%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT400^1 : 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 : n020.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 08:45:39 AM UTC 2026
% Result : Theorem 1.81s 1.41s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 254 ( 75 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 919 ( 38 ~; 30 |; 4 &; 821 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 58 ( 0 ^; 54 !; 4 ?; 58 :)
% 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 ).
thf(func_def_18,type,
sK1: list ).
thf(f136,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f135,f86]) ).
thf(f86,plain,
( $true
!= ( listStar @ sK0 @ ( rev @ sK0 @ ( rev @ sK0 @ sK1 ) ) @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
thf(f77,plain,
( ( $true
!= ( listStar @ sK0 @ ( rev @ sK0 @ ( rev @ sK0 @ sK1 ) ) @ sK1 ) )
& ( ( listStar @ sK0 @ sK1 @ sK1 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f75,f76]) ).
thf(f76,plain,
( ? [X0: nat,X1: list] :
( ( $true
!= ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ X1 ) )
& ( $true
= ( listStar @ X0 @ X1 @ X1 ) ) )
=> ( ( $true
!= ( listStar @ sK0 @ ( rev @ sK0 @ ( rev @ sK0 @ sK1 ) ) @ sK1 ) )
& ( ( listStar @ sK0 @ sK1 @ sK1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f75,plain,
? [X0: nat,X1: list] :
( ( $true
!= ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ X1 ) )
& ( $true
= ( listStar @ X0 @ X1 @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f65]) ).
thf(f65,plain,
~ ! [X0: nat,X1: list] :
( ( $true
= ( listStar @ X0 @ X1 @ X1 ) )
=> ( $true
= ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f64]) ).
thf(f64,plain,
~ ! [X0: nat,X1: list] :
( ( listStar @ X0 @ X1 @ X1 )
=> ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ X1 ) ),
inference(rectify,[status(thm)],[f26]) ).
thf(f26,negated_conjecture,
~ ! [X6: nat,X13: list] :
( ( listStar @ X6 @ X13 @ X13 )
=> ( listStar @ X6 @ ( rev @ X6 @ ( rev @ X6 @ X13 ) ) @ X13 ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
thf(f25,conjecture,
! [X6: nat,X13: list] :
( ( listStar @ X6 @ X13 @ X13 )
=> ( listStar @ X6 @ ( rev @ X6 @ ( rev @ X6 @ X13 ) ) @ X13 ) ),
file('/export/starexec/sandbox/tmp/tmp.bglDpxLIIQ/DTF2THF_2542.p',list_rev_invol) ).
thf(f135,plain,
( $true
= ( listStar @ sK0 @ ( rev @ sK0 @ ( rev @ sK0 @ sK1 ) ) @ sK1 ) ),
inference(subsumption_resolution,[status(thm)],[f133,f85]) ).
thf(f85,plain,
( ( listStar @ sK0 @ sK1 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f77]) ).
thf(f133,plain,
( ( ( listStar @ sK0 @ sK1 @ sK1 )
!= $true )
| ( $true
= ( listStar @ sK0 @ ( rev @ sK0 @ ( rev @ sK0 @ sK1 ) ) @ sK1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f131]) ).
thf(f131,plain,
( ( $true != $true )
| ( $true
= ( listStar @ sK0 @ ( rev @ sK0 @ ( rev @ sK0 @ sK1 ) ) @ sK1 ) )
| ( ( listStar @ sK0 @ sK1 @ sK1 )
!= $true ) ),
inference(superposition,[status(thm)],[f83,f128]) ).
thf(f128,plain,
( ( listStar @ sK0 @ ( rev @ sK0 @ ( rev @ sK0 @ sK1 ) ) @ ( app @ zero @ sK0 @ nil @ sK1 ) )
= $true ),
inference(subsumption_resolution,[status(thm)],[f126,f85]) ).
thf(f126,plain,
( ( ( listStar @ sK0 @ ( rev @ sK0 @ ( rev @ sK0 @ sK1 ) ) @ ( app @ zero @ sK0 @ nil @ sK1 ) )
= $true )
| ( ( listStar @ sK0 @ sK1 @ sK1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f124]) ).
thf(f124,plain,
( ( ( listStar @ sK0 @ sK1 @ sK1 )
!= $true )
| ( ( listStar @ sK0 @ ( rev @ sK0 @ ( rev @ sK0 @ sK1 ) ) @ ( app @ zero @ sK0 @ nil @ sK1 ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f79,f123]) ).
thf(f123,plain,
( $true
= ( listStar @ sK0 @ ( rev @ sK0 @ ( rev @ sK0 @ sK1 ) ) @ ( app @ zero @ sK0 @ ( rev @ zero @ nil ) @ sK1 ) ) ),
inference(subsumption_resolution,[status(thm)],[f121,f85]) ).
thf(f121,plain,
( ( $true
= ( listStar @ sK0 @ ( rev @ sK0 @ ( rev @ sK0 @ sK1 ) ) @ ( app @ zero @ sK0 @ ( rev @ zero @ nil ) @ sK1 ) ) )
| ( ( listStar @ sK0 @ sK1 @ sK1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f119]) ).
thf(f119,plain,
( ( ( listStar @ sK0 @ sK1 @ sK1 )
!= $true )
| ( $true != $true )
| ( $true
= ( listStar @ sK0 @ ( rev @ sK0 @ ( rev @ sK0 @ sK1 ) ) @ ( app @ zero @ sK0 @ ( rev @ zero @ nil ) @ sK1 ) ) ) ),
inference(superposition,[status(thm)],[f80,f95]) ).
thf(f95,plain,
( ( listStar @ sK0 @ ( rev @ sK0 @ ( rev @ sK0 @ sK1 ) ) @ ( rev @ ( plus @ sK0 @ zero ) @ ( app @ sK0 @ zero @ ( rev @ sK0 @ sK1 ) @ nil ) ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f93]) ).
thf(f93,plain,
( ( $true != $true )
| ( ( listStar @ sK0 @ ( rev @ sK0 @ ( rev @ sK0 @ sK1 ) ) @ ( rev @ ( plus @ sK0 @ zero ) @ ( app @ sK0 @ zero @ ( rev @ sK0 @ sK1 ) @ nil ) ) )
= $true ) ),
inference(superposition,[status(thm)],[f78,f85]) ).
thf(f78,plain,
! [X0: nat,X1: list] :
( ( $true
!= ( listStar @ X0 @ X1 @ X1 ) )
| ( ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( rev @ ( plus @ X0 @ zero ) @ ( app @ X0 @ zero @ ( rev @ X0 @ X1 ) @ nil ) ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
thf(f68,plain,
! [X0: nat,X1: list] :
( ( ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( rev @ ( plus @ X0 @ zero ) @ ( app @ X0 @ zero @ ( rev @ X0 @ X1 ) @ nil ) ) )
= $true )
| ( $true
!= ( listStar @ X0 @ X1 @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f49]) ).
thf(f49,plain,
! [X0: nat,X1: list] :
( ( $true
= ( listStar @ X0 @ X1 @ X1 ) )
=> ( ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( rev @ ( plus @ X0 @ zero ) @ ( app @ X0 @ zero @ ( rev @ X0 @ X1 ) @ nil ) ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f48]) ).
thf(f48,plain,
! [X0: nat,X1: list] :
( ( listStar @ X0 @ X1 @ X1 )
=> ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( rev @ ( plus @ X0 @ zero ) @ ( app @ X0 @ zero @ ( rev @ X0 @ X1 ) @ nil ) ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,axiom,
! [X6: nat,X13: list] :
( ( listStar @ X6 @ X13 @ X13 )
=> ( listStar @ X6 @ ( rev @ X6 @ ( rev @ X6 @ X13 ) ) @ ( rev @ ( plus @ X6 @ zero ) @ ( app @ X6 @ zero @ ( rev @ X6 @ X13 ) @ nil ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bglDpxLIIQ/DTF2THF_2542.p',list_rev_invol_step1) ).
thf(f80,plain,
! [X0: nat,X1: list] :
( ( ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( rev @ ( plus @ X0 @ zero ) @ ( app @ X0 @ zero @ ( rev @ X0 @ X1 ) @ nil ) ) )
!= $true )
| ( $true
= ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( app @ zero @ X0 @ ( rev @ zero @ nil ) @ X1 ) ) )
| ( $true
!= ( listStar @ X0 @ X1 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
thf(f72,plain,
! [X0: nat,X1: list] :
( ( $true
!= ( listStar @ X0 @ X1 @ X1 ) )
| ( ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( rev @ ( plus @ X0 @ zero ) @ ( app @ X0 @ zero @ ( rev @ X0 @ X1 ) @ nil ) ) )
!= $true )
| ( $true
= ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( app @ zero @ X0 @ ( rev @ zero @ nil ) @ X1 ) ) ) ),
inference(flattening,[status(thm)],[f71]) ).
thf(f71,plain,
! [X0: nat,X1: list] :
( ( $true
= ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( app @ zero @ X0 @ ( rev @ zero @ nil ) @ X1 ) ) )
| ( ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( rev @ ( plus @ X0 @ zero ) @ ( app @ X0 @ zero @ ( rev @ X0 @ X1 ) @ nil ) ) )
!= $true )
| ( $true
!= ( listStar @ X0 @ X1 @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f45]) ).
thf(f45,plain,
! [X0: nat,X1: list] :
( ( $true
= ( listStar @ X0 @ X1 @ X1 ) )
=> ( ( ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( rev @ ( plus @ X0 @ zero ) @ ( app @ X0 @ zero @ ( rev @ X0 @ X1 ) @ nil ) ) )
= $true )
=> ( $true
= ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( app @ zero @ X0 @ ( rev @ zero @ nil ) @ X1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f44]) ).
thf(f44,plain,
! [X0: nat,X1: list] :
( ( listStar @ X0 @ X1 @ X1 )
=> ( ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( rev @ ( plus @ X0 @ zero ) @ ( app @ X0 @ zero @ ( rev @ X0 @ X1 ) @ nil ) ) )
=> ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( app @ zero @ X0 @ ( rev @ zero @ nil ) @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f22]) ).
thf(f22,axiom,
! [X6: nat,X13: list] :
( ( listStar @ X6 @ X13 @ X13 )
=> ( ( listStar @ X6 @ ( rev @ X6 @ ( rev @ X6 @ X13 ) ) @ ( rev @ ( plus @ X6 @ zero ) @ ( app @ X6 @ zero @ ( rev @ X6 @ X13 ) @ nil ) ) )
=> ( listStar @ X6 @ ( rev @ X6 @ ( rev @ X6 @ X13 ) ) @ ( app @ zero @ X6 @ ( rev @ zero @ nil ) @ X13 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bglDpxLIIQ/DTF2THF_2542.p',list_rev_invol_step2) ).
thf(f79,plain,
! [X0: nat,X1: list] :
( ( $true
!= ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( app @ zero @ X0 @ ( rev @ zero @ nil ) @ X1 ) ) )
| ( $true
= ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( app @ zero @ X0 @ nil @ X1 ) ) )
| ( $true
!= ( listStar @ X0 @ X1 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
thf(f74,plain,
! [X0: nat,X1: list] :
( ( $true
!= ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( app @ zero @ X0 @ ( rev @ zero @ nil ) @ X1 ) ) )
| ( $true
= ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( app @ zero @ X0 @ nil @ X1 ) ) )
| ( $true
!= ( listStar @ X0 @ X1 @ X1 ) ) ),
inference(flattening,[status(thm)],[f73]) ).
thf(f73,plain,
! [X0: nat,X1: list] :
( ( $true
= ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( app @ zero @ X0 @ nil @ X1 ) ) )
| ( $true
!= ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( app @ zero @ X0 @ ( rev @ zero @ nil ) @ X1 ) ) )
| ( $true
!= ( listStar @ X0 @ X1 @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f61]) ).
thf(f61,plain,
! [X0: nat,X1: list] :
( ( $true
= ( listStar @ X0 @ X1 @ X1 ) )
=> ( ( $true
= ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( app @ zero @ X0 @ ( rev @ zero @ nil ) @ X1 ) ) )
=> ( $true
= ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( app @ zero @ X0 @ nil @ X1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f60]) ).
thf(f60,plain,
! [X0: nat,X1: list] :
( ( listStar @ X0 @ X1 @ X1 )
=> ( ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( app @ zero @ X0 @ ( rev @ zero @ nil ) @ X1 ) )
=> ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( app @ zero @ X0 @ nil @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f23]) ).
thf(f23,axiom,
! [X6: nat,X13: list] :
( ( listStar @ X6 @ X13 @ X13 )
=> ( ( listStar @ X6 @ ( rev @ X6 @ ( rev @ X6 @ X13 ) ) @ ( app @ zero @ X6 @ ( rev @ zero @ nil ) @ X13 ) )
=> ( listStar @ X6 @ ( rev @ X6 @ ( rev @ X6 @ X13 ) ) @ ( app @ zero @ X6 @ nil @ X13 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bglDpxLIIQ/DTF2THF_2542.p',list_rev_invol_step3) ).
thf(f83,plain,
! [X0: nat,X1: list] :
( ( $true
!= ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( app @ zero @ X0 @ nil @ X1 ) ) )
| ( $true
!= ( listStar @ X0 @ X1 @ X1 ) )
| ( $true
= ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
thf(f70,plain,
! [X0: nat,X1: list] :
( ( $true
!= ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( app @ zero @ X0 @ nil @ X1 ) ) )
| ( $true
!= ( listStar @ X0 @ X1 @ X1 ) )
| ( $true
= ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ X1 ) ) ),
inference(flattening,[status(thm)],[f69]) ).
thf(f69,plain,
! [X0: nat,X1: list] :
( ( $true
= ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ X1 ) )
| ( $true
!= ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( app @ zero @ X0 @ nil @ X1 ) ) )
| ( $true
!= ( listStar @ X0 @ X1 @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: nat,X1: list] :
( ( $true
= ( listStar @ X0 @ X1 @ X1 ) )
=> ( ( $true
= ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( app @ zero @ X0 @ nil @ X1 ) ) )
=> ( $true
= ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: nat,X1: list] :
( ( listStar @ X0 @ X1 @ X1 )
=> ( ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ ( app @ zero @ X0 @ nil @ X1 ) )
=> ( listStar @ X0 @ ( rev @ X0 @ ( rev @ X0 @ X1 ) ) @ X1 ) ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,axiom,
! [X6: nat,X13: list] :
( ( listStar @ X6 @ X13 @ X13 )
=> ( ( listStar @ X6 @ ( rev @ X6 @ ( rev @ X6 @ X13 ) ) @ ( app @ zero @ X6 @ nil @ X13 ) )
=> ( listStar @ X6 @ ( rev @ X6 @ ( rev @ X6 @ X13 ) ) @ X13 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bglDpxLIIQ/DTF2THF_2542.p',list_rev_invol_step4) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT400^1 : TPTP v9.2.1. Released v9.2.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n020.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 06:17:27 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.49 ---- Original DTF file ---
% 0.28/0.49 thf(spec,logic,$$dhol).
% 0.28/0.49 %------------------------------------------------------------------------------
% 0.28/0.49 % File : DAT400^1 : TPTP v9.2.1. Released v9.2.0.
% 0.28/0.49 % Domain : Data Structures
% 0.28/0.49 % Problem : List reversal involution, step 5
% 0.28/0.49 % Version : Especial.
% 0.28/0.49 % English : List reversal involution. The proof is split into smaller steps.
% 0.28/0.49 % To simplify proof search, the axioms in each problem file have
% 0.28/0.49 % been preselected.
% 0.28/0.49
% 0.28/0.49 % Refs : [RRB23] Rothgang et al. (2023), Theorem Proving in Dependently
% 0.28/0.49 % : [Rot25] Rothgang (2025), Email to Geoff Sutcliffe
% 0.28/0.49 % : [RK+25] Ranalter et al. (2025), The Dependently Typed Higher-O
% 0.28/0.49 % Source : [Rot25]
% 0.28/0.49 % Names : ListReversalInvolution/list-rev-invol-step5.p [Rot25]
% 0.28/0.49
% 0.28/0.49 % Status : Theorem
% 0.28/0.49 % Rating : ? v9.2.0
% 0.28/0.49 % Syntax : Number of formulae : 27 ( 12 unt; 10 typ; 0 def)
% 0.28/0.49 % Number of atoms : 20 ( 20 equ; 0 cnn)
% 0.28/0.49 % Maximal formula atoms : 2 ( 1 avg)
% 0.28/0.49 % Number of connectives : 170 ( 3 ~; 0 |; 0 &; 160 @)
% 0.28/0.49 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.28/0.49 % Maximal formula depth : 8 ( 4 avg)
% 0.28/0.49 % Number of types : 3 ( 2 usr)
% 0.28/0.49 % Number of type decls : 10 ( 0 !>P; 3 !>D)
% 0.28/0.49 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.28/0.49 % Number of symbols : 9 ( 8 usr; 2 con; 0-4 aty)
% 0.28/0.49 % Number of variables : 38 ( 0 ^; 34 !; 0 ?; 38 :)
% 0.28/0.49 % ( 4 !>; 0 ?*; 0 @-; 0 @+)
% 0.28/0.49 % SPC : DH0_THM_EQU_NAR
% 0.28/0.49
% 0.28/0.49 % Comments :
% 0.28/0.49 %------------------------------------------------------------------------------
% 0.28/0.49 thf(elem_type,type,
% 0.28/0.49 elem: $tType ).
% 0.28/0.49
% 0.28/0.49 thf(nat_type,type,
% 0.28/0.49 nat: $tType ).
% 0.28/0.49
% 0.28/0.49 thf(zero_type,type,
% 0.28/0.49 zero: nat ).
% 0.28/0.49
% 0.28/0.49 thf(suc_type,type,
% 0.28/0.49 suc: nat > nat ).
% 0.28/0.49
% 0.28/0.49 thf(plus_type,type,
% 0.28/0.49 plus: nat > nat > nat ).
% 0.28/0.49
% 0.28/0.49 thf(list_type,type,
% 0.28/0.49 list: nat > $tType ).
% 0.28/0.49
% 0.28/0.49 thf(nil_type,type,
% 0.28/0.49 nil: list @ zero ).
% 0.28/0.49
% 0.28/0.49 thf(cons_type,type,
% 0.28/0.49 cons:
% 0.28/0.49 !>[N: nat] : ( elem > ( list @ N ) > ( list @ ( suc @ N ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(app_type,type,
% 0.28/0.49 app:
% 0.28/0.49 !>[N: nat,M: nat] : ( ( list @ N ) > ( list @ M ) > ( list @ ( plus @ N @ M ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(rev_type,type,
% 0.28/0.49 rev:
% 0.28/0.49 !>[N: nat] : ( ( list @ N ) > ( list @ N ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(peano1,axiom,
% 0.28/0.49 ! [N: nat] :
% 0.28/0.49 ( ( suc @ N )
% 0.28/0.49 != zero ) ).
% 0.28/0.49
% 0.28/0.49 thf(peano2,axiom,
% 0.28/0.49 ! [N: nat,M: nat] :
% 0.28/0.49 ( ( N != M )
% 0.28/0.49 => ( ( suc @ N )
% 0.28/0.49 != ( suc @ M ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(peano3,axiom,
% 0.28/0.49 ! [P: nat > $o] :
% 0.28/0.49 ( ( P @ zero )
% 0.28/0.49 => ( ! [M: nat] :
% 0.28/0.49 ( ( P @ M )
% 0.28/0.49 => ( P @ ( suc @ M ) ) )
% 0.28/0.49 => ! [N: nat] : ( P @ N ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(ax1,axiom,
% 0.28/0.49 ! [N: nat] :
% 0.28/0.49 ( ( plus @ zero @ N )
% 0.28/0.49 = N ) ).
% 0.28/0.49
% 0.28/0.49 thf(ax2,axiom,
% 0.28/0.49 ! [N: nat,M: nat] :
% 0.28/0.49 ( ( plus @ ( suc @ N ) @ M )
% 0.28/0.49 = ( suc @ ( plus @ N @ M ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(ax3,axiom,
% 0.28/0.49 ! [N: nat,X: list @ N] :
% 0.28/0.49 ( ( app @ zero @ N @ nil @ X )
% 0.28/0.49 = X ) ).
% 0.28/0.49
% 0.28/0.49 thf(ax4,axiom,
% 0.28/0.49 ! [N: nat,M: nat,X: elem,Y: list @ N,Z: list @ M] :
% 0.28/0.49 ( ( app @ ( suc @ N ) @ M @ ( cons @ N @ X @ Y ) @ Z )
% 0.28/0.49 = ( cons @ ( plus @ N @ M ) @ X @ ( app @ N @ M @ Y @ Z ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(ax5,axiom,
% 0.28/0.49 ( ( rev @ zero @ nil )
% 0.28/0.49 = nil ) ).
% 0.28/0.49
% 0.28/0.49 thf(ax6,axiom,
% 0.28/0.49 ! [N: nat,X: elem,Y: list @ N] :
% 0.28/0.49 ( ( rev @ ( suc @ N ) @ ( cons @ N @ X @ Y ) )
% 0.28/0.49 = ( app @ N @ ( suc @ zero ) @ ( rev @ N @ Y ) @ ( cons @ zero @ X @ nil ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(plus_com,axiom,
% 0.28/0.49 ! [N: nat,M: nat] :
% 0.28/0.49 ( ( plus @ N @ M )
% 0.28/0.49 = ( plus @ M @ N ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(plus1r,axiom,
% 0.28/0.49 ! [N: nat] :
% 0.28/0.49 ( ( suc @ N )
% 0.28/0.49 = ( plus @ N @ ( suc @ zero ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(list_app_nil,axiom,
% 0.28/0.49 ! [N: nat,L: list @ N] :
% 0.28/0.49 ( ( app @ N @ zero @ L @ nil )
% 0.28/0.49 = L ) ).
% 0.28/0.49
% 0.28/0.49 thf(list_rev_invol_step1,axiom,
% 0.28/0.49 ! [N: nat,L: list @ N] :
% 0.28/0.49 ( ( rev @ N @ ( rev @ N @ L ) )
% 0.28/0.49 = ( rev @ ( plus @ N @ zero ) @ ( app @ N @ zero @ ( rev @ N @ L ) @ nil ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(list_rev_invol_step2,axiom,
% 0.28/0.49 ! [N: nat,L: list @ N] :
% 0.28/0.49 ( ( ( rev @ N @ ( rev @ N @ L ) )
% 0.28/0.49 = ( rev @ ( plus @ N @ zero ) @ ( app @ N @ zero @ ( rev @ N @ L ) @ nil ) ) )
% 0.28/0.49 => ( ( rev @ N @ ( rev @ N @ L ) )
% 0.28/0.49 = ( app @ zero @ N @ ( rev @ zero @ nil ) @ L ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(list_rev_invol_step3,axiom,
% 0.28/0.49 ! [N: nat,L: list @ N] :
% 0.28/0.49 ( ( ( rev @ N @ ( rev @ N @ L ) )
% 0.28/0.49 = ( app @ zero @ N @ ( rev @ zero @ nil ) @ L ) )
% 0.28/0.49 => ( ( rev @ N @ ( rev @ N @ L ) )
% 0.28/0.49 = ( app @ zero @ N @ nil @ L ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(list_rev_invol_step4,axiom,
% 0.28/0.49 ! [N: nat,L: list @ N] :
% 0.28/0.49 ( ( ( rev @ N @ ( rev @ N @ L ) )
% 0.28/0.49 = ( app @ zero @ N @ nil @ L ) )
% 0.28/0.49 => ( ( rev @ N @ ( rev @ N @ L ) )
% 0.28/0.49 = L ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(list_rev_invol,conjecture,
% 0.28/0.49 ! [N: nat,L: list @ N] :
% 0.28/0.49 ( ( rev @ N @ ( rev @ N @ L ) )
% 0.28/0.49 = L ) ).
% 0.28/0.49
% 0.28/0.49 %------------------------------------------------------------------------------
% 0.28/0.49 ------------------------
% 1.77/1.30 ---- Embedded in THF ---
% 1.77/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.77/1.31 %%% Generated on Tue Feb 24 06:17:28 EST 2026
% 1.77/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.77/1.31 %%% Logic specification used:
% 1.77/1.31 %%% thf(spec, logic, $$dhol).
% 1.77/1.31
% 1.77/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.bglDpxLIIQ/DTF2DTF2542.p
% See solution above
% 1.77/1.31 ------------------------
% 1.77/1.32 ---- Cleaned THF ---
% 1.77/1.32 thf(is_per_type,type,
% 1.77/1.32 isPer:
% 1.77/1.32 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 1.77/1.32
% 1.77/1.32 thf(is_per,definition,
% 1.77/1.32 ! [A: $tType,AStar: A > A > $o] :
% 1.77/1.32 ( ( isPer @ A @ AStar )
% 1.77/1.32 <=> ( ! [X: A,Y: A] :
% 1.77/1.32 ( ( AStar @ X @ Y )
% 1.77/1.32 => ( AStar @ Y @ X ) )
% 1.77/1.32 & ! [X: A,Y: A,Z: A] :
% 1.77/1.32 ( ( AStar @ X @ Y )
% 1.77/1.32 => ( ( AStar @ Y @ Z )
% 1.77/1.32 => ( AStar @ X @ Z ) ) ) ) ) ).
% 1.77/1.32
% 1.77/1.32 thf(elem_type,type,
% 1.77/1.32 elem: $tType ).
% 1.77/1.32
% 1.77/1.32 thf(elemStar,type,
% 1.77/1.32 elemStar: elem > elem > $o ).
% 1.77/1.32
% 1.77/1.32 thf(elemStar_is_eq,axiom,
% 1.77/1.32 ! [X: elem,Y: elem] :
% 1.77/1.32 ( ( elemStar @ X @ Y )
% 1.77/1.32 <=> ( X = Y ) ) ).
% 1.77/1.32
% 1.77/1.32 thf(nat_type,type,
% 1.77/1.32 nat: $tType ).
% 1.77/1.32
% 1.77/1.32 thf(natStar,type,
% 1.77/1.32 natStar: nat > nat > $o ).
% 1.77/1.32
% 1.77/1.32 thf(natStar_is_eq,axiom,
% 1.77/1.32 ! [X: nat,Y: nat] :
% 1.77/1.32 ( ( natStar @ X @ Y )
% 1.77/1.32 <=> ( X = Y ) ) ).
% 1.77/1.32
% 1.77/1.32 thf(zero_type,type,
% 1.77/1.32 zero: nat ).
% 1.77/1.32
% 1.77/1.32 thf(suc_type,type,
% 1.77/1.32 suc: nat > nat ).
% 1.77/1.32
% 1.77/1.32 thf(plus_type,type,
% 1.77/1.32 plus: nat > nat > nat ).
% 1.77/1.32
% 1.77/1.32 thf(list_type,type,
% 1.77/1.32 list: $tType ).
% 1.77/1.32
% 1.77/1.32 thf(listStar,type,
% 1.77/1.32 listStar: nat > list > list > $o ).
% 1.77/1.32
% 1.77/1.32 thf('\'listStar\'_is_per',axiom,
% 1.77/1.32 ! [C: nat] : ( isPer @ list @ ( listStar @ C ) ) ).
% 1.77/1.32
% 1.77/1.32 thf(nil_type,type,
% 1.77/1.32 nil: list ).
% 1.77/1.32
% 1.77/1.32 thf(nil_tp_ax,axiom,
% 1.77/1.32 listStar @ zero @ nil @ nil ).
% 1.77/1.32
% 1.77/1.32 thf(cons_type,type,
% 1.77/1.32 cons: nat > elem > list > list ).
% 1.77/1.32
% 1.77/1.32 thf(cons_tp_ax,axiom,
% 1.77/1.32 ! [N: nat,D: elem,D0: list,D0_prime: list] :
% 1.77/1.32 ( ( listStar @ N @ D0 @ D0_prime )
% 1.77/1.32 => ( listStar @ ( suc @ N ) @ ( cons @ N @ D @ D0 ) @ ( cons @ N @ D @ D0_prime ) ) ) ).
% 1.77/1.32
% 1.77/1.32 thf(app_type,type,
% 1.77/1.32 app: nat > nat > list > list > list ).
% 1.77/1.32
% 1.77/1.32 thf(app_tp_ax,axiom,
% 1.77/1.32 ! [N: nat,M: nat,D: list,D_prime: list] :
% 1.77/1.32 ( ( listStar @ N @ D @ D_prime )
% 1.77/1.32 => ! [D0: list,D0_prime: list] :
% 1.77/1.32 ( ( listStar @ M @ D0 @ D0_prime )
% 1.77/1.32 => ( listStar @ ( plus @ N @ M ) @ ( app @ N @ M @ D @ D0 ) @ ( app @ N @ M @ D_prime @ D0_prime ) ) ) ) ).
% 1.77/1.32
% 1.77/1.32 thf(rev_type,type,
% 1.77/1.32 rev: nat > list > list ).
% 1.77/1.32
% 1.77/1.32 thf(rev_tp_ax,axiom,
% 1.77/1.32 ! [N: nat,D: list,D_prime: list] :
% 1.77/1.32 ( ( listStar @ N @ D @ D_prime )
% 1.77/1.32 => ( listStar @ N @ ( rev @ N @ D ) @ ( rev @ N @ D_prime ) ) ) ).
% 1.77/1.32
% 1.77/1.32 thf(peano1,axiom,
% 1.77/1.32 ! [N: nat] :
% 1.77/1.32 ( ( suc @ N )
% 1.77/1.32 != zero ) ).
% 1.77/1.32
% 1.77/1.32 thf(peano2,axiom,
% 1.77/1.32 ! [N: nat,M: nat] :
% 1.77/1.32 ( ( N != M )
% 1.77/1.32 => ( ( suc @ N )
% 1.77/1.32 != ( suc @ M ) ) ) ).
% 1.77/1.32
% 1.77/1.32 thf(peano3,axiom,
% 1.77/1.32 ! [P: nat > $o] :
% 1.77/1.32 ( ( P @ zero )
% 1.77/1.32 => ( ! [M: nat] :
% 1.77/1.32 ( ( P @ M )
% 1.77/1.32 => ( P @ ( suc @ M ) ) )
% 1.77/1.32 => ! [N: nat] : ( P @ N ) ) ) ).
% 1.77/1.32
% 1.77/1.32 thf(ax1,axiom,
% 1.77/1.32 ! [N: nat] :
% 1.77/1.32 ( ( plus @ zero @ N )
% 1.77/1.32 = N ) ).
% 1.77/1.32
% 1.77/1.32 thf(ax2,axiom,
% 1.77/1.32 ! [N: nat,M: nat] :
% 1.77/1.32 ( ( plus @ ( suc @ N ) @ M )
% 1.77/1.32 = ( suc @ ( plus @ N @ M ) ) ) ).
% 1.77/1.32
% 1.77/1.32 thf(ax3,axiom,
% 1.77/1.32 ! [N: nat,X: list] :
% 1.77/1.32 ( ( listStar @ N @ X @ X )
% 1.77/1.32 => ( listStar @ ( plus @ zero @ N ) @ ( app @ zero @ N @ nil @ X ) @ X ) ) ).
% 1.77/1.32
% 1.77/1.32 thf(ax4,axiom,
% 1.77/1.32 ! [N: nat,M: nat,X: elem,Y: list,Z: list] :
% 1.77/1.32 ( ( listStar @ N @ Y @ Y )
% 1.77/1.32 => ( ( listStar @ M @ Z @ Z )
% 1.77/1.32 => ( listStar @ ( plus @ ( suc @ N ) @ M ) @ ( app @ ( suc @ N ) @ M @ ( cons @ N @ X @ Y ) @ Z ) @ ( cons @ ( plus @ N @ M ) @ X @ ( app @ N @ M @ Y @ Z ) ) ) ) ) ).
% 1.77/1.32
% 1.77/1.32 thf(ax5,axiom,
% 1.77/1.32 listStar @ zero @ ( rev @ zero @ nil ) @ nil ).
% 1.77/1.32
% 1.77/1.32 thf(ax6,axiom,
% 1.77/1.32 ! [N: nat,X: elem,Y: list] :
% 1.77/1.32 ( ( listStar @ N @ Y @ Y )
% 1.77/1.32 => ( listStar @ ( suc @ N ) @ ( rev @ ( suc @ N ) @ ( cons @ N @ X @ Y ) ) @ ( app @ N @ ( suc @ zero ) @ ( rev @ N @ Y ) @ ( cons @ zero @ X @ nil ) ) ) ) ).
% 1.77/1.32
% 1.77/1.32 thf(plus_com,axiom,
% 1.77/1.32 ! [N: nat,M: nat] :
% 1.77/1.32 ( ( plus @ N @ M )
% 1.77/1.32 = ( plus @ M @ N ) ) ).
% 1.77/1.32
% 1.77/1.32 thf(plus1r,axiom,
% 1.77/1.32 ! [N: nat] :
% 1.77/1.32 ( ( suc @ N )
% 1.77/1.32 = ( plus @ N @ ( suc @ zero ) ) ) ).
% 1.77/1.32
% 1.77/1.32 thf(list_app_nil,axiom,
% 1.77/1.32 ! [N: nat,L: list] :
% 1.77/1.32 ( ( listStar @ N @ L @ L )
% 1.77/1.32 => ( listStar @ ( plus @ N @ zero ) @ ( app @ N @ zero @ L @ nil ) @ L ) ) ).
% 1.77/1.32
% 1.77/1.32 thf(list_rev_invol_step1,axiom,
% 1.77/1.32 ! [N: nat,L: list] :
% 1.77/1.32 ( ( listStar @ N @ L @ L )
% 1.77/1.32 => ( listStar @ N @ ( rev @ N @ ( rev @ N @ L ) ) @ ( rev @ ( plus @ N @ zero ) @ ( app @ N @ zero @ ( rev @ N @ L ) @ nil ) ) ) ) ).
% 1.77/1.32
% 1.77/1.32 thf(list_rev_invol_step2,axiom,
% 1.77/1.32 ! [N: nat,L: list] :
% 1.77/1.32 ( ( listStar @ N @ L @ L )
% 1.77/1.32 => ( ( listStar @ N @ ( rev @ N @ ( rev @ N @ L ) ) @ ( rev @ ( plus @ N @ zero ) @ ( app @ N @ zero @ ( rev @ N @ L ) @ nil ) ) )
% 1.77/1.32 => ( listStar @ N @ ( rev @ N @ ( rev @ N @ L ) ) @ ( app @ zero @ N @ ( rev @ zero @ nil ) @ L ) ) ) ) ).
% 1.77/1.32
% 1.77/1.32 thf(list_rev_invol_step3,axiom,
% 1.77/1.32 ! [N: nat,L: list] :
% 1.77/1.32 ( ( listStar @ N @ L @ L )
% 1.77/1.32 => ( ( listStar @ N @ ( rev @ N @ ( rev @ N @ L ) ) @ ( app @ zero @ N @ ( rev @ zero @ nil ) @ L ) )
% 1.77/1.32 => ( listStar @ N @ ( rev @ N @ ( rev @ N @ L ) ) @ ( app @ zero @ N @ nil @ L ) ) ) ) ).
% 1.77/1.32
% 1.77/1.32 thf(list_rev_invol_step4,axiom,
% 1.77/1.32 ! [N: nat,L: list] :
% 1.77/1.32 ( ( listStar @ N @ L @ L )
% 1.77/1.32 => ( ( listStar @ N @ ( rev @ N @ ( rev @ N @ L ) ) @ ( app @ zero @ N @ nil @ L ) )
% 1.77/1.32 => ( listStar @ N @ ( rev @ N @ ( rev @ N @ L ) ) @ L ) ) ) ).
% 1.77/1.32
% 1.77/1.32 thf(list_rev_invol,conjecture,
% 1.77/1.32 ! [N: nat,L: list] :
% 1.77/1.32 ( ( listStar @ N @ L @ L )
% 1.77/1.32 => ( listStar @ N @ ( rev @ N @ ( rev @ N @ L ) ) @ L ) ) ).
% 1.77/1.32 ------------------------
% 1.77/1.34 % (2871)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_2542 for (2999ds/4Mi)
% 1.77/1.34 % (2873)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2542 for (2999ds/2Mi)
% 1.77/1.34 % (2871)Instruction limit reached!
% 1.77/1.34 % (2871)------------------------------
% 1.77/1.34 % (2871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.34 % (2871)Termination reason: Unknown
% 1.77/1.34 % (2871)Termination phase: Property scanning
% 1.77/1.34
% 1.77/1.34 % (2871)Memory used [KB]: 1023
% 1.77/1.34 % (2871)Time elapsed: 0.003 s
% 1.77/1.34 % (2871)Instructions burned: 6 (million)
% 1.77/1.34 % (2871)------------------------------
% 1.77/1.34 % (2871)------------------------------
% 1.77/1.34 % (2873)Instruction limit reached!
% 1.77/1.34 % (2873)------------------------------
% 1.77/1.34 % (2873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.34 % (2873)Termination reason: Unknown
% 1.77/1.34 % (2873)Termination phase: shuffling
% 1.77/1.34
% 1.77/1.34 % (2873)Memory used [KB]: 1023
% 1.77/1.34 % (2873)Time elapsed: 0.002 s
% 1.77/1.34 % (2873)Instructions burned: 3 (million)
% 1.77/1.34 % (2873)------------------------------
% 1.77/1.34 % (2873)------------------------------
% 1.77/1.34 % (2870)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2542 for (2999ds/183Mi)
% 1.77/1.34 % (2872)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_2542 for (2999ds/27Mi)
% 1.77/1.35 % (2874)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_2542 for (2999ds/2Mi)
% 1.77/1.35 % (2875)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_2542 for (2999ds/275Mi)
% 1.77/1.35 % (2876)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2542 for (2999ds/18Mi)
% 1.77/1.35 % (2874)Instruction limit reached!
% 1.77/1.35 % (2874)------------------------------
% 1.77/1.35 % (2874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.35 % (2874)Termination reason: Unknown
% 1.77/1.35 % (2874)Termination phase: shuffling
% 1.77/1.35
% 1.77/1.35 % (2874)Memory used [KB]: 1023
% 1.77/1.35 % (2874)Time elapsed: 0.003 s
% 1.77/1.35 % (2874)Instructions burned: 2 (million)
% 1.77/1.35 % (2874)------------------------------
% 1.77/1.35 % (2874)------------------------------
% 1.77/1.35 % (2877)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2542 for (2999ds/3Mi)
% 1.77/1.35 % (2878)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_2542 for (2999ds/37Mi)
% 1.77/1.35 % (2877)Instruction limit reached!
% 1.77/1.35 % (2877)------------------------------
% 1.77/1.35 % (2877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.35 % (2877)Termination reason: Unknown
% 1.77/1.35 % (2877)Termination phase: shuffling
% 1.77/1.35
% 1.77/1.35 % (2877)Memory used [KB]: 1023
% 1.77/1.35 % (2877)Time elapsed: 0.002 s
% 1.77/1.35 % (2877)Instructions burned: 4 (million)
% 1.77/1.35 % (2877)------------------------------
% 1.77/1.35 % (2877)------------------------------
% 1.77/1.35 % (2875)Refutation not found, incomplete strategy
% 1.77/1.35 % (2875)------------------------------
% 1.77/1.35 % (2875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.35 % (2875)Termination reason: Refutation not found, incomplete strategy
% 1.77/1.35
% 1.77/1.35
% 1.77/1.35 % (2875)Memory used [KB]: 5628
% 1.77/1.35 % (2875)Time elapsed: 0.008 s
% 1.77/1.35 % (2875)Instructions burned: 9 (million)
% 1.77/1.35 % (2875)------------------------------
% 1.77/1.35 % (2875)------------------------------
% 1.77/1.36 % (2876)Instruction limit reached!
% 1.77/1.36 % (2876)------------------------------
% 1.77/1.36 % (2876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.36 % (2876)Termination reason: Unknown
% 1.77/1.36 % (2876)Termination phase: Saturation
% 1.77/1.36
% 1.77/1.36 % (2876)Memory used [KB]: 5628
% 1.77/1.36 % (2876)Time elapsed: 0.013 s
% 1.77/1.36 % (2876)Instructions burned: 18 (million)
% 1.77/1.36 % (2876)------------------------------
% 1.77/1.36 % (2876)------------------------------
% 1.77/1.36 % (2872)Instruction limit reached!
% 1.77/1.36 % (2872)------------------------------
% 1.77/1.36 % (2872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.36 % (2872)Termination reason: Unknown
% 1.77/1.36 % (2872)Termination phase: Saturation
% 1.77/1.36
% 1.77/1.36 % (2872)Memory used [KB]: 5628
% 1.77/1.36 % (2872)Time elapsed: 0.018 s
% 1.77/1.36 % (2872)Instructions burned: 28 (million)
% 1.77/1.36 % (2872)------------------------------
% 1.77/1.36 % (2872)------------------------------
% 1.77/1.36 % (2878)Instruction limit reached!
% 1.77/1.36 % (2878)------------------------------
% 1.77/1.36 % (2878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.36 % (2878)Termination reason: Unknown
% 1.77/1.36 % (2878)Termination phase: Saturation
% 1.77/1.36
% 1.77/1.36 % (2878)Memory used [KB]: 5884
% 1.77/1.36 % (2878)Time elapsed: 0.014 s
% 1.77/1.36 % (2878)Instructions burned: 38 (million)
% 1.77/1.36 % (2878)------------------------------
% 1.77/1.36 % (2878)------------------------------
% 1.77/1.36 % (2879)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_2542 for (2999ds/15Mi)
% 1.77/1.37 % (2880)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_2542 for (2999ds/3Mi)
% 1.77/1.37 % (2880)Instruction limit reached!
% 1.77/1.37 % (2880)------------------------------
% 1.77/1.37 % (2880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.37 % (2880)Termination reason: Unknown
% 1.77/1.37 % (2880)Termination phase: shuffling
% 1.77/1.37
% 1.77/1.37 % (2880)Memory used [KB]: 1023
% 1.77/1.37 % (2880)Time elapsed: 0.004 s
% 1.77/1.37 % (2880)Instructions burned: 4 (million)
% 1.77/1.37 % (2880)------------------------------
% 1.77/1.37 % (2880)------------------------------
% 1.77/1.37 % (2881)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_2542 for (2999ds/1041Mi)
% 1.77/1.37 % (2884)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_2542 for (2999ds/3Mi)
% 1.77/1.37 % (2883)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_2542 for (2999ds/16Mi)
% 1.77/1.37 % (2879)Instruction limit reached!
% 1.77/1.37 % (2879)------------------------------
% 1.77/1.37 % (2879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.37 % (2879)Termination reason: Unknown
% 1.77/1.37 % (2879)Termination phase: Saturation
% 1.77/1.37
% 1.77/1.37 % (2879)Memory used [KB]: 5756
% 1.77/1.37 % (2879)Time elapsed: 0.011 s
% 1.77/1.37 % (2879)Instructions burned: 15 (million)
% 1.77/1.37 % (2879)------------------------------
% 1.77/1.37 % (2879)------------------------------
% 1.77/1.37 % (2884)Instruction limit reached!
% 1.77/1.37 % (2884)------------------------------
% 1.77/1.37 % (2884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.37 % (2884)Termination reason: Unknown
% 1.77/1.37 % (2884)Termination phase: Property scanning
% 1.77/1.37
% 1.77/1.37 % (2884)Memory used [KB]: 1023
% 1.77/1.37 % (2884)Time elapsed: 0.003 s
% 1.77/1.37 % (2884)Instructions burned: 4 (million)
% 1.77/1.37 % (2884)------------------------------
% 1.77/1.37 % (2884)------------------------------
% 1.77/1.37 % (2882)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_2542 for (2999ds/7Mi)
% 1.77/1.38 % (2883)Instruction limit reached!
% 1.77/1.38 % (2883)------------------------------
% 1.77/1.38 % (2883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.38 % (2883)Termination reason: Unknown
% 1.77/1.38 % (2883)Termination phase: Saturation
% 1.77/1.38
% 1.77/1.38 % (2883)Memory used [KB]: 5628
% 1.77/1.38 % (2883)Time elapsed: 0.007 s
% 1.77/1.38 % (2883)Instructions burned: 17 (million)
% 1.77/1.38 % (2883)------------------------------
% 1.77/1.38 % (2883)------------------------------
% 1.77/1.38 % (2882)Instruction limit reached!
% 1.77/1.38 % (2882)------------------------------
% 1.77/1.38 % (2882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.38 % (2882)Termination reason: Unknown
% 1.77/1.38 % (2882)Termination phase: Property scanning
% 1.77/1.38
% 1.77/1.38 % (2882)Memory used [KB]: 1023
% 1.77/1.38 % (2882)Time elapsed: 0.006 s
% 1.77/1.38 % (2882)Instructions burned: 7 (million)
% 1.77/1.38 % (2882)------------------------------
% 1.77/1.38 % (2882)------------------------------
% 1.77/1.38 % (2886)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_2542 for (2999ds/7Mi)
% 1.77/1.38 % (2886)Instruction limit reached!
% 1.77/1.38 % (2886)------------------------------
% 1.77/1.38 % (2886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.38 % (2886)Termination reason: Unknown
% 1.77/1.38 % (2886)Termination phase: Property scanning
% 1.77/1.38
% 1.77/1.38 % (2886)Memory used [KB]: 1023
% 1.77/1.38 % (2886)Time elapsed: 0.004 s
% 1.77/1.38 % (2886)Instructions burned: 7 (million)
% 1.77/1.38 % (2886)------------------------------
% 1.77/1.38 % (2886)------------------------------
% 1.77/1.39 % (2885)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_2542 for (2999ds/3Mi)
% 1.77/1.39 % (2888)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_2542 for (2999ds/4Mi)
% 1.77/1.39 % (2885)Instruction limit reached!
% 1.77/1.39 % (2885)------------------------------
% 1.77/1.39 % (2885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.39 % (2885)Termination reason: Unknown
% 1.77/1.39 % (2885)Termination phase: shuffling
% 1.77/1.39
% 1.77/1.39 % (2885)Memory used [KB]: 1023
% 1.77/1.39 % (2885)Time elapsed: 0.004 s
% 1.77/1.39 % (2885)Instructions burned: 4 (million)
% 1.77/1.39 % (2885)------------------------------
% 1.77/1.39 % (2885)------------------------------
% 1.77/1.39 % (2888)Instruction limit reached!
% 1.77/1.39 % (2888)------------------------------
% 1.77/1.39 % (2888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.39 % (2888)Termination reason: Unknown
% 1.77/1.39 % (2888)Termination phase: Property scanning
% 1.77/1.39
% 1.77/1.39 % (2888)Memory used [KB]: 1023
% 1.77/1.39 % (2888)Time elapsed: 0.003 s
% 1.77/1.39 % (2888)Instructions burned: 4 (million)
% 1.77/1.39 % (2888)------------------------------
% 1.77/1.39 % (2888)------------------------------
% 1.77/1.39 % (2887)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_2542 for (2999ds/3Mi)
% 1.77/1.39 % (2887)Instruction limit reached!
% 1.77/1.39 % (2887)------------------------------
% 1.77/1.39 % (2887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.39 % (2887)Termination reason: Unknown
% 1.77/1.39 % (2887)Termination phase: shuffling
% 1.77/1.39
% 1.77/1.39 % (2887)Memory used [KB]: 1023
% 1.77/1.39 % (2887)Time elapsed: 0.004 s
% 1.77/1.39 % (2887)Instructions burned: 4 (million)
% 1.77/1.39 % (2887)------------------------------
% 1.77/1.39 % (2887)------------------------------
% 1.77/1.39 % (2890)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_2542 for (2999ds/710Mi)
% 1.77/1.39 % (2889)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_2542 for (2999ds/18Mi)
% 1.81/1.40 % (2892)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_2542 for (2999ds/902Mi)
% 1.81/1.40 % (2890)First to succeed.
% 1.81/1.40 % (2889)Instruction limit reached!
% 1.81/1.40 % (2889)------------------------------
% 1.81/1.40 % (2889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.40 % (2889)Termination reason: Unknown
% 1.81/1.40 % (2889)Termination phase: Saturation
% 1.81/1.40
% 1.81/1.40 % (2889)Memory used [KB]: 5628
% 1.81/1.40 % (2889)Time elapsed: 0.012 s
% 1.81/1.40 % (2889)Instructions burned: 18 (million)
% 1.81/1.40 % (2889)------------------------------
% 1.81/1.40 % (2889)------------------------------
% 1.81/1.41 % (2891)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_2542 for (2999ds/6Mi)
% 1.81/1.41 % (2890)Refutation found. Thanks to Tanya!
% 1.81/1.41 % SZS status Theorem for DTF2THF_2542
% 1.81/1.41 % SZS output start Proof for DTF2THF_2542
% 1.81/1.41 thf(type_def_6, type, elem: $tType).
% 1.81/1.41 thf(type_def_7, type, nat: $tType).
% 1.81/1.41 thf(type_def_8, type, list: $tType).
% 1.81/1.41 thf(func_def_0, type, isPer: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 1.81/1.41 thf(func_def_2, type, elem: $tType).
% 1.81/1.41 thf(func_def_3, type, elemStar: elem > elem > $o).
% 1.81/1.41 thf(func_def_4, type, nat: $tType).
% 1.81/1.41 thf(func_def_5, type, natStar: nat > nat > $o).
% 1.81/1.41 thf(func_def_6, type, zero: nat).
% 1.81/1.41 thf(func_def_7, type, suc: nat > nat).
% 1.81/1.41 thf(func_def_8, type, plus: nat > nat > nat).
% 1.81/1.41 thf(func_def_9, type, list: $tType).
% 1.81/1.41 thf(func_def_10, type, listStar: nat > list > list > $o).
% 1.81/1.41 thf(func_def_11, type, nil: list).
% 1.81/1.41 thf(func_def_12, type, cons: nat > elem > list > list).
% 1.81/1.41 thf(func_def_13, type, app: nat > nat > list > list > list).
% 1.81/1.41 thf(func_def_14, type, rev: nat > list > list).
% 1.81/1.41 thf(func_def_17, type, sK0: nat).
% 1.81/1.41 thf(func_def_18, type, sK1: list).
% 1.81/1.41 thf(f136,plain,(
% 1.81/1.41 $false),
% 1.81/1.41 inference(subsumption_resolution,[status(thm)],[f135,f86])).
% 1.81/1.41 thf(f86,plain,(
% 1.81/1.41 ($true != (listStar @ sK0 @ (rev @ sK0 @ (rev @ sK0 @ sK1)) @ sK1))),
% 1.81/1.41 inference(cnf_transformation,[status(thm)],[f77])).
% 1.81/1.41 thf(f77,plain,(
% 1.81/1.41 ($true != (listStar @ sK0 @ (rev @ sK0 @ (rev @ sK0 @ sK1)) @ sK1)) & ((listStar @ sK0 @ sK1 @ sK1) = $true)),
% 1.81/1.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f75,f76])).
% 1.81/1.41 thf(f76,plain,(
% 1.81/1.41 ? [X0 : nat,X1 : list] : (($true != (listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ X1)) & ($true = (listStar @ X0 @ X1 @ X1))) => (($true != (listStar @ sK0 @ (rev @ sK0 @ (rev @ sK0 @ sK1)) @ sK1)) & ((listStar @ sK0 @ sK1 @ sK1) = $true))),
% 1.81/1.41 introduced(definition,[],[choice_axiom])).
% 1.81/1.41 thf(f75,plain,(
% 1.81/1.41 ? [X0 : nat,X1 : list] : (($true != (listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ X1)) & ($true = (listStar @ X0 @ X1 @ X1)))),
% 1.81/1.41 inference(ennf_transformation,[status(thm)],[f65])).
% 1.81/1.41 thf(f65,plain,(
% 1.81/1.41 ~! [X0 : nat,X1 : list] : (($true = (listStar @ X0 @ X1 @ X1)) => ($true = (listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ X1)))),
% 1.81/1.41 inference(fool_elimination,[status(thm)],[f64])).
% 1.81/1.41 thf(f64,plain,(
% 1.81/1.41 ~! [X0 : nat,X1 : list] : ((listStar @ X0 @ X1 @ X1) => (listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ X1))),
% 1.81/1.41 inference(rectify,[status(thm)],[f26])).
% 1.81/1.41 thf(f26,negated_conjecture,(
% 1.81/1.41 ~! [X6 : nat,X13 : list] : ((listStar @ X6 @ X13 @ X13) => (listStar @ X6 @ (rev @ X6 @ (rev @ X6 @ X13)) @ X13))),
% 1.81/1.41 inference(negated_conjecture,[status(cth)],[f25])).
% 1.81/1.41 thf(f25,conjecture,(
% 1.81/1.41 ! [X6 : nat,X13 : list] : ((listStar @ X6 @ X13 @ X13) => (listStar @ X6 @ (rev @ X6 @ (rev @ X6 @ X13)) @ X13))),
% 1.81/1.41 file('/export/starexec/sandbox/tmp/tmp.bglDpxLIIQ/DTF2THF_2542.p',list_rev_invol)).
% 1.81/1.41 thf(f135,plain,(
% 1.81/1.41 ($true = (listStar @ sK0 @ (rev @ sK0 @ (rev @ sK0 @ sK1)) @ sK1))),
% 1.81/1.41 inference(subsumption_resolution,[status(thm)],[f133,f85])).
% 1.81/1.41 thf(f85,plain,(
% 1.81/1.41 ((listStar @ sK0 @ sK1 @ sK1) = $true)),
% 1.81/1.41 inference(cnf_transformation,[status(thm)],[f77])).
% 1.81/1.41 thf(f133,plain,(
% 1.81/1.41 ((listStar @ sK0 @ sK1 @ sK1) != $true) | ($true = (listStar @ sK0 @ (rev @ sK0 @ (rev @ sK0 @ sK1)) @ sK1))),
% 1.81/1.41 inference(trivial_inequality_removal,[status(thm)],[f131])).
% 1.81/1.41 thf(f131,plain,(
% 1.81/1.41 ($true != $true) | ($true = (listStar @ sK0 @ (rev @ sK0 @ (rev @ sK0 @ sK1)) @ sK1)) | ((listStar @ sK0 @ sK1 @ sK1) != $true)),
% 1.81/1.41 inference(superposition,[status(thm)],[f83,f128])).
% 1.81/1.41 thf(f128,plain,(
% 1.81/1.41 ((listStar @ sK0 @ (rev @ sK0 @ (rev @ sK0 @ sK1)) @ (app @ zero @ sK0 @ nil @ sK1)) = $true)),
% 1.81/1.41 inference(subsumption_resolution,[status(thm)],[f126,f85])).
% 1.81/1.41 thf(f126,plain,(
% 1.81/1.41 ((listStar @ sK0 @ (rev @ sK0 @ (rev @ sK0 @ sK1)) @ (app @ zero @ sK0 @ nil @ sK1)) = $true) | ((listStar @ sK0 @ sK1 @ sK1) != $true)),
% 1.81/1.41 inference(trivial_inequality_removal,[status(thm)],[f124])).
% 1.81/1.41 thf(f124,plain,(
% 1.81/1.41 ((listStar @ sK0 @ sK1 @ sK1) != $true) | ((listStar @ sK0 @ (rev @ sK0 @ (rev @ sK0 @ sK1)) @ (app @ zero @ sK0 @ nil @ sK1)) = $true) | ($true != $true)),
% 1.81/1.41 inference(superposition,[status(thm)],[f79,f123])).
% 1.81/1.41 thf(f123,plain,(
% 1.81/1.41 ($true = (listStar @ sK0 @ (rev @ sK0 @ (rev @ sK0 @ sK1)) @ (app @ zero @ sK0 @ (rev @ zero @ nil) @ sK1)))),
% 1.81/1.41 inference(subsumption_resolution,[status(thm)],[f121,f85])).
% 1.81/1.41 thf(f121,plain,(
% 1.81/1.41 ($true = (listStar @ sK0 @ (rev @ sK0 @ (rev @ sK0 @ sK1)) @ (app @ zero @ sK0 @ (rev @ zero @ nil) @ sK1))) | ((listStar @ sK0 @ sK1 @ sK1) != $true)),
% 1.81/1.41 inference(trivial_inequality_removal,[status(thm)],[f119])).
% 1.81/1.41 thf(f119,plain,(
% 1.81/1.41 ((listStar @ sK0 @ sK1 @ sK1) != $true) | ($true != $true) | ($true = (listStar @ sK0 @ (rev @ sK0 @ (rev @ sK0 @ sK1)) @ (app @ zero @ sK0 @ (rev @ zero @ nil) @ sK1)))),
% 1.81/1.41 inference(superposition,[status(thm)],[f80,f95])).
% 1.81/1.41 thf(f95,plain,(
% 1.81/1.41 ((listStar @ sK0 @ (rev @ sK0 @ (rev @ sK0 @ sK1)) @ (rev @ (plus @ sK0 @ zero) @ (app @ sK0 @ zero @ (rev @ sK0 @ sK1) @ nil))) = $true)),
% 1.81/1.41 inference(trivial_inequality_removal,[status(thm)],[f93])).
% 1.81/1.41 thf(f93,plain,(
% 1.81/1.41 ($true != $true) | ((listStar @ sK0 @ (rev @ sK0 @ (rev @ sK0 @ sK1)) @ (rev @ (plus @ sK0 @ zero) @ (app @ sK0 @ zero @ (rev @ sK0 @ sK1) @ nil))) = $true)),
% 1.81/1.41 inference(superposition,[status(thm)],[f78,f85])).
% 1.81/1.41 thf(f78,plain,(
% 1.81/1.41 ( ! [X0 : nat,X1 : list] : (($true != (listStar @ X0 @ X1 @ X1)) | ((listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (rev @ (plus @ X0 @ zero) @ (app @ X0 @ zero @ (rev @ X0 @ X1) @ nil))) = $true)) )),
% 1.81/1.41 inference(cnf_transformation,[status(thm)],[f68])).
% 1.81/1.41 thf(f68,plain,(
% 1.81/1.41 ! [X0 : nat,X1 : list] : (((listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (rev @ (plus @ X0 @ zero) @ (app @ X0 @ zero @ (rev @ X0 @ X1) @ nil))) = $true) | ($true != (listStar @ X0 @ X1 @ X1)))),
% 1.81/1.41 inference(ennf_transformation,[status(thm)],[f49])).
% 1.81/1.41 thf(f49,plain,(
% 1.81/1.41 ! [X0 : nat,X1 : list] : (($true = (listStar @ X0 @ X1 @ X1)) => ((listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (rev @ (plus @ X0 @ zero) @ (app @ X0 @ zero @ (rev @ X0 @ X1) @ nil))) = $true))),
% 1.81/1.41 inference(fool_elimination,[status(thm)],[f48])).
% 1.81/1.41 thf(f48,plain,(
% 1.81/1.41 ! [X0 : nat,X1 : list] : ((listStar @ X0 @ X1 @ X1) => (listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (rev @ (plus @ X0 @ zero) @ (app @ X0 @ zero @ (rev @ X0 @ X1) @ nil))))),
% 1.81/1.41 inference(rectify,[status(thm)],[f21])).
% 1.81/1.41 thf(f21,axiom,(
% 1.81/1.41 ! [X6 : nat,X13 : list] : ((listStar @ X6 @ X13 @ X13) => (listStar @ X6 @ (rev @ X6 @ (rev @ X6 @ X13)) @ (rev @ (plus @ X6 @ zero) @ (app @ X6 @ zero @ (rev @ X6 @ X13) @ nil))))),
% 1.81/1.41 file('/export/starexec/sandbox/tmp/tmp.bglDpxLIIQ/DTF2THF_2542.p',list_rev_invol_step1)).
% 1.81/1.41 thf(f80,plain,(
% 1.81/1.41 ( ! [X0 : nat,X1 : list] : (((listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (rev @ (plus @ X0 @ zero) @ (app @ X0 @ zero @ (rev @ X0 @ X1) @ nil))) != $true) | ($true = (listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (app @ zero @ X0 @ (rev @ zero @ nil) @ X1))) | ($true != (listStar @ X0 @ X1 @ X1))) )),
% 1.81/1.41 inference(cnf_transformation,[status(thm)],[f72])).
% 1.81/1.41 thf(f72,plain,(
% 1.81/1.41 ! [X0 : nat,X1 : list] : (($true != (listStar @ X0 @ X1 @ X1)) | ((listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (rev @ (plus @ X0 @ zero) @ (app @ X0 @ zero @ (rev @ X0 @ X1) @ nil))) != $true) | ($true = (listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (app @ zero @ X0 @ (rev @ zero @ nil) @ X1))))),
% 1.81/1.41 inference(flattening,[status(thm)],[f71])).
% 1.81/1.41 thf(f71,plain,(
% 1.81/1.41 ! [X0 : nat,X1 : list] : ((($true = (listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (app @ zero @ X0 @ (rev @ zero @ nil) @ X1))) | ((listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (rev @ (plus @ X0 @ zero) @ (app @ X0 @ zero @ (rev @ X0 @ X1) @ nil))) != $true)) | ($true != (listStar @ X0 @ X1 @ X1)))),
% 1.81/1.41 inference(ennf_transformation,[status(thm)],[f45])).
% 1.81/1.41 thf(f45,plain,(
% 1.81/1.41 ! [X0 : nat,X1 : list] : (($true = (listStar @ X0 @ X1 @ X1)) => (((listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (rev @ (plus @ X0 @ zero) @ (app @ X0 @ zero @ (rev @ X0 @ X1) @ nil))) = $true) => ($true = (listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (app @ zero @ X0 @ (rev @ zero @ nil) @ X1)))))),
% 1.81/1.41 inference(fool_elimination,[status(thm)],[f44])).
% 1.81/1.41 thf(f44,plain,(
% 1.81/1.41 ! [X0 : nat,X1 : list] : ((listStar @ X0 @ X1 @ X1) => ((listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (rev @ (plus @ X0 @ zero) @ (app @ X0 @ zero @ (rev @ X0 @ X1) @ nil))) => (listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (app @ zero @ X0 @ (rev @ zero @ nil) @ X1))))),
% 1.81/1.41 inference(rectify,[status(thm)],[f22])).
% 1.81/1.41 thf(f22,axiom,(
% 1.81/1.41 ! [X6 : nat,X13 : list] : ((listStar @ X6 @ X13 @ X13) => ((listStar @ X6 @ (rev @ X6 @ (rev @ X6 @ X13)) @ (rev @ (plus @ X6 @ zero) @ (app @ X6 @ zero @ (rev @ X6 @ X13) @ nil))) => (listStar @ X6 @ (rev @ X6 @ (rev @ X6 @ X13)) @ (app @ zero @ X6 @ (rev @ zero @ nil) @ X13))))),
% 1.81/1.41 file('/export/starexec/sandbox/tmp/tmp.bglDpxLIIQ/DTF2THF_2542.p',list_rev_invol_step2)).
% 1.81/1.41 thf(f79,plain,(
% 1.81/1.41 ( ! [X0 : nat,X1 : list] : (($true != (listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (app @ zero @ X0 @ (rev @ zero @ nil) @ X1))) | ($true = (listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (app @ zero @ X0 @ nil @ X1))) | ($true != (listStar @ X0 @ X1 @ X1))) )),
% 1.81/1.41 inference(cnf_transformation,[status(thm)],[f74])).
% 1.81/1.41 thf(f74,plain,(
% 1.81/1.41 ! [X0 : nat,X1 : list] : (($true != (listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (app @ zero @ X0 @ (rev @ zero @ nil) @ X1))) | ($true = (listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (app @ zero @ X0 @ nil @ X1))) | ($true != (listStar @ X0 @ X1 @ X1)))),
% 1.81/1.41 inference(flattening,[status(thm)],[f73])).
% 1.81/1.41 thf(f73,plain,(
% 1.81/1.41 ! [X0 : nat,X1 : list] : ((($true = (listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (app @ zero @ X0 @ nil @ X1))) | ($true != (listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (app @ zero @ X0 @ (rev @ zero @ nil) @ X1)))) | ($true != (listStar @ X0 @ X1 @ X1)))),
% 1.81/1.41 inference(ennf_transformation,[status(thm)],[f61])).
% 1.81/1.41 thf(f61,plain,(
% 1.81/1.41 ! [X0 : nat,X1 : list] : (($true = (listStar @ X0 @ X1 @ X1)) => (($true = (listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (app @ zero @ X0 @ (rev @ zero @ nil) @ X1))) => ($true = (listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (app @ zero @ X0 @ nil @ X1)))))),
% 1.81/1.41 inference(fool_elimination,[status(thm)],[f60])).
% 1.81/1.41 thf(f60,plain,(
% 1.81/1.41 ! [X0 : nat,X1 : list] : ((listStar @ X0 @ X1 @ X1) => ((listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (app @ zero @ X0 @ (rev @ zero @ nil) @ X1)) => (listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (app @ zero @ X0 @ nil @ X1))))),
% 1.81/1.41 inference(rectify,[status(thm)],[f23])).
% 1.81/1.41 thf(f23,axiom,(
% 1.81/1.41 ! [X6 : nat,X13 : list] : ((listStar @ X6 @ X13 @ X13) => ((listStar @ X6 @ (rev @ X6 @ (rev @ X6 @ X13)) @ (app @ zero @ X6 @ (rev @ zero @ nil) @ X13)) => (listStar @ X6 @ (rev @ X6 @ (rev @ X6 @ X13)) @ (app @ zero @ X6 @ nil @ X13))))),
% 1.81/1.41 file('/export/starexec/sandbox/tmp/tmp.bglDpxLIIQ/DTF2THF_2542.p',list_rev_invol_step3)).
% 1.81/1.41 thf(f83,plain,(
% 1.81/1.41 ( ! [X0 : nat,X1 : list] : (($true != (listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (app @ zero @ X0 @ nil @ X1))) | ($true != (listStar @ X0 @ X1 @ X1)) | ($true = (listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ X1))) )),
% 1.81/1.41 inference(cnf_transformation,[status(thm)],[f70])).
% 1.81/1.41 thf(f70,plain,(
% 1.81/1.41 ! [X0 : nat,X1 : list] : (($true != (listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (app @ zero @ X0 @ nil @ X1))) | ($true != (listStar @ X0 @ X1 @ X1)) | ($true = (listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ X1)))),
% 1.81/1.41 inference(flattening,[status(thm)],[f69])).
% 1.81/1.41 thf(f69,plain,(
% 1.81/1.41 ! [X0 : nat,X1 : list] : ((($true = (listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ X1)) | ($true != (listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (app @ zero @ X0 @ nil @ X1)))) | ($true != (listStar @ X0 @ X1 @ X1)))),
% 1.81/1.41 inference(ennf_transformation,[status(thm)],[f31])).
% 1.81/1.41 thf(f31,plain,(
% 1.81/1.41 ! [X0 : nat,X1 : list] : (($true = (listStar @ X0 @ X1 @ X1)) => (($true = (listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (app @ zero @ X0 @ nil @ X1))) => ($true = (listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ X1))))),
% 1.81/1.41 inference(fool_elimination,[status(thm)],[f30])).
% 1.81/1.41 thf(f30,plain,(
% 1.81/1.41 ! [X0 : nat,X1 : list] : ((listStar @ X0 @ X1 @ X1) => ((listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ (app @ zero @ X0 @ nil @ X1)) => (listStar @ X0 @ (rev @ X0 @ (rev @ X0 @ X1)) @ X1)))),
% 1.81/1.41 inference(rectify,[status(thm)],[f24])).
% 1.81/1.41 thf(f24,axiom,(
% 1.81/1.41 ! [X6 : nat,X13 : list] : ((listStar @ X6 @ X13 @ X13) => ((listStar @ X6 @ (rev @ X6 @ (rev @ X6 @ X13)) @ (app @ zero @ X6 @ nil @ X13)) => (listStar @ X6 @ (rev @ X6 @ (rev @ X6 @ X13)) @ X13)))),
% 1.81/1.41 file('/export/starexec/sandbox/tmp/tmp.bglDpxLIIQ/DTF2THF_2542.p',list_rev_invol_step4)).
% 1.81/1.41 % SZS output end Proof for DTF2THF_2542
% 1.81/1.41 % (2890)------------------------------
% 1.81/1.41 % (2890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.41 % (2890)Termination reason: Refutation
% 1.81/1.41
% 1.81/1.41 % (2890)Memory used [KB]: 5756
% 1.81/1.41 % (2890)Time elapsed: 0.013 s
% 1.81/1.41 % (2890)Instructions burned: 27 (million)
% 1.81/1.41 % (2890)------------------------------
% 1.81/1.41 % (2890)------------------------------
% 1.81/1.41 % (2869)Success in time 0.072 s
%------------------------------------------------------------------------------