TSTP Solution File: KLE027+2 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : KLE027+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n016.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 02:26:15 EDT 2022
% Result : Theorem 1.82s 2.05s
% Output : Refutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 18
% Syntax : Number of clauses : 43 ( 31 unt; 0 nHn; 26 RR)
% Number of literals : 59 ( 31 equ; 20 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 43 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
addition(X,zero) = X,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
cnf(2,axiom,
addition(X,X) = X,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_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/KLE001+0.ax',multiplicative_associativity) ).
cnf(6,axiom,
multiplication(one,X) = X,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+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/KLE001+0.ax',right_distributivity) ).
cnf(8,axiom,
multiplication(addition(X,Y),Z) = addition(multiplication(X,Z),multiplication(Y,Z)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
cnf(10,axiom,
multiplication(zero,X) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
cnf(11,axiom,
( ~ leq(X,Y)
| addition(X,Y) = Y ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
cnf(12,axiom,
( leq(X,Y)
| addition(X,Y) != Y ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
cnf(13,axiom,
( ~ test(X)
| complement('SKOLEMAAAW1'(X),X) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).
cnf(15,axiom,
( ~ complement(X,Y)
| multiplication(Y,X) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).
cnf(16,axiom,
( ~ complement(X,Y)
| multiplication(X,Y) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).
cnf(17,axiom,
( ~ complement(X,Y)
| addition(X,Y) = one ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).
cnf(18,axiom,
( complement(X,Y)
| multiplication(Y,X) != zero
| multiplication(X,Y) != zero
| addition(X,Y) != one ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).
cnf(19,axiom,
( ~ test(X)
| c(X) != Y
| complement(X,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).
cnf(20,axiom,
( ~ test(X)
| c(X) = Y
| ~ complement(X,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).
cnf(22,negated_conjecture,
test('SKOLEMAAAW5'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(24,negated_conjecture,
( ~ leq(addition(multiplication('SKOLEMAAAW5',addition(multiplication('SKOLEMAAAW5','SKOLEMAAAW2'),multiplication(c('SKOLEMAAAW5'),'SKOLEMAAAW3'))),multiplication(c('SKOLEMAAAW5'),'SKOLEMAAAW4')),addition(multiplication('SKOLEMAAAW5','SKOLEMAAAW2'),multiplication(c('SKOLEMAAAW5'),'SKOLEMAAAW4')))
| ~ leq(addition(multiplication('SKOLEMAAAW5','SKOLEMAAAW2'),multiplication(c('SKOLEMAAAW5'),'SKOLEMAAAW4')),addition(multiplication('SKOLEMAAAW5',addition(multiplication('SKOLEMAAAW5','SKOLEMAAAW2'),multiplication(c('SKOLEMAAAW5'),'SKOLEMAAAW3'))),multiplication(c('SKOLEMAAAW5'),'SKOLEMAAAW4'))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(25,plain,
( ~ leq(addition(multiplication('SKOLEMAAAW5',multiplication('SKOLEMAAAW5','SKOLEMAAAW2')),addition(multiplication('SKOLEMAAAW5',multiplication(c('SKOLEMAAAW5'),'SKOLEMAAAW3')),multiplication(c('SKOLEMAAAW5'),'SKOLEMAAAW4'))),addition(multiplication('SKOLEMAAAW5','SKOLEMAAAW2'),multiplication(c('SKOLEMAAAW5'),'SKOLEMAAAW4')))
| ~ leq(addition(multiplication('SKOLEMAAAW5','SKOLEMAAAW2'),multiplication(c('SKOLEMAAAW5'),'SKOLEMAAAW4')),addition(multiplication('SKOLEMAAAW5',multiplication('SKOLEMAAAW5','SKOLEMAAAW2')),addition(multiplication('SKOLEMAAAW5',multiplication(c('SKOLEMAAAW5'),'SKOLEMAAAW3')),multiplication(c('SKOLEMAAAW5'),'SKOLEMAAAW4')))) ),
inference('REWRITE',[status(thm)],[24,7,theory(equality)]) ).
cnf(27,plain,
complement('SKOLEMAAAW1'('SKOLEMAAAW5'),'SKOLEMAAAW5'),
inference('HYPERRESOLVE',[status(thm)],[13,22]) ).
cnf(30,plain,
leq(X,X),
inference('HYPERRESOLVE',[status(thm)],[12,2]) ).
cnf(31,plain,
leq(X,addition(X,Y)),
inference('HYPERRESOLVE',[status(thm)],[12,3]) ).
cnf(36,plain,
complement('SKOLEMAAAW5',c('SKOLEMAAAW5')),
inference('HYPERRESOLVE',[status(thm)],[19,22,theory(equality)]) ).
cnf(83,plain,
addition('SKOLEMAAAW1'('SKOLEMAAAW5'),'SKOLEMAAAW5') = one,
inference('HYPERRESOLVE',[status(thm)],[17,27]) ).
cnf(85,plain,
multiplication('SKOLEMAAAW1'('SKOLEMAAAW5'),'SKOLEMAAAW5') = zero,
inference('HYPERRESOLVE',[status(thm)],[16,27]) ).
cnf(86,plain,
multiplication('SKOLEMAAAW5','SKOLEMAAAW1'('SKOLEMAAAW5')) = zero,
inference('HYPERRESOLVE',[status(thm)],[15,27]) ).
cnf(96,plain,
multiplication('SKOLEMAAAW5',c('SKOLEMAAAW5')) = zero,
inference('HYPERRESOLVE',[status(thm)],[16,36]) ).
cnf(97,plain,
multiplication(c('SKOLEMAAAW5'),'SKOLEMAAAW5') = zero,
inference('HYPERRESOLVE',[status(thm)],[15,36]) ).
cnf(135,plain,
leq('SKOLEMAAAW5',one),
inference('PARAMODULATE',[status(thm)],[31,83,theory(equality)]) ).
cnf(139,plain,
X = addition(multiplication('SKOLEMAAAW1'('SKOLEMAAAW5'),X),multiplication('SKOLEMAAAW5',X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,83,theory(equality)]),6,theory(equality)]) ).
cnf(143,plain,
complement('SKOLEMAAAW5','SKOLEMAAAW1'('SKOLEMAAAW5')),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[18,83,theory(equality)]),86,85,theory(equality)]) ).
cnf(144,plain,
addition('SKOLEMAAAW5',one) = one,
inference('HYPERRESOLVE',[status(thm)],[11,135]) ).
cnf(149,plain,
c('SKOLEMAAAW5') = 'SKOLEMAAAW1'('SKOLEMAAAW5'),
inference('HYPERRESOLVE',[status(thm)],[20,143,22]) ).
cnf(155,plain,
X = addition(multiplication(c('SKOLEMAAAW5'),X),multiplication('SKOLEMAAAW5',X)),
inference('REWRITE',[status(thm)],[139,149,theory(equality)]) ).
cnf(205,plain,
multiplication('SKOLEMAAAW5',multiplication(c('SKOLEMAAAW5'),X)) = zero,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[4,96,theory(equality)]),10,theory(equality)]) ).
cnf(206,plain,
( ~ leq(addition(multiplication(c('SKOLEMAAAW5'),'SKOLEMAAAW4'),multiplication('SKOLEMAAAW5',multiplication('SKOLEMAAAW5','SKOLEMAAAW2'))),addition(multiplication('SKOLEMAAAW5','SKOLEMAAAW2'),multiplication(c('SKOLEMAAAW5'),'SKOLEMAAAW4')))
| ~ leq(addition(multiplication('SKOLEMAAAW5','SKOLEMAAAW2'),multiplication(c('SKOLEMAAAW5'),'SKOLEMAAAW4')),addition(multiplication(c('SKOLEMAAAW5'),'SKOLEMAAAW4'),multiplication('SKOLEMAAAW5',multiplication('SKOLEMAAAW5','SKOLEMAAAW2')))) ),
inference('REWRITE',[status(thm)],[25,1,205,theory(equality)]) ).
cnf(207,plain,
multiplication(c('SKOLEMAAAW5'),multiplication('SKOLEMAAAW5',X)) = zero,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[4,97,theory(equality)]),10,theory(equality)]) ).
cnf(227,plain,
X = addition(multiplication('SKOLEMAAAW5',X),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,144,theory(equality)]),6,theory(equality)]) ).
cnf(441,plain,
leq(addition(multiplication('SKOLEMAAAW5',X),Y),addition(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[31,227,theory(equality)]),227,7,theory(equality)]) ).
cnf(442,plain,
~ leq(addition(multiplication('SKOLEMAAAW5','SKOLEMAAAW2'),multiplication(c('SKOLEMAAAW5'),'SKOLEMAAAW4')),addition(multiplication(c('SKOLEMAAAW5'),'SKOLEMAAAW4'),multiplication('SKOLEMAAAW5',multiplication('SKOLEMAAAW5','SKOLEMAAAW2')))),
inference('REWRITE',[status(thm)],[206,441]) ).
cnf(1224,plain,
multiplication('SKOLEMAAAW5',X) = multiplication('SKOLEMAAAW5',multiplication('SKOLEMAAAW5',X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[155,207,theory(equality)]),1,theory(equality)]) ).
cnf(1225,plain,
$false,
inference('REWRITE',[status(thm)],[442,30,1224,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.14 % Problem : KLE027+2 : TPTP v8.1.0. Released v4.0.0.
% 0.14/0.15 % Command : run-snark %s %d
% 0.14/0.36 % Computer : n016.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 09:38:34 EDT 2022
% 0.14/0.37 % CPUTime :
% 0.22/0.50 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.51 *
% 0.22/0.51 *
% 0.22/0.51 #<PACKAGE "SNARK-USER">
% 0.22/0.51 *
% 0.22/0.51 SNARK-TPTP-OPTIONS
% 0.22/0.51 *
% 0.22/0.51 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.22/0.51 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.22/0.51 (USE-FACTORING :POS)
% 0.22/0.51 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.22/0.51 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.22/0.51 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.22/0.51 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.22/0.51 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.22/0.51 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.22/0.51 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.22/0.51 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.22/0.51 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.22/0.51 (DECLARE-TPTP-SYMBOLS2))
% 0.22/0.51 *
% 0.22/0.51 "."
% 0.22/0.51 *
% 0.22/0.51 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-16T09:38:34
% 0.22/0.52 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n016.cluster.edu at 2022-06-16T09:38:34
% 0.22/0.53
% 0.22/0.53 ; Recognized commutativity assertion (= (|addition| ?X ?Y) (|addition| ?Y ?X)).
% 0.22/0.53 ; Recognized associativity assertion (= (|addition| ?X (|addition| ?Y ?Z)) (|addition| (|addition| ?X ?Y) ?Z)).
% 0.22/0.53 ; Recognized right identity assertion (= (|addition| ?X |zero|) ?X).
% 0.22/0.53 ; Recognized associativity assertion (= (|multiplication| ?X (|multiplication| ?Y ?Z)) (|multiplication| (|multiplication| ?X ?Y) ?Z)).
% 0.22/0.53 ; Recognized right identity assertion (= (|multiplication| ?X |one|) ?X).
% 0.22/0.53 ; Recognized left identity assertion (= (|multiplication| |one| ?X) ?X).
% 0.22/0.53 ; Declaring addition to be commutative.
% 1.82/2.05 ; Declaring addition to be associative-commutative.
% 1.82/2.05
% 1.82/2.05 #||
% 1.82/2.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.82/2.05 % SZS output start Refutation
% See solution above
% 1.82/2.05 ||#
% 1.82/2.05
% 1.82/2.05 ; Summary of computation:
% 1.82/2.05 ; 8530 formulas have been input or derived (from 186 formulas).
% 1.82/2.05 ; 1225 (14%) were retained. Of these,
% 1.82/2.05 ; 270 (22%) were simplified or subsumed later,
% 1.82/2.05 ; 955 (78%) are still being kept.
% 1.82/2.05 ;
% 1.82/2.05 ; Run time in seconds excluding printing time:
% 1.82/2.05 ; 0.005 0% Read assertion file (1 call)
% 1.82/2.05 ; 0.001 0% Assert (17 calls)
% 1.82/2.05 ; 0.126 8% Process new row (8,081 calls)
% 1.82/2.05 ; 0.038 2% Resolution (370 calls)
% 1.82/2.05 ; 0.103 7% Paramodulation (185 calls)
% 1.82/2.05 ; 0.000 0% Factoring (4 calls)
% 1.82/2.05 ; 0.000 0% Embedding (112 calls)
% 1.82/2.05 ; 0.046 3% Condensing (890 calls)
% 1.82/2.05 ; 0.054 4% Forward subsumption (890 calls)
% 1.82/2.05 ; 0.015 1% Backward subsumption (352 calls)
% 1.82/2.05 ; 0.024 2% Clause clause subsumption (3,011 calls)
% 1.82/2.05 ; 1.004 65% Forward simplification (7,932 calls)
% 1.82/2.05 ; 0.028 2% Backward simplification (1,115 calls)
% 1.82/2.05 ; 0.021 1% Ordering (5,290 calls)
% 1.82/2.05 ; 0.006 0% Ordering ac (944 calls)
% 1.82/2.05 ; 0.000 0% Sortal reasoning (32 calls)
% 1.82/2.05 ; 0.000 0% Purity testing (1 call)
% 1.82/2.05 ; 0.065 4% Other
% 1.82/2.05 ; 1.536 Total
% 1.82/2.05 ; 1.539 Real time
% 1.82/2.05 ;
% 1.82/2.05 ; Term-hash-array has 2,496 terms in all.
% 1.82/2.05 ; Feature-vector-row-index has 304 entries (318 at peak, 352 added, 48 deleted).
% 1.82/2.05 ; Feature-vector-row-index has 1,392 nodes (1,510 at peak, 1,852 added, 460 deleted).
% 1.82/2.05 ; Retrieved 3,868 possibly forward subsuming rows in 890 calls.
% 1.82/2.05 ; Retrieved 392 possibly backward subsumed rows in 352 calls.
% 1.82/2.05 ; Path-index has 2,023 entries (2,167 at peak, 2,528 added, 505 deleted).
% 1.82/2.05 ; Path-index has 601 nodes (616 at peak, 762 added, 161 deleted).
% 1.82/2.05 ; Trie-index has 2,023 entries (2,167 at peak, 2,528 added, 505 deleted).
% 1.82/2.05 ; Trie-index has 1,129 nodes (1,140 at peak, 1,469 added, 340 deleted).
% 1.82/2.05 ; Retrieved 1,219,282 generalization terms in 45,880 calls.
% 1.82/2.05 ; Retrieved 2,224 instance terms in 780 calls.
% 1.82/2.05 ; Retrieved 35,393 unifiable terms in 1,952 calls.
% 1.82/2.05 ;
% 1.82/2.05 ; The agenda of backward simplifiable rows to process has 1 entry:
% 1.82/2.05 ; 1 with value 0
% 1.82/2.05 ; The agenda of rows to process has 30 entries:
% 1.82/2.05 ; 12 with value 20 6 with value 24 1 with value 27
% 1.82/2.05 ; 2 with value 22 3 with value 25 1 with value 30
% 1.82/2.05 ; 1 with value 23 2 with value 26 2 with value 47
% 1.82/2.05 ; The agenda of rows to give has 798 entries:
% 1.82/2.06 ; 1 with value (4 11) 18 with value (4 29) 12 with value (4 53)
% 1.82/2.06 ; 1 with value (4 13) 21 with value (4 30) 4 with value (4 55)
% 1.82/2.06 ; 1 with value (4 15) 4 with value (4 31) 8 with value (4 56)
% 1.82/2.06 ; 1 with value (4 16) 27 with value (4 32) 5 with value (4 59)
% 1.82/2.06 ; 43 with value (4 17) 6 with value (4 33) 1 with value (4 61)
% 1.82/2.06 ; 53 with value (4 18) 22 with value (4 34) 4 with value (4 63)
% 1.82/2.06 ; 75 with value (4 19) 2 with value (4 35) 8 with value (4 65)
% 1.82/2.06 ; 78 with value (4 20) 16 with value (4 36) 4 with value (4 67)
% 1.82/2.06 ; 54 with value (4 21) 8 with value (4 37) 4 with value (4 68)
% 1.82/2.06 ; 26 with value (4 22) 5 with value (4 38) 4 with value (4 70)
% 1.82/2.06 ; 53 with value (4 23) 10 with value (4 39) 8 with value (4 77)
% 1.82/2.06 ; 54 with value (4 24) 2 with value (4 41) 2 with value (4 79)
% 1.82/2.06 ; 57 with value (4 25) 4 with value (4 46) 4 with value (4 93)
% 1.82/2.06 ; 32 with value (4 26) 4 with value (4 47) 8 with value (4 97)
% 1.82/2.06 ; 23 with value (4 27) 2 with value (4 51) 1 with value (4 107)
% 1.82/2.06 ; 18 with value (4 28)
% 1.82/2.06 Evaluation took:
% 1.82/2.06 1.54 seconds of real time
% 1.82/2.06 1.483978 seconds of user run time
% 1.82/2.06 0.056292 seconds of system run time
% 1.82/2.06 [Run times include 0.056 seconds GC run time.]
% 1.82/2.06 0 calls to %EVAL
% 1.82/2.06 0 page faults and
% 1.82/2.06 148,921,616 bytes consed.
% 1.82/2.06 :PROOF-FOUND
% 1.82/2.06 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-16T09:38:35
% 1.82/2.06 :PROOF-FOUND
% 1.82/2.06 *
%------------------------------------------------------------------------------