TSTP Solution File: SET622+3 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET622+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n023.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 00:52:36 EDT 2022
% Result : Theorem 0.23s 1.41s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 24 unt; 0 def)
% Number of atoms : 24 ( 23 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th98,conjecture,
! [X1,X2,X3] : difference(X1,symmetric_difference(X2,X3)) = union(difference(X1,union(X2,X3)),intersection(intersection(X1,X2),X3)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_th98) ).
fof(symmetric_difference_and_difference,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = difference(union(X1,X2),intersection(X1,X2)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',symmetric_difference_and_difference) ).
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(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_of_union) ).
fof(associativity_of_intersection,axiom,
! [X1,X2,X3] : intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',associativity_of_intersection) ).
fof(difference_difference_union2,axiom,
! [X1,X2,X3] : difference(X1,difference(X2,X3)) = union(difference(X1,X2),intersection(X1,X3)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',difference_difference_union2) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X3] : difference(X1,symmetric_difference(X2,X3)) = union(difference(X1,union(X2,X3)),intersection(intersection(X1,X2),X3)),
inference(assume_negation,[status(cth)],[prove_th98]) ).
fof(c_0_7,negated_conjecture,
difference(esk1_0,symmetric_difference(esk2_0,esk3_0)) != union(difference(esk1_0,union(esk2_0,esk3_0)),intersection(intersection(esk1_0,esk2_0),esk3_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_8,plain,
! [X3,X4] : symmetric_difference(X3,X4) = difference(union(X3,X4),intersection(X3,X4)),
inference(variable_rename,[status(thm)],[symmetric_difference_and_difference]) ).
cnf(c_0_9,negated_conjecture,
difference(esk1_0,symmetric_difference(esk2_0,esk3_0)) != union(difference(esk1_0,union(esk2_0,esk3_0)),intersection(intersection(esk1_0,esk2_0),esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
symmetric_difference(X1,X2) = difference(union(X1,X2),intersection(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
fof(c_0_12,plain,
! [X3,X4] : union(X3,X4) = union(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
fof(c_0_13,plain,
! [X4,X5,X6] : intersection(intersection(X4,X5),X6) = intersection(X4,intersection(X5,X6)),
inference(variable_rename,[status(thm)],[associativity_of_intersection]) ).
fof(c_0_14,plain,
! [X4,X5,X6] : difference(X4,difference(X5,X6)) = union(difference(X4,X5),intersection(X4,X6)),
inference(variable_rename,[status(thm)],[difference_difference_union2]) ).
cnf(c_0_15,negated_conjecture,
difference(esk1_0,difference(union(esk2_0,esk3_0),intersection(esk2_0,esk3_0))) != union(difference(esk1_0,union(esk2_0,esk3_0)),intersection(intersection(esk1_0,esk2_0),esk3_0)),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_16,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
difference(X1,difference(X2,X3)) = union(difference(X1,X2),intersection(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
union(intersection(esk3_0,intersection(esk1_0,esk2_0)),difference(esk1_0,union(esk2_0,esk3_0))) != difference(esk1_0,difference(union(esk2_0,esk3_0),intersection(esk2_0,esk3_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_21,plain,
intersection(X1,intersection(X2,X3)) = intersection(X3,intersection(X1,X2)),
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_22,plain,
union(intersection(X1,X2),difference(X1,X3)) = difference(X1,difference(X3,X2)),
inference(spm,[status(thm)],[c_0_17,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET622+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 00:49:25 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 : 24
% 0.23/1.41 # Proof object clause steps : 11
% 0.23/1.41 # Proof object formula steps : 13
% 0.23/1.41 # Proof object conjectures : 7
% 0.23/1.41 # Proof object clause conjectures : 4
% 0.23/1.41 # Proof object formula conjectures : 3
% 0.23/1.41 # Proof object initial clauses used : 6
% 0.23/1.41 # Proof object initial formulas used : 6
% 0.23/1.41 # Proof object generating inferences : 2
% 0.23/1.41 # Proof object simplifying inferences : 6
% 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 : 3
% 0.23/1.41 # Initial clauses : 21
% 0.23/1.41 # Removed in clause preprocessing : 3
% 0.23/1.41 # Initial clauses in saturation : 18
% 0.23/1.41 # Processed clauses : 36
% 0.23/1.41 # ...of these trivial : 8
% 0.23/1.41 # ...subsumed : 2
% 0.23/1.41 # ...remaining for further processing : 26
% 0.23/1.41 # Other redundant clauses eliminated : 0
% 0.23/1.41 # Clauses deleted for lack of memory : 0
% 0.23/1.41 # Backward-subsumed : 0
% 0.23/1.41 # Backward-rewritten : 2
% 0.23/1.41 # Generated clauses : 172
% 0.23/1.41 # ...of the previous two non-trivial : 109
% 0.23/1.41 # Contextual simplify-reflections : 0
% 0.23/1.41 # Paramodulations : 170
% 0.23/1.41 # Factorizations : 2
% 0.23/1.41 # Equation resolutions : 0
% 0.23/1.41 # Current number of processed clauses : 24
% 0.23/1.41 # Positive orientable unit clauses : 8
% 0.23/1.41 # Positive unorientable unit clauses: 3
% 0.23/1.41 # Negative unit clauses : 0
% 0.23/1.41 # Non-unit-clauses : 13
% 0.23/1.41 # Current number of unprocessed clauses: 91
% 0.23/1.41 # ...number of literals in the above : 190
% 0.23/1.41 # Current number of archived formulas : 0
% 0.23/1.41 # Current number of archived clauses : 3
% 0.23/1.41 # Clause-clause subsumption calls (NU) : 22
% 0.23/1.41 # Rec. Clause-clause subsumption calls : 21
% 0.23/1.41 # Non-unit clause-clause subsumptions : 2
% 0.23/1.41 # Unit Clause-clause subsumption calls : 3
% 0.23/1.41 # Rewrite failures with RHS unbound : 0
% 0.23/1.41 # BW rewrite match attempts : 26
% 0.23/1.41 # BW rewrite match successes : 22
% 0.23/1.41 # Condensation attempts : 0
% 0.23/1.41 # Condensation successes : 0
% 0.23/1.41 # Termbank termtop insertions : 2810
% 0.23/1.41
% 0.23/1.41 # -------------------------------------------------
% 0.23/1.41 # User time : 0.017 s
% 0.23/1.41 # System time : 0.001 s
% 0.23/1.41 # Total time : 0.018 s
% 0.23/1.41 # Maximum resident set size: 2780 pages
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