TSTP Solution File: SET666+3 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET666+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n006.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 00:52:59 EDT 2022
% Result : Theorem 0.26s 1.44s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 49 ( 11 unt; 0 def)
% Number of atoms : 194 ( 0 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 245 ( 100 ~; 101 |; 15 &)
% ( 6 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-2 aty)
% Number of variables : 88 ( 2 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p14,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( subset(X1,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',p14) ).
fof(p24,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p24) ).
fof(p3,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> subset(identity_relation_of(X1),cross_product(X1,X1)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p3) ).
fof(p16,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',p16) ).
fof(p22,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',p22) ).
fof(prove_relset_1_29,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ilf_type(identity_relation_of(X1),identity_relation_of_type(X1)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_relset_1_29) ).
fof(p6,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ilf_type(X2,identity_relation_of_type(X1))
<=> ilf_type(X2,relation_type(X1,X1)) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p6) ).
fof(p18,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',p18) ).
fof(p1,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',p1) ).
fof(p12,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',p12) ).
fof(c_0_10,plain,
! [X4,X5,X6] :
( ( ~ subset(X4,X5)
| ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ilf_type(esk4_2(X4,X5),set_type)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk4_2(X4,X5),X4)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk4_2(X4,X5),X5)
| subset(X4,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)],[p14])])])])])])]) ).
fof(c_0_11,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[p24]) ).
fof(c_0_12,plain,
! [X2] :
( ~ ilf_type(X2,set_type)
| subset(identity_relation_of(X2),cross_product(X2,X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p3])]) ).
fof(c_0_13,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(esk12_2(X4,X5),set_type)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk12_2(X4,X5),X4)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk12_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)],[p16])])])])])])]) ).
cnf(c_0_14,plain,
( member(X3,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( subset(identity_relation_of(X1),cross_product(X1,X1))
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,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)],[p22])])])])])])])]) ).
cnf(c_0_18,plain,
( member(X1,power_set(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(esk12_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ subset(X3,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_15]),c_0_15])]) ).
cnf(c_0_20,plain,
subset(identity_relation_of(X1),cross_product(X1,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_15])]) ).
fof(c_0_21,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ilf_type(identity_relation_of(X1),identity_relation_of_type(X1)) ),
inference(assume_negation,[status(cth)],[prove_relset_1_29]) ).
fof(c_0_22,plain,
! [X3,X4] :
( ( ~ ilf_type(X4,identity_relation_of_type(X3))
| ilf_type(X4,relation_type(X3,X3))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) )
& ( ~ ilf_type(X4,relation_type(X3,X3))
| ilf_type(X4,identity_relation_of_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)],[p6])])])])])]) ).
fof(c_0_23,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)],[p18])])])])])])]) ).
cnf(c_0_24,plain,
( ~ ilf_type(X1,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
( member(X1,power_set(X2))
| ~ member(esk12_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_15]),c_0_15])]) ).
cnf(c_0_26,plain,
( member(X1,cross_product(X2,X2))
| ~ member(X1,identity_relation_of(X2)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,plain,
( member(X1,power_set(X2))
| member(esk12_2(X1,X2),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_28,negated_conjecture,
( ilf_type(esk1_0,set_type)
& ~ ilf_type(identity_relation_of(esk1_0),identity_relation_of_type(esk1_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
cnf(c_0_29,plain,
( ilf_type(X2,identity_relation_of_type(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X2,relation_type(X1,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_30,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)],[p1])])])])])]) ).
fof(c_0_31,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)],[p12])])])])])]) ).
cnf(c_0_32,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_23]) ).
cnf(c_0_33,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_15]),c_0_15])]) ).
cnf(c_0_34,plain,
( member(X1,power_set(cross_product(X2,X2)))
| ~ member(esk12_2(X1,cross_product(X2,X2)),identity_relation_of(X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_35,plain,
( member(esk12_2(X1,X2),X1)
| member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_15]),c_0_15])]) ).
cnf(c_0_36,negated_conjecture,
~ ilf_type(identity_relation_of(esk1_0),identity_relation_of_type(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_37,plain,
( ilf_type(X1,identity_relation_of_type(X2))
| ~ ilf_type(X1,relation_type(X2,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_15]),c_0_15])]) ).
cnf(c_0_38,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_30]) ).
cnf(c_0_39,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_31]) ).
cnf(c_0_40,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_32,c_0_15]),c_0_15])]),c_0_33]) ).
cnf(c_0_41,plain,
member(identity_relation_of(X1),power_set(cross_product(X1,X1))),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,negated_conjecture,
~ ilf_type(identity_relation_of(esk1_0),relation_type(esk1_0,esk1_0)),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_43,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_38,c_0_15]),c_0_15])]) ).
cnf(c_0_44,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_39,c_0_15]),c_0_15])]) ).
cnf(c_0_45,plain,
ilf_type(identity_relation_of(X1),member_type(power_set(cross_product(X1,X1)))),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,negated_conjecture,
~ ilf_type(identity_relation_of(esk1_0),subset_type(cross_product(esk1_0,esk1_0))),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,plain,
ilf_type(identity_relation_of(X1),subset_type(cross_product(X1,X1))),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET666+3 : TPTP v8.1.0. Released v2.2.0.
% 0.08/0.14 % Command : run_ET %s %d
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jul 10 17:09:36 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.26/1.44 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.26/1.44 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.26/1.44 # Preprocessing time : 0.019 s
% 0.26/1.44
% 0.26/1.44 # Proof found!
% 0.26/1.44 # SZS status Theorem
% 0.26/1.44 # SZS output start CNFRefutation
% See solution above
% 0.26/1.44 # Proof object total steps : 49
% 0.26/1.44 # Proof object clause steps : 28
% 0.26/1.44 # Proof object formula steps : 21
% 0.26/1.44 # Proof object conjectures : 7
% 0.26/1.44 # Proof object clause conjectures : 4
% 0.26/1.44 # Proof object formula conjectures : 3
% 0.26/1.44 # Proof object initial clauses used : 11
% 0.26/1.44 # Proof object initial formulas used : 10
% 0.26/1.44 # Proof object generating inferences : 7
% 0.26/1.44 # Proof object simplifying inferences : 30
% 0.26/1.44 # Training examples: 0 positive, 0 negative
% 0.26/1.44 # Parsed axioms : 25
% 0.26/1.44 # Removed by relevancy pruning/SinE : 0
% 0.26/1.44 # Initial clauses : 48
% 0.26/1.44 # Removed in clause preprocessing : 1
% 0.26/1.44 # Initial clauses in saturation : 47
% 0.26/1.44 # Processed clauses : 159
% 0.26/1.44 # ...of these trivial : 10
% 0.26/1.44 # ...subsumed : 20
% 0.26/1.44 # ...remaining for further processing : 129
% 0.26/1.44 # Other redundant clauses eliminated : 1
% 0.26/1.44 # Clauses deleted for lack of memory : 0
% 0.26/1.44 # Backward-subsumed : 0
% 0.26/1.44 # Backward-rewritten : 2
% 0.26/1.44 # Generated clauses : 318
% 0.26/1.44 # ...of the previous two non-trivial : 289
% 0.26/1.44 # Contextual simplify-reflections : 4
% 0.26/1.44 # Paramodulations : 316
% 0.26/1.44 # Factorizations : 0
% 0.26/1.44 # Equation resolutions : 2
% 0.26/1.44 # Current number of processed clauses : 126
% 0.26/1.44 # Positive orientable unit clauses : 43
% 0.26/1.44 # Positive unorientable unit clauses: 0
% 0.26/1.44 # Negative unit clauses : 3
% 0.26/1.44 # Non-unit-clauses : 80
% 0.26/1.44 # Current number of unprocessed clauses: 177
% 0.26/1.44 # ...number of literals in the above : 462
% 0.26/1.44 # Current number of archived formulas : 0
% 0.26/1.44 # Current number of archived clauses : 2
% 0.26/1.44 # Clause-clause subsumption calls (NU) : 828
% 0.26/1.44 # Rec. Clause-clause subsumption calls : 686
% 0.26/1.44 # Non-unit clause-clause subsumptions : 17
% 0.26/1.44 # Unit Clause-clause subsumption calls : 38
% 0.26/1.44 # Rewrite failures with RHS unbound : 0
% 0.26/1.44 # BW rewrite match attempts : 10
% 0.26/1.44 # BW rewrite match successes : 2
% 0.26/1.44 # Condensation attempts : 0
% 0.26/1.44 # Condensation successes : 0
% 0.26/1.44 # Termbank termtop insertions : 8203
% 0.26/1.44
% 0.26/1.44 # -------------------------------------------------
% 0.26/1.44 # User time : 0.021 s
% 0.26/1.44 # System time : 0.008 s
% 0.26/1.44 # Total time : 0.029 s
% 0.26/1.44 # Maximum resident set size: 3604 pages
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