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E---3.5.1.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : E---3.5.1
% Problem  : SWC160+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM

% Computer : n006.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 : Thu Sep 24 02:43:15 PM UTC 2026

% Result   : Theorem 0.17s 0.55s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   55 (  22 unt;   0 def)
%            Number of atoms       :  283 (  59 equ)
%            Maximal formula atoms :   32 (   5 avg)
%            Number of connectives :  338 ( 110   ~; 115   |;  54   &)
%                                         (   1 <=>;  58  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   31 (   6 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   19 (  19 usr;  12 con; 0-2 aty)
%            Number of variables   :  113 (   0 sgn  77   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(co1,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( ( nil = X3
                      & nil != X4 )
                    | ! [X10] :
                        ( ssItem(X10)
                       => ! [X11] :
                            ( ssItem(X11)
                           => ! [X12] :
                                ( ssList(X12)
                               => ! [X13] :
                                    ( ssList(X13)
                                   => ! [X14] :
                                        ( ssList(X14)
                                       => ( ( leq(X10,X11)
                                            & ! [X15] :
                                                ( ssItem(X15)
                                               => ( ( leq(X15,X11)
                                                    & leq(X10,X15) )
                                                  | ~ memberP(X13,X15) ) ) )
                                          | ~ leq(X11,X10)
                                          | app(app(app(app(X12,cons(X10,nil)),X13),cons(X11,nil)),X14) != X1 ) ) ) ) ) )
                    | ! [X5] :
                        ( ssList(X5)
                       => ( ? [X6] :
                              ( ? [X7] :
                                  ( ? [X8] :
                                      ( ? [X9] :
                                          ( lt(X8,X6)
                                          & app(X9,cons(X8,nil)) = X3
                                          & ssList(X9) )
                                      & ssItem(X8) )
                                  & app(cons(X6,nil),X7) = X5
                                  & ssList(X7) )
                              & ssItem(X6) )
                          | ~ strictorderedP(X3)
                          | app(X3,X5) != X4 ) )
                    | X1 != X3
                    | X2 != X4 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

fof(ax82,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax82) ).

fof(ax16,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ssList(cons(X2,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).

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

fof(ax81,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => cons(X2,X1) = app(cons(X2,nil),X1) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).

fof(ax26,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ssList(app(X1,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).

fof(ax33,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ( lt(X1,X2)
           => ~ lt(X2,X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax33) ).

fof(ax92,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ( leq(X1,X2)
           => ( lt(X1,X2)
              | X1 = X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax92) ).

fof(ax12,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( strictorderedP(X1)
      <=> ! [X2] :
            ( ssItem(X2)
           => ! [X3] :
                ( ssItem(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ! [X5] :
                        ( ssList(X5)
                       => ! [X6] :
                            ( ssList(X6)
                           => ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
                             => lt(X2,X3) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax12) ).

fof(c_0_9,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( ( nil = X3
                        & nil != X4 )
                      | ! [X10] :
                          ( ssItem(X10)
                         => ! [X11] :
                              ( ssItem(X11)
                             => ! [X12] :
                                  ( ssList(X12)
                                 => ! [X13] :
                                      ( ssList(X13)
                                     => ! [X14] :
                                          ( ssList(X14)
                                         => ( ( leq(X10,X11)
                                              & ! [X15] :
                                                  ( ssItem(X15)
                                                 => ( ( leq(X15,X11)
                                                      & leq(X10,X15) )
                                                    | ~ memberP(X13,X15) ) ) )
                                            | ~ leq(X11,X10)
                                            | app(app(app(app(X12,cons(X10,nil)),X13),cons(X11,nil)),X14) != X1 ) ) ) ) ) )
                      | ! [X5] :
                          ( ssList(X5)
                         => ( ? [X6] :
                                ( ? [X7] :
                                    ( ? [X8] :
                                        ( ? [X9] :
                                            ( lt(X8,X6)
                                            & app(X9,cons(X8,nil)) = X3
                                            & ssList(X9) )
                                        & ssItem(X8) )
                                    & app(cons(X6,nil),X7) = X5
                                    & ssList(X7) )
                                & ssItem(X6) )
                            | ~ strictorderedP(X3)
                            | app(X3,X5) != X4 ) )
                      | X1 != X3
                      | X2 != X4 ) ) ) ) ),
    inference(assume_negation,[status(cth)],[co1]) ).

fof(c_0_10,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( ( nil = X3
                        & nil != X4 )
                      | ! [X10] :
                          ( ssItem(X10)
                         => ! [X11] :
                              ( ssItem(X11)
                             => ! [X12] :
                                  ( ssList(X12)
                                 => ! [X13] :
                                      ( ssList(X13)
                                     => ! [X14] :
                                          ( ssList(X14)
                                         => ( ( leq(X10,X11)
                                              & ! [X15] :
                                                  ( ssItem(X15)
                                                 => ( ( leq(X15,X11)
                                                      & leq(X10,X15) )
                                                    | ~ memberP(X13,X15) ) ) )
                                            | ~ leq(X11,X10)
                                            | app(app(app(app(X12,cons(X10,nil)),X13),cons(X11,nil)),X14) != X1 ) ) ) ) ) )
                      | ! [X5] :
                          ( ssList(X5)
                         => ( ? [X6] :
                                ( ? [X7] :
                                    ( ? [X8] :
                                        ( ? [X9] :
                                            ( lt(X8,X6)
                                            & app(X9,cons(X8,nil)) = X3
                                            & ssList(X9) )
                                        & ssItem(X8) )
                                    & app(cons(X6,nil),X7) = X5
                                    & ssList(X7) )
                                & ssItem(X6) )
                            | ~ strictorderedP(X3)
                            | app(X3,X5) != X4 ) )
                      | X1 != X3
                      | X2 != X4 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_9]) ).

fof(c_0_11,negated_conjecture,
    ! [X265,X266,X267,X268] :
      ( ( nil != esk50_0
        | nil = esk51_0 )
      & ( ~ leq(esk53_0,esk54_0)
        | ~ leq(esk58_0,esk54_0)
        | ~ leq(esk53_0,esk58_0) )
      & ( ~ leq(esk53_0,esk54_0)
        | memberP(esk56_0,esk58_0) )
      & ( ~ leq(esk53_0,esk54_0)
        | ssItem(esk58_0) )
      & leq(esk54_0,esk53_0)
      & app(app(app(app(esk55_0,cons(esk53_0,nil)),esk56_0),cons(esk54_0,nil)),esk57_0) = esk48_0
      & ssList(esk57_0)
      & ssList(esk56_0)
      & ssList(esk55_0)
      & ssItem(esk54_0)
      & ssItem(esk53_0)
      & ( ~ lt(X267,X265)
        | app(X268,cons(X267,nil)) != esk50_0
        | ~ ssList(X268)
        | ~ ssItem(X267)
        | app(cons(X265,nil),X266) != esk52_0
        | ~ ssList(X266)
        | ~ ssItem(X265) )
      & strictorderedP(esk50_0)
      & app(esk50_0,esk52_0) = esk51_0
      & ssList(esk52_0)
      & esk48_0 = esk50_0
      & esk49_0 = esk51_0
      & ssList(esk51_0)
      & ssList(esk50_0)
      & ssList(esk49_0)
      & ssList(esk48_0) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])])]) ).

cnf(c_0_12,negated_conjecture,
    app(app(app(app(esk55_0,cons(esk53_0,nil)),esk56_0),cons(esk54_0,nil)),esk57_0) = esk48_0,
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_13,negated_conjecture,
    esk48_0 = esk50_0,
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_14,plain,
    ! [X231,X232,X233] :
      ( app(app(X231,X232),X233) = app(X231,app(X232,X233))
      | ~ ssList(X233)
      | ~ ssList(X232)
      | ~ ssList(X231) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).

cnf(c_0_15,negated_conjecture,
    app(app(app(app(esk55_0,cons(esk53_0,nil)),esk56_0),cons(esk54_0,nil)),esk57_0) = esk50_0,
    inference(rw,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_16,plain,
    ( ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | app(app(X1,X2),X3) = app(X1,app(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_17,negated_conjecture,
    ssList(esk56_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_18,negated_conjecture,
    ssList(esk55_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_19,plain,
    ! [X120,X121] :
      ( ssList(cons(X121,X120))
      | ~ ssItem(X121)
      | ~ ssList(X120) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).

cnf(c_0_20,negated_conjecture,
    ( ~ ssList(cons(esk53_0,nil))
    | app(app(app(esk55_0,app(cons(esk53_0,nil),esk56_0)),cons(esk54_0,nil)),esk57_0) = esk50_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18])]) ).

cnf(c_0_21,plain,
    ( ~ ssItem(X2)
    | ~ ssList(X1)
    | ssList(cons(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_22,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[ax17]) ).

cnf(c_0_23,negated_conjecture,
    ssItem(esk53_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_24,plain,
    ! [X229,X230] :
      ( cons(X230,X229) = app(cons(X230,nil),X229)
      | ~ ssItem(X230)
      | ~ ssList(X229) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).

cnf(c_0_25,negated_conjecture,
    app(app(app(esk55_0,app(cons(esk53_0,nil),esk56_0)),cons(esk54_0,nil)),esk57_0) = esk50_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23])]) ).

cnf(c_0_26,plain,
    ( ~ ssItem(X2)
    | ~ ssList(X1)
    | cons(X2,X1) = app(cons(X2,nil),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_27,negated_conjecture,
    app(app(app(esk55_0,cons(esk53_0,esk56_0)),cons(esk54_0,nil)),esk57_0) = esk50_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_17]),c_0_23])]) ).

cnf(c_0_28,negated_conjecture,
    ssList(esk57_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_29,negated_conjecture,
    ( ~ ssList(cons(esk54_0,nil))
    | ~ ssList(app(esk55_0,cons(esk53_0,esk56_0)))
    | app(app(esk55_0,cons(esk53_0,esk56_0)),app(cons(esk54_0,nil),esk57_0)) = esk50_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_27]),c_0_28])]) ).

cnf(c_0_30,negated_conjecture,
    ssItem(esk54_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_31,plain,
    ! [X139,X140] :
      ( ssList(app(X139,X140))
      | ~ ssList(X140)
      | ~ ssList(X139) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).

cnf(c_0_32,negated_conjecture,
    ( ~ ssList(app(esk55_0,cons(esk53_0,esk56_0)))
    | app(app(esk55_0,cons(esk53_0,esk56_0)),app(cons(esk54_0,nil),esk57_0)) = esk50_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_21]),c_0_22]),c_0_30])]) ).

cnf(c_0_33,plain,
    ( ~ ssList(X2)
    | ~ ssList(X1)
    | ssList(app(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

fof(c_0_34,plain,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ( lt(X1,X2)
           => ~ lt(X2,X1) ) ) ),
    inference(fof_simplification,[status(thm)],[ax33]) ).

fof(c_0_35,plain,
    ! [X251,X252] :
      ( lt(X251,X252)
      | X251 = X252
      | ~ leq(X251,X252)
      | ~ ssItem(X252)
      | ~ ssItem(X251) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax92])])])]) ).

fof(c_0_36,plain,
    ! [X87,X88,X89,X90,X91,X92] :
      ( ( ~ ssList(X87)
        | strictorderedP(X87)
        | ~ lt(esk30_1(X87),esk31_1(X87)) )
      & ( ~ ssList(X87)
        | strictorderedP(X87)
        | app(app(esk32_1(X87),cons(esk30_1(X87),esk33_1(X87))),cons(esk31_1(X87),esk34_1(X87))) = X87 )
      & ( ~ ssList(X87)
        | strictorderedP(X87)
        | ssList(esk34_1(X87)) )
      & ( ~ ssList(X87)
        | strictorderedP(X87)
        | ssList(esk33_1(X87)) )
      & ( ~ ssList(X87)
        | strictorderedP(X87)
        | ssList(esk32_1(X87)) )
      & ( ~ ssList(X87)
        | strictorderedP(X87)
        | ssItem(esk31_1(X87)) )
      & ( ~ ssList(X87)
        | strictorderedP(X87)
        | ssItem(esk30_1(X87)) )
      & ( ~ ssList(X87)
        | lt(X88,X89)
        | app(app(X90,cons(X88,X91)),cons(X89,X92)) != X87
        | ~ ssList(X92)
        | ~ ssList(X91)
        | ~ ssList(X90)
        | ~ ssItem(X89)
        | ~ ssItem(X88)
        | ~ strictorderedP(X87) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax12])])])])])]) ).

cnf(c_0_37,negated_conjecture,
    ( ~ ssList(cons(esk53_0,esk56_0))
    | app(app(esk55_0,cons(esk53_0,esk56_0)),app(cons(esk54_0,nil),esk57_0)) = esk50_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_18])]) ).

fof(c_0_38,plain,
    ! [X153,X154] :
      ( ~ lt(X154,X153)
      | ~ lt(X153,X154)
      | ~ ssItem(X154)
      | ~ ssItem(X153) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])])]) ).

cnf(c_0_39,plain,
    ( ~ leq(X1,X2)
    | ~ ssItem(X2)
    | ~ ssItem(X1)
    | lt(X1,X2)
    | X1 = X2 ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_40,negated_conjecture,
    leq(esk54_0,esk53_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_41,plain,
    ( ~ ssList(X1)
    | app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
    | ~ ssList(X6)
    | ~ ssList(X5)
    | ~ ssList(X4)
    | ~ ssItem(X3)
    | ~ ssItem(X2)
    | ~ strictorderedP(X1)
    | lt(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_42,negated_conjecture,
    app(app(esk55_0,cons(esk53_0,esk56_0)),app(cons(esk54_0,nil),esk57_0)) = esk50_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_21]),c_0_17]),c_0_23])]) ).

cnf(c_0_43,negated_conjecture,
    ssList(esk48_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_44,plain,
    ( ~ lt(X2,X1)
    | ~ lt(X1,X2)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_45,negated_conjecture,
    ( lt(esk54_0,esk53_0)
    | esk54_0 = esk53_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_23]),c_0_30])]) ).

cnf(c_0_46,plain,
    ( ~ ssItem(X1)
    | ~ ssItem(X2)
    | ~ ssList(X3)
    | ~ ssList(X4)
    | ~ ssList(X5)
    | ~ ssList(app(app(X3,cons(X1,X4)),cons(X2,X5)))
    | ~ strictorderedP(app(app(X3,cons(X1,X4)),cons(X2,X5)))
    | lt(X1,X2) ),
    inference(er,[status(thm)],[c_0_41]) ).

cnf(c_0_47,negated_conjecture,
    app(app(esk55_0,cons(esk53_0,esk56_0)),cons(esk54_0,esk57_0)) = esk50_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_26]),c_0_28]),c_0_30])]) ).

cnf(c_0_48,negated_conjecture,
    strictorderedP(esk50_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_49,negated_conjecture,
    ssList(esk50_0),
    inference(rw,[status(thm)],[c_0_43,c_0_13]) ).

cnf(c_0_50,negated_conjecture,
    ( ~ lt(esk53_0,esk54_0)
    | esk54_0 = esk53_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_30]),c_0_23])]) ).

cnf(c_0_51,negated_conjecture,
    lt(esk53_0,esk54_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_49]),c_0_28]),c_0_17]),c_0_18]),c_0_30]),c_0_23])]) ).

cnf(c_0_52,negated_conjecture,
    esk54_0 = esk53_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51])]) ).

cnf(c_0_53,negated_conjecture,
    lt(esk53_0,esk53_0),
    inference(rw,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_54,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_53]),c_0_53]),c_0_23])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWC160+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05  % Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40  % Computer : n006.cluster.edu
% 0.11/0.40  % Model    : x86_64 x86_64
% 0.11/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40  % Memory   : 8046.5625MB
% 0.11/0.40  % OS       : Linux 6.8.0-71-generic
% 0.11/0.40  % CPULimit : 300
% 0.11/0.40  % WCLimit  : 300
% 0.11/0.40  % DateTime : Mon Sep 21 07:59:16 UTC 2026
% 0.11/0.40  % CPUTime  : 
% 0.11/0.40  Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.44  Running first-order theorem proving
% 0.11/0.44  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.55  % Version: 3.5.1
% 0.17/0.55  % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.55  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.55  % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.55  % Starting new_bool_3 with 300s (1) cores
% 0.17/0.55  % Starting new_bool_1 with 300s (1) cores
% 0.17/0.55  % Starting sh5l with 300s (1) cores
% 0.17/0.55  % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2371395 completed with status 0
% 0.17/0.55  % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.17/0.55  % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.55  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.55  % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.55  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.17/0.55  % No SInE strategy applied
% 0.17/0.55  % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.17/0.55  % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.55  % Starting SubtermCWHack with 136s (1) cores
% 0.17/0.55  % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.17/0.55  % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.17/0.55  % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 0.17/0.55  % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 0.17/0.55  % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2371403 completed with status 0
% 0.17/0.55  % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.17/0.55  % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.17/0.55  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.55  % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.17/0.55  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.17/0.55  % No SInE strategy applied
% 0.17/0.55  % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.17/0.55  % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.55  % Starting SubtermCWHack with 136s (1) cores
% 0.17/0.55  % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.17/0.55  % Preprocessing time       : 0.004 s
% 0.17/0.55  % Presaturation interreduction done
% 0.17/0.55  
% 0.17/0.55  % Proof found!
% 0.17/0.55  % SZS status Theorem
% 0.17/0.55  % SZS output start CNFRefutation
% See solution above
% 0.17/0.55  % Parsed axioms                        : 96
% 0.17/0.55  % Removed by relevancy pruning/SinE    : 0
% 0.17/0.55  % Initial clauses                      : 211
% 0.17/0.55  % Removed in clause preprocessing      : 2
% 0.17/0.55  % Initial clauses in saturation        : 209
% 0.17/0.55  % Processed clauses                    : 678
% 0.17/0.55  % ...of these trivial                  : 3
% 0.17/0.55  % ...subsumed                          : 86
% 0.17/0.55  % ...remaining for further processing  : 589
% 0.17/0.55  % Other redundant clauses eliminated   : 65
% 0.17/0.55  % Clauses deleted for lack of memory   : 0
% 0.17/0.55  % Backward-subsumed                    : 12
% 0.17/0.55  % Backward-rewritten                   : 34
% 0.17/0.55  % Generated clauses                    : 1380
% 0.17/0.55  % ...of the previous two non-redundant : 1242
% 0.17/0.55  % ...aggressively subsumed             : 0
% 0.17/0.55  % Contextual simplify-reflections      : 40
% 0.17/0.55  % Paramodulations                      : 1312
% 0.17/0.55  % Factorizations                       : 0
% 0.17/0.55  % NegExts                              : 0
% 0.17/0.55  % Equation resolutions                 : 70
% 0.17/0.55  % Disequality decompositions           : 0
% 0.17/0.55  % Total rewrite steps                  : 1103
% 0.17/0.55  % ...of those cached                   : 1053
% 0.17/0.55  % Propositional unsat checks           : 0
% 0.17/0.55  %    Propositional check models        : 0
% 0.17/0.55  %    Propositional check unsatisfiable : 0
% 0.17/0.55  %    Propositional clauses             : 0
% 0.17/0.55  %    Propositional clauses after purity: 0
% 0.17/0.55  %    Propositional unsat core size     : 0
% 0.17/0.55  %    Propositional preprocessing time  : 0.000
% 0.17/0.55  %    Propositional encoding time       : 0.000
% 0.17/0.55  %    Propositional solver time         : 0.000
% 0.17/0.55  %    Success case prop preproc time    : 0.000
% 0.17/0.55  %    Success case prop encoding time   : 0.000
% 0.17/0.55  %    Success case prop solver time     : 0.000
% 0.17/0.55  % Current number of processed clauses  : 317
% 0.17/0.55  %    Positive orientable unit clauses  : 59
% 0.17/0.55  %    Positive unorientable unit clauses: 0
% 0.17/0.55  %    Negative unit clauses             : 2
% 0.17/0.55  %    Non-unit-clauses                  : 256
% 0.17/0.55  % Current number of unprocessed clauses: 969
% 0.17/0.55  % ...number of literals in the above   : 5271
% 0.17/0.55  % Current number of archived formulas  : 0
% 0.17/0.55  % Current number of archived clauses   : 249
% 0.17/0.55  % Clause-clause subsumption calls (NU) : 23039
% 0.17/0.55  % Rec. Clause-clause subsumption calls : 6871
% 0.17/0.55  % Non-unit clause-clause subsumptions  : 105
% 0.17/0.55  % Unit Clause-clause subsumption calls : 692
% 0.17/0.55  % Rewrite failures with RHS unbound    : 0
% 0.17/0.55  % BW rewrite match attempts            : 33
% 0.17/0.55  % BW rewrite match successes           : 14
% 0.17/0.55  % Condensation attempts                : 0
% 0.17/0.55  % Condensation successes               : 0
% 0.17/0.55  % Termbank termtop insertions          : 49321
% 0.17/0.55  % Search garbage collected termcells   : 4543
% 0.17/0.55  
% 0.17/0.55  % -------------------------------------------------
% 0.17/0.55  % User time                : 0.084 s
% 0.17/0.55  % System time              : 0.007 s
% 0.17/0.55  % Total time               : 0.091 s
% 0.17/0.55  % Maximum resident set size: 4028 pages
% 0.17/0.55  
% 0.17/0.55  % -------------------------------------------------
% 0.17/0.55  % User time                : 0.356 s
% 0.17/0.55  % System time              : 0.033 s
% 0.17/0.55  % Total time               : 0.389 s
% 0.17/0.55  % Maximum resident set size: 4608 pages
% 0.17/0.55  % E exiting
%------------------------------------------------------------------------------