%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT391^1 : 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 : n006.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 08:45:38 AM UTC 2026
% Result : Theorem 1.57s 1.39s
% Output : Refutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of formulae : 56 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 460 ( 169 equ; 0 cnn)
% Maximal formula atoms : 12 ( 8 avg)
% Number of connectives : 2081 ( 81 ~; 54 |; 55 &;1850 @)
% ( 5 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 9 con; 0-4 aty)
% Number of variables : 195 ( 0 ^; 156 !; 39 ?; 195 :)
% 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(func_def_17,type,
sK0: ( nat > $o ) > nat ).
thf(func_def_18,type,
sK1: nat ).
thf(func_def_19,type,
sK2: elem ).
thf(func_def_20,type,
sK3: list ).
thf(func_def_21,type,
sK4: nat ).
thf(func_def_22,type,
sK5: list ).
thf(func_def_23,type,
sK6:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_24,type,
sK7:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_25,type,
sK8:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_26,type,
sK9:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_27,type,
sK10:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_29,type,
ph12:
!>[X0: $tType] : X0 ).
thf(f390,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f387]) ).
thf(f387,plain,
$true != $true,
inference(superposition,[status(thm)],[f279,f88]) ).
thf(f88,plain,
( ( listStar @ sK4 @ sK5 @ sK5 )
= $true ),
inference(cnf_transformation,[status(thm)],[f74]) ).
thf(f74,plain,
( ( ( listStar @ sK1 @ sK3 @ sK3 )
= $true )
& ! [X3: nat,X4: list] :
( ( ( listStar @ ( plus @ sK1 @ X3 ) @ ( rev @ ( plus @ sK1 @ X3 ) @ ( app @ sK1 @ X3 @ ( rev @ sK1 @ sK3 ) @ X4 ) ) @ ( app @ X3 @ sK1 @ ( rev @ X3 @ X4 ) @ sK3 ) )
= $true )
| ( ( listStar @ X3 @ X4 @ X4 )
!= $true ) )
& ( ( listStar @ ( plus @ ( suc @ sK1 ) @ sK4 ) @ ( rev @ ( plus @ ( suc @ sK1 ) @ sK4 ) @ ( app @ ( suc @ sK1 ) @ sK4 @ ( rev @ ( suc @ sK1 ) @ ( cons @ sK1 @ sK2 @ sK3 ) ) @ sK5 ) ) @ ( app @ ( suc @ sK4 ) @ sK1 @ ( rev @ ( suc @ sK4 ) @ ( cons @ sK4 @ sK2 @ sK5 ) ) @ sK3 ) )
!= $true )
& ( ( listStar @ sK4 @ sK5 @ sK5 )
= $true )
& ( ( listStar @ ( plus @ ( suc @ sK1 ) @ sK4 ) @ ( rev @ ( plus @ ( suc @ sK1 ) @ sK4 ) @ ( app @ ( suc @ sK1 ) @ sK4 @ ( rev @ ( suc @ sK1 ) @ ( cons @ sK1 @ sK2 @ sK3 ) ) @ sK5 ) ) @ ( rev @ ( plus @ sK1 @ ( suc @ sK4 ) ) @ ( app @ sK1 @ ( suc @ sK4 ) @ ( rev @ sK1 @ sK3 ) @ ( cons @ sK4 @ sK2 @ sK5 ) ) ) )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5])],[f58,f73,f72]) ).
thf(f72,plain,
( ? [X0: nat,X1: elem,X2: list] :
( ( ( listStar @ X0 @ X2 @ X2 )
= $true )
& ! [X3: nat,X4: list] :
( ( ( listStar @ ( plus @ X0 @ X3 ) @ ( rev @ ( plus @ X0 @ X3 ) @ ( app @ X0 @ X3 @ ( rev @ X0 @ X2 ) @ X4 ) ) @ ( app @ X3 @ X0 @ ( rev @ X3 @ X4 ) @ X2 ) )
= $true )
| ( ( listStar @ X3 @ X4 @ X4 )
!= $true ) )
& ? [X5: nat,X6: list] :
( ( ( listStar @ ( plus @ ( suc @ X0 ) @ X5 ) @ ( rev @ ( plus @ ( suc @ X0 ) @ X5 ) @ ( app @ ( suc @ X0 ) @ X5 @ ( rev @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) ) @ X6 ) ) @ ( app @ ( suc @ X5 ) @ X0 @ ( rev @ ( suc @ X5 ) @ ( cons @ X5 @ X1 @ X6 ) ) @ X2 ) )
!= $true )
& ( $true
= ( 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 ) ) @ ( rev @ ( plus @ X0 @ ( suc @ X5 ) ) @ ( app @ X0 @ ( suc @ X5 ) @ ( rev @ X0 @ X2 ) @ ( cons @ X5 @ X1 @ X6 ) ) ) )
= $true ) ) )
=> ( ( ( listStar @ sK1 @ sK3 @ sK3 )
= $true )
& ! [X4: list,X3: nat] :
( ( ( listStar @ ( plus @ sK1 @ X3 ) @ ( rev @ ( plus @ sK1 @ X3 ) @ ( app @ sK1 @ X3 @ ( rev @ sK1 @ sK3 ) @ X4 ) ) @ ( app @ X3 @ sK1 @ ( rev @ X3 @ X4 ) @ sK3 ) )
= $true )
| ( ( listStar @ X3 @ X4 @ X4 )
!= $true ) )
& ? [X6: list,X5: nat] :
( ( $true
!= ( listStar @ ( plus @ ( suc @ sK1 ) @ X5 ) @ ( rev @ ( plus @ ( suc @ sK1 ) @ X5 ) @ ( app @ ( suc @ sK1 ) @ X5 @ ( rev @ ( suc @ sK1 ) @ ( cons @ sK1 @ sK2 @ sK3 ) ) @ X6 ) ) @ ( app @ ( suc @ X5 ) @ sK1 @ ( rev @ ( suc @ X5 ) @ ( cons @ X5 @ sK2 @ X6 ) ) @ sK3 ) ) )
& ( $true
= ( listStar @ X5 @ X6 @ X6 ) )
& ( ( listStar @ ( plus @ ( suc @ sK1 ) @ X5 ) @ ( rev @ ( plus @ ( suc @ sK1 ) @ X5 ) @ ( app @ ( suc @ sK1 ) @ X5 @ ( rev @ ( suc @ sK1 ) @ ( cons @ sK1 @ sK2 @ sK3 ) ) @ X6 ) ) @ ( rev @ ( plus @ sK1 @ ( suc @ X5 ) ) @ ( app @ sK1 @ ( suc @ X5 ) @ ( rev @ sK1 @ sK3 ) @ ( cons @ X5 @ sK2 @ X6 ) ) ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f73,plain,
( ? [X6: list,X5: nat] :
( ( $true
!= ( listStar @ ( plus @ ( suc @ sK1 ) @ X5 ) @ ( rev @ ( plus @ ( suc @ sK1 ) @ X5 ) @ ( app @ ( suc @ sK1 ) @ X5 @ ( rev @ ( suc @ sK1 ) @ ( cons @ sK1 @ sK2 @ sK3 ) ) @ X6 ) ) @ ( app @ ( suc @ X5 ) @ sK1 @ ( rev @ ( suc @ X5 ) @ ( cons @ X5 @ sK2 @ X6 ) ) @ sK3 ) ) )
& ( $true
= ( listStar @ X5 @ X6 @ X6 ) )
& ( ( listStar @ ( plus @ ( suc @ sK1 ) @ X5 ) @ ( rev @ ( plus @ ( suc @ sK1 ) @ X5 ) @ ( app @ ( suc @ sK1 ) @ X5 @ ( rev @ ( suc @ sK1 ) @ ( cons @ sK1 @ sK2 @ sK3 ) ) @ X6 ) ) @ ( rev @ ( plus @ sK1 @ ( suc @ X5 ) ) @ ( app @ sK1 @ ( suc @ X5 ) @ ( rev @ sK1 @ sK3 ) @ ( cons @ X5 @ sK2 @ X6 ) ) ) )
= $true ) )
=> ( ( ( listStar @ ( plus @ ( suc @ sK1 ) @ sK4 ) @ ( rev @ ( plus @ ( suc @ sK1 ) @ sK4 ) @ ( app @ ( suc @ sK1 ) @ sK4 @ ( rev @ ( suc @ sK1 ) @ ( cons @ sK1 @ sK2 @ sK3 ) ) @ sK5 ) ) @ ( app @ ( suc @ sK4 ) @ sK1 @ ( rev @ ( suc @ sK4 ) @ ( cons @ sK4 @ sK2 @ sK5 ) ) @ sK3 ) )
!= $true )
& ( ( listStar @ sK4 @ sK5 @ sK5 )
= $true )
& ( ( listStar @ ( plus @ ( suc @ sK1 ) @ sK4 ) @ ( rev @ ( plus @ ( suc @ sK1 ) @ sK4 ) @ ( app @ ( suc @ sK1 ) @ sK4 @ ( rev @ ( suc @ sK1 ) @ ( cons @ sK1 @ sK2 @ sK3 ) ) @ sK5 ) ) @ ( rev @ ( plus @ sK1 @ ( suc @ sK4 ) ) @ ( app @ sK1 @ ( suc @ sK4 ) @ ( rev @ sK1 @ sK3 ) @ ( cons @ sK4 @ sK2 @ sK5 ) ) ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f58,plain,
? [X0: nat,X1: elem,X2: list] :
( ( ( listStar @ X0 @ X2 @ X2 )
= $true )
& ! [X3: nat,X4: list] :
( ( ( listStar @ ( plus @ X0 @ X3 ) @ ( rev @ ( plus @ X0 @ X3 ) @ ( app @ X0 @ X3 @ ( rev @ X0 @ X2 ) @ X4 ) ) @ ( app @ X3 @ X0 @ ( rev @ X3 @ X4 ) @ X2 ) )
= $true )
| ( ( listStar @ X3 @ X4 @ X4 )
!= $true ) )
& ? [X5: nat,X6: list] :
( ( ( listStar @ ( plus @ ( suc @ X0 ) @ X5 ) @ ( rev @ ( plus @ ( suc @ X0 ) @ X5 ) @ ( app @ ( suc @ X0 ) @ X5 @ ( rev @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) ) @ X6 ) ) @ ( app @ ( suc @ X5 ) @ X0 @ ( rev @ ( suc @ X5 ) @ ( cons @ X5 @ X1 @ X6 ) ) @ X2 ) )
!= $true )
& ( $true
= ( 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 ) ) @ ( rev @ ( plus @ X0 @ ( suc @ X5 ) ) @ ( app @ X0 @ ( suc @ X5 ) @ ( rev @ X0 @ X2 ) @ ( cons @ X5 @ X1 @ X6 ) ) ) )
= $true ) ) ),
inference(flattening,[status(thm)],[f57]) ).
thf(f57,plain,
? [X0: nat,X1: elem,X2: list] :
( ? [X5: nat,X6: list] :
( ( ( listStar @ ( plus @ ( suc @ X0 ) @ X5 ) @ ( rev @ ( plus @ ( suc @ X0 ) @ X5 ) @ ( app @ ( suc @ X0 ) @ X5 @ ( rev @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) ) @ X6 ) ) @ ( app @ ( suc @ X5 ) @ X0 @ ( rev @ ( suc @ X5 ) @ ( cons @ X5 @ X1 @ X6 ) ) @ X2 ) )
!= $true )
& ( ( listStar @ ( plus @ ( suc @ X0 ) @ X5 ) @ ( rev @ ( plus @ ( suc @ X0 ) @ X5 ) @ ( app @ ( suc @ X0 ) @ X5 @ ( rev @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) ) @ X6 ) ) @ ( rev @ ( plus @ X0 @ ( suc @ X5 ) ) @ ( app @ X0 @ ( suc @ X5 ) @ ( rev @ X0 @ X2 ) @ ( cons @ X5 @ X1 @ X6 ) ) ) )
= $true )
& ( $true
= ( listStar @ X5 @ X6 @ X6 ) ) )
& ! [X3: nat,X4: list] :
( ( ( listStar @ ( plus @ X0 @ X3 ) @ ( rev @ ( plus @ X0 @ X3 ) @ ( app @ X0 @ X3 @ ( rev @ X0 @ X2 ) @ X4 ) ) @ ( app @ X3 @ X0 @ ( rev @ X3 @ X4 ) @ X2 ) )
= $true )
| ( ( listStar @ X3 @ X4 @ X4 )
!= $true ) )
& ( ( listStar @ X0 @ X2 @ X2 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
~ ! [X0: nat,X1: elem,X2: list] :
( ( ( listStar @ X0 @ X2 @ X2 )
= $true )
=> ( ! [X3: nat,X4: list] :
( ( ( listStar @ X3 @ X4 @ X4 )
= $true )
=> ( ( listStar @ ( plus @ X0 @ X3 ) @ ( rev @ ( plus @ X0 @ X3 ) @ ( app @ X0 @ X3 @ ( rev @ X0 @ X2 ) @ X4 ) ) @ ( app @ X3 @ X0 @ ( rev @ X3 @ X4 ) @ X2 ) )
= $true ) )
=> ! [X5: nat,X6: list] :
( ( $true
= ( 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 ) ) @ ( rev @ ( plus @ X0 @ ( suc @ X5 ) ) @ ( app @ X0 @ ( suc @ X5 ) @ ( rev @ X0 @ X2 ) @ ( cons @ X5 @ X1 @ X6 ) ) ) )
= $true )
=> ( ( listStar @ ( plus @ ( suc @ X0 ) @ X5 ) @ ( rev @ ( plus @ ( suc @ X0 ) @ X5 ) @ ( app @ ( suc @ X0 ) @ X5 @ ( rev @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) ) @ X6 ) ) @ ( app @ ( suc @ X5 ) @ X0 @ ( rev @ ( suc @ X5 ) @ ( cons @ X5 @ X1 @ X6 ) ) @ X2 ) )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f34]) ).
thf(f34,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 ) ) @ ( rev @ ( plus @ X0 @ ( suc @ X5 ) ) @ ( app @ X0 @ ( suc @ X5 ) @ ( rev @ X0 @ X2 ) @ ( cons @ X5 @ X1 @ X6 ) ) ) )
=> ( listStar @ ( plus @ ( suc @ X0 ) @ X5 ) @ ( rev @ ( plus @ ( suc @ X0 ) @ X5 ) @ ( app @ ( suc @ X0 ) @ X5 @ ( rev @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) ) @ X6 ) ) @ ( app @ ( suc @ X5 ) @ X0 @ ( rev @ ( suc @ X5 ) @ ( cons @ X5 @ X1 @ X6 ) ) @ X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f22]) ).
thf(f22,negated_conjecture,
~ ! [X6: nat,X2: elem,X16: list] :
( ( listStar @ X6 @ X16 @ X16 )
=> ( ! [X14: nat,X17: list] :
( ( listStar @ X14 @ X17 @ X17 )
=> ( listStar @ ( plus @ X6 @ X14 ) @ ( rev @ ( plus @ X6 @ X14 ) @ ( app @ X6 @ X14 @ ( rev @ X6 @ X16 ) @ X17 ) ) @ ( app @ X14 @ X6 @ ( rev @ X14 @ X17 ) @ X16 ) ) )
=> ! [X14: nat,X17: list] :
( ( listStar @ X14 @ X17 @ X17 )
=> ( ( listStar @ ( plus @ ( suc @ X6 ) @ X14 ) @ ( rev @ ( plus @ ( suc @ X6 ) @ X14 ) @ ( app @ ( suc @ X6 ) @ X14 @ ( rev @ ( suc @ X6 ) @ ( cons @ X6 @ X2 @ X16 ) ) @ X17 ) ) @ ( rev @ ( plus @ X6 @ ( suc @ X14 ) ) @ ( app @ X6 @ ( suc @ X14 ) @ ( rev @ X6 @ X16 ) @ ( cons @ X14 @ X2 @ X17 ) ) ) )
=> ( listStar @ ( plus @ ( suc @ X6 ) @ X14 ) @ ( rev @ ( plus @ ( suc @ X6 ) @ X14 ) @ ( app @ ( suc @ X6 ) @ X14 @ ( rev @ ( suc @ X6 ) @ ( cons @ X6 @ X2 @ X16 ) ) @ X17 ) ) @ ( app @ ( suc @ X14 ) @ X6 @ ( rev @ ( suc @ X14 ) @ ( cons @ X14 @ X2 @ X17 ) ) @ X16 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
thf(f21,conjecture,
! [X6: nat,X2: elem,X16: list] :
( ( listStar @ X6 @ X16 @ X16 )
=> ( ! [X14: nat,X17: list] :
( ( listStar @ X14 @ X17 @ X17 )
=> ( listStar @ ( plus @ X6 @ X14 ) @ ( rev @ ( plus @ X6 @ X14 ) @ ( app @ X6 @ X14 @ ( rev @ X6 @ X16 ) @ X17 ) ) @ ( app @ X14 @ X6 @ ( rev @ X14 @ X17 ) @ X16 ) ) )
=> ! [X14: nat,X17: list] :
( ( listStar @ X14 @ X17 @ X17 )
=> ( ( listStar @ ( plus @ ( suc @ X6 ) @ X14 ) @ ( rev @ ( plus @ ( suc @ X6 ) @ X14 ) @ ( app @ ( suc @ X6 ) @ X14 @ ( rev @ ( suc @ X6 ) @ ( cons @ X6 @ X2 @ X16 ) ) @ X17 ) ) @ ( rev @ ( plus @ X6 @ ( suc @ X14 ) ) @ ( app @ X6 @ ( suc @ X14 ) @ ( rev @ X6 @ X16 ) @ ( cons @ X14 @ X2 @ X17 ) ) ) )
=> ( listStar @ ( plus @ ( suc @ X6 ) @ X14 ) @ ( rev @ ( plus @ ( suc @ X6 ) @ X14 ) @ ( app @ ( suc @ X6 ) @ X14 @ ( rev @ ( suc @ X6 ) @ ( cons @ X6 @ X2 @ X16 ) ) @ X17 ) ) @ ( app @ ( suc @ X14 ) @ X6 @ ( rev @ ( suc @ X14 ) @ ( cons @ X14 @ X2 @ X17 ) ) @ X16 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EoxrKmOWLf/DTF2THF_13150.p',list_rev_invol_lem_indstep4) ).
thf(f279,plain,
( ( listStar @ sK4 @ sK5 @ sK5 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f275]) ).
thf(f275,plain,
( ( ( listStar @ sK4 @ sK5 @ sK5 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f217,f116]) ).
thf(f116,plain,
! [X2: list,X3: list,X0: nat,X1: elem] :
( ( ( listStar @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) @ ( cons @ X0 @ X1 @ X3 ) )
= $true )
| ( ( listStar @ X0 @ X2 @ X3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
thf(f69,plain,
! [X0: nat,X1: elem,X2: list,X3: list] :
( ( ( listStar @ X0 @ X2 @ X3 )
!= $true )
| ( ( listStar @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) @ ( cons @ X0 @ X1 @ X3 ) )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: nat,X1: elem,X2: list,X3: list] :
( ( ( listStar @ X0 @ X2 @ X3 )
= $true )
=> ( ( listStar @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) @ ( cons @ X0 @ X1 @ X3 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: nat,X1: elem,X2: list,X3: list] :
( ( listStar @ X0 @ X2 @ X3 )
=> ( listStar @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) @ ( cons @ X0 @ X1 @ X3 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X6: nat,X7: elem,X8: list,X9: list] :
( ( listStar @ X6 @ X8 @ X9 )
=> ( listStar @ ( suc @ X6 ) @ ( cons @ X6 @ X7 @ X8 ) @ ( cons @ X6 @ X7 @ X9 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EoxrKmOWLf/DTF2THF_13150.p',cons_tp_ax) ).
thf(f217,plain,
( ( listStar @ ( suc @ sK4 ) @ ( cons @ sK4 @ sK2 @ sK5 ) @ ( cons @ sK4 @ sK2 @ sK5 ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f211]) ).
thf(f211,plain,
( ( $true != $true )
| ( ( listStar @ ( suc @ sK4 ) @ ( cons @ sK4 @ sK2 @ sK5 ) @ ( cons @ sK4 @ sK2 @ sK5 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f159,f140]) ).
thf(f140,plain,
! [X0: nat,X1: list] :
( ( ( listStar @ ( plus @ sK1 @ X0 ) @ ( rev @ ( plus @ sK1 @ X0 ) @ ( app @ sK1 @ X0 @ ( rev @ sK1 @ sK3 ) @ X1 ) ) @ ( app @ X0 @ sK1 @ ( rev @ X0 @ X1 ) @ sK3 ) )
= $true )
| ( $true
!= ( listStar @ X0 @ X1 @ X1 ) ) ),
inference(superposition,[status(thm)],[f124,f113]) ).
thf(f113,plain,
! [X0: nat,X1: nat] :
( ( plus @ X1 @ X0 )
= ( plus @ X0 @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
thf(f53,plain,
! [X0: nat,X1: nat] :
( ( plus @ X1 @ X0 )
= ( plus @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f17]) ).
thf(f17,axiom,
! [X6: nat,X10: nat] :
( ( plus @ X6 @ X10 )
= ( plus @ X10 @ X6 ) ),
file('/export/starexec/sandbox/tmp/tmp.EoxrKmOWLf/DTF2THF_13150.p',plus_com) ).
thf(f124,plain,
! [X0: nat,X1: list] :
( ( ( listStar @ ( plus @ X0 @ sK1 ) @ ( rev @ ( plus @ X0 @ sK1 ) @ ( app @ sK1 @ X0 @ ( rev @ sK1 @ sK3 ) @ X1 ) ) @ ( app @ X0 @ sK1 @ ( rev @ X0 @ X1 ) @ sK3 ) )
= $true )
| ( $true
!= ( listStar @ X0 @ X1 @ X1 ) ) ),
inference(superposition,[status(thm)],[f90,f113]) ).
thf(f90,plain,
! [X3: nat,X4: list] :
( ( ( listStar @ ( plus @ sK1 @ X3 ) @ ( rev @ ( plus @ sK1 @ X3 ) @ ( app @ sK1 @ X3 @ ( rev @ sK1 @ sK3 ) @ X4 ) ) @ ( app @ X3 @ sK1 @ ( rev @ X3 @ X4 ) @ sK3 ) )
= $true )
| ( ( listStar @ X3 @ X4 @ X4 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
thf(f159,plain,
( $true
!= ( listStar @ ( plus @ sK1 @ ( suc @ sK4 ) ) @ ( rev @ ( plus @ sK1 @ ( suc @ sK4 ) ) @ ( app @ sK1 @ ( suc @ sK4 ) @ ( rev @ sK1 @ sK3 ) @ ( cons @ sK4 @ sK2 @ sK5 ) ) ) @ ( app @ ( suc @ sK4 ) @ sK1 @ ( rev @ ( suc @ sK4 ) @ ( cons @ sK4 @ sK2 @ sK5 ) ) @ sK3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f154]) ).
thf(f154,plain,
( ( $true != $true )
| ( $true
!= ( listStar @ ( plus @ sK1 @ ( suc @ sK4 ) ) @ ( rev @ ( plus @ sK1 @ ( suc @ sK4 ) ) @ ( app @ sK1 @ ( suc @ sK4 ) @ ( rev @ sK1 @ sK3 ) @ ( cons @ sK4 @ sK2 @ sK5 ) ) ) @ ( app @ ( suc @ sK4 ) @ sK1 @ ( rev @ ( suc @ sK4 ) @ ( cons @ sK4 @ sK2 @ sK5 ) ) @ sK3 ) ) ) ),
inference(superposition,[status(thm)],[f131,f121]) ).
thf(f121,plain,
( ( listStar @ ( plus @ sK1 @ ( suc @ sK4 ) ) @ ( rev @ ( plus @ sK1 @ ( suc @ sK4 ) ) @ ( app @ ( suc @ sK1 ) @ sK4 @ ( rev @ ( suc @ sK1 ) @ ( cons @ sK1 @ sK2 @ sK3 ) ) @ sK5 ) ) @ ( rev @ ( plus @ sK1 @ ( suc @ sK4 ) ) @ ( app @ sK1 @ ( suc @ sK4 ) @ ( rev @ sK1 @ sK3 ) @ ( cons @ sK4 @ sK2 @ sK5 ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f87,f94]) ).
thf(f94,plain,
! [X0: nat,X1: nat] :
( ( plus @ ( suc @ X0 ) @ X1 )
= ( plus @ X0 @ ( suc @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
thf(f49,plain,
! [X0: nat,X1: nat] :
( ( plus @ ( suc @ X0 ) @ X1 )
= ( plus @ X0 @ ( suc @ X1 ) ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,axiom,
! [X6: nat,X10: nat] :
( ( plus @ ( suc @ X6 ) @ X10 )
= ( plus @ X6 @ ( suc @ X10 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EoxrKmOWLf/DTF2THF_13150.p',plus_s_l_r) ).
thf(f87,plain,
( ( listStar @ ( plus @ ( suc @ sK1 ) @ sK4 ) @ ( rev @ ( plus @ ( suc @ sK1 ) @ sK4 ) @ ( app @ ( suc @ sK1 ) @ sK4 @ ( rev @ ( suc @ sK1 ) @ ( cons @ sK1 @ sK2 @ sK3 ) ) @ sK5 ) ) @ ( rev @ ( plus @ sK1 @ ( suc @ sK4 ) ) @ ( app @ sK1 @ ( suc @ sK4 ) @ ( rev @ sK1 @ sK3 ) @ ( cons @ sK4 @ sK2 @ sK5 ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f74]) ).
thf(f131,plain,
! [X0: list] :
( ( ( listStar @ ( plus @ sK1 @ ( suc @ sK4 ) ) @ ( rev @ ( plus @ sK1 @ ( suc @ sK4 ) ) @ ( app @ ( suc @ sK1 ) @ sK4 @ ( rev @ ( suc @ sK1 ) @ ( cons @ sK1 @ sK2 @ sK3 ) ) @ sK5 ) ) @ X0 )
!= $true )
| ( $true
!= ( listStar @ ( plus @ sK1 @ ( suc @ sK4 ) ) @ X0 @ ( app @ ( suc @ sK4 ) @ sK1 @ ( rev @ ( suc @ sK4 ) @ ( cons @ sK4 @ sK2 @ sK5 ) ) @ sK3 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f130]) ).
thf(f130,plain,
! [X0: list] :
( ( ( listStar @ ( plus @ sK1 @ ( suc @ sK4 ) ) @ ( rev @ ( plus @ sK1 @ ( suc @ sK4 ) ) @ ( app @ ( suc @ sK1 ) @ sK4 @ ( rev @ ( suc @ sK1 ) @ ( cons @ sK1 @ sK2 @ sK3 ) ) @ sK5 ) ) @ X0 )
!= $true )
| ( $true
!= ( listStar @ ( plus @ sK1 @ ( suc @ sK4 ) ) @ X0 @ ( app @ ( suc @ sK4 ) @ sK1 @ ( rev @ ( suc @ sK4 ) @ ( cons @ sK4 @ sK2 @ sK5 ) ) @ sK3 ) ) )
| ( $true != $true ) ),
inference(forward_demodulation,[status(thm)],[f129,f106]) ).
thf(f106,plain,
! [X0: nat] :
( ( isPer @ list @ ( listStar @ X0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: nat] :
( ( isPer @ list @ ( listStar @ X0 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: nat] : ( isPer @ list @ ( listStar @ X0 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X5: nat] : ( isPer @ list @ ( listStar @ X5 ) ),
file('/export/starexec/sandbox/tmp/tmp.EoxrKmOWLf/DTF2THF_13150.p','\'listStar\'_is_per') ).
thf(f129,plain,
! [X0: list] :
( ( $true
!= ( listStar @ ( plus @ sK1 @ ( suc @ sK4 ) ) @ X0 @ ( app @ ( suc @ sK4 ) @ sK1 @ ( rev @ ( suc @ sK4 ) @ ( cons @ sK4 @ sK2 @ sK5 ) ) @ sK3 ) ) )
| ( $true
!= ( isPer @ list @ ( listStar @ ( plus @ sK1 @ ( suc @ sK4 ) ) ) ) )
| ( ( listStar @ ( plus @ sK1 @ ( suc @ sK4 ) ) @ ( rev @ ( plus @ sK1 @ ( suc @ sK4 ) ) @ ( app @ ( suc @ sK1 ) @ sK4 @ ( rev @ ( suc @ sK1 ) @ ( cons @ sK1 @ sK2 @ sK3 ) ) @ sK5 ) ) @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f126]) ).
thf(f126,plain,
! [X0: list] :
( ( ( listStar @ ( plus @ sK1 @ ( suc @ sK4 ) ) @ ( rev @ ( plus @ sK1 @ ( suc @ sK4 ) ) @ ( app @ ( suc @ sK1 ) @ sK4 @ ( rev @ ( suc @ sK1 ) @ ( cons @ sK1 @ sK2 @ sK3 ) ) @ sK5 ) ) @ X0 )
!= $true )
| ( $true
!= ( listStar @ ( plus @ sK1 @ ( suc @ sK4 ) ) @ X0 @ ( app @ ( suc @ sK4 ) @ sK1 @ ( rev @ ( suc @ sK4 ) @ ( cons @ sK4 @ sK2 @ sK5 ) ) @ sK3 ) ) )
| ( $true != $true )
| ( $true
!= ( isPer @ list @ ( listStar @ ( plus @ sK1 @ ( suc @ sK4 ) ) ) ) ) ),
inference(superposition,[status(thm)],[f120,f98]) ).
thf(f98,plain,
! [X0: $tType,X10: X0,X11: X0,X1: X0 > X0 > $o,X9: X0] :
( ( $true
= ( X1 @ X9 @ X11 ) )
| ( ( isPer @ X0 @ X1 )
!= $true )
| ( ( X1 @ X9 @ X10 )
!= $true )
| ( ( X1 @ X10 @ X11 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f81]) ).
thf(f81,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ( ( isPer @ X0 @ X1 )
= $true )
| ( ( ( X1 @ ( sK7 @ X0 @ X1 ) @ ( sK6 @ X0 @ X1 ) )
!= $true )
& ( ( X1 @ ( sK6 @ X0 @ X1 ) @ ( sK7 @ X0 @ X1 ) )
= $true ) )
| ( ( ( X1 @ ( sK9 @ X0 @ X1 ) @ ( sK10 @ X0 @ X1 ) )
= $true )
& ( ( X1 @ ( sK8 @ X0 @ X1 ) @ ( sK9 @ X0 @ X1 ) )
= $true )
& ( ( X1 @ ( sK8 @ X0 @ X1 ) @ ( sK10 @ X0 @ X1 ) )
!= $true ) ) )
& ( ( ! [X7: X0,X8: X0] :
( ( $true
= ( X1 @ X8 @ X7 ) )
| ( $true
!= ( X1 @ X7 @ X8 ) ) )
& ! [X9: X0,X10: X0,X11: X0] :
( ( ( X1 @ X10 @ X11 )
!= $true )
| ( ( X1 @ X9 @ X10 )
!= $true )
| ( $true
= ( X1 @ X9 @ X11 ) ) ) )
| ( ( isPer @ X0 @ X1 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10])],[f78,f80,f79]) ).
thf(f79,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ? [X2: X0,X3: X0] :
( ( ( X1 @ X3 @ X2 )
!= $true )
& ( ( X1 @ X2 @ X3 )
= $true ) )
=> ( ( ( X1 @ ( sK7 @ X0 @ X1 ) @ ( sK6 @ X0 @ X1 ) )
!= $true )
& ( ( X1 @ ( sK6 @ X0 @ X1 ) @ ( sK7 @ X0 @ X1 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f80,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ? [X4: X0,X5: X0,X6: X0] :
( ( ( X1 @ X5 @ X6 )
= $true )
& ( $true
= ( X1 @ X4 @ X5 ) )
& ( ( X1 @ X4 @ X6 )
!= $true ) )
=> ( ( ( X1 @ ( sK9 @ X0 @ X1 ) @ ( sK10 @ X0 @ X1 ) )
= $true )
& ( ( X1 @ ( sK8 @ X0 @ X1 ) @ ( sK9 @ X0 @ X1 ) )
= $true )
& ( ( X1 @ ( sK8 @ X0 @ X1 ) @ ( sK10 @ X0 @ X1 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f78,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ( ( isPer @ X0 @ X1 )
= $true )
| ? [X2: X0,X3: X0] :
( ( ( X1 @ X3 @ X2 )
!= $true )
& ( ( X1 @ X2 @ X3 )
= $true ) )
| ? [X4: X0,X5: X0,X6: X0] :
( ( ( X1 @ X5 @ X6 )
= $true )
& ( $true
= ( X1 @ X4 @ X5 ) )
& ( ( X1 @ X4 @ X6 )
!= $true ) ) )
& ( ( ! [X7: X0,X8: X0] :
( ( $true
= ( X1 @ X8 @ X7 ) )
| ( $true
!= ( X1 @ X7 @ X8 ) ) )
& ! [X9: X0,X10: X0,X11: X0] :
( ( ( X1 @ X10 @ X11 )
!= $true )
| ( ( X1 @ X9 @ X10 )
!= $true )
| ( $true
= ( X1 @ X9 @ X11 ) ) ) )
| ( ( isPer @ X0 @ X1 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f77]) ).
thf(f77,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ( ( isPer @ X0 @ X1 )
= $true )
| ? [X5: X0,X6: X0] :
( ( ( X1 @ X6 @ X5 )
!= $true )
& ( ( X1 @ X5 @ X6 )
= $true ) )
| ? [X2: X0,X3: X0,X4: X0] :
( ( ( X1 @ X3 @ X4 )
= $true )
& ( ( X1 @ X2 @ X3 )
= $true )
& ( ( X1 @ X2 @ X4 )
!= $true ) ) )
& ( ( ! [X5: X0,X6: X0] :
( ( ( X1 @ X6 @ X5 )
= $true )
| ( ( X1 @ X5 @ X6 )
!= $true ) )
& ! [X2: X0,X3: X0,X4: X0] :
( ( ( X1 @ X3 @ X4 )
!= $true )
| ( ( X1 @ X2 @ X3 )
!= $true )
| ( ( X1 @ X2 @ X4 )
= $true ) ) )
| ( ( isPer @ X0 @ X1 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f76]) ).
thf(f76,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ( ( isPer @ X0 @ X1 )
= $true )
| ? [X5: X0,X6: X0] :
( ( ( X1 @ X6 @ X5 )
!= $true )
& ( ( X1 @ X5 @ X6 )
= $true ) )
| ? [X2: X0,X3: X0,X4: X0] :
( ( ( X1 @ X3 @ X4 )
= $true )
& ( ( X1 @ X2 @ X3 )
= $true )
& ( ( X1 @ X2 @ X4 )
!= $true ) ) )
& ( ( ! [X5: X0,X6: X0] :
( ( ( X1 @ X6 @ X5 )
= $true )
| ( ( X1 @ X5 @ X6 )
!= $true ) )
& ! [X2: X0,X3: X0,X4: X0] :
( ( ( X1 @ X3 @ X4 )
!= $true )
| ( ( X1 @ X2 @ X3 )
!= $true )
| ( ( X1 @ X2 @ X4 )
= $true ) ) )
| ( ( isPer @ X0 @ X1 )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f61]) ).
thf(f61,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ( isPer @ X0 @ X1 )
= $true )
<=> ( ! [X5: X0,X6: X0] :
( ( ( X1 @ X6 @ X5 )
= $true )
| ( ( X1 @ X5 @ X6 )
!= $true ) )
& ! [X2: X0,X3: X0,X4: X0] :
( ( ( X1 @ X3 @ X4 )
!= $true )
| ( ( X1 @ X2 @ X3 )
!= $true )
| ( ( X1 @ X2 @ X4 )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f60]) ).
thf(f60,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ( isPer @ X0 @ X1 )
= $true )
<=> ( ! [X5: X0,X6: X0] :
( ( ( X1 @ X6 @ X5 )
= $true )
| ( ( X1 @ X5 @ X6 )
!= $true ) )
& ! [X2: X0,X3: X0,X4: X0] :
( ( ( X1 @ X2 @ X4 )
= $true )
| ( ( X1 @ X3 @ X4 )
!= $true )
| ( ( X1 @ X2 @ X3 )
!= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f39]) ).
thf(f39,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ( isPer @ X0 @ X1 )
= $true )
<=> ( ! [X5: X0,X6: X0] :
( ( ( X1 @ X5 @ X6 )
= $true )
=> ( ( X1 @ X6 @ X5 )
= $true ) )
& ! [X2: X0,X3: X0,X4: X0] :
( ( ( X1 @ X2 @ X3 )
= $true )
=> ( ( ( X1 @ X3 @ X4 )
= $true )
=> ( ( X1 @ X2 @ X4 )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f38]) ).
thf(f38,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( isPer @ X0 @ X1 )
<=> ( ! [X2: X0,X3: X0,X4: X0] :
( ( X1 @ X2 @ X3 )
=> ( ( X1 @ X3 @ X4 )
=> ( X1 @ X2 @ X4 ) ) )
& ! [X5: X0,X6: X0] :
( ( X1 @ X5 @ X6 )
=> ( X1 @ X6 @ X5 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( isPer @ X0 @ X1 )
<=> ( ! [X2: X0,X3: X0,X4: X0] :
( ( X1 @ X2 @ X3 )
=> ( ( X1 @ X3 @ X4 )
=> ( X1 @ X2 @ X4 ) ) )
& ! [X2: X0,X3: X0] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EoxrKmOWLf/DTF2THF_13150.p',is_per) ).
thf(f120,plain,
( $true
!= ( listStar @ ( plus @ sK1 @ ( suc @ sK4 ) ) @ ( rev @ ( plus @ sK1 @ ( suc @ sK4 ) ) @ ( app @ ( suc @ sK1 ) @ sK4 @ ( rev @ ( suc @ sK1 ) @ ( cons @ sK1 @ sK2 @ sK3 ) ) @ sK5 ) ) @ ( app @ ( suc @ sK4 ) @ sK1 @ ( rev @ ( suc @ sK4 ) @ ( cons @ sK4 @ sK2 @ sK5 ) ) @ sK3 ) ) ),
inference(forward_demodulation,[status(thm)],[f89,f94]) ).
thf(f89,plain,
( ( listStar @ ( plus @ ( suc @ sK1 ) @ sK4 ) @ ( rev @ ( plus @ ( suc @ sK1 ) @ sK4 ) @ ( app @ ( suc @ sK1 ) @ sK4 @ ( rev @ ( suc @ sK1 ) @ ( cons @ sK1 @ sK2 @ sK3 ) ) @ sK5 ) ) @ ( app @ ( suc @ sK4 ) @ sK1 @ ( rev @ ( suc @ sK4 ) @ ( cons @ sK4 @ sK2 @ sK5 ) ) @ sK3 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : DAT391^1 : TPTP v9.2.1. Released v9.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue Feb 24 06:16:30 EST 2026
% 0.11/0.32 % CPUTime :
% 0.11/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.42 ---- Original DTF file ---
% 0.18/0.42 thf(spec,logic,$$dhol).
% 0.18/0.42 %------------------------------------------------------------------------------
% 0.18/0.42 % File : DAT391^1 : TPTP v9.2.1. Released v9.2.0.
% 0.18/0.42 % Domain : Data Structures
% 0.18/0.42 % Problem : List involution lemma, induction step 4
% 0.18/0.42 % Version : Especial.
% 0.18/0.42 % English : List involution lemma. The proof is by induction with a separate
% 0.18/0.42 % problem file for the base and step case (with multiple subcases)
% 0.18/0.42 % as well as the correct instantiation of the induction axiom for
% 0.18/0.42 % lists. The main file uses the conjectures of the other files as
% 0.18/0.42 % lemmas in order to prove the final result. To simplify proof
% 0.18/0.42 % search, the axioms in each problem file have been preselected.
% 0.18/0.42 % For the actual induction proof, it is sufficient to consider the
% 0.18/0.42 % "step" problem files.
% 0.18/0.42
% 0.18/0.42 % Refs : [RRB23] Rothgang et al. (2023), Theorem Proving in Dependently
% 0.18/0.42 % : [Rot25] Rothgang (2025), Email to Geoff Sutcliffe
% 0.18/0.42 % : [RK+25] Ranalter et al. (2025), The Dependently Typed Higher-O
% 0.18/0.42 % Source : [Rot25]
% 0.18/0.42 % Names : ListReversalInvolutionLemma/list-rev-invol-lem-indstep4.p [Rot25]
% 0.18/0.42
% 0.18/0.42 % Status : Theorem
% 0.18/0.42 % Rating : ? v9.2.0
% 0.18/0.42 % Syntax : Number of formulae : 23 ( 10 unt; 10 typ; 0 def)
% 0.18/0.42 % Number of atoms : 15 ( 15 equ; 0 cnn)
% 0.18/0.42 % Maximal formula atoms : 3 ( 1 avg)
% 0.18/0.42 % Number of connectives : 161 ( 3 ~; 0 |; 0 &; 152 @)
% 0.18/0.42 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.18/0.42 % Maximal formula depth : 8 ( 4 avg)
% 0.18/0.42 % Number of types : 3 ( 2 usr)
% 0.18/0.42 % Number of type decls : 10 ( 0 !>P; 3 !>D)
% 0.18/0.42 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.18/0.42 % Number of symbols : 9 ( 8 usr; 2 con; 0-4 aty)
% 0.18/0.42 % Number of variables : 36 ( 0 ^; 32 !; 0 ?; 36 :)
% 0.18/0.42 % ( 4 !>; 0 ?*; 0 @-; 0 @+)
% 0.18/0.42 % SPC : DH0_THM_EQU_NAR
% 0.18/0.42
% 0.18/0.42 % Comments :
% 0.18/0.42 %------------------------------------------------------------------------------
% 0.18/0.42 thf(elem_type,type,
% 0.18/0.42 elem: $tType ).
% 0.18/0.42
% 0.18/0.42 thf(nat_type,type,
% 0.18/0.42 nat: $tType ).
% 0.18/0.42
% 0.18/0.42 thf(zero_type,type,
% 0.18/0.42 zero: nat ).
% 0.18/0.42
% 0.18/0.42 thf(suc_type,type,
% 0.18/0.42 suc: nat > nat ).
% 0.18/0.42
% 0.18/0.42 thf(plus_type,type,
% 0.18/0.42 plus: nat > nat > nat ).
% 0.18/0.42
% 0.18/0.42 thf(list_type,type,
% 0.18/0.42 list: nat > $tType ).
% 0.18/0.42
% 0.18/0.42 thf(nil_type,type,
% 0.18/0.42 nil: list @ zero ).
% 0.18/0.42
% 0.18/0.42 thf(cons_type,type,
% 0.18/0.42 cons:
% 0.18/0.42 !>[N: nat] : ( elem > ( list @ N ) > ( list @ ( suc @ N ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(app_type,type,
% 0.18/0.42 app:
% 0.18/0.42 !>[N: nat,M: nat] : ( ( list @ N ) > ( list @ M ) > ( list @ ( plus @ N @ M ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(rev_type,type,
% 0.18/0.42 rev:
% 0.18/0.42 !>[N: nat] : ( ( list @ N ) > ( list @ N ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(peano1,axiom,
% 0.18/0.42 ! [N: nat] :
% 0.18/0.42 ( ( suc @ N )
% 0.18/0.42 != zero ) ).
% 0.18/0.42
% 0.18/0.42 thf(peano2,axiom,
% 0.18/0.42 ! [N: nat,M: nat] :
% 0.18/0.42 ( ( N != M )
% 0.18/0.42 => ( ( suc @ N )
% 0.18/0.42 != ( suc @ M ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(peano3,axiom,
% 0.18/0.42 ! [P: nat > $o] :
% 0.18/0.42 ( ( P @ zero )
% 0.18/0.42 => ( ! [M: nat] :
% 0.18/0.42 ( ( P @ M )
% 0.18/0.42 => ( P @ ( suc @ M ) ) )
% 0.18/0.42 => ! [N: nat] : ( P @ N ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(ax1,axiom,
% 0.18/0.42 ! [N: nat] :
% 0.18/0.42 ( ( plus @ zero @ N )
% 0.18/0.42 = N ) ).
% 0.18/0.42
% 0.18/0.42 thf(ax2,axiom,
% 0.18/0.42 ! [N: nat,M: nat] :
% 0.18/0.42 ( ( plus @ ( suc @ N ) @ M )
% 0.18/0.42 = ( suc @ ( plus @ N @ M ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(ax3,axiom,
% 0.18/0.42 ! [N: nat,X: list @ N] :
% 0.18/0.42 ( ( app @ zero @ N @ nil @ X )
% 0.18/0.42 = X ) ).
% 0.18/0.42
% 0.18/0.42 thf(ax4,axiom,
% 0.18/0.42 ! [N: nat,M: nat,X: elem,Y: list @ N,Z: list @ M] :
% 0.18/0.42 ( ( app @ ( suc @ N ) @ M @ ( cons @ N @ X @ Y ) @ Z )
% 0.18/0.42 = ( cons @ ( plus @ N @ M ) @ X @ ( app @ N @ M @ Y @ Z ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(plus_zero_r,axiom,
% 0.18/0.42 ! [M: nat] :
% 0.18/0.42 ( ( plus @ M @ zero )
% 0.18/0.42 = M ) ).
% 0.18/0.42
% 0.18/0.42 thf(plus_com,axiom,
% 0.18/0.42 ! [N: nat,M: nat] :
% 0.18/0.42 ( ( plus @ N @ M )
% 0.18/0.42 = ( plus @ M @ N ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(plus_assoc,axiom,
% 0.18/0.42 ! [M1: nat,M2: nat,M3: nat] :
% 0.18/0.42 ( ( plus @ M1 @ ( plus @ M2 @ M3 ) )
% 0.18/0.42 = ( plus @ ( plus @ M1 @ M2 ) @ M3 ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(plus1r,axiom,
% 0.18/0.42 ! [N: nat] :
% 0.18/0.42 ( ( suc @ N )
% 0.18/0.42 = ( plus @ N @ ( suc @ zero ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(plus_s_l_r,axiom,
% 0.18/0.42 ! [N: nat,M: nat] :
% 0.18/0.42 ( ( plus @ ( suc @ N ) @ M )
% 0.18/0.42 = ( plus @ N @ ( suc @ M ) ) ) ).
% 0.18/0.42
% 0.18/0.42 thf(list_rev_invol_lem_indstep4,conjecture,
% 0.18/0.42 ! [N: nat,X: elem,L: list @ N] :
% 0.18/0.42 ( ! [M2: nat,L2: list @ M2] :
% 0.18/0.42 ( ( rev @ ( plus @ N @ M2 ) @ ( app @ N @ M2 @ ( rev @ N @ L ) @ L2 ) )
% 0.18/0.42 = ( app @ M2 @ N @ ( rev @ M2 @ L2 ) @ L ) )
% 0.18/0.42 => ! [M2: nat,L2: list @ M2] :
% 0.18/0.42 ( ( ( rev @ ( plus @ ( suc @ N ) @ M2 ) @ ( app @ ( suc @ N ) @ M2 @ ( rev @ ( suc @ N ) @ ( cons @ N @ X @ L ) ) @ L2 ) )
% 0.18/0.42 = ( rev @ ( plus @ N @ ( suc @ M2 ) ) @ ( app @ N @ ( suc @ M2 ) @ ( rev @ N @ L ) @ ( cons @ M2 @ X @ L2 ) ) ) )
% 0.18/0.42 => ( ( rev @ ( plus @ ( suc @ N ) @ M2 ) @ ( app @ ( suc @ N ) @ M2 @ ( rev @ ( suc @ N ) @ ( cons @ N @ X @ L ) ) @ L2 ) )
% 0.18/0.42 = ( app @ ( suc @ M2 ) @ N @ ( rev @ ( suc @ M2 ) @ ( cons @ M2 @ X @ L2 ) ) @ L ) ) ) ) ).
% 0.18/0.42
% 0.18/0.42 %------------------------------------------------------------------------------
% 0.18/0.42 ------------------------
% 1.36/1.19 ---- Embedded in THF ---
% 1.36/1.19 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.36/1.19 %%% Generated on Tue Feb 24 06:16:31 EST 2026
% 1.36/1.19 %%% using '$$dhol' embedding, version 1.3.0.
% 1.36/1.19 %%% Logic specification used:
% 1.36/1.19 %%% thf(spec, logic, $$dhol).
% 1.36/1.19
% 1.36/1.19 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.EoxrKmOWLf/DTF2DTF13150.p
% See solution above
% 1.36/1.20 ------------------------
% 1.55/1.21 ---- Cleaned THF ---
% 1.55/1.21 thf(is_per_type,type,
% 1.55/1.21 isPer:
% 1.55/1.21 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 1.55/1.21
% 1.55/1.21 thf(is_per,definition,
% 1.55/1.21 ! [A: $tType,AStar: A > A > $o] :
% 1.55/1.21 ( ( isPer @ A @ AStar )
% 1.55/1.21 <=> ( ! [X: A,Y: A] :
% 1.55/1.21 ( ( AStar @ X @ Y )
% 1.55/1.21 => ( AStar @ Y @ X ) )
% 1.55/1.21 & ! [X: A,Y: A,Z: A] :
% 1.55/1.21 ( ( AStar @ X @ Y )
% 1.55/1.21 => ( ( AStar @ Y @ Z )
% 1.55/1.21 => ( AStar @ X @ Z ) ) ) ) ) ).
% 1.55/1.21
% 1.55/1.21 thf(elem_type,type,
% 1.55/1.21 elem: $tType ).
% 1.55/1.21
% 1.55/1.21 thf(elemStar,type,
% 1.55/1.21 elemStar: elem > elem > $o ).
% 1.55/1.21
% 1.55/1.21 thf(elemStar_is_eq,axiom,
% 1.55/1.21 ! [X: elem,Y: elem] :
% 1.55/1.21 ( ( elemStar @ X @ Y )
% 1.55/1.21 <=> ( X = Y ) ) ).
% 1.55/1.21
% 1.55/1.21 thf(nat_type,type,
% 1.55/1.21 nat: $tType ).
% 1.55/1.21
% 1.55/1.21 thf(natStar,type,
% 1.55/1.21 natStar: nat > nat > $o ).
% 1.55/1.21
% 1.55/1.21 thf(natStar_is_eq,axiom,
% 1.55/1.21 ! [X: nat,Y: nat] :
% 1.55/1.21 ( ( natStar @ X @ Y )
% 1.55/1.21 <=> ( X = Y ) ) ).
% 1.55/1.21
% 1.55/1.21 thf(zero_type,type,
% 1.55/1.21 zero: nat ).
% 1.55/1.21
% 1.55/1.21 thf(suc_type,type,
% 1.55/1.21 suc: nat > nat ).
% 1.55/1.21
% 1.55/1.21 thf(plus_type,type,
% 1.55/1.21 plus: nat > nat > nat ).
% 1.55/1.21
% 1.55/1.21 thf(list_type,type,
% 1.55/1.21 list: $tType ).
% 1.55/1.21
% 1.55/1.21 thf(listStar,type,
% 1.55/1.21 listStar: nat > list > list > $o ).
% 1.55/1.21
% 1.55/1.21 thf('\'listStar\'_is_per',axiom,
% 1.55/1.21 ! [C: nat] : ( isPer @ list @ ( listStar @ C ) ) ).
% 1.55/1.21
% 1.55/1.21 thf(nil_type,type,
% 1.55/1.21 nil: list ).
% 1.55/1.21
% 1.55/1.21 thf(nil_tp_ax,axiom,
% 1.55/1.21 listStar @ zero @ nil @ nil ).
% 1.55/1.21
% 1.55/1.21 thf(cons_type,type,
% 1.55/1.21 cons: nat > elem > list > list ).
% 1.55/1.21
% 1.55/1.21 thf(cons_tp_ax,axiom,
% 1.55/1.21 ! [N: nat,D: elem,D0: list,D0_prime: list] :
% 1.55/1.21 ( ( listStar @ N @ D0 @ D0_prime )
% 1.55/1.21 => ( listStar @ ( suc @ N ) @ ( cons @ N @ D @ D0 ) @ ( cons @ N @ D @ D0_prime ) ) ) ).
% 1.55/1.21
% 1.55/1.21 thf(app_type,type,
% 1.55/1.21 app: nat > nat > list > list > list ).
% 1.55/1.21
% 1.55/1.21 thf(app_tp_ax,axiom,
% 1.55/1.21 ! [N: nat,M: nat,D: list,D_prime: list] :
% 1.55/1.21 ( ( listStar @ N @ D @ D_prime )
% 1.55/1.21 => ! [D0: list,D0_prime: list] :
% 1.55/1.21 ( ( listStar @ M @ D0 @ D0_prime )
% 1.55/1.21 => ( listStar @ ( plus @ N @ M ) @ ( app @ N @ M @ D @ D0 ) @ ( app @ N @ M @ D_prime @ D0_prime ) ) ) ) ).
% 1.55/1.21
% 1.55/1.21 thf(rev_type,type,
% 1.55/1.21 rev: nat > list > list ).
% 1.55/1.21
% 1.55/1.21 thf(rev_tp_ax,axiom,
% 1.55/1.21 ! [N: nat,D: list,D_prime: list] :
% 1.55/1.21 ( ( listStar @ N @ D @ D_prime )
% 1.55/1.21 => ( listStar @ N @ ( rev @ N @ D ) @ ( rev @ N @ D_prime ) ) ) ).
% 1.55/1.21
% 1.55/1.21 thf(peano1,axiom,
% 1.55/1.21 ! [N: nat] :
% 1.55/1.21 ( ( suc @ N )
% 1.55/1.21 != zero ) ).
% 1.55/1.21
% 1.55/1.21 thf(peano2,axiom,
% 1.55/1.21 ! [N: nat,M: nat] :
% 1.55/1.21 ( ( N != M )
% 1.55/1.21 => ( ( suc @ N )
% 1.55/1.21 != ( suc @ M ) ) ) ).
% 1.55/1.21
% 1.55/1.21 thf(peano3,axiom,
% 1.55/1.21 ! [P: nat > $o] :
% 1.55/1.21 ( ( P @ zero )
% 1.55/1.21 => ( ! [M: nat] :
% 1.55/1.21 ( ( P @ M )
% 1.55/1.21 => ( P @ ( suc @ M ) ) )
% 1.55/1.21 => ! [N: nat] : ( P @ N ) ) ) ).
% 1.55/1.21
% 1.55/1.21 thf(ax1,axiom,
% 1.55/1.21 ! [N: nat] :
% 1.55/1.21 ( ( plus @ zero @ N )
% 1.55/1.21 = N ) ).
% 1.55/1.21
% 1.55/1.21 thf(ax2,axiom,
% 1.55/1.21 ! [N: nat,M: nat] :
% 1.55/1.21 ( ( plus @ ( suc @ N ) @ M )
% 1.55/1.21 = ( suc @ ( plus @ N @ M ) ) ) ).
% 1.55/1.21
% 1.55/1.21 thf(ax3,axiom,
% 1.55/1.21 ! [N: nat,X: list] :
% 1.55/1.21 ( ( listStar @ N @ X @ X )
% 1.55/1.21 => ( listStar @ ( plus @ zero @ N ) @ ( app @ zero @ N @ nil @ X ) @ X ) ) ).
% 1.55/1.21
% 1.55/1.21 thf(ax4,axiom,
% 1.55/1.21 ! [N: nat,M: nat,X: elem,Y: list,Z: list] :
% 1.55/1.21 ( ( listStar @ N @ Y @ Y )
% 1.55/1.21 => ( ( listStar @ M @ Z @ Z )
% 1.55/1.21 => ( listStar @ ( plus @ ( suc @ N ) @ M ) @ ( app @ ( suc @ N ) @ M @ ( cons @ N @ X @ Y ) @ Z ) @ ( cons @ ( plus @ N @ M ) @ X @ ( app @ N @ M @ Y @ Z ) ) ) ) ) ).
% 1.55/1.21
% 1.55/1.21 thf(plus_zero_r,axiom,
% 1.55/1.21 ! [M: nat] :
% 1.55/1.21 ( ( plus @ M @ zero )
% 1.55/1.21 = M ) ).
% 1.55/1.21
% 1.55/1.21 thf(plus_com,axiom,
% 1.55/1.21 ! [N: nat,M: nat] :
% 1.55/1.21 ( ( plus @ N @ M )
% 1.55/1.21 = ( plus @ M @ N ) ) ).
% 1.55/1.21
% 1.55/1.21 thf(plus_assoc,axiom,
% 1.55/1.21 ! [M1: nat,M2: nat,M3: nat] :
% 1.55/1.21 ( ( plus @ M1 @ ( plus @ M2 @ M3 ) )
% 1.55/1.21 = ( plus @ ( plus @ M1 @ M2 ) @ M3 ) ) ).
% 1.55/1.21
% 1.55/1.21 thf(plus1r,axiom,
% 1.55/1.21 ! [N: nat] :
% 1.55/1.21 ( ( suc @ N )
% 1.55/1.21 = ( plus @ N @ ( suc @ zero ) ) ) ).
% 1.55/1.21
% 1.55/1.21 thf(plus_s_l_r,axiom,
% 1.55/1.21 ! [N: nat,M: nat] :
% 1.55/1.21 ( ( plus @ ( suc @ N ) @ M )
% 1.55/1.21 = ( plus @ N @ ( suc @ M ) ) ) ).
% 1.55/1.21
% 1.55/1.21 thf(list_rev_invol_lem_indstep4,conjecture,
% 1.55/1.21 ! [N: nat,X: elem,L: list] :
% 1.55/1.21 ( ( listStar @ N @ L @ L )
% 1.55/1.21 => ( ! [M2: nat,L2: list] :
% 1.55/1.21 ( ( listStar @ M2 @ L2 @ L2 )
% 1.55/1.21 => ( listStar @ ( plus @ N @ M2 ) @ ( rev @ ( plus @ N @ M2 ) @ ( app @ N @ M2 @ ( rev @ N @ L ) @ L2 ) ) @ ( app @ M2 @ N @ ( rev @ M2 @ L2 ) @ L ) ) )
% 1.55/1.21 => ! [M2: nat,L2: list] :
% 1.55/1.21 ( ( listStar @ M2 @ L2 @ L2 )
% 1.55/1.21 => ( ( listStar @ ( plus @ ( suc @ N ) @ M2 ) @ ( rev @ ( plus @ ( suc @ N ) @ M2 ) @ ( app @ ( suc @ N ) @ M2 @ ( rev @ ( suc @ N ) @ ( cons @ N @ X @ L ) ) @ L2 ) ) @ ( rev @ ( plus @ N @ ( suc @ M2 ) ) @ ( app @ N @ ( suc @ M2 ) @ ( rev @ N @ L ) @ ( cons @ M2 @ X @ L2 ) ) ) )
% 1.55/1.21 => ( listStar @ ( plus @ ( suc @ N ) @ M2 ) @ ( rev @ ( plus @ ( suc @ N ) @ M2 ) @ ( app @ ( suc @ N ) @ M2 @ ( rev @ ( suc @ N ) @ ( cons @ N @ X @ L ) ) @ L2 ) ) @ ( app @ ( suc @ M2 ) @ N @ ( rev @ ( suc @ M2 ) @ ( cons @ M2 @ X @ L2 ) ) @ L ) ) ) ) ) ) ).
% 1.55/1.21 ------------------------
% 1.55/1.22 % (13253)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13150 for (2999ds/183Mi)
% 1.55/1.23 % (13257)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_13150 for (2999ds/2Mi)
% 1.55/1.23 % (13258)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_13150 for (2999ds/275Mi)
% 1.55/1.23 % (13254)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_13150 for (2999ds/4Mi)
% 1.55/1.23 % (13256)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13150 for (2999ds/2Mi)
% 1.55/1.23 % (13255)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_13150 for (2999ds/27Mi)
% 1.55/1.23 % (13259)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13150 for (2999ds/18Mi)
% 1.55/1.23 % (13256)Instruction limit reached!
% 1.55/1.23 % (13256)------------------------------
% 1.55/1.23 % (13256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.23 % (13257)Instruction limit reached!
% 1.55/1.23 % (13257)------------------------------
% 1.55/1.23 % (13257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.23 % (13256)Termination reason: Unknown
% 1.55/1.23 % (13256)Termination phase: shuffling
% 1.55/1.23
% 1.55/1.23 % (13256)Memory used [KB]: 1023
% 1.55/1.23 % (13256)Time elapsed: 0.002 s
% 1.55/1.23 % (13256)Instructions burned: 2 (million)
% 1.55/1.23 % (13256)------------------------------
% 1.55/1.23 % (13256)------------------------------
% 1.55/1.23 % (13257)Termination reason: Unknown
% 1.55/1.23 % (13257)Termination phase: shuffling
% 1.55/1.23
% 1.55/1.23 % (13257)Memory used [KB]: 1023
% 1.55/1.23 % (13257)Time elapsed: 0.002 s
% 1.55/1.23 % (13257)Instructions burned: 2 (million)
% 1.55/1.23 % (13257)------------------------------
% 1.55/1.23 % (13257)------------------------------
% 1.55/1.23 % (13254)Instruction limit reached!
% 1.55/1.23 % (13254)------------------------------
% 1.55/1.23 % (13254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.23 % (13254)Termination reason: Unknown
% 1.55/1.23 % (13254)Termination phase: Property scanning
% 1.55/1.23
% 1.55/1.23 % (13254)Memory used [KB]: 1023
% 1.55/1.23 % (13254)Time elapsed: 0.004 s
% 1.55/1.23 % (13254)Instructions burned: 6 (million)
% 1.55/1.23 % (13254)------------------------------
% 1.55/1.23 % (13254)------------------------------
% 1.55/1.23 % (13259)Instruction limit reached!
% 1.55/1.23 % (13259)------------------------------
% 1.55/1.23 % (13259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.23 % (13259)Termination reason: Unknown
% 1.55/1.23 % (13259)Termination phase: Saturation
% 1.55/1.23
% 1.55/1.23 % (13259)Memory used [KB]: 5628
% 1.55/1.23 % (13259)Time elapsed: 0.010 s
% 1.55/1.23 % (13259)Instructions burned: 18 (million)
% 1.55/1.23 % (13259)------------------------------
% 1.55/1.23 % (13259)------------------------------
% 1.55/1.24 % (13255)Instruction limit reached!
% 1.55/1.24 % (13255)------------------------------
% 1.55/1.24 % (13255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.24 % (13255)Termination reason: Unknown
% 1.55/1.24 % (13255)Termination phase: Saturation
% 1.55/1.24
% 1.55/1.24 % (13255)Memory used [KB]: 5628
% 1.55/1.24 % (13255)Time elapsed: 0.016 s
% 1.55/1.24 % (13255)Instructions burned: 28 (million)
% 1.55/1.24 % (13255)------------------------------
% 1.55/1.24 % (13255)------------------------------
% 1.55/1.24 % (13260)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13150 for (2999ds/3Mi)
% 1.55/1.24 % (13261)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_13150 for (2999ds/37Mi)
% 1.55/1.24 % (13260)Instruction limit reached!
% 1.55/1.24 % (13260)------------------------------
% 1.55/1.24 % (13260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.24 % (13260)Termination reason: Unknown
% 1.55/1.24 % (13260)Termination phase: Property scanning
% 1.55/1.24
% 1.55/1.24 % (13260)Memory used [KB]: 1023
% 1.55/1.24 % (13260)Time elapsed: 0.003 s
% 1.55/1.24 % (13260)Instructions burned: 4 (million)
% 1.55/1.24 % (13260)------------------------------
% 1.55/1.24 % (13260)------------------------------
% 1.55/1.24 % (13262)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_13150 for (2999ds/15Mi)
% 1.55/1.25 % (13263)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_13150 for (2999ds/3Mi)
% 1.55/1.25 % (13262)Instruction limit reached!
% 1.55/1.25 % (13262)------------------------------
% 1.55/1.25 % (13262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.25 % (13262)Termination reason: Unknown
% 1.55/1.25 % (13263)Instruction limit reached!
% 1.55/1.25 % (13263)------------------------------
% 1.55/1.25 % (13263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.25 % (13262)Termination phase: Saturation
% 1.55/1.25
% 1.55/1.25 % (13262)Memory used [KB]: 5756
% 1.55/1.25 % (13262)Time elapsed: 0.009 s
% 1.55/1.25 % (13262)Instructions burned: 16 (million)
% 1.55/1.25 % (13262)------------------------------
% 1.55/1.25 % (13262)------------------------------
% 1.55/1.25 % (13263)Termination reason: Unknown
% 1.55/1.25 % (13263)Termination phase: Property scanning
% 1.55/1.25
% 1.55/1.25 % (13263)Memory used [KB]: 1023
% 1.55/1.25 % (13263)Time elapsed: 0.003 s
% 1.55/1.25 % (13263)Instructions burned: 4 (million)
% 1.55/1.25 % (13263)------------------------------
% 1.55/1.25 % (13263)------------------------------
% 1.55/1.26 % (13264)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_13150 for (2999ds/1041Mi)
% 1.55/1.26 % (13265)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_13150 for (2999ds/7Mi)
% 1.55/1.26 % (13261)Instruction limit reached!
% 1.55/1.26 % (13261)------------------------------
% 1.55/1.26 % (13261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.26 % (13261)Termination reason: Unknown
% 1.55/1.26 % (13261)Termination phase: Saturation
% 1.55/1.26
% 1.55/1.26 % (13261)Memory used [KB]: 5884
% 1.55/1.26 % (13261)Time elapsed: 0.019 s
% 1.55/1.26 % (13261)Instructions burned: 37 (million)
% 1.55/1.26 % (13261)------------------------------
% 1.55/1.26 % (13261)------------------------------
% 1.55/1.26 % (13265)Instruction limit reached!
% 1.55/1.26 % (13265)------------------------------
% 1.55/1.26 % (13265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.26 % (13265)Termination reason: Unknown
% 1.55/1.26 % (13265)Termination phase: Property scanning
% 1.55/1.26
% 1.55/1.26 % (13265)Memory used [KB]: 1023
% 1.55/1.26 % (13265)Time elapsed: 0.005 s
% 1.55/1.26 % (13265)Instructions burned: 9 (million)
% 1.55/1.26 % (13265)------------------------------
% 1.55/1.26 % (13265)------------------------------
% 1.55/1.27 % (13266)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_13150 for (2999ds/16Mi)
% 1.55/1.27 % (13267)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_13150 for (2999ds/3Mi)
% 1.55/1.27 % (13267)Instruction limit reached!
% 1.55/1.27 % (13267)------------------------------
% 1.55/1.27 % (13267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.27 % (13267)Termination reason: Unknown
% 1.55/1.27 % (13267)Termination phase: Property scanning
% 1.55/1.27
% 1.55/1.27 % (13267)Memory used [KB]: 1023
% 1.55/1.27 % (13267)Time elapsed: 0.003 s
% 1.55/1.27 % (13267)Instructions burned: 4 (million)
% 1.55/1.27 % (13267)------------------------------
% 1.55/1.27 % (13267)------------------------------
% 1.55/1.28 % (13266)Instruction limit reached!
% 1.55/1.28 % (13266)------------------------------
% 1.55/1.28 % (13266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.28 % (13266)Termination reason: Unknown
% 1.55/1.28 % (13266)Termination phase: Saturation
% 1.55/1.28
% 1.55/1.28 % (13266)Memory used [KB]: 5628
% 1.55/1.28 % (13266)Time elapsed: 0.009 s
% 1.55/1.28 % (13266)Instructions burned: 16 (million)
% 1.55/1.28 % (13266)------------------------------
% 1.55/1.28 % (13266)------------------------------
% 1.55/1.28 % (13268)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_13150 for (2999ds/3Mi)
% 1.55/1.28 % (13253)Instruction limit reached!
% 1.55/1.28 % (13253)------------------------------
% 1.55/1.28 % (13253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.28 % (13253)Termination reason: Unknown
% 1.55/1.28 % (13253)Termination phase: Saturation
% 1.55/1.28
% 1.55/1.28 % (13253)Memory used [KB]: 6524
% 1.55/1.28 % (13253)Time elapsed: 0.059 s
% 1.55/1.28 % (13253)Instructions burned: 185 (million)
% 1.55/1.28 % (13253)------------------------------
% 1.55/1.28 % (13253)------------------------------
% 1.55/1.28 % (13268)Instruction limit reached!
% 1.55/1.28 % (13268)------------------------------
% 1.55/1.28 % (13268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.28 % (13268)Termination reason: Unknown
% 1.55/1.28 % (13268)Termination phase: Property scanning
% 1.55/1.28
% 1.55/1.28 % (13268)Memory used [KB]: 1023
% 1.55/1.28 % (13268)Time elapsed: 0.003 s
% 1.55/1.28 % (13268)Instructions burned: 4 (million)
% 1.55/1.28 % (13268)------------------------------
% 1.55/1.28 % (13268)------------------------------
% 1.55/1.28 % (13269)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_13150 for (2999ds/7Mi)
% 1.55/1.28 % (13269)Instruction limit reached!
% 1.55/1.28 % (13269)------------------------------
% 1.55/1.28 % (13269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.28 % (13269)Termination reason: Unknown
% 1.55/1.28 % (13269)Termination phase: Property scanning
% 1.55/1.28
% 1.55/1.28 % (13269)Memory used [KB]: 1023
% 1.55/1.28 % (13269)Time elapsed: 0.005 s
% 1.55/1.28 % (13269)Instructions burned: 9 (million)
% 1.55/1.28 % (13269)------------------------------
% 1.55/1.28 % (13269)------------------------------
% 1.55/1.29 % (13270)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_13150 for (2999ds/3Mi)
% 1.55/1.29 % (13272)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_13150 for (2999ds/18Mi)
% 1.55/1.29 % (13270)Instruction limit reached!
% 1.55/1.29 % (13270)------------------------------
% 1.55/1.29 % (13270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.29 % (13270)Termination reason: Unknown
% 1.55/1.29 % (13270)Termination phase: shuffling
% 1.55/1.29
% 1.55/1.29 % (13270)Memory used [KB]: 1023
% 1.55/1.29 % (13270)Time elapsed: 0.003 s
% 1.55/1.29 % (13270)Instructions burned: 4 (million)
% 1.55/1.29 % (13270)------------------------------
% 1.55/1.29 % (13270)------------------------------
% 1.55/1.29 % (13271)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_13150 for (2999ds/4Mi)
% 1.55/1.29 % (13271)Instruction limit reached!
% 1.55/1.29 % (13271)------------------------------
% 1.55/1.29 % (13271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.29 % (13271)Termination reason: Unknown
% 1.55/1.29 % (13271)Termination phase: Property scanning
% 1.55/1.29
% 1.55/1.29 % (13271)Memory used [KB]: 1023
% 1.55/1.29 % (13271)Time elapsed: 0.003 s
% 1.55/1.29 % (13271)Instructions burned: 4 (million)
% 1.55/1.29 % (13271)------------------------------
% 1.55/1.29 % (13271)------------------------------
% 1.55/1.29 % (13272)Instruction limit reached!
% 1.55/1.29 % (13272)------------------------------
% 1.55/1.29 % (13272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.29 % (13272)Termination reason: Unknown
% 1.55/1.29 % (13272)Termination phase: Saturation
% 1.55/1.29
% 1.55/1.29 % (13272)Memory used [KB]: 5628
% 1.55/1.29 % (13272)Time elapsed: 0.007 s
% 1.55/1.29 % (13272)Instructions burned: 20 (million)
% 1.55/1.29 % (13272)------------------------------
% 1.55/1.29 % (13272)------------------------------
% 1.55/1.29 % (13273)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_13150 for (2999ds/710Mi)
% 1.57/1.30 % (13274)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_13150 for (2999ds/6Mi)
% 1.57/1.30 % (13275)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_13150 for (2999ds/902Mi)
% 1.57/1.30 % (13274)Instruction limit reached!
% 1.57/1.30 % (13274)------------------------------
% 1.57/1.30 % (13274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.30 % (13274)Termination reason: Unknown
% 1.57/1.30 % (13274)Termination phase: Preprocessing 3
% 1.57/1.30
% 1.57/1.30 % (13274)Memory used [KB]: 1023
% 1.57/1.30 % (13274)Time elapsed: 0.003 s
% 1.57/1.30 % (13274)Instructions burned: 7 (million)
% 1.57/1.30 % (13274)------------------------------
% 1.57/1.30 % (13274)------------------------------
% 1.57/1.31 % (13277)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_13150 for (2999ds/5Mi)
% 1.57/1.31 % (13276)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_13150 for (2999ds/21Mi)
% 1.57/1.31 % (13277)Instruction limit reached!
% 1.57/1.31 % (13277)------------------------------
% 1.57/1.31 % (13277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.31 % (13277)Termination reason: Unknown
% 1.57/1.31 % (13277)Termination phase: Property scanning
% 1.57/1.31
% 1.57/1.31 % (13277)Memory used [KB]: 1023
% 1.57/1.31 % (13277)Time elapsed: 0.004 s
% 1.57/1.31 % (13277)Instructions burned: 7 (million)
% 1.57/1.31 % (13277)------------------------------
% 1.57/1.31 % (13277)------------------------------
% 1.57/1.31 % (13278)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_13150 for (2999ds/6Mi)
% 1.57/1.32 % (13278)Instruction limit reached!
% 1.57/1.32 % (13278)------------------------------
% 1.57/1.32 % (13278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.32 % (13278)Termination reason: Unknown
% 1.57/1.32 % (13278)Termination phase: SInE selection
% 1.57/1.32
% 1.57/1.32 % (13278)Memory used [KB]: 1023
% 1.57/1.32 % (13278)Time elapsed: 0.003 s
% 1.57/1.32 % (13278)Instructions burned: 8 (million)
% 1.57/1.32 % (13278)------------------------------
% 1.57/1.32 % (13278)------------------------------
% 1.57/1.32 % (13276)Instruction limit reached!
% 1.57/1.32 % (13276)------------------------------
% 1.57/1.32 % (13276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.32 % (13276)Termination reason: Unknown
% 1.57/1.32 % (13276)Termination phase: Saturation
% 1.57/1.32
% 1.57/1.32 % (13276)Memory used [KB]: 5756
% 1.57/1.32 % (13276)Time elapsed: 0.012 s
% 1.57/1.32 % (13276)Instructions burned: 21 (million)
% 1.57/1.32 % (13276)------------------------------
% 1.57/1.32 % (13276)------------------------------
% 1.57/1.32 % (13280)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_13150 for (2999ds/779Mi)
% 1.57/1.33 % (13279)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_13150 for (2999ds/377Mi)
% 1.57/1.34 % (13281)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_13150 for (2998ds/19Mi)
% 1.57/1.35 % (13281)Instruction limit reached!
% 1.57/1.35 % (13281)------------------------------
% 1.57/1.35 % (13281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.35 % (13281)Termination reason: Unknown
% 1.57/1.35 % (13281)Termination phase: Saturation
% 1.57/1.35
% 1.57/1.35 % (13281)Memory used [KB]: 5628
% 1.57/1.35 % (13281)Time elapsed: 0.011 s
% 1.57/1.35 % (13281)Instructions burned: 20 (million)
% 1.57/1.35 % (13281)------------------------------
% 1.57/1.35 % (13281)------------------------------
% 1.57/1.35 % (13258)Instruction limit reached!
% 1.57/1.35 % (13258)------------------------------
% 1.57/1.35 % (13258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.35 % (13258)Termination reason: Unknown
% 1.57/1.35 % (13258)Termination phase: Saturation
% 1.57/1.35
% 1.57/1.35 % (13258)Memory used [KB]: 6396
% 1.57/1.35 % (13258)Time elapsed: 0.130 s
% 1.57/1.35 % (13258)Instructions burned: 275 (million)
% 1.57/1.35 % (13258)------------------------------
% 1.57/1.35 % (13258)------------------------------
% 1.57/1.37 % (13282)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_13150 for (2998ds/879Mi)
% 1.57/1.37 % (13283)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_13150 for (2998ds/17Mi)
% 1.57/1.38 % (13283)Instruction limit reached!
% 1.57/1.38 % (13283)------------------------------
% 1.57/1.38 % (13283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.38 % (13283)Termination reason: Unknown
% 1.57/1.38 % (13283)Termination phase: Saturation
% 1.57/1.38
% 1.57/1.38 % (13283)Memory used [KB]: 5756
% 1.57/1.38 % (13283)Time elapsed: 0.011 s
% 1.57/1.38 % (13283)Instructions burned: 18 (million)
% 1.57/1.38 % (13283)------------------------------
% 1.57/1.38 % (13283)------------------------------
% 1.57/1.39 % (13275)First to succeed.
% 1.57/1.39 % (13275)Refutation found. Thanks to Tanya!
% 1.57/1.39 % SZS status Theorem for DTF2THF_13150
% 1.57/1.39 % SZS output start Proof for DTF2THF_13150
% 1.57/1.39 thf(type_def_6, type, elem: $tType).
% 1.57/1.39 thf(type_def_7, type, nat: $tType).
% 1.57/1.39 thf(type_def_8, type, list: $tType).
% 1.57/1.39 thf(func_def_0, type, isPer: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 1.57/1.39 thf(func_def_2, type, elem: $tType).
% 1.57/1.39 thf(func_def_3, type, elemStar: elem > elem > $o).
% 1.57/1.39 thf(func_def_4, type, nat: $tType).
% 1.57/1.39 thf(func_def_5, type, natStar: nat > nat > $o).
% 1.57/1.39 thf(func_def_6, type, zero: nat).
% 1.57/1.39 thf(func_def_7, type, suc: nat > nat).
% 1.57/1.39 thf(func_def_8, type, plus: nat > nat > nat).
% 1.57/1.39 thf(func_def_9, type, list: $tType).
% 1.57/1.39 thf(func_def_10, type, listStar: nat > list > list > $o).
% 1.57/1.39 thf(func_def_11, type, nil: list).
% 1.57/1.39 thf(func_def_12, type, cons: nat > elem > list > list).
% 1.57/1.39 thf(func_def_13, type, app: nat > nat > list > list > list).
% 1.57/1.39 thf(func_def_14, type, rev: nat > list > list).
% 1.57/1.39 thf(func_def_17, type, sK0: (nat > $o) > nat).
% 1.57/1.39 thf(func_def_18, type, sK1: nat).
% 1.57/1.39 thf(func_def_19, type, sK2: elem).
% 1.57/1.39 thf(func_def_20, type, sK3: list).
% 1.57/1.39 thf(func_def_21, type, sK4: nat).
% 1.57/1.39 thf(func_def_22, type, sK5: list).
% 1.57/1.39 thf(func_def_23, type, sK6: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.57/1.39 thf(func_def_24, type, sK7: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.57/1.39 thf(func_def_25, type, sK8: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.57/1.39 thf(func_def_26, type, sK9: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.57/1.39 thf(func_def_27, type, sK10: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.57/1.39 thf(func_def_29, type, ph12: !>[X0: $tType]:(X0)).
% 1.57/1.39 thf(f390,plain,(
% 1.57/1.39 $false),
% 1.57/1.39 inference(trivial_inequality_removal,[status(thm)],[f387])).
% 1.57/1.39 thf(f387,plain,(
% 1.57/1.39 ($true != $true)),
% 1.57/1.39 inference(superposition,[status(thm)],[f279,f88])).
% 1.57/1.39 thf(f88,plain,(
% 1.57/1.39 ((listStar @ sK4 @ sK5 @ sK5) = $true)),
% 1.57/1.39 inference(cnf_transformation,[status(thm)],[f74])).
% 1.57/1.39 thf(f74,plain,(
% 1.57/1.39 ((listStar @ sK1 @ sK3 @ sK3) = $true) & ! [X3 : nat,X4 : list] : (((listStar @ (plus @ sK1 @ X3) @ (rev @ (plus @ sK1 @ X3) @ (app @ sK1 @ X3 @ (rev @ sK1 @ sK3) @ X4)) @ (app @ X3 @ sK1 @ (rev @ X3 @ X4) @ sK3)) = $true) | ((listStar @ X3 @ X4 @ X4) != $true)) & (((listStar @ (plus @ (suc @ sK1) @ sK4) @ (rev @ (plus @ (suc @ sK1) @ sK4) @ (app @ (suc @ sK1) @ sK4 @ (rev @ (suc @ sK1) @ (cons @ sK1 @ sK2 @ sK3)) @ sK5)) @ (app @ (suc @ sK4) @ sK1 @ (rev @ (suc @ sK4) @ (cons @ sK4 @ sK2 @ sK5)) @ sK3)) != $true) & ((listStar @ sK4 @ sK5 @ sK5) = $true) & ((listStar @ (plus @ (suc @ sK1) @ sK4) @ (rev @ (plus @ (suc @ sK1) @ sK4) @ (app @ (suc @ sK1) @ sK4 @ (rev @ (suc @ sK1) @ (cons @ sK1 @ sK2 @ sK3)) @ sK5)) @ (rev @ (plus @ sK1 @ (suc @ sK4)) @ (app @ sK1 @ (suc @ sK4) @ (rev @ sK1 @ sK3) @ (cons @ sK4 @ sK2 @ sK5)))) = $true))),
% 1.57/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5])],[f58,f73,f72])).
% 1.57/1.39 thf(f72,plain,(
% 1.57/1.39 ? [X0 : nat,X1 : elem,X2 : list] : (((listStar @ X0 @ X2 @ X2) = $true) & ! [X3 : nat,X4 : list] : (((listStar @ (plus @ X0 @ X3) @ (rev @ (plus @ X0 @ X3) @ (app @ X0 @ X3 @ (rev @ X0 @ X2) @ X4)) @ (app @ X3 @ X0 @ (rev @ X3 @ X4) @ X2)) = $true) | ((listStar @ X3 @ X4 @ X4) != $true)) & ? [X5 : nat,X6 : list] : (((listStar @ (plus @ (suc @ X0) @ X5) @ (rev @ (plus @ (suc @ X0) @ X5) @ (app @ (suc @ X0) @ X5 @ (rev @ (suc @ X0) @ (cons @ X0 @ X1 @ X2)) @ X6)) @ (app @ (suc @ X5) @ X0 @ (rev @ (suc @ X5) @ (cons @ X5 @ X1 @ X6)) @ X2)) != $true) & ($true = (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)) @ (rev @ (plus @ X0 @ (suc @ X5)) @ (app @ X0 @ (suc @ X5) @ (rev @ X0 @ X2) @ (cons @ X5 @ X1 @ X6)))) = $true))) => (((listStar @ sK1 @ sK3 @ sK3) = $true) & ! [X4 : list,X3 : nat] : (((listStar @ (plus @ sK1 @ X3) @ (rev @ (plus @ sK1 @ X3) @ (app @ sK1 @ X3 @ (rev @ sK1 @ sK3) @ X4)) @ (app @ X3 @ sK1 @ (rev @ X3 @ X4) @ sK3)) = $true) | ((listStar @ X3 @ X4 @ X4) != $true)) & ? [X6 : list,X5 : nat] : (($true != (listStar @ (plus @ (suc @ sK1) @ X5) @ (rev @ (plus @ (suc @ sK1) @ X5) @ (app @ (suc @ sK1) @ X5 @ (rev @ (suc @ sK1) @ (cons @ sK1 @ sK2 @ sK3)) @ X6)) @ (app @ (suc @ X5) @ sK1 @ (rev @ (suc @ X5) @ (cons @ X5 @ sK2 @ X6)) @ sK3))) & ($true = (listStar @ X5 @ X6 @ X6)) & ((listStar @ (plus @ (suc @ sK1) @ X5) @ (rev @ (plus @ (suc @ sK1) @ X5) @ (app @ (suc @ sK1) @ X5 @ (rev @ (suc @ sK1) @ (cons @ sK1 @ sK2 @ sK3)) @ X6)) @ (rev @ (plus @ sK1 @ (suc @ X5)) @ (app @ sK1 @ (suc @ X5) @ (rev @ sK1 @ sK3) @ (cons @ X5 @ sK2 @ X6)))) = $true)))),
% 1.57/1.39 introduced(definition,[],[choice_axiom])).
% 1.57/1.39 thf(f73,plain,(
% 1.57/1.39 ? [X6 : list,X5 : nat] : (($true != (listStar @ (plus @ (suc @ sK1) @ X5) @ (rev @ (plus @ (suc @ sK1) @ X5) @ (app @ (suc @ sK1) @ X5 @ (rev @ (suc @ sK1) @ (cons @ sK1 @ sK2 @ sK3)) @ X6)) @ (app @ (suc @ X5) @ sK1 @ (rev @ (suc @ X5) @ (cons @ X5 @ sK2 @ X6)) @ sK3))) & ($true = (listStar @ X5 @ X6 @ X6)) & ((listStar @ (plus @ (suc @ sK1) @ X5) @ (rev @ (plus @ (suc @ sK1) @ X5) @ (app @ (suc @ sK1) @ X5 @ (rev @ (suc @ sK1) @ (cons @ sK1 @ sK2 @ sK3)) @ X6)) @ (rev @ (plus @ sK1 @ (suc @ X5)) @ (app @ sK1 @ (suc @ X5) @ (rev @ sK1 @ sK3) @ (cons @ X5 @ sK2 @ X6)))) = $true)) => (((listStar @ (plus @ (suc @ sK1) @ sK4) @ (rev @ (plus @ (suc @ sK1) @ sK4) @ (app @ (suc @ sK1) @ sK4 @ (rev @ (suc @ sK1) @ (cons @ sK1 @ sK2 @ sK3)) @ sK5)) @ (app @ (suc @ sK4) @ sK1 @ (rev @ (suc @ sK4) @ (cons @ sK4 @ sK2 @ sK5)) @ sK3)) != $true) & ((listStar @ sK4 @ sK5 @ sK5) = $true) & ((listStar @ (plus @ (suc @ sK1) @ sK4) @ (rev @ (plus @ (suc @ sK1) @ sK4) @ (app @ (suc @ sK1) @ sK4 @ (rev @ (suc @ sK1) @ (cons @ sK1 @ sK2 @ sK3)) @ sK5)) @ (rev @ (plus @ sK1 @ (suc @ sK4)) @ (app @ sK1 @ (suc @ sK4) @ (rev @ sK1 @ sK3) @ (cons @ sK4 @ sK2 @ sK5)))) = $true))),
% 1.57/1.39 introduced(definition,[],[choice_axiom])).
% 1.57/1.39 thf(f58,plain,(
% 1.57/1.39 ? [X0 : nat,X1 : elem,X2 : list] : (((listStar @ X0 @ X2 @ X2) = $true) & ! [X3 : nat,X4 : list] : (((listStar @ (plus @ X0 @ X3) @ (rev @ (plus @ X0 @ X3) @ (app @ X0 @ X3 @ (rev @ X0 @ X2) @ X4)) @ (app @ X3 @ X0 @ (rev @ X3 @ X4) @ X2)) = $true) | ((listStar @ X3 @ X4 @ X4) != $true)) & ? [X5 : nat,X6 : list] : (((listStar @ (plus @ (suc @ X0) @ X5) @ (rev @ (plus @ (suc @ X0) @ X5) @ (app @ (suc @ X0) @ X5 @ (rev @ (suc @ X0) @ (cons @ X0 @ X1 @ X2)) @ X6)) @ (app @ (suc @ X5) @ X0 @ (rev @ (suc @ X5) @ (cons @ X5 @ X1 @ X6)) @ X2)) != $true) & ($true = (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)) @ (rev @ (plus @ X0 @ (suc @ X5)) @ (app @ X0 @ (suc @ X5) @ (rev @ X0 @ X2) @ (cons @ X5 @ X1 @ X6)))) = $true)))),
% 1.57/1.39 inference(flattening,[status(thm)],[f57])).
% 1.57/1.39 thf(f57,plain,(
% 1.57/1.39 ? [X0 : nat,X1 : elem,X2 : list] : ((? [X5 : nat,X6 : list] : ((((listStar @ (plus @ (suc @ X0) @ X5) @ (rev @ (plus @ (suc @ X0) @ X5) @ (app @ (suc @ X0) @ X5 @ (rev @ (suc @ X0) @ (cons @ X0 @ X1 @ X2)) @ X6)) @ (app @ (suc @ X5) @ X0 @ (rev @ (suc @ X5) @ (cons @ X5 @ X1 @ X6)) @ X2)) != $true) & ((listStar @ (plus @ (suc @ X0) @ X5) @ (rev @ (plus @ (suc @ X0) @ X5) @ (app @ (suc @ X0) @ X5 @ (rev @ (suc @ X0) @ (cons @ X0 @ X1 @ X2)) @ X6)) @ (rev @ (plus @ X0 @ (suc @ X5)) @ (app @ X0 @ (suc @ X5) @ (rev @ X0 @ X2) @ (cons @ X5 @ X1 @ X6)))) = $true)) & ($true = (listStar @ X5 @ X6 @ X6))) & ! [X3 : nat,X4 : list] : (((listStar @ (plus @ X0 @ X3) @ (rev @ (plus @ X0 @ X3) @ (app @ X0 @ X3 @ (rev @ X0 @ X2) @ X4)) @ (app @ X3 @ X0 @ (rev @ X3 @ X4) @ X2)) = $true) | ((listStar @ X3 @ X4 @ X4) != $true))) & ((listStar @ X0 @ X2 @ X2) = $true))),
% 1.57/1.39 inference(ennf_transformation,[status(thm)],[f35])).
% 1.57/1.39 thf(f35,plain,(
% 1.57/1.39 ~! [X0 : nat,X1 : elem,X2 : list] : (((listStar @ X0 @ X2 @ X2) = $true) => (! [X3 : nat,X4 : list] : (((listStar @ X3 @ X4 @ X4) = $true) => ((listStar @ (plus @ X0 @ X3) @ (rev @ (plus @ X0 @ X3) @ (app @ X0 @ X3 @ (rev @ X0 @ X2) @ X4)) @ (app @ X3 @ X0 @ (rev @ X3 @ X4) @ X2)) = $true)) => ! [X5 : nat,X6 : list] : (($true = (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)) @ (rev @ (plus @ X0 @ (suc @ X5)) @ (app @ X0 @ (suc @ X5) @ (rev @ X0 @ X2) @ (cons @ X5 @ X1 @ X6)))) = $true) => ((listStar @ (plus @ (suc @ X0) @ X5) @ (rev @ (plus @ (suc @ X0) @ X5) @ (app @ (suc @ X0) @ X5 @ (rev @ (suc @ X0) @ (cons @ X0 @ X1 @ X2)) @ X6)) @ (app @ (suc @ X5) @ X0 @ (rev @ (suc @ X5) @ (cons @ X5 @ X1 @ X6)) @ X2)) = $true)))))),
% 1.57/1.39 inference(fool_elimination,[status(thm)],[f34])).
% 1.57/1.39 thf(f34,plain,(
% 1.57/1.39 ~! [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)) @ (rev @ (plus @ X0 @ (suc @ X5)) @ (app @ X0 @ (suc @ X5) @ (rev @ X0 @ X2) @ (cons @ X5 @ X1 @ X6)))) => (listStar @ (plus @ (suc @ X0) @ X5) @ (rev @ (plus @ (suc @ X0) @ X5) @ (app @ (suc @ X0) @ X5 @ (rev @ (suc @ X0) @ (cons @ X0 @ X1 @ X2)) @ X6)) @ (app @ (suc @ X5) @ X0 @ (rev @ (suc @ X5) @ (cons @ X5 @ X1 @ X6)) @ X2))))))),
% 1.57/1.39 inference(rectify,[status(thm)],[f22])).
% 1.57/1.39 thf(f22,negated_conjecture,(
% 1.57/1.39 ~! [X6 : nat,X2 : elem,X16 : list] : ((listStar @ X6 @ X16 @ X16) => (! [X14 : nat,X17 : list] : ((listStar @ X14 @ X17 @ X17) => (listStar @ (plus @ X6 @ X14) @ (rev @ (plus @ X6 @ X14) @ (app @ X6 @ X14 @ (rev @ X6 @ X16) @ X17)) @ (app @ X14 @ X6 @ (rev @ X14 @ X17) @ X16))) => ! [X14 : nat,X17 : list] : ((listStar @ X14 @ X17 @ X17) => ((listStar @ (plus @ (suc @ X6) @ X14) @ (rev @ (plus @ (suc @ X6) @ X14) @ (app @ (suc @ X6) @ X14 @ (rev @ (suc @ X6) @ (cons @ X6 @ X2 @ X16)) @ X17)) @ (rev @ (plus @ X6 @ (suc @ X14)) @ (app @ X6 @ (suc @ X14) @ (rev @ X6 @ X16) @ (cons @ X14 @ X2 @ X17)))) => (listStar @ (plus @ (suc @ X6) @ X14) @ (rev @ (plus @ (suc @ X6) @ X14) @ (app @ (suc @ X6) @ X14 @ (rev @ (suc @ X6) @ (cons @ X6 @ X2 @ X16)) @ X17)) @ (app @ (suc @ X14) @ X6 @ (rev @ (suc @ X14) @ (cons @ X14 @ X2 @ X17)) @ X16))))))),
% 1.57/1.39 inference(negated_conjecture,[status(cth)],[f21])).
% 1.57/1.39 thf(f21,conjecture,(
% 1.57/1.39 ! [X6 : nat,X2 : elem,X16 : list] : ((listStar @ X6 @ X16 @ X16) => (! [X14 : nat,X17 : list] : ((listStar @ X14 @ X17 @ X17) => (listStar @ (plus @ X6 @ X14) @ (rev @ (plus @ X6 @ X14) @ (app @ X6 @ X14 @ (rev @ X6 @ X16) @ X17)) @ (app @ X14 @ X6 @ (rev @ X14 @ X17) @ X16))) => ! [X14 : nat,X17 : list] : ((listStar @ X14 @ X17 @ X17) => ((listStar @ (plus @ (suc @ X6) @ X14) @ (rev @ (plus @ (suc @ X6) @ X14) @ (app @ (suc @ X6) @ X14 @ (rev @ (suc @ X6) @ (cons @ X6 @ X2 @ X16)) @ X17)) @ (rev @ (plus @ X6 @ (suc @ X14)) @ (app @ X6 @ (suc @ X14) @ (rev @ X6 @ X16) @ (cons @ X14 @ X2 @ X17)))) => (listStar @ (plus @ (suc @ X6) @ X14) @ (rev @ (plus @ (suc @ X6) @ X14) @ (app @ (suc @ X6) @ X14 @ (rev @ (suc @ X6) @ (cons @ X6 @ X2 @ X16)) @ X17)) @ (app @ (suc @ X14) @ X6 @ (rev @ (suc @ X14) @ (cons @ X14 @ X2 @ X17)) @ X16))))))),
% 1.57/1.39 file('/export/starexec/sandbox/tmp/tmp.EoxrKmOWLf/DTF2THF_13150.p',list_rev_invol_lem_indstep4)).
% 1.57/1.39 thf(f279,plain,(
% 1.57/1.39 ((listStar @ sK4 @ sK5 @ sK5) != $true)),
% 1.57/1.39 inference(trivial_inequality_removal,[status(thm)],[f275])).
% 1.57/1.39 thf(f275,plain,(
% 1.57/1.39 ((listStar @ sK4 @ sK5 @ sK5) != $true) | ($true != $true)),
% 1.57/1.39 inference(superposition,[status(thm)],[f217,f116])).
% 1.57/1.39 thf(f116,plain,(
% 1.57/1.39 ( ! [X2 : list,X3 : list,X0 : nat,X1 : elem] : (((listStar @ (suc @ X0) @ (cons @ X0 @ X1 @ X2) @ (cons @ X0 @ X1 @ X3)) = $true) | ((listStar @ X0 @ X2 @ X3) != $true)) )),
% 1.57/1.39 inference(cnf_transformation,[status(thm)],[f69])).
% 1.57/1.39 thf(f69,plain,(
% 1.57/1.39 ! [X0 : nat,X1 : elem,X2 : list,X3 : list] : (((listStar @ X0 @ X2 @ X3) != $true) | ((listStar @ (suc @ X0) @ (cons @ X0 @ X1 @ X2) @ (cons @ X0 @ X1 @ X3)) = $true))),
% 1.57/1.39 inference(ennf_transformation,[status(thm)],[f31])).
% 1.57/1.39 thf(f31,plain,(
% 1.57/1.39 ! [X0 : nat,X1 : elem,X2 : list,X3 : list] : (((listStar @ X0 @ X2 @ X3) = $true) => ((listStar @ (suc @ X0) @ (cons @ X0 @ X1 @ X2) @ (cons @ X0 @ X1 @ X3)) = $true))),
% 1.57/1.39 inference(fool_elimination,[status(thm)],[f30])).
% 1.57/1.39 thf(f30,plain,(
% 1.57/1.39 ! [X0 : nat,X1 : elem,X2 : list,X3 : list] : ((listStar @ X0 @ X2 @ X3) => (listStar @ (suc @ X0) @ (cons @ X0 @ X1 @ X2) @ (cons @ X0 @ X1 @ X3)))),
% 1.57/1.39 inference(rectify,[status(thm)],[f6])).
% 1.57/1.39 thf(f6,axiom,(
% 1.57/1.39 ! [X6 : nat,X7 : elem,X8 : list,X9 : list] : ((listStar @ X6 @ X8 @ X9) => (listStar @ (suc @ X6) @ (cons @ X6 @ X7 @ X8) @ (cons @ X6 @ X7 @ X9)))),
% 1.57/1.39 file('/export/starexec/sandbox/tmp/tmp.EoxrKmOWLf/DTF2THF_13150.p',cons_tp_ax)).
% 1.57/1.39 thf(f217,plain,(
% 1.57/1.39 ((listStar @ (suc @ sK4) @ (cons @ sK4 @ sK2 @ sK5) @ (cons @ sK4 @ sK2 @ sK5)) != $true)),
% 1.57/1.39 inference(trivial_inequality_removal,[status(thm)],[f211])).
% 1.57/1.39 thf(f211,plain,(
% 1.57/1.39 ($true != $true) | ((listStar @ (suc @ sK4) @ (cons @ sK4 @ sK2 @ sK5) @ (cons @ sK4 @ sK2 @ sK5)) != $true)),
% 1.57/1.39 inference(superposition,[status(thm)],[f159,f140])).
% 1.57/1.39 thf(f140,plain,(
% 1.57/1.39 ( ! [X0 : nat,X1 : list] : (((listStar @ (plus @ sK1 @ X0) @ (rev @ (plus @ sK1 @ X0) @ (app @ sK1 @ X0 @ (rev @ sK1 @ sK3) @ X1)) @ (app @ X0 @ sK1 @ (rev @ X0 @ X1) @ sK3)) = $true) | ($true != (listStar @ X0 @ X1 @ X1))) )),
% 1.57/1.39 inference(superposition,[status(thm)],[f124,f113])).
% 1.57/1.39 thf(f113,plain,(
% 1.57/1.39 ( ! [X0 : nat,X1 : nat] : (((plus @ X1 @ X0) = (plus @ X0 @ X1))) )),
% 1.57/1.39 inference(cnf_transformation,[status(thm)],[f53])).
% 1.57/1.39 thf(f53,plain,(
% 1.57/1.39 ! [X0 : nat,X1 : nat] : ((plus @ X1 @ X0) = (plus @ X0 @ X1))),
% 1.57/1.39 inference(rectify,[status(thm)],[f17])).
% 1.57/1.39 thf(f17,axiom,(
% 1.57/1.39 ! [X6 : nat,X10 : nat] : ((plus @ X6 @ X10) = (plus @ X10 @ X6))),
% 1.57/1.39 file('/export/starexec/sandbox/tmp/tmp.EoxrKmOWLf/DTF2THF_13150.p',plus_com)).
% 1.57/1.39 thf(f124,plain,(
% 1.57/1.39 ( ! [X0 : nat,X1 : list] : (((listStar @ (plus @ X0 @ sK1) @ (rev @ (plus @ X0 @ sK1) @ (app @ sK1 @ X0 @ (rev @ sK1 @ sK3) @ X1)) @ (app @ X0 @ sK1 @ (rev @ X0 @ X1) @ sK3)) = $true) | ($true != (listStar @ X0 @ X1 @ X1))) )),
% 1.57/1.39 inference(superposition,[status(thm)],[f90,f113])).
% 1.57/1.39 thf(f90,plain,(
% 1.57/1.39 ( ! [X3 : nat,X4 : list] : (((listStar @ (plus @ sK1 @ X3) @ (rev @ (plus @ sK1 @ X3) @ (app @ sK1 @ X3 @ (rev @ sK1 @ sK3) @ X4)) @ (app @ X3 @ sK1 @ (rev @ X3 @ X4) @ sK3)) = $true) | ((listStar @ X3 @ X4 @ X4) != $true)) )),
% 1.57/1.39 inference(cnf_transformation,[status(thm)],[f74])).
% 1.57/1.39 thf(f159,plain,(
% 1.57/1.39 ($true != (listStar @ (plus @ sK1 @ (suc @ sK4)) @ (rev @ (plus @ sK1 @ (suc @ sK4)) @ (app @ sK1 @ (suc @ sK4) @ (rev @ sK1 @ sK3) @ (cons @ sK4 @ sK2 @ sK5))) @ (app @ (suc @ sK4) @ sK1 @ (rev @ (suc @ sK4) @ (cons @ sK4 @ sK2 @ sK5)) @ sK3)))),
% 1.57/1.39 inference(trivial_inequality_removal,[status(thm)],[f154])).
% 1.57/1.39 thf(f154,plain,(
% 1.57/1.39 ($true != $true) | ($true != (listStar @ (plus @ sK1 @ (suc @ sK4)) @ (rev @ (plus @ sK1 @ (suc @ sK4)) @ (app @ sK1 @ (suc @ sK4) @ (rev @ sK1 @ sK3) @ (cons @ sK4 @ sK2 @ sK5))) @ (app @ (suc @ sK4) @ sK1 @ (rev @ (suc @ sK4) @ (cons @ sK4 @ sK2 @ sK5)) @ sK3)))),
% 1.57/1.39 inference(superposition,[status(thm)],[f131,f121])).
% 1.57/1.39 thf(f121,plain,(
% 1.57/1.39 ((listStar @ (plus @ sK1 @ (suc @ sK4)) @ (rev @ (plus @ sK1 @ (suc @ sK4)) @ (app @ (suc @ sK1) @ sK4 @ (rev @ (suc @ sK1) @ (cons @ sK1 @ sK2 @ sK3)) @ sK5)) @ (rev @ (plus @ sK1 @ (suc @ sK4)) @ (app @ sK1 @ (suc @ sK4) @ (rev @ sK1 @ sK3) @ (cons @ sK4 @ sK2 @ sK5)))) = $true)),
% 1.57/1.39 inference(forward_demodulation,[status(thm)],[f87,f94])).
% 1.57/1.39 thf(f94,plain,(
% 1.57/1.39 ( ! [X0 : nat,X1 : nat] : (((plus @ (suc @ X0) @ X1) = (plus @ X0 @ (suc @ X1)))) )),
% 1.57/1.39 inference(cnf_transformation,[status(thm)],[f49])).
% 1.57/1.39 thf(f49,plain,(
% 1.57/1.39 ! [X0 : nat,X1 : nat] : ((plus @ (suc @ X0) @ X1) = (plus @ X0 @ (suc @ X1)))),
% 1.57/1.39 inference(rectify,[status(thm)],[f20])).
% 1.57/1.39 thf(f20,axiom,(
% 1.57/1.39 ! [X6 : nat,X10 : nat] : ((plus @ (suc @ X6) @ X10) = (plus @ X6 @ (suc @ X10)))),
% 1.57/1.39 file('/export/starexec/sandbox/tmp/tmp.EoxrKmOWLf/DTF2THF_13150.p',plus_s_l_r)).
% 1.57/1.39 thf(f87,plain,(
% 1.57/1.39 ((listStar @ (plus @ (suc @ sK1) @ sK4) @ (rev @ (plus @ (suc @ sK1) @ sK4) @ (app @ (suc @ sK1) @ sK4 @ (rev @ (suc @ sK1) @ (cons @ sK1 @ sK2 @ sK3)) @ sK5)) @ (rev @ (plus @ sK1 @ (suc @ sK4)) @ (app @ sK1 @ (suc @ sK4) @ (rev @ sK1 @ sK3) @ (cons @ sK4 @ sK2 @ sK5)))) = $true)),
% 1.57/1.39 inference(cnf_transformation,[status(thm)],[f74])).
% 1.57/1.39 thf(f131,plain,(
% 1.57/1.39 ( ! [X0 : list] : (((listStar @ (plus @ sK1 @ (suc @ sK4)) @ (rev @ (plus @ sK1 @ (suc @ sK4)) @ (app @ (suc @ sK1) @ sK4 @ (rev @ (suc @ sK1) @ (cons @ sK1 @ sK2 @ sK3)) @ sK5)) @ X0) != $true) | ($true != (listStar @ (plus @ sK1 @ (suc @ sK4)) @ X0 @ (app @ (suc @ sK4) @ sK1 @ (rev @ (suc @ sK4) @ (cons @ sK4 @ sK2 @ sK5)) @ sK3)))) )),
% 1.57/1.39 inference(trivial_inequality_removal,[status(thm)],[f130])).
% 1.57/1.39 thf(f130,plain,(
% 1.57/1.39 ( ! [X0 : list] : (((listStar @ (plus @ sK1 @ (suc @ sK4)) @ (rev @ (plus @ sK1 @ (suc @ sK4)) @ (app @ (suc @ sK1) @ sK4 @ (rev @ (suc @ sK1) @ (cons @ sK1 @ sK2 @ sK3)) @ sK5)) @ X0) != $true) | ($true != (listStar @ (plus @ sK1 @ (suc @ sK4)) @ X0 @ (app @ (suc @ sK4) @ sK1 @ (rev @ (suc @ sK4) @ (cons @ sK4 @ sK2 @ sK5)) @ sK3))) | ($true != $true)) )),
% 1.57/1.39 inference(forward_demodulation,[status(thm)],[f129,f106])).
% 1.57/1.39 thf(f106,plain,(
% 1.57/1.39 ( ! [X0 : nat] : (((isPer @ list @ (listStar @ X0)) = $true)) )),
% 1.57/1.39 inference(cnf_transformation,[status(thm)],[f41])).
% 1.57/1.39 thf(f41,plain,(
% 1.57/1.39 ! [X0 : nat] : ((isPer @ list @ (listStar @ X0)) = $true)),
% 1.57/1.39 inference(fool_elimination,[status(thm)],[f40])).
% 1.57/1.39 thf(f40,plain,(
% 1.57/1.39 ! [X0 : nat] : (isPer @ list @ (listStar @ X0))),
% 1.57/1.39 inference(rectify,[status(thm)],[f4])).
% 1.57/1.39 thf(f4,axiom,(
% 1.57/1.39 ! [X5 : nat] : (isPer @ list @ (listStar @ X5))),
% 1.57/1.39 file('/export/starexec/sandbox/tmp/tmp.EoxrKmOWLf/DTF2THF_13150.p','\'listStar\'_is_per')).
% 1.57/1.39 thf(f129,plain,(
% 1.57/1.39 ( ! [X0 : list] : (($true != (listStar @ (plus @ sK1 @ (suc @ sK4)) @ X0 @ (app @ (suc @ sK4) @ sK1 @ (rev @ (suc @ sK4) @ (cons @ sK4 @ sK2 @ sK5)) @ sK3))) | ($true != (isPer @ list @ (listStar @ (plus @ sK1 @ (suc @ sK4))))) | ((listStar @ (plus @ sK1 @ (suc @ sK4)) @ (rev @ (plus @ sK1 @ (suc @ sK4)) @ (app @ (suc @ sK1) @ sK4 @ (rev @ (suc @ sK1) @ (cons @ sK1 @ sK2 @ sK3)) @ sK5)) @ X0) != $true)) )),
% 1.57/1.39 inference(trivial_inequality_removal,[status(thm)],[f126])).
% 1.57/1.39 thf(f126,plain,(
% 1.57/1.39 ( ! [X0 : list] : (((listStar @ (plus @ sK1 @ (suc @ sK4)) @ (rev @ (plus @ sK1 @ (suc @ sK4)) @ (app @ (suc @ sK1) @ sK4 @ (rev @ (suc @ sK1) @ (cons @ sK1 @ sK2 @ sK3)) @ sK5)) @ X0) != $true) | ($true != (listStar @ (plus @ sK1 @ (suc @ sK4)) @ X0 @ (app @ (suc @ sK4) @ sK1 @ (rev @ (suc @ sK4) @ (cons @ sK4 @ sK2 @ sK5)) @ sK3))) | ($true != $true) | ($true != (isPer @ list @ (listStar @ (plus @ sK1 @ (suc @ sK4)))))) )),
% 1.57/1.39 inference(superposition,[status(thm)],[f120,f98])).
% 1.57/1.39 thf(f98,plain,(
% 1.57/1.39 ( ! [X0 : $tType,X10 : X0,X11 : X0,X1 : X0 > X0 > $o,X9 : X0] : (($true = (X1 @ X9 @ X11)) | ((isPer @ X0 @ X1) != $true) | ((X1 @ X9 @ X10) != $true) | ((X1 @ X10 @ X11) != $true)) )),
% 1.57/1.39 inference(cnf_transformation,[status(thm)],[f81])).
% 1.57/1.39 thf(f81,plain,(
% 1.57/1.39 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((((isPer @ X0 @ X1) = $true) | (((X1 @ (sK7 @ X0 @ X1) @ (sK6 @ X0 @ X1)) != $true) & ((X1 @ (sK6 @ X0 @ X1) @ (sK7 @ X0 @ X1)) = $true)) | (((X1 @ (sK9 @ X0 @ X1) @ (sK10 @ X0 @ X1)) = $true) & ((X1 @ (sK8 @ X0 @ X1) @ (sK9 @ X0 @ X1)) = $true) & ((X1 @ (sK8 @ X0 @ X1) @ (sK10 @ X0 @ X1)) != $true))) & ((! [X7 : X0,X8 : X0] : (($true = (X1 @ X8 @ X7)) | ($true != (X1 @ X7 @ X8))) & ! [X9 : X0,X10 : X0,X11 : X0] : (((X1 @ X10 @ X11) != $true) | ((X1 @ X9 @ X10) != $true) | ($true = (X1 @ X9 @ X11)))) | ((isPer @ X0 @ X1) != $true)))),
% 1.57/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10])],[f78,f80,f79])).
% 1.57/1.39 thf(f79,plain,(
% 1.57/1.39 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X2 : X0,X3 : X0] : (((X1 @ X3 @ X2) != $true) & ((X1 @ X2 @ X3) = $true)) => (((X1 @ (sK7 @ X0 @ X1) @ (sK6 @ X0 @ X1)) != $true) & ((X1 @ (sK6 @ X0 @ X1) @ (sK7 @ X0 @ X1)) = $true)))),
% 1.57/1.39 introduced(definition,[],[choice_axiom])).
% 1.57/1.39 thf(f80,plain,(
% 1.57/1.39 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X4 : X0,X5 : X0,X6 : X0] : (((X1 @ X5 @ X6) = $true) & ($true = (X1 @ X4 @ X5)) & ((X1 @ X4 @ X6) != $true)) => (((X1 @ (sK9 @ X0 @ X1) @ (sK10 @ X0 @ X1)) = $true) & ((X1 @ (sK8 @ X0 @ X1) @ (sK9 @ X0 @ X1)) = $true) & ((X1 @ (sK8 @ X0 @ X1) @ (sK10 @ X0 @ X1)) != $true)))),
% 1.57/1.39 introduced(definition,[],[choice_axiom])).
% 1.57/1.39 thf(f78,plain,(
% 1.57/1.39 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((((isPer @ X0 @ X1) = $true) | ? [X2 : X0,X3 : X0] : (((X1 @ X3 @ X2) != $true) & ((X1 @ X2 @ X3) = $true)) | ? [X4 : X0,X5 : X0,X6 : X0] : (((X1 @ X5 @ X6) = $true) & ($true = (X1 @ X4 @ X5)) & ((X1 @ X4 @ X6) != $true))) & ((! [X7 : X0,X8 : X0] : (($true = (X1 @ X8 @ X7)) | ($true != (X1 @ X7 @ X8))) & ! [X9 : X0,X10 : X0,X11 : X0] : (((X1 @ X10 @ X11) != $true) | ((X1 @ X9 @ X10) != $true) | ($true = (X1 @ X9 @ X11)))) | ((isPer @ X0 @ X1) != $true)))),
% 1.57/1.39 inference(rectify,[status(thm)],[f77])).
% 1.57/1.39 thf(f77,plain,(
% 1.57/1.39 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((((isPer @ X0 @ X1) = $true) | ? [X5 : X0,X6 : X0] : (((X1 @ X6 @ X5) != $true) & ((X1 @ X5 @ X6) = $true)) | ? [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X3 @ X4) = $true) & ((X1 @ X2 @ X3) = $true) & ((X1 @ X2 @ X4) != $true))) & ((! [X5 : X0,X6 : X0] : (((X1 @ X6 @ X5) = $true) | ((X1 @ X5 @ X6) != $true)) & ! [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X3 @ X4) != $true) | ((X1 @ X2 @ X3) != $true) | ((X1 @ X2 @ X4) = $true))) | ((isPer @ X0 @ X1) != $true)))),
% 1.57/1.39 inference(flattening,[status(thm)],[f76])).
% 1.57/1.39 thf(f76,plain,(
% 1.57/1.39 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((((isPer @ X0 @ X1) = $true) | (? [X5 : X0,X6 : X0] : (((X1 @ X6 @ X5) != $true) & ((X1 @ X5 @ X6) = $true)) | ? [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X3 @ X4) = $true) & ((X1 @ X2 @ X3) = $true) & ((X1 @ X2 @ X4) != $true)))) & ((! [X5 : X0,X6 : X0] : (((X1 @ X6 @ X5) = $true) | ((X1 @ X5 @ X6) != $true)) & ! [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X3 @ X4) != $true) | ((X1 @ X2 @ X3) != $true) | ((X1 @ X2 @ X4) = $true))) | ((isPer @ X0 @ X1) != $true)))),
% 1.57/1.39 inference(nnf_transformation,[status(thm)],[f61])).
% 1.57/1.39 thf(f61,plain,(
% 1.57/1.39 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) <=> (! [X5 : X0,X6 : X0] : (((X1 @ X6 @ X5) = $true) | ((X1 @ X5 @ X6) != $true)) & ! [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X3 @ X4) != $true) | ((X1 @ X2 @ X3) != $true) | ((X1 @ X2 @ X4) = $true))))),
% 1.57/1.39 inference(flattening,[status(thm)],[f60])).
% 1.57/1.39 thf(f60,plain,(
% 1.57/1.39 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) <=> (! [X5 : X0,X6 : X0] : (((X1 @ X6 @ X5) = $true) | ((X1 @ X5 @ X6) != $true)) & ! [X2 : X0,X3 : X0,X4 : X0] : ((((X1 @ X2 @ X4) = $true) | ((X1 @ X3 @ X4) != $true)) | ((X1 @ X2 @ X3) != $true))))),
% 1.57/1.39 inference(ennf_transformation,[status(thm)],[f39])).
% 1.57/1.39 thf(f39,plain,(
% 1.57/1.39 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((isPer @ X0 @ X1) = $true) <=> (! [X5 : X0,X6 : X0] : (((X1 @ X5 @ X6) = $true) => ((X1 @ X6 @ X5) = $true)) & ! [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X2 @ X3) = $true) => (((X1 @ X3 @ X4) = $true) => ((X1 @ X2 @ X4) = $true)))))),
% 1.57/1.39 inference(fool_elimination,[status(thm)],[f38])).
% 1.57/1.39 thf(f38,plain,(
% 1.57/1.39 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) <=> (! [X2 : X0,X3 : X0,X4 : X0] : ((X1 @ X2 @ X3) => ((X1 @ X3 @ X4) => (X1 @ X2 @ X4))) & ! [X5 : X0,X6 : X0] : ((X1 @ X5 @ X6) => (X1 @ X6 @ X5))))),
% 1.57/1.39 inference(rectify,[status(thm)],[f1])).
% 1.57/1.39 thf(f1,axiom,(
% 1.57/1.39 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) <=> (! [X2 : X0,X3 : X0,X4 : X0] : ((X1 @ X2 @ X3) => ((X1 @ X3 @ X4) => (X1 @ X2 @ X4))) & ! [X2 : X0,X3 : X0] : ((X1 @ X2 @ X3) => (X1 @ X3 @ X2))))),
% 1.57/1.39 file('/export/starexec/sandbox/tmp/tmp.EoxrKmOWLf/DTF2THF_13150.p',is_per)).
% 1.57/1.39 thf(f120,plain,(
% 1.57/1.39 ($true != (listStar @ (plus @ sK1 @ (suc @ sK4)) @ (rev @ (plus @ sK1 @ (suc @ sK4)) @ (app @ (suc @ sK1) @ sK4 @ (rev @ (suc @ sK1) @ (cons @ sK1 @ sK2 @ sK3)) @ sK5)) @ (app @ (suc @ sK4) @ sK1 @ (rev @ (suc @ sK4) @ (cons @ sK4 @ sK2 @ sK5)) @ sK3)))),
% 1.57/1.39 inference(forward_demodulation,[status(thm)],[f89,f94])).
% 1.57/1.39 thf(f89,plain,(
% 1.57/1.39 ((listStar @ (plus @ (suc @ sK1) @ sK4) @ (rev @ (plus @ (suc @ sK1) @ sK4) @ (app @ (suc @ sK1) @ sK4 @ (rev @ (suc @ sK1) @ (cons @ sK1 @ sK2 @ sK3)) @ sK5)) @ (app @ (suc @ sK4) @ sK1 @ (rev @ (suc @ sK4) @ (cons @ sK4 @ sK2 @ sK5)) @ sK3)) != $true)),
% 1.57/1.39 inference(cnf_transformation,[status(thm)],[f74])).
% 1.57/1.39 % SZS output end Proof for DTF2THF_13150
% 1.57/1.39 % (13275)------------------------------
% 1.57/1.39 % (13275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.39 % (13275)Termination reason: Refutation
% 1.57/1.39
% 1.57/1.39 % (13275)Memory used [KB]: 6012
% 1.57/1.39 % (13275)Time elapsed: 0.089 s
% 1.57/1.39 % (13275)Instructions burned: 181 (million)
% 1.57/1.39 % (13275)------------------------------
% 1.57/1.39 % (13275)------------------------------
% 1.57/1.39 % (13252)Success in time 0.173 s
%------------------------------------------------------------------------------