TSTP Solution File: SET586+3 by ET---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET586+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n014.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 00:52:11 EDT 2022
% Result : Theorem 0.23s 1.41s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 9 unt; 0 def)
% Number of atoms : 66 ( 3 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 59 ( 23 ~; 25 |; 6 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 65 ( 9 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_intersection_of_subset,conjecture,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(intersection(X1,X3),intersection(X2,X3)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_intersection_of_subset) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',subset_defn) ).
fof(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',intersection_defn) ).
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(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(X1,X2)
=> subset(intersection(X1,X3),intersection(X2,X3)) ),
inference(assume_negation,[status(cth)],[prove_intersection_of_subset]) ).
fof(c_0_5,plain,
! [X4,X5,X6,X4,X5] :
( ( ~ subset(X4,X5)
| ~ member(X6,X4)
| member(X6,X5) )
& ( member(esk4_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ member(esk4_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subset_defn])])])])])])]) ).
fof(c_0_6,negated_conjecture,
( subset(esk1_0,esk2_0)
& ~ subset(intersection(esk1_0,esk3_0),intersection(esk2_0,esk3_0)) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
cnf(c_0_7,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
subset(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X4,X5,X6,X4,X5,X6] :
( ( member(X6,X4)
| ~ member(X6,intersection(X4,X5)) )
& ( member(X6,X5)
| ~ member(X6,intersection(X4,X5)) )
& ( ~ member(X6,X4)
| ~ member(X6,X5)
| member(X6,intersection(X4,X5)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])])])]) ).
cnf(c_0_10,plain,
( subset(X1,X2)
| ~ member(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,negated_conjecture,
( member(X1,esk2_0)
| ~ member(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( subset(X1,X2)
| member(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_14,negated_conjecture,
( subset(X1,esk2_0)
| ~ member(esk4_2(X1,esk2_0),esk1_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( subset(intersection(X1,X2),X3)
| member(esk4_2(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,negated_conjecture,
subset(intersection(esk1_0,X1),esk2_0),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,negated_conjecture,
( member(X1,esk2_0)
| ~ member(X1,intersection(esk1_0,X2)) ),
inference(spm,[status(thm)],[c_0_7,c_0_16]) ).
cnf(c_0_19,plain,
( subset(X1,intersection(X2,X3))
| ~ member(esk4_2(X1,intersection(X2,X3)),X3)
| ~ member(esk4_2(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
( subset(intersection(esk1_0,X1),X2)
| member(esk4_2(intersection(esk1_0,X1),X2),esk2_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_13]) ).
cnf(c_0_21,plain,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_22,negated_conjecture,
( subset(intersection(esk1_0,X1),intersection(X2,esk2_0))
| ~ member(esk4_2(intersection(esk1_0,X1),intersection(X2,esk2_0)),X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
( subset(intersection(X1,X2),X3)
| member(esk4_2(intersection(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_13]) ).
fof(c_0_24,plain,
! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_25,negated_conjecture,
subset(intersection(esk1_0,X1),intersection(X1,esk2_0)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_27,negated_conjecture,
~ subset(intersection(esk1_0,esk3_0),intersection(esk2_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_28,negated_conjecture,
subset(intersection(esk1_0,X1),intersection(esk2_0,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET586+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n014.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 07:24:34 EDT 2022
% 0.13/0.34 % 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 : 0.014 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 : 30
% 0.23/1.41 # Proof object clause steps : 21
% 0.23/1.41 # Proof object formula steps : 9
% 0.23/1.41 # Proof object conjectures : 14
% 0.23/1.41 # Proof object clause conjectures : 11
% 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 : 4
% 0.23/1.41 # Proof object generating inferences : 11
% 0.23/1.41 # Proof object simplifying inferences : 2
% 0.23/1.41 # Training examples: 0 positive, 0 negative
% 0.23/1.41 # Parsed axioms : 6
% 0.23/1.41 # Removed by relevancy pruning/SinE : 0
% 0.23/1.41 # Initial clauses : 14
% 0.23/1.41 # Removed in clause preprocessing : 2
% 0.23/1.41 # Initial clauses in saturation : 12
% 0.23/1.41 # Processed clauses : 73
% 0.23/1.41 # ...of these trivial : 5
% 0.23/1.41 # ...subsumed : 26
% 0.23/1.41 # ...remaining for further processing : 42
% 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 : 208
% 0.23/1.41 # ...of the previous two non-trivial : 177
% 0.23/1.41 # Contextual simplify-reflections : 2
% 0.23/1.41 # Paramodulations : 198
% 0.23/1.41 # Factorizations : 10
% 0.23/1.41 # Equation resolutions : 0
% 0.23/1.41 # Current number of processed clauses : 40
% 0.23/1.41 # Positive orientable unit clauses : 12
% 0.23/1.41 # Positive unorientable unit clauses: 1
% 0.23/1.41 # Negative unit clauses : 0
% 0.23/1.41 # Non-unit-clauses : 27
% 0.23/1.41 # Current number of unprocessed clauses: 115
% 0.23/1.41 # ...number of literals in the above : 283
% 0.23/1.41 # Current number of archived formulas : 0
% 0.23/1.41 # Current number of archived clauses : 2
% 0.23/1.41 # Clause-clause subsumption calls (NU) : 226
% 0.23/1.41 # Rec. Clause-clause subsumption calls : 183
% 0.23/1.41 # Non-unit clause-clause subsumptions : 28
% 0.23/1.41 # Unit Clause-clause subsumption calls : 14
% 0.23/1.41 # Rewrite failures with RHS unbound : 0
% 0.23/1.41 # BW rewrite match attempts : 20
% 0.23/1.41 # BW rewrite match successes : 6
% 0.23/1.41 # Condensation attempts : 0
% 0.23/1.41 # Condensation successes : 0
% 0.23/1.41 # Termbank termtop insertions : 3109
% 0.23/1.41
% 0.23/1.41 # -------------------------------------------------
% 0.23/1.41 # User time : 0.018 s
% 0.23/1.41 # System time : 0.002 s
% 0.23/1.41 # Total time : 0.020 s
% 0.23/1.41 # Maximum resident set size: 3024 pages
%------------------------------------------------------------------------------