TSTP Solution File: SWV370+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SWV370+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n015.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 20:46:52 EDT 2024

% Result   : Theorem 0.20s 0.38s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   70 (   5 unt;   0 def)
%            Number of atoms       :  193 (  20 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  199 (  76   ~;  87   |;  20   &)
%                                         (  13 <=>;   2  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :   10 (   8 usr;   6 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-3 aty)
%            Number of variables   :  148 ( 130   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f9,axiom,
    ! [U,V,W] :
      ( contains_pq(insert_pq(U,V),W)
    <=> ( contains_pq(U,W)
        | V = W ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f21,axiom,
    ! [U,V,W,X] :
      ( contains_slb(insert_slb(U,pair(V,X)),W)
    <=> ( contains_slb(U,W)
        | V = W ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f39,axiom,
    ! [U,V,W,X] :
      ( contains_cpq(triple(U,V,W),X)
    <=> contains_slb(V,X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f55,axiom,
    ! [U,V,W,X,Y] : i(triple(U,insert_slb(V,pair(X,Y)),W)) = insert_pq(i(triple(U,V,W)),X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f63,conjecture,
    ! [U] :
      ( ! [V,W,X] :
          ( contains_cpq(triple(V,U,W),X)
        <=> contains_pq(i(triple(V,U,W)),X) )
     => ! [Y,Z,X1,X2,X3] :
          ( contains_cpq(triple(Y,insert_slb(U,pair(X1,X2)),Z),X3)
        <=> contains_pq(i(triple(Y,insert_slb(U,pair(X1,X2)),Z)),X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f64,negated_conjecture,
    ~ ! [U] :
        ( ! [V,W,X] :
            ( contains_cpq(triple(V,U,W),X)
          <=> contains_pq(i(triple(V,U,W)),X) )
       => ! [Y,Z,X1,X2,X3] :
            ( contains_cpq(triple(Y,insert_slb(U,pair(X1,X2)),Z),X3)
          <=> contains_pq(i(triple(Y,insert_slb(U,pair(X1,X2)),Z)),X3) ) ),
    inference(negated_conjecture,[status(cth)],[f63]) ).

fof(f79,plain,
    ! [U,V,W] :
      ( ( ~ contains_pq(insert_pq(U,V),W)
        | contains_pq(U,W)
        | V = W )
      & ( contains_pq(insert_pq(U,V),W)
        | ( ~ contains_pq(U,W)
          & V != W ) ) ),
    inference(NNF_transformation,[status(esa)],[f9]) ).

fof(f80,plain,
    ( ! [U,V,W] :
        ( ~ contains_pq(insert_pq(U,V),W)
        | contains_pq(U,W)
        | V = W )
    & ! [U,V,W] :
        ( contains_pq(insert_pq(U,V),W)
        | ( ~ contains_pq(U,W)
          & V != W ) ) ),
    inference(miniscoping,[status(esa)],[f79]) ).

fof(f81,plain,
    ! [X0,X1,X2] :
      ( ~ contains_pq(insert_pq(X0,X1),X2)
      | contains_pq(X0,X2)
      | X1 = X2 ),
    inference(cnf_transformation,[status(esa)],[f80]) ).

fof(f82,plain,
    ! [X0,X1,X2] :
      ( contains_pq(insert_pq(X0,X1),X2)
      | ~ contains_pq(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f80]) ).

fof(f83,plain,
    ! [X0,X1,X2] :
      ( contains_pq(insert_pq(X0,X1),X2)
      | X1 != X2 ),
    inference(cnf_transformation,[status(esa)],[f80]) ).

fof(f106,plain,
    ! [U,V,W,X] :
      ( ( ~ contains_slb(insert_slb(U,pair(V,X)),W)
        | contains_slb(U,W)
        | V = W )
      & ( contains_slb(insert_slb(U,pair(V,X)),W)
        | ( ~ contains_slb(U,W)
          & V != W ) ) ),
    inference(NNF_transformation,[status(esa)],[f21]) ).

fof(f107,plain,
    ( ! [U,V,W] :
        ( ! [X] : ~ contains_slb(insert_slb(U,pair(V,X)),W)
        | contains_slb(U,W)
        | V = W )
    & ! [U,V,W] :
        ( ! [X] : contains_slb(insert_slb(U,pair(V,X)),W)
        | ( ~ contains_slb(U,W)
          & V != W ) ) ),
    inference(miniscoping,[status(esa)],[f106]) ).

fof(f108,plain,
    ! [X0,X1,X2,X3] :
      ( ~ contains_slb(insert_slb(X0,pair(X1,X2)),X3)
      | contains_slb(X0,X3)
      | X1 = X3 ),
    inference(cnf_transformation,[status(esa)],[f107]) ).

fof(f109,plain,
    ! [X0,X1,X2,X3] :
      ( contains_slb(insert_slb(X0,pair(X1,X2)),X3)
      | ~ contains_slb(X0,X3) ),
    inference(cnf_transformation,[status(esa)],[f107]) ).

fof(f110,plain,
    ! [X0,X1,X2,X3] :
      ( contains_slb(insert_slb(X0,pair(X1,X2)),X3)
      | X1 != X3 ),
    inference(cnf_transformation,[status(esa)],[f107]) ).

fof(f155,plain,
    ! [U,V,W,X] :
      ( ( ~ contains_cpq(triple(U,V,W),X)
        | contains_slb(V,X) )
      & ( contains_cpq(triple(U,V,W),X)
        | ~ contains_slb(V,X) ) ),
    inference(NNF_transformation,[status(esa)],[f39]) ).

fof(f156,plain,
    ( ! [V,X] :
        ( ! [U,W] : ~ contains_cpq(triple(U,V,W),X)
        | contains_slb(V,X) )
    & ! [V,X] :
        ( ! [U,W] : contains_cpq(triple(U,V,W),X)
        | ~ contains_slb(V,X) ) ),
    inference(miniscoping,[status(esa)],[f155]) ).

fof(f157,plain,
    ! [X0,X1,X2,X3] :
      ( ~ contains_cpq(triple(X0,X1,X2),X3)
      | contains_slb(X1,X3) ),
    inference(cnf_transformation,[status(esa)],[f156]) ).

fof(f158,plain,
    ! [X0,X1,X2,X3] :
      ( contains_cpq(triple(X0,X1,X2),X3)
      | ~ contains_slb(X1,X3) ),
    inference(cnf_transformation,[status(esa)],[f156]) ).

fof(f193,plain,
    ! [X0,X1,X2,X3,X4] : i(triple(X0,insert_slb(X1,pair(X2,X3)),X4)) = insert_pq(i(triple(X0,X1,X4)),X2),
    inference(cnf_transformation,[status(esa)],[f55]) ).

fof(f229,plain,
    ? [U] :
      ( ! [V,W,X] :
          ( contains_cpq(triple(V,U,W),X)
        <=> contains_pq(i(triple(V,U,W)),X) )
      & ? [Y,Z,X1,X2,X3] :
          ( contains_cpq(triple(Y,insert_slb(U,pair(X1,X2)),Z),X3)
        <~> contains_pq(i(triple(Y,insert_slb(U,pair(X1,X2)),Z)),X3) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f64]) ).

fof(f230,plain,
    ? [U] :
      ( ! [V,W,X] :
          ( ( ~ contains_cpq(triple(V,U,W),X)
            | contains_pq(i(triple(V,U,W)),X) )
          & ( contains_cpq(triple(V,U,W),X)
            | ~ contains_pq(i(triple(V,U,W)),X) ) )
      & ? [Y,Z,X1,X2,X3] :
          ( ( contains_cpq(triple(Y,insert_slb(U,pair(X1,X2)),Z),X3)
            | contains_pq(i(triple(Y,insert_slb(U,pair(X1,X2)),Z)),X3) )
          & ( ~ contains_cpq(triple(Y,insert_slb(U,pair(X1,X2)),Z),X3)
            | ~ contains_pq(i(triple(Y,insert_slb(U,pair(X1,X2)),Z)),X3) ) ) ),
    inference(NNF_transformation,[status(esa)],[f229]) ).

fof(f231,plain,
    ? [U] :
      ( ! [V,W,X] :
          ( ~ contains_cpq(triple(V,U,W),X)
          | contains_pq(i(triple(V,U,W)),X) )
      & ! [V,W,X] :
          ( contains_cpq(triple(V,U,W),X)
          | ~ contains_pq(i(triple(V,U,W)),X) )
      & ? [Y,Z,X1,X2,X3] :
          ( ( contains_cpq(triple(Y,insert_slb(U,pair(X1,X2)),Z),X3)
            | contains_pq(i(triple(Y,insert_slb(U,pair(X1,X2)),Z)),X3) )
          & ( ~ contains_cpq(triple(Y,insert_slb(U,pair(X1,X2)),Z),X3)
            | ~ contains_pq(i(triple(Y,insert_slb(U,pair(X1,X2)),Z)),X3) ) ) ),
    inference(miniscoping,[status(esa)],[f230]) ).

fof(f232,plain,
    ( ! [V,W,X] :
        ( ~ contains_cpq(triple(V,sk0_4,W),X)
        | contains_pq(i(triple(V,sk0_4,W)),X) )
    & ! [V,W,X] :
        ( contains_cpq(triple(V,sk0_4,W),X)
        | ~ contains_pq(i(triple(V,sk0_4,W)),X) )
    & ( contains_cpq(triple(sk0_5,insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_6),sk0_9)
      | contains_pq(i(triple(sk0_5,insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_6)),sk0_9) )
    & ( ~ contains_cpq(triple(sk0_5,insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_6),sk0_9)
      | ~ contains_pq(i(triple(sk0_5,insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_6)),sk0_9) ) ),
    inference(skolemization,[status(esa)],[f231]) ).

fof(f233,plain,
    ! [X0,X1,X2] :
      ( ~ contains_cpq(triple(X0,sk0_4,X1),X2)
      | contains_pq(i(triple(X0,sk0_4,X1)),X2) ),
    inference(cnf_transformation,[status(esa)],[f232]) ).

fof(f234,plain,
    ! [X0,X1,X2] :
      ( contains_cpq(triple(X0,sk0_4,X1),X2)
      | ~ contains_pq(i(triple(X0,sk0_4,X1)),X2) ),
    inference(cnf_transformation,[status(esa)],[f232]) ).

fof(f235,plain,
    ( contains_cpq(triple(sk0_5,insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_6),sk0_9)
    | contains_pq(i(triple(sk0_5,insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_6)),sk0_9) ),
    inference(cnf_transformation,[status(esa)],[f232]) ).

fof(f236,plain,
    ( ~ contains_cpq(triple(sk0_5,insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_6),sk0_9)
    | ~ contains_pq(i(triple(sk0_5,insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_6)),sk0_9) ),
    inference(cnf_transformation,[status(esa)],[f232]) ).

fof(f237,plain,
    ( spl0_0
  <=> contains_cpq(triple(sk0_5,insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_6),sk0_9) ),
    introduced(split_symbol_definition) ).

fof(f238,plain,
    ( contains_cpq(triple(sk0_5,insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_6),sk0_9)
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f237]) ).

fof(f239,plain,
    ( ~ contains_cpq(triple(sk0_5,insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_6),sk0_9)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f237]) ).

fof(f240,plain,
    ( spl0_1
  <=> contains_pq(i(triple(sk0_5,insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_6)),sk0_9) ),
    introduced(split_symbol_definition) ).

fof(f241,plain,
    ( contains_pq(i(triple(sk0_5,insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_6)),sk0_9)
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f240]) ).

fof(f242,plain,
    ( ~ contains_pq(i(triple(sk0_5,insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_6)),sk0_9)
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f240]) ).

fof(f243,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f235,f237,f240]) ).

fof(f244,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f236,f237,f240]) ).

fof(f246,plain,
    ! [X0,X1] : contains_pq(insert_pq(X0,X1),X1),
    inference(destructive_equality_resolution,[status(esa)],[f83]) ).

fof(f247,plain,
    ! [X0,X1,X2] : contains_slb(insert_slb(X0,pair(X1,X2)),X1),
    inference(destructive_equality_resolution,[status(esa)],[f110]) ).

fof(f250,plain,
    ( contains_pq(insert_pq(i(triple(sk0_5,sk0_4,sk0_6)),sk0_7),sk0_9)
    | ~ spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f193,f241]) ).

fof(f258,plain,
    ( spl0_2
  <=> contains_pq(i(triple(sk0_5,sk0_4,sk0_6)),sk0_9) ),
    introduced(split_symbol_definition) ).

fof(f259,plain,
    ( contains_pq(i(triple(sk0_5,sk0_4,sk0_6)),sk0_9)
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f258]) ).

fof(f261,plain,
    ( spl0_3
  <=> sk0_7 = sk0_9 ),
    introduced(split_symbol_definition) ).

fof(f262,plain,
    ( sk0_7 = sk0_9
    | ~ spl0_3 ),
    inference(component_clause,[status(thm)],[f261]) ).

fof(f264,plain,
    ( contains_pq(i(triple(sk0_5,sk0_4,sk0_6)),sk0_9)
    | sk0_7 = sk0_9
    | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f250,f81]) ).

fof(f265,plain,
    ( spl0_2
    | spl0_3
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f264,f258,f261,f240]) ).

fof(f267,plain,
    ( contains_cpq(triple(sk0_5,sk0_4,sk0_6),sk0_9)
    | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f259,f234]) ).

fof(f269,plain,
    ( contains_slb(sk0_4,sk0_9)
    | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f267,f157]) ).

fof(f271,plain,
    ( ~ contains_slb(insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_9)
    | spl0_0 ),
    inference(resolution,[status(thm)],[f239,f158]) ).

fof(f392,plain,
    ( ~ contains_slb(sk0_4,sk0_9)
    | spl0_0 ),
    inference(resolution,[status(thm)],[f109,f271]) ).

fof(f393,plain,
    ( $false
    | ~ spl0_2
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f392,f269]) ).

fof(f394,plain,
    ( ~ spl0_2
    | spl0_0 ),
    inference(contradiction_clause,[status(thm)],[f393]) ).

fof(f395,plain,
    ( ~ contains_pq(insert_pq(i(triple(sk0_5,sk0_4,sk0_6)),sk0_7),sk0_9)
    | spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f193,f242]) ).

fof(f396,plain,
    ( ~ contains_pq(i(triple(sk0_5,sk0_4,sk0_6)),sk0_9)
    | spl0_1 ),
    inference(resolution,[status(thm)],[f395,f82]) ).

fof(f397,plain,
    ( ~ contains_cpq(triple(sk0_5,sk0_4,sk0_6),sk0_9)
    | spl0_1 ),
    inference(resolution,[status(thm)],[f396,f233]) ).

fof(f399,plain,
    ( ~ contains_slb(sk0_4,sk0_9)
    | spl0_1 ),
    inference(resolution,[status(thm)],[f397,f158]) ).

fof(f401,plain,
    ( contains_slb(insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_9)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f238,f157]) ).

fof(f402,plain,
    ( spl0_7
  <=> contains_slb(sk0_4,sk0_9) ),
    introduced(split_symbol_definition) ).

fof(f403,plain,
    ( contains_slb(sk0_4,sk0_9)
    | ~ spl0_7 ),
    inference(component_clause,[status(thm)],[f402]) ).

fof(f405,plain,
    ( contains_slb(sk0_4,sk0_9)
    | sk0_7 = sk0_9
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f401,f108]) ).

fof(f406,plain,
    ( spl0_7
    | spl0_3
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f405,f402,f261,f237]) ).

fof(f410,plain,
    ( ~ contains_slb(insert_slb(sk0_4,pair(sk0_7,sk0_8)),sk0_7)
    | ~ spl0_3
    | spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f262,f271]) ).

fof(f411,plain,
    ( $false
    | ~ spl0_3
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f410,f247]) ).

fof(f412,plain,
    ( ~ spl0_3
    | spl0_0 ),
    inference(contradiction_clause,[status(thm)],[f411]) ).

fof(f413,plain,
    ( $false
    | ~ spl0_7
    | spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f399,f403]) ).

fof(f414,plain,
    ( ~ spl0_7
    | spl0_1 ),
    inference(contradiction_clause,[status(thm)],[f413]) ).

fof(f421,plain,
    ( ~ contains_pq(insert_pq(i(triple(sk0_5,sk0_4,sk0_6)),sk0_7),sk0_7)
    | ~ spl0_3
    | spl0_1 ),
    inference(backward_demodulation,[status(thm)],[f262,f395]) ).

fof(f422,plain,
    ( $false
    | ~ spl0_3
    | spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f421,f246]) ).

fof(f423,plain,
    ( ~ spl0_3
    | spl0_1 ),
    inference(contradiction_clause,[status(thm)],[f422]) ).

fof(f424,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f243,f244,f265,f394,f406,f412,f414,f423]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWV370+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n015.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Tue Apr 30 01:02:02 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.20/0.36  % Drodi V3.6.0
% 0.20/0.38  % Refutation found
% 0.20/0.38  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.38  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.40  % Elapsed time: 0.042457 seconds
% 0.20/0.40  % CPU time: 0.192979 seconds
% 0.20/0.40  % Total memory used: 37.237 MB
% 0.20/0.40  % Net memory used: 37.033 MB
%------------------------------------------------------------------------------