TSTP Solution File: KLE141+2 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : KLE141+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n003.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 02:26:49 EDT 2022
% Result : Theorem 0.48s 0.64s
% Output : Refutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of clauses : 21 ( 16 unt; 0 nHn; 7 RR)
% Number of literals : 26 ( 13 equ; 8 neg)
% Maximal clause size : 2 ( 1 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 : 31 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
addition(X,X) = X,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',idempotence) ).
cnf(3,plain,
addition(X,addition(X,Y)) = addition(X,Y),
inference('EMBED',[status(thm)],[2]) ).
cnf(4,axiom,
multiplication(X,multiplication(Y,Z)) = multiplication(multiplication(X,Y),Z),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_associativity) ).
cnf(5,axiom,
multiplication(X,one) = X,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
cnf(6,axiom,
multiplication(one,X) = X,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
cnf(8,axiom,
multiplication(addition(X,Y),Z) = addition(multiplication(X,Z),multiplication(Y,Z)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',distributivity2) ).
cnf(9,axiom,
multiplication(zero,X) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
cnf(18,axiom,
( ~ leq(X,addition(multiplication(Y,X),Z))
| leq(X,multiplication(strong_iteration(Y),Z)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).
cnf(19,axiom,
strong_iteration(X) = addition(star(X),multiplication(strong_iteration(X),zero)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',isolation) ).
cnf(21,axiom,
( ~ leq(X,Y)
| addition(X,Y) = Y ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',order) ).
cnf(22,axiom,
( leq(X,Y)
| addition(X,Y) != Y ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',order) ).
cnf(23,negated_conjecture,
( ~ leq(multiplication(strong_iteration(one),'SKOLEMAAAU1'),strong_iteration(one))
| ~ leq(strong_iteration(one),multiplication(strong_iteration(one),'SKOLEMAAAU1')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(26,plain,
leq(X,addition(X,Y)),
inference('HYPERRESOLVE',[status(thm)],[22,3]) ).
cnf(82,plain,
multiplication(X,zero) = multiplication(multiplication(X,zero),Y),
inference('PARAMODULATE',[status(thm)],[4,9,theory(equality)]) ).
cnf(132,plain,
multiplication(strong_iteration(X),Y) = addition(multiplication(star(X),Y),multiplication(strong_iteration(X),zero)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,19,theory(equality)]),82,theory(equality)]) ).
cnf(134,plain,
( ~ leq(addition(multiplication(star(one),'SKOLEMAAAU1'),multiplication(strong_iteration(one),zero)),strong_iteration(one))
| ~ leq(strong_iteration(one),addition(multiplication(star(one),'SKOLEMAAAU1'),multiplication(strong_iteration(one),zero))) ),
inference('REWRITE',[status(thm)],[23,132,theory(equality)]) ).
cnf(180,plain,
leq(X,multiplication(strong_iteration(one),Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[18,6,theory(equality)]),26]) ).
cnf(224,plain,
leq(X,strong_iteration(one)),
inference('PARAMODULATE',[status(thm)],[180,5,theory(equality)]) ).
cnf(225,plain,
~ leq(strong_iteration(one),addition(multiplication(star(one),'SKOLEMAAAU1'),multiplication(strong_iteration(one),zero))),
inference('REWRITE',[status(thm)],[134,224]) ).
cnf(227,plain,
addition(X,multiplication(strong_iteration(one),Y)) = multiplication(strong_iteration(one),Y),
inference('HYPERRESOLVE',[status(thm)],[21,180]) ).
cnf(229,plain,
$false,
inference('REWRITE',[status(thm)],[225,180,227,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE141+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : run-snark %s %d
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 15:08:26 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.45 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.46 *
% 0.20/0.47 *
% 0.20/0.47 #<PACKAGE "SNARK-USER">
% 0.20/0.47 *
% 0.20/0.47 SNARK-TPTP-OPTIONS
% 0.20/0.47 *
% 0.20/0.47 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.47 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.47 (USE-FACTORING :POS)
% 0.20/0.47 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.47 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.47 *
% 0.20/0.47 "."
% 0.20/0.47 *
% 0.20/0.47 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-16T15:08:27
% 0.20/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n003.cluster.edu at 2022-06-16T15:08:27
% 0.20/0.49
% 0.20/0.49 ; Recognized commutativity assertion (= (|addition| ?X ?Y) (|addition| ?Y ?X)).
% 0.20/0.49 ; Recognized associativity assertion (= (|addition| ?X (|addition| ?Y ?Z)) (|addition| (|addition| ?X ?Y) ?Z)).
% 0.20/0.49 ; Recognized right identity assertion (= (|addition| ?X |zero|) ?X).
% 0.20/0.49 ; Recognized associativity assertion (= (|multiplication| ?X (|multiplication| ?Y ?Z)) (|multiplication| (|multiplication| ?X ?Y) ?Z)).
% 0.20/0.49 ; Recognized right identity assertion (= (|multiplication| ?X |one|) ?X).
% 0.20/0.49 ; Recognized left identity assertion (= (|multiplication| |one| ?X) ?X).
% 0.20/0.49 ; Declaring addition to be commutative.
% 0.48/0.64 ; Declaring addition to be associative-commutative.
% 0.48/0.64
% 0.48/0.64 #||
% 0.48/0.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.48/0.64 % SZS output start Refutation
% See solution above
% 0.48/0.64 ||#
% 0.48/0.64
% 0.48/0.64 ; Summary of computation:
% 0.48/0.64 ; 644 formulas have been input or derived (from 34 formulas).
% 0.48/0.64 ; 229 (36%) were retained. Of these,
% 0.48/0.64 ; 16 ( 7%) were simplified or subsumed later,
% 0.48/0.64 ; 213 (93%) are still being kept.
% 0.48/0.64 ;
% 0.48/0.64 ; Run time in seconds excluding printing time:
% 0.48/0.64 ; 0.004 2% Read assertion file (1 call)
% 0.48/0.64 ; 0.002 1% Assert (19 calls)
% 0.48/0.64 ; 0.020 12% Process new row (622 calls)
% 0.48/0.64 ; 0.004 2% Resolution (66 calls)
% 0.48/0.64 ; 0.015 9% Paramodulation (33 calls)
% 0.48/0.64 ; 0.000 0% Embedding (45 calls)
% 0.48/0.64 ; 0.007 4% Condensing (157 calls)
% 0.48/0.64 ; 0.008 5% Forward subsumption (157 calls)
% 0.48/0.64 ; 0.001 1% Backward subsumption (91 calls)
% 0.48/0.64 ; 0.002 1% Clause clause subsumption (239 calls)
% 0.48/0.64 ; 0.067 39% Forward simplification (580 calls)
% 0.48/0.64 ; 0.003 2% Backward simplification (187 calls)
% 0.48/0.64 ; 0.005 3% Ordering (909 calls)
% 0.48/0.64 ; 0.006 4% Ordering ac (246 calls)
% 0.48/0.64 ; 0.000 0% Sortal reasoning (32 calls)
% 0.48/0.64 ; 0.000 0% Purity testing (1 call)
% 0.48/0.64 ; 0.026 15% Other
% 0.48/0.64 ; 0.170 Total
% 0.48/0.64 ; 0.171 Real time
% 0.48/0.64 ;
% 0.48/0.64 ; Term-hash-array has 624 terms in all.
% 0.48/0.64 ; Feature-vector-row-index has 89 entries (90 at peak, 91 added, 2 deleted).
% 0.48/0.64 ; Feature-vector-row-index has 560 nodes (582 at peak, 595 added, 35 deleted).
% 0.48/0.64 ; Retrieved 255 possibly forward subsuming rows in 157 calls.
% 0.48/0.64 ; Retrieved 26 possibly backward subsumed rows in 91 calls.
% 0.48/0.64 ; Path-index has 590 entries (592 at peak, 638 added, 48 deleted).
% 0.48/0.64 ; Path-index has 503 nodes (511 at peak, 540 added, 37 deleted).
% 0.48/0.65 ; Trie-index has 590 entries (592 at peak, 638 added, 48 deleted).
% 0.48/0.65 ; Trie-index has 465 nodes (470 at peak, 494 added, 29 deleted).
% 0.48/0.65 ; Retrieved 47,317 generalization terms in 5,479 calls.
% 0.48/0.65 ; Retrieved 314 instance terms in 128 calls.
% 0.48/0.65 ; Retrieved 1,678 unifiable terms in 181 calls.
% 0.48/0.65 ;
% 0.48/0.65 ; The agenda of rows to process has 1 entry:
% 0.48/0.65 ; 1 with value 17
% 0.48/0.65 ; The agenda of rows to give has 180 entries:
% 0.48/0.65 ; 1 with value (4 8) 21 with value (4 19) 8 with value (4 27)
% 0.48/0.65 ; 7 with value (4 11) 14 with value (4 20) 22 with value (4 28)
% 0.48/0.65 ; 7 with value (4 12) 3 with value (4 21) 2 with value (4 29)
% 0.48/0.65 ; 3 with value (4 13) 6 with value (4 22) 1 with value (4 30)
% 0.48/0.65 ; 7 with value (4 14) 3 with value (4 23) 3 with value (4 32)
% 0.48/0.65 ; 14 with value (4 15) 4 with value (4 24) 3 with value (4 33)
% 0.48/0.65 ; 4 with value (4 16) 6 with value (4 25) 5 with value (4 35)
% 0.48/0.65 ; 13 with value (4 17) 13 with value (4 26) 1 with value (4 40)
% 0.48/0.65 ; 9 with value (4 18)
% 0.48/0.65 Evaluation took:
% 0.48/0.65 0.173 seconds of real time
% 0.48/0.65 0.158516 seconds of user run time
% 0.48/0.65 0.014281 seconds of system run time
% 0.48/0.65 0 calls to %EVAL
% 0.48/0.65 0 page faults and
% 0.48/0.65 9,598,680 bytes consed.
% 0.48/0.65 :PROOF-FOUND
% 0.48/0.65 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-16T15:08:27
% 0.48/0.65 :PROOF-FOUND
% 0.48/0.65 *
%------------------------------------------------------------------------------