TSTP Solution File: SWC109+1 by Enigma---0.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Enigma---0.5.1
% Problem  : SWC109+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : enigmatic-eprover.py %s %d 1

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Tue Jul 19 20:13:40 EDT 2022

% Result   : Theorem 7.72s 2.47s
% Output   : CNFRefutation 7.72s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   51 (  13 unt;   0 def)
%            Number of atoms       :  243 (  82 equ)
%            Maximal formula atoms :   52 (   4 avg)
%            Number of connectives :  303 ( 111   ~; 123   |;  45   &)
%                                         (   3 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   29 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   8 con; 0-2 aty)
%            Number of variables   :   59 (   0 sgn  38   !;   6   ?)

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

fof(ax7,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( segmentP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & ? [X4] :
                    ( ssList(X4)
                    & app(app(X3,X2),X4) = X1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).

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

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

fof(ax54,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( ( segmentP(X1,X2)
              & segmentP(X2,X1) )
           => X1 = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax54) ).

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(ax57,axiom,
    ! [X1] :
      ( ssList(X1)
     => segmentP(X1,nil) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax57) ).

fof(ax58,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( segmentP(nil,X1)
      <=> nil = X1 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax58) ).

fof(c_0_8,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ~ ssList(X4)
                    | X2 != X4
                    | X1 != X3
                    | ( ! [X5] :
                          ( ssItem(X5)
                         => ! [X6] :
                              ( ssList(X6)
                             => ! [X7] :
                                  ( ~ ssList(X7)
                                  | cons(X5,nil) != X3
                                  | app(app(X6,X3),X7) != X4
                                  | ? [X8] :
                                      ( ssItem(X8)
                                      & memberP(X6,X8)
                                      & lt(X5,X8) )
                                  | ? [X9] :
                                      ( ssItem(X9)
                                      & memberP(X7,X9)
                                      & lt(X9,X5) ) ) ) )
                      & ( nil != X4
                        | nil != X3 ) )
                    | ( ( nil != X2
                        | nil = X1 )
                      & ( ~ neq(X2,nil)
                        | ( neq(X1,nil)
                          & segmentP(X2,X1) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[co1]) ).

fof(c_0_9,plain,
    ! [X31,X32,X35,X36] :
      ( ( ssList(esk8_2(X31,X32))
        | ~ segmentP(X31,X32)
        | ~ ssList(X32)
        | ~ ssList(X31) )
      & ( ssList(esk9_2(X31,X32))
        | ~ segmentP(X31,X32)
        | ~ ssList(X32)
        | ~ ssList(X31) )
      & ( app(app(esk8_2(X31,X32),X32),esk9_2(X31,X32)) = X31
        | ~ segmentP(X31,X32)
        | ~ ssList(X32)
        | ~ ssList(X31) )
      & ( ~ ssList(X35)
        | ~ ssList(X36)
        | app(app(X35,X32),X36) != X31
        | segmentP(X31,X32)
        | ~ ssList(X32)
        | ~ ssList(X31) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax7])])])])]) ).

fof(c_0_10,negated_conjecture,
    ! [X261,X262] :
      ( ssList(esk48_0)
      & ssList(esk49_0)
      & ssList(esk50_0)
      & ssList(esk51_0)
      & esk49_0 = esk51_0
      & esk48_0 = esk50_0
      & ( nil = esk51_0
        | ssItem(esk52_0) )
      & ( nil = esk50_0
        | ssItem(esk52_0) )
      & ( nil = esk51_0
        | ssList(esk53_0) )
      & ( nil = esk50_0
        | ssList(esk53_0) )
      & ( nil = esk51_0
        | ssList(esk54_0) )
      & ( nil = esk50_0
        | ssList(esk54_0) )
      & ( nil = esk51_0
        | cons(esk52_0,nil) = esk50_0 )
      & ( nil = esk50_0
        | cons(esk52_0,nil) = esk50_0 )
      & ( nil = esk51_0
        | app(app(esk53_0,esk50_0),esk54_0) = esk51_0 )
      & ( nil = esk50_0
        | app(app(esk53_0,esk50_0),esk54_0) = esk51_0 )
      & ( nil = esk51_0
        | ~ ssItem(X261)
        | ~ memberP(esk53_0,X261)
        | ~ lt(esk52_0,X261) )
      & ( nil = esk50_0
        | ~ ssItem(X261)
        | ~ memberP(esk53_0,X261)
        | ~ lt(esk52_0,X261) )
      & ( nil = esk51_0
        | ~ ssItem(X262)
        | ~ memberP(esk54_0,X262)
        | ~ lt(X262,esk52_0) )
      & ( nil = esk50_0
        | ~ ssItem(X262)
        | ~ memberP(esk54_0,X262)
        | ~ lt(X262,esk52_0) )
      & ( neq(esk49_0,nil)
        | nil = esk49_0 )
      & ( ~ neq(esk48_0,nil)
        | ~ segmentP(esk49_0,esk48_0)
        | nil = esk49_0 )
      & ( neq(esk49_0,nil)
        | nil != esk48_0 )
      & ( ~ neq(esk48_0,nil)
        | ~ segmentP(esk49_0,esk48_0)
        | nil != esk48_0 ) ),
    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_8])])])])])]) ).

cnf(c_0_11,plain,
    ( segmentP(X4,X3)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | app(app(X1,X3),X2) != X4
    | ~ ssList(X3)
    | ~ ssList(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_12,negated_conjecture,
    ssList(esk49_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

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

cnf(c_0_14,negated_conjecture,
    ssList(esk48_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]) ).

fof(c_0_16,plain,
    ! [X125,X126] :
      ( ~ ssList(X125)
      | ~ ssItem(X126)
      | nil != cons(X126,X125) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).

cnf(c_0_17,negated_conjecture,
    ( nil = esk49_0
    | ~ neq(esk48_0,nil)
    | ~ segmentP(esk49_0,esk48_0) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_18,plain,
    ( segmentP(app(app(X1,X2),X3),X2)
    | ~ ssList(app(app(X1,X2),X3))
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ ssList(X1) ),
    inference(er,[status(thm)],[c_0_11]) ).

cnf(c_0_19,negated_conjecture,
    ( nil = esk50_0
    | app(app(esk53_0,esk50_0),esk54_0) = esk51_0 ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_20,negated_conjecture,
    ssList(esk51_0),
    inference(rw,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_21,negated_conjecture,
    ssList(esk50_0),
    inference(rw,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_22,negated_conjecture,
    ( nil = esk50_0
    | ssList(esk53_0) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_23,negated_conjecture,
    ( nil = esk50_0
    | ssList(esk54_0) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_24,plain,
    ( ~ ssList(X1)
    | ~ ssItem(X2)
    | nil != cons(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_25,negated_conjecture,
    ( nil = esk51_0
    | cons(esk52_0,nil) = esk50_0 ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_26,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[ax17]) ).

cnf(c_0_27,negated_conjecture,
    ( nil = esk51_0
    | ssItem(esk52_0) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_28,plain,
    ! [X190,X191] :
      ( ~ ssList(X190)
      | ~ ssList(X191)
      | ~ segmentP(X190,X191)
      | ~ segmentP(X191,X190)
      | X190 = X191 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax54])])]) ).

cnf(c_0_29,negated_conjecture,
    ( esk51_0 = nil
    | ~ segmentP(esk51_0,esk50_0)
    | ~ neq(esk50_0,nil) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_13]),c_0_15]),c_0_13]),c_0_15]) ).

cnf(c_0_30,negated_conjecture,
    ( esk50_0 = nil
    | segmentP(esk51_0,esk50_0) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]),c_0_22]),c_0_23]) ).

cnf(c_0_31,negated_conjecture,
    ( esk51_0 = nil
    | esk50_0 != nil ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]),c_0_27]) ).

fof(c_0_32,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_33,plain,
    ( X1 = X2
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ segmentP(X1,X2)
    | ~ segmentP(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_34,negated_conjecture,
    ( esk51_0 = nil
    | ~ neq(esk50_0,nil) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).

cnf(c_0_35,plain,
    ( X1 = X2
    | neq(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_36,negated_conjecture,
    ( esk50_0 = nil
    | esk51_0 = esk50_0
    | ~ segmentP(esk50_0,esk51_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_30]),c_0_20]),c_0_21])]) ).

cnf(c_0_37,negated_conjecture,
    esk51_0 = nil,
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_26]),c_0_21])]),c_0_31]) ).

fof(c_0_38,plain,
    ! [X197] :
      ( ~ ssList(X197)
      | segmentP(X197,nil) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])]) ).

fof(c_0_39,plain,
    ! [X198] :
      ( ( ~ segmentP(nil,X198)
        | nil = X198
        | ~ ssList(X198) )
      & ( nil != X198
        | segmentP(nil,X198)
        | ~ ssList(X198) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax58])])]) ).

cnf(c_0_40,negated_conjecture,
    ( ~ neq(esk48_0,nil)
    | ~ segmentP(esk49_0,esk48_0)
    | nil != esk48_0 ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_41,negated_conjecture,
    ( esk50_0 = nil
    | ~ segmentP(esk50_0,nil) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_37])]) ).

cnf(c_0_42,plain,
    ( segmentP(X1,nil)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_43,plain,
    ( segmentP(nil,X1)
    | nil != X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_44,negated_conjecture,
    ( neq(esk49_0,nil)
    | nil != esk48_0 ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_45,negated_conjecture,
    ( esk50_0 != nil
    | ~ segmentP(esk51_0,esk50_0)
    | ~ neq(esk50_0,nil) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_15]),c_0_15]),c_0_13]),c_0_15]) ).

cnf(c_0_46,negated_conjecture,
    esk50_0 = nil,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_21])]) ).

cnf(c_0_47,plain,
    segmentP(nil,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_43]),c_0_26])]) ).

cnf(c_0_48,negated_conjecture,
    ( neq(esk51_0,nil)
    | esk50_0 != nil ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_13]),c_0_15]) ).

cnf(c_0_49,negated_conjecture,
    ~ neq(nil,nil),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_37]),c_0_46]),c_0_46]),c_0_47]),c_0_46])]) ).

cnf(c_0_50,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_37]),c_0_46])]),c_0_49]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWC109+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13  % Command  : enigmatic-eprover.py %s %d 1
% 0.13/0.34  % Computer : n009.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sun Jun 12 02:48:24 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.46  # ENIGMATIC: Selected SinE mode:
% 0.20/0.46  # Parsing /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.46  # Filter: axfilter_auto   0 goes into file theBenchmark_axfilter_auto   0.p
% 0.20/0.46  # Filter: axfilter_auto   1 goes into file theBenchmark_axfilter_auto   1.p
% 0.20/0.46  # Filter: axfilter_auto   2 goes into file theBenchmark_axfilter_auto   2.p
% 7.72/2.47  # ENIGMATIC: Solved by autoschedule:
% 7.72/2.47  # No SInE strategy applied
% 7.72/2.47  # Trying AutoSched0 for 150 seconds
% 7.72/2.47  # AutoSched0-Mode selected heuristic G_E___207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 7.72/2.47  # and selection function SelectNewComplexAHP.
% 7.72/2.47  #
% 7.72/2.47  # Preprocessing time       : 0.019 s
% 7.72/2.47  # Presaturation interreduction done
% 7.72/2.47  
% 7.72/2.47  # Proof found!
% 7.72/2.47  # SZS status Theorem
% 7.72/2.47  # SZS output start CNFRefutation
% See solution above
% 7.72/2.47  # Training examples: 0 positive, 0 negative
% 7.72/2.47  
% 7.72/2.47  # -------------------------------------------------
% 7.72/2.47  # User time                : 0.044 s
% 7.72/2.47  # System time              : 0.004 s
% 7.72/2.47  # Total time               : 0.047 s
% 7.72/2.47  # Maximum resident set size: 7124 pages
% 7.72/2.47  
%------------------------------------------------------------------------------