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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : SWC270+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 : n011.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 03:09:05 PM UTC 2026

% Result   : Theorem 4.88s 22.62s
% Output   : CNFRefutation 4.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   62 (  11 unt;   0 def)
%            Number of atoms       :  354 (  38 equ)
%            Maximal formula atoms :   17 (   5 avg)
%            Number of connectives :  480 ( 188   ~; 198   |;  64   &)
%                                         (   8 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   8 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   4 con; 0-2 aty)
%            Number of variables   :  147 (   0 sgn 123   !;  24   ?;  15   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f11,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( totalorderedP(X0)
      <=> ! [X1] :
            ( ssItem(X1)
           => ! [X2] :
                ( ssItem(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                             => leq(X1,X2) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax11) ).

fof(f12,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( strictorderedP(X0)
      <=> ! [X1] :
            ( ssItem(X1)
           => ! [X2] :
                ( ssItem(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                             => lt(X1,X2) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax12) ).

fof(f93,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( lt(X0,X1)
          <=> ( leq(X0,X1)
              & X0 != X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax93) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( totalorderedP(X0)
                  | ~ strictorderedP(X2)
                  | ~ segmentP(X3,X2)
                  | X0 != X2
                  | X1 != X3
                  | ~ ssList(X3) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( totalorderedP(X0)
                    | ~ strictorderedP(X2)
                    | ~ segmentP(X3,X2)
                    | X0 != X2
                    | X1 != X3
                    | ~ ssList(X3) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f96]) ).

fof(f98,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ~ totalorderedP(X0)
                  & strictorderedP(X2)
                  & segmentP(X3,X2)
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) ) ) ) ),
    inference(ennf_transformation,[],[f97]) ).

fof(f111,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( totalorderedP(X0)
      <=> ! [X1] :
            ( ~ ssItem(X1)
            | ! [X2] :
                ( ~ ssItem(X2)
                | ! [X3] :
                    ( ~ ssList(X3)
                    | ! [X4] :
                        ( ~ ssList(X4)
                        | ! [X5] :
                            ( ~ ssList(X5)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | leq(X1,X2) ) ) ) ) ) ) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f112,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( totalorderedP(X0)
      <=> ! [X1] :
            ( ~ ssItem(X1)
            | ! [X2] :
                ( ~ ssItem(X2)
                | ! [X3] :
                    ( ~ ssList(X3)
                    | ! [X4] :
                        ( ~ ssList(X4)
                        | ! [X5] :
                            ( ~ ssList(X5)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | leq(X1,X2) ) ) ) ) ) ) ),
    inference(flattening,[],[f111]) ).

fof(f115,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( strictorderedP(X0)
      <=> ! [X1] :
            ( ~ ssItem(X1)
            | ! [X2] :
                ( ~ ssItem(X2)
                | ! [X3] :
                    ( ~ ssList(X3)
                    | ! [X4] :
                        ( ~ ssList(X4)
                        | ! [X5] :
                            ( ~ ssList(X5)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | lt(X1,X2) ) ) ) ) ) ) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f116,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( strictorderedP(X0)
      <=> ! [X1] :
            ( ~ ssItem(X1)
            | ! [X2] :
                ( ~ ssItem(X2)
                | ! [X3] :
                    ( ~ ssList(X3)
                    | ! [X4] :
                        ( ~ ssList(X4)
                        | ! [X5] :
                            ( ~ ssList(X5)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | lt(X1,X2) ) ) ) ) ) ) ),
    inference(flattening,[],[f115]) ).

fof(f146,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ! [X1] :
          ( ~ ssItem(X1)
          | ( lt(X0,X1)
          <=> ( leq(X0,X1)
              & X0 != X1 ) ) ) ),
    inference(ennf_transformation,[],[f93]) ).

fof(f168,plain,
    ( ssList(sK0)
    & ssList(sK1)
    & ssList(sK2)
    & ~ totalorderedP(sK0)
    & strictorderedP(sK2)
    & segmentP(sK3,sK2)
    & sK0 = sK2
    & sK1 = sK3
    & ssList(sK3) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f98]) ).

fof(f176,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( ( ~ totalorderedP(X0)
          | ! [X1] :
              ( ~ ssItem(X1)
              | ! [X2] :
                  ( ~ ssItem(X2)
                  | ! [X3] :
                      ( ~ ssList(X3)
                      | ! [X4] :
                          ( ~ ssList(X4)
                          | ! [X5] :
                              ( ~ ssList(X5)
                              | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                              | leq(X1,X2) ) ) ) ) ) )
        & ( ? [X1] :
              ( ssItem(X1)
              & ? [X2] :
                  ( ssItem(X2)
                  & ? [X3] :
                      ( ssList(X3)
                      & ? [X4] :
                          ( ssList(X4)
                          & ? [X5] :
                              ( ssList(X5)
                              & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                              & ~ leq(X1,X2) ) ) ) ) )
          | totalorderedP(X0) ) ) ),
    inference(nnf_transformation,[],[f112]) ).

fof(f177,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( ( ~ totalorderedP(X0)
          | ! [X6] :
              ( ~ ssItem(X6)
              | ! [X7] :
                  ( ~ ssItem(X7)
                  | ! [X8] :
                      ( ~ ssList(X8)
                      | ! [X9] :
                          ( ~ ssList(X9)
                          | ! [X10] :
                              ( ~ ssList(X10)
                              | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                              | leq(X6,X7) ) ) ) ) ) )
        & ( ? [X1] :
              ( ssItem(X1)
              & ? [X2] :
                  ( ssItem(X2)
                  & ? [X3] :
                      ( ssList(X3)
                      & ? [X4] :
                          ( ssList(X4)
                          & ? [X5] :
                              ( ssList(X5)
                              & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                              & ~ leq(X1,X2) ) ) ) ) )
          | totalorderedP(X0) ) ) ),
    inference(rectify,[],[f176]) ).

fof(f178,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( ( ~ totalorderedP(X0)
          | ! [X6] :
              ( ~ ssItem(X6)
              | ! [X7] :
                  ( ~ ssItem(X7)
                  | ! [X8] :
                      ( ~ ssList(X8)
                      | ! [X9] :
                          ( ~ ssList(X9)
                          | ! [X10] :
                              ( ~ ssList(X10)
                              | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                              | leq(X6,X7) ) ) ) ) ) )
        & ( ( ssItem(sK8(X0))
            & ssItem(sK9(X0))
            & ssList(sK10(X0))
            & ssList(sK11(X0))
            & ssList(sK12(X0))
            & app(app(sK10(X0),cons(sK8(X0),sK11(X0))),cons(sK9(X0),sK12(X0))) = X0
            & ~ leq(sK8(X0),sK9(X0)) )
          | totalorderedP(X0) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12]),skolemize(X1,sK8(X0)),skolemize(X2,sK9(X0)),skolemize(X3,sK10(X0)),skolemize(X4,sK11(X0)),skolemize(X5,sK12(X0))],[f177]) ).

fof(f181,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( ( ~ strictorderedP(X0)
          | ! [X1] :
              ( ~ ssItem(X1)
              | ! [X2] :
                  ( ~ ssItem(X2)
                  | ! [X3] :
                      ( ~ ssList(X3)
                      | ! [X4] :
                          ( ~ ssList(X4)
                          | ! [X5] :
                              ( ~ ssList(X5)
                              | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                              | lt(X1,X2) ) ) ) ) ) )
        & ( ? [X1] :
              ( ssItem(X1)
              & ? [X2] :
                  ( ssItem(X2)
                  & ? [X3] :
                      ( ssList(X3)
                      & ? [X4] :
                          ( ssList(X4)
                          & ? [X5] :
                              ( ssList(X5)
                              & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                              & ~ lt(X1,X2) ) ) ) ) )
          | strictorderedP(X0) ) ) ),
    inference(nnf_transformation,[],[f116]) ).

fof(f182,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( ( ~ strictorderedP(X0)
          | ! [X6] :
              ( ~ ssItem(X6)
              | ! [X7] :
                  ( ~ ssItem(X7)
                  | ! [X8] :
                      ( ~ ssList(X8)
                      | ! [X9] :
                          ( ~ ssList(X9)
                          | ! [X10] :
                              ( ~ ssList(X10)
                              | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                              | lt(X6,X7) ) ) ) ) ) )
        & ( ? [X1] :
              ( ssItem(X1)
              & ? [X2] :
                  ( ssItem(X2)
                  & ? [X3] :
                      ( ssList(X3)
                      & ? [X4] :
                          ( ssList(X4)
                          & ? [X5] :
                              ( ssList(X5)
                              & app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                              & ~ lt(X1,X2) ) ) ) ) )
          | strictorderedP(X0) ) ) ),
    inference(rectify,[],[f181]) ).

fof(f183,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( ( ~ strictorderedP(X0)
          | ! [X6] :
              ( ~ ssItem(X6)
              | ! [X7] :
                  ( ~ ssItem(X7)
                  | ! [X8] :
                      ( ~ ssList(X8)
                      | ! [X9] :
                          ( ~ ssList(X9)
                          | ! [X10] :
                              ( ~ ssList(X10)
                              | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
                              | lt(X6,X7) ) ) ) ) ) )
        & ( ( ssItem(sK13(X0))
            & ssItem(sK14(X0))
            & ssList(sK15(X0))
            & ssList(sK16(X0))
            & ssList(sK17(X0))
            & app(app(sK15(X0),cons(sK13(X0),sK16(X0))),cons(sK14(X0),sK17(X0))) = X0
            & ~ lt(sK13(X0),sK14(X0)) )
          | strictorderedP(X0) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16,sK17]),skolemize(X1,sK13(X0)),skolemize(X2,sK14(X0)),skolemize(X3,sK15(X0)),skolemize(X4,sK16(X0)),skolemize(X5,sK17(X0))],[f182]) ).

fof(f188,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ! [X1] :
          ( ~ ssItem(X1)
          | ( ( ~ lt(X0,X1)
              | ( leq(X0,X1)
                & X0 != X1 ) )
            & ( ~ leq(X0,X1)
              | X0 = X1
              | lt(X0,X1) ) ) ) ),
    inference(nnf_transformation,[],[f146]) ).

fof(f189,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ! [X1] :
          ( ~ ssItem(X1)
          | ( ( ~ lt(X0,X1)
              | ( leq(X0,X1)
                & X0 != X1 ) )
            & ( ~ leq(X0,X1)
              | X0 = X1
              | lt(X0,X1) ) ) ) ),
    inference(flattening,[],[f188]) ).

fof(f191,plain,
    ssList(sK0),
    inference(cnf_transformation,[],[f168]) ).

fof(f194,plain,
    ~ totalorderedP(sK0),
    inference(cnf_transformation,[],[f168]) ).

fof(f195,plain,
    strictorderedP(sK2),
    inference(cnf_transformation,[],[f168]) ).

fof(f197,plain,
    sK0 = sK2,
    inference(cnf_transformation,[],[f168]) ).

fof(f222,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ssItem(sK8(X0))
      | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f178]) ).

fof(f223,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ssItem(sK9(X0))
      | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f178]) ).

fof(f224,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ssList(sK10(X0))
      | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f178]) ).

fof(f225,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ssList(sK11(X0))
      | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f178]) ).

fof(f226,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ssList(sK12(X0))
      | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f178]) ).

fof(f227,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(app(sK10(X0),cons(sK8(X0),sK11(X0))),cons(sK9(X0),sK12(X0))) = X0
      | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f178]) ).

fof(f228,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ~ leq(sK8(X0),sK9(X0))
      | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f178]) ).

fof(f236,plain,
    ! [X10,X0,X8,X6,X9,X7] :
      ( ~ ssList(X0)
      | ~ strictorderedP(X0)
      | ~ ssItem(X6)
      | ~ ssItem(X7)
      | ~ ssList(X8)
      | ~ ssList(X9)
      | ~ ssList(X10)
      | app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
      | lt(X6,X7) ),
    inference(cnf_transformation,[],[f183]) ).

fof(f271,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssItem(X1)
      | ~ lt(X0,X1)
      | leq(X0,X1) ),
    inference(cnf_transformation,[],[f189]) ).

fof(f287,plain,
    ~ totalorderedP(sK2),
    inference(definition_unfolding,[],[f194,f197]) ).

fof(f289,plain,
    ssList(sK2),
    inference(definition_unfolding,[],[f191,f197]) ).

fof(f297,plain,
    ! [X10,X8,X6,X9,X7] :
      ( ~ ssList(app(app(X8,cons(X6,X9)),cons(X7,X10)))
      | ~ strictorderedP(app(app(X8,cons(X6,X9)),cons(X7,X10)))
      | ~ ssItem(X6)
      | ~ ssItem(X7)
      | ~ ssList(X8)
      | ~ ssList(X9)
      | ~ ssList(X10)
      | lt(X6,X7) ),
    inference(equality_resolution,[],[f236]) ).

tcf(c_51,negated_conjecture,
    strictorderedP(sK2),
    inference(cnf_transformation,[],[f195]) ).

tcf(c_52,negated_conjecture,
    ~ totalorderedP(sK2),
    inference(cnf_transformation,[],[f287]) ).

tcf(c_55,negated_conjecture,
    ssList(sK2),
    inference(cnf_transformation,[],[f289]) ).

tcf(c_76,plain,
    ! [X0: $i] :
      ( totalorderedP(X0)
      | ~ ssList(X0)
      | ~ leq(sK8(X0),sK9(X0)) ),
    inference(cnf_transformation,[],[f228]) ).

tcf(c_77,plain,
    ! [X0: $i] :
      ( totalorderedP(X0)
      | ( app(app(sK10(X0),cons(sK8(X0),sK11(X0))),cons(sK9(X0),sK12(X0))) = X0 )
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f227]) ).

tcf(c_78,plain,
    ! [X0: $i] :
      ( totalorderedP(X0)
      | ssList(sK12(X0))
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f226]) ).

tcf(c_79,plain,
    ! [X0: $i] :
      ( totalorderedP(X0)
      | ssList(sK11(X0))
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f225]) ).

tcf(c_80,plain,
    ! [X0: $i] :
      ( totalorderedP(X0)
      | ssList(sK10(X0))
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f224]) ).

tcf(c_81,plain,
    ! [X0: $i] :
      ( totalorderedP(X0)
      | ssItem(sK9(X0))
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f223]) ).

tcf(c_82,plain,
    ! [X0: $i] :
      ( totalorderedP(X0)
      | ssItem(sK8(X0))
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f222]) ).

tcf(c_97,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( lt(X1,X3)
      | ~ ssItem(X3)
      | ~ ssItem(X1)
      | ~ ssList(X4)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
      | ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4))) ),
    inference(cnf_transformation,[],[f297]) ).

tcf(c_127,plain,
    ! [X0: $i,X1: $i] :
      ( leq(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ lt(X0,X1) ),
    inference(cnf_transformation,[],[f271]) ).

tcf(c_4597,plain,
    ( totalorderedP(sK2)
    | ssList(sK12(sK2))
    | ~ ssList(sK2) ),
    inference(instantiation,[status(thm)],[c_78]) ).

tcf(c_4598,plain,
    ( totalorderedP(sK2)
    | ssList(sK11(sK2))
    | ~ ssList(sK2) ),
    inference(instantiation,[status(thm)],[c_79]) ).

tcf(c_4599,plain,
    ( totalorderedP(sK2)
    | ssList(sK10(sK2))
    | ~ ssList(sK2) ),
    inference(instantiation,[status(thm)],[c_80]) ).

tcf(c_4600,plain,
    ( totalorderedP(sK2)
    | ssItem(sK9(sK2))
    | ~ ssList(sK2) ),
    inference(instantiation,[status(thm)],[c_81]) ).

tcf(c_4601,plain,
    ( totalorderedP(sK2)
    | ssItem(sK8(sK2))
    | ~ ssList(sK2) ),
    inference(instantiation,[status(thm)],[c_82]) ).

tcf(c_4656,plain,
    ( totalorderedP(sK2)
    | ~ ssList(sK2)
    | ~ leq(sK8(sK2),sK9(sK2)) ),
    inference(instantiation,[status(thm)],[c_76]) ).

tcf(c_5231,plain,
    ! [X0: $i] :
      ( leq(sK8(sK2),X0)
      | ~ ssItem(X0)
      | ~ ssItem(sK8(sK2))
      | ~ lt(sK8(sK2),X0) ),
    inference(instantiation,[status(thm)],[c_127]) ).

tcf(c_9398,plain,
    ( totalorderedP(sK2)
    | ( app(app(sK10(sK2),cons(sK8(sK2),sK11(sK2))),cons(sK9(sK2),sK12(sK2))) = sK2 ) ),
    inference(superposition,[status(thm)],[c_55,c_77]) ).

tcf(c_9419,plain,
    app(app(sK10(sK2),cons(sK8(sK2),sK11(sK2))),cons(sK9(sK2),sK12(sK2))) = sK2,
    inference(forward_subsumption_resolution,[status(thm)],[c_9398,c_52]) ).

tcf(c_13331,plain,
    ( leq(sK8(sK2),sK9(sK2))
    | ~ ssItem(sK9(sK2))
    | ~ ssItem(sK8(sK2))
    | ~ lt(sK8(sK2),sK9(sK2)) ),
    inference(instantiation,[status(thm)],[c_5231]) ).

tcf(c_15182,plain,
    ( lt(sK8(sK2),sK9(sK2))
    | ~ ssList(sK2)
    | ~ ssItem(sK9(sK2))
    | ~ ssItem(sK8(sK2))
    | ~ ssList(sK12(sK2))
    | ~ ssList(sK11(sK2))
    | ~ ssList(sK10(sK2))
    | ~ strictorderedP(app(app(sK10(sK2),cons(sK8(sK2),sK11(sK2))),cons(sK9(sK2),sK12(sK2)))) ),
    inference(superposition,[status(thm)],[c_9419,c_97]) ).

tcf(c_15215,plain,
    ( lt(sK8(sK2),sK9(sK2))
    | ~ strictorderedP(sK2)
    | ~ ssList(sK2)
    | ~ ssItem(sK9(sK2))
    | ~ ssItem(sK8(sK2))
    | ~ ssList(sK12(sK2))
    | ~ ssList(sK11(sK2))
    | ~ ssList(sK10(sK2)) ),
    inference(light_normalisation,[status(thm)],[c_15182,c_9419]) ).

tcf(c_15216,plain,
    ( lt(sK8(sK2),sK9(sK2))
    | ~ ssItem(sK9(sK2))
    | ~ ssItem(sK8(sK2))
    | ~ ssList(sK12(sK2))
    | ~ ssList(sK11(sK2))
    | ~ ssList(sK10(sK2)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_15215,c_51,c_55]) ).

tcf(c_15247,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_15216,c_13331,c_4656,c_4601,c_4600,c_4599,c_4598,c_4597,c_52,c_55]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWC270+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.34   % Computer : n011.cluster.edu
% 0.08/0.34   % Model    : x86_64 x86_64
% 0.08/0.34   % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34   % Memory   : 8046.5625MB
% 0.08/0.34   % OS       : Linux 6.8.0-71-generic
% 0.08/21.70  % CPULimit : 300
% 0.08/21.70  % WCLimit  : 300
% 0.08/21.70  % DateTime : Thu Sep 24 17:20:26 UTC 2026
% 0.08/21.70  % CPUTime  : 
% 0.08/21.70  Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/21.74  Running first-order theorem proving
% 0.08/21.74  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
% 0.08/21.75  
% 0.08/21.75  % ======== iProver multi-core TPTP/SMT =========
% 0.08/21.75  
% 0.08/21.75  % Detected problem language: tptp
% 0.08/21.77  % Proving...
% 4.88/22.62  % SZS status Started for theBenchmark.p
% 4.88/22.62  % SZS status Theorem for theBenchmark.p
% 4.88/22.62  
% 4.88/22.62  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.88/22.62  
% 4.88/22.62  % ------  iProver source info
% 4.88/22.62  
% 4.88/22.62  % git: date: 2026-07-19 20:42:38 +0200
% 4.88/22.62  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.88/22.62  % git: non_committed_changes: false
% 4.88/22.62  
% 4.88/22.62  % ------ Parsing...
% 4.88/22.62  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 4.88/22.62  
% 4.88/22.62  % ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e % 
% 4.88/22.62  
% 4.88/22.62  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 4.88/22.62  
% 4.88/22.62  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 4.88/22.62  % ------ Proving...
% 4.88/22.62  % ------ Problem Properties 
% 4.88/22.62  
% 4.88/22.62  % 
% 4.88/22.62  % clauses                               86
% 4.88/22.62  % conjectures                           5
% 4.88/22.62  % EPR                                   26
% 4.88/22.62  % Horn                                  54
% 4.88/22.62  % unary                                 13
% 4.88/22.62  % binary                                8
% 4.88/22.62  % lits                                  296
% 4.88/22.62  % lits eq                               59
% 4.88/22.62  % fd_pure                               0
% 4.88/22.62  % fd_pseudo                             0
% 4.88/22.62  % fd_cond                               19
% 4.88/22.62  % fd_pseudo_cond                        8
% 4.88/22.62  % AC symbols                            0
% 4.88/22.62  
% 4.88/22.62  % ------ Schedule dynamic 5 is on 
% 4.88/22.62  
% 4.88/22.62  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.88/22.62  
% 4.88/22.62  
% 4.88/22.62  % ------ 
% 4.88/22.62  % Current options:
% 4.88/22.62  % ------ 
% 4.88/22.62  
% 4.88/22.62  
% 4.88/22.62  % 
% 4.88/22.62  
% 4.88/22.62  % ------ Proving...
% 4.88/22.62  % 
% 4.88/22.62  
% 4.88/22.62  % SZS status Theorem for theBenchmark.p
% 4.88/22.62  
% 4.88/22.62  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.88/22.62  
% 4.88/22.62  
%------------------------------------------------------------------------------