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E---3.5.1.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : E---3.5.1
% Problem  : SWC299+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 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 : Thu Sep 24 02:43:50 PM UTC 2026

% Result   : Theorem 0.29s 0.81s
% Output   : CNFRefutation 0.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   57 (  23 unt;   0 def)
%            Number of atoms       :  282 (  68 equ)
%            Maximal formula atoms :   49 (   4 avg)
%            Number of connectives :  331 ( 106   ~; 117   |;  48   &)
%                                         (   1 <=>;  59  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   33 (   5 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   20 (  20 usr;  13 con; 0-2 aty)
%            Number of variables   :  105 (   0 sgn  76   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(co1,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( ( ( nil != X3
                        | nil != X4 )
                      & ! [X10] :
                          ( ssItem(X10)
                         => ! [X11] :
                              ( ssList(X11)
                             => ! [X12] :
                                  ( ssList(X12)
                                 => ( ? [X14] :
                                        ( lt(X14,X10)
                                        & memberP(X12,X14)
                                        & ssItem(X14) )
                                    | ? [X13] :
                                        ( lt(X10,X13)
                                        & memberP(X11,X13)
                                        & ssItem(X13) )
                                    | app(app(X11,X3),X12) != X4
                                    | cons(X10,nil) != X3 ) ) ) ) )
                    | ! [X5] :
                        ( ssItem(X5)
                       => ! [X6] :
                            ( ssItem(X6)
                           => ! [X7] :
                                ( ssList(X7)
                               => ! [X8] :
                                    ( ssList(X8)
                                   => ! [X9] :
                                        ( ssList(X9)
                                       => ( ~ lt(X6,X5)
                                          | app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) != X1 ) ) ) ) ) )
                    | X1 != X3
                    | X2 != X4 ) ) ) ) ),
    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(ax33,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ( lt(X1,X2)
           => ~ lt(X2,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax33) ).

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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax12) ).

fof(ax68,axiom,
    ! [X1] :
      ( ssItem(X1)
     => strictorderedP(cons(X1,nil)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax68) ).

fof(ax69,axiom,
    strictorderedP(nil),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax69) ).

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

fof(c_0_11,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( ( ( nil != X3
                          | nil != X4 )
                        & ! [X10] :
                            ( ssItem(X10)
                           => ! [X11] :
                                ( ssList(X11)
                               => ! [X12] :
                                    ( ssList(X12)
                                   => ( ? [X14] :
                                          ( lt(X14,X10)
                                          & memberP(X12,X14)
                                          & ssItem(X14) )
                                      | ? [X13] :
                                          ( lt(X10,X13)
                                          & memberP(X11,X13)
                                          & ssItem(X13) )
                                      | app(app(X11,X3),X12) != X4
                                      | cons(X10,nil) != X3 ) ) ) ) )
                      | ! [X5] :
                          ( ssItem(X5)
                         => ! [X6] :
                              ( ssItem(X6)
                             => ! [X7] :
                                  ( ssList(X7)
                                 => ! [X8] :
                                      ( ssList(X8)
                                     => ! [X9] :
                                          ( ssList(X9)
                                         => ( ~ lt(X6,X5)
                                            | app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) != X1 ) ) ) ) ) )
                      | X1 != X3
                      | X2 != X4 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_10]) ).

fof(c_0_12,negated_conjecture,
    ! [X271,X272] :
      ( ( ~ lt(X272,esk57_0)
        | ~ memberP(esk59_0,X272)
        | ~ ssItem(X272)
        | nil = esk50_0 )
      & ( ~ lt(X272,esk57_0)
        | ~ memberP(esk59_0,X272)
        | ~ ssItem(X272)
        | nil = esk51_0 )
      & ( ~ lt(esk57_0,X271)
        | ~ memberP(esk58_0,X271)
        | ~ ssItem(X271)
        | nil = esk50_0 )
      & ( ~ lt(esk57_0,X271)
        | ~ memberP(esk58_0,X271)
        | ~ ssItem(X271)
        | nil = esk51_0 )
      & ( app(app(esk58_0,esk50_0),esk59_0) = esk51_0
        | nil = esk50_0 )
      & ( app(app(esk58_0,esk50_0),esk59_0) = esk51_0
        | nil = esk51_0 )
      & ( cons(esk57_0,nil) = esk50_0
        | nil = esk50_0 )
      & ( cons(esk57_0,nil) = esk50_0
        | nil = esk51_0 )
      & ( ssList(esk59_0)
        | nil = esk50_0 )
      & ( ssList(esk59_0)
        | nil = esk51_0 )
      & ( ssList(esk58_0)
        | nil = esk50_0 )
      & ( ssList(esk58_0)
        | nil = esk51_0 )
      & ( ssItem(esk57_0)
        | nil = esk50_0 )
      & ( ssItem(esk57_0)
        | nil = esk51_0 )
      & lt(esk53_0,esk52_0)
      & app(app(app(app(esk54_0,cons(esk52_0,nil)),esk55_0),cons(esk53_0,nil)),esk56_0) = esk48_0
      & ssList(esk56_0)
      & ssList(esk55_0)
      & ssList(esk54_0)
      & ssItem(esk53_0)
      & ssItem(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_11])])])])])]) ).

cnf(c_0_13,negated_conjecture,
    app(app(app(app(esk54_0,cons(esk52_0,nil)),esk55_0),cons(esk53_0,nil)),esk56_0) = esk48_0,
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

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

fof(c_0_15,plain,
    ! [X230,X231,X232] :
      ( app(app(X230,X231),X232) = app(X230,app(X231,X232))
      | ~ ssList(X232)
      | ~ ssList(X231)
      | ~ ssList(X230) ),
    inference(fof_nnf,[status(thm)],[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(esk54_0,cons(esk52_0,nil)),esk55_0),cons(esk53_0,nil)),esk56_0) = esk50_0,
    inference(rw,[status(thm)],[c_0_13,c_0_14]) ).

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

cnf(c_0_18,negated_conjecture,
    ssList(esk55_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_19,negated_conjecture,
    ssList(esk54_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_20,plain,
    ! [X119,X120] :
      ( ssList(cons(X120,X119))
      | ~ ssItem(X120)
      | ~ ssList(X119) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).

cnf(c_0_21,negated_conjecture,
    ( ~ ssList(cons(esk52_0,nil))
    | app(app(app(esk54_0,app(cons(esk52_0,nil),esk55_0)),cons(esk53_0,nil)),esk56_0) = esk50_0 ),
    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,
    ( ~ ssItem(X2)
    | ~ ssList(X1)
    | ssList(cons(X2,X1)) ),
    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(esk52_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_25,plain,
    ! [X228,X229] :
      ( cons(X229,X228) = app(cons(X229,nil),X228)
      | ~ ssItem(X229)
      | ~ ssList(X228) ),
    inference(fof_nnf,[status(thm)],[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(esk54_0,app(cons(esk52_0,nil),esk55_0)),cons(esk53_0,nil)),esk56_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,
    ( ~ ssItem(X2)
    | ~ ssList(X1)
    | cons(X2,X1) = app(cons(X2,nil),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_28,negated_conjecture,
    app(app(app(esk54_0,cons(esk52_0,esk55_0)),cons(esk53_0,nil)),esk56_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(esk56_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_30,negated_conjecture,
    ( ~ ssList(cons(esk53_0,nil))
    | ~ ssList(app(esk54_0,cons(esk52_0,esk55_0)))
    | app(app(esk54_0,cons(esk52_0,esk55_0)),app(cons(esk53_0,nil),esk56_0)) = esk50_0 ),
    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(esk53_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_32,plain,
    ! [X138,X139] :
      ( ssList(app(X138,X139))
      | ~ ssList(X139)
      | ~ ssList(X138) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).

cnf(c_0_33,negated_conjecture,
    ( ~ ssList(app(esk54_0,cons(esk52_0,esk55_0)))
    | app(app(esk54_0,cons(esk52_0,esk55_0)),app(cons(esk53_0,nil),esk56_0)) = esk50_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(X2)
    | ~ ssList(X1)
    | ssList(app(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

fof(c_0_35,plain,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ( lt(X1,X2)
           => ~ lt(X2,X1) ) ) ),
    inference(fof_simplification,[status(thm)],[ax33]) ).

fof(c_0_36,plain,
    ! [X86,X87,X88,X89,X90,X91] :
      ( ( ~ ssList(X86)
        | strictorderedP(X86)
        | ~ lt(esk30_1(X86),esk31_1(X86)) )
      & ( ~ ssList(X86)
        | strictorderedP(X86)
        | app(app(esk32_1(X86),cons(esk30_1(X86),esk33_1(X86))),cons(esk31_1(X86),esk34_1(X86))) = X86 )
      & ( ~ ssList(X86)
        | strictorderedP(X86)
        | ssList(esk34_1(X86)) )
      & ( ~ ssList(X86)
        | strictorderedP(X86)
        | ssList(esk33_1(X86)) )
      & ( ~ ssList(X86)
        | strictorderedP(X86)
        | ssList(esk32_1(X86)) )
      & ( ~ ssList(X86)
        | strictorderedP(X86)
        | ssItem(esk31_1(X86)) )
      & ( ~ ssList(X86)
        | strictorderedP(X86)
        | ssItem(esk30_1(X86)) )
      & ( ~ ssList(X86)
        | lt(X87,X88)
        | app(app(X89,cons(X87,X90)),cons(X88,X91)) != X86
        | ~ ssList(X91)
        | ~ ssList(X90)
        | ~ ssList(X89)
        | ~ ssItem(X88)
        | ~ ssItem(X87)
        | ~ strictorderedP(X86) ) ),
    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(esk52_0,esk55_0))
    | app(app(esk54_0,cons(esk52_0,esk55_0)),app(cons(esk53_0,nil),esk56_0)) = esk50_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,
    ! [X152,X153] :
      ( ~ lt(X153,X152)
      | ~ lt(X152,X153)
      | ~ ssItem(X153)
      | ~ ssItem(X152) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])])]) ).

fof(c_0_39,plain,
    ! [X210] :
      ( strictorderedP(cons(X210,nil))
      | ~ ssItem(X210) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax68])])]) ).

cnf(c_0_40,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_41,negated_conjecture,
    app(app(esk54_0,cons(esk52_0,esk55_0)),app(cons(esk53_0,nil),esk56_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_42,negated_conjecture,
    ssList(esk48_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_43,plain,
    ( ~ lt(X2,X1)
    | ~ lt(X1,X2)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_44,negated_conjecture,
    lt(esk53_0,esk52_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_45,plain,
    ( ~ ssItem(X1)
    | strictorderedP(cons(X1,nil)) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_46,negated_conjecture,
    ( cons(esk57_0,nil) = esk50_0
    | nil = esk50_0 ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_47,negated_conjecture,
    ( ssItem(esk57_0)
    | nil = esk50_0 ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_48,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_40]) ).

cnf(c_0_49,negated_conjecture,
    app(app(esk54_0,cons(esk52_0,esk55_0)),cons(esk53_0,esk56_0)) = esk50_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_27]),c_0_29]),c_0_31])]) ).

cnf(c_0_50,negated_conjecture,
    ssList(esk50_0),
    inference(rw,[status(thm)],[c_0_42,c_0_14]) ).

cnf(c_0_51,negated_conjecture,
    ~ lt(esk52_0,esk53_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_31]),c_0_24])]) ).

cnf(c_0_52,negated_conjecture,
    ( strictorderedP(esk50_0)
    | esk50_0 = nil ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).

cnf(c_0_53,negated_conjecture,
    ~ strictorderedP(esk50_0),
    inference(sr,[status(thm)],[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(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_29]),c_0_18]),c_0_19]),c_0_31]),c_0_24])]),c_0_51]) ).

cnf(c_0_54,negated_conjecture,
    esk50_0 = nil,
    inference(sr,[status(thm)],[c_0_52,c_0_53]) ).

cnf(c_0_55,plain,
    strictorderedP(nil),
    inference(split_conjunct,[status(thm)],[ax69]) ).

cnf(c_0_56,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54]),c_0_55])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWC299+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07  % Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.47  % Computer : n011.cluster.edu
% 0.19/0.47  % Model    : x86_64 x86_64
% 0.19/0.47  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.47  % Memory   : 8046.5625MB
% 0.19/0.47  % OS       : Linux 6.8.0-71-generic
% 0.19/0.47  % CPULimit : 300
% 0.19/0.47  % WCLimit  : 300
% 0.19/0.47  % DateTime : Mon Sep 21 08:13:25 UTC 2026
% 0.19/0.48  % CPUTime  : 
% 0.19/0.48  Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.56  Running first-order theorem proving
% 0.23/0.56  Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.29/0.81  % Version: 3.5.1
% 0.29/0.81  % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.29/0.81  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.81  % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.29/0.81  % Starting new_bool_3 with 300s (1) cores
% 0.29/0.81  % Starting new_bool_1 with 300s (1) cores
% 0.29/0.81  % Starting sh5l with 300s (1) cores
% 0.29/0.81  % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1430459 completed with status 0
% 0.29/0.81  % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.29/0.81  % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.29/0.81  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.81  % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.29/0.81  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.29/0.81  % No SInE strategy applied
% 0.29/0.81  % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.29/0.81  % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.29/0.81  % Starting SubtermCWHack with 136s (1) cores
% 0.29/0.81  % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.29/0.81  % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.29/0.81  % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 0.29/0.81  % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 0.29/0.81  % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1430466 completed with status 0
% 0.29/0.81  % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.29/0.81  % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.29/0.81  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.81  % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.29/0.81  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.29/0.81  % No SInE strategy applied
% 0.29/0.81  % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.29/0.81  % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.29/0.81  % Starting SubtermCWHack with 136s (1) cores
% 0.29/0.81  % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.29/0.81  % Preprocessing time       : 0.007 s
% 0.29/0.81  % Presaturation interreduction done
% 0.29/0.81  
% 0.29/0.81  % Proof found!
% 0.29/0.81  % SZS status Theorem
% 0.29/0.81  % SZS output start CNFRefutation
% See solution above
% 0.29/0.82  % Parsed axioms                        : 96
% 0.29/0.82  % Removed by relevancy pruning/SinE    : 0
% 0.29/0.82  % Initial clauses                      : 217
% 0.29/0.82  % Removed in clause preprocessing      : 2
% 0.29/0.82  % Initial clauses in saturation        : 215
% 0.29/0.82  % Processed clauses                    : 1022
% 0.29/0.82  % ...of these trivial                  : 3
% 0.29/0.82  % ...subsumed                          : 266
% 0.29/0.82  % ...remaining for further processing  : 753
% 0.29/0.82  % Other redundant clauses eliminated   : 69
% 0.29/0.82  % Clauses deleted for lack of memory   : 0
% 0.29/0.82  % Backward-subsumed                    : 35
% 0.29/0.82  % Backward-rewritten                   : 184
% 0.29/0.82  % Generated clauses                    : 2363
% 0.29/0.82  % ...of the previous two non-redundant : 2130
% 0.29/0.82  % ...aggressively subsumed             : 0
% 0.29/0.82  % Contextual simplify-reflections      : 193
% 0.29/0.82  % Paramodulations                      : 2289
% 0.29/0.82  % Factorizations                       : 0
% 0.29/0.82  % NegExts                              : 0
% 0.29/0.82  % Equation resolutions                 : 74
% 0.29/0.82  % Disequality decompositions           : 0
% 0.29/0.82  % Total rewrite steps                  : 1484
% 0.29/0.82  % ...of those cached                   : 1443
% 0.29/0.82  % Propositional unsat checks           : 0
% 0.29/0.82  %    Propositional check models        : 0
% 0.29/0.82  %    Propositional check unsatisfiable : 0
% 0.29/0.82  %    Propositional clauses             : 0
% 0.29/0.82  %    Propositional clauses after purity: 0
% 0.29/0.82  %    Propositional unsat core size     : 0
% 0.29/0.82  %    Propositional preprocessing time  : 0.000
% 0.29/0.82  %    Propositional encoding time       : 0.000
% 0.29/0.82  %    Propositional solver time         : 0.000
% 0.29/0.82  %    Success case prop preproc time    : 0.000
% 0.29/0.82  %    Success case prop encoding time   : 0.000
% 0.29/0.82  %    Success case prop solver time     : 0.000
% 0.29/0.82  % Current number of processed clauses  : 300
% 0.29/0.82  %    Positive orientable unit clauses  : 32
% 0.29/0.82  %    Positive unorientable unit clauses: 0
% 0.29/0.82  %    Negative unit clauses             : 4
% 0.29/0.82  %    Non-unit-clauses                  : 264
% 0.29/0.82  % Current number of unprocessed clauses: 1512
% 0.29/0.82  % ...number of literals in the above   : 8699
% 0.29/0.82  % Current number of archived formulas  : 0
% 0.29/0.82  % Current number of archived clauses   : 430
% 0.29/0.82  % Clause-clause subsumption calls (NU) : 35460
% 0.29/0.82  % Rec. Clause-clause subsumption calls : 13210
% 0.29/0.82  % Non-unit clause-clause subsumptions  : 464
% 0.29/0.82  % Unit Clause-clause subsumption calls : 336
% 0.29/0.82  % Rewrite failures with RHS unbound    : 0
% 0.29/0.82  % BW rewrite match attempts            : 32
% 0.29/0.82  % BW rewrite match successes           : 13
% 0.29/0.82  % Condensation attempts                : 0
% 0.29/0.82  % Condensation successes               : 0
% 0.29/0.82  % Termbank termtop insertions          : 66497
% 0.29/0.82  % Search garbage collected termcells   : 4514
% 0.29/0.82  
% 0.29/0.82  % -------------------------------------------------
% 0.29/0.82  % User time                : 0.195 s
% 0.29/0.82  % System time              : 0.012 s
% 0.29/0.82  % Total time               : 0.207 s
% 0.29/0.82  % Maximum resident set size: 4280 pages
% 0.29/0.82  
% 0.29/0.82  % -------------------------------------------------
% 0.29/0.82  % User time                : 0.879 s
% 0.29/0.82  % System time              : 0.051 s
% 0.29/0.82  % Total time               : 0.929 s
% 0.29/0.82  % Maximum resident set size: 4608 pages
% 0.29/0.82  % E exiting
%------------------------------------------------------------------------------