TSTP Solution File: SWC099+1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SWC099+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n029.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 04:23:19 EDT 2024

% Result   : Theorem 1.66s 0.69s
% Output   : CNFRefutation 1.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   91 (  13 unt;   0 def)
%            Number of atoms       :  347 (  89 equ)
%            Maximal formula atoms :   23 (   3 avg)
%            Number of connectives :  439 ( 183   ~; 175   |;  36   &)
%                                         (   5 <=>;  40  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   5 con; 0-2 aty)
%            Number of variables   :  115 (   0 sgn  63   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(co1,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ~ frontsegP(X4,X3)
                    | ~ equalelemsP(X3)
                    | ? [X5] :
                        ( ssList(X5)
                        & neq(X3,X5)
                        & frontsegP(X4,X5)
                        & segmentP(X5,X3)
                        & equalelemsP(X5) )
                    | ( ( nil != X2
                        | nil = X1 )
                      & ( ~ neq(X2,nil)
                        | ( neq(X1,nil)
                          & frontsegP(X2,X1) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(ax15,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( neq(X1,X2)
          <=> X1 != X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).

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

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(ax21,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => nil != cons(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).

fof(ax46,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( frontsegP(nil,X1)
      <=> nil = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax46) ).

fof(ax18,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => cons(X2,X1) != X1 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).

fof(ax23,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => hd(cons(X2,X1)) = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax23) ).

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

fof(ax25,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => tl(cons(X2,X1)) = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax25) ).

fof(ax4,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( singletonP(X1)
      <=> ? [X2] :
            ( ssItem(X2)
            & cons(X2,nil) = X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).

fof(ax57,axiom,
    ! [X1] :
      ( ssList(X1)
     => segmentP(X1,nil) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax57) ).

fof(ax44,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( frontsegP(cons(X1,X3),cons(X2,X4))
                  <=> ( X1 = X2
                      & frontsegP(X3,X4) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax44) ).

fof(ax73,axiom,
    ! [X1] :
      ( ssItem(X1)
     => equalelemsP(cons(X1,nil)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax73) ).

fof(ax20,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil = X1
        | ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( ssItem(X3)
                & cons(X3,X2) = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax20) ).

fof(ax45,axiom,
    ! [X1] :
      ( ssList(X1)
     => frontsegP(X1,nil) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax45) ).

fof(c_0_16,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ~ frontsegP(X4,X3)
                      | ~ equalelemsP(X3)
                      | ? [X5] :
                          ( ssList(X5)
                          & neq(X3,X5)
                          & frontsegP(X4,X5)
                          & segmentP(X5,X3)
                          & equalelemsP(X5) )
                      | ( ( nil != X2
                          | nil = X1 )
                        & ( ~ neq(X2,nil)
                          | ( neq(X1,nil)
                            & frontsegP(X2,X1) ) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).

fof(c_0_17,negated_conjecture,
    ! [X255] :
      ( ssList(esk48_0)
      & ssList(esk49_0)
      & ssList(esk50_0)
      & ssList(esk51_0)
      & esk49_0 = esk51_0
      & esk48_0 = esk50_0
      & frontsegP(esk51_0,esk50_0)
      & equalelemsP(esk50_0)
      & ( ~ ssList(X255)
        | ~ neq(esk50_0,X255)
        | ~ frontsegP(esk51_0,X255)
        | ~ segmentP(X255,esk50_0)
        | ~ equalelemsP(X255) )
      & ( neq(esk49_0,nil)
        | nil = esk49_0 )
      & ( ~ neq(esk48_0,nil)
        | ~ frontsegP(esk49_0,esk48_0)
        | nil = esk49_0 )
      & ( neq(esk49_0,nil)
        | nil != esk48_0 )
      & ( ~ neq(esk48_0,nil)
        | ~ frontsegP(esk49_0,esk48_0)
        | nil != 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_16])])])])])]) ).

cnf(c_0_18,negated_conjecture,
    frontsegP(esk51_0,esk50_0),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_19,negated_conjecture,
    esk49_0 = esk51_0,
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_20,negated_conjecture,
    esk48_0 = esk50_0,
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

fof(c_0_21,plain,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( neq(X1,X2)
          <=> X1 != X2 ) ) ),
    inference(fof_simplification,[status(thm)],[ax15]) ).

cnf(c_0_22,negated_conjecture,
    ( nil = esk49_0
    | ~ neq(esk48_0,nil)
    | ~ frontsegP(esk49_0,esk48_0) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_23,negated_conjecture,
    frontsegP(esk49_0,esk48_0),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).

fof(c_0_24,plain,
    ! [X109,X110] :
      ( ( ~ neq(X109,X110)
        | X109 != X110
        | ~ ssList(X110)
        | ~ ssList(X109) )
      & ( X109 = X110
        | neq(X109,X110)
        | ~ ssList(X110)
        | ~ ssList(X109) ) ),
    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_21])])])])]) ).

cnf(c_0_25,negated_conjecture,
    ( esk49_0 = nil
    | ~ neq(esk48_0,nil) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).

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

cnf(c_0_27,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[ax17]) ).

cnf(c_0_28,negated_conjecture,
    ssList(esk48_0),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

fof(c_0_29,plain,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => cons(hd(X1),tl(X1)) = X1 ) ),
    inference(fof_simplification,[status(thm)],[ax78]) ).

fof(c_0_30,plain,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => nil != cons(X2,X1) ) ),
    inference(fof_simplification,[status(thm)],[ax21]) ).

fof(c_0_31,plain,
    ! [X172] :
      ( ( ~ frontsegP(nil,X172)
        | nil = X172
        | ~ ssList(X172) )
      & ( nil != X172
        | frontsegP(nil,X172)
        | ~ ssList(X172) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax46])])])]) ).

cnf(c_0_32,negated_conjecture,
    ( esk48_0 = nil
    | esk49_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])]) ).

fof(c_0_33,plain,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => cons(X2,X1) != X1 ) ),
    inference(fof_simplification,[status(thm)],[ax18]) ).

fof(c_0_34,plain,
    ! [X213] :
      ( ~ ssList(X213)
      | nil = X213
      | cons(hd(X213),tl(X213)) = X213 ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])]) ).

fof(c_0_35,plain,
    ! [X125,X126] :
      ( ~ ssList(X125)
      | ~ ssItem(X126)
      | hd(cons(X126,X125)) = X126 ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])])]) ).

fof(c_0_36,plain,
    ! [X111,X112] :
      ( ~ ssList(X111)
      | ~ ssItem(X112)
      | ssList(cons(X112,X111)) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).

fof(c_0_37,plain,
    ! [X122,X123] :
      ( ~ ssList(X122)
      | ~ ssItem(X123)
      | nil != cons(X123,X122) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])])]) ).

fof(c_0_38,plain,
    ! [X128,X129] :
      ( ~ ssList(X128)
      | ~ ssItem(X129)
      | tl(cons(X129,X128)) = X128 ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])])]) ).

fof(c_0_39,plain,
    ! [X17,X19] :
      ( ( ssItem(esk5_1(X17))
        | ~ singletonP(X17)
        | ~ ssList(X17) )
      & ( cons(esk5_1(X17),nil) = X17
        | ~ singletonP(X17)
        | ~ ssList(X17) )
      & ( ~ ssItem(X19)
        | cons(X19,nil) != X17
        | singletonP(X17)
        | ~ ssList(X17) ) ),
    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)],[ax4])])])])])]) ).

cnf(c_0_40,negated_conjecture,
    ( ~ ssList(X1)
    | ~ neq(esk50_0,X1)
    | ~ frontsegP(esk51_0,X1)
    | ~ segmentP(X1,esk50_0)
    | ~ equalelemsP(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_41,plain,
    ( nil = X1
    | ~ frontsegP(nil,X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_42,negated_conjecture,
    ( esk48_0 = nil
    | frontsegP(nil,esk48_0) ),
    inference(spm,[status(thm)],[c_0_23,c_0_32]) ).

fof(c_0_43,plain,
    ! [X194] :
      ( ~ ssList(X194)
      | segmentP(X194,nil) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])])]) ).

fof(c_0_44,plain,
    ! [X113,X114] :
      ( ~ ssList(X113)
      | ~ ssItem(X114)
      | cons(X114,X113) != X113 ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])])]) ).

cnf(c_0_45,plain,
    ( nil = X1
    | cons(hd(X1),tl(X1)) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_46,plain,
    ( hd(cons(X2,X1)) = X2
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_47,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_48,plain,
    ( ~ ssList(X1)
    | ~ ssItem(X2)
    | nil != cons(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_49,plain,
    ( tl(cons(X2,X1)) = X1
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_50,plain,
    ( cons(esk5_1(X1),nil) = X1
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_51,plain,
    ( ssItem(esk5_1(X1))
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_52,plain,
    ( singletonP(X2)
    | ~ ssItem(X1)
    | cons(X1,nil) != X2
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_53,negated_conjecture,
    ( ~ equalelemsP(X1)
    | ~ segmentP(X1,esk48_0)
    | ~ frontsegP(esk49_0,X1)
    | ~ ssList(X1)
    | ~ neq(esk48_0,X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_20]),c_0_20]),c_0_19]) ).

cnf(c_0_54,negated_conjecture,
    esk48_0 = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_28])]) ).

cnf(c_0_55,plain,
    ( segmentP(X1,nil)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

fof(c_0_56,plain,
    ! [X167,X168,X169,X170] :
      ( ( X167 = X168
        | ~ frontsegP(cons(X167,X169),cons(X168,X170))
        | ~ ssList(X170)
        | ~ ssList(X169)
        | ~ ssItem(X168)
        | ~ ssItem(X167) )
      & ( frontsegP(X169,X170)
        | ~ frontsegP(cons(X167,X169),cons(X168,X170))
        | ~ ssList(X170)
        | ~ ssList(X169)
        | ~ ssItem(X168)
        | ~ ssItem(X167) )
      & ( X167 != X168
        | ~ frontsegP(X169,X170)
        | frontsegP(cons(X167,X169),cons(X168,X170))
        | ~ ssList(X170)
        | ~ ssList(X169)
        | ~ ssItem(X168)
        | ~ ssItem(X167) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])])])])]) ).

cnf(c_0_57,plain,
    ( ~ ssList(X1)
    | ~ ssItem(X2)
    | cons(X2,X1) != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_58,plain,
    ( cons(X1,tl(cons(X1,X2))) = cons(X1,X2)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_48]) ).

cnf(c_0_59,plain,
    ( tl(X1) = nil
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_27])]),c_0_51]) ).

cnf(c_0_60,plain,
    ( singletonP(cons(X1,nil))
    | ~ ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(er,[status(thm)],[c_0_52]) ).

cnf(c_0_61,negated_conjecture,
    ( ~ equalelemsP(X1)
    | ~ frontsegP(esk49_0,X1)
    | ~ ssList(X1)
    | ~ neq(nil,X1) ),
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54]),c_0_54]),c_0_55]) ).

fof(c_0_62,plain,
    ! [X206] :
      ( ~ ssItem(X206)
      | equalelemsP(cons(X206,nil)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax73])])]) ).

cnf(c_0_63,plain,
    ( frontsegP(cons(X1,X3),cons(X2,X4))
    | X1 != X2
    | ~ frontsegP(X3,X4)
    | ~ ssList(X4)
    | ~ ssList(X3)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

fof(c_0_64,plain,
    ! [X119] :
      ( ( ssList(esk44_1(X119))
        | nil = X119
        | ~ ssList(X119) )
      & ( ssItem(esk45_1(X119))
        | nil = X119
        | ~ ssList(X119) )
      & ( cons(esk45_1(X119),esk44_1(X119)) = X119
        | nil = X119
        | ~ ssList(X119) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])])]) ).

cnf(c_0_65,plain,
    ( tl(cons(X1,X2)) != cons(X1,X2)
    | ~ ssList(tl(cons(X1,X2)))
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[c_0_57,c_0_58]) ).

cnf(c_0_66,plain,
    ( tl(cons(X1,nil)) = nil
    | ~ ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[c_0_59,c_0_60]) ).

cnf(c_0_67,negated_conjecture,
    ( nil = X1
    | ~ equalelemsP(X1)
    | ~ frontsegP(esk49_0,X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_26]),c_0_27])]) ).

cnf(c_0_68,plain,
    ( equalelemsP(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_69,plain,
    ( frontsegP(cons(X1,X2),cons(X1,X3))
    | ~ frontsegP(X2,X3)
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(er,[status(thm)],[c_0_63]) ).

cnf(c_0_70,plain,
    ( cons(esk45_1(X1),esk44_1(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_64]) ).

cnf(c_0_71,plain,
    ( ssItem(esk45_1(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_64]) ).

cnf(c_0_72,plain,
    ( ssList(esk44_1(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_64]) ).

cnf(c_0_73,plain,
    ( cons(X1,nil) != nil
    | ~ ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_27])]) ).

cnf(c_0_74,negated_conjecture,
    ( cons(X1,nil) = nil
    | ~ frontsegP(esk49_0,cons(X1,nil))
    | ~ ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[c_0_67,c_0_68]) ).

cnf(c_0_75,plain,
    ( nil = X1
    | frontsegP(X1,cons(esk45_1(X1),X2))
    | ~ frontsegP(esk44_1(X1),X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]),c_0_72]) ).

cnf(c_0_76,negated_conjecture,
    ssList(esk49_0),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_77,plain,
    ( cons(X1,nil) != nil
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_47]),c_0_27])]) ).

fof(c_0_78,plain,
    ! [X171] :
      ( ~ ssList(X171)
      | frontsegP(X171,nil) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])])]) ).

cnf(c_0_79,negated_conjecture,
    ( esk49_0 = nil
    | ~ frontsegP(esk44_1(esk49_0),nil)
    | ~ ssList(cons(esk45_1(esk49_0),nil))
    | ~ ssItem(esk45_1(esk49_0)) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_27]),c_0_76])]),c_0_77]) ).

cnf(c_0_80,plain,
    ( frontsegP(X1,nil)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_78]) ).

cnf(c_0_81,negated_conjecture,
    ( esk49_0 = nil
    | ~ ssList(cons(esk45_1(esk49_0),nil))
    | ~ ssList(esk44_1(esk49_0))
    | ~ ssItem(esk45_1(esk49_0)) ),
    inference(spm,[status(thm)],[c_0_79,c_0_80]) ).

cnf(c_0_82,negated_conjecture,
    ( esk49_0 = nil
    | ~ ssList(esk44_1(esk49_0))
    | ~ ssItem(esk45_1(esk49_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_47]),c_0_27])]) ).

cnf(c_0_83,negated_conjecture,
    ( ~ neq(esk48_0,nil)
    | ~ frontsegP(esk49_0,esk48_0)
    | nil != esk48_0 ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_84,negated_conjecture,
    ( neq(esk49_0,nil)
    | nil != esk48_0 ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_85,negated_conjecture,
    ( esk49_0 = nil
    | ~ ssList(esk44_1(esk49_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_71]),c_0_76])]) ).

cnf(c_0_86,negated_conjecture,
    ( esk48_0 != nil
    | ~ neq(esk48_0,nil) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_23])]) ).

cnf(c_0_87,negated_conjecture,
    neq(esk49_0,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_54])]) ).

cnf(c_0_88,negated_conjecture,
    esk49_0 = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_72]),c_0_76])]) ).

cnf(c_0_89,negated_conjecture,
    ~ neq(nil,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_54]),c_0_54])]) ).

cnf(c_0_90,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_88]),c_0_89]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : SWC099+1 : TPTP v8.2.0. Released v2.4.0.
% 0.00/0.09  % Command    : run_E %s %d THM
% 0.09/0.29  % Computer : n029.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit   : 300
% 0.09/0.30  % WCLimit    : 300
% 0.09/0.30  % DateTime   : Sun May 19 03:46:08 EDT 2024
% 0.09/0.30  % CPUTime    : 
% 0.15/0.40  Running first-order theorem proving
% 0.15/0.40  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
% 1.66/0.69  # Version: 3.1.0
% 1.66/0.69  # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.66/0.69  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.66/0.69  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.66/0.69  # Starting new_bool_3 with 300s (1) cores
% 1.66/0.69  # Starting new_bool_1 with 300s (1) cores
% 1.66/0.69  # Starting sh5l with 300s (1) cores
% 1.66/0.69  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 24302 completed with status 0
% 1.66/0.69  # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.66/0.69  # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.66/0.69  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.66/0.69  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.66/0.69  # No SInE strategy applied
% 1.66/0.69  # Search class: FGHSF-FSLM21-MFFFFFNN
% 1.66/0.69  # Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 1.66/0.69  # Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 1.66/0.69  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.66/0.69  # Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 1.66/0.69  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 1.66/0.69  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2o with 136s (1) cores
% 1.66/0.69  # G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with pid 24311 completed with status 0
% 1.66/0.69  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y
% 1.66/0.69  # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.66/0.69  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.66/0.69  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.66/0.69  # No SInE strategy applied
% 1.66/0.69  # Search class: FGHSF-FSLM21-MFFFFFNN
% 1.66/0.69  # Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 1.66/0.69  # Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 1.66/0.69  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.66/0.69  # Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 1.66/0.69  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 1.66/0.69  # Preprocessing time       : 0.003 s
% 1.66/0.69  # Presaturation interreduction done
% 1.66/0.69  
% 1.66/0.69  # Proof found!
% 1.66/0.69  # SZS status Theorem
% 1.66/0.69  # SZS output start CNFRefutation
% See solution above
% 1.66/0.69  # Parsed axioms                        : 96
% 1.66/0.69  # Removed by relevancy pruning/SinE    : 0
% 1.66/0.69  # Initial clauses                      : 203
% 1.66/0.69  # Removed in clause preprocessing      : 2
% 1.66/0.69  # Initial clauses in saturation        : 201
% 1.66/0.69  # Processed clauses                    : 1973
% 1.66/0.69  # ...of these trivial                  : 16
% 1.66/0.69  # ...subsumed                          : 1142
% 1.66/0.69  # ...remaining for further processing  : 815
% 1.66/0.69  # Other redundant clauses eliminated   : 237
% 1.66/0.69  # Clauses deleted for lack of memory   : 0
% 1.66/0.69  # Backward-subsumed                    : 43
% 1.66/0.69  # Backward-rewritten                   : 29
% 1.66/0.69  # Generated clauses                    : 6379
% 1.66/0.69  # ...of the previous two non-redundant : 5523
% 1.66/0.69  # ...aggressively subsumed             : 0
% 1.66/0.69  # Contextual simplify-reflections      : 260
% 1.66/0.69  # Paramodulations                      : 6136
% 1.66/0.69  # Factorizations                       : 0
% 1.66/0.69  # NegExts                              : 0
% 1.66/0.69  # Equation resolutions                 : 245
% 1.66/0.69  # Disequality decompositions           : 0
% 1.66/0.69  # Total rewrite steps                  : 3211
% 1.66/0.69  # ...of those cached                   : 3187
% 1.66/0.69  # Propositional unsat checks           : 0
% 1.66/0.69  #    Propositional check models        : 0
% 1.66/0.69  #    Propositional check unsatisfiable : 0
% 1.66/0.69  #    Propositional clauses             : 0
% 1.66/0.69  #    Propositional clauses after purity: 0
% 1.66/0.69  #    Propositional unsat core size     : 0
% 1.66/0.69  #    Propositional preprocessing time  : 0.000
% 1.66/0.69  #    Propositional encoding time       : 0.000
% 1.66/0.69  #    Propositional solver time         : 0.000
% 1.66/0.69  #    Success case prop preproc time    : 0.000
% 1.66/0.69  #    Success case prop encoding time   : 0.000
% 1.66/0.69  #    Success case prop solver time     : 0.000
% 1.66/0.69  # Current number of processed clauses  : 525
% 1.66/0.69  #    Positive orientable unit clauses  : 22
% 1.66/0.69  #    Positive unorientable unit clauses: 0
% 1.66/0.69  #    Negative unit clauses             : 3
% 1.66/0.69  #    Non-unit-clauses                  : 500
% 1.66/0.69  # Current number of unprocessed clauses: 3845
% 1.66/0.69  # ...number of literals in the above   : 27128
% 1.66/0.69  # Current number of archived formulas  : 0
% 1.66/0.69  # Current number of archived clauses   : 267
% 1.66/0.69  # Clause-clause subsumption calls (NU) : 97651
% 1.66/0.69  # Rec. Clause-clause subsumption calls : 16391
% 1.66/0.69  # Non-unit clause-clause subsumptions  : 1245
% 1.66/0.69  # Unit Clause-clause subsumption calls : 112
% 1.66/0.69  # Rewrite failures with RHS unbound    : 0
% 1.66/0.69  # BW rewrite match attempts            : 7
% 1.66/0.69  # BW rewrite match successes           : 7
% 1.66/0.69  # Condensation attempts                : 0
% 1.66/0.69  # Condensation successes               : 0
% 1.66/0.69  # Termbank termtop insertions          : 140704
% 1.66/0.69  # Search garbage collected termcells   : 4315
% 1.66/0.69  
% 1.66/0.69  # -------------------------------------------------
% 1.66/0.69  # User time                : 0.202 s
% 1.66/0.69  # System time              : 0.009 s
% 1.66/0.69  # Total time               : 0.211 s
% 1.66/0.69  # Maximum resident set size: 2468 pages
% 1.66/0.69  
% 1.66/0.69  # -------------------------------------------------
% 1.66/0.69  # User time                : 1.143 s
% 1.66/0.69  # System time              : 0.038 s
% 1.66/0.69  # Total time               : 1.181 s
% 1.66/0.69  # Maximum resident set size: 1820 pages
% 1.66/0.69  % E---3.1 exiting
% 1.66/0.70  % E exiting
%------------------------------------------------------------------------------