TSTP Solution File: GRP578-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP578-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n024.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 11:39:30 EDT 2022

% Result   : Unsatisfiable 0.19s 0.49s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   30 (  30 unt;   0 nHn;   7 RR)
%            Number of literals    :   30 (  29 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   :   35 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
    double_divide(double_divide(X,double_divide(double_divide(double_divide(Y,X),Z),double_divide(Y,identity))),double_divide(identity,identity)) = 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_2,negated_conjecture,
    multiply(identity,a2) != a2,
    file('/export/starexec/sandbox/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(X,double_divide(double_divide(double_divide(Y,X),Z),inverse(Y))),inverse(identity)) = Z,
    inference('REWRITE',[status(thm)],[single_axiom,inverse,theory(equality)]) ).

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

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

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

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

cnf(18,plain,
    double_divide(double_divide(inverse(identity),X),inverse(identity)) = double_divide(double_divide(inverse(Y),X),inverse(Y)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9,8,theory(equality)]),inverse,theory(equality)]) ).

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

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

cnf(27,plain,
    inverse(double_divide(identity,inverse(double_divide(identity,X)))) = X,
    inference('REWRITE',[status(thm)],[16,26,theory(equality)]) ).

cnf(28,plain,
    inverse(double_divide(identity,inverse(inverse(identity)))) = identity,
    inference('REWRITE',[status(thm)],[22,26,theory(equality)]) ).

cnf(29,plain,
    double_divide(double_divide(inverse(identity),inverse(inverse(X))),inverse(identity)) = double_divide(identity,inverse(X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9,10,theory(equality)]),inverse,theory(equality)]) ).

cnf(33,plain,
    double_divide(double_divide(inverse(identity),double_divide(double_divide(inverse(double_divide(identity,X)),Y),inverse(inverse(X)))),inverse(identity)) = Y,
    inference('PARAMODULATE',[status(thm)],[8,26,theory(equality)]) ).

cnf(43,plain,
    double_divide(double_divide(X,double_divide(inverse(identity),X)),inverse(identity)) = identity,
    inference('PARAMODULATE',[status(thm)],[17,27,theory(equality)]) ).

cnf(45,plain,
    inverse(double_divide(identity,X)) = double_divide(inverse(identity),double_divide(identity,X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,43,theory(equality)]),26,inverse,theory(equality)]) ).

cnf(47,plain,
    inverse(identity) = inverse(inverse(identity)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[45,identity,theory(equality)]),inverse,theory(equality)]) ).

cnf(49,plain,
    inverse(identity) = identity,
    inference('REWRITE',[status(thm)],[28,identity,47,theory(equality)]) ).

cnf(58,plain,
    inverse(double_divide(identity,X)) = double_divide(double_divide(inverse(Y),X),inverse(Y)),
    inference('REWRITE',[status(thm)],[18,inverse,49,theory(equality)]) ).

cnf(62,plain,
    inverse(inverse(X)) = inverse(double_divide(identity,X)),
    inference('REWRITE',[status(thm)],[26,inverse,49,theory(equality)]) ).

cnf(65,plain,
    inverse(inverse(inverse(inverse(X)))) = X,
    inference('REWRITE',[status(thm)],[27,62,theory(equality)]) ).

cnf(67,plain,
    inverse(inverse(X)) = double_divide(double_divide(inverse(Y),X),inverse(Y)),
    inference('REWRITE',[status(thm)],[58,62,theory(equality)]) ).

cnf(68,plain,
    X = double_divide(identity,inverse(X)),
    inference('REWRITE',[status(thm)],[29,65,62,inverse,49,theory(equality)]) ).

cnf(74,plain,
    inverse(inverse(X)) = X,
    inference('REWRITE',[status(thm)],[33,inverse,68,67,62,49,theory(equality)]) ).

cnf(80,plain,
    $false,
    inference('REWRITE',[status(thm)],[7,74,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GRP578-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.13  % Command  : run-snark %s %d
% 0.12/0.34  % Computer : n024.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Mon Jun 13 23:58:48 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.46  /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p 2022-06-13T23:58:48
% 0.19/0.47  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n024.cluster.edu at 2022-06-13T23:58:48
% 0.19/0.48  
% 0.19/0.49  ; Recognized possible right inverse assertion (= |identity| (|double_divide| ?X (|inverse| ?X))).
% 0.19/0.49  
% 0.19/0.49  #||
% 0.19/0.49  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.49  % SZS output start Refutation
% See solution above
% 0.19/0.50  ||#
% 0.19/0.50  
% 0.19/0.50  ; Summary of computation:
% 0.19/0.50  ;       143 formulas have been input or derived (from 18 formulas).
% 0.19/0.50  ;        80 (56%) were retained.  Of these,
% 0.19/0.50  ;           60 (75%) were simplified or subsumed later,
% 0.19/0.50  ;           20 (25%) are still being kept.
% 0.19/0.50  ; 
% 0.19/0.50  ; Run time in seconds excluding printing time:
% 0.19/0.50  ;     0.001   4%   Read assertion file          (1 call)
% 0.19/0.50  ;     0.000   0%   Assert                       (5 calls)
% 0.19/0.50  ;     0.009  35%   Process new row              (125 calls)
% 0.19/0.50  ;     0.000   0%   Resolution                   (34 calls)
% 0.19/0.50  ;     0.001   4%   Paramodulation               (17 calls)
% 0.19/0.50  ;     0.002   8%   Forward simplification       (121 calls)
% 0.19/0.50  ;     0.001   4%   Backward simplification      (80 calls)
% 0.19/0.50  ;     0.000   0%   Ordering                     (271 calls)
% 0.19/0.50  ;     0.001   4%   Sortal reasoning             (32 calls)
% 0.19/0.50  ;     0.000   0%   Purity testing               (1 call)
% 0.19/0.50  ;     0.011  42%   Other
% 0.19/0.50  ;     0.026        Total
% 0.19/0.50  ;     0.028        Real time
% 0.19/0.50  ; 
% 0.19/0.50  ; Term-hash-array has 267 terms in all.
% 0.19/0.50  ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.19/0.50  ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.19/0.50  ; Path-index has 69 entries (180 at peak, 331 added, 262 deleted).
% 0.19/0.50  ; Path-index has 592 nodes (639 at peak, 992 added, 400 deleted).
% 0.19/0.50  ; Trie-index has 69 entries (180 at peak, 331 added, 262 deleted).
% 0.19/0.50  ; Trie-index has 294 nodes (954 at peak, 1,674 added, 1,380 deleted).
% 0.19/0.50  ; Retrieved 241 generalization terms in 712 calls.
% 0.19/0.50  ; Retrieved 137 instance terms in 84 calls.
% 0.19/0.50  ; Retrieved 229 unifiable terms in 129 calls.
% 0.19/0.50  ; 
% 0.19/0.50  ; The agenda of backward simplifiable rows to process has 13 entries:
% 0.19/0.50  ;    13 with value 0
% 0.19/0.50  ; The agenda of rows to process has 5 entries:
% 0.19/0.50  ;     2 with value 17              1 with value 24               1 with value 31
% 0.19/0.50  ;     1 with value 23
% 0.19/0.50  ; The agenda of input rows to give has 1 entry:
% 0.19/0.50  ;     1 with value 19
% 0.19/0.50  ; The agenda of rows to give has 15 entries:
% 0.19/0.50  ;     1 with value (4 9)           1 with value (4 13)           1 with value (4 21)
% 0.19/0.50  ;     4 with value (4 11)          2 with value (4 19)           1 with value (4 23)
% 0.19/0.50  ;     1 with value (4 12)          3 with value (4 20)           1 with value (4 24)
% 0.19/0.50  Evaluation took:
% 0.19/0.50    0.028 seconds of real time
% 0.19/0.50    0.022981 seconds of user run time
% 0.19/0.50    0.005007 seconds of system run time
% 0.19/0.50    0 calls to %EVAL
% 0.19/0.50    0 page faults and
% 0.19/0.50    4,877,000 bytes consed.
% 0.19/0.50  :PROOF-FOUND
% 0.19/0.50  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T23:58:48
% 0.19/0.50  :PROOF-FOUND
% 0.19/0.50  * 
%------------------------------------------------------------------------------