TSTP Solution File: SWC418+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWC418+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n023.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 : Thu Aug 31 20:22:27 EDT 2023

% Result   : Theorem 0.55s 0.74s
% Output   : CNFRefutation 0.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :   90
% Syntax   : Number of formulae    :  167 (  13 unt;  75 typ;   0 def)
%            Number of atoms       :  358 ( 160 equ)
%            Maximal formula atoms :   26 (   3 avg)
%            Number of connectives :  438 ( 172   ~; 185   |;  45   &)
%                                         (   2 <=>;  34  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   30 (   5 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   85 (  68   >;  17   *;   0   +;   0  <<)
%            Number of predicates  :   21 (  19 usr;   1 prp; 0-2 aty)
%            Number of functors    :   56 (  56 usr;   7 con; 0-2 aty)
%            Number of variables   :  113 (   0 sgn;  57   !;  14   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    ssItem: $i > $o ).

tff(decl_23,type,
    neq: ( $i * $i ) > $o ).

tff(decl_24,type,
    ssList: $i > $o ).

tff(decl_25,type,
    memberP: ( $i * $i ) > $o ).

tff(decl_26,type,
    cons: ( $i * $i ) > $i ).

tff(decl_27,type,
    app: ( $i * $i ) > $i ).

tff(decl_28,type,
    singletonP: $i > $o ).

tff(decl_29,type,
    nil: $i ).

tff(decl_30,type,
    frontsegP: ( $i * $i ) > $o ).

tff(decl_31,type,
    rearsegP: ( $i * $i ) > $o ).

tff(decl_32,type,
    segmentP: ( $i * $i ) > $o ).

tff(decl_33,type,
    cyclefreeP: $i > $o ).

tff(decl_34,type,
    leq: ( $i * $i ) > $o ).

tff(decl_35,type,
    totalorderP: $i > $o ).

tff(decl_36,type,
    strictorderP: $i > $o ).

tff(decl_37,type,
    lt: ( $i * $i ) > $o ).

tff(decl_38,type,
    totalorderedP: $i > $o ).

tff(decl_39,type,
    strictorderedP: $i > $o ).

tff(decl_40,type,
    duplicatefreeP: $i > $o ).

tff(decl_41,type,
    equalelemsP: $i > $o ).

tff(decl_42,type,
    hd: $i > $i ).

tff(decl_43,type,
    tl: $i > $i ).

tff(decl_44,type,
    geq: ( $i * $i ) > $o ).

tff(decl_45,type,
    gt: ( $i * $i ) > $o ).

tff(decl_46,type,
    esk1_0: $i ).

tff(decl_47,type,
    esk2_0: $i ).

tff(decl_48,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_49,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_50,type,
    esk5_1: $i > $i ).

tff(decl_51,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_52,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_53,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_54,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_55,type,
    esk10_1: $i > $i ).

tff(decl_56,type,
    esk11_1: $i > $i ).

tff(decl_57,type,
    esk12_1: $i > $i ).

tff(decl_58,type,
    esk13_1: $i > $i ).

tff(decl_59,type,
    esk14_1: $i > $i ).

tff(decl_60,type,
    esk15_1: $i > $i ).

tff(decl_61,type,
    esk16_1: $i > $i ).

tff(decl_62,type,
    esk17_1: $i > $i ).

tff(decl_63,type,
    esk18_1: $i > $i ).

tff(decl_64,type,
    esk19_1: $i > $i ).

tff(decl_65,type,
    esk20_1: $i > $i ).

tff(decl_66,type,
    esk21_1: $i > $i ).

tff(decl_67,type,
    esk22_1: $i > $i ).

tff(decl_68,type,
    esk23_1: $i > $i ).

tff(decl_69,type,
    esk24_1: $i > $i ).

tff(decl_70,type,
    esk25_1: $i > $i ).

tff(decl_71,type,
    esk26_1: $i > $i ).

tff(decl_72,type,
    esk27_1: $i > $i ).

tff(decl_73,type,
    esk28_1: $i > $i ).

tff(decl_74,type,
    esk29_1: $i > $i ).

tff(decl_75,type,
    esk30_1: $i > $i ).

tff(decl_76,type,
    esk31_1: $i > $i ).

tff(decl_77,type,
    esk32_1: $i > $i ).

tff(decl_78,type,
    esk33_1: $i > $i ).

tff(decl_79,type,
    esk34_1: $i > $i ).

tff(decl_80,type,
    esk35_1: $i > $i ).

tff(decl_81,type,
    esk36_1: $i > $i ).

tff(decl_82,type,
    esk37_1: $i > $i ).

tff(decl_83,type,
    esk38_1: $i > $i ).

tff(decl_84,type,
    esk39_1: $i > $i ).

tff(decl_85,type,
    esk40_1: $i > $i ).

tff(decl_86,type,
    esk41_1: $i > $i ).

tff(decl_87,type,
    esk42_1: $i > $i ).

tff(decl_88,type,
    esk43_1: $i > $i ).

tff(decl_89,type,
    esk44_1: $i > $i ).

tff(decl_90,type,
    esk45_1: $i > $i ).

tff(decl_91,type,
    esk46_1: $i > $i ).

tff(decl_92,type,
    esk47_1: $i > $i ).

tff(decl_93,type,
    esk48_0: $i ).

tff(decl_94,type,
    esk49_0: $i ).

tff(decl_95,type,
    esk50_0: $i ).

tff(decl_96,type,
    esk51_0: $i ).

fof(co1,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ~ neq(X2,nil)
                    | ? [X5] :
                        ( ssItem(X5)
                        & ? [X6] :
                            ( ssList(X6)
                            & ? [X7] :
                                ( ssList(X7)
                                & app(app(X6,cons(X5,nil)),X7) = X2
                                & app(app(X7,cons(X5,nil)),X6) = X1 ) ) )
                    | ( nil != X3
                      & nil = X4 )
                    | ( ? [X8] :
                          ( ssList(X8)
                          & X3 != X8
                          & ? [X9] :
                              ( ssList(X9)
                              & ? [X10] :
                                  ( ssList(X10)
                                  & tl(X4) = X9
                                  & app(X9,X10) = X8
                                  & ? [X11] :
                                      ( ssItem(X11)
                                      & cons(X11,nil) = X10
                                      & hd(X4) = X11
                                      & neq(nil,X4) )
                                  & neq(nil,X4) ) ) )
                      & neq(X4,nil) ) ) ) ) ) ),
    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(ax16,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ssList(cons(X2,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).

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

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

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

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

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(c_0_15,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ~ neq(X2,nil)
                      | ? [X5] :
                          ( ssItem(X5)
                          & ? [X6] :
                              ( ssList(X6)
                              & ? [X7] :
                                  ( ssList(X7)
                                  & app(app(X6,cons(X5,nil)),X7) = X2
                                  & app(app(X7,cons(X5,nil)),X6) = X1 ) ) )
                      | ( nil != X3
                        & nil = X4 )
                      | ( ? [X8] :
                            ( ssList(X8)
                            & X3 != X8
                            & ? [X9] :
                                ( ssList(X9)
                                & ? [X10] :
                                    ( ssList(X10)
                                    & tl(X4) = X9
                                    & app(X9,X10) = X8
                                    & ? [X11] :
                                        ( ssItem(X11)
                                        & cons(X11,nil) = X10
                                        & hd(X4) = X11
                                        & neq(nil,X4) )
                                    & neq(nil,X4) ) ) )
                        & neq(X4,nil) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).

fof(c_0_16,negated_conjecture,
    ! [X260,X261,X262,X263,X264,X265,X266] :
      ( ssList(esk48_0)
      & ssList(esk49_0)
      & ssList(esk50_0)
      & ssList(esk51_0)
      & esk49_0 = esk51_0
      & esk48_0 = esk50_0
      & neq(esk49_0,nil)
      & ( ~ ssItem(X260)
        | ~ ssList(X261)
        | ~ ssList(X262)
        | app(app(X261,cons(X260,nil)),X262) != esk49_0
        | app(app(X262,cons(X260,nil)),X261) != esk48_0 )
      & ( nil = esk50_0
        | nil != esk51_0 )
      & ( ~ ssList(X263)
        | esk50_0 = X263
        | ~ ssList(X264)
        | ~ ssList(X265)
        | tl(esk51_0) != X264
        | app(X264,X265) != X263
        | ~ ssItem(X266)
        | cons(X266,nil) != X265
        | hd(esk51_0) != X266
        | ~ neq(nil,esk51_0)
        | ~ neq(nil,esk51_0)
        | ~ neq(esk51_0,nil) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).

cnf(c_0_17,negated_conjecture,
    ( esk50_0 = X1
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | tl(esk51_0) != X2
    | app(X2,X3) != X1
    | ~ ssItem(X4)
    | cons(X4,nil) != X3
    | hd(esk51_0) != X4
    | ~ neq(nil,esk51_0)
    | ~ neq(nil,esk51_0)
    | ~ neq(esk51_0,nil) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_18,negated_conjecture,
    neq(esk49_0,nil),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_19,negated_conjecture,
    esk49_0 = esk51_0,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_20,plain,
    ! [X135,X136] :
      ( ~ ssList(X135)
      | ~ ssList(X136)
      | ssList(app(X135,X136)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).

cnf(c_0_21,negated_conjecture,
    ( esk50_0 = X1
    | hd(esk51_0) != X4
    | tl(esk51_0) != X2
    | app(X2,X3) != X1
    | cons(X4,nil) != X3
    | ~ ssItem(X4)
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ neq(nil,esk51_0)
    | ~ neq(esk51_0,nil) ),
    inference(cn,[status(thm)],[c_0_17]) ).

cnf(c_0_22,negated_conjecture,
    neq(esk51_0,nil),
    inference(rw,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_23,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

fof(c_0_24,plain,
    ! [X132] :
      ( ~ ssList(X132)
      | nil = X132
      | ssList(tl(X132)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).

cnf(c_0_25,negated_conjecture,
    ssList(esk49_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_26,negated_conjecture,
    ( app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk50_0
    | ~ ssList(cons(hd(esk51_0),nil))
    | ~ ssList(tl(esk51_0))
    | ~ neq(nil,esk51_0)
    | ~ ssItem(hd(esk51_0)) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])])])])])]),c_0_23]) ).

cnf(c_0_27,plain,
    ( nil = X1
    | ssList(tl(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_28,negated_conjecture,
    ssList(esk51_0),
    inference(rw,[status(thm)],[c_0_25,c_0_19]) ).

fof(c_0_29,plain,
    ! [X116,X117] :
      ( ~ ssList(X116)
      | ~ ssItem(X117)
      | ssList(cons(X117,X116)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).

cnf(c_0_30,negated_conjecture,
    ( app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk50_0
    | esk51_0 = nil
    | ~ ssList(cons(hd(esk51_0),nil))
    | ~ neq(nil,esk51_0)
    | ~ ssItem(hd(esk51_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,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

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

fof(c_0_33,plain,
    ! [X129] :
      ( ~ ssList(X129)
      | nil = X129
      | ssItem(hd(X129)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).

fof(c_0_34,plain,
    ! [X218] :
      ( ~ ssList(X218)
      | nil = X218
      | cons(hd(X218),tl(X218)) = X218 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).

fof(c_0_35,plain,
    ! [X235,X236] :
      ( ~ ssList(X235)
      | ~ ssList(X236)
      | nil = X235
      | tl(app(X235,X236)) = app(tl(X235),X236) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax86])])]) ).

fof(c_0_36,plain,
    ! [X230,X231] :
      ( ( nil = X231
        | nil != app(X230,X231)
        | ~ ssList(X231)
        | ~ ssList(X230) )
      & ( nil = X230
        | nil != app(X230,X231)
        | ~ ssList(X231)
        | ~ ssList(X230) )
      & ( nil != X231
        | nil != X230
        | nil = app(X230,X231)
        | ~ ssList(X231)
        | ~ ssList(X230) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).

cnf(c_0_37,negated_conjecture,
    ( app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk50_0
    | esk51_0 = nil
    | ~ neq(nil,esk51_0)
    | ~ ssItem(hd(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).

cnf(c_0_38,plain,
    ( nil = X1
    | ssItem(hd(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

fof(c_0_39,plain,
    ! [X114,X115] :
      ( ( ~ neq(X114,X115)
        | X114 != X115
        | ~ ssList(X115)
        | ~ ssList(X114) )
      & ( X114 = X115
        | neq(X114,X115)
        | ~ ssList(X115)
        | ~ ssList(X114) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).

cnf(c_0_40,plain,
    ( nil = X1
    | cons(hd(X1),tl(X1)) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

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

cnf(c_0_42,plain,
    ( nil = X1
    | nil != app(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_43,negated_conjecture,
    ( app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk50_0
    | esk51_0 = nil
    | ~ neq(nil,esk51_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_28])]) ).

cnf(c_0_44,plain,
    ( X1 = X2
    | neq(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_45,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_40,c_0_41]),c_0_23]),c_0_42]) ).

cnf(c_0_46,negated_conjecture,
    ( app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk50_0
    | esk51_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_28]),c_0_32])]) ).

cnf(c_0_47,negated_conjecture,
    ( cons(hd(app(esk51_0,cons(hd(esk51_0),nil))),esk50_0) = app(esk51_0,cons(hd(esk51_0),nil))
    | esk51_0 = nil
    | ~ ssList(cons(hd(esk51_0),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_28])]) ).

cnf(c_0_48,negated_conjecture,
    ( cons(hd(app(esk51_0,cons(hd(esk51_0),nil))),esk50_0) = app(esk51_0,cons(hd(esk51_0),nil))
    | esk51_0 = nil
    | ~ ssItem(hd(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_31]),c_0_32])]) ).

fof(c_0_49,plain,
    ! [X233,X234] :
      ( ~ ssList(X233)
      | ~ ssList(X234)
      | nil = X233
      | hd(app(X233,X234)) = hd(X233) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax85])])]) ).

cnf(c_0_50,negated_conjecture,
    ( cons(hd(app(esk51_0,cons(hd(esk51_0),nil))),esk50_0) = app(esk51_0,cons(hd(esk51_0),nil))
    | esk51_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_38]),c_0_28])]) ).

cnf(c_0_51,plain,
    ( nil = X1
    | hd(app(X1,X2)) = hd(X1)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

fof(c_0_52,plain,
    ! [X127,X128] :
      ( ~ ssList(X127)
      | ~ ssItem(X128)
      | nil != cons(X128,X127) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).

cnf(c_0_53,negated_conjecture,
    ssList(esk48_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_54,negated_conjecture,
    esk48_0 = esk50_0,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_55,negated_conjecture,
    ( app(esk51_0,cons(hd(esk51_0),nil)) = cons(hd(esk51_0),esk50_0)
    | esk51_0 = nil
    | ~ ssList(cons(hd(esk51_0),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_28])]) ).

cnf(c_0_56,plain,
    ( ~ ssList(X1)
    | ~ ssItem(X2)
    | nil != cons(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

cnf(c_0_57,negated_conjecture,
    ssList(esk50_0),
    inference(rw,[status(thm)],[c_0_53,c_0_54]) ).

cnf(c_0_58,negated_conjecture,
    ( app(esk51_0,cons(hd(esk51_0),nil)) = cons(hd(esk51_0),esk50_0)
    | esk51_0 = nil
    | ~ ssItem(hd(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_31]),c_0_32])]) ).

cnf(c_0_59,negated_conjecture,
    ( esk51_0 = nil
    | app(esk51_0,cons(hd(esk51_0),nil)) != nil
    | ~ ssItem(hd(app(esk51_0,cons(hd(esk51_0),nil)))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_50]),c_0_57])]) ).

cnf(c_0_60,negated_conjecture,
    ( app(esk51_0,cons(hd(esk51_0),nil)) = cons(hd(esk51_0),esk50_0)
    | esk51_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_38]),c_0_28])]) ).

cnf(c_0_61,negated_conjecture,
    ( esk51_0 = nil
    | app(esk51_0,cons(hd(esk51_0),nil)) != nil
    | ~ ssList(cons(hd(esk51_0),nil))
    | ~ ssItem(hd(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_51]),c_0_28])]) ).

cnf(c_0_62,negated_conjecture,
    ( hd(cons(hd(esk51_0),esk50_0)) = hd(esk51_0)
    | esk51_0 = nil
    | ~ ssList(cons(hd(esk51_0),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_60]),c_0_28])]) ).

cnf(c_0_63,negated_conjecture,
    ( esk51_0 = nil
    | ssList(cons(hd(esk51_0),esk50_0))
    | ~ ssList(cons(hd(esk51_0),nil)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_60]),c_0_28])]) ).

cnf(c_0_64,negated_conjecture,
    ( esk51_0 = nil
    | app(esk51_0,cons(hd(esk51_0),nil)) != nil
    | ~ ssItem(hd(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_31]),c_0_32])]) ).

cnf(c_0_65,negated_conjecture,
    ( ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | app(app(X2,cons(X1,nil)),X3) != esk49_0
    | app(app(X3,cons(X1,nil)),X2) != esk48_0 ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_66,plain,
    ! [X232] :
      ( ~ ssList(X232)
      | app(X232,nil) = X232 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).

cnf(c_0_67,negated_conjecture,
    ( hd(cons(hd(esk51_0),esk50_0)) = hd(esk51_0)
    | esk51_0 = nil
    | ~ ssItem(hd(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_31]),c_0_32])]) ).

cnf(c_0_68,negated_conjecture,
    ( esk51_0 = nil
    | ssList(cons(hd(esk51_0),esk50_0))
    | ~ ssItem(hd(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_31]),c_0_32])]) ).

cnf(c_0_69,negated_conjecture,
    ( esk51_0 = nil
    | app(esk51_0,cons(hd(esk51_0),nil)) != nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_38]),c_0_28])]) ).

cnf(c_0_70,negated_conjecture,
    ( app(app(X1,cons(X2,nil)),X3) != esk50_0
    | app(app(X3,cons(X2,nil)),X1) != esk51_0
    | ~ ssList(X1)
    | ~ ssList(X3)
    | ~ ssItem(X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_54]),c_0_19]) ).

cnf(c_0_71,plain,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

cnf(c_0_72,negated_conjecture,
    ( hd(cons(hd(esk51_0),esk50_0)) = hd(esk51_0)
    | esk51_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_38]),c_0_28])]) ).

cnf(c_0_73,negated_conjecture,
    ( esk51_0 = nil
    | ssList(cons(hd(esk51_0),esk50_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_38]),c_0_28])]) ).

cnf(c_0_74,negated_conjecture,
    ( esk51_0 = nil
    | cons(hd(esk51_0),esk50_0) != nil ),
    inference(spm,[status(thm)],[c_0_69,c_0_60]) ).

cnf(c_0_75,negated_conjecture,
    ( app(app(nil,cons(X1,nil)),X2) != esk51_0
    | app(X2,cons(X1,nil)) != esk50_0
    | ~ ssList(app(X2,cons(X1,nil)))
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_32])]) ).

cnf(c_0_76,negated_conjecture,
    ( esk51_0 = nil
    | ssItem(hd(esk51_0)) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_72]),c_0_73]),c_0_74]) ).

cnf(c_0_77,negated_conjecture,
    ( esk51_0 = nil
    | app(app(nil,cons(hd(esk51_0),nil)),tl(esk51_0)) != esk51_0
    | ~ ssList(tl(esk51_0)) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_46]),c_0_57])]),c_0_76]) ).

fof(c_0_78,plain,
    ! [X140] :
      ( ~ ssList(X140)
      | app(nil,X140) = X140 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).

cnf(c_0_79,negated_conjecture,
    ( esk51_0 = nil
    | app(app(nil,cons(hd(esk51_0),nil)),tl(esk51_0)) != esk51_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_27]),c_0_28])]) ).

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

cnf(c_0_81,negated_conjecture,
    ( esk51_0 = nil
    | app(cons(hd(esk51_0),nil),tl(esk51_0)) != esk51_0
    | ~ ssList(cons(hd(esk51_0),nil)) ),
    inference(spm,[status(thm)],[c_0_79,c_0_80]) ).

fof(c_0_82,plain,
    ! [X225,X226] :
      ( ~ ssList(X225)
      | ~ ssItem(X226)
      | cons(X226,X225) = app(cons(X226,nil),X225) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).

cnf(c_0_83,negated_conjecture,
    ( esk51_0 = nil
    | app(cons(hd(esk51_0),nil),tl(esk51_0)) != esk51_0 ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_31]),c_0_32])]),c_0_76]) ).

cnf(c_0_84,plain,
    ( cons(X2,X1) = app(cons(X2,nil),X1)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_82]) ).

cnf(c_0_85,negated_conjecture,
    ( esk51_0 = nil
    | cons(hd(esk51_0),tl(esk51_0)) != esk51_0
    | ~ ssList(tl(esk51_0)) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_76]) ).

cnf(c_0_86,negated_conjecture,
    ( esk51_0 = nil
    | cons(hd(esk51_0),tl(esk51_0)) != esk51_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_27]),c_0_28])]) ).

cnf(c_0_87,plain,
    ( ~ neq(X1,X2)
    | X1 != X2
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_88,negated_conjecture,
    esk51_0 = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_40]),c_0_28])]) ).

cnf(c_0_89,plain,
    ( ~ ssList(X1)
    | ~ neq(X1,X1) ),
    inference(er,[status(thm)],[c_0_87]) ).

cnf(c_0_90,negated_conjecture,
    neq(nil,nil),
    inference(rw,[status(thm)],[c_0_22,c_0_88]) ).

cnf(c_0_91,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_32])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SWC418+1 : TPTP v8.1.2. Released v2.4.0.
% 0.03/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33  % Computer : n023.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Mon Aug 28 19:14:10 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.52/0.57  start to proof: theBenchmark
% 0.55/0.74  % Version  : CSE_E---1.5
% 0.55/0.74  % Problem  : theBenchmark.p
% 0.55/0.74  % Proof found
% 0.55/0.74  % SZS status Theorem for theBenchmark.p
% 0.55/0.74  % SZS output start Proof
% See solution above
% 0.55/0.75  % Total time : 0.156000 s
% 0.55/0.75  % SZS output end Proof
% 0.55/0.75  % Total time : 0.161000 s
%------------------------------------------------------------------------------