TSTP Solution File: FLD026-3 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : FLD026-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n028.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 02:27:03 EDT 2022

% Result   : Unsatisfiable 2.87s 3.05s
% Output   : Refutation 2.87s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   25 (  18 unt;   4 nHn;  25 RR)
%            Number of literals    :   39 (   0 equ;  13 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    :    5 (   5 usr;   4 con; 0-1 aty)
%            Number of variables   :   16 (   0 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/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(a_is_defined,hypothesis,
    defined(a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).

cnf(b_is_defined,hypothesis,
    defined(b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).

cnf(not_sum_3,negated_conjecture,
    ~ sum(additive_identity,a,additive_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_3) ).

cnf(product_4,negated_conjecture,
    product(multiplicative_identity,a,b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_4) ).

cnf(not_product_5,negated_conjecture,
    ~ product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_5) ).

cnf(33,plain,
    product(multiplicative_identity,a,a),
    inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_multiplication,a_is_defined]) ).

cnf(34,plain,
    product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
    inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_multiplication,well_definedness_of_multiplicative_identity]) ).

cnf(35,plain,
    product(multiplicative_identity,additive_identity,additive_identity),
    inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_multiplication,well_definedness_of_additive_identity]) ).

cnf(77,plain,
    ( defined(multiplicative_inverse(b))
    | sum(additive_identity,b,additive_identity) ),
    inference('HYPERRESOLVE',[status(thm)],[well_definedness_of_multiplicative_inverse,b_is_defined]) ).

cnf(121,plain,
    product(multiplicative_inverse(a),a,multiplicative_identity),
    inference('UR-RESOLVE',[status(thm)],[existence_of_inverse_multiplication,not_sum_3,a_is_defined]) ).

cnf(122,plain,
    ( product(multiplicative_inverse(b),b,multiplicative_identity)
    | sum(additive_identity,b,additive_identity) ),
    inference('HYPERRESOLVE',[status(thm)],[existence_of_inverse_multiplication,b_is_defined]) ).

cnf(128,plain,
    product(multiplicative_identity,b,a),
    inference('HYPERRESOLVE',[status(thm)],[associativity_multiplication_1,33,product_4,33]) ).

cnf(8250,plain,
    ~ sum(additive_identity,b,additive_identity),
    inference('UR-RESOLVE',[status(thm)],[distributivity_1,128,not_sum_3,35,35]) ).

cnf(8251,plain,
    defined(multiplicative_inverse(b)),
    inference('REWRITE',[status(thm)],[77,8250]) ).

cnf(8252,plain,
    product(multiplicative_inverse(b),b,multiplicative_identity),
    inference('REWRITE',[status(thm)],[122,8250]) ).

cnf(8263,plain,
    product(multiplicative_identity,multiplicative_inverse(b),multiplicative_inverse(b)),
    inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_multiplication,8251]) ).

cnf(8730,plain,
    product(multiplicative_inverse(a),b,multiplicative_identity),
    inference('HYPERRESOLVE',[status(thm)],[associativity_multiplication_1,121,product_4,34]) ).

cnf(14623,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[associativity_multiplication_1,8730,not_product_5,8252]),8263]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : FLD026-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.14/0.15  % Command  : run-snark %s %d
% 0.14/0.36  % Computer : n028.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Tue Jun  7 03:25:59 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.21/0.49  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.50  * 
% 0.21/0.50  * 
% 0.21/0.51  #<PACKAGE "SNARK-USER">
% 0.21/0.51  * 
% 0.21/0.51  SNARK-TPTP-OPTIONS
% 0.21/0.51  * 
% 0.21/0.51  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.21/0.51   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.21/0.51   (USE-FACTORING :POS)
% 0.21/0.51   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.21/0.51   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.21/0.51   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.21/0.51   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.21/0.51   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.21/0.51   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.21/0.51   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.21/0.51   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.21/0.51   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.21/0.51   (DECLARE-TPTP-SYMBOLS2))
% 0.21/0.51  * 
% 0.21/0.51  "."
% 0.21/0.51  * 
% 0.21/0.51  ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-07T03:25:59
% 0.21/0.51  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n028.cluster.edu at 2022-06-07T03:25:59
% 0.21/0.53  
% 0.21/0.53  ; Recognized possible associativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?X ?U ?V)) (NOT (|sum| ?U ?W ?Y)) (NOT (|sum| ?V ?W ?Z))).
% 0.21/0.53  ; Recognized possible associativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?U ?V ?X)) (NOT (|sum| ?V ?Y ?W)) (NOT (|sum| ?U ?W ?Z))).
% 0.21/0.53  ; Recognized commutativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?Y ?X ?Z))).
% 0.21/0.53  ; Recognized possible associativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?X ?U ?V)) (NOT (|product| ?U ?W ?Y)) (NOT (|product| ?V ?W ?Z))).
% 0.21/0.53  ; Recognized possible associativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?U ?V ?X)) (NOT (|product| ?V ?Y ?W)) (NOT (|product| ?U ?W ?Z))).
% 0.21/0.53  ; Recognized commutativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?Y ?X ?Z))).
% 0.21/0.53  ; Declaring sum to be commutative.
% 2.87/3.05  ; Declaring product to be commutative.
% 2.87/3.05  
% 2.87/3.05  #||
% 2.87/3.05  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.87/3.05  % SZS output start Refutation
% See solution above
% 2.87/3.05  ||#
% 2.87/3.05  
% 2.87/3.05  ; Summary of computation:
% 2.87/3.05  ;     34086 formulas have been input or derived (from 189 formulas).
% 2.87/3.05  ;     14623 (43%) were retained.  Of these,
% 2.87/3.05  ;           95 ( 1%) were simplified or subsumed later,
% 2.87/3.05  ;        14528 (99%) are still being kept.
% 2.87/3.05  ; 
% 2.87/3.05  ; Run time in seconds excluding printing time:
% 2.87/3.05  ;     0.006   0%   Read assertion file          (1 call)
% 2.87/3.05  ;     0.000   0%   Assert                       (31 calls)
% 2.87/3.05  ;     0.902  36%   Process new row              (32,735 calls)
% 2.87/3.05  ;     1.071  42%   Resolution                   (376 calls)
% 2.87/3.05  ;     0.002   0%   Paramodulation               (188 calls)
% 2.87/3.05  ;     0.000   0%   Factoring                    (5 calls)
% 2.87/3.05  ;     0.004   0%   Condensing                   (3,192 calls)
% 2.87/3.05  ;     0.100   4%   Forward subsumption          (3,192 calls)
% 2.87/3.05  ;     0.036   1%   Backward subsumption         (1,736 calls)
% 2.87/3.05  ;     0.011   0%   Clause clause subsumption    (10,157 calls)
% 2.87/3.05  ;     0.184   7%   Forward simplification       (32,735 calls)
% 2.87/3.05  ;     0.100   4%   Backward simplification      (14,623 calls)
% 2.87/3.05  ;     0.002   0%   Ordering                     (2,076 calls)
% 2.87/3.05  ;     0.000   0%   Sortal reasoning             (32 calls)
% 2.87/3.05  ;     0.000   0%   Purity testing               (1 call)
% 2.87/3.05  ;     0.121   5%   Other
% 2.87/3.05  ;     2.539        Total
% 2.87/3.05  ;     2.540        Real time
% 2.87/3.05  ; 
% 2.87/3.05  ; Term-hash-array has 21,443 terms in all.
% 2.87/3.05  ; Feature-vector-row-index has 1,663 entries (1,663 at peak, 1,736 added, 73 deleted).
% 2.87/3.05  ; Feature-vector-row-index has 1,946 nodes (1,946 at peak, 2,016 added, 70 deleted).
% 2.87/3.05  ;  Retrieved 22,993 possibly forward subsuming rows in 3,192 calls.
% 2.87/3.05  ;  Retrieved 8,396 possibly backward subsumed rows in 1,736 calls.
% 2.87/3.05  ; Path-index has 21,412 entries (21,412 at peak, 21,527 added, 115 deleted).
% 2.87/3.05  ; Path-index has 1,170 nodes (1,170 at peak, 1,187 added, 17 deleted).
% 2.87/3.05  ; Trie-index has 21,412 entries (21,412 at peak, 21,527 added, 115 deleted).
% 2.87/3.05  ; Trie-index has 60,342 nodes (60,342 at peak, 60,518 added, 176 deleted).
% 2.87/3.05  ; Retrieved 16,669 generalization terms in 35,999 calls.
% 2.87/3.05  ; Retrieved 13,065 instance terms in 12,886 calls.
% 2.87/3.05  ; Retrieved 2,685,822 unifiable terms in 36,836 calls.
% 2.87/3.05  ; 
% 2.87/3.05  ; The agenda of rows to process has 133 entries:
% 2.87/3.05  ;    34 with value 11             18 with value 13              36 with value 14
% 2.87/3.05  ;    45 with value 12
% 2.87/3.05  ; The agenda of rows to give has 14345 entries:
% 2.87/3.05  ;    27 with value (4 9)        2250 with value (4 15)         478 with value (4 20)
% 2.87/3.05  ;   335 with value (4 10)        149 with value (4 16)        1560 with value (4 21)
% 2.87/3.05  ;   924 with value (4 11)       1062 with value (4 17)          17 with value (4 22)
% 2.87/3.05  ;  1352 with value (4 12)        241 with value (4 18)         365 with value (4 23)
% 2.87/3.05  ;  2694 with value (4 13)       2370 with value (4 19)          10 with value (4 25)
% 2.87/3.05  ;   511 with value (4 14)
% 2.87/3.05  Evaluation took:
% 2.87/3.05    2.541 seconds of real time
% 2.87/3.05    2.364499 seconds of user run time
% 2.87/3.05    0.177548 seconds of system run time
% 2.87/3.05    [Run times include 0.296 seconds GC run time.]
% 2.87/3.05    0 calls to %EVAL
% 2.87/3.05    0 page faults and
% 2.87/3.05    172,060,800 bytes consed.
% 2.87/3.05  :PROOF-FOUND
% 2.87/3.05  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-07T03:26:02
% 2.87/3.05  :PROOF-FOUND
% 2.87/3.05  * 
%------------------------------------------------------------------------------