TSTP Solution File: SWW299+1 by Vampire---4.9

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%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : SWW299+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% Computer : n020.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 18:31:56 EDT 2024

% Result   : Theorem 0.49s 0.77s
% Output   : Refutation 0.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   30 (   6 unt;   0 def)
%            Number of atoms       :   99 (   0 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  113 (  44   ~;  33   |;  17   &)
%                                         (   1 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    6 (   5 usr;   2 prp; 0-3 aty)
%            Number of functors    :   16 (  16 usr;   8 con; 0-4 aty)
%            Number of variables   :   78 (  62   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f5579,plain,
    $false,
    inference(avatar_sat_refutation,[],[f5571,f5578]) ).

fof(f5578,plain,
    ~ spl15_1,
    inference(avatar_contradiction_clause,[],[f5577]) ).

fof(f5577,plain,
    ( $false
    | ~ spl15_1 ),
    inference(subsumption_resolution,[],[f5576,f5395]) ).

fof(f5395,plain,
    v_P(sK1,sK2),
    inference(cnf_transformation,[],[f5350]) ).

fof(f5350,plain,
    ( ! [X2,X3] :
        ( ( ~ v_Q(sK1,sK3(X2,X3))
          & ! [X5] :
              ( hBOOL(hAPP(hAPP(X3,X5),sK3(X2,X3)))
              | ~ hBOOL(hAPP(hAPP(X2,X5),sK2)) ) )
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,X2,v_c,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) )
    & v_P(sK1,sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f5298,f5349,f5348]) ).

fof(f5348,plain,
    ( ? [X0,X1] :
        ( ! [X2,X3] :
            ( ? [X4] :
                ( ~ v_Q(X0,X4)
                & ! [X5] :
                    ( hBOOL(hAPP(hAPP(X3,X5),X4))
                    | ~ hBOOL(hAPP(hAPP(X2,X5),X1)) ) )
            | ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,X2,v_c,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) )
        & v_P(X0,X1) )
   => ( ! [X3,X2] :
          ( ? [X4] :
              ( ~ v_Q(sK1,X4)
              & ! [X5] :
                  ( hBOOL(hAPP(hAPP(X3,X5),X4))
                  | ~ hBOOL(hAPP(hAPP(X2,X5),sK2)) ) )
          | ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,X2,v_c,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) )
      & v_P(sK1,sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f5349,plain,
    ! [X2,X3] :
      ( ? [X4] :
          ( ~ v_Q(sK1,X4)
          & ! [X5] :
              ( hBOOL(hAPP(hAPP(X3,X5),X4))
              | ~ hBOOL(hAPP(hAPP(X2,X5),sK2)) ) )
     => ( ~ v_Q(sK1,sK3(X2,X3))
        & ! [X5] :
            ( hBOOL(hAPP(hAPP(X3,X5),sK3(X2,X3)))
            | ~ hBOOL(hAPP(hAPP(X2,X5),sK2)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f5298,plain,
    ? [X0,X1] :
      ( ! [X2,X3] :
          ( ? [X4] :
              ( ~ v_Q(X0,X4)
              & ! [X5] :
                  ( hBOOL(hAPP(hAPP(X3,X5),X4))
                  | ~ hBOOL(hAPP(hAPP(X2,X5),X1)) ) )
          | ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,X2,v_c,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) )
      & v_P(X0,X1) ),
    inference(ennf_transformation,[],[f5226]) ).

fof(f5226,plain,
    ~ ! [X0,X1] :
        ( v_P(X0,X1)
       => ? [X2,X3] :
            ( ! [X4] :
                ( ! [X5] :
                    ( hBOOL(hAPP(hAPP(X2,X5),X1))
                   => hBOOL(hAPP(hAPP(X3,X5),X4)) )
               => v_Q(X0,X4) )
            & c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,X2,v_c,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ) ),
    inference(rectify,[],[f5225]) ).

fof(f5225,negated_conjecture,
    ~ ! [X299,X300] :
        ( v_P(X299,X300)
       => ? [X303,X304] :
            ( ! [X301] :
                ( ! [X302] :
                    ( hBOOL(hAPP(hAPP(X303,X302),X300))
                   => hBOOL(hAPP(hAPP(X304,X302),X301)) )
               => v_Q(X299,X301) )
            & c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,X303,v_c,X304)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ) ),
    inference(negated_conjecture,[],[f5224]) ).

fof(f5224,conjecture,
    ! [X299,X300] :
      ( v_P(X299,X300)
     => ? [X303,X304] :
          ( ! [X301] :
              ( ! [X302] :
                  ( hBOOL(hAPP(hAPP(X303,X302),X300))
                 => hBOOL(hAPP(hAPP(X304,X302),X301)) )
             => v_Q(X299,X301) )
          & c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,X303,v_c,X304)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f5576,plain,
    ( ~ v_P(sK1,sK2)
    | ~ spl15_1 ),
    inference(resolution,[],[f5570,f5554]) ).

fof(f5554,plain,
    ~ v_Q(sK1,sK3(v_P_H,v_Q_H)),
    inference(resolution,[],[f5397,f5398]) ).

fof(f5398,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P_H,v_c,v_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
    inference(cnf_transformation,[],[f5222]) ).

fof(f5222,axiom,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P_H,v_c,v_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f5397,plain,
    ! [X2,X3] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,X2,v_c,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
      | ~ v_Q(sK1,sK3(X2,X3)) ),
    inference(cnf_transformation,[],[f5350]) ).

fof(f5570,plain,
    ( ! [X1] :
        ( v_Q(X1,sK3(v_P_H,v_Q_H))
        | ~ v_P(X1,sK2) )
    | ~ spl15_1 ),
    inference(avatar_component_clause,[],[f5569]) ).

fof(f5569,plain,
    ( spl15_1
  <=> ! [X1] :
        ( v_Q(X1,sK3(v_P_H,v_Q_H))
        | ~ v_P(X1,sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_1])]) ).

fof(f5571,plain,
    ( spl15_1
    | spl15_1 ),
    inference(avatar_split_clause,[],[f5567,f5569,f5569]) ).

fof(f5567,plain,
    ! [X0,X1] :
      ( v_Q(X0,sK3(v_P_H,v_Q_H))
      | ~ v_P(X0,sK2)
      | v_Q(X1,sK3(v_P_H,v_Q_H))
      | ~ v_P(X1,sK2) ),
    inference(resolution,[],[f5562,f5399]) ).

fof(f5399,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP(hAPP(v_P_H,sK4(X1,X2)),X1))
      | v_Q(X0,X2)
      | ~ v_P(X0,X1) ),
    inference(cnf_transformation,[],[f5352]) ).

fof(f5352,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( v_Q(X0,X2)
          | ( ~ hBOOL(hAPP(hAPP(v_Q_H,sK4(X1,X2)),X2))
            & hBOOL(hAPP(hAPP(v_P_H,sK4(X1,X2)),X1)) ) )
      | ~ v_P(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f5299,f5351]) ).

fof(f5351,plain,
    ! [X1,X2] :
      ( ? [X3] :
          ( ~ hBOOL(hAPP(hAPP(v_Q_H,X3),X2))
          & hBOOL(hAPP(hAPP(v_P_H,X3),X1)) )
     => ( ~ hBOOL(hAPP(hAPP(v_Q_H,sK4(X1,X2)),X2))
        & hBOOL(hAPP(hAPP(v_P_H,sK4(X1,X2)),X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f5299,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( v_Q(X0,X2)
          | ? [X3] :
              ( ~ hBOOL(hAPP(hAPP(v_Q_H,X3),X2))
              & hBOOL(hAPP(hAPP(v_P_H,X3),X1)) ) )
      | ~ v_P(X0,X1) ),
    inference(ennf_transformation,[],[f5227]) ).

fof(f5227,plain,
    ! [X0,X1] :
      ( v_P(X0,X1)
     => ! [X2] :
          ( ! [X3] :
              ( hBOOL(hAPP(hAPP(v_P_H,X3),X1))
             => hBOOL(hAPP(hAPP(v_Q_H,X3),X2)) )
         => v_Q(X0,X2) ) ),
    inference(rectify,[],[f5223]) ).

fof(f5223,axiom,
    ! [X299,X300] :
      ( v_P(X299,X300)
     => ! [X301] :
          ( ! [X302] :
              ( hBOOL(hAPP(hAPP(v_P_H,X302),X300))
             => hBOOL(hAPP(hAPP(v_Q_H,X302),X301)) )
         => v_Q(X299,X301) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f5562,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP(hAPP(v_P_H,sK4(X0,sK3(v_P_H,v_Q_H))),sK2))
      | v_Q(X1,sK3(v_P_H,v_Q_H))
      | ~ v_P(X1,X0) ),
    inference(resolution,[],[f5558,f5400]) ).

fof(f5400,plain,
    ! [X2,X0,X1] :
      ( ~ hBOOL(hAPP(hAPP(v_Q_H,sK4(X1,X2)),X2))
      | v_Q(X0,X2)
      | ~ v_P(X0,X1) ),
    inference(cnf_transformation,[],[f5352]) ).

fof(f5558,plain,
    ! [X0] :
      ( hBOOL(hAPP(hAPP(v_Q_H,X0),sK3(v_P_H,v_Q_H)))
      | ~ hBOOL(hAPP(hAPP(v_P_H,X0),sK2)) ),
    inference(resolution,[],[f5396,f5398]) ).

fof(f5396,plain,
    ! [X2,X3,X5] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,X2,v_c,X3)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(X2,X5),sK2))
      | hBOOL(hAPP(hAPP(X3,X5),sK3(X2,X3))) ),
    inference(cnf_transformation,[],[f5350]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SWW299+1 : TPTP v8.2.0. Released v5.2.0.
% 0.03/0.12  % Command    : run_vampire %s %d THM
% 0.12/0.33  % Computer : n020.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Wed Jun 19 05:50:54 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.20/0.35  This is a FOF_CAX_RFO_SEQ problem
% 0.20/0.35  Running first-order theorem proving
% 0.20/0.35  Running /export/starexec/sandbox/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.49/0.72  % (17361)Running in auto input_syntax mode. Trying TPTP
% 0.49/0.72  % (17362)lrs+10_1:628_anc=all_dependent:bsr=unit_only:sil=256000:sp=frequency:i=136310:newcnf=on_0 on theBenchmark for (2999ds/136310Mi)
% 0.49/0.72  % (17361)Running in auto input_syntax mode. Trying TPTP
% 0.49/0.72  % (17364)lrs+11_1:12_to=lpo:sil=128000:sp=const_min:i=103397:ss=included:sgt=16:av=off:fsd=on:nm=16_0 on theBenchmark for (2999ds/103397Mi)
% 0.49/0.72  % (17361)Running in auto input_syntax mode. Trying TPTP
% 0.49/0.72  % (17365)dis+2_1:50_sil=256000:flr=on:sac=on:i=218245:fsr=off:uhcvi=on_0 on theBenchmark for (2999ds/218245Mi)
% 0.49/0.72  % (17361)Running in auto input_syntax mode. Trying TPTP
% 0.49/0.72  % (17366)lrs-1010_1:1_sil=2000:i=250:sd=1:ss=axioms:sgt=32:sos=on_0 on theBenchmark for (2999ds/250Mi)
% 0.49/0.72  % (17361)Running in auto input_syntax mode. Trying TPTP
% 0.49/0.72  % (17367)lrs-1011_8:1_sil=16000:sos=all:i=346:sd=1:ep=R:ss=axioms_0 on theBenchmark for (2999ds/346Mi)
% 0.49/0.72  % (17361)Running in auto input_syntax mode. Trying TPTP
% 0.49/0.72  % (17368)lrs+1002_1:1_to=lpo:sil=2000:sp=frequency:sos=on:st=3.0:i=282:sd=2:ss=axioms_0 on theBenchmark for (2999ds/282Mi)
% 0.49/0.72  % (17361)Running in auto input_syntax mode. Trying TPTP
% 0.49/0.72  % (17363)lrs+2_3:1_to=lpo:sil=256000:irw=on:fde=unused:sp=unary_first:bce=on:nwc=6.0:s2agt=30:newcnf=on:s2a=on:i=140573:nm=2_0 on theBenchmark for (2999ds/140573Mi)
% 0.49/0.76  % (17366)First to succeed.
% 0.49/0.76  % (17366)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-17361"
% 0.49/0.77  % (17361)Running in auto input_syntax mode. Trying TPTP
% 0.49/0.77  % (17366)Refutation found. Thanks to Tanya!
% 0.49/0.77  % SZS status Theorem for theBenchmark
% 0.49/0.77  % SZS output start Proof for theBenchmark
% See solution above
% 0.49/0.77  % (17366)------------------------------
% 0.49/0.77  % (17366)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.49/0.77  % (17366)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.49/0.77  % (17366)Termination reason: Refutation
% 0.49/0.77  
% 0.49/0.77  % (17366)Memory used [KB]: 6287
% 0.49/0.77  % (17366)Time elapsed: 0.047 s
% 0.49/0.77  % (17366)Instructions burned: 65 (million)
% 0.49/0.77  % (17366)------------------------------
% 0.49/0.77  % (17366)------------------------------
% 0.49/0.77  % (17361)Success in time 0.123 s
%------------------------------------------------------------------------------