TSTP Solution File: GRP078-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP078-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n019.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 0.22s 0.56s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   43 (  40 unt;   0 nHn;  10 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   :   63 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
    double_divide(double_divide(identity,X),double_divide(identity,double_divide(double_divide(double_divide(X,Y),identity),double_divide(Z,Y)))) = Z,
    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,negated_conjecture,
    ( multiply(inverse(a1),a1) != identity
    | multiply(identity,a2) != a2
    | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
    file('/export/starexec/sandbox/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,X),double_divide(identity,double_divide(inverse(double_divide(X,Y)),double_divide(Z,Y)))) = Z,
    inference('REWRITE',[status(thm)],[single_axiom,inverse,theory(equality)]) ).

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

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

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

cnf(18,plain,
    double_divide(identity,double_divide(identity,double_divide(inverse(inverse(inverse(identity))),inverse(X)))) = X,
    inference('PARAMODULATE',[status(thm)],[10,identity,theory(equality)]) ).

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

cnf(23,plain,
    double_divide(identity,double_divide(identity,double_divide(identity,inverse(X)))) = X,
    inference('REWRITE',[status(thm)],[18,22,theory(equality)]) ).

cnf(25,plain,
    double_divide(double_divide(identity,X),double_divide(identity,double_divide(inverse(double_divide(X,inverse(identity))),inverse(inverse(Y))))) = double_divide(identity,Y),
    inference('PARAMODULATE',[status(thm)],[8,16,theory(equality)]) ).

cnf(27,plain,
    double_divide(double_divide(identity,X),double_divide(identity,inverse(inverse(inverse(X))))) = inverse(inverse(identity)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,22,theory(equality)]),inverse,theory(equality)]) ).

cnf(29,plain,
    inverse(identity) = inverse(inverse(identity)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[23,22,theory(equality)]),identity,inverse,theory(equality)]) ).

cnf(32,plain,
    inverse(identity) = identity,
    inference('REWRITE',[status(thm)],[22,29,theory(equality)]) ).

cnf(33,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)],[7,32,theory(equality)]) ).

cnf(34,plain,
    double_divide(identity,double_divide(identity,double_divide(inverse(double_divide(identity,X)),double_divide(Y,X)))) = Y,
    inference('REWRITE',[status(thm)],[9,32,theory(equality)]) ).

cnf(36,plain,
    inverse(double_divide(identity,X)) = inverse(inverse(X)),
    inference('REWRITE',[status(thm)],[16,inverse,32,theory(equality)]) ).

cnf(37,plain,
    double_divide(identity,double_divide(identity,double_divide(inverse(inverse(X)),double_divide(Y,X)))) = Y,
    inference('REWRITE',[status(thm)],[34,36,theory(equality)]) ).

cnf(39,plain,
    inverse(X) = double_divide(identity,X),
    inference('REWRITE',[status(thm)],[25,10,inverse,32,theory(equality)]) ).

cnf(40,plain,
    inverse(inverse(double_divide(inverse(inverse(X)),double_divide(Y,X)))) = Y,
    inference('REWRITE',[status(thm)],[37,39,theory(equality)]) ).

cnf(41,plain,
    inverse(inverse(inverse(inverse(X)))) = X,
    inference('REWRITE',[status(thm)],[23,39,theory(equality)]) ).

cnf(42,plain,
    double_divide(inverse(X),inverse(double_divide(inverse(double_divide(X,Y)),double_divide(Z,Y)))) = Z,
    inference('REWRITE',[status(thm)],[8,39,theory(equality)]) ).

cnf(50,plain,
    double_divide(inverse(X),X) = identity,
    inference('REWRITE',[status(thm)],[27,32,41,39,29,theory(equality)]) ).

cnf(52,plain,
    inverse(inverse(X)) = X,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[42,50,theory(equality)]),inverse,32,theory(equality)]) ).

cnf(56,plain,
    double_divide(X,double_divide(Y,X)) = Y,
    inference('REWRITE',[status(thm)],[40,52,theory(equality)]) ).

cnf(59,plain,
    inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
    inference('REWRITE',[status(thm)],[33,52,theory(equality)]) ).

cnf(60,plain,
    double_divide(inverse(X),inverse(double_divide(X,Y))) = inverse(Y),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[42,50,theory(equality)]),52,inverse,theory(equality)]) ).

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

cnf(64,plain,
    double_divide(inverse(X),inverse(double_divide(inverse(double_divide(X,double_divide(Y,Z))),Y))) = Z,
    inference('PARAMODULATE',[status(thm)],[42,56,theory(equality)]) ).

cnf(68,plain,
    double_divide(inverse(X),inverse(Y)) = inverse(double_divide(Y,X)),
    inference('PARAMODULATE',[status(thm)],[61,60,theory(equality)]) ).

cnf(70,plain,
    inverse(double_divide(double_divide(inverse(double_divide(X,double_divide(Y,Z))),Y),X)) = Z,
    inference('REWRITE',[status(thm)],[64,68,theory(equality)]) ).

cnf(73,plain,
    double_divide(X,inverse(Y)) = inverse(double_divide(Y,inverse(X))),
    inference('PARAMODULATE',[status(thm)],[68,52,theory(equality)]) ).

cnf(75,plain,
    double_divide(double_divide(b3,a3),inverse(c3)) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
    inference('REWRITE',[status(thm)],[59,73,theory(equality)]) ).

cnf(76,plain,
    double_divide(inverse(X),Y) = inverse(double_divide(inverse(Y),X)),
    inference('PARAMODULATE',[status(thm)],[68,52,theory(equality)]) ).

cnf(77,plain,
    double_divide(inverse(X),double_divide(inverse(Y),double_divide(X,double_divide(Y,Z)))) = Z,
    inference('REWRITE',[status(thm)],[70,52,76,theory(equality)]) ).

cnf(79,plain,
    double_divide(double_divide(b3,a3),inverse(c3)) != double_divide(inverse(a3),double_divide(c3,b3)),
    inference('REWRITE',[status(thm)],[75,76,theory(equality)]) ).

cnf(80,plain,
    double_divide(X,inverse(Y)) = double_divide(inverse(Z),double_divide(Y,double_divide(Z,X))),
    inference('PARAMODULATE',[status(thm)],[61,77,theory(equality)]) ).

cnf(81,plain,
    double_divide(double_divide(X,Y),inverse(Z)) = double_divide(inverse(Y),double_divide(Z,X)),
    inference('PARAMODULATE',[status(thm)],[80,56,theory(equality)]) ).

cnf(82,plain,
    $false,
    inference('REWRITE',[status(thm)],[79,81,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : GRP078-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.08/0.15  % Command  : run-snark %s %d
% 0.15/0.36  % Computer : n019.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 600
% 0.15/0.36  % DateTime : Mon Jun 13 16:45:54 EDT 2022
% 0.15/0.36  % CPUTime  : 
% 0.22/0.49  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.50  * 
% 0.22/0.50  * 
% 0.22/0.51  #<PACKAGE "SNARK-USER">
% 0.22/0.51  * 
% 0.22/0.51  SNARK-TPTP-OPTIONS
% 0.22/0.51  * 
% 0.22/0.51  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.22/0.51   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.22/0.51   (USE-FACTORING :POS)
% 0.22/0.51   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.22/0.51   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.22/0.51   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.22/0.51   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.22/0.51   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.22/0.51   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.22/0.51   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.22/0.51   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.22/0.51   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.22/0.51   (DECLARE-TPTP-SYMBOLS2))
% 0.22/0.51  * 
% 0.22/0.51  "."
% 0.22/0.51  * 
% 0.22/0.51  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T16:45:55
% 0.22/0.51  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n019.cluster.edu at 2022-06-13T16:45:55
% 0.22/0.52  
% 0.22/0.56  ; Recognized possible right inverse assertion (= |identity| (|double_divide| ?X (|inverse| ?X))).
% 0.22/0.56  
% 0.22/0.56  #||
% 0.22/0.56  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.56  % SZS output start Refutation
% See solution above
% 0.22/0.57  ||#
% 0.22/0.57  
% 0.22/0.57  ; Summary of computation:
% 0.22/0.57  ;       217 formulas have been input or derived (from 25 formulas).
% 0.22/0.57  ;        82 (38%) were retained.  Of these,
% 0.22/0.57  ;           65 (79%) were simplified or subsumed later,
% 0.22/0.57  ;           17 (21%) are still being kept.
% 0.22/0.57  ; 
% 0.22/0.57  ; Run time in seconds excluding printing time:
% 0.22/0.57  ;     0.002   3%   Read assertion file          (1 call)
% 0.22/0.57  ;     0.000   0%   Assert                       (5 calls)
% 0.22/0.57  ;     0.012  21%   Process new row              (205 calls)
% 0.22/0.57  ;     0.001   2%   Resolution                   (48 calls)
% 0.22/0.57  ;     0.003   5%   Paramodulation               (24 calls)
% 0.22/0.57  ;     0.000   0%   Condensing                   (3 calls)
% 0.22/0.57  ;     0.000   0%   Forward subsumption          (3 calls)
% 0.22/0.57  ;     0.000   0%   Backward subsumption         (3 calls)
% 0.22/0.57  ;     0.007  12%   Forward simplification       (174 calls)
% 0.22/0.57  ;     0.008  14%   Backward simplification      (82 calls)
% 0.22/0.57  ;     0.003   5%   Ordering                     (426 calls)
% 0.22/0.57  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.22/0.57  ;     0.000   0%   Purity testing               (1 call)
% 0.22/0.57  ;     0.022  38%   Other
% 0.22/0.57  ;     0.058        Total
% 0.22/0.57  ;     0.064        Real time
% 0.22/0.57  ; 
% 0.22/0.57  ; Term-hash-array has 328 terms in all.
% 0.22/0.57  ; Feature-vector-row-index has 0 entries (1 at peak, 3 added, 3 deleted).
% 0.22/0.57  ; Feature-vector-row-index has 1 node (26 at peak, 69 added, 68 deleted).
% 0.22/0.57  ;  Retrieved 0 possibly forward subsuming rows in 3 calls.
% 0.22/0.57  ;  Retrieved 0 possibly backward subsumed rows in 3 calls.
% 0.22/0.57  ; Path-index has 54 entries (143 at peak, 446 added, 392 deleted).
% 0.22/0.57  ; Path-index has 642 nodes (694 at peak, 1,228 added, 586 deleted).
% 0.22/0.57  ; Trie-index has 54 entries (143 at peak, 446 added, 392 deleted).
% 0.22/0.57  ; Trie-index has 169 nodes (600 at peak, 1,675 added, 1,506 deleted).
% 0.22/0.57  ; Retrieved 445 generalization terms in 967 calls.
% 0.22/0.57  ; Retrieved 181 instance terms in 84 calls.
% 0.22/0.57  ; Retrieved 459 unifiable terms in 195 calls.
% 0.22/0.57  ; 
% 0.22/0.57  ; The agenda of backward simplifiable rows to process has 1 entry:
% 0.22/0.57  ;     1 with value 0
% 0.22/0.57  ; The agenda of rows to process has 11 entries:
% 0.22/0.57  ;     1 with value 20              2 with value 22               1 with value 24
% 0.22/0.57  ;     4 with value 21              1 with value 23               2 with value 28
% 0.22/0.57  ; The agenda of rows to give has 5 entries:
% 0.22/0.57  ;     1 with value (4 20)          3 with value (4 21)           1 with value (4 22)
% 0.22/0.57  Evaluation took:
% 0.22/0.57    0.064 seconds of real time
% 0.22/0.57    0.057871 seconds of user run time
% 0.22/0.57    0.005962 seconds of system run time
% 0.22/0.57    0 calls to %EVAL
% 0.22/0.57    0 page faults and
% 0.22/0.57    6,764,488 bytes consed.
% 0.22/0.57  :PROOF-FOUND
% 0.22/0.57  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T16:45:55
% 0.22/0.57  :PROOF-FOUND
% 0.22/0.57  * 
%------------------------------------------------------------------------------