%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT384^1 : TPTP v9.2.1. Released v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 08:45:37 AM UTC 2026
% Result : Theorem 2.00s 1.54s
% Output : Refutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 220 ( 14 equ; 0 cnn)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 1500 ( 5 ~; 0 |; 0 &;1327 @)
% ( 0 <=>; 86 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 11 usr; 5 con; 0-4 aty)
% ( 82 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 138 ( 82 ^; 56 !; 0 ?; 138 :)
% 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_14,type,
rev: nat > list > list ).
thf(f103,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f102]) ).
thf(f102,plain,
$false = $true,
inference(boolean_simplification,[status(thm)],[f101]) ).
thf(f101,plain,
( ( ~ $true ) = $true ),
inference(backward_demodulation,[status(thm)],[f83,f100]) ).
thf(f100,plain,
( ( !! @ list
@ ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list
@ ^ [Y2: list] :
( !! @ nat
@ ^ [Y3: nat] :
( ( listStar @ Y3 @ Y2 @ Y2 )
=> ( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( listStar @ ( plus @ Y3 @ Y1 ) @ ( rev @ ( plus @ Y3 @ Y1 ) @ ( app @ Y3 @ Y1 @ ( rev @ Y3 @ Y2 ) @ Y0 ) ) @ ( app @ Y1 @ Y3 @ ( rev @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f99]) ).
thf(f99,plain,
( ( $true
=> ( !! @ list
@ ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list
@ ^ [Y2: list] :
( !! @ nat
@ ^ [Y3: nat] :
( ( listStar @ Y3 @ Y2 @ Y2 )
=> ( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( listStar @ ( plus @ Y3 @ Y1 ) @ ( rev @ ( plus @ Y3 @ Y1 ) @ ( app @ Y3 @ Y1 @ ( rev @ Y3 @ Y2 ) @ Y0 ) ) @ ( app @ Y1 @ Y3 @ ( rev @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f98,f76]) ).
thf(f76,plain,
( ( !! @ list
@ ^ [Y0: list] :
( !! @ elem
@ ^ [Y1: elem] :
( !! @ nat
@ ^ [Y2: nat] :
( ( listStar @ Y2 @ Y0 @ Y0 )
=> ( ( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( listStar @ ( plus @ Y2 @ Y4 ) @ ( rev @ ( plus @ Y2 @ Y4 ) @ ( app @ Y2 @ Y4 @ ( rev @ Y2 @ Y0 ) @ Y3 ) ) @ ( app @ Y4 @ Y2 @ ( rev @ Y4 @ Y3 ) @ Y0 ) ) ) ) )
=> ( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( listStar @ ( plus @ ( suc @ Y2 ) @ Y4 ) @ ( rev @ ( plus @ ( suc @ Y2 ) @ Y4 ) @ ( app @ ( suc @ Y2 ) @ Y4 @ ( rev @ ( suc @ Y2 ) @ ( cons @ Y2 @ Y1 @ Y0 ) ) @ Y3 ) ) @ ( app @ Y4 @ ( suc @ Y2 ) @ ( rev @ Y4 @ Y3 ) @ ( cons @ Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f55]) ).
thf(f55,plain,
( ( !! @ list
@ ^ [Y0: list] :
( !! @ elem
@ ^ [Y1: elem] :
( !! @ nat
@ ^ [Y2: nat] :
( ( listStar @ Y2 @ Y0 @ Y0 )
=> ( ( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( listStar @ ( plus @ Y2 @ Y4 ) @ ( rev @ ( plus @ Y2 @ Y4 ) @ ( app @ Y2 @ Y4 @ ( rev @ Y2 @ Y0 ) @ Y3 ) ) @ ( app @ Y4 @ Y2 @ ( rev @ Y4 @ Y3 ) @ Y0 ) ) ) ) )
=> ( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( listStar @ ( plus @ ( suc @ Y2 ) @ Y4 ) @ ( rev @ ( plus @ ( suc @ Y2 ) @ Y4 ) @ ( app @ ( suc @ Y2 ) @ Y4 @ ( rev @ ( suc @ Y2 ) @ ( cons @ Y2 @ Y1 @ Y0 ) ) @ Y3 ) ) @ ( app @ Y4 @ ( suc @ Y2 ) @ ( rev @ Y4 @ Y3 ) @ ( cons @ Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f54]) ).
thf(f54,plain,
! [X0: nat,X1: elem,X2: list] :
( ( listStar @ X0 @ X2 @ X2 )
=> ( ! [X3: nat,X4: list] :
( ( listStar @ X3 @ X4 @ X4 )
=> ( listStar @ ( plus @ X0 @ X3 ) @ ( rev @ ( plus @ X0 @ X3 ) @ ( app @ X0 @ X3 @ ( rev @ X0 @ X2 ) @ X4 ) ) @ ( app @ X3 @ X0 @ ( rev @ X3 @ X4 ) @ X2 ) ) )
=> ! [X5: nat,X6: list] :
( ( listStar @ X5 @ X6 @ X6 )
=> ( listStar @ ( plus @ ( suc @ X0 ) @ X5 ) @ ( rev @ ( plus @ ( suc @ X0 ) @ X5 ) @ ( app @ ( suc @ X0 ) @ X5 @ ( rev @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) ) @ X6 ) ) @ ( app @ X5 @ ( suc @ X0 ) @ ( rev @ X5 @ X6 ) @ ( cons @ X0 @ X1 @ X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f22]) ).
thf(f22,axiom,
! [X6: nat,X2: elem,X15: list] :
( ( listStar @ X6 @ X15 @ X15 )
=> ( ! [X13: nat,X14: list] :
( ( listStar @ X13 @ X14 @ X14 )
=> ( listStar @ ( plus @ X6 @ X13 ) @ ( rev @ ( plus @ X6 @ X13 ) @ ( app @ X6 @ X13 @ ( rev @ X6 @ X15 ) @ X14 ) ) @ ( app @ X13 @ X6 @ ( rev @ X13 @ X14 ) @ X15 ) ) )
=> ! [X13: nat,X14: list] :
( ( listStar @ X13 @ X14 @ X14 )
=> ( listStar @ ( plus @ ( suc @ X6 ) @ X13 ) @ ( rev @ ( plus @ ( suc @ X6 ) @ X13 ) @ ( app @ ( suc @ X6 ) @ X13 @ ( rev @ ( suc @ X6 ) @ ( cons @ X6 @ X2 @ X15 ) ) @ X14 ) ) @ ( app @ X13 @ ( suc @ X6 ) @ ( rev @ X13 @ X14 ) @ ( cons @ X6 @ X2 @ X15 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.K4a8wmNMBS/DTF2THF_3850.p',list_rev_invol_lem_indstep) ).
thf(f98,plain,
( ( ( !! @ list
@ ^ [Y0: list] :
( !! @ elem
@ ^ [Y1: elem] :
( !! @ nat
@ ^ [Y2: nat] :
( ( listStar @ Y2 @ Y0 @ Y0 )
=> ( ( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( listStar @ ( plus @ Y2 @ Y4 ) @ ( rev @ ( plus @ Y2 @ Y4 ) @ ( app @ Y2 @ Y4 @ ( rev @ Y2 @ Y0 ) @ Y3 ) ) @ ( app @ Y4 @ Y2 @ ( rev @ Y4 @ Y3 ) @ Y0 ) ) ) ) )
=> ( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( listStar @ ( plus @ ( suc @ Y2 ) @ Y4 ) @ ( rev @ ( plus @ ( suc @ Y2 ) @ Y4 ) @ ( app @ ( suc @ Y2 ) @ Y4 @ ( rev @ ( suc @ Y2 ) @ ( cons @ Y2 @ Y1 @ Y0 ) ) @ Y3 ) ) @ ( app @ Y4 @ ( suc @ Y2 ) @ ( rev @ Y4 @ Y3 ) @ ( cons @ Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ list
@ ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list
@ ^ [Y2: list] :
( !! @ nat
@ ^ [Y3: nat] :
( ( listStar @ Y3 @ Y2 @ Y2 )
=> ( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( listStar @ ( plus @ Y3 @ Y1 ) @ ( rev @ ( plus @ Y3 @ Y1 ) @ ( app @ Y3 @ Y1 @ ( rev @ Y3 @ Y2 ) @ Y0 ) ) @ ( app @ Y1 @ Y3 @ ( rev @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f97]) ).
thf(f97,plain,
( ( $true
=> ( ( !! @ list
@ ^ [Y0: list] :
( !! @ elem
@ ^ [Y1: elem] :
( !! @ nat
@ ^ [Y2: nat] :
( ( listStar @ Y2 @ Y0 @ Y0 )
=> ( ( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( listStar @ ( plus @ Y2 @ Y4 ) @ ( rev @ ( plus @ Y2 @ Y4 ) @ ( app @ Y2 @ Y4 @ ( rev @ Y2 @ Y0 ) @ Y3 ) ) @ ( app @ Y4 @ Y2 @ ( rev @ Y4 @ Y3 ) @ Y0 ) ) ) ) )
=> ( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( listStar @ ( plus @ ( suc @ Y2 ) @ Y4 ) @ ( rev @ ( plus @ ( suc @ Y2 ) @ Y4 ) @ ( app @ ( suc @ Y2 ) @ Y4 @ ( rev @ ( suc @ Y2 ) @ ( cons @ Y2 @ Y1 @ Y0 ) ) @ Y3 ) ) @ ( app @ Y4 @ ( suc @ Y2 ) @ ( rev @ Y4 @ Y3 ) @ ( cons @ Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ list
@ ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list
@ ^ [Y2: list] :
( !! @ nat
@ ^ [Y3: nat] :
( ( listStar @ Y3 @ Y2 @ Y2 )
=> ( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( listStar @ ( plus @ Y3 @ Y1 ) @ ( rev @ ( plus @ Y3 @ Y1 ) @ ( app @ Y3 @ Y1 @ ( rev @ Y3 @ Y2 ) @ Y0 ) ) @ ( app @ Y1 @ Y3 @ ( rev @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f75,f78]) ).
thf(f78,plain,
( ( !! @ list
@ ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( listStar @ ( plus @ zero @ Y1 ) @ ( rev @ ( plus @ zero @ Y1 ) @ ( app @ zero @ Y1 @ ( rev @ zero @ nil ) @ Y0 ) ) @ ( app @ Y1 @ zero @ ( rev @ Y1 @ Y0 ) @ nil ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f59]) ).
thf(f59,plain,
( ( !! @ list
@ ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( listStar @ ( plus @ zero @ Y1 ) @ ( rev @ ( plus @ zero @ Y1 ) @ ( app @ zero @ Y1 @ ( rev @ zero @ nil ) @ Y0 ) ) @ ( app @ Y1 @ zero @ ( rev @ Y1 @ Y0 ) @ nil ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f58]) ).
thf(f58,plain,
! [X0: nat,X1: list] :
( ( listStar @ X0 @ X1 @ X1 )
=> ( listStar @ ( plus @ zero @ X0 ) @ ( rev @ ( plus @ zero @ X0 ) @ ( app @ zero @ X0 @ ( rev @ zero @ nil ) @ X1 ) ) @ ( app @ X0 @ zero @ ( rev @ X0 @ X1 ) @ nil ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,axiom,
! [X13: nat,X14: list] :
( ( listStar @ X13 @ X14 @ X14 )
=> ( listStar @ ( plus @ zero @ X13 ) @ ( rev @ ( plus @ zero @ X13 ) @ ( app @ zero @ X13 @ ( rev @ zero @ nil ) @ X14 ) ) @ ( app @ X13 @ zero @ ( rev @ X13 @ X14 ) @ nil ) ) ),
file('/export/starexec/sandbox/tmp/tmp.K4a8wmNMBS/DTF2THF_3850.p',list_rev_invol_lem_base) ).
thf(f75,plain,
( ( ( !! @ list
@ ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( listStar @ ( plus @ zero @ Y1 ) @ ( rev @ ( plus @ zero @ Y1 ) @ ( app @ zero @ Y1 @ ( rev @ zero @ nil ) @ Y0 ) ) @ ( app @ Y1 @ zero @ ( rev @ Y1 @ Y0 ) @ nil ) ) ) ) )
=> ( ( !! @ list
@ ^ [Y0: list] :
( !! @ elem
@ ^ [Y1: elem] :
( !! @ nat
@ ^ [Y2: nat] :
( ( listStar @ Y2 @ Y0 @ Y0 )
=> ( ( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( listStar @ ( plus @ Y2 @ Y4 ) @ ( rev @ ( plus @ Y2 @ Y4 ) @ ( app @ Y2 @ Y4 @ ( rev @ Y2 @ Y0 ) @ Y3 ) ) @ ( app @ Y4 @ Y2 @ ( rev @ Y4 @ Y3 ) @ Y0 ) ) ) ) )
=> ( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( listStar @ ( plus @ ( suc @ Y2 ) @ Y4 ) @ ( rev @ ( plus @ ( suc @ Y2 ) @ Y4 ) @ ( app @ ( suc @ Y2 ) @ Y4 @ ( rev @ ( suc @ Y2 ) @ ( cons @ Y2 @ Y1 @ Y0 ) ) @ Y3 ) ) @ ( app @ Y4 @ ( suc @ Y2 ) @ ( rev @ Y4 @ Y3 ) @ ( cons @ Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ list
@ ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list
@ ^ [Y2: list] :
( !! @ nat
@ ^ [Y3: nat] :
( ( listStar @ Y3 @ Y2 @ Y2 )
=> ( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( listStar @ ( plus @ Y3 @ Y1 ) @ ( rev @ ( plus @ Y3 @ Y1 ) @ ( app @ Y3 @ Y1 @ ( rev @ Y3 @ Y2 ) @ Y0 ) ) @ ( app @ Y1 @ Y3 @ ( rev @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f67]) ).
thf(f67,plain,
( ( ( !! @ list
@ ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( listStar @ ( plus @ zero @ Y1 ) @ ( rev @ ( plus @ zero @ Y1 ) @ ( app @ zero @ Y1 @ ( rev @ zero @ nil ) @ Y0 ) ) @ ( app @ Y1 @ zero @ ( rev @ Y1 @ Y0 ) @ nil ) ) ) ) )
=> ( ( !! @ list
@ ^ [Y0: list] :
( !! @ elem
@ ^ [Y1: elem] :
( !! @ nat
@ ^ [Y2: nat] :
( ( listStar @ Y2 @ Y0 @ Y0 )
=> ( ( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( listStar @ ( plus @ Y2 @ Y4 ) @ ( rev @ ( plus @ Y2 @ Y4 ) @ ( app @ Y2 @ Y4 @ ( rev @ Y2 @ Y0 ) @ Y3 ) ) @ ( app @ Y4 @ Y2 @ ( rev @ Y4 @ Y3 ) @ Y0 ) ) ) ) )
=> ( !! @ list
@ ^ [Y3: list] :
( !! @ nat
@ ^ [Y4: nat] :
( ( listStar @ Y4 @ Y3 @ Y3 )
=> ( listStar @ ( plus @ ( suc @ Y2 ) @ Y4 ) @ ( rev @ ( plus @ ( suc @ Y2 ) @ Y4 ) @ ( app @ ( suc @ Y2 ) @ Y4 @ ( rev @ ( suc @ Y2 ) @ ( cons @ Y2 @ Y1 @ Y0 ) ) @ Y3 ) ) @ ( app @ Y4 @ ( suc @ Y2 ) @ ( rev @ Y4 @ Y3 ) @ ( cons @ Y2 @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) )
=> ( !! @ list
@ ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list
@ ^ [Y2: list] :
( !! @ nat
@ ^ [Y3: nat] :
( ( listStar @ Y3 @ Y2 @ Y2 )
=> ( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( listStar @ ( plus @ Y3 @ Y1 ) @ ( rev @ ( plus @ Y3 @ Y1 ) @ ( app @ Y3 @ Y1 @ ( rev @ Y3 @ Y2 ) @ Y0 ) ) @ ( app @ Y1 @ Y3 @ ( rev @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f66]) ).
thf(f66,plain,
( ! [X0: nat,X1: list] :
( ( listStar @ X0 @ X1 @ X1 )
=> ( listStar @ ( plus @ zero @ X0 ) @ ( rev @ ( plus @ zero @ X0 ) @ ( app @ zero @ X0 @ ( rev @ zero @ nil ) @ X1 ) ) @ ( app @ X0 @ zero @ ( rev @ X0 @ X1 ) @ nil ) ) )
=> ( ! [X2: nat,X3: elem,X4: list] :
( ( listStar @ X2 @ X4 @ X4 )
=> ( ! [X5: nat,X6: list] :
( ( listStar @ X5 @ X6 @ X6 )
=> ( listStar @ ( plus @ X2 @ X5 ) @ ( rev @ ( plus @ X2 @ X5 ) @ ( app @ X2 @ X5 @ ( rev @ X2 @ X4 ) @ X6 ) ) @ ( app @ X5 @ X2 @ ( rev @ X5 @ X6 ) @ X4 ) ) )
=> ! [X7: nat,X8: list] :
( ( listStar @ X7 @ X8 @ X8 )
=> ( listStar @ ( plus @ ( suc @ X2 ) @ X7 ) @ ( rev @ ( plus @ ( suc @ X2 ) @ X7 ) @ ( app @ ( suc @ X2 ) @ X7 @ ( rev @ ( suc @ X2 ) @ ( cons @ X2 @ X3 @ X4 ) ) @ X8 ) ) @ ( app @ X7 @ ( suc @ X2 ) @ ( rev @ X7 @ X8 ) @ ( cons @ X2 @ X3 @ X4 ) ) ) ) ) )
=> ! [X9: nat,X10: list,X11: nat,X12: list] :
( ( listStar @ X9 @ X10 @ X10 )
=> ( ( listStar @ X11 @ X12 @ X12 )
=> ( listStar @ ( plus @ X9 @ X11 ) @ ( rev @ ( plus @ X9 @ X11 ) @ ( app @ X9 @ X11 @ ( rev @ X9 @ X10 ) @ X12 ) ) @ ( app @ X11 @ X9 @ ( rev @ X11 @ X12 ) @ X10 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,axiom,
( ! [X13: nat,X14: list] :
( ( listStar @ X13 @ X14 @ X14 )
=> ( listStar @ ( plus @ zero @ X13 ) @ ( rev @ ( plus @ zero @ X13 ) @ ( app @ zero @ X13 @ ( rev @ zero @ nil ) @ X14 ) ) @ ( app @ X13 @ zero @ ( rev @ X13 @ X14 ) @ nil ) ) )
=> ( ! [X6: nat,X2: elem,X15: list] :
( ( listStar @ X6 @ X15 @ X15 )
=> ( ! [X13: nat,X14: list] :
( ( listStar @ X13 @ X14 @ X14 )
=> ( listStar @ ( plus @ X6 @ X13 ) @ ( rev @ ( plus @ X6 @ X13 ) @ ( app @ X6 @ X13 @ ( rev @ X6 @ X15 ) @ X14 ) ) @ ( app @ X13 @ X6 @ ( rev @ X13 @ X14 ) @ X15 ) ) )
=> ! [X13: nat,X14: list] :
( ( listStar @ X13 @ X14 @ X14 )
=> ( listStar @ ( plus @ ( suc @ X6 ) @ X13 ) @ ( rev @ ( plus @ ( suc @ X6 ) @ X13 ) @ ( app @ ( suc @ X6 ) @ X13 @ ( rev @ ( suc @ X6 ) @ ( cons @ X6 @ X2 @ X15 ) ) @ X14 ) ) @ ( app @ X13 @ ( suc @ X6 ) @ ( rev @ X13 @ X14 ) @ ( cons @ X6 @ X2 @ X15 ) ) ) ) ) )
=> ! [X6: nat,X15: list,X13: nat,X14: list] :
( ( listStar @ X6 @ X15 @ X15 )
=> ( ( listStar @ X13 @ X14 @ X14 )
=> ( listStar @ ( plus @ X6 @ X13 ) @ ( rev @ ( plus @ X6 @ X13 ) @ ( app @ X6 @ X13 @ ( rev @ X6 @ X15 ) @ X14 ) ) @ ( app @ X13 @ X6 @ ( rev @ X13 @ X14 ) @ X15 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.K4a8wmNMBS/DTF2THF_3850.p',list_rev_invol_lem_indinst) ).
thf(f83,plain,
( ( ~ ( !! @ list
@ ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list
@ ^ [Y2: list] :
( !! @ nat
@ ^ [Y3: nat] :
( ( listStar @ Y3 @ Y2 @ Y2 )
=> ( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( listStar @ ( plus @ Y3 @ Y1 ) @ ( rev @ ( plus @ Y3 @ Y1 ) @ ( app @ Y3 @ Y1 @ ( rev @ Y3 @ Y2 ) @ Y0 ) ) @ ( app @ Y1 @ Y3 @ ( rev @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f61]) ).
thf(f61,plain,
( ( ~ ( !! @ list
@ ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( !! @ list
@ ^ [Y2: list] :
( !! @ nat
@ ^ [Y3: nat] :
( ( listStar @ Y3 @ Y2 @ Y2 )
=> ( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( listStar @ ( plus @ Y3 @ Y1 ) @ ( rev @ ( plus @ Y3 @ Y1 ) @ ( app @ Y3 @ Y1 @ ( rev @ Y3 @ Y2 ) @ Y0 ) ) @ ( app @ Y1 @ Y3 @ ( rev @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f60]) ).
thf(f60,plain,
~ ! [X0: nat,X1: list,X2: nat,X3: list] :
( ( listStar @ X0 @ X1 @ X1 )
=> ( ( listStar @ X2 @ X3 @ X3 )
=> ( listStar @ ( plus @ X0 @ X2 ) @ ( rev @ ( plus @ X0 @ X2 ) @ ( app @ X0 @ X2 @ ( rev @ X0 @ X1 ) @ X3 ) ) @ ( app @ X2 @ X0 @ ( rev @ X2 @ X3 ) @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,negated_conjecture,
~ ! [X6: nat,X15: list,X13: nat,X14: list] :
( ( listStar @ X6 @ X15 @ X15 )
=> ( ( listStar @ X13 @ X14 @ X14 )
=> ( listStar @ ( plus @ X6 @ X13 ) @ ( rev @ ( plus @ X6 @ X13 ) @ ( app @ X6 @ X13 @ ( rev @ X6 @ X15 ) @ X14 ) ) @ ( app @ X13 @ X6 @ ( rev @ X13 @ X14 ) @ X15 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
thf(f23,conjecture,
! [X6: nat,X15: list,X13: nat,X14: list] :
( ( listStar @ X6 @ X15 @ X15 )
=> ( ( listStar @ X13 @ X14 @ X14 )
=> ( listStar @ ( plus @ X6 @ X13 ) @ ( rev @ ( plus @ X6 @ X13 ) @ ( app @ X6 @ X13 @ ( rev @ X6 @ X15 ) @ X14 ) ) @ ( app @ X13 @ X6 @ ( rev @ X13 @ X14 ) @ X15 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.K4a8wmNMBS/DTF2THF_3850.p',list_rev_invol_lem) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT384^1 : TPTP v9.2.1. Released v9.2.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n019.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 06:18:24 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : DAT384^1 : TPTP v9.2.1. Released v9.2.0.
% 0.28/0.46 % Domain : Data Structures
% 0.28/0.46 % Problem : List involution lemma
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English : List involution lemma. The proof is by induction with a separate
% 0.28/0.46 % problem file for the base and step case (with multiple subcases)
% 0.28/0.46 % as well as the correct instantiation of the induction axiom for
% 0.28/0.46 % lists. The main file uses the conjectures of the other files as
% 0.28/0.46 % lemmas in order to prove the final result. To simplify proof
% 0.28/0.46 % search, the axioms in each problem file have been preselected.
% 0.28/0.46 % For the actual induction proof, it is sufficient to consider the
% 0.28/0.46 % "step" problem files.
% 0.28/0.46
% 0.28/0.46 % Refs : [RRB23] Rothgang et al. (2023), Theorem Proving in Dependently
% 0.28/0.46 % : [Rot25] Rothgang (2025), Email to Geoff Sutcliffe
% 0.28/0.46 % : [RK+25] Ranalter et al. (2025), The Dependently Typed Higher-O
% 0.28/0.46 % Source : [Rot25]
% 0.28/0.46 % Names : ListReversalInvolutionLemma/list-rev-invol-lem.p [Rot25]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : ? v9.2.0
% 0.28/0.46 % Syntax : Number of formulae : 25 ( 11 unt; 10 typ; 0 def)
% 0.28/0.46 % Number of atoms : 19 ( 19 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 4 ( 1 avg)
% 0.28/0.46 % Number of connectives : 249 ( 3 ~; 0 |; 0 &; 238 @)
% 0.28/0.46 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 9 ( 4 avg)
% 0.28/0.46 % Number of types : 3 ( 2 usr)
% 0.28/0.46 % Number of type decls : 10 ( 0 !>P; 3 !>D)
% 0.28/0.46 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 9 ( 8 usr; 2 con; 0-4 aty)
% 0.28/0.46 % Number of variables : 52 ( 0 ^; 48 !; 0 ?; 52 :)
% 0.28/0.46 % ( 4 !>; 0 ?*; 0 @-; 0 @+)
% 0.28/0.46 % SPC : DH0_THM_EQU_NAR
% 0.28/0.46
% 0.28/0.46 % Comments :
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(elem_type,type,
% 0.28/0.46 elem: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(nat_type,type,
% 0.28/0.46 nat: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(zero_type,type,
% 0.28/0.46 zero: nat ).
% 0.28/0.46
% 0.28/0.46 thf(suc_type,type,
% 0.28/0.46 suc: nat > nat ).
% 0.28/0.46
% 0.28/0.46 thf(plus_type,type,
% 0.28/0.46 plus: nat > nat > nat ).
% 0.28/0.46
% 0.28/0.46 thf(list_type,type,
% 0.28/0.46 list: nat > $tType ).
% 0.28/0.46
% 0.28/0.46 thf(nil_type,type,
% 0.28/0.46 nil: list @ zero ).
% 0.28/0.46
% 0.28/0.46 thf(cons_type,type,
% 0.28/0.46 cons:
% 0.28/0.46 !>[N: nat] : ( elem > ( list @ N ) > ( list @ ( suc @ N ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(app_type,type,
% 0.28/0.46 app:
% 0.28/0.46 !>[N: nat,M: nat] : ( ( list @ N ) > ( list @ M ) > ( list @ ( plus @ N @ M ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(rev_type,type,
% 0.28/0.46 rev:
% 0.28/0.46 !>[N: nat] : ( ( list @ N ) > ( list @ N ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(peano1,axiom,
% 0.28/0.46 ! [N: nat] :
% 0.28/0.46 ( ( suc @ N )
% 0.28/0.46 != zero ) ).
% 0.28/0.46
% 0.28/0.46 thf(peano2,axiom,
% 0.28/0.46 ! [N: nat,M: nat] :
% 0.28/0.46 ( ( N != M )
% 0.28/0.46 => ( ( suc @ N )
% 0.28/0.46 != ( suc @ M ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(peano3,axiom,
% 0.28/0.46 ! [P: nat > $o] :
% 0.28/0.46 ( ( P @ zero )
% 0.28/0.46 => ( ! [M: nat] :
% 0.28/0.46 ( ( P @ M )
% 0.28/0.46 => ( P @ ( suc @ M ) ) )
% 0.28/0.46 => ! [N: nat] : ( P @ N ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(ax1,axiom,
% 0.28/0.46 ! [N: nat] :
% 0.28/0.46 ( ( plus @ zero @ N )
% 0.28/0.46 = N ) ).
% 0.28/0.46
% 0.28/0.46 thf(ax2,axiom,
% 0.28/0.46 ! [N: nat,M: nat] :
% 0.28/0.46 ( ( plus @ ( suc @ N ) @ M )
% 0.28/0.46 = ( suc @ ( plus @ N @ M ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(ax3,axiom,
% 0.28/0.46 ! [N: nat,X: list @ N] :
% 0.28/0.46 ( ( app @ zero @ N @ nil @ X )
% 0.28/0.46 = X ) ).
% 0.28/0.46
% 0.28/0.46 thf(ax4,axiom,
% 0.28/0.46 ! [N: nat,M: nat,X: elem,Y: list @ N,Z: list @ M] :
% 0.28/0.46 ( ( app @ ( suc @ N ) @ M @ ( cons @ N @ X @ Y ) @ Z )
% 0.28/0.46 = ( cons @ ( plus @ N @ M ) @ X @ ( app @ N @ M @ Y @ Z ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(ax5,axiom,
% 0.28/0.46 ( ( rev @ zero @ nil )
% 0.28/0.46 = nil ) ).
% 0.28/0.46
% 0.28/0.46 thf(ax6,axiom,
% 0.28/0.46 ! [N: nat,X: elem,Y: list @ N] :
% 0.28/0.46 ( ( rev @ ( suc @ N ) @ ( cons @ N @ X @ Y ) )
% 0.28/0.46 = ( app @ N @ ( suc @ zero ) @ ( rev @ N @ Y ) @ ( cons @ zero @ X @ nil ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(plus_com,axiom,
% 0.28/0.46 ! [N: nat,M: nat] :
% 0.28/0.46 ( ( plus @ N @ M )
% 0.28/0.46 = ( plus @ M @ N ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(plus1r,axiom,
% 0.28/0.46 ! [N: nat] :
% 0.28/0.46 ( ( suc @ N )
% 0.28/0.46 = ( plus @ N @ ( suc @ zero ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(list_rev_invol_lem_indinst,axiom,
% 0.28/0.46 ( ! [M2: nat,L2: list @ M2] :
% 0.28/0.46 ( ( rev @ ( plus @ zero @ M2 ) @ ( app @ zero @ M2 @ ( rev @ zero @ nil ) @ L2 ) )
% 0.28/0.46 = ( app @ M2 @ zero @ ( rev @ M2 @ L2 ) @ nil ) )
% 0.28/0.46 => ( ! [N: nat,X: elem,L: list @ N] :
% 0.28/0.46 ( ! [M2: nat,L2: list @ M2] :
% 0.28/0.46 ( ( rev @ ( plus @ N @ M2 ) @ ( app @ N @ M2 @ ( rev @ N @ L ) @ L2 ) )
% 0.28/0.46 = ( app @ M2 @ N @ ( rev @ M2 @ L2 ) @ L ) )
% 0.28/0.46 => ! [M2: nat,L2: list @ M2] :
% 0.28/0.46 ( ( rev @ ( plus @ ( suc @ N ) @ M2 ) @ ( app @ ( suc @ N ) @ M2 @ ( rev @ ( suc @ N ) @ ( cons @ N @ X @ L ) ) @ L2 ) )
% 0.28/0.46 = ( app @ M2 @ ( suc @ N ) @ ( rev @ M2 @ L2 ) @ ( cons @ N @ X @ L ) ) ) )
% 0.28/0.46 => ! [N: nat,L: list @ N,M2: nat,L2: list @ M2] :
% 0.28/0.46 ( ( rev @ ( plus @ N @ M2 ) @ ( app @ N @ M2 @ ( rev @ N @ L ) @ L2 ) )
% 0.28/0.46 = ( app @ M2 @ N @ ( rev @ M2 @ L2 ) @ L ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(list_rev_invol_lem_base,axiom,
% 0.28/0.46 ! [M2: nat,L2: list @ M2] :
% 0.28/0.46 ( ( rev @ ( plus @ zero @ M2 ) @ ( app @ zero @ M2 @ ( rev @ zero @ nil ) @ L2 ) )
% 0.28/0.46 = ( app @ M2 @ zero @ ( rev @ M2 @ L2 ) @ nil ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(list_rev_invol_lem_indstep,axiom,
% 0.28/0.46 ! [N: nat,X: elem,L: list @ N] :
% 0.28/0.46 ( ! [M2: nat,L2: list @ M2] :
% 0.28/0.46 ( ( rev @ ( plus @ N @ M2 ) @ ( app @ N @ M2 @ ( rev @ N @ L ) @ L2 ) )
% 0.28/0.46 = ( app @ M2 @ N @ ( rev @ M2 @ L2 ) @ L ) )
% 0.28/0.46 => ! [M2: nat,L2: list @ M2] :
% 0.28/0.46 ( ( rev @ ( plus @ ( suc @ N ) @ M2 ) @ ( app @ ( suc @ N ) @ M2 @ ( rev @ ( suc @ N ) @ ( cons @ N @ X @ L ) ) @ L2 ) )
% 0.28/0.46 = ( app @ M2 @ ( suc @ N ) @ ( rev @ M2 @ L2 ) @ ( cons @ N @ X @ L ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(list_rev_invol_lem,conjecture,
% 0.28/0.46 ! [N: nat,L: list @ N,M2: nat,L2: list @ M2] :
% 0.28/0.46 ( ( rev @ ( plus @ N @ M2 ) @ ( app @ N @ M2 @ ( rev @ N @ L ) @ L2 ) )
% 0.28/0.46 = ( app @ M2 @ N @ ( rev @ M2 @ L2 ) @ L ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 1.90/1.43 ---- Embedded in THF ---
% 1.90/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.90/1.43 %%% Generated on Tue Feb 24 06:18:25 EST 2026
% 1.90/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 1.90/1.43 %%% Logic specification used:
% 1.90/1.43 %%% thf(spec, logic, $$dhol).
% 1.90/1.43
% 1.90/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.K4a8wmNMBS/DTF2DTF3850.p
% See solution above
% 1.90/1.43 ------------------------
% 1.90/1.44 ---- Cleaned THF ---
% 1.90/1.44 thf(is_per_type,type,
% 1.90/1.44 isPer:
% 1.90/1.44 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 1.90/1.44
% 1.90/1.44 thf(is_per,definition,
% 1.90/1.44 ! [A: $tType,AStar: A > A > $o] :
% 1.90/1.44 ( ( isPer @ A @ AStar )
% 1.90/1.44 <=> ( ! [X: A,Y: A] :
% 1.90/1.44 ( ( AStar @ X @ Y )
% 1.90/1.44 => ( AStar @ Y @ X ) )
% 1.90/1.44 & ! [X: A,Y: A,Z: A] :
% 1.90/1.44 ( ( AStar @ X @ Y )
% 1.90/1.44 => ( ( AStar @ Y @ Z )
% 1.90/1.44 => ( AStar @ X @ Z ) ) ) ) ) ).
% 1.90/1.44
% 1.90/1.44 thf(elem_type,type,
% 1.90/1.44 elem: $tType ).
% 1.90/1.44
% 1.90/1.44 thf(elemStar,type,
% 1.90/1.44 elemStar: elem > elem > $o ).
% 1.90/1.44
% 1.90/1.44 thf(elemStar_is_eq,axiom,
% 1.90/1.44 ! [X: elem,Y: elem] :
% 1.90/1.44 ( ( elemStar @ X @ Y )
% 1.90/1.44 <=> ( X = Y ) ) ).
% 1.90/1.44
% 1.90/1.44 thf(nat_type,type,
% 1.90/1.44 nat: $tType ).
% 1.90/1.44
% 1.90/1.44 thf(natStar,type,
% 1.90/1.44 natStar: nat > nat > $o ).
% 1.90/1.44
% 1.90/1.44 thf(natStar_is_eq,axiom,
% 1.90/1.44 ! [X: nat,Y: nat] :
% 1.90/1.44 ( ( natStar @ X @ Y )
% 1.90/1.44 <=> ( X = Y ) ) ).
% 1.90/1.44
% 1.90/1.44 thf(zero_type,type,
% 1.90/1.44 zero: nat ).
% 1.90/1.44
% 1.90/1.44 thf(suc_type,type,
% 1.90/1.44 suc: nat > nat ).
% 1.90/1.44
% 1.90/1.44 thf(plus_type,type,
% 1.90/1.44 plus: nat > nat > nat ).
% 1.90/1.44
% 1.90/1.44 thf(list_type,type,
% 1.90/1.44 list: $tType ).
% 1.90/1.44
% 1.90/1.44 thf(listStar,type,
% 1.90/1.44 listStar: nat > list > list > $o ).
% 1.90/1.44
% 1.90/1.44 thf('\'listStar\'_is_per',axiom,
% 1.90/1.44 ! [C: nat] : ( isPer @ list @ ( listStar @ C ) ) ).
% 1.90/1.44
% 1.90/1.44 thf(nil_type,type,
% 1.90/1.44 nil: list ).
% 1.90/1.44
% 1.90/1.44 thf(nil_tp_ax,axiom,
% 1.90/1.44 listStar @ zero @ nil @ nil ).
% 1.90/1.44
% 1.90/1.44 thf(cons_type,type,
% 1.90/1.44 cons: nat > elem > list > list ).
% 1.90/1.44
% 1.90/1.44 thf(cons_tp_ax,axiom,
% 1.90/1.44 ! [N: nat,D: elem,D0: list,D0_prime: list] :
% 1.90/1.44 ( ( listStar @ N @ D0 @ D0_prime )
% 1.90/1.44 => ( listStar @ ( suc @ N ) @ ( cons @ N @ D @ D0 ) @ ( cons @ N @ D @ D0_prime ) ) ) ).
% 1.90/1.44
% 1.90/1.44 thf(app_type,type,
% 1.90/1.44 app: nat > nat > list > list > list ).
% 1.90/1.44
% 1.90/1.44 thf(app_tp_ax,axiom,
% 1.90/1.44 ! [N: nat,M: nat,D: list,D_prime: list] :
% 1.90/1.44 ( ( listStar @ N @ D @ D_prime )
% 1.90/1.44 => ! [D0: list,D0_prime: list] :
% 1.90/1.44 ( ( listStar @ M @ D0 @ D0_prime )
% 1.90/1.44 => ( listStar @ ( plus @ N @ M ) @ ( app @ N @ M @ D @ D0 ) @ ( app @ N @ M @ D_prime @ D0_prime ) ) ) ) ).
% 1.90/1.44
% 1.90/1.44 thf(rev_type,type,
% 1.90/1.44 rev: nat > list > list ).
% 1.90/1.44
% 1.90/1.44 thf(rev_tp_ax,axiom,
% 1.90/1.44 ! [N: nat,D: list,D_prime: list] :
% 1.90/1.44 ( ( listStar @ N @ D @ D_prime )
% 1.90/1.44 => ( listStar @ N @ ( rev @ N @ D ) @ ( rev @ N @ D_prime ) ) ) ).
% 1.90/1.44
% 1.90/1.44 thf(peano1,axiom,
% 1.90/1.44 ! [N: nat] :
% 1.90/1.44 ( ( suc @ N )
% 1.90/1.44 != zero ) ).
% 1.90/1.44
% 1.90/1.44 thf(peano2,axiom,
% 1.90/1.44 ! [N: nat,M: nat] :
% 1.90/1.44 ( ( N != M )
% 1.90/1.44 => ( ( suc @ N )
% 1.90/1.44 != ( suc @ M ) ) ) ).
% 1.90/1.44
% 1.90/1.44 thf(peano3,axiom,
% 1.90/1.44 ! [P: nat > $o] :
% 1.90/1.44 ( ( P @ zero )
% 1.90/1.44 => ( ! [M: nat] :
% 1.90/1.44 ( ( P @ M )
% 1.90/1.44 => ( P @ ( suc @ M ) ) )
% 1.90/1.44 => ! [N: nat] : ( P @ N ) ) ) ).
% 1.90/1.44
% 1.90/1.44 thf(ax1,axiom,
% 1.90/1.44 ! [N: nat] :
% 1.90/1.44 ( ( plus @ zero @ N )
% 1.90/1.44 = N ) ).
% 1.90/1.44
% 1.90/1.44 thf(ax2,axiom,
% 1.90/1.44 ! [N: nat,M: nat] :
% 1.90/1.44 ( ( plus @ ( suc @ N ) @ M )
% 1.90/1.44 = ( suc @ ( plus @ N @ M ) ) ) ).
% 1.90/1.44
% 1.90/1.44 thf(ax3,axiom,
% 1.90/1.44 ! [N: nat,X: list] :
% 1.90/1.44 ( ( listStar @ N @ X @ X )
% 1.90/1.44 => ( listStar @ ( plus @ zero @ N ) @ ( app @ zero @ N @ nil @ X ) @ X ) ) ).
% 1.90/1.44
% 1.90/1.44 thf(ax4,axiom,
% 1.90/1.44 ! [N: nat,M: nat,X: elem,Y: list,Z: list] :
% 1.90/1.44 ( ( listStar @ N @ Y @ Y )
% 1.90/1.44 => ( ( listStar @ M @ Z @ Z )
% 1.90/1.44 => ( listStar @ ( plus @ ( suc @ N ) @ M ) @ ( app @ ( suc @ N ) @ M @ ( cons @ N @ X @ Y ) @ Z ) @ ( cons @ ( plus @ N @ M ) @ X @ ( app @ N @ M @ Y @ Z ) ) ) ) ) ).
% 1.90/1.45
% 1.90/1.45 thf(ax5,axiom,
% 1.90/1.45 listStar @ zero @ ( rev @ zero @ nil ) @ nil ).
% 1.90/1.45
% 1.90/1.45 thf(ax6,axiom,
% 1.90/1.45 ! [N: nat,X: elem,Y: list] :
% 1.90/1.45 ( ( listStar @ N @ Y @ Y )
% 1.90/1.45 => ( listStar @ ( suc @ N ) @ ( rev @ ( suc @ N ) @ ( cons @ N @ X @ Y ) ) @ ( app @ N @ ( suc @ zero ) @ ( rev @ N @ Y ) @ ( cons @ zero @ X @ nil ) ) ) ) ).
% 1.90/1.45
% 1.90/1.45 thf(plus_com,axiom,
% 1.90/1.45 ! [N: nat,M: nat] :
% 1.90/1.45 ( ( plus @ N @ M )
% 1.90/1.45 = ( plus @ M @ N ) ) ).
% 1.90/1.45
% 1.90/1.45 thf(plus1r,axiom,
% 1.90/1.45 ! [N: nat] :
% 1.90/1.45 ( ( suc @ N )
% 1.90/1.45 = ( plus @ N @ ( suc @ zero ) ) ) ).
% 1.90/1.45
% 1.90/1.45 thf(list_rev_invol_lem_indinst,axiom,
% 1.90/1.45 ( ! [M2: nat,L2: list] :
% 1.90/1.45 ( ( listStar @ M2 @ L2 @ L2 )
% 1.90/1.45 => ( listStar @ ( plus @ zero @ M2 ) @ ( rev @ ( plus @ zero @ M2 ) @ ( app @ zero @ M2 @ ( rev @ zero @ nil ) @ L2 ) ) @ ( app @ M2 @ zero @ ( rev @ M2 @ L2 ) @ nil ) ) )
% 1.90/1.45 => ( ! [N: nat,X: elem,L: list] :
% 1.90/1.45 ( ( listStar @ N @ L @ L )
% 1.90/1.45 => ( ! [M2: nat,L2: list] :
% 1.90/1.45 ( ( listStar @ M2 @ L2 @ L2 )
% 1.90/1.45 => ( listStar @ ( plus @ N @ M2 ) @ ( rev @ ( plus @ N @ M2 ) @ ( app @ N @ M2 @ ( rev @ N @ L ) @ L2 ) ) @ ( app @ M2 @ N @ ( rev @ M2 @ L2 ) @ L ) ) )
% 1.90/1.45 => ! [M2: nat,L2: list] :
% 1.90/1.45 ( ( listStar @ M2 @ L2 @ L2 )
% 1.90/1.45 => ( listStar @ ( plus @ ( suc @ N ) @ M2 ) @ ( rev @ ( plus @ ( suc @ N ) @ M2 ) @ ( app @ ( suc @ N ) @ M2 @ ( rev @ ( suc @ N ) @ ( cons @ N @ X @ L ) ) @ L2 ) ) @ ( app @ M2 @ ( suc @ N ) @ ( rev @ M2 @ L2 ) @ ( cons @ N @ X @ L ) ) ) ) ) )
% 1.90/1.45 => ! [N: nat,L: list,M2: nat,L2: list] :
% 1.90/1.45 ( ( listStar @ N @ L @ L )
% 1.90/1.45 => ( ( listStar @ M2 @ L2 @ L2 )
% 1.90/1.45 => ( listStar @ ( plus @ N @ M2 ) @ ( rev @ ( plus @ N @ M2 ) @ ( app @ N @ M2 @ ( rev @ N @ L ) @ L2 ) ) @ ( app @ M2 @ N @ ( rev @ M2 @ L2 ) @ L ) ) ) ) ) ) ).
% 1.90/1.45
% 1.90/1.45 thf(list_rev_invol_lem_base,axiom,
% 1.90/1.45 ! [M2: nat,L2: list] :
% 1.90/1.45 ( ( listStar @ M2 @ L2 @ L2 )
% 1.90/1.45 => ( listStar @ ( plus @ zero @ M2 ) @ ( rev @ ( plus @ zero @ M2 ) @ ( app @ zero @ M2 @ ( rev @ zero @ nil ) @ L2 ) ) @ ( app @ M2 @ zero @ ( rev @ M2 @ L2 ) @ nil ) ) ) ).
% 1.90/1.45
% 1.90/1.45 thf(list_rev_invol_lem_indstep,axiom,
% 1.90/1.45 ! [N: nat,X: elem,L: list] :
% 1.90/1.45 ( ( listStar @ N @ L @ L )
% 1.90/1.45 => ( ! [M2: nat,L2: list] :
% 1.90/1.45 ( ( listStar @ M2 @ L2 @ L2 )
% 1.90/1.45 => ( listStar @ ( plus @ N @ M2 ) @ ( rev @ ( plus @ N @ M2 ) @ ( app @ N @ M2 @ ( rev @ N @ L ) @ L2 ) ) @ ( app @ M2 @ N @ ( rev @ M2 @ L2 ) @ L ) ) )
% 1.90/1.45 => ! [M2: nat,L2: list] :
% 1.90/1.45 ( ( listStar @ M2 @ L2 @ L2 )
% 1.90/1.45 => ( listStar @ ( plus @ ( suc @ N ) @ M2 ) @ ( rev @ ( plus @ ( suc @ N ) @ M2 ) @ ( app @ ( suc @ N ) @ M2 @ ( rev @ ( suc @ N ) @ ( cons @ N @ X @ L ) ) @ L2 ) ) @ ( app @ M2 @ ( suc @ N ) @ ( rev @ M2 @ L2 ) @ ( cons @ N @ X @ L ) ) ) ) ) ) ).
% 1.90/1.45
% 1.90/1.45 thf(list_rev_invol_lem,conjecture,
% 1.90/1.45 ! [N: nat,L: list,M2: nat,L2: list] :
% 1.90/1.45 ( ( listStar @ N @ L @ L )
% 1.90/1.45 => ( ( listStar @ M2 @ L2 @ L2 )
% 1.90/1.45 => ( listStar @ ( plus @ N @ M2 ) @ ( rev @ ( plus @ N @ M2 ) @ ( app @ N @ M2 @ ( rev @ N @ L ) @ L2 ) ) @ ( app @ M2 @ N @ ( rev @ M2 @ L2 ) @ L ) ) ) ) ).
% 1.90/1.45 ------------------------
% 1.90/1.47 % (4057)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_3850 for (2999ds/275Mi)
% 1.90/1.47 % (4054)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_3850 for (2999ds/27Mi)
% 1.90/1.47 % (4055)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3850 for (2999ds/2Mi)
% 1.90/1.47 % (4055)Instruction limit reached!
% 1.90/1.47 % (4055)------------------------------
% 1.90/1.47 % (4055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/1.47 % (4055)Termination reason: Unknown
% 1.90/1.47 % (4055)Termination phase: shuffling
% 1.90/1.47
% 1.90/1.47 % (4055)Memory used [KB]: 1023
% 1.90/1.47 % (4055)Time elapsed: 0.002 s
% 1.90/1.47 % (4055)Instructions burned: 2 (million)
% 1.90/1.47 % (4055)------------------------------
% 1.90/1.47 % (4055)------------------------------
% 1.90/1.47 % (4052)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3850 for (2999ds/183Mi)
% 1.90/1.47 % (4057)Refutation not found, incomplete strategy
% 1.90/1.47 % (4057)------------------------------
% 1.90/1.47 % (4057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/1.47 % (4057)Termination reason: Refutation not found, incomplete strategy
% 1.90/1.47
% 1.90/1.47
% 1.90/1.47 % (4057)Memory used [KB]: 5628
% 1.90/1.47 % (4057)Time elapsed: 0.005 s
% 1.90/1.47 % (4057)Instructions burned: 10 (million)
% 1.90/1.47 % (4057)------------------------------
% 1.90/1.47 % (4057)------------------------------
% 1.90/1.48 % (4054)Instruction limit reached!
% 1.90/1.48 % (4054)------------------------------
% 1.90/1.48 % (4054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/1.48 % (4054)Termination reason: Unknown
% 1.90/1.48 % (4054)Termination phase: Saturation
% 1.90/1.48
% 1.90/1.48 % (4054)Memory used [KB]: 5756
% 1.90/1.48 % (4054)Time elapsed: 0.010 s
% 1.90/1.48 % (4054)Instructions burned: 27 (million)
% 1.90/1.48 % (4054)------------------------------
% 1.90/1.48 % (4054)------------------------------
% 1.90/1.48 % (4058)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3850 for (2999ds/18Mi)
% 1.90/1.48 % (4053)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_3850 for (2999ds/4Mi)
% 1.90/1.48 % (4056)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_3850 for (2999ds/2Mi)
% 1.90/1.48 % (4056)Instruction limit reached!
% 1.90/1.48 % (4056)------------------------------
% 1.90/1.48 % (4056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/1.48 % (4056)Termination reason: Unknown
% 1.90/1.48 % (4056)Termination phase: shuffling
% 1.90/1.48
% 1.90/1.48 % (4056)Memory used [KB]: 1023
% 1.90/1.48 % (4056)Time elapsed: 0.004 s
% 1.90/1.48 % (4056)Instructions burned: 2 (million)
% 1.90/1.48 % (4056)------------------------------
% 1.90/1.48 % (4056)------------------------------
% 1.90/1.48 % (4053)Instruction limit reached!
% 1.90/1.48 % (4053)------------------------------
% 1.90/1.48 % (4053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/1.48 % (4053)Termination reason: Unknown
% 1.90/1.48 % (4053)Termination phase: shuffling
% 1.90/1.48
% 1.90/1.48 % (4053)Memory used [KB]: 1023
% 1.90/1.48 % (4053)Time elapsed: 0.006 s
% 1.90/1.48 % (4053)Instructions burned: 4 (million)
% 1.90/1.48 % (4053)------------------------------
% 1.90/1.48 % (4053)------------------------------
% 1.90/1.49 % (4063)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_3850 for (2999ds/37Mi)
% 1.90/1.49 % (4064)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_3850 for (2999ds/15Mi)
% 1.90/1.49 % (4062)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3850 for (2999ds/3Mi)
% 1.90/1.49 % (4062)Instruction limit reached!
% 1.90/1.49 % (4062)------------------------------
% 1.90/1.49 % (4062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/1.49 % (4062)Termination reason: Unknown
% 1.90/1.49 % (4062)Termination phase: shuffling
% 1.90/1.49
% 1.90/1.49 % (4062)Memory used [KB]: 1023
% 1.90/1.49 % (4062)Time elapsed: 0.003 s
% 1.90/1.49 % (4062)Instructions burned: 4 (million)
% 1.90/1.49 % (4062)------------------------------
% 1.90/1.49 % (4062)------------------------------
% 1.90/1.49 % (4058)Instruction limit reached!
% 1.90/1.49 % (4058)------------------------------
% 1.90/1.49 % (4058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/1.49 % (4058)Termination reason: Unknown
% 1.90/1.49 % (4058)Termination phase: Saturation
% 1.90/1.49
% 1.90/1.49 % (4058)Memory used [KB]: 5628
% 1.90/1.49 % (4058)Time elapsed: 0.015 s
% 1.90/1.49 % (4058)Instructions burned: 18 (million)
% 1.90/1.49 % (4058)------------------------------
% 1.90/1.49 % (4058)------------------------------
% 1.90/1.49 % (4064)Instruction limit reached!
% 1.90/1.49 % (4064)------------------------------
% 1.90/1.49 % (4064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.90/1.49 % (4064)Termination reason: Unknown
% 1.90/1.49 % (4064)Termination phase: Property scanning
% 1.90/1.49
% 1.90/1.49 % (4064)Memory used [KB]: 1151
% 1.90/1.49 % (4064)Time elapsed: 0.008 s
% 1.90/1.49 % (4064)Instructions burned: 15 (million)
% 1.90/1.49 % (4064)------------------------------
% 1.90/1.49 % (4064)------------------------------
% 2.00/1.50 % (4063)Instruction limit reached!
% 2.00/1.50 % (4063)------------------------------
% 2.00/1.50 % (4063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.00/1.50 % (4063)Termination reason: Unknown
% 2.00/1.50 % (4063)Termination phase: Saturation
% 2.00/1.50
% 2.00/1.50 % (4063)Memory used [KB]: 5884
% 2.00/1.50 % (4063)Time elapsed: 0.013 s
% 2.00/1.50 % (4063)Instructions burned: 38 (million)
% 2.00/1.50 % (4063)------------------------------
% 2.00/1.50 % (4063)------------------------------
% 2.00/1.51 % (4070)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3850 for (2999ds/16Mi)
% 2.00/1.51 % (4071)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_3850 for (2999ds/3Mi)
% 2.00/1.51 % (4071)Instruction limit reached!
% 2.00/1.51 % (4071)------------------------------
% 2.00/1.51 % (4071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.00/1.51 % (4071)Termination reason: Unknown
% 2.00/1.51 % (4071)Termination phase: shuffling
% 2.00/1.51
% 2.00/1.51 % (4071)Memory used [KB]: 1023
% 2.00/1.51 % (4071)Time elapsed: 0.003 s
% 2.00/1.51 % (4071)Instructions burned: 4 (million)
% 2.00/1.51 % (4071)------------------------------
% 2.00/1.51 % (4071)------------------------------
% 2.00/1.51 % (4067)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_3850 for (2999ds/3Mi)
% 2.00/1.51 % (4067)Instruction limit reached!
% 2.00/1.51 % (4067)------------------------------
% 2.00/1.51 % (4067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.00/1.51 % (4067)Termination reason: Unknown
% 2.00/1.51 % (4067)Termination phase: shuffling
% 2.00/1.51
% 2.00/1.51 % (4067)Memory used [KB]: 1023
% 2.00/1.51 % (4067)Time elapsed: 0.004 s
% 2.00/1.51 % (4067)Instructions burned: 3 (million)
% 2.00/1.51 % (4067)------------------------------
% 2.00/1.51 % (4067)------------------------------
% 2.00/1.51 % (4070)Instruction limit reached!
% 2.00/1.51 % (4070)------------------------------
% 2.00/1.51 % (4070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.00/1.51 % (4070)Termination reason: Unknown
% 2.00/1.51 % (4070)Termination phase: Property scanning
% 2.00/1.51
% 2.00/1.51 % (4070)Memory used [KB]: 1151
% 2.00/1.51 % (4070)Time elapsed: 0.009 s
% 2.00/1.51 % (4070)Instructions burned: 17 (million)
% 2.00/1.51 % (4070)------------------------------
% 2.00/1.51 % (4070)------------------------------
% 2.00/1.51 % (4069)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3850 for (2999ds/7Mi)
% 2.00/1.51 % (4068)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_3850 for (2999ds/1041Mi)
% 2.00/1.52 % (4069)Instruction limit reached!
% 2.00/1.52 % (4069)------------------------------
% 2.00/1.52 % (4069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.00/1.52 % (4069)Termination reason: Unknown
% 2.00/1.52 % (4069)Termination phase: Property scanning
% 2.00/1.52
% 2.00/1.52 % (4069)Memory used [KB]: 1023
% 2.00/1.52 % (4069)Time elapsed: 0.005 s
% 2.00/1.52 % (4069)Instructions burned: 7 (million)
% 2.00/1.52 % (4069)------------------------------
% 2.00/1.52 % (4069)------------------------------
% 2.00/1.53 % (4073)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_3850 for (2999ds/3Mi)
% 2.00/1.53 % (4078)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3850 for (2999ds/7Mi)
% 2.00/1.53 % (4073)Instruction limit reached!
% 2.00/1.53 % (4073)------------------------------
% 2.00/1.53 % (4073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.00/1.53 % (4073)Termination reason: Unknown
% 2.00/1.53 % (4073)Termination phase: shuffling
% 2.00/1.53
% 2.00/1.53 % (4073)Memory used [KB]: 1023
% 2.00/1.53 % (4073)Time elapsed: 0.004 s
% 2.00/1.53 % (4073)Instructions burned: 3 (million)
% 2.00/1.53 % (4073)------------------------------
% 2.00/1.53 % (4073)------------------------------
% 2.00/1.53 % (4080)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3850 for (2999ds/4Mi)
% 2.00/1.53 % (4080)Instruction limit reached!
% 2.00/1.53 % (4080)------------------------------
% 2.00/1.53 % (4080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.00/1.53 % (4080)Termination reason: Unknown
% 2.00/1.53 % (4080)Termination phase: shuffling
% 2.00/1.53
% 2.00/1.53 % (4080)Memory used [KB]: 1023
% 2.00/1.53 % (4080)Time elapsed: 0.003 s
% 2.00/1.53 % (4080)Instructions burned: 4 (million)
% 2.00/1.53 % (4080)------------------------------
% 2.00/1.53 % (4080)------------------------------
% 2.00/1.53 % (4078)Instruction limit reached!
% 2.00/1.53 % (4078)------------------------------
% 2.00/1.53 % (4078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.00/1.53 % (4078)Termination reason: Unknown
% 2.00/1.53 % (4078)Termination phase: Preprocessing 3
% 2.00/1.53
% 2.00/1.53 % (4078)Memory used [KB]: 1023
% 2.00/1.53 % (4078)Time elapsed: 0.006 s
% 2.00/1.53 % (4078)Instructions burned: 8 (million)
% 2.00/1.53 % (4078)------------------------------
% 2.00/1.53 % (4078)------------------------------
% 2.00/1.53 % (4068)First to succeed.
% 2.00/1.53 % (4081)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3850 for (2999ds/18Mi)
% 2.00/1.53 % (4079)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3850 for (2999ds/3Mi)
% 2.00/1.54 % (4079)Instruction limit reached!
% 2.00/1.54 % (4079)------------------------------
% 2.00/1.54 % (4079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.00/1.54 % (4079)Termination reason: Unknown
% 2.00/1.54 % (4079)Termination phase: shuffling
% 2.00/1.54
% 2.00/1.54 % (4079)Memory used [KB]: 1023
% 2.00/1.54 % (4079)Time elapsed: 0.003 s
% 2.00/1.54 % (4079)Instructions burned: 3 (million)
% 2.00/1.54 % (4079)------------------------------
% 2.00/1.54 % (4079)------------------------------
% 2.00/1.54 % (4068)Refutation found. Thanks to Tanya!
% 2.00/1.54 % SZS status Theorem for DTF2THF_3850
% 2.00/1.54 % SZS output start Proof for DTF2THF_3850
% 2.00/1.54 thf(type_def_6, type, elem: $tType).
% 2.00/1.54 thf(type_def_7, type, nat: $tType).
% 2.00/1.54 thf(type_def_8, type, list: $tType).
% 2.00/1.54 thf(func_def_0, type, isPer: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 2.00/1.54 thf(func_def_2, type, elem: $tType).
% 2.00/1.54 thf(func_def_3, type, elemStar: elem > elem > $o).
% 2.00/1.54 thf(func_def_4, type, nat: $tType).
% 2.00/1.54 thf(func_def_5, type, natStar: nat > nat > $o).
% 2.00/1.54 thf(func_def_6, type, zero: nat).
% 2.00/1.54 thf(func_def_7, type, suc: nat > nat).
% 2.00/1.54 thf(func_def_8, type, plus: nat > nat > nat).
% 2.00/1.54 thf(func_def_9, type, list: $tType).
% 2.00/1.54 thf(func_def_10, type, listStar: nat > list > list > $o).
% 2.00/1.54 thf(func_def_11, type, nil: list).
% 2.00/1.54 thf(func_def_12, type, cons: nat > elem > list > list).
% 2.00/1.54 thf(func_def_13, type, app: nat > nat > list > list > list).
% 2.00/1.54 thf(func_def_14, type, rev: nat > list > list).
% 2.00/1.54 thf(f103,plain,(
% 2.00/1.54 $false),
% 2.00/1.54 inference(trivial_inequality_removal,[status(thm)],[f102])).
% 2.00/1.54 thf(f102,plain,(
% 2.00/1.54 ($false = $true)),
% 2.00/1.54 inference(boolean_simplification,[status(thm)],[f101])).
% 2.00/1.54 thf(f101,plain,(
% 2.00/1.54 ((~ $true) = $true)),
% 2.00/1.54 inference(backward_demodulation,[status(thm)],[f83,f100])).
% 2.00/1.54 thf(f100,plain,(
% 2.00/1.54 ((!! @ list @ (^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: (!! @ list @ (^[Y2 : list]: (!! @ nat @ (^[Y3 : nat]: ((listStar @ Y3 @ Y2 @ Y2) => ((listStar @ Y1 @ Y0 @ Y0) => (listStar @ (plus @ Y3 @ Y1) @ (rev @ (plus @ Y3 @ Y1) @ (app @ Y3 @ Y1 @ (rev @ Y3 @ Y2) @ Y0)) @ (app @ Y1 @ Y3 @ (rev @ Y1 @ Y0) @ Y2)))))))))))) = $true)),
% 2.00/1.54 inference(boolean_simplification,[status(thm)],[f99])).
% 2.00/1.54 thf(f99,plain,(
% 2.00/1.54 (($true => (!! @ list @ (^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: (!! @ list @ (^[Y2 : list]: (!! @ nat @ (^[Y3 : nat]: ((listStar @ Y3 @ Y2 @ Y2) => ((listStar @ Y1 @ Y0 @ Y0) => (listStar @ (plus @ Y3 @ Y1) @ (rev @ (plus @ Y3 @ Y1) @ (app @ Y3 @ Y1 @ (rev @ Y3 @ Y2) @ Y0)) @ (app @ Y1 @ Y3 @ (rev @ Y1 @ Y0) @ Y2))))))))))))) = $true)),
% 2.00/1.54 inference(forward_demodulation,[status(thm)],[f98,f76])).
% 2.00/1.54 thf(f76,plain,(
% 2.00/1.54 ((!! @ list @ (^[Y0 : list]: (!! @ elem @ (^[Y1 : elem]: (!! @ nat @ (^[Y2 : nat]: ((listStar @ Y2 @ Y0 @ Y0) => ((!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: ((listStar @ Y4 @ Y3 @ Y3) => (listStar @ (plus @ Y2 @ Y4) @ (rev @ (plus @ Y2 @ Y4) @ (app @ Y2 @ Y4 @ (rev @ Y2 @ Y0) @ Y3)) @ (app @ Y4 @ Y2 @ (rev @ Y4 @ Y3) @ Y0))))))) => (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: ((listStar @ Y4 @ Y3 @ Y3) => (listStar @ (plus @ (suc @ Y2) @ Y4) @ (rev @ (plus @ (suc @ Y2) @ Y4) @ (app @ (suc @ Y2) @ Y4 @ (rev @ (suc @ Y2) @ (cons @ Y2 @ Y1 @ Y0)) @ Y3)) @ (app @ Y4 @ (suc @ Y2) @ (rev @ Y4 @ Y3) @ (cons @ Y2 @ Y1 @ Y0)))))))))))))))) = $true)),
% 2.00/1.54 inference(cnf_transformation,[status(thm)],[f55])).
% 2.00/1.54 thf(f55,plain,(
% 2.00/1.54 ((!! @ list @ (^[Y0 : list]: (!! @ elem @ (^[Y1 : elem]: (!! @ nat @ (^[Y2 : nat]: ((listStar @ Y2 @ Y0 @ Y0) => ((!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: ((listStar @ Y4 @ Y3 @ Y3) => (listStar @ (plus @ Y2 @ Y4) @ (rev @ (plus @ Y2 @ Y4) @ (app @ Y2 @ Y4 @ (rev @ Y2 @ Y0) @ Y3)) @ (app @ Y4 @ Y2 @ (rev @ Y4 @ Y3) @ Y0))))))) => (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: ((listStar @ Y4 @ Y3 @ Y3) => (listStar @ (plus @ (suc @ Y2) @ Y4) @ (rev @ (plus @ (suc @ Y2) @ Y4) @ (app @ (suc @ Y2) @ Y4 @ (rev @ (suc @ Y2) @ (cons @ Y2 @ Y1 @ Y0)) @ Y3)) @ (app @ Y4 @ (suc @ Y2) @ (rev @ Y4 @ Y3) @ (cons @ Y2 @ Y1 @ Y0)))))))))))))))) = $true)),
% 2.00/1.54 inference(fool_elimination,[status(thm)],[f54])).
% 2.00/1.54 thf(f54,plain,(
% 2.00/1.54 ! [X0 : nat,X1 : elem,X2 : list] : ((listStar @ X0 @ X2 @ X2) => (! [X3 : nat,X4 : list] : ((listStar @ X3 @ X4 @ X4) => (listStar @ (plus @ X0 @ X3) @ (rev @ (plus @ X0 @ X3) @ (app @ X0 @ X3 @ (rev @ X0 @ X2) @ X4)) @ (app @ X3 @ X0 @ (rev @ X3 @ X4) @ X2))) => ! [X5 : nat,X6 : list] : ((listStar @ X5 @ X6 @ X6) => (listStar @ (plus @ (suc @ X0) @ X5) @ (rev @ (plus @ (suc @ X0) @ X5) @ (app @ (suc @ X0) @ X5 @ (rev @ (suc @ X0) @ (cons @ X0 @ X1 @ X2)) @ X6)) @ (app @ X5 @ (suc @ X0) @ (rev @ X5 @ X6) @ (cons @ X0 @ X1 @ X2))))))),
% 2.00/1.54 inference(rectify,[status(thm)],[f22])).
% 2.00/1.54 thf(f22,axiom,(
% 2.00/1.54 ! [X6 : nat,X2 : elem,X15 : list] : ((listStar @ X6 @ X15 @ X15) => (! [X13 : nat,X14 : list] : ((listStar @ X13 @ X14 @ X14) => (listStar @ (plus @ X6 @ X13) @ (rev @ (plus @ X6 @ X13) @ (app @ X6 @ X13 @ (rev @ X6 @ X15) @ X14)) @ (app @ X13 @ X6 @ (rev @ X13 @ X14) @ X15))) => ! [X13 : nat,X14 : list] : ((listStar @ X13 @ X14 @ X14) => (listStar @ (plus @ (suc @ X6) @ X13) @ (rev @ (plus @ (suc @ X6) @ X13) @ (app @ (suc @ X6) @ X13 @ (rev @ (suc @ X6) @ (cons @ X6 @ X2 @ X15)) @ X14)) @ (app @ X13 @ (suc @ X6) @ (rev @ X13 @ X14) @ (cons @ X6 @ X2 @ X15))))))),
% 2.00/1.54 file('/export/starexec/sandbox/tmp/tmp.K4a8wmNMBS/DTF2THF_3850.p',list_rev_invol_lem_indstep)).
% 2.00/1.54 thf(f98,plain,(
% 2.00/1.54 (((!! @ list @ (^[Y0 : list]: (!! @ elem @ (^[Y1 : elem]: (!! @ nat @ (^[Y2 : nat]: ((listStar @ Y2 @ Y0 @ Y0) => ((!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: ((listStar @ Y4 @ Y3 @ Y3) => (listStar @ (plus @ Y2 @ Y4) @ (rev @ (plus @ Y2 @ Y4) @ (app @ Y2 @ Y4 @ (rev @ Y2 @ Y0) @ Y3)) @ (app @ Y4 @ Y2 @ (rev @ Y4 @ Y3) @ Y0))))))) => (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: ((listStar @ Y4 @ Y3 @ Y3) => (listStar @ (plus @ (suc @ Y2) @ Y4) @ (rev @ (plus @ (suc @ Y2) @ Y4) @ (app @ (suc @ Y2) @ Y4 @ (rev @ (suc @ Y2) @ (cons @ Y2 @ Y1 @ Y0)) @ Y3)) @ (app @ Y4 @ (suc @ Y2) @ (rev @ Y4 @ Y3) @ (cons @ Y2 @ Y1 @ Y0)))))))))))))))) => (!! @ list @ (^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: (!! @ list @ (^[Y2 : list]: (!! @ nat @ (^[Y3 : nat]: ((listStar @ Y3 @ Y2 @ Y2) => ((listStar @ Y1 @ Y0 @ Y0) => (listStar @ (plus @ Y3 @ Y1) @ (rev @ (plus @ Y3 @ Y1) @ (app @ Y3 @ Y1 @ (rev @ Y3 @ Y2) @ Y0)) @ (app @ Y1 @ Y3 @ (rev @ Y1 @ Y0) @ Y2))))))))))))) = $true)),
% 2.00/1.54 inference(boolean_simplification,[status(thm)],[f97])).
% 2.00/1.54 thf(f97,plain,(
% 2.00/1.54 (($true => ((!! @ list @ (^[Y0 : list]: (!! @ elem @ (^[Y1 : elem]: (!! @ nat @ (^[Y2 : nat]: ((listStar @ Y2 @ Y0 @ Y0) => ((!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: ((listStar @ Y4 @ Y3 @ Y3) => (listStar @ (plus @ Y2 @ Y4) @ (rev @ (plus @ Y2 @ Y4) @ (app @ Y2 @ Y4 @ (rev @ Y2 @ Y0) @ Y3)) @ (app @ Y4 @ Y2 @ (rev @ Y4 @ Y3) @ Y0))))))) => (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: ((listStar @ Y4 @ Y3 @ Y3) => (listStar @ (plus @ (suc @ Y2) @ Y4) @ (rev @ (plus @ (suc @ Y2) @ Y4) @ (app @ (suc @ Y2) @ Y4 @ (rev @ (suc @ Y2) @ (cons @ Y2 @ Y1 @ Y0)) @ Y3)) @ (app @ Y4 @ (suc @ Y2) @ (rev @ Y4 @ Y3) @ (cons @ Y2 @ Y1 @ Y0)))))))))))))))) => (!! @ list @ (^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: (!! @ list @ (^[Y2 : list]: (!! @ nat @ (^[Y3 : nat]: ((listStar @ Y3 @ Y2 @ Y2) => ((listStar @ Y1 @ Y0 @ Y0) => (listStar @ (plus @ Y3 @ Y1) @ (rev @ (plus @ Y3 @ Y1) @ (app @ Y3 @ Y1 @ (rev @ Y3 @ Y2) @ Y0)) @ (app @ Y1 @ Y3 @ (rev @ Y1 @ Y0) @ Y2)))))))))))))) = $true)),
% 2.00/1.54 inference(forward_demodulation,[status(thm)],[f75,f78])).
% 2.00/1.54 thf(f78,plain,(
% 2.00/1.54 ((!! @ list @ (^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ Y1 @ Y0 @ Y0) => (listStar @ (plus @ zero @ Y1) @ (rev @ (plus @ zero @ Y1) @ (app @ zero @ Y1 @ (rev @ zero @ nil) @ Y0)) @ (app @ Y1 @ zero @ (rev @ Y1 @ Y0) @ nil))))))) = $true)),
% 2.00/1.54 inference(cnf_transformation,[status(thm)],[f59])).
% 2.00/1.54 thf(f59,plain,(
% 2.00/1.54 ((!! @ list @ (^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ Y1 @ Y0 @ Y0) => (listStar @ (plus @ zero @ Y1) @ (rev @ (plus @ zero @ Y1) @ (app @ zero @ Y1 @ (rev @ zero @ nil) @ Y0)) @ (app @ Y1 @ zero @ (rev @ Y1 @ Y0) @ nil))))))) = $true)),
% 2.00/1.54 inference(fool_elimination,[status(thm)],[f58])).
% 2.00/1.54 thf(f58,plain,(
% 2.00/1.54 ! [X0 : nat,X1 : list] : ((listStar @ X0 @ X1 @ X1) => (listStar @ (plus @ zero @ X0) @ (rev @ (plus @ zero @ X0) @ (app @ zero @ X0 @ (rev @ zero @ nil) @ X1)) @ (app @ X0 @ zero @ (rev @ X0 @ X1) @ nil)))),
% 2.00/1.54 inference(rectify,[status(thm)],[f21])).
% 2.00/1.54 thf(f21,axiom,(
% 2.00/1.54 ! [X13 : nat,X14 : list] : ((listStar @ X13 @ X14 @ X14) => (listStar @ (plus @ zero @ X13) @ (rev @ (plus @ zero @ X13) @ (app @ zero @ X13 @ (rev @ zero @ nil) @ X14)) @ (app @ X13 @ zero @ (rev @ X13 @ X14) @ nil)))),
% 2.00/1.54 file('/export/starexec/sandbox/tmp/tmp.K4a8wmNMBS/DTF2THF_3850.p',list_rev_invol_lem_base)).
% 2.00/1.54 thf(f75,plain,(
% 2.00/1.54 (((!! @ list @ (^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ Y1 @ Y0 @ Y0) => (listStar @ (plus @ zero @ Y1) @ (rev @ (plus @ zero @ Y1) @ (app @ zero @ Y1 @ (rev @ zero @ nil) @ Y0)) @ (app @ Y1 @ zero @ (rev @ Y1 @ Y0) @ nil))))))) => ((!! @ list @ (^[Y0 : list]: (!! @ elem @ (^[Y1 : elem]: (!! @ nat @ (^[Y2 : nat]: ((listStar @ Y2 @ Y0 @ Y0) => ((!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: ((listStar @ Y4 @ Y3 @ Y3) => (listStar @ (plus @ Y2 @ Y4) @ (rev @ (plus @ Y2 @ Y4) @ (app @ Y2 @ Y4 @ (rev @ Y2 @ Y0) @ Y3)) @ (app @ Y4 @ Y2 @ (rev @ Y4 @ Y3) @ Y0))))))) => (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: ((listStar @ Y4 @ Y3 @ Y3) => (listStar @ (plus @ (suc @ Y2) @ Y4) @ (rev @ (plus @ (suc @ Y2) @ Y4) @ (app @ (suc @ Y2) @ Y4 @ (rev @ (suc @ Y2) @ (cons @ Y2 @ Y1 @ Y0)) @ Y3)) @ (app @ Y4 @ (suc @ Y2) @ (rev @ Y4 @ Y3) @ (cons @ Y2 @ Y1 @ Y0)))))))))))))))) => (!! @ list @ (^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: (!! @ list @ (^[Y2 : list]: (!! @ nat @ (^[Y3 : nat]: ((listStar @ Y3 @ Y2 @ Y2) => ((listStar @ Y1 @ Y0 @ Y0) => (listStar @ (plus @ Y3 @ Y1) @ (rev @ (plus @ Y3 @ Y1) @ (app @ Y3 @ Y1 @ (rev @ Y3 @ Y2) @ Y0)) @ (app @ Y1 @ Y3 @ (rev @ Y1 @ Y0) @ Y2)))))))))))))) = $true)),
% 2.00/1.54 inference(cnf_transformation,[status(thm)],[f67])).
% 2.00/1.54 thf(f67,plain,(
% 2.00/1.54 (((!! @ list @ (^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ Y1 @ Y0 @ Y0) => (listStar @ (plus @ zero @ Y1) @ (rev @ (plus @ zero @ Y1) @ (app @ zero @ Y1 @ (rev @ zero @ nil) @ Y0)) @ (app @ Y1 @ zero @ (rev @ Y1 @ Y0) @ nil))))))) => ((!! @ list @ (^[Y0 : list]: (!! @ elem @ (^[Y1 : elem]: (!! @ nat @ (^[Y2 : nat]: ((listStar @ Y2 @ Y0 @ Y0) => ((!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: ((listStar @ Y4 @ Y3 @ Y3) => (listStar @ (plus @ Y2 @ Y4) @ (rev @ (plus @ Y2 @ Y4) @ (app @ Y2 @ Y4 @ (rev @ Y2 @ Y0) @ Y3)) @ (app @ Y4 @ Y2 @ (rev @ Y4 @ Y3) @ Y0))))))) => (!! @ list @ (^[Y3 : list]: (!! @ nat @ (^[Y4 : nat]: ((listStar @ Y4 @ Y3 @ Y3) => (listStar @ (plus @ (suc @ Y2) @ Y4) @ (rev @ (plus @ (suc @ Y2) @ Y4) @ (app @ (suc @ Y2) @ Y4 @ (rev @ (suc @ Y2) @ (cons @ Y2 @ Y1 @ Y0)) @ Y3)) @ (app @ Y4 @ (suc @ Y2) @ (rev @ Y4 @ Y3) @ (cons @ Y2 @ Y1 @ Y0)))))))))))))))) => (!! @ list @ (^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: (!! @ list @ (^[Y2 : list]: (!! @ nat @ (^[Y3 : nat]: ((listStar @ Y3 @ Y2 @ Y2) => ((listStar @ Y1 @ Y0 @ Y0) => (listStar @ (plus @ Y3 @ Y1) @ (rev @ (plus @ Y3 @ Y1) @ (app @ Y3 @ Y1 @ (rev @ Y3 @ Y2) @ Y0)) @ (app @ Y1 @ Y3 @ (rev @ Y1 @ Y0) @ Y2)))))))))))))) = $true)),
% 2.00/1.54 inference(fool_elimination,[status(thm)],[f66])).
% 2.00/1.54 thf(f66,plain,(
% 2.00/1.54 ! [X0 : nat,X1 : list] : ((listStar @ X0 @ X1 @ X1) => (listStar @ (plus @ zero @ X0) @ (rev @ (plus @ zero @ X0) @ (app @ zero @ X0 @ (rev @ zero @ nil) @ X1)) @ (app @ X0 @ zero @ (rev @ X0 @ X1) @ nil))) => (! [X2 : nat,X3 : elem,X4 : list] : ((listStar @ X2 @ X4 @ X4) => (! [X5 : nat,X6 : list] : ((listStar @ X5 @ X6 @ X6) => (listStar @ (plus @ X2 @ X5) @ (rev @ (plus @ X2 @ X5) @ (app @ X2 @ X5 @ (rev @ X2 @ X4) @ X6)) @ (app @ X5 @ X2 @ (rev @ X5 @ X6) @ X4))) => ! [X7 : nat,X8 : list] : ((listStar @ X7 @ X8 @ X8) => (listStar @ (plus @ (suc @ X2) @ X7) @ (rev @ (plus @ (suc @ X2) @ X7) @ (app @ (suc @ X2) @ X7 @ (rev @ (suc @ X2) @ (cons @ X2 @ X3 @ X4)) @ X8)) @ (app @ X7 @ (suc @ X2) @ (rev @ X7 @ X8) @ (cons @ X2 @ X3 @ X4)))))) => ! [X9 : nat,X10 : list,X11 : nat,X12 : list] : ((listStar @ X9 @ X10 @ X10) => ((listStar @ X11 @ X12 @ X12) => (listStar @ (plus @ X9 @ X11) @ (rev @ (plus @ X9 @ X11) @ (app @ X9 @ X11 @ (rev @ X9 @ X10) @ X12)) @ (app @ X11 @ X9 @ (rev @ X11 @ X12) @ X10)))))),
% 2.00/1.54 inference(rectify,[status(thm)],[f20])).
% 2.00/1.54 thf(f20,axiom,(
% 2.00/1.54 ! [X13 : nat,X14 : list] : ((listStar @ X13 @ X14 @ X14) => (listStar @ (plus @ zero @ X13) @ (rev @ (plus @ zero @ X13) @ (app @ zero @ X13 @ (rev @ zero @ nil) @ X14)) @ (app @ X13 @ zero @ (rev @ X13 @ X14) @ nil))) => (! [X6 : nat,X2 : elem,X15 : list] : ((listStar @ X6 @ X15 @ X15) => (! [X13 : nat,X14 : list] : ((listStar @ X13 @ X14 @ X14) => (listStar @ (plus @ X6 @ X13) @ (rev @ (plus @ X6 @ X13) @ (app @ X6 @ X13 @ (rev @ X6 @ X15) @ X14)) @ (app @ X13 @ X6 @ (rev @ X13 @ X14) @ X15))) => ! [X13 : nat,X14 : list] : ((listStar @ X13 @ X14 @ X14) => (listStar @ (plus @ (suc @ X6) @ X13) @ (rev @ (plus @ (suc @ X6) @ X13) @ (app @ (suc @ X6) @ X13 @ (rev @ (suc @ X6) @ (cons @ X6 @ X2 @ X15)) @ X14)) @ (app @ X13 @ (suc @ X6) @ (rev @ X13 @ X14) @ (cons @ X6 @ X2 @ X15)))))) => ! [X6 : nat,X15 : list,X13 : nat,X14 : list] : ((listStar @ X6 @ X15 @ X15) => ((listStar @ X13 @ X14 @ X14) => (listStar @ (plus @ X6 @ X13) @ (rev @ (plus @ X6 @ X13) @ (app @ X6 @ X13 @ (rev @ X6 @ X15) @ X14)) @ (app @ X13 @ X6 @ (rev @ X13 @ X14) @ X15)))))),
% 2.00/1.54 file('/export/starexec/sandbox/tmp/tmp.K4a8wmNMBS/DTF2THF_3850.p',list_rev_invol_lem_indinst)).
% 2.00/1.54 thf(f83,plain,(
% 2.00/1.54 ((~ (!! @ list @ (^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: (!! @ list @ (^[Y2 : list]: (!! @ nat @ (^[Y3 : nat]: ((listStar @ Y3 @ Y2 @ Y2) => ((listStar @ Y1 @ Y0 @ Y0) => (listStar @ (plus @ Y3 @ Y1) @ (rev @ (plus @ Y3 @ Y1) @ (app @ Y3 @ Y1 @ (rev @ Y3 @ Y2) @ Y0)) @ (app @ Y1 @ Y3 @ (rev @ Y1 @ Y0) @ Y2))))))))))))) = $true)),
% 2.00/1.54 inference(cnf_transformation,[status(thm)],[f61])).
% 2.00/1.54 thf(f61,plain,(
% 2.00/1.54 ((~ (!! @ list @ (^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: (!! @ list @ (^[Y2 : list]: (!! @ nat @ (^[Y3 : nat]: ((listStar @ Y3 @ Y2 @ Y2) => ((listStar @ Y1 @ Y0 @ Y0) => (listStar @ (plus @ Y3 @ Y1) @ (rev @ (plus @ Y3 @ Y1) @ (app @ Y3 @ Y1 @ (rev @ Y3 @ Y2) @ Y0)) @ (app @ Y1 @ Y3 @ (rev @ Y1 @ Y0) @ Y2))))))))))))) = $true)),
% 2.00/1.54 inference(fool_elimination,[status(thm)],[f60])).
% 2.00/1.54 thf(f60,plain,(
% 2.00/1.54 ~! [X0 : nat,X1 : list,X2 : nat,X3 : list] : ((listStar @ X0 @ X1 @ X1) => ((listStar @ X2 @ X3 @ X3) => (listStar @ (plus @ X0 @ X2) @ (rev @ (plus @ X0 @ X2) @ (app @ X0 @ X2 @ (rev @ X0 @ X1) @ X3)) @ (app @ X2 @ X0 @ (rev @ X2 @ X3) @ X1))))),
% 2.00/1.54 inference(rectify,[status(thm)],[f24])).
% 2.00/1.54 thf(f24,negated_conjecture,(
% 2.00/1.54 ~! [X6 : nat,X15 : list,X13 : nat,X14 : list] : ((listStar @ X6 @ X15 @ X15) => ((listStar @ X13 @ X14 @ X14) => (listStar @ (plus @ X6 @ X13) @ (rev @ (plus @ X6 @ X13) @ (app @ X6 @ X13 @ (rev @ X6 @ X15) @ X14)) @ (app @ X13 @ X6 @ (rev @ X13 @ X14) @ X15))))),
% 2.00/1.54 inference(negated_conjecture,[status(cth)],[f23])).
% 2.00/1.54 thf(f23,conjecture,(
% 2.00/1.54 ! [X6 : nat,X15 : list,X13 : nat,X14 : list] : ((listStar @ X6 @ X15 @ X15) => ((listStar @ X13 @ X14 @ X14) => (listStar @ (plus @ X6 @ X13) @ (rev @ (plus @ X6 @ X13) @ (app @ X6 @ X13 @ (rev @ X6 @ X15) @ X14)) @ (app @ X13 @ X6 @ (rev @ X13 @ X14) @ X15))))),
% 2.00/1.54 file('/export/starexec/sandbox/tmp/tmp.K4a8wmNMBS/DTF2THF_3850.p',list_rev_invol_lem)).
% 2.00/1.54 % SZS output end Proof for DTF2THF_3850
% 2.00/1.54 % (4068)------------------------------
% 2.00/1.54 % (4068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.00/1.54 % (4068)Termination reason: Refutation
% 2.00/1.54
% 2.00/1.54 % (4068)Memory used [KB]: 5756
% 2.00/1.54 % (4068)Time elapsed: 0.025 s
% 2.00/1.54 % (4068)Instructions burned: 19 (million)
% 2.00/1.54 % (4068)------------------------------
% 2.00/1.54 % (4068)------------------------------
% 2.00/1.54 % (4042)Success in time 0.081 s
%------------------------------------------------------------------------------