TSTP Solution File: SWC005+1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SWC005+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n028.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 21 04:22:32 EDT 2024

% Result   : Theorem 0.20s 0.55s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   83 (  12 unt;   0 def)
%            Number of atoms       :  322 ( 118 equ)
%            Maximal formula atoms :   34 (   3 avg)
%            Number of connectives :  391 ( 152   ~; 156   |;  36   &)
%                                         (   2 <=>;  45  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   5 con; 0-2 aty)
%            Number of variables   :  111 (   0 sgn  63   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(co1,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ( ( ~ neq(X2,nil)
                        | ? [X5] :
                            ( ssList(X5)
                            & ? [X6] :
                                ( ssList(X6)
                                & ? [X7] :
                                    ( ssList(X7)
                                    & app(app(X5,X6),X7) = X2
                                    & app(X5,X7) = X1
                                    & neq(X6,nil) ) ) )
                        | ? [X8] :
                            ( ssList(X8)
                            & X3 != X8
                            & tl(X4) = X8
                            & neq(nil,X4) ) )
                      & ( ~ neq(X2,nil)
                        | neq(X4,nil) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

fof(ax15,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( neq(X1,X2)
          <=> X1 != X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).

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

fof(ax21,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => nil != cons(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).

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

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

fof(ax19,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssItem(X3)
             => ! [X4] :
                  ( ssItem(X4)
                 => ( cons(X3,X1) = cons(X4,X2)
                   => ( X3 = X4
                      & X2 = X1 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax19) ).

fof(ax20,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil = X1
        | ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( ssItem(X3)
                & cons(X3,X2) = X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax20) ).

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

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

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

fof(ax23,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => hd(cons(X2,X1)) = X2 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax23) ).

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(ax18,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => cons(X2,X1) != X1 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax18) ).

fof(c_0_14,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ( ( ~ neq(X2,nil)
                          | ? [X5] :
                              ( ssList(X5)
                              & ? [X6] :
                                  ( ssList(X6)
                                  & ? [X7] :
                                      ( ssList(X7)
                                      & app(app(X5,X6),X7) = X2
                                      & app(X5,X7) = X1
                                      & neq(X6,nil) ) ) )
                          | ? [X8] :
                              ( ssList(X8)
                              & X3 != X8
                              & tl(X4) = X8
                              & neq(nil,X4) ) )
                        & ( ~ neq(X2,nil)
                          | neq(X4,nil) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).

fof(c_0_15,negated_conjecture,
    ! [X13,X14,X15,X16] :
      ( ssList(esk1_0)
      & ssList(esk2_0)
      & ssList(esk3_0)
      & ssList(esk4_0)
      & esk2_0 = esk4_0
      & esk1_0 = esk3_0
      & ( neq(esk2_0,nil)
        | neq(esk2_0,nil) )
      & ( ~ neq(esk4_0,nil)
        | neq(esk2_0,nil) )
      & ( neq(esk2_0,nil)
        | ~ ssList(X13)
        | ~ ssList(X14)
        | ~ ssList(X15)
        | app(app(X13,X14),X15) != esk2_0
        | app(X13,X15) != esk1_0
        | ~ neq(X14,nil) )
      & ( ~ neq(esk4_0,nil)
        | ~ ssList(X13)
        | ~ ssList(X14)
        | ~ ssList(X15)
        | app(app(X13,X14),X15) != esk2_0
        | app(X13,X15) != esk1_0
        | ~ neq(X14,nil) )
      & ( neq(esk2_0,nil)
        | ~ ssList(X16)
        | esk3_0 = X16
        | tl(esk4_0) != X16
        | ~ neq(nil,esk4_0) )
      & ( ~ neq(esk4_0,nil)
        | ~ ssList(X16)
        | esk3_0 = X16
        | tl(esk4_0) != X16
        | ~ neq(nil,esk4_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])])])])])]) ).

cnf(c_0_16,negated_conjecture,
    ( neq(esk2_0,nil)
    | neq(esk2_0,nil) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_17,negated_conjecture,
    neq(esk2_0,nil),
    inference(cn,[status(thm)],[c_0_16]) ).

cnf(c_0_18,negated_conjecture,
    esk2_0 = esk4_0,
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_19,plain,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( neq(X1,X2)
          <=> X1 != X2 ) ) ),
    inference(fof_simplification,[status(thm)],[ax15]) ).

cnf(c_0_20,negated_conjecture,
    ( esk3_0 = X1
    | ~ neq(esk4_0,nil)
    | ~ ssList(X1)
    | tl(esk4_0) != X1
    | ~ neq(nil,esk4_0) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_21,negated_conjecture,
    esk1_0 = esk3_0,
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_22,negated_conjecture,
    neq(esk4_0,nil),
    inference(rw,[status(thm)],[c_0_17,c_0_18]) ).

fof(c_0_23,plain,
    ! [X19,X20] :
      ( ( ~ neq(X19,X20)
        | X19 != X20
        | ~ ssList(X20)
        | ~ ssList(X19) )
      & ( X19 = X20
        | neq(X19,X20)
        | ~ ssList(X20)
        | ~ ssList(X19) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])])]) ).

cnf(c_0_24,negated_conjecture,
    ssList(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_25,plain,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => ssList(tl(X1)) ) ),
    inference(fof_simplification,[status(thm)],[ax24]) ).

fof(c_0_26,plain,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => nil != cons(X2,X1) ) ),
    inference(fof_simplification,[status(thm)],[ax21]) ).

fof(c_0_27,plain,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => cons(hd(X1),tl(X1)) = X1 ) ),
    inference(fof_simplification,[status(thm)],[ax78]) ).

cnf(c_0_28,negated_conjecture,
    ( tl(esk4_0) = esk1_0
    | ~ ssList(tl(esk4_0))
    | ~ neq(nil,esk4_0) ),
    inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_22])])]) ).

cnf(c_0_29,plain,
    ( X1 = X2
    | neq(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_30,negated_conjecture,
    ssList(esk4_0),
    inference(rw,[status(thm)],[c_0_24,c_0_18]) ).

cnf(c_0_31,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[ax17]) ).

fof(c_0_32,plain,
    ! [X26] :
      ( ~ ssList(X26)
      | nil = X26
      | ssList(tl(X26)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])]) ).

fof(c_0_33,plain,
    ! [X62,X63,X64,X65] :
      ( ( X64 = X65
        | cons(X64,X62) != cons(X65,X63)
        | ~ ssItem(X65)
        | ~ ssItem(X64)
        | ~ ssList(X63)
        | ~ ssList(X62) )
      & ( X63 = X62
        | cons(X64,X62) != cons(X65,X63)
        | ~ ssItem(X65)
        | ~ ssItem(X64)
        | ~ ssList(X63)
        | ~ ssList(X62) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax19])])])])]) ).

fof(c_0_34,plain,
    ! [X21] :
      ( ( ssList(esk5_1(X21))
        | nil = X21
        | ~ ssList(X21) )
      & ( ssItem(esk6_1(X21))
        | nil = X21
        | ~ ssList(X21) )
      & ( cons(esk6_1(X21),esk5_1(X21)) = X21
        | nil = X21
        | ~ ssList(X21) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])])]) ).

fof(c_0_35,plain,
    ! [X58,X59] :
      ( ~ ssList(X58)
      | ~ ssItem(X59)
      | ssList(cons(X59,X58)) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).

fof(c_0_36,plain,
    ! [X24,X25] :
      ( ~ ssList(X24)
      | ~ ssItem(X25)
      | nil != cons(X25,X24) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])]) ).

fof(c_0_37,plain,
    ! [X33] :
      ( ~ ssList(X33)
      | nil = X33
      | cons(hd(X33),tl(X33)) = X33 ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])]) ).

cnf(c_0_38,negated_conjecture,
    ( tl(esk4_0) = esk1_0
    | esk4_0 = nil
    | ~ ssList(tl(esk4_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31])]) ).

cnf(c_0_39,plain,
    ( nil = X1
    | ssList(tl(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_40,plain,
    ( X1 = X2
    | cons(X3,X2) != cons(X4,X1)
    | ~ ssItem(X4)
    | ~ ssItem(X3)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_41,plain,
    ( cons(esk6_1(X1),esk5_1(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_42,plain,
    ( ssItem(esk6_1(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_43,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_44,plain,
    ( ~ ssList(X1)
    | ~ ssItem(X2)
    | nil != cons(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_45,plain,
    ( nil = X1
    | cons(hd(X1),tl(X1)) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_46,negated_conjecture,
    ( tl(esk4_0) = esk1_0
    | esk4_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_30])]) ).

fof(c_0_47,plain,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => ssItem(hd(X1)) ) ),
    inference(fof_simplification,[status(thm)],[ax22]) ).

cnf(c_0_48,plain,
    ( esk5_1(cons(X1,X2)) = X2
    | ~ ssList(esk5_1(cons(X1,X2)))
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41])]),c_0_42]),c_0_43]),c_0_44]) ).

cnf(c_0_49,negated_conjecture,
    ( cons(hd(esk4_0),esk1_0) = esk4_0
    | esk4_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_30])]) ).

cnf(c_0_50,negated_conjecture,
    ssList(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_51,plain,
    ! [X66] :
      ( ~ ssList(X66)
      | nil = X66
      | ssItem(hd(X66)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])]) ).

cnf(c_0_52,negated_conjecture,
    ( esk5_1(esk4_0) = esk1_0
    | esk4_0 = nil
    | ~ ssList(esk5_1(esk4_0))
    | ~ ssItem(hd(esk4_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50])]) ).

cnf(c_0_53,plain,
    ( nil = X1
    | ssItem(hd(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

cnf(c_0_54,negated_conjecture,
    ( ~ neq(esk4_0,nil)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | app(app(X1,X2),X3) != esk2_0
    | app(X1,X3) != esk1_0
    | ~ neq(X2,nil) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_55,plain,
    ! [X41] :
      ( ~ ssList(X41)
      | app(nil,X41) = X41 ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).

cnf(c_0_56,negated_conjecture,
    ( esk5_1(esk4_0) = esk1_0
    | esk4_0 = nil
    | ~ ssList(esk5_1(esk4_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_30])]) ).

cnf(c_0_57,plain,
    ( ssList(esk5_1(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_58,negated_conjecture,
    ( app(app(X1,X2),X3) != esk4_0
    | app(X1,X3) != esk1_0
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ neq(X2,nil) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_18]),c_0_22])]) ).

cnf(c_0_59,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_55]) ).

fof(c_0_60,plain,
    ! [X67,X68] :
      ( ~ ssList(X67)
      | ~ ssItem(X68)
      | hd(cons(X68,X67)) = X68 ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])])]) ).

cnf(c_0_61,negated_conjecture,
    ( esk5_1(esk4_0) = esk1_0
    | esk4_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_30])]) ).

cnf(c_0_62,negated_conjecture,
    ( app(app(nil,X1),esk1_0) != esk4_0
    | ~ ssList(X1)
    | ~ neq(X1,nil) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_31])])]),c_0_50])]) ).

fof(c_0_63,plain,
    ! [X48,X49] :
      ( ~ ssList(X48)
      | ~ ssItem(X49)
      | cons(X49,X48) = app(cons(X49,nil),X48) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).

cnf(c_0_64,plain,
    ( hd(cons(X2,X1)) = X2
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_60]) ).

cnf(c_0_65,negated_conjecture,
    ( cons(esk6_1(esk4_0),esk1_0) = esk4_0
    | esk4_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_61]),c_0_30])]) ).

cnf(c_0_66,negated_conjecture,
    ( app(X1,esk1_0) != esk4_0
    | ~ ssList(X1)
    | ~ neq(X1,nil) ),
    inference(spm,[status(thm)],[c_0_62,c_0_59]) ).

cnf(c_0_67,plain,
    ( cons(X2,X1) = app(cons(X2,nil),X1)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_63]) ).

cnf(c_0_68,negated_conjecture,
    ( esk6_1(esk4_0) = hd(esk4_0)
    | esk4_0 = nil
    | ~ ssItem(esk6_1(esk4_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_50])]) ).

cnf(c_0_69,negated_conjecture,
    ( cons(X1,esk1_0) != esk4_0
    | ~ ssList(cons(X1,nil))
    | ~ neq(cons(X1,nil),nil)
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_50])]) ).

cnf(c_0_70,negated_conjecture,
    ( esk6_1(esk4_0) = hd(esk4_0)
    | esk4_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_42]),c_0_30])]) ).

fof(c_0_71,plain,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => cons(X2,X1) != X1 ) ),
    inference(fof_simplification,[status(thm)],[ax18]) ).

cnf(c_0_72,negated_conjecture,
    ( esk4_0 = nil
    | ~ ssList(cons(hd(esk4_0),nil))
    | ~ neq(cons(hd(esk4_0),nil),nil)
    | ~ ssItem(hd(esk4_0)) ),
    inference(spm,[status(thm)],[c_0_69,c_0_49]) ).

cnf(c_0_73,negated_conjecture,
    ( esk4_0 = nil
    | ssItem(hd(esk4_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_70]),c_0_30])]) ).

fof(c_0_74,plain,
    ! [X60,X61] :
      ( ~ ssList(X60)
      | ~ ssItem(X61)
      | cons(X61,X60) != X60 ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_71])])])]) ).

cnf(c_0_75,negated_conjecture,
    ( cons(hd(esk4_0),nil) = nil
    | esk4_0 = nil
    | ~ ssList(cons(hd(esk4_0),nil)) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_29]),c_0_31])]),c_0_73]) ).

cnf(c_0_76,plain,
    ( ~ ssList(X1)
    | ~ ssItem(X2)
    | cons(X2,X1) != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_74]) ).

cnf(c_0_77,negated_conjecture,
    ( cons(hd(esk4_0),nil) = nil
    | esk4_0 = nil ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_43]),c_0_31])]),c_0_73]) ).

cnf(c_0_78,plain,
    ( ~ neq(X1,X2)
    | X1 != X2
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_79,negated_conjecture,
    esk4_0 = nil,
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_31])]),c_0_73]) ).

cnf(c_0_80,plain,
    ( ~ ssList(X1)
    | ~ neq(X1,X1) ),
    inference(er,[status(thm)],[c_0_78]) ).

cnf(c_0_81,negated_conjecture,
    neq(nil,nil),
    inference(rw,[status(thm)],[c_0_22,c_0_79]) ).

cnf(c_0_82,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_31])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : SWC005+1 : TPTP v8.2.0. Released v2.4.0.
% 0.08/0.14  % Command    : run_E %s %d THM
% 0.14/0.35  % Computer : n028.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun May 19 02:49:53 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  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
% 0.20/0.55  # Version: 3.1.0
% 0.20/0.55  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.20/0.55  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.55  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.20/0.55  # Starting new_bool_3 with 300s (1) cores
% 0.20/0.55  # Starting new_bool_1 with 300s (1) cores
% 0.20/0.55  # Starting sh5l with 300s (1) cores
% 0.20/0.55  # new_bool_1 with pid 15794 completed with status 0
% 0.20/0.55  # Result found by new_bool_1
% 0.20/0.55  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.20/0.55  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.55  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.20/0.55  # Starting new_bool_3 with 300s (1) cores
% 0.20/0.55  # Starting new_bool_1 with 300s (1) cores
% 0.20/0.55  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.55  # Search class: FGHSF-FFMM21-SFFFFFNN
% 0.20/0.55  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.55  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with 163s (1) cores
% 0.20/0.55  # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with pid 15797 completed with status 0
% 0.20/0.55  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v
% 0.20/0.55  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.20/0.55  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.55  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.20/0.55  # Starting new_bool_3 with 300s (1) cores
% 0.20/0.55  # Starting new_bool_1 with 300s (1) cores
% 0.20/0.55  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.55  # Search class: FGHSF-FFMM21-SFFFFFNN
% 0.20/0.55  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.55  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with 163s (1) cores
% 0.20/0.55  # Preprocessing time       : 0.002 s
% 0.20/0.55  # Presaturation interreduction done
% 0.20/0.55  
% 0.20/0.55  # Proof found!
% 0.20/0.55  # SZS status Theorem
% 0.20/0.55  # SZS output start CNFRefutation
% See solution above
% 0.20/0.55  # Parsed axioms                        : 96
% 0.20/0.55  # Removed by relevancy pruning/SinE    : 67
% 0.20/0.55  # Initial clauses                      : 51
% 0.20/0.55  # Removed in clause preprocessing      : 0
% 0.20/0.55  # Initial clauses in saturation        : 51
% 0.20/0.55  # Processed clauses                    : 672
% 0.20/0.55  # ...of these trivial                  : 6
% 0.20/0.55  # ...subsumed                          : 377
% 0.20/0.55  # ...remaining for further processing  : 289
% 0.20/0.55  # Other redundant clauses eliminated   : 29
% 0.20/0.55  # Clauses deleted for lack of memory   : 0
% 0.20/0.55  # Backward-subsumed                    : 49
% 0.20/0.55  # Backward-rewritten                   : 102
% 0.20/0.55  # Generated clauses                    : 1220
% 0.20/0.55  # ...of the previous two non-redundant : 1127
% 0.20/0.55  # ...aggressively subsumed             : 0
% 0.20/0.55  # Contextual simplify-reflections      : 79
% 0.20/0.55  # Paramodulations                      : 1187
% 0.20/0.55  # Factorizations                       : 0
% 0.20/0.55  # NegExts                              : 0
% 0.20/0.55  # Equation resolutions                 : 34
% 0.20/0.55  # Disequality decompositions           : 0
% 0.20/0.55  # Total rewrite steps                  : 832
% 0.20/0.55  # ...of those cached                   : 823
% 0.20/0.55  # Propositional unsat checks           : 0
% 0.20/0.55  #    Propositional check models        : 0
% 0.20/0.55  #    Propositional check unsatisfiable : 0
% 0.20/0.55  #    Propositional clauses             : 0
% 0.20/0.55  #    Propositional clauses after purity: 0
% 0.20/0.55  #    Propositional unsat core size     : 0
% 0.20/0.55  #    Propositional preprocessing time  : 0.000
% 0.20/0.55  #    Propositional encoding time       : 0.000
% 0.20/0.55  #    Propositional solver time         : 0.000
% 0.20/0.55  #    Success case prop preproc time    : 0.000
% 0.20/0.55  #    Success case prop encoding time   : 0.000
% 0.20/0.55  #    Success case prop solver time     : 0.000
% 0.20/0.55  # Current number of processed clauses  : 88
% 0.20/0.55  #    Positive orientable unit clauses  : 9
% 0.20/0.55  #    Positive unorientable unit clauses: 0
% 0.20/0.55  #    Negative unit clauses             : 2
% 0.20/0.55  #    Non-unit-clauses                  : 77
% 0.20/0.55  # Current number of unprocessed clauses: 528
% 0.20/0.55  # ...number of literals in the above   : 2973
% 0.20/0.55  # Current number of archived formulas  : 0
% 0.20/0.55  # Current number of archived clauses   : 197
% 0.20/0.55  # Clause-clause subsumption calls (NU) : 9362
% 0.20/0.55  # Rec. Clause-clause subsumption calls : 3396
% 0.20/0.55  # Non-unit clause-clause subsumptions  : 488
% 0.20/0.55  # Unit Clause-clause subsumption calls : 96
% 0.20/0.55  # Rewrite failures with RHS unbound    : 0
% 0.20/0.55  # BW rewrite match attempts            : 2
% 0.20/0.55  # BW rewrite match successes           : 2
% 0.20/0.55  # Condensation attempts                : 0
% 0.20/0.55  # Condensation successes               : 0
% 0.20/0.55  # Termbank termtop insertions          : 24916
% 0.20/0.55  # Search garbage collected termcells   : 1554
% 0.20/0.55  
% 0.20/0.55  # -------------------------------------------------
% 0.20/0.55  # User time                : 0.053 s
% 0.20/0.55  # System time              : 0.001 s
% 0.20/0.55  # Total time               : 0.055 s
% 0.20/0.55  # Maximum resident set size: 2016 pages
% 0.20/0.55  
% 0.20/0.55  # -------------------------------------------------
% 0.20/0.55  # User time                : 0.056 s
% 0.20/0.55  # System time              : 0.005 s
% 0.20/0.55  # Total time               : 0.061 s
% 0.20/0.55  # Maximum resident set size: 1828 pages
% 0.20/0.55  % E---3.1 exiting
% 0.20/0.55  % E exiting
%------------------------------------------------------------------------------