%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT390^1 : 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 : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:45:38 AM UTC 2026
% Result : Theorem 1.88s 1.40s
% Output : Refutation 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 100 ( 31 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 924 ( 10 ~; 0 |; 15 &; 886 @)
% ( 0 <=>; 13 =>; 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 : 19 ( 16 usr; 9 con; 0-4 aty)
% Number of variables : 41 ( 0 ^; 26 !; 15 ?; 41 :)
% 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: elem ).
thf(func_def_19,type,
sK2: list ).
thf(func_def_20,type,
sK3: nat ).
thf(func_def_21,type,
sK4: list ).
thf(f78,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f77,f76]) ).
thf(f76,plain,
( ( listStar @ ( plus @ sK0 @ ( suc @ sK3 ) ) @ ( rev @ ( plus @ sK0 @ ( suc @ sK3 ) ) @ ( app @ ( suc @ sK0 ) @ sK3 @ ( rev @ ( suc @ sK0 ) @ ( cons @ sK0 @ sK1 @ sK2 ) ) @ sK4 ) ) @ ( rev @ ( plus @ sK0 @ ( suc @ sK3 ) ) @ ( app @ sK0 @ ( suc @ sK3 ) @ ( rev @ sK0 @ sK2 ) @ ( cons @ sK3 @ sK1 @ sK4 ) ) ) )
!= $true ),
inference(forward_demodulation,[status(thm)],[f73,f67]) ).
thf(f67,plain,
! [X0: nat,X1: nat] :
( ( plus @ ( suc @ X0 ) @ X1 )
= ( plus @ X0 @ ( suc @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
thf(f50,plain,
! [X0: nat,X1: nat] :
( ( plus @ ( suc @ X0 ) @ X1 )
= ( plus @ X0 @ ( suc @ X1 ) ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,axiom,
! [X6: nat,X10: nat] :
( ( plus @ ( suc @ X6 ) @ X10 )
= ( plus @ X6 @ ( suc @ X10 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lmrxhHgLnQ/DTF2THF_25022.p',plus_s_l_r) ).
thf(f73,plain,
( ( listStar @ ( plus @ ( suc @ sK0 ) @ sK3 ) @ ( rev @ ( plus @ ( suc @ sK0 ) @ sK3 ) @ ( app @ ( suc @ sK0 ) @ sK3 @ ( rev @ ( suc @ sK0 ) @ ( cons @ sK0 @ sK1 @ sK2 ) ) @ sK4 ) ) @ ( rev @ ( plus @ sK0 @ ( suc @ sK3 ) ) @ ( app @ sK0 @ ( suc @ sK3 ) @ ( rev @ sK0 @ sK2 ) @ ( cons @ sK3 @ sK1 @ sK4 ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f62]) ).
thf(f62,plain,
( ( ( listStar @ ( plus @ ( suc @ sK0 ) @ sK3 ) @ ( rev @ ( plus @ ( suc @ sK0 ) @ sK3 ) @ ( app @ ( suc @ sK0 ) @ sK3 @ ( rev @ ( suc @ sK0 ) @ ( cons @ sK0 @ sK1 @ sK2 ) ) @ sK4 ) ) @ ( rev @ ( plus @ sK0 @ ( suc @ sK3 ) ) @ ( app @ sK0 @ ( suc @ sK3 ) @ ( rev @ sK0 @ sK2 ) @ ( cons @ sK3 @ sK1 @ sK4 ) ) ) )
!= $true )
& ( ( listStar @ ( plus @ ( suc @ sK0 ) @ sK3 ) @ ( rev @ ( plus @ ( suc @ sK0 ) @ sK3 ) @ ( app @ ( suc @ sK0 ) @ sK3 @ ( rev @ ( suc @ sK0 ) @ ( cons @ sK0 @ sK1 @ sK2 ) ) @ sK4 ) ) @ ( rev @ ( plus @ ( suc @ sK0 ) @ sK3 ) @ ( app @ sK0 @ ( suc @ sK3 ) @ ( rev @ sK0 @ sK2 ) @ ( cons @ sK3 @ sK1 @ sK4 ) ) ) )
= $true )
& ( ( listStar @ sK3 @ sK4 @ sK4 )
= $true )
& ( ( listStar @ sK0 @ sK2 @ sK2 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f56,f61]) ).
thf(f61,plain,
( ? [X0: nat,X1: elem,X2: list,X3: nat,X4: list] :
( ( $true
!= ( listStar @ ( plus @ ( suc @ X0 ) @ X3 ) @ ( rev @ ( plus @ ( suc @ X0 ) @ X3 ) @ ( app @ ( suc @ X0 ) @ X3 @ ( rev @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) ) @ X4 ) ) @ ( rev @ ( plus @ X0 @ ( suc @ X3 ) ) @ ( app @ X0 @ ( suc @ X3 ) @ ( rev @ X0 @ X2 ) @ ( cons @ X3 @ X1 @ X4 ) ) ) ) )
& ( ( listStar @ ( plus @ ( suc @ X0 ) @ X3 ) @ ( rev @ ( plus @ ( suc @ X0 ) @ X3 ) @ ( app @ ( suc @ X0 ) @ X3 @ ( rev @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) ) @ X4 ) ) @ ( rev @ ( plus @ ( suc @ X0 ) @ X3 ) @ ( app @ X0 @ ( suc @ X3 ) @ ( rev @ X0 @ X2 ) @ ( cons @ X3 @ X1 @ X4 ) ) ) )
= $true )
& ( $true
= ( listStar @ X3 @ X4 @ X4 ) )
& ( $true
= ( listStar @ X0 @ X2 @ X2 ) ) )
=> ( ( ( listStar @ ( plus @ ( suc @ sK0 ) @ sK3 ) @ ( rev @ ( plus @ ( suc @ sK0 ) @ sK3 ) @ ( app @ ( suc @ sK0 ) @ sK3 @ ( rev @ ( suc @ sK0 ) @ ( cons @ sK0 @ sK1 @ sK2 ) ) @ sK4 ) ) @ ( rev @ ( plus @ sK0 @ ( suc @ sK3 ) ) @ ( app @ sK0 @ ( suc @ sK3 ) @ ( rev @ sK0 @ sK2 ) @ ( cons @ sK3 @ sK1 @ sK4 ) ) ) )
!= $true )
& ( ( listStar @ ( plus @ ( suc @ sK0 ) @ sK3 ) @ ( rev @ ( plus @ ( suc @ sK0 ) @ sK3 ) @ ( app @ ( suc @ sK0 ) @ sK3 @ ( rev @ ( suc @ sK0 ) @ ( cons @ sK0 @ sK1 @ sK2 ) ) @ sK4 ) ) @ ( rev @ ( plus @ ( suc @ sK0 ) @ sK3 ) @ ( app @ sK0 @ ( suc @ sK3 ) @ ( rev @ sK0 @ sK2 ) @ ( cons @ sK3 @ sK1 @ sK4 ) ) ) )
= $true )
& ( ( listStar @ sK3 @ sK4 @ sK4 )
= $true )
& ( ( listStar @ sK0 @ sK2 @ sK2 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f56,plain,
? [X0: nat,X1: elem,X2: list,X3: nat,X4: list] :
( ( $true
!= ( listStar @ ( plus @ ( suc @ X0 ) @ X3 ) @ ( rev @ ( plus @ ( suc @ X0 ) @ X3 ) @ ( app @ ( suc @ X0 ) @ X3 @ ( rev @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) ) @ X4 ) ) @ ( rev @ ( plus @ X0 @ ( suc @ X3 ) ) @ ( app @ X0 @ ( suc @ X3 ) @ ( rev @ X0 @ X2 ) @ ( cons @ X3 @ X1 @ X4 ) ) ) ) )
& ( ( listStar @ ( plus @ ( suc @ X0 ) @ X3 ) @ ( rev @ ( plus @ ( suc @ X0 ) @ X3 ) @ ( app @ ( suc @ X0 ) @ X3 @ ( rev @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) ) @ X4 ) ) @ ( rev @ ( plus @ ( suc @ X0 ) @ X3 ) @ ( app @ X0 @ ( suc @ X3 ) @ ( rev @ X0 @ X2 ) @ ( cons @ X3 @ X1 @ X4 ) ) ) )
= $true )
& ( $true
= ( listStar @ X3 @ X4 @ X4 ) )
& ( $true
= ( listStar @ X0 @ X2 @ X2 ) ) ),
inference(flattening,[status(thm)],[f55]) ).
thf(f55,plain,
? [X0: nat,X1: elem,X2: list,X3: nat,X4: list] :
( ( $true
!= ( listStar @ ( plus @ ( suc @ X0 ) @ X3 ) @ ( rev @ ( plus @ ( suc @ X0 ) @ X3 ) @ ( app @ ( suc @ X0 ) @ X3 @ ( rev @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) ) @ X4 ) ) @ ( rev @ ( plus @ X0 @ ( suc @ X3 ) ) @ ( app @ X0 @ ( suc @ X3 ) @ ( rev @ X0 @ X2 ) @ ( cons @ X3 @ X1 @ X4 ) ) ) ) )
& ( ( listStar @ ( plus @ ( suc @ X0 ) @ X3 ) @ ( rev @ ( plus @ ( suc @ X0 ) @ X3 ) @ ( app @ ( suc @ X0 ) @ X3 @ ( rev @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) ) @ X4 ) ) @ ( rev @ ( plus @ ( suc @ X0 ) @ X3 ) @ ( app @ X0 @ ( suc @ X3 ) @ ( rev @ X0 @ X2 ) @ ( cons @ X3 @ X1 @ X4 ) ) ) )
= $true )
& ( $true
= ( listStar @ X3 @ X4 @ X4 ) )
& ( $true
= ( listStar @ X0 @ X2 @ X2 ) ) ),
inference(ennf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
~ ! [X0: nat,X1: elem,X2: list,X3: nat,X4: list] :
( ( $true
= ( listStar @ X0 @ X2 @ X2 ) )
=> ( ( $true
= ( listStar @ X3 @ X4 @ X4 ) )
=> ( ( ( listStar @ ( plus @ ( suc @ X0 ) @ X3 ) @ ( rev @ ( plus @ ( suc @ X0 ) @ X3 ) @ ( app @ ( suc @ X0 ) @ X3 @ ( rev @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) ) @ X4 ) ) @ ( rev @ ( plus @ ( suc @ X0 ) @ X3 ) @ ( app @ X0 @ ( suc @ X3 ) @ ( rev @ X0 @ X2 ) @ ( cons @ X3 @ X1 @ X4 ) ) ) )
= $true )
=> ( $true
= ( listStar @ ( plus @ ( suc @ X0 ) @ X3 ) @ ( rev @ ( plus @ ( suc @ X0 ) @ X3 ) @ ( app @ ( suc @ X0 ) @ X3 @ ( rev @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) ) @ X4 ) ) @ ( rev @ ( plus @ X0 @ ( suc @ X3 ) ) @ ( app @ X0 @ ( suc @ X3 ) @ ( rev @ X0 @ X2 ) @ ( cons @ X3 @ X1 @ X4 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f32]) ).
thf(f32,plain,
~ ! [X0: nat,X1: elem,X2: list,X3: nat,X4: list] :
( ( listStar @ X0 @ X2 @ X2 )
=> ( ( listStar @ X3 @ X4 @ X4 )
=> ( ( listStar @ ( plus @ ( suc @ X0 ) @ X3 ) @ ( rev @ ( plus @ ( suc @ X0 ) @ X3 ) @ ( app @ ( suc @ X0 ) @ X3 @ ( rev @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) ) @ X4 ) ) @ ( rev @ ( plus @ ( suc @ X0 ) @ X3 ) @ ( app @ X0 @ ( suc @ X3 ) @ ( rev @ X0 @ X2 ) @ ( cons @ X3 @ X1 @ X4 ) ) ) )
=> ( listStar @ ( plus @ ( suc @ X0 ) @ X3 ) @ ( rev @ ( plus @ ( suc @ X0 ) @ X3 ) @ ( app @ ( suc @ X0 ) @ X3 @ ( rev @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) ) @ X4 ) ) @ ( rev @ ( plus @ X0 @ ( suc @ X3 ) ) @ ( app @ X0 @ ( suc @ X3 ) @ ( rev @ X0 @ X2 ) @ ( cons @ X3 @ X1 @ X4 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f22]) ).
thf(f22,negated_conjecture,
~ ! [X6: nat,X2: elem,X16: list,X14: nat,X17: list] :
( ( listStar @ X6 @ X16 @ X16 )
=> ( ( 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 @ X6 @ ( suc @ X14 ) @ ( rev @ X6 @ X16 ) @ ( cons @ X14 @ X2 @ X17 ) ) ) )
=> ( listStar @ ( plus @ ( suc @ X6 ) @ X14 ) @ ( rev @ ( plus @ ( suc @ X6 ) @ X14 ) @ ( app @ ( suc @ X6 ) @ X14 @ ( rev @ ( suc @ X6 ) @ ( cons @ X6 @ X2 @ X16 ) ) @ X17 ) ) @ ( rev @ ( plus @ X6 @ ( suc @ X14 ) ) @ ( app @ X6 @ ( suc @ X14 ) @ ( rev @ X6 @ X16 ) @ ( cons @ X14 @ X2 @ X17 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
thf(f21,conjecture,
! [X6: nat,X2: elem,X16: list,X14: nat,X17: list] :
( ( listStar @ X6 @ X16 @ X16 )
=> ( ( 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 @ X6 @ ( suc @ X14 ) @ ( rev @ X6 @ X16 ) @ ( cons @ X14 @ X2 @ X17 ) ) ) )
=> ( listStar @ ( plus @ ( suc @ X6 ) @ X14 ) @ ( rev @ ( plus @ ( suc @ X6 ) @ X14 ) @ ( app @ ( suc @ X6 ) @ X14 @ ( rev @ ( suc @ X6 ) @ ( cons @ X6 @ X2 @ X16 ) ) @ X17 ) ) @ ( rev @ ( plus @ X6 @ ( suc @ X14 ) ) @ ( app @ X6 @ ( suc @ X14 ) @ ( rev @ X6 @ X16 ) @ ( cons @ X14 @ X2 @ X17 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lmrxhHgLnQ/DTF2THF_25022.p',list_rev_invol_lem_indstep3) ).
thf(f77,plain,
( ( listStar @ ( plus @ sK0 @ ( suc @ sK3 ) ) @ ( rev @ ( plus @ sK0 @ ( suc @ sK3 ) ) @ ( app @ ( suc @ sK0 ) @ sK3 @ ( rev @ ( suc @ sK0 ) @ ( cons @ sK0 @ sK1 @ sK2 ) ) @ sK4 ) ) @ ( rev @ ( plus @ sK0 @ ( suc @ sK3 ) ) @ ( app @ sK0 @ ( suc @ sK3 ) @ ( rev @ sK0 @ sK2 ) @ ( cons @ sK3 @ sK1 @ sK4 ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f72,f67]) ).
thf(f72,plain,
( ( listStar @ ( plus @ ( suc @ sK0 ) @ sK3 ) @ ( rev @ ( plus @ ( suc @ sK0 ) @ sK3 ) @ ( app @ ( suc @ sK0 ) @ sK3 @ ( rev @ ( suc @ sK0 ) @ ( cons @ sK0 @ sK1 @ sK2 ) ) @ sK4 ) ) @ ( rev @ ( plus @ ( suc @ sK0 ) @ sK3 ) @ ( app @ sK0 @ ( suc @ sK3 ) @ ( rev @ sK0 @ sK2 ) @ ( cons @ sK3 @ sK1 @ sK4 ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT390^1 : 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
% 0.17/0.34 % Computer : n004.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 06:16:26 EST 2026
% 0.21/0.35 % CPUTime :
% 0.21/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.32/0.50 ---- Original DTF file ---
% 0.32/0.50 thf(spec,logic,$$dhol).
% 0.32/0.50 %------------------------------------------------------------------------------
% 0.32/0.50 % File : DAT390^1 : TPTP v9.2.1. Released v9.2.0.
% 0.32/0.50 % Domain : Data Structures
% 0.32/0.50 % Problem : List involution lemma, induction step 3
% 0.32/0.50 % Version : Especial.
% 0.32/0.50 % English : List involution lemma. The proof is by induction with a separate
% 0.32/0.50 % problem file for the base and step case (with multiple subcases)
% 0.32/0.50 % as well as the correct instantiation of the induction axiom for
% 0.32/0.50 % lists. The main file uses the conjectures of the other files as
% 0.32/0.50 % lemmas in order to prove the final result. To simplify proof
% 0.32/0.50 % search, the axioms in each problem file have been preselected.
% 0.32/0.50 % For the actual induction proof, it is sufficient to consider the
% 0.32/0.50 % "step" problem files.
% 0.32/0.50
% 0.32/0.50 % Refs : [RRB23] Rothgang et al. (2023), Theorem Proving in Dependently
% 0.32/0.50 % : [Rot25] Rothgang (2025), Email to Geoff Sutcliffe
% 0.32/0.50 % : [RK+25] Ranalter et al. (2025), The Dependently Typed Higher-O
% 0.32/0.50 % Source : [Rot25]
% 0.32/0.50 % Names : ListReversalInvolutionLemma/list-rev-invol-lem-indstep3.p [Rot25]
% 0.32/0.50
% 0.32/0.50 % Status : Theorem
% 0.32/0.50 % Rating : ? v9.2.0
% 0.32/0.50 % Syntax : Number of formulae : 23 ( 10 unt; 10 typ; 0 def)
% 0.32/0.50 % Number of atoms : 14 ( 14 equ; 0 cnn)
% 0.32/0.50 % Maximal formula atoms : 2 ( 1 avg)
% 0.32/0.50 % Number of connectives : 147 ( 3 ~; 0 |; 0 &; 139 @)
% 0.32/0.50 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.32/0.50 % Maximal formula depth : 8 ( 4 avg)
% 0.32/0.50 % Number of types : 3 ( 2 usr)
% 0.32/0.50 % Number of type decls : 10 ( 0 !>P; 3 !>D)
% 0.32/0.50 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.32/0.50 % Number of symbols : 9 ( 8 usr; 2 con; 0-4 aty)
% 0.32/0.50 % Number of variables : 34 ( 0 ^; 30 !; 0 ?; 34 :)
% 0.32/0.50 % ( 4 !>; 0 ?*; 0 @-; 0 @+)
% 0.32/0.50 % SPC : DH0_THM_EQU_NAR
% 0.32/0.50
% 0.32/0.50 % Comments :
% 0.32/0.50 %------------------------------------------------------------------------------
% 0.32/0.50 thf(elem_type,type,
% 0.32/0.50 elem: $tType ).
% 0.32/0.50
% 0.32/0.50 thf(nat_type,type,
% 0.32/0.50 nat: $tType ).
% 0.32/0.50
% 0.32/0.50 thf(zero_type,type,
% 0.32/0.50 zero: nat ).
% 0.32/0.50
% 0.32/0.50 thf(suc_type,type,
% 0.32/0.50 suc: nat > nat ).
% 0.32/0.50
% 0.32/0.50 thf(plus_type,type,
% 0.32/0.50 plus: nat > nat > nat ).
% 0.32/0.50
% 0.32/0.50 thf(list_type,type,
% 0.32/0.50 list: nat > $tType ).
% 0.32/0.50
% 0.32/0.50 thf(nil_type,type,
% 0.32/0.50 nil: list @ zero ).
% 0.32/0.50
% 0.32/0.50 thf(cons_type,type,
% 0.32/0.50 cons:
% 0.32/0.50 !>[N: nat] : ( elem > ( list @ N ) > ( list @ ( suc @ N ) ) ) ).
% 0.32/0.50
% 0.32/0.50 thf(app_type,type,
% 0.32/0.50 app:
% 0.32/0.50 !>[N: nat,M: nat] : ( ( list @ N ) > ( list @ M ) > ( list @ ( plus @ N @ M ) ) ) ).
% 0.32/0.50
% 0.32/0.50 thf(rev_type,type,
% 0.32/0.50 rev:
% 0.32/0.50 !>[N: nat] : ( ( list @ N ) > ( list @ N ) ) ).
% 0.32/0.50
% 0.32/0.50 thf(peano1,axiom,
% 0.32/0.50 ! [N: nat] :
% 0.32/0.50 ( ( suc @ N )
% 0.32/0.50 != zero ) ).
% 0.32/0.50
% 0.32/0.50 thf(peano2,axiom,
% 0.32/0.50 ! [N: nat,M: nat] :
% 0.32/0.50 ( ( N != M )
% 0.32/0.50 => ( ( suc @ N )
% 0.32/0.50 != ( suc @ M ) ) ) ).
% 0.32/0.50
% 0.32/0.50 thf(peano3,axiom,
% 0.32/0.50 ! [P: nat > $o] :
% 0.32/0.50 ( ( P @ zero )
% 0.32/0.50 => ( ! [M: nat] :
% 0.32/0.50 ( ( P @ M )
% 0.32/0.50 => ( P @ ( suc @ M ) ) )
% 0.32/0.50 => ! [N: nat] : ( P @ N ) ) ) ).
% 0.32/0.50
% 0.32/0.50 thf(ax1,axiom,
% 0.32/0.50 ! [N: nat] :
% 0.32/0.50 ( ( plus @ zero @ N )
% 0.32/0.50 = N ) ).
% 0.32/0.50
% 0.32/0.50 thf(ax2,axiom,
% 0.32/0.50 ! [N: nat,M: nat] :
% 0.32/0.50 ( ( plus @ ( suc @ N ) @ M )
% 0.32/0.50 = ( suc @ ( plus @ N @ M ) ) ) ).
% 0.32/0.50
% 0.32/0.50 thf(ax3,axiom,
% 0.32/0.50 ! [N: nat,X: list @ N] :
% 0.32/0.50 ( ( app @ zero @ N @ nil @ X )
% 0.32/0.50 = X ) ).
% 0.32/0.50
% 0.32/0.50 thf(ax4,axiom,
% 0.32/0.50 ! [N: nat,M: nat,X: elem,Y: list @ N,Z: list @ M] :
% 0.32/0.50 ( ( app @ ( suc @ N ) @ M @ ( cons @ N @ X @ Y ) @ Z )
% 0.32/0.50 = ( cons @ ( plus @ N @ M ) @ X @ ( app @ N @ M @ Y @ Z ) ) ) ).
% 0.32/0.50
% 0.32/0.50 thf(plus_zero_r,axiom,
% 0.32/0.50 ! [M: nat] :
% 0.32/0.50 ( ( plus @ M @ zero )
% 0.32/0.50 = M ) ).
% 0.32/0.50
% 0.32/0.50 thf(plus_com,axiom,
% 0.32/0.50 ! [N: nat,M: nat] :
% 0.32/0.50 ( ( plus @ N @ M )
% 0.32/0.50 = ( plus @ M @ N ) ) ).
% 0.32/0.50
% 0.32/0.50 thf(plus_assoc,axiom,
% 0.32/0.50 ! [M1: nat,M2: nat,M3: nat] :
% 0.32/0.50 ( ( plus @ M1 @ ( plus @ M2 @ M3 ) )
% 0.32/0.50 = ( plus @ ( plus @ M1 @ M2 ) @ M3 ) ) ).
% 0.32/0.50
% 0.32/0.50 thf(plus1r,axiom,
% 0.32/0.50 ! [N: nat] :
% 0.32/0.50 ( ( suc @ N )
% 0.32/0.50 = ( plus @ N @ ( suc @ zero ) ) ) ).
% 0.32/0.50
% 0.32/0.50 thf(plus_s_l_r,axiom,
% 0.32/0.50 ! [N: nat,M: nat] :
% 0.32/0.50 ( ( plus @ ( suc @ N ) @ M )
% 0.32/0.50 = ( plus @ N @ ( suc @ M ) ) ) ).
% 0.32/0.50
% 0.32/0.50 thf(list_rev_invol_lem_indstep3,conjecture,
% 0.32/0.50 ! [N: nat,X: elem,L: list @ N,M2: nat,L2: list @ M2] :
% 0.32/0.50 ( ( ( rev @ ( plus @ ( suc @ N ) @ M2 ) @ ( app @ ( suc @ N ) @ M2 @ ( rev @ ( suc @ N ) @ ( cons @ N @ X @ L ) ) @ L2 ) )
% 0.32/0.50 = ( rev @ ( plus @ ( suc @ N ) @ M2 ) @ ( app @ N @ ( suc @ M2 ) @ ( rev @ N @ L ) @ ( cons @ M2 @ X @ L2 ) ) ) )
% 0.32/0.50 => ( ( rev @ ( plus @ ( suc @ N ) @ M2 ) @ ( app @ ( suc @ N ) @ M2 @ ( rev @ ( suc @ N ) @ ( cons @ N @ X @ L ) ) @ L2 ) )
% 0.32/0.50 = ( rev @ ( plus @ N @ ( suc @ M2 ) ) @ ( app @ N @ ( suc @ M2 ) @ ( rev @ N @ L ) @ ( cons @ M2 @ X @ L2 ) ) ) ) ) ).
% 0.32/0.50
% 0.32/0.50 %------------------------------------------------------------------------------
% 0.32/0.50 ------------------------
% 1.72/1.36 ---- Embedded in THF ---
% 1.72/1.36 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.72/1.36 %%% Generated on Tue Feb 24 06:16:27 EST 2026
% 1.72/1.36 %%% using '$$dhol' embedding, version 1.3.0.
% 1.72/1.36 %%% Logic specification used:
% 1.72/1.36 %%% thf(spec, logic, $$dhol).
% 1.72/1.36
% 1.72/1.36 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.lmrxhHgLnQ/DTF2DTF25022.p
% See solution above
% 1.72/1.36 ------------------------
% 1.72/1.37 ---- Cleaned THF ---
% 1.72/1.37 thf(is_per_type,type,
% 1.72/1.37 isPer:
% 1.72/1.37 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 1.72/1.37
% 1.72/1.37 thf(is_per,definition,
% 1.72/1.37 ! [A: $tType,AStar: A > A > $o] :
% 1.72/1.37 ( ( isPer @ A @ AStar )
% 1.72/1.37 <=> ( ! [X: A,Y: A] :
% 1.72/1.37 ( ( AStar @ X @ Y )
% 1.72/1.37 => ( AStar @ Y @ X ) )
% 1.72/1.37 & ! [X: A,Y: A,Z: A] :
% 1.72/1.37 ( ( AStar @ X @ Y )
% 1.72/1.37 => ( ( AStar @ Y @ Z )
% 1.72/1.37 => ( AStar @ X @ Z ) ) ) ) ) ).
% 1.72/1.37
% 1.72/1.37 thf(elem_type,type,
% 1.72/1.37 elem: $tType ).
% 1.72/1.37
% 1.72/1.37 thf(elemStar,type,
% 1.72/1.37 elemStar: elem > elem > $o ).
% 1.72/1.37
% 1.72/1.37 thf(elemStar_is_eq,axiom,
% 1.72/1.37 ! [X: elem,Y: elem] :
% 1.72/1.37 ( ( elemStar @ X @ Y )
% 1.72/1.37 <=> ( X = Y ) ) ).
% 1.72/1.37
% 1.72/1.37 thf(nat_type,type,
% 1.72/1.37 nat: $tType ).
% 1.72/1.37
% 1.72/1.37 thf(natStar,type,
% 1.72/1.37 natStar: nat > nat > $o ).
% 1.72/1.37
% 1.72/1.37 thf(natStar_is_eq,axiom,
% 1.72/1.37 ! [X: nat,Y: nat] :
% 1.72/1.37 ( ( natStar @ X @ Y )
% 1.72/1.37 <=> ( X = Y ) ) ).
% 1.72/1.37
% 1.72/1.37 thf(zero_type,type,
% 1.72/1.37 zero: nat ).
% 1.72/1.37
% 1.72/1.37 thf(suc_type,type,
% 1.72/1.37 suc: nat > nat ).
% 1.72/1.37
% 1.72/1.37 thf(plus_type,type,
% 1.72/1.37 plus: nat > nat > nat ).
% 1.72/1.37
% 1.72/1.37 thf(list_type,type,
% 1.72/1.37 list: $tType ).
% 1.72/1.37
% 1.72/1.37 thf(listStar,type,
% 1.72/1.37 listStar: nat > list > list > $o ).
% 1.72/1.37
% 1.72/1.37 thf('\'listStar\'_is_per',axiom,
% 1.72/1.37 ! [C: nat] : ( isPer @ list @ ( listStar @ C ) ) ).
% 1.72/1.37
% 1.72/1.37 thf(nil_type,type,
% 1.72/1.37 nil: list ).
% 1.72/1.37
% 1.72/1.37 thf(nil_tp_ax,axiom,
% 1.72/1.37 listStar @ zero @ nil @ nil ).
% 1.72/1.37
% 1.72/1.37 thf(cons_type,type,
% 1.72/1.37 cons: nat > elem > list > list ).
% 1.72/1.37
% 1.72/1.37 thf(cons_tp_ax,axiom,
% 1.72/1.37 ! [N: nat,D: elem,D0: list,D0_prime: list] :
% 1.72/1.37 ( ( listStar @ N @ D0 @ D0_prime )
% 1.72/1.37 => ( listStar @ ( suc @ N ) @ ( cons @ N @ D @ D0 ) @ ( cons @ N @ D @ D0_prime ) ) ) ).
% 1.72/1.37
% 1.72/1.37 thf(app_type,type,
% 1.72/1.37 app: nat > nat > list > list > list ).
% 1.72/1.37
% 1.72/1.37 thf(app_tp_ax,axiom,
% 1.72/1.37 ! [N: nat,M: nat,D: list,D_prime: list] :
% 1.72/1.37 ( ( listStar @ N @ D @ D_prime )
% 1.72/1.37 => ! [D0: list,D0_prime: list] :
% 1.72/1.37 ( ( listStar @ M @ D0 @ D0_prime )
% 1.72/1.37 => ( listStar @ ( plus @ N @ M ) @ ( app @ N @ M @ D @ D0 ) @ ( app @ N @ M @ D_prime @ D0_prime ) ) ) ) ).
% 1.72/1.37
% 1.72/1.37 thf(rev_type,type,
% 1.72/1.37 rev: nat > list > list ).
% 1.72/1.37
% 1.72/1.37 thf(rev_tp_ax,axiom,
% 1.72/1.37 ! [N: nat,D: list,D_prime: list] :
% 1.72/1.37 ( ( listStar @ N @ D @ D_prime )
% 1.72/1.37 => ( listStar @ N @ ( rev @ N @ D ) @ ( rev @ N @ D_prime ) ) ) ).
% 1.72/1.37
% 1.72/1.37 thf(peano1,axiom,
% 1.72/1.37 ! [N: nat] :
% 1.72/1.37 ( ( suc @ N )
% 1.72/1.37 != zero ) ).
% 1.72/1.37
% 1.72/1.37 thf(peano2,axiom,
% 1.72/1.37 ! [N: nat,M: nat] :
% 1.72/1.37 ( ( N != M )
% 1.72/1.37 => ( ( suc @ N )
% 1.72/1.37 != ( suc @ M ) ) ) ).
% 1.72/1.37
% 1.72/1.37 thf(peano3,axiom,
% 1.72/1.37 ! [P: nat > $o] :
% 1.72/1.37 ( ( P @ zero )
% 1.72/1.37 => ( ! [M: nat] :
% 1.72/1.37 ( ( P @ M )
% 1.72/1.37 => ( P @ ( suc @ M ) ) )
% 1.72/1.37 => ! [N: nat] : ( P @ N ) ) ) ).
% 1.72/1.37
% 1.72/1.37 thf(ax1,axiom,
% 1.72/1.37 ! [N: nat] :
% 1.72/1.37 ( ( plus @ zero @ N )
% 1.72/1.37 = N ) ).
% 1.72/1.37
% 1.72/1.37 thf(ax2,axiom,
% 1.72/1.37 ! [N: nat,M: nat] :
% 1.72/1.37 ( ( plus @ ( suc @ N ) @ M )
% 1.72/1.37 = ( suc @ ( plus @ N @ M ) ) ) ).
% 1.72/1.37
% 1.72/1.37 thf(ax3,axiom,
% 1.72/1.37 ! [N: nat,X: list] :
% 1.72/1.37 ( ( listStar @ N @ X @ X )
% 1.72/1.37 => ( listStar @ ( plus @ zero @ N ) @ ( app @ zero @ N @ nil @ X ) @ X ) ) ).
% 1.72/1.37
% 1.72/1.37 thf(ax4,axiom,
% 1.72/1.37 ! [N: nat,M: nat,X: elem,Y: list,Z: list] :
% 1.72/1.37 ( ( listStar @ N @ Y @ Y )
% 1.72/1.37 => ( ( listStar @ M @ Z @ Z )
% 1.72/1.37 => ( listStar @ ( plus @ ( suc @ N ) @ M ) @ ( app @ ( suc @ N ) @ M @ ( cons @ N @ X @ Y ) @ Z ) @ ( cons @ ( plus @ N @ M ) @ X @ ( app @ N @ M @ Y @ Z ) ) ) ) ) ).
% 1.72/1.37
% 1.72/1.37 thf(plus_zero_r,axiom,
% 1.72/1.37 ! [M: nat] :
% 1.72/1.37 ( ( plus @ M @ zero )
% 1.72/1.37 = M ) ).
% 1.72/1.37
% 1.72/1.37 thf(plus_com,axiom,
% 1.72/1.37 ! [N: nat,M: nat] :
% 1.72/1.37 ( ( plus @ N @ M )
% 1.72/1.37 = ( plus @ M @ N ) ) ).
% 1.72/1.37
% 1.72/1.37 thf(plus_assoc,axiom,
% 1.72/1.37 ! [M1: nat,M2: nat,M3: nat] :
% 1.72/1.37 ( ( plus @ M1 @ ( plus @ M2 @ M3 ) )
% 1.72/1.37 = ( plus @ ( plus @ M1 @ M2 ) @ M3 ) ) ).
% 1.72/1.37
% 1.72/1.37 thf(plus1r,axiom,
% 1.72/1.37 ! [N: nat] :
% 1.72/1.37 ( ( suc @ N )
% 1.72/1.37 = ( plus @ N @ ( suc @ zero ) ) ) ).
% 1.72/1.37
% 1.72/1.37 thf(plus_s_l_r,axiom,
% 1.72/1.37 ! [N: nat,M: nat] :
% 1.72/1.37 ( ( plus @ ( suc @ N ) @ M )
% 1.72/1.37 = ( plus @ N @ ( suc @ M ) ) ) ).
% 1.72/1.37
% 1.72/1.37 thf(list_rev_invol_lem_indstep3,conjecture,
% 1.72/1.37 ! [N: nat,X: elem,L: list,M2: nat,L2: list] :
% 1.72/1.37 ( ( listStar @ N @ L @ L )
% 1.72/1.37 => ( ( listStar @ M2 @ L2 @ L2 )
% 1.72/1.37 => ( ( 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 @ N @ ( suc @ M2 ) @ ( rev @ N @ L ) @ ( cons @ M2 @ X @ L2 ) ) ) )
% 1.72/1.37 => ( listStar @ ( plus @ ( suc @ N ) @ M2 ) @ ( rev @ ( plus @ ( suc @ N ) @ M2 ) @ ( app @ ( suc @ N ) @ M2 @ ( rev @ ( suc @ N ) @ ( cons @ N @ X @ L ) ) @ L2 ) ) @ ( rev @ ( plus @ N @ ( suc @ M2 ) ) @ ( app @ N @ ( suc @ M2 ) @ ( rev @ N @ L ) @ ( cons @ M2 @ X @ L2 ) ) ) ) ) ) ) ).
% 1.72/1.37 ------------------------
% 1.72/1.39 % (25355)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_25022 for (2999ds/2Mi)
% 1.72/1.39 % (25355)Instruction limit reached!
% 1.72/1.39 % (25355)------------------------------
% 1.72/1.39 % (25355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.39 % (25355)Termination reason: Unknown
% 1.72/1.39 % (25355)Termination phase: shuffling
% 1.72/1.39
% 1.72/1.39 % (25355)Memory used [KB]: 1023
% 1.72/1.39 % (25355)Time elapsed: 0.002 s
% 1.72/1.39 % (25355)Instructions burned: 3 (million)
% 1.72/1.39 % (25355)------------------------------
% 1.72/1.39 % (25355)------------------------------
% 1.72/1.39 % (25353)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_25022 for (2999ds/27Mi)
% 1.72/1.40 % (25351)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25022 for (2999ds/183Mi)
% 1.72/1.40 % (25352)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_25022 for (2999ds/4Mi)
% 1.72/1.40 % (25354)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_25022 for (2999ds/2Mi)
% 1.72/1.40 % (25356)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_25022 for (2999ds/275Mi)
% 1.72/1.40 % (25357)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_25022 for (2999ds/18Mi)
% 1.72/1.40 % (25354)Instruction limit reached!
% 1.72/1.40 % (25354)------------------------------
% 1.72/1.40 % (25354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.40 % (25354)Termination reason: Unknown
% 1.72/1.40 % (25354)Termination phase: shuffling
% 1.72/1.40
% 1.72/1.40 % (25354)Memory used [KB]: 1023
% 1.72/1.40 % (25354)Time elapsed: 0.003 s
% 1.72/1.40 % (25354)Instructions burned: 2 (million)
% 1.72/1.40 % (25354)------------------------------
% 1.72/1.40 % (25354)------------------------------
% 1.88/1.40 % (25352)Instruction limit reached!
% 1.88/1.40 % (25352)------------------------------
% 1.88/1.40 % (25352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.40 % (25352)Termination reason: Unknown
% 1.88/1.40 % (25352)Termination phase: shuffling
% 1.88/1.40
% 1.88/1.40 % (25352)Memory used [KB]: 1023
% 1.88/1.40 % (25352)Time elapsed: 0.004 s
% 1.88/1.40 % (25352)Instructions burned: 4 (million)
% 1.88/1.40 % (25352)------------------------------
% 1.88/1.40 % (25352)------------------------------
% 1.88/1.40 % (25358)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_25022 for (2999ds/3Mi)
% 1.88/1.40 % (25353)Instruction limit reached!
% 1.88/1.40 % (25353)------------------------------
% 1.88/1.40 % (25353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.40 % (25353)Termination reason: Unknown
% 1.88/1.40 % (25353)Termination phase: Saturation
% 1.88/1.40
% 1.88/1.40 % (25353)Memory used [KB]: 5628
% 1.88/1.40 % (25353)Time elapsed: 0.011 s
% 1.88/1.40 % (25353)Instructions burned: 27 (million)
% 1.88/1.40 % (25353)------------------------------
% 1.88/1.40 % (25353)------------------------------
% 1.88/1.40 % (25358)Instruction limit reached!
% 1.88/1.40 % (25358)------------------------------
% 1.88/1.40 % (25358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.40 % (25358)Termination reason: Unknown
% 1.88/1.40 % (25358)Termination phase: shuffling
% 1.88/1.40
% 1.88/1.40 % (25358)Memory used [KB]: 1023
% 1.88/1.40 % (25358)Time elapsed: 0.002 s
% 1.88/1.40 % (25358)Instructions burned: 3 (million)
% 1.88/1.40 % (25358)------------------------------
% 1.88/1.40 % (25358)------------------------------
% 1.88/1.40 % (25356)First to succeed.
% 1.88/1.40 % (25356)Refutation found. Thanks to Tanya!
% 1.88/1.40 % SZS status Theorem for DTF2THF_25022
% 1.88/1.40 % SZS output start Proof for DTF2THF_25022
% 1.88/1.40 thf(type_def_6, type, elem: $tType).
% 1.88/1.40 thf(type_def_7, type, nat: $tType).
% 1.88/1.40 thf(type_def_8, type, list: $tType).
% 1.88/1.40 thf(func_def_0, type, isPer: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 1.88/1.40 thf(func_def_2, type, elem: $tType).
% 1.88/1.40 thf(func_def_3, type, elemStar: elem > elem > $o).
% 1.88/1.40 thf(func_def_4, type, nat: $tType).
% 1.88/1.40 thf(func_def_5, type, natStar: nat > nat > $o).
% 1.88/1.40 thf(func_def_6, type, zero: nat).
% 1.88/1.40 thf(func_def_7, type, suc: nat > nat).
% 1.88/1.40 thf(func_def_8, type, plus: nat > nat > nat).
% 1.88/1.40 thf(func_def_9, type, list: $tType).
% 1.88/1.40 thf(func_def_10, type, listStar: nat > list > list > $o).
% 1.88/1.40 thf(func_def_11, type, nil: list).
% 1.88/1.40 thf(func_def_12, type, cons: nat > elem > list > list).
% 1.88/1.40 thf(func_def_13, type, app: nat > nat > list > list > list).
% 1.88/1.40 thf(func_def_14, type, rev: nat > list > list).
% 1.88/1.40 thf(func_def_17, type, sK0: nat).
% 1.88/1.40 thf(func_def_18, type, sK1: elem).
% 1.88/1.40 thf(func_def_19, type, sK2: list).
% 1.88/1.40 thf(func_def_20, type, sK3: nat).
% 1.88/1.40 thf(func_def_21, type, sK4: list).
% 1.88/1.40 thf(f78,plain,(
% 1.88/1.40 $false),
% 1.88/1.40 inference(subsumption_resolution,[status(thm)],[f77,f76])).
% 1.88/1.40 thf(f76,plain,(
% 1.88/1.40 ((listStar @ (plus @ sK0 @ (suc @ sK3)) @ (rev @ (plus @ sK0 @ (suc @ sK3)) @ (app @ (suc @ sK0) @ sK3 @ (rev @ (suc @ sK0) @ (cons @ sK0 @ sK1 @ sK2)) @ sK4)) @ (rev @ (plus @ sK0 @ (suc @ sK3)) @ (app @ sK0 @ (suc @ sK3) @ (rev @ sK0 @ sK2) @ (cons @ sK3 @ sK1 @ sK4)))) != $true)),
% 1.88/1.40 inference(forward_demodulation,[status(thm)],[f73,f67])).
% 1.88/1.40 thf(f67,plain,(
% 1.88/1.40 ( ! [X0 : nat,X1 : nat] : (((plus @ (suc @ X0) @ X1) = (plus @ X0 @ (suc @ X1)))) )),
% 1.88/1.40 inference(cnf_transformation,[status(thm)],[f50])).
% 1.88/1.40 thf(f50,plain,(
% 1.88/1.40 ! [X0 : nat,X1 : nat] : ((plus @ (suc @ X0) @ X1) = (plus @ X0 @ (suc @ X1)))),
% 1.88/1.40 inference(rectify,[status(thm)],[f20])).
% 1.88/1.40 thf(f20,axiom,(
% 1.88/1.40 ! [X6 : nat,X10 : nat] : ((plus @ (suc @ X6) @ X10) = (plus @ X6 @ (suc @ X10)))),
% 1.88/1.40 file('/export/starexec/sandbox/tmp/tmp.lmrxhHgLnQ/DTF2THF_25022.p',plus_s_l_r)).
% 1.88/1.40 thf(f73,plain,(
% 1.88/1.40 ((listStar @ (plus @ (suc @ sK0) @ sK3) @ (rev @ (plus @ (suc @ sK0) @ sK3) @ (app @ (suc @ sK0) @ sK3 @ (rev @ (suc @ sK0) @ (cons @ sK0 @ sK1 @ sK2)) @ sK4)) @ (rev @ (plus @ sK0 @ (suc @ sK3)) @ (app @ sK0 @ (suc @ sK3) @ (rev @ sK0 @ sK2) @ (cons @ sK3 @ sK1 @ sK4)))) != $true)),
% 1.88/1.40 inference(cnf_transformation,[status(thm)],[f62])).
% 1.88/1.40 thf(f62,plain,(
% 1.88/1.40 ((listStar @ (plus @ (suc @ sK0) @ sK3) @ (rev @ (plus @ (suc @ sK0) @ sK3) @ (app @ (suc @ sK0) @ sK3 @ (rev @ (suc @ sK0) @ (cons @ sK0 @ sK1 @ sK2)) @ sK4)) @ (rev @ (plus @ sK0 @ (suc @ sK3)) @ (app @ sK0 @ (suc @ sK3) @ (rev @ sK0 @ sK2) @ (cons @ sK3 @ sK1 @ sK4)))) != $true) & ((listStar @ (plus @ (suc @ sK0) @ sK3) @ (rev @ (plus @ (suc @ sK0) @ sK3) @ (app @ (suc @ sK0) @ sK3 @ (rev @ (suc @ sK0) @ (cons @ sK0 @ sK1 @ sK2)) @ sK4)) @ (rev @ (plus @ (suc @ sK0) @ sK3) @ (app @ sK0 @ (suc @ sK3) @ (rev @ sK0 @ sK2) @ (cons @ sK3 @ sK1 @ sK4)))) = $true) & ((listStar @ sK3 @ sK4 @ sK4) = $true) & ((listStar @ sK0 @ sK2 @ sK2) = $true)),
% 1.88/1.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f56,f61])).
% 1.88/1.40 thf(f61,plain,(
% 1.88/1.40 ? [X0 : nat,X1 : elem,X2 : list,X3 : nat,X4 : list] : (($true != (listStar @ (plus @ (suc @ X0) @ X3) @ (rev @ (plus @ (suc @ X0) @ X3) @ (app @ (suc @ X0) @ X3 @ (rev @ (suc @ X0) @ (cons @ X0 @ X1 @ X2)) @ X4)) @ (rev @ (plus @ X0 @ (suc @ X3)) @ (app @ X0 @ (suc @ X3) @ (rev @ X0 @ X2) @ (cons @ X3 @ X1 @ X4))))) & ((listStar @ (plus @ (suc @ X0) @ X3) @ (rev @ (plus @ (suc @ X0) @ X3) @ (app @ (suc @ X0) @ X3 @ (rev @ (suc @ X0) @ (cons @ X0 @ X1 @ X2)) @ X4)) @ (rev @ (plus @ (suc @ X0) @ X3) @ (app @ X0 @ (suc @ X3) @ (rev @ X0 @ X2) @ (cons @ X3 @ X1 @ X4)))) = $true) & ($true = (listStar @ X3 @ X4 @ X4)) & ($true = (listStar @ X0 @ X2 @ X2))) => (((listStar @ (plus @ (suc @ sK0) @ sK3) @ (rev @ (plus @ (suc @ sK0) @ sK3) @ (app @ (suc @ sK0) @ sK3 @ (rev @ (suc @ sK0) @ (cons @ sK0 @ sK1 @ sK2)) @ sK4)) @ (rev @ (plus @ sK0 @ (suc @ sK3)) @ (app @ sK0 @ (suc @ sK3) @ (rev @ sK0 @ sK2) @ (cons @ sK3 @ sK1 @ sK4)))) != $true) & ((listStar @ (plus @ (suc @ sK0) @ sK3) @ (rev @ (plus @ (suc @ sK0) @ sK3) @ (app @ (suc @ sK0) @ sK3 @ (rev @ (suc @ sK0) @ (cons @ sK0 @ sK1 @ sK2)) @ sK4)) @ (rev @ (plus @ (suc @ sK0) @ sK3) @ (app @ sK0 @ (suc @ sK3) @ (rev @ sK0 @ sK2) @ (cons @ sK3 @ sK1 @ sK4)))) = $true) & ((listStar @ sK3 @ sK4 @ sK4) = $true) & ((listStar @ sK0 @ sK2 @ sK2) = $true))),
% 1.88/1.40 introduced(definition,[],[choice_axiom])).
% 1.88/1.40 thf(f56,plain,(
% 1.88/1.40 ? [X0 : nat,X1 : elem,X2 : list,X3 : nat,X4 : list] : (($true != (listStar @ (plus @ (suc @ X0) @ X3) @ (rev @ (plus @ (suc @ X0) @ X3) @ (app @ (suc @ X0) @ X3 @ (rev @ (suc @ X0) @ (cons @ X0 @ X1 @ X2)) @ X4)) @ (rev @ (plus @ X0 @ (suc @ X3)) @ (app @ X0 @ (suc @ X3) @ (rev @ X0 @ X2) @ (cons @ X3 @ X1 @ X4))))) & ((listStar @ (plus @ (suc @ X0) @ X3) @ (rev @ (plus @ (suc @ X0) @ X3) @ (app @ (suc @ X0) @ X3 @ (rev @ (suc @ X0) @ (cons @ X0 @ X1 @ X2)) @ X4)) @ (rev @ (plus @ (suc @ X0) @ X3) @ (app @ X0 @ (suc @ X3) @ (rev @ X0 @ X2) @ (cons @ X3 @ X1 @ X4)))) = $true) & ($true = (listStar @ X3 @ X4 @ X4)) & ($true = (listStar @ X0 @ X2 @ X2)))),
% 1.88/1.40 inference(flattening,[status(thm)],[f55])).
% 1.88/1.40 thf(f55,plain,(
% 1.88/1.40 ? [X0 : nat,X1 : elem,X2 : list,X3 : nat,X4 : list] : (((($true != (listStar @ (plus @ (suc @ X0) @ X3) @ (rev @ (plus @ (suc @ X0) @ X3) @ (app @ (suc @ X0) @ X3 @ (rev @ (suc @ X0) @ (cons @ X0 @ X1 @ X2)) @ X4)) @ (rev @ (plus @ X0 @ (suc @ X3)) @ (app @ X0 @ (suc @ X3) @ (rev @ X0 @ X2) @ (cons @ X3 @ X1 @ X4))))) & ((listStar @ (plus @ (suc @ X0) @ X3) @ (rev @ (plus @ (suc @ X0) @ X3) @ (app @ (suc @ X0) @ X3 @ (rev @ (suc @ X0) @ (cons @ X0 @ X1 @ X2)) @ X4)) @ (rev @ (plus @ (suc @ X0) @ X3) @ (app @ X0 @ (suc @ X3) @ (rev @ X0 @ X2) @ (cons @ X3 @ X1 @ X4)))) = $true)) & ($true = (listStar @ X3 @ X4 @ X4))) & ($true = (listStar @ X0 @ X2 @ X2)))),
% 1.88/1.40 inference(ennf_transformation,[status(thm)],[f33])).
% 1.88/1.40 thf(f33,plain,(
% 1.88/1.40 ~! [X0 : nat,X1 : elem,X2 : list,X3 : nat,X4 : list] : (($true = (listStar @ X0 @ X2 @ X2)) => (($true = (listStar @ X3 @ X4 @ X4)) => (((listStar @ (plus @ (suc @ X0) @ X3) @ (rev @ (plus @ (suc @ X0) @ X3) @ (app @ (suc @ X0) @ X3 @ (rev @ (suc @ X0) @ (cons @ X0 @ X1 @ X2)) @ X4)) @ (rev @ (plus @ (suc @ X0) @ X3) @ (app @ X0 @ (suc @ X3) @ (rev @ X0 @ X2) @ (cons @ X3 @ X1 @ X4)))) = $true) => ($true = (listStar @ (plus @ (suc @ X0) @ X3) @ (rev @ (plus @ (suc @ X0) @ X3) @ (app @ (suc @ X0) @ X3 @ (rev @ (suc @ X0) @ (cons @ X0 @ X1 @ X2)) @ X4)) @ (rev @ (plus @ X0 @ (suc @ X3)) @ (app @ X0 @ (suc @ X3) @ (rev @ X0 @ X2) @ (cons @ X3 @ X1 @ X4))))))))),
% 1.88/1.40 inference(fool_elimination,[status(thm)],[f32])).
% 1.88/1.40 thf(f32,plain,(
% 1.88/1.40 ~! [X0 : nat,X1 : elem,X2 : list,X3 : nat,X4 : list] : ((listStar @ X0 @ X2 @ X2) => ((listStar @ X3 @ X4 @ X4) => ((listStar @ (plus @ (suc @ X0) @ X3) @ (rev @ (plus @ (suc @ X0) @ X3) @ (app @ (suc @ X0) @ X3 @ (rev @ (suc @ X0) @ (cons @ X0 @ X1 @ X2)) @ X4)) @ (rev @ (plus @ (suc @ X0) @ X3) @ (app @ X0 @ (suc @ X3) @ (rev @ X0 @ X2) @ (cons @ X3 @ X1 @ X4)))) => (listStar @ (plus @ (suc @ X0) @ X3) @ (rev @ (plus @ (suc @ X0) @ X3) @ (app @ (suc @ X0) @ X3 @ (rev @ (suc @ X0) @ (cons @ X0 @ X1 @ X2)) @ X4)) @ (rev @ (plus @ X0 @ (suc @ X3)) @ (app @ X0 @ (suc @ X3) @ (rev @ X0 @ X2) @ (cons @ X3 @ X1 @ X4)))))))),
% 1.88/1.40 inference(rectify,[status(thm)],[f22])).
% 1.88/1.40 thf(f22,negated_conjecture,(
% 1.88/1.40 ~! [X6 : nat,X2 : elem,X16 : list,X14 : nat,X17 : list] : ((listStar @ X6 @ X16 @ X16) => ((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 @ X6 @ (suc @ X14) @ (rev @ X6 @ X16) @ (cons @ X14 @ X2 @ X17)))) => (listStar @ (plus @ (suc @ X6) @ X14) @ (rev @ (plus @ (suc @ X6) @ X14) @ (app @ (suc @ X6) @ X14 @ (rev @ (suc @ X6) @ (cons @ X6 @ X2 @ X16)) @ X17)) @ (rev @ (plus @ X6 @ (suc @ X14)) @ (app @ X6 @ (suc @ X14) @ (rev @ X6 @ X16) @ (cons @ X14 @ X2 @ X17)))))))),
% 1.88/1.40 inference(negated_conjecture,[status(cth)],[f21])).
% 1.88/1.40 thf(f21,conjecture,(
% 1.88/1.40 ! [X6 : nat,X2 : elem,X16 : list,X14 : nat,X17 : list] : ((listStar @ X6 @ X16 @ X16) => ((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 @ X6 @ (suc @ X14) @ (rev @ X6 @ X16) @ (cons @ X14 @ X2 @ X17)))) => (listStar @ (plus @ (suc @ X6) @ X14) @ (rev @ (plus @ (suc @ X6) @ X14) @ (app @ (suc @ X6) @ X14 @ (rev @ (suc @ X6) @ (cons @ X6 @ X2 @ X16)) @ X17)) @ (rev @ (plus @ X6 @ (suc @ X14)) @ (app @ X6 @ (suc @ X14) @ (rev @ X6 @ X16) @ (cons @ X14 @ X2 @ X17)))))))),
% 1.88/1.40 file('/export/starexec/sandbox/tmp/tmp.lmrxhHgLnQ/DTF2THF_25022.p',list_rev_invol_lem_indstep3)).
% 1.88/1.40 thf(f77,plain,(
% 1.88/1.40 ((listStar @ (plus @ sK0 @ (suc @ sK3)) @ (rev @ (plus @ sK0 @ (suc @ sK3)) @ (app @ (suc @ sK0) @ sK3 @ (rev @ (suc @ sK0) @ (cons @ sK0 @ sK1 @ sK2)) @ sK4)) @ (rev @ (plus @ sK0 @ (suc @ sK3)) @ (app @ sK0 @ (suc @ sK3) @ (rev @ sK0 @ sK2) @ (cons @ sK3 @ sK1 @ sK4)))) = $true)),
% 1.88/1.40 inference(forward_demodulation,[status(thm)],[f72,f67])).
% 1.88/1.40 thf(f72,plain,(
% 1.88/1.40 ((listStar @ (plus @ (suc @ sK0) @ sK3) @ (rev @ (plus @ (suc @ sK0) @ sK3) @ (app @ (suc @ sK0) @ sK3 @ (rev @ (suc @ sK0) @ (cons @ sK0 @ sK1 @ sK2)) @ sK4)) @ (rev @ (plus @ (suc @ sK0) @ sK3) @ (app @ sK0 @ (suc @ sK3) @ (rev @ sK0 @ sK2) @ (cons @ sK3 @ sK1 @ sK4)))) = $true)),
% 1.88/1.40 inference(cnf_transformation,[status(thm)],[f62])).
% 1.88/1.40 % SZS output end Proof for DTF2THF_25022
% 1.88/1.40 % (25356)------------------------------
% 1.88/1.40 % (25356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.40 % (25356)Termination reason: Refutation
% 1.88/1.40
% 1.88/1.40 % (25356)Memory used [KB]: 5628
% 1.88/1.40 % (25356)Time elapsed: 0.010 s
% 1.88/1.40 % (25356)Instructions burned: 8 (million)
% 1.88/1.40 % (25356)------------------------------
% 1.88/1.40 % (25356)------------------------------
% 1.88/1.40 % (25350)Success in time 0.024 s
%------------------------------------------------------------------------------