TSTP Solution File: SET351+4 by Enigma---0.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Enigma---0.5.1
% Problem  : SET351+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : enigmatic-eprover.py %s %d 1

% Computer : n003.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 00:11:10 EDT 2022

% Result   : Theorem 6.85s 2.91s
% Output   : CNFRefutation 6.85s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   38 (   9 unt;   0 def)
%            Number of atoms       :   90 (   9 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   91 (  39   ~;  38   |;   9   &)
%                                         (   4 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :   46 (   0 sgn  25   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(thI39,conjecture,
    ! [X1] : equal_set(sum(singleton(X1)),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI39) ).

fof(equal_set,axiom,
    ! [X1,X2] :
      ( equal_set(X1,X2)
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).

fof(subset,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).

fof(sum,axiom,
    ! [X3,X1] :
      ( member(X3,sum(X1))
    <=> ? [X5] :
          ( member(X5,X1)
          & member(X3,X5) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',sum) ).

fof(singleton,axiom,
    ! [X3,X1] :
      ( member(X3,singleton(X1))
    <=> X3 = X1 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',singleton) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X1] : equal_set(sum(singleton(X1)),X1),
    inference(assume_negation,[status(cth)],[thI39]) ).

fof(c_0_6,negated_conjecture,
    ~ equal_set(sum(singleton(esk4_0)),esk4_0),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

fof(c_0_7,plain,
    ! [X12,X13] :
      ( ( subset(X12,X13)
        | ~ equal_set(X12,X13) )
      & ( subset(X13,X12)
        | ~ equal_set(X12,X13) )
      & ( ~ subset(X12,X13)
        | ~ subset(X13,X12)
        | equal_set(X12,X13) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])]) ).

cnf(c_0_8,negated_conjecture,
    ~ equal_set(sum(singleton(esk4_0)),esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_9,plain,
    ( equal_set(X1,X2)
    | ~ subset(X1,X2)
    | ~ subset(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_10,plain,
    ! [X6,X7,X8,X9,X10] :
      ( ( ~ subset(X6,X7)
        | ~ member(X8,X6)
        | member(X8,X7) )
      & ( member(esk1_2(X9,X10),X9)
        | subset(X9,X10) )
      & ( ~ member(esk1_2(X9,X10),X10)
        | subset(X9,X10) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[subset])])])])])]) ).

cnf(c_0_11,negated_conjecture,
    ( ~ subset(esk4_0,sum(singleton(esk4_0)))
    | ~ subset(sum(singleton(esk4_0)),esk4_0) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_12,plain,
    ( member(esk1_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_13,plain,
    ! [X31,X32,X34,X35,X36] :
      ( ( member(esk2_2(X31,X32),X32)
        | ~ member(X31,sum(X32)) )
      & ( member(X31,esk2_2(X31,X32))
        | ~ member(X31,sum(X32)) )
      & ( ~ member(X36,X35)
        | ~ member(X34,X36)
        | member(X34,sum(X35)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[sum])])])])])]) ).

cnf(c_0_14,negated_conjecture,
    ( member(esk1_2(sum(singleton(esk4_0)),esk4_0),sum(singleton(esk4_0)))
    | ~ subset(esk4_0,sum(singleton(esk4_0))) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_15,plain,
    ( subset(X1,X2)
    | ~ member(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_16,plain,
    ! [X26,X27] :
      ( ( ~ member(X26,singleton(X27))
        | X26 = X27 )
      & ( X26 != X27
        | member(X26,singleton(X27)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[singleton])]) ).

cnf(c_0_17,plain,
    ( member(esk2_2(X1,X2),X2)
    | ~ member(X1,sum(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_18,negated_conjecture,
    ( member(esk1_2(sum(singleton(esk4_0)),esk4_0),sum(singleton(esk4_0)))
    | member(esk1_2(esk4_0,sum(singleton(esk4_0))),esk4_0) ),
    inference(spm,[status(thm)],[c_0_14,c_0_12]) ).

cnf(c_0_19,negated_conjecture,
    ( member(esk1_2(sum(singleton(esk4_0)),esk4_0),sum(singleton(esk4_0)))
    | ~ member(esk1_2(esk4_0,sum(singleton(esk4_0))),sum(singleton(esk4_0))) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_20,plain,
    ( X1 = X2
    | ~ member(X1,singleton(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_21,negated_conjecture,
    ( member(esk2_2(esk1_2(sum(singleton(esk4_0)),esk4_0),singleton(esk4_0)),singleton(esk4_0))
    | member(esk1_2(esk4_0,sum(singleton(esk4_0))),esk4_0) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_22,negated_conjecture,
    ( member(esk2_2(esk1_2(sum(singleton(esk4_0)),esk4_0),singleton(esk4_0)),singleton(esk4_0))
    | ~ member(esk1_2(esk4_0,sum(singleton(esk4_0))),sum(singleton(esk4_0))) ),
    inference(spm,[status(thm)],[c_0_17,c_0_19]) ).

cnf(c_0_23,plain,
    ( member(X3,sum(X2))
    | ~ member(X1,X2)
    | ~ member(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_24,negated_conjecture,
    ( esk2_2(esk1_2(sum(singleton(esk4_0)),esk4_0),singleton(esk4_0)) = esk4_0
    | member(esk1_2(esk4_0,sum(singleton(esk4_0))),esk4_0) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_25,plain,
    ( member(X1,singleton(X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_26,negated_conjecture,
    ( esk2_2(esk1_2(sum(singleton(esk4_0)),esk4_0),singleton(esk4_0)) = esk4_0
    | ~ member(esk1_2(esk4_0,sum(singleton(esk4_0))),sum(singleton(esk4_0))) ),
    inference(spm,[status(thm)],[c_0_20,c_0_22]) ).

cnf(c_0_27,negated_conjecture,
    ( esk2_2(esk1_2(sum(singleton(esk4_0)),esk4_0),singleton(esk4_0)) = esk4_0
    | member(esk1_2(esk4_0,sum(singleton(esk4_0))),sum(X1))
    | ~ member(esk4_0,X1) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_28,plain,
    member(X1,singleton(X1)),
    inference(er,[status(thm)],[c_0_25]) ).

cnf(c_0_29,negated_conjecture,
    ( ~ member(esk1_2(sum(singleton(esk4_0)),esk4_0),esk4_0)
    | ~ subset(esk4_0,sum(singleton(esk4_0))) ),
    inference(spm,[status(thm)],[c_0_11,c_0_15]) ).

cnf(c_0_30,plain,
    ( member(X1,esk2_2(X1,X2))
    | ~ member(X1,sum(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_31,negated_conjecture,
    esk2_2(esk1_2(sum(singleton(esk4_0)),esk4_0),singleton(esk4_0)) = esk4_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_32,negated_conjecture,
    ( member(esk1_2(esk4_0,sum(singleton(esk4_0))),esk4_0)
    | ~ member(esk1_2(sum(singleton(esk4_0)),esk4_0),esk4_0) ),
    inference(spm,[status(thm)],[c_0_29,c_0_12]) ).

cnf(c_0_33,negated_conjecture,
    ( ~ member(esk1_2(esk4_0,sum(singleton(esk4_0))),sum(singleton(esk4_0)))
    | ~ member(esk1_2(sum(singleton(esk4_0)),esk4_0),esk4_0) ),
    inference(spm,[status(thm)],[c_0_29,c_0_15]) ).

cnf(c_0_34,negated_conjecture,
    member(esk1_2(esk4_0,sum(singleton(esk4_0))),esk4_0),
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_18]),c_0_31]),c_0_32]) ).

cnf(c_0_35,negated_conjecture,
    ~ member(esk1_2(esk4_0,sum(singleton(esk4_0))),sum(singleton(esk4_0))),
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_19]),c_0_31]),c_0_33]) ).

cnf(c_0_36,negated_conjecture,
    ( member(esk1_2(esk4_0,sum(singleton(esk4_0))),sum(X1))
    | ~ member(esk4_0,X1) ),
    inference(spm,[status(thm)],[c_0_23,c_0_34]) ).

cnf(c_0_37,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_28])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : SET351+4 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.14  % Command  : enigmatic-eprover.py %s %d 1
% 0.14/0.35  % Computer : n003.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Mon Jul 11 04:14:31 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.21/0.46  # ENIGMATIC: Selected SinE mode:
% 0.21/0.46  # Parsing /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.46  # Filter: axfilter_auto   0 goes into file theBenchmark_axfilter_auto   0.p
% 0.21/0.46  # Filter: axfilter_auto   1 goes into file theBenchmark_axfilter_auto   1.p
% 0.21/0.46  # Filter: axfilter_auto   2 goes into file theBenchmark_axfilter_auto   2.p
% 6.85/2.91  # ENIGMATIC: Solved by autoschedule:
% 6.85/2.91  # No SInE strategy applied
% 6.85/2.91  # Trying AutoSched0 for 150 seconds
% 6.85/2.91  # AutoSched0-Mode selected heuristic G_E___208_C09_12_F1_SE_CS_SP_PS_S070I
% 6.85/2.91  # and selection function SelectVGNonCR.
% 6.85/2.91  #
% 6.85/2.91  # Preprocessing time       : 0.015 s
% 6.85/2.91  # Presaturation interreduction done
% 6.85/2.91  
% 6.85/2.91  # Proof found!
% 6.85/2.91  # SZS status Theorem
% 6.85/2.91  # SZS output start CNFRefutation
% See solution above
% 6.85/2.91  # Training examples: 0 positive, 0 negative
% 6.85/2.91  
% 6.85/2.91  # -------------------------------------------------
% 6.85/2.91  # User time                : 0.022 s
% 6.85/2.91  # System time              : 0.003 s
% 6.85/2.91  # Total time               : 0.026 s
% 6.85/2.91  # Maximum resident set size: 7116 pages
% 6.85/2.91  
%------------------------------------------------------------------------------