TSTP Solution File: SET662+3 by ET---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET662+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n015.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 00:52:58 EDT 2022
% Result : Theorem 0.23s 1.41s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 36 ( 10 unt; 0 def)
% Number of atoms : 135 ( 0 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 167 ( 68 ~; 64 |; 12 &)
% ( 4 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 62 ( 6 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p11,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p11) ).
fof(p20,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p20) ).
fof(p4,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,empty_set) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p4) ).
fof(p12,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X1,power_set(X2))
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> member(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p12) ).
fof(p14,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p14) ).
fof(prove_relset_1_25,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ilf_type(empty_set,relation_type(X1,X2)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_relset_1_25) ).
fof(p2,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> ilf_type(X3,relation_type(X1,X2)) )
& ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ilf_type(X4,subset_type(cross_product(X1,X2))) ) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p2) ).
fof(p7,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ilf_type(X2,subset_type(X1))
<=> ilf_type(X2,member_type(power_set(X1))) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p7) ).
fof(c_0_8,plain,
! [X3,X4] :
( ( ~ empty(X3)
| ~ ilf_type(X4,set_type)
| ~ member(X4,X3)
| ~ ilf_type(X3,set_type) )
& ( ilf_type(esk5_1(X3),set_type)
| empty(X3)
| ~ ilf_type(X3,set_type) )
& ( member(esk5_1(X3),X3)
| empty(X3)
| ~ ilf_type(X3,set_type) ) ),
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)],[inference(fof_simplification,[status(thm)],[p11])])])])])])])]) ).
fof(c_0_9,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[p20]) ).
fof(c_0_10,plain,
! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,empty_set) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[p4])])]) ).
fof(c_0_11,plain,
! [X4,X5,X6] :
( ( ~ member(X4,power_set(X5))
| ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ilf_type(esk7_2(X4,X5),set_type)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk7_2(X4,X5),X4)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk7_2(X4,X5),X5)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
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)],[p12])])])])])])]) ).
fof(c_0_12,plain,
! [X3,X4] :
( ( ~ ilf_type(X3,member_type(X4))
| member(X3,X4)
| empty(X4)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) )
& ( ~ member(X3,X4)
| ilf_type(X3,member_type(X4))
| empty(X4)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[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)],[p14])])])])])])]) ).
cnf(c_0_13,plain,
( ~ ilf_type(X1,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( ~ member(X1,empty_set)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( member(X1,power_set(X2))
| member(esk7_2(X1,X2),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ilf_type(empty_set,relation_type(X1,X2)) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_25]) ).
fof(c_0_18,plain,
! [X5,X6,X7,X8] :
( ( ~ ilf_type(X7,subset_type(cross_product(X5,X6)))
| ilf_type(X7,relation_type(X5,X6))
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( ~ ilf_type(X8,relation_type(X5,X6))
| ilf_type(X8,subset_type(cross_product(X5,X6)))
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])])])])]) ).
fof(c_0_19,plain,
! [X3,X4] :
( ( ~ ilf_type(X4,subset_type(X3))
| ilf_type(X4,member_type(power_set(X3)))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) )
& ( ~ ilf_type(X4,member_type(power_set(X3)))
| ilf_type(X4,subset_type(X3))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p7])])])])])]) ).
cnf(c_0_20,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_14])]) ).
cnf(c_0_22,plain,
~ member(X1,empty_set),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_14])]) ).
cnf(c_0_23,plain,
( member(esk7_2(X1,X2),X1)
| member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_14]),c_0_14])]) ).
fof(c_0_24,negated_conjecture,
( ilf_type(esk1_0,set_type)
& ilf_type(esk2_0,set_type)
& ~ ilf_type(empty_set,relation_type(esk1_0,esk2_0)) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])])]) ).
cnf(c_0_25,plain,
( ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
( ilf_type(X2,subset_type(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X2,member_type(power_set(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
( ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_14]),c_0_14])]),c_0_21]) ).
cnf(c_0_28,plain,
member(empty_set,power_set(X1)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,negated_conjecture,
~ ilf_type(empty_set,relation_type(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
( ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X1,subset_type(cross_product(X2,X3))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_14]),c_0_14])]) ).
cnf(c_0_31,plain,
( ilf_type(X1,subset_type(X2))
| ~ ilf_type(X1,member_type(power_set(X2))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_14]),c_0_14])]) ).
cnf(c_0_32,plain,
ilf_type(empty_set,member_type(power_set(X1))),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,negated_conjecture,
~ ilf_type(empty_set,subset_type(cross_product(esk1_0,esk2_0))),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
ilf_type(empty_set,subset_type(X1)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET662+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n015.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 : Sun Jul 10 03:49:23 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 : 0.017 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 : 36
% 0.23/1.41 # Proof object clause steps : 19
% 0.23/1.41 # Proof object formula steps : 17
% 0.23/1.41 # Proof object conjectures : 6
% 0.23/1.41 # Proof object clause conjectures : 3
% 0.23/1.41 # Proof object formula conjectures : 3
% 0.23/1.41 # Proof object initial clauses used : 8
% 0.23/1.41 # Proof object initial formulas used : 8
% 0.23/1.41 # Proof object generating inferences : 4
% 0.23/1.41 # Proof object simplifying inferences : 20
% 0.23/1.41 # Training examples: 0 positive, 0 negative
% 0.23/1.41 # Parsed axioms : 22
% 0.23/1.41 # Removed by relevancy pruning/SinE : 3
% 0.23/1.41 # Initial clauses : 33
% 0.23/1.41 # Removed in clause preprocessing : 0
% 0.23/1.41 # Initial clauses in saturation : 33
% 0.23/1.41 # Processed clauses : 40
% 0.23/1.41 # ...of these trivial : 5
% 0.23/1.41 # ...subsumed : 1
% 0.23/1.41 # ...remaining for further processing : 34
% 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 : 4
% 0.23/1.41 # Generated clauses : 31
% 0.23/1.41 # ...of the previous two non-trivial : 23
% 0.23/1.41 # Contextual simplify-reflections : 1
% 0.23/1.41 # Paramodulations : 31
% 0.23/1.41 # Factorizations : 0
% 0.23/1.41 # Equation resolutions : 0
% 0.23/1.41 # Current number of processed clauses : 30
% 0.23/1.41 # Positive orientable unit clauses : 10
% 0.23/1.41 # Positive unorientable unit clauses: 0
% 0.23/1.41 # Negative unit clauses : 3
% 0.23/1.41 # Non-unit-clauses : 17
% 0.23/1.41 # Current number of unprocessed clauses: 16
% 0.23/1.41 # ...number of literals in the above : 30
% 0.23/1.41 # Current number of archived formulas : 0
% 0.23/1.41 # Current number of archived clauses : 4
% 0.23/1.41 # Clause-clause subsumption calls (NU) : 46
% 0.23/1.41 # Rec. Clause-clause subsumption calls : 42
% 0.23/1.41 # Non-unit clause-clause subsumptions : 1
% 0.23/1.41 # Unit Clause-clause subsumption calls : 6
% 0.23/1.41 # Rewrite failures with RHS unbound : 0
% 0.23/1.41 # BW rewrite match attempts : 4
% 0.23/1.41 # BW rewrite match successes : 4
% 0.23/1.41 # Condensation attempts : 0
% 0.23/1.41 # Condensation successes : 0
% 0.23/1.41 # Termbank termtop insertions : 2931
% 0.23/1.41
% 0.23/1.41 # -------------------------------------------------
% 0.23/1.41 # User time : 0.016 s
% 0.23/1.41 # System time : 0.002 s
% 0.23/1.41 # Total time : 0.018 s
% 0.23/1.41 # Maximum resident set size: 3012 pages
%------------------------------------------------------------------------------