TSTP Solution File: SWC204+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWC204+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n022.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 : Fri May  3 03:11:34 EDT 2024

% Result   : Theorem 8.16s 1.69s
% Output   : CNFRefutation 8.16s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f604)

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

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

fof(f18,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => cons(X1,X0) != X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).

fof(f24,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ssList(tl(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).

fof(f26,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ssList(app(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).

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

fof(f58,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( segmentP(nil,X0)
      <=> nil = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).

fof(f75,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ? [X1] :
            ( hd(X0) = X1
            & ssItem(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax75) ).

fof(f78,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => cons(hd(X0),tl(X0)) = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax78) ).

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

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

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

fof(f120,plain,
    ! [X0] :
      ( ! [X1] :
          ( cons(X1,X0) != X0
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f129,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f130,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f129]) ).

fof(f132,plain,
    ! [X0] :
      ( ! [X1] :
          ( ssList(app(X0,X1))
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f134,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f176,plain,
    ! [X0] :
      ( ( segmentP(nil,X0)
      <=> nil = X0 )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f58]) ).

fof(f186,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f75]) ).

fof(f187,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f186]) ).

fof(f192,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f78]) ).

fof(f193,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f192]) ).

fof(f221,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( ~ neq(X0,nil)
                      & ! [X4] :
                          ( ! [X5] :
                              ( ~ neq(nil,X3)
                              | app(X2,X5) != X4
                              | tl(X3) != X5
                              | ~ ssList(X5) )
                          | X3 = X4
                          | ~ ssList(X4) )
                      & neq(X1,nil) ) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f97]) ).

fof(f222,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( ~ neq(X0,nil)
                      & ! [X4] :
                          ( ! [X5] :
                              ( ~ neq(nil,X3)
                              | app(X2,X5) != X4
                              | tl(X3) != X5
                              | ~ ssList(X5) )
                          | X3 = X4
                          | ~ ssList(X4) )
                      & neq(X1,nil) ) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f221]) ).

fof(f316,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f118]) ).

fof(f330,plain,
    ! [X0] :
      ( ( ( segmentP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ segmentP(nil,X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f176]) ).

fof(f335,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
     => ( hd(X0) = sK51(X0)
        & ssItem(sK51(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f336,plain,
    ! [X0] :
      ( ( hd(X0) = sK51(X0)
        & ssItem(sK51(X0)) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK51])],[f187,f335]) ).

fof(f343,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( ~ neq(X3,nil)
                        & neq(X1,nil) )
                      | ( ~ neq(X0,nil)
                        & ! [X4] :
                            ( ! [X5] :
                                ( ~ neq(nil,X3)
                                | app(X2,X5) != X4
                                | tl(X3) != X5
                                | ~ ssList(X5) )
                            | X3 = X4
                            | ~ ssList(X4) )
                        & neq(X1,nil) ) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( ~ neq(sK53,nil)
                      & ! [X4] :
                          ( ! [X5] :
                              ( ~ neq(nil,X3)
                              | app(X2,X5) != X4
                              | tl(X3) != X5
                              | ~ ssList(X5) )
                          | X3 = X4
                          | ~ ssList(X4) )
                      & neq(X1,nil) ) )
                  & sK53 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK53) ) ),
    introduced(choice_axiom,[]) ).

fof(f344,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( ~ neq(X3,nil)
                    & neq(X1,nil) )
                  | ( ~ neq(sK53,nil)
                    & ! [X4] :
                        ( ! [X5] :
                            ( ~ neq(nil,X3)
                            | app(X2,X5) != X4
                            | tl(X3) != X5
                            | ~ ssList(X5) )
                        | X3 = X4
                        | ~ ssList(X4) )
                    & neq(X1,nil) ) )
                & sK53 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( ~ neq(X3,nil)
                  & neq(sK54,nil) )
                | ( ~ neq(sK53,nil)
                  & ! [X4] :
                      ( ! [X5] :
                          ( ~ neq(nil,X3)
                          | app(X2,X5) != X4
                          | tl(X3) != X5
                          | ~ ssList(X5) )
                      | X3 = X4
                      | ~ ssList(X4) )
                  & neq(sK54,nil) ) )
              & sK53 = X2
              & sK54 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK54) ) ),
    introduced(choice_axiom,[]) ).

fof(f345,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( ~ neq(X3,nil)
                & neq(sK54,nil) )
              | ( ~ neq(sK53,nil)
                & ! [X4] :
                    ( ! [X5] :
                        ( ~ neq(nil,X3)
                        | app(X2,X5) != X4
                        | tl(X3) != X5
                        | ~ ssList(X5) )
                    | X3 = X4
                    | ~ ssList(X4) )
                & neq(sK54,nil) ) )
            & sK53 = X2
            & sK54 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( ~ neq(X3,nil)
              & neq(sK54,nil) )
            | ( ~ neq(sK53,nil)
              & ! [X4] :
                  ( ! [X5] :
                      ( ~ neq(nil,X3)
                      | app(sK55,X5) != X4
                      | tl(X3) != X5
                      | ~ ssList(X5) )
                  | X3 = X4
                  | ~ ssList(X4) )
              & neq(sK54,nil) ) )
          & sK53 = sK55
          & sK54 = X3
          & ssList(X3) )
      & ssList(sK55) ) ),
    introduced(choice_axiom,[]) ).

fof(f346,plain,
    ( ? [X3] :
        ( ( ( ~ neq(X3,nil)
            & neq(sK54,nil) )
          | ( ~ neq(sK53,nil)
            & ! [X4] :
                ( ! [X5] :
                    ( ~ neq(nil,X3)
                    | app(sK55,X5) != X4
                    | tl(X3) != X5
                    | ~ ssList(X5) )
                | X3 = X4
                | ~ ssList(X4) )
            & neq(sK54,nil) ) )
        & sK53 = sK55
        & sK54 = X3
        & ssList(X3) )
   => ( ( ( ~ neq(sK56,nil)
          & neq(sK54,nil) )
        | ( ~ neq(sK53,nil)
          & ! [X4] :
              ( ! [X5] :
                  ( ~ neq(nil,sK56)
                  | app(sK55,X5) != X4
                  | tl(sK56) != X5
                  | ~ ssList(X5) )
              | sK56 = X4
              | ~ ssList(X4) )
          & neq(sK54,nil) ) )
      & sK53 = sK55
      & sK54 = sK56
      & ssList(sK56) ) ),
    introduced(choice_axiom,[]) ).

fof(f347,plain,
    ( ( ( ~ neq(sK56,nil)
        & neq(sK54,nil) )
      | ( ~ neq(sK53,nil)
        & ! [X4] :
            ( ! [X5] :
                ( ~ neq(nil,sK56)
                | app(sK55,X5) != X4
                | tl(sK56) != X5
                | ~ ssList(X5) )
            | sK56 = X4
            | ~ ssList(X4) )
        & neq(sK54,nil) ) )
    & sK53 = sK55
    & sK54 = sK56
    & ssList(sK56)
    & ssList(sK55)
    & ssList(sK54)
    & ssList(sK53) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56])],[f222,f346,f345,f344,f343]) ).

fof(f438,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f316]) ).

fof(f440,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f441,plain,
    ! [X0,X1] :
      ( cons(X1,X0) != X0
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f450,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f130]) ).

fof(f452,plain,
    ! [X0,X1] :
      ( ssList(app(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f132]) ).

fof(f454,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f134]) ).

fof(f494,plain,
    ! [X0] :
      ( nil = X0
      | ~ segmentP(nil,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f330]) ).

fof(f495,plain,
    ! [X0] :
      ( segmentP(nil,X0)
      | nil != X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f330]) ).

fof(f520,plain,
    ! [X0] :
      ( ssItem(sK51(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f336]) ).

fof(f521,plain,
    ! [X0] :
      ( hd(X0) = sK51(X0)
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f336]) ).

fof(f525,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f193]) ).

fof(f547,plain,
    ssList(sK53),
    inference(cnf_transformation,[],[f347]) ).

fof(f548,plain,
    ssList(sK54),
    inference(cnf_transformation,[],[f347]) ).

fof(f551,plain,
    sK54 = sK56,
    inference(cnf_transformation,[],[f347]) ).

fof(f552,plain,
    sK53 = sK55,
    inference(cnf_transformation,[],[f347]) ).

fof(f554,plain,
    ! [X4,X5] :
      ( neq(sK54,nil)
      | ~ neq(nil,sK56)
      | app(sK55,X5) != X4
      | tl(sK56) != X5
      | ~ ssList(X5)
      | sK56 = X4
      | ~ ssList(X4) ),
    inference(cnf_transformation,[],[f347]) ).

fof(f557,plain,
    ! [X4,X5] :
      ( ~ neq(sK56,nil)
      | ~ neq(nil,sK56)
      | app(sK55,X5) != X4
      | tl(sK56) != X5
      | ~ ssList(X5)
      | sK56 = X4
      | ~ ssList(X4) ),
    inference(cnf_transformation,[],[f347]) ).

fof(f558,plain,
    ( ~ neq(sK56,nil)
    | ~ neq(sK53,nil) ),
    inference(cnf_transformation,[],[f347]) ).

fof(f559,plain,
    ( ~ neq(sK56,nil)
    | ~ neq(sK55,nil) ),
    inference(definition_unfolding,[],[f558,f552]) ).

fof(f562,plain,
    ! [X4,X5] :
      ( neq(sK56,nil)
      | ~ neq(nil,sK56)
      | app(sK55,X5) != X4
      | tl(sK56) != X5
      | ~ ssList(X5)
      | sK56 = X4
      | ~ ssList(X4) ),
    inference(definition_unfolding,[],[f554,f551]) ).

fof(f564,plain,
    ssList(sK56),
    inference(definition_unfolding,[],[f548,f551]) ).

fof(f565,plain,
    ssList(sK55),
    inference(definition_unfolding,[],[f547,f552]) ).

fof(f585,plain,
    ( segmentP(nil,nil)
    | ~ ssList(nil) ),
    inference(equality_resolution,[],[f495]) ).

fof(f593,plain,
    ! [X5] :
      ( ~ neq(sK56,nil)
      | ~ neq(nil,sK56)
      | tl(sK56) != X5
      | ~ ssList(X5)
      | app(sK55,X5) = sK56
      | ~ ssList(app(sK55,X5)) ),
    inference(equality_resolution,[],[f557]) ).

fof(f594,plain,
    ( ~ neq(sK56,nil)
    | ~ neq(nil,sK56)
    | ~ ssList(tl(sK56))
    | sK56 = app(sK55,tl(sK56))
    | ~ ssList(app(sK55,tl(sK56))) ),
    inference(equality_resolution,[],[f593]) ).

fof(f595,plain,
    ! [X5] :
      ( neq(sK56,nil)
      | ~ neq(nil,sK56)
      | tl(sK56) != X5
      | ~ ssList(X5)
      | app(sK55,X5) = sK56
      | ~ ssList(app(sK55,X5)) ),
    inference(equality_resolution,[],[f562]) ).

fof(f596,plain,
    ( neq(sK56,nil)
    | ~ neq(nil,sK56)
    | ~ ssList(tl(sK56))
    | sK56 = app(sK55,tl(sK56))
    | ~ ssList(app(sK55,tl(sK56))) ),
    inference(equality_resolution,[],[f595]) ).

cnf(c_138,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | X0 = X1
    | neq(X0,X1) ),
    inference(cnf_transformation,[],[f438]) ).

cnf(c_139,plain,
    ( ~ neq(X0,X0)
    | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f599]) ).

cnf(c_141,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f440]) ).

cnf(c_142,plain,
    ( cons(X0,X1) != X1
    | ~ ssItem(X0)
    | ~ ssList(X1) ),
    inference(cnf_transformation,[],[f441]) ).

cnf(c_151,plain,
    ( ~ ssList(X0)
    | X0 = nil
    | ssList(tl(X0)) ),
    inference(cnf_transformation,[],[f450]) ).

cnf(c_153,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | ssList(app(X0,X1)) ),
    inference(cnf_transformation,[],[f452]) ).

cnf(c_155,plain,
    ( ~ ssList(X0)
    | app(nil,X0) = X0 ),
    inference(cnf_transformation,[],[f454]) ).

cnf(c_195,plain,
    ( ~ ssList(nil)
    | segmentP(nil,nil) ),
    inference(cnf_transformation,[],[f585]) ).

cnf(c_196,plain,
    ( ~ segmentP(nil,X0)
    | ~ ssList(X0)
    | X0 = nil ),
    inference(cnf_transformation,[],[f494]) ).

cnf(c_219,plain,
    ( ~ ssList(X0)
    | hd(X0) = sK51(X0)
    | X0 = nil ),
    inference(cnf_transformation,[],[f521]) ).

cnf(c_220,plain,
    ( ~ ssList(X0)
    | X0 = nil
    | ssItem(sK51(X0)) ),
    inference(cnf_transformation,[],[f520]) ).

cnf(c_224,plain,
    ( ~ ssList(X0)
    | cons(hd(X0),tl(X0)) = X0
    | X0 = nil ),
    inference(cnf_transformation,[],[f525]) ).

cnf(c_246,negated_conjecture,
    ( ~ neq(sK56,nil)
    | ~ neq(sK55,nil) ),
    inference(cnf_transformation,[],[f559]) ).

cnf(c_247,negated_conjecture,
    ( ~ ssList(app(sK55,tl(sK56)))
    | ~ neq(nil,sK56)
    | ~ neq(sK56,nil)
    | ~ ssList(tl(sK56))
    | app(sK55,tl(sK56)) = sK56 ),
    inference(cnf_transformation,[],[f594]) ).

cnf(c_249,negated_conjecture,
    ( ~ ssList(app(sK55,tl(sK56)))
    | ~ neq(nil,sK56)
    | ~ ssList(tl(sK56))
    | app(sK55,tl(sK56)) = sK56
    | neq(sK56,nil) ),
    inference(cnf_transformation,[],[f596]) ).

cnf(c_250,negated_conjecture,
    neq(sK56,nil),
    inference(cnf_transformation,[],[f604]) ).

cnf(c_253,negated_conjecture,
    ssList(sK56),
    inference(cnf_transformation,[],[f564]) ).

cnf(c_254,negated_conjecture,
    ssList(sK55),
    inference(cnf_transformation,[],[f565]) ).

cnf(c_304,plain,
    ( ~ segmentP(nil,nil)
    | ~ ssList(nil)
    | nil = nil ),
    inference(instantiation,[status(thm)],[c_196]) ).

cnf(c_369,negated_conjecture,
    ~ neq(sK55,nil),
    inference(global_subsumption_just,[status(thm)],[c_246,c_250,c_246]) ).

cnf(c_383,negated_conjecture,
    neq(sK56,nil),
    inference(global_subsumption_just,[status(thm)],[c_249,c_250]) ).

cnf(c_385,plain,
    ( ~ neq(nil,sK56)
    | ~ ssList(app(sK55,tl(sK56)))
    | ~ ssList(tl(sK56))
    | app(sK55,tl(sK56)) = sK56 ),
    inference(global_subsumption_just,[status(thm)],[c_247,c_250,c_247]) ).

cnf(c_386,negated_conjecture,
    ( ~ ssList(app(sK55,tl(sK56)))
    | ~ neq(nil,sK56)
    | ~ ssList(tl(sK56))
    | app(sK55,tl(sK56)) = sK56 ),
    inference(renaming,[status(thm)],[c_385]) ).

cnf(c_3222,plain,
    ( X0 != sK55
    | X1 != nil
    | ~ ssList(X0)
    | ~ ssList(X1)
    | X0 = X1 ),
    inference(resolution_lifted,[status(thm)],[c_138,c_369]) ).

cnf(c_3223,plain,
    ( ~ ssList(nil)
    | ~ ssList(sK55)
    | sK55 = nil ),
    inference(unflattening,[status(thm)],[c_3222]) ).

cnf(c_3224,plain,
    sK55 = nil,
    inference(global_subsumption_just,[status(thm)],[c_3223,c_254,c_141,c_3223]) ).

cnf(c_3231,plain,
    ( X0 != nil
    | X1 != sK56
    | ~ ssList(app(sK55,tl(sK56)))
    | ~ ssList(tl(sK56))
    | ~ ssList(X0)
    | ~ ssList(X1)
    | app(sK55,tl(sK56)) = sK56
    | X0 = X1 ),
    inference(resolution_lifted,[status(thm)],[c_138,c_386]) ).

cnf(c_3232,plain,
    ( ~ ssList(app(sK55,tl(sK56)))
    | ~ ssList(tl(sK56))
    | ~ ssList(nil)
    | ~ ssList(sK56)
    | app(sK55,tl(sK56)) = sK56
    | nil = sK56 ),
    inference(unflattening,[status(thm)],[c_3231]) ).

cnf(c_3233,plain,
    ( ~ ssList(app(sK55,tl(sK56)))
    | ~ ssList(tl(sK56))
    | app(sK55,tl(sK56)) = sK56
    | nil = sK56 ),
    inference(global_subsumption_just,[status(thm)],[c_3232,c_253,c_141,c_3232]) ).

cnf(c_3251,plain,
    ( X0 != nil
    | X0 != sK56
    | ~ ssList(X0) ),
    inference(resolution_lifted,[status(thm)],[c_139,c_383]) ).

cnf(c_3252,plain,
    ( nil != sK56
    | ~ ssList(nil) ),
    inference(unflattening,[status(thm)],[c_3251]) ).

cnf(c_3253,plain,
    nil != sK56,
    inference(global_subsumption_just,[status(thm)],[c_3252,c_141,c_3252]) ).

cnf(c_3258,plain,
    ( ~ ssList(app(sK55,tl(sK56)))
    | ~ ssList(tl(sK56))
    | app(sK55,tl(sK56)) = sK56 ),
    inference(backward_subsumption_resolution,[status(thm)],[c_3233,c_3253]) ).

cnf(c_3261,plain,
    ( nil != nil
    | sK56 != sK55 ),
    inference(resolution_lifted,[status(thm)],[c_383,c_369]) ).

cnf(c_3262,plain,
    sK56 != sK55,
    inference(global_subsumption_just,[status(thm)],[c_3261,c_141,c_195,c_304,c_3261]) ).

cnf(c_6080,plain,
    nil != sK56,
    inference(light_normalisation,[status(thm)],[c_3262,c_3224]) ).

cnf(c_6643,plain,
    ( ~ ssList(app(nil,tl(sK56)))
    | ~ ssList(tl(sK56))
    | app(nil,tl(sK56)) = sK56 ),
    inference(light_normalisation,[status(thm)],[c_3258,c_3224]) ).

cnf(c_12906,negated_conjecture,
    ssList(sK56),
    inference(demodulation,[status(thm)],[c_253]) ).

cnf(c_16225,plain,
    ( ~ ssList(X0)
    | app(nil,tl(X0)) = tl(X0)
    | X0 = nil ),
    inference(superposition,[status(thm)],[c_151,c_155]) ).

cnf(c_16243,plain,
    ( ~ ssList(tl(sK56))
    | ~ ssList(nil)
    | app(nil,tl(sK56)) = sK56 ),
    inference(superposition,[status(thm)],[c_153,c_6643]) ).

cnf(c_16244,plain,
    ( ~ ssList(tl(sK56))
    | app(nil,tl(sK56)) = sK56 ),
    inference(forward_subsumption_resolution,[status(thm)],[c_16243,c_141]) ).

cnf(c_16259,plain,
    ( ~ ssList(sK56)
    | app(nil,tl(sK56)) = sK56
    | nil = sK56 ),
    inference(superposition,[status(thm)],[c_151,c_16244]) ).

cnf(c_16260,plain,
    app(nil,tl(sK56)) = sK56,
    inference(forward_subsumption_resolution,[status(thm)],[c_16259,c_6080,c_12906]) ).

cnf(c_17072,plain,
    ( app(nil,tl(sK56)) = tl(sK56)
    | nil = sK56 ),
    inference(superposition,[status(thm)],[c_12906,c_16225]) ).

cnf(c_17073,plain,
    ( tl(sK56) = sK56
    | nil = sK56 ),
    inference(light_normalisation,[status(thm)],[c_17072,c_16260]) ).

cnf(c_17074,plain,
    tl(sK56) = sK56,
    inference(forward_subsumption_resolution,[status(thm)],[c_17073,c_6080]) ).

cnf(c_18067,plain,
    ( hd(sK56) = sK51(sK56)
    | nil = sK56 ),
    inference(superposition,[status(thm)],[c_12906,c_219]) ).

cnf(c_18068,plain,
    hd(sK56) = sK51(sK56),
    inference(forward_subsumption_resolution,[status(thm)],[c_18067,c_6080]) ).

cnf(c_18231,plain,
    ( ~ ssList(sK56)
    | nil = sK56
    | ssItem(hd(sK56)) ),
    inference(superposition,[status(thm)],[c_18068,c_220]) ).

cnf(c_18232,plain,
    ssItem(hd(sK56)),
    inference(forward_subsumption_resolution,[status(thm)],[c_18231,c_6080,c_12906]) ).

cnf(c_21121,plain,
    ( cons(hd(sK56),tl(sK56)) = sK56
    | nil = sK56 ),
    inference(superposition,[status(thm)],[c_12906,c_224]) ).

cnf(c_21122,plain,
    ( cons(hd(sK56),sK56) = sK56
    | nil = sK56 ),
    inference(light_normalisation,[status(thm)],[c_21121,c_17074]) ).

cnf(c_21123,plain,
    cons(hd(sK56),sK56) = sK56,
    inference(forward_subsumption_resolution,[status(thm)],[c_21122,c_6080]) ).

cnf(c_21637,plain,
    ( ~ ssItem(hd(sK56))
    | ~ ssList(sK56) ),
    inference(superposition,[status(thm)],[c_21123,c_142]) ).

cnf(c_21640,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_21637,c_12906,c_18232]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SWC204+1 : TPTP v8.1.2. Released v2.4.0.
% 0.08/0.14  % Command  : run_iprover %s %d THM
% 0.14/0.35  % Computer : n022.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu May  2 23:30:42 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.16/1.69  % SZS status Started for theBenchmark.p
% 8.16/1.69  % SZS status Theorem for theBenchmark.p
% 8.16/1.69  
% 8.16/1.69  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 8.16/1.69  
% 8.16/1.69  ------  iProver source info
% 8.16/1.69  
% 8.16/1.69  git: date: 2024-05-02 19:28:25 +0000
% 8.16/1.69  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 8.16/1.69  git: non_committed_changes: false
% 8.16/1.69  
% 8.16/1.69  ------ Parsing...
% 8.16/1.69  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 8.16/1.69  
% 8.16/1.69  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe_e  sup_sim: 5  sf_s  rm: 5 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 5 0s  sf_e  pe_s  pe_e 
% 8.16/1.69  
% 8.16/1.69  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 8.16/1.69  
% 8.16/1.69  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 8.16/1.69  ------ Proving...
% 8.16/1.69  ------ Problem Properties 
% 8.16/1.69  
% 8.16/1.69  
% 8.16/1.69  clauses                                 184
% 8.16/1.69  conjectures                             1
% 8.16/1.69  EPR                                     52
% 8.16/1.69  Horn                                    116
% 8.16/1.69  unary                                   19
% 8.16/1.69  binary                                  40
% 8.16/1.69  lits                                    624
% 8.16/1.69  lits eq                                 81
% 8.16/1.69  fd_pure                                 0
% 8.16/1.69  fd_pseudo                               0
% 8.16/1.69  fd_cond                                 21
% 8.16/1.69  fd_pseudo_cond                          14
% 8.16/1.69  AC symbols                              0
% 8.16/1.69  
% 8.16/1.69  ------ Schedule dynamic 5 is on 
% 8.16/1.69  
% 8.16/1.69  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.16/1.69  
% 8.16/1.69  
% 8.16/1.69  ------ 
% 8.16/1.69  Current options:
% 8.16/1.69  ------ 
% 8.16/1.69  
% 8.16/1.69  
% 8.16/1.69  
% 8.16/1.69  
% 8.16/1.69  ------ Proving...
% 8.16/1.69  
% 8.16/1.69  
% 8.16/1.69  % SZS status Theorem for theBenchmark.p
% 8.16/1.69  
% 8.16/1.69  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.16/1.69  
% 8.16/1.69  
%------------------------------------------------------------------------------