TSTP Solution File: SWW360+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SWW360+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n010.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 : Tue Apr 30 20:50:07 EDT 2024

% Result   : Theorem 28.30s 4.17s
% Output   : CNFRefutation 28.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   37 (  17 unt;   0 def)
%            Number of atoms       :   65 (  22 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   54 (  26   ~;  16   |;   6   &)
%                                         (   2 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   6 con; 0-3 aty)
%            Number of variables   :   77 (  76   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f6,axiom,
    ! [V_B_2,V_a_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [V_G_2,V_ts_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),V_ts_2),V_G_2))
     => v_P(V_G_2,V_ts_2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f106,axiom,
    ! [V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
    <=> hBOOL(hAPP(V_A_2,V_x_2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f118,axiom,
    ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f121,axiom,
    ! [V_C_2,V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f125,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
    <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f135,axiom,
    ! [V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5226,conjecture,
    ! [B_x] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_U))
     => v_P(hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,B_x)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5227,negated_conjecture,
    ~ ! [B_x] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_U))
       => v_P(hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,B_x)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))) ),
    inference(negated_conjecture,[status(cth)],[f5226]) ).

fof(f5243,plain,
    ! [X0,X1,X2,X3,X4] : hAPP(c_Set_Oimage(X0,X1,X2),hAPP(hAPP(c_Set_Oinsert(X0),X3),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X0,X1,X2),X4)),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f5244,plain,
    ! [V_G_2,V_ts_2] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),V_ts_2),V_G_2))
      | v_P(V_G_2,V_ts_2) ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f5245,plain,
    ! [X0,X1] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),X0),X1))
      | v_P(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f5244]) ).

fof(f5562,plain,
    ! [V_A_2,V_x_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
        | hBOOL(hAPP(V_A_2,V_x_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
        | ~ hBOOL(hAPP(V_A_2,V_x_2)) ) ),
    inference(NNF_transformation,[status(esa)],[f106]) ).

fof(f5563,plain,
    ( ! [V_A_2,V_x_2] :
        ( ! [T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
        | hBOOL(hAPP(V_A_2,V_x_2)) )
    & ! [V_A_2,V_x_2] :
        ( ! [T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
        | ~ hBOOL(hAPP(V_A_2,V_x_2)) ) ),
    inference(miniscoping,[status(esa)],[f5562]) ).

fof(f5564,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X0),X1),X2))
      | hBOOL(hAPP(X2,X1)) ),
    inference(cnf_transformation,[status(esa)],[f5563]) ).

fof(f5565,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(hAPP(c_member(X0),X1),X2))
      | ~ hBOOL(hAPP(X2,X1)) ),
    inference(cnf_transformation,[status(esa)],[f5563]) ).

fof(f5595,plain,
    ! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),X1) = X1,
    inference(cnf_transformation,[status(esa)],[f118]) ).

fof(f5604,plain,
    ! [X0,X1,X2,X3] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)),X3) = hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X2),X3)),
    inference(cnf_transformation,[status(esa)],[f121]) ).

fof(f5608,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != V_B_2 ) ),
    inference(NNF_transformation,[status(esa)],[f125]) ).

fof(f5609,plain,
    ( ! [V_B_2,V_A_2,T_b] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 )
    & ! [V_B_2,V_A_2,T_b] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != V_B_2 ) ),
    inference(miniscoping,[status(esa)],[f5608]) ).

fof(f5611,plain,
    ! [X0,X1,X2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X1),X2))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X1),X2) != X2 ),
    inference(cnf_transformation,[status(esa)],[f5609]) ).

fof(f5637,plain,
    ! [V_A_2,V_a_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ),
    inference(pre_NNF_transformation,[status(esa)],[f135]) ).

fof(f5638,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X0),X1),X2))
      | hAPP(hAPP(c_Set_Oinsert(X0),X1),X2) = X2 ),
    inference(cnf_transformation,[status(esa)],[f5637]) ).

fof(f20151,plain,
    ? [B_x] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_U))
      & ~ v_P(hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,B_x)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))) ),
    inference(pre_NNF_transformation,[status(esa)],[f5227]) ).

fof(f20152,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),sk0_569),v_U))
    & ~ v_P(hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,sk0_569)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))) ),
    inference(skolemization,[status(esa)],[f20151]) ).

fof(f20153,plain,
    hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),sk0_569),v_U)),
    inference(cnf_transformation,[status(esa)],[f20152]) ).

fof(f20154,plain,
    ~ v_P(hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,sk0_569)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))),
    inference(cnf_transformation,[status(esa)],[f20152]) ).

fof(f20938,plain,
    hBOOL(hAPP(v_U,sk0_569)),
    inference(resolution,[status(thm)],[f5564,f20153]) ).

fof(f20959,plain,
    ! [X0,X1,X2] :
      ( hAPP(hAPP(c_Set_Oinsert(X0),X1),X2) = X2
      | ~ hBOOL(hAPP(X2,X1)) ),
    inference(resolution,[status(thm)],[f5638,f5565]) ).

fof(f21490,plain,
    ! [X0] : hAPP(hAPP(c_Set_Oinsert(X0),sk0_569),v_U) = v_U,
    inference(resolution,[status(thm)],[f20959,f20938]) ).

fof(f32093,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,sk0_569)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
    inference(resolution,[status(thm)],[f20154,f5245]) ).

fof(f32669,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(t_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,sk0_569)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)) != hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),
    inference(resolution,[status(thm)],[f32093,f5611]) ).

fof(f32670,plain,
    hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,sk0_569)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(t_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool))),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) != hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),
    inference(forward_demodulation,[status(thm)],[f5604,f32669]) ).

fof(f32671,plain,
    hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,sk0_569)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)) != hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),
    inference(forward_demodulation,[status(thm)],[f5595,f32670]) ).

fof(f32672,plain,
    hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),sk0_569),v_U)) != hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),
    inference(forward_demodulation,[status(thm)],[f5243,f32671]) ).

fof(f32673,plain,
    hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U) != hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),
    inference(forward_demodulation,[status(thm)],[f21490,f32672]) ).

fof(f32674,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f32673]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem  : SWW360+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.07  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.26  % Computer : n010.cluster.edu
% 0.07/0.26  % Model    : x86_64 x86_64
% 0.07/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26  % Memory   : 8042.1875MB
% 0.07/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26  % CPULimit : 300
% 0.07/0.26  % WCLimit  : 300
% 0.07/0.26  % DateTime : Mon Apr 29 22:53:05 EDT 2024
% 0.07/0.26  % CPUTime  : 
% 0.37/0.60  % Drodi V3.6.0
% 28.30/4.17  % Refutation found
% 28.30/4.17  % SZS status Theorem for theBenchmark: Theorem is valid
% 28.30/4.17  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 29.37/4.36  % Elapsed time: 4.085459 seconds
% 29.37/4.36  % CPU time: 29.323278 seconds
% 29.37/4.36  % Total memory used: 1.106 GB
% 29.37/4.36  % Net memory used: 1.099 GB
%------------------------------------------------------------------------------