TSTP Solution File: KLE167+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : KLE167+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n008.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 01:56:22 EDT 2022
% Result : Theorem 0.25s 1.43s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 43 ( 29 unt; 0 def)
% Number of atoms : 63 ( 39 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 37 ( 17 ~; 12 |; 4 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 68 ( 2 sgn 40 !; 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(goals,conjecture,
! [X4,X5] :
( ( multiplication(X4,X5) = zero
=> leq(multiplication(X4,star(X5)),X4) )
& leq(X4,multiplication(X4,star(X5))) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',goals) ).
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(star_unfold2,axiom,
! [X1] : addition(one,multiplication(star(X1),X1)) = star(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_unfold2) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
fof(star_induction2,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X3,X1),X2),X3)
=> leq(multiplication(X2,star(X1)),X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_induction2) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
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,negated_conjecture,
~ ! [X4,X5] :
( ( multiplication(X4,X5) = zero
=> leq(multiplication(X4,star(X5)),X4) )
& leq(X4,multiplication(X4,star(X5))) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_13,plain,
! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
inference(variable_rename,[status(thm)],[distributivity1]) ).
fof(c_0_14,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
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]) ).
fof(c_0_17,plain,
! [X2] : addition(one,multiplication(star(X2),X2)) = star(X2),
inference(variable_rename,[status(thm)],[star_unfold2]) ).
fof(c_0_18,negated_conjecture,
( ( multiplication(esk1_0,esk2_0) = zero
| ~ leq(esk3_0,multiplication(esk3_0,star(esk4_0))) )
& ( ~ leq(multiplication(esk1_0,star(esk2_0)),esk1_0)
| ~ leq(esk3_0,multiplication(esk3_0,star(esk4_0))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])])]) ).
fof(c_0_19,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_20,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_23,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,negated_conjecture,
( ~ leq(esk3_0,multiplication(esk3_0,star(esk4_0)))
| ~ leq(multiplication(esk1_0,star(esk2_0)),esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_28,plain,
! [X4,X5,X6] :
( ~ leq(addition(multiplication(X6,X4),X5),X6)
| leq(multiplication(X5,star(X4)),X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction2])]) ).
cnf(c_0_29,negated_conjecture,
( multiplication(esk1_0,esk2_0) = zero
| ~ leq(esk3_0,multiplication(esk3_0,star(esk4_0))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_30,plain,
! [X2] : addition(X2,zero) = X2,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_31,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_32,negated_conjecture,
( addition(esk3_0,multiplication(esk3_0,star(esk4_0))) != multiplication(esk3_0,star(esk4_0))
| ~ leq(multiplication(esk1_0,star(esk2_0)),esk1_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_33,plain,
addition(X1,multiplication(X1,star(X2))) = multiplication(X1,star(X2)),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,plain,
( leq(multiplication(X1,star(X2)),X3)
| ~ leq(addition(multiplication(X3,X2),X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,negated_conjecture,
( multiplication(esk1_0,esk2_0) = zero
| addition(esk3_0,multiplication(esk3_0,star(esk4_0))) != multiplication(esk3_0,star(esk4_0)) ),
inference(spm,[status(thm)],[c_0_29,c_0_25]) ).
cnf(c_0_36,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,negated_conjecture,
~ leq(multiplication(esk1_0,star(esk2_0)),esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]) ).
cnf(c_0_39,plain,
( leq(multiplication(X1,star(X2)),X3)
| addition(multiplication(X3,X2),addition(X1,X3)) != X3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_25]),c_0_15]) ).
cnf(c_0_40,negated_conjecture,
multiplication(esk1_0,esk2_0) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_33])]) ).
cnf(c_0_41,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_16]),c_0_41])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KLE167+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14 % Command : run_ET %s %d
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jun 16 14:46:22 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.25/1.43 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.25/1.43 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.25/1.43 # Preprocessing time : 0.015 s
% 0.25/1.43
% 0.25/1.43 # Proof found!
% 0.25/1.43 # SZS status Theorem
% 0.25/1.43 # SZS output start CNFRefutation
% See solution above
% 0.25/1.43 # Proof object total steps : 43
% 0.25/1.43 # Proof object clause steps : 22
% 0.25/1.43 # Proof object formula steps : 21
% 0.25/1.43 # Proof object conjectures : 10
% 0.25/1.43 # Proof object clause conjectures : 7
% 0.25/1.43 # Proof object formula conjectures : 3
% 0.25/1.43 # Proof object initial clauses used : 11
% 0.25/1.43 # Proof object initial formulas used : 10
% 0.25/1.43 # Proof object generating inferences : 9
% 0.25/1.43 # Proof object simplifying inferences : 9
% 0.25/1.43 # Training examples: 0 positive, 0 negative
% 0.25/1.43 # Parsed axioms : 19
% 0.25/1.43 # Removed by relevancy pruning/SinE : 0
% 0.25/1.43 # Initial clauses : 21
% 0.25/1.43 # Removed in clause preprocessing : 0
% 0.25/1.43 # Initial clauses in saturation : 21
% 0.25/1.43 # Processed clauses : 174
% 0.25/1.43 # ...of these trivial : 9
% 0.25/1.43 # ...subsumed : 55
% 0.25/1.43 # ...remaining for further processing : 110
% 0.25/1.43 # Other redundant clauses eliminated : 0
% 0.25/1.43 # Clauses deleted for lack of memory : 0
% 0.25/1.43 # Backward-subsumed : 10
% 0.25/1.43 # Backward-rewritten : 16
% 0.25/1.43 # Generated clauses : 895
% 0.25/1.43 # ...of the previous two non-trivial : 629
% 0.25/1.43 # Contextual simplify-reflections : 12
% 0.25/1.43 # Paramodulations : 895
% 0.25/1.43 # Factorizations : 0
% 0.25/1.43 # Equation resolutions : 0
% 0.25/1.43 # Current number of processed clauses : 84
% 0.25/1.43 # Positive orientable unit clauses : 29
% 0.25/1.43 # Positive unorientable unit clauses: 4
% 0.25/1.43 # Negative unit clauses : 1
% 0.25/1.43 # Non-unit-clauses : 50
% 0.25/1.43 # Current number of unprocessed clauses: 464
% 0.25/1.43 # ...number of literals in the above : 915
% 0.25/1.43 # Current number of archived formulas : 0
% 0.25/1.43 # Current number of archived clauses : 26
% 0.25/1.43 # Clause-clause subsumption calls (NU) : 448
% 0.25/1.43 # Rec. Clause-clause subsumption calls : 433
% 0.25/1.43 # Non-unit clause-clause subsumptions : 73
% 0.25/1.43 # Unit Clause-clause subsumption calls : 41
% 0.25/1.43 # Rewrite failures with RHS unbound : 0
% 0.25/1.43 # BW rewrite match attempts : 71
% 0.25/1.43 # BW rewrite match successes : 24
% 0.25/1.43 # Condensation attempts : 0
% 0.25/1.43 # Condensation successes : 0
% 0.25/1.43 # Termbank termtop insertions : 11097
% 0.25/1.43
% 0.25/1.43 # -------------------------------------------------
% 0.25/1.43 # User time : 0.033 s
% 0.25/1.43 # System time : 0.002 s
% 0.25/1.43 # Total time : 0.035 s
% 0.25/1.43 # Maximum resident set size: 3612 pages
% 0.25/23.43 eprover: CPU time limit exceeded, terminating
% 0.25/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.45 eprover: No such file or directory
% 0.25/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.45 eprover: No such file or directory
% 0.25/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.46 eprover: No such file or directory
% 0.25/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.47 eprover: No such file or directory
% 0.25/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.47 eprover: No such file or directory
% 0.25/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.48 eprover: No such file or directory
% 0.25/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.48 eprover: No such file or directory
% 0.25/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.49 eprover: No such file or directory
% 0.25/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.50 eprover: No such file or directory
% 0.25/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.50 eprover: No such file or directory
% 0.25/23.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.51 eprover: No such file or directory
%------------------------------------------------------------------------------