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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : SWC384+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM

% Computer : n017.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 03:09:33 PM UTC 2026

% Result   : Theorem 2.30s 7.06s
% Output   : CNFRefutation 2.30s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f274ERROR: Could not build tree for root c_8325ERROR: MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( singletonP(X0)
      <=> ? [X1] :
            ( cons(X1,nil) = X0
            & ssItem(X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).

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/Axioms/SWC001+0.ax',ax7) ).

fof(f16,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ssList(cons(X1,X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).

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

fof(f98,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ssList(X3)
                  & ( ~ segmentP(X1,X0)
                    | ~ singletonP(X0) )
                  & ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( ssItem(X4)
                        & ? [X5] :
                            ( ssList(X5)
                            & ? [X6] :
                                ( ssList(X6)
                                & ! [X8] :
                                    ( ~ lt(X8,X4)
                                    | ~ memberP(X6,X8)
                                    | ~ ssItem(X8) )
                                & ! [X7] :
                                    ( ~ lt(X4,X7)
                                    | ~ memberP(X5,X7)
                                    | ~ ssItem(X7) )
                                & app(app(X5,X2),X6) = X3
                                & cons(X4,nil) = X2 ) ) ) )
                  & neq(X1,nil)
                  & X0 = X2
                  & X1 = X3 ) ) ) ),
    inference(ennf_transformation,[],[f97]) ).

fof(f99,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ssList(X3)
                  & ( ~ segmentP(X1,X0)
                    | ~ singletonP(X0) )
                  & ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( ssItem(X4)
                        & ? [X5] :
                            ( ssList(X5)
                            & ? [X6] :
                                ( ssList(X6)
                                & ! [X8] :
                                    ( ~ lt(X8,X4)
                                    | ~ memberP(X6,X8)
                                    | ~ ssItem(X8) )
                                & ! [X7] :
                                    ( ~ lt(X4,X7)
                                    | ~ memberP(X5,X7)
                                    | ~ ssItem(X7) )
                                & app(app(X5,X2),X6) = X3
                                & cons(X4,nil) = X2 ) ) ) )
                  & neq(X1,nil)
                  & X0 = X2
                  & X1 = X3 ) ) ) ),
    inference(flattening,[],[f98]) ).

fof(f108,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssItem(X1)
          | ssList(cons(X1,X0)) ) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f124,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( singletonP(X0)
      <=> ? [X1] :
            ( cons(X1,nil) = X0
            & ssItem(X1) ) ) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f134,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(f155,plain,
    ( ssList(sK4)
    & ssList(sK5)
    & ssList(sK6)
    & ssList(sK7)
    & ( ~ segmentP(sK5,sK4)
      | ~ singletonP(sK4) )
    & ( ( nil = sK6
        & nil = sK7 )
      | sP0(sK6,sK7) )
    & neq(sK5,nil)
    & sK4 = sK6
    & sK5 = sK7 ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7)],[f151]) ).

fof(f169,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( ( ~ singletonP(X0)
          | ? [X1] :
              ( cons(X1,nil) = X0
              & ssItem(X1) ) )
        & ( ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) )
          | singletonP(X0) ) ) ),
    inference(nnf_transformation,[],[f124]) ).

fof(f170,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( ( ~ singletonP(X0)
          | ? [X2] :
              ( cons(X2,nil) = X0
              & ssItem(X2) ) )
        & ( ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) )
          | singletonP(X0) ) ) ),
    inference(rectify,[],[f169]) ).

fof(f171,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( ( ~ singletonP(X0)
          | ( cons(sK14(X0),nil) = X0
            & ssItem(sK14(X0)) ) )
        & ( ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) )
          | singletonP(X0) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X2,sK14(X0))],[f170]) ).

fof(f173,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,[],[f134]) ).

fof(f174,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,[],[f173]) ).

fof(f175,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( ( ~ segmentP(X0,X1)
              | ( app(app(sK15(X0,X1),X1),sK16(X0,X1)) = X0
                & ssList(sK16(X0,X1))
                & ssList(sK15(X0,X1)) ) )
            & ( ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) )
              | segmentP(X0,X1) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16]),skolemize(X4,sK15(X0,X1)),skolemize(X5,sK16(X0,X1))],[f174]) ).

fof(f185,plain,
    ssList(sK4),
    inference(cnf_transformation,[],[f155]) ).

fof(f186,plain,
    ssList(sK5),
    inference(cnf_transformation,[],[f155]) ).

fof(f189,plain,
    ( ~ segmentP(sK5,sK4)
    | ~ singletonP(sK4) ),
    inference(cnf_transformation,[],[f155]) ).

fof(f191,plain,
    ( nil = sK7
    | sP0(sK6,sK7) ),
    inference(cnf_transformation,[],[f155]) ).

fof(f192,plain,
    neq(sK5,nil),
    inference(cnf_transformation,[],[f155]) ).

fof(f193,plain,
    sK4 = sK6,
    inference(cnf_transformation,[],[f155]) ).

fof(f194,plain,
    sK5 = sK7,
    inference(cnf_transformation,[],[f155]) ).

fof(f207,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssItem(X1)
      | ssList(cons(X1,X0)) ),
    inference(cnf_transformation,[],[f108]) ).

fof(f221,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f236,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | cons(X1,nil) != X0
      | ~ ssItem(X1)
      | singletonP(X0) ),
    inference(cnf_transformation,[],[f171]) ).

fof(f247,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,[],[f175]) ).

fof(f259,plain,
    neq(sK7,nil),
    inference(definition_unfolding,[],[f192,f194]) ).

fof(f260,plain,
    ( ~ segmentP(sK7,sK6)
    | ~ singletonP(sK6) ),
    inference(definition_unfolding,[],[f189,f193,f194,f193]) ).

fof(f261,plain,
    ssList(sK7),
    inference(definition_unfolding,[],[f186,f194]) ).

fof(f262,plain,
    ssList(sK6),
    inference(definition_unfolding,[],[f185,f193]) ).

fof(f269,plain,
    ! [X1] :
      ( ~ ssList(cons(X1,nil))
      | ~ ssItem(X1)
      | singletonP(cons(X1,nil)) ),
    inference(equality_resolution,[],[f236]) ).

fof(f271,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,[],[f247]) ).

tcf(c_56,negated_conjecture,
    neq(sK7,nil),
    inference(cnf_transformation,[],[f259]) ).

tcf(c_57,negated_conjecture,
    ( sP0(sK6,sK7)
    | ( nil = sK7 ) ),
    inference(cnf_transformation,[],[f191]) ).

tcf(c_59,negated_conjecture,
    ( ~ singletonP(sK6)
    | ~ segmentP(sK7,sK6) ),
    inference(cnf_transformation,[],[f260]) ).

tcf(c_62,negated_conjecture,
    ssList(sK7),
    inference(cnf_transformation,[],[f261]) ).

tcf(c_63,negated_conjecture,
    ssList(sK6),
    inference(cnf_transformation,[],[f262]) ).

tcf(c_76,plain,
    ! [X0: $i,X1: $i] :
      ( ssList(cons(X0,X1))
      | ~ ssList(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f207]) ).

tcf(c_87,plain,
    ! [X0: $i] :
      ( ~ ssList(X0)
      | ~ neq(X0,X0) ),
    inference(cnf_transformation,[],[f274]) ).

tcf(c_90,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f221]) ).

tcf(c_103,plain,
    ! [X0: $i] :
      ( singletonP(cons(X0,nil))
      | ~ ssItem(X0)
      | ~ ssList(cons(X0,nil)) ),
    inference(cnf_transformation,[],[f269]) ).

tcf(c_113,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,[],[f271]) ).

tcf(c_1238,plain,
    ! [X0: $i] :
      ( ~ ssList(X0)
      | ( X0 != sK7 )
      | ( X0 != nil ) ),
    inference(resolution_lifted,[status(thm)],[c_56,c_87]) ).

tcf(c_1239,plain,
    ( ~ ssList(nil)
    | ( nil != sK7 ) ),
    inference(unflattening,[status(thm)],[c_1238]) ).

tcf(c_1240,plain,
    nil != sK7,
    inference(global_subsumption_just,[status(thm)],[c_1239,c_90,c_1239]) ).

tcf(c_1254,plain,
    sP0(sK6,sK7),
    inference(backward_subsumption_resolution,[status(thm)],[c_57,c_1240]) ).

tcf(c_3515,plain,
    ! [X0: $i] :
      ( singletonP(cons(X0,nil))
      | ~ ssList(nil)
      | ~ ssItem(X0) ),
    inference(superposition,[status(thm)],[c_76,c_103]) ).

tcf(c_3517,plain,
    ! [X0: $i] :
      ( singletonP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_3515,c_90]) ).

fof(f150,definition,
    ! [X2,X3] :
      ( ~ sP0(X2,X3)
      | ? [X4] :
          ( ssItem(X4)
          & ? [X5] :
              ( ssList(X5)
              & ? [X6] :
                  ( ssList(X6)
                  & ! [X8] :
                      ( ~ lt(X8,X4)
                      | ~ memberP(X6,X8)
                      | ~ ssItem(X8) )
                  & ! [X7] :
                      ( ~ lt(X4,X7)
                      | ~ memberP(X5,X7)
                      | ~ ssItem(X7) )
                  & app(app(X5,X2),X6) = X3
                  & cons(X4,nil) = X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).

fof(f151,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ssList(X3)
                  & ( ~ segmentP(X1,X0)
                    | ~ singletonP(X0) )
                  & ( ( nil = X2
                      & nil = X3 )
                    | sP0(X2,X3) )
                  & neq(X1,nil)
                  & X0 = X2
                  & X1 = X3 ) ) ) ),
    inference(definition_folding,[],[f99,f150]) ).

fof(f152,plain,
    ! [X2,X3] :
      ( ~ sP0(X2,X3)
      | ? [X4] :
          ( ssItem(X4)
          & ? [X5] :
              ( ssList(X5)
              & ? [X6] :
                  ( ssList(X6)
                  & ! [X8] :
                      ( ~ lt(X8,X4)
                      | ~ memberP(X6,X8)
                      | ~ ssItem(X8) )
                  & ! [X7] :
                      ( ~ lt(X4,X7)
                      | ~ memberP(X5,X7)
                      | ~ ssItem(X7) )
                  & app(app(X5,X2),X6) = X3
                  & cons(X4,nil) = X2 ) ) ) ),
    inference(nnf_transformation,[],[f150]) ).

fof(f153,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | ? [X2] :
          ( ssItem(X2)
          & ? [X3] :
              ( ssList(X3)
              & ? [X4] :
                  ( ssList(X4)
                  & ! [X6] :
                      ( ~ lt(X6,X2)
                      | ~ memberP(X4,X6)
                      | ~ ssItem(X6) )
                  & ! [X5] :
                      ( ~ lt(X2,X5)
                      | ~ memberP(X3,X5)
                      | ~ ssItem(X5) )
                  & app(app(X3,X0),X4) = X1
                  & cons(X2,nil) = X0 ) ) ) ),
    inference(rectify,[],[f152]) ).

fof(f154,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | ( ssItem(sK1(X0,X1))
        & ssList(sK2(X0,X1))
        & ssList(sK3(X0,X1))
        & ! [X6] :
            ( ~ lt(X6,sK1(X0,X1))
            | ~ memberP(sK3(X0,X1),X6)
            | ~ ssItem(X6) )
        & ! [X5] :
            ( ~ lt(sK1(X0,X1),X5)
            | ~ memberP(sK2(X0,X1),X5)
            | ~ ssItem(X5) )
        & app(app(sK2(X0,X1),X0),sK3(X0,X1)) = X1
        & cons(sK1(X0,X1),nil) = X0 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(X0,X1)),skolemize(X3,sK2(X0,X1)),skolemize(X4,sK3(X0,X1))],[f153]) ).

fof(f178,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | ssItem(sK1(X0,X1)) ),
    inference(cnf_transformation,[],[f154]) ).

fof(f179,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | ssList(sK2(X0,X1)) ),
    inference(cnf_transformation,[],[f154]) ).

fof(f180,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | ssList(sK3(X0,X1)) ),
    inference(cnf_transformation,[],[f154]) ).

fof(f183,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | app(app(sK2(X0,X1),X0),sK3(X0,X1)) = X1 ),
    inference(cnf_transformation,[],[f154]) ).

fof(f184,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | cons(sK1(X0,X1),nil) = X0 ),
    inference(cnf_transformation,[],[f154]) ).

tcf(c_49,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(sK1(X0,X1),nil) = X0 )
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f184]) ).

tcf(c_50,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(sK2(X0,X1),X0),sK3(X0,X1)) = X1 )
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f183]) ).

tcf(c_53,plain,
    ! [X0: $i,X1: $i] :
      ( ssList(sK3(X0,X1))
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f180]) ).

tcf(c_54,plain,
    ! [X0: $i,X1: $i] :
      ( ssList(sK2(X0,X1))
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f179]) ).

tcf(c_55,plain,
    ! [X0: $i,X1: $i] :
      ( ssItem(sK1(X0,X1))
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f178]) ).

tcf(c_1255,plain,
    ! [X0: $i,X1: $i] :
      ( ssItem(sK1(X0,X1))
      | ( X1 != sK7 )
      | ( X0 != sK6 ) ),
    inference(resolution_lifted,[status(thm)],[c_55,c_1254]) ).

tcf(c_1256,plain,
    ssItem(sK1(sK6,sK7)),
    inference(unflattening,[status(thm)],[c_1255]) ).

tcf(c_1262,plain,
    ! [X0: $i,X1: $i] :
      ( ssList(sK2(X0,X1))
      | ( X1 != sK7 )
      | ( X0 != sK6 ) ),
    inference(resolution_lifted,[status(thm)],[c_54,c_1254]) ).

tcf(c_1263,plain,
    ssList(sK2(sK6,sK7)),
    inference(unflattening,[status(thm)],[c_1262]) ).

tcf(c_1269,plain,
    ! [X0: $i,X1: $i] :
      ( ssList(sK3(X0,X1))
      | ( X1 != sK7 )
      | ( X0 != sK6 ) ),
    inference(resolution_lifted,[status(thm)],[c_53,c_1254]) ).

tcf(c_1270,plain,
    ssList(sK3(sK6,sK7)),
    inference(unflattening,[status(thm)],[c_1269]) ).

tcf(c_1304,plain,
    ! [X0: $i,X1: $i] :
      ( ( app(app(sK2(X0,X1),X0),sK3(X0,X1)) = X1 )
      | ( X1 != sK7 )
      | ( X0 != sK6 ) ),
    inference(resolution_lifted,[status(thm)],[c_50,c_1254]) ).

tcf(c_1305,plain,
    app(app(sK2(sK6,sK7),sK6),sK3(sK6,sK7)) = sK7,
    inference(unflattening,[status(thm)],[c_1304]) ).

tcf(c_1311,plain,
    ! [X0: $i,X1: $i] :
      ( ( cons(sK1(X0,X1),nil) = X0 )
      | ( X1 != sK7 )
      | ( X0 != sK6 ) ),
    inference(resolution_lifted,[status(thm)],[c_49,c_1254]) ).

tcf(c_1312,plain,
    cons(sK1(sK6,sK7),nil) = sK6,
    inference(unflattening,[status(thm)],[c_1311]) ).

tcf(c_3590,plain,
    ( singletonP(sK6)
    | ~ ssItem(sK1(sK6,sK7)) ),
    inference(superposition,[status(thm)],[c_1312,c_3517]) ).

tcf(c_3592,plain,
    singletonP(sK6),
    inference(forward_subsumption_resolution,[status(thm)],[c_3590,c_1256]) ).

tcf(c_3596,plain,
    ~ segmentP(sK7,sK6),
    inference(backward_subsumption_resolution,[status(thm)],[c_59,c_3592]) ).

tcf(c_8161,plain,
    ( segmentP(sK7,sK6)
    | ~ ssList(sK6)
    | ~ ssList(sK3(sK6,sK7))
    | ~ ssList(sK2(sK6,sK7))
    | ~ ssList(app(app(sK2(sK6,sK7),sK6),sK3(sK6,sK7))) ),
    inference(superposition,[status(thm)],[c_1305,c_113]) ).

tcf(c_8324,plain,
    ( segmentP(sK7,sK6)
    | ~ ssList(sK6)
    | ~ ssList(sK7)
    | ~ ssList(sK3(sK6,sK7))
    | ~ ssList(sK2(sK6,sK7)) ),
    inference(light_normalisation,[status(thm)],[c_8161,c_1305]) ).

tcf(c_8325,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_8324,c_3596,c_63,c_62,c_1270,c_1263]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWC384+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/5.59  % Computer : n017.cluster.edu
% 0.12/5.59  % Model    : x86_64 x86_64
% 0.12/5.59  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.59  % Memory   : 8046.5625MB
% 0.12/5.59  % OS       : Linux 6.8.0-71-generic
% 0.12/5.59  % CPULimit : 300
% 0.12/5.59  % WCLimit  : 300
% 0.12/5.59  % DateTime : Thu Sep 24 17:53:08 UTC 2026
% 0.16/5.60  % CPUTime  : 
% 0.16/5.60  Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.65  Running first-order theorem proving
% 0.16/5.65  Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.67  
% 0.16/5.67  % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.67  
% 0.16/5.67  % Detected problem language: tptp
% 0.16/5.68  % Proving...
% 2.30/7.06  % SZS status Started for theBenchmark.p
% 2.30/7.06  % SZS status Theorem for theBenchmark.p
% 2.30/7.06  
% 2.30/7.06  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.30/7.06  
% 2.30/7.06  % ------  iProver source info
% 2.30/7.06  
% 2.30/7.06  % git: date: 2026-07-19 20:42:38 +0200
% 2.30/7.06  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.30/7.06  % git: non_committed_changes: false
% 2.30/7.06  
% 2.30/7.06  % ------ Parsing...
% 2.30/7.06  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 2.30/7.06  
% 2.30/7.06  % ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 0  sf_s  rm: 3 0s  sf_e  pe_s  pe_e % 
% 2.30/7.06  
% 2.30/7.06  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 2.30/7.06  
% 2.30/7.06  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.30/7.06  % ------ Proving...
% 2.30/7.06  % ------ Problem Properties 
% 2.30/7.06  
% 2.30/7.06  % 
% 2.30/7.06  % clauses                               69
% 2.30/7.06  % conjectures                           3
% 2.30/7.06  % EPR                                   25
% 2.30/7.06  % Horn                                  63
% 2.30/7.06  % unary                                 15
% 2.30/7.06  % binary                                8
% 2.30/7.06  % lits                                  228
% 2.30/7.06  % lits eq                               36
% 2.30/7.06  % fd_pure                               0
% 2.30/7.06  % fd_pseudo                             0
% 2.30/7.06  % fd_cond                               5
% 2.30/7.06  % fd_pseudo_cond                        8
% 2.30/7.06  % AC symbols                            0
% 2.30/7.06  
% 2.30/7.06  % ------ Schedule dynamic 5 is on 
% 2.30/7.06  
% 2.30/7.06  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.30/7.06  
% 2.30/7.06  
% 2.30/7.06  % ------ 
% 2.30/7.06  % Current options:
% 2.30/7.06  % ------ 
% 2.30/7.06  
% 2.30/7.06  
% 2.30/7.06  % 
% 2.30/7.06  
% 2.30/7.06  % ------ Proving...
% 2.30/7.06  % 
% 2.30/7.06  
% 2.30/7.06  % SZS status Theorem for theBenchmark.p
% 2.30/7.06  
% 2.30/7.06  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.30/7.06  
% 2.30/7.06  
%------------------------------------------------------------------------------