TSTP Solution File: GRP100-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP100-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n011.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 11:36:09 EDT 2022

% Result   : Unsatisfiable 0.46s 0.70s
% Output   : Refutation 0.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   45 (  40 unt;   0 nHn;  10 RR)
%            Number of literals    :   55 (  54 equ;  17 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   8 con; 0-2 aty)
%            Number of variables   :   76 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
    double_divide(double_divide(X,double_divide(double_divide(Y,double_divide(X,Z)),double_divide(Z,identity))),double_divide(identity,identity)) = Y,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).

cnf(multiply,axiom,
    multiply(X,Y) = double_divide(double_divide(Y,X),identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).

cnf(inverse,axiom,
    inverse(X) = double_divide(X,identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).

cnf(identity,axiom,
    identity = double_divide(X,inverse(X)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).

cnf(prove_these_axioms,negated_conjecture,
    ( multiply(inverse(a1),a1) != identity
    | multiply(identity,a2) != a2
    | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
    | multiply(a4,b4) != multiply(b4,a4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).

cnf(6,plain,
    multiply(X,Y) = inverse(double_divide(Y,X)),
    inference('REWRITE',[status(thm)],[multiply,inverse,theory(equality)]) ).

cnf(7,plain,
    ( inverse(identity) != identity
    | inverse(inverse(a2)) != a2
    | inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3))
    | inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)) ),
    inference('REWRITE',[status(thm)],[prove_these_axioms,inverse,identity,6,theory(equality)]) ).

cnf(8,plain,
    double_divide(double_divide(X,double_divide(double_divide(Y,double_divide(X,Z)),inverse(Z))),inverse(identity)) = Y,
    inference('REWRITE',[status(thm)],[single_axiom,inverse,theory(equality)]) ).

cnf(9,plain,
    double_divide(double_divide(X,double_divide(double_divide(Y,inverse(X)),inverse(identity))),inverse(identity)) = Y,
    inference('PARAMODULATE',[status(thm)],[8,inverse,theory(equality)]) ).

cnf(10,plain,
    double_divide(double_divide(X,double_divide(inverse(Y),inverse(inverse(X)))),inverse(identity)) = Y,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,identity,theory(equality)]),inverse,theory(equality)]) ).

cnf(12,plain,
    double_divide(inverse(X),inverse(identity)) = X,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,identity,theory(equality)]),inverse,theory(equality)]) ).

cnf(15,plain,
    double_divide(double_divide(identity,double_divide(X,inverse(identity))),inverse(identity)) = inverse(X),
    inference('PARAMODULATE',[status(thm)],[9,12,theory(equality)]) ).

cnf(16,plain,
    inverse(X) = double_divide(Y,double_divide(inverse(X),inverse(inverse(Y)))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9,10,theory(equality)]),15,theory(equality)]) ).

cnf(17,plain,
    inverse(X) = double_divide(Y,double_divide(double_divide(X,inverse(Y)),inverse(identity))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9,9,theory(equality)]),15,theory(equality)]) ).

cnf(18,plain,
    double_divide(double_divide(inverse(X),double_divide(inverse(X),inverse(inverse(inverse(Y))))),inverse(identity)) = Y,
    inference('PARAMODULATE',[status(thm)],[8,16,theory(equality)]) ).

cnf(20,plain,
    inverse(inverse(X)) = double_divide(identity,double_divide(X,inverse(identity))),
    inference('PARAMODULATE',[status(thm)],[17,12,theory(equality)]) ).

cnf(22,plain,
    inverse(double_divide(X,double_divide(double_divide(Y,double_divide(X,Z)),inverse(Z)))) = inverse(inverse(Y)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[17,8,theory(equality)]),20,theory(equality)]) ).

cnf(24,plain,
    inverse(inverse(identity)) = inverse(identity),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[20,identity,theory(equality)]),inverse,theory(equality)]) ).

cnf(30,plain,
    inverse(identity) = identity,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12,24,theory(equality)]),12,theory(equality)]) ).

cnf(31,plain,
    ( inverse(inverse(a2)) != a2
    | inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3))
    | inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)) ),
    inference('REWRITE',[status(thm)],[7,30,theory(equality)]) ).

cnf(32,plain,
    inverse(inverse(X)) = X,
    inference('REWRITE',[status(thm)],[8,22,inverse,30,theory(equality)]) ).

cnf(34,plain,
    inverse(X) = double_divide(Y,double_divide(inverse(X),Y)),
    inference('REWRITE',[status(thm)],[16,32,theory(equality)]) ).

cnf(35,plain,
    inverse(double_divide(X,double_divide(double_divide(Y,double_divide(X,Z)),inverse(Z)))) = Y,
    inference('REWRITE',[status(thm)],[22,32,theory(equality)]) ).

cnf(36,plain,
    ( inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3))
    | inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)) ),
    inference('REWRITE',[status(thm)],[31,32,theory(equality)]) ).

cnf(37,plain,
    inverse(X) = double_divide(Y,inverse(double_divide(X,inverse(Y)))),
    inference('REWRITE',[status(thm)],[17,inverse,30,theory(equality)]) ).

cnf(38,plain,
    inverse(double_divide(inverse(X),double_divide(inverse(X),inverse(Y)))) = Y,
    inference('REWRITE',[status(thm)],[18,inverse,32,30,theory(equality)]) ).

cnf(45,plain,
    X = double_divide(Y,double_divide(X,Y)),
    inference('PARAMODULATE',[status(thm)],[34,32,theory(equality)]) ).

cnf(46,plain,
    X = double_divide(double_divide(Y,X),Y),
    inference('PARAMODULATE',[status(thm)],[45,45,theory(equality)]) ).

cnf(48,plain,
    inverse(double_divide(X,inverse(Y))) = double_divide(inverse(X),Y),
    inference('PARAMODULATE',[status(thm)],[46,37,theory(equality)]) ).

cnf(49,plain,
    ( double_divide(inverse(c3),double_divide(b3,a3)) != double_divide(double_divide(c3,b3),inverse(a3))
    | inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)) ),
    inference('REWRITE',[status(thm)],[36,32,48,theory(equality)]) ).

cnf(51,plain,
    inverse(double_divide(X,double_divide(X,inverse(Y)))) = Y,
    inference('PARAMODULATE',[status(thm)],[38,38,theory(equality)]) ).

cnf(52,plain,
    inverse(X) = double_divide(Y,double_divide(Y,inverse(X))),
    inference('PARAMODULATE',[status(thm)],[32,51,theory(equality)]) ).

cnf(53,plain,
    X = double_divide(Y,double_divide(Y,X)),
    inference('PARAMODULATE',[status(thm)],[52,32,theory(equality)]) ).

cnf(54,plain,
    double_divide(X,Y) = double_divide(Y,X),
    inference('PARAMODULATE',[status(thm)],[46,53,theory(equality)]) ).

cnf(56,plain,
    double_divide(inverse(c3),double_divide(b3,a3)) != double_divide(double_divide(c3,b3),inverse(a3)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[49,54,theory(equality)]),theory(equality)]) ).

cnf(93,plain,
    inverse(X) = double_divide(Y,double_divide(double_divide(X,double_divide(Y,Z)),inverse(Z))),
    inference('PARAMODULATE',[status(thm)],[32,35,theory(equality)]) ).

cnf(130,plain,
    double_divide(double_divide(X,double_divide(Y,Z)),inverse(Z)) = double_divide(inverse(X),Y),
    inference('PARAMODULATE',[status(thm)],[46,93,theory(equality)]) ).

cnf(131,plain,
    double_divide(double_divide(X,Y),inverse(Z)) = double_divide(inverse(X),double_divide(Z,Y)),
    inference('PARAMODULATE',[status(thm)],[130,46,theory(equality)]) ).

cnf(132,plain,
    double_divide(inverse(c3),double_divide(b3,a3)) != double_divide(inverse(c3),double_divide(a3,b3)),
    inference('REWRITE',[status(thm)],[56,131,theory(equality)]) ).

cnf(134,plain,
    double_divide(X,double_divide(Y,Z)) = double_divide(inverse(Z),double_divide(inverse(X),Y)),
    inference('PARAMODULATE',[status(thm)],[45,130,theory(equality)]) ).

cnf(167,plain,
    double_divide(double_divide(X,Y),inverse(Z)) = double_divide(inverse(Y),double_divide(Z,X)),
    inference('PARAMODULATE',[status(thm)],[131,54,theory(equality)]) ).

cnf(171,plain,
    double_divide(inverse(double_divide(X,Y)),double_divide(Y,Z)) = double_divide(inverse(Z),X),
    inference('REWRITE',[status(thm)],[130,167,theory(equality)]) ).

cnf(213,plain,
    double_divide(inverse(X),double_divide(Y,Z)) = double_divide(inverse(Z),double_divide(Y,X)),
    inference('PARAMODULATE',[status(thm)],[171,46,theory(equality)]) ).

cnf(265,plain,
    double_divide(inverse(X),double_divide(Y,Z)) = double_divide(inverse(X),double_divide(Z,Y)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[213,134,theory(equality)]),32,theory(equality)]) ).

cnf(266,plain,
    $false,
    inference('REWRITE',[status(thm)],[132,265,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : GRP100-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.12/0.12  % Command  : run-snark %s %d
% 0.12/0.33  % Computer : n011.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Tue Jun 14 11:30:49 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.44  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45  * 
% 0.18/0.45  * 
% 0.18/0.46  #<PACKAGE "SNARK-USER">
% 0.18/0.46  * 
% 0.18/0.46  SNARK-TPTP-OPTIONS
% 0.18/0.46  * 
% 0.18/0.46  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.18/0.46   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.18/0.46   (USE-FACTORING :POS)
% 0.18/0.46   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.18/0.46   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.18/0.46   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.18/0.46   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.18/0.46   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.18/0.46   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.18/0.46   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.18/0.46   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.18/0.46   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.18/0.46   (DECLARE-TPTP-SYMBOLS2))
% 0.18/0.46  * 
% 0.18/0.46  "."
% 0.18/0.46  * 
% 0.18/0.46  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-14T11:30:49
% 0.18/0.46  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n011.cluster.edu at 2022-06-14T11:30:49
% 0.18/0.47  
% 0.46/0.70  ; Recognized possible right inverse assertion (= |identity| (|double_divide| ?X (|inverse| ?X))).
% 0.46/0.70  
% 0.46/0.70  #||
% 0.46/0.70  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.46/0.70  % SZS output start Refutation
% See solution above
% 0.53/0.71  ||#
% 0.53/0.71  
% 0.53/0.71  ; Summary of computation:
% 0.53/0.71  ;      1190 formulas have been input or derived (from 44 formulas).
% 0.53/0.71  ;       266 (22%) were retained.  Of these,
% 0.53/0.71  ;           80 (30%) were simplified or subsumed later,
% 0.53/0.71  ;          186 (70%) are still being kept.
% 0.53/0.71  ; 
% 0.53/0.71  ; Run time in seconds excluding printing time:
% 0.53/0.71  ;     0.001   0%   Read assertion file          (1 call)
% 0.53/0.71  ;     0.000   0%   Assert                       (5 calls)
% 0.53/0.71  ;     0.021   9%   Process new row              (1,088 calls)
% 0.53/0.71  ;     0.002   1%   Resolution                   (86 calls)
% 0.53/0.71  ;     0.022   9%   Paramodulation               (43 calls)
% 0.53/0.71  ;     0.000   0%   Condensing                   (5 calls)
% 0.53/0.71  ;     0.000   0%   Forward subsumption          (5 calls)
% 0.53/0.71  ;     0.000   0%   Backward subsumption         (5 calls)
% 0.53/0.71  ;     0.043  18%   Forward simplification       (929 calls)
% 0.53/0.71  ;     0.018   8%   Backward simplification      (266 calls)
% 0.53/0.71  ;     0.104  44%   Ordering                     (13,323 calls)
% 0.53/0.71  ;     0.001   0%   Sortal reasoning             (32 calls)
% 0.53/0.71  ;     0.000   0%   Purity testing               (1 call)
% 0.53/0.71  ;     0.027  11%   Other
% 0.53/0.71  ;     0.239        Total
% 0.53/0.71  ;     0.249        Real time
% 0.53/0.71  ; 
% 0.53/0.71  ; Term-hash-array has 709 terms in all.
% 0.53/0.71  ; Feature-vector-row-index has 0 entries (1 at peak, 5 added, 5 deleted).
% 0.53/0.71  ; Feature-vector-row-index has 1 node (29 at peak, 127 added, 126 deleted).
% 0.53/0.71  ;  Retrieved 0 possibly forward subsuming rows in 5 calls.
% 0.53/0.71  ;  Retrieved 0 possibly backward subsumed rows in 5 calls.
% 0.53/0.71  ; Path-index has 467 entries (476 at peak, 825 added, 358 deleted).
% 0.53/0.71  ; Path-index has 535 nodes (553 at peak, 1,014 added, 479 deleted).
% 0.53/0.71  ; Trie-index has 467 entries (476 at peak, 825 added, 358 deleted).
% 0.53/0.71  ; Trie-index has 1,629 nodes (1,653 at peak, 3,066 added, 1,437 deleted).
% 0.53/0.71  ; Retrieved 10,159 generalization terms in 6,339 calls.
% 0.53/0.71  ; Retrieved 3,653 instance terms in 489 calls.
% 0.53/0.71  ; Retrieved 2,053 unifiable terms in 344 calls.
% 0.53/0.71  ; 
% 0.53/0.71  ; The agenda of rows to process has 61 entries:
% 0.53/0.71  ;     7 with value 27              7 with value 29              18 with value 31
% 0.53/0.71  ;    10 with value 28             13 with value 30               6 with value 32
% 0.53/0.71  ; The agenda of rows to give has 163 entries:
% 0.53/0.71  ;     1 with value (4 21)         17 with value (4 26)          21 with value (4 30)
% 0.53/0.71  ;     5 with value (4 23)         14 with value (4 27)           6 with value (4 31)
% 0.53/0.71  ;    22 with value (4 24)         24 with value (4 28)           8 with value (4 32)
% 0.53/0.71  ;    12 with value (4 25)         31 with value (4 29)           2 with value (4 35)
% 0.53/0.71  Evaluation took:
% 0.53/0.71    0.249 seconds of real time
% 0.53/0.71    0.2158 seconds of user run time
% 0.53/0.71    0.032919 seconds of system run time
% 0.53/0.71    [Run times include 0.005 seconds GC run time.]
% 0.53/0.71    0 calls to %EVAL
% 0.53/0.71    0 page faults and
% 0.53/0.71    16,392,696 bytes consed.
% 0.53/0.71  :PROOF-FOUND
% 0.53/0.71  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-14T11:30:50
% 0.53/0.71  :PROOF-FOUND
% 0.53/0.71  * 
%------------------------------------------------------------------------------