TSTP Solution File: FLD010-5 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : FLD010-5 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n027.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 02:26:57 EDT 2022

% Result   : Unsatisfiable 0.48s 0.69s
% Output   : Refutation 0.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   18 (  12 unt;   2 nHn;  18 RR)
%            Number of literals    :   31 (   0 equ;  14 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-1 aty)
%            Number of variables   :   17 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(existence_of_identity_addition,axiom,
    ( sum(additive_identity,X,X)
    | ~ defined(X) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).

cnf(associativity_multiplication_1,axiom,
    ( product(X,Y,Z)
    | ~ product(X,U,V)
    | ~ product(U,W,Y)
    | ~ product(V,W,Z) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).

cnf(existence_of_identity_multiplication,axiom,
    ( product(multiplicative_identity,X,X)
    | ~ defined(X) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).

cnf(existence_of_inverse_multiplication,axiom,
    ( product(multiplicative_inverse(X),X,multiplicative_identity)
    | sum(additive_identity,X,additive_identity)
    | ~ defined(X) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).

cnf(distributivity_1,axiom,
    ( sum(X,Y,Z)
    | ~ sum(U,V,W)
    | ~ product(W,X1,Z)
    | ~ product(U,X1,X)
    | ~ product(V,X1,Y) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).

cnf(well_definedness_of_additive_identity,axiom,
    defined(additive_identity),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).

cnf(well_definedness_of_multiplicative_identity,axiom,
    defined(multiplicative_identity),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).

cnf(well_definedness_of_multiplicative_inverse,axiom,
    ( defined(multiplicative_inverse(X))
    | ~ defined(X)
    | sum(additive_identity,X,additive_identity) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).

cnf(not_sum_1,negated_conjecture,
    ~ sum(additive_identity,multiplicative_identity,additive_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_1) ).

cnf(not_sum_2,negated_conjecture,
    ~ sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_2) ).

cnf(25,plain,
    sum(additive_identity,multiplicative_identity,multiplicative_identity),
    inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_addition,well_definedness_of_multiplicative_identity]) ).

cnf(27,plain,
    product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
    inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_multiplication,well_definedness_of_multiplicative_identity]) ).

cnf(28,plain,
    product(multiplicative_identity,additive_identity,additive_identity),
    inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_multiplication,well_definedness_of_additive_identity]) ).

cnf(41,plain,
    defined(multiplicative_inverse(multiplicative_identity)),
    inference('UR-RESOLVE',[status(thm)],[well_definedness_of_multiplicative_inverse,well_definedness_of_multiplicative_identity,not_sum_1]) ).

cnf(53,plain,
    product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity),
    inference('UR-RESOLVE',[status(thm)],[existence_of_inverse_multiplication,not_sum_1,well_definedness_of_multiplicative_identity]) ).

cnf(58,plain,
    ~ product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(multiplicative_identity)),
    inference('UR-RESOLVE',[status(thm)],[distributivity_1,28,not_sum_2,25,27]) ).

cnf(130,plain,
    product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_inverse(multiplicative_identity)),
    inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_multiplication,41]) ).

cnf(1087,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[associativity_multiplication_1,58,53]),130]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : FLD010-5 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13  % Command  : run-snark %s %d
% 0.13/0.34  % Computer : n027.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  6 15:18:39 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.46  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.47  * 
% 0.19/0.47  * 
% 0.19/0.48  #<PACKAGE "SNARK-USER">
% 0.19/0.48  * 
% 0.19/0.48  SNARK-TPTP-OPTIONS
% 0.19/0.48  * 
% 0.19/0.48  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.48   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.48   (USE-FACTORING :POS)
% 0.19/0.48   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.48   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.48   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.48   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.48   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.48   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.48   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.48   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.48   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.48   (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.48  * 
% 0.19/0.48  "."
% 0.19/0.48  * 
% 0.19/0.48  ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-06T15:18:39
% 0.19/0.48  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n027.cluster.edu at 2022-06-06T15:18:39
% 0.19/0.50  
% 0.19/0.50  ; Recognized possible associativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?X ?U ?V)) (NOT (|sum| ?U ?W ?Y)) (NOT (|sum| ?V ?W ?Z))).
% 0.19/0.50  ; Recognized possible associativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?U ?V ?X)) (NOT (|sum| ?V ?Y ?W)) (NOT (|sum| ?U ?W ?Z))).
% 0.19/0.50  ; Recognized commutativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?Y ?X ?Z))).
% 0.19/0.50  ; Recognized possible associativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?X ?U ?V)) (NOT (|product| ?U ?W ?Y)) (NOT (|product| ?V ?W ?Z))).
% 0.19/0.50  ; Recognized possible associativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?U ?V ?X)) (NOT (|product| ?V ?Y ?W)) (NOT (|product| ?U ?W ?Z))).
% 0.19/0.50  ; Recognized commutativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?Y ?X ?Z))).
% 0.19/0.50  ; Declaring sum to be commutative.
% 0.48/0.69  ; Declaring product to be commutative.
% 0.48/0.69  
% 0.48/0.69  #||
% 0.48/0.69  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.48/0.69  % SZS output start Refutation
% See solution above
% 0.48/0.70  ||#
% 0.48/0.70  
% 0.48/0.70  ; Summary of computation:
% 0.48/0.70  ;      2837 formulas have been input or derived (from 61 formulas).
% 0.48/0.70  ;      1087 (38%) were retained.  Of these,
% 0.48/0.70  ;           28 ( 3%) were simplified or subsumed later,
% 0.48/0.70  ;         1059 (97%) are still being kept.
% 0.48/0.70  ; 
% 0.48/0.70  ; Run time in seconds excluding printing time:
% 0.48/0.70  ;     0.006   3%   Read assertion file          (1 call)
% 0.48/0.70  ;     0.002   1%   Assert                       (28 calls)
% 0.48/0.70  ;     0.060  29%   Process new row              (2,525 calls)
% 0.48/0.70  ;     0.067  33%   Resolution                   (120 calls)
% 0.48/0.70  ;     0.000   0%   Paramodulation               (60 calls)
% 0.48/0.70  ;     0.000   0%   Factoring                    (1 call)
% 0.48/0.70  ;     0.001   0%   Condensing                   (224 calls)
% 0.48/0.70  ;     0.006   3%   Forward subsumption          (224 calls)
% 0.48/0.70  ;     0.004   2%   Backward subsumption         (136 calls)
% 0.48/0.70  ;     0.000   0%   Clause clause subsumption    (325 calls)
% 0.48/0.70  ;     0.016   8%   Forward simplification       (2,525 calls)
% 0.48/0.70  ;     0.005   2%   Backward simplification      (1,087 calls)
% 0.48/0.70  ;     0.000   0%   Ordering                     (180 calls)
% 0.48/0.70  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.48/0.70  ;     0.000   0%   Purity testing               (1 call)
% 0.48/0.70  ;     0.039  19%   Other
% 0.48/0.70  ;     0.206        Total
% 0.48/0.70  ;     0.218        Real time
% 0.48/0.70  ; 
% 0.48/0.70  ; Term-hash-array has 1,515 terms in all.
% 0.48/0.70  ; Feature-vector-row-index has 113 entries (117 at peak, 136 added, 23 deleted).
% 0.48/0.70  ; Feature-vector-row-index has 267 nodes (319 at peak, 345 added, 78 deleted).
% 0.48/0.70  ;  Retrieved 300 possibly forward subsuming rows in 224 calls.
% 0.48/0.70  ;  Retrieved 80 possibly backward subsumed rows in 136 calls.
% 0.48/0.70  ; Path-index has 1,499 entries (1,499 at peak, 1,536 added, 37 deleted).
% 0.48/0.70  ; Path-index has 537 nodes (543 at peak, 549 added, 12 deleted).
% 0.48/0.70  ; Trie-index has 1,499 entries (1,499 at peak, 1,536 added, 37 deleted).
% 0.48/0.70  ; Trie-index has 4,511 nodes (4,511 at peak, 4,585 added, 74 deleted).
% 0.48/0.70  ; Retrieved 1,355 generalization terms in 2,732 calls.
% 0.48/0.70  ; Retrieved 1,014 instance terms in 950 calls.
% 0.48/0.70  ; Retrieved 81,859 unifiable terms in 4,405 calls.
% 0.48/0.70  ; 
% 0.48/0.70  ; The agenda of rows to process has 12 entries:
% 0.48/0.70  ;     7 with value 12              1 with value 13               4 with value 14
% 0.48/0.70  ; The agenda of rows to give has 1000 entries:
% 0.48/0.70  ;    27 with value (4 9)          36 with value (4 14)          25 with value (4 18)
% 0.48/0.70  ;    84 with value (4 10)         90 with value (4 15)         128 with value (4 19)
% 0.48/0.70  ;   125 with value (4 11)         15 with value (4 16)          27 with value (4 20)
% 0.48/0.70  ;   161 with value (4 12)         96 with value (4 17)           1 with value (4 22)
% 0.48/0.70  ;   185 with value (4 13)
% 0.48/0.70  Evaluation took:
% 0.48/0.70    0.219 seconds of real time
% 0.48/0.70    0.195806 seconds of user run time
% 0.48/0.70    0.022601 seconds of system run time
% 0.48/0.70    [Run times include 0.011 seconds GC run time.]
% 0.48/0.70    0 calls to %EVAL
% 0.48/0.70    0 page faults and
% 0.48/0.70    13,263,856 bytes consed.
% 0.48/0.70  :PROOF-FOUND
% 0.48/0.70  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-06T15:18:40
% 0.48/0.70  :PROOF-FOUND
% 0.48/0.70  * 
%------------------------------------------------------------------------------