TSTP Solution File: KLE144+2 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : KLE144+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n024.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 0.24s 1.41s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 54 ( 39 unt; 0 def)
% Number of atoms : 71 ( 42 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 34 ( 17 ~; 12 |; 3 &)
% ( 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 86 ( 8 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
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(idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',idempotence) ).
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(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
fof(goals,conjecture,
! [X4] :
( leq(strong_iteration(star(X4)),strong_iteration(one))
& leq(strong_iteration(one),strong_iteration(star(X4))) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',goals) ).
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(star_unfold2,axiom,
! [X1] : addition(one,multiplication(star(X1),X1)) = star(X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_unfold2) ).
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(c_0_11,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_12,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
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)],[idempotence]) ).
cnf(c_0_15,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(multiplication(X2,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
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]) ).
cnf(c_0_20,plain,
( leq(X1,multiplication(strong_iteration(one),X2))
| ~ leq(X1,addition(X1,X2)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_22,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_23,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( leq(X1,multiplication(strong_iteration(one),X2))
| ~ leq(X1,addition(X2,X1)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
fof(c_0_27,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_28,negated_conjecture,
~ ! [X4] :
( leq(strong_iteration(star(X4)),strong_iteration(one))
& leq(strong_iteration(one),strong_iteration(star(X4))) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_29,plain,
leq(X1,multiplication(strong_iteration(one),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_30,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_31,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_32,plain,
! [X2] : addition(one,multiplication(star(X2),X2)) = star(X2),
inference(variable_rename,[status(thm)],[star_unfold2]) ).
fof(c_0_33,negated_conjecture,
( ~ leq(strong_iteration(star(esk1_0)),strong_iteration(one))
| ~ leq(strong_iteration(one),strong_iteration(star(esk2_0))) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])]) ).
cnf(c_0_34,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_35,plain,
leq(X1,strong_iteration(one)),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_38,plain,
! [X2] : strong_iteration(X2) = addition(multiplication(X2,strong_iteration(X2)),one),
inference(variable_rename,[status(thm)],[infty_unfold1]) ).
cnf(c_0_39,negated_conjecture,
( ~ leq(strong_iteration(one),strong_iteration(star(esk2_0)))
| ~ leq(strong_iteration(star(esk1_0)),strong_iteration(one)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,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_15,c_0_25]) ).
cnf(c_0_41,plain,
addition(X1,strong_iteration(one)) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(spm,[status(thm)],[c_0_36,c_0_16]) ).
cnf(c_0_43,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_23,c_0_37]) ).
cnf(c_0_44,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_45,negated_conjecture,
~ leq(strong_iteration(one),strong_iteration(star(esk2_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_35])]) ).
cnf(c_0_46,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_40,c_0_30]),c_0_21]),c_0_21]) ).
cnf(c_0_47,plain,
addition(strong_iteration(one),X1) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_21,c_0_41]) ).
cnf(c_0_48,plain,
addition(X1,multiplication(star(X2),X1)) = multiplication(star(X2),X1),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_44,c_0_21]) ).
cnf(c_0_50,negated_conjecture,
addition(one,multiplication(star(esk2_0),strong_iteration(one))) != strong_iteration(one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_51,plain,
multiplication(star(X1),strong_iteration(one)) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_48,c_0_47]) ).
cnf(c_0_52,plain,
addition(one,strong_iteration(X1)) = strong_iteration(X1),
inference(spm,[status(thm)],[c_0_23,c_0_49]) ).
cnf(c_0_53,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51]),c_0_52])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE144+2 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : run_ET %s %d
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 16 08:21:03 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.24/1.41 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.41 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.41 # Preprocessing time : 0.015 s
% 0.24/1.41
% 0.24/1.41 # Proof found!
% 0.24/1.41 # SZS status Theorem
% 0.24/1.41 # SZS output start CNFRefutation
% See solution above
% 0.24/1.41 # Proof object total steps : 54
% 0.24/1.41 # Proof object clause steps : 31
% 0.24/1.41 # Proof object formula steps : 23
% 0.24/1.41 # Proof object conjectures : 7
% 0.24/1.41 # Proof object clause conjectures : 4
% 0.24/1.41 # Proof object formula conjectures : 3
% 0.24/1.41 # Proof object initial clauses used : 12
% 0.24/1.41 # Proof object initial formulas used : 11
% 0.24/1.41 # Proof object generating inferences : 16
% 0.24/1.41 # Proof object simplifying inferences : 11
% 0.24/1.41 # Training examples: 0 positive, 0 negative
% 0.24/1.41 # Parsed axioms : 19
% 0.24/1.41 # Removed by relevancy pruning/SinE : 0
% 0.24/1.41 # Initial clauses : 20
% 0.24/1.41 # Removed in clause preprocessing : 0
% 0.24/1.41 # Initial clauses in saturation : 20
% 0.24/1.41 # Processed clauses : 988
% 0.24/1.41 # ...of these trivial : 113
% 0.24/1.41 # ...subsumed : 498
% 0.24/1.41 # ...remaining for further processing : 377
% 0.24/1.41 # Other redundant clauses eliminated : 0
% 0.24/1.41 # Clauses deleted for lack of memory : 0
% 0.24/1.41 # Backward-subsumed : 27
% 0.24/1.41 # Backward-rewritten : 117
% 0.24/1.41 # Generated clauses : 12324
% 0.24/1.41 # ...of the previous two non-trivial : 10434
% 0.24/1.41 # Contextual simplify-reflections : 136
% 0.24/1.41 # Paramodulations : 12323
% 0.24/1.41 # Factorizations : 0
% 0.24/1.41 # Equation resolutions : 1
% 0.24/1.41 # Current number of processed clauses : 233
% 0.24/1.41 # Positive orientable unit clauses : 74
% 0.24/1.41 # Positive unorientable unit clauses: 16
% 0.24/1.41 # Negative unit clauses : 4
% 0.24/1.41 # Non-unit-clauses : 139
% 0.24/1.41 # Current number of unprocessed clauses: 8437
% 0.24/1.41 # ...number of literals in the above : 13981
% 0.24/1.41 # Current number of archived formulas : 0
% 0.24/1.41 # Current number of archived clauses : 144
% 0.24/1.41 # Clause-clause subsumption calls (NU) : 5319
% 0.24/1.41 # Rec. Clause-clause subsumption calls : 5293
% 0.24/1.41 # Non-unit clause-clause subsumptions : 617
% 0.24/1.41 # Unit Clause-clause subsumption calls : 214
% 0.24/1.41 # Rewrite failures with RHS unbound : 0
% 0.24/1.41 # BW rewrite match attempts : 199
% 0.24/1.41 # BW rewrite match successes : 95
% 0.24/1.41 # Condensation attempts : 0
% 0.24/1.41 # Condensation successes : 0
% 0.24/1.41 # Termbank termtop insertions : 176693
% 0.24/1.41
% 0.24/1.41 # -------------------------------------------------
% 0.24/1.41 # User time : 0.199 s
% 0.24/1.41 # System time : 0.007 s
% 0.24/1.41 # Total time : 0.206 s
% 0.24/1.41 # Maximum resident set size: 13108 pages
%------------------------------------------------------------------------------