TSTP Solution File: KLE039+1 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : KLE039+1 : TPTP v8.1.0. Released v4.0.0.
% 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 : Sun Jul 17 01:55:32 EDT 2022
% Result : Theorem 0.29s 1.46s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 59 ( 50 unt; 0 def)
% Number of atoms : 70 ( 46 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 22 ( 11 ~; 8 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 102 ( 2 sgn 52 !; 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/KLE002+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_idempotence) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',order) ).
fof(star_unfold_right,axiom,
! [X1] : leq(addition(one,multiplication(X1,star(X1))),star(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_unfold_right) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_commutativity) ).
fof(star_unfold_left,axiom,
! [X1] : leq(addition(one,multiplication(star(X1),X1)),star(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_unfold_left) ).
fof(star_induction_right,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X1,X2),X3),X1)
=> leq(multiplication(X3,star(X2)),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_induction_right) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_left_identity) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',left_distributivity) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_associativity) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',right_distributivity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_right_identity) ).
fof(goals,conjecture,
! [X4] : star(star(X4)) = star(X4),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',goals) ).
fof(c_0_13,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_14,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_15,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])])])]) ).
fof(c_0_16,plain,
! [X2] : leq(addition(one,multiplication(X2,star(X2))),star(X2)),
inference(variable_rename,[status(thm)],[star_unfold_right]) ).
fof(c_0_17,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_18,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_20,plain,
! [X2] : leq(addition(one,multiplication(star(X2),X2)),star(X2)),
inference(variable_rename,[status(thm)],[star_unfold_left]) ).
fof(c_0_21,plain,
! [X4,X5,X6] :
( ~ leq(addition(multiplication(X4,X5),X6),X4)
| leq(multiplication(X6,star(X5)),X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction_right])]) ).
cnf(c_0_22,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
leq(addition(one,multiplication(X1,star(X1))),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,plain,
leq(addition(one,multiplication(star(X1),X1)),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( leq(multiplication(X1,star(X2)),X3)
| ~ leq(addition(multiplication(X3,X2),X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_28,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_29,plain,
! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_30,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_18]),c_0_24]) ).
fof(c_0_31,plain,
! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_32,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_33,plain,
addition(one,addition(star(X1),multiplication(star(X1),X1))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_26]),c_0_18]),c_0_24]) ).
cnf(c_0_34,plain,
( leq(multiplication(X1,star(X2)),X3)
| ~ leq(addition(X1,multiplication(X3,X2)),X3) ),
inference(spm,[status(thm)],[c_0_27,c_0_24]) ).
cnf(c_0_35,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_36,plain,
! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_37,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_38,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_25,c_0_30]) ).
cnf(c_0_40,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_41,plain,
addition(star(X1),multiplication(star(X1),X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_18]),c_0_24]),c_0_25]) ).
cnf(c_0_42,plain,
leq(star(X1),star(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_26]),c_0_35]) ).
cnf(c_0_43,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,plain,
addition(star(X1),multiplication(X1,star(X1))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_30]),c_0_18]),c_0_24]),c_0_25]) ).
cnf(c_0_46,plain,
addition(X1,multiplication(star(X2),X1)) = multiplication(star(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_35]) ).
fof(c_0_47,negated_conjecture,
~ ! [X4] : star(star(X4)) = star(X4),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_48,plain,
( leq(multiplication(X1,multiplication(X2,star(X2))),X1)
| ~ leq(multiplication(X1,X2),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_19]),c_0_40]) ).
cnf(c_0_49,plain,
leq(multiplication(star(X1),star(X1)),star(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_41]),c_0_42])]) ).
cnf(c_0_50,plain,
addition(X1,multiplication(X1,star(X2))) = multiplication(X1,star(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_39]),c_0_44]) ).
cnf(c_0_51,plain,
multiplication(star(X1),star(star(X1))) = star(star(X1)),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
fof(c_0_52,negated_conjecture,
star(star(esk1_0)) != star(esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])]) ).
cnf(c_0_53,plain,
( addition(X1,multiplication(X1,multiplication(X2,star(X2)))) = X1
| ~ leq(multiplication(X1,X2),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_48]),c_0_24]) ).
cnf(c_0_54,plain,
multiplication(star(X1),star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_49]),c_0_24]),c_0_46]) ).
cnf(c_0_55,plain,
addition(star(X1),star(star(X1))) = star(star(X1)),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_56,negated_conjecture,
star(star(esk1_0)) != star(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_57,plain,
star(star(X1)) = star(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_51]),c_0_51]),c_0_55]),c_0_42])]) ).
cnf(c_0_58,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : KLE039+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.15 % Command : run_ET %s %d
% 0.15/0.37 % Computer : n025.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Thu Jun 16 12:52:56 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.29/1.46 # Running protocol protocol_eprover_29fa5c60d0ee03ec4f64b055553dc135fbe4ee3a for 23 seconds:
% 0.29/1.46 # Preprocessing time : 0.014 s
% 0.29/1.46
% 0.29/1.46 # Proof found!
% 0.29/1.46 # SZS status Theorem
% 0.29/1.46 # SZS output start CNFRefutation
% See solution above
% 0.29/1.46 # Proof object total steps : 59
% 0.29/1.46 # Proof object clause steps : 32
% 0.29/1.46 # Proof object formula steps : 27
% 0.29/1.46 # Proof object conjectures : 5
% 0.29/1.46 # Proof object clause conjectures : 2
% 0.29/1.46 # Proof object formula conjectures : 3
% 0.29/1.46 # Proof object initial clauses used : 13
% 0.29/1.46 # Proof object initial formulas used : 13
% 0.29/1.46 # Proof object generating inferences : 18
% 0.29/1.46 # Proof object simplifying inferences : 26
% 0.29/1.46 # Training examples: 0 positive, 0 negative
% 0.29/1.46 # Parsed axioms : 17
% 0.29/1.46 # Removed by relevancy pruning/SinE : 0
% 0.29/1.46 # Initial clauses : 18
% 0.29/1.46 # Removed in clause preprocessing : 0
% 0.29/1.46 # Initial clauses in saturation : 18
% 0.29/1.46 # Processed clauses : 587
% 0.29/1.46 # ...of these trivial : 42
% 0.29/1.46 # ...subsumed : 321
% 0.29/1.46 # ...remaining for further processing : 224
% 0.29/1.46 # Other redundant clauses eliminated : 0
% 0.29/1.46 # Clauses deleted for lack of memory : 0
% 0.29/1.46 # Backward-subsumed : 0
% 0.29/1.46 # Backward-rewritten : 84
% 0.29/1.46 # Generated clauses : 8977
% 0.29/1.46 # ...of the previous two non-trivial : 6714
% 0.29/1.46 # Contextual simplify-reflections : 2
% 0.29/1.46 # Paramodulations : 8970
% 0.29/1.46 # Factorizations : 0
% 0.29/1.46 # Equation resolutions : 0
% 0.29/1.46 # Current number of processed clauses : 137
% 0.29/1.46 # Positive orientable unit clauses : 54
% 0.29/1.46 # Positive unorientable unit clauses: 4
% 0.29/1.46 # Negative unit clauses : 9
% 0.29/1.46 # Non-unit-clauses : 70
% 0.29/1.46 # Current number of unprocessed clauses: 2385
% 0.29/1.46 # ...number of literals in the above : 4109
% 0.29/1.46 # Current number of archived formulas : 0
% 0.29/1.46 # Current number of archived clauses : 85
% 0.29/1.46 # Clause-clause subsumption calls (NU) : 768
% 0.29/1.46 # Rec. Clause-clause subsumption calls : 754
% 0.29/1.46 # Non-unit clause-clause subsumptions : 15
% 0.29/1.46 # Unit Clause-clause subsumption calls : 108
% 0.29/1.46 # Rewrite failures with RHS unbound : 0
% 0.29/1.46 # BW rewrite match attempts : 485
% 0.29/1.46 # BW rewrite match successes : 59
% 0.29/1.46 # Condensation attempts : 0
% 0.29/1.46 # Condensation successes : 0
% 0.29/1.46 # Termbank termtop insertions : 177715
% 0.29/1.46
% 0.29/1.46 # -------------------------------------------------
% 0.29/1.46 # User time : 0.131 s
% 0.29/1.46 # System time : 0.006 s
% 0.29/1.46 # Total time : 0.138 s
% 0.29/1.46 # Maximum resident set size: 9416 pages
% 0.29/23.46 eprover: CPU time limit exceeded, terminating
% 0.29/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.47 eprover: No such file or directory
% 0.29/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.48 eprover: No such file or directory
% 0.29/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.48 eprover: No such file or directory
% 0.29/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.49 eprover: No such file or directory
% 0.29/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.50 eprover: No such file or directory
% 0.29/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.50 eprover: No such file or directory
% 0.29/23.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.51 eprover: No such file or directory
% 0.29/23.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.51 eprover: No such file or directory
% 0.29/23.52 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.52 eprover: No such file or directory
% 0.29/23.52 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.52 eprover: No such file or directory
% 0.29/23.53 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.53 eprover: No such file or directory
%------------------------------------------------------------------------------