TSTP Solution File: SWW225+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SWW225+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n008.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 12:44:31 EDT 2023

% Result   : Theorem 1.78s 0.66s
% Output   : CNFRefutation 1.78s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   40 (  15 unt;   0 def)
%            Number of atoms       :   76 (   8 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   65 (  29   ~;  26   |;   4   &)
%                                         (   4 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   3 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-3 aty)
%            Number of variables   :   36 (;  36   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f19,axiom,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
       => V_m = V_n ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f23,axiom,
    ! [V_m_2,V_n_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f69,axiom,
    ! [V_m_2,V_n_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f80,axiom,
    ! [V_w,V_z] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f81,axiom,
    ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f1269,conjecture,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f1270,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
    inference(negated_conjecture,[status(cth)],[f1269]) ).

fof(f1275,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f1279,plain,
    ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f1314,plain,
    ! [V_n,V_m] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
      | V_m = V_n ),
    inference(pre_NNF_transformation,[status(esa)],[f19]) ).

fof(f1315,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f1314]) ).

fof(f1322,plain,
    ! [V_m_2,V_n_2] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ) ),
    inference(NNF_transformation,[status(esa)],[f23]) ).

fof(f1323,plain,
    ( ! [V_m_2,V_n_2] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) )
    & ! [V_m_2,V_n_2] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ) ),
    inference(miniscoping,[status(esa)],[f1322]) ).

fof(f1324,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),c_Nat_OSuc(X1))
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f1323]) ).

fof(f1465,plain,
    ! [V_m_2,V_n_2] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ) ),
    inference(NNF_transformation,[status(esa)],[f69]) ).

fof(f1466,plain,
    ( ! [V_m_2,V_n_2] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) )
    & ! [V_m_2,V_n_2] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ) ),
    inference(miniscoping,[status(esa)],[f1465]) ).

fof(f1467,plain,
    ! [X0,X1] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1))
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f1466]) ).

fof(f1500,plain,
    ! [X0,X1] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f80]) ).

fof(f1501,plain,
    ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X0),
    inference(cnf_transformation,[status(esa)],[f81]) ).

fof(f4720,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
    inference(cnf_transformation,[status(esa)],[f1270]) ).

fof(f4890,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Nat_OSuc(v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
    inference(backward_demodulation,[status(thm)],[f1279,f4720]) ).

fof(f4905,plain,
    ( spl0_0
  <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) ),
    introduced(split_symbol_definition) ).

fof(f4907,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f4905]) ).

fof(f4908,plain,
    ( spl0_1
  <=> hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____) ),
    introduced(split_symbol_definition) ).

fof(f4909,plain,
    ( hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f4908]) ).

fof(f4911,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))
    | hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____) ),
    inference(resolution,[status(thm)],[f1315,f1275]) ).

fof(f4912,plain,
    ( ~ spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f4911,f4905,f4908]) ).

fof(f4931,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Nat_OSuc(v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
    | ~ spl0_1 ),
    inference(backward_demodulation,[status(thm)],[f4909,f4890]) ).

fof(f4932,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Nat_OSuc(v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Nat_OSuc(v_N2____))))
    | ~ spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f1279,f4931]) ).

fof(f4933,plain,
    ( $false
    | ~ spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f4932,f1501]) ).

fof(f4934,plain,
    ~ spl0_1,
    inference(contradiction_clause,[status(thm)],[f4933]) ).

fof(f5441,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))
    | spl0_0 ),
    inference(resolution,[status(thm)],[f4907,f1324]) ).

fof(f5442,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Nat_OSuc(v_N2____)))
    | spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f1279,f5441]) ).

fof(f5460,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Nat_OSuc(v_N2____)))),
    inference(resolution,[status(thm)],[f4890,f1500]) ).

fof(f7254,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Nat_OSuc(v_N2____))),
    inference(resolution,[status(thm)],[f5460,f1467]) ).

fof(f7255,plain,
    ( $false
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f7254,f5442]) ).

fof(f7256,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f7255]) ).

fof(f7257,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f4912,f4934,f7256]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWW225+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 : n008.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 10:57:23 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.43  % Drodi V3.5.1
% 1.78/0.66  % Refutation found
% 1.78/0.66  % SZS status Theorem for theBenchmark: Theorem is valid
% 1.78/0.66  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.78/0.69  % Elapsed time: 0.343367 seconds
% 1.78/0.69  % CPU time: 1.946194 seconds
% 1.78/0.69  % Memory used: 163.322 MB
%------------------------------------------------------------------------------