TSTP Solution File: SWC053+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWC053+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n021.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 03:11:03 EDT 2024

% Result   : Theorem 13.77s 2.63s
% Output   : CNFRefutation 13.77s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f602)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( frontsegP(X0,X1)
          <=> ? [X2] :
                ( app(X1,X2) = X0
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox2/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/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(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).

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

fof(f28,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(nil,X0) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).

fof(f41,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( ( frontsegP(X1,X0)
              & frontsegP(X0,X1) )
           => X0 = X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41) ).

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

fof(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( ( ? [X4] :
                              ( segmentP(X0,X4)
                              & segmentP(X1,X4)
                              & neq(X4,nil)
                              & ssList(X4) )
                          | ~ neq(X1,nil) )
                        & ( nil = X0
                          | nil != X1 ) )
                      | ( ( nil != X2
                          | nil != X3 )
                        & ! [X5] :
                            ( ssList(X5)
                           => ( ~ frontsegP(X2,X5)
                              | ~ frontsegP(X3,X5)
                              | ~ neq(X5,nil) ) ) )
                      | 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(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(f152,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ frontsegP(X1,X0)
          | ~ frontsegP(X0,X1)
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f41]) ).

fof(f153,plain,
    ! [X0] :
      ( ! [X1] :
          ( X0 = X1
          | ~ frontsegP(X1,X0)
          | ~ frontsegP(X0,X1)
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f152]) ).

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

fof(f223,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ! [X4] :
                          ( ~ segmentP(X0,X4)
                          | ~ segmentP(X1,X4)
                          | ~ neq(X4,nil)
                          | ~ ssList(X4) )
                      & neq(X1,nil) )
                    | ( nil != X0
                      & nil = X1 ) )
                  & ( ( nil = X2
                      & nil = X3 )
                    | ? [X5] :
                        ( frontsegP(X2,X5)
                        & frontsegP(X3,X5)
                        & neq(X5,nil)
                        & ssList(X5) ) )
                  & 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(f344,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( ! [X4] :
                            ( ~ segmentP(X0,X4)
                            | ~ segmentP(X1,X4)
                            | ~ neq(X4,nil)
                            | ~ ssList(X4) )
                        & neq(X1,nil) )
                      | ( nil != X0
                        & nil = X1 ) )
                    & ( ( nil = X2
                        & nil = X3 )
                      | ? [X5] :
                          ( frontsegP(X2,X5)
                          & frontsegP(X3,X5)
                          & neq(X5,nil)
                          & ssList(X5) ) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ! [X4] :
                          ( ~ segmentP(sK53,X4)
                          | ~ segmentP(X1,X4)
                          | ~ neq(X4,nil)
                          | ~ ssList(X4) )
                      & neq(X1,nil) )
                    | ( nil != sK53
                      & nil = X1 ) )
                  & ( ( nil = X2
                      & nil = X3 )
                    | ? [X5] :
                        ( frontsegP(X2,X5)
                        & frontsegP(X3,X5)
                        & neq(X5,nil)
                        & ssList(X5) ) )
                  & sK53 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK53) ) ),
    introduced(choice_axiom,[]) ).

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

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

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

fof(f348,plain,
    ( ? [X5] :
        ( frontsegP(sK55,X5)
        & frontsegP(sK56,X5)
        & neq(X5,nil)
        & ssList(X5) )
   => ( frontsegP(sK55,sK57)
      & frontsegP(sK56,sK57)
      & neq(sK57,nil)
      & ssList(sK57) ) ),
    introduced(choice_axiom,[]) ).

fof(f349,plain,
    ( ( ( ! [X4] :
            ( ~ segmentP(sK53,X4)
            | ~ segmentP(sK54,X4)
            | ~ neq(X4,nil)
            | ~ ssList(X4) )
        & neq(sK54,nil) )
      | ( nil != sK53
        & nil = sK54 ) )
    & ( ( nil = sK55
        & nil = sK56 )
      | ( frontsegP(sK55,sK57)
        & frontsegP(sK56,sK57)
        & neq(sK57,nil)
        & 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])],[f223,f348,f347,f346,f345,f344]) ).

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

fof(f363,plain,
    ! [X0,X1] :
      ( app(X1,sK11(X0,X1)) = X0
      | ~ frontsegP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f249]) ).

fof(f364,plain,
    ! [X2,X0,X1] :
      ( frontsegP(X0,X1)
      | app(X1,X2) != X0
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f249]) ).

fof(f371,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(f440,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f317]) ).

fof(f442,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f454,plain,
    ! [X0,X1] :
      ( ssList(app(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f133]) ).

fof(f456,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f135]) ).

fof(f475,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ frontsegP(X1,X0)
      | ~ frontsegP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f153]) ).

fof(f549,plain,
    ssList(sK53),
    inference(cnf_transformation,[],[f349]) ).

fof(f550,plain,
    ssList(sK54),
    inference(cnf_transformation,[],[f349]) ).

fof(f553,plain,
    sK54 = sK56,
    inference(cnf_transformation,[],[f349]) ).

fof(f554,plain,
    sK53 = sK55,
    inference(cnf_transformation,[],[f349]) ).

fof(f555,plain,
    ( nil = sK56
    | ssList(sK57) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f556,plain,
    ( nil = sK56
    | neq(sK57,nil) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f557,plain,
    ( nil = sK56
    | frontsegP(sK56,sK57) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f558,plain,
    ( nil = sK56
    | frontsegP(sK55,sK57) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f559,plain,
    ( nil = sK55
    | ssList(sK57) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f560,plain,
    ( nil = sK55
    | neq(sK57,nil) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f561,plain,
    ( nil = sK55
    | frontsegP(sK56,sK57) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f562,plain,
    ( nil = sK55
    | frontsegP(sK55,sK57) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f564,plain,
    ( neq(sK54,nil)
    | nil != sK53 ),
    inference(cnf_transformation,[],[f349]) ).

fof(f565,plain,
    ! [X4] :
      ( ~ segmentP(sK53,X4)
      | ~ segmentP(sK54,X4)
      | ~ neq(X4,nil)
      | ~ ssList(X4)
      | nil = sK54 ),
    inference(cnf_transformation,[],[f349]) ).

fof(f568,plain,
    ! [X4] :
      ( ~ segmentP(sK55,X4)
      | ~ segmentP(sK56,X4)
      | ~ neq(X4,nil)
      | ~ ssList(X4)
      | nil = sK56 ),
    inference(definition_unfolding,[],[f565,f554,f553,f553]) ).

fof(f569,plain,
    ( neq(sK56,nil)
    | nil != sK55 ),
    inference(definition_unfolding,[],[f564,f553,f554]) ).

fof(f571,plain,
    ssList(sK56),
    inference(definition_unfolding,[],[f550,f553]) ).

fof(f572,plain,
    ssList(sK55),
    inference(definition_unfolding,[],[f549,f554]) ).

fof(f576,plain,
    ! [X2,X1] :
      ( frontsegP(app(X1,X2),X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(app(X1,X2)) ),
    inference(equality_resolution,[],[f364]) ).

fof(f578,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,[],[f371]) ).

cnf(c_61,plain,
    ( ~ ssList(app(X0,X1))
    | ~ ssList(X0)
    | ~ ssList(X1)
    | frontsegP(app(X0,X1),X0) ),
    inference(cnf_transformation,[],[f576]) ).

cnf(c_62,plain,
    ( ~ frontsegP(X0,X1)
    | ~ ssList(X0)
    | ~ ssList(X1)
    | app(X1,sK11(X0,X1)) = X0 ),
    inference(cnf_transformation,[],[f363]) ).

cnf(c_63,plain,
    ( ~ frontsegP(X0,X1)
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ssList(sK11(X0,X1)) ),
    inference(cnf_transformation,[],[f362]) ).

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,[],[f578]) ).

cnf(c_138,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | X0 = X1
    | neq(X0,X1) ),
    inference(cnf_transformation,[],[f440]) ).

cnf(c_139,plain,
    ( ~ neq(X0,X0)
    | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f602]) ).

cnf(c_141,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f442]) ).

cnf(c_153,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | ssList(app(X0,X1)) ),
    inference(cnf_transformation,[],[f454]) ).

cnf(c_155,plain,
    ( ~ ssList(X0)
    | app(nil,X0) = X0 ),
    inference(cnf_transformation,[],[f456]) ).

cnf(c_174,plain,
    ( ~ frontsegP(X0,X1)
    | ~ frontsegP(X1,X0)
    | ~ ssList(X0)
    | ~ ssList(X1)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f475]) ).

cnf(c_247,negated_conjecture,
    ( ~ neq(X0,nil)
    | ~ segmentP(sK55,X0)
    | ~ segmentP(sK56,X0)
    | ~ ssList(X0)
    | nil = sK56 ),
    inference(cnf_transformation,[],[f568]) ).

cnf(c_248,negated_conjecture,
    ( nil != sK55
    | neq(sK56,nil) ),
    inference(cnf_transformation,[],[f569]) ).

cnf(c_250,negated_conjecture,
    ( nil = sK55
    | frontsegP(sK55,sK57) ),
    inference(cnf_transformation,[],[f562]) ).

cnf(c_251,negated_conjecture,
    ( nil = sK55
    | frontsegP(sK56,sK57) ),
    inference(cnf_transformation,[],[f561]) ).

cnf(c_252,negated_conjecture,
    ( nil = sK55
    | neq(sK57,nil) ),
    inference(cnf_transformation,[],[f560]) ).

cnf(c_253,negated_conjecture,
    ( nil = sK55
    | ssList(sK57) ),
    inference(cnf_transformation,[],[f559]) ).

cnf(c_254,negated_conjecture,
    ( nil = sK56
    | frontsegP(sK55,sK57) ),
    inference(cnf_transformation,[],[f558]) ).

cnf(c_255,negated_conjecture,
    ( nil = sK56
    | frontsegP(sK56,sK57) ),
    inference(cnf_transformation,[],[f557]) ).

cnf(c_256,negated_conjecture,
    ( nil = sK56
    | neq(sK57,nil) ),
    inference(cnf_transformation,[],[f556]) ).

cnf(c_257,negated_conjecture,
    ( nil = sK56
    | ssList(sK57) ),
    inference(cnf_transformation,[],[f555]) ).

cnf(c_260,negated_conjecture,
    ssList(sK56),
    inference(cnf_transformation,[],[f571]) ).

cnf(c_261,negated_conjecture,
    ssList(sK55),
    inference(cnf_transformation,[],[f572]) ).

cnf(c_385,plain,
    ( ~ ssList(X0)
    | ~ ssList(X1)
    | frontsegP(app(X0,X1),X0) ),
    inference(global_subsumption_just,[status(thm)],[c_61,c_153,c_61]) ).

cnf(c_4876,plain,
    ( X0 != X1
    | X2 != nil
    | ~ segmentP(sK55,X1)
    | ~ segmentP(sK56,X1)
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | X0 = X2
    | nil = sK56 ),
    inference(resolution_lifted,[status(thm)],[c_138,c_247]) ).

cnf(c_4877,plain,
    ( ~ segmentP(sK55,X0)
    | ~ segmentP(sK56,X0)
    | ~ ssList(X0)
    | ~ ssList(nil)
    | X0 = nil
    | nil = sK56 ),
    inference(unflattening,[status(thm)],[c_4876]) ).

cnf(c_4879,plain,
    ( ~ ssList(X0)
    | ~ segmentP(sK56,X0)
    | ~ segmentP(sK55,X0)
    | X0 = nil
    | nil = sK56 ),
    inference(global_subsumption_just,[status(thm)],[c_4877,c_141,c_4877]) ).

cnf(c_4880,plain,
    ( ~ segmentP(sK55,X0)
    | ~ segmentP(sK56,X0)
    | ~ ssList(X0)
    | X0 = nil
    | nil = sK56 ),
    inference(renaming,[status(thm)],[c_4879]) ).

cnf(c_4928,plain,
    ( X0 != nil
    | X0 != sK56
    | nil != sK55
    | ~ ssList(X0) ),
    inference(resolution_lifted,[status(thm)],[c_139,c_248]) ).

cnf(c_4929,plain,
    ( nil != sK55
    | nil != sK56
    | ~ ssList(nil) ),
    inference(unflattening,[status(thm)],[c_4928]) ).

cnf(c_4942,plain,
    ( X0 != nil
    | X0 != sK57
    | ~ ssList(X0)
    | nil = sK56 ),
    inference(resolution_lifted,[status(thm)],[c_139,c_256]) ).

cnf(c_4943,plain,
    ( nil != sK57
    | ~ ssList(nil)
    | nil = sK56 ),
    inference(unflattening,[status(thm)],[c_4942]) ).

cnf(c_4944,plain,
    ( nil != sK57
    | nil = sK56 ),
    inference(global_subsumption_just,[status(thm)],[c_4943,c_141,c_4943]) ).

cnf(c_4952,plain,
    ( X0 != nil
    | X0 != sK57
    | ~ ssList(X0)
    | nil = sK55 ),
    inference(resolution_lifted,[status(thm)],[c_139,c_252]) ).

cnf(c_4953,plain,
    ( nil != sK57
    | ~ ssList(nil)
    | nil = sK55 ),
    inference(unflattening,[status(thm)],[c_4952]) ).

cnf(c_4954,plain,
    nil != sK57,
    inference(global_subsumption_just,[status(thm)],[c_4953,c_141,c_4929,c_4944,c_4953]) ).

cnf(c_5042,negated_conjecture,
    ssList(sK57),
    inference(global_subsumption_just,[status(thm)],[c_257,c_141,c_257,c_253,c_4929]) ).

cnf(c_5044,negated_conjecture,
    frontsegP(sK56,sK57),
    inference(global_subsumption_just,[status(thm)],[c_255,c_141,c_255,c_251,c_4929]) ).

cnf(c_5046,negated_conjecture,
    frontsegP(sK55,sK57),
    inference(global_subsumption_just,[status(thm)],[c_254,c_141,c_254,c_250,c_4929]) ).

cnf(c_5048,negated_conjecture,
    ssList(sK57),
    inference(global_subsumption_just,[status(thm)],[c_253,c_5042]) ).

cnf(c_5050,negated_conjecture,
    frontsegP(sK56,sK57),
    inference(global_subsumption_just,[status(thm)],[c_251,c_5044]) ).

cnf(c_5052,negated_conjecture,
    frontsegP(sK55,sK57),
    inference(global_subsumption_just,[status(thm)],[c_250,c_5046]) ).

cnf(c_13282,negated_conjecture,
    frontsegP(sK55,sK57),
    inference(demodulation,[status(thm)],[c_5052]) ).

cnf(c_13283,negated_conjecture,
    frontsegP(sK56,sK57),
    inference(demodulation,[status(thm)],[c_5050]) ).

cnf(c_13284,negated_conjecture,
    ssList(sK57),
    inference(demodulation,[status(thm)],[c_5048]) ).

cnf(c_13285,negated_conjecture,
    ssList(sK55),
    inference(demodulation,[status(thm)],[c_261]) ).

cnf(c_13286,negated_conjecture,
    ssList(sK56),
    inference(demodulation,[status(thm)],[c_260]) ).

cnf(c_16526,plain,
    app(nil,sK57) = sK57,
    inference(superposition,[status(thm)],[c_13284,c_155]) ).

cnf(c_16580,plain,
    ( ~ ssList(nil)
    | ~ ssList(sK57)
    | frontsegP(sK57,nil) ),
    inference(superposition,[status(thm)],[c_16526,c_385]) ).

cnf(c_16581,plain,
    frontsegP(sK57,nil),
    inference(forward_subsumption_resolution,[status(thm)],[c_16580,c_13284,c_141]) ).

cnf(c_22082,plain,
    ( ~ ssList(sK55)
    | ~ ssList(sK57)
    | app(sK57,sK11(sK55,sK57)) = sK55 ),
    inference(superposition,[status(thm)],[c_13282,c_62]) ).

cnf(c_22083,plain,
    ( ~ ssList(sK56)
    | ~ ssList(sK57)
    | app(sK57,sK11(sK56,sK57)) = sK56 ),
    inference(superposition,[status(thm)],[c_13283,c_62]) ).

cnf(c_22099,plain,
    app(sK57,sK11(sK56,sK57)) = sK56,
    inference(forward_subsumption_resolution,[status(thm)],[c_22083,c_13284,c_13286]) ).

cnf(c_22100,plain,
    app(sK57,sK11(sK55,sK57)) = sK55,
    inference(forward_subsumption_resolution,[status(thm)],[c_22082,c_13284,c_13285]) ).

cnf(c_22901,plain,
    ( ~ frontsegP(nil,sK57)
    | ~ ssList(nil)
    | ~ ssList(sK57)
    | nil = sK57 ),
    inference(superposition,[status(thm)],[c_16581,c_174]) ).

cnf(c_22913,plain,
    ~ frontsegP(nil,sK57),
    inference(forward_subsumption_resolution,[status(thm)],[c_22901,c_4954,c_13284,c_141]) ).

cnf(c_31742,plain,
    ( ~ ssList(app(app(nil,sK57),X0))
    | ~ ssList(X0)
    | ~ ssList(nil)
    | ~ ssList(sK57)
    | segmentP(app(sK57,X0),sK57) ),
    inference(superposition,[status(thm)],[c_16526,c_67]) ).

cnf(c_31846,plain,
    ( ~ ssList(app(sK57,X0))
    | ~ ssList(X0)
    | ~ ssList(nil)
    | ~ ssList(sK57)
    | segmentP(app(sK57,X0),sK57) ),
    inference(light_normalisation,[status(thm)],[c_31742,c_16526]) ).

cnf(c_31847,plain,
    ( ~ ssList(app(sK57,X0))
    | ~ ssList(X0)
    | segmentP(app(sK57,X0),sK57) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_31846,c_13284,c_141]) ).

cnf(c_36956,plain,
    ( ~ ssList(app(sK57,sK11(sK55,sK57)))
    | ~ ssList(sK11(sK55,sK57))
    | segmentP(sK55,sK57) ),
    inference(superposition,[status(thm)],[c_22100,c_31847]) ).

cnf(c_36957,plain,
    ( ~ ssList(app(sK57,sK11(sK56,sK57)))
    | ~ ssList(sK11(sK56,sK57))
    | segmentP(sK56,sK57) ),
    inference(superposition,[status(thm)],[c_22099,c_31847]) ).

cnf(c_36964,plain,
    ( ~ ssList(sK11(sK56,sK57))
    | ~ ssList(sK56)
    | segmentP(sK56,sK57) ),
    inference(light_normalisation,[status(thm)],[c_36957,c_22099]) ).

cnf(c_36965,plain,
    ( ~ ssList(sK11(sK56,sK57))
    | segmentP(sK56,sK57) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_36964,c_13286]) ).

cnf(c_36968,plain,
    ( ~ ssList(sK11(sK55,sK57))
    | ~ ssList(sK55)
    | segmentP(sK55,sK57) ),
    inference(light_normalisation,[status(thm)],[c_36956,c_22100]) ).

cnf(c_36969,plain,
    ( ~ ssList(sK11(sK55,sK57))
    | segmentP(sK55,sK57) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_36968,c_13285]) ).

cnf(c_37061,plain,
    ( ~ frontsegP(sK56,sK57)
    | ~ ssList(sK56)
    | ~ ssList(sK57)
    | segmentP(sK56,sK57) ),
    inference(superposition,[status(thm)],[c_63,c_36965]) ).

cnf(c_37062,plain,
    segmentP(sK56,sK57),
    inference(forward_subsumption_resolution,[status(thm)],[c_37061,c_13284,c_13286,c_13283]) ).

cnf(c_37082,plain,
    ( ~ frontsegP(sK55,sK57)
    | ~ ssList(sK55)
    | ~ ssList(sK57)
    | segmentP(sK55,sK57) ),
    inference(superposition,[status(thm)],[c_63,c_36969]) ).

cnf(c_37083,plain,
    segmentP(sK55,sK57),
    inference(forward_subsumption_resolution,[status(thm)],[c_37082,c_13284,c_13285,c_13282]) ).

cnf(c_37358,plain,
    ( ~ segmentP(sK56,sK57)
    | ~ ssList(sK57)
    | nil = sK56
    | nil = sK57 ),
    inference(superposition,[status(thm)],[c_37083,c_4880]) ).

cnf(c_37362,plain,
    nil = sK56,
    inference(forward_subsumption_resolution,[status(thm)],[c_37358,c_4954,c_13284,c_37062]) ).

cnf(c_37432,plain,
    frontsegP(nil,sK57),
    inference(demodulation,[status(thm)],[c_13283,c_37362]) ).

cnf(c_37473,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_37432,c_22913]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SWC053+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.11  % Command  : run_iprover %s %d THM
% 0.11/0.32  % Computer : n021.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Thu May  2 23:40:43 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.17/0.44  Running first-order theorem proving
% 0.17/0.44  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 13.77/2.63  % SZS status Started for theBenchmark.p
% 13.77/2.63  % SZS status Theorem for theBenchmark.p
% 13.77/2.63  
% 13.77/2.63  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 13.77/2.63  
% 13.77/2.63  ------  iProver source info
% 13.77/2.63  
% 13.77/2.63  git: date: 2024-05-02 19:28:25 +0000
% 13.77/2.63  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 13.77/2.63  git: non_committed_changes: false
% 13.77/2.63  
% 13.77/2.63  ------ Parsing...
% 13.77/2.63  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 13.77/2.63  
% 13.77/2.63  ------ 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  sup_sim: 0  sf_s  rm: 5 0s  sf_e  pe_s  pe_e 
% 13.77/2.63  
% 13.77/2.63  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 13.77/2.63  
% 13.77/2.63  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 13.77/2.63  ------ Proving...
% 13.77/2.63  ------ Problem Properties 
% 13.77/2.63  
% 13.77/2.63  
% 13.77/2.63  clauses                                 192
% 13.77/2.63  conjectures                             5
% 13.77/2.63  EPR                                     61
% 13.77/2.63  Horn                                    123
% 13.77/2.63  unary                                   22
% 13.77/2.63  binary                                  41
% 13.77/2.63  lits                                    645
% 13.77/2.63  lits eq                                 88
% 13.77/2.63  fd_pure                                 0
% 13.77/2.63  fd_pseudo                               0
% 13.77/2.63  fd_cond                                 23
% 13.77/2.63  fd_pseudo_cond                          14
% 13.77/2.63  AC symbols                              0
% 13.77/2.63  
% 13.77/2.63  ------ Schedule dynamic 5 is on 
% 13.77/2.63  
% 13.77/2.63  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 13.77/2.63  
% 13.77/2.63  
% 13.77/2.63  ------ 
% 13.77/2.63  Current options:
% 13.77/2.63  ------ 
% 13.77/2.63  
% 13.77/2.63  
% 13.77/2.63  
% 13.77/2.63  
% 13.77/2.63  ------ Proving...
% 13.77/2.63  
% 13.77/2.63  
% 13.77/2.63  % SZS status Theorem for theBenchmark.p
% 13.77/2.63  
% 13.77/2.63  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 13.77/2.63  
% 13.77/2.64  
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