TSTP Solution File: KLE150+2 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : KLE150+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n023.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 01:56:16 EDT 2022
% Result : Theorem 0.24s 1.43s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 45 ( 37 unt; 0 def)
% Number of atoms : 55 ( 40 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 21 ( 11 ~; 6 |; 3 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 70 ( 3 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_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(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
fof(goals,conjecture,
! [X4] :
( leq(strong_iteration(multiplication(X4,zero)),addition(one,multiplication(X4,zero)))
& leq(addition(one,multiplication(X4,zero)),strong_iteration(multiplication(X4,zero))) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_associativity) ).
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(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
fof(c_0_11,plain,
! [X2] : strong_iteration(X2) = addition(multiplication(X2,strong_iteration(X2)),one),
inference(variable_rename,[status(thm)],[infty_unfold1]) ).
fof(c_0_12,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_13,plain,
! [X2] : addition(X2,zero) = X2,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_14,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_15,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_16,negated_conjecture,
~ ! [X4] :
( leq(strong_iteration(multiplication(X4,zero)),addition(one,multiplication(X4,zero)))
& leq(addition(one,multiplication(X4,zero)),strong_iteration(multiplication(X4,zero))) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_17,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_19,plain,
! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_20,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_23,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_24,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[idempotence]) ).
fof(c_0_25,negated_conjecture,
( ~ leq(strong_iteration(multiplication(esk1_0,zero)),addition(one,multiplication(esk1_0,zero)))
| ~ leq(addition(one,multiplication(esk2_0,zero)),strong_iteration(multiplication(esk2_0,zero))) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
fof(c_0_26,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_27,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_28,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_30,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_31,plain,
! [X2] : multiplication(zero,X2) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_32,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,negated_conjecture,
( ~ leq(addition(one,multiplication(esk2_0,zero)),strong_iteration(multiplication(esk2_0,zero)))
| ~ leq(strong_iteration(multiplication(esk1_0,zero)),addition(one,multiplication(esk1_0,zero))) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_35,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,plain,
addition(one,multiplication(X1,multiplication(X2,strong_iteration(multiplication(X1,X2))))) = strong_iteration(multiplication(X1,X2)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_37,plain,
multiplication(addition(one,X1),zero) = multiplication(X1,zero),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_38,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_39,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_40,negated_conjecture,
( addition(one,addition(multiplication(esk2_0,zero),strong_iteration(multiplication(esk2_0,zero)))) != strong_iteration(multiplication(esk2_0,zero))
| ~ leq(strong_iteration(multiplication(esk1_0,zero)),addition(one,multiplication(esk1_0,zero))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_32]) ).
cnf(c_0_41,plain,
strong_iteration(multiplication(X1,zero)) = addition(one,multiplication(X1,zero)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_37]) ).
cnf(c_0_42,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_39,c_0_18]) ).
cnf(c_0_43,negated_conjecture,
~ leq(addition(one,multiplication(esk1_0,zero)),addition(one,multiplication(esk1_0,zero))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_39]),c_0_41]),c_0_41])]) ).
cnf(c_0_44,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_43,c_0_35]),c_0_32]),c_0_42]),c_0_39])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : KLE150+2 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.14 % Command : run_ET %s %d
% 0.14/0.36 % Computer : n023.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 08:53:20 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.24/1.43 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.43 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.43 # Preprocessing time : 0.009 s
% 0.24/1.43
% 0.24/1.43 # Proof found!
% 0.24/1.43 # SZS status Theorem
% 0.24/1.43 # SZS output start CNFRefutation
% See solution above
% 0.24/1.43 # Proof object total steps : 45
% 0.24/1.43 # Proof object clause steps : 22
% 0.24/1.43 # Proof object formula steps : 23
% 0.24/1.43 # Proof object conjectures : 7
% 0.24/1.43 # Proof object clause conjectures : 4
% 0.24/1.43 # Proof object formula conjectures : 3
% 0.24/1.43 # Proof object initial clauses used : 11
% 0.24/1.43 # Proof object initial formulas used : 11
% 0.24/1.43 # Proof object generating inferences : 9
% 0.24/1.43 # Proof object simplifying inferences : 14
% 0.24/1.43 # Training examples: 0 positive, 0 negative
% 0.24/1.43 # Parsed axioms : 19
% 0.24/1.43 # Removed by relevancy pruning/SinE : 0
% 0.24/1.43 # Initial clauses : 20
% 0.24/1.43 # Removed in clause preprocessing : 0
% 0.24/1.43 # Initial clauses in saturation : 20
% 0.24/1.43 # Processed clauses : 341
% 0.24/1.43 # ...of these trivial : 73
% 0.24/1.43 # ...subsumed : 62
% 0.24/1.43 # ...remaining for further processing : 206
% 0.24/1.43 # Other redundant clauses eliminated : 0
% 0.24/1.43 # Clauses deleted for lack of memory : 0
% 0.24/1.43 # Backward-subsumed : 4
% 0.24/1.43 # Backward-rewritten : 88
% 0.24/1.43 # Generated clauses : 3889
% 0.24/1.43 # ...of the previous two non-trivial : 2937
% 0.24/1.43 # Contextual simplify-reflections : 1
% 0.24/1.43 # Paramodulations : 3889
% 0.24/1.43 # Factorizations : 0
% 0.24/1.43 # Equation resolutions : 0
% 0.24/1.43 # Current number of processed clauses : 114
% 0.24/1.43 # Positive orientable unit clauses : 52
% 0.24/1.43 # Positive unorientable unit clauses: 7
% 0.24/1.43 # Negative unit clauses : 1
% 0.24/1.43 # Non-unit-clauses : 54
% 0.24/1.43 # Current number of unprocessed clauses: 2034
% 0.24/1.43 # ...number of literals in the above : 3387
% 0.24/1.43 # Current number of archived formulas : 0
% 0.24/1.43 # Current number of archived clauses : 92
% 0.24/1.43 # Clause-clause subsumption calls (NU) : 633
% 0.24/1.43 # Rec. Clause-clause subsumption calls : 633
% 0.24/1.43 # Non-unit clause-clause subsumptions : 49
% 0.24/1.43 # Unit Clause-clause subsumption calls : 52
% 0.24/1.43 # Rewrite failures with RHS unbound : 0
% 0.24/1.43 # BW rewrite match attempts : 181
% 0.24/1.43 # BW rewrite match successes : 100
% 0.24/1.43 # Condensation attempts : 0
% 0.24/1.43 # Condensation successes : 0
% 0.24/1.43 # Termbank termtop insertions : 50161
% 0.24/1.43
% 0.24/1.43 # -------------------------------------------------
% 0.24/1.43 # User time : 0.047 s
% 0.24/1.43 # System time : 0.005 s
% 0.24/1.43 # Total time : 0.052 s
% 0.24/1.43 # Maximum resident set size: 5720 pages
%------------------------------------------------------------------------------