TSTP Solution File: LAT257-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : LAT257-1 : TPTP v8.1.0. Released v3.1.0.
% 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 : Sun Jul 17 06:43:03 EDT 2022

% Result   : Unsatisfiable 256.64s 256.83s
% Output   : Refutation 256.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   30 (  28 unt;   0 nHn;   9 RR)
%            Number of literals    :   33 (  32 equ;   5 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   42 (   7 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(idempotence_of_meet,axiom,
    meet(X,X) = X,
    file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',idempotence_of_meet) ).

cnf(idempotence_of_join,axiom,
    join(X,X) = X,
    file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',idempotence_of_join) ).

cnf(4,plain,
    join(X,join(X,Y)) = join(X,Y),
    inference('EMBED',[status(thm)],[idempotence_of_join]) ).

cnf(absorption1,axiom,
    meet(X,join(X,Y)) = X,
    file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption1) ).

cnf(6,plain,
    meet(X,meet(join(X,Y),Z)) = meet(X,Z),
    inference('EMBED',[status(thm)],[absorption1]) ).

cnf(absorption2,axiom,
    join(X,meet(X,Y)) = X,
    file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption2) ).

cnf(complement_join,axiom,
    join(X,complement(X)) = one,
    file('/export/starexec/sandbox/benchmark/Axioms/LAT001-4.ax',complement_join) ).

cnf(10,plain,
    join(X,join(complement(X),Y)) = join(one,Y),
    inference('EMBED',[status(thm)],[complement_join]) ).

cnf(complement_meet,axiom,
    meet(X,complement(X)) = zero,
    file('/export/starexec/sandbox/benchmark/Axioms/LAT001-4.ax',complement_meet) ).

cnf(meet_join_complement,axiom,
    ( meet(X,Y) != zero
    | join(X,Y) != one
    | complement(X) = Y ),
    file('/export/starexec/sandbox/benchmark/Axioms/LAT001-4.ax',meet_join_complement) ).

cnf(equation_H82,axiom,
    meet(X,join(meet(Y,join(X,Z)),meet(Z,join(X,Y)))) = join(meet(X,Y),meet(X,Z)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H82) ).

cnf(15,plain,
    meet(X,meet(join(meet(Y,join(X,Z)),meet(Z,join(X,Y))),U)) = meet(join(meet(X,Y),meet(X,Z)),U),
    inference('EMBED',[status(thm)],[equation_H82]) ).

cnf(prove_distributivity_hypothesis,hypothesis,
    meet(b,a) = a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity_hypothesis) ).

cnf(17,plain,
    meet(b,meet(a,X)) = meet(a,X),
    inference('EMBED',[status(thm)],[prove_distributivity_hypothesis]) ).

cnf(prove_distributivity,negated_conjecture,
    join(complement(b),complement(a)) != complement(a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity) ).

cnf(19,plain,
    join(one,X) = one,
    inference('PARAMODULATE',[status(thm)],[4,10,theory(equality)]) ).

cnf(27,plain,
    meet(X,one) = X,
    inference('PARAMODULATE',[status(thm)],[absorption1,complement_join,theory(equality)]) ).

cnf(34,plain,
    meet(a,X) = meet(a,meet(X,join(meet(X,b),Y))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[17,6,theory(equality)]),prove_distributivity_hypothesis,theory(equality)]) ).

cnf(46,plain,
    join(b,a) = b,
    inference('PARAMODULATE',[status(thm)],[absorption2,prove_distributivity_hypothesis,theory(equality)]) ).

cnf(47,plain,
    join(b,join(a,X)) = join(b,X),
    inference('EMBED',[status(thm)],[46]) ).

cnf(48,plain,
    join(X,zero) = X,
    inference('PARAMODULATE',[status(thm)],[absorption2,complement_meet,theory(equality)]) ).

cnf(93,plain,
    complement(complement(X)) = X,
    inference('HYPERRESOLVE',[status(thm)],[meet_join_complement,complement_meet,complement_join]) ).

cnf(110,plain,
    ( meet(join(X,Y),complement(X)) != zero
    | X = join(X,Y) ),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[meet_join_complement,10,theory(equality)]),93,19,theory(equality)]) ).

cnf(167,plain,
    meet(X,join(Y,meet(join(X,Y),complement(X)))) = meet(X,Y),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[equation_H82,complement_join,theory(equality)]),48,27,theory(equality)]) ).

cnf(275,plain,
    meet(join(meet(X,Y),meet(X,Z)),join(X,U)) = join(meet(X,Y),meet(X,Z)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[6,15,theory(equality)]),equation_H82,theory(equality)]) ).

cnf(365,plain,
    join(b,complement(a)) = one,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,47,theory(equality)]),19,theory(equality)]) ).

cnf(1689,plain,
    meet(a,X) = meet(a,join(meet(X,Y),meet(X,b))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[15,34,theory(equality)]),275,idempotence_of_meet,absorption1,theory(equality)]) ).

cnf(4088,plain,
    meet(join(complement(b),complement(a)),a) != zero,
    inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[110,prove_distributivity]),93,theory(equality)]) ).

cnf(8626,plain,
    meet(b,join(complement(b),complement(a))) = meet(b,complement(a)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[167,365,theory(equality)]),27,theory(equality)]) ).

cnf(9469,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1689,8626,theory(equality)]),4088,prove_distributivity_hypothesis,idempotence_of_join,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12  % Problem  : LAT257-1 : TPTP v8.1.0. Released v3.1.0.
% 0.09/0.12  % Command  : run-snark %s %d
% 0.12/0.33  % Computer : n020.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Wed Jun 29 18:26:16 EDT 2022
% 0.12/0.33  % 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 2022-06-29T18:26:16
% 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 2022-06-29T18:26:16
% 0.19/0.48  
% 0.19/0.48  ; Recognized commutativity assertion (= (|meet| ?X ?Y) (|meet| ?Y ?X)).
% 0.19/0.48  ; Recognized commutativity assertion (= (|join| ?X ?Y) (|join| ?Y ?X)).
% 0.19/0.48  ; Recognized associativity assertion (= (|meet| (|meet| ?X ?Y) ?Z) (|meet| ?X (|meet| ?Y ?Z))).
% 0.19/0.48  ; Recognized associativity assertion (= (|join| (|join| ?X ?Y) ?Z) (|join| ?X (|join| ?Y ?Z))).
% 0.19/0.48  ; Recognized possible right inverse assertion (= (|join| ?X (|complement| ?X)) |one|).
% 0.19/0.48  ; Recognized possible right inverse assertion (= (|meet| ?X (|complement| ?X)) |zero|).
% 0.19/0.48  ; Declaring meet to be commutative.
% 0.19/0.48  ; Declaring meet to be associative-commutative.
% 0.19/0.48  ; Declaring join to be commutative.
% 256.64/256.83  ; Declaring join to be associative-commutative.
% 256.64/256.83  
% 256.64/256.83  #||
% 256.64/256.83  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 256.64/256.83  % SZS output start Refutation
% See solution above
% 256.64/256.83  ||#
% 256.64/256.83  
% 256.64/256.83  ; Summary of computation:
% 256.64/256.83  ;     88952 formulas have been input or derived (from 174 formulas).
% 256.64/256.83  ;      9469 (11%) were retained.  Of these,
% 256.64/256.83  ;          304 ( 3%) were simplified or subsumed later,
% 256.64/256.83  ;         9165 (97%) are still being kept.
% 256.64/256.83  ; 
% 256.64/256.83  ; Run time in seconds excluding printing time:
% 256.64/256.83  ;     0.003   0%   Read assertion file          (1 call)
% 256.64/256.83  ;     0.000   0%   Assert                       (14 calls)
% 256.64/256.83  ;     3.240   1%   Process new row              (84,543 calls)
% 256.64/256.83  ;     0.413   0%   Resolution                   (346 calls)
% 256.64/256.83  ;     2.070   1%   Paramodulation               (173 calls)
% 256.64/256.83  ;     0.112   0%   Embedding                    (4,112 calls)
% 256.64/256.83  ;     0.233   0%   Condensing                   (3,989 calls)
% 256.64/256.83  ;     0.387   0%   Forward subsumption          (3,989 calls)
% 256.64/256.83  ;     0.081   0%   Backward subsumption         (1,238 calls)
% 256.64/256.83  ;     0.332   0%   Clause clause subsumption    (19,310 calls)
% 256.64/256.83  ;   214.048  83%   Forward simplification       (80,432 calls)
% 256.64/256.83  ;    11.400   4%   Backward simplification      (5,358 calls)
% 256.64/256.83  ;     0.090   0%   Ordering                     (34,355 calls)
% 256.64/256.83  ;    23.567   9%   Ordering ac                  (17,452 calls)
% 256.64/256.83  ;     0.000   0%   Sortal reasoning             (32 calls)
% 256.64/256.83  ;     0.000   0%   Purity testing               (1 call)
% 256.64/256.83  ;     0.386   0%   Other
% 256.64/256.83  ;   256.362        Total
% 256.64/256.83  ;   256.365        Real time
% 256.64/256.83  ; 
% 256.64/256.83  ; Term-hash-array has 29,582 terms in all.
% 256.64/256.83  ; Feature-vector-row-index has 1,237 entries (1,237 at peak, 1,238 added, 1 deleted).
% 256.64/256.83  ; Feature-vector-row-index has 10,876 nodes (10,876 at peak, 10,882 added, 6 deleted).
% 256.64/256.83  ;  Retrieved 18,883 possibly forward subsuming rows in 3,989 calls.
% 256.64/256.83  ;  Retrieved 1,870 possibly backward subsumed rows in 1,238 calls.
% 256.64/256.83  ; Path-index has 28,754 entries (28,754 at peak, 29,720 added, 966 deleted).
% 256.64/256.83  ; Path-index has 969 nodes (969 at peak, 990 added, 21 deleted).
% 256.64/256.83  ; Trie-index has 28,754 entries (28,754 at peak, 29,720 added, 966 deleted).
% 256.64/256.83  ; Trie-index has 106 nodes (106 at peak, 107 added, 1 deleted).
% 256.64/256.83  ; Retrieved 577,836,632 generalization terms in 718,914 calls.
% 256.64/256.83  ; Retrieved 518,237 instance terms in 4,125 calls.
% 256.64/256.83  ; Retrieved 853,447 unifiable terms in 4,651 calls.
% 256.64/256.83  ; 
% 256.64/256.83  ; The agenda of rows to process has 22 entries:
% 256.64/256.83  ;     1 with value 28              4 with value 32               5 with value 36
% 256.64/256.83  ;     1 with value 29              2 with value 33               3 with value 37
% 256.64/256.83  ;     1 with value 30              1 with value 35               1 with value 38
% 256.64/256.83  ;     3 with value 31
% 256.64/256.83  ; The agenda of rows to give has 8991 entries:
% 256.64/256.83  ;     1 with value (4 19)        205 with value (4 46)          26 with value (4 72)
% 256.64/256.83  ;    24 with value (4 20)        174 with value (4 47)          10 with value (4 73)
% 256.64/256.83  ;    79 with value (4 21)        168 with value (4 48)           6 with value (4 74)
% 256.64/256.83  ;    95 with value (4 22)        161 with value (4 49)           8 with value (4 75)
% 256.64/256.83  ;   135 with value (4 23)        159 with value (4 50)          18 with value (4 76)
% 256.64/256.83  ;   139 with value (4 24)        149 with value (4 51)           9 with value (4 77)
% 256.64/256.83  ;   206 with value (4 25)        138 with value (4 52)           6 with value (4 78)
% 256.64/256.83  ;   251 with value (4 26)        138 with value (4 53)          10 with value (4 79)
% 256.64/256.83  ;   240 with value (4 27)        100 with value (4 54)          17 with value (4 80)
% 256.64/256.83  ;   299 with value (4 28)         87 with value (4 55)           5 with value (4 81)
% 256.64/256.83  ;   328 with value (4 29)        104 with value (4 56)           4 with value (4 82)
% 256.64/256.83  ;   369 with value (4 30)         77 with value (4 57)           6 with value (4 83)
% 256.64/256.83  ;   336 with value (4 31)         96 with value (4 58)           9 with value (4 84)
% 256.64/256.83  ;   397 with value (4 32)         81 with value (4 59)           7 with value (4 85)
% 256.64/256.83  ;   287 with value (4 33)         65 with value (4 60)           2 with value (4 87)
% 256.64/256.83  ;   383 with value (4 34)         58 with value (4 61)           6 with value (4 88)
% 256.64/256.83  ;   313 with value (4 35)         51 with value (4 62)           8 with value (4 89)
% 256.64/256.83  ;   338 with value (4 36)         44 with value (4 63)           2 with value (4 90)
% 256.64/256.83  ;   293 with value (4 37)         53 with value (4 64)           2 with value (4 92)
% 256.64/256.83  ;   274 with value (4 38)         31 with value (4 65)           3 with value (4 93)
% 256.64/256.83  ;   268 with value (4 39)         41 with value (4 66)           2 with value (4 94)
% 256.64/256.83  ;   292 with value (4 40)         40 with value (4 67)           2 with value (4 96)
% 256.64/256.83  ;   254 with value (4 41)         30 with value (4 68)           2 with value (4 98)
% 256.64/256.83  ;   259 with value (4 42)         17 with value (4 69)           2 with value (4 104)
% 256.64/256.83  ;   225 with value (4 43)         26 with value (4 70)           2 with value (4 108)
% 256.64/256.83  ;   182 with value (4 44)         24 with value (4 71)           2 with value (4 118)
% 256.64/256.83  ;   231 with value (4 45)
% 256.64/256.83  Evaluation took:
% 256.64/256.83    256.367 seconds of real time
% 256.64/256.83    255.36034 seconds of user run time
% 256.64/256.83    1.006102 seconds of system run time
% 256.64/256.83    [Run times include 7.186 seconds GC run time.]
% 256.64/256.83    0 calls to %EVAL
% 256.64/256.83    0 page faults and
% 256.64/256.83    10,553,109,976 bytes consed.
% 256.64/256.83  :PROOF-FOUND
% 256.64/256.83  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-29T18:30:32
% 256.64/256.83  :PROOF-FOUND
% 256.64/256.83  * 
%------------------------------------------------------------------------------