TSTP Solution File: FLD009-3 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : FLD009-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 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 02:26:57 EDT 2022

% Result   : Unsatisfiable 1.44s 1.66s
% Output   : Refutation 1.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   15 (  10 unt;   2 nHn;  15 RR)
%            Number of literals    :   25 (   0 equ;  11 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   13 (   2 sgn)

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

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

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

cnf(totality_of_multiplication,axiom,
    ( product(X,Y,multiply(X,Y))
    | ~ defined(X)
    | ~ defined(Y) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_multiplication) ).

cnf(a_is_defined,hypothesis,
    defined(a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).

cnf(b_is_defined,hypothesis,
    defined(b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).

cnf(not_sum_3,negated_conjecture,
    ~ sum(additive_identity,a,additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_3) ).

cnf(not_product_4,negated_conjecture,
    ~ product(a,X,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_4) ).

cnf(31,plain,
    product(multiplicative_identity,b,b),
    inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_multiplication,b_is_defined]) ).

cnf(75,plain,
    defined(multiplicative_inverse(a)),
    inference('UR-RESOLVE',[status(thm)],[well_definedness_of_multiplicative_inverse,a_is_defined,not_sum_3]) ).

cnf(120,plain,
    product(multiplicative_inverse(a),a,multiplicative_identity),
    inference('UR-RESOLVE',[status(thm)],[existence_of_inverse_multiplication,not_sum_3,a_is_defined]) ).

cnf(416,plain,
    product(multiplicative_inverse(a),b,multiply(multiplicative_inverse(a),b)),
    inference('HYPERRESOLVE',[status(thm)],[totality_of_multiplication,75,b_is_defined]) ).

cnf(8313,plain,
    ~ product(multiplicative_inverse(a),b,X),
    inference('UR-RESOLVE',[status(thm)],[associativity_multiplication_1,120,not_product_4,31]) ).

cnf(8314,plain,
    $false,
    inference('REWRITE',[status(thm)],[416,8313]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : FLD009-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.10/0.13  % Command  : run-snark %s %d
% 0.13/0.34  % Computer : n024.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 23:57:35 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.45  /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 2022-06-06T23:57:35
% 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 2022-06-06T23:57:35
% 0.19/0.49  
% 0.19/0.49  ; Recognized possible associativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?X ?U ?V)) (NOT (|sum| ?U ?W ?Y)) (NOT (|sum| ?V ?W ?Z))).
% 0.19/0.49  ; Recognized possible associativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?U ?V ?X)) (NOT (|sum| ?V ?Y ?W)) (NOT (|sum| ?U ?W ?Z))).
% 0.19/0.49  ; Recognized commutativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?Y ?X ?Z))).
% 0.19/0.49  ; Recognized possible associativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?X ?U ?V)) (NOT (|product| ?U ?W ?Y)) (NOT (|product| ?V ?W ?Z))).
% 0.19/0.49  ; Recognized possible associativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?U ?V ?X)) (NOT (|product| ?V ?Y ?W)) (NOT (|product| ?U ?W ?Z))).
% 0.19/0.49  ; Recognized commutativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?Y ?X ?Z))).
% 0.19/0.49  ; Declaring sum to be commutative.
% 1.44/1.66  ; Declaring product to be commutative.
% 1.44/1.66  
% 1.44/1.66  #||
% 1.44/1.66  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.44/1.66  % SZS output start Refutation
% See solution above
% 1.44/1.66  ||#
% 1.44/1.66  
% 1.44/1.66  ; Summary of computation:
% 1.44/1.66  ;     17407 formulas have been input or derived (from 97 formulas).
% 1.44/1.66  ;      8314 (48%) were retained.  Of these,
% 1.44/1.66  ;           12 ( 0%) were simplified or subsumed later,
% 1.44/1.66  ;         8302 (100%) are still being kept.
% 1.44/1.66  ; 
% 1.44/1.66  ; Run time in seconds:
% 1.44/1.66  ;     0.006   1%   Read assertion file          (1 call)
% 1.44/1.66  ;     0.002   0%   Assert                       (30 calls)
% 1.44/1.66  ;     0.460  39%   Process new row              (17,118 calls)
% 1.44/1.66  ;     0.357  30%   Resolution                   (192 calls)
% 1.44/1.66  ;     0.000   0%   Paramodulation               (96 calls)
% 1.44/1.66  ;     0.004   0%   Condensing                   (1,820 calls)
% 1.44/1.66  ;     0.046   4%   Forward subsumption          (1,820 calls)
% 1.44/1.66  ;     0.022   2%   Backward subsumption         (958 calls)
% 1.44/1.66  ;     0.008   1%   Clause clause subsumption    (5,275 calls)
% 1.44/1.66  ;     0.154  13%   Forward simplification       (17,118 calls)
% 1.44/1.66  ;     0.052   4%   Backward simplification      (8,314 calls)
% 1.44/1.66  ;     0.001   0%   Ordering                     (760 calls)
% 1.44/1.66  ;     0.000   0%   Sortal reasoning             (32 calls)
% 1.44/1.66  ;     0.000   0%   Purity testing               (1 call)
% 1.44/1.66  ;     0.078   7%   Other
% 1.44/1.66  ;     1.190        Total
% 1.44/1.66  ;     1.191        Real time
% 1.44/1.66  ; 
% 1.44/1.66  ; Term-hash-array has 12,840 terms in all.
% 1.44/1.66  ; Feature-vector-row-index has 952 entries (956 at peak, 958 added, 6 deleted).
% 1.44/1.66  ; Feature-vector-row-index has 751 nodes (767 at peak, 779 added, 28 deleted).
% 1.44/1.66  ;  Retrieved 13,387 possibly forward subsuming rows in 1,820 calls.
% 1.44/1.66  ;  Retrieved 5,958 possibly backward subsumed rows in 958 calls.
% 1.44/1.66  ; Path-index has 12,838 entries (12,840 at peak, 12,853 added, 15 deleted).
% 1.44/1.66  ; Path-index has 848 nodes (848 at peak, 857 added, 9 deleted).
% 1.44/1.66  ; Trie-index has 12,838 entries (12,840 at peak, 12,853 added, 15 deleted).
% 1.44/1.66  ; Trie-index has 36,216 nodes (36,224 at peak, 36,242 added, 26 deleted).
% 1.44/1.66  ; Retrieved 7,942 generalization terms in 18,908 calls.
% 1.44/1.66  ; Retrieved 7,380 instance terms in 7,355 calls.
% 1.44/1.66  ; Retrieved 1,000,826 unifiable terms in 5,799 calls.
% 1.44/1.66  ; 
% 1.44/1.66  ; The agenda of rows to process has 16 entries:
% 1.44/1.66  ;    11 with value 10              5 with value 11
% 1.44/1.66  ; The agenda of rows to give has 8207 entries:
% 1.44/1.66  ;     2 with value (4 7)         840 with value (4 12)         768 with value (4 17)
% 1.44/1.66  ;     9 with value (4 8)        2143 with value (4 13)         224 with value (4 18)
% 1.44/1.66  ;    72 with value (4 9)          56 with value (4 14)        2051 with value (4 19)
% 1.44/1.66  ;   161 with value (4 10)        584 with value (4 15)         496 with value (4 20)
% 1.44/1.66  ;   623 with value (4 11)        146 with value (4 16)          32 with value (4 22)
% 1.44/1.66  Evaluation took:
% 1.44/1.66    1.192 seconds of real time
% 1.44/1.66    1.071406 seconds of user run time
% 1.44/1.66    0.120351 seconds of system run time
% 1.44/1.66    [Run times include 0.136 seconds GC run time.]
% 1.44/1.66    0 calls to %EVAL
% 1.44/1.66    0 page faults and
% 1.44/1.66    86,322,776 bytes consed.
% 1.44/1.66  :PROOF-FOUND
% 1.44/1.66  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-06T23:57:36
% 1.44/1.66  :PROOF-FOUND
% 1.44/1.66  * 
%------------------------------------------------------------------------------