TSTP Solution File: SWC005+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWC005+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 : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 20:19:00 EDT 2023

% Result   : Theorem 0.85s 0.93s
% Output   : CNFRefutation 0.85s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   94
% Syntax   : Number of formulae    :  182 (  13 unt;  75 typ;   0 def)
%            Number of atoms       :  418 ( 144 equ)
%            Maximal formula atoms :   34 (   3 avg)
%            Number of connectives :  523 ( 212   ~; 222   |;  42   &)
%                                         (   3 <=>;  44  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   5 avg)
%            Maximal term depth    :    3 (   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   :  160 (   0 sgn;  77   !;  11   ?;   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] :
                            ( ssList(X5)
                            & ? [X6] :
                                ( ssList(X6)
                                & ? [X7] :
                                    ( ssList(X7)
                                    & app(app(X5,X6),X7) = X2
                                    & app(X5,X7) = X1
                                    & neq(X6,nil) ) ) )
                        | ? [X8] :
                            ( ssList(X8)
                            & X3 != X8
                            & tl(X4) = X8
                            & neq(nil,X4) ) )
                      & ( ~ neq(X2,nil)
                        | neq(X4,nil) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

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(ax19,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssItem(X3)
             => ! [X4] :
                  ( ssItem(X4)
                 => ( cons(X3,X1) = cons(X4,X2)
                   => ( X3 = X4
                      & X2 = X1 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax19) ).

fof(ax20,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil = X1
        | ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( ssItem(X3)
                & cons(X3,X2) = X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax20) ).

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

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

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

fof(ax6,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( rearsegP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & app(X3,X2) = X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax6) ).

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

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

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

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

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

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

fof(ax18,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => cons(X2,X1) != X1 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax18) ).

fof(c_0_19,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ( ( ~ neq(X2,nil)
                          | ? [X5] :
                              ( ssList(X5)
                              & ? [X6] :
                                  ( ssList(X6)
                                  & ? [X7] :
                                      ( ssList(X7)
                                      & app(app(X5,X6),X7) = X2
                                      & app(X5,X7) = X1
                                      & neq(X6,nil) ) ) )
                          | ? [X8] :
                              ( ssList(X8)
                              & X3 != X8
                              & tl(X4) = X8
                              & neq(nil,X4) ) )
                        & ( ~ neq(X2,nil)
                          | neq(X4,nil) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).

fof(c_0_20,negated_conjecture,
    ! [X257,X258,X259,X260] :
      ( ssList(esk48_0)
      & ssList(esk49_0)
      & ssList(esk50_0)
      & ssList(esk51_0)
      & esk49_0 = esk51_0
      & esk48_0 = esk50_0
      & ( neq(esk49_0,nil)
        | neq(esk49_0,nil) )
      & ( ~ neq(esk51_0,nil)
        | neq(esk49_0,nil) )
      & ( neq(esk49_0,nil)
        | ~ ssList(X257)
        | ~ ssList(X258)
        | ~ ssList(X259)
        | app(app(X257,X258),X259) != esk49_0
        | app(X257,X259) != esk48_0
        | ~ neq(X258,nil) )
      & ( ~ neq(esk51_0,nil)
        | ~ ssList(X257)
        | ~ ssList(X258)
        | ~ ssList(X259)
        | app(app(X257,X258),X259) != esk49_0
        | app(X257,X259) != esk48_0
        | ~ neq(X258,nil) )
      & ( neq(esk49_0,nil)
        | ~ ssList(X260)
        | esk50_0 = X260
        | tl(esk51_0) != X260
        | ~ neq(nil,esk51_0) )
      & ( ~ neq(esk51_0,nil)
        | ~ ssList(X260)
        | esk50_0 = X260
        | tl(esk51_0) != X260
        | ~ neq(nil,esk51_0) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])])]) ).

cnf(c_0_21,negated_conjecture,
    ( neq(esk49_0,nil)
    | neq(esk49_0,nil) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_22,negated_conjecture,
    neq(esk49_0,nil),
    inference(cn,[status(thm)],[c_0_21]) ).

cnf(c_0_23,negated_conjecture,
    esk49_0 = esk51_0,
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_24,negated_conjecture,
    ( esk50_0 = X1
    | ~ neq(esk51_0,nil)
    | ~ ssList(X1)
    | tl(esk51_0) != X1
    | ~ neq(nil,esk51_0) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_25,negated_conjecture,
    esk48_0 = esk50_0,
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_26,negated_conjecture,
    neq(esk51_0,nil),
    inference(rw,[status(thm)],[c_0_22,c_0_23]) ).

fof(c_0_27,plain,
    ! [X129] :
      ( ~ ssList(X129)
      | nil = X129
      | ssList(tl(X129)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).

cnf(c_0_28,negated_conjecture,
    ssList(esk49_0),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_29,negated_conjecture,
    ( tl(esk51_0) = esk48_0
    | ~ ssList(tl(esk51_0))
    | ~ neq(nil,esk51_0) ),
    inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_26])])]) ).

cnf(c_0_30,plain,
    ( nil = X1
    | ssList(tl(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_31,negated_conjecture,
    ssList(esk51_0),
    inference(rw,[status(thm)],[c_0_28,c_0_23]) ).

fof(c_0_32,plain,
    ! [X111,X112] :
      ( ( ~ neq(X111,X112)
        | X111 != X112
        | ~ ssList(X112)
        | ~ ssList(X111) )
      & ( X111 = X112
        | neq(X111,X112)
        | ~ ssList(X112)
        | ~ ssList(X111) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).

fof(c_0_33,plain,
    ! [X117,X118,X119,X120] :
      ( ( X119 = X120
        | cons(X119,X117) != cons(X120,X118)
        | ~ ssItem(X120)
        | ~ ssItem(X119)
        | ~ ssList(X118)
        | ~ ssList(X117) )
      & ( X118 = X117
        | cons(X119,X117) != cons(X120,X118)
        | ~ ssItem(X120)
        | ~ ssItem(X119)
        | ~ ssList(X118)
        | ~ ssList(X117) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax19])])])]) ).

fof(c_0_34,plain,
    ! [X121] :
      ( ( ssList(esk44_1(X121))
        | nil = X121
        | ~ ssList(X121) )
      & ( ssItem(esk45_1(X121))
        | nil = X121
        | ~ ssList(X121) )
      & ( cons(esk45_1(X121),esk44_1(X121)) = X121
        | nil = X121
        | ~ ssList(X121) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])]) ).

fof(c_0_35,plain,
    ! [X113,X114] :
      ( ~ ssList(X113)
      | ~ ssItem(X114)
      | ssList(cons(X114,X113)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).

fof(c_0_36,plain,
    ! [X124,X125] :
      ( ~ ssList(X124)
      | ~ ssItem(X125)
      | nil != cons(X125,X124) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).

fof(c_0_37,plain,
    ! [X215] :
      ( ~ ssList(X215)
      | nil = X215
      | cons(hd(X215),tl(X215)) = X215 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).

cnf(c_0_38,negated_conjecture,
    ( tl(esk51_0) = esk48_0
    | esk51_0 = nil
    | ~ neq(nil,esk51_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).

cnf(c_0_39,plain,
    ( X1 = X2
    | neq(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_40,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[ax17]) ).

cnf(c_0_41,plain,
    ( X1 = X2
    | cons(X3,X2) != cons(X4,X1)
    | ~ ssItem(X4)
    | ~ ssItem(X3)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_42,plain,
    ( cons(esk45_1(X1),esk44_1(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_43,plain,
    ( ssItem(esk45_1(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_44,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_45,plain,
    ( ~ ssList(X1)
    | ~ ssItem(X2)
    | nil != cons(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_46,plain,
    ( nil = X1
    | cons(hd(X1),tl(X1)) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_47,negated_conjecture,
    ( tl(esk51_0) = esk48_0
    | esk51_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_31]),c_0_40])]) ).

fof(c_0_48,plain,
    ! [X26,X27,X29] :
      ( ( ssList(esk7_2(X26,X27))
        | ~ rearsegP(X26,X27)
        | ~ ssList(X27)
        | ~ ssList(X26) )
      & ( app(esk7_2(X26,X27),X27) = X26
        | ~ rearsegP(X26,X27)
        | ~ ssList(X27)
        | ~ ssList(X26) )
      & ( ~ ssList(X29)
        | app(X29,X27) != X26
        | rearsegP(X26,X27)
        | ~ ssList(X27)
        | ~ ssList(X26) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])])])])]) ).

fof(c_0_49,plain,
    ! [X132,X133] :
      ( ~ ssList(X132)
      | ~ ssList(X133)
      | ssList(app(X132,X133)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).

cnf(c_0_50,plain,
    ( esk44_1(cons(X1,X2)) = X2
    | ~ ssList(esk44_1(cons(X1,X2)))
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42])]),c_0_43]),c_0_44]),c_0_45]) ).

cnf(c_0_51,negated_conjecture,
    ( cons(hd(esk51_0),esk48_0) = esk51_0
    | esk51_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_31])]) ).

cnf(c_0_52,negated_conjecture,
    ssList(esk48_0),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_53,plain,
    ( rearsegP(X3,X2)
    | ~ ssList(X1)
    | app(X1,X2) != X3
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

cnf(c_0_54,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

fof(c_0_55,plain,
    ! [X222,X223] :
      ( ~ ssList(X222)
      | ~ ssItem(X223)
      | cons(X223,X222) = app(cons(X223,nil),X222) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).

cnf(c_0_56,negated_conjecture,
    ( esk44_1(esk51_0) = esk48_0
    | esk51_0 = nil
    | ~ ssList(esk44_1(esk51_0))
    | ~ ssItem(hd(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52])]) ).

cnf(c_0_57,plain,
    ( ssList(esk44_1(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

fof(c_0_58,plain,
    ! [X126] :
      ( ~ ssList(X126)
      | nil = X126
      | ssItem(hd(X126)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).

cnf(c_0_59,plain,
    ( rearsegP(app(X1,X2),X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_53]),c_0_54]) ).

cnf(c_0_60,plain,
    ( cons(X2,X1) = app(cons(X2,nil),X1)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_55]) ).

cnf(c_0_61,negated_conjecture,
    ( esk44_1(esk51_0) = esk48_0
    | esk51_0 = nil
    | ~ ssItem(hd(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_31])]) ).

cnf(c_0_62,plain,
    ( nil = X1
    | ssItem(hd(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_58]) ).

fof(c_0_63,plain,
    ! [X224,X225,X226] :
      ( ~ ssList(X224)
      | ~ ssList(X225)
      | ~ ssList(X226)
      | app(app(X224,X225),X226) = app(X224,app(X225,X226)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).

fof(c_0_64,plain,
    ! [X227,X228] :
      ( ( nil = X228
        | nil != app(X227,X228)
        | ~ ssList(X228)
        | ~ ssList(X227) )
      & ( nil = X227
        | nil != app(X227,X228)
        | ~ ssList(X228)
        | ~ ssList(X227) )
      & ( nil != X228
        | nil != X227
        | nil = app(X227,X228)
        | ~ ssList(X228)
        | ~ ssList(X227) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).

cnf(c_0_65,plain,
    ( rearsegP(cons(X1,X2),X2)
    | ~ ssList(cons(X1,nil))
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[c_0_59,c_0_60]) ).

cnf(c_0_66,negated_conjecture,
    ( esk44_1(esk51_0) = esk48_0
    | esk51_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_31])]) ).

fof(c_0_67,plain,
    ! [X229] :
      ( ~ ssList(X229)
      | app(X229,nil) = X229 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).

fof(c_0_68,plain,
    ! [X134,X135,X136] :
      ( ~ ssList(X134)
      | ~ ssList(X135)
      | ~ ssItem(X136)
      | cons(X136,app(X135,X134)) = app(cons(X136,X135),X134) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).

cnf(c_0_69,plain,
    ( app(app(X1,X2),X3) = app(X1,app(X2,X3))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_63]) ).

cnf(c_0_70,plain,
    ( nil = app(X2,X1)
    | nil != X1
    | nil != X2
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_64]) ).

cnf(c_0_71,negated_conjecture,
    ( ~ neq(esk51_0,nil)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | app(app(X1,X2),X3) != esk49_0
    | app(X1,X3) != esk48_0
    | ~ neq(X2,nil) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

fof(c_0_72,plain,
    ! [X137] :
      ( ~ ssList(X137)
      | app(nil,X137) = X137 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).

cnf(c_0_73,plain,
    ( rearsegP(cons(X1,X2),X2)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_44]),c_0_40])]) ).

cnf(c_0_74,negated_conjecture,
    ( cons(esk45_1(esk51_0),esk48_0) = esk51_0
    | esk51_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_66]),c_0_31])]) ).

fof(c_0_75,plain,
    ! [X115,X116] :
      ( ~ ssList(X115)
      | ~ ssItem(X116)
      | cons(X116,X115) != X115 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])]) ).

cnf(c_0_76,plain,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_67]) ).

cnf(c_0_77,plain,
    ( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssItem(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_68]) ).

cnf(c_0_78,plain,
    ( ssList(app(X1,app(X2,X3)))
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_69]),c_0_54]) ).

cnf(c_0_79,plain,
    app(nil,nil) = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_70])]),c_0_40])]) ).

cnf(c_0_80,negated_conjecture,
    ( app(app(X1,X2),X3) != esk51_0
    | app(X1,X3) != esk48_0
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ neq(X2,nil) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_23]),c_0_26])]) ).

cnf(c_0_81,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_72]) ).

cnf(c_0_82,negated_conjecture,
    ( esk51_0 = nil
    | rearsegP(esk51_0,esk48_0)
    | ~ ssItem(esk45_1(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_52])]) ).

cnf(c_0_83,plain,
    ( ~ ssList(X1)
    | ~ ssItem(X2)
    | cons(X2,X1) != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_75]) ).

cnf(c_0_84,plain,
    ( cons(X1,app(X2,nil)) = cons(X1,X2)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_40])]),c_0_44]) ).

cnf(c_0_85,plain,
    ( ssList(app(X1,nil))
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_40])]) ).

cnf(c_0_86,negated_conjecture,
    ( app(app(nil,X1),esk48_0) != esk51_0
    | ~ ssList(X1)
    | ~ neq(X1,nil) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_40])])]),c_0_52])]) ).

cnf(c_0_87,plain,
    ( app(esk7_2(X1,X2),X2) = X1
    | ~ rearsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

cnf(c_0_88,negated_conjecture,
    ( esk51_0 = nil
    | rearsegP(esk51_0,esk48_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_43]),c_0_31])]) ).

cnf(c_0_89,plain,
    ( ssList(esk7_2(X1,X2))
    | ~ rearsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

cnf(c_0_90,plain,
    ( cons(X1,X2) != app(X2,nil)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]) ).

cnf(c_0_91,negated_conjecture,
    ( app(X1,esk48_0) != esk51_0
    | ~ ssList(X1)
    | ~ neq(X1,nil) ),
    inference(spm,[status(thm)],[c_0_86,c_0_81]) ).

cnf(c_0_92,negated_conjecture,
    ( app(esk7_2(esk51_0,esk48_0),esk48_0) = esk51_0
    | esk51_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_52]),c_0_31])]) ).

cnf(c_0_93,negated_conjecture,
    ( esk51_0 = nil
    | ssList(esk7_2(esk51_0,esk48_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_88]),c_0_52]),c_0_31])]) ).

cnf(c_0_94,negated_conjecture,
    ( esk51_0 = nil
    | app(esk48_0,nil) != esk51_0
    | ~ ssItem(esk45_1(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_74]),c_0_52])]) ).

cnf(c_0_95,plain,
    ( app(X1,app(X2,nil)) = app(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_69]),c_0_40])]),c_0_54]) ).

cnf(c_0_96,plain,
    ( app(nil,app(X1,X2)) = app(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_81]),c_0_40])]) ).

cnf(c_0_97,negated_conjecture,
    ( esk51_0 = nil
    | ~ neq(esk7_2(esk51_0,esk48_0),nil) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]) ).

cnf(c_0_98,negated_conjecture,
    ( esk51_0 = nil
    | app(esk48_0,nil) != esk51_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_43]),c_0_31])]) ).

cnf(c_0_99,plain,
    ( app(X1,nil) = app(nil,X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_40])]) ).

cnf(c_0_100,negated_conjecture,
    ( esk7_2(esk51_0,esk48_0) = nil
    | esk51_0 = nil ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_39]),c_0_40])]),c_0_93]) ).

cnf(c_0_101,negated_conjecture,
    ( esk51_0 = nil
    | app(nil,esk48_0) != esk51_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_52])]) ).

cnf(c_0_102,plain,
    ( ~ neq(X1,X2)
    | X1 != X2
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_103,negated_conjecture,
    esk51_0 = nil,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_100]),c_0_101]) ).

cnf(c_0_104,plain,
    ( ~ ssList(X1)
    | ~ neq(X1,X1) ),
    inference(er,[status(thm)],[c_0_102]) ).

cnf(c_0_105,negated_conjecture,
    neq(nil,nil),
    inference(rw,[status(thm)],[c_0_26,c_0_103]) ).

cnf(c_0_106,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_40])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWC005+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.33  % Computer : n015.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit   : 300
% 0.14/0.33  % WCLimit    : 300
% 0.14/0.33  % DateTime   : Mon Aug 28 15:32:10 EDT 2023
% 0.14/0.33  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.85/0.93  % Version  : CSE_E---1.5
% 0.85/0.93  % Problem  : theBenchmark.p
% 0.85/0.93  % Proof found
% 0.85/0.93  % SZS status Theorem for theBenchmark.p
% 0.85/0.93  % SZS output start Proof
% See solution above
% 0.85/0.94  % Total time : 0.367000 s
% 0.85/0.94  % SZS output end Proof
% 0.85/0.94  % Total time : 0.372000 s
%------------------------------------------------------------------------------