TSTP Solution File: GRP169-2 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP169-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 : Sat Jul 16 11:37:15 EDT 2022

% Result   : Unsatisfiable 0.83s 1.07s
% Output   : Refutation 0.83s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   23 (  23 unt;   0 nHn;   6 RR)
%            Number of literals    :   23 (  22 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   30 (   2 sgn)

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

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

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

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

cnf(monotony_lub1,axiom,
    multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_lub1) ).

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(p02b_1,hypothesis,
    greatest_lower_bound(inverse(a),inverse(b)) = inverse(a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p02b_1) ).

cnf(prove_p02b,negated_conjecture,
    greatest_lower_bound(a,b) != b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p02b) ).

cnf(68,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(69,plain,
    multiply(multiply(X,inverse(Y)),Y) = multiply(X,identity),
    inference('PARAMODULATE',[status(thm)],[associativity,left_inverse,theory(equality)]) ).

cnf(93,plain,
    multiply(inverse(a),X) = greatest_lower_bound(multiply(inverse(a),X),multiply(inverse(b),X)),
    inference('PARAMODULATE',[status(thm)],[monotony_glb2,p02b_1,theory(equality)]) ).

cnf(110,plain,
    X = multiply(inverse(inverse(X)),identity),
    inference('PARAMODULATE',[status(thm)],[68,left_inverse,theory(equality)]) ).

cnf(111,plain,
    multiply(X,Y) = multiply(inverse(inverse(X)),Y),
    inference('PARAMODULATE',[status(thm)],[68,68,theory(equality)]) ).

cnf(112,plain,
    X = multiply(X,identity),
    inference('REWRITE',[status(thm)],[110,111,theory(equality)]) ).

cnf(113,plain,
    multiply(multiply(X,inverse(Y)),Y) = X,
    inference('REWRITE',[status(thm)],[69,112,theory(equality)]) ).

cnf(121,plain,
    X = inverse(inverse(X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[113,left_inverse,theory(equality)]),left_identity,theory(equality)]) ).

cnf(129,plain,
    X = multiply(Y,multiply(inverse(Y),X)),
    inference('PARAMODULATE',[status(thm)],[68,121,theory(equality)]) ).

cnf(292,plain,
    multiply(inverse(a),b) = greatest_lower_bound(multiply(inverse(a),b),identity),
    inference('PARAMODULATE',[status(thm)],[93,left_inverse,theory(equality)]) ).

cnf(360,plain,
    least_upper_bound(identity,multiply(inverse(a),b)) = identity,
    inference('PARAMODULATE',[status(thm)],[lub_absorbtion,292,theory(equality)]) ).

cnf(368,plain,
    X = least_upper_bound(X,multiply(X,multiply(inverse(a),b))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[monotony_lub1,360,theory(equality)]),112,theory(equality)]) ).

cnf(528,plain,
    a = least_upper_bound(a,b),
    inference('PARAMODULATE',[status(thm)],[368,129,theory(equality)]) ).

cnf(550,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[glb_absorbtion,528,theory(equality)]),prove_p02b]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GRP169-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.13  % Command  : run-snark %s %d
% 0.13/0.34  % Computer : n015.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 : Mon Jun 13 12:11:38 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.46  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.47  * 
% 0.19/0.47  * 
% 0.19/0.48  #<PACKAGE "SNARK-USER">
% 0.19/0.48  * 
% 0.19/0.48  SNARK-TPTP-OPTIONS
% 0.19/0.48  * 
% 0.19/0.48  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.48   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.48   (USE-FACTORING :POS)
% 0.19/0.48   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.48   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.48   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.48   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.48   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.48   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.48   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.48   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.48   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.48   (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.48  * 
% 0.19/0.48  "."
% 0.19/0.48  * 
% 0.19/0.48  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T12:11:38
% 0.19/0.48  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n015.cluster.edu at 2022-06-13T12:11:38
% 0.19/0.49  
% 0.19/0.49  ; Recognized left identity assertion (= (|multiply| |identity| ?X) ?X).
% 0.19/0.49  ; Recognized possible left inverse assertion (= (|multiply| (|inverse| ?X) ?X) |identity|).
% 0.19/0.49  ; Recognized associativity assertion (= (|multiply| (|multiply| ?X ?Y) ?Z) (|multiply| ?X (|multiply| ?Y ?Z))).
% 0.19/0.49  ; Recognized commutativity assertion (= (|greatest_lower_bound| ?X ?Y) (|greatest_lower_bound| ?Y ?X)).
% 0.19/0.49  ; Recognized commutativity assertion (= (|least_upper_bound| ?X ?Y) (|least_upper_bound| ?Y ?X)).
% 0.19/0.49  ; Recognized associativity assertion (= (|greatest_lower_bound| ?X (|greatest_lower_bound| ?Y ?Z)) (|greatest_lower_bound| (|greatest_lower_bound| ?X ?Y) ?Z)).
% 0.19/0.49  ; Recognized associativity assertion (= (|least_upper_bound| ?X (|least_upper_bound| ?Y ?Z)) (|least_upper_bound| (|least_upper_bound| ?X ?Y) ?Z)).
% 0.19/0.49  ; Declaring greatest_lower_bound to be commutative.
% 0.19/0.49  ; Declaring greatest_lower_bound to be associative-commutative.
% 0.19/0.49  ; Declaring least_upper_bound to be commutative.
% 0.83/1.07  ; Declaring least_upper_bound to be associative-commutative.
% 0.83/1.07  
% 0.83/1.07  #||
% 0.83/1.07  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.83/1.07  % SZS output start Refutation
% See solution above
% 0.83/1.07  ||#
% 0.83/1.07  
% 0.83/1.07  ; Summary of computation:
% 0.83/1.07  ;      2648 formulas have been input or derived (from 66 formulas).
% 0.83/1.07  ;       550 (21%) were retained.  Of these,
% 0.83/1.07  ;           49 ( 9%) were simplified or subsumed later,
% 0.83/1.07  ;          501 (91%) are still being kept.
% 0.83/1.07  ; 
% 0.83/1.07  ; Run time in seconds excluding printing time:
% 0.83/1.07  ;     0.004   1%   Read assertion file          (1 call)
% 0.83/1.07  ;     0.000   0%   Assert                       (17 calls)
% 0.83/1.07  ;     0.064  11%   Process new row              (2,592 calls)
% 0.83/1.07  ;     0.002   0%   Resolution                   (130 calls)
% 0.83/1.07  ;     0.055   9%   Paramodulation               (65 calls)
% 0.83/1.07  ;     0.002   0%   Embedding                    (242 calls)
% 0.83/1.07  ;     0.363  61%   Forward simplification       (2,294 calls)
% 0.83/1.07  ;     0.016   3%   Backward simplification      (312 calls)
% 0.83/1.07  ;     0.045   8%   Ordering                     (10,362 calls)
% 0.83/1.07  ;     0.007   1%   Ordering ac                  (865 calls)
% 0.83/1.07  ;     0.001   0%   Sortal reasoning             (32 calls)
% 0.83/1.07  ;     0.000   0%   Purity testing               (1 call)
% 0.83/1.07  ;     0.035   6%   Other
% 0.83/1.07  ;     0.594        Total
% 0.83/1.07  ;     0.596        Real time
% 0.83/1.07  ; 
% 0.83/1.07  ; Term-hash-array has 1,642 terms in all.
% 0.83/1.07  ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.83/1.07  ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.83/1.07  ; Path-index has 1,515 entries (1,515 at peak, 1,656 added, 141 deleted).
% 0.83/1.07  ; Path-index has 1,534 nodes (1,534 at peak, 1,558 added, 24 deleted).
% 0.83/1.07  ; Trie-index has 1,515 entries (1,515 at peak, 1,656 added, 141 deleted).
% 0.83/1.07  ; Trie-index has 1,036 nodes (1,036 at peak, 1,168 added, 132 deleted).
% 0.83/1.07  ; Retrieved 480,118 generalization terms in 26,693 calls.
% 0.83/1.07  ; Retrieved 1,118 instance terms in 394 calls.
% 0.83/1.08  ; Retrieved 8,379 unifiable terms in 396 calls.
% 0.83/1.08  ; 
% 0.83/1.08  ; The agenda of rows to process has 2 entries:
% 0.83/1.08  ;     2 with value 20
% 0.83/1.08  ; The agenda of rows to give has 438 entries:
% 0.83/1.08  ;     1 with value (4 12)         40 with value (4 25)          16 with value (4 32)
% 0.83/1.08  ;     7 with value (4 19)         37 with value (4 26)           6 with value (4 33)
% 0.83/1.08  ;    28 with value (4 20)         58 with value (4 27)           6 with value (4 34)
% 0.83/1.08  ;    20 with value (4 21)         44 with value (4 28)           4 with value (4 35)
% 0.83/1.08  ;    22 with value (4 22)         22 with value (4 29)          10 with value (4 36)
% 0.83/1.08  ;    35 with value (4 23)         26 with value (4 30)           2 with value (4 40)
% 0.83/1.08  ;    34 with value (4 24)         18 with value (4 31)           2 with value (4 42)
% 0.83/1.08  Evaluation took:
% 0.83/1.08    0.596 seconds of real time
% 0.83/1.08    0.561606 seconds of user run time
% 0.83/1.08    0.034629 seconds of system run time
% 0.83/1.08    [Run times include 0.012 seconds GC run time.]
% 0.83/1.08    0 calls to %EVAL
% 0.83/1.08    0 page faults and
% 0.83/1.08    33,597,520 bytes consed.
% 0.83/1.08  :PROOF-FOUND
% 0.83/1.08  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T12:11:38
% 0.83/1.08  :PROOF-FOUND
% 0.83/1.08  * 
%------------------------------------------------------------------------------