TSTP Solution File: REL013+1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : REL013+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n007.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 : Mon Jul 18 19:59:18 EDT 2022

% Result   : Theorem 1.10s 1.28s
% Output   : Refutation 1.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   53 (  52 unt;   0 nHn;  12 RR)
%            Number of literals    :   54 (  53 equ;   3 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :   69 (  10 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    X = join(complement(join(complement(X),complement(Y))),complement(join(complement(X),Y))),
    file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux3_a_kind_of_de_Morgan) ).

cnf(2,plain,
    join(complement(join(complement(X),complement(Y))),join(complement(join(complement(X),Y)),Z)) = join(X,Z),
    inference('EMBED',[status(thm)],[1]) ).

cnf(3,axiom,
    meet(X,Y) = complement(join(complement(X),complement(Y))),
    file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux4_definiton_of_meet) ).

cnf(5,axiom,
    composition(X,one) = X,
    file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',composition_identity) ).

cnf(6,axiom,
    composition(join(X,Y),Z) = join(composition(X,Z),composition(Y,Z)),
    file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).

cnf(7,plain,
    join(composition(X,Y),join(composition(Z,Y),U)) = join(composition(join(X,Z),Y),U),
    inference('EMBED',[status(thm)],[6]) ).

cnf(8,axiom,
    converse(converse(X)) = X,
    file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).

cnf(9,axiom,
    converse(join(X,Y)) = join(converse(X),converse(Y)),
    file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_additivity) ).

cnf(11,axiom,
    converse(composition(X,Y)) = composition(converse(Y),converse(X)),
    file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_multiplicativity) ).

cnf(12,axiom,
    join(composition(converse(X),complement(composition(X,Y))),complement(Y)) = complement(Y),
    file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_cancellativity) ).

cnf(13,plain,
    join(composition(converse(X),complement(composition(X,Y))),join(complement(Y),Z)) = join(complement(Y),Z),
    inference('EMBED',[status(thm)],[12]) ).

cnf(14,axiom,
    top = join(X,complement(X)),
    file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',def_top) ).

cnf(15,plain,
    join(X,join(complement(X),Y)) = join(top,Y),
    inference('EMBED',[status(thm)],[14]) ).

cnf(16,axiom,
    zero = meet(X,complement(X)),
    file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',def_zero) ).

cnf(17,plain,
    zero = complement(top),
    inference('REWRITE',[status(thm)],[16,3,theory(equality)]) ).

cnf(18,negated_conjecture,
    ( composition('SKOLEMAAAV1',zero) != zero
    | composition(zero,'SKOLEMAAAV1') != zero ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

cnf(25,plain,
    join(top,X) = join(top,complement(join(Y,complement(join(X,Y))))),
    inference('PARAMODULATE',[status(thm)],[15,15,theory(equality)]) ).

cnf(27,plain,
    converse(join(converse(X),Y)) = join(X,converse(Y)),
    inference('PARAMODULATE',[status(thm)],[9,8,theory(equality)]) ).

cnf(34,plain,
    converse(composition(converse(X),Y)) = composition(converse(Y),X),
    inference('PARAMODULATE',[status(thm)],[11,8,theory(equality)]) ).

cnf(47,plain,
    join(composition(join(X,Y),Z),complement(composition(X,Z))) = join(top,composition(Y,Z)),
    inference('PARAMODULATE',[status(thm)],[15,7,theory(equality)]) ).

cnf(53,plain,
    join(composition(converse(X),complement(composition(X,top))),zero) = zero,
    inference('PARAMODULATE',[status(thm)],[12,17,theory(equality)]) ).

cnf(65,plain,
    join(complement(X),complement(composition(converse(Y),complement(composition(Y,X))))) = join(top,complement(X)),
    inference('PARAMODULATE',[status(thm)],[15,13,theory(equality)]) ).

cnf(77,plain,
    complement(X) = join(zero,complement(join(complement(complement(X)),X))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1,14,theory(equality)]),17,theory(equality)]) ).

cnf(79,plain,
    X = complement(complement(X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1,14,theory(equality)]),77,17,theory(equality)]) ).

cnf(84,plain,
    X = join(complement(join(top,complement(X))),X),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1,12,theory(equality)]),79,65,theory(equality)]) ).

cnf(100,plain,
    join(top,complement(X)) = join(top,complement(join(complement(Y),X))),
    inference('PARAMODULATE',[status(thm)],[15,2,theory(equality)]) ).

cnf(102,plain,
    join(top,X) = join(top,complement(Y)),
    inference('REWRITE',[status(thm)],[25,100,theory(equality)]) ).

cnf(123,plain,
    top = join(top,X),
    inference('PARAMODULATE',[status(thm)],[14,102,theory(equality)]) ).

cnf(129,plain,
    join(composition(join(X,Y),Z),complement(composition(X,Z))) = top,
    inference('REWRITE',[status(thm)],[47,123,theory(equality)]) ).

cnf(143,plain,
    X = join(zero,X),
    inference('REWRITE',[status(thm)],[84,17,123,theory(equality)]) ).

cnf(147,plain,
    composition(converse(X),complement(composition(X,top))) = zero,
    inference('REWRITE',[status(thm)],[53,143,theory(equality)]) ).

cnf(162,plain,
    converse(top) = join(X,converse(top)),
    inference('PARAMODULATE',[status(thm)],[27,123,theory(equality)]) ).

cnf(164,plain,
    X = join(X,converse(zero)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[27,143,theory(equality)]),8,theory(equality)]) ).

cnf(182,plain,
    converse(zero) = zero,
    inference('PARAMODULATE',[status(thm)],[143,164,theory(equality)]) ).

cnf(188,plain,
    top = converse(top),
    inference('PARAMODULATE',[status(thm)],[14,162,theory(equality)]) ).

cnf(195,plain,
    composition(top,complement(composition(top,top))) = zero,
    inference('PARAMODULATE',[status(thm)],[147,188,theory(equality)]) ).

cnf(218,plain,
    X = composition(converse(one),X),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[34,5,theory(equality)]),8,theory(equality)]) ).

cnf(242,plain,
    one = converse(one),
    inference('PARAMODULATE',[status(thm)],[5,218,theory(equality)]) ).

cnf(243,plain,
    X = composition(one,X),
    inference('REWRITE',[status(thm)],[218,242,theory(equality)]) ).

cnf(246,plain,
    composition(join(one,X),Y) = join(composition(X,Y),Y),
    inference('PARAMODULATE',[status(thm)],[6,243,theory(equality)]) ).

cnf(501,plain,
    join(composition(X,Y),complement(composition(zero,Y))) = top,
    inference('PARAMODULATE',[status(thm)],[129,143,theory(equality)]) ).

cnf(503,plain,
    join(composition(top,X),complement(composition(Y,X))) = top,
    inference('PARAMODULATE',[status(thm)],[129,14,theory(equality)]) ).

cnf(598,plain,
    join(X,complement(composition(zero,X))) = top,
    inference('PARAMODULATE',[status(thm)],[501,243,theory(equality)]) ).

cnf(614,plain,
    complement(composition(zero,zero)) = top,
    inference('PARAMODULATE',[status(thm)],[143,598,theory(equality)]) ).

cnf(625,plain,
    composition(zero,zero) = zero,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[79,614,theory(equality)]),17,theory(equality)]) ).

cnf(631,plain,
    composition(X,zero) = composition(join(one,X),zero),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[6,625,theory(equality)]),246,143,theory(equality)]) ).

cnf(669,plain,
    join(composition(top,X),complement(X)) = top,
    inference('PARAMODULATE',[status(thm)],[503,243,theory(equality)]) ).

cnf(686,plain,
    composition(top,top) = top,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[669,17,theory(equality)]),143,theory(equality)]) ).

cnf(687,plain,
    composition(top,zero) = zero,
    inference('REWRITE',[status(thm)],[195,17,686,theory(equality)]) ).

cnf(704,plain,
    zero = composition(X,zero),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[6,687,theory(equality)]),631,246,687,123,theory(equality)]) ).

cnf(713,plain,
    composition(zero,'SKOLEMAAAV1') != zero,
    inference('REWRITE',[status(thm)],[18,704,theory(equality)]) ).

cnf(714,plain,
    zero = composition(zero,X),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[34,704,theory(equality)]),182,theory(equality)]) ).

cnf(715,plain,
    $false,
    inference('REWRITE',[status(thm)],[713,714,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : REL013+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : run-snark %s %d
% 0.13/0.33  % Computer : n007.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
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Fri Jul  8 12:02:00 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 2022-07-08T12:02:00
% 0.19/0.47  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n007.cluster.edu at 2022-07-08T12:02:00
% 0.19/0.48  
% 0.19/0.48  ; Recognized commutativity assertion (= (|join| ?X ?Y) (|join| ?Y ?X)).
% 0.19/0.48  ; Recognized associativity assertion (= (|join| ?X (|join| ?Y ?Z)) (|join| (|join| ?X ?Y) ?Z)).
% 0.19/0.48  ; Recognized associativity assertion (= (|composition| ?X (|composition| ?Y ?Z)) (|composition| (|composition| ?X ?Y) ?Z)).
% 0.19/0.48  ; Recognized right identity assertion (= (|composition| ?X |one|) ?X).
% 0.19/0.48  ; Recognized possible right inverse assertion (= |top| (|join| ?X (|complement| ?X))).
% 0.19/0.48  ; Recognized possible right inverse assertion (= |zero| (|meet| ?X (|complement| ?X))).
% 0.19/0.48  ; Declaring join to be commutative.
% 1.10/1.28  ; Declaring join to be associative-commutative.
% 1.10/1.28  
% 1.10/1.28  #||
% 1.10/1.28  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.10/1.28  % SZS output start Refutation
% See solution above
% 1.10/1.28  ||#
% 1.10/1.28  
% 1.10/1.28  ; Summary of computation:
% 1.10/1.28  ;      3185 formulas have been input or derived (from 78 formulas).
% 1.10/1.28  ;       715 (22%) were retained.  Of these,
% 1.10/1.28  ;          334 (47%) were simplified or subsumed later,
% 1.10/1.28  ;          381 (53%) are still being kept.
% 1.10/1.28  ; 
% 1.10/1.28  ; Run time in seconds excluding printing time:
% 1.10/1.28  ;     0.004   0%   Read assertion file          (1 call)
% 1.10/1.28  ;     0.001   0%   Assert                       (14 calls)
% 1.10/1.28  ;     0.063   8%   Process new row              (3,093 calls)
% 1.10/1.28  ;     0.003   0%   Resolution                   (154 calls)
% 1.10/1.28  ;     0.059   7%   Paramodulation               (77 calls)
% 1.10/1.28  ;     0.003   0%   Embedding                    (285 calls)
% 1.10/1.28  ;     0.000   0%   Condensing                   (1 call)
% 1.10/1.28  ;     0.001   0%   Forward subsumption          (1 call)
% 1.10/1.28  ;     0.000   0%   Backward subsumption         (1 call)
% 1.10/1.28  ;     0.294  36%   Forward simplification       (2,474 calls)
% 1.10/1.28  ;     0.029   4%   Backward simplification      (436 calls)
% 1.10/1.28  ;     0.029   4%   Ordering                     (7,264 calls)
% 1.10/1.28  ;     0.291  36%   Ordering ac                  (4,547 calls)
% 1.10/1.28  ;     0.000   0%   Sortal reasoning             (32 calls)
% 1.10/1.28  ;     0.000   0%   Purity testing               (1 call)
% 1.10/1.28  ;     0.033   4%   Other
% 1.10/1.28  ;     0.810        Total
% 1.10/1.28  ;     0.815        Real time
% 1.10/1.28  ; 
% 1.10/1.28  ; Term-hash-array has 2,156 terms in all.
% 1.10/1.28  ; Feature-vector-row-index has 0 entries (1 at peak, 1 added, 1 deleted).
% 1.10/1.28  ; Feature-vector-row-index has 1 node (11 at peak, 11 added, 10 deleted).
% 1.10/1.28  ;  Retrieved 0 possibly forward subsuming rows in 1 call.
% 1.10/1.28  ;  Retrieved 0 possibly backward subsumed rows in 1 call.
% 1.10/1.28  ; Path-index has 1,297 entries (1,787 at peak, 2,242 added, 945 deleted).
% 1.10/1.28  ; Path-index has 1,631 nodes (1,909 at peak, 2,042 added, 411 deleted).
% 1.10/1.28  ; Trie-index has 1,297 entries (1,787 at peak, 2,242 added, 945 deleted).
% 1.10/1.28  ; Trie-index has 877 nodes (1,314 at peak, 1,626 added, 749 deleted).
% 1.10/1.28  ; Retrieved 645,134 generalization terms in 20,908 calls.
% 1.10/1.28  ; Retrieved 1,556 instance terms in 529 calls.
% 1.10/1.28  ; Retrieved 11,105 unifiable terms in 455 calls.
% 1.10/1.28  ; 
% 1.10/1.28  ; The agenda of backward simplifiable rows to process has 29 entries:
% 1.10/1.28  ;    29 with value 0
% 1.10/1.28  ; The agenda of rows to process has 13 entries:
% 1.10/1.28  ;     4 with value 18              3 with value 21               1 with value 22
% 1.10/1.28  ;     5 with value 19
% 1.10/1.28  ; The agenda of rows to give has 336 entries:
% 1.10/1.28  ;     2 with value (4 14)         51 with value (4 22)          19 with value (4 30)
% 1.10/1.28  ;     1 with value (4 15)         41 with value (4 23)           8 with value (4 31)
% 1.10/1.28  ;     3 with value (4 16)         34 with value (4 24)           9 with value (4 32)
% 1.10/1.28  ;    14 with value (4 17)         13 with value (4 25)           4 with value (4 33)
% 1.10/1.28  ;     6 with value (4 18)         16 with value (4 26)           2 with value (4 34)
% 1.10/1.28  ;     5 with value (4 19)         11 with value (4 27)           2 with value (4 36)
% 1.10/1.28  ;    26 with value (4 20)         31 with value (4 28)           4 with value (4 37)
% 1.10/1.28  ;    29 with value (4 21)          3 with value (4 29)           2 with value (4 39)
% 1.10/1.28  Evaluation took:
% 1.10/1.28    0.815 seconds of real time
% 1.10/1.28    0.79293 seconds of user run time
% 1.10/1.28    0.021665 seconds of system run time
% 1.10/1.28    [Run times include 0.017 seconds GC run time.]
% 1.10/1.28    0 calls to %EVAL
% 1.10/1.28    0 page faults and
% 1.10/1.28    44,131,456 bytes consed.
% 1.10/1.28  :PROOF-FOUND
% 1.10/1.28  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-08T12:02:01
% 1.10/1.28  :PROOF-FOUND
% 1.10/1.28  * 
%------------------------------------------------------------------------------