%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT388^1 : 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 : n001.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 1.89s 1.76s
% Output : Refutation 1.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 247 ( 75 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 1360 ( 37 ~; 18 |; 17 &;1258 @)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 9 con; 0-4 aty)
% Number of variables : 121 ( 0 ^; 102 !; 19 ?; 121 :)
% 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:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_18,type,
sK1:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_26,type,
sK2: ( nat > $o ) > nat ).
thf(func_def_27,type,
sK3:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_28,type,
sK4:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_29,type,
sK5:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_30,type,
sK6:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_31,type,
sK7:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_32,type,
sK8: nat ).
thf(func_def_33,type,
sK9: elem ).
thf(func_def_34,type,
sK10: list ).
thf(func_def_35,type,
sK11: nat ).
thf(func_def_36,type,
sK12: list ).
thf(func_def_38,type,
ph14:
!>[X0: $tType] : X0 ).
thf(f255,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f254,f144]) ).
thf(f144,plain,
( ( listStar @ sK8 @ sK10 @ sK10 )
= $true ),
inference(cnf_transformation,[status(thm)],[f116]) ).
thf(f116,plain,
( ! [X3: nat,X4: list] :
( ( $true
!= ( listStar @ X3 @ X4 @ X4 ) )
| ( $true
= ( listStar @ ( plus @ sK8 @ X3 ) @ ( rev @ ( plus @ sK8 @ X3 ) @ ( app @ sK8 @ X3 @ ( rev @ sK8 @ sK10 ) @ X4 ) ) @ ( app @ X3 @ sK8 @ ( rev @ X3 @ X4 ) @ sK10 ) ) ) )
& ( ( listStar @ ( plus @ ( suc @ sK8 ) @ sK11 ) @ ( rev @ ( plus @ ( suc @ sK8 ) @ sK11 ) @ ( app @ ( suc @ sK8 ) @ sK11 @ ( rev @ ( suc @ sK8 ) @ ( cons @ sK8 @ sK9 @ sK10 ) ) @ sK12 ) ) @ ( rev @ ( plus @ ( suc @ sK8 ) @ sK11 ) @ ( app @ ( plus @ sK8 @ ( suc @ zero ) ) @ sK11 @ ( app @ sK8 @ ( suc @ zero ) @ ( rev @ sK8 @ sK10 ) @ ( cons @ zero @ sK9 @ nil ) ) @ sK12 ) ) )
!= $true )
& ( $true
= ( listStar @ sK11 @ sK12 @ sK12 ) )
& ( ( listStar @ sK8 @ sK10 @ sK10 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12])],[f90,f115,f114]) ).
thf(f114,plain,
( ? [X0: nat,X1: elem,X2: list] :
( ! [X3: nat,X4: list] :
( ( $true
!= ( 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 ) )
= $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 ) ) @ ( rev @ ( plus @ ( suc @ X0 ) @ X5 ) @ ( app @ ( plus @ X0 @ ( suc @ zero ) ) @ X5 @ ( app @ X0 @ ( suc @ zero ) @ ( rev @ X0 @ X2 ) @ ( cons @ zero @ X1 @ nil ) ) @ X6 ) ) )
!= $true )
& ( ( listStar @ X5 @ X6 @ X6 )
= $true ) )
& ( ( listStar @ X0 @ X2 @ X2 )
= $true ) )
=> ( ! [X4: list,X3: nat] :
( ( $true
!= ( listStar @ X3 @ X4 @ X4 ) )
| ( $true
= ( listStar @ ( plus @ sK8 @ X3 ) @ ( rev @ ( plus @ sK8 @ X3 ) @ ( app @ sK8 @ X3 @ ( rev @ sK8 @ sK10 ) @ X4 ) ) @ ( app @ X3 @ sK8 @ ( rev @ X3 @ X4 ) @ sK10 ) ) ) )
& ? [X6: list,X5: nat] :
( ( ( listStar @ ( plus @ ( suc @ sK8 ) @ X5 ) @ ( rev @ ( plus @ ( suc @ sK8 ) @ X5 ) @ ( app @ ( suc @ sK8 ) @ X5 @ ( rev @ ( suc @ sK8 ) @ ( cons @ sK8 @ sK9 @ sK10 ) ) @ X6 ) ) @ ( rev @ ( plus @ ( suc @ sK8 ) @ X5 ) @ ( app @ ( plus @ sK8 @ ( suc @ zero ) ) @ X5 @ ( app @ sK8 @ ( suc @ zero ) @ ( rev @ sK8 @ sK10 ) @ ( cons @ zero @ sK9 @ nil ) ) @ X6 ) ) )
!= $true )
& ( ( listStar @ X5 @ X6 @ X6 )
= $true ) )
& ( ( listStar @ sK8 @ sK10 @ sK10 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f115,plain,
( ? [X6: list,X5: nat] :
( ( ( listStar @ ( plus @ ( suc @ sK8 ) @ X5 ) @ ( rev @ ( plus @ ( suc @ sK8 ) @ X5 ) @ ( app @ ( suc @ sK8 ) @ X5 @ ( rev @ ( suc @ sK8 ) @ ( cons @ sK8 @ sK9 @ sK10 ) ) @ X6 ) ) @ ( rev @ ( plus @ ( suc @ sK8 ) @ X5 ) @ ( app @ ( plus @ sK8 @ ( suc @ zero ) ) @ X5 @ ( app @ sK8 @ ( suc @ zero ) @ ( rev @ sK8 @ sK10 ) @ ( cons @ zero @ sK9 @ nil ) ) @ X6 ) ) )
!= $true )
& ( ( listStar @ X5 @ X6 @ X6 )
= $true ) )
=> ( ( ( listStar @ ( plus @ ( suc @ sK8 ) @ sK11 ) @ ( rev @ ( plus @ ( suc @ sK8 ) @ sK11 ) @ ( app @ ( suc @ sK8 ) @ sK11 @ ( rev @ ( suc @ sK8 ) @ ( cons @ sK8 @ sK9 @ sK10 ) ) @ sK12 ) ) @ ( rev @ ( plus @ ( suc @ sK8 ) @ sK11 ) @ ( app @ ( plus @ sK8 @ ( suc @ zero ) ) @ sK11 @ ( app @ sK8 @ ( suc @ zero ) @ ( rev @ sK8 @ sK10 ) @ ( cons @ zero @ sK9 @ nil ) ) @ sK12 ) ) )
!= $true )
& ( $true
= ( listStar @ sK11 @ sK12 @ sK12 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f90,plain,
? [X0: nat,X1: elem,X2: list] :
( ! [X3: nat,X4: list] :
( ( $true
!= ( 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 ) )
= $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 ) ) @ ( rev @ ( plus @ ( suc @ X0 ) @ X5 ) @ ( app @ ( plus @ X0 @ ( suc @ zero ) ) @ X5 @ ( app @ X0 @ ( suc @ zero ) @ ( rev @ X0 @ X2 ) @ ( cons @ zero @ X1 @ nil ) ) @ X6 ) ) )
!= $true )
& ( ( listStar @ X5 @ X6 @ X6 )
= $true ) )
& ( ( listStar @ X0 @ X2 @ X2 )
= $true ) ),
inference(flattening,[status(thm)],[f89]) ).
thf(f89,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 ) ) @ ( rev @ ( plus @ ( suc @ X0 ) @ X5 ) @ ( app @ ( plus @ X0 @ ( suc @ zero ) ) @ X5 @ ( app @ X0 @ ( suc @ zero ) @ ( rev @ X0 @ X2 ) @ ( cons @ zero @ X1 @ nil ) ) @ X6 ) ) )
!= $true )
& ( ( listStar @ X5 @ X6 @ X6 )
= $true ) )
& ! [X3: nat,X4: list] :
( ( $true
!= ( 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 ) )
= $true ) )
& ( ( listStar @ X0 @ X2 @ X2 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f67]) ).
thf(f67,plain,
~ ! [X0: nat,X1: elem,X2: list] :
( ( ( listStar @ X0 @ X2 @ X2 )
= $true )
=> ( ! [X3: nat,X4: list] :
( ( $true
= ( 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 ) )
= $true ) )
=> ! [X5: nat,X6: list] :
( ( ( listStar @ X5 @ X6 @ X6 )
= $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 @ ( suc @ X0 ) @ X5 ) @ ( app @ ( plus @ X0 @ ( suc @ zero ) ) @ X5 @ ( app @ X0 @ ( suc @ zero ) @ ( rev @ X0 @ X2 ) @ ( cons @ zero @ X1 @ nil ) ) @ X6 ) ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f66]) ).
thf(f66,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 @ ( suc @ X0 ) @ X5 ) @ ( app @ ( plus @ X0 @ ( suc @ zero ) ) @ X5 @ ( app @ X0 @ ( suc @ zero ) @ ( rev @ X0 @ X2 ) @ ( cons @ zero @ X1 @ nil ) ) @ X6 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,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 @ ( suc @ X6 ) @ X14 ) @ ( app @ ( plus @ X6 @ ( suc @ zero ) ) @ X14 @ ( app @ X6 @ ( suc @ zero ) @ ( rev @ X6 @ X16 ) @ ( cons @ zero @ X2 @ nil ) ) @ X17 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
thf(f23,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 @ ( suc @ X6 ) @ X14 ) @ ( app @ ( plus @ X6 @ ( suc @ zero ) ) @ X14 @ ( app @ X6 @ ( suc @ zero ) @ ( rev @ X6 @ X16 ) @ ( cons @ zero @ X2 @ nil ) ) @ X17 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.o1aRMkv1xQ/DTF2THF_3954.p',list_rev_invol_lem_indstep1) ).
thf(f254,plain,
( ( listStar @ sK8 @ sK10 @ sK10 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f249]) ).
thf(f249,plain,
( ( ( listStar @ sK8 @ sK10 @ sK10 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f236,f152]) ).
thf(f152,plain,
! [X2: list,X0: nat,X1: elem] :
( ( $true
= ( listStar @ ( suc @ X0 ) @ ( rev @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) ) @ ( app @ X0 @ ( suc @ zero ) @ ( rev @ X0 @ X2 ) @ ( cons @ zero @ X1 @ nil ) ) ) )
| ( ( listStar @ X0 @ X2 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f93]) ).
thf(f93,plain,
! [X0: nat,X1: elem,X2: list] :
( ( $true
= ( listStar @ ( suc @ X0 ) @ ( rev @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) ) @ ( app @ X0 @ ( suc @ zero ) @ ( rev @ X0 @ X2 ) @ ( cons @ zero @ X1 @ nil ) ) ) )
| ( ( listStar @ X0 @ X2 @ X2 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f59]) ).
thf(f59,plain,
! [X0: nat,X1: elem,X2: list] :
( ( ( listStar @ X0 @ X2 @ X2 )
= $true )
=> ( $true
= ( listStar @ ( suc @ X0 ) @ ( rev @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) ) @ ( app @ X0 @ ( suc @ zero ) @ ( rev @ X0 @ X2 ) @ ( cons @ zero @ X1 @ nil ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f58]) ).
thf(f58,plain,
! [X0: nat,X1: elem,X2: list] :
( ( listStar @ X0 @ X2 @ X2 )
=> ( listStar @ ( suc @ X0 ) @ ( rev @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) ) @ ( app @ X0 @ ( suc @ zero ) @ ( rev @ X0 @ X2 ) @ ( cons @ zero @ X1 @ nil ) ) ) ),
inference(rectify,[status(thm)],[f17]) ).
thf(f17,axiom,
! [X6: nat,X2: elem,X3: list] :
( ( listStar @ X6 @ X3 @ X3 )
=> ( listStar @ ( suc @ X6 ) @ ( rev @ ( suc @ X6 ) @ ( cons @ X6 @ X2 @ X3 ) ) @ ( app @ X6 @ ( suc @ zero ) @ ( rev @ X6 @ X3 ) @ ( cons @ zero @ X2 @ nil ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.o1aRMkv1xQ/DTF2THF_3954.p',ax6) ).
thf(f236,plain,
( ( listStar @ ( suc @ sK8 ) @ ( rev @ ( suc @ sK8 ) @ ( cons @ sK8 @ sK9 @ sK10 ) ) @ ( app @ sK8 @ ( suc @ zero ) @ ( rev @ sK8 @ sK10 ) @ ( cons @ zero @ sK9 @ nil ) ) )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f233,f145]) ).
thf(f145,plain,
( $true
= ( listStar @ sK11 @ sK12 @ sK12 ) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
thf(f233,plain,
( ( $true
!= ( listStar @ sK11 @ sK12 @ sK12 ) )
| ( ( listStar @ ( suc @ sK8 ) @ ( rev @ ( suc @ sK8 ) @ ( cons @ sK8 @ sK9 @ sK10 ) ) @ ( app @ sK8 @ ( suc @ zero ) @ ( rev @ sK8 @ sK10 ) @ ( cons @ zero @ sK9 @ nil ) ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f229]) ).
thf(f229,plain,
( ( $true != $true )
| ( ( listStar @ ( suc @ sK8 ) @ ( rev @ ( suc @ sK8 ) @ ( cons @ sK8 @ sK9 @ sK10 ) ) @ ( app @ sK8 @ ( suc @ zero ) @ ( rev @ sK8 @ sK10 ) @ ( cons @ zero @ sK9 @ nil ) ) )
!= $true )
| ( $true
!= ( listStar @ sK11 @ sK12 @ sK12 ) ) ),
inference(superposition,[status(thm)],[f178,f130]) ).
thf(f130,plain,
! [X2: list,X3: list,X0: nat,X1: nat,X4: list,X5: list] :
( ( ( listStar @ ( plus @ X0 @ X1 ) @ ( app @ X0 @ X1 @ X2 @ X4 ) @ ( app @ X0 @ X1 @ X3 @ X5 ) )
= $true )
| ( ( listStar @ X0 @ X2 @ X3 )
!= $true )
| ( $true
!= ( listStar @ X1 @ X4 @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
thf(f99,plain,
! [X0: nat,X1: nat,X2: list,X3: list] :
( ! [X4: list,X5: list] :
( ( $true
!= ( listStar @ X1 @ X4 @ X5 ) )
| ( ( listStar @ ( plus @ X0 @ X1 ) @ ( app @ X0 @ X1 @ X2 @ X4 ) @ ( app @ X0 @ X1 @ X3 @ X5 ) )
= $true ) )
| ( ( listStar @ X0 @ X2 @ X3 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f55]) ).
thf(f55,plain,
! [X0: nat,X1: nat,X2: list,X3: list] :
( ( ( listStar @ X0 @ X2 @ X3 )
= $true )
=> ! [X4: list,X5: list] :
( ( $true
= ( listStar @ X1 @ X4 @ X5 ) )
=> ( ( listStar @ ( plus @ X0 @ X1 ) @ ( app @ X0 @ X1 @ X2 @ X4 ) @ ( app @ X0 @ X1 @ X3 @ X5 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f54]) ).
thf(f54,plain,
! [X0: nat,X1: nat,X2: list,X3: list] :
( ( listStar @ X0 @ X2 @ X3 )
=> ! [X4: list,X5: list] :
( ( listStar @ X1 @ X4 @ X5 )
=> ( listStar @ ( plus @ X0 @ X1 ) @ ( app @ X0 @ X1 @ X2 @ X4 ) @ ( app @ X0 @ X1 @ X3 @ X5 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
! [X6: nat,X10: nat,X7: list,X11: list] :
( ( listStar @ X6 @ X7 @ X11 )
=> ! [X8: list,X9: list] :
( ( listStar @ X10 @ X8 @ X9 )
=> ( listStar @ ( plus @ X6 @ X10 ) @ ( app @ X6 @ X10 @ X7 @ X8 ) @ ( app @ X6 @ X10 @ X11 @ X9 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.o1aRMkv1xQ/DTF2THF_3954.p',app_tp_ax) ).
thf(f178,plain,
( $true
!= ( listStar @ ( plus @ ( suc @ sK8 ) @ sK11 ) @ ( app @ ( suc @ sK8 ) @ sK11 @ ( rev @ ( suc @ sK8 ) @ ( cons @ sK8 @ sK9 @ sK10 ) ) @ sK12 ) @ ( app @ ( suc @ sK8 ) @ sK11 @ ( app @ sK8 @ ( suc @ zero ) @ ( rev @ sK8 @ sK10 ) @ ( cons @ zero @ sK9 @ nil ) ) @ sK12 ) ) ),
inference(superposition,[status(thm)],[f168,f142]) ).
thf(f142,plain,
! [X0: nat] :
( ( plus @ X0 @ ( suc @ zero ) )
= ( suc @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
! [X0: nat] :
( ( plus @ X0 @ ( suc @ zero ) )
= ( suc @ X0 ) ),
inference(fool_elimination,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: nat] :
( ( plus @ X0 @ ( suc @ zero ) )
= ( suc @ X0 ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,axiom,
! [X6: nat] :
( ( suc @ X6 )
= ( plus @ X6 @ ( suc @ zero ) ) ),
file('/export/starexec/sandbox/tmp/tmp.o1aRMkv1xQ/DTF2THF_3954.p',plus1r) ).
thf(f168,plain,
( $true
!= ( listStar @ ( plus @ ( suc @ sK8 ) @ sK11 ) @ ( app @ ( suc @ sK8 ) @ sK11 @ ( rev @ ( suc @ sK8 ) @ ( cons @ sK8 @ sK9 @ sK10 ) ) @ sK12 ) @ ( app @ ( plus @ sK8 @ ( suc @ zero ) ) @ sK11 @ ( app @ sK8 @ ( suc @ zero ) @ ( rev @ sK8 @ sK10 ) @ ( cons @ zero @ sK9 @ nil ) ) @ sK12 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f165]) ).
thf(f165,plain,
( ( $true
!= ( listStar @ ( plus @ ( suc @ sK8 ) @ sK11 ) @ ( app @ ( suc @ sK8 ) @ sK11 @ ( rev @ ( suc @ sK8 ) @ ( cons @ sK8 @ sK9 @ sK10 ) ) @ sK12 ) @ ( app @ ( plus @ sK8 @ ( suc @ zero ) ) @ sK11 @ ( app @ sK8 @ ( suc @ zero ) @ ( rev @ sK8 @ sK10 ) @ ( cons @ zero @ sK9 @ nil ) ) @ sK12 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f146,f132]) ).
thf(f132,plain,
! [X2: list,X0: nat,X1: list] :
( ( $true
= ( listStar @ X0 @ ( rev @ X0 @ X1 ) @ ( rev @ X0 @ X2 ) ) )
| ( ( listStar @ X0 @ X1 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f92]) ).
thf(f92,plain,
! [X0: nat,X1: list,X2: list] :
( ( ( listStar @ X0 @ X1 @ X2 )
!= $true )
| ( $true
= ( listStar @ X0 @ ( rev @ X0 @ X1 ) @ ( rev @ X0 @ X2 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f43]) ).
thf(f43,plain,
! [X0: nat,X1: list,X2: list] :
( ( ( listStar @ X0 @ X1 @ X2 )
= $true )
=> ( $true
= ( listStar @ X0 @ ( rev @ X0 @ X1 ) @ ( rev @ X0 @ X2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f42]) ).
thf(f42,plain,
! [X0: nat,X1: list,X2: list] :
( ( listStar @ X0 @ X1 @ X2 )
=> ( listStar @ X0 @ ( rev @ X0 @ X1 ) @ ( rev @ X0 @ X2 ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
! [X6: nat,X7: list,X11: list] :
( ( listStar @ X6 @ X7 @ X11 )
=> ( listStar @ X6 @ ( rev @ X6 @ X7 ) @ ( rev @ X6 @ X11 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.o1aRMkv1xQ/DTF2THF_3954.p',rev_tp_ax) ).
thf(f146,plain,
( ( listStar @ ( plus @ ( suc @ sK8 ) @ sK11 ) @ ( rev @ ( plus @ ( suc @ sK8 ) @ sK11 ) @ ( app @ ( suc @ sK8 ) @ sK11 @ ( rev @ ( suc @ sK8 ) @ ( cons @ sK8 @ sK9 @ sK10 ) ) @ sK12 ) ) @ ( rev @ ( plus @ ( suc @ sK8 ) @ sK11 ) @ ( app @ ( plus @ sK8 @ ( suc @ zero ) ) @ sK11 @ ( app @ sK8 @ ( suc @ zero ) @ ( rev @ sK8 @ sK10 ) @ ( cons @ zero @ sK9 @ nil ) ) @ sK12 ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT388^1 : TPTP v9.2.1. Released v9.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n001.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 06:17:35 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.49 ---- Original DTF file ---
% 0.29/0.49 thf(spec,logic,$$dhol).
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 % File : DAT388^1 : TPTP v9.2.1. Released v9.2.0.
% 0.29/0.49 % Domain : Data Structures
% 0.29/0.49 % Problem : List involution lemma, induction step 1
% 0.29/0.49 % Version : Especial.
% 0.29/0.49 % English : List involution lemma. The proof is by induction with a separate
% 0.29/0.49 % problem file for the base and step case (with multiple subcases)
% 0.29/0.49 % as well as the correct instantiation of the induction axiom for
% 0.29/0.49 % lists. The main file uses the conjectures of the other files as
% 0.29/0.49 % lemmas in order to prove the final result. To simplify proof
% 0.29/0.49 % search, the axioms in each problem file have been preselected.
% 0.29/0.49 % For the actual induction proof, it is sufficient to consider the
% 0.29/0.49 % "step" problem files.
% 0.29/0.49
% 0.29/0.49 % Refs : [RRB23] Rothgang et al. (2023), Theorem Proving in Dependently
% 0.29/0.49 % : [Rot25] Rothgang (2025), Email to Geoff Sutcliffe
% 0.29/0.49 % : [RK+25] Ranalter et al. (2025), The Dependently Typed Higher-O
% 0.29/0.49 % Source : [Rot25]
% 0.29/0.49 % Names : ListReversalInvolutionLemma/list-rev-invol-lem-indstep1.p [Rot25]
% 0.29/0.49
% 0.29/0.49 % Status : Theorem
% 0.29/0.49 % Rating : ? v9.2.0
% 0.29/0.49 % Syntax : Number of formulae : 25 ( 12 unt; 10 typ; 0 def)
% 0.29/0.49 % Number of atoms : 16 ( 16 equ; 0 cnn)
% 0.29/0.49 % Maximal formula atoms : 2 ( 1 avg)
% 0.29/0.49 % Number of connectives : 176 ( 3 ~; 0 |; 0 &; 168 @)
% 0.29/0.49 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.29/0.49 % Maximal formula depth : 8 ( 4 avg)
% 0.29/0.49 % Number of types : 3 ( 2 usr)
% 0.29/0.49 % Number of type decls : 10 ( 0 !>P; 3 !>D)
% 0.29/0.49 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.29/0.49 % Number of symbols : 9 ( 8 usr; 2 con; 0-4 aty)
% 0.29/0.49 % Number of variables : 43 ( 0 ^; 39 !; 0 ?; 43 :)
% 0.29/0.49 % ( 4 !>; 0 ?*; 0 @-; 0 @+)
% 0.29/0.49 % SPC : DH0_THM_EQU_NAR
% 0.29/0.49
% 0.29/0.49 % Comments :
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 thf(elem_type,type,
% 0.29/0.49 elem: $tType ).
% 0.29/0.49
% 0.29/0.49 thf(nat_type,type,
% 0.29/0.49 nat: $tType ).
% 0.29/0.49
% 0.29/0.49 thf(zero_type,type,
% 0.29/0.49 zero: nat ).
% 0.29/0.49
% 0.29/0.49 thf(suc_type,type,
% 0.29/0.49 suc: nat > nat ).
% 0.29/0.49
% 0.29/0.49 thf(plus_type,type,
% 0.29/0.49 plus: nat > nat > nat ).
% 0.29/0.49
% 0.29/0.49 thf(list_type,type,
% 0.29/0.49 list: nat > $tType ).
% 0.29/0.49
% 0.29/0.49 thf(nil_type,type,
% 0.29/0.49 nil: list @ zero ).
% 0.29/0.49
% 0.29/0.49 thf(cons_type,type,
% 0.29/0.49 cons:
% 0.29/0.49 !>[N: nat] : ( elem > ( list @ N ) > ( list @ ( suc @ N ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(app_type,type,
% 0.29/0.49 app:
% 0.29/0.49 !>[N: nat,M: nat] : ( ( list @ N ) > ( list @ M ) > ( list @ ( plus @ N @ M ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(rev_type,type,
% 0.29/0.49 rev:
% 0.29/0.49 !>[N: nat] : ( ( list @ N ) > ( list @ N ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(peano1,axiom,
% 0.29/0.49 ! [N: nat] :
% 0.29/0.49 ( ( suc @ N )
% 0.29/0.49 != zero ) ).
% 0.29/0.49
% 0.29/0.49 thf(peano2,axiom,
% 0.29/0.49 ! [N: nat,M: nat] :
% 0.29/0.49 ( ( N != M )
% 0.29/0.49 => ( ( suc @ N )
% 0.29/0.49 != ( suc @ M ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(peano3,axiom,
% 0.29/0.49 ! [P: nat > $o] :
% 0.29/0.49 ( ( P @ zero )
% 0.29/0.49 => ( ! [M: nat] :
% 0.29/0.49 ( ( P @ M )
% 0.29/0.49 => ( P @ ( suc @ M ) ) )
% 0.29/0.49 => ! [N: nat] : ( P @ N ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax1,axiom,
% 0.29/0.49 ! [N: nat] :
% 0.29/0.49 ( ( plus @ zero @ N )
% 0.29/0.49 = N ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax2,axiom,
% 0.29/0.49 ! [N: nat,M: nat] :
% 0.29/0.49 ( ( plus @ ( suc @ N ) @ M )
% 0.29/0.49 = ( suc @ ( plus @ N @ M ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax3,axiom,
% 0.29/0.49 ! [N: nat,X: list @ N] :
% 0.29/0.49 ( ( app @ zero @ N @ nil @ X )
% 0.29/0.49 = X ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax4,axiom,
% 0.29/0.49 ! [N: nat,M: nat,X: elem,Y: list @ N,Z: list @ M] :
% 0.29/0.49 ( ( app @ ( suc @ N ) @ M @ ( cons @ N @ X @ Y ) @ Z )
% 0.29/0.49 = ( cons @ ( plus @ N @ M ) @ X @ ( app @ N @ M @ Y @ Z ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax5,axiom,
% 0.29/0.49 ( ( rev @ zero @ nil )
% 0.29/0.49 = nil ) ).
% 0.29/0.49
% 0.29/0.49 thf(ax6,axiom,
% 0.29/0.49 ! [N: nat,X: elem,Y: list @ N] :
% 0.29/0.49 ( ( rev @ ( suc @ N ) @ ( cons @ N @ X @ Y ) )
% 0.29/0.49 = ( app @ N @ ( suc @ zero ) @ ( rev @ N @ Y ) @ ( cons @ zero @ X @ nil ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(plus_zero_r,axiom,
% 0.29/0.49 ! [M: nat] :
% 0.29/0.49 ( ( plus @ M @ zero )
% 0.29/0.49 = M ) ).
% 0.29/0.49
% 0.29/0.49 thf(plus_com,axiom,
% 0.29/0.49 ! [N: nat,M: nat] :
% 0.29/0.49 ( ( plus @ N @ M )
% 0.29/0.49 = ( plus @ M @ N ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(plus_assoc,axiom,
% 0.29/0.49 ! [M1: nat,M2: nat,M3: nat] :
% 0.29/0.49 ( ( plus @ M1 @ ( plus @ M2 @ M3 ) )
% 0.29/0.49 = ( plus @ ( plus @ M1 @ M2 ) @ M3 ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(plus1r,axiom,
% 0.29/0.49 ! [N: nat] :
% 0.29/0.49 ( ( suc @ N )
% 0.29/0.49 = ( plus @ N @ ( suc @ zero ) ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(list_app_assoc,axiom,
% 0.29/0.49 ! [M: nat,L: list @ M,M2: nat,L2: list @ M2,M3: nat,L3: list @ M3] :
% 0.29/0.49 ( ( app @ M @ ( plus @ M2 @ M3 ) @ L @ ( app @ M2 @ M3 @ L2 @ L3 ) )
% 0.29/0.49 = ( app @ ( plus @ M @ M2 ) @ M3 @ ( app @ M @ M2 @ L @ L2 ) @ L3 ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(list_rev_invol_lem_indstep1,conjecture,
% 0.29/0.49 ! [N: nat,X: elem,L: list @ N] :
% 0.29/0.49 ( ! [M2: nat,L2: list @ M2] :
% 0.29/0.49 ( ( rev @ ( plus @ N @ M2 ) @ ( app @ N @ M2 @ ( rev @ N @ L ) @ L2 ) )
% 0.29/0.49 = ( app @ M2 @ N @ ( rev @ M2 @ L2 ) @ L ) )
% 0.29/0.49 => ! [M2: nat,L2: list @ M2] :
% 0.29/0.49 ( ( rev @ ( plus @ ( suc @ N ) @ M2 ) @ ( app @ ( suc @ N ) @ M2 @ ( rev @ ( suc @ N ) @ ( cons @ N @ X @ L ) ) @ L2 ) )
% 0.29/0.49 = ( rev @ ( plus @ ( suc @ N ) @ M2 ) @ ( app @ ( plus @ N @ ( suc @ zero ) ) @ M2 @ ( app @ N @ ( suc @ zero ) @ ( rev @ N @ L ) @ ( cons @ zero @ X @ nil ) ) @ L2 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 ------------------------
% 1.76/1.36 ---- Embedded in THF ---
% 1.76/1.37 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.76/1.37 %%% Generated on Tue Feb 24 06:17:36 EST 2026
% 1.76/1.37 %%% using '$$dhol' embedding, version 1.3.0.
% 1.76/1.37 %%% Logic specification used:
% 1.76/1.37 %%% thf(spec, logic, $$dhol).
% 1.76/1.37
% 1.76/1.37 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.o1aRMkv1xQ/DTF2DTF3954.p
% See solution above
% 1.76/1.37 ------------------------
% 1.76/1.38 ---- Cleaned THF ---
% 1.76/1.38 thf(is_per_type,type,
% 1.76/1.38 isPer:
% 1.76/1.38 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 1.76/1.38
% 1.76/1.38 thf(is_per,definition,
% 1.76/1.38 ! [A: $tType,AStar: A > A > $o] :
% 1.76/1.38 ( ( isPer @ A @ AStar )
% 1.76/1.38 <=> ( ! [X: A,Y: A] :
% 1.76/1.38 ( ( AStar @ X @ Y )
% 1.76/1.38 => ( AStar @ Y @ X ) )
% 1.76/1.38 & ! [X: A,Y: A,Z: A] :
% 1.76/1.38 ( ( AStar @ X @ Y )
% 1.76/1.38 => ( ( AStar @ Y @ Z )
% 1.76/1.38 => ( AStar @ X @ Z ) ) ) ) ) ).
% 1.76/1.38
% 1.76/1.38 thf(elem_type,type,
% 1.76/1.38 elem: $tType ).
% 1.76/1.38
% 1.76/1.38 thf(elemStar,type,
% 1.76/1.38 elemStar: elem > elem > $o ).
% 1.76/1.38
% 1.76/1.38 thf(elemStar_is_eq,axiom,
% 1.76/1.38 ! [X: elem,Y: elem] :
% 1.76/1.38 ( ( elemStar @ X @ Y )
% 1.76/1.38 <=> ( X = Y ) ) ).
% 1.76/1.38
% 1.76/1.38 thf(nat_type,type,
% 1.76/1.38 nat: $tType ).
% 1.76/1.38
% 1.76/1.38 thf(natStar,type,
% 1.76/1.38 natStar: nat > nat > $o ).
% 1.76/1.38
% 1.76/1.38 thf(natStar_is_eq,axiom,
% 1.76/1.38 ! [X: nat,Y: nat] :
% 1.76/1.38 ( ( natStar @ X @ Y )
% 1.76/1.38 <=> ( X = Y ) ) ).
% 1.76/1.38
% 1.76/1.38 thf(zero_type,type,
% 1.76/1.38 zero: nat ).
% 1.76/1.38
% 1.76/1.38 thf(suc_type,type,
% 1.76/1.38 suc: nat > nat ).
% 1.76/1.38
% 1.76/1.38 thf(plus_type,type,
% 1.76/1.38 plus: nat > nat > nat ).
% 1.76/1.38
% 1.76/1.38 thf(list_type,type,
% 1.76/1.38 list: $tType ).
% 1.76/1.38
% 1.76/1.38 thf(listStar,type,
% 1.76/1.38 listStar: nat > list > list > $o ).
% 1.76/1.38
% 1.76/1.38 thf('\'listStar\'_is_per',axiom,
% 1.76/1.38 ! [C: nat] : ( isPer @ list @ ( listStar @ C ) ) ).
% 1.76/1.38
% 1.76/1.38 thf(nil_type,type,
% 1.76/1.38 nil: list ).
% 1.76/1.38
% 1.76/1.38 thf(nil_tp_ax,axiom,
% 1.76/1.38 listStar @ zero @ nil @ nil ).
% 1.76/1.38
% 1.76/1.38 thf(cons_type,type,
% 1.76/1.38 cons: nat > elem > list > list ).
% 1.76/1.38
% 1.76/1.38 thf(cons_tp_ax,axiom,
% 1.76/1.38 ! [N: nat,D: elem,D0: list,D0_prime: list] :
% 1.76/1.38 ( ( listStar @ N @ D0 @ D0_prime )
% 1.76/1.38 => ( listStar @ ( suc @ N ) @ ( cons @ N @ D @ D0 ) @ ( cons @ N @ D @ D0_prime ) ) ) ).
% 1.76/1.38
% 1.76/1.38 thf(app_type,type,
% 1.76/1.38 app: nat > nat > list > list > list ).
% 1.76/1.38
% 1.76/1.38 thf(app_tp_ax,axiom,
% 1.76/1.38 ! [N: nat,M: nat,D: list,D_prime: list] :
% 1.76/1.38 ( ( listStar @ N @ D @ D_prime )
% 1.76/1.38 => ! [D0: list,D0_prime: list] :
% 1.76/1.38 ( ( listStar @ M @ D0 @ D0_prime )
% 1.76/1.38 => ( listStar @ ( plus @ N @ M ) @ ( app @ N @ M @ D @ D0 ) @ ( app @ N @ M @ D_prime @ D0_prime ) ) ) ) ).
% 1.76/1.38
% 1.76/1.38 thf(rev_type,type,
% 1.76/1.38 rev: nat > list > list ).
% 1.76/1.38
% 1.76/1.38 thf(rev_tp_ax,axiom,
% 1.76/1.38 ! [N: nat,D: list,D_prime: list] :
% 1.76/1.38 ( ( listStar @ N @ D @ D_prime )
% 1.76/1.38 => ( listStar @ N @ ( rev @ N @ D ) @ ( rev @ N @ D_prime ) ) ) ).
% 1.76/1.38
% 1.76/1.38 thf(peano1,axiom,
% 1.76/1.38 ! [N: nat] :
% 1.76/1.38 ( ( suc @ N )
% 1.76/1.38 != zero ) ).
% 1.76/1.38
% 1.76/1.38 thf(peano2,axiom,
% 1.76/1.38 ! [N: nat,M: nat] :
% 1.76/1.38 ( ( N != M )
% 1.76/1.38 => ( ( suc @ N )
% 1.76/1.38 != ( suc @ M ) ) ) ).
% 1.76/1.38
% 1.76/1.38 thf(peano3,axiom,
% 1.76/1.38 ! [P: nat > $o] :
% 1.76/1.38 ( ( P @ zero )
% 1.76/1.38 => ( ! [M: nat] :
% 1.76/1.38 ( ( P @ M )
% 1.76/1.38 => ( P @ ( suc @ M ) ) )
% 1.76/1.38 => ! [N: nat] : ( P @ N ) ) ) ).
% 1.76/1.38
% 1.76/1.38 thf(ax1,axiom,
% 1.76/1.38 ! [N: nat] :
% 1.76/1.38 ( ( plus @ zero @ N )
% 1.76/1.38 = N ) ).
% 1.76/1.38
% 1.76/1.38 thf(ax2,axiom,
% 1.76/1.38 ! [N: nat,M: nat] :
% 1.76/1.38 ( ( plus @ ( suc @ N ) @ M )
% 1.76/1.38 = ( suc @ ( plus @ N @ M ) ) ) ).
% 1.76/1.38
% 1.76/1.38 thf(ax3,axiom,
% 1.76/1.38 ! [N: nat,X: list] :
% 1.76/1.38 ( ( listStar @ N @ X @ X )
% 1.76/1.38 => ( listStar @ ( plus @ zero @ N ) @ ( app @ zero @ N @ nil @ X ) @ X ) ) ).
% 1.76/1.38
% 1.76/1.38 thf(ax4,axiom,
% 1.76/1.38 ! [N: nat,M: nat,X: elem,Y: list,Z: list] :
% 1.76/1.38 ( ( listStar @ N @ Y @ Y )
% 1.76/1.38 => ( ( listStar @ M @ Z @ Z )
% 1.76/1.38 => ( listStar @ ( plus @ ( suc @ N ) @ M ) @ ( app @ ( suc @ N ) @ M @ ( cons @ N @ X @ Y ) @ Z ) @ ( cons @ ( plus @ N @ M ) @ X @ ( app @ N @ M @ Y @ Z ) ) ) ) ) ).
% 1.76/1.38
% 1.76/1.38 thf(ax5,axiom,
% 1.76/1.38 listStar @ zero @ ( rev @ zero @ nil ) @ nil ).
% 1.76/1.38
% 1.76/1.38 thf(ax6,axiom,
% 1.76/1.38 ! [N: nat,X: elem,Y: list] :
% 1.76/1.38 ( ( listStar @ N @ Y @ Y )
% 1.76/1.38 => ( listStar @ ( suc @ N ) @ ( rev @ ( suc @ N ) @ ( cons @ N @ X @ Y ) ) @ ( app @ N @ ( suc @ zero ) @ ( rev @ N @ Y ) @ ( cons @ zero @ X @ nil ) ) ) ) ).
% 1.76/1.38
% 1.76/1.38 thf(plus_zero_r,axiom,
% 1.76/1.38 ! [M: nat] :
% 1.76/1.38 ( ( plus @ M @ zero )
% 1.76/1.38 = M ) ).
% 1.76/1.38
% 1.76/1.38 thf(plus_com,axiom,
% 1.76/1.38 ! [N: nat,M: nat] :
% 1.76/1.38 ( ( plus @ N @ M )
% 1.76/1.38 = ( plus @ M @ N ) ) ).
% 1.76/1.38
% 1.76/1.38 thf(plus_assoc,axiom,
% 1.76/1.38 ! [M1: nat,M2: nat,M3: nat] :
% 1.76/1.38 ( ( plus @ M1 @ ( plus @ M2 @ M3 ) )
% 1.76/1.38 = ( plus @ ( plus @ M1 @ M2 ) @ M3 ) ) ).
% 1.76/1.38
% 1.76/1.38 thf(plus1r,axiom,
% 1.76/1.38 ! [N: nat] :
% 1.76/1.38 ( ( suc @ N )
% 1.76/1.38 = ( plus @ N @ ( suc @ zero ) ) ) ).
% 1.76/1.38
% 1.76/1.38 thf(list_app_assoc,axiom,
% 1.76/1.38 ! [M: nat,L: list,M2: nat,L2: list,M3: nat,L3: list] :
% 1.76/1.38 ( ( listStar @ M @ L @ L )
% 1.76/1.38 => ( ( listStar @ M2 @ L2 @ L2 )
% 1.76/1.38 => ( ( listStar @ M3 @ L3 @ L3 )
% 1.76/1.38 => ( listStar @ ( plus @ ( plus @ M2 @ M3 ) @ ( plus @ M2 @ M3 ) ) @ ( app @ M @ ( plus @ M2 @ M3 ) @ L @ ( app @ M2 @ M3 @ L2 @ L3 ) ) @ ( app @ ( plus @ M @ M2 ) @ M3 @ ( app @ M @ M2 @ L @ L2 ) @ L3 ) ) ) ) ) ).
% 1.76/1.38
% 1.76/1.38 thf(list_rev_invol_lem_indstep1,conjecture,
% 1.76/1.38 ! [N: nat,X: elem,L: list] :
% 1.76/1.38 ( ( listStar @ N @ L @ L )
% 1.76/1.38 => ( ! [M2: nat,L2: list] :
% 1.76/1.38 ( ( listStar @ M2 @ L2 @ L2 )
% 1.76/1.38 => ( listStar @ ( plus @ N @ M2 ) @ ( rev @ ( plus @ N @ M2 ) @ ( app @ N @ M2 @ ( rev @ N @ L ) @ L2 ) ) @ ( app @ M2 @ N @ ( rev @ M2 @ L2 ) @ L ) ) )
% 1.76/1.38 => ! [M2: nat,L2: list] :
% 1.76/1.38 ( ( listStar @ M2 @ L2 @ L2 )
% 1.76/1.38 => ( listStar @ ( plus @ ( suc @ N ) @ M2 ) @ ( rev @ ( plus @ ( suc @ N ) @ M2 ) @ ( app @ ( suc @ N ) @ M2 @ ( rev @ ( suc @ N ) @ ( cons @ N @ X @ L ) ) @ L2 ) ) @ ( rev @ ( plus @ ( suc @ N ) @ M2 ) @ ( app @ ( plus @ N @ ( suc @ zero ) ) @ M2 @ ( app @ N @ ( suc @ zero ) @ ( rev @ N @ L ) @ ( cons @ zero @ X @ nil ) ) @ L2 ) ) ) ) ) ) ).
% 1.76/1.38 ------------------------
% 1.89/1.40 % (4293)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3954 for (2999ds/2Mi)
% 1.89/1.40 % (4293)Instruction limit reached!
% 1.89/1.40 % (4293)------------------------------
% 1.89/1.40 % (4293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.40 % (4293)Termination reason: Unknown
% 1.89/1.40 % (4293)Termination phase: shuffling
% 1.89/1.40
% 1.89/1.40 % (4293)Memory used [KB]: 1023
% 1.89/1.40 % (4293)Time elapsed: 0.002 s
% 1.89/1.40 % (4293)Instructions burned: 2 (million)
% 1.89/1.40 % (4293)------------------------------
% 1.89/1.40 % (4293)------------------------------
% 1.89/1.40 % (4294)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_3954 for (2999ds/2Mi)
% 1.89/1.40 % (4294)Instruction limit reached!
% 1.89/1.40 % (4294)------------------------------
% 1.89/1.40 % (4294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.40 % (4294)Termination reason: Unknown
% 1.89/1.40 % (4294)Termination phase: shuffling
% 1.89/1.40
% 1.89/1.40 % (4294)Memory used [KB]: 1023
% 1.89/1.40 % (4294)Time elapsed: 0.002 s
% 1.89/1.40 % (4294)Instructions burned: 3 (million)
% 1.89/1.40 % (4294)------------------------------
% 1.89/1.40 % (4294)------------------------------
% 1.89/1.40 % (4290)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3954 for (2999ds/183Mi)
% 1.89/1.40 % (4291)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_3954 for (2999ds/4Mi)
% 1.89/1.40 % (4292)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_3954 for (2999ds/27Mi)
% 1.89/1.41 % (4296)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3954 for (2999ds/18Mi)
% 1.89/1.41 % (4295)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_3954 for (2999ds/275Mi)
% 1.89/1.41 % (4291)Instruction limit reached!
% 1.89/1.41 % (4291)------------------------------
% 1.89/1.41 % (4291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.41 % (4291)Termination reason: Unknown
% 1.89/1.41 % (4291)Termination phase: shuffling
% 1.89/1.41
% 1.89/1.41 % (4291)Memory used [KB]: 1023
% 1.89/1.41 % (4291)Time elapsed: 0.004 s
% 1.89/1.41 % (4291)Instructions burned: 4 (million)
% 1.89/1.41 % (4291)------------------------------
% 1.89/1.41 % (4291)------------------------------
% 1.89/1.41 % (4297)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3954 for (2999ds/3Mi)
% 1.89/1.41 % (4297)Instruction limit reached!
% 1.89/1.41 % (4297)------------------------------
% 1.89/1.41 % (4297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.41 % (4297)Termination reason: Unknown
% 1.89/1.41 % (4297)Termination phase: shuffling
% 1.89/1.41
% 1.89/1.41 % (4297)Memory used [KB]: 1023
% 1.89/1.41 % (4297)Time elapsed: 0.002 s
% 1.89/1.41 % (4297)Instructions burned: 4 (million)
% 1.89/1.41 % (4297)------------------------------
% 1.89/1.41 % (4297)------------------------------
% 1.89/1.41 % (4298)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_3954 for (2999ds/37Mi)
% 1.89/1.42 % (4296)Instruction limit reached!
% 1.89/1.42 % (4296)------------------------------
% 1.89/1.42 % (4296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.42 % (4296)Termination reason: Unknown
% 1.89/1.42 % (4296)Termination phase: Saturation
% 1.89/1.42
% 1.89/1.42 % (4296)Memory used [KB]: 5628
% 1.89/1.42 % (4296)Time elapsed: 0.013 s
% 1.89/1.42 % (4296)Instructions burned: 19 (million)
% 1.89/1.42 % (4296)------------------------------
% 1.89/1.42 % (4296)------------------------------
% 1.89/1.42 % (4300)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_3954 for (2999ds/3Mi)
% 1.89/1.42 % (4300)Instruction limit reached!
% 1.89/1.42 % (4300)------------------------------
% 1.89/1.42 % (4300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.42 % (4300)Termination reason: Unknown
% 1.89/1.42 % (4300)Termination phase: shuffling
% 1.89/1.42
% 1.89/1.42 % (4300)Memory used [KB]: 1023
% 1.89/1.42 % (4300)Time elapsed: 0.002 s
% 1.89/1.42 % (4300)Instructions burned: 4 (million)
% 1.89/1.42 % (4300)------------------------------
% 1.89/1.42 % (4300)------------------------------
% 1.89/1.42 % (4298)Instruction limit reached!
% 1.89/1.42 % (4298)------------------------------
% 1.89/1.42 % (4298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.42 % (4298)Termination reason: Unknown
% 1.89/1.42 % (4298)Termination phase: Saturation
% 1.89/1.42
% 1.89/1.42 % (4298)Memory used [KB]: 5884
% 1.89/1.42 % (4298)Time elapsed: 0.014 s
% 1.89/1.42 % (4298)Instructions burned: 39 (million)
% 1.89/1.42 % (4298)------------------------------
% 1.89/1.42 % (4298)------------------------------
% 1.89/1.42 % (4292)Instruction limit reached!
% 1.89/1.42 % (4292)------------------------------
% 1.89/1.42 % (4292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.42 % (4292)Termination reason: Unknown
% 1.89/1.42 % (4292)Termination phase: Saturation
% 1.89/1.42
% 1.89/1.42 % (4292)Memory used [KB]: 5628
% 1.89/1.42 % (4292)Time elapsed: 0.019 s
% 1.89/1.42 % (4292)Instructions burned: 27 (million)
% 1.89/1.42 % (4292)------------------------------
% 1.89/1.42 % (4292)------------------------------
% 1.89/1.42 % (4299)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_3954 for (2999ds/15Mi)
% 1.89/1.43 % (4302)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3954 for (2999ds/7Mi)
% 1.89/1.43 % (4302)Instruction limit reached!
% 1.89/1.43 % (4302)------------------------------
% 1.89/1.43 % (4302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.43 % (4302)Termination reason: Unknown
% 1.89/1.43 % (4302)Termination phase: Preprocessing 3
% 1.89/1.43
% 1.89/1.43 % (4302)Memory used [KB]: 1023
% 1.89/1.43 % (4302)Time elapsed: 0.003 s
% 1.89/1.43 % (4302)Instructions burned: 7 (million)
% 1.89/1.43 % (4302)------------------------------
% 1.89/1.43 % (4302)------------------------------
% 1.89/1.43 % (4301)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_3954 for (2999ds/1041Mi)
% 1.89/1.43 % (4303)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3954 for (2999ds/16Mi)
% 1.89/1.43 % (4299)Instruction limit reached!
% 1.89/1.43 % (4299)------------------------------
% 1.89/1.43 % (4299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.43 % (4299)Termination reason: Unknown
% 1.89/1.43 % (4299)Termination phase: Saturation
% 1.89/1.43
% 1.89/1.43 % (4299)Memory used [KB]: 1151
% 1.89/1.43 % (4299)Time elapsed: 0.010 s
% 1.89/1.43 % (4299)Instructions burned: 15 (million)
% 1.89/1.43 % (4299)------------------------------
% 1.89/1.43 % (4299)------------------------------
% 1.89/1.44 % (4303)Instruction limit reached!
% 1.89/1.44 % (4303)------------------------------
% 1.89/1.44 % (4303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.44 % (4303)Termination reason: Unknown
% 1.89/1.44 % (4303)Termination phase: Saturation
% 1.89/1.44
% 1.89/1.44 % (4303)Memory used [KB]: 5628
% 1.89/1.44 % (4303)Time elapsed: 0.007 s
% 1.89/1.44 % (4303)Instructions burned: 16 (million)
% 1.89/1.44 % (4303)------------------------------
% 1.89/1.44 % (4303)------------------------------
% 1.89/1.44 % (4304)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_3954 for (2999ds/3Mi)
% 1.89/1.44 % (4304)Instruction limit reached!
% 1.89/1.44 % (4304)------------------------------
% 1.89/1.44 % (4304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.44 % (4304)Termination reason: Unknown
% 1.89/1.44 % (4304)Termination phase: shuffling
% 1.89/1.44
% 1.89/1.44 % (4304)Memory used [KB]: 1023
% 1.89/1.44 % (4304)Time elapsed: 0.003 s
% 1.89/1.44 % (4304)Instructions burned: 3 (million)
% 1.89/1.44 % (4304)------------------------------
% 1.89/1.44 % (4304)------------------------------
% 1.89/1.44 % (4305)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_3954 for (2999ds/3Mi)
% 1.89/1.44 % (4305)Instruction limit reached!
% 1.89/1.44 % (4305)------------------------------
% 1.89/1.44 % (4305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.44 % (4305)Termination reason: Unknown
% 1.89/1.44 % (4305)Termination phase: shuffling
% 1.89/1.44
% 1.89/1.44 % (4305)Memory used [KB]: 1023
% 1.89/1.44 % (4305)Time elapsed: 0.002 s
% 1.89/1.44 % (4305)Instructions burned: 4 (million)
% 1.89/1.44 % (4305)------------------------------
% 1.89/1.44 % (4305)------------------------------
% 1.89/1.45 % (4307)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3954 for (2999ds/3Mi)
% 1.89/1.45 % (4307)Instruction limit reached!
% 1.89/1.45 % (4307)------------------------------
% 1.89/1.45 % (4307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.45 % (4307)Termination reason: Unknown
% 1.89/1.45 % (4307)Termination phase: shuffling
% 1.89/1.45
% 1.89/1.45 % (4307)Memory used [KB]: 1023
% 1.89/1.45 % (4307)Time elapsed: 0.003 s
% 1.89/1.45 % (4307)Instructions burned: 5 (million)
% 1.89/1.45 % (4307)------------------------------
% 1.89/1.45 % (4307)------------------------------
% 1.89/1.45 % (4309)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3954 for (2999ds/18Mi)
% 1.89/1.45 % (4308)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3954 for (2999ds/4Mi)
% 1.89/1.45 % (4306)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3954 for (2999ds/7Mi)
% 1.89/1.45 % (4308)Instruction limit reached!
% 1.89/1.45 % (4308)------------------------------
% 1.89/1.45 % (4308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.45 % (4308)Termination reason: Unknown
% 1.89/1.45 % (4308)Termination phase: Property scanning
% 1.89/1.45
% 1.89/1.45 % (4308)Memory used [KB]: 1023
% 1.89/1.45 % (4308)Time elapsed: 0.003 s
% 1.89/1.45 % (4308)Instructions burned: 4 (million)
% 1.89/1.45 % (4308)------------------------------
% 1.89/1.45 % (4308)------------------------------
% 1.89/1.45 % (4306)Instruction limit reached!
% 1.89/1.45 % (4306)------------------------------
% 1.89/1.45 % (4306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.45 % (4306)Termination reason: Unknown
% 1.89/1.45 % (4306)Termination phase: Property scanning
% 1.89/1.45
% 1.89/1.45 % (4306)Memory used [KB]: 1023
% 1.89/1.45 % (4306)Time elapsed: 0.006 s
% 1.89/1.45 % (4306)Instructions burned: 8 (million)
% 1.89/1.45 % (4306)------------------------------
% 1.89/1.45 % (4306)------------------------------
% 1.89/1.45 % (4309)Instruction limit reached!
% 1.89/1.45 % (4309)------------------------------
% 1.89/1.45 % (4309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.45 % (4309)Termination reason: Unknown
% 1.89/1.45 % (4309)Termination phase: Saturation
% 1.89/1.45
% 1.89/1.46 % (4309)Memory used [KB]: 5628
% 1.89/1.46 % (4309)Time elapsed: 0.007 s
% 1.89/1.46 % (4309)Instructions burned: 20 (million)
% 1.89/1.46 % (4309)------------------------------
% 1.89/1.46 % (4309)------------------------------
% 1.89/1.46 % (4310)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_3954 for (2999ds/710Mi)
% 1.89/1.46 % (4311)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3954 for (2999ds/6Mi)
% 1.89/1.46 % (4311)Instruction limit reached!
% 1.89/1.46 % (4311)------------------------------
% 1.89/1.46 % (4311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.46 % (4311)Termination reason: Unknown
% 1.89/1.46 % (4311)Termination phase: Property scanning
% 1.89/1.46
% 1.89/1.46 % (4311)Memory used [KB]: 1023
% 1.89/1.46 % (4311)Time elapsed: 0.004 s
% 1.89/1.46 % (4311)Instructions burned: 8 (million)
% 1.89/1.46 % (4311)------------------------------
% 1.89/1.46 % (4311)------------------------------
% 1.89/1.46 % (4313)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_3954 for (2999ds/21Mi)
% 1.89/1.47 % (4312)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_3954 for (2999ds/902Mi)
% 1.89/1.47 % (4313)Instruction limit reached!
% 1.89/1.47 % (4313)------------------------------
% 1.89/1.47 % (4313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.47 % (4313)Termination reason: Unknown
% 1.89/1.47 % (4313)Termination phase: Saturation
% 1.89/1.47
% 1.89/1.47 % (4313)Memory used [KB]: 5756
% 1.89/1.47 % (4313)Time elapsed: 0.008 s
% 1.89/1.47 % (4313)Instructions burned: 21 (million)
% 1.89/1.47 % (4313)------------------------------
% 1.89/1.47 % (4313)------------------------------
% 1.89/1.47 % (4314)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_3954 for (2999ds/5Mi)
% 1.89/1.47 % (4314)Instruction limit reached!
% 1.89/1.47 % (4314)------------------------------
% 1.89/1.47 % (4314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.47 % (4314)Termination reason: Unknown
% 1.89/1.47 % (4314)Termination phase: shuffling
% 1.89/1.47
% 1.89/1.47 % (4314)Memory used [KB]: 1023
% 1.89/1.47 % (4314)Time elapsed: 0.003 s
% 1.89/1.47 % (4314)Instructions burned: 5 (million)
% 1.89/1.47 % (4314)------------------------------
% 1.89/1.47 % (4314)------------------------------
% 1.89/1.48 % (4315)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_3954 for (2999ds/6Mi)
% 1.89/1.48 % (4315)Instruction limit reached!
% 1.89/1.48 % (4315)------------------------------
% 1.89/1.48 % (4315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.48 % (4315)Termination reason: Unknown
% 1.89/1.48 % (4315)Termination phase: Property scanning
% 1.89/1.48
% 1.89/1.48 % (4315)Memory used [KB]: 1023
% 1.89/1.48 % (4315)Time elapsed: 0.003 s
% 1.89/1.48 % (4315)Instructions burned: 8 (million)
% 1.89/1.48 % (4315)------------------------------
% 1.89/1.48 % (4315)------------------------------
% 1.89/1.48 % (4316)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_3954 for (2999ds/377Mi)
% 1.89/1.49 % (4317)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_3954 for (2999ds/779Mi)
% 1.89/1.51 % (4290)Instruction limit reached!
% 1.89/1.51 % (4290)------------------------------
% 1.89/1.51 % (4290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.51 % (4290)Termination reason: Unknown
% 1.89/1.51 % (4290)Termination phase: Saturation
% 1.89/1.51
% 1.89/1.51 % (4290)Memory used [KB]: 6396
% 1.89/1.51 % (4290)Time elapsed: 0.107 s
% 1.89/1.51 % (4290)Instructions burned: 185 (million)
% 1.89/1.51 % (4290)------------------------------
% 1.89/1.51 % (4290)------------------------------
% 1.89/1.52 % (4318)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_3954 for (2998ds/19Mi)
% 1.89/1.53 % (4318)Instruction limit reached!
% 1.89/1.53 % (4318)------------------------------
% 1.89/1.53 % (4318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.53 % (4318)Termination reason: Unknown
% 1.89/1.53 % (4318)Termination phase: Saturation
% 1.89/1.53
% 1.89/1.53 % (4318)Memory used [KB]: 5628
% 1.89/1.53 % (4318)Time elapsed: 0.007 s
% 1.89/1.53 % (4318)Instructions burned: 19 (million)
% 1.89/1.53 % (4318)------------------------------
% 1.89/1.53 % (4318)------------------------------
% 1.89/1.53 % (4295)Instruction limit reached!
% 1.89/1.53 % (4295)------------------------------
% 1.89/1.53 % (4295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.53 % (4295)Termination reason: Unknown
% 1.89/1.53 % (4295)Termination phase: Saturation
% 1.89/1.53
% 1.89/1.53 % (4295)Memory used [KB]: 6396
% 1.89/1.53 % (4295)Time elapsed: 0.129 s
% 1.89/1.53 % (4295)Instructions burned: 275 (million)
% 1.89/1.53 % (4295)------------------------------
% 1.89/1.53 % (4295)------------------------------
% 1.89/1.54 % (4319)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_3954 for (2998ds/879Mi)
% 1.89/1.54 % (4320)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_3954 for (2998ds/17Mi)
% 1.89/1.55 % (4320)Instruction limit reached!
% 1.89/1.55 % (4320)------------------------------
% 1.89/1.55 % (4320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.55 % (4320)Termination reason: Unknown
% 1.89/1.55 % (4320)Termination phase: Saturation
% 1.89/1.55
% 1.89/1.55 % (4320)Memory used [KB]: 5756
% 1.89/1.55 % (4320)Time elapsed: 0.008 s
% 1.89/1.55 % (4320)Instructions burned: 18 (million)
% 1.89/1.55 % (4320)------------------------------
% 1.89/1.55 % (4320)------------------------------
% 1.89/1.56 % (4321)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_3954 for (2998ds/3Mi)
% 1.89/1.56 % (4321)Instruction limit reached!
% 1.89/1.56 % (4321)------------------------------
% 1.89/1.56 % (4321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.56 % (4321)Termination reason: Unknown
% 1.89/1.56 % (4321)Termination phase: Property scanning
% 1.89/1.56
% 1.89/1.56 % (4321)Memory used [KB]: 1023
% 1.89/1.56 % (4321)Time elapsed: 0.003 s
% 1.89/1.56 % (4321)Instructions burned: 5 (million)
% 1.89/1.56 % (4321)------------------------------
% 1.89/1.56 % (4321)------------------------------
% 1.89/1.57 % (4322)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_3954 for (2998ds/30Mi)
% 1.89/1.58 % (4322)Instruction limit reached!
% 1.89/1.58 % (4322)------------------------------
% 1.89/1.58 % (4322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.58 % (4322)Termination reason: Unknown
% 1.89/1.58 % (4322)Termination phase: Saturation
% 1.89/1.58
% 1.89/1.58 % (4322)Memory used [KB]: 5756
% 1.89/1.58 % (4322)Time elapsed: 0.012 s
% 1.89/1.58 % (4322)Instructions burned: 30 (million)
% 1.89/1.58 % (4322)------------------------------
% 1.89/1.58 % (4322)------------------------------
% 1.89/1.59 % (4323)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_3954 for (2998ds/127Mi)
% 1.89/1.61 % (4316)Instruction limit reached!
% 1.89/1.61 % (4316)------------------------------
% 1.89/1.61 % (4316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.61 % (4316)Termination reason: Unknown
% 1.89/1.61 % (4316)Termination phase: Saturation
% 1.89/1.61
% 1.89/1.61 % (4316)Memory used [KB]: 6268
% 1.89/1.61 % (4316)Time elapsed: 0.129 s
% 1.89/1.61 % (4316)Instructions burned: 378 (million)
% 1.89/1.61 % (4316)------------------------------
% 1.89/1.61 % (4316)------------------------------
% 1.89/1.62 % (4324)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_3954 for (2997ds/100Mi)
% 1.89/1.63 % (4323)Instruction limit reached!
% 1.89/1.63 % (4323)------------------------------
% 1.89/1.63 % (4323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.63 % (4323)Termination reason: Unknown
% 1.89/1.63 % (4323)Termination phase: Saturation
% 1.89/1.63
% 1.89/1.63 % (4323)Memory used [KB]: 6012
% 1.89/1.63 % (4323)Time elapsed: 0.045 s
% 1.89/1.63 % (4323)Instructions burned: 129 (million)
% 1.89/1.63 % (4323)------------------------------
% 1.89/1.63 % (4323)------------------------------
% 1.89/1.64 % (4325)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_3954 for (2997ds/3Mi)
% 1.89/1.65 % (4325)Instruction limit reached!
% 1.89/1.65 % (4325)------------------------------
% 1.89/1.65 % (4325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.65 % (4325)Termination reason: Unknown
% 1.89/1.65 % (4325)Termination phase: shuffling
% 1.89/1.65
% 1.89/1.65 % (4325)Memory used [KB]: 1023
% 1.89/1.65 % (4325)Time elapsed: 0.003 s
% 1.89/1.65 % (4325)Instructions burned: 5 (million)
% 1.89/1.65 % (4325)------------------------------
% 1.89/1.65 % (4325)------------------------------
% 1.89/1.65 % (4324)Instruction limit reached!
% 1.89/1.65 % (4324)------------------------------
% 1.89/1.65 % (4324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.65 % (4324)Termination reason: Unknown
% 1.89/1.65 % (4324)Termination phase: Saturation
% 1.89/1.65
% 1.89/1.65 % (4324)Memory used [KB]: 6012
% 1.89/1.65 % (4324)Time elapsed: 0.035 s
% 1.89/1.65 % (4324)Instructions burned: 102 (million)
% 1.89/1.65 % (4324)------------------------------
% 1.89/1.65 % (4324)------------------------------
% 1.89/1.66 % (4326)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_3954 for (2997ds/20Mi)
% 1.89/1.66 % (4326)Instruction limit reached!
% 1.89/1.66 % (4326)------------------------------
% 1.89/1.66 % (4326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.66 % (4326)Termination reason: Unknown
% 1.89/1.66 % (4326)Termination phase: Saturation
% 1.89/1.66
% 1.89/1.66 % (4326)Memory used [KB]: 5628
% 1.89/1.66 % (4326)Time elapsed: 0.008 s
% 1.89/1.66 % (4326)Instructions burned: 20 (million)
% 1.89/1.66 % (4326)------------------------------
% 1.89/1.66 % (4326)------------------------------
% 1.89/1.66 % (4327)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_3954 for (2997ds/86Mi)
% 1.89/1.67 % (4328)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_3954 for (2997ds/107Mi)
% 1.89/1.68 % (4310)Instruction limit reached!
% 1.89/1.68 % (4310)------------------------------
% 1.89/1.68 % (4310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.68 % (4310)Termination reason: Unknown
% 1.89/1.68 % (4310)Termination phase: Saturation
% 1.89/1.68
% 1.89/1.68 % (4310)Memory used [KB]: 7291
% 1.89/1.68 % (4310)Time elapsed: 0.223 s
% 1.89/1.68 % (4310)Instructions burned: 711 (million)
% 1.89/1.68 % (4310)------------------------------
% 1.89/1.68 % (4310)------------------------------
% 1.89/1.69 % (4329)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_3954 for (2997ds/39Mi)
% 1.89/1.69 % (4327)Instruction limit reached!
% 1.89/1.69 % (4327)------------------------------
% 1.89/1.69 % (4327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.69 % (4327)Termination reason: Unknown
% 1.89/1.69 % (4327)Termination phase: Saturation
% 1.89/1.69
% 1.89/1.69 % (4327)Memory used [KB]: 6140
% 1.89/1.69 % (4327)Time elapsed: 0.030 s
% 1.89/1.69 % (4327)Instructions burned: 86 (million)
% 1.89/1.69 % (4327)------------------------------
% 1.89/1.69 % (4327)------------------------------
% 1.89/1.70 % (4329)Instruction limit reached!
% 1.89/1.70 % (4329)------------------------------
% 1.89/1.70 % (4329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.70 % (4329)Termination reason: Unknown
% 1.89/1.70 % (4329)Termination phase: Saturation
% 1.89/1.70
% 1.89/1.70 % (4329)Memory used [KB]: 5756
% 1.89/1.70 % (4329)Time elapsed: 0.035 s
% 1.89/1.70 % (4329)Instructions burned: 40 (million)
% 1.89/1.70 % (4329)------------------------------
% 1.89/1.70 % (4329)------------------------------
% 1.89/1.70 % (4330)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_3954 for (2996ds/448Mi)
% 1.89/1.71 % (4328)Instruction limit reached!
% 1.89/1.71 % (4328)------------------------------
% 1.89/1.71 % (4328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.71 % (4328)Termination reason: Unknown
% 1.89/1.71 % (4328)Termination phase: Saturation
% 1.89/1.71
% 1.89/1.71 % (4328)Memory used [KB]: 5884
% 1.89/1.71 % (4328)Time elapsed: 0.038 s
% 1.89/1.71 % (4328)Instructions burned: 107 (million)
% 1.89/1.71 % (4328)------------------------------
% 1.89/1.71 % (4328)------------------------------
% 1.89/1.71 % (4331)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_3954 for (2996ds/46Mi)
% 1.89/1.72 % (4332)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_3954 for (2996ds/98Mi)
% 1.89/1.72 % (4317)Instruction limit reached!
% 1.89/1.72 % (4317)------------------------------
% 1.89/1.72 % (4317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.72 % (4317)Termination reason: Unknown
% 1.89/1.72 % (4317)Termination phase: Saturation
% 1.89/1.72
% 1.89/1.72 % (4317)Memory used [KB]: 7036
% 1.89/1.72 % (4317)Time elapsed: 0.233 s
% 1.89/1.72 % (4317)Instructions burned: 781 (million)
% 1.89/1.72 % (4317)------------------------------
% 1.89/1.72 % (4317)------------------------------
% 1.89/1.73 % (4331)Instruction limit reached!
% 1.89/1.73 % (4331)------------------------------
% 1.89/1.73 % (4331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.73 % (4331)Termination reason: Unknown
% 1.89/1.73 % (4331)Termination phase: Saturation
% 1.89/1.73
% 1.89/1.73 % (4331)Memory used [KB]: 5884
% 1.89/1.73 % (4331)Time elapsed: 0.016 s
% 1.89/1.73 % (4331)Instructions burned: 46 (million)
% 1.89/1.73 % (4331)------------------------------
% 1.89/1.73 % (4331)------------------------------
% 1.89/1.73 % (4333)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_3954 for (2996ds/507Mi)
% 1.89/1.74 % (4334)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_3954 for (2996ds/149Mi)
% 1.89/1.75 % (4332)Instruction limit reached!
% 1.89/1.75 % (4332)------------------------------
% 1.89/1.75 % (4332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.75 % (4332)Termination reason: Unknown
% 1.89/1.75 % (4332)Termination phase: Saturation
% 1.89/1.75
% 1.89/1.75 % (4332)Memory used [KB]: 1407
% 1.89/1.75 % (4332)Time elapsed: 0.034 s
% 1.89/1.75 % (4332)Instructions burned: 100 (million)
% 1.89/1.75 % (4332)------------------------------
% 1.89/1.75 % (4332)------------------------------
% 1.89/1.76 % (4333)First to succeed.
% 1.89/1.76 % (4333)Refutation found. Thanks to Tanya!
% 1.89/1.76 % SZS status Theorem for DTF2THF_3954
% 1.89/1.76 % SZS output start Proof for DTF2THF_3954
% 1.89/1.76 thf(type_def_6, type, elem: $tType).
% 1.89/1.76 thf(type_def_7, type, nat: $tType).
% 1.89/1.76 thf(type_def_8, type, list: $tType).
% 1.89/1.76 thf(func_def_0, type, isPer: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 1.89/1.76 thf(func_def_2, type, elem: $tType).
% 1.89/1.76 thf(func_def_3, type, elemStar: elem > elem > $o).
% 1.89/1.76 thf(func_def_4, type, nat: $tType).
% 1.89/1.76 thf(func_def_5, type, natStar: nat > nat > $o).
% 1.89/1.76 thf(func_def_6, type, zero: nat).
% 1.89/1.76 thf(func_def_7, type, suc: nat > nat).
% 1.89/1.76 thf(func_def_8, type, plus: nat > nat > nat).
% 1.89/1.76 thf(func_def_9, type, list: $tType).
% 1.89/1.76 thf(func_def_10, type, listStar: nat > list > list > $o).
% 1.89/1.76 thf(func_def_11, type, nil: list).
% 1.89/1.76 thf(func_def_12, type, cons: nat > elem > list > list).
% 1.89/1.76 thf(func_def_13, type, app: nat > nat > list > list > list).
% 1.89/1.76 thf(func_def_14, type, rev: nat > list > list).
% 1.89/1.76 thf(func_def_17, type, sK0: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.89/1.76 thf(func_def_18, type, sK1: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.89/1.76 thf(func_def_26, type, sK2: (nat > $o) > nat).
% 1.89/1.76 thf(func_def_27, type, sK3: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.89/1.76 thf(func_def_28, type, sK4: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.89/1.76 thf(func_def_29, type, sK5: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.89/1.76 thf(func_def_30, type, sK6: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.89/1.76 thf(func_def_31, type, sK7: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.89/1.76 thf(func_def_32, type, sK8: nat).
% 1.89/1.76 thf(func_def_33, type, sK9: elem).
% 1.89/1.76 thf(func_def_34, type, sK10: list).
% 1.89/1.76 thf(func_def_35, type, sK11: nat).
% 1.89/1.76 thf(func_def_36, type, sK12: list).
% 1.89/1.76 thf(func_def_38, type, ph14: !>[X0: $tType]:(X0)).
% 1.89/1.76 thf(f255,plain,(
% 1.89/1.76 $false),
% 1.89/1.76 inference(subsumption_resolution,[status(thm)],[f254,f144])).
% 1.89/1.76 thf(f144,plain,(
% 1.89/1.76 ((listStar @ sK8 @ sK10 @ sK10) = $true)),
% 1.89/1.76 inference(cnf_transformation,[status(thm)],[f116])).
% 1.89/1.76 thf(f116,plain,(
% 1.89/1.76 ! [X3 : nat,X4 : list] : (($true != (listStar @ X3 @ X4 @ X4)) | ($true = (listStar @ (plus @ sK8 @ X3) @ (rev @ (plus @ sK8 @ X3) @ (app @ sK8 @ X3 @ (rev @ sK8 @ sK10) @ X4)) @ (app @ X3 @ sK8 @ (rev @ X3 @ X4) @ sK10)))) & (((listStar @ (plus @ (suc @ sK8) @ sK11) @ (rev @ (plus @ (suc @ sK8) @ sK11) @ (app @ (suc @ sK8) @ sK11 @ (rev @ (suc @ sK8) @ (cons @ sK8 @ sK9 @ sK10)) @ sK12)) @ (rev @ (plus @ (suc @ sK8) @ sK11) @ (app @ (plus @ sK8 @ (suc @ zero)) @ sK11 @ (app @ sK8 @ (suc @ zero) @ (rev @ sK8 @ sK10) @ (cons @ zero @ sK9 @ nil)) @ sK12))) != $true) & ($true = (listStar @ sK11 @ sK12 @ sK12))) & ((listStar @ sK8 @ sK10 @ sK10) = $true)),
% 1.89/1.76 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12])],[f90,f115,f114])).
% 1.89/1.76 thf(f114,plain,(
% 1.89/1.76 ? [X0 : nat,X1 : elem,X2 : list] : (! [X3 : nat,X4 : list] : (($true != (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)) = $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)) @ (rev @ (plus @ (suc @ X0) @ X5) @ (app @ (plus @ X0 @ (suc @ zero)) @ X5 @ (app @ X0 @ (suc @ zero) @ (rev @ X0 @ X2) @ (cons @ zero @ X1 @ nil)) @ X6))) != $true) & ((listStar @ X5 @ X6 @ X6) = $true)) & ((listStar @ X0 @ X2 @ X2) = $true)) => (! [X4 : list,X3 : nat] : (($true != (listStar @ X3 @ X4 @ X4)) | ($true = (listStar @ (plus @ sK8 @ X3) @ (rev @ (plus @ sK8 @ X3) @ (app @ sK8 @ X3 @ (rev @ sK8 @ sK10) @ X4)) @ (app @ X3 @ sK8 @ (rev @ X3 @ X4) @ sK10)))) & ? [X6 : list,X5 : nat] : (((listStar @ (plus @ (suc @ sK8) @ X5) @ (rev @ (plus @ (suc @ sK8) @ X5) @ (app @ (suc @ sK8) @ X5 @ (rev @ (suc @ sK8) @ (cons @ sK8 @ sK9 @ sK10)) @ X6)) @ (rev @ (plus @ (suc @ sK8) @ X5) @ (app @ (plus @ sK8 @ (suc @ zero)) @ X5 @ (app @ sK8 @ (suc @ zero) @ (rev @ sK8 @ sK10) @ (cons @ zero @ sK9 @ nil)) @ X6))) != $true) & ((listStar @ X5 @ X6 @ X6) = $true)) & ((listStar @ sK8 @ sK10 @ sK10) = $true))),
% 1.89/1.76 introduced(definition,[],[choice_axiom])).
% 1.89/1.76 thf(f115,plain,(
% 1.89/1.76 ? [X6 : list,X5 : nat] : (((listStar @ (plus @ (suc @ sK8) @ X5) @ (rev @ (plus @ (suc @ sK8) @ X5) @ (app @ (suc @ sK8) @ X5 @ (rev @ (suc @ sK8) @ (cons @ sK8 @ sK9 @ sK10)) @ X6)) @ (rev @ (plus @ (suc @ sK8) @ X5) @ (app @ (plus @ sK8 @ (suc @ zero)) @ X5 @ (app @ sK8 @ (suc @ zero) @ (rev @ sK8 @ sK10) @ (cons @ zero @ sK9 @ nil)) @ X6))) != $true) & ((listStar @ X5 @ X6 @ X6) = $true)) => (((listStar @ (plus @ (suc @ sK8) @ sK11) @ (rev @ (plus @ (suc @ sK8) @ sK11) @ (app @ (suc @ sK8) @ sK11 @ (rev @ (suc @ sK8) @ (cons @ sK8 @ sK9 @ sK10)) @ sK12)) @ (rev @ (plus @ (suc @ sK8) @ sK11) @ (app @ (plus @ sK8 @ (suc @ zero)) @ sK11 @ (app @ sK8 @ (suc @ zero) @ (rev @ sK8 @ sK10) @ (cons @ zero @ sK9 @ nil)) @ sK12))) != $true) & ($true = (listStar @ sK11 @ sK12 @ sK12)))),
% 1.89/1.76 introduced(definition,[],[choice_axiom])).
% 1.89/1.76 thf(f90,plain,(
% 1.89/1.76 ? [X0 : nat,X1 : elem,X2 : list] : (! [X3 : nat,X4 : list] : (($true != (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)) = $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)) @ (rev @ (plus @ (suc @ X0) @ X5) @ (app @ (plus @ X0 @ (suc @ zero)) @ X5 @ (app @ X0 @ (suc @ zero) @ (rev @ X0 @ X2) @ (cons @ zero @ X1 @ nil)) @ X6))) != $true) & ((listStar @ X5 @ X6 @ X6) = $true)) & ((listStar @ X0 @ X2 @ X2) = $true))),
% 1.89/1.76 inference(flattening,[status(thm)],[f89])).
% 1.89/1.76 thf(f89,plain,(
% 1.89/1.76 ? [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)) @ (rev @ (plus @ (suc @ X0) @ X5) @ (app @ (plus @ X0 @ (suc @ zero)) @ X5 @ (app @ X0 @ (suc @ zero) @ (rev @ X0 @ X2) @ (cons @ zero @ X1 @ nil)) @ X6))) != $true) & ((listStar @ X5 @ X6 @ X6) = $true)) & ! [X3 : nat,X4 : list] : (($true != (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)) = $true))) & ((listStar @ X0 @ X2 @ X2) = $true))),
% 1.89/1.76 inference(ennf_transformation,[status(thm)],[f67])).
% 1.89/1.76 thf(f67,plain,(
% 1.89/1.76 ~! [X0 : nat,X1 : elem,X2 : list] : (((listStar @ X0 @ X2 @ X2) = $true) => (! [X3 : nat,X4 : list] : (($true = (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)) = $true)) => ! [X5 : nat,X6 : list] : (((listStar @ X5 @ X6 @ X6) = $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 @ (suc @ X0) @ X5) @ (app @ (plus @ X0 @ (suc @ zero)) @ X5 @ (app @ X0 @ (suc @ zero) @ (rev @ X0 @ X2) @ (cons @ zero @ X1 @ nil)) @ X6))) = $true))))),
% 1.89/1.76 inference(fool_elimination,[status(thm)],[f66])).
% 1.89/1.76 thf(f66,plain,(
% 1.89/1.76 ~! [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 @ (suc @ X0) @ X5) @ (app @ (plus @ X0 @ (suc @ zero)) @ X5 @ (app @ X0 @ (suc @ zero) @ (rev @ X0 @ X2) @ (cons @ zero @ X1 @ nil)) @ X6))))))),
% 1.89/1.76 inference(rectify,[status(thm)],[f24])).
% 1.89/1.76 thf(f24,negated_conjecture,(
% 1.89/1.76 ~! [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 @ (suc @ X6) @ X14) @ (app @ (plus @ X6 @ (suc @ zero)) @ X14 @ (app @ X6 @ (suc @ zero) @ (rev @ X6 @ X16) @ (cons @ zero @ X2 @ nil)) @ X17))))))),
% 1.89/1.76 inference(negated_conjecture,[status(cth)],[f23])).
% 1.89/1.76 thf(f23,conjecture,(
% 1.89/1.76 ! [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 @ (suc @ X6) @ X14) @ (app @ (plus @ X6 @ (suc @ zero)) @ X14 @ (app @ X6 @ (suc @ zero) @ (rev @ X6 @ X16) @ (cons @ zero @ X2 @ nil)) @ X17))))))),
% 1.89/1.76 file('/export/starexec/sandbox/tmp/tmp.o1aRMkv1xQ/DTF2THF_3954.p',list_rev_invol_lem_indstep1)).
% 1.89/1.76 thf(f254,plain,(
% 1.89/1.76 ((listStar @ sK8 @ sK10 @ sK10) != $true)),
% 1.89/1.76 inference(trivial_inequality_removal,[status(thm)],[f249])).
% 1.89/1.76 thf(f249,plain,(
% 1.89/1.76 ((listStar @ sK8 @ sK10 @ sK10) != $true) | ($true != $true)),
% 1.89/1.76 inference(superposition,[status(thm)],[f236,f152])).
% 1.89/1.76 thf(f152,plain,(
% 1.89/1.76 ( ! [X2 : list,X0 : nat,X1 : elem] : (($true = (listStar @ (suc @ X0) @ (rev @ (suc @ X0) @ (cons @ X0 @ X1 @ X2)) @ (app @ X0 @ (suc @ zero) @ (rev @ X0 @ X2) @ (cons @ zero @ X1 @ nil)))) | ((listStar @ X0 @ X2 @ X2) != $true)) )),
% 1.89/1.76 inference(cnf_transformation,[status(thm)],[f93])).
% 1.89/1.76 thf(f93,plain,(
% 1.89/1.76 ! [X0 : nat,X1 : elem,X2 : list] : (($true = (listStar @ (suc @ X0) @ (rev @ (suc @ X0) @ (cons @ X0 @ X1 @ X2)) @ (app @ X0 @ (suc @ zero) @ (rev @ X0 @ X2) @ (cons @ zero @ X1 @ nil)))) | ((listStar @ X0 @ X2 @ X2) != $true))),
% 1.89/1.76 inference(ennf_transformation,[status(thm)],[f59])).
% 1.89/1.76 thf(f59,plain,(
% 1.89/1.76 ! [X0 : nat,X1 : elem,X2 : list] : (((listStar @ X0 @ X2 @ X2) = $true) => ($true = (listStar @ (suc @ X0) @ (rev @ (suc @ X0) @ (cons @ X0 @ X1 @ X2)) @ (app @ X0 @ (suc @ zero) @ (rev @ X0 @ X2) @ (cons @ zero @ X1 @ nil)))))),
% 1.89/1.76 inference(fool_elimination,[status(thm)],[f58])).
% 1.89/1.76 thf(f58,plain,(
% 1.89/1.76 ! [X0 : nat,X1 : elem,X2 : list] : ((listStar @ X0 @ X2 @ X2) => (listStar @ (suc @ X0) @ (rev @ (suc @ X0) @ (cons @ X0 @ X1 @ X2)) @ (app @ X0 @ (suc @ zero) @ (rev @ X0 @ X2) @ (cons @ zero @ X1 @ nil))))),
% 1.89/1.76 inference(rectify,[status(thm)],[f17])).
% 1.89/1.76 thf(f17,axiom,(
% 1.89/1.76 ! [X6 : nat,X2 : elem,X3 : list] : ((listStar @ X6 @ X3 @ X3) => (listStar @ (suc @ X6) @ (rev @ (suc @ X6) @ (cons @ X6 @ X2 @ X3)) @ (app @ X6 @ (suc @ zero) @ (rev @ X6 @ X3) @ (cons @ zero @ X2 @ nil))))),
% 1.89/1.76 file('/export/starexec/sandbox/tmp/tmp.o1aRMkv1xQ/DTF2THF_3954.p',ax6)).
% 1.89/1.76 thf(f236,plain,(
% 1.89/1.76 ((listStar @ (suc @ sK8) @ (rev @ (suc @ sK8) @ (cons @ sK8 @ sK9 @ sK10)) @ (app @ sK8 @ (suc @ zero) @ (rev @ sK8 @ sK10) @ (cons @ zero @ sK9 @ nil))) != $true)),
% 1.89/1.76 inference(subsumption_resolution,[status(thm)],[f233,f145])).
% 1.89/1.76 thf(f145,plain,(
% 1.89/1.76 ($true = (listStar @ sK11 @ sK12 @ sK12))),
% 1.89/1.76 inference(cnf_transformation,[status(thm)],[f116])).
% 1.89/1.76 thf(f233,plain,(
% 1.89/1.76 ($true != (listStar @ sK11 @ sK12 @ sK12)) | ((listStar @ (suc @ sK8) @ (rev @ (suc @ sK8) @ (cons @ sK8 @ sK9 @ sK10)) @ (app @ sK8 @ (suc @ zero) @ (rev @ sK8 @ sK10) @ (cons @ zero @ sK9 @ nil))) != $true)),
% 1.89/1.76 inference(trivial_inequality_removal,[status(thm)],[f229])).
% 1.89/1.76 thf(f229,plain,(
% 1.89/1.76 ($true != $true) | ((listStar @ (suc @ sK8) @ (rev @ (suc @ sK8) @ (cons @ sK8 @ sK9 @ sK10)) @ (app @ sK8 @ (suc @ zero) @ (rev @ sK8 @ sK10) @ (cons @ zero @ sK9 @ nil))) != $true) | ($true != (listStar @ sK11 @ sK12 @ sK12))),
% 1.89/1.76 inference(superposition,[status(thm)],[f178,f130])).
% 1.89/1.76 thf(f130,plain,(
% 1.89/1.76 ( ! [X2 : list,X3 : list,X0 : nat,X1 : nat,X4 : list,X5 : list] : (((listStar @ (plus @ X0 @ X1) @ (app @ X0 @ X1 @ X2 @ X4) @ (app @ X0 @ X1 @ X3 @ X5)) = $true) | ((listStar @ X0 @ X2 @ X3) != $true) | ($true != (listStar @ X1 @ X4 @ X5))) )),
% 1.89/1.76 inference(cnf_transformation,[status(thm)],[f99])).
% 1.89/1.76 thf(f99,plain,(
% 1.89/1.76 ! [X0 : nat,X1 : nat,X2 : list,X3 : list] : (! [X4 : list,X5 : list] : (($true != (listStar @ X1 @ X4 @ X5)) | ((listStar @ (plus @ X0 @ X1) @ (app @ X0 @ X1 @ X2 @ X4) @ (app @ X0 @ X1 @ X3 @ X5)) = $true)) | ((listStar @ X0 @ X2 @ X3) != $true))),
% 1.89/1.76 inference(ennf_transformation,[status(thm)],[f55])).
% 1.89/1.76 thf(f55,plain,(
% 1.89/1.76 ! [X0 : nat,X1 : nat,X2 : list,X3 : list] : (((listStar @ X0 @ X2 @ X3) = $true) => ! [X4 : list,X5 : list] : (($true = (listStar @ X1 @ X4 @ X5)) => ((listStar @ (plus @ X0 @ X1) @ (app @ X0 @ X1 @ X2 @ X4) @ (app @ X0 @ X1 @ X3 @ X5)) = $true)))),
% 1.89/1.76 inference(fool_elimination,[status(thm)],[f54])).
% 1.89/1.76 thf(f54,plain,(
% 1.89/1.76 ! [X0 : nat,X1 : nat,X2 : list,X3 : list] : ((listStar @ X0 @ X2 @ X3) => ! [X4 : list,X5 : list] : ((listStar @ X1 @ X4 @ X5) => (listStar @ (plus @ X0 @ X1) @ (app @ X0 @ X1 @ X2 @ X4) @ (app @ X0 @ X1 @ X3 @ X5))))),
% 1.89/1.76 inference(rectify,[status(thm)],[f7])).
% 1.89/1.76 thf(f7,axiom,(
% 1.89/1.76 ! [X6 : nat,X10 : nat,X7 : list,X11 : list] : ((listStar @ X6 @ X7 @ X11) => ! [X8 : list,X9 : list] : ((listStar @ X10 @ X8 @ X9) => (listStar @ (plus @ X6 @ X10) @ (app @ X6 @ X10 @ X7 @ X8) @ (app @ X6 @ X10 @ X11 @ X9))))),
% 1.89/1.76 file('/export/starexec/sandbox/tmp/tmp.o1aRMkv1xQ/DTF2THF_3954.p',app_tp_ax)).
% 1.89/1.76 thf(f178,plain,(
% 1.89/1.76 ($true != (listStar @ (plus @ (suc @ sK8) @ sK11) @ (app @ (suc @ sK8) @ sK11 @ (rev @ (suc @ sK8) @ (cons @ sK8 @ sK9 @ sK10)) @ sK12) @ (app @ (suc @ sK8) @ sK11 @ (app @ sK8 @ (suc @ zero) @ (rev @ sK8 @ sK10) @ (cons @ zero @ sK9 @ nil)) @ sK12)))),
% 1.89/1.76 inference(superposition,[status(thm)],[f168,f142])).
% 1.89/1.76 thf(f142,plain,(
% 1.89/1.76 ( ! [X0 : nat] : (((plus @ X0 @ (suc @ zero)) = (suc @ X0))) )),
% 1.89/1.76 inference(cnf_transformation,[status(thm)],[f37])).
% 1.89/1.76 thf(f37,plain,(
% 1.89/1.76 ! [X0 : nat] : ((plus @ X0 @ (suc @ zero)) = (suc @ X0))),
% 1.89/1.76 inference(fool_elimination,[status(thm)],[f36])).
% 1.89/1.76 thf(f36,plain,(
% 1.89/1.76 ! [X0 : nat] : ((plus @ X0 @ (suc @ zero)) = (suc @ X0))),
% 1.89/1.76 inference(rectify,[status(thm)],[f21])).
% 1.89/1.76 thf(f21,axiom,(
% 1.89/1.76 ! [X6 : nat] : ((suc @ X6) = (plus @ X6 @ (suc @ zero)))),
% 1.89/1.76 file('/export/starexec/sandbox/tmp/tmp.o1aRMkv1xQ/DTF2THF_3954.p',plus1r)).
% 1.89/1.76 thf(f168,plain,(
% 1.89/1.76 ($true != (listStar @ (plus @ (suc @ sK8) @ sK11) @ (app @ (suc @ sK8) @ sK11 @ (rev @ (suc @ sK8) @ (cons @ sK8 @ sK9 @ sK10)) @ sK12) @ (app @ (plus @ sK8 @ (suc @ zero)) @ sK11 @ (app @ sK8 @ (suc @ zero) @ (rev @ sK8 @ sK10) @ (cons @ zero @ sK9 @ nil)) @ sK12)))),
% 1.89/1.76 inference(trivial_inequality_removal,[status(thm)],[f165])).
% 1.89/1.76 thf(f165,plain,(
% 1.89/1.76 ($true != (listStar @ (plus @ (suc @ sK8) @ sK11) @ (app @ (suc @ sK8) @ sK11 @ (rev @ (suc @ sK8) @ (cons @ sK8 @ sK9 @ sK10)) @ sK12) @ (app @ (plus @ sK8 @ (suc @ zero)) @ sK11 @ (app @ sK8 @ (suc @ zero) @ (rev @ sK8 @ sK10) @ (cons @ zero @ sK9 @ nil)) @ sK12))) | ($true != $true)),
% 1.89/1.76 inference(superposition,[status(thm)],[f146,f132])).
% 1.89/1.76 thf(f132,plain,(
% 1.89/1.76 ( ! [X2 : list,X0 : nat,X1 : list] : (($true = (listStar @ X0 @ (rev @ X0 @ X1) @ (rev @ X0 @ X2))) | ((listStar @ X0 @ X1 @ X2) != $true)) )),
% 1.89/1.76 inference(cnf_transformation,[status(thm)],[f92])).
% 1.89/1.76 thf(f92,plain,(
% 1.89/1.76 ! [X0 : nat,X1 : list,X2 : list] : (((listStar @ X0 @ X1 @ X2) != $true) | ($true = (listStar @ X0 @ (rev @ X0 @ X1) @ (rev @ X0 @ X2))))),
% 1.89/1.76 inference(ennf_transformation,[status(thm)],[f43])).
% 1.89/1.76 thf(f43,plain,(
% 1.89/1.76 ! [X0 : nat,X1 : list,X2 : list] : (((listStar @ X0 @ X1 @ X2) = $true) => ($true = (listStar @ X0 @ (rev @ X0 @ X1) @ (rev @ X0 @ X2))))),
% 1.89/1.76 inference(fool_elimination,[status(thm)],[f42])).
% 1.89/1.76 thf(f42,plain,(
% 1.89/1.76 ! [X0 : nat,X1 : list,X2 : list] : ((listStar @ X0 @ X1 @ X2) => (listStar @ X0 @ (rev @ X0 @ X1) @ (rev @ X0 @ X2)))),
% 1.89/1.76 inference(rectify,[status(thm)],[f8])).
% 1.89/1.76 thf(f8,axiom,(
% 1.89/1.76 ! [X6 : nat,X7 : list,X11 : list] : ((listStar @ X6 @ X7 @ X11) => (listStar @ X6 @ (rev @ X6 @ X7) @ (rev @ X6 @ X11)))),
% 1.89/1.76 file('/export/starexec/sandbox/tmp/tmp.o1aRMkv1xQ/DTF2THF_3954.p',rev_tp_ax)).
% 1.89/1.76 thf(f146,plain,(
% 1.89/1.76 ((listStar @ (plus @ (suc @ sK8) @ sK11) @ (rev @ (plus @ (suc @ sK8) @ sK11) @ (app @ (suc @ sK8) @ sK11 @ (rev @ (suc @ sK8) @ (cons @ sK8 @ sK9 @ sK10)) @ sK12)) @ (rev @ (plus @ (suc @ sK8) @ sK11) @ (app @ (plus @ sK8 @ (suc @ zero)) @ sK11 @ (app @ sK8 @ (suc @ zero) @ (rev @ sK8 @ sK10) @ (cons @ zero @ sK9 @ nil)) @ sK12))) != $true)),
% 1.89/1.76 inference(cnf_transformation,[status(thm)],[f116])).
% 1.89/1.76 % SZS output end Proof for DTF2THF_3954
% 1.89/1.76 % (4333)------------------------------
% 1.89/1.76 % (4333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.76 % (4333)Termination reason: Refutation
% 1.89/1.76
% 1.89/1.76 % (4333)Memory used [KB]: 6012
% 1.89/1.76 % (4333)Time elapsed: 0.025 s
% 1.89/1.76 % (4333)Instructions burned: 73 (million)
% 1.89/1.76 % (4333)------------------------------
% 1.89/1.76 % (4333)------------------------------
% 1.89/1.76 % (4289)Success in time 0.372 s
%------------------------------------------------------------------------------