TSTP Solution File: GRP172-2 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP172-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n009.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 : Sat Jul 16 11:37:17 EDT 2022

% Result   : Unsatisfiable 0.78s 0.94s
% Output   : Refutation 0.78s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   11 (  11 unt;   0 nHn;   5 RR)
%            Number of literals    :   11 (  10 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   10 (   1 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
    multiply(identity,X) = X,
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).

cnf(lub_absorbtion,axiom,
    least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',lub_absorbtion) ).

cnf(monotony_glb2,axiom,
    multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).

cnf(p04d_1,hypothesis,
    greatest_lower_bound(identity,a) = identity,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p04d_1) ).

cnf(p04d_2,hypothesis,
    greatest_lower_bound(identity,b) = identity,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p04d_2) ).

cnf(19,plain,
    greatest_lower_bound(identity,greatest_lower_bound(b,X)) = greatest_lower_bound(identity,X),
    inference('EMBED',[status(thm)],[p04d_2]) ).

cnf(prove_p04d,negated_conjecture,
    least_upper_bound(identity,multiply(a,b)) != multiply(a,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p04d) ).

cnf(111,plain,
    X = greatest_lower_bound(X,multiply(a,X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[monotony_glb2,p04d_1,theory(equality)]),left_identity,theory(equality)]) ).

cnf(112,plain,
    greatest_lower_bound(X,greatest_lower_bound(multiply(a,X),Y)) = greatest_lower_bound(X,Y),
    inference('EMBED',[status(thm)],[111]) ).

cnf(215,plain,
    identity = greatest_lower_bound(identity,multiply(a,b)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[19,112,theory(equality)]),p04d_2,theory(equality)]) ).

cnf(401,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[lub_absorbtion,215,theory(equality)]),prove_p04d]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : GRP172-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.10/0.13  % Command  : run-snark %s %d
% 0.14/0.34  % Computer : n009.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Mon Jun 13 19:26:23 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.21/0.46  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.47  * 
% 0.21/0.47  * 
% 0.21/0.47  #<PACKAGE "SNARK-USER">
% 0.21/0.47  * 
% 0.21/0.47  SNARK-TPTP-OPTIONS
% 0.21/0.47  * 
% 0.21/0.47  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.21/0.47   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.21/0.47   (USE-FACTORING :POS)
% 0.21/0.47   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.21/0.47   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.21/0.47   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.21/0.47   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.21/0.47   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.21/0.47   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.21/0.47   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.21/0.47   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.21/0.47   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.21/0.47   (DECLARE-TPTP-SYMBOLS2))
% 0.21/0.47  * 
% 0.21/0.47  "."
% 0.21/0.47  * 
% 0.21/0.47  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T19:26:23
% 0.21/0.47  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n009.cluster.edu at 2022-06-13T19:26:23
% 0.21/0.49  
% 0.21/0.49  ; Recognized left identity assertion (= (|multiply| |identity| ?X) ?X).
% 0.21/0.49  ; Recognized possible left inverse assertion (= (|multiply| (|inverse| ?X) ?X) |identity|).
% 0.21/0.49  ; Recognized associativity assertion (= (|multiply| (|multiply| ?X ?Y) ?Z) (|multiply| ?X (|multiply| ?Y ?Z))).
% 0.21/0.49  ; Recognized commutativity assertion (= (|greatest_lower_bound| ?X ?Y) (|greatest_lower_bound| ?Y ?X)).
% 0.21/0.49  ; Recognized commutativity assertion (= (|least_upper_bound| ?X ?Y) (|least_upper_bound| ?Y ?X)).
% 0.21/0.49  ; Recognized associativity assertion (= (|greatest_lower_bound| ?X (|greatest_lower_bound| ?Y ?Z)) (|greatest_lower_bound| (|greatest_lower_bound| ?X ?Y) ?Z)).
% 0.21/0.49  ; Recognized associativity assertion (= (|least_upper_bound| ?X (|least_upper_bound| ?Y ?Z)) (|least_upper_bound| (|least_upper_bound| ?X ?Y) ?Z)).
% 0.21/0.49  ; Declaring greatest_lower_bound to be commutative.
% 0.21/0.49  ; Declaring greatest_lower_bound to be associative-commutative.
% 0.21/0.49  ; Declaring least_upper_bound to be commutative.
% 0.78/0.94  ; Declaring least_upper_bound to be associative-commutative.
% 0.78/0.94  
% 0.78/0.94  #||
% 0.78/0.94  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.78/0.94  % SZS output start Refutation
% See solution above
% 0.78/0.94  ||#
% 0.78/0.94  
% 0.78/0.94  ; Summary of computation:
% 0.78/0.94  ;      2307 formulas have been input or derived (from 51 formulas).
% 0.78/0.94  ;       401 (17%) were retained.  Of these,
% 0.78/0.94  ;           56 (14%) were simplified or subsumed later,
% 0.78/0.94  ;          345 (86%) are still being kept.
% 0.78/0.94  ; 
% 0.78/0.94  ; Run time in seconds excluding printing time:
% 0.78/0.94  ;     0.004   1%   Read assertion file          (1 call)
% 0.78/0.94  ;     0.001   0%   Assert                       (18 calls)
% 0.78/0.94  ;     0.036   8%   Process new row              (2,228 calls)
% 0.78/0.94  ;     0.002   0%   Resolution                   (100 calls)
% 0.78/0.94  ;     0.055  12%   Paramodulation               (50 calls)
% 0.78/0.94  ;     0.003   1%   Embedding                    (192 calls)
% 0.78/0.94  ;     0.305  66%   Forward simplification       (2,040 calls)
% 0.78/0.94  ;     0.010   2%   Backward simplification      (213 calls)
% 0.78/0.94  ;     0.006   1%   Ordering                     (2,136 calls)
% 0.78/0.94  ;     0.008   2%   Ordering ac                  (702 calls)
% 0.78/0.94  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.78/0.94  ;     0.000   0%   Purity testing               (1 call)
% 0.78/0.94  ;     0.033   7%   Other
% 0.78/0.94  ;     0.463        Total
% 0.78/0.94  ;     0.468        Real time
% 0.78/0.94  ; 
% 0.78/0.94  ; Term-hash-array has 1,078 terms in all.
% 0.78/0.94  ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.78/0.94  ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.78/0.94  ; Path-index has 955 entries (955 at peak, 1,095 added, 140 deleted).
% 0.78/0.94  ; Path-index has 419 nodes (419 at peak, 434 added, 15 deleted).
% 0.78/0.94  ; Trie-index has 955 entries (955 at peak, 1,095 added, 140 deleted).
% 0.78/0.94  ; Trie-index has 310 nodes (310 at peak, 344 added, 34 deleted).
% 0.78/0.94  ; Retrieved 415,901 generalization terms in 20,218 calls.
% 0.78/0.94  ; Retrieved 562 instance terms in 236 calls.
% 0.78/0.94  ; Retrieved 5,209 unifiable terms in 261 calls.
% 0.78/0.94  ; 
% 0.78/0.94  ; The agenda of rows to process has 2 entries:
% 0.78/0.94  ;     2 with value 20
% 0.78/0.94  ; The agenda of rows to give has 294 entries:
% 0.78/0.94  ;     5 with value (4 12)         20 with value (4 19)           4 with value (4 26)
% 0.78/0.94  ;     1 with value (4 13)          9 with value (4 20)           4 with value (4 27)
% 0.78/0.94  ;     8 with value (4 14)         32 with value (4 21)          12 with value (4 28)
% 0.78/0.94  ;    47 with value (4 15)         26 with value (4 22)           4 with value (4 30)
% 0.78/0.94  ;    50 with value (4 16)         22 with value (4 23)           4 with value (4 31)
% 0.78/0.94  ;    14 with value (4 17)         10 with value (4 24)           4 with value (4 33)
% 0.78/0.94  ;    10 with value (4 18)          4 with value (4 25)           4 with value (4 36)
% 0.78/0.94  Evaluation took:
% 0.78/0.94    0.469 seconds of real time
% 0.78/0.94    0.441344 seconds of user run time
% 0.78/0.94    0.023019 seconds of system run time
% 0.78/0.94    [Run times include 0.006 seconds GC run time.]
% 0.78/0.94    0 calls to %EVAL
% 0.78/0.94    0 page faults and
% 0.78/0.94    22,299,096 bytes consed.
% 0.78/0.94  :PROOF-FOUND
% 0.78/0.94  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T19:26:23
% 0.78/0.94  :PROOF-FOUND
% 0.78/0.94  * 
%------------------------------------------------------------------------------