TSTP Solution File: SWW306+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWW306+1 : TPTP v8.1.2. Released v5.2.0.
% 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 : n018.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 : Fri Sep  1 01:00:49 EDT 2023

% Result   : Theorem 8.31s 2.38s
% Output   : Refutation 8.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   44 (  18 unt;   0 def)
%            Number of atoms       :  100 (  15 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :   98 (  42   ~;  30   |;  13   &)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :   19 (  19 usr;   8 con; 0-4 aty)
%            Number of variables   :  120 (; 106   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f24392,plain,
    $false,
    inference(subsumption_resolution,[],[f24391,f24377]) ).

fof(f24377,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(t_a,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK1)),v_c,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(sK0))))),
    inference(resolution,[],[f24368,f16539]) ).

fof(f16539,plain,
    v_P(sK0,sK1),
    inference(cnf_transformation,[],[f14392]) ).

fof(f14392,plain,
    ( ! [X2,X3] :
        ( ( ~ hBOOL(hAPP(v_Q(sK0),sK2(X2,X3)))
          & ! [X5] :
              ( hBOOL(hAPP(hAPP(X3,X5),sK2(X2,X3)))
              | ~ hBOOL(hAPP(hAPP(X2,X5),sK1)) ) )
        | ~ 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(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f10315,f14391,f14390]) ).

fof(f14390,plain,
    ( ? [X0,X1] :
        ( ! [X2,X3] :
            ( ? [X4] :
                ( ~ hBOOL(hAPP(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] :
              ( ~ hBOOL(hAPP(v_Q(sK0),X4))
              & ! [X5] :
                  ( hBOOL(hAPP(hAPP(X3,X5),X4))
                  | ~ hBOOL(hAPP(hAPP(X2,X5),sK1)) ) )
          | ~ 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(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f14391,plain,
    ! [X2,X3] :
      ( ? [X4] :
          ( ~ hBOOL(hAPP(v_Q(sK0),X4))
          & ! [X5] :
              ( hBOOL(hAPP(hAPP(X3,X5),X4))
              | ~ hBOOL(hAPP(hAPP(X2,X5),sK1)) ) )
     => ( ~ hBOOL(hAPP(v_Q(sK0),sK2(X2,X3)))
        & ! [X5] :
            ( hBOOL(hAPP(hAPP(X3,X5),sK2(X2,X3)))
            | ~ hBOOL(hAPP(hAPP(X2,X5),sK1)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f10315,plain,
    ? [X0,X1] :
      ( ! [X2,X3] :
          ( ? [X4] :
              ( ~ hBOOL(hAPP(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,[],[f5232]) ).

fof(f5232,plain,
    ~ ! [X0,X1] :
        ( v_P(X0,X1)
       => ? [X2,X3] :
            ( ! [X4] :
                ( ! [X5] :
                    ( hBOOL(hAPP(hAPP(X2,X5),X1))
                   => hBOOL(hAPP(hAPP(X3,X5),X4)) )
               => hBOOL(hAPP(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,[],[f5231]) ).

fof(f5231,negated_conjecture,
    ~ ! [X27,X28] :
        ( v_P(X27,X28)
       => ? [X311,X312] :
            ( ! [X32] :
                ( ! [X33] :
                    ( hBOOL(hAPP(hAPP(X311,X33),X28))
                   => hBOOL(hAPP(hAPP(X312,X33),X32)) )
               => hBOOL(hAPP(v_Q(X27),X32)) )
            & 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,X311,v_c,X312)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ) ),
    inference(negated_conjecture,[],[f5230]) ).

fof(f5230,conjecture,
    ! [X27,X28] :
      ( v_P(X27,X28)
     => ? [X311,X312] :
          ( ! [X32] :
              ( ! [X33] :
                  ( hBOOL(hAPP(hAPP(X311,X33),X28))
                 => hBOOL(hAPP(hAPP(X312,X33),X32)) )
             => hBOOL(hAPP(v_Q(X27),X32)) )
          & 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,X311,v_c,X312)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox/tmp/tmp.OFGxk04q8m/Vampire---4.8_26193',conj_1) ).

fof(f24368,plain,
    ! [X0,X1] :
      ( ~ v_P(X0,X1)
      | c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(t_a,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),X1)),v_c,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(X0))))) ),
    inference(forward_demodulation,[],[f24367,f17415]) ).

fof(f17415,plain,
    ! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0,
    inference(cnf_transformation,[],[f5701]) ).

fof(f5701,plain,
    ! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0,
    inference(rectify,[],[f38]) ).

fof(f38,axiom,
    ! [X22,X4] : hAPP(c_Set_OCollect(X4),X22) = X22,
    file('/export/starexec/sandbox/tmp/tmp.OFGxk04q8m/Vampire---4.8_26193',fact_Collect__def) ).

fof(f24367,plain,
    ! [X0,X1] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(c_Set_OCollect(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(t_a,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),X1)),v_c,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(X0))))))
      | ~ v_P(X0,X1) ),
    inference(forward_demodulation,[],[f16542,f17616]) ).

fof(f17616,plain,
    ! [X0,X1] : hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X1),hAPP(c_fequal,X0)),
    inference(cnf_transformation,[],[f5902]) ).

fof(f5902,plain,
    ! [X0,X1] : hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X1),hAPP(c_fequal,X0)),
    inference(rectify,[],[f31]) ).

fof(f31,axiom,
    ! [X5,X4] : hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X4),hAPP(c_fequal,X5)),
    file('/export/starexec/sandbox/tmp/tmp.OFGxk04q8m/Vampire---4.8_26193',fact_singleton__conv2) ).

fof(f16542,plain,
    ! [X0,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,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),X1)),v_c,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(X0)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
      | ~ v_P(X0,X1) ),
    inference(cnf_transformation,[],[f10316]) ).

fof(f10316,plain,
    ! [X0,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,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),X1)),v_c,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(X0)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
      | ~ v_P(X0,X1) ),
    inference(ennf_transformation,[],[f5233]) ).

fof(f5233,plain,
    ! [X0,X1] :
      ( v_P(X0,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,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),X1)),v_c,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(X0)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ),
    inference(rectify,[],[f5229]) ).

fof(f5229,axiom,
    ! [X27,X28] :
      ( v_P(X27,X28)
     => 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,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),X28)),v_c,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(X27)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox/tmp/tmp.OFGxk04q8m/Vampire---4.8_26193',conj_0) ).

fof(f24391,plain,
    ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(t_a,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK1)),v_c,hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(sK0))))),
    inference(resolution,[],[f24384,f24364]) ).

fof(f24364,plain,
    ! [X2,X3] :
      ( ~ hBOOL(hAPP(v_Q(sK0),sK2(X2,X3)))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(t_a,X2,v_c,X3))) ),
    inference(forward_demodulation,[],[f24363,f17415]) ).

fof(f24363,plain,
    ! [X2,X3] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(c_Set_OCollect(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(t_a,X2,v_c,X3))))
      | ~ hBOOL(hAPP(v_Q(sK0),sK2(X2,X3))) ),
    inference(forward_demodulation,[],[f16541,f17616]) ).

fof(f16541,plain,
    ! [X2,X3] :
      ( ~ hBOOL(hAPP(v_Q(sK0),sK2(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)))) ),
    inference(cnf_transformation,[],[f14392]) ).

fof(f24384,plain,
    hBOOL(hAPP(v_Q(sK0),sK2(hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK1)),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(sK0))))),
    inference(subsumption_resolution,[],[f24383,f23731]) ).

fof(f23731,plain,
    ! [X1] : hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
    inference(equality_resolution,[],[f17911]) ).

fof(f17911,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(hAPP(c_fequal,X1),X0))
      | X0 != X1 ),
    inference(cnf_transformation,[],[f6138]) ).

fof(f6138,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(hAPP(c_fequal,X1),X0))
      | X0 != X1 ),
    inference(rectify,[],[f5215]) ).

fof(f5215,axiom,
    ! [X30,X15] :
      ( hBOOL(hAPP(hAPP(c_fequal,X15),X30))
      | X15 != X30 ),
    file('/export/starexec/sandbox/tmp/tmp.OFGxk04q8m/Vampire---4.8_26193',help_c__fequal__2) ).

fof(f24383,plain,
    ( ~ hBOOL(hAPP(hAPP(c_fequal,sK1),sK1))
    | hBOOL(hAPP(v_Q(sK0),sK2(hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK1)),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(sK0))))) ),
    inference(forward_demodulation,[],[f24382,f23198]) ).

fof(f23198,plain,
    ! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(X2,X0),X1) = hAPP(hAPP(hAPP(c_COMBC(X5,X4,X3),X2),X1),X0),
    inference(cnf_transformation,[],[f9754]) ).

fof(f9754,plain,
    ! [X0,X1,X2,X3,X4,X5] : hAPP(hAPP(X2,X0),X1) = hAPP(hAPP(hAPP(c_COMBC(X5,X4,X3),X2),X1),X0),
    inference(rectify,[],[f5212]) ).

fof(f5212,axiom,
    ! [X31,X25,X22,X4,X47,X16] : hAPP(hAPP(hAPP(c_COMBC(X16,X47,X4),X22),X25),X31) = hAPP(hAPP(X22,X31),X25),
    file('/export/starexec/sandbox/tmp/tmp.OFGxk04q8m/Vampire---4.8_26193',help_c__COMBC__1) ).

fof(f24382,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK1),sK1))
    | hBOOL(hAPP(v_Q(sK0),sK2(hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK1)),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(sK0))))) ),
    inference(forward_demodulation,[],[f24381,f21114]) ).

fof(f21114,plain,
    ! [X2,X3,X0,X1] : hAPP(hAPP(c_COMBK(X3,X2),X1),X0) = X1,
    inference(cnf_transformation,[],[f8247]) ).

fof(f8247,plain,
    ! [X0,X1,X2,X3] : hAPP(hAPP(c_COMBK(X3,X2),X1),X0) = X1,
    inference(rectify,[],[f5210]) ).

fof(f5210,axiom,
    ! [X310,X309,X4,X38] : hAPP(hAPP(c_COMBK(X38,X4),X309),X310) = X309,
    file('/export/starexec/sandbox/tmp/tmp.OFGxk04q8m/Vampire---4.8_26193',help_c__COMBK__1) ).

fof(f24381,plain,
    ! [X0] :
      ( hBOOL(hAPP(v_Q(sK0),sK2(hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK1)),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(sK0)))))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK1)),X0),sK1)) ),
    inference(forward_demodulation,[],[f24378,f21114]) ).

fof(f24378,plain,
    ! [X0] :
      ( hBOOL(hAPP(hAPP(hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(sK0)),X0),sK2(hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK1)),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),v_Q(sK0)))))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),t_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK1)),X0),sK1)) ),
    inference(resolution,[],[f24377,f24366]) ).

fof(f24366,plain,
    ! [X2,X3,X5] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(t_a,X2,v_c,X3)))
      | hBOOL(hAPP(hAPP(X3,X5),sK2(X2,X3)))
      | ~ hBOOL(hAPP(hAPP(X2,X5),sK1)) ),
    inference(forward_demodulation,[],[f24365,f17415]) ).

fof(f24365,plain,
    ! [X2,X3,X5] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(c_Set_OCollect(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(t_a,X2,v_c,X3))))
      | hBOOL(hAPP(hAPP(X3,X5),sK2(X2,X3)))
      | ~ hBOOL(hAPP(hAPP(X2,X5),sK1)) ),
    inference(forward_demodulation,[],[f16540,f17616]) ).

fof(f16540,plain,
    ! [X2,X3,X5] :
      ( hBOOL(hAPP(hAPP(X3,X5),sK2(X2,X3)))
      | ~ hBOOL(hAPP(hAPP(X2,X5),sK1))
      | ~ 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(cnf_transformation,[],[f14392]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.63/0.88  % Problem    : SWW306+1 : TPTP v8.1.2. Released v5.2.0.
% 0.63/0.89  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.90/1.11  % Computer : n018.cluster.edu
% 0.90/1.11  % Model    : x86_64 x86_64
% 0.90/1.11  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.90/1.11  % Memory   : 8042.1875MB
% 0.90/1.11  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.90/1.11  % CPULimit   : 300
% 0.90/1.11  % WCLimit    : 300
% 0.90/1.11  % DateTime   : Sun Aug 27 19:55:47 EDT 2023
% 0.90/1.11  % CPUTime    : 
% 0.90/1.11  This is a FOF_CAX_RFO_SEQ problem
% 0.90/1.11  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.OFGxk04q8m/Vampire---4.8_26193
% 0.90/1.11  % (26336)Running in auto input_syntax mode. Trying TPTP
% 0.97/1.37  % (26343)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_394 on Vampire---4 for (394ds/0Mi)
% 0.97/1.39  % (26339)ott-11_3:1_afr=on:anc=all_dependent:bd=preordered:bce=on:er=filter:fsd=off:fde=unused:nm=4:sos=all:sac=on:tgt=full:urr=on_476 on Vampire---4 for (476ds/0Mi)
% 0.97/1.39  % (26338)dis-1002_1_bd=off:fsd=off:fsr=off:fde=none:nwc=1.3:sims=off:sos=all_501 on Vampire---4 for (501ds/0Mi)
% 0.97/1.39  % (26342)dis+1011_2:1_add=off:afr=on:er=known:fde=unused:nwc=1.3:nicw=on:sas=z3:sims=off:sos=on:sac=on:tgt=full_398 on Vampire---4 for (398ds/0Mi)
% 0.97/1.40  % (26340)ott+1010_3_aac=none:bs=unit_only:bce=on:ep=R:er=filter:fsd=off:fde=none:gsp=on:irw=on:lcm=predicate:nwc=10.0:sos=all:sp=occurrence_449 on Vampire---4 for (449ds/0Mi)
% 0.97/1.40  % (26337)dis+1011_3_av=off:bd=off:er=known:fsd=off:fde=unused:irw=on:nm=64:nwc=1.3:sos=on:sp=reverse_arity_577 on Vampire---4 for (577ds/0Mi)
% 0.97/1.40  % (26341)dis+3_3:2_aac=none:fsd=off:fde=none:lcm=reverse:nm=32:nicw=on:sos=on:sac=on:sp=occurrence_419 on Vampire---4 for (419ds/0Mi)
% 8.31/2.38  % (26337)First to succeed.
% 8.31/2.38  % (26337)Refutation found. Thanks to Tanya!
% 8.31/2.38  % SZS status Theorem for Vampire---4
% 8.31/2.38  % SZS output start Proof for Vampire---4
% See solution above
% 8.47/2.39  % (26337)------------------------------
% 8.47/2.39  % (26337)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 8.47/2.39  % (26337)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 8.47/2.39  % (26337)Termination reason: Refutation
% 8.47/2.39  
% 8.47/2.39  % (26337)Memory used [KB]: 24562
% 8.47/2.39  % (26337)Time elapsed: 0.985 s
% 8.47/2.39  % (26337)------------------------------
% 8.47/2.39  % (26337)------------------------------
% 8.47/2.39  % (26336)Success in time 1.265 s
% 8.47/2.39  % Vampire---4.8 exiting
%------------------------------------------------------------------------------