TSTP Solution File: GRP491-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP491-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n008.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 11:39:07 EDT 2022

% Result   : Unsatisfiable 0.20s 0.52s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   23 (  23 unt;   0 nHn;   6 RR)
%            Number of literals    :   23 (  22 equ;   2 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    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   27 (   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/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_2,negated_conjecture,
    multiply(identity,a2) != a2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).

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

cnf(7,plain,
    inverse(inverse(a2)) != a2,
    inference('REWRITE',[status(thm)],[prove_these_axioms_2,inverse,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(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,
    identity = inverse(identity),
    inference('REWRITE',[status(thm)],[22,29,theory(equality)]) ).

cnf(38,plain,
    inverse(X) = double_divide(identity,X),
    inference('REWRITE',[status(thm)],[25,10,inverse,32,theory(equality)]) ).

cnf(40,plain,
    inverse(inverse(inverse(inverse(X)))) = X,
    inference('REWRITE',[status(thm)],[23,38,theory(equality)]) ).

cnf(41,plain,
    double_divide(inverse(X),inverse(double_divide(inverse(double_divide(X,Y)),double_divide(Z,Y)))) = Z,
    inference('REWRITE',[status(thm)],[8,38,theory(equality)]) ).

cnf(49,plain,
    double_divide(inverse(X),X) = identity,
    inference('REWRITE',[status(thm)],[27,32,40,38,29,theory(equality)]) ).

cnf(51,plain,
    inverse(inverse(X)) = X,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[41,49,theory(equality)]),inverse,32,theory(equality)]) ).

cnf(58,plain,
    $false,
    inference('REWRITE',[status(thm)],[7,51,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP491-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13  % Command  : run-snark %s %d
% 0.13/0.34  % Computer : n008.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 14:58:22 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.46  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.47  * 
% 0.20/0.47  * 
% 0.20/0.47  #<PACKAGE "SNARK-USER">
% 0.20/0.47  * 
% 0.20/0.47  SNARK-TPTP-OPTIONS
% 0.20/0.47  * 
% 0.20/0.48  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.48   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.48   (USE-FACTORING :POS)
% 0.20/0.48   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.48   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.48   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.48   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.48   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.48   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.48   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.48   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.48   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.48   (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.48  * 
% 0.20/0.48  "."
% 0.20/0.48  * 
% 0.20/0.48  ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T14:58:22
% 0.20/0.48  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n008.cluster.edu at 2022-06-13T14:58:22
% 0.20/0.49  
% 0.20/0.52  ; Recognized possible right inverse assertion (= |identity| (|double_divide| ?X (|inverse| ?X))).
% 0.20/0.52  
% 0.20/0.52  #||
% 0.20/0.52  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.52  % SZS output start Refutation
% See solution above
% 0.20/0.52  ||#
% 0.20/0.52  
% 0.20/0.52  ; Summary of computation:
% 0.20/0.52  ;       107 formulas have been input or derived (from 15 formulas).
% 0.20/0.52  ;        58 (54%) were retained.  Of these,
% 0.20/0.52  ;           42 (72%) were simplified or subsumed later,
% 0.20/0.52  ;           16 (28%) are still being kept.
% 0.20/0.52  ; 
% 0.20/0.52  ; Run time in seconds excluding printing time:
% 0.20/0.52  ;     0.001   2%   Read assertion file          (1 call)
% 0.20/0.52  ;     0.001   2%   Assert                       (5 calls)
% 0.20/0.52  ;     0.011  26%   Process new row              (105 calls)
% 0.20/0.52  ;     0.000   0%   Resolution                   (28 calls)
% 0.20/0.52  ;     0.001   2%   Paramodulation               (14 calls)
% 0.20/0.52  ;     0.002   5%   Forward simplification       (100 calls)
% 0.20/0.52  ;     0.004   9%   Backward simplification      (58 calls)
% 0.20/0.52  ;     0.001   2%   Ordering                     (175 calls)
% 0.20/0.52  ;     0.001   2%   Sortal reasoning             (32 calls)
% 0.20/0.52  ;     0.000   0%   Purity testing               (1 call)
% 0.20/0.52  ;     0.021  49%   Other
% 0.20/0.52  ;     0.043        Total
% 0.20/0.52  ;     0.047        Real time
% 0.20/0.52  ; 
% 0.20/0.52  ; Term-hash-array has 231 terms in all.
% 0.20/0.52  ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.20/0.52  ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.20/0.52  ; Path-index has 72 entries (129 at peak, 284 added, 212 deleted).
% 0.20/0.52  ; Path-index has 552 nodes (578 at peak, 844 added, 292 deleted).
% 0.20/0.52  ; Trie-index has 72 entries (129 at peak, 284 added, 212 deleted).
% 0.20/0.52  ; Trie-index has 259 nodes (559 at peak, 1,160 added, 901 deleted).
% 0.20/0.52  ; Retrieved 192 generalization terms in 625 calls.
% 0.20/0.52  ; Retrieved 106 instance terms in 57 calls.
% 0.20/0.52  ; Retrieved 171 unifiable terms in 95 calls.
% 0.20/0.52  ; 
% 0.20/0.52  ; The agenda of rows to process has 2 entries:
% 0.20/0.52  ;     1 with value 23              1 with value 24
% 0.20/0.52  ; The agenda of rows to give has 8 entries:
% 0.20/0.52  ;     1 with value (4 11)          1 with value (4 23)           1 with value (4 29)
% 0.20/0.52  ;     1 with value (4 13)          1 with value (4 25)           1 with value (4 32)
% 0.20/0.52  ;     1 with value (4 16)          1 with value (4 28)
% 0.20/0.52  Evaluation took:
% 0.20/0.52    0.047 seconds of real time
% 0.20/0.52    0.044616 seconds of user run time
% 0.20/0.52    0.002116 seconds of system run time
% 0.20/0.52    0 calls to %EVAL
% 0.20/0.52    0 page faults and
% 0.20/0.52    3,975,344 bytes consed.
% 0.20/0.52  :PROOF-FOUND
% 0.20/0.52  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T14:58:22
% 0.20/0.52  :PROOF-FOUND
% 0.20/0.52  * 
%------------------------------------------------------------------------------