TSTP Solution File: KLE011+2 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : KLE011+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n021.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 02:26:07 EDT 2022

% Result   : Theorem 0.74s 0.92s
% Output   : Refutation 0.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   17
% Syntax   : Number of clauses     :   45 (  33 unt;   0 nHn;  31 RR)
%            Number of literals    :   61 (  32 equ;  21 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    7 (   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   :   38 (   1 sgn)

% Comments : 
%------------------------------------------------------------------------------
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(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(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('SKOLEMAAAW3'),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

cnf(23,negated_conjecture,
    test('SKOLEMAAAW2'),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

cnf(24,negated_conjecture,
    ( ~ leq(one,addition(multiplication(addition('SKOLEMAAAW3',c('SKOLEMAAAW3')),'SKOLEMAAAW2'),addition(multiplication(addition('SKOLEMAAAW2',c('SKOLEMAAAW2')),'SKOLEMAAAW3'),multiplication(c('SKOLEMAAAW2'),c('SKOLEMAAAW3')))))
    | ~ leq(addition(multiplication(addition('SKOLEMAAAW3',c('SKOLEMAAAW3')),'SKOLEMAAAW2'),addition(multiplication(addition('SKOLEMAAAW2',c('SKOLEMAAAW2')),'SKOLEMAAAW3'),multiplication(c('SKOLEMAAAW2'),c('SKOLEMAAAW3')))),one) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

cnf(25,plain,
    ( ~ leq(one,addition(multiplication('SKOLEMAAAW3','SKOLEMAAAW2'),addition(multiplication(c('SKOLEMAAAW3'),'SKOLEMAAAW2'),addition(multiplication('SKOLEMAAAW2','SKOLEMAAAW3'),addition(multiplication(c('SKOLEMAAAW2'),'SKOLEMAAAW3'),multiplication(c('SKOLEMAAAW2'),c('SKOLEMAAAW3')))))))
    | ~ leq(addition(multiplication('SKOLEMAAAW3','SKOLEMAAAW2'),addition(multiplication(c('SKOLEMAAAW3'),'SKOLEMAAAW2'),addition(multiplication('SKOLEMAAAW2','SKOLEMAAAW3'),addition(multiplication(c('SKOLEMAAAW2'),'SKOLEMAAAW3'),multiplication(c('SKOLEMAAAW2'),c('SKOLEMAAAW3')))))),one) ),
    inference('REWRITE',[status(thm)],[24,8,theory(equality)]) ).

cnf(26,plain,
    complement('SKOLEMAAAW1'('SKOLEMAAAW3'),'SKOLEMAAAW3'),
    inference('HYPERRESOLVE',[status(thm)],[13,22]) ).

cnf(27,plain,
    complement('SKOLEMAAAW1'('SKOLEMAAAW2'),'SKOLEMAAAW2'),
    inference('HYPERRESOLVE',[status(thm)],[13,23]) ).

cnf(31,plain,
    leq(X,addition(X,Y)),
    inference('HYPERRESOLVE',[status(thm)],[12,3]) ).

cnf(36,plain,
    complement('SKOLEMAAAW2',c('SKOLEMAAAW2')),
    inference('HYPERRESOLVE',[status(thm)],[19,23,theory(equality)]) ).

cnf(78,plain,
    addition('SKOLEMAAAW1'('SKOLEMAAAW3'),'SKOLEMAAAW3') = one,
    inference('HYPERRESOLVE',[status(thm)],[17,26]) ).

cnf(80,plain,
    multiplication('SKOLEMAAAW1'('SKOLEMAAAW3'),'SKOLEMAAAW3') = zero,
    inference('HYPERRESOLVE',[status(thm)],[16,26]) ).

cnf(81,plain,
    multiplication('SKOLEMAAAW3','SKOLEMAAAW1'('SKOLEMAAAW3')) = zero,
    inference('HYPERRESOLVE',[status(thm)],[15,26]) ).

cnf(83,plain,
    addition('SKOLEMAAAW1'('SKOLEMAAAW2'),'SKOLEMAAAW2') = one,
    inference('HYPERRESOLVE',[status(thm)],[17,27]) ).

cnf(94,plain,
    addition('SKOLEMAAAW2',c('SKOLEMAAAW2')) = one,
    inference('HYPERRESOLVE',[status(thm)],[17,36]) ).

cnf(108,plain,
    leq('SKOLEMAAAW3',one),
    inference('PARAMODULATE',[status(thm)],[31,78,theory(equality)]) ).

cnf(112,plain,
    X = addition(multiplication('SKOLEMAAAW1'('SKOLEMAAAW3'),X),multiplication('SKOLEMAAAW3',X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,78,theory(equality)]),6,theory(equality)]) ).

cnf(114,plain,
    X = addition(multiplication(X,'SKOLEMAAAW1'('SKOLEMAAAW3')),multiplication(X,'SKOLEMAAAW3')),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[7,78,theory(equality)]),5,theory(equality)]) ).

cnf(116,plain,
    complement('SKOLEMAAAW3','SKOLEMAAAW1'('SKOLEMAAAW3')),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[18,78,theory(equality)]),81,80,theory(equality)]) ).

cnf(117,plain,
    addition('SKOLEMAAAW3',one) = one,
    inference('HYPERRESOLVE',[status(thm)],[11,108]) ).

cnf(122,plain,
    c('SKOLEMAAAW3') = 'SKOLEMAAAW1'('SKOLEMAAAW3'),
    inference('HYPERRESOLVE',[status(thm)],[20,116,22]) ).

cnf(128,plain,
    X = addition(multiplication(c('SKOLEMAAAW3'),X),multiplication('SKOLEMAAAW3',X)),
    inference('REWRITE',[status(thm)],[112,122,theory(equality)]) ).

cnf(130,plain,
    ( ~ leq(one,addition(multiplication('SKOLEMAAAW2','SKOLEMAAAW3'),addition(multiplication(c('SKOLEMAAAW2'),'SKOLEMAAAW3'),addition(multiplication(c('SKOLEMAAAW2'),c('SKOLEMAAAW3')),'SKOLEMAAAW2'))))
    | ~ leq(addition(multiplication('SKOLEMAAAW2','SKOLEMAAAW3'),addition(multiplication(c('SKOLEMAAAW2'),'SKOLEMAAAW3'),addition(multiplication(c('SKOLEMAAAW2'),c('SKOLEMAAAW3')),'SKOLEMAAAW2'))),one) ),
    inference('REWRITE',[status(thm)],[25,128,theory(equality)]) ).

cnf(131,plain,
    X = addition(multiplication(X,c('SKOLEMAAAW3')),multiplication(X,'SKOLEMAAAW3')),
    inference('REWRITE',[status(thm)],[114,122,theory(equality)]) ).

cnf(133,plain,
    ~ leq(addition(multiplication('SKOLEMAAAW2','SKOLEMAAAW3'),one),one),
    inference('REWRITE',[status(thm)],[130,31,94,131,theory(equality)]) ).

cnf(136,plain,
    addition(multiplication('SKOLEMAAAW2','SKOLEMAAAW3'),one) != one,
    inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[12,133]),2,theory(equality)]) ).

cnf(138,plain,
    leq('SKOLEMAAAW2',one),
    inference('PARAMODULATE',[status(thm)],[31,83,theory(equality)]) ).

cnf(147,plain,
    addition('SKOLEMAAAW2',one) = one,
    inference('HYPERRESOLVE',[status(thm)],[11,138]) ).

cnf(148,plain,
    addition('SKOLEMAAAW2',addition(one,X)) = addition(one,X),
    inference('EMBED',[status(thm)],[147]) ).

cnf(214,plain,
    X = addition(multiplication(X,'SKOLEMAAAW3'),X),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[7,117,theory(equality)]),5,theory(equality)]) ).

cnf(215,plain,
    addition(multiplication(X,'SKOLEMAAAW3'),addition(X,Y)) = addition(X,Y),
    inference('EMBED',[status(thm)],[214]) ).

cnf(418,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[148,215,theory(equality)]),136,147,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : KLE011+2 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.15  % Command  : run-snark %s %d
% 0.15/0.37  % Computer : n021.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 600
% 0.15/0.37  % DateTime : Thu Jun 16 10:04:14 EDT 2022
% 0.15/0.37  % CPUTime  : 
% 0.23/0.51  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.52  * 
% 0.23/0.52  * 
% 0.23/0.53  #<PACKAGE "SNARK-USER">
% 0.23/0.53  * 
% 0.23/0.53  SNARK-TPTP-OPTIONS
% 0.23/0.53  * 
% 0.23/0.53  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.23/0.53   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.23/0.53   (USE-FACTORING :POS)
% 0.23/0.53   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.23/0.53   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.23/0.53   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.23/0.53   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.23/0.53   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.23/0.53   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.23/0.53   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.23/0.53   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.23/0.53   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.23/0.53   (DECLARE-TPTP-SYMBOLS2))
% 0.23/0.53  * 
% 0.23/0.53  "."
% 0.23/0.53  * 
% 0.23/0.53  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-16T10:04:15
% 0.23/0.53  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n021.cluster.edu at 2022-06-16T10:04:15
% 0.23/0.55  
% 0.23/0.55  ; Recognized commutativity assertion (= (|addition| ?X ?Y) (|addition| ?Y ?X)).
% 0.23/0.55  ; Recognized associativity assertion (= (|addition| ?X (|addition| ?Y ?Z)) (|addition| (|addition| ?X ?Y) ?Z)).
% 0.23/0.55  ; Recognized right identity assertion (= (|addition| ?X |zero|) ?X).
% 0.23/0.55  ; Recognized associativity assertion (= (|multiplication| ?X (|multiplication| ?Y ?Z)) (|multiplication| (|multiplication| ?X ?Y) ?Z)).
% 0.23/0.55  ; Recognized right identity assertion (= (|multiplication| ?X |one|) ?X).
% 0.23/0.55  ; Recognized left identity assertion (= (|multiplication| |one| ?X) ?X).
% 0.23/0.55  ; Declaring addition to be commutative.
% 0.74/0.92  ; Declaring addition to be associative-commutative.
% 0.74/0.92  
% 0.74/0.92  #||
% 0.74/0.92  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.74/0.92  % SZS output start Refutation
% See solution above
% 0.74/0.93  ||#
% 0.74/0.93  
% 0.74/0.93  ; Summary of computation:
% 0.74/0.93  ;      3035 formulas have been input or derived (from 134 formulas).
% 0.74/0.93  ;       418 (14%) were retained.  Of these,
% 0.74/0.93  ;           48 (11%) were simplified or subsumed later,
% 0.74/0.93  ;          370 (89%) are still being kept.
% 0.74/0.93  ; 
% 0.74/0.93  ; Run time in seconds excluding printing time:
% 0.74/0.93  ;     0.005   1%   Read assertion file          (1 call)
% 0.74/0.93  ;     0.001   0%   Assert                       (17 calls)
% 0.74/0.93  ;     0.043  11%   Process new row              (2,595 calls)
% 0.74/0.93  ;     0.023   6%   Resolution                   (266 calls)
% 0.74/0.93  ;     0.036   9%   Paramodulation               (133 calls)
% 0.74/0.93  ;     0.000   0%   Factoring                    (4 calls)
% 0.74/0.93  ;     0.000   0%   Embedding                    (44 calls)
% 0.74/0.93  ;     0.034   9%   Condensing                   (422 calls)
% 0.74/0.93  ;     0.021   5%   Forward subsumption          (422 calls)
% 0.74/0.93  ;     0.008   2%   Backward subsumption         (192 calls)
% 0.74/0.93  ;     0.010   3%   Clause clause subsumption    (917 calls)
% 0.74/0.93  ;     0.151  39%   Forward simplification       (2,530 calls)
% 0.74/0.93  ;     0.007   2%   Backward simplification      (376 calls)
% 0.74/0.93  ;     0.009   2%   Ordering                     (1,804 calls)
% 0.74/0.93  ;     0.001   0%   Ordering ac                  (255 calls)
% 0.74/0.93  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.74/0.93  ;     0.001   0%   Purity testing               (1 call)
% 0.74/0.93  ;     0.035   9%   Other
% 0.74/0.93  ;     0.385        Total
% 0.74/0.93  ;     0.395        Real time
% 0.74/0.93  ; 
% 0.74/0.93  ; Term-hash-array has 938 terms in all.
% 0.74/0.93  ; Feature-vector-row-index has 180 entries (180 at peak, 192 added, 12 deleted).
% 0.74/0.93  ; Feature-vector-row-index has 1,048 nodes (1,048 at peak, 1,154 added, 106 deleted).
% 0.74/0.93  ;  Retrieved 1,122 possibly forward subsuming rows in 422 calls.
% 0.74/0.93  ;  Retrieved 114 possibly backward subsumed rows in 192 calls.
% 0.74/0.93  ; Path-index has 856 entries (856 at peak, 954 added, 98 deleted).
% 0.74/0.93  ; Path-index has 487 nodes (487 at peak, 572 added, 85 deleted).
% 0.74/0.93  ; Trie-index has 856 entries (856 at peak, 954 added, 98 deleted).
% 0.74/0.93  ; Trie-index has 682 nodes (682 at peak, 789 added, 107 deleted).
% 0.74/0.93  ; Retrieved 123,531 generalization terms in 14,391 calls.
% 0.74/0.93  ; Retrieved 333 instance terms in 201 calls.
% 0.74/0.93  ; Retrieved 11,620 unifiable terms in 1,292 calls.
% 0.74/0.93  ; 
% 0.74/0.93  ; The agenda of rows to process has 274 entries:
% 0.74/0.93  ;     5 with value 18              9 with value 30               6 with value 41
% 0.74/0.93  ;    18 with value 19              6 with value 31               1 with value 43
% 0.74/0.93  ;    17 with value 20             13 with value 32               2 with value 44
% 0.74/0.93  ;    18 with value 21              6 with value 33               1 with value 45
% 0.74/0.93  ;    16 with value 22              2 with value 34               2 with value 46
% 0.74/0.93  ;    19 with value 23             15 with value 35               1 with value 48
% 0.74/0.93  ;    14 with value 24              1 with value 36               4 with value 49
% 0.74/0.93  ;    17 with value 25              2 with value 37               1 with value 51
% 0.74/0.93  ;    11 with value 26              2 with value 38               4 with value 57
% 0.74/0.93  ;    20 with value 27              4 with value 39               4 with value 66
% 0.74/0.93  ;    19 with value 28              2 with value 40               2 with value 74
% 0.74/0.93  ;    10 with value 29
% 0.74/0.93  ; The agenda of rows to give has 247 entries:
% 0.74/0.93  ;     7 with value (4 15)          8 with value (4 28)           2 with value (4 51)
% 0.74/0.93  ;    19 with value (4 16)          5 with value (4 29)           4 with value (4 53)
% 0.74/0.93  ;    26 with value (4 17)          4 with value (4 30)           4 with value (4 55)
% 0.74/0.93  ;    16 with value (4 18)          1 with value (4 32)           2 with value (4 56)
% 0.74/0.93  ;    13 with value (4 19)          4 with value (4 33)           5 with value (4 59)
% 0.74/0.93  ;    16 with value (4 20)          9 with value (4 34)           1 with value (4 61)
% 0.74/0.93  ;    11 with value (4 21)         12 with value (4 36)           4 with value (4 63)
% 0.74/0.93  ;     4 with value (4 22)          4 with value (4 37)           2 with value (4 65)
% 0.74/0.93  ;    12 with value (4 23)          4 with value (4 38)           2 with value (4 77)
% 0.74/0.93  ;     6 with value (4 24)          8 with value (4 39)           2 with value (4 79)
% 0.74/0.93  ;    14 with value (4 25)          2 with value (4 41)           2 with value (4 97)
% 0.74/0.93  ;     3 with value (4 26)          4 with value (4 46)           1 with value (4 107)
% 0.74/0.93  ;     4 with value (4 27)
% 0.74/0.93  Evaluation took:
% 0.74/0.93    0.396 seconds of real time
% 0.74/0.93    0.365571 seconds of user run time
% 0.74/0.93    0.029751 seconds of system run time
% 0.74/0.93    [Run times include 0.012 seconds GC run time.]
% 0.74/0.93    0 calls to %EVAL
% 0.74/0.93    0 page faults and
% 0.74/0.93    27,840,376 bytes consed.
% 0.74/0.93  :PROOF-FOUND
% 0.74/0.93  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-16T10:04:15
% 0.74/0.93  :PROOF-FOUND
% 0.74/0.93  * 
%------------------------------------------------------------------------------