TSTP Solution File: SWC106-1 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SWC106-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n010.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 12:39:16 EDT 2023

% Result   : Unsatisfiable 0.12s 0.35s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   72 (   9 unt;   0 def)
%            Number of atoms       :  181 (  26 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  207 (  98   ~;  98   |;   0   &)
%                                         (  11 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   17 (  15 usr;  12 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :   31 (;  31   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f8,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f85,axiom,
    ! [U,V] :
      ( ~ ssList(U)
      | ~ ssList(V)
      | ssList(app(V,U)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f86,axiom,
    ! [U,V] :
      ( ~ ssItem(U)
      | ~ ssList(V)
      | ssList(cons(U,V)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f99,axiom,
    ! [U,V] :
      ( cons(U,V) != V
      | ~ ssItem(U)
      | ~ ssList(V) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f100,axiom,
    ! [U,V] :
      ( ~ ssList(U)
      | ~ ssList(V)
      | neq(V,U)
      | V = U ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f143,axiom,
    ! [U,V,W] :
      ( app(U,V) != W
      | ~ ssList(U)
      | ~ ssList(V)
      | ~ ssList(W)
      | rearsegP(W,V) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f190,negated_conjecture,
    sk2 = sk4,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f191,negated_conjecture,
    sk1 = sk3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f192,negated_conjecture,
    ( neq(sk2,nil)
    | neq(sk2,nil) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f199,negated_conjecture,
    ( ssItem(sk5)
    | ~ neq(sk4,nil) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f200,negated_conjecture,
    ( ssList(sk6)
    | ~ neq(sk4,nil) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f201,negated_conjecture,
    ( cons(sk5,nil) = sk3
    | ~ neq(sk4,nil) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f202,negated_conjecture,
    ( app(sk6,cons(sk5,nil)) = sk4
    | ~ neq(sk4,nil) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f203,negated_conjecture,
    ( ~ neq(sk1,nil)
    | ~ rearsegP(sk2,sk1)
    | ~ neq(sk4,nil) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f211,plain,
    ssList(nil),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f289,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | ssList(app(X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f85]) ).

fof(f290,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | ssList(cons(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f86]) ).

fof(f304,plain,
    ! [V] :
      ( ! [U] :
          ( cons(U,V) != V
          | ~ ssItem(U) )
      | ~ ssList(V) ),
    inference(miniscoping,[status(esa)],[f99]) ).

fof(f305,plain,
    ! [X0,X1] :
      ( cons(X0,X1) != X1
      | ~ ssItem(X0)
      | ~ ssList(X1) ),
    inference(cnf_transformation,[status(esa)],[f304]) ).

fof(f306,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | neq(X1,X0)
      | X1 = X0 ),
    inference(cnf_transformation,[status(esa)],[f100]) ).

fof(f361,plain,
    ! [V,W] :
      ( ! [U] :
          ( app(U,V) != W
          | ~ ssList(U) )
      | ~ ssList(V)
      | ~ ssList(W)
      | rearsegP(W,V) ),
    inference(miniscoping,[status(esa)],[f143]) ).

fof(f362,plain,
    ! [X0,X1,X2] :
      ( app(X0,X1) != X2
      | ~ ssList(X0)
      | ~ ssList(X1)
      | ~ ssList(X2)
      | rearsegP(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f361]) ).

fof(f438,plain,
    sk2 = sk4,
    inference(cnf_transformation,[status(esa)],[f190]) ).

fof(f439,plain,
    sk1 = sk3,
    inference(cnf_transformation,[status(esa)],[f191]) ).

fof(f440,plain,
    ( neq(sk2,nil)
    | neq(sk2,nil) ),
    inference(cnf_transformation,[status(esa)],[f192]) ).

fof(f447,plain,
    ( ssItem(sk5)
    | ~ neq(sk4,nil) ),
    inference(cnf_transformation,[status(esa)],[f199]) ).

fof(f448,plain,
    ( ssList(sk6)
    | ~ neq(sk4,nil) ),
    inference(cnf_transformation,[status(esa)],[f200]) ).

fof(f449,plain,
    ( cons(sk5,nil) = sk3
    | ~ neq(sk4,nil) ),
    inference(cnf_transformation,[status(esa)],[f201]) ).

fof(f450,plain,
    ( app(sk6,cons(sk5,nil)) = sk4
    | ~ neq(sk4,nil) ),
    inference(cnf_transformation,[status(esa)],[f202]) ).

fof(f451,plain,
    ( ~ neq(sk1,nil)
    | ~ rearsegP(sk2,sk1)
    | ~ neq(sk4,nil) ),
    inference(cnf_transformation,[status(esa)],[f203]) ).

fof(f459,plain,
    ( spl0_2
  <=> neq(sk2,nil) ),
    introduced(split_symbol_definition) ).

fof(f460,plain,
    ( neq(sk2,nil)
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f459]) ).

fof(f462,plain,
    spl0_2,
    inference(split_clause,[status(thm)],[f440,f459]) ).

fof(f463,plain,
    ( spl0_3
  <=> neq(sk4,nil) ),
    introduced(split_symbol_definition) ).

fof(f465,plain,
    ( ~ neq(sk4,nil)
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f463]) ).

fof(f467,plain,
    ( spl0_4
  <=> ssItem(sk5) ),
    introduced(split_symbol_definition) ).

fof(f471,plain,
    ( spl0_5
  <=> ssList(sk6) ),
    introduced(split_symbol_definition) ).

fof(f475,plain,
    ( spl0_6
  <=> cons(sk5,nil) = sk3 ),
    introduced(split_symbol_definition) ).

fof(f476,plain,
    ( cons(sk5,nil) = sk3
    | ~ spl0_6 ),
    inference(component_clause,[status(thm)],[f475]) ).

fof(f479,plain,
    ( spl0_7
  <=> app(sk6,cons(sk5,nil)) = sk4 ),
    introduced(split_symbol_definition) ).

fof(f480,plain,
    ( app(sk6,cons(sk5,nil)) = sk4
    | ~ spl0_7 ),
    inference(component_clause,[status(thm)],[f479]) ).

fof(f483,plain,
    ( spl0_8
  <=> neq(sk1,nil) ),
    introduced(split_symbol_definition) ).

fof(f485,plain,
    ( ~ neq(sk1,nil)
    | spl0_8 ),
    inference(component_clause,[status(thm)],[f483]) ).

fof(f486,plain,
    ( spl0_9
  <=> rearsegP(sk2,sk1) ),
    introduced(split_symbol_definition) ).

fof(f490,plain,
    ( spl0_4
    | ~ spl0_3 ),
    inference(split_clause,[status(thm)],[f447,f467,f463]) ).

fof(f491,plain,
    ( spl0_5
    | ~ spl0_3 ),
    inference(split_clause,[status(thm)],[f448,f471,f463]) ).

fof(f492,plain,
    ( spl0_6
    | ~ spl0_3 ),
    inference(split_clause,[status(thm)],[f449,f475,f463]) ).

fof(f493,plain,
    ( spl0_7
    | ~ spl0_3 ),
    inference(split_clause,[status(thm)],[f450,f479,f463]) ).

fof(f494,plain,
    ( ~ spl0_8
    | ~ spl0_9
    | ~ spl0_3 ),
    inference(split_clause,[status(thm)],[f451,f483,f486,f463]) ).

fof(f509,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | ~ ssList(app(X0,X1))
      | rearsegP(app(X0,X1),X1) ),
    inference(destructive_equality_resolution,[status(esa)],[f362]) ).

fof(f526,plain,
    ( spl0_10
  <=> ssList(nil) ),
    introduced(split_symbol_definition) ).

fof(f528,plain,
    ( ~ ssList(nil)
    | spl0_10 ),
    inference(component_clause,[status(thm)],[f526]) ).

fof(f536,plain,
    ( $false
    | spl0_10 ),
    inference(forward_subsumption_resolution,[status(thm)],[f528,f211]) ).

fof(f537,plain,
    spl0_10,
    inference(contradiction_clause,[status(thm)],[f536]) ).

fof(f538,plain,
    ( ~ neq(sk2,nil)
    | spl0_3 ),
    inference(forward_demodulation,[status(thm)],[f438,f465]) ).

fof(f539,plain,
    ( $false
    | spl0_3
    | ~ spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f460,f538]) ).

fof(f540,plain,
    ( spl0_3
    | ~ spl0_2 ),
    inference(contradiction_clause,[status(thm)],[f539]) ).

fof(f541,plain,
    ( cons(sk5,nil) = sk1
    | ~ spl0_6 ),
    inference(forward_demodulation,[status(thm)],[f439,f476]) ).

fof(f542,plain,
    ( app(sk6,cons(sk5,nil)) = sk2
    | ~ spl0_7 ),
    inference(forward_demodulation,[status(thm)],[f438,f480]) ).

fof(f544,plain,
    ( spl0_12
  <=> ssList(sk1) ),
    introduced(split_symbol_definition) ).

fof(f547,plain,
    ( ~ ssItem(sk5)
    | ~ ssList(nil)
    | ssList(sk1)
    | ~ spl0_6 ),
    inference(paramodulation,[status(thm)],[f541,f290]) ).

fof(f548,plain,
    ( ~ spl0_4
    | ~ spl0_10
    | spl0_12
    | ~ spl0_6 ),
    inference(split_clause,[status(thm)],[f547,f467,f526,f544,f475]) ).

fof(f549,plain,
    ( spl0_13
  <=> sk1 = nil ),
    introduced(split_symbol_definition) ).

fof(f552,plain,
    ( sk1 != nil
    | ~ ssItem(sk5)
    | ~ ssList(nil)
    | ~ spl0_6 ),
    inference(paramodulation,[status(thm)],[f541,f305]) ).

fof(f553,plain,
    ( ~ spl0_13
    | ~ spl0_4
    | ~ spl0_10
    | ~ spl0_6 ),
    inference(split_clause,[status(thm)],[f552,f549,f467,f526,f475]) ).

fof(f554,plain,
    ( app(sk6,sk1) = sk2
    | ~ spl0_6
    | ~ spl0_7 ),
    inference(forward_demodulation,[status(thm)],[f541,f542]) ).

fof(f600,plain,
    ( ~ ssList(nil)
    | ~ ssList(sk1)
    | sk1 = nil
    | spl0_8 ),
    inference(resolution,[status(thm)],[f306,f485]) ).

fof(f601,plain,
    ( ~ spl0_10
    | ~ spl0_12
    | spl0_13
    | spl0_8 ),
    inference(split_clause,[status(thm)],[f600,f526,f544,f549,f483]) ).

fof(f629,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | rearsegP(app(X0,X1),X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[f509,f289]) ).

fof(f633,plain,
    ( ~ ssList(sk6)
    | ~ ssList(sk1)
    | rearsegP(sk2,sk1)
    | ~ spl0_6
    | ~ spl0_7 ),
    inference(paramodulation,[status(thm)],[f554,f629]) ).

fof(f634,plain,
    ( ~ spl0_5
    | ~ spl0_12
    | spl0_9
    | ~ spl0_6
    | ~ spl0_7 ),
    inference(split_clause,[status(thm)],[f633,f471,f544,f486,f475,f479]) ).

fof(f635,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f462,f490,f491,f492,f493,f494,f537,f540,f548,f553,f601,f634]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SWC106-1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n010.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Tue May 30 11:10:07 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  % Drodi V3.5.1
% 0.12/0.35  % Refutation found
% 0.12/0.35  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.35  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.58  % Elapsed time: 0.025073 seconds
% 0.18/0.58  % CPU time: 0.024204 seconds
% 0.18/0.58  % Memory used: 4.137 MB
%------------------------------------------------------------------------------