TSTP Solution File: SYO385^5 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYO385^5 : 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 17:33:43 EDT 2022
% Result : Theorem 0.20s 0.52s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 11
% Syntax : Number of formulae : 126 ( 95 unt; 10 typ; 0 def)
% Number of atoms : 1140 ( 170 equ; 0 cnn)
% Maximal formula atoms : 24 ( 9 avg)
% Number of connectives : 3891 (1133 ~; 606 |; 78 &;2074 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 648 ( 0 ^ 648 !; 0 ?; 648 :)
% 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_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_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 ) )
& ! [Xx: $i,Xy: $i,Xz: $i] :
~ ( cQ_3 @ Xx @ Xy @ Xz ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM409_2) ).
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 ) )
& ! [Xx: $i,Xy: $i,Xz: $i] :
~ ( cQ_3 @ 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 ) )
& ! [Xx: $i,Xy: $i,Xz: $i] :
~ ( cQ_3 @ 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 ) )
& ! [Xx: $i,Xy: $i,Xz: $i] :
~ ( cQ_3 @ Xx @ Xy @ Xz ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
~ ( cQ_3 @ Xx @ Xy @ Xz )
& ! [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 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
~ ( cQ_3 @ Xx @ Xy @ Xz )
& ! [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 ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ~ ( ~ ! [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(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( cQ_3 @ SX0 @ SX1 @ SX2 )
| ~ ~ ( ~ ! [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)],[7]) ).
thf(9,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( cQ_3 @ 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_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)],[8]) ).
thf(11,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( cQ_3 @ 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_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)],[10]) ).
thf(13,plain,
! [SV1: $i] :
( ( ! [SY21: $i,SY22: $i] :
~ ( cQ_3 @ SV1 @ SY21 @ SY22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(14,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)],[12]) ).
thf(15,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY23: $i] :
~ ( cQ_3 @ SV1 @ SV2 @ SY23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(16,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)],[14]) ).
thf(17,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)],[14]) ).
thf(18,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ( cQ_3 @ 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_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)],[16]) ).
thf(20,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)],[17]) ).
thf(21,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( cQ_3 @ SV1 @ SV2 @ SV3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
! [SV4: $i] :
( ( ! [SY24: $i,SY25: $i,SY26: $i,SY27: $i,SY28: $i] :
( ( cQ_3 @ SY26 @ SY27 @ SY28 )
| ~ ( cQ_2 @ SV4 @ SY24 @ SY25 )
| ~ ( cP_2 @ ( f @ SV4 ) @ SY26 )
| ~ ( cP_2 @ ( f @ SY24 ) @ SY27 )
| ~ ( cP_2 @ ( f @ SY25 ) @ SY28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(23,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)],[20]) ).
thf(24,plain,
! [SV5: $i,SV4: $i] :
( ( ! [SY29: $i,SY30: $i,SY31: $i,SY32: $i] :
( ( cQ_3 @ SY30 @ SY31 @ SY32 )
| ~ ( cQ_2 @ SV4 @ SV5 @ SY29 )
| ~ ( cP_2 @ ( f @ SV4 ) @ SY30 )
| ~ ( cP_2 @ ( f @ SV5 ) @ SY31 )
| ~ ( cP_2 @ ( f @ SY29 ) @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(25,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(26,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)],[23]) ).
thf(27,plain,
! [SV6: $i,SV5: $i,SV4: $i] :
( ( ! [SY33: $i,SY34: $i,SY35: $i] :
( ( cQ_3 @ SY33 @ SY34 @ SY35 )
| ~ ( cQ_2 @ SV4 @ SV5 @ SV6 )
| ~ ( cP_2 @ ( f @ SV4 ) @ SY33 )
| ~ ( cP_2 @ ( f @ SV5 ) @ SY34 )
| ~ ( cP_2 @ ( f @ SV6 ) @ SY35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(28,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( cP_2 @ SX0 @ SX1 )
| ( cP_2 @ ( f @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(29,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)],[26]) ).
thf(30,plain,
! [SV6: $i,SV5: $i,SV4: $i,SV7: $i] :
( ( ! [SY36: $i,SY37: $i] :
( ( cQ_3 @ SV7 @ SY36 @ SY37 )
| ~ ( cQ_2 @ SV4 @ SV5 @ SV6 )
| ~ ( cP_2 @ ( f @ SV4 ) @ SV7 )
| ~ ( cP_2 @ ( f @ SV5 ) @ SY36 )
| ~ ( cP_2 @ ( f @ SV6 ) @ SY37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV8: $i] :
( ( ! [SY38: $i] :
( ~ ( cP_2 @ SV8 @ SY38 )
| ( cP_2 @ ( f @ SV8 ) @ SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(32,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)],[29]) ).
thf(33,plain,
! [SV6: $i,SV5: $i,SV4: $i,SV9: $i,SV7: $i] :
( ( ! [SY39: $i] :
( ( cQ_3 @ SV7 @ SV9 @ SY39 )
| ~ ( cQ_2 @ SV4 @ SV5 @ SV6 )
| ~ ( cP_2 @ ( f @ SV4 ) @ SV7 )
| ~ ( cP_2 @ ( f @ SV5 ) @ SV9 )
| ~ ( cP_2 @ ( f @ SV6 ) @ SY39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV10: $i,SV8: $i] :
( ( ~ ( cP_2 @ SV8 @ SV10 )
| ( cP_2 @ ( f @ SV8 ) @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(35,plain,
( ( ~ ! [SX0: $i] : ( cP_2 @ 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_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)],[32]) ).
thf(37,plain,
! [SV6: $i,SV5: $i,SV4: $i,SV11: $i,SV9: $i,SV7: $i] :
( ( ( cQ_3 @ SV7 @ SV9 @ SV11 )
| ~ ( cQ_2 @ SV4 @ SV5 @ SV6 )
| ~ ( cP_2 @ ( f @ SV4 ) @ SV7 )
| ~ ( cP_2 @ ( f @ SV5 ) @ SV9 )
| ~ ( cP_2 @ ( f @ SV6 ) @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV10: $i,SV8: $i] :
( ( ( ~ ( cP_2 @ SV8 @ SV10 ) )
= $true )
| ( ( cP_2 @ ( f @ SV8 ) @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(39,plain,
( ( ! [SX0: $i] : ( cP_2 @ 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_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)],[36]) ).
thf(41,plain,
! [SV6: $i,SV5: $i,SV4: $i,SV11: $i,SV9: $i,SV7: $i] :
( ( ( cQ_3 @ SV7 @ SV9 @ SV11 )
= $true )
| ( ( ~ ( cQ_2 @ SV4 @ SV5 @ SV6 )
| ~ ( cP_2 @ ( f @ SV4 ) @ SV7 )
| ~ ( cP_2 @ ( f @ SV5 ) @ SV9 )
| ~ ( cP_2 @ ( f @ SV6 ) @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV10: $i,SV8: $i] :
( ( ( cP_2 @ SV8 @ SV10 )
= $false )
| ( ( cP_2 @ ( f @ SV8 ) @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV12: $i] :
( ( cP_2 @ 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_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)],[40]) ).
thf(45,plain,
! [SV11: $i,SV9: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i] :
( ( ( ~ ( cQ_2 @ SV4 @ SV5 @ SV6 )
| ~ ( cP_2 @ ( f @ SV4 ) @ SV7 )
| ~ ( cP_2 @ ( f @ SV5 ) @ SV9 ) )
= $true )
| ( ( ~ ( cP_2 @ ( f @ SV6 ) @ SV11 ) )
= $true )
| ( ( cQ_3 @ 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_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)],[44]) ).
thf(47,plain,
( ( ~ ( cP_2 @ 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_2 @ SV4 @ SV5 @ SV6 )
| ~ ( cP_2 @ ( f @ SV4 ) @ SV7 ) )
= $true )
| ( ( ~ ( cP_2 @ ( f @ SV5 ) @ SV9 ) )
= $true )
| ( ( ~ ( cP_2 @ ( f @ SV6 ) @ SV11 ) )
= $true )
| ( ( cQ_3 @ 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_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)],[46]) ).
thf(50,plain,
( ( cP_2 @ 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_2 @ SV4 @ SV5 @ SV6 ) )
= $true )
| ( ( ~ ( cP_2 @ ( f @ SV4 ) @ SV7 ) )
= $true )
| ( ( ~ ( cP_2 @ ( f @ SV5 ) @ SV9 ) )
= $true )
| ( ( ~ ( cP_2 @ ( f @ SV6 ) @ SV11 ) )
= $true )
| ( ( cQ_3 @ 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_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)],[49]) ).
thf(53,plain,
! [SV11: $i,SV9: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i] :
( ( ( cQ_2 @ SV4 @ SV5 @ SV6 )
= $false )
| ( ( ~ ( cP_2 @ ( f @ SV4 ) @ SV7 ) )
= $true )
| ( ( ~ ( cP_2 @ ( f @ SV5 ) @ SV9 ) )
= $true )
| ( ( ~ ( cP_2 @ ( f @ SV6 ) @ SV11 ) )
= $true )
| ( ( cQ_3 @ 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_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)],[52]) ).
thf(55,plain,
( ( ~ ( cP_2 @ 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_2 @ ( f @ SV4 ) @ SV7 )
= $false )
| ( ( cQ_2 @ SV4 @ SV5 @ SV6 )
= $false )
| ( ( ~ ( cP_2 @ ( f @ SV5 ) @ SV9 ) )
= $true )
| ( ( ~ ( cP_2 @ ( f @ SV6 ) @ SV11 ) )
= $true )
| ( ( cQ_3 @ 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_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)],[54]) ).
thf(58,plain,
( ( cP_2 @ 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_2 @ ( f @ SV5 ) @ SV9 )
= $false )
| ( ( cQ_2 @ SV4 @ SV5 @ SV6 )
= $false )
| ( ( cP_2 @ ( f @ SV4 ) @ SV7 )
= $false )
| ( ( ~ ( cP_2 @ ( f @ SV6 ) @ SV11 ) )
= $true )
| ( ( cQ_3 @ 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_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)],[57]) ).
thf(61,plain,
! [SV9: $i,SV5: $i,SV7: $i,SV4: $i,SV11: $i,SV6: $i] :
( ( ( cP_2 @ ( f @ SV6 ) @ SV11 )
= $false )
| ( ( cP_2 @ ( f @ SV4 ) @ SV7 )
= $false )
| ( ( cQ_2 @ SV4 @ SV5 @ SV6 )
= $false )
| ( ( cP_2 @ ( f @ SV5 ) @ SV9 )
= $false )
| ( ( cQ_3 @ 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_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)],[60]) ).
thf(63,plain,
( ( ~ ( cP_2 @ 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_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)],[62]) ).
thf(65,plain,
( ( cP_2 @ 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_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)],[64]) ).
thf(67,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)],[66]) ).
thf(68,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)],[66]) ).
thf(69,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)],[67]) ).
thf(70,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)],[68]) ).
thf(71,plain,
! [SV13: $i] :
( ( ! [SY40: $i,SY41: $i,SY42: $i,SY43: $i,SY44: $i] :
( ( cQ_2 @ SY42 @ SY43 @ SY44 )
| ~ ( cQ_1 @ SV13 @ SY40 @ SY41 )
| ~ ( cP_1 @ ( f @ SV13 ) @ SY42 )
| ~ ( cP_1 @ ( f @ SY40 ) @ SY43 )
| ~ ( cP_1 @ ( f @ SY41 ) @ SY44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(72,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)],[70]) ).
thf(73,plain,
! [SV14: $i,SV13: $i] :
( ( ! [SY45: $i,SY46: $i,SY47: $i,SY48: $i] :
( ( cQ_2 @ SY46 @ SY47 @ SY48 )
| ~ ( cQ_1 @ SV13 @ SV14 @ SY45 )
| ~ ( cP_1 @ ( f @ SV13 ) @ SY46 )
| ~ ( cP_1 @ ( f @ SV14 ) @ SY47 )
| ~ ( cP_1 @ ( f @ SY45 ) @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(74,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(75,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)],[72]) ).
thf(76,plain,
! [SV15: $i,SV14: $i,SV13: $i] :
( ( ! [SY49: $i,SY50: $i,SY51: $i] :
( ( cQ_2 @ SY49 @ SY50 @ SY51 )
| ~ ( cQ_1 @ SV13 @ SV14 @ SV15 )
| ~ ( cP_1 @ ( f @ SV13 ) @ SY49 )
| ~ ( cP_1 @ ( f @ SV14 ) @ SY50 )
| ~ ( cP_1 @ ( f @ SV15 ) @ SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(77,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( cP_1 @ SX0 @ SX1 )
| ( cP_1 @ ( f @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(78,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)],[75]) ).
thf(79,plain,
! [SV15: $i,SV14: $i,SV13: $i,SV16: $i] :
( ( ! [SY52: $i,SY53: $i] :
( ( cQ_2 @ SV16 @ SY52 @ SY53 )
| ~ ( cQ_1 @ SV13 @ SV14 @ SV15 )
| ~ ( cP_1 @ ( f @ SV13 ) @ SV16 )
| ~ ( cP_1 @ ( f @ SV14 ) @ SY52 )
| ~ ( cP_1 @ ( f @ SV15 ) @ SY53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(80,plain,
! [SV17: $i] :
( ( ! [SY54: $i] :
( ~ ( cP_1 @ SV17 @ SY54 )
| ( cP_1 @ ( f @ SV17 ) @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(81,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)],[78]) ).
thf(82,plain,
! [SV15: $i,SV14: $i,SV13: $i,SV18: $i,SV16: $i] :
( ( ! [SY55: $i] :
( ( cQ_2 @ SV16 @ SV18 @ SY55 )
| ~ ( cQ_1 @ SV13 @ SV14 @ SV15 )
| ~ ( cP_1 @ ( f @ SV13 ) @ SV16 )
| ~ ( cP_1 @ ( f @ SV14 ) @ SV18 )
| ~ ( cP_1 @ ( f @ SV15 ) @ SY55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(83,plain,
! [SV19: $i,SV17: $i] :
( ( ~ ( cP_1 @ SV17 @ SV19 )
| ( cP_1 @ ( f @ SV17 ) @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(84,plain,
( ( ~ ! [SX0: $i] : ( cP_1 @ d @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(85,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)],[81]) ).
thf(86,plain,
! [SV15: $i,SV14: $i,SV13: $i,SV20: $i,SV18: $i,SV16: $i] :
( ( ( cQ_2 @ SV16 @ SV18 @ SV20 )
| ~ ( cQ_1 @ SV13 @ SV14 @ SV15 )
| ~ ( cP_1 @ ( f @ SV13 ) @ SV16 )
| ~ ( cP_1 @ ( f @ SV14 ) @ SV18 )
| ~ ( cP_1 @ ( f @ SV15 ) @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(87,plain,
! [SV19: $i,SV17: $i] :
( ( ( ~ ( cP_1 @ SV17 @ SV19 ) )
= $true )
| ( ( cP_1 @ ( f @ SV17 ) @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(88,plain,
( ( ! [SX0: $i] : ( cP_1 @ d @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(89,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)],[85]) ).
thf(90,plain,
! [SV15: $i,SV14: $i,SV13: $i,SV20: $i,SV18: $i,SV16: $i] :
( ( ( cQ_2 @ SV16 @ SV18 @ SV20 )
= $true )
| ( ( ~ ( cQ_1 @ SV13 @ SV14 @ SV15 )
| ~ ( cP_1 @ ( f @ SV13 ) @ SV16 )
| ~ ( cP_1 @ ( f @ SV14 ) @ SV18 )
| ~ ( cP_1 @ ( f @ SV15 ) @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(91,plain,
! [SV19: $i,SV17: $i] :
( ( ( cP_1 @ SV17 @ SV19 )
= $false )
| ( ( cP_1 @ ( f @ SV17 ) @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(92,plain,
! [SV21: $i] :
( ( cP_1 @ d @ SV21 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(93,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)],[89]) ).
thf(94,plain,
! [SV20: $i,SV18: $i,SV16: $i,SV15: $i,SV14: $i,SV13: $i] :
( ( ( ~ ( cQ_1 @ SV13 @ SV14 @ SV15 )
| ~ ( cP_1 @ ( f @ SV13 ) @ SV16 )
| ~ ( cP_1 @ ( f @ SV14 ) @ SV18 ) )
= $true )
| ( ( ~ ( cP_1 @ ( f @ SV15 ) @ SV20 ) )
= $true )
| ( ( cQ_2 @ SV16 @ SV18 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(95,plain,
( ( ~ ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(96,plain,
( ( ~ ( cP_1 @ 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_1 @ SV13 @ SV14 @ SV15 )
| ~ ( cP_1 @ ( f @ SV13 ) @ SV16 ) )
= $true )
| ( ( ~ ( cP_1 @ ( f @ SV14 ) @ SV18 ) )
= $true )
| ( ( ~ ( cP_1 @ ( f @ SV15 ) @ SV20 ) )
= $true )
| ( ( cQ_2 @ SV16 @ SV18 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(98,plain,
( ( ~ ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ b @ b ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(99,plain,
( ( cP_1 @ 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_1 @ SV13 @ SV14 @ SV15 ) )
= $true )
| ( ( ~ ( cP_1 @ ( f @ SV13 ) @ SV16 ) )
= $true )
| ( ( ~ ( cP_1 @ ( f @ SV14 ) @ SV18 ) )
= $true )
| ( ( ~ ( cP_1 @ ( f @ SV15 ) @ SV20 ) )
= $true )
| ( ( cQ_2 @ SV16 @ SV18 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(101,plain,
( ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
| ~ ( cP_1 @ 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_1 @ SV13 @ SV14 @ SV15 )
= $false )
| ( ( ~ ( cP_1 @ ( f @ SV13 ) @ SV16 ) )
= $true )
| ( ( ~ ( cP_1 @ ( f @ SV14 ) @ SV18 ) )
= $true )
| ( ( ~ ( cP_1 @ ( f @ SV15 ) @ SV20 ) )
= $true )
| ( ( cQ_2 @ SV16 @ SV18 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(103,plain,
( ( ~ ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(104,plain,
( ( ~ ( cP_1 @ 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_1 @ ( f @ SV13 ) @ SV16 )
= $false )
| ( ( cQ_1 @ SV13 @ SV14 @ SV15 )
= $false )
| ( ( ~ ( cP_1 @ ( f @ SV14 ) @ SV18 ) )
= $true )
| ( ( ~ ( cP_1 @ ( f @ SV15 ) @ SV20 ) )
= $true )
| ( ( cQ_2 @ SV16 @ SV18 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(106,plain,
( ( ~ ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(107,plain,
( ( cP_1 @ 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_1 @ ( f @ SV14 ) @ SV18 )
= $false )
| ( ( cQ_1 @ SV13 @ SV14 @ SV15 )
= $false )
| ( ( cP_1 @ ( f @ SV13 ) @ SV16 )
= $false )
| ( ( ~ ( cP_1 @ ( f @ SV15 ) @ SV20 ) )
= $true )
| ( ( cQ_2 @ SV16 @ SV18 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(109,plain,
( ( ~ ( cP_1 @ a @ a )
| ~ ( cQ_1 @ a @ b @ c ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(110,plain,
! [SV18: $i,SV14: $i,SV16: $i,SV13: $i,SV20: $i,SV15: $i] :
( ( ( cP_1 @ ( f @ SV15 ) @ SV20 )
= $false )
| ( ( cP_1 @ ( f @ SV13 ) @ SV16 )
= $false )
| ( ( cQ_1 @ SV13 @ SV14 @ SV15 )
= $false )
| ( ( cP_1 @ ( f @ SV14 ) @ SV18 )
= $false )
| ( ( cQ_2 @ SV16 @ SV18 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(111,plain,
( ( ~ ( cP_1 @ a @ a ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(112,plain,
( ( ~ ( cQ_1 @ a @ b @ c ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(113,plain,
( ( cP_1 @ a @ a )
= $true ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(114,plain,
( ( cQ_1 @ a @ b @ c )
= $true ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(115,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[21,114,113,110,107,99,92,91,65,61,58,50,43,42]) ).
thf(116,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYO385^5 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jul 9 13:32:51 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.37
% 0.20/0.37 No.of.Axioms: 0
% 0.20/0.37
% 0.20/0.37 Length.of.Defs: 0
% 0.20/0.37
% 0.20/0.37 Contains.Choice.Funs: false
% 0.20/0.39 (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)..........
% 0.20/0.52
% 0.20/0.52 ********************************
% 0.20/0.52 * All subproblems solved! *
% 0.20/0.52 ********************************
% 0.20/0.52 % SZS status Theorem for /export/starexec/sandbox2/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:115,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.52
% 0.20/0.52 %**** Beginning of derivation protocol ****
% 0.20/0.52 % SZS output start CNFRefutation
% See solution above
% 0.20/0.52
% 0.20/0.52 %**** End of derivation protocol ****
% 0.20/0.52 %**** no. of clauses in derivation: 116 ****
% 0.20/0.52 %**** clause counter: 115 ****
% 0.20/0.52
% 0.20/0.52 % SZS status Theorem for /export/starexec/sandbox2/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:115,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------