%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT349^1 : 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 : n022.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 08:45:32 AM UTC 2026
% Result : Theorem 1.80s 1.72s
% Output : Refutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 198 ( 58 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 918 ( 33 ~; 18 |; 10 &; 836 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 9 con; 0-4 aty)
% Number of variables : 91 ( 0 ^; 76 !; 15 ?; 91 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
elem: $tType ).
thf(type_def_7,type,
nat: $tType ).
thf(type_def_8,type,
list: $tType ).
thf(func_def_0,type,
isPer:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > $o ) ).
thf(func_def_2,type,
elem: $tType ).
thf(func_def_3,type,
elemStar: elem > elem > $o ).
thf(func_def_4,type,
nat: $tType ).
thf(func_def_5,type,
natStar: nat > nat > $o ).
thf(func_def_6,type,
zero: nat ).
thf(func_def_7,type,
suc: nat > nat ).
thf(func_def_8,type,
plus: nat > nat > nat ).
thf(func_def_9,type,
list: $tType ).
thf(func_def_10,type,
listStar: nat > list > list > $o ).
thf(func_def_11,type,
nil: list ).
thf(func_def_12,type,
cons: nat > elem > list > list ).
thf(func_def_13,type,
app: nat > nat > list > list > list ).
thf(func_def_14,type,
rev: nat > list > list ).
thf(func_def_17,type,
sK0:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_18,type,
sK1:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_26,type,
sK2:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_27,type,
sK3:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_28,type,
sK4:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_29,type,
sK5:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_30,type,
sK6:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_31,type,
sK7: nat ).
thf(func_def_32,type,
sK8: list ).
thf(func_def_33,type,
sK9: elem ).
thf(func_def_34,type,
sK10: nat ).
thf(func_def_35,type,
sK11: list ).
thf(func_def_36,type,
sK12: ( nat > $o ) > nat ).
thf(func_def_38,type,
ph14:
!>[X0: $tType] : X0 ).
thf(f157,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f154,f119]) ).
thf(f119,plain,
( ( listStar @ zero @ nil @ nil )
= $true ),
inference(cnf_transformation,[status(thm)],[f55]) ).
thf(f55,plain,
( ( listStar @ zero @ nil @ nil )
= $true ),
inference(fool_elimination,[status(thm)],[f54]) ).
thf(f54,plain,
listStar @ zero @ nil @ nil,
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
listStar @ zero @ nil @ nil,
file('/export/starexec/sandbox/tmp/tmp.Lt8swKET46/DTF2THF_11343.p',nil_tp_ax) ).
thf(f154,plain,
( ( listStar @ zero @ nil @ nil )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f150]) ).
thf(f150,plain,
( ( ( listStar @ zero @ nil @ nil )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f147,f122]) ).
thf(f122,plain,
! [X2: list,X3: list,X0: nat,X1: elem] :
( ( $true
= ( listStar @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) @ ( cons @ X0 @ X1 @ X3 ) ) )
| ( $true
!= ( listStar @ X0 @ X2 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
thf(f83,plain,
! [X0: nat,X1: elem,X2: list,X3: list] :
( ( $true
!= ( listStar @ X0 @ X2 @ X3 ) )
| ( $true
= ( listStar @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) @ ( cons @ X0 @ X1 @ X3 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: nat,X1: elem,X2: list,X3: list] :
( ( $true
= ( listStar @ X0 @ X2 @ X3 ) )
=> ( $true
= ( listStar @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) @ ( cons @ X0 @ X1 @ X3 ) ) ) ),
inference(fool_elimination,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: nat,X1: elem,X2: list,X3: list] :
( ( listStar @ X0 @ X2 @ X3 )
=> ( listStar @ ( suc @ X0 ) @ ( cons @ X0 @ X1 @ X2 ) @ ( cons @ X0 @ X1 @ X3 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X6: nat,X7: elem,X8: list,X9: list] :
( ( listStar @ X6 @ X8 @ X9 )
=> ( listStar @ ( suc @ X6 ) @ ( cons @ X6 @ X7 @ X8 ) @ ( cons @ X6 @ X7 @ X9 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Lt8swKET46/DTF2THF_11343.p',cons_tp_ax) ).
thf(f147,plain,
( $true
!= ( listStar @ ( suc @ zero ) @ ( cons @ zero @ sK9 @ nil ) @ ( cons @ zero @ sK9 @ nil ) ) ),
inference(subsumption_resolution,[status(thm)],[f146,f110]) ).
thf(f110,plain,
( ( listStar @ sK7 @ sK8 @ sK8 )
= $true ),
inference(cnf_transformation,[status(thm)],[f96]) ).
thf(f96,plain,
( ( ( listStar @ sK10 @ sK11 @ sK11 )
= $true )
& ( $true
!= ( listStar @ ( plus @ ( plus @ ( suc @ zero ) @ sK10 ) @ ( plus @ ( suc @ zero ) @ sK10 ) ) @ ( app @ sK7 @ ( plus @ ( suc @ zero ) @ sK10 ) @ sK8 @ ( app @ ( suc @ zero ) @ sK10 @ ( cons @ zero @ sK9 @ nil ) @ sK11 ) ) @ ( app @ ( plus @ sK7 @ ( suc @ zero ) ) @ sK10 @ ( app @ sK7 @ ( suc @ zero ) @ sK8 @ ( cons @ zero @ sK9 @ nil ) ) @ sK11 ) ) )
& ( ( listStar @ sK7 @ sK8 @ sK8 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11])],[f82,f95]) ).
thf(f95,plain,
( ? [X0: nat,X1: list,X2: elem,X3: nat,X4: list] :
( ( $true
= ( listStar @ X3 @ X4 @ X4 ) )
& ( ( listStar @ ( plus @ ( plus @ ( suc @ zero ) @ X3 ) @ ( plus @ ( suc @ zero ) @ X3 ) ) @ ( app @ X0 @ ( plus @ ( suc @ zero ) @ X3 ) @ X1 @ ( app @ ( suc @ zero ) @ X3 @ ( cons @ zero @ X2 @ nil ) @ X4 ) ) @ ( app @ ( plus @ X0 @ ( suc @ zero ) ) @ X3 @ ( app @ X0 @ ( suc @ zero ) @ X1 @ ( cons @ zero @ X2 @ nil ) ) @ X4 ) )
!= $true )
& ( ( listStar @ X0 @ X1 @ X1 )
= $true ) )
=> ( ( ( listStar @ sK10 @ sK11 @ sK11 )
= $true )
& ( $true
!= ( listStar @ ( plus @ ( plus @ ( suc @ zero ) @ sK10 ) @ ( plus @ ( suc @ zero ) @ sK10 ) ) @ ( app @ sK7 @ ( plus @ ( suc @ zero ) @ sK10 ) @ sK8 @ ( app @ ( suc @ zero ) @ sK10 @ ( cons @ zero @ sK9 @ nil ) @ sK11 ) ) @ ( app @ ( plus @ sK7 @ ( suc @ zero ) ) @ sK10 @ ( app @ sK7 @ ( suc @ zero ) @ sK8 @ ( cons @ zero @ sK9 @ nil ) ) @ sK11 ) ) )
& ( ( listStar @ sK7 @ sK8 @ sK8 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f82,plain,
? [X0: nat,X1: list,X2: elem,X3: nat,X4: list] :
( ( $true
= ( listStar @ X3 @ X4 @ X4 ) )
& ( ( listStar @ ( plus @ ( plus @ ( suc @ zero ) @ X3 ) @ ( plus @ ( suc @ zero ) @ X3 ) ) @ ( app @ X0 @ ( plus @ ( suc @ zero ) @ X3 ) @ X1 @ ( app @ ( suc @ zero ) @ X3 @ ( cons @ zero @ X2 @ nil ) @ X4 ) ) @ ( app @ ( plus @ X0 @ ( suc @ zero ) ) @ X3 @ ( app @ X0 @ ( suc @ zero ) @ X1 @ ( cons @ zero @ X2 @ nil ) ) @ X4 ) )
!= $true )
& ( ( listStar @ X0 @ X1 @ X1 )
= $true ) ),
inference(flattening,[status(thm)],[f81]) ).
thf(f81,plain,
? [X0: nat,X1: list,X2: elem,X3: nat,X4: list] :
( ( ( listStar @ ( plus @ ( plus @ ( suc @ zero ) @ X3 ) @ ( plus @ ( suc @ zero ) @ X3 ) ) @ ( app @ X0 @ ( plus @ ( suc @ zero ) @ X3 ) @ X1 @ ( app @ ( suc @ zero ) @ X3 @ ( cons @ zero @ X2 @ nil ) @ X4 ) ) @ ( app @ ( plus @ X0 @ ( suc @ zero ) ) @ X3 @ ( app @ X0 @ ( suc @ zero ) @ X1 @ ( cons @ zero @ X2 @ nil ) ) @ X4 ) )
!= $true )
& ( $true
= ( listStar @ X3 @ X4 @ X4 ) )
& ( ( listStar @ X0 @ X1 @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f53]) ).
thf(f53,plain,
~ ! [X0: nat,X1: list,X2: elem,X3: nat,X4: list] :
( ( ( listStar @ X0 @ X1 @ X1 )
= $true )
=> ( ( $true
= ( listStar @ X3 @ X4 @ X4 ) )
=> ( ( listStar @ ( plus @ ( plus @ ( suc @ zero ) @ X3 ) @ ( plus @ ( suc @ zero ) @ X3 ) ) @ ( app @ X0 @ ( plus @ ( suc @ zero ) @ X3 ) @ X1 @ ( app @ ( suc @ zero ) @ X3 @ ( cons @ zero @ X2 @ nil ) @ X4 ) ) @ ( app @ ( plus @ X0 @ ( suc @ zero ) ) @ X3 @ ( app @ X0 @ ( suc @ zero ) @ X1 @ ( cons @ zero @ X2 @ nil ) ) @ X4 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f52]) ).
thf(f52,plain,
~ ! [X0: nat,X1: list,X2: elem,X3: nat,X4: list] :
( ( listStar @ X0 @ X1 @ X1 )
=> ( ( listStar @ X3 @ X4 @ X4 )
=> ( listStar @ ( plus @ ( plus @ ( suc @ zero ) @ X3 ) @ ( plus @ ( suc @ zero ) @ X3 ) ) @ ( app @ X0 @ ( plus @ ( suc @ zero ) @ X3 ) @ X1 @ ( app @ ( suc @ zero ) @ X3 @ ( cons @ zero @ X2 @ nil ) @ X4 ) ) @ ( app @ ( plus @ X0 @ ( suc @ zero ) ) @ X3 @ ( app @ X0 @ ( suc @ zero ) @ X1 @ ( cons @ zero @ X2 @ nil ) ) @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,negated_conjecture,
~ ! [X10: nat,X16: list,X2: elem,X15: nat,X18: list] :
( ( listStar @ X10 @ X16 @ X16 )
=> ( ( listStar @ X15 @ X18 @ X18 )
=> ( listStar @ ( plus @ ( plus @ ( suc @ zero ) @ X15 ) @ ( plus @ ( suc @ zero ) @ X15 ) ) @ ( app @ X10 @ ( plus @ ( suc @ zero ) @ X15 ) @ X16 @ ( app @ ( suc @ zero ) @ X15 @ ( cons @ zero @ X2 @ nil ) @ X18 ) ) @ ( app @ ( plus @ X10 @ ( suc @ zero ) ) @ X15 @ ( app @ X10 @ ( suc @ zero ) @ X16 @ ( cons @ zero @ X2 @ nil ) ) @ X18 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
thf(f19,conjecture,
! [X10: nat,X16: list,X2: elem,X15: nat,X18: list] :
( ( listStar @ X10 @ X16 @ X16 )
=> ( ( listStar @ X15 @ X18 @ X18 )
=> ( listStar @ ( plus @ ( plus @ ( suc @ zero ) @ X15 ) @ ( plus @ ( suc @ zero ) @ X15 ) ) @ ( app @ X10 @ ( plus @ ( suc @ zero ) @ X15 ) @ X16 @ ( app @ ( suc @ zero ) @ X15 @ ( cons @ zero @ X2 @ nil ) @ X18 ) ) @ ( app @ ( plus @ X10 @ ( suc @ zero ) ) @ X15 @ ( app @ X10 @ ( suc @ zero ) @ X16 @ ( cons @ zero @ X2 @ nil ) ) @ X18 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Lt8swKET46/DTF2THF_11343.p',list_app_assoc_m1_step1) ).
thf(f146,plain,
( ( $true
!= ( listStar @ ( suc @ zero ) @ ( cons @ zero @ sK9 @ nil ) @ ( cons @ zero @ sK9 @ nil ) ) )
| ( ( listStar @ sK7 @ sK8 @ sK8 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f145,f112]) ).
thf(f112,plain,
( ( listStar @ sK10 @ sK11 @ sK11 )
= $true ),
inference(cnf_transformation,[status(thm)],[f96]) ).
thf(f145,plain,
( ( ( listStar @ sK10 @ sK11 @ sK11 )
!= $true )
| ( ( listStar @ sK7 @ sK8 @ sK8 )
!= $true )
| ( $true
!= ( listStar @ ( suc @ zero ) @ ( cons @ zero @ sK9 @ nil ) @ ( cons @ zero @ sK9 @ nil ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f140]) ).
thf(f140,plain,
( ( $true != $true )
| ( $true
!= ( listStar @ ( suc @ zero ) @ ( cons @ zero @ sK9 @ nil ) @ ( cons @ zero @ sK9 @ nil ) ) )
| ( ( listStar @ sK7 @ sK8 @ sK8 )
!= $true )
| ( ( listStar @ sK10 @ sK11 @ sK11 )
!= $true ) ),
inference(superposition,[status(thm)],[f111,f117]) ).
thf(f117,plain,
! [X2: nat,X3: list,X0: nat,X1: 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 @ X2 @ X3 @ X3 ) )
| ( ( listStar @ X0 @ X1 @ X1 )
!= $true )
| ( $true
!= ( listStar @ X4 @ X5 @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f88]) ).
thf(f88,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 ) ) )
| ( ( listStar @ X0 @ X1 @ X1 )
!= $true )
| ( $true
!= ( listStar @ X4 @ X5 @ X5 ) )
| ( $true
!= ( listStar @ X2 @ X3 @ X3 ) ) ),
inference(flattening,[status(thm)],[f87]) ).
thf(f87,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 ) )
| ( ( listStar @ X0 @ X1 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: nat,X1: list,X2: nat,X3: list,X4: nat,X5: list] :
( ( ( listStar @ X0 @ X1 @ X1 )
= $true )
=> ( ( $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)],[f26]) ).
thf(f26,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)],[f18]) ).
thf(f18,axiom,
! [X10: nat,X16: list,X14: nat,X17: list,X15: nat,X18: list] :
( ( listStar @ X10 @ X16 @ X16 )
=> ( ( listStar @ X14 @ X17 @ X17 )
=> ( ( listStar @ X15 @ X18 @ X18 )
=> ( listStar @ ( plus @ ( plus @ X14 @ X15 ) @ ( plus @ X14 @ X15 ) ) @ ( app @ X10 @ ( plus @ X14 @ X15 ) @ X16 @ ( app @ X14 @ X15 @ X17 @ X18 ) ) @ ( app @ ( plus @ X10 @ X14 ) @ X15 @ ( app @ X10 @ X14 @ X16 @ X17 ) @ X18 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Lt8swKET46/DTF2THF_11343.p',list_app_assoc) ).
thf(f111,plain,
( $true
!= ( listStar @ ( plus @ ( plus @ ( suc @ zero ) @ sK10 ) @ ( plus @ ( suc @ zero ) @ sK10 ) ) @ ( app @ sK7 @ ( plus @ ( suc @ zero ) @ sK10 ) @ sK8 @ ( app @ ( suc @ zero ) @ sK10 @ ( cons @ zero @ sK9 @ nil ) @ sK11 ) ) @ ( app @ ( plus @ sK7 @ ( suc @ zero ) ) @ sK10 @ ( app @ sK7 @ ( suc @ zero ) @ sK8 @ ( cons @ zero @ sK9 @ nil ) ) @ sK11 ) ) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : DAT349^1 : TPTP v9.2.1. Released v9.2.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.32 % Computer : n022.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue Feb 24 06:15:21 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.46 ---- Original DTF file ---
% 0.18/0.47 thf(spec,logic,$$dhol).
% 0.18/0.47 %------------------------------------------------------------------------------
% 0.18/0.47 % File : DAT349^1 : TPTP v9.2.1. Released v9.2.0.
% 0.18/0.47 % Domain : Data Structures
% 0.18/0.47 % Problem : Corollary of the associativity of append, step 1
% 0.18/0.47 % Version : Especial.
% 0.18/0.47 % English : Corollary of the associativity of append. The proof is split into
% 0.18/0.47 % smaller steps. To simplify proof search, the axioms in each
% 0.18/0.47 % problem file have been preselected.
% 0.18/0.47
% 0.18/0.47 % Refs : [RRB23] Rothgang et al. (2023), Theorem Proving in Dependently
% 0.18/0.47 % : [Rot25] Rothgang (2025), Email to Geoff Sutcliffe
% 0.18/0.47 % : [RK+25] Ranalter et al. (2025), The Dependently Typed Higher-O
% 0.18/0.47 % Source : [Rot25]
% 0.18/0.47 % Names : ListAppAssocM1/list-app-assoc-m1-step1.p [Rot25]
% 0.18/0.47
% 0.18/0.47 % Status : Theorem
% 0.18/0.47 % Rating : ? v9.2.0
% 0.18/0.47 % Syntax : Number of formulae : 21 ( 9 unt; 10 typ; 0 def)
% 0.18/0.47 % Number of atoms : 11 ( 11 equ; 0 cnn)
% 0.18/0.47 % Maximal formula atoms : 2 ( 1 avg)
% 0.18/0.47 % Number of connectives : 107 ( 3 ~; 0 |; 0 &; 100 @)
% 0.18/0.47 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.18/0.47 % Maximal formula depth : 8 ( 4 avg)
% 0.18/0.47 % Number of types : 3 ( 2 usr)
% 0.18/0.47 % Number of type decls : 10 ( 0 !>P; 3 !>D)
% 0.18/0.47 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.18/0.47 % Number of symbols : 9 ( 8 usr; 2 con; 0-4 aty)
% 0.18/0.47 % Number of variables : 31 ( 0 ^; 27 !; 0 ?; 31 :)
% 0.18/0.47 % ( 4 !>; 0 ?*; 0 @-; 0 @+)
% 0.18/0.47 % SPC : DH0_THM_EQU_NAR
% 0.18/0.47
% 0.18/0.47 % Comments :
% 0.18/0.47 %------------------------------------------------------------------------------
% 0.18/0.47 thf(elem_type,type,
% 0.18/0.47 elem: $tType ).
% 0.18/0.47
% 0.18/0.47 thf(nat_type,type,
% 0.18/0.47 nat: $tType ).
% 0.18/0.47
% 0.18/0.47 thf(zero_type,type,
% 0.18/0.47 zero: nat ).
% 0.18/0.47
% 0.18/0.47 thf(suc_type,type,
% 0.18/0.47 suc: nat > nat ).
% 0.18/0.47
% 0.18/0.47 thf(plus_type,type,
% 0.18/0.47 plus: nat > nat > nat ).
% 0.18/0.47
% 0.18/0.47 thf(list_type,type,
% 0.18/0.47 list: nat > $tType ).
% 0.18/0.47
% 0.18/0.47 thf(nil_type,type,
% 0.18/0.47 nil: list @ zero ).
% 0.18/0.47
% 0.18/0.47 thf(cons_type,type,
% 0.18/0.47 cons:
% 0.18/0.47 !>[N: nat] : ( elem > ( list @ N ) > ( list @ ( suc @ N ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(app_type,type,
% 0.18/0.47 app:
% 0.18/0.47 !>[N: nat,M: nat] : ( ( list @ N ) > ( list @ M ) > ( list @ ( plus @ N @ M ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(rev_type,type,
% 0.18/0.47 rev:
% 0.18/0.47 !>[N: nat] : ( ( list @ N ) > ( list @ N ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(peano1,axiom,
% 0.18/0.47 ! [N: nat] :
% 0.18/0.47 ( ( suc @ N )
% 0.18/0.47 != zero ) ).
% 0.18/0.47
% 0.18/0.47 thf(peano2,axiom,
% 0.18/0.47 ! [N: nat,M: nat] :
% 0.18/0.47 ( ( N != M )
% 0.18/0.47 => ( ( suc @ N )
% 0.18/0.47 != ( suc @ M ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(peano3,axiom,
% 0.18/0.47 ! [P: nat > $o] :
% 0.18/0.47 ( ( P @ zero )
% 0.18/0.47 => ( ! [M: nat] :
% 0.18/0.47 ( ( P @ M )
% 0.18/0.47 => ( P @ ( suc @ M ) ) )
% 0.18/0.47 => ! [N: nat] : ( P @ N ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(ax1,axiom,
% 0.18/0.47 ! [N: nat] :
% 0.18/0.47 ( ( plus @ zero @ N )
% 0.18/0.47 = N ) ).
% 0.18/0.47
% 0.18/0.47 thf(ax2,axiom,
% 0.18/0.47 ! [N: nat,M: nat] :
% 0.18/0.47 ( ( plus @ ( suc @ N ) @ M )
% 0.18/0.47 = ( suc @ ( plus @ N @ M ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(plus_zero_r,axiom,
% 0.18/0.47 ! [M: nat] :
% 0.18/0.47 ( ( plus @ M @ zero )
% 0.18/0.47 = M ) ).
% 0.18/0.47
% 0.18/0.47 thf(plus_com,axiom,
% 0.18/0.47 ! [N: nat,M: nat] :
% 0.18/0.47 ( ( plus @ N @ M )
% 0.18/0.47 = ( plus @ M @ N ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(plus_assoc,axiom,
% 0.18/0.47 ! [M1: nat,M2: nat,M3: nat] :
% 0.18/0.47 ( ( plus @ M1 @ ( plus @ M2 @ M3 ) )
% 0.18/0.47 = ( plus @ ( plus @ M1 @ M2 ) @ M3 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(plus1r,axiom,
% 0.18/0.47 ! [N: nat] :
% 0.18/0.47 ( ( suc @ N )
% 0.18/0.47 = ( plus @ N @ ( suc @ zero ) ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(list_app_assoc,axiom,
% 0.18/0.47 ! [M: nat,L: list @ M,M2: nat,L2: list @ M2,M3: nat,L3: list @ M3] :
% 0.18/0.47 ( ( app @ M @ ( plus @ M2 @ M3 ) @ L @ ( app @ M2 @ M3 @ L2 @ L3 ) )
% 0.18/0.47 = ( app @ ( plus @ M @ M2 ) @ M3 @ ( app @ M @ M2 @ L @ L2 ) @ L3 ) ) ).
% 0.18/0.47
% 0.18/0.47 thf(list_app_assoc_m1_step1,conjecture,
% 0.18/0.47 ! [M: nat,L: list @ M,X: elem,M3: nat,L3: list @ M3] :
% 0.18/0.47 ( ( app @ M @ ( plus @ ( suc @ zero ) @ M3 ) @ L @ ( app @ ( suc @ zero ) @ M3 @ ( cons @ zero @ X @ nil ) @ L3 ) )
% 0.18/0.47 = ( app @ ( plus @ M @ ( suc @ zero ) ) @ M3 @ ( app @ M @ ( suc @ zero ) @ L @ ( cons @ zero @ X @ nil ) ) @ L3 ) ) ).
% 0.18/0.47
% 0.18/0.47 %------------------------------------------------------------------------------
% 0.18/0.47 ------------------------
% 1.71/1.34 ---- Embedded in THF ---
% 1.71/1.34 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.71/1.34 %%% Generated on Tue Feb 24 06:15:22 EST 2026
% 1.71/1.34 %%% using '$$dhol' embedding, version 1.3.0.
% 1.71/1.34 %%% Logic specification used:
% 1.71/1.34 %%% thf(spec, logic, $$dhol).
% 1.71/1.34
% 1.71/1.34 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Lt8swKET46/DTF2DTF11343.p
% See solution above
% 1.71/1.34 ------------------------
% 1.71/1.35 ---- Cleaned THF ---
% 1.71/1.35 thf(is_per_type,type,
% 1.71/1.35 isPer:
% 1.71/1.35 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 1.71/1.35
% 1.71/1.35 thf(is_per,definition,
% 1.71/1.35 ! [A: $tType,AStar: A > A > $o] :
% 1.71/1.35 ( ( isPer @ A @ AStar )
% 1.71/1.35 <=> ( ! [X: A,Y: A] :
% 1.71/1.35 ( ( AStar @ X @ Y )
% 1.71/1.35 => ( AStar @ Y @ X ) )
% 1.71/1.35 & ! [X: A,Y: A,Z: A] :
% 1.71/1.35 ( ( AStar @ X @ Y )
% 1.71/1.35 => ( ( AStar @ Y @ Z )
% 1.71/1.35 => ( AStar @ X @ Z ) ) ) ) ) ).
% 1.71/1.35
% 1.71/1.35 thf(elem_type,type,
% 1.71/1.35 elem: $tType ).
% 1.71/1.35
% 1.71/1.35 thf(elemStar,type,
% 1.71/1.35 elemStar: elem > elem > $o ).
% 1.71/1.35
% 1.71/1.35 thf(elemStar_is_eq,axiom,
% 1.71/1.35 ! [X: elem,Y: elem] :
% 1.71/1.35 ( ( elemStar @ X @ Y )
% 1.71/1.35 <=> ( X = Y ) ) ).
% 1.71/1.35
% 1.71/1.35 thf(nat_type,type,
% 1.71/1.35 nat: $tType ).
% 1.71/1.35
% 1.71/1.35 thf(natStar,type,
% 1.71/1.35 natStar: nat > nat > $o ).
% 1.71/1.35
% 1.71/1.35 thf(natStar_is_eq,axiom,
% 1.71/1.35 ! [X: nat,Y: nat] :
% 1.71/1.35 ( ( natStar @ X @ Y )
% 1.71/1.35 <=> ( X = Y ) ) ).
% 1.71/1.35
% 1.71/1.35 thf(zero_type,type,
% 1.71/1.35 zero: nat ).
% 1.71/1.35
% 1.71/1.35 thf(suc_type,type,
% 1.71/1.35 suc: nat > nat ).
% 1.71/1.35
% 1.71/1.35 thf(plus_type,type,
% 1.71/1.35 plus: nat > nat > nat ).
% 1.71/1.35
% 1.71/1.35 thf(list_type,type,
% 1.71/1.35 list: $tType ).
% 1.71/1.35
% 1.71/1.35 thf(listStar,type,
% 1.71/1.35 listStar: nat > list > list > $o ).
% 1.71/1.35
% 1.71/1.35 thf('\'listStar\'_is_per',axiom,
% 1.71/1.35 ! [C: nat] : ( isPer @ list @ ( listStar @ C ) ) ).
% 1.71/1.35
% 1.71/1.35 thf(nil_type,type,
% 1.71/1.35 nil: list ).
% 1.71/1.35
% 1.71/1.35 thf(nil_tp_ax,axiom,
% 1.71/1.35 listStar @ zero @ nil @ nil ).
% 1.71/1.35
% 1.71/1.35 thf(cons_type,type,
% 1.71/1.35 cons: nat > elem > list > list ).
% 1.71/1.35
% 1.71/1.35 thf(cons_tp_ax,axiom,
% 1.71/1.35 ! [N: nat,D: elem,D0: list,D0_prime: list] :
% 1.71/1.35 ( ( listStar @ N @ D0 @ D0_prime )
% 1.71/1.35 => ( listStar @ ( suc @ N ) @ ( cons @ N @ D @ D0 ) @ ( cons @ N @ D @ D0_prime ) ) ) ).
% 1.71/1.35
% 1.71/1.35 thf(app_type,type,
% 1.71/1.35 app: nat > nat > list > list > list ).
% 1.71/1.35
% 1.71/1.35 thf(app_tp_ax,axiom,
% 1.71/1.35 ! [N: nat,M: nat,D: list,D_prime: list] :
% 1.71/1.35 ( ( listStar @ N @ D @ D_prime )
% 1.71/1.35 => ! [D0: list,D0_prime: list] :
% 1.71/1.35 ( ( listStar @ M @ D0 @ D0_prime )
% 1.71/1.35 => ( listStar @ ( plus @ N @ M ) @ ( app @ N @ M @ D @ D0 ) @ ( app @ N @ M @ D_prime @ D0_prime ) ) ) ) ).
% 1.71/1.35
% 1.71/1.35 thf(rev_type,type,
% 1.71/1.35 rev: nat > list > list ).
% 1.71/1.35
% 1.71/1.35 thf(rev_tp_ax,axiom,
% 1.71/1.35 ! [N: nat,D: list,D_prime: list] :
% 1.71/1.35 ( ( listStar @ N @ D @ D_prime )
% 1.71/1.35 => ( listStar @ N @ ( rev @ N @ D ) @ ( rev @ N @ D_prime ) ) ) ).
% 1.71/1.35
% 1.71/1.35 thf(peano1,axiom,
% 1.71/1.35 ! [N: nat] :
% 1.71/1.35 ( ( suc @ N )
% 1.71/1.35 != zero ) ).
% 1.71/1.35
% 1.71/1.35 thf(peano2,axiom,
% 1.71/1.35 ! [N: nat,M: nat] :
% 1.71/1.35 ( ( N != M )
% 1.71/1.35 => ( ( suc @ N )
% 1.71/1.35 != ( suc @ M ) ) ) ).
% 1.71/1.35
% 1.71/1.35 thf(peano3,axiom,
% 1.71/1.35 ! [P: nat > $o] :
% 1.71/1.35 ( ( P @ zero )
% 1.71/1.35 => ( ! [M: nat] :
% 1.71/1.35 ( ( P @ M )
% 1.71/1.35 => ( P @ ( suc @ M ) ) )
% 1.71/1.35 => ! [N: nat] : ( P @ N ) ) ) ).
% 1.71/1.35
% 1.71/1.35 thf(ax1,axiom,
% 1.71/1.35 ! [N: nat] :
% 1.71/1.35 ( ( plus @ zero @ N )
% 1.71/1.35 = N ) ).
% 1.71/1.35
% 1.71/1.35 thf(ax2,axiom,
% 1.71/1.35 ! [N: nat,M: nat] :
% 1.71/1.35 ( ( plus @ ( suc @ N ) @ M )
% 1.71/1.35 = ( suc @ ( plus @ N @ M ) ) ) ).
% 1.71/1.35
% 1.71/1.35 thf(plus_zero_r,axiom,
% 1.71/1.35 ! [M: nat] :
% 1.71/1.35 ( ( plus @ M @ zero )
% 1.71/1.35 = M ) ).
% 1.71/1.35
% 1.71/1.35 thf(plus_com,axiom,
% 1.71/1.35 ! [N: nat,M: nat] :
% 1.71/1.35 ( ( plus @ N @ M )
% 1.71/1.35 = ( plus @ M @ N ) ) ).
% 1.71/1.35
% 1.71/1.35 thf(plus_assoc,axiom,
% 1.71/1.35 ! [M1: nat,M2: nat,M3: nat] :
% 1.71/1.35 ( ( plus @ M1 @ ( plus @ M2 @ M3 ) )
% 1.71/1.35 = ( plus @ ( plus @ M1 @ M2 ) @ M3 ) ) ).
% 1.71/1.35
% 1.71/1.35 thf(plus1r,axiom,
% 1.71/1.35 ! [N: nat] :
% 1.71/1.35 ( ( suc @ N )
% 1.71/1.35 = ( plus @ N @ ( suc @ zero ) ) ) ).
% 1.71/1.35
% 1.71/1.35 thf(list_app_assoc,axiom,
% 1.71/1.35 ! [M: nat,L: list,M2: nat,L2: list,M3: nat,L3: list] :
% 1.71/1.35 ( ( listStar @ M @ L @ L )
% 1.71/1.35 => ( ( listStar @ M2 @ L2 @ L2 )
% 1.71/1.35 => ( ( listStar @ M3 @ L3 @ L3 )
% 1.71/1.35 => ( 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 ) ) ) ) ) ).
% 1.71/1.35
% 1.71/1.35 thf(list_app_assoc_m1_step1,conjecture,
% 1.71/1.35 ! [M: nat,L: list,X: elem,M3: nat,L3: list] :
% 1.71/1.35 ( ( listStar @ M @ L @ L )
% 1.71/1.35 => ( ( listStar @ M3 @ L3 @ L3 )
% 1.71/1.35 => ( listStar @ ( plus @ ( plus @ ( suc @ zero ) @ M3 ) @ ( plus @ ( suc @ zero ) @ M3 ) ) @ ( app @ M @ ( plus @ ( suc @ zero ) @ M3 ) @ L @ ( app @ ( suc @ zero ) @ M3 @ ( cons @ zero @ X @ nil ) @ L3 ) ) @ ( app @ ( plus @ M @ ( suc @ zero ) ) @ M3 @ ( app @ M @ ( suc @ zero ) @ L @ ( cons @ zero @ X @ nil ) ) @ L3 ) ) ) ) ).
% 1.71/1.35 ------------------------
% 1.71/1.37 % (11726)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_11343 for (2999ds/275Mi)
% 1.71/1.37 % (11725)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_11343 for (2999ds/2Mi)
% 1.71/1.37 % (11725)Instruction limit reached!
% 1.71/1.37 % (11725)------------------------------
% 1.71/1.37 % (11725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.37 % (11725)Termination reason: Unknown
% 1.71/1.37 % (11725)Termination phase: shuffling
% 1.71/1.37
% 1.71/1.37 % (11725)Memory used [KB]: 1023
% 1.71/1.37 % (11725)Time elapsed: 0.002 s
% 1.71/1.37 % (11725)Instructions burned: 3 (million)
% 1.71/1.37 % (11725)------------------------------
% 1.71/1.37 % (11725)------------------------------
% 1.71/1.37 % (11726)Refutation not found, incomplete strategy
% 1.71/1.37 % (11726)------------------------------
% 1.71/1.37 % (11726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.37 % (11726)Termination reason: Refutation not found, incomplete strategy
% 1.71/1.37
% 1.71/1.37
% 1.71/1.37 % (11726)Memory used [KB]: 5628
% 1.71/1.37 % (11726)Time elapsed: 0.005 s
% 1.71/1.37 % (11726)Instructions burned: 10 (million)
% 1.71/1.37 % (11726)------------------------------
% 1.71/1.37 % (11726)------------------------------
% 1.71/1.37 % (11721)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11343 for (2999ds/183Mi)
% 1.71/1.37 % (11722)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_11343 for (2999ds/4Mi)
% 1.71/1.37 % (11723)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_11343 for (2999ds/27Mi)
% 1.71/1.37 % (11724)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11343 for (2999ds/2Mi)
% 1.71/1.37 % (11727)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11343 for (2999ds/18Mi)
% 1.71/1.37 % (11724)Instruction limit reached!
% 1.71/1.37 % (11724)------------------------------
% 1.71/1.37 % (11724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.37 % (11724)Termination reason: Unknown
% 1.71/1.37 % (11724)Termination phase: shuffling
% 1.71/1.37
% 1.71/1.37 % (11724)Memory used [KB]: 1023
% 1.71/1.37 % (11724)Time elapsed: 0.003 s
% 1.71/1.37 % (11724)Instructions burned: 2 (million)
% 1.71/1.37 % (11724)------------------------------
% 1.71/1.37 % (11724)------------------------------
% 1.71/1.38 % (11722)Instruction limit reached!
% 1.71/1.38 % (11722)------------------------------
% 1.71/1.38 % (11722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.38 % (11722)Termination reason: Unknown
% 1.71/1.38 % (11722)Termination phase: shuffling
% 1.71/1.38
% 1.71/1.38 % (11722)Memory used [KB]: 1023
% 1.71/1.38 % (11722)Time elapsed: 0.004 s
% 1.71/1.38 % (11722)Instructions burned: 4 (million)
% 1.71/1.38 % (11722)------------------------------
% 1.71/1.38 % (11722)------------------------------
% 1.71/1.38 % (11728)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_11343 for (2999ds/3Mi)
% 1.71/1.38 % (11728)Instruction limit reached!
% 1.71/1.38 % (11728)------------------------------
% 1.71/1.38 % (11728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.38 % (11728)Termination reason: Unknown
% 1.71/1.38 % (11728)Termination phase: Property scanning
% 1.71/1.38
% 1.71/1.38 % (11728)Memory used [KB]: 1023
% 1.71/1.38 % (11728)Time elapsed: 0.003 s
% 1.71/1.38 % (11728)Instructions burned: 4 (million)
% 1.71/1.38 % (11728)------------------------------
% 1.71/1.38 % (11728)------------------------------
% 1.71/1.38 % (11729)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_11343 for (2999ds/37Mi)
% 1.71/1.38 % (11727)Instruction limit reached!
% 1.71/1.38 % (11727)------------------------------
% 1.71/1.38 % (11727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.38 % (11727)Termination reason: Unknown
% 1.71/1.38 % (11727)Termination phase: Saturation
% 1.71/1.38
% 1.71/1.38 % (11727)Memory used [KB]: 5628
% 1.71/1.38 % (11727)Time elapsed: 0.013 s
% 1.71/1.38 % (11727)Instructions burned: 18 (million)
% 1.71/1.38 % (11727)------------------------------
% 1.71/1.38 % (11727)------------------------------
% 1.71/1.39 % (11732)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_11343 for (2999ds/1041Mi)
% 1.71/1.39 % (11723)Instruction limit reached!
% 1.71/1.39 % (11723)------------------------------
% 1.71/1.39 % (11723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.39 % (11723)Termination reason: Unknown
% 1.71/1.39 % (11723)Termination phase: Saturation
% 1.71/1.39
% 1.71/1.39 % (11723)Memory used [KB]: 5628
% 1.71/1.39 % (11723)Time elapsed: 0.019 s
% 1.71/1.39 % (11723)Instructions burned: 27 (million)
% 1.71/1.39 % (11723)------------------------------
% 1.71/1.39 % (11723)------------------------------
% 1.71/1.39 % (11729)Instruction limit reached!
% 1.71/1.39 % (11729)------------------------------
% 1.71/1.39 % (11729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.39 % (11729)Termination reason: Unknown
% 1.71/1.39 % (11729)Termination phase: Saturation
% 1.71/1.39
% 1.71/1.39 % (11729)Memory used [KB]: 5884
% 1.71/1.39 % (11729)Time elapsed: 0.013 s
% 1.71/1.39 % (11729)Instructions burned: 38 (million)
% 1.71/1.39 % (11729)------------------------------
% 1.71/1.39 % (11729)------------------------------
% 1.71/1.39 % (11730)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_11343 for (2999ds/15Mi)
% 1.71/1.39 % (11731)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_11343 for (2999ds/3Mi)
% 1.71/1.39 % (11731)Instruction limit reached!
% 1.71/1.39 % (11731)------------------------------
% 1.71/1.39 % (11731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.71/1.39 % (11731)Termination reason: Unknown
% 1.71/1.39 % (11731)Termination phase: Property scanning
% 1.71/1.39
% 1.71/1.39 % (11731)Memory used [KB]: 1023
% 1.71/1.39 % (11731)Time elapsed: 0.004 s
% 1.71/1.39 % (11731)Instructions burned: 4 (million)
% 1.71/1.39 % (11731)------------------------------
% 1.71/1.39 % (11731)------------------------------
% 1.80/1.40 % (11730)Instruction limit reached!
% 1.80/1.40 % (11730)------------------------------
% 1.80/1.40 % (11730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.40 % (11730)Termination reason: Unknown
% 1.80/1.40 % (11730)Termination phase: Saturation
% 1.80/1.40
% 1.80/1.40 % (11730)Memory used [KB]: 5756
% 1.80/1.40 % (11730)Time elapsed: 0.011 s
% 1.80/1.40 % (11730)Instructions burned: 15 (million)
% 1.80/1.40 % (11730)------------------------------
% 1.80/1.40 % (11730)------------------------------
% 1.80/1.40 % (11735)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_11343 for (2999ds/3Mi)
% 1.80/1.40 % (11735)Instruction limit reached!
% 1.80/1.40 % (11735)------------------------------
% 1.80/1.40 % (11735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.40 % (11735)Termination reason: Unknown
% 1.80/1.40 % (11735)Termination phase: shuffling
% 1.80/1.40
% 1.80/1.40 % (11735)Memory used [KB]: 1023
% 1.80/1.40 % (11735)Time elapsed: 0.002 s
% 1.80/1.40 % (11735)Instructions burned: 3 (million)
% 1.80/1.40 % (11735)------------------------------
% 1.80/1.40 % (11735)------------------------------
% 1.80/1.40 % (11733)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_11343 for (2999ds/7Mi)
% 1.80/1.41 % (11733)Instruction limit reached!
% 1.80/1.41 % (11733)------------------------------
% 1.80/1.41 % (11733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.41 % (11733)Termination reason: Unknown
% 1.80/1.41 % (11733)Termination phase: Property scanning
% 1.80/1.41
% 1.80/1.41 % (11733)Memory used [KB]: 1023
% 1.80/1.41 % (11733)Time elapsed: 0.006 s
% 1.80/1.41 % (11733)Instructions burned: 8 (million)
% 1.80/1.41 % (11733)------------------------------
% 1.80/1.41 % (11733)------------------------------
% 1.80/1.41 % (11734)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_11343 for (2999ds/16Mi)
% 1.80/1.41 % (11738)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_11343 for (2999ds/3Mi)
% 1.80/1.41 % (11736)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_11343 for (2999ds/3Mi)
% 1.80/1.41 % (11738)Instruction limit reached!
% 1.80/1.41 % (11738)------------------------------
% 1.80/1.41 % (11738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.41 % (11738)Termination reason: Unknown
% 1.80/1.41 % (11738)Termination phase: shuffling
% 1.80/1.41
% 1.80/1.41 % (11738)Memory used [KB]: 1023
% 1.80/1.41 % (11738)Time elapsed: 0.002 s
% 1.80/1.41 % (11738)Instructions burned: 4 (million)
% 1.80/1.41 % (11738)------------------------------
% 1.80/1.41 % (11738)------------------------------
% 1.80/1.41 % (11736)Instruction limit reached!
% 1.80/1.41 % (11736)------------------------------
% 1.80/1.41 % (11736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.41 % (11736)Termination reason: Unknown
% 1.80/1.41 % (11736)Termination phase: Property scanning
% 1.80/1.41
% 1.80/1.41 % (11736)Memory used [KB]: 1023
% 1.80/1.41 % (11736)Time elapsed: 0.004 s
% 1.80/1.41 % (11736)Instructions burned: 4 (million)
% 1.80/1.41 % (11736)------------------------------
% 1.80/1.41 % (11736)------------------------------
% 1.80/1.42 % (11734)Instruction limit reached!
% 1.80/1.42 % (11734)------------------------------
% 1.80/1.42 % (11734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.42 % (11734)Termination reason: Unknown
% 1.80/1.42 % (11734)Termination phase: Saturation
% 1.80/1.42
% 1.80/1.42 % (11734)Memory used [KB]: 5756
% 1.80/1.42 % (11734)Time elapsed: 0.012 s
% 1.80/1.42 % (11734)Instructions burned: 17 (million)
% 1.80/1.42 % (11734)------------------------------
% 1.80/1.42 % (11734)------------------------------
% 1.80/1.42 % (11737)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_11343 for (2999ds/7Mi)
% 1.80/1.42 % (11739)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_11343 for (2999ds/4Mi)
% 1.80/1.42 % (11740)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_11343 for (2999ds/18Mi)
% 1.80/1.42 % (11737)Instruction limit reached!
% 1.80/1.42 % (11737)------------------------------
% 1.80/1.42 % (11737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.42 % (11737)Termination reason: Unknown
% 1.80/1.42 % (11737)Termination phase: Property scanning
% 1.80/1.42
% 1.80/1.42 % (11737)Memory used [KB]: 1023
% 1.80/1.42 % (11737)Time elapsed: 0.006 s
% 1.80/1.42 % (11737)Instructions burned: 8 (million)
% 1.80/1.42 % (11737)------------------------------
% 1.80/1.42 % (11737)------------------------------
% 1.80/1.42 % (11739)Instruction limit reached!
% 1.80/1.42 % (11739)------------------------------
% 1.80/1.42 % (11739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.42 % (11739)Termination reason: Unknown
% 1.80/1.42 % (11739)Termination phase: Preprocessing 1
% 1.80/1.42
% 1.80/1.42 % (11739)Memory used [KB]: 1023
% 1.80/1.42 % (11739)Time elapsed: 0.003 s
% 1.80/1.42 % (11739)Instructions burned: 4 (million)
% 1.80/1.42 % (11739)------------------------------
% 1.80/1.42 % (11739)------------------------------
% 1.80/1.43 % (11740)Instruction limit reached!
% 1.80/1.43 % (11740)------------------------------
% 1.80/1.43 % (11740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.43 % (11740)Termination reason: Unknown
% 1.80/1.43 % (11740)Termination phase: Saturation
% 1.80/1.43
% 1.80/1.43 % (11740)Memory used [KB]: 5628
% 1.80/1.43 % (11740)Time elapsed: 0.007 s
% 1.80/1.43 % (11740)Instructions burned: 19 (million)
% 1.80/1.43 % (11740)------------------------------
% 1.80/1.43 % (11740)------------------------------
% 1.80/1.43 % (11741)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_11343 for (2999ds/710Mi)
% 1.80/1.43 % (11744)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_11343 for (2999ds/21Mi)
% 1.80/1.44 % (11742)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_11343 for (2999ds/6Mi)
% 1.80/1.44 % (11745)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_11343 for (2999ds/5Mi)
% 1.80/1.44 % (11742)Instruction limit reached!
% 1.80/1.44 % (11742)------------------------------
% 1.80/1.44 % (11742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.44 % (11742)Termination reason: Unknown
% 1.80/1.44 % (11742)Termination phase: Property scanning
% 1.80/1.44
% 1.80/1.44 % (11742)Memory used [KB]: 1023
% 1.80/1.44 % (11742)Time elapsed: 0.005 s
% 1.80/1.44 % (11742)Instructions burned: 6 (million)
% 1.80/1.44 % (11742)------------------------------
% 1.80/1.44 % (11742)------------------------------
% 1.80/1.44 % (11745)Instruction limit reached!
% 1.80/1.44 % (11745)------------------------------
% 1.80/1.44 % (11745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.44 % (11745)Termination reason: Unknown
% 1.80/1.44 % (11745)Termination phase: Property scanning
% 1.80/1.44
% 1.80/1.44 % (11745)Memory used [KB]: 1023
% 1.80/1.44 % (11745)Time elapsed: 0.003 s
% 1.80/1.44 % (11745)Instructions burned: 7 (million)
% 1.80/1.44 % (11745)------------------------------
% 1.80/1.44 % (11745)------------------------------
% 1.80/1.44 % (11743)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_11343 for (2999ds/902Mi)
% 1.80/1.44 % (11744)Instruction limit reached!
% 1.80/1.44 % (11744)------------------------------
% 1.80/1.44 % (11744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.44 % (11744)Termination reason: Unknown
% 1.80/1.44 % (11744)Termination phase: Saturation
% 1.80/1.44
% 1.80/1.44 % (11744)Memory used [KB]: 5756
% 1.80/1.44 % (11744)Time elapsed: 0.009 s
% 1.80/1.44 % (11744)Instructions burned: 22 (million)
% 1.80/1.44 % (11744)------------------------------
% 1.80/1.44 % (11744)------------------------------
% 1.80/1.45 % (11747)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_11343 for (2999ds/377Mi)
% 1.80/1.45 % (11748)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_11343 for (2999ds/779Mi)
% 1.80/1.46 % (11746)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_11343 for (2999ds/6Mi)
% 1.80/1.46 % (11746)Instruction limit reached!
% 1.80/1.46 % (11746)------------------------------
% 1.80/1.46 % (11746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.46 % (11746)Termination reason: Unknown
% 1.80/1.46 % (11746)Termination phase: SInE selection
% 1.80/1.46
% 1.80/1.46 % (11746)Memory used [KB]: 1023
% 1.80/1.46 % (11746)Time elapsed: 0.005 s
% 1.80/1.46 % (11746)Instructions burned: 6 (million)
% 1.80/1.46 % (11746)------------------------------
% 1.80/1.46 % (11746)------------------------------
% 1.80/1.48 % (11749)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_11343 for (2999ds/19Mi)
% 1.80/1.48 % (11721)Instruction limit reached!
% 1.80/1.48 % (11721)------------------------------
% 1.80/1.48 % (11721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.48 % (11721)Termination reason: Unknown
% 1.80/1.48 % (11721)Termination phase: Saturation
% 1.80/1.48
% 1.80/1.48 % (11721)Memory used [KB]: 6396
% 1.80/1.48 % (11721)Time elapsed: 0.110 s
% 1.80/1.48 % (11721)Instructions burned: 184 (million)
% 1.80/1.48 % (11721)------------------------------
% 1.80/1.48 % (11721)------------------------------
% 1.80/1.49 % (11749)Instruction limit reached!
% 1.80/1.49 % (11749)------------------------------
% 1.80/1.49 % (11749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.49 % (11749)Termination reason: Unknown
% 1.80/1.49 % (11749)Termination phase: Saturation
% 1.80/1.49
% 1.80/1.49 % (11749)Memory used [KB]: 5756
% 1.80/1.49 % (11749)Time elapsed: 0.013 s
% 1.80/1.49 % (11749)Instructions burned: 19 (million)
% 1.80/1.49 % (11749)------------------------------
% 1.80/1.49 % (11749)------------------------------
% 1.80/1.50 % (11750)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_11343 for (2998ds/879Mi)
% 1.80/1.50 % (11751)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_11343 for (2998ds/17Mi)
% 1.80/1.52 % (11751)Instruction limit reached!
% 1.80/1.52 % (11751)------------------------------
% 1.80/1.52 % (11751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.52 % (11751)Termination reason: Unknown
% 1.80/1.52 % (11751)Termination phase: Saturation
% 1.80/1.52
% 1.80/1.52 % (11751)Memory used [KB]: 5756
% 1.80/1.52 % (11751)Time elapsed: 0.013 s
% 1.80/1.52 % (11751)Instructions burned: 18 (million)
% 1.80/1.52 % (11751)------------------------------
% 1.80/1.52 % (11751)------------------------------
% 1.80/1.53 % (11752)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_11343 for (2998ds/3Mi)
% 1.80/1.53 % (11752)Instruction limit reached!
% 1.80/1.53 % (11752)------------------------------
% 1.80/1.53 % (11752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.53 % (11752)Termination reason: Unknown
% 1.80/1.53 % (11752)Termination phase: Preprocessing 3
% 1.80/1.53
% 1.80/1.53 % (11752)Memory used [KB]: 1023
% 1.80/1.53 % (11752)Time elapsed: 0.003 s
% 1.80/1.53 % (11752)Instructions burned: 5 (million)
% 1.80/1.53 % (11752)------------------------------
% 1.80/1.53 % (11752)------------------------------
% 1.80/1.54 % (11753)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_11343 for (2998ds/30Mi)
% 1.80/1.55 % (11753)Instruction limit reached!
% 1.80/1.55 % (11753)------------------------------
% 1.80/1.55 % (11753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.55 % (11753)Termination reason: Unknown
% 1.80/1.55 % (11753)Termination phase: Saturation
% 1.80/1.55
% 1.80/1.55 % (11753)Memory used [KB]: 5756
% 1.80/1.55 % (11753)Time elapsed: 0.012 s
% 1.80/1.55 % (11753)Instructions burned: 30 (million)
% 1.80/1.55 % (11753)------------------------------
% 1.80/1.55 % (11753)------------------------------
% 1.80/1.56 % (11754)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_11343 for (2998ds/127Mi)
% 1.80/1.57 % (11747)Instruction limit reached!
% 1.80/1.57 % (11747)------------------------------
% 1.80/1.57 % (11747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.57 % (11747)Termination reason: Unknown
% 1.80/1.57 % (11747)Termination phase: Saturation
% 1.80/1.57
% 1.80/1.57 % (11747)Memory used [KB]: 6140
% 1.80/1.57 % (11747)Time elapsed: 0.119 s
% 1.80/1.57 % (11747)Instructions burned: 377 (million)
% 1.80/1.57 % (11747)------------------------------
% 1.80/1.57 % (11747)------------------------------
% 1.80/1.58 % (11755)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_11343 for (2998ds/100Mi)
% 1.80/1.61 % (11755)Instruction limit reached!
% 1.80/1.61 % (11755)------------------------------
% 1.80/1.61 % (11755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.61 % (11755)Termination reason: Unknown
% 1.80/1.61 % (11755)Termination phase: Saturation
% 1.80/1.61
% 1.80/1.61 % (11755)Memory used [KB]: 6012
% 1.80/1.61 % (11755)Time elapsed: 0.052 s
% 1.80/1.61 % (11755)Instructions burned: 100 (million)
% 1.80/1.61 % (11755)------------------------------
% 1.80/1.61 % (11755)------------------------------
% 1.80/1.61 % (11754)Instruction limit reached!
% 1.80/1.61 % (11754)------------------------------
% 1.80/1.61 % (11754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.61 % (11754)Termination reason: Unknown
% 1.80/1.61 % (11754)Termination phase: Saturation
% 1.80/1.61
% 1.80/1.61 % (11754)Memory used [KB]: 6012
% 1.80/1.61 % (11754)Time elapsed: 0.067 s
% 1.80/1.61 % (11754)Instructions burned: 129 (million)
% 1.80/1.61 % (11754)------------------------------
% 1.80/1.61 % (11754)------------------------------
% 1.80/1.62 % (11756)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_11343 for (2997ds/3Mi)
% 1.80/1.62 % (11756)Instruction limit reached!
% 1.80/1.62 % (11756)------------------------------
% 1.80/1.62 % (11756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.62 % (11756)Termination reason: Unknown
% 1.80/1.62 % (11756)Termination phase: shuffling
% 1.80/1.62
% 1.80/1.62 % (11756)Memory used [KB]: 1023
% 1.80/1.62 % (11756)Time elapsed: 0.002 s
% 1.80/1.62 % (11756)Instructions burned: 4 (million)
% 1.80/1.62 % (11756)------------------------------
% 1.80/1.62 % (11756)------------------------------
% 1.80/1.62 % (11757)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_11343 for (2997ds/20Mi)
% 1.80/1.62 % (11757)Instruction limit reached!
% 1.80/1.62 % (11757)------------------------------
% 1.80/1.62 % (11757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.62 % (11757)Termination reason: Unknown
% 1.80/1.62 % (11757)Termination phase: Saturation
% 1.80/1.62
% 1.80/1.62 % (11757)Memory used [KB]: 5628
% 1.80/1.62 % (11757)Time elapsed: 0.009 s
% 1.80/1.62 % (11757)Instructions burned: 21 (million)
% 1.80/1.62 % (11757)------------------------------
% 1.80/1.62 % (11757)------------------------------
% 1.80/1.63 % (11758)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_11343 for (2997ds/86Mi)
% 1.80/1.63 % (11759)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_11343 for (2997ds/107Mi)
% 1.80/1.65 % (11758)Instruction limit reached!
% 1.80/1.65 % (11758)------------------------------
% 1.80/1.65 % (11758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.65 % (11758)Termination reason: Unknown
% 1.80/1.65 % (11758)Termination phase: Saturation
% 1.80/1.65
% 1.80/1.65 % (11758)Memory used [KB]: 6140
% 1.80/1.65 % (11758)Time elapsed: 0.051 s
% 1.80/1.65 % (11758)Instructions burned: 86 (million)
% 1.80/1.65 % (11758)------------------------------
% 1.80/1.65 % (11758)------------------------------
% 1.80/1.66 % (11760)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_11343 for (2997ds/39Mi)
% 1.80/1.67 % (11759)Instruction limit reached!
% 1.80/1.67 % (11759)------------------------------
% 1.80/1.67 % (11759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.67 % (11759)Termination reason: Unknown
% 1.80/1.67 % (11759)Termination phase: Saturation
% 1.80/1.67
% 1.80/1.67 % (11759)Memory used [KB]: 5884
% 1.80/1.67 % (11759)Time elapsed: 0.060 s
% 1.80/1.67 % (11759)Instructions burned: 107 (million)
% 1.80/1.67 % (11759)------------------------------
% 1.80/1.67 % (11759)------------------------------
% 1.80/1.67 % (11760)Instruction limit reached!
% 1.80/1.67 % (11760)------------------------------
% 1.80/1.67 % (11760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.67 % (11760)Termination reason: Unknown
% 1.80/1.67 % (11760)Termination phase: Saturation
% 1.80/1.67
% 1.80/1.67 % (11760)Memory used [KB]: 5756
% 1.80/1.67 % (11760)Time elapsed: 0.014 s
% 1.80/1.67 % (11760)Instructions burned: 41 (million)
% 1.80/1.67 % (11760)------------------------------
% 1.80/1.67 % (11760)------------------------------
% 1.80/1.68 % (11761)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_11343 for (2996ds/448Mi)
% 1.80/1.68 % (11762)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_11343 for (2996ds/46Mi)
% 1.80/1.70 % (11762)Instruction limit reached!
% 1.80/1.70 % (11762)------------------------------
% 1.80/1.70 % (11762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.70 % (11762)Termination reason: Unknown
% 1.80/1.70 % (11762)Termination phase: Saturation
% 1.80/1.70
% 1.80/1.70 % (11762)Memory used [KB]: 5884
% 1.80/1.70 % (11762)Time elapsed: 0.017 s
% 1.80/1.70 % (11762)Instructions burned: 46 (million)
% 1.80/1.70 % (11762)------------------------------
% 1.80/1.70 % (11762)------------------------------
% 1.80/1.70 % (11748)Instruction limit reached!
% 1.80/1.70 % (11748)------------------------------
% 1.80/1.70 % (11748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.70 % (11748)Termination reason: Unknown
% 1.80/1.70 % (11748)Termination phase: Saturation
% 1.80/1.70
% 1.80/1.70 % (11748)Memory used [KB]: 6908
% 1.80/1.70 % (11748)Time elapsed: 0.253 s
% 1.80/1.70 % (11748)Instructions burned: 781 (million)
% 1.80/1.70 % (11748)------------------------------
% 1.80/1.70 % (11748)------------------------------
% 1.80/1.71 % (11741)Instruction limit reached!
% 1.80/1.71 % (11741)------------------------------
% 1.80/1.71 % (11741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.71 % (11741)Termination reason: Unknown
% 1.80/1.71 % (11741)Termination phase: Saturation
% 1.80/1.71
% 1.80/1.71 % (11741)Memory used [KB]: 7164
% 1.80/1.71 % (11741)Time elapsed: 0.277 s
% 1.80/1.71 % (11741)Instructions burned: 713 (million)
% 1.80/1.71 % (11741)------------------------------
% 1.80/1.71 % (11741)------------------------------
% 1.80/1.71 % (11763)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_11343 for (2996ds/98Mi)
% 1.80/1.71 % (11732)Instruction limit reached!
% 1.80/1.71 % (11732)------------------------------
% 1.80/1.71 % (11732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.71 % (11732)Termination reason: Unknown
% 1.80/1.71 % (11732)Termination phase: Saturation
% 1.80/1.71
% 1.80/1.71 % (11732)Memory used [KB]: 7547
% 1.80/1.71 % (11732)Time elapsed: 0.324 s
% 1.80/1.71 % (11732)Instructions burned: 1041 (million)
% 1.80/1.71 % (11732)------------------------------
% 1.80/1.71 % (11732)------------------------------
% 1.80/1.71 % (11764)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_11343 for (2996ds/507Mi)
% 1.80/1.72 % (11765)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_11343 for (2996ds/149Mi)
% 1.80/1.72 % (11764)First to succeed.
% 1.80/1.72 % (11766)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_11343 for (2996ds/39Mi)
% 1.80/1.72 % (11764)Refutation found. Thanks to Tanya!
% 1.80/1.72 % SZS status Theorem for DTF2THF_11343
% 1.80/1.72 % SZS output start Proof for DTF2THF_11343
% 1.80/1.72 thf(type_def_6, type, elem: $tType).
% 1.80/1.72 thf(type_def_7, type, nat: $tType).
% 1.80/1.72 thf(type_def_8, type, list: $tType).
% 1.80/1.72 thf(func_def_0, type, isPer: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 1.80/1.72 thf(func_def_2, type, elem: $tType).
% 1.80/1.72 thf(func_def_3, type, elemStar: elem > elem > $o).
% 1.80/1.72 thf(func_def_4, type, nat: $tType).
% 1.80/1.72 thf(func_def_5, type, natStar: nat > nat > $o).
% 1.80/1.72 thf(func_def_6, type, zero: nat).
% 1.80/1.72 thf(func_def_7, type, suc: nat > nat).
% 1.80/1.72 thf(func_def_8, type, plus: nat > nat > nat).
% 1.80/1.72 thf(func_def_9, type, list: $tType).
% 1.80/1.72 thf(func_def_10, type, listStar: nat > list > list > $o).
% 1.80/1.72 thf(func_def_11, type, nil: list).
% 1.80/1.72 thf(func_def_12, type, cons: nat > elem > list > list).
% 1.80/1.72 thf(func_def_13, type, app: nat > nat > list > list > list).
% 1.80/1.72 thf(func_def_14, type, rev: nat > list > list).
% 1.80/1.72 thf(func_def_17, type, sK0: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.80/1.72 thf(func_def_18, type, sK1: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.80/1.72 thf(func_def_26, type, sK2: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.80/1.72 thf(func_def_27, type, sK3: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.80/1.72 thf(func_def_28, type, sK4: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.80/1.72 thf(func_def_29, type, sK5: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.80/1.72 thf(func_def_30, type, sK6: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 1.80/1.72 thf(func_def_31, type, sK7: nat).
% 1.80/1.72 thf(func_def_32, type, sK8: list).
% 1.80/1.72 thf(func_def_33, type, sK9: elem).
% 1.80/1.72 thf(func_def_34, type, sK10: nat).
% 1.80/1.72 thf(func_def_35, type, sK11: list).
% 1.80/1.72 thf(func_def_36, type, sK12: (nat > $o) > nat).
% 1.80/1.72 thf(func_def_38, type, ph14: !>[X0: $tType]:(X0)).
% 1.80/1.72 thf(f157,plain,(
% 1.80/1.72 $false),
% 1.80/1.72 inference(subsumption_resolution,[status(thm)],[f154,f119])).
% 1.80/1.72 thf(f119,plain,(
% 1.80/1.72 ((listStar @ zero @ nil @ nil) = $true)),
% 1.80/1.72 inference(cnf_transformation,[status(thm)],[f55])).
% 1.80/1.72 thf(f55,plain,(
% 1.80/1.72 ((listStar @ zero @ nil @ nil) = $true)),
% 1.80/1.72 inference(fool_elimination,[status(thm)],[f54])).
% 1.80/1.72 thf(f54,plain,(
% 1.80/1.72 (listStar @ zero @ nil @ nil)),
% 1.80/1.72 inference(rectify,[status(thm)],[f5])).
% 1.80/1.72 thf(f5,axiom,(
% 1.80/1.72 (listStar @ zero @ nil @ nil)),
% 1.80/1.72 file('/export/starexec/sandbox/tmp/tmp.Lt8swKET46/DTF2THF_11343.p',nil_tp_ax)).
% 1.80/1.72 thf(f154,plain,(
% 1.80/1.72 ((listStar @ zero @ nil @ nil) != $true)),
% 1.80/1.72 inference(trivial_inequality_removal,[status(thm)],[f150])).
% 1.80/1.72 thf(f150,plain,(
% 1.80/1.72 ((listStar @ zero @ nil @ nil) != $true) | ($true != $true)),
% 1.80/1.72 inference(superposition,[status(thm)],[f147,f122])).
% 1.80/1.72 thf(f122,plain,(
% 1.80/1.72 ( ! [X2 : list,X3 : list,X0 : nat,X1 : elem] : (($true = (listStar @ (suc @ X0) @ (cons @ X0 @ X1 @ X2) @ (cons @ X0 @ X1 @ X3))) | ($true != (listStar @ X0 @ X2 @ X3))) )),
% 1.80/1.72 inference(cnf_transformation,[status(thm)],[f83])).
% 1.80/1.72 thf(f83,plain,(
% 1.80/1.72 ! [X0 : nat,X1 : elem,X2 : list,X3 : list] : (($true != (listStar @ X0 @ X2 @ X3)) | ($true = (listStar @ (suc @ X0) @ (cons @ X0 @ X1 @ X2) @ (cons @ X0 @ X1 @ X3))))),
% 1.80/1.72 inference(ennf_transformation,[status(thm)],[f41])).
% 1.80/1.72 thf(f41,plain,(
% 1.80/1.72 ! [X0 : nat,X1 : elem,X2 : list,X3 : list] : (($true = (listStar @ X0 @ X2 @ X3)) => ($true = (listStar @ (suc @ X0) @ (cons @ X0 @ X1 @ X2) @ (cons @ X0 @ X1 @ X3))))),
% 1.80/1.72 inference(fool_elimination,[status(thm)],[f40])).
% 1.80/1.72 thf(f40,plain,(
% 1.80/1.72 ! [X0 : nat,X1 : elem,X2 : list,X3 : list] : ((listStar @ X0 @ X2 @ X3) => (listStar @ (suc @ X0) @ (cons @ X0 @ X1 @ X2) @ (cons @ X0 @ X1 @ X3)))),
% 1.80/1.72 inference(rectify,[status(thm)],[f6])).
% 1.80/1.72 thf(f6,axiom,(
% 1.80/1.72 ! [X6 : nat,X7 : elem,X8 : list,X9 : list] : ((listStar @ X6 @ X8 @ X9) => (listStar @ (suc @ X6) @ (cons @ X6 @ X7 @ X8) @ (cons @ X6 @ X7 @ X9)))),
% 1.80/1.72 file('/export/starexec/sandbox/tmp/tmp.Lt8swKET46/DTF2THF_11343.p',cons_tp_ax)).
% 1.80/1.72 thf(f147,plain,(
% 1.80/1.72 ($true != (listStar @ (suc @ zero) @ (cons @ zero @ sK9 @ nil) @ (cons @ zero @ sK9 @ nil)))),
% 1.80/1.72 inference(subsumption_resolution,[status(thm)],[f146,f110])).
% 1.80/1.72 thf(f110,plain,(
% 1.80/1.72 ((listStar @ sK7 @ sK8 @ sK8) = $true)),
% 1.80/1.72 inference(cnf_transformation,[status(thm)],[f96])).
% 1.80/1.72 thf(f96,plain,(
% 1.80/1.72 ((listStar @ sK10 @ sK11 @ sK11) = $true) & ($true != (listStar @ (plus @ (plus @ (suc @ zero) @ sK10) @ (plus @ (suc @ zero) @ sK10)) @ (app @ sK7 @ (plus @ (suc @ zero) @ sK10) @ sK8 @ (app @ (suc @ zero) @ sK10 @ (cons @ zero @ sK9 @ nil) @ sK11)) @ (app @ (plus @ sK7 @ (suc @ zero)) @ sK10 @ (app @ sK7 @ (suc @ zero) @ sK8 @ (cons @ zero @ sK9 @ nil)) @ sK11))) & ((listStar @ sK7 @ sK8 @ sK8) = $true)),
% 1.80/1.72 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11])],[f82,f95])).
% 1.80/1.72 thf(f95,plain,(
% 1.80/1.72 ? [X0 : nat,X1 : list,X2 : elem,X3 : nat,X4 : list] : (($true = (listStar @ X3 @ X4 @ X4)) & ((listStar @ (plus @ (plus @ (suc @ zero) @ X3) @ (plus @ (suc @ zero) @ X3)) @ (app @ X0 @ (plus @ (suc @ zero) @ X3) @ X1 @ (app @ (suc @ zero) @ X3 @ (cons @ zero @ X2 @ nil) @ X4)) @ (app @ (plus @ X0 @ (suc @ zero)) @ X3 @ (app @ X0 @ (suc @ zero) @ X1 @ (cons @ zero @ X2 @ nil)) @ X4)) != $true) & ((listStar @ X0 @ X1 @ X1) = $true)) => (((listStar @ sK10 @ sK11 @ sK11) = $true) & ($true != (listStar @ (plus @ (plus @ (suc @ zero) @ sK10) @ (plus @ (suc @ zero) @ sK10)) @ (app @ sK7 @ (plus @ (suc @ zero) @ sK10) @ sK8 @ (app @ (suc @ zero) @ sK10 @ (cons @ zero @ sK9 @ nil) @ sK11)) @ (app @ (plus @ sK7 @ (suc @ zero)) @ sK10 @ (app @ sK7 @ (suc @ zero) @ sK8 @ (cons @ zero @ sK9 @ nil)) @ sK11))) & ((listStar @ sK7 @ sK8 @ sK8) = $true))),
% 1.80/1.72 introduced(definition,[],[choice_axiom])).
% 1.80/1.72 thf(f82,plain,(
% 1.80/1.72 ? [X0 : nat,X1 : list,X2 : elem,X3 : nat,X4 : list] : (($true = (listStar @ X3 @ X4 @ X4)) & ((listStar @ (plus @ (plus @ (suc @ zero) @ X3) @ (plus @ (suc @ zero) @ X3)) @ (app @ X0 @ (plus @ (suc @ zero) @ X3) @ X1 @ (app @ (suc @ zero) @ X3 @ (cons @ zero @ X2 @ nil) @ X4)) @ (app @ (plus @ X0 @ (suc @ zero)) @ X3 @ (app @ X0 @ (suc @ zero) @ X1 @ (cons @ zero @ X2 @ nil)) @ X4)) != $true) & ((listStar @ X0 @ X1 @ X1) = $true))),
% 1.80/1.72 inference(flattening,[status(thm)],[f81])).
% 1.80/1.72 thf(f81,plain,(
% 1.80/1.72 ? [X0 : nat,X1 : list,X2 : elem,X3 : nat,X4 : list] : ((((listStar @ (plus @ (plus @ (suc @ zero) @ X3) @ (plus @ (suc @ zero) @ X3)) @ (app @ X0 @ (plus @ (suc @ zero) @ X3) @ X1 @ (app @ (suc @ zero) @ X3 @ (cons @ zero @ X2 @ nil) @ X4)) @ (app @ (plus @ X0 @ (suc @ zero)) @ X3 @ (app @ X0 @ (suc @ zero) @ X1 @ (cons @ zero @ X2 @ nil)) @ X4)) != $true) & ($true = (listStar @ X3 @ X4 @ X4))) & ((listStar @ X0 @ X1 @ X1) = $true))),
% 1.80/1.72 inference(ennf_transformation,[status(thm)],[f53])).
% 1.80/1.72 thf(f53,plain,(
% 1.80/1.72 ~! [X0 : nat,X1 : list,X2 : elem,X3 : nat,X4 : list] : (((listStar @ X0 @ X1 @ X1) = $true) => (($true = (listStar @ X3 @ X4 @ X4)) => ((listStar @ (plus @ (plus @ (suc @ zero) @ X3) @ (plus @ (suc @ zero) @ X3)) @ (app @ X0 @ (plus @ (suc @ zero) @ X3) @ X1 @ (app @ (suc @ zero) @ X3 @ (cons @ zero @ X2 @ nil) @ X4)) @ (app @ (plus @ X0 @ (suc @ zero)) @ X3 @ (app @ X0 @ (suc @ zero) @ X1 @ (cons @ zero @ X2 @ nil)) @ X4)) = $true)))),
% 1.80/1.72 inference(fool_elimination,[status(thm)],[f52])).
% 1.80/1.72 thf(f52,plain,(
% 1.80/1.72 ~! [X0 : nat,X1 : list,X2 : elem,X3 : nat,X4 : list] : ((listStar @ X0 @ X1 @ X1) => ((listStar @ X3 @ X4 @ X4) => (listStar @ (plus @ (plus @ (suc @ zero) @ X3) @ (plus @ (suc @ zero) @ X3)) @ (app @ X0 @ (plus @ (suc @ zero) @ X3) @ X1 @ (app @ (suc @ zero) @ X3 @ (cons @ zero @ X2 @ nil) @ X4)) @ (app @ (plus @ X0 @ (suc @ zero)) @ X3 @ (app @ X0 @ (suc @ zero) @ X1 @ (cons @ zero @ X2 @ nil)) @ X4))))),
% 1.80/1.72 inference(rectify,[status(thm)],[f20])).
% 1.80/1.72 thf(f20,negated_conjecture,(
% 1.80/1.72 ~! [X10 : nat,X16 : list,X2 : elem,X15 : nat,X18 : list] : ((listStar @ X10 @ X16 @ X16) => ((listStar @ X15 @ X18 @ X18) => (listStar @ (plus @ (plus @ (suc @ zero) @ X15) @ (plus @ (suc @ zero) @ X15)) @ (app @ X10 @ (plus @ (suc @ zero) @ X15) @ X16 @ (app @ (suc @ zero) @ X15 @ (cons @ zero @ X2 @ nil) @ X18)) @ (app @ (plus @ X10 @ (suc @ zero)) @ X15 @ (app @ X10 @ (suc @ zero) @ X16 @ (cons @ zero @ X2 @ nil)) @ X18))))),
% 1.80/1.72 inference(negated_conjecture,[status(cth)],[f19])).
% 1.80/1.72 thf(f19,conjecture,(
% 1.80/1.72 ! [X10 : nat,X16 : list,X2 : elem,X15 : nat,X18 : list] : ((listStar @ X10 @ X16 @ X16) => ((listStar @ X15 @ X18 @ X18) => (listStar @ (plus @ (plus @ (suc @ zero) @ X15) @ (plus @ (suc @ zero) @ X15)) @ (app @ X10 @ (plus @ (suc @ zero) @ X15) @ X16 @ (app @ (suc @ zero) @ X15 @ (cons @ zero @ X2 @ nil) @ X18)) @ (app @ (plus @ X10 @ (suc @ zero)) @ X15 @ (app @ X10 @ (suc @ zero) @ X16 @ (cons @ zero @ X2 @ nil)) @ X18))))),
% 1.80/1.72 file('/export/starexec/sandbox/tmp/tmp.Lt8swKET46/DTF2THF_11343.p',list_app_assoc_m1_step1)).
% 1.80/1.72 thf(f146,plain,(
% 1.80/1.72 ($true != (listStar @ (suc @ zero) @ (cons @ zero @ sK9 @ nil) @ (cons @ zero @ sK9 @ nil))) | ((listStar @ sK7 @ sK8 @ sK8) != $true)),
% 1.80/1.72 inference(subsumption_resolution,[status(thm)],[f145,f112])).
% 1.80/1.72 thf(f112,plain,(
% 1.80/1.72 ((listStar @ sK10 @ sK11 @ sK11) = $true)),
% 1.80/1.72 inference(cnf_transformation,[status(thm)],[f96])).
% 1.80/1.72 thf(f145,plain,(
% 1.80/1.72 ((listStar @ sK10 @ sK11 @ sK11) != $true) | ((listStar @ sK7 @ sK8 @ sK8) != $true) | ($true != (listStar @ (suc @ zero) @ (cons @ zero @ sK9 @ nil) @ (cons @ zero @ sK9 @ nil)))),
% 1.80/1.72 inference(trivial_inequality_removal,[status(thm)],[f140])).
% 1.80/1.72 thf(f140,plain,(
% 1.80/1.72 ($true != $true) | ($true != (listStar @ (suc @ zero) @ (cons @ zero @ sK9 @ nil) @ (cons @ zero @ sK9 @ nil))) | ((listStar @ sK7 @ sK8 @ sK8) != $true) | ((listStar @ sK10 @ sK11 @ sK11) != $true)),
% 1.80/1.72 inference(superposition,[status(thm)],[f111,f117])).
% 1.80/1.72 thf(f117,plain,(
% 1.80/1.72 ( ! [X2 : nat,X3 : list,X0 : nat,X1 : list,X4 : nat,X5 : list] : (($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 @ X2 @ X3 @ X3)) | ((listStar @ X0 @ X1 @ X1) != $true) | ($true != (listStar @ X4 @ X5 @ X5))) )),
% 1.80/1.72 inference(cnf_transformation,[status(thm)],[f88])).
% 1.80/1.72 thf(f88,plain,(
% 1.80/1.72 ! [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))) | ((listStar @ X0 @ X1 @ X1) != $true) | ($true != (listStar @ X4 @ X5 @ X5)) | ($true != (listStar @ X2 @ X3 @ X3)))),
% 1.80/1.72 inference(flattening,[status(thm)],[f87])).
% 1.80/1.72 thf(f87,plain,(
% 1.80/1.72 ! [X0 : nat,X1 : list,X2 : nat,X3 : list,X4 : nat,X5 : list] : (((($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))) | ((listStar @ X0 @ X1 @ X1) != $true))),
% 1.80/1.72 inference(ennf_transformation,[status(thm)],[f27])).
% 1.80/1.72 thf(f27,plain,(
% 1.80/1.72 ! [X0 : nat,X1 : list,X2 : nat,X3 : list,X4 : nat,X5 : list] : (((listStar @ X0 @ X1 @ X1) = $true) => (($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))))))),
% 1.80/1.72 inference(fool_elimination,[status(thm)],[f26])).
% 1.80/1.72 thf(f26,plain,(
% 1.80/1.72 ! [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)))))),
% 1.80/1.72 inference(rectify,[status(thm)],[f18])).
% 1.80/1.72 thf(f18,axiom,(
% 1.80/1.72 ! [X10 : nat,X16 : list,X14 : nat,X17 : list,X15 : nat,X18 : list] : ((listStar @ X10 @ X16 @ X16) => ((listStar @ X14 @ X17 @ X17) => ((listStar @ X15 @ X18 @ X18) => (listStar @ (plus @ (plus @ X14 @ X15) @ (plus @ X14 @ X15)) @ (app @ X10 @ (plus @ X14 @ X15) @ X16 @ (app @ X14 @ X15 @ X17 @ X18)) @ (app @ (plus @ X10 @ X14) @ X15 @ (app @ X10 @ X14 @ X16 @ X17) @ X18)))))),
% 1.80/1.72 file('/export/starexec/sandbox/tmp/tmp.Lt8swKET46/DTF2THF_11343.p',list_app_assoc)).
% 1.80/1.72 thf(f111,plain,(
% 1.80/1.72 ($true != (listStar @ (plus @ (plus @ (suc @ zero) @ sK10) @ (plus @ (suc @ zero) @ sK10)) @ (app @ sK7 @ (plus @ (suc @ zero) @ sK10) @ sK8 @ (app @ (suc @ zero) @ sK10 @ (cons @ zero @ sK9 @ nil) @ sK11)) @ (app @ (plus @ sK7 @ (suc @ zero)) @ sK10 @ (app @ sK7 @ (suc @ zero) @ sK8 @ (cons @ zero @ sK9 @ nil)) @ sK11)))),
% 1.80/1.72 inference(cnf_transformation,[status(thm)],[f96])).
% 1.80/1.72 % SZS output end Proof for DTF2THF_11343
% 1.80/1.72 % (11764)------------------------------
% 1.80/1.72 % (11764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.72 % (11764)Termination reason: Refutation
% 1.80/1.72
% 1.80/1.72 % (11764)Memory used [KB]: 5756
% 1.80/1.72 % (11764)Time elapsed: 0.009 s
% 1.80/1.72 % (11764)Instructions burned: 19 (million)
% 1.80/1.72 % (11764)------------------------------
% 1.80/1.72 % (11764)------------------------------
% 1.80/1.72 % (11720)Success in time 0.366 s
%------------------------------------------------------------------------------