%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT340^1 : TPTP v9.2.1. Released v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n018.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 08:45:31 AM UTC 2026
% Result : Theorem 1.50s 1.61s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of formulae : 59 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 412 ( 152 equ; 0 cnn)
% Maximal formula atoms : 12 ( 6 avg)
% Number of connectives : 1211 ( 78 ~; 54 |; 41 &;1004 @)
% ( 5 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 7 con; 0-4 aty)
% Number of variables : 174 ( 0 ^; 145 !; 29 ?; 174 :)
% 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_16,type,
sK0:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_17,type,
sK1:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_25,type,
sK2:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_26,type,
sK3:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_27,type,
sK4:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_28,type,
sK5:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_29,type,
sK6:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_30,type,
sK7: nat ).
thf(func_def_31,type,
sK8: elem ).
thf(func_def_32,type,
sK9: list ).
thf(func_def_34,type,
ph11:
!>[X0: $tType] : X0 ).
thf(f222,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f221,f96]) ).
thf(f96,plain,
( $true
= ( listStar @ sK7 @ ( app @ sK7 @ zero @ sK9 @ nil ) @ sK9 ) ),
inference(superposition,[status(thm)],[f88,f82]) ).
thf(f82,plain,
! [X0: nat] :
( ( plus @ X0 @ zero )
= X0 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: nat] :
( ( plus @ X0 @ zero )
= X0 ),
inference(fool_elimination,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: nat] :
( ( plus @ X0 @ zero )
= X0 ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,axiom,
! [X10: nat] :
( ( plus @ X10 @ zero )
= X10 ),
file('/export/starexec/sandbox2/tmp/tmp.gmviLDLzUA/DTF2THF_29509.p',plus_zero_r) ).
thf(f88,plain,
( ( listStar @ ( plus @ sK7 @ zero ) @ ( app @ sK7 @ zero @ sK9 @ nil ) @ sK9 )
= $true ),
inference(cnf_transformation,[status(thm)],[f69]) ).
thf(f69,plain,
( ( $true
!= ( listStar @ ( plus @ ( suc @ sK7 ) @ zero ) @ ( app @ ( suc @ sK7 ) @ zero @ ( cons @ sK7 @ sK8 @ sK9 ) @ nil ) @ ( cons @ sK7 @ sK8 @ sK9 ) ) )
& ( $true
= ( listStar @ sK7 @ sK9 @ sK9 ) )
& ( ( listStar @ ( plus @ sK7 @ zero ) @ ( app @ sK7 @ zero @ sK9 @ nil ) @ sK9 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f54,f68]) ).
thf(f68,plain,
( ? [X0: nat,X1: elem,X2: list] :
( ( $true
!= ( listStar @ ( plus @ ( suc @ X0 ) @ zero ) @ ( app @ ( suc @ X0 ) @ zero @ ( cons @ X0 @ X1 @ X2 ) @ nil ) @ ( cons @ X0 @ X1 @ X2 ) ) )
& ( ( listStar @ X0 @ X2 @ X2 )
= $true )
& ( ( listStar @ ( plus @ X0 @ zero ) @ ( app @ X0 @ zero @ X2 @ nil ) @ X2 )
= $true ) )
=> ( ( $true
!= ( listStar @ ( plus @ ( suc @ sK7 ) @ zero ) @ ( app @ ( suc @ sK7 ) @ zero @ ( cons @ sK7 @ sK8 @ sK9 ) @ nil ) @ ( cons @ sK7 @ sK8 @ sK9 ) ) )
& ( $true
= ( listStar @ sK7 @ sK9 @ sK9 ) )
& ( ( listStar @ ( plus @ sK7 @ zero ) @ ( app @ sK7 @ zero @ sK9 @ nil ) @ sK9 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f54,plain,
? [X0: nat,X1: elem,X2: list] :
( ( $true
!= ( listStar @ ( plus @ ( suc @ X0 ) @ zero ) @ ( app @ ( suc @ X0 ) @ zero @ ( cons @ X0 @ X1 @ X2 ) @ nil ) @ ( cons @ X0 @ X1 @ X2 ) ) )
& ( ( listStar @ X0 @ X2 @ X2 )
= $true )
& ( ( listStar @ ( plus @ X0 @ zero ) @ ( app @ X0 @ zero @ X2 @ nil ) @ X2 )
= $true ) ),
inference(flattening,[status(thm)],[f53]) ).
thf(f53,plain,
? [X0: nat,X1: elem,X2: list] :
( ( $true
!= ( listStar @ ( plus @ ( suc @ X0 ) @ zero ) @ ( app @ ( suc @ X0 ) @ zero @ ( cons @ X0 @ X1 @ X2 ) @ nil ) @ ( cons @ X0 @ X1 @ X2 ) ) )
& ( ( listStar @ ( plus @ X0 @ zero ) @ ( app @ X0 @ zero @ X2 @ nil ) @ X2 )
= $true )
& ( ( listStar @ X0 @ X2 @ X2 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
~ ! [X0: nat,X1: elem,X2: list] :
( ( ( listStar @ X0 @ X2 @ X2 )
= $true )
=> ( ( ( listStar @ ( plus @ X0 @ zero ) @ ( app @ X0 @ zero @ X2 @ nil ) @ X2 )
= $true )
=> ( $true
= ( listStar @ ( plus @ ( suc @ X0 ) @ zero ) @ ( app @ ( suc @ X0 ) @ zero @ ( cons @ X0 @ X1 @ X2 ) @ nil ) @ ( cons @ X0 @ X1 @ X2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f34]) ).
thf(f34,plain,
~ ! [X0: nat,X1: elem,X2: list] :
( ( listStar @ X0 @ X2 @ X2 )
=> ( ( listStar @ ( plus @ X0 @ zero ) @ ( app @ X0 @ zero @ X2 @ nil ) @ X2 )
=> ( listStar @ ( plus @ ( suc @ X0 ) @ zero ) @ ( app @ ( suc @ X0 ) @ zero @ ( cons @ X0 @ X1 @ X2 ) @ nil ) @ ( cons @ X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,negated_conjecture,
~ ! [X6: nat,X2: elem,X12: list] :
( ( listStar @ X6 @ X12 @ X12 )
=> ( ( listStar @ ( plus @ X6 @ zero ) @ ( app @ X6 @ zero @ X12 @ nil ) @ X12 )
=> ( listStar @ ( plus @ ( suc @ X6 ) @ zero ) @ ( app @ ( suc @ X6 ) @ zero @ ( cons @ X6 @ X2 @ X12 ) @ nil ) @ ( cons @ X6 @ X2 @ X12 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
thf(f11,conjecture,
! [X6: nat,X2: elem,X12: list] :
( ( listStar @ X6 @ X12 @ X12 )
=> ( ( listStar @ ( plus @ X6 @ zero ) @ ( app @ X6 @ zero @ X12 @ nil ) @ X12 )
=> ( listStar @ ( plus @ ( suc @ X6 ) @ zero ) @ ( app @ ( suc @ X6 ) @ zero @ ( cons @ X6 @ X2 @ X12 ) @ nil ) @ ( cons @ X6 @ X2 @ X12 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.gmviLDLzUA/DTF2THF_29509.p',list_app_nil_indstep) ).
thf(f221,plain,
( $true
!= ( listStar @ sK7 @ ( app @ sK7 @ zero @ sK9 @ nil ) @ sK9 ) ),
inference(trivial_inequality_removal,[status(thm)],[f216]) ).
thf(f216,plain,
( ( $true
!= ( listStar @ sK7 @ ( app @ sK7 @ zero @ sK9 @ nil ) @ sK9 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f190,f85]) ).
thf(f85,plain,
! [X2: list,X3: list,X0: nat,X1: elem] :
( ( ( listStar @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) @ ( cons @ X0 @ X1 @ X3 ) )
= $true )
| ( ( listStar @ X0 @ X2 @ X3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
thf(f57,plain,
! [X0: nat,X1: elem,X2: list,X3: list] :
( ( ( listStar @ X0 @ X2 @ X3 )
!= $true )
| ( ( listStar @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) @ ( cons @ X0 @ X1 @ X3 ) )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: nat,X1: elem,X2: list,X3: list] :
( ( ( listStar @ X0 @ X2 @ X3 )
= $true )
=> ( ( listStar @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) @ ( cons @ X0 @ X1 @ X3 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: nat,X1: elem,X2: list,X3: list] :
( ( listStar @ X0 @ X2 @ X3 )
=> ( listStar @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) @ ( cons @ X0 @ X1 @ X3 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X6: nat,X7: elem,X8: list,X9: list] :
( ( listStar @ X6 @ X8 @ X9 )
=> ( listStar @ ( suc @ X6 ) @ ( cons @ X6 @ X7 @ X8 ) @ ( cons @ X6 @ X7 @ X9 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.gmviLDLzUA/DTF2THF_29509.p',cons_tp_ax) ).
thf(f190,plain,
( ( listStar @ ( suc @ sK7 ) @ ( cons @ sK7 @ sK8 @ ( app @ sK7 @ zero @ sK9 @ nil ) ) @ ( cons @ sK7 @ sK8 @ sK9 ) )
!= $true ),
inference(superposition,[status(thm)],[f162,f82]) ).
thf(f162,plain,
( ( listStar @ ( plus @ ( suc @ sK7 ) @ zero ) @ ( cons @ sK7 @ sK8 @ ( app @ sK7 @ zero @ sK9 @ nil ) ) @ ( cons @ sK7 @ sK8 @ sK9 ) )
!= $true ),
inference(superposition,[status(thm)],[f150,f82]) ).
thf(f150,plain,
( $true
!= ( listStar @ ( plus @ ( suc @ sK7 ) @ zero ) @ ( cons @ ( plus @ sK7 @ zero ) @ sK8 @ ( app @ sK7 @ zero @ sK9 @ nil ) ) @ ( cons @ sK7 @ sK8 @ sK9 ) ) ),
inference(subsumption_resolution,[status(thm)],[f149,f71]) ).
thf(f71,plain,
( ( listStar @ zero @ nil @ nil )
= $true ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( listStar @ zero @ nil @ nil )
= $true ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
listStar @ zero @ nil @ nil,
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
listStar @ zero @ nil @ nil,
file('/export/starexec/sandbox2/tmp/tmp.gmviLDLzUA/DTF2THF_29509.p',nil_tp_ax) ).
thf(f149,plain,
( ( ( listStar @ zero @ nil @ nil )
!= $true )
| ( $true
!= ( listStar @ ( plus @ ( suc @ sK7 ) @ zero ) @ ( cons @ ( plus @ sK7 @ zero ) @ sK8 @ ( app @ sK7 @ zero @ sK9 @ nil ) ) @ ( cons @ sK7 @ sK8 @ sK9 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f148,f89]) ).
thf(f89,plain,
( $true
= ( listStar @ sK7 @ sK9 @ sK9 ) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
thf(f148,plain,
( ( $true
!= ( listStar @ sK7 @ sK9 @ sK9 ) )
| ( $true
!= ( listStar @ ( plus @ ( suc @ sK7 ) @ zero ) @ ( cons @ ( plus @ sK7 @ zero ) @ sK8 @ ( app @ sK7 @ zero @ sK9 @ nil ) ) @ ( cons @ sK7 @ sK8 @ sK9 ) ) )
| ( ( listStar @ zero @ nil @ nil )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f138]) ).
thf(f138,plain,
( ( ( listStar @ zero @ nil @ nil )
!= $true )
| ( $true
!= ( listStar @ ( plus @ ( suc @ sK7 ) @ zero ) @ ( cons @ ( plus @ sK7 @ zero ) @ sK8 @ ( app @ sK7 @ zero @ sK9 @ nil ) ) @ ( cons @ sK7 @ sK8 @ sK9 ) ) )
| ( $true
!= ( listStar @ sK7 @ sK9 @ sK9 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f104,f87]) ).
thf(f87,plain,
! [X2: elem,X3: list,X0: nat,X1: nat,X4: list] :
( ( $true
= ( listStar @ ( plus @ ( suc @ X0 ) @ X1 ) @ ( app @ ( suc @ X0 ) @ X1 @ ( cons @ X0 @ X2 @ X3 ) @ X4 ) @ ( cons @ ( plus @ X0 @ X1 ) @ X2 @ ( app @ X0 @ X1 @ X3 @ X4 ) ) ) )
| ( $true
!= ( listStar @ X0 @ X3 @ X3 ) )
| ( $true
!= ( listStar @ X1 @ X4 @ X4 ) ) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
thf(f60,plain,
! [X0: nat,X1: nat,X2: elem,X3: list,X4: list] :
( ( $true
!= ( listStar @ X1 @ X4 @ X4 ) )
| ( $true
= ( listStar @ ( plus @ ( suc @ X0 ) @ X1 ) @ ( app @ ( suc @ X0 ) @ X1 @ ( cons @ X0 @ X2 @ X3 ) @ X4 ) @ ( cons @ ( plus @ X0 @ X1 ) @ X2 @ ( app @ X0 @ X1 @ X3 @ X4 ) ) ) )
| ( $true
!= ( listStar @ X0 @ X3 @ X3 ) ) ),
inference(flattening,[status(thm)],[f59]) ).
thf(f59,plain,
! [X0: nat,X1: nat,X2: elem,X3: list,X4: list] :
( ( $true
= ( listStar @ ( plus @ ( suc @ X0 ) @ X1 ) @ ( app @ ( suc @ X0 ) @ X1 @ ( cons @ X0 @ X2 @ X3 ) @ X4 ) @ ( cons @ ( plus @ X0 @ X1 ) @ X2 @ ( app @ X0 @ X1 @ X3 @ X4 ) ) ) )
| ( $true
!= ( listStar @ X1 @ X4 @ X4 ) )
| ( $true
!= ( listStar @ X0 @ X3 @ X3 ) ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: nat,X1: nat,X2: elem,X3: list,X4: list] :
( ( $true
= ( listStar @ X0 @ X3 @ X3 ) )
=> ( ( $true
= ( listStar @ X1 @ X4 @ X4 ) )
=> ( $true
= ( listStar @ ( plus @ ( suc @ X0 ) @ X1 ) @ ( app @ ( suc @ X0 ) @ X1 @ ( cons @ X0 @ X2 @ X3 ) @ X4 ) @ ( cons @ ( plus @ X0 @ X1 ) @ X2 @ ( app @ X0 @ X1 @ X3 @ X4 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: nat,X1: nat,X2: elem,X3: list,X4: list] :
( ( listStar @ X0 @ X3 @ X3 )
=> ( ( listStar @ X1 @ X4 @ X4 )
=> ( listStar @ ( plus @ ( suc @ X0 ) @ X1 ) @ ( app @ ( suc @ X0 ) @ X1 @ ( cons @ X0 @ X2 @ X3 ) @ X4 ) @ ( cons @ ( plus @ X0 @ X1 ) @ X2 @ ( app @ X0 @ X1 @ X3 @ X4 ) ) ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,axiom,
! [X6: nat,X10: nat,X2: elem,X3: list,X4: list] :
( ( listStar @ X6 @ X3 @ X3 )
=> ( ( listStar @ X10 @ X4 @ X4 )
=> ( listStar @ ( plus @ ( suc @ X6 ) @ X10 ) @ ( app @ ( suc @ X6 ) @ X10 @ ( cons @ X6 @ X2 @ X3 ) @ X4 ) @ ( cons @ ( plus @ X6 @ X10 ) @ X2 @ ( app @ X6 @ X10 @ X3 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.gmviLDLzUA/DTF2THF_29509.p',ax4) ).
thf(f104,plain,
! [X0: list] :
( ( $true
!= ( listStar @ ( plus @ ( suc @ sK7 ) @ zero ) @ ( app @ ( suc @ sK7 ) @ zero @ ( cons @ sK7 @ sK8 @ sK9 ) @ nil ) @ X0 ) )
| ( $true
!= ( listStar @ ( plus @ ( suc @ sK7 ) @ zero ) @ X0 @ ( cons @ sK7 @ sK8 @ sK9 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f101,f86]) ).
thf(f86,plain,
! [X0: nat] :
( $true
= ( isPer @ list @ ( listStar @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: nat] :
( $true
= ( isPer @ list @ ( listStar @ X0 ) ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: nat] : ( isPer @ list @ ( listStar @ X0 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X5: nat] : ( isPer @ list @ ( listStar @ X5 ) ),
file('/export/starexec/sandbox2/tmp/tmp.gmviLDLzUA/DTF2THF_29509.p','\'listStar\'_is_per') ).
thf(f101,plain,
! [X0: list] :
( ( $true
!= ( listStar @ ( plus @ ( suc @ sK7 ) @ zero ) @ X0 @ ( cons @ sK7 @ sK8 @ sK9 ) ) )
| ( ( isPer @ list @ ( listStar @ ( plus @ ( suc @ sK7 ) @ zero ) ) )
!= $true )
| ( $true
!= ( listStar @ ( plus @ ( suc @ sK7 ) @ zero ) @ ( app @ ( suc @ sK7 ) @ zero @ ( cons @ sK7 @ sK8 @ sK9 ) @ nil ) @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f100]) ).
thf(f100,plain,
! [X0: list] :
( ( $true != $true )
| ( $true
!= ( listStar @ ( plus @ ( suc @ sK7 ) @ zero ) @ ( app @ ( suc @ sK7 ) @ zero @ ( cons @ sK7 @ sK8 @ sK9 ) @ nil ) @ X0 ) )
| ( $true
!= ( listStar @ ( plus @ ( suc @ sK7 ) @ zero ) @ X0 @ ( cons @ sK7 @ sK8 @ sK9 ) ) )
| ( ( isPer @ list @ ( listStar @ ( plus @ ( suc @ sK7 ) @ zero ) ) )
!= $true ) ),
inference(superposition,[status(thm)],[f90,f81]) ).
thf(f81,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0 > X0 > $o,X4: X0] :
( ( ( X1 @ X2 @ X4 )
= $true )
| ( ( isPer @ X0 @ X1 )
!= $true )
| ( ( X1 @ X2 @ X3 )
!= $true )
| ( ( X1 @ X3 @ X4 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
thf(f67,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ( ! [X2: X0,X3: X0,X4: X0] :
( ( ( X1 @ X2 @ X3 )
!= $true )
| ( ( X1 @ X2 @ X4 )
= $true )
| ( ( X1 @ X3 @ X4 )
!= $true ) )
& ! [X5: X0,X6: X0] :
( ( ( X1 @ X5 @ X6 )
!= $true )
| ( $true
= ( X1 @ X6 @ X5 ) ) ) )
| ( ( isPer @ X0 @ X1 )
!= $true ) )
& ( ( ( isPer @ X0 @ X1 )
= $true )
| ( ( $true
= ( X1 @ ( sK2 @ X0 @ X1 ) @ ( sK3 @ X0 @ X1 ) ) )
& ( ( X1 @ ( sK2 @ X0 @ X1 ) @ ( sK4 @ X0 @ X1 ) )
!= $true )
& ( $true
= ( X1 @ ( sK3 @ X0 @ X1 ) @ ( sK4 @ X0 @ X1 ) ) ) )
| ( ( $true
= ( X1 @ ( sK5 @ X0 @ X1 ) @ ( sK6 @ X0 @ X1 ) ) )
& ( $true
!= ( X1 @ ( sK6 @ X0 @ X1 ) @ ( sK5 @ X0 @ X1 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6])],[f64,f66,f65]) ).
thf(f65,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ? [X7: X0,X8: X0,X9: X0] :
( ( $true
= ( X1 @ X7 @ X8 ) )
& ( $true
!= ( X1 @ X7 @ X9 ) )
& ( ( X1 @ X8 @ X9 )
= $true ) )
=> ( ( $true
= ( X1 @ ( sK2 @ X0 @ X1 ) @ ( sK3 @ X0 @ X1 ) ) )
& ( ( X1 @ ( sK2 @ X0 @ X1 ) @ ( sK4 @ X0 @ X1 ) )
!= $true )
& ( $true
= ( X1 @ ( sK3 @ X0 @ X1 ) @ ( sK4 @ X0 @ X1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f66,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ? [X10: X0,X11: X0] :
( ( $true
= ( X1 @ X10 @ X11 ) )
& ( $true
!= ( X1 @ X11 @ X10 ) ) )
=> ( ( $true
= ( X1 @ ( sK5 @ X0 @ X1 ) @ ( sK6 @ X0 @ X1 ) ) )
& ( $true
!= ( X1 @ ( sK6 @ X0 @ X1 ) @ ( sK5 @ X0 @ X1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f64,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ( ! [X2: X0,X3: X0,X4: X0] :
( ( ( X1 @ X2 @ X3 )
!= $true )
| ( ( X1 @ X2 @ X4 )
= $true )
| ( ( X1 @ X3 @ X4 )
!= $true ) )
& ! [X5: X0,X6: X0] :
( ( ( X1 @ X5 @ X6 )
!= $true )
| ( $true
= ( X1 @ X6 @ X5 ) ) ) )
| ( ( isPer @ X0 @ X1 )
!= $true ) )
& ( ( ( isPer @ X0 @ X1 )
= $true )
| ? [X7: X0,X8: X0,X9: X0] :
( ( $true
= ( X1 @ X7 @ X8 ) )
& ( $true
!= ( X1 @ X7 @ X9 ) )
& ( ( X1 @ X8 @ X9 )
= $true ) )
| ? [X10: X0,X11: X0] :
( ( $true
= ( X1 @ X10 @ X11 ) )
& ( $true
!= ( X1 @ X11 @ X10 ) ) ) ) ),
inference(rectify,[status(thm)],[f63]) ).
thf(f63,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ( ! [X2: X0,X3: X0,X4: X0] :
( ( ( X1 @ X2 @ X3 )
!= $true )
| ( ( X1 @ X2 @ X4 )
= $true )
| ( ( X1 @ X3 @ X4 )
!= $true ) )
& ! [X5: X0,X6: X0] :
( ( ( X1 @ X5 @ X6 )
!= $true )
| ( $true
= ( X1 @ X6 @ X5 ) ) ) )
| ( ( isPer @ X0 @ X1 )
!= $true ) )
& ( ( ( isPer @ X0 @ X1 )
= $true )
| ? [X2: X0,X3: X0,X4: X0] :
( ( ( X1 @ X2 @ X3 )
= $true )
& ( ( X1 @ X2 @ X4 )
!= $true )
& ( ( X1 @ X3 @ X4 )
= $true ) )
| ? [X5: X0,X6: X0] :
( ( ( X1 @ X5 @ X6 )
= $true )
& ( $true
!= ( X1 @ X6 @ X5 ) ) ) ) ),
inference(flattening,[status(thm)],[f62]) ).
thf(f62,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ( ! [X2: X0,X3: X0,X4: X0] :
( ( ( X1 @ X2 @ X3 )
!= $true )
| ( ( X1 @ X2 @ X4 )
= $true )
| ( ( X1 @ X3 @ X4 )
!= $true ) )
& ! [X5: X0,X6: X0] :
( ( ( X1 @ X5 @ X6 )
!= $true )
| ( $true
= ( X1 @ X6 @ X5 ) ) ) )
| ( ( isPer @ X0 @ X1 )
!= $true ) )
& ( ( ( isPer @ X0 @ X1 )
= $true )
| ? [X2: X0,X3: X0,X4: X0] :
( ( ( X1 @ X2 @ X3 )
= $true )
& ( ( X1 @ X2 @ X4 )
!= $true )
& ( ( X1 @ X3 @ X4 )
= $true ) )
| ? [X5: X0,X6: X0] :
( ( ( X1 @ X5 @ X6 )
= $true )
& ( $true
!= ( X1 @ X6 @ X5 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f56]) ).
thf(f56,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ! [X2: X0,X3: X0,X4: X0] :
( ( ( X1 @ X2 @ X3 )
!= $true )
| ( ( X1 @ X2 @ X4 )
= $true )
| ( ( X1 @ X3 @ X4 )
!= $true ) )
& ! [X5: X0,X6: X0] :
( ( ( X1 @ X5 @ X6 )
!= $true )
| ( $true
= ( X1 @ X6 @ X5 ) ) ) )
<=> ( ( isPer @ X0 @ X1 )
= $true ) ),
inference(flattening,[status(thm)],[f55]) ).
thf(f55,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ! [X2: X0,X3: X0,X4: X0] :
( ( ( X1 @ X2 @ X4 )
= $true )
| ( ( X1 @ X3 @ X4 )
!= $true )
| ( ( X1 @ X2 @ X3 )
!= $true ) )
& ! [X5: X0,X6: X0] :
( ( ( X1 @ X5 @ X6 )
!= $true )
| ( $true
= ( X1 @ X6 @ X5 ) ) ) )
<=> ( ( isPer @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ! [X2: X0,X3: X0,X4: X0] :
( ( ( X1 @ X2 @ X3 )
= $true )
=> ( ( ( X1 @ X3 @ X4 )
= $true )
=> ( ( X1 @ X2 @ X4 )
= $true ) ) )
& ! [X5: X0,X6: X0] :
( ( ( X1 @ X5 @ X6 )
= $true )
=> ( $true
= ( X1 @ X6 @ X5 ) ) ) )
<=> ( ( isPer @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( isPer @ X0 @ X1 )
<=> ( ! [X2: X0,X3: X0,X4: X0] :
( ( X1 @ X2 @ X3 )
=> ( ( X1 @ X3 @ X4 )
=> ( X1 @ X2 @ X4 ) ) )
& ! [X5: X0,X6: X0] :
( ( X1 @ X5 @ X6 )
=> ( X1 @ X6 @ X5 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( isPer @ X0 @ X1 )
<=> ( ! [X2: X0,X3: X0,X4: X0] :
( ( X1 @ X2 @ X3 )
=> ( ( X1 @ X3 @ X4 )
=> ( X1 @ X2 @ X4 ) ) )
& ! [X2: X0,X3: X0] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.gmviLDLzUA/DTF2THF_29509.p',is_per) ).
thf(f90,plain,
( $true
!= ( listStar @ ( plus @ ( suc @ sK7 ) @ zero ) @ ( app @ ( suc @ sK7 ) @ zero @ ( cons @ sK7 @ sK8 @ sK9 ) @ nil ) @ ( cons @ sK7 @ sK8 @ sK9 ) ) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : DAT340^1 : TPTP v9.2.1. Released v9.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.31 % Computer : n018.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Feb 24 06:15:46 EST 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.31 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.40 ---- Original DTF file ---
% 0.16/0.40 thf(spec,logic,$$dhol).
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 % File : DAT340^1 : TPTP v9.2.1. Released v9.2.0.
% 0.16/0.40 % Domain : Data Structures
% 0.16/0.40 % Problem : Nil is a right-neutral element of app, step case
% 0.16/0.40 % Version : Especial.
% 0.16/0.40 % English : Nil is a right-neutral element of app. The proof is by induction
% 0.16/0.40 % with a separate problem file for the base and step case as well as
% 0.16/0.40 % the correct instantiation of the induction axiom for lists. The
% 0.16/0.40 % main file uses the conjectures of the other files as lemmas in
% 0.16/0.40 % order to prove the final result. To simplify proof search, the
% 0.16/0.40 % lemmas in the problem file for the induction step have been
% 0.16/0.40 % preselected.
% 0.16/0.40
% 0.16/0.40 % Refs : [RRB23] Rothgang et al. (2023), Theorem Proving in Dependently
% 0.16/0.40 % : [Rot25] Rothgang (2025), Email to Geoff Sutcliffe
% 0.16/0.40 % : [RK+25] Ranalter et al. (2025), The Dependently Typed Higher-O
% 0.16/0.40 % Source : [Rot25]
% 0.16/0.40 % Names : ListAppNil/list-app-nil-indstep.p [Rot25]
% 0.16/0.40
% 0.16/0.40 % Status : Theorem
% 0.16/0.40 % Rating : ? v9.2.0
% 0.16/0.40 % Syntax : Number of formulae : 13 ( 3 unt; 9 typ; 0 def)
% 0.16/0.40 % Number of atoms : 5 ( 5 equ; 0 cnn)
% 0.16/0.40 % Maximal formula atoms : 2 ( 1 avg)
% 0.16/0.40 % Number of connectives : 53 ( 0 ~; 0 |; 0 &; 52 @)
% 0.16/0.40 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.16/0.40 % Maximal formula depth : 6 ( 4 avg)
% 0.16/0.40 % Number of types : 2 ( 2 usr)
% 0.16/0.40 % Number of type decls : 9 ( 0 !>P; 2 !>D)
% 0.16/0.40 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.16/0.40 % Number of symbols : 8 ( 7 usr; 2 con; 0-4 aty)
% 0.16/0.40 % Number of variables : 14 ( 0 ^; 11 !; 0 ?; 14 :)
% 0.16/0.40 % ( 3 !>; 0 ?*; 0 @-; 0 @+)
% 0.16/0.40 % SPC : DH0_THM_EQU_NAR
% 0.16/0.40
% 0.16/0.40 % Comments :
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 thf(elem_type,type,
% 0.16/0.40 elem: $tType ).
% 0.16/0.40
% 0.16/0.40 thf(nat_type,type,
% 0.16/0.40 nat: $tType ).
% 0.16/0.40
% 0.16/0.40 thf(zero_type,type,
% 0.16/0.40 zero: nat ).
% 0.16/0.40
% 0.16/0.40 thf(suc_type,type,
% 0.16/0.40 suc: nat > nat ).
% 0.16/0.40
% 0.16/0.40 thf(plus_type,type,
% 0.16/0.40 plus: nat > nat > nat ).
% 0.16/0.40
% 0.16/0.40 thf(list_type,type,
% 0.16/0.40 list: nat > $tType ).
% 0.16/0.40
% 0.16/0.40 thf(nil_type,type,
% 0.16/0.40 nil: list @ zero ).
% 0.16/0.40
% 0.16/0.40 thf(cons_type,type,
% 0.16/0.40 cons:
% 0.16/0.40 !>[N: nat] : ( elem > ( list @ N ) > ( list @ ( suc @ N ) ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(app_type,type,
% 0.16/0.40 app:
% 0.16/0.40 !>[N: nat,M: nat] : ( ( list @ N ) > ( list @ M ) > ( list @ ( plus @ N @ M ) ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(ax2,axiom,
% 0.16/0.40 ! [N: nat,M: nat] :
% 0.16/0.40 ( ( plus @ ( suc @ N ) @ M )
% 0.16/0.40 = ( suc @ ( plus @ N @ M ) ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(ax4,axiom,
% 0.16/0.40 ! [N: nat,M: nat,X: elem,Y: list @ N,Z: list @ M] :
% 0.16/0.40 ( ( app @ ( suc @ N ) @ M @ ( cons @ N @ X @ Y ) @ Z )
% 0.16/0.40 = ( cons @ ( plus @ N @ M ) @ X @ ( app @ N @ M @ Y @ Z ) ) ) ).
% 0.16/0.40
% 0.16/0.40 thf(plus_zero_r,axiom,
% 0.16/0.40 ! [M: nat] :
% 0.16/0.40 ( ( plus @ M @ zero )
% 0.16/0.40 = M ) ).
% 0.16/0.40
% 0.16/0.40 thf(list_app_nil_indstep,conjecture,
% 0.16/0.40 ! [N: nat,X: elem,L: list @ N] :
% 0.16/0.40 ( ( ( app @ N @ zero @ L @ nil )
% 0.16/0.40 = L )
% 0.16/0.40 => ( ( app @ ( suc @ N ) @ zero @ ( cons @ N @ X @ L ) @ nil )
% 0.16/0.40 = ( cons @ N @ X @ L ) ) ) ).
% 0.16/0.40
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 ------------------------
% 1.43/1.15 ---- Embedded in THF ---
% 1.43/1.15 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.43/1.15 %%% Generated on Tue Feb 24 06:15:46 EST 2026
% 1.43/1.15 %%% using '$$dhol' embedding, version 1.3.0.
% 1.43/1.15 %%% Logic specification used:
% 1.43/1.15 %%% thf(spec, logic, $$dhol).
% 1.43/1.15
% 1.43/1.15 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.gmviLDLzUA/DTF2DTF29509.p
% See solution above
% 1.43/1.15 ------------------------
% 1.43/1.16 ---- Cleaned THF ---
% 1.43/1.16 thf(is_per_type,type,
% 1.43/1.16 isPer:
% 1.43/1.16 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 1.43/1.16
% 1.43/1.16 thf(is_per,definition,
% 1.43/1.16 ! [A: $tType,AStar: A > A > $o] :
% 1.43/1.16 ( ( isPer @ A @ AStar )
% 1.43/1.16 <=> ( ! [X: A,Y: A] :
% 1.43/1.16 ( ( AStar @ X @ Y )
% 1.43/1.16 => ( AStar @ Y @ X ) )
% 1.43/1.16 & ! [X: A,Y: A,Z: A] :
% 1.43/1.16 ( ( AStar @ X @ Y )
% 1.43/1.16 => ( ( AStar @ Y @ Z )
% 1.43/1.16 => ( AStar @ X @ Z ) ) ) ) ) ).
% 1.43/1.16
% 1.43/1.16 thf(elem_type,type,
% 1.43/1.16 elem: $tType ).
% 1.43/1.16
% 1.43/1.16 thf(elemStar,type,
% 1.43/1.16 elemStar: elem > elem > $o ).
% 1.43/1.16
% 1.43/1.16 thf(elemStar_is_eq,axiom,
% 1.43/1.16 ! [X: elem,Y: elem] :
% 1.43/1.16 ( ( elemStar @ X @ Y )
% 1.43/1.16 <=> ( X = Y ) ) ).
% 1.43/1.16
% 1.43/1.16 thf(nat_type,type,
% 1.43/1.16 nat: $tType ).
% 1.43/1.16
% 1.43/1.16 thf(natStar,type,
% 1.43/1.16 natStar: nat > nat > $o ).
% 1.43/1.16
% 1.43/1.16 thf(natStar_is_eq,axiom,
% 1.43/1.16 ! [X: nat,Y: nat] :
% 1.43/1.16 ( ( natStar @ X @ Y )
% 1.43/1.16 <=> ( X = Y ) ) ).
% 1.43/1.16
% 1.43/1.16 thf(zero_type,type,
% 1.43/1.16 zero: nat ).
% 1.43/1.16
% 1.43/1.16 thf(suc_type,type,
% 1.43/1.16 suc: nat > nat ).
% 1.43/1.16
% 1.43/1.16 thf(plus_type,type,
% 1.43/1.16 plus: nat > nat > nat ).
% 1.43/1.16
% 1.43/1.16 thf(list_type,type,
% 1.43/1.16 list: $tType ).
% 1.43/1.16
% 1.43/1.16 thf(listStar,type,
% 1.43/1.16 listStar: nat > list > list > $o ).
% 1.43/1.16
% 1.43/1.16 thf('\'listStar\'_is_per',axiom,
% 1.43/1.16 ! [C: nat] : ( isPer @ list @ ( listStar @ C ) ) ).
% 1.43/1.16
% 1.43/1.16 thf(nil_type,type,
% 1.43/1.16 nil: list ).
% 1.43/1.16
% 1.43/1.16 thf(nil_tp_ax,axiom,
% 1.43/1.16 listStar @ zero @ nil @ nil ).
% 1.43/1.16
% 1.43/1.16 thf(cons_type,type,
% 1.43/1.16 cons: nat > elem > list > list ).
% 1.43/1.16
% 1.43/1.16 thf(cons_tp_ax,axiom,
% 1.43/1.16 ! [N: nat,D: elem,D0: list,D0_prime: list] :
% 1.43/1.16 ( ( listStar @ N @ D0 @ D0_prime )
% 1.43/1.16 => ( listStar @ ( suc @ N ) @ ( cons @ N @ D @ D0 ) @ ( cons @ N @ D @ D0_prime ) ) ) ).
% 1.43/1.16
% 1.43/1.16 thf(app_type,type,
% 1.43/1.16 app: nat > nat > list > list > list ).
% 1.43/1.16
% 1.43/1.16 thf(app_tp_ax,axiom,
% 1.43/1.16 ! [N: nat,M: nat,D: list,D_prime: list] :
% 1.43/1.16 ( ( listStar @ N @ D @ D_prime )
% 1.43/1.16 => ! [D0: list,D0_prime: list] :
% 1.43/1.16 ( ( listStar @ M @ D0 @ D0_prime )
% 1.43/1.16 => ( listStar @ ( plus @ N @ M ) @ ( app @ N @ M @ D @ D0 ) @ ( app @ N @ M @ D_prime @ D0_prime ) ) ) ) ).
% 1.43/1.16
% 1.43/1.16 thf(ax2,axiom,
% 1.43/1.16 ! [N: nat,M: nat] :
% 1.43/1.16 ( ( plus @ ( suc @ N ) @ M )
% 1.43/1.16 = ( suc @ ( plus @ N @ M ) ) ) ).
% 1.43/1.16
% 1.43/1.16 thf(ax4,axiom,
% 1.43/1.16 ! [N: nat,M: nat,X: elem,Y: list,Z: list] :
% 1.43/1.16 ( ( listStar @ N @ Y @ Y )
% 1.43/1.16 => ( ( listStar @ M @ Z @ Z )
% 1.43/1.16 => ( listStar @ ( plus @ ( suc @ N ) @ M ) @ ( app @ ( suc @ N ) @ M @ ( cons @ N @ X @ Y ) @ Z ) @ ( cons @ ( plus @ N @ M ) @ X @ ( app @ N @ M @ Y @ Z ) ) ) ) ) ).
% 1.43/1.16
% 1.43/1.16 thf(plus_zero_r,axiom,
% 1.43/1.16 ! [M: nat] :
% 1.43/1.16 ( ( plus @ M @ zero )
% 1.43/1.16 = M ) ).
% 1.43/1.16
% 1.43/1.16 thf(list_app_nil_indstep,conjecture,
% 1.43/1.16 ! [N: nat,X: elem,L: list] :
% 1.43/1.16 ( ( listStar @ N @ L @ L )
% 1.43/1.16 => ( ( listStar @ ( plus @ N @ zero ) @ ( app @ N @ zero @ L @ nil ) @ L )
% 1.43/1.16 => ( listStar @ ( plus @ ( suc @ N ) @ zero ) @ ( app @ ( suc @ N ) @ zero @ ( cons @ N @ X @ L ) @ nil ) @ ( cons @ N @ X @ L ) ) ) ) ).
% 1.43/1.16 ------------------------
% 1.43/1.18 % (29608)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29509 for (2999ds/183Mi)
% 1.43/1.18 % (29611)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29509 for (2999ds/2Mi)
% 1.43/1.18 % (29610)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_29509 for (2999ds/27Mi)
% 1.43/1.18 % (29614)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29509 for (2999ds/18Mi)
% 1.43/1.18 % (29612)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_29509 for (2999ds/2Mi)
% 1.43/1.18 % (29613)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_29509 for (2999ds/275Mi)
% 1.43/1.18 % (29611)Instruction limit reached!
% 1.43/1.18 % (29611)------------------------------
% 1.43/1.18 % (29611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.18 % (29611)Termination reason: Unknown
% 1.43/1.18 % (29611)Termination phase: shuffling
% 1.43/1.18
% 1.43/1.18 % (29612)Instruction limit reached!
% 1.43/1.18 % (29612)------------------------------
% 1.43/1.18 % (29612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.18 % (29612)Termination reason: Unknown
% 1.43/1.18 % (29612)Termination phase: shuffling
% 1.43/1.18
% 1.43/1.18 % (29612)Memory used [KB]: 1023
% 1.43/1.18 % (29612)Time elapsed: 0.002 s
% 1.43/1.18 % (29612)Instructions burned: 2 (million)
% 1.43/1.18 % (29612)------------------------------
% 1.43/1.18 % (29612)------------------------------
% 1.43/1.18 % (29611)Memory used [KB]: 1023
% 1.43/1.18 % (29611)Time elapsed: 0.002 s
% 1.43/1.18 % (29611)Instructions burned: 2 (million)
% 1.43/1.18 % (29611)------------------------------
% 1.43/1.18 % (29611)------------------------------
% 1.43/1.19 % (29613)Refutation not found, incomplete strategy
% 1.43/1.19 % (29613)------------------------------
% 1.43/1.19 % (29613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.19 % (29613)Termination reason: Refutation not found, incomplete strategy
% 1.43/1.19
% 1.43/1.19
% 1.43/1.19 % (29613)Memory used [KB]: 5500
% 1.43/1.19 % (29613)Time elapsed: 0.004 s
% 1.43/1.19 % (29613)Instructions burned: 5 (million)
% 1.43/1.19 % (29613)------------------------------
% 1.43/1.19 % (29613)------------------------------
% 1.43/1.19 % (29609)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_29509 for (2999ds/4Mi)
% 1.43/1.19 % (29609)Instruction limit reached!
% 1.43/1.19 % (29609)------------------------------
% 1.43/1.19 % (29609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.19 % (29609)Termination reason: Unknown
% 1.43/1.19 % (29609)Termination phase: Property scanning
% 1.43/1.19
% 1.43/1.19 % (29609)Memory used [KB]: 1023
% 1.43/1.19 % (29609)Time elapsed: 0.003 s
% 1.43/1.19 % (29609)Instructions burned: 4 (million)
% 1.43/1.19 % (29609)------------------------------
% 1.43/1.19 % (29609)------------------------------
% 1.43/1.19 % (29614)Instruction limit reached!
% 1.43/1.19 % (29614)------------------------------
% 1.43/1.19 % (29614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.19 % (29614)Termination reason: Unknown
% 1.43/1.19 % (29614)Termination phase: Saturation
% 1.43/1.19
% 1.43/1.19 % (29614)Memory used [KB]: 5628
% 1.43/1.19 % (29614)Time elapsed: 0.011 s
% 1.43/1.19 % (29614)Instructions burned: 19 (million)
% 1.43/1.19 % (29614)------------------------------
% 1.43/1.19 % (29614)------------------------------
% 1.50/1.20 % (29610)Instruction limit reached!
% 1.50/1.20 % (29610)------------------------------
% 1.50/1.20 % (29610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.20 % (29610)Termination reason: Unknown
% 1.50/1.20 % (29610)Termination phase: Saturation
% 1.50/1.20
% 1.50/1.20 % (29610)Memory used [KB]: 5756
% 1.50/1.20 % (29610)Time elapsed: 0.016 s
% 1.50/1.20 % (29610)Instructions burned: 28 (million)
% 1.50/1.20 % (29610)------------------------------
% 1.50/1.20 % (29610)------------------------------
% 1.50/1.21 % (29616)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_29509 for (2999ds/37Mi)
% 1.50/1.21 % (29615)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_29509 for (2999ds/3Mi)
% 1.50/1.21 % (29617)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_29509 for (2999ds/15Mi)
% 1.50/1.21 % (29618)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_29509 for (2999ds/3Mi)
% 1.50/1.21 % (29619)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_29509 for (2999ds/1041Mi)
% 1.50/1.21 % (29615)Instruction limit reached!
% 1.50/1.21 % (29615)------------------------------
% 1.50/1.21 % (29615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.21 % (29615)Termination reason: Unknown
% 1.50/1.21 % (29615)Termination phase: Preprocessing 3
% 1.50/1.21
% 1.50/1.21 % (29615)Memory used [KB]: 1023
% 1.50/1.21 % (29615)Time elapsed: 0.003 s
% 1.50/1.21 % (29615)Instructions burned: 4 (million)
% 1.50/1.21 % (29615)------------------------------
% 1.50/1.21 % (29615)------------------------------
% 1.50/1.21 % (29618)Instruction limit reached!
% 1.50/1.21 % (29618)------------------------------
% 1.50/1.21 % (29618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.21 % (29618)Termination reason: Unknown
% 1.50/1.21 % (29618)Termination phase: Preprocessing 3
% 1.50/1.21
% 1.50/1.21 % (29618)Memory used [KB]: 1023
% 1.50/1.21 % (29618)Time elapsed: 0.003 s
% 1.50/1.21 % (29618)Instructions burned: 4 (million)
% 1.50/1.21 % (29618)------------------------------
% 1.50/1.21 % (29618)------------------------------
% 1.50/1.21 % (29620)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_29509 for (2999ds/7Mi)
% 1.50/1.22 % (29617)Instruction limit reached!
% 1.50/1.22 % (29617)------------------------------
% 1.50/1.22 % (29617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.22 % (29617)Termination reason: Unknown
% 1.50/1.22 % (29617)Termination phase: Saturation
% 1.50/1.22
% 1.50/1.22 % (29617)Memory used [KB]: 5756
% 1.50/1.22 % (29617)Time elapsed: 0.009 s
% 1.50/1.22 % (29617)Instructions burned: 15 (million)
% 1.50/1.22 % (29617)------------------------------
% 1.50/1.22 % (29617)------------------------------
% 1.50/1.22 % (29620)Instruction limit reached!
% 1.50/1.22 % (29620)------------------------------
% 1.50/1.22 % (29620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.22 % (29620)Termination reason: Unknown
% 1.50/1.22 % (29620)Termination phase: Saturation
% 1.50/1.22
% 1.50/1.22 % (29620)Memory used [KB]: 1023
% 1.50/1.22 % (29620)Time elapsed: 0.005 s
% 1.50/1.22 % (29620)Instructions burned: 8 (million)
% 1.50/1.22 % (29620)------------------------------
% 1.50/1.22 % (29620)------------------------------
% 1.50/1.22 % (29621)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_29509 for (2999ds/16Mi)
% 1.50/1.23 % (29622)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_29509 for (2999ds/3Mi)
% 1.50/1.23 % (29616)Instruction limit reached!
% 1.50/1.23 % (29616)------------------------------
% 1.50/1.23 % (29616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.23 % (29616)Termination reason: Unknown
% 1.50/1.23 % (29616)Termination phase: Saturation
% 1.50/1.23
% 1.50/1.23 % (29616)Memory used [KB]: 5756
% 1.50/1.23 % (29616)Time elapsed: 0.019 s
% 1.50/1.23 % (29616)Instructions burned: 37 (million)
% 1.50/1.23 % (29616)------------------------------
% 1.50/1.23 % (29616)------------------------------
% 1.50/1.23 % (29622)Instruction limit reached!
% 1.50/1.23 % (29622)------------------------------
% 1.50/1.23 % (29622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.23 % (29622)Termination reason: Unknown
% 1.50/1.23 % (29622)Termination phase: Preprocessing 3
% 1.50/1.23
% 1.50/1.23 % (29622)Memory used [KB]: 1023
% 1.50/1.23 % (29622)Time elapsed: 0.003 s
% 1.50/1.23 % (29622)Instructions burned: 4 (million)
% 1.50/1.23 % (29622)------------------------------
% 1.50/1.23 % (29622)------------------------------
% 1.50/1.23 % (29623)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_29509 for (2999ds/3Mi)
% 1.50/1.23 % (29621)Instruction limit reached!
% 1.50/1.23 % (29621)------------------------------
% 1.50/1.23 % (29621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.23 % (29621)Termination reason: Unknown
% 1.50/1.23 % (29621)Termination phase: Saturation
% 1.50/1.23
% 1.50/1.23 % (29621)Memory used [KB]: 5756
% 1.50/1.23 % (29621)Time elapsed: 0.009 s
% 1.50/1.23 % (29621)Instructions burned: 16 (million)
% 1.50/1.23 % (29621)------------------------------
% 1.50/1.23 % (29621)------------------------------
% 1.50/1.23 % (29608)Instruction limit reached!
% 1.50/1.23 % (29608)------------------------------
% 1.50/1.23 % (29608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.23 % (29608)Termination reason: Unknown
% 1.50/1.23 % (29608)Termination phase: Saturation
% 1.50/1.23
% 1.50/1.23 % (29608)Memory used [KB]: 7164
% 1.50/1.23 % (29623)Instruction limit reached!
% 1.50/1.23 % (29623)------------------------------
% 1.50/1.23 % (29623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.23 % (29608)Time elapsed: 0.057 s
% 1.50/1.23 % (29608)Instructions burned: 186 (million)
% 1.50/1.23 % (29608)------------------------------
% 1.50/1.23 % (29608)------------------------------
% 1.50/1.23 % (29623)Termination reason: Unknown
% 1.50/1.23 % (29623)Termination phase: Preprocessing 3
% 1.50/1.23
% 1.50/1.23 % (29623)Memory used [KB]: 1023
% 1.50/1.23 % (29623)Time elapsed: 0.003 s
% 1.50/1.23 % (29623)Instructions burned: 4 (million)
% 1.50/1.23 % (29623)------------------------------
% 1.50/1.23 % (29623)------------------------------
% 1.50/1.23 % (29624)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_29509 for (2999ds/7Mi)
% 1.50/1.24 % (29624)Instruction limit reached!
% 1.50/1.24 % (29624)------------------------------
% 1.50/1.24 % (29624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.24 % (29624)Termination reason: Unknown
% 1.50/1.24 % (29624)Termination phase: Saturation
% 1.50/1.24
% 1.50/1.24 % (29624)Memory used [KB]: 5500
% 1.50/1.24 % (29624)Time elapsed: 0.005 s
% 1.50/1.24 % (29624)Instructions burned: 8 (million)
% 1.50/1.24 % (29624)------------------------------
% 1.50/1.24 % (29624)------------------------------
% 1.50/1.24 % (29625)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_29509 for (2999ds/3Mi)
% 1.50/1.24 % (29628)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_29509 for (2999ds/710Mi)
% 1.50/1.24 % (29626)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_29509 for (2999ds/4Mi)
% 1.50/1.24 % (29625)Instruction limit reached!
% 1.50/1.24 % (29625)------------------------------
% 1.50/1.24 % (29625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.24 % (29625)Termination reason: Unknown
% 1.50/1.24 % (29625)Termination phase: Preprocessing 1
% 1.50/1.24
% 1.50/1.24 % (29625)Memory used [KB]: 1023
% 1.50/1.24 % (29625)Time elapsed: 0.003 s
% 1.50/1.24 % (29625)Instructions burned: 4 (million)
% 1.50/1.24 % (29625)------------------------------
% 1.50/1.24 % (29625)------------------------------
% 1.50/1.24 % (29626)Instruction limit reached!
% 1.50/1.24 % (29626)------------------------------
% 1.50/1.24 % (29626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.24 % (29626)Termination reason: Unknown
% 1.50/1.24 % (29626)Termination phase: Property scanning
% 1.50/1.24
% 1.50/1.24 % (29626)Memory used [KB]: 1023
% 1.50/1.24 % (29626)Time elapsed: 0.003 s
% 1.50/1.24 % (29626)Instructions burned: 4 (million)
% 1.50/1.24 % (29626)------------------------------
% 1.50/1.24 % (29626)------------------------------
% 1.50/1.25 % (29627)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_29509 for (2999ds/18Mi)
% 1.50/1.25 % (29629)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_29509 for (2999ds/6Mi)
% 1.50/1.25 % (29629)Instruction limit reached!
% 1.50/1.25 % (29629)------------------------------
% 1.50/1.25 % (29629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.25 % (29629)Termination reason: Unknown
% 1.50/1.25 % (29629)Termination phase: Saturation
% 1.50/1.25
% 1.50/1.25 % (29629)Memory used [KB]: 5500
% 1.50/1.25 % (29629)Time elapsed: 0.004 s
% 1.50/1.25 % (29629)Instructions burned: 6 (million)
% 1.50/1.25 % (29629)------------------------------
% 1.50/1.25 % (29629)------------------------------
% 1.50/1.25 % (29630)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_29509 for (2999ds/902Mi)
% 1.50/1.26 % (29627)Instruction limit reached!
% 1.50/1.26 % (29627)------------------------------
% 1.50/1.26 % (29627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.26 % (29627)Termination reason: Unknown
% 1.50/1.26 % (29627)Termination phase: Saturation
% 1.50/1.26
% 1.50/1.26 % (29627)Memory used [KB]: 5628
% 1.50/1.26 % (29627)Time elapsed: 0.011 s
% 1.50/1.26 % (29627)Instructions burned: 19 (million)
% 1.50/1.26 % (29627)------------------------------
% 1.50/1.26 % (29627)------------------------------
% 1.50/1.26 % (29631)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_29509 for (2999ds/21Mi)
% 1.50/1.26 % (29632)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_29509 for (2999ds/5Mi)
% 1.50/1.26 % (29632)Instruction limit reached!
% 1.50/1.26 % (29632)------------------------------
% 1.50/1.26 % (29632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.26 % (29632)Termination reason: Unknown
% 1.50/1.26 % (29632)Termination phase: Saturation
% 1.50/1.26
% 1.50/1.26 % (29632)Memory used [KB]: 5500
% 1.50/1.26 % (29632)Time elapsed: 0.004 s
% 1.50/1.26 % (29632)Instructions burned: 6 (million)
% 1.50/1.26 % (29632)------------------------------
% 1.50/1.26 % (29632)------------------------------
% 1.50/1.26 % (29633)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_29509 for (2999ds/6Mi)
% 1.50/1.27 % (29633)Instruction limit reached!
% 1.50/1.27 % (29633)------------------------------
% 1.50/1.27 % (29633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.27 % (29633)Termination reason: Unknown
% 1.50/1.27 % (29633)Termination phase: Saturation
% 1.50/1.27
% 1.50/1.27 % (29633)Memory used [KB]: 5500
% 1.50/1.27 % (29633)Time elapsed: 0.003 s
% 1.50/1.27 % (29633)Instructions burned: 6 (million)
% 1.50/1.27 % (29633)------------------------------
% 1.50/1.27 % (29633)------------------------------
% 1.50/1.27 % (29631)Instruction limit reached!
% 1.50/1.27 % (29631)------------------------------
% 1.50/1.27 % (29631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.27 % (29631)Termination reason: Unknown
% 1.50/1.27 % (29631)Termination phase: Saturation
% 1.50/1.27
% 1.50/1.27 % (29631)Memory used [KB]: 5756
% 1.50/1.27 % (29631)Time elapsed: 0.012 s
% 1.50/1.27 % (29631)Instructions burned: 21 (million)
% 1.50/1.27 % (29631)------------------------------
% 1.50/1.27 % (29631)------------------------------
% 1.50/1.27 % (29634)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_29509 for (2999ds/377Mi)
% 1.50/1.28 % (29636)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_29509 for (2999ds/19Mi)
% 1.50/1.28 % (29636)Refutation not found, incomplete strategy
% 1.50/1.28 % (29636)------------------------------
% 1.50/1.28 % (29636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.28 % (29636)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.28
% 1.50/1.28
% 1.50/1.28 % (29636)Memory used [KB]: 5628
% 1.50/1.28 % (29636)Time elapsed: 0.003 s
% 1.50/1.28 % (29636)Instructions burned: 7 (million)
% 1.50/1.28 % (29636)------------------------------
% 1.50/1.28 % (29636)------------------------------
% 1.50/1.28 % (29635)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_29509 for (2999ds/779Mi)
% 1.50/1.29 % (29637)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_29509 for (2999ds/879Mi)
% 1.50/1.29 % (29638)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_29509 for (2998ds/17Mi)
% 1.50/1.29 % (29638)Instruction limit reached!
% 1.50/1.29 % (29638)------------------------------
% 1.50/1.29 % (29638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (29638)Termination reason: Unknown
% 1.50/1.29 % (29638)Termination phase: Saturation
% 1.50/1.29
% 1.50/1.29 % (29638)Memory used [KB]: 5756
% 1.50/1.29 % (29638)Time elapsed: 0.007 s
% 1.50/1.29 % (29638)Instructions burned: 19 (million)
% 1.50/1.29 % (29638)------------------------------
% 1.50/1.29 % (29638)------------------------------
% 1.50/1.30 % (29639)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_29509 for (2998ds/3Mi)
% 1.50/1.30 % (29639)Instruction limit reached!
% 1.50/1.30 % (29639)------------------------------
% 1.50/1.30 % (29639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.30 % (29639)Termination reason: Unknown
% 1.50/1.30 % (29639)Termination phase: Preprocessing 3
% 1.50/1.30
% 1.50/1.30 % (29639)Memory used [KB]: 1023
% 1.50/1.30 % (29639)Time elapsed: 0.002 s
% 1.50/1.30 % (29639)Instructions burned: 4 (million)
% 1.50/1.30 % (29639)------------------------------
% 1.50/1.30 % (29639)------------------------------
% 1.50/1.31 % (29640)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_29509 for (2998ds/30Mi)
% 1.50/1.32 % (29640)Instruction limit reached!
% 1.50/1.32 % (29640)------------------------------
% 1.50/1.32 % (29640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.32 % (29640)Termination reason: Unknown
% 1.50/1.32 % (29640)Termination phase: Saturation
% 1.50/1.32
% 1.50/1.32 % (29640)Memory used [KB]: 5756
% 1.50/1.32 % (29640)Time elapsed: 0.011 s
% 1.50/1.32 % (29640)Instructions burned: 31 (million)
% 1.50/1.32 % (29640)------------------------------
% 1.50/1.32 % (29640)------------------------------
% 1.50/1.33 % (29641)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_29509 for (2998ds/127Mi)
% 1.50/1.37 % (29641)Instruction limit reached!
% 1.50/1.37 % (29641)------------------------------
% 1.50/1.37 % (29641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.37 % (29641)Termination reason: Unknown
% 1.50/1.37 % (29641)Termination phase: Saturation
% 1.50/1.37
% 1.50/1.37 % (29641)Memory used [KB]: 6268
% 1.50/1.37 % (29641)Time elapsed: 0.039 s
% 1.50/1.37 % (29641)Instructions burned: 128 (million)
% 1.50/1.37 % (29641)------------------------------
% 1.50/1.37 % (29641)------------------------------
% 1.50/1.38 % (29642)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_29509 for (2998ds/100Mi)
% 1.50/1.41 % (29642)Instruction limit reached!
% 1.50/1.41 % (29642)------------------------------
% 1.50/1.41 % (29642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.41 % (29642)Termination reason: Unknown
% 1.50/1.41 % (29642)Termination phase: Saturation
% 1.50/1.41
% 1.50/1.41 % (29642)Memory used [KB]: 6140
% 1.50/1.41 % (29642)Time elapsed: 0.033 s
% 1.50/1.41 % (29642)Instructions burned: 100 (million)
% 1.50/1.41 % (29642)------------------------------
% 1.50/1.41 % (29642)------------------------------
% 1.50/1.42 % (29643)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_29509 for (2997ds/3Mi)
% 1.50/1.42 % (29643)Instruction limit reached!
% 1.50/1.42 % (29643)------------------------------
% 1.50/1.42 % (29643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.42 % (29643)Termination reason: Unknown
% 1.50/1.42 % (29643)Termination phase: Property scanning
% 1.50/1.42
% 1.50/1.42 % (29643)Memory used [KB]: 1023
% 1.50/1.42 % (29643)Time elapsed: 0.002 s
% 1.50/1.42 % (29643)Instructions burned: 4 (million)
% 1.50/1.42 % (29643)------------------------------
% 1.50/1.42 % (29643)------------------------------
% 1.50/1.43 % (29644)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_29509 for (2997ds/20Mi)
% 1.50/1.44 % (29644)Instruction limit reached!
% 1.50/1.44 % (29644)------------------------------
% 1.50/1.44 % (29644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.44 % (29644)Termination reason: Unknown
% 1.50/1.44 % (29644)Termination phase: Saturation
% 1.50/1.44
% 1.50/1.44 % (29644)Memory used [KB]: 5756
% 1.50/1.44 % (29644)Time elapsed: 0.008 s
% 1.50/1.44 % (29644)Instructions burned: 22 (million)
% 1.50/1.44 % (29644)------------------------------
% 1.50/1.44 % (29644)------------------------------
% 1.50/1.45 % (29645)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_29509 for (2997ds/86Mi)
% 1.50/1.45 % (29634)Instruction limit reached!
% 1.50/1.45 % (29634)------------------------------
% 1.50/1.45 % (29634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.45 % (29634)Termination reason: Unknown
% 1.50/1.45 % (29634)Termination phase: Saturation
% 1.50/1.45
% 1.50/1.45 % (29634)Memory used [KB]: 6268
% 1.50/1.45 % (29634)Time elapsed: 0.180 s
% 1.50/1.45 % (29634)Instructions burned: 378 (million)
% 1.50/1.45 % (29634)------------------------------
% 1.50/1.45 % (29634)------------------------------
% 1.50/1.47 % (29646)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_29509 for (2997ds/107Mi)
% 1.50/1.49 % (29645)Instruction limit reached!
% 1.50/1.49 % (29645)------------------------------
% 1.50/1.49 % (29645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.49 % (29645)Termination reason: Unknown
% 1.50/1.49 % (29645)Termination phase: Saturation
% 1.50/1.49
% 1.50/1.49 % (29645)Memory used [KB]: 6268
% 1.50/1.49 % (29645)Time elapsed: 0.039 s
% 1.50/1.49 % (29645)Instructions burned: 87 (million)
% 1.50/1.49 % (29645)------------------------------
% 1.50/1.49 % (29645)------------------------------
% 1.50/1.50 % (29647)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_29509 for (2996ds/39Mi)
% 1.50/1.52 % (29647)Instruction limit reached!
% 1.50/1.52 % (29647)------------------------------
% 1.50/1.52 % (29647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.52 % (29647)Termination reason: Unknown
% 1.50/1.52 % (29647)Termination phase: Saturation
% 1.50/1.52
% 1.50/1.52 % (29647)Memory used [KB]: 5884
% 1.50/1.52 % (29647)Time elapsed: 0.021 s
% 1.50/1.52 % (29647)Instructions burned: 39 (million)
% 1.50/1.52 % (29647)------------------------------
% 1.50/1.52 % (29647)------------------------------
% 1.50/1.52 % (29646)Instruction limit reached!
% 1.50/1.52 % (29646)------------------------------
% 1.50/1.52 % (29646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.52 % (29646)Termination reason: Unknown
% 1.50/1.52 % (29646)Termination phase: Saturation
% 1.50/1.52
% 1.50/1.52 % (29646)Memory used [KB]: 6140
% 1.50/1.52 % (29646)Time elapsed: 0.056 s
% 1.50/1.52 % (29646)Instructions burned: 108 (million)
% 1.50/1.52 % (29646)------------------------------
% 1.50/1.52 % (29646)------------------------------
% 1.50/1.54 % (29649)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_29509 for (2996ds/46Mi)
% 1.50/1.55 % (29648)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_29509 for (2996ds/448Mi)
% 1.50/1.56 % (29628)Instruction limit reached!
% 1.50/1.56 % (29628)------------------------------
% 1.50/1.56 % (29628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.56 % (29628)Termination reason: Unknown
% 1.50/1.56 % (29628)Termination phase: Saturation
% 1.50/1.56
% 1.50/1.56 % (29628)Memory used [KB]: 7931
% 1.50/1.56 % (29628)Time elapsed: 0.318 s
% 1.50/1.56 % (29628)Instructions burned: 712 (million)
% 1.50/1.56 % (29628)------------------------------
% 1.50/1.56 % (29628)------------------------------
% 1.50/1.56 % (29649)Instruction limit reached!
% 1.50/1.56 % (29649)------------------------------
% 1.50/1.56 % (29649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.56 % (29649)Termination reason: Unknown
% 1.50/1.56 % (29649)Termination phase: Saturation
% 1.50/1.56
% 1.50/1.56 % (29649)Memory used [KB]: 5756
% 1.50/1.56 % (29649)Time elapsed: 0.025 s
% 1.50/1.56 % (29649)Instructions burned: 47 (million)
% 1.50/1.56 % (29649)------------------------------
% 1.50/1.56 % (29649)------------------------------
% 1.50/1.58 % (29650)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_29509 for (2996ds/98Mi)
% 1.50/1.58 % (29651)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_29509 for (2996ds/507Mi)
% 1.50/1.60 % (29651)First to succeed.
% 1.50/1.61 % (29651)Refutation found. Thanks to Tanya!
% 1.50/1.61 % SZS status Theorem for DTF2THF_29509
% 1.50/1.61 % SZS output start Proof for DTF2THF_29509
% 1.50/1.61 thf(type_def_6, type, elem: $tType).
% 1.50/1.61 thf(type_def_7, type, nat: $tType).
% 1.50/1.61 thf(type_def_8, type, list: $tType).
% 1.50/1.61 thf(func_def_0, type, isPer: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 1.50/1.61 thf(func_def_2, type, elem: $tType).
% 1.50/1.61 thf(func_def_3, type, elemStar: elem > elem > $o).
% 1.50/1.61 thf(func_def_4, type, nat: $tType).
% 1.50/1.61 thf(func_def_5, type, natStar: nat > nat > $o).
% 1.50/1.61 thf(func_def_6, type, zero: nat).
% 1.50/1.61 thf(func_def_7, type, suc: nat > nat).
% 1.50/1.61 thf(func_def_8, type, plus: nat > nat > nat).
% 1.50/1.61 thf(func_def_9, type, list: $tType).
% 1.50/1.61 thf(func_def_10, type, listStar: nat > list > list > $o).
% 1.50/1.61 thf(func_def_11, type, nil: list).
% 1.50/1.61 thf(func_def_12, type, cons: nat > elem > list > list).
% 1.50/1.61 thf(func_def_13, type, app: nat > nat > list > list > list).
% 1.50/1.61 thf(func_def_16, type, sK0: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.50/1.61 thf(func_def_17, type, sK1: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.50/1.61 thf(func_def_25, type, sK2: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.50/1.61 thf(func_def_26, type, sK3: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.50/1.61 thf(func_def_27, type, sK4: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.50/1.61 thf(func_def_28, type, sK5: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.50/1.61 thf(func_def_29, type, sK6: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.50/1.61 thf(func_def_30, type, sK7: nat).
% 1.50/1.61 thf(func_def_31, type, sK8: elem).
% 1.50/1.61 thf(func_def_32, type, sK9: list).
% 1.50/1.61 thf(func_def_34, type, ph11: !>[X0: $tType]:(X0)).
% 1.50/1.61 thf(f222,plain,(
% 1.50/1.61 $false),
% 1.50/1.61 inference(subsumption_resolution,[status(thm)],[f221,f96])).
% 1.50/1.61 thf(f96,plain,(
% 1.50/1.61 ($true = (listStar @ sK7 @ (app @ sK7 @ zero @ sK9 @ nil) @ sK9))),
% 1.50/1.61 inference(superposition,[status(thm)],[f88,f82])).
% 1.50/1.61 thf(f82,plain,(
% 1.50/1.61 ( ! [X0 : nat] : (((plus @ X0 @ zero) = X0)) )),
% 1.50/1.61 inference(cnf_transformation,[status(thm)],[f25])).
% 1.50/1.61 thf(f25,plain,(
% 1.50/1.61 ! [X0 : nat] : ((plus @ X0 @ zero) = X0)),
% 1.50/1.61 inference(fool_elimination,[status(thm)],[f24])).
% 1.50/1.61 thf(f24,plain,(
% 1.50/1.61 ! [X0 : nat] : ((plus @ X0 @ zero) = X0)),
% 1.50/1.61 inference(rectify,[status(thm)],[f10])).
% 1.50/1.61 thf(f10,axiom,(
% 1.50/1.61 ! [X10 : nat] : ((plus @ X10 @ zero) = X10)),
% 1.50/1.61 file('/export/starexec/sandbox2/tmp/tmp.gmviLDLzUA/DTF2THF_29509.p',plus_zero_r)).
% 1.50/1.61 thf(f88,plain,(
% 1.50/1.61 ((listStar @ (plus @ sK7 @ zero) @ (app @ sK7 @ zero @ sK9 @ nil) @ sK9) = $true)),
% 1.50/1.61 inference(cnf_transformation,[status(thm)],[f69])).
% 1.50/1.61 thf(f69,plain,(
% 1.50/1.61 ($true != (listStar @ (plus @ (suc @ sK7) @ zero) @ (app @ (suc @ sK7) @ zero @ (cons @ sK7 @ sK8 @ sK9) @ nil) @ (cons @ sK7 @ sK8 @ sK9))) & ($true = (listStar @ sK7 @ sK9 @ sK9)) & ((listStar @ (plus @ sK7 @ zero) @ (app @ sK7 @ zero @ sK9 @ nil) @ sK9) = $true)),
% 1.50/1.61 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f54,f68])).
% 1.50/1.61 thf(f68,plain,(
% 1.50/1.61 ? [X0 : nat,X1 : elem,X2 : list] : (($true != (listStar @ (plus @ (suc @ X0) @ zero) @ (app @ (suc @ X0) @ zero @ (cons @ X0 @ X1 @ X2) @ nil) @ (cons @ X0 @ X1 @ X2))) & ((listStar @ X0 @ X2 @ X2) = $true) & ((listStar @ (plus @ X0 @ zero) @ (app @ X0 @ zero @ X2 @ nil) @ X2) = $true)) => (($true != (listStar @ (plus @ (suc @ sK7) @ zero) @ (app @ (suc @ sK7) @ zero @ (cons @ sK7 @ sK8 @ sK9) @ nil) @ (cons @ sK7 @ sK8 @ sK9))) & ($true = (listStar @ sK7 @ sK9 @ sK9)) & ((listStar @ (plus @ sK7 @ zero) @ (app @ sK7 @ zero @ sK9 @ nil) @ sK9) = $true))),
% 1.50/1.61 introduced(definition,[],[choice_axiom])).
% 1.50/1.61 thf(f54,plain,(
% 1.50/1.61 ? [X0 : nat,X1 : elem,X2 : list] : (($true != (listStar @ (plus @ (suc @ X0) @ zero) @ (app @ (suc @ X0) @ zero @ (cons @ X0 @ X1 @ X2) @ nil) @ (cons @ X0 @ X1 @ X2))) & ((listStar @ X0 @ X2 @ X2) = $true) & ((listStar @ (plus @ X0 @ zero) @ (app @ X0 @ zero @ X2 @ nil) @ X2) = $true))),
% 1.50/1.61 inference(flattening,[status(thm)],[f53])).
% 1.50/1.61 thf(f53,plain,(
% 1.50/1.61 ? [X0 : nat,X1 : elem,X2 : list] : ((($true != (listStar @ (plus @ (suc @ X0) @ zero) @ (app @ (suc @ X0) @ zero @ (cons @ X0 @ X1 @ X2) @ nil) @ (cons @ X0 @ X1 @ X2))) & ((listStar @ (plus @ X0 @ zero) @ (app @ X0 @ zero @ X2 @ nil) @ X2) = $true)) & ((listStar @ X0 @ X2 @ X2) = $true))),
% 1.50/1.61 inference(ennf_transformation,[status(thm)],[f35])).
% 1.50/1.61 thf(f35,plain,(
% 1.50/1.61 ~! [X0 : nat,X1 : elem,X2 : list] : (((listStar @ X0 @ X2 @ X2) = $true) => (((listStar @ (plus @ X0 @ zero) @ (app @ X0 @ zero @ X2 @ nil) @ X2) = $true) => ($true = (listStar @ (plus @ (suc @ X0) @ zero) @ (app @ (suc @ X0) @ zero @ (cons @ X0 @ X1 @ X2) @ nil) @ (cons @ X0 @ X1 @ X2)))))),
% 1.50/1.61 inference(fool_elimination,[status(thm)],[f34])).
% 1.50/1.61 thf(f34,plain,(
% 1.50/1.61 ~! [X0 : nat,X1 : elem,X2 : list] : ((listStar @ X0 @ X2 @ X2) => ((listStar @ (plus @ X0 @ zero) @ (app @ X0 @ zero @ X2 @ nil) @ X2) => (listStar @ (plus @ (suc @ X0) @ zero) @ (app @ (suc @ X0) @ zero @ (cons @ X0 @ X1 @ X2) @ nil) @ (cons @ X0 @ X1 @ X2))))),
% 1.50/1.61 inference(rectify,[status(thm)],[f12])).
% 1.50/1.61 thf(f12,negated_conjecture,(
% 1.50/1.61 ~! [X6 : nat,X2 : elem,X12 : list] : ((listStar @ X6 @ X12 @ X12) => ((listStar @ (plus @ X6 @ zero) @ (app @ X6 @ zero @ X12 @ nil) @ X12) => (listStar @ (plus @ (suc @ X6) @ zero) @ (app @ (suc @ X6) @ zero @ (cons @ X6 @ X2 @ X12) @ nil) @ (cons @ X6 @ X2 @ X12))))),
% 1.50/1.61 inference(negated_conjecture,[status(cth)],[f11])).
% 1.50/1.61 thf(f11,conjecture,(
% 1.50/1.61 ! [X6 : nat,X2 : elem,X12 : list] : ((listStar @ X6 @ X12 @ X12) => ((listStar @ (plus @ X6 @ zero) @ (app @ X6 @ zero @ X12 @ nil) @ X12) => (listStar @ (plus @ (suc @ X6) @ zero) @ (app @ (suc @ X6) @ zero @ (cons @ X6 @ X2 @ X12) @ nil) @ (cons @ X6 @ X2 @ X12))))),
% 1.50/1.61 file('/export/starexec/sandbox2/tmp/tmp.gmviLDLzUA/DTF2THF_29509.p',list_app_nil_indstep)).
% 1.50/1.61 thf(f221,plain,(
% 1.50/1.61 ($true != (listStar @ sK7 @ (app @ sK7 @ zero @ sK9 @ nil) @ sK9))),
% 1.50/1.61 inference(trivial_inequality_removal,[status(thm)],[f216])).
% 1.50/1.61 thf(f216,plain,(
% 1.50/1.61 ($true != (listStar @ sK7 @ (app @ sK7 @ zero @ sK9 @ nil) @ sK9)) | ($true != $true)),
% 1.50/1.61 inference(superposition,[status(thm)],[f190,f85])).
% 1.50/1.61 thf(f85,plain,(
% 1.50/1.61 ( ! [X2 : list,X3 : list,X0 : nat,X1 : elem] : (((listStar @ (suc @ X0) @ (cons @ X0 @ X1 @ X2) @ (cons @ X0 @ X1 @ X3)) = $true) | ((listStar @ X0 @ X2 @ X3) != $true)) )),
% 1.50/1.61 inference(cnf_transformation,[status(thm)],[f57])).
% 1.50/1.61 thf(f57,plain,(
% 1.50/1.61 ! [X0 : nat,X1 : elem,X2 : list,X3 : list] : (((listStar @ X0 @ X2 @ X3) != $true) | ((listStar @ (suc @ X0) @ (cons @ X0 @ X1 @ X2) @ (cons @ X0 @ X1 @ X3)) = $true))),
% 1.50/1.61 inference(ennf_transformation,[status(thm)],[f23])).
% 1.50/1.61 thf(f23,plain,(
% 1.50/1.61 ! [X0 : nat,X1 : elem,X2 : list,X3 : list] : (((listStar @ X0 @ X2 @ X3) = $true) => ((listStar @ (suc @ X0) @ (cons @ X0 @ X1 @ X2) @ (cons @ X0 @ X1 @ X3)) = $true))),
% 1.50/1.61 inference(fool_elimination,[status(thm)],[f22])).
% 1.50/1.61 thf(f22,plain,(
% 1.50/1.61 ! [X0 : nat,X1 : elem,X2 : list,X3 : list] : ((listStar @ X0 @ X2 @ X3) => (listStar @ (suc @ X0) @ (cons @ X0 @ X1 @ X2) @ (cons @ X0 @ X1 @ X3)))),
% 1.50/1.61 inference(rectify,[status(thm)],[f6])).
% 1.50/1.61 thf(f6,axiom,(
% 1.50/1.61 ! [X6 : nat,X7 : elem,X8 : list,X9 : list] : ((listStar @ X6 @ X8 @ X9) => (listStar @ (suc @ X6) @ (cons @ X6 @ X7 @ X8) @ (cons @ X6 @ X7 @ X9)))),
% 1.50/1.61 file('/export/starexec/sandbox2/tmp/tmp.gmviLDLzUA/DTF2THF_29509.p',cons_tp_ax)).
% 1.50/1.61 thf(f190,plain,(
% 1.50/1.61 ((listStar @ (suc @ sK7) @ (cons @ sK7 @ sK8 @ (app @ sK7 @ zero @ sK9 @ nil)) @ (cons @ sK7 @ sK8 @ sK9)) != $true)),
% 1.50/1.61 inference(superposition,[status(thm)],[f162,f82])).
% 1.50/1.61 thf(f162,plain,(
% 1.50/1.61 ((listStar @ (plus @ (suc @ sK7) @ zero) @ (cons @ sK7 @ sK8 @ (app @ sK7 @ zero @ sK9 @ nil)) @ (cons @ sK7 @ sK8 @ sK9)) != $true)),
% 1.50/1.61 inference(superposition,[status(thm)],[f150,f82])).
% 1.50/1.61 thf(f150,plain,(
% 1.50/1.61 ($true != (listStar @ (plus @ (suc @ sK7) @ zero) @ (cons @ (plus @ sK7 @ zero) @ sK8 @ (app @ sK7 @ zero @ sK9 @ nil)) @ (cons @ sK7 @ sK8 @ sK9)))),
% 1.50/1.61 inference(subsumption_resolution,[status(thm)],[f149,f71])).
% 1.50/1.61 thf(f71,plain,(
% 1.50/1.61 ((listStar @ zero @ nil @ nil) = $true)),
% 1.50/1.61 inference(cnf_transformation,[status(thm)],[f21])).
% 1.50/1.61 thf(f21,plain,(
% 1.50/1.61 ((listStar @ zero @ nil @ nil) = $true)),
% 1.50/1.61 inference(fool_elimination,[status(thm)],[f20])).
% 1.50/1.61 thf(f20,plain,(
% 1.50/1.61 (listStar @ zero @ nil @ nil)),
% 1.50/1.61 inference(rectify,[status(thm)],[f5])).
% 1.50/1.61 thf(f5,axiom,(
% 1.50/1.61 (listStar @ zero @ nil @ nil)),
% 1.50/1.61 file('/export/starexec/sandbox2/tmp/tmp.gmviLDLzUA/DTF2THF_29509.p',nil_tp_ax)).
% 1.50/1.61 thf(f149,plain,(
% 1.50/1.61 ((listStar @ zero @ nil @ nil) != $true) | ($true != (listStar @ (plus @ (suc @ sK7) @ zero) @ (cons @ (plus @ sK7 @ zero) @ sK8 @ (app @ sK7 @ zero @ sK9 @ nil)) @ (cons @ sK7 @ sK8 @ sK9)))),
% 1.50/1.61 inference(subsumption_resolution,[status(thm)],[f148,f89])).
% 1.50/1.61 thf(f89,plain,(
% 1.50/1.61 ($true = (listStar @ sK7 @ sK9 @ sK9))),
% 1.50/1.61 inference(cnf_transformation,[status(thm)],[f69])).
% 1.50/1.61 thf(f148,plain,(
% 1.50/1.61 ($true != (listStar @ sK7 @ sK9 @ sK9)) | ($true != (listStar @ (plus @ (suc @ sK7) @ zero) @ (cons @ (plus @ sK7 @ zero) @ sK8 @ (app @ sK7 @ zero @ sK9 @ nil)) @ (cons @ sK7 @ sK8 @ sK9))) | ((listStar @ zero @ nil @ nil) != $true)),
% 1.50/1.61 inference(trivial_inequality_removal,[status(thm)],[f138])).
% 1.50/1.61 thf(f138,plain,(
% 1.50/1.61 ((listStar @ zero @ nil @ nil) != $true) | ($true != (listStar @ (plus @ (suc @ sK7) @ zero) @ (cons @ (plus @ sK7 @ zero) @ sK8 @ (app @ sK7 @ zero @ sK9 @ nil)) @ (cons @ sK7 @ sK8 @ sK9))) | ($true != (listStar @ sK7 @ sK9 @ sK9)) | ($true != $true)),
% 1.50/1.61 inference(superposition,[status(thm)],[f104,f87])).
% 1.50/1.61 thf(f87,plain,(
% 1.50/1.61 ( ! [X2 : elem,X3 : list,X0 : nat,X1 : nat,X4 : list] : (($true = (listStar @ (plus @ (suc @ X0) @ X1) @ (app @ (suc @ X0) @ X1 @ (cons @ X0 @ X2 @ X3) @ X4) @ (cons @ (plus @ X0 @ X1) @ X2 @ (app @ X0 @ X1 @ X3 @ X4)))) | ($true != (listStar @ X0 @ X3 @ X3)) | ($true != (listStar @ X1 @ X4 @ X4))) )),
% 1.50/1.61 inference(cnf_transformation,[status(thm)],[f60])).
% 1.50/1.61 thf(f60,plain,(
% 1.50/1.61 ! [X0 : nat,X1 : nat,X2 : elem,X3 : list,X4 : list] : (($true != (listStar @ X1 @ X4 @ X4)) | ($true = (listStar @ (plus @ (suc @ X0) @ X1) @ (app @ (suc @ X0) @ X1 @ (cons @ X0 @ X2 @ X3) @ X4) @ (cons @ (plus @ X0 @ X1) @ X2 @ (app @ X0 @ X1 @ X3 @ X4)))) | ($true != (listStar @ X0 @ X3 @ X3)))),
% 1.50/1.61 inference(flattening,[status(thm)],[f59])).
% 1.50/1.61 thf(f59,plain,(
% 1.50/1.61 ! [X0 : nat,X1 : nat,X2 : elem,X3 : list,X4 : list] : ((($true = (listStar @ (plus @ (suc @ X0) @ X1) @ (app @ (suc @ X0) @ X1 @ (cons @ X0 @ X2 @ X3) @ X4) @ (cons @ (plus @ X0 @ X1) @ X2 @ (app @ X0 @ X1 @ X3 @ X4)))) | ($true != (listStar @ X1 @ X4 @ X4))) | ($true != (listStar @ X0 @ X3 @ X3)))),
% 1.50/1.61 inference(ennf_transformation,[status(thm)],[f15])).
% 1.50/1.61 thf(f15,plain,(
% 1.50/1.61 ! [X0 : nat,X1 : nat,X2 : elem,X3 : list,X4 : list] : (($true = (listStar @ X0 @ X3 @ X3)) => (($true = (listStar @ X1 @ X4 @ X4)) => ($true = (listStar @ (plus @ (suc @ X0) @ X1) @ (app @ (suc @ X0) @ X1 @ (cons @ X0 @ X2 @ X3) @ X4) @ (cons @ (plus @ X0 @ X1) @ X2 @ (app @ X0 @ X1 @ X3 @ X4))))))),
% 1.50/1.61 inference(fool_elimination,[status(thm)],[f14])).
% 1.50/1.61 thf(f14,plain,(
% 1.50/1.61 ! [X0 : nat,X1 : nat,X2 : elem,X3 : list,X4 : list] : ((listStar @ X0 @ X3 @ X3) => ((listStar @ X1 @ X4 @ X4) => (listStar @ (plus @ (suc @ X0) @ X1) @ (app @ (suc @ X0) @ X1 @ (cons @ X0 @ X2 @ X3) @ X4) @ (cons @ (plus @ X0 @ X1) @ X2 @ (app @ X0 @ X1 @ X3 @ X4)))))),
% 1.50/1.61 inference(rectify,[status(thm)],[f9])).
% 1.50/1.61 thf(f9,axiom,(
% 1.50/1.61 ! [X6 : nat,X10 : nat,X2 : elem,X3 : list,X4 : list] : ((listStar @ X6 @ X3 @ X3) => ((listStar @ X10 @ X4 @ X4) => (listStar @ (plus @ (suc @ X6) @ X10) @ (app @ (suc @ X6) @ X10 @ (cons @ X6 @ X2 @ X3) @ X4) @ (cons @ (plus @ X6 @ X10) @ X2 @ (app @ X6 @ X10 @ X3 @ X4)))))),
% 1.50/1.61 file('/export/starexec/sandbox2/tmp/tmp.gmviLDLzUA/DTF2THF_29509.p',ax4)).
% 1.50/1.61 thf(f104,plain,(
% 1.50/1.61 ( ! [X0 : list] : (($true != (listStar @ (plus @ (suc @ sK7) @ zero) @ (app @ (suc @ sK7) @ zero @ (cons @ sK7 @ sK8 @ sK9) @ nil) @ X0)) | ($true != (listStar @ (plus @ (suc @ sK7) @ zero) @ X0 @ (cons @ sK7 @ sK8 @ sK9)))) )),
% 1.50/1.61 inference(subsumption_resolution,[status(thm)],[f101,f86])).
% 1.50/1.61 thf(f86,plain,(
% 1.50/1.61 ( ! [X0 : nat] : (($true = (isPer @ list @ (listStar @ X0)))) )),
% 1.50/1.61 inference(cnf_transformation,[status(thm)],[f19])).
% 1.50/1.61 thf(f19,plain,(
% 1.50/1.61 ! [X0 : nat] : ($true = (isPer @ list @ (listStar @ X0)))),
% 1.50/1.61 inference(fool_elimination,[status(thm)],[f18])).
% 1.50/1.61 thf(f18,plain,(
% 1.50/1.61 ! [X0 : nat] : (isPer @ list @ (listStar @ X0))),
% 1.50/1.61 inference(rectify,[status(thm)],[f4])).
% 1.50/1.61 thf(f4,axiom,(
% 1.50/1.61 ! [X5 : nat] : (isPer @ list @ (listStar @ X5))),
% 1.50/1.61 file('/export/starexec/sandbox2/tmp/tmp.gmviLDLzUA/DTF2THF_29509.p','\'listStar\'_is_per')).
% 1.50/1.61 thf(f101,plain,(
% 1.50/1.61 ( ! [X0 : list] : (($true != (listStar @ (plus @ (suc @ sK7) @ zero) @ X0 @ (cons @ sK7 @ sK8 @ sK9))) | ((isPer @ list @ (listStar @ (plus @ (suc @ sK7) @ zero))) != $true) | ($true != (listStar @ (plus @ (suc @ sK7) @ zero) @ (app @ (suc @ sK7) @ zero @ (cons @ sK7 @ sK8 @ sK9) @ nil) @ X0))) )),
% 1.50/1.61 inference(trivial_inequality_removal,[status(thm)],[f100])).
% 1.50/1.61 thf(f100,plain,(
% 1.50/1.61 ( ! [X0 : list] : (($true != $true) | ($true != (listStar @ (plus @ (suc @ sK7) @ zero) @ (app @ (suc @ sK7) @ zero @ (cons @ sK7 @ sK8 @ sK9) @ nil) @ X0)) | ($true != (listStar @ (plus @ (suc @ sK7) @ zero) @ X0 @ (cons @ sK7 @ sK8 @ sK9))) | ((isPer @ list @ (listStar @ (plus @ (suc @ sK7) @ zero))) != $true)) )),
% 1.50/1.61 inference(superposition,[status(thm)],[f90,f81])).
% 1.50/1.61 thf(f81,plain,(
% 1.50/1.61 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o,X4 : X0] : (((X1 @ X2 @ X4) = $true) | ((isPer @ X0 @ X1) != $true) | ((X1 @ X2 @ X3) != $true) | ((X1 @ X3 @ X4) != $true)) )),
% 1.50/1.61 inference(cnf_transformation,[status(thm)],[f67])).
% 1.50/1.61 thf(f67,plain,(
% 1.50/1.61 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((! [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X2 @ X4) = $true) | ((X1 @ X3 @ X4) != $true)) & ! [X5 : X0,X6 : X0] : (((X1 @ X5 @ X6) != $true) | ($true = (X1 @ X6 @ X5)))) | ((isPer @ X0 @ X1) != $true)) & (((isPer @ X0 @ X1) = $true) | (($true = (X1 @ (sK2 @ X0 @ X1) @ (sK3 @ X0 @ X1))) & ((X1 @ (sK2 @ X0 @ X1) @ (sK4 @ X0 @ X1)) != $true) & ($true = (X1 @ (sK3 @ X0 @ X1) @ (sK4 @ X0 @ X1)))) | (($true = (X1 @ (sK5 @ X0 @ X1) @ (sK6 @ X0 @ X1))) & ($true != (X1 @ (sK6 @ X0 @ X1) @ (sK5 @ X0 @ X1))))))),
% 1.50/1.61 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6])],[f64,f66,f65])).
% 1.50/1.61 thf(f65,plain,(
% 1.50/1.61 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X7 : X0,X8 : X0,X9 : X0] : (($true = (X1 @ X7 @ X8)) & ($true != (X1 @ X7 @ X9)) & ((X1 @ X8 @ X9) = $true)) => (($true = (X1 @ (sK2 @ X0 @ X1) @ (sK3 @ X0 @ X1))) & ((X1 @ (sK2 @ X0 @ X1) @ (sK4 @ X0 @ X1)) != $true) & ($true = (X1 @ (sK3 @ X0 @ X1) @ (sK4 @ X0 @ X1)))))),
% 1.50/1.61 introduced(definition,[],[choice_axiom])).
% 1.50/1.61 thf(f66,plain,(
% 1.50/1.61 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X10 : X0,X11 : X0] : (($true = (X1 @ X10 @ X11)) & ($true != (X1 @ X11 @ X10))) => (($true = (X1 @ (sK5 @ X0 @ X1) @ (sK6 @ X0 @ X1))) & ($true != (X1 @ (sK6 @ X0 @ X1) @ (sK5 @ X0 @ X1)))))),
% 1.50/1.61 introduced(definition,[],[choice_axiom])).
% 1.50/1.61 thf(f64,plain,(
% 1.50/1.61 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((! [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X2 @ X4) = $true) | ((X1 @ X3 @ X4) != $true)) & ! [X5 : X0,X6 : X0] : (((X1 @ X5 @ X6) != $true) | ($true = (X1 @ X6 @ X5)))) | ((isPer @ X0 @ X1) != $true)) & (((isPer @ X0 @ X1) = $true) | ? [X7 : X0,X8 : X0,X9 : X0] : (($true = (X1 @ X7 @ X8)) & ($true != (X1 @ X7 @ X9)) & ((X1 @ X8 @ X9) = $true)) | ? [X10 : X0,X11 : X0] : (($true = (X1 @ X10 @ X11)) & ($true != (X1 @ X11 @ X10)))))),
% 1.50/1.61 inference(rectify,[status(thm)],[f63])).
% 1.50/1.61 thf(f63,plain,(
% 1.50/1.61 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((! [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X2 @ X4) = $true) | ((X1 @ X3 @ X4) != $true)) & ! [X5 : X0,X6 : X0] : (((X1 @ X5 @ X6) != $true) | ($true = (X1 @ X6 @ X5)))) | ((isPer @ X0 @ X1) != $true)) & (((isPer @ X0 @ X1) = $true) | ? [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X2 @ X3) = $true) & ((X1 @ X2 @ X4) != $true) & ((X1 @ X3 @ X4) = $true)) | ? [X5 : X0,X6 : X0] : (((X1 @ X5 @ X6) = $true) & ($true != (X1 @ X6 @ X5)))))),
% 1.50/1.61 inference(flattening,[status(thm)],[f62])).
% 1.50/1.61 thf(f62,plain,(
% 1.50/1.61 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((! [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X2 @ X4) = $true) | ((X1 @ X3 @ X4) != $true)) & ! [X5 : X0,X6 : X0] : (((X1 @ X5 @ X6) != $true) | ($true = (X1 @ X6 @ X5)))) | ((isPer @ X0 @ X1) != $true)) & (((isPer @ X0 @ X1) = $true) | (? [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X2 @ X3) = $true) & ((X1 @ X2 @ X4) != $true) & ((X1 @ X3 @ X4) = $true)) | ? [X5 : X0,X6 : X0] : (((X1 @ X5 @ X6) = $true) & ($true != (X1 @ X6 @ X5))))))),
% 1.50/1.61 inference(nnf_transformation,[status(thm)],[f56])).
% 1.50/1.61 thf(f56,plain,(
% 1.50/1.61 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X2 @ X3) != $true) | ((X1 @ X2 @ X4) = $true) | ((X1 @ X3 @ X4) != $true)) & ! [X5 : X0,X6 : X0] : (((X1 @ X5 @ X6) != $true) | ($true = (X1 @ X6 @ X5)))) <=> ((isPer @ X0 @ X1) = $true))),
% 1.50/1.61 inference(flattening,[status(thm)],[f55])).
% 1.50/1.61 thf(f55,plain,(
% 1.50/1.61 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X2 : X0,X3 : X0,X4 : X0] : ((((X1 @ X2 @ X4) = $true) | ((X1 @ X3 @ X4) != $true)) | ((X1 @ X2 @ X3) != $true)) & ! [X5 : X0,X6 : X0] : (((X1 @ X5 @ X6) != $true) | ($true = (X1 @ X6 @ X5)))) <=> ((isPer @ X0 @ X1) = $true))),
% 1.50/1.61 inference(ennf_transformation,[status(thm)],[f27])).
% 1.50/1.61 thf(f27,plain,(
% 1.50/1.61 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X2 : X0,X3 : X0,X4 : X0] : (((X1 @ X2 @ X3) = $true) => (((X1 @ X3 @ X4) = $true) => ((X1 @ X2 @ X4) = $true))) & ! [X5 : X0,X6 : X0] : (((X1 @ X5 @ X6) = $true) => ($true = (X1 @ X6 @ X5)))) <=> ((isPer @ X0 @ X1) = $true))),
% 1.50/1.61 inference(fool_elimination,[status(thm)],[f26])).
% 1.50/1.61 thf(f26,plain,(
% 1.50/1.61 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) <=> (! [X2 : X0,X3 : X0,X4 : X0] : ((X1 @ X2 @ X3) => ((X1 @ X3 @ X4) => (X1 @ X2 @ X4))) & ! [X5 : X0,X6 : X0] : ((X1 @ X5 @ X6) => (X1 @ X6 @ X5))))),
% 1.50/1.61 inference(rectify,[status(thm)],[f1])).
% 1.50/1.61 thf(f1,axiom,(
% 1.50/1.61 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) <=> (! [X2 : X0,X3 : X0,X4 : X0] : ((X1 @ X2 @ X3) => ((X1 @ X3 @ X4) => (X1 @ X2 @ X4))) & ! [X2 : X0,X3 : X0] : ((X1 @ X2 @ X3) => (X1 @ X3 @ X2))))),
% 1.50/1.61 file('/export/starexec/sandbox2/tmp/tmp.gmviLDLzUA/DTF2THF_29509.p',is_per)).
% 1.50/1.61 thf(f90,plain,(
% 1.50/1.61 ($true != (listStar @ (plus @ (suc @ sK7) @ zero) @ (app @ (suc @ sK7) @ zero @ (cons @ sK7 @ sK8 @ sK9) @ nil) @ (cons @ sK7 @ sK8 @ sK9)))),
% 1.50/1.61 inference(cnf_transformation,[status(thm)],[f69])).
% 1.50/1.61 % SZS output end Proof for DTF2THF_29509
% 1.50/1.61 % (29651)------------------------------
% 1.50/1.61 % (29651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.61 % (29651)Termination reason: Refutation
% 1.50/1.61
% 1.50/1.61 % (29651)Memory used [KB]: 5756
% 1.50/1.61 % (29651)Time elapsed: 0.025 s
% 1.50/1.61 % (29651)Instructions burned: 40 (million)
% 1.50/1.61 % (29651)------------------------------
% 1.50/1.61 % (29651)------------------------------
% 1.50/1.61 % (29607)Success in time 0.428 s
%------------------------------------------------------------------------------