TSTP Solution File: KLE009+4 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : KLE009+4 : 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 02:26:06 EDT 2022
% Result : Theorem 2.60s 2.79s
% Output : Refutation 2.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of clauses : 46 ( 32 unt; 0 nHn; 36 RR)
% Number of literals : 65 ( 32 equ; 23 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
addition(X,X) = X,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
cnf(5,axiom,
multiplication(X,one) = X,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
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(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('SKOLEMAAAV1'(X),X) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).
cnf(14,axiom,
( test(X)
| ~ complement(Y,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,axiom,
( ~ test(X)
| ~ test(Y)
| c(addition(X,Y)) = multiplication(c(X),c(Y)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+2.ax',test_deMorgan1) ).
cnf(24,negated_conjecture,
test('SKOLEMAAAV3'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(25,negated_conjecture,
test('SKOLEMAAAV2'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(26,negated_conjecture,
( ~ leq(one,addition(multiplication('SKOLEMAAAV2','SKOLEMAAAV3'),addition(multiplication('SKOLEMAAAV2',c('SKOLEMAAAV3')),addition(multiplication(c('SKOLEMAAAV2'),'SKOLEMAAAV3'),multiplication(c('SKOLEMAAAV2'),c('SKOLEMAAAV3'))))))
| ~ leq(addition(multiplication('SKOLEMAAAV2','SKOLEMAAAV3'),addition(multiplication('SKOLEMAAAV2',c('SKOLEMAAAV3')),addition(multiplication(c('SKOLEMAAAV2'),'SKOLEMAAAV3'),multiplication(c('SKOLEMAAAV2'),c('SKOLEMAAAV3'))))),one) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(27,plain,
complement('SKOLEMAAAV1'('SKOLEMAAAV3'),'SKOLEMAAAV3'),
inference('HYPERRESOLVE',[status(thm)],[13,24]) ).
cnf(31,plain,
leq(X,X),
inference('HYPERRESOLVE',[status(thm)],[12,2]) ).
cnf(36,plain,
complement('SKOLEMAAAV3',c('SKOLEMAAAV3')),
inference('HYPERRESOLVE',[status(thm)],[19,24,theory(equality)]) ).
cnf(37,plain,
complement('SKOLEMAAAV2',c('SKOLEMAAAV2')),
inference('HYPERRESOLVE',[status(thm)],[19,25,theory(equality)]) ).
cnf(51,plain,
c(addition('SKOLEMAAAV3','SKOLEMAAAV2')) = multiplication(c('SKOLEMAAAV3'),c('SKOLEMAAAV2')),
inference('HYPERRESOLVE',[status(thm)],[22,24,25]) ).
cnf(52,plain,
c(addition('SKOLEMAAAV3','SKOLEMAAAV2')) = multiplication(c('SKOLEMAAAV2'),c('SKOLEMAAAV3')),
inference('HYPERRESOLVE',[status(thm)],[22,25,24]) ).
cnf(53,plain,
( ~ leq(one,addition(multiplication('SKOLEMAAAV2','SKOLEMAAAV3'),addition(multiplication('SKOLEMAAAV2',c('SKOLEMAAAV3')),addition(multiplication(c('SKOLEMAAAV2'),'SKOLEMAAAV3'),c(addition('SKOLEMAAAV3','SKOLEMAAAV2'))))))
| ~ leq(addition(multiplication('SKOLEMAAAV2','SKOLEMAAAV3'),addition(multiplication('SKOLEMAAAV2',c('SKOLEMAAAV3')),addition(multiplication(c('SKOLEMAAAV2'),'SKOLEMAAAV3'),c(addition('SKOLEMAAAV3','SKOLEMAAAV2'))))),one) ),
inference('REWRITE',[status(thm)],[26,52,theory(equality)]) ).
cnf(106,plain,
addition('SKOLEMAAAV1'('SKOLEMAAAV3'),'SKOLEMAAAV3') = one,
inference('HYPERRESOLVE',[status(thm)],[17,27]) ).
cnf(108,plain,
multiplication('SKOLEMAAAV1'('SKOLEMAAAV3'),'SKOLEMAAAV3') = zero,
inference('HYPERRESOLVE',[status(thm)],[16,27]) ).
cnf(109,plain,
multiplication('SKOLEMAAAV3','SKOLEMAAAV1'('SKOLEMAAAV3')) = zero,
inference('HYPERRESOLVE',[status(thm)],[15,27]) ).
cnf(116,plain,
test(c('SKOLEMAAAV3')),
inference('HYPERRESOLVE',[status(thm)],[14,36]) ).
cnf(122,plain,
addition('SKOLEMAAAV2',c('SKOLEMAAAV2')) = one,
inference('HYPERRESOLVE',[status(thm)],[17,37]) ).
cnf(134,plain,
c(addition(c('SKOLEMAAAV3'),'SKOLEMAAAV2')) = multiplication(c(c('SKOLEMAAAV3')),c('SKOLEMAAAV2')),
inference('HYPERRESOLVE',[status(thm)],[22,116,25]) ).
cnf(137,plain,
c(addition(c('SKOLEMAAAV3'),'SKOLEMAAAV2')) = multiplication(c('SKOLEMAAAV2'),c(c('SKOLEMAAAV3'))),
inference('HYPERRESOLVE',[status(thm)],[22,116,25]) ).
cnf(178,plain,
X = addition(multiplication('SKOLEMAAAV1'('SKOLEMAAAV3'),X),multiplication('SKOLEMAAAV3',X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,106,theory(equality)]),6,theory(equality)]) ).
cnf(180,plain,
X = addition(multiplication(X,'SKOLEMAAAV1'('SKOLEMAAAV3')),multiplication(X,'SKOLEMAAAV3')),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[7,106,theory(equality)]),5,theory(equality)]) ).
cnf(182,plain,
complement('SKOLEMAAAV3','SKOLEMAAAV1'('SKOLEMAAAV3')),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[18,106,theory(equality)]),109,108,theory(equality)]) ).
cnf(188,plain,
c('SKOLEMAAAV3') = 'SKOLEMAAAV1'('SKOLEMAAAV3'),
inference('HYPERRESOLVE',[status(thm)],[20,182,24]) ).
cnf(189,plain,
complement(c('SKOLEMAAAV3'),'SKOLEMAAAV3'),
inference('REWRITE',[status(thm)],[27,188,theory(equality)]) ).
cnf(194,plain,
X = addition(multiplication(c('SKOLEMAAAV3'),X),multiplication('SKOLEMAAAV3',X)),
inference('REWRITE',[status(thm)],[178,188,theory(equality)]) ).
cnf(196,plain,
X = addition(multiplication(X,c('SKOLEMAAAV3')),multiplication(X,'SKOLEMAAAV3')),
inference('REWRITE',[status(thm)],[180,188,theory(equality)]) ).
cnf(198,plain,
( ~ leq(one,addition(multiplication(c('SKOLEMAAAV2'),'SKOLEMAAAV3'),addition(c(addition('SKOLEMAAAV3','SKOLEMAAAV2')),'SKOLEMAAAV2')))
| ~ leq(addition(multiplication(c('SKOLEMAAAV2'),'SKOLEMAAAV3'),addition(c(addition('SKOLEMAAAV3','SKOLEMAAAV2')),'SKOLEMAAAV2')),one) ),
inference('REWRITE',[status(thm)],[53,196,theory(equality)]) ).
cnf(199,plain,
c(c('SKOLEMAAAV3')) = 'SKOLEMAAAV3',
inference('HYPERRESOLVE',[status(thm)],[20,189,116]) ).
cnf(201,plain,
c(addition(c('SKOLEMAAAV3'),'SKOLEMAAAV2')) = multiplication('SKOLEMAAAV3',c('SKOLEMAAAV2')),
inference('REWRITE',[status(thm)],[134,199,theory(equality)]) ).
cnf(206,plain,
c(addition(c('SKOLEMAAAV3'),'SKOLEMAAAV2')) = multiplication(c('SKOLEMAAAV2'),'SKOLEMAAAV3'),
inference('REWRITE',[status(thm)],[137,199,theory(equality)]) ).
cnf(207,plain,
( ~ leq(one,addition(c(addition(c('SKOLEMAAAV3'),'SKOLEMAAAV2')),addition(c(addition('SKOLEMAAAV3','SKOLEMAAAV2')),'SKOLEMAAAV2')))
| ~ leq(addition(c(addition(c('SKOLEMAAAV3'),'SKOLEMAAAV2')),addition(c(addition('SKOLEMAAAV3','SKOLEMAAAV2')),'SKOLEMAAAV2')),one) ),
inference('REWRITE',[status(thm)],[198,206,theory(equality)]) ).
cnf(1399,plain,
c('SKOLEMAAAV2') = addition(c(addition('SKOLEMAAAV3','SKOLEMAAAV2')),c(addition(c('SKOLEMAAAV3'),'SKOLEMAAAV2'))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[194,51,theory(equality)]),201,theory(equality)]) ).
cnf(1401,plain,
$false,
inference('REWRITE',[status(thm)],[207,31,122,1399,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : KLE009+4 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : run-snark %s %d
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 16:00:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.44 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 *
% 0.19/0.45 *
% 0.19/0.46 #<PACKAGE "SNARK-USER">
% 0.19/0.46 *
% 0.19/0.46 SNARK-TPTP-OPTIONS
% 0.19/0.46 *
% 0.19/0.46 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.46 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.46 (USE-FACTORING :POS)
% 0.19/0.46 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.46 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.46 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.46 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.46 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.46 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.46 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.46 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.46 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.46 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.46 *
% 0.19/0.46 "."
% 0.19/0.46 *
% 0.19/0.46 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-16T16:00:27
% 0.19/0.46 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n003.cluster.edu at 2022-06-16T16:00:27
% 0.19/0.48
% 0.19/0.48 ; Recognized commutativity assertion (= (|addition| ?X ?Y) (|addition| ?Y ?X)).
% 0.19/0.48 ; Recognized associativity assertion (= (|addition| ?X (|addition| ?Y ?Z)) (|addition| (|addition| ?X ?Y) ?Z)).
% 0.19/0.48 ; Recognized right identity assertion (= (|addition| ?X |zero|) ?X).
% 0.19/0.48 ; Recognized associativity assertion (= (|multiplication| ?X (|multiplication| ?Y ?Z)) (|multiplication| (|multiplication| ?X ?Y) ?Z)).
% 0.19/0.48 ; Recognized right identity assertion (= (|multiplication| ?X |one|) ?X).
% 0.19/0.48 ; Recognized left identity assertion (= (|multiplication| |one| ?X) ?X).
% 0.19/0.48 ; Declaring addition to be commutative.
% 2.60/2.79 ; Declaring addition to be associative-commutative.
% 2.60/2.79
% 2.60/2.79 #||
% 2.60/2.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.60/2.79 % SZS output start Refutation
% See solution above
% 2.60/2.80 ||#
% 2.60/2.80
% 2.60/2.80 ; Summary of computation:
% 2.60/2.80 ; 10732 formulas have been input or derived (from 200 formulas).
% 2.60/2.80 ; 1401 (13%) were retained. Of these,
% 2.60/2.80 ; 149 (11%) were simplified or subsumed later,
% 2.60/2.80 ; 1252 (89%) are still being kept.
% 2.60/2.80 ;
% 2.60/2.80 ; Run time in seconds excluding printing time:
% 2.60/2.80 ; 0.006 0% Read assertion file (1 call)
% 2.60/2.80 ; 0.001 0% Assert (19 calls)
% 2.60/2.80 ; 0.141 6% Process new row (10,368 calls)
% 2.60/2.80 ; 0.036 2% Resolution (398 calls)
% 2.60/2.80 ; 0.117 5% Paramodulation (199 calls)
% 2.60/2.80 ; 0.000 0% Factoring (4 calls)
% 2.60/2.80 ; 0.001 0% Embedding (118 calls)
% 2.60/2.80 ; 0.054 2% Condensing (996 calls)
% 2.60/2.80 ; 0.043 2% Forward subsumption (996 calls)
% 2.60/2.80 ; 0.013 1% Backward subsumption (416 calls)
% 2.60/2.80 ; 0.038 2% Clause clause subsumption (3,048 calls)
% 2.60/2.80 ; 1.776 76% Forward simplification (10,225 calls)
% 2.60/2.80 ; 0.019 1% Backward simplification (1,298 calls)
% 2.60/2.80 ; 0.019 1% Ordering (6,295 calls)
% 2.60/2.80 ; 0.008 0% Ordering ac (891 calls)
% 2.60/2.80 ; 0.000 0% Sortal reasoning (32 calls)
% 2.60/2.80 ; 0.000 0% Purity testing (1 call)
% 2.60/2.80 ; 0.062 3% Other
% 2.60/2.80 ; 2.334 Total
% 2.60/2.80 ; 2.341 Real time
% 2.60/2.80 ;
% 2.60/2.80 ; Term-hash-array has 2,900 terms in all.
% 2.60/2.80 ; Feature-vector-row-index has 382 entries (384 at peak, 416 added, 34 deleted).
% 2.60/2.80 ; Feature-vector-row-index has 1,740 nodes (1,771 at peak, 2,026 added, 286 deleted).
% 2.60/2.80 ; Retrieved 3,955 possibly forward subsuming rows in 996 calls.
% 2.60/2.80 ; Retrieved 518 possibly backward subsumed rows in 416 calls.
% 2.60/2.80 ; Path-index has 2,628 entries (2,630 at peak, 2,936 added, 308 deleted).
% 2.60/2.80 ; Path-index has 795 nodes (798 at peak, 990 added, 195 deleted).
% 2.60/2.80 ; Trie-index has 2,628 entries (2,630 at peak, 2,936 added, 308 deleted).
% 2.60/2.80 ; Trie-index has 1,411 nodes (1,417 at peak, 1,823 added, 412 deleted).
% 2.60/2.80 ; Retrieved 1,871,072 generalization terms in 66,666 calls.
% 2.60/2.80 ; Retrieved 2,950 instance terms in 899 calls.
% 2.60/2.80 ; Retrieved 41,110 unifiable terms in 2,302 calls.
% 2.60/2.80 ;
% 2.60/2.80 ; The agenda of rows to process has 20 entries:
% 2.60/2.80 ; 2 with value 22 3 with value 25 1 with value 30
% 2.60/2.80 ; 2 with value 23 2 with value 26 2 with value 47
% 2.60/2.80 ; 7 with value 24 1 with value 27
% 2.60/2.80 ; The agenda of rows to give has 1075 entries:
% 2.60/2.80 ; 39 with value (4 17) 36 with value (4 32) 8 with value (4 56)
% 2.60/2.80 ; 40 with value (4 18) 22 with value (4 33) 8 with value (4 58)
% 2.60/2.80 ; 90 with value (4 19) 36 with value (4 34) 5 with value (4 59)
% 2.60/2.80 ; 108 with value (4 20) 8 with value (4 35) 1 with value (4 61)
% 2.60/2.80 ; 76 with value (4 21) 20 with value (4 36) 4 with value (4 62)
% 2.60/2.80 ; 33 with value (4 22) 12 with value (4 37) 8 with value (4 63)
% 2.60/2.80 ; 71 with value (4 23) 5 with value (4 38) 8 with value (4 65)
% 2.60/2.80 ; 64 with value (4 24) 16 with value (4 39) 8 with value (4 70)
% 2.60/2.80 ; 87 with value (4 25) 2 with value (4 41) 8 with value (4 77)
% 2.60/2.80 ; 50 with value (4 26) 8 with value (4 42) 2 with value (4 79)
% 2.60/2.80 ; 54 with value (4 27) 4 with value (4 45) 8 with value (4 84)
% 2.60/2.80 ; 31 with value (4 28) 2 with value (4 51) 8 with value (4 97)
% 2.60/2.80 ; 24 with value (4 29) 8 with value (4 53) 8 with value (4 104)
% 2.60/2.80 ; 24 with value (4 30) 4 with value (4 55) 1 with value (4 107)
% 2.60/2.80 ; 16 with value (4 31)
% 2.60/2.80 Evaluation took:
% 2.60/2.80 2.342 seconds of real time
% 2.60/2.80 2.269462 seconds of user run time
% 2.60/2.80 0.072801 seconds of system run time
% 2.60/2.80 [Run times include 0.101 seconds GC run time.]
% 2.60/2.80 0 calls to %EVAL
% 2.60/2.80 0 page faults and
% 2.60/2.80 254,298,008 bytes consed.
% 2.60/2.80 :PROOF-FOUND
% 2.60/2.80 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-16T16:00:29
% 2.60/2.80 :PROOF-FOUND
% 2.60/2.80 *
%------------------------------------------------------------------------------