TSTP Solution File: DAT070_1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT070_1 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n019.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 : Tue Apr 30 11:03:58 EDT 2024
% Result : Theorem 0.15s 0.34s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 81
% Syntax : Number of formulae : 204 ( 65 unt; 11 typ; 0 def)
% Number of atoms : 413 ( 131 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 378 ( 158 ~; 151 |; 16 &)
% ( 46 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 387 ( 59 atm; 100 fun; 62 num; 166 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 9 ( 6 >; 3 *; 0 +; 0 <<)
% Number of predicates : 46 ( 43 usr; 43 prp; 0-2 aty)
% Number of functors : 13 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 282 ( 276 !; 6 ?; 282 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
heap: $tType ).
tff(func_def_0,type,
empty: heap ).
tff(func_def_1,type,
toop: heap > $int ).
tff(func_def_2,type,
sel: ( heap * $int ) > $int ).
tff(func_def_3,type,
length: heap > $int ).
tff(func_def_4,type,
app: ( heap * $int ) > heap ).
tff(func_def_5,type,
get: heap > heap ).
tff(func_def_10,type,
sK0: $int ).
tff(func_def_11,type,
sK1: $int ).
tff(func_def_12,type,
sK2: heap ).
tff(pred_def_1,type,
lsls: ( heap * heap ) > $o ).
tff(f368,plain,
$false,
inference(avatar_sat_refutation,[],[f81,f86,f90,f94,f98,f103,f107,f111,f115,f119,f123,f127,f131,f135,f139,f143,f147,f151,f162,f166,f170,f174,f178,f193,f197,f201,f205,f209,f213,f217,f261,f265,f290,f300,f310,f320,f326,f330,f344,f348,f352,f356,f367]) ).
tff(f367,plain,
( ~ spl3_3
| ~ spl3_36 ),
inference(avatar_contradiction_clause,[],[f365]) ).
tff(f365,plain,
( $false
| ~ spl3_3
| ~ spl3_36 ),
inference(resolution,[],[f319,f89]) ).
tff(f89,plain,
( ! [X0: $int] : ~ $less(X0,X0)
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f88]) ).
tff(f88,plain,
( spl3_3
<=> ! [X0: $int] : ~ $less(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
tff(f319,plain,
( $less(sK1,sK1)
| ~ spl3_36 ),
inference(avatar_component_clause,[],[f317]) ).
tff(f317,plain,
( spl3_36
<=> $less(sK1,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_36])]) ).
tff(f356,plain,
( spl3_42
| ~ spl3_12
| ~ spl3_31 ),
inference(avatar_split_clause,[],[f281,f259,f125,f354]) ).
tff(f354,plain,
( spl3_42
<=> ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_42])]) ).
tff(f125,plain,
( spl3_12
<=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).
tff(f259,plain,
( spl3_31
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_31])]) ).
tff(f281,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 )
| ~ spl3_12
| ~ spl3_31 ),
inference(evaluation,[],[f266]) ).
tff(f266,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = $sum(0,X1) )
| ~ spl3_12
| ~ spl3_31 ),
inference(superposition,[],[f260,f126]) ).
tff(f126,plain,
( ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) )
| ~ spl3_12 ),
inference(avatar_component_clause,[],[f125]) ).
tff(f260,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) )
| ~ spl3_31 ),
inference(avatar_component_clause,[],[f259]) ).
tff(f352,plain,
( spl3_41
| ~ spl3_11
| ~ spl3_23 ),
inference(avatar_split_clause,[],[f188,f176,f121,f350]) ).
tff(f350,plain,
( spl3_41
<=> ! [X2: heap,X0: heap,X1: $int] :
( ~ lsls(app(X0,X1),X2)
| lsls(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_41])]) ).
tff(f121,plain,
( spl3_11
<=> ! [X2: heap,X0: $int] : lsls(X2,app(X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).
tff(f176,plain,
( spl3_23
<=> ! [X2: heap,X0: heap,X1: heap] :
( lsls(X1,X2)
| ~ lsls(X0,X2)
| ~ lsls(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_23])]) ).
tff(f188,plain,
( ! [X2: heap,X0: heap,X1: $int] :
( ~ lsls(app(X0,X1),X2)
| lsls(X0,X2) )
| ~ spl3_11
| ~ spl3_23 ),
inference(resolution,[],[f177,f122]) ).
tff(f122,plain,
( ! [X2: heap,X0: $int] : lsls(X2,app(X2,X0))
| ~ spl3_11 ),
inference(avatar_component_clause,[],[f121]) ).
tff(f177,plain,
( ! [X2: heap,X0: heap,X1: heap] :
( ~ lsls(X1,X0)
| ~ lsls(X0,X2)
| lsls(X1,X2) )
| ~ spl3_23 ),
inference(avatar_component_clause,[],[f176]) ).
tff(f348,plain,
( spl3_40
| ~ spl3_15
| ~ spl3_17 ),
inference(avatar_split_clause,[],[f156,f145,f137,f346]) ).
tff(f346,plain,
( spl3_40
<=> ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_40])]) ).
tff(f137,plain,
( spl3_15
<=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_15])]) ).
tff(f145,plain,
( spl3_17
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_17])]) ).
tff(f156,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) )
| ~ spl3_15
| ~ spl3_17 ),
inference(superposition,[],[f146,f138]) ).
tff(f138,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) )
| ~ spl3_15 ),
inference(avatar_component_clause,[],[f137]) ).
tff(f146,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) )
| ~ spl3_17 ),
inference(avatar_component_clause,[],[f145]) ).
tff(f344,plain,
( spl3_39
| ~ spl3_15
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f153,f141,f137,f342]) ).
tff(f342,plain,
( spl3_39
<=> ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_39])]) ).
tff(f141,plain,
( spl3_16
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).
tff(f153,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) )
| ~ spl3_15
| ~ spl3_16 ),
inference(superposition,[],[f142,f138]) ).
tff(f142,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) )
| ~ spl3_16 ),
inference(avatar_component_clause,[],[f141]) ).
tff(f330,plain,
( spl3_38
| ~ spl3_6
| ~ spl3_30 ),
inference(avatar_split_clause,[],[f255,f215,f100,f328]) ).
tff(f328,plain,
( spl3_38
<=> ! [X0: $int] : ( sel(app(empty,X0),1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_38])]) ).
tff(f100,plain,
( spl3_6
<=> ( 0 = length(empty) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
tff(f215,plain,
( spl3_30
<=> ! [X2: $int,X0: heap] : ( sel(app(X0,X2),$sum(1,length(X0))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_30])]) ).
tff(f255,plain,
( ! [X0: $int] : ( sel(app(empty,X0),1) = X0 )
| ~ spl3_6
| ~ spl3_30 ),
inference(evaluation,[],[f252]) ).
tff(f252,plain,
( ! [X0: $int] : ( sel(app(empty,X0),$sum(1,0)) = X0 )
| ~ spl3_6
| ~ spl3_30 ),
inference(superposition,[],[f216,f102]) ).
tff(f102,plain,
( ( 0 = length(empty) )
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f100]) ).
tff(f216,plain,
( ! [X2: $int,X0: heap] : ( sel(app(X0,X2),$sum(1,length(X0))) = X2 )
| ~ spl3_30 ),
inference(avatar_component_clause,[],[f215]) ).
tff(f326,plain,
( spl3_37
| ~ spl3_11
| ~ spl3_27 ),
inference(avatar_split_clause,[],[f243,f203,f121,f324]) ).
tff(f324,plain,
( spl3_37
<=> ! [X0: heap] :
( lsls(get(X0),X0)
| ( empty = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_37])]) ).
tff(f203,plain,
( spl3_27
<=> ! [X0: heap] :
( ( app(get(X0),toop(X0)) = X0 )
| ( empty = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_27])]) ).
tff(f243,plain,
( ! [X0: heap] :
( lsls(get(X0),X0)
| ( empty = X0 ) )
| ~ spl3_11
| ~ spl3_27 ),
inference(superposition,[],[f122,f204]) ).
tff(f204,plain,
( ! [X0: heap] :
( ( app(get(X0),toop(X0)) = X0 )
| ( empty = X0 ) )
| ~ spl3_27 ),
inference(avatar_component_clause,[],[f203]) ).
tff(f320,plain,
( spl3_36
| ~ spl3_1
| ~ spl3_34 ),
inference(avatar_split_clause,[],[f302,f297,f78,f317]) ).
tff(f78,plain,
( spl3_1
<=> $less(sK1,$sum(1,length(sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
tff(f297,plain,
( spl3_34
<=> ( sK1 = $sum(1,length(sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_34])]) ).
tff(f302,plain,
( $less(sK1,sK1)
| ~ spl3_1
| ~ spl3_34 ),
inference(superposition,[],[f80,f299]) ).
tff(f299,plain,
( ( sK1 = $sum(1,length(sK2)) )
| ~ spl3_34 ),
inference(avatar_component_clause,[],[f297]) ).
tff(f80,plain,
( $less(sK1,$sum(1,length(sK2)))
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f78]) ).
tff(f310,plain,
( spl3_35
| ~ spl3_4
| ~ spl3_18 ),
inference(avatar_split_clause,[],[f158,f149,f92,f308]) ).
tff(f308,plain,
( spl3_35
<=> ! [X0: heap,X1: $int] : ~ lsls(app(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_35])]) ).
tff(f92,plain,
( spl3_4
<=> ! [X0: heap] : ~ lsls(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
tff(f149,plain,
( spl3_18
<=> ! [X2: heap,X0: $int,X1: heap] :
( lsls(X1,app(X2,X0))
| ~ lsls(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_18])]) ).
tff(f158,plain,
( ! [X0: heap,X1: $int] : ~ lsls(app(X0,X1),X0)
| ~ spl3_4
| ~ spl3_18 ),
inference(resolution,[],[f150,f93]) ).
tff(f93,plain,
( ! [X0: heap] : ~ lsls(X0,X0)
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f92]) ).
tff(f150,plain,
( ! [X2: heap,X0: $int,X1: heap] :
( lsls(X1,app(X2,X0))
| ~ lsls(X1,X2) )
| ~ spl3_18 ),
inference(avatar_component_clause,[],[f149]) ).
tff(f300,plain,
( spl3_34
| spl3_2
| ~ spl3_33 ),
inference(avatar_split_clause,[],[f295,f288,f83,f297]) ).
tff(f83,plain,
( spl3_2
<=> ( sel(app(sK2,sK0),sK1) = sel(sK2,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
tff(f288,plain,
( spl3_33
<=> ! [X2: $int,X0: $int,X1: heap] :
( ( sel(app(X1,X0),X2) = sel(X1,X2) )
| ( $sum(1,length(X1)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_33])]) ).
tff(f295,plain,
( ( sK1 = $sum(1,length(sK2)) )
| spl3_2
| ~ spl3_33 ),
inference(trivial_inequality_removal,[],[f293]) ).
tff(f293,plain,
( ( sel(sK2,sK1) != sel(sK2,sK1) )
| ( sK1 = $sum(1,length(sK2)) )
| spl3_2
| ~ spl3_33 ),
inference(superposition,[],[f85,f289]) ).
tff(f289,plain,
( ! [X2: $int,X0: $int,X1: heap] :
( ( sel(app(X1,X0),X2) = sel(X1,X2) )
| ( $sum(1,length(X1)) = X2 ) )
| ~ spl3_33 ),
inference(avatar_component_clause,[],[f288]) ).
tff(f85,plain,
( ( sel(app(sK2,sK0),sK1) != sel(sK2,sK1) )
| spl3_2 ),
inference(avatar_component_clause,[],[f83]) ).
tff(f290,plain,
spl3_33,
inference(avatar_split_clause,[],[f64,f288]) ).
tff(f64,plain,
! [X2: $int,X0: $int,X1: heap] :
( ( sel(app(X1,X0),X2) = sel(X1,X2) )
| ( $sum(1,length(X1)) = X2 ) ),
inference(cnf_transformation,[],[f43]) ).
tff(f43,plain,
! [X0: $int,X1: heap,X2: $int] :
( ( sel(app(X1,X0),X2) = sel(X1,X2) )
| ( $sum(1,length(X1)) = X2 ) ),
inference(ennf_transformation,[],[f37]) ).
tff(f37,plain,
! [X0: $int,X1: heap,X2: $int] :
( ( $sum(1,length(X1)) != X2 )
=> ( sel(app(X1,X0),X2) = sel(X1,X2) ) ),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
! [X2: $int,X1: heap,X0: $int] :
( ( $sum(1,length(X1)) != X0 )
=> ( sel(app(X1,X2),X0) = sel(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_3) ).
tff(f265,plain,
spl3_32,
inference(avatar_split_clause,[],[f67,f263]) ).
tff(f263,plain,
( spl3_32
<=> ! [X2: heap,X0: $int,X1: heap] :
( lsls(X1,X2)
| ( X1 = X2 )
| ~ lsls(X1,app(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_32])]) ).
tff(f67,plain,
! [X2: heap,X0: $int,X1: heap] :
( lsls(X1,X2)
| ( X1 = X2 )
| ~ lsls(X1,app(X2,X0)) ),
inference(cnf_transformation,[],[f50]) ).
tff(f50,plain,
! [X0: $int,X1: heap,X2: heap] :
( ( lsls(X1,app(X2,X0))
| ( ~ lsls(X1,X2)
& ( X1 != X2 ) ) )
& ( lsls(X1,X2)
| ( X1 = X2 )
| ~ lsls(X1,app(X2,X0)) ) ),
inference(flattening,[],[f49]) ).
tff(f49,plain,
! [X0: $int,X1: heap,X2: heap] :
( ( lsls(X1,app(X2,X0))
| ( ~ lsls(X1,X2)
& ( X1 != X2 ) ) )
& ( lsls(X1,X2)
| ( X1 = X2 )
| ~ lsls(X1,app(X2,X0)) ) ),
inference(nnf_transformation,[],[f40]) ).
tff(f40,plain,
! [X0: $int,X1: heap,X2: heap] :
( lsls(X1,app(X2,X0))
<=> ( lsls(X1,X2)
| ( X1 = X2 ) ) ),
inference(rectify,[],[f14]) ).
tff(f14,axiom,
! [X2: $int,X3: heap,X1: heap] :
( lsls(X3,app(X1,X2))
<=> ( lsls(X3,X1)
| ( X1 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_30) ).
tff(f261,plain,
spl3_31,
inference(avatar_split_clause,[],[f18,f259]) ).
tff(f18,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f217,plain,
spl3_30,
inference(avatar_split_clause,[],[f73,f215]) ).
tff(f73,plain,
! [X2: $int,X0: heap] : ( sel(app(X0,X2),$sum(1,length(X0))) = X2 ),
inference(equality_resolution,[],[f65]) ).
tff(f65,plain,
! [X2: $int,X0: heap,X1: $int] :
( ( sel(app(X0,X2),X1) = X2 )
| ( $sum(1,length(X0)) != X1 ) ),
inference(cnf_transformation,[],[f44]) ).
tff(f44,plain,
! [X0: heap,X1: $int,X2: $int] :
( ( sel(app(X0,X2),X1) = X2 )
| ( $sum(1,length(X0)) != X1 ) ),
inference(ennf_transformation,[],[f38]) ).
tff(f38,plain,
! [X0: heap,X1: $int,X2: $int] :
( ( $sum(1,length(X0)) = X1 )
=> ( sel(app(X0,X2),X1) = X2 ) ),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X1: heap,X0: $int,X2: $int] :
( ( $sum(1,length(X1)) = X0 )
=> ( sel(app(X1,X2),X0) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_2) ).
tff(f213,plain,
spl3_29,
inference(avatar_split_clause,[],[f71,f211]) ).
tff(f211,plain,
( spl3_29
<=> ! [X2: $int,X0: heap,X1: heap,X3: $int] :
( ( X2 = X3 )
| ( app(X0,X2) != app(X1,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_29])]) ).
tff(f71,plain,
! [X2: $int,X3: $int,X0: heap,X1: heap] :
( ( X2 = X3 )
| ( app(X0,X2) != app(X1,X3) ) ),
inference(cnf_transformation,[],[f52]) ).
tff(f52,plain,
! [X0: heap,X1: heap,X2: $int,X3: $int] :
( ( ( app(X0,X2) = app(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) )
& ( ( ( X2 = X3 )
& ( X0 = X1 ) )
| ( app(X0,X2) != app(X1,X3) ) ) ),
inference(flattening,[],[f51]) ).
tff(f51,plain,
! [X0: heap,X1: heap,X2: $int,X3: $int] :
( ( ( app(X0,X2) = app(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) )
& ( ( ( X2 = X3 )
& ( X0 = X1 ) )
| ( app(X0,X2) != app(X1,X3) ) ) ),
inference(nnf_transformation,[],[f41]) ).
tff(f41,plain,
! [X0: heap,X1: heap,X2: $int,X3: $int] :
( ( app(X0,X2) = app(X1,X3) )
<=> ( ( X2 = X3 )
& ( X0 = X1 ) ) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X1: heap,X3: heap,X2: $int,X4: $int] :
( ( app(X1,X2) = app(X3,X4) )
<=> ( ( X2 = X4 )
& ( X1 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_22) ).
tff(f209,plain,
spl3_28,
inference(avatar_split_clause,[],[f70,f207]) ).
tff(f207,plain,
( spl3_28
<=> ! [X0: heap,X3: $int,X2: $int,X1: heap] :
( ( X0 = X1 )
| ( app(X0,X2) != app(X1,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_28])]) ).
tff(f70,plain,
! [X2: $int,X3: $int,X0: heap,X1: heap] :
( ( X0 = X1 )
| ( app(X0,X2) != app(X1,X3) ) ),
inference(cnf_transformation,[],[f52]) ).
tff(f205,plain,
spl3_27,
inference(avatar_split_clause,[],[f59,f203]) ).
tff(f59,plain,
! [X0: heap] :
( ( app(get(X0),toop(X0)) = X0 )
| ( empty = X0 ) ),
inference(cnf_transformation,[],[f32]) ).
tff(f32,plain,
! [X0: heap] :
( ( app(get(X0),toop(X0)) = X0 )
| ( empty = X0 ) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X1: heap] :
( ( app(get(X1),toop(X1)) = X1 )
| ( empty = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_24) ).
tff(f201,plain,
( spl3_26
| ~ spl3_1
| ~ spl3_20 ),
inference(avatar_split_clause,[],[f179,f164,f78,f199]) ).
tff(f199,plain,
( spl3_26
<=> ! [X0: $int] :
( ~ $less(X0,sK1)
| $less(X0,$sum(1,length(sK2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_26])]) ).
tff(f164,plain,
( spl3_20
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_20])]) ).
tff(f179,plain,
( ! [X0: $int] :
( ~ $less(X0,sK1)
| $less(X0,$sum(1,length(sK2))) )
| ~ spl3_1
| ~ spl3_20 ),
inference(resolution,[],[f165,f80]) ).
tff(f165,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X2)
| ~ $less(X0,X1)
| $less(X0,X2) )
| ~ spl3_20 ),
inference(avatar_component_clause,[],[f164]) ).
tff(f197,plain,
spl3_25,
inference(avatar_split_clause,[],[f25,f195]) ).
tff(f195,plain,
( spl3_25
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_25])]) ).
tff(f25,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_145,[]) ).
tff(f193,plain,
spl3_24,
inference(avatar_split_clause,[],[f20,f191]) ).
tff(f191,plain,
( spl3_24
<=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_24])]) ).
tff(f20,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_139,[]) ).
tff(f178,plain,
spl3_23,
inference(avatar_split_clause,[],[f66,f176]) ).
tff(f66,plain,
! [X2: heap,X0: heap,X1: heap] :
( lsls(X1,X2)
| ~ lsls(X0,X2)
| ~ lsls(X1,X0) ),
inference(cnf_transformation,[],[f46]) ).
tff(f46,plain,
! [X0: heap,X1: heap,X2: heap] :
( lsls(X1,X2)
| ~ lsls(X0,X2)
| ~ lsls(X1,X0) ),
inference(flattening,[],[f45]) ).
tff(f45,plain,
! [X0: heap,X1: heap,X2: heap] :
( lsls(X1,X2)
| ~ lsls(X0,X2)
| ~ lsls(X1,X0) ),
inference(ennf_transformation,[],[f39]) ).
tff(f39,plain,
! [X0: heap,X1: heap,X2: heap] :
( ( lsls(X0,X2)
& lsls(X1,X0) )
=> lsls(X1,X2) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X3: heap,X1: heap,X5: heap] :
( ( lsls(X3,X5)
& lsls(X1,X3) )
=> lsls(X1,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_28) ).
tff(f174,plain,
spl3_22,
inference(avatar_split_clause,[],[f63,f172]) ).
tff(f172,plain,
( spl3_22
<=> ! [X0: $int,X1: heap] : ( $sum(1,length(X1)) = length(app(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_22])]) ).
tff(f63,plain,
! [X0: $int,X1: heap] : ( $sum(1,length(X1)) = length(app(X1,X0)) ),
inference(cnf_transformation,[],[f36]) ).
tff(f36,plain,
! [X0: $int,X1: heap] : ( $sum(1,length(X1)) = length(app(X1,X0)) ),
inference(rectify,[],[f10]) ).
tff(f10,axiom,
! [X2: $int,X1: heap] : ( $sum(1,length(X1)) = length(app(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_26) ).
tff(f170,plain,
spl3_21,
inference(avatar_split_clause,[],[f24,f168]) ).
tff(f168,plain,
( spl3_21
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_21])]) ).
tff(f24,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f166,plain,
spl3_20,
inference(avatar_split_clause,[],[f23,f164]) ).
tff(f23,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f162,plain,
( spl3_19
| ~ spl3_3
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f152,f141,f88,f160]) ).
tff(f160,plain,
( spl3_19
<=> ! [X0: $int] : $less(X0,$sum(X0,1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_19])]) ).
tff(f152,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl3_3
| ~ spl3_16 ),
inference(resolution,[],[f142,f89]) ).
tff(f151,plain,
spl3_18,
inference(avatar_split_clause,[],[f69,f149]) ).
tff(f69,plain,
! [X2: heap,X0: $int,X1: heap] :
( lsls(X1,app(X2,X0))
| ~ lsls(X1,X2) ),
inference(cnf_transformation,[],[f50]) ).
tff(f147,plain,
spl3_17,
inference(avatar_split_clause,[],[f28,f145]) ).
tff(f28,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_161,[]) ).
tff(f143,plain,
spl3_16,
inference(avatar_split_clause,[],[f26,f141]) ).
tff(f26,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_147,[]) ).
tff(f139,plain,
spl3_15,
inference(avatar_split_clause,[],[f17,f137]) ).
tff(f17,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f135,plain,
spl3_14,
inference(avatar_split_clause,[],[f62,f133]) ).
tff(f133,plain,
( spl3_14
<=> ! [X0: heap,X1: $int] : ( toop(app(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).
tff(f62,plain,
! [X0: heap,X1: $int] : ( toop(app(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f35]) ).
tff(f35,plain,
! [X0: heap,X1: $int] : ( toop(app(X0,X1)) = X1 ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X1: heap,X2: $int] : ( toop(app(X1,X2)) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_21) ).
tff(f131,plain,
spl3_13,
inference(avatar_split_clause,[],[f61,f129]) ).
tff(f129,plain,
( spl3_13
<=> ! [X0: $int,X1: heap] : ( get(app(X1,X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).
tff(f61,plain,
! [X0: $int,X1: heap] : ( get(app(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f34]) ).
tff(f34,plain,
! [X0: $int,X1: heap] : ( get(app(X1,X0)) = X1 ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X2: $int,X1: heap] : ( get(app(X1,X2)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_20) ).
tff(f127,plain,
spl3_12,
inference(avatar_split_clause,[],[f21,f125]) ).
tff(f21,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f123,plain,
spl3_11,
inference(avatar_split_clause,[],[f74,f121]) ).
tff(f74,plain,
! [X2: heap,X0: $int] : lsls(X2,app(X2,X0)),
inference(equality_resolution,[],[f68]) ).
tff(f68,plain,
! [X2: heap,X0: $int,X1: heap] :
( lsls(X1,app(X2,X0))
| ( X1 != X2 ) ),
inference(cnf_transformation,[],[f50]) ).
tff(f119,plain,
spl3_10,
inference(avatar_split_clause,[],[f60,f117]) ).
tff(f117,plain,
( spl3_10
<=> ! [X0: heap,X1: $int] : ( empty != app(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).
tff(f60,plain,
! [X0: heap,X1: $int] : ( empty != app(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
tff(f33,plain,
! [X0: heap,X1: $int] : ( empty != app(X0,X1) ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X1: heap,X2: $int] : ( empty != app(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_23) ).
tff(f115,plain,
spl3_9,
inference(avatar_split_clause,[],[f58,f113]) ).
tff(f113,plain,
( spl3_9
<=> ! [X0: $int] : ( sel(empty,X0) = 0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).
tff(f58,plain,
! [X0: $int] : ( sel(empty,X0) = 0 ),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: $int] : ( sel(empty,X0) = 0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_1) ).
tff(f111,plain,
spl3_8,
inference(avatar_split_clause,[],[f27,f109]) ).
tff(f109,plain,
( spl3_8
<=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).
tff(f27,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_148,[]) ).
tff(f107,plain,
spl3_7,
inference(avatar_split_clause,[],[f19,f105]) ).
tff(f105,plain,
( spl3_7
<=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).
tff(f19,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f103,plain,
spl3_6,
inference(avatar_split_clause,[],[f55,f100]) ).
tff(f55,plain,
0 = length(empty),
inference(cnf_transformation,[],[f9]) ).
tff(f9,axiom,
0 = length(empty),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_25) ).
tff(f98,plain,
spl3_5,
inference(avatar_split_clause,[],[f57,f96]) ).
tff(f96,plain,
( spl3_5
<=> ! [X0: heap] : ~ lsls(X0,empty) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
tff(f57,plain,
! [X0: heap] : ~ lsls(X0,empty),
inference(cnf_transformation,[],[f31]) ).
tff(f31,plain,
! [X0: heap] : ~ lsls(X0,empty),
inference(rectify,[],[f13]) ).
tff(f13,axiom,
! [X1: heap] : ~ lsls(X1,empty),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_29) ).
tff(f94,plain,
spl3_4,
inference(avatar_split_clause,[],[f56,f92]) ).
tff(f56,plain,
! [X0: heap] : ~ lsls(X0,X0),
inference(cnf_transformation,[],[f30]) ).
tff(f30,plain,
! [X0: heap] : ~ lsls(X0,X0),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X1: heap] : ~ lsls(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_27) ).
tff(f90,plain,
spl3_3,
inference(avatar_split_clause,[],[f22,f88]) ).
tff(f22,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f86,plain,
~ spl3_2,
inference(avatar_split_clause,[],[f53,f83]) ).
tff(f53,plain,
sel(app(sK2,sK0),sK1) != sel(sK2,sK1),
inference(cnf_transformation,[],[f48]) ).
tff(f48,plain,
( $less(sK1,$sum(1,length(sK2)))
& ( sel(app(sK2,sK0),sK1) != sel(sK2,sK1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f42,f47]) ).
tff(f47,plain,
( ? [X0: $int,X1: $int,X2: heap] :
( $less(X1,$sum(1,length(X2)))
& ( sel(app(X2,X0),X1) != sel(X2,X1) ) )
=> ( $less(sK1,$sum(1,length(sK2)))
& ( sel(app(sK2,sK0),sK1) != sel(sK2,sK1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f42,plain,
? [X0: $int,X1: $int,X2: heap] :
( $less(X1,$sum(1,length(X2)))
& ( sel(app(X2,X0),X1) != sel(X2,X1) ) ),
inference(ennf_transformation,[],[f29]) ).
tff(f29,plain,
~ ! [X0: $int,X1: $int,X2: heap] :
( ~ $less(X1,$sum(1,length(X2)))
| ( sel(app(X2,X0),X1) = sel(X2,X1) ) ),
inference(rectify,[],[f16]) ).
tff(f16,negated_conjecture,
~ ! [X2: $int,X0: $int,X1: heap] :
( ~ $less(X0,$sum(1,length(X1)))
| ( sel(app(X1,X2),X0) = sel(X1,X0) ) ),
inference(negated_conjecture,[],[f15]) ).
tff(f15,conjecture,
! [X2: $int,X0: $int,X1: heap] :
( ~ $less(X0,$sum(1,length(X1)))
| ( sel(app(X1,X2),X0) = sel(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',th_5) ).
tff(f81,plain,
spl3_1,
inference(avatar_split_clause,[],[f54,f78]) ).
tff(f54,plain,
$less(sK1,$sum(1,length(sK2))),
inference(cnf_transformation,[],[f48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : DAT070_1 : TPTP v8.1.2. Released v5.5.0.
% 0.10/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n019.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Apr 29 22:16:59 EDT 2024
% 0.15/0.31 % CPUTime :
% 0.15/0.31 % (27657)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.33 % (27660)WARNING: value z3 for option sas not known
% 0.15/0.33 % (27662)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.33 % (27663)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.33 % (27659)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.33 % (27661)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.33 % (27664)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.33 % (27660)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.33 % (27658)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.33 % (27659)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.33 % (27659)Terminated due to inappropriate strategy.
% 0.15/0.33 % (27659)------------------------------
% 0.15/0.33 % (27659)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.33 % (27661)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.33 % (27659)Termination reason: Inappropriate
% 0.15/0.33
% 0.15/0.33 % (27659)Memory used [KB]: 749
% 0.15/0.33 % (27659)Time elapsed: 0.003 s
% 0.15/0.33 % (27659)Instructions burned: 3 (million)
% 0.15/0.33 % (27659)------------------------------
% 0.15/0.33 % (27659)------------------------------
% 0.15/0.33 % (27661)Terminated due to inappropriate strategy.
% 0.15/0.33 % (27661)------------------------------
% 0.15/0.33 % (27661)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.33 % (27661)Termination reason: Inappropriate
% 0.15/0.33
% 0.15/0.33 % (27661)Memory used [KB]: 749
% 0.15/0.33 % (27661)Time elapsed: 0.003 s
% 0.15/0.33 % (27661)Instructions burned: 3 (million)
% 0.15/0.33 % (27661)------------------------------
% 0.15/0.33 % (27661)------------------------------
% 0.15/0.33 % (27658)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.33 % (27658)Terminated due to inappropriate strategy.
% 0.15/0.33 % (27658)------------------------------
% 0.15/0.33 % (27658)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.33 % (27658)Termination reason: Inappropriate
% 0.15/0.33
% 0.15/0.33 % (27658)Memory used [KB]: 749
% 0.15/0.33 % (27658)Time elapsed: 0.002 s
% 0.15/0.33 % (27658)Instructions burned: 3 (million)
% 0.15/0.33 % (27658)------------------------------
% 0.15/0.33 % (27658)------------------------------
% 0.15/0.34 % (27662)First to succeed.
% 0.15/0.34 % (27662)Refutation found. Thanks to Tanya!
% 0.15/0.34 % SZS status Theorem for theBenchmark
% 0.15/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.34 % (27662)------------------------------
% 0.15/0.34 % (27662)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.34 % (27662)Termination reason: Refutation
% 0.15/0.34
% 0.15/0.34 % (27662)Memory used [KB]: 936
% 0.15/0.34 % (27662)Time elapsed: 0.013 s
% 0.15/0.34 % (27662)Instructions burned: 18 (million)
% 0.15/0.34 % (27662)------------------------------
% 0.15/0.34 % (27662)------------------------------
% 0.15/0.34 % (27657)Success in time 0.025 s
%------------------------------------------------------------------------------