%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT360^1 : 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 : n028.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 08:45:33 AM UTC 2026
% Result : Theorem 6.85s 2.13s
% Output : Refutation 6.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 81 ( 16 unt; 0 typ; 4 def)
% Number of atoms : 530 ( 176 equ; 0 cnn)
% Maximal formula atoms : 12 ( 6 avg)
% Number of connectives : 1469 ( 106 ~; 91 |; 41 &;1193 @)
% ( 9 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 12 con; 0-4 aty)
% Number of variables : 176 ( 0 ^; 144 !; 32 ?; 176 :)
% 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: nat ).
thf(func_def_17,type,
sK1: list ).
thf(func_def_18,type,
sK2: nat ).
thf(func_def_19,type,
sK3: list ).
thf(func_def_20,type,
sK4:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_21,type,
sK5:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_22,type,
sK6:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_23,type,
sK7:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_24,type,
sK8:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_25,type,
sP9: $o > $o ).
thf(func_def_27,type,
ph11:
!>[X0: $tType] : X0 ).
thf(f1026,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f77,f964,f995,f1020,f1025]) ).
thf(f1025,plain,
~ spl10_1,
inference(avatar_contradiction_clause,[status(thm)],[f1024]) ).
thf(f1024,plain,
( $false
| ~ spl10_1 ),
inference(trivial_inequality_removal,[status(thm)],[f1023]) ).
thf(f1023,plain,
( ( $false = $true )
| ~ spl10_1 ),
inference(backward_demodulation,[status(thm)],[f66,f72]) ).
thf(f72,plain,
( ( ( sP9 @ $true )
= $false )
| ~ spl10_1 ),
inference(avatar_component_clause,[status(thm)],[f70]) ).
thf(f70,definition,
( spl10_1
<=> ( ( sP9 @ $true )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl10_1])],[avatar_definition]) ).
thf(f66,plain,
( ( sP9 @ $true )
= $true ),
inference(inequality_splitting,[status(thm)],[f53,f65]) ).
thf(f65,plain,
( ( sP9 @ ( listStar @ ( plus @ zero @ ( plus @ sK0 @ sK2 ) ) @ ( app @ zero @ ( plus @ sK0 @ sK2 ) @ nil @ ( app @ sK0 @ sK2 @ sK1 @ sK3 ) ) @ ( app @ ( plus @ zero @ sK0 ) @ sK2 @ ( app @ zero @ sK0 @ nil @ sK1 ) @ sK3 ) ) )
= $false ),
introduced(definition,[new_symbols(naming,[sP9])],[inequality_splitting_name_introduction]) ).
thf(f53,plain,
( ( listStar @ ( plus @ zero @ ( plus @ sK0 @ sK2 ) ) @ ( app @ zero @ ( plus @ sK0 @ sK2 ) @ nil @ ( app @ sK0 @ sK2 @ sK1 @ sK3 ) ) @ ( app @ ( plus @ zero @ sK0 ) @ sK2 @ ( app @ zero @ sK0 @ nil @ sK1 ) @ sK3 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ( listStar @ ( plus @ zero @ ( plus @ sK0 @ sK2 ) ) @ ( app @ zero @ ( plus @ sK0 @ sK2 ) @ nil @ ( app @ sK0 @ sK2 @ sK1 @ sK3 ) ) @ ( app @ ( plus @ zero @ sK0 ) @ sK2 @ ( app @ zero @ sK0 @ nil @ sK1 ) @ sK3 ) )
!= $true )
& ( ( listStar @ sK0 @ sK1 @ sK1 )
= $true )
& ( ( listStar @ sK2 @ sK3 @ sK3 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f35,f40]) ).
thf(f40,plain,
( ? [X0: nat,X1: list,X2: nat,X3: list] :
( ( ( listStar @ ( plus @ zero @ ( plus @ X0 @ X2 ) ) @ ( app @ zero @ ( plus @ X0 @ X2 ) @ nil @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ zero @ X0 ) @ X2 @ ( app @ zero @ X0 @ nil @ X1 ) @ X3 ) )
!= $true )
& ( ( listStar @ X0 @ X1 @ X1 )
= $true )
& ( ( listStar @ X2 @ X3 @ X3 )
= $true ) )
=> ( ( ( listStar @ ( plus @ zero @ ( plus @ sK0 @ sK2 ) ) @ ( app @ zero @ ( plus @ sK0 @ sK2 ) @ nil @ ( app @ sK0 @ sK2 @ sK1 @ sK3 ) ) @ ( app @ ( plus @ zero @ sK0 ) @ sK2 @ ( app @ zero @ sK0 @ nil @ sK1 ) @ sK3 ) )
!= $true )
& ( ( listStar @ sK0 @ sK1 @ sK1 )
= $true )
& ( ( listStar @ sK2 @ sK3 @ sK3 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f35,plain,
? [X0: nat,X1: list,X2: nat,X3: list] :
( ( ( listStar @ ( plus @ zero @ ( plus @ X0 @ X2 ) ) @ ( app @ zero @ ( plus @ X0 @ X2 ) @ nil @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ zero @ X0 ) @ X2 @ ( app @ zero @ X0 @ nil @ X1 ) @ X3 ) )
!= $true )
& ( ( listStar @ X0 @ X1 @ X1 )
= $true )
& ( ( listStar @ X2 @ X3 @ X3 )
= $true ) ),
inference(flattening,[status(thm)],[f34]) ).
thf(f34,plain,
? [X0: nat,X1: list,X2: nat,X3: list] :
( ( ( listStar @ ( plus @ zero @ ( plus @ X0 @ X2 ) ) @ ( app @ zero @ ( plus @ X0 @ X2 ) @ nil @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ zero @ X0 ) @ X2 @ ( app @ zero @ X0 @ nil @ X1 ) @ X3 ) )
!= $true )
& ( ( listStar @ X2 @ X3 @ X3 )
= $true )
& ( ( listStar @ X0 @ X1 @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
~ ! [X0: nat,X1: list,X2: nat,X3: list] :
( ( ( listStar @ X0 @ X1 @ X1 )
= $true )
=> ( ( ( listStar @ X2 @ X3 @ X3 )
= $true )
=> ( ( listStar @ ( plus @ zero @ ( plus @ X0 @ X2 ) ) @ ( app @ zero @ ( plus @ X0 @ X2 ) @ nil @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ zero @ X0 ) @ X2 @ ( app @ zero @ X0 @ nil @ X1 ) @ X3 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
~ ! [X0: nat,X1: list,X2: nat,X3: list] :
( ( listStar @ X0 @ X1 @ X1 )
=> ( ( listStar @ X2 @ X3 @ X3 )
=> ( listStar @ ( plus @ zero @ ( plus @ X0 @ X2 ) ) @ ( app @ zero @ ( plus @ X0 @ X2 ) @ nil @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ zero @ X0 ) @ X2 @ ( app @ zero @ X0 @ nil @ X1 ) @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,negated_conjecture,
~ ! [X13: nat,X15: list,X14: nat,X16: list] :
( ( listStar @ X13 @ X15 @ X15 )
=> ( ( listStar @ X14 @ X16 @ X16 )
=> ( listStar @ ( plus @ zero @ ( plus @ X13 @ X14 ) ) @ ( app @ zero @ ( plus @ X13 @ X14 ) @ nil @ ( app @ X13 @ X14 @ X15 @ X16 ) ) @ ( app @ ( plus @ zero @ X13 ) @ X14 @ ( app @ zero @ X13 @ nil @ X15 ) @ X16 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
thf(f11,conjecture,
! [X13: nat,X15: list,X14: nat,X16: list] :
( ( listStar @ X13 @ X15 @ X15 )
=> ( ( listStar @ X14 @ X16 @ X16 )
=> ( listStar @ ( plus @ zero @ ( plus @ X13 @ X14 ) ) @ ( app @ zero @ ( plus @ X13 @ X14 ) @ nil @ ( app @ X13 @ X14 @ X15 @ X16 ) ) @ ( app @ ( plus @ zero @ X13 ) @ X14 @ ( app @ zero @ X13 @ nil @ X15 ) @ X16 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.v0WQauavVr/DTF2THF_27475.p',list_app_assoc_base) ).
thf(f1020,plain,
spl10_8,
inference(avatar_contradiction_clause,[status(thm)],[f1019]) ).
thf(f1019,plain,
( $false
| spl10_8 ),
inference(subsumption_resolution,[status(thm)],[f1015,f52]) ).
thf(f52,plain,
( ( listStar @ sK0 @ sK1 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f1015,plain,
( ( ( listStar @ sK0 @ sK1 @ sK1 )
!= $true )
| spl10_8 ),
inference(trivial_inequality_removal,[status(thm)],[f1012]) ).
thf(f1012,plain,
( ( ( listStar @ sK0 @ sK1 @ sK1 )
!= $true )
| ( $true != $true )
| spl10_8 ),
inference(superposition,[status(thm)],[f1010,f947]) ).
thf(f947,plain,
! [X0: nat,X1: list] :
( ( ( listStar @ X0 @ ( app @ zero @ X0 @ nil @ X1 ) @ X1 )
= $true )
| ( ( listStar @ X0 @ X1 @ X1 )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f48,f49]) ).
thf(f49,plain,
! [X0: nat] :
( ( plus @ zero @ X0 )
= X0 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
! [X0: nat] :
( ( plus @ zero @ X0 )
= X0 ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
! [X6: nat] :
( ( plus @ zero @ X6 )
= X6 ),
file('/export/starexec/sandbox/tmp/tmp.v0WQauavVr/DTF2THF_27475.p',ax1) ).
thf(f48,plain,
! [X0: nat,X1: list] :
( ( ( listStar @ X0 @ X1 @ X1 )
!= $true )
| ( ( listStar @ ( plus @ zero @ X0 ) @ ( app @ zero @ X0 @ nil @ X1 ) @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
! [X0: nat,X1: list] :
( ( ( listStar @ ( plus @ zero @ X0 ) @ ( app @ zero @ X0 @ nil @ X1 ) @ X1 )
= $true )
| ( ( listStar @ X0 @ X1 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: nat,X1: list] :
( ( ( listStar @ X0 @ X1 @ X1 )
= $true )
=> ( ( listStar @ ( plus @ zero @ X0 ) @ ( app @ zero @ X0 @ nil @ X1 ) @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: nat,X1: list] :
( ( listStar @ X0 @ X1 @ X1 )
=> ( listStar @ ( plus @ zero @ X0 ) @ ( app @ zero @ X0 @ nil @ X1 ) @ X1 ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,axiom,
! [X6: nat,X2: list] :
( ( listStar @ X6 @ X2 @ X2 )
=> ( listStar @ ( plus @ zero @ X6 ) @ ( app @ zero @ X6 @ nil @ X2 ) @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.v0WQauavVr/DTF2THF_27475.p',ax3) ).
thf(f1010,plain,
( ( ( listStar @ sK0 @ ( app @ zero @ sK0 @ nil @ sK1 ) @ sK1 )
!= $true )
| spl10_8 ),
inference(subsumption_resolution,[status(thm)],[f1009,f50]) ).
thf(f50,plain,
! [X0: nat] :
( ( isPer @ list @ ( listStar @ X0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: nat] :
( ( isPer @ list @ ( listStar @ X0 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: nat] : ( isPer @ list @ ( listStar @ X0 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X5: nat] : ( isPer @ list @ ( listStar @ X5 ) ),
file('/export/starexec/sandbox/tmp/tmp.v0WQauavVr/DTF2THF_27475.p','\'listStar\'_is_per') ).
thf(f1009,plain,
( ( ( listStar @ sK0 @ ( app @ zero @ sK0 @ nil @ sK1 ) @ sK1 )
!= $true )
| ( ( isPer @ list @ ( listStar @ sK0 ) )
!= $true )
| spl10_8 ),
inference(trivial_inequality_removal,[status(thm)],[f1006]) ).
thf(f1006,plain,
( ( $true != $true )
| ( ( isPer @ list @ ( listStar @ sK0 ) )
!= $true )
| ( ( listStar @ sK0 @ ( app @ zero @ sK0 @ nil @ sK1 ) @ sK1 )
!= $true )
| spl10_8 ),
inference(superposition,[status(thm)],[f1005,f63]) ).
thf(f63,plain,
! [X0: $tType,X1: X0 > X0 > $o,X6: X0,X5: X0] :
( ( ( X1 @ X6 @ X5 )
= $true )
| ( ( X1 @ X5 @ X6 )
!= $true )
| ( ( isPer @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f47,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 @ X6 @ X5 )
= $true )
| ( ( X1 @ X5 @ X6 )
!= $true ) ) )
| ( ( isPer @ X0 @ X1 )
!= $true ) )
& ( ( ( isPer @ X0 @ X1 )
= $true )
| ( ( ( X1 @ ( sK4 @ X0 @ X1 ) @ ( sK6 @ X0 @ X1 ) )
!= $true )
& ( ( X1 @ ( sK5 @ X0 @ X1 ) @ ( sK6 @ X0 @ X1 ) )
= $true )
& ( ( X1 @ ( sK4 @ X0 @ X1 ) @ ( sK5 @ X0 @ X1 ) )
= $true ) )
| ( ( ( X1 @ ( sK8 @ X0 @ X1 ) @ ( sK7 @ X0 @ X1 ) )
!= $true )
& ( ( X1 @ ( sK7 @ X0 @ X1 ) @ ( sK8 @ X0 @ X1 ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f44,f46,f45]) ).
thf(f45,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ? [X7: X0,X8: X0,X9: X0] :
( ( ( X1 @ X7 @ X9 )
!= $true )
& ( ( X1 @ X8 @ X9 )
= $true )
& ( ( X1 @ X7 @ X8 )
= $true ) )
=> ( ( ( X1 @ ( sK4 @ X0 @ X1 ) @ ( sK6 @ X0 @ X1 ) )
!= $true )
& ( ( X1 @ ( sK5 @ X0 @ X1 ) @ ( sK6 @ X0 @ X1 ) )
= $true )
& ( ( X1 @ ( sK4 @ X0 @ X1 ) @ ( sK5 @ X0 @ X1 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f46,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ? [X10: X0,X11: X0] :
( ( ( X1 @ X11 @ X10 )
!= $true )
& ( ( X1 @ X10 @ X11 )
= $true ) )
=> ( ( ( X1 @ ( sK8 @ X0 @ X1 ) @ ( sK7 @ X0 @ X1 ) )
!= $true )
& ( ( X1 @ ( sK7 @ X0 @ X1 ) @ ( sK8 @ X0 @ X1 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f44,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 @ X6 @ X5 )
= $true )
| ( ( X1 @ X5 @ X6 )
!= $true ) ) )
| ( ( isPer @ X0 @ X1 )
!= $true ) )
& ( ( ( isPer @ X0 @ X1 )
= $true )
| ? [X7: X0,X8: X0,X9: X0] :
( ( ( X1 @ X7 @ X9 )
!= $true )
& ( ( X1 @ X8 @ X9 )
= $true )
& ( ( X1 @ X7 @ X8 )
= $true ) )
| ? [X10: X0,X11: X0] :
( ( ( X1 @ X11 @ X10 )
!= $true )
& ( ( X1 @ X10 @ X11 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f43]) ).
thf(f43,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ( ! [X4: X0,X5: X0,X6: X0] :
( ( ( X1 @ X4 @ X6 )
= $true )
| ( ( X1 @ X5 @ X6 )
!= $true )
| ( ( X1 @ X4 @ X5 )
!= $true ) )
& ! [X2: X0,X3: X0] :
( ( ( X1 @ X3 @ X2 )
= $true )
| ( ( X1 @ X2 @ X3 )
!= $true ) ) )
| ( ( isPer @ X0 @ X1 )
!= $true ) )
& ( ( ( isPer @ X0 @ X1 )
= $true )
| ? [X4: X0,X5: X0,X6: X0] :
( ( ( X1 @ X4 @ X6 )
!= $true )
& ( ( X1 @ X5 @ X6 )
= $true )
& ( ( X1 @ X4 @ X5 )
= $true ) )
| ? [X2: X0,X3: X0] :
( ( ( X1 @ X3 @ X2 )
!= $true )
& ( ( X1 @ X2 @ X3 )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f42]) ).
thf(f42,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ( ! [X4: X0,X5: X0,X6: X0] :
( ( ( X1 @ X4 @ X6 )
= $true )
| ( ( X1 @ X5 @ X6 )
!= $true )
| ( ( X1 @ X4 @ X5 )
!= $true ) )
& ! [X2: X0,X3: X0] :
( ( ( X1 @ X3 @ X2 )
= $true )
| ( ( X1 @ X2 @ X3 )
!= $true ) ) )
| ( ( isPer @ X0 @ X1 )
!= $true ) )
& ( ( ( isPer @ X0 @ X1 )
= $true )
| ? [X4: X0,X5: X0,X6: X0] :
( ( ( X1 @ X4 @ X6 )
!= $true )
& ( ( X1 @ X5 @ X6 )
= $true )
& ( ( X1 @ X4 @ X5 )
= $true ) )
| ? [X2: X0,X3: X0] :
( ( ( X1 @ X3 @ X2 )
!= $true )
& ( ( X1 @ X2 @ X3 )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
thf(f39,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ! [X4: X0,X5: X0,X6: X0] :
( ( ( X1 @ X4 @ X6 )
= $true )
| ( ( X1 @ X5 @ X6 )
!= $true )
| ( ( X1 @ X4 @ X5 )
!= $true ) )
& ! [X2: X0,X3: X0] :
( ( ( X1 @ X3 @ X2 )
= $true )
| ( ( X1 @ X2 @ X3 )
!= $true ) ) )
<=> ( ( isPer @ X0 @ X1 )
= $true ) ),
inference(flattening,[status(thm)],[f38]) ).
thf(f38,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ! [X2: X0,X3: X0] :
( ( ( X1 @ X3 @ X2 )
= $true )
| ( ( X1 @ X2 @ X3 )
!= $true ) )
& ! [X4: X0,X5: X0,X6: X0] :
( ( ( X1 @ X4 @ X6 )
= $true )
| ( ( X1 @ X5 @ X6 )
!= $true )
| ( ( X1 @ X4 @ X5 )
!= $true ) ) )
<=> ( ( isPer @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( ! [X2: X0,X3: X0] :
( ( ( X1 @ X2 @ X3 )
= $true )
=> ( ( X1 @ X3 @ X2 )
= $true ) )
& ! [X4: X0,X5: X0,X6: X0] :
( ( ( X1 @ X4 @ X5 )
= $true )
=> ( ( ( X1 @ X5 @ X6 )
= $true )
=> ( ( X1 @ X4 @ X6 )
= $true ) ) ) )
<=> ( ( 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] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) )
& ! [X4: X0,X5: X0,X6: X0] :
( ( X1 @ X4 @ X5 )
=> ( ( X1 @ X5 @ X6 )
=> ( X1 @ X4 @ X6 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > X0 > $o] :
( ( isPer @ X0 @ X1 )
<=> ( ! [X2: X0,X3: X0] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) )
& ! [X2: X0,X3: X0,X4: X0] :
( ( X1 @ X2 @ X3 )
=> ( ( X1 @ X3 @ X4 )
=> ( X1 @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.v0WQauavVr/DTF2THF_27475.p',is_per) ).
thf(f1005,plain,
( ( ( listStar @ sK0 @ sK1 @ ( app @ zero @ sK0 @ nil @ sK1 ) )
!= $true )
| spl10_8 ),
inference(subsumption_resolution,[status(thm)],[f999,f51]) ).
thf(f51,plain,
( ( listStar @ sK2 @ sK3 @ sK3 )
= $true ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f999,plain,
( ( ( listStar @ sK2 @ sK3 @ sK3 )
!= $true )
| ( ( listStar @ sK0 @ sK1 @ ( app @ zero @ sK0 @ nil @ sK1 ) )
!= $true )
| spl10_8 ),
inference(trivial_inequality_removal,[status(thm)],[f996]) ).
thf(f996,plain,
( ( ( listStar @ sK2 @ sK3 @ sK3 )
!= $true )
| ( $true != $true )
| ( ( listStar @ sK0 @ sK1 @ ( app @ zero @ sK0 @ nil @ sK1 ) )
!= $true )
| spl10_8 ),
inference(superposition,[status(thm)],[f959,f56]) ).
thf(f56,plain,
! [X2: list,X3: list,X0: nat,X1: nat,X4: list,X5: list] :
( ( ( listStar @ ( plus @ X0 @ X1 ) @ ( app @ X0 @ X1 @ X2 @ X4 ) @ ( app @ X0 @ X1 @ X3 @ X5 ) )
= $true )
| ( ( listStar @ X1 @ X4 @ X5 )
!= $true )
| ( ( listStar @ X0 @ X2 @ X3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: nat,X1: nat,X2: list,X3: list] :
( ( ( listStar @ X0 @ X2 @ X3 )
!= $true )
| ! [X4: list,X5: list] :
( ( ( listStar @ ( plus @ X0 @ X1 ) @ ( app @ X0 @ X1 @ X2 @ X4 ) @ ( app @ X0 @ X1 @ X3 @ X5 ) )
= $true )
| ( ( listStar @ X1 @ X4 @ X5 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: nat,X1: nat,X2: list,X3: list] :
( ( ( listStar @ X0 @ X2 @ X3 )
= $true )
=> ! [X4: list,X5: list] :
( ( ( listStar @ X1 @ X4 @ X5 )
= $true )
=> ( ( listStar @ ( plus @ X0 @ X1 ) @ ( app @ X0 @ X1 @ X2 @ X4 ) @ ( app @ X0 @ X1 @ X3 @ X5 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: nat,X1: nat,X2: list,X3: list] :
( ( listStar @ X0 @ X2 @ X3 )
=> ! [X4: list,X5: list] :
( ( listStar @ X1 @ X4 @ X5 )
=> ( listStar @ ( plus @ X0 @ X1 ) @ ( app @ X0 @ X1 @ X2 @ X4 ) @ ( app @ X0 @ X1 @ X3 @ X5 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
! [X6: nat,X10: nat,X7: list,X11: list] :
( ( listStar @ X6 @ X7 @ X11 )
=> ! [X8: list,X9: list] :
( ( listStar @ X10 @ X8 @ X9 )
=> ( listStar @ ( plus @ X6 @ X10 ) @ ( app @ X6 @ X10 @ X7 @ X8 ) @ ( app @ X6 @ X10 @ X11 @ X9 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.v0WQauavVr/DTF2THF_27475.p',app_tp_ax) ).
thf(f959,plain,
( ( ( listStar @ ( plus @ sK0 @ sK2 ) @ ( app @ sK0 @ sK2 @ sK1 @ sK3 ) @ ( app @ sK0 @ sK2 @ ( app @ zero @ sK0 @ nil @ sK1 ) @ sK3 ) )
!= $true )
| spl10_8 ),
inference(avatar_component_clause,[status(thm)],[f957]) ).
thf(f957,definition,
( spl10_8
<=> ( ( listStar @ ( plus @ sK0 @ sK2 ) @ ( app @ sK0 @ sK2 @ sK1 @ sK3 ) @ ( app @ sK0 @ sK2 @ ( app @ zero @ sK0 @ nil @ sK1 ) @ sK3 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl10_8])],[avatar_definition]) ).
thf(f995,plain,
spl10_9,
inference(avatar_contradiction_clause,[status(thm)],[f994]) ).
thf(f994,plain,
( $false
| spl10_9 ),
inference(subsumption_resolution,[status(thm)],[f993,f52]) ).
thf(f993,plain,
( ( ( listStar @ sK0 @ sK1 @ sK1 )
!= $true )
| spl10_9 ),
inference(subsumption_resolution,[status(thm)],[f992,f51]) ).
thf(f992,plain,
( ( ( listStar @ sK2 @ sK3 @ sK3 )
!= $true )
| ( ( listStar @ sK0 @ sK1 @ sK1 )
!= $true )
| spl10_9 ),
inference(trivial_inequality_removal,[status(thm)],[f991]) ).
thf(f991,plain,
( ( ( listStar @ sK2 @ sK3 @ sK3 )
!= $true )
| ( $true != $true )
| ( ( listStar @ sK0 @ sK1 @ sK1 )
!= $true )
| spl10_9 ),
inference(superposition,[status(thm)],[f963,f56]) ).
thf(f963,plain,
( ( ( listStar @ ( plus @ sK0 @ sK2 ) @ ( app @ sK0 @ sK2 @ sK1 @ sK3 ) @ ( app @ sK0 @ sK2 @ sK1 @ sK3 ) )
!= $true )
| spl10_9 ),
inference(avatar_component_clause,[status(thm)],[f961]) ).
thf(f961,definition,
( spl10_9
<=> ( ( listStar @ ( plus @ sK0 @ sK2 ) @ ( app @ sK0 @ sK2 @ sK1 @ sK3 ) @ ( app @ sK0 @ sK2 @ sK1 @ sK3 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl10_9])],[avatar_definition]) ).
thf(f964,plain,
( ~ spl10_8
| ~ spl10_9
| ~ spl10_2 ),
inference(avatar_split_clause,[status(thm)],[f955,f74,f961,f957]) ).
thf(f74,definition,
( spl10_2
<=> ( $false
= ( listStar @ ( plus @ zero @ ( plus @ sK0 @ sK2 ) ) @ ( app @ zero @ ( plus @ sK0 @ sK2 ) @ nil @ ( app @ sK0 @ sK2 @ sK1 @ sK3 ) ) @ ( app @ ( plus @ zero @ sK0 ) @ sK2 @ ( app @ zero @ sK0 @ nil @ sK1 ) @ sK3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl10_2])],[avatar_definition]) ).
thf(f955,plain,
( ( ( listStar @ ( plus @ sK0 @ sK2 ) @ ( app @ sK0 @ sK2 @ sK1 @ sK3 ) @ ( app @ sK0 @ sK2 @ ( app @ zero @ sK0 @ nil @ sK1 ) @ sK3 ) )
!= $true )
| ( ( listStar @ ( plus @ sK0 @ sK2 ) @ ( app @ sK0 @ sK2 @ sK1 @ sK3 ) @ ( app @ sK0 @ sK2 @ sK1 @ sK3 ) )
!= $true )
| ~ spl10_2 ),
inference(trivial_inequality_removal,[status(thm)],[f949]) ).
thf(f949,plain,
( ( ( listStar @ ( plus @ sK0 @ sK2 ) @ ( app @ sK0 @ sK2 @ sK1 @ sK3 ) @ ( app @ sK0 @ sK2 @ sK1 @ sK3 ) )
!= $true )
| ( $true != $true )
| ( ( listStar @ ( plus @ sK0 @ sK2 ) @ ( app @ sK0 @ sK2 @ sK1 @ sK3 ) @ ( app @ sK0 @ sK2 @ ( app @ zero @ sK0 @ nil @ sK1 ) @ sK3 ) )
!= $true )
| ~ spl10_2 ),
inference(superposition,[status(thm)],[f507,f947]) ).
thf(f507,plain,
( ! [X0: list] :
( ( ( listStar @ ( plus @ sK0 @ sK2 ) @ ( app @ zero @ ( plus @ sK0 @ sK2 ) @ nil @ ( app @ sK0 @ sK2 @ sK1 @ sK3 ) ) @ X0 )
!= $true )
| ( ( listStar @ ( plus @ sK0 @ sK2 ) @ X0 @ ( app @ sK0 @ sK2 @ ( app @ zero @ sK0 @ nil @ sK1 ) @ sK3 ) )
!= $true ) )
| ~ spl10_2 ),
inference(subsumption_resolution,[status(thm)],[f502,f50]) ).
thf(f502,plain,
( ! [X0: list] :
( ( ( isPer @ list @ ( listStar @ ( plus @ sK0 @ sK2 ) ) )
!= $true )
| ( ( listStar @ ( plus @ sK0 @ sK2 ) @ X0 @ ( app @ sK0 @ sK2 @ ( app @ zero @ sK0 @ nil @ sK1 ) @ sK3 ) )
!= $true )
| ( ( listStar @ ( plus @ sK0 @ sK2 ) @ ( app @ zero @ ( plus @ sK0 @ sK2 ) @ nil @ ( app @ sK0 @ sK2 @ sK1 @ sK3 ) ) @ X0 )
!= $true ) )
| ~ spl10_2 ),
inference(trivial_inequality_removal,[status(thm)],[f187]) ).
thf(f187,plain,
( ! [X0: list] :
( ( ( isPer @ list @ ( listStar @ ( plus @ sK0 @ sK2 ) ) )
!= $true )
| ( ( listStar @ ( plus @ sK0 @ sK2 ) @ ( app @ zero @ ( plus @ sK0 @ sK2 ) @ nil @ ( app @ sK0 @ sK2 @ sK1 @ sK3 ) ) @ X0 )
!= $true )
| ( ( listStar @ ( plus @ sK0 @ sK2 ) @ X0 @ ( app @ sK0 @ sK2 @ ( app @ zero @ sK0 @ nil @ sK1 ) @ sK3 ) )
!= $true )
| ( $false = $true ) )
| ~ spl10_2 ),
inference(superposition,[status(thm)],[f64,f88]) ).
thf(f88,plain,
( ( $false
= ( listStar @ ( plus @ sK0 @ sK2 ) @ ( app @ zero @ ( plus @ sK0 @ sK2 ) @ nil @ ( app @ sK0 @ sK2 @ sK1 @ sK3 ) ) @ ( app @ sK0 @ sK2 @ ( app @ zero @ sK0 @ nil @ sK1 ) @ sK3 ) ) )
| ~ spl10_2 ),
inference(forward_demodulation,[status(thm)],[f87,f49]) ).
thf(f87,plain,
( ( $false
= ( listStar @ ( plus @ sK0 @ sK2 ) @ ( app @ zero @ ( plus @ sK0 @ sK2 ) @ nil @ ( app @ sK0 @ sK2 @ sK1 @ sK3 ) ) @ ( app @ ( plus @ zero @ sK0 ) @ sK2 @ ( app @ zero @ sK0 @ nil @ sK1 ) @ sK3 ) ) )
| ~ spl10_2 ),
inference(forward_demodulation,[status(thm)],[f76,f49]) ).
thf(f76,plain,
( ( $false
= ( listStar @ ( plus @ zero @ ( plus @ sK0 @ sK2 ) ) @ ( app @ zero @ ( plus @ sK0 @ sK2 ) @ nil @ ( app @ sK0 @ sK2 @ sK1 @ sK3 ) ) @ ( app @ ( plus @ zero @ sK0 ) @ sK2 @ ( app @ zero @ sK0 @ nil @ sK1 ) @ sK3 ) ) )
| ~ spl10_2 ),
inference(avatar_component_clause,[status(thm)],[f74]) ).
thf(f64,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0 > X0 > $o,X4: X0] :
( ( ( X1 @ X2 @ X4 )
= $true )
| ( ( isPer @ X0 @ X1 )
!= $true )
| ( ( X1 @ X3 @ X4 )
!= $true )
| ( ( X1 @ X2 @ X3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f77,plain,
( spl10_1
| spl10_2 ),
inference(avatar_split_clause,[status(thm)],[f67,f74,f70]) ).
thf(f67,plain,
( ( ( sP9 @ $true )
= $false )
| ( $false
= ( listStar @ ( plus @ zero @ ( plus @ sK0 @ sK2 ) ) @ ( app @ zero @ ( plus @ sK0 @ sK2 ) @ nil @ ( app @ sK0 @ sK2 @ sK1 @ sK3 ) ) @ ( app @ ( plus @ zero @ sK0 ) @ sK2 @ ( app @ zero @ sK0 @ nil @ sK1 ) @ sK3 ) ) ) ),
inference(cases_simplifying,[status(thm)],[f65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT360^1 : TPTP v9.2.1. Released v9.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n028.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 06:16:42 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.45 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : DAT360^1 : TPTP v9.2.1. Released v9.2.0.
% 0.20/0.46 % Domain : Data Structures
% 0.20/0.46 % Problem : Associativity of list append, base case
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English : Associativity of list append. The proof is by induction with a
% 0.20/0.46 % problem file for the base and step case (with multiple subcases)
% 0.20/0.46 % as well as the correct instantiation of the induction axiom for
% 0.20/0.46 % lists. The main file uses the conjectures of the other files as
% 0.20/0.46 % lemmas in order to prove the final result. To simplify proof
% 0.20/0.46 % search, the axioms in each problem file have been preselected.
% 0.20/0.46
% 0.20/0.46 % Refs : [RRB23] Rothgang et al. (2023), Theorem Proving in Dependently
% 0.20/0.46 % : [Rot25] Rothgang (2025), Email to Geoff Sutcliffe
% 0.20/0.46 % : [RK+25] Ranalter et al. (2025), The Dependently Typed Higher-O
% 0.20/0.46 % Source : [Rot25]
% 0.20/0.46 % Names : ListAppAssoc/list-app-assoc-base.p [Rot25]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : ? v9.2.0
% 0.20/0.46 % Syntax : Number of formulae : 13 ( 4 unt; 9 typ; 0 def)
% 0.20/0.46 % Number of atoms : 4 ( 4 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.20/0.46 % Number of connectives : 46 ( 0 ~; 0 |; 0 &; 46 @)
% 0.20/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 5 ( 4 avg)
% 0.20/0.46 % Number of types : 2 ( 2 usr)
% 0.20/0.46 % Number of type decls : 9 ( 0 !>P; 2 !>D)
% 0.20/0.46 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 8 ( 7 usr; 2 con; 0-4 aty)
% 0.20/0.46 % Number of variables : 13 ( 0 ^; 10 !; 0 ?; 13 :)
% 0.20/0.46 % ( 3 !>; 0 ?*; 0 @-; 0 @+)
% 0.20/0.46 % SPC : DH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments :
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(elem_type,type,
% 0.20/0.46 elem: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(nat_type,type,
% 0.20/0.46 nat: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(zero_type,type,
% 0.20/0.46 zero: nat ).
% 0.20/0.46
% 0.20/0.46 thf(suc_type,type,
% 0.20/0.46 suc: nat > nat ).
% 0.20/0.46
% 0.20/0.46 thf(plus_type,type,
% 0.20/0.46 plus: nat > nat > nat ).
% 0.20/0.46
% 0.20/0.46 thf(list_type,type,
% 0.20/0.46 list: nat > $tType ).
% 0.20/0.46
% 0.20/0.46 thf(nil_type,type,
% 0.20/0.46 nil: list @ zero ).
% 0.20/0.46
% 0.20/0.46 thf(cons_type,type,
% 0.20/0.46 cons:
% 0.20/0.46 !>[N: nat] : ( elem > ( list @ N ) > ( list @ ( suc @ N ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(app_type,type,
% 0.20/0.46 app:
% 0.20/0.46 !>[N: nat,M: nat] : ( ( list @ N ) > ( list @ M ) > ( list @ ( plus @ N @ M ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ax1,axiom,
% 0.20/0.46 ! [N: nat] :
% 0.20/0.46 ( ( plus @ zero @ N )
% 0.20/0.46 = N ) ).
% 0.20/0.46
% 0.20/0.46 thf(ax3,axiom,
% 0.20/0.46 ! [N: nat,X: list @ N] :
% 0.20/0.46 ( ( app @ zero @ N @ nil @ X )
% 0.20/0.46 = X ) ).
% 0.20/0.46
% 0.20/0.46 thf(plus_assoc,axiom,
% 0.20/0.46 ! [M1: nat,M2: nat,M3: nat] :
% 0.20/0.46 ( ( plus @ M1 @ ( plus @ M2 @ M3 ) )
% 0.20/0.46 = ( plus @ ( plus @ M1 @ M2 ) @ M3 ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(list_app_assoc_base,conjecture,
% 0.20/0.46 ! [M2: nat,L2: list @ M2,M3: nat,L3: list @ M3] :
% 0.20/0.46 ( ( app @ zero @ ( plus @ M2 @ M3 ) @ nil @ ( app @ M2 @ M3 @ L2 @ L3 ) )
% 0.20/0.46 = ( app @ ( plus @ zero @ M2 ) @ M3 @ ( app @ zero @ M2 @ nil @ L2 ) @ L3 ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.50/1.29 ---- Embedded in THF ---
% 1.50/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.29 %%% Generated on Tue Feb 24 06:16:42 EST 2026
% 1.50/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.29 %%% Logic specification used:
% 1.50/1.29 %%% thf(spec, logic, $$dhol).
% 1.50/1.29
% 1.50/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.v0WQauavVr/DTF2DTF27475.p
% See solution above
% 1.50/1.29 ------------------------
% 1.74/1.30 ---- Cleaned THF ---
% 1.74/1.30 thf(is_per_type,type,
% 1.74/1.30 isPer:
% 1.74/1.30 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 1.74/1.30
% 1.74/1.30 thf(is_per,definition,
% 1.74/1.30 ! [A: $tType,AStar: A > A > $o] :
% 1.74/1.30 ( ( isPer @ A @ AStar )
% 1.74/1.30 <=> ( ! [X: A,Y: A] :
% 1.74/1.30 ( ( AStar @ X @ Y )
% 1.74/1.30 => ( AStar @ Y @ X ) )
% 1.74/1.30 & ! [X: A,Y: A,Z: A] :
% 1.74/1.30 ( ( AStar @ X @ Y )
% 1.74/1.30 => ( ( AStar @ Y @ Z )
% 1.74/1.30 => ( AStar @ X @ Z ) ) ) ) ) ).
% 1.74/1.30
% 1.74/1.30 thf(elem_type,type,
% 1.74/1.30 elem: $tType ).
% 1.74/1.30
% 1.74/1.30 thf(elemStar,type,
% 1.74/1.30 elemStar: elem > elem > $o ).
% 1.74/1.30
% 1.74/1.30 thf(elemStar_is_eq,axiom,
% 1.74/1.30 ! [X: elem,Y: elem] :
% 1.74/1.30 ( ( elemStar @ X @ Y )
% 1.74/1.30 <=> ( X = Y ) ) ).
% 1.74/1.30
% 1.74/1.30 thf(nat_type,type,
% 1.74/1.30 nat: $tType ).
% 1.74/1.30
% 1.74/1.30 thf(natStar,type,
% 1.74/1.30 natStar: nat > nat > $o ).
% 1.74/1.30
% 1.74/1.30 thf(natStar_is_eq,axiom,
% 1.74/1.30 ! [X: nat,Y: nat] :
% 1.74/1.30 ( ( natStar @ X @ Y )
% 1.74/1.30 <=> ( X = Y ) ) ).
% 1.74/1.30
% 1.74/1.30 thf(zero_type,type,
% 1.74/1.30 zero: nat ).
% 1.74/1.30
% 1.74/1.30 thf(suc_type,type,
% 1.74/1.30 suc: nat > nat ).
% 1.74/1.30
% 1.74/1.30 thf(plus_type,type,
% 1.74/1.30 plus: nat > nat > nat ).
% 1.74/1.30
% 1.74/1.30 thf(list_type,type,
% 1.74/1.30 list: $tType ).
% 1.74/1.30
% 1.74/1.30 thf(listStar,type,
% 1.74/1.30 listStar: nat > list > list > $o ).
% 1.74/1.30
% 1.74/1.30 thf('\'listStar\'_is_per',axiom,
% 1.74/1.30 ! [C: nat] : ( isPer @ list @ ( listStar @ C ) ) ).
% 1.74/1.30
% 1.74/1.30 thf(nil_type,type,
% 1.74/1.30 nil: list ).
% 1.74/1.30
% 1.74/1.30 thf(nil_tp_ax,axiom,
% 1.74/1.30 listStar @ zero @ nil @ nil ).
% 1.74/1.30
% 1.74/1.30 thf(cons_type,type,
% 1.74/1.30 cons: nat > elem > list > list ).
% 1.74/1.30
% 1.74/1.30 thf(cons_tp_ax,axiom,
% 1.74/1.30 ! [N: nat,D: elem,D0: list,D0_prime: list] :
% 1.74/1.30 ( ( listStar @ N @ D0 @ D0_prime )
% 1.74/1.30 => ( listStar @ ( suc @ N ) @ ( cons @ N @ D @ D0 ) @ ( cons @ N @ D @ D0_prime ) ) ) ).
% 1.74/1.30
% 1.74/1.30 thf(app_type,type,
% 1.74/1.30 app: nat > nat > list > list > list ).
% 1.74/1.30
% 1.74/1.30 thf(app_tp_ax,axiom,
% 1.74/1.30 ! [N: nat,M: nat,D: list,D_prime: list] :
% 1.74/1.30 ( ( listStar @ N @ D @ D_prime )
% 1.74/1.30 => ! [D0: list,D0_prime: list] :
% 1.74/1.30 ( ( listStar @ M @ D0 @ D0_prime )
% 1.74/1.30 => ( listStar @ ( plus @ N @ M ) @ ( app @ N @ M @ D @ D0 ) @ ( app @ N @ M @ D_prime @ D0_prime ) ) ) ) ).
% 1.74/1.30
% 1.74/1.30 thf(ax1,axiom,
% 1.74/1.30 ! [N: nat] :
% 1.74/1.30 ( ( plus @ zero @ N )
% 1.74/1.30 = N ) ).
% 1.74/1.30
% 1.74/1.30 thf(ax3,axiom,
% 1.74/1.30 ! [N: nat,X: list] :
% 1.74/1.30 ( ( listStar @ N @ X @ X )
% 1.74/1.30 => ( listStar @ ( plus @ zero @ N ) @ ( app @ zero @ N @ nil @ X ) @ X ) ) ).
% 1.74/1.30
% 1.74/1.30 thf(plus_assoc,axiom,
% 1.74/1.30 ! [M1: nat,M2: nat,M3: nat] :
% 1.74/1.30 ( ( plus @ M1 @ ( plus @ M2 @ M3 ) )
% 1.74/1.30 = ( plus @ ( plus @ M1 @ M2 ) @ M3 ) ) ).
% 1.74/1.30
% 1.74/1.30 thf(list_app_assoc_base,conjecture,
% 1.74/1.30 ! [M2: nat,L2: list,M3: nat,L3: list] :
% 1.74/1.30 ( ( listStar @ M2 @ L2 @ L2 )
% 1.74/1.30 => ( ( listStar @ M3 @ L3 @ L3 )
% 1.74/1.30 => ( listStar @ ( plus @ zero @ ( plus @ M2 @ M3 ) ) @ ( app @ zero @ ( plus @ M2 @ M3 ) @ nil @ ( app @ M2 @ M3 @ L2 @ L3 ) ) @ ( app @ ( plus @ zero @ M2 ) @ M3 @ ( app @ zero @ M2 @ nil @ L2 ) @ L3 ) ) ) ) ).
% 1.74/1.30 ------------------------
% 1.74/1.31 % (27663)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27475 for (2999ds/183Mi)
% 1.74/1.31 % (27668)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_27475 for (2999ds/275Mi)
% 1.74/1.31 % (27664)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_27475 for (2999ds/4Mi)
% 1.74/1.31 % (27664)Instruction limit reached!
% 1.74/1.31 % (27664)------------------------------
% 1.74/1.31 % (27664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.31 % (27664)Termination reason: Unknown
% 1.74/1.31 % (27664)Termination phase: Property scanning
% 1.74/1.31
% 1.74/1.31 % (27664)Memory used [KB]: 1023
% 1.74/1.31 % (27664)Time elapsed: 0.002 s
% 1.74/1.31 % (27664)Instructions burned: 4 (million)
% 1.74/1.31 % (27664)------------------------------
% 1.74/1.31 % (27664)------------------------------
% 1.74/1.31 % (27668)Refutation not found, incomplete strategy
% 1.74/1.31 % (27668)------------------------------
% 1.74/1.31 % (27668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.31 % (27668)Termination reason: Refutation not found, incomplete strategy
% 1.74/1.31
% 1.74/1.31
% 1.74/1.31 % (27668)Memory used [KB]: 5500
% 1.74/1.31 % (27668)Time elapsed: 0.003 s
% 1.74/1.31 % (27668)Instructions burned: 5 (million)
% 1.74/1.31 % (27668)------------------------------
% 1.74/1.31 % (27668)------------------------------
% 1.74/1.32 % (27666)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27475 for (2999ds/2Mi)
% 1.74/1.32 % (27665)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_27475 for (2999ds/27Mi)
% 1.74/1.32 % (27666)Instruction limit reached!
% 1.74/1.32 % (27666)------------------------------
% 1.74/1.32 % (27666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.32 % (27666)Termination reason: Unknown
% 1.74/1.32 % (27666)Termination phase: Property scanning
% 1.74/1.32
% 1.74/1.32 % (27666)Memory used [KB]: 1023
% 1.74/1.32 % (27666)Time elapsed: 0.003 s
% 1.74/1.32 % (27666)Instructions burned: 2 (million)
% 1.74/1.32 % (27666)------------------------------
% 1.74/1.32 % (27666)------------------------------
% 1.74/1.32 % (27667)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_27475 for (2999ds/2Mi)
% 1.74/1.32 % (27671)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_27475 for (2999ds/37Mi)
% 1.74/1.32 % (27670)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27475 for (2999ds/3Mi)
% 1.74/1.32 % (27667)Instruction limit reached!
% 1.74/1.32 % (27667)------------------------------
% 1.74/1.32 % (27667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.32 % (27667)Termination reason: Unknown
% 1.74/1.32 % (27667)Termination phase: shuffling
% 1.74/1.32
% 1.74/1.32 % (27667)Memory used [KB]: 1023
% 1.74/1.32 % (27667)Time elapsed: 0.002 s
% 1.74/1.32 % (27667)Instructions burned: 3 (million)
% 1.74/1.32 % (27667)------------------------------
% 1.74/1.32 % (27667)------------------------------
% 1.74/1.32 % (27669)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27475 for (2999ds/18Mi)
% 1.74/1.33 % (27670)Instruction limit reached!
% 1.74/1.33 % (27670)------------------------------
% 1.74/1.33 % (27670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.33 % (27670)Termination reason: Unknown
% 1.74/1.33 % (27670)Termination phase: Property scanning
% 1.74/1.33
% 1.74/1.33 % (27670)Memory used [KB]: 1023
% 1.74/1.33 % (27670)Time elapsed: 0.003 s
% 1.74/1.33 % (27670)Instructions burned: 4 (million)
% 1.74/1.33 % (27670)------------------------------
% 1.74/1.33 % (27670)------------------------------
% 1.74/1.34 % (27671)Instruction limit reached!
% 1.74/1.34 % (27671)------------------------------
% 1.74/1.34 % (27671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.34 % (27671)Termination reason: Unknown
% 1.74/1.34 % (27671)Termination phase: Saturation
% 1.74/1.34
% 1.74/1.34 % (27671)Memory used [KB]: 5756
% 1.74/1.34 % (27671)Time elapsed: 0.012 s
% 1.74/1.34 % (27671)Instructions burned: 37 (million)
% 1.74/1.34 % (27671)------------------------------
% 1.74/1.34 % (27671)------------------------------
% 1.74/1.34 % (27672)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_27475 for (2999ds/15Mi)
% 1.74/1.34 % (27665)Instruction limit reached!
% 1.74/1.34 % (27665)------------------------------
% 1.74/1.34 % (27665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.34 % (27665)Termination reason: Unknown
% 1.74/1.34 % (27665)Termination phase: Saturation
% 1.74/1.34
% 1.74/1.34 % (27665)Memory used [KB]: 5628
% 1.74/1.34 % (27665)Time elapsed: 0.019 s
% 1.74/1.34 % (27665)Instructions burned: 27 (million)
% 1.74/1.34 % (27665)------------------------------
% 1.74/1.34 % (27665)------------------------------
% 1.74/1.34 % (27669)Instruction limit reached!
% 1.74/1.34 % (27669)------------------------------
% 1.74/1.34 % (27669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.34 % (27669)Termination reason: Unknown
% 1.74/1.34 % (27669)Termination phase: Saturation
% 1.74/1.34
% 1.74/1.34 % (27669)Memory used [KB]: 5628
% 1.74/1.34 % (27669)Time elapsed: 0.015 s
% 1.74/1.34 % (27669)Instructions burned: 18 (million)
% 1.74/1.34 % (27669)------------------------------
% 1.74/1.34 % (27669)------------------------------
% 1.74/1.34 % (27674)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_27475 for (2999ds/1041Mi)
% 1.74/1.34 % (27673)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_27475 for (2999ds/3Mi)
% 1.74/1.34 % (27673)Instruction limit reached!
% 1.74/1.34 % (27673)------------------------------
% 1.74/1.34 % (27673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.34 % (27673)Termination reason: Unknown
% 1.74/1.34 % (27673)Termination phase: Preprocessing 3
% 1.74/1.34
% 1.74/1.34 % (27673)Memory used [KB]: 1023
% 1.74/1.34 % (27673)Time elapsed: 0.003 s
% 1.74/1.34 % (27673)Instructions burned: 3 (million)
% 1.74/1.34 % (27673)------------------------------
% 1.74/1.34 % (27673)------------------------------
% 1.74/1.34 % (27672)Instruction limit reached!
% 1.74/1.34 % (27672)------------------------------
% 1.74/1.34 % (27672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.34 % (27672)Termination reason: Unknown
% 1.74/1.34 % (27672)Termination phase: Saturation
% 1.74/1.34
% 1.74/1.34 % (27672)Memory used [KB]: 5756
% 1.74/1.34 % (27672)Time elapsed: 0.007 s
% 1.74/1.34 % (27672)Instructions burned: 15 (million)
% 1.74/1.34 % (27672)------------------------------
% 1.74/1.34 % (27672)------------------------------
% 1.74/1.34 % (27675)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_27475 for (2999ds/7Mi)
% 1.74/1.35 % (27675)Instruction limit reached!
% 1.74/1.35 % (27675)------------------------------
% 1.74/1.35 % (27675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.35 % (27675)Termination reason: Unknown
% 1.74/1.35 % (27675)Termination phase: Saturation
% 1.74/1.35
% 1.74/1.35 % (27675)Memory used [KB]: 1023
% 1.74/1.35 % (27675)Time elapsed: 0.003 s
% 1.74/1.35 % (27675)Instructions burned: 7 (million)
% 1.74/1.35 % (27675)------------------------------
% 1.74/1.35 % (27675)------------------------------
% 1.74/1.35 % (27679)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_27475 for (2999ds/7Mi)
% 1.74/1.36 % (27676)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_27475 for (2999ds/16Mi)
% 1.74/1.36 % (27679)Instruction limit reached!
% 1.74/1.36 % (27679)------------------------------
% 1.74/1.36 % (27679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.36 % (27679)Termination reason: Unknown
% 1.74/1.36 % (27679)Termination phase: Saturation
% 1.74/1.36
% 1.74/1.36 % (27679)Memory used [KB]: 5500
% 1.74/1.36 % (27679)Time elapsed: 0.004 s
% 1.74/1.36 % (27679)Instructions burned: 7 (million)
% 1.74/1.36 % (27679)------------------------------
% 1.74/1.36 % (27679)------------------------------
% 1.74/1.36 % (27680)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_27475 for (2999ds/3Mi)
% 1.74/1.36 % (27680)Instruction limit reached!
% 1.74/1.36 % (27680)------------------------------
% 1.74/1.36 % (27680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.36 % (27680)Termination reason: Unknown
% 1.74/1.36 % (27680)Termination phase: Property scanning
% 1.74/1.36
% 1.74/1.36 % (27680)Memory used [KB]: 1023
% 1.74/1.36 % (27680)Time elapsed: 0.002 s
% 1.74/1.36 % (27680)Instructions burned: 4 (million)
% 1.74/1.36 % (27680)------------------------------
% 1.74/1.36 % (27680)------------------------------
% 1.74/1.36 % (27663)Instruction limit reached!
% 1.74/1.36 % (27663)------------------------------
% 1.74/1.36 % (27663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.36 % (27663)Termination reason: Unknown
% 1.74/1.36 % (27663)Termination phase: Saturation
% 1.74/1.36
% 1.74/1.36 % (27663)Memory used [KB]: 7036
% 1.74/1.36 % (27663)Time elapsed: 0.049 s
% 1.74/1.36 % (27663)Instructions burned: 184 (million)
% 1.74/1.36 % (27663)------------------------------
% 1.74/1.36 % (27663)------------------------------
% 1.74/1.36 % (27677)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_27475 for (2999ds/3Mi)
% 1.74/1.36 % (27678)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_27475 for (2999ds/3Mi)
% 1.74/1.36 % (27677)Instruction limit reached!
% 1.74/1.36 % (27677)------------------------------
% 1.74/1.36 % (27677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.36 % (27678)Instruction limit reached!
% 1.74/1.36 % (27678)------------------------------
% 1.74/1.36 % (27678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.36 % (27678)Termination reason: Unknown
% 1.74/1.36 % (27678)Termination phase: Property scanning
% 1.74/1.36
% 1.74/1.36 % (27678)Memory used [KB]: 1023
% 1.74/1.36 % (27678)Time elapsed: 0.003 s
% 1.74/1.36 % (27678)Instructions burned: 3 (million)
% 1.74/1.36 % (27678)------------------------------
% 1.74/1.36 % (27678)------------------------------
% 1.74/1.36 % (27677)Termination reason: Unknown
% 1.74/1.36 % (27677)Termination phase: Preprocessing 3
% 1.74/1.36
% 1.74/1.36 % (27677)Memory used [KB]: 1023
% 1.74/1.36 % (27677)Time elapsed: 0.004 s
% 1.74/1.36 % (27677)Instructions burned: 3 (million)
% 1.74/1.36 % (27677)------------------------------
% 1.74/1.36 % (27677)------------------------------
% 1.74/1.37 % (27676)Instruction limit reached!
% 1.74/1.37 % (27676)------------------------------
% 1.74/1.37 % (27676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.37 % (27676)Termination reason: Unknown
% 1.74/1.37 % (27676)Termination phase: Saturation
% 1.74/1.37
% 1.74/1.37 % (27676)Memory used [KB]: 5756
% 1.74/1.37 % (27676)Time elapsed: 0.012 s
% 1.74/1.37 % (27676)Instructions burned: 16 (million)
% 1.74/1.37 % (27676)------------------------------
% 1.74/1.37 % (27676)------------------------------
% 1.74/1.37 % (27681)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_27475 for (2999ds/4Mi)
% 1.74/1.37 % (27682)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_27475 for (2999ds/18Mi)
% 1.74/1.37 % (27681)Instruction limit reached!
% 1.74/1.37 % (27681)------------------------------
% 1.74/1.37 % (27681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.37 % (27681)Termination reason: Unknown
% 1.74/1.37 % (27681)Termination phase: Property scanning
% 1.74/1.37
% 1.74/1.37 % (27681)Memory used [KB]: 1023
% 1.74/1.37 % (27681)Time elapsed: 0.003 s
% 1.74/1.37 % (27681)Instructions burned: 4 (million)
% 1.74/1.37 % (27681)------------------------------
% 1.74/1.37 % (27681)------------------------------
% 1.74/1.37 % (27683)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_27475 for (2999ds/710Mi)
% 1.74/1.37 % (27682)Instruction limit reached!
% 1.74/1.37 % (27682)------------------------------
% 1.74/1.37 % (27682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.37 % (27682)Termination reason: Unknown
% 1.74/1.37 % (27682)Termination phase: Saturation
% 1.74/1.37
% 1.74/1.37 % (27682)Memory used [KB]: 5628
% 1.74/1.37 % (27682)Time elapsed: 0.009 s
% 1.74/1.37 % (27682)Instructions burned: 18 (million)
% 1.74/1.37 % (27682)------------------------------
% 1.74/1.37 % (27682)------------------------------
% 1.74/1.37 % (27684)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_27475 for (2999ds/6Mi)
% 1.74/1.38 % (27684)Instruction limit reached!
% 1.74/1.38 % (27684)------------------------------
% 1.74/1.38 % (27684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.38 % (27684)Termination reason: Unknown
% 1.74/1.38 % (27687)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_27475 for (2999ds/5Mi)
% 1.74/1.38 % (27684)Termination phase: Saturation
% 1.74/1.38
% 1.74/1.38 % (27684)Memory used [KB]: 5500
% 1.74/1.38 % (27684)Time elapsed: 0.003 s
% 1.74/1.38 % (27684)Instructions burned: 6 (million)
% 1.74/1.38 % (27684)------------------------------
% 1.74/1.38 % (27684)------------------------------
% 1.74/1.38 % (27687)Instruction limit reached!
% 1.74/1.38 % (27687)------------------------------
% 1.74/1.38 % (27687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.38 % (27687)Termination reason: Unknown
% 1.74/1.38 % (27687)Termination phase: Saturation
% 1.74/1.38
% 1.74/1.38 % (27687)Memory used [KB]: 5500
% 1.74/1.38 % (27687)Time elapsed: 0.004 s
% 1.74/1.38 % (27687)Instructions burned: 7 (million)
% 1.74/1.38 % (27687)------------------------------
% 1.74/1.38 % (27687)------------------------------
% 1.74/1.38 % (27685)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_27475 for (2999ds/902Mi)
% 1.74/1.38 % (27686)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_27475 for (2999ds/21Mi)
% 1.74/1.39 % (27689)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_27475 for (2999ds/377Mi)
% 1.74/1.39 % (27690)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_27475 for (2999ds/779Mi)
% 1.74/1.39 % (27688)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_27475 for (2999ds/6Mi)
% 1.74/1.39 % (27688)Instruction limit reached!
% 1.74/1.39 % (27688)------------------------------
% 1.74/1.39 % (27688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.39 % (27688)Termination reason: Unknown
% 1.74/1.39 % (27688)Termination phase: Saturation
% 1.74/1.39
% 1.74/1.39 % (27688)Memory used [KB]: 5500
% 1.74/1.39 % (27688)Time elapsed: 0.005 s
% 1.74/1.39 % (27688)Instructions burned: 9 (million)
% 1.74/1.39 % (27688)------------------------------
% 1.74/1.39 % (27688)------------------------------
% 1.74/1.40 % (27686)Instruction limit reached!
% 1.74/1.40 % (27686)------------------------------
% 1.74/1.40 % (27686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.40 % (27686)Termination reason: Unknown
% 1.74/1.40 % (27686)Termination phase: Saturation
% 1.74/1.40
% 1.74/1.40 % (27686)Memory used [KB]: 5628
% 1.74/1.40 % (27686)Time elapsed: 0.015 s
% 1.74/1.40 % (27686)Instructions burned: 21 (million)
% 1.74/1.40 % (27686)------------------------------
% 1.74/1.40 % (27686)------------------------------
% 1.74/1.40 % (27691)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_27475 for (2999ds/19Mi)
% 1.74/1.41 % (27691)Refutation not found, incomplete strategy
% 1.74/1.41 % (27691)------------------------------
% 1.74/1.41 % (27691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.41 % (27691)Termination reason: Refutation not found, incomplete strategy
% 1.74/1.41
% 1.74/1.41
% 1.74/1.41 % (27691)Memory used [KB]: 5628
% 1.74/1.41 % (27691)Time elapsed: 0.004 s
% 1.74/1.41 % (27691)Instructions burned: 10 (million)
% 1.74/1.41 % (27691)------------------------------
% 1.74/1.41 % (27691)------------------------------
% 1.74/1.42 % (27693)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_27475 for (2999ds/17Mi)
% 1.74/1.42 % (27693)Instruction limit reached!
% 1.74/1.42 % (27693)------------------------------
% 1.74/1.42 % (27693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.42 % (27693)Termination reason: Unknown
% 1.74/1.42 % (27693)Termination phase: Saturation
% 1.74/1.42
% 1.74/1.42 % (27693)Memory used [KB]: 5756
% 1.74/1.42 % (27693)Time elapsed: 0.007 s
% 1.74/1.42 % (27693)Instructions burned: 18 (million)
% 1.74/1.42 % (27693)------------------------------
% 1.74/1.42 % (27693)------------------------------
% 1.74/1.42 % (27692)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_27475 for (2999ds/879Mi)
% 1.74/1.43 % (27694)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_27475 for (2998ds/3Mi)
% 1.74/1.43 % (27694)Instruction limit reached!
% 1.74/1.43 % (27694)------------------------------
% 1.74/1.43 % (27694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.43 % (27694)Termination reason: Unknown
% 1.74/1.43 % (27694)Termination phase: Preprocessing 3
% 1.74/1.43
% 1.74/1.43 % (27694)Memory used [KB]: 1023
% 1.74/1.43 % (27694)Time elapsed: 0.002 s
% 1.74/1.43 % (27694)Instructions burned: 4 (million)
% 1.74/1.43 % (27694)------------------------------
% 1.74/1.43 % (27694)------------------------------
% 1.74/1.44 % (27695)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_27475 for (2998ds/30Mi)
% 1.74/1.45 % (27695)Instruction limit reached!
% 1.74/1.45 % (27695)------------------------------
% 1.74/1.45 % (27695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.45 % (27695)Termination reason: Unknown
% 1.74/1.45 % (27695)Termination phase: Saturation
% 1.74/1.45
% 1.74/1.45 % (27695)Memory used [KB]: 5756
% 1.74/1.45 % (27695)Time elapsed: 0.011 s
% 1.74/1.45 % (27695)Instructions burned: 31 (million)
% 1.74/1.45 % (27695)------------------------------
% 1.74/1.45 % (27695)------------------------------
% 1.74/1.46 % (27701)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_27475 for (2998ds/127Mi)
% 1.74/1.52 % (27701)Instruction limit reached!
% 1.74/1.52 % (27701)------------------------------
% 1.74/1.52 % (27701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.52 % (27701)Termination reason: Unknown
% 1.74/1.52 % (27701)Termination phase: Saturation
% 1.74/1.52
% 1.74/1.52 % (27701)Memory used [KB]: 6268
% 1.74/1.52 % (27701)Time elapsed: 0.059 s
% 1.74/1.52 % (27701)Instructions burned: 127 (million)
% 1.74/1.52 % (27701)------------------------------
% 1.74/1.52 % (27701)------------------------------
% 1.74/1.52 % (27689)Instruction limit reached!
% 1.74/1.52 % (27689)------------------------------
% 1.74/1.52 % (27689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.52 % (27689)Termination reason: Unknown
% 1.74/1.52 % (27689)Termination phase: Saturation
% 1.74/1.52
% 1.74/1.52 % (27689)Memory used [KB]: 6140
% 1.74/1.52 % (27689)Time elapsed: 0.134 s
% 1.74/1.52 % (27689)Instructions burned: 377 (million)
% 1.74/1.52 % (27689)------------------------------
% 1.74/1.52 % (27689)------------------------------
% 1.74/1.53 % (27723)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_27475 for (2997ds/3Mi)
% 1.74/1.53 % (27723)Instruction limit reached!
% 1.74/1.53 % (27723)------------------------------
% 1.74/1.53 % (27723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.53 % (27723)Termination reason: Unknown
% 1.74/1.53 % (27723)Termination phase: shuffling
% 1.74/1.53
% 1.74/1.53 % (27723)Memory used [KB]: 1023
% 1.74/1.53 % (27723)Time elapsed: 0.003 s
% 1.74/1.53 % (27723)Instructions burned: 3 (million)
% 1.74/1.53 % (27723)------------------------------
% 1.74/1.53 % (27723)------------------------------
% 1.74/1.54 % (27722)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_27475 for (2997ds/100Mi)
% 1.74/1.55 % (27729)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_27475 for (2997ds/20Mi)
% 1.74/1.57 % (27729)Instruction limit reached!
% 1.74/1.57 % (27729)------------------------------
% 1.74/1.57 % (27729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.57 % (27729)Termination reason: Unknown
% 1.74/1.57 % (27729)Termination phase: Saturation
% 1.74/1.57
% 1.74/1.57 % (27729)Memory used [KB]: 5628
% 1.74/1.57 % (27729)Time elapsed: 0.014 s
% 1.74/1.57 % (27729)Instructions burned: 21 (million)
% 1.74/1.57 % (27729)------------------------------
% 1.74/1.57 % (27729)------------------------------
% 1.74/1.58 % (27722)Instruction limit reached!
% 1.74/1.58 % (27722)------------------------------
% 1.74/1.58 % (27722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.58 % (27722)Termination reason: Unknown
% 1.74/1.58 % (27722)Termination phase: Saturation
% 1.74/1.58
% 1.74/1.58 % (27722)Memory used [KB]: 6012
% 1.74/1.58 % (27722)Time elapsed: 0.046 s
% 1.74/1.58 % (27722)Instructions burned: 102 (million)
% 1.74/1.58 % (27722)------------------------------
% 1.74/1.58 % (27722)------------------------------
% 1.74/1.58 % (27737)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_27475 for (2997ds/86Mi)
% 1.74/1.59 % (27738)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_27475 for (2997ds/107Mi)
% 1.74/1.62 % (27737)Instruction limit reached!
% 1.74/1.62 % (27737)------------------------------
% 1.74/1.62 % (27737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.62 % (27737)Termination reason: Unknown
% 1.74/1.62 % (27737)Termination phase: Saturation
% 1.74/1.62
% 1.74/1.62 % (27737)Memory used [KB]: 6140
% 1.74/1.62 % (27737)Time elapsed: 0.043 s
% 1.74/1.62 % (27737)Instructions burned: 87 (million)
% 1.74/1.62 % (27737)------------------------------
% 1.74/1.62 % (27737)------------------------------
% 1.74/1.64 % (27738)Instruction limit reached!
% 1.74/1.64 % (27738)------------------------------
% 1.74/1.64 % (27738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.64 % (27738)Termination reason: Unknown
% 1.74/1.64 % (27738)Termination phase: Saturation
% 1.74/1.64
% 1.74/1.64 % (27738)Memory used [KB]: 6012
% 1.74/1.64 % (27738)Time elapsed: 0.048 s
% 1.74/1.64 % (27742)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_27475 for (2996ds/39Mi)
% 1.74/1.64 % (27738)Instructions burned: 109 (million)
% 1.74/1.64 % (27738)------------------------------
% 1.74/1.64 % (27738)------------------------------
% 1.74/1.65 % (27743)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_27475 for (2996ds/448Mi)
% 1.74/1.66 % (27742)Instruction limit reached!
% 1.74/1.66 % (27742)------------------------------
% 1.74/1.66 % (27742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.66 % (27742)Termination reason: Unknown
% 1.74/1.66 % (27742)Termination phase: Saturation
% 1.74/1.66
% 1.74/1.66 % (27742)Memory used [KB]: 5756
% 1.74/1.66 % (27742)Time elapsed: 0.018 s
% 1.74/1.66 % (27742)Instructions burned: 40 (million)
% 1.74/1.66 % (27742)------------------------------
% 1.74/1.66 % (27742)------------------------------
% 1.74/1.66 % (27683)Instruction limit reached!
% 1.74/1.66 % (27683)------------------------------
% 1.74/1.66 % (27683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.66 % (27683)Termination reason: Unknown
% 1.74/1.66 % (27683)Termination phase: Saturation
% 1.74/1.66
% 1.74/1.66 % (27683)Memory used [KB]: 7931
% 1.74/1.66 % (27683)Time elapsed: 0.294 s
% 1.74/1.66 % (27683)Instructions burned: 712 (million)
% 1.74/1.66 % (27683)------------------------------
% 1.74/1.66 % (27683)------------------------------
% 1.74/1.67 % (27745)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_27475 for (2996ds/46Mi)
% 1.74/1.68 % (27746)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_27475 for (2996ds/98Mi)
% 1.74/1.68 % (27745)Instruction limit reached!
% 1.74/1.68 % (27745)------------------------------
% 1.74/1.68 % (27745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.68 % (27745)Termination reason: Unknown
% 1.74/1.68 % (27745)Termination phase: Saturation
% 1.74/1.68
% 1.74/1.68 % (27745)Memory used [KB]: 5756
% 1.74/1.68 % (27745)Time elapsed: 0.017 s
% 1.74/1.68 % (27745)Instructions burned: 46 (million)
% 1.74/1.68 % (27745)------------------------------
% 1.74/1.68 % (27745)------------------------------
% 1.74/1.70 % (27690)Instruction limit reached!
% 1.74/1.70 % (27690)------------------------------
% 1.74/1.70 % (27690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.70 % (27690)Termination reason: Unknown
% 1.74/1.70 % (27690)Termination phase: Saturation
% 1.74/1.70
% 1.74/1.70 % (27690)Memory used [KB]: 6908
% 1.74/1.70 % (27690)Time elapsed: 0.312 s
% 1.74/1.70 % (27690)Instructions burned: 779 (million)
% 1.74/1.70 % (27690)------------------------------
% 1.74/1.70 % (27690)------------------------------
% 1.74/1.70 % (27747)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_27475 for (2996ds/507Mi)
% 1.74/1.72 % (27748)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_27475 for (2996ds/149Mi)
% 1.74/1.72 % (27746)Instruction limit reached!
% 1.74/1.72 % (27746)------------------------------
% 1.74/1.72 % (27746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.72 % (27746)Termination reason: Unknown
% 1.74/1.72 % (27746)Termination phase: Saturation
% 1.74/1.72
% 1.74/1.72 % (27746)Memory used [KB]: 1407
% 1.74/1.72 % (27746)Time elapsed: 0.047 s
% 1.74/1.72 % (27746)Instructions burned: 98 (million)
% 1.74/1.72 % (27746)------------------------------
% 1.74/1.72 % (27746)------------------------------
% 1.74/1.74 % (27674)Instruction limit reached!
% 1.74/1.74 % (27674)------------------------------
% 1.74/1.74 % (27674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.74 % (27674)Termination reason: Unknown
% 1.74/1.74 % (27674)Termination phase: Saturation
% 1.74/1.74
% 1.74/1.74 % (27674)Memory used [KB]: 8699
% 1.74/1.74 % (27674)Time elapsed: 0.406 s
% 1.74/1.74 % (27674)Instructions burned: 1043 (million)
% 1.74/1.74 % (27674)------------------------------
% 1.74/1.74 % (27674)------------------------------
% 1.74/1.75 % (27749)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_27475 for (2995ds/39Mi)
% 1.74/1.76 % (27751)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_27475 for (2995ds/6Mi)
% 1.74/1.76 % (27751)Instruction limit reached!
% 1.74/1.76 % (27751)------------------------------
% 1.74/1.76 % (27751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.76 % (27751)Termination reason: Unknown
% 1.74/1.76 % (27751)Termination phase: Saturation
% 1.74/1.76
% 1.74/1.76 % (27751)Memory used [KB]: 9978
% 1.74/1.76 % (27751)Time elapsed: 0.005 s
% 1.74/1.76 % (27751)Instructions burned: 7 (million)
% 1.74/1.76 % (27751)------------------------------
% 1.74/1.76 % (27751)------------------------------
% 1.74/1.77 % (27752)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_27475 for (2995ds/1087Mi)
% 1.74/1.78 % (27749)Instruction limit reached!
% 1.74/1.78 % (27749)------------------------------
% 1.74/1.78 % (27749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.78 % (27749)Termination reason: Unknown
% 1.74/1.78 % (27749)Termination phase: Saturation
% 1.74/1.78
% 1.74/1.78 % (27749)Memory used [KB]: 5756
% 1.74/1.78 % (27749)Time elapsed: 0.050 s
% 1.74/1.78 % (27749)Instructions burned: 40 (million)
% 1.74/1.78 % (27749)------------------------------
% 1.74/1.78 % (27749)------------------------------
% 1.74/1.79 % (27754)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_27475 for (2995ds/47Mi)
% 1.74/1.79 % (27748)Instruction limit reached!
% 1.74/1.79 % (27748)------------------------------
% 1.74/1.79 % (27748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.79 % (27748)Termination reason: Unknown
% 1.74/1.79 % (27748)Termination phase: Saturation
% 1.74/1.79
% 1.74/1.79 % (27748)Memory used [KB]: 6140
% 1.74/1.79 % (27748)Time elapsed: 0.077 s
% 1.74/1.79 % (27748)Instructions burned: 150 (million)
% 1.74/1.79 % (27748)------------------------------
% 1.74/1.79 % (27748)------------------------------
% 1.74/1.81 % (27754)Instruction limit reached!
% 1.74/1.81 % (27754)------------------------------
% 1.74/1.81 % (27754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.81 % (27754)Termination reason: Unknown
% 1.74/1.81 % (27754)Termination phase: Saturation
% 1.74/1.81
% 1.74/1.81 % (27754)Memory used [KB]: 5884
% 1.74/1.81 % (27754)Time elapsed: 0.047 s
% 1.74/1.81 % (27754)Instructions burned: 48 (million)
% 1.74/1.81 % (27754)------------------------------
% 1.74/1.81 % (27754)------------------------------
% 1.74/1.82 % (27756)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_27475 for (2995ds/44Mi)
% 1.74/1.82 % (27756)Refutation not found, incomplete strategy
% 1.74/1.82 % (27756)------------------------------
% 1.74/1.82 % (27756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.82 % (27756)Termination reason: Refutation not found, incomplete strategy
% 1.74/1.82
% 1.74/1.82
% 1.74/1.82 % (27756)Memory used [KB]: 1151
% 1.74/1.82 % (27756)Time elapsed: 0.004 s
% 1.74/1.82 % (27756)Instructions burned: 10 (million)
% 1.74/1.82 % (27756)------------------------------
% 1.74/1.82 % (27756)------------------------------
% 1.74/1.83 % (27685)Instruction limit reached!
% 1.74/1.83 % (27685)------------------------------
% 1.74/1.83 % (27685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.83 % (27685)Termination reason: Unknown
% 1.74/1.83 % (27685)Termination phase: Saturation
% 1.74/1.83
% 1.74/1.83 % (27685)Memory used [KB]: 6524
% 1.74/1.83 % (27685)Time elapsed: 0.448 s
% 1.74/1.83 % (27685)Instructions burned: 902 (million)
% 1.74/1.83 % (27685)------------------------------
% 1.74/1.83 % (27685)------------------------------
% 1.74/1.83 % (27759)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_27475 for (2994ds/432Mi)
% 1.74/1.84 % (27760)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_27475 for (2994ds/62Mi)
% 1.74/1.85 % (27692)Instruction limit reached!
% 1.74/1.85 % (27692)------------------------------
% 1.74/1.85 % (27692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.85 % (27692)Termination reason: Unknown
% 1.74/1.85 % (27692)Termination phase: Saturation
% 1.74/1.85
% 1.74/1.85 % (27692)Memory used [KB]: 7291
% 1.74/1.85 % (27692)Time elapsed: 0.424 s
% 1.74/1.85 % (27692)Instructions burned: 879 (million)
% 1.74/1.85 % (27692)------------------------------
% 1.74/1.85 % (27692)------------------------------
% 1.74/1.85 % (27761)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_27475 for (2994ds/31Mi)
% 1.74/1.86 % (27743)Instruction limit reached!
% 1.74/1.86 % (27743)------------------------------
% 1.74/1.86 % (27743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.86 % (27743)Termination reason: Unknown
% 1.74/1.86 % (27743)Termination phase: Saturation
% 1.74/1.86
% 1.74/1.86 % (27743)Memory used [KB]: 6652
% 1.74/1.86 % (27743)Time elapsed: 0.221 s
% 1.74/1.86 % (27743)Instructions burned: 448 (million)
% 1.74/1.86 % (27743)------------------------------
% 1.74/1.86 % (27743)------------------------------
% 1.74/1.86 % (27761)Instruction limit reached!
% 1.74/1.86 % (27761)------------------------------
% 1.74/1.86 % (27761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.86 % (27761)Termination reason: Unknown
% 1.74/1.86 % (27761)Termination phase: Saturation
% 1.74/1.86
% 1.74/1.86 % (27761)Memory used [KB]: 5884
% 1.74/1.86 % (27761)Time elapsed: 0.016 s
% 1.74/1.86 % (27761)Instructions burned: 32 (million)
% 1.74/1.86 % (27761)------------------------------
% 1.74/1.86 % (27761)------------------------------
% 1.74/1.87 % (27767)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_27475 for (2994ds/71Mi)
% 1.74/1.87 % (27760)Instruction limit reached!
% 1.74/1.87 % (27760)------------------------------
% 1.74/1.87 % (27760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.87 % (27760)Termination reason: Unknown
% 1.74/1.87 % (27760)Termination phase: Saturation
% 1.74/1.87
% 1.74/1.87 % (27760)Memory used [KB]: 6012
% 1.74/1.87 % (27760)Time elapsed: 0.033 s
% 1.74/1.87 % (27760)Instructions burned: 63 (million)
% 1.74/1.87 % (27760)------------------------------
% 1.74/1.87 % (27760)------------------------------
% 1.74/1.88 % (27764)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_27475 for (2994ds/96Mi)
% 1.74/1.88 % (27766)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_27475 for (2994ds/453Mi)
% 1.74/1.89 % (27747)Instruction limit reached!
% 1.74/1.89 % (27747)------------------------------
% 1.74/1.89 % (27747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.89 % (27747)Termination reason: Unknown
% 1.74/1.89 % (27747)Termination phase: Saturation
% 1.74/1.89
% 1.74/1.89 % (27747)Memory used [KB]: 6268
% 1.74/1.89 % (27747)Time elapsed: 0.190 s
% 1.74/1.89 % (27747)Instructions burned: 507 (million)
% 1.74/1.89 % (27747)------------------------------
% 1.74/1.89 % (27747)------------------------------
% 1.74/1.89 % (27769)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_27475 for (2994ds/83Mi)
% 1.74/1.90 % (27767)Instruction limit reached!
% 1.74/1.90 % (27767)------------------------------
% 1.74/1.90 % (27767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.91 % (27767)Termination reason: Unknown
% 1.74/1.91 % (27767)Termination phase: Saturation
% 1.74/1.91
% 1.74/1.91 % (27767)Memory used [KB]: 6012
% 1.74/1.91 % (27767)Time elapsed: 0.034 s
% 1.74/1.91 % (27767)Instructions burned: 71 (million)
% 1.74/1.91 % (27767)------------------------------
% 1.74/1.91 % (27767)------------------------------
% 1.74/1.92 % (27770)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_27475 for (2994ds/11Mi)
% 1.74/1.92 % (27772)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_27475 for (2994ds/41Mi)
% 1.74/1.92 % (27770)Instruction limit reached!
% 1.74/1.92 % (27770)------------------------------
% 1.74/1.92 % (27770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.92 % (27770)Termination reason: Unknown
% 1.74/1.92 % (27770)Termination phase: Saturation
% 1.74/1.92
% 1.74/1.92 % (27770)Memory used [KB]: 5628
% 1.74/1.92 % (27770)Time elapsed: 0.005 s
% 1.74/1.92 % (27770)Instructions burned: 13 (million)
% 1.74/1.92 % (27770)------------------------------
% 1.74/1.92 % (27770)------------------------------
% 1.74/1.92 % (27764)Instruction limit reached!
% 1.74/1.92 % (27764)------------------------------
% 1.74/1.92 % (27764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.92 % (27764)Termination reason: Unknown
% 1.74/1.92 % (27764)Termination phase: Saturation
% 1.74/1.92
% 1.74/1.92 % (27764)Memory used [KB]: 6012
% 1.74/1.92 % (27764)Time elapsed: 0.050 s
% 1.74/1.92 % (27764)Instructions burned: 97 (million)
% 1.74/1.92 % (27764)------------------------------
% 1.74/1.92 % (27764)------------------------------
% 1.74/1.93 % (27769)Instruction limit reached!
% 1.74/1.93 % (27769)------------------------------
% 1.74/1.93 % (27769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.93 % (27769)Termination reason: Unknown
% 1.74/1.93 % (27769)Termination phase: Saturation
% 1.74/1.93
% 1.74/1.93 % (27769)Memory used [KB]: 5756
% 1.74/1.93 % (27769)Time elapsed: 0.040 s
% 1.74/1.93 % (27769)Instructions burned: 83 (million)
% 1.74/1.93 % (27769)------------------------------
% 1.74/1.93 % (27769)------------------------------
% 1.74/1.93 % (27774)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_27475 for (2993ds/6Mi)
% 1.74/1.93 % (27774)Instruction limit reached!
% 1.74/1.93 % (27774)------------------------------
% 1.74/1.93 % (27774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.93 % (27774)Termination reason: Unknown
% 1.74/1.93 % (27774)Termination phase: Saturation
% 1.74/1.93
% 1.74/1.93 % (27774)Memory used [KB]: 5500
% 1.74/1.93 % (27774)Time elapsed: 0.003 s
% 1.74/1.93 % (27774)Instructions burned: 6 (million)
% 1.74/1.93 % (27774)------------------------------
% 1.74/1.93 % (27774)------------------------------
% 1.74/1.94 % (27775)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_27475 for (2993ds/150Mi)
% 1.74/1.94 % (27772)Instruction limit reached!
% 1.74/1.94 % (27772)------------------------------
% 1.74/1.94 % (27772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.94 % (27772)Termination reason: Unknown
% 1.74/1.94 % (27772)Termination phase: Saturation
% 1.74/1.94
% 1.74/1.94 % (27772)Memory used [KB]: 5884
% 1.74/1.94 % (27772)Time elapsed: 0.021 s
% 1.74/1.94 % (27772)Instructions burned: 41 (million)
% 1.74/1.94 % (27772)------------------------------
% 1.74/1.94 % (27772)------------------------------
% 1.74/1.95 % (27776)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_27475 for (2993ds/343Mi)
% 1.74/1.95 % (27778)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_27475 for (2993ds/109Mi)
% 1.74/1.96 % (27780)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_27475 for (2993ds/253Mi)
% 1.74/1.98 % (27775)Instruction limit reached!
% 1.74/1.98 % (27775)------------------------------
% 1.74/1.98 % (27775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.98 % (27775)Termination reason: Unknown
% 1.74/1.98 % (27775)Termination phase: Saturation
% 1.74/1.98
% 1.74/1.98 % (27775)Memory used [KB]: 6268
% 1.74/1.98 % (27775)Time elapsed: 0.045 s
% 1.74/1.98 % (27775)Instructions burned: 152 (million)
% 1.74/1.98 % (27775)------------------------------
% 1.74/1.98 % (27775)------------------------------
% 1.74/1.99 % (27783)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_27475 for (2993ds/140Mi)
% 1.74/2.00 % (27778)Instruction limit reached!
% 1.74/2.00 % (27778)------------------------------
% 1.74/2.00 % (27778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/2.00 % (27778)Termination reason: Unknown
% 1.74/2.00 % (27778)Termination phase: Saturation
% 1.74/2.00
% 1.74/2.00 % (27778)Memory used [KB]: 6268
% 1.74/2.00 % (27778)Time elapsed: 0.053 s
% 1.74/2.00 % (27778)Instructions burned: 110 (million)
% 1.74/2.00 % (27778)------------------------------
% 1.74/2.00 % (27778)------------------------------
% 1.74/2.02 % (27759)Instruction limit reached!
% 1.74/2.02 % (27759)------------------------------
% 1.74/2.02 % (27759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/2.02 % (27759)Termination reason: Unknown
% 1.74/2.02 % (27759)Termination phase: Saturation
% 1.74/2.02
% 1.74/2.02 % (27759)Memory used [KB]: 2430
% 1.74/2.02 % (27759)Time elapsed: 0.190 s
% 1.74/2.02 % (27759)Instructions burned: 432 (million)
% 1.74/2.02 % (27759)------------------------------
% 1.74/2.02 % (27759)------------------------------
% 1.74/2.02 % (27784)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_27475 for (2993ds/614Mi)
% 6.55/2.04 % (27787)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_27475 for (2992ds/202Mi)
% 6.55/2.04 % (27783)Instruction limit reached!
% 6.55/2.04 % (27783)------------------------------
% 6.55/2.04 % (27783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.55/2.04 % (27783)Termination reason: Unknown
% 6.55/2.04 % (27783)Termination phase: Saturation
% 6.55/2.04
% 6.55/2.04 % (27783)Memory used [KB]: 6140
% 6.55/2.04 % (27783)Time elapsed: 0.052 s
% 6.55/2.04 % (27783)Instructions burned: 140 (million)
% 6.55/2.04 % (27783)------------------------------
% 6.55/2.04 % (27783)------------------------------
% 6.55/2.04 % (27787)Refutation not found, incomplete strategy
% 6.55/2.04 % (27787)------------------------------
% 6.55/2.04 % (27787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.55/2.04 % (27787)Termination reason: Refutation not found, incomplete strategy
% 6.55/2.04
% 6.55/2.04
% 6.55/2.04 % (27787)Memory used [KB]: 5500
% 6.55/2.04 % (27787)Time elapsed: 0.004 s
% 6.55/2.04 % (27787)Instructions burned: 5 (million)
% 6.55/2.04 % (27787)------------------------------
% 6.55/2.04 % (27787)------------------------------
% 6.55/2.06 % (27791)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=283:si=on:rtra=on_0 on DTF2THF_27475 for (2992ds/283Mi)
% 6.55/2.06 % (27790)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_27475 for (2992ds/339Mi)
% 6.55/2.07 % (27766)Instruction limit reached!
% 6.55/2.07 % (27766)------------------------------
% 6.55/2.07 % (27766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.55/2.07 % (27766)Termination reason: Unknown
% 6.55/2.07 % (27766)Termination phase: Saturation
% 6.55/2.07
% 6.55/2.07 % (27766)Memory used [KB]: 6652
% 6.55/2.07 % (27766)Time elapsed: 0.183 s
% 6.55/2.07 % (27766)Instructions burned: 454 (million)
% 6.55/2.07 % (27766)------------------------------
% 6.55/2.07 % (27766)------------------------------
% 6.55/2.07 % (27780)Instruction limit reached!
% 6.55/2.07 % (27780)------------------------------
% 6.55/2.07 % (27780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.55/2.07 % (27780)Termination reason: Unknown
% 6.55/2.07 % (27780)Termination phase: Saturation
% 6.55/2.07
% 6.55/2.07 % (27780)Memory used [KB]: 6268
% 6.55/2.07 % (27780)Time elapsed: 0.119 s
% 6.55/2.07 % (27780)Instructions burned: 254 (million)
% 6.55/2.07 % (27780)------------------------------
% 6.55/2.07 % (27780)------------------------------
% 6.55/2.08 % (27776)Instruction limit reached!
% 6.55/2.08 % (27776)------------------------------
% 6.55/2.08 % (27776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.55/2.08 % (27776)Termination reason: Unknown
% 6.55/2.08 % (27776)Termination phase: Saturation
% 6.55/2.08
% 6.55/2.08 % (27776)Memory used [KB]: 6652
% 6.55/2.08 % (27776)Time elapsed: 0.131 s
% 6.55/2.08 % (27776)Instructions burned: 344 (million)
% 6.55/2.08 % (27776)------------------------------
% 6.55/2.08 % (27776)------------------------------
% 6.55/2.09 % (27796)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_27475 for (2992ds/134Mi)
% 6.55/2.09 % (27797)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_27475 for (2992ds/298Mi)
% 6.55/2.10 % (27798)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_27475 for (2992ds/192Mi)
% 6.55/2.12 % (27790)First to succeed.
% 6.85/2.13 % (27790)Refutation found. Thanks to Tanya!
% 6.85/2.13 % SZS status Theorem for DTF2THF_27475
% 6.85/2.13 % SZS output start Proof for DTF2THF_27475
% 6.85/2.13 thf(type_def_6, type, elem: $tType).
% 6.85/2.13 thf(type_def_7, type, nat: $tType).
% 6.85/2.13 thf(type_def_8, type, list: $tType).
% 6.85/2.13 thf(func_def_0, type, isPer: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 6.85/2.13 thf(func_def_2, type, elem: $tType).
% 6.85/2.13 thf(func_def_3, type, elemStar: elem > elem > $o).
% 6.85/2.13 thf(func_def_4, type, nat: $tType).
% 6.85/2.13 thf(func_def_5, type, natStar: nat > nat > $o).
% 6.85/2.13 thf(func_def_6, type, zero: nat).
% 6.85/2.13 thf(func_def_7, type, suc: nat > nat).
% 6.85/2.13 thf(func_def_8, type, plus: nat > nat > nat).
% 6.85/2.13 thf(func_def_9, type, list: $tType).
% 6.85/2.13 thf(func_def_10, type, listStar: nat > list > list > $o).
% 6.85/2.13 thf(func_def_11, type, nil: list).
% 6.85/2.13 thf(func_def_12, type, cons: nat > elem > list > list).
% 6.85/2.13 thf(func_def_13, type, app: nat > nat > list > list > list).
% 6.85/2.13 thf(func_def_16, type, sK0: nat).
% 6.85/2.13 thf(func_def_17, type, sK1: list).
% 6.85/2.13 thf(func_def_18, type, sK2: nat).
% 6.85/2.13 thf(func_def_19, type, sK3: list).
% 6.85/2.13 thf(func_def_20, type, sK4: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 6.85/2.13 thf(func_def_21, type, sK5: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 6.85/2.13 thf(func_def_22, type, sK6: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 6.85/2.13 thf(func_def_23, type, sK7: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 6.85/2.13 thf(func_def_24, type, sK8: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 6.85/2.13 thf(func_def_25, type, sP9: $o > $o).
% 6.85/2.13 thf(func_def_27, type, ph11: !>[X0: $tType]:(X0)).
% 6.85/2.13 thf(f1026,plain,(
% 6.85/2.13 $false),
% 6.85/2.13 inference(avatar_sat_refutation,[status(thm)],[f77,f964,f995,f1020,f1025])).
% 6.85/2.13 thf(f1025,plain,(
% 6.85/2.13 ~spl10_1),
% 6.85/2.13 inference(avatar_contradiction_clause,[status(thm)],[f1024])).
% 6.85/2.13 thf(f1024,plain,(
% 6.85/2.13 $false | ~spl10_1),
% 6.85/2.13 inference(trivial_inequality_removal,[status(thm)],[f1023])).
% 6.85/2.13 thf(f1023,plain,(
% 6.85/2.13 ($false = $true) | ~spl10_1),
% 6.85/2.13 inference(backward_demodulation,[status(thm)],[f66,f72])).
% 6.85/2.13 thf(f72,plain,(
% 6.85/2.13 ((sP9 @ $true) = $false) | ~spl10_1),
% 6.85/2.13 inference(avatar_component_clause,[status(thm)],[f70])).
% 6.85/2.13 thf(f70,definition,(
% 6.85/2.13 spl10_1 <=> ((sP9 @ $true) = $false)),
% 6.85/2.13 introduced(definition,[new_symbols(naming,[spl10_1])],[avatar_definition])).
% 6.85/2.13 thf(f66,plain,(
% 6.85/2.13 ((sP9 @ $true) = $true)),
% 6.85/2.13 inference(inequality_splitting,[status(thm)],[f53,f65])).
% 6.85/2.13 thf(f65,plain,(
% 6.85/2.13 ((sP9 @ (listStar @ (plus @ zero @ (plus @ sK0 @ sK2)) @ (app @ zero @ (plus @ sK0 @ sK2) @ nil @ (app @ sK0 @ sK2 @ sK1 @ sK3)) @ (app @ (plus @ zero @ sK0) @ sK2 @ (app @ zero @ sK0 @ nil @ sK1) @ sK3))) = $false)),
% 6.85/2.13 introduced(definition,[new_symbols(naming,[sP9])],[inequality_splitting_name_introduction])).
% 6.85/2.13 thf(f53,plain,(
% 6.85/2.13 ((listStar @ (plus @ zero @ (plus @ sK0 @ sK2)) @ (app @ zero @ (plus @ sK0 @ sK2) @ nil @ (app @ sK0 @ sK2 @ sK1 @ sK3)) @ (app @ (plus @ zero @ sK0) @ sK2 @ (app @ zero @ sK0 @ nil @ sK1) @ sK3)) != $true)),
% 6.85/2.13 inference(cnf_transformation,[status(thm)],[f41])).
% 6.85/2.13 thf(f41,plain,(
% 6.85/2.13 ((listStar @ (plus @ zero @ (plus @ sK0 @ sK2)) @ (app @ zero @ (plus @ sK0 @ sK2) @ nil @ (app @ sK0 @ sK2 @ sK1 @ sK3)) @ (app @ (plus @ zero @ sK0) @ sK2 @ (app @ zero @ sK0 @ nil @ sK1) @ sK3)) != $true) & ((listStar @ sK0 @ sK1 @ sK1) = $true) & ((listStar @ sK2 @ sK3 @ sK3) = $true)),
% 6.85/2.13 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f35,f40])).
% 6.85/2.13 thf(f40,plain,(
% 6.85/2.13 ? [X0 : nat,X1 : list,X2 : nat,X3 : list] : (((listStar @ (plus @ zero @ (plus @ X0 @ X2)) @ (app @ zero @ (plus @ X0 @ X2) @ nil @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ zero @ X0) @ X2 @ (app @ zero @ X0 @ nil @ X1) @ X3)) != $true) & ((listStar @ X0 @ X1 @ X1) = $true) & ((listStar @ X2 @ X3 @ X3) = $true)) => (((listStar @ (plus @ zero @ (plus @ sK0 @ sK2)) @ (app @ zero @ (plus @ sK0 @ sK2) @ nil @ (app @ sK0 @ sK2 @ sK1 @ sK3)) @ (app @ (plus @ zero @ sK0) @ sK2 @ (app @ zero @ sK0 @ nil @ sK1) @ sK3)) != $true) & ((listStar @ sK0 @ sK1 @ sK1) = $true) & ((listStar @ sK2 @ sK3 @ sK3) = $true))),
% 6.85/2.13 introduced(definition,[],[choice_axiom])).
% 6.85/2.13 thf(f35,plain,(
% 6.85/2.13 ? [X0 : nat,X1 : list,X2 : nat,X3 : list] : (((listStar @ (plus @ zero @ (plus @ X0 @ X2)) @ (app @ zero @ (plus @ X0 @ X2) @ nil @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ zero @ X0) @ X2 @ (app @ zero @ X0 @ nil @ X1) @ X3)) != $true) & ((listStar @ X0 @ X1 @ X1) = $true) & ((listStar @ X2 @ X3 @ X3) = $true))),
% 6.85/2.13 inference(flattening,[status(thm)],[f34])).
% 6.85/2.13 thf(f34,plain,(
% 6.85/2.13 ? [X0 : nat,X1 : list,X2 : nat,X3 : list] : ((((listStar @ (plus @ zero @ (plus @ X0 @ X2)) @ (app @ zero @ (plus @ X0 @ X2) @ nil @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ zero @ X0) @ X2 @ (app @ zero @ X0 @ nil @ X1) @ X3)) != $true) & ((listStar @ X2 @ X3 @ X3) = $true)) & ((listStar @ X0 @ X1 @ X1) = $true))),
% 6.85/2.13 inference(ennf_transformation,[status(thm)],[f19])).
% 6.85/2.13 thf(f19,plain,(
% 6.85/2.13 ~! [X0 : nat,X1 : list,X2 : nat,X3 : list] : (((listStar @ X0 @ X1 @ X1) = $true) => (((listStar @ X2 @ X3 @ X3) = $true) => ((listStar @ (plus @ zero @ (plus @ X0 @ X2)) @ (app @ zero @ (plus @ X0 @ X2) @ nil @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ zero @ X0) @ X2 @ (app @ zero @ X0 @ nil @ X1) @ X3)) = $true)))),
% 6.85/2.13 inference(fool_elimination,[status(thm)],[f18])).
% 6.85/2.13 thf(f18,plain,(
% 6.85/2.13 ~! [X0 : nat,X1 : list,X2 : nat,X3 : list] : ((listStar @ X0 @ X1 @ X1) => ((listStar @ X2 @ X3 @ X3) => (listStar @ (plus @ zero @ (plus @ X0 @ X2)) @ (app @ zero @ (plus @ X0 @ X2) @ nil @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ zero @ X0) @ X2 @ (app @ zero @ X0 @ nil @ X1) @ X3))))),
% 6.85/2.13 inference(rectify,[status(thm)],[f12])).
% 6.85/2.13 thf(f12,negated_conjecture,(
% 6.85/2.13 ~! [X13 : nat,X15 : list,X14 : nat,X16 : list] : ((listStar @ X13 @ X15 @ X15) => ((listStar @ X14 @ X16 @ X16) => (listStar @ (plus @ zero @ (plus @ X13 @ X14)) @ (app @ zero @ (plus @ X13 @ X14) @ nil @ (app @ X13 @ X14 @ X15 @ X16)) @ (app @ (plus @ zero @ X13) @ X14 @ (app @ zero @ X13 @ nil @ X15) @ X16))))),
% 6.85/2.13 inference(negated_conjecture,[status(cth)],[f11])).
% 6.85/2.13 thf(f11,conjecture,(
% 6.85/2.13 ! [X13 : nat,X15 : list,X14 : nat,X16 : list] : ((listStar @ X13 @ X15 @ X15) => ((listStar @ X14 @ X16 @ X16) => (listStar @ (plus @ zero @ (plus @ X13 @ X14)) @ (app @ zero @ (plus @ X13 @ X14) @ nil @ (app @ X13 @ X14 @ X15 @ X16)) @ (app @ (plus @ zero @ X13) @ X14 @ (app @ zero @ X13 @ nil @ X15) @ X16))))),
% 6.85/2.13 file('/export/starexec/sandbox/tmp/tmp.v0WQauavVr/DTF2THF_27475.p',list_app_assoc_base)).
% 6.85/2.13 thf(f1020,plain,(
% 6.85/2.13 spl10_8),
% 6.85/2.13 inference(avatar_contradiction_clause,[status(thm)],[f1019])).
% 6.85/2.13 thf(f1019,plain,(
% 6.85/2.13 $false | spl10_8),
% 6.85/2.13 inference(subsumption_resolution,[status(thm)],[f1015,f52])).
% 6.85/2.13 thf(f52,plain,(
% 6.85/2.13 ((listStar @ sK0 @ sK1 @ sK1) = $true)),
% 6.85/2.13 inference(cnf_transformation,[status(thm)],[f41])).
% 6.85/2.13 thf(f1015,plain,(
% 6.85/2.13 ((listStar @ sK0 @ sK1 @ sK1) != $true) | spl10_8),
% 6.85/2.13 inference(trivial_inequality_removal,[status(thm)],[f1012])).
% 6.85/2.13 thf(f1012,plain,(
% 6.85/2.13 ((listStar @ sK0 @ sK1 @ sK1) != $true) | ($true != $true) | spl10_8),
% 6.85/2.13 inference(superposition,[status(thm)],[f1010,f947])).
% 6.85/2.13 thf(f947,plain,(
% 6.85/2.13 ( ! [X0 : nat,X1 : list] : (((listStar @ X0 @ (app @ zero @ X0 @ nil @ X1) @ X1) = $true) | ((listStar @ X0 @ X1 @ X1) != $true)) )),
% 6.85/2.13 inference(forward_demodulation,[status(thm)],[f48,f49])).
% 6.85/2.13 thf(f49,plain,(
% 6.85/2.13 ( ! [X0 : nat] : (((plus @ zero @ X0) = X0)) )),
% 6.85/2.13 inference(cnf_transformation,[status(thm)],[f32])).
% 6.85/2.13 thf(f32,plain,(
% 6.85/2.13 ! [X0 : nat] : ((plus @ zero @ X0) = X0)),
% 6.85/2.13 inference(rectify,[status(thm)],[f8])).
% 6.85/2.13 thf(f8,axiom,(
% 6.85/2.13 ! [X6 : nat] : ((plus @ zero @ X6) = X6)),
% 6.85/2.13 file('/export/starexec/sandbox/tmp/tmp.v0WQauavVr/DTF2THF_27475.p',ax1)).
% 6.85/2.13 thf(f48,plain,(
% 6.85/2.13 ( ! [X0 : nat,X1 : list] : (((listStar @ X0 @ X1 @ X1) != $true) | ((listStar @ (plus @ zero @ X0) @ (app @ zero @ X0 @ nil @ X1) @ X1) = $true)) )),
% 6.85/2.13 inference(cnf_transformation,[status(thm)],[f37])).
% 6.85/2.13 thf(f37,plain,(
% 6.85/2.13 ! [X0 : nat,X1 : list] : (((listStar @ (plus @ zero @ X0) @ (app @ zero @ X0 @ nil @ X1) @ X1) = $true) | ((listStar @ X0 @ X1 @ X1) != $true))),
% 6.85/2.13 inference(ennf_transformation,[status(thm)],[f29])).
% 6.85/2.13 thf(f29,plain,(
% 6.85/2.13 ! [X0 : nat,X1 : list] : (((listStar @ X0 @ X1 @ X1) = $true) => ((listStar @ (plus @ zero @ X0) @ (app @ zero @ X0 @ nil @ X1) @ X1) = $true))),
% 6.85/2.13 inference(fool_elimination,[status(thm)],[f28])).
% 6.85/2.13 thf(f28,plain,(
% 6.85/2.13 ! [X0 : nat,X1 : list] : ((listStar @ X0 @ X1 @ X1) => (listStar @ (plus @ zero @ X0) @ (app @ zero @ X0 @ nil @ X1) @ X1))),
% 6.85/2.13 inference(rectify,[status(thm)],[f9])).
% 6.85/2.13 thf(f9,axiom,(
% 6.85/2.13 ! [X6 : nat,X2 : list] : ((listStar @ X6 @ X2 @ X2) => (listStar @ (plus @ zero @ X6) @ (app @ zero @ X6 @ nil @ X2) @ X2))),
% 6.85/2.13 file('/export/starexec/sandbox/tmp/tmp.v0WQauavVr/DTF2THF_27475.p',ax3)).
% 6.85/2.13 thf(f1010,plain,(
% 6.85/2.13 ((listStar @ sK0 @ (app @ zero @ sK0 @ nil @ sK1) @ sK1) != $true) | spl10_8),
% 6.85/2.13 inference(subsumption_resolution,[status(thm)],[f1009,f50])).
% 6.85/2.13 thf(f50,plain,(
% 6.85/2.13 ( ! [X0 : nat] : (((isPer @ list @ (listStar @ X0)) = $true)) )),
% 6.85/2.13 inference(cnf_transformation,[status(thm)],[f15])).
% 6.85/2.13 thf(f15,plain,(
% 6.85/2.13 ! [X0 : nat] : ((isPer @ list @ (listStar @ X0)) = $true)),
% 6.85/2.13 inference(fool_elimination,[status(thm)],[f14])).
% 6.85/2.13 thf(f14,plain,(
% 6.85/2.13 ! [X0 : nat] : (isPer @ list @ (listStar @ X0))),
% 6.85/2.13 inference(rectify,[status(thm)],[f4])).
% 6.85/2.13 thf(f4,axiom,(
% 6.85/2.13 ! [X5 : nat] : (isPer @ list @ (listStar @ X5))),
% 6.85/2.13 file('/export/starexec/sandbox/tmp/tmp.v0WQauavVr/DTF2THF_27475.p','\'listStar\'_is_per')).
% 6.85/2.13 thf(f1009,plain,(
% 6.85/2.13 ((listStar @ sK0 @ (app @ zero @ sK0 @ nil @ sK1) @ sK1) != $true) | ((isPer @ list @ (listStar @ sK0)) != $true) | spl10_8),
% 6.85/2.13 inference(trivial_inequality_removal,[status(thm)],[f1006])).
% 6.85/2.13 thf(f1006,plain,(
% 6.85/2.13 ($true != $true) | ((isPer @ list @ (listStar @ sK0)) != $true) | ((listStar @ sK0 @ (app @ zero @ sK0 @ nil @ sK1) @ sK1) != $true) | spl10_8),
% 6.85/2.13 inference(superposition,[status(thm)],[f1005,f63])).
% 6.85/2.13 thf(f63,plain,(
% 6.85/2.13 ( ! [X0 : $tType,X1 : X0 > X0 > $o,X6 : X0,X5 : X0] : (((X1 @ X6 @ X5) = $true) | ((X1 @ X5 @ X6) != $true) | ((isPer @ X0 @ X1) != $true)) )),
% 6.85/2.13 inference(cnf_transformation,[status(thm)],[f47])).
% 6.85/2.13 thf(f47,plain,(
% 6.85/2.13 ! [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 @ X6 @ X5) = $true) | ((X1 @ X5 @ X6) != $true))) | ((isPer @ X0 @ X1) != $true)) & (((isPer @ X0 @ X1) = $true) | (((X1 @ (sK4 @ X0 @ X1) @ (sK6 @ X0 @ X1)) != $true) & ((X1 @ (sK5 @ X0 @ X1) @ (sK6 @ X0 @ X1)) = $true) & ((X1 @ (sK4 @ X0 @ X1) @ (sK5 @ X0 @ X1)) = $true)) | (((X1 @ (sK8 @ X0 @ X1) @ (sK7 @ X0 @ X1)) != $true) & ((X1 @ (sK7 @ X0 @ X1) @ (sK8 @ X0 @ X1)) = $true))))),
% 6.85/2.13 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f44,f46,f45])).
% 6.85/2.13 thf(f45,plain,(
% 6.85/2.13 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X7 : X0,X8 : X0,X9 : X0] : (((X1 @ X7 @ X9) != $true) & ((X1 @ X8 @ X9) = $true) & ((X1 @ X7 @ X8) = $true)) => (((X1 @ (sK4 @ X0 @ X1) @ (sK6 @ X0 @ X1)) != $true) & ((X1 @ (sK5 @ X0 @ X1) @ (sK6 @ X0 @ X1)) = $true) & ((X1 @ (sK4 @ X0 @ X1) @ (sK5 @ X0 @ X1)) = $true)))),
% 6.85/2.13 introduced(definition,[],[choice_axiom])).
% 6.85/2.13 thf(f46,plain,(
% 6.85/2.13 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X10 : X0,X11 : X0] : (((X1 @ X11 @ X10) != $true) & ((X1 @ X10 @ X11) = $true)) => (((X1 @ (sK8 @ X0 @ X1) @ (sK7 @ X0 @ X1)) != $true) & ((X1 @ (sK7 @ X0 @ X1) @ (sK8 @ X0 @ X1)) = $true)))),
% 6.85/2.13 introduced(definition,[],[choice_axiom])).
% 6.85/2.13 thf(f44,plain,(
% 6.85/2.13 ! [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 @ X6 @ X5) = $true) | ((X1 @ X5 @ X6) != $true))) | ((isPer @ X0 @ X1) != $true)) & (((isPer @ X0 @ X1) = $true) | ? [X7 : X0,X8 : X0,X9 : X0] : (((X1 @ X7 @ X9) != $true) & ((X1 @ X8 @ X9) = $true) & ((X1 @ X7 @ X8) = $true)) | ? [X10 : X0,X11 : X0] : (((X1 @ X11 @ X10) != $true) & ((X1 @ X10 @ X11) = $true))))),
% 6.85/2.13 inference(rectify,[status(thm)],[f43])).
% 6.85/2.13 thf(f43,plain,(
% 6.85/2.13 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((! [X4 : X0,X5 : X0,X6 : X0] : (((X1 @ X4 @ X6) = $true) | ((X1 @ X5 @ X6) != $true) | ((X1 @ X4 @ X5) != $true)) & ! [X2 : X0,X3 : X0] : (((X1 @ X3 @ X2) = $true) | ((X1 @ X2 @ X3) != $true))) | ((isPer @ X0 @ X1) != $true)) & (((isPer @ X0 @ X1) = $true) | ? [X4 : X0,X5 : X0,X6 : X0] : (((X1 @ X4 @ X6) != $true) & ((X1 @ X5 @ X6) = $true) & ((X1 @ X4 @ X5) = $true)) | ? [X2 : X0,X3 : X0] : (((X1 @ X3 @ X2) != $true) & ((X1 @ X2 @ X3) = $true))))),
% 6.85/2.13 inference(flattening,[status(thm)],[f42])).
% 6.85/2.13 thf(f42,plain,(
% 6.85/2.13 ! [X0 : $tType,X1 : X0 > X0 > $o] : (((! [X4 : X0,X5 : X0,X6 : X0] : (((X1 @ X4 @ X6) = $true) | ((X1 @ X5 @ X6) != $true) | ((X1 @ X4 @ X5) != $true)) & ! [X2 : X0,X3 : X0] : (((X1 @ X3 @ X2) = $true) | ((X1 @ X2 @ X3) != $true))) | ((isPer @ X0 @ X1) != $true)) & (((isPer @ X0 @ X1) = $true) | (? [X4 : X0,X5 : X0,X6 : X0] : (((X1 @ X4 @ X6) != $true) & ((X1 @ X5 @ X6) = $true) & ((X1 @ X4 @ X5) = $true)) | ? [X2 : X0,X3 : X0] : (((X1 @ X3 @ X2) != $true) & ((X1 @ X2 @ X3) = $true)))))),
% 6.85/2.13 inference(nnf_transformation,[status(thm)],[f39])).
% 6.85/2.13 thf(f39,plain,(
% 6.85/2.13 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X4 : X0,X5 : X0,X6 : X0] : (((X1 @ X4 @ X6) = $true) | ((X1 @ X5 @ X6) != $true) | ((X1 @ X4 @ X5) != $true)) & ! [X2 : X0,X3 : X0] : (((X1 @ X3 @ X2) = $true) | ((X1 @ X2 @ X3) != $true))) <=> ((isPer @ X0 @ X1) = $true))),
% 6.85/2.13 inference(flattening,[status(thm)],[f38])).
% 6.85/2.13 thf(f38,plain,(
% 6.85/2.13 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X2 : X0,X3 : X0] : (((X1 @ X3 @ X2) = $true) | ((X1 @ X2 @ X3) != $true)) & ! [X4 : X0,X5 : X0,X6 : X0] : ((((X1 @ X4 @ X6) = $true) | ((X1 @ X5 @ X6) != $true)) | ((X1 @ X4 @ X5) != $true))) <=> ((isPer @ X0 @ X1) = $true))),
% 6.85/2.13 inference(ennf_transformation,[status(thm)],[f27])).
% 6.85/2.13 thf(f27,plain,(
% 6.85/2.13 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((! [X2 : X0,X3 : X0] : (((X1 @ X2 @ X3) = $true) => ((X1 @ X3 @ X2) = $true)) & ! [X4 : X0,X5 : X0,X6 : X0] : (((X1 @ X4 @ X5) = $true) => (((X1 @ X5 @ X6) = $true) => ((X1 @ X4 @ X6) = $true)))) <=> ((isPer @ X0 @ X1) = $true))),
% 6.85/2.13 inference(fool_elimination,[status(thm)],[f26])).
% 6.85/2.13 thf(f26,plain,(
% 6.85/2.13 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) <=> (! [X2 : X0,X3 : X0] : ((X1 @ X2 @ X3) => (X1 @ X3 @ X2)) & ! [X4 : X0,X5 : X0,X6 : X0] : ((X1 @ X4 @ X5) => ((X1 @ X5 @ X6) => (X1 @ X4 @ X6)))))),
% 6.85/2.13 inference(rectify,[status(thm)],[f1])).
% 6.85/2.13 thf(f1,axiom,(
% 6.85/2.13 ! [X0 : $tType,X1 : X0 > X0 > $o] : ((isPer @ X0 @ X1) <=> (! [X2 : X0,X3 : X0] : ((X1 @ X2 @ X3) => (X1 @ X3 @ X2)) & ! [X2 : X0,X3 : X0,X4 : X0] : ((X1 @ X2 @ X3) => ((X1 @ X3 @ X4) => (X1 @ X2 @ X4)))))),
% 6.85/2.13 file('/export/starexec/sandbox/tmp/tmp.v0WQauavVr/DTF2THF_27475.p',is_per)).
% 6.85/2.13 thf(f1005,plain,(
% 6.85/2.13 ((listStar @ sK0 @ sK1 @ (app @ zero @ sK0 @ nil @ sK1)) != $true) | spl10_8),
% 6.85/2.13 inference(subsumption_resolution,[status(thm)],[f999,f51])).
% 6.85/2.13 thf(f51,plain,(
% 6.85/2.13 ((listStar @ sK2 @ sK3 @ sK3) = $true)),
% 6.85/2.13 inference(cnf_transformation,[status(thm)],[f41])).
% 6.85/2.13 thf(f999,plain,(
% 6.85/2.13 ((listStar @ sK2 @ sK3 @ sK3) != $true) | ((listStar @ sK0 @ sK1 @ (app @ zero @ sK0 @ nil @ sK1)) != $true) | spl10_8),
% 6.85/2.13 inference(trivial_inequality_removal,[status(thm)],[f996])).
% 6.85/2.13 thf(f996,plain,(
% 6.85/2.13 ((listStar @ sK2 @ sK3 @ sK3) != $true) | ($true != $true) | ((listStar @ sK0 @ sK1 @ (app @ zero @ sK0 @ nil @ sK1)) != $true) | spl10_8),
% 6.85/2.13 inference(superposition,[status(thm)],[f959,f56])).
% 6.85/2.13 thf(f56,plain,(
% 6.85/2.13 ( ! [X2 : list,X3 : list,X0 : nat,X1 : nat,X4 : list,X5 : list] : (((listStar @ (plus @ X0 @ X1) @ (app @ X0 @ X1 @ X2 @ X4) @ (app @ X0 @ X1 @ X3 @ X5)) = $true) | ((listStar @ X1 @ X4 @ X5) != $true) | ((listStar @ X0 @ X2 @ X3) != $true)) )),
% 6.85/2.13 inference(cnf_transformation,[status(thm)],[f36])).
% 6.85/2.13 thf(f36,plain,(
% 6.85/2.13 ! [X0 : nat,X1 : nat,X2 : list,X3 : list] : (((listStar @ X0 @ X2 @ X3) != $true) | ! [X4 : list,X5 : list] : (((listStar @ (plus @ X0 @ X1) @ (app @ X0 @ X1 @ X2 @ X4) @ (app @ X0 @ X1 @ X3 @ X5)) = $true) | ((listStar @ X1 @ X4 @ X5) != $true)))),
% 6.85/2.13 inference(ennf_transformation,[status(thm)],[f31])).
% 6.85/2.13 thf(f31,plain,(
% 6.85/2.13 ! [X0 : nat,X1 : nat,X2 : list,X3 : list] : (((listStar @ X0 @ X2 @ X3) = $true) => ! [X4 : list,X5 : list] : (((listStar @ X1 @ X4 @ X5) = $true) => ((listStar @ (plus @ X0 @ X1) @ (app @ X0 @ X1 @ X2 @ X4) @ (app @ X0 @ X1 @ X3 @ X5)) = $true)))),
% 6.85/2.13 inference(fool_elimination,[status(thm)],[f30])).
% 6.85/2.13 thf(f30,plain,(
% 6.85/2.13 ! [X0 : nat,X1 : nat,X2 : list,X3 : list] : ((listStar @ X0 @ X2 @ X3) => ! [X4 : list,X5 : list] : ((listStar @ X1 @ X4 @ X5) => (listStar @ (plus @ X0 @ X1) @ (app @ X0 @ X1 @ X2 @ X4) @ (app @ X0 @ X1 @ X3 @ X5))))),
% 6.85/2.13 inference(rectify,[status(thm)],[f7])).
% 6.85/2.13 thf(f7,axiom,(
% 6.85/2.13 ! [X6 : nat,X10 : nat,X7 : list,X11 : list] : ((listStar @ X6 @ X7 @ X11) => ! [X8 : list,X9 : list] : ((listStar @ X10 @ X8 @ X9) => (listStar @ (plus @ X6 @ X10) @ (app @ X6 @ X10 @ X7 @ X8) @ (app @ X6 @ X10 @ X11 @ X9))))),
% 6.85/2.13 file('/export/starexec/sandbox/tmp/tmp.v0WQauavVr/DTF2THF_27475.p',app_tp_ax)).
% 6.85/2.13 thf(f959,plain,(
% 6.85/2.13 ((listStar @ (plus @ sK0 @ sK2) @ (app @ sK0 @ sK2 @ sK1 @ sK3) @ (app @ sK0 @ sK2 @ (app @ zero @ sK0 @ nil @ sK1) @ sK3)) != $true) | spl10_8),
% 6.85/2.13 inference(avatar_component_clause,[status(thm)],[f957])).
% 6.85/2.13 thf(f957,definition,(
% 6.85/2.13 spl10_8 <=> ((listStar @ (plus @ sK0 @ sK2) @ (app @ sK0 @ sK2 @ sK1 @ sK3) @ (app @ sK0 @ sK2 @ (app @ zero @ sK0 @ nil @ sK1) @ sK3)) = $true)),
% 6.85/2.13 introduced(definition,[new_symbols(naming,[spl10_8])],[avatar_definition])).
% 6.85/2.13 thf(f995,plain,(
% 6.85/2.13 spl10_9),
% 6.85/2.13 inference(avatar_contradiction_clause,[status(thm)],[f994])).
% 6.85/2.13 thf(f994,plain,(
% 6.85/2.13 $false | spl10_9),
% 6.85/2.13 inference(subsumption_resolution,[status(thm)],[f993,f52])).
% 6.85/2.13 thf(f993,plain,(
% 6.85/2.13 ((listStar @ sK0 @ sK1 @ sK1) != $true) | spl10_9),
% 6.85/2.13 inference(subsumption_resolution,[status(thm)],[f992,f51])).
% 6.85/2.13 thf(f992,plain,(
% 6.85/2.13 ((listStar @ sK2 @ sK3 @ sK3) != $true) | ((listStar @ sK0 @ sK1 @ sK1) != $true) | spl10_9),
% 6.85/2.13 inference(trivial_inequality_removal,[status(thm)],[f991])).
% 6.85/2.13 thf(f991,plain,(
% 6.85/2.13 ((listStar @ sK2 @ sK3 @ sK3) != $true) | ($true != $true) | ((listStar @ sK0 @ sK1 @ sK1) != $true) | spl10_9),
% 6.85/2.13 inference(superposition,[status(thm)],[f963,f56])).
% 6.85/2.13 thf(f963,plain,(
% 6.85/2.13 ((listStar @ (plus @ sK0 @ sK2) @ (app @ sK0 @ sK2 @ sK1 @ sK3) @ (app @ sK0 @ sK2 @ sK1 @ sK3)) != $true) | spl10_9),
% 6.85/2.13 inference(avatar_component_clause,[status(thm)],[f961])).
% 6.85/2.13 thf(f961,definition,(
% 6.85/2.13 spl10_9 <=> ((listStar @ (plus @ sK0 @ sK2) @ (app @ sK0 @ sK2 @ sK1 @ sK3) @ (app @ sK0 @ sK2 @ sK1 @ sK3)) = $true)),
% 6.85/2.13 introduced(definition,[new_symbols(naming,[spl10_9])],[avatar_definition])).
% 6.85/2.13 thf(f964,plain,(
% 6.85/2.13 ~spl10_8 | ~spl10_9 | ~spl10_2),
% 6.85/2.13 inference(avatar_split_clause,[status(thm)],[f955,f74,f961,f957])).
% 6.85/2.13 thf(f74,definition,(
% 6.85/2.13 spl10_2 <=> ($false = (listStar @ (plus @ zero @ (plus @ sK0 @ sK2)) @ (app @ zero @ (plus @ sK0 @ sK2) @ nil @ (app @ sK0 @ sK2 @ sK1 @ sK3)) @ (app @ (plus @ zero @ sK0) @ sK2 @ (app @ zero @ sK0 @ nil @ sK1) @ sK3)))),
% 6.85/2.13 introduced(definition,[new_symbols(naming,[spl10_2])],[avatar_definition])).
% 6.85/2.13 thf(f955,plain,(
% 6.85/2.13 ((listStar @ (plus @ sK0 @ sK2) @ (app @ sK0 @ sK2 @ sK1 @ sK3) @ (app @ sK0 @ sK2 @ (app @ zero @ sK0 @ nil @ sK1) @ sK3)) != $true) | ((listStar @ (plus @ sK0 @ sK2) @ (app @ sK0 @ sK2 @ sK1 @ sK3) @ (app @ sK0 @ sK2 @ sK1 @ sK3)) != $true) | ~spl10_2),
% 6.85/2.13 inference(trivial_inequality_removal,[status(thm)],[f949])).
% 6.85/2.13 thf(f949,plain,(
% 6.85/2.13 ((listStar @ (plus @ sK0 @ sK2) @ (app @ sK0 @ sK2 @ sK1 @ sK3) @ (app @ sK0 @ sK2 @ sK1 @ sK3)) != $true) | ($true != $true) | ((listStar @ (plus @ sK0 @ sK2) @ (app @ sK0 @ sK2 @ sK1 @ sK3) @ (app @ sK0 @ sK2 @ (app @ zero @ sK0 @ nil @ sK1) @ sK3)) != $true) | ~spl10_2),
% 6.85/2.13 inference(superposition,[status(thm)],[f507,f947])).
% 6.85/2.13 thf(f507,plain,(
% 6.85/2.13 ( ! [X0 : list] : (((listStar @ (plus @ sK0 @ sK2) @ (app @ zero @ (plus @ sK0 @ sK2) @ nil @ (app @ sK0 @ sK2 @ sK1 @ sK3)) @ X0) != $true) | ((listStar @ (plus @ sK0 @ sK2) @ X0 @ (app @ sK0 @ sK2 @ (app @ zero @ sK0 @ nil @ sK1) @ sK3)) != $true)) ) | ~spl10_2),
% 6.85/2.13 inference(subsumption_resolution,[status(thm)],[f502,f50])).
% 6.85/2.13 thf(f502,plain,(
% 6.85/2.13 ( ! [X0 : list] : (((isPer @ list @ (listStar @ (plus @ sK0 @ sK2))) != $true) | ((listStar @ (plus @ sK0 @ sK2) @ X0 @ (app @ sK0 @ sK2 @ (app @ zero @ sK0 @ nil @ sK1) @ sK3)) != $true) | ((listStar @ (plus @ sK0 @ sK2) @ (app @ zero @ (plus @ sK0 @ sK2) @ nil @ (app @ sK0 @ sK2 @ sK1 @ sK3)) @ X0) != $true)) ) | ~spl10_2),
% 6.85/2.13 inference(trivial_inequality_removal,[status(thm)],[f187])).
% 6.85/2.13 thf(f187,plain,(
% 6.85/2.13 ( ! [X0 : list] : (((isPer @ list @ (listStar @ (plus @ sK0 @ sK2))) != $true) | ((listStar @ (plus @ sK0 @ sK2) @ (app @ zero @ (plus @ sK0 @ sK2) @ nil @ (app @ sK0 @ sK2 @ sK1 @ sK3)) @ X0) != $true) | ((listStar @ (plus @ sK0 @ sK2) @ X0 @ (app @ sK0 @ sK2 @ (app @ zero @ sK0 @ nil @ sK1) @ sK3)) != $true) | ($false = $true)) ) | ~spl10_2),
% 6.85/2.13 inference(superposition,[status(thm)],[f64,f88])).
% 6.85/2.13 thf(f88,plain,(
% 6.85/2.13 ($false = (listStar @ (plus @ sK0 @ sK2) @ (app @ zero @ (plus @ sK0 @ sK2) @ nil @ (app @ sK0 @ sK2 @ sK1 @ sK3)) @ (app @ sK0 @ sK2 @ (app @ zero @ sK0 @ nil @ sK1) @ sK3))) | ~spl10_2),
% 6.85/2.13 inference(forward_demodulation,[status(thm)],[f87,f49])).
% 6.85/2.13 thf(f87,plain,(
% 6.85/2.13 ($false = (listStar @ (plus @ sK0 @ sK2) @ (app @ zero @ (plus @ sK0 @ sK2) @ nil @ (app @ sK0 @ sK2 @ sK1 @ sK3)) @ (app @ (plus @ zero @ sK0) @ sK2 @ (app @ zero @ sK0 @ nil @ sK1) @ sK3))) | ~spl10_2),
% 6.85/2.13 inference(forward_demodulation,[status(thm)],[f76,f49])).
% 6.85/2.13 thf(f76,plain,(
% 6.85/2.13 ($false = (listStar @ (plus @ zero @ (plus @ sK0 @ sK2)) @ (app @ zero @ (plus @ sK0 @ sK2) @ nil @ (app @ sK0 @ sK2 @ sK1 @ sK3)) @ (app @ (plus @ zero @ sK0) @ sK2 @ (app @ zero @ sK0 @ nil @ sK1) @ sK3))) | ~spl10_2),
% 6.85/2.13 inference(avatar_component_clause,[status(thm)],[f74])).
% 6.85/2.13 thf(f64,plain,(
% 6.85/2.13 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o,X4 : X0] : (((X1 @ X2 @ X4) = $true) | ((isPer @ X0 @ X1) != $true) | ((X1 @ X3 @ X4) != $true) | ((X1 @ X2 @ X3) != $true)) )),
% 6.85/2.13 inference(cnf_transformation,[status(thm)],[f47])).
% 6.85/2.13 thf(f77,plain,(
% 6.85/2.13 spl10_1 | spl10_2),
% 6.85/2.13 inference(avatar_split_clause,[status(thm)],[f67,f74,f70])).
% 6.85/2.13 thf(f67,plain,(
% 6.85/2.13 ((sP9 @ $true) = $false) | ($false = (listStar @ (plus @ zero @ (plus @ sK0 @ sK2)) @ (app @ zero @ (plus @ sK0 @ sK2) @ nil @ (app @ sK0 @ sK2 @ sK1 @ sK3)) @ (app @ (plus @ zero @ sK0) @ sK2 @ (app @ zero @ sK0 @ nil @ sK1) @ sK3)))),
% 6.85/2.13 inference(cases_simplifying,[status(thm)],[f65])).
% 6.85/2.13 % SZS output end Proof for DTF2THF_27475
% 6.85/2.13 % (27790)------------------------------
% 6.85/2.13 % (27790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.85/2.13 % (27790)Termination reason: Refutation
% 6.85/2.13
% 6.85/2.13 % (27790)Memory used [KB]: 5884
% 6.85/2.13 % (27790)Time elapsed: 0.090 s
% 6.85/2.13 % (27790)Instructions burned: 127 (million)
% 6.85/2.13 % (27790)------------------------------
% 6.85/2.13 % (27790)------------------------------
% 6.85/2.13 % (27662)Success in time 0.814 s
%------------------------------------------------------------------------------