TSTP Solution File: KLE020+2 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : KLE020+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n015.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 02:26:11 EDT 2022

% Result   : Theorem 4.76s 4.93s
% Output   : Refutation 4.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   19
% Syntax   : Number of clauses     :   45 (  34 unt;   0 nHn;  32 RR)
%            Number of literals    :   60 (  31 equ;  17 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :   36 (   1 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(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('SKOLEMAAAV1'(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('SKOLEMAAAV2'),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

cnf(23,negated_conjecture,
    test('SKOLEMAAAV3'),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

cnf(24,negated_conjecture,
    test('SKOLEMAAAV4'),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

cnf(25,negated_conjecture,
    ( ~ leq(addition('SKOLEMAAAV2',multiplication('SKOLEMAAAV3','SKOLEMAAAV4')),multiplication(addition('SKOLEMAAAV2','SKOLEMAAAV3'),addition('SKOLEMAAAV2','SKOLEMAAAV4')))
    | ~ leq(multiplication(addition('SKOLEMAAAV2','SKOLEMAAAV3'),addition('SKOLEMAAAV2','SKOLEMAAAV4')),addition('SKOLEMAAAV2',multiplication('SKOLEMAAAV3','SKOLEMAAAV4'))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

cnf(26,plain,
    ( ~ leq(addition('SKOLEMAAAV2',multiplication('SKOLEMAAAV3','SKOLEMAAAV4')),addition(multiplication('SKOLEMAAAV2','SKOLEMAAAV2'),addition(multiplication('SKOLEMAAAV2','SKOLEMAAAV4'),addition(multiplication('SKOLEMAAAV3','SKOLEMAAAV2'),multiplication('SKOLEMAAAV3','SKOLEMAAAV4')))))
    | ~ leq(addition(multiplication('SKOLEMAAAV2','SKOLEMAAAV2'),addition(multiplication('SKOLEMAAAV2','SKOLEMAAAV4'),addition(multiplication('SKOLEMAAAV3','SKOLEMAAAV2'),multiplication('SKOLEMAAAV3','SKOLEMAAAV4')))),addition('SKOLEMAAAV2',multiplication('SKOLEMAAAV3','SKOLEMAAAV4'))) ),
    inference('REWRITE',[status(thm)],[25,7,8,theory(equality)]) ).

cnf(27,plain,
    complement('SKOLEMAAAV1'('SKOLEMAAAV4'),'SKOLEMAAAV4'),
    inference('HYPERRESOLVE',[status(thm)],[13,24]) ).

cnf(28,plain,
    complement('SKOLEMAAAV1'('SKOLEMAAAV3'),'SKOLEMAAAV3'),
    inference('HYPERRESOLVE',[status(thm)],[13,23]) ).

cnf(29,plain,
    complement('SKOLEMAAAV1'('SKOLEMAAAV2'),'SKOLEMAAAV2'),
    inference('HYPERRESOLVE',[status(thm)],[13,22]) ).

cnf(32,plain,
    leq(X,X),
    inference('HYPERRESOLVE',[status(thm)],[12,2]) ).

cnf(33,plain,
    leq(X,addition(X,Y)),
    inference('HYPERRESOLVE',[status(thm)],[12,3]) ).

cnf(39,plain,
    complement('SKOLEMAAAV2',c('SKOLEMAAAV2')),
    inference('HYPERRESOLVE',[status(thm)],[19,22,theory(equality)]) ).

cnf(81,plain,
    addition('SKOLEMAAAV1'('SKOLEMAAAV4'),'SKOLEMAAAV4') = one,
    inference('HYPERRESOLVE',[status(thm)],[17,27]) ).

cnf(86,plain,
    addition('SKOLEMAAAV1'('SKOLEMAAAV3'),'SKOLEMAAAV3') = one,
    inference('HYPERRESOLVE',[status(thm)],[17,28]) ).

cnf(91,plain,
    addition('SKOLEMAAAV1'('SKOLEMAAAV2'),'SKOLEMAAAV2') = one,
    inference('HYPERRESOLVE',[status(thm)],[17,29]) ).

cnf(93,plain,
    multiplication('SKOLEMAAAV1'('SKOLEMAAAV2'),'SKOLEMAAAV2') = zero,
    inference('HYPERRESOLVE',[status(thm)],[16,29]) ).

cnf(94,plain,
    multiplication('SKOLEMAAAV2','SKOLEMAAAV1'('SKOLEMAAAV2')) = zero,
    inference('HYPERRESOLVE',[status(thm)],[15,29]) ).

cnf(110,plain,
    multiplication(c('SKOLEMAAAV2'),'SKOLEMAAAV2') = zero,
    inference('HYPERRESOLVE',[status(thm)],[15,39]) ).

cnf(123,plain,
    leq('SKOLEMAAAV4',one),
    inference('PARAMODULATE',[status(thm)],[33,81,theory(equality)]) ).

cnf(132,plain,
    addition('SKOLEMAAAV4',one) = one,
    inference('HYPERRESOLVE',[status(thm)],[11,123]) ).

cnf(150,plain,
    leq('SKOLEMAAAV3',one),
    inference('PARAMODULATE',[status(thm)],[33,86,theory(equality)]) ).

cnf(159,plain,
    addition('SKOLEMAAAV3',one) = one,
    inference('HYPERRESOLVE',[status(thm)],[11,150]) ).

cnf(181,plain,
    X = addition(multiplication('SKOLEMAAAV1'('SKOLEMAAAV2'),X),multiplication('SKOLEMAAAV2',X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,91,theory(equality)]),6,theory(equality)]) ).

cnf(185,plain,
    complement('SKOLEMAAAV2','SKOLEMAAAV1'('SKOLEMAAAV2')),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[18,91,theory(equality)]),94,93,theory(equality)]) ).

cnf(191,plain,
    c('SKOLEMAAAV2') = 'SKOLEMAAAV1'('SKOLEMAAAV2'),
    inference('HYPERRESOLVE',[status(thm)],[20,185,22]) ).

cnf(197,plain,
    X = addition(multiplication(c('SKOLEMAAAV2'),X),multiplication('SKOLEMAAAV2',X)),
    inference('REWRITE',[status(thm)],[181,191,theory(equality)]) ).

cnf(275,plain,
    X = addition(multiplication(X,'SKOLEMAAAV4'),X),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[7,132,theory(equality)]),5,theory(equality)]) ).

cnf(290,plain,
    X = addition(multiplication('SKOLEMAAAV3',X),X),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,159,theory(equality)]),6,theory(equality)]) ).

cnf(2726,plain,
    'SKOLEMAAAV2' = multiplication('SKOLEMAAAV2','SKOLEMAAAV2'),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[197,110,theory(equality)]),1,theory(equality)]) ).

cnf(2727,plain,
    $false,
    inference('REWRITE',[status(thm)],[26,32,275,290,2726,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : KLE020+2 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13  % Command  : run-snark %s %d
% 0.12/0.34  % Computer : n015.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Thu Jun 16 12:53:26 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.20/0.46  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.47  * 
% 0.20/0.47  * 
% 0.20/0.48  #<PACKAGE "SNARK-USER">
% 0.20/0.48  * 
% 0.20/0.48  SNARK-TPTP-OPTIONS
% 0.20/0.48  * 
% 0.20/0.48  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.48   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.48   (USE-FACTORING :POS)
% 0.20/0.48   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.48   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.48   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.48   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.48   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.48   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.48   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.48   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.48   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.48   (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.48  * 
% 0.20/0.48  "."
% 0.20/0.48  * 
% 0.20/0.48  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-16T12:53:26
% 0.20/0.48  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n015.cluster.edu at 2022-06-16T12:53:26
% 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.
% 4.76/4.93  ; Declaring addition to be associative-commutative.
% 4.76/4.93  
% 4.76/4.93  #||
% 4.76/4.93  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.76/4.93  % SZS output start Refutation
% See solution above
% 4.76/4.93  ||#
% 4.76/4.93  
% 4.76/4.93  ; Summary of computation:
% 4.76/4.93  ;     18944 formulas have been input or derived (from 294 formulas).
% 4.76/4.93  ;      2727 (14%) were retained.  Of these,
% 4.76/4.93  ;          508 (19%) were simplified or subsumed later,
% 4.76/4.93  ;         2219 (81%) are still being kept.
% 4.76/4.94  ; 
% 4.76/4.94  ; Run time in seconds excluding printing time:
% 4.76/4.94  ;     0.004   0%   Read assertion file          (1 call)
% 4.76/4.94  ;     0.002   0%   Assert                       (17 calls)
% 4.76/4.94  ;     0.259   6%   Process new row              (17,731 calls)
% 4.76/4.94  ;     0.077   2%   Resolution                   (586 calls)
% 4.76/4.94  ;     0.223   5%   Paramodulation               (293 calls)
% 4.76/4.94  ;     0.000   0%   Factoring                    (4 calls)
% 4.76/4.94  ;     0.001   0%   Embedding                    (242 calls)
% 4.76/4.94  ;     0.069   2%   Condensing                   (1,382 calls)
% 4.76/4.94  ;     0.072   2%   Forward subsumption          (1,382 calls)
% 4.76/4.94  ;     0.019   0%   Backward subsumption         (564 calls)
% 4.76/4.94  ;     0.028   1%   Clause clause subsumption    (5,143 calls)
% 4.76/4.94  ;     3.500  79%   Forward simplification       (17,437 calls)
% 4.76/4.94  ;     0.066   1%   Backward simplification      (2,487 calls)
% 4.76/4.94  ;     0.027   1%   Ordering                     (11,717 calls)
% 4.76/4.94  ;     0.015   0%   Ordering ac                  (2,325 calls)
% 4.76/4.94  ;     0.001   0%   Sortal reasoning             (32 calls)
% 4.76/4.94  ;     0.000   0%   Purity testing               (1 call)
% 4.76/4.94  ;     0.089   2%   Other
% 4.76/4.94  ;     4.452        Total
% 4.76/4.94  ;     4.457        Real time
% 4.76/4.94  ; 
% 4.76/4.94  ; Term-hash-array has 5,218 terms in all.
% 4.76/4.94  ; Feature-vector-row-index has 495 entries (510 at peak, 564 added, 69 deleted).
% 4.76/4.94  ; Feature-vector-row-index has 2,491 nodes (2,649 at peak, 3,158 added, 667 deleted).
% 4.76/4.94  ;  Retrieved 6,030 possibly forward subsuming rows in 1,382 calls.
% 4.76/4.94  ;  Retrieved 586 possibly backward subsumed rows in 564 calls.
% 4.76/4.94  ; Path-index has 4,356 entries (4,549 at peak, 5,241 added, 885 deleted).
% 4.76/4.94  ; Path-index has 720 nodes (720 at peak, 854 added, 134 deleted).
% 4.76/4.94  ; Trie-index has 4,356 entries (4,549 at peak, 5,241 added, 885 deleted).
% 4.76/4.94  ; Trie-index has 1,933 nodes (1,992 at peak, 2,468 added, 535 deleted).
% 4.76/4.94  ; Retrieved 6,228,603 generalization terms in 93,956 calls.
% 4.76/4.94  ; Retrieved 6,020 instance terms in 1,940 calls.
% 4.76/4.94  ; Retrieved 93,397 unifiable terms in 3,158 calls.
% 4.76/4.94  ; 
% 4.76/4.94  ; The agenda of backward simplifiable rows to process has 98 entries:
% 4.76/4.94  ;    98 with value 0
% 4.76/4.94  ; The agenda of rows to process has 71 entries:
% 4.76/4.94  ;     1 with value 14              7 with value 19               3 with value 25
% 4.76/4.94  ;     1 with value 15             16 with value 20               2 with value 26
% 4.76/4.94  ;     6 with value 16              2 with value 22               1 with value 27
% 4.76/4.94  ;     6 with value 17              1 with value 23               1 with value 30
% 4.76/4.94  ;    14 with value 18              8 with value 24               2 with value 47
% 4.76/4.94  ; The agenda of rows to give has 1964 entries:
% 4.76/4.94  ;     1 with value (4 11)         47 with value (4 30)           6 with value (4 55)
% 4.76/4.94  ;     1 with value (4 13)         10 with value (4 31)          12 with value (4 56)
% 4.76/4.94  ;    99 with value (4 17)         66 with value (4 32)           7 with value (4 59)
% 4.76/4.94  ;   145 with value (4 18)         12 with value (4 33)           1 with value (4 61)
% 4.76/4.94  ;   190 with value (4 19)         48 with value (4 34)           6 with value (4 63)
% 4.76/4.94  ;   250 with value (4 20)          6 with value (4 35)          12 with value (4 65)
% 4.76/4.94  ;   141 with value (4 21)         26 with value (4 36)           8 with value (4 67)
% 4.76/4.94  ;    72 with value (4 22)         12 with value (4 37)           8 with value (4 68)
% 4.76/4.94  ;   124 with value (4 23)          5 with value (4 38)          12 with value (4 70)
% 4.76/4.94  ;   153 with value (4 24)         14 with value (4 39)          12 with value (4 77)
% 4.76/4.94  ;   136 with value (4 25)          2 with value (4 41)           2 with value (4 79)
% 4.76/4.94  ;   117 with value (4 26)          6 with value (4 46)           8 with value (4 93)
% 4.76/4.94  ;    56 with value (4 27)          8 with value (4 47)          12 with value (4 97)
% 4.76/4.94  ;    52 with value (4 28)          2 with value (4 51)           1 with value (4 107)
% 4.76/4.94  ;    32 with value (4 29)         24 with value (4 53)
% 4.76/4.94  Evaluation took:
% 4.76/4.94    4.458 seconds of real time
% 4.76/4.94    4.323028 seconds of user run time
% 4.76/4.94    0.133645 seconds of system run time
% 4.76/4.94    [Run times include 0.173 seconds GC run time.]
% 4.76/4.94    0 calls to %EVAL
% 4.76/4.94    0 page faults and
% 4.76/4.94    399,058,200 bytes consed.
% 4.76/4.94  :PROOF-FOUND
% 4.76/4.94  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-16T12:53:30
% 4.76/4.94  :PROOF-FOUND
% 4.76/4.94  * 
%------------------------------------------------------------------------------