TSTP Solution File: SWW520_5 by Vampire---4.9

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%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : SWW520_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% Computer : n029.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 18:33:22 EDT 2024

% Result   : Theorem 0.22s 0.44s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   22 (  15 unt;   0 typ;   0 def)
%            Number of atoms       :   47 (   7 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   44 (  19   ~;   7   |;  13   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   15 (  13 usr;   1 prp; 0-6 aty)
%            Number of functors    :   49 (  49 usr;   5 con; 0-4 aty)
%            Number of variables   :   37 (  28   !;   9   ?;  37   :)

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

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

tff(type_def_7,type,
    hoare_28830079triple: $tType > $tType ).

tff(type_def_8,type,
    nat: $tType ).

tff(type_def_9,type,
    pred: $tType > $tType ).

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

tff(func_def_0,type,
    combk: 
      !>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).

tff(func_def_1,type,
    complete_Sup_Sup: 
      !>[X0: $tType] : ( fun(X0,bool) > X0 ) ).

tff(func_def_2,type,
    suc: nat > nat ).

tff(func_def_3,type,
    semiri532925092at_aux: 
      !>[X0: $tType] : ( ( fun(X0,X0) * nat * X0 ) > X0 ) ).

tff(func_def_4,type,
    bot_bot: 
      !>[X0: $tType] : X0 ).

tff(func_def_5,type,
    powp: 
      !>[X0: $tType] : ( fun(X0,bool) > fun(fun(X0,bool),bool) ) ).

tff(func_def_6,type,
    pred1: 
      !>[X0: $tType] : ( fun(X0,bool) > pred(X0) ) ).

tff(func_def_7,type,
    pred_case: 
      !>[X0: $tType,X1: $tType] : ( ( fun(fun(X0,bool),X1) * pred(X0) ) > X1 ) ).

tff(func_def_8,type,
    pred_rec: 
      !>[X0: $tType,X1: $tType] : ( ( fun(fun(X0,bool),X1) * pred(X0) ) > X1 ) ).

tff(func_def_9,type,
    collect: 
      !>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).

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

tff(func_def_11,type,
    fFalse: bool ).

tff(func_def_12,type,
    fTrue: bool ).

tff(func_def_13,type,
    ga: fun(hoare_28830079triple(a),bool) ).

tff(func_def_14,type,
    sK0: nat ).

tff(func_def_15,type,
    sK1: hoare_28830079triple(a) ).

tff(func_def_16,type,
    sK2: 
      !>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > X0 ) ).

tff(func_def_17,type,
    sK3: 
      !>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > X0 ) ).

tff(func_def_18,type,
    sK4: 
      !>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > X0 ) ).

tff(func_def_19,type,
    sK5: 
      !>[X0: $tType] : ( fun(nat,X0) > nat ) ).

tff(func_def_20,type,
    sK6: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).

tff(func_def_21,type,
    sK7: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).

tff(func_def_22,type,
    sK8: nat > nat ).

tff(func_def_23,type,
    sK9: 
      !>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).

tff(func_def_24,type,
    sK10: 
      !>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).

tff(func_def_25,type,
    sK11: 
      !>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).

tff(func_def_26,type,
    sK12: 
      !>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).

tff(func_def_27,type,
    sK13: 
      !>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).

tff(func_def_28,type,
    sK14: 
      !>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).

tff(func_def_29,type,
    sK15: 
      !>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).

tff(func_def_30,type,
    sK16: 
      !>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).

tff(func_def_31,type,
    sK17: 
      !>[X0: $tType] : ( fun(X0,bool) > X0 ) ).

tff(func_def_32,type,
    sK18: 
      !>[X0: $tType] : ( fun(X0,bool) > X0 ) ).

tff(func_def_33,type,
    sK19: 
      !>[X0: $tType] : ( fun(X0,bool) > X0 ) ).

tff(func_def_34,type,
    sK20: 
      !>[X0: $tType] : ( fun(X0,bool) > X0 ) ).

tff(func_def_35,type,
    sK21: 
      !>[X0: $tType] : ( fun(X0,bool) > X0 ) ).

tff(func_def_36,type,
    sK22: 
      !>[X0: $tType] : ( pred(X0) > fun(X0,bool) ) ).

tff(func_def_37,type,
    sK23: 
      !>[X0: $tType] : ( ( fun(fun(X0,bool),bool) * X0 ) > fun(X0,bool) ) ).

tff(func_def_38,type,
    sK24: 
      !>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) ) > X0 ) ).

tff(func_def_39,type,
    sK25: 
      !>[X0: $tType] : ( ( nat * fun(hoare_28830079triple(X0),bool) ) > hoare_28830079triple(X0) ) ).

tff(func_def_40,type,
    sK26: 
      !>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) ) > X0 ) ).

tff(func_def_41,type,
    sK27: 
      !>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) ) > X0 ) ).

tff(func_def_42,type,
    sK28: 
      !>[X0: $tType] : ( ( fun(X0,bool) * fun(fun(X0,bool),bool) ) > fun(X0,bool) ) ).

tff(func_def_43,type,
    sK29: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).

tff(func_def_44,type,
    sK30: 
      !>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) ) > X0 ) ).

tff(func_def_45,type,
    sK31: 
      !>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) * fun(X0,bool) ) > X0 ) ).

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

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

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

tff(pred_def_4,type,
    semiring_1: 
      !>[X0: $tType] : $o ).

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

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

tff(pred_def_7,type,
    comple187826305attice: 
      !>[X0: $tType] : $o ).

tff(pred_def_8,type,
    hoare_592965047valids: 
      !>[X0: $tType] : ( ( fun(hoare_28830079triple(X0),bool) * fun(hoare_28830079triple(X0),bool) ) > $o ) ).

tff(pred_def_9,type,
    hoare_1633586161_valid: 
      !>[X0: $tType] : ( ( nat * hoare_28830079triple(X0) ) > $o ) ).

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

tff(pred_def_11,type,
    inv_imagep: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X0,bool)) * fun(X1,X0) * X1 * X1 ) > $o ) ).

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

tff(pred_def_13,type,
    pp: bool > $o ).

tff(f621,plain,
    $false,
    inference(subsumption_resolution,[],[f613,f619]) ).

tff(f619,plain,
    ! [X0: $tType,X1: X0] : ~ member(X0,X1,combk(bool,X0,fFalse)),
    inference(backward_demodulation,[],[f482,f612]) ).

tff(f612,plain,
    ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = combk(bool,X0,fFalse) ),
    inference(backward_demodulation,[],[f448,f484]) ).

tff(f484,plain,
    ! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
    inference(cnf_transformation,[],[f167]) ).

tff(f167,plain,
    ! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
    inference(rectify,[],[f76]) ).

tff(f76,axiom,
    ! [X1: $tType,X3: fun(X1,bool)] : ( collect(X1,X3) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

tff(f448,plain,
    ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse)) ),
    inference(cnf_transformation,[],[f139]) ).

tff(f139,plain,
    ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse)) ),
    inference(rectify,[],[f11]) ).

tff(f11,axiom,
    ! [X1: $tType] : ( bot_bot(fun(X1,bool)) = collect(X1,combk(bool,X1,fFalse)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

tff(f482,plain,
    ! [X0: $tType,X1: X0] : ~ member(X0,X1,bot_bot(fun(X0,bool))),
    inference(cnf_transformation,[],[f165]) ).

tff(f165,plain,
    ! [X0: $tType,X1: X0] : ~ member(X0,X1,bot_bot(fun(X0,bool))),
    inference(rectify,[],[f4]) ).

tff(f4,axiom,
    ! [X1: $tType,X7: X1] : ~ member(X1,X7,bot_bot(fun(X1,bool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

tff(f613,plain,
    member(hoare_28830079triple(a),sK1,combk(bool,hoare_28830079triple(a),fFalse)),
    inference(backward_demodulation,[],[f611,f484]) ).

tff(f611,plain,
    member(hoare_28830079triple(a),sK1,collect(hoare_28830079triple(a),combk(bool,hoare_28830079triple(a),fFalse))),
    inference(backward_demodulation,[],[f421,f448]) ).

tff(f421,plain,
    member(hoare_28830079triple(a),sK1,bot_bot(fun(hoare_28830079triple(a),bool))),
    inference(cnf_transformation,[],[f339]) ).

tff(f339,plain,
    ( ~ hoare_1633586161_valid(a,sK0,sK1)
    & member(hoare_28830079triple(a),sK1,bot_bot(fun(hoare_28830079triple(a),bool)))
    & ! [X2: hoare_28830079triple(a)] :
        ( hoare_1633586161_valid(a,sK0,X2)
        | ~ member(hoare_28830079triple(a),X2,ga) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f239,f338,f337]) ).

tff(f337,plain,
    ( ? [X0: nat] :
        ( ? [X1: hoare_28830079triple(a)] :
            ( ~ hoare_1633586161_valid(a,X0,X1)
            & member(hoare_28830079triple(a),X1,bot_bot(fun(hoare_28830079triple(a),bool))) )
        & ! [X2: hoare_28830079triple(a)] :
            ( hoare_1633586161_valid(a,X0,X2)
            | ~ member(hoare_28830079triple(a),X2,ga) ) )
   => ( ? [X1: hoare_28830079triple(a)] :
          ( ~ hoare_1633586161_valid(a,sK0,X1)
          & member(hoare_28830079triple(a),X1,bot_bot(fun(hoare_28830079triple(a),bool))) )
      & ! [X2: hoare_28830079triple(a)] :
          ( hoare_1633586161_valid(a,sK0,X2)
          | ~ member(hoare_28830079triple(a),X2,ga) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f338,plain,
    ( ? [X1: hoare_28830079triple(a)] :
        ( ~ hoare_1633586161_valid(a,sK0,X1)
        & member(hoare_28830079triple(a),X1,bot_bot(fun(hoare_28830079triple(a),bool))) )
   => ( ~ hoare_1633586161_valid(a,sK0,sK1)
      & member(hoare_28830079triple(a),sK1,bot_bot(fun(hoare_28830079triple(a),bool))) ) ),
    introduced(choice_axiom,[]) ).

tff(f239,plain,
    ? [X0: nat] :
      ( ? [X1: hoare_28830079triple(a)] :
          ( ~ hoare_1633586161_valid(a,X0,X1)
          & member(hoare_28830079triple(a),X1,bot_bot(fun(hoare_28830079triple(a),bool))) )
      & ! [X2: hoare_28830079triple(a)] :
          ( hoare_1633586161_valid(a,X0,X2)
          | ~ member(hoare_28830079triple(a),X2,ga) ) ),
    inference(ennf_transformation,[],[f128]) ).

tff(f128,plain,
    ~ ! [X0: nat] :
        ( ! [X1: hoare_28830079triple(a)] :
            ( member(hoare_28830079triple(a),X1,bot_bot(fun(hoare_28830079triple(a),bool)))
           => hoare_1633586161_valid(a,X0,X1) )
        | ? [X2: hoare_28830079triple(a)] :
            ( ~ hoare_1633586161_valid(a,X0,X2)
            & member(hoare_28830079triple(a),X2,ga) ) ),
    inference(rectify,[],[f127]) ).

tff(f127,negated_conjecture,
    ~ ! [X51: nat] :
        ( ! [X19: hoare_28830079triple(a)] :
            ( member(hoare_28830079triple(a),X19,bot_bot(fun(hoare_28830079triple(a),bool)))
           => hoare_1633586161_valid(a,X51,X19) )
        | ? [X4: hoare_28830079triple(a)] :
            ( ~ hoare_1633586161_valid(a,X51,X4)
            & member(hoare_28830079triple(a),X4,ga) ) ),
    inference(negated_conjecture,[],[f126]) ).

tff(f126,conjecture,
    ! [X51: nat] :
      ( ! [X19: hoare_28830079triple(a)] :
          ( member(hoare_28830079triple(a),X19,bot_bot(fun(hoare_28830079triple(a),bool)))
         => hoare_1633586161_valid(a,X51,X19) )
      | ? [X4: hoare_28830079triple(a)] :
          ( ~ hoare_1633586161_valid(a,X51,X4)
          & member(hoare_28830079triple(a),X4,ga) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWW520_5 : TPTP v8.2.0. Released v6.0.0.
% 0.07/0.12  % Command    : run_vampire %s %d THM
% 0.12/0.34  % Computer : n029.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Wed Jun 19 09:45:09 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.12/0.36  This is a TF1_THM_EQU_NAR problem
% 0.12/0.36  Running first-order theorem proving
% 0.12/0.36  Running /export/starexec/sandbox/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.43  % (23275)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43  % (23279)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)
% 0.22/0.43  % (23275)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43  % (23276)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)
% 0.22/0.43  % (23275)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43  % (23278)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)
% 0.22/0.44  % (23279)First to succeed.
% 0.22/0.44  % (23279)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-23275"
% 0.22/0.44  % (23275)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.44  % (23279)Refutation found. Thanks to Tanya!
% 0.22/0.44  % SZS status Theorem for theBenchmark
% 0.22/0.44  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.44  % (23279)------------------------------
% 0.22/0.44  % (23279)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.44  % (23279)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.44  % (23279)Termination reason: Refutation
% 0.22/0.44  
% 0.22/0.44  % (23279)Memory used [KB]: 1401
% 0.22/0.44  % (23279)Time elapsed: 0.010 s
% 0.22/0.44  % (23279)Instructions burned: 12 (million)
% 0.22/0.44  % (23279)------------------------------
% 0.22/0.44  % (23279)------------------------------
% 0.22/0.44  % (23275)Success in time 0.071 s
%------------------------------------------------------------------------------