TSTP Solution File: KLE144+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : KLE144+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n026.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 : Sun Jul 17 01:56:12 EDT 2022
% Result : Theorem 0.23s 1.40s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 49 ( 41 unt; 0 def)
% Number of atoms : 59 ( 40 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 20 ( 10 ~; 7 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 80 ( 15 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).
fof(idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(infty_coinduction,axiom,
! [X1,X2,X3] :
( leq(X3,addition(multiplication(X1,X3),X2))
=> leq(X3,multiplication(strong_iteration(X1),X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
fof(distributivity2,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',distributivity2) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
fof(star_unfold2,axiom,
! [X1] : addition(one,multiplication(star(X1),X1)) = star(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_unfold2) ).
fof(goals,conjecture,
! [X4] : strong_iteration(star(X4)) = strong_iteration(one),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',goals) ).
fof(c_0_10,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_11,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[idempotence]) ).
fof(c_0_12,plain,
! [X4,X5,X6] :
( ~ leq(X6,addition(multiplication(X4,X6),X5))
| leq(X6,multiplication(strong_iteration(X4),X5)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[infty_coinduction])]) ).
fof(c_0_13,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_14,plain,
! [X3,X4,X3,X4] :
( ( ~ leq(X3,X4)
| addition(X3,X4) = X4 )
& ( addition(X3,X4) != X4
| leq(X3,X4) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])])]) ).
cnf(c_0_15,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(multiplication(X2,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( leq(X1,multiplication(strong_iteration(one),X2))
| ~ leq(X1,addition(X1,X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
leq(X1,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_23,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_24,plain,
leq(X1,multiplication(strong_iteration(one),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]) ).
cnf(c_0_25,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_26,plain,
! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
inference(variable_rename,[status(thm)],[distributivity2]) ).
fof(c_0_27,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_28,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_29,plain,
leq(X1,strong_iteration(one)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_30,plain,
! [X2] : addition(one,multiplication(star(X2),X2)) = star(X2),
inference(variable_rename,[status(thm)],[star_unfold2]) ).
cnf(c_0_31,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
addition(X1,strong_iteration(one)) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_18]),c_0_32]) ).
cnf(c_0_36,plain,
addition(strong_iteration(one),X1) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_20,c_0_34]) ).
cnf(c_0_38,plain,
multiplication(addition(X1,one),strong_iteration(one)) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,plain,
addition(star(X1),one) = star(X1),
inference(spm,[status(thm)],[c_0_32,c_0_37]) ).
cnf(c_0_40,plain,
multiplication(star(X1),strong_iteration(one)) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_41,plain,
leq(X1,X1),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
fof(c_0_42,negated_conjecture,
~ ! [X4] : strong_iteration(star(X4)) = strong_iteration(one),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_43,plain,
leq(strong_iteration(one),multiplication(strong_iteration(star(X1)),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_40]),c_0_36]),c_0_41])]) ).
fof(c_0_44,negated_conjecture,
strong_iteration(star(esk1_0)) != strong_iteration(one),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])]) ).
cnf(c_0_45,plain,
strong_iteration(one) = multiplication(strong_iteration(star(X1)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_43]),c_0_36]) ).
cnf(c_0_46,negated_conjecture,
strong_iteration(star(esk1_0)) != strong_iteration(one),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_47,plain,
strong_iteration(one) = strong_iteration(star(X1)),
inference(spm,[status(thm)],[c_0_25,c_0_45]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KLE144+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n026.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 : Thu Jun 16 16:47:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.23/1.40 # Running protocol protocol_eprover_2d86bd69119e7e9cc4417c0ee581499eaf828bb2 for 23 seconds:
% 0.23/1.40 # SinE strategy is GSinE(CountFormulas,,1.1,,02,500,1.0)
% 0.23/1.40 # Preprocessing time : 0.014 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 : 49
% 0.23/1.40 # Proof object clause steps : 28
% 0.23/1.40 # Proof object formula steps : 21
% 0.23/1.40 # Proof object conjectures : 5
% 0.23/1.40 # Proof object clause conjectures : 2
% 0.23/1.40 # Proof object formula conjectures : 3
% 0.23/1.40 # Proof object initial clauses used : 11
% 0.23/1.40 # Proof object initial formulas used : 10
% 0.23/1.40 # Proof object generating inferences : 15
% 0.23/1.40 # Proof object simplifying inferences : 9
% 0.23/1.40 # Training examples: 0 positive, 0 negative
% 0.23/1.40 # Parsed axioms : 19
% 0.23/1.40 # Removed by relevancy pruning/SinE : 3
% 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 : 1805
% 0.23/1.40 # ...of these trivial : 701
% 0.23/1.40 # ...subsumed : 342
% 0.23/1.40 # ...remaining for further processing : 762
% 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 : 5
% 0.23/1.40 # Backward-rewritten : 510
% 0.23/1.40 # Generated clauses : 50947
% 0.23/1.40 # ...of the previous two non-trivial : 38128
% 0.23/1.40 # Contextual simplify-reflections : 0
% 0.23/1.40 # Paramodulations : 50945
% 0.23/1.40 # Factorizations : 0
% 0.23/1.40 # Equation resolutions : 2
% 0.23/1.40 # Current number of processed clauses : 247
% 0.23/1.40 # Positive orientable unit clauses : 114
% 0.23/1.40 # Positive unorientable unit clauses: 41
% 0.23/1.40 # Negative unit clauses : 0
% 0.23/1.40 # Non-unit-clauses : 92
% 0.23/1.40 # Current number of unprocessed clauses: 17693
% 0.23/1.40 # ...number of literals in the above : 24368
% 0.23/1.40 # Current number of archived formulas : 0
% 0.23/1.40 # Current number of archived clauses : 515
% 0.23/1.40 # Clause-clause subsumption calls (NU) : 3683
% 0.23/1.40 # Rec. Clause-clause subsumption calls : 3683
% 0.23/1.40 # Non-unit clause-clause subsumptions : 163
% 0.23/1.40 # Unit Clause-clause subsumption calls : 1452
% 0.23/1.40 # Rewrite failures with RHS unbound : 53
% 0.23/1.40 # BW rewrite match attempts : 3053
% 0.23/1.40 # BW rewrite match successes : 397
% 0.23/1.40 # Condensation attempts : 0
% 0.23/1.40 # Condensation successes : 0
% 0.23/1.40 # Termbank termtop insertions : 1006364
% 0.23/1.40
% 0.23/1.40 # -------------------------------------------------
% 0.23/1.40 # User time : 0.535 s
% 0.23/1.40 # System time : 0.018 s
% 0.23/1.40 # Total time : 0.553 s
% 0.23/1.40 # Maximum resident set size: 31860 pages
%------------------------------------------------------------------------------