TSTP Solution File: SEU420+2 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU420+2 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n023.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 12:37:01 EDT 2023

% Result   : Theorem 0.65s 1.08s
% Output   : CNFRefutation 3.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   52 (  13 unt;   0 def)
%            Number of atoms       :  116 (   2 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  108 (  44   ~;  41   |;   7   &)
%                                         (   6 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   7 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   54 (;  48   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f57,axiom,
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f86,axiom,
    ! [A,B] : r1_tarski(k3_xboole_0(A,B),A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f88,axiom,
    ! [A,B,C] :
      ( ( r1_tarski(A,B)
        & r1_tarski(A,C) )
     => r1_tarski(A,k3_xboole_0(B,C)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f563,axiom,
    ! [A,B] :
      ( v1_relat_1(B)
     => ( r1_tarski(A,B)
       => v1_relat_1(A) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f729,axiom,
    ! [A,B] :
      ( v1_relat_1(B)
     => ! [C] :
          ( v1_relat_1(C)
         => ( r1_tarski(B,C)
           => r1_tarski(k9_relat_1(B,A),k9_relat_1(C,A)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4482,conjecture,
    ! [A,B] :
      ( v1_relat_1(B)
     => ! [C] :
          ( v1_relat_1(C)
         => r1_tarski(k9_relat_1(k3_xboole_0(B,C),k3_pua2mss1(A)),k3_xboole_0(k9_relat_1(B,k3_pua2mss1(A)),k9_relat_1(C,k3_pua2mss1(A)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4483,negated_conjecture,
    ~ ! [A,B] :
        ( v1_relat_1(B)
       => ! [C] :
            ( v1_relat_1(C)
           => r1_tarski(k9_relat_1(k3_xboole_0(B,C),k3_pua2mss1(A)),k3_xboole_0(k9_relat_1(B,k3_pua2mss1(A)),k9_relat_1(C,k3_pua2mss1(A)))) ) ),
    inference(negated_conjecture,[status(cth)],[f4482]) ).

fof(f4692,plain,
    ! [X0,X1] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
    inference(cnf_transformation,[status(esa)],[f57]) ).

fof(f4743,plain,
    ! [X0,X1] : r1_tarski(k3_xboole_0(X0,X1),X0),
    inference(cnf_transformation,[status(esa)],[f86]) ).

fof(f4747,plain,
    ! [A,B,C] :
      ( ~ r1_tarski(A,B)
      | ~ r1_tarski(A,C)
      | r1_tarski(A,k3_xboole_0(B,C)) ),
    inference(pre_NNF_transformation,[status(esa)],[f88]) ).

fof(f4748,plain,
    ! [X0,X1,X2] :
      ( ~ r1_tarski(X0,X1)
      | ~ r1_tarski(X0,X2)
      | r1_tarski(X0,k3_xboole_0(X1,X2)) ),
    inference(cnf_transformation,[status(esa)],[f4747]) ).

fof(f5876,plain,
    ! [A,B] :
      ( ~ v1_relat_1(B)
      | ~ r1_tarski(A,B)
      | v1_relat_1(A) ),
    inference(pre_NNF_transformation,[status(esa)],[f563]) ).

fof(f5877,plain,
    ! [B] :
      ( ~ v1_relat_1(B)
      | ! [A] :
          ( ~ r1_tarski(A,B)
          | v1_relat_1(A) ) ),
    inference(miniscoping,[status(esa)],[f5876]) ).

fof(f5878,plain,
    ! [X0,X1] :
      ( ~ v1_relat_1(X0)
      | ~ r1_tarski(X1,X0)
      | v1_relat_1(X1) ),
    inference(cnf_transformation,[status(esa)],[f5877]) ).

fof(f6333,plain,
    ! [A,B] :
      ( ~ v1_relat_1(B)
      | ! [C] :
          ( ~ v1_relat_1(C)
          | ~ r1_tarski(B,C)
          | r1_tarski(k9_relat_1(B,A),k9_relat_1(C,A)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f729]) ).

fof(f6334,plain,
    ! [B] :
      ( ~ v1_relat_1(B)
      | ! [C] :
          ( ~ v1_relat_1(C)
          | ~ r1_tarski(B,C)
          | ! [A] : r1_tarski(k9_relat_1(B,A),k9_relat_1(C,A)) ) ),
    inference(miniscoping,[status(esa)],[f6333]) ).

fof(f6335,plain,
    ! [X0,X1,X2] :
      ( ~ v1_relat_1(X0)
      | ~ v1_relat_1(X1)
      | ~ r1_tarski(X0,X1)
      | r1_tarski(k9_relat_1(X0,X2),k9_relat_1(X1,X2)) ),
    inference(cnf_transformation,[status(esa)],[f6334]) ).

fof(f17518,plain,
    ? [A,B] :
      ( v1_relat_1(B)
      & ? [C] :
          ( v1_relat_1(C)
          & ~ r1_tarski(k9_relat_1(k3_xboole_0(B,C),k3_pua2mss1(A)),k3_xboole_0(k9_relat_1(B,k3_pua2mss1(A)),k9_relat_1(C,k3_pua2mss1(A)))) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f4483]) ).

fof(f17519,plain,
    ? [B] :
      ( v1_relat_1(B)
      & ? [C] :
          ( v1_relat_1(C)
          & ? [A] : ~ r1_tarski(k9_relat_1(k3_xboole_0(B,C),k3_pua2mss1(A)),k3_xboole_0(k9_relat_1(B,k3_pua2mss1(A)),k9_relat_1(C,k3_pua2mss1(A)))) ) ),
    inference(miniscoping,[status(esa)],[f17518]) ).

fof(f17520,plain,
    ( v1_relat_1(sk0_1204)
    & v1_relat_1(sk0_1205)
    & ~ r1_tarski(k9_relat_1(k3_xboole_0(sk0_1204,sk0_1205),k3_pua2mss1(sk0_1206)),k3_xboole_0(k9_relat_1(sk0_1204,k3_pua2mss1(sk0_1206)),k9_relat_1(sk0_1205,k3_pua2mss1(sk0_1206)))) ),
    inference(skolemization,[status(esa)],[f17519]) ).

fof(f17521,plain,
    v1_relat_1(sk0_1204),
    inference(cnf_transformation,[status(esa)],[f17520]) ).

fof(f17522,plain,
    v1_relat_1(sk0_1205),
    inference(cnf_transformation,[status(esa)],[f17520]) ).

fof(f17523,plain,
    ~ r1_tarski(k9_relat_1(k3_xboole_0(sk0_1204,sk0_1205),k3_pua2mss1(sk0_1206)),k3_xboole_0(k9_relat_1(sk0_1204,k3_pua2mss1(sk0_1206)),k9_relat_1(sk0_1205,k3_pua2mss1(sk0_1206)))),
    inference(cnf_transformation,[status(esa)],[f17520]) ).

fof(f21722,plain,
    ! [X0,X1] : r1_tarski(k3_xboole_0(X0,X1),X1),
    inference(paramodulation,[status(thm)],[f4692,f4743]) ).

fof(f21874,plain,
    ( spl0_623
  <=> r1_tarski(k9_relat_1(k3_xboole_0(sk0_1204,sk0_1205),k3_pua2mss1(sk0_1206)),k9_relat_1(sk0_1204,k3_pua2mss1(sk0_1206))) ),
    introduced(split_symbol_definition) ).

fof(f21876,plain,
    ( ~ r1_tarski(k9_relat_1(k3_xboole_0(sk0_1204,sk0_1205),k3_pua2mss1(sk0_1206)),k9_relat_1(sk0_1204,k3_pua2mss1(sk0_1206)))
    | spl0_623 ),
    inference(component_clause,[status(thm)],[f21874]) ).

fof(f21877,plain,
    ( spl0_624
  <=> r1_tarski(k9_relat_1(k3_xboole_0(sk0_1204,sk0_1205),k3_pua2mss1(sk0_1206)),k9_relat_1(sk0_1205,k3_pua2mss1(sk0_1206))) ),
    introduced(split_symbol_definition) ).

fof(f21879,plain,
    ( ~ r1_tarski(k9_relat_1(k3_xboole_0(sk0_1204,sk0_1205),k3_pua2mss1(sk0_1206)),k9_relat_1(sk0_1205,k3_pua2mss1(sk0_1206)))
    | spl0_624 ),
    inference(component_clause,[status(thm)],[f21877]) ).

fof(f21880,plain,
    ( ~ r1_tarski(k9_relat_1(k3_xboole_0(sk0_1204,sk0_1205),k3_pua2mss1(sk0_1206)),k9_relat_1(sk0_1204,k3_pua2mss1(sk0_1206)))
    | ~ r1_tarski(k9_relat_1(k3_xboole_0(sk0_1204,sk0_1205),k3_pua2mss1(sk0_1206)),k9_relat_1(sk0_1205,k3_pua2mss1(sk0_1206))) ),
    inference(resolution,[status(thm)],[f4748,f17523]) ).

fof(f21881,plain,
    ( ~ spl0_623
    | ~ spl0_624 ),
    inference(split_clause,[status(thm)],[f21880,f21874,f21877]) ).

fof(f25917,plain,
    ! [X0,X1,X2] :
      ( ~ v1_relat_1(X0)
      | ~ r1_tarski(X1,X0)
      | r1_tarski(k9_relat_1(X1,X2),k9_relat_1(X0,X2)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f6335,f5878]) ).

fof(f25918,plain,
    ( spl0_774
  <=> v1_relat_1(sk0_1205) ),
    introduced(split_symbol_definition) ).

fof(f25920,plain,
    ( ~ v1_relat_1(sk0_1205)
    | spl0_774 ),
    inference(component_clause,[status(thm)],[f25918]) ).

fof(f25921,plain,
    ( spl0_775
  <=> r1_tarski(k3_xboole_0(sk0_1204,sk0_1205),sk0_1205) ),
    introduced(split_symbol_definition) ).

fof(f25923,plain,
    ( ~ r1_tarski(k3_xboole_0(sk0_1204,sk0_1205),sk0_1205)
    | spl0_775 ),
    inference(component_clause,[status(thm)],[f25921]) ).

fof(f25924,plain,
    ( ~ v1_relat_1(sk0_1205)
    | ~ r1_tarski(k3_xboole_0(sk0_1204,sk0_1205),sk0_1205)
    | spl0_624 ),
    inference(resolution,[status(thm)],[f25917,f21879]) ).

fof(f25925,plain,
    ( ~ spl0_774
    | ~ spl0_775
    | spl0_624 ),
    inference(split_clause,[status(thm)],[f25924,f25918,f25921,f21877]) ).

fof(f25926,plain,
    ( spl0_776
  <=> v1_relat_1(sk0_1204) ),
    introduced(split_symbol_definition) ).

fof(f25928,plain,
    ( ~ v1_relat_1(sk0_1204)
    | spl0_776 ),
    inference(component_clause,[status(thm)],[f25926]) ).

fof(f25929,plain,
    ( spl0_777
  <=> r1_tarski(k3_xboole_0(sk0_1204,sk0_1205),sk0_1204) ),
    introduced(split_symbol_definition) ).

fof(f25931,plain,
    ( ~ r1_tarski(k3_xboole_0(sk0_1204,sk0_1205),sk0_1204)
    | spl0_777 ),
    inference(component_clause,[status(thm)],[f25929]) ).

fof(f25932,plain,
    ( ~ v1_relat_1(sk0_1204)
    | ~ r1_tarski(k3_xboole_0(sk0_1204,sk0_1205),sk0_1204)
    | spl0_623 ),
    inference(resolution,[status(thm)],[f25917,f21876]) ).

fof(f25933,plain,
    ( ~ spl0_776
    | ~ spl0_777
    | spl0_623 ),
    inference(split_clause,[status(thm)],[f25932,f25926,f25929,f21874]) ).

fof(f25945,plain,
    ( $false
    | spl0_776 ),
    inference(forward_subsumption_resolution,[status(thm)],[f25928,f17521]) ).

fof(f25946,plain,
    spl0_776,
    inference(contradiction_clause,[status(thm)],[f25945]) ).

fof(f25947,plain,
    ( $false
    | spl0_777 ),
    inference(forward_subsumption_resolution,[status(thm)],[f25931,f4743]) ).

fof(f25948,plain,
    spl0_777,
    inference(contradiction_clause,[status(thm)],[f25947]) ).

fof(f25949,plain,
    ( $false
    | spl0_775 ),
    inference(forward_subsumption_resolution,[status(thm)],[f25923,f21722]) ).

fof(f25950,plain,
    spl0_775,
    inference(contradiction_clause,[status(thm)],[f25949]) ).

fof(f25951,plain,
    ( $false
    | spl0_774 ),
    inference(forward_subsumption_resolution,[status(thm)],[f25920,f17522]) ).

fof(f25952,plain,
    spl0_774,
    inference(contradiction_clause,[status(thm)],[f25951]) ).

fof(f25953,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f21881,f25925,f25933,f25946,f25948,f25950,f25952]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SEU420+2 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32  % Computer : n023.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit : 300
% 0.10/0.32  % WCLimit  : 300
% 0.10/0.32  % DateTime : Tue May 30 09:37:08 EDT 2023
% 0.10/0.32  % CPUTime  : 
% 0.46/0.66  % Drodi V3.5.1
% 0.65/1.08  % Refutation found
% 0.65/1.08  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.65/1.08  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.04/1.18  % Elapsed time: 0.849655 seconds
% 3.04/1.18  % CPU time: 3.515390 seconds
% 3.04/1.18  % Memory used: 658.922 MB
%------------------------------------------------------------------------------