TSTP Solution File: SET971+1 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET971+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n025.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 00:55:47 EDT 2022
% Result : Theorem 0.22s 1.40s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 25 unt; 0 def)
% Number of atoms : 40 ( 28 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 15 ( 6 ~; 2 |; 4 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 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 : 58 ( 1 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t123_zfmisc_1,axiom,
! [X1,X2,X3,X4] : cartesian_product2(set_intersection2(X1,X2),set_intersection2(X3,X4)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t123_zfmisc_1) ).
fof(idempotence_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',idempotence_k3_xboole_0) ).
fof(t124_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> set_intersection2(cartesian_product2(X1,X4),cartesian_product2(X2,X3)) = cartesian_product2(X1,X3) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t124_zfmisc_1) ).
fof(t28_xboole_1,axiom,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t28_xboole_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',commutativity_k3_xboole_0) ).
fof(c_0_5,plain,
! [X5,X6,X7,X8] : cartesian_product2(set_intersection2(X5,X6),set_intersection2(X7,X8)) = set_intersection2(cartesian_product2(X5,X7),cartesian_product2(X6,X8)),
inference(variable_rename,[status(thm)],[t123_zfmisc_1]) ).
fof(c_0_6,plain,
! [X3] : set_intersection2(X3,X3) = X3,
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[idempotence_k3_xboole_0])]) ).
cnf(c_0_7,plain,
cartesian_product2(set_intersection2(X1,X2),set_intersection2(X3,X4)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> set_intersection2(cartesian_product2(X1,X4),cartesian_product2(X2,X3)) = cartesian_product2(X1,X3) ),
inference(assume_negation,[status(cth)],[t124_zfmisc_1]) ).
cnf(c_0_10,plain,
cartesian_product2(set_intersection2(X1,X2),X3) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X3)),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
fof(c_0_11,plain,
! [X3,X4] :
( ~ subset(X3,X4)
| set_intersection2(X3,X4) = X3 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])]) ).
fof(c_0_12,negated_conjecture,
( subset(esk1_0,esk2_0)
& subset(esk3_0,esk4_0)
& set_intersection2(cartesian_product2(esk1_0,esk4_0),cartesian_product2(esk2_0,esk3_0)) != cartesian_product2(esk1_0,esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_13,plain,
! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_0_14,plain,
set_intersection2(cartesian_product2(X1,set_intersection2(X2,X3)),cartesian_product2(X4,set_intersection2(X2,X3))) = set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X4,X3)),
inference(rw,[status(thm)],[c_0_7,c_0_10]) ).
cnf(c_0_15,plain,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
subset(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
subset(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
cartesian_product2(X1,set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X1,X3)),
inference(spm,[status(thm)],[c_0_8,c_0_14]) ).
cnf(c_0_20,negated_conjecture,
set_intersection2(esk4_0,esk3_0) = esk3_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_21,negated_conjecture,
set_intersection2(esk2_0,esk1_0) = esk1_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_18]),c_0_17]) ).
cnf(c_0_22,plain,
set_intersection2(set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X1,X3)),set_intersection2(cartesian_product2(X4,X2),cartesian_product2(X4,X3))) = set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X4,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_19]),c_0_19]) ).
cnf(c_0_23,negated_conjecture,
set_intersection2(cartesian_product2(X1,esk4_0),cartesian_product2(X1,esk3_0)) = cartesian_product2(X1,esk3_0),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
set_intersection2(cartesian_product2(esk2_0,X1),cartesian_product2(esk1_0,X1)) = cartesian_product2(esk1_0,X1),
inference(spm,[status(thm)],[c_0_10,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
set_intersection2(cartesian_product2(X1,esk3_0),cartesian_product2(X2,esk3_0)) = set_intersection2(cartesian_product2(X1,esk4_0),cartesian_product2(X2,esk3_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_23]) ).
cnf(c_0_26,negated_conjecture,
set_intersection2(cartesian_product2(esk1_0,esk4_0),cartesian_product2(esk2_0,esk3_0)) != cartesian_product2(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_27,negated_conjecture,
set_intersection2(cartesian_product2(esk2_0,esk4_0),cartesian_product2(esk1_0,esk3_0)) = cartesian_product2(esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,plain,
set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)) = set_intersection2(cartesian_product2(X3,X2),cartesian_product2(X1,X4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_22]),c_0_22]) ).
cnf(c_0_29,negated_conjecture,
cartesian_product2(esk1_0,esk3_0) != set_intersection2(cartesian_product2(esk2_0,esk3_0),cartesian_product2(esk1_0,esk4_0)),
inference(rw,[status(thm)],[c_0_26,c_0_17]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_17]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET971+1 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.12 % Command : run_ET %s %d
% 0.13/0.33 % Computer : n025.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 : Sun Jul 10 08:30:31 EDT 2022
% 0.13/0.33 % 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 : 0.014 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 : 31
% 0.22/1.40 # Proof object clause steps : 20
% 0.22/1.40 # Proof object formula steps : 11
% 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 : 7
% 0.22/1.40 # Proof object initial formulas used : 5
% 0.22/1.40 # Proof object generating inferences : 9
% 0.22/1.40 # Proof object simplifying inferences : 11
% 0.22/1.40 # Training examples: 0 positive, 0 negative
% 0.22/1.40 # Parsed axioms : 8
% 0.22/1.40 # Removed by relevancy pruning/SinE : 2
% 0.22/1.40 # Initial clauses : 8
% 0.22/1.40 # Removed in clause preprocessing : 0
% 0.22/1.40 # Initial clauses in saturation : 8
% 0.22/1.40 # Processed clauses : 72
% 0.22/1.40 # ...of these trivial : 7
% 0.22/1.40 # ...subsumed : 2
% 0.22/1.40 # ...remaining for further processing : 63
% 0.22/1.40 # Other redundant clauses eliminated : 0
% 0.22/1.40 # Clauses deleted for lack of memory : 0
% 0.22/1.40 # Backward-subsumed : 1
% 0.22/1.40 # Backward-rewritten : 20
% 0.22/1.40 # Generated clauses : 434
% 0.22/1.40 # ...of the previous two non-trivial : 369
% 0.22/1.40 # Contextual simplify-reflections : 0
% 0.22/1.40 # Paramodulations : 434
% 0.22/1.40 # Factorizations : 0
% 0.22/1.40 # Equation resolutions : 0
% 0.22/1.40 # Current number of processed clauses : 42
% 0.22/1.40 # Positive orientable unit clauses : 37
% 0.22/1.40 # Positive unorientable unit clauses: 3
% 0.22/1.40 # Negative unit clauses : 1
% 0.22/1.40 # Non-unit-clauses : 1
% 0.22/1.40 # Current number of unprocessed clauses: 198
% 0.22/1.40 # ...number of literals in the above : 198
% 0.22/1.40 # Current number of archived formulas : 0
% 0.22/1.40 # Current number of archived clauses : 21
% 0.22/1.40 # Clause-clause subsumption calls (NU) : 0
% 0.22/1.40 # Rec. Clause-clause subsumption calls : 0
% 0.22/1.40 # Non-unit clause-clause subsumptions : 0
% 0.22/1.40 # Unit Clause-clause subsumption calls : 19
% 0.22/1.40 # Rewrite failures with RHS unbound : 0
% 0.22/1.40 # BW rewrite match attempts : 194
% 0.22/1.40 # BW rewrite match successes : 107
% 0.22/1.40 # Condensation attempts : 0
% 0.22/1.40 # Condensation successes : 0
% 0.22/1.40 # Termbank termtop insertions : 8831
% 0.22/1.40
% 0.22/1.40 # -------------------------------------------------
% 0.22/1.40 # User time : 0.022 s
% 0.22/1.40 # System time : 0.004 s
% 0.22/1.40 # Total time : 0.026 s
% 0.22/1.40 # Maximum resident set size: 3300 pages
%------------------------------------------------------------------------------