TSTP Solution File: SET009+3 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET009+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n022.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 00:47:33 EDT 2022
% Result : Theorem 0.21s 1.41s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 4 unt; 0 def)
% Number of atoms : 57 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 56 ( 22 ~; 23 |; 6 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 55 ( 7 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_subset_difference,conjecture,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(difference(X3,X2),difference(X3,X1)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_subset_difference) ).
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',difference_defn) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',subset_defn) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(X1,X2)
=> subset(difference(X3,X2),difference(X3,X1)) ),
inference(assume_negation,[status(cth)],[prove_subset_difference]) ).
fof(c_0_4,plain,
! [X4,X5,X6,X4,X5,X6] :
( ( member(X6,X4)
| ~ member(X6,difference(X4,X5)) )
& ( ~ member(X6,X5)
| ~ member(X6,difference(X4,X5)) )
& ( ~ member(X6,X4)
| member(X6,X5)
| member(X6,difference(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)],[inference(fof_simplification,[status(thm)],[difference_defn])])])])])]) ).
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(difference(esk3_0,esk2_0),difference(esk3_0,esk1_0)) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).
cnf(c_0_7,plain,
( ~ member(X1,difference(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( subset(X1,X2)
| member(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
subset(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( subset(X1,X2)
| ~ member(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,plain,
( member(X1,difference(X2,X3))
| member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_13,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_14,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk4_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_15,negated_conjecture,
( member(X1,esk2_0)
| ~ member(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_16,plain,
( subset(X1,difference(X2,X3))
| member(esk4_2(X1,difference(X2,X3)),X3)
| ~ member(esk4_2(X1,difference(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( subset(difference(X1,X2),X3)
| member(esk4_2(difference(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_8]) ).
cnf(c_0_18,negated_conjecture,
( subset(difference(X1,esk2_0),X2)
| ~ member(esk4_2(difference(X1,esk2_0),X2),esk1_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
( subset(difference(X1,X2),difference(X1,X3))
| member(esk4_2(difference(X1,X2),difference(X1,X3)),X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
~ subset(difference(esk3_0,esk2_0),difference(esk3_0,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_21,negated_conjecture,
subset(difference(X1,esk2_0),difference(X1,esk1_0)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET009+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n022.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 : Mon Jul 11 09:53:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.21/1.41 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.21/1.41 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.21/1.41 # Preprocessing time : 0.014 s
% 0.21/1.41
% 0.21/1.41 # Proof found!
% 0.21/1.41 # SZS status Theorem
% 0.21/1.41 # SZS output start CNFRefutation
% See solution above
% 0.21/1.41 # Proof object total steps : 23
% 0.21/1.41 # Proof object clause steps : 16
% 0.21/1.41 # Proof object formula steps : 7
% 0.21/1.41 # Proof object conjectures : 9
% 0.21/1.41 # Proof object clause conjectures : 6
% 0.21/1.41 # Proof object formula conjectures : 3
% 0.21/1.41 # Proof object initial clauses used : 8
% 0.21/1.41 # Proof object initial formulas used : 3
% 0.21/1.41 # Proof object generating inferences : 7
% 0.21/1.41 # Proof object simplifying inferences : 2
% 0.21/1.41 # Training examples: 0 positive, 0 negative
% 0.21/1.41 # Parsed axioms : 4
% 0.21/1.41 # Removed by relevancy pruning/SinE : 0
% 0.21/1.41 # Initial clauses : 9
% 0.21/1.41 # Removed in clause preprocessing : 0
% 0.21/1.41 # Initial clauses in saturation : 9
% 0.21/1.41 # Processed clauses : 57
% 0.21/1.41 # ...of these trivial : 2
% 0.21/1.41 # ...subsumed : 11
% 0.21/1.41 # ...remaining for further processing : 44
% 0.21/1.41 # Other redundant clauses eliminated : 0
% 0.21/1.41 # Clauses deleted for lack of memory : 0
% 0.21/1.41 # Backward-subsumed : 0
% 0.21/1.41 # Backward-rewritten : 1
% 0.21/1.41 # Generated clauses : 127
% 0.21/1.41 # ...of the previous two non-trivial : 108
% 0.21/1.41 # Contextual simplify-reflections : 8
% 0.21/1.41 # Paramodulations : 127
% 0.21/1.41 # Factorizations : 0
% 0.21/1.41 # Equation resolutions : 0
% 0.21/1.41 # Current number of processed clauses : 43
% 0.21/1.41 # Positive orientable unit clauses : 13
% 0.21/1.41 # Positive unorientable unit clauses: 0
% 0.21/1.41 # Negative unit clauses : 0
% 0.21/1.41 # Non-unit-clauses : 30
% 0.21/1.41 # Current number of unprocessed clauses: 60
% 0.21/1.41 # ...number of literals in the above : 115
% 0.21/1.41 # Current number of archived formulas : 0
% 0.21/1.41 # Current number of archived clauses : 1
% 0.21/1.41 # Clause-clause subsumption calls (NU) : 210
% 0.21/1.41 # Rec. Clause-clause subsumption calls : 208
% 0.21/1.41 # Non-unit clause-clause subsumptions : 19
% 0.21/1.41 # Unit Clause-clause subsumption calls : 23
% 0.21/1.41 # Rewrite failures with RHS unbound : 0
% 0.21/1.41 # BW rewrite match attempts : 39
% 0.21/1.41 # BW rewrite match successes : 1
% 0.21/1.41 # Condensation attempts : 0
% 0.21/1.41 # Condensation successes : 0
% 0.21/1.41 # Termbank termtop insertions : 2382
% 0.21/1.41
% 0.21/1.41 # -------------------------------------------------
% 0.21/1.41 # User time : 0.016 s
% 0.21/1.41 # System time : 0.002 s
% 0.21/1.41 # Total time : 0.018 s
% 0.21/1.41 # Maximum resident set size: 2764 pages
%------------------------------------------------------------------------------