TSTP Solution File: SEU408+3 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SEU408+3 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n011.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 20:42:14 EDT 2024

% Result   : Theorem 26.90s 6.04s
% Output   : CNFRefutation 29.28s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   47 (  11 unt;   0 def)
%            Number of atoms       :  205 (  27 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  236 (  78   ~;  71   |;  69   &)
%                                         (   7 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   14 (  12 usr;   4 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-6 aty)
%            Number of variables   :   75 (  70   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f30,axiom,
    ! [A,B,C] :
      ( C = k2_xboole_0(A,B)
    <=> ! [D] :
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            | r2_hidden(D,B) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f675,axiom,
    ! [A,B] :
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f19022,axiom,
    ! [A,B] :
      ( ( l1_orders_2(A)
        & l1_orders_2(B) )
     => ( v1_orders_2(k1_latsum_1(A,B))
        & l1_orders_2(k1_latsum_1(A,B)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f19025,axiom,
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ! [C] :
              ( ( v1_orders_2(C)
                & l1_orders_2(C) )
             => ( C = k1_latsum_1(A,B)
              <=> ( u1_struct_0(C) = k2_xboole_0(u1_struct_0(A),u1_struct_0(B))
                  & u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A),u1_orders_2(B)),k7_relset_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_orders_2(A),u1_orders_2(B))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f19037,conjecture,
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & v1_lattice3(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( r2_hidden(C,u1_struct_0(B))
             => m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f19038,negated_conjecture,
    ~ ! [A] :
        ( ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & l1_orders_2(A) )
       => ! [B] :
            ( ( ~ v3_struct_0(B)
              & v2_orders_2(B)
              & v3_orders_2(B)
              & v4_orders_2(B)
              & v1_lattice3(B)
              & l1_orders_2(B) )
           => ! [C] :
                ( r2_hidden(C,u1_struct_0(B))
               => m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B))) ) ) ),
    inference(negated_conjecture,[status(cth)],[f19037]) ).

fof(f19133,plain,
    ! [A,B,C] :
      ( ( C != k2_xboole_0(A,B)
        | ! [D] :
            ( ( ~ r2_hidden(D,C)
              | r2_hidden(D,A)
              | r2_hidden(D,B) )
            & ( r2_hidden(D,C)
              | ( ~ r2_hidden(D,A)
                & ~ r2_hidden(D,B) ) ) ) )
      & ( C = k2_xboole_0(A,B)
        | ? [D] :
            ( ( ~ r2_hidden(D,C)
              | ( ~ r2_hidden(D,A)
                & ~ r2_hidden(D,B) ) )
            & ( r2_hidden(D,C)
              | r2_hidden(D,A)
              | r2_hidden(D,B) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f30]) ).

fof(f19134,plain,
    ( ! [A,B,C] :
        ( C != k2_xboole_0(A,B)
        | ( ! [D] :
              ( ~ r2_hidden(D,C)
              | r2_hidden(D,A)
              | r2_hidden(D,B) )
          & ! [D] :
              ( r2_hidden(D,C)
              | ( ~ r2_hidden(D,A)
                & ~ r2_hidden(D,B) ) ) ) )
    & ! [A,B,C] :
        ( C = k2_xboole_0(A,B)
        | ? [D] :
            ( ( ~ r2_hidden(D,C)
              | ( ~ r2_hidden(D,A)
                & ~ r2_hidden(D,B) ) )
            & ( r2_hidden(D,C)
              | r2_hidden(D,A)
              | r2_hidden(D,B) ) ) ) ),
    inference(miniscoping,[status(esa)],[f19133]) ).

fof(f19135,plain,
    ( ! [A,B,C] :
        ( C != k2_xboole_0(A,B)
        | ( ! [D] :
              ( ~ r2_hidden(D,C)
              | r2_hidden(D,A)
              | r2_hidden(D,B) )
          & ! [D] :
              ( r2_hidden(D,C)
              | ( ~ r2_hidden(D,A)
                & ~ r2_hidden(D,B) ) ) ) )
    & ! [A,B,C] :
        ( C = k2_xboole_0(A,B)
        | ( ( ~ r2_hidden(sk0_23(C,B,A),C)
            | ( ~ r2_hidden(sk0_23(C,B,A),A)
              & ~ r2_hidden(sk0_23(C,B,A),B) ) )
          & ( r2_hidden(sk0_23(C,B,A),C)
            | r2_hidden(sk0_23(C,B,A),A)
            | r2_hidden(sk0_23(C,B,A),B) ) ) ) ),
    inference(skolemization,[status(esa)],[f19134]) ).

fof(f19138,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != k2_xboole_0(X1,X2)
      | r2_hidden(X3,X0)
      | ~ r2_hidden(X3,X2) ),
    inference(cnf_transformation,[status(esa)],[f19135]) ).

fof(f20501,plain,
    ! [A,B] :
      ( ~ r2_hidden(A,B)
      | m1_subset_1(A,B) ),
    inference(pre_NNF_transformation,[status(esa)],[f675]) ).

fof(f20502,plain,
    ! [X0,X1] :
      ( ~ r2_hidden(X0,X1)
      | m1_subset_1(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f20501]) ).

fof(f89021,plain,
    ! [A,B] :
      ( ~ l1_orders_2(A)
      | ~ l1_orders_2(B)
      | ( v1_orders_2(k1_latsum_1(A,B))
        & l1_orders_2(k1_latsum_1(A,B)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f19022]) ).

fof(f89022,plain,
    ! [X0,X1] :
      ( ~ l1_orders_2(X0)
      | ~ l1_orders_2(X1)
      | v1_orders_2(k1_latsum_1(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f89021]) ).

fof(f89023,plain,
    ! [X0,X1] :
      ( ~ l1_orders_2(X0)
      | ~ l1_orders_2(X1)
      | l1_orders_2(k1_latsum_1(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f89021]) ).

fof(f89040,plain,
    ! [A] :
      ( ~ l1_orders_2(A)
      | ! [B] :
          ( ~ l1_orders_2(B)
          | ! [C] :
              ( ~ v1_orders_2(C)
              | ~ l1_orders_2(C)
              | ( C = k1_latsum_1(A,B)
              <=> ( u1_struct_0(C) = k2_xboole_0(u1_struct_0(A),u1_struct_0(B))
                  & u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A),u1_orders_2(B)),k7_relset_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_orders_2(A),u1_orders_2(B))) ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f19025]) ).

fof(f89041,plain,
    ! [A] :
      ( ~ l1_orders_2(A)
      | ! [B] :
          ( ~ l1_orders_2(B)
          | ! [C] :
              ( ~ v1_orders_2(C)
              | ~ l1_orders_2(C)
              | ( ( C != k1_latsum_1(A,B)
                  | ( u1_struct_0(C) = k2_xboole_0(u1_struct_0(A),u1_struct_0(B))
                    & u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A),u1_orders_2(B)),k7_relset_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_orders_2(A),u1_orders_2(B))) ) )
                & ( C = k1_latsum_1(A,B)
                  | u1_struct_0(C) != k2_xboole_0(u1_struct_0(A),u1_struct_0(B))
                  | u1_orders_2(C) != k2_xboole_0(k2_xboole_0(u1_orders_2(A),u1_orders_2(B)),k7_relset_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_orders_2(A),u1_orders_2(B))) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f89040]) ).

fof(f89042,plain,
    ! [X0,X1,X2] :
      ( ~ l1_orders_2(X0)
      | ~ l1_orders_2(X1)
      | ~ v1_orders_2(X2)
      | ~ l1_orders_2(X2)
      | X2 != k1_latsum_1(X0,X1)
      | u1_struct_0(X2) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) ),
    inference(cnf_transformation,[status(esa)],[f89041]) ).

fof(f89076,plain,
    ? [A] :
      ( ~ v3_struct_0(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v1_lattice3(A)
      & l1_orders_2(A)
      & ? [B] :
          ( ~ v3_struct_0(B)
          & v2_orders_2(B)
          & v3_orders_2(B)
          & v4_orders_2(B)
          & v1_lattice3(B)
          & l1_orders_2(B)
          & ? [C] :
              ( r2_hidden(C,u1_struct_0(B))
              & ~ m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B))) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f19038]) ).

fof(f89077,plain,
    ( ~ v3_struct_0(sk0_6519)
    & v2_orders_2(sk0_6519)
    & v3_orders_2(sk0_6519)
    & v4_orders_2(sk0_6519)
    & v1_lattice3(sk0_6519)
    & l1_orders_2(sk0_6519)
    & ~ v3_struct_0(sk0_6520)
    & v2_orders_2(sk0_6520)
    & v3_orders_2(sk0_6520)
    & v4_orders_2(sk0_6520)
    & v1_lattice3(sk0_6520)
    & l1_orders_2(sk0_6520)
    & r2_hidden(sk0_6521,u1_struct_0(sk0_6520))
    & ~ m1_subset_1(sk0_6521,u1_struct_0(k1_latsum_1(sk0_6519,sk0_6520))) ),
    inference(skolemization,[status(esa)],[f89076]) ).

fof(f89083,plain,
    l1_orders_2(sk0_6519),
    inference(cnf_transformation,[status(esa)],[f89077]) ).

fof(f89089,plain,
    l1_orders_2(sk0_6520),
    inference(cnf_transformation,[status(esa)],[f89077]) ).

fof(f89090,plain,
    r2_hidden(sk0_6521,u1_struct_0(sk0_6520)),
    inference(cnf_transformation,[status(esa)],[f89077]) ).

fof(f89091,plain,
    ~ m1_subset_1(sk0_6521,u1_struct_0(k1_latsum_1(sk0_6519,sk0_6520))),
    inference(cnf_transformation,[status(esa)],[f89077]) ).

fof(f103458,plain,
    ! [X0,X1,X2] :
      ( r2_hidden(X0,k2_xboole_0(X1,X2))
      | ~ r2_hidden(X0,X2) ),
    inference(destructive_equality_resolution,[status(esa)],[f19138]) ).

fof(f107910,plain,
    ! [X0,X1] :
      ( ~ l1_orders_2(X0)
      | ~ l1_orders_2(X1)
      | ~ v1_orders_2(k1_latsum_1(X0,X1))
      | ~ l1_orders_2(k1_latsum_1(X0,X1))
      | u1_struct_0(k1_latsum_1(X0,X1)) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) ),
    inference(destructive_equality_resolution,[status(esa)],[f89042]) ).

fof(f108184,plain,
    ( spl0_2346
  <=> l1_orders_2(sk0_6520) ),
    introduced(split_symbol_definition) ).

fof(f108186,plain,
    ( ~ l1_orders_2(sk0_6520)
    | spl0_2346 ),
    inference(component_clause,[status(thm)],[f108184]) ).

fof(f108192,plain,
    ( spl0_2348
  <=> l1_orders_2(sk0_6519) ),
    introduced(split_symbol_definition) ).

fof(f108194,plain,
    ( ~ l1_orders_2(sk0_6519)
    | spl0_2348 ),
    inference(component_clause,[status(thm)],[f108192]) ).

fof(f108200,plain,
    ( $false
    | spl0_2348 ),
    inference(forward_subsumption_resolution,[status(thm)],[f108194,f89083]) ).

fof(f108201,plain,
    spl0_2348,
    inference(contradiction_clause,[status(thm)],[f108200]) ).

fof(f108202,plain,
    ( $false
    | spl0_2346 ),
    inference(forward_subsumption_resolution,[status(thm)],[f108186,f89089]) ).

fof(f108203,plain,
    spl0_2346,
    inference(contradiction_clause,[status(thm)],[f108202]) ).

fof(f108214,plain,
    ! [X0] :
      ( ~ l1_orders_2(X0)
      | l1_orders_2(k1_latsum_1(sk0_6519,X0)) ),
    inference(resolution,[status(thm)],[f89023,f89083]) ).

fof(f108248,plain,
    l1_orders_2(k1_latsum_1(sk0_6519,sk0_6520)),
    inference(resolution,[status(thm)],[f108214,f89089]) ).

fof(f108307,plain,
    ! [X0,X1] :
      ( ~ l1_orders_2(X0)
      | ~ l1_orders_2(X1)
      | ~ l1_orders_2(k1_latsum_1(X0,X1))
      | u1_struct_0(k1_latsum_1(X0,X1)) = k2_xboole_0(u1_struct_0(X0),u1_struct_0(X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f107910,f89022]) ).

fof(f108313,plain,
    ( spl0_2357
  <=> u1_struct_0(k1_latsum_1(sk0_6519,sk0_6520)) = k2_xboole_0(u1_struct_0(sk0_6519),u1_struct_0(sk0_6520)) ),
    introduced(split_symbol_definition) ).

fof(f108314,plain,
    ( u1_struct_0(k1_latsum_1(sk0_6519,sk0_6520)) = k2_xboole_0(u1_struct_0(sk0_6519),u1_struct_0(sk0_6520))
    | ~ spl0_2357 ),
    inference(component_clause,[status(thm)],[f108313]) ).

fof(f108316,plain,
    ( ~ l1_orders_2(sk0_6519)
    | ~ l1_orders_2(sk0_6520)
    | u1_struct_0(k1_latsum_1(sk0_6519,sk0_6520)) = k2_xboole_0(u1_struct_0(sk0_6519),u1_struct_0(sk0_6520)) ),
    inference(resolution,[status(thm)],[f108307,f108248]) ).

fof(f108317,plain,
    ( ~ spl0_2348
    | ~ spl0_2346
    | spl0_2357 ),
    inference(split_clause,[status(thm)],[f108316,f108192,f108184,f108313]) ).

fof(f112381,plain,
    ! [X0] : r2_hidden(sk0_6521,k2_xboole_0(X0,u1_struct_0(sk0_6520))),
    inference(resolution,[status(thm)],[f103458,f89090]) ).

fof(f113025,plain,
    ! [X0] : m1_subset_1(sk0_6521,k2_xboole_0(X0,u1_struct_0(sk0_6520))),
    inference(resolution,[status(thm)],[f112381,f20502]) ).

fof(f113035,plain,
    ( m1_subset_1(sk0_6521,u1_struct_0(k1_latsum_1(sk0_6519,sk0_6520)))
    | ~ spl0_2357 ),
    inference(paramodulation,[status(thm)],[f108314,f113025]) ).

fof(f113036,plain,
    ( $false
    | ~ spl0_2357 ),
    inference(forward_subsumption_resolution,[status(thm)],[f113035,f89091]) ).

fof(f113037,plain,
    ~ spl0_2357,
    inference(contradiction_clause,[status(thm)],[f113036]) ).

fof(f113038,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f108201,f108203,f108317,f113037]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13  % Problem  : SEU408+3 : TPTP v8.1.2. Released v3.4.0.
% 0.06/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.34  % Computer : n011.cluster.edu
% 0.10/0.34  % Model    : x86_64 x86_64
% 0.10/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34  % Memory   : 8042.1875MB
% 0.10/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.34  % CPULimit : 300
% 0.10/0.34  % WCLimit  : 300
% 0.10/0.34  % DateTime : Mon Apr 29 19:49:03 EDT 2024
% 0.10/0.34  % CPUTime  : 
% 2.63/2.88  % Drodi V3.6.0
% 26.90/6.04  % Refutation found
% 26.90/6.04  % SZS status Theorem for theBenchmark: Theorem is valid
% 26.90/6.04  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 30.90/6.58  % Elapsed time: 6.171194 seconds
% 30.90/6.58  % CPU time: 28.435842 seconds
% 30.90/6.58  % Total memory used: 5.210 GB
% 30.90/6.58  % Net memory used: 5.184 GB
%------------------------------------------------------------------------------