TSTP Solution File: KLE142+1 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : KLE142+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n028.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 01:56:11 EDT 2022
% Result : Theorem 0.26s 1.45s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 56 ( 47 unt; 0 def)
% Number of atoms : 67 ( 48 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 : 93 ( 11 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/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(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',order) ).
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(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
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(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
fof(distributivity1,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',distributivity1) ).
fof(goals,conjecture,
! [X4] : strong_iteration(strong_iteration(X4)) = strong_iteration(one),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',goals) ).
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]) ).
fof(c_0_21,plain,
! [X2] : strong_iteration(X2) = addition(multiplication(X2,strong_iteration(X2)),one),
inference(variable_rename,[status(thm)],[infty_unfold1]) ).
fof(c_0_22,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_23,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_24,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_26,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
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,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
leq(X1,multiplication(strong_iteration(one),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_31,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_35,plain,
leq(X1,strong_iteration(one)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
fof(c_0_36,plain,
! [X2] : addition(X2,zero) = X2,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_37,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(spm,[status(thm)],[c_0_32,c_0_17]) ).
cnf(c_0_38,plain,
addition(one,strong_iteration(X1)) = strong_iteration(X1),
inference(spm,[status(thm)],[c_0_25,c_0_33]) ).
cnf(c_0_39,plain,
addition(X1,strong_iteration(one)) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_41,plain,
addition(X1,multiplication(strong_iteration(X2),X1)) = multiplication(strong_iteration(X2),X1),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,plain,
addition(strong_iteration(one),X1) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_29,c_0_39]) ).
fof(c_0_43,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_44,plain,
( leq(X1,multiplication(strong_iteration(X2),zero))
| ~ leq(X1,multiplication(X2,X1)) ),
inference(spm,[status(thm)],[c_0_16,c_0_40]) ).
cnf(c_0_45,plain,
multiplication(strong_iteration(X1),strong_iteration(one)) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
fof(c_0_46,negated_conjecture,
~ ! [X4] : strong_iteration(strong_iteration(X4)) = strong_iteration(one),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_47,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_48,plain,
leq(strong_iteration(one),multiplication(strong_iteration(strong_iteration(X1)),zero)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_35])]) ).
fof(c_0_49,negated_conjecture,
strong_iteration(strong_iteration(esk1_0)) != strong_iteration(one),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])])]) ).
cnf(c_0_50,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_31]),c_0_29]) ).
cnf(c_0_51,plain,
multiplication(strong_iteration(strong_iteration(X1)),zero) = strong_iteration(one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_48]),c_0_42]) ).
cnf(c_0_52,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_40]) ).
cnf(c_0_53,negated_conjecture,
strong_iteration(strong_iteration(esk1_0)) != strong_iteration(one),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_54,plain,
strong_iteration(strong_iteration(X1)) = strong_iteration(one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_39]),c_0_52]),c_0_31]) ).
cnf(c_0_55,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : KLE142+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : run_ET %s %d
% 0.14/0.36 % Computer : n028.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Thu Jun 16 15:36:11 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.26/1.45 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.26/1.45 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.26/1.45 # Preprocessing time : 0.015 s
% 0.26/1.45
% 0.26/1.45 # Proof found!
% 0.26/1.45 # SZS status Theorem
% 0.26/1.45 # SZS output start CNFRefutation
% See solution above
% 0.26/1.45 # Proof object total steps : 56
% 0.26/1.45 # Proof object clause steps : 31
% 0.26/1.45 # Proof object formula steps : 25
% 0.26/1.45 # Proof object conjectures : 5
% 0.26/1.45 # Proof object clause conjectures : 2
% 0.26/1.45 # Proof object formula conjectures : 3
% 0.26/1.45 # Proof object initial clauses used : 13
% 0.26/1.45 # Proof object initial formulas used : 12
% 0.26/1.45 # Proof object generating inferences : 16
% 0.26/1.45 # Proof object simplifying inferences : 12
% 0.26/1.45 # Training examples: 0 positive, 0 negative
% 0.26/1.45 # Parsed axioms : 19
% 0.26/1.45 # Removed by relevancy pruning/SinE : 0
% 0.26/1.45 # Initial clauses : 20
% 0.26/1.45 # Removed in clause preprocessing : 0
% 0.26/1.45 # Initial clauses in saturation : 20
% 0.26/1.45 # Processed clauses : 1179
% 0.26/1.45 # ...of these trivial : 122
% 0.26/1.45 # ...subsumed : 791
% 0.26/1.45 # ...remaining for further processing : 266
% 0.26/1.45 # Other redundant clauses eliminated : 0
% 0.26/1.45 # Clauses deleted for lack of memory : 0
% 0.26/1.45 # Backward-subsumed : 3
% 0.26/1.45 # Backward-rewritten : 43
% 0.26/1.45 # Generated clauses : 14714
% 0.26/1.45 # ...of the previous two non-trivial : 12226
% 0.26/1.45 # Contextual simplify-reflections : 94
% 0.26/1.45 # Paramodulations : 14714
% 0.26/1.45 # Factorizations : 0
% 0.26/1.45 # Equation resolutions : 0
% 0.26/1.45 # Current number of processed clauses : 220
% 0.26/1.45 # Positive orientable unit clauses : 86
% 0.26/1.45 # Positive unorientable unit clauses: 18
% 0.26/1.45 # Negative unit clauses : 12
% 0.26/1.45 # Non-unit-clauses : 104
% 0.26/1.45 # Current number of unprocessed clauses: 8742
% 0.26/1.45 # ...number of literals in the above : 13282
% 0.26/1.45 # Current number of archived formulas : 0
% 0.26/1.45 # Current number of archived clauses : 46
% 0.26/1.45 # Clause-clause subsumption calls (NU) : 1520
% 0.26/1.45 # Rec. Clause-clause subsumption calls : 1507
% 0.26/1.45 # Non-unit clause-clause subsumptions : 325
% 0.26/1.45 # Unit Clause-clause subsumption calls : 340
% 0.26/1.45 # Rewrite failures with RHS unbound : 0
% 0.26/1.45 # BW rewrite match attempts : 298
% 0.26/1.45 # BW rewrite match successes : 162
% 0.26/1.45 # Condensation attempts : 0
% 0.26/1.45 # Condensation successes : 0
% 0.26/1.45 # Termbank termtop insertions : 172009
% 0.26/1.45
% 0.26/1.45 # -------------------------------------------------
% 0.26/1.45 # User time : 0.191 s
% 0.26/1.45 # System time : 0.007 s
% 0.26/1.45 # Total time : 0.198 s
% 0.26/1.45 # Maximum resident set size: 12848 pages
%------------------------------------------------------------------------------