TSTP Solution File: ALG006-1 by SNARK---20120808r022

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%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : ALG006-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n021.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 17:59:35 EDT 2022

% Result   : Unsatisfiable 0.41s 0.62s
% Output   : Refutation 0.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   30 (  30 unt;   0 nHn;   2 RR)
%            Number of literals    :   30 (  29 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    5 (   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   :   72 (   6 sgn)

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

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

cnf(set_difference_3,axiom,
    difference(difference(X,Y),Z) = difference(difference(X,Z),difference(Y,Z)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_3) ).

cnf(prove_set_difference_3_simplified,negated_conjecture,
    difference(difference(a,c),b) != difference(difference(a,b),c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_set_difference_3_simplified) ).

cnf(5,plain,
    difference(difference(X,Y),Y) = difference(X,Y),
    inference('PARAMODULATE',[status(thm)],[set_difference_1,set_difference_1,theory(equality)]) ).

cnf(7,plain,
    difference(X,X) = difference(difference(Y,X),difference(Y,X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[set_difference_2,set_difference_1,theory(equality)]),5,theory(equality)]) ).

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(12,plain,
    difference(difference(X,Y),difference(Z,X)) = difference(X,difference(Y,difference(Z,X))),
    inference('PARAMODULATE',[status(thm)],[set_difference_3,set_difference_1,theory(equality)]) ).

cnf(13,plain,
    difference(X,difference(X,difference(X,Y))) = difference(difference(X,Y),difference(Y,X)),
    inference('REWRITE',[status(thm)],[8,12,theory(equality)]) ).

cnf(14,plain,
    difference(difference(X,Y),difference(Z,Y)) = difference(difference(X,difference(Z,Y)),Y),
    inference('PARAMODULATE',[status(thm)],[set_difference_3,set_difference_1,theory(equality)]) ).

cnf(16,plain,
    difference(X,difference(X,difference(Y,Z))) = difference(difference(Y,Z),difference(difference(Y,X),difference(Z,X))),
    inference('PARAMODULATE',[status(thm)],[set_difference_2,set_difference_3,theory(equality)]) ).

cnf(28,plain,
    difference(difference(difference(X,Y),Z),Y) = difference(difference(X,Y),difference(Z,Y)),
    inference('PARAMODULATE',[status(thm)],[set_difference_3,5,theory(equality)]) ).

cnf(31,plain,
    difference(difference(X,Y),X) = difference(X,X),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[5,7,theory(equality)]),set_difference_3,theory(equality)]) ).

cnf(34,plain,
    difference(X,X) = difference(Y,Y),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[7,set_difference_2,theory(equality)]),7,theory(equality)]) ).

cnf(35,plain,
    difference(X,difference(Y,Y)) = X,
    inference('PARAMODULATE',[status(thm)],[set_difference_1,34,theory(equality)]) ).

cnf(36,plain,
    difference(difference(X,X),Y) = difference(X,X),
    inference('PARAMODULATE',[status(thm)],[5,34,theory(equality)]) ).

cnf(37,plain,
    difference(difference(X,Y),difference(Y,X)) = difference(X,Y),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[set_difference_2,31,theory(equality)]),35,13,theory(equality)]) ).

cnf(38,plain,
    difference(X,difference(X,difference(X,Y))) = difference(X,Y),
    inference('REWRITE',[status(thm)],[13,37,theory(equality)]) ).

cnf(39,plain,
    difference(X,X) = difference(difference(difference(X,Y),Z),difference(X,Z)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[set_difference_3,31,theory(equality)]),36,theory(equality)]) ).

cnf(41,plain,
    difference(difference(X,difference(Y,Z)),Y) = difference(X,Y),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[set_difference_3,31,theory(equality)]),5,set_difference_3,theory(equality)]) ).

cnf(43,plain,
    difference(difference(X,Y),Z) = difference(difference(X,Z),difference(difference(X,difference(X,Y)),Z)),
    inference('PARAMODULATE',[status(thm)],[set_difference_3,38,theory(equality)]) ).

cnf(44,plain,
    difference(difference(X,Y),difference(difference(X,Y),difference(difference(X,Z),Y))) = difference(difference(X,Z),Y),
    inference('PARAMODULATE',[status(thm)],[38,set_difference_3,theory(equality)]) ).

cnf(85,plain,
    difference(difference(X,Y),difference(X,difference(Y,Z))) = difference(difference(X,difference(Y,Z)),difference(X,difference(Y,Z))),
    inference('PARAMODULATE',[status(thm)],[31,41,theory(equality)]) ).

cnf(99,plain,
    difference(X,X) = difference(difference(X,Y),difference(X,difference(Y,Z))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[31,14,theory(equality)]),85,39,theory(equality)]) ).

cnf(139,plain,
    difference(difference(X,Y),Z) = difference(difference(X,Y),difference(Z,Y)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[38,28,theory(equality)]),35,99,theory(equality)]) ).

cnf(168,plain,
    difference(difference(X,Y),difference(difference(X,Y),difference(X,Z))) = difference(difference(X,Z),Y),
    inference('REWRITE',[status(thm)],[44,139,theory(equality)]) ).

cnf(169,plain,
    difference(difference(X,Y),Z) = difference(difference(X,Z),difference(X,difference(X,Y))),
    inference('REWRITE',[status(thm)],[43,139,theory(equality)]) ).

cnf(177,plain,
    difference(X,difference(X,difference(Y,Z))) = difference(difference(Y,Z),difference(Y,X)),
    inference('REWRITE',[status(thm)],[16,139,theory(equality)]) ).

cnf(178,plain,
    difference(difference(X,Y),Z) = difference(difference(X,Z),Y),
    inference('REWRITE',[status(thm)],[168,169,177,theory(equality)]) ).

cnf(179,plain,
    $false,
    inference('REWRITE',[status(thm)],[prove_set_difference_3_simplified,178,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : ALG006-1 : TPTP v8.1.0. Released v2.2.0.
% 0.00/0.09  % Command  : run-snark %s %d
% 0.09/0.29  % Computer : n021.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit : 300
% 0.09/0.29  % WCLimit  : 600
% 0.09/0.29  % DateTime : Thu Jun  9 06:22:38 EDT 2022
% 0.09/0.29  % CPUTime  : 
% 0.13/0.38  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.38  * 
% 0.13/0.38  * 
% 0.13/0.39  #<PACKAGE "SNARK-USER">
% 0.13/0.39  * 
% 0.13/0.39  SNARK-TPTP-OPTIONS
% 0.13/0.39  * 
% 0.13/0.39  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.13/0.39   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.13/0.39   (USE-FACTORING :POS)
% 0.13/0.39   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.13/0.39   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.13/0.39   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.13/0.39   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.13/0.39   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.13/0.39   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.13/0.39   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.13/0.39   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.13/0.39   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.13/0.39   (DECLARE-TPTP-SYMBOLS2))
% 0.13/0.39  * 
% 0.13/0.39  "."
% 0.13/0.39  * 
% 0.13/0.39  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-09T06:22:38
% 0.13/0.39  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n021.cluster.edu at 2022-06-09T06:22:38
% 0.41/0.62  
% 0.41/0.62  
% 0.41/0.62  #||
% 0.41/0.62  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.41/0.62  % SZS output start Refutation
% See solution above
% 0.44/0.63  ||#
% 0.44/0.63  
% 0.44/0.63  ; Summary of computation:
% 0.44/0.63  ;      1009 formulas have been input or derived (from 22 formulas).
% 0.44/0.63  ;       179 (18%) were retained.  Of these,
% 0.44/0.63  ;          116 (65%) were simplified or subsumed later,
% 0.44/0.63  ;           63 (35%) are still being kept.
% 0.44/0.63  ; 
% 0.44/0.63  ; Run time in seconds excluding printing time:
% 0.44/0.63  ;     0.001   0%   Read assertion file          (1 call)
% 0.44/0.63  ;     0.000   0%   Assert                       (4 calls)
% 0.44/0.63  ;     0.026  11%   Process new row              (933 calls)
% 0.44/0.63  ;     0.000   0%   Resolution                   (42 calls)
% 0.44/0.63  ;     0.020   9%   Paramodulation               (21 calls)
% 0.44/0.63  ;     0.073  32%   Forward simplification       (931 calls)
% 0.44/0.63  ;     0.015   7%   Backward simplification      (179 calls)
% 0.44/0.63  ;     0.073  32%   Ordering                     (5,194 calls)
% 0.44/0.63  ;     0.001   0%   Sortal reasoning             (32 calls)
% 0.44/0.63  ;     0.000   0%   Purity testing               (1 call)
% 0.44/0.63  ;     0.021   9%   Other
% 0.44/0.63  ;     0.230        Total
% 0.44/0.63  ;     0.240        Real time
% 0.44/0.63  ; 
% 0.44/0.63  ; Term-hash-array has 473 terms in all.
% 0.44/0.63  ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.44/0.63  ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.44/0.63  ; Path-index has 191 entries (370 at peak, 517 added, 326 deleted).
% 0.44/0.63  ; Path-index has 161 nodes (187 at peak, 195 added, 34 deleted).
% 0.44/0.63  ; Trie-index has 191 entries (370 at peak, 517 added, 326 deleted).
% 0.44/0.63  ; Trie-index has 570 nodes (1,276 at peak, 1,688 added, 1,118 deleted).
% 0.44/0.63  ; Retrieved 24,009 generalization terms in 7,607 calls.
% 0.44/0.63  ; Retrieved 1,868 instance terms in 217 calls.
% 0.44/0.63  ; Retrieved 2,855 unifiable terms in 130 calls.
% 0.44/0.63  ; 
% 0.44/0.63  ; The agenda of backward simplifiable rows to process has 36 entries:
% 0.44/0.63  ;    36 with value 0
% 0.44/0.63  ; The agenda of rows to process has 10 entries:
% 0.44/0.63  ;     5 with value 36              2 with value 39               1 with value 47
% 0.44/0.63  ;     2 with value 38
% 0.44/0.63  ; The agenda of rows to give has 51 entries:
% 0.44/0.63  ;     1 with value (4 16)          9 with value (4 23)           2 with value (4 28)
% 0.44/0.63  ;     1 with value (4 17)          7 with value (4 24)           1 with value (4 29)
% 0.44/0.63  ;     2 with value (4 19)          4 with value (4 25)           1 with value (4 31)
% 0.44/0.63  ;     1 with value (4 20)         11 with value (4 26)           1 with value (4 32)
% 0.44/0.63  ;     2 with value (4 21)          2 with value (4 27)           1 with value (4 33)
% 0.44/0.63  ;     5 with value (4 22)
% 0.44/0.63  Evaluation took:
% 0.44/0.63    0.24 seconds of real time
% 0.44/0.63    0.226097 seconds of user run time
% 0.44/0.63    0.014274 seconds of system run time
% 0.44/0.63    [Run times include 0.006 seconds GC run time.]
% 0.44/0.63    0 calls to %EVAL
% 0.44/0.63    0 page faults and
% 0.44/0.63    13,222,024 bytes consed.
% 0.44/0.63  :PROOF-FOUND
% 0.44/0.63  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-09T06:22:38
% 0.44/0.63  :PROOF-FOUND
% 0.44/0.63  * 
%------------------------------------------------------------------------------