TSTP Solution File: SET638+3 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SET638+3 : TPTP v8.1.0. Released v2.2.0.
% 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 00:52:47 EDT 2022

% Result   : Theorem 0.23s 1.41s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   32 (  25 unt;   0 def)
%            Number of atoms       :   42 (  25 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   16 (   6   ~;   3   |;   4   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   48 (   1 sgn  30   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(prove_th120,conjecture,
    ! [X1,X2,X3] :
      ( ( subset(X1,union(X2,X3))
        & intersection(X1,X3) = empty_set )
     => subset(X1,X2) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_th120) ).

fof(intersection_distributes_over_union,axiom,
    ! [X1,X2,X3] : intersection(X1,union(X2,X3)) = union(intersection(X1,X2),intersection(X1,X3)),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',intersection_distributes_over_union) ).

fof(commutativity_of_intersection,axiom,
    ! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_of_intersection) ).

fof(union_empty_set,axiom,
    ! [X1] : union(X1,empty_set) = X1,
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',union_empty_set) ).

fof(commutativity_of_union,axiom,
    ! [X1,X2] : union(X1,X2) = union(X2,X1),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_of_union) ).

fof(subset_intersection,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
     => intersection(X1,X2) = X1 ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',subset_intersection) ).

fof(intersection_is_subset,axiom,
    ! [X1,X2] : subset(intersection(X1,X2),X1),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',intersection_is_subset) ).

fof(c_0_7,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( subset(X1,union(X2,X3))
          & intersection(X1,X3) = empty_set )
       => subset(X1,X2) ),
    inference(assume_negation,[status(cth)],[prove_th120]) ).

fof(c_0_8,plain,
    ! [X4,X5,X6] : intersection(X4,union(X5,X6)) = union(intersection(X4,X5),intersection(X4,X6)),
    inference(variable_rename,[status(thm)],[intersection_distributes_over_union]) ).

fof(c_0_9,plain,
    ! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
    inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).

fof(c_0_10,negated_conjecture,
    ( subset(esk1_0,union(esk2_0,esk3_0))
    & intersection(esk1_0,esk3_0) = empty_set
    & ~ subset(esk1_0,esk2_0) ),
    inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).

cnf(c_0_11,plain,
    intersection(X1,union(X2,X3)) = union(intersection(X1,X2),intersection(X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,plain,
    intersection(X1,X2) = intersection(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,negated_conjecture,
    intersection(esk1_0,esk3_0) = empty_set,
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_14,plain,
    ! [X2] : union(X2,empty_set) = X2,
    inference(variable_rename,[status(thm)],[union_empty_set]) ).

cnf(c_0_15,plain,
    union(intersection(X1,X2),intersection(X3,X1)) = intersection(X1,union(X2,X3)),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_16,negated_conjecture,
    intersection(esk3_0,esk1_0) = empty_set,
    inference(rw,[status(thm)],[c_0_13,c_0_12]) ).

cnf(c_0_17,plain,
    union(X1,empty_set) = X1,
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_18,plain,
    ! [X3,X4] : union(X3,X4) = union(X4,X3),
    inference(variable_rename,[status(thm)],[commutativity_of_union]) ).

fof(c_0_19,plain,
    ! [X3,X4] :
      ( ~ subset(X3,X4)
      | intersection(X3,X4) = X3 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subset_intersection])]) ).

cnf(c_0_20,negated_conjecture,
    intersection(esk1_0,union(X1,esk3_0)) = intersection(esk1_0,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).

cnf(c_0_21,plain,
    union(X1,X2) = union(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_22,plain,
    ( intersection(X1,X2) = X1
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_23,negated_conjecture,
    intersection(esk1_0,union(esk3_0,X1)) = intersection(esk1_0,X1),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_24,negated_conjecture,
    subset(esk1_0,union(esk2_0,esk3_0)),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

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

cnf(c_0_26,negated_conjecture,
    ( intersection(esk1_0,X1) = esk1_0
    | ~ subset(esk1_0,union(esk3_0,X1)) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_27,negated_conjecture,
    subset(esk1_0,union(esk3_0,esk2_0)),
    inference(rw,[status(thm)],[c_0_24,c_0_21]) ).

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

cnf(c_0_29,negated_conjecture,
    intersection(esk2_0,esk1_0) = esk1_0,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_12]) ).

cnf(c_0_30,negated_conjecture,
    ~ subset(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_31,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET638+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13  % Command  : run_ET %s %d
% 0.12/0.34  % Computer : n007.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 : Sun Jul 10 23:33:47 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.23/1.41  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/1.41  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/1.41  # Preprocessing time       : 0.015 s
% 0.23/1.41  
% 0.23/1.41  # Proof found!
% 0.23/1.41  # SZS status Theorem
% 0.23/1.41  # SZS output start CNFRefutation
% See solution above
% 0.23/1.41  # Proof object total steps             : 32
% 0.23/1.41  # Proof object clause steps            : 17
% 0.23/1.41  # Proof object formula steps           : 15
% 0.23/1.41  # Proof object conjectures             : 13
% 0.23/1.41  # Proof object clause conjectures      : 10
% 0.23/1.41  # Proof object formula conjectures     : 3
% 0.23/1.41  # Proof object initial clauses used    : 9
% 0.23/1.41  # Proof object initial formulas used   : 7
% 0.23/1.41  # Proof object generating inferences   : 6
% 0.23/1.41  # Proof object simplifying inferences  : 5
% 0.23/1.41  # Training examples: 0 positive, 0 negative
% 0.23/1.41  # Parsed axioms                        : 15
% 0.23/1.41  # Removed by relevancy pruning/SinE    : 1
% 0.23/1.41  # Initial clauses                      : 27
% 0.23/1.41  # Removed in clause preprocessing      : 2
% 0.23/1.41  # Initial clauses in saturation        : 25
% 0.23/1.41  # Processed clauses                    : 77
% 0.23/1.41  # ...of these trivial                  : 8
% 0.23/1.41  # ...subsumed                          : 15
% 0.23/1.41  # ...remaining for further processing  : 54
% 0.23/1.41  # Other redundant clauses eliminated   : 2
% 0.23/1.41  # Clauses deleted for lack of memory   : 0
% 0.23/1.41  # Backward-subsumed                    : 1
% 0.23/1.41  # Backward-rewritten                   : 3
% 0.23/1.41  # Generated clauses                    : 313
% 0.23/1.41  # ...of the previous two non-trivial   : 235
% 0.23/1.41  # Contextual simplify-reflections      : 0
% 0.23/1.41  # Paramodulations                      : 309
% 0.23/1.41  # Factorizations                       : 2
% 0.23/1.41  # Equation resolutions                 : 2
% 0.23/1.41  # Current number of processed clauses  : 48
% 0.23/1.41  #    Positive orientable unit clauses  : 18
% 0.23/1.41  #    Positive unorientable unit clauses: 2
% 0.23/1.41  #    Negative unit clauses             : 2
% 0.23/1.41  #    Non-unit-clauses                  : 26
% 0.23/1.41  # Current number of unprocessed clauses: 180
% 0.23/1.41  # ...number of literals in the above   : 367
% 0.23/1.41  # Current number of archived formulas  : 0
% 0.23/1.41  # Current number of archived clauses   : 4
% 0.23/1.41  # Clause-clause subsumption calls (NU) : 50
% 0.23/1.41  # Rec. Clause-clause subsumption calls : 50
% 0.23/1.41  # Non-unit clause-clause subsumptions  : 11
% 0.23/1.41  # Unit Clause-clause subsumption calls : 0
% 0.23/1.41  # Rewrite failures with RHS unbound    : 0
% 0.23/1.41  # BW rewrite match attempts            : 14
% 0.23/1.41  # BW rewrite match successes           : 9
% 0.23/1.41  # Condensation attempts                : 0
% 0.23/1.41  # Condensation successes               : 0
% 0.23/1.41  # Termbank termtop insertions          : 3766
% 0.23/1.41  
% 0.23/1.41  # -------------------------------------------------
% 0.23/1.41  # User time                : 0.019 s
% 0.23/1.41  # System time              : 0.002 s
% 0.23/1.41  # Total time               : 0.021 s
% 0.23/1.41  # Maximum resident set size: 3044 pages
%------------------------------------------------------------------------------