%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT362^1 : 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 : n011.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 08:45:34 AM UTC 2026
% Result : Theorem 1.88s 1.78s
% Output : Refutation 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 77 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 735 ( 236 equ; 0 cnn)
% Maximal formula atoms : 8 ( 9 avg)
% Number of connectives : 4255 ( 140 ~; 120 |; 31 &;3911 @)
% ( 0 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 10 con; 0-4 aty)
% Number of variables : 325 ( 0 ^; 289 !; 36 ?; 325 :)
% 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,
sP0: nat > nat > list > list > $o ).
thf(func_def_17,type,
sK1: nat > nat > list > list > nat ).
thf(func_def_18,type,
sK2: nat > nat > list > list > elem ).
thf(func_def_19,type,
sK3: nat > nat > list > list > list ).
thf(func_def_20,type,
sK4: nat ).
thf(func_def_21,type,
sK5: list ).
thf(func_def_22,type,
sK6: nat ).
thf(func_def_23,type,
sK7: list ).
thf(func_def_24,type,
sK8: nat ).
thf(func_def_25,type,
sK9: list ).
thf(f241,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f240,f72]) ).
thf(f72,plain,
( $true
= ( listStar @ sK8 @ sK9 @ sK9 ) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
thf(f60,plain,
( ( $true
!= ( listStar @ ( plus @ ( plus @ sK6 @ sK8 ) @ ( plus @ sK6 @ sK8 ) ) @ ( app @ sK4 @ ( plus @ sK6 @ sK8 ) @ sK5 @ ( app @ sK6 @ sK8 @ sK7 @ sK9 ) ) @ ( app @ ( plus @ sK4 @ sK6 ) @ sK8 @ ( app @ sK4 @ sK6 @ sK5 @ sK7 ) @ sK9 ) ) )
& ( $true
= ( listStar @ sK4 @ sK5 @ sK5 ) )
& ( $true
= ( listStar @ sK8 @ sK9 @ sK9 ) )
& ( $true
= ( listStar @ sK6 @ sK7 @ sK7 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8,sK9])],[f51,f59]) ).
thf(f59,plain,
( ? [X0: nat,X1: list,X2: nat,X3: list,X4: nat,X5: list] :
( ( $true
!= ( listStar @ ( plus @ ( plus @ X2 @ X4 ) @ ( plus @ X2 @ X4 ) ) @ ( app @ X0 @ ( plus @ X2 @ X4 ) @ X1 @ ( app @ X2 @ X4 @ X3 @ X5 ) ) @ ( app @ ( plus @ X0 @ X2 ) @ X4 @ ( app @ X0 @ X2 @ X1 @ X3 ) @ X5 ) ) )
& ( $true
= ( listStar @ X0 @ X1 @ X1 ) )
& ( $true
= ( listStar @ X4 @ X5 @ X5 ) )
& ( $true
= ( listStar @ X2 @ X3 @ X3 ) ) )
=> ( ( $true
!= ( listStar @ ( plus @ ( plus @ sK6 @ sK8 ) @ ( plus @ sK6 @ sK8 ) ) @ ( app @ sK4 @ ( plus @ sK6 @ sK8 ) @ sK5 @ ( app @ sK6 @ sK8 @ sK7 @ sK9 ) ) @ ( app @ ( plus @ sK4 @ sK6 ) @ sK8 @ ( app @ sK4 @ sK6 @ sK5 @ sK7 ) @ sK9 ) ) )
& ( $true
= ( listStar @ sK4 @ sK5 @ sK5 ) )
& ( $true
= ( listStar @ sK8 @ sK9 @ sK9 ) )
& ( $true
= ( listStar @ sK6 @ sK7 @ sK7 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f51,plain,
? [X0: nat,X1: list,X2: nat,X3: list,X4: nat,X5: list] :
( ( $true
!= ( listStar @ ( plus @ ( plus @ X2 @ X4 ) @ ( plus @ X2 @ X4 ) ) @ ( app @ X0 @ ( plus @ X2 @ X4 ) @ X1 @ ( app @ X2 @ X4 @ X3 @ X5 ) ) @ ( app @ ( plus @ X0 @ X2 ) @ X4 @ ( app @ X0 @ X2 @ X1 @ X3 ) @ X5 ) ) )
& ( $true
= ( listStar @ X0 @ X1 @ X1 ) )
& ( $true
= ( listStar @ X4 @ X5 @ X5 ) )
& ( $true
= ( listStar @ X2 @ X3 @ X3 ) ) ),
inference(flattening,[status(thm)],[f50]) ).
thf(f50,plain,
? [X0: nat,X1: list,X2: nat,X3: list,X4: nat,X5: list] :
( ( $true
!= ( listStar @ ( plus @ ( plus @ X2 @ X4 ) @ ( plus @ X2 @ X4 ) ) @ ( app @ X0 @ ( plus @ X2 @ X4 ) @ X1 @ ( app @ X2 @ X4 @ X3 @ X5 ) ) @ ( app @ ( plus @ X0 @ X2 ) @ X4 @ ( app @ X0 @ X2 @ X1 @ X3 ) @ X5 ) ) )
& ( $true
= ( listStar @ X4 @ X5 @ X5 ) )
& ( $true
= ( listStar @ X2 @ X3 @ X3 ) )
& ( $true
= ( listStar @ X0 @ X1 @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
~ ! [X0: nat,X1: list,X2: nat,X3: list,X4: nat,X5: list] :
( ( $true
= ( listStar @ X0 @ X1 @ X1 ) )
=> ( ( $true
= ( listStar @ X2 @ X3 @ X3 ) )
=> ( ( $true
= ( listStar @ X4 @ X5 @ X5 ) )
=> ( $true
= ( listStar @ ( plus @ ( plus @ X2 @ X4 ) @ ( plus @ X2 @ X4 ) ) @ ( app @ X0 @ ( plus @ X2 @ X4 ) @ X1 @ ( app @ X2 @ X4 @ X3 @ X5 ) ) @ ( app @ ( plus @ X0 @ X2 ) @ X4 @ ( app @ X0 @ X2 @ X1 @ X3 ) @ X5 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f21]) ).
thf(f21,plain,
~ ! [X0: nat,X1: list,X2: nat,X3: list,X4: nat,X5: list] :
( ( listStar @ X0 @ X1 @ X1 )
=> ( ( listStar @ X2 @ X3 @ X3 )
=> ( ( listStar @ X4 @ X5 @ X5 )
=> ( listStar @ ( plus @ ( plus @ X2 @ X4 ) @ ( plus @ X2 @ X4 ) ) @ ( app @ X0 @ ( plus @ X2 @ X4 ) @ X1 @ ( app @ X2 @ X4 @ X3 @ X5 ) ) @ ( app @ ( plus @ X0 @ X2 ) @ X4 @ ( app @ X0 @ X2 @ X1 @ X3 ) @ X5 ) ) ) ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,negated_conjecture,
~ ! [X10: nat,X17: list,X13: nat,X15: list,X14: nat,X16: list] :
( ( listStar @ X10 @ X17 @ X17 )
=> ( ( listStar @ X13 @ X15 @ X15 )
=> ( ( listStar @ X14 @ X16 @ X16 )
=> ( listStar @ ( plus @ ( plus @ X13 @ X14 ) @ ( plus @ X13 @ X14 ) ) @ ( app @ X10 @ ( plus @ X13 @ X14 ) @ X17 @ ( app @ X13 @ X14 @ X15 @ X16 ) ) @ ( app @ ( plus @ X10 @ X13 ) @ X14 @ ( app @ X10 @ X13 @ X17 @ X15 ) @ X16 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
thf(f14,conjecture,
! [X10: nat,X17: list,X13: nat,X15: list,X14: nat,X16: list] :
( ( listStar @ X10 @ X17 @ X17 )
=> ( ( listStar @ X13 @ X15 @ X15 )
=> ( ( listStar @ X14 @ X16 @ X16 )
=> ( listStar @ ( plus @ ( plus @ X13 @ X14 ) @ ( plus @ X13 @ X14 ) ) @ ( app @ X10 @ ( plus @ X13 @ X14 ) @ X17 @ ( app @ X13 @ X14 @ X15 @ X16 ) ) @ ( app @ ( plus @ X10 @ X13 ) @ X14 @ ( app @ X10 @ X13 @ X17 @ X15 ) @ X16 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MXj1wRhtZr/DTF2THF_8110.p',list_app_assoc) ).
thf(f240,plain,
( $true
!= ( listStar @ sK8 @ sK9 @ sK9 ) ),
inference(subsumption_resolution,[status(thm)],[f239,f71]) ).
thf(f71,plain,
( $true
= ( listStar @ sK6 @ sK7 @ sK7 ) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
thf(f239,plain,
( ( $true
!= ( listStar @ sK6 @ sK7 @ sK7 ) )
| ( $true
!= ( listStar @ sK8 @ sK9 @ sK9 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f238]) ).
thf(f238,plain,
( ( $true
!= ( listStar @ sK6 @ sK7 @ sK7 ) )
| ( $true
!= ( listStar @ sK8 @ sK9 @ sK9 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f237,f156]) ).
thf(f156,plain,
( $true
= ( sP0 @ sK8 @ sK6 @ sK7 @ sK9 ) ),
inference(subsumption_resolution,[status(thm)],[f155,f73]) ).
thf(f73,plain,
( $true
= ( listStar @ sK4 @ sK5 @ sK5 ) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
thf(f155,plain,
( ( $true
!= ( listStar @ sK4 @ sK5 @ sK5 ) )
| ( $true
= ( sP0 @ sK8 @ sK6 @ sK7 @ sK9 ) ) ),
inference(subsumption_resolution,[status(thm)],[f154,f72]) ).
thf(f154,plain,
( ( $true
!= ( listStar @ sK8 @ sK9 @ sK9 ) )
| ( $true
!= ( listStar @ sK4 @ sK5 @ sK5 ) )
| ( $true
= ( sP0 @ sK8 @ sK6 @ sK7 @ sK9 ) ) ),
inference(subsumption_resolution,[status(thm)],[f150,f71]) ).
thf(f150,plain,
( ( $true
!= ( listStar @ sK6 @ sK7 @ sK7 ) )
| ( $true
!= ( listStar @ sK8 @ sK9 @ sK9 ) )
| ( $true
= ( sP0 @ sK8 @ sK6 @ sK7 @ sK9 ) )
| ( $true
!= ( listStar @ sK4 @ sK5 @ sK5 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f149]) ).
thf(f149,plain,
( ( $true
= ( sP0 @ sK8 @ sK6 @ sK7 @ sK9 ) )
| ( $true
!= ( listStar @ sK4 @ sK5 @ sK5 ) )
| ( $true != $true )
| ( $true
!= ( listStar @ sK8 @ sK9 @ sK9 ) )
| ( $true
!= ( listStar @ sK6 @ sK7 @ sK7 ) ) ),
inference(superposition,[status(thm)],[f77,f118]) ).
thf(f118,plain,
! [X2: nat,X3: list,X0: nat,X1: list,X4: nat,X5: list] :
( ( $true
= ( listStar @ ( plus @ X0 @ ( plus @ X2 @ ( plus @ X0 @ X2 ) ) ) @ ( app @ X4 @ ( plus @ X0 @ X2 ) @ X5 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ X4 @ X0 ) @ X2 @ ( app @ X4 @ X0 @ X5 @ X1 ) @ X3 ) ) )
| ( $true
= ( sP0 @ X2 @ X0 @ X1 @ X3 ) )
| ( $true
!= ( listStar @ X2 @ X3 @ X3 ) )
| ( $true
!= ( listStar @ X0 @ X1 @ X1 ) )
| ( $true
!= ( listStar @ X4 @ X5 @ X5 ) ) ),
inference(subsumption_resolution,[status(thm)],[f117,f89]) ).
thf(f89,plain,
! [X2: nat,X3: list,X0: nat,X1: list] :
( ( $true
= ( listStar @ ( plus @ X0 @ X2 ) @ ( app @ zero @ ( plus @ X0 @ X2 ) @ nil @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ X0 @ X2 @ ( app @ zero @ X0 @ nil @ X1 ) @ X3 ) ) )
| ( $true
!= ( listStar @ X0 @ X1 @ X1 ) )
| ( $true
!= ( listStar @ X2 @ X3 @ X3 ) ) ),
inference(forward_demodulation,[status(thm)],[f88,f61]) ).
thf(f61,plain,
! [X0: nat] :
( ( plus @ zero @ X0 )
= X0 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f41,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.MXj1wRhtZr/DTF2THF_8110.p',ax1) ).
thf(f88,plain,
! [X2: nat,X3: list,X0: nat,X1: list] :
( ( $true
!= ( listStar @ X0 @ X1 @ X1 ) )
| ( $true
= ( listStar @ ( 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 ) ) ),
inference(forward_demodulation,[status(thm)],[f63,f61]) ).
thf(f63,plain,
! [X2: nat,X3: list,X0: nat,X1: list] :
( ( $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
!= ( listStar @ X0 @ X1 @ X1 ) )
| ( $true
!= ( listStar @ X2 @ X3 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
thf(f49,plain,
! [X0: nat,X1: list,X2: nat,X3: list] :
( ( $true
!= ( listStar @ X2 @ X3 @ X3 ) )
| ( $true
!= ( listStar @ X0 @ X1 @ X1 ) )
| ( $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 ) ) ) ),
inference(flattening,[status(thm)],[f48]) ).
thf(f48,plain,
! [X0: nat,X1: list,X2: nat,X3: list] :
( ( $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
!= ( listStar @ X2 @ X3 @ X3 ) )
| ( $true
!= ( listStar @ X0 @ X1 @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: nat,X1: list,X2: nat,X3: list] :
( ( $true
= ( 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 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f23]) ).
thf(f23,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,axiom,
! [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.MXj1wRhtZr/DTF2THF_8110.p',list_app_assoc_base) ).
thf(f117,plain,
! [X2: nat,X3: list,X0: nat,X1: list,X4: nat,X5: list] :
( ( $true
!= ( listStar @ X4 @ X5 @ X5 ) )
| ( $true
= ( listStar @ ( plus @ X0 @ ( plus @ X2 @ ( plus @ X0 @ X2 ) ) ) @ ( app @ X4 @ ( plus @ X0 @ X2 ) @ X5 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ X4 @ X0 ) @ X2 @ ( app @ X4 @ X0 @ X5 @ X1 ) @ X3 ) ) )
| ( $true
= ( sP0 @ X2 @ X0 @ X1 @ X3 ) )
| ( $true
!= ( listStar @ X2 @ X3 @ X3 ) )
| ( $true
!= ( listStar @ ( plus @ X0 @ X2 ) @ ( app @ zero @ ( plus @ X0 @ X2 ) @ nil @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ X0 @ X2 @ ( app @ zero @ X0 @ nil @ X1 ) @ X3 ) ) )
| ( $true
!= ( listStar @ X0 @ X1 @ X1 ) ) ),
inference(forward_demodulation,[status(thm)],[f116,f61]) ).
thf(f116,plain,
! [X2: nat,X3: list,X0: nat,X1: list,X4: nat,X5: list] :
( ( $true
= ( sP0 @ X2 @ X0 @ X1 @ X3 ) )
| ( $true
!= ( listStar @ X2 @ X3 @ X3 ) )
| ( $true
!= ( listStar @ ( 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 @ X4 @ X5 @ X5 ) )
| ( $true
= ( listStar @ ( plus @ X0 @ ( plus @ X2 @ ( plus @ X0 @ X2 ) ) ) @ ( app @ X4 @ ( plus @ X0 @ X2 ) @ X5 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ X4 @ X0 ) @ X2 @ ( app @ X4 @ X0 @ X5 @ X1 ) @ X3 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f115,f68]) ).
thf(f68,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( plus @ X0 @ ( plus @ X1 @ X2 ) )
= ( plus @ ( plus @ X0 @ X1 ) @ X2 ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f39,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( plus @ X0 @ ( plus @ X1 @ X2 ) )
= ( plus @ ( plus @ X0 @ X1 ) @ X2 ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,axiom,
! [X12: nat,X13: nat,X14: nat] :
( ( plus @ X12 @ ( plus @ X13 @ X14 ) )
= ( plus @ ( plus @ X12 @ X13 ) @ X14 ) ),
file('/export/starexec/sandbox/tmp/tmp.MXj1wRhtZr/DTF2THF_8110.p',plus_assoc) ).
thf(f115,plain,
! [X2: nat,X3: list,X0: nat,X1: list,X4: nat,X5: list] :
( ( $true
= ( listStar @ ( plus @ ( plus @ X0 @ X2 ) @ ( plus @ X0 @ X2 ) ) @ ( app @ X4 @ ( plus @ X0 @ X2 ) @ X5 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ X4 @ X0 ) @ X2 @ ( app @ X4 @ X0 @ X5 @ X1 ) @ X3 ) ) )
| ( $true
!= ( listStar @ ( 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
= ( sP0 @ X2 @ X0 @ X1 @ X3 ) )
| ( $true
!= ( listStar @ X2 @ X3 @ X3 ) )
| ( $true
!= ( listStar @ X0 @ X1 @ X1 ) )
| ( $true
!= ( listStar @ X4 @ X5 @ X5 ) ) ),
inference(forward_demodulation,[status(thm)],[f67,f61]) ).
thf(f67,plain,
! [X2: nat,X3: list,X0: nat,X1: list,X4: nat,X5: list] :
( ( $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
= ( sP0 @ X2 @ X0 @ X1 @ X3 ) )
| ( $true
!= ( listStar @ X4 @ X5 @ X5 ) )
| ( $true
= ( listStar @ ( plus @ ( plus @ X0 @ X2 ) @ ( plus @ X0 @ X2 ) ) @ ( app @ X4 @ ( plus @ X0 @ X2 ) @ X5 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ X4 @ X0 ) @ X2 @ ( app @ X4 @ X0 @ X5 @ X1 ) @ X3 ) ) )
| ( $true
!= ( listStar @ X0 @ X1 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
thf(f58,plain,
! [X0: nat,X1: list,X2: nat,X3: list] :
( ! [X4: nat,X5: list] :
( ( $true
!= ( listStar @ X4 @ X5 @ X5 ) )
| ( $true
= ( listStar @ ( plus @ ( plus @ X0 @ X2 ) @ ( plus @ X0 @ X2 ) ) @ ( app @ X4 @ ( plus @ X0 @ X2 ) @ X5 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ X4 @ X0 ) @ X2 @ ( app @ X4 @ X0 @ X5 @ X1 ) @ X3 ) ) ) )
| ( $true
= ( sP0 @ X2 @ X0 @ X1 @ X3 ) )
| ( $true
!= ( listStar @ X2 @ X3 @ X3 ) )
| ( $true
!= ( listStar @ X0 @ X1 @ X1 ) )
| ( $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 ) ) ) ),
inference(rectify,[status(thm)],[f53]) ).
thf(f53,plain,
! [X0: nat,X1: list,X2: nat,X3: list] :
( ! [X7: nat,X8: list] :
( ( $true
!= ( listStar @ X7 @ X8 @ X8 ) )
| ( $true
= ( listStar @ ( plus @ ( plus @ X0 @ X2 ) @ ( plus @ X0 @ X2 ) ) @ ( app @ X7 @ ( plus @ X0 @ X2 ) @ X8 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ X7 @ X0 ) @ X2 @ ( app @ X7 @ X0 @ X8 @ X1 ) @ X3 ) ) ) )
| ( $true
= ( sP0 @ X2 @ X0 @ X1 @ X3 ) )
| ( $true
!= ( listStar @ X2 @ X3 @ X3 ) )
| ( $true
!= ( listStar @ X0 @ X1 @ X1 ) )
| ( $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 ) ) ) ),
inference(definition_folding,[status(thm)],[f44,f52]) ).
thf(f52,plain,
! [X3: list,X1: list,X0: nat,X2: nat] :
( ? [X4: nat,X5: elem,X6: list] :
( ( $true
= ( listStar @ ( plus @ ( plus @ X0 @ X2 ) @ ( plus @ X0 @ X2 ) ) @ ( app @ X4 @ ( plus @ X0 @ X2 ) @ X6 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ X4 @ X0 ) @ X2 @ ( app @ X4 @ X0 @ X6 @ X1 ) @ X3 ) ) )
& ( $true
= ( listStar @ X4 @ X6 @ X6 ) )
& ( $true
!= ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X2 ) ) @ ( plus @ X0 @ X2 ) ) @ ( app @ ( suc @ X4 ) @ ( plus @ X0 @ X2 ) @ ( cons @ X4 @ X5 @ X6 ) @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ ( suc @ X4 ) @ X0 ) @ X2 @ ( app @ ( suc @ X4 ) @ X0 @ ( cons @ X4 @ X5 @ X6 ) @ X1 ) @ X3 ) ) ) )
| ( $true
!= ( sP0 @ X2 @ X0 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f44,plain,
! [X0: nat,X1: list,X2: nat,X3: list] :
( ! [X7: nat,X8: list] :
( ( $true
!= ( listStar @ X7 @ X8 @ X8 ) )
| ( $true
= ( listStar @ ( plus @ ( plus @ X0 @ X2 ) @ ( plus @ X0 @ X2 ) ) @ ( app @ X7 @ ( plus @ X0 @ X2 ) @ X8 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ X7 @ X0 ) @ X2 @ ( app @ X7 @ X0 @ X8 @ X1 ) @ X3 ) ) ) )
| ? [X4: nat,X5: elem,X6: list] :
( ( $true
= ( listStar @ ( plus @ ( plus @ X0 @ X2 ) @ ( plus @ X0 @ X2 ) ) @ ( app @ X4 @ ( plus @ X0 @ X2 ) @ X6 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ X4 @ X0 ) @ X2 @ ( app @ X4 @ X0 @ X6 @ X1 ) @ X3 ) ) )
& ( $true
= ( listStar @ X4 @ X6 @ X6 ) )
& ( $true
!= ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X2 ) ) @ ( plus @ X0 @ X2 ) ) @ ( app @ ( suc @ X4 ) @ ( plus @ X0 @ X2 ) @ ( cons @ X4 @ X5 @ X6 ) @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ ( suc @ X4 ) @ X0 ) @ X2 @ ( app @ ( suc @ X4 ) @ X0 @ ( cons @ X4 @ X5 @ X6 ) @ X1 ) @ X3 ) ) ) )
| ( $true
!= ( listStar @ X2 @ X3 @ X3 ) )
| ( $true
!= ( listStar @ X0 @ X1 @ X1 ) )
| ( $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 ) ) ) ),
inference(flattening,[status(thm)],[f43]) ).
thf(f43,plain,
! [X0: nat,X1: list,X2: nat,X3: list] :
( ! [X7: nat,X8: list] :
( ( $true
!= ( listStar @ X7 @ X8 @ X8 ) )
| ( $true
= ( listStar @ ( plus @ ( plus @ X0 @ X2 ) @ ( plus @ X0 @ X2 ) ) @ ( app @ X7 @ ( plus @ X0 @ X2 ) @ X8 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ X7 @ X0 ) @ X2 @ ( app @ X7 @ X0 @ X8 @ X1 ) @ X3 ) ) ) )
| ? [X4: nat,X5: elem,X6: list] :
( ( $true
!= ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X2 ) ) @ ( plus @ X0 @ X2 ) ) @ ( app @ ( suc @ X4 ) @ ( plus @ X0 @ X2 ) @ ( cons @ X4 @ X5 @ X6 ) @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ ( suc @ X4 ) @ X0 ) @ X2 @ ( app @ ( suc @ X4 ) @ X0 @ ( cons @ X4 @ X5 @ X6 ) @ X1 ) @ X3 ) ) )
& ( $true
= ( listStar @ ( plus @ ( plus @ X0 @ X2 ) @ ( plus @ X0 @ X2 ) ) @ ( app @ X4 @ ( plus @ X0 @ X2 ) @ X6 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ X4 @ X0 ) @ X2 @ ( app @ X4 @ X0 @ X6 @ X1 ) @ X3 ) ) )
& ( $true
= ( listStar @ X4 @ X6 @ X6 ) ) )
| ( $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
!= ( listStar @ X2 @ X3 @ X3 ) )
| ( $true
!= ( listStar @ X0 @ X1 @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: nat,X1: list,X2: nat,X3: list] :
( ( $true
= ( 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 ) ) )
=> ( ! [X4: nat,X5: elem,X6: list] :
( ( $true
= ( listStar @ X4 @ X6 @ X6 ) )
=> ( ( $true
= ( listStar @ ( plus @ ( plus @ X0 @ X2 ) @ ( plus @ X0 @ X2 ) ) @ ( app @ X4 @ ( plus @ X0 @ X2 ) @ X6 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ X4 @ X0 ) @ X2 @ ( app @ X4 @ X0 @ X6 @ X1 ) @ X3 ) ) )
=> ( $true
= ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X2 ) ) @ ( plus @ X0 @ X2 ) ) @ ( app @ ( suc @ X4 ) @ ( plus @ X0 @ X2 ) @ ( cons @ X4 @ X5 @ X6 ) @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ ( suc @ X4 ) @ X0 ) @ X2 @ ( app @ ( suc @ X4 ) @ X0 @ ( cons @ X4 @ X5 @ X6 ) @ X1 ) @ X3 ) ) ) ) )
=> ! [X7: nat,X8: list] :
( ( $true
= ( listStar @ X7 @ X8 @ X8 ) )
=> ( $true
= ( listStar @ ( plus @ ( plus @ X0 @ X2 ) @ ( plus @ X0 @ X2 ) ) @ ( app @ X7 @ ( plus @ X0 @ X2 ) @ X8 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ X7 @ X0 ) @ X2 @ ( app @ X7 @ X0 @ X8 @ X1 ) @ X3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,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 ) )
=> ( ! [X4: nat,X5: elem,X6: list] :
( ( listStar @ X4 @ X6 @ X6 )
=> ( ( listStar @ ( plus @ ( plus @ X0 @ X2 ) @ ( plus @ X0 @ X2 ) ) @ ( app @ X4 @ ( plus @ X0 @ X2 ) @ X6 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ X4 @ X0 ) @ X2 @ ( app @ X4 @ X0 @ X6 @ X1 ) @ X3 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X2 ) ) @ ( plus @ X0 @ X2 ) ) @ ( app @ ( suc @ X4 ) @ ( plus @ X0 @ X2 ) @ ( cons @ X4 @ X5 @ X6 ) @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ ( suc @ X4 ) @ X0 ) @ X2 @ ( app @ ( suc @ X4 ) @ X0 @ ( cons @ X4 @ X5 @ X6 ) @ X1 ) @ X3 ) ) ) )
=> ! [X7: nat,X8: list] :
( ( listStar @ X7 @ X8 @ X8 )
=> ( listStar @ ( plus @ ( plus @ X0 @ X2 ) @ ( plus @ X0 @ X2 ) ) @ ( app @ X7 @ ( plus @ X0 @ X2 ) @ X8 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ X7 @ X0 ) @ X2 @ ( app @ X7 @ X0 @ X8 @ X1 ) @ X3 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,axiom,
! [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 ) )
=> ( ! [X10: nat,X2: elem,X17: list] :
( ( listStar @ X10 @ X17 @ X17 )
=> ( ( listStar @ ( plus @ ( plus @ X13 @ X14 ) @ ( plus @ X13 @ X14 ) ) @ ( app @ X10 @ ( plus @ X13 @ X14 ) @ X17 @ ( app @ X13 @ X14 @ X15 @ X16 ) ) @ ( app @ ( plus @ X10 @ X13 ) @ X14 @ ( app @ X10 @ X13 @ X17 @ X15 ) @ X16 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X13 @ X14 ) ) @ ( plus @ X13 @ X14 ) ) @ ( app @ ( suc @ X10 ) @ ( plus @ X13 @ X14 ) @ ( cons @ X10 @ X2 @ X17 ) @ ( app @ X13 @ X14 @ X15 @ X16 ) ) @ ( app @ ( plus @ ( suc @ X10 ) @ X13 ) @ X14 @ ( app @ ( suc @ X10 ) @ X13 @ ( cons @ X10 @ X2 @ X17 ) @ X15 ) @ X16 ) ) ) )
=> ! [X10: nat,X17: list] :
( ( listStar @ X10 @ X17 @ X17 )
=> ( listStar @ ( plus @ ( plus @ X13 @ X14 ) @ ( plus @ X13 @ X14 ) ) @ ( app @ X10 @ ( plus @ X13 @ X14 ) @ X17 @ ( app @ X13 @ X14 @ X15 @ X16 ) ) @ ( app @ ( plus @ X10 @ X13 ) @ X14 @ ( app @ X10 @ X13 @ X17 @ X15 ) @ X16 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MXj1wRhtZr/DTF2THF_8110.p',list_app_assoc_indinst) ).
thf(f77,plain,
( $true
!= ( listStar @ ( plus @ sK6 @ ( plus @ sK8 @ ( plus @ sK6 @ sK8 ) ) ) @ ( app @ sK4 @ ( plus @ sK6 @ sK8 ) @ sK5 @ ( app @ sK6 @ sK8 @ sK7 @ sK9 ) ) @ ( app @ ( plus @ sK4 @ sK6 ) @ sK8 @ ( app @ sK4 @ sK6 @ sK5 @ sK7 ) @ sK9 ) ) ),
inference(backward_demodulation,[status(thm)],[f74,f68]) ).
thf(f74,plain,
( $true
!= ( listStar @ ( plus @ ( plus @ sK6 @ sK8 ) @ ( plus @ sK6 @ sK8 ) ) @ ( app @ sK4 @ ( plus @ sK6 @ sK8 ) @ sK5 @ ( app @ sK6 @ sK8 @ sK7 @ sK9 ) ) @ ( app @ ( plus @ sK4 @ sK6 ) @ sK8 @ ( app @ sK4 @ sK6 @ sK5 @ sK7 ) @ sK9 ) ) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
thf(f237,plain,
! [X2: list,X3: list,X0: nat,X1: nat] :
( ( $true
!= ( sP0 @ X1 @ X0 @ X2 @ X3 ) )
| ( $true
!= ( listStar @ X0 @ X2 @ X2 ) )
| ( $true
!= ( listStar @ X1 @ X3 @ X3 ) ) ),
inference(subsumption_resolution,[status(thm)],[f236,f96]) ).
thf(f96,plain,
! [X2: nat,X3: nat,X0: list,X1: list] :
( ( $true
= ( listStar @ ( plus @ X2 @ ( plus @ X3 @ ( plus @ X2 @ X3 ) ) ) @ ( app @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ ( plus @ X2 @ X3 ) @ ( sK3 @ X3 @ X2 @ X1 @ X0 ) @ ( app @ X2 @ X3 @ X1 @ X0 ) ) @ ( app @ ( plus @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ X2 ) @ X3 @ ( app @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ X2 @ ( sK3 @ X3 @ X2 @ X1 @ X0 ) @ X1 ) @ X0 ) ) )
| ( $true
!= ( sP0 @ X3 @ X2 @ X1 @ X0 ) ) ),
inference(forward_demodulation,[status(thm)],[f66,f68]) ).
thf(f66,plain,
! [X2: nat,X3: nat,X0: list,X1: list] :
( ( $true
!= ( sP0 @ X3 @ X2 @ X1 @ X0 ) )
| ( $true
= ( listStar @ ( plus @ ( plus @ X2 @ X3 ) @ ( plus @ X2 @ X3 ) ) @ ( app @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ ( plus @ X2 @ X3 ) @ ( sK3 @ X3 @ X2 @ X1 @ X0 ) @ ( app @ X2 @ X3 @ X1 @ X0 ) ) @ ( app @ ( plus @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ X2 ) @ X3 @ ( app @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ X2 @ ( sK3 @ X3 @ X2 @ X1 @ X0 ) @ X1 ) @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
thf(f57,plain,
! [X0: list,X1: list,X2: nat,X3: nat] :
( ( ( $true
= ( listStar @ ( plus @ ( plus @ X2 @ X3 ) @ ( plus @ X2 @ X3 ) ) @ ( app @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ ( plus @ X2 @ X3 ) @ ( sK3 @ X3 @ X2 @ X1 @ X0 ) @ ( app @ X2 @ X3 @ X1 @ X0 ) ) @ ( app @ ( plus @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ X2 ) @ X3 @ ( app @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ X2 @ ( sK3 @ X3 @ X2 @ X1 @ X0 ) @ X1 ) @ X0 ) ) )
& ( $true
= ( listStar @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ ( sK3 @ X3 @ X2 @ X1 @ X0 ) @ ( sK3 @ X3 @ X2 @ X1 @ X0 ) ) )
& ( $true
!= ( listStar @ ( plus @ ( suc @ ( plus @ X2 @ X3 ) ) @ ( plus @ X2 @ X3 ) ) @ ( app @ ( suc @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) ) @ ( plus @ X2 @ X3 ) @ ( cons @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ ( sK2 @ X3 @ X2 @ X1 @ X0 ) @ ( sK3 @ X3 @ X2 @ X1 @ X0 ) ) @ ( app @ X2 @ X3 @ X1 @ X0 ) ) @ ( app @ ( plus @ ( suc @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) ) @ X2 ) @ X3 @ ( app @ ( suc @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) ) @ X2 @ ( cons @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ ( sK2 @ X3 @ X2 @ X1 @ X0 ) @ ( sK3 @ X3 @ X2 @ X1 @ X0 ) ) @ X1 ) @ X0 ) ) ) )
| ( $true
!= ( sP0 @ X3 @ X2 @ X1 @ X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f55,f56]) ).
thf(f56,plain,
! [X0: list,X1: list,X2: nat,X3: nat] :
( ? [X4: nat,X5: elem,X6: list] :
( ( $true
= ( listStar @ ( plus @ ( plus @ X2 @ X3 ) @ ( plus @ X2 @ X3 ) ) @ ( app @ X4 @ ( plus @ X2 @ X3 ) @ X6 @ ( app @ X2 @ X3 @ X1 @ X0 ) ) @ ( app @ ( plus @ X4 @ X2 ) @ X3 @ ( app @ X4 @ X2 @ X6 @ X1 ) @ X0 ) ) )
& ( $true
= ( listStar @ X4 @ X6 @ X6 ) )
& ( $true
!= ( listStar @ ( plus @ ( suc @ ( plus @ X2 @ X3 ) ) @ ( plus @ X2 @ X3 ) ) @ ( app @ ( suc @ X4 ) @ ( plus @ X2 @ X3 ) @ ( cons @ X4 @ X5 @ X6 ) @ ( app @ X2 @ X3 @ X1 @ X0 ) ) @ ( app @ ( plus @ ( suc @ X4 ) @ X2 ) @ X3 @ ( app @ ( suc @ X4 ) @ X2 @ ( cons @ X4 @ X5 @ X6 ) @ X1 ) @ X0 ) ) ) )
=> ( ( $true
= ( listStar @ ( plus @ ( plus @ X2 @ X3 ) @ ( plus @ X2 @ X3 ) ) @ ( app @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ ( plus @ X2 @ X3 ) @ ( sK3 @ X3 @ X2 @ X1 @ X0 ) @ ( app @ X2 @ X3 @ X1 @ X0 ) ) @ ( app @ ( plus @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ X2 ) @ X3 @ ( app @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ X2 @ ( sK3 @ X3 @ X2 @ X1 @ X0 ) @ X1 ) @ X0 ) ) )
& ( $true
= ( listStar @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ ( sK3 @ X3 @ X2 @ X1 @ X0 ) @ ( sK3 @ X3 @ X2 @ X1 @ X0 ) ) )
& ( $true
!= ( listStar @ ( plus @ ( suc @ ( plus @ X2 @ X3 ) ) @ ( plus @ X2 @ X3 ) ) @ ( app @ ( suc @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) ) @ ( plus @ X2 @ X3 ) @ ( cons @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ ( sK2 @ X3 @ X2 @ X1 @ X0 ) @ ( sK3 @ X3 @ X2 @ X1 @ X0 ) ) @ ( app @ X2 @ X3 @ X1 @ X0 ) ) @ ( app @ ( plus @ ( suc @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) ) @ X2 ) @ X3 @ ( app @ ( suc @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) ) @ X2 @ ( cons @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ ( sK2 @ X3 @ X2 @ X1 @ X0 ) @ ( sK3 @ X3 @ X2 @ X1 @ X0 ) ) @ X1 ) @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f55,plain,
! [X0: list,X1: list,X2: nat,X3: nat] :
( ? [X4: nat,X5: elem,X6: list] :
( ( $true
= ( listStar @ ( plus @ ( plus @ X2 @ X3 ) @ ( plus @ X2 @ X3 ) ) @ ( app @ X4 @ ( plus @ X2 @ X3 ) @ X6 @ ( app @ X2 @ X3 @ X1 @ X0 ) ) @ ( app @ ( plus @ X4 @ X2 ) @ X3 @ ( app @ X4 @ X2 @ X6 @ X1 ) @ X0 ) ) )
& ( $true
= ( listStar @ X4 @ X6 @ X6 ) )
& ( $true
!= ( listStar @ ( plus @ ( suc @ ( plus @ X2 @ X3 ) ) @ ( plus @ X2 @ X3 ) ) @ ( app @ ( suc @ X4 ) @ ( plus @ X2 @ X3 ) @ ( cons @ X4 @ X5 @ X6 ) @ ( app @ X2 @ X3 @ X1 @ X0 ) ) @ ( app @ ( plus @ ( suc @ X4 ) @ X2 ) @ X3 @ ( app @ ( suc @ X4 ) @ X2 @ ( cons @ X4 @ X5 @ X6 ) @ X1 ) @ X0 ) ) ) )
| ( $true
!= ( sP0 @ X3 @ X2 @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f54]) ).
thf(f54,plain,
! [X3: list,X1: list,X0: nat,X2: nat] :
( ? [X4: nat,X5: elem,X6: list] :
( ( $true
= ( listStar @ ( plus @ ( plus @ X0 @ X2 ) @ ( plus @ X0 @ X2 ) ) @ ( app @ X4 @ ( plus @ X0 @ X2 ) @ X6 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ X4 @ X0 ) @ X2 @ ( app @ X4 @ X0 @ X6 @ X1 ) @ X3 ) ) )
& ( $true
= ( listStar @ X4 @ X6 @ X6 ) )
& ( $true
!= ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X2 ) ) @ ( plus @ X0 @ X2 ) ) @ ( app @ ( suc @ X4 ) @ ( plus @ X0 @ X2 ) @ ( cons @ X4 @ X5 @ X6 ) @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ ( suc @ X4 ) @ X0 ) @ X2 @ ( app @ ( suc @ X4 ) @ X0 @ ( cons @ X4 @ X5 @ X6 ) @ X1 ) @ X3 ) ) ) )
| ( $true
!= ( sP0 @ X2 @ X0 @ X1 @ X3 ) ) ),
inference(nnf_transformation,[status(thm)],[f52]) ).
thf(f236,plain,
! [X2: list,X3: list,X0: nat,X1: nat] :
( ( $true
!= ( listStar @ ( plus @ X0 @ ( plus @ X1 @ ( plus @ X0 @ X1 ) ) ) @ ( app @ ( sK1 @ X1 @ X0 @ X2 @ X3 ) @ ( plus @ X0 @ X1 ) @ ( sK3 @ X1 @ X0 @ X2 @ X3 ) @ ( app @ X0 @ X1 @ X2 @ X3 ) ) @ ( app @ ( plus @ ( sK1 @ X1 @ X0 @ X2 @ X3 ) @ X0 ) @ X1 @ ( app @ ( sK1 @ X1 @ X0 @ X2 @ X3 ) @ X0 @ ( sK3 @ X1 @ X0 @ X2 @ X3 ) @ X2 ) @ X3 ) ) )
| ( $true
!= ( sP0 @ X1 @ X0 @ X2 @ X3 ) )
| ( $true
!= ( listStar @ X0 @ X2 @ X2 ) )
| ( $true
!= ( listStar @ X1 @ X3 @ X3 ) ) ),
inference(subsumption_resolution,[status(thm)],[f229,f65]) ).
thf(f65,plain,
! [X2: nat,X3: nat,X0: list,X1: list] :
( ( $true
= ( listStar @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ ( sK3 @ X3 @ X2 @ X1 @ X0 ) @ ( sK3 @ X3 @ X2 @ X1 @ X0 ) ) )
| ( $true
!= ( sP0 @ X3 @ X2 @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
thf(f229,plain,
! [X2: list,X3: list,X0: nat,X1: nat] :
( ( $true
!= ( listStar @ ( sK1 @ X1 @ X0 @ X2 @ X3 ) @ ( sK3 @ X1 @ X0 @ X2 @ X3 ) @ ( sK3 @ X1 @ X0 @ X2 @ X3 ) ) )
| ( $true
!= ( listStar @ X0 @ X2 @ X2 ) )
| ( $true
!= ( listStar @ X1 @ X3 @ X3 ) )
| ( $true
!= ( listStar @ ( plus @ X0 @ ( plus @ X1 @ ( plus @ X0 @ X1 ) ) ) @ ( app @ ( sK1 @ X1 @ X0 @ X2 @ X3 ) @ ( plus @ X0 @ X1 ) @ ( sK3 @ X1 @ X0 @ X2 @ X3 ) @ ( app @ X0 @ X1 @ X2 @ X3 ) ) @ ( app @ ( plus @ ( sK1 @ X1 @ X0 @ X2 @ X3 ) @ X0 ) @ X1 @ ( app @ ( sK1 @ X1 @ X0 @ X2 @ X3 ) @ X0 @ ( sK3 @ X1 @ X0 @ X2 @ X3 ) @ X2 ) @ X3 ) ) )
| ( $true
!= ( sP0 @ X1 @ X0 @ X2 @ X3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f228]) ).
thf(f228,plain,
! [X2: list,X3: list,X0: nat,X1: nat] :
( ( $true
!= ( listStar @ X0 @ X2 @ X2 ) )
| ( $true
!= ( listStar @ ( sK1 @ X1 @ X0 @ X2 @ X3 ) @ ( sK3 @ X1 @ X0 @ X2 @ X3 ) @ ( sK3 @ X1 @ X0 @ X2 @ X3 ) ) )
| ( $true
!= ( listStar @ X1 @ X3 @ X3 ) )
| ( $true
!= ( sP0 @ X1 @ X0 @ X2 @ X3 ) )
| ( $true != $true )
| ( $true
!= ( listStar @ ( plus @ X0 @ ( plus @ X1 @ ( plus @ X0 @ X1 ) ) ) @ ( app @ ( sK1 @ X1 @ X0 @ X2 @ X3 ) @ ( plus @ X0 @ X1 ) @ ( sK3 @ X1 @ X0 @ X2 @ X3 ) @ ( app @ X0 @ X1 @ X2 @ X3 ) ) @ ( app @ ( plus @ ( sK1 @ X1 @ X0 @ X2 @ X3 ) @ X0 ) @ X1 @ ( app @ ( sK1 @ X1 @ X0 @ X2 @ X3 ) @ X0 @ ( sK3 @ X1 @ X0 @ X2 @ X3 ) @ X2 ) @ X3 ) ) ) ),
inference(superposition,[status(thm)],[f204,f163]) ).
thf(f163,plain,
! [X2: nat,X3: list,X0: nat,X1: list,X6: list,X4: nat,X5: elem] :
( ( $true
= ( listStar @ ( suc @ ( plus @ X0 @ ( plus @ X2 @ ( plus @ X0 @ X2 ) ) ) ) @ ( app @ ( suc @ X4 ) @ ( plus @ X0 @ X2 ) @ ( cons @ X4 @ X5 @ X6 ) @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( suc @ ( plus @ X4 @ X0 ) ) @ X2 @ ( app @ ( suc @ X4 ) @ X0 @ ( cons @ X4 @ X5 @ X6 ) @ X1 ) @ X3 ) ) )
| ( $true
!= ( listStar @ X2 @ X3 @ X3 ) )
| ( $true
!= ( listStar @ ( plus @ X0 @ ( plus @ X2 @ ( plus @ X0 @ X2 ) ) ) @ ( app @ X4 @ ( plus @ X0 @ X2 ) @ X6 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ X4 @ X0 ) @ X2 @ ( app @ X4 @ X0 @ X6 @ X1 ) @ X3 ) ) )
| ( $true
!= ( listStar @ X4 @ X6 @ X6 ) )
| ( $true
!= ( listStar @ X0 @ X1 @ X1 ) ) ),
inference(forward_demodulation,[status(thm)],[f162,f70]) ).
thf(f70,plain,
! [X0: nat,X1: nat] :
( ( plus @ ( suc @ X0 ) @ X1 )
= ( suc @ ( plus @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: nat,X1: nat] :
( ( plus @ ( suc @ X0 ) @ X1 )
= ( suc @ ( plus @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,axiom,
! [X6: nat,X10: nat] :
( ( plus @ ( suc @ X6 ) @ X10 )
= ( suc @ ( plus @ X6 @ X10 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MXj1wRhtZr/DTF2THF_8110.p',ax2) ).
thf(f162,plain,
! [X2: nat,X3: list,X0: nat,X1: list,X6: list,X4: nat,X5: elem] :
( ( $true
!= ( listStar @ X4 @ X6 @ X6 ) )
| ( $true
= ( listStar @ ( suc @ ( plus @ X0 @ ( plus @ X2 @ ( plus @ X0 @ X2 ) ) ) ) @ ( app @ ( suc @ X4 ) @ ( plus @ X0 @ X2 ) @ ( cons @ X4 @ X5 @ X6 ) @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ ( suc @ X4 ) @ X0 ) @ X2 @ ( app @ ( suc @ X4 ) @ X0 @ ( cons @ X4 @ X5 @ X6 ) @ X1 ) @ X3 ) ) )
| ( $true
!= ( listStar @ X2 @ X3 @ X3 ) )
| ( $true
!= ( listStar @ X0 @ X1 @ X1 ) )
| ( $true
!= ( listStar @ ( plus @ X0 @ ( plus @ X2 @ ( plus @ X0 @ X2 ) ) ) @ ( app @ X4 @ ( plus @ X0 @ X2 ) @ X6 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ X4 @ X0 ) @ X2 @ ( app @ X4 @ X0 @ X6 @ X1 ) @ X3 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f161,f68]) ).
thf(f161,plain,
! [X2: nat,X3: list,X0: nat,X1: list,X6: list,X4: nat,X5: elem] :
( ( $true
= ( listStar @ ( suc @ ( plus @ ( plus @ X0 @ X2 ) @ ( plus @ X0 @ X2 ) ) ) @ ( app @ ( suc @ X4 ) @ ( plus @ X0 @ X2 ) @ ( cons @ X4 @ X5 @ X6 ) @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ ( suc @ X4 ) @ X0 ) @ X2 @ ( app @ ( suc @ X4 ) @ X0 @ ( cons @ X4 @ X5 @ X6 ) @ X1 ) @ X3 ) ) )
| ( $true
!= ( listStar @ X2 @ X3 @ X3 ) )
| ( $true
!= ( listStar @ X4 @ X6 @ X6 ) )
| ( $true
!= ( listStar @ X0 @ X1 @ X1 ) )
| ( $true
!= ( listStar @ ( plus @ X0 @ ( plus @ X2 @ ( plus @ X0 @ X2 ) ) ) @ ( app @ X4 @ ( plus @ X0 @ X2 ) @ X6 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ X4 @ X0 ) @ X2 @ ( app @ X4 @ X0 @ X6 @ X1 ) @ X3 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f160,f70]) ).
thf(f160,plain,
! [X2: nat,X3: list,X0: nat,X1: list,X6: list,X4: nat,X5: elem] :
( ( $true
!= ( listStar @ X0 @ X1 @ X1 ) )
| ( $true
!= ( listStar @ X4 @ X6 @ X6 ) )
| ( $true
!= ( listStar @ ( plus @ X0 @ ( plus @ X2 @ ( plus @ X0 @ X2 ) ) ) @ ( app @ X4 @ ( plus @ X0 @ X2 ) @ X6 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ X4 @ X0 ) @ X2 @ ( app @ X4 @ X0 @ X6 @ X1 ) @ X3 ) ) )
| ( $true
= ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X2 ) ) @ ( plus @ X0 @ X2 ) ) @ ( app @ ( suc @ X4 ) @ ( plus @ X0 @ X2 ) @ ( cons @ X4 @ X5 @ X6 ) @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ ( suc @ X4 ) @ X0 ) @ X2 @ ( app @ ( suc @ X4 ) @ X0 @ ( cons @ X4 @ X5 @ X6 ) @ X1 ) @ X3 ) ) )
| ( $true
!= ( listStar @ X2 @ X3 @ X3 ) ) ),
inference(forward_demodulation,[status(thm)],[f75,f68]) ).
thf(f75,plain,
! [X2: nat,X3: list,X0: nat,X1: list,X6: list,X4: nat,X5: elem] :
( ( $true
!= ( listStar @ X2 @ X3 @ X3 ) )
| ( $true
!= ( listStar @ X4 @ X6 @ X6 ) )
| ( $true
!= ( listStar @ ( plus @ ( plus @ X0 @ X2 ) @ ( plus @ X0 @ X2 ) ) @ ( app @ X4 @ ( plus @ X0 @ X2 ) @ X6 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ X4 @ X0 ) @ X2 @ ( app @ X4 @ X0 @ X6 @ X1 ) @ X3 ) ) )
| ( $true
= ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X2 ) ) @ ( plus @ X0 @ X2 ) ) @ ( app @ ( suc @ X4 ) @ ( plus @ X0 @ X2 ) @ ( cons @ X4 @ X5 @ X6 ) @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ ( suc @ X4 ) @ X0 ) @ X2 @ ( app @ ( suc @ X4 ) @ X0 @ ( cons @ X4 @ X5 @ X6 ) @ X1 ) @ X3 ) ) )
| ( $true
!= ( listStar @ X0 @ X1 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f46,plain,
! [X0: nat,X1: list,X2: nat,X3: list,X4: nat,X5: elem,X6: list] :
( ( $true
!= ( listStar @ ( plus @ ( plus @ X0 @ X2 ) @ ( plus @ X0 @ X2 ) ) @ ( app @ X4 @ ( plus @ X0 @ X2 ) @ X6 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ X4 @ X0 ) @ X2 @ ( app @ X4 @ X0 @ X6 @ X1 ) @ X3 ) ) )
| ( $true
!= ( listStar @ X2 @ X3 @ X3 ) )
| ( $true
!= ( listStar @ X0 @ X1 @ X1 ) )
| ( $true
= ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X2 ) ) @ ( plus @ X0 @ X2 ) ) @ ( app @ ( suc @ X4 ) @ ( plus @ X0 @ X2 ) @ ( cons @ X4 @ X5 @ X6 ) @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ ( suc @ X4 ) @ X0 ) @ X2 @ ( app @ ( suc @ X4 ) @ X0 @ ( cons @ X4 @ X5 @ X6 ) @ X1 ) @ X3 ) ) )
| ( $true
!= ( listStar @ X4 @ X6 @ X6 ) ) ),
inference(flattening,[status(thm)],[f45]) ).
thf(f45,plain,
! [X0: nat,X1: list,X2: nat,X3: list,X4: nat,X5: elem,X6: list] :
( ( $true
= ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X2 ) ) @ ( plus @ X0 @ X2 ) ) @ ( app @ ( suc @ X4 ) @ ( plus @ X0 @ X2 ) @ ( cons @ X4 @ X5 @ X6 ) @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ ( suc @ X4 ) @ X0 ) @ X2 @ ( app @ ( suc @ X4 ) @ X0 @ ( cons @ X4 @ X5 @ X6 ) @ X1 ) @ X3 ) ) )
| ( $true
!= ( listStar @ ( plus @ ( plus @ X0 @ X2 ) @ ( plus @ X0 @ X2 ) ) @ ( app @ X4 @ ( plus @ X0 @ X2 ) @ X6 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ X4 @ X0 ) @ X2 @ ( app @ X4 @ X0 @ X6 @ X1 ) @ X3 ) ) )
| ( $true
!= ( listStar @ X4 @ X6 @ X6 ) )
| ( $true
!= ( listStar @ X2 @ X3 @ X3 ) )
| ( $true
!= ( listStar @ X0 @ X1 @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
! [X0: nat,X1: list,X2: nat,X3: list,X4: nat,X5: elem,X6: list] :
( ( $true
= ( listStar @ X0 @ X1 @ X1 ) )
=> ( ( $true
= ( listStar @ X2 @ X3 @ X3 ) )
=> ( ( $true
= ( listStar @ X4 @ X6 @ X6 ) )
=> ( ( $true
= ( listStar @ ( plus @ ( plus @ X0 @ X2 ) @ ( plus @ X0 @ X2 ) ) @ ( app @ X4 @ ( plus @ X0 @ X2 ) @ X6 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ X4 @ X0 ) @ X2 @ ( app @ X4 @ X0 @ X6 @ X1 ) @ X3 ) ) )
=> ( $true
= ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X2 ) ) @ ( plus @ X0 @ X2 ) ) @ ( app @ ( suc @ X4 ) @ ( plus @ X0 @ X2 ) @ ( cons @ X4 @ X5 @ X6 ) @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ ( suc @ X4 ) @ X0 ) @ X2 @ ( app @ ( suc @ X4 ) @ X0 @ ( cons @ X4 @ X5 @ X6 ) @ X1 ) @ X3 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f37]) ).
thf(f37,plain,
! [X0: nat,X1: list,X2: nat,X3: list,X4: nat,X5: elem,X6: list] :
( ( listStar @ X0 @ X1 @ X1 )
=> ( ( listStar @ X2 @ X3 @ X3 )
=> ( ( listStar @ X4 @ X6 @ X6 )
=> ( ( listStar @ ( plus @ ( plus @ X0 @ X2 ) @ ( plus @ X0 @ X2 ) ) @ ( app @ X4 @ ( plus @ X0 @ X2 ) @ X6 @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ X4 @ X0 ) @ X2 @ ( app @ X4 @ X0 @ X6 @ X1 ) @ X3 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X0 @ X2 ) ) @ ( plus @ X0 @ X2 ) ) @ ( app @ ( suc @ X4 ) @ ( plus @ X0 @ X2 ) @ ( cons @ X4 @ X5 @ X6 ) @ ( app @ X0 @ X2 @ X1 @ X3 ) ) @ ( app @ ( plus @ ( suc @ X4 ) @ X0 ) @ X2 @ ( app @ ( suc @ X4 ) @ X0 @ ( cons @ X4 @ X5 @ X6 ) @ X1 ) @ X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,axiom,
! [X13: nat,X15: list,X14: nat,X16: list,X10: nat,X2: elem,X17: list] :
( ( listStar @ X13 @ X15 @ X15 )
=> ( ( listStar @ X14 @ X16 @ X16 )
=> ( ( listStar @ X10 @ X17 @ X17 )
=> ( ( listStar @ ( plus @ ( plus @ X13 @ X14 ) @ ( plus @ X13 @ X14 ) ) @ ( app @ X10 @ ( plus @ X13 @ X14 ) @ X17 @ ( app @ X13 @ X14 @ X15 @ X16 ) ) @ ( app @ ( plus @ X10 @ X13 ) @ X14 @ ( app @ X10 @ X13 @ X17 @ X15 ) @ X16 ) )
=> ( listStar @ ( plus @ ( suc @ ( plus @ X13 @ X14 ) ) @ ( plus @ X13 @ X14 ) ) @ ( app @ ( suc @ X10 ) @ ( plus @ X13 @ X14 ) @ ( cons @ X10 @ X2 @ X17 ) @ ( app @ X13 @ X14 @ X15 @ X16 ) ) @ ( app @ ( plus @ ( suc @ X10 ) @ X13 ) @ X14 @ ( app @ ( suc @ X10 ) @ X13 @ ( cons @ X10 @ X2 @ X17 ) @ X15 ) @ X16 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MXj1wRhtZr/DTF2THF_8110.p',list_app_assoc_indstep) ).
thf(f204,plain,
! [X2: nat,X3: nat,X0: list,X1: list] :
( ( $true
!= ( listStar @ ( suc @ ( plus @ X2 @ ( plus @ X3 @ ( plus @ X2 @ X3 ) ) ) ) @ ( app @ ( suc @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) ) @ ( plus @ X2 @ X3 ) @ ( cons @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ ( sK2 @ X3 @ X2 @ X1 @ X0 ) @ ( sK3 @ X3 @ X2 @ X1 @ X0 ) ) @ ( app @ X2 @ X3 @ X1 @ X0 ) ) @ ( app @ ( suc @ ( plus @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ X2 ) ) @ X3 @ ( app @ ( suc @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) ) @ X2 @ ( cons @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ ( sK2 @ X3 @ X2 @ X1 @ X0 ) @ ( sK3 @ X3 @ X2 @ X1 @ X0 ) ) @ X1 ) @ X0 ) ) )
| ( $true
!= ( sP0 @ X3 @ X2 @ X1 @ X0 ) ) ),
inference(forward_demodulation,[status(thm)],[f203,f70]) ).
thf(f203,plain,
! [X2: nat,X3: nat,X0: list,X1: list] :
( ( $true
!= ( listStar @ ( suc @ ( plus @ X2 @ ( plus @ X3 @ ( plus @ X2 @ X3 ) ) ) ) @ ( app @ ( suc @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) ) @ ( plus @ X2 @ X3 ) @ ( cons @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ ( sK2 @ X3 @ X2 @ X1 @ X0 ) @ ( sK3 @ X3 @ X2 @ X1 @ X0 ) ) @ ( app @ X2 @ X3 @ X1 @ X0 ) ) @ ( app @ ( plus @ ( suc @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) ) @ X2 ) @ X3 @ ( app @ ( suc @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) ) @ X2 @ ( cons @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ ( sK2 @ X3 @ X2 @ X1 @ X0 ) @ ( sK3 @ X3 @ X2 @ X1 @ X0 ) ) @ X1 ) @ X0 ) ) )
| ( $true
!= ( sP0 @ X3 @ X2 @ X1 @ X0 ) ) ),
inference(forward_demodulation,[status(thm)],[f202,f68]) ).
thf(f202,plain,
! [X2: nat,X3: nat,X0: list,X1: list] :
( ( $true
!= ( sP0 @ X3 @ X2 @ X1 @ X0 ) )
| ( $true
!= ( listStar @ ( suc @ ( plus @ ( plus @ X2 @ X3 ) @ ( plus @ X2 @ X3 ) ) ) @ ( app @ ( suc @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) ) @ ( plus @ X2 @ X3 ) @ ( cons @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ ( sK2 @ X3 @ X2 @ X1 @ X0 ) @ ( sK3 @ X3 @ X2 @ X1 @ X0 ) ) @ ( app @ X2 @ X3 @ X1 @ X0 ) ) @ ( app @ ( plus @ ( suc @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) ) @ X2 ) @ X3 @ ( app @ ( suc @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) ) @ X2 @ ( cons @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ ( sK2 @ X3 @ X2 @ X1 @ X0 ) @ ( sK3 @ X3 @ X2 @ X1 @ X0 ) ) @ X1 ) @ X0 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f64,f70]) ).
thf(f64,plain,
! [X2: nat,X3: nat,X0: list,X1: list] :
( ( $true
!= ( sP0 @ X3 @ X2 @ X1 @ X0 ) )
| ( $true
!= ( listStar @ ( plus @ ( suc @ ( plus @ X2 @ X3 ) ) @ ( plus @ X2 @ X3 ) ) @ ( app @ ( suc @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) ) @ ( plus @ X2 @ X3 ) @ ( cons @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ ( sK2 @ X3 @ X2 @ X1 @ X0 ) @ ( sK3 @ X3 @ X2 @ X1 @ X0 ) ) @ ( app @ X2 @ X3 @ X1 @ X0 ) ) @ ( app @ ( plus @ ( suc @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) ) @ X2 ) @ X3 @ ( app @ ( suc @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) ) @ X2 @ ( cons @ ( sK1 @ X3 @ X2 @ X1 @ X0 ) @ ( sK2 @ X3 @ X2 @ X1 @ X0 ) @ ( sK3 @ X3 @ X2 @ X1 @ X0 ) ) @ X1 ) @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT362^1 : 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
% 0.15/0.34 % Computer : n011.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 06:16:02 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.26/0.46 ---- Original DTF file ---
% 0.26/0.46 thf(spec,logic,$$dhol).
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 % File : DAT362^1 : TPTP v9.2.1. Released v9.2.0.
% 0.26/0.46 % Domain : Data Structures
% 0.26/0.46 % Problem : Associativity of list append
% 0.26/0.46 % Version : Especial.
% 0.26/0.46 % English : Associativity of list append. The proof is by induction with a
% 0.26/0.46 % problem file for the base and step case (with multiple subcases)
% 0.26/0.46 % as well as the correct instantiation of the induction axiom for
% 0.26/0.46 % lists. The main file uses the conjectures of the other files as
% 0.26/0.46 % lemmas in order to prove the final result. To simplify proof
% 0.26/0.46 % search, the axioms in each problem file have been preselected.
% 0.26/0.46
% 0.26/0.46 % Refs : [RRB23] Rothgang et al. (2023), Theorem Proving in Dependently
% 0.26/0.46 % : [Rot25] Rothgang (2025), Email to Geoff Sutcliffe
% 0.26/0.46 % : [RK+25] Ranalter et al. (2025), The Dependently Typed Higher-O
% 0.26/0.46 % Source : [Rot25]
% 0.26/0.46 % Names : ListAppAssoc/list-app-assoc.p [Rot25]
% 0.26/0.46
% 0.26/0.46 % Status : Theorem
% 0.26/0.46 % Rating : ? v9.2.0
% 0.26/0.46 % Syntax : Number of formulae : 16 ( 5 unt; 9 typ; 0 def)
% 0.26/0.46 % Number of atoms : 11 ( 11 equ; 0 cnn)
% 0.26/0.46 % Maximal formula atoms : 4 ( 1 avg)
% 0.26/0.46 % Number of connectives : 219 ( 0 ~; 0 |; 0 &; 215 @)
% 0.26/0.46 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.26/0.46 % Maximal formula depth : 11 ( 6 avg)
% 0.26/0.46 % Number of types : 2 ( 2 usr)
% 0.26/0.46 % Number of type decls : 9 ( 0 !>P; 2 !>D)
% 0.26/0.46 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.26/0.46 % Number of symbols : 8 ( 7 usr; 2 con; 0-4 aty)
% 0.26/0.46 % Number of variables : 35 ( 0 ^; 32 !; 0 ?; 35 :)
% 0.26/0.46 % ( 3 !>; 0 ?*; 0 @-; 0 @+)
% 0.26/0.46 % SPC : DH0_THM_EQU_NAR
% 0.26/0.46
% 0.26/0.46 % Comments :
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 thf(elem_type,type,
% 0.26/0.46 elem: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(nat_type,type,
% 0.26/0.46 nat: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(zero_type,type,
% 0.26/0.46 zero: nat ).
% 0.26/0.46
% 0.26/0.46 thf(suc_type,type,
% 0.26/0.46 suc: nat > nat ).
% 0.26/0.46
% 0.26/0.46 thf(plus_type,type,
% 0.26/0.46 plus: nat > nat > nat ).
% 0.26/0.46
% 0.26/0.46 thf(list_type,type,
% 0.26/0.46 list: nat > $tType ).
% 0.26/0.46
% 0.26/0.46 thf(nil_type,type,
% 0.26/0.46 nil: list @ zero ).
% 0.26/0.46
% 0.26/0.46 thf(cons_type,type,
% 0.26/0.46 cons:
% 0.26/0.46 !>[N: nat] : ( elem > ( list @ N ) > ( list @ ( suc @ N ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(app_type,type,
% 0.26/0.46 app:
% 0.26/0.46 !>[N: nat,M: nat] : ( ( list @ N ) > ( list @ M ) > ( list @ ( plus @ N @ M ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(ax1,axiom,
% 0.26/0.46 ! [N: nat] :
% 0.26/0.46 ( ( plus @ zero @ N )
% 0.26/0.46 = N ) ).
% 0.26/0.46
% 0.26/0.46 thf(ax2,axiom,
% 0.26/0.46 ! [N: nat,M: nat] :
% 0.26/0.46 ( ( plus @ ( suc @ N ) @ M )
% 0.26/0.46 = ( suc @ ( plus @ N @ M ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(plus_assoc,axiom,
% 0.26/0.46 ! [M1: nat,M2: nat,M3: nat] :
% 0.26/0.46 ( ( plus @ M1 @ ( plus @ M2 @ M3 ) )
% 0.26/0.46 = ( plus @ ( plus @ M1 @ M2 ) @ M3 ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(list_app_assoc_indinst,axiom,
% 0.26/0.46 ! [M2: nat,L2: list @ M2,M3: nat,L3: list @ M3] :
% 0.26/0.46 ( ( ( app @ zero @ ( plus @ M2 @ M3 ) @ nil @ ( app @ M2 @ M3 @ L2 @ L3 ) )
% 0.26/0.46 = ( app @ ( plus @ zero @ M2 ) @ M3 @ ( app @ zero @ M2 @ nil @ L2 ) @ L3 ) )
% 0.26/0.46 => ( ! [M: nat,X: elem,L: list @ M] :
% 0.26/0.46 ( ( ( app @ M @ ( plus @ M2 @ M3 ) @ L @ ( app @ M2 @ M3 @ L2 @ L3 ) )
% 0.26/0.46 = ( app @ ( plus @ M @ M2 ) @ M3 @ ( app @ M @ M2 @ L @ L2 ) @ L3 ) )
% 0.26/0.46 => ( ( app @ ( suc @ M ) @ ( plus @ M2 @ M3 ) @ ( cons @ M @ X @ L ) @ ( app @ M2 @ M3 @ L2 @ L3 ) )
% 0.26/0.46 = ( app @ ( plus @ ( suc @ M ) @ M2 ) @ M3 @ ( app @ ( suc @ M ) @ M2 @ ( cons @ M @ X @ L ) @ L2 ) @ L3 ) ) )
% 0.26/0.46 => ! [M: nat,L: list @ M] :
% 0.26/0.46 ( ( app @ M @ ( plus @ M2 @ M3 ) @ L @ ( app @ M2 @ M3 @ L2 @ L3 ) )
% 0.26/0.46 = ( app @ ( plus @ M @ M2 ) @ M3 @ ( app @ M @ M2 @ L @ L2 ) @ L3 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(list_app_assoc_base,axiom,
% 0.26/0.46 ! [M2: nat,L2: list @ M2,M3: nat,L3: list @ M3] :
% 0.26/0.46 ( ( app @ zero @ ( plus @ M2 @ M3 ) @ nil @ ( app @ M2 @ M3 @ L2 @ L3 ) )
% 0.26/0.46 = ( app @ ( plus @ zero @ M2 ) @ M3 @ ( app @ zero @ M2 @ nil @ L2 ) @ L3 ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(list_app_assoc_indstep,axiom,
% 0.26/0.46 ! [M2: nat,L2: list @ M2,M3: nat,L3: list @ M3,M: nat,X: elem,L: list @ M] :
% 0.26/0.46 ( ( ( app @ M @ ( plus @ M2 @ M3 ) @ L @ ( app @ M2 @ M3 @ L2 @ L3 ) )
% 0.26/0.46 = ( app @ ( plus @ M @ M2 ) @ M3 @ ( app @ M @ M2 @ L @ L2 ) @ L3 ) )
% 0.26/0.46 => ( ( app @ ( suc @ M ) @ ( plus @ M2 @ M3 ) @ ( cons @ M @ X @ L ) @ ( app @ M2 @ M3 @ L2 @ L3 ) )
% 0.26/0.46 = ( app @ ( plus @ ( suc @ M ) @ M2 ) @ M3 @ ( app @ ( suc @ M ) @ M2 @ ( cons @ M @ X @ L ) @ L2 ) @ L3 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf(list_app_assoc,conjecture,
% 0.26/0.46 ! [M: nat,L: list @ M,M2: nat,L2: list @ M2,M3: nat,L3: list @ M3] :
% 0.26/0.46 ( ( app @ M @ ( plus @ M2 @ M3 ) @ L @ ( app @ M2 @ M3 @ L2 @ L3 ) )
% 0.26/0.46 = ( app @ ( plus @ M @ M2 ) @ M3 @ ( app @ M @ M2 @ L @ L2 ) @ L3 ) ) ).
% 0.26/0.46
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 ------------------------
% 1.81/1.33 ---- Embedded in THF ---
% 1.81/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.81/1.33 %%% Generated on Tue Feb 24 06:16:03 EST 2026
% 1.81/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.81/1.33 %%% Logic specification used:
% 1.81/1.33 %%% thf(spec, logic, $$dhol).
% 1.81/1.33
% 1.81/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.MXj1wRhtZr/DTF2DTF8110.p
% See solution above
% 1.81/1.33 ------------------------
% 1.81/1.35 ---- Cleaned THF ---
% 1.81/1.35 thf(is_per_type,type,
% 1.81/1.35 isPer:
% 1.81/1.35 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 1.81/1.35
% 1.81/1.35 thf(is_per,definition,
% 1.81/1.35 ! [A: $tType,AStar: A > A > $o] :
% 1.81/1.35 ( ( isPer @ A @ AStar )
% 1.81/1.35 <=> ( ! [X: A,Y: A] :
% 1.81/1.35 ( ( AStar @ X @ Y )
% 1.81/1.35 => ( AStar @ Y @ X ) )
% 1.81/1.35 & ! [X: A,Y: A,Z: A] :
% 1.81/1.35 ( ( AStar @ X @ Y )
% 1.81/1.35 => ( ( AStar @ Y @ Z )
% 1.81/1.35 => ( AStar @ X @ Z ) ) ) ) ) ).
% 1.81/1.35
% 1.81/1.35 thf(elem_type,type,
% 1.81/1.35 elem: $tType ).
% 1.81/1.35
% 1.81/1.35 thf(elemStar,type,
% 1.81/1.35 elemStar: elem > elem > $o ).
% 1.81/1.35
% 1.81/1.35 thf(elemStar_is_eq,axiom,
% 1.81/1.35 ! [X: elem,Y: elem] :
% 1.81/1.35 ( ( elemStar @ X @ Y )
% 1.81/1.35 <=> ( X = Y ) ) ).
% 1.81/1.35
% 1.81/1.35 thf(nat_type,type,
% 1.81/1.35 nat: $tType ).
% 1.81/1.35
% 1.81/1.35 thf(natStar,type,
% 1.81/1.35 natStar: nat > nat > $o ).
% 1.81/1.35
% 1.81/1.35 thf(natStar_is_eq,axiom,
% 1.81/1.35 ! [X: nat,Y: nat] :
% 1.81/1.35 ( ( natStar @ X @ Y )
% 1.81/1.35 <=> ( X = Y ) ) ).
% 1.81/1.35
% 1.81/1.35 thf(zero_type,type,
% 1.81/1.35 zero: nat ).
% 1.81/1.35
% 1.81/1.35 thf(suc_type,type,
% 1.81/1.35 suc: nat > nat ).
% 1.81/1.35
% 1.81/1.35 thf(plus_type,type,
% 1.81/1.35 plus: nat > nat > nat ).
% 1.81/1.35
% 1.81/1.35 thf(list_type,type,
% 1.81/1.35 list: $tType ).
% 1.81/1.35
% 1.81/1.35 thf(listStar,type,
% 1.81/1.35 listStar: nat > list > list > $o ).
% 1.81/1.35
% 1.81/1.35 thf('\'listStar\'_is_per',axiom,
% 1.81/1.35 ! [C: nat] : ( isPer @ list @ ( listStar @ C ) ) ).
% 1.81/1.35
% 1.81/1.35 thf(nil_type,type,
% 1.81/1.35 nil: list ).
% 1.81/1.35
% 1.81/1.35 thf(nil_tp_ax,axiom,
% 1.81/1.35 listStar @ zero @ nil @ nil ).
% 1.81/1.35
% 1.81/1.35 thf(cons_type,type,
% 1.81/1.35 cons: nat > elem > list > list ).
% 1.81/1.35
% 1.81/1.35 thf(cons_tp_ax,axiom,
% 1.81/1.35 ! [N: nat,D: elem,D0: list,D0_prime: list] :
% 1.81/1.35 ( ( listStar @ N @ D0 @ D0_prime )
% 1.81/1.35 => ( listStar @ ( suc @ N ) @ ( cons @ N @ D @ D0 ) @ ( cons @ N @ D @ D0_prime ) ) ) ).
% 1.81/1.35
% 1.81/1.35 thf(app_type,type,
% 1.81/1.35 app: nat > nat > list > list > list ).
% 1.81/1.35
% 1.81/1.35 thf(app_tp_ax,axiom,
% 1.81/1.35 ! [N: nat,M: nat,D: list,D_prime: list] :
% 1.81/1.35 ( ( listStar @ N @ D @ D_prime )
% 1.81/1.35 => ! [D0: list,D0_prime: list] :
% 1.81/1.35 ( ( listStar @ M @ D0 @ D0_prime )
% 1.81/1.35 => ( listStar @ ( plus @ N @ M ) @ ( app @ N @ M @ D @ D0 ) @ ( app @ N @ M @ D_prime @ D0_prime ) ) ) ) ).
% 1.81/1.35
% 1.81/1.35 thf(ax1,axiom,
% 1.81/1.35 ! [N: nat] :
% 1.81/1.35 ( ( plus @ zero @ N )
% 1.81/1.35 = N ) ).
% 1.81/1.35
% 1.81/1.35 thf(ax2,axiom,
% 1.81/1.35 ! [N: nat,M: nat] :
% 1.81/1.35 ( ( plus @ ( suc @ N ) @ M )
% 1.81/1.35 = ( suc @ ( plus @ N @ M ) ) ) ).
% 1.81/1.35
% 1.81/1.35 thf(plus_assoc,axiom,
% 1.81/1.35 ! [M1: nat,M2: nat,M3: nat] :
% 1.81/1.35 ( ( plus @ M1 @ ( plus @ M2 @ M3 ) )
% 1.81/1.35 = ( plus @ ( plus @ M1 @ M2 ) @ M3 ) ) ).
% 1.81/1.35
% 1.81/1.35 thf(list_app_assoc_indinst,axiom,
% 1.81/1.35 ! [M2: nat,L2: list,M3: nat,L3: list] :
% 1.81/1.35 ( ( listStar @ M2 @ L2 @ L2 )
% 1.81/1.35 => ( ( listStar @ M3 @ L3 @ L3 )
% 1.81/1.35 => ( ( 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 ) )
% 1.81/1.35 => ( ! [M: nat,X: elem,L: list] :
% 1.81/1.35 ( ( listStar @ M @ L @ L )
% 1.81/1.35 => ( ( listStar @ ( plus @ ( plus @ M2 @ M3 ) @ ( plus @ M2 @ M3 ) ) @ ( app @ M @ ( plus @ M2 @ M3 ) @ L @ ( app @ M2 @ M3 @ L2 @ L3 ) ) @ ( app @ ( plus @ M @ M2 ) @ M3 @ ( app @ M @ M2 @ L @ L2 ) @ L3 ) )
% 1.81/1.35 => ( listStar @ ( plus @ ( suc @ ( plus @ M2 @ M3 ) ) @ ( plus @ M2 @ M3 ) ) @ ( app @ ( suc @ M ) @ ( plus @ M2 @ M3 ) @ ( cons @ M @ X @ L ) @ ( app @ M2 @ M3 @ L2 @ L3 ) ) @ ( app @ ( plus @ ( suc @ M ) @ M2 ) @ M3 @ ( app @ ( suc @ M ) @ M2 @ ( cons @ M @ X @ L ) @ L2 ) @ L3 ) ) ) )
% 1.81/1.35 => ! [M: nat,L: list] :
% 1.81/1.35 ( ( listStar @ M @ L @ L )
% 1.81/1.35 => ( listStar @ ( plus @ ( plus @ M2 @ M3 ) @ ( plus @ M2 @ M3 ) ) @ ( app @ M @ ( plus @ M2 @ M3 ) @ L @ ( app @ M2 @ M3 @ L2 @ L3 ) ) @ ( app @ ( plus @ M @ M2 ) @ M3 @ ( app @ M @ M2 @ L @ L2 ) @ L3 ) ) ) ) ) ) ) ).
% 1.81/1.35
% 1.81/1.35 thf(list_app_assoc_base,axiom,
% 1.81/1.35 ! [M2: nat,L2: list,M3: nat,L3: list] :
% 1.81/1.35 ( ( listStar @ M2 @ L2 @ L2 )
% 1.81/1.35 => ( ( listStar @ M3 @ L3 @ L3 )
% 1.81/1.35 => ( 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 ) ) ) ) ).
% 1.81/1.35
% 1.81/1.35 thf(list_app_assoc_indstep,axiom,
% 1.81/1.35 ! [M2: nat,L2: list,M3: nat,L3: list,M: nat,X: elem,L: list] :
% 1.81/1.35 ( ( listStar @ M2 @ L2 @ L2 )
% 1.81/1.35 => ( ( listStar @ M3 @ L3 @ L3 )
% 1.81/1.35 => ( ( listStar @ M @ L @ L )
% 1.81/1.35 => ( ( listStar @ ( plus @ ( plus @ M2 @ M3 ) @ ( plus @ M2 @ M3 ) ) @ ( app @ M @ ( plus @ M2 @ M3 ) @ L @ ( app @ M2 @ M3 @ L2 @ L3 ) ) @ ( app @ ( plus @ M @ M2 ) @ M3 @ ( app @ M @ M2 @ L @ L2 ) @ L3 ) )
% 1.81/1.35 => ( listStar @ ( plus @ ( suc @ ( plus @ M2 @ M3 ) ) @ ( plus @ M2 @ M3 ) ) @ ( app @ ( suc @ M ) @ ( plus @ M2 @ M3 ) @ ( cons @ M @ X @ L ) @ ( app @ M2 @ M3 @ L2 @ L3 ) ) @ ( app @ ( plus @ ( suc @ M ) @ M2 ) @ M3 @ ( app @ ( suc @ M ) @ M2 @ ( cons @ M @ X @ L ) @ L2 ) @ L3 ) ) ) ) ) ) ).
% 1.81/1.35
% 1.81/1.35 thf(list_app_assoc,conjecture,
% 1.81/1.35 ! [M: nat,L: list,M2: nat,L2: list,M3: nat,L3: list] :
% 1.81/1.35 ( ( listStar @ M @ L @ L )
% 1.81/1.35 => ( ( listStar @ M2 @ L2 @ L2 )
% 1.81/1.35 => ( ( listStar @ M3 @ L3 @ L3 )
% 1.81/1.35 => ( listStar @ ( plus @ ( plus @ M2 @ M3 ) @ ( plus @ M2 @ M3 ) ) @ ( app @ M @ ( plus @ M2 @ M3 ) @ L @ ( app @ M2 @ M3 @ L2 @ L3 ) ) @ ( app @ ( plus @ M @ M2 ) @ M3 @ ( app @ M @ M2 @ L @ L2 ) @ L3 ) ) ) ) ) ).
% 1.81/1.35 ------------------------
% 1.81/1.36 % (8438)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_8110 for (2999ds/4Mi)
% 1.81/1.36 % (8443)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8110 for (2999ds/18Mi)
% 1.81/1.36 % (8438)Instruction limit reached!
% 1.81/1.36 % (8438)------------------------------
% 1.81/1.36 % (8438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.36 % (8438)Termination reason: Unknown
% 1.81/1.36 % (8438)Termination phase: shuffling
% 1.81/1.36
% 1.81/1.36 % (8438)Memory used [KB]: 1023
% 1.81/1.36 % (8438)Time elapsed: 0.002 s
% 1.81/1.36 % (8438)Instructions burned: 4 (million)
% 1.81/1.36 % (8438)------------------------------
% 1.81/1.36 % (8438)------------------------------
% 1.81/1.37 % (8443)Instruction limit reached!
% 1.81/1.37 % (8443)------------------------------
% 1.81/1.37 % (8443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.37 % (8443)Termination reason: Unknown
% 1.81/1.37 % (8443)Termination phase: Saturation
% 1.81/1.37
% 1.81/1.37 % (8443)Memory used [KB]: 5628
% 1.81/1.37 % (8443)Time elapsed: 0.007 s
% 1.81/1.37 % (8443)Instructions burned: 19 (million)
% 1.81/1.37 % (8443)------------------------------
% 1.81/1.37 % (8443)------------------------------
% 1.81/1.37 % (8437)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8110 for (2999ds/183Mi)
% 1.81/1.37 % (8440)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8110 for (2999ds/2Mi)
% 1.81/1.37 % (8439)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_8110 for (2999ds/27Mi)
% 1.81/1.37 % (8441)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_8110 for (2999ds/2Mi)
% 1.81/1.37 % (8442)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_8110 for (2999ds/275Mi)
% 1.81/1.37 % (8440)Instruction limit reached!
% 1.81/1.37 % (8440)------------------------------
% 1.81/1.37 % (8440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.37 % (8440)Termination reason: Unknown
% 1.81/1.37 % (8440)Termination phase: shuffling
% 1.81/1.37
% 1.81/1.37 % (8440)Memory used [KB]: 1023
% 1.81/1.37 % (8440)Time elapsed: 0.003 s
% 1.81/1.37 % (8440)Instructions burned: 3 (million)
% 1.81/1.37 % (8440)------------------------------
% 1.81/1.37 % (8440)------------------------------
% 1.81/1.37 % (8441)Instruction limit reached!
% 1.81/1.37 % (8441)------------------------------
% 1.81/1.37 % (8441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.37 % (8441)Termination reason: Unknown
% 1.81/1.37 % (8441)Termination phase: shuffling
% 1.81/1.37
% 1.81/1.37 % (8441)Memory used [KB]: 1023
% 1.81/1.37 % (8441)Time elapsed: 0.003 s
% 1.81/1.37 % (8441)Instructions burned: 3 (million)
% 1.81/1.37 % (8441)------------------------------
% 1.81/1.37 % (8441)------------------------------
% 1.81/1.37 % (8444)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_8110 for (2999ds/3Mi)
% 1.81/1.37 % (8444)Instruction limit reached!
% 1.81/1.37 % (8444)------------------------------
% 1.81/1.37 % (8444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.37 % (8444)Termination reason: Unknown
% 1.81/1.37 % (8444)Termination phase: shuffling
% 1.81/1.37
% 1.81/1.37 % (8444)Memory used [KB]: 1023
% 1.81/1.37 % (8444)Time elapsed: 0.002 s
% 1.81/1.37 % (8444)Instructions burned: 3 (million)
% 1.81/1.37 % (8444)------------------------------
% 1.81/1.37 % (8444)------------------------------
% 1.81/1.38 % (8442)Refutation not found, incomplete strategy
% 1.81/1.38 % (8442)------------------------------
% 1.81/1.38 % (8442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.38 % (8442)Termination reason: Refutation not found, incomplete strategy
% 1.81/1.38
% 1.81/1.38
% 1.81/1.38 % (8442)Memory used [KB]: 5500
% 1.81/1.38 % (8442)Time elapsed: 0.007 s
% 1.81/1.38 % (8442)Instructions burned: 9 (million)
% 1.81/1.38 % (8442)------------------------------
% 1.81/1.38 % (8442)------------------------------
% 1.81/1.38 % (8445)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_8110 for (2999ds/37Mi)
% 1.81/1.38 % (8448)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_8110 for (2999ds/1041Mi)
% 1.81/1.39 % (8439)Instruction limit reached!
% 1.81/1.39 % (8439)------------------------------
% 1.81/1.39 % (8439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.39 % (8439)Termination reason: Unknown
% 1.81/1.39 % (8439)Termination phase: Saturation
% 1.81/1.39
% 1.81/1.39 % (8439)Memory used [KB]: 5756
% 1.81/1.39 % (8439)Time elapsed: 0.018 s
% 1.81/1.39 % (8439)Instructions burned: 28 (million)
% 1.81/1.39 % (8439)------------------------------
% 1.81/1.39 % (8439)------------------------------
% 1.81/1.39 % (8446)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_8110 for (2999ds/15Mi)
% 1.81/1.39 % (8447)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_8110 for (2999ds/3Mi)
% 1.81/1.39 % (8445)Instruction limit reached!
% 1.81/1.39 % (8445)------------------------------
% 1.81/1.39 % (8445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.39 % (8445)Termination reason: Unknown
% 1.81/1.39 % (8445)Termination phase: Saturation
% 1.81/1.39
% 1.81/1.39 % (8445)Memory used [KB]: 5756
% 1.81/1.39 % (8445)Time elapsed: 0.013 s
% 1.81/1.39 % (8445)Instructions burned: 37 (million)
% 1.81/1.39 % (8445)------------------------------
% 1.81/1.39 % (8445)------------------------------
% 1.81/1.39 % (8447)Instruction limit reached!
% 1.81/1.39 % (8447)------------------------------
% 1.81/1.39 % (8447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.39 % (8447)Termination reason: Unknown
% 1.81/1.39 % (8447)Termination phase: shuffling
% 1.81/1.39
% 1.81/1.39 % (8447)Memory used [KB]: 1023
% 1.81/1.39 % (8447)Time elapsed: 0.004 s
% 1.81/1.39 % (8447)Instructions burned: 4 (million)
% 1.81/1.39 % (8447)------------------------------
% 1.81/1.39 % (8447)------------------------------
% 1.81/1.39 % (8449)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_8110 for (2999ds/7Mi)
% 1.88/1.40 % (8446)Instruction limit reached!
% 1.88/1.40 % (8446)------------------------------
% 1.88/1.40 % (8446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.40 % (8446)Termination reason: Unknown
% 1.88/1.40 % (8446)Termination phase: Saturation
% 1.88/1.40
% 1.88/1.40 % (8446)Memory used [KB]: 1151
% 1.88/1.40 % (8446)Time elapsed: 0.010 s
% 1.88/1.40 % (8446)Instructions burned: 15 (million)
% 1.88/1.40 % (8446)------------------------------
% 1.88/1.40 % (8446)------------------------------
% 1.88/1.40 % (8449)Instruction limit reached!
% 1.88/1.40 % (8449)------------------------------
% 1.88/1.40 % (8449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.40 % (8449)Termination reason: Unknown
% 1.88/1.40 % (8449)Termination phase: Naming
% 1.88/1.40
% 1.88/1.40 % (8449)Memory used [KB]: 1023
% 1.88/1.40 % (8449)Time elapsed: 0.006 s
% 1.88/1.40 % (8449)Instructions burned: 8 (million)
% 1.88/1.40 % (8449)------------------------------
% 1.88/1.40 % (8449)------------------------------
% 1.88/1.40 % (8451)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_8110 for (2999ds/3Mi)
% 1.88/1.40 % (8451)Instruction limit reached!
% 1.88/1.40 % (8451)------------------------------
% 1.88/1.40 % (8451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.40 % (8451)Termination reason: Unknown
% 1.88/1.40 % (8451)Termination phase: shuffling
% 1.88/1.40
% 1.88/1.40 % (8451)Memory used [KB]: 1023
% 1.88/1.40 % (8451)Time elapsed: 0.003 s
% 1.88/1.40 % (8451)Instructions burned: 4 (million)
% 1.88/1.40 % (8451)------------------------------
% 1.88/1.40 % (8451)------------------------------
% 1.88/1.40 % (8450)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_8110 for (2999ds/16Mi)
% 1.88/1.41 % (8452)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_8110 for (2999ds/3Mi)
% 1.88/1.41 % (8450)Instruction limit reached!
% 1.88/1.41 % (8450)------------------------------
% 1.88/1.41 % (8450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.41 % (8450)Termination reason: Unknown
% 1.88/1.41 % (8450)Termination phase: Saturation
% 1.88/1.41
% 1.88/1.41 % (8450)Memory used [KB]: 5628
% 1.88/1.41 % (8450)Time elapsed: 0.009 s
% 1.88/1.41 % (8450)Instructions burned: 17 (million)
% 1.88/1.41 % (8450)------------------------------
% 1.88/1.41 % (8450)------------------------------
% 1.88/1.41 % (8452)Instruction limit reached!
% 1.88/1.41 % (8452)------------------------------
% 1.88/1.41 % (8452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.41 % (8452)Termination reason: Unknown
% 1.88/1.41 % (8452)Termination phase: shuffling
% 1.88/1.41
% 1.88/1.41 % (8452)Memory used [KB]: 1023
% 1.88/1.41 % (8452)Time elapsed: 0.004 s
% 1.88/1.41 % (8452)Instructions burned: 4 (million)
% 1.88/1.41 % (8452)------------------------------
% 1.88/1.41 % (8452)------------------------------
% 1.88/1.41 % (8455)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_8110 for (2999ds/4Mi)
% 1.88/1.41 % (8455)Instruction limit reached!
% 1.88/1.41 % (8455)------------------------------
% 1.88/1.41 % (8455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.41 % (8455)Termination reason: Unknown
% 1.88/1.41 % (8455)Termination phase: shuffling
% 1.88/1.41
% 1.88/1.41 % (8455)Memory used [KB]: 1023
% 1.88/1.41 % (8455)Time elapsed: 0.003 s
% 1.88/1.41 % (8455)Instructions burned: 4 (million)
% 1.88/1.41 % (8455)------------------------------
% 1.88/1.41 % (8455)------------------------------
% 1.88/1.41 % (8453)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_8110 for (2999ds/7Mi)
% 1.88/1.42 % (8454)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_8110 for (2999ds/3Mi)
% 1.88/1.42 % (8454)Instruction limit reached!
% 1.88/1.42 % (8454)------------------------------
% 1.88/1.42 % (8454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.42 % (8454)Termination reason: Unknown
% 1.88/1.42 % (8454)Termination phase: shuffling
% 1.88/1.42
% 1.88/1.42 % (8454)Memory used [KB]: 1023
% 1.88/1.42 % (8454)Time elapsed: 0.003 s
% 1.88/1.42 % (8454)Instructions burned: 3 (million)
% 1.88/1.42 % (8454)------------------------------
% 1.88/1.42 % (8454)------------------------------
% 1.88/1.42 % (8453)Instruction limit reached!
% 1.88/1.42 % (8453)------------------------------
% 1.88/1.42 % (8453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.42 % (8453)Termination reason: Unknown
% 1.88/1.42 % (8453)Termination phase: Preprocessing 3
% 1.88/1.42
% 1.88/1.42 % (8453)Memory used [KB]: 1023
% 1.88/1.42 % (8453)Time elapsed: 0.006 s
% 1.88/1.42 % (8453)Instructions burned: 8 (million)
% 1.88/1.42 % (8453)------------------------------
% 1.88/1.42 % (8453)------------------------------
% 1.88/1.42 % (8456)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_8110 for (2999ds/18Mi)
% 1.88/1.42 % (8458)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_8110 for (2999ds/6Mi)
% 1.88/1.42 % (8458)Instruction limit reached!
% 1.88/1.42 % (8458)------------------------------
% 1.88/1.42 % (8458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.42 % (8458)Termination reason: Unknown
% 1.88/1.42 % (8458)Termination phase: Preprocessing 3
% 1.88/1.42
% 1.88/1.42 % (8458)Memory used [KB]: 1023
% 1.88/1.42 % (8458)Time elapsed: 0.004 s
% 1.88/1.42 % (8458)Instructions burned: 7 (million)
% 1.88/1.42 % (8458)------------------------------
% 1.88/1.42 % (8458)------------------------------
% 1.88/1.43 % (8456)Instruction limit reached!
% 1.88/1.43 % (8456)------------------------------
% 1.88/1.43 % (8456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.43 % (8456)Termination reason: Unknown
% 1.88/1.43 % (8456)Termination phase: Saturation
% 1.88/1.43
% 1.88/1.43 % (8456)Memory used [KB]: 5628
% 1.88/1.43 % (8456)Time elapsed: 0.008 s
% 1.88/1.43 % (8456)Instructions burned: 20 (million)
% 1.88/1.43 % (8456)------------------------------
% 1.88/1.43 % (8456)------------------------------
% 1.88/1.43 % (8457)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_8110 for (2999ds/710Mi)
% 1.88/1.43 % (8459)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_8110 for (2999ds/902Mi)
% 1.88/1.43 % (8461)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_8110 for (2999ds/5Mi)
% 1.88/1.44 % (8460)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_8110 for (2999ds/21Mi)
% 1.88/1.44 % (8461)Instruction limit reached!
% 1.88/1.44 % (8461)------------------------------
% 1.88/1.44 % (8461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.44 % (8461)Termination reason: Unknown
% 1.88/1.44 % (8461)Termination phase: shuffling
% 1.88/1.44
% 1.88/1.44 % (8461)Memory used [KB]: 1023
% 1.88/1.44 % (8461)Time elapsed: 0.003 s
% 1.88/1.44 % (8461)Instructions burned: 5 (million)
% 1.88/1.44 % (8461)------------------------------
% 1.88/1.44 % (8461)------------------------------
% 1.88/1.44 % (8462)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_8110 for (2999ds/6Mi)
% 1.88/1.44 % (8462)Instruction limit reached!
% 1.88/1.44 % (8462)------------------------------
% 1.88/1.44 % (8462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.44 % (8462)Termination reason: Unknown
% 1.88/1.44 % (8462)Termination phase: Property scanning
% 1.88/1.44
% 1.88/1.44 % (8462)Memory used [KB]: 1023
% 1.88/1.44 % (8462)Time elapsed: 0.004 s
% 1.88/1.44 % (8462)Instructions burned: 8 (million)
% 1.88/1.44 % (8462)------------------------------
% 1.88/1.44 % (8462)------------------------------
% 1.88/1.45 % (8463)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_8110 for (2999ds/377Mi)
% 1.88/1.45 % (8460)Instruction limit reached!
% 1.88/1.45 % (8460)------------------------------
% 1.88/1.45 % (8460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.45 % (8460)Termination reason: Unknown
% 1.88/1.45 % (8460)Termination phase: Saturation
% 1.88/1.45
% 1.88/1.45 % (8460)Memory used [KB]: 5628
% 1.88/1.45 % (8460)Time elapsed: 0.014 s
% 1.88/1.45 % (8460)Instructions burned: 22 (million)
% 1.88/1.45 % (8460)------------------------------
% 1.88/1.45 % (8460)------------------------------
% 1.88/1.45 % (8464)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_8110 for (2999ds/779Mi)
% 1.88/1.46 % (8465)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_8110 for (2999ds/19Mi)
% 1.88/1.47 % (8437)Instruction limit reached!
% 1.88/1.47 % (8437)------------------------------
% 1.88/1.47 % (8437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.47 % (8437)Termination reason: Unknown
% 1.88/1.47 % (8437)Termination phase: Saturation
% 1.88/1.47
% 1.88/1.47 % (8437)Memory used [KB]: 6652
% 1.88/1.47 % (8437)Time elapsed: 0.101 s
% 1.88/1.47 % (8437)Instructions burned: 185 (million)
% 1.88/1.47 % (8437)------------------------------
% 1.88/1.47 % (8437)------------------------------
% 1.88/1.47 % (8465)Refutation not found, incomplete strategy
% 1.88/1.47 % (8465)------------------------------
% 1.88/1.47 % (8465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.47 % (8465)Termination reason: Refutation not found, incomplete strategy
% 1.88/1.47
% 1.88/1.47
% 1.88/1.47 % (8465)Memory used [KB]: 5628
% 1.88/1.47 % (8465)Time elapsed: 0.008 s
% 1.88/1.47 % (8465)Instructions burned: 13 (million)
% 1.88/1.47 % (8465)------------------------------
% 1.88/1.47 % (8465)------------------------------
% 1.88/1.48 % (8466)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_8110 for (2998ds/879Mi)
% 1.88/1.48 % (8467)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_8110 for (2998ds/17Mi)
% 1.88/1.49 % (8467)Instruction limit reached!
% 1.88/1.49 % (8467)------------------------------
% 1.88/1.49 % (8467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.49 % (8467)Termination reason: Unknown
% 1.88/1.49 % (8467)Termination phase: Saturation
% 1.88/1.49
% 1.88/1.49 % (8467)Memory used [KB]: 5628
% 1.88/1.49 % (8467)Time elapsed: 0.007 s
% 1.88/1.49 % (8467)Instructions burned: 17 (million)
% 1.88/1.49 % (8467)------------------------------
% 1.88/1.49 % (8467)------------------------------
% 1.88/1.50 % (8468)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_8110 for (2998ds/3Mi)
% 1.88/1.50 % (8468)Instruction limit reached!
% 1.88/1.50 % (8468)------------------------------
% 1.88/1.50 % (8468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.50 % (8468)Termination reason: Unknown
% 1.88/1.50 % (8468)Termination phase: shuffling
% 1.88/1.50
% 1.88/1.50 % (8468)Memory used [KB]: 1023
% 1.88/1.50 % (8468)Time elapsed: 0.003 s
% 1.88/1.50 % (8468)Instructions burned: 4 (million)
% 1.88/1.50 % (8468)------------------------------
% 1.88/1.50 % (8468)------------------------------
% 1.88/1.51 % (8469)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_8110 for (2998ds/30Mi)
% 1.88/1.52 % (8469)Instruction limit reached!
% 1.88/1.52 % (8469)------------------------------
% 1.88/1.52 % (8469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.52 % (8469)Termination reason: Unknown
% 1.88/1.52 % (8469)Termination phase: Saturation
% 1.88/1.52
% 1.88/1.52 % (8469)Memory used [KB]: 5756
% 1.88/1.52 % (8469)Time elapsed: 0.012 s
% 1.88/1.52 % (8469)Instructions burned: 32 (million)
% 1.88/1.52 % (8469)------------------------------
% 1.88/1.52 % (8469)------------------------------
% 1.88/1.53 % (8470)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_8110 for (2998ds/127Mi)
% 1.88/1.57 % (8470)Instruction limit reached!
% 1.88/1.57 % (8470)------------------------------
% 1.88/1.57 % (8470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.57 % (8470)Termination reason: Unknown
% 1.88/1.57 % (8470)Termination phase: Saturation
% 1.88/1.57
% 1.88/1.57 % (8470)Memory used [KB]: 6268
% 1.88/1.57 % (8470)Time elapsed: 0.065 s
% 1.88/1.57 % (8470)Instructions burned: 127 (million)
% 1.88/1.57 % (8470)------------------------------
% 1.88/1.57 % (8470)------------------------------
% 1.88/1.58 % (8463)Instruction limit reached!
% 1.88/1.58 % (8463)------------------------------
% 1.88/1.58 % (8463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.58 % (8463)Termination reason: Unknown
% 1.88/1.58 % (8463)Termination phase: Saturation
% 1.88/1.58
% 1.88/1.58 % (8463)Memory used [KB]: 6524
% 1.88/1.58 % (8463)Time elapsed: 0.153 s
% 1.88/1.58 % (8463)Instructions burned: 377 (million)
% 1.88/1.58 % (8463)------------------------------
% 1.88/1.58 % (8463)------------------------------
% 1.88/1.58 % (8471)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_8110 for (2997ds/100Mi)
% 1.88/1.59 % (8472)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_8110 for (2997ds/3Mi)
% 1.88/1.59 % (8472)Instruction limit reached!
% 1.88/1.59 % (8472)------------------------------
% 1.88/1.59 % (8472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.59 % (8472)Termination reason: Unknown
% 1.88/1.59 % (8472)Termination phase: shuffling
% 1.88/1.59
% 1.88/1.59 % (8472)Memory used [KB]: 1023
% 1.88/1.59 % (8472)Time elapsed: 0.003 s
% 1.88/1.59 % (8472)Instructions burned: 5 (million)
% 1.88/1.59 % (8472)------------------------------
% 1.88/1.59 % (8472)------------------------------
% 1.88/1.60 % (8473)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_8110 for (2997ds/20Mi)
% 1.88/1.60 % (8473)Instruction limit reached!
% 1.88/1.60 % (8473)------------------------------
% 1.88/1.60 % (8473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.60 % (8473)Termination reason: Unknown
% 1.88/1.60 % (8473)Termination phase: Saturation
% 1.88/1.60
% 1.88/1.60 % (8473)Memory used [KB]: 5628
% 1.88/1.60 % (8473)Time elapsed: 0.035 s
% 1.88/1.60 % (8473)Instructions burned: 22 (million)
% 1.88/1.60 % (8473)------------------------------
% 1.88/1.60 % (8473)------------------------------
% 1.88/1.61 % (8471)Instruction limit reached!
% 1.88/1.61 % (8471)------------------------------
% 1.88/1.61 % (8471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.61 % (8471)Termination reason: Unknown
% 1.88/1.61 % (8471)Termination phase: Saturation
% 1.88/1.61
% 1.88/1.61 % (8471)Memory used [KB]: 6140
% 1.88/1.61 % (8471)Time elapsed: 0.033 s
% 1.88/1.61 % (8471)Instructions burned: 101 (million)
% 1.88/1.61 % (8471)------------------------------
% 1.88/1.61 % (8471)------------------------------
% 1.88/1.61 % (8474)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_8110 for (2997ds/86Mi)
% 1.88/1.62 % (8475)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_8110 for (2997ds/107Mi)
% 1.88/1.64 % (8474)Instruction limit reached!
% 1.88/1.64 % (8474)------------------------------
% 1.88/1.64 % (8474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.64 % (8474)Termination reason: Unknown
% 1.88/1.64 % (8474)Termination phase: Saturation
% 1.88/1.64
% 1.88/1.64 % (8474)Memory used [KB]: 6268
% 1.88/1.64 % (8474)Time elapsed: 0.029 s
% 1.88/1.64 % (8474)Instructions burned: 88 (million)
% 1.88/1.64 % (8474)------------------------------
% 1.88/1.64 % (8474)------------------------------
% 1.88/1.65 % (8476)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_8110 for (2997ds/39Mi)
% 1.88/1.65 % (8475)Instruction limit reached!
% 1.88/1.65 % (8475)------------------------------
% 1.88/1.65 % (8475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.65 % (8475)Termination reason: Unknown
% 1.88/1.65 % (8475)Termination phase: Saturation
% 1.88/1.65
% 1.88/1.65 % (8475)Memory used [KB]: 6140
% 1.88/1.65 % (8475)Time elapsed: 0.037 s
% 1.88/1.65 % (8475)Instructions burned: 107 (million)
% 1.88/1.65 % (8475)------------------------------
% 1.88/1.65 % (8475)------------------------------
% 1.88/1.66 % (8476)Instruction limit reached!
% 1.88/1.66 % (8476)------------------------------
% 1.88/1.66 % (8476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.66 % (8476)Termination reason: Unknown
% 1.88/1.66 % (8476)Termination phase: Saturation
% 1.88/1.66
% 1.88/1.66 % (8476)Memory used [KB]: 5756
% 1.88/1.66 % (8476)Time elapsed: 0.013 s
% 1.88/1.66 % (8476)Instructions burned: 40 (million)
% 1.88/1.66 % (8476)------------------------------
% 1.88/1.66 % (8476)------------------------------
% 1.88/1.66 % (8477)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_8110 for (2996ds/448Mi)
% 1.88/1.67 % (8477)Refutation not found, incomplete strategy
% 1.88/1.67 % (8477)------------------------------
% 1.88/1.67 % (8477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.67 % (8477)Termination reason: Refutation not found, incomplete strategy
% 1.88/1.67
% 1.88/1.67
% 1.88/1.67 % (8477)Memory used [KB]: 5628
% 1.88/1.67 % (8477)Time elapsed: 0.007 s
% 1.88/1.67 % (8477)Instructions burned: 18 (million)
% 1.88/1.67 % (8477)------------------------------
% 1.88/1.67 % (8477)------------------------------
% 1.88/1.67 % (8478)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_8110 for (2996ds/46Mi)
% 1.88/1.68 % (8457)Instruction limit reached!
% 1.88/1.68 % (8457)------------------------------
% 1.88/1.68 % (8457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.68 % (8457)Termination reason: Unknown
% 1.88/1.68 % (8457)Termination phase: Saturation
% 1.88/1.68
% 1.88/1.68 % (8457)Memory used [KB]: 7675
% 1.88/1.68 % (8457)Time elapsed: 0.250 s
% 1.88/1.68 % (8457)Instructions burned: 710 (million)
% 1.88/1.68 % (8457)------------------------------
% 1.88/1.68 % (8457)------------------------------
% 1.88/1.68 % (8479)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_8110 for (2996ds/98Mi)
% 1.88/1.69 % (8478)Instruction limit reached!
% 1.88/1.69 % (8478)------------------------------
% 1.88/1.69 % (8478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.69 % (8478)Termination reason: Unknown
% 1.88/1.69 % (8478)Termination phase: Saturation
% 1.88/1.69
% 1.88/1.69 % (8478)Memory used [KB]: 5756
% 1.88/1.69 % (8478)Time elapsed: 0.015 s
% 1.88/1.69 % (8478)Instructions burned: 47 (million)
% 1.88/1.69 % (8478)------------------------------
% 1.88/1.69 % (8478)------------------------------
% 1.88/1.69 % (8480)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_8110 for (2996ds/507Mi)
% 1.88/1.69 % (8464)Instruction limit reached!
% 1.88/1.69 % (8464)------------------------------
% 1.88/1.69 % (8464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.69 % (8464)Termination reason: Unknown
% 1.88/1.69 % (8464)Termination phase: Saturation
% 1.88/1.69
% 1.88/1.69 % (8464)Memory used [KB]: 7164
% 1.88/1.69 % (8464)Time elapsed: 0.264 s
% 1.88/1.69 % (8464)Instructions burned: 782 (million)
% 1.88/1.69 % (8464)------------------------------
% 1.88/1.69 % (8464)------------------------------
% 1.88/1.69 % (8448)Instruction limit reached!
% 1.88/1.69 % (8448)------------------------------
% 1.88/1.69 % (8448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.69 % (8448)Termination reason: Unknown
% 1.88/1.69 % (8448)Termination phase: Saturation
% 1.88/1.69
% 1.88/1.69 % (8448)Memory used [KB]: 8955
% 1.88/1.69 % (8448)Time elapsed: 0.310 s
% 1.88/1.69 % (8448)Instructions burned: 1043 (million)
% 1.88/1.69 % (8448)------------------------------
% 1.88/1.69 % (8448)------------------------------
% 1.88/1.70 % (8481)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_8110 for (2996ds/149Mi)
% 1.88/1.70 % (8482)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_8110 for (2996ds/39Mi)
% 1.88/1.70 % (8483)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_8110 for (2996ds/6Mi)
% 1.88/1.70 % (8483)Instruction limit reached!
% 1.88/1.70 % (8483)------------------------------
% 1.88/1.70 % (8483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.70 % (8483)Termination reason: Unknown
% 1.88/1.70 % (8483)Termination phase: Property scanning
% 1.88/1.70
% 1.88/1.70 % (8483)Memory used [KB]: 1023
% 1.88/1.70 % (8483)Time elapsed: 0.003 s
% 1.88/1.70 % (8483)Instructions burned: 7 (million)
% 1.88/1.70 % (8483)------------------------------
% 1.88/1.70 % (8483)------------------------------
% 1.88/1.71 % (8482)Instruction limit reached!
% 1.88/1.71 % (8482)------------------------------
% 1.88/1.71 % (8482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.71 % (8482)Termination reason: Unknown
% 1.88/1.71 % (8482)Termination phase: Saturation
% 1.88/1.71
% 1.88/1.71 % (8482)Memory used [KB]: 5756
% 1.88/1.71 % (8482)Time elapsed: 0.014 s
% 1.88/1.71 % (8482)Instructions burned: 40 (million)
% 1.88/1.71 % (8482)------------------------------
% 1.88/1.71 % (8482)------------------------------
% 1.88/1.71 % (8479)Instruction limit reached!
% 1.88/1.71 % (8479)------------------------------
% 1.88/1.71 % (8479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.71 % (8479)Termination reason: Unknown
% 1.88/1.71 % (8479)Termination phase: Saturation
% 1.88/1.71
% 1.88/1.71 % (8479)Memory used [KB]: 1535
% 1.88/1.71 % (8479)Time elapsed: 0.034 s
% 1.88/1.71 % (8479)Instructions burned: 100 (million)
% 1.88/1.71 % (8479)------------------------------
% 1.88/1.71 % (8479)------------------------------
% 1.88/1.71 % (8484)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_8110 for (2996ds/1087Mi)
% 1.88/1.72 % (8485)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_8110 for (2996ds/47Mi)
% 1.88/1.72 % (8486)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_8110 for (2996ds/44Mi)
% 1.88/1.73 % (8486)Refutation not found, incomplete strategy
% 1.88/1.73 % (8486)------------------------------
% 1.88/1.73 % (8486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.73 % (8486)Termination reason: Refutation not found, incomplete strategy
% 1.88/1.73
% 1.88/1.73
% 1.88/1.73 % (8486)Memory used [KB]: 1151
% 1.88/1.73 % (8486)Time elapsed: 0.007 s
% 1.88/1.73 % (8486)Instructions burned: 15 (million)
% 1.88/1.73 % (8486)------------------------------
% 1.88/1.73 % (8486)------------------------------
% 1.88/1.74 % (8485)Instruction limit reached!
% 1.88/1.74 % (8485)------------------------------
% 1.88/1.74 % (8485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.74 % (8485)Termination reason: Unknown
% 1.88/1.74 % (8485)Termination phase: Saturation
% 1.88/1.74
% 1.88/1.74 % (8485)Memory used [KB]: 5884
% 1.88/1.74 % (8485)Time elapsed: 0.017 s
% 1.88/1.74 % (8485)Instructions burned: 47 (million)
% 1.88/1.74 % (8485)------------------------------
% 1.88/1.74 % (8485)------------------------------
% 1.88/1.74 % (8487)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_8110 for (2996ds/432Mi)
% 1.88/1.74 % (8459)Instruction limit reached!
% 1.88/1.74 % (8459)------------------------------
% 1.88/1.74 % (8459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.74 % (8459)Termination reason: Unknown
% 1.88/1.74 % (8459)Termination phase: Saturation
% 1.88/1.74
% 1.88/1.74 % (8459)Memory used [KB]: 6396
% 1.88/1.74 % (8459)Time elapsed: 0.308 s
% 1.88/1.74 % (8459)Instructions burned: 903 (million)
% 1.88/1.74 % (8459)------------------------------
% 1.88/1.74 % (8459)------------------------------
% 1.88/1.74 % (8481)Instruction limit reached!
% 1.88/1.74 % (8481)------------------------------
% 1.88/1.74 % (8481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.74 % (8481)Termination reason: Unknown
% 1.88/1.74 % (8481)Termination phase: Saturation
% 1.88/1.74
% 1.88/1.74 % (8481)Memory used [KB]: 6140
% 1.88/1.74 % (8481)Time elapsed: 0.047 s
% 1.88/1.74 % (8481)Instructions burned: 150 (million)
% 1.88/1.74 % (8481)------------------------------
% 1.88/1.74 % (8481)------------------------------
% 1.88/1.75 % (8488)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_8110 for (2996ds/62Mi)
% 1.88/1.75 % (8489)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_8110 for (2996ds/31Mi)
% 1.88/1.75 % (8490)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_8110 for (2996ds/96Mi)
% 1.88/1.76 % (8489)Instruction limit reached!
% 1.88/1.76 % (8489)------------------------------
% 1.88/1.76 % (8489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.76 % (8489)Termination reason: Unknown
% 1.88/1.76 % (8489)Termination phase: Saturation
% 1.88/1.76
% 1.88/1.76 % (8489)Memory used [KB]: 5756
% 1.88/1.76 % (8489)Time elapsed: 0.012 s
% 1.88/1.76 % (8489)Instructions burned: 33 (million)
% 1.88/1.76 % (8489)------------------------------
% 1.88/1.76 % (8489)------------------------------
% 1.88/1.76 % (8466)Instruction limit reached!
% 1.88/1.76 % (8466)------------------------------
% 1.88/1.76 % (8466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.76 % (8466)Termination reason: Unknown
% 1.88/1.76 % (8466)Termination phase: Saturation
% 1.88/1.76
% 1.88/1.76 % (8466)Memory used [KB]: 7931
% 1.88/1.76 % (8466)Time elapsed: 0.309 s
% 1.88/1.76 % (8466)Instructions burned: 881 (million)
% 1.88/1.76 % (8466)------------------------------
% 1.88/1.76 % (8466)------------------------------
% 1.88/1.77 % (8488)Instruction limit reached!
% 1.88/1.77 % (8488)------------------------------
% 1.88/1.77 % (8488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.77 % (8488)Termination reason: Unknown
% 1.88/1.77 % (8488)Termination phase: Saturation
% 1.88/1.77
% 1.88/1.77 % (8488)Memory used [KB]: 5884
% 1.88/1.77 % (8488)Time elapsed: 0.023 s
% 1.88/1.77 % (8488)Instructions burned: 64 (million)
% 1.88/1.77 % (8488)------------------------------
% 1.88/1.77 % (8488)------------------------------
% 1.88/1.77 % (8491)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_8110 for (2995ds/453Mi)
% 1.88/1.77 % (8492)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_8110 for (2995ds/71Mi)
% 1.88/1.78 % (8484)First to succeed.
% 1.88/1.78 % (8493)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_8110 for (2995ds/83Mi)
% 1.88/1.78 % (8484)Refutation found. Thanks to Tanya!
% 1.88/1.78 % SZS status Theorem for DTF2THF_8110
% 1.88/1.78 % SZS output start Proof for DTF2THF_8110
% 1.88/1.78 thf(type_def_6, type, elem: $tType).
% 1.88/1.78 thf(type_def_7, type, nat: $tType).
% 1.88/1.78 thf(type_def_8, type, list: $tType).
% 1.88/1.78 thf(func_def_0, type, isPer: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 1.88/1.78 thf(func_def_2, type, elem: $tType).
% 1.88/1.78 thf(func_def_3, type, elemStar: elem > elem > $o).
% 1.88/1.78 thf(func_def_4, type, nat: $tType).
% 1.88/1.78 thf(func_def_5, type, natStar: nat > nat > $o).
% 1.88/1.78 thf(func_def_6, type, zero: nat).
% 1.88/1.78 thf(func_def_7, type, suc: nat > nat).
% 1.88/1.78 thf(func_def_8, type, plus: nat > nat > nat).
% 1.88/1.78 thf(func_def_9, type, list: $tType).
% 1.88/1.78 thf(func_def_10, type, listStar: nat > list > list > $o).
% 1.88/1.78 thf(func_def_11, type, nil: list).
% 1.88/1.78 thf(func_def_12, type, cons: nat > elem > list > list).
% 1.88/1.78 thf(func_def_13, type, app: nat > nat > list > list > list).
% 1.88/1.78 thf(func_def_16, type, sP0: nat > nat > list > list > $o).
% 1.88/1.78 thf(func_def_17, type, sK1: nat > nat > list > list > nat).
% 1.88/1.78 thf(func_def_18, type, sK2: nat > nat > list > list > elem).
% 1.88/1.78 thf(func_def_19, type, sK3: nat > nat > list > list > list).
% 1.88/1.78 thf(func_def_20, type, sK4: nat).
% 1.88/1.78 thf(func_def_21, type, sK5: list).
% 1.88/1.78 thf(func_def_22, type, sK6: nat).
% 1.88/1.78 thf(func_def_23, type, sK7: list).
% 1.88/1.78 thf(func_def_24, type, sK8: nat).
% 1.88/1.78 thf(func_def_25, type, sK9: list).
% 1.88/1.78 thf(f241,plain,(
% 1.88/1.78 $false),
% 1.88/1.78 inference(subsumption_resolution,[status(thm)],[f240,f72])).
% 1.88/1.78 thf(f72,plain,(
% 1.88/1.78 ($true = (listStar @ sK8 @ sK9 @ sK9))),
% 1.88/1.78 inference(cnf_transformation,[status(thm)],[f60])).
% 1.88/1.78 thf(f60,plain,(
% 1.88/1.78 ($true != (listStar @ (plus @ (plus @ sK6 @ sK8) @ (plus @ sK6 @ sK8)) @ (app @ sK4 @ (plus @ sK6 @ sK8) @ sK5 @ (app @ sK6 @ sK8 @ sK7 @ sK9)) @ (app @ (plus @ sK4 @ sK6) @ sK8 @ (app @ sK4 @ sK6 @ sK5 @ sK7) @ sK9))) & ($true = (listStar @ sK4 @ sK5 @ sK5)) & ($true = (listStar @ sK8 @ sK9 @ sK9)) & ($true = (listStar @ sK6 @ sK7 @ sK7))),
% 1.88/1.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8,sK9])],[f51,f59])).
% 1.88/1.78 thf(f59,plain,(
% 1.88/1.78 ? [X0 : nat,X1 : list,X2 : nat,X3 : list,X4 : nat,X5 : list] : (($true != (listStar @ (plus @ (plus @ X2 @ X4) @ (plus @ X2 @ X4)) @ (app @ X0 @ (plus @ X2 @ X4) @ X1 @ (app @ X2 @ X4 @ X3 @ X5)) @ (app @ (plus @ X0 @ X2) @ X4 @ (app @ X0 @ X2 @ X1 @ X3) @ X5))) & ($true = (listStar @ X0 @ X1 @ X1)) & ($true = (listStar @ X4 @ X5 @ X5)) & ($true = (listStar @ X2 @ X3 @ X3))) => (($true != (listStar @ (plus @ (plus @ sK6 @ sK8) @ (plus @ sK6 @ sK8)) @ (app @ sK4 @ (plus @ sK6 @ sK8) @ sK5 @ (app @ sK6 @ sK8 @ sK7 @ sK9)) @ (app @ (plus @ sK4 @ sK6) @ sK8 @ (app @ sK4 @ sK6 @ sK5 @ sK7) @ sK9))) & ($true = (listStar @ sK4 @ sK5 @ sK5)) & ($true = (listStar @ sK8 @ sK9 @ sK9)) & ($true = (listStar @ sK6 @ sK7 @ sK7)))),
% 1.88/1.78 introduced(definition,[],[choice_axiom])).
% 1.88/1.78 thf(f51,plain,(
% 1.88/1.78 ? [X0 : nat,X1 : list,X2 : nat,X3 : list,X4 : nat,X5 : list] : (($true != (listStar @ (plus @ (plus @ X2 @ X4) @ (plus @ X2 @ X4)) @ (app @ X0 @ (plus @ X2 @ X4) @ X1 @ (app @ X2 @ X4 @ X3 @ X5)) @ (app @ (plus @ X0 @ X2) @ X4 @ (app @ X0 @ X2 @ X1 @ X3) @ X5))) & ($true = (listStar @ X0 @ X1 @ X1)) & ($true = (listStar @ X4 @ X5 @ X5)) & ($true = (listStar @ X2 @ X3 @ X3)))),
% 1.88/1.78 inference(flattening,[status(thm)],[f50])).
% 1.88/1.78 thf(f50,plain,(
% 1.88/1.78 ? [X0 : nat,X1 : list,X2 : nat,X3 : list,X4 : nat,X5 : list] : (((($true != (listStar @ (plus @ (plus @ X2 @ X4) @ (plus @ X2 @ X4)) @ (app @ X0 @ (plus @ X2 @ X4) @ X1 @ (app @ X2 @ X4 @ X3 @ X5)) @ (app @ (plus @ X0 @ X2) @ X4 @ (app @ X0 @ X2 @ X1 @ X3) @ X5))) & ($true = (listStar @ X4 @ X5 @ X5))) & ($true = (listStar @ X2 @ X3 @ X3))) & ($true = (listStar @ X0 @ X1 @ X1)))),
% 1.88/1.78 inference(ennf_transformation,[status(thm)],[f22])).
% 1.88/1.78 thf(f22,plain,(
% 1.88/1.78 ~! [X0 : nat,X1 : list,X2 : nat,X3 : list,X4 : nat,X5 : list] : (($true = (listStar @ X0 @ X1 @ X1)) => (($true = (listStar @ X2 @ X3 @ X3)) => (($true = (listStar @ X4 @ X5 @ X5)) => ($true = (listStar @ (plus @ (plus @ X2 @ X4) @ (plus @ X2 @ X4)) @ (app @ X0 @ (plus @ X2 @ X4) @ X1 @ (app @ X2 @ X4 @ X3 @ X5)) @ (app @ (plus @ X0 @ X2) @ X4 @ (app @ X0 @ X2 @ X1 @ X3) @ X5))))))),
% 1.88/1.78 inference(fool_elimination,[status(thm)],[f21])).
% 1.88/1.78 thf(f21,plain,(
% 1.88/1.78 ~! [X0 : nat,X1 : list,X2 : nat,X3 : list,X4 : nat,X5 : list] : ((listStar @ X0 @ X1 @ X1) => ((listStar @ X2 @ X3 @ X3) => ((listStar @ X4 @ X5 @ X5) => (listStar @ (plus @ (plus @ X2 @ X4) @ (plus @ X2 @ X4)) @ (app @ X0 @ (plus @ X2 @ X4) @ X1 @ (app @ X2 @ X4 @ X3 @ X5)) @ (app @ (plus @ X0 @ X2) @ X4 @ (app @ X0 @ X2 @ X1 @ X3) @ X5)))))),
% 1.88/1.78 inference(rectify,[status(thm)],[f15])).
% 1.88/1.78 thf(f15,negated_conjecture,(
% 1.88/1.78 ~! [X10 : nat,X17 : list,X13 : nat,X15 : list,X14 : nat,X16 : list] : ((listStar @ X10 @ X17 @ X17) => ((listStar @ X13 @ X15 @ X15) => ((listStar @ X14 @ X16 @ X16) => (listStar @ (plus @ (plus @ X13 @ X14) @ (plus @ X13 @ X14)) @ (app @ X10 @ (plus @ X13 @ X14) @ X17 @ (app @ X13 @ X14 @ X15 @ X16)) @ (app @ (plus @ X10 @ X13) @ X14 @ (app @ X10 @ X13 @ X17 @ X15) @ X16)))))),
% 1.88/1.78 inference(negated_conjecture,[status(cth)],[f14])).
% 1.88/1.78 thf(f14,conjecture,(
% 1.88/1.78 ! [X10 : nat,X17 : list,X13 : nat,X15 : list,X14 : nat,X16 : list] : ((listStar @ X10 @ X17 @ X17) => ((listStar @ X13 @ X15 @ X15) => ((listStar @ X14 @ X16 @ X16) => (listStar @ (plus @ (plus @ X13 @ X14) @ (plus @ X13 @ X14)) @ (app @ X10 @ (plus @ X13 @ X14) @ X17 @ (app @ X13 @ X14 @ X15 @ X16)) @ (app @ (plus @ X10 @ X13) @ X14 @ (app @ X10 @ X13 @ X17 @ X15) @ X16)))))),
% 1.88/1.78 file('/export/starexec/sandbox/tmp/tmp.MXj1wRhtZr/DTF2THF_8110.p',list_app_assoc)).
% 1.88/1.78 thf(f240,plain,(
% 1.88/1.78 ($true != (listStar @ sK8 @ sK9 @ sK9))),
% 1.88/1.78 inference(subsumption_resolution,[status(thm)],[f239,f71])).
% 1.88/1.78 thf(f71,plain,(
% 1.88/1.78 ($true = (listStar @ sK6 @ sK7 @ sK7))),
% 1.88/1.78 inference(cnf_transformation,[status(thm)],[f60])).
% 1.88/1.78 thf(f239,plain,(
% 1.88/1.78 ($true != (listStar @ sK6 @ sK7 @ sK7)) | ($true != (listStar @ sK8 @ sK9 @ sK9))),
% 1.88/1.78 inference(trivial_inequality_removal,[status(thm)],[f238])).
% 1.88/1.78 thf(f238,plain,(
% 1.88/1.78 ($true != (listStar @ sK6 @ sK7 @ sK7)) | ($true != (listStar @ sK8 @ sK9 @ sK9)) | ($true != $true)),
% 1.88/1.78 inference(superposition,[status(thm)],[f237,f156])).
% 1.88/1.78 thf(f156,plain,(
% 1.88/1.78 ($true = (sP0 @ sK8 @ sK6 @ sK7 @ sK9))),
% 1.88/1.78 inference(subsumption_resolution,[status(thm)],[f155,f73])).
% 1.88/1.78 thf(f73,plain,(
% 1.88/1.78 ($true = (listStar @ sK4 @ sK5 @ sK5))),
% 1.88/1.78 inference(cnf_transformation,[status(thm)],[f60])).
% 1.88/1.78 thf(f155,plain,(
% 1.88/1.78 ($true != (listStar @ sK4 @ sK5 @ sK5)) | ($true = (sP0 @ sK8 @ sK6 @ sK7 @ sK9))),
% 1.88/1.78 inference(subsumption_resolution,[status(thm)],[f154,f72])).
% 1.88/1.78 thf(f154,plain,(
% 1.88/1.78 ($true != (listStar @ sK8 @ sK9 @ sK9)) | ($true != (listStar @ sK4 @ sK5 @ sK5)) | ($true = (sP0 @ sK8 @ sK6 @ sK7 @ sK9))),
% 1.88/1.78 inference(subsumption_resolution,[status(thm)],[f150,f71])).
% 1.88/1.78 thf(f150,plain,(
% 1.88/1.78 ($true != (listStar @ sK6 @ sK7 @ sK7)) | ($true != (listStar @ sK8 @ sK9 @ sK9)) | ($true = (sP0 @ sK8 @ sK6 @ sK7 @ sK9)) | ($true != (listStar @ sK4 @ sK5 @ sK5))),
% 1.88/1.78 inference(trivial_inequality_removal,[status(thm)],[f149])).
% 1.88/1.78 thf(f149,plain,(
% 1.88/1.78 ($true = (sP0 @ sK8 @ sK6 @ sK7 @ sK9)) | ($true != (listStar @ sK4 @ sK5 @ sK5)) | ($true != $true) | ($true != (listStar @ sK8 @ sK9 @ sK9)) | ($true != (listStar @ sK6 @ sK7 @ sK7))),
% 1.88/1.78 inference(superposition,[status(thm)],[f77,f118])).
% 1.88/1.78 thf(f118,plain,(
% 1.88/1.78 ( ! [X2 : nat,X3 : list,X0 : nat,X1 : list,X4 : nat,X5 : list] : (($true = (listStar @ (plus @ X0 @ (plus @ X2 @ (plus @ X0 @ X2))) @ (app @ X4 @ (plus @ X0 @ X2) @ X5 @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ X4 @ X0) @ X2 @ (app @ X4 @ X0 @ X5 @ X1) @ X3))) | ($true = (sP0 @ X2 @ X0 @ X1 @ X3)) | ($true != (listStar @ X2 @ X3 @ X3)) | ($true != (listStar @ X0 @ X1 @ X1)) | ($true != (listStar @ X4 @ X5 @ X5))) )),
% 1.88/1.78 inference(subsumption_resolution,[status(thm)],[f117,f89])).
% 1.88/1.78 thf(f89,plain,(
% 1.88/1.78 ( ! [X2 : nat,X3 : list,X0 : nat,X1 : list] : (($true = (listStar @ (plus @ X0 @ X2) @ (app @ zero @ (plus @ X0 @ X2) @ nil @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ X0 @ X2 @ (app @ zero @ X0 @ nil @ X1) @ X3))) | ($true != (listStar @ X0 @ X1 @ X1)) | ($true != (listStar @ X2 @ X3 @ X3))) )),
% 1.88/1.78 inference(forward_demodulation,[status(thm)],[f88,f61])).
% 1.88/1.78 thf(f61,plain,(
% 1.88/1.78 ( ! [X0 : nat] : (((plus @ zero @ X0) = X0)) )),
% 1.88/1.78 inference(cnf_transformation,[status(thm)],[f41])).
% 1.88/1.78 thf(f41,plain,(
% 1.88/1.78 ! [X0 : nat] : ((plus @ zero @ X0) = X0)),
% 1.88/1.78 inference(rectify,[status(thm)],[f8])).
% 1.88/1.78 thf(f8,axiom,(
% 1.88/1.78 ! [X6 : nat] : ((plus @ zero @ X6) = X6)),
% 1.88/1.78 file('/export/starexec/sandbox/tmp/tmp.MXj1wRhtZr/DTF2THF_8110.p',ax1)).
% 1.88/1.78 thf(f88,plain,(
% 1.88/1.78 ( ! [X2 : nat,X3 : list,X0 : nat,X1 : list] : (($true != (listStar @ X0 @ X1 @ X1)) | ($true = (listStar @ (plus @ X0 @ X2) @ (app @ zero @ (plus @ X0 @ X2) @ nil @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ zero @ X0) @ X2 @ (app @ zero @ X0 @ nil @ X1) @ X3))) | ($true != (listStar @ X2 @ X3 @ X3))) )),
% 1.88/1.78 inference(forward_demodulation,[status(thm)],[f63,f61])).
% 1.88/1.78 thf(f63,plain,(
% 1.88/1.78 ( ! [X2 : nat,X3 : list,X0 : nat,X1 : list] : (($true = (listStar @ (plus @ zero @ (plus @ X0 @ X2)) @ (app @ zero @ (plus @ X0 @ X2) @ nil @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ zero @ X0) @ X2 @ (app @ zero @ X0 @ nil @ X1) @ X3))) | ($true != (listStar @ X0 @ X1 @ X1)) | ($true != (listStar @ X2 @ X3 @ X3))) )),
% 1.88/1.78 inference(cnf_transformation,[status(thm)],[f49])).
% 1.88/1.78 thf(f49,plain,(
% 1.88/1.78 ! [X0 : nat,X1 : list,X2 : nat,X3 : list] : (($true != (listStar @ X2 @ X3 @ X3)) | ($true != (listStar @ X0 @ X1 @ X1)) | ($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))))),
% 1.88/1.78 inference(flattening,[status(thm)],[f48])).
% 1.88/1.78 thf(f48,plain,(
% 1.88/1.78 ! [X0 : nat,X1 : list,X2 : nat,X3 : list] : ((($true = (listStar @ (plus @ zero @ (plus @ X0 @ X2)) @ (app @ zero @ (plus @ X0 @ X2) @ nil @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ zero @ X0) @ X2 @ (app @ zero @ X0 @ nil @ X1) @ X3))) | ($true != (listStar @ X2 @ X3 @ X3))) | ($true != (listStar @ X0 @ X1 @ X1)))),
% 1.88/1.78 inference(ennf_transformation,[status(thm)],[f24])).
% 1.88/1.78 thf(f24,plain,(
% 1.88/1.78 ! [X0 : nat,X1 : list,X2 : nat,X3 : list] : (($true = (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)))))),
% 1.88/1.78 inference(fool_elimination,[status(thm)],[f23])).
% 1.88/1.78 thf(f23,plain,(
% 1.88/1.78 ! [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))))),
% 1.88/1.78 inference(rectify,[status(thm)],[f12])).
% 1.88/1.78 thf(f12,axiom,(
% 1.88/1.78 ! [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))))),
% 1.88/1.78 file('/export/starexec/sandbox/tmp/tmp.MXj1wRhtZr/DTF2THF_8110.p',list_app_assoc_base)).
% 1.88/1.78 thf(f117,plain,(
% 1.88/1.78 ( ! [X2 : nat,X3 : list,X0 : nat,X1 : list,X4 : nat,X5 : list] : (($true != (listStar @ X4 @ X5 @ X5)) | ($true = (listStar @ (plus @ X0 @ (plus @ X2 @ (plus @ X0 @ X2))) @ (app @ X4 @ (plus @ X0 @ X2) @ X5 @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ X4 @ X0) @ X2 @ (app @ X4 @ X0 @ X5 @ X1) @ X3))) | ($true = (sP0 @ X2 @ X0 @ X1 @ X3)) | ($true != (listStar @ X2 @ X3 @ X3)) | ($true != (listStar @ (plus @ X0 @ X2) @ (app @ zero @ (plus @ X0 @ X2) @ nil @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ X0 @ X2 @ (app @ zero @ X0 @ nil @ X1) @ X3))) | ($true != (listStar @ X0 @ X1 @ X1))) )),
% 1.88/1.78 inference(forward_demodulation,[status(thm)],[f116,f61])).
% 1.88/1.78 thf(f116,plain,(
% 1.88/1.78 ( ! [X2 : nat,X3 : list,X0 : nat,X1 : list,X4 : nat,X5 : list] : (($true = (sP0 @ X2 @ X0 @ X1 @ X3)) | ($true != (listStar @ X2 @ X3 @ X3)) | ($true != (listStar @ (plus @ X0 @ X2) @ (app @ zero @ (plus @ X0 @ X2) @ nil @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ zero @ X0) @ X2 @ (app @ zero @ X0 @ nil @ X1) @ X3))) | ($true != (listStar @ X0 @ X1 @ X1)) | ($true != (listStar @ X4 @ X5 @ X5)) | ($true = (listStar @ (plus @ X0 @ (plus @ X2 @ (plus @ X0 @ X2))) @ (app @ X4 @ (plus @ X0 @ X2) @ X5 @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ X4 @ X0) @ X2 @ (app @ X4 @ X0 @ X5 @ X1) @ X3)))) )),
% 1.88/1.78 inference(forward_demodulation,[status(thm)],[f115,f68])).
% 1.88/1.78 thf(f68,plain,(
% 1.88/1.78 ( ! [X2 : nat,X0 : nat,X1 : nat] : (((plus @ X0 @ (plus @ X1 @ X2)) = (plus @ (plus @ X0 @ X1) @ X2))) )),
% 1.88/1.78 inference(cnf_transformation,[status(thm)],[f39])).
% 1.88/1.78 thf(f39,plain,(
% 1.88/1.78 ! [X0 : nat,X1 : nat,X2 : nat] : ((plus @ X0 @ (plus @ X1 @ X2)) = (plus @ (plus @ X0 @ X1) @ X2))),
% 1.88/1.78 inference(rectify,[status(thm)],[f10])).
% 1.88/1.78 thf(f10,axiom,(
% 1.88/1.78 ! [X12 : nat,X13 : nat,X14 : nat] : ((plus @ X12 @ (plus @ X13 @ X14)) = (plus @ (plus @ X12 @ X13) @ X14))),
% 1.88/1.78 file('/export/starexec/sandbox/tmp/tmp.MXj1wRhtZr/DTF2THF_8110.p',plus_assoc)).
% 1.88/1.78 thf(f115,plain,(
% 1.88/1.78 ( ! [X2 : nat,X3 : list,X0 : nat,X1 : list,X4 : nat,X5 : list] : (($true = (listStar @ (plus @ (plus @ X0 @ X2) @ (plus @ X0 @ X2)) @ (app @ X4 @ (plus @ X0 @ X2) @ X5 @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ X4 @ X0) @ X2 @ (app @ X4 @ X0 @ X5 @ X1) @ X3))) | ($true != (listStar @ (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))) | ($true = (sP0 @ X2 @ X0 @ X1 @ X3)) | ($true != (listStar @ X2 @ X3 @ X3)) | ($true != (listStar @ X0 @ X1 @ X1)) | ($true != (listStar @ X4 @ X5 @ X5))) )),
% 1.88/1.78 inference(forward_demodulation,[status(thm)],[f67,f61])).
% 1.88/1.78 thf(f67,plain,(
% 1.88/1.78 ( ! [X2 : nat,X3 : list,X0 : nat,X1 : list,X4 : nat,X5 : list] : (($true != (listStar @ X2 @ X3 @ X3)) | ($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))) | ($true = (sP0 @ X2 @ X0 @ X1 @ X3)) | ($true != (listStar @ X4 @ X5 @ X5)) | ($true = (listStar @ (plus @ (plus @ X0 @ X2) @ (plus @ X0 @ X2)) @ (app @ X4 @ (plus @ X0 @ X2) @ X5 @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ X4 @ X0) @ X2 @ (app @ X4 @ X0 @ X5 @ X1) @ X3))) | ($true != (listStar @ X0 @ X1 @ X1))) )),
% 1.88/1.78 inference(cnf_transformation,[status(thm)],[f58])).
% 1.88/1.78 thf(f58,plain,(
% 1.88/1.78 ! [X0 : nat,X1 : list,X2 : nat,X3 : list] : (! [X4 : nat,X5 : list] : (($true != (listStar @ X4 @ X5 @ X5)) | ($true = (listStar @ (plus @ (plus @ X0 @ X2) @ (plus @ X0 @ X2)) @ (app @ X4 @ (plus @ X0 @ X2) @ X5 @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ X4 @ X0) @ X2 @ (app @ X4 @ X0 @ X5 @ X1) @ X3)))) | ($true = (sP0 @ X2 @ X0 @ X1 @ X3)) | ($true != (listStar @ X2 @ X3 @ X3)) | ($true != (listStar @ X0 @ X1 @ X1)) | ($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))))),
% 1.88/1.78 inference(rectify,[status(thm)],[f53])).
% 1.88/1.78 thf(f53,plain,(
% 1.88/1.78 ! [X0 : nat,X1 : list,X2 : nat,X3 : list] : (! [X7 : nat,X8 : list] : (($true != (listStar @ X7 @ X8 @ X8)) | ($true = (listStar @ (plus @ (plus @ X0 @ X2) @ (plus @ X0 @ X2)) @ (app @ X7 @ (plus @ X0 @ X2) @ X8 @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ X7 @ X0) @ X2 @ (app @ X7 @ X0 @ X8 @ X1) @ X3)))) | ($true = (sP0 @ X2 @ X0 @ X1 @ X3)) | ($true != (listStar @ X2 @ X3 @ X3)) | ($true != (listStar @ X0 @ X1 @ X1)) | ($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))))),
% 1.88/1.78 inference(definition_folding,[status(thm)],[f44,f52])).
% 1.88/1.78 thf(f52,plain,(
% 1.88/1.78 ! [X3 : list,X1 : list,X0 : nat,X2 : nat] : (? [X4 : nat,X5 : elem,X6 : list] : (($true = (listStar @ (plus @ (plus @ X0 @ X2) @ (plus @ X0 @ X2)) @ (app @ X4 @ (plus @ X0 @ X2) @ X6 @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ X4 @ X0) @ X2 @ (app @ X4 @ X0 @ X6 @ X1) @ X3))) & ($true = (listStar @ X4 @ X6 @ X6)) & ($true != (listStar @ (plus @ (suc @ (plus @ X0 @ X2)) @ (plus @ X0 @ X2)) @ (app @ (suc @ X4) @ (plus @ X0 @ X2) @ (cons @ X4 @ X5 @ X6) @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ (suc @ X4) @ X0) @ X2 @ (app @ (suc @ X4) @ X0 @ (cons @ X4 @ X5 @ X6) @ X1) @ X3)))) | ~($true = (sP0 @ X2 @ X0 @ X1 @ X3)))),
% 1.88/1.78 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.88/1.78 thf(f44,plain,(
% 1.88/1.78 ! [X0 : nat,X1 : list,X2 : nat,X3 : list] : (! [X7 : nat,X8 : list] : (($true != (listStar @ X7 @ X8 @ X8)) | ($true = (listStar @ (plus @ (plus @ X0 @ X2) @ (plus @ X0 @ X2)) @ (app @ X7 @ (plus @ X0 @ X2) @ X8 @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ X7 @ X0) @ X2 @ (app @ X7 @ X0 @ X8 @ X1) @ X3)))) | ? [X4 : nat,X5 : elem,X6 : list] : (($true = (listStar @ (plus @ (plus @ X0 @ X2) @ (plus @ X0 @ X2)) @ (app @ X4 @ (plus @ X0 @ X2) @ X6 @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ X4 @ X0) @ X2 @ (app @ X4 @ X0 @ X6 @ X1) @ X3))) & ($true = (listStar @ X4 @ X6 @ X6)) & ($true != (listStar @ (plus @ (suc @ (plus @ X0 @ X2)) @ (plus @ X0 @ X2)) @ (app @ (suc @ X4) @ (plus @ X0 @ X2) @ (cons @ X4 @ X5 @ X6) @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ (suc @ X4) @ X0) @ X2 @ (app @ (suc @ X4) @ X0 @ (cons @ X4 @ X5 @ X6) @ X1) @ X3)))) | ($true != (listStar @ X2 @ X3 @ X3)) | ($true != (listStar @ X0 @ X1 @ X1)) | ($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))))),
% 1.88/1.78 inference(flattening,[status(thm)],[f43])).
% 1.88/1.78 thf(f43,plain,(
% 1.88/1.78 ! [X0 : nat,X1 : list,X2 : nat,X3 : list] : ((((! [X7 : nat,X8 : list] : (($true != (listStar @ X7 @ X8 @ X8)) | ($true = (listStar @ (plus @ (plus @ X0 @ X2) @ (plus @ X0 @ X2)) @ (app @ X7 @ (plus @ X0 @ X2) @ X8 @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ X7 @ X0) @ X2 @ (app @ X7 @ X0 @ X8 @ X1) @ X3)))) | ? [X4 : nat,X5 : elem,X6 : list] : ((($true != (listStar @ (plus @ (suc @ (plus @ X0 @ X2)) @ (plus @ X0 @ X2)) @ (app @ (suc @ X4) @ (plus @ X0 @ X2) @ (cons @ X4 @ X5 @ X6) @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ (suc @ X4) @ X0) @ X2 @ (app @ (suc @ X4) @ X0 @ (cons @ X4 @ X5 @ X6) @ X1) @ X3))) & ($true = (listStar @ (plus @ (plus @ X0 @ X2) @ (plus @ X0 @ X2)) @ (app @ X4 @ (plus @ X0 @ X2) @ X6 @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ X4 @ X0) @ X2 @ (app @ X4 @ X0 @ X6 @ X1) @ X3)))) & ($true = (listStar @ X4 @ X6 @ X6)))) | ($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)))) | ($true != (listStar @ X2 @ X3 @ X3))) | ($true != (listStar @ X0 @ X1 @ X1)))),
% 1.88/1.78 inference(ennf_transformation,[status(thm)],[f18])).
% 1.88/1.78 thf(f18,plain,(
% 1.88/1.78 ! [X0 : nat,X1 : list,X2 : nat,X3 : list] : (($true = (listStar @ X0 @ X1 @ X1)) => (($true = (listStar @ X2 @ X3 @ X3)) => (($true = (listStar @ (plus @ zero @ (plus @ X0 @ X2)) @ (app @ zero @ (plus @ X0 @ X2) @ nil @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ zero @ X0) @ X2 @ (app @ zero @ X0 @ nil @ X1) @ X3))) => (! [X4 : nat,X5 : elem,X6 : list] : (($true = (listStar @ X4 @ X6 @ X6)) => (($true = (listStar @ (plus @ (plus @ X0 @ X2) @ (plus @ X0 @ X2)) @ (app @ X4 @ (plus @ X0 @ X2) @ X6 @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ X4 @ X0) @ X2 @ (app @ X4 @ X0 @ X6 @ X1) @ X3))) => ($true = (listStar @ (plus @ (suc @ (plus @ X0 @ X2)) @ (plus @ X0 @ X2)) @ (app @ (suc @ X4) @ (plus @ X0 @ X2) @ (cons @ X4 @ X5 @ X6) @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ (suc @ X4) @ X0) @ X2 @ (app @ (suc @ X4) @ X0 @ (cons @ X4 @ X5 @ X6) @ X1) @ X3))))) => ! [X7 : nat,X8 : list] : (($true = (listStar @ X7 @ X8 @ X8)) => ($true = (listStar @ (plus @ (plus @ X0 @ X2) @ (plus @ X0 @ X2)) @ (app @ X7 @ (plus @ X0 @ X2) @ X8 @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ X7 @ X0) @ X2 @ (app @ X7 @ X0 @ X8 @ X1) @ X3))))))))),
% 1.88/1.78 inference(fool_elimination,[status(thm)],[f17])).
% 1.88/1.78 thf(f17,plain,(
% 1.88/1.78 ! [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)) => (! [X4 : nat,X5 : elem,X6 : list] : ((listStar @ X4 @ X6 @ X6) => ((listStar @ (plus @ (plus @ X0 @ X2) @ (plus @ X0 @ X2)) @ (app @ X4 @ (plus @ X0 @ X2) @ X6 @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ X4 @ X0) @ X2 @ (app @ X4 @ X0 @ X6 @ X1) @ X3)) => (listStar @ (plus @ (suc @ (plus @ X0 @ X2)) @ (plus @ X0 @ X2)) @ (app @ (suc @ X4) @ (plus @ X0 @ X2) @ (cons @ X4 @ X5 @ X6) @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ (suc @ X4) @ X0) @ X2 @ (app @ (suc @ X4) @ X0 @ (cons @ X4 @ X5 @ X6) @ X1) @ X3)))) => ! [X7 : nat,X8 : list] : ((listStar @ X7 @ X8 @ X8) => (listStar @ (plus @ (plus @ X0 @ X2) @ (plus @ X0 @ X2)) @ (app @ X7 @ (plus @ X0 @ X2) @ X8 @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ X7 @ X0) @ X2 @ (app @ X7 @ X0 @ X8 @ X1) @ X3)))))))),
% 1.88/1.78 inference(rectify,[status(thm)],[f11])).
% 1.88/1.78 thf(f11,axiom,(
% 1.88/1.78 ! [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)) => (! [X10 : nat,X2 : elem,X17 : list] : ((listStar @ X10 @ X17 @ X17) => ((listStar @ (plus @ (plus @ X13 @ X14) @ (plus @ X13 @ X14)) @ (app @ X10 @ (plus @ X13 @ X14) @ X17 @ (app @ X13 @ X14 @ X15 @ X16)) @ (app @ (plus @ X10 @ X13) @ X14 @ (app @ X10 @ X13 @ X17 @ X15) @ X16)) => (listStar @ (plus @ (suc @ (plus @ X13 @ X14)) @ (plus @ X13 @ X14)) @ (app @ (suc @ X10) @ (plus @ X13 @ X14) @ (cons @ X10 @ X2 @ X17) @ (app @ X13 @ X14 @ X15 @ X16)) @ (app @ (plus @ (suc @ X10) @ X13) @ X14 @ (app @ (suc @ X10) @ X13 @ (cons @ X10 @ X2 @ X17) @ X15) @ X16)))) => ! [X10 : nat,X17 : list] : ((listStar @ X10 @ X17 @ X17) => (listStar @ (plus @ (plus @ X13 @ X14) @ (plus @ X13 @ X14)) @ (app @ X10 @ (plus @ X13 @ X14) @ X17 @ (app @ X13 @ X14 @ X15 @ X16)) @ (app @ (plus @ X10 @ X13) @ X14 @ (app @ X10 @ X13 @ X17 @ X15) @ X16)))))))),
% 1.88/1.78 file('/export/starexec/sandbox/tmp/tmp.MXj1wRhtZr/DTF2THF_8110.p',list_app_assoc_indinst)).
% 1.88/1.78 thf(f77,plain,(
% 1.88/1.78 ($true != (listStar @ (plus @ sK6 @ (plus @ sK8 @ (plus @ sK6 @ sK8))) @ (app @ sK4 @ (plus @ sK6 @ sK8) @ sK5 @ (app @ sK6 @ sK8 @ sK7 @ sK9)) @ (app @ (plus @ sK4 @ sK6) @ sK8 @ (app @ sK4 @ sK6 @ sK5 @ sK7) @ sK9)))),
% 1.88/1.78 inference(backward_demodulation,[status(thm)],[f74,f68])).
% 1.88/1.78 thf(f74,plain,(
% 1.88/1.78 ($true != (listStar @ (plus @ (plus @ sK6 @ sK8) @ (plus @ sK6 @ sK8)) @ (app @ sK4 @ (plus @ sK6 @ sK8) @ sK5 @ (app @ sK6 @ sK8 @ sK7 @ sK9)) @ (app @ (plus @ sK4 @ sK6) @ sK8 @ (app @ sK4 @ sK6 @ sK5 @ sK7) @ sK9)))),
% 1.88/1.78 inference(cnf_transformation,[status(thm)],[f60])).
% 1.88/1.78 thf(f237,plain,(
% 1.88/1.78 ( ! [X2 : list,X3 : list,X0 : nat,X1 : nat] : (($true != (sP0 @ X1 @ X0 @ X2 @ X3)) | ($true != (listStar @ X0 @ X2 @ X2)) | ($true != (listStar @ X1 @ X3 @ X3))) )),
% 1.88/1.78 inference(subsumption_resolution,[status(thm)],[f236,f96])).
% 1.88/1.78 thf(f96,plain,(
% 1.88/1.78 ( ! [X2 : nat,X3 : nat,X0 : list,X1 : list] : (($true = (listStar @ (plus @ X2 @ (plus @ X3 @ (plus @ X2 @ X3))) @ (app @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (plus @ X2 @ X3) @ (sK3 @ X3 @ X2 @ X1 @ X0) @ (app @ X2 @ X3 @ X1 @ X0)) @ (app @ (plus @ (sK1 @ X3 @ X2 @ X1 @ X0) @ X2) @ X3 @ (app @ (sK1 @ X3 @ X2 @ X1 @ X0) @ X2 @ (sK3 @ X3 @ X2 @ X1 @ X0) @ X1) @ X0))) | ($true != (sP0 @ X3 @ X2 @ X1 @ X0))) )),
% 1.88/1.78 inference(forward_demodulation,[status(thm)],[f66,f68])).
% 1.88/1.78 thf(f66,plain,(
% 1.88/1.78 ( ! [X2 : nat,X3 : nat,X0 : list,X1 : list] : (($true != (sP0 @ X3 @ X2 @ X1 @ X0)) | ($true = (listStar @ (plus @ (plus @ X2 @ X3) @ (plus @ X2 @ X3)) @ (app @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (plus @ X2 @ X3) @ (sK3 @ X3 @ X2 @ X1 @ X0) @ (app @ X2 @ X3 @ X1 @ X0)) @ (app @ (plus @ (sK1 @ X3 @ X2 @ X1 @ X0) @ X2) @ X3 @ (app @ (sK1 @ X3 @ X2 @ X1 @ X0) @ X2 @ (sK3 @ X3 @ X2 @ X1 @ X0) @ X1) @ X0)))) )),
% 1.88/1.78 inference(cnf_transformation,[status(thm)],[f57])).
% 1.88/1.78 thf(f57,plain,(
% 1.88/1.78 ! [X0 : list,X1 : list,X2 : nat,X3 : nat] : ((($true = (listStar @ (plus @ (plus @ X2 @ X3) @ (plus @ X2 @ X3)) @ (app @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (plus @ X2 @ X3) @ (sK3 @ X3 @ X2 @ X1 @ X0) @ (app @ X2 @ X3 @ X1 @ X0)) @ (app @ (plus @ (sK1 @ X3 @ X2 @ X1 @ X0) @ X2) @ X3 @ (app @ (sK1 @ X3 @ X2 @ X1 @ X0) @ X2 @ (sK3 @ X3 @ X2 @ X1 @ X0) @ X1) @ X0))) & ($true = (listStar @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (sK3 @ X3 @ X2 @ X1 @ X0) @ (sK3 @ X3 @ X2 @ X1 @ X0))) & ($true != (listStar @ (plus @ (suc @ (plus @ X2 @ X3)) @ (plus @ X2 @ X3)) @ (app @ (suc @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ (plus @ X2 @ X3) @ (cons @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (sK2 @ X3 @ X2 @ X1 @ X0) @ (sK3 @ X3 @ X2 @ X1 @ X0)) @ (app @ X2 @ X3 @ X1 @ X0)) @ (app @ (plus @ (suc @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ X2) @ X3 @ (app @ (suc @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ X2 @ (cons @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (sK2 @ X3 @ X2 @ X1 @ X0) @ (sK3 @ X3 @ X2 @ X1 @ X0)) @ X1) @ X0)))) | ($true != (sP0 @ X3 @ X2 @ X1 @ X0)))),
% 1.88/1.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f55,f56])).
% 1.88/1.78 thf(f56,plain,(
% 1.88/1.78 ! [X0 : list,X1 : list,X2 : nat,X3 : nat] : (? [X4 : nat,X5 : elem,X6 : list] : (($true = (listStar @ (plus @ (plus @ X2 @ X3) @ (plus @ X2 @ X3)) @ (app @ X4 @ (plus @ X2 @ X3) @ X6 @ (app @ X2 @ X3 @ X1 @ X0)) @ (app @ (plus @ X4 @ X2) @ X3 @ (app @ X4 @ X2 @ X6 @ X1) @ X0))) & ($true = (listStar @ X4 @ X6 @ X6)) & ($true != (listStar @ (plus @ (suc @ (plus @ X2 @ X3)) @ (plus @ X2 @ X3)) @ (app @ (suc @ X4) @ (plus @ X2 @ X3) @ (cons @ X4 @ X5 @ X6) @ (app @ X2 @ X3 @ X1 @ X0)) @ (app @ (plus @ (suc @ X4) @ X2) @ X3 @ (app @ (suc @ X4) @ X2 @ (cons @ X4 @ X5 @ X6) @ X1) @ X0)))) => (($true = (listStar @ (plus @ (plus @ X2 @ X3) @ (plus @ X2 @ X3)) @ (app @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (plus @ X2 @ X3) @ (sK3 @ X3 @ X2 @ X1 @ X0) @ (app @ X2 @ X3 @ X1 @ X0)) @ (app @ (plus @ (sK1 @ X3 @ X2 @ X1 @ X0) @ X2) @ X3 @ (app @ (sK1 @ X3 @ X2 @ X1 @ X0) @ X2 @ (sK3 @ X3 @ X2 @ X1 @ X0) @ X1) @ X0))) & ($true = (listStar @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (sK3 @ X3 @ X2 @ X1 @ X0) @ (sK3 @ X3 @ X2 @ X1 @ X0))) & ($true != (listStar @ (plus @ (suc @ (plus @ X2 @ X3)) @ (plus @ X2 @ X3)) @ (app @ (suc @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ (plus @ X2 @ X3) @ (cons @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (sK2 @ X3 @ X2 @ X1 @ X0) @ (sK3 @ X3 @ X2 @ X1 @ X0)) @ (app @ X2 @ X3 @ X1 @ X0)) @ (app @ (plus @ (suc @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ X2) @ X3 @ (app @ (suc @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ X2 @ (cons @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (sK2 @ X3 @ X2 @ X1 @ X0) @ (sK3 @ X3 @ X2 @ X1 @ X0)) @ X1) @ X0)))))),
% 1.88/1.78 introduced(definition,[],[choice_axiom])).
% 1.88/1.78 thf(f55,plain,(
% 1.88/1.78 ! [X0 : list,X1 : list,X2 : nat,X3 : nat] : (? [X4 : nat,X5 : elem,X6 : list] : (($true = (listStar @ (plus @ (plus @ X2 @ X3) @ (plus @ X2 @ X3)) @ (app @ X4 @ (plus @ X2 @ X3) @ X6 @ (app @ X2 @ X3 @ X1 @ X0)) @ (app @ (plus @ X4 @ X2) @ X3 @ (app @ X4 @ X2 @ X6 @ X1) @ X0))) & ($true = (listStar @ X4 @ X6 @ X6)) & ($true != (listStar @ (plus @ (suc @ (plus @ X2 @ X3)) @ (plus @ X2 @ X3)) @ (app @ (suc @ X4) @ (plus @ X2 @ X3) @ (cons @ X4 @ X5 @ X6) @ (app @ X2 @ X3 @ X1 @ X0)) @ (app @ (plus @ (suc @ X4) @ X2) @ X3 @ (app @ (suc @ X4) @ X2 @ (cons @ X4 @ X5 @ X6) @ X1) @ X0)))) | ($true != (sP0 @ X3 @ X2 @ X1 @ X0)))),
% 1.88/1.78 inference(rectify,[status(thm)],[f54])).
% 1.88/1.78 thf(f54,plain,(
% 1.88/1.78 ! [X3 : list,X1 : list,X0 : nat,X2 : nat] : (? [X4 : nat,X5 : elem,X6 : list] : (($true = (listStar @ (plus @ (plus @ X0 @ X2) @ (plus @ X0 @ X2)) @ (app @ X4 @ (plus @ X0 @ X2) @ X6 @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ X4 @ X0) @ X2 @ (app @ X4 @ X0 @ X6 @ X1) @ X3))) & ($true = (listStar @ X4 @ X6 @ X6)) & ($true != (listStar @ (plus @ (suc @ (plus @ X0 @ X2)) @ (plus @ X0 @ X2)) @ (app @ (suc @ X4) @ (plus @ X0 @ X2) @ (cons @ X4 @ X5 @ X6) @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ (suc @ X4) @ X0) @ X2 @ (app @ (suc @ X4) @ X0 @ (cons @ X4 @ X5 @ X6) @ X1) @ X3)))) | ($true != (sP0 @ X2 @ X0 @ X1 @ X3)))),
% 1.88/1.78 inference(nnf_transformation,[status(thm)],[f52])).
% 1.88/1.78 thf(f236,plain,(
% 1.88/1.78 ( ! [X2 : list,X3 : list,X0 : nat,X1 : nat] : (($true != (listStar @ (plus @ X0 @ (plus @ X1 @ (plus @ X0 @ X1))) @ (app @ (sK1 @ X1 @ X0 @ X2 @ X3) @ (plus @ X0 @ X1) @ (sK3 @ X1 @ X0 @ X2 @ X3) @ (app @ X0 @ X1 @ X2 @ X3)) @ (app @ (plus @ (sK1 @ X1 @ X0 @ X2 @ X3) @ X0) @ X1 @ (app @ (sK1 @ X1 @ X0 @ X2 @ X3) @ X0 @ (sK3 @ X1 @ X0 @ X2 @ X3) @ X2) @ X3))) | ($true != (sP0 @ X1 @ X0 @ X2 @ X3)) | ($true != (listStar @ X0 @ X2 @ X2)) | ($true != (listStar @ X1 @ X3 @ X3))) )),
% 1.88/1.78 inference(subsumption_resolution,[status(thm)],[f229,f65])).
% 1.88/1.78 thf(f65,plain,(
% 1.88/1.78 ( ! [X2 : nat,X3 : nat,X0 : list,X1 : list] : (($true = (listStar @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (sK3 @ X3 @ X2 @ X1 @ X0) @ (sK3 @ X3 @ X2 @ X1 @ X0))) | ($true != (sP0 @ X3 @ X2 @ X1 @ X0))) )),
% 1.88/1.78 inference(cnf_transformation,[status(thm)],[f57])).
% 1.88/1.78 thf(f229,plain,(
% 1.88/1.78 ( ! [X2 : list,X3 : list,X0 : nat,X1 : nat] : (($true != (listStar @ (sK1 @ X1 @ X0 @ X2 @ X3) @ (sK3 @ X1 @ X0 @ X2 @ X3) @ (sK3 @ X1 @ X0 @ X2 @ X3))) | ($true != (listStar @ X0 @ X2 @ X2)) | ($true != (listStar @ X1 @ X3 @ X3)) | ($true != (listStar @ (plus @ X0 @ (plus @ X1 @ (plus @ X0 @ X1))) @ (app @ (sK1 @ X1 @ X0 @ X2 @ X3) @ (plus @ X0 @ X1) @ (sK3 @ X1 @ X0 @ X2 @ X3) @ (app @ X0 @ X1 @ X2 @ X3)) @ (app @ (plus @ (sK1 @ X1 @ X0 @ X2 @ X3) @ X0) @ X1 @ (app @ (sK1 @ X1 @ X0 @ X2 @ X3) @ X0 @ (sK3 @ X1 @ X0 @ X2 @ X3) @ X2) @ X3))) | ($true != (sP0 @ X1 @ X0 @ X2 @ X3))) )),
% 1.88/1.78 inference(trivial_inequality_removal,[status(thm)],[f228])).
% 1.88/1.78 thf(f228,plain,(
% 1.88/1.78 ( ! [X2 : list,X3 : list,X0 : nat,X1 : nat] : (($true != (listStar @ X0 @ X2 @ X2)) | ($true != (listStar @ (sK1 @ X1 @ X0 @ X2 @ X3) @ (sK3 @ X1 @ X0 @ X2 @ X3) @ (sK3 @ X1 @ X0 @ X2 @ X3))) | ($true != (listStar @ X1 @ X3 @ X3)) | ($true != (sP0 @ X1 @ X0 @ X2 @ X3)) | ($true != $true) | ($true != (listStar @ (plus @ X0 @ (plus @ X1 @ (plus @ X0 @ X1))) @ (app @ (sK1 @ X1 @ X0 @ X2 @ X3) @ (plus @ X0 @ X1) @ (sK3 @ X1 @ X0 @ X2 @ X3) @ (app @ X0 @ X1 @ X2 @ X3)) @ (app @ (plus @ (sK1 @ X1 @ X0 @ X2 @ X3) @ X0) @ X1 @ (app @ (sK1 @ X1 @ X0 @ X2 @ X3) @ X0 @ (sK3 @ X1 @ X0 @ X2 @ X3) @ X2) @ X3)))) )),
% 1.88/1.78 inference(superposition,[status(thm)],[f204,f163])).
% 1.88/1.78 thf(f163,plain,(
% 1.88/1.78 ( ! [X2 : nat,X3 : list,X0 : nat,X1 : list,X6 : list,X4 : nat,X5 : elem] : (($true = (listStar @ (suc @ (plus @ X0 @ (plus @ X2 @ (plus @ X0 @ X2)))) @ (app @ (suc @ X4) @ (plus @ X0 @ X2) @ (cons @ X4 @ X5 @ X6) @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (suc @ (plus @ X4 @ X0)) @ X2 @ (app @ (suc @ X4) @ X0 @ (cons @ X4 @ X5 @ X6) @ X1) @ X3))) | ($true != (listStar @ X2 @ X3 @ X3)) | ($true != (listStar @ (plus @ X0 @ (plus @ X2 @ (plus @ X0 @ X2))) @ (app @ X4 @ (plus @ X0 @ X2) @ X6 @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ X4 @ X0) @ X2 @ (app @ X4 @ X0 @ X6 @ X1) @ X3))) | ($true != (listStar @ X4 @ X6 @ X6)) | ($true != (listStar @ X0 @ X1 @ X1))) )),
% 1.88/1.78 inference(forward_demodulation,[status(thm)],[f162,f70])).
% 1.88/1.78 thf(f70,plain,(
% 1.88/1.78 ( ! [X0 : nat,X1 : nat] : (((plus @ (suc @ X0) @ X1) = (suc @ (plus @ X0 @ X1)))) )),
% 1.88/1.78 inference(cnf_transformation,[status(thm)],[f40])).
% 1.88/1.78 thf(f40,plain,(
% 1.88/1.78 ! [X0 : nat,X1 : nat] : ((plus @ (suc @ X0) @ X1) = (suc @ (plus @ X0 @ X1)))),
% 1.88/1.78 inference(rectify,[status(thm)],[f9])).
% 1.88/1.78 thf(f9,axiom,(
% 1.88/1.78 ! [X6 : nat,X10 : nat] : ((plus @ (suc @ X6) @ X10) = (suc @ (plus @ X6 @ X10)))),
% 1.88/1.78 file('/export/starexec/sandbox/tmp/tmp.MXj1wRhtZr/DTF2THF_8110.p',ax2)).
% 1.88/1.78 thf(f162,plain,(
% 1.88/1.78 ( ! [X2 : nat,X3 : list,X0 : nat,X1 : list,X6 : list,X4 : nat,X5 : elem] : (($true != (listStar @ X4 @ X6 @ X6)) | ($true = (listStar @ (suc @ (plus @ X0 @ (plus @ X2 @ (plus @ X0 @ X2)))) @ (app @ (suc @ X4) @ (plus @ X0 @ X2) @ (cons @ X4 @ X5 @ X6) @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ (suc @ X4) @ X0) @ X2 @ (app @ (suc @ X4) @ X0 @ (cons @ X4 @ X5 @ X6) @ X1) @ X3))) | ($true != (listStar @ X2 @ X3 @ X3)) | ($true != (listStar @ X0 @ X1 @ X1)) | ($true != (listStar @ (plus @ X0 @ (plus @ X2 @ (plus @ X0 @ X2))) @ (app @ X4 @ (plus @ X0 @ X2) @ X6 @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ X4 @ X0) @ X2 @ (app @ X4 @ X0 @ X6 @ X1) @ X3)))) )),
% 1.88/1.78 inference(forward_demodulation,[status(thm)],[f161,f68])).
% 1.88/1.78 thf(f161,plain,(
% 1.88/1.78 ( ! [X2 : nat,X3 : list,X0 : nat,X1 : list,X6 : list,X4 : nat,X5 : elem] : (($true = (listStar @ (suc @ (plus @ (plus @ X0 @ X2) @ (plus @ X0 @ X2))) @ (app @ (suc @ X4) @ (plus @ X0 @ X2) @ (cons @ X4 @ X5 @ X6) @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ (suc @ X4) @ X0) @ X2 @ (app @ (suc @ X4) @ X0 @ (cons @ X4 @ X5 @ X6) @ X1) @ X3))) | ($true != (listStar @ X2 @ X3 @ X3)) | ($true != (listStar @ X4 @ X6 @ X6)) | ($true != (listStar @ X0 @ X1 @ X1)) | ($true != (listStar @ (plus @ X0 @ (plus @ X2 @ (plus @ X0 @ X2))) @ (app @ X4 @ (plus @ X0 @ X2) @ X6 @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ X4 @ X0) @ X2 @ (app @ X4 @ X0 @ X6 @ X1) @ X3)))) )),
% 1.88/1.78 inference(forward_demodulation,[status(thm)],[f160,f70])).
% 1.88/1.78 thf(f160,plain,(
% 1.88/1.78 ( ! [X2 : nat,X3 : list,X0 : nat,X1 : list,X6 : list,X4 : nat,X5 : elem] : (($true != (listStar @ X0 @ X1 @ X1)) | ($true != (listStar @ X4 @ X6 @ X6)) | ($true != (listStar @ (plus @ X0 @ (plus @ X2 @ (plus @ X0 @ X2))) @ (app @ X4 @ (plus @ X0 @ X2) @ X6 @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ X4 @ X0) @ X2 @ (app @ X4 @ X0 @ X6 @ X1) @ X3))) | ($true = (listStar @ (plus @ (suc @ (plus @ X0 @ X2)) @ (plus @ X0 @ X2)) @ (app @ (suc @ X4) @ (plus @ X0 @ X2) @ (cons @ X4 @ X5 @ X6) @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ (suc @ X4) @ X0) @ X2 @ (app @ (suc @ X4) @ X0 @ (cons @ X4 @ X5 @ X6) @ X1) @ X3))) | ($true != (listStar @ X2 @ X3 @ X3))) )),
% 1.88/1.78 inference(forward_demodulation,[status(thm)],[f75,f68])).
% 1.88/1.78 thf(f75,plain,(
% 1.88/1.78 ( ! [X2 : nat,X3 : list,X0 : nat,X1 : list,X6 : list,X4 : nat,X5 : elem] : (($true != (listStar @ X2 @ X3 @ X3)) | ($true != (listStar @ X4 @ X6 @ X6)) | ($true != (listStar @ (plus @ (plus @ X0 @ X2) @ (plus @ X0 @ X2)) @ (app @ X4 @ (plus @ X0 @ X2) @ X6 @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ X4 @ X0) @ X2 @ (app @ X4 @ X0 @ X6 @ X1) @ X3))) | ($true = (listStar @ (plus @ (suc @ (plus @ X0 @ X2)) @ (plus @ X0 @ X2)) @ (app @ (suc @ X4) @ (plus @ X0 @ X2) @ (cons @ X4 @ X5 @ X6) @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ (suc @ X4) @ X0) @ X2 @ (app @ (suc @ X4) @ X0 @ (cons @ X4 @ X5 @ X6) @ X1) @ X3))) | ($true != (listStar @ X0 @ X1 @ X1))) )),
% 1.88/1.78 inference(cnf_transformation,[status(thm)],[f46])).
% 1.88/1.78 thf(f46,plain,(
% 1.88/1.78 ! [X0 : nat,X1 : list,X2 : nat,X3 : list,X4 : nat,X5 : elem,X6 : list] : (($true != (listStar @ (plus @ (plus @ X0 @ X2) @ (plus @ X0 @ X2)) @ (app @ X4 @ (plus @ X0 @ X2) @ X6 @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ X4 @ X0) @ X2 @ (app @ X4 @ X0 @ X6 @ X1) @ X3))) | ($true != (listStar @ X2 @ X3 @ X3)) | ($true != (listStar @ X0 @ X1 @ X1)) | ($true = (listStar @ (plus @ (suc @ (plus @ X0 @ X2)) @ (plus @ X0 @ X2)) @ (app @ (suc @ X4) @ (plus @ X0 @ X2) @ (cons @ X4 @ X5 @ X6) @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ (suc @ X4) @ X0) @ X2 @ (app @ (suc @ X4) @ X0 @ (cons @ X4 @ X5 @ X6) @ X1) @ X3))) | ($true != (listStar @ X4 @ X6 @ X6)))),
% 1.88/1.78 inference(flattening,[status(thm)],[f45])).
% 1.88/1.78 thf(f45,plain,(
% 1.88/1.78 ! [X0 : nat,X1 : list,X2 : nat,X3 : list,X4 : nat,X5 : elem,X6 : list] : ((((($true = (listStar @ (plus @ (suc @ (plus @ X0 @ X2)) @ (plus @ X0 @ X2)) @ (app @ (suc @ X4) @ (plus @ X0 @ X2) @ (cons @ X4 @ X5 @ X6) @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ (suc @ X4) @ X0) @ X2 @ (app @ (suc @ X4) @ X0 @ (cons @ X4 @ X5 @ X6) @ X1) @ X3))) | ($true != (listStar @ (plus @ (plus @ X0 @ X2) @ (plus @ X0 @ X2)) @ (app @ X4 @ (plus @ X0 @ X2) @ X6 @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ X4 @ X0) @ X2 @ (app @ X4 @ X0 @ X6 @ X1) @ X3)))) | ($true != (listStar @ X4 @ X6 @ X6))) | ($true != (listStar @ X2 @ X3 @ X3))) | ($true != (listStar @ X0 @ X1 @ X1)))),
% 1.88/1.78 inference(ennf_transformation,[status(thm)],[f38])).
% 1.88/1.78 thf(f38,plain,(
% 1.88/1.78 ! [X0 : nat,X1 : list,X2 : nat,X3 : list,X4 : nat,X5 : elem,X6 : list] : (($true = (listStar @ X0 @ X1 @ X1)) => (($true = (listStar @ X2 @ X3 @ X3)) => (($true = (listStar @ X4 @ X6 @ X6)) => (($true = (listStar @ (plus @ (plus @ X0 @ X2) @ (plus @ X0 @ X2)) @ (app @ X4 @ (plus @ X0 @ X2) @ X6 @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ X4 @ X0) @ X2 @ (app @ X4 @ X0 @ X6 @ X1) @ X3))) => ($true = (listStar @ (plus @ (suc @ (plus @ X0 @ X2)) @ (plus @ X0 @ X2)) @ (app @ (suc @ X4) @ (plus @ X0 @ X2) @ (cons @ X4 @ X5 @ X6) @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ (suc @ X4) @ X0) @ X2 @ (app @ (suc @ X4) @ X0 @ (cons @ X4 @ X5 @ X6) @ X1) @ X3)))))))),
% 1.88/1.78 inference(fool_elimination,[status(thm)],[f37])).
% 1.88/1.78 thf(f37,plain,(
% 1.88/1.78 ! [X0 : nat,X1 : list,X2 : nat,X3 : list,X4 : nat,X5 : elem,X6 : list] : ((listStar @ X0 @ X1 @ X1) => ((listStar @ X2 @ X3 @ X3) => ((listStar @ X4 @ X6 @ X6) => ((listStar @ (plus @ (plus @ X0 @ X2) @ (plus @ X0 @ X2)) @ (app @ X4 @ (plus @ X0 @ X2) @ X6 @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ X4 @ X0) @ X2 @ (app @ X4 @ X0 @ X6 @ X1) @ X3)) => (listStar @ (plus @ (suc @ (plus @ X0 @ X2)) @ (plus @ X0 @ X2)) @ (app @ (suc @ X4) @ (plus @ X0 @ X2) @ (cons @ X4 @ X5 @ X6) @ (app @ X0 @ X2 @ X1 @ X3)) @ (app @ (plus @ (suc @ X4) @ X0) @ X2 @ (app @ (suc @ X4) @ X0 @ (cons @ X4 @ X5 @ X6) @ X1) @ X3))))))),
% 1.88/1.78 inference(rectify,[status(thm)],[f13])).
% 1.88/1.78 thf(f13,axiom,(
% 1.88/1.78 ! [X13 : nat,X15 : list,X14 : nat,X16 : list,X10 : nat,X2 : elem,X17 : list] : ((listStar @ X13 @ X15 @ X15) => ((listStar @ X14 @ X16 @ X16) => ((listStar @ X10 @ X17 @ X17) => ((listStar @ (plus @ (plus @ X13 @ X14) @ (plus @ X13 @ X14)) @ (app @ X10 @ (plus @ X13 @ X14) @ X17 @ (app @ X13 @ X14 @ X15 @ X16)) @ (app @ (plus @ X10 @ X13) @ X14 @ (app @ X10 @ X13 @ X17 @ X15) @ X16)) => (listStar @ (plus @ (suc @ (plus @ X13 @ X14)) @ (plus @ X13 @ X14)) @ (app @ (suc @ X10) @ (plus @ X13 @ X14) @ (cons @ X10 @ X2 @ X17) @ (app @ X13 @ X14 @ X15 @ X16)) @ (app @ (plus @ (suc @ X10) @ X13) @ X14 @ (app @ (suc @ X10) @ X13 @ (cons @ X10 @ X2 @ X17) @ X15) @ X16))))))),
% 1.88/1.78 file('/export/starexec/sandbox/tmp/tmp.MXj1wRhtZr/DTF2THF_8110.p',list_app_assoc_indstep)).
% 1.88/1.78 thf(f204,plain,(
% 1.88/1.78 ( ! [X2 : nat,X3 : nat,X0 : list,X1 : list] : (($true != (listStar @ (suc @ (plus @ X2 @ (plus @ X3 @ (plus @ X2 @ X3)))) @ (app @ (suc @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ (plus @ X2 @ X3) @ (cons @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (sK2 @ X3 @ X2 @ X1 @ X0) @ (sK3 @ X3 @ X2 @ X1 @ X0)) @ (app @ X2 @ X3 @ X1 @ X0)) @ (app @ (suc @ (plus @ (sK1 @ X3 @ X2 @ X1 @ X0) @ X2)) @ X3 @ (app @ (suc @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ X2 @ (cons @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (sK2 @ X3 @ X2 @ X1 @ X0) @ (sK3 @ X3 @ X2 @ X1 @ X0)) @ X1) @ X0))) | ($true != (sP0 @ X3 @ X2 @ X1 @ X0))) )),
% 1.88/1.78 inference(forward_demodulation,[status(thm)],[f203,f70])).
% 1.88/1.78 thf(f203,plain,(
% 1.88/1.78 ( ! [X2 : nat,X3 : nat,X0 : list,X1 : list] : (($true != (listStar @ (suc @ (plus @ X2 @ (plus @ X3 @ (plus @ X2 @ X3)))) @ (app @ (suc @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ (plus @ X2 @ X3) @ (cons @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (sK2 @ X3 @ X2 @ X1 @ X0) @ (sK3 @ X3 @ X2 @ X1 @ X0)) @ (app @ X2 @ X3 @ X1 @ X0)) @ (app @ (plus @ (suc @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ X2) @ X3 @ (app @ (suc @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ X2 @ (cons @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (sK2 @ X3 @ X2 @ X1 @ X0) @ (sK3 @ X3 @ X2 @ X1 @ X0)) @ X1) @ X0))) | ($true != (sP0 @ X3 @ X2 @ X1 @ X0))) )),
% 1.88/1.78 inference(forward_demodulation,[status(thm)],[f202,f68])).
% 1.88/1.78 thf(f202,plain,(
% 1.88/1.78 ( ! [X2 : nat,X3 : nat,X0 : list,X1 : list] : (($true != (sP0 @ X3 @ X2 @ X1 @ X0)) | ($true != (listStar @ (suc @ (plus @ (plus @ X2 @ X3) @ (plus @ X2 @ X3))) @ (app @ (suc @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ (plus @ X2 @ X3) @ (cons @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (sK2 @ X3 @ X2 @ X1 @ X0) @ (sK3 @ X3 @ X2 @ X1 @ X0)) @ (app @ X2 @ X3 @ X1 @ X0)) @ (app @ (plus @ (suc @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ X2) @ X3 @ (app @ (suc @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ X2 @ (cons @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (sK2 @ X3 @ X2 @ X1 @ X0) @ (sK3 @ X3 @ X2 @ X1 @ X0)) @ X1) @ X0)))) )),
% 1.88/1.78 inference(forward_demodulation,[status(thm)],[f64,f70])).
% 1.88/1.78 thf(f64,plain,(
% 1.88/1.78 ( ! [X2 : nat,X3 : nat,X0 : list,X1 : list] : (($true != (sP0 @ X3 @ X2 @ X1 @ X0)) | ($true != (listStar @ (plus @ (suc @ (plus @ X2 @ X3)) @ (plus @ X2 @ X3)) @ (app @ (suc @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ (plus @ X2 @ X3) @ (cons @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (sK2 @ X3 @ X2 @ X1 @ X0) @ (sK3 @ X3 @ X2 @ X1 @ X0)) @ (app @ X2 @ X3 @ X1 @ X0)) @ (app @ (plus @ (suc @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ X2) @ X3 @ (app @ (suc @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ X2 @ (cons @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (sK2 @ X3 @ X2 @ X1 @ X0) @ (sK3 @ X3 @ X2 @ X1 @ X0)) @ X1) @ X0)))) )),
% 1.88/1.78 inference(cnf_transformation,[status(thm)],[f57])).
% 1.88/1.78 % SZS output end Proof for DTF2THF_8110
% 1.88/1.78 % (8484)------------------------------
% 1.88/1.78 % (8484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.78 % (8484)Termination reason: Refutation
% 1.88/1.78
% 1.88/1.78 % (8484)Memory used [KB]: 6396
% 1.88/1.78 % (8484)Time elapsed: 0.068 s
% 1.88/1.78 % (8484)Instructions burned: 208 (million)
% 1.88/1.78 % (8484)------------------------------
% 1.88/1.78 % (8484)------------------------------
% 1.88/1.78 % (8436)Success in time 0.426 s
%------------------------------------------------------------------------------