Y7 @ ( Y6 @ ( Y9 @ Y14 @ Y15 ) ) )
= ( Y13 @ ( Y7 @ ( Y6 @ Y14 ) ) @ ( Y7 @ ( Y6 @ Y15 ) ) ) ) ) ) )
& ( !!
@ ^ [Y14: g] :
( ( Y8 @ Y14 )
=> ( Y12 @ ( Y7 @ ( Y6 @ Y14 ) ) ) ) )
& ( !!
@ ^ [Y14: a] :
( !!
@ ^ [Y15: a] :
( ( ( Y12 @ Y15 )
& ( Y12 @ Y14 ) )
=> ( Y12 @ ( Y13 @ Y14 @ Y15 ) ) ) ) )
& ( !!
@ ^ [Y14: g] :
( !!
@ ^ [Y15: g] :
( ( ( Y8 @ Y15 )
& ( Y8 @ Y14 ) )
=> ( Y8 @ ( Y9 @ Y14 @ Y15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl2,plain,
~ ( !!
@ ^ [Y0: b > a] :
( !!
@ ^ [Y1: g > $o] :
( !!
@ ^ [Y2: g > g > g] :
( !!
@ ^ [Y3: b > $o] :
( !!
@ ^ [Y4: b > b > b] :
( !!
@ ^ [Y5: g > b] :
( !!
@ ^ [Y6: b > a] :
( !!
@ ^ [Y7: g > $o] :
( !!
@ ^ [Y8: g > g > g] :
( !!
@ ^ [Y9: b > $o] :
( !!
@ ^ [Y10: b > b > b] :
( !!
@ ^ [Y11: a > $o] :
( !!
@ ^ [Y12: a > a > a] :
( ( ( !!
@ ^ [Y13: g] :
( ( Y7 @ Y13 )
=> ( Y9 @ ( Y5 @ Y13 ) ) ) )
& ( !!
@ ^ [Y13: b] :
( ( Y9 @ Y13 )
=> ( Y11 @ ( Y6 @ Y13 ) ) ) )
& ( !!
@ ^ [Y13: b] :
( !!
@ ^ [Y14: b] :
( ( ( Y9 @ Y14 )
& ( Y9 @ Y13 ) )
=> ( ( Y6 @ ( Y10 @ Y13 @ Y14 ) )
= ( Y12 @ ( Y6 @ Y13 ) @ ( Y6 @ Y14 ) ) ) ) ) )
& ( !!
@ ^ [Y13: a] :
( !!
@ ^ [Y14: a] :
( ( ( Y11 @ Y14 )
& ( Y11 @ Y13 ) )
=> ( Y11 @ ( Y12 @ Y13 @ Y14 ) ) ) ) )
& ( !!
@ ^ [Y13: g] :
( !!
@ ^ [Y14: g] :
( ( ( Y7 @ Y14 )
& ( Y7 @ Y13 ) )
=> ( ( Y5 @ ( Y8 @ Y13 @ Y14 ) )
= ( Y10 @ ( Y5 @ Y13 ) @ ( Y5 @ Y14 ) ) ) ) ) )
& ( !!
@ ^ [Y13: g] :
( !!
@ ^ [Y14: g] :
( ( ( Y7 @ Y14 )
& ( Y7 @ Y13 ) )
=> ( Y7 @ ( Y8 @ Y13 @ Y14 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y13: g] :
( !!
@ ^ [Y14: g] :
( ( ( Y7 @ Y13 )
& ( Y7 @ Y14 ) )
=> ( ( Y6 @ ( Y5 @ ( Y8 @ Y13 @ Y14 ) ) )
= ( Y12 @ ( Y6 @ ( Y5 @ Y13 ) ) @ ( Y6 @ ( Y5 @ Y14 ) ) ) ) ) ) )
& ( !!
@ ^ [Y13: g] :
( ( Y7 @ Y13 )
=> ( Y11 @ ( Y6 @ ( Y5 @ Y13 ) ) ) ) )
& ( !!
@ ^ [Y13: a] :
( !!
@ ^ [Y14: a] :
( ( ( Y11 @ Y14 )
& ( Y11 @ Y13 ) )
=> ( Y11 @ ( Y12 @ Y13 @ Y14 ) ) ) ) )
& ( !!
@ ^ [Y13: g] :
( !!
@ ^ [Y14: g] :
( ( ( Y7 @ Y14 )
& ( Y7 @ Y13 ) )
=> ( Y7 @ ( Y8 @ Y13 @ Y14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl3,plain,
~ ( !!
@ ^ [Y0: g > $o] :
( !!
@ ^ [Y1: g > g > g] :
( !!
@ ^ [Y2: b > $o] :
( !!
@ ^ [Y3: b > b > b] :
( !!
@ ^ [Y4: g > b] :
( !!
@ ^ [Y5: b > a] :
( !!
@ ^ [Y6: g > $o] :
( !!
@ ^ [Y7: g > g > g] :
( !!
@ ^ [Y8: b > $o] :
( !!
@ ^ [Y9: b > b > b] :
( !!
@ ^ [Y10: a > $o] :
( !!
@ ^ [Y11: a > a > a] :
( ( ( !!
@ ^ [Y12: g] :
( ( Y6 @ Y12 )
=> ( Y8 @ ( Y4 @ Y12 ) ) ) )
& ( !!
@ ^ [Y12: b] :
( ( Y8 @ Y12 )
=> ( Y10 @ ( Y5 @ Y12 ) ) ) )
& ( !!
@ ^ [Y12: b] :
( !!
@ ^ [Y13: b] :
( ( ( Y8 @ Y13 )
& ( Y8 @ Y12 ) )
=> ( ( Y5 @ ( Y9 @ Y12 @ Y13 ) )
= ( Y11 @ ( Y5 @ Y12 ) @ ( Y5 @ Y13 ) ) ) ) ) )
& ( !!
@ ^ [Y12: a] :
( !!
@ ^ [Y13: a] :
( ( ( Y10 @ Y13 )
& ( Y10 @ Y12 ) )
=> ( Y10 @ ( Y11 @ Y12 @ Y13 ) ) ) ) )
& ( !!
@ ^ [Y12: g] :
( !!
@ ^ [Y13: g] :
( ( ( Y6 @ Y13 )
& ( Y6 @ Y12 ) )
=> ( ( Y4 @ ( Y7 @ Y12 @ Y13 ) )
= ( Y9 @ ( Y4 @ Y12 ) @ ( Y4 @ Y13 ) ) ) ) ) )
& ( !!
@ ^ [Y12: g] :
( !!
@ ^ [Y13: g] :
( ( ( Y6 @ Y13 )
& ( Y6 @ Y12 ) )
=> ( Y6 @ ( Y7 @ Y12 @ Y13 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y12: g] :
( !!
@ ^ [Y13: g] :
( ( ( Y6 @ Y12 )
& ( Y6 @ Y13 ) )
=> ( ( Y5 @ ( Y4 @ ( Y7 @ Y12 @ Y13 ) ) )
= ( Y11 @ ( Y5 @ ( Y4 @ Y12 ) ) @ ( Y5 @ ( Y4 @ Y13 ) ) ) ) ) ) )
& ( !!
@ ^ [Y12: g] :
( ( Y6 @ Y12 )
=> ( Y10 @ ( Y5 @ ( Y4 @ Y12 ) ) ) ) )
& ( !!
@ ^ [Y12: a] :
( !!
@ ^ [Y13: a] :
( ( ( Y10 @ Y13 )
& ( Y10 @ Y12 ) )
=> ( Y10 @ ( Y11 @ Y12 @ Y13 ) ) ) ) )
& ( !!
@ ^ [Y12: g] :
( !!
@ ^ [Y13: g] :
( ( ( Y6 @ Y13 )
& ( Y6 @ Y12 ) )
=> ( Y6 @ ( Y7 @ Y12 @ Y13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl4,plain,
~ ( !!
@ ^ [Y0: g > g > g] :
( !!
@ ^ [Y1: b > $o] :
( !!
@ ^ [Y2: b > b > b] :
( !!
@ ^ [Y3: g > b] :
( !!
@ ^ [Y4: b > a] :
( !!
@ ^ [Y5: g > $o] :
( !!
@ ^ [Y6: g > g > g] :
( !!
@ ^ [Y7: b > $o] :
( !!
@ ^ [Y8: b > b > b] :
( !!
@ ^ [Y9: a > $o] :
( !!
@ ^ [Y10: a > a > a] :
( ( ( !!
@ ^ [Y11: g] :
( ( Y5 @ Y11 )
=> ( Y7 @ ( Y3 @ Y11 ) ) ) )
& ( !!
@ ^ [Y11: b] :
( ( Y7 @ Y11 )
=> ( Y9 @ ( Y4 @ Y11 ) ) ) )
& ( !!
@ ^ [Y11: b] :
( !!
@ ^ [Y12: b] :
( ( ( Y7 @ Y12 )
& ( Y7 @ Y11 ) )
=> ( ( Y4 @ ( Y8 @ Y11 @ Y12 ) )
= ( Y10 @ ( Y4 @ Y11 ) @ ( Y4 @ Y12 ) ) ) ) ) )
& ( !!
@ ^ [Y11: a] :
( !!
@ ^ [Y12: a] :
( ( ( Y9 @ Y12 )
& ( Y9 @ Y11 ) )
=> ( Y9 @ ( Y10 @ Y11 @ Y12 ) ) ) ) )
& ( !!
@ ^ [Y11: g] :
( !!
@ ^ [Y12: g] :
( ( ( Y5 @ Y12 )
& ( Y5 @ Y11 ) )
=> ( ( Y3 @ ( Y6 @ Y11 @ Y12 ) )
= ( Y8 @ ( Y3 @ Y11 ) @ ( Y3 @ Y12 ) ) ) ) ) )
& ( !!
@ ^ [Y11: g] :
( !!
@ ^ [Y12: g] :
( ( ( Y5 @ Y12 )
& ( Y5 @ Y11 ) )
=> ( Y5 @ ( Y6 @ Y11 @ Y12 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y11: g] :
( !!
@ ^ [Y12: g] :
( ( ( Y5 @ Y11 )
& ( Y5 @ Y12 ) )
=> ( ( Y4 @ ( Y3 @ ( Y6 @ Y11 @ Y12 ) ) )
= ( Y10 @ ( Y4 @ ( Y3 @ Y11 ) ) @ ( Y4 @ ( Y3 @ Y12 ) ) ) ) ) ) )
& ( !!
@ ^ [Y11: g] :
( ( Y5 @ Y11 )
=> ( Y9 @ ( Y4 @ ( Y3 @ Y11 ) ) ) ) )
& ( !!
@ ^ [Y11: a] :
( !!
@ ^ [Y12: a] :
( ( ( Y9 @ Y12 )
& ( Y9 @ Y11 ) )
=> ( Y9 @ ( Y10 @ Y11 @ Y12 ) ) ) ) )
& ( !!
@ ^ [Y11: g] :
( !!
@ ^ [Y12: g] :
( ( ( Y5 @ Y12 )
& ( Y5 @ Y11 ) )
=> ( Y5 @ ( Y6 @ Y11 @ Y12 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl5,plain,
~ ( !!
@ ^ [Y0: b > $o] :
( !!
@ ^ [Y1: b > b > b] :
( !!
@ ^ [Y2: g > b] :
( !!
@ ^ [Y3: b > a] :
( !!
@ ^ [Y4: g > $o] :
( !!
@ ^ [Y5: g > g > g] :
( !!
@ ^ [Y6: b > $o] :
( !!
@ ^ [Y7: b > b > b] :
( !!
@ ^ [Y8: a > $o] :
( !!
@ ^ [Y9: a > a > a] :
( ( ( !!
@ ^ [Y10: g] :
( ( Y4 @ Y10 )
=> ( Y6 @ ( Y2 @ Y10 ) ) ) )
& ( !!
@ ^ [Y10: b] :
( ( Y6 @ Y10 )
=> ( Y8 @ ( Y3 @ Y10 ) ) ) )
& ( !!
@ ^ [Y10: b] :
( !!
@ ^ [Y11: b] :
( ( ( Y6 @ Y11 )
& ( Y6 @ Y10 ) )
=> ( ( Y3 @ ( Y7 @ Y10 @ Y11 ) )
= ( Y9 @ ( Y3 @ Y10 ) @ ( Y3 @ Y11 ) ) ) ) ) )
& ( !!
@ ^ [Y10: a] :
( !!
@ ^ [Y11: a] :
( ( ( Y8 @ Y11 )
& ( Y8 @ Y10 ) )
=> ( Y8 @ ( Y9 @ Y10 @ Y11 ) ) ) ) )
& ( !!
@ ^ [Y10: g] :
( !!
@ ^ [Y11: g] :
( ( ( Y4 @ Y11 )
& ( Y4 @ Y10 ) )
=> ( ( Y2 @ ( Y5 @ Y10 @ Y11 ) )
= ( Y7 @ ( Y2 @ Y10 ) @ ( Y2 @ Y11 ) ) ) ) ) )
& ( !!
@ ^ [Y10: g] :
( !!
@ ^ [Y11: g] :
( ( ( Y4 @ Y11 )
& ( Y4 @ Y10 ) )
=> ( Y4 @ ( Y5 @ Y10 @ Y11 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y10: g] :
( !!
@ ^ [Y11: g] :
( ( ( Y4 @ Y10 )
& ( Y4 @ Y11 ) )
=> ( ( Y3 @ ( Y2 @ ( Y5 @ Y10 @ Y11 ) ) )
= ( Y9 @ ( Y3 @ ( Y2 @ Y10 ) ) @ ( Y3 @ ( Y2 @ Y11 ) ) ) ) ) ) )
& ( !!
@ ^ [Y10: g] :
( ( Y4 @ Y10 )
=> ( Y8 @ ( Y3 @ ( Y2 @ Y10 ) ) ) ) )
& ( !!
@ ^ [Y10: a] :
( !!
@ ^ [Y11: a] :
( ( ( Y8 @ Y11 )
& ( Y8 @ Y10 ) )
=> ( Y8 @ ( Y9 @ Y10 @ Y11 ) ) ) ) )
& ( !!
@ ^ [Y10: g] :
( !!
@ ^ [Y11: g] :
( ( ( Y4 @ Y11 )
& ( Y4 @ Y10 ) )
=> ( Y4 @ ( Y5 @ Y10 @ Y11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl6,plain,
~ ( !!
@ ^ [Y0: b > b > b] :
( !!
@ ^ [Y1: g > b] :
( !!
@ ^ [Y2: b > a] :
( !!
@ ^ [Y3: g > $o] :
( !!
@ ^ [Y4: g > g > g] :
( !!
@ ^ [Y5: b > $o] :
( !!
@ ^ [Y6: b > b > b] :
( !!
@ ^ [Y7: a > $o] :
( !!
@ ^ [Y8: a > a > a] :
( ( ( !!
@ ^ [Y9: g] :
( ( Y3 @ Y9 )
=> ( Y5 @ ( Y1 @ Y9 ) ) ) )
& ( !!
@ ^ [Y9: b] :
( ( Y5 @ Y9 )
=> ( Y7 @ ( Y2 @ Y9 ) ) ) )
& ( !!
@ ^ [Y9: b] :
( !!
@ ^ [Y10: b] :
( ( ( Y5 @ Y10 )
& ( Y5 @ Y9 ) )
=> ( ( Y2 @ ( Y6 @ Y9 @ Y10 ) )
= ( Y8 @ ( Y2 @ Y9 ) @ ( Y2 @ Y10 ) ) ) ) ) )
& ( !!
@ ^ [Y9: a] :
( !!
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 )
& ( Y7 @ Y9 ) )
=> ( Y7 @ ( Y8 @ Y9 @ Y10 ) ) ) ) )
& ( !!
@ ^ [Y9: g] :
( !!
@ ^ [Y10: g] :
( ( ( Y3 @ Y10 )
& ( Y3 @ Y9 ) )
=> ( ( Y1 @ ( Y4 @ Y9 @ Y10 ) )
= ( Y6 @ ( Y1 @ Y9 ) @ ( Y1 @ Y10 ) ) ) ) ) )
& ( !!
@ ^ [Y9: g] :
( !!
@ ^ [Y10: g] :
( ( ( Y3 @ Y10 )
& ( Y3 @ Y9 ) )
=> ( Y3 @ ( Y4 @ Y9 @ Y10 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y9: g] :
( !!
@ ^ [Y10: g] :
( ( ( Y3 @ Y9 )
& ( Y3 @ Y10 ) )
=> ( ( Y2 @ ( Y1 @ ( Y4 @ Y9 @ Y10 ) ) )
= ( Y8 @ ( Y2 @ ( Y1 @ Y9 ) ) @ ( Y2 @ ( Y1 @ Y10 ) ) ) ) ) ) )
& ( !!
@ ^ [Y9: g] :
( ( Y3 @ Y9 )
=> ( Y7 @ ( Y2 @ ( Y1 @ Y9 ) ) ) ) )
& ( !!
@ ^ [Y9: a] :
( !!
@ ^ [Y10: a] :
( ( ( Y7 @ Y10 )
& ( Y7 @ Y9 ) )
=> ( Y7 @ ( Y8 @ Y9 @ Y10 ) ) ) ) )
& ( !!
@ ^ [Y9: g] :
( !!
@ ^ [Y10: g] :
( ( ( Y3 @ Y10 )
& ( Y3 @ Y9 ) )
=> ( Y3 @ ( Y4 @ Y9 @ Y10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl7,plain,
~ ( !!
@ ^ [Y0: g > b] :
( !!
@ ^ [Y1: b > a] :
( !!
@ ^ [Y2: g > $o] :
( !!
@ ^ [Y3: g > g > g] :
( !!
@ ^ [Y4: b > $o] :
( !!
@ ^ [Y5: b > b > b] :
( !!
@ ^ [Y6: a > $o] :
( !!
@ ^ [Y7: a > a > a] :
( ( ( !!
@ ^ [Y8: g] :
( ( Y2 @ Y8 )
=> ( Y4 @ ( Y0 @ Y8 ) ) ) )
& ( !!
@ ^ [Y8: b] :
( ( Y4 @ Y8 )
=> ( Y6 @ ( Y1 @ Y8 ) ) ) )
& ( !!
@ ^ [Y8: b] :
( !!
@ ^ [Y9: b] :
( ( ( Y4 @ Y9 )
& ( Y4 @ Y8 ) )
=> ( ( Y1 @ ( Y5 @ Y8 @ Y9 ) )
= ( Y7 @ ( Y1 @ Y8 ) @ ( Y1 @ Y9 ) ) ) ) ) )
& ( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ ( Y7 @ Y8 @ Y9 ) ) ) ) )
& ( !!
@ ^ [Y8: g] :
( !!
@ ^ [Y9: g] :
( ( ( Y2 @ Y9 )
& ( Y2 @ Y8 ) )
=> ( ( Y0 @ ( Y3 @ Y8 @ Y9 ) )
= ( Y5 @ ( Y0 @ Y8 ) @ ( Y0 @ Y9 ) ) ) ) ) )
& ( !!
@ ^ [Y8: g] :
( !!
@ ^ [Y9: g] :
( ( ( Y2 @ Y9 )
& ( Y2 @ Y8 ) )
=> ( Y2 @ ( Y3 @ Y8 @ Y9 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y8: g] :
( !!
@ ^ [Y9: g] :
( ( ( Y2 @ Y8 )
& ( Y2 @ Y9 ) )
=> ( ( Y1 @ ( Y0 @ ( Y3 @ Y8 @ Y9 ) ) )
= ( Y7 @ ( Y1 @ ( Y0 @ Y8 ) ) @ ( Y1 @ ( Y0 @ Y9 ) ) ) ) ) ) )
& ( !!
@ ^ [Y8: g] :
( ( Y2 @ Y8 )
=> ( Y6 @ ( Y1 @ ( Y0 @ Y8 ) ) ) ) )
& ( !!
@ ^ [Y8: a] :
( !!
@ ^ [Y9: a] :
( ( ( Y6 @ Y9 )
& ( Y6 @ Y8 ) )
=> ( Y6 @ ( Y7 @ Y8 @ Y9 ) ) ) ) )
& ( !!
@ ^ [Y8: g] :
( !!
@ ^ [Y9: g] :
( ( ( Y2 @ Y9 )
& ( Y2 @ Y8 ) )
=> ( Y2 @ ( Y3 @ Y8 @ Y9 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl8,plain,
~ ( !!
@ ^ [Y0: b > a] :
( !!
@ ^ [Y1: g > $o] :
( !!
@ ^ [Y2: g > g > g] :
( !!
@ ^ [Y3: b > $o] :
( !!
@ ^ [Y4: b > b > b] :
( !!
@ ^ [Y5: a > $o] :
( !!
@ ^ [Y6: a > a > a] :
( ( ( !!
@ ^ [Y7: g] :
( ( Y1 @ Y7 )
=> ( Y3 @ ( '#sk7' @ Y7 ) ) ) )
& ( !!
@ ^ [Y7: b] :
( ( Y3 @ Y7 )
=> ( Y5 @ ( Y0 @ Y7 ) ) ) )
& ( !!
@ ^ [Y7: b] :
( !!
@ ^ [Y8: b] :
( ( ( Y3 @ Y8 )
& ( Y3 @ Y7 ) )
=> ( ( Y0 @ ( Y4 @ Y7 @ Y8 ) )
= ( Y6 @ ( Y0 @ Y7 ) @ ( Y0 @ Y8 ) ) ) ) ) )
& ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 )
& ( Y5 @ Y7 ) )
=> ( Y5 @ ( Y6 @ Y7 @ Y8 ) ) ) ) )
& ( !!
@ ^ [Y7: g] :
( !!
@ ^ [Y8: g] :
( ( ( Y1 @ Y8 )
& ( Y1 @ Y7 ) )
=> ( ( '#sk7' @ ( Y2 @ Y7 @ Y8 ) )
= ( Y4 @ ( '#sk7' @ Y7 ) @ ( '#sk7' @ Y8 ) ) ) ) ) )
& ( !!
@ ^ [Y7: g] :
( !!
@ ^ [Y8: g] :
( ( ( Y1 @ Y8 )
& ( Y1 @ Y7 ) )
=> ( Y1 @ ( Y2 @ Y7 @ Y8 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y7: g] :
( !!
@ ^ [Y8: g] :
( ( ( Y1 @ Y7 )
& ( Y1 @ Y8 ) )
=> ( ( Y0 @ ( '#sk7' @ ( Y2 @ Y7 @ Y8 ) ) )
= ( Y6 @ ( Y0 @ ( '#sk7' @ Y7 ) ) @ ( Y0 @ ( '#sk7' @ Y8 ) ) ) ) ) ) )
& ( !!
@ ^ [Y7: g] :
( ( Y1 @ Y7 )
=> ( Y5 @ ( Y0 @ ( '#sk7' @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y7: a] :
( !!
@ ^ [Y8: a] :
( ( ( Y5 @ Y8 )
& ( Y5 @ Y7 ) )
=> ( Y5 @ ( Y6 @ Y7 @ Y8 ) ) ) ) )
& ( !!
@ ^ [Y7: g] :
( !!
@ ^ [Y8: g] :
( ( ( Y1 @ Y8 )
& ( Y1 @ Y7 ) )
=> ( Y1 @ ( Y2 @ Y7 @ Y8 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl9,plain,
~ ( !!
@ ^ [Y0: g > $o] :
( !!
@ ^ [Y1: g > g > g] :
( !!
@ ^ [Y2: b > $o] :
( !!
@ ^ [Y3: b > b > b] :
( !!
@ ^ [Y4: a > $o] :
( !!
@ ^ [Y5: a > a > a] :
( ( ( !!
@ ^ [Y6: g] :
( ( Y0 @ Y6 )
=> ( Y2 @ ( '#sk7' @ Y6 ) ) ) )
& ( !!
@ ^ [Y6: b] :
( ( Y2 @ Y6 )
=> ( Y4 @ ( '#sk8' @ Y6 ) ) ) )
& ( !!
@ ^ [Y6: b] :
( !!
@ ^ [Y7: b] :
( ( ( Y2 @ Y7 )
& ( Y2 @ Y6 ) )
=> ( ( '#sk8' @ ( Y3 @ Y6 @ Y7 ) )
= ( Y5 @ ( '#sk8' @ Y6 ) @ ( '#sk8' @ Y7 ) ) ) ) ) )
& ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ ( Y5 @ Y6 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y6: g] :
( !!
@ ^ [Y7: g] :
( ( ( Y0 @ Y7 )
& ( Y0 @ Y6 ) )
=> ( ( '#sk7' @ ( Y1 @ Y6 @ Y7 ) )
= ( Y3 @ ( '#sk7' @ Y6 ) @ ( '#sk7' @ Y7 ) ) ) ) ) )
& ( !!
@ ^ [Y6: g] :
( !!
@ ^ [Y7: g] :
( ( ( Y0 @ Y7 )
& ( Y0 @ Y6 ) )
=> ( Y0 @ ( Y1 @ Y6 @ Y7 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y6: g] :
( !!
@ ^ [Y7: g] :
( ( ( Y0 @ Y6 )
& ( Y0 @ Y7 ) )
=> ( ( '#sk8' @ ( '#sk7' @ ( Y1 @ Y6 @ Y7 ) ) )
= ( Y5 @ ( '#sk8' @ ( '#sk7' @ Y6 ) ) @ ( '#sk8' @ ( '#sk7' @ Y7 ) ) ) ) ) ) )
& ( !!
@ ^ [Y6: g] :
( ( Y0 @ Y6 )
=> ( Y4 @ ( '#sk8' @ ( '#sk7' @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y6: a] :
( !!
@ ^ [Y7: a] :
( ( ( Y4 @ Y7 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ ( Y5 @ Y6 @ Y7 ) ) ) ) )
& ( !!
@ ^ [Y6: g] :
( !!
@ ^ [Y7: g] :
( ( ( Y0 @ Y7 )
& ( Y0 @ Y6 ) )
=> ( Y0 @ ( Y1 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl10,plain,
~ ( !!
@ ^ [Y0: g > g > g] :
( !!
@ ^ [Y1: b > $o] :
( !!
@ ^ [Y2: b > b > b] :
( !!
@ ^ [Y3: a > $o] :
( !!
@ ^ [Y4: a > a > a] :
( ( ( !!
@ ^ [Y5: g] :
( ( '#sk9' @ Y5 )
=> ( Y1 @ ( '#sk7' @ Y5 ) ) ) )
& ( !!
@ ^ [Y5: b] :
( ( Y1 @ Y5 )
=> ( Y3 @ ( '#sk8' @ Y5 ) ) ) )
& ( !!
@ ^ [Y5: b] :
( !!
@ ^ [Y6: b] :
( ( ( Y1 @ Y6 )
& ( Y1 @ Y5 ) )
=> ( ( '#sk8' @ ( Y2 @ Y5 @ Y6 ) )
= ( Y4 @ ( '#sk8' @ Y5 ) @ ( '#sk8' @ Y6 ) ) ) ) ) )
& ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y5: g] :
( !!
@ ^ [Y6: g] :
( ( ( '#sk9' @ Y6 )
& ( '#sk9' @ Y5 ) )
=> ( ( '#sk7' @ ( Y0 @ Y5 @ Y6 ) )
= ( Y2 @ ( '#sk7' @ Y5 ) @ ( '#sk7' @ Y6 ) ) ) ) ) )
& ( !!
@ ^ [Y5: g] :
( !!
@ ^ [Y6: g] :
( ( ( '#sk9' @ Y6 )
& ( '#sk9' @ Y5 ) )
=> ( '#sk9' @ ( Y0 @ Y5 @ Y6 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y5: g] :
( !!
@ ^ [Y6: g] :
( ( ( '#sk9' @ Y5 )
& ( '#sk9' @ Y6 ) )
=> ( ( '#sk8' @ ( '#sk7' @ ( Y0 @ Y5 @ Y6 ) ) )
= ( Y4 @ ( '#sk8' @ ( '#sk7' @ Y5 ) ) @ ( '#sk8' @ ( '#sk7' @ Y6 ) ) ) ) ) ) )
& ( !!
@ ^ [Y5: g] :
( ( '#sk9' @ Y5 )
=> ( Y3 @ ( '#sk8' @ ( '#sk7' @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y5: a] :
( !!
@ ^ [Y6: a] :
( ( ( Y3 @ Y6 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ ( Y4 @ Y5 @ Y6 ) ) ) ) )
& ( !!
@ ^ [Y5: g] :
( !!
@ ^ [Y6: g] :
( ( ( '#sk9' @ Y6 )
& ( '#sk9' @ Y5 ) )
=> ( '#sk9' @ ( Y0 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl11,plain,
~ ( !!
@ ^ [Y0: b > $o] :
( !!
@ ^ [Y1: b > b > b] :
( !!
@ ^ [Y2: a > $o] :
( !!
@ ^ [Y3: a > a > a] :
( ( ( !!
@ ^ [Y4: g] :
( ( '#sk9' @ Y4 )
=> ( Y0 @ ( '#sk7' @ Y4 ) ) ) )
& ( !!
@ ^ [Y4: b] :
( ( Y0 @ Y4 )
=> ( Y2 @ ( '#sk8' @ Y4 ) ) ) )
& ( !!
@ ^ [Y4: b] :
( !!
@ ^ [Y5: b] :
( ( ( Y0 @ Y5 )
& ( Y0 @ Y4 ) )
=> ( ( '#sk8' @ ( Y1 @ Y4 @ Y5 ) )
= ( Y3 @ ( '#sk8' @ Y4 ) @ ( '#sk8' @ Y5 ) ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y4: g] :
( !!
@ ^ [Y5: g] :
( ( ( '#sk9' @ Y5 )
& ( '#sk9' @ Y4 ) )
=> ( ( '#sk7' @ ( '#sk10' @ Y4 @ Y5 ) )
= ( Y1 @ ( '#sk7' @ Y4 ) @ ( '#sk7' @ Y5 ) ) ) ) ) )
& ( !!
@ ^ [Y4: g] :
( !!
@ ^ [Y5: g] :
( ( ( '#sk9' @ Y5 )
& ( '#sk9' @ Y4 ) )
=> ( '#sk9' @ ( '#sk10' @ Y4 @ Y5 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y4: g] :
( !!
@ ^ [Y5: g] :
( ( ( '#sk9' @ Y4 )
& ( '#sk9' @ Y5 ) )
=> ( ( '#sk8' @ ( '#sk7' @ ( '#sk10' @ Y4 @ Y5 ) ) )
= ( Y3 @ ( '#sk8' @ ( '#sk7' @ Y4 ) ) @ ( '#sk8' @ ( '#sk7' @ Y5 ) ) ) ) ) ) )
& ( !!
@ ^ [Y4: g] :
( ( '#sk9' @ Y4 )
=> ( Y2 @ ( '#sk8' @ ( '#sk7' @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y4: a] :
( !!
@ ^ [Y5: a] :
( ( ( Y2 @ Y5 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ ( Y3 @ Y4 @ Y5 ) ) ) ) )
& ( !!
@ ^ [Y4: g] :
( !!
@ ^ [Y5: g] :
( ( ( '#sk9' @ Y5 )
& ( '#sk9' @ Y4 ) )
=> ( '#sk9' @ ( '#sk10' @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl12,plain,
~ ( !!
@ ^ [Y0: b > b > b] :
( !!
@ ^ [Y1: a > $o] :
( !!
@ ^ [Y2: a > a > a] :
( ( ( !!
@ ^ [Y3: g] :
( ( '#sk9' @ Y3 )
=> ( '#sk11' @ ( '#sk7' @ Y3 ) ) ) )
& ( !!
@ ^ [Y3: b] :
( ( '#sk11' @ Y3 )
=> ( Y1 @ ( '#sk8' @ Y3 ) ) ) )
& ( !!
@ ^ [Y3: b] :
( !!
@ ^ [Y4: b] :
( ( ( '#sk11' @ Y4 )
& ( '#sk11' @ Y3 ) )
=> ( ( '#sk8' @ ( Y0 @ Y3 @ Y4 ) )
= ( Y2 @ ( '#sk8' @ Y3 ) @ ( '#sk8' @ Y4 ) ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y3: g] :
( !!
@ ^ [Y4: g] :
( ( ( '#sk9' @ Y4 )
& ( '#sk9' @ Y3 ) )
=> ( ( '#sk7' @ ( '#sk10' @ Y3 @ Y4 ) )
= ( Y0 @ ( '#sk7' @ Y3 ) @ ( '#sk7' @ Y4 ) ) ) ) ) )
& ( !!
@ ^ [Y3: g] :
( !!
@ ^ [Y4: g] :
( ( ( '#sk9' @ Y4 )
& ( '#sk9' @ Y3 ) )
=> ( '#sk9' @ ( '#sk10' @ Y3 @ Y4 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y3: g] :
( !!
@ ^ [Y4: g] :
( ( ( '#sk9' @ Y3 )
& ( '#sk9' @ Y4 ) )
=> ( ( '#sk8' @ ( '#sk7' @ ( '#sk10' @ Y3 @ Y4 ) ) )
= ( Y2 @ ( '#sk8' @ ( '#sk7' @ Y3 ) ) @ ( '#sk8' @ ( '#sk7' @ Y4 ) ) ) ) ) ) )
& ( !!
@ ^ [Y3: g] :
( ( '#sk9' @ Y3 )
=> ( Y1 @ ( '#sk8' @ ( '#sk7' @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y3: a] :
( !!
@ ^ [Y4: a] :
( ( ( Y1 @ Y4 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ ( Y2 @ Y3 @ Y4 ) ) ) ) )
& ( !!
@ ^ [Y3: g] :
( !!
@ ^ [Y4: g] :
( ( ( '#sk9' @ Y4 )
& ( '#sk9' @ Y3 ) )
=> ( '#sk9' @ ( '#sk10' @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl13,plain,
~ ( !!
@ ^ [Y0: a > $o] :
( !!
@ ^ [Y1: a > a > a] :
( ( ( !!
@ ^ [Y2: g] :
( ( '#sk9' @ Y2 )
=> ( '#sk11' @ ( '#sk7' @ Y2 ) ) ) )
& ( !!
@ ^ [Y2: b] :
( ( '#sk11' @ Y2 )
=> ( Y0 @ ( '#sk8' @ Y2 ) ) ) )
& ( !!
@ ^ [Y2: b] :
( !!
@ ^ [Y3: b] :
( ( ( '#sk11' @ Y3 )
& ( '#sk11' @ Y2 ) )
=> ( ( '#sk8' @ ( '#sk12' @ Y2 @ Y3 ) )
= ( Y1 @ ( '#sk8' @ Y2 ) @ ( '#sk8' @ Y3 ) ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y2: g] :
( !!
@ ^ [Y3: g] :
( ( ( '#sk9' @ Y3 )
& ( '#sk9' @ Y2 ) )
=> ( ( '#sk7' @ ( '#sk10' @ Y2 @ Y3 ) )
= ( '#sk12' @ ( '#sk7' @ Y2 ) @ ( '#sk7' @ Y3 ) ) ) ) ) )
& ( !!
@ ^ [Y2: g] :
( !!
@ ^ [Y3: g] :
( ( ( '#sk9' @ Y3 )
& ( '#sk9' @ Y2 ) )
=> ( '#sk9' @ ( '#sk10' @ Y2 @ Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y2: g] :
( !!
@ ^ [Y3: g] :
( ( ( '#sk9' @ Y2 )
& ( '#sk9' @ Y3 ) )
=> ( ( '#sk8' @ ( '#sk7' @ ( '#sk10' @ Y2 @ Y3 ) ) )
= ( Y1 @ ( '#sk8' @ ( '#sk7' @ Y2 ) ) @ ( '#sk8' @ ( '#sk7' @ Y3 ) ) ) ) ) ) )
& ( !!
@ ^ [Y2: g] :
( ( '#sk9' @ Y2 )
=> ( Y0 @ ( '#sk8' @ ( '#sk7' @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y2: a] :
( !!
@ ^ [Y3: a] :
( ( ( Y0 @ Y3 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ ( Y1 @ Y2 @ Y3 ) ) ) ) )
& ( !!
@ ^ [Y2: g] :
( !!
@ ^ [Y3: g] :
( ( ( '#sk9' @ Y3 )
& ( '#sk9' @ Y2 ) )
=> ( '#sk9' @ ( '#sk10' @ Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl14,plain,
~ ( !!
@ ^ [Y0: a > a > a] :
( ( ( !!
@ ^ [Y1: g] :
( ( '#sk9' @ Y1 )
=> ( '#sk11' @ ( '#sk7' @ Y1 ) ) ) )
& ( !!
@ ^ [Y1: b] :
( ( '#sk11' @ Y1 )
=> ( '#sk13' @ ( '#sk8' @ Y1 ) ) ) )
& ( !!
@ ^ [Y1: b] :
( !!
@ ^ [Y2: b] :
( ( ( '#sk11' @ Y2 )
& ( '#sk11' @ Y1 ) )
=> ( ( '#sk8' @ ( '#sk12' @ Y1 @ Y2 ) )
= ( Y0 @ ( '#sk8' @ Y1 ) @ ( '#sk8' @ Y2 ) ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk13' @ Y2 )
& ( '#sk13' @ Y1 ) )
=> ( '#sk13' @ ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( ( '#sk9' @ Y2 )
& ( '#sk9' @ Y1 ) )
=> ( ( '#sk7' @ ( '#sk10' @ Y1 @ Y2 ) )
= ( '#sk12' @ ( '#sk7' @ Y1 ) @ ( '#sk7' @ Y2 ) ) ) ) ) )
& ( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( ( '#sk9' @ Y2 )
& ( '#sk9' @ Y1 ) )
=> ( '#sk9' @ ( '#sk10' @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( ( '#sk9' @ Y1 )
& ( '#sk9' @ Y2 ) )
=> ( ( '#sk8' @ ( '#sk7' @ ( '#sk10' @ Y1 @ Y2 ) ) )
= ( Y0 @ ( '#sk8' @ ( '#sk7' @ Y1 ) ) @ ( '#sk8' @ ( '#sk7' @ Y2 ) ) ) ) ) ) )
& ( !!
@ ^ [Y1: g] :
( ( '#sk9' @ Y1 )
=> ( '#sk13' @ ( '#sk8' @ ( '#sk7' @ Y1 ) ) ) ) )
& ( !!
@ ^ [Y1: a] :
( !!
@ ^ [Y2: a] :
( ( ( '#sk13' @ Y2 )
& ( '#sk13' @ Y1 ) )
=> ( '#sk13' @ ( Y0 @ Y1 @ Y2 ) ) ) ) )
& ( !!
@ ^ [Y1: g] :
( !!
@ ^ [Y2: g] :
( ( ( '#sk9' @ Y2 )
& ( '#sk9' @ Y1 ) )
=> ( '#sk9' @ ( '#sk10' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl15,plain,
~ ( ( ( !!
@ ^ [Y0: g] :
( ( '#sk9' @ Y0 )
=> ( '#sk11' @ ( '#sk7' @ Y0 ) ) ) )
& ( !!
@ ^ [Y0: b] :
( ( '#sk11' @ Y0 )
=> ( '#sk13' @ ( '#sk8' @ Y0 ) ) ) )
& ( !!
@ ^ [Y0: b] :
( !!
@ ^ [Y1: b] :
( ( ( '#sk11' @ Y1 )
& ( '#sk11' @ Y0 ) )
=> ( ( '#sk8' @ ( '#sk12' @ Y0 @ Y1 ) )
= ( '#sk14' @ ( '#sk8' @ Y0 ) @ ( '#sk8' @ Y1 ) ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk13' @ Y1 )
& ( '#sk13' @ Y0 ) )
=> ( '#sk13' @ ( '#sk14' @ Y0 @ Y1 ) ) ) ) )
& ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ( '#sk9' @ Y1 )
& ( '#sk9' @ Y0 ) )
=> ( ( '#sk7' @ ( '#sk10' @ Y0 @ Y1 ) )
= ( '#sk12' @ ( '#sk7' @ Y0 ) @ ( '#sk7' @ Y1 ) ) ) ) ) )
& ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ( '#sk9' @ Y1 )
& ( '#sk9' @ Y0 ) )
=> ( '#sk9' @ ( '#sk10' @ Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ( '#sk9' @ Y0 )
& ( '#sk9' @ Y1 ) )
=> ( ( '#sk8' @ ( '#sk7' @ ( '#sk10' @ Y0 @ Y1 ) ) )
= ( '#sk14' @ ( '#sk8' @ ( '#sk7' @ Y0 ) ) @ ( '#sk8' @ ( '#sk7' @ Y1 ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: g] :
( ( '#sk9' @ Y0 )
=> ( '#sk13' @ ( '#sk8' @ ( '#sk7' @ Y0 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk13' @ Y1 )
& ( '#sk13' @ Y0 ) )
=> ( '#sk13' @ ( '#sk14' @ Y0 @ Y1 ) ) ) ) )
& ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ( '#sk9' @ Y1 )
& ( '#sk9' @ Y0 ) )
=> ( '#sk9' @ ( '#sk10' @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl16,plain,
( ( !!
@ ^ [Y0: g] :
( ( '#sk9' @ Y0 )
=> ( '#sk11' @ ( '#sk7' @ Y0 ) ) ) )
& ( !!
@ ^ [Y0: b] :
( ( '#sk11' @ Y0 )
=> ( '#sk13' @ ( '#sk8' @ Y0 ) ) ) )
& ( !!
@ ^ [Y0: b] :
( !!
@ ^ [Y1: b] :
( ( ( '#sk11' @ Y1 )
& ( '#sk11' @ Y0 ) )
=> ( ( '#sk8' @ ( '#sk12' @ Y0 @ Y1 ) )
= ( '#sk14' @ ( '#sk8' @ Y0 ) @ ( '#sk8' @ Y1 ) ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk13' @ Y1 )
& ( '#sk13' @ Y0 ) )
=> ( '#sk13' @ ( '#sk14' @ Y0 @ Y1 ) ) ) ) )
& ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ( '#sk9' @ Y1 )
& ( '#sk9' @ Y0 ) )
=> ( ( '#sk7' @ ( '#sk10' @ Y0 @ Y1 ) )
= ( '#sk12' @ ( '#sk7' @ Y0 ) @ ( '#sk7' @ Y1 ) ) ) ) ) )
& ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ( '#sk9' @ Y1 )
& ( '#sk9' @ Y0 ) )
=> ( '#sk9' @ ( '#sk10' @ Y0 @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl22,plain,
( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ( '#sk9' @ Y1 )
& ( '#sk9' @ Y0 ) )
=> ( ( '#sk7' @ ( '#sk10' @ Y0 @ Y1 ) )
= ( '#sk12' @ ( '#sk7' @ Y0 ) @ ( '#sk7' @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl29,plain,
! [X2: g] :
( !!
@ ^ [Y0: g] :
( ( ( '#sk9' @ Y0 )
& ( '#sk9' @ X2 ) )
=> ( ( '#sk7' @ ( '#sk10' @ X2 @ Y0 ) )
= ( '#sk12' @ ( '#sk7' @ X2 ) @ ( '#sk7' @ Y0 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl36,plain,
! [X2: g,X4: g] :
( ( ( '#sk9' @ X4 )
& ( '#sk9' @ X2 ) )
=> ( ( '#sk7' @ ( '#sk10' @ X2 @ X4 ) )
= ( '#sk12' @ ( '#sk7' @ X2 ) @ ( '#sk7' @ X4 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl41,plain,
! [X2: g,X4: g] :
( ~ ( ( '#sk9' @ X4 )
& ( '#sk9' @ X2 ) )
| ( ( '#sk7' @ ( '#sk10' @ X2 @ X4 ) )
= ( '#sk12' @ ( '#sk7' @ X2 ) @ ( '#sk7' @ X4 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl48,plain,
! [X2: g,X4: g] :
( ~ ( ( '#sk9' @ X4 )
& ( '#sk9' @ X2 ) )
| ( ( '#sk7' @ ( '#sk10' @ X2 @ X4 ) )
= ( '#sk12' @ ( '#sk7' @ X2 ) @ ( '#sk7' @ X4 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl49,plain,
! [X2: g,X4: g] :
( ~ ( '#sk9' @ X4 )
| ~ ( '#sk9' @ X2 )
| ( ( '#sk7' @ ( '#sk10' @ X2 @ X4 ) )
= ( '#sk12' @ ( '#sk7' @ X2 ) @ ( '#sk7' @ X4 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl18,plain,
( !!
@ ^ [Y0: g] :
( ( '#sk9' @ Y0 )
=> ( '#sk11' @ ( '#sk7' @ Y0 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl25,plain,
! [X2: g] :
( ( '#sk9' @ X2 )
=> ( '#sk11' @ ( '#sk7' @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl32,plain,
! [X2: g] :
( ~ ( '#sk9' @ X2 )
| ( '#sk11' @ ( '#sk7' @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl32_001,plain,
! [X2: g] :
( ~ ( '#sk9' @ X2 )
| ( '#sk11' @ ( '#sk7' @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl20,plain,
( !!
@ ^ [Y0: b] :
( !!
@ ^ [Y1: b] :
( ( ( '#sk11' @ Y1 )
& ( '#sk11' @ Y0 ) )
=> ( ( '#sk8' @ ( '#sk12' @ Y0 @ Y1 ) )
= ( '#sk14' @ ( '#sk8' @ Y0 ) @ ( '#sk8' @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl27,plain,
! [X2: b] :
( !!
@ ^ [Y0: b] :
( ( ( '#sk11' @ Y0 )
& ( '#sk11' @ X2 ) )
=> ( ( '#sk8' @ ( '#sk12' @ X2 @ Y0 ) )
= ( '#sk14' @ ( '#sk8' @ X2 ) @ ( '#sk8' @ Y0 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl34,plain,
! [X2: b,X4: b] :
( ( ( '#sk11' @ X4 )
& ( '#sk11' @ X2 ) )
=> ( ( '#sk8' @ ( '#sk12' @ X2 @ X4 ) )
= ( '#sk14' @ ( '#sk8' @ X2 ) @ ( '#sk8' @ X4 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl39,plain,
! [X2: b,X4: b] :
( ~ ( ( '#sk11' @ X4 )
& ( '#sk11' @ X2 ) )
| ( ( '#sk8' @ ( '#sk12' @ X2 @ X4 ) )
= ( '#sk14' @ ( '#sk8' @ X2 ) @ ( '#sk8' @ X4 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl45,plain,
! [X2: b,X4: b] :
( ~ ( ( '#sk11' @ X4 )
& ( '#sk11' @ X2 ) )
| ( ( '#sk8' @ ( '#sk12' @ X2 @ X4 ) )
= ( '#sk14' @ ( '#sk8' @ X2 ) @ ( '#sk8' @ X4 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl46,plain,
! [X2: b,X4: b] :
( ~ ( '#sk11' @ X4 )
| ~ ( '#sk11' @ X2 )
| ( ( '#sk8' @ ( '#sk12' @ X2 @ X4 ) )
= ( '#sk14' @ ( '#sk8' @ X2 ) @ ( '#sk8' @ X4 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl17,plain,
~ ( ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ( '#sk9' @ Y0 )
& ( '#sk9' @ Y1 ) )
=> ( ( '#sk8' @ ( '#sk7' @ ( '#sk10' @ Y0 @ Y1 ) ) )
= ( '#sk14' @ ( '#sk8' @ ( '#sk7' @ Y0 ) ) @ ( '#sk8' @ ( '#sk7' @ Y1 ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: g] :
( ( '#sk9' @ Y0 )
=> ( '#sk13' @ ( '#sk8' @ ( '#sk7' @ Y0 ) ) ) ) )
& ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk13' @ Y1 )
& ( '#sk13' @ Y0 ) )
=> ( '#sk13' @ ( '#sk14' @ Y0 @ Y1 ) ) ) ) )
& ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ( '#sk9' @ Y1 )
& ( '#sk9' @ Y0 ) )
=> ( '#sk9' @ ( '#sk10' @ Y0 @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl24,plain,
( ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ( '#sk9' @ Y0 )
& ( '#sk9' @ Y1 ) )
=> ( ( '#sk8' @ ( '#sk7' @ ( '#sk10' @ Y0 @ Y1 ) ) )
= ( '#sk14' @ ( '#sk8' @ ( '#sk7' @ Y0 ) ) @ ( '#sk8' @ ( '#sk7' @ Y1 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( ( '#sk9' @ Y0 )
=> ( '#sk13' @ ( '#sk8' @ ( '#sk7' @ Y0 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk13' @ Y1 )
& ( '#sk13' @ Y0 ) )
=> ( '#sk13' @ ( '#sk14' @ Y0 @ Y1 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ( '#sk9' @ Y1 )
& ( '#sk9' @ Y0 ) )
=> ( '#sk9' @ ( '#sk10' @ Y0 @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl31,plain,
( ~ ( !!
@ ^ [Y0: g] :
( ( ( '#sk9' @ '#sk15' )
& ( '#sk9' @ Y0 ) )
=> ( ( '#sk8' @ ( '#sk7' @ ( '#sk10' @ '#sk15' @ Y0 ) ) )
= ( '#sk14' @ ( '#sk8' @ ( '#sk7' @ '#sk15' ) ) @ ( '#sk8' @ ( '#sk7' @ Y0 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ( '#sk9' @ Y1 )
& ( '#sk9' @ Y0 ) )
=> ( '#sk9' @ ( '#sk10' @ Y0 @ Y1 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk13' @ Y1 )
& ( '#sk13' @ Y0 ) )
=> ( '#sk13' @ ( '#sk14' @ Y0 @ Y1 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( ( '#sk9' @ Y0 )
=> ( '#sk13' @ ( '#sk8' @ ( '#sk7' @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl38,plain,
( ~ ( ( ( '#sk9' @ '#sk15' )
& ( '#sk9' @ '#sk16' ) )
=> ( ( '#sk8' @ ( '#sk7' @ ( '#sk10' @ '#sk15' @ '#sk16' ) ) )
= ( '#sk14' @ ( '#sk8' @ ( '#sk7' @ '#sk15' ) ) @ ( '#sk8' @ ( '#sk7' @ '#sk16' ) ) ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( ( '#sk9' @ Y0 )
=> ( '#sk13' @ ( '#sk8' @ ( '#sk7' @ Y0 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk13' @ Y1 )
& ( '#sk13' @ Y0 ) )
=> ( '#sk13' @ ( '#sk14' @ Y0 @ Y1 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ( '#sk9' @ Y1 )
& ( '#sk9' @ Y0 ) )
=> ( '#sk9' @ ( '#sk10' @ Y0 @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl44,plain,
( ( ( '#sk8' @ ( '#sk7' @ ( '#sk10' @ '#sk15' @ '#sk16' ) ) )
!= ( '#sk14' @ ( '#sk8' @ ( '#sk7' @ '#sk15' ) ) @ ( '#sk8' @ ( '#sk7' @ '#sk16' ) ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ( '#sk9' @ Y1 )
& ( '#sk9' @ Y0 ) )
=> ( '#sk9' @ ( '#sk10' @ Y0 @ Y1 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk13' @ Y1 )
& ( '#sk13' @ Y0 ) )
=> ( '#sk13' @ ( '#sk14' @ Y0 @ Y1 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( ( '#sk9' @ Y0 )
=> ( '#sk13' @ ( '#sk8' @ ( '#sk7' @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl53,plain,
( ( ( '#sk8' @ ( '#sk7' @ ( '#sk10' @ '#sk15' @ '#sk16' ) ) )
!= ( '#sk14' @ ( '#sk8' @ ( '#sk7' @ '#sk15' ) ) @ ( '#sk8' @ ( '#sk7' @ '#sk16' ) ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ( '#sk9' @ Y1 )
& ( '#sk9' @ Y0 ) )
=> ( '#sk9' @ ( '#sk10' @ Y0 @ Y1 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk13' @ Y1 )
& ( '#sk13' @ Y0 ) )
=> ( '#sk13' @ ( '#sk14' @ Y0 @ Y1 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( ( '#sk9' @ Y0 )
=> ( '#sk13' @ ( '#sk8' @ ( '#sk7' @ Y0 ) ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl53_002,plain,
( ( ( '#sk8' @ ( '#sk7' @ ( '#sk10' @ '#sk15' @ '#sk16' ) ) )
!= ( '#sk14' @ ( '#sk8' @ ( '#sk7' @ '#sk15' ) ) @ ( '#sk8' @ ( '#sk7' @ '#sk16' ) ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ( '#sk9' @ Y1 )
& ( '#sk9' @ Y0 ) )
=> ( '#sk9' @ ( '#sk10' @ Y0 @ Y1 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk13' @ Y1 )
& ( '#sk13' @ Y0 ) )
=> ( '#sk13' @ ( '#sk14' @ Y0 @ Y1 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( ( '#sk9' @ Y0 )
=> ( '#sk13' @ ( '#sk8' @ ( '#sk7' @ Y0 ) ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl54,plain,
( '#form17'
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ( '#sk9' @ Y1 )
& ( '#sk9' @ Y0 ) )
=> ( '#sk9' @ ( '#sk10' @ Y0 @ Y1 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl56,plain,
( ~ '#form17'
| ~ ( !!
@ ^ [Y0: g] :
( ( '#sk9' @ Y0 )
=> ( '#sk13' @ ( '#sk8' @ ( '#sk7' @ Y0 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk13' @ Y1 )
& ( '#sk13' @ Y0 ) )
=> ( '#sk13' @ ( '#sk14' @ Y0 @ Y1 ) ) ) ) )
| ( ( '#sk8' @ ( '#sk7' @ ( '#sk10' @ '#sk15' @ '#sk16' ) ) )
!= ( '#sk14' @ ( '#sk8' @ ( '#sk7' @ '#sk15' ) ) @ ( '#sk8' @ ( '#sk7' @ '#sk16' ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl53,zip_derived_cl54]) ).
thf(zip_derived_cl43,plain,
( ( ( '#sk9' @ '#sk15' )
& ( '#sk9' @ '#sk16' ) )
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ( '#sk9' @ Y1 )
& ( '#sk9' @ Y0 ) )
=> ( '#sk9' @ ( '#sk10' @ Y0 @ Y1 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk13' @ Y1 )
& ( '#sk13' @ Y0 ) )
=> ( '#sk13' @ ( '#sk14' @ Y0 @ Y1 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( ( '#sk9' @ Y0 )
=> ( '#sk13' @ ( '#sk8' @ ( '#sk7' @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl51,plain,
( ( '#sk9' @ '#sk15' )
| ~ ( !!
@ ^ [Y0: g] :
( ( '#sk9' @ Y0 )
=> ( '#sk13' @ ( '#sk8' @ ( '#sk7' @ Y0 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk13' @ Y1 )
& ( '#sk13' @ Y0 ) )
=> ( '#sk13' @ ( '#sk14' @ Y0 @ Y1 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ( '#sk9' @ Y1 )
& ( '#sk9' @ Y0 ) )
=> ( '#sk9' @ ( '#sk10' @ Y0 @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl57,plain,
( '#form19'
| ~ ( !!
@ ^ [Y0: g] :
( ( '#sk9' @ Y0 )
=> ( '#sk13' @ ( '#sk8' @ ( '#sk7' @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl61,plain,
( ~ '#form19'
| ( ( '#sk8' @ ( '#sk7' @ ( '#sk10' @ '#sk15' @ '#sk16' ) ) )
!= ( '#sk14' @ ( '#sk8' @ ( '#sk7' @ '#sk15' ) ) @ ( '#sk8' @ ( '#sk7' @ '#sk16' ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk13' @ Y1 )
& ( '#sk13' @ Y0 ) )
=> ( '#sk13' @ ( '#sk14' @ Y0 @ Y1 ) ) ) ) )
| ~ '#form17' ),
inference(renaming,[status(thm)],[zip_derived_cl56,zip_derived_cl57]) ).
thf(zip_derived_cl61_003,plain,
( ~ '#form19'
| ( ( '#sk8' @ ( '#sk7' @ ( '#sk10' @ '#sk15' @ '#sk16' ) ) )
!= ( '#sk14' @ ( '#sk8' @ ( '#sk7' @ '#sk15' ) ) @ ( '#sk8' @ ( '#sk7' @ '#sk16' ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk13' @ Y1 )
& ( '#sk13' @ Y0 ) )
=> ( '#sk13' @ ( '#sk14' @ Y0 @ Y1 ) ) ) ) )
| ~ '#form17' ),
inference(renaming,[status(thm)],[zip_derived_cl56,zip_derived_cl57]) ).
thf(zip_derived_cl67,plain,
( '#form22'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk13' @ Y1 )
& ( '#sk13' @ Y0 ) )
=> ( '#sk13' @ ( '#sk14' @ Y0 @ Y1 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl69,plain,
( ~ '#form22'
| ~ '#form17'
| ( ( '#sk8' @ ( '#sk7' @ ( '#sk10' @ '#sk15' @ '#sk16' ) ) )
!= ( '#sk14' @ ( '#sk8' @ ( '#sk7' @ '#sk15' ) ) @ ( '#sk8' @ ( '#sk7' @ '#sk16' ) ) ) )
| ~ '#form19' ),
inference(renaming,[status(thm)],[zip_derived_cl61,zip_derived_cl67]) ).
thf(zip_derived_cl57_004,plain,
( '#form19'
| ~ ( !!
@ ^ [Y0: g] :
( ( '#sk9' @ Y0 )
=> ( '#sk13' @ ( '#sk8' @ ( '#sk7' @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl58,plain,
( ~ ( ( '#sk9' @ '#sk20' )
=> ( '#sk13' @ ( '#sk8' @ ( '#sk7' @ '#sk20' ) ) ) )
| '#form19' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl65,plain,
( ~ ( '#sk13' @ ( '#sk8' @ ( '#sk7' @ '#sk20' ) ) )
| '#form19' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl19,plain,
( !!
@ ^ [Y0: b] :
( ( '#sk11' @ Y0 )
=> ( '#sk13' @ ( '#sk8' @ Y0 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl26,plain,
! [X2: b] :
( ( '#sk11' @ X2 )
=> ( '#sk13' @ ( '#sk8' @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl33,plain,
! [X2: b] :
( ~ ( '#sk11' @ X2 )
| ( '#sk13' @ ( '#sk8' @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl81,plain,
( '#form19'
| ~ ( '#sk11' @ ( '#sk7' @ '#sk20' ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl65,zip_derived_cl33]) ).
thf(zip_derived_cl32_005,plain,
! [X2: g] :
( ~ ( '#sk9' @ X2 )
| ( '#sk11' @ ( '#sk7' @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl85,plain,
( '#form19'
| ~ ( '#sk9' @ '#sk20' ) ),
inference('sup+',[status(thm)],[zip_derived_cl81,zip_derived_cl32]) ).
thf(zip_derived_cl64,plain,
( ( '#sk9' @ '#sk20' )
| '#form19' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl89,plain,
'#form19',
inference(clc,[status(thm)],[zip_derived_cl85,zip_derived_cl64]) ).
thf(zip_derived_cl92,plain,
( ~ '#form22'
| ~ '#form17'
| ( ( '#sk8' @ ( '#sk7' @ ( '#sk10' @ '#sk15' @ '#sk16' ) ) )
!= ( '#sk14' @ ( '#sk8' @ ( '#sk7' @ '#sk15' ) ) @ ( '#sk8' @ ( '#sk7' @ '#sk16' ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl69,zip_derived_cl89]) ).
thf(zip_derived_cl21,plain,
( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk13' @ Y1 )
& ( '#sk13' @ Y0 ) )
=> ( '#sk13' @ ( '#sk14' @ Y0 @ Y1 ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl28,plain,
! [X2: a] :
( !!
@ ^ [Y0: a] :
( ( ( '#sk13' @ Y0 )
& ( '#sk13' @ X2 ) )
=> ( '#sk13' @ ( '#sk14' @ X2 @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl35,plain,
! [X2: a,X4: a] :
( ( ( '#sk13' @ X4 )
& ( '#sk13' @ X2 ) )
=> ( '#sk13' @ ( '#sk14' @ X2 @ X4 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl40,plain,
! [X2: a,X4: a] :
( ~ ( ( '#sk13' @ X4 )
& ( '#sk13' @ X2 ) )
| ( '#sk13' @ ( '#sk14' @ X2 @ X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl47,plain,
! [X2: a,X4: a] :
( ~ ( '#sk13' @ X4 )
| ~ ( '#sk13' @ X2 )
| ( '#sk13' @ ( '#sk14' @ X2 @ X4 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl67_006,plain,
( '#form22'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk13' @ Y1 )
& ( '#sk13' @ Y0 ) )
=> ( '#sk13' @ ( '#sk14' @ Y0 @ Y1 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl68,plain,
( ~ ( !!
@ ^ [Y0: a] :
( ( ( '#sk13' @ Y0 )
& ( '#sk13' @ '#sk23' ) )
=> ( '#sk13' @ ( '#sk14' @ '#sk23' @ Y0 ) ) ) )
| '#form22' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl74,plain,
( ~ ( ( ( '#sk13' @ '#sk24' )
& ( '#sk13' @ '#sk23' ) )
=> ( '#sk13' @ ( '#sk14' @ '#sk23' @ '#sk24' ) ) )
| '#form22' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl78,plain,
( ~ ( '#sk13' @ ( '#sk14' @ '#sk23' @ '#sk24' ) )
| '#form22' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl74]) ).
thf(zip_derived_cl93,plain,
( ~ ( '#sk13' @ '#sk23' )
| ~ ( '#sk13' @ '#sk24' )
| '#form22' ),
inference('sup-',[status(thm)],[zip_derived_cl47,zip_derived_cl78]) ).
thf(zip_derived_cl77,plain,
( ( ( '#sk13' @ '#sk24' )
& ( '#sk13' @ '#sk23' ) )
| '#form22' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl74]) ).
thf(zip_derived_cl80,plain,
( ( '#sk13' @ '#sk23' )
| '#form22' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl77]) ).
thf(zip_derived_cl97,plain,
( '#form22'
| ~ ( '#sk13' @ '#sk24' ) ),
inference(clc,[status(thm)],[zip_derived_cl93,zip_derived_cl80]) ).
thf(zip_derived_cl79,plain,
( ( '#sk13' @ '#sk24' )
| '#form22' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl77]) ).
thf(zip_derived_cl98,plain,
'#form22',
inference(clc,[status(thm)],[zip_derived_cl97,zip_derived_cl79]) ).
thf(zip_derived_cl101,plain,
( ~ '#form17'
| ( ( '#sk8' @ ( '#sk7' @ ( '#sk10' @ '#sk15' @ '#sk16' ) ) )
!= ( '#sk14' @ ( '#sk8' @ ( '#sk7' @ '#sk15' ) ) @ ( '#sk8' @ ( '#sk7' @ '#sk16' ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl92,zip_derived_cl98]) ).
thf(zip_derived_cl23,plain,
( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ( '#sk9' @ Y1 )
& ( '#sk9' @ Y0 ) )
=> ( '#sk9' @ ( '#sk10' @ Y0 @ Y1 ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl30,plain,
! [X2: g] :
( !!
@ ^ [Y0: g] :
( ( ( '#sk9' @ Y0 )
& ( '#sk9' @ X2 ) )
=> ( '#sk9' @ ( '#sk10' @ X2 @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl37,plain,
! [X2: g,X4: g] :
( ( ( '#sk9' @ X4 )
& ( '#sk9' @ X2 ) )
=> ( '#sk9' @ ( '#sk10' @ X2 @ X4 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl42,plain,
! [X2: g,X4: g] :
( ~ ( ( '#sk9' @ X4 )
& ( '#sk9' @ X2 ) )
| ( '#sk9' @ ( '#sk10' @ X2 @ X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl50,plain,
! [X2: g,X4: g] :
( ~ ( '#sk9' @ X4 )
| ~ ( '#sk9' @ X2 )
| ( '#sk9' @ ( '#sk10' @ X2 @ X4 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl54_007,plain,
( '#form17'
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ( '#sk9' @ Y1 )
& ( '#sk9' @ Y0 ) )
=> ( '#sk9' @ ( '#sk10' @ Y0 @ Y1 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl55,plain,
( ~ ( !!
@ ^ [Y0: g] :
( ( ( '#sk9' @ Y0 )
& ( '#sk9' @ '#sk18' ) )
=> ( '#sk9' @ ( '#sk10' @ '#sk18' @ Y0 ) ) ) )
| '#form17' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl62,plain,
( ~ ( ( ( '#sk9' @ '#sk21' )
& ( '#sk9' @ '#sk18' ) )
=> ( '#sk9' @ ( '#sk10' @ '#sk18' @ '#sk21' ) ) )
| '#form17' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl71,plain,
( ~ ( '#sk9' @ ( '#sk10' @ '#sk18' @ '#sk21' ) )
| '#form17' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl104,plain,
( ~ ( '#sk9' @ '#sk18' )
| ~ ( '#sk9' @ '#sk21' )
| '#form17' ),
inference('sup-',[status(thm)],[zip_derived_cl50,zip_derived_cl71]) ).
thf(zip_derived_cl70,plain,
( ( ( '#sk9' @ '#sk21' )
& ( '#sk9' @ '#sk18' ) )
| '#form17' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl76,plain,
( ( '#sk9' @ '#sk18' )
| '#form17' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl108,plain,
( '#form17'
| ~ ( '#sk9' @ '#sk21' ) ),
inference(clc,[status(thm)],[zip_derived_cl104,zip_derived_cl76]) ).
thf(zip_derived_cl75,plain,
( ( '#sk9' @ '#sk21' )
| '#form17' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl109,plain,
'#form17',
inference(clc,[status(thm)],[zip_derived_cl108,zip_derived_cl75]) ).
thf(zip_derived_cl112,plain,
( ( '#sk8' @ ( '#sk7' @ ( '#sk10' @ '#sk15' @ '#sk16' ) ) )
!= ( '#sk14' @ ( '#sk8' @ ( '#sk7' @ '#sk15' ) ) @ ( '#sk8' @ ( '#sk7' @ '#sk16' ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl101,zip_derived_cl109]) ).
thf(zip_derived_cl113,plain,
( ( ( '#sk8' @ ( '#sk7' @ ( '#sk10' @ '#sk15' @ '#sk16' ) ) )
!= ( '#sk8' @ ( '#sk12' @ ( '#sk7' @ '#sk15' ) @ ( '#sk7' @ '#sk16' ) ) ) )
| ~ ( '#sk11' @ ( '#sk7' @ '#sk15' ) )
| ~ ( '#sk11' @ ( '#sk7' @ '#sk16' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl46,zip_derived_cl112]) ).
thf(zip_derived_cl115,plain,
( ~ ( '#sk9' @ '#sk15' )
| ~ ( '#sk11' @ ( '#sk7' @ '#sk16' ) )
| ( ( '#sk8' @ ( '#sk7' @ ( '#sk10' @ '#sk15' @ '#sk16' ) ) )
!= ( '#sk8' @ ( '#sk12' @ ( '#sk7' @ '#sk15' ) @ ( '#sk7' @ '#sk16' ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl32,zip_derived_cl113]) ).
thf(zip_derived_cl51_008,plain,
( ( '#sk9' @ '#sk15' )
| ~ ( !!
@ ^ [Y0: g] :
( ( '#sk9' @ Y0 )
=> ( '#sk13' @ ( '#sk8' @ ( '#sk7' @ Y0 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk13' @ Y1 )
& ( '#sk13' @ Y0 ) )
=> ( '#sk13' @ ( '#sk14' @ Y0 @ Y1 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ( '#sk9' @ Y1 )
& ( '#sk9' @ Y0 ) )
=> ( '#sk9' @ ( '#sk10' @ Y0 @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl57_009,plain,
( '#form19'
| ~ ( !!
@ ^ [Y0: g] :
( ( '#sk9' @ Y0 )
=> ( '#sk13' @ ( '#sk8' @ ( '#sk7' @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl59,plain,
( ~ '#form19'
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ( '#sk9' @ Y1 )
& ( '#sk9' @ Y0 ) )
=> ( '#sk9' @ ( '#sk10' @ Y0 @ Y1 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk13' @ Y1 )
& ( '#sk13' @ Y0 ) )
=> ( '#sk13' @ ( '#sk14' @ Y0 @ Y1 ) ) ) ) )
| ( '#sk9' @ '#sk15' ) ),
inference(renaming,[status(thm)],[zip_derived_cl51,zip_derived_cl57]) ).
thf(zip_derived_cl54_010,plain,
( '#form17'
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ( '#sk9' @ Y1 )
& ( '#sk9' @ Y0 ) )
=> ( '#sk9' @ ( '#sk10' @ Y0 @ Y1 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl63,plain,
( ~ '#form17'
| ( '#sk9' @ '#sk15' )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk13' @ Y1 )
& ( '#sk13' @ Y0 ) )
=> ( '#sk13' @ ( '#sk14' @ Y0 @ Y1 ) ) ) ) )
| ~ '#form19' ),
inference(renaming,[status(thm)],[zip_derived_cl59,zip_derived_cl54]) ).
thf(zip_derived_cl67_011,plain,
( '#form22'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk13' @ Y1 )
& ( '#sk13' @ Y0 ) )
=> ( '#sk13' @ ( '#sk14' @ Y0 @ Y1 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl72,plain,
( ~ '#form22'
| ~ '#form19'
| ( '#sk9' @ '#sk15' )
| ~ '#form17' ),
inference(renaming,[status(thm)],[zip_derived_cl63,zip_derived_cl67]) ).
thf(zip_derived_cl89_012,plain,
'#form19',
inference(clc,[status(thm)],[zip_derived_cl85,zip_derived_cl64]) ).
thf(zip_derived_cl90,plain,
( ~ '#form22'
| ( '#sk9' @ '#sk15' )
| ~ '#form17' ),
inference(demod,[status(thm)],[zip_derived_cl72,zip_derived_cl89]) ).
thf(zip_derived_cl98_013,plain,
'#form22',
inference(clc,[status(thm)],[zip_derived_cl97,zip_derived_cl79]) ).
thf(zip_derived_cl99,plain,
( ( '#sk9' @ '#sk15' )
| ~ '#form17' ),
inference(demod,[status(thm)],[zip_derived_cl90,zip_derived_cl98]) ).
thf(zip_derived_cl109_014,plain,
'#form17',
inference(clc,[status(thm)],[zip_derived_cl108,zip_derived_cl75]) ).
thf(zip_derived_cl110,plain,
'#sk9' @ '#sk15',
inference(demod,[status(thm)],[zip_derived_cl99,zip_derived_cl109]) ).
thf(zip_derived_cl117,plain,
( ~ ( '#sk11' @ ( '#sk7' @ '#sk16' ) )
| ( ( '#sk8' @ ( '#sk7' @ ( '#sk10' @ '#sk15' @ '#sk16' ) ) )
!= ( '#sk8' @ ( '#sk12' @ ( '#sk7' @ '#sk15' ) @ ( '#sk7' @ '#sk16' ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl115,zip_derived_cl110]) ).
thf(zip_derived_cl119,plain,
( ~ ( '#sk9' @ '#sk16' )
| ( ( '#sk8' @ ( '#sk7' @ ( '#sk10' @ '#sk15' @ '#sk16' ) ) )
!= ( '#sk8' @ ( '#sk12' @ ( '#sk7' @ '#sk15' ) @ ( '#sk7' @ '#sk16' ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl32,zip_derived_cl117]) ).
thf(zip_derived_cl52,plain,
( ( '#sk9' @ '#sk16' )
| ~ ( !!
@ ^ [Y0: g] :
( ( '#sk9' @ Y0 )
=> ( '#sk13' @ ( '#sk8' @ ( '#sk7' @ Y0 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk13' @ Y1 )
& ( '#sk13' @ Y0 ) )
=> ( '#sk13' @ ( '#sk14' @ Y0 @ Y1 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ( '#sk9' @ Y1 )
& ( '#sk9' @ Y0 ) )
=> ( '#sk9' @ ( '#sk10' @ Y0 @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl57_015,plain,
( '#form19'
| ~ ( !!
@ ^ [Y0: g] :
( ( '#sk9' @ Y0 )
=> ( '#sk13' @ ( '#sk8' @ ( '#sk7' @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl60,plain,
( ~ '#form19'
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ( '#sk9' @ Y1 )
& ( '#sk9' @ Y0 ) )
=> ( '#sk9' @ ( '#sk10' @ Y0 @ Y1 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk13' @ Y1 )
& ( '#sk13' @ Y0 ) )
=> ( '#sk13' @ ( '#sk14' @ Y0 @ Y1 ) ) ) ) )
| ( '#sk9' @ '#sk16' ) ),
inference(renaming,[status(thm)],[zip_derived_cl52,zip_derived_cl57]) ).
thf(zip_derived_cl54_016,plain,
( '#form17'
| ~ ( !!
@ ^ [Y0: g] :
( !!
@ ^ [Y1: g] :
( ( ( '#sk9' @ Y1 )
& ( '#sk9' @ Y0 ) )
=> ( '#sk9' @ ( '#sk10' @ Y0 @ Y1 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl66,plain,
( ~ '#form17'
| ( '#sk9' @ '#sk16' )
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk13' @ Y1 )
& ( '#sk13' @ Y0 ) )
=> ( '#sk13' @ ( '#sk14' @ Y0 @ Y1 ) ) ) ) )
| ~ '#form19' ),
inference(renaming,[status(thm)],[zip_derived_cl60,zip_derived_cl54]) ).
thf(zip_derived_cl67_017,plain,
( '#form22'
| ~ ( !!
@ ^ [Y0: a] :
( !!
@ ^ [Y1: a] :
( ( ( '#sk13' @ Y1 )
& ( '#sk13' @ Y0 ) )
=> ( '#sk13' @ ( '#sk14' @ Y0 @ Y1 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl73,plain,
( ~ '#form22'
| ~ '#form19'
| ( '#sk9' @ '#sk16' )
| ~ '#form17' ),
inference(renaming,[status(thm)],[zip_derived_cl66,zip_derived_cl67]) ).
thf(zip_derived_cl89_018,plain,
'#form19',
inference(clc,[status(thm)],[zip_derived_cl85,zip_derived_cl64]) ).
thf(zip_derived_cl91,plain,
( ~ '#form22'
| ( '#sk9' @ '#sk16' )
| ~ '#form17' ),
inference(demod,[status(thm)],[zip_derived_cl73,zip_derived_cl89]) ).
thf(zip_derived_cl98_019,plain,
'#form22',
inference(clc,[status(thm)],[zip_derived_cl97,zip_derived_cl79]) ).
thf(zip_derived_cl100,plain,
( ( '#sk9' @ '#sk16' )
| ~ '#form17' ),
inference(demod,[status(thm)],[zip_derived_cl91,zip_derived_cl98]) ).
thf(zip_derived_cl109_020,plain,
'#form17',
inference(clc,[status(thm)],[zip_derived_cl108,zip_derived_cl75]) ).
thf(zip_derived_cl111,plain,
'#sk9' @ '#sk16',
inference(demod,[status(thm)],[zip_derived_cl100,zip_derived_cl109]) ).
thf(zip_derived_cl121,plain,
( ( '#sk8' @ ( '#sk7' @ ( '#sk10' @ '#sk15' @ '#sk16' ) ) )
!= ( '#sk8' @ ( '#sk12' @ ( '#sk7' @ '#sk15' ) @ ( '#sk7' @ '#sk16' ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl119,zip_derived_cl111]) ).
thf(zip_derived_cl123,plain,
( ( ( '#sk8' @ ( '#sk7' @ ( '#sk10' @ '#sk15' @ '#sk16' ) ) )
!= ( '#sk8' @ ( '#sk7' @ ( '#sk10' @ '#sk15' @ '#sk16' ) ) ) )
| ~ ( '#sk9' @ '#sk15' )
| ~ ( '#sk9' @ '#sk16' ) ),
inference('sup-',[status(thm)],[zip_derived_cl49,zip_derived_cl121]) ).
thf(zip_derived_cl110_021,plain,
'#sk9' @ '#sk15',
inference(demod,[status(thm)],[zip_derived_cl99,zip_derived_cl109]) ).
thf(zip_derived_cl111_022,plain,
'#sk9' @ '#sk16',
inference(demod,[status(thm)],[zip_derived_cl100,zip_derived_cl109]) ).
thf(zip_derived_cl125,plain,
( ( '#sk8' @ ( '#sk7' @ ( '#sk10' @ '#sk15' @ '#sk16' ) ) )
!= ( '#sk8' @ ( '#sk7' @ ( '#sk10' @ '#sk15' @ '#sk16' ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl123,zip_derived_cl110,zip_derived_cl111]) ).
thf(zip_derived_cl126,plain,
$false,
inference(simplify,[status(thm)],[zip_derived_cl125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO225^5 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.RMeJwo7gPb true
% 0.13/0.34 % Computer : n002.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 : Sat Aug 26 01:21:17 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in HO mode
% 0.21/0.66 % Total configuration time : 828
% 0.21/0.66 % Estimated wc time : 1656
% 0.21/0.66 % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.74 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.40/0.76 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.40/0.76 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.40/0.76 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.40/0.76 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.42/0.94 % Solved by lams/20_acsne_simpl.sh.
% 1.42/0.94 % done 30 iterations in 0.073s
% 1.42/0.94 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.42/0.94 % SZS output start Refutation
% See solution above
% 1.42/0.95
% 1.42/0.95
% 1.42/0.95 % Terminating...
% 2.77/1.06 % Runner terminated.
% 2.80/1.07 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------