TSTP Solution File: KLE144+2 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : KLE144+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n008.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 2.96s 3.19s
% Output   : Refutation 3.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   42 (  36 unt;   0 nHn;   8 RR)
%            Number of literals    :   48 (  26 equ;   8 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   :   66 (  13 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    addition(X,zero) = X,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_identity) ).

cnf(2,axiom,
    addition(X,X) = X,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',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/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).

cnf(6,axiom,
    multiplication(one,X) = X,
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/KLE004+0.ax',distributivity1) ).

cnf(8,axiom,
    multiplication(addition(X,Y),Z) = addition(multiplication(X,Z),multiplication(Y,Z)),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',distributivity2) ).

cnf(10,axiom,
    addition(one,multiplication(X,star(X))) = star(X),
    file('/export/starexec/sandbox2/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/sandbox2/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(18,axiom,
    ( ~ leq(X,addition(multiplication(Y,X),Z))
    | leq(X,multiplication(strong_iteration(Y),Z)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).

cnf(21,axiom,
    ( ~ leq(X,Y)
    | addition(X,Y) = Y ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).

cnf(22,axiom,
    ( leq(X,Y)
    | addition(X,Y) != Y ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).

cnf(23,negated_conjecture,
    ( ~ leq(strong_iteration(star('SKOLEMAAAV1')),strong_iteration(one))
    | ~ leq(strong_iteration(one),strong_iteration(star('SKOLEMAAAV1'))) ),
    file('/export/starexec/sandbox2/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(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(224,plain,
    ~ leq(strong_iteration(one),strong_iteration(star('SKOLEMAAAV1'))),
    inference('REWRITE',[status(thm)],[23,223]) ).

cnf(229,plain,
    addition(strong_iteration(one),X) = strong_iteration(one),
    inference('HYPERRESOLVE',[status(thm)],[21,223]) ).

cnf(233,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(234,plain,
    addition(X,addition(multiplication(star(Y),X),Z)) = addition(multiplication(star(Y),X),Z),
    inference('EMBED',[status(thm)],[233]) ).

cnf(365,plain,
    X = addition(X,multiplication(X,zero)),
    inference('PARAMODULATE',[status(thm)],[108,5,theory(equality)]) ).

cnf(366,plain,
    addition(X,addition(multiplication(X,zero),Y)) = addition(X,Y),
    inference('EMBED',[status(thm)],[365]) ).

cnf(1165,plain,
    leq(X,multiplication(star(Y),X)),
    inference('HYPERRESOLVE',[status(thm)],[22,233]) ).

cnf(1263,plain,
    leq(X,multiplication(strong_iteration(star(Y)),zero)),
    inference('HYPERRESOLVE',[status(thm)],[180,1165]) ).

cnf(1285,plain,
    addition(X,multiplication(strong_iteration(star(Y)),zero)) = multiplication(strong_iteration(star(Y)),zero),
    inference('HYPERRESOLVE',[status(thm)],[21,1263]) ).

cnf(1317,plain,
    star(X) = addition(star(X),X),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[13,234,theory(equality)]),12,theory(equality)]) ).

cnf(1458,plain,
    leq(X,star(X)),
    inference('HYPERRESOLVE',[status(thm)],[22,1317]) ).

cnf(1459,plain,
    leq(X,strong_iteration(star(X))),
    inference('REWRITE',[status(thm)],[181,1458]) ).

cnf(1537,plain,
    addition(X,strong_iteration(star(X))) = strong_iteration(star(X)),
    inference('HYPERRESOLVE',[status(thm)],[21,1459]) ).

cnf(1538,plain,
    addition(X,addition(strong_iteration(star(X)),Y)) = addition(strong_iteration(star(X)),Y),
    inference('EMBED',[status(thm)],[1537]) ).

cnf(2332,plain,
    leq(addition(X,Y),addition(strong_iteration(star(X)),addition(Y,Z))),
    inference('PARAMODULATE',[status(thm)],[26,1538,theory(equality)]) ).

cnf(2395,plain,
    multiplication(strong_iteration(star(X)),zero) = strong_iteration(star(X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[366,1538,theory(equality)]),1537,1285,theory(equality)]) ).

cnf(2396,plain,
    addition(X,strong_iteration(star(Y))) = strong_iteration(star(Y)),
    inference('REWRITE',[status(thm)],[1285,2395,theory(equality)]) ).

cnf(2406,plain,
    leq(addition(X,Y),strong_iteration(star(X))),
    inference('REWRITE',[status(thm)],[2332,2396,theory(equality)]) ).

cnf(2412,plain,
    leq(strong_iteration(one),strong_iteration(star(X))),
    inference('PARAMODULATE',[status(thm)],[2406,229,theory(equality)]) ).

cnf(2413,plain,
    $false,
    inference('REWRITE',[status(thm)],[224,2412]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : KLE144+2 : TPTP v8.1.0. Released v4.0.0.
% 0.14/0.13  % Command  : run-snark %s %d
% 0.14/0.35  % Computer : n008.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Thu Jun 16 08:23:22 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.21/0.47  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.48  * 
% 0.21/0.48  * 
% 0.21/0.49  #<PACKAGE "SNARK-USER">
% 0.21/0.49  * 
% 0.21/0.49  SNARK-TPTP-OPTIONS
% 0.21/0.49  * 
% 0.21/0.49  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.21/0.49   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.21/0.49   (USE-FACTORING :POS)
% 0.21/0.49   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.21/0.49   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.21/0.49   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.21/0.49   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.21/0.49   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.21/0.49   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.21/0.49   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.21/0.49   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.21/0.49   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.21/0.49   (DECLARE-TPTP-SYMBOLS2))
% 0.21/0.49  * 
% 0.21/0.49  "."
% 0.21/0.49  * 
% 0.21/0.49  ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-16T08:23:22
% 0.21/0.49  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n008.cluster.edu at 2022-06-16T08:23:22
% 0.21/0.50  
% 0.21/0.50  ; Recognized commutativity assertion (= (|addition| ?X ?Y) (|addition| ?Y ?X)).
% 0.21/0.50  ; Recognized associativity assertion (= (|addition| ?X (|addition| ?Y ?Z)) (|addition| (|addition| ?X ?Y) ?Z)).
% 0.21/0.50  ; Recognized right identity assertion (= (|addition| ?X |zero|) ?X).
% 0.21/0.50  ; Recognized associativity assertion (= (|multiplication| ?X (|multiplication| ?Y ?Z)) (|multiplication| (|multiplication| ?X ?Y) ?Z)).
% 0.21/0.50  ; Recognized right identity assertion (= (|multiplication| ?X |one|) ?X).
% 0.21/0.50  ; Recognized left identity assertion (= (|multiplication| |one| ?X) ?X).
% 0.21/0.50  ; Declaring addition to be commutative.
% 2.96/3.19  ; Declaring addition to be associative-commutative.
% 2.96/3.19  
% 2.96/3.19  #||
% 2.96/3.19  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.96/3.19  % SZS output start Refutation
% See solution above
% 3.02/3.20  ||#
% 3.02/3.20  
% 3.02/3.20  ; Summary of computation:
% 3.02/3.20  ;     14183 formulas have been input or derived (from 211 formulas).
% 3.02/3.20  ;      2413 (17%) were retained.  Of these,
% 3.02/3.20  ;          507 (21%) were simplified or subsumed later,
% 3.02/3.20  ;         1906 (79%) are still being kept.
% 3.02/3.20  ; 
% 3.02/3.20  ; Run time in seconds excluding printing time:
% 3.02/3.20  ;     0.004   0%   Read assertion file          (1 call)
% 3.02/3.20  ;     0.002   0%   Assert                       (19 calls)
% 3.02/3.20  ;     0.231   9%   Process new row              (13,366 calls)
% 3.02/3.20  ;     0.037   1%   Resolution                   (420 calls)
% 3.02/3.20  ;     0.187   7%   Paramodulation               (210 calls)
% 3.02/3.20  ;     0.001   0%   Embedding                    (210 calls)
% 3.02/3.20  ;     0.049   2%   Condensing                   (1,515 calls)
% 3.02/3.20  ;     0.129   5%   Forward subsumption          (1,515 calls)
% 3.02/3.20  ;     0.028   1%   Backward subsumption         (747 calls)
% 3.02/3.20  ;     0.046   2%   Clause clause subsumption    (5,907 calls)
% 3.02/3.20  ;     1.785  66%   Forward simplification       (12,462 calls)
% 3.02/3.20  ;     0.072   3%   Backward simplification      (2,208 calls)
% 3.02/3.20  ;     0.041   2%   Ordering                     (9,775 calls)
% 3.02/3.20  ;     0.013   0%   Ordering ac                  (1,681 calls)
% 3.02/3.20  ;     0.000   0%   Sortal reasoning             (32 calls)
% 3.02/3.20  ;     0.000   0%   Purity testing               (1 call)
% 3.02/3.20  ;     0.071   3%   Other
% 3.02/3.20  ;     2.696        Total
% 3.02/3.20  ;     2.710        Real time
% 3.02/3.20  ; 
% 3.02/3.20  ; Term-hash-array has 4,804 terms in all.
% 3.02/3.20  ; Feature-vector-row-index has 670 entries (672 at peak, 747 added, 77 deleted).
% 3.02/3.20  ; Feature-vector-row-index has 4,569 nodes (4,590 at peak, 5,214 added, 645 deleted).
% 3.02/3.20  ;  Retrieved 6,713 possibly forward subsuming rows in 1,515 calls.
% 3.02/3.20  ;  Retrieved 1,109 possibly backward subsumed rows in 747 calls.
% 3.02/3.20  ; Path-index has 3,926 entries (4,076 at peak, 4,890 added, 964 deleted).
% 3.02/3.20  ; Path-index has 2,282 nodes (2,341 at peak, 2,528 added, 246 deleted).
% 3.02/3.20  ; Trie-index has 3,926 entries (4,076 at peak, 4,890 added, 964 deleted).
% 3.02/3.20  ; Trie-index has 1,941 nodes (1,959 at peak, 2,265 added, 324 deleted).
% 3.02/3.20  ; Retrieved 2,575,159 generalization terms in 86,915 calls.
% 3.02/3.20  ; Retrieved 7,603 instance terms in 1,493 calls.
% 3.02/3.20  ; Retrieved 38,403 unifiable terms in 1,618 calls.
% 3.02/3.20  ; 
% 3.02/3.20  ; The agenda of rows to process has 263 entries:
% 3.02/3.20  ;     3 with value 13             36 with value 20               9 with value 27
% 3.02/3.20  ;    10 with value 14             13 with value 21               3 with value 28
% 3.02/3.20  ;    36 with value 15             20 with value 22               4 with value 29
% 3.02/3.20  ;    11 with value 16             18 with value 23               1 with value 30
% 3.02/3.20  ;    34 with value 17             12 with value 24               1 with value 31
% 3.02/3.20  ;    24 with value 18             13 with value 25               1 with value 33
% 3.02/3.20  ;    11 with value 19              3 with value 26
% 3.02/3.20  ; The agenda of rows to give has 1714 entries:
% 3.02/3.20  ;     1 with value (4 13)         98 with value (4 28)          11 with value (4 41)
% 3.02/3.20  ;    10 with value (4 15)         70 with value (4 29)          10 with value (4 42)
% 3.02/3.20  ;    39 with value (4 16)         40 with value (4 30)           8 with value (4 43)
% 3.02/3.20  ;    81 with value (4 17)         32 with value (4 31)           4 with value (4 45)
% 3.02/3.20  ;    96 with value (4 18)         43 with value (4 32)           5 with value (4 46)
% 3.02/3.20  ;   126 with value (4 19)         30 with value (4 33)           7 with value (4 47)
% 3.02/3.20  ;   118 with value (4 20)         28 with value (4 34)           1 with value (4 49)
% 3.02/3.20  ;   137 with value (4 21)         18 with value (4 35)           4 with value (4 50)
% 3.02/3.20  ;   142 with value (4 22)         27 with value (4 36)           3 with value (4 51)
% 3.02/3.20  ;   108 with value (4 23)         15 with value (4 37)           1 with value (4 52)
% 3.02/3.20  ;   100 with value (4 24)         13 with value (4 38)           3 with value (4 55)
% 3.02/3.20  ;    82 with value (4 25)         24 with value (4 39)           1 with value (4 56)
% 3.02/3.20  ;    93 with value (4 26)         16 with value (4 40)           1 with value (4 62)
% 3.02/3.20  ;    68 with value (4 27)
% 3.02/3.20  Evaluation took:
% 3.02/3.20    2.711 seconds of real time
% 3.02/3.20    2.57499 seconds of user run time
% 3.02/3.20    0.124094 seconds of system run time
% 3.02/3.20    [Run times include 0.101 seconds GC run time.]
% 3.02/3.20    0 calls to %EVAL
% 3.02/3.20    0 page faults and
% 3.02/3.20    176,099,608 bytes consed.
% 3.02/3.21  :PROOF-FOUND
% 3.02/3.21  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-16T08:23:25
% 3.02/3.21  :PROOF-FOUND
% 3.02/3.21  * 
%------------------------------------------------------------------------------