TSTP Solution File: SWC218+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SWC218+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n002.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 Aug 31 20:41:46 EDT 2023

% Result   : Theorem 6.77s 1.65s
% Output   : CNFRefutation 6.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   20
% Syntax   : Number of formulae    :  100 (  24 unt;   0 def)
%            Number of atoms       :  456 ( 124 equ)
%            Maximal formula atoms :   24 (   4 avg)
%            Number of connectives :  528 ( 172   ~; 151   |; 157   &)
%                                         (  10 <=>;  38  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   8 con; 0-2 aty)
%            Number of variables   :  197 (   0 sgn;  95   !;  80   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f6,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( rearsegP(X0,X1)
          <=> ? [X2] :
                ( app(X2,X1) = X0
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).

fof(f7,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( segmentP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(app(X2,X1),X3) = X0
                    & ssList(X3) )
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).

fof(f15,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( neq(X0,X1)
          <=> X0 != X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).

fof(f16,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ssList(cons(X1,X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).

fof(f21,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => nil != cons(X1,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).

fof(f26,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ssList(app(X0,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).

fof(f52,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( rearsegP(nil,X0)
      <=> nil = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).

fof(f58,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( segmentP(nil,X0)
      <=> nil = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( neq(X0,nil)
                    | ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( ! [X6] :
                                  ( ssItem(X6)
                                 => app(app(X4,cons(X6,nil)),X5) != X2 )
                              | app(X4,X5) != X3 ) ) )
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

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

fof(f102,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( rearsegP(X0,X1)
          <=> ? [X2] :
                ( app(X2,X1) = X0
                & ssList(X2) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f103,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( segmentP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(app(X2,X1),X3) = X0
                    & ssList(X3) )
                & ssList(X2) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f7]) ).

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

fof(f119,plain,
    ! [X0] :
      ( ! [X1] :
          ( ssList(cons(X1,X0))
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f125,plain,
    ! [X0] :
      ( ! [X1] :
          ( nil != cons(X1,X0)
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f21]) ).

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

fof(f167,plain,
    ! [X0] :
      ( ( rearsegP(nil,X0)
      <=> nil = X0 )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f52]) ).

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

fof(f221,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ neq(X0,nil)
                  & ? [X4] :
                      ( ? [X5] :
                          ( ? [X6] :
                              ( app(app(X4,cons(X6,nil)),X5) = X2
                              & ssItem(X6) )
                          & app(X4,X5) = X3
                          & ssList(X5) )
                      & ssList(X4) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f97]) ).

fof(f222,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ neq(X0,nil)
                  & ? [X4] :
                      ( ? [X5] :
                          ( ? [X6] :
                              ( app(app(X4,cons(X6,nil)),X5) = X2
                              & ssItem(X6) )
                          & app(X4,X5) = X3
                          & ssList(X5) )
                      & ssList(X4) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f221]) ).

fof(f249,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( rearsegP(X0,X1)
              | ! [X2] :
                  ( app(X2,X1) != X0
                  | ~ ssList(X2) ) )
            & ( ? [X2] :
                  ( app(X2,X1) = X0
                  & ssList(X2) )
              | ~ rearsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f102]) ).

fof(f250,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( rearsegP(X0,X1)
              | ! [X2] :
                  ( app(X2,X1) != X0
                  | ~ ssList(X2) ) )
            & ( ? [X3] :
                  ( app(X3,X1) = X0
                  & ssList(X3) )
              | ~ rearsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f249]) ).

fof(f251,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( app(X3,X1) = X0
          & ssList(X3) )
     => ( app(sK12(X0,X1),X1) = X0
        & ssList(sK12(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f252,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( rearsegP(X0,X1)
              | ! [X2] :
                  ( app(X2,X1) != X0
                  | ~ ssList(X2) ) )
            & ( ( app(sK12(X0,X1),X1) = X0
                & ssList(sK12(X0,X1)) )
              | ~ rearsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f250,f251]) ).

fof(f253,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ? [X2] :
                  ( ? [X3] :
                      ( app(app(X2,X1),X3) = X0
                      & ssList(X3) )
                  & ssList(X2) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f103]) ).

fof(f254,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ? [X4] :
                  ( ? [X5] :
                      ( app(app(X4,X1),X5) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f253]) ).

fof(f255,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( app(app(X4,X1),X5) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( app(app(sK13(X0,X1),X1),X5) = X0
            & ssList(X5) )
        & ssList(sK13(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f256,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( app(app(sK13(X0,X1),X1),X5) = X0
          & ssList(X5) )
     => ( app(app(sK13(X0,X1),X1),sK14(X0,X1)) = X0
        & ssList(sK14(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f257,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ( app(app(sK13(X0,X1),X1),sK14(X0,X1)) = X0
                & ssList(sK14(X0,X1))
                & ssList(sK13(X0,X1)) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14])],[f254,f256,f255]) ).

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

fof(f329,plain,
    ! [X0] :
      ( ( ( rearsegP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ rearsegP(nil,X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f167]) ).

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

fof(f343,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ~ neq(X0,nil)
                    & ? [X4] :
                        ( ? [X5] :
                            ( ? [X6] :
                                ( app(app(X4,cons(X6,nil)),X5) = X2
                                & ssItem(X6) )
                            & app(X4,X5) = X3
                            & ssList(X5) )
                        & ssList(X4) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ neq(sK53,nil)
                  & ? [X4] :
                      ( ? [X5] :
                          ( ? [X6] :
                              ( app(app(X4,cons(X6,nil)),X5) = X2
                              & ssItem(X6) )
                          & app(X4,X5) = X3
                          & ssList(X5) )
                      & ssList(X4) )
                  & sK53 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK53) ) ),
    introduced(choice_axiom,[]) ).

fof(f344,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ~ neq(sK53,nil)
                & ? [X4] :
                    ( ? [X5] :
                        ( ? [X6] :
                            ( app(app(X4,cons(X6,nil)),X5) = X2
                            & ssItem(X6) )
                        & app(X4,X5) = X3
                        & ssList(X5) )
                    & ssList(X4) )
                & sK53 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ~ neq(sK53,nil)
              & ? [X4] :
                  ( ? [X5] :
                      ( ? [X6] :
                          ( app(app(X4,cons(X6,nil)),X5) = X2
                          & ssItem(X6) )
                      & app(X4,X5) = X3
                      & ssList(X5) )
                  & ssList(X4) )
              & sK53 = X2
              & sK54 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK54) ) ),
    introduced(choice_axiom,[]) ).

fof(f345,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ~ neq(sK53,nil)
            & ? [X4] :
                ( ? [X5] :
                    ( ? [X6] :
                        ( app(app(X4,cons(X6,nil)),X5) = X2
                        & ssItem(X6) )
                    & app(X4,X5) = X3
                    & ssList(X5) )
                & ssList(X4) )
            & sK53 = X2
            & sK54 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ~ neq(sK53,nil)
          & ? [X4] :
              ( ? [X5] :
                  ( ? [X6] :
                      ( app(app(X4,cons(X6,nil)),X5) = sK55
                      & ssItem(X6) )
                  & app(X4,X5) = X3
                  & ssList(X5) )
              & ssList(X4) )
          & sK53 = sK55
          & sK54 = X3
          & ssList(X3) )
      & ssList(sK55) ) ),
    introduced(choice_axiom,[]) ).

fof(f346,plain,
    ( ? [X3] :
        ( ~ neq(sK53,nil)
        & ? [X4] :
            ( ? [X5] :
                ( ? [X6] :
                    ( app(app(X4,cons(X6,nil)),X5) = sK55
                    & ssItem(X6) )
                & app(X4,X5) = X3
                & ssList(X5) )
            & ssList(X4) )
        & sK53 = sK55
        & sK54 = X3
        & ssList(X3) )
   => ( ~ neq(sK53,nil)
      & ? [X4] :
          ( ? [X5] :
              ( ? [X6] :
                  ( app(app(X4,cons(X6,nil)),X5) = sK55
                  & ssItem(X6) )
              & app(X4,X5) = sK56
              & ssList(X5) )
          & ssList(X4) )
      & sK53 = sK55
      & sK54 = sK56
      & ssList(sK56) ) ),
    introduced(choice_axiom,[]) ).

fof(f347,plain,
    ( ? [X4] :
        ( ? [X5] :
            ( ? [X6] :
                ( app(app(X4,cons(X6,nil)),X5) = sK55
                & ssItem(X6) )
            & app(X4,X5) = sK56
            & ssList(X5) )
        & ssList(X4) )
   => ( ? [X5] :
          ( ? [X6] :
              ( sK55 = app(app(sK57,cons(X6,nil)),X5)
              & ssItem(X6) )
          & sK56 = app(sK57,X5)
          & ssList(X5) )
      & ssList(sK57) ) ),
    introduced(choice_axiom,[]) ).

fof(f348,plain,
    ( ? [X5] :
        ( ? [X6] :
            ( sK55 = app(app(sK57,cons(X6,nil)),X5)
            & ssItem(X6) )
        & sK56 = app(sK57,X5)
        & ssList(X5) )
   => ( ? [X6] :
          ( sK55 = app(app(sK57,cons(X6,nil)),sK58)
          & ssItem(X6) )
      & sK56 = app(sK57,sK58)
      & ssList(sK58) ) ),
    introduced(choice_axiom,[]) ).

fof(f349,plain,
    ( ? [X6] :
        ( sK55 = app(app(sK57,cons(X6,nil)),sK58)
        & ssItem(X6) )
   => ( sK55 = app(app(sK57,cons(sK59,nil)),sK58)
      & ssItem(sK59) ) ),
    introduced(choice_axiom,[]) ).

fof(f350,plain,
    ( ~ neq(sK53,nil)
    & sK55 = app(app(sK57,cons(sK59,nil)),sK58)
    & ssItem(sK59)
    & sK56 = app(sK57,sK58)
    & ssList(sK58)
    & ssList(sK57)
    & sK53 = sK55
    & sK54 = sK56
    & ssList(sK56)
    & ssList(sK55)
    & ssList(sK54)
    & ssList(sK53) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58,sK59])],[f222,f349,f348,f347,f346,f345,f344,f343]) ).

fof(f368,plain,
    ! [X2,X0,X1] :
      ( rearsegP(X0,X1)
      | app(X2,X1) != X0
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f252]) ).

fof(f372,plain,
    ! [X2,X3,X0,X1] :
      ( segmentP(X0,X1)
      | app(app(X2,X1),X3) != X0
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f257]) ).

fof(f441,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f316]) ).

fof(f442,plain,
    ! [X0,X1] :
      ( ssList(cons(X1,X0))
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f119]) ).

fof(f443,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f450,plain,
    ! [X0,X1] :
      ( nil != cons(X1,X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f125]) ).

fof(f455,plain,
    ! [X0,X1] :
      ( ssList(app(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f132]) ).

fof(f490,plain,
    ! [X0] :
      ( nil = X0
      | ~ rearsegP(nil,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f329]) ).

fof(f497,plain,
    ! [X0] :
      ( nil = X0
      | ~ segmentP(nil,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f330]) ).

fof(f550,plain,
    ssList(sK53),
    inference(cnf_transformation,[],[f350]) ).

fof(f555,plain,
    sK53 = sK55,
    inference(cnf_transformation,[],[f350]) ).

fof(f556,plain,
    ssList(sK57),
    inference(cnf_transformation,[],[f350]) ).

fof(f557,plain,
    ssList(sK58),
    inference(cnf_transformation,[],[f350]) ).

fof(f559,plain,
    ssItem(sK59),
    inference(cnf_transformation,[],[f350]) ).

fof(f560,plain,
    sK55 = app(app(sK57,cons(sK59,nil)),sK58),
    inference(cnf_transformation,[],[f350]) ).

fof(f561,plain,
    ~ neq(sK53,nil),
    inference(cnf_transformation,[],[f350]) ).

fof(f562,plain,
    ~ neq(sK55,nil),
    inference(definition_unfolding,[],[f561,f555]) ).

fof(f564,plain,
    ssList(sK55),
    inference(definition_unfolding,[],[f550,f555]) ).

fof(f569,plain,
    ! [X2,X1] :
      ( rearsegP(app(X2,X1),X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(app(X2,X1)) ),
    inference(equality_resolution,[],[f368]) ).

fof(f570,plain,
    ! [X2,X3,X1] :
      ( segmentP(app(app(X2,X1),X3),X1)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(app(app(X2,X1),X3)) ),
    inference(equality_resolution,[],[f372]) ).

cnf(c_64,plain,
    ( ~ ssList(app(X0,X1))
    | ~ ssList(X0)
    | ~ ssList(X1)
    | rearsegP(app(X0,X1),X1) ),
    inference(cnf_transformation,[],[f569]) ).

cnf(c_67,plain,
    ( ~ ssList(app(app(X0,X1),X2))
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | segmentP(app(app(X0,X1),X2),X1) ),
    inference(cnf_transformation,[],[f570]) ).

cnf(c_138,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | X0 = X1
    | neq(X0,X1) ),
    inference(cnf_transformation,[],[f441]) ).

cnf(c_140,plain,
    ( ~ ssItem(X0)
    | ~ ssList(X1)
    | ssList(cons(X0,X1)) ),
    inference(cnf_transformation,[],[f442]) ).

cnf(c_141,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f443]) ).

cnf(c_148,plain,
    ( cons(X0,X1) != nil
    | ~ ssItem(X0)
    | ~ ssList(X1) ),
    inference(cnf_transformation,[],[f450]) ).

cnf(c_153,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | ssList(app(X0,X1)) ),
    inference(cnf_transformation,[],[f455]) ).

cnf(c_189,plain,
    ( ~ rearsegP(nil,X0)
    | ~ ssList(X0)
    | X0 = nil ),
    inference(cnf_transformation,[],[f490]) ).

cnf(c_196,plain,
    ( ~ segmentP(nil,X0)
    | ~ ssList(X0)
    | X0 = nil ),
    inference(cnf_transformation,[],[f497]) ).

cnf(c_246,negated_conjecture,
    ~ neq(sK55,nil),
    inference(cnf_transformation,[],[f562]) ).

cnf(c_247,negated_conjecture,
    app(app(sK57,cons(sK59,nil)),sK58) = sK55,
    inference(cnf_transformation,[],[f560]) ).

cnf(c_248,negated_conjecture,
    ssItem(sK59),
    inference(cnf_transformation,[],[f559]) ).

cnf(c_250,negated_conjecture,
    ssList(sK58),
    inference(cnf_transformation,[],[f557]) ).

cnf(c_251,negated_conjecture,
    ssList(sK57),
    inference(cnf_transformation,[],[f556]) ).

cnf(c_255,negated_conjecture,
    ssList(sK55),
    inference(cnf_transformation,[],[f564]) ).

cnf(c_374,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | rearsegP(app(X0,X1),X1) ),
    inference(global_subsumption_just,[status(thm)],[c_64,c_153,c_64]) ).

cnf(c_3207,plain,
    ( X0 != sK55
    | X1 != nil
    | ~ ssList(X0)
    | ~ ssList(X1)
    | X0 = X1 ),
    inference(resolution_lifted,[status(thm)],[c_138,c_246]) ).

cnf(c_3208,plain,
    ( ~ ssList(nil)
    | ~ ssList(sK55)
    | sK55 = nil ),
    inference(unflattening,[status(thm)],[c_3207]) ).

cnf(c_3209,plain,
    sK55 = nil,
    inference(global_subsumption_just,[status(thm)],[c_3208,c_255,c_141,c_3208]) ).

cnf(c_6289,plain,
    app(app(sK57,cons(sK59,nil)),sK58) = nil,
    inference(light_normalisation,[status(thm)],[c_247,c_3209]) ).

cnf(c_16956,plain,
    ( ~ ssList(app(sK57,cons(sK59,nil)))
    | ~ ssList(sK58)
    | rearsegP(nil,sK58) ),
    inference(superposition,[status(thm)],[c_6289,c_374]) ).

cnf(c_16991,plain,
    ( ~ ssList(app(sK57,cons(sK59,nil)))
    | rearsegP(nil,sK58) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_16956,c_250]) ).

cnf(c_17028,plain,
    ( ~ ssList(cons(sK59,nil))
    | ~ ssList(sK57)
    | rearsegP(nil,sK58) ),
    inference(superposition,[status(thm)],[c_153,c_16991]) ).

cnf(c_17029,plain,
    ( ~ ssList(cons(sK59,nil))
    | rearsegP(nil,sK58) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_17028,c_251]) ).

cnf(c_17036,plain,
    ( ~ ssItem(sK59)
    | ~ ssList(nil)
    | rearsegP(nil,sK58) ),
    inference(superposition,[status(thm)],[c_140,c_17029]) ).

cnf(c_17037,plain,
    rearsegP(nil,sK58),
    inference(forward_subsumption_resolution,[status(thm)],[c_17036,c_141,c_248]) ).

cnf(c_17038,plain,
    ( ~ ssList(sK58)
    | nil = sK58 ),
    inference(superposition,[status(thm)],[c_17037,c_189]) ).

cnf(c_17039,plain,
    nil = sK58,
    inference(forward_subsumption_resolution,[status(thm)],[c_17038,c_250]) ).

cnf(c_17050,plain,
    app(app(sK57,cons(sK59,nil)),nil) = nil,
    inference(demodulation,[status(thm)],[c_6289,c_17039]) ).

cnf(c_17326,plain,
    ( ~ ssList(X0)
    | ~ ssItem(sK59)
    | ssList(cons(sK59,X0)) ),
    inference(instantiation,[status(thm)],[c_140]) ).

cnf(c_17327,plain,
    ( ~ ssItem(sK59)
    | ~ ssList(nil)
    | ssList(cons(sK59,nil)) ),
    inference(instantiation,[status(thm)],[c_17326]) ).

cnf(c_17332,plain,
    ( cons(sK59,X0) != nil
    | ~ ssList(X0)
    | ~ ssItem(sK59) ),
    inference(instantiation,[status(thm)],[c_148]) ).

cnf(c_17333,plain,
    ( cons(sK59,nil) != nil
    | ~ ssItem(sK59)
    | ~ ssList(nil) ),
    inference(instantiation,[status(thm)],[c_17332]) ).

cnf(c_18512,plain,
    ( ~ segmentP(nil,cons(sK59,X0))
    | ~ ssList(cons(sK59,X0))
    | cons(sK59,X0) = nil ),
    inference(instantiation,[status(thm)],[c_196]) ).

cnf(c_18525,plain,
    ( ~ segmentP(nil,cons(sK59,nil))
    | ~ ssList(cons(sK59,nil))
    | cons(sK59,nil) = nil ),
    inference(instantiation,[status(thm)],[c_18512]) ).

cnf(c_31785,plain,
    ( ~ ssList(app(app(sK57,cons(sK59,nil)),nil))
    | ~ ssList(cons(sK59,nil))
    | ~ ssList(nil)
    | ~ ssList(sK57)
    | segmentP(nil,cons(sK59,nil)) ),
    inference(superposition,[status(thm)],[c_17050,c_67]) ).

cnf(c_31865,plain,
    ( ~ ssList(cons(sK59,nil))
    | ~ ssList(nil)
    | ~ ssList(sK57)
    | segmentP(nil,cons(sK59,nil)) ),
    inference(light_normalisation,[status(thm)],[c_31785,c_17050]) ).

cnf(c_31866,plain,
    ( ~ ssList(cons(sK59,nil))
    | segmentP(nil,cons(sK59,nil)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31865,c_251,c_141]) ).

cnf(c_32064,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_31866,c_18525,c_17333,c_17327,c_141,c_248]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWC218+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n002.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 : Mon Aug 28 18:41:50 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.46  Running first-order theorem proving
% 0.20/0.46  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.77/1.65  % SZS status Started for theBenchmark.p
% 6.77/1.65  % SZS status Theorem for theBenchmark.p
% 6.77/1.65  
% 6.77/1.65  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 6.77/1.65  
% 6.77/1.65  ------  iProver source info
% 6.77/1.65  
% 6.77/1.65  git: date: 2023-05-31 18:12:56 +0000
% 6.77/1.65  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 6.77/1.65  git: non_committed_changes: false
% 6.77/1.65  git: last_make_outside_of_git: false
% 6.77/1.65  
% 6.77/1.65  ------ Parsing...
% 6.77/1.65  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 6.77/1.65  
% 6.77/1.65  ------ 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: 3  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 
% 6.77/1.65  
% 6.77/1.65  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 6.77/1.65  
% 6.77/1.65  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 6.77/1.65  ------ Proving...
% 6.77/1.65  ------ Problem Properties 
% 6.77/1.65  
% 6.77/1.65  
% 6.77/1.65  clauses                                 187
% 6.77/1.65  conjectures                             5
% 6.77/1.65  EPR                                     54
% 6.77/1.65  Horn                                    119
% 6.77/1.65  unary                                   23
% 6.77/1.65  binary                                  40
% 6.77/1.65  lits                                    625
% 6.77/1.65  lits eq                                 81
% 6.77/1.65  fd_pure                                 0
% 6.77/1.65  fd_pseudo                               0
% 6.77/1.65  fd_cond                                 21
% 6.77/1.65  fd_pseudo_cond                          14
% 6.77/1.65  AC symbols                              0
% 6.77/1.65  
% 6.77/1.65  ------ Schedule dynamic 5 is on 
% 6.77/1.65  
% 6.77/1.65  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.77/1.65  
% 6.77/1.65  
% 6.77/1.65  ------ 
% 6.77/1.65  Current options:
% 6.77/1.65  ------ 
% 6.77/1.65  
% 6.77/1.65  
% 6.77/1.65  
% 6.77/1.65  
% 6.77/1.65  ------ Proving...
% 6.77/1.65  
% 6.77/1.65  
% 6.77/1.65  % SZS status Theorem for theBenchmark.p
% 6.77/1.65  
% 6.77/1.65  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.77/1.66  
% 6.77/1.66  
%------------------------------------------------------------------------------