%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET902+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n019.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 00:55:19 EDT 2022
% Result : Theorem 0.23s 1.40s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 17 unt; 0 def)
% Number of atoms : 67 ( 55 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 65 ( 29 ~; 18 |; 17 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 5 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t43_zfmisc_1,conjecture,
! [X1,X2,X3] :
~ ( singleton(X1) = set_union2(X2,X3)
& ~ ( X2 = singleton(X1)
& X3 = singleton(X1) )
& ~ ( X2 = empty_set
& X3 = singleton(X1) )
& ~ ( X2 = singleton(X1)
& X3 = empty_set ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t43_zfmisc_1) ).
fof(t7_xboole_1,axiom,
! [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_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_k2_xboole_0) ).
fof(l4_zfmisc_1,axiom,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',l4_zfmisc_1) ).
fof(idempotence_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',idempotence_k2_xboole_0) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( singleton(X1) = set_union2(X2,X3)
& ~ ( X2 = singleton(X1)
& X3 = singleton(X1) )
& ~ ( X2 = empty_set
& X3 = singleton(X1) )
& ~ ( X2 = singleton(X1)
& X3 = empty_set ) ),
inference(assume_negation,[status(cth)],[t43_zfmisc_1]) ).
fof(c_0_6,plain,
! [X3,X4] : subset(X3,set_union2(X3,X4)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(c_0_7,plain,
! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_8,negated_conjecture,
( singleton(esk1_0) = set_union2(esk2_0,esk3_0)
& ( esk2_0 != singleton(esk1_0)
| esk3_0 != singleton(esk1_0) )
& ( esk2_0 != empty_set
| esk3_0 != singleton(esk1_0) )
& ( esk2_0 != singleton(esk1_0)
| esk3_0 != empty_set ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_9,plain,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X3,X4,X3,X4] :
( ( ~ subset(X3,singleton(X4))
| X3 = empty_set
| X3 = singleton(X4) )
& ( X3 != empty_set
| subset(X3,singleton(X4)) )
& ( X3 != singleton(X4)
| subset(X3,singleton(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)],[l4_zfmisc_1])])])])]) ).
cnf(c_0_12,negated_conjecture,
singleton(esk1_0) = set_union2(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
subset(X1,set_union2(X2,X1)),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
subset(esk2_0,singleton(esk1_0)),
inference(spm,[status(thm)],[c_0_9,c_0_12]) ).
cnf(c_0_16,negated_conjecture,
subset(esk3_0,singleton(esk1_0)),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
( esk3_0 != empty_set
| esk2_0 != singleton(esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,negated_conjecture,
( singleton(esk1_0) = esk2_0
| empty_set = esk2_0 ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
( esk3_0 != singleton(esk1_0)
| esk2_0 != singleton(esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,negated_conjecture,
( esk3_0 != singleton(esk1_0)
| esk2_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,negated_conjecture,
( singleton(esk1_0) = esk3_0
| empty_set = esk3_0 ),
inference(spm,[status(thm)],[c_0_14,c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( empty_set = esk2_0
| empty_set != esk3_0 ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( empty_set = esk2_0
| esk3_0 != esk2_0 ),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
( empty_set = esk3_0
| empty_set != esk2_0 ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
empty_set = esk2_0,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_21]),c_0_22]),c_0_23]) ).
fof(c_0_26,plain,
! [X3] : set_union2(X3,X3) = X3,
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[idempotence_k2_xboole_0])]) ).
cnf(c_0_27,negated_conjecture,
esk3_0 = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_25])]) ).
cnf(c_0_28,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_29,negated_conjecture,
singleton(esk1_0) != esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_25]),c_0_27])]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_27]),c_0_28]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET902+1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n019.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 Jul 10 02:21:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.23/1.40 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/1.40 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/1.40 # Preprocessing time : 0.015 s
% 0.23/1.40
% 0.23/1.40 # Proof found!
% 0.23/1.40 # SZS status Theorem
% 0.23/1.40 # SZS output start CNFRefutation
% See solution above
% 0.23/1.40 # Proof object total steps : 31
% 0.23/1.40 # Proof object clause steps : 20
% 0.23/1.40 # Proof object formula steps : 11
% 0.23/1.40 # Proof object conjectures : 18
% 0.23/1.40 # Proof object clause conjectures : 15
% 0.23/1.40 # Proof object formula conjectures : 3
% 0.23/1.40 # Proof object initial clauses used : 8
% 0.23/1.40 # Proof object initial formulas used : 5
% 0.23/1.40 # Proof object generating inferences : 9
% 0.23/1.40 # Proof object simplifying inferences : 11
% 0.23/1.40 # Training examples: 0 positive, 0 negative
% 0.23/1.40 # Parsed axioms : 12
% 0.23/1.40 # Removed by relevancy pruning/SinE : 0
% 0.23/1.40 # Initial clauses : 17
% 0.23/1.40 # Removed in clause preprocessing : 0
% 0.23/1.40 # Initial clauses in saturation : 17
% 0.23/1.40 # Processed clauses : 37
% 0.23/1.40 # ...of these trivial : 1
% 0.23/1.40 # ...subsumed : 1
% 0.23/1.40 # ...remaining for further processing : 34
% 0.23/1.40 # Other redundant clauses eliminated : 0
% 0.23/1.40 # Clauses deleted for lack of memory : 0
% 0.23/1.40 # Backward-subsumed : 1
% 0.23/1.40 # Backward-rewritten : 18
% 0.23/1.40 # Generated clauses : 51
% 0.23/1.40 # ...of the previous two non-trivial : 42
% 0.23/1.40 # Contextual simplify-reflections : 2
% 0.23/1.40 # Paramodulations : 51
% 0.23/1.40 # Factorizations : 0
% 0.23/1.40 # Equation resolutions : 0
% 0.23/1.40 # Current number of processed clauses : 15
% 0.23/1.40 # Positive orientable unit clauses : 8
% 0.23/1.40 # Positive unorientable unit clauses: 1
% 0.23/1.40 # Negative unit clauses : 2
% 0.23/1.40 # Non-unit-clauses : 4
% 0.23/1.40 # Current number of unprocessed clauses: 13
% 0.23/1.40 # ...number of literals in the above : 22
% 0.23/1.40 # Current number of archived formulas : 0
% 0.23/1.40 # Current number of archived clauses : 19
% 0.23/1.40 # Clause-clause subsumption calls (NU) : 8
% 0.23/1.40 # Rec. Clause-clause subsumption calls : 8
% 0.23/1.40 # Non-unit clause-clause subsumptions : 2
% 0.23/1.40 # Unit Clause-clause subsumption calls : 5
% 0.23/1.40 # Rewrite failures with RHS unbound : 0
% 0.23/1.40 # BW rewrite match attempts : 10
% 0.23/1.40 # BW rewrite match successes : 8
% 0.23/1.40 # Condensation attempts : 0
% 0.23/1.40 # Condensation successes : 0
% 0.23/1.40 # Termbank termtop insertions : 942
% 0.23/1.40
% 0.23/1.40 # -------------------------------------------------
% 0.23/1.40 # User time : 0.017 s
% 0.23/1.40 # System time : 0.000 s
% 0.23/1.40 # Total time : 0.017 s
% 0.23/1.40 # Maximum resident set size: 2776 pages
%------------------------------------------------------------------------------