TSTP Solution File: GRP184-4 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP184-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 11:37:24 EDT 2022

% Result   : Unsatisfiable 0.20s 0.57s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   20 (  20 unt;   0 nHn;   6 RR)
%            Number of literals    :   20 (  19 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   :   26 (   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(idempotence_of_gld,axiom,
    greatest_lower_bound(X,X) = X,
    file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',idempotence_of_gld) ).

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(p21x_1,hypothesis,
    inverse(identity) = identity,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21x_1) ).

cnf(p21x_2,hypothesis,
    inverse(inverse(X)) = X,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21x_2) ).

cnf(p21x_3,hypothesis,
    inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21x_3) ).

cnf(p21x_4,hypothesis,
    inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21x_4) ).

cnf(prove_p21x,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_p21x) ).

cnf(23,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_p21x,monotony_lub1,left_identity,monotony_lub2,theory(equality)]) ).

cnf(24,plain,
    multiply(X,inverse(X)) = identity,
    inference('PARAMODULATE',[status(thm)],[left_inverse,p21x_2,theory(equality)]) ).

cnf(62,plain,
    inverse(X) = multiply(inverse(X),identity),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[p21x_3,p21x_1,theory(equality)]),left_identity,theory(equality)]) ).

cnf(63,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)],[23,62,theory(equality)]) ).

cnf(64,plain,
    inverse(multiply(X,inverse(Y))) = multiply(Y,inverse(X)),
    inference('PARAMODULATE',[status(thm)],[p21x_3,p21x_2,theory(equality)]) ).

cnf(65,plain,
    inverse(greatest_lower_bound(a,greatest_lower_bound(inverse(a),identity))) != least_upper_bound(multiply(inverse(greatest_lower_bound(a,identity)),a),inverse(greatest_lower_bound(a,identity))),
    inference('REWRITE',[status(thm)],[63,idempotence_of_gld,p21x_4,left_identity,24,monotony_glb2,64,theory(equality)]) ).

cnf(66,plain,
    inverse(multiply(inverse(X),Y)) = multiply(inverse(Y),X),
    inference('PARAMODULATE',[status(thm)],[p21x_3,p21x_2,theory(equality)]) ).

cnf(67,plain,
    $false,
    inference('REWRITE',[status(thm)],[65,idempotence_of_gld,p21x_4,62,left_inverse,monotony_glb1,66,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP184-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13  % Command  : run-snark %s %d
% 0.13/0.35  % Computer : n024.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Mon Jun 13 10:46:48 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.20/0.47  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.48  * 
% 0.20/0.48  * 
% 0.20/0.48  #<PACKAGE "SNARK-USER">
% 0.20/0.48  * 
% 0.20/0.48  SNARK-TPTP-OPTIONS
% 0.20/0.48  * 
% 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/sandbox/benchmark/theBenchmark.p 2022-06-13T10:46:48
% 0.20/0.49  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n024.cluster.edu at 2022-06-13T10:46:48
% 0.20/0.50  
% 0.20/0.50  ; Recognized left identity assertion (= (|multiply| |identity| ?X) ?X).
% 0.20/0.50  ; Recognized possible left inverse assertion (= (|multiply| (|inverse| ?X) ?X) |identity|).
% 0.20/0.50  ; Recognized associativity assertion (= (|multiply| (|multiply| ?X ?Y) ?Z) (|multiply| ?X (|multiply| ?Y ?Z))).
% 0.20/0.50  ; Recognized commutativity assertion (= (|greatest_lower_bound| ?X ?Y) (|greatest_lower_bound| ?Y ?X)).
% 0.20/0.50  ; Recognized commutativity assertion (= (|least_upper_bound| ?X ?Y) (|least_upper_bound| ?Y ?X)).
% 0.20/0.50  ; Recognized associativity assertion (= (|greatest_lower_bound| ?X (|greatest_lower_bound| ?Y ?Z)) (|greatest_lower_bound| (|greatest_lower_bound| ?X ?Y) ?Z)).
% 0.20/0.50  ; Recognized associativity assertion (= (|least_upper_bound| ?X (|least_upper_bound| ?Y ?Z)) (|least_upper_bound| (|least_upper_bound| ?X ?Y) ?Z)).
% 0.20/0.50  ; Declaring greatest_lower_bound to be commutative.
% 0.20/0.50  ; Declaring greatest_lower_bound to be associative-commutative.
% 0.20/0.50  ; Declaring least_upper_bound to be commutative.
% 0.20/0.57  ; Declaring least_upper_bound to be associative-commutative.
% 0.20/0.57  
% 0.20/0.57  #||
% 0.20/0.57  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.57  % SZS output start Refutation
% See solution above
% 0.20/0.57  ||#
% 0.20/0.57  
% 0.20/0.57  ; Summary of computation:
% 0.20/0.57  ;       276 formulas have been input or derived (from 14 formulas).
% 0.20/0.57  ;        67 (24%) were retained.  Of these,
% 0.20/0.57  ;            4 ( 6%) were simplified or subsumed later,
% 0.20/0.57  ;           63 (94%) are still being kept.
% 0.20/0.57  ; 
% 0.20/0.57  ; Run time in seconds excluding printing time:
% 0.20/0.57  ;     0.004   5%   Read assertion file          (1 call)
% 0.20/0.57  ;     0.001   1%   Assert                       (21 calls)
% 0.20/0.57  ;     0.008  10%   Process new row              (265 calls)
% 0.20/0.57  ;     0.000   0%   Resolution                   (26 calls)
% 0.20/0.57  ;     0.006   8%   Paramodulation               (13 calls)
% 0.20/0.57  ;     0.001   1%   Embedding                    (28 calls)
% 0.20/0.57  ;     0.027  34%   Forward simplification       (242 calls)
% 0.20/0.57  ;     0.004   5%   Backward simplification      (43 calls)
% 0.20/0.57  ;     0.000   0%   Ordering                     (181 calls)
% 0.20/0.57  ;     0.002   2%   Ordering ac                  (60 calls)
% 0.20/0.57  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.20/0.57  ;     0.000   0%   Purity testing               (1 call)
% 0.20/0.57  ;     0.027  34%   Other
% 0.20/0.57  ;     0.080        Total
% 0.20/0.57  ;     0.083        Real time
% 0.20/0.57  ; 
% 0.20/0.57  ; Term-hash-array has 211 terms in all.
% 0.20/0.57  ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.20/0.57  ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.20/0.57  ; Path-index has 199 entries (207 at peak, 225 added, 26 deleted).
% 0.20/0.57  ; Path-index has 186 nodes (209 at peak, 266 added, 80 deleted).
% 0.20/0.57  ; Trie-index has 199 entries (207 at peak, 225 added, 26 deleted).
% 0.20/0.57  ; Trie-index has 127 nodes (130 at peak, 144 added, 17 deleted).
% 0.20/0.57  ; Retrieved 5,902 generalization terms in 1,338 calls.
% 0.20/0.57  ; Retrieved 188 instance terms in 48 calls.
% 0.20/0.57  ; Retrieved 183 unifiable terms in 60 calls.
% 0.20/0.57  ; 
% 0.20/0.57  ; The agenda of input rows to give has 8 entries:
% 0.20/0.57  ;     3 with value 13              1 with value 14               4 with value 16
% 0.20/0.57  ; The agenda of rows to give has 41 entries:
% 0.20/0.57  ;     1 with value (4 10)          4 with value (4 21)           4 with value (4 27)
% 0.20/0.57  ;     2 with value (4 11)          4 with value (4 22)           4 with value (4 30)
% 0.20/0.57  ;     2 with value (4 15)          4 with value (4 24)           4 with value (4 31)
% 0.20/0.57  ;     4 with value (4 20)          4 with value (4 25)           4 with value (4 33)
% 0.20/0.57  Evaluation took:
% 0.20/0.57    0.084 seconds of real time
% 0.20/0.57    0.077747 seconds of user run time
% 0.20/0.57    0.006094 seconds of system run time
% 0.20/0.57    0 calls to %EVAL
% 0.20/0.57    0 page faults and
% 0.20/0.57    5,757,440 bytes consed.
% 0.20/0.57  :PROOF-FOUND
% 0.20/0.57  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T10:46:49
% 0.20/0.57  :PROOF-FOUND
% 0.20/0.57  * 
%------------------------------------------------------------------------------