TSTP Solution File: KLE144+1 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : KLE144+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n027.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 23.27s 23.48s
% Output : Refutation 23.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of clauses : 49 ( 44 unt; 0 nHn; 7 RR)
% Number of literals : 54 ( 38 equ; 6 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 : 75 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
addition(X,zero) = X,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
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(7,axiom,
multiplication(X,addition(Y,Z)) = addition(multiplication(X,Y),multiplication(X,Z)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',distributivity1) ).
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(10,axiom,
addition(one,multiplication(X,star(X))) = star(X),
file('/export/starexec/sandbox/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/sandbox/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(16,axiom,
strong_iteration(X) = addition(multiplication(X,strong_iteration(X)),one),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).
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(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,
strong_iteration(star('SKOLEMAAAV1')) != strong_iteration(one),
file('/export/starexec/sandbox/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(82,plain,
multiplication(X,zero) = multiplication(multiplication(X,zero),Y),
inference('PARAMODULATE',[status(thm)],[4,9,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(227,plain,
addition(strong_iteration(one),X) = strong_iteration(one),
inference('HYPERRESOLVE',[status(thm)],[21,223]) ).
cnf(230,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(231,plain,
addition(X,addition(multiplication(star(Y),X),Z)) = addition(multiplication(star(Y),X),Z),
inference('EMBED',[status(thm)],[230]) ).
cnf(276,plain,
addition(one,multiplication(X,zero)) = star(multiplication(X,zero)),
inference('PARAMODULATE',[status(thm)],[10,82,theory(equality)]) ).
cnf(278,plain,
strong_iteration(multiplication(X,zero)) = star(multiplication(X,zero)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[16,82,theory(equality)]),276,theory(equality)]) ).
cnf(362,plain,
X = addition(X,multiplication(X,zero)),
inference('PARAMODULATE',[status(thm)],[108,5,theory(equality)]) ).
cnf(363,plain,
addition(X,addition(multiplication(X,zero),Y)) = addition(X,Y),
inference('EMBED',[status(thm)],[362]) ).
cnf(1162,plain,
leq(X,multiplication(star(Y),X)),
inference('HYPERRESOLVE',[status(thm)],[22,230]) ).
cnf(1168,plain,
multiplication(star(X),strong_iteration(one)) = strong_iteration(one),
inference('PARAMODULATE',[status(thm)],[227,230,theory(equality)]) ).
cnf(1260,plain,
leq(X,multiplication(strong_iteration(star(Y)),zero)),
inference('HYPERRESOLVE',[status(thm)],[180,1162]) ).
cnf(1282,plain,
addition(X,multiplication(strong_iteration(star(Y)),zero)) = multiplication(strong_iteration(star(Y)),zero),
inference('HYPERRESOLVE',[status(thm)],[21,1260]) ).
cnf(1314,plain,
star(X) = addition(star(X),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[13,231,theory(equality)]),12,theory(equality)]) ).
cnf(1455,plain,
leq(X,star(X)),
inference('HYPERRESOLVE',[status(thm)],[22,1314]) ).
cnf(1456,plain,
leq(X,strong_iteration(star(X))),
inference('REWRITE',[status(thm)],[181,1455]) ).
cnf(1534,plain,
addition(X,strong_iteration(star(X))) = strong_iteration(star(X)),
inference('HYPERRESOLVE',[status(thm)],[21,1456]) ).
cnf(1535,plain,
addition(X,addition(strong_iteration(star(X)),Y)) = addition(strong_iteration(star(X)),Y),
inference('EMBED',[status(thm)],[1534]) ).
cnf(2392,plain,
multiplication(strong_iteration(star(X)),zero) = strong_iteration(star(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[363,1535,theory(equality)]),1534,1282,theory(equality)]) ).
cnf(2393,plain,
addition(X,strong_iteration(star(Y))) = strong_iteration(star(Y)),
inference('REWRITE',[status(thm)],[1282,2392,theory(equality)]) ).
cnf(2809,plain,
strong_iteration(strong_iteration(star(X))) = star(strong_iteration(star(X))),
inference('PARAMODULATE',[status(thm)],[278,2392,theory(equality)]) ).
cnf(2810,plain,
strong_iteration(star(X)) = multiplication(strong_iteration(star(X)),Y),
inference('PARAMODULATE',[status(thm)],[82,2392,theory(equality)]) ).
cnf(5540,plain,
star(strong_iteration(star(X))) = strong_iteration(star(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[16,2809,theory(equality)]),2393,2810,theory(equality)]) ).
cnf(5872,plain,
strong_iteration(star(X)) = strong_iteration(one),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1168,5540,theory(equality)]),2810,theory(equality)]) ).
cnf(5873,plain,
$false,
inference('REWRITE',[status(thm)],[23,5872,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE144+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : run-snark %s %d
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 16 16:50:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.18/0.45 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.46 *
% 0.18/0.46 *
% 0.18/0.46 #<PACKAGE "SNARK-USER">
% 0.18/0.46 *
% 0.18/0.46 SNARK-TPTP-OPTIONS
% 0.18/0.46 *
% 0.18/0.47 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.18/0.47 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.18/0.47 (USE-FACTORING :POS)
% 0.18/0.47 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.18/0.47 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.18/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.18/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.18/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.18/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.18/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.18/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.18/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.18/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.18/0.47 *
% 0.18/0.47 "."
% 0.18/0.47 *
% 0.18/0.47 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-16T16:50:06
% 0.18/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n027.cluster.edu at 2022-06-16T16:50:06
% 0.18/0.48
% 0.18/0.48 ; Recognized commutativity assertion (= (|addition| ?X ?Y) (|addition| ?Y ?X)).
% 0.18/0.48 ; Recognized associativity assertion (= (|addition| ?X (|addition| ?Y ?Z)) (|addition| (|addition| ?X ?Y) ?Z)).
% 0.18/0.48 ; Recognized right identity assertion (= (|addition| ?X |zero|) ?X).
% 0.18/0.48 ; Recognized associativity assertion (= (|multiplication| ?X (|multiplication| ?Y ?Z)) (|multiplication| (|multiplication| ?X ?Y) ?Z)).
% 0.18/0.48 ; Recognized right identity assertion (= (|multiplication| ?X |one|) ?X).
% 0.18/0.48 ; Recognized left identity assertion (= (|multiplication| |one| ?X) ?X).
% 0.18/0.48 ; Declaring addition to be commutative.
% 23.27/23.48 ; Declaring addition to be associative-commutative.
% 23.27/23.48
% 23.27/23.48 #||
% 23.27/23.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.27/23.48 % SZS output start Refutation
% See solution above
% 23.27/23.49 ||#
% 23.27/23.49
% 23.27/23.49 ; Summary of computation:
% 23.27/23.49 ; 41482 formulas have been input or derived (from 379 formulas).
% 23.27/23.49 ; 5873 (14%) were retained. Of these,
% 23.27/23.49 ; 1297 (22%) were simplified or subsumed later,
% 23.27/23.49 ; 4576 (78%) are still being kept.
% 23.27/23.49 ;
% 23.27/23.49 ; Run time in seconds excluding printing time:
% 23.27/23.49 ; 0.004 0% Read assertion file (1 call)
% 23.27/23.49 ; 0.001 0% Assert (19 calls)
% 23.27/23.49 ; 0.699 3% Process new row (40,114 calls)
% 23.27/23.49 ; 0.116 1% Resolution (756 calls)
% 23.27/23.49 ; 0.497 2% Paramodulation (378 calls)
% 23.27/23.49 ; 0.004 0% Embedding (362 calls)
% 23.27/23.49 ; 0.090 0% Condensing (2,727 calls)
% 23.27/23.49 ; 0.208 1% Forward subsumption (2,727 calls)
% 23.27/23.49 ; 0.064 0% Backward subsumption (1,245 calls)
% 23.27/23.49 ; 0.132 1% Clause clause subsumption (13,897 calls)
% 23.27/23.49 ; 20.580 89% Forward simplification (38,899 calls)
% 23.27/23.49 ; 0.274 1% Backward simplification (5,516 calls)
% 23.27/23.49 ; 0.131 1% Ordering (36,223 calls)
% 23.27/23.49 ; 0.062 0% Ordering ac (5,073 calls)
% 23.27/23.49 ; 0.000 0% Sortal reasoning (32 calls)
% 23.27/23.49 ; 0.000 0% Purity testing (1 call)
% 23.27/23.49 ; 0.154 1% Other
% 23.27/23.49 ; 23.016 Total
% 23.27/23.49 ; 23.025 Real time
% 23.27/23.49 ;
% 23.27/23.49 ; Term-hash-array has 11,400 terms in all.
% 23.27/23.49 ; Feature-vector-row-index has 1,088 entries (1,096 at peak, 1,245 added, 157 deleted).
% 23.27/23.49 ; Feature-vector-row-index has 7,165 nodes (7,212 at peak, 8,540 added, 1,375 deleted).
% 23.27/23.49 ; Retrieved 17,616 possibly forward subsuming rows in 2,727 calls.
% 23.27/23.49 ; Retrieved 1,878 possibly backward subsumed rows in 1,245 calls.
% 23.27/23.49 ; Path-index has 9,129 entries (9,204 at peak, 11,740 added, 2,611 deleted).
% 23.27/23.49 ; Path-index has 3,744 nodes (3,799 at peak, 4,253 added, 509 deleted).
% 23.27/23.49 ; Trie-index has 9,129 entries (9,204 at peak, 11,740 added, 2,611 deleted).
% 23.27/23.49 ; Trie-index has 3,207 nodes (3,345 at peak, 4,199 added, 992 deleted).
% 23.27/23.49 ; Retrieved 23,583,036 generalization terms in 296,709 calls.
% 23.27/23.49 ; Retrieved 28,173 instance terms in 4,303 calls.
% 23.27/23.49 ; Retrieved 113,543 unifiable terms in 3,150 calls.
% 23.27/23.49 ;
% 23.27/23.49 ; The agenda of rows to process has 157 entries:
% 23.27/23.49 ; 8 with value 19 14 with value 23 7 with value 27
% 23.27/23.49 ; 29 with value 20 22 with value 24 1 with value 28
% 23.27/23.49 ; 38 with value 21 7 with value 25 1 with value 30
% 23.27/23.49 ; 26 with value 22 4 with value 26
% 23.27/23.49 ; The agenda of rows to give has 4247 entries:
% 23.27/23.49 ; 1 with value (4 15) 53 with value (4 34) 13 with value (4 52)
% 23.27/23.49 ; 2 with value (4 17) 55 with value (4 35) 3 with value (4 53)
% 23.27/23.49 ; 155 with value (4 18) 70 with value (4 36) 13 with value (4 54)
% 23.27/23.49 ; 220 with value (4 19) 50 with value (4 37) 13 with value (4 55)
% 23.27/23.49 ; 217 with value (4 20) 47 with value (4 38) 12 with value (4 56)
% 23.27/23.49 ; 304 with value (4 21) 41 with value (4 39) 2 with value (4 57)
% 23.27/23.49 ; 347 with value (4 22) 36 with value (4 40) 4 with value (4 58)
% 23.27/23.49 ; 342 with value (4 23) 30 with value (4 41) 1 with value (4 59)
% 23.27/23.49 ; 287 with value (4 24) 25 with value (4 42) 1 with value (4 60)
% 23.27/23.49 ; 336 with value (4 25) 21 with value (4 43) 1 with value (4 61)
% 23.27/23.49 ; 301 with value (4 26) 21 with value (4 44) 7 with value (4 62)
% 23.27/23.49 ; 207 with value (4 27) 19 with value (4 45) 4 with value (4 63)
% 23.27/23.49 ; 226 with value (4 28) 25 with value (4 46) 5 with value (4 64)
% 23.27/23.49 ; 177 with value (4 29) 21 with value (4 47) 2 with value (4 65)
% 23.27/23.49 ; 139 with value (4 30) 9 with value (4 48) 1 with value (4 69)
% 23.27/23.49 ; 141 with value (4 31) 3 with value (4 49) 1 with value (4 70)
% 23.27/23.49 ; 129 with value (4 32) 13 with value (4 50) 1 with value (4 77)
% 23.27/23.49 ; 80 with value (4 33) 13 with value (4 51)
% 23.27/23.49 Evaluation took:
% 23.27/23.49 23.026 seconds of real time
% 23.27/23.49 22.682892 seconds of user run time
% 23.27/23.49 0.344783 seconds of system run time
% 23.27/23.49 [Run times include 0.999 seconds GC run time.]
% 23.27/23.49 0 calls to %EVAL
% 23.27/23.49 0 page faults and
% 23.27/23.49 1,714,084,912 bytes consed.
% 23.27/23.49 :PROOF-FOUND
% 23.27/23.49 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-16T16:50:29
% 23.27/23.49 :PROOF-FOUND
% 23.27/23.49 *
%------------------------------------------------------------------------------