TSTP Solution File: SWC124+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWC124+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n027.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 03:11:19 EDT 2024

% Result   : Theorem 10.20s 2.15s
% Output   : CNFRefutation 10.20s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

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

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

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

fof(f221,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ segmentP(X1,X0)
                    | ~ neq(X0,nil) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X4] :
                      ( ! [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( ! [X8] :
                                      ( ~ leq(X7,X5)
                                      | app(X8,cons(X7,nil)) != X2
                                      | ~ ssList(X8) )
                                  | ~ ssItem(X7) )
                              | app(cons(X5,nil),X6) != X4
                              | ~ ssList(X6) )
                          | ~ ssItem(X5) )
                      & totalorderedP(X2)
                      & app(X2,X4) = X3
                      & ssList(X4) )
                  & neq(X1,nil)
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f97]) ).

fof(f222,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ segmentP(X1,X0)
                    | ~ neq(X0,nil) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X4] :
                      ( ! [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( ! [X8] :
                                      ( ~ leq(X7,X5)
                                      | app(X8,cons(X7,nil)) != X2
                                      | ~ ssList(X8) )
                                  | ~ ssItem(X7) )
                              | app(cons(X5,nil),X6) != X4
                              | ~ ssList(X6) )
                          | ~ ssItem(X5) )
                      & totalorderedP(X2)
                      & app(X2,X4) = X3
                      & ssList(X4) )
                  & neq(X1,nil)
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f221]) ).

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(f343,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ~ segmentP(X1,X0)
                      | ~ neq(X0,nil) )
                    & ( nil != X2
                      | nil = X3 )
                    & ? [X4] :
                        ( ! [X5] :
                            ( ! [X6] :
                                ( ! [X7] :
                                    ( ! [X8] :
                                        ( ~ leq(X7,X5)
                                        | app(X8,cons(X7,nil)) != X2
                                        | ~ ssList(X8) )
                                    | ~ ssItem(X7) )
                                | app(cons(X5,nil),X6) != X4
                                | ~ ssList(X6) )
                            | ~ ssItem(X5) )
                        & totalorderedP(X2)
                        & app(X2,X4) = X3
                        & ssList(X4) )
                    & neq(X1,nil)
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ segmentP(X1,sK53)
                    | ~ neq(sK53,nil) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X4] :
                      ( ! [X5] :
                          ( ! [X6] :
                              ( ! [X7] :
                                  ( ! [X8] :
                                      ( ~ leq(X7,X5)
                                      | app(X8,cons(X7,nil)) != X2
                                      | ~ ssList(X8) )
                                  | ~ ssItem(X7) )
                              | app(cons(X5,nil),X6) != X4
                              | ~ ssList(X6) )
                          | ~ ssItem(X5) )
                      & totalorderedP(X2)
                      & app(X2,X4) = X3
                      & ssList(X4) )
                  & neq(X1,nil)
                  & sK53 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK53) ) ),
    introduced(choice_axiom,[]) ).

fof(f344,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ~ segmentP(X1,sK53)
                  | ~ neq(sK53,nil) )
                & ( nil != X2
                  | nil = X3 )
                & ? [X4] :
                    ( ! [X5] :
                        ( ! [X6] :
                            ( ! [X7] :
                                ( ! [X8] :
                                    ( ~ leq(X7,X5)
                                    | app(X8,cons(X7,nil)) != X2
                                    | ~ ssList(X8) )
                                | ~ ssItem(X7) )
                            | app(cons(X5,nil),X6) != X4
                            | ~ ssList(X6) )
                        | ~ ssItem(X5) )
                    & totalorderedP(X2)
                    & app(X2,X4) = X3
                    & ssList(X4) )
                & neq(X1,nil)
                & sK53 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ~ segmentP(sK54,sK53)
                | ~ neq(sK53,nil) )
              & ( nil != X2
                | nil = X3 )
              & ? [X4] :
                  ( ! [X5] :
                      ( ! [X6] :
                          ( ! [X7] :
                              ( ! [X8] :
                                  ( ~ leq(X7,X5)
                                  | app(X8,cons(X7,nil)) != X2
                                  | ~ ssList(X8) )
                              | ~ ssItem(X7) )
                          | app(cons(X5,nil),X6) != X4
                          | ~ ssList(X6) )
                      | ~ ssItem(X5) )
                  & totalorderedP(X2)
                  & app(X2,X4) = X3
                  & ssList(X4) )
              & neq(sK54,nil)
              & sK53 = X2
              & sK54 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK54) ) ),
    introduced(choice_axiom,[]) ).

fof(f345,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ~ segmentP(sK54,sK53)
              | ~ neq(sK53,nil) )
            & ( nil != X2
              | nil = X3 )
            & ? [X4] :
                ( ! [X5] :
                    ( ! [X6] :
                        ( ! [X7] :
                            ( ! [X8] :
                                ( ~ leq(X7,X5)
                                | app(X8,cons(X7,nil)) != X2
                                | ~ ssList(X8) )
                            | ~ ssItem(X7) )
                        | app(cons(X5,nil),X6) != X4
                        | ~ ssList(X6) )
                    | ~ ssItem(X5) )
                & totalorderedP(X2)
                & app(X2,X4) = X3
                & ssList(X4) )
            & neq(sK54,nil)
            & sK53 = X2
            & sK54 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ~ segmentP(sK54,sK53)
            | ~ neq(sK53,nil) )
          & ( nil != sK55
            | nil = X3 )
          & ? [X4] :
              ( ! [X5] :
                  ( ! [X6] :
                      ( ! [X7] :
                          ( ! [X8] :
                              ( ~ leq(X7,X5)
                              | app(X8,cons(X7,nil)) != sK55
                              | ~ ssList(X8) )
                          | ~ ssItem(X7) )
                      | app(cons(X5,nil),X6) != X4
                      | ~ ssList(X6) )
                  | ~ ssItem(X5) )
              & totalorderedP(sK55)
              & app(sK55,X4) = X3
              & ssList(X4) )
          & neq(sK54,nil)
          & sK53 = sK55
          & sK54 = X3
          & ssList(X3) )
      & ssList(sK55) ) ),
    introduced(choice_axiom,[]) ).

fof(f346,plain,
    ( ? [X3] :
        ( ( ~ segmentP(sK54,sK53)
          | ~ neq(sK53,nil) )
        & ( nil != sK55
          | nil = X3 )
        & ? [X4] :
            ( ! [X5] :
                ( ! [X6] :
                    ( ! [X7] :
                        ( ! [X8] :
                            ( ~ leq(X7,X5)
                            | app(X8,cons(X7,nil)) != sK55
                            | ~ ssList(X8) )
                        | ~ ssItem(X7) )
                    | app(cons(X5,nil),X6) != X4
                    | ~ ssList(X6) )
                | ~ ssItem(X5) )
            & totalorderedP(sK55)
            & app(sK55,X4) = X3
            & ssList(X4) )
        & neq(sK54,nil)
        & sK53 = sK55
        & sK54 = X3
        & ssList(X3) )
   => ( ( ~ segmentP(sK54,sK53)
        | ~ neq(sK53,nil) )
      & ( nil != sK55
        | nil = sK56 )
      & ? [X4] :
          ( ! [X5] :
              ( ! [X6] :
                  ( ! [X7] :
                      ( ! [X8] :
                          ( ~ leq(X7,X5)
                          | app(X8,cons(X7,nil)) != sK55
                          | ~ ssList(X8) )
                      | ~ ssItem(X7) )
                  | app(cons(X5,nil),X6) != X4
                  | ~ ssList(X6) )
              | ~ ssItem(X5) )
          & totalorderedP(sK55)
          & app(sK55,X4) = sK56
          & ssList(X4) )
      & neq(sK54,nil)
      & sK53 = sK55
      & sK54 = sK56
      & ssList(sK56) ) ),
    introduced(choice_axiom,[]) ).

fof(f347,plain,
    ( ? [X4] :
        ( ! [X5] :
            ( ! [X6] :
                ( ! [X7] :
                    ( ! [X8] :
                        ( ~ leq(X7,X5)
                        | app(X8,cons(X7,nil)) != sK55
                        | ~ ssList(X8) )
                    | ~ ssItem(X7) )
                | app(cons(X5,nil),X6) != X4
                | ~ ssList(X6) )
            | ~ ssItem(X5) )
        & totalorderedP(sK55)
        & app(sK55,X4) = sK56
        & ssList(X4) )
   => ( ! [X5] :
          ( ! [X6] :
              ( ! [X7] :
                  ( ! [X8] :
                      ( ~ leq(X7,X5)
                      | app(X8,cons(X7,nil)) != sK55
                      | ~ ssList(X8) )
                  | ~ ssItem(X7) )
              | app(cons(X5,nil),X6) != sK57
              | ~ ssList(X6) )
          | ~ ssItem(X5) )
      & totalorderedP(sK55)
      & sK56 = app(sK55,sK57)
      & ssList(sK57) ) ),
    introduced(choice_axiom,[]) ).

fof(f348,plain,
    ( ( ~ segmentP(sK54,sK53)
      | ~ neq(sK53,nil) )
    & ( nil != sK55
      | nil = sK56 )
    & ! [X5] :
        ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( ~ leq(X7,X5)
                    | app(X8,cons(X7,nil)) != sK55
                    | ~ ssList(X8) )
                | ~ ssItem(X7) )
            | app(cons(X5,nil),X6) != sK57
            | ~ ssList(X6) )
        | ~ ssItem(X5) )
    & totalorderedP(sK55)
    & sK56 = app(sK55,sK57)
    & ssList(sK57)
    & neq(sK54,nil)
    & sK53 = sK55
    & sK54 = sK56
    & ssList(sK56)
    & ssList(sK55)
    & ssList(sK54)
    & ssList(sK53) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57])],[f222,f347,f346,f345,f344,f343]) ).

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,[],[f257]) ).

fof(f439,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f316]) ).

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

fof(f455,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f134]) ).

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,
    neq(sK54,nil),
    inference(cnf_transformation,[],[f348]) ).

fof(f555,plain,
    ssList(sK57),
    inference(cnf_transformation,[],[f348]) ).

fof(f556,plain,
    sK56 = app(sK55,sK57),
    inference(cnf_transformation,[],[f348]) ).

fof(f559,plain,
    ( nil != sK55
    | nil = sK56 ),
    inference(cnf_transformation,[],[f348]) ).

fof(f560,plain,
    ( ~ segmentP(sK54,sK53)
    | ~ neq(sK53,nil) ),
    inference(cnf_transformation,[],[f348]) ).

fof(f561,plain,
    ( ~ segmentP(sK56,sK55)
    | ~ neq(sK55,nil) ),
    inference(definition_unfolding,[],[f560,f552,f553,f553]) ).

fof(f562,plain,
    neq(sK56,nil),
    inference(definition_unfolding,[],[f554,f552]) ).

fof(f563,plain,
    ssList(sK56),
    inference(definition_unfolding,[],[f549,f552]) ).

fof(f564,plain,
    ssList(sK55),
    inference(definition_unfolding,[],[f548,f553]) ).

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,[],[f370]) ).

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,[],[f439]) ).

cnf(c_139,plain,
    ( ~ neq(X0,X0)
    | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f594]) ).

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

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

cnf(c_246,negated_conjecture,
    ( ~ neq(sK55,nil)
    | ~ segmentP(sK56,sK55) ),
    inference(cnf_transformation,[],[f561]) ).

cnf(c_247,negated_conjecture,
    ( nil != sK55
    | nil = sK56 ),
    inference(cnf_transformation,[],[f559]) ).

cnf(c_250,negated_conjecture,
    app(sK55,sK57) = sK56,
    inference(cnf_transformation,[],[f556]) ).

cnf(c_251,negated_conjecture,
    ssList(sK57),
    inference(cnf_transformation,[],[f555]) ).

cnf(c_252,negated_conjecture,
    neq(sK56,nil),
    inference(cnf_transformation,[],[f562]) ).

cnf(c_255,negated_conjecture,
    ssList(sK56),
    inference(cnf_transformation,[],[f563]) ).

cnf(c_256,negated_conjecture,
    ssList(sK55),
    inference(cnf_transformation,[],[f564]) ).

cnf(c_3249,plain,
    ( X0 != sK55
    | X1 != nil
    | ~ segmentP(sK56,sK55)
    | ~ ssList(X0)
    | ~ ssList(X1)
    | X0 = X1 ),
    inference(resolution_lifted,[status(thm)],[c_138,c_246]) ).

cnf(c_3250,plain,
    ( ~ segmentP(sK56,sK55)
    | ~ ssList(nil)
    | ~ ssList(sK55)
    | sK55 = nil ),
    inference(unflattening,[status(thm)],[c_3249]) ).

cnf(c_3251,plain,
    ( ~ segmentP(sK56,sK55)
    | sK55 = nil ),
    inference(global_subsumption_just,[status(thm)],[c_3250,c_256,c_141,c_3250]) ).

cnf(c_3263,plain,
    ( X0 != nil
    | X0 != sK56
    | ~ ssList(X0) ),
    inference(resolution_lifted,[status(thm)],[c_139,c_252]) ).

cnf(c_3264,plain,
    ( nil != sK56
    | ~ ssList(nil) ),
    inference(unflattening,[status(thm)],[c_3263]) ).

cnf(c_3265,plain,
    nil != sK56,
    inference(global_subsumption_just,[status(thm)],[c_3264,c_141,c_3264]) ).

cnf(c_3284,plain,
    nil != sK55,
    inference(backward_subsumption_resolution,[status(thm)],[c_247,c_3265]) ).

cnf(c_8916,plain,
    app(sK55,sK57) = sP0_iProver_def,
    definition ).

cnf(c_8917,negated_conjecture,
    ssList(sK55),
    inference(demodulation,[status(thm)],[c_256]) ).

cnf(c_8918,negated_conjecture,
    ssList(sK56),
    inference(demodulation,[status(thm)],[c_255]) ).

cnf(c_8919,negated_conjecture,
    ssList(sK57),
    inference(demodulation,[status(thm)],[c_251]) ).

cnf(c_8920,negated_conjecture,
    sP0_iProver_def = sK56,
    inference(demodulation,[status(thm)],[c_250,c_8916]) ).

cnf(c_11770,plain,
    ssList(sP0_iProver_def),
    inference(light_normalisation,[status(thm)],[c_8918,c_8920]) ).

cnf(c_11779,plain,
    ( ~ segmentP(sP0_iProver_def,sK55)
    | nil = sK55 ),
    inference(light_normalisation,[status(thm)],[c_3251,c_8920]) ).

cnf(c_11780,plain,
    ~ segmentP(sP0_iProver_def,sK55),
    inference(forward_subsumption_resolution,[status(thm)],[c_11779,c_3284]) ).

cnf(c_12103,plain,
    app(nil,sK55) = sK55,
    inference(superposition,[status(thm)],[c_8917,c_155]) ).

cnf(c_28303,plain,
    ( ~ ssList(app(app(nil,sK55),X0))
    | ~ ssList(X0)
    | ~ ssList(nil)
    | ~ ssList(sK55)
    | segmentP(app(sK55,X0),sK55) ),
    inference(superposition,[status(thm)],[c_12103,c_67]) ).

cnf(c_28378,plain,
    ( ~ ssList(app(sK55,X0))
    | ~ ssList(X0)
    | ~ ssList(nil)
    | ~ ssList(sK55)
    | segmentP(app(sK55,X0),sK55) ),
    inference(light_normalisation,[status(thm)],[c_28303,c_12103]) ).

cnf(c_28379,plain,
    ( ~ ssList(app(sK55,X0))
    | ~ ssList(X0)
    | segmentP(app(sK55,X0),sK55) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_28378,c_8917,c_141]) ).

cnf(c_30074,plain,
    ( ~ ssList(app(sK55,sK57))
    | ~ ssList(sK57)
    | segmentP(sP0_iProver_def,sK55) ),
    inference(superposition,[status(thm)],[c_8916,c_28379]) ).

cnf(c_30083,plain,
    ( ~ ssList(sK57)
    | ~ ssList(sP0_iProver_def)
    | segmentP(sP0_iProver_def,sK55) ),
    inference(light_normalisation,[status(thm)],[c_30074,c_8916]) ).

cnf(c_30084,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_30083,c_11780,c_11770,c_8919]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SWC124+1 : TPTP v8.1.2. Released v2.4.0.
% 0.03/0.12  % Command  : run_iprover %s %d THM
% 0.12/0.33  % Computer : n027.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu May  2 23:58:05 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.18/0.45  Running first-order theorem proving
% 0.18/0.45  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
% 10.20/2.15  % SZS status Started for theBenchmark.p
% 10.20/2.15  % SZS status Theorem for theBenchmark.p
% 10.20/2.15  
% 10.20/2.15  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 10.20/2.15  
% 10.20/2.15  ------  iProver source info
% 10.20/2.15  
% 10.20/2.15  git: date: 2024-05-02 19:28:25 +0000
% 10.20/2.15  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 10.20/2.15  git: non_committed_changes: false
% 10.20/2.15  
% 10.20/2.15  ------ Parsing...
% 10.20/2.15  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 10.20/2.15  
% 10.20/2.15  ------ 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 
% 10.20/2.15  
% 10.20/2.15  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 10.20/2.15  
% 10.20/2.15  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 10.20/2.15  ------ Proving...
% 10.20/2.15  ------ Problem Properties 
% 10.20/2.15  
% 10.20/2.15  
% 10.20/2.15  clauses                                 191
% 10.20/2.15  conjectures                             6
% 10.20/2.15  EPR                                     58
% 10.20/2.15  Horn                                    123
% 10.20/2.15  unary                                   24
% 10.20/2.15  binary                                  42
% 10.20/2.15  lits                                    637
% 10.20/2.15  lits eq                                 86
% 10.20/2.15  fd_pure                                 0
% 10.20/2.15  fd_pseudo                               0
% 10.20/2.15  fd_cond                                 21
% 10.20/2.15  fd_pseudo_cond                          14
% 10.20/2.15  AC symbols                              0
% 10.20/2.15  
% 10.20/2.15  ------ Schedule dynamic 5 is on 
% 10.20/2.15  
% 10.20/2.15  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.20/2.15  
% 10.20/2.15  
% 10.20/2.15  ------ 
% 10.20/2.15  Current options:
% 10.20/2.15  ------ 
% 10.20/2.15  
% 10.20/2.15  
% 10.20/2.15  
% 10.20/2.15  
% 10.20/2.15  ------ Proving...
% 10.20/2.15  
% 10.20/2.15  
% 10.20/2.15  % SZS status Theorem for theBenchmark.p
% 10.20/2.15  
% 10.20/2.15  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.20/2.15  
% 10.20/2.15  
%------------------------------------------------------------------------------