TSTP Solution File: SWC255+1 by PyRes---1.5

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%------------------------------------------------------------------------------
% File     : PyRes---1.5
% Problem  : SWC255+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s

% Computer : n016.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 : Thu May  9 17:43:41 EDT 2024

% Result   : Theorem 7.55s 7.75s
% Output   : Refutation 7.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   26 (  10 unt;   0 def)
%            Number of atoms       :  116 (  26 equ)
%            Maximal formula atoms :   18 (   4 avg)
%            Number of connectives :  132 (  42   ~;  37   |;  41   &)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   32 (   0 sgn  12   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(co1,conjecture,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ! [X] :
                  ( ssList(X)
                 => ( V != X
                    | U != W
                    | ( ( ~ neq(V,nil)
                        | ~ singletonP(W)
                        | singletonP(U) )
                      & ( ~ neq(V,nil)
                        | neq(X,nil) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(c23,negated_conjecture,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X] :
                    ( ssList(X)
                   => ( V != X
                      | U != W
                      | ( ( ~ neq(V,nil)
                          | ~ singletonP(W)
                          | singletonP(U) )
                        & ( ~ neq(V,nil)
                          | neq(X,nil) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[co1]) ).

fof(c24,negated_conjecture,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X] :
                    ( ssList(X)
                   => ( V != X
                      | U != W
                      | ( ( ~ neq(V,nil)
                          | ~ singletonP(W)
                          | singletonP(U) )
                        & ( ~ neq(V,nil)
                          | neq(X,nil) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[c23]) ).

fof(c25,negated_conjecture,
    ? [U] :
      ( ssList(U)
      & ? [V] :
          ( ssList(V)
          & ? [W] :
              ( ssList(W)
              & ? [X] :
                  ( ssList(X)
                  & V = X
                  & U = W
                  & ( ( neq(V,nil)
                      & singletonP(W)
                      & ~ singletonP(U) )
                    | ( neq(V,nil)
                      & ~ neq(X,nil) ) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[c24]) ).

fof(c26,negated_conjecture,
    ? [X2] :
      ( ssList(X2)
      & ? [X3] :
          ( ssList(X3)
          & ? [X4] :
              ( ssList(X4)
              & ? [X5] :
                  ( ssList(X5)
                  & X3 = X5
                  & X2 = X4
                  & ( ( neq(X3,nil)
                      & singletonP(X4)
                      & ~ singletonP(X2) )
                    | ( neq(X3,nil)
                      & ~ neq(X5,nil) ) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[c25]) ).

fof(c27,negated_conjecture,
    ( ssList(skolem0001)
    & ssList(skolem0002)
    & ssList(skolem0003)
    & ssList(skolem0004)
    & skolem0002 = skolem0004
    & skolem0001 = skolem0003
    & ( ( neq(skolem0002,nil)
        & singletonP(skolem0003)
        & ~ singletonP(skolem0001) )
      | ( neq(skolem0002,nil)
        & ~ neq(skolem0004,nil) ) ) ),
    inference(skolemize,[status(esa)],[c26]) ).

fof(c28,negated_conjecture,
    ( ssList(skolem0001)
    & ssList(skolem0002)
    & ssList(skolem0003)
    & ssList(skolem0004)
    & skolem0002 = skolem0004
    & skolem0001 = skolem0003
    & ( neq(skolem0002,nil)
      | neq(skolem0002,nil) )
    & ( neq(skolem0002,nil)
      | ~ neq(skolem0004,nil) )
    & ( singletonP(skolem0003)
      | neq(skolem0002,nil) )
    & ( singletonP(skolem0003)
      | ~ neq(skolem0004,nil) )
    & ( ~ singletonP(skolem0001)
      | neq(skolem0002,nil) )
    & ( ~ singletonP(skolem0001)
      | ~ neq(skolem0004,nil) ) ),
    inference(distribute,[status(thm)],[c27]) ).

cnf(c40,negated_conjecture,
    ( ~ singletonP(skolem0001)
    | ~ neq(skolem0004,nil) ),
    inference(split_conjunct,[status(thm)],[c28]) ).

cnf(c33,negated_conjecture,
    skolem0002 = skolem0004,
    inference(split_conjunct,[status(thm)],[c28]) ).

cnf(reflexivity,axiom,
    X250 = X250,
    theory(equality) ).

cnf(c5,axiom,
    ( X276 != X277
    | X278 != X275
    | ~ neq(X276,X278)
    | neq(X277,X275) ),
    theory(equality) ).

cnf(c35,negated_conjecture,
    ( neq(skolem0002,nil)
    | neq(skolem0002,nil) ),
    inference(split_conjunct,[status(thm)],[c28]) ).

cnf(c664,plain,
    neq(skolem0002,nil),
    inference(factor,[status(thm)],[c35]) ).

cnf(c667,plain,
    ( skolem0002 != X855
    | nil != X856
    | neq(X855,X856) ),
    inference(resolution,[status(thm)],[c664,c5]) ).

cnf(c20587,plain,
    ( skolem0002 != X886
    | neq(X886,nil) ),
    inference(resolution,[status(thm)],[c667,reflexivity]) ).

cnf(c21095,plain,
    neq(skolem0004,nil),
    inference(resolution,[status(thm)],[c20587,c33]) ).

cnf(c21098,plain,
    ~ singletonP(skolem0001),
    inference(resolution,[status(thm)],[c21095,c40]) ).

cnf(symmetry,axiom,
    ( X252 != X251
    | X251 = X252 ),
    theory(equality) ).

cnf(c34,negated_conjecture,
    skolem0001 = skolem0003,
    inference(split_conjunct,[status(thm)],[c28]) ).

cnf(c520,plain,
    skolem0003 = skolem0001,
    inference(resolution,[status(thm)],[c34,symmetry]) ).

cnf(c8,axiom,
    ( X290 != X291
    | ~ singletonP(X290)
    | singletonP(X291) ),
    theory(equality) ).

cnf(c577,plain,
    ( ~ singletonP(skolem0003)
    | singletonP(skolem0001) ),
    inference(resolution,[status(thm)],[c8,c520]) ).

cnf(c38,negated_conjecture,
    ( singletonP(skolem0003)
    | ~ neq(skolem0004,nil) ),
    inference(split_conjunct,[status(thm)],[c28]) ).

cnf(c21100,plain,
    singletonP(skolem0003),
    inference(resolution,[status(thm)],[c21095,c38]) ).

cnf(c21138,plain,
    singletonP(skolem0001),
    inference(resolution,[status(thm)],[c21100,c577]) ).

cnf(c21141,plain,
    $false,
    inference(resolution,[status(thm)],[c21138,c21098]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SWC255+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14  % Command  : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.13/0.35  % Computer : n016.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 : Thu May  9 02:28:53 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 7.55/7.75  % Version:  1.5
% 7.55/7.75  % SZS status Theorem
% 7.55/7.75  % SZS output start CNFRefutation
% See solution above
% 7.55/7.75  
% 7.55/7.75  % Initial clauses    : 228
% 7.55/7.75  % Processed clauses  : 974
% 7.55/7.75  % Factors computed   : 45
% 7.55/7.75  % Resolvents computed: 20588
% 7.55/7.75  % Tautologies deleted: 21
% 7.55/7.75  % Forward subsumed   : 423
% 7.55/7.75  % Backward subsumed  : 8
% 7.55/7.75  % -------- CPU Time ---------
% 7.55/7.75  % User time          : 7.329 s
% 7.55/7.75  % System time        : 0.055 s
% 7.55/7.75  % Total time         : 7.384 s
%------------------------------------------------------------------------------