TSTP Solution File: GRP101-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP101-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 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 11:36:09 EDT 2022

% Result   : Unsatisfiable 0.53s 0.75s
% Output   : Refutation 0.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   48 (  44 unt;   0 nHn;  10 RR)
%            Number of literals    :   57 (  56 equ;  16 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :   10 (   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   :   84 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
    double_divide(double_divide(X,double_divide(double_divide(Y,double_divide(Z,X)),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(Z,X)),inverse(Z))),inverse(identity)) = Y,
    inference('REWRITE',[status(thm)],[single_axiom,inverse,theory(equality)]) ).

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

cnf(11,plain,
    double_divide(double_divide(inverse(identity),double_divide(double_divide(X,Y),inverse(double_divide(Z,double_divide(double_divide(Y,double_divide(U,Z)),inverse(U)))))),inverse(identity)) = X,
    inference('PARAMODULATE',[status(thm)],[8,8,theory(equality)]) ).

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

cnf(14,plain,
    double_divide(double_divide(inverse(identity),X),inverse(identity)) = inverse(inverse(X)),
    inference('PARAMODULATE',[status(thm)],[9,12,theory(equality)]) ).

cnf(16,plain,
    inverse(inverse(double_divide(double_divide(X,Y),inverse(double_divide(Z,double_divide(double_divide(Y,double_divide(U,Z)),inverse(U))))))) = X,
    inference('REWRITE',[status(thm)],[11,14,theory(equality)]) ).

cnf(20,plain,
    identity = inverse(inverse(inverse(inverse(identity)))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[14,identity,theory(equality)]),identity,theory(equality)]) ).

cnf(24,plain,
    inverse(identity) = identity,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12,20,theory(equality)]),identity,theory(equality)]) ).

cnf(25,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)],[7,24,theory(equality)]) ).

cnf(26,plain,
    inverse(double_divide(X,double_divide(double_divide(Y,double_divide(Z,X)),inverse(Z)))) = Y,
    inference('REWRITE',[status(thm)],[8,inverse,24,theory(equality)]) ).

cnf(27,plain,
    inverse(inverse(double_divide(double_divide(X,Y),Y))) = X,
    inference('REWRITE',[status(thm)],[16,26,theory(equality)]) ).

cnf(28,plain,
    inverse(double_divide(inverse(X),double_divide(inverse(Y),inverse(X)))) = Y,
    inference('REWRITE',[status(thm)],[9,inverse,24,theory(equality)]) ).

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

cnf(31,plain,
    inverse(double_divide(identity,X)) = inverse(inverse(X)),
    inference('REWRITE',[status(thm)],[14,inverse,24,theory(equality)]) ).

cnf(34,plain,
    inverse(double_divide(X,double_divide(double_divide(Y,double_divide(double_divide(Z,double_divide(double_divide(U,double_divide(V,Z)),inverse(V))),X)),U))) = Y,
    inference('PARAMODULATE',[status(thm)],[26,26,theory(equality)]) ).

cnf(37,plain,
    inverse(inverse(inverse(X))) = double_divide(Y,double_divide(double_divide(X,double_divide(Z,Y)),inverse(Z))),
    inference('PARAMODULATE',[status(thm)],[30,26,theory(equality)]) ).

cnf(38,plain,
    inverse(double_divide(X,double_divide(double_divide(Y,double_divide(inverse(inverse(inverse(Z))),X)),Z))) = Y,
    inference('REWRITE',[status(thm)],[34,37,theory(equality)]) ).

cnf(40,plain,
    inverse(X) = double_divide(identity,X),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[30,31,theory(equality)]),30,theory(equality)]) ).

cnf(42,plain,
    inverse(inverse(X)) = double_divide(double_divide(X,Y),Y),
    inference('PARAMODULATE',[status(thm)],[30,27,theory(equality)]) ).

cnf(43,plain,
    identity = double_divide(inverse(X),X),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[42,40,theory(equality)]),24,theory(equality)]) ).

cnf(44,plain,
    inverse(inverse(double_divide(X,Y))) = double_divide(inverse(inverse(X)),Y),
    inference('PARAMODULATE',[status(thm)],[42,42,theory(equality)]) ).

cnf(45,plain,
    inverse(double_divide(X,double_divide(double_divide(Y,inverse(inverse(double_divide(inverse(Z),X)))),Z))) = Y,
    inference('REWRITE',[status(thm)],[38,44,theory(equality)]) ).

cnf(46,plain,
    inverse(inverse(inverse(X))) = inverse(X),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[42,43,theory(equality)]),40,theory(equality)]) ).

cnf(47,plain,
    inverse(inverse(X)) = X,
    inference('REWRITE',[status(thm)],[30,46,theory(equality)]) ).

cnf(48,plain,
    inverse(double_divide(X,double_divide(double_divide(Y,double_divide(inverse(Z),X)),Z))) = Y,
    inference('REWRITE',[status(thm)],[45,47,theory(equality)]) ).

cnf(49,plain,
    X = double_divide(double_divide(X,Y),Y),
    inference('REWRITE',[status(thm)],[42,47,theory(equality)]) ).

cnf(50,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)],[25,47,theory(equality)]) ).

cnf(51,plain,
    inverse(X) = double_divide(Y,double_divide(double_divide(X,double_divide(Z,Y)),inverse(Z))),
    inference('REWRITE',[status(thm)],[37,46,theory(equality)]) ).

cnf(52,plain,
    inverse(double_divide(X,double_divide(inverse(Y),X))) = Y,
    inference('PARAMODULATE',[status(thm)],[28,28,theory(equality)]) ).

cnf(53,plain,
    inverse(X) = double_divide(Y,double_divide(inverse(X),Y)),
    inference('PARAMODULATE',[status(thm)],[47,52,theory(equality)]) ).

cnf(54,plain,
    X = double_divide(Y,double_divide(X,Y)),
    inference('PARAMODULATE',[status(thm)],[53,47,theory(equality)]) ).

cnf(55,plain,
    double_divide(X,Y) = double_divide(Y,X),
    inference('PARAMODULATE',[status(thm)],[54,49,theory(equality)]) ).

cnf(58,plain,
    inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[50,55,theory(equality)]),theory(equality)]) ).

cnf(59,plain,
    inverse(double_divide(X,double_divide(Y,Z))) = double_divide(Y,double_divide(inverse(Z),X)),
    inference('PARAMODULATE',[status(thm)],[48,49,theory(equality)]) ).

cnf(60,plain,
    inverse(double_divide(X,double_divide(Y,Z))) = double_divide(Z,double_divide(X,inverse(Y))),
    inference('PARAMODULATE',[status(thm)],[51,49,theory(equality)]) ).

cnf(62,plain,
    inverse(double_divide(X,inverse(Y))) = double_divide(Y,inverse(X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[59,inverse,theory(equality)]),40,24,theory(equality)]) ).

cnf(63,plain,
    double_divide(double_divide(b3,a3),inverse(c3)) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
    inference('REWRITE',[status(thm)],[58,47,62,theory(equality)]) ).

cnf(87,plain,
    double_divide(inverse(X),Y) = inverse(double_divide(X,inverse(Y))),
    inference('PARAMODULATE',[status(thm)],[55,62,theory(equality)]) ).

cnf(88,plain,
    double_divide(double_divide(b3,a3),inverse(c3)) != double_divide(double_divide(c3,b3),inverse(a3)),
    inference('REWRITE',[status(thm)],[63,47,87,theory(equality)]) ).

cnf(175,plain,
    inverse(double_divide(inverse(X),double_divide(Y,Z))) = double_divide(Z,inverse(double_divide(X,Y))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[60,87,theory(equality)]),47,theory(equality)]) ).

cnf(310,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[88,62,theory(equality)]),55,47,175,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP101-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.13  % 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 23:52:23 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.46  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.47  * 
% 0.20/0.47  * 
% 0.20/0.48  #<PACKAGE "SNARK-USER">
% 0.20/0.48  * 
% 0.20/0.48  SNARK-TPTP-OPTIONS
% 0.20/0.48  * 
% 0.20/0.48  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.48   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.48   (USE-FACTORING :POS)
% 0.20/0.48   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.48   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.48   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.48   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.48   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.48   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.48   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.48   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.48   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.48   (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.48  * 
% 0.20/0.48  "."
% 0.20/0.48  * 
% 0.20/0.48  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T23:52:23
% 0.20/0.48  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n015.cluster.edu at 2022-06-13T23:52:23
% 0.20/0.49  
% 0.53/0.75  ; Recognized possible right inverse assertion (= |identity| (|double_divide| ?X (|inverse| ?X))).
% 0.53/0.75  
% 0.53/0.75  #||
% 0.53/0.75  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.53/0.75  % SZS output start Refutation
% See solution above
% 0.53/0.75  ||#
% 0.53/0.75  
% 0.53/0.75  ; Summary of computation:
% 0.53/0.75  ;       950 formulas have been input or derived (from 42 formulas).
% 0.53/0.75  ;       310 (33%) were retained.  Of these,
% 0.53/0.75  ;           67 (22%) were simplified or subsumed later,
% 0.53/0.75  ;          243 (78%) are still being kept.
% 0.53/0.75  ; 
% 0.53/0.75  ; Run time in seconds excluding printing time:
% 0.53/0.76  ;     0.002   1%   Read assertion file          (1 call)
% 0.53/0.76  ;     0.000   0%   Assert                       (5 calls)
% 0.53/0.76  ;     0.041  15%   Process new row              (918 calls)
% 0.53/0.76  ;     0.001   0%   Resolution                   (82 calls)
% 0.53/0.76  ;     0.014   5%   Paramodulation               (41 calls)
% 0.53/0.76  ;     0.000   0%   Condensing                   (4 calls)
% 0.53/0.76  ;     0.002   1%   Forward subsumption          (4 calls)
% 0.53/0.76  ;     0.001   0%   Backward subsumption         (4 calls)
% 0.53/0.76  ;     0.048  18%   Forward simplification       (829 calls)
% 0.53/0.76  ;     0.023   8%   Backward simplification      (310 calls)
% 0.53/0.76  ;     0.116  42%   Ordering                     (17,583 calls)
% 0.53/0.76  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.53/0.76  ;     0.000   0%   Purity testing               (1 call)
% 0.53/0.76  ;     0.025   9%   Other
% 0.53/0.76  ;     0.273        Total
% 0.53/0.76  ;     0.278        Real time
% 0.53/0.76  ; 
% 0.53/0.76  ; Term-hash-array has 872 terms in all.
% 0.53/0.76  ; Feature-vector-row-index has 0 entries (1 at peak, 4 added, 4 deleted).
% 0.53/0.76  ; Feature-vector-row-index has 1 node (29 at peak, 104 added, 103 deleted).
% 0.53/0.76  ;  Retrieved 0 possibly forward subsuming rows in 4 calls.
% 0.53/0.76  ;  Retrieved 0 possibly backward subsumed rows in 4 calls.
% 0.53/0.76  ; Path-index has 652 entries (652 at peak, 999 added, 347 deleted).
% 0.53/0.76  ; Path-index has 755 nodes (755 at peak, 1,285 added, 530 deleted).
% 0.53/0.76  ; Trie-index has 652 entries (652 at peak, 999 added, 347 deleted).
% 0.53/0.76  ; Trie-index has 2,124 nodes (2,124 at peak, 3,453 added, 1,329 deleted).
% 0.53/0.76  ; Retrieved 11,276 generalization terms in 5,615 calls.
% 0.53/0.76  ; Retrieved 3,973 instance terms in 659 calls.
% 0.53/0.76  ; Retrieved 1,982 unifiable terms in 335 calls.
% 0.53/0.76  ; 
% 0.53/0.76  ; The agenda of rows to process has 1 entry:
% 0.53/0.76  ;     1 with value 26
% 0.53/0.76  ; The agenda of rows to give has 219 entries:
% 0.53/0.76  ;     4 with value (4 22)         20 with value (4 26)          38 with value (4 30)
% 0.53/0.76  ;    29 with value (4 23)         34 with value (4 27)          23 with value (4 31)
% 0.53/0.76  ;    12 with value (4 24)         21 with value (4 28)          10 with value (4 32)
% 0.53/0.76  ;    15 with value (4 25)          9 with value (4 29)           4 with value (4 33)
% 0.53/0.76  Evaluation took:
% 0.53/0.76    0.278 seconds of real time
% 0.53/0.76    0.240986 seconds of user run time
% 0.53/0.76    0.036963 seconds of system run time
% 0.53/0.76    [Run times include 0.007 seconds GC run time.]
% 0.53/0.76    0 calls to %EVAL
% 0.53/0.76    0 page faults and
% 0.53/0.76    17,747,120 bytes consed.
% 0.53/0.76  :PROOF-FOUND
% 0.53/0.76  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T23:52:23
% 0.53/0.76  :PROOF-FOUND
% 0.53/0.76  * 
%------------------------------------------------------------------------------