TSTP Solution File: KLE141+1 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : KLE141+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n017.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 0.22s 1.41s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 55 ( 46 unt; 0 def)
% Number of atoms : 66 ( 47 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 : 4 ( 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 : 85 ( 10 sgn 46 !; 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/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/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/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(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
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(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
fof(goals,conjecture,
! [X4] : multiplication(strong_iteration(one),X4) = strong_iteration(one),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',goals) ).
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(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
fof(c_0_12,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_13,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
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]) ).
fof(c_0_15,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[idempotence]) ).
cnf(c_0_16,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(multiplication(X2,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,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_19,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( leq(X1,multiplication(strong_iteration(one),X2))
| ~ leq(X1,addition(X1,X2)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_24,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_25,plain,
leq(X1,multiplication(strong_iteration(one),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_26,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_27,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_28,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_29,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_30,plain,
leq(X1,strong_iteration(one)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,plain,
addition(X1,strong_iteration(one)) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
fof(c_0_34,plain,
! [X2] : addition(X2,zero) = X2,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_35,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_26]),c_0_32]) ).
cnf(c_0_36,plain,
addition(strong_iteration(one),X1) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_38,plain,
multiplication(strong_iteration(one),addition(X1,one)) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,plain,
( leq(X1,multiplication(strong_iteration(X2),zero))
| ~ leq(X1,multiplication(X2,X1)) ),
inference(spm,[status(thm)],[c_0_16,c_0_37]) ).
cnf(c_0_40,plain,
multiplication(strong_iteration(one),strong_iteration(one)) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_38,c_0_36]) ).
cnf(c_0_41,plain,
leq(strong_iteration(one),multiplication(strong_iteration(strong_iteration(one)),zero)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_30])]) ).
cnf(c_0_42,plain,
multiplication(strong_iteration(strong_iteration(one)),zero) = strong_iteration(one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_41]),c_0_36]) ).
cnf(c_0_43,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_37,c_0_32]) ).
fof(c_0_44,negated_conjecture,
~ ! [X4] : multiplication(strong_iteration(one),X4) = strong_iteration(one),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_45,plain,
! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_46,plain,
strong_iteration(strong_iteration(one)) = strong_iteration(one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_42]),c_0_33]),c_0_43]),c_0_26]) ).
fof(c_0_47,plain,
! [X2] : multiplication(zero,X2) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(c_0_48,negated_conjecture,
multiplication(strong_iteration(one),esk1_0) != strong_iteration(one),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])]) ).
cnf(c_0_49,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_50,plain,
multiplication(strong_iteration(one),zero) = strong_iteration(one),
inference(rw,[status(thm)],[c_0_42,c_0_46]) ).
cnf(c_0_51,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_52,negated_conjecture,
multiplication(strong_iteration(one),esk1_0) != strong_iteration(one),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_53,plain,
multiplication(strong_iteration(one),X1) = strong_iteration(one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_50]) ).
cnf(c_0_54,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_53])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE141+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : run_ET %s %d
% 0.14/0.33 % Computer : n017.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Thu Jun 16 12:19:55 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.22/1.41 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.22/1.41 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.22/1.41 # Preprocessing time : 0.015 s
% 0.22/1.41
% 0.22/1.41 # Proof found!
% 0.22/1.41 # SZS status Theorem
% 0.22/1.41 # SZS output start CNFRefutation
% See solution above
% 0.22/1.41 # Proof object total steps : 55
% 0.22/1.41 # Proof object clause steps : 30
% 0.22/1.41 # Proof object formula steps : 25
% 0.22/1.41 # Proof object conjectures : 5
% 0.22/1.41 # Proof object clause conjectures : 2
% 0.22/1.41 # Proof object formula conjectures : 3
% 0.22/1.41 # Proof object initial clauses used : 13
% 0.22/1.41 # Proof object initial formulas used : 12
% 0.22/1.41 # Proof object generating inferences : 15
% 0.22/1.41 # Proof object simplifying inferences : 14
% 0.22/1.41 # Training examples: 0 positive, 0 negative
% 0.22/1.41 # Parsed axioms : 19
% 0.22/1.41 # Removed by relevancy pruning/SinE : 0
% 0.22/1.41 # Initial clauses : 20
% 0.22/1.41 # Removed in clause preprocessing : 0
% 0.22/1.41 # Initial clauses in saturation : 20
% 0.22/1.41 # Processed clauses : 163
% 0.22/1.41 # ...of these trivial : 17
% 0.22/1.41 # ...subsumed : 55
% 0.22/1.41 # ...remaining for further processing : 91
% 0.22/1.41 # Other redundant clauses eliminated : 0
% 0.22/1.41 # Clauses deleted for lack of memory : 0
% 0.22/1.41 # Backward-subsumed : 3
% 0.22/1.41 # Backward-rewritten : 22
% 0.22/1.41 # Generated clauses : 1648
% 0.22/1.41 # ...of the previous two non-trivial : 1159
% 0.22/1.41 # Contextual simplify-reflections : 0
% 0.22/1.41 # Paramodulations : 1648
% 0.22/1.41 # Factorizations : 0
% 0.22/1.41 # Equation resolutions : 0
% 0.22/1.41 # Current number of processed clauses : 66
% 0.22/1.41 # Positive orientable unit clauses : 41
% 0.22/1.41 # Positive unorientable unit clauses: 7
% 0.22/1.41 # Negative unit clauses : 2
% 0.22/1.41 # Non-unit-clauses : 16
% 0.22/1.41 # Current number of unprocessed clauses: 817
% 0.22/1.41 # ...number of literals in the above : 1089
% 0.22/1.41 # Current number of archived formulas : 0
% 0.22/1.41 # Current number of archived clauses : 25
% 0.22/1.41 # Clause-clause subsumption calls (NU) : 37
% 0.22/1.41 # Rec. Clause-clause subsumption calls : 37
% 0.22/1.41 # Non-unit clause-clause subsumptions : 7
% 0.22/1.41 # Unit Clause-clause subsumption calls : 23
% 0.22/1.41 # Rewrite failures with RHS unbound : 0
% 0.22/1.41 # BW rewrite match attempts : 102
% 0.22/1.41 # BW rewrite match successes : 51
% 0.22/1.41 # Condensation attempts : 0
% 0.22/1.41 # Condensation successes : 0
% 0.22/1.41 # Termbank termtop insertions : 18229
% 0.22/1.41
% 0.22/1.41 # -------------------------------------------------
% 0.22/1.41 # User time : 0.037 s
% 0.22/1.41 # System time : 0.002 s
% 0.22/1.41 # Total time : 0.039 s
% 0.22/1.41 # Maximum resident set size: 3872 pages
%------------------------------------------------------------------------------