TSTP Solution File: SWC410+1 by Enigma---0.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Enigma---0.5.1
% Problem  : SWC410+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : enigmatic-eprover.py %s %d 1

% Computer : n032.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  : 600s
% DateTime : Tue Jul 19 20:15:31 EDT 2022

% Result   : Theorem 12.55s 2.87s
% Output   : CNFRefutation 12.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   32
%            Number of leaves      :   17
% Syntax   : Number of formulae    :  110 (  19 unt;   0 def)
%            Number of atoms       :  476 ( 152 equ)
%            Maximal formula atoms :   30 (   4 avg)
%            Number of connectives :  596 ( 230   ~; 266   |;  50   &)
%                                         (   5 <=>;  45  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   30 (   5 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   6 con; 0-2 aty)
%            Number of variables   :  141 (   0 sgn  72   !;   8   ?)

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

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

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

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

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

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

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

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

fof(ax86,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( nil != X1
           => tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax86) ).

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(ax85,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( nil != X1
           => hd(app(X1,X2)) = hd(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax85) ).

fof(ax13,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( duplicatefreeP(X1)
      <=> ! [X2] :
            ( ssItem(X2)
           => ! [X3] :
                ( ssItem(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ! [X5] :
                        ( ssList(X5)
                       => ! [X6] :
                            ( ssList(X6)
                           => ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
                             => X2 != X3 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax13) ).

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

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(ax72,axiom,
    duplicatefreeP(nil),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax72) ).

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(ax38,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ~ memberP(nil,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).

fof(c_0_17,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ! [X5] :
                          ( ssItem(X5)
                         => ( ~ memberP(X2,X5)
                            | memberP(X1,X5) ) )
                      | ( nil != X3
                        & nil = X4 )
                      | ( neq(X4,nil)
                        & ( ~ neq(X3,nil)
                          | ? [X6] :
                              ( ssList(X6)
                              & X4 != X6
                              & ? [X7] :
                                  ( ssList(X7)
                                  & ? [X8] :
                                      ( ssList(X8)
                                      & tl(X3) = X7
                                      & app(X7,X8) = X6
                                      & ? [X9] :
                                          ( ssItem(X9)
                                          & cons(X9,nil) = X8
                                          & hd(X3) = X9
                                          & neq(nil,X3) )
                                      & neq(nil,X3) ) ) ) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[co1]) ).

fof(c_0_18,negated_conjecture,
    ! [X259,X260,X261,X262] :
      ( ssList(esk48_0)
      & ssList(esk49_0)
      & ssList(esk50_0)
      & ssList(esk51_0)
      & esk49_0 = esk51_0
      & esk48_0 = esk50_0
      & ssItem(esk52_0)
      & memberP(esk49_0,esk52_0)
      & ~ memberP(esk48_0,esk52_0)
      & ( nil = esk50_0
        | nil != esk51_0 )
      & ( neq(esk50_0,nil)
        | ~ neq(esk51_0,nil) )
      & ( ~ ssList(X259)
        | esk51_0 = X259
        | ~ ssList(X260)
        | ~ ssList(X261)
        | tl(esk50_0) != X260
        | app(X260,X261) != X259
        | ~ ssItem(X262)
        | cons(X262,nil) != X261
        | hd(esk50_0) != X262
        | ~ neq(nil,esk50_0)
        | ~ neq(nil,esk50_0)
        | ~ neq(esk51_0,nil) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_17])])])])])]) ).

cnf(c_0_19,negated_conjecture,
    ( esk51_0 = X1
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | tl(esk50_0) != X2
    | app(X2,X3) != X1
    | ~ ssItem(X4)
    | cons(X4,nil) != X3
    | hd(esk50_0) != X4
    | ~ neq(nil,esk50_0)
    | ~ neq(nil,esk50_0)
    | ~ neq(esk51_0,nil) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

fof(c_0_20,plain,
    ! [X133,X134] :
      ( ~ ssList(X133)
      | ~ ssList(X134)
      | ssList(app(X133,X134)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).

cnf(c_0_21,negated_conjecture,
    ( esk51_0 = X1
    | hd(esk50_0) != X4
    | tl(esk50_0) != X2
    | app(X2,X3) != X1
    | cons(X4,nil) != X3
    | ~ ssItem(X4)
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ neq(nil,esk50_0)
    | ~ neq(esk51_0,nil) ),
    inference(cn,[status(thm)],[c_0_19]) ).

cnf(c_0_22,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

fof(c_0_23,plain,
    ! [X130] :
      ( ~ ssList(X130)
      | nil = X130
      | ssList(tl(X130)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).

cnf(c_0_24,negated_conjecture,
    ssList(esk48_0),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_25,negated_conjecture,
    esk48_0 = esk50_0,
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_26,negated_conjecture,
    ( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
    | ~ ssList(cons(hd(esk50_0),nil))
    | ~ ssList(tl(esk50_0))
    | ~ neq(nil,esk50_0)
    | ~ neq(esk51_0,nil)
    | ~ ssItem(hd(esk50_0)) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_21])])])]),c_0_22]) ).

cnf(c_0_27,plain,
    ( nil = X1
    | ssList(tl(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_28,negated_conjecture,
    ssList(esk50_0),
    inference(rw,[status(thm)],[c_0_24,c_0_25]) ).

fof(c_0_29,plain,
    ! [X112,X113] :
      ( ( ~ neq(X112,X113)
        | X112 != X113
        | ~ ssList(X113)
        | ~ ssList(X112) )
      & ( X112 = X113
        | neq(X112,X113)
        | ~ ssList(X113)
        | ~ ssList(X112) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).

cnf(c_0_30,negated_conjecture,
    ( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
    | esk50_0 = nil
    | ~ ssList(cons(hd(esk50_0),nil))
    | ~ neq(nil,esk50_0)
    | ~ neq(esk51_0,nil)
    | ~ ssItem(hd(esk50_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).

cnf(c_0_31,plain,
    ( X1 = X2
    | neq(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_32,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[ax17]) ).

cnf(c_0_33,negated_conjecture,
    ssList(esk49_0),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_34,negated_conjecture,
    esk49_0 = esk51_0,
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_35,negated_conjecture,
    ( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
    | esk50_0 = nil
    | ~ ssList(cons(hd(esk50_0),nil))
    | ~ neq(esk51_0,nil)
    | ~ ssItem(hd(esk50_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_28]),c_0_32])]) ).

cnf(c_0_36,negated_conjecture,
    ssList(esk51_0),
    inference(rw,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_37,negated_conjecture,
    ( nil = esk50_0
    | nil != esk51_0 ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

fof(c_0_38,plain,
    ! [X127] :
      ( ~ ssList(X127)
      | nil = X127
      | ssItem(hd(X127)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).

cnf(c_0_39,negated_conjecture,
    ( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
    | esk50_0 = nil
    | ~ ssList(cons(hd(esk50_0),nil))
    | ~ ssItem(hd(esk50_0)) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_31]),c_0_32]),c_0_36])]),c_0_37]) ).

cnf(c_0_40,plain,
    ( nil = X1
    | ssItem(hd(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

fof(c_0_41,plain,
    ! [X114,X115] :
      ( ~ ssList(X114)
      | ~ ssItem(X115)
      | ssList(cons(X115,X114)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).

fof(c_0_42,plain,
    ! [X216] :
      ( ~ ssList(X216)
      | nil = X216
      | cons(hd(X216),tl(X216)) = X216 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).

fof(c_0_43,plain,
    ! [X233,X234] :
      ( ~ ssList(X233)
      | ~ ssList(X234)
      | nil = X233
      | tl(app(X233,X234)) = app(tl(X233),X234) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax86])])]) ).

fof(c_0_44,plain,
    ! [X228,X229] :
      ( ( nil = X229
        | nil != app(X228,X229)
        | ~ ssList(X229)
        | ~ ssList(X228) )
      & ( nil = X228
        | nil != app(X228,X229)
        | ~ ssList(X229)
        | ~ ssList(X228) )
      & ( nil != X229
        | nil != X228
        | nil = app(X228,X229)
        | ~ ssList(X229)
        | ~ ssList(X228) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).

cnf(c_0_45,negated_conjecture,
    ( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
    | esk50_0 = nil
    | ~ ssList(cons(hd(esk50_0),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_28])]) ).

cnf(c_0_46,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_47,plain,
    ( nil = X1
    | cons(hd(X1),tl(X1)) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

cnf(c_0_48,plain,
    ( nil = X1
    | tl(app(X1,X2)) = app(tl(X1),X2)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_49,plain,
    ( nil = X1
    | nil != app(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_50,negated_conjecture,
    ( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
    | esk50_0 = nil
    | ~ ssItem(hd(esk50_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_32])]) ).

cnf(c_0_51,plain,
    ( cons(hd(app(X1,X2)),app(tl(X1),X2)) = app(X1,X2)
    | nil = X1
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_22]),c_0_49]) ).

cnf(c_0_52,negated_conjecture,
    ( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
    | esk50_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_40]),c_0_28])]) ).

cnf(c_0_53,negated_conjecture,
    ( cons(hd(app(esk50_0,cons(hd(esk50_0),nil))),esk51_0) = app(esk50_0,cons(hd(esk50_0),nil))
    | esk50_0 = nil
    | ~ ssList(cons(hd(esk50_0),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_28])]) ).

cnf(c_0_54,negated_conjecture,
    ( cons(hd(app(esk50_0,cons(hd(esk50_0),nil))),esk51_0) = app(esk50_0,cons(hd(esk50_0),nil))
    | esk50_0 = nil
    | ~ ssItem(hd(esk50_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_46]),c_0_32])]) ).

fof(c_0_55,plain,
    ! [X231,X232] :
      ( ~ ssList(X231)
      | ~ ssList(X232)
      | nil = X231
      | hd(app(X231,X232)) = hd(X231) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax85])])]) ).

cnf(c_0_56,negated_conjecture,
    ( cons(hd(app(esk50_0,cons(hd(esk50_0),nil))),esk51_0) = app(esk50_0,cons(hd(esk50_0),nil))
    | esk50_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_40]),c_0_28])]) ).

cnf(c_0_57,plain,
    ( nil = X1
    | hd(app(X1,X2)) = hd(X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_55]) ).

cnf(c_0_58,negated_conjecture,
    ( app(esk50_0,cons(hd(esk50_0),nil)) = cons(hd(esk50_0),esk51_0)
    | esk50_0 = nil
    | ~ ssList(cons(hd(esk50_0),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_28])]) ).

fof(c_0_59,plain,
    ! [X92,X93,X94,X95,X96,X97] :
      ( ( ~ duplicatefreeP(X92)
        | ~ ssItem(X93)
        | ~ ssItem(X94)
        | ~ ssList(X95)
        | ~ ssList(X96)
        | ~ ssList(X97)
        | app(app(X95,cons(X93,X96)),cons(X94,X97)) != X92
        | X93 != X94
        | ~ ssList(X92) )
      & ( ssItem(esk35_1(X92))
        | duplicatefreeP(X92)
        | ~ ssList(X92) )
      & ( ssItem(esk36_1(X92))
        | duplicatefreeP(X92)
        | ~ ssList(X92) )
      & ( ssList(esk37_1(X92))
        | duplicatefreeP(X92)
        | ~ ssList(X92) )
      & ( ssList(esk38_1(X92))
        | duplicatefreeP(X92)
        | ~ ssList(X92) )
      & ( ssList(esk39_1(X92))
        | duplicatefreeP(X92)
        | ~ ssList(X92) )
      & ( app(app(esk37_1(X92),cons(esk35_1(X92),esk38_1(X92))),cons(esk36_1(X92),esk39_1(X92))) = X92
        | duplicatefreeP(X92)
        | ~ ssList(X92) )
      & ( esk35_1(X92) = esk36_1(X92)
        | duplicatefreeP(X92)
        | ~ ssList(X92) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax13])])])])]) ).

cnf(c_0_60,negated_conjecture,
    ( app(esk50_0,cons(hd(esk50_0),nil)) = cons(hd(esk50_0),esk51_0)
    | esk50_0 = nil
    | ~ ssItem(hd(esk50_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_46]),c_0_32])]) ).

cnf(c_0_61,plain,
    ( ~ duplicatefreeP(X1)
    | ~ ssItem(X2)
    | ~ ssItem(X3)
    | ~ ssList(X4)
    | ~ ssList(X5)
    | ~ ssList(X6)
    | app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
    | X2 != X3
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_59]) ).

fof(c_0_62,plain,
    ! [X138] :
      ( ~ ssList(X138)
      | app(nil,X138) = X138 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).

cnf(c_0_63,negated_conjecture,
    ( app(esk50_0,cons(hd(esk50_0),nil)) = cons(hd(esk50_0),esk51_0)
    | esk50_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_40]),c_0_28])]) ).

cnf(c_0_64,plain,
    ( ~ duplicatefreeP(app(app(X1,cons(X2,X3)),cons(X2,X4)))
    | ~ ssList(app(app(X1,cons(X2,X3)),cons(X2,X4)))
    | ~ ssList(X4)
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_61])]) ).

cnf(c_0_65,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_66,negated_conjecture,
    ( esk50_0 = nil
    | ssList(cons(hd(esk50_0),esk51_0))
    | ~ ssList(cons(hd(esk50_0),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_63]),c_0_28])]) ).

cnf(c_0_67,negated_conjecture,
    ( hd(cons(hd(esk50_0),esk51_0)) = hd(esk50_0)
    | esk50_0 = nil
    | ~ ssList(cons(hd(esk50_0),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_63]),c_0_28])]) ).

fof(c_0_68,plain,
    ! [X157,X158,X159] :
      ( ( ~ memberP(cons(X158,X159),X157)
        | X157 = X158
        | memberP(X159,X157)
        | ~ ssList(X159)
        | ~ ssItem(X158)
        | ~ ssItem(X157) )
      & ( X157 != X158
        | memberP(cons(X158,X159),X157)
        | ~ ssList(X159)
        | ~ ssItem(X158)
        | ~ ssItem(X157) )
      & ( ~ memberP(X159,X157)
        | memberP(cons(X158,X159),X157)
        | ~ ssList(X159)
        | ~ ssItem(X158)
        | ~ ssItem(X157) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])]) ).

cnf(c_0_69,negated_conjecture,
    memberP(esk49_0,esk52_0),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_70,plain,
    ( ~ duplicatefreeP(app(cons(X1,X2),cons(X1,X3)))
    | ~ ssList(app(cons(X1,X2),cons(X1,X3)))
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_32])]),c_0_46]) ).

cnf(c_0_71,negated_conjecture,
    ( esk50_0 = nil
    | ssList(cons(hd(esk50_0),esk51_0))
    | ~ ssItem(hd(esk50_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_46]),c_0_32])]) ).

cnf(c_0_72,negated_conjecture,
    ( hd(cons(hd(esk50_0),esk51_0)) = hd(esk50_0)
    | esk50_0 = nil
    | ~ ssItem(hd(esk50_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_46]),c_0_32])]) ).

cnf(c_0_73,plain,
    ( memberP(cons(X3,X1),X2)
    | ~ memberP(X1,X2)
    | ~ ssList(X1)
    | ~ ssItem(X3)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_68]) ).

cnf(c_0_74,negated_conjecture,
    memberP(esk51_0,esk52_0),
    inference(rw,[status(thm)],[c_0_69,c_0_34]) ).

cnf(c_0_75,negated_conjecture,
    ssItem(esk52_0),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_76,plain,
    ( nil = X1
    | ~ duplicatefreeP(app(X1,cons(hd(X1),X2)))
    | ~ ssList(app(X1,cons(hd(X1),X2)))
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_47]),c_0_40]),c_0_27]) ).

cnf(c_0_77,negated_conjecture,
    ( esk50_0 = nil
    | ssList(cons(hd(esk50_0),esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_40]),c_0_28])]) ).

cnf(c_0_78,negated_conjecture,
    ( hd(cons(hd(esk50_0),esk51_0)) = hd(esk50_0)
    | esk50_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_40]),c_0_28])]) ).

cnf(c_0_79,negated_conjecture,
    ( memberP(cons(X1,esk51_0),esk52_0)
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_36]),c_0_75])]) ).

cnf(c_0_80,negated_conjecture,
    ( esk50_0 = nil
    | ~ duplicatefreeP(cons(hd(esk50_0),esk51_0)) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_63]),c_0_32]),c_0_28])]),c_0_77]) ).

cnf(c_0_81,negated_conjecture,
    ( cons(hd(esk50_0),esk51_0) = nil
    | esk50_0 = nil
    | ssItem(hd(esk50_0)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_78]),c_0_77]) ).

cnf(c_0_82,plain,
    duplicatefreeP(nil),
    inference(split_conjunct,[status(thm)],[ax72]) ).

cnf(c_0_83,negated_conjecture,
    ( esk50_0 = nil
    | memberP(app(esk50_0,cons(hd(esk50_0),nil)),esk52_0)
    | ~ ssItem(hd(app(esk50_0,cons(hd(esk50_0),nil)))) ),
    inference(spm,[status(thm)],[c_0_79,c_0_56]) ).

cnf(c_0_84,negated_conjecture,
    ( esk50_0 = nil
    | ssItem(hd(esk50_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82])]) ).

fof(c_0_85,plain,
    ! [X154,X155,X156] :
      ( ( ~ memberP(app(X155,X156),X154)
        | memberP(X155,X154)
        | memberP(X156,X154)
        | ~ ssList(X156)
        | ~ ssList(X155)
        | ~ ssItem(X154) )
      & ( ~ memberP(X155,X154)
        | memberP(app(X155,X156),X154)
        | ~ ssList(X156)
        | ~ ssList(X155)
        | ~ ssItem(X154) )
      & ( ~ memberP(X156,X154)
        | memberP(app(X155,X156),X154)
        | ~ ssList(X156)
        | ~ ssList(X155)
        | ~ ssItem(X154) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])])]) ).

cnf(c_0_86,negated_conjecture,
    ( esk50_0 = nil
    | memberP(app(esk50_0,cons(hd(esk50_0),nil)),esk52_0)
    | ~ ssList(cons(hd(esk50_0),nil)) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_57]),c_0_28])]),c_0_84]) ).

cnf(c_0_87,negated_conjecture,
    ~ memberP(esk48_0,esk52_0),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_88,plain,
    ( memberP(X1,X3)
    | memberP(X2,X3)
    | ~ memberP(app(X1,X2),X3)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssItem(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_85]) ).

cnf(c_0_89,negated_conjecture,
    ( esk50_0 = nil
    | memberP(app(esk50_0,cons(hd(esk50_0),nil)),esk52_0) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_46]),c_0_32])]),c_0_84]) ).

cnf(c_0_90,negated_conjecture,
    ~ memberP(esk50_0,esk52_0),
    inference(rw,[status(thm)],[c_0_87,c_0_25]) ).

cnf(c_0_91,plain,
    ( memberP(cons(X2,X3),X1)
    | X1 != X2
    | ~ ssList(X3)
    | ~ ssItem(X2)
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_68]) ).

cnf(c_0_92,negated_conjecture,
    ( esk50_0 = nil
    | memberP(cons(hd(esk50_0),nil),esk52_0)
    | ~ ssList(cons(hd(esk50_0),nil)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_28]),c_0_75])]),c_0_90]) ).

cnf(c_0_93,plain,
    ( memberP(cons(X1,X2),X1)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(er,[status(thm)],[c_0_91]) ).

cnf(c_0_94,plain,
    ( X3 = X1
    | memberP(X2,X3)
    | ~ memberP(cons(X1,X2),X3)
    | ~ ssList(X2)
    | ~ ssItem(X1)
    | ~ ssItem(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_68]) ).

cnf(c_0_95,negated_conjecture,
    ( esk50_0 = nil
    | memberP(cons(hd(esk50_0),nil),esk52_0) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_46]),c_0_32])]),c_0_84]) ).

fof(c_0_96,plain,
    ! [X160] :
      ( ~ ssItem(X160)
      | ~ memberP(nil,X160) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax38])])]) ).

cnf(c_0_97,plain,
    ( nil = X1
    | memberP(X1,hd(X1))
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_47]),c_0_40]),c_0_27]) ).

cnf(c_0_98,negated_conjecture,
    ( hd(esk50_0) = esk52_0
    | esk50_0 = nil
    | memberP(nil,esk52_0) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_32]),c_0_75])]),c_0_84]) ).

cnf(c_0_99,negated_conjecture,
    ( neq(esk50_0,nil)
    | ~ neq(esk51_0,nil) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_100,plain,
    ( ~ ssItem(X1)
    | ~ memberP(nil,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_96]) ).

cnf(c_0_101,negated_conjecture,
    ( esk50_0 = nil
    | memberP(nil,esk52_0) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_28])]),c_0_90]) ).

cnf(c_0_102,plain,
    ( ~ neq(X1,X2)
    | X1 != X2
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_103,negated_conjecture,
    ( esk51_0 = nil
    | neq(esk50_0,nil) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_31]),c_0_32]),c_0_36])]) ).

cnf(c_0_104,negated_conjecture,
    esk50_0 = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_75])]) ).

cnf(c_0_105,plain,
    ( ~ ssList(X1)
    | ~ neq(X1,X1) ),
    inference(er,[status(thm)],[c_0_102]) ).

cnf(c_0_106,negated_conjecture,
    ( esk51_0 = nil
    | neq(nil,nil) ),
    inference(rw,[status(thm)],[c_0_103,c_0_104]) ).

cnf(c_0_107,negated_conjecture,
    esk51_0 = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_32])]) ).

cnf(c_0_108,negated_conjecture,
    ~ memberP(nil,esk52_0),
    inference(rw,[status(thm)],[c_0_90,c_0_104]) ).

cnf(c_0_109,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_107]),c_0_108]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SWC410+1 : TPTP v8.1.0. Released v2.4.0.
% 0.00/0.10  % Command  : enigmatic-eprover.py %s %d 1
% 0.09/0.30  % Computer : n032.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit : 300
% 0.09/0.30  % WCLimit  : 600
% 0.09/0.30  % DateTime : Sun Jun 12 00:33:27 EDT 2022
% 0.09/0.30  % CPUTime  : 
% 0.15/0.38  # ENIGMATIC: Selected SinE mode:
% 0.15/0.39  # Parsing /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.39  # Filter: axfilter_auto   0 goes into file theBenchmark_axfilter_auto   0.p
% 0.15/0.39  # Filter: axfilter_auto   1 goes into file theBenchmark_axfilter_auto   1.p
% 0.15/0.39  # Filter: axfilter_auto   2 goes into file theBenchmark_axfilter_auto   2.p
% 12.55/2.87  # ENIGMATIC: Solved by autoschedule:
% 12.55/2.87  # No SInE strategy applied
% 12.55/2.87  # Trying AutoSched0 for 150 seconds
% 12.55/2.87  # AutoSched0-Mode selected heuristic G_E___207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 12.55/2.87  # and selection function SelectNewComplexAHP.
% 12.55/2.87  #
% 12.55/2.87  # Preprocessing time       : 0.028 s
% 12.55/2.87  # Presaturation interreduction done
% 12.55/2.87  
% 12.55/2.87  # Proof found!
% 12.55/2.87  # SZS status Theorem
% 12.55/2.87  # SZS output start CNFRefutation
% See solution above
% 12.55/2.87  # Training examples: 0 positive, 0 negative
% 12.55/2.87  
% 12.55/2.87  # -------------------------------------------------
% 12.55/2.87  # User time                : 0.747 s
% 12.55/2.87  # System time              : 0.020 s
% 12.55/2.87  # Total time               : 0.767 s
% 12.55/2.87  # Maximum resident set size: 7120 pages
% 12.55/2.87  
%------------------------------------------------------------------------------