%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT359^1 : TPTP v9.2.1. Released v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:45:33 AM UTC 2026
% Result : Theorem 1.81s 1.45s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 5
% Syntax : Number of formulae : 135 ( 92 unt; 0 typ; 0 def)
% Number of atoms : 1391 ( 231 equ; 0 cnn)
% Maximal formula atoms : 9 ( 10 avg)
% Number of connectives : 11960 ( 4 ~; 108 |; 0 &;11162 @)
% ( 0 <=>; 399 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 17 usr; 12 con; 0-4 aty)
% ( 287 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 798 ( 322 ^; 476 !; 0 ?; 798 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
elem: $tType ).
thf(type_def_7,type,
nat: $tType ).
thf(type_def_8,type,
list: $tType ).
thf(func_def_0,type,
isPer:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > $o ) ).
thf(func_def_2,type,
elem: $tType ).
thf(func_def_3,type,
elemStar: elem > elem > $o ).
thf(func_def_4,type,
nat: $tType ).
thf(func_def_5,type,
natStar: nat > nat > $o ).
thf(func_def_6,type,
zero: nat ).
thf(func_def_7,type,
suc: nat > nat ).
thf(func_def_8,type,
plus: nat > nat > nat ).
thf(func_def_9,type,
list: $tType ).
thf(func_def_10,type,
listStar: nat > list > list > $o ).
thf(func_def_11,type,
nil: list ).
thf(func_def_12,type,
cons: nat > elem > list > list ).
thf(func_def_13,type,
app: nat > nat > list > list > list ).
thf(func_def_31,type,
sK1: list ).
thf(func_def_32,type,
sK2: elem ).
thf(func_def_33,type,
sK3: nat ).
thf(func_def_34,type,
sK4: list ).
thf(func_def_35,type,
sK5: nat ).
thf(func_def_36,type,
sK6: list ).
thf(func_def_37,type,
sK7: nat ).
thf(f251,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f248]) ).
thf(f248,plain,
$false = $true,
inference(backward_demodulation,[status(thm)],[f126,f241]) ).
thf(f241,plain,
( ( listStar @ ( plus @ ( plus @ sK7 @ sK5 ) @ ( plus @ sK7 @ sK5 ) ) @ ( app @ sK3 @ ( plus @ sK7 @ sK5 ) @ sK1 @ ( app @ sK7 @ sK5 @ sK6 @ sK4 ) ) @ ( app @ ( plus @ sK3 @ sK7 ) @ sK5 @ ( app @ sK3 @ sK7 @ sK1 @ sK6 ) @ sK4 ) )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f240]) ).
thf(f240,plain,
( ( $false = $true )
| ( ( listStar @ ( plus @ ( plus @ sK7 @ sK5 ) @ ( plus @ sK7 @ sK5 ) ) @ ( app @ sK3 @ ( plus @ sK7 @ sK5 ) @ sK1 @ ( app @ sK7 @ sK5 @ sK6 @ sK4 ) ) @ ( app @ ( plus @ sK3 @ sK7 ) @ sK5 @ ( app @ sK3 @ sK7 @ sK1 @ sK6 ) @ sK4 ) )
= $false ) ),
inference(forward_demodulation,[status(thm)],[f239,f124]) ).
thf(f124,plain,
( ( listStar @ sK3 @ sK1 @ sK1 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f121]) ).
thf(f121,plain,
( ( ( listStar @ sK3 @ sK1 @ sK1 )
=> ( ( listStar @ ( plus @ ( plus @ sK7 @ sK5 ) @ ( plus @ sK7 @ sK5 ) ) @ ( app @ sK3 @ ( plus @ sK7 @ sK5 ) @ sK1 @ ( app @ sK7 @ sK5 @ sK6 @ sK4 ) ) @ ( app @ ( plus @ sK3 @ sK7 ) @ sK5 @ ( app @ sK3 @ sK7 @ sK1 @ sK6 ) @ sK4 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ sK7 @ sK5 ) ) @ ( plus @ sK7 @ sK5 ) ) @ ( app @ ( suc @ sK3 ) @ ( plus @ sK7 @ sK5 ) @ ( cons @ sK3 @ sK2 @ sK1 ) @ ( app @ sK7 @ sK5 @ sK6 @ sK4 ) ) @ ( app @ ( plus @ ( suc @ sK3 ) @ sK7 ) @ sK5 @ ( app @ ( suc @ sK3 ) @ sK7 @ ( cons @ sK3 @ sK2 @ sK1 ) @ sK6 ) @ sK4 ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f119]) ).
thf(f119,plain,
( ( ( listStar @ sK5 @ sK4 @ sK4 )
=> ( ( listStar @ sK3 @ sK1 @ sK1 )
=> ( ( listStar @ ( plus @ ( plus @ sK7 @ sK5 ) @ ( plus @ sK7 @ sK5 ) ) @ ( app @ sK3 @ ( plus @ sK7 @ sK5 ) @ sK1 @ ( app @ sK7 @ sK5 @ sK6 @ sK4 ) ) @ ( app @ ( plus @ sK3 @ sK7 ) @ sK5 @ ( app @ sK3 @ sK7 @ sK1 @ sK6 ) @ sK4 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ sK7 @ sK5 ) ) @ ( plus @ sK7 @ sK5 ) ) @ ( app @ ( suc @ sK3 ) @ ( plus @ sK7 @ sK5 ) @ ( cons @ sK3 @ sK2 @ sK1 ) @ ( app @ sK7 @ sK5 @ sK6 @ sK4 ) ) @ ( app @ ( plus @ ( suc @ sK3 ) @ sK7 ) @ sK5 @ ( app @ ( suc @ sK3 ) @ sK7 @ ( cons @ sK3 @ sK2 @ sK1 ) @ sK6 ) @ sK4 ) ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f118]) ).
thf(f118,plain,
( $false
= ( ( listStar @ sK7 @ sK6 @ sK6 )
=> ( ( listStar @ sK5 @ sK4 @ sK4 )
=> ( ( listStar @ sK3 @ sK1 @ sK1 )
=> ( ( listStar @ ( plus @ ( plus @ sK7 @ sK5 ) @ ( plus @ sK7 @ sK5 ) ) @ ( app @ sK3 @ ( plus @ sK7 @ sK5 ) @ sK1 @ ( app @ sK7 @ sK5 @ sK6 @ sK4 ) ) @ ( app @ ( plus @ sK3 @ sK7 ) @ sK5 @ ( app @ sK3 @ sK7 @ sK1 @ sK6 ) @ sK4 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ sK7 @ sK5 ) ) @ ( plus @ sK7 @ sK5 ) ) @ ( app @ ( suc @ sK3 ) @ ( plus @ sK7 @ sK5 ) @ ( cons @ sK3 @ sK2 @ sK1 ) @ ( app @ sK7 @ sK5 @ sK6 @ sK4 ) ) @ ( app @ ( plus @ ( suc @ sK3 ) @ sK7 ) @ sK5 @ ( app @ ( suc @ sK3 ) @ sK7 @ ( cons @ sK3 @ sK2 @ sK1 ) @ sK6 ) @ sK4 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f117]) ).
thf(f117,plain,
( $false
= ( ^ [Y0: nat] :
( ( listStar @ Y0 @ sK6 @ sK6 )
=> ( ( listStar @ sK5 @ sK4 @ sK4 )
=> ( ( listStar @ sK3 @ sK1 @ sK1 )
=> ( ( listStar @ ( plus @ ( plus @ Y0 @ sK5 ) @ ( plus @ Y0 @ sK5 ) ) @ ( app @ sK3 @ ( plus @ Y0 @ sK5 ) @ sK1 @ ( app @ Y0 @ sK5 @ sK6 @ sK4 ) ) @ ( app @ ( plus @ sK3 @ Y0 ) @ sK5 @ ( app @ sK3 @ Y0 @ sK1 @ sK6 ) @ sK4 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y0 @ sK5 ) ) @ ( plus @ Y0 @ sK5 ) ) @ ( app @ ( suc @ sK3 ) @ ( plus @ Y0 @ sK5 ) @ ( cons @ sK3 @ sK2 @ sK1 ) @ ( app @ Y0 @ sK5 @ sK6 @ sK4 ) ) @ ( app @ ( plus @ ( suc @ sK3 ) @ Y0 ) @ sK5 @ ( app @ ( suc @ sK3 ) @ Y0 @ ( cons @ sK3 @ sK2 @ sK1 ) @ sK6 ) @ sK4 ) ) ) ) ) )
@ sK7 ) ),
inference(sigma_clausification,[status(thm)],[f116]) ).
thf(f116,plain,
( $false
= ( !! @ nat
@ ^ [Y0: nat] :
( ( listStar @ Y0 @ sK6 @ sK6 )
=> ( ( listStar @ sK5 @ sK4 @ sK4 )
=> ( ( listStar @ sK3 @ sK1 @ sK1 )
=> ( ( listStar @ ( plus @ ( plus @ Y0 @ sK5 ) @ ( plus @ Y0 @ sK5 ) ) @ ( app @ sK3 @ ( plus @ Y0 @ sK5 ) @ sK1 @ ( app @ Y0 @ sK5 @ sK6 @ sK4 ) ) @ ( app @ ( plus @ sK3 @ Y0 ) @ sK5 @ ( app @ sK3 @ Y0 @ sK1 @ sK6 ) @ sK4 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y0 @ sK5 ) ) @ ( plus @ Y0 @ sK5 ) ) @ ( app @ ( suc @ sK3 ) @ ( plus @ Y0 @ sK5 ) @ ( cons @ sK3 @ sK2 @ sK1 ) @ ( app @ Y0 @ sK5 @ sK6 @ sK4 ) ) @ ( app @ ( plus @ ( suc @ sK3 ) @ Y0 ) @ sK5 @ ( app @ ( suc @ sK3 ) @ Y0 @ ( cons @ sK3 @ sK2 @ sK1 ) @ sK6 ) @ sK4 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f115]) ).
thf(f115,plain,
( ( ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( ( listStar @ sK5 @ sK4 @ sK4 )
=> ( ( listStar @ sK3 @ sK1 @ sK1 )
=> ( ( listStar @ ( plus @ ( plus @ Y1 @ sK5 ) @ ( plus @ Y1 @ sK5 ) ) @ ( app @ sK3 @ ( plus @ Y1 @ sK5 ) @ sK1 @ ( app @ Y1 @ sK5 @ Y0 @ sK4 ) ) @ ( app @ ( plus @ sK3 @ Y1 ) @ sK5 @ ( app @ sK3 @ Y1 @ sK1 @ Y0 ) @ sK4 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y1 @ sK5 ) ) @ ( plus @ Y1 @ sK5 ) ) @ ( app @ ( suc @ sK3 ) @ ( plus @ Y1 @ sK5 ) @ ( cons @ sK3 @ sK2 @ sK1 ) @ ( app @ Y1 @ sK5 @ Y0 @ sK4 ) ) @ ( app @ ( plus @ ( suc @ sK3 ) @ Y1 ) @ sK5 @ ( app @ ( suc @ sK3 ) @ Y1 @ ( cons @ sK3 @ sK2 @ sK1 ) @ Y0 ) @ sK4 ) ) ) ) ) ) )
@ sK6 )
= $false ),
inference(sigma_clausification,[status(thm)],[f114]) ).
thf(f114,plain,
( ( !! @ list
@ ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( ( listStar @ sK5 @ sK4 @ sK4 )
=> ( ( listStar @ sK3 @ sK1 @ sK1 )
=> ( ( listStar @ ( plus @ ( plus @ Y1 @ sK5 ) @ ( plus @ Y1 @ sK5 ) ) @ ( app @ sK3 @ ( plus @ Y1 @ sK5 ) @ sK1 @ ( app @ Y1 @ sK5 @ Y0 @ sK4 ) ) @ ( app @ ( plus @ sK3 @ Y1 ) @ sK5 @ ( app @ sK3 @ Y1 @ sK1 @ Y0 ) @ sK4 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y1 @ sK5 ) ) @ ( plus @ Y1 @ sK5 ) ) @ ( app @ ( suc @ sK3 ) @ ( plus @ Y1 @ sK5 ) @ ( cons @ sK3 @ sK2 @ sK1 ) @ ( app @ Y1 @ sK5 @ Y0 @ sK4 ) ) @ ( app @ ( plus @ ( suc @ sK3 ) @ Y1 ) @ sK5 @ ( app @ ( suc @ sK3 ) @ Y1 @ ( cons @ sK3 @ sK2 @ sK1 ) @ Y0 ) @ sK4 ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f113]) ).
thf(f113,plain,
( ( ^ [Y0: nat] :
( !! @ list
@ ^ [Y1: list] :
( !! @ nat
@ ^ [Y2: nat] :
( ( listStar @ Y2 @ Y1 @ Y1 )
=> ( ( listStar @ Y0 @ sK4 @ sK4 )
=> ( ( listStar @ sK3 @ sK1 @ sK1 )
=> ( ( listStar @ ( plus @ ( plus @ Y2 @ Y0 ) @ ( plus @ Y2 @ Y0 ) ) @ ( app @ sK3 @ ( plus @ Y2 @ Y0 ) @ sK1 @ ( app @ Y2 @ Y0 @ Y1 @ sK4 ) ) @ ( app @ ( plus @ sK3 @ Y2 ) @ Y0 @ ( app @ sK3 @ Y2 @ sK1 @ Y1 ) @ sK4 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y2 @ Y0 ) ) @ ( plus @ Y2 @ Y0 ) ) @ ( app @ ( suc @ sK3 ) @ ( plus @ Y2 @ Y0 ) @ ( cons @ sK3 @ sK2 @ sK1 ) @ ( app @ Y2 @ Y0 @ Y1 @ sK4 ) ) @ ( app @ ( plus @ ( suc @ sK3 ) @ Y2 ) @ Y0 @ ( app @ ( suc @ sK3 ) @ Y2 @ ( cons @ sK3 @ sK2 @ sK1 ) @ Y1 ) @ sK4 ) ) ) ) ) ) ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[status(thm)],[f112]) ).
thf(f112,plain,
( $false
= ( !! @ nat
@ ^ [Y0: nat] :
( !! @ list
@ ^ [Y1: list] :
( !! @ nat
@ ^ [Y2: nat] :
( ( listStar @ Y2 @ Y1 @ Y1 )
=> ( ( listStar @ Y0 @ sK4 @ sK4 )
=> ( ( listStar @ sK3 @ sK1 @ sK1 )
=> ( ( listStar @ ( plus @ ( plus @ Y2 @ Y0 ) @ ( plus @ Y2 @ Y0 ) ) @ ( app @ sK3 @ ( plus @ Y2 @ Y0 ) @ sK1 @ ( app @ Y2 @ Y0 @ Y1 @ sK4 ) ) @ ( app @ ( plus @ sK3 @ Y2 ) @ Y0 @ ( app @ sK3 @ Y2 @ sK1 @ Y1 ) @ sK4 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y2 @ Y0 ) ) @ ( plus @ Y2 @ Y0 ) ) @ ( app @ ( suc @ sK3 ) @ ( plus @ Y2 @ Y0 ) @ ( cons @ sK3 @ sK2 @ sK1 ) @ ( app @ Y2 @ Y0 @ Y1 @ sK4 ) ) @ ( app @ ( plus @ ( suc @ sK3 ) @ Y2 ) @ Y0 @ ( app @ ( suc @ sK3 ) @ Y2 @ ( cons @ sK3 @ sK2 @ sK1 ) @ Y1 ) @ sK4 ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f111]) ).
thf(f111,plain,
( $false
= ( ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list
@ ^ [Y2: list] :
( !! @ nat
@ ^ [Y3: nat] :
( ( listStar @ Y3 @ Y2 @ Y2 )
=> ( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( ( listStar @ sK3 @ sK1 @ sK1 )
=> ( ( listStar @ ( plus @ ( plus @ Y3 @ Y1 ) @ ( plus @ Y3 @ Y1 ) ) @ ( app @ sK3 @ ( plus @ Y3 @ Y1 ) @ sK1 @ ( app @ Y3 @ Y1 @ Y2 @ Y0 ) ) @ ( app @ ( plus @ sK3 @ Y3 ) @ Y1 @ ( app @ sK3 @ Y3 @ sK1 @ Y2 ) @ Y0 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y3 @ Y1 ) ) @ ( plus @ Y3 @ Y1 ) ) @ ( app @ ( suc @ sK3 ) @ ( plus @ Y3 @ Y1 ) @ ( cons @ sK3 @ sK2 @ sK1 ) @ ( app @ Y3 @ Y1 @ Y2 @ Y0 ) ) @ ( app @ ( plus @ ( suc @ sK3 ) @ Y3 ) @ Y1 @ ( app @ ( suc @ sK3 ) @ Y3 @ ( cons @ sK3 @ sK2 @ sK1 ) @ Y2 ) @ Y0 ) ) ) ) ) ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f110]) ).
thf(f110,plain,
( ( !! @ list
@ ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list
@ ^ [Y2: list] :
( !! @ nat
@ ^ [Y3: nat] :
( ( listStar @ Y3 @ Y2 @ Y2 )
=> ( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( ( listStar @ sK3 @ sK1 @ sK1 )
=> ( ( listStar @ ( plus @ ( plus @ Y3 @ Y1 ) @ ( plus @ Y3 @ Y1 ) ) @ ( app @ sK3 @ ( plus @ Y3 @ Y1 ) @ sK1 @ ( app @ Y3 @ Y1 @ Y2 @ Y0 ) ) @ ( app @ ( plus @ sK3 @ Y3 ) @ Y1 @ ( app @ sK3 @ Y3 @ sK1 @ Y2 ) @ Y0 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y3 @ Y1 ) ) @ ( plus @ Y3 @ Y1 ) ) @ ( app @ ( suc @ sK3 ) @ ( plus @ Y3 @ Y1 ) @ ( cons @ sK3 @ sK2 @ sK1 ) @ ( app @ Y3 @ Y1 @ Y2 @ Y0 ) ) @ ( app @ ( plus @ ( suc @ sK3 ) @ Y3 ) @ Y1 @ ( app @ ( suc @ sK3 ) @ Y3 @ ( cons @ sK3 @ sK2 @ sK1 ) @ Y2 ) @ Y0 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f109]) ).
thf(f109,plain,
( ( ^ [Y0: nat] :
( !! @ list
@ ^ [Y1: list] :
( !! @ nat
@ ^ [Y2: nat] :
( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( ( listStar @ Y2 @ Y1 @ Y1 )
=> ( ( listStar @ Y0 @ sK1 @ sK1 )
=> ( ( listStar @ ( plus @ ( plus @ Y4 @ Y2 ) @ ( plus @ Y4 @ Y2 ) ) @ ( app @ Y0 @ ( plus @ Y4 @ Y2 ) @ sK1 @ ( app @ Y4 @ Y2 @ Y3 @ Y1 ) ) @ ( app @ ( plus @ Y0 @ Y4 ) @ Y2 @ ( app @ Y0 @ Y4 @ sK1 @ Y3 ) @ Y1 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y4 @ Y2 ) ) @ ( plus @ Y4 @ Y2 ) ) @ ( app @ ( suc @ Y0 ) @ ( plus @ Y4 @ Y2 ) @ ( cons @ Y0 @ sK2 @ sK1 ) @ ( app @ Y4 @ Y2 @ Y3 @ Y1 ) ) @ ( app @ ( plus @ ( suc @ Y0 ) @ Y4 ) @ Y2 @ ( app @ ( suc @ Y0 ) @ Y4 @ ( cons @ Y0 @ sK2 @ sK1 ) @ Y3 ) @ Y1 ) ) ) ) ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f108]) ).
thf(f108,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ list
@ ^ [Y1: list] :
( !! @ nat
@ ^ [Y2: nat] :
( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( ( listStar @ Y2 @ Y1 @ Y1 )
=> ( ( listStar @ Y0 @ sK1 @ sK1 )
=> ( ( listStar @ ( plus @ ( plus @ Y4 @ Y2 ) @ ( plus @ Y4 @ Y2 ) ) @ ( app @ Y0 @ ( plus @ Y4 @ Y2 ) @ sK1 @ ( app @ Y4 @ Y2 @ Y3 @ Y1 ) ) @ ( app @ ( plus @ Y0 @ Y4 ) @ Y2 @ ( app @ Y0 @ Y4 @ sK1 @ Y3 ) @ Y1 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y4 @ Y2 ) ) @ ( plus @ Y4 @ Y2 ) ) @ ( app @ ( suc @ Y0 ) @ ( plus @ Y4 @ Y2 ) @ ( cons @ Y0 @ sK2 @ sK1 ) @ ( app @ Y4 @ Y2 @ Y3 @ Y1 ) ) @ ( app @ ( plus @ ( suc @ Y0 ) @ Y4 ) @ Y2 @ ( app @ ( suc @ Y0 ) @ Y4 @ ( cons @ Y0 @ sK2 @ sK1 ) @ Y3 ) @ Y1 ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f107]) ).
thf(f107,plain,
( $false
= ( ^ [Y0: elem] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list
@ ^ [Y2: list] :
( !! @ nat
@ ^ [Y3: nat] :
( !! @ list
@ ^ [Y4: list] :
( !! @ nat
@ ^ [Y5: nat] :
( ( listStar @ Y5 @ Y4 @ Y4 )
=> ( ( listStar @ Y3 @ Y2 @ Y2 )
=> ( ( listStar @ Y1 @ sK1 @ sK1 )
=> ( ( listStar @ ( plus @ ( plus @ Y5 @ Y3 ) @ ( plus @ Y5 @ Y3 ) ) @ ( app @ Y1 @ ( plus @ Y5 @ Y3 ) @ sK1 @ ( app @ Y5 @ Y3 @ Y4 @ Y2 ) ) @ ( app @ ( plus @ Y1 @ Y5 ) @ Y3 @ ( app @ Y1 @ Y5 @ sK1 @ Y4 ) @ Y2 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y5 @ Y3 ) ) @ ( plus @ Y5 @ Y3 ) ) @ ( app @ ( suc @ Y1 ) @ ( plus @ Y5 @ Y3 ) @ ( cons @ Y1 @ Y0 @ sK1 ) @ ( app @ Y5 @ Y3 @ Y4 @ Y2 ) ) @ ( app @ ( plus @ ( suc @ Y1 ) @ Y5 ) @ Y3 @ ( app @ ( suc @ Y1 ) @ Y5 @ ( cons @ Y1 @ Y0 @ sK1 ) @ Y4 ) @ Y2 ) ) ) ) ) ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f106]) ).
thf(f106,plain,
( ( !! @ elem
@ ^ [Y0: elem] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list
@ ^ [Y2: list] :
( !! @ nat
@ ^ [Y3: nat] :
( !! @ list
@ ^ [Y4: list] :
( !! @ nat
@ ^ [Y5: nat] :
( ( listStar @ Y5 @ Y4 @ Y4 )
=> ( ( listStar @ Y3 @ Y2 @ Y2 )
=> ( ( listStar @ Y1 @ sK1 @ sK1 )
=> ( ( listStar @ ( plus @ ( plus @ Y5 @ Y3 ) @ ( plus @ Y5 @ Y3 ) ) @ ( app @ Y1 @ ( plus @ Y5 @ Y3 ) @ sK1 @ ( app @ Y5 @ Y3 @ Y4 @ Y2 ) ) @ ( app @ ( plus @ Y1 @ Y5 ) @ Y3 @ ( app @ Y1 @ Y5 @ sK1 @ Y4 ) @ Y2 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y5 @ Y3 ) ) @ ( plus @ Y5 @ Y3 ) ) @ ( app @ ( suc @ Y1 ) @ ( plus @ Y5 @ Y3 ) @ ( cons @ Y1 @ Y0 @ sK1 ) @ ( app @ Y5 @ Y3 @ Y4 @ Y2 ) ) @ ( app @ ( plus @ ( suc @ Y1 ) @ Y5 ) @ Y3 @ ( app @ ( suc @ Y1 ) @ Y5 @ ( cons @ Y1 @ Y0 @ sK1 ) @ Y4 ) @ Y2 ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f105]) ).
thf(f105,plain,
( $false
= ( ^ [Y0: list] :
( !! @ elem
@ ^ [Y1: elem] :
( !! @ nat
@ ^ [Y2: nat] :
( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( !! @ list
@ ^ [Y5: list] :
( !! @ nat
@ ^ [Y6: nat] :
( ( listStar @ Y6 @ Y5 @ Y5 )
=> ( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( ( listStar @ Y2 @ Y0 @ Y0 )
=> ( ( listStar @ ( plus @ ( plus @ Y6 @ Y4 ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ Y2 @ ( plus @ Y6 @ Y4 ) @ Y0 @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( app @ ( plus @ Y2 @ Y6 ) @ Y4 @ ( app @ Y2 @ Y6 @ Y0 @ Y5 ) @ Y3 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y6 @ Y4 ) ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ ( suc @ Y2 ) @ ( plus @ Y6 @ Y4 ) @ ( cons @ Y2 @ Y1 @ Y0 ) @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( app @ ( plus @ ( suc @ Y2 ) @ Y6 ) @ Y4 @ ( app @ ( suc @ Y2 ) @ Y6 @ ( cons @ Y2 @ Y1 @ Y0 ) @ Y5 ) @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_clausification,[status(thm)],[f104]) ).
thf(f104,plain,
( $false
= ( !! @ list
@ ^ [Y0: list] :
( !! @ elem
@ ^ [Y1: elem] :
( !! @ nat
@ ^ [Y2: nat] :
( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( !! @ list
@ ^ [Y5: list] :
( !! @ nat
@ ^ [Y6: nat] :
( ( listStar @ Y6 @ Y5 @ Y5 )
=> ( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( ( listStar @ Y2 @ Y0 @ Y0 )
=> ( ( listStar @ ( plus @ ( plus @ Y6 @ Y4 ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ Y2 @ ( plus @ Y6 @ Y4 ) @ Y0 @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( app @ ( plus @ Y2 @ Y6 ) @ Y4 @ ( app @ Y2 @ Y6 @ Y0 @ Y5 ) @ Y3 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y6 @ Y4 ) ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ ( suc @ Y2 ) @ ( plus @ Y6 @ Y4 ) @ ( cons @ Y2 @ Y1 @ Y0 ) @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( app @ ( plus @ ( suc @ Y2 ) @ Y6 ) @ Y4 @ ( app @ ( suc @ Y2 ) @ Y6 @ ( cons @ Y2 @ Y1 @ Y0 ) @ Y5 ) @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ~ ( !! @ list
@ ^ [Y0: list] :
( !! @ elem
@ ^ [Y1: elem] :
( !! @ nat
@ ^ [Y2: nat] :
( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( !! @ list
@ ^ [Y5: list] :
( !! @ nat
@ ^ [Y6: nat] :
( ( listStar @ Y6 @ Y5 @ Y5 )
=> ( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( ( listStar @ Y2 @ Y0 @ Y0 )
=> ( ( listStar @ ( plus @ ( plus @ Y6 @ Y4 ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ Y2 @ ( plus @ Y6 @ Y4 ) @ Y0 @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( app @ ( plus @ Y2 @ Y6 ) @ Y4 @ ( app @ Y2 @ Y6 @ Y0 @ Y5 ) @ Y3 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y6 @ Y4 ) ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ ( suc @ Y2 ) @ ( plus @ Y6 @ Y4 ) @ ( cons @ Y2 @ Y1 @ Y0 ) @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( app @ ( plus @ ( suc @ Y2 ) @ Y6 ) @ Y4 @ ( app @ ( suc @ Y2 ) @ Y6 @ ( cons @ Y2 @ Y1 @ Y0 ) @ Y5 ) @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ~ ( !! @ list
@ ^ [Y0: list] :
( !! @ elem
@ ^ [Y1: elem] :
( !! @ nat
@ ^ [Y2: nat] :
( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( !! @ list
@ ^ [Y5: list] :
( !! @ nat
@ ^ [Y6: nat] :
( ( listStar @ Y6 @ Y5 @ Y5 )
=> ( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( ( listStar @ Y2 @ Y0 @ Y0 )
=> ( ( listStar @ ( plus @ ( plus @ Y6 @ Y4 ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ Y2 @ ( plus @ Y6 @ Y4 ) @ Y0 @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( app @ ( plus @ Y2 @ Y6 ) @ Y4 @ ( app @ Y2 @ Y6 @ Y0 @ Y5 ) @ Y3 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y6 @ Y4 ) ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ ( suc @ Y2 ) @ ( plus @ Y6 @ Y4 ) @ ( cons @ Y2 @ Y1 @ Y0 ) @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( app @ ( plus @ ( suc @ Y2 ) @ Y6 ) @ Y4 @ ( app @ ( suc @ Y2 ) @ Y6 @ ( cons @ Y2 @ Y1 @ Y0 ) @ Y5 ) @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f47]) ).
thf(f47,plain,
~ ! [X0: nat,X1: list,X2: nat,X3: list,X4: nat,X5: elem,X6: list] :
( ( listStar @ X0 @ X1 @ X1 )
=> ( ( listStar @ X2 @ X3 @ X3 )
=> ( ( listStar @ X4 @ X6 @ X6 )
=> ( ( listStar @ ( plus @ ( plus @ X0 @ X2 ) @ ( plus @ X0 @ X2 ) ) @ ( app @ X4 @ ( plus @ X0 @ X2 ) @ X6 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ X4 @ X0 ) @ X2 @ ( app @ X4 @ X0 @ X6 @ X1 ) @ X3 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X2 ) ) @ ( plus @ X0 @ X2 ) ) @ ( app @ ( suc @ X4 ) @ ( plus @ X0 @ X2 ) @ ( cons @ X4 @ X5 @ X6 ) @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ ( suc @ X4 ) @ X0 ) @ X2 @ ( app @ ( suc @ X4 ) @ X0 @ ( cons @ X4 @ X5 @ X6 ) @ X1 ) @ X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f17]) ).
thf(f17,negated_conjecture,
~ ! [X13: nat,X16: list,X14: nat,X17: list,X10: nat,X2: elem,X18: list] :
( ( listStar @ X13 @ X16 @ X16 )
=> ( ( listStar @ X14 @ X17 @ X17 )
=> ( ( listStar @ X10 @ X18 @ X18 )
=> ( ( listStar @ ( plus @ ( plus @ X13 @ X14 ) @ ( plus @ X13 @ X14 ) ) @ ( app @ X10 @ ( plus @ X13 @ X14 ) @ X18 @ ( app @ X13 @ X14 @ X16 @ X17 ) ) @ ( app @ ( plus @ X10 @ X13 ) @ X14 @ ( app @ X10 @ X13 @ X18 @ X16 ) @ X17 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X13 @ X14 ) ) @ ( plus @ X13 @ X14 ) ) @ ( app @ ( suc @ X10 ) @ ( plus @ X13 @ X14 ) @ ( cons @ X10 @ X2 @ X18 ) @ ( app @ X13 @ X14 @ X16 @ X17 ) ) @ ( app @ ( plus @ ( suc @ X10 ) @ X13 ) @ X14 @ ( app @ ( suc @ X10 ) @ X13 @ ( cons @ X10 @ X2 @ X18 ) @ X16 ) @ X17 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
thf(f16,conjecture,
! [X13: nat,X16: list,X14: nat,X17: list,X10: nat,X2: elem,X18: list] :
( ( listStar @ X13 @ X16 @ X16 )
=> ( ( listStar @ X14 @ X17 @ X17 )
=> ( ( listStar @ X10 @ X18 @ X18 )
=> ( ( listStar @ ( plus @ ( plus @ X13 @ X14 ) @ ( plus @ X13 @ X14 ) ) @ ( app @ X10 @ ( plus @ X13 @ X14 ) @ X18 @ ( app @ X13 @ X14 @ X16 @ X17 ) ) @ ( app @ ( plus @ X10 @ X13 ) @ X14 @ ( app @ X10 @ X13 @ X18 @ X16 ) @ X17 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X13 @ X14 ) ) @ ( plus @ X13 @ X14 ) ) @ ( app @ ( suc @ X10 ) @ ( plus @ X13 @ X14 ) @ ( cons @ X10 @ X2 @ X18 ) @ ( app @ X13 @ X14 @ X16 @ X17 ) ) @ ( app @ ( plus @ ( suc @ X10 ) @ X13 ) @ X14 @ ( app @ ( suc @ X10 ) @ X13 @ ( cons @ X10 @ X2 @ X18 ) @ X16 ) @ X17 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.PLL0ptdnA4/DTF2THF_4359.p',list_app_assoc_indstep) ).
thf(f239,plain,
( ( ( listStar @ ( plus @ ( plus @ sK7 @ sK5 ) @ ( plus @ sK7 @ sK5 ) ) @ ( app @ sK3 @ ( plus @ sK7 @ sK5 ) @ sK1 @ ( app @ sK7 @ sK5 @ sK6 @ sK4 ) ) @ ( app @ ( plus @ sK3 @ sK7 ) @ sK5 @ ( app @ sK3 @ sK7 @ sK1 @ sK6 ) @ sK4 ) )
= $false )
| ( ( listStar @ sK3 @ sK1 @ sK1 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f238]) ).
thf(f238,plain,
( ( ( listStar @ ( plus @ ( plus @ sK7 @ sK5 ) @ ( plus @ sK7 @ sK5 ) ) @ ( app @ sK3 @ ( plus @ sK7 @ sK5 ) @ sK1 @ ( app @ sK7 @ sK5 @ sK6 @ sK4 ) ) @ ( app @ ( plus @ sK3 @ sK7 ) @ sK5 @ ( app @ sK3 @ sK7 @ sK1 @ sK6 ) @ sK4 ) )
= $false )
| ( $false = $true )
| ( ( listStar @ sK3 @ sK1 @ sK1 )
= $false ) ),
inference(forward_demodulation,[status(thm)],[f237,f120]) ).
thf(f120,plain,
( $true
= ( listStar @ sK7 @ sK6 @ sK6 ) ),
inference(binary_proxy_clausification,[status(thm)],[f118]) ).
thf(f237,plain,
( ( ( listStar @ ( plus @ ( plus @ sK7 @ sK5 ) @ ( plus @ sK7 @ sK5 ) ) @ ( app @ sK3 @ ( plus @ sK7 @ sK5 ) @ sK1 @ ( app @ sK7 @ sK5 @ sK6 @ sK4 ) ) @ ( app @ ( plus @ sK3 @ sK7 ) @ sK5 @ ( app @ sK3 @ sK7 @ sK1 @ sK6 ) @ sK4 ) )
= $false )
| ( $false
= ( listStar @ sK7 @ sK6 @ sK6 ) )
| ( ( listStar @ sK3 @ sK1 @ sK1 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f236]) ).
thf(f236,plain,
( ( $false = $true )
| ( ( listStar @ ( plus @ ( plus @ sK7 @ sK5 ) @ ( plus @ sK7 @ sK5 ) ) @ ( app @ sK3 @ ( plus @ sK7 @ sK5 ) @ sK1 @ ( app @ sK7 @ sK5 @ sK6 @ sK4 ) ) @ ( app @ ( plus @ sK3 @ sK7 ) @ sK5 @ ( app @ sK3 @ sK7 @ sK1 @ sK6 ) @ sK4 ) )
= $false )
| ( ( listStar @ sK3 @ sK1 @ sK1 )
= $false )
| ( $false
= ( listStar @ sK7 @ sK6 @ sK6 ) ) ),
inference(forward_demodulation,[status(thm)],[f235,f122]) ).
thf(f122,plain,
( ( listStar @ sK5 @ sK4 @ sK4 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f119]) ).
thf(f235,plain,
( ( ( listStar @ sK5 @ sK4 @ sK4 )
= $false )
| ( ( listStar @ sK3 @ sK1 @ sK1 )
= $false )
| ( $false
= ( listStar @ sK7 @ sK6 @ sK6 ) )
| ( ( listStar @ ( plus @ ( plus @ sK7 @ sK5 ) @ ( plus @ sK7 @ sK5 ) ) @ ( app @ sK3 @ ( plus @ sK7 @ sK5 ) @ sK1 @ ( app @ sK7 @ sK5 @ sK6 @ sK4 ) ) @ ( app @ ( plus @ sK3 @ sK7 ) @ sK5 @ ( app @ sK3 @ sK7 @ sK1 @ sK6 ) @ sK4 ) )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f232]) ).
thf(f232,plain,
( ( $false
= ( listStar @ sK7 @ sK6 @ sK6 ) )
| ( $false = $true )
| ( ( listStar @ sK5 @ sK4 @ sK4 )
= $false )
| ( ( listStar @ sK3 @ sK1 @ sK1 )
= $false )
| ( ( listStar @ ( plus @ ( plus @ sK7 @ sK5 ) @ ( plus @ sK7 @ sK5 ) ) @ ( app @ sK3 @ ( plus @ sK7 @ sK5 ) @ sK1 @ ( app @ sK7 @ sK5 @ sK6 @ sK4 ) ) @ ( app @ ( plus @ sK3 @ sK7 ) @ sK5 @ ( app @ sK3 @ sK7 @ sK1 @ sK6 ) @ sK4 ) )
= $false ) ),
inference(superposition,[status(thm)],[f228,f125]) ).
thf(f125,plain,
( $false
= ( listStar @ ( plus @ ( suc @ ( plus @ sK7 @ sK5 ) ) @ ( plus @ sK7 @ sK5 ) ) @ ( app @ ( suc @ sK3 ) @ ( plus @ sK7 @ sK5 ) @ ( cons @ sK3 @ sK2 @ sK1 ) @ ( app @ sK7 @ sK5 @ sK6 @ sK4 ) ) @ ( app @ ( plus @ ( suc @ sK3 ) @ sK7 ) @ sK5 @ ( app @ ( suc @ sK3 ) @ sK7 @ ( cons @ sK3 @ sK2 @ sK1 ) @ sK6 ) @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f123]) ).
thf(f123,plain,
( $false
= ( ( listStar @ ( plus @ ( plus @ sK7 @ sK5 ) @ ( plus @ sK7 @ sK5 ) ) @ ( app @ sK3 @ ( plus @ sK7 @ sK5 ) @ sK1 @ ( app @ sK7 @ sK5 @ sK6 @ sK4 ) ) @ ( app @ ( plus @ sK3 @ sK7 ) @ sK5 @ ( app @ sK3 @ sK7 @ sK1 @ sK6 ) @ sK4 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ sK7 @ sK5 ) ) @ ( plus @ sK7 @ sK5 ) ) @ ( app @ ( suc @ sK3 ) @ ( plus @ sK7 @ sK5 ) @ ( cons @ sK3 @ sK2 @ sK1 ) @ ( app @ sK7 @ sK5 @ sK6 @ sK4 ) ) @ ( app @ ( plus @ ( suc @ sK3 ) @ sK7 ) @ sK5 @ ( app @ ( suc @ sK3 ) @ sK7 @ ( cons @ sK3 @ sK2 @ sK1 ) @ sK6 ) @ sK4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f121]) ).
thf(f228,plain,
! [X2: nat,X3: elem,X0: nat,X1: nat,X6: list,X4: list,X5: list] :
( ( $true
= ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X1 ) ) @ ( plus @ X0 @ X1 ) ) @ ( app @ ( suc @ X2 ) @ ( plus @ X0 @ X1 ) @ ( cons @ X2 @ X3 @ X4 ) @ ( app @ X0 @ X1 @ X5 @ X6 ) ) @ ( app @ ( plus @ ( suc @ X2 ) @ X0 ) @ X1 @ ( app @ ( suc @ X2 ) @ X0 @ ( cons @ X2 @ X3 @ X4 ) @ X5 ) @ X6 ) ) )
| ( $false
= ( listStar @ X2 @ X4 @ X4 ) )
| ( $false
= ( listStar @ X0 @ X5 @ X5 ) )
| ( ( listStar @ X1 @ X6 @ X6 )
= $false )
| ( ( listStar @ ( plus @ ( plus @ X0 @ X1 ) @ ( plus @ X0 @ X1 ) ) @ ( app @ X2 @ ( plus @ X0 @ X1 ) @ X4 @ ( app @ X0 @ X1 @ X5 @ X6 ) ) @ ( app @ ( plus @ X2 @ X0 ) @ X1 @ ( app @ X2 @ X0 @ X4 @ X5 ) @ X6 ) )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f227]) ).
thf(f227,plain,
! [X2: nat,X3: elem,X0: nat,X1: nat,X6: list,X4: list,X5: list] :
( ( $true
= ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X1 ) ) @ ( plus @ X0 @ X1 ) ) @ ( app @ ( suc @ X2 ) @ ( plus @ X0 @ X1 ) @ ( cons @ X2 @ X3 @ X4 ) @ ( app @ X0 @ X1 @ X5 @ X6 ) ) @ ( app @ ( plus @ ( suc @ X2 ) @ X0 ) @ X1 @ ( app @ ( suc @ X2 ) @ X0 @ ( cons @ X2 @ X3 @ X4 ) @ X5 ) @ X6 ) ) )
| ( $false
= ( listStar @ X0 @ X5 @ X5 ) )
| ( $false = $true )
| ( $false
= ( listStar @ X2 @ X4 @ X4 ) )
| ( ( listStar @ ( plus @ ( plus @ X0 @ X1 ) @ ( plus @ X0 @ X1 ) ) @ ( app @ X2 @ ( plus @ X0 @ X1 ) @ X4 @ ( app @ X0 @ X1 @ X5 @ X6 ) ) @ ( app @ ( plus @ X2 @ X0 ) @ X1 @ ( app @ X2 @ X0 @ X4 @ X5 ) @ X6 ) )
= $false )
| ( ( listStar @ X1 @ X6 @ X6 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f226]) ).
thf(f226,plain,
! [X2: nat,X3: elem,X0: nat,X1: nat,X6: list,X4: list,X5: list] :
( ( $false
= ( listStar @ X2 @ X4 @ X4 ) )
| ( ( listStar @ ( plus @ ( plus @ X0 @ X1 ) @ ( plus @ X0 @ X1 ) ) @ ( app @ X2 @ ( plus @ X0 @ X1 ) @ X4 @ ( app @ X0 @ X1 @ X5 @ X6 ) ) @ ( app @ ( plus @ X2 @ X0 ) @ X1 @ ( app @ X2 @ X0 @ X4 @ X5 ) @ X6 ) )
= $false )
| ( $false
= ( listStar @ X0 @ X5 @ X5 ) )
| ( $true
= ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X1 ) ) @ ( plus @ X0 @ X1 ) ) @ ( app @ ( suc @ X2 ) @ ( plus @ X0 @ X1 ) @ ( cons @ X2 @ X3 @ X4 ) @ ( app @ X0 @ X1 @ X5 @ X6 ) ) @ ( app @ ( plus @ ( suc @ X2 ) @ X0 ) @ X1 @ ( app @ ( suc @ X2 ) @ X0 @ ( cons @ X2 @ X3 @ X4 ) @ X5 ) @ X6 ) ) )
| ( ( listStar @ X1 @ X6 @ X6 )
= $false )
| ( $false
= ( listStar @ X0 @ X5 @ X5 ) )
| ( ( listStar @ X1 @ X6 @ X6 )
= $false )
| ( $false = $true )
| ( $false
= ( listStar @ X2 @ X4 @ X4 ) ) ),
inference(superposition,[status(thm)],[f76,f221]) ).
thf(f221,plain,
! [X2: nat,X3: elem,X0: nat,X1: nat,X6: list,X4: list,X5: list] :
( ( ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X1 ) ) @ ( plus @ X0 @ X1 ) ) @ ( app @ ( suc @ X2 ) @ ( plus @ X0 @ X1 ) @ ( cons @ X2 @ X3 @ X4 ) @ ( app @ X0 @ X1 @ X5 @ X6 ) ) @ ( app @ ( suc @ ( plus @ X2 @ X0 ) ) @ X1 @ ( cons @ ( plus @ X2 @ X0 ) @ X3 @ ( app @ X2 @ X0 @ X4 @ X5 ) ) @ X6 ) )
= $true )
| ( ( listStar @ X1 @ X6 @ X6 )
= $false )
| ( $false
= ( listStar @ X0 @ X5 @ X5 ) )
| ( $false
= ( listStar @ X2 @ X4 @ X4 ) )
| ( ( listStar @ ( plus @ ( plus @ X0 @ X1 ) @ ( plus @ X0 @ X1 ) ) @ ( app @ X2 @ ( plus @ X0 @ X1 ) @ X4 @ ( app @ X0 @ X1 @ X5 @ X6 ) ) @ ( app @ ( plus @ X2 @ X0 ) @ X1 @ ( app @ X2 @ X0 @ X4 @ X5 ) @ X6 ) )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f220]) ).
thf(f220,plain,
! [X2: nat,X3: elem,X0: nat,X1: nat,X6: list,X4: list,X5: list] :
( ( ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X1 ) ) @ ( plus @ X0 @ X1 ) ) @ ( app @ ( suc @ X2 ) @ ( plus @ X0 @ X1 ) @ ( cons @ X2 @ X3 @ X4 ) @ ( app @ X0 @ X1 @ X5 @ X6 ) ) @ ( app @ ( suc @ ( plus @ X2 @ X0 ) ) @ X1 @ ( cons @ ( plus @ X2 @ X0 ) @ X3 @ ( app @ X2 @ X0 @ X4 @ X5 ) ) @ X6 ) )
= $true )
| ( $false = $true )
| ( ( listStar @ ( plus @ ( plus @ X0 @ X1 ) @ ( plus @ X0 @ X1 ) ) @ ( app @ X2 @ ( plus @ X0 @ X1 ) @ X4 @ ( app @ X0 @ X1 @ X5 @ X6 ) ) @ ( app @ ( plus @ X2 @ X0 ) @ X1 @ ( app @ X2 @ X0 @ X4 @ X5 ) @ X6 ) )
= $false )
| ( ( listStar @ X1 @ X6 @ X6 )
= $false )
| ( $false
= ( listStar @ X0 @ X5 @ X5 ) )
| ( $false
= ( listStar @ X2 @ X4 @ X4 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f219]) ).
thf(f219,plain,
! [X2: nat,X3: elem,X0: nat,X1: nat,X6: list,X4: list,X5: list] :
( ( $false
= ( listStar @ X0 @ X5 @ X5 ) )
| ( ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X1 ) ) @ ( plus @ X0 @ X1 ) ) @ ( app @ ( suc @ X2 ) @ ( plus @ X0 @ X1 ) @ ( cons @ X2 @ X3 @ X4 ) @ ( app @ X0 @ X1 @ X5 @ X6 ) ) @ ( app @ ( suc @ ( plus @ X2 @ X0 ) ) @ X1 @ ( cons @ ( plus @ X2 @ X0 ) @ X3 @ ( app @ X2 @ X0 @ X4 @ X5 ) ) @ X6 ) )
= $true )
| ( $false
= ( listStar @ X2 @ X4 @ X4 ) )
| ( $false
= ( listStar @ X0 @ X5 @ X5 ) )
| ( ( listStar @ X1 @ X6 @ X6 )
= $false )
| ( $false = $true )
| ( ( listStar @ X1 @ X6 @ X6 )
= $false )
| ( ( listStar @ ( plus @ ( plus @ X0 @ X1 ) @ ( plus @ X0 @ X1 ) ) @ ( app @ X2 @ ( plus @ X0 @ X1 ) @ X4 @ ( app @ X0 @ X1 @ X5 @ X6 ) ) @ ( app @ ( plus @ X2 @ X0 ) @ X1 @ ( app @ X2 @ X0 @ X4 @ X5 ) @ X6 ) )
= $false )
| ( $false
= ( listStar @ X2 @ X4 @ X4 ) ) ),
inference(superposition,[status(thm)],[f103,f209]) ).
thf(f209,plain,
! [X2: nat,X3: elem,X0: nat,X1: nat,X6: list,X4: list,X5: list] :
( ( ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X1 ) ) @ ( plus @ X0 @ X1 ) ) @ ( app @ ( suc @ X2 ) @ ( plus @ X0 @ X1 ) @ ( cons @ X2 @ X3 @ X4 ) @ ( app @ X0 @ X1 @ X5 @ X6 ) ) @ ( cons @ ( plus @ ( plus @ X2 @ X0 ) @ X1 ) @ X3 @ ( app @ ( plus @ X2 @ X0 ) @ X1 @ ( app @ X2 @ X0 @ X4 @ X5 ) @ X6 ) ) )
= $true )
| ( $false
= ( listStar @ X2 @ X4 @ X4 ) )
| ( ( listStar @ X1 @ X6 @ X6 )
= $false )
| ( $false
= ( listStar @ X0 @ X5 @ X5 ) )
| ( ( listStar @ ( plus @ ( plus @ X0 @ X1 ) @ ( plus @ X0 @ X1 ) ) @ ( app @ X2 @ ( plus @ X0 @ X1 ) @ X4 @ ( app @ X0 @ X1 @ X5 @ X6 ) ) @ ( app @ ( plus @ X2 @ X0 ) @ X1 @ ( app @ X2 @ X0 @ X4 @ X5 ) @ X6 ) )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f208]) ).
thf(f208,plain,
! [X2: nat,X3: elem,X0: nat,X1: nat,X6: list,X4: list,X5: list] :
( ( ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X1 ) ) @ ( plus @ X0 @ X1 ) ) @ ( app @ ( suc @ X2 ) @ ( plus @ X0 @ X1 ) @ ( cons @ X2 @ X3 @ X4 ) @ ( app @ X0 @ X1 @ X5 @ X6 ) ) @ ( cons @ ( plus @ ( plus @ X2 @ X0 ) @ X1 ) @ X3 @ ( app @ ( plus @ X2 @ X0 ) @ X1 @ ( app @ X2 @ X0 @ X4 @ X5 ) @ X6 ) ) )
= $true )
| ( $false = $true )
| ( $false
= ( listStar @ X0 @ X5 @ X5 ) )
| ( $false
= ( listStar @ X2 @ X4 @ X4 ) )
| ( ( listStar @ ( plus @ ( plus @ X0 @ X1 ) @ ( plus @ X0 @ X1 ) ) @ ( app @ X2 @ ( plus @ X0 @ X1 ) @ X4 @ ( app @ X0 @ X1 @ X5 @ X6 ) ) @ ( app @ ( plus @ X2 @ X0 ) @ X1 @ ( app @ X2 @ X0 @ X4 @ X5 ) @ X6 ) )
= $false )
| ( ( listStar @ X1 @ X6 @ X6 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f206]) ).
thf(f206,plain,
! [X2: nat,X3: elem,X0: nat,X1: nat,X6: list,X4: list,X5: list] :
( ( $false
= ( listStar @ X2 @ X4 @ X4 ) )
| ( $false
= ( listStar @ X0 @ X5 @ X5 ) )
| ( ( listStar @ ( plus @ ( plus @ X0 @ X1 ) @ ( plus @ X0 @ X1 ) ) @ ( app @ X2 @ ( plus @ X0 @ X1 ) @ X4 @ ( app @ X0 @ X1 @ X5 @ X6 ) ) @ ( app @ ( plus @ X2 @ X0 ) @ X1 @ ( app @ X2 @ X0 @ X4 @ X5 ) @ X6 ) )
= $false )
| ( $false = $true )
| ( ( listStar @ X1 @ X6 @ X6 )
= $false )
| ( ( listStar @ X1 @ X6 @ X6 )
= $false )
| ( $false
= ( listStar @ X2 @ X4 @ X4 ) )
| ( $false
= ( listStar @ X0 @ X5 @ X5 ) )
| ( ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X1 ) ) @ ( plus @ X0 @ X1 ) ) @ ( app @ ( suc @ X2 ) @ ( plus @ X0 @ X1 ) @ ( cons @ X2 @ X3 @ X4 ) @ ( app @ X0 @ X1 @ X5 @ X6 ) ) @ ( cons @ ( plus @ ( plus @ X2 @ X0 ) @ X1 ) @ X3 @ ( app @ ( plus @ X2 @ X0 ) @ X1 @ ( app @ X2 @ X0 @ X4 @ X5 ) @ X6 ) ) )
= $true ) ),
inference(superposition,[status(thm)],[f188,f157]) ).
thf(f157,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X7: nat,X4: list,X5: nat] :
( ( $false
= ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ X3 @ ( plus @ X7 @ X5 ) ) @ X2 @ ( app @ X3 @ ( plus @ X7 @ X5 ) @ X1 @ ( app @ X7 @ X5 @ X6 @ X4 ) ) ) ) )
| ( $false
= ( listStar @ X3 @ X1 @ X1 ) )
| ( ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ ( plus @ X3 @ X7 ) @ X5 ) @ X2 @ ( app @ ( plus @ X3 @ X7 ) @ X5 @ ( app @ X3 @ X7 @ X1 @ X6 ) @ X4 ) ) )
= $true )
| ( $false
= ( listStar @ X7 @ X6 @ X6 ) )
| ( $false
= ( listStar @ X5 @ X4 @ X4 ) )
| ( $false
= ( listStar @ ( plus @ ( plus @ X7 @ X5 ) @ ( plus @ X7 @ X5 ) ) @ ( app @ X3 @ ( plus @ X7 @ X5 ) @ X1 @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( app @ ( plus @ X3 @ X7 ) @ X5 @ ( app @ X3 @ X7 @ X1 @ X6 ) @ X4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f156]) ).
thf(f156,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X7: nat,X4: list,X5: nat] :
( ( $false
= ( listStar @ X3 @ X1 @ X1 ) )
| ( $false
= ( listStar @ ( plus @ ( plus @ X7 @ X5 ) @ ( plus @ X7 @ X5 ) ) @ ( app @ X3 @ ( plus @ X7 @ X5 ) @ X1 @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( app @ ( plus @ X3 @ X7 ) @ X5 @ ( app @ X3 @ X7 @ X1 @ X6 ) @ X4 ) ) )
| ( $true
= ( ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ X3 @ ( plus @ X7 @ X5 ) ) @ X2 @ ( app @ X3 @ ( plus @ X7 @ X5 ) @ X1 @ ( app @ X7 @ X5 @ X6 @ X4 ) ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ ( plus @ X3 @ X7 ) @ X5 ) @ X2 @ ( app @ ( plus @ X3 @ X7 ) @ X5 @ ( app @ X3 @ X7 @ X1 @ X6 ) @ X4 ) ) ) ) )
| ( $false
= ( listStar @ X7 @ X6 @ X6 ) )
| ( $false
= ( listStar @ X5 @ X4 @ X4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f155]) ).
thf(f155,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X7: nat,X4: list,X5: nat] :
( ( $false
= ( listStar @ X7 @ X6 @ X6 ) )
| ( $false
= ( listStar @ X5 @ X4 @ X4 ) )
| ( $false
= ( listStar @ X3 @ X1 @ X1 ) )
| ( ( ( listStar @ ( plus @ ( plus @ X7 @ X5 ) @ ( plus @ X7 @ X5 ) ) @ ( app @ X3 @ ( plus @ X7 @ X5 ) @ X1 @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( app @ ( plus @ X3 @ X7 ) @ X5 @ ( app @ X3 @ X7 @ X1 @ X6 ) @ X4 ) )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ X3 @ ( plus @ X7 @ X5 ) ) @ X2 @ ( app @ X3 @ ( plus @ X7 @ X5 ) @ X1 @ ( app @ X7 @ X5 @ X6 @ X4 ) ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ ( plus @ X3 @ X7 ) @ X5 ) @ X2 @ ( app @ ( plus @ X3 @ X7 ) @ X5 @ ( app @ X3 @ X7 @ X1 @ X6 ) @ X4 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f154]) ).
thf(f154,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X7: nat,X4: list,X5: nat] :
( ( $false
= ( listStar @ X7 @ X6 @ X6 ) )
| ( ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( plus @ X7 @ X5 ) @ ( plus @ X7 @ X5 ) ) @ ( app @ X3 @ ( plus @ X7 @ X5 ) @ X1 @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( app @ ( plus @ X3 @ X7 ) @ X5 @ ( app @ X3 @ X7 @ X1 @ X6 ) @ X4 ) )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ X3 @ ( plus @ X7 @ X5 ) ) @ X2 @ ( app @ X3 @ ( plus @ X7 @ X5 ) @ X1 @ ( app @ X7 @ X5 @ X6 @ X4 ) ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ ( plus @ X3 @ X7 ) @ X5 ) @ X2 @ ( app @ ( plus @ X3 @ X7 ) @ X5 @ ( app @ X3 @ X7 @ X1 @ X6 ) @ X4 ) ) ) ) ) )
= $true )
| ( $false
= ( listStar @ X5 @ X4 @ X4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f153]) ).
thf(f153,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X7: nat,X4: list,X5: nat] :
( ( $false
= ( listStar @ X7 @ X6 @ X6 ) )
| ( ( ( listStar @ X5 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( plus @ X7 @ X5 ) @ ( plus @ X7 @ X5 ) ) @ ( app @ X3 @ ( plus @ X7 @ X5 ) @ X1 @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( app @ ( plus @ X3 @ X7 ) @ X5 @ ( app @ X3 @ X7 @ X1 @ X6 ) @ X4 ) )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ X3 @ ( plus @ X7 @ X5 ) ) @ X2 @ ( app @ X3 @ ( plus @ X7 @ X5 ) @ X1 @ ( app @ X7 @ X5 @ X6 @ X4 ) ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ ( plus @ X3 @ X7 ) @ X5 ) @ X2 @ ( app @ ( plus @ X3 @ X7 ) @ X5 @ ( app @ X3 @ X7 @ X1 @ X6 ) @ X4 ) ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f152]) ).
thf(f152,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X7: nat,X4: list,X5: nat] :
( $true
= ( ( listStar @ X7 @ X6 @ X6 )
=> ( ( listStar @ X5 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( plus @ X7 @ X5 ) @ ( plus @ X7 @ X5 ) ) @ ( app @ X3 @ ( plus @ X7 @ X5 ) @ X1 @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( app @ ( plus @ X3 @ X7 ) @ X5 @ ( app @ X3 @ X7 @ X1 @ X6 ) @ X4 ) )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ X3 @ ( plus @ X7 @ X5 ) ) @ X2 @ ( app @ X3 @ ( plus @ X7 @ X5 ) @ X1 @ ( app @ X7 @ X5 @ X6 @ X4 ) ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ ( plus @ X3 @ X7 ) @ X5 ) @ X2 @ ( app @ ( plus @ X3 @ X7 ) @ X5 @ ( app @ X3 @ X7 @ X1 @ X6 ) @ X4 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f151]) ).
thf(f151,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X7: nat,X4: list,X5: nat] :
( $true
= ( ^ [Y0: nat] :
( ( listStar @ Y0 @ X6 @ X6 )
=> ( ( listStar @ X5 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( plus @ Y0 @ X5 ) @ ( plus @ Y0 @ X5 ) ) @ ( app @ X3 @ ( plus @ Y0 @ X5 ) @ X1 @ ( app @ Y0 @ X5 @ X6 @ X4 ) ) @ ( app @ ( plus @ X3 @ Y0 ) @ X5 @ ( app @ X3 @ Y0 @ X1 @ X6 ) @ X4 ) )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y0 @ X5 ) ) @ ( plus @ Y0 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y0 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y0 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ X3 @ ( plus @ Y0 @ X5 ) ) @ X2 @ ( app @ X3 @ ( plus @ Y0 @ X5 ) @ X1 @ ( app @ Y0 @ X5 @ X6 @ X4 ) ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y0 @ X5 ) ) @ ( plus @ Y0 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y0 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y0 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ ( plus @ X3 @ Y0 ) @ X5 ) @ X2 @ ( app @ ( plus @ X3 @ Y0 ) @ X5 @ ( app @ X3 @ Y0 @ X1 @ X6 ) @ X4 ) ) ) ) ) ) ) )
@ X7 ) ),
inference(pi_clausification,[status(thm)],[f150]) ).
thf(f150,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X4: list,X5: nat] :
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( listStar @ Y0 @ X6 @ X6 )
=> ( ( listStar @ X5 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( plus @ Y0 @ X5 ) @ ( plus @ Y0 @ X5 ) ) @ ( app @ X3 @ ( plus @ Y0 @ X5 ) @ X1 @ ( app @ Y0 @ X5 @ X6 @ X4 ) ) @ ( app @ ( plus @ X3 @ Y0 ) @ X5 @ ( app @ X3 @ Y0 @ X1 @ X6 ) @ X4 ) )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y0 @ X5 ) ) @ ( plus @ Y0 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y0 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y0 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ X3 @ ( plus @ Y0 @ X5 ) ) @ X2 @ ( app @ X3 @ ( plus @ Y0 @ X5 ) @ X1 @ ( app @ Y0 @ X5 @ X6 @ X4 ) ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y0 @ X5 ) ) @ ( plus @ Y0 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y0 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y0 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ ( plus @ X3 @ Y0 ) @ X5 ) @ X2 @ ( app @ ( plus @ X3 @ Y0 ) @ X5 @ ( app @ X3 @ Y0 @ X1 @ X6 ) @ X4 ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f149]) ).
thf(f149,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X4: list,X5: nat] :
( ( ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( ( listStar @ X5 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( plus @ Y1 @ X5 ) @ ( plus @ Y1 @ X5 ) ) @ ( app @ X3 @ ( plus @ Y1 @ X5 ) @ X1 @ ( app @ Y1 @ X5 @ Y0 @ X4 ) ) @ ( app @ ( plus @ X3 @ Y1 ) @ X5 @ ( app @ X3 @ Y1 @ X1 @ Y0 ) @ X4 ) )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y1 @ X5 ) ) @ ( plus @ Y1 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y1 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y1 @ X5 @ Y0 @ X4 ) ) @ ( cons @ ( plus @ X3 @ ( plus @ Y1 @ X5 ) ) @ X2 @ ( app @ X3 @ ( plus @ Y1 @ X5 ) @ X1 @ ( app @ Y1 @ X5 @ Y0 @ X4 ) ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y1 @ X5 ) ) @ ( plus @ Y1 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y1 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y1 @ X5 @ Y0 @ X4 ) ) @ ( cons @ ( plus @ ( plus @ X3 @ Y1 ) @ X5 ) @ X2 @ ( app @ ( plus @ X3 @ Y1 ) @ X5 @ ( app @ X3 @ Y1 @ X1 @ Y0 ) @ X4 ) ) ) ) ) ) ) ) )
@ X6 )
= $true ),
inference(pi_clausification,[status(thm)],[f148]) ).
thf(f148,plain,
! [X2: elem,X3: nat,X1: list,X4: list,X5: nat] :
( ( !! @ list
@ ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( ( listStar @ X5 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( plus @ Y1 @ X5 ) @ ( plus @ Y1 @ X5 ) ) @ ( app @ X3 @ ( plus @ Y1 @ X5 ) @ X1 @ ( app @ Y1 @ X5 @ Y0 @ X4 ) ) @ ( app @ ( plus @ X3 @ Y1 ) @ X5 @ ( app @ X3 @ Y1 @ X1 @ Y0 ) @ X4 ) )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y1 @ X5 ) ) @ ( plus @ Y1 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y1 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y1 @ X5 @ Y0 @ X4 ) ) @ ( cons @ ( plus @ X3 @ ( plus @ Y1 @ X5 ) ) @ X2 @ ( app @ X3 @ ( plus @ Y1 @ X5 ) @ X1 @ ( app @ Y1 @ X5 @ Y0 @ X4 ) ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y1 @ X5 ) ) @ ( plus @ Y1 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y1 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y1 @ X5 @ Y0 @ X4 ) ) @ ( cons @ ( plus @ ( plus @ X3 @ Y1 ) @ X5 ) @ X2 @ ( app @ ( plus @ X3 @ Y1 ) @ X5 @ ( app @ X3 @ Y1 @ X1 @ Y0 ) @ X4 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f147]) ).
thf(f147,plain,
! [X2: elem,X3: nat,X1: list,X4: list,X5: nat] :
( ( ^ [Y0: nat] :
( !! @ list
@ ^ [Y1: list] :
( !! @ nat
@ ^ [Y2: nat] :
( ( listStar @ Y2 @ Y1 @ Y1 )
=> ( ( listStar @ Y0 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( plus @ Y2 @ Y0 ) @ ( plus @ Y2 @ Y0 ) ) @ ( app @ X3 @ ( plus @ Y2 @ Y0 ) @ X1 @ ( app @ Y2 @ Y0 @ Y1 @ X4 ) ) @ ( app @ ( plus @ X3 @ Y2 ) @ Y0 @ ( app @ X3 @ Y2 @ X1 @ Y1 ) @ X4 ) )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y2 @ Y0 ) ) @ ( plus @ Y2 @ Y0 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y2 @ Y0 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y2 @ Y0 @ Y1 @ X4 ) ) @ ( cons @ ( plus @ X3 @ ( plus @ Y2 @ Y0 ) ) @ X2 @ ( app @ X3 @ ( plus @ Y2 @ Y0 ) @ X1 @ ( app @ Y2 @ Y0 @ Y1 @ X4 ) ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y2 @ Y0 ) ) @ ( plus @ Y2 @ Y0 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y2 @ Y0 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y2 @ Y0 @ Y1 @ X4 ) ) @ ( cons @ ( plus @ ( plus @ X3 @ Y2 ) @ Y0 ) @ X2 @ ( app @ ( plus @ X3 @ Y2 ) @ Y0 @ ( app @ X3 @ Y2 @ X1 @ Y1 ) @ X4 ) ) ) ) ) ) ) ) ) )
@ X5 )
= $true ),
inference(pi_clausification,[status(thm)],[f146]) ).
thf(f146,plain,
! [X2: elem,X3: nat,X1: list,X4: list] :
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ list
@ ^ [Y1: list] :
( !! @ nat
@ ^ [Y2: nat] :
( ( listStar @ Y2 @ Y1 @ Y1 )
=> ( ( listStar @ Y0 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( plus @ Y2 @ Y0 ) @ ( plus @ Y2 @ Y0 ) ) @ ( app @ X3 @ ( plus @ Y2 @ Y0 ) @ X1 @ ( app @ Y2 @ Y0 @ Y1 @ X4 ) ) @ ( app @ ( plus @ X3 @ Y2 ) @ Y0 @ ( app @ X3 @ Y2 @ X1 @ Y1 ) @ X4 ) )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y2 @ Y0 ) ) @ ( plus @ Y2 @ Y0 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y2 @ Y0 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y2 @ Y0 @ Y1 @ X4 ) ) @ ( cons @ ( plus @ X3 @ ( plus @ Y2 @ Y0 ) ) @ X2 @ ( app @ X3 @ ( plus @ Y2 @ Y0 ) @ X1 @ ( app @ Y2 @ Y0 @ Y1 @ X4 ) ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y2 @ Y0 ) ) @ ( plus @ Y2 @ Y0 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y2 @ Y0 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y2 @ Y0 @ Y1 @ X4 ) ) @ ( cons @ ( plus @ ( plus @ X3 @ Y2 ) @ Y0 ) @ X2 @ ( app @ ( plus @ X3 @ Y2 ) @ Y0 @ ( app @ X3 @ Y2 @ X1 @ Y1 ) @ X4 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f145]) ).
thf(f145,plain,
! [X2: elem,X3: nat,X1: list,X4: list] :
( ( ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list
@ ^ [Y2: list] :
( !! @ nat
@ ^ [Y3: nat] :
( ( listStar @ Y3 @ Y2 @ Y2 )
=> ( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( plus @ Y3 @ Y1 ) @ ( plus @ Y3 @ Y1 ) ) @ ( app @ X3 @ ( plus @ Y3 @ Y1 ) @ X1 @ ( app @ Y3 @ Y1 @ Y2 @ Y0 ) ) @ ( app @ ( plus @ X3 @ Y3 ) @ Y1 @ ( app @ X3 @ Y3 @ X1 @ Y2 ) @ Y0 ) )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y3 @ Y1 ) ) @ ( plus @ Y3 @ Y1 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y3 @ Y1 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y3 @ Y1 @ Y2 @ Y0 ) ) @ ( cons @ ( plus @ X3 @ ( plus @ Y3 @ Y1 ) ) @ X2 @ ( app @ X3 @ ( plus @ Y3 @ Y1 ) @ X1 @ ( app @ Y3 @ Y1 @ Y2 @ Y0 ) ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y3 @ Y1 ) ) @ ( plus @ Y3 @ Y1 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y3 @ Y1 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y3 @ Y1 @ Y2 @ Y0 ) ) @ ( cons @ ( plus @ ( plus @ X3 @ Y3 ) @ Y1 ) @ X2 @ ( app @ ( plus @ X3 @ Y3 ) @ Y1 @ ( app @ X3 @ Y3 @ X1 @ Y2 ) @ Y0 ) ) ) ) ) ) ) ) ) ) )
@ X4 )
= $true ),
inference(pi_clausification,[status(thm)],[f144]) ).
thf(f144,plain,
! [X2: elem,X3: nat,X1: list] :
( ( !! @ list
@ ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list
@ ^ [Y2: list] :
( !! @ nat
@ ^ [Y3: nat] :
( ( listStar @ Y3 @ Y2 @ Y2 )
=> ( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( plus @ Y3 @ Y1 ) @ ( plus @ Y3 @ Y1 ) ) @ ( app @ X3 @ ( plus @ Y3 @ Y1 ) @ X1 @ ( app @ Y3 @ Y1 @ Y2 @ Y0 ) ) @ ( app @ ( plus @ X3 @ Y3 ) @ Y1 @ ( app @ X3 @ Y3 @ X1 @ Y2 ) @ Y0 ) )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y3 @ Y1 ) ) @ ( plus @ Y3 @ Y1 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y3 @ Y1 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y3 @ Y1 @ Y2 @ Y0 ) ) @ ( cons @ ( plus @ X3 @ ( plus @ Y3 @ Y1 ) ) @ X2 @ ( app @ X3 @ ( plus @ Y3 @ Y1 ) @ X1 @ ( app @ Y3 @ Y1 @ Y2 @ Y0 ) ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y3 @ Y1 ) ) @ ( plus @ Y3 @ Y1 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y3 @ Y1 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y3 @ Y1 @ Y2 @ Y0 ) ) @ ( cons @ ( plus @ ( plus @ X3 @ Y3 ) @ Y1 ) @ X2 @ ( app @ ( plus @ X3 @ Y3 ) @ Y1 @ ( app @ X3 @ Y3 @ X1 @ Y2 ) @ Y0 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f143]) ).
thf(f143,plain,
! [X2: elem,X3: nat,X1: list] :
( ( ^ [Y0: nat] :
( !! @ list
@ ^ [Y1: list] :
( !! @ nat
@ ^ [Y2: nat] :
( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( ( listStar @ Y2 @ Y1 @ Y1 )
=> ( ( listStar @ Y0 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( plus @ Y4 @ Y2 ) @ ( plus @ Y4 @ Y2 ) ) @ ( app @ Y0 @ ( plus @ Y4 @ Y2 ) @ X1 @ ( app @ Y4 @ Y2 @ Y3 @ Y1 ) ) @ ( app @ ( plus @ Y0 @ Y4 ) @ Y2 @ ( app @ Y0 @ Y4 @ X1 @ Y3 ) @ Y1 ) )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y4 @ Y2 ) ) @ ( plus @ Y4 @ Y2 ) ) @ ( app @ ( suc @ Y0 ) @ ( plus @ Y4 @ Y2 ) @ ( cons @ Y0 @ X2 @ X1 ) @ ( app @ Y4 @ Y2 @ Y3 @ Y1 ) ) @ ( cons @ ( plus @ Y0 @ ( plus @ Y4 @ Y2 ) ) @ X2 @ ( app @ Y0 @ ( plus @ Y4 @ Y2 ) @ X1 @ ( app @ Y4 @ Y2 @ Y3 @ Y1 ) ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y4 @ Y2 ) ) @ ( plus @ Y4 @ Y2 ) ) @ ( app @ ( suc @ Y0 ) @ ( plus @ Y4 @ Y2 ) @ ( cons @ Y0 @ X2 @ X1 ) @ ( app @ Y4 @ Y2 @ Y3 @ Y1 ) ) @ ( cons @ ( plus @ ( plus @ Y0 @ Y4 ) @ Y2 ) @ X2 @ ( app @ ( plus @ Y0 @ Y4 ) @ Y2 @ ( app @ Y0 @ Y4 @ X1 @ Y3 ) @ Y1 ) ) ) ) ) ) ) ) ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f142]) ).
thf(f142,plain,
! [X2: elem,X1: list] :
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( !! @ list
@ ^ [Y1: list] :
( !! @ nat
@ ^ [Y2: nat] :
( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( ( listStar @ Y2 @ Y1 @ Y1 )
=> ( ( listStar @ Y0 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( plus @ Y4 @ Y2 ) @ ( plus @ Y4 @ Y2 ) ) @ ( app @ Y0 @ ( plus @ Y4 @ Y2 ) @ X1 @ ( app @ Y4 @ Y2 @ Y3 @ Y1 ) ) @ ( app @ ( plus @ Y0 @ Y4 ) @ Y2 @ ( app @ Y0 @ Y4 @ X1 @ Y3 ) @ Y1 ) )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y4 @ Y2 ) ) @ ( plus @ Y4 @ Y2 ) ) @ ( app @ ( suc @ Y0 ) @ ( plus @ Y4 @ Y2 ) @ ( cons @ Y0 @ X2 @ X1 ) @ ( app @ Y4 @ Y2 @ Y3 @ Y1 ) ) @ ( cons @ ( plus @ Y0 @ ( plus @ Y4 @ Y2 ) ) @ X2 @ ( app @ Y0 @ ( plus @ Y4 @ Y2 ) @ X1 @ ( app @ Y4 @ Y2 @ Y3 @ Y1 ) ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y4 @ Y2 ) ) @ ( plus @ Y4 @ Y2 ) ) @ ( app @ ( suc @ Y0 ) @ ( plus @ Y4 @ Y2 ) @ ( cons @ Y0 @ X2 @ X1 ) @ ( app @ Y4 @ Y2 @ Y3 @ Y1 ) ) @ ( cons @ ( plus @ ( plus @ Y0 @ Y4 ) @ Y2 ) @ X2 @ ( app @ ( plus @ Y0 @ Y4 ) @ Y2 @ ( app @ Y0 @ Y4 @ X1 @ Y3 ) @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f141]) ).
thf(f141,plain,
! [X2: elem,X1: list] :
( ( ^ [Y0: elem] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list
@ ^ [Y2: list] :
( !! @ nat
@ ^ [Y3: nat] :
( !! @ list
@ ^ [Y4: list] :
( !! @ nat
@ ^ [Y5: nat] :
( ( listStar @ Y5 @ Y4 @ Y4 )
=> ( ( listStar @ Y3 @ Y2 @ Y2 )
=> ( ( listStar @ Y1 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( plus @ Y5 @ Y3 ) @ ( plus @ Y5 @ Y3 ) ) @ ( app @ Y1 @ ( plus @ Y5 @ Y3 ) @ X1 @ ( app @ Y5 @ Y3 @ Y4 @ Y2 ) ) @ ( app @ ( plus @ Y1 @ Y5 ) @ Y3 @ ( app @ Y1 @ Y5 @ X1 @ Y4 ) @ Y2 ) )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y5 @ Y3 ) ) @ ( plus @ Y5 @ Y3 ) ) @ ( app @ ( suc @ Y1 ) @ ( plus @ Y5 @ Y3 ) @ ( cons @ Y1 @ Y0 @ X1 ) @ ( app @ Y5 @ Y3 @ Y4 @ Y2 ) ) @ ( cons @ ( plus @ Y1 @ ( plus @ Y5 @ Y3 ) ) @ Y0 @ ( app @ Y1 @ ( plus @ Y5 @ Y3 ) @ X1 @ ( app @ Y5 @ Y3 @ Y4 @ Y2 ) ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y5 @ Y3 ) ) @ ( plus @ Y5 @ Y3 ) ) @ ( app @ ( suc @ Y1 ) @ ( plus @ Y5 @ Y3 ) @ ( cons @ Y1 @ Y0 @ X1 ) @ ( app @ Y5 @ Y3 @ Y4 @ Y2 ) ) @ ( cons @ ( plus @ ( plus @ Y1 @ Y5 ) @ Y3 ) @ Y0 @ ( app @ ( plus @ Y1 @ Y5 ) @ Y3 @ ( app @ Y1 @ Y5 @ X1 @ Y4 ) @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f140]) ).
thf(f140,plain,
! [X1: list] :
( $true
= ( !! @ elem
@ ^ [Y0: elem] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list
@ ^ [Y2: list] :
( !! @ nat
@ ^ [Y3: nat] :
( !! @ list
@ ^ [Y4: list] :
( !! @ nat
@ ^ [Y5: nat] :
( ( listStar @ Y5 @ Y4 @ Y4 )
=> ( ( listStar @ Y3 @ Y2 @ Y2 )
=> ( ( listStar @ Y1 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( plus @ Y5 @ Y3 ) @ ( plus @ Y5 @ Y3 ) ) @ ( app @ Y1 @ ( plus @ Y5 @ Y3 ) @ X1 @ ( app @ Y5 @ Y3 @ Y4 @ Y2 ) ) @ ( app @ ( plus @ Y1 @ Y5 ) @ Y3 @ ( app @ Y1 @ Y5 @ X1 @ Y4 ) @ Y2 ) )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y5 @ Y3 ) ) @ ( plus @ Y5 @ Y3 ) ) @ ( app @ ( suc @ Y1 ) @ ( plus @ Y5 @ Y3 ) @ ( cons @ Y1 @ Y0 @ X1 ) @ ( app @ Y5 @ Y3 @ Y4 @ Y2 ) ) @ ( cons @ ( plus @ Y1 @ ( plus @ Y5 @ Y3 ) ) @ Y0 @ ( app @ Y1 @ ( plus @ Y5 @ Y3 ) @ X1 @ ( app @ Y5 @ Y3 @ Y4 @ Y2 ) ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y5 @ Y3 ) ) @ ( plus @ Y5 @ Y3 ) ) @ ( app @ ( suc @ Y1 ) @ ( plus @ Y5 @ Y3 ) @ ( cons @ Y1 @ Y0 @ X1 ) @ ( app @ Y5 @ Y3 @ Y4 @ Y2 ) ) @ ( cons @ ( plus @ ( plus @ Y1 @ Y5 ) @ Y3 ) @ Y0 @ ( app @ ( plus @ Y1 @ Y5 ) @ Y3 @ ( app @ Y1 @ Y5 @ X1 @ Y4 ) @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f139]) ).
thf(f139,plain,
! [X1: list] :
( ( ^ [Y0: list] :
( !! @ elem
@ ^ [Y1: elem] :
( !! @ nat
@ ^ [Y2: nat] :
( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( !! @ list
@ ^ [Y5: list] :
( !! @ nat
@ ^ [Y6: nat] :
( ( listStar @ Y6 @ Y5 @ Y5 )
=> ( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( ( listStar @ Y2 @ Y0 @ Y0 )
=> ( ( listStar @ ( plus @ ( plus @ Y6 @ Y4 ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ Y2 @ ( plus @ Y6 @ Y4 ) @ Y0 @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( app @ ( plus @ Y2 @ Y6 ) @ Y4 @ ( app @ Y2 @ Y6 @ Y0 @ Y5 ) @ Y3 ) )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y6 @ Y4 ) ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ ( suc @ Y2 ) @ ( plus @ Y6 @ Y4 ) @ ( cons @ Y2 @ Y1 @ Y0 ) @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( cons @ ( plus @ Y2 @ ( plus @ Y6 @ Y4 ) ) @ Y1 @ ( app @ Y2 @ ( plus @ Y6 @ Y4 ) @ Y0 @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y6 @ Y4 ) ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ ( suc @ Y2 ) @ ( plus @ Y6 @ Y4 ) @ ( cons @ Y2 @ Y1 @ Y0 ) @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( cons @ ( plus @ ( plus @ Y2 @ Y6 ) @ Y4 ) @ Y1 @ ( app @ ( plus @ Y2 @ Y6 ) @ Y4 @ ( app @ Y2 @ Y6 @ Y0 @ Y5 ) @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( $true
= ( !! @ list
@ ^ [Y0: list] :
( !! @ elem
@ ^ [Y1: elem] :
( !! @ nat
@ ^ [Y2: nat] :
( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( !! @ list
@ ^ [Y5: list] :
( !! @ nat
@ ^ [Y6: nat] :
( ( listStar @ Y6 @ Y5 @ Y5 )
=> ( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( ( listStar @ Y2 @ Y0 @ Y0 )
=> ( ( listStar @ ( plus @ ( plus @ Y6 @ Y4 ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ Y2 @ ( plus @ Y6 @ Y4 ) @ Y0 @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( app @ ( plus @ Y2 @ Y6 ) @ Y4 @ ( app @ Y2 @ Y6 @ Y0 @ Y5 ) @ Y3 ) )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y6 @ Y4 ) ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ ( suc @ Y2 ) @ ( plus @ Y6 @ Y4 ) @ ( cons @ Y2 @ Y1 @ Y0 ) @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( cons @ ( plus @ Y2 @ ( plus @ Y6 @ Y4 ) ) @ Y1 @ ( app @ Y2 @ ( plus @ Y6 @ Y4 ) @ Y0 @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y6 @ Y4 ) ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ ( suc @ Y2 ) @ ( plus @ Y6 @ Y4 ) @ ( cons @ Y2 @ Y1 @ Y0 ) @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( cons @ ( plus @ ( plus @ Y2 @ Y6 ) @ Y4 ) @ Y1 @ ( app @ ( plus @ Y2 @ Y6 ) @ Y4 @ ( app @ Y2 @ Y6 @ Y0 @ Y5 ) @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
( $true
= ( !! @ list
@ ^ [Y0: list] :
( !! @ elem
@ ^ [Y1: elem] :
( !! @ nat
@ ^ [Y2: nat] :
( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( !! @ list
@ ^ [Y5: list] :
( !! @ nat
@ ^ [Y6: nat] :
( ( listStar @ Y6 @ Y5 @ Y5 )
=> ( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( ( listStar @ Y2 @ Y0 @ Y0 )
=> ( ( listStar @ ( plus @ ( plus @ Y6 @ Y4 ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ Y2 @ ( plus @ Y6 @ Y4 ) @ Y0 @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( app @ ( plus @ Y2 @ Y6 ) @ Y4 @ ( app @ Y2 @ Y6 @ Y0 @ Y5 ) @ Y3 ) )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y6 @ Y4 ) ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ ( suc @ Y2 ) @ ( plus @ Y6 @ Y4 ) @ ( cons @ Y2 @ Y1 @ Y0 ) @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( cons @ ( plus @ Y2 @ ( plus @ Y6 @ Y4 ) ) @ Y1 @ ( app @ Y2 @ ( plus @ Y6 @ Y4 ) @ Y0 @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y6 @ Y4 ) ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ ( suc @ Y2 ) @ ( plus @ Y6 @ Y4 ) @ ( cons @ Y2 @ Y1 @ Y0 ) @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( cons @ ( plus @ ( plus @ Y2 @ Y6 ) @ Y4 ) @ Y1 @ ( app @ ( plus @ Y2 @ Y6 ) @ Y4 @ ( app @ Y2 @ Y6 @ Y0 @ Y5 ) @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f37]) ).
thf(f37,plain,
! [X0: nat,X1: list,X2: nat,X3: list,X4: nat,X5: elem,X6: list] :
( ( listStar @ X0 @ X1 @ X1 )
=> ( ( listStar @ X2 @ X3 @ X3 )
=> ( ( listStar @ X4 @ X6 @ X6 )
=> ( ( listStar @ ( plus @ ( plus @ X0 @ X2 ) @ ( plus @ X0 @ X2 ) ) @ ( app @ X4 @ ( plus @ X0 @ X2 ) @ X6 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ X4 @ X0 ) @ X2 @ ( app @ X4 @ X0 @ X6 @ X1 ) @ X3 ) )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X2 ) ) @ ( plus @ X0 @ X2 ) ) @ ( app @ ( suc @ X4 ) @ ( plus @ X0 @ X2 ) @ ( cons @ X4 @ X5 @ X6 ) @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( cons @ ( plus @ X4 @ ( plus @ X0 @ X2 ) ) @ X5 @ ( app @ X4 @ ( plus @ X0 @ X2 ) @ X6 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X2 ) ) @ ( plus @ X0 @ X2 ) ) @ ( app @ ( suc @ X4 ) @ ( plus @ X0 @ X2 ) @ ( cons @ X4 @ X5 @ X6 ) @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( cons @ ( plus @ ( plus @ X4 @ X0 ) @ X2 ) @ X5 @ ( app @ ( plus @ X4 @ X0 ) @ X2 @ ( app @ X4 @ X0 @ X6 @ X1 ) @ X3 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
! [X13: nat,X16: list,X14: nat,X17: list,X10: nat,X2: elem,X18: list] :
( ( listStar @ X13 @ X16 @ X16 )
=> ( ( listStar @ X14 @ X17 @ X17 )
=> ( ( listStar @ X10 @ X18 @ X18 )
=> ( ( listStar @ ( plus @ ( plus @ X13 @ X14 ) @ ( plus @ X13 @ X14 ) ) @ ( app @ X10 @ ( plus @ X13 @ X14 ) @ X18 @ ( app @ X13 @ X14 @ X16 @ X17 ) ) @ ( app @ ( plus @ X10 @ X13 ) @ X14 @ ( app @ X10 @ X13 @ X18 @ X16 ) @ X17 ) )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ X13 @ X14 ) ) @ ( plus @ X13 @ X14 ) ) @ ( app @ ( suc @ X10 ) @ ( plus @ X13 @ X14 ) @ ( cons @ X10 @ X2 @ X18 ) @ ( app @ X13 @ X14 @ X16 @ X17 ) ) @ ( cons @ ( plus @ X10 @ ( plus @ X13 @ X14 ) ) @ X2 @ ( app @ X10 @ ( plus @ X13 @ X14 ) @ X18 @ ( app @ X13 @ X14 @ X16 @ X17 ) ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X13 @ X14 ) ) @ ( plus @ X13 @ X14 ) ) @ ( app @ ( suc @ X10 ) @ ( plus @ X13 @ X14 ) @ ( cons @ X10 @ X2 @ X18 ) @ ( app @ X13 @ X14 @ X16 @ X17 ) ) @ ( cons @ ( plus @ ( plus @ X10 @ X13 ) @ X14 ) @ X2 @ ( app @ ( plus @ X10 @ X13 ) @ X14 @ ( app @ X10 @ X13 @ X18 @ X16 ) @ X17 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.PLL0ptdnA4/DTF2THF_4359.p',list_app_assoc_indstep3) ).
thf(f188,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X7: nat,X4: list,X5: nat] :
( ( $true
= ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ X3 @ ( plus @ X7 @ X5 ) ) @ X2 @ ( app @ X3 @ ( plus @ X7 @ X5 ) @ X1 @ ( app @ X7 @ X5 @ X6 @ X4 ) ) ) ) )
| ( $false
= ( listStar @ X3 @ X1 @ X1 ) )
| ( $false
= ( listStar @ X7 @ X6 @ X6 ) )
| ( $false
= ( listStar @ X5 @ X4 @ X4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f187]) ).
thf(f187,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X7: nat,X4: list,X5: nat] :
( ( $false
= ( listStar @ X7 @ X6 @ X6 ) )
| ( ( ( listStar @ X3 @ X1 @ X1 )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ X3 @ ( plus @ X7 @ X5 ) ) @ X2 @ ( app @ X3 @ ( plus @ X7 @ X5 ) @ X1 @ ( app @ X7 @ X5 @ X6 @ X4 ) ) ) ) )
= $true )
| ( $false
= ( listStar @ X5 @ X4 @ X4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f186]) ).
thf(f186,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X7: nat,X4: list,X5: nat] :
( ( $false
= ( listStar @ X7 @ X6 @ X6 ) )
| ( ( ( listStar @ X5 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ X3 @ ( plus @ X7 @ X5 ) ) @ X2 @ ( app @ X3 @ ( plus @ X7 @ X5 ) @ X1 @ ( app @ X7 @ X5 @ X6 @ X4 ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f185]) ).
thf(f185,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X7: nat,X4: list,X5: nat] :
( ( ( listStar @ X7 @ X6 @ X6 )
=> ( ( listStar @ X5 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ X3 @ ( plus @ X7 @ X5 ) ) @ X2 @ ( app @ X3 @ ( plus @ X7 @ X5 ) @ X1 @ ( app @ X7 @ X5 @ X6 @ X4 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f184]) ).
thf(f184,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X7: nat,X4: list,X5: nat] :
( $true
= ( ^ [Y0: nat] :
( ( listStar @ Y0 @ X6 @ X6 )
=> ( ( listStar @ X5 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y0 @ X5 ) ) @ ( plus @ Y0 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y0 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y0 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ X3 @ ( plus @ Y0 @ X5 ) ) @ X2 @ ( app @ X3 @ ( plus @ Y0 @ X5 ) @ X1 @ ( app @ Y0 @ X5 @ X6 @ X4 ) ) ) ) ) ) )
@ X7 ) ),
inference(pi_clausification,[status(thm)],[f183]) ).
thf(f183,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X4: list,X5: nat] :
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( listStar @ Y0 @ X6 @ X6 )
=> ( ( listStar @ X5 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y0 @ X5 ) ) @ ( plus @ Y0 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y0 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y0 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ X3 @ ( plus @ Y0 @ X5 ) ) @ X2 @ ( app @ X3 @ ( plus @ Y0 @ X5 ) @ X1 @ ( app @ Y0 @ X5 @ X6 @ X4 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f182]) ).
thf(f182,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X4: list,X5: nat] :
( ( ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( ( listStar @ X5 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y1 @ X5 ) ) @ ( plus @ Y1 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y1 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y1 @ X5 @ Y0 @ X4 ) ) @ ( cons @ ( plus @ X3 @ ( plus @ Y1 @ X5 ) ) @ X2 @ ( app @ X3 @ ( plus @ Y1 @ X5 ) @ X1 @ ( app @ Y1 @ X5 @ Y0 @ X4 ) ) ) ) ) ) ) )
@ X6 )
= $true ),
inference(pi_clausification,[status(thm)],[f181]) ).
thf(f181,plain,
! [X2: elem,X3: nat,X1: list,X4: list,X5: nat] :
( ( !! @ list
@ ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( ( listStar @ X5 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y1 @ X5 ) ) @ ( plus @ Y1 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y1 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y1 @ X5 @ Y0 @ X4 ) ) @ ( cons @ ( plus @ X3 @ ( plus @ Y1 @ X5 ) ) @ X2 @ ( app @ X3 @ ( plus @ Y1 @ X5 ) @ X1 @ ( app @ Y1 @ X5 @ Y0 @ X4 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f180]) ).
thf(f180,plain,
! [X2: elem,X3: nat,X1: list,X4: list,X5: nat] :
( ( ^ [Y0: nat] :
( !! @ list
@ ^ [Y1: list] :
( !! @ nat
@ ^ [Y2: nat] :
( ( listStar @ Y2 @ Y1 @ Y1 )
=> ( ( listStar @ Y0 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y2 @ Y0 ) ) @ ( plus @ Y2 @ Y0 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y2 @ Y0 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y2 @ Y0 @ Y1 @ X4 ) ) @ ( cons @ ( plus @ X3 @ ( plus @ Y2 @ Y0 ) ) @ X2 @ ( app @ X3 @ ( plus @ Y2 @ Y0 ) @ X1 @ ( app @ Y2 @ Y0 @ Y1 @ X4 ) ) ) ) ) ) ) ) )
@ X5 )
= $true ),
inference(pi_clausification,[status(thm)],[f179]) ).
thf(f179,plain,
! [X2: elem,X3: nat,X1: list,X4: list] :
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ list
@ ^ [Y1: list] :
( !! @ nat
@ ^ [Y2: nat] :
( ( listStar @ Y2 @ Y1 @ Y1 )
=> ( ( listStar @ Y0 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y2 @ Y0 ) ) @ ( plus @ Y2 @ Y0 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y2 @ Y0 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y2 @ Y0 @ Y1 @ X4 ) ) @ ( cons @ ( plus @ X3 @ ( plus @ Y2 @ Y0 ) ) @ X2 @ ( app @ X3 @ ( plus @ Y2 @ Y0 ) @ X1 @ ( app @ Y2 @ Y0 @ Y1 @ X4 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f178]) ).
thf(f178,plain,
! [X2: elem,X3: nat,X1: list,X4: list] :
( ( ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list
@ ^ [Y2: list] :
( !! @ nat
@ ^ [Y3: nat] :
( ( listStar @ Y3 @ Y2 @ Y2 )
=> ( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y3 @ Y1 ) ) @ ( plus @ Y3 @ Y1 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y3 @ Y1 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y3 @ Y1 @ Y2 @ Y0 ) ) @ ( cons @ ( plus @ X3 @ ( plus @ Y3 @ Y1 ) ) @ X2 @ ( app @ X3 @ ( plus @ Y3 @ Y1 ) @ X1 @ ( app @ Y3 @ Y1 @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
@ X4 )
= $true ),
inference(pi_clausification,[status(thm)],[f177]) ).
thf(f177,plain,
! [X2: elem,X3: nat,X1: list] :
( $true
= ( !! @ list
@ ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list
@ ^ [Y2: list] :
( !! @ nat
@ ^ [Y3: nat] :
( ( listStar @ Y3 @ Y2 @ Y2 )
=> ( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y3 @ Y1 ) ) @ ( plus @ Y3 @ Y1 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y3 @ Y1 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y3 @ Y1 @ Y2 @ Y0 ) ) @ ( cons @ ( plus @ X3 @ ( plus @ Y3 @ Y1 ) ) @ X2 @ ( app @ X3 @ ( plus @ Y3 @ Y1 ) @ X1 @ ( app @ Y3 @ Y1 @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f176]) ).
thf(f176,plain,
! [X2: elem,X3: nat,X1: list] :
( $true
= ( ^ [Y0: nat] :
( !! @ list
@ ^ [Y1: list] :
( !! @ nat
@ ^ [Y2: nat] :
( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( ( listStar @ Y2 @ Y1 @ Y1 )
=> ( ( listStar @ Y0 @ X1 @ X1 )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y4 @ Y2 ) ) @ ( plus @ Y4 @ Y2 ) ) @ ( app @ ( suc @ Y0 ) @ ( plus @ Y4 @ Y2 ) @ ( cons @ Y0 @ X2 @ X1 ) @ ( app @ Y4 @ Y2 @ Y3 @ Y1 ) ) @ ( cons @ ( plus @ Y0 @ ( plus @ Y4 @ Y2 ) ) @ X2 @ ( app @ Y0 @ ( plus @ Y4 @ Y2 ) @ X1 @ ( app @ Y4 @ Y2 @ Y3 @ Y1 ) ) ) ) ) ) ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f175]) ).
thf(f175,plain,
! [X2: elem,X1: list] :
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( !! @ list
@ ^ [Y1: list] :
( !! @ nat
@ ^ [Y2: nat] :
( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( ( listStar @ Y2 @ Y1 @ Y1 )
=> ( ( listStar @ Y0 @ X1 @ X1 )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y4 @ Y2 ) ) @ ( plus @ Y4 @ Y2 ) ) @ ( app @ ( suc @ Y0 ) @ ( plus @ Y4 @ Y2 ) @ ( cons @ Y0 @ X2 @ X1 ) @ ( app @ Y4 @ Y2 @ Y3 @ Y1 ) ) @ ( cons @ ( plus @ Y0 @ ( plus @ Y4 @ Y2 ) ) @ X2 @ ( app @ Y0 @ ( plus @ Y4 @ Y2 ) @ X1 @ ( app @ Y4 @ Y2 @ Y3 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f174]) ).
thf(f174,plain,
! [X2: elem,X1: list] :
( $true
= ( ^ [Y0: elem] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list
@ ^ [Y2: list] :
( !! @ nat
@ ^ [Y3: nat] :
( !! @ list
@ ^ [Y4: list] :
( !! @ nat
@ ^ [Y5: nat] :
( ( listStar @ Y5 @ Y4 @ Y4 )
=> ( ( listStar @ Y3 @ Y2 @ Y2 )
=> ( ( listStar @ Y1 @ X1 @ X1 )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y5 @ Y3 ) ) @ ( plus @ Y5 @ Y3 ) ) @ ( app @ ( suc @ Y1 ) @ ( plus @ Y5 @ Y3 ) @ ( cons @ Y1 @ Y0 @ X1 ) @ ( app @ Y5 @ Y3 @ Y4 @ Y2 ) ) @ ( cons @ ( plus @ Y1 @ ( plus @ Y5 @ Y3 ) ) @ Y0 @ ( app @ Y1 @ ( plus @ Y5 @ Y3 ) @ X1 @ ( app @ Y5 @ Y3 @ Y4 @ Y2 ) ) ) ) ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f173]) ).
thf(f173,plain,
! [X1: list] :
( $true
= ( !! @ elem
@ ^ [Y0: elem] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list
@ ^ [Y2: list] :
( !! @ nat
@ ^ [Y3: nat] :
( !! @ list
@ ^ [Y4: list] :
( !! @ nat
@ ^ [Y5: nat] :
( ( listStar @ Y5 @ Y4 @ Y4 )
=> ( ( listStar @ Y3 @ Y2 @ Y2 )
=> ( ( listStar @ Y1 @ X1 @ X1 )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y5 @ Y3 ) ) @ ( plus @ Y5 @ Y3 ) ) @ ( app @ ( suc @ Y1 ) @ ( plus @ Y5 @ Y3 ) @ ( cons @ Y1 @ Y0 @ X1 ) @ ( app @ Y5 @ Y3 @ Y4 @ Y2 ) ) @ ( cons @ ( plus @ Y1 @ ( plus @ Y5 @ Y3 ) ) @ Y0 @ ( app @ Y1 @ ( plus @ Y5 @ Y3 ) @ X1 @ ( app @ Y5 @ Y3 @ Y4 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f172]) ).
thf(f172,plain,
! [X1: list] :
( $true
= ( ^ [Y0: list] :
( !! @ elem
@ ^ [Y1: elem] :
( !! @ nat
@ ^ [Y2: nat] :
( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( !! @ list
@ ^ [Y5: list] :
( !! @ nat
@ ^ [Y6: nat] :
( ( listStar @ Y6 @ Y5 @ Y5 )
=> ( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( ( listStar @ Y2 @ Y0 @ Y0 )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y6 @ Y4 ) ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ ( suc @ Y2 ) @ ( plus @ Y6 @ Y4 ) @ ( cons @ Y2 @ Y1 @ Y0 ) @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( cons @ ( plus @ Y2 @ ( plus @ Y6 @ Y4 ) ) @ Y1 @ ( app @ Y2 @ ( plus @ Y6 @ Y4 ) @ Y0 @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
( ( !! @ list
@ ^ [Y0: list] :
( !! @ elem
@ ^ [Y1: elem] :
( !! @ nat
@ ^ [Y2: nat] :
( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( !! @ list
@ ^ [Y5: list] :
( !! @ nat
@ ^ [Y6: nat] :
( ( listStar @ Y6 @ Y5 @ Y5 )
=> ( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( ( listStar @ Y2 @ Y0 @ Y0 )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y6 @ Y4 ) ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ ( suc @ Y2 ) @ ( plus @ Y6 @ Y4 ) @ ( cons @ Y2 @ Y1 @ Y0 ) @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( cons @ ( plus @ Y2 @ ( plus @ Y6 @ Y4 ) ) @ Y1 @ ( app @ Y2 @ ( plus @ Y6 @ Y4 ) @ Y0 @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ( !! @ list
@ ^ [Y0: list] :
( !! @ elem
@ ^ [Y1: elem] :
( !! @ nat
@ ^ [Y2: nat] :
( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( !! @ list
@ ^ [Y5: list] :
( !! @ nat
@ ^ [Y6: nat] :
( ( listStar @ Y6 @ Y5 @ Y5 )
=> ( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( ( listStar @ Y2 @ Y0 @ Y0 )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y6 @ Y4 ) ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ ( suc @ Y2 ) @ ( plus @ Y6 @ Y4 ) @ ( cons @ Y2 @ Y1 @ Y0 ) @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( cons @ ( plus @ Y2 @ ( plus @ Y6 @ Y4 ) ) @ Y1 @ ( app @ Y2 @ ( plus @ Y6 @ Y4 ) @ Y0 @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: nat,X1: list,X2: nat,X3: list,X4: nat,X5: elem,X6: list] :
( ( listStar @ X0 @ X1 @ X1 )
=> ( ( listStar @ X2 @ X3 @ X3 )
=> ( ( listStar @ X4 @ X6 @ X6 )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X2 ) ) @ ( plus @ X0 @ X2 ) ) @ ( app @ ( suc @ X4 ) @ ( plus @ X0 @ X2 ) @ ( cons @ X4 @ X5 @ X6 ) @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( cons @ ( plus @ X4 @ ( plus @ X0 @ X2 ) ) @ X5 @ ( app @ X4 @ ( plus @ X0 @ X2 ) @ X6 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,axiom,
! [X13: nat,X16: list,X14: nat,X17: list,X10: nat,X2: elem,X18: list] :
( ( listStar @ X13 @ X16 @ X16 )
=> ( ( listStar @ X14 @ X17 @ X17 )
=> ( ( listStar @ X10 @ X18 @ X18 )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X13 @ X14 ) ) @ ( plus @ X13 @ X14 ) ) @ ( app @ ( suc @ X10 ) @ ( plus @ X13 @ X14 ) @ ( cons @ X10 @ X2 @ X18 ) @ ( app @ X13 @ X14 @ X16 @ X17 ) ) @ ( cons @ ( plus @ X10 @ ( plus @ X13 @ X14 ) ) @ X2 @ ( app @ X10 @ ( plus @ X13 @ X14 ) @ X18 @ ( app @ X13 @ X14 @ X16 @ X17 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.PLL0ptdnA4/DTF2THF_4359.p',list_app_assoc_indstep4) ).
thf(f103,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X7: nat,X4: list,X5: nat] :
( ( $false
= ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ ( plus @ X3 @ X7 ) @ X5 ) @ X2 @ ( app @ ( plus @ X3 @ X7 ) @ X5 @ ( app @ X3 @ X7 @ X1 @ X6 ) @ X4 ) ) ) )
| ( $false
= ( listStar @ X7 @ X6 @ X6 ) )
| ( $false
= ( listStar @ X3 @ X1 @ X1 ) )
| ( $false
= ( listStar @ X5 @ X4 @ X4 ) )
| ( ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( app @ ( suc @ ( plus @ X3 @ X7 ) ) @ X5 @ ( cons @ ( plus @ X3 @ X7 ) @ X2 @ ( app @ X3 @ X7 @ X1 @ X6 ) ) @ X4 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f102]) ).
thf(f102,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X7: nat,X4: list,X5: nat] :
( ( $false
= ( listStar @ X7 @ X6 @ X6 ) )
| ( $false
= ( listStar @ X3 @ X1 @ X1 ) )
| ( $true
= ( ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ ( plus @ X3 @ X7 ) @ X5 ) @ X2 @ ( app @ ( plus @ X3 @ X7 ) @ X5 @ ( app @ X3 @ X7 @ X1 @ X6 ) @ X4 ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( app @ ( suc @ ( plus @ X3 @ X7 ) ) @ X5 @ ( cons @ ( plus @ X3 @ X7 ) @ X2 @ ( app @ X3 @ X7 @ X1 @ X6 ) ) @ X4 ) ) ) )
| ( $false
= ( listStar @ X5 @ X4 @ X4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f101]) ).
thf(f101,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X7: nat,X4: list,X5: nat] :
( ( $false
= ( listStar @ X7 @ X6 @ X6 ) )
| ( $false
= ( listStar @ X5 @ X4 @ X4 ) )
| ( ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ ( plus @ X3 @ X7 ) @ X5 ) @ X2 @ ( app @ ( plus @ X3 @ X7 ) @ X5 @ ( app @ X3 @ X7 @ X1 @ X6 ) @ X4 ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( app @ ( suc @ ( plus @ X3 @ X7 ) ) @ X5 @ ( cons @ ( plus @ X3 @ X7 ) @ X2 @ ( app @ X3 @ X7 @ X1 @ X6 ) ) @ X4 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X7: nat,X4: list,X5: nat] :
( ( $false
= ( listStar @ X7 @ X6 @ X6 ) )
| ( ( ( listStar @ X5 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ ( plus @ X3 @ X7 ) @ X5 ) @ X2 @ ( app @ ( plus @ X3 @ X7 ) @ X5 @ ( app @ X3 @ X7 @ X1 @ X6 ) @ X4 ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( app @ ( suc @ ( plus @ X3 @ X7 ) ) @ X5 @ ( cons @ ( plus @ X3 @ X7 ) @ X2 @ ( app @ X3 @ X7 @ X1 @ X6 ) ) @ X4 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f99]) ).
thf(f99,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X7: nat,X4: list,X5: nat] :
( ( ( listStar @ X7 @ X6 @ X6 )
=> ( ( listStar @ X5 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ ( plus @ X3 @ X7 ) @ X5 ) @ X2 @ ( app @ ( plus @ X3 @ X7 ) @ X5 @ ( app @ X3 @ X7 @ X1 @ X6 ) @ X4 ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( app @ ( suc @ ( plus @ X3 @ X7 ) ) @ X5 @ ( cons @ ( plus @ X3 @ X7 ) @ X2 @ ( app @ X3 @ X7 @ X1 @ X6 ) ) @ X4 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f98]) ).
thf(f98,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X7: nat,X4: list,X5: nat] :
( ( ^ [Y0: nat] :
( ( listStar @ Y0 @ X6 @ X6 )
=> ( ( listStar @ X5 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y0 @ X5 ) ) @ ( plus @ Y0 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y0 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y0 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ ( plus @ X3 @ Y0 ) @ X5 ) @ X2 @ ( app @ ( plus @ X3 @ Y0 ) @ X5 @ ( app @ X3 @ Y0 @ X1 @ X6 ) @ X4 ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y0 @ X5 ) ) @ ( plus @ Y0 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y0 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y0 @ X5 @ X6 @ X4 ) ) @ ( app @ ( suc @ ( plus @ X3 @ Y0 ) ) @ X5 @ ( cons @ ( plus @ X3 @ Y0 ) @ X2 @ ( app @ X3 @ Y0 @ X1 @ X6 ) ) @ X4 ) ) ) ) ) )
@ X7 )
= $true ),
inference(pi_clausification,[status(thm)],[f97]) ).
thf(f97,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X4: list,X5: nat] :
( ( !! @ nat
@ ^ [Y0: nat] :
( ( listStar @ Y0 @ X6 @ X6 )
=> ( ( listStar @ X5 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y0 @ X5 ) ) @ ( plus @ Y0 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y0 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y0 @ X5 @ X6 @ X4 ) ) @ ( cons @ ( plus @ ( plus @ X3 @ Y0 ) @ X5 ) @ X2 @ ( app @ ( plus @ X3 @ Y0 ) @ X5 @ ( app @ X3 @ Y0 @ X1 @ X6 ) @ X4 ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y0 @ X5 ) ) @ ( plus @ Y0 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y0 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y0 @ X5 @ X6 @ X4 ) ) @ ( app @ ( suc @ ( plus @ X3 @ Y0 ) ) @ X5 @ ( cons @ ( plus @ X3 @ Y0 ) @ X2 @ ( app @ X3 @ Y0 @ X1 @ X6 ) ) @ X4 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f96]) ).
thf(f96,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X4: list,X5: nat] :
( ( ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( ( listStar @ X5 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y1 @ X5 ) ) @ ( plus @ Y1 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y1 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y1 @ X5 @ Y0 @ X4 ) ) @ ( cons @ ( plus @ ( plus @ X3 @ Y1 ) @ X5 ) @ X2 @ ( app @ ( plus @ X3 @ Y1 ) @ X5 @ ( app @ X3 @ Y1 @ X1 @ Y0 ) @ X4 ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y1 @ X5 ) ) @ ( plus @ Y1 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y1 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y1 @ X5 @ Y0 @ X4 ) ) @ ( app @ ( suc @ ( plus @ X3 @ Y1 ) ) @ X5 @ ( cons @ ( plus @ X3 @ Y1 ) @ X2 @ ( app @ X3 @ Y1 @ X1 @ Y0 ) ) @ X4 ) ) ) ) ) ) )
@ X6 )
= $true ),
inference(pi_clausification,[status(thm)],[f95]) ).
thf(f95,plain,
! [X2: elem,X3: nat,X1: list,X4: list,X5: nat] :
( ( !! @ list
@ ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( ( listStar @ X5 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y1 @ X5 ) ) @ ( plus @ Y1 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y1 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y1 @ X5 @ Y0 @ X4 ) ) @ ( cons @ ( plus @ ( plus @ X3 @ Y1 ) @ X5 ) @ X2 @ ( app @ ( plus @ X3 @ Y1 ) @ X5 @ ( app @ X3 @ Y1 @ X1 @ Y0 ) @ X4 ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y1 @ X5 ) ) @ ( plus @ Y1 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y1 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y1 @ X5 @ Y0 @ X4 ) ) @ ( app @ ( suc @ ( plus @ X3 @ Y1 ) ) @ X5 @ ( cons @ ( plus @ X3 @ Y1 ) @ X2 @ ( app @ X3 @ Y1 @ X1 @ Y0 ) ) @ X4 ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f94]) ).
thf(f94,plain,
! [X2: elem,X3: nat,X1: list,X4: list,X5: nat] :
( ( ^ [Y0: nat] :
( !! @ list
@ ^ [Y1: list] :
( !! @ nat
@ ^ [Y2: nat] :
( ( listStar @ Y2 @ Y1 @ Y1 )
=> ( ( listStar @ Y0 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y2 @ Y0 ) ) @ ( plus @ Y2 @ Y0 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y2 @ Y0 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y2 @ Y0 @ Y1 @ X4 ) ) @ ( cons @ ( plus @ ( plus @ X3 @ Y2 ) @ Y0 ) @ X2 @ ( app @ ( plus @ X3 @ Y2 ) @ Y0 @ ( app @ X3 @ Y2 @ X1 @ Y1 ) @ X4 ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y2 @ Y0 ) ) @ ( plus @ Y2 @ Y0 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y2 @ Y0 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y2 @ Y0 @ Y1 @ X4 ) ) @ ( app @ ( suc @ ( plus @ X3 @ Y2 ) ) @ Y0 @ ( cons @ ( plus @ X3 @ Y2 ) @ X2 @ ( app @ X3 @ Y2 @ X1 @ Y1 ) ) @ X4 ) ) ) ) ) ) ) )
@ X5 )
= $true ),
inference(pi_clausification,[status(thm)],[f93]) ).
thf(f93,plain,
! [X2: elem,X3: nat,X1: list,X4: list] :
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ list
@ ^ [Y1: list] :
( !! @ nat
@ ^ [Y2: nat] :
( ( listStar @ Y2 @ Y1 @ Y1 )
=> ( ( listStar @ Y0 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y2 @ Y0 ) ) @ ( plus @ Y2 @ Y0 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y2 @ Y0 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y2 @ Y0 @ Y1 @ X4 ) ) @ ( cons @ ( plus @ ( plus @ X3 @ Y2 ) @ Y0 ) @ X2 @ ( app @ ( plus @ X3 @ Y2 ) @ Y0 @ ( app @ X3 @ Y2 @ X1 @ Y1 ) @ X4 ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y2 @ Y0 ) ) @ ( plus @ Y2 @ Y0 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y2 @ Y0 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y2 @ Y0 @ Y1 @ X4 ) ) @ ( app @ ( suc @ ( plus @ X3 @ Y2 ) ) @ Y0 @ ( cons @ ( plus @ X3 @ Y2 ) @ X2 @ ( app @ X3 @ Y2 @ X1 @ Y1 ) ) @ X4 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f92]) ).
thf(f92,plain,
! [X2: elem,X3: nat,X1: list,X4: list] :
( ( ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list
@ ^ [Y2: list] :
( !! @ nat
@ ^ [Y3: nat] :
( ( listStar @ Y3 @ Y2 @ Y2 )
=> ( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y3 @ Y1 ) ) @ ( plus @ Y3 @ Y1 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y3 @ Y1 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y3 @ Y1 @ Y2 @ Y0 ) ) @ ( cons @ ( plus @ ( plus @ X3 @ Y3 ) @ Y1 ) @ X2 @ ( app @ ( plus @ X3 @ Y3 ) @ Y1 @ ( app @ X3 @ Y3 @ X1 @ Y2 ) @ Y0 ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y3 @ Y1 ) ) @ ( plus @ Y3 @ Y1 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y3 @ Y1 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y3 @ Y1 @ Y2 @ Y0 ) ) @ ( app @ ( suc @ ( plus @ X3 @ Y3 ) ) @ Y1 @ ( cons @ ( plus @ X3 @ Y3 ) @ X2 @ ( app @ X3 @ Y3 @ X1 @ Y2 ) ) @ Y0 ) ) ) ) ) ) ) ) )
@ X4 )
= $true ),
inference(pi_clausification,[status(thm)],[f91]) ).
thf(f91,plain,
! [X2: elem,X3: nat,X1: list] :
( $true
= ( !! @ list
@ ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list
@ ^ [Y2: list] :
( !! @ nat
@ ^ [Y3: nat] :
( ( listStar @ Y3 @ Y2 @ Y2 )
=> ( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y3 @ Y1 ) ) @ ( plus @ Y3 @ Y1 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y3 @ Y1 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y3 @ Y1 @ Y2 @ Y0 ) ) @ ( cons @ ( plus @ ( plus @ X3 @ Y3 ) @ Y1 ) @ X2 @ ( app @ ( plus @ X3 @ Y3 ) @ Y1 @ ( app @ X3 @ Y3 @ X1 @ Y2 ) @ Y0 ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y3 @ Y1 ) ) @ ( plus @ Y3 @ Y1 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y3 @ Y1 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y3 @ Y1 @ Y2 @ Y0 ) ) @ ( app @ ( suc @ ( plus @ X3 @ Y3 ) ) @ Y1 @ ( cons @ ( plus @ X3 @ Y3 ) @ X2 @ ( app @ X3 @ Y3 @ X1 @ Y2 ) ) @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f90]) ).
thf(f90,plain,
! [X2: elem,X3: nat,X1: list] :
( ( ^ [Y0: nat] :
( !! @ list
@ ^ [Y1: list] :
( !! @ nat
@ ^ [Y2: nat] :
( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( ( listStar @ Y2 @ Y1 @ Y1 )
=> ( ( listStar @ Y0 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y4 @ Y2 ) ) @ ( plus @ Y4 @ Y2 ) ) @ ( app @ ( suc @ Y0 ) @ ( plus @ Y4 @ Y2 ) @ ( cons @ Y0 @ X2 @ X1 ) @ ( app @ Y4 @ Y2 @ Y3 @ Y1 ) ) @ ( cons @ ( plus @ ( plus @ Y0 @ Y4 ) @ Y2 ) @ X2 @ ( app @ ( plus @ Y0 @ Y4 ) @ Y2 @ ( app @ Y0 @ Y4 @ X1 @ Y3 ) @ Y1 ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y4 @ Y2 ) ) @ ( plus @ Y4 @ Y2 ) ) @ ( app @ ( suc @ Y0 ) @ ( plus @ Y4 @ Y2 ) @ ( cons @ Y0 @ X2 @ X1 ) @ ( app @ Y4 @ Y2 @ Y3 @ Y1 ) ) @ ( app @ ( suc @ ( plus @ Y0 @ Y4 ) ) @ Y2 @ ( cons @ ( plus @ Y0 @ Y4 ) @ X2 @ ( app @ Y0 @ Y4 @ X1 @ Y3 ) ) @ Y1 ) ) ) ) ) ) ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f89]) ).
thf(f89,plain,
! [X2: elem,X1: list] :
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ list
@ ^ [Y1: list] :
( !! @ nat
@ ^ [Y2: nat] :
( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( ( listStar @ Y2 @ Y1 @ Y1 )
=> ( ( listStar @ Y0 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y4 @ Y2 ) ) @ ( plus @ Y4 @ Y2 ) ) @ ( app @ ( suc @ Y0 ) @ ( plus @ Y4 @ Y2 ) @ ( cons @ Y0 @ X2 @ X1 ) @ ( app @ Y4 @ Y2 @ Y3 @ Y1 ) ) @ ( cons @ ( plus @ ( plus @ Y0 @ Y4 ) @ Y2 ) @ X2 @ ( app @ ( plus @ Y0 @ Y4 ) @ Y2 @ ( app @ Y0 @ Y4 @ X1 @ Y3 ) @ Y1 ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y4 @ Y2 ) ) @ ( plus @ Y4 @ Y2 ) ) @ ( app @ ( suc @ Y0 ) @ ( plus @ Y4 @ Y2 ) @ ( cons @ Y0 @ X2 @ X1 ) @ ( app @ Y4 @ Y2 @ Y3 @ Y1 ) ) @ ( app @ ( suc @ ( plus @ Y0 @ Y4 ) ) @ Y2 @ ( cons @ ( plus @ Y0 @ Y4 ) @ X2 @ ( app @ Y0 @ Y4 @ X1 @ Y3 ) ) @ Y1 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f88]) ).
thf(f88,plain,
! [X2: elem,X1: list] :
( ( ^ [Y0: elem] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list
@ ^ [Y2: list] :
( !! @ nat
@ ^ [Y3: nat] :
( !! @ list
@ ^ [Y4: list] :
( !! @ nat
@ ^ [Y5: nat] :
( ( listStar @ Y5 @ Y4 @ Y4 )
=> ( ( listStar @ Y3 @ Y2 @ Y2 )
=> ( ( listStar @ Y1 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y5 @ Y3 ) ) @ ( plus @ Y5 @ Y3 ) ) @ ( app @ ( suc @ Y1 ) @ ( plus @ Y5 @ Y3 ) @ ( cons @ Y1 @ Y0 @ X1 ) @ ( app @ Y5 @ Y3 @ Y4 @ Y2 ) ) @ ( cons @ ( plus @ ( plus @ Y1 @ Y5 ) @ Y3 ) @ Y0 @ ( app @ ( plus @ Y1 @ Y5 ) @ Y3 @ ( app @ Y1 @ Y5 @ X1 @ Y4 ) @ Y2 ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y5 @ Y3 ) ) @ ( plus @ Y5 @ Y3 ) ) @ ( app @ ( suc @ Y1 ) @ ( plus @ Y5 @ Y3 ) @ ( cons @ Y1 @ Y0 @ X1 ) @ ( app @ Y5 @ Y3 @ Y4 @ Y2 ) ) @ ( app @ ( suc @ ( plus @ Y1 @ Y5 ) ) @ Y3 @ ( cons @ ( plus @ Y1 @ Y5 ) @ Y0 @ ( app @ Y1 @ Y5 @ X1 @ Y4 ) ) @ Y2 ) ) ) ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f87]) ).
thf(f87,plain,
! [X1: list] :
( ( !! @ elem
@ ^ [Y0: elem] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list
@ ^ [Y2: list] :
( !! @ nat
@ ^ [Y3: nat] :
( !! @ list
@ ^ [Y4: list] :
( !! @ nat
@ ^ [Y5: nat] :
( ( listStar @ Y5 @ Y4 @ Y4 )
=> ( ( listStar @ Y3 @ Y2 @ Y2 )
=> ( ( listStar @ Y1 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y5 @ Y3 ) ) @ ( plus @ Y5 @ Y3 ) ) @ ( app @ ( suc @ Y1 ) @ ( plus @ Y5 @ Y3 ) @ ( cons @ Y1 @ Y0 @ X1 ) @ ( app @ Y5 @ Y3 @ Y4 @ Y2 ) ) @ ( cons @ ( plus @ ( plus @ Y1 @ Y5 ) @ Y3 ) @ Y0 @ ( app @ ( plus @ Y1 @ Y5 ) @ Y3 @ ( app @ Y1 @ Y5 @ X1 @ Y4 ) @ Y2 ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y5 @ Y3 ) ) @ ( plus @ Y5 @ Y3 ) ) @ ( app @ ( suc @ Y1 ) @ ( plus @ Y5 @ Y3 ) @ ( cons @ Y1 @ Y0 @ X1 ) @ ( app @ Y5 @ Y3 @ Y4 @ Y2 ) ) @ ( app @ ( suc @ ( plus @ Y1 @ Y5 ) ) @ Y3 @ ( cons @ ( plus @ Y1 @ Y5 ) @ Y0 @ ( app @ Y1 @ Y5 @ X1 @ Y4 ) ) @ Y2 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f86]) ).
thf(f86,plain,
! [X1: list] :
( ( ^ [Y0: list] :
( !! @ elem
@ ^ [Y1: elem] :
( !! @ nat
@ ^ [Y2: nat] :
( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( !! @ list
@ ^ [Y5: list] :
( !! @ nat
@ ^ [Y6: nat] :
( ( listStar @ Y6 @ Y5 @ Y5 )
=> ( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( ( listStar @ Y2 @ Y0 @ Y0 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y6 @ Y4 ) ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ ( suc @ Y2 ) @ ( plus @ Y6 @ Y4 ) @ ( cons @ Y2 @ Y1 @ Y0 ) @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( cons @ ( plus @ ( plus @ Y2 @ Y6 ) @ Y4 ) @ Y1 @ ( app @ ( plus @ Y2 @ Y6 ) @ Y4 @ ( app @ Y2 @ Y6 @ Y0 @ Y5 ) @ Y3 ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y6 @ Y4 ) ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ ( suc @ Y2 ) @ ( plus @ Y6 @ Y4 ) @ ( cons @ Y2 @ Y1 @ Y0 ) @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( app @ ( suc @ ( plus @ Y2 @ Y6 ) ) @ Y4 @ ( cons @ ( plus @ Y2 @ Y6 ) @ Y1 @ ( app @ Y2 @ Y6 @ Y0 @ Y5 ) ) @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
( $true
= ( !! @ list
@ ^ [Y0: list] :
( !! @ elem
@ ^ [Y1: elem] :
( !! @ nat
@ ^ [Y2: nat] :
( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( !! @ list
@ ^ [Y5: list] :
( !! @ nat
@ ^ [Y6: nat] :
( ( listStar @ Y6 @ Y5 @ Y5 )
=> ( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( ( listStar @ Y2 @ Y0 @ Y0 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y6 @ Y4 ) ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ ( suc @ Y2 ) @ ( plus @ Y6 @ Y4 ) @ ( cons @ Y2 @ Y1 @ Y0 ) @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( cons @ ( plus @ ( plus @ Y2 @ Y6 ) @ Y4 ) @ Y1 @ ( app @ ( plus @ Y2 @ Y6 ) @ Y4 @ ( app @ Y2 @ Y6 @ Y0 @ Y5 ) @ Y3 ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y6 @ Y4 ) ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ ( suc @ Y2 ) @ ( plus @ Y6 @ Y4 ) @ ( cons @ Y2 @ Y1 @ Y0 ) @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( app @ ( suc @ ( plus @ Y2 @ Y6 ) ) @ Y4 @ ( cons @ ( plus @ Y2 @ Y6 ) @ Y1 @ ( app @ Y2 @ Y6 @ Y0 @ Y5 ) ) @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( $true
= ( !! @ list
@ ^ [Y0: list] :
( !! @ elem
@ ^ [Y1: elem] :
( !! @ nat
@ ^ [Y2: nat] :
( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( !! @ list
@ ^ [Y5: list] :
( !! @ nat
@ ^ [Y6: nat] :
( ( listStar @ Y6 @ Y5 @ Y5 )
=> ( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( ( listStar @ Y2 @ Y0 @ Y0 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y6 @ Y4 ) ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ ( suc @ Y2 ) @ ( plus @ Y6 @ Y4 ) @ ( cons @ Y2 @ Y1 @ Y0 ) @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( cons @ ( plus @ ( plus @ Y2 @ Y6 ) @ Y4 ) @ Y1 @ ( app @ ( plus @ Y2 @ Y6 ) @ Y4 @ ( app @ Y2 @ Y6 @ Y0 @ Y5 ) @ Y3 ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y6 @ Y4 ) ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ ( suc @ Y2 ) @ ( plus @ Y6 @ Y4 ) @ ( cons @ Y2 @ Y1 @ Y0 ) @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( app @ ( suc @ ( plus @ Y2 @ Y6 ) ) @ Y4 @ ( cons @ ( plus @ Y2 @ Y6 ) @ Y1 @ ( app @ Y2 @ Y6 @ Y0 @ Y5 ) ) @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: nat,X1: list,X2: nat,X3: list,X4: nat,X5: elem,X6: list] :
( ( listStar @ X0 @ X1 @ X1 )
=> ( ( listStar @ X2 @ X3 @ X3 )
=> ( ( listStar @ X4 @ X6 @ X6 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X2 ) ) @ ( plus @ X0 @ X2 ) ) @ ( app @ ( suc @ X4 ) @ ( plus @ X0 @ X2 ) @ ( cons @ X4 @ X5 @ X6 ) @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( cons @ ( plus @ ( plus @ X4 @ X0 ) @ X2 ) @ X5 @ ( app @ ( plus @ X4 @ X0 ) @ X2 @ ( app @ X4 @ X0 @ X6 @ X1 ) @ X3 ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X2 ) ) @ ( plus @ X0 @ X2 ) ) @ ( app @ ( suc @ X4 ) @ ( plus @ X0 @ X2 ) @ ( cons @ X4 @ X5 @ X6 ) @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( suc @ ( plus @ X4 @ X0 ) ) @ X2 @ ( cons @ ( plus @ X4 @ X0 ) @ X5 @ ( app @ X4 @ X0 @ X6 @ X1 ) ) @ X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,axiom,
! [X13: nat,X16: list,X14: nat,X17: list,X10: nat,X2: elem,X18: list] :
( ( listStar @ X13 @ X16 @ X16 )
=> ( ( listStar @ X14 @ X17 @ X17 )
=> ( ( listStar @ X10 @ X18 @ X18 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ X13 @ X14 ) ) @ ( plus @ X13 @ X14 ) ) @ ( app @ ( suc @ X10 ) @ ( plus @ X13 @ X14 ) @ ( cons @ X10 @ X2 @ X18 ) @ ( app @ X13 @ X14 @ X16 @ X17 ) ) @ ( cons @ ( plus @ ( plus @ X10 @ X13 ) @ X14 ) @ X2 @ ( app @ ( plus @ X10 @ X13 ) @ X14 @ ( app @ X10 @ X13 @ X18 @ X16 ) @ X17 ) ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X13 @ X14 ) ) @ ( plus @ X13 @ X14 ) ) @ ( app @ ( suc @ X10 ) @ ( plus @ X13 @ X14 ) @ ( cons @ X10 @ X2 @ X18 ) @ ( app @ X13 @ X14 @ X16 @ X17 ) ) @ ( app @ ( suc @ ( plus @ X10 @ X13 ) ) @ X14 @ ( cons @ ( plus @ X10 @ X13 ) @ X2 @ ( app @ X10 @ X13 @ X18 @ X16 ) ) @ X17 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.PLL0ptdnA4/DTF2THF_4359.p',list_app_assoc_indstep2) ).
thf(f76,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X7: nat,X4: list,X5: nat] :
( ( ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( app @ ( suc @ ( plus @ X3 @ X7 ) ) @ X5 @ ( cons @ ( plus @ X3 @ X7 ) @ X2 @ ( app @ X3 @ X7 @ X1 @ X6 ) ) @ X4 ) )
= $false )
| ( $true
= ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( app @ ( plus @ ( suc @ X3 ) @ X7 ) @ X5 @ ( app @ ( suc @ X3 ) @ X7 @ ( cons @ X3 @ X2 @ X1 ) @ X6 ) @ X4 ) ) )
| ( $false
= ( listStar @ X3 @ X1 @ X1 ) )
| ( $false
= ( listStar @ X7 @ X6 @ X6 ) )
| ( $false
= ( listStar @ X5 @ X4 @ X4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f75]) ).
thf(f75,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X7: nat,X4: list,X5: nat] :
( ( $true
= ( ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( app @ ( suc @ ( plus @ X3 @ X7 ) ) @ X5 @ ( cons @ ( plus @ X3 @ X7 ) @ X2 @ ( app @ X3 @ X7 @ X1 @ X6 ) ) @ X4 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( app @ ( plus @ ( suc @ X3 ) @ X7 ) @ X5 @ ( app @ ( suc @ X3 ) @ X7 @ ( cons @ X3 @ X2 @ X1 ) @ X6 ) @ X4 ) ) ) )
| ( $false
= ( listStar @ X5 @ X4 @ X4 ) )
| ( $false
= ( listStar @ X3 @ X1 @ X1 ) )
| ( $false
= ( listStar @ X7 @ X6 @ X6 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X7: nat,X4: list,X5: nat] :
( ( $false
= ( listStar @ X7 @ X6 @ X6 ) )
| ( $true
= ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( app @ ( suc @ ( plus @ X3 @ X7 ) ) @ X5 @ ( cons @ ( plus @ X3 @ X7 ) @ X2 @ ( app @ X3 @ X7 @ X1 @ X6 ) ) @ X4 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( app @ ( plus @ ( suc @ X3 ) @ X7 ) @ X5 @ ( app @ ( suc @ X3 ) @ X7 @ ( cons @ X3 @ X2 @ X1 ) @ X6 ) @ X4 ) ) ) ) )
| ( $false
= ( listStar @ X5 @ X4 @ X4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X7: nat,X4: list,X5: nat] :
( ( $false
= ( listStar @ X7 @ X6 @ X6 ) )
| ( ( ( listStar @ X5 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( app @ ( suc @ ( plus @ X3 @ X7 ) ) @ X5 @ ( cons @ ( plus @ X3 @ X7 ) @ X2 @ ( app @ X3 @ X7 @ X1 @ X6 ) ) @ X4 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( app @ ( plus @ ( suc @ X3 ) @ X7 ) @ X5 @ ( app @ ( suc @ X3 ) @ X7 @ ( cons @ X3 @ X2 @ X1 ) @ X6 ) @ X4 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X7: nat,X4: list,X5: nat] :
( ( ( listStar @ X7 @ X6 @ X6 )
=> ( ( listStar @ X5 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( app @ ( suc @ ( plus @ X3 @ X7 ) ) @ X5 @ ( cons @ ( plus @ X3 @ X7 ) @ X2 @ ( app @ X3 @ X7 @ X1 @ X6 ) ) @ X4 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X7 @ X5 ) ) @ ( plus @ X7 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ X7 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ X7 @ X5 @ X6 @ X4 ) ) @ ( app @ ( plus @ ( suc @ X3 ) @ X7 ) @ X5 @ ( app @ ( suc @ X3 ) @ X7 @ ( cons @ X3 @ X2 @ X1 ) @ X6 ) @ X4 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f71]) ).
thf(f71,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X7: nat,X4: list,X5: nat] :
( ( ^ [Y0: nat] :
( ( listStar @ Y0 @ X6 @ X6 )
=> ( ( listStar @ X5 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y0 @ X5 ) ) @ ( plus @ Y0 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y0 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y0 @ X5 @ X6 @ X4 ) ) @ ( app @ ( suc @ ( plus @ X3 @ Y0 ) ) @ X5 @ ( cons @ ( plus @ X3 @ Y0 ) @ X2 @ ( app @ X3 @ Y0 @ X1 @ X6 ) ) @ X4 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y0 @ X5 ) ) @ ( plus @ Y0 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y0 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y0 @ X5 @ X6 @ X4 ) ) @ ( app @ ( plus @ ( suc @ X3 ) @ Y0 ) @ X5 @ ( app @ ( suc @ X3 ) @ Y0 @ ( cons @ X3 @ X2 @ X1 ) @ X6 ) @ X4 ) ) ) ) ) )
@ X7 )
= $true ),
inference(pi_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X4: list,X5: nat] :
( ( !! @ nat
@ ^ [Y0: nat] :
( ( listStar @ Y0 @ X6 @ X6 )
=> ( ( listStar @ X5 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y0 @ X5 ) ) @ ( plus @ Y0 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y0 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y0 @ X5 @ X6 @ X4 ) ) @ ( app @ ( suc @ ( plus @ X3 @ Y0 ) ) @ X5 @ ( cons @ ( plus @ X3 @ Y0 ) @ X2 @ ( app @ X3 @ Y0 @ X1 @ X6 ) ) @ X4 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y0 @ X5 ) ) @ ( plus @ Y0 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y0 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y0 @ X5 @ X6 @ X4 ) ) @ ( app @ ( plus @ ( suc @ X3 ) @ Y0 ) @ X5 @ ( app @ ( suc @ X3 ) @ Y0 @ ( cons @ X3 @ X2 @ X1 ) @ X6 ) @ X4 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
! [X2: elem,X3: nat,X1: list,X6: list,X4: list,X5: nat] :
( ( ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( ( listStar @ X5 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y1 @ X5 ) ) @ ( plus @ Y1 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y1 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y1 @ X5 @ Y0 @ X4 ) ) @ ( app @ ( suc @ ( plus @ X3 @ Y1 ) ) @ X5 @ ( cons @ ( plus @ X3 @ Y1 ) @ X2 @ ( app @ X3 @ Y1 @ X1 @ Y0 ) ) @ X4 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y1 @ X5 ) ) @ ( plus @ Y1 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y1 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y1 @ X5 @ Y0 @ X4 ) ) @ ( app @ ( plus @ ( suc @ X3 ) @ Y1 ) @ X5 @ ( app @ ( suc @ X3 ) @ Y1 @ ( cons @ X3 @ X2 @ X1 ) @ Y0 ) @ X4 ) ) ) ) ) ) )
@ X6 )
= $true ),
inference(pi_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
! [X2: elem,X3: nat,X1: list,X4: list,X5: nat] :
( ( !! @ list
@ ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( ( listStar @ X5 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y1 @ X5 ) ) @ ( plus @ Y1 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y1 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y1 @ X5 @ Y0 @ X4 ) ) @ ( app @ ( suc @ ( plus @ X3 @ Y1 ) ) @ X5 @ ( cons @ ( plus @ X3 @ Y1 ) @ X2 @ ( app @ X3 @ Y1 @ X1 @ Y0 ) ) @ X4 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y1 @ X5 ) ) @ ( plus @ Y1 @ X5 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y1 @ X5 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y1 @ X5 @ Y0 @ X4 ) ) @ ( app @ ( plus @ ( suc @ X3 ) @ Y1 ) @ X5 @ ( app @ ( suc @ X3 ) @ Y1 @ ( cons @ X3 @ X2 @ X1 ) @ Y0 ) @ X4 ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f67]) ).
thf(f67,plain,
! [X2: elem,X3: nat,X1: list,X4: list,X5: nat] :
( ( ^ [Y0: nat] :
( !! @ list
@ ^ [Y1: list] :
( !! @ nat
@ ^ [Y2: nat] :
( ( listStar @ Y2 @ Y1 @ Y1 )
=> ( ( listStar @ Y0 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y2 @ Y0 ) ) @ ( plus @ Y2 @ Y0 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y2 @ Y0 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y2 @ Y0 @ Y1 @ X4 ) ) @ ( app @ ( suc @ ( plus @ X3 @ Y2 ) ) @ Y0 @ ( cons @ ( plus @ X3 @ Y2 ) @ X2 @ ( app @ X3 @ Y2 @ X1 @ Y1 ) ) @ X4 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y2 @ Y0 ) ) @ ( plus @ Y2 @ Y0 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y2 @ Y0 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y2 @ Y0 @ Y1 @ X4 ) ) @ ( app @ ( plus @ ( suc @ X3 ) @ Y2 ) @ Y0 @ ( app @ ( suc @ X3 ) @ Y2 @ ( cons @ X3 @ X2 @ X1 ) @ Y1 ) @ X4 ) ) ) ) ) ) ) )
@ X5 )
= $true ),
inference(pi_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
! [X2: elem,X3: nat,X1: list,X4: list] :
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ list
@ ^ [Y1: list] :
( !! @ nat
@ ^ [Y2: nat] :
( ( listStar @ Y2 @ Y1 @ Y1 )
=> ( ( listStar @ Y0 @ X4 @ X4 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y2 @ Y0 ) ) @ ( plus @ Y2 @ Y0 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y2 @ Y0 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y2 @ Y0 @ Y1 @ X4 ) ) @ ( app @ ( suc @ ( plus @ X3 @ Y2 ) ) @ Y0 @ ( cons @ ( plus @ X3 @ Y2 ) @ X2 @ ( app @ X3 @ Y2 @ X1 @ Y1 ) ) @ X4 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y2 @ Y0 ) ) @ ( plus @ Y2 @ Y0 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y2 @ Y0 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y2 @ Y0 @ Y1 @ X4 ) ) @ ( app @ ( plus @ ( suc @ X3 ) @ Y2 ) @ Y0 @ ( app @ ( suc @ X3 ) @ Y2 @ ( cons @ X3 @ X2 @ X1 ) @ Y1 ) @ X4 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f65]) ).
thf(f65,plain,
! [X2: elem,X3: nat,X1: list,X4: list] :
( ( ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list
@ ^ [Y2: list] :
( !! @ nat
@ ^ [Y3: nat] :
( ( listStar @ Y3 @ Y2 @ Y2 )
=> ( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y3 @ Y1 ) ) @ ( plus @ Y3 @ Y1 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y3 @ Y1 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y3 @ Y1 @ Y2 @ Y0 ) ) @ ( app @ ( suc @ ( plus @ X3 @ Y3 ) ) @ Y1 @ ( cons @ ( plus @ X3 @ Y3 ) @ X2 @ ( app @ X3 @ Y3 @ X1 @ Y2 ) ) @ Y0 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y3 @ Y1 ) ) @ ( plus @ Y3 @ Y1 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y3 @ Y1 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y3 @ Y1 @ Y2 @ Y0 ) ) @ ( app @ ( plus @ ( suc @ X3 ) @ Y3 ) @ Y1 @ ( app @ ( suc @ X3 ) @ Y3 @ ( cons @ X3 @ X2 @ X1 ) @ Y2 ) @ Y0 ) ) ) ) ) ) ) ) )
@ X4 )
= $true ),
inference(pi_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
! [X2: elem,X3: nat,X1: list] :
( $true
= ( !! @ list
@ ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list
@ ^ [Y2: list] :
( !! @ nat
@ ^ [Y3: nat] :
( ( listStar @ Y3 @ Y2 @ Y2 )
=> ( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( ( listStar @ X3 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y3 @ Y1 ) ) @ ( plus @ Y3 @ Y1 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y3 @ Y1 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y3 @ Y1 @ Y2 @ Y0 ) ) @ ( app @ ( suc @ ( plus @ X3 @ Y3 ) ) @ Y1 @ ( cons @ ( plus @ X3 @ Y3 ) @ X2 @ ( app @ X3 @ Y3 @ X1 @ Y2 ) ) @ Y0 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y3 @ Y1 ) ) @ ( plus @ Y3 @ Y1 ) ) @ ( app @ ( suc @ X3 ) @ ( plus @ Y3 @ Y1 ) @ ( cons @ X3 @ X2 @ X1 ) @ ( app @ Y3 @ Y1 @ Y2 @ Y0 ) ) @ ( app @ ( plus @ ( suc @ X3 ) @ Y3 ) @ Y1 @ ( app @ ( suc @ X3 ) @ Y3 @ ( cons @ X3 @ X2 @ X1 ) @ Y2 ) @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f63]) ).
thf(f63,plain,
! [X2: elem,X3: nat,X1: list] :
( $true
= ( ^ [Y0: nat] :
( !! @ list
@ ^ [Y1: list] :
( !! @ nat
@ ^ [Y2: nat] :
( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( ( listStar @ Y2 @ Y1 @ Y1 )
=> ( ( listStar @ Y0 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y4 @ Y2 ) ) @ ( plus @ Y4 @ Y2 ) ) @ ( app @ ( suc @ Y0 ) @ ( plus @ Y4 @ Y2 ) @ ( cons @ Y0 @ X2 @ X1 ) @ ( app @ Y4 @ Y2 @ Y3 @ Y1 ) ) @ ( app @ ( suc @ ( plus @ Y0 @ Y4 ) ) @ Y2 @ ( cons @ ( plus @ Y0 @ Y4 ) @ X2 @ ( app @ Y0 @ Y4 @ X1 @ Y3 ) ) @ Y1 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y4 @ Y2 ) ) @ ( plus @ Y4 @ Y2 ) ) @ ( app @ ( suc @ Y0 ) @ ( plus @ Y4 @ Y2 ) @ ( cons @ Y0 @ X2 @ X1 ) @ ( app @ Y4 @ Y2 @ Y3 @ Y1 ) ) @ ( app @ ( plus @ ( suc @ Y0 ) @ Y4 ) @ Y2 @ ( app @ ( suc @ Y0 ) @ Y4 @ ( cons @ Y0 @ X2 @ X1 ) @ Y3 ) @ Y1 ) ) ) ) ) ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
! [X2: elem,X1: list] :
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( !! @ list
@ ^ [Y1: list] :
( !! @ nat
@ ^ [Y2: nat] :
( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( ( listStar @ Y2 @ Y1 @ Y1 )
=> ( ( listStar @ Y0 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y4 @ Y2 ) ) @ ( plus @ Y4 @ Y2 ) ) @ ( app @ ( suc @ Y0 ) @ ( plus @ Y4 @ Y2 ) @ ( cons @ Y0 @ X2 @ X1 ) @ ( app @ Y4 @ Y2 @ Y3 @ Y1 ) ) @ ( app @ ( suc @ ( plus @ Y0 @ Y4 ) ) @ Y2 @ ( cons @ ( plus @ Y0 @ Y4 ) @ X2 @ ( app @ Y0 @ Y4 @ X1 @ Y3 ) ) @ Y1 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y4 @ Y2 ) ) @ ( plus @ Y4 @ Y2 ) ) @ ( app @ ( suc @ Y0 ) @ ( plus @ Y4 @ Y2 ) @ ( cons @ Y0 @ X2 @ X1 ) @ ( app @ Y4 @ Y2 @ Y3 @ Y1 ) ) @ ( app @ ( plus @ ( suc @ Y0 ) @ Y4 ) @ Y2 @ ( app @ ( suc @ Y0 ) @ Y4 @ ( cons @ Y0 @ X2 @ X1 ) @ Y3 ) @ Y1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: elem,X1: list] :
( $true
= ( ^ [Y0: elem] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list
@ ^ [Y2: list] :
( !! @ nat
@ ^ [Y3: nat] :
( !! @ list
@ ^ [Y4: list] :
( !! @ nat
@ ^ [Y5: nat] :
( ( listStar @ Y5 @ Y4 @ Y4 )
=> ( ( listStar @ Y3 @ Y2 @ Y2 )
=> ( ( listStar @ Y1 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y5 @ Y3 ) ) @ ( plus @ Y5 @ Y3 ) ) @ ( app @ ( suc @ Y1 ) @ ( plus @ Y5 @ Y3 ) @ ( cons @ Y1 @ Y0 @ X1 ) @ ( app @ Y5 @ Y3 @ Y4 @ Y2 ) ) @ ( app @ ( suc @ ( plus @ Y1 @ Y5 ) ) @ Y3 @ ( cons @ ( plus @ Y1 @ Y5 ) @ Y0 @ ( app @ Y1 @ Y5 @ X1 @ Y4 ) ) @ Y2 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y5 @ Y3 ) ) @ ( plus @ Y5 @ Y3 ) ) @ ( app @ ( suc @ Y1 ) @ ( plus @ Y5 @ Y3 ) @ ( cons @ Y1 @ Y0 @ X1 ) @ ( app @ Y5 @ Y3 @ Y4 @ Y2 ) ) @ ( app @ ( plus @ ( suc @ Y1 ) @ Y5 ) @ Y3 @ ( app @ ( suc @ Y1 ) @ Y5 @ ( cons @ Y1 @ Y0 @ X1 ) @ Y4 ) @ Y2 ) ) ) ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
! [X1: list] :
( ( !! @ elem
@ ^ [Y0: elem] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list
@ ^ [Y2: list] :
( !! @ nat
@ ^ [Y3: nat] :
( !! @ list
@ ^ [Y4: list] :
( !! @ nat
@ ^ [Y5: nat] :
( ( listStar @ Y5 @ Y4 @ Y4 )
=> ( ( listStar @ Y3 @ Y2 @ Y2 )
=> ( ( listStar @ Y1 @ X1 @ X1 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y5 @ Y3 ) ) @ ( plus @ Y5 @ Y3 ) ) @ ( app @ ( suc @ Y1 ) @ ( plus @ Y5 @ Y3 ) @ ( cons @ Y1 @ Y0 @ X1 ) @ ( app @ Y5 @ Y3 @ Y4 @ Y2 ) ) @ ( app @ ( suc @ ( plus @ Y1 @ Y5 ) ) @ Y3 @ ( cons @ ( plus @ Y1 @ Y5 ) @ Y0 @ ( app @ Y1 @ Y5 @ X1 @ Y4 ) ) @ Y2 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y5 @ Y3 ) ) @ ( plus @ Y5 @ Y3 ) ) @ ( app @ ( suc @ Y1 ) @ ( plus @ Y5 @ Y3 ) @ ( cons @ Y1 @ Y0 @ X1 ) @ ( app @ Y5 @ Y3 @ Y4 @ Y2 ) ) @ ( app @ ( plus @ ( suc @ Y1 ) @ Y5 ) @ Y3 @ ( app @ ( suc @ Y1 ) @ Y5 @ ( cons @ Y1 @ Y0 @ X1 ) @ Y4 ) @ Y2 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f59]) ).
thf(f59,plain,
! [X1: list] :
( ( ^ [Y0: list] :
( !! @ elem
@ ^ [Y1: elem] :
( !! @ nat
@ ^ [Y2: nat] :
( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( !! @ list
@ ^ [Y5: list] :
( !! @ nat
@ ^ [Y6: nat] :
( ( listStar @ Y6 @ Y5 @ Y5 )
=> ( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( ( listStar @ Y2 @ Y0 @ Y0 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y6 @ Y4 ) ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ ( suc @ Y2 ) @ ( plus @ Y6 @ Y4 ) @ ( cons @ Y2 @ Y1 @ Y0 ) @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( app @ ( suc @ ( plus @ Y2 @ Y6 ) ) @ Y4 @ ( cons @ ( plus @ Y2 @ Y6 ) @ Y1 @ ( app @ Y2 @ Y6 @ Y0 @ Y5 ) ) @ Y3 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y6 @ Y4 ) ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ ( suc @ Y2 ) @ ( plus @ Y6 @ Y4 ) @ ( cons @ Y2 @ Y1 @ Y0 ) @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( app @ ( plus @ ( suc @ Y2 ) @ Y6 ) @ Y4 @ ( app @ ( suc @ Y2 ) @ Y6 @ ( cons @ Y2 @ Y1 @ Y0 ) @ Y5 ) @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
( ( !! @ list
@ ^ [Y0: list] :
( !! @ elem
@ ^ [Y1: elem] :
( !! @ nat
@ ^ [Y2: nat] :
( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( !! @ list
@ ^ [Y5: list] :
( !! @ nat
@ ^ [Y6: nat] :
( ( listStar @ Y6 @ Y5 @ Y5 )
=> ( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( ( listStar @ Y2 @ Y0 @ Y0 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y6 @ Y4 ) ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ ( suc @ Y2 ) @ ( plus @ Y6 @ Y4 ) @ ( cons @ Y2 @ Y1 @ Y0 ) @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( app @ ( suc @ ( plus @ Y2 @ Y6 ) ) @ Y4 @ ( cons @ ( plus @ Y2 @ Y6 ) @ Y1 @ ( app @ Y2 @ Y6 @ Y0 @ Y5 ) ) @ Y3 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y6 @ Y4 ) ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ ( suc @ Y2 ) @ ( plus @ Y6 @ Y4 ) @ ( cons @ Y2 @ Y1 @ Y0 ) @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( app @ ( plus @ ( suc @ Y2 ) @ Y6 ) @ Y4 @ ( app @ ( suc @ Y2 ) @ Y6 @ ( cons @ Y2 @ Y1 @ Y0 ) @ Y5 ) @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f44]) ).
thf(f44,plain,
( ( !! @ list
@ ^ [Y0: list] :
( !! @ elem
@ ^ [Y1: elem] :
( !! @ nat
@ ^ [Y2: nat] :
( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( !! @ list
@ ^ [Y5: list] :
( !! @ nat
@ ^ [Y6: nat] :
( ( listStar @ Y6 @ Y5 @ Y5 )
=> ( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( ( listStar @ Y2 @ Y0 @ Y0 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ Y6 @ Y4 ) ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ ( suc @ Y2 ) @ ( plus @ Y6 @ Y4 ) @ ( cons @ Y2 @ Y1 @ Y0 ) @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( app @ ( suc @ ( plus @ Y2 @ Y6 ) ) @ Y4 @ ( cons @ ( plus @ Y2 @ Y6 ) @ Y1 @ ( app @ Y2 @ Y6 @ Y0 @ Y5 ) ) @ Y3 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ Y6 @ Y4 ) ) @ ( plus @ Y6 @ Y4 ) ) @ ( app @ ( suc @ Y2 ) @ ( plus @ Y6 @ Y4 ) @ ( cons @ Y2 @ Y1 @ Y0 ) @ ( app @ Y6 @ Y4 @ Y5 @ Y3 ) ) @ ( app @ ( plus @ ( suc @ Y2 ) @ Y6 ) @ Y4 @ ( app @ ( suc @ Y2 ) @ Y6 @ ( cons @ Y2 @ Y1 @ Y0 ) @ Y5 ) @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f43]) ).
thf(f43,plain,
! [X0: nat,X1: list,X2: nat,X3: list,X4: nat,X5: elem,X6: list] :
( ( listStar @ X0 @ X1 @ X1 )
=> ( ( listStar @ X2 @ X3 @ X3 )
=> ( ( listStar @ X4 @ X6 @ X6 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X2 ) ) @ ( plus @ X0 @ X2 ) ) @ ( app @ ( suc @ X4 ) @ ( plus @ X0 @ X2 ) @ ( cons @ X4 @ X5 @ X6 ) @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( suc @ ( plus @ X4 @ X0 ) ) @ X2 @ ( cons @ ( plus @ X4 @ X0 ) @ X5 @ ( app @ X4 @ X0 @ X6 @ X1 ) ) @ X3 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X2 ) ) @ ( plus @ X0 @ X2 ) ) @ ( app @ ( suc @ X4 ) @ ( plus @ X0 @ X2 ) @ ( cons @ X4 @ X5 @ X6 ) @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ ( suc @ X4 ) @ X0 ) @ X2 @ ( app @ ( suc @ X4 ) @ X0 @ ( cons @ X4 @ X5 @ X6 ) @ X1 ) @ X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,axiom,
! [X13: nat,X16: list,X14: nat,X17: list,X10: nat,X2: elem,X18: list] :
( ( listStar @ X13 @ X16 @ X16 )
=> ( ( listStar @ X14 @ X17 @ X17 )
=> ( ( listStar @ X10 @ X18 @ X18 )
=> ( ( listStar @ ( plus @ ( suc @ ( plus @ X13 @ X14 ) ) @ ( plus @ X13 @ X14 ) ) @ ( app @ ( suc @ X10 ) @ ( plus @ X13 @ X14 ) @ ( cons @ X10 @ X2 @ X18 ) @ ( app @ X13 @ X14 @ X16 @ X17 ) ) @ ( app @ ( suc @ ( plus @ X10 @ X13 ) ) @ X14 @ ( cons @ ( plus @ X10 @ X13 ) @ X2 @ ( app @ X10 @ X13 @ X18 @ X16 ) ) @ X17 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X13 @ X14 ) ) @ ( plus @ X13 @ X14 ) ) @ ( app @ ( suc @ X10 ) @ ( plus @ X13 @ X14 ) @ ( cons @ X10 @ X2 @ X18 ) @ ( app @ X13 @ X14 @ X16 @ X17 ) ) @ ( app @ ( plus @ ( suc @ X10 ) @ X13 ) @ X14 @ ( app @ ( suc @ X10 ) @ X13 @ ( cons @ X10 @ X2 @ X18 ) @ X16 ) @ X17 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.PLL0ptdnA4/DTF2THF_4359.p',list_app_assoc_indstep1) ).
thf(f126,plain,
( ( listStar @ ( plus @ ( plus @ sK7 @ sK5 ) @ ( plus @ sK7 @ sK5 ) ) @ ( app @ sK3 @ ( plus @ sK7 @ sK5 ) @ sK1 @ ( app @ sK7 @ sK5 @ sK6 @ sK4 ) ) @ ( app @ ( plus @ sK3 @ sK7 ) @ sK5 @ ( app @ sK3 @ sK7 @ sK1 @ sK6 ) @ sK4 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : DAT359^1 : TPTP v9.2.1. Released v9.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n031.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 06:17:33 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.44 ---- Original DTF file ---
% 0.15/0.44 thf(spec,logic,$$dhol).
% 0.15/0.44 %------------------------------------------------------------------------------
% 0.15/0.44 % File : DAT359^1 : TPTP v9.2.1. Released v9.2.0.
% 0.15/0.44 % Domain : Data Structures
% 0.15/0.44 % Problem : Associativity of list append, induction step 5
% 0.15/0.44 % Version : Especial.
% 0.15/0.44 % English :
% 0.15/0.44
% 0.15/0.44 % Refs : [RRB23] Rothgang et al. (2023), Theorem Proving in Dependently
% 0.15/0.44 % : [Rot25] Rothgang (2025), Email to Geoff Sutcliffe
% 0.15/0.44 % : [RK+25] Ranalter et al. (2025), The Dependently Typed Higher-O
% 0.15/0.44 % Source : [Rot25]
% 0.15/0.44 % Names : ListAppAssoc/list-app-assoc-indstep5.p [Rot25]
% 0.15/0.44
% 0.15/0.44 % Status : Theorem
% 0.15/0.44 % Rating : ? v9.2.0
% 0.15/0.44 % Syntax : Number of formulae : 18 ( 5 unt; 9 typ; 0 def)
% 0.15/0.44 % Number of atoms : 14 ( 14 equ; 0 cnn)
% 0.15/0.44 % Maximal formula atoms : 3 ( 1 avg)
% 0.15/0.44 % Number of connectives : 354 ( 0 ~; 0 |; 0 &; 349 @)
% 0.15/0.44 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.15/0.44 % Maximal formula depth : 10 ( 7 avg)
% 0.15/0.44 % Number of types : 2 ( 2 usr)
% 0.15/0.44 % Number of type decls : 9 ( 0 !>P; 2 !>D)
% 0.15/0.44 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.15/0.44 % Number of symbols : 8 ( 7 usr; 2 con; 0-4 aty)
% 0.15/0.44 % Number of variables : 51 ( 0 ^; 48 !; 0 ?; 51 :)
% 0.15/0.44 % ( 3 !>; 0 ?*; 0 @-; 0 @+)
% 0.15/0.44 % SPC : DH0_THM_EQU_NAR
% 0.15/0.44
% 0.15/0.44 % Comments :
% 0.15/0.44 %------------------------------------------------------------------------------
% 0.15/0.44 thf(elem_type,type,
% 0.15/0.44 elem: $tType ).
% 0.15/0.44
% 0.15/0.44 thf(nat_type,type,
% 0.15/0.44 nat: $tType ).
% 0.15/0.44
% 0.15/0.44 thf(zero_type,type,
% 0.15/0.44 zero: nat ).
% 0.15/0.44
% 0.15/0.44 thf(suc_type,type,
% 0.15/0.44 suc: nat > nat ).
% 0.15/0.44
% 0.15/0.44 thf(plus_type,type,
% 0.15/0.44 plus: nat > nat > nat ).
% 0.15/0.44
% 0.15/0.44 thf(list_type,type,
% 0.15/0.44 list: nat > $tType ).
% 0.15/0.44
% 0.15/0.44 thf(nil_type,type,
% 0.15/0.44 nil: list @ zero ).
% 0.15/0.44
% 0.15/0.44 thf(cons_type,type,
% 0.15/0.44 cons:
% 0.15/0.44 !>[N: nat] : ( elem > ( list @ N ) > ( list @ ( suc @ N ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(app_type,type,
% 0.15/0.44 app:
% 0.15/0.44 !>[N: nat,M: nat] : ( ( list @ N ) > ( list @ M ) > ( list @ ( plus @ N @ M ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(ax2,axiom,
% 0.15/0.44 ! [N: nat,M: nat] :
% 0.15/0.44 ( ( plus @ ( suc @ N ) @ M )
% 0.15/0.44 = ( suc @ ( plus @ N @ M ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(ax4,axiom,
% 0.15/0.44 ! [N: nat,M: nat,X: elem,Y: list @ N,Z: list @ M] :
% 0.15/0.44 ( ( app @ ( suc @ N ) @ M @ ( cons @ N @ X @ Y ) @ Z )
% 0.15/0.44 = ( cons @ ( plus @ N @ M ) @ X @ ( app @ N @ M @ Y @ Z ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(plus_assoc,axiom,
% 0.15/0.44 ! [M1: nat,M2: nat,M3: nat] :
% 0.15/0.44 ( ( plus @ M1 @ ( plus @ M2 @ M3 ) )
% 0.15/0.44 = ( plus @ ( plus @ M1 @ M2 ) @ M3 ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(plus_s_a,axiom,
% 0.15/0.44 ! [N: nat,M: nat,K: nat] :
% 0.15/0.44 ( ( suc @ ( plus @ ( plus @ N @ M ) @ K ) )
% 0.15/0.44 = ( plus @ ( suc @ N ) @ ( plus @ M @ K ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(list_app_assoc_indstep1,axiom,
% 0.15/0.44 ! [M2: nat,L2: list @ M2,M3: nat,L3: list @ M3,M: nat,X: elem,L: list @ M] :
% 0.15/0.44 ( ( ( app @ ( suc @ M ) @ ( plus @ M2 @ M3 ) @ ( cons @ M @ X @ L ) @ ( app @ M2 @ M3 @ L2 @ L3 ) )
% 0.15/0.44 = ( app @ ( suc @ ( plus @ M @ M2 ) ) @ M3 @ ( cons @ ( plus @ M @ M2 ) @ X @ ( app @ M @ M2 @ L @ L2 ) ) @ L3 ) )
% 0.15/0.44 => ( ( app @ ( suc @ M ) @ ( plus @ M2 @ M3 ) @ ( cons @ M @ X @ L ) @ ( app @ M2 @ M3 @ L2 @ L3 ) )
% 0.15/0.44 = ( app @ ( plus @ ( suc @ M ) @ M2 ) @ M3 @ ( app @ ( suc @ M ) @ M2 @ ( cons @ M @ X @ L ) @ L2 ) @ L3 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(list_app_assoc_indstep2,axiom,
% 0.15/0.44 ! [M2: nat,L2: list @ M2,M3: nat,L3: list @ M3,M: nat,X: elem,L: list @ M] :
% 0.15/0.44 ( ( ( app @ ( suc @ M ) @ ( plus @ M2 @ M3 ) @ ( cons @ M @ X @ L ) @ ( app @ M2 @ M3 @ L2 @ L3 ) )
% 0.15/0.44 = ( cons @ ( plus @ ( plus @ M @ M2 ) @ M3 ) @ X @ ( app @ ( plus @ M @ M2 ) @ M3 @ ( app @ M @ M2 @ L @ L2 ) @ L3 ) ) )
% 0.15/0.44 => ( ( app @ ( suc @ M ) @ ( plus @ M2 @ M3 ) @ ( cons @ M @ X @ L ) @ ( app @ M2 @ M3 @ L2 @ L3 ) )
% 0.15/0.44 = ( app @ ( suc @ ( plus @ M @ M2 ) ) @ M3 @ ( cons @ ( plus @ M @ M2 ) @ X @ ( app @ M @ M2 @ L @ L2 ) ) @ L3 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(list_app_assoc_indstep3,axiom,
% 0.15/0.44 ! [M2: nat,L2: list @ M2,M3: nat,L3: list @ M3,M: nat,X: elem,L: list @ M] :
% 0.15/0.44 ( ( ( app @ M @ ( plus @ M2 @ M3 ) @ L @ ( app @ M2 @ M3 @ L2 @ L3 ) )
% 0.15/0.44 = ( app @ ( plus @ M @ M2 ) @ M3 @ ( app @ M @ M2 @ L @ L2 ) @ L3 ) )
% 0.15/0.44 => ( ( ( app @ ( suc @ M ) @ ( plus @ M2 @ M3 ) @ ( cons @ M @ X @ L ) @ ( app @ M2 @ M3 @ L2 @ L3 ) )
% 0.15/0.44 = ( cons @ ( plus @ M @ ( plus @ M2 @ M3 ) ) @ X @ ( app @ M @ ( plus @ M2 @ M3 ) @ L @ ( app @ M2 @ M3 @ L2 @ L3 ) ) ) )
% 0.15/0.44 => ( ( app @ ( suc @ M ) @ ( plus @ M2 @ M3 ) @ ( cons @ M @ X @ L ) @ ( app @ M2 @ M3 @ L2 @ L3 ) )
% 0.15/0.44 = ( cons @ ( plus @ ( plus @ M @ M2 ) @ M3 ) @ X @ ( app @ ( plus @ M @ M2 ) @ M3 @ ( app @ M @ M2 @ L @ L2 ) @ L3 ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(list_app_assoc_indstep4,axiom,
% 0.15/0.44 ! [M2: nat,L2: list @ M2,M3: nat,L3: list @ M3,M: nat,X: elem,L: list @ M] :
% 0.15/0.44 ( ( app @ ( suc @ M ) @ ( plus @ M2 @ M3 ) @ ( cons @ M @ X @ L ) @ ( app @ M2 @ M3 @ L2 @ L3 ) )
% 0.15/0.44 = ( cons @ ( plus @ M @ ( plus @ M2 @ M3 ) ) @ X @ ( app @ M @ ( plus @ M2 @ M3 ) @ L @ ( app @ M2 @ M3 @ L2 @ L3 ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(list_app_assoc_indstep,conjecture,
% 0.15/0.44 ! [M2: nat,L2: list @ M2,M3: nat,L3: list @ M3,M: nat,X: elem,L: list @ M] :
% 0.15/0.44 ( ( ( app @ M @ ( plus @ M2 @ M3 ) @ L @ ( app @ M2 @ M3 @ L2 @ L3 ) )
% 0.15/0.44 = ( app @ ( plus @ M @ M2 ) @ M3 @ ( app @ M @ M2 @ L @ L2 ) @ L3 ) )
% 0.15/0.44 => ( ( app @ ( suc @ M ) @ ( plus @ M2 @ M3 ) @ ( cons @ M @ X @ L ) @ ( app @ M2 @ M3 @ L2 @ L3 ) )
% 0.15/0.44 = ( app @ ( plus @ ( suc @ M ) @ M2 ) @ M3 @ ( app @ ( suc @ M ) @ M2 @ ( cons @ M @ X @ L ) @ L2 ) @ L3 ) ) ) ).
% 0.15/0.44
% 0.15/0.44 %------------------------------------------------------------------------------
% 0.15/0.44 ------------------------
% 1.53/1.29 ---- Embedded in THF ---
% 1.53/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.53/1.29 %%% Generated on Tue Feb 24 06:17:33 EST 2026
% 1.53/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.53/1.29 %%% Logic specification used:
% 1.53/1.29 %%% thf(spec, logic, $$dhol).
% 1.53/1.29
% 1.53/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.PLL0ptdnA4/DTF2DTF4359.p
% See solution above
% 1.53/1.29 ------------------------
% 1.80/1.30 ---- Cleaned THF ---
% 1.80/1.30 thf(is_per_type,type,
% 1.80/1.30 isPer:
% 1.80/1.30 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 1.80/1.30
% 1.80/1.30 thf(is_per,definition,
% 1.80/1.30 ! [A: $tType,AStar: A > A > $o] :
% 1.80/1.30 ( ( isPer @ A @ AStar )
% 1.80/1.30 <=> ( ! [X: A,Y: A] :
% 1.80/1.30 ( ( AStar @ X @ Y )
% 1.80/1.30 => ( AStar @ Y @ X ) )
% 1.80/1.30 & ! [X: A,Y: A,Z: A] :
% 1.80/1.30 ( ( AStar @ X @ Y )
% 1.80/1.30 => ( ( AStar @ Y @ Z )
% 1.80/1.30 => ( AStar @ X @ Z ) ) ) ) ) ).
% 1.80/1.30
% 1.80/1.30 thf(elem_type,type,
% 1.80/1.30 elem: $tType ).
% 1.80/1.30
% 1.80/1.30 thf(elemStar,type,
% 1.80/1.30 elemStar: elem > elem > $o ).
% 1.80/1.30
% 1.80/1.30 thf(elemStar_is_eq,axiom,
% 1.80/1.30 ! [X: elem,Y: elem] :
% 1.80/1.30 ( ( elemStar @ X @ Y )
% 1.80/1.30 <=> ( X = Y ) ) ).
% 1.80/1.30
% 1.80/1.30 thf(nat_type,type,
% 1.80/1.30 nat: $tType ).
% 1.80/1.30
% 1.80/1.30 thf(natStar,type,
% 1.80/1.30 natStar: nat > nat > $o ).
% 1.80/1.30
% 1.80/1.30 thf(natStar_is_eq,axiom,
% 1.80/1.30 ! [X: nat,Y: nat] :
% 1.80/1.30 ( ( natStar @ X @ Y )
% 1.80/1.30 <=> ( X = Y ) ) ).
% 1.80/1.30
% 1.80/1.30 thf(zero_type,type,
% 1.80/1.30 zero: nat ).
% 1.80/1.30
% 1.80/1.30 thf(suc_type,type,
% 1.80/1.30 suc: nat > nat ).
% 1.80/1.30
% 1.80/1.30 thf(plus_type,type,
% 1.80/1.30 plus: nat > nat > nat ).
% 1.80/1.30
% 1.80/1.30 thf(list_type,type,
% 1.80/1.30 list: $tType ).
% 1.80/1.30
% 1.80/1.30 thf(listStar,type,
% 1.80/1.30 listStar: nat > list > list > $o ).
% 1.80/1.30
% 1.80/1.30 thf('\'listStar\'_is_per',axiom,
% 1.80/1.30 ! [C: nat] : ( isPer @ list @ ( listStar @ C ) ) ).
% 1.80/1.30
% 1.80/1.30 thf(nil_type,type,
% 1.80/1.30 nil: list ).
% 1.80/1.30
% 1.80/1.30 thf(nil_tp_ax,axiom,
% 1.80/1.30 listStar @ zero @ nil @ nil ).
% 1.80/1.30
% 1.80/1.30 thf(cons_type,type,
% 1.80/1.30 cons: nat > elem > list > list ).
% 1.80/1.30
% 1.80/1.30 thf(cons_tp_ax,axiom,
% 1.80/1.30 ! [N: nat,D: elem,D0: list,D0_prime: list] :
% 1.80/1.30 ( ( listStar @ N @ D0 @ D0_prime )
% 1.80/1.30 => ( listStar @ ( suc @ N ) @ ( cons @ N @ D @ D0 ) @ ( cons @ N @ D @ D0_prime ) ) ) ).
% 1.80/1.30
% 1.80/1.30 thf(app_type,type,
% 1.80/1.30 app: nat > nat > list > list > list ).
% 1.80/1.30
% 1.80/1.30 thf(app_tp_ax,axiom,
% 1.80/1.30 ! [N: nat,M: nat,D: list,D_prime: list] :
% 1.80/1.30 ( ( listStar @ N @ D @ D_prime )
% 1.80/1.30 => ! [D0: list,D0_prime: list] :
% 1.80/1.30 ( ( listStar @ M @ D0 @ D0_prime )
% 1.80/1.30 => ( listStar @ ( plus @ N @ M ) @ ( app @ N @ M @ D @ D0 ) @ ( app @ N @ M @ D_prime @ D0_prime ) ) ) ) ).
% 1.80/1.30
% 1.80/1.30 thf(ax2,axiom,
% 1.80/1.30 ! [N: nat,M: nat] :
% 1.80/1.30 ( ( plus @ ( suc @ N ) @ M )
% 1.80/1.30 = ( suc @ ( plus @ N @ M ) ) ) ).
% 1.80/1.30
% 1.80/1.30 thf(ax4,axiom,
% 1.80/1.30 ! [N: nat,M: nat,X: elem,Y: list,Z: list] :
% 1.80/1.30 ( ( listStar @ N @ Y @ Y )
% 1.80/1.30 => ( ( listStar @ M @ Z @ Z )
% 1.80/1.30 => ( listStar @ ( plus @ ( suc @ N ) @ M ) @ ( app @ ( suc @ N ) @ M @ ( cons @ N @ X @ Y ) @ Z ) @ ( cons @ ( plus @ N @ M ) @ X @ ( app @ N @ M @ Y @ Z ) ) ) ) ) ).
% 1.80/1.30
% 1.80/1.30 thf(plus_assoc,axiom,
% 1.80/1.30 ! [M1: nat,M2: nat,M3: nat] :
% 1.80/1.30 ( ( plus @ M1 @ ( plus @ M2 @ M3 ) )
% 1.80/1.30 = ( plus @ ( plus @ M1 @ M2 ) @ M3 ) ) ).
% 1.80/1.30
% 1.80/1.30 thf(plus_s_a,axiom,
% 1.80/1.30 ! [N: nat,M: nat,K: nat] :
% 1.80/1.30 ( ( suc @ ( plus @ ( plus @ N @ M ) @ K ) )
% 1.80/1.30 = ( plus @ ( suc @ N ) @ ( plus @ M @ K ) ) ) ).
% 1.80/1.30
% 1.80/1.30 thf(list_app_assoc_indstep1,axiom,
% 1.80/1.30 ! [M2: nat,L2: list,M3: nat,L3: list,M: nat,X: elem,L: list] :
% 1.80/1.30 ( ( listStar @ M2 @ L2 @ L2 )
% 1.80/1.30 => ( ( listStar @ M3 @ L3 @ L3 )
% 1.80/1.30 => ( ( listStar @ M @ L @ L )
% 1.80/1.30 => ( ( listStar @ ( plus @ ( suc @ ( plus @ M2 @ M3 ) ) @ ( plus @ M2 @ M3 ) ) @ ( app @ ( suc @ M ) @ ( plus @ M2 @ M3 ) @ ( cons @ M @ X @ L ) @ ( app @ M2 @ M3 @ L2 @ L3 ) ) @ ( app @ ( suc @ ( plus @ M @ M2 ) ) @ M3 @ ( cons @ ( plus @ M @ M2 ) @ X @ ( app @ M @ M2 @ L @ L2 ) ) @ L3 ) )
% 1.80/1.30 => ( listStar @ ( plus @ ( suc @ ( plus @ M2 @ M3 ) ) @ ( plus @ M2 @ M3 ) ) @ ( app @ ( suc @ M ) @ ( plus @ M2 @ M3 ) @ ( cons @ M @ X @ L ) @ ( app @ M2 @ M3 @ L2 @ L3 ) ) @ ( app @ ( plus @ ( suc @ M ) @ M2 ) @ M3 @ ( app @ ( suc @ M ) @ M2 @ ( cons @ M @ X @ L ) @ L2 ) @ L3 ) ) ) ) ) ) ).
% 1.80/1.30
% 1.80/1.30 thf(list_app_assoc_indstep2,axiom,
% 1.80/1.30 ! [M2: nat,L2: list,M3: nat,L3: list,M: nat,X: elem,L: list] :
% 1.80/1.30 ( ( listStar @ M2 @ L2 @ L2 )
% 1.80/1.30 => ( ( listStar @ M3 @ L3 @ L3 )
% 1.80/1.30 => ( ( listStar @ M @ L @ L )
% 1.80/1.30 => ( ( listStar @ ( plus @ ( suc @ ( plus @ M2 @ M3 ) ) @ ( plus @ M2 @ M3 ) ) @ ( app @ ( suc @ M ) @ ( plus @ M2 @ M3 ) @ ( cons @ M @ X @ L ) @ ( app @ M2 @ M3 @ L2 @ L3 ) ) @ ( cons @ ( plus @ ( plus @ M @ M2 ) @ M3 ) @ X @ ( app @ ( plus @ M @ M2 ) @ M3 @ ( app @ M @ M2 @ L @ L2 ) @ L3 ) ) )
% 1.80/1.30 => ( listStar @ ( plus @ ( suc @ ( plus @ M2 @ M3 ) ) @ ( plus @ M2 @ M3 ) ) @ ( app @ ( suc @ M ) @ ( plus @ M2 @ M3 ) @ ( cons @ M @ X @ L ) @ ( app @ M2 @ M3 @ L2 @ L3 ) ) @ ( app @ ( suc @ ( plus @ M @ M2 ) ) @ M3 @ ( cons @ ( plus @ M @ M2 ) @ X @ ( app @ M @ M2 @ L @ L2 ) ) @ L3 ) ) ) ) ) ) ).
% 1.80/1.30
% 1.80/1.30 thf(list_app_assoc_indstep3,axiom,
% 1.80/1.30 ! [M2: nat,L2: list,M3: nat,L3: list,M: nat,X: elem,L: list] :
% 1.80/1.30 ( ( listStar @ M2 @ L2 @ L2 )
% 1.80/1.30 => ( ( listStar @ M3 @ L3 @ L3 )
% 1.80/1.30 => ( ( listStar @ M @ L @ L )
% 1.80/1.30 => ( ( listStar @ ( plus @ ( plus @ M2 @ M3 ) @ ( plus @ M2 @ M3 ) ) @ ( app @ M @ ( plus @ M2 @ M3 ) @ L @ ( app @ M2 @ M3 @ L2 @ L3 ) ) @ ( app @ ( plus @ M @ M2 ) @ M3 @ ( app @ M @ M2 @ L @ L2 ) @ L3 ) )
% 1.80/1.30 => ( ( listStar @ ( plus @ ( suc @ ( plus @ M2 @ M3 ) ) @ ( plus @ M2 @ M3 ) ) @ ( app @ ( suc @ M ) @ ( plus @ M2 @ M3 ) @ ( cons @ M @ X @ L ) @ ( app @ M2 @ M3 @ L2 @ L3 ) ) @ ( cons @ ( plus @ M @ ( plus @ M2 @ M3 ) ) @ X @ ( app @ M @ ( plus @ M2 @ M3 ) @ L @ ( app @ M2 @ M3 @ L2 @ L3 ) ) ) )
% 1.80/1.30 => ( listStar @ ( plus @ ( suc @ ( plus @ M2 @ M3 ) ) @ ( plus @ M2 @ M3 ) ) @ ( app @ ( suc @ M ) @ ( plus @ M2 @ M3 ) @ ( cons @ M @ X @ L ) @ ( app @ M2 @ M3 @ L2 @ L3 ) ) @ ( cons @ ( plus @ ( plus @ M @ M2 ) @ M3 ) @ X @ ( app @ ( plus @ M @ M2 ) @ M3 @ ( app @ M @ M2 @ L @ L2 ) @ L3 ) ) ) ) ) ) ) ) ).
% 1.80/1.30
% 1.80/1.30 thf(list_app_assoc_indstep4,axiom,
% 1.80/1.30 ! [M2: nat,L2: list,M3: nat,L3: list,M: nat,X: elem,L: list] :
% 1.80/1.30 ( ( listStar @ M2 @ L2 @ L2 )
% 1.80/1.30 => ( ( listStar @ M3 @ L3 @ L3 )
% 1.80/1.30 => ( ( listStar @ M @ L @ L )
% 1.80/1.30 => ( listStar @ ( plus @ ( suc @ ( plus @ M2 @ M3 ) ) @ ( plus @ M2 @ M3 ) ) @ ( app @ ( suc @ M ) @ ( plus @ M2 @ M3 ) @ ( cons @ M @ X @ L ) @ ( app @ M2 @ M3 @ L2 @ L3 ) ) @ ( cons @ ( plus @ M @ ( plus @ M2 @ M3 ) ) @ X @ ( app @ M @ ( plus @ M2 @ M3 ) @ L @ ( app @ M2 @ M3 @ L2 @ L3 ) ) ) ) ) ) ) ).
% 1.80/1.30
% 1.80/1.30 thf(list_app_assoc_indstep,conjecture,
% 1.80/1.30 ! [M2: nat,L2: list,M3: nat,L3: list,M: nat,X: elem,L: list] :
% 1.80/1.30 ( ( listStar @ M2 @ L2 @ L2 )
% 1.80/1.30 => ( ( listStar @ M3 @ L3 @ L3 )
% 1.80/1.30 => ( ( listStar @ M @ L @ L )
% 1.80/1.30 => ( ( listStar @ ( plus @ ( plus @ M2 @ M3 ) @ ( plus @ M2 @ M3 ) ) @ ( app @ M @ ( plus @ M2 @ M3 ) @ L @ ( app @ M2 @ M3 @ L2 @ L3 ) ) @ ( app @ ( plus @ M @ M2 ) @ M3 @ ( app @ M @ M2 @ L @ L2 ) @ L3 ) )
% 1.80/1.30 => ( listStar @ ( plus @ ( suc @ ( plus @ M2 @ M3 ) ) @ ( plus @ M2 @ M3 ) ) @ ( app @ ( suc @ M ) @ ( plus @ M2 @ M3 ) @ ( cons @ M @ X @ L ) @ ( app @ M2 @ M3 @ L2 @ L3 ) ) @ ( app @ ( plus @ ( suc @ M ) @ M2 ) @ M3 @ ( app @ ( suc @ M ) @ M2 @ ( cons @ M @ X @ L ) @ L2 ) @ L3 ) ) ) ) ) ) ).
% 1.80/1.30 ------------------------
% 1.80/1.31 % (4460)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/183Mi)
% 1.80/1.32 % (4461)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/4Mi)
% 1.80/1.32 % (4462)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/27Mi)
% 1.80/1.32 % (4464)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/2Mi)
% 1.80/1.32 % (4465)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/275Mi)
% 1.80/1.32 % (4463)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/2Mi)
% 1.80/1.32 % (4466)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/18Mi)
% 1.80/1.32 % (4464)Instruction limit reached!
% 1.80/1.32 % (4464)------------------------------
% 1.80/1.32 % (4464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.32 % (4464)Termination reason: Unknown
% 1.80/1.32 % (4464)Termination phase: shuffling
% 1.80/1.32
% 1.80/1.32 % (4464)Memory used [KB]: 1023
% 1.80/1.32 % (4464)Time elapsed: 0.002 s
% 1.80/1.32 % (4464)Instructions burned: 2 (million)
% 1.80/1.32 % (4464)------------------------------
% 1.80/1.32 % (4464)------------------------------
% 1.80/1.32 % (4461)Instruction limit reached!
% 1.80/1.32 % (4461)------------------------------
% 1.80/1.32 % (4461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.32 % (4461)Termination reason: Unknown
% 1.80/1.32 % (4461)Termination phase: shuffling
% 1.80/1.32
% 1.80/1.32 % (4461)Memory used [KB]: 1023
% 1.80/1.32 % (4461)Time elapsed: 0.003 s
% 1.80/1.32 % (4461)Instructions burned: 4 (million)
% 1.80/1.32 % (4461)------------------------------
% 1.80/1.32 % (4461)------------------------------
% 1.80/1.32 % (4463)Instruction limit reached!
% 1.80/1.32 % (4463)------------------------------
% 1.80/1.32 % (4463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.32 % (4463)Termination reason: Unknown
% 1.80/1.32 % (4463)Termination phase: shuffling
% 1.80/1.32
% 1.80/1.32 % (4463)Memory used [KB]: 1023
% 1.80/1.32 % (4463)Time elapsed: 0.003 s
% 1.80/1.32 % (4463)Instructions burned: 4 (million)
% 1.80/1.32 % (4463)------------------------------
% 1.80/1.32 % (4463)------------------------------
% 1.80/1.33 % (4466)Instruction limit reached!
% 1.80/1.33 % (4466)------------------------------
% 1.80/1.33 % (4466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.33 % (4466)Termination reason: Unknown
% 1.80/1.33 % (4466)Termination phase: Saturation
% 1.80/1.33
% 1.80/1.33 % (4466)Memory used [KB]: 5628
% 1.80/1.33 % (4466)Time elapsed: 0.010 s
% 1.80/1.33 % (4466)Instructions burned: 19 (million)
% 1.80/1.33 % (4466)------------------------------
% 1.80/1.33 % (4466)------------------------------
% 1.80/1.33 % (4465)Refutation not found, incomplete strategy
% 1.80/1.33 % (4465)------------------------------
% 1.80/1.33 % (4465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.33 % (4465)Termination reason: Refutation not found, incomplete strategy
% 1.80/1.33
% 1.80/1.33
% 1.80/1.33 % (4465)Memory used [KB]: 5628
% 1.80/1.33 % (4465)Time elapsed: 0.011 s
% 1.80/1.33 % (4465)Instructions burned: 21 (million)
% 1.80/1.33 % (4465)------------------------------
% 1.80/1.33 % (4465)------------------------------
% 1.80/1.33 % (4462)Instruction limit reached!
% 1.80/1.33 % (4462)------------------------------
% 1.80/1.33 % (4462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.33 % (4462)Termination reason: Unknown
% 1.80/1.33 % (4462)Termination phase: Saturation
% 1.80/1.33
% 1.80/1.33 % (4462)Memory used [KB]: 5628
% 1.80/1.33 % (4462)Time elapsed: 0.015 s
% 1.80/1.33 % (4462)Instructions burned: 27 (million)
% 1.80/1.33 % (4462)------------------------------
% 1.80/1.33 % (4462)------------------------------
% 1.80/1.34 % (4467)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/3Mi)
% 1.80/1.34 % (4468)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/37Mi)
% 1.80/1.34 % (4467)Instruction limit reached!
% 1.80/1.34 % (4467)------------------------------
% 1.80/1.34 % (4467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.34 % (4467)Termination reason: Unknown
% 1.80/1.34 % (4467)Termination phase: shuffling
% 1.80/1.34
% 1.80/1.34 % (4467)Memory used [KB]: 1023
% 1.80/1.34 % (4467)Time elapsed: 0.003 s
% 1.80/1.34 % (4467)Instructions burned: 4 (million)
% 1.80/1.34 % (4467)------------------------------
% 1.80/1.34 % (4467)------------------------------
% 1.80/1.34 % (4469)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/15Mi)
% 1.80/1.34 % (4469)Instruction limit reached!
% 1.80/1.34 % (4469)------------------------------
% 1.80/1.34 % (4469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.34 % (4469)Termination reason: Unknown
% 1.80/1.34 % (4469)Termination phase: Property scanning
% 1.80/1.34
% 1.80/1.34 % (4469)Memory used [KB]: 1151
% 1.80/1.34 % (4469)Time elapsed: 0.008 s
% 1.80/1.34 % (4469)Instructions burned: 15 (million)
% 1.80/1.34 % (4469)------------------------------
% 1.80/1.34 % (4469)------------------------------
% 1.80/1.34 % (4470)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/3Mi)
% 1.80/1.35 % (4470)Instruction limit reached!
% 1.80/1.35 % (4470)------------------------------
% 1.80/1.35 % (4470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.35 % (4470)Termination reason: Unknown
% 1.80/1.35 % (4470)Termination phase: shuffling
% 1.80/1.35
% 1.80/1.35 % (4470)Memory used [KB]: 1023
% 1.80/1.35 % (4470)Time elapsed: 0.003 s
% 1.80/1.35 % (4470)Instructions burned: 4 (million)
% 1.80/1.35 % (4470)------------------------------
% 1.80/1.35 % (4470)------------------------------
% 1.80/1.35 % (4471)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/1041Mi)
% 1.80/1.35 % (4474)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/16Mi)
% 1.80/1.35 % (4474)Instruction limit reached!
% 1.80/1.35 % (4474)------------------------------
% 1.80/1.35 % (4474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.35 % (4474)Termination reason: Unknown
% 1.80/1.35 % (4474)Termination phase: Saturation
% 1.80/1.35
% 1.80/1.35 % (4474)Memory used [KB]: 5628
% 1.80/1.35 % (4474)Time elapsed: 0.006 s
% 1.80/1.35 % (4474)Instructions burned: 18 (million)
% 1.80/1.35 % (4474)------------------------------
% 1.80/1.35 % (4474)------------------------------
% 1.80/1.35 % (4472)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/7Mi)
% 1.80/1.35 % (4468)Instruction limit reached!
% 1.80/1.35 % (4468)------------------------------
% 1.80/1.35 % (4468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.35 % (4468)Termination reason: Unknown
% 1.80/1.35 % (4468)Termination phase: Saturation
% 1.80/1.35
% 1.80/1.35 % (4468)Memory used [KB]: 5756
% 1.80/1.35 % (4468)Time elapsed: 0.018 s
% 1.80/1.35 % (4468)Instructions burned: 38 (million)
% 1.80/1.35 % (4468)------------------------------
% 1.80/1.35 % (4468)------------------------------
% 1.80/1.36 % (4472)Instruction limit reached!
% 1.80/1.36 % (4472)------------------------------
% 1.80/1.36 % (4472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.36 % (4472)Termination reason: Unknown
% 1.80/1.36 % (4472)Termination phase: Property scanning
% 1.80/1.36
% 1.80/1.36 % (4472)Memory used [KB]: 1023
% 1.80/1.36 % (4472)Time elapsed: 0.005 s
% 1.80/1.36 % (4472)Instructions burned: 8 (million)
% 1.80/1.36 % (4472)------------------------------
% 1.80/1.36 % (4472)------------------------------
% 1.80/1.36 % (4475)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/3Mi)
% 1.80/1.36 % (4475)Instruction limit reached!
% 1.80/1.36 % (4475)------------------------------
% 1.80/1.36 % (4475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.36 % (4475)Termination reason: Unknown
% 1.80/1.36 % (4475)Termination phase: shuffling
% 1.80/1.36
% 1.80/1.36 % (4475)Memory used [KB]: 1023
% 1.80/1.36 % (4475)Time elapsed: 0.003 s
% 1.80/1.36 % (4475)Instructions burned: 4 (million)
% 1.80/1.36 % (4475)------------------------------
% 1.80/1.36 % (4475)------------------------------
% 1.80/1.36 % (4476)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/3Mi)
% 1.80/1.36 % (4476)Instruction limit reached!
% 1.80/1.36 % (4476)------------------------------
% 1.80/1.36 % (4476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.36 % (4476)Termination reason: Unknown
% 1.80/1.36 % (4476)Termination phase: shuffling
% 1.80/1.36
% 1.80/1.36 % (4476)Memory used [KB]: 1023
% 1.80/1.36 % (4476)Time elapsed: 0.003 s
% 1.80/1.36 % (4476)Instructions burned: 4 (million)
% 1.80/1.36 % (4476)------------------------------
% 1.80/1.36 % (4476)------------------------------
% 1.80/1.37 % (4478)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/3Mi)
% 1.80/1.37 % (4478)Instruction limit reached!
% 1.80/1.37 % (4478)------------------------------
% 1.80/1.37 % (4478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.37 % (4478)Termination reason: Unknown
% 1.80/1.37 % (4478)Termination phase: shuffling
% 1.80/1.37
% 1.80/1.37 % (4478)Memory used [KB]: 1023
% 1.80/1.37 % (4478)Time elapsed: 0.003 s
% 1.80/1.37 % (4478)Instructions burned: 4 (million)
% 1.80/1.37 % (4478)------------------------------
% 1.80/1.37 % (4478)------------------------------
% 1.80/1.37 % (4460)Instruction limit reached!
% 1.80/1.37 % (4460)------------------------------
% 1.80/1.37 % (4460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.37 % (4460)Termination reason: Unknown
% 1.80/1.37 % (4460)Termination phase: Saturation
% 1.80/1.37
% 1.80/1.37 % (4460)Memory used [KB]: 7036
% 1.80/1.37 % (4460)Time elapsed: 0.059 s
% 1.80/1.37 % (4460)Instructions burned: 183 (million)
% 1.80/1.37 % (4460)------------------------------
% 1.80/1.37 % (4460)------------------------------
% 1.80/1.37 % (4477)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/7Mi)
% 1.80/1.37 % (4479)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/4Mi)
% 1.80/1.37 % (4479)Instruction limit reached!
% 1.80/1.37 % (4479)------------------------------
% 1.80/1.37 % (4479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.37 % (4479)Termination reason: Unknown
% 1.80/1.37 % (4479)Termination phase: shuffling
% 1.80/1.37
% 1.80/1.37 % (4479)Memory used [KB]: 1023
% 1.80/1.37 % (4479)Time elapsed: 0.003 s
% 1.80/1.37 % (4479)Instructions burned: 4 (million)
% 1.80/1.37 % (4479)------------------------------
% 1.80/1.37 % (4479)------------------------------
% 1.80/1.38 % (4477)Instruction limit reached!
% 1.80/1.38 % (4477)------------------------------
% 1.80/1.38 % (4477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.38 % (4477)Termination reason: Unknown
% 1.80/1.38 % (4477)Termination phase: Property scanning
% 1.80/1.38
% 1.80/1.38 % (4477)Memory used [KB]: 1023
% 1.80/1.38 % (4477)Time elapsed: 0.005 s
% 1.80/1.38 % (4477)Instructions burned: 8 (million)
% 1.80/1.38 % (4477)------------------------------
% 1.80/1.38 % (4477)------------------------------
% 1.80/1.38 % (4480)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/18Mi)
% 1.80/1.38 % (4481)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/710Mi)
% 1.80/1.38 % (4482)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/6Mi)
% 1.80/1.38 % (4482)Instruction limit reached!
% 1.80/1.38 % (4482)------------------------------
% 1.80/1.38 % (4482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.38 % (4482)Termination reason: Unknown
% 1.80/1.38 % (4482)Termination phase: Property scanning
% 1.80/1.38
% 1.80/1.38 % (4482)Memory used [KB]: 1023
% 1.80/1.38 % (4482)Time elapsed: 0.003 s
% 1.80/1.38 % (4482)Instructions burned: 7 (million)
% 1.80/1.38 % (4482)------------------------------
% 1.80/1.38 % (4482)------------------------------
% 1.80/1.39 % (4480)Instruction limit reached!
% 1.80/1.39 % (4480)------------------------------
% 1.80/1.39 % (4480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.39 % (4480)Termination reason: Unknown
% 1.80/1.39 % (4480)Termination phase: Saturation
% 1.80/1.39
% 1.80/1.39 % (4480)Memory used [KB]: 5628
% 1.80/1.39 % (4480)Time elapsed: 0.010 s
% 1.80/1.39 % (4480)Instructions burned: 19 (million)
% 1.80/1.39 % (4480)------------------------------
% 1.80/1.39 % (4480)------------------------------
% 1.80/1.39 % (4484)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/21Mi)
% 1.80/1.39 % (4483)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/902Mi)
% 1.80/1.39 % (4485)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/5Mi)
% 1.80/1.39 % (4486)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/6Mi)
% 1.80/1.39 % (4485)Instruction limit reached!
% 1.80/1.39 % (4485)------------------------------
% 1.80/1.39 % (4485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.39 % (4485)Termination reason: Unknown
% 1.80/1.39 % (4485)Termination phase: shuffling
% 1.80/1.39
% 1.80/1.39 % (4485)Memory used [KB]: 1023
% 1.80/1.39 % (4485)Time elapsed: 0.004 s
% 1.80/1.39 % (4485)Instructions burned: 7 (million)
% 1.80/1.39 % (4485)------------------------------
% 1.80/1.39 % (4485)------------------------------
% 1.80/1.39 % (4486)Instruction limit reached!
% 1.80/1.39 % (4486)------------------------------
% 1.80/1.39 % (4486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.39 % (4486)Termination reason: Unknown
% 1.80/1.39 % (4486)Termination phase: Property scanning
% 1.80/1.39
% 1.80/1.39 % (4486)Memory used [KB]: 1023
% 1.80/1.39 % (4486)Time elapsed: 0.003 s
% 1.80/1.39 % (4486)Instructions burned: 8 (million)
% 1.80/1.39 % (4486)------------------------------
% 1.80/1.39 % (4486)------------------------------
% 1.81/1.40 % (4484)Instruction limit reached!
% 1.81/1.40 % (4484)------------------------------
% 1.81/1.40 % (4484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.40 % (4484)Termination reason: Unknown
% 1.81/1.40 % (4484)Termination phase: Saturation
% 1.81/1.40
% 1.81/1.40 % (4484)Memory used [KB]: 5628
% 1.81/1.40 % (4484)Time elapsed: 0.011 s
% 1.81/1.40 % (4484)Instructions burned: 21 (million)
% 1.81/1.40 % (4484)------------------------------
% 1.81/1.40 % (4484)------------------------------
% 1.81/1.40 % (4488)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/779Mi)
% 1.81/1.40 % (4487)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/377Mi)
% 1.81/1.41 % (4489)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/19Mi)
% 1.81/1.42 % (4490)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_4359 for (2999ds/879Mi)
% 1.81/1.42 % (4489)Instruction limit reached!
% 1.81/1.42 % (4489)------------------------------
% 1.81/1.42 % (4489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.42 % (4489)Termination reason: Unknown
% 1.81/1.42 % (4489)Termination phase: Saturation
% 1.81/1.42
% 1.81/1.42 % (4489)Memory used [KB]: 5628
% 1.81/1.42 % (4489)Time elapsed: 0.010 s
% 1.81/1.42 % (4489)Instructions burned: 21 (million)
% 1.81/1.42 % (4489)------------------------------
% 1.81/1.42 % (4489)------------------------------
% 1.81/1.43 % (4488)First to succeed.
% 1.81/1.44 % (4491)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_4359 for (2998ds/17Mi)
% 1.81/1.45 % (4491)Instruction limit reached!
% 1.81/1.45 % (4491)------------------------------
% 1.81/1.45 % (4491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.45 % (4491)Termination reason: Unknown
% 1.81/1.45 % (4491)Termination phase: Saturation
% 1.81/1.45
% 1.81/1.45 % (4491)Memory used [KB]: 5500
% 1.81/1.45 % (4491)Time elapsed: 0.010 s
% 1.81/1.45 % (4491)Instructions burned: 18 (million)
% 1.81/1.45 % (4491)------------------------------
% 1.81/1.45 % (4491)------------------------------
% 1.81/1.45 % (4488)Refutation found. Thanks to Tanya!
% 1.81/1.45 % SZS status Theorem for DTF2THF_4359
% 1.81/1.45 % SZS output start Proof for DTF2THF_4359
% 1.81/1.45 thf(type_def_6, type, elem: $tType).
% 1.81/1.45 thf(type_def_7, type, nat: $tType).
% 1.81/1.45 thf(type_def_8, type, list: $tType).
% 1.81/1.45 thf(func_def_0, type, isPer: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 1.81/1.45 thf(func_def_2, type, elem: $tType).
% 1.81/1.45 thf(func_def_3, type, elemStar: elem > elem > $o).
% 1.81/1.45 thf(func_def_4, type, nat: $tType).
% 1.81/1.45 thf(func_def_5, type, natStar: nat > nat > $o).
% 1.81/1.45 thf(func_def_6, type, zero: nat).
% 1.81/1.45 thf(func_def_7, type, suc: nat > nat).
% 1.81/1.45 thf(func_def_8, type, plus: nat > nat > nat).
% 1.81/1.45 thf(func_def_9, type, list: $tType).
% 1.81/1.45 thf(func_def_10, type, listStar: nat > list > list > $o).
% 1.81/1.45 thf(func_def_11, type, nil: list).
% 1.81/1.45 thf(func_def_12, type, cons: nat > elem > list > list).
% 1.81/1.45 thf(func_def_13, type, app: nat > nat > list > list > list).
% 1.81/1.45 thf(func_def_31, type, sK1: list).
% 1.81/1.45 thf(func_def_32, type, sK2: elem).
% 1.81/1.45 thf(func_def_33, type, sK3: nat).
% 1.81/1.45 thf(func_def_34, type, sK4: list).
% 1.81/1.45 thf(func_def_35, type, sK5: nat).
% 1.81/1.45 thf(func_def_36, type, sK6: list).
% 1.81/1.45 thf(func_def_37, type, sK7: nat).
% 1.81/1.45 thf(f251,plain,(
% 1.81/1.45 $false),
% 1.81/1.45 inference(trivial_inequality_removal,[status(thm)],[f248])).
% 1.81/1.45 thf(f248,plain,(
% 1.81/1.45 ($false = $true)),
% 1.81/1.45 inference(backward_demodulation,[status(thm)],[f126,f241])).
% 1.81/1.45 thf(f241,plain,(
% 1.81/1.45 ((listStar @ (plus @ (plus @ sK7 @ sK5) @ (plus @ sK7 @ sK5)) @ (app @ sK3 @ (plus @ sK7 @ sK5) @ sK1 @ (app @ sK7 @ sK5 @ sK6 @ sK4)) @ (app @ (plus @ sK3 @ sK7) @ sK5 @ (app @ sK3 @ sK7 @ sK1 @ sK6) @ sK4)) = $false)),
% 1.81/1.45 inference(trivial_inequality_removal,[status(thm)],[f240])).
% 1.81/1.45 thf(f240,plain,(
% 1.81/1.45 ($false = $true) | ((listStar @ (plus @ (plus @ sK7 @ sK5) @ (plus @ sK7 @ sK5)) @ (app @ sK3 @ (plus @ sK7 @ sK5) @ sK1 @ (app @ sK7 @ sK5 @ sK6 @ sK4)) @ (app @ (plus @ sK3 @ sK7) @ sK5 @ (app @ sK3 @ sK7 @ sK1 @ sK6) @ sK4)) = $false)),
% 1.81/1.45 inference(forward_demodulation,[status(thm)],[f239,f124])).
% 1.81/1.45 thf(f124,plain,(
% 1.81/1.45 ((listStar @ sK3 @ sK1 @ sK1) = $true)),
% 1.81/1.45 inference(binary_proxy_clausification,[status(thm)],[f121])).
% 1.81/1.45 thf(f121,plain,(
% 1.81/1.45 (((listStar @ sK3 @ sK1 @ sK1) => ((listStar @ (plus @ (plus @ sK7 @ sK5) @ (plus @ sK7 @ sK5)) @ (app @ sK3 @ (plus @ sK7 @ sK5) @ sK1 @ (app @ sK7 @ sK5 @ sK6 @ sK4)) @ (app @ (plus @ sK3 @ sK7) @ sK5 @ (app @ sK3 @ sK7 @ sK1 @ sK6) @ sK4)) => (listStar @ (plus @ (suc @ (plus @ sK7 @ sK5)) @ (plus @ sK7 @ sK5)) @ (app @ (suc @ sK3) @ (plus @ sK7 @ sK5) @ (cons @ sK3 @ sK2 @ sK1) @ (app @ sK7 @ sK5 @ sK6 @ sK4)) @ (app @ (plus @ (suc @ sK3) @ sK7) @ sK5 @ (app @ (suc @ sK3) @ sK7 @ (cons @ sK3 @ sK2 @ sK1) @ sK6) @ sK4)))) = $false)),
% 1.81/1.45 inference(binary_proxy_clausification,[status(thm)],[f119])).
% 1.81/1.45 thf(f119,plain,(
% 1.81/1.45 (((listStar @ sK5 @ sK4 @ sK4) => ((listStar @ sK3 @ sK1 @ sK1) => ((listStar @ (plus @ (plus @ sK7 @ sK5) @ (plus @ sK7 @ sK5)) @ (app @ sK3 @ (plus @ sK7 @ sK5) @ sK1 @ (app @ sK7 @ sK5 @ sK6 @ sK4)) @ (app @ (plus @ sK3 @ sK7) @ sK5 @ (app @ sK3 @ sK7 @ sK1 @ sK6) @ sK4)) => (listStar @ (plus @ (suc @ (plus @ sK7 @ sK5)) @ (plus @ sK7 @ sK5)) @ (app @ (suc @ sK3) @ (plus @ sK7 @ sK5) @ (cons @ sK3 @ sK2 @ sK1) @ (app @ sK7 @ sK5 @ sK6 @ sK4)) @ (app @ (plus @ (suc @ sK3) @ sK7) @ sK5 @ (app @ (suc @ sK3) @ sK7 @ (cons @ sK3 @ sK2 @ sK1) @ sK6) @ sK4))))) = $false)),
% 1.81/1.45 inference(binary_proxy_clausification,[status(thm)],[f118])).
% 1.81/1.45 thf(f118,plain,(
% 1.81/1.45 ($false = ((listStar @ sK7 @ sK6 @ sK6) => ((listStar @ sK5 @ sK4 @ sK4) => ((listStar @ sK3 @ sK1 @ sK1) => ((listStar @ (plus @ (plus @ sK7 @ sK5) @ (plus @ sK7 @ sK5)) @ (app @ sK3 @ (plus @ sK7 @ sK5) @ sK1 @ (app @ sK7 @ sK5 @ sK6 @ sK4)) @ (app @ (plus @ sK3 @ sK7) @ sK5 @ (app @ sK3 @ sK7 @ sK1 @ sK6) @ sK4)) => (listStar @ (plus @ (suc @ (plus @ sK7 @ sK5)) @ (plus @ sK7 @ sK5)) @ (app @ (suc @ sK3) @ (plus @ sK7 @ sK5) @ (cons @ sK3 @ sK2 @ sK1) @ (app @ sK7 @ sK5 @ sK6 @ sK4)) @ (app @ (plus @ (suc @ sK3) @ sK7) @ sK5 @ (app @ (suc @ sK3) @ sK7 @ (cons @ sK3 @ sK2 @ sK1) @ sK6) @ sK4)))))))),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f117])).
% 1.81/1.45 thf(f117,plain,(
% 1.81/1.45 ($false = ((^[Y0 : nat]: ((listStar @ Y0 @ sK6 @ sK6) => ((listStar @ sK5 @ sK4 @ sK4) => ((listStar @ sK3 @ sK1 @ sK1) => ((listStar @ (plus @ (plus @ Y0 @ sK5) @ (plus @ Y0 @ sK5)) @ (app @ sK3 @ (plus @ Y0 @ sK5) @ sK1 @ (app @ Y0 @ sK5 @ sK6 @ sK4)) @ (app @ (plus @ sK3 @ Y0) @ sK5 @ (app @ sK3 @ Y0 @ sK1 @ sK6) @ sK4)) => (listStar @ (plus @ (suc @ (plus @ Y0 @ sK5)) @ (plus @ Y0 @ sK5)) @ (app @ (suc @ sK3) @ (plus @ Y0 @ sK5) @ (cons @ sK3 @ sK2 @ sK1) @ (app @ Y0 @ sK5 @ sK6 @ sK4)) @ (app @ (plus @ (suc @ sK3) @ Y0) @ sK5 @ (app @ (suc @ sK3) @ Y0 @ (cons @ sK3 @ sK2 @ sK1) @ sK6) @ sK4))))))) @ sK7))),
% 1.81/1.45 inference(sigma_clausification,[status(thm)],[f116])).
% 1.81/1.45 thf(f116,plain,(
% 1.81/1.45 ($false = (!! @ nat @ (^[Y0 : nat]: ((listStar @ Y0 @ sK6 @ sK6) => ((listStar @ sK5 @ sK4 @ sK4) => ((listStar @ sK3 @ sK1 @ sK1) => ((listStar @ (plus @ (plus @ Y0 @ sK5) @ (plus @ Y0 @ sK5)) @ (app @ sK3 @ (plus @ Y0 @ sK5) @ sK1 @ (app @ Y0 @ sK5 @ sK6 @ sK4)) @ (app @ (plus @ sK3 @ Y0) @ sK5 @ (app @ sK3 @ Y0 @ sK1 @ sK6) @ sK4)) => (listStar @ (plus @ (suc @ (plus @ Y0 @ sK5)) @ (plus @ Y0 @ sK5)) @ (app @ (suc @ sK3) @ (plus @ Y0 @ sK5) @ (cons @ sK3 @ sK2 @ sK1) @ (app @ Y0 @ sK5 @ sK6 @ sK4)) @ (app @ (plus @ (suc @ sK3) @ Y0) @ sK5 @ (app @ (suc @ sK3) @ Y0 @ (cons @ sK3 @ sK2 @ sK1) @ sK6) @ sK4)))))))))),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f115])).
% 1.81/1.45 thf(f115,plain,(
% 1.81/1.45 (((^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ Y1 @ Y0 @ Y0) => ((listStar @ sK5 @ sK4 @ sK4) => ((listStar @ sK3 @ sK1 @ sK1) => ((listStar @ (plus @ (plus @ Y1 @ sK5) @ (plus @ Y1 @ sK5)) @ (app @ sK3 @ (plus @ Y1 @ sK5) @ sK1 @ (app @ Y1 @ sK5 @ Y0 @ sK4)) @ (app @ (plus @ sK3 @ Y1) @ sK5 @ (app @ sK3 @ Y1 @ sK1 @ Y0) @ sK4)) => (listStar @ (plus @ (suc @ (plus @ Y1 @ sK5)) @ (plus @ Y1 @ sK5)) @ (app @ (suc @ sK3) @ (plus @ Y1 @ sK5) @ (cons @ sK3 @ sK2 @ sK1) @ (app @ Y1 @ sK5 @ Y0 @ sK4)) @ (app @ (plus @ (suc @ sK3) @ Y1) @ sK5 @ (app @ (suc @ sK3) @ Y1 @ (cons @ sK3 @ sK2 @ sK1) @ Y0) @ sK4))))))))) @ sK6) = $false)),
% 1.81/1.45 inference(sigma_clausification,[status(thm)],[f114])).
% 1.81/1.45 thf(f114,plain,(
% 1.81/1.45 ((!! @ list @ (^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ Y1 @ Y0 @ Y0) => ((listStar @ sK5 @ sK4 @ sK4) => ((listStar @ sK3 @ sK1 @ sK1) => ((listStar @ (plus @ (plus @ Y1 @ sK5) @ (plus @ Y1 @ sK5)) @ (app @ sK3 @ (plus @ Y1 @ sK5) @ sK1 @ (app @ Y1 @ sK5 @ Y0 @ sK4)) @ (app @ (plus @ sK3 @ Y1) @ sK5 @ (app @ sK3 @ Y1 @ sK1 @ Y0) @ sK4)) => (listStar @ (plus @ (suc @ (plus @ Y1 @ sK5)) @ (plus @ Y1 @ sK5)) @ (app @ (suc @ sK3) @ (plus @ Y1 @ sK5) @ (cons @ sK3 @ sK2 @ sK1) @ (app @ Y1 @ sK5 @ Y0 @ sK4)) @ (app @ (plus @ (suc @ sK3) @ Y1) @ sK5 @ (app @ (suc @ sK3) @ Y1 @ (cons @ sK3 @ sK2 @ sK1) @ Y0) @ sK4)))))))))) = $false)),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f113])).
% 1.81/1.45 thf(f113,plain,(
% 1.81/1.45 (((^[Y0 : nat]: (!! @ list @ (^[Y1 : list]: (!! @ nat @ (^[Y2 : nat]: ((listStar @ Y2 @ Y1 @ Y1) => ((listStar @ Y0 @ sK4 @ sK4) => ((listStar @ sK3 @ sK1 @ sK1) => ((listStar @ (plus @ (plus @ Y2 @ Y0) @ (plus @ Y2 @ Y0)) @ (app @ sK3 @ (plus @ Y2 @ Y0) @ sK1 @ (app @ Y2 @ Y0 @ Y1 @ sK4)) @ (app @ (plus @ sK3 @ Y2) @ Y0 @ (app @ sK3 @ Y2 @ sK1 @ Y1) @ sK4)) => (listStar @ (plus @ (suc @ (plus @ Y2 @ Y0)) @ (plus @ Y2 @ Y0)) @ (app @ (suc @ sK3) @ (plus @ Y2 @ Y0) @ (cons @ sK3 @ sK2 @ sK1) @ (app @ Y2 @ Y0 @ Y1 @ sK4)) @ (app @ (plus @ (suc @ sK3) @ Y2) @ Y0 @ (app @ (suc @ sK3) @ Y2 @ (cons @ sK3 @ sK2 @ sK1) @ Y1) @ sK4))))))))))) @ sK5) = $false)),
% 1.81/1.45 inference(sigma_clausification,[status(thm)],[f112])).
% 1.81/1.45 thf(f112,plain,(
% 1.81/1.45 ($false = (!! @ nat @ (^[Y0 : nat]: (!! @ list @ (^[Y1 : list]: (!! @ nat @ (^[Y2 : nat]: ((listStar @ Y2 @ Y1 @ Y1) => ((listStar @ Y0 @ sK4 @ sK4) => ((listStar @ sK3 @ sK1 @ sK1) => ((listStar @ (plus @ (plus @ Y2 @ Y0) @ (plus @ Y2 @ Y0)) @ (app @ sK3 @ (plus @ Y2 @ Y0) @ sK1 @ (app @ Y2 @ Y0 @ Y1 @ sK4)) @ (app @ (plus @ sK3 @ Y2) @ Y0 @ (app @ sK3 @ Y2 @ sK1 @ Y1) @ sK4)) => (listStar @ (plus @ (suc @ (plus @ Y2 @ Y0)) @ (plus @ Y2 @ Y0)) @ (app @ (suc @ sK3) @ (plus @ Y2 @ Y0) @ (cons @ sK3 @ sK2 @ sK1) @ (app @ Y2 @ Y0 @ Y1 @ sK4)) @ (app @ (plus @ (suc @ sK3) @ Y2) @ Y0 @ (app @ (suc @ sK3) @ Y2 @ (cons @ sK3 @ sK2 @ sK1) @ Y1) @ sK4)))))))))))))),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f111])).
% 1.81/1.45 thf(f111,plain,(
% 1.81/1.45 ($false = ((^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: (!! @ list @ (^[Y2 : list]: (!! @ nat @ (^[Y3 : nat]: ((listStar @ Y3 @ Y2 @ Y2) => ((listStar @ Y1 @ Y0 @ Y0) => ((listStar @ sK3 @ sK1 @ sK1) => ((listStar @ (plus @ (plus @ Y3 @ Y1) @ (plus @ Y3 @ Y1)) @ (app @ sK3 @ (plus @ Y3 @ Y1) @ sK1 @ (app @ Y3 @ Y1 @ Y2 @ Y0)) @ (app @ (plus @ sK3 @ Y3) @ Y1 @ (app @ sK3 @ Y3 @ sK1 @ Y2) @ Y0)) => (listStar @ (plus @ (suc @ (plus @ Y3 @ Y1)) @ (plus @ Y3 @ Y1)) @ (app @ (suc @ sK3) @ (plus @ Y3 @ Y1) @ (cons @ sK3 @ sK2 @ sK1) @ (app @ Y3 @ Y1 @ Y2 @ Y0)) @ (app @ (plus @ (suc @ sK3) @ Y3) @ Y1 @ (app @ (suc @ sK3) @ Y3 @ (cons @ sK3 @ sK2 @ sK1) @ Y2) @ Y0))))))))))))) @ sK4))),
% 1.81/1.45 inference(sigma_clausification,[status(thm)],[f110])).
% 1.81/1.45 thf(f110,plain,(
% 1.81/1.45 ((!! @ list @ (^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: (!! @ list @ (^[Y2 : list]: (!! @ nat @ (^[Y3 : nat]: ((listStar @ Y3 @ Y2 @ Y2) => ((listStar @ Y1 @ Y0 @ Y0) => ((listStar @ sK3 @ sK1 @ sK1) => ((listStar @ (plus @ (plus @ Y3 @ Y1) @ (plus @ Y3 @ Y1)) @ (app @ sK3 @ (plus @ Y3 @ Y1) @ sK1 @ (app @ Y3 @ Y1 @ Y2 @ Y0)) @ (app @ (plus @ sK3 @ Y3) @ Y1 @ (app @ sK3 @ Y3 @ sK1 @ Y2) @ Y0)) => (listStar @ (plus @ (suc @ (plus @ Y3 @ Y1)) @ (plus @ Y3 @ Y1)) @ (app @ (suc @ sK3) @ (plus @ Y3 @ Y1) @ (cons @ sK3 @ sK2 @ sK1) @ (app @ Y3 @ Y1 @ Y2 @ Y0)) @ (app @ (plus @ (suc @ sK3) @ Y3) @ Y1 @ (app @ (suc @ sK3) @ Y3 @ (cons @ sK3 @ sK2 @ sK1) @ Y2) @ Y0)))))))))))))) = $false)),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f109])).
% 1.81/1.45 thf(f109,plain,(
% 1.81/1.45 (((^[Y0 : nat]: (!! @ list @ (^[Y1 : list]: (!! @ nat @ (^[Y2 : nat]: (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: ((listStar @ Y4 @ Y3 @ Y3) => ((listStar @ Y2 @ Y1 @ Y1) => ((listStar @ Y0 @ sK1 @ sK1) => ((listStar @ (plus @ (plus @ Y4 @ Y2) @ (plus @ Y4 @ Y2)) @ (app @ Y0 @ (plus @ Y4 @ Y2) @ sK1 @ (app @ Y4 @ Y2 @ Y3 @ Y1)) @ (app @ (plus @ Y0 @ Y4) @ Y2 @ (app @ Y0 @ Y4 @ sK1 @ Y3) @ Y1)) => (listStar @ (plus @ (suc @ (plus @ Y4 @ Y2)) @ (plus @ Y4 @ Y2)) @ (app @ (suc @ Y0) @ (plus @ Y4 @ Y2) @ (cons @ Y0 @ sK2 @ sK1) @ (app @ Y4 @ Y2 @ Y3 @ Y1)) @ (app @ (plus @ (suc @ Y0) @ Y4) @ Y2 @ (app @ (suc @ Y0) @ Y4 @ (cons @ Y0 @ sK2 @ sK1) @ Y3) @ Y1))))))))))))))) @ sK3) = $false)),
% 1.81/1.45 inference(sigma_clausification,[status(thm)],[f108])).
% 1.81/1.45 thf(f108,plain,(
% 1.81/1.45 ((!! @ nat @ (^[Y0 : nat]: (!! @ list @ (^[Y1 : list]: (!! @ nat @ (^[Y2 : nat]: (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: ((listStar @ Y4 @ Y3 @ Y3) => ((listStar @ Y2 @ Y1 @ Y1) => ((listStar @ Y0 @ sK1 @ sK1) => ((listStar @ (plus @ (plus @ Y4 @ Y2) @ (plus @ Y4 @ Y2)) @ (app @ Y0 @ (plus @ Y4 @ Y2) @ sK1 @ (app @ Y4 @ Y2 @ Y3 @ Y1)) @ (app @ (plus @ Y0 @ Y4) @ Y2 @ (app @ Y0 @ Y4 @ sK1 @ Y3) @ Y1)) => (listStar @ (plus @ (suc @ (plus @ Y4 @ Y2)) @ (plus @ Y4 @ Y2)) @ (app @ (suc @ Y0) @ (plus @ Y4 @ Y2) @ (cons @ Y0 @ sK2 @ sK1) @ (app @ Y4 @ Y2 @ Y3 @ Y1)) @ (app @ (plus @ (suc @ Y0) @ Y4) @ Y2 @ (app @ (suc @ Y0) @ Y4 @ (cons @ Y0 @ sK2 @ sK1) @ Y3) @ Y1)))))))))))))))) = $false)),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f107])).
% 1.81/1.45 thf(f107,plain,(
% 1.81/1.45 ($false = ((^[Y0 : elem]: (!! @ nat @ (^[Y1 : nat]: (!! @ list @ (^[Y2 : list]: (!! @ nat @ (^[Y3 : nat]: (!! @ list @ (^[Y4 : list]: (!! @ nat @ (^[Y5 : nat]: ((listStar @ Y5 @ Y4 @ Y4) => ((listStar @ Y3 @ Y2 @ Y2) => ((listStar @ Y1 @ sK1 @ sK1) => ((listStar @ (plus @ (plus @ Y5 @ Y3) @ (plus @ Y5 @ Y3)) @ (app @ Y1 @ (plus @ Y5 @ Y3) @ sK1 @ (app @ Y5 @ Y3 @ Y4 @ Y2)) @ (app @ (plus @ Y1 @ Y5) @ Y3 @ (app @ Y1 @ Y5 @ sK1 @ Y4) @ Y2)) => (listStar @ (plus @ (suc @ (plus @ Y5 @ Y3)) @ (plus @ Y5 @ Y3)) @ (app @ (suc @ Y1) @ (plus @ Y5 @ Y3) @ (cons @ Y1 @ Y0 @ sK1) @ (app @ Y5 @ Y3 @ Y4 @ Y2)) @ (app @ (plus @ (suc @ Y1) @ Y5) @ Y3 @ (app @ (suc @ Y1) @ Y5 @ (cons @ Y1 @ Y0 @ sK1) @ Y4) @ Y2))))))))))))))))) @ sK2))),
% 1.81/1.45 inference(sigma_clausification,[status(thm)],[f106])).
% 1.81/1.45 thf(f106,plain,(
% 1.81/1.45 ((!! @ elem @ (^[Y0 : elem]: (!! @ nat @ (^[Y1 : nat]: (!! @ list @ (^[Y2 : list]: (!! @ nat @ (^[Y3 : nat]: (!! @ list @ (^[Y4 : list]: (!! @ nat @ (^[Y5 : nat]: ((listStar @ Y5 @ Y4 @ Y4) => ((listStar @ Y3 @ Y2 @ Y2) => ((listStar @ Y1 @ sK1 @ sK1) => ((listStar @ (plus @ (plus @ Y5 @ Y3) @ (plus @ Y5 @ Y3)) @ (app @ Y1 @ (plus @ Y5 @ Y3) @ sK1 @ (app @ Y5 @ Y3 @ Y4 @ Y2)) @ (app @ (plus @ Y1 @ Y5) @ Y3 @ (app @ Y1 @ Y5 @ sK1 @ Y4) @ Y2)) => (listStar @ (plus @ (suc @ (plus @ Y5 @ Y3)) @ (plus @ Y5 @ Y3)) @ (app @ (suc @ Y1) @ (plus @ Y5 @ Y3) @ (cons @ Y1 @ Y0 @ sK1) @ (app @ Y5 @ Y3 @ Y4 @ Y2)) @ (app @ (plus @ (suc @ Y1) @ Y5) @ Y3 @ (app @ (suc @ Y1) @ Y5 @ (cons @ Y1 @ Y0 @ sK1) @ Y4) @ Y2)))))))))))))))))) = $false)),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f105])).
% 1.81/1.45 thf(f105,plain,(
% 1.81/1.45 ($false = ((^[Y0 : list]: (!! @ elem @ (^[Y1 : elem]: (!! @ nat @ (^[Y2 : nat]: (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: (!! @ list @ (^[Y5 : list]: (!! @ nat @ (^[Y6 : nat]: ((listStar @ Y6 @ Y5 @ Y5) => ((listStar @ Y4 @ Y3 @ Y3) => ((listStar @ Y2 @ Y0 @ Y0) => ((listStar @ (plus @ (plus @ Y6 @ Y4) @ (plus @ Y6 @ Y4)) @ (app @ Y2 @ (plus @ Y6 @ Y4) @ Y0 @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (app @ (plus @ Y2 @ Y6) @ Y4 @ (app @ Y2 @ Y6 @ Y0 @ Y5) @ Y3)) => (listStar @ (plus @ (suc @ (plus @ Y6 @ Y4)) @ (plus @ Y6 @ Y4)) @ (app @ (suc @ Y2) @ (plus @ Y6 @ Y4) @ (cons @ Y2 @ Y1 @ Y0) @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (app @ (plus @ (suc @ Y2) @ Y6) @ Y4 @ (app @ (suc @ Y2) @ Y6 @ (cons @ Y2 @ Y1 @ Y0) @ Y5) @ Y3))))))))))))))))))) @ sK1))),
% 1.81/1.45 inference(sigma_clausification,[status(thm)],[f104])).
% 1.81/1.45 thf(f104,plain,(
% 1.81/1.45 ($false = (!! @ list @ (^[Y0 : list]: (!! @ elem @ (^[Y1 : elem]: (!! @ nat @ (^[Y2 : nat]: (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: (!! @ list @ (^[Y5 : list]: (!! @ nat @ (^[Y6 : nat]: ((listStar @ Y6 @ Y5 @ Y5) => ((listStar @ Y4 @ Y3 @ Y3) => ((listStar @ Y2 @ Y0 @ Y0) => ((listStar @ (plus @ (plus @ Y6 @ Y4) @ (plus @ Y6 @ Y4)) @ (app @ Y2 @ (plus @ Y6 @ Y4) @ Y0 @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (app @ (plus @ Y2 @ Y6) @ Y4 @ (app @ Y2 @ Y6 @ Y0 @ Y5) @ Y3)) => (listStar @ (plus @ (suc @ (plus @ Y6 @ Y4)) @ (plus @ Y6 @ Y4)) @ (app @ (suc @ Y2) @ (plus @ Y6 @ Y4) @ (cons @ Y2 @ Y1 @ Y0) @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (app @ (plus @ (suc @ Y2) @ Y6) @ Y4 @ (app @ (suc @ Y2) @ Y6 @ (cons @ Y2 @ Y1 @ Y0) @ Y5) @ Y3)))))))))))))))))))))),
% 1.81/1.45 inference(not_proxy_clausification,[status(thm)],[f55])).
% 1.81/1.45 thf(f55,plain,(
% 1.81/1.45 ((~ (!! @ list @ (^[Y0 : list]: (!! @ elem @ (^[Y1 : elem]: (!! @ nat @ (^[Y2 : nat]: (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: (!! @ list @ (^[Y5 : list]: (!! @ nat @ (^[Y6 : nat]: ((listStar @ Y6 @ Y5 @ Y5) => ((listStar @ Y4 @ Y3 @ Y3) => ((listStar @ Y2 @ Y0 @ Y0) => ((listStar @ (plus @ (plus @ Y6 @ Y4) @ (plus @ Y6 @ Y4)) @ (app @ Y2 @ (plus @ Y6 @ Y4) @ Y0 @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (app @ (plus @ Y2 @ Y6) @ Y4 @ (app @ Y2 @ Y6 @ Y0 @ Y5) @ Y3)) => (listStar @ (plus @ (suc @ (plus @ Y6 @ Y4)) @ (plus @ Y6 @ Y4)) @ (app @ (suc @ Y2) @ (plus @ Y6 @ Y4) @ (cons @ Y2 @ Y1 @ Y0) @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (app @ (plus @ (suc @ Y2) @ Y6) @ Y4 @ (app @ (suc @ Y2) @ Y6 @ (cons @ Y2 @ Y1 @ Y0) @ Y5) @ Y3))))))))))))))))))))) = $true)),
% 1.81/1.45 inference(cnf_transformation,[status(thm)],[f48])).
% 1.81/1.45 thf(f48,plain,(
% 1.81/1.45 ((~ (!! @ list @ (^[Y0 : list]: (!! @ elem @ (^[Y1 : elem]: (!! @ nat @ (^[Y2 : nat]: (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: (!! @ list @ (^[Y5 : list]: (!! @ nat @ (^[Y6 : nat]: ((listStar @ Y6 @ Y5 @ Y5) => ((listStar @ Y4 @ Y3 @ Y3) => ((listStar @ Y2 @ Y0 @ Y0) => ((listStar @ (plus @ (plus @ Y6 @ Y4) @ (plus @ Y6 @ Y4)) @ (app @ Y2 @ (plus @ Y6 @ Y4) @ Y0 @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (app @ (plus @ Y2 @ Y6) @ Y4 @ (app @ Y2 @ Y6 @ Y0 @ Y5) @ Y3)) => (listStar @ (plus @ (suc @ (plus @ Y6 @ Y4)) @ (plus @ Y6 @ Y4)) @ (app @ (suc @ Y2) @ (plus @ Y6 @ Y4) @ (cons @ Y2 @ Y1 @ Y0) @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (app @ (plus @ (suc @ Y2) @ Y6) @ Y4 @ (app @ (suc @ Y2) @ Y6 @ (cons @ Y2 @ Y1 @ Y0) @ Y5) @ Y3))))))))))))))))))))) = $true)),
% 1.81/1.45 inference(fool_elimination,[status(thm)],[f47])).
% 1.81/1.45 thf(f47,plain,(
% 1.81/1.45 ~! [X0 : nat,X1 : list,X2 : nat,X3 : list,X4 : nat,X5 : elem,X6 : list] : ((listStar @ X0 @ X1 @ X1) => ((listStar @ X2 @ X3 @ X3) => ((listStar @ X4 @ X6 @ X6) => ((listStar @ (plus @ (plus @ X0 @ X2) @ (plus @ X0 @ X2)) @ (app @ X4 @ (plus @ X0 @ X2) @ X6 @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ X4 @ X0) @ X2 @ (app @ X4 @ X0 @ X6 @ X1) @ X3)) => (listStar @ (plus @ (suc @ (plus @ X0 @ X2)) @ (plus @ X0 @ X2)) @ (app @ (suc @ X4) @ (plus @ X0 @ X2) @ (cons @ X4 @ X5 @ X6) @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ (suc @ X4) @ X0) @ X2 @ (app @ (suc @ X4) @ X0 @ (cons @ X4 @ X5 @ X6) @ X1) @ X3))))))),
% 1.81/1.45 inference(rectify,[status(thm)],[f17])).
% 1.81/1.45 thf(f17,negated_conjecture,(
% 1.81/1.45 ~! [X13 : nat,X16 : list,X14 : nat,X17 : list,X10 : nat,X2 : elem,X18 : list] : ((listStar @ X13 @ X16 @ X16) => ((listStar @ X14 @ X17 @ X17) => ((listStar @ X10 @ X18 @ X18) => ((listStar @ (plus @ (plus @ X13 @ X14) @ (plus @ X13 @ X14)) @ (app @ X10 @ (plus @ X13 @ X14) @ X18 @ (app @ X13 @ X14 @ X16 @ X17)) @ (app @ (plus @ X10 @ X13) @ X14 @ (app @ X10 @ X13 @ X18 @ X16) @ X17)) => (listStar @ (plus @ (suc @ (plus @ X13 @ X14)) @ (plus @ X13 @ X14)) @ (app @ (suc @ X10) @ (plus @ X13 @ X14) @ (cons @ X10 @ X2 @ X18) @ (app @ X13 @ X14 @ X16 @ X17)) @ (app @ (plus @ (suc @ X10) @ X13) @ X14 @ (app @ (suc @ X10) @ X13 @ (cons @ X10 @ X2 @ X18) @ X16) @ X17))))))),
% 1.81/1.45 inference(negated_conjecture,[status(cth)],[f16])).
% 1.81/1.45 thf(f16,conjecture,(
% 1.81/1.45 ! [X13 : nat,X16 : list,X14 : nat,X17 : list,X10 : nat,X2 : elem,X18 : list] : ((listStar @ X13 @ X16 @ X16) => ((listStar @ X14 @ X17 @ X17) => ((listStar @ X10 @ X18 @ X18) => ((listStar @ (plus @ (plus @ X13 @ X14) @ (plus @ X13 @ X14)) @ (app @ X10 @ (plus @ X13 @ X14) @ X18 @ (app @ X13 @ X14 @ X16 @ X17)) @ (app @ (plus @ X10 @ X13) @ X14 @ (app @ X10 @ X13 @ X18 @ X16) @ X17)) => (listStar @ (plus @ (suc @ (plus @ X13 @ X14)) @ (plus @ X13 @ X14)) @ (app @ (suc @ X10) @ (plus @ X13 @ X14) @ (cons @ X10 @ X2 @ X18) @ (app @ X13 @ X14 @ X16 @ X17)) @ (app @ (plus @ (suc @ X10) @ X13) @ X14 @ (app @ (suc @ X10) @ X13 @ (cons @ X10 @ X2 @ X18) @ X16) @ X17))))))),
% 1.81/1.45 file('/export/starexec/sandbox2/tmp/tmp.PLL0ptdnA4/DTF2THF_4359.p',list_app_assoc_indstep)).
% 1.81/1.45 thf(f239,plain,(
% 1.81/1.45 ((listStar @ (plus @ (plus @ sK7 @ sK5) @ (plus @ sK7 @ sK5)) @ (app @ sK3 @ (plus @ sK7 @ sK5) @ sK1 @ (app @ sK7 @ sK5 @ sK6 @ sK4)) @ (app @ (plus @ sK3 @ sK7) @ sK5 @ (app @ sK3 @ sK7 @ sK1 @ sK6) @ sK4)) = $false) | ((listStar @ sK3 @ sK1 @ sK1) = $false)),
% 1.81/1.45 inference(trivial_inequality_removal,[status(thm)],[f238])).
% 1.81/1.45 thf(f238,plain,(
% 1.81/1.45 ((listStar @ (plus @ (plus @ sK7 @ sK5) @ (plus @ sK7 @ sK5)) @ (app @ sK3 @ (plus @ sK7 @ sK5) @ sK1 @ (app @ sK7 @ sK5 @ sK6 @ sK4)) @ (app @ (plus @ sK3 @ sK7) @ sK5 @ (app @ sK3 @ sK7 @ sK1 @ sK6) @ sK4)) = $false) | ($false = $true) | ((listStar @ sK3 @ sK1 @ sK1) = $false)),
% 1.81/1.45 inference(forward_demodulation,[status(thm)],[f237,f120])).
% 1.81/1.45 thf(f120,plain,(
% 1.81/1.45 ($true = (listStar @ sK7 @ sK6 @ sK6))),
% 1.81/1.45 inference(binary_proxy_clausification,[status(thm)],[f118])).
% 1.81/1.45 thf(f237,plain,(
% 1.81/1.45 ((listStar @ (plus @ (plus @ sK7 @ sK5) @ (plus @ sK7 @ sK5)) @ (app @ sK3 @ (plus @ sK7 @ sK5) @ sK1 @ (app @ sK7 @ sK5 @ sK6 @ sK4)) @ (app @ (plus @ sK3 @ sK7) @ sK5 @ (app @ sK3 @ sK7 @ sK1 @ sK6) @ sK4)) = $false) | ($false = (listStar @ sK7 @ sK6 @ sK6)) | ((listStar @ sK3 @ sK1 @ sK1) = $false)),
% 1.81/1.45 inference(trivial_inequality_removal,[status(thm)],[f236])).
% 1.81/1.45 thf(f236,plain,(
% 1.81/1.45 ($false = $true) | ((listStar @ (plus @ (plus @ sK7 @ sK5) @ (plus @ sK7 @ sK5)) @ (app @ sK3 @ (plus @ sK7 @ sK5) @ sK1 @ (app @ sK7 @ sK5 @ sK6 @ sK4)) @ (app @ (plus @ sK3 @ sK7) @ sK5 @ (app @ sK3 @ sK7 @ sK1 @ sK6) @ sK4)) = $false) | ((listStar @ sK3 @ sK1 @ sK1) = $false) | ($false = (listStar @ sK7 @ sK6 @ sK6))),
% 1.81/1.45 inference(forward_demodulation,[status(thm)],[f235,f122])).
% 1.81/1.45 thf(f122,plain,(
% 1.81/1.45 ((listStar @ sK5 @ sK4 @ sK4) = $true)),
% 1.81/1.45 inference(binary_proxy_clausification,[status(thm)],[f119])).
% 1.81/1.45 thf(f235,plain,(
% 1.81/1.45 ((listStar @ sK5 @ sK4 @ sK4) = $false) | ((listStar @ sK3 @ sK1 @ sK1) = $false) | ($false = (listStar @ sK7 @ sK6 @ sK6)) | ((listStar @ (plus @ (plus @ sK7 @ sK5) @ (plus @ sK7 @ sK5)) @ (app @ sK3 @ (plus @ sK7 @ sK5) @ sK1 @ (app @ sK7 @ sK5 @ sK6 @ sK4)) @ (app @ (plus @ sK3 @ sK7) @ sK5 @ (app @ sK3 @ sK7 @ sK1 @ sK6) @ sK4)) = $false)),
% 1.81/1.45 inference(trivial_inequality_removal,[status(thm)],[f232])).
% 1.81/1.45 thf(f232,plain,(
% 1.81/1.45 ($false = (listStar @ sK7 @ sK6 @ sK6)) | ($false = $true) | ((listStar @ sK5 @ sK4 @ sK4) = $false) | ((listStar @ sK3 @ sK1 @ sK1) = $false) | ((listStar @ (plus @ (plus @ sK7 @ sK5) @ (plus @ sK7 @ sK5)) @ (app @ sK3 @ (plus @ sK7 @ sK5) @ sK1 @ (app @ sK7 @ sK5 @ sK6 @ sK4)) @ (app @ (plus @ sK3 @ sK7) @ sK5 @ (app @ sK3 @ sK7 @ sK1 @ sK6) @ sK4)) = $false)),
% 1.81/1.45 inference(superposition,[status(thm)],[f228,f125])).
% 1.81/1.45 thf(f125,plain,(
% 1.81/1.45 ($false = (listStar @ (plus @ (suc @ (plus @ sK7 @ sK5)) @ (plus @ sK7 @ sK5)) @ (app @ (suc @ sK3) @ (plus @ sK7 @ sK5) @ (cons @ sK3 @ sK2 @ sK1) @ (app @ sK7 @ sK5 @ sK6 @ sK4)) @ (app @ (plus @ (suc @ sK3) @ sK7) @ sK5 @ (app @ (suc @ sK3) @ sK7 @ (cons @ sK3 @ sK2 @ sK1) @ sK6) @ sK4)))),
% 1.81/1.45 inference(binary_proxy_clausification,[status(thm)],[f123])).
% 1.81/1.45 thf(f123,plain,(
% 1.81/1.45 ($false = ((listStar @ (plus @ (plus @ sK7 @ sK5) @ (plus @ sK7 @ sK5)) @ (app @ sK3 @ (plus @ sK7 @ sK5) @ sK1 @ (app @ sK7 @ sK5 @ sK6 @ sK4)) @ (app @ (plus @ sK3 @ sK7) @ sK5 @ (app @ sK3 @ sK7 @ sK1 @ sK6) @ sK4)) => (listStar @ (plus @ (suc @ (plus @ sK7 @ sK5)) @ (plus @ sK7 @ sK5)) @ (app @ (suc @ sK3) @ (plus @ sK7 @ sK5) @ (cons @ sK3 @ sK2 @ sK1) @ (app @ sK7 @ sK5 @ sK6 @ sK4)) @ (app @ (plus @ (suc @ sK3) @ sK7) @ sK5 @ (app @ (suc @ sK3) @ sK7 @ (cons @ sK3 @ sK2 @ sK1) @ sK6) @ sK4))))),
% 1.81/1.45 inference(binary_proxy_clausification,[status(thm)],[f121])).
% 1.81/1.45 thf(f228,plain,(
% 1.81/1.45 ( ! [X2 : nat,X3 : elem,X0 : nat,X1 : nat,X6 : list,X4 : list,X5 : list] : (($true = (listStar @ (plus @ (suc @ (plus @ X0 @ X1)) @ (plus @ X0 @ X1)) @ (app @ (suc @ X2) @ (plus @ X0 @ X1) @ (cons @ X2 @ X3 @ X4) @ (app @ X0 @ X1 @ X5 @ X6)) @ (app @ (plus @ (suc @ X2) @ X0) @ X1 @ (app @ (suc @ X2) @ X0 @ (cons @ X2 @ X3 @ X4) @ X5) @ X6))) | ($false = (listStar @ X2 @ X4 @ X4)) | ($false = (listStar @ X0 @ X5 @ X5)) | ((listStar @ X1 @ X6 @ X6) = $false) | ((listStar @ (plus @ (plus @ X0 @ X1) @ (plus @ X0 @ X1)) @ (app @ X2 @ (plus @ X0 @ X1) @ X4 @ (app @ X0 @ X1 @ X5 @ X6)) @ (app @ (plus @ X2 @ X0) @ X1 @ (app @ X2 @ X0 @ X4 @ X5) @ X6)) = $false)) )),
% 1.81/1.45 inference(trivial_inequality_removal,[status(thm)],[f227])).
% 1.81/1.45 thf(f227,plain,(
% 1.81/1.45 ( ! [X2 : nat,X3 : elem,X0 : nat,X1 : nat,X6 : list,X4 : list,X5 : list] : (($true = (listStar @ (plus @ (suc @ (plus @ X0 @ X1)) @ (plus @ X0 @ X1)) @ (app @ (suc @ X2) @ (plus @ X0 @ X1) @ (cons @ X2 @ X3 @ X4) @ (app @ X0 @ X1 @ X5 @ X6)) @ (app @ (plus @ (suc @ X2) @ X0) @ X1 @ (app @ (suc @ X2) @ X0 @ (cons @ X2 @ X3 @ X4) @ X5) @ X6))) | ($false = (listStar @ X0 @ X5 @ X5)) | ($false = $true) | ($false = (listStar @ X2 @ X4 @ X4)) | ((listStar @ (plus @ (plus @ X0 @ X1) @ (plus @ X0 @ X1)) @ (app @ X2 @ (plus @ X0 @ X1) @ X4 @ (app @ X0 @ X1 @ X5 @ X6)) @ (app @ (plus @ X2 @ X0) @ X1 @ (app @ X2 @ X0 @ X4 @ X5) @ X6)) = $false) | ((listStar @ X1 @ X6 @ X6) = $false)) )),
% 1.81/1.45 inference(duplicate_literal_removal,[status(thm)],[f226])).
% 1.81/1.45 thf(f226,plain,(
% 1.81/1.45 ( ! [X2 : nat,X3 : elem,X0 : nat,X1 : nat,X6 : list,X4 : list,X5 : list] : (($false = (listStar @ X2 @ X4 @ X4)) | ((listStar @ (plus @ (plus @ X0 @ X1) @ (plus @ X0 @ X1)) @ (app @ X2 @ (plus @ X0 @ X1) @ X4 @ (app @ X0 @ X1 @ X5 @ X6)) @ (app @ (plus @ X2 @ X0) @ X1 @ (app @ X2 @ X0 @ X4 @ X5) @ X6)) = $false) | ($false = (listStar @ X0 @ X5 @ X5)) | ($true = (listStar @ (plus @ (suc @ (plus @ X0 @ X1)) @ (plus @ X0 @ X1)) @ (app @ (suc @ X2) @ (plus @ X0 @ X1) @ (cons @ X2 @ X3 @ X4) @ (app @ X0 @ X1 @ X5 @ X6)) @ (app @ (plus @ (suc @ X2) @ X0) @ X1 @ (app @ (suc @ X2) @ X0 @ (cons @ X2 @ X3 @ X4) @ X5) @ X6))) | ((listStar @ X1 @ X6 @ X6) = $false) | ($false = (listStar @ X0 @ X5 @ X5)) | ((listStar @ X1 @ X6 @ X6) = $false) | ($false = $true) | ($false = (listStar @ X2 @ X4 @ X4))) )),
% 1.81/1.45 inference(superposition,[status(thm)],[f76,f221])).
% 1.81/1.45 thf(f221,plain,(
% 1.81/1.45 ( ! [X2 : nat,X3 : elem,X0 : nat,X1 : nat,X6 : list,X4 : list,X5 : list] : (((listStar @ (plus @ (suc @ (plus @ X0 @ X1)) @ (plus @ X0 @ X1)) @ (app @ (suc @ X2) @ (plus @ X0 @ X1) @ (cons @ X2 @ X3 @ X4) @ (app @ X0 @ X1 @ X5 @ X6)) @ (app @ (suc @ (plus @ X2 @ X0)) @ X1 @ (cons @ (plus @ X2 @ X0) @ X3 @ (app @ X2 @ X0 @ X4 @ X5)) @ X6)) = $true) | ((listStar @ X1 @ X6 @ X6) = $false) | ($false = (listStar @ X0 @ X5 @ X5)) | ($false = (listStar @ X2 @ X4 @ X4)) | ((listStar @ (plus @ (plus @ X0 @ X1) @ (plus @ X0 @ X1)) @ (app @ X2 @ (plus @ X0 @ X1) @ X4 @ (app @ X0 @ X1 @ X5 @ X6)) @ (app @ (plus @ X2 @ X0) @ X1 @ (app @ X2 @ X0 @ X4 @ X5) @ X6)) = $false)) )),
% 1.81/1.45 inference(trivial_inequality_removal,[status(thm)],[f220])).
% 1.81/1.45 thf(f220,plain,(
% 1.81/1.45 ( ! [X2 : nat,X3 : elem,X0 : nat,X1 : nat,X6 : list,X4 : list,X5 : list] : (((listStar @ (plus @ (suc @ (plus @ X0 @ X1)) @ (plus @ X0 @ X1)) @ (app @ (suc @ X2) @ (plus @ X0 @ X1) @ (cons @ X2 @ X3 @ X4) @ (app @ X0 @ X1 @ X5 @ X6)) @ (app @ (suc @ (plus @ X2 @ X0)) @ X1 @ (cons @ (plus @ X2 @ X0) @ X3 @ (app @ X2 @ X0 @ X4 @ X5)) @ X6)) = $true) | ($false = $true) | ((listStar @ (plus @ (plus @ X0 @ X1) @ (plus @ X0 @ X1)) @ (app @ X2 @ (plus @ X0 @ X1) @ X4 @ (app @ X0 @ X1 @ X5 @ X6)) @ (app @ (plus @ X2 @ X0) @ X1 @ (app @ X2 @ X0 @ X4 @ X5) @ X6)) = $false) | ((listStar @ X1 @ X6 @ X6) = $false) | ($false = (listStar @ X0 @ X5 @ X5)) | ($false = (listStar @ X2 @ X4 @ X4))) )),
% 1.81/1.45 inference(duplicate_literal_removal,[status(thm)],[f219])).
% 1.81/1.45 thf(f219,plain,(
% 1.81/1.45 ( ! [X2 : nat,X3 : elem,X0 : nat,X1 : nat,X6 : list,X4 : list,X5 : list] : (($false = (listStar @ X0 @ X5 @ X5)) | ((listStar @ (plus @ (suc @ (plus @ X0 @ X1)) @ (plus @ X0 @ X1)) @ (app @ (suc @ X2) @ (plus @ X0 @ X1) @ (cons @ X2 @ X3 @ X4) @ (app @ X0 @ X1 @ X5 @ X6)) @ (app @ (suc @ (plus @ X2 @ X0)) @ X1 @ (cons @ (plus @ X2 @ X0) @ X3 @ (app @ X2 @ X0 @ X4 @ X5)) @ X6)) = $true) | ($false = (listStar @ X2 @ X4 @ X4)) | ($false = (listStar @ X0 @ X5 @ X5)) | ((listStar @ X1 @ X6 @ X6) = $false) | ($false = $true) | ((listStar @ X1 @ X6 @ X6) = $false) | ((listStar @ (plus @ (plus @ X0 @ X1) @ (plus @ X0 @ X1)) @ (app @ X2 @ (plus @ X0 @ X1) @ X4 @ (app @ X0 @ X1 @ X5 @ X6)) @ (app @ (plus @ X2 @ X0) @ X1 @ (app @ X2 @ X0 @ X4 @ X5) @ X6)) = $false) | ($false = (listStar @ X2 @ X4 @ X4))) )),
% 1.81/1.45 inference(superposition,[status(thm)],[f103,f209])).
% 1.81/1.45 thf(f209,plain,(
% 1.81/1.45 ( ! [X2 : nat,X3 : elem,X0 : nat,X1 : nat,X6 : list,X4 : list,X5 : list] : (((listStar @ (plus @ (suc @ (plus @ X0 @ X1)) @ (plus @ X0 @ X1)) @ (app @ (suc @ X2) @ (plus @ X0 @ X1) @ (cons @ X2 @ X3 @ X4) @ (app @ X0 @ X1 @ X5 @ X6)) @ (cons @ (plus @ (plus @ X2 @ X0) @ X1) @ X3 @ (app @ (plus @ X2 @ X0) @ X1 @ (app @ X2 @ X0 @ X4 @ X5) @ X6))) = $true) | ($false = (listStar @ X2 @ X4 @ X4)) | ((listStar @ X1 @ X6 @ X6) = $false) | ($false = (listStar @ X0 @ X5 @ X5)) | ((listStar @ (plus @ (plus @ X0 @ X1) @ (plus @ X0 @ X1)) @ (app @ X2 @ (plus @ X0 @ X1) @ X4 @ (app @ X0 @ X1 @ X5 @ X6)) @ (app @ (plus @ X2 @ X0) @ X1 @ (app @ X2 @ X0 @ X4 @ X5) @ X6)) = $false)) )),
% 1.81/1.45 inference(trivial_inequality_removal,[status(thm)],[f208])).
% 1.81/1.45 thf(f208,plain,(
% 1.81/1.45 ( ! [X2 : nat,X3 : elem,X0 : nat,X1 : nat,X6 : list,X4 : list,X5 : list] : (((listStar @ (plus @ (suc @ (plus @ X0 @ X1)) @ (plus @ X0 @ X1)) @ (app @ (suc @ X2) @ (plus @ X0 @ X1) @ (cons @ X2 @ X3 @ X4) @ (app @ X0 @ X1 @ X5 @ X6)) @ (cons @ (plus @ (plus @ X2 @ X0) @ X1) @ X3 @ (app @ (plus @ X2 @ X0) @ X1 @ (app @ X2 @ X0 @ X4 @ X5) @ X6))) = $true) | ($false = $true) | ($false = (listStar @ X0 @ X5 @ X5)) | ($false = (listStar @ X2 @ X4 @ X4)) | ((listStar @ (plus @ (plus @ X0 @ X1) @ (plus @ X0 @ X1)) @ (app @ X2 @ (plus @ X0 @ X1) @ X4 @ (app @ X0 @ X1 @ X5 @ X6)) @ (app @ (plus @ X2 @ X0) @ X1 @ (app @ X2 @ X0 @ X4 @ X5) @ X6)) = $false) | ((listStar @ X1 @ X6 @ X6) = $false)) )),
% 1.81/1.45 inference(duplicate_literal_removal,[status(thm)],[f206])).
% 1.81/1.45 thf(f206,plain,(
% 1.81/1.45 ( ! [X2 : nat,X3 : elem,X0 : nat,X1 : nat,X6 : list,X4 : list,X5 : list] : (($false = (listStar @ X2 @ X4 @ X4)) | ($false = (listStar @ X0 @ X5 @ X5)) | ((listStar @ (plus @ (plus @ X0 @ X1) @ (plus @ X0 @ X1)) @ (app @ X2 @ (plus @ X0 @ X1) @ X4 @ (app @ X0 @ X1 @ X5 @ X6)) @ (app @ (plus @ X2 @ X0) @ X1 @ (app @ X2 @ X0 @ X4 @ X5) @ X6)) = $false) | ($false = $true) | ((listStar @ X1 @ X6 @ X6) = $false) | ((listStar @ X1 @ X6 @ X6) = $false) | ($false = (listStar @ X2 @ X4 @ X4)) | ($false = (listStar @ X0 @ X5 @ X5)) | ((listStar @ (plus @ (suc @ (plus @ X0 @ X1)) @ (plus @ X0 @ X1)) @ (app @ (suc @ X2) @ (plus @ X0 @ X1) @ (cons @ X2 @ X3 @ X4) @ (app @ X0 @ X1 @ X5 @ X6)) @ (cons @ (plus @ (plus @ X2 @ X0) @ X1) @ X3 @ (app @ (plus @ X2 @ X0) @ X1 @ (app @ X2 @ X0 @ X4 @ X5) @ X6))) = $true)) )),
% 1.81/1.45 inference(superposition,[status(thm)],[f188,f157])).
% 1.81/1.45 thf(f157,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X7 : nat,X4 : list,X5 : nat] : (($false = (listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (cons @ (plus @ X3 @ (plus @ X7 @ X5)) @ X2 @ (app @ X3 @ (plus @ X7 @ X5) @ X1 @ (app @ X7 @ X5 @ X6 @ X4))))) | ($false = (listStar @ X3 @ X1 @ X1)) | ((listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (cons @ (plus @ (plus @ X3 @ X7) @ X5) @ X2 @ (app @ (plus @ X3 @ X7) @ X5 @ (app @ X3 @ X7 @ X1 @ X6) @ X4))) = $true) | ($false = (listStar @ X7 @ X6 @ X6)) | ($false = (listStar @ X5 @ X4 @ X4)) | ($false = (listStar @ (plus @ (plus @ X7 @ X5) @ (plus @ X7 @ X5)) @ (app @ X3 @ (plus @ X7 @ X5) @ X1 @ (app @ X7 @ X5 @ X6 @ X4)) @ (app @ (plus @ X3 @ X7) @ X5 @ (app @ X3 @ X7 @ X1 @ X6) @ X4)))) )),
% 1.81/1.45 inference(binary_proxy_clausification,[status(thm)],[f156])).
% 1.81/1.45 thf(f156,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X7 : nat,X4 : list,X5 : nat] : (($false = (listStar @ X3 @ X1 @ X1)) | ($false = (listStar @ (plus @ (plus @ X7 @ X5) @ (plus @ X7 @ X5)) @ (app @ X3 @ (plus @ X7 @ X5) @ X1 @ (app @ X7 @ X5 @ X6 @ X4)) @ (app @ (plus @ X3 @ X7) @ X5 @ (app @ X3 @ X7 @ X1 @ X6) @ X4))) | ($true = ((listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (cons @ (plus @ X3 @ (plus @ X7 @ X5)) @ X2 @ (app @ X3 @ (plus @ X7 @ X5) @ X1 @ (app @ X7 @ X5 @ X6 @ X4)))) => (listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (cons @ (plus @ (plus @ X3 @ X7) @ X5) @ X2 @ (app @ (plus @ X3 @ X7) @ X5 @ (app @ X3 @ X7 @ X1 @ X6) @ X4))))) | ($false = (listStar @ X7 @ X6 @ X6)) | ($false = (listStar @ X5 @ X4 @ X4))) )),
% 1.81/1.45 inference(binary_proxy_clausification,[status(thm)],[f155])).
% 1.81/1.45 thf(f155,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X7 : nat,X4 : list,X5 : nat] : (($false = (listStar @ X7 @ X6 @ X6)) | ($false = (listStar @ X5 @ X4 @ X4)) | ($false = (listStar @ X3 @ X1 @ X1)) | (((listStar @ (plus @ (plus @ X7 @ X5) @ (plus @ X7 @ X5)) @ (app @ X3 @ (plus @ X7 @ X5) @ X1 @ (app @ X7 @ X5 @ X6 @ X4)) @ (app @ (plus @ X3 @ X7) @ X5 @ (app @ X3 @ X7 @ X1 @ X6) @ X4)) => ((listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (cons @ (plus @ X3 @ (plus @ X7 @ X5)) @ X2 @ (app @ X3 @ (plus @ X7 @ X5) @ X1 @ (app @ X7 @ X5 @ X6 @ X4)))) => (listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (cons @ (plus @ (plus @ X3 @ X7) @ X5) @ X2 @ (app @ (plus @ X3 @ X7) @ X5 @ (app @ X3 @ X7 @ X1 @ X6) @ X4))))) = $true)) )),
% 1.81/1.45 inference(binary_proxy_clausification,[status(thm)],[f154])).
% 1.81/1.45 thf(f154,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X7 : nat,X4 : list,X5 : nat] : (($false = (listStar @ X7 @ X6 @ X6)) | (((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (plus @ X7 @ X5) @ (plus @ X7 @ X5)) @ (app @ X3 @ (plus @ X7 @ X5) @ X1 @ (app @ X7 @ X5 @ X6 @ X4)) @ (app @ (plus @ X3 @ X7) @ X5 @ (app @ X3 @ X7 @ X1 @ X6) @ X4)) => ((listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (cons @ (plus @ X3 @ (plus @ X7 @ X5)) @ X2 @ (app @ X3 @ (plus @ X7 @ X5) @ X1 @ (app @ X7 @ X5 @ X6 @ X4)))) => (listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (cons @ (plus @ (plus @ X3 @ X7) @ X5) @ X2 @ (app @ (plus @ X3 @ X7) @ X5 @ (app @ X3 @ X7 @ X1 @ X6) @ X4)))))) = $true) | ($false = (listStar @ X5 @ X4 @ X4))) )),
% 1.81/1.45 inference(binary_proxy_clausification,[status(thm)],[f153])).
% 1.81/1.45 thf(f153,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X7 : nat,X4 : list,X5 : nat] : (($false = (listStar @ X7 @ X6 @ X6)) | (((listStar @ X5 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (plus @ X7 @ X5) @ (plus @ X7 @ X5)) @ (app @ X3 @ (plus @ X7 @ X5) @ X1 @ (app @ X7 @ X5 @ X6 @ X4)) @ (app @ (plus @ X3 @ X7) @ X5 @ (app @ X3 @ X7 @ X1 @ X6) @ X4)) => ((listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (cons @ (plus @ X3 @ (plus @ X7 @ X5)) @ X2 @ (app @ X3 @ (plus @ X7 @ X5) @ X1 @ (app @ X7 @ X5 @ X6 @ X4)))) => (listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (cons @ (plus @ (plus @ X3 @ X7) @ X5) @ X2 @ (app @ (plus @ X3 @ X7) @ X5 @ (app @ X3 @ X7 @ X1 @ X6) @ X4))))))) = $true)) )),
% 1.81/1.45 inference(binary_proxy_clausification,[status(thm)],[f152])).
% 1.81/1.45 thf(f152,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X7 : nat,X4 : list,X5 : nat] : (($true = ((listStar @ X7 @ X6 @ X6) => ((listStar @ X5 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (plus @ X7 @ X5) @ (plus @ X7 @ X5)) @ (app @ X3 @ (plus @ X7 @ X5) @ X1 @ (app @ X7 @ X5 @ X6 @ X4)) @ (app @ (plus @ X3 @ X7) @ X5 @ (app @ X3 @ X7 @ X1 @ X6) @ X4)) => ((listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (cons @ (plus @ X3 @ (plus @ X7 @ X5)) @ X2 @ (app @ X3 @ (plus @ X7 @ X5) @ X1 @ (app @ X7 @ X5 @ X6 @ X4)))) => (listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (cons @ (plus @ (plus @ X3 @ X7) @ X5) @ X2 @ (app @ (plus @ X3 @ X7) @ X5 @ (app @ X3 @ X7 @ X1 @ X6) @ X4)))))))))) )),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f151])).
% 1.81/1.45 thf(f151,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X7 : nat,X4 : list,X5 : nat] : (($true = ((^[Y0 : nat]: ((listStar @ Y0 @ X6 @ X6) => ((listStar @ X5 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (plus @ Y0 @ X5) @ (plus @ Y0 @ X5)) @ (app @ X3 @ (plus @ Y0 @ X5) @ X1 @ (app @ Y0 @ X5 @ X6 @ X4)) @ (app @ (plus @ X3 @ Y0) @ X5 @ (app @ X3 @ Y0 @ X1 @ X6) @ X4)) => ((listStar @ (plus @ (suc @ (plus @ Y0 @ X5)) @ (plus @ Y0 @ X5)) @ (app @ (suc @ X3) @ (plus @ Y0 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ Y0 @ X5 @ X6 @ X4)) @ (cons @ (plus @ X3 @ (plus @ Y0 @ X5)) @ X2 @ (app @ X3 @ (plus @ Y0 @ X5) @ X1 @ (app @ Y0 @ X5 @ X6 @ X4)))) => (listStar @ (plus @ (suc @ (plus @ Y0 @ X5)) @ (plus @ Y0 @ X5)) @ (app @ (suc @ X3) @ (plus @ Y0 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ Y0 @ X5 @ X6 @ X4)) @ (cons @ (plus @ (plus @ X3 @ Y0) @ X5) @ X2 @ (app @ (plus @ X3 @ Y0) @ X5 @ (app @ X3 @ Y0 @ X1 @ X6) @ X4))))))))) @ X7))) )),
% 1.81/1.45 inference(pi_clausification,[status(thm)],[f150])).
% 1.81/1.45 thf(f150,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X4 : list,X5 : nat] : (($true = (!! @ nat @ (^[Y0 : nat]: ((listStar @ Y0 @ X6 @ X6) => ((listStar @ X5 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (plus @ Y0 @ X5) @ (plus @ Y0 @ X5)) @ (app @ X3 @ (plus @ Y0 @ X5) @ X1 @ (app @ Y0 @ X5 @ X6 @ X4)) @ (app @ (plus @ X3 @ Y0) @ X5 @ (app @ X3 @ Y0 @ X1 @ X6) @ X4)) => ((listStar @ (plus @ (suc @ (plus @ Y0 @ X5)) @ (plus @ Y0 @ X5)) @ (app @ (suc @ X3) @ (plus @ Y0 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ Y0 @ X5 @ X6 @ X4)) @ (cons @ (plus @ X3 @ (plus @ Y0 @ X5)) @ X2 @ (app @ X3 @ (plus @ Y0 @ X5) @ X1 @ (app @ Y0 @ X5 @ X6 @ X4)))) => (listStar @ (plus @ (suc @ (plus @ Y0 @ X5)) @ (plus @ Y0 @ X5)) @ (app @ (suc @ X3) @ (plus @ Y0 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ Y0 @ X5 @ X6 @ X4)) @ (cons @ (plus @ (plus @ X3 @ Y0) @ X5) @ X2 @ (app @ (plus @ X3 @ Y0) @ X5 @ (app @ X3 @ Y0 @ X1 @ X6) @ X4)))))))))))) )),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f149])).
% 1.81/1.45 thf(f149,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X4 : list,X5 : nat] : ((((^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ Y1 @ Y0 @ Y0) => ((listStar @ X5 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (plus @ Y1 @ X5) @ (plus @ Y1 @ X5)) @ (app @ X3 @ (plus @ Y1 @ X5) @ X1 @ (app @ Y1 @ X5 @ Y0 @ X4)) @ (app @ (plus @ X3 @ Y1) @ X5 @ (app @ X3 @ Y1 @ X1 @ Y0) @ X4)) => ((listStar @ (plus @ (suc @ (plus @ Y1 @ X5)) @ (plus @ Y1 @ X5)) @ (app @ (suc @ X3) @ (plus @ Y1 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ Y1 @ X5 @ Y0 @ X4)) @ (cons @ (plus @ X3 @ (plus @ Y1 @ X5)) @ X2 @ (app @ X3 @ (plus @ Y1 @ X5) @ X1 @ (app @ Y1 @ X5 @ Y0 @ X4)))) => (listStar @ (plus @ (suc @ (plus @ Y1 @ X5)) @ (plus @ Y1 @ X5)) @ (app @ (suc @ X3) @ (plus @ Y1 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ Y1 @ X5 @ Y0 @ X4)) @ (cons @ (plus @ (plus @ X3 @ Y1) @ X5) @ X2 @ (app @ (plus @ X3 @ Y1) @ X5 @ (app @ X3 @ Y1 @ X1 @ Y0) @ X4))))))))))) @ X6) = $true)) )),
% 1.81/1.45 inference(pi_clausification,[status(thm)],[f148])).
% 1.81/1.45 thf(f148,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X4 : list,X5 : nat] : (((!! @ list @ (^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ Y1 @ Y0 @ Y0) => ((listStar @ X5 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (plus @ Y1 @ X5) @ (plus @ Y1 @ X5)) @ (app @ X3 @ (plus @ Y1 @ X5) @ X1 @ (app @ Y1 @ X5 @ Y0 @ X4)) @ (app @ (plus @ X3 @ Y1) @ X5 @ (app @ X3 @ Y1 @ X1 @ Y0) @ X4)) => ((listStar @ (plus @ (suc @ (plus @ Y1 @ X5)) @ (plus @ Y1 @ X5)) @ (app @ (suc @ X3) @ (plus @ Y1 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ Y1 @ X5 @ Y0 @ X4)) @ (cons @ (plus @ X3 @ (plus @ Y1 @ X5)) @ X2 @ (app @ X3 @ (plus @ Y1 @ X5) @ X1 @ (app @ Y1 @ X5 @ Y0 @ X4)))) => (listStar @ (plus @ (suc @ (plus @ Y1 @ X5)) @ (plus @ Y1 @ X5)) @ (app @ (suc @ X3) @ (plus @ Y1 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ Y1 @ X5 @ Y0 @ X4)) @ (cons @ (plus @ (plus @ X3 @ Y1) @ X5) @ X2 @ (app @ (plus @ X3 @ Y1) @ X5 @ (app @ X3 @ Y1 @ X1 @ Y0) @ X4)))))))))))) = $true)) )),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f147])).
% 1.81/1.45 thf(f147,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X4 : list,X5 : nat] : ((((^[Y0 : nat]: (!! @ list @ (^[Y1 : list]: (!! @ nat @ (^[Y2 : nat]: ((listStar @ Y2 @ Y1 @ Y1) => ((listStar @ Y0 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (plus @ Y2 @ Y0) @ (plus @ Y2 @ Y0)) @ (app @ X3 @ (plus @ Y2 @ Y0) @ X1 @ (app @ Y2 @ Y0 @ Y1 @ X4)) @ (app @ (plus @ X3 @ Y2) @ Y0 @ (app @ X3 @ Y2 @ X1 @ Y1) @ X4)) => ((listStar @ (plus @ (suc @ (plus @ Y2 @ Y0)) @ (plus @ Y2 @ Y0)) @ (app @ (suc @ X3) @ (plus @ Y2 @ Y0) @ (cons @ X3 @ X2 @ X1) @ (app @ Y2 @ Y0 @ Y1 @ X4)) @ (cons @ (plus @ X3 @ (plus @ Y2 @ Y0)) @ X2 @ (app @ X3 @ (plus @ Y2 @ Y0) @ X1 @ (app @ Y2 @ Y0 @ Y1 @ X4)))) => (listStar @ (plus @ (suc @ (plus @ Y2 @ Y0)) @ (plus @ Y2 @ Y0)) @ (app @ (suc @ X3) @ (plus @ Y2 @ Y0) @ (cons @ X3 @ X2 @ X1) @ (app @ Y2 @ Y0 @ Y1 @ X4)) @ (cons @ (plus @ (plus @ X3 @ Y2) @ Y0) @ X2 @ (app @ (plus @ X3 @ Y2) @ Y0 @ (app @ X3 @ Y2 @ X1 @ Y1) @ X4))))))))))))) @ X5) = $true)) )),
% 1.81/1.45 inference(pi_clausification,[status(thm)],[f146])).
% 1.81/1.45 thf(f146,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X4 : list] : (((!! @ nat @ (^[Y0 : nat]: (!! @ list @ (^[Y1 : list]: (!! @ nat @ (^[Y2 : nat]: ((listStar @ Y2 @ Y1 @ Y1) => ((listStar @ Y0 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (plus @ Y2 @ Y0) @ (plus @ Y2 @ Y0)) @ (app @ X3 @ (plus @ Y2 @ Y0) @ X1 @ (app @ Y2 @ Y0 @ Y1 @ X4)) @ (app @ (plus @ X3 @ Y2) @ Y0 @ (app @ X3 @ Y2 @ X1 @ Y1) @ X4)) => ((listStar @ (plus @ (suc @ (plus @ Y2 @ Y0)) @ (plus @ Y2 @ Y0)) @ (app @ (suc @ X3) @ (plus @ Y2 @ Y0) @ (cons @ X3 @ X2 @ X1) @ (app @ Y2 @ Y0 @ Y1 @ X4)) @ (cons @ (plus @ X3 @ (plus @ Y2 @ Y0)) @ X2 @ (app @ X3 @ (plus @ Y2 @ Y0) @ X1 @ (app @ Y2 @ Y0 @ Y1 @ X4)))) => (listStar @ (plus @ (suc @ (plus @ Y2 @ Y0)) @ (plus @ Y2 @ Y0)) @ (app @ (suc @ X3) @ (plus @ Y2 @ Y0) @ (cons @ X3 @ X2 @ X1) @ (app @ Y2 @ Y0 @ Y1 @ X4)) @ (cons @ (plus @ (plus @ X3 @ Y2) @ Y0) @ X2 @ (app @ (plus @ X3 @ Y2) @ Y0 @ (app @ X3 @ Y2 @ X1 @ Y1) @ X4)))))))))))))) = $true)) )),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f145])).
% 1.81/1.45 thf(f145,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X4 : list] : ((((^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: (!! @ list @ (^[Y2 : list]: (!! @ nat @ (^[Y3 : nat]: ((listStar @ Y3 @ Y2 @ Y2) => ((listStar @ Y1 @ Y0 @ Y0) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (plus @ Y3 @ Y1) @ (plus @ Y3 @ Y1)) @ (app @ X3 @ (plus @ Y3 @ Y1) @ X1 @ (app @ Y3 @ Y1 @ Y2 @ Y0)) @ (app @ (plus @ X3 @ Y3) @ Y1 @ (app @ X3 @ Y3 @ X1 @ Y2) @ Y0)) => ((listStar @ (plus @ (suc @ (plus @ Y3 @ Y1)) @ (plus @ Y3 @ Y1)) @ (app @ (suc @ X3) @ (plus @ Y3 @ Y1) @ (cons @ X3 @ X2 @ X1) @ (app @ Y3 @ Y1 @ Y2 @ Y0)) @ (cons @ (plus @ X3 @ (plus @ Y3 @ Y1)) @ X2 @ (app @ X3 @ (plus @ Y3 @ Y1) @ X1 @ (app @ Y3 @ Y1 @ Y2 @ Y0)))) => (listStar @ (plus @ (suc @ (plus @ Y3 @ Y1)) @ (plus @ Y3 @ Y1)) @ (app @ (suc @ X3) @ (plus @ Y3 @ Y1) @ (cons @ X3 @ X2 @ X1) @ (app @ Y3 @ Y1 @ Y2 @ Y0)) @ (cons @ (plus @ (plus @ X3 @ Y3) @ Y1) @ X2 @ (app @ (plus @ X3 @ Y3) @ Y1 @ (app @ X3 @ Y3 @ X1 @ Y2) @ Y0))))))))))))))) @ X4) = $true)) )),
% 1.81/1.45 inference(pi_clausification,[status(thm)],[f144])).
% 1.81/1.45 thf(f144,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list] : (((!! @ list @ (^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: (!! @ list @ (^[Y2 : list]: (!! @ nat @ (^[Y3 : nat]: ((listStar @ Y3 @ Y2 @ Y2) => ((listStar @ Y1 @ Y0 @ Y0) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (plus @ Y3 @ Y1) @ (plus @ Y3 @ Y1)) @ (app @ X3 @ (plus @ Y3 @ Y1) @ X1 @ (app @ Y3 @ Y1 @ Y2 @ Y0)) @ (app @ (plus @ X3 @ Y3) @ Y1 @ (app @ X3 @ Y3 @ X1 @ Y2) @ Y0)) => ((listStar @ (plus @ (suc @ (plus @ Y3 @ Y1)) @ (plus @ Y3 @ Y1)) @ (app @ (suc @ X3) @ (plus @ Y3 @ Y1) @ (cons @ X3 @ X2 @ X1) @ (app @ Y3 @ Y1 @ Y2 @ Y0)) @ (cons @ (plus @ X3 @ (plus @ Y3 @ Y1)) @ X2 @ (app @ X3 @ (plus @ Y3 @ Y1) @ X1 @ (app @ Y3 @ Y1 @ Y2 @ Y0)))) => (listStar @ (plus @ (suc @ (plus @ Y3 @ Y1)) @ (plus @ Y3 @ Y1)) @ (app @ (suc @ X3) @ (plus @ Y3 @ Y1) @ (cons @ X3 @ X2 @ X1) @ (app @ Y3 @ Y1 @ Y2 @ Y0)) @ (cons @ (plus @ (plus @ X3 @ Y3) @ Y1) @ X2 @ (app @ (plus @ X3 @ Y3) @ Y1 @ (app @ X3 @ Y3 @ X1 @ Y2) @ Y0)))))))))))))))) = $true)) )),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f143])).
% 1.81/1.45 thf(f143,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list] : ((((^[Y0 : nat]: (!! @ list @ (^[Y1 : list]: (!! @ nat @ (^[Y2 : nat]: (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: ((listStar @ Y4 @ Y3 @ Y3) => ((listStar @ Y2 @ Y1 @ Y1) => ((listStar @ Y0 @ X1 @ X1) => ((listStar @ (plus @ (plus @ Y4 @ Y2) @ (plus @ Y4 @ Y2)) @ (app @ Y0 @ (plus @ Y4 @ Y2) @ X1 @ (app @ Y4 @ Y2 @ Y3 @ Y1)) @ (app @ (plus @ Y0 @ Y4) @ Y2 @ (app @ Y0 @ Y4 @ X1 @ Y3) @ Y1)) => ((listStar @ (plus @ (suc @ (plus @ Y4 @ Y2)) @ (plus @ Y4 @ Y2)) @ (app @ (suc @ Y0) @ (plus @ Y4 @ Y2) @ (cons @ Y0 @ X2 @ X1) @ (app @ Y4 @ Y2 @ Y3 @ Y1)) @ (cons @ (plus @ Y0 @ (plus @ Y4 @ Y2)) @ X2 @ (app @ Y0 @ (plus @ Y4 @ Y2) @ X1 @ (app @ Y4 @ Y2 @ Y3 @ Y1)))) => (listStar @ (plus @ (suc @ (plus @ Y4 @ Y2)) @ (plus @ Y4 @ Y2)) @ (app @ (suc @ Y0) @ (plus @ Y4 @ Y2) @ (cons @ Y0 @ X2 @ X1) @ (app @ Y4 @ Y2 @ Y3 @ Y1)) @ (cons @ (plus @ (plus @ Y0 @ Y4) @ Y2) @ X2 @ (app @ (plus @ Y0 @ Y4) @ Y2 @ (app @ Y0 @ Y4 @ X1 @ Y3) @ Y1))))))))))))))))) @ X3) = $true)) )),
% 1.81/1.45 inference(pi_clausification,[status(thm)],[f142])).
% 1.81/1.45 thf(f142,plain,(
% 1.81/1.45 ( ! [X2 : elem,X1 : list] : (($true = (!! @ nat @ (^[Y0 : nat]: (!! @ list @ (^[Y1 : list]: (!! @ nat @ (^[Y2 : nat]: (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: ((listStar @ Y4 @ Y3 @ Y3) => ((listStar @ Y2 @ Y1 @ Y1) => ((listStar @ Y0 @ X1 @ X1) => ((listStar @ (plus @ (plus @ Y4 @ Y2) @ (plus @ Y4 @ Y2)) @ (app @ Y0 @ (plus @ Y4 @ Y2) @ X1 @ (app @ Y4 @ Y2 @ Y3 @ Y1)) @ (app @ (plus @ Y0 @ Y4) @ Y2 @ (app @ Y0 @ Y4 @ X1 @ Y3) @ Y1)) => ((listStar @ (plus @ (suc @ (plus @ Y4 @ Y2)) @ (plus @ Y4 @ Y2)) @ (app @ (suc @ Y0) @ (plus @ Y4 @ Y2) @ (cons @ Y0 @ X2 @ X1) @ (app @ Y4 @ Y2 @ Y3 @ Y1)) @ (cons @ (plus @ Y0 @ (plus @ Y4 @ Y2)) @ X2 @ (app @ Y0 @ (plus @ Y4 @ Y2) @ X1 @ (app @ Y4 @ Y2 @ Y3 @ Y1)))) => (listStar @ (plus @ (suc @ (plus @ Y4 @ Y2)) @ (plus @ Y4 @ Y2)) @ (app @ (suc @ Y0) @ (plus @ Y4 @ Y2) @ (cons @ Y0 @ X2 @ X1) @ (app @ Y4 @ Y2 @ Y3 @ Y1)) @ (cons @ (plus @ (plus @ Y0 @ Y4) @ Y2) @ X2 @ (app @ (plus @ Y0 @ Y4) @ Y2 @ (app @ Y0 @ Y4 @ X1 @ Y3) @ Y1)))))))))))))))))))) )),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f141])).
% 1.81/1.45 thf(f141,plain,(
% 1.81/1.45 ( ! [X2 : elem,X1 : list] : ((((^[Y0 : elem]: (!! @ nat @ (^[Y1 : nat]: (!! @ list @ (^[Y2 : list]: (!! @ nat @ (^[Y3 : nat]: (!! @ list @ (^[Y4 : list]: (!! @ nat @ (^[Y5 : nat]: ((listStar @ Y5 @ Y4 @ Y4) => ((listStar @ Y3 @ Y2 @ Y2) => ((listStar @ Y1 @ X1 @ X1) => ((listStar @ (plus @ (plus @ Y5 @ Y3) @ (plus @ Y5 @ Y3)) @ (app @ Y1 @ (plus @ Y5 @ Y3) @ X1 @ (app @ Y5 @ Y3 @ Y4 @ Y2)) @ (app @ (plus @ Y1 @ Y5) @ Y3 @ (app @ Y1 @ Y5 @ X1 @ Y4) @ Y2)) => ((listStar @ (plus @ (suc @ (plus @ Y5 @ Y3)) @ (plus @ Y5 @ Y3)) @ (app @ (suc @ Y1) @ (plus @ Y5 @ Y3) @ (cons @ Y1 @ Y0 @ X1) @ (app @ Y5 @ Y3 @ Y4 @ Y2)) @ (cons @ (plus @ Y1 @ (plus @ Y5 @ Y3)) @ Y0 @ (app @ Y1 @ (plus @ Y5 @ Y3) @ X1 @ (app @ Y5 @ Y3 @ Y4 @ Y2)))) => (listStar @ (plus @ (suc @ (plus @ Y5 @ Y3)) @ (plus @ Y5 @ Y3)) @ (app @ (suc @ Y1) @ (plus @ Y5 @ Y3) @ (cons @ Y1 @ Y0 @ X1) @ (app @ Y5 @ Y3 @ Y4 @ Y2)) @ (cons @ (plus @ (plus @ Y1 @ Y5) @ Y3) @ Y0 @ (app @ (plus @ Y1 @ Y5) @ Y3 @ (app @ Y1 @ Y5 @ X1 @ Y4) @ Y2))))))))))))))))))) @ X2) = $true)) )),
% 1.81/1.45 inference(pi_clausification,[status(thm)],[f140])).
% 1.81/1.45 thf(f140,plain,(
% 1.81/1.45 ( ! [X1 : list] : (($true = (!! @ elem @ (^[Y0 : elem]: (!! @ nat @ (^[Y1 : nat]: (!! @ list @ (^[Y2 : list]: (!! @ nat @ (^[Y3 : nat]: (!! @ list @ (^[Y4 : list]: (!! @ nat @ (^[Y5 : nat]: ((listStar @ Y5 @ Y4 @ Y4) => ((listStar @ Y3 @ Y2 @ Y2) => ((listStar @ Y1 @ X1 @ X1) => ((listStar @ (plus @ (plus @ Y5 @ Y3) @ (plus @ Y5 @ Y3)) @ (app @ Y1 @ (plus @ Y5 @ Y3) @ X1 @ (app @ Y5 @ Y3 @ Y4 @ Y2)) @ (app @ (plus @ Y1 @ Y5) @ Y3 @ (app @ Y1 @ Y5 @ X1 @ Y4) @ Y2)) => ((listStar @ (plus @ (suc @ (plus @ Y5 @ Y3)) @ (plus @ Y5 @ Y3)) @ (app @ (suc @ Y1) @ (plus @ Y5 @ Y3) @ (cons @ Y1 @ Y0 @ X1) @ (app @ Y5 @ Y3 @ Y4 @ Y2)) @ (cons @ (plus @ Y1 @ (plus @ Y5 @ Y3)) @ Y0 @ (app @ Y1 @ (plus @ Y5 @ Y3) @ X1 @ (app @ Y5 @ Y3 @ Y4 @ Y2)))) => (listStar @ (plus @ (suc @ (plus @ Y5 @ Y3)) @ (plus @ Y5 @ Y3)) @ (app @ (suc @ Y1) @ (plus @ Y5 @ Y3) @ (cons @ Y1 @ Y0 @ X1) @ (app @ Y5 @ Y3 @ Y4 @ Y2)) @ (cons @ (plus @ (plus @ Y1 @ Y5) @ Y3) @ Y0 @ (app @ (plus @ Y1 @ Y5) @ Y3 @ (app @ Y1 @ Y5 @ X1 @ Y4) @ Y2)))))))))))))))))))))) )),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f139])).
% 1.81/1.45 thf(f139,plain,(
% 1.81/1.45 ( ! [X1 : list] : ((((^[Y0 : list]: (!! @ elem @ (^[Y1 : elem]: (!! @ nat @ (^[Y2 : nat]: (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: (!! @ list @ (^[Y5 : list]: (!! @ nat @ (^[Y6 : nat]: ((listStar @ Y6 @ Y5 @ Y5) => ((listStar @ Y4 @ Y3 @ Y3) => ((listStar @ Y2 @ Y0 @ Y0) => ((listStar @ (plus @ (plus @ Y6 @ Y4) @ (plus @ Y6 @ Y4)) @ (app @ Y2 @ (plus @ Y6 @ Y4) @ Y0 @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (app @ (plus @ Y2 @ Y6) @ Y4 @ (app @ Y2 @ Y6 @ Y0 @ Y5) @ Y3)) => ((listStar @ (plus @ (suc @ (plus @ Y6 @ Y4)) @ (plus @ Y6 @ Y4)) @ (app @ (suc @ Y2) @ (plus @ Y6 @ Y4) @ (cons @ Y2 @ Y1 @ Y0) @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (cons @ (plus @ Y2 @ (plus @ Y6 @ Y4)) @ Y1 @ (app @ Y2 @ (plus @ Y6 @ Y4) @ Y0 @ (app @ Y6 @ Y4 @ Y5 @ Y3)))) => (listStar @ (plus @ (suc @ (plus @ Y6 @ Y4)) @ (plus @ Y6 @ Y4)) @ (app @ (suc @ Y2) @ (plus @ Y6 @ Y4) @ (cons @ Y2 @ Y1 @ Y0) @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (cons @ (plus @ (plus @ Y2 @ Y6) @ Y4) @ Y1 @ (app @ (plus @ Y2 @ Y6) @ Y4 @ (app @ Y2 @ Y6 @ Y0 @ Y5) @ Y3))))))))))))))))))))) @ X1) = $true)) )),
% 1.81/1.45 inference(pi_clausification,[status(thm)],[f53])).
% 1.81/1.45 thf(f53,plain,(
% 1.81/1.45 ($true = (!! @ list @ (^[Y0 : list]: (!! @ elem @ (^[Y1 : elem]: (!! @ nat @ (^[Y2 : nat]: (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: (!! @ list @ (^[Y5 : list]: (!! @ nat @ (^[Y6 : nat]: ((listStar @ Y6 @ Y5 @ Y5) => ((listStar @ Y4 @ Y3 @ Y3) => ((listStar @ Y2 @ Y0 @ Y0) => ((listStar @ (plus @ (plus @ Y6 @ Y4) @ (plus @ Y6 @ Y4)) @ (app @ Y2 @ (plus @ Y6 @ Y4) @ Y0 @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (app @ (plus @ Y2 @ Y6) @ Y4 @ (app @ Y2 @ Y6 @ Y0 @ Y5) @ Y3)) => ((listStar @ (plus @ (suc @ (plus @ Y6 @ Y4)) @ (plus @ Y6 @ Y4)) @ (app @ (suc @ Y2) @ (plus @ Y6 @ Y4) @ (cons @ Y2 @ Y1 @ Y0) @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (cons @ (plus @ Y2 @ (plus @ Y6 @ Y4)) @ Y1 @ (app @ Y2 @ (plus @ Y6 @ Y4) @ Y0 @ (app @ Y6 @ Y4 @ Y5 @ Y3)))) => (listStar @ (plus @ (suc @ (plus @ Y6 @ Y4)) @ (plus @ Y6 @ Y4)) @ (app @ (suc @ Y2) @ (plus @ Y6 @ Y4) @ (cons @ Y2 @ Y1 @ Y0) @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (cons @ (plus @ (plus @ Y2 @ Y6) @ Y4) @ Y1 @ (app @ (plus @ Y2 @ Y6) @ Y4 @ (app @ Y2 @ Y6 @ Y0 @ Y5) @ Y3)))))))))))))))))))))))),
% 1.81/1.45 inference(cnf_transformation,[status(thm)],[f38])).
% 1.81/1.45 thf(f38,plain,(
% 1.81/1.45 ($true = (!! @ list @ (^[Y0 : list]: (!! @ elem @ (^[Y1 : elem]: (!! @ nat @ (^[Y2 : nat]: (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: (!! @ list @ (^[Y5 : list]: (!! @ nat @ (^[Y6 : nat]: ((listStar @ Y6 @ Y5 @ Y5) => ((listStar @ Y4 @ Y3 @ Y3) => ((listStar @ Y2 @ Y0 @ Y0) => ((listStar @ (plus @ (plus @ Y6 @ Y4) @ (plus @ Y6 @ Y4)) @ (app @ Y2 @ (plus @ Y6 @ Y4) @ Y0 @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (app @ (plus @ Y2 @ Y6) @ Y4 @ (app @ Y2 @ Y6 @ Y0 @ Y5) @ Y3)) => ((listStar @ (plus @ (suc @ (plus @ Y6 @ Y4)) @ (plus @ Y6 @ Y4)) @ (app @ (suc @ Y2) @ (plus @ Y6 @ Y4) @ (cons @ Y2 @ Y1 @ Y0) @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (cons @ (plus @ Y2 @ (plus @ Y6 @ Y4)) @ Y1 @ (app @ Y2 @ (plus @ Y6 @ Y4) @ Y0 @ (app @ Y6 @ Y4 @ Y5 @ Y3)))) => (listStar @ (plus @ (suc @ (plus @ Y6 @ Y4)) @ (plus @ Y6 @ Y4)) @ (app @ (suc @ Y2) @ (plus @ Y6 @ Y4) @ (cons @ Y2 @ Y1 @ Y0) @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (cons @ (plus @ (plus @ Y2 @ Y6) @ Y4) @ Y1 @ (app @ (plus @ Y2 @ Y6) @ Y4 @ (app @ Y2 @ Y6 @ Y0 @ Y5) @ Y3)))))))))))))))))))))))),
% 1.81/1.45 inference(fool_elimination,[status(thm)],[f37])).
% 1.81/1.45 thf(f37,plain,(
% 1.81/1.45 ! [X0 : nat,X1 : list,X2 : nat,X3 : list,X4 : nat,X5 : elem,X6 : list] : ((listStar @ X0 @ X1 @ X1) => ((listStar @ X2 @ X3 @ X3) => ((listStar @ X4 @ X6 @ X6) => ((listStar @ (plus @ (plus @ X0 @ X2) @ (plus @ X0 @ X2)) @ (app @ X4 @ (plus @ X0 @ X2) @ X6 @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ X4 @ X0) @ X2 @ (app @ X4 @ X0 @ X6 @ X1) @ X3)) => ((listStar @ (plus @ (suc @ (plus @ X0 @ X2)) @ (plus @ X0 @ X2)) @ (app @ (suc @ X4) @ (plus @ X0 @ X2) @ (cons @ X4 @ X5 @ X6) @ (app @ X0 @ X2 @ X1 @ X3)) @ (cons @ (plus @ X4 @ (plus @ X0 @ X2)) @ X5 @ (app @ X4 @ (plus @ X0 @ X2) @ X6 @ (app @ X0 @ X2 @ X1 @ X3)))) => (listStar @ (plus @ (suc @ (plus @ X0 @ X2)) @ (plus @ X0 @ X2)) @ (app @ (suc @ X4) @ (plus @ X0 @ X2) @ (cons @ X4 @ X5 @ X6) @ (app @ X0 @ X2 @ X1 @ X3)) @ (cons @ (plus @ (plus @ X4 @ X0) @ X2) @ X5 @ (app @ (plus @ X4 @ X0) @ X2 @ (app @ X4 @ X0 @ X6 @ X1) @ X3))))))))),
% 1.81/1.45 inference(rectify,[status(thm)],[f14])).
% 1.81/1.45 thf(f14,axiom,(
% 1.81/1.45 ! [X13 : nat,X16 : list,X14 : nat,X17 : list,X10 : nat,X2 : elem,X18 : list] : ((listStar @ X13 @ X16 @ X16) => ((listStar @ X14 @ X17 @ X17) => ((listStar @ X10 @ X18 @ X18) => ((listStar @ (plus @ (plus @ X13 @ X14) @ (plus @ X13 @ X14)) @ (app @ X10 @ (plus @ X13 @ X14) @ X18 @ (app @ X13 @ X14 @ X16 @ X17)) @ (app @ (plus @ X10 @ X13) @ X14 @ (app @ X10 @ X13 @ X18 @ X16) @ X17)) => ((listStar @ (plus @ (suc @ (plus @ X13 @ X14)) @ (plus @ X13 @ X14)) @ (app @ (suc @ X10) @ (plus @ X13 @ X14) @ (cons @ X10 @ X2 @ X18) @ (app @ X13 @ X14 @ X16 @ X17)) @ (cons @ (plus @ X10 @ (plus @ X13 @ X14)) @ X2 @ (app @ X10 @ (plus @ X13 @ X14) @ X18 @ (app @ X13 @ X14 @ X16 @ X17)))) => (listStar @ (plus @ (suc @ (plus @ X13 @ X14)) @ (plus @ X13 @ X14)) @ (app @ (suc @ X10) @ (plus @ X13 @ X14) @ (cons @ X10 @ X2 @ X18) @ (app @ X13 @ X14 @ X16 @ X17)) @ (cons @ (plus @ (plus @ X10 @ X13) @ X14) @ X2 @ (app @ (plus @ X10 @ X13) @ X14 @ (app @ X10 @ X13 @ X18 @ X16) @ X17))))))))),
% 1.81/1.45 file('/export/starexec/sandbox2/tmp/tmp.PLL0ptdnA4/DTF2THF_4359.p',list_app_assoc_indstep3)).
% 1.81/1.45 thf(f188,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X7 : nat,X4 : list,X5 : nat] : (($true = (listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (cons @ (plus @ X3 @ (plus @ X7 @ X5)) @ X2 @ (app @ X3 @ (plus @ X7 @ X5) @ X1 @ (app @ X7 @ X5 @ X6 @ X4))))) | ($false = (listStar @ X3 @ X1 @ X1)) | ($false = (listStar @ X7 @ X6 @ X6)) | ($false = (listStar @ X5 @ X4 @ X4))) )),
% 1.81/1.45 inference(binary_proxy_clausification,[status(thm)],[f187])).
% 1.81/1.45 thf(f187,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X7 : nat,X4 : list,X5 : nat] : (($false = (listStar @ X7 @ X6 @ X6)) | (((listStar @ X3 @ X1 @ X1) => (listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (cons @ (plus @ X3 @ (plus @ X7 @ X5)) @ X2 @ (app @ X3 @ (plus @ X7 @ X5) @ X1 @ (app @ X7 @ X5 @ X6 @ X4))))) = $true) | ($false = (listStar @ X5 @ X4 @ X4))) )),
% 1.81/1.45 inference(binary_proxy_clausification,[status(thm)],[f186])).
% 1.81/1.45 thf(f186,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X7 : nat,X4 : list,X5 : nat] : (($false = (listStar @ X7 @ X6 @ X6)) | (((listStar @ X5 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => (listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (cons @ (plus @ X3 @ (plus @ X7 @ X5)) @ X2 @ (app @ X3 @ (plus @ X7 @ X5) @ X1 @ (app @ X7 @ X5 @ X6 @ X4)))))) = $true)) )),
% 1.81/1.45 inference(binary_proxy_clausification,[status(thm)],[f185])).
% 1.81/1.45 thf(f185,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X7 : nat,X4 : list,X5 : nat] : ((((listStar @ X7 @ X6 @ X6) => ((listStar @ X5 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => (listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (cons @ (plus @ X3 @ (plus @ X7 @ X5)) @ X2 @ (app @ X3 @ (plus @ X7 @ X5) @ X1 @ (app @ X7 @ X5 @ X6 @ X4))))))) = $true)) )),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f184])).
% 1.81/1.45 thf(f184,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X7 : nat,X4 : list,X5 : nat] : (($true = ((^[Y0 : nat]: ((listStar @ Y0 @ X6 @ X6) => ((listStar @ X5 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => (listStar @ (plus @ (suc @ (plus @ Y0 @ X5)) @ (plus @ Y0 @ X5)) @ (app @ (suc @ X3) @ (plus @ Y0 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ Y0 @ X5 @ X6 @ X4)) @ (cons @ (plus @ X3 @ (plus @ Y0 @ X5)) @ X2 @ (app @ X3 @ (plus @ Y0 @ X5) @ X1 @ (app @ Y0 @ X5 @ X6 @ X4)))))))) @ X7))) )),
% 1.81/1.45 inference(pi_clausification,[status(thm)],[f183])).
% 1.81/1.45 thf(f183,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X4 : list,X5 : nat] : (($true = (!! @ nat @ (^[Y0 : nat]: ((listStar @ Y0 @ X6 @ X6) => ((listStar @ X5 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => (listStar @ (plus @ (suc @ (plus @ Y0 @ X5)) @ (plus @ Y0 @ X5)) @ (app @ (suc @ X3) @ (plus @ Y0 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ Y0 @ X5 @ X6 @ X4)) @ (cons @ (plus @ X3 @ (plus @ Y0 @ X5)) @ X2 @ (app @ X3 @ (plus @ Y0 @ X5) @ X1 @ (app @ Y0 @ X5 @ X6 @ X4))))))))))) )),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f182])).
% 1.81/1.45 thf(f182,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X4 : list,X5 : nat] : ((((^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ Y1 @ Y0 @ Y0) => ((listStar @ X5 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => (listStar @ (plus @ (suc @ (plus @ Y1 @ X5)) @ (plus @ Y1 @ X5)) @ (app @ (suc @ X3) @ (plus @ Y1 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ Y1 @ X5 @ Y0 @ X4)) @ (cons @ (plus @ X3 @ (plus @ Y1 @ X5)) @ X2 @ (app @ X3 @ (plus @ Y1 @ X5) @ X1 @ (app @ Y1 @ X5 @ Y0 @ X4)))))))))) @ X6) = $true)) )),
% 1.81/1.45 inference(pi_clausification,[status(thm)],[f181])).
% 1.81/1.45 thf(f181,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X4 : list,X5 : nat] : (((!! @ list @ (^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ Y1 @ Y0 @ Y0) => ((listStar @ X5 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => (listStar @ (plus @ (suc @ (plus @ Y1 @ X5)) @ (plus @ Y1 @ X5)) @ (app @ (suc @ X3) @ (plus @ Y1 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ Y1 @ X5 @ Y0 @ X4)) @ (cons @ (plus @ X3 @ (plus @ Y1 @ X5)) @ X2 @ (app @ X3 @ (plus @ Y1 @ X5) @ X1 @ (app @ Y1 @ X5 @ Y0 @ X4))))))))))) = $true)) )),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f180])).
% 1.81/1.45 thf(f180,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X4 : list,X5 : nat] : ((((^[Y0 : nat]: (!! @ list @ (^[Y1 : list]: (!! @ nat @ (^[Y2 : nat]: ((listStar @ Y2 @ Y1 @ Y1) => ((listStar @ Y0 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => (listStar @ (plus @ (suc @ (plus @ Y2 @ Y0)) @ (plus @ Y2 @ Y0)) @ (app @ (suc @ X3) @ (plus @ Y2 @ Y0) @ (cons @ X3 @ X2 @ X1) @ (app @ Y2 @ Y0 @ Y1 @ X4)) @ (cons @ (plus @ X3 @ (plus @ Y2 @ Y0)) @ X2 @ (app @ X3 @ (plus @ Y2 @ Y0) @ X1 @ (app @ Y2 @ Y0 @ Y1 @ X4)))))))))))) @ X5) = $true)) )),
% 1.81/1.45 inference(pi_clausification,[status(thm)],[f179])).
% 1.81/1.45 thf(f179,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X4 : list] : (((!! @ nat @ (^[Y0 : nat]: (!! @ list @ (^[Y1 : list]: (!! @ nat @ (^[Y2 : nat]: ((listStar @ Y2 @ Y1 @ Y1) => ((listStar @ Y0 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => (listStar @ (plus @ (suc @ (plus @ Y2 @ Y0)) @ (plus @ Y2 @ Y0)) @ (app @ (suc @ X3) @ (plus @ Y2 @ Y0) @ (cons @ X3 @ X2 @ X1) @ (app @ Y2 @ Y0 @ Y1 @ X4)) @ (cons @ (plus @ X3 @ (plus @ Y2 @ Y0)) @ X2 @ (app @ X3 @ (plus @ Y2 @ Y0) @ X1 @ (app @ Y2 @ Y0 @ Y1 @ X4))))))))))))) = $true)) )),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f178])).
% 1.81/1.45 thf(f178,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X4 : list] : ((((^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: (!! @ list @ (^[Y2 : list]: (!! @ nat @ (^[Y3 : nat]: ((listStar @ Y3 @ Y2 @ Y2) => ((listStar @ Y1 @ Y0 @ Y0) => ((listStar @ X3 @ X1 @ X1) => (listStar @ (plus @ (suc @ (plus @ Y3 @ Y1)) @ (plus @ Y3 @ Y1)) @ (app @ (suc @ X3) @ (plus @ Y3 @ Y1) @ (cons @ X3 @ X2 @ X1) @ (app @ Y3 @ Y1 @ Y2 @ Y0)) @ (cons @ (plus @ X3 @ (plus @ Y3 @ Y1)) @ X2 @ (app @ X3 @ (plus @ Y3 @ Y1) @ X1 @ (app @ Y3 @ Y1 @ Y2 @ Y0)))))))))))))) @ X4) = $true)) )),
% 1.81/1.45 inference(pi_clausification,[status(thm)],[f177])).
% 1.81/1.45 thf(f177,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list] : (($true = (!! @ list @ (^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: (!! @ list @ (^[Y2 : list]: (!! @ nat @ (^[Y3 : nat]: ((listStar @ Y3 @ Y2 @ Y2) => ((listStar @ Y1 @ Y0 @ Y0) => ((listStar @ X3 @ X1 @ X1) => (listStar @ (plus @ (suc @ (plus @ Y3 @ Y1)) @ (plus @ Y3 @ Y1)) @ (app @ (suc @ X3) @ (plus @ Y3 @ Y1) @ (cons @ X3 @ X2 @ X1) @ (app @ Y3 @ Y1 @ Y2 @ Y0)) @ (cons @ (plus @ X3 @ (plus @ Y3 @ Y1)) @ X2 @ (app @ X3 @ (plus @ Y3 @ Y1) @ X1 @ (app @ Y3 @ Y1 @ Y2 @ Y0))))))))))))))))) )),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f176])).
% 1.81/1.45 thf(f176,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list] : (($true = ((^[Y0 : nat]: (!! @ list @ (^[Y1 : list]: (!! @ nat @ (^[Y2 : nat]: (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: ((listStar @ Y4 @ Y3 @ Y3) => ((listStar @ Y2 @ Y1 @ Y1) => ((listStar @ Y0 @ X1 @ X1) => (listStar @ (plus @ (suc @ (plus @ Y4 @ Y2)) @ (plus @ Y4 @ Y2)) @ (app @ (suc @ Y0) @ (plus @ Y4 @ Y2) @ (cons @ Y0 @ X2 @ X1) @ (app @ Y4 @ Y2 @ Y3 @ Y1)) @ (cons @ (plus @ Y0 @ (plus @ Y4 @ Y2)) @ X2 @ (app @ Y0 @ (plus @ Y4 @ Y2) @ X1 @ (app @ Y4 @ Y2 @ Y3 @ Y1)))))))))))))))) @ X3))) )),
% 1.81/1.45 inference(pi_clausification,[status(thm)],[f175])).
% 1.81/1.45 thf(f175,plain,(
% 1.81/1.45 ( ! [X2 : elem,X1 : list] : (($true = (!! @ nat @ (^[Y0 : nat]: (!! @ list @ (^[Y1 : list]: (!! @ nat @ (^[Y2 : nat]: (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: ((listStar @ Y4 @ Y3 @ Y3) => ((listStar @ Y2 @ Y1 @ Y1) => ((listStar @ Y0 @ X1 @ X1) => (listStar @ (plus @ (suc @ (plus @ Y4 @ Y2)) @ (plus @ Y4 @ Y2)) @ (app @ (suc @ Y0) @ (plus @ Y4 @ Y2) @ (cons @ Y0 @ X2 @ X1) @ (app @ Y4 @ Y2 @ Y3 @ Y1)) @ (cons @ (plus @ Y0 @ (plus @ Y4 @ Y2)) @ X2 @ (app @ Y0 @ (plus @ Y4 @ Y2) @ X1 @ (app @ Y4 @ Y2 @ Y3 @ Y1))))))))))))))))))) )),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f174])).
% 1.81/1.45 thf(f174,plain,(
% 1.81/1.45 ( ! [X2 : elem,X1 : list] : (($true = ((^[Y0 : elem]: (!! @ nat @ (^[Y1 : nat]: (!! @ list @ (^[Y2 : list]: (!! @ nat @ (^[Y3 : nat]: (!! @ list @ (^[Y4 : list]: (!! @ nat @ (^[Y5 : nat]: ((listStar @ Y5 @ Y4 @ Y4) => ((listStar @ Y3 @ Y2 @ Y2) => ((listStar @ Y1 @ X1 @ X1) => (listStar @ (plus @ (suc @ (plus @ Y5 @ Y3)) @ (plus @ Y5 @ Y3)) @ (app @ (suc @ Y1) @ (plus @ Y5 @ Y3) @ (cons @ Y1 @ Y0 @ X1) @ (app @ Y5 @ Y3 @ Y4 @ Y2)) @ (cons @ (plus @ Y1 @ (plus @ Y5 @ Y3)) @ Y0 @ (app @ Y1 @ (plus @ Y5 @ Y3) @ X1 @ (app @ Y5 @ Y3 @ Y4 @ Y2)))))))))))))))))) @ X2))) )),
% 1.81/1.45 inference(pi_clausification,[status(thm)],[f173])).
% 1.81/1.45 thf(f173,plain,(
% 1.81/1.45 ( ! [X1 : list] : (($true = (!! @ elem @ (^[Y0 : elem]: (!! @ nat @ (^[Y1 : nat]: (!! @ list @ (^[Y2 : list]: (!! @ nat @ (^[Y3 : nat]: (!! @ list @ (^[Y4 : list]: (!! @ nat @ (^[Y5 : nat]: ((listStar @ Y5 @ Y4 @ Y4) => ((listStar @ Y3 @ Y2 @ Y2) => ((listStar @ Y1 @ X1 @ X1) => (listStar @ (plus @ (suc @ (plus @ Y5 @ Y3)) @ (plus @ Y5 @ Y3)) @ (app @ (suc @ Y1) @ (plus @ Y5 @ Y3) @ (cons @ Y1 @ Y0 @ X1) @ (app @ Y5 @ Y3 @ Y4 @ Y2)) @ (cons @ (plus @ Y1 @ (plus @ Y5 @ Y3)) @ Y0 @ (app @ Y1 @ (plus @ Y5 @ Y3) @ X1 @ (app @ Y5 @ Y3 @ Y4 @ Y2))))))))))))))))))))) )),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f172])).
% 1.81/1.45 thf(f172,plain,(
% 1.81/1.45 ( ! [X1 : list] : (($true = ((^[Y0 : list]: (!! @ elem @ (^[Y1 : elem]: (!! @ nat @ (^[Y2 : nat]: (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: (!! @ list @ (^[Y5 : list]: (!! @ nat @ (^[Y6 : nat]: ((listStar @ Y6 @ Y5 @ Y5) => ((listStar @ Y4 @ Y3 @ Y3) => ((listStar @ Y2 @ Y0 @ Y0) => (listStar @ (plus @ (suc @ (plus @ Y6 @ Y4)) @ (plus @ Y6 @ Y4)) @ (app @ (suc @ Y2) @ (plus @ Y6 @ Y4) @ (cons @ Y2 @ Y1 @ Y0) @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (cons @ (plus @ Y2 @ (plus @ Y6 @ Y4)) @ Y1 @ (app @ Y2 @ (plus @ Y6 @ Y4) @ Y0 @ (app @ Y6 @ Y4 @ Y5 @ Y3)))))))))))))))))))) @ X1))) )),
% 1.81/1.45 inference(pi_clausification,[status(thm)],[f54])).
% 1.81/1.45 thf(f54,plain,(
% 1.81/1.45 ((!! @ list @ (^[Y0 : list]: (!! @ elem @ (^[Y1 : elem]: (!! @ nat @ (^[Y2 : nat]: (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: (!! @ list @ (^[Y5 : list]: (!! @ nat @ (^[Y6 : nat]: ((listStar @ Y6 @ Y5 @ Y5) => ((listStar @ Y4 @ Y3 @ Y3) => ((listStar @ Y2 @ Y0 @ Y0) => (listStar @ (plus @ (suc @ (plus @ Y6 @ Y4)) @ (plus @ Y6 @ Y4)) @ (app @ (suc @ Y2) @ (plus @ Y6 @ Y4) @ (cons @ Y2 @ Y1 @ Y0) @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (cons @ (plus @ Y2 @ (plus @ Y6 @ Y4)) @ Y1 @ (app @ Y2 @ (plus @ Y6 @ Y4) @ Y0 @ (app @ Y6 @ Y4 @ Y5 @ Y3))))))))))))))))))))) = $true)),
% 1.81/1.45 inference(cnf_transformation,[status(thm)],[f30])).
% 1.81/1.45 thf(f30,plain,(
% 1.81/1.45 ((!! @ list @ (^[Y0 : list]: (!! @ elem @ (^[Y1 : elem]: (!! @ nat @ (^[Y2 : nat]: (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: (!! @ list @ (^[Y5 : list]: (!! @ nat @ (^[Y6 : nat]: ((listStar @ Y6 @ Y5 @ Y5) => ((listStar @ Y4 @ Y3 @ Y3) => ((listStar @ Y2 @ Y0 @ Y0) => (listStar @ (plus @ (suc @ (plus @ Y6 @ Y4)) @ (plus @ Y6 @ Y4)) @ (app @ (suc @ Y2) @ (plus @ Y6 @ Y4) @ (cons @ Y2 @ Y1 @ Y0) @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (cons @ (plus @ Y2 @ (plus @ Y6 @ Y4)) @ Y1 @ (app @ Y2 @ (plus @ Y6 @ Y4) @ Y0 @ (app @ Y6 @ Y4 @ Y5 @ Y3))))))))))))))))))))) = $true)),
% 1.81/1.45 inference(fool_elimination,[status(thm)],[f29])).
% 1.81/1.45 thf(f29,plain,(
% 1.81/1.45 ! [X0 : nat,X1 : list,X2 : nat,X3 : list,X4 : nat,X5 : elem,X6 : list] : ((listStar @ X0 @ X1 @ X1) => ((listStar @ X2 @ X3 @ X3) => ((listStar @ X4 @ X6 @ X6) => (listStar @ (plus @ (suc @ (plus @ X0 @ X2)) @ (plus @ X0 @ X2)) @ (app @ (suc @ X4) @ (plus @ X0 @ X2) @ (cons @ X4 @ X5 @ X6) @ (app @ X0 @ X2 @ X1 @ X3)) @ (cons @ (plus @ X4 @ (plus @ X0 @ X2)) @ X5 @ (app @ X4 @ (plus @ X0 @ X2) @ X6 @ (app @ X0 @ X2 @ X1 @ X3)))))))),
% 1.81/1.45 inference(rectify,[status(thm)],[f15])).
% 1.81/1.45 thf(f15,axiom,(
% 1.81/1.45 ! [X13 : nat,X16 : list,X14 : nat,X17 : list,X10 : nat,X2 : elem,X18 : list] : ((listStar @ X13 @ X16 @ X16) => ((listStar @ X14 @ X17 @ X17) => ((listStar @ X10 @ X18 @ X18) => (listStar @ (plus @ (suc @ (plus @ X13 @ X14)) @ (plus @ X13 @ X14)) @ (app @ (suc @ X10) @ (plus @ X13 @ X14) @ (cons @ X10 @ X2 @ X18) @ (app @ X13 @ X14 @ X16 @ X17)) @ (cons @ (plus @ X10 @ (plus @ X13 @ X14)) @ X2 @ (app @ X10 @ (plus @ X13 @ X14) @ X18 @ (app @ X13 @ X14 @ X16 @ X17)))))))),
% 1.81/1.45 file('/export/starexec/sandbox2/tmp/tmp.PLL0ptdnA4/DTF2THF_4359.p',list_app_assoc_indstep4)).
% 1.81/1.45 thf(f103,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X7 : nat,X4 : list,X5 : nat] : (($false = (listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (cons @ (plus @ (plus @ X3 @ X7) @ X5) @ X2 @ (app @ (plus @ X3 @ X7) @ X5 @ (app @ X3 @ X7 @ X1 @ X6) @ X4)))) | ($false = (listStar @ X7 @ X6 @ X6)) | ($false = (listStar @ X3 @ X1 @ X1)) | ($false = (listStar @ X5 @ X4 @ X4)) | ((listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (app @ (suc @ (plus @ X3 @ X7)) @ X5 @ (cons @ (plus @ X3 @ X7) @ X2 @ (app @ X3 @ X7 @ X1 @ X6)) @ X4)) = $true)) )),
% 1.81/1.45 inference(binary_proxy_clausification,[status(thm)],[f102])).
% 1.81/1.45 thf(f102,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X7 : nat,X4 : list,X5 : nat] : (($false = (listStar @ X7 @ X6 @ X6)) | ($false = (listStar @ X3 @ X1 @ X1)) | ($true = ((listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (cons @ (plus @ (plus @ X3 @ X7) @ X5) @ X2 @ (app @ (plus @ X3 @ X7) @ X5 @ (app @ X3 @ X7 @ X1 @ X6) @ X4))) => (listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (app @ (suc @ (plus @ X3 @ X7)) @ X5 @ (cons @ (plus @ X3 @ X7) @ X2 @ (app @ X3 @ X7 @ X1 @ X6)) @ X4)))) | ($false = (listStar @ X5 @ X4 @ X4))) )),
% 1.81/1.45 inference(binary_proxy_clausification,[status(thm)],[f101])).
% 1.81/1.45 thf(f101,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X7 : nat,X4 : list,X5 : nat] : (($false = (listStar @ X7 @ X6 @ X6)) | ($false = (listStar @ X5 @ X4 @ X4)) | (((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (cons @ (plus @ (plus @ X3 @ X7) @ X5) @ X2 @ (app @ (plus @ X3 @ X7) @ X5 @ (app @ X3 @ X7 @ X1 @ X6) @ X4))) => (listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (app @ (suc @ (plus @ X3 @ X7)) @ X5 @ (cons @ (plus @ X3 @ X7) @ X2 @ (app @ X3 @ X7 @ X1 @ X6)) @ X4)))) = $true)) )),
% 1.81/1.45 inference(binary_proxy_clausification,[status(thm)],[f100])).
% 1.81/1.45 thf(f100,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X7 : nat,X4 : list,X5 : nat] : (($false = (listStar @ X7 @ X6 @ X6)) | (((listStar @ X5 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (cons @ (plus @ (plus @ X3 @ X7) @ X5) @ X2 @ (app @ (plus @ X3 @ X7) @ X5 @ (app @ X3 @ X7 @ X1 @ X6) @ X4))) => (listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (app @ (suc @ (plus @ X3 @ X7)) @ X5 @ (cons @ (plus @ X3 @ X7) @ X2 @ (app @ X3 @ X7 @ X1 @ X6)) @ X4))))) = $true)) )),
% 1.81/1.45 inference(binary_proxy_clausification,[status(thm)],[f99])).
% 1.81/1.45 thf(f99,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X7 : nat,X4 : list,X5 : nat] : ((((listStar @ X7 @ X6 @ X6) => ((listStar @ X5 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (cons @ (plus @ (plus @ X3 @ X7) @ X5) @ X2 @ (app @ (plus @ X3 @ X7) @ X5 @ (app @ X3 @ X7 @ X1 @ X6) @ X4))) => (listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (app @ (suc @ (plus @ X3 @ X7)) @ X5 @ (cons @ (plus @ X3 @ X7) @ X2 @ (app @ X3 @ X7 @ X1 @ X6)) @ X4)))))) = $true)) )),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f98])).
% 1.81/1.45 thf(f98,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X7 : nat,X4 : list,X5 : nat] : ((((^[Y0 : nat]: ((listStar @ Y0 @ X6 @ X6) => ((listStar @ X5 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ Y0 @ X5)) @ (plus @ Y0 @ X5)) @ (app @ (suc @ X3) @ (plus @ Y0 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ Y0 @ X5 @ X6 @ X4)) @ (cons @ (plus @ (plus @ X3 @ Y0) @ X5) @ X2 @ (app @ (plus @ X3 @ Y0) @ X5 @ (app @ X3 @ Y0 @ X1 @ X6) @ X4))) => (listStar @ (plus @ (suc @ (plus @ Y0 @ X5)) @ (plus @ Y0 @ X5)) @ (app @ (suc @ X3) @ (plus @ Y0 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ Y0 @ X5 @ X6 @ X4)) @ (app @ (suc @ (plus @ X3 @ Y0)) @ X5 @ (cons @ (plus @ X3 @ Y0) @ X2 @ (app @ X3 @ Y0 @ X1 @ X6)) @ X4))))))) @ X7) = $true)) )),
% 1.81/1.45 inference(pi_clausification,[status(thm)],[f97])).
% 1.81/1.45 thf(f97,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X4 : list,X5 : nat] : (((!! @ nat @ (^[Y0 : nat]: ((listStar @ Y0 @ X6 @ X6) => ((listStar @ X5 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ Y0 @ X5)) @ (plus @ Y0 @ X5)) @ (app @ (suc @ X3) @ (plus @ Y0 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ Y0 @ X5 @ X6 @ X4)) @ (cons @ (plus @ (plus @ X3 @ Y0) @ X5) @ X2 @ (app @ (plus @ X3 @ Y0) @ X5 @ (app @ X3 @ Y0 @ X1 @ X6) @ X4))) => (listStar @ (plus @ (suc @ (plus @ Y0 @ X5)) @ (plus @ Y0 @ X5)) @ (app @ (suc @ X3) @ (plus @ Y0 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ Y0 @ X5 @ X6 @ X4)) @ (app @ (suc @ (plus @ X3 @ Y0)) @ X5 @ (cons @ (plus @ X3 @ Y0) @ X2 @ (app @ X3 @ Y0 @ X1 @ X6)) @ X4)))))))) = $true)) )),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f96])).
% 1.81/1.45 thf(f96,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X4 : list,X5 : nat] : ((((^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ Y1 @ Y0 @ Y0) => ((listStar @ X5 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ Y1 @ X5)) @ (plus @ Y1 @ X5)) @ (app @ (suc @ X3) @ (plus @ Y1 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ Y1 @ X5 @ Y0 @ X4)) @ (cons @ (plus @ (plus @ X3 @ Y1) @ X5) @ X2 @ (app @ (plus @ X3 @ Y1) @ X5 @ (app @ X3 @ Y1 @ X1 @ Y0) @ X4))) => (listStar @ (plus @ (suc @ (plus @ Y1 @ X5)) @ (plus @ Y1 @ X5)) @ (app @ (suc @ X3) @ (plus @ Y1 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ Y1 @ X5 @ Y0 @ X4)) @ (app @ (suc @ (plus @ X3 @ Y1)) @ X5 @ (cons @ (plus @ X3 @ Y1) @ X2 @ (app @ X3 @ Y1 @ X1 @ Y0)) @ X4))))))))) @ X6) = $true)) )),
% 1.81/1.45 inference(pi_clausification,[status(thm)],[f95])).
% 1.81/1.45 thf(f95,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X4 : list,X5 : nat] : (((!! @ list @ (^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ Y1 @ Y0 @ Y0) => ((listStar @ X5 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ Y1 @ X5)) @ (plus @ Y1 @ X5)) @ (app @ (suc @ X3) @ (plus @ Y1 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ Y1 @ X5 @ Y0 @ X4)) @ (cons @ (plus @ (plus @ X3 @ Y1) @ X5) @ X2 @ (app @ (plus @ X3 @ Y1) @ X5 @ (app @ X3 @ Y1 @ X1 @ Y0) @ X4))) => (listStar @ (plus @ (suc @ (plus @ Y1 @ X5)) @ (plus @ Y1 @ X5)) @ (app @ (suc @ X3) @ (plus @ Y1 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ Y1 @ X5 @ Y0 @ X4)) @ (app @ (suc @ (plus @ X3 @ Y1)) @ X5 @ (cons @ (plus @ X3 @ Y1) @ X2 @ (app @ X3 @ Y1 @ X1 @ Y0)) @ X4)))))))))) = $true)) )),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f94])).
% 1.81/1.45 thf(f94,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X4 : list,X5 : nat] : ((((^[Y0 : nat]: (!! @ list @ (^[Y1 : list]: (!! @ nat @ (^[Y2 : nat]: ((listStar @ Y2 @ Y1 @ Y1) => ((listStar @ Y0 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ Y2 @ Y0)) @ (plus @ Y2 @ Y0)) @ (app @ (suc @ X3) @ (plus @ Y2 @ Y0) @ (cons @ X3 @ X2 @ X1) @ (app @ Y2 @ Y0 @ Y1 @ X4)) @ (cons @ (plus @ (plus @ X3 @ Y2) @ Y0) @ X2 @ (app @ (plus @ X3 @ Y2) @ Y0 @ (app @ X3 @ Y2 @ X1 @ Y1) @ X4))) => (listStar @ (plus @ (suc @ (plus @ Y2 @ Y0)) @ (plus @ Y2 @ Y0)) @ (app @ (suc @ X3) @ (plus @ Y2 @ Y0) @ (cons @ X3 @ X2 @ X1) @ (app @ Y2 @ Y0 @ Y1 @ X4)) @ (app @ (suc @ (plus @ X3 @ Y2)) @ Y0 @ (cons @ (plus @ X3 @ Y2) @ X2 @ (app @ X3 @ Y2 @ X1 @ Y1)) @ X4))))))))))) @ X5) = $true)) )),
% 1.81/1.45 inference(pi_clausification,[status(thm)],[f93])).
% 1.81/1.45 thf(f93,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X4 : list] : (((!! @ nat @ (^[Y0 : nat]: (!! @ list @ (^[Y1 : list]: (!! @ nat @ (^[Y2 : nat]: ((listStar @ Y2 @ Y1 @ Y1) => ((listStar @ Y0 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ Y2 @ Y0)) @ (plus @ Y2 @ Y0)) @ (app @ (suc @ X3) @ (plus @ Y2 @ Y0) @ (cons @ X3 @ X2 @ X1) @ (app @ Y2 @ Y0 @ Y1 @ X4)) @ (cons @ (plus @ (plus @ X3 @ Y2) @ Y0) @ X2 @ (app @ (plus @ X3 @ Y2) @ Y0 @ (app @ X3 @ Y2 @ X1 @ Y1) @ X4))) => (listStar @ (plus @ (suc @ (plus @ Y2 @ Y0)) @ (plus @ Y2 @ Y0)) @ (app @ (suc @ X3) @ (plus @ Y2 @ Y0) @ (cons @ X3 @ X2 @ X1) @ (app @ Y2 @ Y0 @ Y1 @ X4)) @ (app @ (suc @ (plus @ X3 @ Y2)) @ Y0 @ (cons @ (plus @ X3 @ Y2) @ X2 @ (app @ X3 @ Y2 @ X1 @ Y1)) @ X4)))))))))))) = $true)) )),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f92])).
% 1.81/1.45 thf(f92,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X4 : list] : ((((^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: (!! @ list @ (^[Y2 : list]: (!! @ nat @ (^[Y3 : nat]: ((listStar @ Y3 @ Y2 @ Y2) => ((listStar @ Y1 @ Y0 @ Y0) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ Y3 @ Y1)) @ (plus @ Y3 @ Y1)) @ (app @ (suc @ X3) @ (plus @ Y3 @ Y1) @ (cons @ X3 @ X2 @ X1) @ (app @ Y3 @ Y1 @ Y2 @ Y0)) @ (cons @ (plus @ (plus @ X3 @ Y3) @ Y1) @ X2 @ (app @ (plus @ X3 @ Y3) @ Y1 @ (app @ X3 @ Y3 @ X1 @ Y2) @ Y0))) => (listStar @ (plus @ (suc @ (plus @ Y3 @ Y1)) @ (plus @ Y3 @ Y1)) @ (app @ (suc @ X3) @ (plus @ Y3 @ Y1) @ (cons @ X3 @ X2 @ X1) @ (app @ Y3 @ Y1 @ Y2 @ Y0)) @ (app @ (suc @ (plus @ X3 @ Y3)) @ Y1 @ (cons @ (plus @ X3 @ Y3) @ X2 @ (app @ X3 @ Y3 @ X1 @ Y2)) @ Y0))))))))))))) @ X4) = $true)) )),
% 1.81/1.45 inference(pi_clausification,[status(thm)],[f91])).
% 1.81/1.45 thf(f91,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list] : (($true = (!! @ list @ (^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: (!! @ list @ (^[Y2 : list]: (!! @ nat @ (^[Y3 : nat]: ((listStar @ Y3 @ Y2 @ Y2) => ((listStar @ Y1 @ Y0 @ Y0) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ Y3 @ Y1)) @ (plus @ Y3 @ Y1)) @ (app @ (suc @ X3) @ (plus @ Y3 @ Y1) @ (cons @ X3 @ X2 @ X1) @ (app @ Y3 @ Y1 @ Y2 @ Y0)) @ (cons @ (plus @ (plus @ X3 @ Y3) @ Y1) @ X2 @ (app @ (plus @ X3 @ Y3) @ Y1 @ (app @ X3 @ Y3 @ X1 @ Y2) @ Y0))) => (listStar @ (plus @ (suc @ (plus @ Y3 @ Y1)) @ (plus @ Y3 @ Y1)) @ (app @ (suc @ X3) @ (plus @ Y3 @ Y1) @ (cons @ X3 @ X2 @ X1) @ (app @ Y3 @ Y1 @ Y2 @ Y0)) @ (app @ (suc @ (plus @ X3 @ Y3)) @ Y1 @ (cons @ (plus @ X3 @ Y3) @ X2 @ (app @ X3 @ Y3 @ X1 @ Y2)) @ Y0)))))))))))))))) )),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f90])).
% 1.81/1.45 thf(f90,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list] : ((((^[Y0 : nat]: (!! @ list @ (^[Y1 : list]: (!! @ nat @ (^[Y2 : nat]: (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: ((listStar @ Y4 @ Y3 @ Y3) => ((listStar @ Y2 @ Y1 @ Y1) => ((listStar @ Y0 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ Y4 @ Y2)) @ (plus @ Y4 @ Y2)) @ (app @ (suc @ Y0) @ (plus @ Y4 @ Y2) @ (cons @ Y0 @ X2 @ X1) @ (app @ Y4 @ Y2 @ Y3 @ Y1)) @ (cons @ (plus @ (plus @ Y0 @ Y4) @ Y2) @ X2 @ (app @ (plus @ Y0 @ Y4) @ Y2 @ (app @ Y0 @ Y4 @ X1 @ Y3) @ Y1))) => (listStar @ (plus @ (suc @ (plus @ Y4 @ Y2)) @ (plus @ Y4 @ Y2)) @ (app @ (suc @ Y0) @ (plus @ Y4 @ Y2) @ (cons @ Y0 @ X2 @ X1) @ (app @ Y4 @ Y2 @ Y3 @ Y1)) @ (app @ (suc @ (plus @ Y0 @ Y4)) @ Y2 @ (cons @ (plus @ Y0 @ Y4) @ X2 @ (app @ Y0 @ Y4 @ X1 @ Y3)) @ Y1))))))))))))))) @ X3) = $true)) )),
% 1.81/1.45 inference(pi_clausification,[status(thm)],[f89])).
% 1.81/1.45 thf(f89,plain,(
% 1.81/1.45 ( ! [X2 : elem,X1 : list] : (((!! @ nat @ (^[Y0 : nat]: (!! @ list @ (^[Y1 : list]: (!! @ nat @ (^[Y2 : nat]: (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: ((listStar @ Y4 @ Y3 @ Y3) => ((listStar @ Y2 @ Y1 @ Y1) => ((listStar @ Y0 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ Y4 @ Y2)) @ (plus @ Y4 @ Y2)) @ (app @ (suc @ Y0) @ (plus @ Y4 @ Y2) @ (cons @ Y0 @ X2 @ X1) @ (app @ Y4 @ Y2 @ Y3 @ Y1)) @ (cons @ (plus @ (plus @ Y0 @ Y4) @ Y2) @ X2 @ (app @ (plus @ Y0 @ Y4) @ Y2 @ (app @ Y0 @ Y4 @ X1 @ Y3) @ Y1))) => (listStar @ (plus @ (suc @ (plus @ Y4 @ Y2)) @ (plus @ Y4 @ Y2)) @ (app @ (suc @ Y0) @ (plus @ Y4 @ Y2) @ (cons @ Y0 @ X2 @ X1) @ (app @ Y4 @ Y2 @ Y3 @ Y1)) @ (app @ (suc @ (plus @ Y0 @ Y4)) @ Y2 @ (cons @ (plus @ Y0 @ Y4) @ X2 @ (app @ Y0 @ Y4 @ X1 @ Y3)) @ Y1)))))))))))))))) = $true)) )),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f88])).
% 1.81/1.45 thf(f88,plain,(
% 1.81/1.45 ( ! [X2 : elem,X1 : list] : ((((^[Y0 : elem]: (!! @ nat @ (^[Y1 : nat]: (!! @ list @ (^[Y2 : list]: (!! @ nat @ (^[Y3 : nat]: (!! @ list @ (^[Y4 : list]: (!! @ nat @ (^[Y5 : nat]: ((listStar @ Y5 @ Y4 @ Y4) => ((listStar @ Y3 @ Y2 @ Y2) => ((listStar @ Y1 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ Y5 @ Y3)) @ (plus @ Y5 @ Y3)) @ (app @ (suc @ Y1) @ (plus @ Y5 @ Y3) @ (cons @ Y1 @ Y0 @ X1) @ (app @ Y5 @ Y3 @ Y4 @ Y2)) @ (cons @ (plus @ (plus @ Y1 @ Y5) @ Y3) @ Y0 @ (app @ (plus @ Y1 @ Y5) @ Y3 @ (app @ Y1 @ Y5 @ X1 @ Y4) @ Y2))) => (listStar @ (plus @ (suc @ (plus @ Y5 @ Y3)) @ (plus @ Y5 @ Y3)) @ (app @ (suc @ Y1) @ (plus @ Y5 @ Y3) @ (cons @ Y1 @ Y0 @ X1) @ (app @ Y5 @ Y3 @ Y4 @ Y2)) @ (app @ (suc @ (plus @ Y1 @ Y5)) @ Y3 @ (cons @ (plus @ Y1 @ Y5) @ Y0 @ (app @ Y1 @ Y5 @ X1 @ Y4)) @ Y2))))))))))))))))) @ X2) = $true)) )),
% 1.81/1.45 inference(pi_clausification,[status(thm)],[f87])).
% 1.81/1.45 thf(f87,plain,(
% 1.81/1.45 ( ! [X1 : list] : (((!! @ elem @ (^[Y0 : elem]: (!! @ nat @ (^[Y1 : nat]: (!! @ list @ (^[Y2 : list]: (!! @ nat @ (^[Y3 : nat]: (!! @ list @ (^[Y4 : list]: (!! @ nat @ (^[Y5 : nat]: ((listStar @ Y5 @ Y4 @ Y4) => ((listStar @ Y3 @ Y2 @ Y2) => ((listStar @ Y1 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ Y5 @ Y3)) @ (plus @ Y5 @ Y3)) @ (app @ (suc @ Y1) @ (plus @ Y5 @ Y3) @ (cons @ Y1 @ Y0 @ X1) @ (app @ Y5 @ Y3 @ Y4 @ Y2)) @ (cons @ (plus @ (plus @ Y1 @ Y5) @ Y3) @ Y0 @ (app @ (plus @ Y1 @ Y5) @ Y3 @ (app @ Y1 @ Y5 @ X1 @ Y4) @ Y2))) => (listStar @ (plus @ (suc @ (plus @ Y5 @ Y3)) @ (plus @ Y5 @ Y3)) @ (app @ (suc @ Y1) @ (plus @ Y5 @ Y3) @ (cons @ Y1 @ Y0 @ X1) @ (app @ Y5 @ Y3 @ Y4 @ Y2)) @ (app @ (suc @ (plus @ Y1 @ Y5)) @ Y3 @ (cons @ (plus @ Y1 @ Y5) @ Y0 @ (app @ Y1 @ Y5 @ X1 @ Y4)) @ Y2)))))))))))))))))) = $true)) )),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f86])).
% 1.81/1.45 thf(f86,plain,(
% 1.81/1.45 ( ! [X1 : list] : ((((^[Y0 : list]: (!! @ elem @ (^[Y1 : elem]: (!! @ nat @ (^[Y2 : nat]: (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: (!! @ list @ (^[Y5 : list]: (!! @ nat @ (^[Y6 : nat]: ((listStar @ Y6 @ Y5 @ Y5) => ((listStar @ Y4 @ Y3 @ Y3) => ((listStar @ Y2 @ Y0 @ Y0) => ((listStar @ (plus @ (suc @ (plus @ Y6 @ Y4)) @ (plus @ Y6 @ Y4)) @ (app @ (suc @ Y2) @ (plus @ Y6 @ Y4) @ (cons @ Y2 @ Y1 @ Y0) @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (cons @ (plus @ (plus @ Y2 @ Y6) @ Y4) @ Y1 @ (app @ (plus @ Y2 @ Y6) @ Y4 @ (app @ Y2 @ Y6 @ Y0 @ Y5) @ Y3))) => (listStar @ (plus @ (suc @ (plus @ Y6 @ Y4)) @ (plus @ Y6 @ Y4)) @ (app @ (suc @ Y2) @ (plus @ Y6 @ Y4) @ (cons @ Y2 @ Y1 @ Y0) @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (app @ (suc @ (plus @ Y2 @ Y6)) @ Y4 @ (cons @ (plus @ Y2 @ Y6) @ Y1 @ (app @ Y2 @ Y6 @ Y0 @ Y5)) @ Y3))))))))))))))))))) @ X1) = $true)) )),
% 1.81/1.45 inference(pi_clausification,[status(thm)],[f58])).
% 1.81/1.45 thf(f58,plain,(
% 1.81/1.45 ($true = (!! @ list @ (^[Y0 : list]: (!! @ elem @ (^[Y1 : elem]: (!! @ nat @ (^[Y2 : nat]: (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: (!! @ list @ (^[Y5 : list]: (!! @ nat @ (^[Y6 : nat]: ((listStar @ Y6 @ Y5 @ Y5) => ((listStar @ Y4 @ Y3 @ Y3) => ((listStar @ Y2 @ Y0 @ Y0) => ((listStar @ (plus @ (suc @ (plus @ Y6 @ Y4)) @ (plus @ Y6 @ Y4)) @ (app @ (suc @ Y2) @ (plus @ Y6 @ Y4) @ (cons @ Y2 @ Y1 @ Y0) @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (cons @ (plus @ (plus @ Y2 @ Y6) @ Y4) @ Y1 @ (app @ (plus @ Y2 @ Y6) @ Y4 @ (app @ Y2 @ Y6 @ Y0 @ Y5) @ Y3))) => (listStar @ (plus @ (suc @ (plus @ Y6 @ Y4)) @ (plus @ Y6 @ Y4)) @ (app @ (suc @ Y2) @ (plus @ Y6 @ Y4) @ (cons @ Y2 @ Y1 @ Y0) @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (app @ (suc @ (plus @ Y2 @ Y6)) @ Y4 @ (cons @ (plus @ Y2 @ Y6) @ Y1 @ (app @ Y2 @ Y6 @ Y0 @ Y5)) @ Y3)))))))))))))))))))))),
% 1.81/1.45 inference(cnf_transformation,[status(thm)],[f22])).
% 1.81/1.45 thf(f22,plain,(
% 1.81/1.45 ($true = (!! @ list @ (^[Y0 : list]: (!! @ elem @ (^[Y1 : elem]: (!! @ nat @ (^[Y2 : nat]: (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: (!! @ list @ (^[Y5 : list]: (!! @ nat @ (^[Y6 : nat]: ((listStar @ Y6 @ Y5 @ Y5) => ((listStar @ Y4 @ Y3 @ Y3) => ((listStar @ Y2 @ Y0 @ Y0) => ((listStar @ (plus @ (suc @ (plus @ Y6 @ Y4)) @ (plus @ Y6 @ Y4)) @ (app @ (suc @ Y2) @ (plus @ Y6 @ Y4) @ (cons @ Y2 @ Y1 @ Y0) @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (cons @ (plus @ (plus @ Y2 @ Y6) @ Y4) @ Y1 @ (app @ (plus @ Y2 @ Y6) @ Y4 @ (app @ Y2 @ Y6 @ Y0 @ Y5) @ Y3))) => (listStar @ (plus @ (suc @ (plus @ Y6 @ Y4)) @ (plus @ Y6 @ Y4)) @ (app @ (suc @ Y2) @ (plus @ Y6 @ Y4) @ (cons @ Y2 @ Y1 @ Y0) @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (app @ (suc @ (plus @ Y2 @ Y6)) @ Y4 @ (cons @ (plus @ Y2 @ Y6) @ Y1 @ (app @ Y2 @ Y6 @ Y0 @ Y5)) @ Y3)))))))))))))))))))))),
% 1.81/1.45 inference(fool_elimination,[status(thm)],[f21])).
% 1.81/1.45 thf(f21,plain,(
% 1.81/1.45 ! [X0 : nat,X1 : list,X2 : nat,X3 : list,X4 : nat,X5 : elem,X6 : list] : ((listStar @ X0 @ X1 @ X1) => ((listStar @ X2 @ X3 @ X3) => ((listStar @ X4 @ X6 @ X6) => ((listStar @ (plus @ (suc @ (plus @ X0 @ X2)) @ (plus @ X0 @ X2)) @ (app @ (suc @ X4) @ (plus @ X0 @ X2) @ (cons @ X4 @ X5 @ X6) @ (app @ X0 @ X2 @ X1 @ X3)) @ (cons @ (plus @ (plus @ X4 @ X0) @ X2) @ X5 @ (app @ (plus @ X4 @ X0) @ X2 @ (app @ X4 @ X0 @ X6 @ X1) @ X3))) => (listStar @ (plus @ (suc @ (plus @ X0 @ X2)) @ (plus @ X0 @ X2)) @ (app @ (suc @ X4) @ (plus @ X0 @ X2) @ (cons @ X4 @ X5 @ X6) @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (suc @ (plus @ X4 @ X0)) @ X2 @ (cons @ (plus @ X4 @ X0) @ X5 @ (app @ X4 @ X0 @ X6 @ X1)) @ X3))))))),
% 1.81/1.45 inference(rectify,[status(thm)],[f13])).
% 1.81/1.45 thf(f13,axiom,(
% 1.81/1.45 ! [X13 : nat,X16 : list,X14 : nat,X17 : list,X10 : nat,X2 : elem,X18 : list] : ((listStar @ X13 @ X16 @ X16) => ((listStar @ X14 @ X17 @ X17) => ((listStar @ X10 @ X18 @ X18) => ((listStar @ (plus @ (suc @ (plus @ X13 @ X14)) @ (plus @ X13 @ X14)) @ (app @ (suc @ X10) @ (plus @ X13 @ X14) @ (cons @ X10 @ X2 @ X18) @ (app @ X13 @ X14 @ X16 @ X17)) @ (cons @ (plus @ (plus @ X10 @ X13) @ X14) @ X2 @ (app @ (plus @ X10 @ X13) @ X14 @ (app @ X10 @ X13 @ X18 @ X16) @ X17))) => (listStar @ (plus @ (suc @ (plus @ X13 @ X14)) @ (plus @ X13 @ X14)) @ (app @ (suc @ X10) @ (plus @ X13 @ X14) @ (cons @ X10 @ X2 @ X18) @ (app @ X13 @ X14 @ X16 @ X17)) @ (app @ (suc @ (plus @ X10 @ X13)) @ X14 @ (cons @ (plus @ X10 @ X13) @ X2 @ (app @ X10 @ X13 @ X18 @ X16)) @ X17))))))),
% 1.81/1.45 file('/export/starexec/sandbox2/tmp/tmp.PLL0ptdnA4/DTF2THF_4359.p',list_app_assoc_indstep2)).
% 1.81/1.45 thf(f76,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X7 : nat,X4 : list,X5 : nat] : (((listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (app @ (suc @ (plus @ X3 @ X7)) @ X5 @ (cons @ (plus @ X3 @ X7) @ X2 @ (app @ X3 @ X7 @ X1 @ X6)) @ X4)) = $false) | ($true = (listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (app @ (plus @ (suc @ X3) @ X7) @ X5 @ (app @ (suc @ X3) @ X7 @ (cons @ X3 @ X2 @ X1) @ X6) @ X4))) | ($false = (listStar @ X3 @ X1 @ X1)) | ($false = (listStar @ X7 @ X6 @ X6)) | ($false = (listStar @ X5 @ X4 @ X4))) )),
% 1.81/1.45 inference(binary_proxy_clausification,[status(thm)],[f75])).
% 1.81/1.45 thf(f75,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X7 : nat,X4 : list,X5 : nat] : (($true = ((listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (app @ (suc @ (plus @ X3 @ X7)) @ X5 @ (cons @ (plus @ X3 @ X7) @ X2 @ (app @ X3 @ X7 @ X1 @ X6)) @ X4)) => (listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (app @ (plus @ (suc @ X3) @ X7) @ X5 @ (app @ (suc @ X3) @ X7 @ (cons @ X3 @ X2 @ X1) @ X6) @ X4)))) | ($false = (listStar @ X5 @ X4 @ X4)) | ($false = (listStar @ X3 @ X1 @ X1)) | ($false = (listStar @ X7 @ X6 @ X6))) )),
% 1.81/1.45 inference(binary_proxy_clausification,[status(thm)],[f74])).
% 1.81/1.45 thf(f74,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X7 : nat,X4 : list,X5 : nat] : (($false = (listStar @ X7 @ X6 @ X6)) | ($true = ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (app @ (suc @ (plus @ X3 @ X7)) @ X5 @ (cons @ (plus @ X3 @ X7) @ X2 @ (app @ X3 @ X7 @ X1 @ X6)) @ X4)) => (listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (app @ (plus @ (suc @ X3) @ X7) @ X5 @ (app @ (suc @ X3) @ X7 @ (cons @ X3 @ X2 @ X1) @ X6) @ X4))))) | ($false = (listStar @ X5 @ X4 @ X4))) )),
% 1.81/1.45 inference(binary_proxy_clausification,[status(thm)],[f73])).
% 1.81/1.45 thf(f73,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X7 : nat,X4 : list,X5 : nat] : (($false = (listStar @ X7 @ X6 @ X6)) | (((listStar @ X5 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (app @ (suc @ (plus @ X3 @ X7)) @ X5 @ (cons @ (plus @ X3 @ X7) @ X2 @ (app @ X3 @ X7 @ X1 @ X6)) @ X4)) => (listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (app @ (plus @ (suc @ X3) @ X7) @ X5 @ (app @ (suc @ X3) @ X7 @ (cons @ X3 @ X2 @ X1) @ X6) @ X4))))) = $true)) )),
% 1.81/1.45 inference(binary_proxy_clausification,[status(thm)],[f72])).
% 1.81/1.45 thf(f72,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X7 : nat,X4 : list,X5 : nat] : ((((listStar @ X7 @ X6 @ X6) => ((listStar @ X5 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (app @ (suc @ (plus @ X3 @ X7)) @ X5 @ (cons @ (plus @ X3 @ X7) @ X2 @ (app @ X3 @ X7 @ X1 @ X6)) @ X4)) => (listStar @ (plus @ (suc @ (plus @ X7 @ X5)) @ (plus @ X7 @ X5)) @ (app @ (suc @ X3) @ (plus @ X7 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ X7 @ X5 @ X6 @ X4)) @ (app @ (plus @ (suc @ X3) @ X7) @ X5 @ (app @ (suc @ X3) @ X7 @ (cons @ X3 @ X2 @ X1) @ X6) @ X4)))))) = $true)) )),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f71])).
% 1.81/1.45 thf(f71,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X7 : nat,X4 : list,X5 : nat] : ((((^[Y0 : nat]: ((listStar @ Y0 @ X6 @ X6) => ((listStar @ X5 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ Y0 @ X5)) @ (plus @ Y0 @ X5)) @ (app @ (suc @ X3) @ (plus @ Y0 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ Y0 @ X5 @ X6 @ X4)) @ (app @ (suc @ (plus @ X3 @ Y0)) @ X5 @ (cons @ (plus @ X3 @ Y0) @ X2 @ (app @ X3 @ Y0 @ X1 @ X6)) @ X4)) => (listStar @ (plus @ (suc @ (plus @ Y0 @ X5)) @ (plus @ Y0 @ X5)) @ (app @ (suc @ X3) @ (plus @ Y0 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ Y0 @ X5 @ X6 @ X4)) @ (app @ (plus @ (suc @ X3) @ Y0) @ X5 @ (app @ (suc @ X3) @ Y0 @ (cons @ X3 @ X2 @ X1) @ X6) @ X4))))))) @ X7) = $true)) )),
% 1.81/1.45 inference(pi_clausification,[status(thm)],[f70])).
% 1.81/1.45 thf(f70,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X4 : list,X5 : nat] : (((!! @ nat @ (^[Y0 : nat]: ((listStar @ Y0 @ X6 @ X6) => ((listStar @ X5 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ Y0 @ X5)) @ (plus @ Y0 @ X5)) @ (app @ (suc @ X3) @ (plus @ Y0 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ Y0 @ X5 @ X6 @ X4)) @ (app @ (suc @ (plus @ X3 @ Y0)) @ X5 @ (cons @ (plus @ X3 @ Y0) @ X2 @ (app @ X3 @ Y0 @ X1 @ X6)) @ X4)) => (listStar @ (plus @ (suc @ (plus @ Y0 @ X5)) @ (plus @ Y0 @ X5)) @ (app @ (suc @ X3) @ (plus @ Y0 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ Y0 @ X5 @ X6 @ X4)) @ (app @ (plus @ (suc @ X3) @ Y0) @ X5 @ (app @ (suc @ X3) @ Y0 @ (cons @ X3 @ X2 @ X1) @ X6) @ X4)))))))) = $true)) )),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.81/1.45 thf(f69,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X6 : list,X4 : list,X5 : nat] : ((((^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ Y1 @ Y0 @ Y0) => ((listStar @ X5 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ Y1 @ X5)) @ (plus @ Y1 @ X5)) @ (app @ (suc @ X3) @ (plus @ Y1 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ Y1 @ X5 @ Y0 @ X4)) @ (app @ (suc @ (plus @ X3 @ Y1)) @ X5 @ (cons @ (plus @ X3 @ Y1) @ X2 @ (app @ X3 @ Y1 @ X1 @ Y0)) @ X4)) => (listStar @ (plus @ (suc @ (plus @ Y1 @ X5)) @ (plus @ Y1 @ X5)) @ (app @ (suc @ X3) @ (plus @ Y1 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ Y1 @ X5 @ Y0 @ X4)) @ (app @ (plus @ (suc @ X3) @ Y1) @ X5 @ (app @ (suc @ X3) @ Y1 @ (cons @ X3 @ X2 @ X1) @ Y0) @ X4))))))))) @ X6) = $true)) )),
% 1.81/1.45 inference(pi_clausification,[status(thm)],[f68])).
% 1.81/1.45 thf(f68,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X4 : list,X5 : nat] : (((!! @ list @ (^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ Y1 @ Y0 @ Y0) => ((listStar @ X5 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ Y1 @ X5)) @ (plus @ Y1 @ X5)) @ (app @ (suc @ X3) @ (plus @ Y1 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ Y1 @ X5 @ Y0 @ X4)) @ (app @ (suc @ (plus @ X3 @ Y1)) @ X5 @ (cons @ (plus @ X3 @ Y1) @ X2 @ (app @ X3 @ Y1 @ X1 @ Y0)) @ X4)) => (listStar @ (plus @ (suc @ (plus @ Y1 @ X5)) @ (plus @ Y1 @ X5)) @ (app @ (suc @ X3) @ (plus @ Y1 @ X5) @ (cons @ X3 @ X2 @ X1) @ (app @ Y1 @ X5 @ Y0 @ X4)) @ (app @ (plus @ (suc @ X3) @ Y1) @ X5 @ (app @ (suc @ X3) @ Y1 @ (cons @ X3 @ X2 @ X1) @ Y0) @ X4)))))))))) = $true)) )),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f67])).
% 1.81/1.45 thf(f67,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X4 : list,X5 : nat] : ((((^[Y0 : nat]: (!! @ list @ (^[Y1 : list]: (!! @ nat @ (^[Y2 : nat]: ((listStar @ Y2 @ Y1 @ Y1) => ((listStar @ Y0 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ Y2 @ Y0)) @ (plus @ Y2 @ Y0)) @ (app @ (suc @ X3) @ (plus @ Y2 @ Y0) @ (cons @ X3 @ X2 @ X1) @ (app @ Y2 @ Y0 @ Y1 @ X4)) @ (app @ (suc @ (plus @ X3 @ Y2)) @ Y0 @ (cons @ (plus @ X3 @ Y2) @ X2 @ (app @ X3 @ Y2 @ X1 @ Y1)) @ X4)) => (listStar @ (plus @ (suc @ (plus @ Y2 @ Y0)) @ (plus @ Y2 @ Y0)) @ (app @ (suc @ X3) @ (plus @ Y2 @ Y0) @ (cons @ X3 @ X2 @ X1) @ (app @ Y2 @ Y0 @ Y1 @ X4)) @ (app @ (plus @ (suc @ X3) @ Y2) @ Y0 @ (app @ (suc @ X3) @ Y2 @ (cons @ X3 @ X2 @ X1) @ Y1) @ X4))))))))))) @ X5) = $true)) )),
% 1.81/1.45 inference(pi_clausification,[status(thm)],[f66])).
% 1.81/1.45 thf(f66,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X4 : list] : (((!! @ nat @ (^[Y0 : nat]: (!! @ list @ (^[Y1 : list]: (!! @ nat @ (^[Y2 : nat]: ((listStar @ Y2 @ Y1 @ Y1) => ((listStar @ Y0 @ X4 @ X4) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ Y2 @ Y0)) @ (plus @ Y2 @ Y0)) @ (app @ (suc @ X3) @ (plus @ Y2 @ Y0) @ (cons @ X3 @ X2 @ X1) @ (app @ Y2 @ Y0 @ Y1 @ X4)) @ (app @ (suc @ (plus @ X3 @ Y2)) @ Y0 @ (cons @ (plus @ X3 @ Y2) @ X2 @ (app @ X3 @ Y2 @ X1 @ Y1)) @ X4)) => (listStar @ (plus @ (suc @ (plus @ Y2 @ Y0)) @ (plus @ Y2 @ Y0)) @ (app @ (suc @ X3) @ (plus @ Y2 @ Y0) @ (cons @ X3 @ X2 @ X1) @ (app @ Y2 @ Y0 @ Y1 @ X4)) @ (app @ (plus @ (suc @ X3) @ Y2) @ Y0 @ (app @ (suc @ X3) @ Y2 @ (cons @ X3 @ X2 @ X1) @ Y1) @ X4)))))))))))) = $true)) )),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f65])).
% 1.81/1.45 thf(f65,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list,X4 : list] : ((((^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: (!! @ list @ (^[Y2 : list]: (!! @ nat @ (^[Y3 : nat]: ((listStar @ Y3 @ Y2 @ Y2) => ((listStar @ Y1 @ Y0 @ Y0) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ Y3 @ Y1)) @ (plus @ Y3 @ Y1)) @ (app @ (suc @ X3) @ (plus @ Y3 @ Y1) @ (cons @ X3 @ X2 @ X1) @ (app @ Y3 @ Y1 @ Y2 @ Y0)) @ (app @ (suc @ (plus @ X3 @ Y3)) @ Y1 @ (cons @ (plus @ X3 @ Y3) @ X2 @ (app @ X3 @ Y3 @ X1 @ Y2)) @ Y0)) => (listStar @ (plus @ (suc @ (plus @ Y3 @ Y1)) @ (plus @ Y3 @ Y1)) @ (app @ (suc @ X3) @ (plus @ Y3 @ Y1) @ (cons @ X3 @ X2 @ X1) @ (app @ Y3 @ Y1 @ Y2 @ Y0)) @ (app @ (plus @ (suc @ X3) @ Y3) @ Y1 @ (app @ (suc @ X3) @ Y3 @ (cons @ X3 @ X2 @ X1) @ Y2) @ Y0))))))))))))) @ X4) = $true)) )),
% 1.81/1.45 inference(pi_clausification,[status(thm)],[f64])).
% 1.81/1.45 thf(f64,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list] : (($true = (!! @ list @ (^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: (!! @ list @ (^[Y2 : list]: (!! @ nat @ (^[Y3 : nat]: ((listStar @ Y3 @ Y2 @ Y2) => ((listStar @ Y1 @ Y0 @ Y0) => ((listStar @ X3 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ Y3 @ Y1)) @ (plus @ Y3 @ Y1)) @ (app @ (suc @ X3) @ (plus @ Y3 @ Y1) @ (cons @ X3 @ X2 @ X1) @ (app @ Y3 @ Y1 @ Y2 @ Y0)) @ (app @ (suc @ (plus @ X3 @ Y3)) @ Y1 @ (cons @ (plus @ X3 @ Y3) @ X2 @ (app @ X3 @ Y3 @ X1 @ Y2)) @ Y0)) => (listStar @ (plus @ (suc @ (plus @ Y3 @ Y1)) @ (plus @ Y3 @ Y1)) @ (app @ (suc @ X3) @ (plus @ Y3 @ Y1) @ (cons @ X3 @ X2 @ X1) @ (app @ Y3 @ Y1 @ Y2 @ Y0)) @ (app @ (plus @ (suc @ X3) @ Y3) @ Y1 @ (app @ (suc @ X3) @ Y3 @ (cons @ X3 @ X2 @ X1) @ Y2) @ Y0)))))))))))))))) )),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f63])).
% 1.81/1.45 thf(f63,plain,(
% 1.81/1.45 ( ! [X2 : elem,X3 : nat,X1 : list] : (($true = ((^[Y0 : nat]: (!! @ list @ (^[Y1 : list]: (!! @ nat @ (^[Y2 : nat]: (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: ((listStar @ Y4 @ Y3 @ Y3) => ((listStar @ Y2 @ Y1 @ Y1) => ((listStar @ Y0 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ Y4 @ Y2)) @ (plus @ Y4 @ Y2)) @ (app @ (suc @ Y0) @ (plus @ Y4 @ Y2) @ (cons @ Y0 @ X2 @ X1) @ (app @ Y4 @ Y2 @ Y3 @ Y1)) @ (app @ (suc @ (plus @ Y0 @ Y4)) @ Y2 @ (cons @ (plus @ Y0 @ Y4) @ X2 @ (app @ Y0 @ Y4 @ X1 @ Y3)) @ Y1)) => (listStar @ (plus @ (suc @ (plus @ Y4 @ Y2)) @ (plus @ Y4 @ Y2)) @ (app @ (suc @ Y0) @ (plus @ Y4 @ Y2) @ (cons @ Y0 @ X2 @ X1) @ (app @ Y4 @ Y2 @ Y3 @ Y1)) @ (app @ (plus @ (suc @ Y0) @ Y4) @ Y2 @ (app @ (suc @ Y0) @ Y4 @ (cons @ Y0 @ X2 @ X1) @ Y3) @ Y1))))))))))))))) @ X3))) )),
% 1.81/1.45 inference(pi_clausification,[status(thm)],[f62])).
% 1.81/1.45 thf(f62,plain,(
% 1.81/1.45 ( ! [X2 : elem,X1 : list] : (($true = (!! @ nat @ (^[Y0 : nat]: (!! @ list @ (^[Y1 : list]: (!! @ nat @ (^[Y2 : nat]: (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: ((listStar @ Y4 @ Y3 @ Y3) => ((listStar @ Y2 @ Y1 @ Y1) => ((listStar @ Y0 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ Y4 @ Y2)) @ (plus @ Y4 @ Y2)) @ (app @ (suc @ Y0) @ (plus @ Y4 @ Y2) @ (cons @ Y0 @ X2 @ X1) @ (app @ Y4 @ Y2 @ Y3 @ Y1)) @ (app @ (suc @ (plus @ Y0 @ Y4)) @ Y2 @ (cons @ (plus @ Y0 @ Y4) @ X2 @ (app @ Y0 @ Y4 @ X1 @ Y3)) @ Y1)) => (listStar @ (plus @ (suc @ (plus @ Y4 @ Y2)) @ (plus @ Y4 @ Y2)) @ (app @ (suc @ Y0) @ (plus @ Y4 @ Y2) @ (cons @ Y0 @ X2 @ X1) @ (app @ Y4 @ Y2 @ Y3 @ Y1)) @ (app @ (plus @ (suc @ Y0) @ Y4) @ Y2 @ (app @ (suc @ Y0) @ Y4 @ (cons @ Y0 @ X2 @ X1) @ Y3) @ Y1)))))))))))))))))) )),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f61])).
% 1.81/1.45 thf(f61,plain,(
% 1.81/1.45 ( ! [X2 : elem,X1 : list] : (($true = ((^[Y0 : elem]: (!! @ nat @ (^[Y1 : nat]: (!! @ list @ (^[Y2 : list]: (!! @ nat @ (^[Y3 : nat]: (!! @ list @ (^[Y4 : list]: (!! @ nat @ (^[Y5 : nat]: ((listStar @ Y5 @ Y4 @ Y4) => ((listStar @ Y3 @ Y2 @ Y2) => ((listStar @ Y1 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ Y5 @ Y3)) @ (plus @ Y5 @ Y3)) @ (app @ (suc @ Y1) @ (plus @ Y5 @ Y3) @ (cons @ Y1 @ Y0 @ X1) @ (app @ Y5 @ Y3 @ Y4 @ Y2)) @ (app @ (suc @ (plus @ Y1 @ Y5)) @ Y3 @ (cons @ (plus @ Y1 @ Y5) @ Y0 @ (app @ Y1 @ Y5 @ X1 @ Y4)) @ Y2)) => (listStar @ (plus @ (suc @ (plus @ Y5 @ Y3)) @ (plus @ Y5 @ Y3)) @ (app @ (suc @ Y1) @ (plus @ Y5 @ Y3) @ (cons @ Y1 @ Y0 @ X1) @ (app @ Y5 @ Y3 @ Y4 @ Y2)) @ (app @ (plus @ (suc @ Y1) @ Y5) @ Y3 @ (app @ (suc @ Y1) @ Y5 @ (cons @ Y1 @ Y0 @ X1) @ Y4) @ Y2))))))))))))))))) @ X2))) )),
% 1.81/1.45 inference(pi_clausification,[status(thm)],[f60])).
% 1.81/1.45 thf(f60,plain,(
% 1.81/1.45 ( ! [X1 : list] : (((!! @ elem @ (^[Y0 : elem]: (!! @ nat @ (^[Y1 : nat]: (!! @ list @ (^[Y2 : list]: (!! @ nat @ (^[Y3 : nat]: (!! @ list @ (^[Y4 : list]: (!! @ nat @ (^[Y5 : nat]: ((listStar @ Y5 @ Y4 @ Y4) => ((listStar @ Y3 @ Y2 @ Y2) => ((listStar @ Y1 @ X1 @ X1) => ((listStar @ (plus @ (suc @ (plus @ Y5 @ Y3)) @ (plus @ Y5 @ Y3)) @ (app @ (suc @ Y1) @ (plus @ Y5 @ Y3) @ (cons @ Y1 @ Y0 @ X1) @ (app @ Y5 @ Y3 @ Y4 @ Y2)) @ (app @ (suc @ (plus @ Y1 @ Y5)) @ Y3 @ (cons @ (plus @ Y1 @ Y5) @ Y0 @ (app @ Y1 @ Y5 @ X1 @ Y4)) @ Y2)) => (listStar @ (plus @ (suc @ (plus @ Y5 @ Y3)) @ (plus @ Y5 @ Y3)) @ (app @ (suc @ Y1) @ (plus @ Y5 @ Y3) @ (cons @ Y1 @ Y0 @ X1) @ (app @ Y5 @ Y3 @ Y4 @ Y2)) @ (app @ (plus @ (suc @ Y1) @ Y5) @ Y3 @ (app @ (suc @ Y1) @ Y5 @ (cons @ Y1 @ Y0 @ X1) @ Y4) @ Y2)))))))))))))))))) = $true)) )),
% 1.81/1.45 inference(beta_eta_normalization,[status(thm)],[f59])).
% 1.81/1.45 thf(f59,plain,(
% 1.81/1.45 ( ! [X1 : list] : ((((^[Y0 : list]: (!! @ elem @ (^[Y1 : elem]: (!! @ nat @ (^[Y2 : nat]: (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: (!! @ list @ (^[Y5 : list]: (!! @ nat @ (^[Y6 : nat]: ((listStar @ Y6 @ Y5 @ Y5) => ((listStar @ Y4 @ Y3 @ Y3) => ((listStar @ Y2 @ Y0 @ Y0) => ((listStar @ (plus @ (suc @ (plus @ Y6 @ Y4)) @ (plus @ Y6 @ Y4)) @ (app @ (suc @ Y2) @ (plus @ Y6 @ Y4) @ (cons @ Y2 @ Y1 @ Y0) @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (app @ (suc @ (plus @ Y2 @ Y6)) @ Y4 @ (cons @ (plus @ Y2 @ Y6) @ Y1 @ (app @ Y2 @ Y6 @ Y0 @ Y5)) @ Y3)) => (listStar @ (plus @ (suc @ (plus @ Y6 @ Y4)) @ (plus @ Y6 @ Y4)) @ (app @ (suc @ Y2) @ (plus @ Y6 @ Y4) @ (cons @ Y2 @ Y1 @ Y0) @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (app @ (plus @ (suc @ Y2) @ Y6) @ Y4 @ (app @ (suc @ Y2) @ Y6 @ (cons @ Y2 @ Y1 @ Y0) @ Y5) @ Y3))))))))))))))))))) @ X1) = $true)) )),
% 1.81/1.45 inference(pi_clausification,[status(thm)],[f57])).
% 1.81/1.45 thf(f57,plain,(
% 1.81/1.45 ((!! @ list @ (^[Y0 : list]: (!! @ elem @ (^[Y1 : elem]: (!! @ nat @ (^[Y2 : nat]: (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: (!! @ list @ (^[Y5 : list]: (!! @ nat @ (^[Y6 : nat]: ((listStar @ Y6 @ Y5 @ Y5) => ((listStar @ Y4 @ Y3 @ Y3) => ((listStar @ Y2 @ Y0 @ Y0) => ((listStar @ (plus @ (suc @ (plus @ Y6 @ Y4)) @ (plus @ Y6 @ Y4)) @ (app @ (suc @ Y2) @ (plus @ Y6 @ Y4) @ (cons @ Y2 @ Y1 @ Y0) @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (app @ (suc @ (plus @ Y2 @ Y6)) @ Y4 @ (cons @ (plus @ Y2 @ Y6) @ Y1 @ (app @ Y2 @ Y6 @ Y0 @ Y5)) @ Y3)) => (listStar @ (plus @ (suc @ (plus @ Y6 @ Y4)) @ (plus @ Y6 @ Y4)) @ (app @ (suc @ Y2) @ (plus @ Y6 @ Y4) @ (cons @ Y2 @ Y1 @ Y0) @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (app @ (plus @ (suc @ Y2) @ Y6) @ Y4 @ (app @ (suc @ Y2) @ Y6 @ (cons @ Y2 @ Y1 @ Y0) @ Y5) @ Y3)))))))))))))))))))) = $true)),
% 1.81/1.45 inference(cnf_transformation,[status(thm)],[f44])).
% 1.81/1.45 thf(f44,plain,(
% 1.81/1.45 ((!! @ list @ (^[Y0 : list]: (!! @ elem @ (^[Y1 : elem]: (!! @ nat @ (^[Y2 : nat]: (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: (!! @ list @ (^[Y5 : list]: (!! @ nat @ (^[Y6 : nat]: ((listStar @ Y6 @ Y5 @ Y5) => ((listStar @ Y4 @ Y3 @ Y3) => ((listStar @ Y2 @ Y0 @ Y0) => ((listStar @ (plus @ (suc @ (plus @ Y6 @ Y4)) @ (plus @ Y6 @ Y4)) @ (app @ (suc @ Y2) @ (plus @ Y6 @ Y4) @ (cons @ Y2 @ Y1 @ Y0) @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (app @ (suc @ (plus @ Y2 @ Y6)) @ Y4 @ (cons @ (plus @ Y2 @ Y6) @ Y1 @ (app @ Y2 @ Y6 @ Y0 @ Y5)) @ Y3)) => (listStar @ (plus @ (suc @ (plus @ Y6 @ Y4)) @ (plus @ Y6 @ Y4)) @ (app @ (suc @ Y2) @ (plus @ Y6 @ Y4) @ (cons @ Y2 @ Y1 @ Y0) @ (app @ Y6 @ Y4 @ Y5 @ Y3)) @ (app @ (plus @ (suc @ Y2) @ Y6) @ Y4 @ (app @ (suc @ Y2) @ Y6 @ (cons @ Y2 @ Y1 @ Y0) @ Y5) @ Y3)))))))))))))))))))) = $true)),
% 1.81/1.45 inference(fool_elimination,[status(thm)],[f43])).
% 1.81/1.45 thf(f43,plain,(
% 1.81/1.45 ! [X0 : nat,X1 : list,X2 : nat,X3 : list,X4 : nat,X5 : elem,X6 : list] : ((listStar @ X0 @ X1 @ X1) => ((listStar @ X2 @ X3 @ X3) => ((listStar @ X4 @ X6 @ X6) => ((listStar @ (plus @ (suc @ (plus @ X0 @ X2)) @ (plus @ X0 @ X2)) @ (app @ (suc @ X4) @ (plus @ X0 @ X2) @ (cons @ X4 @ X5 @ X6) @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (suc @ (plus @ X4 @ X0)) @ X2 @ (cons @ (plus @ X4 @ X0) @ X5 @ (app @ X4 @ X0 @ X6 @ X1)) @ X3)) => (listStar @ (plus @ (suc @ (plus @ X0 @ X2)) @ (plus @ X0 @ X2)) @ (app @ (suc @ X4) @ (plus @ X0 @ X2) @ (cons @ X4 @ X5 @ X6) @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ (suc @ X4) @ X0) @ X2 @ (app @ (suc @ X4) @ X0 @ (cons @ X4 @ X5 @ X6) @ X1) @ X3))))))),
% 1.81/1.45 inference(rectify,[status(thm)],[f12])).
% 1.81/1.45 thf(f12,axiom,(
% 1.81/1.45 ! [X13 : nat,X16 : list,X14 : nat,X17 : list,X10 : nat,X2 : elem,X18 : list] : ((listStar @ X13 @ X16 @ X16) => ((listStar @ X14 @ X17 @ X17) => ((listStar @ X10 @ X18 @ X18) => ((listStar @ (plus @ (suc @ (plus @ X13 @ X14)) @ (plus @ X13 @ X14)) @ (app @ (suc @ X10) @ (plus @ X13 @ X14) @ (cons @ X10 @ X2 @ X18) @ (app @ X13 @ X14 @ X16 @ X17)) @ (app @ (suc @ (plus @ X10 @ X13)) @ X14 @ (cons @ (plus @ X10 @ X13) @ X2 @ (app @ X10 @ X13 @ X18 @ X16)) @ X17)) => (listStar @ (plus @ (suc @ (plus @ X13 @ X14)) @ (plus @ X13 @ X14)) @ (app @ (suc @ X10) @ (plus @ X13 @ X14) @ (cons @ X10 @ X2 @ X18) @ (app @ X13 @ X14 @ X16 @ X17)) @ (app @ (plus @ (suc @ X10) @ X13) @ X14 @ (app @ (suc @ X10) @ X13 @ (cons @ X10 @ X2 @ X18) @ X16) @ X17))))))),
% 1.81/1.45 file('/export/starexec/sandbox2/tmp/tmp.PLL0ptdnA4/DTF2THF_4359.p',list_app_assoc_indstep1)).
% 1.81/1.45 thf(f126,plain,(
% 1.81/1.45 ((listStar @ (plus @ (plus @ sK7 @ sK5) @ (plus @ sK7 @ sK5)) @ (app @ sK3 @ (plus @ sK7 @ sK5) @ sK1 @ (app @ sK7 @ sK5 @ sK6 @ sK4)) @ (app @ (plus @ sK3 @ sK7) @ sK5 @ (app @ sK3 @ sK7 @ sK1 @ sK6) @ sK4)) = $true)),
% 1.81/1.45 inference(binary_proxy_clausification,[status(thm)],[f123])).
% 1.81/1.45 % SZS output end Proof for DTF2THF_4359
% 1.81/1.45 % (4488)------------------------------
% 1.81/1.45 % (4488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.45 % (4488)Termination reason: Refutation
% 1.81/1.45
% 1.81/1.45 % (4488)Memory used [KB]: 6396
% 1.81/1.45 % (4488)Time elapsed: 0.063 s
% 1.81/1.45 % (4488)Instructions burned: 103 (million)
% 1.81/1.45 % (4488)------------------------------
% 1.81/1.45 % (4488)------------------------------
% 1.81/1.45 % (4459)Success in time 0.15 s
%------------------------------------------------------------------------------