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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : SWC264+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 : n001.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 03:09:04 PM UTC 2026

% Result   : Theorem 7.37s 1.77s
% Output   : CNFRefutation 7.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   62 (  11 unt;   0 def)
%            Number of atoms       :  350 (  38 equ)
%            Maximal formula atoms :   17 (   5 avg)
%            Number of connectives :  474 ( 186   ~; 196   |;  62   &)
%                                         (   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  :    8 (   6 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)
                  | 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)
                    | 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)
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) ) ) ) ),
    inference(ennf_transformation,[],[f97]) ).

fof(f101,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(f102,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,[],[f101]) ).

fof(f105,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(f106,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,[],[f105]) ).

fof(f127,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ! [X1] :
          ( ~ ssItem(X1)
          | ( lt(X0,X1)
          <=> ( leq(X0,X1)
              & X0 != X1 ) ) ) ),
    inference(ennf_transformation,[],[f93]) ).

fof(f158,plain,
    ( ssList(sK0)
    & ssList(sK1)
    & ssList(sK2)
    & ~ totalorderedP(sK0)
    & strictorderedP(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(f162,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,[],[f102]) ).

fof(f163,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,[],[f162]) ).

fof(f164,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(sK6(X0))
            & ssItem(sK7(X0))
            & ssList(sK8(X0))
            & ssList(sK9(X0))
            & ssList(sK10(X0))
            & app(app(sK8(X0),cons(sK6(X0),sK9(X0))),cons(sK7(X0),sK10(X0))) = X0
            & ~ leq(sK6(X0),sK7(X0)) )
          | totalorderedP(X0) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10]),skolemize(X1,sK6(X0)),skolemize(X2,sK7(X0)),skolemize(X3,sK8(X0)),skolemize(X4,sK9(X0)),skolemize(X5,sK10(X0))],[f163]) ).

fof(f167,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,[],[f106]) ).

fof(f168,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,[],[f167]) ).

fof(f169,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(sK11(X0))
            & ssItem(sK12(X0))
            & ssList(sK13(X0))
            & ssList(sK14(X0))
            & ssList(sK15(X0))
            & app(app(sK13(X0),cons(sK11(X0),sK14(X0))),cons(sK12(X0),sK15(X0))) = X0
            & ~ lt(sK11(X0),sK12(X0)) )
          | strictorderedP(X0) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14,sK15]),skolemize(X1,sK11(X0)),skolemize(X2,sK12(X0)),skolemize(X3,sK13(X0)),skolemize(X4,sK14(X0)),skolemize(X5,sK15(X0))],[f168]) ).

fof(f172,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,[],[f127]) ).

fof(f173,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,[],[f172]) ).

fof(f177,plain,
    ssList(sK0),
    inference(cnf_transformation,[],[f158]) ).

fof(f180,plain,
    ~ totalorderedP(sK0),
    inference(cnf_transformation,[],[f158]) ).

fof(f181,plain,
    strictorderedP(sK2),
    inference(cnf_transformation,[],[f158]) ).

fof(f182,plain,
    sK0 = sK2,
    inference(cnf_transformation,[],[f158]) ).

fof(f196,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ssItem(sK6(X0))
      | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f164]) ).

fof(f197,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ssItem(sK7(X0))
      | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f164]) ).

fof(f198,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ssList(sK8(X0))
      | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f164]) ).

fof(f199,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ssList(sK9(X0))
      | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f164]) ).

fof(f200,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ssList(sK10(X0))
      | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f164]) ).

fof(f201,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(app(sK8(X0),cons(sK6(X0),sK9(X0))),cons(sK7(X0),sK10(X0))) = X0
      | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f164]) ).

fof(f202,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ~ leq(sK6(X0),sK7(X0))
      | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f164]) ).

fof(f210,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,[],[f169]) ).

fof(f236,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssItem(X1)
      | ~ lt(X0,X1)
      | leq(X0,X1) ),
    inference(cnf_transformation,[],[f173]) ).

fof(f261,plain,
    ~ totalorderedP(sK2),
    inference(definition_unfolding,[],[f180,f182]) ).

fof(f263,plain,
    ssList(sK2),
    inference(definition_unfolding,[],[f177,f182]) ).

fof(f269,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,[],[f210]) ).

tcf(c_50,negated_conjecture,
    strictorderedP(sK2),
    inference(cnf_transformation,[],[f181]) ).

tcf(c_51,negated_conjecture,
    ~ totalorderedP(sK2),
    inference(cnf_transformation,[],[f261]) ).

tcf(c_54,negated_conjecture,
    ssList(sK2),
    inference(cnf_transformation,[],[f263]) ).

tcf(c_64,plain,
    ! [X0: $i] :
      ( totalorderedP(X0)
      | ~ ssList(X0)
      | ~ leq(sK6(X0),sK7(X0)) ),
    inference(cnf_transformation,[],[f202]) ).

tcf(c_65,plain,
    ! [X0: $i] :
      ( totalorderedP(X0)
      | ( app(app(sK8(X0),cons(sK6(X0),sK9(X0))),cons(sK7(X0),sK10(X0))) = X0 )
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f201]) ).

tcf(c_66,plain,
    ! [X0: $i] :
      ( totalorderedP(X0)
      | ssList(sK10(X0))
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f200]) ).

tcf(c_67,plain,
    ! [X0: $i] :
      ( totalorderedP(X0)
      | ssList(sK9(X0))
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f199]) ).

tcf(c_68,plain,
    ! [X0: $i] :
      ( totalorderedP(X0)
      | ssList(sK8(X0))
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f198]) ).

tcf(c_69,plain,
    ! [X0: $i] :
      ( totalorderedP(X0)
      | ssItem(sK7(X0))
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f197]) ).

tcf(c_70,plain,
    ! [X0: $i] :
      ( totalorderedP(X0)
      | ssItem(sK6(X0))
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f196]) ).

tcf(c_85,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,[],[f269]) ).

tcf(c_106,plain,
    ! [X0: $i,X1: $i] :
      ( leq(X0,X1)
      | ~ ssItem(X1)
      | ~ ssItem(X0)
      | ~ lt(X0,X1) ),
    inference(cnf_transformation,[],[f236]) ).

tcf(c_3873,plain,
    ( totalorderedP(sK2)
    | ssList(sK10(sK2))
    | ~ ssList(sK2) ),
    inference(instantiation,[status(thm)],[c_66]) ).

tcf(c_3874,plain,
    ( totalorderedP(sK2)
    | ssList(sK9(sK2))
    | ~ ssList(sK2) ),
    inference(instantiation,[status(thm)],[c_67]) ).

tcf(c_3875,plain,
    ( totalorderedP(sK2)
    | ssList(sK8(sK2))
    | ~ ssList(sK2) ),
    inference(instantiation,[status(thm)],[c_68]) ).

tcf(c_3885,plain,
    ( totalorderedP(sK2)
    | ssItem(sK7(sK2))
    | ~ ssList(sK2) ),
    inference(instantiation,[status(thm)],[c_69]) ).

tcf(c_3895,plain,
    ( totalorderedP(sK2)
    | ssItem(sK6(sK2))
    | ~ ssList(sK2) ),
    inference(instantiation,[status(thm)],[c_70]) ).

tcf(c_4037,plain,
    ( totalorderedP(sK2)
    | ~ ssList(sK2)
    | ~ leq(sK6(sK2),sK7(sK2)) ),
    inference(instantiation,[status(thm)],[c_64]) ).

tcf(c_4595,plain,
    ! [X0: $i] :
      ( leq(sK6(sK2),X0)
      | ~ ssItem(X0)
      | ~ ssItem(sK6(sK2))
      | ~ lt(sK6(sK2),X0) ),
    inference(instantiation,[status(thm)],[c_106]) ).

tcf(c_7132,plain,
    ( totalorderedP(sK2)
    | ( app(app(sK8(sK2),cons(sK6(sK2),sK9(sK2))),cons(sK7(sK2),sK10(sK2))) = sK2 ) ),
    inference(superposition,[status(thm)],[c_54,c_65]) ).

tcf(c_7150,plain,
    app(app(sK8(sK2),cons(sK6(sK2),sK9(sK2))),cons(sK7(sK2),sK10(sK2))) = sK2,
    inference(forward_subsumption_resolution,[status(thm)],[c_7132,c_51]) ).

tcf(c_9294,plain,
    ( lt(sK6(sK2),sK7(sK2))
    | ~ ssList(sK2)
    | ~ ssItem(sK7(sK2))
    | ~ ssItem(sK6(sK2))
    | ~ ssList(sK10(sK2))
    | ~ ssList(sK9(sK2))
    | ~ ssList(sK8(sK2))
    | ~ strictorderedP(app(app(sK8(sK2),cons(sK6(sK2),sK9(sK2))),cons(sK7(sK2),sK10(sK2)))) ),
    inference(superposition,[status(thm)],[c_7150,c_85]) ).

tcf(c_9371,plain,
    ( lt(sK6(sK2),sK7(sK2))
    | ~ strictorderedP(sK2)
    | ~ ssList(sK2)
    | ~ ssItem(sK7(sK2))
    | ~ ssItem(sK6(sK2))
    | ~ ssList(sK10(sK2))
    | ~ ssList(sK9(sK2))
    | ~ ssList(sK8(sK2)) ),
    inference(light_normalisation,[status(thm)],[c_9294,c_7150]) ).

tcf(c_9372,plain,
    ( lt(sK6(sK2),sK7(sK2))
    | ~ ssItem(sK7(sK2))
    | ~ ssItem(sK6(sK2))
    | ~ ssList(sK10(sK2))
    | ~ ssList(sK9(sK2))
    | ~ ssList(sK8(sK2)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_9371,c_50,c_54]) ).

tcf(c_10105,plain,
    ( leq(sK6(sK2),sK7(sK2))
    | ~ ssItem(sK7(sK2))
    | ~ ssItem(sK6(sK2))
    | ~ lt(sK6(sK2),sK7(sK2)) ),
    inference(instantiation,[status(thm)],[c_4595]) ).

tcf(c_10106,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_10105,c_9372,c_4037,c_3895,c_3885,c_3875,c_3874,c_3873,c_51,c_54]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWC264+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.38  % Computer : n001.cluster.edu
% 0.11/0.38  % Model    : x86_64 x86_64
% 0.11/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38  % Memory   : 8046.5625MB
% 0.11/0.38  % OS       : Linux 6.8.0-71-generic
% 0.11/0.38  % CPULimit : 300
% 0.11/0.38  % WCLimit  : 300
% 0.11/0.38  % DateTime : Thu Sep 24 17:23:38 UTC 2026
% 0.11/0.39  % CPUTime  : 
% 0.11/0.39  Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.43  Running first-order theorem proving
% 0.11/0.43  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
% 0.11/0.44  
% 0.11/0.44  % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.44  
% 0.11/0.44  % Detected problem language: tptp
% 0.11/0.45  % Proving...
% 7.37/1.77  % SZS status Started for theBenchmark.p
% 7.37/1.77  % SZS status Theorem for theBenchmark.p
% 7.37/1.77  
% 7.37/1.77  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.37/1.77  
% 7.37/1.77  % ------  iProver source info
% 7.37/1.77  
% 7.37/1.77  % git: date: 2026-07-19 20:42:38 +0200
% 7.37/1.77  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.37/1.77  % git: non_committed_changes: false
% 7.37/1.77  
% 7.37/1.77  % ------ Parsing...
% 7.37/1.77  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 7.37/1.77  
% 7.37/1.77  % ------ 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 % 
% 7.37/1.77  
% 7.37/1.77  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 7.37/1.77  
% 7.37/1.77  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 7.37/1.77  % ------ Proving...
% 7.37/1.77  % ------ Problem Properties 
% 7.37/1.77  
% 7.37/1.77  % 
% 7.37/1.77  % clauses                               74
% 7.37/1.77  % conjectures                           4
% 7.37/1.77  % EPR                                   19
% 7.37/1.77  % Horn                                  42
% 7.37/1.77  % unary                                 11
% 7.37/1.77  % binary                                6
% 7.37/1.77  % lits                                  253
% 7.37/1.77  % lits eq                               56
% 7.37/1.77  % fd_pure                               0
% 7.37/1.77  % fd_pseudo                             0
% 7.37/1.77  % fd_cond                               18
% 7.37/1.77  % fd_pseudo_cond                        7
% 7.37/1.77  % AC symbols                            0
% 7.37/1.77  
% 7.37/1.77  % ------ Schedule dynamic 5 is on 
% 7.37/1.77  
% 7.37/1.77  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.37/1.77  
% 7.37/1.77  
% 7.37/1.77  % ------ 
% 7.37/1.77  % Current options:
% 7.37/1.77  % ------ 
% 7.37/1.77  
% 7.37/1.77  
% 7.37/1.77  % 
% 7.37/1.77  
% 7.37/1.77  % ------ Proving...
% 7.37/1.77  % 
% 7.37/1.77  
% 7.37/1.77  % SZS status Theorem for theBenchmark.p
% 7.37/1.77  
% 7.37/1.77  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.37/1.77  
% 7.37/1.77  
%------------------------------------------------------------------------------