TSTP Solution File: SWC343+1 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : SWC343+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 04:29:09 EDT 2024

% Result   : Theorem 0.13s 0.43s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   12
% Syntax   : Number of formulae    :  109 (  29 unt;   0 def)
%            Number of atoms       :  450 ( 196 equ)
%            Maximal formula atoms :   88 (   4 avg)
%            Number of connectives :  571 ( 230   ~; 246   |;  49   &)
%                                         (   1 <=>;  45  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   35 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   6 con; 0-2 aty)
%            Number of variables   :  127 (   0 sgn  65   !;  10   ?)

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

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

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

fof(ax27,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssItem(X3)
             => cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax27) ).

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

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

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

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

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

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(c_0_12,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ! [X5] :
                          ( ssList(X5)
                         => ( app(X3,X5) != X4
                            | ~ strictorderedP(X3)
                            | ? [X6] :
                                ( ssItem(X6)
                                & ? [X7] :
                                    ( ssList(X7)
                                    & app(cons(X6,nil),X7) = X5
                                    & ? [X8] :
                                        ( ssItem(X8)
                                        & ? [X9] :
                                            ( ssList(X9)
                                            & app(X9,cons(X8,nil)) = X3
                                            & lt(X8,X6) ) ) ) ) ) )
                      | ( nil != X4
                        & nil = X3 )
                      | ( ? [X10] :
                            ( ssList(X10)
                            & app(X1,X10) = X2
                            & ! [X11] :
                                ( ssItem(X11)
                               => ! [X12] :
                                    ( ssList(X12)
                                   => ( app(cons(X11,nil),X12) != X10
                                      | ! [X13] :
                                          ( ssItem(X13)
                                         => ! [X14] :
                                              ( ssList(X14)
                                             => ( app(X14,cons(X13,nil)) != X1
                                                | ~ lt(X13,X11) ) ) ) ) ) )
                            & strictorderedP(X1) )
                        & ( nil != X1
                          | nil = X2 ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).

fof(c_0_13,negated_conjecture,
    ! [X20,X21,X22,X23,X24] :
      ( ssList(esk1_0)
      & ssList(esk2_0)
      & ssList(esk3_0)
      & ssList(esk4_0)
      & esk2_0 = esk4_0
      & esk1_0 = esk3_0
      & ssList(esk5_0)
      & app(esk3_0,esk5_0) = esk4_0
      & strictorderedP(esk3_0)
      & ( ~ ssItem(X20)
        | ~ ssList(X21)
        | app(cons(X20,nil),X21) != esk5_0
        | ~ ssItem(X22)
        | ~ ssList(X23)
        | app(X23,cons(X22,nil)) != esk3_0
        | ~ lt(X22,X20) )
      & ( nil = esk4_0
        | nil != esk3_0 )
      & ( nil = esk1_0
        | ssItem(esk6_1(X24))
        | ~ ssList(X24)
        | app(esk1_0,X24) != esk2_0
        | ~ strictorderedP(esk1_0) )
      & ( nil != esk2_0
        | ssItem(esk6_1(X24))
        | ~ ssList(X24)
        | app(esk1_0,X24) != esk2_0
        | ~ strictorderedP(esk1_0) )
      & ( nil = esk1_0
        | ssList(esk7_1(X24))
        | ~ ssList(X24)
        | app(esk1_0,X24) != esk2_0
        | ~ strictorderedP(esk1_0) )
      & ( nil != esk2_0
        | ssList(esk7_1(X24))
        | ~ ssList(X24)
        | app(esk1_0,X24) != esk2_0
        | ~ strictorderedP(esk1_0) )
      & ( nil = esk1_0
        | app(cons(esk6_1(X24),nil),esk7_1(X24)) = X24
        | ~ ssList(X24)
        | app(esk1_0,X24) != esk2_0
        | ~ strictorderedP(esk1_0) )
      & ( nil != esk2_0
        | app(cons(esk6_1(X24),nil),esk7_1(X24)) = X24
        | ~ ssList(X24)
        | app(esk1_0,X24) != esk2_0
        | ~ strictorderedP(esk1_0) )
      & ( nil = esk1_0
        | ssItem(esk8_1(X24))
        | ~ ssList(X24)
        | app(esk1_0,X24) != esk2_0
        | ~ strictorderedP(esk1_0) )
      & ( nil != esk2_0
        | ssItem(esk8_1(X24))
        | ~ ssList(X24)
        | app(esk1_0,X24) != esk2_0
        | ~ strictorderedP(esk1_0) )
      & ( nil = esk1_0
        | ssList(esk9_1(X24))
        | ~ ssList(X24)
        | app(esk1_0,X24) != esk2_0
        | ~ strictorderedP(esk1_0) )
      & ( nil != esk2_0
        | ssList(esk9_1(X24))
        | ~ ssList(X24)
        | app(esk1_0,X24) != esk2_0
        | ~ strictorderedP(esk1_0) )
      & ( nil = esk1_0
        | app(esk9_1(X24),cons(esk8_1(X24),nil)) = esk1_0
        | ~ ssList(X24)
        | app(esk1_0,X24) != esk2_0
        | ~ strictorderedP(esk1_0) )
      & ( nil != esk2_0
        | app(esk9_1(X24),cons(esk8_1(X24),nil)) = esk1_0
        | ~ ssList(X24)
        | app(esk1_0,X24) != esk2_0
        | ~ strictorderedP(esk1_0) )
      & ( nil = esk1_0
        | lt(esk8_1(X24),esk6_1(X24))
        | ~ ssList(X24)
        | app(esk1_0,X24) != esk2_0
        | ~ strictorderedP(esk1_0) )
      & ( nil != esk2_0
        | lt(esk8_1(X24),esk6_1(X24))
        | ~ ssList(X24)
        | app(esk1_0,X24) != esk2_0
        | ~ strictorderedP(esk1_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_12])])])])])]) ).

fof(c_0_14,plain,
    ! [X78,X79] :
      ( ( nil = X79
        | nil != app(X78,X79)
        | ~ ssList(X79)
        | ~ ssList(X78) )
      & ( nil = X78
        | nil != app(X78,X79)
        | ~ ssList(X79)
        | ~ ssList(X78) )
      & ( nil != X79
        | nil != X78
        | nil = app(X78,X79)
        | ~ ssList(X79)
        | ~ ssList(X78) ) ),
    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_15,negated_conjecture,
    app(esk3_0,esk5_0) = esk4_0,
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_16,negated_conjecture,
    esk1_0 = esk3_0,
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_17,negated_conjecture,
    esk2_0 = esk4_0,
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_18,negated_conjecture,
    strictorderedP(esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_19,plain,
    ( nil = X1
    | nil != app(X2,X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_20,negated_conjecture,
    app(esk1_0,esk5_0) = esk2_0,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).

cnf(c_0_21,negated_conjecture,
    ssList(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_22,negated_conjecture,
    ssList(esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_23,plain,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => nil != cons(X2,X1) ) ),
    inference(fof_simplification,[status(thm)],[ax21]) ).

cnf(c_0_24,negated_conjecture,
    ( app(cons(esk6_1(X1),nil),esk7_1(X1)) = X1
    | nil != esk2_0
    | ~ ssList(X1)
    | app(esk1_0,X1) != esk2_0
    | ~ strictorderedP(esk1_0) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_25,negated_conjecture,
    strictorderedP(esk1_0),
    inference(rw,[status(thm)],[c_0_18,c_0_16]) ).

cnf(c_0_26,negated_conjecture,
    ( esk5_0 = nil
    | esk2_0 != nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22])]) ).

fof(c_0_27,plain,
    ! [X32,X33] :
      ( ~ ssList(X32)
      | ~ ssItem(X33)
      | nil != cons(X33,X32) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])]) ).

fof(c_0_28,plain,
    ! [X63,X64,X65] :
      ( ~ ssList(X63)
      | ~ ssList(X64)
      | ~ ssItem(X65)
      | cons(X65,app(X64,X63)) = app(cons(X65,X64),X63) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])])]) ).

fof(c_0_29,plain,
    ! [X61,X62] :
      ( ~ ssList(X61)
      | ~ ssList(X62)
      | ssList(app(X61,X62)) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).

cnf(c_0_30,negated_conjecture,
    ( app(cons(esk6_1(X1),nil),esk7_1(X1)) = X1
    | app(esk1_0,X1) != esk2_0
    | esk2_0 != nil
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).

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

cnf(c_0_32,negated_conjecture,
    ( app(esk1_0,nil) = esk2_0
    | esk2_0 != nil ),
    inference(spm,[status(thm)],[c_0_20,c_0_26]) ).

fof(c_0_33,plain,
    ! [X81,X82] :
      ( ~ ssList(X81)
      | ~ ssItem(X82)
      | ssList(cons(X82,X81)) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).

cnf(c_0_34,plain,
    ( ~ ssList(X1)
    | ~ ssItem(X2)
    | nil != cons(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_35,plain,
    ( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssItem(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_36,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_37,negated_conjecture,
    ( esk7_1(nil) = nil
    | esk2_0 != nil
    | ~ ssList(cons(esk6_1(nil),nil))
    | ~ ssList(esk7_1(nil)) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_30])]),c_0_31])]),c_0_32]) ).

cnf(c_0_38,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_39,negated_conjecture,
    ( ssItem(esk6_1(X1))
    | nil != esk2_0
    | ~ ssList(X1)
    | app(esk1_0,X1) != esk2_0
    | ~ strictorderedP(esk1_0) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_40,plain,
    ( app(cons(X1,X2),X3) != nil
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).

cnf(c_0_41,negated_conjecture,
    ( esk7_1(nil) = nil
    | esk2_0 != nil
    | ~ ssList(esk7_1(nil))
    | ~ ssItem(esk6_1(nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_31])]) ).

cnf(c_0_42,negated_conjecture,
    ( ssItem(esk6_1(X1))
    | app(esk1_0,X1) != esk2_0
    | esk2_0 != nil
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_25])]) ).

cnf(c_0_43,negated_conjecture,
    ( ssList(esk7_1(X1))
    | nil != esk2_0
    | ~ ssList(X1)
    | app(esk1_0,X1) != esk2_0
    | ~ strictorderedP(esk1_0) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_44,negated_conjecture,
    ( nil = esk1_0
    | app(cons(esk6_1(X1),nil),esk7_1(X1)) = X1
    | ~ ssList(X1)
    | app(esk1_0,X1) != esk2_0
    | ~ strictorderedP(esk1_0) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_45,negated_conjecture,
    ( nil = esk1_0
    | ssItem(esk6_1(X1))
    | ~ ssList(X1)
    | app(esk1_0,X1) != esk2_0
    | ~ strictorderedP(esk1_0) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_46,negated_conjecture,
    ( nil = esk1_0
    | ssList(esk7_1(X1))
    | ~ ssList(X1)
    | app(esk1_0,X1) != esk2_0
    | ~ strictorderedP(esk1_0) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_47,negated_conjecture,
    ( esk2_0 != nil
    | ~ ssList(esk7_1(nil))
    | ~ ssItem(esk6_1(nil)) ),
    inference(csr,[status(thm)],[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_40,c_0_30]),c_0_31])])]),c_0_31])]),c_0_32]) ).

cnf(c_0_48,negated_conjecture,
    ( esk7_1(nil) = nil
    | esk2_0 != nil
    | ~ ssList(esk7_1(nil)) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_31])]),c_0_32]) ).

cnf(c_0_49,negated_conjecture,
    ( ssList(esk7_1(X1))
    | app(esk1_0,X1) != esk2_0
    | esk2_0 != nil
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_25])]) ).

fof(c_0_50,plain,
    ! [X73,X74] :
      ( ~ ssList(X73)
      | ~ ssItem(X74)
      | cons(X74,X73) = app(cons(X74,nil),X73) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).

cnf(c_0_51,negated_conjecture,
    ( app(cons(esk6_1(X1),nil),esk7_1(X1)) = X1
    | esk1_0 = nil
    | app(esk1_0,X1) != esk2_0
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_25])]) ).

cnf(c_0_52,negated_conjecture,
    ( esk1_0 = nil
    | ssItem(esk6_1(X1))
    | app(esk1_0,X1) != esk2_0
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_25])]) ).

cnf(c_0_53,negated_conjecture,
    ( esk1_0 = nil
    | ssList(esk7_1(X1))
    | app(esk1_0,X1) != esk2_0
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_25])]) ).

cnf(c_0_54,negated_conjecture,
    ( esk2_0 != nil
    | ~ ssList(esk7_1(nil)) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_42]),c_0_31])]),c_0_32]) ).

cnf(c_0_55,negated_conjecture,
    ( esk7_1(nil) = nil
    | esk2_0 != nil ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_31])]),c_0_32]) ).

cnf(c_0_56,negated_conjecture,
    ( nil = esk4_0
    | nil != esk3_0 ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_57,plain,
    ( cons(X2,X1) = app(cons(X2,nil),X1)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_58,negated_conjecture,
    ( app(cons(esk6_1(esk5_0),nil),esk7_1(esk5_0)) = esk5_0
    | esk1_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_20]),c_0_22])]) ).

cnf(c_0_59,negated_conjecture,
    ( esk1_0 = nil
    | ssItem(esk6_1(esk5_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_20]),c_0_22])]) ).

cnf(c_0_60,negated_conjecture,
    ( esk1_0 = nil
    | ssList(esk7_1(esk5_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_20]),c_0_22])]) ).

cnf(c_0_61,negated_conjecture,
    esk2_0 != nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_31])]) ).

cnf(c_0_62,negated_conjecture,
    ( esk2_0 = nil
    | esk1_0 != nil ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_17]),c_0_16]) ).

fof(c_0_63,plain,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => ssItem(hd(X1)) ) ),
    inference(fof_simplification,[status(thm)],[ax22]) ).

fof(c_0_64,plain,
    ! [X92,X93] :
      ( ~ ssList(X92)
      | ~ ssItem(X93)
      | hd(cons(X93,X92)) = X93 ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])])]) ).

cnf(c_0_65,negated_conjecture,
    ( cons(esk6_1(esk5_0),esk7_1(esk5_0)) = esk5_0
    | esk1_0 = nil ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_60]) ).

cnf(c_0_66,negated_conjecture,
    esk1_0 != nil,
    inference(spm,[status(thm)],[c_0_61,c_0_62]) ).

fof(c_0_67,plain,
    ! [X91] :
      ( ~ ssList(X91)
      | nil = X91
      | ssItem(hd(X91)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_63])])]) ).

cnf(c_0_68,negated_conjecture,
    ( nil = esk1_0
    | app(esk9_1(X1),cons(esk8_1(X1),nil)) = esk1_0
    | ~ ssList(X1)
    | app(esk1_0,X1) != esk2_0
    | ~ strictorderedP(esk1_0) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_69,negated_conjecture,
    ( nil = esk1_0
    | ssList(esk9_1(X1))
    | ~ ssList(X1)
    | app(esk1_0,X1) != esk2_0
    | ~ strictorderedP(esk1_0) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_70,negated_conjecture,
    ( nil = esk1_0
    | ssItem(esk8_1(X1))
    | ~ ssList(X1)
    | app(esk1_0,X1) != esk2_0
    | ~ strictorderedP(esk1_0) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_71,plain,
    ( hd(cons(X2,X1)) = X2
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_64]) ).

cnf(c_0_72,negated_conjecture,
    cons(esk6_1(esk5_0),esk7_1(esk5_0)) = esk5_0,
    inference(sr,[status(thm)],[c_0_65,c_0_66]) ).

cnf(c_0_73,negated_conjecture,
    ssList(esk7_1(esk5_0)),
    inference(sr,[status(thm)],[c_0_60,c_0_66]) ).

cnf(c_0_74,negated_conjecture,
    ssItem(esk6_1(esk5_0)),
    inference(sr,[status(thm)],[c_0_59,c_0_66]) ).

cnf(c_0_75,plain,
    ( nil = X1
    | ssItem(hd(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_67]) ).

cnf(c_0_76,negated_conjecture,
    ( nil = esk1_0
    | lt(esk8_1(X1),esk6_1(X1))
    | ~ ssList(X1)
    | app(esk1_0,X1) != esk2_0
    | ~ strictorderedP(esk1_0) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_77,plain,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => ssList(tl(X1)) ) ),
    inference(fof_simplification,[status(thm)],[ax24]) ).

cnf(c_0_78,negated_conjecture,
    ( app(esk9_1(X1),cons(esk8_1(X1),nil)) = esk1_0
    | esk1_0 = nil
    | app(esk1_0,X1) != esk2_0
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_25])]) ).

cnf(c_0_79,negated_conjecture,
    ( esk1_0 = nil
    | ssList(esk9_1(X1))
    | app(esk1_0,X1) != esk2_0
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_25])]) ).

cnf(c_0_80,negated_conjecture,
    ( esk1_0 = nil
    | ssItem(esk8_1(X1))
    | app(esk1_0,X1) != esk2_0
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_25])]) ).

fof(c_0_81,plain,
    ! [X108,X109] :
      ( ~ ssList(X108)
      | ~ ssItem(X109)
      | tl(cons(X109,X108)) = X108 ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])])]) ).

cnf(c_0_82,negated_conjecture,
    esk6_1(esk5_0) = hd(esk5_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]),c_0_74])]) ).

cnf(c_0_83,negated_conjecture,
    ( esk5_0 = nil
    | ssItem(hd(esk5_0)) ),
    inference(spm,[status(thm)],[c_0_75,c_0_22]) ).

cnf(c_0_84,negated_conjecture,
    esk5_0 != nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_72]),c_0_73]),c_0_74])]) ).

cnf(c_0_85,negated_conjecture,
    ( esk1_0 = nil
    | lt(esk8_1(X1),esk6_1(X1))
    | app(esk1_0,X1) != esk2_0
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_25])]) ).

fof(c_0_86,plain,
    ! [X107] :
      ( ~ ssList(X107)
      | nil = X107
      | ssList(tl(X107)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_77])])]) ).

cnf(c_0_87,negated_conjecture,
    ( ~ ssItem(X1)
    | ~ ssList(X2)
    | app(cons(X1,nil),X2) != esk5_0
    | ~ ssItem(X3)
    | ~ ssList(X4)
    | app(X4,cons(X3,nil)) != esk3_0
    | ~ lt(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_88,negated_conjecture,
    ( app(esk9_1(esk5_0),cons(esk8_1(esk5_0),nil)) = esk1_0
    | esk1_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_20]),c_0_22])]) ).

cnf(c_0_89,negated_conjecture,
    ( esk1_0 = nil
    | ssList(esk9_1(esk5_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_20]),c_0_22])]) ).

cnf(c_0_90,negated_conjecture,
    ( esk1_0 = nil
    | ssItem(esk8_1(esk5_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_20]),c_0_22])]) ).

cnf(c_0_91,plain,
    ( tl(cons(X2,X1)) = X1
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_81]) ).

cnf(c_0_92,negated_conjecture,
    cons(hd(esk5_0),esk7_1(esk5_0)) = esk5_0,
    inference(rw,[status(thm)],[c_0_72,c_0_82]) ).

cnf(c_0_93,negated_conjecture,
    ssItem(hd(esk5_0)),
    inference(sr,[status(thm)],[c_0_83,c_0_84]) ).

cnf(c_0_94,negated_conjecture,
    ( esk1_0 = nil
    | lt(esk8_1(esk5_0),esk6_1(esk5_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_20]),c_0_22])]) ).

cnf(c_0_95,plain,
    ( nil = X1
    | ssList(tl(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_86]) ).

cnf(c_0_96,negated_conjecture,
    ( app(X1,cons(X2,nil)) != esk1_0
    | app(cons(X3,nil),X4) != esk5_0
    | ~ lt(X2,X3)
    | ~ ssList(X1)
    | ~ ssList(X4)
    | ~ ssItem(X2)
    | ~ ssItem(X3) ),
    inference(rw,[status(thm)],[c_0_87,c_0_16]) ).

cnf(c_0_97,negated_conjecture,
    app(esk9_1(esk5_0),cons(esk8_1(esk5_0),nil)) = esk1_0,
    inference(sr,[status(thm)],[c_0_88,c_0_66]) ).

cnf(c_0_98,negated_conjecture,
    ssList(esk9_1(esk5_0)),
    inference(sr,[status(thm)],[c_0_89,c_0_66]) ).

cnf(c_0_99,negated_conjecture,
    ssItem(esk8_1(esk5_0)),
    inference(sr,[status(thm)],[c_0_90,c_0_66]) ).

cnf(c_0_100,negated_conjecture,
    app(cons(hd(esk5_0),nil),esk7_1(esk5_0)) = esk5_0,
    inference(rw,[status(thm)],[inference(sr,[status(thm)],[c_0_58,c_0_66]),c_0_82]) ).

cnf(c_0_101,negated_conjecture,
    esk7_1(esk5_0) = tl(esk5_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_73]),c_0_93])]) ).

cnf(c_0_102,negated_conjecture,
    lt(esk8_1(esk5_0),esk6_1(esk5_0)),
    inference(sr,[status(thm)],[c_0_94,c_0_66]) ).

cnf(c_0_103,negated_conjecture,
    ( esk5_0 = nil
    | ssList(tl(esk5_0)) ),
    inference(spm,[status(thm)],[c_0_95,c_0_22]) ).

cnf(c_0_104,negated_conjecture,
    ( app(cons(X1,nil),X2) != esk5_0
    | ~ lt(esk8_1(esk5_0),X1)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_98]),c_0_99])]) ).

cnf(c_0_105,negated_conjecture,
    app(cons(hd(esk5_0),nil),tl(esk5_0)) = esk5_0,
    inference(rw,[status(thm)],[c_0_100,c_0_101]) ).

cnf(c_0_106,negated_conjecture,
    lt(esk8_1(esk5_0),hd(esk5_0)),
    inference(rw,[status(thm)],[c_0_102,c_0_82]) ).

cnf(c_0_107,negated_conjecture,
    ssList(tl(esk5_0)),
    inference(sr,[status(thm)],[c_0_103,c_0_84]) ).

cnf(c_0_108,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_106]),c_0_107]),c_0_93])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem    : SWC343+1 : TPTP v8.2.0. Released v2.4.0.
% 0.07/0.09  % Command    : run_E %s %d THM
% 0.07/0.28  % Computer : n029.cluster.edu
% 0.07/0.28  % Model    : x86_64 x86_64
% 0.07/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.28  % Memory   : 8042.1875MB
% 0.07/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.28  % CPULimit   : 300
% 0.07/0.28  % WCLimit    : 300
% 0.07/0.28  % DateTime   : Sun May 19 03:45:53 EDT 2024
% 0.07/0.28  % CPUTime    : 
% 0.13/0.38  Running first-order model finding
% 0.13/0.38  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.43  # Version: 3.1.0
% 0.13/0.43  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/0.43  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.43  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/0.43  # Starting new_bool_3 with 300s (1) cores
% 0.13/0.43  # Starting new_bool_1 with 300s (1) cores
% 0.13/0.43  # Starting sh5l with 300s (1) cores
% 0.13/0.43  # new_bool_1 with pid 22675 completed with status 0
% 0.13/0.43  # Result found by new_bool_1
% 0.13/0.43  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/0.43  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.43  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/0.43  # Starting new_bool_3 with 300s (1) cores
% 0.13/0.43  # Starting new_bool_1 with 300s (1) cores
% 0.13/0.43  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.43  # Search class: FGHSF-FFMM21-MFFFFFNN
% 0.13/0.43  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.43  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 0.13/0.43  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 22677 completed with status 0
% 0.13/0.43  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.13/0.43  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/0.43  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.43  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/0.43  # Starting new_bool_3 with 300s (1) cores
% 0.13/0.43  # Starting new_bool_1 with 300s (1) cores
% 0.13/0.43  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.43  # Search class: FGHSF-FFMM21-MFFFFFNN
% 0.13/0.43  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.43  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 0.13/0.43  # Preprocessing time       : 0.002 s
% 0.13/0.43  # Presaturation interreduction done
% 0.13/0.43  
% 0.13/0.43  # Proof found!
% 0.13/0.43  # SZS status Theorem
% 0.13/0.43  # SZS output start CNFRefutation
% See solution above
% 0.13/0.43  # Parsed axioms                        : 96
% 0.13/0.43  # Removed by relevancy pruning/SinE    : 56
% 0.13/0.43  # Initial clauses                      : 86
% 0.13/0.43  # Removed in clause preprocessing      : 1
% 0.13/0.43  # Initial clauses in saturation        : 85
% 0.13/0.43  # Processed clauses                    : 468
% 0.13/0.43  # ...of these trivial                  : 11
% 0.13/0.43  # ...subsumed                          : 115
% 0.13/0.43  # ...remaining for further processing  : 342
% 0.13/0.43  # Other redundant clauses eliminated   : 14
% 0.13/0.43  # Clauses deleted for lack of memory   : 0
% 0.13/0.43  # Backward-subsumed                    : 47
% 0.13/0.43  # Backward-rewritten                   : 15
% 0.13/0.43  # Generated clauses                    : 1431
% 0.13/0.43  # ...of the previous two non-redundant : 1329
% 0.13/0.43  # ...aggressively subsumed             : 0
% 0.13/0.43  # Contextual simplify-reflections      : 20
% 0.13/0.43  # Paramodulations                      : 1380
% 0.13/0.43  # Factorizations                       : 0
% 0.13/0.43  # NegExts                              : 0
% 0.13/0.43  # Equation resolutions                 : 18
% 0.13/0.43  # Disequality decompositions           : 0
% 0.13/0.43  # Total rewrite steps                  : 569
% 0.13/0.43  # ...of those cached                   : 539
% 0.13/0.43  # Propositional unsat checks           : 0
% 0.13/0.43  #    Propositional check models        : 0
% 0.13/0.43  #    Propositional check unsatisfiable : 0
% 0.13/0.43  #    Propositional clauses             : 0
% 0.13/0.43  #    Propositional clauses after purity: 0
% 0.13/0.43  #    Propositional unsat core size     : 0
% 0.13/0.43  #    Propositional preprocessing time  : 0.000
% 0.13/0.43  #    Propositional encoding time       : 0.000
% 0.13/0.43  #    Propositional solver time         : 0.000
% 0.13/0.43  #    Success case prop preproc time    : 0.000
% 0.13/0.43  #    Success case prop encoding time   : 0.000
% 0.13/0.43  #    Success case prop solver time     : 0.000
% 0.13/0.43  # Current number of processed clauses  : 162
% 0.13/0.43  #    Positive orientable unit clauses  : 40
% 0.13/0.43  #    Positive unorientable unit clauses: 0
% 0.13/0.43  #    Negative unit clauses             : 9
% 0.13/0.43  #    Non-unit-clauses                  : 113
% 0.13/0.43  # Current number of unprocessed clauses: 895
% 0.13/0.43  # ...number of literals in the above   : 3328
% 0.13/0.43  # Current number of archived formulas  : 0
% 0.13/0.43  # Current number of archived clauses   : 176
% 0.13/0.43  # Clause-clause subsumption calls (NU) : 5207
% 0.13/0.43  # Rec. Clause-clause subsumption calls : 2805
% 0.13/0.43  # Non-unit clause-clause subsumptions  : 138
% 0.13/0.43  # Unit Clause-clause subsumption calls : 891
% 0.13/0.43  # Rewrite failures with RHS unbound    : 0
% 0.13/0.43  # BW rewrite match attempts            : 7
% 0.13/0.43  # BW rewrite match successes           : 7
% 0.13/0.43  # Condensation attempts                : 0
% 0.13/0.43  # Condensation successes               : 0
% 0.13/0.43  # Termbank termtop insertions          : 27750
% 0.13/0.43  # Search garbage collected termcells   : 2211
% 0.13/0.43  
% 0.13/0.43  # -------------------------------------------------
% 0.13/0.43  # User time                : 0.038 s
% 0.13/0.43  # System time              : 0.002 s
% 0.13/0.43  # Total time               : 0.041 s
% 0.13/0.43  # Maximum resident set size: 2056 pages
% 0.13/0.43  
% 0.13/0.43  # -------------------------------------------------
% 0.13/0.43  # User time                : 0.041 s
% 0.13/0.43  # System time              : 0.004 s
% 0.13/0.43  # Total time               : 0.044 s
% 0.13/0.43  # Maximum resident set size: 1828 pages
% 0.13/0.43  % E---3.1 exiting
%------------------------------------------------------------------------------