TSTP Solution File: GRP080-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP080-1 : 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 11:36:03 EDT 2022

% Result   : Unsatisfiable 0.38s 0.54s
% Output   : Refutation 0.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   43 (  40 unt;   0 nHn;   8 RR)
%            Number of literals    :   48 (  47 equ;  11 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    7 (   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   :   67 (   0 sgn)

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

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

cnf(10,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)],[7,9,theory(equality)]) ).

cnf(11,plain,
    double_divide(identity,inverse(double_divide(X,double_divide(Y,X)))) = Y,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,identity,theory(equality)]),9,inverse,theory(equality)]) ).

cnf(12,plain,
    double_divide(double_divide(identity,double_divide(identity,inverse(X))),inverse(double_divide(X,inverse(Y)))) = Y,
    inference('PARAMODULATE',[status(thm)],[8,inverse,theory(equality)]) ).

cnf(16,plain,
    double_divide(double_divide(identity,inverse(X)),inverse(double_divide(identity,double_divide(Y,X)))) = Y,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,9,theory(equality)]),inverse,theory(equality)]) ).

cnf(17,plain,
    double_divide(identity,inverse(double_divide(identity,inverse(X)))) = X,
    inference('PARAMODULATE',[status(thm)],[11,inverse,theory(equality)]) ).

cnf(18,plain,
    double_divide(identity,inverse(inverse(inverse(X)))) = X,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[11,identity,theory(equality)]),inverse,theory(equality)]) ).

cnf(25,plain,
    double_divide(identity,inverse(X)) = inverse(inverse(X)),
    inference('PARAMODULATE',[status(thm)],[17,18,theory(equality)]) ).

cnf(28,plain,
    inverse(inverse(inverse(inverse(X)))) = X,
    inference('REWRITE',[status(thm)],[18,25,theory(equality)]) ).

cnf(29,plain,
    double_divide(inverse(inverse(inverse(X))),inverse(double_divide(X,inverse(Y)))) = Y,
    inference('REWRITE',[status(thm)],[12,25,theory(equality)]) ).

cnf(30,plain,
    double_divide(inverse(inverse(X)),inverse(double_divide(identity,double_divide(Y,X)))) = Y,
    inference('REWRITE',[status(thm)],[16,25,theory(equality)]) ).

cnf(31,plain,
    inverse(inverse(double_divide(X,double_divide(Y,X)))) = Y,
    inference('REWRITE',[status(thm)],[11,25,theory(equality)]) ).

cnf(33,plain,
    double_divide(identity,X) = inverse(X),
    inference('PARAMODULATE',[status(thm)],[25,28,theory(equality)]) ).

cnf(34,plain,
    double_divide(inverse(inverse(X)),inverse(inverse(double_divide(Y,X)))) = Y,
    inference('REWRITE',[status(thm)],[30,33,theory(equality)]) ).

cnf(43,plain,
    double_divide(inverse(double_divide(X,inverse(Y))),inverse(double_divide(Y,double_divide(Z,X)))) = Z,
    inference('REWRITE',[status(thm)],[8,33,theory(equality)]) ).

cnf(45,plain,
    double_divide(inverse(double_divide(X,Y)),inverse(double_divide(inverse(inverse(inverse(Y))),double_divide(Z,X)))) = Z,
    inference('PARAMODULATE',[status(thm)],[43,28,theory(equality)]) ).

cnf(47,plain,
    inverse(inverse(X)) = double_divide(Y,double_divide(X,Y)),
    inference('PARAMODULATE',[status(thm)],[28,31,theory(equality)]) ).

cnf(53,plain,
    double_divide(inverse(inverse(inverse(X))),inverse(inverse(X))) = identity,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[29,9,theory(equality)]),inverse,theory(equality)]) ).

cnf(54,plain,
    double_divide(inverse(inverse(inverse(X))),inverse(double_divide(X,Y))) = inverse(inverse(inverse(Y))),
    inference('PARAMODULATE',[status(thm)],[29,28,theory(equality)]) ).

cnf(55,plain,
    double_divide(inverse(X),X) = identity,
    inference('PARAMODULATE',[status(thm)],[53,28,theory(equality)]) ).

cnf(56,plain,
    inverse(inverse(inverse(X))) = inverse(X),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[47,55,theory(equality)]),inverse,theory(equality)]) ).

cnf(58,plain,
    double_divide(inverse(double_divide(X,Y)),inverse(double_divide(inverse(Y),double_divide(Z,X)))) = Z,
    inference('REWRITE',[status(thm)],[45,56,theory(equality)]) ).

cnf(59,plain,
    inverse(inverse(X)) = X,
    inference('REWRITE',[status(thm)],[28,56,theory(equality)]) ).

cnf(60,plain,
    double_divide(X,double_divide(Y,X)) = Y,
    inference('REWRITE',[status(thm)],[34,59,theory(equality)]) ).

cnf(63,plain,
    inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
    inference('REWRITE',[status(thm)],[10,59,theory(equality)]) ).

cnf(66,plain,
    double_divide(inverse(X),inverse(double_divide(X,Y))) = inverse(Y),
    inference('REWRITE',[status(thm)],[54,59,56,theory(equality)]) ).

cnf(68,plain,
    double_divide(inverse(X),inverse(Y)) = inverse(double_divide(Y,X)),
    inference('PARAMODULATE',[status(thm)],[66,60,theory(equality)]) ).

cnf(70,plain,
    inverse(double_divide(double_divide(inverse(X),double_divide(Y,Z)),double_divide(Z,X))) = Y,
    inference('REWRITE',[status(thm)],[58,68,theory(equality)]) ).

cnf(72,plain,
    double_divide(X,inverse(Y)) = inverse(double_divide(Y,inverse(X))),
    inference('PARAMODULATE',[status(thm)],[68,59,theory(equality)]) ).

cnf(73,plain,
    double_divide(double_divide(b3,a3),inverse(c3)) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
    inference('REWRITE',[status(thm)],[63,72,theory(equality)]) ).

cnf(74,plain,
    double_divide(inverse(X),Y) = inverse(double_divide(inverse(Y),X)),
    inference('PARAMODULATE',[status(thm)],[68,59,theory(equality)]) ).

cnf(76,plain,
    double_divide(double_divide(b3,a3),inverse(c3)) != double_divide(inverse(a3),double_divide(c3,b3)),
    inference('REWRITE',[status(thm)],[73,74,theory(equality)]) ).

cnf(87,plain,
    inverse(X) = double_divide(double_divide(inverse(Y),double_divide(X,Z)),double_divide(Z,Y)),
    inference('PARAMODULATE',[status(thm)],[59,70,theory(equality)]) ).

cnf(96,plain,
    double_divide(double_divide(X,Y),inverse(Z)) = double_divide(inverse(Y),double_divide(Z,X)),
    inference('PARAMODULATE',[status(thm)],[60,87,theory(equality)]) ).

cnf(97,plain,
    $false,
    inference('REWRITE',[status(thm)],[76,96,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP080-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.07/0.13  % Command  : run-snark %s %d
% 0.13/0.34  % Computer : n006.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 11:55:57 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  * 
% 0.19/0.47  #<PACKAGE "SNARK-USER">
% 0.19/0.47  * 
% 0.19/0.47  SNARK-TPTP-OPTIONS
% 0.19/0.47  * 
% 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 2022-06-13T11:55:57
% 0.19/0.47  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n006.cluster.edu at 2022-06-13T11:55:57
% 0.19/0.48  
% 0.38/0.54  ; Recognized possible right inverse assertion (= |identity| (|double_divide| ?X (|inverse| ?X))).
% 0.38/0.54  
% 0.38/0.54  #||
% 0.38/0.54  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.38/0.54  % SZS output start Refutation
% See solution above
% 0.38/0.55  ||#
% 0.38/0.55  
% 0.38/0.55  ; Summary of computation:
% 0.38/0.55  ;       419 formulas have been input or derived (from 33 formulas).
% 0.38/0.55  ;        97 (23%) were retained.  Of these,
% 0.38/0.55  ;           61 (63%) were simplified or subsumed later,
% 0.38/0.55  ;           36 (37%) are still being kept.
% 0.38/0.55  ; 
% 0.38/0.55  ; Run time in seconds excluding printing time:
% 0.38/0.55  ;     0.001   1%   Read assertion file          (1 call)
% 0.38/0.55  ;     0.000   0%   Assert                       (5 calls)
% 0.38/0.55  ;     0.014  19%   Process new row              (387 calls)
% 0.38/0.55  ;     0.000   0%   Resolution                   (64 calls)
% 0.38/0.55  ;     0.009  12%   Paramodulation               (32 calls)
% 0.38/0.55  ;     0.000   0%   Condensing                   (3 calls)
% 0.38/0.55  ;     0.001   1%   Forward subsumption          (3 calls)
% 0.38/0.55  ;     0.000   0%   Backward subsumption         (3 calls)
% 0.38/0.55  ;     0.006   8%   Forward simplification       (317 calls)
% 0.38/0.55  ;     0.007  10%   Backward simplification      (97 calls)
% 0.38/0.55  ;     0.007  10%   Ordering                     (969 calls)
% 0.38/0.55  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.38/0.55  ;     0.001   1%   Purity testing               (1 call)
% 0.38/0.55  ;     0.027  37%   Other
% 0.38/0.55  ;     0.073        Total
% 0.38/0.55  ;     0.078        Real time
% 0.38/0.55  ; 
% 0.38/0.55  ; Term-hash-array has 312 terms in all.
% 0.38/0.55  ; Feature-vector-row-index has 0 entries (1 at peak, 3 added, 3 deleted).
% 0.38/0.55  ; Feature-vector-row-index has 1 node (26 at peak, 69 added, 68 deleted).
% 0.38/0.55  ;  Retrieved 0 possibly forward subsuming rows in 3 calls.
% 0.38/0.55  ;  Retrieved 0 possibly backward subsumed rows in 3 calls.
% 0.38/0.55  ; Path-index has 119 entries (129 at peak, 432 added, 313 deleted).
% 0.38/0.55  ; Path-index has 525 nodes (546 at peak, 948 added, 423 deleted).
% 0.38/0.55  ; Trie-index has 119 entries (129 at peak, 432 added, 313 deleted).
% 0.38/0.55  ; Trie-index has 533 nodes (560 at peak, 1,722 added, 1,189 deleted).
% 0.38/0.55  ; Retrieved 1,022 generalization terms in 1,869 calls.
% 0.38/0.55  ; Retrieved 246 instance terms in 116 calls.
% 0.38/0.55  ; Retrieved 747 unifiable terms in 243 calls.
% 0.38/0.55  ; 
% 0.38/0.55  ; The agenda of rows to process has 30 entries:
% 0.38/0.55  ;     7 with value 21              3 with value 26               4 with value 29
% 0.38/0.55  ;     6 with value 22              2 with value 27               3 with value 30
% 0.38/0.55  ;     2 with value 23              3 with value 28
% 0.38/0.55  ; The agenda of rows to give has 20 entries:
% 0.38/0.55  ;     1 with value (4 21)          1 with value (4 24)           1 with value (4 27)
% 0.38/0.55  ;     1 with value (4 23)          8 with value (4 26)           8 with value (4 28)
% 0.38/0.55  Evaluation took:
% 0.38/0.55    0.079 seconds of real time
% 0.38/0.55    0.071783 seconds of user run time
% 0.38/0.55    0.007107 seconds of system run time
% 0.38/0.55    0 calls to %EVAL
% 0.38/0.55    0 page faults and
% 0.38/0.55    7,058,864 bytes consed.
% 0.38/0.55  :PROOF-FOUND
% 0.38/0.55  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T11:55:57
% 0.38/0.55  :PROOF-FOUND
% 0.38/0.55  * 
%------------------------------------------------------------------------------