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E---3.5.1.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : E---3.5.1
% Problem  : SWC234+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 02:43:34 PM UTC 2026

% Result   : Theorem 2.15s 0.74s
% Output   : CNFRefutation 2.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   65 (  16 unt;   0 def)
%            Number of atoms       :  300 ( 103 equ)
%            Maximal formula atoms :   42 (   4 avg)
%            Number of connectives :  393 ( 158   ~; 149   |;  46   &)
%                                         (   1 <=>;  39  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-3 aty)
%            Number of variables   :  118 (   0 sgn  60   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(co1,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ( nil = X3
                    & nil != X4 )
                  | ! [X9] :
                      ( ? [X10] :
                          ( ? [X11] :
                              ( ? [X12] :
                                  ( app(X12,cons(X10,nil)) = X3
                                  & ssList(X12) )
                              & app(cons(X10,nil),X11) = X9
                              & ssList(X11) )
                          & ssItem(X10) )
                      | ~ equalelemsP(X3)
                      | app(X3,X9) != X4
                      | ~ ssList(X9) )
                  | ? [X5] :
                      ( ? [X6] :
                          ( ? [X7] :
                              ( ! [X8] :
                                  ( lt(X5,X8)
                                  | ~ leq(X5,X8)
                                  | ~ memberP(X7,X8)
                                  | ~ memberP(X6,X8)
                                  | ~ ssItem(X8) )
                              & app(app(X6,cons(X5,nil)),X7) = X1
                              & ssList(X7) )
                          & ssList(X6) )
                      & ssItem(X5) )
                  | nil = X1
                  | X1 != X3
                  | X2 != X4
                  | ~ ssList(X4) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(ax38,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ~ memberP(nil,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).

fof(ax92,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ( leq(X1,X2)
           => ( lt(X1,X2)
              | X1 = X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax92) ).

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

fof(ax28,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(nil,X1) = X1 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).

fof(ax85,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( nil != X1
           => hd(app(X1,X2)) = hd(X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax85) ).

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(ax22,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => ssItem(hd(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).

fof(ax83,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( nil = app(X1,X2)
          <=> ( nil = X1
              & nil = X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).

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

fof(ax78,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => cons(hd(X1),tl(X1)) = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).

fof(ax24,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => ssList(tl(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).

fof(c_0_12,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ( nil = X3
                      & nil != X4 )
                    | ! [X9] :
                        ( ? [X10] :
                            ( ? [X11] :
                                ( ? [X12] :
                                    ( app(X12,cons(X10,nil)) = X3
                                    & ssList(X12) )
                                & app(cons(X10,nil),X11) = X9
                                & ssList(X11) )
                            & ssItem(X10) )
                        | ~ equalelemsP(X3)
                        | app(X3,X9) != X4
                        | ~ ssList(X9) )
                    | ? [X5] :
                        ( ? [X6] :
                            ( ? [X7] :
                                ( ! [X8] :
                                    ( lt(X5,X8)
                                    | ~ leq(X5,X8)
                                    | ~ memberP(X7,X8)
                                    | ~ memberP(X6,X8)
                                    | ~ ssItem(X8) )
                                & app(app(X6,cons(X5,nil)),X7) = X1
                                & ssList(X7) )
                            & ssList(X6) )
                        & ssItem(X5) )
                    | nil = X1
                    | X1 != X3
                    | X2 != X4
                    | ~ ssList(X4) ) ) ) ),
    inference(assume_negation,[status(cth)],[co1]) ).

fof(c_0_13,plain,
    ! [X1] :
      ( ssItem(X1)
     => ~ memberP(nil,X1) ),
    inference(fof_simplification,[status(thm)],[ax38]) ).

fof(c_0_14,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ( nil = X3
                      & nil != X4 )
                    | ! [X9] :
                        ( ? [X10] :
                            ( ? [X11] :
                                ( ? [X12] :
                                    ( app(X12,cons(X10,nil)) = X3
                                    & ssList(X12) )
                                & app(cons(X10,nil),X11) = X9
                                & ssList(X11) )
                            & ssItem(X10) )
                        | ~ equalelemsP(X3)
                        | app(X3,X9) != X4
                        | ~ ssList(X9) )
                    | ? [X5] :
                        ( ? [X6] :
                            ( ? [X7] :
                                ( ! [X8] :
                                    ( lt(X5,X8)
                                    | ~ leq(X5,X8)
                                    | ~ memberP(X7,X8)
                                    | ~ memberP(X6,X8)
                                    | ~ ssItem(X8) )
                                & app(app(X6,cons(X5,nil)),X7) = X1
                                & ssList(X7) )
                            & ssList(X6) )
                        & ssItem(X5) )
                    | nil = X1
                    | X1 != X3
                    | X2 != X4
                    | ~ ssList(X4) ) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_12]) ).

fof(c_0_15,plain,
    ! [X163] :
      ( ~ memberP(nil,X163)
      | ~ ssItem(X163) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).

fof(c_0_16,negated_conjecture,
    ! [X261,X262,X263,X266,X267,X268] :
      ( ( nil != esk50_0
        | nil = esk51_0 )
      & ( app(X268,cons(X266,nil)) != esk50_0
        | ~ ssList(X268)
        | app(cons(X266,nil),X267) != esk53_0
        | ~ ssList(X267)
        | ~ ssItem(X266) )
      & equalelemsP(esk50_0)
      & app(esk50_0,esk53_0) = esk51_0
      & ssList(esk53_0)
      & ( ~ ssItem(X261)
        | ~ ssList(X262)
        | app(app(X262,cons(X261,nil)),X263) != esk48_0
        | ~ ssList(X263)
        | ~ lt(X261,esk52_3(X261,X262,X263)) )
      & ( ~ ssItem(X261)
        | ~ ssList(X262)
        | app(app(X262,cons(X261,nil)),X263) != esk48_0
        | ~ ssList(X263)
        | leq(X261,esk52_3(X261,X262,X263)) )
      & ( ~ ssItem(X261)
        | ~ ssList(X262)
        | app(app(X262,cons(X261,nil)),X263) != esk48_0
        | ~ ssList(X263)
        | memberP(X263,esk52_3(X261,X262,X263)) )
      & ( ~ ssItem(X261)
        | ~ ssList(X262)
        | app(app(X262,cons(X261,nil)),X263) != esk48_0
        | ~ ssList(X263)
        | memberP(X262,esk52_3(X261,X262,X263)) )
      & ( ~ ssItem(X261)
        | ~ ssList(X262)
        | app(app(X262,cons(X261,nil)),X263) != esk48_0
        | ~ ssList(X263)
        | ssItem(esk52_3(X261,X262,X263)) )
      & nil != esk48_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_14])])])])])]) ).

fof(c_0_17,plain,
    ! [X248,X249] :
      ( lt(X248,X249)
      | X248 = X249
      | ~ leq(X248,X249)
      | ~ ssItem(X249)
      | ~ ssItem(X248) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax92])])])]) ).

cnf(c_0_18,plain,
    ( ~ memberP(nil,X1)
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_19,negated_conjecture,
    ( ~ ssItem(X2)
    | ~ ssList(X1)
    | app(app(X1,cons(X2,nil)),X3) != esk48_0
    | ~ ssList(X3)
    | memberP(X1,esk52_3(X2,X1,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_20,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[ax17]) ).

cnf(c_0_21,negated_conjecture,
    ( ~ ssItem(X1)
    | ~ ssList(X2)
    | app(app(X2,cons(X1,nil)),X3) != esk48_0
    | ~ ssList(X3)
    | ~ lt(X1,esk52_3(X1,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_22,plain,
    ( ~ leq(X1,X2)
    | ~ ssItem(X2)
    | ~ ssItem(X1)
    | lt(X1,X2)
    | X1 = X2 ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_23,negated_conjecture,
    ( ~ ssItem(X1)
    | ~ ssList(X2)
    | app(app(X2,cons(X1,nil)),X3) != esk48_0
    | ~ ssList(X3)
    | ssItem(esk52_3(X1,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_24,negated_conjecture,
    ( ~ ssItem(X1)
    | ~ ssList(X2)
    | app(app(X2,cons(X1,nil)),X3) != esk48_0
    | ~ ssList(X3)
    | leq(X1,esk52_3(X1,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_25,negated_conjecture,
    ( ~ ssItem(X1)
    | ~ ssItem(esk52_3(X1,nil,X2))
    | ~ ssList(X2)
    | app(app(nil,cons(X1,nil)),X2) != esk48_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).

cnf(c_0_26,negated_conjecture,
    ( ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | app(app(X2,cons(X1,nil)),X3) != esk48_0
    | esk52_3(X1,X2,X3) = X1 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24]) ).

fof(c_0_27,plain,
    ! [X141] :
      ( app(nil,X141) = X141
      | ~ ssList(X141) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).

fof(c_0_28,plain,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( nil != X1
           => hd(app(X1,X2)) = hd(X1) ) ) ),
    inference(fof_simplification,[status(thm)],[ax85]) ).

cnf(c_0_29,negated_conjecture,
    ( ~ ssItem(X1)
    | ~ ssList(X2)
    | app(app(nil,cons(X1,nil)),X2) != esk48_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_20])]) ).

cnf(c_0_30,plain,
    ( ~ ssList(X1)
    | app(nil,X1) = X1 ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

fof(c_0_31,plain,
    ! [X226,X227] :
      ( cons(X227,X226) = app(cons(X227,nil),X226)
      | ~ ssItem(X227)
      | ~ ssList(X226) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).

fof(c_0_32,plain,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => ssItem(hd(X1)) ) ),
    inference(fof_simplification,[status(thm)],[ax22]) ).

fof(c_0_33,plain,
    ! [X234,X235] :
      ( hd(app(X234,X235)) = hd(X234)
      | nil = X234
      | ~ ssList(X235)
      | ~ ssList(X234) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])]) ).

cnf(c_0_34,negated_conjecture,
    app(esk50_0,esk53_0) = esk51_0,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_35,negated_conjecture,
    esk48_0 = esk50_0,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_36,plain,
    ! [X231,X232] :
      ( ( ~ ssList(X231)
        | ~ ssList(X232)
        | nil = app(X231,X232)
        | nil != X231
        | nil != X232 )
      & ( ~ ssList(X231)
        | ~ ssList(X232)
        | nil != app(X231,X232)
        | nil = X231 )
      & ( ~ ssList(X231)
        | ~ ssList(X232)
        | nil != app(X231,X232)
        | nil = X232 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])])]) ).

cnf(c_0_37,negated_conjecture,
    ( ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(cons(X1,nil))
    | app(cons(X1,nil),X2) != esk48_0 ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_38,plain,
    ( ~ ssItem(X2)
    | ~ ssList(X1)
    | cons(X2,X1) = app(cons(X2,nil),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

fof(c_0_39,plain,
    ! [X117,X118] :
      ( ssList(cons(X118,X117))
      | ~ ssItem(X118)
      | ~ ssList(X117) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).

fof(c_0_40,plain,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => cons(hd(X1),tl(X1)) = X1 ) ),
    inference(fof_simplification,[status(thm)],[ax78]) ).

fof(c_0_41,plain,
    ! [X130] :
      ( ssItem(hd(X130))
      | nil = X130
      | ~ ssList(X130) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])]) ).

cnf(c_0_42,plain,
    ( ~ ssList(X2)
    | ~ ssList(X1)
    | hd(app(X1,X2)) = hd(X1)
    | nil = X1 ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_43,negated_conjecture,
    app(esk48_0,esk53_0) = esk51_0,
    inference(rw,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_44,negated_conjecture,
    ssList(esk53_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_45,negated_conjecture,
    ssList(esk48_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_46,negated_conjecture,
    nil != esk48_0,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_47,negated_conjecture,
    ssList(esk49_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_48,negated_conjecture,
    esk49_0 = esk51_0,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_49,plain,
    ( ~ ssList(X1)
    | ~ ssList(X2)
    | nil != app(X1,X2)
    | nil = X1 ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_50,negated_conjecture,
    ( ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(cons(X1,nil))
    | cons(X1,X2) != esk48_0 ),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_51,plain,
    ( ~ ssItem(X2)
    | ~ ssList(X1)
    | ssList(cons(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

fof(c_0_52,plain,
    ! [X219] :
      ( cons(hd(X219),tl(X219)) = X219
      | nil = X219
      | ~ ssList(X219) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])]) ).

cnf(c_0_53,plain,
    ( ~ ssList(X1)
    | ssItem(hd(X1))
    | nil = X1 ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_54,negated_conjecture,
    hd(esk51_0) = hd(esk48_0),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_45])]),c_0_46]) ).

cnf(c_0_55,negated_conjecture,
    ssList(esk51_0),
    inference(rw,[status(thm)],[c_0_47,c_0_48]) ).

cnf(c_0_56,negated_conjecture,
    esk51_0 != nil,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_43]),c_0_44]),c_0_45])]),c_0_46]) ).

fof(c_0_57,plain,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => ssList(tl(X1)) ) ),
    inference(fof_simplification,[status(thm)],[ax24]) ).

cnf(c_0_58,negated_conjecture,
    ( ~ ssItem(X1)
    | ~ ssList(X2)
    | cons(X1,X2) != esk48_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_20])]) ).

cnf(c_0_59,plain,
    ( ~ ssList(X1)
    | cons(hd(X1),tl(X1)) = X1
    | nil = X1 ),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

cnf(c_0_60,negated_conjecture,
    ssItem(hd(esk48_0)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55])]),c_0_56]) ).

fof(c_0_61,plain,
    ! [X133] :
      ( ssList(tl(X133))
      | nil = X133
      | ~ ssList(X133) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])]) ).

cnf(c_0_62,negated_conjecture,
    ~ ssList(tl(esk48_0)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59])]),c_0_60]),c_0_45])]),c_0_46]) ).

cnf(c_0_63,plain,
    ( ~ ssList(X1)
    | ssList(tl(X1))
    | nil = X1 ),
    inference(split_conjunct,[status(thm)],[c_0_61]) ).

cnf(c_0_64,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_45])]),c_0_46]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SWC234+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04  % Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36  % Computer : n011.cluster.edu
% 0.09/0.36  % Model    : x86_64 x86_64
% 0.09/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36  % Memory   : 8046.5625MB
% 0.09/0.36  % OS       : Linux 6.8.0-71-generic
% 0.09/0.36  % CPULimit : 300
% 0.09/0.36  % WCLimit  : 300
% 0.09/0.36  % DateTime : Mon Sep 21 08:07:11 UTC 2026
% 0.09/0.37  % CPUTime  : 
% 0.09/0.37  Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41  Running first-order theorem proving
% 0.09/0.41  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
% 2.15/0.74  % Version: 3.5.1
% 2.15/0.74  % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.15/0.74  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.15/0.74  % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.15/0.74  % Starting new_bool_3 with 300s (1) cores
% 2.15/0.74  % Starting new_bool_1 with 300s (1) cores
% 2.15/0.74  % Starting sh5l with 300s (1) cores
% 2.15/0.74  % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1420365 completed with status 0
% 2.15/0.74  % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 2.15/0.74  % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.15/0.74  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.15/0.74  % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.15/0.74  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.15/0.74  % No SInE strategy applied
% 2.15/0.74  % Search class: FGHSF-FSLM31-MFFFFFNN
% 2.15/0.74  % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.15/0.74  % Starting SubtermCWHack with 136s (1) cores
% 2.15/0.74  % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 2.15/0.74  % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 2.15/0.74  % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 2.15/0.74  % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S070I with 136s (1) cores
% 2.15/0.74  % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 1420374 completed with status 0
% 2.15/0.74  % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 2.15/0.74  % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.15/0.74  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.15/0.74  % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.15/0.74  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.15/0.74  % No SInE strategy applied
% 2.15/0.74  % Search class: FGHSF-FSLM31-MFFFFFNN
% 2.15/0.74  % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.15/0.74  % Starting SubtermCWHack with 136s (1) cores
% 2.15/0.74  % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 2.15/0.74  % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 2.15/0.74  % Preprocessing time       : 0.004 s
% 2.15/0.74  % Presaturation interreduction done
% 2.15/0.74  
% 2.15/0.74  % Proof found!
% 2.15/0.74  % SZS status Theorem
% 2.15/0.74  % SZS output start CNFRefutation
% See solution above
% 2.15/0.74  % Parsed axioms                        : 96
% 2.15/0.74  % Removed by relevancy pruning/SinE    : 0
% 2.15/0.74  % Initial clauses                      : 207
% 2.15/0.74  % Removed in clause preprocessing      : 2
% 2.15/0.74  % Initial clauses in saturation        : 205
% 2.15/0.74  % Processed clauses                    : 2511
% 2.15/0.74  % ...of these trivial                  : 47
% 2.15/0.74  % ...subsumed                          : 1307
% 2.15/0.74  % ...remaining for further processing  : 1157
% 2.15/0.74  % Other redundant clauses eliminated   : 245
% 2.15/0.74  % Clauses deleted for lack of memory   : 0
% 2.15/0.74  % Backward-subsumed                    : 230
% 2.15/0.74  % Backward-rewritten                   : 15
% 2.15/0.74  % Generated clauses                    : 6956
% 2.15/0.74  % ...of the previous two non-redundant : 6132
% 2.15/0.74  % ...aggressively subsumed             : 0
% 2.15/0.74  % Contextual simplify-reflections      : 207
% 2.15/0.74  % Paramodulations                      : 6708
% 2.15/0.74  % Factorizations                       : 0
% 2.15/0.74  % NegExts                              : 0
% 2.15/0.74  % Equation resolutions                 : 250
% 2.15/0.74  % Disequality decompositions           : 0
% 2.15/0.74  % Total rewrite steps                  : 5759
% 2.15/0.74  % ...of those cached                   : 5717
% 2.15/0.74  % Propositional unsat checks           : 0
% 2.15/0.74  %    Propositional check models        : 0
% 2.15/0.74  %    Propositional check unsatisfiable : 0
% 2.15/0.74  %    Propositional clauses             : 0
% 2.15/0.74  %    Propositional clauses after purity: 0
% 2.15/0.74  %    Propositional unsat core size     : 0
% 2.15/0.74  %    Propositional preprocessing time  : 0.000
% 2.15/0.74  %    Propositional encoding time       : 0.000
% 2.15/0.74  %    Propositional solver time         : 0.000
% 2.15/0.74  %    Success case prop preproc time    : 0.000
% 2.15/0.74  %    Success case prop encoding time   : 0.000
% 2.15/0.74  %    Success case prop solver time     : 0.000
% 2.15/0.74  % Current number of processed clauses  : 691
% 2.15/0.74  %    Positive orientable unit clauses  : 45
% 2.15/0.74  %    Positive unorientable unit clauses: 0
% 2.15/0.74  %    Negative unit clauses             : 16
% 2.15/0.74  %    Non-unit-clauses                  : 630
% 2.15/0.74  % Current number of unprocessed clauses: 3818
% 2.15/0.74  % ...number of literals in the above   : 23893
% 2.15/0.74  % Current number of archived formulas  : 0
% 2.15/0.74  % Current number of archived clauses   : 443
% 2.15/0.74  % Clause-clause subsumption calls (NU) : 101916
% 2.15/0.74  % Rec. Clause-clause subsumption calls : 25244
% 2.15/0.74  % Non-unit clause-clause subsumptions  : 1278
% 2.15/0.74  % Unit Clause-clause subsumption calls : 1653
% 2.15/0.74  % Rewrite failures with RHS unbound    : 0
% 2.15/0.74  % BW rewrite match attempts            : 13
% 2.15/0.74  % BW rewrite match successes           : 13
% 2.15/0.74  % Condensation attempts                : 0
% 2.15/0.74  % Condensation successes               : 0
% 2.15/0.74  % Termbank termtop insertions          : 145005
% 2.15/0.74  % Search garbage collected termcells   : 4444
% 2.15/0.74  
% 2.15/0.74  % -------------------------------------------------
% 2.15/0.74  % User time                : 0.295 s
% 2.15/0.74  % System time              : 0.011 s
% 2.15/0.74  % Total time               : 0.306 s
% 2.15/0.74  % Maximum resident set size: 4228 pages
% 2.15/0.74  
% 2.15/0.74  % -------------------------------------------------
% 2.15/0.74  % User time                : 1.364 s
% 2.15/0.74  % System time              : 0.069 s
% 2.15/0.74  % Total time               : 1.433 s
% 2.15/0.74  % Maximum resident set size: 4608 pages
% 2.15/0.74  % E exiting
%------------------------------------------------------------------------------