TSTP Solution File: SET763+4 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SET763+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n007.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 00:53:49 EDT 2022

% Result   : Theorem 0.16s 1.35s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   35 (  14 unt;   0 def)
%            Number of atoms       :  148 (   4 equ)
%            Maximal formula atoms :   55 (   4 avg)
%            Number of connectives :  175 (  62   ~;  69   |;  34   &)
%                                         (   4 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   30 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   5 con; 0-4 aty)
%            Number of variables   :   85 (  16 sgn  52   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(thIIa13,conjecture,
    ! [X6,X1,X2,X3] :
      ( ( maps(X6,X1,X2)
        & subset(X3,X1)
        & equal_set(image2(X6,X3),empty_set) )
     => equal_set(X3,empty_set) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',thIIa13) ).

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(empty_set,axiom,
    ! [X3] : ~ member(X3,empty_set),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',empty_set) ).

fof(image2,axiom,
    ! [X6,X1,X5] :
      ( member(X5,image2(X6,X1))
    <=> ? [X3] :
          ( member(X3,X1)
          & apply(X6,X3,X5) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',image2) ).

fof(maps,axiom,
    ! [X6,X1,X2] :
      ( maps(X6,X1,X2)
    <=> ( ! [X3] :
            ( member(X3,X1)
           => ? [X5] :
                ( member(X5,X2)
                & apply(X6,X3,X5) ) )
        & ! [X3,X7,X8] :
            ( ( member(X3,X1)
              & member(X7,X2)
              & member(X8,X2) )
           => ( ( apply(X6,X3,X7)
                & apply(X6,X3,X8) )
             => X7 = X8 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',maps) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X6,X1,X2,X3] :
        ( ( maps(X6,X1,X2)
          & subset(X3,X1)
          & equal_set(image2(X6,X3),empty_set) )
       => equal_set(X3,empty_set) ),
    inference(assume_negation,[status(cth)],[thIIa13]) ).

fof(c_0_7,plain,
    ! [X3,X4,X3,X4] :
      ( ( subset(X3,X4)
        | ~ equal_set(X3,X4) )
      & ( subset(X4,X3)
        | ~ equal_set(X3,X4) )
      & ( ~ subset(X3,X4)
        | ~ subset(X4,X3)
        | equal_set(X3,X4) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])])])]) ).

fof(c_0_8,negated_conjecture,
    ( maps(esk1_0,esk2_0,esk3_0)
    & subset(esk4_0,esk2_0)
    & equal_set(image2(esk1_0,esk4_0),empty_set)
    & ~ equal_set(esk4_0,empty_set) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).

fof(c_0_9,plain,
    ! [X4,X5,X6,X4,X5] :
      ( ( ~ subset(X4,X5)
        | ~ member(X6,X4)
        | member(X6,X5) )
      & ( member(esk6_2(X4,X5),X4)
        | subset(X4,X5) )
      & ( ~ member(esk6_2(X4,X5),X5)
        | subset(X4,X5) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subset])])])])])])]) ).

cnf(c_0_10,plain,
    ( subset(X1,X2)
    | ~ equal_set(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,negated_conjecture,
    equal_set(image2(esk1_0,esk4_0),empty_set),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_12,plain,
    ! [X4] : ~ member(X4,empty_set),
    inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[empty_set])]) ).

fof(c_0_13,plain,
    ! [X7,X8,X9,X7,X8,X9,X11] :
      ( ( member(esk5_3(X7,X8,X9),X8)
        | ~ member(X9,image2(X7,X8)) )
      & ( apply(X7,esk5_3(X7,X8,X9),X9)
        | ~ member(X9,image2(X7,X8)) )
      & ( ~ member(X11,X8)
        | ~ apply(X7,X11,X9)
        | member(X9,image2(X7,X8)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[image2])])])])])])]) ).

fof(c_0_14,plain,
    ! [X9,X10,X11,X12,X14,X15,X16,X9,X10,X11,X18] :
      ( ( member(esk7_4(X9,X10,X11,X12),X11)
        | ~ member(X12,X10)
        | ~ maps(X9,X10,X11) )
      & ( apply(X9,X12,esk7_4(X9,X10,X11,X12))
        | ~ member(X12,X10)
        | ~ maps(X9,X10,X11) )
      & ( ~ member(X14,X10)
        | ~ member(X15,X11)
        | ~ member(X16,X11)
        | ~ apply(X9,X14,X15)
        | ~ apply(X9,X14,X16)
        | X15 = X16
        | ~ maps(X9,X10,X11) )
      & ( member(esk9_3(X9,X10,X11),X10)
        | member(esk8_3(X9,X10,X11),X10)
        | maps(X9,X10,X11) )
      & ( member(esk10_3(X9,X10,X11),X11)
        | member(esk8_3(X9,X10,X11),X10)
        | maps(X9,X10,X11) )
      & ( member(esk11_3(X9,X10,X11),X11)
        | member(esk8_3(X9,X10,X11),X10)
        | maps(X9,X10,X11) )
      & ( apply(X9,esk9_3(X9,X10,X11),esk10_3(X9,X10,X11))
        | member(esk8_3(X9,X10,X11),X10)
        | maps(X9,X10,X11) )
      & ( apply(X9,esk9_3(X9,X10,X11),esk11_3(X9,X10,X11))
        | member(esk8_3(X9,X10,X11),X10)
        | maps(X9,X10,X11) )
      & ( esk10_3(X9,X10,X11) != esk11_3(X9,X10,X11)
        | member(esk8_3(X9,X10,X11),X10)
        | maps(X9,X10,X11) )
      & ( member(esk9_3(X9,X10,X11),X10)
        | ~ member(X18,X11)
        | ~ apply(X9,esk8_3(X9,X10,X11),X18)
        | maps(X9,X10,X11) )
      & ( member(esk10_3(X9,X10,X11),X11)
        | ~ member(X18,X11)
        | ~ apply(X9,esk8_3(X9,X10,X11),X18)
        | maps(X9,X10,X11) )
      & ( member(esk11_3(X9,X10,X11),X11)
        | ~ member(X18,X11)
        | ~ apply(X9,esk8_3(X9,X10,X11),X18)
        | maps(X9,X10,X11) )
      & ( apply(X9,esk9_3(X9,X10,X11),esk10_3(X9,X10,X11))
        | ~ member(X18,X11)
        | ~ apply(X9,esk8_3(X9,X10,X11),X18)
        | maps(X9,X10,X11) )
      & ( apply(X9,esk9_3(X9,X10,X11),esk11_3(X9,X10,X11))
        | ~ member(X18,X11)
        | ~ apply(X9,esk8_3(X9,X10,X11),X18)
        | maps(X9,X10,X11) )
      & ( esk10_3(X9,X10,X11) != esk11_3(X9,X10,X11)
        | ~ member(X18,X11)
        | ~ apply(X9,esk8_3(X9,X10,X11),X18)
        | maps(X9,X10,X11) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[maps])])])])])])]) ).

cnf(c_0_15,plain,
    ( member(X1,X2)
    | ~ member(X1,X3)
    | ~ subset(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_16,negated_conjecture,
    subset(image2(esk1_0,esk4_0),empty_set),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_17,plain,
    ~ member(X1,empty_set),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_18,plain,
    ( member(X1,image2(X2,X3))
    | ~ apply(X2,X4,X1)
    | ~ member(X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_19,plain,
    ( apply(X1,X4,esk7_4(X1,X2,X3,X4))
    | ~ maps(X1,X2,X3)
    | ~ member(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_20,negated_conjecture,
    ~ member(X1,image2(esk1_0,esk4_0)),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).

cnf(c_0_21,plain,
    ( member(esk7_4(X1,X2,X3,X4),image2(X1,X5))
    | ~ maps(X1,X2,X3)
    | ~ member(X4,X5)
    | ~ member(X4,X2) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_22,negated_conjecture,
    subset(esk4_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_23,negated_conjecture,
    ~ equal_set(esk4_0,empty_set),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_24,plain,
    ( equal_set(X1,X2)
    | ~ subset(X2,X1)
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_25,plain,
    ( subset(X1,X2)
    | member(esk6_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_26,negated_conjecture,
    ( ~ maps(esk1_0,X1,X2)
    | ~ member(X3,esk4_0)
    | ~ member(X3,X1) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_27,negated_conjecture,
    maps(esk1_0,esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_28,negated_conjecture,
    ( member(X1,esk2_0)
    | ~ member(X1,esk4_0) ),
    inference(spm,[status(thm)],[c_0_15,c_0_22]) ).

cnf(c_0_29,negated_conjecture,
    ( ~ subset(empty_set,esk4_0)
    | ~ subset(esk4_0,empty_set) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_30,plain,
    subset(empty_set,X1),
    inference(spm,[status(thm)],[c_0_17,c_0_25]) ).

cnf(c_0_31,negated_conjecture,
    ~ member(X1,esk4_0),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).

cnf(c_0_32,negated_conjecture,
    ~ subset(esk4_0,empty_set),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).

cnf(c_0_33,negated_conjecture,
    subset(esk4_0,X1),
    inference(spm,[status(thm)],[c_0_31,c_0_25]) ).

cnf(c_0_34,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : SET763+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.09/0.09  % Command  : run_ET %s %d
% 0.09/0.29  % Computer : n007.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit : 300
% 0.09/0.29  % WCLimit  : 600
% 0.09/0.29  % DateTime : Sun Jul 10 03:24:31 EDT 2022
% 0.09/0.29  % CPUTime  : 
% 0.16/1.35  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.16/1.35  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.16/1.35  # Preprocessing time       : 0.013 s
% 0.16/1.35  
% 0.16/1.35  # Proof found!
% 0.16/1.35  # SZS status Theorem
% 0.16/1.35  # SZS output start CNFRefutation
% See solution above
% 0.16/1.35  # Proof object total steps             : 35
% 0.16/1.35  # Proof object clause steps            : 22
% 0.16/1.35  # Proof object formula steps           : 13
% 0.16/1.35  # Proof object conjectures             : 16
% 0.16/1.35  # Proof object clause conjectures      : 13
% 0.16/1.35  # Proof object formula conjectures     : 3
% 0.16/1.35  # Proof object initial clauses used    : 11
% 0.16/1.35  # Proof object initial formulas used   : 6
% 0.16/1.35  # Proof object generating inferences   : 9
% 0.16/1.35  # Proof object simplifying inferences  : 6
% 0.16/1.35  # Training examples: 0 positive, 0 negative
% 0.16/1.35  # Parsed axioms                        : 29
% 0.16/1.35  # Removed by relevancy pruning/SinE    : 23
% 0.16/1.35  # Initial clauses                      : 29
% 0.16/1.35  # Removed in clause preprocessing      : 0
% 0.16/1.35  # Initial clauses in saturation        : 29
% 0.16/1.35  # Processed clauses                    : 72
% 0.16/1.35  # ...of these trivial                  : 0
% 0.16/1.35  # ...subsumed                          : 9
% 0.16/1.35  # ...remaining for further processing  : 63
% 0.16/1.35  # Other redundant clauses eliminated   : 0
% 0.16/1.35  # Clauses deleted for lack of memory   : 0
% 0.16/1.35  # Backward-subsumed                    : 0
% 0.16/1.35  # Backward-rewritten                   : 9
% 0.16/1.35  # Generated clauses                    : 108
% 0.16/1.35  # ...of the previous two non-trivial   : 98
% 0.16/1.35  # Contextual simplify-reflections      : 1
% 0.16/1.35  # Paramodulations                      : 108
% 0.16/1.35  # Factorizations                       : 0
% 0.16/1.35  # Equation resolutions                 : 0
% 0.16/1.35  # Current number of processed clauses  : 54
% 0.16/1.35  #    Positive orientable unit clauses  : 12
% 0.16/1.35  #    Positive unorientable unit clauses: 0
% 0.16/1.35  #    Negative unit clauses             : 6
% 0.16/1.35  #    Non-unit-clauses                  : 36
% 0.16/1.35  # Current number of unprocessed clauses: 50
% 0.16/1.35  # ...number of literals in the above   : 156
% 0.16/1.35  # Current number of archived formulas  : 0
% 0.16/1.35  # Current number of archived clauses   : 9
% 0.16/1.35  # Clause-clause subsumption calls (NU) : 110
% 0.16/1.35  # Rec. Clause-clause subsumption calls : 54
% 0.16/1.35  # Non-unit clause-clause subsumptions  : 2
% 0.16/1.35  # Unit Clause-clause subsumption calls : 49
% 0.16/1.35  # Rewrite failures with RHS unbound    : 0
% 0.16/1.35  # BW rewrite match attempts            : 16
% 0.16/1.35  # BW rewrite match successes           : 9
% 0.16/1.35  # Condensation attempts                : 0
% 0.16/1.35  # Condensation successes               : 0
% 0.16/1.35  # Termbank termtop insertions          : 3432
% 0.16/1.35  
% 0.16/1.35  # -------------------------------------------------
% 0.16/1.35  # User time                : 0.016 s
% 0.16/1.35  # System time              : 0.001 s
% 0.16/1.35  # Total time               : 0.017 s
% 0.16/1.35  # Maximum resident set size: 3052 pages
%------------------------------------------------------------------------------