TSTP Solution File: SEU422+2 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SEU422+2 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n032.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 20:42:18 EDT 2024

% Result   : Theorem 40.90s 5.86s
% Output   : CNFRefutation 41.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   75 (  25 unt;   0 def)
%            Number of atoms       :  178 (  24 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  174 (  71   ~;  65   |;  21   &)
%                                         (   7 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   3 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   3 con; 0-2 aty)
%            Number of variables   :  128 ( 122   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f8,axiom,
    ! [A,B] :
      ( r1_tarski(A,B)
    <=> ! [C] :
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f54,axiom,
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f64,axiom,
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f79,axiom,
    ! [A,B,C] :
      ( r1_tarski(A,B)
     => r1_tarski(A,k2_xboole_0(C,B)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f81,axiom,
    ! [A,B] :
      ( r1_tarski(A,B)
     => k2_xboole_0(A,B) = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f105,axiom,
    ! [A,B] : r1_tarski(k4_xboole_0(A,B),A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f185,axiom,
    ! [A,B] :
      ( B = k1_zfmisc_1(A)
    <=> ! [C] :
          ( r2_hidden(C,B)
        <=> r1_tarski(C,A) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f267,axiom,
    ! [A,B] :
      ( r1_tarski(A,B)
     => r1_tarski(k1_zfmisc_1(A),k1_zfmisc_1(B)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f288,axiom,
    ! [A] : r1_tarski(A,k1_zfmisc_1(k3_tarski(A))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f540,axiom,
    ! [A,B] :
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4486,axiom,
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => B = k3_tarski(a_2_0_relset_2(A,B)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4487,conjecture,
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => m1_subset_1(a_2_0_relset_2(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4488,negated_conjecture,
    ~ ! [A] :
        ( ~ v1_xboole_0(A)
       => ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(A))
           => m1_subset_1(a_2_0_relset_2(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
    inference(negated_conjecture,[status(cth)],[f4487]) ).

fof(f4512,plain,
    ! [A,B] :
      ( r1_tarski(A,B)
    <=> ! [C] :
          ( ~ r2_hidden(C,A)
          | r2_hidden(C,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f8]) ).

fof(f4513,plain,
    ! [A,B] :
      ( ( ~ r1_tarski(A,B)
        | ! [C] :
            ( ~ r2_hidden(C,A)
            | r2_hidden(C,B) ) )
      & ( r1_tarski(A,B)
        | ? [C] :
            ( r2_hidden(C,A)
            & ~ r2_hidden(C,B) ) ) ),
    inference(NNF_transformation,[status(esa)],[f4512]) ).

fof(f4514,plain,
    ( ! [A,B] :
        ( ~ r1_tarski(A,B)
        | ! [C] :
            ( ~ r2_hidden(C,A)
            | r2_hidden(C,B) ) )
    & ! [A,B] :
        ( r1_tarski(A,B)
        | ? [C] :
            ( r2_hidden(C,A)
            & ~ r2_hidden(C,B) ) ) ),
    inference(miniscoping,[status(esa)],[f4513]) ).

fof(f4515,plain,
    ( ! [A,B] :
        ( ~ r1_tarski(A,B)
        | ! [C] :
            ( ~ r2_hidden(C,A)
            | r2_hidden(C,B) ) )
    & ! [A,B] :
        ( r1_tarski(A,B)
        | ( r2_hidden(sk0_3(B,A),A)
          & ~ r2_hidden(sk0_3(B,A),B) ) ) ),
    inference(skolemization,[status(esa)],[f4514]) ).

fof(f4516,plain,
    ! [X0,X1,X2] :
      ( ~ r1_tarski(X0,X1)
      | ~ r2_hidden(X2,X0)
      | r2_hidden(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f4515]) ).

fof(f4694,plain,
    ! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
    inference(cnf_transformation,[status(esa)],[f54]) ).

fof(f4703,plain,
    ! [X0] : k4_xboole_0(X0,k1_xboole_0) = X0,
    inference(cnf_transformation,[status(esa)],[f64]) ).

fof(f4729,plain,
    ! [A,B,C] :
      ( ~ r1_tarski(A,B)
      | r1_tarski(A,k2_xboole_0(C,B)) ),
    inference(pre_NNF_transformation,[status(esa)],[f79]) ).

fof(f4730,plain,
    ! [A,B] :
      ( ~ r1_tarski(A,B)
      | ! [C] : r1_tarski(A,k2_xboole_0(C,B)) ),
    inference(miniscoping,[status(esa)],[f4729]) ).

fof(f4731,plain,
    ! [X0,X1,X2] :
      ( ~ r1_tarski(X0,X1)
      | r1_tarski(X0,k2_xboole_0(X2,X1)) ),
    inference(cnf_transformation,[status(esa)],[f4730]) ).

fof(f4735,plain,
    ! [A,B] :
      ( ~ r1_tarski(A,B)
      | k2_xboole_0(A,B) = B ),
    inference(pre_NNF_transformation,[status(esa)],[f81]) ).

fof(f4736,plain,
    ! [X0,X1] :
      ( ~ r1_tarski(X0,X1)
      | k2_xboole_0(X0,X1) = X1 ),
    inference(cnf_transformation,[status(esa)],[f4735]) ).

fof(f4786,plain,
    ! [X0,X1] : r1_tarski(k4_xboole_0(X0,X1),X0),
    inference(cnf_transformation,[status(esa)],[f105]) ).

fof(f4947,plain,
    ! [A,B] :
      ( ( B != k1_zfmisc_1(A)
        | ! [C] :
            ( ( ~ r2_hidden(C,B)
              | r1_tarski(C,A) )
            & ( r2_hidden(C,B)
              | ~ r1_tarski(C,A) ) ) )
      & ( B = k1_zfmisc_1(A)
        | ? [C] :
            ( ( ~ r2_hidden(C,B)
              | ~ r1_tarski(C,A) )
            & ( r2_hidden(C,B)
              | r1_tarski(C,A) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f185]) ).

fof(f4948,plain,
    ( ! [A,B] :
        ( B != k1_zfmisc_1(A)
        | ( ! [C] :
              ( ~ r2_hidden(C,B)
              | r1_tarski(C,A) )
          & ! [C] :
              ( r2_hidden(C,B)
              | ~ r1_tarski(C,A) ) ) )
    & ! [A,B] :
        ( B = k1_zfmisc_1(A)
        | ? [C] :
            ( ( ~ r2_hidden(C,B)
              | ~ r1_tarski(C,A) )
            & ( r2_hidden(C,B)
              | r1_tarski(C,A) ) ) ) ),
    inference(miniscoping,[status(esa)],[f4947]) ).

fof(f4949,plain,
    ( ! [A,B] :
        ( B != k1_zfmisc_1(A)
        | ( ! [C] :
              ( ~ r2_hidden(C,B)
              | r1_tarski(C,A) )
          & ! [C] :
              ( r2_hidden(C,B)
              | ~ r1_tarski(C,A) ) ) )
    & ! [A,B] :
        ( B = k1_zfmisc_1(A)
        | ( ( ~ r2_hidden(sk0_36(B,A),B)
            | ~ r1_tarski(sk0_36(B,A),A) )
          & ( r2_hidden(sk0_36(B,A),B)
            | r1_tarski(sk0_36(B,A),A) ) ) ) ),
    inference(skolemization,[status(esa)],[f4948]) ).

fof(f4950,plain,
    ! [X0,X1,X2] :
      ( X0 != k1_zfmisc_1(X1)
      | ~ r2_hidden(X2,X0)
      | r1_tarski(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f4949]) ).

fof(f4951,plain,
    ! [X0,X1,X2] :
      ( X0 != k1_zfmisc_1(X1)
      | r2_hidden(X2,X0)
      | ~ r1_tarski(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f4949]) ).

fof(f5149,plain,
    ! [A,B] :
      ( ~ r1_tarski(A,B)
      | r1_tarski(k1_zfmisc_1(A),k1_zfmisc_1(B)) ),
    inference(pre_NNF_transformation,[status(esa)],[f267]) ).

fof(f5150,plain,
    ! [X0,X1] :
      ( ~ r1_tarski(X0,X1)
      | r1_tarski(k1_zfmisc_1(X0),k1_zfmisc_1(X1)) ),
    inference(cnf_transformation,[status(esa)],[f5149]) ).

fof(f5174,plain,
    ! [X0] : r1_tarski(X0,k1_zfmisc_1(k3_tarski(X0))),
    inference(cnf_transformation,[status(esa)],[f288]) ).

fof(f5819,plain,
    ! [A,B] :
      ( ( ~ m1_subset_1(A,k1_zfmisc_1(B))
        | r1_tarski(A,B) )
      & ( m1_subset_1(A,k1_zfmisc_1(B))
        | ~ r1_tarski(A,B) ) ),
    inference(NNF_transformation,[status(esa)],[f540]) ).

fof(f5820,plain,
    ( ! [A,B] :
        ( ~ m1_subset_1(A,k1_zfmisc_1(B))
        | r1_tarski(A,B) )
    & ! [A,B] :
        ( m1_subset_1(A,k1_zfmisc_1(B))
        | ~ r1_tarski(A,B) ) ),
    inference(miniscoping,[status(esa)],[f5819]) ).

fof(f5821,plain,
    ! [X0,X1] :
      ( ~ m1_subset_1(X0,k1_zfmisc_1(X1))
      | r1_tarski(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f5820]) ).

fof(f5822,plain,
    ! [X0,X1] :
      ( m1_subset_1(X0,k1_zfmisc_1(X1))
      | ~ r1_tarski(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f5820]) ).

fof(f17538,plain,
    ! [A] :
      ( v1_xboole_0(A)
      | ! [B] :
          ( ~ m1_subset_1(B,k1_zfmisc_1(A))
          | B = k3_tarski(a_2_0_relset_2(A,B)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f4486]) ).

fof(f17539,plain,
    ! [X0,X1] :
      ( v1_xboole_0(X0)
      | ~ m1_subset_1(X1,k1_zfmisc_1(X0))
      | X1 = k3_tarski(a_2_0_relset_2(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f17538]) ).

fof(f17540,plain,
    ? [A] :
      ( ~ v1_xboole_0(A)
      & ? [B] :
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ m1_subset_1(a_2_0_relset_2(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f4488]) ).

fof(f17541,plain,
    ( ~ v1_xboole_0(sk0_1205)
    & m1_subset_1(sk0_1206,k1_zfmisc_1(sk0_1205))
    & ~ m1_subset_1(a_2_0_relset_2(sk0_1205,sk0_1206),k1_zfmisc_1(k1_zfmisc_1(sk0_1205))) ),
    inference(skolemization,[status(esa)],[f17540]) ).

fof(f17542,plain,
    ~ v1_xboole_0(sk0_1205),
    inference(cnf_transformation,[status(esa)],[f17541]) ).

fof(f17543,plain,
    m1_subset_1(sk0_1206,k1_zfmisc_1(sk0_1205)),
    inference(cnf_transformation,[status(esa)],[f17541]) ).

fof(f17544,plain,
    ~ m1_subset_1(a_2_0_relset_2(sk0_1205,sk0_1206),k1_zfmisc_1(k1_zfmisc_1(sk0_1205))),
    inference(cnf_transformation,[status(esa)],[f17541]) ).

fof(f20831,plain,
    ! [X0,X1] :
      ( ~ r2_hidden(X0,k1_zfmisc_1(X1))
      | r1_tarski(X0,X1) ),
    inference(destructive_equality_resolution,[status(esa)],[f4950]) ).

fof(f20832,plain,
    ! [X0,X1] :
      ( r2_hidden(X0,k1_zfmisc_1(X1))
      | ~ r1_tarski(X0,X1) ),
    inference(destructive_equality_resolution,[status(esa)],[f4951]) ).

fof(f21745,plain,
    r1_tarski(sk0_1206,sk0_1205),
    inference(resolution,[status(thm)],[f5821,f17543]) ).

fof(f21761,plain,
    ! [X0,X1] :
      ( ~ r1_tarski(X0,X1)
      | r2_hidden(k1_zfmisc_1(X0),k1_zfmisc_1(k1_zfmisc_1(X1))) ),
    inference(resolution,[status(thm)],[f5150,f20832]) ).

fof(f21781,plain,
    r2_hidden(k1_zfmisc_1(sk0_1206),k1_zfmisc_1(k1_zfmisc_1(sk0_1205))),
    inference(resolution,[status(thm)],[f21761,f21745]) ).

fof(f21782,plain,
    r1_tarski(k1_zfmisc_1(sk0_1206),k1_zfmisc_1(sk0_1205)),
    inference(resolution,[status(thm)],[f21781,f20831]) ).

fof(f21889,plain,
    ~ r1_tarski(a_2_0_relset_2(sk0_1205,sk0_1206),k1_zfmisc_1(sk0_1205)),
    inference(resolution,[status(thm)],[f5822,f17544]) ).

fof(f21960,plain,
    ( spl0_641
  <=> v1_xboole_0(sk0_1205) ),
    introduced(split_symbol_definition) ).

fof(f21961,plain,
    ( v1_xboole_0(sk0_1205)
    | ~ spl0_641 ),
    inference(component_clause,[status(thm)],[f21960]) ).

fof(f21963,plain,
    ( spl0_642
  <=> sk0_1206 = k3_tarski(a_2_0_relset_2(sk0_1205,sk0_1206)) ),
    introduced(split_symbol_definition) ).

fof(f21964,plain,
    ( sk0_1206 = k3_tarski(a_2_0_relset_2(sk0_1205,sk0_1206))
    | ~ spl0_642 ),
    inference(component_clause,[status(thm)],[f21963]) ).

fof(f21966,plain,
    ( v1_xboole_0(sk0_1205)
    | sk0_1206 = k3_tarski(a_2_0_relset_2(sk0_1205,sk0_1206)) ),
    inference(resolution,[status(thm)],[f17539,f17543]) ).

fof(f21967,plain,
    ( spl0_641
    | spl0_642 ),
    inference(split_clause,[status(thm)],[f21966,f21960,f21963]) ).

fof(f21969,plain,
    ( $false
    | ~ spl0_641 ),
    inference(forward_subsumption_resolution,[status(thm)],[f21961,f17542]) ).

fof(f21970,plain,
    ~ spl0_641,
    inference(contradiction_clause,[status(thm)],[f21969]) ).

fof(f24250,plain,
    ! [X0,X1] : r2_hidden(k4_xboole_0(X0,X1),k1_zfmisc_1(X0)),
    inference(resolution,[status(thm)],[f4786,f20832]) ).

fof(f24509,plain,
    ! [X0] :
      ( ~ r2_hidden(X0,k1_zfmisc_1(sk0_1206))
      | r2_hidden(X0,k1_zfmisc_1(sk0_1205)) ),
    inference(resolution,[status(thm)],[f21782,f4516]) ).

fof(f25786,plain,
    ( r1_tarski(a_2_0_relset_2(sk0_1205,sk0_1206),k1_zfmisc_1(sk0_1206))
    | ~ spl0_642 ),
    inference(paramodulation,[status(thm)],[f21964,f5174]) ).

fof(f26510,plain,
    ! [X0] : r2_hidden(k4_xboole_0(sk0_1206,X0),k1_zfmisc_1(sk0_1205)),
    inference(resolution,[status(thm)],[f24509,f24250]) ).

fof(f26541,plain,
    ! [X0] : r1_tarski(k4_xboole_0(sk0_1206,X0),sk0_1205),
    inference(resolution,[status(thm)],[f26510,f20831]) ).

fof(f26551,plain,
    ! [X0] : r2_hidden(k1_zfmisc_1(k4_xboole_0(sk0_1206,X0)),k1_zfmisc_1(k1_zfmisc_1(sk0_1205))),
    inference(resolution,[status(thm)],[f26541,f21761]) ).

fof(f26563,plain,
    ! [X0] : r1_tarski(k1_zfmisc_1(k4_xboole_0(sk0_1206,X0)),k1_zfmisc_1(sk0_1205)),
    inference(resolution,[status(thm)],[f26551,f20831]) ).

fof(f33794,plain,
    ! [X0] : k2_xboole_0(k1_zfmisc_1(k4_xboole_0(sk0_1206,X0)),k1_zfmisc_1(sk0_1205)) = k1_zfmisc_1(sk0_1205),
    inference(resolution,[status(thm)],[f4736,f26563]) ).

fof(f33795,plain,
    ! [X0] : k2_xboole_0(k1_zfmisc_1(sk0_1205),k1_zfmisc_1(k4_xboole_0(sk0_1206,X0))) = k1_zfmisc_1(sk0_1205),
    inference(forward_demodulation,[status(thm)],[f4694,f33794]) ).

fof(f34042,plain,
    ! [X0,X1] :
      ( ~ r1_tarski(X0,k1_zfmisc_1(k4_xboole_0(sk0_1206,X1)))
      | r1_tarski(X0,k1_zfmisc_1(sk0_1205)) ),
    inference(paramodulation,[status(thm)],[f33795,f4731]) ).

fof(f34074,plain,
    ! [X0] :
      ( ~ r1_tarski(X0,k1_zfmisc_1(sk0_1206))
      | r1_tarski(X0,k1_zfmisc_1(sk0_1205)) ),
    inference(paramodulation,[status(thm)],[f4703,f34042]) ).

fof(f34548,plain,
    ( r1_tarski(a_2_0_relset_2(sk0_1205,sk0_1206),k1_zfmisc_1(sk0_1205))
    | ~ spl0_642 ),
    inference(resolution,[status(thm)],[f25786,f34074]) ).

fof(f34549,plain,
    ( $false
    | ~ spl0_642 ),
    inference(forward_subsumption_resolution,[status(thm)],[f34548,f21889]) ).

fof(f34550,plain,
    ~ spl0_642,
    inference(contradiction_clause,[status(thm)],[f34549]) ).

fof(f34551,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f21967,f21970,f34550]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : SEU422+2 : TPTP v8.1.2. Released v3.4.0.
% 0.08/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.33  % Computer : n032.cluster.edu
% 0.10/0.33  % Model    : x86_64 x86_64
% 0.10/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.33  % Memory   : 8042.1875MB
% 0.10/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.33  % CPULimit : 300
% 0.10/0.33  % WCLimit  : 300
% 0.10/0.33  % DateTime : Mon Apr 29 19:48:51 EDT 2024
% 0.10/0.33  % CPUTime  : 
% 0.43/0.67  % Drodi V3.6.0
% 40.90/5.86  % Refutation found
% 40.90/5.86  % SZS status Theorem for theBenchmark: Theorem is valid
% 40.90/5.86  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 42.39/6.03  % Elapsed time: 5.677651 seconds
% 42.39/6.03  % CPU time: 41.922589 seconds
% 42.39/6.03  % Total memory used: 837.087 MB
% 42.39/6.03  % Net memory used: 828.731 MB
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