TSTP Solution File: SET968+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SET968+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n017.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 00:55:46 EDT 2022

% Result   : Theorem 0.25s 1.42s
% Output   : CNFRefutation 0.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   17 (  15 unt;   0 def)
%            Number of atoms       :   19 (  18 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    5 (   3   ~;   0   |;   2   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   43 (   3 sgn  27   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t121_zfmisc_1,conjecture,
    ! [X1,X2,X3,X4] : cartesian_product2(set_union2(X1,X2),set_union2(X3,X4)) = set_union2(set_union2(set_union2(cartesian_product2(X1,X3),cartesian_product2(X1,X4)),cartesian_product2(X2,X3)),cartesian_product2(X2,X4)),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t121_zfmisc_1) ).

fof(commutativity_k2_xboole_0,axiom,
    ! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_k2_xboole_0) ).

fof(t4_xboole_1,axiom,
    ! [X1,X2,X3] : set_union2(set_union2(X1,X2),X3) = set_union2(X1,set_union2(X2,X3)),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t4_xboole_1) ).

fof(t120_zfmisc_1,axiom,
    ! [X1,X2,X3] :
      ( cartesian_product2(set_union2(X1,X2),X3) = set_union2(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
      & cartesian_product2(X3,set_union2(X1,X2)) = set_union2(cartesian_product2(X3,X1),cartesian_product2(X3,X2)) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t120_zfmisc_1) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X1,X2,X3,X4] : cartesian_product2(set_union2(X1,X2),set_union2(X3,X4)) = set_union2(set_union2(set_union2(cartesian_product2(X1,X3),cartesian_product2(X1,X4)),cartesian_product2(X2,X3)),cartesian_product2(X2,X4)),
    inference(assume_negation,[status(cth)],[t121_zfmisc_1]) ).

fof(c_0_5,plain,
    ! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
    inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).

fof(c_0_6,plain,
    ! [X4,X5,X6] : set_union2(set_union2(X4,X5),X6) = set_union2(X4,set_union2(X5,X6)),
    inference(variable_rename,[status(thm)],[t4_xboole_1]) ).

fof(c_0_7,negated_conjecture,
    cartesian_product2(set_union2(esk1_0,esk2_0),set_union2(esk3_0,esk4_0)) != set_union2(set_union2(set_union2(cartesian_product2(esk1_0,esk3_0),cartesian_product2(esk1_0,esk4_0)),cartesian_product2(esk2_0,esk3_0)),cartesian_product2(esk2_0,esk4_0)),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

fof(c_0_8,plain,
    ! [X4,X5,X6,X4,X5,X6] :
      ( cartesian_product2(set_union2(X4,X5),X6) = set_union2(cartesian_product2(X4,X6),cartesian_product2(X5,X6))
      & cartesian_product2(X6,set_union2(X4,X5)) = set_union2(cartesian_product2(X6,X4),cartesian_product2(X6,X5)) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[t120_zfmisc_1])])]) ).

cnf(c_0_9,plain,
    set_union2(X1,X2) = set_union2(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_10,plain,
    set_union2(set_union2(X1,X2),X3) = set_union2(X1,set_union2(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,negated_conjecture,
    cartesian_product2(set_union2(esk1_0,esk2_0),set_union2(esk3_0,esk4_0)) != set_union2(set_union2(set_union2(cartesian_product2(esk1_0,esk3_0),cartesian_product2(esk1_0,esk4_0)),cartesian_product2(esk2_0,esk3_0)),cartesian_product2(esk2_0,esk4_0)),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,plain,
    cartesian_product2(X1,set_union2(X2,X3)) = set_union2(cartesian_product2(X1,X2),cartesian_product2(X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,plain,
    cartesian_product2(set_union2(X1,X2),X3) = set_union2(cartesian_product2(X1,X3),cartesian_product2(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,plain,
    set_union2(X1,X2) = set_union2(X2,X1),
    c_0_9 ).

cnf(c_0_15,plain,
    set_union2(set_union2(X1,X2),X3) = set_union2(X1,set_union2(X2,X3)),
    c_0_10 ).

cnf(c_0_16,negated_conjecture,
    $false,
    inference(ar,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_13]),c_0_10]),c_0_10]),c_0_10]),c_0_10]),c_0_14,c_0_15]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET968+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13  % Command  : run_ET %s %d
% 0.13/0.34  % Computer : n017.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 : Mon Jul 11 02:10:33 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.25/1.42  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.25/1.42  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.25/1.42  # Preprocessing time       : 0.014 s
% 0.25/1.42  
% 0.25/1.42  # Proof found!
% 0.25/1.42  # SZS status Theorem
% 0.25/1.42  # SZS output start CNFRefutation
% See solution above
% 0.25/1.42  # Proof object total steps             : 17
% 0.25/1.42  # Proof object clause steps            : 8
% 0.25/1.42  # Proof object formula steps           : 9
% 0.25/1.42  # Proof object conjectures             : 5
% 0.25/1.42  # Proof object clause conjectures      : 2
% 0.25/1.42  # Proof object formula conjectures     : 3
% 0.25/1.42  # Proof object initial clauses used    : 5
% 0.25/1.42  # Proof object initial formulas used   : 4
% 0.25/1.42  # Proof object generating inferences   : 0
% 0.25/1.42  # Proof object simplifying inferences  : 8
% 0.25/1.42  # Training examples: 0 positive, 0 negative
% 0.25/1.42  # Parsed axioms                        : 9
% 0.25/1.42  # Removed by relevancy pruning/SinE    : 4
% 0.25/1.42  # Initial clauses                      : 6
% 0.25/1.42  # Removed in clause preprocessing      : 0
% 0.25/1.42  # Initial clauses in saturation        : 6
% 0.25/1.42  # Processed clauses                    : 11
% 0.25/1.42  # ...of these trivial                  : 2
% 0.25/1.42  # ...subsumed                          : 0
% 0.25/1.42  # ...remaining for further processing  : 8
% 0.25/1.42  # Other redundant clauses eliminated   : 0
% 0.25/1.42  # Clauses deleted for lack of memory   : 0
% 0.25/1.42  # Backward-subsumed                    : 0
% 0.25/1.42  # Backward-rewritten                   : 1
% 0.25/1.42  # Generated clauses                    : 38
% 0.25/1.42  # ...of the previous two non-trivial   : 19
% 0.25/1.42  # Contextual simplify-reflections      : 0
% 0.25/1.42  # Paramodulations                      : 38
% 0.25/1.42  # Factorizations                       : 0
% 0.25/1.42  # Equation resolutions                 : 0
% 0.25/1.42  # Current number of processed clauses  : 7
% 0.25/1.42  #    Positive orientable unit clauses  : 6
% 0.25/1.42  #    Positive unorientable unit clauses: 1
% 0.25/1.42  #    Negative unit clauses             : 0
% 0.25/1.42  #    Non-unit-clauses                  : 0
% 0.25/1.42  # Current number of unprocessed clauses: 14
% 0.25/1.42  # ...number of literals in the above   : 14
% 0.25/1.42  # Current number of archived formulas  : 0
% 0.25/1.42  # Current number of archived clauses   : 1
% 0.25/1.42  # Clause-clause subsumption calls (NU) : 0
% 0.25/1.42  # Rec. Clause-clause subsumption calls : 0
% 0.25/1.42  # Non-unit clause-clause subsumptions  : 0
% 0.25/1.42  # Unit Clause-clause subsumption calls : 2
% 0.25/1.42  # Rewrite failures with RHS unbound    : 0
% 0.25/1.42  # BW rewrite match attempts            : 19
% 0.25/1.42  # BW rewrite match successes           : 11
% 0.25/1.42  # Condensation attempts                : 0
% 0.25/1.42  # Condensation successes               : 0
% 0.25/1.42  # Termbank termtop insertions          : 666
% 0.25/1.42  
% 0.25/1.42  # -------------------------------------------------
% 0.25/1.42  # User time                : 0.011 s
% 0.25/1.42  # System time              : 0.004 s
% 0.25/1.42  # Total time               : 0.015 s
% 0.25/1.42  # Maximum resident set size: 2768 pages
%------------------------------------------------------------------------------