%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT386^1 : 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 : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:45:37 AM UTC 2026
% Result : Theorem 1.76s 1.43s
% Output : Refutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 47 ( 40 unt; 0 typ; 0 def)
% Number of atoms : 180 ( 43 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 578 ( 6 ~; 0 |; 0 &; 511 @)
% ( 0 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 14 usr; 7 con; 0-4 aty)
% ( 28 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 77 ( 36 ^; 41 !; 0 ?; 77 :)
% 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_31,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
sK2: list ).
thf(func_def_33,type,
sK3: nat ).
thf(f423,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f422]) ).
thf(f422,plain,
$true = $false,
inference(boolean_simplification,[status(thm)],[f421]) ).
thf(f421,plain,
( $true = ( ~ $true ) ),
inference(forward_demodulation,[status(thm)],[f418,f412]) ).
thf(f412,plain,
( $true
= ( listStar @ sK3 @ ( rev @ sK3 @ sK2 ) @ ( rev @ sK3 @ sK2 ) ) ),
inference(boolean_simplification,[status(thm)],[f411]) ).
thf(f411,plain,
( $true
= ( $true
=> ( listStar @ sK3 @ ( rev @ sK3 @ sK2 ) @ ( rev @ sK3 @ sK2 ) ) ) ),
inference(superposition,[status(thm)],[f261,f406]) ).
thf(f406,plain,
( $true
= ( listStar @ sK3 @ sK2 @ sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f389]) ).
thf(f389,plain,
( ( ( listStar @ sK3 @ sK2 @ sK2 )
=> ( listStar @ sK3 @ ( app @ sK3 @ zero @ ( rev @ sK3 @ sK2 ) @ nil ) @ ( rev @ sK3 @ sK2 ) ) )
= $false ),
inference(forward_demodulation,[status(thm)],[f385,f88]) ).
thf(f88,plain,
! [X1: nat] :
( ( plus @ X1 @ zero )
= X1 ),
inference(equality_proxy_clausification,[status(thm)],[f87]) ).
thf(f87,plain,
! [X1: nat] :
( $true
= ( ( plus @ X1 @ zero )
= X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f86]) ).
thf(f86,plain,
! [X1: nat] :
( ( ^ [Y0: nat] :
( ( plus @ Y0 @ zero )
= Y0 )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( plus @ Y0 @ zero )
= Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
thf(f43,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( plus @ Y0 @ zero )
= Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f42]) ).
thf(f42,plain,
! [X0: nat] :
( ( plus @ X0 @ zero )
= X0 ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
! [X10: nat] :
( ( plus @ X10 @ zero )
= X10 ),
file('/export/starexec/sandbox/tmp/tmp.wmjoDlDinY/DTF2THF_16462.p',plus_zero_r) ).
thf(f385,plain,
( ( ( listStar @ sK3 @ sK2 @ sK2 )
=> ( listStar @ ( plus @ sK3 @ zero ) @ ( app @ sK3 @ zero @ ( rev @ sK3 @ sK2 ) @ nil ) @ ( rev @ sK3 @ sK2 ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f383]) ).
thf(f383,plain,
( ( ^ [Y0: nat] :
( ( listStar @ Y0 @ sK2 @ sK2 )
=> ( listStar @ ( plus @ Y0 @ zero ) @ ( app @ Y0 @ zero @ ( rev @ Y0 @ sK2 ) @ nil ) @ ( rev @ Y0 @ sK2 ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f376]) ).
thf(f376,plain,
( $false
= ( !! @ nat
@ ^ [Y0: nat] :
( ( listStar @ Y0 @ sK2 @ sK2 )
=> ( listStar @ ( plus @ Y0 @ zero ) @ ( app @ Y0 @ zero @ ( rev @ Y0 @ sK2 ) @ nil ) @ ( rev @ Y0 @ sK2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f375]) ).
thf(f375,plain,
( ( ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( listStar @ ( plus @ Y1 @ zero ) @ ( app @ Y1 @ zero @ ( rev @ Y1 @ Y0 ) @ nil ) @ ( rev @ Y1 @ Y0 ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f365]) ).
thf(f365,plain,
( ( !! @ list
@ ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( listStar @ ( plus @ Y1 @ zero ) @ ( app @ Y1 @ zero @ ( rev @ Y1 @ Y0 ) @ nil ) @ ( rev @ Y1 @ Y0 ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
( ( ~ ( !! @ list
@ ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( listStar @ ( plus @ Y1 @ zero ) @ ( app @ Y1 @ zero @ ( rev @ Y1 @ Y0 ) @ nil ) @ ( rev @ Y1 @ Y0 ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f49]) ).
thf(f49,plain,
( ( ~ ( !! @ list
@ ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( listStar @ ( plus @ Y1 @ zero ) @ ( app @ Y1 @ zero @ ( rev @ Y1 @ Y0 ) @ nil ) @ ( rev @ Y1 @ Y0 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f48]) ).
thf(f48,plain,
~ ! [X0: nat,X1: list] :
( ( listStar @ X0 @ X1 @ X1 )
=> ( listStar @ ( plus @ X0 @ zero ) @ ( app @ X0 @ zero @ ( rev @ X0 @ X1 ) @ nil ) @ ( rev @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f18]) ).
thf(f18,negated_conjecture,
~ ! [X14: nat,X15: list] :
( ( listStar @ X14 @ X15 @ X15 )
=> ( listStar @ ( plus @ X14 @ zero ) @ ( app @ X14 @ zero @ ( rev @ X14 @ X15 ) @ nil ) @ ( rev @ X14 @ X15 ) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
thf(f17,conjecture,
! [X14: nat,X15: list] :
( ( listStar @ X14 @ X15 @ X15 )
=> ( listStar @ ( plus @ X14 @ zero ) @ ( app @ X14 @ zero @ ( rev @ X14 @ X15 ) @ nil ) @ ( rev @ X14 @ X15 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.wmjoDlDinY/DTF2THF_16462.p',list_rev_invol_lem_base_step2) ).
thf(f261,plain,
! [X2: list,X3: nat,X1: list] :
( ( ( listStar @ X3 @ X2 @ X1 )
=> ( listStar @ X3 @ ( rev @ X3 @ X2 ) @ ( rev @ X3 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f256]) ).
thf(f256,plain,
! [X2: list,X3: nat,X1: list] :
( $true
= ( ^ [Y0: nat] :
( ( listStar @ Y0 @ X2 @ X1 )
=> ( listStar @ Y0 @ ( rev @ Y0 @ X2 ) @ ( rev @ Y0 @ X1 ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f248]) ).
thf(f248,plain,
! [X2: list,X1: list] :
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( listStar @ Y0 @ X2 @ X1 )
=> ( listStar @ Y0 @ ( rev @ Y0 @ X2 ) @ ( rev @ Y0 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f247]) ).
thf(f247,plain,
! [X2: list,X1: list] :
( $true
= ( ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( ( listStar @ Y1 @ Y0 @ X1 )
=> ( listStar @ Y1 @ ( rev @ Y1 @ Y0 ) @ ( rev @ Y1 @ X1 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f240]) ).
thf(f240,plain,
! [X1: list] :
( $true
= ( !! @ list
@ ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( ( listStar @ Y1 @ Y0 @ X1 )
=> ( listStar @ Y1 @ ( rev @ Y1 @ Y0 ) @ ( rev @ Y1 @ X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f239]) ).
thf(f239,plain,
! [X1: list] :
( $true
= ( ^ [Y0: list] :
( !! @ list
@ ^ [Y1: list] :
( !! @ nat
@ ^ [Y2: nat] :
( ( listStar @ Y2 @ Y1 @ Y0 )
=> ( listStar @ Y2 @ ( rev @ Y2 @ Y1 ) @ ( rev @ Y2 @ Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( $true
= ( !! @ list
@ ^ [Y0: list] :
( !! @ list
@ ^ [Y1: list] :
( !! @ nat
@ ^ [Y2: nat] :
( ( listStar @ Y2 @ Y1 @ Y0 )
=> ( listStar @ Y2 @ ( rev @ Y2 @ Y1 ) @ ( rev @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f39,plain,
( $true
= ( !! @ list
@ ^ [Y0: list] :
( !! @ list
@ ^ [Y1: list] :
( !! @ nat
@ ^ [Y2: nat] :
( ( listStar @ Y2 @ Y1 @ Y0 )
=> ( listStar @ Y2 @ ( rev @ Y2 @ Y1 ) @ ( rev @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f38]) ).
thf(f38,plain,
! [X0: nat,X1: list,X2: list] :
( ( listStar @ X0 @ X1 @ X2 )
=> ( listStar @ X0 @ ( rev @ X0 @ X1 ) @ ( rev @ X0 @ X2 ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
! [X6: nat,X7: list,X11: list] :
( ( listStar @ X6 @ X7 @ X11 )
=> ( listStar @ X6 @ ( rev @ X6 @ X7 ) @ ( rev @ X6 @ X11 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.wmjoDlDinY/DTF2THF_16462.p',rev_tp_ax) ).
thf(f418,plain,
( $true
= ( ~ ( listStar @ sK3 @ ( rev @ sK3 @ sK2 ) @ ( rev @ sK3 @ sK2 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f415]) ).
thf(f415,plain,
( $true
= ( ( listStar @ sK3 @ ( rev @ sK3 @ sK2 ) @ ( rev @ sK3 @ sK2 ) )
=> $false ) ),
inference(superposition,[status(thm)],[f290,f408]) ).
thf(f408,plain,
( ( listStar @ sK3 @ ( app @ sK3 @ zero @ ( rev @ sK3 @ sK2 ) @ nil ) @ ( rev @ sK3 @ sK2 ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f407]) ).
thf(f407,plain,
( ( $true
=> ( listStar @ sK3 @ ( app @ sK3 @ zero @ ( rev @ sK3 @ sK2 ) @ nil ) @ ( rev @ sK3 @ sK2 ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f389,f406]) ).
thf(f290,plain,
! [X2: nat,X1: list] :
( $true
= ( ( listStar @ X2 @ X1 @ X1 )
=> ( listStar @ X2 @ ( app @ X2 @ zero @ X1 @ nil ) @ X1 ) ) ),
inference(forward_demodulation,[status(thm)],[f286,f88]) ).
thf(f286,plain,
! [X2: nat,X1: list] :
( $true
= ( ( listStar @ X2 @ X1 @ X1 )
=> ( listStar @ ( plus @ X2 @ zero ) @ ( app @ X2 @ zero @ X1 @ nil ) @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f284]) ).
thf(f284,plain,
! [X2: nat,X1: list] :
( $true
= ( ^ [Y0: nat] :
( ( listStar @ Y0 @ X1 @ X1 )
=> ( listStar @ ( plus @ Y0 @ zero ) @ ( app @ Y0 @ zero @ X1 @ nil ) @ X1 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f276]) ).
thf(f276,plain,
! [X1: list] :
( ( !! @ nat
@ ^ [Y0: nat] :
( ( listStar @ Y0 @ X1 @ X1 )
=> ( listStar @ ( plus @ Y0 @ zero ) @ ( app @ Y0 @ zero @ X1 @ nil ) @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f275]) ).
thf(f275,plain,
! [X1: list] :
( $true
= ( ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( listStar @ ( plus @ Y1 @ zero ) @ ( app @ Y1 @ zero @ Y0 @ nil ) @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( $true
= ( !! @ list
@ ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( listStar @ ( plus @ Y1 @ zero ) @ ( app @ Y1 @ zero @ Y0 @ nil ) @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
thf(f51,plain,
( $true
= ( !! @ list
@ ^ [Y0: list] :
( !! @ nat
@ ^ [Y1: nat] :
( ( listStar @ Y1 @ Y0 @ Y0 )
=> ( listStar @ ( plus @ Y1 @ zero ) @ ( app @ Y1 @ zero @ Y0 @ nil ) @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f50]) ).
thf(f50,plain,
! [X0: nat,X1: list] :
( ( listStar @ X0 @ X1 @ X1 )
=> ( listStar @ ( plus @ X0 @ zero ) @ ( app @ X0 @ zero @ X1 @ nil ) @ X1 ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,axiom,
! [X6: nat,X13: list] :
( ( listStar @ X6 @ X13 @ X13 )
=> ( listStar @ ( plus @ X6 @ zero ) @ ( app @ X6 @ zero @ X13 @ nil ) @ X13 ) ),
file('/export/starexec/sandbox/tmp/tmp.wmjoDlDinY/DTF2THF_16462.p',list_app_nil) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT386^1 : TPTP v9.2.1. Released v9.2.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n023.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 06:18:49 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.32/0.47 ---- Original DTF file ---
% 0.32/0.47 thf(spec,logic,$$dhol).
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 % File : DAT386^1 : TPTP v9.2.1. Released v9.2.0.
% 0.32/0.47 % Domain : Data Structures
% 0.32/0.47 % Problem : List involution lemma, base step 2
% 0.32/0.47 % Version : Especial.
% 0.32/0.47 % English : List involution lemma. The proof is by induction with a separate
% 0.32/0.47 % problem file for the base and step case (with multiple subcases)
% 0.32/0.47 % as well as the correct instantiation of the induction axiom for
% 0.32/0.47 % lists. The main file uses the conjectures of the other files as
% 0.32/0.47 % lemmas in order to prove the final result. To simplify proof
% 0.32/0.47 % search, the axioms in each problem file have been preselected.
% 0.32/0.47 % For the actual induction proof, it is sufficient to consider the
% 0.32/0.47 % "step" problem files.
% 0.32/0.47
% 0.32/0.47 % Refs : [RRB23] Rothgang et al. (2023), Theorem Proving in Dependently
% 0.32/0.47 % : [Rot25] Rothgang (2025), Email to Geoff Sutcliffe
% 0.32/0.47 % : [RK+25] Ranalter et al. (2025), The Dependently Typed Higher-O
% 0.32/0.47 % Source : [Rot25]
% 0.32/0.47 % Names : ListReversalInvolutionLemma/list-rev-invol-lem-base-step2.p [Rot25]
% 0.32/0.47
% 0.32/0.47 % Status : Theorem
% 0.32/0.47 % Rating : ? v9.2.0
% 0.32/0.47 % Syntax : Number of formulae : 19 ( 7 unt; 10 typ; 0 def)
% 0.32/0.47 % Number of atoms : 9 ( 9 equ; 0 cnn)
% 0.32/0.47 % Maximal formula atoms : 2 ( 1 avg)
% 0.32/0.47 % Number of connectives : 54 ( 3 ~; 0 |; 0 &; 47 @)
% 0.32/0.47 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.32/0.47 % Maximal formula depth : 8 ( 3 avg)
% 0.32/0.47 % Number of types : 3 ( 2 usr)
% 0.32/0.47 % Number of type decls : 10 ( 0 !>P; 3 !>D)
% 0.32/0.47 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.32/0.47 % Number of symbols : 9 ( 8 usr; 2 con; 0-4 aty)
% 0.32/0.47 % Number of variables : 19 ( 0 ^; 15 !; 0 ?; 19 :)
% 0.32/0.47 % ( 4 !>; 0 ?*; 0 @-; 0 @+)
% 0.32/0.47 % SPC : DH0_THM_EQU_NAR
% 0.32/0.47
% 0.32/0.47 % Comments :
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 thf(elem_type,type,
% 0.32/0.47 elem: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(nat_type,type,
% 0.32/0.47 nat: $tType ).
% 0.32/0.47
% 0.32/0.47 thf(zero_type,type,
% 0.32/0.47 zero: nat ).
% 0.32/0.47
% 0.32/0.47 thf(suc_type,type,
% 0.32/0.47 suc: nat > nat ).
% 0.32/0.47
% 0.32/0.47 thf(plus_type,type,
% 0.32/0.47 plus: nat > nat > nat ).
% 0.32/0.47
% 0.32/0.47 thf(list_type,type,
% 0.32/0.47 list: nat > $tType ).
% 0.32/0.47
% 0.32/0.47 thf(nil_type,type,
% 0.32/0.47 nil: list @ zero ).
% 0.32/0.47
% 0.32/0.47 thf(cons_type,type,
% 0.32/0.47 cons:
% 0.32/0.47 !>[N: nat] : ( elem > ( list @ N ) > ( list @ ( suc @ N ) ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(app_type,type,
% 0.32/0.47 app:
% 0.32/0.47 !>[N: nat,M: nat] : ( ( list @ N ) > ( list @ M ) > ( list @ ( plus @ N @ M ) ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(rev_type,type,
% 0.32/0.47 rev:
% 0.32/0.47 !>[N: nat] : ( ( list @ N ) > ( list @ N ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(peano1,axiom,
% 0.32/0.47 ! [N: nat] :
% 0.32/0.47 ( ( suc @ N )
% 0.32/0.47 != zero ) ).
% 0.32/0.47
% 0.32/0.47 thf(peano2,axiom,
% 0.32/0.47 ! [N: nat,M: nat] :
% 0.32/0.47 ( ( N != M )
% 0.32/0.47 => ( ( suc @ N )
% 0.32/0.47 != ( suc @ M ) ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(peano3,axiom,
% 0.32/0.47 ! [P: nat > $o] :
% 0.32/0.47 ( ( P @ zero )
% 0.32/0.47 => ( ! [M: nat] :
% 0.32/0.47 ( ( P @ M )
% 0.32/0.47 => ( P @ ( suc @ M ) ) )
% 0.32/0.47 => ! [N: nat] : ( P @ N ) ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(ax1,axiom,
% 0.32/0.47 ! [N: nat] :
% 0.32/0.47 ( ( plus @ zero @ N )
% 0.32/0.47 = N ) ).
% 0.32/0.47
% 0.32/0.47 thf(ax2,axiom,
% 0.32/0.47 ! [N: nat,M: nat] :
% 0.32/0.47 ( ( plus @ ( suc @ N ) @ M )
% 0.32/0.47 = ( suc @ ( plus @ N @ M ) ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(plus_zero_r,axiom,
% 0.32/0.47 ! [M: nat] :
% 0.32/0.47 ( ( plus @ M @ zero )
% 0.32/0.47 = M ) ).
% 0.32/0.47
% 0.32/0.47 thf(plus1r,axiom,
% 0.32/0.47 ! [N: nat] :
% 0.32/0.47 ( ( suc @ N )
% 0.32/0.47 = ( plus @ N @ ( suc @ zero ) ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(list_app_nil,axiom,
% 0.32/0.47 ! [N: nat,L: list @ N] :
% 0.32/0.47 ( ( app @ N @ zero @ L @ nil )
% 0.32/0.47 = L ) ).
% 0.32/0.47
% 0.32/0.47 thf(list_rev_invol_lem_base_step2,conjecture,
% 0.32/0.47 ! [M2: nat,L2: list @ M2] :
% 0.32/0.47 ( ( app @ M2 @ zero @ ( rev @ M2 @ L2 ) @ nil )
% 0.32/0.47 = ( rev @ M2 @ L2 ) ) ).
% 0.32/0.47
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 ------------------------
% 1.70/1.32 ---- Embedded in THF ---
% 1.70/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.70/1.32 %%% Generated on Tue Feb 24 06:18:50 EST 2026
% 1.70/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.70/1.32 %%% Logic specification used:
% 1.70/1.32 %%% thf(spec, logic, $$dhol).
% 1.70/1.32
% 1.70/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.wmjoDlDinY/DTF2DTF16462.p
% See solution above
% 1.70/1.32 ------------------------
% 1.70/1.33 ---- Cleaned THF ---
% 1.70/1.33 thf(is_per_type,type,
% 1.70/1.33 isPer:
% 1.70/1.33 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 1.70/1.33
% 1.70/1.33 thf(is_per,definition,
% 1.70/1.33 ! [A: $tType,AStar: A > A > $o] :
% 1.70/1.33 ( ( isPer @ A @ AStar )
% 1.70/1.33 <=> ( ! [X: A,Y: A] :
% 1.70/1.33 ( ( AStar @ X @ Y )
% 1.70/1.33 => ( AStar @ Y @ X ) )
% 1.70/1.33 & ! [X: A,Y: A,Z: A] :
% 1.70/1.33 ( ( AStar @ X @ Y )
% 1.70/1.33 => ( ( AStar @ Y @ Z )
% 1.70/1.33 => ( AStar @ X @ Z ) ) ) ) ) ).
% 1.70/1.33
% 1.70/1.33 thf(elem_type,type,
% 1.70/1.33 elem: $tType ).
% 1.70/1.33
% 1.70/1.33 thf(elemStar,type,
% 1.70/1.33 elemStar: elem > elem > $o ).
% 1.70/1.33
% 1.70/1.33 thf(elemStar_is_eq,axiom,
% 1.70/1.33 ! [X: elem,Y: elem] :
% 1.70/1.33 ( ( elemStar @ X @ Y )
% 1.70/1.33 <=> ( X = Y ) ) ).
% 1.70/1.33
% 1.70/1.33 thf(nat_type,type,
% 1.70/1.33 nat: $tType ).
% 1.70/1.33
% 1.70/1.33 thf(natStar,type,
% 1.70/1.33 natStar: nat > nat > $o ).
% 1.70/1.33
% 1.70/1.33 thf(natStar_is_eq,axiom,
% 1.70/1.33 ! [X: nat,Y: nat] :
% 1.70/1.33 ( ( natStar @ X @ Y )
% 1.70/1.33 <=> ( X = Y ) ) ).
% 1.70/1.33
% 1.70/1.33 thf(zero_type,type,
% 1.70/1.33 zero: nat ).
% 1.70/1.33
% 1.70/1.33 thf(suc_type,type,
% 1.70/1.33 suc: nat > nat ).
% 1.70/1.33
% 1.70/1.33 thf(plus_type,type,
% 1.70/1.33 plus: nat > nat > nat ).
% 1.70/1.33
% 1.70/1.33 thf(list_type,type,
% 1.70/1.33 list: $tType ).
% 1.70/1.33
% 1.70/1.33 thf(listStar,type,
% 1.70/1.33 listStar: nat > list > list > $o ).
% 1.70/1.33
% 1.70/1.33 thf('\'listStar\'_is_per',axiom,
% 1.70/1.33 ! [C: nat] : ( isPer @ list @ ( listStar @ C ) ) ).
% 1.70/1.33
% 1.70/1.33 thf(nil_type,type,
% 1.70/1.33 nil: list ).
% 1.70/1.33
% 1.70/1.33 thf(nil_tp_ax,axiom,
% 1.70/1.33 listStar @ zero @ nil @ nil ).
% 1.70/1.33
% 1.70/1.33 thf(cons_type,type,
% 1.70/1.33 cons: nat > elem > list > list ).
% 1.70/1.33
% 1.70/1.33 thf(cons_tp_ax,axiom,
% 1.70/1.33 ! [N: nat,D: elem,D0: list,D0_prime: list] :
% 1.70/1.33 ( ( listStar @ N @ D0 @ D0_prime )
% 1.70/1.33 => ( listStar @ ( suc @ N ) @ ( cons @ N @ D @ D0 ) @ ( cons @ N @ D @ D0_prime ) ) ) ).
% 1.70/1.33
% 1.70/1.33 thf(app_type,type,
% 1.70/1.33 app: nat > nat > list > list > list ).
% 1.70/1.33
% 1.70/1.33 thf(app_tp_ax,axiom,
% 1.70/1.33 ! [N: nat,M: nat,D: list,D_prime: list] :
% 1.70/1.33 ( ( listStar @ N @ D @ D_prime )
% 1.70/1.33 => ! [D0: list,D0_prime: list] :
% 1.70/1.33 ( ( listStar @ M @ D0 @ D0_prime )
% 1.70/1.33 => ( listStar @ ( plus @ N @ M ) @ ( app @ N @ M @ D @ D0 ) @ ( app @ N @ M @ D_prime @ D0_prime ) ) ) ) ).
% 1.70/1.33
% 1.70/1.33 thf(rev_type,type,
% 1.70/1.33 rev: nat > list > list ).
% 1.70/1.33
% 1.70/1.33 thf(rev_tp_ax,axiom,
% 1.70/1.33 ! [N: nat,D: list,D_prime: list] :
% 1.70/1.33 ( ( listStar @ N @ D @ D_prime )
% 1.70/1.33 => ( listStar @ N @ ( rev @ N @ D ) @ ( rev @ N @ D_prime ) ) ) ).
% 1.70/1.33
% 1.70/1.33 thf(peano1,axiom,
% 1.70/1.33 ! [N: nat] :
% 1.70/1.33 ( ( suc @ N )
% 1.70/1.33 != zero ) ).
% 1.70/1.33
% 1.70/1.33 thf(peano2,axiom,
% 1.70/1.33 ! [N: nat,M: nat] :
% 1.70/1.33 ( ( N != M )
% 1.70/1.33 => ( ( suc @ N )
% 1.70/1.33 != ( suc @ M ) ) ) ).
% 1.70/1.33
% 1.70/1.33 thf(peano3,axiom,
% 1.70/1.33 ! [P: nat > $o] :
% 1.70/1.33 ( ( P @ zero )
% 1.70/1.33 => ( ! [M: nat] :
% 1.70/1.33 ( ( P @ M )
% 1.70/1.33 => ( P @ ( suc @ M ) ) )
% 1.70/1.33 => ! [N: nat] : ( P @ N ) ) ) ).
% 1.70/1.33
% 1.70/1.33 thf(ax1,axiom,
% 1.70/1.33 ! [N: nat] :
% 1.70/1.33 ( ( plus @ zero @ N )
% 1.70/1.33 = N ) ).
% 1.70/1.33
% 1.70/1.33 thf(ax2,axiom,
% 1.70/1.33 ! [N: nat,M: nat] :
% 1.70/1.33 ( ( plus @ ( suc @ N ) @ M )
% 1.70/1.33 = ( suc @ ( plus @ N @ M ) ) ) ).
% 1.70/1.33
% 1.70/1.33 thf(plus_zero_r,axiom,
% 1.70/1.33 ! [M: nat] :
% 1.70/1.33 ( ( plus @ M @ zero )
% 1.70/1.33 = M ) ).
% 1.70/1.33
% 1.70/1.33 thf(plus1r,axiom,
% 1.70/1.33 ! [N: nat] :
% 1.70/1.33 ( ( suc @ N )
% 1.70/1.33 = ( plus @ N @ ( suc @ zero ) ) ) ).
% 1.70/1.33
% 1.70/1.33 thf(list_app_nil,axiom,
% 1.70/1.33 ! [N: nat,L: list] :
% 1.70/1.33 ( ( listStar @ N @ L @ L )
% 1.70/1.33 => ( listStar @ ( plus @ N @ zero ) @ ( app @ N @ zero @ L @ nil ) @ L ) ) ).
% 1.70/1.33
% 1.70/1.33 thf(list_rev_invol_lem_base_step2,conjecture,
% 1.70/1.33 ! [M2: nat,L2: list] :
% 1.70/1.33 ( ( listStar @ M2 @ L2 @ L2 )
% 1.70/1.33 => ( listStar @ ( plus @ M2 @ zero ) @ ( app @ M2 @ zero @ ( rev @ M2 @ L2 ) @ nil ) @ ( rev @ M2 @ L2 ) ) ) ).
% 1.70/1.33 ------------------------
% 1.70/1.35 % (16796)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_16462 for (2999ds/18Mi)
% 1.70/1.35 % (16795)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_16462 for (2999ds/275Mi)
% 1.70/1.35 % (16795)Refutation not found, incomplete strategy
% 1.70/1.35 % (16795)------------------------------
% 1.70/1.35 % (16795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.35 % (16795)Termination reason: Refutation not found, incomplete strategy
% 1.70/1.35
% 1.70/1.35
% 1.70/1.35 % (16795)Memory used [KB]: 5500
% 1.70/1.35 % (16795)Time elapsed: 0.003 s
% 1.70/1.35 % (16795)Instructions burned: 5 (million)
% 1.70/1.35 % (16795)------------------------------
% 1.70/1.35 % (16795)------------------------------
% 1.70/1.36 % (16796)Instruction limit reached!
% 1.70/1.36 % (16796)------------------------------
% 1.70/1.36 % (16796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.36 % (16796)Termination reason: Unknown
% 1.70/1.36 % (16796)Termination phase: Saturation
% 1.70/1.36
% 1.70/1.36 % (16796)Memory used [KB]: 5628
% 1.70/1.36 % (16796)Time elapsed: 0.008 s
% 1.70/1.36 % (16796)Instructions burned: 19 (million)
% 1.70/1.36 % (16796)------------------------------
% 1.70/1.36 % (16796)------------------------------
% 1.70/1.36 % (16790)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16462 for (2999ds/183Mi)
% 1.70/1.36 % (16791)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_16462 for (2999ds/4Mi)
% 1.70/1.36 % (16792)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_16462 for (2999ds/27Mi)
% 1.70/1.36 % (16793)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16462 for (2999ds/2Mi)
% 1.70/1.36 % (16794)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_16462 for (2999ds/2Mi)
% 1.70/1.36 % (16793)Instruction limit reached!
% 1.70/1.36 % (16793)------------------------------
% 1.70/1.36 % (16793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.36 % (16793)Termination reason: Unknown
% 1.70/1.36 % (16793)Termination phase: shuffling
% 1.70/1.36
% 1.70/1.36 % (16793)Memory used [KB]: 1023
% 1.70/1.36 % (16793)Time elapsed: 0.003 s
% 1.70/1.36 % (16793)Instructions burned: 2 (million)
% 1.70/1.36 % (16793)------------------------------
% 1.70/1.36 % (16793)------------------------------
% 1.70/1.36 % (16794)Instruction limit reached!
% 1.70/1.36 % (16794)------------------------------
% 1.70/1.36 % (16794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.36 % (16794)Termination reason: Unknown
% 1.70/1.36 % (16794)Termination phase: shuffling
% 1.70/1.36
% 1.70/1.36 % (16794)Memory used [KB]: 1023
% 1.70/1.36 % (16794)Time elapsed: 0.003 s
% 1.70/1.36 % (16794)Instructions burned: 2 (million)
% 1.70/1.36 % (16794)------------------------------
% 1.70/1.36 % (16794)------------------------------
% 1.70/1.36 % (16791)Instruction limit reached!
% 1.70/1.36 % (16791)------------------------------
% 1.70/1.36 % (16791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.36 % (16791)Termination reason: Unknown
% 1.70/1.36 % (16791)Termination phase: Property scanning
% 1.70/1.36
% 1.70/1.36 % (16791)Memory used [KB]: 1023
% 1.70/1.36 % (16791)Time elapsed: 0.004 s
% 1.70/1.36 % (16791)Instructions burned: 4 (million)
% 1.70/1.36 % (16791)------------------------------
% 1.70/1.36 % (16791)------------------------------
% 1.70/1.36 % (16797)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_16462 for (2999ds/3Mi)
% 1.70/1.36 % (16797)Instruction limit reached!
% 1.70/1.36 % (16797)------------------------------
% 1.70/1.36 % (16797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.36 % (16797)Termination reason: Unknown
% 1.70/1.36 % (16797)Termination phase: Property scanning
% 1.70/1.36
% 1.70/1.36 % (16797)Memory used [KB]: 1023
% 1.70/1.36 % (16797)Time elapsed: 0.003 s
% 1.70/1.36 % (16797)Instructions burned: 4 (million)
% 1.70/1.36 % (16797)------------------------------
% 1.70/1.36 % (16797)------------------------------
% 1.70/1.36 % (16798)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_16462 for (2999ds/37Mi)
% 1.70/1.37 % (16802)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_16462 for (2999ds/7Mi)
% 1.70/1.37 % (16792)Instruction limit reached!
% 1.70/1.37 % (16792)------------------------------
% 1.70/1.37 % (16792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.37 % (16792)Termination reason: Unknown
% 1.70/1.37 % (16792)Termination phase: Saturation
% 1.70/1.37
% 1.70/1.37 % (16792)Memory used [KB]: 5756
% 1.70/1.37 % (16792)Time elapsed: 0.020 s
% 1.70/1.37 % (16792)Instructions burned: 27 (million)
% 1.70/1.37 % (16792)------------------------------
% 1.70/1.37 % (16792)------------------------------
% 1.70/1.37 % (16799)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_16462 for (2999ds/15Mi)
% 1.70/1.37 % (16800)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_16462 for (2999ds/3Mi)
% 1.70/1.38 % (16801)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_16462 for (2999ds/1041Mi)
% 1.70/1.38 % (16802)Instruction limit reached!
% 1.70/1.38 % (16802)------------------------------
% 1.70/1.38 % (16802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.38 % (16802)Termination reason: Unknown
% 1.70/1.38 % (16802)Termination phase: Saturation
% 1.70/1.38
% 1.70/1.38 % (16802)Memory used [KB]: 1023
% 1.70/1.38 % (16802)Time elapsed: 0.004 s
% 1.70/1.38 % (16802)Instructions burned: 7 (million)
% 1.70/1.38 % (16802)------------------------------
% 1.70/1.38 % (16802)------------------------------
% 1.70/1.38 % (16800)Instruction limit reached!
% 1.70/1.38 % (16800)------------------------------
% 1.70/1.38 % (16800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.38 % (16800)Termination reason: Unknown
% 1.70/1.38 % (16800)Termination phase: Preprocessing 3
% 1.70/1.38
% 1.70/1.38 % (16800)Memory used [KB]: 1023
% 1.70/1.38 % (16800)Time elapsed: 0.004 s
% 1.70/1.38 % (16800)Instructions burned: 4 (million)
% 1.70/1.38 % (16800)------------------------------
% 1.70/1.38 % (16800)------------------------------
% 1.70/1.38 % (16798)Instruction limit reached!
% 1.70/1.38 % (16798)------------------------------
% 1.70/1.38 % (16798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.38 % (16798)Termination reason: Unknown
% 1.70/1.38 % (16798)Termination phase: Saturation
% 1.70/1.38
% 1.70/1.38 % (16798)Memory used [KB]: 5884
% 1.70/1.38 % (16798)Time elapsed: 0.013 s
% 1.70/1.38 % (16798)Instructions burned: 37 (million)
% 1.70/1.38 % (16798)------------------------------
% 1.70/1.38 % (16798)------------------------------
% 1.70/1.38 % (16799)Instruction limit reached!
% 1.70/1.38 % (16799)------------------------------
% 1.70/1.38 % (16799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.38 % (16799)Termination reason: Unknown
% 1.70/1.38 % (16799)Termination phase: Saturation
% 1.70/1.38
% 1.70/1.38 % (16799)Memory used [KB]: 5756
% 1.70/1.38 % (16799)Time elapsed: 0.012 s
% 1.70/1.38 % (16799)Instructions burned: 16 (million)
% 1.70/1.38 % (16799)------------------------------
% 1.70/1.38 % (16799)------------------------------
% 1.70/1.39 % (16804)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_16462 for (2999ds/3Mi)
% 1.70/1.39 % (16806)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_16462 for (2999ds/7Mi)
% 1.70/1.39 % (16804)Instruction limit reached!
% 1.70/1.39 % (16804)------------------------------
% 1.70/1.39 % (16804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.39 % (16804)Termination reason: Unknown
% 1.70/1.39 % (16804)Termination phase: Preprocessing 3
% 1.70/1.39
% 1.70/1.39 % (16804)Memory used [KB]: 1023
% 1.70/1.39 % (16804)Time elapsed: 0.003 s
% 1.70/1.39 % (16804)Instructions burned: 4 (million)
% 1.70/1.39 % (16804)------------------------------
% 1.70/1.39 % (16804)------------------------------
% 1.70/1.39 % (16806)Instruction limit reached!
% 1.70/1.39 % (16806)------------------------------
% 1.70/1.39 % (16806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.39 % (16806)Termination reason: Unknown
% 1.70/1.39 % (16806)Termination phase: Saturation
% 1.70/1.39
% 1.70/1.39 % (16806)Memory used [KB]: 5500
% 1.70/1.39 % (16806)Time elapsed: 0.003 s
% 1.70/1.39 % (16806)Instructions burned: 7 (million)
% 1.70/1.39 % (16806)------------------------------
% 1.70/1.39 % (16806)------------------------------
% 1.70/1.39 % (16803)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_16462 for (2999ds/16Mi)
% 1.70/1.39 % (16805)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_16462 for (2999ds/3Mi)
% 1.70/1.40 % (16805)Instruction limit reached!
% 1.70/1.40 % (16805)------------------------------
% 1.70/1.40 % (16805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.40 % (16805)Termination reason: Unknown
% 1.70/1.40 % (16805)Termination phase: Preprocessing 3
% 1.70/1.40
% 1.70/1.40 % (16805)Memory used [KB]: 1023
% 1.70/1.40 % (16805)Time elapsed: 0.004 s
% 1.70/1.40 % (16805)Instructions burned: 4 (million)
% 1.70/1.40 % (16805)------------------------------
% 1.70/1.40 % (16805)------------------------------
% 1.76/1.40 % (16808)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_16462 for (2999ds/4Mi)
% 1.76/1.40 % (16809)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_16462 for (2999ds/18Mi)
% 1.76/1.40 % (16808)Instruction limit reached!
% 1.76/1.40 % (16808)------------------------------
% 1.76/1.40 % (16808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.40 % (16808)Termination reason: Unknown
% 1.76/1.40 % (16808)Termination phase: Property scanning
% 1.76/1.40
% 1.76/1.40 % (16808)Memory used [KB]: 1023
% 1.76/1.40 % (16808)Time elapsed: 0.003 s
% 1.76/1.40 % (16808)Instructions burned: 4 (million)
% 1.76/1.40 % (16808)------------------------------
% 1.76/1.40 % (16808)------------------------------
% 1.76/1.40 % (16803)Instruction limit reached!
% 1.76/1.40 % (16803)------------------------------
% 1.76/1.40 % (16803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.40 % (16803)Termination reason: Unknown
% 1.76/1.40 % (16803)Termination phase: Saturation
% 1.76/1.40
% 1.76/1.40 % (16803)Memory used [KB]: 5756
% 1.76/1.40 % (16803)Time elapsed: 0.012 s
% 1.76/1.40 % (16803)Instructions burned: 16 (million)
% 1.76/1.40 % (16803)------------------------------
% 1.76/1.40 % (16803)------------------------------
% 1.76/1.40 % (16807)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_16462 for (2999ds/3Mi)
% 1.76/1.40 % (16807)Instruction limit reached!
% 1.76/1.40 % (16807)------------------------------
% 1.76/1.40 % (16807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.40 % (16807)Termination reason: Unknown
% 1.76/1.40 % (16807)Termination phase: shuffling
% 1.76/1.40
% 1.76/1.40 % (16807)Memory used [KB]: 1023
% 1.76/1.40 % (16807)Time elapsed: 0.003 s
% 1.76/1.40 % (16807)Instructions burned: 3 (million)
% 1.76/1.40 % (16807)------------------------------
% 1.76/1.40 % (16807)------------------------------
% 1.76/1.40 % (16809)Instruction limit reached!
% 1.76/1.40 % (16809)------------------------------
% 1.76/1.40 % (16809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.40 % (16809)Termination reason: Unknown
% 1.76/1.40 % (16809)Termination phase: Saturation
% 1.76/1.40
% 1.76/1.40 % (16809)Memory used [KB]: 5628
% 1.76/1.40 % (16809)Time elapsed: 0.007 s
% 1.76/1.40 % (16809)Instructions burned: 18 (million)
% 1.76/1.40 % (16809)------------------------------
% 1.76/1.40 % (16809)------------------------------
% 1.76/1.41 % (16811)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_16462 for (2999ds/6Mi)
% 1.76/1.41 % (16811)Instruction limit reached!
% 1.76/1.41 % (16811)------------------------------
% 1.76/1.41 % (16811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.41 % (16811)Termination reason: Unknown
% 1.76/1.41 % (16811)Termination phase: Saturation
% 1.76/1.41
% 1.76/1.41 % (16811)Memory used [KB]: 5500
% 1.76/1.41 % (16811)Time elapsed: 0.004 s
% 1.76/1.41 % (16811)Instructions burned: 7 (million)
% 1.76/1.41 % (16811)------------------------------
% 1.76/1.41 % (16811)------------------------------
% 1.76/1.41 % (16814)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_16462 for (2999ds/5Mi)
% 1.76/1.41 % (16810)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_16462 for (2999ds/710Mi)
% 1.76/1.41 % (16814)Instruction limit reached!
% 1.76/1.41 % (16814)------------------------------
% 1.76/1.41 % (16814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.41 % (16814)Termination reason: Unknown
% 1.76/1.41 % (16814)Termination phase: Saturation
% 1.76/1.41
% 1.76/1.41 % (16814)Memory used [KB]: 5500
% 1.76/1.41 % (16814)Time elapsed: 0.003 s
% 1.76/1.41 % (16814)Instructions burned: 7 (million)
% 1.76/1.41 % (16814)------------------------------
% 1.76/1.41 % (16814)------------------------------
% 1.76/1.42 % (16812)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_16462 for (2999ds/902Mi)
% 1.76/1.42 % (16813)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_16462 for (2999ds/21Mi)
% 1.76/1.42 % (16815)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_16462 for (2999ds/6Mi)
% 1.76/1.42 % (16815)Instruction limit reached!
% 1.76/1.42 % (16815)------------------------------
% 1.76/1.42 % (16815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.42 % (16815)Termination reason: Unknown
% 1.76/1.42 % (16815)Termination phase: Saturation
% 1.76/1.42
% 1.76/1.42 % (16815)Memory used [KB]: 5500
% 1.76/1.42 % (16815)Time elapsed: 0.004 s
% 1.76/1.42 % (16815)Instructions burned: 7 (million)
% 1.76/1.42 % (16815)------------------------------
% 1.76/1.42 % (16815)------------------------------
% 1.76/1.42 % (16816)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_16462 for (2999ds/377Mi)
% 1.76/1.43 % (16801)First to succeed.
% 1.76/1.43 % (16801)Refutation found. Thanks to Tanya!
% 1.76/1.43 % SZS status Theorem for DTF2THF_16462
% 1.76/1.43 % SZS output start Proof for DTF2THF_16462
% 1.76/1.43 thf(type_def_6, type, elem: $tType).
% 1.76/1.43 thf(type_def_7, type, nat: $tType).
% 1.76/1.43 thf(type_def_8, type, list: $tType).
% 1.76/1.43 thf(func_def_0, type, isPer: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 1.76/1.43 thf(func_def_2, type, elem: $tType).
% 1.76/1.43 thf(func_def_3, type, elemStar: elem > elem > $o).
% 1.76/1.43 thf(func_def_4, type, nat: $tType).
% 1.76/1.43 thf(func_def_5, type, natStar: nat > nat > $o).
% 1.76/1.43 thf(func_def_6, type, zero: nat).
% 1.76/1.43 thf(func_def_7, type, suc: nat > nat).
% 1.76/1.43 thf(func_def_8, type, plus: nat > nat > nat).
% 1.76/1.43 thf(func_def_9, type, list: $tType).
% 1.76/1.43 thf(func_def_10, type, listStar: nat > list > list > $o).
% 1.76/1.43 thf(func_def_11, type, nil: list).
% 1.76/1.43 thf(func_def_12, type, cons: nat > elem > list > list).
% 1.76/1.43 thf(func_def_13, type, app: nat > nat > list > list > list).
% 1.76/1.43 thf(func_def_14, type, rev: nat > list > list).
% 1.76/1.43 thf(func_def_31, type, ph1: !>[X0: $tType]:(X0)).
% 1.76/1.43 thf(func_def_32, type, sK2: list).
% 1.76/1.43 thf(func_def_33, type, sK3: nat).
% 1.76/1.43 thf(f423,plain,(
% 1.76/1.43 $false),
% 1.76/1.43 inference(trivial_inequality_removal,[status(thm)],[f422])).
% 1.76/1.43 thf(f422,plain,(
% 1.76/1.43 ($true = $false)),
% 1.76/1.43 inference(boolean_simplification,[status(thm)],[f421])).
% 1.76/1.43 thf(f421,plain,(
% 1.76/1.43 ($true = (~ $true))),
% 1.76/1.43 inference(forward_demodulation,[status(thm)],[f418,f412])).
% 1.76/1.43 thf(f412,plain,(
% 1.76/1.43 ($true = (listStar @ sK3 @ (rev @ sK3 @ sK2) @ (rev @ sK3 @ sK2)))),
% 1.76/1.43 inference(boolean_simplification,[status(thm)],[f411])).
% 1.76/1.43 thf(f411,plain,(
% 1.76/1.43 ($true = ($true => (listStar @ sK3 @ (rev @ sK3 @ sK2) @ (rev @ sK3 @ sK2))))),
% 1.76/1.43 inference(superposition,[status(thm)],[f261,f406])).
% 1.76/1.43 thf(f406,plain,(
% 1.76/1.43 ($true = (listStar @ sK3 @ sK2 @ sK2))),
% 1.76/1.43 inference(binary_proxy_clausification,[status(thm)],[f389])).
% 1.76/1.43 thf(f389,plain,(
% 1.76/1.43 (((listStar @ sK3 @ sK2 @ sK2) => (listStar @ sK3 @ (app @ sK3 @ zero @ (rev @ sK3 @ sK2) @ nil) @ (rev @ sK3 @ sK2))) = $false)),
% 1.76/1.43 inference(forward_demodulation,[status(thm)],[f385,f88])).
% 1.76/1.43 thf(f88,plain,(
% 1.76/1.43 ( ! [X1 : nat] : (((plus @ X1 @ zero) = X1)) )),
% 1.76/1.43 inference(equality_proxy_clausification,[status(thm)],[f87])).
% 1.76/1.43 thf(f87,plain,(
% 1.76/1.43 ( ! [X1 : nat] : (($true = ((plus @ X1 @ zero) = X1))) )),
% 1.76/1.43 inference(beta_eta_normalization,[status(thm)],[f86])).
% 1.76/1.43 thf(f86,plain,(
% 1.76/1.43 ( ! [X1 : nat] : ((((^[Y0 : nat]: ((plus @ Y0 @ zero) = Y0)) @ X1) = $true)) )),
% 1.76/1.43 inference(pi_clausification,[status(thm)],[f64])).
% 1.76/1.43 thf(f64,plain,(
% 1.76/1.43 ($true = (!! @ nat @ (^[Y0 : nat]: ((plus @ Y0 @ zero) = Y0))))),
% 1.76/1.43 inference(cnf_transformation,[status(thm)],[f43])).
% 1.76/1.43 thf(f43,plain,(
% 1.76/1.43 ($true = (!! @ nat @ (^[Y0 : nat]: ((plus @ Y0 @ zero) = Y0))))),
% 1.76/1.43 inference(fool_elimination,[status(thm)],[f42])).
% 1.76/1.43 thf(f42,plain,(
% 1.76/1.43 ! [X0 : nat] : ((plus @ X0 @ zero) = X0)),
% 1.76/1.43 inference(rectify,[status(thm)],[f14])).
% 1.76/1.43 thf(f14,axiom,(
% 1.76/1.43 ! [X10 : nat] : ((plus @ X10 @ zero) = X10)),
% 1.76/1.43 file('/export/starexec/sandbox/tmp/tmp.wmjoDlDinY/DTF2THF_16462.p',plus_zero_r)).
% 1.76/1.43 thf(f385,plain,(
% 1.76/1.43 (((listStar @ sK3 @ sK2 @ sK2) => (listStar @ (plus @ sK3 @ zero) @ (app @ sK3 @ zero @ (rev @ sK3 @ sK2) @ nil) @ (rev @ sK3 @ sK2))) = $false)),
% 1.76/1.43 inference(beta_eta_normalization,[status(thm)],[f383])).
% 1.76/1.43 thf(f383,plain,(
% 1.76/1.43 (((^[Y0 : nat]: ((listStar @ Y0 @ sK2 @ sK2) => (listStar @ (plus @ Y0 @ zero) @ (app @ Y0 @ zero @ (rev @ Y0 @ sK2) @ nil) @ (rev @ Y0 @ sK2)))) @ sK3) = $false)),
% 1.76/1.43 inference(sigma_clausification,[status(thm)],[f376])).
% 1.76/1.43 thf(f376,plain,(
% 1.76/1.43 ($false = (!! @ nat @ (^[Y0 : nat]: ((listStar @ Y0 @ sK2 @ sK2) => (listStar @ (plus @ Y0 @ zero) @ (app @ Y0 @ zero @ (rev @ Y0 @ sK2) @ nil) @ (rev @ Y0 @ sK2))))))),
% 1.76/1.43 inference(beta_eta_normalization,[status(thm)],[f375])).
% 1.76/1.43 thf(f375,plain,(
% 1.76/1.43 (((^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ Y1 @ Y0 @ Y0) => (listStar @ (plus @ Y1 @ zero) @ (app @ Y1 @ zero @ (rev @ Y1 @ Y0) @ nil) @ (rev @ Y1 @ Y0)))))) @ sK2) = $false)),
% 1.76/1.43 inference(sigma_clausification,[status(thm)],[f365])).
% 1.76/1.43 thf(f365,plain,(
% 1.76/1.43 ((!! @ list @ (^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ Y1 @ Y0 @ Y0) => (listStar @ (plus @ Y1 @ zero) @ (app @ Y1 @ zero @ (rev @ Y1 @ Y0) @ nil) @ (rev @ Y1 @ Y0))))))) = $false)),
% 1.76/1.43 inference(not_proxy_clausification,[status(thm)],[f68])).
% 1.76/1.43 thf(f68,plain,(
% 1.76/1.43 ((~ (!! @ list @ (^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ Y1 @ Y0 @ Y0) => (listStar @ (plus @ Y1 @ zero) @ (app @ Y1 @ zero @ (rev @ Y1 @ Y0) @ nil) @ (rev @ Y1 @ Y0)))))))) = $true)),
% 1.76/1.43 inference(cnf_transformation,[status(thm)],[f49])).
% 1.76/1.43 thf(f49,plain,(
% 1.76/1.43 ((~ (!! @ list @ (^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ Y1 @ Y0 @ Y0) => (listStar @ (plus @ Y1 @ zero) @ (app @ Y1 @ zero @ (rev @ Y1 @ Y0) @ nil) @ (rev @ Y1 @ Y0)))))))) = $true)),
% 1.76/1.43 inference(fool_elimination,[status(thm)],[f48])).
% 1.76/1.43 thf(f48,plain,(
% 1.76/1.43 ~! [X0 : nat,X1 : list] : ((listStar @ X0 @ X1 @ X1) => (listStar @ (plus @ X0 @ zero) @ (app @ X0 @ zero @ (rev @ X0 @ X1) @ nil) @ (rev @ X0 @ X1)))),
% 1.76/1.43 inference(rectify,[status(thm)],[f18])).
% 1.76/1.43 thf(f18,negated_conjecture,(
% 1.76/1.43 ~! [X14 : nat,X15 : list] : ((listStar @ X14 @ X15 @ X15) => (listStar @ (plus @ X14 @ zero) @ (app @ X14 @ zero @ (rev @ X14 @ X15) @ nil) @ (rev @ X14 @ X15)))),
% 1.76/1.43 inference(negated_conjecture,[status(cth)],[f17])).
% 1.76/1.43 thf(f17,conjecture,(
% 1.76/1.43 ! [X14 : nat,X15 : list] : ((listStar @ X14 @ X15 @ X15) => (listStar @ (plus @ X14 @ zero) @ (app @ X14 @ zero @ (rev @ X14 @ X15) @ nil) @ (rev @ X14 @ X15)))),
% 1.76/1.43 file('/export/starexec/sandbox/tmp/tmp.wmjoDlDinY/DTF2THF_16462.p',list_rev_invol_lem_base_step2)).
% 1.76/1.43 thf(f261,plain,(
% 1.76/1.43 ( ! [X2 : list,X3 : nat,X1 : list] : ((((listStar @ X3 @ X2 @ X1) => (listStar @ X3 @ (rev @ X3 @ X2) @ (rev @ X3 @ X1))) = $true)) )),
% 1.76/1.43 inference(beta_eta_normalization,[status(thm)],[f256])).
% 1.76/1.43 thf(f256,plain,(
% 1.76/1.43 ( ! [X2 : list,X3 : nat,X1 : list] : (($true = ((^[Y0 : nat]: ((listStar @ Y0 @ X2 @ X1) => (listStar @ Y0 @ (rev @ Y0 @ X2) @ (rev @ Y0 @ X1)))) @ X3))) )),
% 1.76/1.43 inference(pi_clausification,[status(thm)],[f248])).
% 1.76/1.43 thf(f248,plain,(
% 1.76/1.43 ( ! [X2 : list,X1 : list] : (($true = (!! @ nat @ (^[Y0 : nat]: ((listStar @ Y0 @ X2 @ X1) => (listStar @ Y0 @ (rev @ Y0 @ X2) @ (rev @ Y0 @ X1))))))) )),
% 1.76/1.43 inference(beta_eta_normalization,[status(thm)],[f247])).
% 1.76/1.43 thf(f247,plain,(
% 1.76/1.43 ( ! [X2 : list,X1 : list] : (($true = ((^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ Y1 @ Y0 @ X1) => (listStar @ Y1 @ (rev @ Y1 @ Y0) @ (rev @ Y1 @ X1)))))) @ X2))) )),
% 1.76/1.43 inference(pi_clausification,[status(thm)],[f240])).
% 1.76/1.43 thf(f240,plain,(
% 1.76/1.43 ( ! [X1 : list] : (($true = (!! @ list @ (^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ Y1 @ Y0 @ X1) => (listStar @ Y1 @ (rev @ Y1 @ Y0) @ (rev @ Y1 @ X1))))))))) )),
% 1.76/1.43 inference(beta_eta_normalization,[status(thm)],[f239])).
% 1.76/1.43 thf(f239,plain,(
% 1.76/1.43 ( ! [X1 : list] : (($true = ((^[Y0 : list]: (!! @ list @ (^[Y1 : list]: (!! @ nat @ (^[Y2 : nat]: ((listStar @ Y2 @ Y1 @ Y0) => (listStar @ Y2 @ (rev @ Y2 @ Y1) @ (rev @ Y2 @ Y0)))))))) @ X1))) )),
% 1.76/1.43 inference(pi_clausification,[status(thm)],[f55])).
% 1.76/1.43 thf(f55,plain,(
% 1.76/1.43 ($true = (!! @ list @ (^[Y0 : list]: (!! @ list @ (^[Y1 : list]: (!! @ nat @ (^[Y2 : nat]: ((listStar @ Y2 @ Y1 @ Y0) => (listStar @ Y2 @ (rev @ Y2 @ Y1) @ (rev @ Y2 @ Y0))))))))))),
% 1.76/1.43 inference(cnf_transformation,[status(thm)],[f39])).
% 1.76/1.43 thf(f39,plain,(
% 1.76/1.43 ($true = (!! @ list @ (^[Y0 : list]: (!! @ list @ (^[Y1 : list]: (!! @ nat @ (^[Y2 : nat]: ((listStar @ Y2 @ Y1 @ Y0) => (listStar @ Y2 @ (rev @ Y2 @ Y1) @ (rev @ Y2 @ Y0))))))))))),
% 1.76/1.43 inference(fool_elimination,[status(thm)],[f38])).
% 1.76/1.43 thf(f38,plain,(
% 1.76/1.43 ! [X0 : nat,X1 : list,X2 : list] : ((listStar @ X0 @ X1 @ X2) => (listStar @ X0 @ (rev @ X0 @ X1) @ (rev @ X0 @ X2)))),
% 1.76/1.43 inference(rectify,[status(thm)],[f8])).
% 1.76/1.43 thf(f8,axiom,(
% 1.76/1.43 ! [X6 : nat,X7 : list,X11 : list] : ((listStar @ X6 @ X7 @ X11) => (listStar @ X6 @ (rev @ X6 @ X7) @ (rev @ X6 @ X11)))),
% 1.76/1.43 file('/export/starexec/sandbox/tmp/tmp.wmjoDlDinY/DTF2THF_16462.p',rev_tp_ax)).
% 1.76/1.43 thf(f418,plain,(
% 1.76/1.43 ($true = (~ (listStar @ sK3 @ (rev @ sK3 @ sK2) @ (rev @ sK3 @ sK2))))),
% 1.76/1.43 inference(boolean_simplification,[status(thm)],[f415])).
% 1.76/1.43 thf(f415,plain,(
% 1.76/1.43 ($true = ((listStar @ sK3 @ (rev @ sK3 @ sK2) @ (rev @ sK3 @ sK2)) => $false))),
% 1.76/1.43 inference(superposition,[status(thm)],[f290,f408])).
% 1.76/1.43 thf(f408,plain,(
% 1.76/1.43 ((listStar @ sK3 @ (app @ sK3 @ zero @ (rev @ sK3 @ sK2) @ nil) @ (rev @ sK3 @ sK2)) = $false)),
% 1.76/1.43 inference(boolean_simplification,[status(thm)],[f407])).
% 1.76/1.43 thf(f407,plain,(
% 1.76/1.43 (($true => (listStar @ sK3 @ (app @ sK3 @ zero @ (rev @ sK3 @ sK2) @ nil) @ (rev @ sK3 @ sK2))) = $false)),
% 1.76/1.43 inference(backward_demodulation,[status(thm)],[f389,f406])).
% 1.76/1.43 thf(f290,plain,(
% 1.76/1.43 ( ! [X2 : nat,X1 : list] : (($true = ((listStar @ X2 @ X1 @ X1) => (listStar @ X2 @ (app @ X2 @ zero @ X1 @ nil) @ X1)))) )),
% 1.76/1.43 inference(forward_demodulation,[status(thm)],[f286,f88])).
% 1.76/1.43 thf(f286,plain,(
% 1.76/1.43 ( ! [X2 : nat,X1 : list] : (($true = ((listStar @ X2 @ X1 @ X1) => (listStar @ (plus @ X2 @ zero) @ (app @ X2 @ zero @ X1 @ nil) @ X1)))) )),
% 1.76/1.43 inference(beta_eta_normalization,[status(thm)],[f284])).
% 1.76/1.43 thf(f284,plain,(
% 1.76/1.43 ( ! [X2 : nat,X1 : list] : (($true = ((^[Y0 : nat]: ((listStar @ Y0 @ X1 @ X1) => (listStar @ (plus @ Y0 @ zero) @ (app @ Y0 @ zero @ X1 @ nil) @ X1))) @ X2))) )),
% 1.76/1.43 inference(pi_clausification,[status(thm)],[f276])).
% 1.76/1.43 thf(f276,plain,(
% 1.76/1.43 ( ! [X1 : list] : (((!! @ nat @ (^[Y0 : nat]: ((listStar @ Y0 @ X1 @ X1) => (listStar @ (plus @ Y0 @ zero) @ (app @ Y0 @ zero @ X1 @ nil) @ X1)))) = $true)) )),
% 1.76/1.43 inference(beta_eta_normalization,[status(thm)],[f275])).
% 1.76/1.43 thf(f275,plain,(
% 1.76/1.43 ( ! [X1 : list] : (($true = ((^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ Y1 @ Y0 @ Y0) => (listStar @ (plus @ Y1 @ zero) @ (app @ Y1 @ zero @ Y0 @ nil) @ Y0))))) @ X1))) )),
% 1.76/1.43 inference(pi_clausification,[status(thm)],[f56])).
% 1.76/1.43 thf(f56,plain,(
% 1.76/1.43 ($true = (!! @ list @ (^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ Y1 @ Y0 @ Y0) => (listStar @ (plus @ Y1 @ zero) @ (app @ Y1 @ zero @ Y0 @ nil) @ Y0)))))))),
% 1.76/1.43 inference(cnf_transformation,[status(thm)],[f51])).
% 1.76/1.43 thf(f51,plain,(
% 1.76/1.43 ($true = (!! @ list @ (^[Y0 : list]: (!! @ nat @ (^[Y1 : nat]: ((listStar @ Y1 @ Y0 @ Y0) => (listStar @ (plus @ Y1 @ zero) @ (app @ Y1 @ zero @ Y0 @ nil) @ Y0)))))))),
% 1.76/1.43 inference(fool_elimination,[status(thm)],[f50])).
% 1.76/1.43 thf(f50,plain,(
% 1.76/1.43 ! [X0 : nat,X1 : list] : ((listStar @ X0 @ X1 @ X1) => (listStar @ (plus @ X0 @ zero) @ (app @ X0 @ zero @ X1 @ nil) @ X1))),
% 1.76/1.43 inference(rectify,[status(thm)],[f16])).
% 1.76/1.43 thf(f16,axiom,(
% 1.76/1.43 ! [X6 : nat,X13 : list] : ((listStar @ X6 @ X13 @ X13) => (listStar @ (plus @ X6 @ zero) @ (app @ X6 @ zero @ X13 @ nil) @ X13))),
% 1.76/1.43 file('/export/starexec/sandbox/tmp/tmp.wmjoDlDinY/DTF2THF_16462.p',list_app_nil)).
% 1.76/1.43 % SZS output end Proof for DTF2THF_16462
% 1.76/1.43 % (16801)------------------------------
% 1.76/1.43 % (16801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.76/1.43 % (16801)Termination reason: Refutation
% 1.76/1.43
% 1.76/1.43 % (16801)Memory used [KB]: 6140
% 1.76/1.43 % (16801)Time elapsed: 0.058 s
% 1.76/1.43 % (16801)Instructions burned: 89 (million)
% 1.76/1.43 % (16801)------------------------------
% 1.76/1.43 % (16801)------------------------------
% 1.76/1.43 % (16789)Success in time 0.087 s
%------------------------------------------------------------------------------