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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : SWC067+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM

% Computer : n007.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep 25 03:07:44 PM UTC 2026

% Result   : Theorem 4.17s 1.17s
% Output   : CNFRefutation 4.17s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f548ERROR: Could not build tree for root c_6583ERROR: MakeTreeStats fails)

% 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/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).

fof(f15,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( neq(X0,X1)
          <=> X0 != X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).

fof(f55,axiom,
    ! [X0] :
      ( ssList(X0)
     => segmentP(X0,X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).

fof(f56,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( segmentP(X0,X1)
                   => segmentP(app(app(X2,X0),X3),X1) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax56) ).

fof(f57,axiom,
    ! [X0] :
      ( ssList(X0)
     => segmentP(X0,nil) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax57) ).

fof(f58,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( segmentP(nil,X0)
      <=> nil = X0 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax58) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( ( ? [X14] :
                            ( segmentP(X0,X14)
                            & segmentP(X1,X14)
                            & neq(X14,nil)
                            & ssList(X14) )
                        | ~ neq(X1,nil) )
                      & ( nil = X0
                        | nil != X1 ) )
                    | ( nil = X2
                      & nil != X3 )
                    | ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( ? [X10] :
                                  ( ? [X11] :
                                      ( ? [X12] :
                                          ( ? [X13] :
                                              ( lt(X12,X10)
                                              & app(X13,cons(X12,nil)) = X2
                                              & ssList(X13) )
                                          & ssItem(X12) )
                                      & app(cons(X10,nil),X11) = X5
                                      & ssList(X11) )
                                  & ssItem(X10) )
                              | ? [X6] :
                                  ( ? [X7] :
                                      ( ? [X8] :
                                          ( ? [X9] :
                                              ( lt(X6,X8)
                                              & app(cons(X8,nil),X9) = X2
                                              & ssList(X9) )
                                          & ssItem(X8) )
                                      & app(X7,cons(X6,nil)) = X4
                                      & ssList(X7) )
                                  & ssItem(X6) )
                              | ~ strictorderedP(X2)
                              | app(app(X4,X2),X5) != X3 ) ) )
                    | 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)
                   => ( ( ( ? [X14] :
                              ( segmentP(X0,X14)
                              & segmentP(X1,X14)
                              & neq(X14,nil)
                              & ssList(X14) )
                          | ~ neq(X1,nil) )
                        & ( nil = X0
                          | nil != X1 ) )
                      | ( nil = X2
                        & nil != X3 )
                      | ! [X4] :
                          ( ssList(X4)
                         => ! [X5] :
                              ( ssList(X5)
                             => ( ? [X10] :
                                    ( ? [X11] :
                                        ( ? [X12] :
                                            ( ? [X13] :
                                                ( lt(X12,X10)
                                                & app(X13,cons(X12,nil)) = X2
                                                & ssList(X13) )
                                            & ssItem(X12) )
                                        & app(cons(X10,nil),X11) = X5
                                        & ssList(X11) )
                                    & ssItem(X10) )
                                | ? [X6] :
                                    ( ? [X7] :
                                        ( ? [X8] :
                                            ( ? [X9] :
                                                ( lt(X6,X8)
                                                & app(cons(X8,nil),X9) = X2
                                                & ssList(X9) )
                                            & ssItem(X8) )
                                        & app(X7,cons(X6,nil)) = X4
                                        & ssList(X7) )
                                    & ssItem(X6) )
                                | ~ strictorderedP(X2)
                                | app(app(X4,X2),X5) != X3 ) ) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f96]) ).

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

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

fof(f172,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | segmentP(X0,X0) ),
    inference(ennf_transformation,[],[f55]) ).

fof(f173,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ! [X2] :
              ( ~ ssList(X2)
              | ! [X3] :
                  ( ~ ssList(X3)
                  | ~ segmentP(X0,X1)
                  | segmentP(app(app(X2,X0),X3),X1) ) ) ) ),
    inference(ennf_transformation,[],[f56]) ).

fof(f174,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ! [X2] :
              ( ~ ssList(X2)
              | ! [X3] :
                  ( ~ ssList(X3)
                  | ~ segmentP(X0,X1)
                  | segmentP(app(app(X2,X0),X3),X1) ) ) ) ),
    inference(flattening,[],[f173]) ).

fof(f175,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | segmentP(X0,nil) ),
    inference(ennf_transformation,[],[f57]) ).

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

fof(f221,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ssList(X3)
                  & ( ( ! [X14] :
                          ( ~ segmentP(X0,X14)
                          | ~ segmentP(X1,X14)
                          | ~ neq(X14,nil)
                          | ~ ssList(X14) )
                      & neq(X1,nil) )
                    | ( nil != X0
                      & nil = X1 ) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X4] :
                      ( ssList(X4)
                      & ? [X5] :
                          ( ssList(X5)
                          & ! [X10] :
                              ( ! [X11] :
                                  ( ! [X12] :
                                      ( ! [X13] :
                                          ( ~ lt(X12,X10)
                                          | app(X13,cons(X12,nil)) != X2
                                          | ~ ssList(X13) )
                                      | ~ ssItem(X12) )
                                  | app(cons(X10,nil),X11) != X5
                                  | ~ ssList(X11) )
                              | ~ ssItem(X10) )
                          & ! [X6] :
                              ( ! [X7] :
                                  ( ! [X8] :
                                      ( ! [X9] :
                                          ( ~ lt(X6,X8)
                                          | app(cons(X8,nil),X9) != X2
                                          | ~ ssList(X9) )
                                      | ~ ssItem(X8) )
                                  | app(X7,cons(X6,nil)) != X4
                                  | ~ ssList(X7) )
                              | ~ ssItem(X6) )
                          & strictorderedP(X2)
                          & app(app(X4,X2),X5) = X3 ) )
                  & X0 = X2
                  & X1 = X3 ) ) ) ),
    inference(ennf_transformation,[],[f97]) ).

fof(f222,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ssList(X3)
                  & ( ( ! [X14] :
                          ( ~ segmentP(X0,X14)
                          | ~ segmentP(X1,X14)
                          | ~ neq(X14,nil)
                          | ~ ssList(X14) )
                      & neq(X1,nil) )
                    | ( nil != X0
                      & nil = X1 ) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X4] :
                      ( ssList(X4)
                      & ? [X5] :
                          ( ssList(X5)
                          & ! [X10] :
                              ( ! [X11] :
                                  ( ! [X12] :
                                      ( ! [X13] :
                                          ( ~ lt(X12,X10)
                                          | app(X13,cons(X12,nil)) != X2
                                          | ~ ssList(X13) )
                                      | ~ ssItem(X12) )
                                  | app(cons(X10,nil),X11) != X5
                                  | ~ ssList(X11) )
                              | ~ ssItem(X10) )
                          & ! [X6] :
                              ( ! [X7] :
                                  ( ! [X8] :
                                      ( ! [X9] :
                                          ( ~ lt(X6,X8)
                                          | app(cons(X8,nil),X9) != X2
                                          | ~ ssList(X9) )
                                      | ~ ssItem(X8) )
                                  | app(X7,cons(X6,nil)) != X4
                                  | ~ ssList(X7) )
                              | ~ ssItem(X6) )
                          & strictorderedP(X2)
                          & app(app(X4,X2),X5) = X3 ) )
                  & X0 = X2
                  & X1 = X3 ) ) ) ),
    inference(flattening,[],[f221]) ).

fof(f246,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(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) ) ) ) ),
    inference(nnf_transformation,[],[f103]) ).

fof(f247,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( ( ~ segmentP(X0,X1)
              | ? [X4] :
                  ( ? [X5] :
                      ( app(app(X4,X1),X5) = X0
                      & ssList(X5) )
                  & ssList(X4) ) )
            & ( ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) )
              | segmentP(X0,X1) ) ) ) ),
    inference(rectify,[],[f246]) ).

fof(f248,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( ( ~ segmentP(X0,X1)
              | ( app(app(sK13(X0,X1),X1),sK14(X0,X1)) = X0
                & ssList(sK14(X0,X1))
                & ssList(sK13(X0,X1)) ) )
            & ( ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) )
              | segmentP(X0,X1) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X4,sK13(X0,X1)),skolemize(X5,sK14(X0,X1))],[f247]) ).

fof(f273,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( ( ~ neq(X0,X1)
              | X0 != X1 )
            & ( X0 = X1
              | neq(X0,X1) ) ) ) ),
    inference(nnf_transformation,[],[f118]) ).

fof(f285,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( ( ~ segmentP(nil,X0)
          | nil = X0 )
        & ( nil != X0
          | segmentP(nil,X0) ) ) ),
    inference(nnf_transformation,[],[f176]) ).

fof(f296,plain,
    ( ssList(sK53)
    & ssList(sK54)
    & ssList(sK55)
    & ssList(sK56)
    & ( ( ! [X14] :
            ( ~ segmentP(sK53,X14)
            | ~ segmentP(sK54,X14)
            | ~ neq(X14,nil)
            | ~ ssList(X14) )
        & neq(sK54,nil) )
      | ( nil != sK53
        & nil = sK54 ) )
    & ( nil != sK55
      | nil = sK56 )
    & ssList(sK57)
    & ssList(sK58)
    & ! [X10] :
        ( ! [X11] :
            ( ! [X12] :
                ( ! [X13] :
                    ( ~ lt(X12,X10)
                    | app(X13,cons(X12,nil)) != sK55
                    | ~ ssList(X13) )
                | ~ ssItem(X12) )
            | app(cons(X10,nil),X11) != sK58
            | ~ ssList(X11) )
        | ~ ssItem(X10) )
    & ! [X6] :
        ( ! [X7] :
            ( ! [X8] :
                ( ! [X9] :
                    ( ~ lt(X6,X8)
                    | app(cons(X8,nil),X9) != sK55
                    | ~ ssList(X9) )
                | ~ ssItem(X8) )
            | app(X7,cons(X6,nil)) != sK57
            | ~ ssList(X7) )
        | ~ ssItem(X6) )
    & strictorderedP(sK55)
    & sK56 = app(app(sK57,sK55),sK58)
    & sK53 = sK55
    & sK54 = sK56 ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X4,sK57),skolemize(X5,sK58)],[f222]) ).

fof(f318,plain,
    ! [X2,X3,X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | app(app(X2,X1),X3) != X0
      | ~ ssList(X3)
      | ~ ssList(X2)
      | segmentP(X0,X1) ),
    inference(cnf_transformation,[],[f248]) ).

fof(f387,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | X0 = X1
      | neq(X0,X1) ),
    inference(cnf_transformation,[],[f273]) ).

fof(f389,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f440,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | segmentP(X0,X0) ),
    inference(cnf_transformation,[],[f172]) ).

fof(f441,plain,
    ! [X2,X3,X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | ~ ssList(X2)
      | ~ ssList(X3)
      | ~ segmentP(X0,X1)
      | segmentP(app(app(X2,X0),X3),X1) ),
    inference(cnf_transformation,[],[f174]) ).

fof(f442,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | segmentP(X0,nil) ),
    inference(cnf_transformation,[],[f175]) ).

fof(f443,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ~ segmentP(nil,X0)
      | nil = X0 ),
    inference(cnf_transformation,[],[f285]) ).

fof(f496,plain,
    ssList(sK53),
    inference(cnf_transformation,[],[f296]) ).

fof(f501,plain,
    ( neq(sK54,nil)
    | nil != sK53 ),
    inference(cnf_transformation,[],[f296]) ).

fof(f502,plain,
    ! [X14] :
      ( ~ segmentP(sK53,X14)
      | ~ segmentP(sK54,X14)
      | ~ neq(X14,nil)
      | ~ ssList(X14)
      | nil = sK54 ),
    inference(cnf_transformation,[],[f296]) ).

fof(f504,plain,
    ( nil != sK55
    | nil = sK56 ),
    inference(cnf_transformation,[],[f296]) ).

fof(f505,plain,
    ssList(sK57),
    inference(cnf_transformation,[],[f296]) ).

fof(f506,plain,
    ssList(sK58),
    inference(cnf_transformation,[],[f296]) ).

fof(f510,plain,
    sK56 = app(app(sK57,sK55),sK58),
    inference(cnf_transformation,[],[f296]) ).

fof(f511,plain,
    sK53 = sK55,
    inference(cnf_transformation,[],[f296]) ).

fof(f512,plain,
    sK54 = sK56,
    inference(cnf_transformation,[],[f296]) ).

fof(f514,plain,
    ! [X14] :
      ( ~ segmentP(sK55,X14)
      | ~ segmentP(sK56,X14)
      | ~ neq(X14,nil)
      | ~ ssList(X14)
      | nil = sK56 ),
    inference(definition_unfolding,[],[f502,f512,f512,f511]) ).

fof(f515,plain,
    ( neq(sK56,nil)
    | nil != sK55 ),
    inference(definition_unfolding,[],[f501,f511,f512]) ).

fof(f518,plain,
    ssList(sK55),
    inference(definition_unfolding,[],[f496,f511]) ).

fof(f524,plain,
    ! [X2,X3,X1] :
      ( ~ ssList(app(app(X2,X1),X3))
      | ~ ssList(X1)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | segmentP(app(app(X2,X1),X3),X1) ),
    inference(equality_resolution,[],[f318]) ).

tcf(c_67,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( segmentP(app(app(X0,X1),X2),X1)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ ssList(app(app(X0,X1),X2)) ),
    inference(cnf_transformation,[],[f524]) ).

tcf(c_138,plain,
    ! [X0: $i,X1: $i] :
      ( neq(X0,X1)
      | ( X0 = X1 )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f387]) ).

tcf(c_139,plain,
    ! [X0: $i] :
      ( ~ ssList(X0)
      | ~ neq(X0,X0) ),
    inference(cnf_transformation,[],[f548]) ).

tcf(c_141,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f389]) ).

tcf(c_192,plain,
    ! [X0: $i] :
      ( segmentP(X0,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f440]) ).

tcf(c_193,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( segmentP(app(app(X2,X0),X3),X1)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ segmentP(X0,X1) ),
    inference(cnf_transformation,[],[f441]) ).

tcf(c_194,plain,
    ! [X0: $i] :
      ( segmentP(X0,nil)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f442]) ).

tcf(c_196,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ segmentP(nil,X0) ),
    inference(cnf_transformation,[],[f443]) ).

tcf(c_246,negated_conjecture,
    app(app(sK57,sK55),sK58) = sK56,
    inference(cnf_transformation,[],[f510]) ).

tcf(c_250,negated_conjecture,
    ssList(sK58),
    inference(cnf_transformation,[],[f506]) ).

tcf(c_251,negated_conjecture,
    ssList(sK57),
    inference(cnf_transformation,[],[f505]) ).

tcf(c_252,negated_conjecture,
    ( ( nil = sK56 )
    | ( nil != sK55 ) ),
    inference(cnf_transformation,[],[f504]) ).

tcf(c_254,negated_conjecture,
    ! [X0: $i] :
      ( ( nil = sK56 )
      | ~ ssList(X0)
      | ~ segmentP(sK55,X0)
      | ~ segmentP(sK56,X0)
      | ~ neq(X0,nil) ),
    inference(cnf_transformation,[],[f514]) ).

tcf(c_255,negated_conjecture,
    ( neq(sK56,nil)
    | ( nil != sK55 ) ),
    inference(cnf_transformation,[],[f515]) ).

tcf(c_260,negated_conjecture,
    ssList(sK55),
    inference(cnf_transformation,[],[f518]) ).

tcf(c_532,plain,
    ( ( nil = sK56 )
    | ~ ssList(sK55)
    | ~ segmentP(sK56,sK55)
    | ~ neq(sK55,nil) ),
    inference(superposition,[status(thm)],[c_192,c_254]) ).

tcf(c_533,plain,
    ( ( nil = sK56 )
    | ~ ssList(sK55)
    | ~ ssList(nil)
    | ~ segmentP(sK56,nil)
    | ~ neq(nil,nil) ),
    inference(superposition,[status(thm)],[c_194,c_254]) ).

tcf(c_652,plain,
    ! [X0: $i] :
      ( segmentP(sK56,X0)
      | ~ ssList(sK58)
      | ~ ssList(sK55)
      | ~ ssList(sK57)
      | ~ ssList(X0)
      | ~ segmentP(sK55,X0) ),
    inference(superposition,[status(thm)],[c_246,c_193]) ).

tcf(c_669,plain,
    ( segmentP(sK56,sK55)
    | ~ ssList(sK58)
    | ~ ssList(sK55)
    | ~ ssList(sK57)
    | ~ ssList(app(app(sK57,sK55),sK58)) ),
    inference(superposition,[status(thm)],[c_246,c_67]) ).

tcf(c_1086,negated_conjecture,
    ! [X0: $i] :
      ( ( nil = sK56 )
      | ~ ssList(X0)
      | ~ segmentP(sK55,X0)
      | ~ neq(X0,nil) ),
    inference(global_subsumption_just,[status(thm)],[c_254,c_260,c_251,c_250,c_254,c_652]) ).

tcf(c_1097,plain,
    ( ( nil = sK56 )
    | ~ ssList(sK55)
    | ~ neq(sK55,nil) ),
    inference(superposition,[status(thm)],[c_192,c_1086]) ).

tcf(c_1129,plain,
    ( ( nil = sK56 )
    | ~ neq(sK55,nil) ),
    inference(global_subsumption_just,[status(thm)],[c_532,c_260,c_1097]) ).

tcf(c_1136,plain,
    ( ( nil = sK55 )
    | ( nil = sK56 )
    | ~ ssList(sK55)
    | ~ ssList(nil) ),
    inference(superposition,[status(thm)],[c_138,c_1129]) ).

tcf(c_1148,plain,
    nil = sK56,
    inference(global_subsumption_just,[status(thm)],[c_533,c_260,c_141,c_252,c_1136]) ).

tcf(c_1658,plain,
    ( segmentP(sK56,sK55)
    | ~ ssList(app(app(sK57,sK55),sK58)) ),
    inference(global_subsumption_just,[status(thm)],[c_669,c_260,c_251,c_250,c_669]) ).

tcf(c_1662,plain,
    ( segmentP(nil,sK55)
    | ~ ssList(nil) ),
    inference(light_normalisation,[status(thm)],[c_1658,c_246,c_1148]) ).

tcf(c_1665,plain,
    segmentP(nil,sK55),
    inference(forward_subsumption_resolution,[status(thm)],[c_1662,c_141]) ).

tcf(c_1669,plain,
    ( ( nil = sK55 )
    | ~ ssList(sK55) ),
    inference(superposition,[status(thm)],[c_1665,c_196]) ).

tcf(c_2846,plain,
    nil = sK55,
    inference(global_subsumption_just,[status(thm)],[c_1136,c_260,c_1669]) ).

tcf(c_2864,plain,
    neq(sK56,nil),
    inference(superposition,[status(thm)],[c_2846,c_255]) ).

tcf(c_6580,plain,
    neq(nil,nil),
    inference(light_normalisation,[status(thm)],[c_2864,c_1148]) ).

tcf(c_6582,plain,
    ~ ssList(nil),
    inference(superposition,[status(thm)],[c_6580,c_139]) ).

tcf(c_6583,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[c_141,c_6582]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWC067+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.35  % Computer : n007.cluster.edu
% 0.10/0.35  % Model    : x86_64 x86_64
% 0.10/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35  % Memory   : 8046.5625MB
% 0.10/0.35  % OS       : Linux 6.8.0-71-generic
% 0.10/0.35  % CPULimit : 300
% 0.10/0.35  % WCLimit  : 300
% 0.10/0.35  % DateTime : Thu Sep 24 16:10:08 UTC 2026
% 0.10/0.36  % CPUTime  : 
% 0.10/0.36  Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.39  Running first-order theorem proving
% 0.14/0.39  Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.40  
% 0.14/0.40  % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.40  
% 0.14/0.40  % Detected problem language: tptp
% 0.14/0.41  % Proving...
% 4.17/1.17  % SZS status Started for theBenchmark.p
% 4.17/1.17  % SZS status Theorem for theBenchmark.p
% 4.17/1.17  
% 4.17/1.17  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.17/1.17  
% 4.17/1.17  % ------  iProver source info
% 4.17/1.17  
% 4.17/1.17  % git: date: 2026-07-19 20:42:38 +0200
% 4.17/1.17  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.17/1.17  % git: non_committed_changes: false
% 4.17/1.17  
% 4.17/1.17  % ------ Parsing...
% 4.17/1.17  % ------ Clausification by vclausify_rel  & Parsing by iProver...
% 4.17/1.17  % ------ Proving...
% 4.17/1.17  % ------ Problem Properties 
% 4.17/1.17  
% 4.17/1.17  % 
% 4.17/1.17  % clauses                               212
% 4.17/1.17  % conjectures                           15
% 4.17/1.17  % EPR                                   76
% 4.17/1.17  % Horn                                  140
% 4.17/1.17  % unary                                 20
% 4.17/1.17  % binary                                56
% 4.17/1.17  % lits                                  708
% 4.17/1.17  % lits eq                               92
% 4.17/1.17  % fd_pure                               0
% 4.17/1.17  % fd_pseudo                             0
% 4.17/1.17  % fd_cond                               21
% 4.17/1.17  % fd_pseudo_cond                        17
% 4.17/1.17  % AC symbols                            0
% 4.17/1.17  
% 4.17/1.17  % ------ Input Options Time Limit: Unbounded
% 4.17/1.17  
% 4.17/1.17  
% 4.17/1.17  % ------ 
% 4.17/1.17  % Current options:
% 4.17/1.17  % ------ 
% 4.17/1.17  
% 4.17/1.17  
% 4.17/1.17  % 
% 4.17/1.17  
% 4.17/1.17  % ------ Proving...
% 4.17/1.17  % 
% 4.17/1.17  
% 4.17/1.17  % SZS status Theorem for theBenchmark.p
% 4.17/1.17  
% 4.17/1.17  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.17/1.17  
% 4.17/1.17  
%------------------------------------------------------------------------------