TSTP Solution File: FLD029-3 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : FLD029-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n020.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 02:27:04 EDT 2022

% Result   : Unsatisfiable 6.72s 6.95s
% Output   : Refutation 6.72s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   14
% Syntax   : Number of clauses     :   24 (  16 unt;   2 nHn;  24 RR)
%            Number of literals    :   40 (   0 equ;  19 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    :    8 (   8 usr;   6 con; 0-1 aty)
%            Number of variables   :   23 (   0 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(well_definedness_of_multiplicative_identity,axiom,
    defined(multiplicative_identity),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).

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

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

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,u,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_6) ).

cnf(product_7,negated_conjecture,
    product(a,v,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_7) ).

cnf(not_product_8,negated_conjecture,
    ~ product(multiplicative_identity,u,v),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_8) ).

cnf(35,plain,
    sum(additive_identity,multiplicative_identity,multiplicative_identity),
    inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_addition,well_definedness_of_multiplicative_identity]) ).

cnf(37,plain,
    product(multiplicative_identity,v,v),
    inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_multiplication,v_is_defined]) ).

cnf(49,plain,
    sum(additive_inverse(v),v,additive_identity),
    inference('HYPERRESOLVE',[status(thm)],[existence_of_inverse_addition,v_is_defined]) ).

cnf(228,plain,
    ( product(multiplicative_inverse(a),a,multiplicative_identity)
    | sum(additive_identity,a,additive_identity) ),
    inference('HYPERRESOLVE',[status(thm)],[existence_of_inverse_multiplication,a_is_defined]) ).

cnf(33883,plain,
    ~ sum(b,v,v),
    inference('UR-RESOLVE',[status(thm)],[associativity_addition_1,49,not_sum_5,49]) ).

cnf(33890,plain,
    ~ sum(a,multiplicative_identity,multiplicative_identity),
    inference('UR-RESOLVE',[status(thm)],[distributivity_1,33883,37,product_7,37]) ).

cnf(34003,plain,
    ~ sum(additive_identity,a,additive_identity),
    inference('UR-RESOLVE',[status(thm)],[associativity_addition_1,33890,35,35]) ).

cnf(34005,plain,
    product(multiplicative_inverse(a),a,multiplicative_identity),
    inference('REWRITE',[status(thm)],[228,34003]) ).

cnf(36459,plain,
    product(multiplicative_inverse(a),b,v),
    inference('HYPERRESOLVE',[status(thm)],[associativity_multiplication_1,34005,product_7,37]) ).

cnf(36461,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[associativity_multiplication_1,34005,not_product_8,product_6]),36459]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : FLD029-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.13  % Command  : run-snark %s %d
% 0.13/0.33  % Computer : n020.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Mon Jun  6 18:41:22 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  * 
% 0.19/0.46  #<PACKAGE "SNARK-USER">
% 0.19/0.46  * 
% 0.19/0.46  SNARK-TPTP-OPTIONS
% 0.19/0.46  * 
% 0.19/0.46  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.46   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.46   (USE-FACTORING :POS)
% 0.19/0.46   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.46   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.46   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.46   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.46   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.46   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.46   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.46   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.46   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.46   (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.46  * 
% 0.19/0.46  "."
% 0.19/0.46  * 
% 0.19/0.46  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-06T18:41:22
% 0.19/0.46  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n020.cluster.edu at 2022-06-06T18:41:22
% 0.19/0.48  
% 0.19/0.48  ; Recognized possible associativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?X ?U ?V)) (NOT (|sum| ?U ?W ?Y)) (NOT (|sum| ?V ?W ?Z))).
% 0.19/0.48  ; Recognized possible associativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?U ?V ?X)) (NOT (|sum| ?V ?Y ?W)) (NOT (|sum| ?U ?W ?Z))).
% 0.19/0.48  ; Recognized commutativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?Y ?X ?Z))).
% 0.19/0.48  ; Recognized possible associativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?X ?U ?V)) (NOT (|product| ?U ?W ?Y)) (NOT (|product| ?V ?W ?Z))).
% 0.19/0.48  ; Recognized possible associativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?U ?V ?X)) (NOT (|product| ?V ?Y ?W)) (NOT (|product| ?U ?W ?Z))).
% 0.19/0.48  ; Recognized commutativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?Y ?X ?Z))).
% 0.19/0.48  ; Declaring sum to be commutative.
% 6.72/6.95  ; Declaring product to be commutative.
% 6.72/6.95  
% 6.72/6.95  #||
% 6.72/6.95  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.72/6.95  % SZS output start Refutation
% See solution above
% 6.72/6.95  ||#
% 6.72/6.95  
% 6.72/6.95  ; Summary of computation:
% 6.72/6.95  ;     74468 formulas have been input or derived (from 175 formulas).
% 6.72/6.95  ;     36461 (49%) were retained.  Of these,
% 6.72/6.95  ;           38 ( 0%) were simplified or subsumed later,
% 6.72/6.95  ;        36423 (100%) are still being kept.
% 6.72/6.95  ; 
% 6.72/6.95  ; Run time in seconds excluding printing time:
% 6.72/6.95  ;     0.007   0%   Read assertion file          (1 call)
% 6.72/6.95  ;     0.001   0%   Assert                       (34 calls)
% 6.72/6.95  ;     2.421  37%   Process new row              (73,901 calls)
% 6.72/6.95  ;     2.544  39%   Resolution                   (348 calls)
% 6.72/6.95  ;     0.003   0%   Paramodulation               (174 calls)
% 6.72/6.95  ;     0.016   0%   Condensing                   (8,024 calls)
% 6.72/6.95  ;     0.340   5%   Forward subsumption          (8,024 calls)
% 6.72/6.95  ;     0.117   2%   Backward subsumption         (4,107 calls)
% 6.72/6.95  ;     0.033   1%   Clause clause subsumption    (32,941 calls)
% 6.72/6.95  ;     0.399   6%   Forward simplification       (73,901 calls)
% 6.72/6.95  ;     0.356   5%   Backward simplification      (36,461 calls)
% 6.72/6.95  ;     0.003   0%   Ordering                     (2,252 calls)
% 6.72/6.95  ;     0.000   0%   Sortal reasoning             (32 calls)
% 6.72/6.95  ;     0.000   0%   Purity testing               (1 call)
% 6.72/6.95  ;     0.248   4%   Other
% 6.72/6.95  ;     6.488        Total
% 6.72/6.95  ;     6.488        Real time
% 6.72/6.95  ; 
% 6.72/6.96  ; Term-hash-array has 56,485 terms in all.
% 6.72/6.96  ; Feature-vector-row-index has 4,093 entries (4,093 at peak, 4,107 added, 14 deleted).
% 6.72/6.96  ; Feature-vector-row-index has 2,510 nodes (2,510 at peak, 2,566 added, 56 deleted).
% 6.72/6.96  ;  Retrieved 69,826 possibly forward subsuming rows in 8,024 calls.
% 6.72/6.96  ;  Retrieved 31,746 possibly backward subsumed rows in 4,107 calls.
% 6.72/6.96  ; Path-index has 56,467 entries (56,467 at peak, 56,512 added, 45 deleted).
% 6.72/6.96  ; Path-index has 1,199 nodes (1,199 at peak, 1,220 added, 21 deleted).
% 6.72/6.96  ; Trie-index has 56,467 entries (56,467 at peak, 56,512 added, 45 deleted).
% 6.72/6.96  ; Trie-index has 155,408 nodes (155,408 at peak, 155,465 added, 57 deleted).
% 6.72/6.96  ; Retrieved 33,524 generalization terms in 81,896 calls.
% 6.72/6.96  ; Retrieved 32,430 instance terms in 32,353 calls.
% 6.72/6.96  ; Retrieved 9,167,316 unifiable terms in 13,331 calls.
% 6.72/6.96  ; 
% 6.72/6.96  ; The agenda of rows to process has 41 entries:
% 6.72/6.96  ;     1 with value 9              35 with value 11               1 with value 13
% 6.72/6.96  ;     3 with value 10              1 with value 12
% 6.72/6.96  ; The agenda of rows to give has 36252 entries:
% 6.72/6.96  ;     2 with value (4 8)       10634 with value (4 13)         864 with value (4 18)
% 6.72/6.96  ;   162 with value (4 9)         138 with value (4 14)       10375 with value (4 19)
% 6.72/6.96  ;   390 with value (4 10)       1970 with value (4 15)        2556 with value (4 20)
% 6.80/6.96  ;  2096 with value (4 11)        494 with value (4 16)          72 with value (4 22)
% 6.80/6.96  ;  3331 with value (4 12)       3168 with value (4 17)
% 6.80/6.96  Evaluation took:
% 6.80/6.96    6.491 seconds of real time
% 6.80/6.96    5.984202 seconds of user run time
% 6.80/6.96    0.506883 seconds of system run time
% 6.80/6.96    [Run times include 1.068 seconds GC run time.]
% 6.80/6.96    0 calls to %EVAL
% 6.80/6.96    0 page faults and
% 6.80/6.96    438,780,344 bytes consed.
% 6.80/6.96  :PROOF-FOUND
% 6.80/6.96  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-06T18:41:28
% 6.80/6.96  :PROOF-FOUND
% 6.80/6.96  * 
%------------------------------------------------------------------------------