TSTP Solution File: GRP495-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP495-1 : TPTP v8.1.0. Released v2.6.0.
% 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 11:39:08 EDT 2022

% Result   : Unsatisfiable 0.19s 0.55s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   36 (  36 unt;   0 nHn;   6 RR)
%            Number of literals    :   36 (  35 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   :   57 (   0 sgn)

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

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

cnf(16,plain,
    double_divide(double_divide(identity,X),inverse(identity)) = X,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12,identity,theory(equality)]),inverse,theory(equality)]) ).

cnf(18,plain,
    double_divide(identity,double_divide(identity,double_divide(inverse(identity),inverse(X)))) = X,
    inference('PARAMODULATE',[status(thm)],[12,identity,theory(equality)]) ).

cnf(19,plain,
    double_divide(double_divide(identity,X),double_divide(double_divide(Y,inverse(identity)),double_divide(X,double_divide(identity,double_divide(Z,inverse(Y)))))) = double_divide(identity,Z),
    inference('PARAMODULATE',[status(thm)],[8,12,theory(equality)]) ).

cnf(22,plain,
    identity = inverse(identity),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[16,identity,theory(equality)]),identity,theory(equality)]) ).

cnf(23,plain,
    double_divide(double_divide(identity,X),double_divide(inverse(double_divide(Y,Z)),double_divide(X,Z))) = Y,
    inference('REWRITE',[status(thm)],[8,inverse,22,theory(equality)]) ).

cnf(29,plain,
    inverse(double_divide(identity,X)) = X,
    inference('REWRITE',[status(thm)],[16,inverse,22,theory(equality)]) ).

cnf(30,plain,
    double_divide(identity,double_divide(identity,double_divide(identity,inverse(X)))) = X,
    inference('REWRITE',[status(thm)],[18,22,theory(equality)]) ).

cnf(31,plain,
    double_divide(double_divide(identity,X),double_divide(inverse(Y),double_divide(X,double_divide(identity,double_divide(Z,inverse(Y)))))) = double_divide(identity,Z),
    inference('REWRITE',[status(thm)],[19,inverse,22,theory(equality)]) ).

cnf(34,plain,
    identity = double_divide(double_divide(identity,X),X),
    inference('PARAMODULATE',[status(thm)],[identity,29,theory(equality)]) ).

cnf(36,plain,
    double_divide(double_divide(identity,X),double_divide(identity,double_divide(X,Y))) = double_divide(identity,Y),
    inference('PARAMODULATE',[status(thm)],[12,29,theory(equality)]) ).

cnf(37,plain,
    double_divide(identity,inverse(X)) = X,
    inference('REWRITE',[status(thm)],[12,36,theory(equality)]) ).

cnf(38,plain,
    double_divide(identity,double_divide(identity,X)) = X,
    inference('REWRITE',[status(thm)],[30,37,theory(equality)]) ).

cnf(43,plain,
    inverse(X) = double_divide(identity,X),
    inference('PARAMODULATE',[status(thm)],[29,38,theory(equality)]) ).

cnf(46,plain,
    inverse(inverse(X)) = X,
    inference('REWRITE',[status(thm)],[37,43,theory(equality)]) ).

cnf(48,plain,
    double_divide(inverse(X),double_divide(inverse(double_divide(Y,Z)),double_divide(X,Z))) = Y,
    inference('REWRITE',[status(thm)],[23,43,theory(equality)]) ).

cnf(51,plain,
    double_divide(inverse(X),double_divide(inverse(Y),double_divide(X,inverse(double_divide(Z,inverse(Y)))))) = inverse(Z),
    inference('REWRITE',[status(thm)],[31,43,theory(equality)]) ).

cnf(52,plain,
    identity = double_divide(inverse(X),X),
    inference('REWRITE',[status(thm)],[34,43,theory(equality)]) ).

cnf(55,plain,
    double_divide(X,double_divide(Y,X)) = Y,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[48,52,theory(equality)]),inverse,46,theory(equality)]) ).

cnf(56,plain,
    double_divide(double_divide(X,Y),X) = Y,
    inference('PARAMODULATE',[status(thm)],[55,55,theory(equality)]) ).

cnf(60,plain,
    double_divide(inverse(X),double_divide(inverse(Y),double_divide(X,Z))) = double_divide(Z,Y),
    inference('PARAMODULATE',[status(thm)],[48,56,theory(equality)]) ).

cnf(61,plain,
    double_divide(inverse(double_divide(X,inverse(Y))),Y) = inverse(X),
    inference('REWRITE',[status(thm)],[51,60,theory(equality)]) ).

cnf(64,plain,
    double_divide(X,inverse(Y)) = inverse(double_divide(Y,inverse(X))),
    inference('PARAMODULATE',[status(thm)],[55,61,theory(equality)]) ).

cnf(65,plain,
    double_divide(double_divide(b3,a3),inverse(c3)) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
    inference('REWRITE',[status(thm)],[7,64,theory(equality)]) ).

cnf(66,plain,
    double_divide(inverse(X),Y) = inverse(double_divide(inverse(Y),X)),
    inference('PARAMODULATE',[status(thm)],[61,56,theory(equality)]) ).

cnf(70,plain,
    double_divide(double_divide(b3,a3),inverse(c3)) != double_divide(inverse(a3),double_divide(c3,b3)),
    inference('REWRITE',[status(thm)],[65,66,theory(equality)]) ).

cnf(91,plain,
    double_divide(double_divide(X,Y),inverse(Z)) = double_divide(inverse(Y),double_divide(Z,X)),
    inference('PARAMODULATE',[status(thm)],[56,60,theory(equality)]) ).

cnf(92,plain,
    $false,
    inference('REWRITE',[status(thm)],[70,91,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GRP495-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.13  % 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 : Tue Jun 14 13:49:11 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.46  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.47  * 
% 0.19/0.47  * 
% 0.19/0.48  #<PACKAGE "SNARK-USER">
% 0.19/0.48  * 
% 0.19/0.48  SNARK-TPTP-OPTIONS
% 0.19/0.48  * 
% 0.19/0.48  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.48   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.48   (USE-FACTORING :POS)
% 0.19/0.48   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.48   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.48   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.48   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.48   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.48   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.48   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.48   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.48   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.48   (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.48  * 
% 0.19/0.48  "."
% 0.19/0.48  * 
% 0.19/0.48  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-14T13:49:11
% 0.19/0.48  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n006.cluster.edu at 2022-06-14T13:49:11
% 0.19/0.49  
% 0.19/0.55  ; Recognized possible right inverse assertion (= |identity| (|double_divide| ?X (|inverse| ?X))).
% 0.19/0.55  
% 0.19/0.55  #||
% 0.19/0.55  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.55  % SZS output start Refutation
% See solution above
% 0.19/0.55  ||#
% 0.19/0.55  
% 0.19/0.55  ; Summary of computation:
% 0.19/0.55  ;       421 formulas have been input or derived (from 31 formulas).
% 0.19/0.55  ;        92 (22%) were retained.  Of these,
% 0.19/0.55  ;           57 (62%) were simplified or subsumed later,
% 0.19/0.55  ;           35 (38%) are still being kept.
% 0.19/0.55  ; 
% 0.19/0.55  ; Run time in seconds excluding printing time:
% 0.19/0.55  ;     0.002   3%   Read assertion file          (1 call)
% 0.19/0.55  ;     0.000   0%   Assert                       (5 calls)
% 0.19/0.55  ;     0.010  14%   Process new row              (388 calls)
% 0.19/0.55  ;     0.002   3%   Resolution                   (60 calls)
% 0.19/0.55  ;     0.007  10%   Paramodulation               (30 calls)
% 0.19/0.55  ;     0.010  14%   Forward simplification       (315 calls)
% 0.19/0.55  ;     0.007  10%   Backward simplification      (92 calls)
% 0.19/0.55  ;     0.007  10%   Ordering                     (1,035 calls)
% 0.19/0.55  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.19/0.55  ;     0.000   0%   Purity testing               (1 call)
% 0.19/0.55  ;     0.026  37%   Other
% 0.19/0.56  ;     0.071        Total
% 0.19/0.56  ;     0.076        Real time
% 0.19/0.56  ; 
% 0.19/0.56  ; Term-hash-array has 320 terms in all.
% 0.19/0.56  ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.19/0.56  ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.19/0.56  ; Path-index has 109 entries (136 at peak, 405 added, 296 deleted).
% 0.19/0.56  ; Path-index has 526 nodes (579 at peak, 929 added, 403 deleted).
% 0.19/0.56  ; Trie-index has 109 entries (136 at peak, 405 added, 296 deleted).
% 0.19/0.56  ; Trie-index has 470 nodes (586 at peak, 1,623 added, 1,153 deleted).
% 0.19/0.56  ; Retrieved 1,054 generalization terms in 1,855 calls.
% 0.19/0.56  ; Retrieved 261 instance terms in 113 calls.
% 0.19/0.56  ; Retrieved 810 unifiable terms in 219 calls.
% 0.19/0.56  ; 
% 0.19/0.56  ; The agenda of backward simplifiable rows to process has 1 entry:
% 0.19/0.56  ;     1 with value 0
% 0.19/0.56  ; The agenda of rows to process has 27 entries:
% 0.19/0.56  ;     6 with value 23              1 with value 26               5 with value 29
% 0.19/0.56  ;     5 with value 24              2 with value 27               4 with value 30
% 0.19/0.56  ;     1 with value 25              1 with value 28               2 with value 31
% 0.19/0.56  ; The agenda of rows to give has 19 entries:
% 0.19/0.56  ;     2 with value (4 23)          3 with value (4 26)           4 with value (4 28)
% 0.19/0.56  ;     1 with value (4 24)          5 with value (4 27)           4 with value (4 29)
% 0.19/0.56  Evaluation took:
% 0.19/0.56    0.077 seconds of real time
% 0.19/0.56    0.064933 seconds of user run time
% 0.19/0.56    0.012067 seconds of system run time
% 0.19/0.56    0 calls to %EVAL
% 0.19/0.56    0 page faults and
% 0.19/0.56    6,211,888 bytes consed.
% 0.19/0.56  :PROOF-FOUND
% 0.19/0.56  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-14T13:49:11
% 0.19/0.56  :PROOF-FOUND
% 0.19/0.56  * 
%------------------------------------------------------------------------------