TSTP Solution File: SET636+3 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SET636+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n021.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 00:52:46 EDT 2022

% Result   : Theorem 0.24s 1.42s
% Output   : CNFRefutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   40 (   9 unt;   0 def)
%            Number of atoms       :  103 (  23 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  105 (  42   ~;  45   |;  11   &)
%                                         (   7 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   80 (  13 sgn  41   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(empty_set_defn,axiom,
    ! [X1] : ~ member(X1,empty_set),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',empty_set_defn) ).

fof(equal_member_defn,axiom,
    ! [X1,X2] :
      ( X1 = X2
    <=> ! [X3] :
          ( member(X3,X1)
        <=> member(X3,X2) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',equal_member_defn) ).

fof(intersection_defn,axiom,
    ! [X1,X2,X3] :
      ( member(X3,intersection(X1,X2))
    <=> ( member(X3,X1)
        & member(X3,X2) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',intersection_defn) ).

fof(prove_th118,conjecture,
    ! [X1,X2] :
      ( disjoint(X1,X2)
    <=> intersection(X1,X2) = empty_set ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_th118) ).

fof(intersect_defn,axiom,
    ! [X1,X2] :
      ( intersect(X1,X2)
    <=> ? [X3] :
          ( member(X3,X1)
          & member(X3,X2) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',intersect_defn) ).

fof(disjoint_defn,axiom,
    ! [X1,X2] :
      ( disjoint(X1,X2)
    <=> ~ intersect(X1,X2) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',disjoint_defn) ).

fof(commutativity_of_intersection,axiom,
    ! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_of_intersection) ).

fof(c_0_7,plain,
    ! [X2] : ~ member(X2,empty_set),
    inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[empty_set_defn])]) ).

fof(c_0_8,plain,
    ! [X4,X5,X6,X6,X4,X5] :
      ( ( ~ member(X6,X4)
        | member(X6,X5)
        | X4 != X5 )
      & ( ~ member(X6,X5)
        | member(X6,X4)
        | X4 != X5 )
      & ( ~ member(esk3_2(X4,X5),X4)
        | ~ member(esk3_2(X4,X5),X5)
        | X4 = X5 )
      & ( member(esk3_2(X4,X5),X4)
        | member(esk3_2(X4,X5),X5)
        | 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)],[equal_member_defn])])])])])])]) ).

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

cnf(c_0_10,plain,
    ~ member(X1,empty_set),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,plain,
    ( X1 = X2
    | member(esk3_2(X1,X2),X2)
    | member(esk3_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_12,negated_conjecture,
    ~ ! [X1,X2] :
        ( disjoint(X1,X2)
      <=> intersection(X1,X2) = empty_set ),
    inference(assume_negation,[status(cth)],[prove_th118]) ).

fof(c_0_13,plain,
    ! [X4,X5,X4,X5,X7] :
      ( ( member(esk4_2(X4,X5),X4)
        | ~ intersect(X4,X5) )
      & ( member(esk4_2(X4,X5),X5)
        | ~ intersect(X4,X5) )
      & ( ~ member(X7,X4)
        | ~ member(X7,X5)
        | intersect(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)],[intersect_defn])])])])])])]) ).

cnf(c_0_14,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,plain,
    ( X1 = empty_set
    | member(esk3_2(X1,empty_set),X1) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

fof(c_0_16,plain,
    ! [X3,X4,X3,X4] :
      ( ( ~ disjoint(X3,X4)
        | ~ intersect(X3,X4) )
      & ( intersect(X3,X4)
        | disjoint(X3,X4) ) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[disjoint_defn])])])])]) ).

fof(c_0_17,negated_conjecture,
    ( ( ~ disjoint(esk1_0,esk2_0)
      | intersection(esk1_0,esk2_0) != empty_set )
    & ( disjoint(esk1_0,esk2_0)
      | intersection(esk1_0,esk2_0) = empty_set ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).

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

cnf(c_0_19,plain,
    ( intersection(X1,X2) = empty_set
    | member(esk3_2(intersection(X1,X2),empty_set),X1) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_20,plain,
    ( member(X1,X3)
    | ~ member(X1,intersection(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_21,plain,
    ( ~ intersect(X1,X2)
    | ~ disjoint(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_22,negated_conjecture,
    ( intersection(esk1_0,esk2_0) = empty_set
    | disjoint(esk1_0,esk2_0) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_23,plain,
    ( intersection(X1,X2) = empty_set
    | intersect(X3,X1)
    | ~ member(esk3_2(intersection(X1,X2),empty_set),X3) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_24,plain,
    ( intersection(X1,X2) = X3
    | member(esk3_2(intersection(X1,X2),X3),X3)
    | member(esk3_2(intersection(X1,X2),X3),X2) ),
    inference(spm,[status(thm)],[c_0_20,c_0_11]) ).

fof(c_0_25,plain,
    ! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
    inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).

cnf(c_0_26,negated_conjecture,
    ( intersection(esk1_0,esk2_0) = empty_set
    | ~ intersect(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_27,plain,
    ( intersection(X1,X2) = empty_set
    | intersect(X2,X1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_10]) ).

cnf(c_0_28,plain,
    intersection(X1,X2) = intersection(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_29,plain,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X3)
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_30,negated_conjecture,
    intersection(esk1_0,esk2_0) = empty_set,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).

cnf(c_0_31,negated_conjecture,
    ( intersection(esk1_0,esk2_0) != empty_set
    | ~ disjoint(esk1_0,esk2_0) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_32,plain,
    ( disjoint(X1,X2)
    | intersect(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_33,negated_conjecture,
    ( ~ member(X1,esk2_0)
    | ~ member(X1,esk1_0) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_10]) ).

cnf(c_0_34,plain,
    ( member(esk4_2(X1,X2),X2)
    | ~ intersect(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_35,negated_conjecture,
    ( intersect(esk1_0,esk2_0)
    | intersection(esk1_0,esk2_0) != empty_set ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_36,negated_conjecture,
    ( ~ intersect(X1,esk2_0)
    | ~ member(esk4_2(X1,esk2_0),esk1_0) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_37,plain,
    ( member(esk4_2(X1,X2),X1)
    | ~ intersect(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_38,negated_conjecture,
    intersect(esk1_0,esk2_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_30])]) ).

cnf(c_0_39,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SET636+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13  % Command  : run_ET %s %d
% 0.12/0.34  % Computer : n021.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Mon Jul 11 04:08:08 EDT 2022
% 0.12/0.35  % CPUTime  : 
% 0.24/1.42  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.42  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.42  # Preprocessing time       : 0.016 s
% 0.24/1.42  
% 0.24/1.42  # Proof found!
% 0.24/1.42  # SZS status Theorem
% 0.24/1.42  # SZS output start CNFRefutation
% See solution above
% 0.24/1.42  # Proof object total steps             : 40
% 0.24/1.42  # Proof object clause steps            : 25
% 0.24/1.42  # Proof object formula steps           : 15
% 0.24/1.42  # Proof object conjectures             : 12
% 0.24/1.42  # Proof object clause conjectures      : 9
% 0.24/1.42  # Proof object formula conjectures     : 3
% 0.24/1.42  # Proof object initial clauses used    : 13
% 0.24/1.42  # Proof object initial formulas used   : 7
% 0.24/1.42  # Proof object generating inferences   : 11
% 0.24/1.42  # Proof object simplifying inferences  : 8
% 0.24/1.42  # Training examples: 0 positive, 0 negative
% 0.24/1.42  # Parsed axioms                        : 12
% 0.24/1.42  # Removed by relevancy pruning/SinE    : 4
% 0.24/1.42  # Initial clauses                      : 17
% 0.24/1.42  # Removed in clause preprocessing      : 2
% 0.24/1.42  # Initial clauses in saturation        : 15
% 0.24/1.42  # Processed clauses                    : 201
% 0.24/1.42  # ...of these trivial                  : 7
% 0.24/1.42  # ...subsumed                          : 111
% 0.24/1.42  # ...remaining for further processing  : 83
% 0.24/1.42  # Other redundant clauses eliminated   : 0
% 0.24/1.42  # Clauses deleted for lack of memory   : 0
% 0.24/1.42  # Backward-subsumed                    : 0
% 0.24/1.42  # Backward-rewritten                   : 7
% 0.24/1.42  # Generated clauses                    : 842
% 0.24/1.42  # ...of the previous two non-trivial   : 774
% 0.24/1.42  # Contextual simplify-reflections      : 0
% 0.24/1.42  # Paramodulations                      : 830
% 0.24/1.42  # Factorizations                       : 12
% 0.24/1.42  # Equation resolutions                 : 0
% 0.24/1.42  # Current number of processed clauses  : 76
% 0.24/1.42  #    Positive orientable unit clauses  : 9
% 0.24/1.42  #    Positive unorientable unit clauses: 1
% 0.24/1.42  #    Negative unit clauses             : 4
% 0.24/1.42  #    Non-unit-clauses                  : 62
% 0.24/1.42  # Current number of unprocessed clauses: 588
% 0.24/1.42  # ...number of literals in the above   : 1842
% 0.24/1.42  # Current number of archived formulas  : 0
% 0.24/1.42  # Current number of archived clauses   : 7
% 0.24/1.42  # Clause-clause subsumption calls (NU) : 778
% 0.24/1.42  # Rec. Clause-clause subsumption calls : 674
% 0.24/1.42  # Non-unit clause-clause subsumptions  : 73
% 0.24/1.42  # Unit Clause-clause subsumption calls : 9
% 0.24/1.42  # Rewrite failures with RHS unbound    : 0
% 0.24/1.42  # BW rewrite match attempts            : 3
% 0.24/1.42  # BW rewrite match successes           : 3
% 0.24/1.42  # Condensation attempts                : 0
% 0.24/1.42  # Condensation successes               : 0
% 0.24/1.42  # Termbank termtop insertions          : 9737
% 0.24/1.42  
% 0.24/1.42  # -------------------------------------------------
% 0.24/1.42  # User time                : 0.033 s
% 0.24/1.42  # System time              : 0.001 s
% 0.24/1.42  # Total time               : 0.034 s
% 0.24/1.42  # Maximum resident set size: 3304 pages
%------------------------------------------------------------------------------