TSTP Solution File: KLE144+2 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : KLE144+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %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 02:26:50 EDT 2022
% Result : Theorem 2.96s 3.19s
% Output : Refutation 3.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of clauses : 42 ( 36 unt; 0 nHn; 8 RR)
% Number of literals : 48 ( 26 equ; 8 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 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 : 66 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
addition(X,zero) = X,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
cnf(2,axiom,
addition(X,X) = X,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',idempotence) ).
cnf(3,plain,
addition(X,addition(X,Y)) = addition(X,Y),
inference('EMBED',[status(thm)],[2]) ).
cnf(5,axiom,
multiplication(X,one) = X,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
cnf(6,axiom,
multiplication(one,X) = X,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
cnf(7,axiom,
multiplication(X,addition(Y,Z)) = addition(multiplication(X,Y),multiplication(X,Z)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',distributivity1) ).
cnf(8,axiom,
multiplication(addition(X,Y),Z) = addition(multiplication(X,Z),multiplication(Y,Z)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',distributivity2) ).
cnf(10,axiom,
addition(one,multiplication(X,star(X))) = star(X),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_unfold1) ).
cnf(11,plain,
addition(one,addition(multiplication(X,star(X)),Y)) = addition(star(X),Y),
inference('EMBED',[status(thm)],[10]) ).
cnf(12,axiom,
addition(one,multiplication(star(X),X)) = star(X),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_unfold2) ).
cnf(13,plain,
addition(one,addition(multiplication(star(X),X),Y)) = addition(star(X),Y),
inference('EMBED',[status(thm)],[12]) ).
cnf(18,axiom,
( ~ leq(X,addition(multiplication(Y,X),Z))
| leq(X,multiplication(strong_iteration(Y),Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).
cnf(21,axiom,
( ~ leq(X,Y)
| addition(X,Y) = Y ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
cnf(22,axiom,
( leq(X,Y)
| addition(X,Y) != Y ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
cnf(23,negated_conjecture,
( ~ leq(strong_iteration(star('SKOLEMAAAV1')),strong_iteration(one))
| ~ leq(strong_iteration(one),strong_iteration(star('SKOLEMAAAV1'))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(26,plain,
leq(X,addition(X,Y)),
inference('HYPERRESOLVE',[status(thm)],[22,3]) ).
cnf(35,plain,
addition(star(X),one) = star(X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3,11,theory(equality)]),10,theory(equality)]) ).
cnf(108,plain,
multiplication(X,Y) = addition(multiplication(X,Y),multiplication(X,zero)),
inference('PARAMODULATE',[status(thm)],[7,1,theory(equality)]) ).
cnf(179,plain,
leq(X,multiplication(strong_iteration(one),Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[18,6,theory(equality)]),26]) ).
cnf(180,plain,
( ~ leq(X,multiplication(Y,X))
| leq(X,multiplication(strong_iteration(Y),zero)) ),
inference('PARAMODULATE',[status(thm)],[18,1,theory(equality)]) ).
cnf(181,plain,
( ~ leq(X,star(X))
| leq(X,strong_iteration(star(X))) ),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[18,12,theory(equality)]),5,theory(equality)]) ).
cnf(223,plain,
leq(X,strong_iteration(one)),
inference('PARAMODULATE',[status(thm)],[179,5,theory(equality)]) ).
cnf(224,plain,
~ leq(strong_iteration(one),strong_iteration(star('SKOLEMAAAV1'))),
inference('REWRITE',[status(thm)],[23,223]) ).
cnf(229,plain,
addition(strong_iteration(one),X) = strong_iteration(one),
inference('HYPERRESOLVE',[status(thm)],[21,223]) ).
cnf(233,plain,
multiplication(star(X),Y) = addition(Y,multiplication(star(X),Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,35,theory(equality)]),6,theory(equality)]) ).
cnf(234,plain,
addition(X,addition(multiplication(star(Y),X),Z)) = addition(multiplication(star(Y),X),Z),
inference('EMBED',[status(thm)],[233]) ).
cnf(365,plain,
X = addition(X,multiplication(X,zero)),
inference('PARAMODULATE',[status(thm)],[108,5,theory(equality)]) ).
cnf(366,plain,
addition(X,addition(multiplication(X,zero),Y)) = addition(X,Y),
inference('EMBED',[status(thm)],[365]) ).
cnf(1165,plain,
leq(X,multiplication(star(Y),X)),
inference('HYPERRESOLVE',[status(thm)],[22,233]) ).
cnf(1263,plain,
leq(X,multiplication(strong_iteration(star(Y)),zero)),
inference('HYPERRESOLVE',[status(thm)],[180,1165]) ).
cnf(1285,plain,
addition(X,multiplication(strong_iteration(star(Y)),zero)) = multiplication(strong_iteration(star(Y)),zero),
inference('HYPERRESOLVE',[status(thm)],[21,1263]) ).
cnf(1317,plain,
star(X) = addition(star(X),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[13,234,theory(equality)]),12,theory(equality)]) ).
cnf(1458,plain,
leq(X,star(X)),
inference('HYPERRESOLVE',[status(thm)],[22,1317]) ).
cnf(1459,plain,
leq(X,strong_iteration(star(X))),
inference('REWRITE',[status(thm)],[181,1458]) ).
cnf(1537,plain,
addition(X,strong_iteration(star(X))) = strong_iteration(star(X)),
inference('HYPERRESOLVE',[status(thm)],[21,1459]) ).
cnf(1538,plain,
addition(X,addition(strong_iteration(star(X)),Y)) = addition(strong_iteration(star(X)),Y),
inference('EMBED',[status(thm)],[1537]) ).
cnf(2332,plain,
leq(addition(X,Y),addition(strong_iteration(star(X)),addition(Y,Z))),
inference('PARAMODULATE',[status(thm)],[26,1538,theory(equality)]) ).
cnf(2395,plain,
multiplication(strong_iteration(star(X)),zero) = strong_iteration(star(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[366,1538,theory(equality)]),1537,1285,theory(equality)]) ).
cnf(2396,plain,
addition(X,strong_iteration(star(Y))) = strong_iteration(star(Y)),
inference('REWRITE',[status(thm)],[1285,2395,theory(equality)]) ).
cnf(2406,plain,
leq(addition(X,Y),strong_iteration(star(X))),
inference('REWRITE',[status(thm)],[2332,2396,theory(equality)]) ).
cnf(2412,plain,
leq(strong_iteration(one),strong_iteration(star(X))),
inference('PARAMODULATE',[status(thm)],[2406,229,theory(equality)]) ).
cnf(2413,plain,
$false,
inference('REWRITE',[status(thm)],[224,2412]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : KLE144+2 : TPTP v8.1.0. Released v4.0.0.
% 0.14/0.13 % Command : run-snark %s %d
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Thu Jun 16 08:23:22 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.47 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.48 *
% 0.21/0.48 *
% 0.21/0.49 #<PACKAGE "SNARK-USER">
% 0.21/0.49 *
% 0.21/0.49 SNARK-TPTP-OPTIONS
% 0.21/0.49 *
% 0.21/0.49 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.21/0.49 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.21/0.49 (USE-FACTORING :POS)
% 0.21/0.49 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.21/0.49 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.21/0.49 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.21/0.49 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.21/0.49 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.21/0.49 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.21/0.49 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.21/0.49 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.21/0.49 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.21/0.49 (DECLARE-TPTP-SYMBOLS2))
% 0.21/0.49 *
% 0.21/0.49 "."
% 0.21/0.49 *
% 0.21/0.49 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-16T08:23:22
% 0.21/0.49 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n008.cluster.edu at 2022-06-16T08:23:22
% 0.21/0.50
% 0.21/0.50 ; Recognized commutativity assertion (= (|addition| ?X ?Y) (|addition| ?Y ?X)).
% 0.21/0.50 ; Recognized associativity assertion (= (|addition| ?X (|addition| ?Y ?Z)) (|addition| (|addition| ?X ?Y) ?Z)).
% 0.21/0.50 ; Recognized right identity assertion (= (|addition| ?X |zero|) ?X).
% 0.21/0.50 ; Recognized associativity assertion (= (|multiplication| ?X (|multiplication| ?Y ?Z)) (|multiplication| (|multiplication| ?X ?Y) ?Z)).
% 0.21/0.50 ; Recognized right identity assertion (= (|multiplication| ?X |one|) ?X).
% 0.21/0.50 ; Recognized left identity assertion (= (|multiplication| |one| ?X) ?X).
% 0.21/0.50 ; Declaring addition to be commutative.
% 2.96/3.19 ; Declaring addition to be associative-commutative.
% 2.96/3.19
% 2.96/3.19 #||
% 2.96/3.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.96/3.19 % SZS output start Refutation
% See solution above
% 3.02/3.20 ||#
% 3.02/3.20
% 3.02/3.20 ; Summary of computation:
% 3.02/3.20 ; 14183 formulas have been input or derived (from 211 formulas).
% 3.02/3.20 ; 2413 (17%) were retained. Of these,
% 3.02/3.20 ; 507 (21%) were simplified or subsumed later,
% 3.02/3.20 ; 1906 (79%) are still being kept.
% 3.02/3.20 ;
% 3.02/3.20 ; Run time in seconds excluding printing time:
% 3.02/3.20 ; 0.004 0% Read assertion file (1 call)
% 3.02/3.20 ; 0.002 0% Assert (19 calls)
% 3.02/3.20 ; 0.231 9% Process new row (13,366 calls)
% 3.02/3.20 ; 0.037 1% Resolution (420 calls)
% 3.02/3.20 ; 0.187 7% Paramodulation (210 calls)
% 3.02/3.20 ; 0.001 0% Embedding (210 calls)
% 3.02/3.20 ; 0.049 2% Condensing (1,515 calls)
% 3.02/3.20 ; 0.129 5% Forward subsumption (1,515 calls)
% 3.02/3.20 ; 0.028 1% Backward subsumption (747 calls)
% 3.02/3.20 ; 0.046 2% Clause clause subsumption (5,907 calls)
% 3.02/3.20 ; 1.785 66% Forward simplification (12,462 calls)
% 3.02/3.20 ; 0.072 3% Backward simplification (2,208 calls)
% 3.02/3.20 ; 0.041 2% Ordering (9,775 calls)
% 3.02/3.20 ; 0.013 0% Ordering ac (1,681 calls)
% 3.02/3.20 ; 0.000 0% Sortal reasoning (32 calls)
% 3.02/3.20 ; 0.000 0% Purity testing (1 call)
% 3.02/3.20 ; 0.071 3% Other
% 3.02/3.20 ; 2.696 Total
% 3.02/3.20 ; 2.710 Real time
% 3.02/3.20 ;
% 3.02/3.20 ; Term-hash-array has 4,804 terms in all.
% 3.02/3.20 ; Feature-vector-row-index has 670 entries (672 at peak, 747 added, 77 deleted).
% 3.02/3.20 ; Feature-vector-row-index has 4,569 nodes (4,590 at peak, 5,214 added, 645 deleted).
% 3.02/3.20 ; Retrieved 6,713 possibly forward subsuming rows in 1,515 calls.
% 3.02/3.20 ; Retrieved 1,109 possibly backward subsumed rows in 747 calls.
% 3.02/3.20 ; Path-index has 3,926 entries (4,076 at peak, 4,890 added, 964 deleted).
% 3.02/3.20 ; Path-index has 2,282 nodes (2,341 at peak, 2,528 added, 246 deleted).
% 3.02/3.20 ; Trie-index has 3,926 entries (4,076 at peak, 4,890 added, 964 deleted).
% 3.02/3.20 ; Trie-index has 1,941 nodes (1,959 at peak, 2,265 added, 324 deleted).
% 3.02/3.20 ; Retrieved 2,575,159 generalization terms in 86,915 calls.
% 3.02/3.20 ; Retrieved 7,603 instance terms in 1,493 calls.
% 3.02/3.20 ; Retrieved 38,403 unifiable terms in 1,618 calls.
% 3.02/3.20 ;
% 3.02/3.20 ; The agenda of rows to process has 263 entries:
% 3.02/3.20 ; 3 with value 13 36 with value 20 9 with value 27
% 3.02/3.20 ; 10 with value 14 13 with value 21 3 with value 28
% 3.02/3.20 ; 36 with value 15 20 with value 22 4 with value 29
% 3.02/3.20 ; 11 with value 16 18 with value 23 1 with value 30
% 3.02/3.20 ; 34 with value 17 12 with value 24 1 with value 31
% 3.02/3.20 ; 24 with value 18 13 with value 25 1 with value 33
% 3.02/3.20 ; 11 with value 19 3 with value 26
% 3.02/3.20 ; The agenda of rows to give has 1714 entries:
% 3.02/3.20 ; 1 with value (4 13) 98 with value (4 28) 11 with value (4 41)
% 3.02/3.20 ; 10 with value (4 15) 70 with value (4 29) 10 with value (4 42)
% 3.02/3.20 ; 39 with value (4 16) 40 with value (4 30) 8 with value (4 43)
% 3.02/3.20 ; 81 with value (4 17) 32 with value (4 31) 4 with value (4 45)
% 3.02/3.20 ; 96 with value (4 18) 43 with value (4 32) 5 with value (4 46)
% 3.02/3.20 ; 126 with value (4 19) 30 with value (4 33) 7 with value (4 47)
% 3.02/3.20 ; 118 with value (4 20) 28 with value (4 34) 1 with value (4 49)
% 3.02/3.20 ; 137 with value (4 21) 18 with value (4 35) 4 with value (4 50)
% 3.02/3.20 ; 142 with value (4 22) 27 with value (4 36) 3 with value (4 51)
% 3.02/3.20 ; 108 with value (4 23) 15 with value (4 37) 1 with value (4 52)
% 3.02/3.20 ; 100 with value (4 24) 13 with value (4 38) 3 with value (4 55)
% 3.02/3.20 ; 82 with value (4 25) 24 with value (4 39) 1 with value (4 56)
% 3.02/3.20 ; 93 with value (4 26) 16 with value (4 40) 1 with value (4 62)
% 3.02/3.20 ; 68 with value (4 27)
% 3.02/3.20 Evaluation took:
% 3.02/3.20 2.711 seconds of real time
% 3.02/3.20 2.57499 seconds of user run time
% 3.02/3.20 0.124094 seconds of system run time
% 3.02/3.20 [Run times include 0.101 seconds GC run time.]
% 3.02/3.20 0 calls to %EVAL
% 3.02/3.20 0 page faults and
% 3.02/3.20 176,099,608 bytes consed.
% 3.02/3.21 :PROOF-FOUND
% 3.02/3.21 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-16T08:23:25
% 3.02/3.21 :PROOF-FOUND
% 3.02/3.21 *
%------------------------------------------------------------------------------