TSTP Solution File: SWC204+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWC204+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n016.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 20:20:41 EDT 2023

% Result   : Theorem 0.53s 0.61s
% Output   : CNFRefutation 0.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   84
% Syntax   : Number of formulae    :  126 (  14 unt;  75 typ;   0 def)
%            Number of atoms       :  181 (  65 equ)
%            Maximal formula atoms :   28 (   3 avg)
%            Number of connectives :  208 (  78   ~;  84   |;  24   &)
%                                         (   1 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   4 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   :   46 (   0 sgn;  30   !;   4   ?;   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)
                            & X4 != X5
                            & ? [X6] :
                                ( ssList(X6)
                                & tl(X4) = X6
                                & app(X3,X6) = X5
                                & neq(nil,X4) ) )
                        | neq(X1,nil) )
                      & ( ~ neq(X2,nil)
                        | neq(X4,nil) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(ax24,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => ssList(tl(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).

fof(ax26,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ssList(app(X1,X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).

fof(ax15,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( neq(X1,X2)
          <=> X1 != X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).

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

fof(ax28,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(nil,X1) = X1 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).

fof(ax78,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => cons(hd(X1),tl(X1)) = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).

fof(ax18,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => cons(X2,X1) != X1 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).

fof(ax22,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => ssItem(hd(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).

fof(c_0_9,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ( ( ~ neq(X2,nil)
                          | ? [X5] :
                              ( ssList(X5)
                              & X4 != X5
                              & ? [X6] :
                                  ( ssList(X6)
                                  & tl(X4) = X6
                                  & app(X3,X6) = X5
                                  & neq(nil,X4) ) )
                          | neq(X1,nil) )
                        & ( ~ neq(X2,nil)
                          | neq(X4,nil) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).

fof(c_0_10,negated_conjecture,
    ! [X255,X256] :
      ( 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(X255)
        | esk51_0 = X255
        | ~ ssList(X256)
        | tl(esk51_0) != X256
        | app(esk50_0,X256) != X255
        | ~ neq(nil,esk51_0) )
      & ( ~ neq(esk51_0,nil)
        | ~ ssList(X255)
        | esk51_0 = X255
        | ~ ssList(X256)
        | tl(esk51_0) != X256
        | app(esk50_0,X256) != X255
        | ~ neq(nil,esk51_0) )
      & ( neq(esk49_0,nil)
        | ~ neq(esk48_0,nil) )
      & ( ~ neq(esk51_0,nil)
        | ~ neq(esk48_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)],[c_0_9])])])])]) ).

cnf(c_0_11,negated_conjecture,
    ( neq(esk49_0,nil)
    | neq(esk49_0,nil) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_12,negated_conjecture,
    neq(esk49_0,nil),
    inference(cn,[status(thm)],[c_0_11]) ).

cnf(c_0_13,negated_conjecture,
    esk49_0 = esk51_0,
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,negated_conjecture,
    ( esk51_0 = X1
    | ~ neq(esk51_0,nil)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | tl(esk51_0) != X2
    | app(esk50_0,X2) != X1
    | ~ neq(nil,esk51_0) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_15,negated_conjecture,
    esk48_0 = esk50_0,
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_16,negated_conjecture,
    neq(esk51_0,nil),
    inference(rw,[status(thm)],[c_0_12,c_0_13]) ).

fof(c_0_17,plain,
    ! [X127] :
      ( ~ ssList(X127)
      | nil = X127
      | ssList(tl(X127)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).

cnf(c_0_18,negated_conjecture,
    ssList(esk49_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_19,negated_conjecture,
    ( app(esk48_0,tl(esk51_0)) = esk51_0
    | ~ ssList(app(esk48_0,tl(esk51_0)))
    | ~ ssList(tl(esk51_0))
    | ~ neq(nil,esk51_0) ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_16])])])]) ).

cnf(c_0_20,plain,
    ( nil = X1
    | ssList(tl(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_21,negated_conjecture,
    ssList(esk51_0),
    inference(rw,[status(thm)],[c_0_18,c_0_13]) ).

fof(c_0_22,plain,
    ! [X130,X131] :
      ( ~ ssList(X130)
      | ~ ssList(X131)
      | ssList(app(X130,X131)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).

cnf(c_0_23,negated_conjecture,
    ( app(esk48_0,tl(esk51_0)) = esk51_0
    | esk51_0 = nil
    | ~ ssList(app(esk48_0,tl(esk51_0)))
    | ~ neq(nil,esk51_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).

cnf(c_0_24,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_25,negated_conjecture,
    ssList(esk48_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_26,negated_conjecture,
    ( ~ neq(esk51_0,nil)
    | ~ neq(esk48_0,nil) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_27,plain,
    ! [X109,X110] :
      ( ( ~ neq(X109,X110)
        | X109 != X110
        | ~ ssList(X110)
        | ~ ssList(X109) )
      & ( X109 = X110
        | neq(X109,X110)
        | ~ ssList(X110)
        | ~ ssList(X109) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).

cnf(c_0_28,negated_conjecture,
    ( app(esk48_0,tl(esk51_0)) = esk51_0
    | esk51_0 = nil
    | ~ ssList(tl(esk51_0))
    | ~ neq(nil,esk51_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).

cnf(c_0_29,negated_conjecture,
    ~ neq(esk48_0,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_16])]) ).

cnf(c_0_30,plain,
    ( X1 = X2
    | neq(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_31,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[ax17]) ).

cnf(c_0_32,negated_conjecture,
    ( app(esk48_0,tl(esk51_0)) = esk51_0
    | esk51_0 = nil
    | ~ neq(nil,esk51_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_20]),c_0_21])]) ).

cnf(c_0_33,negated_conjecture,
    esk48_0 = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_25])]) ).

fof(c_0_34,plain,
    ! [X135] :
      ( ~ ssList(X135)
      | app(nil,X135) = X135 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).

cnf(c_0_35,negated_conjecture,
    ( app(nil,tl(esk51_0)) = esk51_0
    | esk51_0 = nil
    | ~ neq(nil,esk51_0) ),
    inference(rw,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_36,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_37,negated_conjecture,
    ( app(nil,tl(esk51_0)) = esk51_0
    | esk51_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_30]),c_0_21]),c_0_31])]) ).

fof(c_0_38,plain,
    ! [X213] :
      ( ~ ssList(X213)
      | nil = X213
      | cons(hd(X213),tl(X213)) = X213 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).

cnf(c_0_39,negated_conjecture,
    ( tl(esk51_0) = esk51_0
    | esk51_0 = nil
    | ~ ssList(tl(esk51_0)) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

fof(c_0_40,plain,
    ! [X113,X114] :
      ( ~ ssList(X113)
      | ~ ssItem(X114)
      | cons(X114,X113) != X113 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])]) ).

cnf(c_0_41,plain,
    ( nil = X1
    | cons(hd(X1),tl(X1)) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_42,negated_conjecture,
    ( tl(esk51_0) = esk51_0
    | esk51_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_20]),c_0_21])]) ).

cnf(c_0_43,plain,
    ( ~ ssList(X1)
    | ~ ssItem(X2)
    | cons(X2,X1) != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_44,negated_conjecture,
    ( cons(hd(esk51_0),esk51_0) = esk51_0
    | esk51_0 = nil ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_21])]) ).

fof(c_0_45,plain,
    ! [X124] :
      ( ~ ssList(X124)
      | nil = X124
      | ssItem(hd(X124)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).

cnf(c_0_46,negated_conjecture,
    ( esk51_0 = nil
    | ~ ssItem(hd(esk51_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_21])]) ).

cnf(c_0_47,plain,
    ( nil = X1
    | ssItem(hd(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

cnf(c_0_48,negated_conjecture,
    esk51_0 = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_21])]) ).

cnf(c_0_49,negated_conjecture,
    ~ neq(nil,nil),
    inference(rw,[status(thm)],[c_0_29,c_0_33]) ).

cnf(c_0_50,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_48]),c_0_49]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SWC204+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n016.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Mon Aug 28 18:30:44 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.21/0.56  start to proof: theBenchmark
% 0.53/0.61  % Version  : CSE_E---1.5
% 0.53/0.61  % Problem  : theBenchmark.p
% 0.53/0.61  % Proof found
% 0.53/0.61  % SZS status Theorem for theBenchmark.p
% 0.53/0.61  % SZS output start Proof
% See solution above
% 0.53/0.62  % Total time : 0.039000 s
% 0.53/0.62  % SZS output end Proof
% 0.53/0.62  % Total time : 0.044000 s
%------------------------------------------------------------------------------