TSTP Solution File: SEU236+2 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SEU236+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n012.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 09:18:10 EDT 2022
% Result : Theorem 0.24s 1.41s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 54 ( 14 unt; 0 def)
% Number of atoms : 145 ( 3 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 153 ( 62 ~; 60 |; 16 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 67 ( 4 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t33_ordinal1,conjecture,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( in(X1,X2)
<=> ordinal_subset(succ(X1),X2) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t33_ordinal1) ).
fof(d1_ordinal1,axiom,
! [X1] : succ(X1) = set_union2(X1,singleton(X1)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d1_ordinal1) ).
fof(redefinition_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
<=> subset(X1,X2) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',redefinition_r1_ordinal1) ).
fof(fc3_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ( ~ empty(succ(X1))
& epsilon_transitive(succ(X1))
& epsilon_connected(succ(X1))
& ordinal(succ(X1)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fc3_ordinal1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d3_tarski) ).
fof(t10_ordinal1,lemma,
! [X1] : in(X1,succ(X1)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t10_ordinal1) ).
fof(connectedness_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',connectedness_r1_ordinal1) ).
fof(t8_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t8_xboole_1) ).
fof(l2_zfmisc_1,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',l2_zfmisc_1) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',antisymmetry_r2_hidden) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( in(X1,X2)
<=> ordinal_subset(succ(X1),X2) ) ) ),
inference(assume_negation,[status(cth)],[t33_ordinal1]) ).
fof(c_0_11,negated_conjecture,
( ordinal(esk1_0)
& ordinal(esk2_0)
& ( ~ in(esk1_0,esk2_0)
| ~ ordinal_subset(succ(esk1_0),esk2_0) )
& ( in(esk1_0,esk2_0)
| ordinal_subset(succ(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_10])])])])]) ).
fof(c_0_12,plain,
! [X2] : succ(X2) = set_union2(X2,singleton(X2)),
inference(variable_rename,[status(thm)],[d1_ordinal1]) ).
fof(c_0_13,plain,
! [X3,X4] :
( ( ~ ordinal_subset(X3,X4)
| subset(X3,X4)
| ~ ordinal(X3)
| ~ ordinal(X4) )
& ( ~ subset(X3,X4)
| ordinal_subset(X3,X4)
| ~ ordinal(X3)
| ~ ordinal(X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r1_ordinal1])])]) ).
cnf(c_0_14,negated_conjecture,
( ordinal_subset(succ(esk1_0),esk2_0)
| in(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
succ(X1) = set_union2(X1,singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X2] :
( ( ~ empty(succ(X2))
| ~ ordinal(X2) )
& ( epsilon_transitive(succ(X2))
| ~ ordinal(X2) )
& ( epsilon_connected(succ(X2))
| ~ ordinal(X2) )
& ( ordinal(succ(X2))
| ~ ordinal(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc3_ordinal1])])])]) ).
cnf(c_0_17,negated_conjecture,
( ~ ordinal_subset(succ(esk1_0),esk2_0)
| ~ in(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ ordinal_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
( in(esk1_0,esk2_0)
| ordinal_subset(set_union2(esk1_0,singleton(esk1_0)),esk2_0) ),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,negated_conjecture,
ordinal(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,plain,
( ordinal(succ(X1))
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( ~ in(esk1_0,esk2_0)
| ~ ordinal_subset(set_union2(esk1_0,singleton(esk1_0)),esk2_0) ),
inference(rw,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_23,plain,
( ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_24,plain,
! [X4,X5,X6,X4,X5] :
( ( ~ subset(X4,X5)
| ~ in(X6,X4)
| in(X6,X5) )
& ( in(esk7_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk7_2(X4,X5),X5)
| subset(X4,X5) ) ),
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)],[d3_tarski])])])])])])]) ).
cnf(c_0_25,negated_conjecture,
( subset(set_union2(esk1_0,singleton(esk1_0)),esk2_0)
| in(esk1_0,esk2_0)
| ~ ordinal(set_union2(esk1_0,singleton(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_26,plain,
( ordinal(set_union2(X1,singleton(X1)))
| ~ ordinal(X1) ),
inference(rw,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_27,negated_conjecture,
ordinal(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_28,lemma,
! [X2] : in(X2,succ(X2)),
inference(variable_rename,[status(thm)],[t10_ordinal1]) ).
fof(c_0_29,plain,
! [X3,X4] :
( ~ ordinal(X3)
| ~ ordinal(X4)
| ordinal_subset(X3,X4)
| ordinal_subset(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[connectedness_r1_ordinal1])]) ).
cnf(c_0_30,negated_conjecture,
( ~ subset(set_union2(esk1_0,singleton(esk1_0)),esk2_0)
| ~ ordinal(set_union2(esk1_0,singleton(esk1_0)))
| ~ in(esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_20])]) ).
fof(c_0_31,lemma,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ subset(X6,X5)
| subset(set_union2(X4,X6),X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_xboole_1])]) ).
fof(c_0_32,lemma,
! [X3,X4,X3,X4] :
( ( ~ subset(singleton(X3),X4)
| in(X3,X4) )
& ( ~ in(X3,X4)
| subset(singleton(X3),X4) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])])])]) ).
cnf(c_0_33,plain,
( in(X1,X2)
| ~ in(X1,X3)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,negated_conjecture,
( subset(set_union2(esk1_0,singleton(esk1_0)),esk2_0)
| in(esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_35,lemma,
in(X1,succ(X1)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,plain,
( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_37,negated_conjecture,
( ~ subset(set_union2(esk1_0,singleton(esk1_0)),esk2_0)
| ~ in(esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_26]),c_0_27])]) ).
cnf(c_0_38,lemma,
( subset(set_union2(X1,X2),X3)
| ~ subset(X2,X3)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_39,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,negated_conjecture,
( in(esk1_0,esk2_0)
| in(X1,esk2_0)
| ~ in(X1,set_union2(esk1_0,singleton(esk1_0))) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_41,lemma,
in(X1,set_union2(X1,singleton(X1))),
inference(rw,[status(thm)],[c_0_35,c_0_15]) ).
cnf(c_0_42,negated_conjecture,
( ordinal_subset(esk2_0,X1)
| ordinal_subset(X1,esk2_0)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_20]) ).
cnf(c_0_43,lemma,
( ~ subset(esk1_0,esk2_0)
| ~ in(esk1_0,esk2_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_44,lemma,
in(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,negated_conjecture,
( ordinal_subset(esk1_0,esk2_0)
| ordinal_subset(esk2_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_42,c_0_27]) ).
cnf(c_0_46,lemma,
~ subset(esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]) ).
cnf(c_0_47,negated_conjecture,
ordinal_subset(esk2_0,esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_45]),c_0_27]),c_0_20])]),c_0_46]) ).
fof(c_0_48,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ in(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden])])]) ).
cnf(c_0_49,negated_conjecture,
subset(esk2_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_47]),c_0_20]),c_0_27])]) ).
cnf(c_0_50,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_51,negated_conjecture,
( in(X1,esk1_0)
| ~ in(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_33,c_0_49]) ).
cnf(c_0_52,negated_conjecture,
( ~ in(esk1_0,X1)
| ~ in(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_53,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_51]),c_0_44])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : SEU236+2 : TPTP v8.1.0. Released v3.3.0.
% 0.09/0.12 % Command : run_ET %s %d
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 20 04:02:52 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.24/1.41 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.41 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.41 # Preprocessing time : 0.028 s
% 0.24/1.41
% 0.24/1.41 # Proof found!
% 0.24/1.41 # SZS status Theorem
% 0.24/1.41 # SZS output start CNFRefutation
% See solution above
% 0.24/1.41 # Proof object total steps : 54
% 0.24/1.41 # Proof object clause steps : 33
% 0.24/1.41 # Proof object formula steps : 21
% 0.24/1.41 # Proof object conjectures : 21
% 0.24/1.41 # Proof object clause conjectures : 18
% 0.24/1.41 # Proof object formula conjectures : 3
% 0.24/1.41 # Proof object initial clauses used : 14
% 0.24/1.41 # Proof object initial formulas used : 10
% 0.24/1.41 # Proof object generating inferences : 14
% 0.24/1.41 # Proof object simplifying inferences : 24
% 0.24/1.41 # Training examples: 0 positive, 0 negative
% 0.24/1.41 # Parsed axioms : 276
% 0.24/1.41 # Removed by relevancy pruning/SinE : 175
% 0.24/1.41 # Initial clauses : 194
% 0.24/1.41 # Removed in clause preprocessing : 4
% 0.24/1.41 # Initial clauses in saturation : 190
% 0.24/1.41 # Processed clauses : 364
% 0.24/1.41 # ...of these trivial : 17
% 0.24/1.41 # ...subsumed : 57
% 0.24/1.41 # ...remaining for further processing : 290
% 0.24/1.41 # Other redundant clauses eliminated : 36
% 0.24/1.41 # Clauses deleted for lack of memory : 0
% 0.24/1.41 # Backward-subsumed : 5
% 0.24/1.41 # Backward-rewritten : 65
% 0.24/1.41 # Generated clauses : 1113
% 0.24/1.41 # ...of the previous two non-trivial : 919
% 0.24/1.41 # Contextual simplify-reflections : 15
% 0.24/1.41 # Paramodulations : 1056
% 0.24/1.41 # Factorizations : 10
% 0.24/1.41 # Equation resolutions : 47
% 0.24/1.41 # Current number of processed clauses : 217
% 0.24/1.41 # Positive orientable unit clauses : 47
% 0.24/1.41 # Positive unorientable unit clauses: 1
% 0.24/1.41 # Negative unit clauses : 20
% 0.24/1.41 # Non-unit-clauses : 149
% 0.24/1.41 # Current number of unprocessed clauses: 569
% 0.24/1.41 # ...number of literals in the above : 1907
% 0.24/1.41 # Current number of archived formulas : 0
% 0.24/1.41 # Current number of archived clauses : 72
% 0.24/1.41 # Clause-clause subsumption calls (NU) : 3575
% 0.24/1.41 # Rec. Clause-clause subsumption calls : 2495
% 0.24/1.41 # Non-unit clause-clause subsumptions : 46
% 0.24/1.41 # Unit Clause-clause subsumption calls : 1893
% 0.24/1.41 # Rewrite failures with RHS unbound : 0
% 0.24/1.41 # BW rewrite match attempts : 24
% 0.24/1.41 # BW rewrite match successes : 20
% 0.24/1.41 # Condensation attempts : 0
% 0.24/1.41 # Condensation successes : 0
% 0.24/1.41 # Termbank termtop insertions : 22403
% 0.24/1.41
% 0.24/1.41 # -------------------------------------------------
% 0.24/1.41 # User time : 0.058 s
% 0.24/1.41 # System time : 0.003 s
% 0.24/1.41 # Total time : 0.061 s
% 0.24/1.41 # Maximum resident set size: 4620 pages
% 0.24/7.18 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/7.18 eprover: No such file or directory
% 0.24/7.18 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/7.18 eprover: No such file or directory
% 0.24/7.19 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/7.19 eprover: No such file or directory
% 0.24/7.20 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/7.20 eprover: No such file or directory
% 0.24/7.20 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/7.20 eprover: No such file or directory
% 0.24/7.21 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/7.21 eprover: No such file or directory
% 0.24/7.21 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/7.21 eprover: No such file or directory
% 0.24/7.22 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/7.22 eprover: No such file or directory
% 0.24/7.23 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/7.23 eprover: No such file or directory
% 0.24/7.23 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/7.23 eprover: No such file or directory
% 0.24/7.24 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/7.24 eprover: No such file or directory
%------------------------------------------------------------------------------