TSTP Solution File: GRP567-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP567-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n014.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 11:39:27 EDT 2022

% Result   : Unsatisfiable 0.20s 0.54s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   43 (  43 unt;   0 nHn;   6 RR)
%            Number of literals    :   43 (  42 equ;   4 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    7 (   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   :   74 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
    double_divide(double_divide(X,double_divide(double_divide(Y,double_divide(X,Z)),double_divide(identity,Z))),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_3,negated_conjecture,
    multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).

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

cnf(7,plain,
    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_3,6,theory(equality)]) ).

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

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

cnf(13,plain,
    double_divide(inverse(X),inverse(identity)) = X,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9,identity,theory(equality)]),inverse,identity,theory(equality)]) ).

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

cnf(15,plain,
    double_divide(double_divide(identity,double_divide(X,inverse(identity))),inverse(identity)) = double_divide(Y,double_divide(double_divide(X,double_divide(Y,Z)),double_divide(identity,Z))),
    inference('PARAMODULATE',[status(thm)],[9,8,theory(equality)]) ).

cnf(16,plain,
    double_divide(double_divide(double_divide(identity,double_divide(X,inverse(identity))),inverse(identity)),inverse(identity)) = X,
    inference('REWRITE',[status(thm)],[8,15,theory(equality)]) ).

cnf(18,plain,
    double_divide(double_divide(identity,X),inverse(identity)) = double_divide(identity,double_divide(X,inverse(identity))),
    inference('PARAMODULATE',[status(thm)],[9,16,theory(equality)]) ).

cnf(19,plain,
    double_divide(double_divide(double_divide(identity,X),inverse(identity)),inverse(identity)) = double_divide(Y,double_divide(double_divide(X,inverse(Y)),inverse(identity))),
    inference('REWRITE',[status(thm)],[14,18,theory(equality)]) ).

cnf(21,plain,
    double_divide(double_divide(double_divide(identity,X),inverse(identity)),inverse(identity)) = double_divide(Y,double_divide(double_divide(X,double_divide(Y,Z)),double_divide(identity,Z))),
    inference('REWRITE',[status(thm)],[15,18,theory(equality)]) ).

cnf(23,plain,
    identity = inverse(identity),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[18,identity,theory(equality)]),13,inverse,theory(equality)]) ).

cnf(24,plain,
    inverse(double_divide(X,double_divide(inverse(Y),double_divide(identity,inverse(X))))) = Y,
    inference('REWRITE',[status(thm)],[10,inverse,23,theory(equality)]) ).

cnf(25,plain,
    inverse(double_divide(X,inverse(double_divide(Y,inverse(X))))) = Y,
    inference('REWRITE',[status(thm)],[11,inverse,23,theory(equality)]) ).

cnf(26,plain,
    inverse(inverse(X)) = X,
    inference('REWRITE',[status(thm)],[13,inverse,23,theory(equality)]) ).

cnf(27,plain,
    inverse(double_divide(identity,X)) = double_divide(identity,inverse(X)),
    inference('REWRITE',[status(thm)],[18,inverse,23,theory(equality)]) ).

cnf(28,plain,
    inverse(double_divide(X,double_divide(inverse(Y),inverse(double_divide(identity,X))))) = Y,
    inference('REWRITE',[status(thm)],[24,27,theory(equality)]) ).

cnf(29,plain,
    double_divide(identity,X) = double_divide(Y,inverse(double_divide(X,inverse(Y)))),
    inference('REWRITE',[status(thm)],[19,26,inverse,23,theory(equality)]) ).

cnf(30,plain,
    inverse(double_divide(identity,X)) = X,
    inference('REWRITE',[status(thm)],[25,29,theory(equality)]) ).

cnf(32,plain,
    inverse(double_divide(X,double_divide(inverse(Y),X))) = Y,
    inference('REWRITE',[status(thm)],[28,30,theory(equality)]) ).

cnf(33,plain,
    inverse(X) = double_divide(Y,double_divide(double_divide(X,double_divide(Y,Z)),double_divide(identity,Z))),
    inference('REWRITE',[status(thm)],[21,30,inverse,23,theory(equality)]) ).

cnf(36,plain,
    inverse(X) = double_divide(identity,X),
    inference('PARAMODULATE',[status(thm)],[26,30,theory(equality)]) ).

cnf(37,plain,
    inverse(X) = double_divide(Y,double_divide(double_divide(X,double_divide(Y,Z)),inverse(Z))),
    inference('REWRITE',[status(thm)],[33,36,theory(equality)]) ).

cnf(38,plain,
    inverse(X) = double_divide(Y,inverse(double_divide(X,inverse(Y)))),
    inference('REWRITE',[status(thm)],[29,36,theory(equality)]) ).

cnf(39,plain,
    inverse(X) = double_divide(Y,double_divide(inverse(X),Y)),
    inference('PARAMODULATE',[status(thm)],[26,32,theory(equality)]) ).

cnf(41,plain,
    X = double_divide(Y,double_divide(X,Y)),
    inference('PARAMODULATE',[status(thm)],[39,26,theory(equality)]) ).

cnf(42,plain,
    X = double_divide(double_divide(Y,X),Y),
    inference('PARAMODULATE',[status(thm)],[41,41,theory(equality)]) ).

cnf(43,plain,
    inverse(double_divide(X,inverse(Y))) = double_divide(inverse(X),Y),
    inference('PARAMODULATE',[status(thm)],[42,38,theory(equality)]) ).

cnf(44,plain,
    double_divide(inverse(c3),double_divide(b3,a3)) != double_divide(double_divide(c3,b3),inverse(a3)),
    inference('REWRITE',[status(thm)],[7,26,43,theory(equality)]) ).

cnf(47,plain,
    X = double_divide(Y,double_divide(Y,X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[37,42,theory(equality)]),26,theory(equality)]) ).

cnf(51,plain,
    inverse(X) = double_divide(double_divide(Y,double_divide(X,Z)),double_divide(inverse(Y),Z)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[37,37,theory(equality)]),26,theory(equality)]) ).

cnf(53,plain,
    double_divide(X,Y) = double_divide(Y,X),
    inference('PARAMODULATE',[status(thm)],[42,47,theory(equality)]) ).

cnf(56,plain,
    double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(double_divide(c3,b3),inverse(a3)),
    inference('PARAMODULATE',[status(thm)],[44,53,theory(equality)]) ).

cnf(72,plain,
    inverse(X) = double_divide(double_divide(inverse(Y),double_divide(X,Z)),double_divide(Y,Z)),
    inference('PARAMODULATE',[status(thm)],[51,26,theory(equality)]) ).

cnf(86,plain,
    double_divide(inverse(X),double_divide(Y,Z)) = double_divide(double_divide(X,Z),inverse(Y)),
    inference('PARAMODULATE',[status(thm)],[41,72,theory(equality)]) ).

cnf(87,plain,
    $false,
    inference('REWRITE',[status(thm)],[56,86,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : GRP567-1 : TPTP v8.1.0. Released v2.6.0.
% 0.12/0.13  % Command  : run-snark %s %d
% 0.13/0.34  % Computer : n014.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 17:19:52 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  * 
% 0.20/0.47  #<PACKAGE "SNARK-USER">
% 0.20/0.47  * 
% 0.20/0.47  SNARK-TPTP-OPTIONS
% 0.20/0.47  * 
% 0.20/0.47  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.47   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.47   (USE-FACTORING :POS)
% 0.20/0.47   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.47   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.47   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.47   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.47   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.47   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.47   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.47   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.47   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.47   (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.47  * 
% 0.20/0.47  "."
% 0.20/0.47  * 
% 0.20/0.47  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T17:19:52
% 0.20/0.47  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n014.cluster.edu at 2022-06-13T17:19:52
% 0.20/0.48  
% 0.20/0.54  ; Recognized possible right inverse assertion (= |identity| (|double_divide| ?X (|inverse| ?X))).
% 0.20/0.54  
% 0.20/0.54  #||
% 0.20/0.54  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.54  % SZS output start Refutation
% See solution above
% 0.20/0.55  ||#
% 0.20/0.55  
% 0.20/0.55  ; Summary of computation:
% 0.20/0.55  ;       470 formulas have been input or derived (from 32 formulas).
% 0.20/0.55  ;        87 (19%) were retained.  Of these,
% 0.20/0.55  ;           45 (52%) were simplified or subsumed later,
% 0.20/0.55  ;           42 (48%) are still being kept.
% 0.20/0.55  ; 
% 0.20/0.55  ; Run time in seconds excluding printing time:
% 0.20/0.55  ;     0.001   1%   Read assertion file          (1 call)
% 0.20/0.55  ;     0.000   0%   Assert                       (5 calls)
% 0.20/0.55  ;     0.009  13%   Process new row              (408 calls)
% 0.20/0.55  ;     0.001   1%   Resolution                   (62 calls)
% 0.20/0.55  ;     0.010  14%   Paramodulation               (31 calls)
% 0.20/0.55  ;     0.011  16%   Forward simplification       (356 calls)
% 0.20/0.55  ;     0.006   9%   Backward simplification      (87 calls)
% 0.20/0.55  ;     0.005   7%   Ordering                     (1,269 calls)
% 0.20/0.55  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.20/0.55  ;     0.000   0%   Purity testing               (1 call)
% 0.20/0.55  ;     0.027  39%   Other
% 0.20/0.55  ;     0.070        Total
% 0.20/0.55  ;     0.076        Real time
% 0.20/0.55  ; 
% 0.20/0.55  ; Term-hash-array has 255 terms in all.
% 0.20/0.55  ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.20/0.55  ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.20/0.55  ; Path-index has 123 entries (143 at peak, 309 added, 186 deleted).
% 0.20/0.55  ; Path-index has 353 nodes (392 at peak, 691 added, 338 deleted).
% 0.20/0.55  ; Trie-index has 123 entries (143 at peak, 309 added, 186 deleted).
% 0.20/0.55  ; Trie-index has 423 nodes (493 at peak, 1,251 added, 828 deleted).
% 0.20/0.55  ; Retrieved 1,243 generalization terms in 1,767 calls.
% 0.20/0.55  ; Retrieved 289 instance terms in 123 calls.
% 0.20/0.55  ; Retrieved 659 unifiable terms in 216 calls.
% 0.20/0.55  ; 
% 0.20/0.55  ; The agenda of backward simplifiable rows to process has 4 entries:
% 0.20/0.55  ;     4 with value 0
% 0.20/0.55  ; The agenda of rows to process has 39 entries:
% 0.20/0.55  ;     7 with value 21              6 with value 25               5 with value 29
% 0.20/0.55  ;     4 with value 22              1 with value 26               3 with value 30
% 0.20/0.55  ;     3 with value 23              1 with value 27               2 with value 31
% 0.20/0.55  ;     4 with value 24              3 with value 28
% 0.20/0.55  ; The agenda of rows to give has 24 entries:
% 0.20/0.55  ;     1 with value (4 21)          5 with value (4 23)          10 with value (4 27)
% 0.20/0.55  ;     4 with value (4 22)          2 with value (4 26)           2 with value (4 28)
% 0.20/0.55  Evaluation took:
% 0.20/0.55    0.077 seconds of real time
% 0.20/0.55    0.067371 seconds of user run time
% 0.20/0.55    0.009134 seconds of system run time
% 0.20/0.55    0 calls to %EVAL
% 0.20/0.55    0 page faults and
% 0.20/0.55    6,764,744 bytes consed.
% 0.20/0.55  :PROOF-FOUND
% 0.20/0.55  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T17:19:52
% 0.20/0.55  :PROOF-FOUND
% 0.20/0.55  * 
%------------------------------------------------------------------------------