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CSE_E---1.7.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SWC303+1 : TPTP v9.2.1. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n001.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May  5 05:19:06 PM UTC 2026

% Result   : Theorem 1.52s 1.79s
% Output   : CNFRefutation 1.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   62 (  25 unt;   0 def)
%            Number of atoms       :  275 (  53 equ)
%            Maximal formula atoms :   30 (   4 avg)
%            Number of connectives :  340 ( 127   ~; 124   |;  43   &)
%                                         (   3 <=>;  43  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   5 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;  11 con; 0-2 aty)
%            Number of variables   :  108 (   0 sgn  72   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(co1,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ~ ssList(X4)
                  | X4 != X2
                  | X3 != X1
                  | ! [X5] :
                      ( ~ ssList(X5)
                      | app(X3,X5) != X4
                      | ~ totalorderedP(X3)
                      | ? [X6] :
                          ( ssItem(X6)
                          & ? [X7] :
                              ( ssList(X7)
                              & app(cons(X6,nil),X7) = X5
                              & ? [X8] :
                                  ( ssItem(X8)
                                  & ? [X9] :
                                      ( ssList(X9)
                                      & app(X9,cons(X8,nil)) = X3
                                      & leq(X8,X6) ) ) ) ) )
                  | ! [X10] :
                      ( ssItem(X10)
                     => ! [X11] :
                          ( ssItem(X11)
                         => ! [X12] :
                              ( ssList(X12)
                             => ! [X13] :
                                  ( ssList(X13)
                                 => ! [X14] :
                                      ( ~ ssList(X14)
                                      | app(app(app(app(X12,cons(X10,nil)),X13),cons(X11,nil)),X14) != X1
                                      | ~ lt(X11,X10) ) ) ) ) )
                  | ( nil != X4
                    & nil = X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax82) ).

fof(ax16,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ssList(cons(X2,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).

fof(ax17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax81) ).

fof(ax26,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ssList(app(X1,X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).

fof(ax93,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ( lt(X1,X2)
          <=> ( X1 != X2
              & leq(X1,X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax93) ).

fof(ax11,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( totalorderedP(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
                             => leq(X2,X3) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax11) ).

fof(ax94,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ( gt(X1,X2)
           => ~ gt(X2,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax94) ).

fof(ax35,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ( gt(X1,X2)
          <=> lt(X2,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax35) ).

fof(ax29,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ( ( leq(X1,X2)
              & leq(X2,X1) )
           => X1 = X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax29) ).

fof(c_0_11,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ~ ssList(X4)
                    | X4 != X2
                    | X3 != X1
                    | ! [X5] :
                        ( ~ ssList(X5)
                        | app(X3,X5) != X4
                        | ~ totalorderedP(X3)
                        | ? [X6] :
                            ( ssItem(X6)
                            & ? [X7] :
                                ( ssList(X7)
                                & app(cons(X6,nil),X7) = X5
                                & ? [X8] :
                                    ( ssItem(X8)
                                    & ? [X9] :
                                        ( ssList(X9)
                                        & app(X9,cons(X8,nil)) = X3
                                        & leq(X8,X6) ) ) ) ) )
                    | ! [X10] :
                        ( ssItem(X10)
                       => ! [X11] :
                            ( ssItem(X11)
                           => ! [X12] :
                                ( ssList(X12)
                               => ! [X13] :
                                    ( ssList(X13)
                                   => ! [X14] :
                                        ( ~ ssList(X14)
                                        | app(app(app(app(X12,cons(X10,nil)),X13),cons(X11,nil)),X14) != X1
                                        | ~ lt(X11,X10) ) ) ) ) )
                    | ( nil != X4
                      & nil = X3 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).

fof(c_0_12,negated_conjecture,
    ! [X481,X482,X483,X484] :
      ( ssList(esk48_0)
      & ssList(esk49_0)
      & ssList(esk50_0)
      & ssList(esk51_0)
      & esk51_0 = esk49_0
      & esk50_0 = esk48_0
      & ssList(esk52_0)
      & app(esk50_0,esk52_0) = esk51_0
      & totalorderedP(esk50_0)
      & ( ~ ssItem(X481)
        | ~ ssList(X482)
        | app(cons(X481,nil),X482) != esk52_0
        | ~ ssItem(X483)
        | ~ ssList(X484)
        | app(X484,cons(X483,nil)) != esk50_0
        | ~ leq(X483,X481) )
      & ssItem(esk53_0)
      & ssItem(esk54_0)
      & ssList(esk55_0)
      & ssList(esk56_0)
      & ssList(esk57_0)
      & app(app(app(app(esk55_0,cons(esk53_0,nil)),esk56_0),cons(esk54_0,nil)),esk57_0) = esk48_0
      & lt(esk54_0,esk53_0)
      & ( nil = esk51_0
        | nil != esk50_0 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).

cnf(c_0_13,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_12]) ).

cnf(c_0_14,negated_conjecture,
    esk50_0 = esk48_0,
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_15,plain,
    ! [X447,X448,X449] :
      ( ~ ssList(X447)
      | ~ ssList(X448)
      | ~ ssList(X449)
      | app(app(X447,X448),X449) = app(X447,app(X448,X449)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).

cnf(c_0_16,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_13,c_0_14]) ).

cnf(c_0_17,plain,
    ( app(app(X1,X2),X3) = app(X1,app(X2,X3))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_18,negated_conjecture,
    ssList(esk56_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_19,negated_conjecture,
    ssList(esk55_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_20,plain,
    ! [X336,X337] :
      ( ~ ssList(X336)
      | ~ ssItem(X337)
      | ssList(cons(X337,X336)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).

cnf(c_0_21,negated_conjecture,
    ( app(app(app(esk55_0,app(cons(esk53_0,nil),esk56_0)),cons(esk54_0,nil)),esk57_0) = esk50_0
    | ~ ssList(cons(esk53_0,nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19])]) ).

cnf(c_0_22,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_23,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[ax17]) ).

cnf(c_0_24,negated_conjecture,
    ssItem(esk53_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_25,plain,
    ! [X445,X446] :
      ( ~ ssList(X445)
      | ~ ssItem(X446)
      | cons(X446,X445) = app(cons(X446,nil),X445) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).

cnf(c_0_26,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_21,c_0_22]),c_0_23]),c_0_24])]) ).

cnf(c_0_27,plain,
    ( cons(X2,X1) = app(cons(X2,nil),X1)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_28,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_26,c_0_27]),c_0_18]),c_0_24])]) ).

cnf(c_0_29,negated_conjecture,
    ssList(esk57_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_30,negated_conjecture,
    ( app(app(esk55_0,cons(esk53_0,esk56_0)),app(cons(esk54_0,nil),esk57_0)) = esk50_0
    | ~ ssList(app(esk55_0,cons(esk53_0,esk56_0)))
    | ~ ssList(cons(esk54_0,nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_28]),c_0_29])]) ).

cnf(c_0_31,negated_conjecture,
    ssItem(esk54_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_32,plain,
    ! [X355,X356] :
      ( ~ ssList(X355)
      | ~ ssList(X356)
      | ssList(app(X355,X356)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).

cnf(c_0_33,negated_conjecture,
    ( app(app(esk55_0,cons(esk53_0,esk56_0)),app(cons(esk54_0,nil),esk57_0)) = esk50_0
    | ~ ssList(app(esk55_0,cons(esk53_0,esk56_0))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_22]),c_0_23]),c_0_31])]) ).

cnf(c_0_34,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

fof(c_0_35,plain,
    ! [X469,X470] :
      ( ( X469 != X470
        | ~ lt(X469,X470)
        | ~ ssItem(X470)
        | ~ ssItem(X469) )
      & ( leq(X469,X470)
        | ~ lt(X469,X470)
        | ~ ssItem(X470)
        | ~ ssItem(X469) )
      & ( X469 = X470
        | ~ leq(X469,X470)
        | lt(X469,X470)
        | ~ ssItem(X470)
        | ~ ssItem(X469) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax93])])])]) ).

fof(c_0_36,plain,
    ! [X292,X293,X294,X295,X296,X297] :
      ( ( ~ totalorderedP(X292)
        | ~ ssItem(X293)
        | ~ ssItem(X294)
        | ~ ssList(X295)
        | ~ ssList(X296)
        | ~ ssList(X297)
        | app(app(X295,cons(X293,X296)),cons(X294,X297)) != X292
        | leq(X293,X294)
        | ~ ssList(X292) )
      & ( ssItem(esk25_1(X292))
        | totalorderedP(X292)
        | ~ ssList(X292) )
      & ( ssItem(esk26_1(X292))
        | totalorderedP(X292)
        | ~ ssList(X292) )
      & ( ssList(esk27_1(X292))
        | totalorderedP(X292)
        | ~ ssList(X292) )
      & ( ssList(esk28_1(X292))
        | totalorderedP(X292)
        | ~ ssList(X292) )
      & ( ssList(esk29_1(X292))
        | totalorderedP(X292)
        | ~ ssList(X292) )
      & ( app(app(esk27_1(X292),cons(esk25_1(X292),esk28_1(X292))),cons(esk26_1(X292),esk29_1(X292))) = X292
        | totalorderedP(X292)
        | ~ ssList(X292) )
      & ( ~ leq(esk25_1(X292),esk26_1(X292))
        | totalorderedP(X292)
        | ~ ssList(X292) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax11])])])])]) ).

cnf(c_0_37,negated_conjecture,
    ( app(app(esk55_0,cons(esk53_0,esk56_0)),app(cons(esk54_0,nil),esk57_0)) = esk50_0
    | ~ ssList(cons(esk53_0,esk56_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_19])]) ).

fof(c_0_38,plain,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ( gt(X1,X2)
           => ~ gt(X2,X1) ) ) ),
    inference(fof_simplification,[status(thm)],[ax94]) ).

fof(c_0_39,plain,
    ! [X374,X375] :
      ( ( ~ gt(X374,X375)
        | lt(X375,X374)
        | ~ ssItem(X375)
        | ~ ssItem(X374) )
      & ( ~ lt(X375,X374)
        | gt(X374,X375)
        | ~ ssItem(X375)
        | ~ ssItem(X374) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax35])])])]) ).

fof(c_0_40,plain,
    ! [X361,X362] :
      ( ~ ssItem(X361)
      | ~ ssItem(X362)
      | ~ leq(X361,X362)
      | ~ leq(X362,X361)
      | X361 = X362 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax29])])]) ).

cnf(c_0_41,plain,
    ( leq(X1,X2)
    | ~ lt(X1,X2)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_42,negated_conjecture,
    lt(esk54_0,esk53_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_43,plain,
    ( leq(X2,X3)
    | ~ totalorderedP(X1)
    | ~ ssItem(X2)
    | ~ ssItem(X3)
    | ~ ssList(X4)
    | ~ ssList(X5)
    | ~ ssList(X6)
    | app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_44,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_22]),c_0_18]),c_0_24])]) ).

cnf(c_0_45,negated_conjecture,
    ssList(esk48_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_46,plain,
    ! [X471,X472] :
      ( ~ ssItem(X471)
      | ~ ssItem(X472)
      | ~ gt(X471,X472)
      | ~ gt(X472,X471) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])]) ).

cnf(c_0_47,plain,
    ( gt(X2,X1)
    | ~ lt(X1,X2)
    | ~ ssItem(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_48,plain,
    ( X1 = X2
    | ~ ssItem(X1)
    | ~ ssItem(X2)
    | ~ leq(X1,X2)
    | ~ leq(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_49,negated_conjecture,
    leq(esk54_0,esk53_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_24]),c_0_31])]) ).

cnf(c_0_50,plain,
    ( leq(X1,X2)
    | ~ totalorderedP(app(app(X3,cons(X1,X4)),cons(X2,X5)))
    | ~ ssList(app(app(X3,cons(X1,X4)),cons(X2,X5)))
    | ~ ssList(X5)
    | ~ ssList(X4)
    | ~ ssList(X3)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    inference(er,[status(thm)],[c_0_43]) ).

cnf(c_0_51,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_44,c_0_27]),c_0_29]),c_0_31])]) ).

cnf(c_0_52,negated_conjecture,
    totalorderedP(esk50_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_53,negated_conjecture,
    ssList(esk50_0),
    inference(rw,[status(thm)],[c_0_45,c_0_14]) ).

cnf(c_0_54,plain,
    ( ~ ssItem(X1)
    | ~ ssItem(X2)
    | ~ gt(X1,X2)
    | ~ gt(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_55,negated_conjecture,
    gt(esk53_0,esk54_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_42]),c_0_24]),c_0_31])]) ).

cnf(c_0_56,negated_conjecture,
    ( esk54_0 = esk53_0
    | ~ leq(esk53_0,esk54_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_31]),c_0_24])]) ).

cnf(c_0_57,negated_conjecture,
    leq(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_50,c_0_51]),c_0_52]),c_0_53]),c_0_29]),c_0_18]),c_0_19]),c_0_31]),c_0_24])]) ).

cnf(c_0_58,negated_conjecture,
    ~ gt(esk54_0,esk53_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_24]),c_0_31])]) ).

cnf(c_0_59,negated_conjecture,
    esk54_0 = esk53_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57])]) ).

cnf(c_0_60,negated_conjecture,
    ~ gt(esk53_0,esk53_0),
    inference(rw,[status(thm)],[c_0_58,c_0_59]) ).

cnf(c_0_61,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_59]),c_0_60]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWC303+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.12  % Command    : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33  % Computer : n001.cluster.edu
% 0.16/0.33  % Model    : x86_64 x86_64
% 0.16/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33  % Memory   : 8042.1875MB
% 0.16/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33  % CPULimit   : 300
% 0.16/0.33  % WCLimit    : 300
% 0.16/0.33  % DateTime   : Tue May  5 04:43:48 EDT 2026
% 0.16/0.33  % CPUTime    : 
% 0.16/0.34  % start to proof: theBenchmark
% 1.52/1.79  % Version  : CSE_E---1.7
% 1.52/1.79  % Problem  : theBenchmark.p
% 1.52/1.79  % SZS status Theorem for theBenchmark.p
% 1.52/1.79  % SZS output start CNFRefutation
% See solution above
% 1.52/1.79  % Total time : 1.373s
%------------------------------------------------------------------------------