TSTP Solution File: SEU244+1 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SEU244+1 : TPTP v8.1.0. Released v3.3.0.
% 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 09:18:14 EDT 2022
% Result : Theorem 0.25s 1.42s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 57 ( 4 unt; 0 def)
% Number of atoms : 252 ( 0 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 349 ( 154 ~; 152 |; 25 &)
% ( 9 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 59 ( 1 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d5_wellord1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( well_orders(X1,X2)
<=> ( is_reflexive_in(X1,X2)
& is_transitive_in(X1,X2)
& is_antisymmetric_in(X1,X2)
& is_connected_in(X1,X2)
& is_well_founded_in(X1,X2) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d5_wellord1) ).
fof(t5_wellord1,axiom,
! [X1] :
( relation(X1)
=> ( well_founded_relation(X1)
<=> is_well_founded_in(X1,relation_field(X1)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t5_wellord1) ).
fof(d9_relat_2,axiom,
! [X1] :
( relation(X1)
=> ( reflexive(X1)
<=> is_reflexive_in(X1,relation_field(X1)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d9_relat_2) ).
fof(d12_relat_2,axiom,
! [X1] :
( relation(X1)
=> ( antisymmetric(X1)
<=> is_antisymmetric_in(X1,relation_field(X1)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d12_relat_2) ).
fof(d14_relat_2,axiom,
! [X1] :
( relation(X1)
=> ( connected(X1)
<=> is_connected_in(X1,relation_field(X1)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d14_relat_2) ).
fof(d16_relat_2,axiom,
! [X1] :
( relation(X1)
=> ( transitive(X1)
<=> is_transitive_in(X1,relation_field(X1)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d16_relat_2) ).
fof(d4_wellord1,axiom,
! [X1] :
( relation(X1)
=> ( well_ordering(X1)
<=> ( reflexive(X1)
& transitive(X1)
& antisymmetric(X1)
& connected(X1)
& well_founded_relation(X1) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d4_wellord1) ).
fof(t8_wellord1,conjecture,
! [X1] :
( relation(X1)
=> ( well_orders(X1,relation_field(X1))
<=> well_ordering(X1) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t8_wellord1) ).
fof(c_0_8,plain,
! [X3,X4,X4] :
( ( is_reflexive_in(X3,X4)
| ~ well_orders(X3,X4)
| ~ relation(X3) )
& ( is_transitive_in(X3,X4)
| ~ well_orders(X3,X4)
| ~ relation(X3) )
& ( is_antisymmetric_in(X3,X4)
| ~ well_orders(X3,X4)
| ~ relation(X3) )
& ( is_connected_in(X3,X4)
| ~ well_orders(X3,X4)
| ~ relation(X3) )
& ( is_well_founded_in(X3,X4)
| ~ well_orders(X3,X4)
| ~ relation(X3) )
& ( ~ is_reflexive_in(X3,X4)
| ~ is_transitive_in(X3,X4)
| ~ is_antisymmetric_in(X3,X4)
| ~ is_connected_in(X3,X4)
| ~ is_well_founded_in(X3,X4)
| well_orders(X3,X4)
| ~ relation(X3) ) ),
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)],[d5_wellord1])])])])])]) ).
fof(c_0_9,plain,
! [X2] :
( ( ~ well_founded_relation(X2)
| is_well_founded_in(X2,relation_field(X2))
| ~ relation(X2) )
& ( ~ is_well_founded_in(X2,relation_field(X2))
| well_founded_relation(X2)
| ~ relation(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_wellord1])])]) ).
cnf(c_0_10,plain,
( well_orders(X1,X2)
| ~ relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ is_connected_in(X1,X2)
| ~ is_antisymmetric_in(X1,X2)
| ~ is_transitive_in(X1,X2)
| ~ is_reflexive_in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,plain,
( is_well_founded_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ well_founded_relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X2] :
( ( ~ reflexive(X2)
| is_reflexive_in(X2,relation_field(X2))
| ~ relation(X2) )
& ( ~ is_reflexive_in(X2,relation_field(X2))
| reflexive(X2)
| ~ relation(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_relat_2])])]) ).
fof(c_0_13,plain,
! [X2] :
( ( ~ antisymmetric(X2)
| is_antisymmetric_in(X2,relation_field(X2))
| ~ relation(X2) )
& ( ~ is_antisymmetric_in(X2,relation_field(X2))
| antisymmetric(X2)
| ~ relation(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d12_relat_2])])]) ).
fof(c_0_14,plain,
! [X2] :
( ( ~ connected(X2)
| is_connected_in(X2,relation_field(X2))
| ~ relation(X2) )
& ( ~ is_connected_in(X2,relation_field(X2))
| connected(X2)
| ~ relation(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d14_relat_2])])]) ).
fof(c_0_15,plain,
! [X2] :
( ( ~ transitive(X2)
| is_transitive_in(X2,relation_field(X2))
| ~ relation(X2) )
& ( ~ is_transitive_in(X2,relation_field(X2))
| transitive(X2)
| ~ relation(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d16_relat_2])])]) ).
cnf(c_0_16,plain,
( well_orders(X1,relation_field(X1))
| ~ is_reflexive_in(X1,relation_field(X1))
| ~ well_founded_relation(X1)
| ~ is_transitive_in(X1,relation_field(X1))
| ~ is_connected_in(X1,relation_field(X1))
| ~ is_antisymmetric_in(X1,relation_field(X1))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_17,plain,
( is_reflexive_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ reflexive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_18,plain,
! [X2] :
( ( reflexive(X2)
| ~ well_ordering(X2)
| ~ relation(X2) )
& ( transitive(X2)
| ~ well_ordering(X2)
| ~ relation(X2) )
& ( antisymmetric(X2)
| ~ well_ordering(X2)
| ~ relation(X2) )
& ( connected(X2)
| ~ well_ordering(X2)
| ~ relation(X2) )
& ( well_founded_relation(X2)
| ~ well_ordering(X2)
| ~ relation(X2) )
& ( ~ reflexive(X2)
| ~ transitive(X2)
| ~ antisymmetric(X2)
| ~ connected(X2)
| ~ well_founded_relation(X2)
| well_ordering(X2)
| ~ relation(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_wellord1])])]) ).
cnf(c_0_19,plain,
( well_founded_relation(X1)
| ~ relation(X1)
| ~ is_well_founded_in(X1,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,plain,
( is_well_founded_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,plain,
( antisymmetric(X1)
| ~ relation(X1)
| ~ is_antisymmetric_in(X1,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,plain,
( is_antisymmetric_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_23,plain,
( connected(X1)
| ~ relation(X1)
| ~ is_connected_in(X1,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,plain,
( transitive(X1)
| ~ relation(X1)
| ~ is_transitive_in(X1,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_26,plain,
( is_transitive_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_27,plain,
( reflexive(X1)
| ~ relation(X1)
| ~ is_reflexive_in(X1,relation_field(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_28,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ well_orders(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_29,negated_conjecture,
~ ! [X1] :
( relation(X1)
=> ( well_orders(X1,relation_field(X1))
<=> well_ordering(X1) ) ),
inference(assume_negation,[status(cth)],[t8_wellord1]) ).
cnf(c_0_30,plain,
( well_orders(X1,relation_field(X1))
| ~ well_founded_relation(X1)
| ~ reflexive(X1)
| ~ is_transitive_in(X1,relation_field(X1))
| ~ is_connected_in(X1,relation_field(X1))
| ~ is_antisymmetric_in(X1,relation_field(X1))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_31,plain,
( is_transitive_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_32,plain,
( well_ordering(X1)
| ~ relation(X1)
| ~ well_founded_relation(X1)
| ~ connected(X1)
| ~ antisymmetric(X1)
| ~ transitive(X1)
| ~ reflexive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_33,plain,
( well_founded_relation(X1)
| ~ well_orders(X1,relation_field(X1))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_34,plain,
( antisymmetric(X1)
| ~ well_orders(X1,relation_field(X1))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_35,plain,
( connected(X1)
| ~ well_orders(X1,relation_field(X1))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_36,plain,
( transitive(X1)
| ~ well_orders(X1,relation_field(X1))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_37,plain,
( reflexive(X1)
| ~ well_orders(X1,relation_field(X1))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_38,negated_conjecture,
( relation(esk1_0)
& ( ~ well_orders(esk1_0,relation_field(esk1_0))
| ~ well_ordering(esk1_0) )
& ( well_orders(esk1_0,relation_field(esk1_0))
| well_ordering(esk1_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])]) ).
cnf(c_0_39,plain,
( well_orders(X1,relation_field(X1))
| ~ well_founded_relation(X1)
| ~ reflexive(X1)
| ~ transitive(X1)
| ~ is_connected_in(X1,relation_field(X1))
| ~ is_antisymmetric_in(X1,relation_field(X1))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_40,plain,
( is_connected_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ connected(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_41,plain,
( well_ordering(X1)
| ~ well_orders(X1,relation_field(X1))
| ~ relation(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_35]),c_0_36]),c_0_37]) ).
cnf(c_0_42,negated_conjecture,
( well_ordering(esk1_0)
| well_orders(esk1_0,relation_field(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_43,negated_conjecture,
relation(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_44,plain,
( well_orders(X1,relation_field(X1))
| ~ well_founded_relation(X1)
| ~ reflexive(X1)
| ~ transitive(X1)
| ~ connected(X1)
| ~ is_antisymmetric_in(X1,relation_field(X1))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,plain,
( is_antisymmetric_in(X1,relation_field(X1))
| ~ relation(X1)
| ~ antisymmetric(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_46,negated_conjecture,
( ~ well_ordering(esk1_0)
| ~ well_orders(esk1_0,relation_field(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_47,negated_conjecture,
well_ordering(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]) ).
cnf(c_0_48,plain,
( well_orders(X1,relation_field(X1))
| ~ well_founded_relation(X1)
| ~ reflexive(X1)
| ~ transitive(X1)
| ~ connected(X1)
| ~ antisymmetric(X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,plain,
( well_founded_relation(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_50,plain,
( antisymmetric(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_51,plain,
( connected(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_52,plain,
( transitive(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_53,plain,
( reflexive(X1)
| ~ relation(X1)
| ~ well_ordering(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_54,negated_conjecture,
~ well_orders(esk1_0,relation_field(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).
cnf(c_0_55,plain,
( well_orders(X1,relation_field(X1))
| ~ well_ordering(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_51]),c_0_52]),c_0_53]) ).
cnf(c_0_56,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_47]),c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU244+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : run_ET %s %d
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 20 10:14:03 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.25/1.42 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.25/1.42 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.25/1.42 # Preprocessing time : 0.016 s
% 0.25/1.42
% 0.25/1.42 # Proof found!
% 0.25/1.42 # SZS status Theorem
% 0.25/1.42 # SZS output start CNFRefutation
% See solution above
% 0.25/1.42 # Proof object total steps : 57
% 0.25/1.42 # Proof object clause steps : 40
% 0.25/1.42 # Proof object formula steps : 17
% 0.25/1.42 # Proof object conjectures : 9
% 0.25/1.42 # Proof object clause conjectures : 6
% 0.25/1.42 # Proof object formula conjectures : 3
% 0.25/1.42 # Proof object initial clauses used : 25
% 0.25/1.42 # Proof object initial formulas used : 8
% 0.25/1.42 # Proof object generating inferences : 14
% 0.25/1.42 # Proof object simplifying inferences : 15
% 0.25/1.42 # Training examples: 0 positive, 0 negative
% 0.25/1.42 # Parsed axioms : 15
% 0.25/1.42 # Removed by relevancy pruning/SinE : 7
% 0.25/1.42 # Initial clauses : 25
% 0.25/1.42 # Removed in clause preprocessing : 0
% 0.25/1.42 # Initial clauses in saturation : 25
% 0.25/1.42 # Processed clauses : 39
% 0.25/1.42 # ...of these trivial : 0
% 0.25/1.42 # ...subsumed : 0
% 0.25/1.42 # ...remaining for further processing : 39
% 0.25/1.42 # Other redundant clauses eliminated : 0
% 0.25/1.42 # Clauses deleted for lack of memory : 0
% 0.25/1.42 # Backward-subsumed : 0
% 0.25/1.42 # Backward-rewritten : 2
% 0.25/1.42 # Generated clauses : 28
% 0.25/1.42 # ...of the previous two non-trivial : 14
% 0.25/1.42 # Contextual simplify-reflections : 8
% 0.25/1.42 # Paramodulations : 28
% 0.25/1.42 # Factorizations : 0
% 0.25/1.42 # Equation resolutions : 0
% 0.25/1.42 # Current number of processed clauses : 37
% 0.25/1.42 # Positive orientable unit clauses : 2
% 0.25/1.42 # Positive unorientable unit clauses: 0
% 0.25/1.42 # Negative unit clauses : 1
% 0.25/1.42 # Non-unit-clauses : 34
% 0.25/1.42 # Current number of unprocessed clauses: 0
% 0.25/1.42 # ...number of literals in the above : 0
% 0.25/1.42 # Current number of archived formulas : 0
% 0.25/1.42 # Current number of archived clauses : 2
% 0.25/1.42 # Clause-clause subsumption calls (NU) : 288
% 0.25/1.42 # Rec. Clause-clause subsumption calls : 89
% 0.25/1.42 # Non-unit clause-clause subsumptions : 8
% 0.25/1.42 # Unit Clause-clause subsumption calls : 0
% 0.25/1.42 # Rewrite failures with RHS unbound : 0
% 0.25/1.42 # BW rewrite match attempts : 1
% 0.25/1.42 # BW rewrite match successes : 1
% 0.25/1.42 # Condensation attempts : 0
% 0.25/1.42 # Condensation successes : 0
% 0.25/1.42 # Termbank termtop insertions : 2106
% 0.25/1.42
% 0.25/1.42 # -------------------------------------------------
% 0.25/1.42 # User time : 0.017 s
% 0.25/1.42 # System time : 0.001 s
% 0.25/1.42 # Total time : 0.018 s
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