TSTP Solution File: SWC077+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWC077+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n023.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 03:11:08 EDT 2024

% Result   : Theorem 239.69s 31.33s
% Output   : CNFRefutation 239.69s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f594)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( frontsegP(X0,X1)
          <=> ? [X2] :
                ( app(X1,X2) = X0
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).

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/sandbox/benchmark/theBenchmark.p',ax7) ).

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

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

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(f22,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ssItem(hd(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).

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(f55,axiom,
    ! [X0] :
      ( ssList(X0)
     => segmentP(X0,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).

fof(f57,axiom,
    ! [X0] :
      ( ssList(X0)
     => segmentP(X0,nil) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax57) ).

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

fof(f68,axiom,
    ! [X0] :
      ( ssItem(X0)
     => strictorderedP(cons(X0,nil)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax68) ).

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

fof(f76,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ? [X1] :
            ( tl(X0) = X1
            & ssList(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax76) ).

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

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

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( nil = X0
                      & nil = X1 )
                    | ? [X5] :
                        ( strictorderedP(X5)
                        & segmentP(X5,X2)
                        & frontsegP(X3,X5)
                        & neq(X2,X5)
                        & ssList(X5) )
                    | ? [X4] :
                        ( segmentP(X0,X4)
                        & segmentP(X1,X4)
                        & neq(X4,nil)
                        & ssList(X4) )
                    | ~ strictorderedP(X2)
                    | ~ frontsegP(X3,X2)
                    | 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)
                   => ( ( nil = X0
                        & nil = X1 )
                      | ? [X5] :
                          ( strictorderedP(X5)
                          & segmentP(X5,X2)
                          & frontsegP(X3,X5)
                          & neq(X2,X5)
                          & ssList(X5) )
                      | ? [X4] :
                          ( segmentP(X0,X4)
                          & segmentP(X1,X4)
                          & neq(X4,nil)
                          & ssList(X4) )
                      | ~ strictorderedP(X2)
                      | ~ frontsegP(X3,X2)
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( nil = X0
                        & nil = X1 )
                      | ? [X4] :
                          ( strictorderedP(X4)
                          & segmentP(X4,X2)
                          & frontsegP(X3,X4)
                          & neq(X2,X4)
                          & ssList(X4) )
                      | ? [X5] :
                          ( segmentP(X0,X5)
                          & segmentP(X1,X5)
                          & neq(X5,nil)
                          & ssList(X5) )
                      | ~ strictorderedP(X2)
                      | ~ frontsegP(X3,X2)
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f102,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( frontsegP(X0,X1)
          <=> ? [X2] :
                ( app(X1,X2) = X0
                & ssList(X2) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f104,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(f119,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( neq(X0,X1)
          <=> X0 != X1 )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f120,plain,
    ! [X0] :
      ( ! [X1] :
          ( ssList(cons(X1,X0))
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f121,plain,
    ! [X0] :
      ( ! [X1] :
          ( cons(X1,X0) != X0
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f127,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f128,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f127]) ).

fof(f133,plain,
    ! [X0] :
      ( ! [X1] :
          ( ssList(app(X0,X1))
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f135,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f173,plain,
    ! [X0] :
      ( segmentP(X0,X0)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f55]) ).

fof(f176,plain,
    ! [X0] :
      ( segmentP(X0,nil)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f57]) ).

fof(f177,plain,
    ! [X0] :
      ( ( segmentP(nil,X0)
      <=> nil = X0 )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f58]) ).

fof(f183,plain,
    ! [X0] :
      ( strictorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f68]) ).

fof(f187,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f75]) ).

fof(f188,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f187]) ).

fof(f189,plain,
    ! [X0] :
      ( ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f76]) ).

fof(f190,plain,
    ! [X0] :
      ( ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f189]) ).

fof(f193,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f78]) ).

fof(f194,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f193]) ).

fof(f199,plain,
    ! [X0] :
      ( ! [X1] :
          ( cons(X1,X0) = app(cons(X1,nil),X0)
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f81]) ).

fof(f202,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f84]) ).

fof(f222,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( nil != X0
                    | nil != X1 )
                  & ! [X4] :
                      ( ~ strictorderedP(X4)
                      | ~ segmentP(X4,X2)
                      | ~ frontsegP(X3,X4)
                      | ~ neq(X2,X4)
                      | ~ ssList(X4) )
                  & ! [X5] :
                      ( ~ segmentP(X0,X5)
                      | ~ segmentP(X1,X5)
                      | ~ neq(X5,nil)
                      | ~ ssList(X5) )
                  & strictorderedP(X2)
                  & frontsegP(X3,X2)
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f223,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( nil != X0
                    | nil != X1 )
                  & ! [X4] :
                      ( ~ strictorderedP(X4)
                      | ~ segmentP(X4,X2)
                      | ~ frontsegP(X3,X4)
                      | ~ neq(X2,X4)
                      | ~ ssList(X4) )
                  & ! [X5] :
                      ( ~ segmentP(X0,X5)
                      | ~ segmentP(X1,X5)
                      | ~ neq(X5,nil)
                      | ~ ssList(X5) )
                  & strictorderedP(X2)
                  & frontsegP(X3,X2)
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f222]) ).

fof(f246,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( frontsegP(X0,X1)
              | ! [X2] :
                  ( app(X1,X2) != X0
                  | ~ ssList(X2) ) )
            & ( ? [X2] :
                  ( app(X1,X2) = X0
                  & ssList(X2) )
              | ~ frontsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f102]) ).

fof(f247,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( frontsegP(X0,X1)
              | ! [X2] :
                  ( app(X1,X2) != X0
                  | ~ ssList(X2) ) )
            & ( ? [X3] :
                  ( app(X1,X3) = X0
                  & ssList(X3) )
              | ~ frontsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f246]) ).

fof(f248,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( app(X1,X3) = X0
          & ssList(X3) )
     => ( app(X1,sK11(X0,X1)) = X0
        & ssList(sK11(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f249,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( frontsegP(X0,X1)
              | ! [X2] :
                  ( app(X1,X2) != X0
                  | ~ ssList(X2) ) )
            & ( ( app(X1,sK11(X0,X1)) = X0
                & ssList(sK11(X0,X1)) )
              | ~ frontsegP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f247,f248]) ).

fof(f254,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,[],[f104]) ).

fof(f255,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,[],[f254]) ).

fof(f256,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(f257,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(f258,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])],[f255,f257,f256]) ).

fof(f317,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f119]) ).

fof(f331,plain,
    ! [X0] :
      ( ( ( segmentP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ segmentP(nil,X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f177]) ).

fof(f336,plain,
    ! [X0] :
      ( ? [X1] :
          ( hd(X0) = X1
          & ssItem(X1) )
     => ( hd(X0) = sK51(X0)
        & ssItem(sK51(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f337,plain,
    ! [X0] :
      ( ( hd(X0) = sK51(X0)
        & ssItem(sK51(X0)) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK51])],[f188,f336]) ).

fof(f338,plain,
    ! [X0] :
      ( ? [X1] :
          ( tl(X0) = X1
          & ssList(X1) )
     => ( tl(X0) = sK52(X0)
        & ssList(sK52(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f339,plain,
    ! [X0] :
      ( ( tl(X0) = sK52(X0)
        & ssList(sK52(X0)) )
      | nil = X0
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f190,f338]) ).

fof(f344,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( nil != X0
                      | nil != X1 )
                    & ! [X4] :
                        ( ~ strictorderedP(X4)
                        | ~ segmentP(X4,X2)
                        | ~ frontsegP(X3,X4)
                        | ~ neq(X2,X4)
                        | ~ ssList(X4) )
                    & ! [X5] :
                        ( ~ segmentP(X0,X5)
                        | ~ segmentP(X1,X5)
                        | ~ neq(X5,nil)
                        | ~ ssList(X5) )
                    & strictorderedP(X2)
                    & frontsegP(X3,X2)
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( nil != sK53
                    | nil != X1 )
                  & ! [X4] :
                      ( ~ strictorderedP(X4)
                      | ~ segmentP(X4,X2)
                      | ~ frontsegP(X3,X4)
                      | ~ neq(X2,X4)
                      | ~ ssList(X4) )
                  & ! [X5] :
                      ( ~ segmentP(sK53,X5)
                      | ~ segmentP(X1,X5)
                      | ~ neq(X5,nil)
                      | ~ ssList(X5) )
                  & strictorderedP(X2)
                  & frontsegP(X3,X2)
                  & sK53 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK53) ) ),
    introduced(choice_axiom,[]) ).

fof(f345,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( nil != sK53
                  | nil != X1 )
                & ! [X4] :
                    ( ~ strictorderedP(X4)
                    | ~ segmentP(X4,X2)
                    | ~ frontsegP(X3,X4)
                    | ~ neq(X2,X4)
                    | ~ ssList(X4) )
                & ! [X5] :
                    ( ~ segmentP(sK53,X5)
                    | ~ segmentP(X1,X5)
                    | ~ neq(X5,nil)
                    | ~ ssList(X5) )
                & strictorderedP(X2)
                & frontsegP(X3,X2)
                & sK53 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( nil != sK53
                | nil != sK54 )
              & ! [X4] :
                  ( ~ strictorderedP(X4)
                  | ~ segmentP(X4,X2)
                  | ~ frontsegP(X3,X4)
                  | ~ neq(X2,X4)
                  | ~ ssList(X4) )
              & ! [X5] :
                  ( ~ segmentP(sK53,X5)
                  | ~ segmentP(sK54,X5)
                  | ~ neq(X5,nil)
                  | ~ ssList(X5) )
              & strictorderedP(X2)
              & frontsegP(X3,X2)
              & sK53 = X2
              & sK54 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK54) ) ),
    introduced(choice_axiom,[]) ).

fof(f346,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( nil != sK53
              | nil != sK54 )
            & ! [X4] :
                ( ~ strictorderedP(X4)
                | ~ segmentP(X4,X2)
                | ~ frontsegP(X3,X4)
                | ~ neq(X2,X4)
                | ~ ssList(X4) )
            & ! [X5] :
                ( ~ segmentP(sK53,X5)
                | ~ segmentP(sK54,X5)
                | ~ neq(X5,nil)
                | ~ ssList(X5) )
            & strictorderedP(X2)
            & frontsegP(X3,X2)
            & sK53 = X2
            & sK54 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( nil != sK53
            | nil != sK54 )
          & ! [X4] :
              ( ~ strictorderedP(X4)
              | ~ segmentP(X4,sK55)
              | ~ frontsegP(X3,X4)
              | ~ neq(sK55,X4)
              | ~ ssList(X4) )
          & ! [X5] :
              ( ~ segmentP(sK53,X5)
              | ~ segmentP(sK54,X5)
              | ~ neq(X5,nil)
              | ~ ssList(X5) )
          & strictorderedP(sK55)
          & frontsegP(X3,sK55)
          & sK53 = sK55
          & sK54 = X3
          & ssList(X3) )
      & ssList(sK55) ) ),
    introduced(choice_axiom,[]) ).

fof(f347,plain,
    ( ? [X3] :
        ( ( nil != sK53
          | nil != sK54 )
        & ! [X4] :
            ( ~ strictorderedP(X4)
            | ~ segmentP(X4,sK55)
            | ~ frontsegP(X3,X4)
            | ~ neq(sK55,X4)
            | ~ ssList(X4) )
        & ! [X5] :
            ( ~ segmentP(sK53,X5)
            | ~ segmentP(sK54,X5)
            | ~ neq(X5,nil)
            | ~ ssList(X5) )
        & strictorderedP(sK55)
        & frontsegP(X3,sK55)
        & sK53 = sK55
        & sK54 = X3
        & ssList(X3) )
   => ( ( nil != sK53
        | nil != sK54 )
      & ! [X4] :
          ( ~ strictorderedP(X4)
          | ~ segmentP(X4,sK55)
          | ~ frontsegP(sK56,X4)
          | ~ neq(sK55,X4)
          | ~ ssList(X4) )
      & ! [X5] :
          ( ~ segmentP(sK53,X5)
          | ~ segmentP(sK54,X5)
          | ~ neq(X5,nil)
          | ~ ssList(X5) )
      & strictorderedP(sK55)
      & frontsegP(sK56,sK55)
      & sK53 = sK55
      & sK54 = sK56
      & ssList(sK56) ) ),
    introduced(choice_axiom,[]) ).

fof(f348,plain,
    ( ( nil != sK53
      | nil != sK54 )
    & ! [X4] :
        ( ~ strictorderedP(X4)
        | ~ segmentP(X4,sK55)
        | ~ frontsegP(sK56,X4)
        | ~ neq(sK55,X4)
        | ~ ssList(X4) )
    & ! [X5] :
        ( ~ segmentP(sK53,X5)
        | ~ segmentP(sK54,X5)
        | ~ neq(X5,nil)
        | ~ ssList(X5) )
    & strictorderedP(sK55)
    & frontsegP(sK56,sK55)
    & sK53 = sK55
    & sK54 = sK56
    & ssList(sK56)
    & ssList(sK55)
    & ssList(sK54)
    & ssList(sK53) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56])],[f223,f347,f346,f345,f344]) ).

fof(f361,plain,
    ! [X0,X1] :
      ( ssList(sK11(X0,X1))
      | ~ frontsegP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f249]) ).

fof(f362,plain,
    ! [X0,X1] :
      ( app(X1,sK11(X0,X1)) = X0
      | ~ frontsegP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f249]) ).

fof(f363,plain,
    ! [X2,X0,X1] :
      ( frontsegP(X0,X1)
      | app(X1,X2) != X0
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f249]) ).

fof(f370,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,[],[f258]) ).

fof(f439,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f317]) ).

fof(f440,plain,
    ! [X0,X1] :
      ( ssList(cons(X1,X0))
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f441,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f442,plain,
    ! [X0,X1] :
      ( cons(X1,X0) != X0
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f121]) ).

fof(f449,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f128]) ).

fof(f453,plain,
    ! [X0,X1] :
      ( ssList(app(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f133]) ).

fof(f455,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f135]) ).

fof(f492,plain,
    ! [X0] :
      ( segmentP(X0,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f173]) ).

fof(f494,plain,
    ! [X0] :
      ( segmentP(X0,nil)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f176]) ).

fof(f495,plain,
    ! [X0] :
      ( nil = X0
      | ~ segmentP(nil,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f331]) ).

fof(f496,plain,
    ! [X0] :
      ( segmentP(nil,X0)
      | nil != X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f331]) ).

fof(f510,plain,
    ! [X0] :
      ( strictorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f183]) ).

fof(f521,plain,
    ! [X0] :
      ( ssItem(sK51(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f337]) ).

fof(f522,plain,
    ! [X0] :
      ( hd(X0) = sK51(X0)
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f337]) ).

fof(f523,plain,
    ! [X0] :
      ( ssList(sK52(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f339]) ).

fof(f524,plain,
    ! [X0] :
      ( tl(X0) = sK52(X0)
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f339]) ).

fof(f526,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f194]) ).

fof(f529,plain,
    ! [X0,X1] :
      ( cons(X1,X0) = app(cons(X1,nil),X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f199]) ).

fof(f534,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f202]) ).

fof(f548,plain,
    ssList(sK53),
    inference(cnf_transformation,[],[f348]) ).

fof(f549,plain,
    ssList(sK54),
    inference(cnf_transformation,[],[f348]) ).

fof(f552,plain,
    sK54 = sK56,
    inference(cnf_transformation,[],[f348]) ).

fof(f553,plain,
    sK53 = sK55,
    inference(cnf_transformation,[],[f348]) ).

fof(f554,plain,
    frontsegP(sK56,sK55),
    inference(cnf_transformation,[],[f348]) ).

fof(f556,plain,
    ! [X5] :
      ( ~ segmentP(sK53,X5)
      | ~ segmentP(sK54,X5)
      | ~ neq(X5,nil)
      | ~ ssList(X5) ),
    inference(cnf_transformation,[],[f348]) ).

fof(f557,plain,
    ! [X4] :
      ( ~ strictorderedP(X4)
      | ~ segmentP(X4,sK55)
      | ~ frontsegP(sK56,X4)
      | ~ neq(sK55,X4)
      | ~ ssList(X4) ),
    inference(cnf_transformation,[],[f348]) ).

fof(f558,plain,
    ( nil != sK53
    | nil != sK54 ),
    inference(cnf_transformation,[],[f348]) ).

fof(f559,plain,
    ( nil != sK55
    | nil != sK56 ),
    inference(definition_unfolding,[],[f558,f553,f552]) ).

fof(f560,plain,
    ! [X5] :
      ( ~ segmentP(sK55,X5)
      | ~ segmentP(sK56,X5)
      | ~ neq(X5,nil)
      | ~ ssList(X5) ),
    inference(definition_unfolding,[],[f556,f553,f552]) ).

fof(f561,plain,
    ssList(sK56),
    inference(definition_unfolding,[],[f549,f552]) ).

fof(f562,plain,
    ssList(sK55),
    inference(definition_unfolding,[],[f548,f553]) ).

fof(f566,plain,
    ! [X2,X1] :
      ( frontsegP(app(X1,X2),X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(app(X1,X2)) ),
    inference(equality_resolution,[],[f363]) ).

fof(f568,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,[],[f370]) ).

fof(f582,plain,
    ( segmentP(nil,nil)
    | ~ ssList(nil) ),
    inference(equality_resolution,[],[f496]) ).

cnf(c_61,plain,
    ( ~ ssList(app(X0,X1))
    | ~ ssList(X0)
    | ~ ssList(X1)
    | frontsegP(app(X0,X1),X0) ),
    inference(cnf_transformation,[],[f566]) ).

cnf(c_62,plain,
    ( ~ frontsegP(X0,X1)
    | ~ ssList(X0)
    | ~ ssList(X1)
    | app(X1,sK11(X0,X1)) = X0 ),
    inference(cnf_transformation,[],[f362]) ).

cnf(c_63,plain,
    ( ~ frontsegP(X0,X1)
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ssList(sK11(X0,X1)) ),
    inference(cnf_transformation,[],[f361]) ).

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,[],[f568]) ).

cnf(c_138,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | X0 = X1
    | neq(X0,X1) ),
    inference(cnf_transformation,[],[f439]) ).

cnf(c_140,plain,
    ( ~ ssItem(X0)
    | ~ ssList(X1)
    | ssList(cons(X0,X1)) ),
    inference(cnf_transformation,[],[f440]) ).

cnf(c_141,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f441]) ).

cnf(c_142,plain,
    ( cons(X0,X1) != X1
    | ~ ssItem(X0)
    | ~ ssList(X1) ),
    inference(cnf_transformation,[],[f442]) ).

cnf(c_149,plain,
    ( ~ ssList(X0)
    | X0 = nil
    | ssItem(hd(X0)) ),
    inference(cnf_transformation,[],[f449]) ).

cnf(c_153,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | ssList(app(X0,X1)) ),
    inference(cnf_transformation,[],[f453]) ).

cnf(c_155,plain,
    ( ~ ssList(X0)
    | app(nil,X0) = X0 ),
    inference(cnf_transformation,[],[f455]) ).

cnf(c_177,plain,
    ( ~ frontsegP(X0,X1)
    | ~ ssItem(X2)
    | ~ ssList(X0)
    | ~ ssList(X1)
    | frontsegP(cons(X2,X0),cons(X2,X1)) ),
    inference(cnf_transformation,[],[f594]) ).

cnf(c_192,plain,
    ( ~ ssList(X0)
    | segmentP(X0,X0) ),
    inference(cnf_transformation,[],[f492]) ).

cnf(c_194,plain,
    ( ~ ssList(X0)
    | segmentP(X0,nil) ),
    inference(cnf_transformation,[],[f494]) ).

cnf(c_195,plain,
    ( ~ ssList(nil)
    | segmentP(nil,nil) ),
    inference(cnf_transformation,[],[f582]) ).

cnf(c_196,plain,
    ( ~ segmentP(nil,X0)
    | ~ ssList(X0)
    | X0 = nil ),
    inference(cnf_transformation,[],[f495]) ).

cnf(c_209,plain,
    ( ~ ssItem(X0)
    | strictorderedP(cons(X0,nil)) ),
    inference(cnf_transformation,[],[f510]) ).

cnf(c_219,plain,
    ( ~ ssList(X0)
    | hd(X0) = sK51(X0)
    | X0 = nil ),
    inference(cnf_transformation,[],[f522]) ).

cnf(c_220,plain,
    ( ~ ssList(X0)
    | X0 = nil
    | ssItem(sK51(X0)) ),
    inference(cnf_transformation,[],[f521]) ).

cnf(c_221,plain,
    ( ~ ssList(X0)
    | tl(X0) = sK52(X0)
    | X0 = nil ),
    inference(cnf_transformation,[],[f524]) ).

cnf(c_222,plain,
    ( ~ ssList(X0)
    | X0 = nil
    | ssList(sK52(X0)) ),
    inference(cnf_transformation,[],[f523]) ).

cnf(c_224,plain,
    ( ~ ssList(X0)
    | cons(hd(X0),tl(X0)) = X0
    | X0 = nil ),
    inference(cnf_transformation,[],[f526]) ).

cnf(c_227,plain,
    ( ~ ssItem(X0)
    | ~ ssList(X1)
    | app(cons(X0,nil),X1) = cons(X0,X1) ),
    inference(cnf_transformation,[],[f529]) ).

cnf(c_232,plain,
    ( ~ ssList(X0)
    | app(X0,nil) = X0 ),
    inference(cnf_transformation,[],[f534]) ).

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

cnf(c_247,negated_conjecture,
    ( ~ neq(sK55,X0)
    | ~ frontsegP(sK56,X0)
    | ~ segmentP(X0,sK55)
    | ~ ssList(X0)
    | ~ strictorderedP(X0) ),
    inference(cnf_transformation,[],[f557]) ).

cnf(c_248,negated_conjecture,
    ( ~ neq(X0,nil)
    | ~ segmentP(sK55,X0)
    | ~ segmentP(sK56,X0)
    | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f560]) ).

cnf(c_250,negated_conjecture,
    frontsegP(sK56,sK55),
    inference(cnf_transformation,[],[f554]) ).

cnf(c_253,negated_conjecture,
    ssList(sK56),
    inference(cnf_transformation,[],[f561]) ).

cnf(c_254,negated_conjecture,
    ssList(sK55),
    inference(cnf_transformation,[],[f562]) ).

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

cnf(c_377,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | frontsegP(app(X0,X1),X0) ),
    inference(global_subsumption_just,[status(thm)],[c_61,c_153,c_61]) ).

cnf(c_3243,plain,
    ( X0 != sK55
    | X1 != X2
    | ~ frontsegP(sK56,X2)
    | ~ segmentP(X2,sK55)
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ strictorderedP(X2)
    | X0 = X1 ),
    inference(resolution_lifted,[status(thm)],[c_138,c_247]) ).

cnf(c_3244,plain,
    ( ~ frontsegP(sK56,X0)
    | ~ segmentP(X0,sK55)
    | ~ ssList(X0)
    | ~ strictorderedP(X0)
    | ~ ssList(sK55)
    | sK55 = X0 ),
    inference(unflattening,[status(thm)],[c_3243]) ).

cnf(c_3246,plain,
    ( ~ strictorderedP(X0)
    | ~ ssList(X0)
    | ~ segmentP(X0,sK55)
    | ~ frontsegP(sK56,X0)
    | sK55 = X0 ),
    inference(global_subsumption_just,[status(thm)],[c_3244,c_254,c_3244]) ).

cnf(c_3247,plain,
    ( ~ frontsegP(sK56,X0)
    | ~ segmentP(X0,sK55)
    | ~ ssList(X0)
    | ~ strictorderedP(X0)
    | sK55 = X0 ),
    inference(renaming,[status(thm)],[c_3246]) ).

cnf(c_3269,plain,
    ( X0 != X1
    | X2 != nil
    | ~ segmentP(sK55,X1)
    | ~ segmentP(sK56,X1)
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | X0 = X2 ),
    inference(resolution_lifted,[status(thm)],[c_138,c_248]) ).

cnf(c_3270,plain,
    ( ~ segmentP(sK55,X0)
    | ~ segmentP(sK56,X0)
    | ~ ssList(X0)
    | ~ ssList(nil)
    | X0 = nil ),
    inference(unflattening,[status(thm)],[c_3269]) ).

cnf(c_3272,plain,
    ( ~ ssList(X0)
    | ~ segmentP(sK56,X0)
    | ~ segmentP(sK55,X0)
    | X0 = nil ),
    inference(global_subsumption_just,[status(thm)],[c_3270,c_141,c_3270]) ).

cnf(c_3273,plain,
    ( ~ segmentP(sK55,X0)
    | ~ segmentP(sK56,X0)
    | ~ ssList(X0)
    | X0 = nil ),
    inference(renaming,[status(thm)],[c_3272]) ).

cnf(c_8923,negated_conjecture,
    ssList(sK55),
    inference(demodulation,[status(thm)],[c_254]) ).

cnf(c_8924,negated_conjecture,
    ssList(sK56),
    inference(demodulation,[status(thm)],[c_253]) ).

cnf(c_8925,negated_conjecture,
    frontsegP(sK56,sK55),
    inference(demodulation,[status(thm)],[c_250]) ).

cnf(c_8927,negated_conjecture,
    ( nil != sK55
    | nil != sK56 ),
    inference(demodulation,[status(thm)],[c_246]) ).

cnf(c_8930,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_12113,plain,
    app(nil,sK55) = sK55,
    inference(superposition,[status(thm)],[c_8923,c_155]) ).

cnf(c_12195,plain,
    app(sK55,nil) = sK55,
    inference(superposition,[status(thm)],[c_8923,c_232]) ).

cnf(c_13204,plain,
    ( ~ ssList(sK55)
    | segmentP(sK55,sK55) ),
    inference(instantiation,[status(thm)],[c_192]) ).

cnf(c_13478,plain,
    ( nil != X0
    | sK55 != X0
    | nil = sK55 ),
    inference(instantiation,[status(thm)],[c_8930]) ).

cnf(c_13479,plain,
    ( nil != nil
    | sK55 != nil
    | nil = sK55 ),
    inference(instantiation,[status(thm)],[c_13478]) ).

cnf(c_14203,plain,
    ( hd(sK56) = sK51(sK56)
    | nil = sK56 ),
    inference(superposition,[status(thm)],[c_8924,c_219]) ).

cnf(c_14356,plain,
    ( tl(sK56) = sK52(sK56)
    | nil = sK56 ),
    inference(superposition,[status(thm)],[c_8924,c_221]) ).

cnf(c_14507,plain,
    ( ~ segmentP(sK55,sK55)
    | ~ segmentP(sK56,sK55)
    | ~ ssList(sK55)
    | sK55 = nil ),
    inference(instantiation,[status(thm)],[c_3273]) ).

cnf(c_14546,plain,
    ( ~ ssList(sK56)
    | nil = sK56
    | ssItem(hd(sK56)) ),
    inference(superposition,[status(thm)],[c_14203,c_220]) ).

cnf(c_14547,plain,
    ( nil = sK56
    | ssItem(hd(sK56)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_14546,c_8924]) ).

cnf(c_14590,plain,
    ( ~ ssList(sK56)
    | nil = sK56
    | ssList(tl(sK56)) ),
    inference(superposition,[status(thm)],[c_14356,c_222]) ).

cnf(c_14591,plain,
    ( nil = sK56
    | ssList(tl(sK56)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_14590,c_8924]) ).

cnf(c_14610,plain,
    ( app(nil,tl(sK56)) = tl(sK56)
    | nil = sK56 ),
    inference(superposition,[status(thm)],[c_14591,c_155]) ).

cnf(c_15346,plain,
    ( ~ ssList(app(X0,X1))
    | ~ ssList(X2)
    | ssList(app(app(X0,X1),X2)) ),
    inference(instantiation,[status(thm)],[c_153]) ).

cnf(c_15390,plain,
    ( ~ ssList(tl(sK56))
    | ~ ssList(nil)
    | nil = sK56
    | frontsegP(tl(sK56),nil) ),
    inference(superposition,[status(thm)],[c_14610,c_377]) ).

cnf(c_15391,plain,
    ( ~ ssList(tl(sK56))
    | nil = sK56
    | frontsegP(tl(sK56),nil) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_15390,c_141]) ).

cnf(c_16843,plain,
    ( cons(hd(sK56),tl(sK56)) = sK56
    | nil = sK56 ),
    inference(superposition,[status(thm)],[c_8924,c_224]) ).

cnf(c_18181,plain,
    ( ~ ssList(sK55)
    | ~ ssList(sK56)
    | app(sK55,sK11(sK56,sK55)) = sK56 ),
    inference(superposition,[status(thm)],[c_8925,c_62]) ).

cnf(c_18193,plain,
    app(sK55,sK11(sK56,sK55)) = sK56,
    inference(forward_subsumption_resolution,[status(thm)],[c_18181,c_8924,c_8923]) ).

cnf(c_21538,plain,
    ( ~ frontsegP(tl(sK56),X0)
    | ~ ssItem(hd(sK56))
    | ~ ssList(tl(sK56))
    | ~ ssList(X0)
    | nil = sK56
    | frontsegP(sK56,cons(hd(sK56),X0)) ),
    inference(superposition,[status(thm)],[c_16843,c_177]) ).

cnf(c_21688,plain,
    ( ~ frontsegP(tl(sK56),nil)
    | ~ ssItem(hd(sK56))
    | ~ ssList(tl(sK56))
    | ~ ssList(nil)
    | nil = sK56
    | frontsegP(sK56,cons(hd(sK56),nil)) ),
    inference(instantiation,[status(thm)],[c_21538]) ).

cnf(c_26910,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | segmentP(app(app(X0,X1),X2),X1) ),
    inference(global_subsumption_just,[status(thm)],[c_67,c_153,c_67,c_15346]) ).

cnf(c_26923,plain,
    ( ~ ssList(X0)
    | ~ ssList(nil)
    | ~ ssList(sK55)
    | segmentP(app(sK55,X0),sK55) ),
    inference(superposition,[status(thm)],[c_12113,c_26910]) ).

cnf(c_26961,plain,
    ( ~ ssList(X0)
    | segmentP(app(sK55,X0),sK55) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_26923,c_8923,c_141]) ).

cnf(c_27793,plain,
    ( ~ ssList(nil)
    | segmentP(sK55,sK55) ),
    inference(superposition,[status(thm)],[c_12195,c_26961]) ).

cnf(c_27794,plain,
    ( ~ ssList(sK11(sK56,sK55))
    | segmentP(sK56,sK55) ),
    inference(superposition,[status(thm)],[c_18193,c_26961]) ).

cnf(c_27800,plain,
    segmentP(sK55,sK55),
    inference(forward_subsumption_resolution,[status(thm)],[c_27793,c_141]) ).

cnf(c_28956,plain,
    ( ~ frontsegP(sK56,sK55)
    | ~ ssList(sK55)
    | ~ ssList(sK56)
    | segmentP(sK56,sK55) ),
    inference(superposition,[status(thm)],[c_63,c_27794]) ).

cnf(c_28957,plain,
    segmentP(sK56,sK55),
    inference(forward_subsumption_resolution,[status(thm)],[c_28956,c_8924,c_8923,c_8925]) ).

cnf(c_28962,plain,
    ( ~ segmentP(sK55,sK55)
    | ~ ssList(sK55)
    | nil = sK55 ),
    inference(superposition,[status(thm)],[c_28957,c_3273]) ).

cnf(c_28963,plain,
    nil = sK55,
    inference(forward_subsumption_resolution,[status(thm)],[c_28962,c_8923,c_27800]) ).

cnf(c_31669,plain,
    ( hd(sK55) = sK51(sK55)
    | nil = sK55 ),
    inference(superposition,[status(thm)],[c_8923,c_219]) ).

cnf(c_34146,plain,
    nil = sK55,
    inference(global_subsumption_just,[status(thm)],[c_31669,c_254,c_141,c_195,c_304,c_13204,c_13479,c_14507,c_28957]) ).

cnf(c_34160,plain,
    ( nil != nil
    | nil != sK56 ),
    inference(demodulation,[status(thm)],[c_8927,c_34146]) ).

cnf(c_34166,plain,
    nil != sK56,
    inference(equality_resolution_simp,[status(thm)],[c_34160]) ).

cnf(c_41281,plain,
    ( cons(X0,nil) != nil
    | ~ ssItem(X0)
    | ~ ssList(nil) ),
    inference(instantiation,[status(thm)],[c_142]) ).

cnf(c_43631,plain,
    ( ~ ssItem(hd(sK56))
    | ~ ssList(X0)
    | ssList(cons(hd(sK56),X0)) ),
    inference(instantiation,[status(thm)],[c_140]) ).

cnf(c_43632,plain,
    ( ~ ssItem(hd(sK56))
    | ~ ssList(nil)
    | ssList(cons(hd(sK56),nil)) ),
    inference(instantiation,[status(thm)],[c_43631]) ).

cnf(c_63976,plain,
    ( cons(hd(sK56),nil) != nil
    | ~ ssItem(hd(sK56))
    | ~ ssList(nil) ),
    inference(instantiation,[status(thm)],[c_41281]) ).

cnf(c_199856,plain,
    ( ~ frontsegP(sK56,X0)
    | ~ segmentP(X0,nil)
    | ~ ssList(X0)
    | ~ strictorderedP(X0)
    | X0 = nil ),
    inference(light_normalisation,[status(thm)],[c_3247,c_28963]) ).

cnf(c_199965,plain,
    ( ~ frontsegP(sK56,X0)
    | ~ ssList(X0)
    | ~ strictorderedP(X0)
    | X0 = nil ),
    inference(backward_subsumption_resolution,[status(thm)],[c_199856,c_194]) ).

cnf(c_202475,plain,
    ( hd(sK56) = sK51(sK56)
    | nil = sK56 ),
    inference(superposition,[status(thm)],[c_8924,c_219]) ).

cnf(c_202476,plain,
    hd(sK56) = sK51(sK56),
    inference(forward_subsumption_resolution,[status(thm)],[c_202475,c_34166]) ).

cnf(c_202600,plain,
    ( tl(sK56) = sK52(sK56)
    | nil = sK56 ),
    inference(superposition,[status(thm)],[c_8924,c_221]) ).

cnf(c_202601,plain,
    tl(sK56) = sK52(sK56),
    inference(forward_subsumption_resolution,[status(thm)],[c_202600,c_34166]) ).

cnf(c_202830,plain,
    ( ~ ssList(sK56)
    | nil = sK56
    | ssItem(hd(sK56)) ),
    inference(superposition,[status(thm)],[c_202476,c_220]) ).

cnf(c_202831,plain,
    ssItem(hd(sK56)),
    inference(forward_subsumption_resolution,[status(thm)],[c_202830,c_34166,c_8924]) ).

cnf(c_202838,plain,
    ( ~ ssList(sK56)
    | nil = sK56
    | ssList(tl(sK56)) ),
    inference(superposition,[status(thm)],[c_202601,c_222]) ).

cnf(c_202839,plain,
    ssList(tl(sK56)),
    inference(forward_subsumption_resolution,[status(thm)],[c_202838,c_34166,c_8924]) ).

cnf(c_204605,plain,
    ( cons(hd(sK56),tl(sK56)) = sK56
    | nil = sK56 ),
    inference(superposition,[status(thm)],[c_8924,c_224]) ).

cnf(c_204608,plain,
    cons(hd(sK56),tl(sK56)) = sK56,
    inference(forward_subsumption_resolution,[status(thm)],[c_204605,c_34166]) ).

cnf(c_204799,plain,
    ( ~ ssList(X0)
    | app(cons(hd(sK56),nil),X0) = cons(hd(sK56),X0) ),
    inference(superposition,[status(thm)],[c_202831,c_227]) ).

cnf(c_205086,plain,
    app(cons(hd(sK56),nil),tl(sK56)) = cons(hd(sK56),tl(sK56)),
    inference(superposition,[status(thm)],[c_202839,c_204799]) ).

cnf(c_205088,plain,
    app(cons(hd(sK56),nil),tl(sK56)) = sK56,
    inference(light_normalisation,[status(thm)],[c_205086,c_204608]) ).

cnf(c_208185,plain,
    ( ~ ssList(cons(hd(sK56),nil))
    | ~ ssList(tl(sK56))
    | frontsegP(sK56,cons(hd(sK56),nil)) ),
    inference(superposition,[status(thm)],[c_205088,c_377]) ).

cnf(c_208193,plain,
    ( ~ ssList(cons(hd(sK56),nil))
    | frontsegP(sK56,cons(hd(sK56),nil)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_208185,c_202839]) ).

cnf(c_209512,plain,
    frontsegP(sK56,cons(hd(sK56),nil)),
    inference(global_subsumption_just,[status(thm)],[c_208193,c_254,c_141,c_195,c_246,c_304,c_13204,c_13479,c_14507,c_14547,c_14591,c_15391,c_21688,c_28957]) ).

cnf(c_209517,plain,
    ( ~ ssList(cons(hd(sK56),nil))
    | ~ strictorderedP(cons(hd(sK56),nil))
    | cons(hd(sK56),nil) = nil ),
    inference(superposition,[status(thm)],[c_209512,c_199965]) ).

cnf(c_491012,plain,
    ( sK56 = nil
    | ssItem(hd(sK56)) ),
    inference(resolution,[status(thm)],[c_149,c_8924]) ).

cnf(c_496824,plain,
    ssItem(hd(sK56)),
    inference(global_subsumption_just,[status(thm)],[c_491012,c_254,c_141,c_195,c_246,c_304,c_13204,c_13479,c_14507,c_14547,c_28957]) ).

cnf(c_496832,plain,
    strictorderedP(cons(hd(sK56),nil)),
    inference(resolution,[status(thm)],[c_496824,c_209]) ).

cnf(c_496836,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_496832,c_209517,c_63976,c_43632,c_28957,c_14547,c_14507,c_13479,c_13204,c_304,c_246,c_195,c_141,c_254]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : SWC077+1 : TPTP v8.1.2. Released v2.4.0.
% 0.13/0.14  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n023.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  2 23:44:24 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.21/0.48  Running first-order theorem proving
% 0.21/0.48  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
% 239.69/31.33  % SZS status Started for theBenchmark.p
% 239.69/31.33  % SZS status Theorem for theBenchmark.p
% 239.69/31.33  
% 239.69/31.33  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 239.69/31.33  
% 239.69/31.33  ------  iProver source info
% 239.69/31.33  
% 239.69/31.33  git: date: 2024-05-02 19:28:25 +0000
% 239.69/31.33  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 239.69/31.33  git: non_committed_changes: false
% 239.69/31.33  
% 239.69/31.33  ------ Parsing...
% 239.69/31.33  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 239.69/31.33  
% 239.69/31.33  ------ 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: 0  sf_s  rm: 5 0s  sf_e  pe_s  pe_e 
% 239.69/31.33  
% 239.69/31.33  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 239.69/31.33  
% 239.69/31.33  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 239.69/31.33  ------ Proving...
% 239.69/31.33  ------ Problem Properties 
% 239.69/31.33  
% 239.69/31.33  
% 239.69/31.33  clauses                                 187
% 239.69/31.33  conjectures                             5
% 239.69/31.33  EPR                                     56
% 239.69/31.33  Horn                                    119
% 239.69/31.33  unary                                   20
% 239.69/31.33  binary                                  41
% 239.69/31.33  lits                                    633
% 239.69/31.33  lits eq                                 82
% 239.69/31.33  fd_pure                                 0
% 239.69/31.33  fd_pseudo                               0
% 239.69/31.33  fd_cond                                 23
% 239.69/31.33  fd_pseudo_cond                          14
% 239.69/31.33  AC symbols                              0
% 239.69/31.33  
% 239.69/31.33  ------ Schedule dynamic 5 is on 
% 239.69/31.33  
% 239.69/31.33  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 239.69/31.33  
% 239.69/31.33  
% 239.69/31.33  ------ 
% 239.69/31.33  Current options:
% 239.69/31.33  ------ 
% 239.69/31.33  
% 239.69/31.33  
% 239.69/31.33  
% 239.69/31.33  
% 239.69/31.33  ------ Proving...
% 239.69/31.33  Proof_search_loop: time out after: 7672 full_loop iterations
% 239.69/31.33  
% 239.69/31.33  ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 239.69/31.33  
% 239.69/31.33  
% 239.69/31.33  ------ 
% 239.69/31.33  Current options:
% 239.69/31.33  ------ 
% 239.69/31.33  
% 239.69/31.33  
% 239.69/31.33  
% 239.69/31.33  
% 239.69/31.33  ------ Proving...
% 239.69/31.33  Proof_search_loop: time out after: 8762 full_loop iterations
% 239.69/31.33  
% 239.69/31.33  ------ Option_1: Negative Selections Time Limit: 35.
% 239.69/31.33  
% 239.69/31.33  
% 239.69/31.33  ------ 
% 239.69/31.33  Current options:
% 239.69/31.33  ------ 
% 239.69/31.33  
% 239.69/31.33  
% 239.69/31.33  
% 239.69/31.33  
% 239.69/31.33  ------ Proving...
% 239.69/31.33  
% 239.69/31.33  
% 239.69/31.33  % SZS status Theorem for theBenchmark.p
% 239.69/31.33  
% 239.69/31.33  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 239.69/31.34  
% 239.69/31.35  
%------------------------------------------------------------------------------