TSTP Solution File: SYO391^5 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYO391^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 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 : 600s
% DateTime : Thu Jul 21 17:33:46 EDT 2022
% Result : Theorem 1.21s 1.44s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 119
% Number of leaves : 19
% Syntax : Number of formulae : 330 ( 251 unt; 18 typ; 0 def)
% Number of atoms : 5680 ( 478 equ; 0 cnn)
% Maximal formula atoms : 68 ( 18 avg)
% Number of connectives : 24859 (8321 ~;4190 |; 222 &;12126 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 53 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 3804 ( 0 ^3804 !; 0 ?;3804 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_cP_1,type,
cP_1: $i > $i > $o ).
thf(tp_cP_2,type,
cP_2: $i > $i > $o ).
thf(tp_cP_3,type,
cP_3: $i > $i > $o ).
thf(tp_cP_4,type,
cP_4: $i > $i > $o ).
thf(tp_cP_5,type,
cP_5: $i > $i > $o ).
thf(tp_cP_6,type,
cP_6: $i > $i > $o ).
thf(tp_cQ_1,type,
cQ_1: $i > $i > $i > $o ).
thf(tp_cQ_2,type,
cQ_2: $i > $i > $i > $o ).
thf(tp_cQ_3,type,
cQ_3: $i > $i > $i > $o ).
thf(tp_cQ_4,type,
cQ_4: $i > $i > $i > $o ).
thf(tp_cQ_5,type,
cQ_5: $i > $i > $i > $o ).
thf(tp_cQ_6,type,
cQ_6: $i > $i > $i > $o ).
thf(tp_cQ_7,type,
cQ_7: $i > $i > $i > $o ).
thf(tp_d,type,
d: $i ).
thf(tp_f,type,
f: $i > $i ).
thf(1,conjecture,
~ ( ( cQ_1 @ a @ b @ c )
& ( cP_1 @ a @ a )
& ( cP_1 @ b @ b )
& ( cP_1 @ c @ c )
& ! [Xx: $i] : ( cP_1 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_1 @ Xx @ Xy )
| ( cP_1 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_1 @ Xx @ Xy @ Xz )
| ~ ( cP_1 @ ( f @ Xx ) @ Xu )
| ~ ( cP_1 @ ( f @ Xy ) @ Xv )
| ~ ( cP_1 @ ( f @ Xz ) @ Xw )
| ( cQ_2 @ Xu @ Xv @ Xw ) )
& ( cP_2 @ a @ a )
& ( cP_2 @ b @ b )
& ( cP_2 @ c @ c )
& ! [Xx: $i] : ( cP_2 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_2 @ Xx @ Xy )
| ( cP_2 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_2 @ Xx @ Xy @ Xz )
| ~ ( cP_2 @ ( f @ Xx ) @ Xu )
| ~ ( cP_2 @ ( f @ Xy ) @ Xv )
| ~ ( cP_2 @ ( f @ Xz ) @ Xw )
| ( cQ_3 @ Xu @ Xv @ Xw ) )
& ( cP_3 @ a @ a )
& ( cP_3 @ b @ b )
& ( cP_3 @ c @ c )
& ! [Xx: $i] : ( cP_3 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_3 @ Xx @ Xy )
| ( cP_3 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_3 @ Xx @ Xy @ Xz )
| ~ ( cP_3 @ ( f @ Xx ) @ Xu )
| ~ ( cP_3 @ ( f @ Xy ) @ Xv )
| ~ ( cP_3 @ ( f @ Xz ) @ Xw )
| ( cQ_4 @ Xu @ Xv @ Xw ) )
& ( cP_4 @ a @ a )
& ( cP_4 @ b @ b )
& ( cP_4 @ c @ c )
& ! [Xx: $i] : ( cP_4 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_4 @ Xx @ Xy )
| ( cP_4 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_4 @ Xx @ Xy @ Xz )
| ~ ( cP_4 @ ( f @ Xx ) @ Xu )
| ~ ( cP_4 @ ( f @ Xy ) @ Xv )
| ~ ( cP_4 @ ( f @ Xz ) @ Xw )
| ( cQ_5 @ Xu @ Xv @ Xw ) )
& ( cP_5 @ a @ a )
& ( cP_5 @ b @ b )
& ( cP_5 @ c @ c )
& ! [Xx: $i] : ( cP_5 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_5 @ Xx @ Xy )
| ( cP_5 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_5 @ Xx @ Xy @ Xz )
| ~ ( cP_5 @ ( f @ Xx ) @ Xu )
| ~ ( cP_5 @ ( f @ Xy ) @ Xv )
| ~ ( cP_5 @ ( f @ Xz ) @ Xw )
| ( cQ_6 @ Xu @ Xv @ Xw ) )
& ( cP_6 @ a @ a )
& ( cP_6 @ b @ b )
& ( cP_6 @ c @ c )
& ! [Xx: $i] : ( cP_6 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_6 @ Xx @ Xy )
| ( cP_6 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_6 @ Xx @ Xy @ Xz )
| ~ ( cP_6 @ ( f @ Xx ) @ Xu )
| ~ ( cP_6 @ ( f @ Xy ) @ Xv )
| ~ ( cP_6 @ ( f @ Xz ) @ Xw )
| ( cQ_7 @ Xu @ Xv @ Xw ) )
& ! [Xx: $i,Xy: $i,Xz: $i] :
~ ( cQ_7 @ Xx @ Xy @ Xz ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM409_6) ).
thf(2,negated_conjecture,
( ( ~ ( ( cQ_1 @ a @ b @ c )
& ( cP_1 @ a @ a )
& ( cP_1 @ b @ b )
& ( cP_1 @ c @ c )
& ! [Xx: $i] : ( cP_1 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_1 @ Xx @ Xy )
| ( cP_1 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_1 @ Xx @ Xy @ Xz )
| ~ ( cP_1 @ ( f @ Xx ) @ Xu )
| ~ ( cP_1 @ ( f @ Xy ) @ Xv )
| ~ ( cP_1 @ ( f @ Xz ) @ Xw )
| ( cQ_2 @ Xu @ Xv @ Xw ) )
& ( cP_2 @ a @ a )
& ( cP_2 @ b @ b )
& ( cP_2 @ c @ c )
& ! [Xx: $i] : ( cP_2 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_2 @ Xx @ Xy )
| ( cP_2 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_2 @ Xx @ Xy @ Xz )
| ~ ( cP_2 @ ( f @ Xx ) @ Xu )
| ~ ( cP_2 @ ( f @ Xy ) @ Xv )
| ~ ( cP_2 @ ( f @ Xz ) @ Xw )
| ( cQ_3 @ Xu @ Xv @ Xw ) )
& ( cP_3 @ a @ a )
& ( cP_3 @ b @ b )
& ( cP_3 @ c @ c )
& ! [Xx: $i] : ( cP_3 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_3 @ Xx @ Xy )
| ( cP_3 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_3 @ Xx @ Xy @ Xz )
| ~ ( cP_3 @ ( f @ Xx ) @ Xu )
| ~ ( cP_3 @ ( f @ Xy ) @ Xv )
| ~ ( cP_3 @ ( f @ Xz ) @ Xw )
| ( cQ_4 @ Xu @ Xv @ Xw ) )
& ( cP_4 @ a @ a )
& ( cP_4 @ b @ b )
& ( cP_4 @ c @ c )
& ! [Xx: $i] : ( cP_4 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_4 @ Xx @ Xy )
| ( cP_4 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_4 @ Xx @ Xy @ Xz )
| ~ ( cP_4 @ ( f @ Xx ) @ Xu )
| ~ ( cP_4 @ ( f @ Xy ) @ Xv )
| ~ ( cP_4 @ ( f @ Xz ) @ Xw )
| ( cQ_5 @ Xu @ Xv @ Xw ) )
& ( cP_5 @ a @ a )
& ( cP_5 @ b @ b )
& ( cP_5 @ c @ c )
& ! [Xx: $i] : ( cP_5 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_5 @ Xx @ Xy )
| ( cP_5 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_5 @ Xx @ Xy @ Xz )
| ~ ( cP_5 @ ( f @ Xx ) @ Xu )
| ~ ( cP_5 @ ( f @ Xy ) @ Xv )
| ~ ( cP_5 @ ( f @ Xz ) @ Xw )
| ( cQ_6 @ Xu @ Xv @ Xw ) )
& ( cP_6 @ a @ a )
& ( cP_6 @ b @ b )
& ( cP_6 @ c @ c )
& ! [Xx: $i] : ( cP_6 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_6 @ Xx @ Xy )
| ( cP_6 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_6 @ Xx @ Xy @ Xz )
| ~ ( cP_6 @ ( f @ Xx ) @ Xu )
| ~ ( cP_6 @ ( f @ Xy ) @ Xv )
| ~ ( cP_6 @ ( f @ Xz ) @ Xw )
| ( cQ_7 @ Xu @ Xv @ Xw ) )
& ! [Xx: $i,Xy: $i,Xz: $i] :
~ ( cQ_7 @ Xx @ Xy @ Xz ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ~ ( ( cQ_1 @ a @ b @ c )
& ( cP_1 @ a @ a )
& ( cP_1 @ b @ b )
& ( cP_1 @ c @ c )
& ! [Xx: $i] : ( cP_1 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_1 @ Xx @ Xy )
| ( cP_1 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_1 @ Xx @ Xy @ Xz )
| ~ ( cP_1 @ ( f @ Xx ) @ Xu )
| ~ ( cP_1 @ ( f @ Xy ) @ Xv )
| ~ ( cP_1 @ ( f @ Xz ) @ Xw )
| ( cQ_2 @ Xu @ Xv @ Xw ) )
& ( cP_2 @ a @ a )
& ( cP_2 @ b @ b )
& ( cP_2 @ c @ c )
& ! [Xx: $i] : ( cP_2 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_2 @ Xx @ Xy )
| ( cP_2 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_2 @ Xx @ Xy @ Xz )
| ~ ( cP_2 @ ( f @ Xx ) @ Xu )
| ~ ( cP_2 @ ( f @ Xy ) @ Xv )
| ~ ( cP_2 @ ( f @ Xz ) @ Xw )
| ( cQ_3 @ Xu @ Xv @ Xw ) )
& ( cP_3 @ a @ a )
& ( cP_3 @ b @ b )
& ( cP_3 @ c @ c )
& ! [Xx: $i] : ( cP_3 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_3 @ Xx @ Xy )
| ( cP_3 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_3 @ Xx @ Xy @ Xz )
| ~ ( cP_3 @ ( f @ Xx ) @ Xu )
| ~ ( cP_3 @ ( f @ Xy ) @ Xv )
| ~ ( cP_3 @ ( f @ Xz ) @ Xw )
| ( cQ_4 @ Xu @ Xv @ Xw ) )
& ( cP_4 @ a @ a )
& ( cP_4 @ b @ b )
& ( cP_4 @ c @ c )
& ! [Xx: $i] : ( cP_4 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_4 @ Xx @ Xy )
| ( cP_4 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_4 @ Xx @ Xy @ Xz )
| ~ ( cP_4 @ ( f @ Xx ) @ Xu )
| ~ ( cP_4 @ ( f @ Xy ) @ Xv )
| ~ ( cP_4 @ ( f @ Xz ) @ Xw )
| ( cQ_5 @ Xu @ Xv @ Xw ) )
& ( cP_5 @ a @ a )
& ( cP_5 @ b @ b )
& ( cP_5 @ c @ c )
& ! [Xx: $i] : ( cP_5 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_5 @ Xx @ Xy )
| ( cP_5 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_5 @ Xx @ Xy @ Xz )
| ~ ( cP_5 @ ( f @ Xx ) @ Xu )
| ~ ( cP_5 @ ( f @ Xy ) @ Xv )
| ~ ( cP_5 @ ( f @ Xz ) @ Xw )
| ( cQ_6 @ Xu @ Xv @ Xw ) )
& ( cP_6 @ a @ a )
& ( cP_6 @ b @ b )
& ( cP_6 @ c @ c )
& ! [Xx: $i] : ( cP_6 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_6 @ Xx @ Xy )
| ( cP_6 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_6 @ Xx @ Xy @ Xz )
| ~ ( cP_6 @ ( f @ Xx ) @ Xu )
| ~ ( cP_6 @ ( f @ Xy ) @ Xv )
| ~ ( cP_6 @ ( f @ Xz ) @ Xw )
| ( cQ_7 @ Xu @ Xv @ Xw ) )
& ! [Xx: $i,Xy: $i,Xz: $i] :
~ ( cQ_7 @ Xx @ Xy @ Xz ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ( cQ_1 @ a @ b @ c )
& ( cP_1 @ a @ a )
& ( cP_1 @ b @ b )
& ( cP_1 @ c @ c )
& ! [Xx: $i] : ( cP_1 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_1 @ Xx @ Xy )
| ( cP_1 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_1 @ Xx @ Xy @ Xz )
| ~ ( cP_1 @ ( f @ Xx ) @ Xu )
| ~ ( cP_1 @ ( f @ Xy ) @ Xv )
| ~ ( cP_1 @ ( f @ Xz ) @ Xw )
| ( cQ_2 @ Xu @ Xv @ Xw ) )
& ( cP_2 @ a @ a )
& ( cP_2 @ b @ b )
& ( cP_2 @ c @ c )
& ! [Xx: $i] : ( cP_2 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_2 @ Xx @ Xy )
| ( cP_2 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_2 @ Xx @ Xy @ Xz )
| ~ ( cP_2 @ ( f @ Xx ) @ Xu )
| ~ ( cP_2 @ ( f @ Xy ) @ Xv )
| ~ ( cP_2 @ ( f @ Xz ) @ Xw )
| ( cQ_3 @ Xu @ Xv @ Xw ) )
& ( cP_3 @ a @ a )
& ( cP_3 @ b @ b )
& ( cP_3 @ c @ c )
& ! [Xx: $i] : ( cP_3 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_3 @ Xx @ Xy )
| ( cP_3 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_3 @ Xx @ Xy @ Xz )
| ~ ( cP_3 @ ( f @ Xx ) @ Xu )
| ~ ( cP_3 @ ( f @ Xy ) @ Xv )
| ~ ( cP_3 @ ( f @ Xz ) @ Xw )
| ( cQ_4 @ Xu @ Xv @ Xw ) )
& ( cP_4 @ a @ a )
& ( cP_4 @ b @ b )
& ( cP_4 @ c @ c )
& ! [Xx: $i] : ( cP_4 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_4 @ Xx @ Xy )
| ( cP_4 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_4 @ Xx @ Xy @ Xz )
| ~ ( cP_4 @ ( f @ Xx ) @ Xu )
| ~ ( cP_4 @ ( f @ Xy ) @ Xv )
| ~ ( cP_4 @ ( f @ Xz ) @ Xw )
| ( cQ_5 @ Xu @ Xv @ Xw ) )
& ( cP_5 @ a @ a )
& ( cP_5 @ b @ b )
& ( cP_5 @ c @ c )
& ! [Xx: $i] : ( cP_5 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_5 @ Xx @ Xy )
| ( cP_5 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_5 @ Xx @ Xy @ Xz )
| ~ ( cP_5 @ ( f @ Xx ) @ Xu )
| ~ ( cP_5 @ ( f @ Xy ) @ Xv )
| ~ ( cP_5 @ ( f @ Xz ) @ Xw )
| ( cQ_6 @ Xu @ Xv @ Xw ) )
& ( cP_6 @ a @ a )
& ( cP_6 @ b @ b )
& ( cP_6 @ c @ c )
& ! [Xx: $i] : ( cP_6 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_6 @ Xx @ Xy )
| ( cP_6 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_6 @ Xx @ Xy @ Xz )
| ~ ( cP_6 @ ( f @ Xx ) @ Xu )
| ~ ( cP_6 @ ( f @ Xy ) @ Xv )
| ~ ( cP_6 @ ( f @ Xz ) @ Xw )
| ( cQ_7 @ Xu @ Xv @ Xw ) )
& ! [Xx: $i,Xy: $i,Xz: $i] :
~ ( cQ_7 @ Xx @ Xy @ Xz ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
~ ( cQ_7 @ Xx @ Xy @ Xz )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ( cQ_7 @ Xu @ Xv @ Xw )
| ~ ( cQ_6 @ Xx @ Xy @ Xz )
| ~ ( cP_6 @ ( f @ Xx ) @ Xu )
| ~ ( cP_6 @ ( f @ Xy ) @ Xv )
| ~ ( cP_6 @ ( f @ Xz ) @ Xw ) )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_6 @ Xx @ Xy )
| ( cP_6 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i] : ( cP_6 @ d @ Xx )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ( cQ_6 @ Xu @ Xv @ Xw )
| ~ ( cQ_5 @ Xx @ Xy @ Xz )
| ~ ( cP_5 @ ( f @ Xx ) @ Xu )
| ~ ( cP_5 @ ( f @ Xy ) @ Xv )
| ~ ( cP_5 @ ( f @ Xz ) @ Xw ) )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_5 @ Xx @ Xy )
| ( cP_5 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i] : ( cP_5 @ d @ Xx )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ( cQ_5 @ Xu @ Xv @ Xw )
| ~ ( cQ_4 @ Xx @ Xy @ Xz )
| ~ ( cP_4 @ ( f @ Xx ) @ Xu )
| ~ ( cP_4 @ ( f @ Xy ) @ Xv )
| ~ ( cP_4 @ ( f @ Xz ) @ Xw ) )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_4 @ Xx @ Xy )
| ( cP_4 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i] : ( cP_4 @ d @ Xx )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ( cQ_4 @ Xu @ Xv @ Xw )
| ~ ( cQ_3 @ Xx @ Xy @ Xz )
| ~ ( cP_3 @ ( f @ Xx ) @ Xu )
| ~ ( cP_3 @ ( f @ Xy ) @ Xv )
| ~ ( cP_3 @ ( f @ Xz ) @ Xw ) )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_3 @ Xx @ Xy )
| ( cP_3 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i] : ( cP_3 @ d @ Xx )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ( cQ_3 @ Xu @ Xv @ Xw )
| ~ ( cQ_2 @ Xx @ Xy @ Xz )
| ~ ( cP_2 @ ( f @ Xx ) @ Xu )
| ~ ( cP_2 @ ( f @ Xy ) @ Xv )
| ~ ( cP_2 @ ( f @ Xz ) @ Xw ) )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_2 @ Xx @ Xy )
| ( cP_2 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i] : ( cP_2 @ d @ Xx )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ( cQ_2 @ Xu @ Xv @ Xw )
| ~ ( cQ_1 @ Xx @ Xy @ Xz )
| ~ ( cP_1 @ ( f @ Xx ) @ Xu )
| ~ ( cP_1 @ ( f @ Xy ) @ Xv )
| ~ ( cP_1 @ ( f @ Xz ) @ Xw ) )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_1 @ Xx @ Xy )
| ( cP_1 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i] : ( cP_1 @ d @ Xx )
& ( cP_1 @ a @ a )
& ( cQ_1 @ a @ b @ c )
& ( cP_1 @ b @ b )
& ( cP_1 @ c @ c )
& ( cP_2 @ a @ a )
& ( cP_2 @ b @ b )
& ( cP_2 @ c @ c )
& ( cP_3 @ a @ a )
& ( cP_3 @ b @ b )
& ( cP_3 @ c @ c )
& ( cP_4 @ a @ a )
& ( cP_4 @ b @ b )
& ( cP_4 @ c @ c )
& ( cP_5 @ a @ a )
& ( cP_5 @ b @ b )
& ( cP_5 @ c @ c )
& ( cP_6 @ a @ a )
& ( cP_6 @ b @ b )
& ( cP_6 @ c @ c ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
~ ( cQ_7 @ Xx @ Xy @ Xz )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ( cQ_7 @ Xu @ Xv @ Xw )
| ~ ( cQ_6 @ Xx @ Xy @ Xz )
| ~ ( cP_6 @ ( f @ Xx ) @ Xu )
| ~ ( cP_6 @ ( f @ Xy ) @ Xv )
| ~ ( cP_6 @ ( f @ Xz ) @ Xw ) )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_6 @ Xx @ Xy )
| ( cP_6 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i] : ( cP_6 @ d @ Xx )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ( cQ_6 @ Xu @ Xv @ Xw )
| ~ ( cQ_5 @ Xx @ Xy @ Xz )
| ~ ( cP_5 @ ( f @ Xx ) @ Xu )
| ~ ( cP_5 @ ( f @ Xy ) @ Xv )
| ~ ( cP_5 @ ( f @ Xz ) @ Xw ) )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_5 @ Xx @ Xy )
| ( cP_5 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i] : ( cP_5 @ d @ Xx )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ( cQ_5 @ Xu @ Xv @ Xw )
| ~ ( cQ_4 @ Xx @ Xy @ Xz )
| ~ ( cP_4 @ ( f @ Xx ) @ Xu )
| ~ ( cP_4 @ ( f @ Xy ) @ Xv )
| ~ ( cP_4 @ ( f @ Xz ) @ Xw ) )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_4 @ Xx @ Xy )
| ( cP_4 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i] : ( cP_4 @ d @ Xx )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ( cQ_4 @ Xu @ Xv @ Xw )
| ~ ( cQ_3 @ Xx @ Xy @ Xz )
| ~ ( cP_3 @ ( f @ Xx ) @ Xu )
| ~ ( cP_3 @ ( f @ Xy ) @ Xv )
| ~ ( cP_3 @ ( f @ Xz ) @ Xw ) )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_3 @ Xx @ Xy )
| ( cP_3 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i] : ( cP_3 @ d @ Xx )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ( cQ_3 @ Xu @ Xv @ Xw )
| ~ ( cQ_2 @ Xx @ Xy @ Xz )
| ~ ( cP_2 @ ( f @ Xx ) @ Xu )
| ~ ( cP_2 @ ( f @ Xy ) @ Xv )
| ~ ( cP_2 @ ( f @ Xz ) @ Xw ) )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_2 @ Xx @ Xy )
| ( cP_2 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i] : ( cP_2 @ d @ Xx )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ( cQ_2 @ Xu @ Xv @ Xw )
| ~ ( cQ_1 @ Xx @ Xy @ Xz )
| ~ ( cP_1 @ ( f @ Xx ) @ Xu )
| ~ ( cP_1 @ ( f @ Xy ) @ Xv )
| ~ ( cP_1 @ ( f @ Xz ) @ Xw ) )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_1 @ Xx @ Xy )
| ( cP_1 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i] : ( cP_1 @ d @ Xx )
& ( cP_1 @ a @ a )
& ( cQ_1 @ a @ b @ c )
& ( cP_1 @ b @ b )
& ( cP_1 @ c @ c )
& ( cP_2 @ a @ a )
& ( cP_2 @ b @ b )
& ( cP_2 @ c @ c )
& ( cP_3 @ a @ a )
& ( cP_3 @ b @ b )
& ( cP_3 @ c @ c )
& ( cP_4 @ a @ a )
& ( cP_4 @ b @ b )
& ( cP_4 @ c @ c )
& ( cP_5 @ a @ a )
& ( cP_5 @ b @ b )
& ( cP_5 @ c @ c )
& ( cP_6 @ a @ a )
& ( cP_6 @ b @ b )
& ( cP_6 @ c @ c ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( cQ_7 @ SX0 @ SX1 @ SX2 )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_7 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_6 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_6 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_6 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_6 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_6 @ SX0 @ SX1 )
| ( cP_6 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_6 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_6 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_5 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_5 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_5 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_5 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_5 @ SX0 @ SX1 )
| ( cP_5 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) ) ) )
| ~ ( cP_6 @ a @ a ) )
| ~ ( cP_6 @ b @ b ) )
| ~ ( cP_6 @ c @ c ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( cQ_7 @ SX0 @ SX1 @ SX2 )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_7 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_6 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_6 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_6 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_6 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_6 @ SX0 @ SX1 )
| ( cP_6 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_6 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_6 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_5 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_5 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_5 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_5 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_5 @ SX0 @ SX1 )
| ( cP_5 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) ) ) )
| ~ ( cP_6 @ a @ a ) )
| ~ ( cP_6 @ b @ b ) )
| ~ ( cP_6 @ c @ c ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7]) ).
thf(9,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( cQ_7 @ SX0 @ SX1 @ SX2 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[8]) ).
thf(10,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_7 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_6 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_6 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_6 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_6 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_6 @ SX0 @ SX1 )
| ( cP_6 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_6 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_6 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_5 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_5 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_5 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_5 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_5 @ SX0 @ SX1 )
| ( cP_5 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) ) ) )
| ~ ( cP_6 @ a @ a ) )
| ~ ( cP_6 @ b @ b ) )
| ~ ( cP_6 @ c @ c ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[8]) ).
thf(11,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( cQ_7 @ SX0 @ SX1 @ SX2 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_7 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_6 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_6 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_6 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_6 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_6 @ SX0 @ SX1 )
| ( cP_6 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_6 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_6 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_5 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_5 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_5 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_5 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_5 @ SX0 @ SX1 )
| ( cP_5 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) ) ) )
| ~ ( cP_6 @ a @ a ) )
| ~ ( cP_6 @ b @ b ) )
| ~ ( cP_6 @ c @ c ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[10]) ).
thf(13,plain,
! [SV1: $i] :
( ( ! [SY57: $i,SY58: $i] :
~ ( cQ_7 @ SV1 @ SY57 @ SY58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_7 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_6 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_6 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_6 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_6 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_6 @ SX0 @ SX1 )
| ( cP_6 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_6 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_6 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_5 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_5 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_5 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_5 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_5 @ SX0 @ SX1 )
| ( cP_5 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) ) ) )
| ~ ( cP_6 @ a @ a ) )
| ~ ( cP_6 @ b @ b ) )
| ~ ( cP_6 @ c @ c ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY59: $i] :
~ ( cQ_7 @ SV1 @ SV2 @ SY59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_7 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_6 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_6 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_6 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_6 @ ( f @ SX2 ) @ SX5 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_6 @ SX0 @ SX1 )
| ( cP_6 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_6 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_6 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_5 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_5 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_5 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_5 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_5 @ SX0 @ SX1 )
| ( cP_5 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) ) ) )
| ~ ( cP_6 @ a @ a ) )
| ~ ( cP_6 @ b @ b ) )
| ~ ( cP_6 @ c @ c ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(18,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ( cQ_7 @ SV1 @ SV2 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_7 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_6 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_6 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_6 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_6 @ ( f @ SX2 ) @ SX5 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_6 @ SX0 @ SX1 )
| ( cP_6 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_6 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_6 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_5 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_5 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_5 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_5 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_5 @ SX0 @ SX1 )
| ( cP_5 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) ) ) )
| ~ ( cP_6 @ a @ a ) )
| ~ ( cP_6 @ b @ b ) )
| ~ ( cP_6 @ c @ c ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( cQ_7 @ SV1 @ SV2 @ SV3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
! [SV4: $i] :
( ( ! [SY60: $i,SY61: $i,SY62: $i,SY63: $i,SY64: $i] :
( ( cQ_7 @ SY62 @ SY63 @ SY64 )
| ~ ( cQ_6 @ SV4 @ SY60 @ SY61 )
| ~ ( cP_6 @ ( f @ SV4 ) @ SY62 )
| ~ ( cP_6 @ ( f @ SY60 ) @ SY63 )
| ~ ( cP_6 @ ( f @ SY61 ) @ SY64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(23,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_6 @ SX0 @ SX1 )
| ( cP_6 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_6 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_6 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_5 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_5 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_5 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_5 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_5 @ SX0 @ SX1 )
| ( cP_5 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) ) ) )
| ~ ( cP_6 @ a @ a ) )
| ~ ( cP_6 @ b @ b ) )
| ~ ( cP_6 @ c @ c ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV5: $i,SV4: $i] :
( ( ! [SY65: $i,SY66: $i,SY67: $i,SY68: $i] :
( ( cQ_7 @ SY66 @ SY67 @ SY68 )
| ~ ( cQ_6 @ SV4 @ SV5 @ SY65 )
| ~ ( cP_6 @ ( f @ SV4 ) @ SY66 )
| ~ ( cP_6 @ ( f @ SV5 ) @ SY67 )
| ~ ( cP_6 @ ( f @ SY65 ) @ SY68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(25,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_6 @ SX0 @ SX1 )
| ( cP_6 @ ( f @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(26,plain,
( ( ~ ~ ( ~ ! [SX0: $i] : ( cP_6 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_6 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_5 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_5 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_5 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_5 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_5 @ SX0 @ SX1 )
| ( cP_5 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) ) ) )
| ~ ( cP_6 @ a @ a ) )
| ~ ( cP_6 @ b @ b ) )
| ~ ( cP_6 @ c @ c ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(27,plain,
! [SV6: $i,SV5: $i,SV4: $i] :
( ( ! [SY69: $i,SY70: $i,SY71: $i] :
( ( cQ_7 @ SY69 @ SY70 @ SY71 )
| ~ ( cQ_6 @ SV4 @ SV5 @ SV6 )
| ~ ( cP_6 @ ( f @ SV4 ) @ SY69 )
| ~ ( cP_6 @ ( f @ SV5 ) @ SY70 )
| ~ ( cP_6 @ ( f @ SV6 ) @ SY71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(28,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( cP_6 @ SX0 @ SX1 )
| ( cP_6 @ ( f @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(29,plain,
( ( ~ ( ~ ! [SX0: $i] : ( cP_6 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_6 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_5 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_5 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_5 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_5 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_5 @ SX0 @ SX1 )
| ( cP_5 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) ) ) )
| ~ ( cP_6 @ a @ a ) )
| ~ ( cP_6 @ b @ b ) )
| ~ ( cP_6 @ c @ c ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(30,plain,
! [SV6: $i,SV5: $i,SV4: $i,SV7: $i] :
( ( ! [SY72: $i,SY73: $i] :
( ( cQ_7 @ SV7 @ SY72 @ SY73 )
| ~ ( cQ_6 @ SV4 @ SV5 @ SV6 )
| ~ ( cP_6 @ ( f @ SV4 ) @ SV7 )
| ~ ( cP_6 @ ( f @ SV5 ) @ SY72 )
| ~ ( cP_6 @ ( f @ SV6 ) @ SY73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV8: $i] :
( ( ! [SY74: $i] :
( ~ ( cP_6 @ SV8 @ SY74 )
| ( cP_6 @ ( f @ SV8 ) @ SY74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(32,plain,
( ( ~ ! [SX0: $i] : ( cP_6 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_6 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_5 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_5 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_5 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_5 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_5 @ SX0 @ SX1 )
| ( cP_5 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) ) ) )
| ~ ( cP_6 @ a @ a ) )
| ~ ( cP_6 @ b @ b ) )
| ~ ( cP_6 @ c @ c ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV6: $i,SV5: $i,SV4: $i,SV9: $i,SV7: $i] :
( ( ! [SY75: $i] :
( ( cQ_7 @ SV7 @ SV9 @ SY75 )
| ~ ( cQ_6 @ SV4 @ SV5 @ SV6 )
| ~ ( cP_6 @ ( f @ SV4 ) @ SV7 )
| ~ ( cP_6 @ ( f @ SV5 ) @ SV9 )
| ~ ( cP_6 @ ( f @ SV6 ) @ SY75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV10: $i,SV8: $i] :
( ( ~ ( cP_6 @ SV8 @ SV10 )
| ( cP_6 @ ( f @ SV8 ) @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(35,plain,
( ( ~ ! [SX0: $i] : ( cP_6 @ d @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(36,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_6 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_5 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_5 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_5 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_5 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_5 @ SX0 @ SX1 )
| ( cP_5 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) ) ) )
| ~ ( cP_6 @ a @ a ) )
| ~ ( cP_6 @ b @ b ) )
| ~ ( cP_6 @ c @ c ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(37,plain,
! [SV6: $i,SV5: $i,SV4: $i,SV11: $i,SV9: $i,SV7: $i] :
( ( ( cQ_7 @ SV7 @ SV9 @ SV11 )
| ~ ( cQ_6 @ SV4 @ SV5 @ SV6 )
| ~ ( cP_6 @ ( f @ SV4 ) @ SV7 )
| ~ ( cP_6 @ ( f @ SV5 ) @ SV9 )
| ~ ( cP_6 @ ( f @ SV6 ) @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV10: $i,SV8: $i] :
( ( ( ~ ( cP_6 @ SV8 @ SV10 ) )
= $true )
| ( ( cP_6 @ ( f @ SV8 ) @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(39,plain,
( ( ! [SX0: $i] : ( cP_6 @ d @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(40,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_6 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_5 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_5 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_5 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_5 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_5 @ SX0 @ SX1 )
| ( cP_5 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) ) ) )
| ~ ( cP_6 @ a @ a ) )
| ~ ( cP_6 @ b @ b ) )
| ~ ( cP_6 @ c @ c ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(41,plain,
! [SV6: $i,SV5: $i,SV4: $i,SV11: $i,SV9: $i,SV7: $i] :
( ( ( cQ_7 @ SV7 @ SV9 @ SV11 )
= $true )
| ( ( ~ ( cQ_6 @ SV4 @ SV5 @ SV6 )
| ~ ( cP_6 @ ( f @ SV4 ) @ SV7 )
| ~ ( cP_6 @ ( f @ SV5 ) @ SV9 )
| ~ ( cP_6 @ ( f @ SV6 ) @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV10: $i,SV8: $i] :
( ( ( cP_6 @ SV8 @ SV10 )
= $false )
| ( ( cP_6 @ ( f @ SV8 ) @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV12: $i] :
( ( cP_6 @ d @ SV12 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(44,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_6 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_5 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_5 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_5 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_5 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_5 @ SX0 @ SX1 )
| ( cP_5 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) ) ) )
| ~ ( cP_6 @ a @ a ) )
| ~ ( cP_6 @ b @ b ) )
| ~ ( cP_6 @ c @ c ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(45,plain,
! [SV11: $i,SV9: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i] :
( ( ( ~ ( cQ_6 @ SV4 @ SV5 @ SV6 )
| ~ ( cP_6 @ ( f @ SV4 ) @ SV7 )
| ~ ( cP_6 @ ( f @ SV5 ) @ SV9 ) )
= $true )
| ( ( ~ ( cP_6 @ ( f @ SV6 ) @ SV11 ) )
= $true )
| ( ( cQ_7 @ SV7 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(46,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_6 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_5 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_5 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_5 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_5 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_5 @ SX0 @ SX1 )
| ( cP_5 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) ) ) )
| ~ ( cP_6 @ a @ a ) )
| ~ ( cP_6 @ b @ b ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(47,plain,
( ( ~ ( cP_6 @ c @ c ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(48,plain,
! [SV11: $i,SV9: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i] :
( ( ( ~ ( cQ_6 @ SV4 @ SV5 @ SV6 )
| ~ ( cP_6 @ ( f @ SV4 ) @ SV7 ) )
= $true )
| ( ( ~ ( cP_6 @ ( f @ SV5 ) @ SV9 ) )
= $true )
| ( ( ~ ( cP_6 @ ( f @ SV6 ) @ SV11 ) )
= $true )
| ( ( cQ_7 @ SV7 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(49,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_6 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_5 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_5 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_5 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_5 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_5 @ SX0 @ SX1 )
| ( cP_5 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) ) ) )
| ~ ( cP_6 @ a @ a ) )
| ~ ( cP_6 @ b @ b ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(50,plain,
( ( cP_6 @ c @ c )
= $true ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(51,plain,
! [SV11: $i,SV9: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i] :
( ( ( ~ ( cQ_6 @ SV4 @ SV5 @ SV6 ) )
= $true )
| ( ( ~ ( cP_6 @ ( f @ SV4 ) @ SV7 ) )
= $true )
| ( ( ~ ( cP_6 @ ( f @ SV5 ) @ SV9 ) )
= $true )
| ( ( ~ ( cP_6 @ ( f @ SV6 ) @ SV11 ) )
= $true )
| ( ( cQ_7 @ SV7 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(52,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_6 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_5 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_5 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_5 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_5 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_5 @ SX0 @ SX1 )
| ( cP_5 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) ) ) )
| ~ ( cP_6 @ a @ a ) )
| ~ ( cP_6 @ b @ b ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(53,plain,
! [SV11: $i,SV9: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i] :
( ( ( cQ_6 @ SV4 @ SV5 @ SV6 )
= $false )
| ( ( ~ ( cP_6 @ ( f @ SV4 ) @ SV7 ) )
= $true )
| ( ( ~ ( cP_6 @ ( f @ SV5 ) @ SV9 ) )
= $true )
| ( ( ~ ( cP_6 @ ( f @ SV6 ) @ SV11 ) )
= $true )
| ( ( cQ_7 @ SV7 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(54,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_6 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_5 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_5 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_5 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_5 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_5 @ SX0 @ SX1 )
| ( cP_5 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) ) ) )
| ~ ( cP_6 @ a @ a ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(55,plain,
( ( ~ ( cP_6 @ b @ b ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[52]) ).
thf(56,plain,
! [SV11: $i,SV9: $i,SV6: $i,SV5: $i,SV7: $i,SV4: $i] :
( ( ( cP_6 @ ( f @ SV4 ) @ SV7 )
= $false )
| ( ( cQ_6 @ SV4 @ SV5 @ SV6 )
= $false )
| ( ( ~ ( cP_6 @ ( f @ SV5 ) @ SV9 ) )
= $true )
| ( ( ~ ( cP_6 @ ( f @ SV6 ) @ SV11 ) )
= $true )
| ( ( cQ_7 @ SV7 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(57,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_6 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_5 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_5 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_5 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_5 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_5 @ SX0 @ SX1 )
| ( cP_5 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) ) ) )
| ~ ( cP_6 @ a @ a ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(58,plain,
( ( cP_6 @ b @ b )
= $true ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(59,plain,
! [SV11: $i,SV7: $i,SV6: $i,SV4: $i,SV9: $i,SV5: $i] :
( ( ( cP_6 @ ( f @ SV5 ) @ SV9 )
= $false )
| ( ( cQ_6 @ SV4 @ SV5 @ SV6 )
= $false )
| ( ( cP_6 @ ( f @ SV4 ) @ SV7 )
= $false )
| ( ( ~ ( cP_6 @ ( f @ SV6 ) @ SV11 ) )
= $true )
| ( ( cQ_7 @ SV7 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(60,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_6 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_5 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_5 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_5 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_5 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_5 @ SX0 @ SX1 )
| ( cP_5 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) ) ) )
| ~ ( cP_6 @ a @ a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(61,plain,
! [SV9: $i,SV5: $i,SV7: $i,SV4: $i,SV11: $i,SV6: $i] :
( ( ( cP_6 @ ( f @ SV6 ) @ SV11 )
= $false )
| ( ( cP_6 @ ( f @ SV4 ) @ SV7 )
= $false )
| ( ( cQ_6 @ SV4 @ SV5 @ SV6 )
= $false )
| ( ( cP_6 @ ( f @ SV5 ) @ SV9 )
= $false )
| ( ( cQ_7 @ SV7 @ SV9 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(62,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_6 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_5 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_5 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_5 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_5 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_5 @ SX0 @ SX1 )
| ( cP_5 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(63,plain,
( ( ~ ( cP_6 @ a @ a ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(64,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_6 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_5 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_5 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_5 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_5 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_5 @ SX0 @ SX1 )
| ( cP_5 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(65,plain,
( ( cP_6 @ a @ a )
= $true ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(66,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_6 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_5 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_5 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_5 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_5 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_5 @ SX0 @ SX1 )
| ( cP_5 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(67,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_6 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_5 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_5 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_5 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_5 @ ( f @ SX2 ) @ SX5 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(68,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_5 @ SX0 @ SX1 )
| ( cP_5 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(69,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_6 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_5 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_5 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_5 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_5 @ ( f @ SX2 ) @ SX5 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(70,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_5 @ SX0 @ SX1 )
| ( cP_5 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(71,plain,
! [SV13: $i] :
( ( ! [SY76: $i,SY77: $i,SY78: $i,SY79: $i,SY80: $i] :
( ( cQ_6 @ SY78 @ SY79 @ SY80 )
| ~ ( cQ_5 @ SV13 @ SY76 @ SY77 )
| ~ ( cP_5 @ ( f @ SV13 ) @ SY78 )
| ~ ( cP_5 @ ( f @ SY76 ) @ SY79 )
| ~ ( cP_5 @ ( f @ SY77 ) @ SY80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(72,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_5 @ SX0 @ SX1 )
| ( cP_5 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(73,plain,
! [SV14: $i,SV13: $i] :
( ( ! [SY81: $i,SY82: $i,SY83: $i,SY84: $i] :
( ( cQ_6 @ SY82 @ SY83 @ SY84 )
| ~ ( cQ_5 @ SV13 @ SV14 @ SY81 )
| ~ ( cP_5 @ ( f @ SV13 ) @ SY82 )
| ~ ( cP_5 @ ( f @ SV14 ) @ SY83 )
| ~ ( cP_5 @ ( f @ SY81 ) @ SY84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(74,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_5 @ SX0 @ SX1 )
| ( cP_5 @ ( f @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(75,plain,
( ( ~ ~ ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(76,plain,
! [SV15: $i,SV14: $i,SV13: $i] :
( ( ! [SY85: $i,SY86: $i,SY87: $i] :
( ( cQ_6 @ SY85 @ SY86 @ SY87 )
| ~ ( cQ_5 @ SV13 @ SV14 @ SV15 )
| ~ ( cP_5 @ ( f @ SV13 ) @ SY85 )
| ~ ( cP_5 @ ( f @ SV14 ) @ SY86 )
| ~ ( cP_5 @ ( f @ SV15 ) @ SY87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(77,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( cP_5 @ SX0 @ SX1 )
| ( cP_5 @ ( f @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(78,plain,
( ( ~ ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(79,plain,
! [SV15: $i,SV14: $i,SV13: $i,SV16: $i] :
( ( ! [SY88: $i,SY89: $i] :
( ( cQ_6 @ SV16 @ SY88 @ SY89 )
| ~ ( cQ_5 @ SV13 @ SV14 @ SV15 )
| ~ ( cP_5 @ ( f @ SV13 ) @ SV16 )
| ~ ( cP_5 @ ( f @ SV14 ) @ SY88 )
| ~ ( cP_5 @ ( f @ SV15 ) @ SY89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(80,plain,
! [SV17: $i] :
( ( ! [SY90: $i] :
( ~ ( cP_5 @ SV17 @ SY90 )
| ( cP_5 @ ( f @ SV17 ) @ SY90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(81,plain,
( ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(82,plain,
! [SV15: $i,SV14: $i,SV13: $i,SV18: $i,SV16: $i] :
( ( ! [SY91: $i] :
( ( cQ_6 @ SV16 @ SV18 @ SY91 )
| ~ ( cQ_5 @ SV13 @ SV14 @ SV15 )
| ~ ( cP_5 @ ( f @ SV13 ) @ SV16 )
| ~ ( cP_5 @ ( f @ SV14 ) @ SV18 )
| ~ ( cP_5 @ ( f @ SV15 ) @ SY91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(83,plain,
! [SV19: $i,SV17: $i] :
( ( ~ ( cP_5 @ SV17 @ SV19 )
| ( cP_5 @ ( f @ SV17 ) @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(84,plain,
( ( ~ ! [SX0: $i] : ( cP_5 @ d @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(85,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(86,plain,
! [SV15: $i,SV14: $i,SV13: $i,SV20: $i,SV18: $i,SV16: $i] :
( ( ( cQ_6 @ SV16 @ SV18 @ SV20 )
| ~ ( cQ_5 @ SV13 @ SV14 @ SV15 )
| ~ ( cP_5 @ ( f @ SV13 ) @ SV16 )
| ~ ( cP_5 @ ( f @ SV14 ) @ SV18 )
| ~ ( cP_5 @ ( f @ SV15 ) @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(87,plain,
! [SV19: $i,SV17: $i] :
( ( ( ~ ( cP_5 @ SV17 @ SV19 ) )
= $true )
| ( ( cP_5 @ ( f @ SV17 ) @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(88,plain,
( ( ! [SX0: $i] : ( cP_5 @ d @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(89,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(90,plain,
! [SV15: $i,SV14: $i,SV13: $i,SV20: $i,SV18: $i,SV16: $i] :
( ( ( cQ_6 @ SV16 @ SV18 @ SV20 )
= $true )
| ( ( ~ ( cQ_5 @ SV13 @ SV14 @ SV15 )
| ~ ( cP_5 @ ( f @ SV13 ) @ SV16 )
| ~ ( cP_5 @ ( f @ SV14 ) @ SV18 )
| ~ ( cP_5 @ ( f @ SV15 ) @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(91,plain,
! [SV19: $i,SV17: $i] :
( ( ( cP_5 @ SV17 @ SV19 )
= $false )
| ( ( cP_5 @ ( f @ SV17 ) @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(92,plain,
! [SV21: $i] :
( ( cP_5 @ d @ SV21 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(93,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
| ~ ( cP_5 @ c @ c ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(94,plain,
! [SV20: $i,SV18: $i,SV16: $i,SV15: $i,SV14: $i,SV13: $i] :
( ( ( ~ ( cQ_5 @ SV13 @ SV14 @ SV15 )
| ~ ( cP_5 @ ( f @ SV13 ) @ SV16 )
| ~ ( cP_5 @ ( f @ SV14 ) @ SV18 ) )
= $true )
| ( ( ~ ( cP_5 @ ( f @ SV15 ) @ SV20 ) )
= $true )
| ( ( cQ_6 @ SV16 @ SV18 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(95,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(96,plain,
( ( ~ ( cP_5 @ c @ c ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(97,plain,
! [SV20: $i,SV18: $i,SV16: $i,SV15: $i,SV14: $i,SV13: $i] :
( ( ( ~ ( cQ_5 @ SV13 @ SV14 @ SV15 )
| ~ ( cP_5 @ ( f @ SV13 ) @ SV16 ) )
= $true )
| ( ( ~ ( cP_5 @ ( f @ SV14 ) @ SV18 ) )
= $true )
| ( ( ~ ( cP_5 @ ( f @ SV15 ) @ SV20 ) )
= $true )
| ( ( cQ_6 @ SV16 @ SV18 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(98,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(99,plain,
( ( cP_5 @ c @ c )
= $true ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(100,plain,
! [SV20: $i,SV18: $i,SV16: $i,SV15: $i,SV14: $i,SV13: $i] :
( ( ( ~ ( cQ_5 @ SV13 @ SV14 @ SV15 ) )
= $true )
| ( ( ~ ( cP_5 @ ( f @ SV13 ) @ SV16 ) )
= $true )
| ( ( ~ ( cP_5 @ ( f @ SV14 ) @ SV18 ) )
= $true )
| ( ( ~ ( cP_5 @ ( f @ SV15 ) @ SV20 ) )
= $true )
| ( ( cQ_6 @ SV16 @ SV18 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(101,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
| ~ ( cP_5 @ b @ b ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(102,plain,
! [SV20: $i,SV18: $i,SV16: $i,SV15: $i,SV14: $i,SV13: $i] :
( ( ( cQ_5 @ SV13 @ SV14 @ SV15 )
= $false )
| ( ( ~ ( cP_5 @ ( f @ SV13 ) @ SV16 ) )
= $true )
| ( ( ~ ( cP_5 @ ( f @ SV14 ) @ SV18 ) )
= $true )
| ( ( ~ ( cP_5 @ ( f @ SV15 ) @ SV20 ) )
= $true )
| ( ( cQ_6 @ SV16 @ SV18 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(103,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(104,plain,
( ( ~ ( cP_5 @ b @ b ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(105,plain,
! [SV20: $i,SV18: $i,SV15: $i,SV14: $i,SV16: $i,SV13: $i] :
( ( ( cP_5 @ ( f @ SV13 ) @ SV16 )
= $false )
| ( ( cQ_5 @ SV13 @ SV14 @ SV15 )
= $false )
| ( ( ~ ( cP_5 @ ( f @ SV14 ) @ SV18 ) )
= $true )
| ( ( ~ ( cP_5 @ ( f @ SV15 ) @ SV20 ) )
= $true )
| ( ( cQ_6 @ SV16 @ SV18 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(106,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(107,plain,
( ( cP_5 @ b @ b )
= $true ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(108,plain,
! [SV20: $i,SV16: $i,SV15: $i,SV13: $i,SV18: $i,SV14: $i] :
( ( ( cP_5 @ ( f @ SV14 ) @ SV18 )
= $false )
| ( ( cQ_5 @ SV13 @ SV14 @ SV15 )
= $false )
| ( ( cP_5 @ ( f @ SV13 ) @ SV16 )
= $false )
| ( ( ~ ( cP_5 @ ( f @ SV15 ) @ SV20 ) )
= $true )
| ( ( cQ_6 @ SV16 @ SV18 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(109,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
| ~ ( cP_5 @ a @ a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(110,plain,
! [SV18: $i,SV14: $i,SV16: $i,SV13: $i,SV20: $i,SV15: $i] :
( ( ( cP_5 @ ( f @ SV15 ) @ SV20 )
= $false )
| ( ( cP_5 @ ( f @ SV13 ) @ SV16 )
= $false )
| ( ( cQ_5 @ SV13 @ SV14 @ SV15 )
= $false )
| ( ( cP_5 @ ( f @ SV14 ) @ SV18 )
= $false )
| ( ( cQ_6 @ SV16 @ SV18 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(111,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(112,plain,
( ( ~ ( cP_5 @ a @ a ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(113,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(114,plain,
( ( cP_5 @ a @ a )
= $true ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(115,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(116,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(117,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[115]) ).
thf(118,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_5 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_4 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_4 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_4 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_4 @ ( f @ SX2 ) @ SX5 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(119,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(120,plain,
! [SV22: $i] :
( ( ! [SY92: $i,SY93: $i,SY94: $i,SY95: $i,SY96: $i] :
( ( cQ_5 @ SY94 @ SY95 @ SY96 )
| ~ ( cQ_4 @ SV22 @ SY92 @ SY93 )
| ~ ( cP_4 @ ( f @ SV22 ) @ SY94 )
| ~ ( cP_4 @ ( f @ SY92 ) @ SY95 )
| ~ ( cP_4 @ ( f @ SY93 ) @ SY96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(121,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(122,plain,
! [SV23: $i,SV22: $i] :
( ( ! [SY97: $i,SY98: $i,SY99: $i,SY100: $i] :
( ( cQ_5 @ SY98 @ SY99 @ SY100 )
| ~ ( cQ_4 @ SV22 @ SV23 @ SY97 )
| ~ ( cP_4 @ ( f @ SV22 ) @ SY98 )
| ~ ( cP_4 @ ( f @ SV23 ) @ SY99 )
| ~ ( cP_4 @ ( f @ SY97 ) @ SY100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(123,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(124,plain,
( ( ~ ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(125,plain,
! [SV24: $i,SV23: $i,SV22: $i] :
( ( ! [SY101: $i,SY102: $i,SY103: $i] :
( ( cQ_5 @ SY101 @ SY102 @ SY103 )
| ~ ( cQ_4 @ SV22 @ SV23 @ SV24 )
| ~ ( cP_4 @ ( f @ SV22 ) @ SY101 )
| ~ ( cP_4 @ ( f @ SV23 ) @ SY102 )
| ~ ( cP_4 @ ( f @ SV24 ) @ SY103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(126,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(127,plain,
( ( ~ ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(128,plain,
! [SV24: $i,SV23: $i,SV22: $i,SV25: $i] :
( ( ! [SY104: $i,SY105: $i] :
( ( cQ_5 @ SV25 @ SY104 @ SY105 )
| ~ ( cQ_4 @ SV22 @ SV23 @ SV24 )
| ~ ( cP_4 @ ( f @ SV22 ) @ SV25 )
| ~ ( cP_4 @ ( f @ SV23 ) @ SY104 )
| ~ ( cP_4 @ ( f @ SV24 ) @ SY105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(129,plain,
! [SV26: $i] :
( ( ! [SY106: $i] :
( ~ ( cP_4 @ SV26 @ SY106 )
| ( cP_4 @ ( f @ SV26 ) @ SY106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(130,plain,
( ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(131,plain,
! [SV24: $i,SV23: $i,SV22: $i,SV27: $i,SV25: $i] :
( ( ! [SY107: $i] :
( ( cQ_5 @ SV25 @ SV27 @ SY107 )
| ~ ( cQ_4 @ SV22 @ SV23 @ SV24 )
| ~ ( cP_4 @ ( f @ SV22 ) @ SV25 )
| ~ ( cP_4 @ ( f @ SV23 ) @ SV27 )
| ~ ( cP_4 @ ( f @ SV24 ) @ SY107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(132,plain,
! [SV28: $i,SV26: $i] :
( ( ~ ( cP_4 @ SV26 @ SV28 )
| ( cP_4 @ ( f @ SV26 ) @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(133,plain,
( ( ~ ! [SX0: $i] : ( cP_4 @ d @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(134,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(135,plain,
! [SV24: $i,SV23: $i,SV22: $i,SV29: $i,SV27: $i,SV25: $i] :
( ( ( cQ_5 @ SV25 @ SV27 @ SV29 )
| ~ ( cQ_4 @ SV22 @ SV23 @ SV24 )
| ~ ( cP_4 @ ( f @ SV22 ) @ SV25 )
| ~ ( cP_4 @ ( f @ SV23 ) @ SV27 )
| ~ ( cP_4 @ ( f @ SV24 ) @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(136,plain,
! [SV28: $i,SV26: $i] :
( ( ( ~ ( cP_4 @ SV26 @ SV28 ) )
= $true )
| ( ( cP_4 @ ( f @ SV26 ) @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(137,plain,
( ( ! [SX0: $i] : ( cP_4 @ d @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(138,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(139,plain,
! [SV24: $i,SV23: $i,SV22: $i,SV29: $i,SV27: $i,SV25: $i] :
( ( ( cQ_5 @ SV25 @ SV27 @ SV29 )
= $true )
| ( ( ~ ( cQ_4 @ SV22 @ SV23 @ SV24 )
| ~ ( cP_4 @ ( f @ SV22 ) @ SV25 )
| ~ ( cP_4 @ ( f @ SV23 ) @ SV27 )
| ~ ( cP_4 @ ( f @ SV24 ) @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(140,plain,
! [SV28: $i,SV26: $i] :
( ( ( cP_4 @ SV26 @ SV28 )
= $false )
| ( ( cP_4 @ ( f @ SV26 ) @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(141,plain,
! [SV30: $i] :
( ( cP_4 @ d @ SV30 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(142,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
| ~ ( cP_4 @ c @ c ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(143,plain,
! [SV29: $i,SV27: $i,SV25: $i,SV24: $i,SV23: $i,SV22: $i] :
( ( ( ~ ( cQ_4 @ SV22 @ SV23 @ SV24 )
| ~ ( cP_4 @ ( f @ SV22 ) @ SV25 )
| ~ ( cP_4 @ ( f @ SV23 ) @ SV27 ) )
= $true )
| ( ( ~ ( cP_4 @ ( f @ SV24 ) @ SV29 ) )
= $true )
| ( ( cQ_5 @ SV25 @ SV27 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(144,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(145,plain,
( ( ~ ( cP_4 @ c @ c ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(146,plain,
! [SV29: $i,SV27: $i,SV25: $i,SV24: $i,SV23: $i,SV22: $i] :
( ( ( ~ ( cQ_4 @ SV22 @ SV23 @ SV24 )
| ~ ( cP_4 @ ( f @ SV22 ) @ SV25 ) )
= $true )
| ( ( ~ ( cP_4 @ ( f @ SV23 ) @ SV27 ) )
= $true )
| ( ( ~ ( cP_4 @ ( f @ SV24 ) @ SV29 ) )
= $true )
| ( ( cQ_5 @ SV25 @ SV27 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(147,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(148,plain,
( ( cP_4 @ c @ c )
= $true ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(149,plain,
! [SV29: $i,SV27: $i,SV25: $i,SV24: $i,SV23: $i,SV22: $i] :
( ( ( ~ ( cQ_4 @ SV22 @ SV23 @ SV24 ) )
= $true )
| ( ( ~ ( cP_4 @ ( f @ SV22 ) @ SV25 ) )
= $true )
| ( ( ~ ( cP_4 @ ( f @ SV23 ) @ SV27 ) )
= $true )
| ( ( ~ ( cP_4 @ ( f @ SV24 ) @ SV29 ) )
= $true )
| ( ( cQ_5 @ SV25 @ SV27 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(150,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
| ~ ( cP_4 @ b @ b ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(151,plain,
! [SV29: $i,SV27: $i,SV25: $i,SV24: $i,SV23: $i,SV22: $i] :
( ( ( cQ_4 @ SV22 @ SV23 @ SV24 )
= $false )
| ( ( ~ ( cP_4 @ ( f @ SV22 ) @ SV25 ) )
= $true )
| ( ( ~ ( cP_4 @ ( f @ SV23 ) @ SV27 ) )
= $true )
| ( ( ~ ( cP_4 @ ( f @ SV24 ) @ SV29 ) )
= $true )
| ( ( cQ_5 @ SV25 @ SV27 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(152,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(153,plain,
( ( ~ ( cP_4 @ b @ b ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(154,plain,
! [SV29: $i,SV27: $i,SV24: $i,SV23: $i,SV25: $i,SV22: $i] :
( ( ( cP_4 @ ( f @ SV22 ) @ SV25 )
= $false )
| ( ( cQ_4 @ SV22 @ SV23 @ SV24 )
= $false )
| ( ( ~ ( cP_4 @ ( f @ SV23 ) @ SV27 ) )
= $true )
| ( ( ~ ( cP_4 @ ( f @ SV24 ) @ SV29 ) )
= $true )
| ( ( cQ_5 @ SV25 @ SV27 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(155,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(156,plain,
( ( cP_4 @ b @ b )
= $true ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(157,plain,
! [SV29: $i,SV25: $i,SV24: $i,SV22: $i,SV27: $i,SV23: $i] :
( ( ( cP_4 @ ( f @ SV23 ) @ SV27 )
= $false )
| ( ( cQ_4 @ SV22 @ SV23 @ SV24 )
= $false )
| ( ( cP_4 @ ( f @ SV22 ) @ SV25 )
= $false )
| ( ( ~ ( cP_4 @ ( f @ SV24 ) @ SV29 ) )
= $true )
| ( ( cQ_5 @ SV25 @ SV27 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(158,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
| ~ ( cP_4 @ a @ a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(159,plain,
! [SV27: $i,SV23: $i,SV25: $i,SV22: $i,SV29: $i,SV24: $i] :
( ( ( cP_4 @ ( f @ SV24 ) @ SV29 )
= $false )
| ( ( cP_4 @ ( f @ SV22 ) @ SV25 )
= $false )
| ( ( cQ_4 @ SV22 @ SV23 @ SV24 )
= $false )
| ( ( cP_4 @ ( f @ SV23 ) @ SV27 )
= $false )
| ( ( cQ_5 @ SV25 @ SV27 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(160,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(161,plain,
( ( ~ ( cP_4 @ a @ a ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(162,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(163,plain,
( ( cP_4 @ a @ a )
= $true ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(164,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(165,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[164]) ).
thf(166,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[164]) ).
thf(167,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_4 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_3 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_3 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_3 @ ( f @ SX2 ) @ SX5 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(168,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(169,plain,
! [SV31: $i] :
( ( ! [SY108: $i,SY109: $i,SY110: $i,SY111: $i,SY112: $i] :
( ( cQ_4 @ SY110 @ SY111 @ SY112 )
| ~ ( cQ_3 @ SV31 @ SY108 @ SY109 )
| ~ ( cP_3 @ ( f @ SV31 ) @ SY110 )
| ~ ( cP_3 @ ( f @ SY108 ) @ SY111 )
| ~ ( cP_3 @ ( f @ SY109 ) @ SY112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(170,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(171,plain,
! [SV32: $i,SV31: $i] :
( ( ! [SY113: $i,SY114: $i,SY115: $i,SY116: $i] :
( ( cQ_4 @ SY114 @ SY115 @ SY116 )
| ~ ( cQ_3 @ SV31 @ SV32 @ SY113 )
| ~ ( cP_3 @ ( f @ SV31 ) @ SY114 )
| ~ ( cP_3 @ ( f @ SV32 ) @ SY115 )
| ~ ( cP_3 @ ( f @ SY113 ) @ SY116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(172,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(173,plain,
( ( ~ ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(174,plain,
! [SV33: $i,SV32: $i,SV31: $i] :
( ( ! [SY117: $i,SY118: $i,SY119: $i] :
( ( cQ_4 @ SY117 @ SY118 @ SY119 )
| ~ ( cQ_3 @ SV31 @ SV32 @ SV33 )
| ~ ( cP_3 @ ( f @ SV31 ) @ SY117 )
| ~ ( cP_3 @ ( f @ SV32 ) @ SY118 )
| ~ ( cP_3 @ ( f @ SV33 ) @ SY119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(175,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(176,plain,
( ( ~ ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(177,plain,
! [SV33: $i,SV32: $i,SV31: $i,SV34: $i] :
( ( ! [SY120: $i,SY121: $i] :
( ( cQ_4 @ SV34 @ SY120 @ SY121 )
| ~ ( cQ_3 @ SV31 @ SV32 @ SV33 )
| ~ ( cP_3 @ ( f @ SV31 ) @ SV34 )
| ~ ( cP_3 @ ( f @ SV32 ) @ SY120 )
| ~ ( cP_3 @ ( f @ SV33 ) @ SY121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(178,plain,
! [SV35: $i] :
( ( ! [SY122: $i] :
( ~ ( cP_3 @ SV35 @ SY122 )
| ( cP_3 @ ( f @ SV35 ) @ SY122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(179,plain,
( ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(180,plain,
! [SV33: $i,SV32: $i,SV31: $i,SV36: $i,SV34: $i] :
( ( ! [SY123: $i] :
( ( cQ_4 @ SV34 @ SV36 @ SY123 )
| ~ ( cQ_3 @ SV31 @ SV32 @ SV33 )
| ~ ( cP_3 @ ( f @ SV31 ) @ SV34 )
| ~ ( cP_3 @ ( f @ SV32 ) @ SV36 )
| ~ ( cP_3 @ ( f @ SV33 ) @ SY123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(181,plain,
! [SV37: $i,SV35: $i] :
( ( ~ ( cP_3 @ SV35 @ SV37 )
| ( cP_3 @ ( f @ SV35 ) @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(182,plain,
( ( ~ ! [SX0: $i] : ( cP_3 @ d @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(183,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(184,plain,
! [SV33: $i,SV32: $i,SV31: $i,SV38: $i,SV36: $i,SV34: $i] :
( ( ( cQ_4 @ SV34 @ SV36 @ SV38 )
| ~ ( cQ_3 @ SV31 @ SV32 @ SV33 )
| ~ ( cP_3 @ ( f @ SV31 ) @ SV34 )
| ~ ( cP_3 @ ( f @ SV32 ) @ SV36 )
| ~ ( cP_3 @ ( f @ SV33 ) @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(185,plain,
! [SV37: $i,SV35: $i] :
( ( ( ~ ( cP_3 @ SV35 @ SV37 ) )
= $true )
| ( ( cP_3 @ ( f @ SV35 ) @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(186,plain,
( ( ! [SX0: $i] : ( cP_3 @ d @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(187,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(188,plain,
! [SV33: $i,SV32: $i,SV31: $i,SV38: $i,SV36: $i,SV34: $i] :
( ( ( cQ_4 @ SV34 @ SV36 @ SV38 )
= $true )
| ( ( ~ ( cQ_3 @ SV31 @ SV32 @ SV33 )
| ~ ( cP_3 @ ( f @ SV31 ) @ SV34 )
| ~ ( cP_3 @ ( f @ SV32 ) @ SV36 )
| ~ ( cP_3 @ ( f @ SV33 ) @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(189,plain,
! [SV37: $i,SV35: $i] :
( ( ( cP_3 @ SV35 @ SV37 )
= $false )
| ( ( cP_3 @ ( f @ SV35 ) @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(190,plain,
! [SV39: $i] :
( ( cP_3 @ d @ SV39 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(191,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
| ~ ( cP_3 @ c @ c ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(192,plain,
! [SV38: $i,SV36: $i,SV34: $i,SV33: $i,SV32: $i,SV31: $i] :
( ( ( ~ ( cQ_3 @ SV31 @ SV32 @ SV33 )
| ~ ( cP_3 @ ( f @ SV31 ) @ SV34 )
| ~ ( cP_3 @ ( f @ SV32 ) @ SV36 ) )
= $true )
| ( ( ~ ( cP_3 @ ( f @ SV33 ) @ SV38 ) )
= $true )
| ( ( cQ_4 @ SV34 @ SV36 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(193,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[191]) ).
thf(194,plain,
( ( ~ ( cP_3 @ c @ c ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[191]) ).
thf(195,plain,
! [SV38: $i,SV36: $i,SV34: $i,SV33: $i,SV32: $i,SV31: $i] :
( ( ( ~ ( cQ_3 @ SV31 @ SV32 @ SV33 )
| ~ ( cP_3 @ ( f @ SV31 ) @ SV34 ) )
= $true )
| ( ( ~ ( cP_3 @ ( f @ SV32 ) @ SV36 ) )
= $true )
| ( ( ~ ( cP_3 @ ( f @ SV33 ) @ SV38 ) )
= $true )
| ( ( cQ_4 @ SV34 @ SV36 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(196,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(197,plain,
( ( cP_3 @ c @ c )
= $true ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(198,plain,
! [SV38: $i,SV36: $i,SV34: $i,SV33: $i,SV32: $i,SV31: $i] :
( ( ( ~ ( cQ_3 @ SV31 @ SV32 @ SV33 ) )
= $true )
| ( ( ~ ( cP_3 @ ( f @ SV31 ) @ SV34 ) )
= $true )
| ( ( ~ ( cP_3 @ ( f @ SV32 ) @ SV36 ) )
= $true )
| ( ( ~ ( cP_3 @ ( f @ SV33 ) @ SV38 ) )
= $true )
| ( ( cQ_4 @ SV34 @ SV36 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(199,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
| ~ ( cP_3 @ b @ b ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(200,plain,
! [SV38: $i,SV36: $i,SV34: $i,SV33: $i,SV32: $i,SV31: $i] :
( ( ( cQ_3 @ SV31 @ SV32 @ SV33 )
= $false )
| ( ( ~ ( cP_3 @ ( f @ SV31 ) @ SV34 ) )
= $true )
| ( ( ~ ( cP_3 @ ( f @ SV32 ) @ SV36 ) )
= $true )
| ( ( ~ ( cP_3 @ ( f @ SV33 ) @ SV38 ) )
= $true )
| ( ( cQ_4 @ SV34 @ SV36 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(201,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(202,plain,
( ( ~ ( cP_3 @ b @ b ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(203,plain,
! [SV38: $i,SV36: $i,SV33: $i,SV32: $i,SV34: $i,SV31: $i] :
( ( ( cP_3 @ ( f @ SV31 ) @ SV34 )
= $false )
| ( ( cQ_3 @ SV31 @ SV32 @ SV33 )
= $false )
| ( ( ~ ( cP_3 @ ( f @ SV32 ) @ SV36 ) )
= $true )
| ( ( ~ ( cP_3 @ ( f @ SV33 ) @ SV38 ) )
= $true )
| ( ( cQ_4 @ SV34 @ SV36 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(204,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(205,plain,
( ( cP_3 @ b @ b )
= $true ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(206,plain,
! [SV38: $i,SV34: $i,SV33: $i,SV31: $i,SV36: $i,SV32: $i] :
( ( ( cP_3 @ ( f @ SV32 ) @ SV36 )
= $false )
| ( ( cQ_3 @ SV31 @ SV32 @ SV33 )
= $false )
| ( ( cP_3 @ ( f @ SV31 ) @ SV34 )
= $false )
| ( ( ~ ( cP_3 @ ( f @ SV33 ) @ SV38 ) )
= $true )
| ( ( cQ_4 @ SV34 @ SV36 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(207,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
| ~ ( cP_3 @ a @ a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(208,plain,
! [SV36: $i,SV32: $i,SV34: $i,SV31: $i,SV38: $i,SV33: $i] :
( ( ( cP_3 @ ( f @ SV33 ) @ SV38 )
= $false )
| ( ( cP_3 @ ( f @ SV31 ) @ SV34 )
= $false )
| ( ( cQ_3 @ SV31 @ SV32 @ SV33 )
= $false )
| ( ( cP_3 @ ( f @ SV32 ) @ SV36 )
= $false )
| ( ( cQ_4 @ SV34 @ SV36 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(209,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(210,plain,
( ( ~ ( cP_3 @ a @ a ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(211,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(212,plain,
( ( cP_3 @ a @ a )
= $true ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(213,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(214,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(215,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(216,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_3 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_2 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_2 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_2 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_2 @ ( f @ SX2 ) @ SX5 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(217,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[215]) ).
thf(218,plain,
! [SV40: $i] :
( ( ! [SY124: $i,SY125: $i,SY126: $i,SY127: $i,SY128: $i] :
( ( cQ_3 @ SY126 @ SY127 @ SY128 )
| ~ ( cQ_2 @ SV40 @ SY124 @ SY125 )
| ~ ( cP_2 @ ( f @ SV40 ) @ SY126 )
| ~ ( cP_2 @ ( f @ SY124 ) @ SY127 )
| ~ ( cP_2 @ ( f @ SY125 ) @ SY128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(219,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(220,plain,
! [SV41: $i,SV40: $i] :
( ( ! [SY129: $i,SY130: $i,SY131: $i,SY132: $i] :
( ( cQ_3 @ SY130 @ SY131 @ SY132 )
| ~ ( cQ_2 @ SV40 @ SV41 @ SY129 )
| ~ ( cP_2 @ ( f @ SV40 ) @ SY130 )
| ~ ( cP_2 @ ( f @ SV41 ) @ SY131 )
| ~ ( cP_2 @ ( f @ SY129 ) @ SY132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(221,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[219]) ).
thf(222,plain,
( ( ~ ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[219]) ).
thf(223,plain,
! [SV42: $i,SV41: $i,SV40: $i] :
( ( ! [SY133: $i,SY134: $i,SY135: $i] :
( ( cQ_3 @ SY133 @ SY134 @ SY135 )
| ~ ( cQ_2 @ SV40 @ SV41 @ SV42 )
| ~ ( cP_2 @ ( f @ SV40 ) @ SY133 )
| ~ ( cP_2 @ ( f @ SV41 ) @ SY134 )
| ~ ( cP_2 @ ( f @ SV42 ) @ SY135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(224,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(225,plain,
( ( ~ ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(226,plain,
! [SV42: $i,SV41: $i,SV40: $i,SV43: $i] :
( ( ! [SY136: $i,SY137: $i] :
( ( cQ_3 @ SV43 @ SY136 @ SY137 )
| ~ ( cQ_2 @ SV40 @ SV41 @ SV42 )
| ~ ( cP_2 @ ( f @ SV40 ) @ SV43 )
| ~ ( cP_2 @ ( f @ SV41 ) @ SY136 )
| ~ ( cP_2 @ ( f @ SV42 ) @ SY137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(227,plain,
! [SV44: $i] :
( ( ! [SY138: $i] :
( ~ ( cP_2 @ SV44 @ SY138 )
| ( cP_2 @ ( f @ SV44 ) @ SY138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(228,plain,
( ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(229,plain,
! [SV42: $i,SV41: $i,SV40: $i,SV45: $i,SV43: $i] :
( ( ! [SY139: $i] :
( ( cQ_3 @ SV43 @ SV45 @ SY139 )
| ~ ( cQ_2 @ SV40 @ SV41 @ SV42 )
| ~ ( cP_2 @ ( f @ SV40 ) @ SV43 )
| ~ ( cP_2 @ ( f @ SV41 ) @ SV45 )
| ~ ( cP_2 @ ( f @ SV42 ) @ SY139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(230,plain,
! [SV46: $i,SV44: $i] :
( ( ~ ( cP_2 @ SV44 @ SV46 )
| ( cP_2 @ ( f @ SV44 ) @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(231,plain,
( ( ~ ! [SX0: $i] : ( cP_2 @ d @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[228]) ).
thf(232,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[228]) ).
thf(233,plain,
! [SV42: $i,SV41: $i,SV40: $i,SV47: $i,SV45: $i,SV43: $i] :
( ( ( cQ_3 @ SV43 @ SV45 @ SV47 )
| ~ ( cQ_2 @ SV40 @ SV41 @ SV42 )
| ~ ( cP_2 @ ( f @ SV40 ) @ SV43 )
| ~ ( cP_2 @ ( f @ SV41 ) @ SV45 )
| ~ ( cP_2 @ ( f @ SV42 ) @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(234,plain,
! [SV46: $i,SV44: $i] :
( ( ( ~ ( cP_2 @ SV44 @ SV46 ) )
= $true )
| ( ( cP_2 @ ( f @ SV44 ) @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(235,plain,
( ( ! [SX0: $i] : ( cP_2 @ d @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(236,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[232]) ).
thf(237,plain,
! [SV42: $i,SV41: $i,SV40: $i,SV47: $i,SV45: $i,SV43: $i] :
( ( ( cQ_3 @ SV43 @ SV45 @ SV47 )
= $true )
| ( ( ~ ( cQ_2 @ SV40 @ SV41 @ SV42 )
| ~ ( cP_2 @ ( f @ SV40 ) @ SV43 )
| ~ ( cP_2 @ ( f @ SV41 ) @ SV45 )
| ~ ( cP_2 @ ( f @ SV42 ) @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(238,plain,
! [SV46: $i,SV44: $i] :
( ( ( cP_2 @ SV44 @ SV46 )
= $false )
| ( ( cP_2 @ ( f @ SV44 ) @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(239,plain,
! [SV48: $i] :
( ( cP_2 @ d @ SV48 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(240,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
| ~ ( cP_2 @ c @ c ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(241,plain,
! [SV47: $i,SV45: $i,SV43: $i,SV42: $i,SV41: $i,SV40: $i] :
( ( ( ~ ( cQ_2 @ SV40 @ SV41 @ SV42 )
| ~ ( cP_2 @ ( f @ SV40 ) @ SV43 )
| ~ ( cP_2 @ ( f @ SV41 ) @ SV45 ) )
= $true )
| ( ( ~ ( cP_2 @ ( f @ SV42 ) @ SV47 ) )
= $true )
| ( ( cQ_3 @ SV43 @ SV45 @ SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(242,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(243,plain,
( ( ~ ( cP_2 @ c @ c ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(244,plain,
! [SV47: $i,SV45: $i,SV43: $i,SV42: $i,SV41: $i,SV40: $i] :
( ( ( ~ ( cQ_2 @ SV40 @ SV41 @ SV42 )
| ~ ( cP_2 @ ( f @ SV40 ) @ SV43 ) )
= $true )
| ( ( ~ ( cP_2 @ ( f @ SV41 ) @ SV45 ) )
= $true )
| ( ( ~ ( cP_2 @ ( f @ SV42 ) @ SV47 ) )
= $true )
| ( ( cQ_3 @ SV43 @ SV45 @ SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(245,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(246,plain,
( ( cP_2 @ c @ c )
= $true ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(247,plain,
! [SV47: $i,SV45: $i,SV43: $i,SV42: $i,SV41: $i,SV40: $i] :
( ( ( ~ ( cQ_2 @ SV40 @ SV41 @ SV42 ) )
= $true )
| ( ( ~ ( cP_2 @ ( f @ SV40 ) @ SV43 ) )
= $true )
| ( ( ~ ( cP_2 @ ( f @ SV41 ) @ SV45 ) )
= $true )
| ( ( ~ ( cP_2 @ ( f @ SV42 ) @ SV47 ) )
= $true )
| ( ( cQ_3 @ SV43 @ SV45 @ SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(248,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
| ~ ( cP_2 @ b @ b ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(249,plain,
! [SV47: $i,SV45: $i,SV43: $i,SV42: $i,SV41: $i,SV40: $i] :
( ( ( cQ_2 @ SV40 @ SV41 @ SV42 )
= $false )
| ( ( ~ ( cP_2 @ ( f @ SV40 ) @ SV43 ) )
= $true )
| ( ( ~ ( cP_2 @ ( f @ SV41 ) @ SV45 ) )
= $true )
| ( ( ~ ( cP_2 @ ( f @ SV42 ) @ SV47 ) )
= $true )
| ( ( cQ_3 @ SV43 @ SV45 @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(250,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[248]) ).
thf(251,plain,
( ( ~ ( cP_2 @ b @ b ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[248]) ).
thf(252,plain,
! [SV47: $i,SV45: $i,SV42: $i,SV41: $i,SV43: $i,SV40: $i] :
( ( ( cP_2 @ ( f @ SV40 ) @ SV43 )
= $false )
| ( ( cQ_2 @ SV40 @ SV41 @ SV42 )
= $false )
| ( ( ~ ( cP_2 @ ( f @ SV41 ) @ SV45 ) )
= $true )
| ( ( ~ ( cP_2 @ ( f @ SV42 ) @ SV47 ) )
= $true )
| ( ( cQ_3 @ SV43 @ SV45 @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(253,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(254,plain,
( ( cP_2 @ b @ b )
= $true ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(255,plain,
! [SV47: $i,SV43: $i,SV42: $i,SV40: $i,SV45: $i,SV41: $i] :
( ( ( cP_2 @ ( f @ SV41 ) @ SV45 )
= $false )
| ( ( cQ_2 @ SV40 @ SV41 @ SV42 )
= $false )
| ( ( cP_2 @ ( f @ SV40 ) @ SV43 )
= $false )
| ( ( ~ ( cP_2 @ ( f @ SV42 ) @ SV47 ) )
= $true )
| ( ( cQ_3 @ SV43 @ SV45 @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(256,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
| ~ ( cP_2 @ a @ a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(257,plain,
! [SV45: $i,SV41: $i,SV43: $i,SV40: $i,SV47: $i,SV42: $i] :
( ( ( cP_2 @ ( f @ SV42 ) @ SV47 )
= $false )
| ( ( cP_2 @ ( f @ SV40 ) @ SV43 )
= $false )
| ( ( cQ_2 @ SV40 @ SV41 @ SV42 )
= $false )
| ( ( cP_2 @ ( f @ SV41 ) @ SV45 )
= $false )
| ( ( cQ_3 @ SV43 @ SV45 @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(258,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(259,plain,
( ( ~ ( cP_2 @ a @ a ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(260,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[258]) ).
thf(261,plain,
( ( cP_2 @ a @ a )
= $true ),
inference(extcnf_not_neg,[status(thm)],[259]) ).
thf(262,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(263,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(264,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(265,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( cQ_2 @ SX3 @ SX4 @ SX5 )
| ~ ( cQ_1 @ SX0 @ SX1 @ SX2 )
| ~ ( cP_1 @ ( f @ SX0 ) @ SX3 )
| ~ ( cP_1 @ ( f @ SX1 ) @ SX4 )
| ~ ( cP_1 @ ( f @ SX2 ) @ SX5 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[263]) ).
thf(266,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(267,plain,
! [SV49: $i] :
( ( ! [SY140: $i,SY141: $i,SY142: $i,SY143: $i,SY144: $i] :
( ( cQ_2 @ SY142 @ SY143 @ SY144 )
| ~ ( cQ_1 @ SV49 @ SY140 @ SY141 )
| ~ ( cP_1 @ ( f @ SV49 ) @ SY142 )
| ~ ( cP_1 @ ( f @ SY140 ) @ SY143 )
| ~ ( cP_1 @ ( f @ SY141 ) @ SY144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(268,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(269,plain,
! [SV50: $i,SV49: $i] :
( ( ! [SY145: $i,SY146: $i,SY147: $i,SY148: $i] :
( ( cQ_2 @ SY146 @ SY147 @ SY148 )
| ~ ( cQ_1 @ SV49 @ SV50 @ SY145 )
| ~ ( cP_1 @ ( f @ SV49 ) @ SY146 )
| ~ ( cP_1 @ ( f @ SV50 ) @ SY147 )
| ~ ( cP_1 @ ( f @ SY145 ) @ SY148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(270,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[268]) ).
thf(271,plain,
( ( ~ ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[268]) ).
thf(272,plain,
! [SV51: $i,SV50: $i,SV49: $i] :
( ( ! [SY149: $i,SY150: $i,SY151: $i] :
( ( cQ_2 @ SY149 @ SY150 @ SY151 )
| ~ ( cQ_1 @ SV49 @ SV50 @ SV51 )
| ~ ( cP_1 @ ( f @ SV49 ) @ SY149 )
| ~ ( cP_1 @ ( f @ SV50 ) @ SY150 )
| ~ ( cP_1 @ ( f @ SV51 ) @ SY151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(273,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[270]) ).
thf(274,plain,
( ( ~ ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(275,plain,
! [SV51: $i,SV50: $i,SV49: $i,SV52: $i] :
( ( ! [SY152: $i,SY153: $i] :
( ( cQ_2 @ SV52 @ SY152 @ SY153 )
| ~ ( cQ_1 @ SV49 @ SV50 @ SV51 )
| ~ ( cP_1 @ ( f @ SV49 ) @ SV52 )
| ~ ( cP_1 @ ( f @ SV50 ) @ SY152 )
| ~ ( cP_1 @ ( f @ SV51 ) @ SY153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(276,plain,
! [SV53: $i] :
( ( ! [SY154: $i] :
( ~ ( cP_1 @ SV53 @ SY154 )
| ( cP_1 @ ( f @ SV53 ) @ SY154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(277,plain,
( ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(278,plain,
! [SV51: $i,SV50: $i,SV49: $i,SV54: $i,SV52: $i] :
( ( ! [SY155: $i] :
( ( cQ_2 @ SV52 @ SV54 @ SY155 )
| ~ ( cQ_1 @ SV49 @ SV50 @ SV51 )
| ~ ( cP_1 @ ( f @ SV49 ) @ SV52 )
| ~ ( cP_1 @ ( f @ SV50 ) @ SV54 )
| ~ ( cP_1 @ ( f @ SV51 ) @ SY155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(279,plain,
! [SV55: $i,SV53: $i] :
( ( ~ ( cP_1 @ SV53 @ SV55 )
| ( cP_1 @ ( f @ SV53 ) @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(280,plain,
( ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[277]) ).
thf(281,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[277]) ).
thf(282,plain,
! [SV51: $i,SV50: $i,SV49: $i,SV56: $i,SV54: $i,SV52: $i] :
( ( ( cQ_2 @ SV52 @ SV54 @ SV56 )
| ~ ( cQ_1 @ SV49 @ SV50 @ SV51 )
| ~ ( cP_1 @ ( f @ SV49 ) @ SV52 )
| ~ ( cP_1 @ ( f @ SV50 ) @ SV54 )
| ~ ( cP_1 @ ( f @ SV51 ) @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(283,plain,
! [SV55: $i,SV53: $i] :
( ( ( ~ ( cP_1 @ SV53 @ SV55 ) )
= $true )
| ( ( cP_1 @ ( f @ SV53 ) @ SV55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(284,plain,
( ( ! [SX0: $i] : ( cP_1 @ d @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(285,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(286,plain,
! [SV51: $i,SV50: $i,SV49: $i,SV56: $i,SV54: $i,SV52: $i] :
( ( ( cQ_2 @ SV52 @ SV54 @ SV56 )
= $true )
| ( ( ~ ( cQ_1 @ SV49 @ SV50 @ SV51 )
| ~ ( cP_1 @ ( f @ SV49 ) @ SV52 )
| ~ ( cP_1 @ ( f @ SV50 ) @ SV54 )
| ~ ( cP_1 @ ( f @ SV51 ) @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(287,plain,
! [SV55: $i,SV53: $i] :
( ( ( cP_1 @ SV53 @ SV55 )
= $false )
| ( ( cP_1 @ ( f @ SV53 ) @ SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(288,plain,
! [SV57: $i] :
( ( cP_1 @ d @ SV57 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(289,plain,
( ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
| ~ ( cP_1 @ c @ c ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(290,plain,
! [SV56: $i,SV54: $i,SV52: $i,SV51: $i,SV50: $i,SV49: $i] :
( ( ( ~ ( cQ_1 @ SV49 @ SV50 @ SV51 )
| ~ ( cP_1 @ ( f @ SV49 ) @ SV52 )
| ~ ( cP_1 @ ( f @ SV50 ) @ SV54 ) )
= $true )
| ( ( ~ ( cP_1 @ ( f @ SV51 ) @ SV56 ) )
= $true )
| ( ( cQ_2 @ SV52 @ SV54 @ SV56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(291,plain,
( ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(292,plain,
( ( ~ ( cP_1 @ c @ c ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(293,plain,
! [SV56: $i,SV54: $i,SV52: $i,SV51: $i,SV50: $i,SV49: $i] :
( ( ( ~ ( cQ_1 @ SV49 @ SV50 @ SV51 )
| ~ ( cP_1 @ ( f @ SV49 ) @ SV52 ) )
= $true )
| ( ( ~ ( cP_1 @ ( f @ SV50 ) @ SV54 ) )
= $true )
| ( ( ~ ( cP_1 @ ( f @ SV51 ) @ SV56 ) )
= $true )
| ( ( cQ_2 @ SV52 @ SV54 @ SV56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(294,plain,
( ( ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[291]) ).
thf(295,plain,
( ( cP_1 @ c @ c )
= $true ),
inference(extcnf_not_neg,[status(thm)],[292]) ).
thf(296,plain,
! [SV56: $i,SV54: $i,SV52: $i,SV51: $i,SV50: $i,SV49: $i] :
( ( ( ~ ( cQ_1 @ SV49 @ SV50 @ SV51 ) )
= $true )
| ( ( ~ ( cP_1 @ ( f @ SV49 ) @ SV52 ) )
= $true )
| ( ( ~ ( cP_1 @ ( f @ SV50 ) @ SV54 ) )
= $true )
| ( ( ~ ( cP_1 @ ( f @ SV51 ) @ SV56 ) )
= $true )
| ( ( cQ_2 @ SV52 @ SV54 @ SV56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(297,plain,
( ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(298,plain,
! [SV56: $i,SV54: $i,SV52: $i,SV51: $i,SV50: $i,SV49: $i] :
( ( ( cQ_1 @ SV49 @ SV50 @ SV51 )
= $false )
| ( ( ~ ( cP_1 @ ( f @ SV49 ) @ SV52 ) )
= $true )
| ( ( ~ ( cP_1 @ ( f @ SV50 ) @ SV54 ) )
= $true )
| ( ( ~ ( cP_1 @ ( f @ SV51 ) @ SV56 ) )
= $true )
| ( ( cQ_2 @ SV52 @ SV54 @ SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(299,plain,
( ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[297]) ).
thf(300,plain,
( ( ~ ( cP_1 @ b @ b ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[297]) ).
thf(301,plain,
! [SV56: $i,SV54: $i,SV51: $i,SV50: $i,SV52: $i,SV49: $i] :
( ( ( cP_1 @ ( f @ SV49 ) @ SV52 )
= $false )
| ( ( cQ_1 @ SV49 @ SV50 @ SV51 )
= $false )
| ( ( ~ ( cP_1 @ ( f @ SV50 ) @ SV54 ) )
= $true )
| ( ( ~ ( cP_1 @ ( f @ SV51 ) @ SV56 ) )
= $true )
| ( ( cQ_2 @ SV52 @ SV54 @ SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(302,plain,
( ( ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[299]) ).
thf(303,plain,
( ( cP_1 @ b @ b )
= $true ),
inference(extcnf_not_neg,[status(thm)],[300]) ).
thf(304,plain,
! [SV56: $i,SV52: $i,SV51: $i,SV49: $i,SV54: $i,SV50: $i] :
( ( ( cP_1 @ ( f @ SV50 ) @ SV54 )
= $false )
| ( ( cQ_1 @ SV49 @ SV50 @ SV51 )
= $false )
| ( ( cP_1 @ ( f @ SV49 ) @ SV52 )
= $false )
| ( ( ~ ( cP_1 @ ( f @ SV51 ) @ SV56 ) )
= $true )
| ( ( cQ_2 @ SV52 @ SV54 @ SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(305,plain,
( ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(306,plain,
! [SV54: $i,SV50: $i,SV52: $i,SV49: $i,SV56: $i,SV51: $i] :
( ( ( cP_1 @ ( f @ SV51 ) @ SV56 )
= $false )
| ( ( cP_1 @ ( f @ SV49 ) @ SV52 )
= $false )
| ( ( cQ_1 @ SV49 @ SV50 @ SV51 )
= $false )
| ( ( cP_1 @ ( f @ SV50 ) @ SV54 )
= $false )
| ( ( cQ_2 @ SV52 @ SV54 @ SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(307,plain,
( ( ~ ( cP_1 @ a @ a ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[305]) ).
thf(308,plain,
( ( ~ ( cQ_1 @ a @ b @ c ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[305]) ).
thf(309,plain,
( ( cP_1 @ a @ a )
= $true ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(310,plain,
( ( cQ_1 @ a @ b @ c )
= $true ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(311,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[21,310,309,306,303,295,288,287,261,257,254,246,239,238,212,208,205,197,190,189,163,159,156,148,141,140,114,110,107,99,92,91,65,61,58,50,43,42]) ).
thf(312,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[311]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO391^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jul 8 22:17:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.56
% 0.19/0.56 No.of.Axioms: 0
% 0.19/0.56
% 0.19/0.56 Length.of.Defs: 0
% 0.19/0.56
% 0.19/0.56 Contains.Choice.Funs: false
% 0.56/0.73 (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)......................................................
% 1.21/1.44
% 1.21/1.44 ********************************
% 1.21/1.44 * All subproblems solved! *
% 1.21/1.44 ********************************
% 1.21/1.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:311,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.33/1.51
% 1.33/1.51 %**** Beginning of derivation protocol ****
% 1.33/1.51 % SZS output start CNFRefutation
% See solution above
% 1.33/1.51
% 1.33/1.51 %**** End of derivation protocol ****
% 1.33/1.51 %**** no. of clauses in derivation: 312 ****
% 1.33/1.51 %**** clause counter: 311 ****
% 1.33/1.51
% 1.33/1.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:311,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------