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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : SWC090+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 : n003.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 03:07:51 PM UTC 2026

% Result   : Theorem 0.98s 1.08s
% Output   : CNFRefutation 0.98s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   92 (  34 unt;   0 def)
%            Number of atoms       :  320 (  64 equ)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  393 ( 165   ~; 152   |;  53   &)
%                                         (   4 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :  104 (   0 sgn  82   !;  22   ?;  25   :)

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

fof(f15,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( neq(X0,X1)
          <=> X0 != X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).

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

fof(f28,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(nil,X0) = X0 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).

fof(f55,axiom,
    ! [X0] :
      ( ssList(X0)
     => segmentP(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).

fof(f84,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(X0,nil) = X0 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ! [X5] :
                        ( ssList(X5)
                       => ! [X6] :
                            ( ssList(X6)
                           => ( app(X6,X5) != X2
                              | app(X5,X6) != X3 ) ) )
                    | ? [X4] :
                        ( segmentP(X0,X4)
                        & segmentP(X1,X4)
                        & neq(X4,nil)
                        & ssList(X4) )
                    | ~ 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)
                   => ( ! [X5] :
                          ( ssList(X5)
                         => ! [X6] :
                              ( ssList(X6)
                             => ( app(X6,X5) != X2
                                | app(X5,X6) != X3 ) ) )
                      | ? [X4] :
                          ( segmentP(X0,X4)
                          & segmentP(X1,X4)
                          & neq(X4,nil)
                          & ssList(X4) )
                      | ~ 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)
                  & ? [X5] :
                      ( ssList(X5)
                      & ? [X6] :
                          ( ssList(X6)
                          & app(X6,X5) = X2
                          & app(X5,X6) = X3 ) )
                  & ! [X4] :
                      ( ~ segmentP(X0,X4)
                      | ~ segmentP(X1,X4)
                      | ~ neq(X4,nil)
                      | ~ ssList(X4) )
                  & 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)
                  & ? [X5] :
                      ( ssList(X5)
                      & ? [X6] :
                          ( ssList(X6)
                          & app(X6,X5) = X2
                          & app(X5,X6) = X3 ) )
                  & ! [X4] :
                      ( ~ segmentP(X0,X4)
                      | ~ segmentP(X1,X4)
                      | ~ neq(X4,nil)
                      | ~ ssList(X4) )
                  & neq(X1,nil)
                  & X0 = X2
                  & X1 = X3 ) ) ) ),
    inference(flattening,[],[f98]) ).

fof(f100,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(X0,nil) = X0 ),
    inference(ennf_transformation,[],[f84]) ).

fof(f108,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(nil,X0) = X0 ),
    inference(ennf_transformation,[],[f28]) ).

fof(f111,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( neq(X0,X1)
          <=> X0 != X1 ) ) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f120,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | segmentP(X0,X0) ),
    inference(ennf_transformation,[],[f55]) ).

fof(f125,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(f130,plain,
    ( ssList(sK0)
    & ssList(sK1)
    & ssList(sK2)
    & ssList(sK3)
    & ssList(sK4)
    & ssList(sK5)
    & sK2 = app(sK5,sK4)
    & sK3 = app(sK4,sK5)
    & ! [X4] :
        ( ~ segmentP(sK0,X4)
        | ~ segmentP(sK1,X4)
        | ~ neq(X4,nil)
        | ~ ssList(X4) )
    & neq(sK1,nil)
    & sK0 = sK2
    & sK1 = sK3 ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X5,sK4),skolemize(X6,sK5)],[f99]) ).

fof(f134,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( ( ~ neq(X0,X1)
              | X0 != X1 )
            & ( X0 = X1
              | neq(X0,X1) ) ) ) ),
    inference(nnf_transformation,[],[f111]) ).

fof(f138,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,[],[f125]) ).

fof(f139,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,[],[f138]) ).

fof(f140,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( ( ~ segmentP(X0,X1)
              | ( app(app(sK10(X0,X1),X1),sK11(X0,X1)) = X0
                & ssList(sK11(X0,X1))
                & ssList(sK10(X0,X1)) ) )
            & ( ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) )
              | segmentP(X0,X1) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X4,sK10(X0,X1)),skolemize(X5,sK11(X0,X1))],[f139]) ).

fof(f141,plain,
    ssList(sK0),
    inference(cnf_transformation,[],[f130]) ).

fof(f142,plain,
    ssList(sK1),
    inference(cnf_transformation,[],[f130]) ).

fof(f145,plain,
    ssList(sK4),
    inference(cnf_transformation,[],[f130]) ).

fof(f146,plain,
    ssList(sK5),
    inference(cnf_transformation,[],[f130]) ).

fof(f147,plain,
    sK2 = app(sK5,sK4),
    inference(cnf_transformation,[],[f130]) ).

fof(f148,plain,
    sK3 = app(sK4,sK5),
    inference(cnf_transformation,[],[f130]) ).

fof(f149,plain,
    ! [X4] :
      ( ~ segmentP(sK0,X4)
      | ~ segmentP(sK1,X4)
      | ~ neq(X4,nil)
      | ~ ssList(X4) ),
    inference(cnf_transformation,[],[f130]) ).

fof(f150,plain,
    neq(sK1,nil),
    inference(cnf_transformation,[],[f130]) ).

fof(f151,plain,
    sK0 = sK2,
    inference(cnf_transformation,[],[f130]) ).

fof(f152,plain,
    sK1 = sK3,
    inference(cnf_transformation,[],[f130]) ).

fof(f156,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(X0,nil) = X0 ),
    inference(cnf_transformation,[],[f100]) ).

fof(f164,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(nil,X0) = X0 ),
    inference(cnf_transformation,[],[f108]) ).

fof(f168,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | X0 = X1
      | neq(X0,X1) ),
    inference(cnf_transformation,[],[f134]) ).

fof(f175,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f180,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | segmentP(X0,X0) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f186,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,[],[f140]) ).

fof(f191,plain,
    neq(sK3,nil),
    inference(definition_unfolding,[],[f150,f152]) ).

fof(f192,plain,
    ! [X4] :
      ( ~ segmentP(sK2,X4)
      | ~ segmentP(sK3,X4)
      | ~ neq(X4,nil)
      | ~ ssList(X4) ),
    inference(definition_unfolding,[],[f149,f152,f151]) ).

fof(f193,plain,
    ssList(sK3),
    inference(definition_unfolding,[],[f142,f152]) ).

fof(f194,plain,
    ssList(sK2),
    inference(definition_unfolding,[],[f141,f151]) ).

fof(f200,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,[],[f186]) ).

tcf(c_49,negated_conjecture,
    neq(sK3,nil),
    inference(cnf_transformation,[],[f191]) ).

tcf(c_50,negated_conjecture,
    ! [X0: $i] :
      ( ~ ssList(X0)
      | ~ segmentP(sK2,X0)
      | ~ segmentP(sK3,X0)
      | ~ neq(X0,nil) ),
    inference(cnf_transformation,[],[f192]) ).

tcf(c_51,negated_conjecture,
    app(sK4,sK5) = sK3,
    inference(cnf_transformation,[],[f148]) ).

tcf(c_52,negated_conjecture,
    app(sK5,sK4) = sK2,
    inference(cnf_transformation,[],[f147]) ).

tcf(c_53,negated_conjecture,
    ssList(sK5),
    inference(cnf_transformation,[],[f146]) ).

tcf(c_54,negated_conjecture,
    ssList(sK4),
    inference(cnf_transformation,[],[f145]) ).

tcf(c_57,negated_conjecture,
    ssList(sK3),
    inference(cnf_transformation,[],[f193]) ).

tcf(c_58,negated_conjecture,
    ssList(sK2),
    inference(cnf_transformation,[],[f194]) ).

tcf(c_62,plain,
    ! [X0: $i] :
      ( ( app(X0,nil) = X0 )
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f156]) ).

tcf(c_70,plain,
    ! [X0: $i] :
      ( ( app(nil,X0) = X0 )
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f164]) ).

tcf(c_73,plain,
    ! [X0: $i,X1: $i] :
      ( neq(X0,X1)
      | ( X0 = X1 )
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f168]) ).

tcf(c_81,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f175]) ).

tcf(c_86,plain,
    ! [X0: $i] :
      ( segmentP(X0,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f180]) ).

tcf(c_89,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,[],[f200]) ).

tcf(c_650,plain,
    ! [X0: $i] :
      ( ~ ssList(X0)
      | ~ segmentP(sK2,X0)
      | ~ segmentP(sK3,X0)
      | ( nil != nil )
      | ( X0 != sK3 ) ),
    inference(resolution_lifted,[status(thm)],[c_49,c_50]) ).

tcf(c_651,plain,
    ( ~ ssList(sK3)
    | ~ segmentP(sK2,sK3)
    | ~ segmentP(sK3,sK3) ),
    inference(unflattening,[status(thm)],[c_650]) ).

tcf(c_652,plain,
    ( ~ segmentP(sK3,sK3)
    | ~ segmentP(sK2,sK3) ),
    inference(global_subsumption_just,[status(thm)],[c_651,c_57,c_651]) ).

tcf(c_653,plain,
    ( ~ segmentP(sK2,sK3)
    | ~ segmentP(sK3,sK3) ),
    inference(renaming,[status(thm)],[c_652]) ).

tcf(c_696,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( X1 = X2 )
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ segmentP(sK2,X0)
      | ~ segmentP(sK3,X0)
      | ( X2 != nil )
      | ( X0 != X1 ) ),
    inference(resolution_lifted,[status(thm)],[c_50,c_73]) ).

tcf(c_697,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ segmentP(sK2,X0)
      | ~ segmentP(sK3,X0) ),
    inference(unflattening,[status(thm)],[c_696]) ).

tcf(c_699,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ segmentP(sK3,X0)
      | ~ segmentP(sK2,X0)
      | ~ ssList(X0) ),
    inference(global_subsumption_just,[status(thm)],[c_697,c_81,c_697]) ).

tcf(c_700,plain,
    ! [X0: $i] :
      ( ( X0 = nil )
      | ~ ssList(X0)
      | ~ segmentP(sK2,X0)
      | ~ segmentP(sK3,X0) ),
    inference(renaming,[status(thm)],[c_699]) ).

tcf(c_1820,plain,
    ( ~ ssList(sK3)
    | ~ segmentP(sK2,sK3) ),
    inference(superposition,[status(thm)],[c_86,c_653]) ).

tcf(c_1821,plain,
    ~ segmentP(sK2,sK3),
    inference(forward_subsumption_resolution,[status(thm)],[c_1820,c_57]) ).

tcf(c_1846,plain,
    app(sK2,nil) = sK2,
    inference(superposition,[status(thm)],[c_58,c_62]) ).

tcf(c_1852,plain,
    app(nil,sK5) = sK5,
    inference(superposition,[status(thm)],[c_53,c_70]) ).

tcf(c_1853,plain,
    app(nil,sK4) = sK4,
    inference(superposition,[status(thm)],[c_54,c_70]) ).

tcf(c_3229,plain,
    ! [X0: $i] :
      ( segmentP(app(sK2,X0),sK4)
      | ~ ssList(sK5)
      | ~ ssList(sK4)
      | ~ ssList(X0)
      | ~ ssList(app(app(sK5,sK4),X0)) ),
    inference(superposition,[status(thm)],[c_52,c_89]) ).

tcf(c_3235,plain,
    ! [X0: $i] :
      ( segmentP(app(sK5,X0),sK5)
      | ~ ssList(sK5)
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(app(nil,sK5),X0)) ),
    inference(superposition,[status(thm)],[c_1852,c_89]) ).

tcf(c_3236,plain,
    ! [X0: $i] :
      ( segmentP(app(sK4,X0),sK4)
      | ~ ssList(sK4)
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(app(nil,sK4),X0)) ),
    inference(superposition,[status(thm)],[c_1853,c_89]) ).

tcf(c_3263,plain,
    ! [X0: $i] :
      ( segmentP(app(sK4,X0),sK4)
      | ~ ssList(sK4)
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sK4,X0)) ),
    inference(light_normalisation,[status(thm)],[c_3236,c_1853]) ).

tcf(c_3264,plain,
    ! [X0: $i] :
      ( segmentP(app(sK4,X0),sK4)
      | ~ ssList(X0)
      | ~ ssList(app(sK4,X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_3263,c_54,c_81]) ).

tcf(c_3268,plain,
    ! [X0: $i] :
      ( segmentP(app(sK5,X0),sK5)
      | ~ ssList(sK5)
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ ssList(app(sK5,X0)) ),
    inference(light_normalisation,[status(thm)],[c_3235,c_1852]) ).

tcf(c_3269,plain,
    ! [X0: $i] :
      ( segmentP(app(sK5,X0),sK5)
      | ~ ssList(X0)
      | ~ ssList(app(sK5,X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_3268,c_53,c_81]) ).

tcf(c_3293,plain,
    ! [X0: $i] :
      ( segmentP(app(sK2,X0),sK4)
      | ~ ssList(sK5)
      | ~ ssList(sK4)
      | ~ ssList(X0)
      | ~ ssList(app(sK2,X0)) ),
    inference(light_normalisation,[status(thm)],[c_3229,c_52]) ).

tcf(c_3294,plain,
    ! [X0: $i] :
      ( segmentP(app(sK2,X0),sK4)
      | ~ ssList(X0)
      | ~ ssList(app(sK2,X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_3293,c_53,c_54]) ).

tcf(c_4434,plain,
    ( segmentP(sK3,sK4)
    | ~ ssList(sK5)
    | ~ ssList(app(sK4,sK5)) ),
    inference(superposition,[status(thm)],[c_51,c_3264]) ).

tcf(c_4441,plain,
    ( segmentP(sK3,sK4)
    | ~ ssList(sK5)
    | ~ ssList(sK3) ),
    inference(light_normalisation,[status(thm)],[c_4434,c_51]) ).

tcf(c_4442,plain,
    segmentP(sK3,sK4),
    inference(forward_subsumption_resolution,[status(thm)],[c_4441,c_53,c_57]) ).

tcf(c_5078,plain,
    ( segmentP(sK2,sK5)
    | ~ ssList(sK4)
    | ~ ssList(app(sK5,sK4)) ),
    inference(superposition,[status(thm)],[c_52,c_3269]) ).

tcf(c_5085,plain,
    ( segmentP(sK2,sK5)
    | ~ ssList(sK4)
    | ~ ssList(sK2) ),
    inference(light_normalisation,[status(thm)],[c_5078,c_52]) ).

tcf(c_5086,plain,
    segmentP(sK2,sK5),
    inference(forward_subsumption_resolution,[status(thm)],[c_5085,c_54,c_58]) ).

tcf(c_5694,plain,
    ( segmentP(sK2,sK4)
    | ~ ssList(nil)
    | ~ ssList(app(sK2,nil)) ),
    inference(superposition,[status(thm)],[c_1846,c_3294]) ).

tcf(c_5698,plain,
    ( segmentP(sK2,sK4)
    | ~ ssList(sK2)
    | ~ ssList(nil) ),
    inference(light_normalisation,[status(thm)],[c_5694,c_1846]) ).

tcf(c_5699,plain,
    segmentP(sK2,sK4),
    inference(forward_subsumption_resolution,[status(thm)],[c_5698,c_58,c_81]) ).

tcf(c_5721,plain,
    ( ( nil = sK4 )
    | ~ ssList(sK4)
    | ~ segmentP(sK3,sK4) ),
    inference(superposition,[status(thm)],[c_5699,c_700]) ).

tcf(c_5725,plain,
    nil = sK4,
    inference(forward_subsumption_resolution,[status(thm)],[c_5721,c_54,c_4442]) ).

tcf(c_5759,plain,
    app(nil,sK5) = sK3,
    inference(demodulation,[status(thm)],[c_51,c_5725]) ).

tcf(c_5761,plain,
    sK3 = sK5,
    inference(demodulation,[status(thm)],[c_1852,c_5759]) ).

tcf(c_5767,plain,
    segmentP(sK2,sK3),
    inference(demodulation,[status(thm)],[c_5086,c_5761]) ).

tcf(c_5790,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_5767,c_1821]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWC090+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36  % Computer : n003.cluster.edu
% 0.09/0.36  % Model    : x86_64 x86_64
% 0.09/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36  % Memory   : 8046.5625MB
% 0.09/0.36  % OS       : Linux 6.8.0-71-generic
% 0.09/0.36  % CPULimit : 300
% 0.09/0.36  % WCLimit  : 300
% 0.09/0.36  % DateTime : Thu Sep 24 16:21:36 UTC 2026
% 0.14/0.36  % CPUTime  : 
% 0.14/0.36  Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.40  Running first-order theorem proving
% 0.14/0.40  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
% 0.14/0.41  
% 0.14/0.41  % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41  
% 0.14/0.41  % Detected problem language: tptp
% 0.14/0.42  % Proving...
% 0.98/1.08  % SZS status Started for theBenchmark.p
% 0.98/1.08  % SZS status Theorem for theBenchmark.p
% 0.98/1.08  
% 0.98/1.08  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.98/1.08  
% 0.98/1.08  % ------  iProver source info
% 0.98/1.08  
% 0.98/1.08  % git: date: 2026-07-19 20:42:38 +0200
% 0.98/1.08  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.98/1.08  % git: non_committed_changes: false
% 0.98/1.08  
% 0.98/1.08  % ------ Parsing...
% 0.98/1.08  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 0.98/1.08  
% 0.98/1.08  % ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e % 
% 0.98/1.08  
% 0.98/1.08  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 0.98/1.08  
% 0.98/1.08  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 0.98/1.08  % ------ Proving...
% 0.98/1.08  % ------ Problem Properties 
% 0.98/1.08  
% 0.98/1.08  % 
% 0.98/1.08  % clauses                               43
% 0.98/1.08  % conjectures                           6
% 0.98/1.08  % EPR                                   17
% 0.98/1.08  % Horn                                  40
% 0.98/1.08  % unary                                 13
% 0.98/1.08  % binary                                5
% 0.98/1.08  % lits                                  126
% 0.98/1.08  % lits eq                               32
% 0.98/1.08  % fd_pure                               0
% 0.98/1.08  % fd_pseudo                             0
% 0.98/1.08  % fd_cond                               6
% 0.98/1.08  % fd_pseudo_cond                        5
% 0.98/1.08  % AC symbols                            0
% 0.98/1.08  
% 0.98/1.08  % ------ Schedule dynamic 5 is on 
% 0.98/1.08  
% 0.98/1.08  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.98/1.08  
% 0.98/1.08  
% 0.98/1.08  % ------ 
% 0.98/1.08  % Current options:
% 0.98/1.08  % ------ 
% 0.98/1.08  
% 0.98/1.08  
% 0.98/1.08  % 
% 0.98/1.08  
% 0.98/1.08  % ------ Proving...
% 0.98/1.08  % 
% 0.98/1.08  
% 0.98/1.08  % SZS status Theorem for theBenchmark.p
% 0.98/1.08  
% 0.98/1.08  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.98/1.08  
% 0.98/1.08  
%------------------------------------------------------------------------------