TSTP Solution File: ALG007-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : ALG007-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n029.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 : Thu Jul 14 17:59:36 EDT 2022

% Result   : Unsatisfiable 1.73s 1.93s
% Output   : Refutation 1.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   40 (  40 unt;   0 nHn;   2 RR)
%            Number of literals    :   40 (  39 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :  120 (  15 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(set_difference_1,axiom,
    difference(X,difference(Y,X)) = X,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_1) ).

cnf(set_difference_2,axiom,
    difference(X,difference(X,Y)) = difference(Y,difference(Y,X)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_2) ).

cnf(set_difference_3_simplified,axiom,
    difference(difference(X,Y),Z) = difference(difference(X,Z),Y),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_3_simplified) ).

cnf(prove_set_difference_3,negated_conjecture,
    difference(difference(a,b),c) != difference(difference(a,c),difference(b,c)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_set_difference_3) ).

cnf(8,plain,
    difference(X,difference(X,difference(X,Y))) = difference(X,difference(Y,difference(Y,X))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[set_difference_2,set_difference_2,theory(equality)]),set_difference_2,theory(equality)]) ).

cnf(9,plain,
    difference(X,difference(difference(Y,X),Z)) = X,
    inference('PARAMODULATE',[status(thm)],[set_difference_1,set_difference_3_simplified,theory(equality)]) ).

cnf(10,plain,
    difference(X,Y) = difference(difference(X,Y),difference(Z,X)),
    inference('PARAMODULATE',[status(thm)],[set_difference_3_simplified,set_difference_1,theory(equality)]) ).

cnf(12,plain,
    difference(difference(X,difference(X,Y)),Z) = difference(difference(Y,Z),difference(Y,X)),
    inference('PARAMODULATE',[status(thm)],[set_difference_3_simplified,set_difference_2,theory(equality)]) ).

cnf(13,plain,
    difference(X,difference(X,difference(Y,Z))) = difference(difference(Y,Z),difference(difference(Y,X),Z)),
    inference('PARAMODULATE',[status(thm)],[set_difference_2,set_difference_3_simplified,theory(equality)]) ).

cnf(16,plain,
    difference(X,difference(difference(difference(Y,X),Z),U)) = X,
    inference('PARAMODULATE',[status(thm)],[9,set_difference_3_simplified,theory(equality)]) ).

cnf(25,plain,
    difference(X,Y) = difference(X,difference(X,difference(X,Y))),
    inference('PARAMODULATE',[status(thm)],[set_difference_2,10,theory(equality)]) ).

cnf(26,plain,
    difference(X,Y) = difference(X,difference(Y,difference(Y,X))),
    inference('REWRITE',[status(thm)],[8,25,theory(equality)]) ).

cnf(29,plain,
    difference(X,difference(X,Y)) = difference(difference(X,difference(X,Y)),difference(Z,Y)),
    inference('PARAMODULATE',[status(thm)],[10,set_difference_2,theory(equality)]) ).

cnf(41,plain,
    difference(difference(X,Y),Z) = difference(difference(X,Z),difference(Y,difference(Y,X))),
    inference('PARAMODULATE',[status(thm)],[set_difference_3_simplified,26,theory(equality)]) ).

cnf(43,plain,
    difference(difference(X,Y),Z) = difference(difference(X,Z),difference(X,difference(X,Y))),
    inference('PARAMODULATE',[status(thm)],[set_difference_3_simplified,25,theory(equality)]) ).

cnf(163,plain,
    difference(difference(X,Y),difference(X,Z)) = difference(difference(Z,Y),difference(Z,X)),
    inference('PARAMODULATE',[status(thm)],[set_difference_3_simplified,12,theory(equality)]) ).

cnf(164,plain,
    difference(X,difference(X,Y)) = difference(difference(Y,difference(Z,X)),difference(Y,X)),
    inference('PARAMODULATE',[status(thm)],[10,12,theory(equality)]) ).

cnf(165,plain,
    difference(X,difference(difference(Y,Z),difference(Y,difference(U,X)))) = X,
    inference('PARAMODULATE',[status(thm)],[16,12,theory(equality)]) ).

cnf(166,plain,
    difference(difference(X,difference(X,Y)),Z) = difference(difference(Y,difference(Y,X)),Z),
    inference('PARAMODULATE',[status(thm)],[set_difference_3_simplified,12,theory(equality)]) ).

cnf(203,plain,
    difference(difference(X,Y),difference(X,Z)) = difference(difference(X,Y),difference(difference(X,Z),difference(difference(Y,difference(Y,X)),Z))),
    inference('PARAMODULATE',[status(thm)],[26,12,theory(equality)]) ).

cnf(252,plain,
    difference(difference(X,Y),difference(difference(X,Y),Z)) = difference(difference(Z,difference(U,X)),difference(Z,difference(X,Y))),
    inference('PARAMODULATE',[status(thm)],[163,10,theory(equality)]) ).

cnf(313,plain,
    difference(difference(X,Y),difference(difference(Z,Y),difference(Z,X))) = difference(difference(difference(X,Y),difference(difference(Z,Y),difference(Z,X))),difference(U,difference(X,Z))),
    inference('PARAMODULATE',[status(thm)],[29,163,theory(equality)]) ).

cnf(352,plain,
    difference(difference(X,difference(Y,Z)),U) = difference(difference(X,U),difference(difference(Y,Z),difference(difference(Y,X),Z))),
    inference('PARAMODULATE',[status(thm)],[41,set_difference_3_simplified,theory(equality)]) ).

cnf(356,plain,
    difference(difference(X,difference(X,Y)),difference(difference(X,difference(X,Y)),difference(Y,Z))) = difference(difference(Y,Z),difference(difference(Y,X),Z)),
    inference('PARAMODULATE',[status(thm)],[set_difference_2,41,theory(equality)]) ).

cnf(503,plain,
    difference(difference(difference(X,Y),Z),difference(difference(U,V),difference(U,Y))) = difference(difference(X,Y),Z),
    inference('PARAMODULATE',[status(thm)],[165,9,theory(equality)]) ).

cnf(565,plain,
    difference(difference(difference(X,Y),difference(difference(Z,Y),difference(Z,X))),U) = difference(difference(difference(X,Z),difference(difference(X,Z),difference(X,Y))),U),
    inference('PARAMODULATE',[status(thm)],[166,163,theory(equality)]) ).

cnf(601,plain,
    difference(difference(X,Y),difference(difference(Z,difference(Z,X)),Y)) = difference(difference(X,Z),difference(difference(X,difference(X,Y)),Z)),
    inference('PARAMODULATE',[status(thm)],[13,12,theory(equality)]) ).

cnf(605,plain,
    difference(difference(X,Y),difference(difference(Z,Y),difference(Z,X))) = difference(difference(X,Z),difference(difference(X,difference(X,Y)),Z)),
    inference('PARAMODULATE',[status(thm)],[13,163,theory(equality)]) ).

cnf(669,plain,
    difference(difference(X,Y),difference(difference(X,Y),difference(X,Z))) = difference(difference(X,Y),Z),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[164,43,theory(equality)]),503,theory(equality)]) ).

cnf(673,plain,
    difference(difference(difference(X,Y),difference(difference(Z,Y),difference(Z,X))),U) = difference(difference(difference(X,Z),Y),U),
    inference('REWRITE',[status(thm)],[565,669,theory(equality)]) ).

cnf(674,plain,
    difference(difference(X,Y),difference(difference(Z,Y),difference(Z,X))) = difference(difference(X,Z),Y),
    inference('REWRITE',[status(thm)],[313,10,673,theory(equality)]) ).

cnf(675,plain,
    difference(difference(X,Y),Z) = difference(difference(X,Y),difference(difference(X,difference(X,Z)),Y)),
    inference('REWRITE',[status(thm)],[605,674,theory(equality)]) ).

cnf(676,plain,
    difference(difference(X,Y),difference(difference(Z,difference(Z,X)),Y)) = difference(difference(X,Z),Y),
    inference('REWRITE',[status(thm)],[601,675,theory(equality)]) ).

cnf(681,plain,
    difference(difference(X,Y),difference(X,Z)) = difference(difference(X,Y),difference(difference(X,Y),Z)),
    inference('REWRITE',[status(thm)],[203,676,theory(equality)]) ).

cnf(685,plain,
    difference(difference(X,difference(X,Y)),difference(X,difference(Y,Z))) = difference(difference(Y,Z),difference(difference(Y,X),Z)),
    inference('REWRITE',[status(thm)],[356,681,theory(equality)]) ).

cnf(703,plain,
    difference(difference(X,Y),difference(X,Z)) = difference(difference(Z,difference(U,X)),difference(Z,difference(X,Y))),
    inference('REWRITE',[status(thm)],[252,681,theory(equality)]) ).

cnf(704,plain,
    difference(difference(X,Y),difference(X,Z)) = difference(difference(X,Y),difference(difference(X,Z),Y)),
    inference('REWRITE',[status(thm)],[685,703,theory(equality)]) ).

cnf(824,plain,
    difference(difference(X,difference(Y,Z)),U) = difference(difference(X,U),difference(difference(Y,Z),difference(Y,X))),
    inference('REWRITE',[status(thm)],[352,704,theory(equality)]) ).

cnf(826,plain,
    difference(difference(X,Y),difference(Z,Y)) = difference(difference(X,Z),Y),
    inference('REWRITE',[status(thm)],[674,set_difference_3_simplified,824,theory(equality)]) ).

cnf(827,plain,
    $false,
    inference('REWRITE',[status(thm)],[prove_set_difference_3,826,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : ALG007-1 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12  % Command  : run-snark %s %d
% 0.12/0.33  % Computer : n029.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  8 13:03:06 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.44  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45  * 
% 0.18/0.45  * 
% 0.18/0.45  #<PACKAGE "SNARK-USER">
% 0.18/0.45  * 
% 0.18/0.46  SNARK-TPTP-OPTIONS
% 0.18/0.46  * 
% 0.18/0.46  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.18/0.46   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.18/0.46   (USE-FACTORING :POS)
% 0.18/0.46   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.18/0.46   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.18/0.46   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.18/0.46   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.18/0.46   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.18/0.46   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.18/0.46   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.18/0.46   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.18/0.46   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.18/0.46   (DECLARE-TPTP-SYMBOLS2))
% 0.18/0.46  * 
% 0.18/0.46  "."
% 0.18/0.46  * 
% 0.18/0.46  ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-08T13:03:06
% 0.18/0.46  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n029.cluster.edu at 2022-06-08T13:03:06
% 1.73/1.93  
% 1.73/1.93  
% 1.73/1.93  #||
% 1.73/1.93  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.73/1.93  % SZS output start Refutation
% See solution above
% 1.73/1.94  ||#
% 1.73/1.94  
% 1.73/1.94  ; Summary of computation:
% 1.73/1.94  ;      6345 formulas have been input or derived (from 41 formulas).
% 1.73/1.94  ;       827 (13%) were retained.  Of these,
% 1.73/1.94  ;          361 (44%) were simplified or subsumed later,
% 1.73/1.94  ;          466 (56%) are still being kept.
% 1.73/1.94  ; 
% 1.73/1.94  ; Run time in seconds excluding printing time:
% 1.73/1.94  ;     0.001   0%   Read assertion file          (1 call)
% 1.73/1.94  ;     0.000   0%   Assert                       (4 calls)
% 1.73/1.94  ;     0.083   6%   Process new row              (5,824 calls)
% 1.73/1.94  ;     0.004   0%   Resolution                   (80 calls)
% 1.73/1.94  ;     0.083   6%   Paramodulation               (40 calls)
% 1.73/1.94  ;     0.547  37%   Forward simplification       (5,824 calls)
% 1.73/1.94  ;     0.107   7%   Backward simplification      (827 calls)
% 1.73/1.94  ;     0.606  41%   Ordering                     (85,180 calls)
% 1.73/1.94  ;     0.000   0%   Sortal reasoning             (32 calls)
% 1.73/1.94  ;     0.001   0%   Purity testing               (1 call)
% 1.73/1.94  ;     0.040   3%   Other
% 1.73/1.94  ;     1.472        Total
% 1.73/1.94  ;     1.480        Real time
% 1.73/1.94  ; 
% 1.73/1.94  ; Term-hash-array has 2,284 terms in all.
% 1.73/1.94  ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 1.73/1.94  ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 1.73/1.94  ; Path-index has 1,345 entries (1,896 at peak, 2,371 added, 1,026 deleted).
% 1.73/1.94  ; Path-index has 413 nodes (447 at peak, 457 added, 44 deleted).
% 1.73/1.94  ; Trie-index has 1,345 entries (1,896 at peak, 2,371 added, 1,026 deleted).
% 1.73/1.94  ; Trie-index has 3,270 nodes (5,014 at peak, 6,242 added, 2,972 deleted).
% 1.73/1.94  ; Retrieved 243,389 generalization terms in 48,859 calls.
% 1.73/1.94  ; Retrieved 31,266 instance terms in 1,351 calls.
% 1.73/1.94  ; Retrieved 21,647 unifiable terms in 281 calls.
% 1.73/1.94  ; 
% 1.73/1.94  ; The agenda of backward simplifiable rows to process has 30 entries:
% 1.73/1.94  ;    30 with value 0
% 1.73/1.94  ; The agenda of rows to process has 98 entries:
% 1.73/1.94  ;    12 with value 33              4 with value 37              25 with value 41
% 1.73/1.94  ;    19 with value 34              8 with value 38               2 with value 42
% 1.73/1.94  ;     3 with value 35              4 with value 39               4 with value 43
% 1.73/1.94  ;    13 with value 36              4 with value 40
% 1.73/1.94  ; The agenda of rows to give has 429 entries:
% 1.73/1.94  ;     1 with value (4 19)         24 with value (4 28)          19 with value (4 36)
% 1.73/1.94  ;     1 with value (4 21)         29 with value (4 29)          11 with value (4 37)
% 1.73/1.94  ;     6 with value (4 22)         24 with value (4 30)           3 with value (4 38)
% 1.73/1.94  ;    10 with value (4 23)         58 with value (4 31)           5 with value (4 40)
% 1.73/1.94  ;    14 with value (4 24)         54 with value (4 32)           7 with value (4 41)
% 1.73/1.94  ;    20 with value (4 25)         19 with value (4 33)           3 with value (4 42)
% 1.73/1.94  ;    39 with value (4 26)         19 with value (4 34)           1 with value (4 53)
% 1.73/1.94  ;    38 with value (4 27)         24 with value (4 35)
% 1.73/1.94  Evaluation took:
% 1.73/1.94    1.48 seconds of real time
% 1.73/1.94    1.356654 seconds of user run time
% 1.73/1.94    0.12386 seconds of system run time
% 1.73/1.94    [Run times include 0.042 seconds GC run time.]
% 1.73/1.94    0 calls to %EVAL
% 1.73/1.94    0 page faults and
% 1.73/1.94    113,724,536 bytes consed.
% 1.73/1.94  :PROOF-FOUND
% 1.73/1.94  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-08T13:03:07
% 1.73/1.94  :PROOF-FOUND
% 1.73/1.94  * 
%------------------------------------------------------------------------------