TSTP Solution File: KLE141+2 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : KLE141+2 : 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 02:26:49 EDT 2022

% Result   : Theorem 0.48s 0.64s
% Output   : Refutation 0.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   21 (  16 unt;   0 nHn;   7 RR)
%            Number of literals    :   26 (  13 equ;   8 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    4 (   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   :   31 (   7 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    addition(X,X) = X,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',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/KLE004+0.ax',multiplicative_associativity) ).

cnf(5,axiom,
    multiplication(X,one) = X,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).

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

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

cnf(9,axiom,
    multiplication(zero,X) = zero,
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).

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

cnf(19,axiom,
    strong_iteration(X) = addition(star(X),multiplication(strong_iteration(X),zero)),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',isolation) ).

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

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

cnf(23,negated_conjecture,
    ( ~ leq(multiplication(strong_iteration(one),'SKOLEMAAAU1'),strong_iteration(one))
    | ~ leq(strong_iteration(one),multiplication(strong_iteration(one),'SKOLEMAAAU1')) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

cnf(26,plain,
    leq(X,addition(X,Y)),
    inference('HYPERRESOLVE',[status(thm)],[22,3]) ).

cnf(82,plain,
    multiplication(X,zero) = multiplication(multiplication(X,zero),Y),
    inference('PARAMODULATE',[status(thm)],[4,9,theory(equality)]) ).

cnf(132,plain,
    multiplication(strong_iteration(X),Y) = addition(multiplication(star(X),Y),multiplication(strong_iteration(X),zero)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,19,theory(equality)]),82,theory(equality)]) ).

cnf(134,plain,
    ( ~ leq(addition(multiplication(star(one),'SKOLEMAAAU1'),multiplication(strong_iteration(one),zero)),strong_iteration(one))
    | ~ leq(strong_iteration(one),addition(multiplication(star(one),'SKOLEMAAAU1'),multiplication(strong_iteration(one),zero))) ),
    inference('REWRITE',[status(thm)],[23,132,theory(equality)]) ).

cnf(180,plain,
    leq(X,multiplication(strong_iteration(one),Y)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[18,6,theory(equality)]),26]) ).

cnf(224,plain,
    leq(X,strong_iteration(one)),
    inference('PARAMODULATE',[status(thm)],[180,5,theory(equality)]) ).

cnf(225,plain,
    ~ leq(strong_iteration(one),addition(multiplication(star(one),'SKOLEMAAAU1'),multiplication(strong_iteration(one),zero))),
    inference('REWRITE',[status(thm)],[134,224]) ).

cnf(227,plain,
    addition(X,multiplication(strong_iteration(one),Y)) = multiplication(strong_iteration(one),Y),
    inference('HYPERRESOLVE',[status(thm)],[21,180]) ).

cnf(229,plain,
    $false,
    inference('REWRITE',[status(thm)],[225,180,227,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : KLE141+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13  % Command  : run-snark %s %d
% 0.13/0.34  % Computer : n003.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Thu Jun 16 15:08:26 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.45  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.46  * 
% 0.20/0.47  * 
% 0.20/0.47  #<PACKAGE "SNARK-USER">
% 0.20/0.47  * 
% 0.20/0.47  SNARK-TPTP-OPTIONS
% 0.20/0.47  * 
% 0.20/0.47  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.47   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.47   (USE-FACTORING :POS)
% 0.20/0.47   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.47   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.47   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.47   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.47   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.47   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.47   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.47   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.47   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.47   (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.47  * 
% 0.20/0.47  "."
% 0.20/0.47  * 
% 0.20/0.47  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-16T15:08:27
% 0.20/0.47  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n003.cluster.edu at 2022-06-16T15:08:27
% 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.
% 0.48/0.64  ; Declaring addition to be associative-commutative.
% 0.48/0.64  
% 0.48/0.64  #||
% 0.48/0.64  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.48/0.64  % SZS output start Refutation
% See solution above
% 0.48/0.64  ||#
% 0.48/0.64  
% 0.48/0.64  ; Summary of computation:
% 0.48/0.64  ;       644 formulas have been input or derived (from 34 formulas).
% 0.48/0.64  ;       229 (36%) were retained.  Of these,
% 0.48/0.64  ;           16 ( 7%) were simplified or subsumed later,
% 0.48/0.64  ;          213 (93%) are still being kept.
% 0.48/0.64  ; 
% 0.48/0.64  ; Run time in seconds excluding printing time:
% 0.48/0.64  ;     0.004   2%   Read assertion file          (1 call)
% 0.48/0.64  ;     0.002   1%   Assert                       (19 calls)
% 0.48/0.64  ;     0.020  12%   Process new row              (622 calls)
% 0.48/0.64  ;     0.004   2%   Resolution                   (66 calls)
% 0.48/0.64  ;     0.015   9%   Paramodulation               (33 calls)
% 0.48/0.64  ;     0.000   0%   Embedding                    (45 calls)
% 0.48/0.64  ;     0.007   4%   Condensing                   (157 calls)
% 0.48/0.64  ;     0.008   5%   Forward subsumption          (157 calls)
% 0.48/0.64  ;     0.001   1%   Backward subsumption         (91 calls)
% 0.48/0.64  ;     0.002   1%   Clause clause subsumption    (239 calls)
% 0.48/0.64  ;     0.067  39%   Forward simplification       (580 calls)
% 0.48/0.64  ;     0.003   2%   Backward simplification      (187 calls)
% 0.48/0.64  ;     0.005   3%   Ordering                     (909 calls)
% 0.48/0.64  ;     0.006   4%   Ordering ac                  (246 calls)
% 0.48/0.64  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.48/0.64  ;     0.000   0%   Purity testing               (1 call)
% 0.48/0.64  ;     0.026  15%   Other
% 0.48/0.64  ;     0.170        Total
% 0.48/0.64  ;     0.171        Real time
% 0.48/0.64  ; 
% 0.48/0.64  ; Term-hash-array has 624 terms in all.
% 0.48/0.64  ; Feature-vector-row-index has 89 entries (90 at peak, 91 added, 2 deleted).
% 0.48/0.64  ; Feature-vector-row-index has 560 nodes (582 at peak, 595 added, 35 deleted).
% 0.48/0.64  ;  Retrieved 255 possibly forward subsuming rows in 157 calls.
% 0.48/0.64  ;  Retrieved 26 possibly backward subsumed rows in 91 calls.
% 0.48/0.64  ; Path-index has 590 entries (592 at peak, 638 added, 48 deleted).
% 0.48/0.64  ; Path-index has 503 nodes (511 at peak, 540 added, 37 deleted).
% 0.48/0.65  ; Trie-index has 590 entries (592 at peak, 638 added, 48 deleted).
% 0.48/0.65  ; Trie-index has 465 nodes (470 at peak, 494 added, 29 deleted).
% 0.48/0.65  ; Retrieved 47,317 generalization terms in 5,479 calls.
% 0.48/0.65  ; Retrieved 314 instance terms in 128 calls.
% 0.48/0.65  ; Retrieved 1,678 unifiable terms in 181 calls.
% 0.48/0.65  ; 
% 0.48/0.65  ; The agenda of rows to process has 1 entry:
% 0.48/0.65  ;     1 with value 17
% 0.48/0.65  ; The agenda of rows to give has 180 entries:
% 0.48/0.65  ;     1 with value (4 8)          21 with value (4 19)           8 with value (4 27)
% 0.48/0.65  ;     7 with value (4 11)         14 with value (4 20)          22 with value (4 28)
% 0.48/0.65  ;     7 with value (4 12)          3 with value (4 21)           2 with value (4 29)
% 0.48/0.65  ;     3 with value (4 13)          6 with value (4 22)           1 with value (4 30)
% 0.48/0.65  ;     7 with value (4 14)          3 with value (4 23)           3 with value (4 32)
% 0.48/0.65  ;    14 with value (4 15)          4 with value (4 24)           3 with value (4 33)
% 0.48/0.65  ;     4 with value (4 16)          6 with value (4 25)           5 with value (4 35)
% 0.48/0.65  ;    13 with value (4 17)         13 with value (4 26)           1 with value (4 40)
% 0.48/0.65  ;     9 with value (4 18)
% 0.48/0.65  Evaluation took:
% 0.48/0.65    0.173 seconds of real time
% 0.48/0.65    0.158516 seconds of user run time
% 0.48/0.65    0.014281 seconds of system run time
% 0.48/0.65    0 calls to %EVAL
% 0.48/0.65    0 page faults and
% 0.48/0.65    9,598,680 bytes consed.
% 0.48/0.65  :PROOF-FOUND
% 0.48/0.65  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-16T15:08:27
% 0.48/0.65  :PROOF-FOUND
% 0.48/0.65  * 
%------------------------------------------------------------------------------