TSTP Solution File: SWW368+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SWW368+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n003.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 : Wed May 31 12:44:49 EDT 2023

% Result   : Theorem 3.61s 1.22s
% Output   : CNFRefutation 3.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   34 (  16 unt;   0 def)
%            Number of atoms       :   64 (   9 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   52 (  22   ~;  18   |;   6   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   3 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   7 con; 0-3 aty)
%            Number of variables   :   61 (;  61   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f10,axiom,
    ! [V_b_2,V_B_2,V_a_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
       => V_a_2 = V_b_2 )
     => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f32,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(f49,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(f53,axiom,
    ! [V_B_2,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2))
    <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_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)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5225,hypothesis,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5228,hypothesis,
    hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),v_U)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5230,conjecture,
    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,v_pn)),v_G)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5231,negated_conjecture,
    ~ 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,v_pn)),v_G)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
    inference(negated_conjecture,[status(cth)],[f5230]) ).

fof(f5258,plain,
    ! [V_b_2,V_B_2,V_a_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
        & V_a_2 != V_b_2 )
      | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ),
    inference(pre_NNF_transformation,[status(esa)],[f10]) ).

fof(f5260,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != X1
      | hBOOL(hAPP(hAPP(c_member(X2),X0),hAPP(hAPP(c_Set_Oinsert(X2),X1),X3))) ),
    inference(cnf_transformation,[status(esa)],[f5258]) ).

fof(f5328,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)],[f32]) ).

fof(f5329,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)],[f5328]) ).

fof(f5381,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)],[f49]) ).

fof(f5396,plain,
    ! [V_B_2,V_A_2,V_x_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2))
        | ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_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)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_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)) ) ),
    inference(NNF_transformation,[status(esa)],[f53]) ).

fof(f5397,plain,
    ( ! [V_B_2,V_A_2,V_x_2,T_b] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2))
        | ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_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)) ) )
    & ! [V_B_2,V_A_2,V_x_2,T_b] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_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)) ) ),
    inference(miniscoping,[status(esa)],[f5396]) ).

fof(f5400,plain,
    ! [X0,X1,X2,X3] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)),X3))
      | ~ hBOOL(hAPP(hAPP(c_member(X0),X1),X3))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X2),X3)) ),
    inference(cnf_transformation,[status(esa)],[f5397]) ).

fof(f20146,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
    inference(cnf_transformation,[status(esa)],[f5225]) ).

fof(f20149,plain,
    hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),v_U)),
    inference(cnf_transformation,[status(esa)],[f5228]) ).

fof(f20151,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,v_pn)),v_G)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
    inference(cnf_transformation,[status(esa)],[f5231]) ).

fof(f20431,plain,
    ! [X0,X1,X2] : hBOOL(hAPP(hAPP(c_member(X0),X1),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2))),
    inference(destructive_equality_resolution,[status(esa)],[f5260]) ).

fof(f20933,plain,
    hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),v_pn),v_U) = v_U,
    inference(resolution,[status(thm)],[f5329,f20149]) ).

fof(f21962,plain,
    ! [X0,X1,X2,X3,X4] : hBOOL(hAPP(hAPP(c_member(X0),hAPP(X1,X2)),hAPP(c_Set_Oimage(X3,X0,X1),hAPP(hAPP(c_Set_Oinsert(X3),X2),X4)))),
    inference(paramodulation,[status(thm)],[f5381,f20431]) ).

fof(f22553,plain,
    ! [X0,X1] : hBOOL(hAPP(hAPP(c_member(X0),hAPP(X1,v_pn)),hAPP(c_Set_Oimage(tc_Com_Opname,X0,X1),v_U))),
    inference(paramodulation,[status(thm)],[f20933,f21962]) ).

fof(f24417,plain,
    ( spl0_30
  <=> hBOOL(hAPP(hAPP(c_member(t_a),hAPP(v_mgt__call,v_pn)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) ),
    introduced(split_symbol_definition) ).

fof(f24419,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(t_a),hAPP(v_mgt__call,v_pn)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
    | spl0_30 ),
    inference(component_clause,[status(thm)],[f24417]) ).

fof(f24420,plain,
    ( spl0_31
  <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) ),
    introduced(split_symbol_definition) ).

fof(f24422,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
    | spl0_31 ),
    inference(component_clause,[status(thm)],[f24420]) ).

fof(f24423,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(t_a),hAPP(v_mgt__call,v_pn)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) ),
    inference(resolution,[status(thm)],[f5400,f20151]) ).

fof(f24424,plain,
    ( ~ spl0_30
    | ~ spl0_31 ),
    inference(split_clause,[status(thm)],[f24423,f24417,f24420]) ).

fof(f24438,plain,
    ( $false
    | spl0_30 ),
    inference(forward_subsumption_resolution,[status(thm)],[f24419,f22553]) ).

fof(f24439,plain,
    spl0_30,
    inference(contradiction_clause,[status(thm)],[f24438]) ).

fof(f24440,plain,
    ( $false
    | spl0_31 ),
    inference(forward_subsumption_resolution,[status(thm)],[f24422,f20146]) ).

fof(f24441,plain,
    spl0_31,
    inference(contradiction_clause,[status(thm)],[f24440]) ).

fof(f24442,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f24424,f24439,f24441]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWW368+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34  % Computer : n003.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Tue May 30 11:01:38 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.61/0.78  % Drodi V3.5.1
% 3.61/1.22  % Refutation found
% 3.61/1.22  % SZS status Theorem for theBenchmark: Theorem is valid
% 3.61/1.22  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.89/1.31  % Elapsed time: 0.951821 seconds
% 3.89/1.31  % CPU time: 4.032932 seconds
% 3.89/1.31  % Memory used: 617.191 MB
%------------------------------------------------------------------------------