TSTP Solution File: SWC294+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SWC294+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n029.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 20:45:14 EDT 2024

% Result   : Theorem 0.13s 0.39s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   75 (  15 unt;   0 def)
%            Number of atoms       :  209 (  37 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  220 (  86   ~;  83   |;  26   &)
%                                         (  14 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   16 (  14 usr;   9 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   39 (  32   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [U] :
      ( ssList(U)
     => ( singletonP(U)
      <=> ? [V] :
            ( ssItem(V)
            & cons(V,nil) = U ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( neq(U,V)
          <=> U != V ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f58,axiom,
    ! [U] :
      ( ssList(U)
     => ( segmentP(nil,U)
      <=> nil = U ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f68,axiom,
    ! [U] :
      ( ssItem(U)
     => strictorderedP(cons(U,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f69,axiom,
    strictorderedP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f96,conjecture,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ! [X] :
                  ( ~ ssList(X)
                  | V != X
                  | U != W
                  | ~ segmentP(X,W)
                  | strictorderedP(U)
                  | ( ~ singletonP(W)
                    & neq(X,nil) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f97,negated_conjecture,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X] :
                    ( ~ ssList(X)
                    | V != X
                    | U != W
                    | ~ segmentP(X,W)
                    | strictorderedP(U)
                    | ( ~ singletonP(W)
                      & neq(X,nil) ) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f96]) ).

fof(f113,plain,
    ! [U] :
      ( ~ ssList(U)
      | ( singletonP(U)
      <=> ? [V] :
            ( ssItem(V)
            & cons(V,nil) = U ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f114,plain,
    ! [U] :
      ( ~ ssList(U)
      | ( ( ~ singletonP(U)
          | ? [V] :
              ( ssItem(V)
              & cons(V,nil) = U ) )
        & ( singletonP(U)
          | ! [V] :
              ( ~ ssItem(V)
              | cons(V,nil) != U ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f113]) ).

fof(f115,plain,
    ! [U] :
      ( ~ ssList(U)
      | ( ( ~ singletonP(U)
          | ( ssItem(sk0_4(U))
            & cons(sk0_4(U),nil) = U ) )
        & ( singletonP(U)
          | ! [V] :
              ( ~ ssItem(V)
              | cons(V,nil) != U ) ) ) ),
    inference(skolemization,[status(esa)],[f114]) ).

fof(f116,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ~ singletonP(X0)
      | ssItem(sk0_4(X0)) ),
    inference(cnf_transformation,[status(esa)],[f115]) ).

fof(f117,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ~ singletonP(X0)
      | cons(sk0_4(X0),nil) = X0 ),
    inference(cnf_transformation,[status(esa)],[f115]) ).

fof(f217,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssList(V)
          | ( neq(U,V)
          <=> U != V ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f15]) ).

fof(f218,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssList(V)
          | ( ( ~ neq(U,V)
              | U != V )
            & ( neq(U,V)
              | U = V ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f217]) ).

fof(f220,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | neq(X0,X1)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f218]) ).

fof(f223,plain,
    ssList(nil),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f324,plain,
    ! [U] :
      ( ~ ssList(U)
      | ( segmentP(nil,U)
      <=> nil = U ) ),
    inference(pre_NNF_transformation,[status(esa)],[f58]) ).

fof(f325,plain,
    ! [U] :
      ( ~ ssList(U)
      | ( ( ~ segmentP(nil,U)
          | nil = U )
        & ( segmentP(nil,U)
          | nil != U ) ) ),
    inference(NNF_transformation,[status(esa)],[f324]) ).

fof(f326,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ~ segmentP(nil,X0)
      | nil = X0 ),
    inference(cnf_transformation,[status(esa)],[f325]) ).

fof(f347,plain,
    ! [U] :
      ( ~ ssItem(U)
      | strictorderedP(cons(U,nil)) ),
    inference(pre_NNF_transformation,[status(esa)],[f68]) ).

fof(f348,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | strictorderedP(cons(X0,nil)) ),
    inference(cnf_transformation,[status(esa)],[f347]) ).

fof(f349,plain,
    strictorderedP(nil),
    inference(cnf_transformation,[status(esa)],[f69]) ).

fof(f415,plain,
    ? [U] :
      ( ssList(U)
      & ? [V] :
          ( ssList(V)
          & ? [W] :
              ( ssList(W)
              & ? [X] :
                  ( ssList(X)
                  & V = X
                  & U = W
                  & segmentP(X,W)
                  & ~ strictorderedP(U)
                  & ( singletonP(W)
                    | ~ neq(X,nil) ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f97]) ).

fof(f416,plain,
    ( ssList(sk0_47)
    & ssList(sk0_48)
    & ssList(sk0_49)
    & ssList(sk0_50)
    & sk0_48 = sk0_50
    & sk0_47 = sk0_49
    & segmentP(sk0_50,sk0_49)
    & ~ strictorderedP(sk0_47)
    & ( singletonP(sk0_49)
      | ~ neq(sk0_50,nil) ) ),
    inference(skolemization,[status(esa)],[f415]) ).

fof(f417,plain,
    ssList(sk0_47),
    inference(cnf_transformation,[status(esa)],[f416]) ).

fof(f418,plain,
    ssList(sk0_48),
    inference(cnf_transformation,[status(esa)],[f416]) ).

fof(f421,plain,
    sk0_48 = sk0_50,
    inference(cnf_transformation,[status(esa)],[f416]) ).

fof(f422,plain,
    sk0_47 = sk0_49,
    inference(cnf_transformation,[status(esa)],[f416]) ).

fof(f423,plain,
    segmentP(sk0_50,sk0_49),
    inference(cnf_transformation,[status(esa)],[f416]) ).

fof(f424,plain,
    ~ strictorderedP(sk0_47),
    inference(cnf_transformation,[status(esa)],[f416]) ).

fof(f425,plain,
    ( singletonP(sk0_49)
    | ~ neq(sk0_50,nil) ),
    inference(cnf_transformation,[status(esa)],[f416]) ).

fof(f426,plain,
    ( spl0_0
  <=> singletonP(sk0_49) ),
    introduced(split_symbol_definition) ).

fof(f427,plain,
    ( singletonP(sk0_49)
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f426]) ).

fof(f429,plain,
    ( spl0_1
  <=> neq(sk0_50,nil) ),
    introduced(split_symbol_definition) ).

fof(f431,plain,
    ( ~ neq(sk0_50,nil)
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f429]) ).

fof(f432,plain,
    ( spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f425,f426,f429]) ).

fof(f465,plain,
    segmentP(sk0_48,sk0_49),
    inference(forward_demodulation,[status(thm)],[f421,f423]) ).

fof(f466,plain,
    segmentP(sk0_48,sk0_47),
    inference(forward_demodulation,[status(thm)],[f422,f465]) ).

fof(f477,plain,
    ( ~ neq(sk0_48,nil)
    | spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f421,f431]) ).

fof(f533,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | neq(sk0_48,X0)
      | sk0_48 = X0 ),
    inference(resolution,[status(thm)],[f220,f418]) ).

fof(f535,plain,
    ( spl0_11
  <=> neq(sk0_48,nil) ),
    introduced(split_symbol_definition) ).

fof(f536,plain,
    ( neq(sk0_48,nil)
    | ~ spl0_11 ),
    inference(component_clause,[status(thm)],[f535]) ).

fof(f538,plain,
    ( spl0_12
  <=> sk0_48 = nil ),
    introduced(split_symbol_definition) ).

fof(f539,plain,
    ( sk0_48 = nil
    | ~ spl0_12 ),
    inference(component_clause,[status(thm)],[f538]) ).

fof(f541,plain,
    ( neq(sk0_48,nil)
    | sk0_48 = nil ),
    inference(resolution,[status(thm)],[f533,f223]) ).

fof(f542,plain,
    ( spl0_11
    | spl0_12 ),
    inference(split_clause,[status(thm)],[f541,f535,f538]) ).

fof(f559,plain,
    ( $false
    | spl0_1
    | ~ spl0_11 ),
    inference(forward_subsumption_resolution,[status(thm)],[f536,f477]) ).

fof(f560,plain,
    ( spl0_1
    | ~ spl0_11 ),
    inference(contradiction_clause,[status(thm)],[f559]) ).

fof(f561,plain,
    ( singletonP(sk0_47)
    | ~ spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f422,f427]) ).

fof(f570,plain,
    ( segmentP(nil,sk0_47)
    | ~ spl0_12 ),
    inference(backward_demodulation,[status(thm)],[f539,f466]) ).

fof(f591,plain,
    ( spl0_19
  <=> sk0_47 = nil ),
    introduced(split_symbol_definition) ).

fof(f592,plain,
    ( sk0_47 = nil
    | ~ spl0_19 ),
    inference(component_clause,[status(thm)],[f591]) ).

fof(f655,plain,
    ( spl0_25
  <=> ssList(sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f657,plain,
    ( ~ ssList(sk0_47)
    | spl0_25 ),
    inference(component_clause,[status(thm)],[f655]) ).

fof(f658,plain,
    ( spl0_26
  <=> ssItem(sk0_4(sk0_47)) ),
    introduced(split_symbol_definition) ).

fof(f659,plain,
    ( ssItem(sk0_4(sk0_47))
    | ~ spl0_26 ),
    inference(component_clause,[status(thm)],[f658]) ).

fof(f661,plain,
    ( ~ ssList(sk0_47)
    | ssItem(sk0_4(sk0_47))
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f116,f561]) ).

fof(f662,plain,
    ( ~ spl0_25
    | spl0_26
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f661,f655,f658,f426]) ).

fof(f663,plain,
    ( $false
    | spl0_25 ),
    inference(forward_subsumption_resolution,[status(thm)],[f657,f417]) ).

fof(f664,plain,
    spl0_25,
    inference(contradiction_clause,[status(thm)],[f663]) ).

fof(f665,plain,
    ( spl0_27
  <=> cons(sk0_4(sk0_47),nil) = sk0_47 ),
    introduced(split_symbol_definition) ).

fof(f666,plain,
    ( cons(sk0_4(sk0_47),nil) = sk0_47
    | ~ spl0_27 ),
    inference(component_clause,[status(thm)],[f665]) ).

fof(f668,plain,
    ( ~ ssList(sk0_47)
    | cons(sk0_4(sk0_47),nil) = sk0_47
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f117,f561]) ).

fof(f669,plain,
    ( ~ spl0_25
    | spl0_27
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f668,f655,f665,f426]) ).

fof(f694,plain,
    ( strictorderedP(cons(sk0_4(sk0_47),nil))
    | ~ spl0_26 ),
    inference(resolution,[status(thm)],[f659,f348]) ).

fof(f721,plain,
    ( strictorderedP(sk0_47)
    | ~ spl0_27
    | ~ spl0_26 ),
    inference(forward_demodulation,[status(thm)],[f666,f694]) ).

fof(f722,plain,
    ( $false
    | ~ spl0_27
    | ~ spl0_26 ),
    inference(forward_subsumption_resolution,[status(thm)],[f721,f424]) ).

fof(f723,plain,
    ( ~ spl0_27
    | ~ spl0_26 ),
    inference(contradiction_clause,[status(thm)],[f722]) ).

fof(f725,plain,
    ( ~ ssList(sk0_47)
    | nil = sk0_47
    | ~ spl0_12 ),
    inference(resolution,[status(thm)],[f570,f326]) ).

fof(f726,plain,
    ( ~ spl0_25
    | spl0_19
    | ~ spl0_12 ),
    inference(split_clause,[status(thm)],[f725,f655,f591,f538]) ).

fof(f749,plain,
    ( ~ strictorderedP(nil)
    | ~ spl0_19 ),
    inference(backward_demodulation,[status(thm)],[f592,f424]) ).

fof(f750,plain,
    ( $false
    | ~ spl0_19 ),
    inference(forward_subsumption_resolution,[status(thm)],[f749,f349]) ).

fof(f751,plain,
    ~ spl0_19,
    inference(contradiction_clause,[status(thm)],[f750]) ).

fof(f752,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f432,f542,f560,f662,f664,f669,f723,f726,f751]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SWC294+1 : TPTP v8.1.2. Released v2.4.0.
% 0.08/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n029.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 00:21:20 EDT 2024
% 0.13/0.36  % CPUTime  : 
% 0.13/0.38  % Drodi V3.6.0
% 0.13/0.39  % Refutation found
% 0.13/0.39  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.42  % Elapsed time: 0.040214 seconds
% 0.21/0.42  % CPU time: 0.069417 seconds
% 0.21/0.42  % Total memory used: 16.888 MB
% 0.21/0.42  % Net memory used: 16.849 MB
%------------------------------------------------------------------------------