TSTP Solution File: SWC420+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWC420+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n017.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 May 21 04:38:51 EDT 2024

% Result   : Theorem 0.66s 0.84s
% Output   : Refutation 0.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   66 (  10 unt;   0 def)
%            Number of atoms       :  413 ( 168 equ)
%            Maximal formula atoms :   36 (   6 avg)
%            Number of connectives :  573 ( 226   ~; 204   |; 117   &)
%                                         (   2 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :  175 ( 130   !;  45   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f529,plain,
    $false,
    inference(subsumption_resolution,[],[f526,f138]) ).

fof(f138,plain,
    ssList(sK3),
    inference(cnf_transformation,[],[f124]) ).

fof(f124,plain,
    ( ( nil != sK3
      | nil = sK2 )
    & ! [X4] :
        ( ! [X5] :
            ( app(cons(X4,nil),X5) != sK3
            | app(X5,cons(X4,nil)) = sK2
            | ~ ssList(X5) )
        | ~ ssItem(X4) )
    & ! [X6] :
        ( ! [X7] :
            ( ! [X8] :
                ( app(app(X8,cons(X6,nil)),X7) != sK0
                | app(app(X7,cons(X6,nil)),X8) != sK1
                | ~ ssList(X8) )
            | ~ ssList(X7) )
        | ~ ssItem(X6) )
    & neq(sK1,nil)
    & sK0 = sK2
    & sK1 = sK3
    & ssList(sK3)
    & ssList(sK2)
    & ssList(sK1)
    & ssList(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f99,f123,f122,f121,f120]) ).

fof(f120,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( nil != X3
                      | nil = X2 )
                    & ! [X4] :
                        ( ! [X5] :
                            ( app(cons(X4,nil),X5) != X3
                            | app(X5,cons(X4,nil)) = X2
                            | ~ ssList(X5) )
                        | ~ ssItem(X4) )
                    & ! [X6] :
                        ( ! [X7] :
                            ( ! [X8] :
                                ( app(app(X8,cons(X6,nil)),X7) != X0
                                | app(app(X7,cons(X6,nil)),X8) != X1
                                | ~ ssList(X8) )
                            | ~ ssList(X7) )
                        | ~ ssItem(X6) )
                    & neq(X1,nil)
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( nil != X3
                    | nil = X2 )
                  & ! [X4] :
                      ( ! [X5] :
                          ( app(cons(X4,nil),X5) != X3
                          | app(X5,cons(X4,nil)) = X2
                          | ~ ssList(X5) )
                      | ~ ssItem(X4) )
                  & ! [X6] :
                      ( ! [X7] :
                          ( ! [X8] :
                              ( app(app(X8,cons(X6,nil)),X7) != sK0
                              | app(app(X7,cons(X6,nil)),X8) != X1
                              | ~ ssList(X8) )
                          | ~ ssList(X7) )
                      | ~ ssItem(X6) )
                  & neq(X1,nil)
                  & sK0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f121,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( nil != X3
                  | nil = X2 )
                & ! [X4] :
                    ( ! [X5] :
                        ( app(cons(X4,nil),X5) != X3
                        | app(X5,cons(X4,nil)) = X2
                        | ~ ssList(X5) )
                    | ~ ssItem(X4) )
                & ! [X6] :
                    ( ! [X7] :
                        ( ! [X8] :
                            ( app(app(X8,cons(X6,nil)),X7) != sK0
                            | app(app(X7,cons(X6,nil)),X8) != X1
                            | ~ ssList(X8) )
                        | ~ ssList(X7) )
                    | ~ ssItem(X6) )
                & neq(X1,nil)
                & sK0 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( nil != X3
                | nil = X2 )
              & ! [X4] :
                  ( ! [X5] :
                      ( app(cons(X4,nil),X5) != X3
                      | app(X5,cons(X4,nil)) = X2
                      | ~ ssList(X5) )
                  | ~ ssItem(X4) )
              & ! [X6] :
                  ( ! [X7] :
                      ( ! [X8] :
                          ( app(app(X8,cons(X6,nil)),X7) != sK0
                          | app(app(X7,cons(X6,nil)),X8) != sK1
                          | ~ ssList(X8) )
                      | ~ ssList(X7) )
                  | ~ ssItem(X6) )
              & neq(sK1,nil)
              & sK0 = X2
              & sK1 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f122,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( nil != X3
              | nil = X2 )
            & ! [X4] :
                ( ! [X5] :
                    ( app(cons(X4,nil),X5) != X3
                    | app(X5,cons(X4,nil)) = X2
                    | ~ ssList(X5) )
                | ~ ssItem(X4) )
            & ! [X6] :
                ( ! [X7] :
                    ( ! [X8] :
                        ( app(app(X8,cons(X6,nil)),X7) != sK0
                        | app(app(X7,cons(X6,nil)),X8) != sK1
                        | ~ ssList(X8) )
                    | ~ ssList(X7) )
                | ~ ssItem(X6) )
            & neq(sK1,nil)
            & sK0 = X2
            & sK1 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( nil != X3
            | nil = sK2 )
          & ! [X4] :
              ( ! [X5] :
                  ( app(cons(X4,nil),X5) != X3
                  | app(X5,cons(X4,nil)) = sK2
                  | ~ ssList(X5) )
              | ~ ssItem(X4) )
          & ! [X6] :
              ( ! [X7] :
                  ( ! [X8] :
                      ( app(app(X8,cons(X6,nil)),X7) != sK0
                      | app(app(X7,cons(X6,nil)),X8) != sK1
                      | ~ ssList(X8) )
                  | ~ ssList(X7) )
              | ~ ssItem(X6) )
          & neq(sK1,nil)
          & sK0 = sK2
          & sK1 = X3
          & ssList(X3) )
      & ssList(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f123,plain,
    ( ? [X3] :
        ( ( nil != X3
          | nil = sK2 )
        & ! [X4] :
            ( ! [X5] :
                ( app(cons(X4,nil),X5) != X3
                | app(X5,cons(X4,nil)) = sK2
                | ~ ssList(X5) )
            | ~ ssItem(X4) )
        & ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( app(app(X8,cons(X6,nil)),X7) != sK0
                    | app(app(X7,cons(X6,nil)),X8) != sK1
                    | ~ ssList(X8) )
                | ~ ssList(X7) )
            | ~ ssItem(X6) )
        & neq(sK1,nil)
        & sK0 = sK2
        & sK1 = X3
        & ssList(X3) )
   => ( ( nil != sK3
        | nil = sK2 )
      & ! [X4] :
          ( ! [X5] :
              ( app(cons(X4,nil),X5) != sK3
              | app(X5,cons(X4,nil)) = sK2
              | ~ ssList(X5) )
          | ~ ssItem(X4) )
      & ! [X6] :
          ( ! [X7] :
              ( ! [X8] :
                  ( app(app(X8,cons(X6,nil)),X7) != sK0
                  | app(app(X7,cons(X6,nil)),X8) != sK1
                  | ~ ssList(X8) )
              | ~ ssList(X7) )
          | ~ ssItem(X6) )
      & neq(sK1,nil)
      & sK0 = sK2
      & sK1 = sK3
      & ssList(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( nil != X3
                    | nil = X2 )
                  & ! [X4] :
                      ( ! [X5] :
                          ( app(cons(X4,nil),X5) != X3
                          | app(X5,cons(X4,nil)) = X2
                          | ~ ssList(X5) )
                      | ~ ssItem(X4) )
                  & ! [X6] :
                      ( ! [X7] :
                          ( ! [X8] :
                              ( app(app(X8,cons(X6,nil)),X7) != X0
                              | app(app(X7,cons(X6,nil)),X8) != X1
                              | ~ ssList(X8) )
                          | ~ ssList(X7) )
                      | ~ ssItem(X6) )
                  & neq(X1,nil)
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ( nil = X3
                      & nil != X2 )
                    | ? [X4] :
                        ( ? [X5] :
                            ( app(cons(X4,nil),X5) = X3
                            & app(X5,cons(X4,nil)) != X2
                            & ssList(X5) )
                        & ssItem(X4) )
                    | ? [X6] :
                        ( ? [X7] :
                            ( ? [X8] :
                                ( app(app(X8,cons(X6,nil)),X7) = X0
                                & app(app(X7,cons(X6,nil)),X8) = X1
                                & ssList(X8) )
                            & ssList(X7) )
                        & ssItem(X6) )
                    | ~ neq(X1,nil)
                    | X0 != X2
                    | X1 != X3
                    | ~ ssList(X3) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ( nil = X3
                      & nil != X2 )
                    | ? [X7] :
                        ( ? [X8] :
                            ( app(cons(X7,nil),X8) = X3
                            & app(X8,cons(X7,nil)) != X2
                            & ssList(X8) )
                        & ssItem(X7) )
                    | ? [X4] :
                        ( ? [X5] :
                            ( ? [X6] :
                                ( app(app(X6,cons(X4,nil)),X5) = X0
                                & app(app(X5,cons(X4,nil)),X6) = X1
                                & ssList(X6) )
                            & ssList(X5) )
                        & ssItem(X4) )
                    | ~ neq(X1,nil)
                    | X0 != X2
                    | X1 != X3
                    | ~ ssList(X3) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ( nil = X3
                    & nil != X2 )
                  | ? [X7] :
                      ( ? [X8] :
                          ( app(cons(X7,nil),X8) = X3
                          & app(X8,cons(X7,nil)) != X2
                          & ssList(X8) )
                      & ssItem(X7) )
                  | ? [X4] :
                      ( ? [X5] :
                          ( ? [X6] :
                              ( app(app(X6,cons(X4,nil)),X5) = X0
                              & app(app(X5,cons(X4,nil)),X6) = X1
                              & ssList(X6) )
                          & ssList(X5) )
                      & ssItem(X4) )
                  | ~ neq(X1,nil)
                  | X0 != X2
                  | X1 != X3
                  | ~ ssList(X3) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

fof(f526,plain,
    ~ ssList(sK3),
    inference(trivial_inequality_removal,[],[f525]) ).

fof(f525,plain,
    ( sK3 != sK3
    | ~ ssList(sK3) ),
    inference(duplicate_literal_removal,[],[f524]) ).

fof(f524,plain,
    ( sK3 != sK3
    | ~ ssList(sK3)
    | ~ ssList(sK3) ),
    inference(resolution,[],[f501,f181]) ).

fof(f181,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1) ),
    inference(duplicate_literal_removal,[],[f178]) ).

fof(f178,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1)
      | ~ ssList(X1) ),
    inference(equality_resolution,[],[f167]) ).

fof(f167,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ neq(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f133]) ).

fof(f133,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f118]) ).

fof(f118,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( neq(X0,X1)
          <=> X0 != X1 )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( neq(X0,X1)
          <=> X0 != X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).

fof(f501,plain,
    ! [X0] :
      ( neq(sK3,X0)
      | sK3 != X0
      | ~ ssList(X0) ),
    inference(superposition,[],[f173,f493]) ).

fof(f493,plain,
    ! [X0] :
      ( nil = X0
      | sK3 != X0
      | ~ ssList(X0) ),
    inference(subsumption_resolution,[],[f492,f150]) ).

fof(f150,plain,
    ! [X0] :
      ( ssItem(sK7(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f130]) ).

fof(f130,plain,
    ! [X0] :
      ( ( cons(sK7(X0),sK6(X0)) = X0
        & ssItem(sK7(X0))
        & ssList(sK6(X0)) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f102,f129,f128]) ).

fof(f128,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( cons(X2,X1) = X0
              & ssItem(X2) )
          & ssList(X1) )
     => ( ? [X2] :
            ( cons(X2,sK6(X0)) = X0
            & ssItem(X2) )
        & ssList(sK6(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f129,plain,
    ! [X0] :
      ( ? [X2] :
          ( cons(X2,sK6(X0)) = X0
          & ssItem(X2) )
     => ( cons(sK7(X0),sK6(X0)) = X0
        & ssItem(sK7(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f102,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( cons(X2,X1) = X0
              & ssItem(X2) )
          & ssList(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f101]) ).

fof(f101,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( cons(X2,X1) = X0
              & ssItem(X2) )
          & ssList(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( ? [X1] :
            ( ? [X2] :
                ( cons(X2,X1) = X0
                & ssItem(X2) )
            & ssList(X1) )
        | nil = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).

fof(f492,plain,
    ! [X0] :
      ( sK3 != X0
      | nil = X0
      | ~ ssList(X0)
      | ~ ssItem(sK7(X0)) ),
    inference(subsumption_resolution,[],[f489,f171]) ).

fof(f171,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).

fof(f489,plain,
    ! [X0] :
      ( sK3 != X0
      | nil = X0
      | ~ ssList(X0)
      | ~ ssItem(sK7(X0))
      | ~ ssList(nil) ),
    inference(resolution,[],[f487,f155]) ).

fof(f155,plain,
    ! [X0,X1] :
      ( ssList(cons(X1,X0))
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f106]) ).

fof(f106,plain,
    ! [X0] :
      ( ! [X1] :
          ( ssList(cons(X1,X0))
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ssList(cons(X1,X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).

fof(f487,plain,
    ! [X0] :
      ( ~ ssList(cons(sK7(X0),nil))
      | sK3 != X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(subsumption_resolution,[],[f486,f150]) ).

fof(f486,plain,
    ! [X0] :
      ( sK3 != X0
      | ~ ssItem(sK7(X0))
      | ~ ssList(cons(sK7(X0),nil))
      | nil = X0
      | ~ ssList(X0) ),
    inference(subsumption_resolution,[],[f477,f149]) ).

fof(f149,plain,
    ! [X0] :
      ( ssList(sK6(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f130]) ).

fof(f477,plain,
    ! [X0] :
      ( sK3 != X0
      | ~ ssList(sK6(X0))
      | ~ ssItem(sK7(X0))
      | ~ ssList(cons(sK7(X0),nil))
      | nil = X0
      | ~ ssList(X0) ),
    inference(superposition,[],[f474,f151]) ).

fof(f151,plain,
    ! [X0] :
      ( cons(sK7(X0),sK6(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f130]) ).

fof(f474,plain,
    ! [X0,X1] :
      ( cons(X0,X1) != sK3
      | ~ ssList(X1)
      | ~ ssItem(X0)
      | ~ ssList(cons(X0,nil)) ),
    inference(duplicate_literal_removal,[],[f469]) ).

fof(f469,plain,
    ! [X0,X1] :
      ( cons(X0,X1) != sK3
      | ~ ssList(X1)
      | ~ ssItem(X0)
      | ~ ssList(cons(X0,nil))
      | ~ ssItem(X0)
      | ~ ssList(X1) ),
    inference(superposition,[],[f454,f161]) ).

fof(f161,plain,
    ! [X0,X1] :
      ( cons(X1,X0) = app(cons(X1,nil),X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f110,plain,
    ! [X0] :
      ( ! [X1] :
          ( cons(X1,X0) = app(cons(X1,nil),X0)
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f81]) ).

fof(f81,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => cons(X1,X0) = app(cons(X1,nil),X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax81) ).

fof(f454,plain,
    ! [X0,X1] :
      ( sK3 != app(cons(X0,nil),X1)
      | ~ ssList(X1)
      | ~ ssItem(X0)
      | ~ ssList(cons(X0,nil)) ),
    inference(subsumption_resolution,[],[f453,f206]) ).

fof(f206,plain,
    ! [X0,X1] :
      ( app(cons(X1,nil),X0) != sK3
      | ssList(app(X0,cons(X1,nil)))
      | ~ ssList(X0)
      | ~ ssItem(X1) ),
    inference(superposition,[],[f137,f143]) ).

fof(f143,plain,
    ! [X4,X5] :
      ( app(X5,cons(X4,nil)) = sK2
      | app(cons(X4,nil),X5) != sK3
      | ~ ssList(X5)
      | ~ ssItem(X4) ),
    inference(cnf_transformation,[],[f124]) ).

fof(f137,plain,
    ssList(sK2),
    inference(cnf_transformation,[],[f124]) ).

fof(f453,plain,
    ! [X0,X1] :
      ( sK3 != app(cons(X0,nil),X1)
      | ~ ssList(X1)
      | ~ ssItem(X0)
      | ~ ssList(app(X1,cons(X0,nil)))
      | ~ ssList(cons(X0,nil)) ),
    inference(subsumption_resolution,[],[f443,f143]) ).

fof(f443,plain,
    ! [X0,X1] :
      ( sK3 != app(cons(X0,nil),X1)
      | sK2 != app(X1,cons(X0,nil))
      | ~ ssList(X1)
      | ~ ssItem(X0)
      | ~ ssList(app(X1,cons(X0,nil)))
      | ~ ssList(cons(X0,nil)) ),
    inference(superposition,[],[f412,f164]) ).

fof(f164,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f115]) ).

fof(f115,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(nil,X0) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).

fof(f412,plain,
    ! [X0,X1] :
      ( sK3 != app(app(nil,cons(X1,nil)),X0)
      | sK2 != app(X0,cons(X1,nil))
      | ~ ssList(X0)
      | ~ ssItem(X1)
      | ~ ssList(app(X0,cons(X1,nil))) ),
    inference(subsumption_resolution,[],[f402,f171]) ).

fof(f402,plain,
    ! [X0,X1] :
      ( sK2 != app(X0,cons(X1,nil))
      | sK3 != app(app(nil,cons(X1,nil)),X0)
      | ~ ssList(X0)
      | ~ ssList(nil)
      | ~ ssItem(X1)
      | ~ ssList(app(X0,cons(X1,nil))) ),
    inference(superposition,[],[f172,f156]) ).

fof(f156,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f107]) ).

fof(f107,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f84]) ).

fof(f84,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(X0,nil) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax84) ).

fof(f172,plain,
    ! [X8,X6,X7] :
      ( app(app(X8,cons(X6,nil)),X7) != sK2
      | app(app(X7,cons(X6,nil)),X8) != sK3
      | ~ ssList(X8)
      | ~ ssList(X7)
      | ~ ssItem(X6) ),
    inference(definition_unfolding,[],[f142,f140,f139]) ).

fof(f139,plain,
    sK1 = sK3,
    inference(cnf_transformation,[],[f124]) ).

fof(f140,plain,
    sK0 = sK2,
    inference(cnf_transformation,[],[f124]) ).

fof(f142,plain,
    ! [X8,X6,X7] :
      ( app(app(X8,cons(X6,nil)),X7) != sK0
      | app(app(X7,cons(X6,nil)),X8) != sK1
      | ~ ssList(X8)
      | ~ ssList(X7)
      | ~ ssItem(X6) ),
    inference(cnf_transformation,[],[f124]) ).

fof(f173,plain,
    neq(sK3,nil),
    inference(definition_unfolding,[],[f141,f139]) ).

fof(f141,plain,
    neq(sK1,nil),
    inference(cnf_transformation,[],[f124]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11  % Problem    : SWC420+1 : TPTP v8.2.0. Released v2.4.0.
% 0.02/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.13/0.34  % Computer : n017.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sun May 19 02:57:07 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.34  This is a FOF_THM_RFO_SEQ problem
% 0.13/0.34  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.60/0.83  % (8679)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on theBenchmark for (2995ds/34Mi)
% 0.60/0.83  % (8682)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on theBenchmark for (2995ds/33Mi)
% 0.60/0.83  % (8681)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on theBenchmark for (2995ds/78Mi)
% 0.60/0.83  % (8680)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on theBenchmark for (2995ds/51Mi)
% 0.60/0.83  % (8683)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on theBenchmark for (2995ds/34Mi)
% 0.60/0.83  % (8684)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on theBenchmark for (2995ds/45Mi)
% 0.60/0.83  % (8685)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on theBenchmark for (2995ds/83Mi)
% 0.60/0.83  % (8686)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on theBenchmark for (2995ds/56Mi)
% 0.66/0.84  % (8684)First to succeed.
% 0.66/0.84  % (8684)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-8678"
% 0.66/0.84  % (8684)Refutation found. Thanks to Tanya!
% 0.66/0.84  % SZS status Theorem for theBenchmark
% 0.66/0.84  % SZS output start Proof for theBenchmark
% See solution above
% 0.66/0.84  % (8684)------------------------------
% 0.66/0.84  % (8684)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.66/0.84  % (8684)Termination reason: Refutation
% 0.66/0.84  
% 0.66/0.84  % (8684)Memory used [KB]: 1285
% 0.66/0.84  % (8684)Time elapsed: 0.015 s
% 0.66/0.84  % (8684)Instructions burned: 24 (million)
% 0.66/0.84  % (8678)Success in time 0.488 s
% 0.66/0.84  % Vampire---4.8 exiting
%------------------------------------------------------------------------------