TSTP Solution File: GRP604-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP604-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n010.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 11:39:37 EDT 2022

% Result   : Unsatisfiable 0.46s 0.66s
% Output   : Refutation 0.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    3
% Syntax   : Number of clauses     :   36 (  36 unt;   0 nHn;   3 RR)
%            Number of literals    :   36 (  35 equ;   2 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :  101 (   0 sgn)

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

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

cnf(prove_these_axioms_4,negated_conjecture,
    multiply(a,b) != multiply(b,a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_4) ).

cnf(4,plain,
    inverse(double_divide(b,a)) != inverse(double_divide(a,b)),
    inference('REWRITE',[status(thm)],[prove_these_axioms_4,multiply,theory(equality)]) ).

cnf(5,plain,
    inverse(double_divide(inverse(double_divide(X,Y)),Z)) = inverse(double_divide(U,inverse(double_divide(Y,double_divide(U,double_divide(X,Z)))))),
    inference('PARAMODULATE',[status(thm)],[single_axiom,single_axiom,theory(equality)]) ).

cnf(6,plain,
    inverse(double_divide(inverse(double_divide(inverse(double_divide(X,Y)),Z)),double_divide(X,Z))) = Y,
    inference('PARAMODULATE',[status(thm)],[single_axiom,5,theory(equality)]) ).

cnf(7,plain,
    inverse(double_divide(X,double_divide(inverse(double_divide(Y,X)),double_divide(Y,Z)))) = Z,
    inference('PARAMODULATE',[status(thm)],[6,6,theory(equality)]) ).

cnf(8,plain,
    inverse(double_divide(inverse(double_divide(X,Y)),double_divide(inverse(double_divide(inverse(double_divide(Z,X)),U)),Y))) = double_divide(Z,U),
    inference('PARAMODULATE',[status(thm)],[6,6,theory(equality)]) ).

cnf(13,plain,
    inverse(double_divide(inverse(double_divide(X,Y)),double_divide(Z,Y))) = double_divide(inverse(double_divide(U,Z)),double_divide(U,X)),
    inference('PARAMODULATE',[status(thm)],[6,7,theory(equality)]) ).

cnf(24,plain,
    double_divide(inverse(double_divide(X,Y)),double_divide(X,inverse(double_divide(Y,Z)))) = Z,
    inference('PARAMODULATE',[status(thm)],[6,13,theory(equality)]) ).

cnf(25,plain,
    double_divide(inverse(double_divide(X,Y)),double_divide(X,Z)) = double_divide(inverse(double_divide(U,Y)),double_divide(U,Z)),
    inference('PARAMODULATE',[status(thm)],[13,13,theory(equality)]) ).

cnf(26,plain,
    inverse(double_divide(X,inverse(double_divide(inverse(double_divide(Y,Z)),double_divide(X,Z))))) = Y,
    inference('PARAMODULATE',[status(thm)],[7,13,theory(equality)]) ).

cnf(63,plain,
    inverse(double_divide(inverse(X),double_divide(Y,double_divide(Y,inverse(double_divide(Z,X)))))) = Z,
    inference('PARAMODULATE',[status(thm)],[6,24,theory(equality)]) ).

cnf(70,plain,
    inverse(double_divide(inverse(double_divide(inverse(X),Y)),double_divide(inverse(double_divide(Z,U)),Y))) = double_divide(Z,inverse(double_divide(U,X))),
    inference('PARAMODULATE',[status(thm)],[6,24,theory(equality)]) ).

cnf(120,plain,
    inverse(double_divide(X,inverse(double_divide(inverse(double_divide(Y,Z)),double_divide(Y,Z))))) = X,
    inference('PARAMODULATE',[status(thm)],[26,25,theory(equality)]) ).

cnf(134,plain,
    double_divide(inverse(double_divide(X,inverse(Y))),double_divide(X,Z)) = double_divide(U,double_divide(U,inverse(double_divide(Z,Y)))),
    inference('PARAMODULATE',[status(thm)],[24,63,theory(equality)]) ).

cnf(138,plain,
    inverse(double_divide(inverse(X),double_divide(Y,double_divide(Y,Z)))) = inverse(double_divide(U,inverse(double_divide(Z,double_divide(U,X))))),
    inference('PARAMODULATE',[status(thm)],[63,single_axiom,theory(equality)]) ).

cnf(144,plain,
    inverse(double_divide(inverse(double_divide(X,Y)),double_divide(double_divide(Z,double_divide(Z,inverse(double_divide(U,V)))),Y))) = double_divide(U,double_divide(inverse(V),X)),
    inference('PARAMODULATE',[status(thm)],[13,63,theory(equality)]) ).

cnf(156,plain,
    inverse(double_divide(X,inverse(double_divide(inverse(Y),Y)))) = X,
    inference('PARAMODULATE',[status(thm)],[120,24,theory(equality)]) ).

cnf(164,plain,
    inverse(double_divide(inverse(inverse(double_divide(inverse(X),X))),double_divide(Y,double_divide(Y,Z)))) = Z,
    inference('PARAMODULATE',[status(thm)],[63,156,theory(equality)]) ).

cnf(167,plain,
    double_divide(X,double_divide(X,Y)) = double_divide(Z,double_divide(Z,Y)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[25,156,theory(equality)]),156,theory(equality)]) ).

cnf(182,plain,
    inverse(double_divide(X,double_divide(X,double_divide(inverse(Y),inverse(double_divide(Z,Y)))))) = Z,
    inference('PARAMODULATE',[status(thm)],[63,167,theory(equality)]) ).

cnf(188,plain,
    double_divide(inverse(double_divide(X,Y)),Z) = double_divide(U,double_divide(U,double_divide(X,inverse(double_divide(Y,Z))))),
    inference('PARAMODULATE',[status(thm)],[167,24,theory(equality)]) ).

cnf(189,plain,
    inverse(double_divide(inverse(double_divide(inverse(X),Y)),X)) = Y,
    inference('REWRITE',[status(thm)],[182,188,theory(equality)]) ).

cnf(209,plain,
    inverse(double_divide(X,double_divide(inverse(Y),X))) = Y,
    inference('PARAMODULATE',[status(thm)],[189,189,theory(equality)]) ).

cnf(211,plain,
    X = inverse(double_divide(inverse(inverse(double_divide(inverse(Y),Y))),X)),
    inference('PARAMODULATE',[status(thm)],[156,189,theory(equality)]) ).

cnf(212,plain,
    double_divide(X,double_divide(X,Y)) = Y,
    inference('REWRITE',[status(thm)],[164,211,theory(equality)]) ).

cnf(226,plain,
    inverse(double_divide(inverse(double_divide(X,Y)),double_divide(inverse(double_divide(Z,U)),Y))) = double_divide(Z,double_divide(inverse(U),X)),
    inference('REWRITE',[status(thm)],[144,212,theory(equality)]) ).

cnf(228,plain,
    double_divide(inverse(double_divide(X,Y)),double_divide(inverse(Z),Y)) = double_divide(X,Z),
    inference('REWRITE',[status(thm)],[8,226,theory(equality)]) ).

cnf(232,plain,
    inverse(double_divide(X,double_divide(Y,Z))) = double_divide(Y,double_divide(inverse(Z),X)),
    inference('REWRITE',[status(thm)],[226,228,theory(equality)]) ).

cnf(274,plain,
    inverse(inverse(X)) = X,
    inference('REWRITE',[status(thm)],[209,212,232,theory(equality)]) ).

cnf(321,plain,
    inverse(double_divide(inverse(X),double_divide(Y,Z))) = double_divide(Y,inverse(double_divide(Z,X))),
    inference('REWRITE',[status(thm)],[70,228,theory(equality)]) ).

cnf(337,plain,
    double_divide(inverse(double_divide(X,inverse(Y))),double_divide(X,Z)) = inverse(double_divide(Z,Y)),
    inference('REWRITE',[status(thm)],[134,212,theory(equality)]) ).

cnf(361,plain,
    inverse(double_divide(inverse(X),Y)) = double_divide(inverse(double_divide(Z,X)),double_divide(Z,Y)),
    inference('REWRITE',[status(thm)],[138,274,321,212,theory(equality)]) ).

cnf(362,plain,
    inverse(double_divide(X,Y)) = inverse(double_divide(Y,X)),
    inference('REWRITE',[status(thm)],[337,274,361,theory(equality)]) ).

cnf(363,plain,
    $false,
    inference('REWRITE',[status(thm)],[4,362,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP604-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.13  % Command  : run-snark %s %d
% 0.12/0.33  % Computer : n010.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 09:42:54 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.18/0.45  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.46  * 
% 0.18/0.46  * 
% 0.18/0.47  #<PACKAGE "SNARK-USER">
% 0.18/0.47  * 
% 0.18/0.47  SNARK-TPTP-OPTIONS
% 0.18/0.47  * 
% 0.18/0.47  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.18/0.47   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.18/0.47   (USE-FACTORING :POS)
% 0.18/0.47   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.18/0.47   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.18/0.47   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.18/0.47   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.18/0.47   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.18/0.47   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.18/0.47   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.18/0.47   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.18/0.47   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.18/0.47   (DECLARE-TPTP-SYMBOLS2))
% 0.18/0.47  * 
% 0.18/0.47  "."
% 0.18/0.47  * 
% 0.18/0.47  ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T09:42:54
% 0.18/0.47  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n010.cluster.edu at 2022-06-14T09:42:54
% 0.46/0.66  
% 0.46/0.66  
% 0.46/0.66  #||
% 0.46/0.66  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.46/0.66  % SZS output start Refutation
% See solution above
% 0.46/0.67  ||#
% 0.46/0.67  
% 0.46/0.67  ; Summary of computation:
% 0.46/0.67  ;       736 formulas have been input or derived (from 17 formulas).
% 0.46/0.67  ;       363 (49%) were retained.  Of these,
% 0.46/0.67  ;          273 (75%) were simplified or subsumed later,
% 0.46/0.67  ;           90 (25%) are still being kept.
% 0.46/0.67  ; 
% 0.46/0.67  ; Run time in seconds excluding printing time:
% 0.46/0.67  ;     0.001   1%   Read assertion file          (1 call)
% 0.46/0.67  ;     0.001   1%   Assert                       (3 calls)
% 0.46/0.67  ;     0.059  31%   Process new row              (620 calls)
% 0.46/0.67  ;     0.000   0%   Resolution                   (32 calls)
% 0.46/0.67  ;     0.014   7%   Paramodulation               (16 calls)
% 0.46/0.67  ;     0.035  19%   Forward simplification       (589 calls)
% 0.46/0.67  ;     0.031  16%   Backward simplification      (362 calls)
% 0.46/0.67  ;     0.023  12%   Ordering                     (2,877 calls)
% 0.46/0.67  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.46/0.67  ;     0.000   0%   Purity testing               (1 call)
% 0.46/0.67  ;     0.025  13%   Other
% 0.46/0.67  ;     0.189        Total
% 0.46/0.67  ;     0.201        Real time
% 0.46/0.67  ; 
% 0.46/0.67  ; Term-hash-array has 1,813 terms in all.
% 0.46/0.67  ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.46/0.67  ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.46/0.67  ; Path-index has 473 entries (1,191 at peak, 1,966 added, 1,493 deleted).
% 0.46/0.67  ; Path-index has 3,265 nodes (3,741 at peak, 4,420 added, 1,155 deleted).
% 0.46/0.67  ; Trie-index has 473 entries (1,191 at peak, 1,966 added, 1,493 deleted).
% 0.46/0.67  ; Trie-index has 2,217 nodes (5,045 at peak, 8,508 added, 6,291 deleted).
% 0.46/0.67  ; Retrieved 1,459 generalization terms in 5,680 calls.
% 0.46/0.67  ; Retrieved 3,113 instance terms in 417 calls.
% 0.46/0.67  ; Retrieved 2,591 unifiable terms in 146 calls.
% 0.46/0.67  ; 
% 0.46/0.67  ; The agenda of backward simplifiable rows to process has 74 entries:
% 0.46/0.67  ;    74 with value 0
% 0.46/0.67  ; The agenda of rows to process has 38 entries:
% 0.46/0.67  ;     2 with value 28              1 with value 33               1 with value 38
% 0.46/0.67  ;     2 with value 29              3 with value 34               1 with value 39
% 0.46/0.67  ;     7 with value 30              5 with value 35               2 with value 40
% 0.46/0.67  ;     2 with value 31              1 with value 36               1 with value 41
% 0.46/0.67  ;     4 with value 32              5 with value 37               1 with value 43
% 0.46/0.67  ; The agenda of input rows to give has 1 entry:
% 0.46/0.67  ;     1 with value 21
% 0.46/0.67  ; The agenda of rows to give has 86 entries:
% 0.46/0.67  ;     3 with value (4 18)          2 with value (4 27)           3 with value (4 35)
% 0.46/0.67  ;     1 with value (4 19)          2 with value (4 28)           2 with value (4 36)
% 0.46/0.67  ;     2 with value (4 20)          8 with value (4 29)           6 with value (4 37)
% 0.46/0.67  ;     1 with value (4 22)          4 with value (4 30)           4 with value (4 38)
% 0.46/0.67  ;     2 with value (4 23)          3 with value (4 31)           1 with value (4 39)
% 0.46/0.67  ;     8 with value (4 24)          7 with value (4 32)           4 with value (4 40)
% 0.46/0.67  ;     5 with value (4 25)          6 with value (4 33)           3 with value (4 41)
% 0.46/0.67  ;     3 with value (4 26)          5 with value (4 34)           1 with value (4 43)
% 0.46/0.67  Evaluation took:
% 0.46/0.67    0.202 seconds of real time
% 0.46/0.67    0.188283 seconds of user run time
% 0.46/0.67    0.013576 seconds of system run time
% 0.46/0.67    [Run times include 0.009 seconds GC run time.]
% 0.46/0.67    0 calls to %EVAL
% 0.46/0.67    0 page faults and
% 0.46/0.67    15,805,296 bytes consed.
% 0.46/0.67  :PROOF-FOUND
% 0.46/0.67  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T09:42:54
% 0.46/0.67  :PROOF-FOUND
% 0.46/0.67  * 
%------------------------------------------------------------------------------