TSTP Solution File: KLE140+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : KLE140+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n015.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 01:56:10 EDT 2022
% Result : Theorem 0.24s 1.42s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 41 ( 29 unt; 0 def)
% Number of atoms : 55 ( 33 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 25 ( 11 ~; 8 |; 2 &)
% ( 1 <=>; 3 =>; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 69 ( 2 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5] :
( leq(X4,X5)
=> leq(strong_iteration(X4),strong_iteration(X5)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',goals) ).
fof(infty_unfold1,axiom,
! [X1] : strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',order) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE004+0.ax',distributivity2) ).
fof(infty_coinduction,axiom,
! [X1,X2,X3] :
( leq(X3,addition(multiplication(X1,X3),X2))
=> leq(X3,multiplication(strong_iteration(X1),X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
fof(idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(c_0_9,negated_conjecture,
~ ! [X4,X5] :
( leq(X4,X5)
=> leq(strong_iteration(X4),strong_iteration(X5)) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_10,plain,
! [X2] : strong_iteration(X2) = addition(multiplication(X2,strong_iteration(X2)),one),
inference(variable_rename,[status(thm)],[infty_unfold1]) ).
fof(c_0_11,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_12,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_13,negated_conjecture,
( leq(esk1_0,esk2_0)
& ~ leq(strong_iteration(esk1_0),strong_iteration(esk2_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_14,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
cnf(c_0_15,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,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_18,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
leq(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
addition(esk1_0,esk2_0) = esk2_0,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_24,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])]) ).
cnf(c_0_25,plain,
addition(one,addition(multiplication(X1,strong_iteration(X1)),X2)) = addition(strong_iteration(X1),X2),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
addition(multiplication(esk1_0,X1),multiplication(esk2_0,X1)) = multiplication(esk2_0,X1),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(multiplication(X2,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_29,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_30,negated_conjecture,
addition(strong_iteration(esk1_0),multiplication(esk2_0,strong_iteration(esk1_0))) = addition(one,multiplication(esk2_0,strong_iteration(esk1_0))),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
fof(c_0_31,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[idempotence]) ).
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_27,c_0_28]) ).
cnf(c_0_33,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_34,negated_conjecture,
addition(strong_iteration(esk1_0),addition(multiplication(esk2_0,strong_iteration(esk1_0)),X1)) = addition(one,addition(multiplication(esk2_0,strong_iteration(esk1_0)),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_30]),c_0_20]) ).
cnf(c_0_35,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,negated_conjecture,
~ leq(strong_iteration(esk1_0),strong_iteration(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_37,plain,
( leq(X1,strong_iteration(X2))
| addition(X1,addition(one,multiplication(X2,X1))) != addition(one,multiplication(X2,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_16]),c_0_16]) ).
cnf(c_0_38,negated_conjecture,
addition(strong_iteration(esk1_0),addition(X1,multiplication(esk2_0,strong_iteration(esk1_0)))) = addition(one,addition(X1,multiplication(esk2_0,strong_iteration(esk1_0)))),
inference(spm,[status(thm)],[c_0_34,c_0_16]) ).
cnf(c_0_39,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_35]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_39])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE140+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 13:36:26 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.24/1.42 # Running protocol protocol_eprover_29fa5c60d0ee03ec4f64b055553dc135fbe4ee3a for 23 seconds:
% 0.24/1.42 # Preprocessing time : 0.014 s
% 0.24/1.42
% 0.24/1.42 # Proof found!
% 0.24/1.42 # SZS status Theorem
% 0.24/1.42 # SZS output start CNFRefutation
% See solution above
% 0.24/1.42 # Proof object total steps : 41
% 0.24/1.42 # Proof object clause steps : 22
% 0.24/1.42 # Proof object formula steps : 19
% 0.24/1.42 # Proof object conjectures : 11
% 0.24/1.42 # Proof object clause conjectures : 8
% 0.24/1.42 # Proof object formula conjectures : 3
% 0.24/1.42 # Proof object initial clauses used : 11
% 0.24/1.42 # Proof object initial formulas used : 9
% 0.24/1.42 # Proof object generating inferences : 10
% 0.24/1.42 # Proof object simplifying inferences : 7
% 0.24/1.42 # Training examples: 0 positive, 0 negative
% 0.24/1.42 # Parsed axioms : 19
% 0.24/1.42 # Removed by relevancy pruning/SinE : 0
% 0.24/1.42 # Initial clauses : 21
% 0.24/1.42 # Removed in clause preprocessing : 0
% 0.24/1.42 # Initial clauses in saturation : 21
% 0.24/1.42 # Processed clauses : 657
% 0.24/1.42 # ...of these trivial : 103
% 0.24/1.42 # ...subsumed : 153
% 0.24/1.42 # ...remaining for further processing : 401
% 0.24/1.42 # Other redundant clauses eliminated : 0
% 0.24/1.42 # Clauses deleted for lack of memory : 0
% 0.24/1.42 # Backward-subsumed : 17
% 0.24/1.42 # Backward-rewritten : 109
% 0.24/1.42 # Generated clauses : 7116
% 0.24/1.42 # ...of the previous two non-trivial : 5250
% 0.24/1.42 # Contextual simplify-reflections : 7
% 0.24/1.42 # Paramodulations : 7116
% 0.24/1.42 # Factorizations : 0
% 0.24/1.42 # Equation resolutions : 0
% 0.24/1.42 # Current number of processed clauses : 275
% 0.24/1.42 # Positive orientable unit clauses : 120
% 0.24/1.42 # Positive unorientable unit clauses: 3
% 0.24/1.42 # Negative unit clauses : 4
% 0.24/1.42 # Non-unit-clauses : 148
% 0.24/1.42 # Current number of unprocessed clauses: 3728
% 0.24/1.42 # ...number of literals in the above : 6138
% 0.24/1.42 # Current number of archived formulas : 0
% 0.24/1.42 # Current number of archived clauses : 126
% 0.24/1.42 # Clause-clause subsumption calls (NU) : 2076
% 0.24/1.42 # Rec. Clause-clause subsumption calls : 2025
% 0.24/1.42 # Non-unit clause-clause subsumptions : 139
% 0.24/1.42 # Unit Clause-clause subsumption calls : 238
% 0.24/1.42 # Rewrite failures with RHS unbound : 0
% 0.24/1.42 # BW rewrite match attempts : 268
% 0.24/1.42 # BW rewrite match successes : 117
% 0.24/1.42 # Condensation attempts : 0
% 0.24/1.42 # Condensation successes : 0
% 0.24/1.42 # Termbank termtop insertions : 105847
% 0.24/1.42
% 0.24/1.42 # -------------------------------------------------
% 0.24/1.42 # User time : 0.123 s
% 0.24/1.42 # System time : 0.006 s
% 0.24/1.42 # Total time : 0.129 s
% 0.24/1.42 # Maximum resident set size: 8892 pages
% 0.24/23.42 eprover: CPU time limit exceeded, terminating
% 0.24/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.43 eprover: No such file or directory
% 0.24/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.43 eprover: No such file or directory
% 0.24/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.44 eprover: No such file or directory
% 0.24/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.44 eprover: No such file or directory
% 0.24/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.44 eprover: No such file or directory
% 0.24/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.45 eprover: No such file or directory
% 0.24/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.45 eprover: No such file or directory
% 0.24/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.45 eprover: No such file or directory
% 0.24/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.46 eprover: No such file or directory
% 0.24/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.46 eprover: No such file or directory
% 0.24/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.24/23.46 eprover: No such file or directory
%------------------------------------------------------------------------------