TSTP Solution File: GRP177-2 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP177-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n025.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 11:37:20 EDT 2022

% Result   : Unsatisfiable 0.69s 0.86s
% Output   : Refutation 0.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   22 (  22 unt;   0 nHn;   8 RR)
%            Number of literals    :   22 (  21 equ;   4 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   22 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
    multiply(identity,X) = X,
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).

cnf(left_inverse,axiom,
    multiply(inverse(X),X) = identity,
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).

cnf(associativity,axiom,
    multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).

cnf(idempotence_of_gld,axiom,
    greatest_lower_bound(X,X) = X,
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',idempotence_of_gld) ).

cnf(monotony_glb1,axiom,
    multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb1) ).

cnf(monotony_glb2,axiom,
    multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).

cnf(p08b_1,hypothesis,
    greatest_lower_bound(identity,a) = identity,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p08b_1) ).

cnf(p08b_2,hypothesis,
    greatest_lower_bound(identity,b) = identity,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p08b_2) ).

cnf(p08b_3,hypothesis,
    greatest_lower_bound(identity,c) = identity,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p08b_3) ).

cnf(prove_p08b,negated_conjecture,
    greatest_lower_bound(a,greatest_lower_bound(multiply(b,c),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) != greatest_lower_bound(a,multiply(b,c)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p08b) ).

cnf(23,plain,
    greatest_lower_bound(multiply(b,a),greatest_lower_bound(multiply(a,c),greatest_lower_bound(multiply(a,a),greatest_lower_bound(a,multiply(b,c))))) != greatest_lower_bound(a,multiply(b,c)),
    inference('REWRITE',[status(thm)],[prove_p08b,idempotence_of_gld,monotony_glb1,monotony_glb2,theory(equality)]) ).

cnf(97,plain,
    X = multiply(inverse(Y),multiply(Y,X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[associativity,left_inverse,theory(equality)]),left_identity,theory(equality)]) ).

cnf(110,plain,
    multiply(X,identity) = greatest_lower_bound(multiply(X,identity),multiply(X,c)),
    inference('PARAMODULATE',[status(thm)],[monotony_glb1,p08b_3,theory(equality)]) ).

cnf(128,plain,
    X = greatest_lower_bound(X,multiply(b,X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[monotony_glb2,p08b_2,theory(equality)]),left_identity,theory(equality)]) ).

cnf(130,plain,
    greatest_lower_bound(multiply(a,c),greatest_lower_bound(multiply(a,a),greatest_lower_bound(multiply(b,c),a))) != greatest_lower_bound(a,multiply(b,c)),
    inference('REWRITE',[status(thm)],[23,128,theory(equality)]) ).

cnf(131,plain,
    X = greatest_lower_bound(X,multiply(a,X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[monotony_glb2,p08b_1,theory(equality)]),left_identity,theory(equality)]) ).

cnf(133,plain,
    greatest_lower_bound(multiply(a,c),greatest_lower_bound(multiply(b,c),a)) != greatest_lower_bound(a,multiply(b,c)),
    inference('REWRITE',[status(thm)],[130,131,theory(equality)]) ).

cnf(337,plain,
    X = multiply(inverse(inverse(X)),identity),
    inference('PARAMODULATE',[status(thm)],[97,left_inverse,theory(equality)]) ).

cnf(338,plain,
    multiply(X,Y) = multiply(inverse(inverse(X)),Y),
    inference('PARAMODULATE',[status(thm)],[97,97,theory(equality)]) ).

cnf(339,plain,
    X = multiply(X,identity),
    inference('REWRITE',[status(thm)],[337,338,theory(equality)]) ).

cnf(341,plain,
    X = greatest_lower_bound(X,multiply(X,c)),
    inference('REWRITE',[status(thm)],[110,339,theory(equality)]) ).

cnf(343,plain,
    $false,
    inference('REWRITE',[status(thm)],[133,341,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : GRP177-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.14  % Command  : run-snark %s %d
% 0.13/0.35  % Computer : n025.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Mon Jun 13 14:33:09 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.20/0.47  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.48  * 
% 0.20/0.48  * 
% 0.20/0.49  #<PACKAGE "SNARK-USER">
% 0.20/0.49  * 
% 0.20/0.49  SNARK-TPTP-OPTIONS
% 0.20/0.49  * 
% 0.20/0.49  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.49   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.49   (USE-FACTORING :POS)
% 0.20/0.49   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.49   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.49   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.49   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.49   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.49   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.49   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.49   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.49   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.49   (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.49  * 
% 0.20/0.49  "."
% 0.20/0.49  * 
% 0.20/0.49  ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T14:33:09
% 0.20/0.49  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n025.cluster.edu at 2022-06-13T14:33:09
% 0.20/0.50  
% 0.20/0.50  ; Recognized left identity assertion (= (|multiply| |identity| ?X) ?X).
% 0.20/0.50  ; Recognized possible left inverse assertion (= (|multiply| (|inverse| ?X) ?X) |identity|).
% 0.20/0.50  ; Recognized associativity assertion (= (|multiply| (|multiply| ?X ?Y) ?Z) (|multiply| ?X (|multiply| ?Y ?Z))).
% 0.20/0.50  ; Recognized commutativity assertion (= (|greatest_lower_bound| ?X ?Y) (|greatest_lower_bound| ?Y ?X)).
% 0.20/0.50  ; Recognized commutativity assertion (= (|least_upper_bound| ?X ?Y) (|least_upper_bound| ?Y ?X)).
% 0.20/0.50  ; Recognized associativity assertion (= (|greatest_lower_bound| ?X (|greatest_lower_bound| ?Y ?Z)) (|greatest_lower_bound| (|greatest_lower_bound| ?X ?Y) ?Z)).
% 0.20/0.50  ; Recognized associativity assertion (= (|least_upper_bound| ?X (|least_upper_bound| ?Y ?Z)) (|least_upper_bound| (|least_upper_bound| ?X ?Y) ?Z)).
% 0.20/0.50  ; Declaring greatest_lower_bound to be commutative.
% 0.20/0.50  ; Declaring greatest_lower_bound to be associative-commutative.
% 0.20/0.50  ; Declaring least_upper_bound to be commutative.
% 0.69/0.86  ; Declaring least_upper_bound to be associative-commutative.
% 0.69/0.86  
% 0.69/0.86  #||
% 0.69/0.86  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.69/0.86  % SZS output start Refutation
% See solution above
% 0.69/0.86  ||#
% 0.69/0.86  
% 0.69/0.86  ; Summary of computation:
% 0.69/0.86  ;      2128 formulas have been input or derived (from 48 formulas).
% 0.69/0.86  ;       343 (16%) were retained.  Of these,
% 0.69/0.86  ;           49 (14%) were simplified or subsumed later,
% 0.69/0.86  ;          294 (86%) are still being kept.
% 0.69/0.86  ; 
% 0.69/0.86  ; Run time in seconds excluding printing time:
% 0.69/0.86  ;     0.005   1%   Read assertion file          (1 call)
% 0.69/0.86  ;     0.000   0%   Assert                       (19 calls)
% 0.69/0.86  ;     0.041  11%   Process new row              (2,014 calls)
% 0.69/0.86  ;     0.001   0%   Resolution                   (94 calls)
% 0.69/0.86  ;     0.049  13%   Paramodulation               (47 calls)
% 0.69/0.86  ;     0.005   1%   Embedding                    (163 calls)
% 0.69/0.86  ;     0.219  59%   Forward simplification       (1,855 calls)
% 0.69/0.86  ;     0.011   3%   Backward simplification      (183 calls)
% 0.69/0.86  ;     0.005   1%   Ordering                     (1,807 calls)
% 0.69/0.86  ;     0.005   1%   Ordering ac                  (629 calls)
% 0.69/0.86  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.69/0.86  ;     0.000   0%   Purity testing               (1 call)
% 0.69/0.86  ;     0.031   8%   Other
% 0.69/0.86  ;     0.372        Total
% 0.69/0.86  ;     0.374        Real time
% 0.69/0.86  ; 
% 0.69/0.86  ; Term-hash-array has 923 terms in all.
% 0.69/0.86  ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.69/0.86  ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.69/0.86  ; Path-index has 813 entries (877 at peak, 942 added, 129 deleted).
% 0.69/0.86  ; Path-index has 408 nodes (422 at peak, 428 added, 20 deleted).
% 0.69/0.86  ; Trie-index has 813 entries (877 at peak, 942 added, 129 deleted).
% 0.69/0.86  ; Trie-index has 250 nodes (271 at peak, 291 added, 41 deleted).
% 0.69/0.86  ; Retrieved 385,512 generalization terms in 17,903 calls.
% 0.69/0.86  ; Retrieved 460 instance terms in 206 calls.
% 0.69/0.86  ; Retrieved 4,595 unifiable terms in 243 calls.
% 0.69/0.86  ; 
% 0.69/0.86  ; The agenda of backward simplifiable rows to process has 11 entries:
% 0.69/0.86  ;    11 with value 0
% 0.69/0.86  ; The agenda of rows to process has 8 entries:
% 0.69/0.86  ;     4 with value 18              4 with value 20
% 0.69/0.86  ; The agenda of rows to give has 247 entries:
% 0.69/0.86  ;     1 with value (4 9)          12 with value (4 18)           4 with value (4 25)
% 0.69/0.86  ;     3 with value (4 11)         18 with value (4 19)           4 with value (4 27)
% 0.69/0.86  ;    18 with value (4 12)          9 with value (4 20)          12 with value (4 28)
% 0.69/0.86  ;     1 with value (4 13)         32 with value (4 21)           4 with value (4 30)
% 0.69/0.86  ;     6 with value (4 14)         22 with value (4 22)           4 with value (4 31)
% 0.69/0.86  ;    31 with value (4 15)         18 with value (4 23)           4 with value (4 33)
% 0.69/0.86  ;    12 with value (4 16)          4 with value (4 24)           4 with value (4 36)
% 0.69/0.86  ;    24 with value (4 17)
% 0.69/0.86  Evaluation took:
% 0.69/0.87    0.375 seconds of real time
% 0.69/0.87    0.358114 seconds of user run time
% 0.69/0.87    0.016843 seconds of system run time
% 0.69/0.87    [Run times include 0.006 seconds GC run time.]
% 0.69/0.87    0 calls to %EVAL
% 0.69/0.87    0 page faults and
% 0.69/0.87    20,718,968 bytes consed.
% 0.69/0.87  :PROOF-FOUND
% 0.69/0.87  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T14:33:09
% 0.69/0.87  :PROOF-FOUND
% 0.69/0.87  * 
%------------------------------------------------------------------------------