%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET960+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n011.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 00:55:44 EDT 2022
% Result : Theorem 0.16s 1.34s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 36 ( 6 unt; 0 def)
% Number of atoms : 120 ( 73 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 141 ( 57 ~; 67 |; 12 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-4 aty)
% Number of variables : 79 ( 23 sgn 25 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d1_xboole_0) ).
fof(d2_zfmisc_1,axiom,
! [X1,X2,X3] :
( X3 = cartesian_product2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5,X6] :
( in(X5,X1)
& in(X6,X2)
& X4 = ordered_pair(X5,X6) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d2_zfmisc_1) ).
fof(t113_zfmisc_1,conjecture,
! [X1,X2] :
( cartesian_product2(X1,X2) = empty_set
<=> ( X1 = empty_set
| X2 = empty_set ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t113_zfmisc_1) ).
fof(c_0_3,plain,
! [X3,X4,X3] :
( ( X3 != empty_set
| ~ in(X4,X3) )
& ( in(esk3_1(X3),X3)
| X3 = empty_set ) ),
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)],[inference(fof_simplification,[status(thm)],[d1_xboole_0])])])])])])]) ).
fof(c_0_4,plain,
! [X7,X8,X9,X10,X10,X13,X14,X7,X8,X9,X16,X17] :
( ( in(esk4_4(X7,X8,X9,X10),X7)
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( in(esk5_4(X7,X8,X9,X10),X8)
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( X10 = ordered_pair(esk4_4(X7,X8,X9,X10),esk5_4(X7,X8,X9,X10))
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( ~ in(X13,X7)
| ~ in(X14,X8)
| X10 != ordered_pair(X13,X14)
| in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( ~ in(esk6_3(X7,X8,X9),X9)
| ~ in(X16,X7)
| ~ in(X17,X8)
| esk6_3(X7,X8,X9) != ordered_pair(X16,X17)
| X9 = cartesian_product2(X7,X8) )
& ( in(esk7_3(X7,X8,X9),X7)
| in(esk6_3(X7,X8,X9),X9)
| X9 = cartesian_product2(X7,X8) )
& ( in(esk8_3(X7,X8,X9),X8)
| in(esk6_3(X7,X8,X9),X9)
| X9 = cartesian_product2(X7,X8) )
& ( esk6_3(X7,X8,X9) = ordered_pair(esk7_3(X7,X8,X9),esk8_3(X7,X8,X9))
| in(esk6_3(X7,X8,X9),X9)
| X9 = cartesian_product2(X7,X8) ) ),
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_zfmisc_1])])])])])])]) ).
cnf(c_0_5,plain,
( ~ in(X1,X2)
| X2 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk6_3(X2,X3,X1),X1)
| in(esk7_3(X2,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2] :
( cartesian_product2(X1,X2) = empty_set
<=> ( X1 = empty_set
| X2 = empty_set ) ),
inference(assume_negation,[status(cth)],[t113_zfmisc_1]) ).
cnf(c_0_8,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk6_3(X2,X3,X1),X1)
| X2 != empty_set ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
fof(c_0_9,negated_conjecture,
( ( esk1_0 != empty_set
| cartesian_product2(esk1_0,esk2_0) != empty_set )
& ( esk2_0 != empty_set
| cartesian_product2(esk1_0,esk2_0) != empty_set )
& ( cartesian_product2(esk1_0,esk2_0) = empty_set
| esk1_0 = empty_set
| esk2_0 = empty_set ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
cnf(c_0_10,plain,
( X1 = cartesian_product2(X2,X3)
| X1 != empty_set
| X2 != empty_set ),
inference(spm,[status(thm)],[c_0_5,c_0_8]) ).
cnf(c_0_11,negated_conjecture,
( cartesian_product2(esk1_0,esk2_0) != empty_set
| esk1_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,plain,
( cartesian_product2(X1,X2) = empty_set
| X1 != empty_set ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_13,plain,
( in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| X4 != ordered_pair(X5,X6)
| ~ in(X6,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_14,negated_conjecture,
( esk2_0 = empty_set
| esk1_0 = empty_set
| cartesian_product2(esk1_0,esk2_0) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
empty_set != esk1_0,
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
( in(ordered_pair(X1,X2),X3)
| X3 != cartesian_product2(X4,X5)
| ~ in(X2,X5)
| ~ in(X1,X4) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
( cartesian_product2(esk1_0,esk2_0) = empty_set
| empty_set = esk2_0 ),
inference(sr,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
( X1 != empty_set
| ~ in(X2,esk2_0)
| ~ in(X3,esk1_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_5]),c_0_5]) ).
cnf(c_0_19,plain,
( X1 = empty_set
| in(esk3_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_20,negated_conjecture,
( empty_set = esk2_0
| X1 != empty_set
| ~ in(X2,esk1_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,negated_conjecture,
( empty_set = esk2_0
| X1 != empty_set ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_19]),c_0_15]) ).
cnf(c_0_22,negated_conjecture,
empty_set = esk2_0,
inference(er,[status(thm)],[c_0_21]) ).
cnf(c_0_23,negated_conjecture,
( X1 != esk2_0
| ~ in(X2,esk2_0)
| ~ in(X3,esk1_0) ),
inference(rw,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_24,plain,
( X1 = cartesian_product2(X2,X3)
| in(esk6_3(X2,X3,X1),X1)
| in(esk8_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_25,negated_conjecture,
( X1 = cartesian_product2(X2,esk2_0)
| in(esk6_3(X2,esk2_0,X1),X1)
| X3 != esk2_0
| ~ in(X4,esk1_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,plain,
( X1 = esk2_0
| in(esk3_1(X1),X1) ),
inference(rw,[status(thm)],[c_0_19,c_0_22]) ).
cnf(c_0_27,negated_conjecture,
esk2_0 != esk1_0,
inference(rw,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_28,negated_conjecture,
( X1 = cartesian_product2(X2,esk2_0)
| in(esk6_3(X2,esk2_0,X1),X1)
| X3 != esk2_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_29,plain,
( X1 != esk2_0
| ~ in(X2,X1) ),
inference(rw,[status(thm)],[c_0_5,c_0_22]) ).
cnf(c_0_30,negated_conjecture,
( X1 = cartesian_product2(X2,esk2_0)
| in(esk6_3(X2,esk2_0,X1),X1) ),
inference(er,[status(thm)],[c_0_28]) ).
cnf(c_0_31,negated_conjecture,
( cartesian_product2(esk1_0,esk2_0) != empty_set
| esk2_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_32,negated_conjecture,
( X1 = cartesian_product2(X2,esk2_0)
| X1 != esk2_0 ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
cartesian_product2(esk1_0,esk2_0) != esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_22]),c_0_22])]) ).
cnf(c_0_34,negated_conjecture,
cartesian_product2(X1,esk2_0) = esk2_0,
inference(er,[status(thm)],[c_0_32]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08 % Problem : SET960+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.09 % Command : run_ET %s %d
% 0.09/0.28 % Computer : n011.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 600
% 0.09/0.28 % DateTime : Sun Jul 10 07:09:41 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.16/1.34 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.16/1.34 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.16/1.34 # Preprocessing time : 0.014 s
% 0.16/1.34
% 0.16/1.34 # Proof found!
% 0.16/1.34 # SZS status Theorem
% 0.16/1.34 # SZS output start CNFRefutation
% See solution above
% 0.16/1.34 # Proof object total steps : 36
% 0.16/1.34 # Proof object clause steps : 29
% 0.16/1.34 # Proof object formula steps : 7
% 0.16/1.34 # Proof object conjectures : 21
% 0.16/1.34 # Proof object clause conjectures : 18
% 0.16/1.34 # Proof object formula conjectures : 3
% 0.16/1.34 # Proof object initial clauses used : 8
% 0.16/1.34 # Proof object initial formulas used : 3
% 0.16/1.34 # Proof object generating inferences : 14
% 0.16/1.34 # Proof object simplifying inferences : 14
% 0.16/1.34 # Training examples: 0 positive, 0 negative
% 0.16/1.34 # Parsed axioms : 10
% 0.16/1.34 # Removed by relevancy pruning/SinE : 2
% 0.16/1.34 # Initial clauses : 18
% 0.16/1.34 # Removed in clause preprocessing : 0
% 0.16/1.34 # Initial clauses in saturation : 18
% 0.16/1.34 # Processed clauses : 64
% 0.16/1.34 # ...of these trivial : 0
% 0.16/1.34 # ...subsumed : 10
% 0.16/1.34 # ...remaining for further processing : 54
% 0.16/1.34 # Other redundant clauses eliminated : 1
% 0.16/1.34 # Clauses deleted for lack of memory : 0
% 0.16/1.34 # Backward-subsumed : 3
% 0.16/1.34 # Backward-rewritten : 16
% 0.16/1.34 # Generated clauses : 94
% 0.16/1.34 # ...of the previous two non-trivial : 95
% 0.16/1.34 # Contextual simplify-reflections : 8
% 0.16/1.34 # Paramodulations : 82
% 0.16/1.34 # Factorizations : 0
% 0.16/1.34 # Equation resolutions : 11
% 0.16/1.34 # Current number of processed clauses : 34
% 0.16/1.34 # Positive orientable unit clauses : 4
% 0.16/1.34 # Positive unorientable unit clauses: 0
% 0.16/1.34 # Negative unit clauses : 3
% 0.16/1.34 # Non-unit-clauses : 27
% 0.16/1.34 # Current number of unprocessed clauses: 22
% 0.16/1.34 # ...number of literals in the above : 78
% 0.16/1.34 # Current number of archived formulas : 0
% 0.16/1.34 # Current number of archived clauses : 20
% 0.16/1.34 # Clause-clause subsumption calls (NU) : 208
% 0.16/1.34 # Rec. Clause-clause subsumption calls : 135
% 0.16/1.34 # Non-unit clause-clause subsumptions : 17
% 0.16/1.34 # Unit Clause-clause subsumption calls : 2
% 0.16/1.34 # Rewrite failures with RHS unbound : 0
% 0.16/1.34 # BW rewrite match attempts : 3
% 0.16/1.34 # BW rewrite match successes : 3
% 0.16/1.34 # Condensation attempts : 0
% 0.16/1.34 # Condensation successes : 0
% 0.16/1.34 # Termbank termtop insertions : 2011
% 0.16/1.34
% 0.16/1.34 # -------------------------------------------------
% 0.16/1.34 # User time : 0.015 s
% 0.16/1.34 # System time : 0.002 s
% 0.16/1.34 # Total time : 0.017 s
% 0.16/1.34 # Maximum resident set size: 2964 pages
%------------------------------------------------------------------------------