TSTP Solution File: COM080_5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : COM080_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n027.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 Aug 30 18:46:36 EDT 2023

% Result   : Theorem 0.23s 0.46s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   78
% Syntax   : Number of formulae    :   93 (   5 unt;  74 typ;   0 def)
%            Number of atoms       :   37 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   31 (  13   ~;   5   |;   5   &)
%                                         (   2 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :   66 (  43   >;  23   *;   0   +;   0  <<)
%            Number of predicates  :   17 (  16 usr;   1 prp; 0-5 aty)
%            Number of functors    :   54 (  54 usr;  13 con; 0-5 aty)
%            Number of variables   :   77 (;  23   !;   2   ?;  77   :)
%                                         (  52  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    bool: $tType ).

tff(type_def_6,type,
    int: $tType ).

tff(type_def_7,type,
    list: $tType > $tType ).

tff(type_def_8,type,
    fm: $tType > $tType ).

tff(type_def_9,type,
    nat: $tType ).

tff(type_def_10,type,
    atom: $tType ).

tff(type_def_11,type,
    fun: ( $tType * $tType ) > $tType ).

tff(type_def_12,type,
    product_prod: ( $tType * $tType ) > $tType ).

tff(func_def_0,type,
    plus_plus: 
      !>[X0: $tType] : fun(X0,fun(X0,X0)) ).

tff(func_def_1,type,
    times_times: 
      !>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).

tff(func_def_2,type,
    zero_zero: 
      !>[X0: $tType] : X0 ).

tff(func_def_3,type,
    iprod: 
      !>[X0: $tType] : ( ( list(X0) * list(X0) ) > X0 ) ).

tff(func_def_4,type,
    zipwith0: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( fun(X0,fun(X1,X2)) > fun(list(X0),fun(list(X1),list(X2))) ) ).

tff(func_def_5,type,
    insert: 
      !>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).

tff(func_def_6,type,
    cons: 
      !>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).

tff(func_def_7,type,
    nil: 
      !>[X0: $tType] : list(X0) ).

tff(func_def_8,type,
    list_case: 
      !>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).

tff(func_def_9,type,
    list_size: 
      !>[X0: $tType] : ( ( fun(X0,nat) * list(X0) ) > nat ) ).

tff(func_def_10,type,
    set: 
      !>[X0: $tType] : ( list(X0) > fun(X0,bool) ) ).

tff(func_def_11,type,
    splice: 
      !>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).

tff(func_def_12,type,
    sublist: 
      !>[X0: $tType] : ( ( list(X0) * fun(nat,bool) ) > list(X0) ) ).

tff(func_def_13,type,
    list_conj: 
      !>[X0: $tType] : ( list(fm(X0)) > fm(X0) ) ).

tff(func_def_14,type,
    list_disj: 
      !>[X0: $tType] : ( list(fm(X0)) > fm(X0) ) ).

tff(func_def_15,type,
    map_fm: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * fm(X0) ) > fm(X1) ) ).

tff(func_def_16,type,
    neg: 
      !>[X0: $tType] : ( fm(X0) > fm(X0) ) ).

tff(func_def_17,type,
    suc: nat > nat ).

tff(func_def_18,type,
    i_Z: fun(atom,fun(list(int),bool)) ).

tff(func_def_19,type,
    asubst: ( int * list(int) ) > fun(atom,atom) ).

tff(func_def_20,type,
    divisor: atom > int ).

tff(func_def_21,type,
    lbounds: list(atom) > list(product_prod(int,list(int))) ).

tff(func_def_22,type,
    qEpres896714165pres_1: list(atom) > fm(atom) ).

tff(func_def_23,type,
    aa: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).

tff(func_def_24,type,
    fFalse: bool ).

tff(func_def_25,type,
    fTrue: bool ).

tff(func_def_26,type,
    as: list(atom) ).

tff(func_def_27,type,
    il: int ).

tff(func_def_28,type,
    ksl: list(int) ).

tff(func_def_29,type,
    m: int ).

tff(func_def_30,type,
    xs: list(int) ).

tff(func_def_31,type,
    sK0: atom ).

tff(func_def_32,type,
    sK1: int ).

tff(func_def_33,type,
    sK2: int ).

tff(func_def_34,type,
    sK3: list(int) ).

tff(func_def_35,type,
    sK4: int ).

tff(func_def_36,type,
    sK5: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

tff(func_def_37,type,
    sK6: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

tff(func_def_38,type,
    sK7: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

tff(func_def_39,type,
    sK8: 
      !>[X0: $tType] : ( list(fm(X0)) > fm(X0) ) ).

tff(func_def_40,type,
    sK9: 
      !>[X0: $tType] : ( list(fm(X0)) > fm(X0) ) ).

tff(func_def_41,type,
    sK10: 
      !>[X0: $tType] : ( list(X0) > X0 ) ).

tff(func_def_42,type,
    sK11: 
      !>[X0: $tType] : ( list(X0) > list(X0) ) ).

tff(func_def_43,type,
    sK12: ( list(int) * list(fm(atom)) ) > fm(atom) ).

tff(func_def_44,type,
    sK13: ( list(int) * list(fm(atom)) ) > fm(atom) ).

tff(func_def_45,type,
    sK14: 
      !>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).

tff(func_def_46,type,
    sK15: 
      !>[X0: $tType] : ( fun(list(X0),bool) > list(X0) ) ).

tff(func_def_47,type,
    sK16: 
      !>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).

tff(func_def_48,type,
    sK17: 
      !>[X0: $tType] : ( ( list(X0) * fun(X0,bool) * X0 ) > X0 ) ).

tff(func_def_49,type,
    sK18: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).

tff(pred_def_1,type,
    ring: 
      !>[X0: $tType] : $o ).

tff(pred_def_2,type,
    cl_Groups_Oplus: 
      !>[X0: $tType] : $o ).

tff(pred_def_3,type,
    zero: 
      !>[X0: $tType] : $o ).

tff(pred_def_4,type,
    monoid_add: 
      !>[X0: $tType] : $o ).

tff(pred_def_5,type,
    comm_semiring_1: 
      !>[X0: $tType] : $o ).

tff(pred_def_6,type,
    comm_monoid_add: 
      !>[X0: $tType] : $o ).

tff(pred_def_7,type,
    ab_semigroup_add: 
      !>[X0: $tType] : $o ).

tff(pred_def_8,type,
    cancel_semigroup_add: 
      !>[X0: $tType] : $o ).

tff(pred_def_9,type,
    cancel146912293up_add: 
      !>[X0: $tType] : $o ).

tff(pred_def_10,type,
    linord219039673up_add: 
      !>[X0: $tType] : $o ).

tff(pred_def_11,type,
    semiri456707255roduct: 
      !>[X0: $tType] : $o ).

tff(pred_def_12,type,
    list_ex1: 
      !>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).

tff(pred_def_13,type,
    interpret: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(list(X1),bool)) * fm(X0) * list(X1) ) > $o ) ).

tff(pred_def_14,type,
    qfree: 
      !>[X0: $tType] : ( fm(X0) > $o ) ).

tff(pred_def_15,type,
    member: 
      !>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).

tff(pred_def_16,type,
    pp: bool > $o ).

tff(f568,plain,
    $false,
    inference(subsumption_resolution,[],[f554,f539]) ).

tff(f539,plain,
    pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m),ksl),sK0)),xs)),
    inference(resolution,[],[f352,f422]) ).

tff(f422,plain,
    ! [X0: atom] :
      ( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m),ksl),X0)),xs))
      | ~ member(atom,X0,set(atom,as)) ),
    inference(cnf_transformation,[],[f258]) ).

tff(f258,plain,
    ! [X0: atom] :
      ( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m),ksl),X0)),xs))
      | ~ member(atom,X0,set(atom,as)) ),
    inference(ennf_transformation,[],[f163]) ).

tff(f163,plain,
    ! [X0: atom] :
      ( member(atom,X0,set(atom,as))
     => pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m),ksl),X0)),xs)) ),
    inference(rectify,[],[f1]) ).

tff(f1,axiom,
    ! [X4: atom] :
      ( member(atom,X4,set(atom,as))
     => pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m),ksl),X4)),xs)) ),
    file('/export/starexec/sandbox/tmp/tmp.EbZcv8Y2FG/Vampire---4.8_2598',fact_0__096ALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_A_Iasubst_A_Iil_A_L_Am_J_Aksl_Aa_J_Axs_096) ).

tff(f352,plain,
    member(atom,sK0,set(atom,as)),
    inference(cnf_transformation,[],[f293]) ).

tff(f293,plain,
    ( ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,sK0),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs)))
    & member(atom,sK0,set(atom,as)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f224,f292]) ).

tff(f292,plain,
    ( ? [X0: atom] :
        ( ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X0),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs)))
        & member(atom,X0,set(atom,as)) )
   => ( ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,sK0),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs)))
      & member(atom,sK0,set(atom,as)) ) ),
    introduced(choice_axiom,[]) ).

tff(f224,plain,
    ? [X0: atom] :
      ( ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X0),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs)))
      & member(atom,X0,set(atom,as)) ),
    inference(ennf_transformation,[],[f125]) ).

tff(f125,plain,
    ~ ! [X0: atom] :
        ( member(atom,X0,set(atom,as))
       => pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X0),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs))) ),
    inference(rectify,[],[f124]) ).

tff(f124,negated_conjecture,
    ~ ! [X22: atom] :
        ( member(atom,X22,set(atom,as))
       => pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X22),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs))) ),
    inference(negated_conjecture,[],[f123]) ).

tff(f123,conjecture,
    ! [X22: atom] :
      ( member(atom,X22,set(atom,as))
     => pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X22),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs))) ),
    file('/export/starexec/sandbox/tmp/tmp.EbZcv8Y2FG/Vampire---4.8_2598',conj_0) ).

tff(f554,plain,
    ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m),ksl),sK0)),xs)),
    inference(resolution,[],[f353,f509]) ).

tff(f509,plain,
    ! [X2: list(int),X3: int,X0: list(int),X1: atom] :
      ( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),iprod(int,X2,X0)),X0)))
      | ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(X3,X2),X1)),X0)) ),
    inference(cnf_transformation,[],[f349]) ).

tff(f349,plain,
    ! [X0: list(int),X1: atom,X2: list(int),X3: int] :
      ( ( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(X3,X2),X1)),X0))
        | ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),iprod(int,X2,X0)),X0))) )
      & ( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),iprod(int,X2,X0)),X0)))
        | ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(X3,X2),X1)),X0)) ) ),
    inference(nnf_transformation,[],[f219]) ).

tff(f219,plain,
    ! [X0: list(int),X1: atom,X2: list(int),X3: int] :
      ( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(X3,X2),X1)),X0))
    <=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X1),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X3),iprod(int,X2,X0)),X0))) ),
    inference(rectify,[],[f5]) ).

tff(f5,axiom,
    ! [X12: list(int),X13: atom,X14: list(int),X15: int] :
      ( pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,aa(atom,atom,asubst(X15,X14),X13)),X12))
    <=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X13),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),X15),iprod(int,X14,X12)),X12))) ),
    file('/export/starexec/sandbox/tmp/tmp.EbZcv8Y2FG/Vampire---4.8_2598',fact_4_IZ__asubst) ).

tff(f353,plain,
    ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,sK0),cons(int,aa(int,int,aa(int,fun(int,int),plus_plus(int),aa(int,int,aa(int,fun(int,int),plus_plus(int),il),m)),iprod(int,ksl,xs)),xs))),
    inference(cnf_transformation,[],[f293]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15  % Problem    : COM080_5 : TPTP v8.1.2. Released v6.0.0.
% 0.00/0.16  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.17/0.37  % Computer : n027.cluster.edu
% 0.17/0.37  % Model    : x86_64 x86_64
% 0.17/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37  % Memory   : 8042.1875MB
% 0.17/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38  % CPULimit   : 300
% 0.17/0.38  % WCLimit    : 300
% 0.17/0.38  % DateTime   : Tue Aug 29 13:15:38 EDT 2023
% 0.17/0.38  % CPUTime    : 
% 0.17/0.38  This is a TF1_THM_EQU_NAR problem
% 0.17/0.38  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.EbZcv8Y2FG/Vampire---4.8_2598
% 0.17/0.38  % (2715)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.45  % (2722)ott+1010_1_aac=none:bce=on:ep=RS:fsd=off:nm=4:nwc=2.0:nicw=on:sas=z3:sims=off_453 on Vampire---4 for (453ds/0Mi)
% 0.23/0.45  % (2717)ott+3_2:7_add=large:amm=off:anc=all:bce=on:drc=off:fsd=off:fde=unused:gs=on:irw=on:lcm=predicate:lma=on:msp=off:nwc=10.0:sac=on_598 on Vampire---4 for (598ds/0Mi)
% 0.23/0.45  % (2718)lrs+11_10:1_bs=unit_only:drc=off:fsd=off:fde=none:gs=on:msp=off:nm=16:nwc=2.0:nicw=on:sos=all:sac=on:sp=reverse_frequency:stl=62_575 on Vampire---4 for (575ds/0Mi)
% 0.23/0.45  % (2721)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_520 on Vampire---4 for (520ds/0Mi)
% 0.23/0.45  % (2720)lrs-1010_20_afr=on:anc=all_dependent:bs=on:bsr=on:cond=on:er=known:fde=none:nm=4:nwc=1.3:sims=off:sp=frequency:urr=on:stl=62_533 on Vampire---4 for (533ds/0Mi)
% 0.23/0.45  % (2716)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_1192 on Vampire---4 for (1192ds/0Mi)
% 0.23/0.45  % (2719)lrs+2_5:4_anc=none:br=off:fde=unused:gsp=on:nm=32:nwc=1.3:sims=off:sos=all:urr=on:stl=62_558 on Vampire---4 for (558ds/0Mi)
% 0.23/0.45  % (2716)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.23/0.45  % (2719)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.23/0.46  % (2718)First to succeed.
% 0.23/0.46  % (2719)Also succeeded, but the first one will report.
% 0.23/0.46  % (2718)Refutation found. Thanks to Tanya!
% 0.23/0.46  % SZS status Theorem for Vampire---4
% 0.23/0.46  % SZS output start Proof for Vampire---4
% See solution above
% 0.23/0.46  % (2718)------------------------------
% 0.23/0.46  % (2718)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.46  % (2718)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.46  % (2718)Termination reason: Refutation
% 0.23/0.46  
% 0.23/0.46  % (2718)Memory used [KB]: 10618
% 0.23/0.46  % (2718)Time elapsed: 0.016 s
% 0.23/0.46  % (2718)------------------------------
% 0.23/0.46  % (2718)------------------------------
% 0.23/0.47  % (2715)Success in time 0.082 s
% 0.23/0.47  % Vampire---4.8 exiting
%------------------------------------------------------------------------------