TSTP Solution File: SWW485_5 by Vampire---4.9

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%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : SWW485_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% Computer : n032.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 : Mon Jun 24 18:33:14 EDT 2024

% Result   : Theorem 0.16s 0.38s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   29 (   6 unt;   0 typ;   0 def)
%            Number of atoms       :   67 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   62 (  24   ~;  17   |;  10   &)
%                                         (   3 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   19 (  18 usr;   5 prp; 0-3 aty)
%            Number of functors    :   25 (  25 usr;   5 con; 0-4 aty)
%            Number of variables   :   26 (  20   !;   6   ?;  26   :)

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

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

tff(type_def_7,type,
    nat: $tType ).

tff(type_def_8,type,
    poly1: $tType > $tType ).

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

tff(type_def_10,type,
    fun: ( $tType * $tType ) > $tType ).

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

tff(func_def_1,type,
    order1: 
      !>[X0: $tType] : ( ( X0 * poly1(X0) ) > nat ) ).

tff(func_def_2,type,
    poly: 
      !>[X0: $tType] : ( poly1(X0) > fun(X0,X0) ) ).

tff(func_def_3,type,
    norm_norm: 
      !>[X0: $tType] : ( X0 > real ) ).

tff(func_def_4,type,
    aa: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).

tff(func_def_5,type,
    fFalse: bool ).

tff(func_def_6,type,
    fTrue: bool ).

tff(func_def_7,type,
    cs: poly1(complex) ).

tff(func_def_8,type,
    r: real ).

tff(func_def_9,type,
    sK0: real > complex ).

tff(func_def_10,type,
    sK1: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).

tff(func_def_11,type,
    sK2: 
      !>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).

tff(func_def_12,type,
    sK3: 
      !>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).

tff(func_def_13,type,
    sK4: 
      !>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).

tff(func_def_14,type,
    sK5: 
      !>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).

tff(func_def_15,type,
    sK6: 
      !>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).

tff(func_def_16,type,
    sK7: 
      !>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).

tff(func_def_17,type,
    sK8: 
      !>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).

tff(func_def_18,type,
    sK9: 
      !>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).

tff(func_def_19,type,
    sK10: 
      !>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).

tff(func_def_20,type,
    sK11: 
      !>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).

tff(func_def_21,type,
    sK12: real ).

tff(func_def_22,type,
    sK13: ( real * real ) > real ).

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

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

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

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

tff(pred_def_5,type,
    ring_char_0: 
      !>[X0: $tType] : $o ).

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

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

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

tff(pred_def_9,type,
    comm_semiring_0: 
      !>[X0: $tType] : $o ).

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

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

tff(pred_def_12,type,
    ord_less: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(pred_def_13,type,
    ord_less_eq: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(pred_def_14,type,
    pp: bool > $o ).

tff(f394,plain,
    $false,
    inference(avatar_sat_refutation,[],[f335,f339,f340,f393]) ).

tff(f393,plain,
    ( ~ spl14_1
    | ~ spl14_3 ),
    inference(avatar_contradiction_clause,[],[f392]) ).

tff(f392,plain,
    ( $false
    | ~ spl14_1
    | ~ spl14_3 ),
    inference(resolution,[],[f373,f338]) ).

tff(f338,plain,
    ( ! [X0: real] : ord_less_eq(real,norm_norm(complex,sK0(X0)),r)
    | ~ spl14_3 ),
    inference(avatar_component_clause,[],[f337]) ).

tff(f337,plain,
    ( spl14_3
  <=> ! [X0: real] : ord_less_eq(real,norm_norm(complex,sK0(X0)),r) ),
    introduced(avatar_definition,[new_symbols(naming,[spl14_3])]) ).

tff(f373,plain,
    ( ~ ord_less_eq(real,norm_norm(complex,sK0(sK12)),r)
    | ~ spl14_1 ),
    inference(resolution,[],[f274,f330]) ).

tff(f330,plain,
    ( ! [X0: real] : ~ ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),sK0(X0))),X0)
    | ~ spl14_1 ),
    inference(avatar_component_clause,[],[f329]) ).

tff(f329,plain,
    ( spl14_1
  <=> ! [X0: real] : ~ ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),sK0(X0))),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl14_1])]) ).

tff(f274,plain,
    ! [X1: complex] :
      ( ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),sK12)
      | ~ ord_less_eq(real,norm_norm(complex,X1),r) ),
    inference(cnf_transformation,[],[f235]) ).

tff(f235,plain,
    ( ! [X1: complex] :
        ( ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),sK12)
        | ~ ord_less_eq(real,norm_norm(complex,X1),r) )
    & ord_less(real,zero_zero(real),sK12) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f197,f234]) ).

tff(f234,plain,
    ( ? [X0: real] :
        ( ! [X1: complex] :
            ( ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),X0)
            | ~ ord_less_eq(real,norm_norm(complex,X1),r) )
        & ord_less(real,zero_zero(real),X0) )
   => ( ! [X1: complex] :
          ( ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),sK12)
          | ~ ord_less_eq(real,norm_norm(complex,X1),r) )
      & ord_less(real,zero_zero(real),sK12) ) ),
    introduced(choice_axiom,[]) ).

tff(f197,plain,
    ? [X0: real] :
      ( ! [X1: complex] :
          ( ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),X0)
          | ~ ord_less_eq(real,norm_norm(complex,X1),r) )
      & ord_less(real,zero_zero(real),X0) ),
    inference(ennf_transformation,[],[f156]) ).

tff(f156,plain,
    ? [X0: real] :
      ( ! [X1: complex] :
          ( ord_less_eq(real,norm_norm(complex,X1),r)
         => ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),X0) )
      & ord_less(real,zero_zero(real),X0) ),
    inference(rectify,[],[f1]) ).

tff(f1,axiom,
    ? [X2: real] :
      ( ! [X3: complex] :
          ( ord_less_eq(real,norm_norm(complex,X3),r)
         => ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X3)),X2) )
      & ord_less(real,zero_zero(real),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

tff(f340,plain,
    ~ spl14_2,
    inference(avatar_split_clause,[],[f249,f332]) ).

tff(f332,plain,
    ( spl14_2
  <=> thesis ),
    introduced(avatar_definition,[new_symbols(naming,[spl14_2])]) ).

tff(f249,plain,
    ~ thesis,
    inference(cnf_transformation,[],[f143]) ).

tff(f143,plain,
    ~ thesis,
    inference(flattening,[],[f142]) ).

tff(f142,negated_conjecture,
    ~ thesis,
    inference(negated_conjecture,[],[f141]) ).

tff(f141,conjecture,
    thesis,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

tff(f339,plain,
    ( spl14_3
    | spl14_2 ),
    inference(avatar_split_clause,[],[f250,f332,f337]) ).

tff(f250,plain,
    ! [X0: real] :
      ( thesis
      | ord_less_eq(real,norm_norm(complex,sK0(X0)),r) ),
    inference(cnf_transformation,[],[f218]) ).

tff(f218,plain,
    ! [X0: real] :
      ( thesis
      | ( ~ ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),sK0(X0))),X0)
        & ord_less_eq(real,norm_norm(complex,sK0(X0)),r) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f179,f217]) ).

tff(f217,plain,
    ! [X0: real] :
      ( ? [X1: complex] :
          ( ~ ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),X0)
          & ord_less_eq(real,norm_norm(complex,X1),r) )
     => ( ~ ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),sK0(X0))),X0)
        & ord_less_eq(real,norm_norm(complex,sK0(X0)),r) ) ),
    introduced(choice_axiom,[]) ).

tff(f179,plain,
    ! [X0: real] :
      ( thesis
      | ? [X1: complex] :
          ( ~ ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),X0)
          & ord_less_eq(real,norm_norm(complex,X1),r) ) ),
    inference(ennf_transformation,[],[f144]) ).

tff(f144,plain,
    ! [X0: real] :
      ( ! [X1: complex] :
          ( ord_less_eq(real,norm_norm(complex,X1),r)
         => ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),X0) )
     => thesis ),
    inference(rectify,[],[f140]) ).

tff(f140,axiom,
    ! [X40: real] :
      ( ! [X41: complex] :
          ( ord_less_eq(real,norm_norm(complex,X41),r)
         => ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X41)),X40) )
     => thesis ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

tff(f335,plain,
    ( spl14_1
    | spl14_2 ),
    inference(avatar_split_clause,[],[f251,f332,f329]) ).

tff(f251,plain,
    ! [X0: real] :
      ( thesis
      | ~ ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),sK0(X0))),X0) ),
    inference(cnf_transformation,[],[f218]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : SWW485_5 : TPTP v8.2.0. Released v6.0.0.
% 0.00/0.09  % Command    : run_vampire %s %d THM
% 0.09/0.29  % Computer : n032.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit   : 300
% 0.09/0.29  % WCLimit    : 300
% 0.09/0.29  % DateTime   : Wed Jun 19 06:36:54 EDT 2024
% 0.09/0.29  % CPUTime    : 
% 0.09/0.31  This is a TF1_THM_EQU_NAR problem
% 0.09/0.31  Running first-order theorem proving
% 0.09/0.31  Running /export/starexec/sandbox2/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.37  % (6770)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.37  % (6774)lrs+1010_2201:262144_anc=all:drc=encompass:sil=256000:sims=off:sp=frequency:spb=goal_then_units:rp=on:lwlo=on:st=3.0:i=179501:bs=unit_only:nm=6:ins=2:fsd=on:ss=axioms:sgt=16:afr=on:tgt=ground:awrs=decay:awrsf=200:acc=on:ccuc=first_0 on theBenchmark for (2999ds/179501Mi)
% 0.16/0.37  % (6770)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.37  % (6776)dis+1011_3:1_sil=256000:tgt=ground:sac=on:i=109:sd=1:ss=included_0 on theBenchmark for (2999ds/109Mi)
% 0.16/0.37  % (6770)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.37  % (6777)dis+1010_1:1_sil=2000:nwc=3.0:s2a=on:i=132:ins=5:fsr=off:ss=axioms:sd=2:fd=off_0 on theBenchmark for (2999ds/132Mi)
% 0.16/0.37  % (6770)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.37  % (6778)dis+1010_159245:1048576_to=lpo:sil=2000:etr=on:sp=unary_frequency:spb=goal:rnwc=on:nwc=10.9066:st=2:i=124:sd=1:nm=3:av=off:ss=axioms:rawr=on:drc=encompass:foolp=on:sgt=5:cond=fast:er=filter:erape=on:erml=2:s2a=on_0 on theBenchmark for (2999ds/124Mi)
% 0.16/0.37  % (6770)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.37  % (6773)dis+11_1:1_nwc=5.0:s2a=on:i=66616:s2at=3.0:sil=128000:bd=off_0 on theBenchmark for (2999ds/66616Mi)
% 0.16/0.37  % (6770)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.37  % (6775)lrs+10_1:3_drc=off:sil=256000:sp=unary_first:lwlo=on:i=216875:kws=precedence:ins=3:rawr=on:nwc=10.0_0 on theBenchmark for (2999ds/216875Mi)
% 0.16/0.37  % (6770)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.37  % (6771)lrs+1011_1:12_anc=none:drc=off:sil=64000:sims=off:sp=unary_first:spb=goal_then_units:lsd=20:rnwc=on:nwc=2.0:i=53554:add=off:awrs=converge:bd=off:uhcvi=on:tgt=ground:afp=300:afq=1.63_0 on theBenchmark for (2999ds/53554Mi)
% 0.16/0.37  % (6777)First to succeed.
% 0.16/0.38  % (6777)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-6770"
% 0.16/0.38  % (6770)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.38  % (6777)Refutation found. Thanks to Tanya!
% 0.16/0.38  % SZS status Theorem for theBenchmark
% 0.16/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.38  % (6777)------------------------------
% 0.16/0.38  % (6777)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.16/0.38  % (6777)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.16/0.38  % (6777)Termination reason: Refutation
% 0.16/0.38  
% 0.16/0.38  % (6777)Memory used [KB]: 1287
% 0.16/0.38  % (6777)Time elapsed: 0.007 s
% 0.16/0.38  % (6777)Instructions burned: 8 (million)
% 0.16/0.38  % (6777)------------------------------
% 0.16/0.38  % (6777)------------------------------
% 0.16/0.38  % (6770)Success in time 0.062 s
%------------------------------------------------------------------------------