TSTP Solution File: SEU180+2 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SEU180+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n020.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 09:17:32 EDT 2022
% Result : Theorem 0.22s 1.40s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 46 ( 21 unt; 0 def)
% Number of atoms : 117 ( 21 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 118 ( 47 ~; 47 |; 13 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 89 ( 14 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d5_tarski) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t69_enumset1) ).
fof(t30_relat_1,conjecture,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_field(X3))
& in(X2,relation_field(X3)) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t30_relat_1) ).
fof(t20_relat_1,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_dom(X3))
& in(X2,relation_rng(X3)) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t20_relat_1) ).
fof(d6_relat_1,axiom,
! [X1] :
( relation(X1)
=> relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d6_relat_1) ).
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(t7_xboole_1,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t7_xboole_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_k2_tarski) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d2_xboole_0) ).
fof(c_0_9,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_10,lemma,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_11,negated_conjecture,
~ ! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_field(X3))
& in(X2,relation_field(X3)) ) ) ),
inference(assume_negation,[status(cth)],[t30_relat_1]) ).
fof(c_0_12,lemma,
! [X4,X5,X6] :
( ( in(X4,relation_dom(X6))
| ~ in(ordered_pair(X4,X5),X6)
| ~ relation(X6) )
& ( in(X5,relation_rng(X6))
| ~ in(ordered_pair(X4,X5),X6)
| ~ relation(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t20_relat_1])])]) ).
cnf(c_0_13,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,negated_conjecture,
( relation(esk3_0)
& in(ordered_pair(esk1_0,esk2_0),esk3_0)
& ( ~ in(esk1_0,relation_field(esk3_0))
| ~ in(esk2_0,relation_field(esk3_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_16,plain,
! [X2] :
( ~ relation(X2)
| relation_field(X2) = set_union2(relation_dom(X2),relation_rng(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_relat_1])]) ).
fof(c_0_17,plain,
! [X4,X5,X6,X4,X5] :
( ( ~ subset(X4,X5)
| ~ in(X6,X4)
| in(X6,X5) )
& ( in(esk4_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk4_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])])])])])])]) ).
fof(c_0_18,lemma,
! [X3,X4] : subset(X3,set_union2(X3,X4)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
cnf(c_0_19,lemma,
( in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_21,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_22,negated_conjecture,
in(ordered_pair(esk1_0,esk2_0),esk3_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,negated_conjecture,
( ~ in(esk2_0,relation_field(esk3_0))
| ~ in(esk1_0,relation_field(esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
( relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,negated_conjecture,
relation(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_26,plain,
( in(X1,X2)
| ~ in(X1,X3)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,lemma,
( in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1) ),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_29,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,negated_conjecture,
in(unordered_pair(unordered_pair(esk1_0,esk2_0),unordered_pair(esk1_0,esk1_0)),esk3_0),
inference(rw,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_31,lemma,
( in(X3,relation_rng(X1))
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_32,negated_conjecture,
( ~ in(esk1_0,set_union2(relation_dom(esk3_0),relation_rng(esk3_0)))
| ~ in(esk2_0,set_union2(relation_dom(esk3_0),relation_rng(esk3_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_33,lemma,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,lemma,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X1,X1)),X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,negated_conjecture,
in(unordered_pair(unordered_pair(esk2_0,esk1_0),unordered_pair(esk1_0,esk1_0)),esk3_0),
inference(rw,[status(thm)],[c_0_30,c_0_29]) ).
fof(c_0_36,plain,
! [X5,X6,X7,X8,X8,X5,X6,X7] :
( ( ~ in(X8,X7)
| in(X8,X5)
| in(X8,X6)
| X7 != set_union2(X5,X6) )
& ( ~ in(X8,X5)
| in(X8,X7)
| X7 != set_union2(X5,X6) )
& ( ~ in(X8,X6)
| in(X8,X7)
| X7 != set_union2(X5,X6) )
& ( ~ in(esk11_3(X5,X6,X7),X5)
| ~ in(esk11_3(X5,X6,X7),X7)
| X7 = set_union2(X5,X6) )
& ( ~ in(esk11_3(X5,X6,X7),X6)
| ~ in(esk11_3(X5,X6,X7),X7)
| X7 = set_union2(X5,X6) )
& ( in(esk11_3(X5,X6,X7),X7)
| in(esk11_3(X5,X6,X7),X5)
| in(esk11_3(X5,X6,X7),X6)
| X7 = set_union2(X5,X6) ) ),
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_xboole_0])])])])])])]) ).
cnf(c_0_37,lemma,
( in(X3,relation_rng(X1))
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)),X1) ),
inference(rw,[status(thm)],[c_0_31,c_0_20]) ).
cnf(c_0_38,negated_conjecture,
( ~ in(esk2_0,set_union2(relation_dom(esk3_0),relation_rng(esk3_0)))
| ~ in(esk1_0,relation_dom(esk3_0)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,negated_conjecture,
in(esk1_0,relation_dom(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_25])]) ).
cnf(c_0_40,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_41,lemma,
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X3,X3)),X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_29]) ).
cnf(c_0_42,negated_conjecture,
~ in(esk2_0,set_union2(relation_dom(esk3_0),relation_rng(esk3_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]) ).
cnf(c_0_43,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_40]) ).
cnf(c_0_44,negated_conjecture,
in(esk2_0,relation_rng(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_35]),c_0_25])]) ).
cnf(c_0_45,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU180+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n020.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 : Sun Jun 19 14:07:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.22/1.40 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.22/1.40 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.22/1.40 # Preprocessing time : 0.025 s
% 0.22/1.40
% 0.22/1.40 # Proof found!
% 0.22/1.40 # SZS status Theorem
% 0.22/1.40 # SZS output start CNFRefutation
% See solution above
% 0.22/1.40 # Proof object total steps : 46
% 0.22/1.40 # Proof object clause steps : 27
% 0.22/1.40 # Proof object formula steps : 19
% 0.22/1.40 # Proof object conjectures : 14
% 0.22/1.40 # Proof object clause conjectures : 11
% 0.22/1.40 # Proof object formula conjectures : 3
% 0.22/1.40 # Proof object initial clauses used : 12
% 0.22/1.40 # Proof object initial formulas used : 9
% 0.22/1.40 # Proof object generating inferences : 9
% 0.22/1.40 # Proof object simplifying inferences : 15
% 0.22/1.40 # Training examples: 0 positive, 0 negative
% 0.22/1.40 # Parsed axioms : 150
% 0.22/1.40 # Removed by relevancy pruning/SinE : 63
% 0.22/1.40 # Initial clauses : 158
% 0.22/1.40 # Removed in clause preprocessing : 2
% 0.22/1.40 # Initial clauses in saturation : 156
% 0.22/1.40 # Processed clauses : 1115
% 0.22/1.40 # ...of these trivial : 43
% 0.22/1.40 # ...subsumed : 636
% 0.22/1.40 # ...remaining for further processing : 436
% 0.22/1.40 # Other redundant clauses eliminated : 60
% 0.22/1.40 # Clauses deleted for lack of memory : 0
% 0.22/1.40 # Backward-subsumed : 8
% 0.22/1.40 # Backward-rewritten : 47
% 0.22/1.40 # Generated clauses : 4285
% 0.22/1.40 # ...of the previous two non-trivial : 3329
% 0.22/1.40 # Contextual simplify-reflections : 29
% 0.22/1.40 # Paramodulations : 4177
% 0.22/1.40 # Factorizations : 10
% 0.22/1.40 # Equation resolutions : 96
% 0.22/1.40 # Current number of processed clauses : 374
% 0.22/1.40 # Positive orientable unit clauses : 69
% 0.22/1.40 # Positive unorientable unit clauses: 2
% 0.22/1.40 # Negative unit clauses : 36
% 0.22/1.40 # Non-unit-clauses : 267
% 0.22/1.40 # Current number of unprocessed clauses: 2169
% 0.22/1.40 # ...number of literals in the above : 6726
% 0.22/1.40 # Current number of archived formulas : 0
% 0.22/1.40 # Current number of archived clauses : 59
% 0.22/1.40 # Clause-clause subsumption calls (NU) : 31296
% 0.22/1.40 # Rec. Clause-clause subsumption calls : 27308
% 0.22/1.40 # Non-unit clause-clause subsumptions : 419
% 0.22/1.40 # Unit Clause-clause subsumption calls : 4530
% 0.22/1.40 # Rewrite failures with RHS unbound : 0
% 0.22/1.40 # BW rewrite match attempts : 70
% 0.22/1.40 # BW rewrite match successes : 40
% 0.22/1.40 # Condensation attempts : 0
% 0.22/1.40 # Condensation successes : 0
% 0.22/1.40 # Termbank termtop insertions : 48445
% 0.22/1.40
% 0.22/1.40 # -------------------------------------------------
% 0.22/1.40 # User time : 0.111 s
% 0.22/1.40 # System time : 0.008 s
% 0.22/1.40 # Total time : 0.119 s
% 0.22/1.40 # Maximum resident set size: 5996 pages
%------------------------------------------------------------------------------