TSTP Solution File: FLD066-3 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : FLD066-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n025.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 02:27:19 EDT 2022

% Result   : Unsatisfiable 24.33s 24.58s
% Output   : Refutation 24.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   14
% Syntax   : Number of clauses     :   26 (  20 unt;   1 nHn;  26 RR)
%            Number of literals    :   39 (   0 equ;  14 neg)
%            Maximal clause size   :    4 (   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;   6 con; 0-1 aty)
%            Number of variables   :   17 (   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(well_definedness_of_additive_identity,axiom,
    defined(additive_identity),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).

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

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

cnf(compatibility_of_order_relation_and_addition,axiom,
    ( less_or_equal(X,Y)
    | ~ less_or_equal(Z,U)
    | ~ sum(Z,V,X)
    | ~ sum(U,V,Y) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_addition) ).

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(sum_6,negated_conjecture,
    sum(a,c,u),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_6) ).

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

cnf(less_or_equal_8,negated_conjecture,
    less_or_equal(u,v),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_8) ).

cnf(not_less_or_equal_9,negated_conjecture,
    ~ less_or_equal(a,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_9) ).

cnf(34,plain,
    sum(additive_identity,c,c),
    inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_addition,c_is_defined]) ).

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

cnf(36,plain,
    sum(additive_identity,a,a),
    inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_addition,a_is_defined]) ).

cnf(55,plain,
    sum(additive_inverse(c),c,additive_identity),
    inference('HYPERRESOLVE',[status(thm)],[existence_of_inverse_addition,c_is_defined]) ).

cnf(268,plain,
    less_or_equal(additive_identity,additive_identity),
    inference('HYPERRESOLVE',[status(thm)],[totality_of_order_relation,well_definedness_of_additive_identity,well_definedness_of_additive_identity]) ).

cnf(269,plain,
    less_or_equal(b,a),
    inference('UR-RESOLVE',[status(thm)],[totality_of_order_relation,not_less_or_equal_9,b_is_defined,a_is_defined]) ).

cnf(295,plain,
    less_or_equal(v,u),
    inference('HYPERRESOLVE',[status(thm)],[compatibility_of_order_relation_and_addition,269,sum_7,sum_6]) ).

cnf(296,plain,
    ~ sum(additive_identity,b,a),
    inference('UR-RESOLVE',[status(thm)],[compatibility_of_order_relation_and_addition,35,not_less_or_equal_9,268]) ).

cnf(1008,plain,
    sum(additive_identity,v,u),
    inference('HYPERRESOLVE',[status(thm)],[antisymmetry_of_order_relation,295,less_or_equal_8]) ).

cnf(58242,plain,
    sum(additive_inverse(c),u,a),
    inference('HYPERRESOLVE',[status(thm)],[associativity_addition_1,55,sum_6,36]) ).

cnf(58298,plain,
    sum(b,c,u),
    inference('HYPERRESOLVE',[status(thm)],[associativity_addition_1,1008,sum_7,34]) ).

cnf(70467,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[associativity_addition_1,58242,296,55]),58298]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : FLD066-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.13  % Command  : run-snark %s %d
% 0.13/0.34  % Computer : n025.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 : Tue Jun  7 00:34:18 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.20/0.46  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.47  * 
% 0.20/0.47  * 
% 0.20/0.48  #<PACKAGE "SNARK-USER">
% 0.20/0.48  * 
% 0.20/0.48  SNARK-TPTP-OPTIONS
% 0.20/0.48  * 
% 0.20/0.48  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.48   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.48   (USE-FACTORING :POS)
% 0.20/0.48   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.48   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.48   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.48   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.48   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.48   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.48   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.48   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.48   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.48   (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.48  * 
% 0.20/0.48  "."
% 0.20/0.48  * 
% 0.20/0.48  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-07T00:34:18
% 0.20/0.48  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n025.cluster.edu at 2022-06-07T00:34:18
% 0.20/0.50  
% 0.20/0.50  ; Recognized possible associativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?X ?U ?V)) (NOT (|sum| ?U ?W ?Y)) (NOT (|sum| ?V ?W ?Z))).
% 0.20/0.50  ; Recognized possible associativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?U ?V ?X)) (NOT (|sum| ?V ?Y ?W)) (NOT (|sum| ?U ?W ?Z))).
% 0.20/0.50  ; Recognized commutativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?Y ?X ?Z))).
% 0.20/0.50  ; Recognized possible associativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?X ?U ?V)) (NOT (|product| ?U ?W ?Y)) (NOT (|product| ?V ?W ?Z))).
% 0.20/0.50  ; Recognized possible associativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?U ?V ?X)) (NOT (|product| ?V ?Y ?W)) (NOT (|product| ?U ?W ?Z))).
% 0.20/0.50  ; Recognized commutativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?Y ?X ?Z))).
% 0.20/0.50  ; Declaring sum to be commutative.
% 24.33/24.58  ; Declaring product to be commutative.
% 24.33/24.58  
% 24.33/24.58  #||
% 24.33/24.58  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.33/24.58  % SZS output start Refutation
% See solution above
% 24.33/24.58  ||#
% 24.33/24.58  
% 24.33/24.58  ; Summary of computation:
% 24.33/24.58  ;    146113 formulas have been input or derived (from 321 formulas).
% 24.33/24.58  ;     70467 (48%) were retained.  Of these,
% 24.33/24.58  ;          128 ( 0%) were simplified or subsumed later,
% 24.33/24.58  ;        70339 (100%) are still being kept.
% 24.33/24.58  ; 
% 24.33/24.58  ; Run time in seconds excluding printing time:
% 24.33/24.58  ;     0.007   0%   Read assertion file          (1 call)
% 24.33/24.58  ;     0.001   0%   Assert                       (35 calls)
% 24.33/24.58  ;     5.091  21%   Process new row              (144,064 calls)
% 24.33/24.58  ;    15.128  63%   Resolution                   (640 calls)
% 24.45/24.61  ;     0.009   0%   Paramodulation               (320 calls)
% 24.45/24.61  ;     0.000   0%   Factoring                    (19 calls)
% 24.45/24.61  ;     0.029   0%   Condensing                   (16,558 calls)
% 24.45/24.61  ;     0.724   3%   Forward subsumption          (16,558 calls)
% 24.45/24.61  ;     0.383   2%   Backward subsumption         (8,980 calls)
% 24.45/24.61  ;     0.090   0%   Clause clause subsumption    (82,269 calls)
% 24.45/24.61  ;     1.214   5%   Forward simplification       (144,064 calls)
% 24.45/24.61  ;     0.950   4%   Backward simplification      (70,467 calls)
% 24.45/24.61  ;     0.011   0%   Ordering                     (8,881 calls)
% 24.45/24.61  ;     0.000   0%   Sortal reasoning             (32 calls)
% 24.45/24.61  ;     0.000   0%   Purity testing               (1 call)
% 24.45/24.61  ;     0.456   2%   Other
% 24.45/24.61  ;    24.093        Total
% 24.45/24.61  ;    24.132        Real time
% 24.45/24.62  ; 
% 24.46/24.62  ; Term-hash-array has 105,739 terms in all.
% 24.46/24.62  ; Feature-vector-row-index has 8,861 entries (8,861 at peak, 8,980 added, 119 deleted).
% 24.46/24.62  ; Feature-vector-row-index has 6,703 nodes (6,703 at peak, 6,743 added, 40 deleted).
% 24.46/24.62  ;  Retrieved 152,698 possibly forward subsuming rows in 16,558 calls.
% 24.46/24.62  ;  Retrieved 66,752 possibly backward subsumed rows in 8,980 calls.
% 24.46/24.62  ; Path-index has 105,692 entries (105,692 at peak, 105,830 added, 138 deleted).
% 24.46/24.62  ; Path-index has 1,478 nodes (1,478 at peak, 1,487 added, 9 deleted).
% 24.46/24.62  ; Trie-index has 105,692 entries (105,692 at peak, 105,830 added, 138 deleted).
% 24.46/24.62  ; Trie-index has 293,882 nodes (293,882 at peak, 294,050 added, 168 deleted).
% 24.46/24.62  ; Retrieved 66,029 generalization terms in 161,076 calls.
% 24.46/24.62  ; Retrieved 61,664 instance terms in 61,486 calls.
% 24.46/24.62  ; Retrieved 26,544,370 unifiable terms in 79,078 calls.
% 24.46/24.62  ; 
% 24.46/24.62  ; The agenda of rows to process has 101 entries:
% 24.46/24.62  ;     2 with value 9              25 with value 11               6 with value 13
% 24.46/24.62  ;     4 with value 10             16 with value 12              48 with value 14
% 24.46/24.62  ; The agenda of rows to give has 70020 entries:
% 24.46/24.62  ;    79 with value (4 9)        7128 with value (4 15)        4684 with value (4 20)
% 24.46/24.62  ;   538 with value (4 10)        785 with value (4 16)        3336 with value (4 21)
% 24.46/24.62  ;  3280 with value (4 11)       3390 with value (4 17)          91 with value (4 22)
% 24.46/24.62  ;  4199 with value (4 12)        875 with value (4 18)         812 with value (4 23)
% 24.46/24.62  ; 20274 with value (4 13)      19525 with value (4 19)           8 with value (4 25)
% 24.46/24.62  ;  1016 with value (4 14)
% 24.46/24.62  Evaluation took:
% 24.46/24.62    24.136 seconds of real time
% 24.46/24.62    23.123764 seconds of user run time
% 24.46/24.62    1.009805 seconds of system run time
% 24.46/24.62    [Run times include 3.118 seconds GC run time.]
% 24.46/24.62    0 calls to %EVAL
% 24.46/24.62    0 page faults and
% 24.46/24.62    969,785,368 bytes consed.
% 24.46/24.62  :PROOF-FOUND
% 24.46/24.62  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-07T00:34:42
% 24.46/24.62  :PROOF-FOUND
% 24.46/24.62  * 
%------------------------------------------------------------------------------