TSTP Solution File: MGT058+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : MGT058+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n009.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 20:28:51 EDT 2024

% Result   : Theorem 0.15s 0.32s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   88 (  10 unt;   0 def)
%            Number of atoms       :  287 (  32 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  305 ( 106   ~; 119   |;  57   &)
%                                         (  17 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   20 (  18 usr;  11 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-2 aty)
%            Number of variables   :   97 (  87   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X,Y] :
      ( smaller_or_equal(X,Y)
    <=> ( smaller(X,Y)
        | X = Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [X,Y] :
      ( greater_or_equal(X,Y)
    <=> ( greater(X,Y)
        | X = Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [X,Y] :
      ( smaller(X,Y)
    <=> greater(Y,X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [X,Y] :
      ~ ( greater(X,Y)
        & greater(Y,X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [X,Y] :
      ( smaller(X,Y)
      | X = Y
      | greater(X,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [X] :
      ( fragile_position(X)
    <=> ! [T] :
          ( ( smaller_or_equal(age(X,T),sigma)
           => positional_advantage(X,T) )
          & ( greater(age(X,T),sigma)
           => ~ positional_advantage(X,T) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [X] :
      ( robust_position(X)
    <=> ! [T] :
          ( ( smaller_or_equal(age(X,T),tau)
           => ~ positional_advantage(X,T) )
          & ( greater(age(X,T),tau)
           => positional_advantage(X,T) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,conjecture,
    ! [X] :
      ( ( organization(X)
        & ? [T0] : age(X,T0) = zero
        & greater_or_equal(sigma,zero)
        & greater_or_equal(tau,zero) )
     => ~ ( fragile_position(X)
          & robust_position(X) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,negated_conjecture,
    ~ ! [X] :
        ( ( organization(X)
          & ? [T0] : age(X,T0) = zero
          & greater_or_equal(sigma,zero)
          & greater_or_equal(tau,zero) )
       => ~ ( fragile_position(X)
            & robust_position(X) ) ),
    inference(negated_conjecture,[status(cth)],[f9]) ).

fof(f11,plain,
    ! [X,Y] :
      ( ( ~ smaller_or_equal(X,Y)
        | smaller(X,Y)
        | X = Y )
      & ( smaller_or_equal(X,Y)
        | ( ~ smaller(X,Y)
          & X != Y ) ) ),
    inference(NNF_transformation,[status(esa)],[f1]) ).

fof(f12,plain,
    ( ! [X,Y] :
        ( ~ smaller_or_equal(X,Y)
        | smaller(X,Y)
        | X = Y )
    & ! [X,Y] :
        ( smaller_or_equal(X,Y)
        | ( ~ smaller(X,Y)
          & X != Y ) ) ),
    inference(miniscoping,[status(esa)],[f11]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( smaller_or_equal(X0,X1)
      | ~ smaller(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( smaller_or_equal(X0,X1)
      | X0 != X1 ),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f16,plain,
    ! [X,Y] :
      ( ( ~ greater_or_equal(X,Y)
        | greater(X,Y)
        | X = Y )
      & ( greater_or_equal(X,Y)
        | ( ~ greater(X,Y)
          & X != Y ) ) ),
    inference(NNF_transformation,[status(esa)],[f2]) ).

fof(f17,plain,
    ( ! [X,Y] :
        ( ~ greater_or_equal(X,Y)
        | greater(X,Y)
        | X = Y )
    & ! [X,Y] :
        ( greater_or_equal(X,Y)
        | ( ~ greater(X,Y)
          & X != Y ) ) ),
    inference(miniscoping,[status(esa)],[f16]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ~ greater_or_equal(X0,X1)
      | greater(X0,X1)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f21,plain,
    ! [X,Y] :
      ( ( ~ smaller(X,Y)
        | greater(Y,X) )
      & ( smaller(X,Y)
        | ~ greater(Y,X) ) ),
    inference(NNF_transformation,[status(esa)],[f3]) ).

fof(f22,plain,
    ( ! [X,Y] :
        ( ~ smaller(X,Y)
        | greater(Y,X) )
    & ! [X,Y] :
        ( smaller(X,Y)
        | ~ greater(Y,X) ) ),
    inference(miniscoping,[status(esa)],[f21]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ~ smaller(X0,X1)
      | greater(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( smaller(X0,X1)
      | ~ greater(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f25,plain,
    ! [X,Y] :
      ( ~ greater(X,Y)
      | ~ greater(Y,X) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ~ greater(X0,X1)
      | ~ greater(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( smaller(X0,X1)
      | X0 = X1
      | greater(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f31,plain,
    ! [X] :
      ( fragile_position(X)
    <=> ! [T] :
          ( ( ~ smaller_or_equal(age(X,T),sigma)
            | positional_advantage(X,T) )
          & ( ~ greater(age(X,T),sigma)
            | ~ positional_advantage(X,T) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f32,plain,
    ! [X] :
      ( ( ~ fragile_position(X)
        | ! [T] :
            ( ( ~ smaller_or_equal(age(X,T),sigma)
              | positional_advantage(X,T) )
            & ( ~ greater(age(X,T),sigma)
              | ~ positional_advantage(X,T) ) ) )
      & ( fragile_position(X)
        | ? [T] :
            ( ( smaller_or_equal(age(X,T),sigma)
              & ~ positional_advantage(X,T) )
            | ( greater(age(X,T),sigma)
              & positional_advantage(X,T) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f31]) ).

fof(f33,plain,
    ( ! [X] :
        ( ~ fragile_position(X)
        | ( ! [T] :
              ( ~ smaller_or_equal(age(X,T),sigma)
              | positional_advantage(X,T) )
          & ! [T] :
              ( ~ greater(age(X,T),sigma)
              | ~ positional_advantage(X,T) ) ) )
    & ! [X] :
        ( fragile_position(X)
        | ? [T] :
            ( smaller_or_equal(age(X,T),sigma)
            & ~ positional_advantage(X,T) )
        | ? [T] :
            ( greater(age(X,T),sigma)
            & positional_advantage(X,T) ) ) ),
    inference(miniscoping,[status(esa)],[f32]) ).

fof(f34,plain,
    ( ! [X] :
        ( ~ fragile_position(X)
        | ( ! [T] :
              ( ~ smaller_or_equal(age(X,T),sigma)
              | positional_advantage(X,T) )
          & ! [T] :
              ( ~ greater(age(X,T),sigma)
              | ~ positional_advantage(X,T) ) ) )
    & ! [X] :
        ( fragile_position(X)
        | ( smaller_or_equal(age(X,sk0_0(X)),sigma)
          & ~ positional_advantage(X,sk0_0(X)) )
        | ( greater(age(X,sk0_1(X)),sigma)
          & positional_advantage(X,sk0_1(X)) ) ) ),
    inference(skolemization,[status(esa)],[f33]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ~ fragile_position(X0)
      | ~ smaller_or_equal(age(X0,X1),sigma)
      | positional_advantage(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f41,plain,
    ! [X] :
      ( robust_position(X)
    <=> ! [T] :
          ( ( ~ smaller_or_equal(age(X,T),tau)
            | ~ positional_advantage(X,T) )
          & ( ~ greater(age(X,T),tau)
            | positional_advantage(X,T) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f8]) ).

fof(f42,plain,
    ! [X] :
      ( ( ~ robust_position(X)
        | ! [T] :
            ( ( ~ smaller_or_equal(age(X,T),tau)
              | ~ positional_advantage(X,T) )
            & ( ~ greater(age(X,T),tau)
              | positional_advantage(X,T) ) ) )
      & ( robust_position(X)
        | ? [T] :
            ( ( smaller_or_equal(age(X,T),tau)
              & positional_advantage(X,T) )
            | ( greater(age(X,T),tau)
              & ~ positional_advantage(X,T) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f41]) ).

fof(f43,plain,
    ( ! [X] :
        ( ~ robust_position(X)
        | ( ! [T] :
              ( ~ smaller_or_equal(age(X,T),tau)
              | ~ positional_advantage(X,T) )
          & ! [T] :
              ( ~ greater(age(X,T),tau)
              | positional_advantage(X,T) ) ) )
    & ! [X] :
        ( robust_position(X)
        | ? [T] :
            ( smaller_or_equal(age(X,T),tau)
            & positional_advantage(X,T) )
        | ? [T] :
            ( greater(age(X,T),tau)
            & ~ positional_advantage(X,T) ) ) ),
    inference(miniscoping,[status(esa)],[f42]) ).

fof(f44,plain,
    ( ! [X] :
        ( ~ robust_position(X)
        | ( ! [T] :
              ( ~ smaller_or_equal(age(X,T),tau)
              | ~ positional_advantage(X,T) )
          & ! [T] :
              ( ~ greater(age(X,T),tau)
              | positional_advantage(X,T) ) ) )
    & ! [X] :
        ( robust_position(X)
        | ( smaller_or_equal(age(X,sk0_2(X)),tau)
          & positional_advantage(X,sk0_2(X)) )
        | ( greater(age(X,sk0_3(X)),tau)
          & ~ positional_advantage(X,sk0_3(X)) ) ) ),
    inference(skolemization,[status(esa)],[f43]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ~ robust_position(X0)
      | ~ smaller_or_equal(age(X0,X1),tau)
      | ~ positional_advantage(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f44]) ).

fof(f51,plain,
    ? [X] :
      ( organization(X)
      & ? [T0] : age(X,T0) = zero
      & greater_or_equal(sigma,zero)
      & greater_or_equal(tau,zero)
      & fragile_position(X)
      & robust_position(X) ),
    inference(pre_NNF_transformation,[status(esa)],[f10]) ).

fof(f52,plain,
    ( organization(sk0_4)
    & age(sk0_4,sk0_5) = zero
    & greater_or_equal(sigma,zero)
    & greater_or_equal(tau,zero)
    & fragile_position(sk0_4)
    & robust_position(sk0_4) ),
    inference(skolemization,[status(esa)],[f51]) ).

fof(f54,plain,
    age(sk0_4,sk0_5) = zero,
    inference(cnf_transformation,[status(esa)],[f52]) ).

fof(f55,plain,
    greater_or_equal(sigma,zero),
    inference(cnf_transformation,[status(esa)],[f52]) ).

fof(f56,plain,
    greater_or_equal(tau,zero),
    inference(cnf_transformation,[status(esa)],[f52]) ).

fof(f57,plain,
    fragile_position(sk0_4),
    inference(cnf_transformation,[status(esa)],[f52]) ).

fof(f58,plain,
    robust_position(sk0_4),
    inference(cnf_transformation,[status(esa)],[f52]) ).

fof(f59,plain,
    ! [X0] : smaller_or_equal(X0,X0),
    inference(destructive_equality_resolution,[status(esa)],[f15]) ).

fof(f61,plain,
    ( spl0_0
  <=> greater(tau,zero) ),
    introduced(split_symbol_definition) ).

fof(f62,plain,
    ( greater(tau,zero)
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f61]) ).

fof(f64,plain,
    ( spl0_1
  <=> tau = zero ),
    introduced(split_symbol_definition) ).

fof(f65,plain,
    ( tau = zero
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f64]) ).

fof(f67,plain,
    ( greater(tau,zero)
    | tau = zero ),
    inference(resolution,[status(thm)],[f18,f56]) ).

fof(f68,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f67,f61,f64]) ).

fof(f69,plain,
    ( spl0_2
  <=> greater(sigma,zero) ),
    introduced(split_symbol_definition) ).

fof(f70,plain,
    ( greater(sigma,zero)
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f69]) ).

fof(f72,plain,
    ( spl0_3
  <=> sigma = zero ),
    introduced(split_symbol_definition) ).

fof(f73,plain,
    ( sigma = zero
    | ~ spl0_3 ),
    inference(component_clause,[status(thm)],[f72]) ).

fof(f75,plain,
    ( greater(sigma,zero)
    | sigma = zero ),
    inference(resolution,[status(thm)],[f18,f55]) ).

fof(f76,plain,
    ( spl0_2
    | spl0_3 ),
    inference(split_clause,[status(thm)],[f75,f69,f72]) ).

fof(f77,plain,
    ( spl0_4
  <=> fragile_position(sk0_4) ),
    introduced(split_symbol_definition) ).

fof(f79,plain,
    ( ~ fragile_position(sk0_4)
    | spl0_4 ),
    inference(component_clause,[status(thm)],[f77]) ).

fof(f80,plain,
    ( spl0_5
  <=> smaller_or_equal(zero,sigma) ),
    introduced(split_symbol_definition) ).

fof(f83,plain,
    ( spl0_6
  <=> positional_advantage(sk0_4,sk0_5) ),
    introduced(split_symbol_definition) ).

fof(f86,plain,
    ( ~ fragile_position(sk0_4)
    | ~ smaller_or_equal(zero,sigma)
    | positional_advantage(sk0_4,sk0_5) ),
    inference(paramodulation,[status(thm)],[f54,f35]) ).

fof(f87,plain,
    ( ~ spl0_4
    | ~ spl0_5
    | spl0_6 ),
    inference(split_clause,[status(thm)],[f86,f77,f80,f83]) ).

fof(f93,plain,
    ( spl0_8
  <=> robust_position(sk0_4) ),
    introduced(split_symbol_definition) ).

fof(f95,plain,
    ( ~ robust_position(sk0_4)
    | spl0_8 ),
    inference(component_clause,[status(thm)],[f93]) ).

fof(f96,plain,
    ( spl0_9
  <=> smaller_or_equal(zero,tau) ),
    introduced(split_symbol_definition) ).

fof(f98,plain,
    ( ~ smaller_or_equal(zero,tau)
    | spl0_9 ),
    inference(component_clause,[status(thm)],[f96]) ).

fof(f99,plain,
    ( ~ robust_position(sk0_4)
    | ~ smaller_or_equal(zero,tau)
    | ~ positional_advantage(sk0_4,sk0_5) ),
    inference(paramodulation,[status(thm)],[f54,f45]) ).

fof(f100,plain,
    ( ~ spl0_8
    | ~ spl0_9
    | ~ spl0_6 ),
    inference(split_clause,[status(thm)],[f99,f93,f96,f83]) ).

fof(f101,plain,
    ( $false
    | spl0_8 ),
    inference(forward_subsumption_resolution,[status(thm)],[f95,f58]) ).

fof(f102,plain,
    spl0_8,
    inference(contradiction_clause,[status(thm)],[f101]) ).

fof(f111,plain,
    ! [X0,X1] :
      ( smaller(X0,X1)
      | X0 = X1
      | smaller(X1,X0) ),
    inference(resolution,[status(thm)],[f30,f24]) ).

fof(f114,plain,
    ! [X0,X1] :
      ( X0 = X1
      | smaller(X1,X0)
      | smaller_or_equal(X0,X1) ),
    inference(resolution,[status(thm)],[f111,f14]) ).

fof(f119,plain,
    ! [X0,X1] :
      ( X0 = X1
      | smaller_or_equal(X0,X1)
      | greater(X0,X1) ),
    inference(resolution,[status(thm)],[f114,f23]) ).

fof(f123,plain,
    ! [X0,X1] :
      ( X0 = X1
      | smaller_or_equal(X0,X1)
      | ~ greater(X1,X0) ),
    inference(resolution,[status(thm)],[f119,f26]) ).

fof(f157,plain,
    ( zero = sigma
    | smaller_or_equal(zero,sigma)
    | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f70,f123]) ).

fof(f158,plain,
    ( spl0_3
    | spl0_5
    | ~ spl0_2 ),
    inference(split_clause,[status(thm)],[f157,f72,f80,f69]) ).

fof(f162,plain,
    ( $false
    | spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f79,f57]) ).

fof(f163,plain,
    spl0_4,
    inference(contradiction_clause,[status(thm)],[f162]) ).

fof(f164,plain,
    ( age(sk0_4,sk0_5) = sigma
    | ~ spl0_3 ),
    inference(backward_demodulation,[status(thm)],[f73,f54]) ).

fof(f189,plain,
    ( spl0_14
  <=> smaller_or_equal(sigma,sigma) ),
    introduced(split_symbol_definition) ).

fof(f191,plain,
    ( ~ smaller_or_equal(sigma,sigma)
    | spl0_14 ),
    inference(component_clause,[status(thm)],[f189]) ).

fof(f204,plain,
    ( ~ fragile_position(sk0_4)
    | ~ smaller_or_equal(sigma,sigma)
    | positional_advantage(sk0_4,sk0_5)
    | ~ spl0_3 ),
    inference(paramodulation,[status(thm)],[f164,f35]) ).

fof(f205,plain,
    ( ~ spl0_4
    | ~ spl0_14
    | spl0_6
    | ~ spl0_3 ),
    inference(split_clause,[status(thm)],[f204,f77,f189,f83,f72]) ).

fof(f206,plain,
    ( $false
    | spl0_14 ),
    inference(forward_subsumption_resolution,[status(thm)],[f191,f59]) ).

fof(f207,plain,
    spl0_14,
    inference(contradiction_clause,[status(thm)],[f206]) ).

fof(f219,plain,
    ( ~ smaller_or_equal(tau,tau)
    | ~ spl0_1
    | spl0_9 ),
    inference(backward_demodulation,[status(thm)],[f65,f98]) ).

fof(f220,plain,
    ( $false
    | ~ spl0_1
    | spl0_9 ),
    inference(forward_subsumption_resolution,[status(thm)],[f219,f59]) ).

fof(f221,plain,
    ( ~ spl0_1
    | spl0_9 ),
    inference(contradiction_clause,[status(thm)],[f220]) ).

fof(f245,plain,
    ( zero = tau
    | smaller_or_equal(zero,tau)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f62,f123]) ).

fof(f246,plain,
    ( spl0_1
    | spl0_9
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f245,f64,f96,f61]) ).

fof(f250,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f68,f76,f87,f100,f102,f158,f163,f205,f207,f221,f246]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10  % Problem  : MGT058+1 : TPTP v8.1.2. Released v2.4.0.
% 0.08/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31  % Computer : n009.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 : Mon Apr 29 23:34:55 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 0.15/0.32  % Drodi V3.6.0
% 0.15/0.32  % Refutation found
% 0.15/0.32  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.32  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.33  % Elapsed time: 0.016931 seconds
% 0.15/0.33  % CPU time: 0.037479 seconds
% 0.15/0.33  % Total memory used: 15.044 MB
% 0.15/0.33  % Net memory used: 14.977 MB
%------------------------------------------------------------------------------