TSTP Solution File: KLE158+1 by ET---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : KLE158+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n032.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 01:56:19 EDT 2022
% Result : Theorem 0.21s 1.38s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 48 ( 37 unt; 0 def)
% Number of atoms : 61 ( 40 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 25 ( 12 ~; 7 |; 2 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 91 ( 2 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(infty_unfold1,axiom,
! [X1] : strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
fof(goals,conjecture,
! [X4,X5,X6] :
( leq(multiplication(X4,X5),multiplication(X6,X4))
=> leq(multiplication(X4,strong_iteration(X5)),multiplication(strong_iteration(X6),X4)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',goals) ).
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(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
fof(distributivity1,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',distributivity1) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
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(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(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_associativity) ).
fof(idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(c_0_11,plain,
! [X2] : strong_iteration(X2) = addition(multiplication(X2,strong_iteration(X2)),one),
inference(variable_rename,[status(thm)],[infty_unfold1]) ).
fof(c_0_12,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_13,negated_conjecture,
~ ! [X4,X5,X6] :
( leq(multiplication(X4,X5),multiplication(X6,X4))
=> leq(multiplication(X4,strong_iteration(X5)),multiplication(strong_iteration(X6),X4)) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_14,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_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,
! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
inference(variable_rename,[status(thm)],[distributivity1]) ).
cnf(c_0_17,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_19,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_20,negated_conjecture,
( leq(multiplication(esk1_0,esk2_0),multiplication(esk3_0,esk1_0))
& ~ leq(multiplication(esk1_0,strong_iteration(esk2_0)),multiplication(strong_iteration(esk3_0),esk1_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
cnf(c_0_21,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(multiplication(X2,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_23,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
cnf(c_0_24,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_27,plain,
! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
inference(variable_rename,[status(thm)],[distributivity2]) ).
cnf(c_0_28,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_29,negated_conjecture,
leq(multiplication(esk1_0,esk2_0),multiplication(esk3_0,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_30,plain,
! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_31,negated_conjecture,
~ leq(multiplication(esk1_0,strong_iteration(esk2_0)),multiplication(strong_iteration(esk3_0),esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_32,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| addition(X1,addition(multiplication(X2,X1),X3)) != addition(multiplication(X2,X1),X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_33,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_34,plain,
addition(X1,multiplication(X1,multiplication(X2,strong_iteration(X2)))) = multiplication(X1,strong_iteration(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_35,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_36,negated_conjecture,
addition(multiplication(esk1_0,esk2_0),multiplication(esk3_0,esk1_0)) = multiplication(esk3_0,esk1_0),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_37,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_38,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[idempotence]) ).
cnf(c_0_39,negated_conjecture,
addition(multiplication(esk1_0,strong_iteration(esk2_0)),addition(esk1_0,multiplication(esk3_0,multiplication(esk1_0,strong_iteration(esk2_0))))) != addition(esk1_0,multiplication(esk3_0,multiplication(esk1_0,strong_iteration(esk2_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_18]),c_0_18]) ).
cnf(c_0_40,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_18]),c_0_33]) ).
cnf(c_0_41,plain,
addition(X1,addition(multiplication(X1,multiplication(X2,strong_iteration(X2))),X3)) = addition(multiplication(X1,strong_iteration(X2)),X3),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_42,negated_conjecture,
addition(multiplication(esk1_0,multiplication(esk2_0,X1)),multiplication(esk3_0,multiplication(esk1_0,X1))) = multiplication(esk3_0,multiplication(esk1_0,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_37]),c_0_37]) ).
cnf(c_0_43,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_44,negated_conjecture,
addition(esk1_0,addition(multiplication(esk1_0,strong_iteration(esk2_0)),multiplication(esk3_0,multiplication(esk1_0,strong_iteration(esk2_0))))) != addition(esk1_0,multiplication(esk3_0,multiplication(esk1_0,strong_iteration(esk2_0)))),
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,negated_conjecture,
addition(multiplication(esk1_0,strong_iteration(esk2_0)),multiplication(esk3_0,multiplication(esk1_0,strong_iteration(esk2_0)))) = addition(esk1_0,multiplication(esk3_0,multiplication(esk1_0,strong_iteration(esk2_0)))),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_33,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45]),c_0_46])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE158+1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.12 % Command : run_ET %s %d
% 0.12/0.32 % Computer : n032.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Thu Jun 16 13:46:00 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.21/1.38 # Running protocol protocol_eprover_29fa5c60d0ee03ec4f64b055553dc135fbe4ee3a for 23 seconds:
% 0.21/1.38 # Preprocessing time : 0.008 s
% 0.21/1.38
% 0.21/1.38 # Proof found!
% 0.21/1.38 # SZS status Theorem
% 0.21/1.38 # SZS output start CNFRefutation
% See solution above
% 0.21/1.38 # Proof object total steps : 48
% 0.21/1.38 # Proof object clause steps : 25
% 0.21/1.38 # Proof object formula steps : 23
% 0.21/1.38 # Proof object conjectures : 11
% 0.21/1.38 # Proof object clause conjectures : 8
% 0.21/1.38 # Proof object formula conjectures : 3
% 0.21/1.38 # Proof object initial clauses used : 13
% 0.21/1.38 # Proof object initial formulas used : 11
% 0.21/1.38 # Proof object generating inferences : 9
% 0.21/1.38 # Proof object simplifying inferences : 12
% 0.21/1.38 # Training examples: 0 positive, 0 negative
% 0.21/1.38 # Parsed axioms : 19
% 0.21/1.38 # Removed by relevancy pruning/SinE : 0
% 0.21/1.38 # Initial clauses : 21
% 0.21/1.38 # Removed in clause preprocessing : 0
% 0.21/1.38 # Initial clauses in saturation : 21
% 0.21/1.38 # Processed clauses : 2017
% 0.21/1.38 # ...of these trivial : 142
% 0.21/1.38 # ...subsumed : 940
% 0.21/1.38 # ...remaining for further processing : 935
% 0.21/1.38 # Other redundant clauses eliminated : 0
% 0.21/1.38 # Clauses deleted for lack of memory : 0
% 0.21/1.38 # Backward-subsumed : 57
% 0.21/1.38 # Backward-rewritten : 83
% 0.21/1.38 # Generated clauses : 30849
% 0.21/1.38 # ...of the previous two non-trivial : 27406
% 0.21/1.38 # Contextual simplify-reflections : 243
% 0.21/1.38 # Paramodulations : 30849
% 0.21/1.38 # Factorizations : 0
% 0.21/1.38 # Equation resolutions : 0
% 0.21/1.38 # Current number of processed clauses : 795
% 0.21/1.38 # Positive orientable unit clauses : 120
% 0.21/1.38 # Positive unorientable unit clauses: 9
% 0.21/1.38 # Negative unit clauses : 4
% 0.21/1.38 # Non-unit-clauses : 662
% 0.21/1.38 # Current number of unprocessed clauses: 20683
% 0.21/1.38 # ...number of literals in the above : 45621
% 0.21/1.38 # Current number of archived formulas : 0
% 0.21/1.38 # Current number of archived clauses : 140
% 0.21/1.38 # Clause-clause subsumption calls (NU) : 30444
% 0.21/1.38 # Rec. Clause-clause subsumption calls : 27550
% 0.21/1.38 # Non-unit clause-clause subsumptions : 941
% 0.21/1.38 # Unit Clause-clause subsumption calls : 962
% 0.21/1.38 # Rewrite failures with RHS unbound : 0
% 0.21/1.38 # BW rewrite match attempts : 1557
% 0.21/1.38 # BW rewrite match successes : 397
% 0.21/1.38 # Condensation attempts : 0
% 0.21/1.38 # Condensation successes : 0
% 0.21/1.38 # Termbank termtop insertions : 584980
% 0.21/1.38
% 0.21/1.38 # -------------------------------------------------
% 0.21/1.38 # User time : 0.395 s
% 0.21/1.38 # System time : 0.015 s
% 0.21/1.38 # Total time : 0.410 s
% 0.21/1.38 # Maximum resident set size: 31856 pages
% 0.21/2.60 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
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% 0.21/23.37 eprover: CPU time limit exceeded, terminating
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% 0.21/23.39 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
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% 0.21/23.41 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
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% 0.21/23.41 eprover: No such file or directory
% 0.21/23.41 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
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% 0.21/23.42 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.21/23.42 eprover: No such file or directory
% 0.21/23.42 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
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% 0.21/23.42 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.21/23.42 eprover: No such file or directory
% 0.21/23.42 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
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% 0.21/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.21/23.43 eprover: No such file or directory
% 0.21/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.21/23.43 eprover: No such file or directory
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% 0.21/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
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% 0.21/23.44 eprover: No such file or directory
% 0.21/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.21/23.44 eprover: No such file or directory
% 0.21/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.21/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.21/23.44 eprover: No such file or directory
% 0.21/23.44 eprover: No such file or directory
% 0.21/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.21/23.45 eprover: No such file or directory
%------------------------------------------------------------------------------