TSTP Solution File: NUM390+1 by ET---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : NUM390+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n016.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 09:32:04 EDT 2022
% Result : Theorem 0.21s 1.39s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 11 unt; 0 def)
% Number of atoms : 127 ( 7 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 131 ( 49 ~; 47 |; 17 &)
% ( 3 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 69 ( 6 sgn 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t22_ordinal1,conjecture,
! [X1] :
( epsilon_transitive(X1)
=> ! [X2] :
( ordinal(X2)
=> ! [X3] :
( ordinal(X3)
=> ( ( subset(X1,X2)
& in(X2,X3) )
=> in(X1,X3) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t22_ordinal1) ).
fof(cc1_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',cc1_ordinal1) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t4_subset) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t3_subset) ).
fof(d2_ordinal1,axiom,
! [X1] :
( epsilon_transitive(X1)
<=> ! [X2] :
( in(X2,X1)
=> subset(X2,X1) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d2_ordinal1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t7_boole) ).
fof(t21_ordinal1,axiom,
! [X1] :
( epsilon_transitive(X1)
=> ! [X2] :
( ordinal(X2)
=> ( proper_subset(X1,X2)
=> in(X1,X2) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t21_ordinal1) ).
fof(d8_xboole_0,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& X1 != X2 ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d8_xboole_0) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t2_subset) ).
fof(c_0_9,negated_conjecture,
~ ! [X1] :
( epsilon_transitive(X1)
=> ! [X2] :
( ordinal(X2)
=> ! [X3] :
( ordinal(X3)
=> ( ( subset(X1,X2)
& in(X2,X3) )
=> in(X1,X3) ) ) ) ),
inference(assume_negation,[status(cth)],[t22_ordinal1]) ).
fof(c_0_10,plain,
! [X2] :
( ( epsilon_transitive(X2)
| ~ ordinal(X2) )
& ( epsilon_connected(X2)
| ~ ordinal(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_ordinal1])])]) ).
fof(c_0_11,negated_conjecture,
( epsilon_transitive(esk14_0)
& ordinal(esk15_0)
& ordinal(esk16_0)
& subset(esk14_0,esk15_0)
& in(esk15_0,esk16_0)
& ~ in(esk14_0,esk16_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_9])])])])]) ).
fof(c_0_12,plain,
! [X4,X5,X6] :
( ~ in(X4,X5)
| ~ element(X5,powerset(X6))
| element(X4,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(c_0_13,plain,
! [X3,X4,X3,X4] :
( ( ~ element(X3,powerset(X4))
| subset(X3,X4) )
& ( ~ subset(X3,X4)
| element(X3,powerset(X4)) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])])]) ).
fof(c_0_14,plain,
! [X3,X4,X3] :
( ( ~ epsilon_transitive(X3)
| ~ in(X4,X3)
| subset(X4,X3) )
& ( in(esk1_1(X3),X3)
| epsilon_transitive(X3) )
& ( ~ subset(esk1_1(X3),X3)
| epsilon_transitive(X3) ) ),
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)],[d2_ordinal1])])])])])])]) ).
cnf(c_0_15,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
ordinal(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( subset(X1,X2)
| ~ in(X1,X2)
| ~ epsilon_transitive(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
epsilon_transitive(esk16_0),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( element(X1,X2)
| ~ subset(X3,X2)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( subset(X1,esk16_0)
| ~ in(X1,esk16_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_23,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ empty(X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(c_0_24,plain,
! [X3,X4] :
( ~ epsilon_transitive(X3)
| ~ ordinal(X4)
| ~ proper_subset(X3,X4)
| in(X3,X4) ),
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)],[t21_ordinal1])])])])]) ).
fof(c_0_25,plain,
! [X3,X4,X3,X4] :
( ( subset(X3,X4)
| ~ proper_subset(X3,X4) )
& ( X3 != X4
| ~ proper_subset(X3,X4) )
& ( ~ subset(X3,X4)
| X3 = X4
| proper_subset(X3,X4) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_xboole_0])])])])]) ).
fof(c_0_26,plain,
! [X3,X4] :
( ~ element(X3,X4)
| empty(X4)
| in(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
cnf(c_0_27,negated_conjecture,
( element(X1,esk16_0)
| ~ in(X2,esk16_0)
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,negated_conjecture,
in(esk15_0,esk16_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_29,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( in(X1,X2)
| ~ proper_subset(X1,X2)
| ~ ordinal(X2)
| ~ epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( proper_subset(X1,X2)
| X1 = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,negated_conjecture,
( element(X1,esk16_0)
| ~ in(X1,esk15_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,negated_conjecture,
~ empty(esk16_0),
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_35,plain,
( X1 = X2
| in(X1,X2)
| ~ subset(X1,X2)
| ~ epsilon_transitive(X1)
| ~ ordinal(X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
subset(esk14_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_37,negated_conjecture,
epsilon_transitive(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_38,negated_conjecture,
ordinal(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_39,negated_conjecture,
~ in(esk14_0,esk16_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_40,negated_conjecture,
( in(X1,esk16_0)
| ~ in(X1,esk15_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_41,negated_conjecture,
( esk14_0 = esk15_0
| in(esk14_0,esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_38])]) ).
cnf(c_0_42,negated_conjecture,
~ in(esk14_0,esk15_0),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,negated_conjecture,
esk14_0 = esk15_0,
inference(sr,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_43]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM390+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n016.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 : Wed Jul 6 07:30:04 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.21/1.39 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.21/1.39 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.21/1.39 # Preprocessing time : 0.016 s
% 0.21/1.39
% 0.21/1.39 # Failure: Out of unprocessed clauses!
% 0.21/1.39 # OLD status GaveUp
% 0.21/1.39 # Parsed axioms : 38
% 0.21/1.39 # Removed by relevancy pruning/SinE : 21
% 0.21/1.39 # Initial clauses : 28
% 0.21/1.39 # Removed in clause preprocessing : 0
% 0.21/1.39 # Initial clauses in saturation : 28
% 0.21/1.39 # Processed clauses : 64
% 0.21/1.39 # ...of these trivial : 0
% 0.21/1.39 # ...subsumed : 10
% 0.21/1.39 # ...remaining for further processing : 54
% 0.21/1.39 # Other redundant clauses eliminated : 1
% 0.21/1.39 # Clauses deleted for lack of memory : 0
% 0.21/1.39 # Backward-subsumed : 0
% 0.21/1.39 # Backward-rewritten : 3
% 0.21/1.39 # Generated clauses : 42
% 0.21/1.39 # ...of the previous two non-trivial : 37
% 0.21/1.39 # Contextual simplify-reflections : 4
% 0.21/1.39 # Paramodulations : 41
% 0.21/1.39 # Factorizations : 0
% 0.21/1.39 # Equation resolutions : 1
% 0.21/1.39 # Current number of processed clauses : 50
% 0.21/1.39 # Positive orientable unit clauses : 10
% 0.21/1.39 # Positive unorientable unit clauses: 0
% 0.21/1.39 # Negative unit clauses : 7
% 0.21/1.39 # Non-unit-clauses : 33
% 0.21/1.39 # Current number of unprocessed clauses: 0
% 0.21/1.39 # ...number of literals in the above : 0
% 0.21/1.39 # Current number of archived formulas : 0
% 0.21/1.39 # Current number of archived clauses : 3
% 0.21/1.39 # Clause-clause subsumption calls (NU) : 96
% 0.21/1.39 # Rec. Clause-clause subsumption calls : 58
% 0.21/1.39 # Non-unit clause-clause subsumptions : 11
% 0.21/1.39 # Unit Clause-clause subsumption calls : 6
% 0.21/1.39 # Rewrite failures with RHS unbound : 0
% 0.21/1.39 # BW rewrite match attempts : 1
% 0.21/1.39 # BW rewrite match successes : 1
% 0.21/1.39 # Condensation attempts : 0
% 0.21/1.39 # Condensation successes : 0
% 0.21/1.39 # Termbank termtop insertions : 1834
% 0.21/1.39
% 0.21/1.39 # -------------------------------------------------
% 0.21/1.39 # User time : 0.013 s
% 0.21/1.39 # System time : 0.005 s
% 0.21/1.39 # Total time : 0.018 s
% 0.21/1.39 # Maximum resident set size: 2968 pages
% 0.21/1.39 # Running protocol protocol_eprover_f171197f65f27d1ba69648a20c844832c84a5dd7 for 23 seconds:
% 0.21/1.39 # Preprocessing time : 0.016 s
% 0.21/1.39
% 0.21/1.39 # Proof found!
% 0.21/1.39 # SZS status Theorem
% 0.21/1.39 # SZS output start CNFRefutation
% See solution above
% 0.21/1.39 # Proof object total steps : 45
% 0.21/1.39 # Proof object clause steps : 26
% 0.21/1.39 # Proof object formula steps : 19
% 0.21/1.39 # Proof object conjectures : 19
% 0.21/1.39 # Proof object clause conjectures : 16
% 0.21/1.39 # Proof object formula conjectures : 3
% 0.21/1.39 # Proof object initial clauses used : 14
% 0.21/1.39 # Proof object initial formulas used : 9
% 0.21/1.39 # Proof object generating inferences : 10
% 0.21/1.39 # Proof object simplifying inferences : 8
% 0.21/1.39 # Training examples: 0 positive, 0 negative
% 0.21/1.39 # Parsed axioms : 38
% 0.21/1.39 # Removed by relevancy pruning/SinE : 0
% 0.21/1.39 # Initial clauses : 68
% 0.21/1.39 # Removed in clause preprocessing : 2
% 0.21/1.39 # Initial clauses in saturation : 66
% 0.21/1.39 # Processed clauses : 192
% 0.21/1.39 # ...of these trivial : 4
% 0.21/1.39 # ...subsumed : 44
% 0.21/1.39 # ...remaining for further processing : 144
% 0.21/1.39 # Other redundant clauses eliminated : 1
% 0.21/1.39 # Clauses deleted for lack of memory : 0
% 0.21/1.39 # Backward-subsumed : 2
% 0.21/1.39 # Backward-rewritten : 46
% 0.21/1.39 # Generated clauses : 270
% 0.21/1.39 # ...of the previous two non-trivial : 264
% 0.21/1.39 # Contextual simplify-reflections : 26
% 0.21/1.39 # Paramodulations : 268
% 0.21/1.39 # Factorizations : 0
% 0.21/1.39 # Equation resolutions : 1
% 0.21/1.39 # Current number of processed clauses : 94
% 0.21/1.39 # Positive orientable unit clauses : 33
% 0.21/1.39 # Positive unorientable unit clauses: 0
% 0.21/1.39 # Negative unit clauses : 7
% 0.21/1.39 # Non-unit-clauses : 54
% 0.21/1.39 # Current number of unprocessed clauses: 78
% 0.21/1.39 # ...number of literals in the above : 204
% 0.21/1.39 # Current number of archived formulas : 0
% 0.21/1.39 # Current number of archived clauses : 49
% 0.21/1.39 # Clause-clause subsumption calls (NU) : 1100
% 0.21/1.39 # Rec. Clause-clause subsumption calls : 949
% 0.21/1.39 # Non-unit clause-clause subsumptions : 64
% 0.21/1.39 # Unit Clause-clause subsumption calls : 203
% 0.21/1.39 # Rewrite failures with RHS unbound : 0
% 0.21/1.39 # BW rewrite match attempts : 7
% 0.21/1.39 # BW rewrite match successes : 4
% 0.21/1.39 # Condensation attempts : 0
% 0.21/1.39 # Condensation successes : 0
% 0.21/1.39 # Termbank termtop insertions : 5274
% 0.21/1.39
% 0.21/1.39 # -------------------------------------------------
% 0.21/1.39 # User time : 0.023 s
% 0.21/1.39 # System time : 0.002 s
% 0.21/1.39 # Total time : 0.025 s
% 0.21/1.39 # Maximum resident set size: 3216 pages
%------------------------------------------------------------------------------