TSTP Solution File: SET617+3 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET617+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n010.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 00:52:33 EDT 2022
% Result : Theorem 0.24s 1.42s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 17 unt; 0 def)
% Number of atoms : 27 ( 26 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 3 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 1 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th92,conjecture,
! [X1] :
( symmetric_difference(X1,empty_set) = X1
& symmetric_difference(empty_set,X1) = X1 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_th92) ).
fof(symmetric_difference_defn,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',symmetric_difference_defn) ).
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(no_difference_with_empty_set2,axiom,
! [X1] : difference(empty_set,X1) = empty_set,
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',no_difference_with_empty_set2) ).
fof(no_difference_with_empty_set1,axiom,
! [X1] : difference(X1,empty_set) = X1,
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',no_difference_with_empty_set1) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( symmetric_difference(X1,empty_set) = X1
& symmetric_difference(empty_set,X1) = X1 ),
inference(assume_negation,[status(cth)],[prove_th92]) ).
fof(c_0_7,negated_conjecture,
( symmetric_difference(esk1_0,empty_set) != esk1_0
| symmetric_difference(empty_set,esk2_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_8,plain,
! [X3,X4] : symmetric_difference(X3,X4) = union(difference(X3,X4),difference(X4,X3)),
inference(variable_rename,[status(thm)],[symmetric_difference_defn]) ).
fof(c_0_9,plain,
! [X2] : union(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[union_empty_set]) ).
fof(c_0_10,plain,
! [X3,X4] : union(X3,X4) = union(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_11,negated_conjecture,
( symmetric_difference(empty_set,esk2_0) != esk2_0
| symmetric_difference(esk1_0,empty_set) != esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X2] : difference(empty_set,X2) = empty_set,
inference(variable_rename,[status(thm)],[no_difference_with_empty_set2]) ).
fof(c_0_14,plain,
! [X2] : difference(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[no_difference_with_empty_set1]) ).
cnf(c_0_15,plain,
union(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
( union(difference(empty_set,esk2_0),difference(esk2_0,empty_set)) != esk2_0
| union(difference(esk1_0,empty_set),difference(empty_set,esk1_0)) != esk1_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_12]) ).
cnf(c_0_18,plain,
difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
union(empty_set,X1) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(cn,[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_17,c_0_18]),c_0_18]),c_0_19]),c_0_20]),c_0_19]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET617+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : run_ET %s %d
% 0.14/0.34 % Computer : n010.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 : Sun Jul 10 07:51:00 EDT 2022
% 0.14/0.34 % 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 : 0.015 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 : 22
% 0.24/1.42 # Proof object clause steps : 9
% 0.24/1.42 # Proof object formula steps : 13
% 0.24/1.42 # Proof object conjectures : 6
% 0.24/1.42 # Proof object clause conjectures : 3
% 0.24/1.42 # Proof object formula conjectures : 3
% 0.24/1.42 # Proof object initial clauses used : 6
% 0.24/1.42 # Proof object initial formulas used : 6
% 0.24/1.42 # Proof object generating inferences : 1
% 0.24/1.42 # Proof object simplifying inferences : 9
% 0.24/1.42 # Training examples: 0 positive, 0 negative
% 0.24/1.42 # Parsed axioms : 13
% 0.24/1.42 # Removed by relevancy pruning/SinE : 1
% 0.24/1.42 # Initial clauses : 19
% 0.24/1.42 # Removed in clause preprocessing : 3
% 0.24/1.42 # Initial clauses in saturation : 16
% 0.24/1.42 # Processed clauses : 21
% 0.24/1.42 # ...of these trivial : 2
% 0.24/1.42 # ...subsumed : 0
% 0.24/1.42 # ...remaining for further processing : 18
% 0.24/1.42 # Other redundant clauses eliminated : 2
% 0.24/1.42 # Clauses deleted for lack of memory : 0
% 0.24/1.42 # Backward-subsumed : 0
% 0.24/1.42 # Backward-rewritten : 1
% 0.24/1.42 # Generated clauses : 16
% 0.24/1.42 # ...of the previous two non-trivial : 8
% 0.24/1.42 # Contextual simplify-reflections : 0
% 0.24/1.42 # Paramodulations : 12
% 0.24/1.42 # Factorizations : 2
% 0.24/1.42 # Equation resolutions : 2
% 0.24/1.42 # Current number of processed clauses : 15
% 0.24/1.42 # Positive orientable unit clauses : 6
% 0.24/1.42 # Positive unorientable unit clauses: 1
% 0.24/1.42 # Negative unit clauses : 1
% 0.24/1.42 # Non-unit-clauses : 7
% 0.24/1.42 # Current number of unprocessed clauses: 3
% 0.24/1.42 # ...number of literals in the above : 6
% 0.24/1.42 # Current number of archived formulas : 0
% 0.24/1.42 # Current number of archived clauses : 2
% 0.24/1.42 # Clause-clause subsumption calls (NU) : 2
% 0.24/1.42 # Rec. Clause-clause subsumption calls : 2
% 0.24/1.42 # Non-unit clause-clause subsumptions : 0
% 0.24/1.42 # Unit Clause-clause subsumption calls : 0
% 0.24/1.42 # Rewrite failures with RHS unbound : 0
% 0.24/1.42 # BW rewrite match attempts : 4
% 0.24/1.42 # BW rewrite match successes : 4
% 0.24/1.42 # Condensation attempts : 0
% 0.24/1.42 # Condensation successes : 0
% 0.24/1.42 # Termbank termtop insertions : 974
% 0.24/1.42
% 0.24/1.42 # -------------------------------------------------
% 0.24/1.42 # User time : 0.014 s
% 0.24/1.42 # System time : 0.002 s
% 0.24/1.42 # Total time : 0.016 s
% 0.24/1.42 # Maximum resident set size: 2776 pages
%------------------------------------------------------------------------------