TSTP Solution File: LCL805_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL805_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n017.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 13:49:43 EDT 2024
% Result : Theorem 0.06s 0.29s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 132
% Syntax : Number of formulae : 207 ( 80 unt; 84 typ; 0 def)
% Number of atoms : 218 ( 53 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 159 ( 64 ~; 40 |; 27 &)
% ( 26 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 112 ( 59 >; 53 *; 0 +; 0 <<)
% Number of predicates : 38 ( 36 usr; 24 prp; 0-6 aty)
% Number of functors : 68 ( 68 usr; 16 con; 0-5 aty)
% Number of variables : 196 ( 136 !; 15 ?; 196 :)
% ( 45 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
dB: $tType ).
tff(type_def_7,type,
list: $tType > $tType ).
tff(type_def_8,type,
nat: $tType ).
tff(type_def_9,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1))) ).
tff(func_def_1,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * X1 ) > fun(X0,X2) ) ).
tff(func_def_2,type,
combi:
!>[X0: $tType] : fun(X0,X0) ).
tff(func_def_3,type,
combk:
!>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).
tff(func_def_4,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * fun(X0,X1) ) > fun(X0,X2) ) ).
tff(func_def_5,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_6,type,
it: fun(dB,bool) ).
tff(func_def_7,type,
beta: fun(dB,fun(dB,bool)) ).
tff(func_def_8,type,
abs: dB > dB ).
tff(func_def_9,type,
app: fun(dB,fun(dB,dB)) ).
tff(func_def_10,type,
var: nat > dB ).
tff(func_def_11,type,
dB_case:
!>[X0: $tType] : ( ( fun(nat,X0) * fun(dB,fun(dB,X0)) * fun(dB,X0) * dB ) > X0 ) ).
tff(func_def_12,type,
dB_size: dB > nat ).
tff(func_def_13,type,
lift: fun(dB,fun(nat,dB)) ).
tff(func_def_14,type,
liftn: ( nat * dB * nat ) > dB ).
tff(func_def_15,type,
subst: fun(dB,fun(dB,fun(nat,dB))) ).
tff(func_def_16,type,
substn: ( dB * dB * nat ) > dB ).
tff(func_def_17,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_18,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_19,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_20,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_21,type,
list_rec:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),fun(X0,X0))) * list(X1) ) > X0 ) ).
tff(func_def_22,type,
list_size:
!>[X0: $tType] : ( ( fun(X0,nat) * list(X0) ) > nat ) ).
tff(func_def_23,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_24,type,
monoid_add_listsum:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_25,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_26,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_27,type,
fFalse: bool ).
tff(func_def_28,type,
fTrue: bool ).
tff(func_def_29,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_30,type,
a: dB ).
tff(func_def_31,type,
as: list(dB) ).
tff(func_def_32,type,
i: nat ).
tff(func_def_33,type,
n: nat ).
tff(func_def_34,type,
rs: list(dB) ).
tff(func_def_35,type,
t: dB ).
tff(func_def_36,type,
u: dB ).
tff(func_def_37,type,
ua: dB ).
tff(func_def_38,type,
sK5: dB > dB ).
tff(func_def_39,type,
sK6: dB > dB ).
tff(func_def_40,type,
sK7: dB > dB ).
tff(func_def_41,type,
sK8: dB > nat ).
tff(func_def_42,type,
sK9: dB > dB ).
tff(func_def_43,type,
sK10: dB > list(dB) ).
tff(func_def_44,type,
sK11: dB > nat ).
tff(func_def_45,type,
sK12: dB > dB ).
tff(func_def_46,type,
sK13: dB > dB ).
tff(func_def_47,type,
sK14: dB > list(dB) ).
tff(func_def_48,type,
sK15: dB > list(dB) ).
tff(func_def_49,type,
sK16: dB > dB ).
tff(func_def_50,type,
sK17: dB > dB ).
tff(func_def_51,type,
sK18: dB > nat ).
tff(func_def_52,type,
sK19: ( dB * dB ) > dB ).
tff(func_def_53,type,
sK20: ( dB * list(dB) * dB ) > dB ).
tff(func_def_54,type,
sK21: ( dB * list(dB) * dB ) > dB ).
tff(func_def_55,type,
sK22: ( dB * list(dB) * dB ) > list(dB) ).
tff(func_def_56,type,
sK23: ( dB * list(dB) * dB ) > list(dB) ).
tff(func_def_57,type,
sK24: ( dB * list(dB) * dB ) > dB ).
tff(func_def_58,type,
sK25: ( dB * list(dB) * nat ) > list(dB) ).
tff(func_def_59,type,
sK26: ( dB * dB * dB ) > dB ).
tff(func_def_60,type,
sK27: ( dB * dB * dB ) > dB ).
tff(func_def_61,type,
sK28: ( dB * dB * dB ) > dB ).
tff(func_def_62,type,
sK29:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_63,type,
sK30:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_64,type,
sK31:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_65,type,
sK32:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X0 ) ).
tff(pred_def_1,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
equal_equal:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_4,type,
step1:
!>[X0: $tType] : ( ( fun(X0,fun(X0,bool)) * list(X0) * list(X0) ) > $o ) ).
tff(pred_def_5,type,
list_ex1:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_6,type,
listsp:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_7,type,
null:
!>[X0: $tType] : ( list(X0) > $o ) ).
tff(pred_def_8,type,
pp: bool > $o ).
tff(pred_def_9,type,
sP0: dB > $o ).
tff(pred_def_10,type,
sP1: dB > $o ).
tff(pred_def_11,type,
sP2: ( dB * list(dB) * dB ) > $o ).
tff(pred_def_12,type,
sP3: ( dB * dB * dB ) > $o ).
tff(pred_def_13,type,
sP4:
!>[X0: $tType] : ( ( list(X0) * list(X0) * fun(X0,fun(X0,bool)) * X0 * X0 ) > $o ) ).
tff(f642,plain,
$false,
inference(avatar_sat_refutation,[],[f538,f543,f548,f553,f557,f561,f565,f569,f573,f578,f583,f588,f592,f596,f600,f604,f609,f613,f617,f621,f625,f632,f639,f641]) ).
tff(f641,plain,
( ~ spl33_8
| spl33_23 ),
inference(avatar_contradiction_clause,[],[f640]) ).
tff(f640,plain,
( $false
| ~ spl33_8
| spl33_23 ),
inference(resolution,[],[f638,f568]) ).
tff(f568,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : listsp(X0,X1,nil(X0))
| ~ spl33_8 ),
inference(avatar_component_clause,[],[f567]) ).
tff(f567,plain,
( spl33_8
<=> ! [X0: $tType,X1: fun(X0,bool)] : listsp(X0,X1,nil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_8])]) ).
tff(f638,plain,
( ~ listsp(dB,it,nil(dB))
| spl33_23 ),
inference(avatar_component_clause,[],[f636]) ).
tff(f636,plain,
( spl33_23
<=> listsp(dB,it,nil(dB)) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_23])]) ).
tff(f639,plain,
( ~ spl33_23
| spl33_22 ),
inference(avatar_split_clause,[],[f634,f629,f636]) ).
tff(f629,plain,
( spl33_22
<=> listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),nil(dB)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_22])]) ).
tff(f634,plain,
( ~ listsp(dB,it,nil(dB))
| spl33_22 ),
inference(forward_demodulation,[],[f633,f402]) ).
tff(f402,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,X1)] : ( nil(X1) = map(X0,X1,X2,nil(X0)) ),
inference(cnf_transformation,[],[f158]) ).
tff(f158,plain,
! [X0: $tType,X1: $tType,X2: fun(X0,X1)] : ( nil(X1) = map(X0,X1,X2,nil(X0)) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X1: $tType,X0: $tType,X9: fun(X1,X0)] : ( nil(X0) = map(X1,X0,X9,nil(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_map_Osimps_I1_J) ).
tff(f633,plain,
( ~ listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),nil(dB)))
| spl33_22 ),
inference(forward_demodulation,[],[f631,f402]) ).
tff(f631,plain,
( ~ listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),nil(dB))))
| spl33_22 ),
inference(avatar_component_clause,[],[f629]) ).
tff(f632,plain,
~ spl33_22,
inference(avatar_split_clause,[],[f327,f629]) ).
tff(f327,plain,
~ listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),nil(dB)))),
inference(cnf_transformation,[],[f114]) ).
tff(f114,plain,
~ listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),nil(dB)))),
inference(flattening,[],[f113]) ).
tff(f113,negated_conjecture,
~ listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),nil(dB)))),
inference(negated_conjecture,[],[f112]) ).
tff(f112,conjecture,
listsp(dB,it,map(dB,dB,combc(dB,nat,dB,lift,zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),nil(dB)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f625,plain,
spl33_21,
inference(avatar_split_clause,[],[f398,f623]) ).
tff(f623,plain,
( spl33_21
<=> ! [X0: $tType,X2: X0,X1: list(X0)] : ( cons(X0,X2,X1) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_21])]) ).
tff(f398,plain,
! [X0: $tType,X2: X0,X1: list(X0)] : ( cons(X0,X2,X1) != X1 ),
inference(cnf_transformation,[],[f154]) ).
tff(f154,plain,
! [X0: $tType,X1: list(X0),X2: X0] : ( cons(X0,X2,X1) != X1 ),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X0: $tType,X77: list(X0),X78: X0] : ( cons(X0,X78,X77) != X77 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_not__Cons__self2) ).
tff(f621,plain,
spl33_20,
inference(avatar_split_clause,[],[f367,f619]) ).
tff(f619,plain,
( spl33_20
<=> ! [X0: nat,X1: dB] : ( liftn(zero_zero(nat),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_20])]) ).
tff(f367,plain,
! [X0: nat,X1: dB] : ( liftn(zero_zero(nat),X1,X0) = X1 ),
inference(cnf_transformation,[],[f129]) ).
tff(f129,plain,
! [X0: nat,X1: dB] : ( liftn(zero_zero(nat),X1,X0) = X1 ),
inference(rectify,[],[f45]) ).
tff(f45,axiom,
! [X13: nat,X5: dB] : ( liftn(zero_zero(nat),X5,X13) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_liftn__0) ).
tff(f617,plain,
spl33_19,
inference(avatar_split_clause,[],[f342,f615]) ).
tff(f615,plain,
( spl33_19
<=> ! [X0: nat] : pp(aa(dB,bool,it,var(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_19])]) ).
tff(f342,plain,
! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
inference(cnf_transformation,[],[f118]) ).
tff(f118,plain,
! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X27: nat] : pp(aa(dB,bool,it,var(X27))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_Var__IT) ).
tff(f613,plain,
spl33_18,
inference(avatar_split_clause,[],[f341,f611]) ).
tff(f611,plain,
( spl33_18
<=> ! [X0: nat] : ( zero_zero(nat) = size_size(dB,var(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_18])]) ).
tff(f341,plain,
! [X0: nat] : ( zero_zero(nat) = size_size(dB,var(X0)) ),
inference(cnf_transformation,[],[f117]) ).
tff(f117,plain,
! [X0: nat] : ( zero_zero(nat) = size_size(dB,var(X0)) ),
inference(rectify,[],[f28]) ).
tff(f28,axiom,
! [X26: nat] : ( zero_zero(nat) = size_size(dB,var(X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_dB_Osize_I4_J) ).
tff(f609,plain,
spl33_17,
inference(avatar_split_clause,[],[f336,f606]) ).
tff(f606,plain,
( spl33_17
<=> ( rs = cons(dB,a,as) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_17])]) ).
tff(f336,plain,
rs = cons(dB,a,as),
inference(cnf_transformation,[],[f99]) ).
tff(f99,axiom,
rs = cons(dB,a,as),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_Cons) ).
tff(f604,plain,
spl33_16,
inference(avatar_split_clause,[],[f397,f602]) ).
tff(f602,plain,
( spl33_16
<=> ! [X0: $tType,X2: fun(X0,fun(X0,bool)),X1: list(X0)] : ~ step1(X0,X2,nil(X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_16])]) ).
tff(f397,plain,
! [X0: $tType,X2: fun(X0,fun(X0,bool)),X1: list(X0)] : ~ step1(X0,X2,nil(X0),X1),
inference(cnf_transformation,[],[f153]) ).
tff(f153,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,fun(X0,bool))] : ~ step1(X0,X2,nil(X0),X1),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X0: $tType,X8: list(X0),X43: fun(X0,fun(X0,bool))] : ~ step1(X0,X43,nil(X0),X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_not__Nil__step1) ).
tff(f600,plain,
spl33_15,
inference(avatar_split_clause,[],[f396,f598]) ).
tff(f598,plain,
( spl33_15
<=> ! [X0: $tType,X2: fun(X0,fun(X0,bool)),X1: list(X0)] : ~ step1(X0,X2,X1,nil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_15])]) ).
tff(f396,plain,
! [X0: $tType,X2: fun(X0,fun(X0,bool)),X1: list(X0)] : ~ step1(X0,X2,X1,nil(X0)),
inference(cnf_transformation,[],[f152]) ).
tff(f152,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,fun(X0,bool))] : ~ step1(X0,X2,X1,nil(X0)),
inference(rectify,[],[f84]) ).
tff(f84,axiom,
! [X0: $tType,X8: list(X0),X43: fun(X0,fun(X0,bool))] : ~ step1(X0,X43,X8,nil(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_not__step1__Nil) ).
tff(f596,plain,
spl33_14,
inference(avatar_split_clause,[],[f395,f594]) ).
tff(f594,plain,
( spl33_14
<=> ! [X0: $tType,X2: X0,X1: list(X0)] : ~ null(X0,cons(X0,X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_14])]) ).
tff(f395,plain,
! [X0: $tType,X2: X0,X1: list(X0)] : ~ null(X0,cons(X0,X2,X1)),
inference(cnf_transformation,[],[f151]) ).
tff(f151,plain,
! [X0: $tType,X1: list(X0),X2: X0] : ~ null(X0,cons(X0,X2,X1)),
inference(rectify,[],[f91]) ).
tff(f91,axiom,
! [X0: $tType,X77: list(X0),X78: X0] : ~ null(X0,cons(X0,X78,X77)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_null__rec_I1_J) ).
tff(f592,plain,
spl33_13,
inference(avatar_split_clause,[],[f340,f590]) ).
tff(f590,plain,
( spl33_13
<=> ! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_13])]) ).
tff(f340,plain,
! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ),
inference(cnf_transformation,[],[f116]) ).
tff(f116,plain,
! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X26: nat] : ( zero_zero(nat) = dB_size(var(X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_dB_Osize_I1_J) ).
tff(f588,plain,
spl33_12,
inference(avatar_split_clause,[],[f335,f585]) ).
tff(f585,plain,
( spl33_12
<=> pp(aa(dB,bool,it,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_12])]) ).
tff(f335,plain,
pp(aa(dB,bool,it,u)),
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
pp(aa(dB,bool,it,u)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_uIT) ).
tff(f583,plain,
spl33_11,
inference(avatar_split_clause,[],[f334,f580]) ).
tff(f580,plain,
( spl33_11
<=> pp(aa(dB,bool,it,ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_11])]) ).
tff(f334,plain,
pp(aa(dB,bool,it,ua)),
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
pp(aa(dB,bool,it,ua)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_Var_I3_J) ).
tff(f578,plain,
spl33_10,
inference(avatar_split_clause,[],[f333,f575]) ).
tff(f575,plain,
( spl33_10
<=> pp(aa(dB,bool,it,t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_10])]) ).
tff(f333,plain,
pp(aa(dB,bool,it,t)),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
pp(aa(dB,bool,it,t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096IT_At_096) ).
tff(f573,plain,
spl33_9,
inference(avatar_split_clause,[],[f508,f571]) ).
tff(f571,plain,
( spl33_9
<=> ! [X0: $tType,X2: list(X0)] : equal_equal(list(X0),X2,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_9])]) ).
tff(f508,plain,
! [X0: $tType,X2: list(X0)] : equal_equal(list(X0),X2,X2),
inference(equality_resolution,[],[f434]) ).
tff(f434,plain,
! [X0: $tType,X2: list(X0),X1: list(X0)] :
( equal_equal(list(X0),X2,X1)
| ( X1 != X2 ) ),
inference(cnf_transformation,[],[f299]) ).
tff(f299,plain,
! [X0: $tType,X1: list(X0),X2: list(X0)] :
( ( equal_equal(list(X0),X2,X1)
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ~ equal_equal(list(X0),X2,X1) ) ),
inference(nnf_transformation,[],[f177]) ).
tff(f177,plain,
! [X0: $tType,X1: list(X0),X2: list(X0)] :
( equal_equal(list(X0),X2,X1)
<=> ( X1 = X2 ) ),
inference(rectify,[],[f65]) ).
tff(f65,axiom,
! [X0: $tType,X52: list(X0),X14: list(X0)] :
( equal_equal(list(X0),X14,X52)
<=> ( X14 = X52 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_equal__list__def) ).
tff(f569,plain,
spl33_8,
inference(avatar_split_clause,[],[f366,f567]) ).
tff(f366,plain,
! [X0: $tType,X1: fun(X0,bool)] : listsp(X0,X1,nil(X0)),
inference(cnf_transformation,[],[f128]) ).
tff(f128,plain,
! [X0: $tType,X1: fun(X0,bool)] : listsp(X0,X1,nil(X0)),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X0: $tType,X7: fun(X0,bool)] : listsp(X0,X7,nil(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_listsp_ONil) ).
tff(f565,plain,
spl33_7,
inference(avatar_split_clause,[],[f364,f563]) ).
tff(f563,plain,
( spl33_7
<=> ! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_7])]) ).
tff(f364,plain,
! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ),
inference(cnf_transformation,[],[f125]) ).
tff(f125,plain,
! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ),
inference(rectify,[],[f63]) ).
tff(f63,axiom,
! [X49: dB,X26: nat] : ( var(X26) != abs(X49) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_dB_Osimps_I6_J) ).
tff(f561,plain,
spl33_6,
inference(avatar_split_clause,[],[f355,f559]) ).
tff(f559,plain,
( spl33_6
<=> ! [X0: dB] :
( sP1(X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_6])]) ).
tff(f355,plain,
! [X0: dB] :
( sP1(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f263]) ).
tff(f263,plain,
! [X0: dB] :
( ( sP1(X0)
| ( ~ sP0(X0)
& ! [X1: dB] :
( ~ pp(aa(dB,bool,it,X1))
| ( abs(X1) != X0 ) )
& ! [X2: list(dB),X3: nat] :
( ~ listsp(dB,it,X2)
| ( foldl(dB,dB,app,var(X3),X2) != X0 ) ) ) )
& ( sP0(X0)
| ( pp(aa(dB,bool,it,sK9(X0)))
& ( abs(sK9(X0)) = X0 ) )
| ( listsp(dB,it,sK10(X0))
& ( foldl(dB,dB,app,var(sK11(X0)),sK10(X0)) = X0 ) )
| ~ sP1(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f260,f262,f261]) ).
tff(f261,plain,
! [X0: dB] :
( ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
=> ( pp(aa(dB,bool,it,sK9(X0)))
& ( abs(sK9(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f262,plain,
! [X0: dB] :
( ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
=> ( listsp(dB,it,sK10(X0))
& ( foldl(dB,dB,app,var(sK11(X0)),sK10(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f260,plain,
! [X0: dB] :
( ( sP1(X0)
| ( ~ sP0(X0)
& ! [X1: dB] :
( ~ pp(aa(dB,bool,it,X1))
| ( abs(X1) != X0 ) )
& ! [X2: list(dB),X3: nat] :
( ~ listsp(dB,it,X2)
| ( foldl(dB,dB,app,var(X3),X2) != X0 ) ) ) )
& ( sP0(X0)
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
| ~ sP1(X0) ) ),
inference(rectify,[],[f259]) ).
tff(f259,plain,
! [X0: dB] :
( ( sP1(X0)
| ( ~ sP0(X0)
& ! [X4: dB] :
( ~ pp(aa(dB,bool,it,X4))
| ( abs(X4) != X0 ) )
& ! [X5: list(dB),X6: nat] :
( ~ listsp(dB,it,X5)
| ( foldl(dB,dB,app,var(X6),X5) != X0 ) ) ) )
& ( sP0(X0)
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
| ~ sP1(X0) ) ),
inference(flattening,[],[f258]) ).
tff(f258,plain,
! [X0: dB] :
( ( sP1(X0)
| ( ~ sP0(X0)
& ! [X4: dB] :
( ~ pp(aa(dB,bool,it,X4))
| ( abs(X4) != X0 ) )
& ! [X5: list(dB),X6: nat] :
( ~ listsp(dB,it,X5)
| ( foldl(dB,dB,app,var(X6),X5) != X0 ) ) ) )
& ( sP0(X0)
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
| ~ sP1(X0) ) ),
inference(nnf_transformation,[],[f244]) ).
tff(f244,plain,
! [X0: dB] :
( sP1(X0)
<=> ( sP0(X0)
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f557,plain,
spl33_5,
inference(avatar_split_clause,[],[f339,f555]) ).
tff(f555,plain,
( spl33_5
<=> ! [X0: $tType] : null(X0,nil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_5])]) ).
tff(f339,plain,
! [X0: $tType] : null(X0,nil(X0)),
inference(cnf_transformation,[],[f115]) ).
tff(f115,plain,
! [X0: $tType] : null(X0,nil(X0)),
inference(rectify,[],[f40]) ).
tff(f40,axiom,
! [X1: $tType] : null(X1,nil(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_null__rec_I2_J) ).
tff(f553,plain,
spl33_4,
inference(avatar_split_clause,[],[f331,f550]) ).
tff(f550,plain,
( spl33_4
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_4])]) ).
tff(f331,plain,
pp(fTrue),
inference(cnf_transformation,[],[f103]) ).
tff(f103,axiom,
pp(fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f548,plain,
spl33_3,
inference(avatar_split_clause,[],[f330,f545]) ).
tff(f545,plain,
( spl33_3
<=> monoid_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_3])]) ).
tff(f330,plain,
monoid_add(nat),
inference(cnf_transformation,[],[f100]) ).
tff(f100,axiom,
monoid_add(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
tff(f543,plain,
spl33_2,
inference(avatar_split_clause,[],[f329,f540]) ).
tff(f540,plain,
( spl33_2
<=> zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_2])]) ).
tff(f329,plain,
zero(nat),
inference(cnf_transformation,[],[f101]) ).
tff(f101,axiom,
zero(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
tff(f538,plain,
~ spl33_1,
inference(avatar_split_clause,[],[f328,f535]) ).
tff(f535,plain,
( spl33_1
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_1])]) ).
tff(f328,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f102]) ).
tff(f102,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : LCL805_5 : TPTP v8.1.2. Released v6.0.0.
% 0.00/0.07 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.06/0.26 % Computer : n017.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 300
% 0.06/0.26 % DateTime : Mon Apr 29 22:06:18 EDT 2024
% 0.06/0.26 % CPUTime :
% 0.06/0.26 % (29536)Running in auto input_syntax mode. Trying TPTP
% 0.06/0.27 % (29544)WARNING: value z3 for option sas not known
% 0.06/0.28 % (29543)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.06/0.28 % (29542)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.06/0.28 % (29546)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.06/0.28 % (29544)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)
% 0.06/0.28 % (29547)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)
% 0.06/0.28 % (29548)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)
% 0.06/0.28 % (29549)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)
% 0.06/0.28 % (29549)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.06/0.28 % Exception at run slice level
% 0.06/0.28 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.06/0.28 % Exception at run slice level
% 0.06/0.28 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.06/0.28 % Exception at run slice level
% 0.06/0.28 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.06/0.28 % (29547)First to succeed.
% 0.06/0.29 % (29548)Also succeeded, but the first one will report.
% 0.06/0.29 % (29547)Refutation found. Thanks to Tanya!
% 0.06/0.29 % SZS status Theorem for theBenchmark
% 0.06/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.29 % (29547)------------------------------
% 0.06/0.29 % (29547)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.06/0.29 % (29547)Termination reason: Refutation
% 0.06/0.29
% 0.06/0.29 % (29547)Memory used [KB]: 1189
% 0.06/0.29 % (29547)Time elapsed: 0.010 s
% 0.06/0.29 % (29547)Instructions burned: 28 (million)
% 0.06/0.29 % (29547)------------------------------
% 0.06/0.29 % (29547)------------------------------
% 0.06/0.29 % (29536)Success in time 0.022 s
%------------------------------------------------------------------------------