TSTP Solution File: GRP775+1 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : GRP775+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n005.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 : Sat Jul 16 09:03:38 EDT 2022
% Result : Theorem 0.25s 1.44s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 52 ( 14 unt; 0 def)
% Number of atoms : 120 ( 69 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 105 ( 37 ~; 50 |; 13 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 67 ( 6 sgn 31 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X11,X12] :
( d(X11,X12)
<=> ( product(X11,product(X12,X11)) = X11
& product(X12,product(X11,X12)) = X12 ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',goals) ).
fof(sos01,axiom,
! [X1,X2,X3] : product(product(X3,X2),X1) = product(X3,product(X2,X1)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',sos01) ).
fof(sos02,axiom,
! [X3] : product(X3,X3) = X3,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',sos02) ).
fof(sos05,axiom,
! [X8,X9] :
( d(X8,X9)
<=> ? [X10] :
( r(X8,X10)
& l(X10,X9) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',sos05) ).
fof(sos04,axiom,
! [X6,X7] :
( r(X6,X7)
<=> ( product(X6,X7) = X7
& product(X7,X6) = X6 ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',sos04) ).
fof(sos03,axiom,
! [X4,X5] :
( l(X4,X5)
<=> ( product(X4,X5) = X4
& product(X5,X4) = X5 ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',sos03) ).
fof(c_0_6,negated_conjecture,
~ ! [X11,X12] :
( d(X11,X12)
<=> ( product(X11,product(X12,X11)) = X11
& product(X12,product(X11,X12)) = X12 ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_7,plain,
! [X4,X5,X6] : product(product(X6,X5),X4) = product(X6,product(X5,X4)),
inference(variable_rename,[status(thm)],[sos01]) ).
fof(c_0_8,plain,
! [X4] : product(X4,X4) = X4,
inference(variable_rename,[status(thm)],[sos02]) ).
fof(c_0_9,plain,
! [X11,X12,X11,X12,X14] :
( ( r(X11,esk3_2(X11,X12))
| ~ d(X11,X12) )
& ( l(esk3_2(X11,X12),X12)
| ~ d(X11,X12) )
& ( ~ r(X11,X14)
| ~ l(X14,X12)
| d(X11,X12) ) ),
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)],[sos05])])])])])])]) ).
fof(c_0_10,negated_conjecture,
( ( ~ d(esk1_0,esk2_0)
| product(esk1_0,product(esk2_0,esk1_0)) != esk1_0
| product(esk2_0,product(esk1_0,esk2_0)) != esk2_0 )
& ( product(esk1_0,product(esk2_0,esk1_0)) = esk1_0
| d(esk1_0,esk2_0) )
& ( product(esk2_0,product(esk1_0,esk2_0)) = esk2_0
| d(esk1_0,esk2_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
cnf(c_0_11,plain,
product(product(X1,X2),X3) = product(X1,product(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
product(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X8,X9,X8,X9] :
( ( product(X8,X9) = X9
| ~ r(X8,X9) )
& ( product(X9,X8) = X8
| ~ r(X8,X9) )
& ( product(X8,X9) != X9
| product(X9,X8) != X8
| r(X8,X9) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos04])])])])]) ).
cnf(c_0_14,plain,
( r(X1,esk3_2(X1,X2))
| ~ d(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
( d(esk1_0,esk2_0)
| product(esk2_0,product(esk1_0,esk2_0)) = esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,plain,
! [X6,X7,X6,X7] :
( ( product(X6,X7) = X6
| ~ l(X6,X7) )
& ( product(X7,X6) = X7
| ~ l(X6,X7) )
& ( product(X6,X7) != X6
| product(X7,X6) != X7
| l(X6,X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos03])])])])]) ).
cnf(c_0_17,plain,
( l(esk3_2(X1,X2),X2)
| ~ d(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,negated_conjecture,
( d(esk1_0,esk2_0)
| product(esk1_0,product(esk2_0,esk1_0)) = esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,plain,
product(X1,product(X1,X2)) = product(X1,X2),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_20,plain,
( product(X1,X2) = X2
| ~ r(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,negated_conjecture,
( product(esk2_0,product(esk1_0,esk2_0)) = esk2_0
| r(esk1_0,esk3_2(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,plain,
( product(X1,X2) = X1
| ~ l(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
( product(esk1_0,product(esk2_0,esk1_0)) = esk1_0
| l(esk3_2(esk1_0,esk2_0),esk2_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,plain,
product(X1,product(X2,product(X1,product(X2,X3)))) = product(X1,product(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_19]),c_0_11]),c_0_11]) ).
cnf(c_0_25,negated_conjecture,
( product(esk1_0,esk3_2(esk1_0,esk2_0)) = esk3_2(esk1_0,esk2_0)
| product(esk2_0,product(esk1_0,esk2_0)) = esk2_0 ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( product(X2,X1) = X2
| ~ l(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_27,negated_conjecture,
( product(esk2_0,product(esk1_0,esk2_0)) = esk2_0
| l(esk3_2(esk1_0,esk2_0),esk2_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_28,plain,
( product(X2,X1) = X1
| ~ r(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_29,negated_conjecture,
( product(esk1_0,product(esk2_0,esk1_0)) = esk1_0
| r(esk1_0,esk3_2(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_30,negated_conjecture,
( product(esk3_2(esk1_0,esk2_0),esk2_0) = esk3_2(esk1_0,esk2_0)
| product(esk1_0,product(esk2_0,esk1_0)) = esk1_0 ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_31,negated_conjecture,
( product(X1,product(esk1_0,product(X1,esk3_2(esk1_0,esk2_0)))) = product(X1,esk3_2(esk1_0,esk2_0))
| product(esk2_0,product(esk1_0,esk2_0)) = esk2_0 ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,negated_conjecture,
( product(esk2_0,product(esk1_0,esk2_0)) = esk2_0
| product(esk2_0,esk3_2(esk1_0,esk2_0)) = esk2_0 ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,negated_conjecture,
( product(esk1_0,product(esk2_0,esk1_0)) = esk1_0
| product(esk3_2(esk1_0,esk2_0),esk1_0) = esk1_0 ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
( product(esk3_2(esk1_0,esk2_0),product(esk2_0,X1)) = product(esk3_2(esk1_0,esk2_0),X1)
| product(esk1_0,product(esk2_0,esk1_0)) = esk1_0 ),
inference(spm,[status(thm)],[c_0_11,c_0_30]) ).
cnf(c_0_35,negated_conjecture,
product(esk2_0,product(esk1_0,esk2_0)) = esk2_0,
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( product(esk3_2(esk1_0,esk2_0),product(esk1_0,X1)) = product(esk1_0,X1)
| product(esk1_0,product(esk2_0,esk1_0)) = esk1_0 ),
inference(spm,[status(thm)],[c_0_11,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
( product(esk3_2(esk1_0,esk2_0),product(esk1_0,esk2_0)) = product(esk3_2(esk1_0,esk2_0),esk2_0)
| product(esk1_0,product(esk2_0,esk1_0)) = esk1_0 ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
( product(esk3_2(esk1_0,esk2_0),esk2_0) = product(esk1_0,esk2_0)
| product(esk1_0,product(esk2_0,esk1_0)) = esk1_0 ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_39,plain,
( r(X1,X2)
| product(X2,X1) != X1
| product(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_40,negated_conjecture,
( product(esk1_0,product(esk2_0,esk1_0)) = esk1_0
| esk3_2(esk1_0,esk2_0) = product(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_38]) ).
cnf(c_0_41,plain,
( r(X1,product(X2,X3))
| product(X1,product(X2,X3)) != product(X2,X3)
| product(X2,product(X3,X1)) != X1 ),
inference(spm,[status(thm)],[c_0_39,c_0_11]) ).
cnf(c_0_42,negated_conjecture,
product(esk1_0,product(esk2_0,esk1_0)) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_40]),c_0_11])]) ).
cnf(c_0_43,negated_conjecture,
( product(esk2_0,product(esk1_0,esk2_0)) != esk2_0
| product(esk1_0,product(esk2_0,esk1_0)) != esk1_0
| ~ d(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_44,plain,
( d(X1,X2)
| ~ l(X3,X2)
| ~ r(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_45,negated_conjecture,
r(esk1_0,product(esk1_0,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_19])]) ).
cnf(c_0_46,plain,
( l(X1,X2)
| product(X2,X1) != X2
| product(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_47,negated_conjecture,
( product(esk1_0,product(esk2_0,esk1_0)) != esk1_0
| ~ d(esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_35])]) ).
cnf(c_0_48,negated_conjecture,
( d(esk1_0,X1)
| ~ l(product(esk1_0,esk2_0),X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,negated_conjecture,
l(product(esk1_0,esk2_0),esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_35]),c_0_11]),c_0_12])]) ).
cnf(c_0_50,negated_conjecture,
~ d(esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_42])]) ).
cnf(c_0_51,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP775+1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : run_ET %s %d
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 13:27:24 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.25/1.44 # Running protocol protocol_eprover_2d86bd69119e7e9cc4417c0ee581499eaf828bb2 for 23 seconds:
% 0.25/1.44 # SinE strategy is GSinE(CountFormulas,,1.1,,02,500,1.0)
% 0.25/1.44 # Preprocessing time : 0.014 s
% 0.25/1.44
% 0.25/1.44 # Proof found!
% 0.25/1.44 # SZS status Theorem
% 0.25/1.44 # SZS output start CNFRefutation
% See solution above
% 0.25/1.44 # Proof object total steps : 52
% 0.25/1.44 # Proof object clause steps : 39
% 0.25/1.44 # Proof object formula steps : 13
% 0.25/1.44 # Proof object conjectures : 28
% 0.25/1.44 # Proof object clause conjectures : 25
% 0.25/1.44 # Proof object formula conjectures : 3
% 0.25/1.44 # Proof object initial clauses used : 14
% 0.25/1.44 # Proof object initial formulas used : 6
% 0.25/1.44 # Proof object generating inferences : 23
% 0.25/1.44 # Proof object simplifying inferences : 14
% 0.25/1.44 # Training examples: 0 positive, 0 negative
% 0.25/1.44 # Parsed axioms : 6
% 0.25/1.44 # Removed by relevancy pruning/SinE : 0
% 0.25/1.44 # Initial clauses : 14
% 0.25/1.44 # Removed in clause preprocessing : 0
% 0.25/1.44 # Initial clauses in saturation : 14
% 0.25/1.44 # Processed clauses : 1126
% 0.25/1.44 # ...of these trivial : 161
% 0.25/1.44 # ...subsumed : 464
% 0.25/1.44 # ...remaining for further processing : 501
% 0.25/1.44 # Other redundant clauses eliminated : 0
% 0.25/1.44 # Clauses deleted for lack of memory : 0
% 0.25/1.44 # Backward-subsumed : 7
% 0.25/1.44 # Backward-rewritten : 323
% 0.25/1.44 # Generated clauses : 26841
% 0.25/1.44 # ...of the previous two non-trivial : 16572
% 0.25/1.44 # Contextual simplify-reflections : 107
% 0.25/1.44 # Paramodulations : 26841
% 0.25/1.44 # Factorizations : 0
% 0.25/1.44 # Equation resolutions : 0
% 0.25/1.44 # Current number of processed clauses : 171
% 0.25/1.44 # Positive orientable unit clauses : 98
% 0.25/1.44 # Positive unorientable unit clauses: 0
% 0.25/1.44 # Negative unit clauses : 1
% 0.25/1.44 # Non-unit-clauses : 72
% 0.25/1.44 # Current number of unprocessed clauses: 5987
% 0.25/1.44 # ...number of literals in the above : 14308
% 0.25/1.44 # Current number of archived formulas : 0
% 0.25/1.44 # Current number of archived clauses : 330
% 0.25/1.44 # Clause-clause subsumption calls (NU) : 5223
% 0.25/1.44 # Rec. Clause-clause subsumption calls : 4095
% 0.25/1.44 # Non-unit clause-clause subsumptions : 578
% 0.25/1.44 # Unit Clause-clause subsumption calls : 280
% 0.25/1.44 # Rewrite failures with RHS unbound : 0
% 0.25/1.44 # BW rewrite match attempts : 2406
% 0.25/1.44 # BW rewrite match successes : 51
% 0.25/1.44 # Condensation attempts : 0
% 0.25/1.44 # Condensation successes : 0
% 0.25/1.44 # Termbank termtop insertions : 919845
% 0.25/1.44
% 0.25/1.44 # -------------------------------------------------
% 0.25/1.44 # User time : 0.333 s
% 0.25/1.44 # System time : 0.011 s
% 0.25/1.44 # Total time : 0.344 s
% 0.25/1.44 # Maximum resident set size: 18608 pages
%------------------------------------------------------------------------------