TSTP Solution File: SWC409+1 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : SWC409+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n015.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 04:29:34 EDT 2024

% Result   : Theorem 13.57s 2.23s
% Output   : CNFRefutation 13.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   16
% Syntax   : Number of formulae    :  106 (  23 unt;   0 def)
%            Number of atoms       :  403 ( 126 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  497 ( 200   ~; 216   |;  34   &)
%                                         (   4 <=>;  43  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   6 con; 0-2 aty)
%            Number of variables   :  164 (   0 sgn  76   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(ax84,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(X1,nil) = X1 ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).

fof(ax82,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax82) ).

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

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

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

fof(ax79,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( app(X3,X2) = app(X1,X2)
               => X3 = X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax79) ).

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

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

fof(ax80,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( app(X2,X3) = app(X2,X1)
               => X3 = X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax80) ).

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

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/sandbox/benchmark/Axioms/SWC001+0.ax',ax27) ).

fof(ax36,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( memberP(app(X2,X3),X1)
              <=> ( memberP(X2,X1)
                  | memberP(X3,X1) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax36) ).

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(ax3,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ( memberP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & ? [X4] :
                    ( ssList(X4)
                    & app(X3,cons(X2,X4)) = X1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax3) ).

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(ax37,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( memberP(cons(X2,X3),X1)
              <=> ( X1 = X2
                  | memberP(X3,X1) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax37) ).

fof(c_0_16,plain,
    ! [X54] :
      ( ~ ssList(X54)
      | app(X54,nil) = X54 ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).

fof(c_0_17,plain,
    ! [X49,X50,X51] :
      ( ~ ssList(X49)
      | ~ ssList(X50)
      | ~ ssList(X51)
      | app(app(X49,X50),X51) = app(X49,app(X50,X51)) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).

fof(c_0_18,plain,
    ! [X35,X36] :
      ( ~ ssList(X35)
      | ~ ssList(X36)
      | ssList(app(X35,X36)) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).

fof(c_0_19,plain,
    ! [X40] :
      ( ~ ssList(X40)
      | app(nil,X40) = X40 ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).

cnf(c_0_20,plain,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_21,plain,
    ( app(app(X1,X2),X3) = app(X1,app(X2,X3))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_22,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[ax17]) ).

cnf(c_0_23,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_24,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

fof(c_0_25,plain,
    ! [X41,X42,X43] :
      ( ~ ssList(X41)
      | ~ ssList(X42)
      | ~ ssList(X43)
      | app(X43,X42) != app(X41,X42)
      | X43 = X41 ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])])]) ).

cnf(c_0_26,plain,
    ( app(X1,app(X2,nil)) = app(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]),c_0_23]) ).

cnf(c_0_27,plain,
    ( app(nil,app(X1,X2)) = app(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_24]),c_0_22])]) ).

fof(c_0_28,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ? [X5] :
                          ( ssItem(X5)
                          & ? [X6] :
                              ( ssList(X6)
                              & app(X6,cons(X5,nil)) != X3
                              & app(cons(X5,nil),X6) = X4 ) )
                      | ! [X7] :
                          ( ssItem(X7)
                         => ( ~ memberP(X2,X7)
                            | memberP(X1,X7) ) )
                      | ( nil != X3
                        & nil = X4 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).

cnf(c_0_29,plain,
    ( X3 = X1
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | app(X3,X2) != app(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_30,plain,
    ( app(X1,nil) = app(nil,X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_22])]) ).

fof(c_0_31,negated_conjecture,
    ! [X12,X13] :
      ( ssList(esk1_0)
      & ssList(esk2_0)
      & ssList(esk3_0)
      & ssList(esk4_0)
      & esk2_0 = esk4_0
      & esk1_0 = esk3_0
      & ( ~ ssItem(X12)
        | ~ ssList(X13)
        | app(X13,cons(X12,nil)) = esk3_0
        | app(cons(X12,nil),X13) != esk4_0 )
      & ssItem(esk5_0)
      & memberP(esk2_0,esk5_0)
      & ~ memberP(esk1_0,esk5_0)
      & ( nil = esk3_0
        | nil != esk4_0 ) ),
    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_28])])])])]) ).

cnf(c_0_32,plain,
    ( X1 = app(X2,X3)
    | app(X1,X4) != app(X2,app(X3,X4))
    | ~ ssList(X4)
    | ~ ssList(X1)
    | ~ ssList(X3)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_21]),c_0_23]) ).

cnf(c_0_33,plain,
    ( app(nil,app(X1,nil)) = app(X1,nil)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_30]),c_0_22])]) ).

cnf(c_0_34,negated_conjecture,
    ssList(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_35,negated_conjecture,
    esk1_0 = esk3_0,
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_36,plain,
    ( X1 = app(nil,X2)
    | app(X1,nil) != app(X2,nil)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_22])]) ).

cnf(c_0_37,negated_conjecture,
    ssList(esk3_0),
    inference(rw,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_38,negated_conjecture,
    ( app(nil,X1) = esk3_0
    | app(esk3_0,nil) != app(X1,nil)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

fof(c_0_39,plain,
    ! [X52,X53] :
      ( ( nil = X53
        | nil != app(X52,X53)
        | ~ ssList(X53)
        | ~ ssList(X52) )
      & ( nil = X52
        | nil != app(X52,X53)
        | ~ ssList(X53)
        | ~ ssList(X52) )
      & ( nil != X53
        | nil != X52
        | nil = app(X52,X53)
        | ~ ssList(X53)
        | ~ ssList(X52) ) ),
    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_40,negated_conjecture,
    ( app(nil,app(esk3_0,nil)) = esk3_0
    | ~ ssList(app(esk3_0,nil)) ),
    inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_20])]) ).

fof(c_0_41,plain,
    ! [X44,X45,X46] :
      ( ~ ssList(X44)
      | ~ ssList(X45)
      | ~ ssList(X46)
      | app(X45,X46) != app(X45,X44)
      | X46 = X44 ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])])]) ).

cnf(c_0_42,plain,
    ( nil = app(X2,X1)
    | nil != X1
    | nil != X2
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_43,negated_conjecture,
    ssList(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_44,negated_conjecture,
    esk2_0 = esk4_0,
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_45,negated_conjecture,
    ( app(esk3_0,nil) = esk3_0
    | ~ ssList(app(esk3_0,nil)) ),
    inference(spm,[status(thm)],[c_0_24,c_0_40]) ).

cnf(c_0_46,plain,
    ( X3 = X1
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | app(X2,X3) != app(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_47,plain,
    app(nil,nil) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_42])]),c_0_22])]) ).

cnf(c_0_48,plain,
    ( ssList(app(X1,app(X2,X3)))
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_21]),c_0_23]) ).

cnf(c_0_49,negated_conjecture,
    ssList(esk4_0),
    inference(rw,[status(thm)],[c_0_43,c_0_44]) ).

cnf(c_0_50,negated_conjecture,
    app(esk3_0,nil) = esk3_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_23]),c_0_22]),c_0_37])]) ).

cnf(c_0_51,plain,
    ( X1 = nil
    | app(nil,X1) != nil
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_22])]) ).

cnf(c_0_52,plain,
    ( ssList(app(X1,nil))
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_47]),c_0_22])]) ).

cnf(c_0_53,negated_conjecture,
    ( app(nil,X1) = esk4_0
    | app(esk4_0,nil) != app(X1,nil)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[c_0_36,c_0_49]) ).

cnf(c_0_54,negated_conjecture,
    ( app(esk3_0,app(nil,X1)) = app(esk3_0,X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_50]),c_0_22]),c_0_37])]) ).

cnf(c_0_55,plain,
    ( app(X1,nil) = nil
    | app(nil,X1) != nil
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_26]),c_0_22])]),c_0_52]) ).

cnf(c_0_56,negated_conjecture,
    app(nil,esk4_0) = esk4_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_53]),c_0_49])]) ).

fof(c_0_57,plain,
    ! [X55,X56] :
      ( ~ ssList(X55)
      | ~ ssItem(X56)
      | ssList(cons(X56,X55)) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).

fof(c_0_58,plain,
    ! [X37,X38,X39] :
      ( ~ ssList(X37)
      | ~ ssList(X38)
      | ~ ssItem(X39)
      | cons(X39,app(X38,X37)) = app(cons(X39,X38),X37) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])])]) ).

fof(c_0_59,plain,
    ! [X26,X27,X28] :
      ( ( ~ memberP(app(X27,X28),X26)
        | memberP(X27,X26)
        | memberP(X28,X26)
        | ~ ssList(X28)
        | ~ ssList(X27)
        | ~ ssItem(X26) )
      & ( ~ memberP(X27,X26)
        | memberP(app(X27,X28),X26)
        | ~ ssList(X28)
        | ~ ssList(X27)
        | ~ ssItem(X26) )
      & ( ~ memberP(X28,X26)
        | memberP(app(X27,X28),X26)
        | ~ ssList(X28)
        | ~ ssList(X27)
        | ~ ssItem(X26) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])])])]) ).

cnf(c_0_60,negated_conjecture,
    ( app(esk3_0,app(X1,nil)) = app(esk3_0,X1)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[c_0_54,c_0_30]) ).

cnf(c_0_61,negated_conjecture,
    ( app(esk4_0,nil) = nil
    | esk4_0 != nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_49])]) ).

fof(c_0_62,plain,
    ! [X15] :
      ( ( ssList(esk6_1(X15))
        | nil = X15
        | ~ ssList(X15) )
      & ( ssItem(esk7_1(X15))
        | nil = X15
        | ~ ssList(X15) )
      & ( cons(esk7_1(X15),esk6_1(X15)) = X15
        | nil = X15
        | ~ ssList(X15) ) ),
    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_63,plain,
    ! [X20,X21,X24,X25] :
      ( ( ssList(esk8_2(X20,X21))
        | ~ memberP(X20,X21)
        | ~ ssItem(X21)
        | ~ ssList(X20) )
      & ( ssList(esk9_2(X20,X21))
        | ~ memberP(X20,X21)
        | ~ ssItem(X21)
        | ~ ssList(X20) )
      & ( app(esk8_2(X20,X21),cons(X21,esk9_2(X20,X21))) = X20
        | ~ memberP(X20,X21)
        | ~ ssItem(X21)
        | ~ ssList(X20) )
      & ( ~ ssList(X24)
        | ~ ssList(X25)
        | app(X24,cons(X21,X25)) != X20
        | memberP(X20,X21)
        | ~ ssItem(X21)
        | ~ ssList(X20) ) ),
    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)],[ax3])])])])])]) ).

fof(c_0_64,plain,
    ! [X47,X48] :
      ( ~ ssList(X47)
      | ~ ssItem(X48)
      | cons(X48,X47) = app(cons(X48,nil),X47) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).

cnf(c_0_65,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

cnf(c_0_66,plain,
    ( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssItem(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_58]) ).

cnf(c_0_67,negated_conjecture,
    ~ memberP(esk1_0,esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_68,plain,
    ( memberP(app(X3,X1),X2)
    | ~ memberP(X1,X2)
    | ~ ssList(X1)
    | ~ ssList(X3)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_59]) ).

cnf(c_0_69,negated_conjecture,
    ( app(esk3_0,esk4_0) = esk3_0
    | esk4_0 != nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_50]),c_0_49])]) ).

cnf(c_0_70,negated_conjecture,
    memberP(esk2_0,esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

fof(c_0_71,plain,
    ! [X29,X30,X31] :
      ( ( ~ memberP(cons(X30,X31),X29)
        | X29 = X30
        | memberP(X31,X29)
        | ~ ssList(X31)
        | ~ ssItem(X30)
        | ~ ssItem(X29) )
      & ( X29 != X30
        | memberP(cons(X30,X31),X29)
        | ~ ssList(X31)
        | ~ ssItem(X30)
        | ~ ssItem(X29) )
      & ( ~ memberP(X31,X29)
        | memberP(cons(X30,X31),X29)
        | ~ ssList(X31)
        | ~ ssItem(X30)
        | ~ ssItem(X29) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])])]) ).

cnf(c_0_72,plain,
    ( cons(esk7_1(X1),esk6_1(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_73,plain,
    ( ssItem(esk7_1(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_74,plain,
    ( ssList(esk6_1(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_75,plain,
    ( memberP(X4,X3)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | app(X1,cons(X3,X2)) != X4
    | ~ ssItem(X3)
    | ~ ssList(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_63]) ).

cnf(c_0_76,negated_conjecture,
    ( app(X2,cons(X1,nil)) = esk3_0
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | app(cons(X1,nil),X2) != esk4_0 ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_77,plain,
    ( cons(X2,X1) = app(cons(X2,nil),X1)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_64]) ).

cnf(c_0_78,plain,
    ( ssList(app(cons(X1,X2),X3))
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_23]) ).

cnf(c_0_79,plain,
    ( app(cons(X1,nil),nil) = cons(X1,nil)
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_47]),c_0_22])]) ).

cnf(c_0_80,negated_conjecture,
    ~ memberP(esk3_0,esk5_0),
    inference(rw,[status(thm)],[c_0_67,c_0_35]) ).

cnf(c_0_81,negated_conjecture,
    ( memberP(esk3_0,X1)
    | esk4_0 != nil
    | ~ memberP(esk4_0,X1)
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_37]),c_0_49])]) ).

cnf(c_0_82,negated_conjecture,
    memberP(esk4_0,esk5_0),
    inference(rw,[status(thm)],[c_0_70,c_0_44]) ).

cnf(c_0_83,negated_conjecture,
    ssItem(esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_84,plain,
    ( X3 = X1
    | memberP(X2,X3)
    | ~ memberP(cons(X1,X2),X3)
    | ~ ssList(X2)
    | ~ ssItem(X1)
    | ~ ssItem(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_71]) ).

cnf(c_0_85,negated_conjecture,
    ( cons(esk7_1(esk4_0),esk6_1(esk4_0)) = esk4_0
    | esk4_0 = nil ),
    inference(spm,[status(thm)],[c_0_72,c_0_49]) ).

cnf(c_0_86,negated_conjecture,
    ( esk4_0 = nil
    | ssItem(esk7_1(esk4_0)) ),
    inference(spm,[status(thm)],[c_0_73,c_0_49]) ).

cnf(c_0_87,negated_conjecture,
    ( esk4_0 = nil
    | ssList(esk6_1(esk4_0)) ),
    inference(spm,[status(thm)],[c_0_74,c_0_49]) ).

cnf(c_0_88,plain,
    ( memberP(app(X1,cons(X2,X3)),X2)
    | ~ ssList(app(X1,cons(X2,X3)))
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(er,[status(thm)],[c_0_75]) ).

cnf(c_0_89,negated_conjecture,
    ( app(X1,cons(X2,nil)) = esk3_0
    | cons(X2,X1) != esk4_0
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(spm,[status(thm)],[c_0_76,c_0_77]) ).

cnf(c_0_90,plain,
    ( memberP(app(X1,X3),X2)
    | ~ memberP(X1,X2)
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_59]) ).

cnf(c_0_91,plain,
    ( ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_22])]) ).

cnf(c_0_92,negated_conjecture,
    esk4_0 != nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]),c_0_83])]) ).

cnf(c_0_93,negated_conjecture,
    ( esk7_1(esk4_0) = X1
    | esk4_0 = nil
    | memberP(esk6_1(esk4_0),X1)
    | ~ memberP(esk4_0,X1)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86]),c_0_87]) ).

cnf(c_0_94,negated_conjecture,
    ( memberP(esk3_0,X1)
    | cons(X1,X2) != esk4_0
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_37]),c_0_22])]) ).

cnf(c_0_95,negated_conjecture,
    ( memberP(esk3_0,X1)
    | cons(X2,X3) != esk4_0
    | ~ memberP(X3,X1)
    | ~ ssList(X3)
    | ~ ssItem(X1)
    | ~ ssItem(X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_89]),c_0_91]) ).

cnf(c_0_96,negated_conjecture,
    cons(esk7_1(esk4_0),esk6_1(esk4_0)) = esk4_0,
    inference(sr,[status(thm)],[c_0_85,c_0_92]) ).

cnf(c_0_97,negated_conjecture,
    ssList(esk6_1(esk4_0)),
    inference(sr,[status(thm)],[c_0_87,c_0_92]) ).

cnf(c_0_98,negated_conjecture,
    ssItem(esk7_1(esk4_0)),
    inference(sr,[status(thm)],[c_0_86,c_0_92]) ).

cnf(c_0_99,negated_conjecture,
    ( esk7_1(esk4_0) = esk5_0
    | esk4_0 = nil
    | memberP(esk6_1(esk4_0),esk5_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_82]),c_0_83])]) ).

cnf(c_0_100,negated_conjecture,
    ( esk4_0 = nil
    | memberP(esk3_0,esk7_1(esk4_0)) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_85]),c_0_86]),c_0_87]) ).

cnf(c_0_101,negated_conjecture,
    ( memberP(esk3_0,X1)
    | ~ memberP(esk6_1(esk4_0),X1)
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97]),c_0_98])]) ).

cnf(c_0_102,negated_conjecture,
    ( esk7_1(esk4_0) = esk5_0
    | memberP(esk6_1(esk4_0),esk5_0) ),
    inference(sr,[status(thm)],[c_0_99,c_0_92]) ).

cnf(c_0_103,negated_conjecture,
    memberP(esk3_0,esk7_1(esk4_0)),
    inference(sr,[status(thm)],[c_0_100,c_0_92]) ).

cnf(c_0_104,negated_conjecture,
    esk7_1(esk4_0) = esk5_0,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_83])]),c_0_80]) ).

cnf(c_0_105,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_104]),c_0_80]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem    : SWC409+1 : TPTP v8.2.0. Released v2.4.0.
% 0.08/0.14  % Command    : run_E %s %d THM
% 0.14/0.35  % Computer : n015.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 03:26:08 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.20/0.48  Running first-order model finding
% 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 --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.57/2.23  # Version: 3.1.0
% 13.57/2.23  # Preprocessing class: FSLSSMSSSSSNFFN.
% 13.57/2.23  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.57/2.23  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 13.57/2.23  # Starting new_bool_3 with 300s (1) cores
% 13.57/2.23  # Starting new_bool_1 with 300s (1) cores
% 13.57/2.23  # Starting sh5l with 300s (1) cores
% 13.57/2.23  # new_bool_1 with pid 27370 completed with status 0
% 13.57/2.23  # Result found by new_bool_1
% 13.57/2.23  # Preprocessing class: FSLSSMSSSSSNFFN.
% 13.57/2.23  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.57/2.23  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 13.57/2.23  # Starting new_bool_3 with 300s (1) cores
% 13.57/2.23  # Starting new_bool_1 with 300s (1) cores
% 13.57/2.23  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 13.57/2.23  # Search class: FGHSF-FFMM21-MFFFFFNN
% 13.57/2.23  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 13.57/2.23  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 13.57/2.23  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 27373 completed with status 0
% 13.57/2.23  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 13.57/2.23  # Preprocessing class: FSLSSMSSSSSNFFN.
% 13.57/2.23  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.57/2.23  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 13.57/2.23  # Starting new_bool_3 with 300s (1) cores
% 13.57/2.23  # Starting new_bool_1 with 300s (1) cores
% 13.57/2.23  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 13.57/2.23  # Search class: FGHSF-FFMM21-MFFFFFNN
% 13.57/2.23  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 13.57/2.23  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 13.57/2.23  # Preprocessing time       : 0.002 s
% 13.57/2.23  # Presaturation interreduction done
% 13.57/2.23  
% 13.57/2.23  # Proof found!
% 13.57/2.23  # SZS status Theorem
% 13.57/2.23  # SZS output start CNFRefutation
% See solution above
% 13.57/2.23  # Parsed axioms                        : 96
% 13.57/2.23  # Removed by relevancy pruning/SinE    : 75
% 13.57/2.23  # Initial clauses                      : 45
% 13.57/2.23  # Removed in clause preprocessing      : 0
% 13.57/2.23  # Initial clauses in saturation        : 45
% 13.57/2.23  # Processed clauses                    : 6403
% 13.57/2.23  # ...of these trivial                  : 592
% 13.57/2.23  # ...subsumed                          : 3521
% 13.57/2.23  # ...remaining for further processing  : 2290
% 13.57/2.23  # Other redundant clauses eliminated   : 45
% 13.57/2.23  # Clauses deleted for lack of memory   : 0
% 13.57/2.23  # Backward-subsumed                    : 148
% 13.57/2.23  # Backward-rewritten                   : 107
% 13.57/2.23  # Generated clauses                    : 163511
% 13.57/2.23  # ...of the previous two non-redundant : 159330
% 13.57/2.23  # ...aggressively subsumed             : 0
% 13.57/2.23  # Contextual simplify-reflections      : 458
% 13.57/2.23  # Paramodulations                      : 163130
% 13.57/2.23  # Factorizations                       : 0
% 13.57/2.23  # NegExts                              : 0
% 13.57/2.23  # Equation resolutions                 : 76
% 13.57/2.23  # Disequality decompositions           : 0
% 13.57/2.23  # Total rewrite steps                  : 32198
% 13.57/2.23  # ...of those cached                   : 31767
% 13.57/2.23  # Propositional unsat checks           : 0
% 13.57/2.23  #    Propositional check models        : 0
% 13.57/2.23  #    Propositional check unsatisfiable : 0
% 13.57/2.23  #    Propositional clauses             : 0
% 13.57/2.23  #    Propositional clauses after purity: 0
% 13.57/2.23  #    Propositional unsat core size     : 0
% 13.57/2.23  #    Propositional preprocessing time  : 0.000
% 13.57/2.23  #    Propositional encoding time       : 0.000
% 13.57/2.23  #    Propositional solver time         : 0.000
% 13.57/2.23  #    Success case prop preproc time    : 0.000
% 13.57/2.23  #    Success case prop encoding time   : 0.000
% 13.57/2.23  #    Success case prop solver time     : 0.000
% 13.57/2.23  # Current number of processed clauses  : 1683
% 13.57/2.23  #    Positive orientable unit clauses  : 672
% 13.57/2.23  #    Positive unorientable unit clauses: 0
% 13.57/2.23  #    Negative unit clauses             : 34
% 13.57/2.23  #    Non-unit-clauses                  : 977
% 13.57/2.23  # Current number of unprocessed clauses: 151818
% 13.57/2.23  # ...number of literals in the above   : 523058
% 13.57/2.23  # Current number of archived formulas  : 0
% 13.57/2.23  # Current number of archived clauses   : 604
% 13.57/2.23  # Clause-clause subsumption calls (NU) : 208851
% 13.57/2.23  # Rec. Clause-clause subsumption calls : 80305
% 13.57/2.23  # Non-unit clause-clause subsumptions  : 3742
% 13.57/2.23  # Unit Clause-clause subsumption calls : 13060
% 13.57/2.23  # Rewrite failures with RHS unbound    : 0
% 13.57/2.23  # BW rewrite match attempts            : 214740
% 13.57/2.23  # BW rewrite match successes           : 5
% 13.57/2.23  # Condensation attempts                : 0
% 13.57/2.23  # Condensation successes               : 0
% 13.57/2.23  # Termbank termtop insertions          : 5407966
% 13.57/2.23  # Search garbage collected termcells   : 1499
% 13.57/2.23  
% 13.57/2.23  # -------------------------------------------------
% 13.57/2.23  # User time                : 1.614 s
% 13.57/2.23  # System time              : 0.083 s
% 13.57/2.23  # Total time               : 1.698 s
% 13.57/2.23  # Maximum resident set size: 1896 pages
% 13.57/2.23  
% 13.57/2.23  # -------------------------------------------------
% 13.57/2.23  # User time                : 1.618 s
% 13.57/2.23  # System time              : 0.086 s
% 13.57/2.23  # Total time               : 1.703 s
% 13.57/2.23  # Maximum resident set size: 1820 pages
% 13.57/2.23  % E---3.1 exiting
%------------------------------------------------------------------------------