TSTP Solution File: SWW360+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% 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 : n004.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 12:44:47 EDT 2023

% Result   : Theorem 16.88s 3.03s
% Output   : CNFRefutation 17.81s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   29 (  13 unt;   0 def)
%            Number of atoms       :   45 (   8 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   29 (  13   ~;   9   |;   2   &)
%                                         (   0 <=>;   5  =>;   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    :   13 (  13 usr;   6 con; 0-3 aty)
%            Number of variables   :   67 (;  66   !;   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(f15,axiom,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f25,axiom,
    ! [V_a_2,V_D_2,V_C_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_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_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_D_2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f36,axiom,
    ! [V_A_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_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(f5263,plain,
    ! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),X1)),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f5292,plain,
    ! [V_a_2,V_D_2,V_C_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_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_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_D_2))) ),
    inference(pre_NNF_transformation,[status(esa)],[f25]) ).

fof(f5293,plain,
    ! [V_D_2,V_C_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))
      | ! [V_a_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_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_D_2))) ),
    inference(miniscoping,[status(esa)],[f5292]) ).

fof(f5294,plain,
    ! [X0,X1,X2,X3] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X1),X2))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X1)),hAPP(hAPP(c_Set_Oinsert(X0),X3),X2))) ),
    inference(cnf_transformation,[status(esa)],[f5293]) ).

fof(f5325,plain,
    ! [X0,X1,X2] : hAPP(hAPP(c_Set_Oinsert(X0),X1),hAPP(hAPP(c_Set_Oinsert(X0),X1),X2)) = hAPP(hAPP(c_Set_Oinsert(X0),X1),X2),
    inference(cnf_transformation,[status(esa)],[f36]) ).

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(f20583,plain,
    hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),sk0_569),v_U) = v_U,
    inference(resolution,[status(thm)],[f5638,f20153]) ).

fof(f21880,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),X0),X1))
      | v_P(hAPP(hAPP(c_Set_Oinsert(t_a),X2),X1),hAPP(hAPP(c_Set_Oinsert(t_a),X2),X0)) ),
    inference(resolution,[status(thm)],[f5294,f5245]) ).

fof(f22383,plain,
    ! [X0,X1,X2] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),X0),hAPP(hAPP(c_Set_Oinsert(t_a),X1),X2)))
      | v_P(hAPP(hAPP(c_Set_Oinsert(t_a),X1),X2),hAPP(hAPP(c_Set_Oinsert(t_a),X1),X0)) ),
    inference(paramodulation,[status(thm)],[f5325,f21880]) ).

fof(f22391,plain,
    ! [X0,X1] : v_P(hAPP(hAPP(c_Set_Oinsert(t_a),X0),X1),hAPP(hAPP(c_Set_Oinsert(t_a),X0),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))),
    inference(resolution,[status(thm)],[f22383,f5263]) ).

fof(f22405,plain,
    ! [X0,X1,X2,X3] : v_P(hAPP(c_Set_Oimage(X0,t_a,X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),X3)),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(X1,X2)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))),
    inference(paramodulation,[status(thm)],[f5243,f22391]) ).

fof(f22415,plain,
    ! [X0] : v_P(hAPP(c_Set_Oimage(tc_Com_Opname,t_a,X0),v_U),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(X0,sk0_569)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))),
    inference(paramodulation,[status(thm)],[f20583,f22405]) ).

fof(f22439,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f20154,f22415]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10  % Problem  : SWW360+1 : TPTP v8.1.2. Released v5.2.0.
% 0.03/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31  % Computer : n004.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Tue May 30 10:50:07 EDT 2023
% 0.10/0.31  % CPUTime  : 
% 0.65/0.86  % Drodi V3.5.1
% 16.88/3.03  % Refutation found
% 16.88/3.03  % SZS status Theorem for theBenchmark: Theorem is valid
% 16.88/3.03  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 18.05/3.18  % Elapsed time: 2.850007 seconds
% 18.05/3.18  % CPU time: 17.684438 seconds
% 18.05/3.18  % Memory used: 709.035 MB
%------------------------------------------------------------------------------