TSTP Solution File: SWC239+1 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : SWC239+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n009.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 04:28:34 EDT 2024

% Result   : Theorem 1.25s 0.61s
% Output   : CNFRefutation 1.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   77 (  21 unt;   0 def)
%            Number of atoms       :  336 ( 104 equ)
%            Maximal formula atoms :   54 (   4 avg)
%            Number of connectives :  427 ( 168   ~; 171   |;  45   &)
%                                         (   4 <=>;  39  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   29 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-3 aty)
%            Number of variables   :  124 (   0 sgn  65   !;   9   ?)

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

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(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(ax43,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( frontsegP(X1,X2)
               => frontsegP(app(X1,X3),X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax43) ).

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

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

fof(ax84,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(X1,nil) = X1 ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax82) ).

fof(ax5,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( frontsegP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & app(X2,X3) = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax5) ).

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(ax80,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( app(X2,X3) = app(X2,X1)
               => X3 = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax80) ).

fof(ax42,axiom,
    ! [X1] :
      ( ssList(X1)
     => frontsegP(X1,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax42) ).

fof(ax93,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ( lt(X1,X2)
          <=> ( X1 != X2
              & leq(X1,X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax93) ).

fof(c_0_13,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | nil = X1
                      | ? [X5] :
                          ( ssItem(X5)
                          & ? [X6] :
                              ( ssList(X6)
                              & ? [X7] :
                                  ( ssList(X7)
                                  & app(app(X6,cons(X5,nil)),X7) = X1
                                  & ! [X8] :
                                      ( ssItem(X8)
                                     => ( ~ memberP(X6,X8)
                                        | ~ memberP(X7,X8)
                                        | ~ lt(X5,X8)
                                        | leq(X5,X8) ) ) ) ) )
                      | ( ! [X9] :
                            ( ssItem(X9)
                           => ( cons(X9,nil) != X3
                              | ~ memberP(X4,X9)
                              | ? [X10] :
                                  ( ssItem(X10)
                                  & X9 != X10
                                  & memberP(X4,X10)
                                  & leq(X9,X10) ) ) )
                        & ( nil != X4
                          | nil != X3 ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).

fof(c_0_14,negated_conjecture,
    ! [X259,X260,X261,X264] :
      ( ssList(esk48_0)
      & ssList(esk49_0)
      & ssList(esk50_0)
      & ssList(esk51_0)
      & esk49_0 = esk51_0
      & esk48_0 = esk50_0
      & nil != esk48_0
      & ( ssItem(esk52_3(X259,X260,X261))
        | ~ ssList(X261)
        | app(app(X260,cons(X259,nil)),X261) != esk48_0
        | ~ ssList(X260)
        | ~ ssItem(X259) )
      & ( memberP(X260,esk52_3(X259,X260,X261))
        | ~ ssList(X261)
        | app(app(X260,cons(X259,nil)),X261) != esk48_0
        | ~ ssList(X260)
        | ~ ssItem(X259) )
      & ( memberP(X261,esk52_3(X259,X260,X261))
        | ~ ssList(X261)
        | app(app(X260,cons(X259,nil)),X261) != esk48_0
        | ~ ssList(X260)
        | ~ ssItem(X259) )
      & ( lt(X259,esk52_3(X259,X260,X261))
        | ~ ssList(X261)
        | app(app(X260,cons(X259,nil)),X261) != esk48_0
        | ~ ssList(X260)
        | ~ ssItem(X259) )
      & ( ~ leq(X259,esk52_3(X259,X260,X261))
        | ~ ssList(X261)
        | app(app(X260,cons(X259,nil)),X261) != esk48_0
        | ~ ssList(X260)
        | ~ ssItem(X259) )
      & ( nil = esk51_0
        | ssItem(esk53_0) )
      & ( nil = esk50_0
        | ssItem(esk53_0) )
      & ( nil = esk51_0
        | cons(esk53_0,nil) = esk50_0 )
      & ( nil = esk50_0
        | cons(esk53_0,nil) = esk50_0 )
      & ( nil = esk51_0
        | memberP(esk51_0,esk53_0) )
      & ( nil = esk50_0
        | memberP(esk51_0,esk53_0) )
      & ( nil = esk51_0
        | ~ ssItem(X264)
        | esk53_0 = X264
        | ~ memberP(esk51_0,X264)
        | ~ leq(esk53_0,X264) )
      & ( nil = esk50_0
        | ~ ssItem(X264)
        | esk53_0 = X264
        | ~ memberP(esk51_0,X264)
        | ~ leq(esk53_0,X264) ) ),
    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_13])])])])])]) ).

fof(c_0_15,plain,
    ! [X136,X137,X138] :
      ( ~ ssList(X136)
      | ~ ssList(X137)
      | ~ ssItem(X138)
      | cons(X138,app(X137,X136)) = app(cons(X138,X137),X136) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])])]) ).

cnf(c_0_16,negated_conjecture,
    ( nil = esk50_0
    | cons(esk53_0,nil) = esk50_0 ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_17,negated_conjecture,
    esk48_0 = esk50_0,
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_18,negated_conjecture,
    nil != esk48_0,
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_19,negated_conjecture,
    ( nil = esk50_0
    | ssItem(esk53_0) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_20,plain,
    ! [X229,X230] :
      ( ( nil = X230
        | nil != app(X229,X230)
        | ~ ssList(X230)
        | ~ ssList(X229) )
      & ( nil = X229
        | nil != app(X229,X230)
        | ~ ssList(X230)
        | ~ ssList(X229) )
      & ( nil != X230
        | nil != X229
        | nil = app(X229,X230)
        | ~ ssList(X230)
        | ~ ssList(X229) ) ),
    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])])])])]) ).

fof(c_0_21,plain,
    ! [X168,X169,X170] :
      ( ~ ssList(X168)
      | ~ ssList(X169)
      | ~ ssList(X170)
      | ~ frontsegP(X168,X169)
      | frontsegP(app(X168,X170),X169) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])])]) ).

fof(c_0_22,plain,
    ! [X175] :
      ( ~ ssList(X175)
      | frontsegP(X175,nil) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])])]) ).

cnf(c_0_23,plain,
    ( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssItem(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_24,negated_conjecture,
    cons(esk53_0,nil) = esk48_0,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_17]),c_0_18]) ).

cnf(c_0_25,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[ax17]) ).

cnf(c_0_26,negated_conjecture,
    ssItem(esk53_0),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_17]),c_0_18]) ).

fof(c_0_27,plain,
    ! [X231] :
      ( ~ ssList(X231)
      | app(X231,nil) = X231 ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).

cnf(c_0_28,plain,
    ( nil = app(X2,X1)
    | nil != X1
    | nil != X2
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_29,plain,
    ( frontsegP(app(X1,X3),X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ frontsegP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_30,plain,
    ( frontsegP(X1,nil)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_31,negated_conjecture,
    ( cons(esk53_0,app(nil,X1)) = app(esk48_0,X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26])]) ).

cnf(c_0_32,plain,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

fof(c_0_33,plain,
    ! [X226,X227,X228] :
      ( ~ ssList(X226)
      | ~ ssList(X227)
      | ~ ssList(X228)
      | app(app(X226,X227),X228) = app(X226,app(X227,X228)) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).

cnf(c_0_34,plain,
    ( app(nil,X1) = nil
    | nil != X1
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_28]),c_0_25])]) ).

fof(c_0_35,plain,
    ! [X24,X25,X27] :
      ( ( ssList(esk6_2(X24,X25))
        | ~ frontsegP(X24,X25)
        | ~ ssList(X25)
        | ~ ssList(X24) )
      & ( app(X25,esk6_2(X24,X25)) = X24
        | ~ frontsegP(X24,X25)
        | ~ ssList(X25)
        | ~ ssList(X24) )
      & ( ~ ssList(X27)
        | app(X25,X27) != X24
        | frontsegP(X24,X25)
        | ~ ssList(X25)
        | ~ ssList(X24) ) ),
    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)],[ax5])])])])])]) ).

cnf(c_0_36,plain,
    ( frontsegP(app(X1,X2),nil)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_25])]) ).

cnf(c_0_37,negated_conjecture,
    app(esk48_0,nil) = esk48_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_24]),c_0_25])]) ).

cnf(c_0_38,negated_conjecture,
    ssList(esk48_0),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_39,plain,
    ( app(app(X1,X2),X3) = app(X1,app(X2,X3))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_40,plain,
    app(nil,nil) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_34]),c_0_25])]) ).

cnf(c_0_41,plain,
    ( app(X1,esk6_2(X2,X1)) = X2
    | ~ frontsegP(X2,X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_42,negated_conjecture,
    frontsegP(esk48_0,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_25]),c_0_38])]) ).

cnf(c_0_43,plain,
    ( ssList(esk6_2(X1,X2))
    | ~ frontsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_44,plain,
    ( app(nil,app(nil,X1)) = app(nil,X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_25])]) ).

cnf(c_0_45,negated_conjecture,
    app(nil,esk6_2(esk48_0,nil)) = esk48_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_38]),c_0_25])]) ).

cnf(c_0_46,negated_conjecture,
    ssList(esk6_2(esk48_0,nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_42]),c_0_25]),c_0_38])]) ).

fof(c_0_47,plain,
    ! [X224,X225] :
      ( ~ ssList(X224)
      | ~ ssItem(X225)
      | cons(X225,X224) = app(cons(X225,nil),X224) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).

cnf(c_0_48,plain,
    ( frontsegP(X3,X2)
    | ~ ssList(X1)
    | app(X2,X1) != X3
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_49,negated_conjecture,
    app(nil,esk48_0) = esk48_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46])]) ).

cnf(c_0_50,plain,
    ( cons(X2,X1) = app(cons(X2,nil),X1)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

fof(c_0_51,plain,
    ! [X221,X222,X223] :
      ( ~ ssList(X221)
      | ~ ssList(X222)
      | ~ ssList(X223)
      | app(X222,X223) != app(X222,X221)
      | X223 = X221 ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])])]) ).

cnf(c_0_52,negated_conjecture,
    ( frontsegP(X1,esk48_0)
    | esk48_0 != X1
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_37]),c_0_38]),c_0_25])]) ).

cnf(c_0_53,negated_conjecture,
    ( app(nil,app(esk48_0,X1)) = app(esk48_0,X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_49]),c_0_38]),c_0_25])]) ).

cnf(c_0_54,negated_conjecture,
    ( app(esk48_0,X1) = cons(esk53_0,X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_24]),c_0_26])]) ).

fof(c_0_55,plain,
    ! [X167] :
      ( ~ ssList(X167)
      | frontsegP(X167,X167) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax42])])]) ).

cnf(c_0_56,plain,
    ( X3 = X1
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | app(X2,X3) != app(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

cnf(c_0_57,negated_conjecture,
    frontsegP(esk48_0,esk48_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_52]),c_0_38])]) ).

fof(c_0_58,plain,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ( lt(X1,X2)
          <=> ( X1 != X2
              & leq(X1,X2) ) ) ) ),
    inference(fof_simplification,[status(thm)],[ax93]) ).

cnf(c_0_59,negated_conjecture,
    ( lt(X1,esk52_3(X1,X2,X3))
    | ~ ssList(X3)
    | app(app(X2,cons(X1,nil)),X3) != esk48_0
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_60,negated_conjecture,
    ( app(nil,cons(esk53_0,X1)) = cons(esk53_0,X1)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[c_0_53,c_0_54]) ).

cnf(c_0_61,plain,
    ( frontsegP(X1,X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_55]) ).

cnf(c_0_62,negated_conjecture,
    ( X1 = nil
    | app(esk48_0,X1) != esk48_0
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_37]),c_0_25]),c_0_38])]) ).

cnf(c_0_63,negated_conjecture,
    app(esk48_0,esk6_2(esk48_0,esk48_0)) = esk48_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_57]),c_0_38])]) ).

cnf(c_0_64,negated_conjecture,
    ssList(esk6_2(esk48_0,esk48_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_57]),c_0_38])]) ).

cnf(c_0_65,negated_conjecture,
    ( ssItem(esk52_3(X1,X2,X3))
    | ~ ssList(X3)
    | app(app(X2,cons(X1,nil)),X3) != esk48_0
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_66,plain,
    ! [X248,X249] :
      ( ( X248 != X249
        | ~ lt(X248,X249)
        | ~ ssItem(X249)
        | ~ ssItem(X248) )
      & ( leq(X248,X249)
        | ~ lt(X248,X249)
        | ~ ssItem(X249)
        | ~ ssItem(X248) )
      & ( X248 = X249
        | ~ leq(X248,X249)
        | lt(X248,X249)
        | ~ ssItem(X249)
        | ~ ssItem(X248) ) ),
    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_58])])])])]) ).

cnf(c_0_67,negated_conjecture,
    ( lt(esk53_0,esk52_3(esk53_0,nil,X1))
    | app(esk48_0,X1) != esk48_0
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_24]),c_0_25]),c_0_26])]) ).

cnf(c_0_68,plain,
    ( app(X1,esk6_2(X1,X1)) = X1
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[c_0_41,c_0_61]) ).

cnf(c_0_69,negated_conjecture,
    esk6_2(esk48_0,esk48_0) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64])]) ).

cnf(c_0_70,negated_conjecture,
    ( ssItem(esk52_3(esk53_0,nil,X1))
    | app(esk48_0,X1) != esk48_0
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_60]),c_0_24]),c_0_25]),c_0_26])]) ).

cnf(c_0_71,plain,
    ( leq(X1,X2)
    | ~ lt(X1,X2)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

cnf(c_0_72,negated_conjecture,
    lt(esk53_0,esk52_3(esk53_0,nil,nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]),c_0_69]),c_0_25]),c_0_38])]) ).

cnf(c_0_73,negated_conjecture,
    ssItem(esk52_3(esk53_0,nil,nil)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_68]),c_0_69]),c_0_69]),c_0_25]),c_0_38])]) ).

cnf(c_0_74,negated_conjecture,
    ( ~ leq(X1,esk52_3(X1,X2,X3))
    | ~ ssList(X3)
    | app(app(X2,cons(X1,nil)),X3) != esk48_0
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_75,negated_conjecture,
    leq(esk53_0,esk52_3(esk53_0,nil,nil)),
    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_26])]) ).

cnf(c_0_76,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_24]),c_0_49]),c_0_37]),c_0_25]),c_0_26])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SWC239+1 : TPTP v8.2.0. Released v2.4.0.
% 0.12/0.14  % Command    : run_E %s %d THM
% 0.13/0.35  % Computer : n009.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sun May 19 02:56:53 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.20/0.46  Running first-order model finding
% 0.20/0.46  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
% 1.25/0.61  # Version: 3.1.0
% 1.25/0.61  # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.25/0.61  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.25/0.61  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.25/0.61  # Starting new_bool_3 with 300s (1) cores
% 1.25/0.61  # Starting new_bool_1 with 300s (1) cores
% 1.25/0.61  # Starting sh5l with 300s (1) cores
% 1.25/0.61  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 16510 completed with status 0
% 1.25/0.61  # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.25/0.61  # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.25/0.61  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.25/0.61  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.25/0.61  # No SInE strategy applied
% 1.25/0.61  # Search class: FGHSF-FSLM31-MFFFFFNN
% 1.25/0.61  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.25/0.61  # Starting G-E--_110_C45_F1_PI_AE_Q4_CS_SP_PS_S4S with 811s (1) cores
% 1.25/0.61  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.25/0.61  # Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 1.25/0.61  # Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S070I with 136s (1) cores
% 1.25/0.61  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S2S with 136s (1) cores
% 1.25/0.61  # G-E--_110_C45_F1_PI_AE_Q4_CS_SP_PS_S4S with pid 16517 completed with status 0
% 1.25/0.61  # Result found by G-E--_110_C45_F1_PI_AE_Q4_CS_SP_PS_S4S
% 1.25/0.61  # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.25/0.61  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.25/0.61  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.25/0.61  # No SInE strategy applied
% 1.25/0.61  # Search class: FGHSF-FSLM31-MFFFFFNN
% 1.25/0.61  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.25/0.61  # Starting G-E--_110_C45_F1_PI_AE_Q4_CS_SP_PS_S4S with 811s (1) cores
% 1.25/0.61  # Preprocessing time       : 0.004 s
% 1.25/0.61  # Presaturation interreduction done
% 1.25/0.61  
% 1.25/0.61  # Proof found!
% 1.25/0.61  # SZS status Theorem
% 1.25/0.61  # SZS output start CNFRefutation
% See solution above
% 1.25/0.61  # Parsed axioms                        : 96
% 1.25/0.61  # Removed by relevancy pruning/SinE    : 0
% 1.25/0.61  # Initial clauses                      : 210
% 1.25/0.61  # Removed in clause preprocessing      : 2
% 1.25/0.61  # Initial clauses in saturation        : 208
% 1.25/0.61  # Processed clauses                    : 1094
% 1.25/0.61  # ...of these trivial                  : 16
% 1.25/0.61  # ...subsumed                          : 347
% 1.25/0.61  # ...remaining for further processing  : 731
% 1.25/0.61  # Other redundant clauses eliminated   : 83
% 1.25/0.61  # Clauses deleted for lack of memory   : 0
% 1.25/0.61  # Backward-subsumed                    : 10
% 1.25/0.61  # Backward-rewritten                   : 35
% 1.25/0.61  # Generated clauses                    : 3283
% 1.25/0.61  # ...of the previous two non-redundant : 2823
% 1.25/0.61  # ...aggressively subsumed             : 0
% 1.25/0.61  # Contextual simplify-reflections      : 86
% 1.25/0.61  # Paramodulations                      : 3126
% 1.25/0.61  # Factorizations                       : 0
% 1.25/0.61  # NegExts                              : 0
% 1.25/0.61  # Equation resolutions                 : 157
% 1.25/0.61  # Disequality decompositions           : 0
% 1.25/0.61  # Total rewrite steps                  : 3013
% 1.25/0.61  # ...of those cached                   : 2936
% 1.25/0.61  # Propositional unsat checks           : 0
% 1.25/0.61  #    Propositional check models        : 0
% 1.25/0.61  #    Propositional check unsatisfiable : 0
% 1.25/0.61  #    Propositional clauses             : 0
% 1.25/0.61  #    Propositional clauses after purity: 0
% 1.25/0.61  #    Propositional unsat core size     : 0
% 1.25/0.61  #    Propositional preprocessing time  : 0.000
% 1.25/0.61  #    Propositional encoding time       : 0.000
% 1.25/0.61  #    Propositional solver time         : 0.000
% 1.25/0.61  #    Success case prop preproc time    : 0.000
% 1.25/0.61  #    Success case prop encoding time   : 0.000
% 1.25/0.61  #    Success case prop solver time     : 0.000
% 1.25/0.61  # Current number of processed clauses  : 480
% 1.25/0.61  #    Positive orientable unit clauses  : 93
% 1.25/0.61  #    Positive unorientable unit clauses: 0
% 1.25/0.61  #    Negative unit clauses             : 20
% 1.25/0.61  #    Non-unit-clauses                  : 367
% 1.25/0.61  # Current number of unprocessed clauses: 2051
% 1.25/0.61  # ...number of literals in the above   : 12464
% 1.25/0.61  # Current number of archived formulas  : 0
% 1.25/0.61  # Current number of archived clauses   : 245
% 1.25/0.61  # Clause-clause subsumption calls (NU) : 34317
% 1.25/0.61  # Rec. Clause-clause subsumption calls : 7245
% 1.25/0.61  # Non-unit clause-clause subsumptions  : 324
% 1.25/0.61  # Unit Clause-clause subsumption calls : 669
% 1.25/0.61  # Rewrite failures with RHS unbound    : 0
% 1.25/0.61  # BW rewrite match attempts            : 31
% 1.25/0.61  # BW rewrite match successes           : 19
% 1.25/0.61  # Condensation attempts                : 0
% 1.25/0.61  # Condensation successes               : 0
% 1.25/0.61  # Termbank termtop insertions          : 80701
% 1.25/0.61  # Search garbage collected termcells   : 4483
% 1.25/0.61  
% 1.25/0.61  # -------------------------------------------------
% 1.25/0.61  # User time                : 0.120 s
% 1.25/0.61  # System time              : 0.014 s
% 1.25/0.61  # Total time               : 0.135 s
% 1.25/0.61  # Maximum resident set size: 2536 pages
% 1.25/0.61  
% 1.25/0.61  # -------------------------------------------------
% 1.25/0.61  # User time                : 0.580 s
% 1.25/0.61  # System time              : 0.042 s
% 1.25/0.61  # Total time               : 0.622 s
% 1.25/0.61  # Maximum resident set size: 1824 pages
% 1.25/0.61  % E---3.1 exiting
%------------------------------------------------------------------------------