TSTP Solution File: GRP110-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP110-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n027.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 11:36:12 EDT 2022

% Result   : Unsatisfiable 0.49s 0.65s
% Output   : Refutation 0.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    3
% Syntax   : Number of clauses     :   54 (  49 unt;   0 nHn;   7 RR)
%            Number of literals    :   67 (  66 equ;  19 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   9 con; 0-2 aty)
%            Number of variables   :  146 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
    inverse(double_divide(inverse(double_divide(inverse(double_divide(X,Y)),Z)),double_divide(X,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,negated_conjecture,
    ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
    | multiply(multiply(inverse(b2),b2),a2) != a2
    | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
    | multiply(a4,b4) != multiply(b4,a4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).

cnf(4,plain,
    ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1)))
    | inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != 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,multiply,theory(equality)]) ).

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

cnf(6,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)],[single_axiom,single_axiom,theory(equality)]) ).

cnf(7,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)],[single_axiom,5,theory(equality)]) ).

cnf(8,plain,
    inverse(double_divide(double_divide(inverse(double_divide(X,Y)),double_divide(X,Z)),double_divide(Z,double_divide(Y,U)))) = U,
    inference('PARAMODULATE',[status(thm)],[5,5,theory(equality)]) ).

cnf(11,plain,
    double_divide(inverse(double_divide(X,Y)),double_divide(X,inverse(double_divide(Y,Z)))) = Z,
    inference('PARAMODULATE',[status(thm)],[single_axiom,7,theory(equality)]) ).

cnf(12,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)],[7,7,theory(equality)]) ).

cnf(13,plain,
    inverse(double_divide(X,inverse(double_divide(inverse(double_divide(Y,Z)),double_divide(X,Z))))) = Y,
    inference('PARAMODULATE',[status(thm)],[5,7,theory(equality)]) ).

cnf(15,plain,
    inverse(inverse(double_divide(inverse(double_divide(X,Y)),double_divide(X,Y)))) = double_divide(inverse(double_divide(Z,U)),double_divide(Z,U)),
    inference('PARAMODULATE',[status(thm)],[7,7,theory(equality)]) ).

cnf(23,plain,
    inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(X,Y)),double_divide(X,Z)),U)),double_divide(inverse(double_divide(Z,V)),U))) = double_divide(Y,V),
    inference('PARAMODULATE',[status(thm)],[single_axiom,7,theory(equality)]) ).

cnf(34,plain,
    inverse(double_divide(inverse(X),double_divide(Y,double_divide(Y,inverse(double_divide(Z,X)))))) = Z,
    inference('PARAMODULATE',[status(thm)],[single_axiom,11,theory(equality)]) ).

cnf(42,plain,
    inverse(double_divide(X,double_divide(inverse(double_divide(inverse(double_divide(Y,Z)),X)),U))) = double_divide(Y,inverse(double_divide(Z,U))),
    inference('PARAMODULATE',[status(thm)],[5,11,theory(equality)]) ).

cnf(69,plain,
    inverse(double_divide(X,inverse(double_divide(inverse(double_divide(Y,Z)),double_divide(Y,Z))))) = X,
    inference('PARAMODULATE',[status(thm)],[13,12,theory(equality)]) ).

cnf(95,plain,
    inverse(double_divide(double_divide(inverse(double_divide(X,inverse(double_divide(Y,Z)))),double_divide(X,U)),double_divide(U,V))) = double_divide(Y,inverse(double_divide(Z,V))),
    inference('PARAMODULATE',[status(thm)],[8,11,theory(equality)]) ).

cnf(113,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)],[7,34,theory(equality)]) ).

cnf(122,plain,
    inverse(double_divide(X,inverse(double_divide(inverse(Y),Y)))) = X,
    inference('PARAMODULATE',[status(thm)],[69,11,theory(equality)]) ).

cnf(130,plain,
    inverse(double_divide(inverse(inverse(double_divide(inverse(X),X))),double_divide(Y,double_divide(Y,Z)))) = Z,
    inference('PARAMODULATE',[status(thm)],[34,122,theory(equality)]) ).

cnf(133,plain,
    double_divide(X,double_divide(X,Y)) = double_divide(Z,double_divide(Z,Y)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12,122,theory(equality)]),122,theory(equality)]) ).

cnf(135,plain,
    inverse(double_divide(X,double_divide(Y,inverse(double_divide(inverse(Z),Z))))) = double_divide(inverse(double_divide(U,Y)),double_divide(U,X)),
    inference('PARAMODULATE',[status(thm)],[7,122,theory(equality)]) ).

cnf(146,plain,
    inverse(double_divide(X,double_divide(X,double_divide(inverse(Y),inverse(double_divide(Z,Y)))))) = Z,
    inference('PARAMODULATE',[status(thm)],[34,133,theory(equality)]) ).

cnf(149,plain,
    double_divide(inverse(double_divide(X,Y)),double_divide(X,inverse(double_divide(Z,double_divide(Z,U))))) = double_divide(Y,U),
    inference('PARAMODULATE',[status(thm)],[11,133,theory(equality)]) ).

cnf(150,plain,
    inverse(double_divide(X,double_divide(inverse(double_divide(Y,X)),double_divide(Z,double_divide(Z,U))))) = double_divide(Y,U),
    inference('PARAMODULATE',[status(thm)],[5,133,theory(equality)]) ).

cnf(151,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)],[133,11,theory(equality)]) ).

cnf(152,plain,
    inverse(double_divide(inverse(double_divide(inverse(X),Y)),X)) = Y,
    inference('REWRITE',[status(thm)],[146,151,theory(equality)]) ).

cnf(160,plain,
    inverse(double_divide(inverse(double_divide(X,Y)),double_divide(Z,double_divide(Z,inverse(double_divide(U,double_divide(U,Y))))))) = X,
    inference('PARAMODULATE',[status(thm)],[34,133,theory(equality)]) ).

cnf(170,plain,
    inverse(double_divide(X,double_divide(inverse(Y),X))) = Y,
    inference('PARAMODULATE',[status(thm)],[152,152,theory(equality)]) ).

cnf(172,plain,
    X = inverse(double_divide(inverse(inverse(double_divide(inverse(Y),Y))),X)),
    inference('PARAMODULATE',[status(thm)],[122,152,theory(equality)]) ).

cnf(173,plain,
    double_divide(X,double_divide(X,Y)) = Y,
    inference('REWRITE',[status(thm)],[130,172,theory(equality)]) ).

cnf(185,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)],[113,173,theory(equality)]) ).

cnf(186,plain,
    double_divide(inverse(double_divide(X,Y)),double_divide(inverse(Z),Y)) = double_divide(X,Z),
    inference('REWRITE',[status(thm)],[6,185,theory(equality)]) ).

cnf(188,plain,
    inverse(double_divide(X,double_divide(Y,Z))) = double_divide(Y,double_divide(inverse(Z),X)),
    inference('REWRITE',[status(thm)],[185,186,theory(equality)]) ).

cnf(194,plain,
    inverse(inverse(double_divide(X,inverse(double_divide(Y,Z))))) = double_divide(Y,inverse(double_divide(Z,X))),
    inference('REWRITE',[status(thm)],[42,173,188,theory(equality)]) ).

cnf(196,plain,
    ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1)))
    | inverse(inverse(inverse(double_divide(inverse(b2),inverse(double_divide(a2,b2)))))) != 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)],[4,194,theory(equality)]) ).

cnf(214,plain,
    inverse(inverse(X)) = X,
    inference('REWRITE',[status(thm)],[170,173,188,theory(equality)]) ).

cnf(235,plain,
    ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1)))
    | inverse(double_divide(inverse(b2),inverse(double_divide(a2,b2)))) != 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)],[196,214,theory(equality)]) ).

cnf(245,plain,
    double_divide(inverse(double_divide(X,Y)),double_divide(X,Y)) = double_divide(inverse(double_divide(Z,U)),double_divide(Z,U)),
    inference('REWRITE',[status(thm)],[15,214,theory(equality)]) ).

cnf(250,plain,
    inverse(double_divide(double_divide(inverse(double_divide(X,Y)),double_divide(X,Z)),double_divide(Z,U))) = double_divide(Y,U),
    inference('REWRITE',[status(thm)],[23,186,theory(equality)]) ).

cnf(253,plain,
    double_divide(inverse(double_divide(X,Y)),Z) = double_divide(X,inverse(double_divide(Y,Z))),
    inference('REWRITE',[status(thm)],[95,250,theory(equality)]) ).

cnf(255,plain,
    inverse(double_divide(inverse(X),inverse(double_divide(Y,X)))) = Y,
    inference('REWRITE',[status(thm)],[152,253,theory(equality)]) ).

cnf(256,plain,
    ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1)))
    | inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)) ),
    inference('REWRITE',[status(thm)],[235,255,253,theory(equality)]) ).

cnf(270,plain,
    inverse(double_divide(inverse(double_divide(X,Y)),inverse(Y))) = X,
    inference('REWRITE',[status(thm)],[160,173,theory(equality)]) ).

cnf(279,plain,
    double_divide(inverse(double_divide(X,Y)),double_divide(X,inverse(Z))) = double_divide(Y,Z),
    inference('REWRITE',[status(thm)],[149,173,theory(equality)]) ).

cnf(290,plain,
    double_divide(X,double_divide(Y,double_divide(Z,Y))) = double_divide(Z,X),
    inference('REWRITE',[status(thm)],[150,214,188,173,theory(equality)]) ).

cnf(309,plain,
    inverse(X) = double_divide(X,inverse(double_divide(inverse(Y),Y))),
    inference('PARAMODULATE',[status(thm)],[214,122,theory(equality)]) ).

cnf(310,plain,
    inverse(double_divide(X,inverse(Y))) = double_divide(inverse(double_divide(Z,Y)),double_divide(Z,X)),
    inference('REWRITE',[status(thm)],[135,309,theory(equality)]) ).

cnf(315,plain,
    inverse(double_divide(inverse(X),inverse(Y))) = double_divide(Y,X),
    inference('REWRITE',[status(thm)],[279,310,theory(equality)]) ).

cnf(326,plain,
    double_divide(X,double_divide(Y,X)) = Y,
    inference('REWRITE',[status(thm)],[270,315,theory(equality)]) ).

cnf(327,plain,
    double_divide(X,Y) = double_divide(Y,X),
    inference('REWRITE',[status(thm)],[290,326,theory(equality)]) ).

cnf(348,plain,
    inverse(double_divide(X,inverse(X))) = inverse(double_divide(Y,inverse(Y))),
    inference('REWRITE',[status(thm)],[245,310,theory(equality)]) ).

cnf(349,plain,
    inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)),
    inference('REWRITE',[status(thm)],[256,348,theory(equality)]) ).

cnf(359,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[349,327,theory(equality)]),theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP110-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.13  % Command  : run-snark %s %d
% 0.13/0.34  % Computer : n027.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 : Tue Jun 14 05:31:33 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.45  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46  * 
% 0.19/0.46  * 
% 0.19/0.46  #<PACKAGE "SNARK-USER">
% 0.19/0.46  * 
% 0.19/0.46  SNARK-TPTP-OPTIONS
% 0.19/0.46  * 
% 0.19/0.47  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.47   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.47   (USE-FACTORING :POS)
% 0.19/0.47   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.47   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.47   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.47   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.47   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.47   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.47   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.47   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.47   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.47   (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.47  * 
% 0.19/0.47  "."
% 0.19/0.47  * 
% 0.19/0.47  ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T05:31:33
% 0.19/0.47  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n027.cluster.edu at 2022-06-14T05:31:33
% 0.49/0.65  
% 0.49/0.65  
% 0.49/0.65  #||
% 0.49/0.65  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.49/0.65  % SZS output start Refutation
% See solution above
% 0.49/0.66  ||#
% 0.49/0.66  
% 0.49/0.66  ; Summary of computation:
% 0.49/0.66  ;       689 formulas have been input or derived (from 21 formulas).
% 0.49/0.66  ;       359 (52%) were retained.  Of these,
% 0.49/0.66  ;          279 (78%) were simplified or subsumed later,
% 0.49/0.66  ;           80 (22%) are still being kept.
% 0.49/0.66  ; 
% 0.49/0.66  ; Run time in seconds excluding printing time:
% 0.49/0.66  ;     0.002   1%   Read assertion file          (1 call)
% 0.49/0.66  ;     0.000   0%   Assert                       (3 calls)
% 0.49/0.66  ;     0.046  25%   Process new row              (683 calls)
% 0.49/0.66  ;     0.001   1%   Resolution                   (40 calls)
% 0.49/0.66  ;     0.012   7%   Paramodulation               (20 calls)
% 0.49/0.66  ;     0.000   0%   Condensing                   (4 calls)
% 0.49/0.66  ;     0.000   0%   Forward subsumption          (4 calls)
% 0.49/0.66  ;     0.000   0%   Backward subsumption         (4 calls)
% 0.49/0.66  ;     0.034  19%   Forward simplification       (622 calls)
% 0.49/0.66  ;     0.025  14%   Backward simplification      (358 calls)
% 0.49/0.66  ;     0.036  20%   Ordering                     (3,118 calls)
% 0.49/0.66  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.49/0.66  ;     0.000   0%   Purity testing               (1 call)
% 0.49/0.66  ;     0.026  14%   Other
% 0.49/0.66  ;     0.182        Total
% 0.49/0.66  ;     0.194        Real time
% 0.49/0.66  ; 
% 0.49/0.66  ; Term-hash-array has 1,646 terms in all.
% 0.49/0.66  ; Feature-vector-row-index has 0 entries (1 at peak, 4 added, 4 deleted).
% 0.49/0.66  ; Feature-vector-row-index has 1 node (36 at peak, 126 added, 125 deleted).
% 0.49/0.66  ;  Retrieved 0 possibly forward subsuming rows in 4 calls.
% 0.49/0.66  ;  Retrieved 0 possibly backward subsumed rows in 4 calls.
% 0.49/0.66  ; Path-index has 362 entries (989 at peak, 1,899 added, 1,537 deleted).
% 0.49/0.66  ; Path-index has 2,422 nodes (2,892 at peak, 3,676 added, 1,254 deleted).
% 0.49/0.66  ; Trie-index has 362 entries (989 at peak, 1,899 added, 1,537 deleted).
% 0.49/0.66  ; Trie-index has 1,649 nodes (4,245 at peak, 7,688 added, 6,039 deleted).
% 0.49/0.66  ; Retrieved 2,052 generalization terms in 5,619 calls.
% 0.49/0.66  ; Retrieved 2,909 instance terms in 423 calls.
% 0.49/0.66  ; Retrieved 2,983 unifiable terms in 199 calls.
% 0.49/0.66  ; 
% 0.49/0.66  ; The agenda of rows to process has 3 entries:
% 0.49/0.66  ;     3 with value 20
% 0.49/0.66  ; The agenda of rows to give has 73 entries:
% 0.49/0.66  ;     2 with value (4 17)          3 with value (4 24)           6 with value (4 30)
% 0.49/0.66  ;     2 with value (4 18)          9 with value (4 25)           4 with value (4 31)
% 0.49/0.66  ;     1 with value (4 20)          4 with value (4 26)           2 with value (4 32)
% 0.49/0.66  ;     5 with value (4 21)          2 with value (4 27)           4 with value (4 33)
% 0.49/0.66  ;     9 with value (4 22)          8 with value (4 28)           2 with value (4 35)
% 0.49/0.66  ;     3 with value (4 23)          5 with value (4 29)           2 with value (4 36)
% 0.49/0.66  Evaluation took:
% 0.49/0.66    0.195 seconds of real time
% 0.49/0.66    0.180633 seconds of user run time
% 0.49/0.66    0.014354 seconds of system run time
% 0.49/0.66    [Run times include 0.007 seconds GC run time.]
% 0.49/0.66    0 calls to %EVAL
% 0.49/0.66    0 page faults and
% 0.49/0.66    17,635,032 bytes consed.
% 0.49/0.66  :PROOF-FOUND
% 0.49/0.66  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T05:31:33
% 0.49/0.66  :PROOF-FOUND
% 0.49/0.66  * 
%------------------------------------------------------------------------------