TSTP Solution File: GRP077-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP077-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n006.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 11:36:02 EDT 2022

% Result   : Unsatisfiable 0.19s 0.54s
% Output   : Refutation 0.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   40 (  37 unt;   0 nHn;   7 RR)
%            Number of literals    :   45 (  44 equ;  10 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :   10 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :   58 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
    double_divide(X,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X,identity),double_divide(Y,Z))),Y),identity)) = Z,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).

cnf(multiply,axiom,
    multiply(X,Y) = double_divide(double_divide(Y,X),identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).

cnf(inverse,axiom,
    inverse(X) = double_divide(X,identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).

cnf(identity,axiom,
    identity = double_divide(X,inverse(X)),
    file('/export/starexec/sandbox2/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)) ),
    file('/export/starexec/sandbox2/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)) ),
    inference('REWRITE',[status(thm)],[prove_these_axioms,inverse,identity,6,theory(equality)]) ).

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

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

cnf(13,plain,
    double_divide(X,inverse(identity)) = inverse(inverse(double_divide(identity,inverse(inverse(X))))),
    inference('PARAMODULATE',[status(thm)],[10,identity,theory(equality)]) ).

cnf(14,plain,
    double_divide(X,double_divide(X,inverse(identity))) = inverse(identity),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,inverse,theory(equality)]),13,theory(equality)]) ).

cnf(19,plain,
    double_divide(X,inverse(Y)) = inverse(inverse(double_divide(double_divide(identity,double_divide(inverse(double_divide(identity,inverse(inverse(X)))),double_divide(Z,Y))),Z))),
    inference('PARAMODULATE',[status(thm)],[10,8,theory(equality)]) ).

cnf(20,plain,
    double_divide(X,inverse(double_divide(identity,inverse(X)))) = inverse(identity),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,14,theory(equality)]),identity,theory(equality)]) ).

cnf(26,plain,
    inverse(identity) = identity,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[20,identity,theory(equality)]),identity,theory(equality)]) ).

cnf(27,plain,
    ( inverse(inverse(a2)) != a2
    | inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)) ),
    inference('REWRITE',[status(thm)],[7,26,theory(equality)]) ).

cnf(28,plain,
    inverse(X) = inverse(inverse(double_divide(identity,inverse(inverse(X))))),
    inference('REWRITE',[status(thm)],[13,inverse,26,theory(equality)]) ).

cnf(31,plain,
    double_divide(X,inverse(double_divide(identity,inverse(X)))) = identity,
    inference('REWRITE',[status(thm)],[20,26,theory(equality)]) ).

cnf(32,plain,
    double_divide(identity,inverse(double_divide(identity,X))) = inverse(X),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,26,theory(equality)]),inverse,26,theory(equality)]) ).

cnf(33,plain,
    double_divide(identity,inverse(double_divide(double_divide(identity,double_divide(identity,double_divide(X,Y))),X))) = Y,
    inference('PARAMODULATE',[status(thm)],[8,26,theory(equality)]) ).

cnf(37,plain,
    inverse(X) = inverse(double_divide(identity,inverse(X))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,31,theory(equality)]),10,inverse,theory(equality)]) ).

cnf(38,plain,
    double_divide(X,inverse(Y)) = inverse(inverse(double_divide(double_divide(identity,double_divide(inverse(inverse(X)),double_divide(Z,Y))),Z))),
    inference('REWRITE',[status(thm)],[19,37,theory(equality)]) ).

cnf(39,plain,
    inverse(X) = inverse(inverse(inverse(X))),
    inference('REWRITE',[status(thm)],[28,37,theory(equality)]) ).

cnf(42,plain,
    double_divide(inverse(X),inverse(double_divide(double_divide(identity,inverse(X)),Y))) = inverse(Y),
    inference('PARAMODULATE',[status(thm)],[10,39,theory(equality)]) ).

cnf(45,plain,
    inverse(double_divide(identity,X)) = inverse(inverse(X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[37,10,theory(equality)]),inverse,26,theory(equality)]) ).

cnf(46,plain,
    double_divide(identity,inverse(inverse(X))) = inverse(X),
    inference('REWRITE',[status(thm)],[32,45,theory(equality)]) ).

cnf(48,plain,
    double_divide(X,inverse(double_divide(inverse(X),Y))) = inverse(Y),
    inference('REWRITE',[status(thm)],[10,46,theory(equality)]) ).

cnf(53,plain,
    inverse(X) = inverse(double_divide(double_divide(identity,double_divide(identity,double_divide(Y,X))),Y)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[45,8,theory(equality)]),39,26,theory(equality)]) ).

cnf(55,plain,
    double_divide(identity,inverse(X)) = X,
    inference('REWRITE',[status(thm)],[33,53,theory(equality)]) ).

cnf(59,plain,
    double_divide(inverse(X),inverse(double_divide(X,Y))) = inverse(Y),
    inference('REWRITE',[status(thm)],[42,55,theory(equality)]) ).

cnf(61,plain,
    X = inverse(inverse(X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[55,39,theory(equality)]),55,theory(equality)]) ).

cnf(64,plain,
    double_divide(X,inverse(Y)) = double_divide(double_divide(identity,double_divide(X,double_divide(Z,Y))),Z),
    inference('REWRITE',[status(thm)],[38,61,theory(equality)]) ).

cnf(69,plain,
    inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
    inference('REWRITE',[status(thm)],[27,61,theory(equality)]) ).

cnf(71,plain,
    double_divide(identity,X) = inverse(X),
    inference('PARAMODULATE',[status(thm)],[55,61,theory(equality)]) ).

cnf(73,plain,
    double_divide(X,inverse(Y)) = double_divide(inverse(double_divide(X,double_divide(Z,Y))),Z),
    inference('REWRITE',[status(thm)],[64,71,theory(equality)]) ).

cnf(74,plain,
    inverse(X) = double_divide(inverse(double_divide(X,inverse(Y))),Y),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[73,inverse,theory(equality)]),inverse,26,theory(equality)]) ).

cnf(83,plain,
    X = double_divide(Y,double_divide(X,Y)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[74,59,theory(equality)]),61,theory(equality)]) ).

cnf(91,plain,
    double_divide(X,inverse(Y)) = inverse(double_divide(Y,inverse(X))),
    inference('PARAMODULATE',[status(thm)],[48,83,theory(equality)]) ).

cnf(93,plain,
    double_divide(double_divide(b3,a3),inverse(c3)) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
    inference('REWRITE',[status(thm)],[69,91,theory(equality)]) ).

cnf(94,plain,
    double_divide(X,inverse(double_divide(Y,Z))) = double_divide(inverse(double_divide(X,Y)),Z),
    inference('PARAMODULATE',[status(thm)],[73,83,theory(equality)]) ).

cnf(95,plain,
    $false,
    inference('REWRITE',[status(thm)],[93,61,91,94,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP077-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.03/0.13  % Command  : run-snark %s %d
% 0.12/0.34  % Computer : n006.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Tue Jun 14 02:37:26 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.46  /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p 2022-06-14T02:37:27
% 0.19/0.48  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n006.cluster.edu at 2022-06-14T02:37:27
% 0.19/0.49  
% 0.19/0.54  ; Recognized possible right inverse assertion (= |identity| (|double_divide| ?X (|inverse| ?X))).
% 0.19/0.54  
% 0.19/0.54  #||
% 0.19/0.54  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.54  % SZS output start Refutation
% See solution above
% 0.39/0.55  ||#
% 0.39/0.55  
% 0.39/0.55  ; Summary of computation:
% 0.39/0.55  ;       259 formulas have been input or derived (from 28 formulas).
% 0.39/0.55  ;        95 (37%) were retained.  Of these,
% 0.39/0.55  ;           73 (77%) were simplified or subsumed later,
% 0.39/0.55  ;           22 (23%) are still being kept.
% 0.39/0.55  ; 
% 0.39/0.55  ; Run time in seconds excluding printing time:
% 0.39/0.55  ;     0.001   2%   Read assertion file          (1 call)
% 0.39/0.55  ;     0.001   2%   Assert                       (5 calls)
% 0.39/0.55  ;     0.014  22%   Process new row              (256 calls)
% 0.39/0.55  ;     0.001   2%   Resolution                   (54 calls)
% 0.39/0.55  ;     0.004   6%   Paramodulation               (27 calls)
% 0.39/0.55  ;     0.000   0%   Condensing                   (3 calls)
% 0.39/0.55  ;     0.000   0%   Forward subsumption          (3 calls)
% 0.39/0.55  ;     0.000   0%   Backward subsumption         (3 calls)
% 0.39/0.55  ;     0.005   8%   Forward simplification       (241 calls)
% 0.39/0.55  ;     0.012  19%   Backward simplification      (95 calls)
% 0.39/0.55  ;     0.001   2%   Ordering                     (551 calls)
% 0.39/0.55  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.39/0.55  ;     0.000   0%   Purity testing               (1 call)
% 0.39/0.55  ;     0.024  38%   Other
% 0.39/0.55  ;     0.063        Total
% 0.39/0.55  ;     0.070        Real time
% 0.39/0.55  ; 
% 0.39/0.55  ; Term-hash-array has 337 terms in all.
% 0.39/0.55  ; Feature-vector-row-index has 0 entries (1 at peak, 3 added, 3 deleted).
% 0.39/0.55  ; Feature-vector-row-index has 1 node (26 at peak, 69 added, 68 deleted).
% 0.39/0.55  ;  Retrieved 0 possibly forward subsuming rows in 3 calls.
% 0.39/0.55  ;  Retrieved 0 possibly backward subsumed rows in 3 calls.
% 0.39/0.55  ; Path-index has 89 entries (131 at peak, 453 added, 364 deleted).
% 0.39/0.55  ; Path-index has 550 nodes (571 at peak, 1,035 added, 485 deleted).
% 0.39/0.55  ; Trie-index has 89 entries (131 at peak, 453 added, 364 deleted).
% 0.39/0.55  ; Trie-index has 295 nodes (532 at peak, 1,683 added, 1,388 deleted).
% 0.39/0.55  ; Retrieved 570 generalization terms in 1,403 calls.
% 0.39/0.55  ; Retrieved 209 instance terms in 106 calls.
% 0.39/0.55  ; Retrieved 455 unifiable terms in 207 calls.
% 0.39/0.55  ; 
% 0.39/0.55  ; The agenda of rows to process has 1 entry:
% 0.39/0.55  ;     1 with value 22
% 0.39/0.55  ; The agenda of rows to give has 11 entries:
% 0.39/0.55  ;     2 with value (4 18)          4 with value (4 22)           1 with value (4 24)
% 0.39/0.55  ;     1 with value (4 19)          1 with value (4 23)           2 with value (4 27)
% 0.39/0.55  Evaluation took:
% 0.39/0.55    0.071 seconds of real time
% 0.39/0.55    0.05713 seconds of user run time
% 0.39/0.55    0.013149 seconds of system run time
% 0.39/0.55    0 calls to %EVAL
% 0.39/0.55    0 page faults and
% 0.39/0.55    6,681,840 bytes consed.
% 0.39/0.55  :PROOF-FOUND
% 0.39/0.55  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T02:37:27
% 0.39/0.55  :PROOF-FOUND
% 0.39/0.55  * 
%------------------------------------------------------------------------------