TSTP Solution File: FLD041-4 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : FLD041-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% 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 02:27:09 EDT 2022

% Result   : Unsatisfiable 3.25s 3.43s
% Output   : Refutation 3.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   14
% Syntax   : Number of clauses     :   22 (  15 unt;   1 nHn;  22 RR)
%            Number of literals    :   37 (   0 equ;  18 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    :    7 (   7 usr;   5 con; 0-1 aty)
%            Number of variables   :   24 (   1 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(associativity_addition_1,axiom,
    ( sum(X,Y,Z)
    | ~ sum(X,U,V)
    | ~ sum(U,W,Y)
    | ~ sum(V,W,Z) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).

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

cnf(existence_of_inverse_addition,axiom,
    ( sum(additive_inverse(X),X,additive_identity)
    | ~ defined(X) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_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/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(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/sandbox/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).

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(c_is_defined,hypothesis,
    defined(c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_is_defined) ).

cnf(not_sum_4,negated_conjecture,
    ~ sum(additive_identity,a,additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_4) ).

cnf(not_sum_5,negated_conjecture,
    ~ sum(additive_identity,b,additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_5) ).

cnf(product_6,negated_conjecture,
    product(a,b,c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_6) ).

cnf(sum_7,negated_conjecture,
    sum(additive_identity,c,additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_7) ).

cnf(30,plain,
    sum(additive_identity,c,c),
    inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_addition,c_is_defined]) ).

cnf(36,plain,
    product(multiplicative_identity,b,b),
    inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_multiplication,b_is_defined]) ).

cnf(46,plain,
    sum(additive_inverse(b),b,additive_identity),
    inference('HYPERRESOLVE',[status(thm)],[existence_of_inverse_addition,b_is_defined]) ).

cnf(168,plain,
    product(multiplicative_inverse(a),a,multiplicative_identity),
    inference('UR-RESOLVE',[status(thm)],[existence_of_inverse_multiplication,not_sum_4,a_is_defined]) ).

cnf(179,plain,
    sum(c,c,c),
    inference('HYPERRESOLVE',[status(thm)],[associativity_addition_1,30,sum_7,30]) ).

cnf(18402,plain,
    ~ sum(b,b,b),
    inference('UR-RESOLVE',[status(thm)],[associativity_addition_1,46,not_sum_5,46]) ).

cnf(18429,plain,
    ~ product(c,X,b),
    inference('UR-RESOLVE',[status(thm)],[distributivity_1,18402,179]) ).

cnf(18532,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[associativity_multiplication_1,168,product_6,36]),18429]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : FLD041-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.12/0.13  % Command  : run-snark %s %d
% 0.13/0.34  % Computer : n029.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 22:19:05 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 2022-06-06T22:19:05
% 0.19/0.47  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n029.cluster.edu at 2022-06-06T22:19:05
% 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.
% 3.25/3.43  ; Declaring product to be commutative.
% 3.25/3.43  
% 3.25/3.43  #||
% 3.25/3.43  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.25/3.43  % SZS output start Refutation
% See solution above
% 3.25/3.43  ||#
% 3.25/3.43  
% 3.25/3.43  ; Summary of computation:
% 3.25/3.43  ;     40784 formulas have been input or derived (from 160 formulas).
% 3.25/3.43  ;     18532 (45%) were retained.  Of these,
% 3.25/3.43  ;           29 ( 0%) were simplified or subsumed later,
% 3.25/3.43  ;        18503 (100%) are still being kept.
% 3.25/3.43  ; 
% 3.25/3.43  ; Run time in seconds excluding printing time:
% 3.25/3.43  ;     0.007   0%   Read assertion file          (1 call)
% 3.25/3.43  ;     0.001   0%   Assert                       (33 calls)
% 3.25/3.43  ;     1.094  37%   Process new row              (40,044 calls)
% 3.25/3.43  ;     1.083  37%   Resolution                   (318 calls)
% 3.25/3.43  ;     0.001   0%   Paramodulation               (159 calls)
% 3.25/3.43  ;     0.011   0%   Condensing                   (4,042 calls)
% 3.25/3.43  ;     0.154   5%   Forward subsumption          (4,042 calls)
% 3.25/3.43  ;     0.051   2%   Backward subsumption         (2,088 calls)
% 3.25/3.43  ;     0.013   0%   Clause clause subsumption    (14,412 calls)
% 3.25/3.43  ;     0.251   8%   Forward simplification       (40,044 calls)
% 3.25/3.43  ;     0.144   5%   Backward simplification      (18,532 calls)
% 3.25/3.43  ;     0.003   0%   Ordering                     (1,386 calls)
% 3.25/3.43  ;     0.000   0%   Sortal reasoning             (32 calls)
% 3.25/3.43  ;     0.001   0%   Purity testing               (1 call)
% 3.25/3.43  ;     0.141   5%   Other
% 3.25/3.43  ;     2.955        Total
% 3.25/3.43  ;     2.958        Real time
% 3.25/3.43  ; 
% 3.25/3.43  ; Term-hash-array has 28,614 terms in all.
% 3.25/3.43  ; Feature-vector-row-index has 2,077 entries (2,085 at peak, 2,088 added, 11 deleted).
% 3.25/3.43  ; Feature-vector-row-index has 1,410 nodes (1,448 at peak, 1,464 added, 54 deleted).
% 3.25/3.43  ;  Retrieved 33,248 possibly forward subsuming rows in 4,042 calls.
% 3.25/3.43  ;  Retrieved 15,054 possibly backward subsumed rows in 2,088 calls.
% 3.25/3.43  ; Path-index has 28,598 entries (28,598 at peak, 28,632 added, 34 deleted).
% 3.25/3.43  ; Path-index has 1,006 nodes (1,009 at peak, 1,021 added, 15 deleted).
% 3.25/3.43  ; Trie-index has 28,598 entries (28,598 at peak, 28,632 added, 34 deleted).
% 3.25/3.43  ; Trie-index has 79,419 nodes (79,419 at peak, 79,462 added, 43 deleted).
% 3.25/3.43  ; Retrieved 19,561 generalization terms in 44,061 calls.
% 3.25/3.43  ; Retrieved 16,521 instance terms in 16,443 calls.
% 3.25/3.43  ; Retrieved 3,540,415 unifiable terms in 18,780 calls.
% 3.25/3.43  ; 
% 3.25/3.43  ; The agenda of rows to process has 29 entries:
% 3.25/3.43  ;     3 with value 9              24 with value 10               2 with value 11
% 3.25/3.43  ; The agenda of rows to give has 18355 entries:
% 3.25/3.43  ;    28 with value (4 8)        5160 with value (4 13)         450 with value (4 18)
% 3.25/3.43  ;   131 with value (4 9)          90 with value (4 14)        5003 with value (4 19)
% 3.25/3.43  ;   307 with value (4 10)       1128 with value (4 15)        1225 with value (4 20)
% 3.25/3.43  ;  1191 with value (4 11)        281 with value (4 16)          50 with value (4 22)
% 3.25/3.43  ;  1711 with value (4 12)       1600 with value (4 17)
% 3.25/3.43  Evaluation took:
% 3.25/3.43    2.96 seconds of real time
% 3.25/3.43    2.730752 seconds of user run time
% 3.25/3.43    0.228143 seconds of system run time
% 3.25/3.43    [Run times include 0.415 seconds GC run time.]
% 3.25/3.43    0 calls to %EVAL
% 3.25/3.43    0 page faults and
% 3.25/3.43    213,453,832 bytes consed.
% 3.25/3.43  :PROOF-FOUND
% 3.25/3.43  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-06T22:19:08
% 3.25/3.43  :PROOF-FOUND
% 3.25/3.43  * 
%------------------------------------------------------------------------------