TSTP Solution File: NUM409+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : NUM409+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n029.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 : Mon Jul 18 09:32:10 EDT 2022
% Result : Theorem 0.23s 1.40s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 48 ( 16 unt; 0 def)
% Number of atoms : 121 ( 10 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 129 ( 56 ~; 48 |; 15 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 47 ( 4 sgn 26 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t8_boole) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',rc1_xboole_0) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t6_boole) ).
fof(fc8_relat_1,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_rng(X1))
& relation(relation_rng(X1)) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fc8_relat_1) ).
fof(t2_xboole_1,axiom,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t2_xboole_1) ).
fof(t45_ordinal1,conjecture,
! [X1] : transfinite_sequence_of(empty_set,X1),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t45_ordinal1) ).
fof(d8_ordinal1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2)
& transfinite_sequence(X2) )
=> ( transfinite_sequence_of(X2,X1)
<=> subset(relation_rng(X2),X1) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d8_ordinal1) ).
fof(cc1_funct_1,axiom,
! [X1] :
( empty(X1)
=> function(X1) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',cc1_funct_1) ).
fof(cc1_relat_1,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',cc1_relat_1) ).
fof(d7_ordinal1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( transfinite_sequence(X1)
<=> ordinal(relation_dom(X1)) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d7_ordinal1) ).
fof(cc3_ordinal1,axiom,
! [X1] :
( empty(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',cc3_ordinal1) ).
fof(fc7_relat_1,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_dom(X1))
& relation(relation_dom(X1)) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fc7_relat_1) ).
fof(c_0_12,plain,
! [X3,X4] :
( ~ empty(X3)
| X3 = X4
| ~ empty(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(c_0_13,plain,
empty(esk8_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
fof(c_0_14,plain,
! [X2] :
( ~ empty(X2)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
cnf(c_0_15,plain,
( X2 = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
empty(esk8_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_17,plain,
! [X2] :
( ( empty(relation_rng(X2))
| ~ empty(X2) )
& ( relation(relation_rng(X2))
| ~ empty(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc8_relat_1])])]) ).
fof(c_0_18,plain,
! [X2] : subset(empty_set,X2),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
cnf(c_0_19,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_20,negated_conjecture,
~ ! [X1] : transfinite_sequence_of(empty_set,X1),
inference(assume_negation,[status(cth)],[t45_ordinal1]) ).
fof(c_0_21,plain,
! [X3,X4] :
( ( ~ transfinite_sequence_of(X4,X3)
| subset(relation_rng(X4),X3)
| ~ relation(X4)
| ~ function(X4)
| ~ transfinite_sequence(X4) )
& ( ~ subset(relation_rng(X4),X3)
| transfinite_sequence_of(X4,X3)
| ~ relation(X4)
| ~ function(X4)
| ~ transfinite_sequence(X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_ordinal1])])]) ).
cnf(c_0_22,plain,
( X1 = esk8_0
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_23,plain,
( empty(relation_rng(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
empty_set = esk8_0,
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
fof(c_0_26,plain,
! [X2] :
( ~ empty(X2)
| function(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_1])]) ).
fof(c_0_27,plain,
! [X2] :
( ~ empty(X2)
| relation(X2) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relat_1])]) ).
fof(c_0_28,negated_conjecture,
~ transfinite_sequence_of(empty_set,esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
cnf(c_0_29,plain,
( transfinite_sequence_of(X1,X2)
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ subset(relation_rng(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,plain,
( relation_rng(X1) = esk8_0
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_31,plain,
subset(esk8_0,X1),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,plain,
( function(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
( relation(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_34,plain,
! [X2] :
( ( ~ transfinite_sequence(X2)
| ordinal(relation_dom(X2))
| ~ relation(X2)
| ~ function(X2) )
& ( ~ ordinal(relation_dom(X2))
| transfinite_sequence(X2)
| ~ relation(X2)
| ~ function(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_ordinal1])])]) ).
cnf(c_0_35,negated_conjecture,
~ transfinite_sequence_of(empty_set,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,plain,
( transfinite_sequence_of(X1,X2)
| ~ transfinite_sequence(X1)
| ~ empty(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]),c_0_32]),c_0_33]) ).
cnf(c_0_37,plain,
( transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ ordinal(relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_38,negated_conjecture,
~ transfinite_sequence_of(esk8_0,esk1_0),
inference(rw,[status(thm)],[c_0_35,c_0_25]) ).
cnf(c_0_39,plain,
( transfinite_sequence_of(X1,X2)
| ~ ordinal(relation_dom(X1))
| ~ empty(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_32]),c_0_33]) ).
fof(c_0_40,plain,
! [X2] :
( ( epsilon_transitive(X2)
| ~ empty(X2) )
& ( epsilon_connected(X2)
| ~ empty(X2) )
& ( ordinal(X2)
| ~ empty(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc3_ordinal1])])]) ).
fof(c_0_41,plain,
! [X2] :
( ( empty(relation_dom(X2))
| ~ empty(X2) )
& ( relation(relation_dom(X2))
| ~ empty(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc7_relat_1])])]) ).
cnf(c_0_42,negated_conjecture,
~ ordinal(relation_dom(esk8_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_16])]) ).
cnf(c_0_43,plain,
( ordinal(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_44,plain,
( empty(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_45,negated_conjecture,
~ empty(relation_dom(esk8_0)),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_46,plain,
( relation_dom(X1) = esk8_0
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_44]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM409+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n029.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 : Thu Jul 7 23:36:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.23/1.40 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/1.40 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/1.40 # Preprocessing time : 0.017 s
% 0.23/1.40
% 0.23/1.40 # Proof found!
% 0.23/1.40 # SZS status Theorem
% 0.23/1.40 # SZS output start CNFRefutation
% See solution above
% 0.23/1.40 # Proof object total steps : 48
% 0.23/1.40 # Proof object clause steps : 23
% 0.23/1.40 # Proof object formula steps : 25
% 0.23/1.40 # Proof object conjectures : 8
% 0.23/1.40 # Proof object clause conjectures : 5
% 0.23/1.40 # Proof object formula conjectures : 3
% 0.23/1.40 # Proof object initial clauses used : 12
% 0.23/1.40 # Proof object initial formulas used : 12
% 0.23/1.40 # Proof object generating inferences : 9
% 0.23/1.40 # Proof object simplifying inferences : 12
% 0.23/1.40 # Training examples: 0 positive, 0 negative
% 0.23/1.40 # Parsed axioms : 51
% 0.23/1.40 # Removed by relevancy pruning/SinE : 13
% 0.23/1.40 # Initial clauses : 62
% 0.23/1.40 # Removed in clause preprocessing : 0
% 0.23/1.40 # Initial clauses in saturation : 62
% 0.23/1.40 # Processed clauses : 373
% 0.23/1.40 # ...of these trivial : 3
% 0.23/1.40 # ...subsumed : 197
% 0.23/1.40 # ...remaining for further processing : 173
% 0.23/1.40 # Other redundant clauses eliminated : 0
% 0.23/1.40 # Clauses deleted for lack of memory : 0
% 0.23/1.40 # Backward-subsumed : 16
% 0.23/1.40 # Backward-rewritten : 13
% 0.23/1.40 # Generated clauses : 669
% 0.23/1.40 # ...of the previous two non-trivial : 526
% 0.23/1.40 # Contextual simplify-reflections : 212
% 0.23/1.40 # Paramodulations : 669
% 0.23/1.40 # Factorizations : 0
% 0.23/1.40 # Equation resolutions : 0
% 0.23/1.40 # Current number of processed clauses : 144
% 0.23/1.40 # Positive orientable unit clauses : 34
% 0.23/1.40 # Positive unorientable unit clauses: 0
% 0.23/1.40 # Negative unit clauses : 6
% 0.23/1.40 # Non-unit-clauses : 104
% 0.23/1.40 # Current number of unprocessed clauses: 162
% 0.23/1.40 # ...number of literals in the above : 650
% 0.23/1.40 # Current number of archived formulas : 0
% 0.23/1.40 # Current number of archived clauses : 29
% 0.23/1.40 # Clause-clause subsumption calls (NU) : 6975
% 0.23/1.40 # Rec. Clause-clause subsumption calls : 5809
% 0.23/1.40 # Non-unit clause-clause subsumptions : 425
% 0.23/1.40 # Unit Clause-clause subsumption calls : 241
% 0.23/1.40 # Rewrite failures with RHS unbound : 0
% 0.23/1.40 # BW rewrite match attempts : 5
% 0.23/1.40 # BW rewrite match successes : 3
% 0.23/1.40 # Condensation attempts : 0
% 0.23/1.40 # Condensation successes : 0
% 0.23/1.40 # Termbank termtop insertions : 9296
% 0.23/1.40
% 0.23/1.40 # -------------------------------------------------
% 0.23/1.40 # User time : 0.032 s
% 0.23/1.40 # System time : 0.003 s
% 0.23/1.40 # Total time : 0.035 s
% 0.23/1.40 # Maximum resident set size: 3316 pages
%------------------------------------------------------------------------------