TSTP Solution File: SWW510_5 by Vampire---4.9

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%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : SWW510_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% Computer : n011.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 18:33:20 EDT 2024

% Result   : Theorem 0.25s 0.48s
% Output   : Refutation 0.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   33 (  11 unt;   0 typ;   0 def)
%            Number of atoms       :   86 (   9 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  100 (  47   ~;  33   |;  16   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-6 aty)
%            Number of functors    :   57 (  57 usr;  11 con; 0-7 aty)
%            Number of variables   :  111 (  94   !;  17   ?; 111   :)

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

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

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

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

tff(type_def_9,type,
    hoare_28830079triple: $tType > $tType ).

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

tff(func_def_0,type,
    combb: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * 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,
    combk: 
      !>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).

tff(func_def_3,type,
    combs: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * fun(X0,X1) ) > fun(X0,X2) ) ).

tff(func_def_4,type,
    skip: com ).

tff(func_def_5,type,
    semi: ( com * com ) > com ).

tff(func_def_6,type,
    finite_fold1: 
      !>[X0: $tType] : ( fun(X0,fun(X0,X0)) > fun(fun(X0,bool),X0) ) ).

tff(func_def_7,type,
    finite_fold1Set: 
      !>[X0: $tType] : ( ( fun(X0,fun(X0,X0)) * fun(X0,bool) ) > fun(X0,bool) ) ).

tff(func_def_8,type,
    the: 
      !>[X0: $tType] : ( fun(X0,bool) > X0 ) ).

tff(func_def_9,type,
    hoare_1841697145triple: 
      !>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * com * fun(X0,fun(state,bool)) ) > hoare_28830079triple(X0) ) ).

tff(func_def_10,type,
    hoare_376461865e_case: 
      !>[X0: $tType,X1: $tType] : ( ( fun(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),X1))) * hoare_28830079triple(X0) ) > X1 ) ).

tff(func_def_11,type,
    hoare_678420151le_rec: 
      !>[X0: $tType,X1: $tType] : ( ( fun(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),X1))) * hoare_28830079triple(X0) ) > X1 ) ).

tff(func_def_12,type,
    bot_bot: 
      !>[X0: $tType] : X0 ).

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

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

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

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

tff(func_def_17,type,
    fFalse: bool ).

tff(func_def_18,type,
    fNot: fun(bool,bool) ).

tff(func_def_19,type,
    fTrue: bool ).

tff(func_def_20,type,
    fconj: fun(bool,fun(bool,bool)) ).

tff(func_def_21,type,
    fdisj: fun(bool,fun(bool,bool)) ).

tff(func_def_22,type,
    fequal: 
      !>[X0: $tType] : fun(X0,fun(X0,bool)) ).

tff(func_def_23,type,
    fimplies: fun(bool,fun(bool,bool)) ).

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

tff(func_def_25,type,
    g: fun(hoare_28830079triple(a),bool) ).

tff(func_def_26,type,
    q: a > fun(state,bool) ).

tff(func_def_27,type,
    c: com ).

tff(func_def_28,type,
    sK0: a ).

tff(func_def_29,type,
    sK1: state ).

tff(func_def_30,type,
    sK2: ( fun(a,fun(state,bool)) * fun(a,fun(state,bool)) ) > state ).

tff(func_def_31,type,
    sK3: 
      !>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) ) > X0 ) ).

tff(func_def_32,type,
    sK4: 
      !>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) ) > state ) ).

tff(func_def_33,type,
    sK5: 
      !>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) ) > state ) ).

tff(func_def_34,type,
    sK6: 
      !>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) ) > X0 ) ).

tff(func_def_35,type,
    sK7: 
      !>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) ) > state ) ).

tff(func_def_36,type,
    sK8: 
      !>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) ) > X0 ) ).

tff(func_def_37,type,
    sK9: 
      !>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) ) > state ) ).

tff(func_def_38,type,
    sK10: 
      !>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * com * fun(hoare_28830079triple(X0),bool) * fun(X0,fun(state,bool)) ) > X0 ) ).

tff(func_def_39,type,
    sK11: 
      !>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * com * fun(hoare_28830079triple(X0),bool) * fun(X0,fun(state,bool)) ) > state ) ).

tff(func_def_40,type,
    sK12: 
      !>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * com * fun(hoare_28830079triple(X0),bool) * fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) ) > state ) ).

tff(func_def_41,type,
    sK13: 
      !>[X0: $tType] : ( hoare_28830079triple(X0) > fun(X0,fun(state,bool)) ) ).

tff(func_def_42,type,
    sK14: 
      !>[X0: $tType] : ( hoare_28830079triple(X0) > com ) ).

tff(func_def_43,type,
    sK15: 
      !>[X0: $tType] : ( hoare_28830079triple(X0) > fun(X0,fun(state,bool)) ) ).

tff(func_def_44,type,
    sK16: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).

tff(func_def_45,type,
    sK17: 
      !>[X0: $tType] : ( fun(X0,bool) > X0 ) ).

tff(func_def_46,type,
    sK18: 
      !>[X0: $tType] : ( fun(X0,bool) > X0 ) ).

tff(func_def_47,type,
    sK19: 
      !>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) ) > X0 ) ).

tff(func_def_48,type,
    sK20: 
      !>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > X0 ) ).

tff(func_def_49,type,
    sK21: 
      !>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) ) > X0 ) ).

tff(func_def_50,type,
    sK22: 
      !>[X0: $tType] : ( ( fun(X0,bool) * X0 ) > X0 ) ).

tff(func_def_51,type,
    sK23: 
      !>[X0: $tType] : ( ( fun(X0,bool) * X0 ) > X0 ) ).

tff(func_def_52,type,
    sK24: 
      !>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > X0 ) ).

tff(func_def_53,type,
    sK25: 
      !>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > X0 ) ).

tff(func_def_54,type,
    sK26: 
      !>[X0: $tType] : ( ( fun(X0,bool) * X0 ) > X0 ) ).

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

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

tff(pred_def_3,type,
    finite_finite1: 
      !>[X0: $tType] : ( fun(X0,bool) > $o ) ).

tff(pred_def_4,type,
    finite_fold_graph: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X1)) * X1 * fun(X0,bool) * X1 ) > $o ) ).

tff(pred_def_5,type,
    finite_folding_one: 
      !>[X0: $tType] : ( ( fun(X0,fun(X0,X0)) * fun(fun(X0,bool),X0) ) > $o ) ).

tff(pred_def_6,type,
    finite2073411215e_idem: 
      !>[X0: $tType] : ( ( fun(X0,fun(X0,X0)) * fun(fun(X0,bool),X0) ) > $o ) ).

tff(pred_def_7,type,
    hoare_992312373derivs: 
      !>[X0: $tType] : ( ( fun(hoare_28830079triple(X0),bool) * fun(hoare_28830079triple(X0),bool) ) > $o ) ).

tff(pred_def_8,type,
    pp: bool > $o ).

tff(pred_def_9,type,
    p: ( a * state ) > $o ).

tff(f443,plain,
    $false,
    inference(resolution,[],[f438,f240]) ).

tff(f240,plain,
    p(sK0,sK1),
    inference(cnf_transformation,[],[f195]) ).

tff(f195,plain,
    ( ! [X2: fun(a,fun(state,bool)),X3: fun(a,fun(state,bool))] :
        ( ( ~ pp(aa(state,bool,q(sK0),sK2(X2,X3)))
          & ! [X5: a] :
              ( pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),sK2(X2,X3)))
              | ~ pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),sK1)) ) )
        | ~ hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3)),bot_bot(fun(hoare_28830079triple(a),bool)))) )
    & p(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f166,f194,f193]) ).

tff(f193,plain,
    ( ? [X0: a,X1: state] :
        ( ! [X2: fun(a,fun(state,bool)),X3: fun(a,fun(state,bool))] :
            ( ? [X4: state] :
                ( ~ pp(aa(state,bool,q(X0),X4))
                & ! [X5: a] :
                    ( pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),X4))
                    | ~ pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),X1)) ) )
            | ~ hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3)),bot_bot(fun(hoare_28830079triple(a),bool)))) )
        & p(X0,X1) )
   => ( ! [X3: fun(a,fun(state,bool)),X2: fun(a,fun(state,bool))] :
          ( ? [X4: state] :
              ( ~ pp(aa(state,bool,q(sK0),X4))
              & ! [X5: a] :
                  ( pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),X4))
                  | ~ pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),sK1)) ) )
          | ~ hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3)),bot_bot(fun(hoare_28830079triple(a),bool)))) )
      & p(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

tff(f194,plain,
    ! [X2: fun(a,fun(state,bool)),X3: fun(a,fun(state,bool))] :
      ( ? [X4: state] :
          ( ~ pp(aa(state,bool,q(sK0),X4))
          & ! [X5: a] :
              ( pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),X4))
              | ~ pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),sK1)) ) )
     => ( ~ pp(aa(state,bool,q(sK0),sK2(X2,X3)))
        & ! [X5: a] :
            ( pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),sK2(X2,X3)))
            | ~ pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),sK1)) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f166,plain,
    ? [X0: a,X1: state] :
      ( ! [X2: fun(a,fun(state,bool)),X3: fun(a,fun(state,bool))] :
          ( ? [X4: state] :
              ( ~ pp(aa(state,bool,q(X0),X4))
              & ! [X5: a] :
                  ( pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),X4))
                  | ~ pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),X1)) ) )
          | ~ hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3)),bot_bot(fun(hoare_28830079triple(a),bool)))) )
      & p(X0,X1) ),
    inference(ennf_transformation,[],[f129]) ).

tff(f129,plain,
    ~ ! [X0: a,X1: state] :
        ( ? [X2: fun(a,fun(state,bool)),X3: fun(a,fun(state,bool))] :
            ( ! [X4: state] :
                ( pp(aa(state,bool,q(X0),X4))
                | ? [X5: a] :
                    ( ~ pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),X4))
                    & pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),X1)) ) )
            & hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3)),bot_bot(fun(hoare_28830079triple(a),bool)))) )
        | ~ p(X0,X1) ),
    inference(rectify,[],[f128]) ).

tff(f128,negated_conjecture,
    ~ ! [X19: a,X20: state] :
        ( ? [X49: fun(a,fun(state,bool)),X50: fun(a,fun(state,bool))] :
            ( ! [X22: state] :
                ( pp(aa(state,bool,q(X19),X22))
                | ? [X23: a] :
                    ( ~ pp(aa(state,bool,aa(a,fun(state,bool),X50,X23),X22))
                    & pp(aa(state,bool,aa(a,fun(state,bool),X49,X23),X20)) ) )
            & hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,X49,c,X50)),bot_bot(fun(hoare_28830079triple(a),bool)))) )
        | ~ p(X19,X20) ),
    inference(negated_conjecture,[],[f127]) ).

tff(f127,conjecture,
    ! [X19: a,X20: state] :
      ( ? [X49: fun(a,fun(state,bool)),X50: fun(a,fun(state,bool))] :
          ( ! [X22: state] :
              ( pp(aa(state,bool,q(X19),X22))
              | ? [X23: a] :
                  ( ~ pp(aa(state,bool,aa(a,fun(state,bool),X50,X23),X22))
                  & pp(aa(state,bool,aa(a,fun(state,bool),X49,X23),X20)) ) )
          & hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,X49,c,X50)),bot_bot(fun(hoare_28830079triple(a),bool)))) )
      | ~ p(X19,X20) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

tff(f438,plain,
    ~ p(sK0,sK1),
    inference(resolution,[],[f432,f346]) ).

tff(f346,plain,
    ! [X0: $tType,X2: X0] : pp(aa(X0,bool,combc(X0,X0,bool,fequal(X0),X2),X2)),
    inference(backward_demodulation,[],[f317,f276]) ).

tff(f276,plain,
    ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
    inference(cnf_transformation,[],[f147]) ).

tff(f147,plain,
    ! [X0: $tType,X1: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
    inference(rectify,[],[f110]) ).

tff(f110,axiom,
    ! [X0: $tType,X2: $tType,X1: $tType,X68: X0,X69: X1,X67: fun(X0,fun(X1,X2))] : ( aa(X0,X2,combc(X0,X1,X2,X67,X69),X68) = aa(X1,X2,aa(X0,fun(X1,X2),X67,X68),X69) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

tff(f317,plain,
    ! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2)),
    inference(equality_resolution,[],[f282]) ).

tff(f282,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1))
      | ( X1 != X2 ) ),
    inference(cnf_transformation,[],[f153]) ).

tff(f153,plain,
    ! [X0: $tType,X1: X0,X2: X0] :
      ( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1))
      | ( X1 != X2 ) ),
    inference(rectify,[],[f122]) ).

tff(f122,axiom,
    ! [X0: $tType,X70: X0,X71: X0] :
      ( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X71),X70))
      | ( X70 != X71 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

tff(f432,plain,
    ! [X0: state] :
      ( ~ pp(aa(state,bool,combc(state,state,bool,fequal(state),X0),sK1))
      | ~ p(sK0,X0) ),
    inference(superposition,[],[f427,f279]) ).

tff(f279,plain,
    ! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ),
    inference(cnf_transformation,[],[f150]) ).

tff(f150,plain,
    ! [X0: $tType,X1: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ),
    inference(rectify,[],[f111]) ).

tff(f111,axiom,
    ! [X1: $tType,X0: $tType,X69: X1,X67: X0] : ( aa(X1,X0,combk(X0,X1,X67),X69) = X67 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

tff(f427,plain,
    ! [X0: state,X1: a] :
      ( ~ pp(aa(state,bool,aa(a,fun(state,bool),combk(fun(state,bool),a,combc(state,state,bool,fequal(state),X0)),X1),sK1))
      | ~ p(sK0,X0) ),
    inference(duplicate_literal_removal,[],[f426]) ).

tff(f426,plain,
    ! [X0: state,X1: a] :
      ( ~ pp(aa(state,bool,aa(a,fun(state,bool),combk(fun(state,bool),a,combc(state,state,bool,fequal(state),X0)),X1),sK1))
      | ~ p(sK0,X0)
      | ~ p(sK0,X0) ),
    inference(resolution,[],[f340,f319]) ).

tff(f319,plain,
    ! [X0: a,X1: state] :
      ( ~ pp(aa(state,bool,q(sK0),sK2(combk(fun(state,bool),a,combc(state,state,bool,fequal(state),X1)),combk(fun(state,bool),a,q(X0)))))
      | ~ p(X0,X1) ),
    inference(resolution,[],[f243,f242]) ).

tff(f242,plain,
    ! [X2: fun(a,fun(state,bool)),X3: fun(a,fun(state,bool))] :
      ( ~ hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3)),bot_bot(fun(hoare_28830079triple(a),bool))))
      | ~ pp(aa(state,bool,q(sK0),sK2(X2,X3))) ),
    inference(cnf_transformation,[],[f195]) ).

tff(f243,plain,
    ! [X0: a,X1: state] :
      ( hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,combk(fun(state,bool),a,combc(state,state,bool,fequal(state),X1)),c,combk(fun(state,bool),a,q(X0)))),bot_bot(fun(hoare_28830079triple(a),bool))))
      | ~ p(X0,X1) ),
    inference(cnf_transformation,[],[f167]) ).

tff(f167,plain,
    ! [X0: a,X1: state] :
      ( hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,combk(fun(state,bool),a,combc(state,state,bool,fequal(state),X1)),c,combk(fun(state,bool),a,q(X0)))),bot_bot(fun(hoare_28830079triple(a),bool))))
      | ~ p(X0,X1) ),
    inference(ennf_transformation,[],[f130]) ).

tff(f130,plain,
    ! [X0: a,X1: state] :
      ( p(X0,X1)
     => hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,combk(fun(state,bool),a,combc(state,state,bool,fequal(state),X1)),c,combk(fun(state,bool),a,q(X0)))),bot_bot(fun(hoare_28830079triple(a),bool)))) ),
    inference(rectify,[],[f126]) ).

tff(f126,axiom,
    ! [X72: a,X73: state] :
      ( p(X72,X73)
     => hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,combk(fun(state,bool),a,combc(state,state,bool,fequal(state),X73)),c,combk(fun(state,bool),a,q(X72)))),bot_bot(fun(hoare_28830079triple(a),bool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).

tff(f340,plain,
    ! [X2: state,X0: a,X1: a] :
      ( pp(aa(state,bool,q(X0),sK2(combk(fun(state,bool),a,combc(state,state,bool,fequal(state),X2)),combk(fun(state,bool),a,q(X0)))))
      | ~ pp(aa(state,bool,aa(a,fun(state,bool),combk(fun(state,bool),a,combc(state,state,bool,fequal(state),X2)),X1),sK1))
      | ~ p(X0,X2) ),
    inference(superposition,[],[f318,f279]) ).

tff(f318,plain,
    ! [X2: a,X0: a,X1: state] :
      ( pp(aa(state,bool,aa(a,fun(state,bool),combk(fun(state,bool),a,q(X0)),X2),sK2(combk(fun(state,bool),a,combc(state,state,bool,fequal(state),X1)),combk(fun(state,bool),a,q(X0)))))
      | ~ pp(aa(state,bool,aa(a,fun(state,bool),combk(fun(state,bool),a,combc(state,state,bool,fequal(state),X1)),X2),sK1))
      | ~ p(X0,X1) ),
    inference(resolution,[],[f243,f241]) ).

tff(f241,plain,
    ! [X2: fun(a,fun(state,bool)),X3: fun(a,fun(state,bool)),X5: a] :
      ( ~ hoare_992312373derivs(a,g,aa(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool),aa(hoare_28830079triple(a),fun(fun(hoare_28830079triple(a),bool),fun(hoare_28830079triple(a),bool)),insert(hoare_28830079triple(a)),hoare_1841697145triple(a,X2,c,X3)),bot_bot(fun(hoare_28830079triple(a),bool))))
      | ~ pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),sK1))
      | pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),sK2(X2,X3))) ),
    inference(cnf_transformation,[],[f195]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : SWW510_5 : TPTP v8.2.0. Released v6.0.0.
% 0.08/0.13  % Command    : run_vampire %s %d THM
% 0.14/0.37  % Computer : n011.cluster.edu
% 0.14/0.37  % Model    : x86_64 x86_64
% 0.14/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37  % Memory   : 8042.1875MB
% 0.14/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37  % CPULimit   : 300
% 0.14/0.37  % WCLimit    : 300
% 0.14/0.37  % DateTime   : Wed Jun 19 05:56:24 EDT 2024
% 0.14/0.37  % CPUTime    : 
% 0.14/0.38  This is a TF1_THM_EQU_NAR problem
% 0.14/0.39  Running first-order theorem proving
% 0.14/0.39  Running /export/starexec/sandbox2/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.25/0.46  % (9935)Running in auto input_syntax mode. Trying TPTP
% 0.25/0.46  % (9937)dis+11_1:1_nwc=5.0:s2a=on:i=66616:s2at=3.0:sil=128000:bd=off_0 on theBenchmark for (2999ds/66616Mi)
% 0.25/0.46  % (9935)Running in auto input_syntax mode. Trying TPTP
% 0.25/0.46  % (9936)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)
% 0.25/0.46  % (9935)Running in auto input_syntax mode. Trying TPTP
% 0.25/0.46  % (9942)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)
% 0.25/0.46  % (9935)Running in auto input_syntax mode. Trying TPTP
% 0.25/0.46  % (9941)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)
% 0.25/0.46  % (9935)Running in auto input_syntax mode. Trying TPTP
% 0.25/0.46  % (9940)dis+1011_3:1_sil=256000:tgt=ground:sac=on:i=109:sd=1:ss=included_0 on theBenchmark for (2999ds/109Mi)
% 0.25/0.46  % (9935)Running in auto input_syntax mode. Trying TPTP
% 0.25/0.46  % (9938)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)
% 0.25/0.46  % (9935)Running in auto input_syntax mode. Trying TPTP
% 0.25/0.46  % (9939)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)
% 0.25/0.48  % (9941)First to succeed.
% 0.25/0.48  % (9942)Also succeeded, but the first one will report.
% 0.25/0.48  % (9941)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-9935"
% 0.25/0.48  % (9935)Running in auto input_syntax mode. Trying TPTP
% 0.25/0.48  % (9941)Refutation found. Thanks to Tanya!
% 0.25/0.48  % SZS status Theorem for theBenchmark
% 0.25/0.48  % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.48  % (9941)------------------------------
% 0.25/0.48  % (9941)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.25/0.48  % (9941)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.25/0.48  % (9941)Termination reason: Refutation
% 0.25/0.48  
% 0.25/0.48  % (9941)Memory used [KB]: 1436
% 0.25/0.48  % (9941)Time elapsed: 0.019 s
% 0.25/0.48  % (9941)Instructions burned: 29 (million)
% 0.25/0.48  % (9941)------------------------------
% 0.25/0.48  % (9941)------------------------------
% 0.25/0.48  % (9935)Success in time 0.077 s
%------------------------------------------------------------------------------