TSTP Solution File: GRP486-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP486-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n011.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 11:39:06 EDT 2022

% Result   : Unsatisfiable 0.39s 0.56s
% Output   : Refutation 0.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   42 (  42 unt;   0 nHn;   6 RR)
%            Number of literals    :   42 (  41 equ;   4 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :   10 (   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   :   72 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
    double_divide(double_divide(X,double_divide(double_divide(double_divide(X,Y),Z),double_divide(Y,identity))),double_divide(identity,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_3,negated_conjecture,
    multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
    file('/export/starexec/sandbox2/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(double_divide(X,Y),Z),inverse(Y))),inverse(identity)) = Z,
    inference('REWRITE',[status(thm)],[single_axiom,inverse,theory(equality)]) ).

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

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

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

cnf(17,plain,
    double_divide(double_divide(X,inverse(double_divide(inverse(X),Y))),inverse(identity)) = double_divide(identity,inverse(Y)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,9,theory(equality)]),inverse,theory(equality)]) ).

cnf(21,plain,
    double_divide(double_divide(X,inverse(inverse(inverse(X)))),inverse(identity)) = identity,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,inverse,theory(equality)]),16,theory(equality)]) ).

cnf(23,plain,
    identity = inverse(identity),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,16,theory(equality)]),21,16,theory(equality)]) ).

cnf(24,plain,
    inverse(double_divide(X,double_divide(double_divide(double_divide(X,Y),Z),inverse(Y)))) = Z,
    inference('REWRITE',[status(thm)],[8,inverse,23,theory(equality)]) ).

cnf(26,plain,
    inverse(double_divide(X,inverse(double_divide(inverse(X),Y)))) = Y,
    inference('REWRITE',[status(thm)],[10,inverse,23,theory(equality)]) ).

cnf(32,plain,
    X = double_divide(identity,inverse(X)),
    inference('REWRITE',[status(thm)],[17,26,inverse,23,theory(equality)]) ).

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

cnf(36,plain,
    inverse(double_divide(X,double_divide(double_divide(double_divide(X,double_divide(Y,double_divide(double_divide(double_divide(Y,Z),U),inverse(Z)))),V),U))) = V,
    inference('PARAMODULATE',[status(thm)],[24,24,theory(equality)]) ).

cnf(37,plain,
    inverse(double_divide(identity,double_divide(double_divide(X,Y),inverse(inverse(X))))) = Y,
    inference('PARAMODULATE',[status(thm)],[24,32,theory(equality)]) ).

cnf(38,plain,
    double_divide(X,double_divide(double_divide(double_divide(X,Y),Z),inverse(Y))) = double_divide(identity,Z),
    inference('PARAMODULATE',[status(thm)],[32,24,theory(equality)]) ).

cnf(39,plain,
    inverse(double_divide(X,double_divide(double_divide(double_divide(X,double_divide(identity,Y)),Z),Y))) = Z,
    inference('REWRITE',[status(thm)],[36,38,theory(equality)]) ).

cnf(40,plain,
    inverse(double_divide(identity,X)) = X,
    inference('REWRITE',[status(thm)],[24,38,theory(equality)]) ).

cnf(41,plain,
    double_divide(double_divide(X,Y),inverse(inverse(X))) = Y,
    inference('REWRITE',[status(thm)],[37,40,theory(equality)]) ).

cnf(45,plain,
    double_divide(X,inverse(inverse(double_divide(Y,X)))) = inverse(inverse(Y)),
    inference('PARAMODULATE',[status(thm)],[41,41,theory(equality)]) ).

cnf(46,plain,
    double_divide(X,inverse(double_divide(inverse(X),Y))) = double_divide(identity,Y),
    inference('PARAMODULATE',[status(thm)],[32,26,theory(equality)]) ).

cnf(47,plain,
    double_divide(X,inverse(inverse(inverse(X)))) = identity,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[32,33,theory(equality)]),23,inverse,theory(equality)]) ).

cnf(49,plain,
    inverse(X) = inverse(inverse(inverse(X))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[41,47,theory(equality)]),32,theory(equality)]) ).

cnf(50,plain,
    X = inverse(inverse(X)),
    inference('PARAMODULATE',[status(thm)],[49,40,theory(equality)]) ).

cnf(51,plain,
    double_divide(X,double_divide(Y,X)) = Y,
    inference('REWRITE',[status(thm)],[45,50,theory(equality)]) ).

cnf(52,plain,
    double_divide(double_divide(X,Y),X) = Y,
    inference('REWRITE',[status(thm)],[41,50,theory(equality)]) ).

cnf(53,plain,
    inverse(X) = double_divide(identity,X),
    inference('PARAMODULATE',[status(thm)],[32,50,theory(equality)]) ).

cnf(57,plain,
    inverse(double_divide(X,double_divide(double_divide(double_divide(X,inverse(Y)),Z),Y))) = Z,
    inference('REWRITE',[status(thm)],[39,53,theory(equality)]) ).

cnf(58,plain,
    double_divide(X,inverse(double_divide(inverse(X),Y))) = inverse(Y),
    inference('REWRITE',[status(thm)],[46,53,theory(equality)]) ).

cnf(63,plain,
    double_divide(inverse(X),Y) = inverse(double_divide(inverse(Y),X)),
    inference('PARAMODULATE',[status(thm)],[52,58,theory(equality)]) ).

cnf(64,plain,
    inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != double_divide(inverse(a3),double_divide(c3,b3)),
    inference('REWRITE',[status(thm)],[7,63,theory(equality)]) ).

cnf(65,plain,
    double_divide(X,inverse(Y)) = inverse(double_divide(Y,inverse(X))),
    inference('PARAMODULATE',[status(thm)],[58,51,theory(equality)]) ).

cnf(67,plain,
    double_divide(double_divide(b3,a3),inverse(c3)) != double_divide(inverse(a3),double_divide(c3,b3)),
    inference('REWRITE',[status(thm)],[64,65,theory(equality)]) ).

cnf(68,plain,
    double_divide(inverse(X),inverse(Y)) = inverse(double_divide(Y,X)),
    inference('PARAMODULATE',[status(thm)],[63,50,theory(equality)]) ).

cnf(87,plain,
    inverse(double_divide(X,double_divide(Y,Z))) = double_divide(Y,double_divide(X,inverse(Z))),
    inference('PARAMODULATE',[status(thm)],[57,51,theory(equality)]) ).

cnf(134,plain,
    inverse(double_divide(X,inverse(double_divide(Y,Z)))) = double_divide(inverse(Z),double_divide(X,Y)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[87,68,theory(equality)]),50,theory(equality)]) ).

cnf(135,plain,
    $false,
    inference('REWRITE',[status(thm)],[67,50,65,134,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : GRP486-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12  % Command  : run-snark %s %d
% 0.12/0.33  % Computer : n011.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 : Mon Jun 13 10:27:48 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.44  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45  * 
% 0.18/0.45  * 
% 0.18/0.46  #<PACKAGE "SNARK-USER">
% 0.18/0.46  * 
% 0.18/0.46  SNARK-TPTP-OPTIONS
% 0.18/0.46  * 
% 0.18/0.46  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.18/0.46   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.18/0.46   (USE-FACTORING :POS)
% 0.18/0.46   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.18/0.46   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.18/0.46   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.18/0.46   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.18/0.46   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.18/0.46   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.18/0.46   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.18/0.46   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.18/0.46   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.18/0.46   (DECLARE-TPTP-SYMBOLS2))
% 0.18/0.46  * 
% 0.18/0.46  "."
% 0.18/0.46  * 
% 0.18/0.46  ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T10:27:48
% 0.18/0.46  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n011.cluster.edu at 2022-06-13T10:27:48
% 0.18/0.47  
% 0.39/0.56  ; Recognized possible right inverse assertion (= |identity| (|double_divide| ?X (|inverse| ?X))).
% 0.39/0.56  
% 0.39/0.56  #||
% 0.39/0.56  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.39/0.56  % SZS output start Refutation
% See solution above
% 0.39/0.57  ||#
% 0.39/0.57  
% 0.39/0.57  ; Summary of computation:
% 0.39/0.57  ;       529 formulas have been input or derived (from 36 formulas).
% 0.39/0.57  ;       135 (26%) were retained.  Of these,
% 0.39/0.57  ;           67 (50%) were simplified or subsumed later,
% 0.39/0.57  ;           68 (50%) are still being kept.
% 0.39/0.57  ; 
% 0.39/0.57  ; Run time in seconds excluding printing time:
% 0.39/0.57  ;     0.001   1%   Read assertion file          (1 call)
% 0.39/0.57  ;     0.001   1%   Assert                       (5 calls)
% 0.39/0.57  ;     0.019  18%   Process new row              (501 calls)
% 0.39/0.57  ;     0.000   0%   Resolution                   (70 calls)
% 0.39/0.57  ;     0.007   7%   Paramodulation               (35 calls)
% 0.39/0.57  ;     0.022  21%   Forward simplification       (432 calls)
% 0.39/0.57  ;     0.014  14%   Backward simplification      (135 calls)
% 0.39/0.57  ;     0.016  16%   Ordering                     (2,277 calls)
% 0.39/0.57  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.39/0.57  ;     0.000   0%   Purity testing               (1 call)
% 0.39/0.57  ;     0.023  22%   Other
% 0.39/0.57  ;     0.103        Total
% 0.39/0.57  ;     0.109        Real time
% 0.39/0.57  ; 
% 0.39/0.57  ; Term-hash-array has 446 terms in all.
% 0.39/0.57  ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.39/0.57  ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.39/0.57  ; Path-index has 250 entries (260 at peak, 524 added, 274 deleted).
% 0.39/0.57  ; Path-index has 701 nodes (719 at peak, 1,182 added, 481 deleted).
% 0.39/0.57  ; Trie-index has 250 entries (260 at peak, 524 added, 274 deleted).
% 0.39/0.57  ; Trie-index has 995 nodes (1,029 at peak, 2,379 added, 1,384 deleted).
% 0.39/0.57  ; Retrieved 2,245 generalization terms in 2,709 calls.
% 0.39/0.57  ; Retrieved 572 instance terms in 214 calls.
% 0.39/0.57  ; Retrieved 917 unifiable terms in 258 calls.
% 0.39/0.57  ; 
% 0.39/0.57  ; The agenda of rows to process has 24 entries:
% 0.39/0.57  ;     2 with value 28              7 with value 30               2 with value 32
% 0.39/0.57  ;     2 with value 29              8 with value 31               3 with value 33
% 0.39/0.57  ; The agenda of rows to give has 53 entries:
% 0.39/0.57  ;     4 with value (4 23)          4 with value (4 27)           1 with value (4 31)
% 0.39/0.57  ;     3 with value (4 24)          4 with value (4 28)           1 with value (4 32)
% 0.39/0.57  ;    13 with value (4 25)          2 with value (4 29)           1 with value (4 33)
% 0.39/0.57  ;    12 with value (4 26)          8 with value (4 30)
% 0.39/0.57  Evaluation took:
% 0.39/0.57    0.109 seconds of real time
% 0.39/0.57    0.093785 seconds of user run time
% 0.39/0.57    0.014847 seconds of system run time
% 0.39/0.57    0 calls to %EVAL
% 0.39/0.57    0 page faults and
% 0.39/0.57    7,955,328 bytes consed.
% 0.39/0.57  :PROOF-FOUND
% 0.39/0.57  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T10:27:49
% 0.39/0.57  :PROOF-FOUND
% 0.39/0.57  * 
%------------------------------------------------------------------------------