%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYO387^5 : 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 : n021.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 17:33:44 EDT 2022
% Result : Theorem 0.61s 0.85s
% Output : CNFRefutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 83
% Number of leaves : 15
% Syntax : Number of formulae : 228 ( 173 unt; 14 typ; 0 def)
% Number of atoms : 3014 ( 324 equ; 0 cnn)
% Maximal formula atoms : 46 ( 14 avg)
% Number of connectives : 12143 (3899 ~;2002 |; 150 &;6092 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 41 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 1902 ( 0 ^1902 !; 0 ?;1902 :)
% 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_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_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 ) )
& ! [Xx: $i,Xy: $i,Xz: $i] :
~ ( cQ_5 @ Xx @ Xy @ Xz ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM409_4) ).
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 ) )
& ! [Xx: $i,Xy: $i,Xz: $i] :
~ ( cQ_5 @ 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 ) )
& ! [Xx: $i,Xy: $i,Xz: $i] :
~ ( cQ_5 @ 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 ) )
& ! [Xx: $i,Xy: $i,Xz: $i] :
~ ( cQ_5 @ Xx @ Xy @ Xz ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
~ ( cQ_5 @ Xx @ Xy @ Xz )
& ! [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 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
~ ( cQ_5 @ Xx @ Xy @ Xz )
& ! [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 ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( cQ_5 @ SX0 @ SX1 @ SX2 )
| ~ ~ ( ~ ! [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(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( cQ_5 @ SX0 @ SX1 @ SX2 )
| ~ ~ ( ~ ! [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)],[7]) ).
thf(9,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( cQ_5 @ 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_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)],[8]) ).
thf(11,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( cQ_5 @ 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_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)],[10]) ).
thf(13,plain,
! [SV1: $i] :
( ( ! [SY39: $i,SY40: $i] :
~ ( cQ_5 @ SV1 @ SY39 @ SY40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(14,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)],[12]) ).
thf(15,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY41: $i] :
~ ( cQ_5 @ SV1 @ SV2 @ SY41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(16,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)],[14]) ).
thf(17,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)],[14]) ).
thf(18,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ( cQ_5 @ 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_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)],[16]) ).
thf(20,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)],[17]) ).
thf(21,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( cQ_5 @ SV1 @ SV2 @ SV3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
! [SV4: $i] :
( ( ! [SY42: $i,SY43: $i,SY44: $i,SY45: $i,SY46: $i] :
( ( cQ_5 @ SY44 @ SY45 @ SY46 )
| ~ ( cQ_4 @ SV4 @ SY42 @ SY43 )
| ~ ( cP_4 @ ( f @ SV4 ) @ SY44 )
| ~ ( cP_4 @ ( f @ SY42 ) @ SY45 )
| ~ ( cP_4 @ ( f @ SY43 ) @ SY46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(23,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)],[20]) ).
thf(24,plain,
! [SV5: $i,SV4: $i] :
( ( ! [SY47: $i,SY48: $i,SY49: $i,SY50: $i] :
( ( cQ_5 @ SY48 @ SY49 @ SY50 )
| ~ ( cQ_4 @ SV4 @ SV5 @ SY47 )
| ~ ( cP_4 @ ( f @ SV4 ) @ SY48 )
| ~ ( cP_4 @ ( f @ SV5 ) @ SY49 )
| ~ ( cP_4 @ ( f @ SY47 ) @ SY50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(25,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(26,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)],[23]) ).
thf(27,plain,
! [SV6: $i,SV5: $i,SV4: $i] :
( ( ! [SY51: $i,SY52: $i,SY53: $i] :
( ( cQ_5 @ SY51 @ SY52 @ SY53 )
| ~ ( cQ_4 @ SV4 @ SV5 @ SV6 )
| ~ ( cP_4 @ ( f @ SV4 ) @ SY51 )
| ~ ( cP_4 @ ( f @ SV5 ) @ SY52 )
| ~ ( cP_4 @ ( f @ SV6 ) @ SY53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(28,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( cP_4 @ SX0 @ SX1 )
| ( cP_4 @ ( f @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(29,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)],[26]) ).
thf(30,plain,
! [SV6: $i,SV5: $i,SV4: $i,SV7: $i] :
( ( ! [SY54: $i,SY55: $i] :
( ( cQ_5 @ SV7 @ SY54 @ SY55 )
| ~ ( cQ_4 @ SV4 @ SV5 @ SV6 )
| ~ ( cP_4 @ ( f @ SV4 ) @ SV7 )
| ~ ( cP_4 @ ( f @ SV5 ) @ SY54 )
| ~ ( cP_4 @ ( f @ SV6 ) @ SY55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV8: $i] :
( ( ! [SY56: $i] :
( ~ ( cP_4 @ SV8 @ SY56 )
| ( cP_4 @ ( f @ SV8 ) @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(32,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)],[29]) ).
thf(33,plain,
! [SV6: $i,SV5: $i,SV4: $i,SV9: $i,SV7: $i] :
( ( ! [SY57: $i] :
( ( cQ_5 @ SV7 @ SV9 @ SY57 )
| ~ ( cQ_4 @ SV4 @ SV5 @ SV6 )
| ~ ( cP_4 @ ( f @ SV4 ) @ SV7 )
| ~ ( cP_4 @ ( f @ SV5 ) @ SV9 )
| ~ ( cP_4 @ ( f @ SV6 ) @ SY57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV10: $i,SV8: $i] :
( ( ~ ( cP_4 @ SV8 @ SV10 )
| ( cP_4 @ ( f @ SV8 ) @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(35,plain,
( ( ~ ! [SX0: $i] : ( cP_4 @ 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_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)],[32]) ).
thf(37,plain,
! [SV6: $i,SV5: $i,SV4: $i,SV11: $i,SV9: $i,SV7: $i] :
( ( ( cQ_5 @ SV7 @ SV9 @ SV11 )
| ~ ( cQ_4 @ SV4 @ SV5 @ SV6 )
| ~ ( cP_4 @ ( f @ SV4 ) @ SV7 )
| ~ ( cP_4 @ ( f @ SV5 ) @ SV9 )
| ~ ( cP_4 @ ( f @ SV6 ) @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV10: $i,SV8: $i] :
( ( ( ~ ( cP_4 @ SV8 @ SV10 ) )
= $true )
| ( ( cP_4 @ ( f @ SV8 ) @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(39,plain,
( ( ! [SX0: $i] : ( cP_4 @ 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_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)],[36]) ).
thf(41,plain,
! [SV6: $i,SV5: $i,SV4: $i,SV11: $i,SV9: $i,SV7: $i] :
( ( ( cQ_5 @ SV7 @ SV9 @ SV11 )
= $true )
| ( ( ~ ( cQ_4 @ SV4 @ SV5 @ SV6 )
| ~ ( cP_4 @ ( f @ SV4 ) @ SV7 )
| ~ ( cP_4 @ ( f @ SV5 ) @ SV9 )
| ~ ( cP_4 @ ( f @ SV6 ) @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV10: $i,SV8: $i] :
( ( ( cP_4 @ SV8 @ SV10 )
= $false )
| ( ( cP_4 @ ( f @ SV8 ) @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV12: $i] :
( ( cP_4 @ 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_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)],[40]) ).
thf(45,plain,
! [SV11: $i,SV9: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i] :
( ( ( ~ ( cQ_4 @ SV4 @ SV5 @ SV6 )
| ~ ( cP_4 @ ( f @ SV4 ) @ SV7 )
| ~ ( cP_4 @ ( f @ SV5 ) @ SV9 ) )
= $true )
| ( ( ~ ( cP_4 @ ( f @ SV6 ) @ SV11 ) )
= $true )
| ( ( cQ_5 @ 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_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)],[44]) ).
thf(47,plain,
( ( ~ ( cP_4 @ 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_4 @ SV4 @ SV5 @ SV6 )
| ~ ( cP_4 @ ( f @ SV4 ) @ SV7 ) )
= $true )
| ( ( ~ ( cP_4 @ ( f @ SV5 ) @ SV9 ) )
= $true )
| ( ( ~ ( cP_4 @ ( f @ SV6 ) @ SV11 ) )
= $true )
| ( ( cQ_5 @ 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_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)],[46]) ).
thf(50,plain,
( ( cP_4 @ 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_4 @ SV4 @ SV5 @ SV6 ) )
= $true )
| ( ( ~ ( cP_4 @ ( f @ SV4 ) @ SV7 ) )
= $true )
| ( ( ~ ( cP_4 @ ( f @ SV5 ) @ SV9 ) )
= $true )
| ( ( ~ ( cP_4 @ ( f @ SV6 ) @ SV11 ) )
= $true )
| ( ( cQ_5 @ 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_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)],[49]) ).
thf(53,plain,
! [SV11: $i,SV9: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i] :
( ( ( cQ_4 @ SV4 @ SV5 @ SV6 )
= $false )
| ( ( ~ ( cP_4 @ ( f @ SV4 ) @ SV7 ) )
= $true )
| ( ( ~ ( cP_4 @ ( f @ SV5 ) @ SV9 ) )
= $true )
| ( ( ~ ( cP_4 @ ( f @ SV6 ) @ SV11 ) )
= $true )
| ( ( cQ_5 @ 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_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)],[52]) ).
thf(55,plain,
( ( ~ ( cP_4 @ 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_4 @ ( f @ SV4 ) @ SV7 )
= $false )
| ( ( cQ_4 @ SV4 @ SV5 @ SV6 )
= $false )
| ( ( ~ ( cP_4 @ ( f @ SV5 ) @ SV9 ) )
= $true )
| ( ( ~ ( cP_4 @ ( f @ SV6 ) @ SV11 ) )
= $true )
| ( ( cQ_5 @ 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_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)],[54]) ).
thf(58,plain,
( ( cP_4 @ 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_4 @ ( f @ SV5 ) @ SV9 )
= $false )
| ( ( cQ_4 @ SV4 @ SV5 @ SV6 )
= $false )
| ( ( cP_4 @ ( f @ SV4 ) @ SV7 )
= $false )
| ( ( ~ ( cP_4 @ ( f @ SV6 ) @ SV11 ) )
= $true )
| ( ( cQ_5 @ 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_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)],[57]) ).
thf(61,plain,
! [SV9: $i,SV5: $i,SV7: $i,SV4: $i,SV11: $i,SV6: $i] :
( ( ( cP_4 @ ( f @ SV6 ) @ SV11 )
= $false )
| ( ( cP_4 @ ( f @ SV4 ) @ SV7 )
= $false )
| ( ( cQ_4 @ SV4 @ SV5 @ SV6 )
= $false )
| ( ( cP_4 @ ( f @ SV5 ) @ SV9 )
= $false )
| ( ( cQ_5 @ 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_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)],[60]) ).
thf(63,plain,
( ( ~ ( cP_4 @ 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_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)],[62]) ).
thf(65,plain,
( ( cP_4 @ 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_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)],[64]) ).
thf(67,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)],[66]) ).
thf(68,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)],[66]) ).
thf(69,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)],[67]) ).
thf(70,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)],[68]) ).
thf(71,plain,
! [SV13: $i] :
( ( ! [SY58: $i,SY59: $i,SY60: $i,SY61: $i,SY62: $i] :
( ( cQ_4 @ SY60 @ SY61 @ SY62 )
| ~ ( cQ_3 @ SV13 @ SY58 @ SY59 )
| ~ ( cP_3 @ ( f @ SV13 ) @ SY60 )
| ~ ( cP_3 @ ( f @ SY58 ) @ SY61 )
| ~ ( cP_3 @ ( f @ SY59 ) @ SY62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(72,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)],[70]) ).
thf(73,plain,
! [SV14: $i,SV13: $i] :
( ( ! [SY63: $i,SY64: $i,SY65: $i,SY66: $i] :
( ( cQ_4 @ SY64 @ SY65 @ SY66 )
| ~ ( cQ_3 @ SV13 @ SV14 @ SY63 )
| ~ ( cP_3 @ ( f @ SV13 ) @ SY64 )
| ~ ( cP_3 @ ( f @ SV14 ) @ SY65 )
| ~ ( cP_3 @ ( f @ SY63 ) @ SY66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(74,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(75,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)],[72]) ).
thf(76,plain,
! [SV15: $i,SV14: $i,SV13: $i] :
( ( ! [SY67: $i,SY68: $i,SY69: $i] :
( ( cQ_4 @ SY67 @ SY68 @ SY69 )
| ~ ( cQ_3 @ SV13 @ SV14 @ SV15 )
| ~ ( cP_3 @ ( f @ SV13 ) @ SY67 )
| ~ ( cP_3 @ ( f @ SV14 ) @ SY68 )
| ~ ( cP_3 @ ( f @ SV15 ) @ SY69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(77,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( cP_3 @ SX0 @ SX1 )
| ( cP_3 @ ( f @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(78,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)],[75]) ).
thf(79,plain,
! [SV15: $i,SV14: $i,SV13: $i,SV16: $i] :
( ( ! [SY70: $i,SY71: $i] :
( ( cQ_4 @ SV16 @ SY70 @ SY71 )
| ~ ( cQ_3 @ SV13 @ SV14 @ SV15 )
| ~ ( cP_3 @ ( f @ SV13 ) @ SV16 )
| ~ ( cP_3 @ ( f @ SV14 ) @ SY70 )
| ~ ( cP_3 @ ( f @ SV15 ) @ SY71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(80,plain,
! [SV17: $i] :
( ( ! [SY72: $i] :
( ~ ( cP_3 @ SV17 @ SY72 )
| ( cP_3 @ ( f @ SV17 ) @ SY72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(81,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)],[78]) ).
thf(82,plain,
! [SV15: $i,SV14: $i,SV13: $i,SV18: $i,SV16: $i] :
( ( ! [SY73: $i] :
( ( cQ_4 @ SV16 @ SV18 @ SY73 )
| ~ ( cQ_3 @ SV13 @ SV14 @ SV15 )
| ~ ( cP_3 @ ( f @ SV13 ) @ SV16 )
| ~ ( cP_3 @ ( f @ SV14 ) @ SV18 )
| ~ ( cP_3 @ ( f @ SV15 ) @ SY73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(83,plain,
! [SV19: $i,SV17: $i] :
( ( ~ ( cP_3 @ SV17 @ SV19 )
| ( cP_3 @ ( f @ SV17 ) @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(84,plain,
( ( ~ ! [SX0: $i] : ( cP_3 @ 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_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)],[81]) ).
thf(86,plain,
! [SV15: $i,SV14: $i,SV13: $i,SV20: $i,SV18: $i,SV16: $i] :
( ( ( cQ_4 @ SV16 @ SV18 @ SV20 )
| ~ ( cQ_3 @ SV13 @ SV14 @ SV15 )
| ~ ( cP_3 @ ( f @ SV13 ) @ SV16 )
| ~ ( cP_3 @ ( f @ SV14 ) @ SV18 )
| ~ ( cP_3 @ ( f @ SV15 ) @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(87,plain,
! [SV19: $i,SV17: $i] :
( ( ( ~ ( cP_3 @ SV17 @ SV19 ) )
= $true )
| ( ( cP_3 @ ( f @ SV17 ) @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(88,plain,
( ( ! [SX0: $i] : ( cP_3 @ 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_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)],[85]) ).
thf(90,plain,
! [SV15: $i,SV14: $i,SV13: $i,SV20: $i,SV18: $i,SV16: $i] :
( ( ( cQ_4 @ SV16 @ SV18 @ SV20 )
= $true )
| ( ( ~ ( cQ_3 @ SV13 @ SV14 @ SV15 )
| ~ ( cP_3 @ ( f @ SV13 ) @ SV16 )
| ~ ( cP_3 @ ( f @ SV14 ) @ SV18 )
| ~ ( cP_3 @ ( f @ SV15 ) @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(91,plain,
! [SV19: $i,SV17: $i] :
( ( ( cP_3 @ SV17 @ SV19 )
= $false )
| ( ( cP_3 @ ( f @ SV17 ) @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(92,plain,
! [SV21: $i] :
( ( cP_3 @ 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_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)],[89]) ).
thf(94,plain,
! [SV20: $i,SV18: $i,SV16: $i,SV15: $i,SV14: $i,SV13: $i] :
( ( ( ~ ( cQ_3 @ SV13 @ SV14 @ SV15 )
| ~ ( cP_3 @ ( f @ SV13 ) @ SV16 )
| ~ ( cP_3 @ ( f @ SV14 ) @ SV18 ) )
= $true )
| ( ( ~ ( cP_3 @ ( f @ SV15 ) @ SV20 ) )
= $true )
| ( ( cQ_4 @ 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_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)],[93]) ).
thf(96,plain,
( ( ~ ( cP_3 @ 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_3 @ SV13 @ SV14 @ SV15 )
| ~ ( cP_3 @ ( f @ SV13 ) @ SV16 ) )
= $true )
| ( ( ~ ( cP_3 @ ( f @ SV14 ) @ SV18 ) )
= $true )
| ( ( ~ ( cP_3 @ ( f @ SV15 ) @ SV20 ) )
= $true )
| ( ( cQ_4 @ 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_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)],[95]) ).
thf(99,plain,
( ( cP_3 @ 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_3 @ SV13 @ SV14 @ SV15 ) )
= $true )
| ( ( ~ ( cP_3 @ ( f @ SV13 ) @ SV16 ) )
= $true )
| ( ( ~ ( cP_3 @ ( f @ SV14 ) @ SV18 ) )
= $true )
| ( ( ~ ( cP_3 @ ( f @ SV15 ) @ SV20 ) )
= $true )
| ( ( cQ_4 @ 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_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)],[98]) ).
thf(102,plain,
! [SV20: $i,SV18: $i,SV16: $i,SV15: $i,SV14: $i,SV13: $i] :
( ( ( cQ_3 @ SV13 @ SV14 @ SV15 )
= $false )
| ( ( ~ ( cP_3 @ ( f @ SV13 ) @ SV16 ) )
= $true )
| ( ( ~ ( cP_3 @ ( f @ SV14 ) @ SV18 ) )
= $true )
| ( ( ~ ( cP_3 @ ( f @ SV15 ) @ SV20 ) )
= $true )
| ( ( cQ_4 @ 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_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)],[101]) ).
thf(104,plain,
( ( ~ ( cP_3 @ 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_3 @ ( f @ SV13 ) @ SV16 )
= $false )
| ( ( cQ_3 @ SV13 @ SV14 @ SV15 )
= $false )
| ( ( ~ ( cP_3 @ ( f @ SV14 ) @ SV18 ) )
= $true )
| ( ( ~ ( cP_3 @ ( f @ SV15 ) @ SV20 ) )
= $true )
| ( ( cQ_4 @ 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_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)],[103]) ).
thf(107,plain,
( ( cP_3 @ 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_3 @ ( f @ SV14 ) @ SV18 )
= $false )
| ( ( cQ_3 @ SV13 @ SV14 @ SV15 )
= $false )
| ( ( cP_3 @ ( f @ SV13 ) @ SV16 )
= $false )
| ( ( ~ ( cP_3 @ ( f @ SV15 ) @ SV20 ) )
= $true )
| ( ( cQ_4 @ 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_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)],[106]) ).
thf(110,plain,
! [SV18: $i,SV14: $i,SV16: $i,SV13: $i,SV20: $i,SV15: $i] :
( ( ( cP_3 @ ( f @ SV15 ) @ SV20 )
= $false )
| ( ( cP_3 @ ( f @ SV13 ) @ SV16 )
= $false )
| ( ( cQ_3 @ SV13 @ SV14 @ SV15 )
= $false )
| ( ( cP_3 @ ( f @ SV14 ) @ SV18 )
= $false )
| ( ( cQ_4 @ 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_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)],[109]) ).
thf(112,plain,
( ( ~ ( cP_3 @ 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_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)],[111]) ).
thf(114,plain,
( ( cP_3 @ 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_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)],[113]) ).
thf(116,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)],[115]) ).
thf(117,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)],[115]) ).
thf(118,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)],[116]) ).
thf(119,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)],[117]) ).
thf(120,plain,
! [SV22: $i] :
( ( ! [SY74: $i,SY75: $i,SY76: $i,SY77: $i,SY78: $i] :
( ( cQ_3 @ SY76 @ SY77 @ SY78 )
| ~ ( cQ_2 @ SV22 @ SY74 @ SY75 )
| ~ ( cP_2 @ ( f @ SV22 ) @ SY76 )
| ~ ( cP_2 @ ( f @ SY74 ) @ SY77 )
| ~ ( cP_2 @ ( f @ SY75 ) @ SY78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(121,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)],[119]) ).
thf(122,plain,
! [SV23: $i,SV22: $i] :
( ( ! [SY79: $i,SY80: $i,SY81: $i,SY82: $i] :
( ( cQ_3 @ SY80 @ SY81 @ SY82 )
| ~ ( cQ_2 @ SV22 @ SV23 @ SY79 )
| ~ ( cP_2 @ ( f @ SV22 ) @ SY80 )
| ~ ( cP_2 @ ( f @ SV23 ) @ SY81 )
| ~ ( cP_2 @ ( f @ SY79 ) @ SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(123,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(124,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)],[121]) ).
thf(125,plain,
! [SV24: $i,SV23: $i,SV22: $i] :
( ( ! [SY83: $i,SY84: $i,SY85: $i] :
( ( cQ_3 @ SY83 @ SY84 @ SY85 )
| ~ ( cQ_2 @ SV22 @ SV23 @ SV24 )
| ~ ( cP_2 @ ( f @ SV22 ) @ SY83 )
| ~ ( cP_2 @ ( f @ SV23 ) @ SY84 )
| ~ ( cP_2 @ ( f @ SV24 ) @ SY85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(126,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(127,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)],[124]) ).
thf(128,plain,
! [SV24: $i,SV23: $i,SV22: $i,SV25: $i] :
( ( ! [SY86: $i,SY87: $i] :
( ( cQ_3 @ SV25 @ SY86 @ SY87 )
| ~ ( cQ_2 @ SV22 @ SV23 @ SV24 )
| ~ ( cP_2 @ ( f @ SV22 ) @ SV25 )
| ~ ( cP_2 @ ( f @ SV23 ) @ SY86 )
| ~ ( cP_2 @ ( f @ SV24 ) @ SY87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(129,plain,
! [SV26: $i] :
( ( ! [SY88: $i] :
( ~ ( cP_2 @ SV26 @ SY88 )
| ( cP_2 @ ( f @ SV26 ) @ SY88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(130,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)],[127]) ).
thf(131,plain,
! [SV24: $i,SV23: $i,SV22: $i,SV27: $i,SV25: $i] :
( ( ! [SY89: $i] :
( ( cQ_3 @ SV25 @ SV27 @ SY89 )
| ~ ( cQ_2 @ SV22 @ SV23 @ SV24 )
| ~ ( cP_2 @ ( f @ SV22 ) @ SV25 )
| ~ ( cP_2 @ ( f @ SV23 ) @ SV27 )
| ~ ( cP_2 @ ( f @ SV24 ) @ SY89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(132,plain,
! [SV28: $i,SV26: $i] :
( ( ~ ( cP_2 @ SV26 @ SV28 )
| ( cP_2 @ ( f @ SV26 ) @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(133,plain,
( ( ~ ! [SX0: $i] : ( cP_2 @ 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_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)],[130]) ).
thf(135,plain,
! [SV24: $i,SV23: $i,SV22: $i,SV29: $i,SV27: $i,SV25: $i] :
( ( ( cQ_3 @ SV25 @ SV27 @ SV29 )
| ~ ( cQ_2 @ SV22 @ SV23 @ SV24 )
| ~ ( cP_2 @ ( f @ SV22 ) @ SV25 )
| ~ ( cP_2 @ ( f @ SV23 ) @ SV27 )
| ~ ( cP_2 @ ( f @ SV24 ) @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(136,plain,
! [SV28: $i,SV26: $i] :
( ( ( ~ ( cP_2 @ SV26 @ SV28 ) )
= $true )
| ( ( cP_2 @ ( f @ SV26 ) @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(137,plain,
( ( ! [SX0: $i] : ( cP_2 @ 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_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)],[134]) ).
thf(139,plain,
! [SV24: $i,SV23: $i,SV22: $i,SV29: $i,SV27: $i,SV25: $i] :
( ( ( cQ_3 @ SV25 @ SV27 @ SV29 )
= $true )
| ( ( ~ ( cQ_2 @ SV22 @ SV23 @ SV24 )
| ~ ( cP_2 @ ( f @ SV22 ) @ SV25 )
| ~ ( cP_2 @ ( f @ SV23 ) @ SV27 )
| ~ ( cP_2 @ ( f @ SV24 ) @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(140,plain,
! [SV28: $i,SV26: $i] :
( ( ( cP_2 @ SV26 @ SV28 )
= $false )
| ( ( cP_2 @ ( f @ SV26 ) @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(141,plain,
! [SV30: $i] :
( ( cP_2 @ 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_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)],[138]) ).
thf(143,plain,
! [SV29: $i,SV27: $i,SV25: $i,SV24: $i,SV23: $i,SV22: $i] :
( ( ( ~ ( cQ_2 @ SV22 @ SV23 @ SV24 )
| ~ ( cP_2 @ ( f @ SV22 ) @ SV25 )
| ~ ( cP_2 @ ( f @ SV23 ) @ SV27 ) )
= $true )
| ( ( ~ ( cP_2 @ ( f @ SV24 ) @ SV29 ) )
= $true )
| ( ( cQ_3 @ 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_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)],[142]) ).
thf(145,plain,
( ( ~ ( cP_2 @ 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_2 @ SV22 @ SV23 @ SV24 )
| ~ ( cP_2 @ ( f @ SV22 ) @ SV25 ) )
= $true )
| ( ( ~ ( cP_2 @ ( f @ SV23 ) @ SV27 ) )
= $true )
| ( ( ~ ( cP_2 @ ( f @ SV24 ) @ SV29 ) )
= $true )
| ( ( cQ_3 @ 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_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)],[144]) ).
thf(148,plain,
( ( cP_2 @ 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_2 @ SV22 @ SV23 @ SV24 ) )
= $true )
| ( ( ~ ( cP_2 @ ( f @ SV22 ) @ SV25 ) )
= $true )
| ( ( ~ ( cP_2 @ ( f @ SV23 ) @ SV27 ) )
= $true )
| ( ( ~ ( cP_2 @ ( f @ SV24 ) @ SV29 ) )
= $true )
| ( ( cQ_3 @ 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_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)],[147]) ).
thf(151,plain,
! [SV29: $i,SV27: $i,SV25: $i,SV24: $i,SV23: $i,SV22: $i] :
( ( ( cQ_2 @ SV22 @ SV23 @ SV24 )
= $false )
| ( ( ~ ( cP_2 @ ( f @ SV22 ) @ SV25 ) )
= $true )
| ( ( ~ ( cP_2 @ ( f @ SV23 ) @ SV27 ) )
= $true )
| ( ( ~ ( cP_2 @ ( f @ SV24 ) @ SV29 ) )
= $true )
| ( ( cQ_3 @ 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_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)],[150]) ).
thf(153,plain,
( ( ~ ( cP_2 @ 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_2 @ ( f @ SV22 ) @ SV25 )
= $false )
| ( ( cQ_2 @ SV22 @ SV23 @ SV24 )
= $false )
| ( ( ~ ( cP_2 @ ( f @ SV23 ) @ SV27 ) )
= $true )
| ( ( ~ ( cP_2 @ ( f @ SV24 ) @ SV29 ) )
= $true )
| ( ( cQ_3 @ 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_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)],[152]) ).
thf(156,plain,
( ( cP_2 @ 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_2 @ ( f @ SV23 ) @ SV27 )
= $false )
| ( ( cQ_2 @ SV22 @ SV23 @ SV24 )
= $false )
| ( ( cP_2 @ ( f @ SV22 ) @ SV25 )
= $false )
| ( ( ~ ( cP_2 @ ( f @ SV24 ) @ SV29 ) )
= $true )
| ( ( cQ_3 @ 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_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)],[155]) ).
thf(159,plain,
! [SV27: $i,SV23: $i,SV25: $i,SV22: $i,SV29: $i,SV24: $i] :
( ( ( cP_2 @ ( f @ SV24 ) @ SV29 )
= $false )
| ( ( cP_2 @ ( f @ SV22 ) @ SV25 )
= $false )
| ( ( cQ_2 @ SV22 @ SV23 @ SV24 )
= $false )
| ( ( cP_2 @ ( f @ SV23 ) @ SV27 )
= $false )
| ( ( cQ_3 @ 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_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)],[158]) ).
thf(161,plain,
( ( ~ ( cP_2 @ 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_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)],[160]) ).
thf(163,plain,
( ( cP_2 @ 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_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)],[162]) ).
thf(165,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)],[164]) ).
thf(166,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)],[164]) ).
thf(167,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)],[165]) ).
thf(168,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)],[166]) ).
thf(169,plain,
! [SV31: $i] :
( ( ! [SY90: $i,SY91: $i,SY92: $i,SY93: $i,SY94: $i] :
( ( cQ_2 @ SY92 @ SY93 @ SY94 )
| ~ ( cQ_1 @ SV31 @ SY90 @ SY91 )
| ~ ( cP_1 @ ( f @ SV31 ) @ SY92 )
| ~ ( cP_1 @ ( f @ SY90 ) @ SY93 )
| ~ ( cP_1 @ ( f @ SY91 ) @ SY94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(170,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)],[168]) ).
thf(171,plain,
! [SV32: $i,SV31: $i] :
( ( ! [SY95: $i,SY96: $i,SY97: $i,SY98: $i] :
( ( cQ_2 @ SY96 @ SY97 @ SY98 )
| ~ ( cQ_1 @ SV31 @ SV32 @ SY95 )
| ~ ( cP_1 @ ( f @ SV31 ) @ SY96 )
| ~ ( cP_1 @ ( f @ SV32 ) @ SY97 )
| ~ ( cP_1 @ ( f @ SY95 ) @ SY98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(172,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(173,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)],[170]) ).
thf(174,plain,
! [SV33: $i,SV32: $i,SV31: $i] :
( ( ! [SY99: $i,SY100: $i,SY101: $i] :
( ( cQ_2 @ SY99 @ SY100 @ SY101 )
| ~ ( cQ_1 @ SV31 @ SV32 @ SV33 )
| ~ ( cP_1 @ ( f @ SV31 ) @ SY99 )
| ~ ( cP_1 @ ( f @ SV32 ) @ SY100 )
| ~ ( cP_1 @ ( f @ SV33 ) @ SY101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(175,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(176,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)],[173]) ).
thf(177,plain,
! [SV33: $i,SV32: $i,SV31: $i,SV34: $i] :
( ( ! [SY102: $i,SY103: $i] :
( ( cQ_2 @ SV34 @ SY102 @ SY103 )
| ~ ( cQ_1 @ SV31 @ SV32 @ SV33 )
| ~ ( cP_1 @ ( f @ SV31 ) @ SV34 )
| ~ ( cP_1 @ ( f @ SV32 ) @ SY102 )
| ~ ( cP_1 @ ( f @ SV33 ) @ SY103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(178,plain,
! [SV35: $i] :
( ( ! [SY104: $i] :
( ~ ( cP_1 @ SV35 @ SY104 )
| ( cP_1 @ ( f @ SV35 ) @ SY104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(179,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)],[176]) ).
thf(180,plain,
! [SV33: $i,SV32: $i,SV31: $i,SV36: $i,SV34: $i] :
( ( ! [SY105: $i] :
( ( cQ_2 @ SV34 @ SV36 @ SY105 )
| ~ ( cQ_1 @ SV31 @ SV32 @ SV33 )
| ~ ( cP_1 @ ( f @ SV31 ) @ SV34 )
| ~ ( cP_1 @ ( f @ SV32 ) @ SV36 )
| ~ ( cP_1 @ ( f @ SV33 ) @ SY105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(181,plain,
! [SV37: $i,SV35: $i] :
( ( ~ ( cP_1 @ SV35 @ SV37 )
| ( cP_1 @ ( f @ SV35 ) @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(182,plain,
( ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(183,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)],[179]) ).
thf(184,plain,
! [SV33: $i,SV32: $i,SV31: $i,SV38: $i,SV36: $i,SV34: $i] :
( ( ( cQ_2 @ SV34 @ SV36 @ SV38 )
| ~ ( cQ_1 @ SV31 @ SV32 @ SV33 )
| ~ ( cP_1 @ ( f @ SV31 ) @ SV34 )
| ~ ( cP_1 @ ( f @ SV32 ) @ SV36 )
| ~ ( cP_1 @ ( f @ SV33 ) @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(185,plain,
! [SV37: $i,SV35: $i] :
( ( ( ~ ( cP_1 @ SV35 @ SV37 ) )
= $true )
| ( ( cP_1 @ ( f @ SV35 ) @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(186,plain,
( ( ! [SX0: $i] : ( cP_1 @ d @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(187,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)],[183]) ).
thf(188,plain,
! [SV33: $i,SV32: $i,SV31: $i,SV38: $i,SV36: $i,SV34: $i] :
( ( ( cQ_2 @ SV34 @ SV36 @ SV38 )
= $true )
| ( ( ~ ( cQ_1 @ SV31 @ SV32 @ SV33 )
| ~ ( cP_1 @ ( f @ SV31 ) @ SV34 )
| ~ ( cP_1 @ ( f @ SV32 ) @ SV36 )
| ~ ( cP_1 @ ( f @ SV33 ) @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(189,plain,
! [SV37: $i,SV35: $i] :
( ( ( cP_1 @ SV35 @ SV37 )
= $false )
| ( ( cP_1 @ ( f @ SV35 ) @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(190,plain,
! [SV39: $i] :
( ( cP_1 @ d @ SV39 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(191,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)],[187]) ).
thf(192,plain,
! [SV38: $i,SV36: $i,SV34: $i,SV33: $i,SV32: $i,SV31: $i] :
( ( ( ~ ( cQ_1 @ SV31 @ SV32 @ SV33 )
| ~ ( cP_1 @ ( f @ SV31 ) @ SV34 )
| ~ ( cP_1 @ ( f @ SV32 ) @ SV36 ) )
= $true )
| ( ( ~ ( cP_1 @ ( f @ SV33 ) @ SV38 ) )
= $true )
| ( ( cQ_2 @ SV34 @ SV36 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(193,plain,
( ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[191]) ).
thf(194,plain,
( ( ~ ( cP_1 @ 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_1 @ SV31 @ SV32 @ SV33 )
| ~ ( cP_1 @ ( f @ SV31 ) @ SV34 ) )
= $true )
| ( ( ~ ( cP_1 @ ( f @ SV32 ) @ SV36 ) )
= $true )
| ( ( ~ ( cP_1 @ ( f @ SV33 ) @ SV38 ) )
= $true )
| ( ( cQ_2 @ SV34 @ SV36 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(196,plain,
( ( ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(197,plain,
( ( cP_1 @ 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_1 @ SV31 @ SV32 @ SV33 ) )
= $true )
| ( ( ~ ( cP_1 @ ( f @ SV31 ) @ SV34 ) )
= $true )
| ( ( ~ ( cP_1 @ ( f @ SV32 ) @ SV36 ) )
= $true )
| ( ( ~ ( cP_1 @ ( f @ SV33 ) @ SV38 ) )
= $true )
| ( ( cQ_2 @ SV34 @ SV36 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(199,plain,
( ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ 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_1 @ SV31 @ SV32 @ SV33 )
= $false )
| ( ( ~ ( cP_1 @ ( f @ SV31 ) @ SV34 ) )
= $true )
| ( ( ~ ( cP_1 @ ( f @ SV32 ) @ SV36 ) )
= $true )
| ( ( ~ ( cP_1 @ ( f @ SV33 ) @ SV38 ) )
= $true )
| ( ( cQ_2 @ SV34 @ SV36 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(201,plain,
( ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(202,plain,
( ( ~ ( cP_1 @ 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_1 @ ( f @ SV31 ) @ SV34 )
= $false )
| ( ( cQ_1 @ SV31 @ SV32 @ SV33 )
= $false )
| ( ( ~ ( cP_1 @ ( f @ SV32 ) @ SV36 ) )
= $true )
| ( ( ~ ( cP_1 @ ( f @ SV33 ) @ SV38 ) )
= $true )
| ( ( cQ_2 @ SV34 @ SV36 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(204,plain,
( ( ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(205,plain,
( ( cP_1 @ 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_1 @ ( f @ SV32 ) @ SV36 )
= $false )
| ( ( cQ_1 @ SV31 @ SV32 @ SV33 )
= $false )
| ( ( cP_1 @ ( f @ SV31 ) @ SV34 )
= $false )
| ( ( ~ ( cP_1 @ ( f @ SV33 ) @ SV38 ) )
= $true )
| ( ( cQ_2 @ SV34 @ SV36 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(207,plain,
( ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(208,plain,
! [SV36: $i,SV32: $i,SV34: $i,SV31: $i,SV38: $i,SV33: $i] :
( ( ( cP_1 @ ( f @ SV33 ) @ SV38 )
= $false )
| ( ( cP_1 @ ( f @ SV31 ) @ SV34 )
= $false )
| ( ( cQ_1 @ SV31 @ SV32 @ SV33 )
= $false )
| ( ( cP_1 @ ( f @ SV32 ) @ SV36 )
= $false )
| ( ( cQ_2 @ SV34 @ SV36 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(209,plain,
( ( ~ ( cP_1 @ a @ a ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(210,plain,
( ( ~ ( cQ_1 @ a @ b @ c ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(211,plain,
( ( cP_1 @ a @ a )
= $true ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(212,plain,
( ( cQ_1 @ a @ b @ c )
= $true ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(213,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[21,212,211,208,205,197,190,189,163,159,156,148,141,140,114,110,107,99,92,91,65,61,58,50,43,42]) ).
thf(214,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[213]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO387^5 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Fri Jul 8 21:53:05 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.44
% 0.19/0.44 No.of.Axioms: 0
% 0.19/0.44
% 0.19/0.44 Length.of.Defs: 0
% 0.19/0.44
% 0.19/0.44 Contains.Choice.Funs: false
% 0.19/0.54 (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)...........................
% 0.61/0.85
% 0.61/0.85 ********************************
% 0.61/0.85 * All subproblems solved! *
% 0.61/0.85 ********************************
% 0.61/0.85 % 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:213,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.69/0.87
% 0.69/0.87 %**** Beginning of derivation protocol ****
% 0.69/0.87 % SZS output start CNFRefutation
% See solution above
% 0.69/0.88
% 0.69/0.88 %**** End of derivation protocol ****
% 0.69/0.88 %**** no. of clauses in derivation: 214 ****
% 0.69/0.88 %**** clause counter: 213 ****
% 0.69/0.88
% 0.69/0.88 % 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:213,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------