TSTP Solution File: GRP184-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP184-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n029.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 11:37:24 EDT 2022

% Result   : Unsatisfiable 0.38s 0.61s
% Output   : Refutation 0.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   26 (  26 unt;   0 nHn;   5 RR)
%            Number of literals    :   26 (  25 equ;   4 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   41 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
    multiply(identity,X) = X,
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).

cnf(left_inverse,axiom,
    multiply(inverse(X),X) = identity,
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).

cnf(associativity,axiom,
    multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).

cnf(monotony_lub1,axiom,
    multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_lub1) ).

cnf(monotony_glb1,axiom,
    multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb1) ).

cnf(monotony_lub2,axiom,
    multiply(least_upper_bound(X,Y),Z) = least_upper_bound(multiply(X,Z),multiply(Y,Z)),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).

cnf(monotony_glb2,axiom,
    multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).

cnf(prove_p21,negated_conjecture,
    multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p21) ).

cnf(17,plain,
    least_upper_bound(multiply(a,inverse(greatest_lower_bound(a,identity))),inverse(greatest_lower_bound(a,identity))) != least_upper_bound(multiply(inverse(greatest_lower_bound(a,identity)),a),multiply(inverse(greatest_lower_bound(a,identity)),identity)),
    inference('REWRITE',[status(thm)],[prove_p21,monotony_lub1,left_identity,monotony_lub2,theory(equality)]) ).

cnf(55,plain,
    X = multiply(inverse(Y),multiply(Y,X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[associativity,left_inverse,theory(equality)]),left_identity,theory(equality)]) ).

cnf(56,plain,
    multiply(multiply(X,inverse(Y)),Y) = multiply(X,identity),
    inference('PARAMODULATE',[status(thm)],[associativity,left_inverse,theory(equality)]) ).

cnf(83,plain,
    X = multiply(inverse(inverse(X)),identity),
    inference('PARAMODULATE',[status(thm)],[55,left_inverse,theory(equality)]) ).

cnf(84,plain,
    multiply(X,Y) = multiply(inverse(inverse(X)),Y),
    inference('PARAMODULATE',[status(thm)],[55,55,theory(equality)]) ).

cnf(85,plain,
    X = multiply(X,identity),
    inference('REWRITE',[status(thm)],[83,84,theory(equality)]) ).

cnf(86,plain,
    multiply(multiply(X,inverse(Y)),Y) = X,
    inference('REWRITE',[status(thm)],[56,85,theory(equality)]) ).

cnf(87,plain,
    least_upper_bound(multiply(a,inverse(greatest_lower_bound(a,identity))),inverse(greatest_lower_bound(a,identity))) != least_upper_bound(multiply(inverse(greatest_lower_bound(a,identity)),a),inverse(greatest_lower_bound(a,identity))),
    inference('REWRITE',[status(thm)],[17,85,theory(equality)]) ).

cnf(95,plain,
    X = inverse(inverse(X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[86,left_inverse,theory(equality)]),left_identity,theory(equality)]) ).

cnf(101,plain,
    multiply(X,inverse(X)) = identity,
    inference('PARAMODULATE',[status(thm)],[left_inverse,95,theory(equality)]) ).

cnf(102,plain,
    multiply(multiply(X,Y),inverse(Y)) = X,
    inference('PARAMODULATE',[status(thm)],[86,95,theory(equality)]) ).

cnf(103,plain,
    X = multiply(Y,multiply(inverse(Y),X)),
    inference('PARAMODULATE',[status(thm)],[55,95,theory(equality)]) ).

cnf(108,plain,
    inverse(X) = multiply(inverse(multiply(Y,X)),Y),
    inference('PARAMODULATE',[status(thm)],[55,102,theory(equality)]) ).

cnf(109,plain,
    multiply(X,inverse(multiply(Y,X))) = inverse(Y),
    inference('PARAMODULATE',[status(thm)],[102,55,theory(equality)]) ).

cnf(121,plain,
    multiply(inverse(X),Y) = inverse(multiply(inverse(Y),X)),
    inference('PARAMODULATE',[status(thm)],[86,108,theory(equality)]) ).

cnf(124,plain,
    least_upper_bound(multiply(a,inverse(greatest_lower_bound(a,identity))),inverse(greatest_lower_bound(a,identity))) != least_upper_bound(inverse(greatest_lower_bound(identity,inverse(a))),inverse(greatest_lower_bound(a,identity))),
    inference('REWRITE',[status(thm)],[87,85,left_inverse,monotony_glb1,121,theory(equality)]) ).

cnf(127,plain,
    inverse(multiply(X,inverse(Y))) = multiply(Y,inverse(X)),
    inference('PARAMODULATE',[status(thm)],[103,109,theory(equality)]) ).

cnf(130,plain,
    $false,
    inference('REWRITE',[status(thm)],[124,left_identity,101,monotony_glb2,127,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP184-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13  % Command  : run-snark %s %d
% 0.13/0.33  % Computer : n029.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Mon Jun 13 14:02:55 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.18/0.45  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.46  * 
% 0.18/0.46  * 
% 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/sandbox/benchmark/theBenchmark.p 2022-06-13T14:02:55
% 0.18/0.46  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n029.cluster.edu at 2022-06-13T14:02:55
% 0.18/0.48  
% 0.18/0.48  ; Recognized left identity assertion (= (|multiply| |identity| ?X) ?X).
% 0.18/0.48  ; Recognized possible left inverse assertion (= (|multiply| (|inverse| ?X) ?X) |identity|).
% 0.18/0.48  ; Recognized associativity assertion (= (|multiply| (|multiply| ?X ?Y) ?Z) (|multiply| ?X (|multiply| ?Y ?Z))).
% 0.18/0.48  ; Recognized commutativity assertion (= (|greatest_lower_bound| ?X ?Y) (|greatest_lower_bound| ?Y ?X)).
% 0.18/0.48  ; Recognized commutativity assertion (= (|least_upper_bound| ?X ?Y) (|least_upper_bound| ?Y ?X)).
% 0.18/0.48  ; Recognized associativity assertion (= (|greatest_lower_bound| ?X (|greatest_lower_bound| ?Y ?Z)) (|greatest_lower_bound| (|greatest_lower_bound| ?X ?Y) ?Z)).
% 0.18/0.48  ; Recognized associativity assertion (= (|least_upper_bound| ?X (|least_upper_bound| ?Y ?Z)) (|least_upper_bound| (|least_upper_bound| ?X ?Y) ?Z)).
% 0.18/0.48  ; Declaring greatest_lower_bound to be commutative.
% 0.18/0.48  ; Declaring greatest_lower_bound to be associative-commutative.
% 0.18/0.48  ; Declaring least_upper_bound to be commutative.
% 0.38/0.61  ; Declaring least_upper_bound to be associative-commutative.
% 0.38/0.61  
% 0.38/0.61  #||
% 0.38/0.61  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.38/0.61  % SZS output start Refutation
% See solution above
% 0.38/0.61  ||#
% 0.38/0.61  
% 0.38/0.61  ; Summary of computation:
% 0.38/0.61  ;       682 formulas have been input or derived (from 29 formulas).
% 0.38/0.61  ;       130 (19%) were retained.  Of these,
% 0.38/0.61  ;           20 (15%) were simplified or subsumed later,
% 0.38/0.61  ;          110 (85%) are still being kept.
% 0.38/0.61  ; 
% 0.38/0.61  ; Run time in seconds excluding printing time:
% 0.38/0.61  ;     0.004   3%   Read assertion file          (1 call)
% 0.38/0.61  ;     0.001   1%   Assert                       (16 calls)
% 0.38/0.61  ;     0.014  10%   Process new row              (655 calls)
% 0.38/0.61  ;     0.002   1%   Resolution                   (56 calls)
% 0.38/0.61  ;     0.016  11%   Paramodulation               (28 calls)
% 0.38/0.61  ;     0.003   2%   Embedding                    (49 calls)
% 0.38/0.61  ;     0.067  47%   Forward simplification       (595 calls)
% 0.38/0.61  ;     0.005   3%   Backward simplification      (84 calls)
% 0.38/0.61  ;     0.005   3%   Ordering                     (906 calls)
% 0.38/0.61  ;     0.001   1%   Ordering ac                  (144 calls)
% 0.38/0.61  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.38/0.61  ;     0.000   0%   Purity testing               (1 call)
% 0.38/0.61  ;     0.026  18%   Other
% 0.38/0.61  ;     0.144        Total
% 0.38/0.61  ;     0.147        Real time
% 0.38/0.61  ; 
% 0.38/0.61  ; Term-hash-array has 441 terms in all.
% 0.38/0.61  ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.38/0.61  ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.38/0.61  ; Path-index has 388 entries (403 at peak, 458 added, 70 deleted).
% 0.38/0.61  ; Path-index has 436 nodes (447 at peak, 524 added, 88 deleted).
% 0.38/0.61  ; Trie-index has 388 entries (403 at peak, 458 added, 70 deleted).
% 0.38/0.61  ; Trie-index has 278 nodes (291 at peak, 358 added, 80 deleted).
% 0.38/0.61  ; Retrieved 33,274 generalization terms in 5,921 calls.
% 0.38/0.61  ; Retrieved 328 instance terms in 111 calls.
% 0.38/0.61  ; Retrieved 1,058 unifiable terms in 163 calls.
% 0.38/0.61  ; 
% 0.38/0.61  ; The agenda of backward simplifiable rows to process has 1 entry:
% 0.38/0.61  ;     1 with value 0
% 0.38/0.61  ; The agenda of rows to process has 15 entries:
% 0.38/0.61  ;     2 with value 19              3 with value 23               4 with value 25
% 0.38/0.61  ;     2 with value 20              1 with value 24               2 with value 31
% 0.38/0.61  ;     1 with value 22
% 0.38/0.61  ; The agenda of rows to give has 86 entries:
% 0.38/0.61  ;     3 with value (4 18)          8 with value (4 24)           4 with value (4 29)
% 0.38/0.61  ;     2 with value (4 19)          4 with value (4 25)           4 with value (4 30)
% 0.38/0.61  ;    11 with value (4 20)          4 with value (4 26)           4 with value (4 31)
% 0.38/0.61  ;     4 with value (4 21)         10 with value (4 27)           4 with value (4 33)
% 0.38/0.61  ;     4 with value (4 22)         16 with value (4 28)           4 with value (4 36)
% 0.38/0.61  Evaluation took:
% 0.38/0.61    0.147 seconds of real time
% 0.38/0.61    0.129667 seconds of user run time
% 0.38/0.61    0.017135 seconds of system run time
% 0.38/0.61    0 calls to %EVAL
% 0.38/0.61    0 page faults and
% 0.38/0.61    10,262,568 bytes consed.
% 0.38/0.61  :PROOF-FOUND
% 0.38/0.61  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T14:02:55
% 0.38/0.61  :PROOF-FOUND
% 0.38/0.61  * 
%------------------------------------------------------------------------------