TSTP Solution File: GRP178-2 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP178-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n032.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 0.89s 1.07s
% Output   : Refutation 0.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   20 (  20 unt;   0 nHn;   4 RR)
%            Number of literals    :   20 (  19 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;   4 con; 0-2 aty)
%            Number of variables   :   26 (   0 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(monotony_glb1,axiom,
    multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
    file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).

cnf(p09b_3,hypothesis,
    greatest_lower_bound(identity,c) = identity,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p09b_3) ).

cnf(p09b_4,hypothesis,
    greatest_lower_bound(a,b) = identity,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p09b_4) ).

cnf(prove_p09b,negated_conjecture,
    greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p09b) ).

cnf(98,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(111,plain,
    multiply(X,identity) = greatest_lower_bound(multiply(X,identity),multiply(X,c)),
    inference('PARAMODULATE',[status(thm)],[monotony_glb1,p09b_3,theory(equality)]) ).

cnf(115,plain,
    multiply(X,identity) = greatest_lower_bound(multiply(X,a),multiply(X,b)),
    inference('PARAMODULATE',[status(thm)],[monotony_glb1,p09b_4,theory(equality)]) ).

cnf(119,plain,
    greatest_lower_bound(multiply(X,a),multiply(X,b)) = greatest_lower_bound(multiply(X,a),greatest_lower_bound(multiply(X,b),multiply(X,c))),
    inference('REWRITE',[status(thm)],[111,115,theory(equality)]) ).

cnf(135,plain,
    X = greatest_lower_bound(multiply(a,X),multiply(b,X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[monotony_glb2,p09b_4,theory(equality)]),left_identity,theory(equality)]) ).

cnf(136,plain,
    greatest_lower_bound(multiply(a,X),greatest_lower_bound(multiply(b,X),Y)) = greatest_lower_bound(X,Y),
    inference('EMBED',[status(thm)],[135]) ).

cnf(336,plain,
    X = greatest_lower_bound(multiply(inverse(inverse(X)),a),multiply(inverse(inverse(X)),b)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[98,left_inverse,theory(equality)]),115,theory(equality)]) ).

cnf(338,plain,
    multiply(X,Y) = multiply(inverse(inverse(X)),Y),
    inference('PARAMODULATE',[status(thm)],[98,98,theory(equality)]) ).

cnf(339,plain,
    X = greatest_lower_bound(multiply(X,a),multiply(X,b)),
    inference('REWRITE',[status(thm)],[336,338,theory(equality)]) ).

cnf(345,plain,
    X = greatest_lower_bound(multiply(X,c),X),
    inference('REWRITE',[status(thm)],[119,339,theory(equality)]) ).

cnf(346,plain,
    greatest_lower_bound(multiply(X,c),greatest_lower_bound(X,Y)) = greatest_lower_bound(X,Y),
    inference('EMBED',[status(thm)],[345]) ).

cnf(708,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[346,136,theory(equality)]),prove_p09b]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10  % Problem  : GRP178-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.11  % Command  : run-snark %s %d
% 0.10/0.31  % Computer : n032.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 600
% 0.10/0.31  % DateTime : Mon Jun 13 08:10:56 EDT 2022
% 0.10/0.31  % CPUTime  : 
% 0.16/0.39  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.40  * 
% 0.16/0.40  * 
% 0.16/0.41  #<PACKAGE "SNARK-USER">
% 0.16/0.41  * 
% 0.16/0.41  SNARK-TPTP-OPTIONS
% 0.16/0.41  * 
% 0.16/0.41  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.16/0.41   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.16/0.41   (USE-FACTORING :POS)
% 0.16/0.41   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.16/0.41   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.16/0.41   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.16/0.41   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.16/0.41   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.16/0.41   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.16/0.41   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.16/0.41   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.16/0.41   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.16/0.41   (DECLARE-TPTP-SYMBOLS2))
% 0.16/0.41  * 
% 0.16/0.41  "."
% 0.16/0.41  * 
% 0.16/0.41  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T08:10:56
% 0.16/0.41  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n032.cluster.edu at 2022-06-13T08:10:56
% 0.16/0.42  
% 0.16/0.42  ; Recognized left identity assertion (= (|multiply| |identity| ?X) ?X).
% 0.16/0.42  ; Recognized possible left inverse assertion (= (|multiply| (|inverse| ?X) ?X) |identity|).
% 0.16/0.42  ; Recognized associativity assertion (= (|multiply| (|multiply| ?X ?Y) ?Z) (|multiply| ?X (|multiply| ?Y ?Z))).
% 0.16/0.42  ; Recognized commutativity assertion (= (|greatest_lower_bound| ?X ?Y) (|greatest_lower_bound| ?Y ?X)).
% 0.16/0.42  ; Recognized commutativity assertion (= (|least_upper_bound| ?X ?Y) (|least_upper_bound| ?Y ?X)).
% 0.16/0.42  ; Recognized associativity assertion (= (|greatest_lower_bound| ?X (|greatest_lower_bound| ?Y ?Z)) (|greatest_lower_bound| (|greatest_lower_bound| ?X ?Y) ?Z)).
% 0.16/0.42  ; Recognized associativity assertion (= (|least_upper_bound| ?X (|least_upper_bound| ?Y ?Z)) (|least_upper_bound| (|least_upper_bound| ?X ?Y) ?Z)).
% 0.16/0.42  ; Declaring greatest_lower_bound to be commutative.
% 0.16/0.42  ; Declaring greatest_lower_bound to be associative-commutative.
% 0.16/0.42  ; Declaring least_upper_bound to be commutative.
% 0.89/1.07  ; Declaring least_upper_bound to be associative-commutative.
% 0.89/1.07  
% 0.89/1.07  #||
% 0.89/1.07  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.89/1.07  % SZS output start Refutation
% See solution above
% 0.89/1.07  ||#
% 0.89/1.07  
% 0.89/1.07  ; Summary of computation:
% 0.89/1.07  ;      4052 formulas have been input or derived (from 84 formulas).
% 0.89/1.07  ;       708 (17%) were retained.  Of these,
% 0.89/1.07  ;           73 (10%) were simplified or subsumed later,
% 0.89/1.07  ;          635 (90%) are still being kept.
% 0.89/1.07  ; 
% 0.89/1.07  ; Run time in seconds excluding printing time:
% 0.89/1.07  ;     0.002   0%   Read assertion file          (1 call)
% 0.89/1.07  ;     0.001   0%   Assert                       (20 calls)
% 0.89/1.07  ;     0.048   7%   Process new row              (3,820 calls)
% 0.89/1.07  ;     0.002   0%   Resolution                   (166 calls)
% 0.89/1.07  ;     0.074  11%   Paramodulation               (83 calls)
% 0.89/1.07  ;     0.006   1%   Embedding                    (347 calls)
% 0.89/1.07  ;     0.456  69%   Forward simplification       (3,479 calls)
% 0.89/1.07  ;     0.011   2%   Backward simplification      (367 calls)
% 0.89/1.07  ;     0.015   2%   Ordering                     (4,675 calls)
% 0.89/1.07  ;     0.010   2%   Ordering ac                  (1,933 calls)
% 0.89/1.07  ;     0.001   0%   Sortal reasoning             (32 calls)
% 0.89/1.07  ;     0.000   0%   Purity testing               (1 call)
% 0.89/1.07  ;     0.032   5%   Other
% 0.89/1.07  ;     0.658        Total
% 0.89/1.07  ;     0.660        Real time
% 0.89/1.07  ; 
% 0.89/1.07  ; Term-hash-array has 1,798 terms in all.
% 0.89/1.07  ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.89/1.07  ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.89/1.07  ; Path-index has 1,636 entries (1,636 at peak, 1,820 added, 184 deleted).
% 0.89/1.07  ; Path-index has 502 nodes (502 at peak, 524 added, 22 deleted).
% 0.89/1.07  ; Trie-index has 1,636 entries (1,636 at peak, 1,820 added, 184 deleted).
% 0.89/1.07  ; Trie-index has 394 nodes (394 at peak, 437 added, 43 deleted).
% 0.89/1.07  ; Retrieved 1,003,558 generalization terms in 31,795 calls.
% 0.89/1.07  ; Retrieved 780 instance terms in 390 calls.
% 0.89/1.07  ; Retrieved 15,800 unifiable terms in 443 calls.
% 0.89/1.07  ; 
% 0.89/1.07  ; The agenda of rows to process has 101 entries:
% 0.89/1.07  ;     5 with value 14             12 with value 21              17 with value 26
% 0.89/1.07  ;     6 with value 15              9 with value 22              11 with value 28
% 0.89/1.07  ;     4 with value 16             12 with value 23               8 with value 30
% 0.89/1.07  ;     2 with value 18              3 with value 24               1 with value 31
% 0.89/1.07  ;     5 with value 20              1 with value 25               5 with value 32
% 0.89/1.07  ; The agenda of rows to give has 551 entries:
% 0.89/1.07  ;     7 with value (4 13)         23 with value (4 20)           4 with value (4 27)
% 0.89/1.07  ;    12 with value (4 14)         54 with value (4 21)          12 with value (4 28)
% 0.89/1.07  ;    95 with value (4 15)         44 with value (4 22)           4 with value (4 30)
% 0.89/1.07  ;   132 with value (4 16)         54 with value (4 23)           4 with value (4 31)
% 0.89/1.07  ;    24 with value (4 17)         22 with value (4 24)           4 with value (4 33)
% 0.89/1.07  ;    18 with value (4 18)          6 with value (4 25)           4 with value (4 36)
% 0.89/1.07  ;    24 with value (4 19)          4 with value (4 26)
% 0.89/1.07  Evaluation took:
% 0.89/1.07    0.66 seconds of real time
% 0.89/1.07    0.627423 seconds of user run time
% 0.89/1.07    0.032524 seconds of system run time
% 0.89/1.07    [Run times include 0.009 seconds GC run time.]
% 0.89/1.07    0 calls to %EVAL
% 0.89/1.07    0 page faults and
% 0.89/1.07    35,124,288 bytes consed.
% 0.89/1.07  :PROOF-FOUND
% 0.89/1.07  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T08:10:57
% 0.89/1.07  :PROOF-FOUND
% 0.89/1.07  * 
%------------------------------------------------------------------------------