TSTP Solution File: REL009+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : REL009+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n024.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 : Mon Jul 18 19:19:02 EDT 2022

% Result   : Theorem 0.26s 5.43s
% Output   : CNFRefutation 0.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   27 (  23 unt;   0 def)
%            Number of atoms       :   34 (  33 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   13 (   6   ~;   2   |;   3   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   47 (   0 sgn  26   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(goals,conjecture,
    ! [X1,X2,X3] :
      ( join(X1,X2) = X2
     => ( join(composition(X1,X3),composition(X2,X3)) = composition(X2,X3)
        & join(composition(X3,X1),composition(X3,X2)) = composition(X3,X2) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',goals) ).

fof(converse_multiplicativity,axiom,
    ! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
    file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_multiplicativity) ).

fof(converse_idempotence,axiom,
    ! [X1] : converse(converse(X1)) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).

fof(maddux1_join_commutativity,axiom,
    ! [X1,X2] : join(X1,X2) = join(X2,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux1_join_commutativity) ).

fof(converse_additivity,axiom,
    ! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_additivity) ).

fof(composition_distributivity,axiom,
    ! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
    file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( join(X1,X2) = X2
       => ( join(composition(X1,X3),composition(X2,X3)) = composition(X2,X3)
          & join(composition(X3,X1),composition(X3,X2)) = composition(X3,X2) ) ),
    inference(assume_negation,[status(cth)],[goals]) ).

fof(c_0_7,plain,
    ! [X3,X4] : converse(composition(X3,X4)) = composition(converse(X4),converse(X3)),
    inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).

fof(c_0_8,plain,
    ! [X2] : converse(converse(X2)) = X2,
    inference(variable_rename,[status(thm)],[converse_idempotence]) ).

fof(c_0_9,negated_conjecture,
    ( join(esk1_0,esk2_0) = esk2_0
    & ( join(composition(esk1_0,esk3_0),composition(esk2_0,esk3_0)) != composition(esk2_0,esk3_0)
      | join(composition(esk4_0,esk1_0),composition(esk4_0,esk2_0)) != composition(esk4_0,esk2_0) ) ),
    inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).

fof(c_0_10,plain,
    ! [X3,X4] : join(X3,X4) = join(X4,X3),
    inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).

fof(c_0_11,plain,
    ! [X3,X4] : converse(join(X3,X4)) = join(converse(X3),converse(X4)),
    inference(variable_rename,[status(thm)],[converse_additivity]) ).

cnf(c_0_12,plain,
    converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_13,plain,
    converse(converse(X1)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_14,plain,
    ! [X4,X5,X6] : composition(join(X4,X5),X6) = join(composition(X4,X6),composition(X5,X6)),
    inference(variable_rename,[status(thm)],[composition_distributivity]) ).

cnf(c_0_15,negated_conjecture,
    join(esk1_0,esk2_0) = esk2_0,
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_16,plain,
    join(X1,X2) = join(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_17,plain,
    converse(join(X1,X2)) = join(converse(X1),converse(X2)),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_18,plain,
    converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_19,plain,
    composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_20,negated_conjecture,
    ( join(composition(esk4_0,esk1_0),composition(esk4_0,esk2_0)) != composition(esk4_0,esk2_0)
    | join(composition(esk1_0,esk3_0),composition(esk2_0,esk3_0)) != composition(esk2_0,esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_21,negated_conjecture,
    join(esk2_0,esk1_0) = esk2_0,
    inference(rw,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_22,plain,
    converse(join(composition(converse(X1),X2),X3)) = join(composition(converse(X2),X1),converse(X3)),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_23,plain,
    join(composition(X1,converse(X2)),converse(composition(X2,X3))) = composition(join(X1,converse(X3)),converse(X2)),
    inference(spm,[status(thm)],[c_0_19,c_0_12]) ).

cnf(c_0_24,negated_conjecture,
    join(composition(esk4_0,esk2_0),composition(esk4_0,esk1_0)) != composition(esk4_0,esk2_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_16]),c_0_16]),c_0_19]),c_0_21])]) ).

cnf(c_0_25,plain,
    join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_17]),c_0_12]),c_0_13]),c_0_13]),c_0_13]) ).

cnf(c_0_26,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_21])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : REL009+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : run_ET %s %d
% 0.14/0.34  % Computer : n024.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Fri Jul  8 10:58:14 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.26/5.43  # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.26/5.43  # Preprocessing time       : 0.014 s
% 0.26/5.43  
% 0.26/5.43  # Proof found!
% 0.26/5.43  # SZS status Theorem
% 0.26/5.43  # SZS output start CNFRefutation
% See solution above
% 0.26/5.43  # Proof object total steps             : 27
% 0.26/5.43  # Proof object clause steps            : 14
% 0.26/5.43  # Proof object formula steps           : 13
% 0.26/5.43  # Proof object conjectures             : 8
% 0.26/5.43  # Proof object clause conjectures      : 5
% 0.26/5.43  # Proof object formula conjectures     : 3
% 0.26/5.43  # Proof object initial clauses used    : 7
% 0.26/5.43  # Proof object initial formulas used   : 6
% 0.26/5.43  # Proof object generating inferences   : 4
% 0.26/5.43  # Proof object simplifying inferences  : 14
% 0.26/5.43  # Training examples: 0 positive, 0 negative
% 0.26/5.43  # Parsed axioms                        : 14
% 0.26/5.43  # Removed by relevancy pruning/SinE    : 0
% 0.26/5.43  # Initial clauses                      : 15
% 0.26/5.43  # Removed in clause preprocessing      : 1
% 0.26/5.43  # Initial clauses in saturation        : 14
% 0.26/5.43  # Processed clauses                    : 6316
% 0.26/5.43  # ...of these trivial                  : 3718
% 0.26/5.43  # ...subsumed                          : 866
% 0.26/5.43  # ...remaining for further processing  : 1732
% 0.26/5.43  # Other redundant clauses eliminated   : 0
% 0.26/5.43  # Clauses deleted for lack of memory   : 92360
% 0.26/5.43  # Backward-subsumed                    : 0
% 0.26/5.43  # Backward-rewritten                   : 475
% 0.26/5.43  # Generated clauses                    : 278373
% 0.26/5.43  # ...of the previous two non-trivial   : 191772
% 0.26/5.43  # Contextual simplify-reflections      : 0
% 0.26/5.43  # Paramodulations                      : 278373
% 0.26/5.43  # Factorizations                       : 0
% 0.26/5.43  # Equation resolutions                 : 0
% 0.26/5.43  # Current number of processed clauses  : 1257
% 0.26/5.43  #    Positive orientable unit clauses  : 1246
% 0.26/5.43  #    Positive unorientable unit clauses: 11
% 0.26/5.43  #    Negative unit clauses             : 0
% 0.26/5.43  #    Non-unit-clauses                  : 0
% 0.26/5.43  # Current number of unprocessed clauses: 66789
% 0.26/5.43  # ...number of literals in the above   : 66789
% 0.26/5.43  # Current number of archived formulas  : 0
% 0.26/5.43  # Current number of archived clauses   : 476
% 0.26/5.43  # Clause-clause subsumption calls (NU) : 0
% 0.26/5.43  # Rec. Clause-clause subsumption calls : 0
% 0.26/5.43  # Non-unit clause-clause subsumptions  : 0
% 0.26/5.43  # Unit Clause-clause subsumption calls : 73
% 0.26/5.43  # Rewrite failures with RHS unbound    : 0
% 0.26/5.43  # BW rewrite match attempts            : 12084
% 0.26/5.43  # BW rewrite match successes           : 524
% 0.26/5.43  # Condensation attempts                : 0
% 0.26/5.43  # Condensation successes               : 0
% 0.26/5.43  # Termbank termtop insertions          : 5998321
% 0.26/5.43  
% 0.26/5.43  # -------------------------------------------------
% 0.26/5.43  # User time                : 3.934 s
% 0.26/5.43  # System time              : 0.084 s
% 0.26/5.43  # Total time               : 4.018 s
% 0.26/5.43  # Maximum resident set size: 147956 pages
% 0.26/23.40  eprover: CPU time limit exceeded, terminating
% 0.26/23.41  eprover: CPU time limit exceeded, terminating
% 0.26/23.41  eprover: CPU time limit exceeded, terminating
% 0.26/23.42  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.26/23.42  eprover: No such file or directory
% 0.26/23.42  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.26/23.42  eprover: No such file or directory
% 0.26/23.42  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.26/23.42  eprover: No such file or directory
% 0.26/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.26/23.43  eprover: No such file or directory
% 0.26/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.26/23.43  eprover: No such file or directory
% 0.26/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.26/23.43  eprover: No such file or directory
% 0.26/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.26/23.43  eprover: No such file or directory
% 0.26/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.26/23.43  eprover: No such file or directory
% 0.26/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.26/23.43  eprover: No such file or directory
% 0.26/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.26/23.44  eprover: No such file or directory
% 0.26/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.26/23.44  eprover: No such file or directory
% 0.26/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.26/23.44  eprover: No such file or directory
% 0.26/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.26/23.44  eprover: No such file or directory
% 0.26/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.26/23.44  eprover: No such file or directory
% 0.26/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.26/23.44  eprover: No such file or directory
% 0.26/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.26/23.44  eprover: No such file or directory
% 0.26/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.26/23.45  eprover: No such file or directory
% 0.26/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.26/23.45  eprover: No such file or directory
% 0.26/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.26/23.45  eprover: No such file or directory
% 0.26/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.26/23.45  eprover: No such file or directory
% 0.26/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.26/23.45  eprover: No such file or directory
% 0.26/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.26/23.45  eprover: No such file or directory
% 0.26/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.26/23.46  eprover: No such file or directory
% 0.26/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.26/23.46  eprover: No such file or directory
% 0.26/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.26/23.46  eprover: No such file or directory
% 0.26/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.26/23.46  eprover: No such file or directory
% 0.26/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.26/23.46  eprover: No such file or directory
% 0.26/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.26/23.46  eprover: No such file or directory
% 0.26/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.26/23.46  eprover: No such file or directory
% 0.26/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.26/23.47  eprover: No such file or directory
% 0.26/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.26/23.47  eprover: No such file or directory
% 0.26/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.26/23.47  eprover: No such file or directory
% 0.26/23.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.26/23.47  eprover: No such file or directory
%------------------------------------------------------------------------------