TSTP Solution File: BOO022-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : BOO022-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n032.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 23:48:58 EDT 2022

% Result   : Unsatisfiable 2.64s 2.80s
% Output   : Refutation 2.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   58 (  58 unt;   0 nHn;   4 RR)
%            Number of literals    :   58 (  57 equ;   3 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    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :  112 (  23 sgn)

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

cnf(multiply_add_property,axiom,
    multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_add_property) ).

cnf(additive_inverse,axiom,
    add(X,inverse(X)) = n1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse) ).

cnf(add_multiply,axiom,
    add(multiply(X,Y),Y) = Y,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_multiply) ).

cnf(add_multiply_property,axiom,
    add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_multiply_property) ).

cnf(6,plain,
    add(X,multiply(Y,Z)) = add(add(multiply(Y,Z),multiply(X,Z)),add(multiply(Y,X),multiply(X,X))),
    inference('REWRITE',[status(thm)],[add_multiply_property,multiply_add_property,theory(equality)]) ).

cnf(multiplicative_inverse,axiom,
    multiply(X,inverse(X)) = n0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse) ).

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

cnf(10,plain,
    multiply(X,X) = X,
    inference('PARAMODULATE',[status(thm)],[multiply_add,add_multiply,theory(equality)]) ).

cnf(11,plain,
    add(X,multiply(Y,Z)) = add(add(multiply(Y,Z),multiply(X,Z)),X),
    inference('REWRITE',[status(thm)],[6,add_multiply,10,theory(equality)]) ).

cnf(12,plain,
    add(X,X) = X,
    inference('PARAMODULATE',[status(thm)],[add_multiply,multiply_add,theory(equality)]) ).

cnf(14,plain,
    multiply(X,n1) = add(multiply(Y,X),multiply(inverse(Y),X)),
    inference('PARAMODULATE',[status(thm)],[multiply_add_property,additive_inverse,theory(equality)]) ).

cnf(15,plain,
    multiply(X,Y) = add(multiply(multiply(Z,Y),X),multiply(Y,X)),
    inference('PARAMODULATE',[status(thm)],[multiply_add_property,add_multiply,theory(equality)]) ).

cnf(19,plain,
    add(X,Y) = add(add(Y,multiply(X,Y)),X),
    inference('PARAMODULATE',[status(thm)],[11,multiply_add,theory(equality)]) ).

cnf(25,plain,
    add(X,multiply(Y,X)) = X,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[11,10,theory(equality)]),12,add_multiply,theory(equality)]) ).

cnf(26,plain,
    add(X,Y) = add(Y,X),
    inference('REWRITE',[status(thm)],[19,25,theory(equality)]) ).

cnf(27,plain,
    multiply(X,Y) = multiply(Y,X),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[multiply_add_property,12,theory(equality)]),12,theory(equality)]) ).

cnf(28,plain,
    add(inverse(X),X) = n1,
    inference('PARAMODULATE',[status(thm)],[additive_inverse,26,theory(equality)]) ).

cnf(46,plain,
    multiply(inverse(X),X) = n0,
    inference('PARAMODULATE',[status(thm)],[multiplicative_inverse,27,theory(equality)]) ).

cnf(51,plain,
    multiply(multiply(b,a),c) != multiply(a,multiply(b,c)),
    inference('PARAMODULATE',[status(thm)],[prove_associativity_of_multiply,27,theory(equality)]) ).

cnf(53,plain,
    multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
    inference('PARAMODULATE',[status(thm)],[multiply_add_property,27,theory(equality)]) ).

cnf(57,plain,
    multiply(X,n1) = add(multiply(inverse(Y),X),multiply(Y,X)),
    inference('PARAMODULATE',[status(thm)],[multiply_add_property,28,theory(equality)]) ).

cnf(59,plain,
    add(X,multiply(X,Y)) = X,
    inference('PARAMODULATE',[status(thm)],[25,27,theory(equality)]) ).

cnf(63,plain,
    add(X,n0) = X,
    inference('PARAMODULATE',[status(thm)],[25,46,theory(equality)]) ).

cnf(66,plain,
    add(n0,X) = X,
    inference('PARAMODULATE',[status(thm)],[add_multiply,46,theory(equality)]) ).

cnf(93,plain,
    multiply(X,n1) = X,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[14,10,theory(equality)]),63,46,theory(equality)]) ).

cnf(95,plain,
    X = add(multiply(Y,X),multiply(inverse(Y),X)),
    inference('REWRITE',[status(thm)],[14,93,theory(equality)]) ).

cnf(96,plain,
    X = add(multiply(inverse(Y),X),multiply(Y,X)),
    inference('REWRITE',[status(thm)],[57,93,theory(equality)]) ).

cnf(108,plain,
    add(inverse(X),multiply(X,Y)) = add(Y,inverse(X)),
    inference('PARAMODULATE',[status(thm)],[11,95,theory(equality)]) ).

cnf(110,plain,
    X = add(multiply(Y,X),multiply(X,inverse(Y))),
    inference('PARAMODULATE',[status(thm)],[95,27,theory(equality)]) ).

cnf(111,plain,
    X = multiply(inverse(inverse(X)),X),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[95,46,theory(equality)]),66,theory(equality)]) ).

cnf(112,plain,
    inverse(inverse(X)) = multiply(X,inverse(inverse(X))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[95,multiplicative_inverse,theory(equality)]),63,theory(equality)]) ).

cnf(113,plain,
    multiply(X,Y) = add(multiply(multiply(Z,Y),X),multiply(multiply(inverse(Z),Y),X)),
    inference('PARAMODULATE',[status(thm)],[multiply_add_property,95,theory(equality)]) ).

cnf(118,plain,
    inverse(inverse(X)) = X,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[27,111,theory(equality)]),112,theory(equality)]) ).

cnf(128,plain,
    add(inverse(X),multiply(Y,X)) = add(Y,inverse(X)),
    inference('PARAMODULATE',[status(thm)],[108,27,theory(equality)]) ).

cnf(163,plain,
    multiply(multiply(b,a),c) != multiply(multiply(b,c),a),
    inference('PARAMODULATE',[status(thm)],[51,27,theory(equality)]) ).

cnf(170,plain,
    X = add(multiply(X,inverse(Y)),multiply(Y,X)),
    inference('PARAMODULATE',[status(thm)],[96,27,theory(equality)]) ).

cnf(229,plain,
    n0 = multiply(multiply(X,Y),inverse(Y)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[15,multiplicative_inverse,theory(equality)]),63,46,theory(equality)]) ).

cnf(245,plain,
    multiply(inverse(X),multiply(Y,X)) = n0,
    inference('PARAMODULATE',[status(thm)],[27,229,theory(equality)]) ).

cnf(246,plain,
    n0 = multiply(multiply(X,Y),inverse(X)),
    inference('PARAMODULATE',[status(thm)],[229,27,theory(equality)]) ).

cnf(248,plain,
    inverse(X) = multiply(inverse(multiply(Y,X)),inverse(X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[95,229,theory(equality)]),66,theory(equality)]) ).

cnf(252,plain,
    n0 = multiply(multiply(X,multiply(Y,Z)),inverse(Z)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[15,229,theory(equality)]),63,245,theory(equality)]) ).

cnf(257,plain,
    multiply(X,multiply(Y,inverse(X))) = n0,
    inference('PARAMODULATE',[status(thm)],[245,118,theory(equality)]) ).

cnf(258,plain,
    n0 = multiply(multiply(X,inverse(Y)),multiply(Z,Y)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[15,245,theory(equality)]),63,229,theory(equality)]) ).

cnf(259,plain,
    n0 = multiply(multiply(inverse(X),Y),X),
    inference('PARAMODULATE',[status(thm)],[246,118,theory(equality)]) ).

cnf(261,plain,
    inverse(X) = multiply(inverse(X),inverse(multiply(X,Y))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[110,246,theory(equality)]),66,theory(equality)]) ).

cnf(283,plain,
    add(inverse(multiply(X,Y)),inverse(Y)) = inverse(multiply(X,Y)),
    inference('PARAMODULATE',[status(thm)],[59,248,theory(equality)]) ).

cnf(293,plain,
    n0 = multiply(multiply(multiply(X,Y),Z),inverse(Y)),
    inference('PARAMODULATE',[status(thm)],[252,27,theory(equality)]) ).

cnf(306,plain,
    X = add(multiply(X,inverse(Y)),multiply(X,Y)),
    inference('PARAMODULATE',[status(thm)],[170,27,theory(equality)]) ).

cnf(322,plain,
    n0 = multiply(multiply(inverse(X),Y),multiply(Z,X)),
    inference('PARAMODULATE',[status(thm)],[258,27,theory(equality)]) ).

cnf(361,plain,
    n0 = multiply(multiply(inverse(X),Y),multiply(X,Z)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[293,261,theory(equality)]),118,theory(equality)]) ).

cnf(478,plain,
    multiply(inverse(X),Y) = multiply(multiply(inverse(X),Y),inverse(multiply(X,Z))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[306,361,theory(equality)]),63,theory(equality)]) ).

cnf(2222,plain,
    multiply(multiply(X,Y),Z) = multiply(multiply(X,Z),multiply(X,Y)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[113,361,theory(equality)]),63,theory(equality)]) ).

cnf(2225,plain,
    multiply(inverse(multiply(X,Y)),Y) = multiply(inverse(X),Y),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[113,multiplicative_inverse,theory(equality)]),66,478,theory(equality)]) ).

cnf(2248,plain,
    multiply(multiply(X,inverse(multiply(inverse(Y),Z))),Z) = multiply(multiply(Y,Z),multiply(X,inverse(multiply(inverse(Y),Z)))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[113,257,theory(equality)]),63,theory(equality)]) ).

cnf(2262,plain,
    add(inverse(X),inverse(Y)) = inverse(multiply(X,Y)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[128,2225,theory(equality)]),283,128,theory(equality)]) ).

cnf(2504,plain,
    multiply(multiply(X,Y),Z) = multiply(multiply(X,Z),Y),
    inference('REWRITE',[status(thm)],[2248,322,2222,63,259,53,multiply_add_property,118,2262,theory(equality)]) ).

cnf(2505,plain,
    $false,
    inference('REWRITE',[status(thm)],[163,2504,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : BOO022-1 : TPTP v8.1.0. Released v2.2.0.
% 0.13/0.12  % Command  : run-snark %s %d
% 0.13/0.32  % Computer : n032.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32  % CPULimit : 300
% 0.13/0.32  % WCLimit  : 600
% 0.13/0.32  % DateTime : Wed Jun  1 22:52:45 EDT 2022
% 0.13/0.32  % CPUTime  : 
% 0.18/0.41  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.42  * 
% 0.18/0.42  * 
% 0.18/0.42  #<PACKAGE "SNARK-USER">
% 0.18/0.42  * 
% 0.18/0.42  SNARK-TPTP-OPTIONS
% 0.18/0.42  * 
% 0.18/0.42  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.18/0.42   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.18/0.43   (USE-FACTORING :POS)
% 0.18/0.43   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.18/0.43   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.18/0.43   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.18/0.43   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.18/0.43   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.18/0.43   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.18/0.43   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.18/0.43   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.18/0.43   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.18/0.43   (DECLARE-TPTP-SYMBOLS2))
% 0.18/0.43  * 
% 0.18/0.43  "."
% 0.18/0.43  * 
% 0.18/0.43  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-01T22:52:45
% 0.18/0.43  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n032.cluster.edu at 2022-06-01T22:52:45
% 0.18/0.43  
% 0.18/0.43  ; Recognized possible right inverse assertion (= (|add| ?X (|inverse| ?X)) |n1|).
% 2.64/2.80  ; Recognized possible right inverse assertion (= (|multiply| ?X (|inverse| ?X)) |n0|).
% 2.64/2.80  
% 2.64/2.80  #||
% 2.64/2.80  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.64/2.80  % SZS output start Refutation
% See solution above
% 2.64/2.81  ||#
% 2.64/2.81  
% 2.64/2.81  ; Summary of computation:
% 2.64/2.81  ;     48203 formulas have been input or derived (from 283 formulas).
% 2.64/2.81  ;      2505 ( 5%) were retained.  Of these,
% 2.64/2.81  ;         1060 (42%) were simplified or subsumed later,
% 2.64/2.81  ;         1445 (58%) are still being kept.
% 2.64/2.81  ; 
% 2.64/2.81  ; Run time in seconds excluding printing time:
% 2.64/2.81  ;     0.001   0%   Read assertion file          (1 call)
% 2.64/2.81  ;     0.000   0%   Assert                       (7 calls)
% 2.64/2.81  ;     0.273  11%   Process new row              (40,604 calls)
% 2.64/2.81  ;     0.030   1%   Resolution                   (564 calls)
% 2.64/2.81  ;     0.484  20%   Paramodulation               (282 calls)
% 2.64/2.81  ;     1.261  53%   Forward simplification       (40,569 calls)
% 2.64/2.81  ;     0.104   4%   Backward simplification      (2,504 calls)
% 2.64/2.81  ;     0.107   4%   Ordering                     (58,514 calls)
% 2.64/2.81  ;     0.001   0%   Sortal reasoning             (32 calls)
% 2.64/2.81  ;     0.000   0%   Purity testing               (1 call)
% 2.64/2.81  ;     0.117   5%   Other
% 2.64/2.81  ;     2.378        Total
% 2.64/2.81  ;     2.382        Real time
% 2.64/2.81  ; 
% 2.64/2.81  ; Term-hash-array has 6,472 terms in all.
% 2.64/2.81  ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 2.64/2.81  ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 2.64/2.81  ; Path-index has 3,853 entries (5,375 at peak, 6,536 added, 2,683 deleted).
% 2.64/2.81  ; Path-index has 4,321 nodes (4,558 at peak, 5,381 added, 1,060 deleted).
% 2.64/2.81  ; Trie-index has 3,853 entries (5,375 at peak, 6,536 added, 2,683 deleted).
% 2.64/2.81  ; Trie-index has 11,216 nodes (15,696 at peak, 20,533 added, 9,317 deleted).
% 2.64/2.81  ; Retrieved 625,238 generalization terms in 286,420 calls.
% 2.64/2.81  ; Retrieved 18,541 instance terms in 2,505 calls.
% 2.64/2.81  ; Retrieved 92,782 unifiable terms in 1,940 calls.
% 2.64/2.81  ; 
% 2.64/2.81  ; The agenda of backward simplifiable rows to process has 298 entries:
% 2.64/2.81  ;   298 with value 0
% 2.64/2.81  ; The agenda of rows to process has 391 entries:
% 2.64/2.81  ;    54 with value 23             27 with value 28               8 with value 33
% 2.64/2.81  ;    67 with value 24             32 with value 29               6 with value 34
% 2.64/2.81  ;    37 with value 25             32 with value 30               3 with value 35
% 2.64/2.81  ;    35 with value 26             41 with value 31               4 with value 36
% 2.64/2.81  ;    29 with value 27             15 with value 32               1 with value 38
% 2.64/2.81  ; The agenda of rows to give has 1236 entries:
% 2.64/2.81  ;     1 with value (4 17)         76 with value (4 30)          14 with value (4 40)
% 2.64/2.81  ;     1 with value (4 21)         54 with value (4 31)           3 with value (4 42)
% 2.64/2.81  ;     3 with value (4 22)         64 with value (4 32)           9 with value (4 43)
% 2.64/2.81  ;    44 with value (4 23)         55 with value (4 33)           1 with value (4 44)
% 2.64/2.81  ;    92 with value (4 24)         32 with value (4 34)           4 with value (4 45)
% 2.64/2.81  ;   111 with value (4 25)         33 with value (4 35)           8 with value (4 46)
% 2.64/2.81  ;   129 with value (4 26)         48 with value (4 36)           4 with value (4 47)
% 2.64/2.81  ;    75 with value (4 27)         48 with value (4 37)           8 with value (4 48)
% 2.64/2.81  ;   216 with value (4 28)         18 with value (4 38)           1 with value (4 50)
% 2.64/2.81  ;    75 with value (4 29)          9 with value (4 39)
% 2.64/2.81  Evaluation took:
% 2.64/2.81    2.383 seconds of real time
% 2.64/2.81    2.142694 seconds of user run time
% 2.64/2.81    0.239675 seconds of system run time
% 2.64/2.81    [Run times include 0.142 seconds GC run time.]
% 2.64/2.81    0 calls to %EVAL
% 2.64/2.81    0 page faults and
% 2.64/2.81    183,095,632 bytes consed.
% 2.64/2.81  :PROOF-FOUND
% 2.64/2.81  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-01T22:52:47
% 2.64/2.81  :PROOF-FOUND
% 2.64/2.81  * 
%------------------------------------------------------------------------------