TSTP Solution File: ALG210+2 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : ALG210+2 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n022.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 : Thu Jul 14 16:50:23 EDT 2022
% Result : Theorem 0.21s 1.40s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 19 unt; 0 def)
% Number of atoms : 54 ( 33 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 41 ( 17 ~; 11 |; 10 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 1 sgn 16 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conjecture_1,conjecture,
! [X1,X2,X3] :
( ( element(X1)
& element(X2)
& X3 = times(X1,X2) )
=> element(X3) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conjecture_1) ).
fof(axiom_1,axiom,
! [X1,X2,X3] : times(times(X1,X2),X3) = times(X2,times(X3,X1)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',axiom_1) ).
fof(axiom_2,axiom,
! [X2] :
( element(X2)
<=> ? [X3] :
( times(X2,X3) = X2
& times(X2,X2) = X3 ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',axiom_2) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2,X3] :
( ( element(X1)
& element(X2)
& X3 = times(X1,X2) )
=> element(X3) ),
inference(assume_negation,[status(cth)],[conjecture_1]) ).
fof(c_0_4,plain,
! [X4,X5,X6] : times(times(X4,X5),X6) = times(X5,times(X6,X4)),
inference(variable_rename,[status(thm)],[axiom_1]) ).
fof(c_0_5,plain,
! [X4,X4,X6] :
( ( times(X4,esk4_1(X4)) = X4
| ~ element(X4) )
& ( times(X4,X4) = esk4_1(X4)
| ~ element(X4) )
& ( times(X4,X6) != X4
| times(X4,X4) != X6
| element(X4) ) ),
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)],[axiom_2])])])])])])]) ).
fof(c_0_6,negated_conjecture,
( element(esk1_0)
& element(esk2_0)
& esk3_0 = times(esk1_0,esk2_0)
& ~ element(esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
cnf(c_0_7,plain,
times(times(X1,X2),X3) = times(X2,times(X3,X1)),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( times(X1,esk4_1(X1)) = X1
| ~ element(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( times(X1,X1) = esk4_1(X1)
| ~ element(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
esk3_0 = times(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
times(times(X1,times(X2,X3)),X4) = times(X3,times(times(X4,X1),X2)),
inference(spm,[status(thm)],[c_0_7,c_0_7]) ).
cnf(c_0_12,plain,
( times(X1,times(X1,X1)) = X1
| ~ element(X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,negated_conjecture,
element(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,negated_conjecture,
times(esk3_0,X1) = times(esk2_0,times(X1,esk1_0)),
inference(spm,[status(thm)],[c_0_7,c_0_10]) ).
cnf(c_0_15,plain,
times(times(X1,times(X2,X3)),X4) = times(X3,times(X1,times(X2,X4))),
inference(spm,[status(thm)],[c_0_11,c_0_7]) ).
cnf(c_0_16,negated_conjecture,
element(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,plain,
( element(X1)
| times(X1,X1) != X2
| times(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,negated_conjecture,
~ element(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
times(esk1_0,times(esk1_0,esk1_0)) = esk1_0,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_20,negated_conjecture,
times(esk1_0,times(esk2_0,times(X1,X2))) = times(X1,times(X2,esk3_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_14]),c_0_15]) ).
cnf(c_0_21,negated_conjecture,
times(esk2_0,times(esk2_0,esk2_0)) = esk2_0,
inference(spm,[status(thm)],[c_0_12,c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( times(esk2_0,times(X1,esk1_0)) != esk3_0
| times(esk3_0,esk3_0) != X1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_14]),c_0_18]) ).
cnf(c_0_23,negated_conjecture,
times(esk1_0,times(esk1_0,times(esk1_0,X1))) = times(esk1_0,X1),
inference(spm,[status(thm)],[c_0_15,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
times(esk2_0,times(esk2_0,esk3_0)) = esk3_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_10]) ).
cnf(c_0_25,negated_conjecture,
( times(esk3_0,X1) != esk3_0
| times(esk3_0,esk3_0) != X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_7]),c_0_10]) ).
cnf(c_0_26,negated_conjecture,
times(esk1_0,times(esk1_0,esk3_0)) = esk3_0,
inference(spm,[status(thm)],[c_0_23,c_0_10]) ).
cnf(c_0_27,negated_conjecture,
times(esk1_0,esk3_0) = times(esk2_0,times(esk3_0,esk3_0)),
inference(spm,[status(thm)],[c_0_20,c_0_24]) ).
cnf(c_0_28,negated_conjecture,
times(esk3_0,times(esk3_0,esk3_0)) != esk3_0,
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_20]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ALG210+2 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n022.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 : Wed Jun 8 22:30:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.21/1.40 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.21/1.40 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.21/1.40 # Preprocessing time : 0.014 s
% 0.21/1.40
% 0.21/1.40 # Proof found!
% 0.21/1.40 # SZS status Theorem
% 0.21/1.40 # SZS output start CNFRefutation
% See solution above
% 0.21/1.40 # Proof object total steps : 30
% 0.21/1.40 # Proof object clause steps : 23
% 0.21/1.40 # Proof object formula steps : 7
% 0.21/1.40 # Proof object conjectures : 19
% 0.21/1.40 # Proof object clause conjectures : 16
% 0.21/1.40 # Proof object formula conjectures : 3
% 0.21/1.40 # Proof object initial clauses used : 8
% 0.21/1.40 # Proof object initial formulas used : 3
% 0.21/1.40 # Proof object generating inferences : 14
% 0.21/1.40 # Proof object simplifying inferences : 7
% 0.21/1.40 # Training examples: 0 positive, 0 negative
% 0.21/1.40 # Parsed axioms : 3
% 0.21/1.40 # Removed by relevancy pruning/SinE : 0
% 0.21/1.40 # Initial clauses : 8
% 0.21/1.40 # Removed in clause preprocessing : 0
% 0.21/1.40 # Initial clauses in saturation : 8
% 0.21/1.40 # Processed clauses : 58
% 0.21/1.40 # ...of these trivial : 3
% 0.21/1.40 # ...subsumed : 4
% 0.21/1.40 # ...remaining for further processing : 51
% 0.21/1.40 # Other redundant clauses eliminated : 0
% 0.21/1.40 # Clauses deleted for lack of memory : 0
% 0.21/1.40 # Backward-subsumed : 1
% 0.21/1.40 # Backward-rewritten : 10
% 0.21/1.40 # Generated clauses : 908
% 0.21/1.40 # ...of the previous two non-trivial : 844
% 0.21/1.40 # Contextual simplify-reflections : 0
% 0.21/1.40 # Paramodulations : 905
% 0.21/1.40 # Factorizations : 0
% 0.21/1.40 # Equation resolutions : 3
% 0.21/1.40 # Current number of processed clauses : 40
% 0.21/1.40 # Positive orientable unit clauses : 21
% 0.21/1.40 # Positive unorientable unit clauses: 5
% 0.21/1.40 # Negative unit clauses : 3
% 0.21/1.40 # Non-unit-clauses : 11
% 0.21/1.40 # Current number of unprocessed clauses: 506
% 0.21/1.40 # ...number of literals in the above : 665
% 0.21/1.40 # Current number of archived formulas : 0
% 0.21/1.40 # Current number of archived clauses : 11
% 0.21/1.40 # Clause-clause subsumption calls (NU) : 23
% 0.21/1.40 # Rec. Clause-clause subsumption calls : 19
% 0.21/1.40 # Non-unit clause-clause subsumptions : 2
% 0.21/1.40 # Unit Clause-clause subsumption calls : 15
% 0.21/1.40 # Rewrite failures with RHS unbound : 0
% 0.21/1.40 # BW rewrite match attempts : 33
% 0.21/1.40 # BW rewrite match successes : 32
% 0.21/1.40 # Condensation attempts : 0
% 0.21/1.40 # Condensation successes : 0
% 0.21/1.40 # Termbank termtop insertions : 11451
% 0.21/1.40
% 0.21/1.40 # -------------------------------------------------
% 0.21/1.40 # User time : 0.029 s
% 0.21/1.40 # System time : 0.002 s
% 0.21/1.40 # Total time : 0.031 s
% 0.21/1.40 # Maximum resident set size: 3288 pages
%------------------------------------------------------------------------------