TSTP Solution File: BOO014-2 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : BOO014-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n023.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 23:48:56 EDT 2022

% Result   : Unsatisfiable 0.77s 0.93s
% Output   : Refutation 0.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   35 (  35 unt;   0 nHn;  13 RR)
%            Number of literals    :   35 (  34 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    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :   38 (   6 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(distributivity1,axiom,
    add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)),
    file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',distributivity1) ).

cnf(distributivity3,axiom,
    multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
    file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',distributivity3) ).

cnf(additive_inverse1,axiom,
    add(X,inverse(X)) = multiplicative_identity,
    file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',additive_inverse1) ).

cnf(multiplicative_inverse1,axiom,
    multiply(X,inverse(X)) = additive_identity,
    file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',multiplicative_inverse1) ).

cnf(multiplicative_id1,axiom,
    multiply(X,multiplicative_identity) = X,
    file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',multiplicative_id1) ).

cnf(additive_id1,axiom,
    add(X,additive_identity) = X,
    file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',additive_id1) ).

cnf(a_plus_b_is_c,hypothesis,
    add(a,b) = c,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_plus_b_is_c) ).

cnf(a_inverse_times_b_inverse_is_d,hypothesis,
    multiply(inverse(a),inverse(b)) = d,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_inverse_times_b_inverse_is_d) ).

cnf(prove_c_inverse_is_d,negated_conjecture,
    inverse(c) != d,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_inverse_is_d) ).

cnf(10,plain,
    add(multiply(X,Y),Z) = add(add(multiply(X,Y),multiply(X,Z)),add(multiply(Y,Z),multiply(Z,Z))),
    inference('REWRITE',[status(thm)],[distributivity1,distributivity3,theory(equality)]) ).

cnf(13,plain,
    multiply(c,X) = add(multiply(a,X),multiply(b,X)),
    inference('PARAMODULATE',[status(thm)],[distributivity3,a_plus_b_is_c,theory(equality)]) ).

cnf(14,plain,
    multiply(X,Y) = add(multiply(X,Y),multiply(additive_identity,Y)),
    inference('PARAMODULATE',[status(thm)],[distributivity3,additive_id1,theory(equality)]) ).

cnf(15,plain,
    X = add(multiply(X,Y),multiply(inverse(Y),X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[distributivity3,additive_inverse1,theory(equality)]),multiplicative_id1,theory(equality)]) ).

cnf(20,plain,
    add(X,Y) = add(add(X,Y),add(multiply(X,Y),multiply(Y,Y))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,multiplicative_id1,theory(equality)]),multiplicative_id1,theory(equality)]) ).

cnf(21,plain,
    X = add(multiply(X,Y),add(multiply(inverse(Y),X),multiply(X,X))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,multiplicative_inverse1,theory(equality)]),additive_id1,theory(equality)]) ).

cnf(39,plain,
    add(multiply(a,inverse(c)),multiply(b,inverse(c))) = additive_identity,
    inference('PARAMODULATE',[status(thm)],[multiplicative_inverse1,13,theory(equality)]) ).

cnf(41,plain,
    additive_identity = multiply(additive_identity,X),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[14,multiplicative_inverse1,theory(equality)]),additive_id1,theory(equality)]) ).

cnf(44,plain,
    X = add(multiply(X,Y),multiply(X,X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,41,theory(equality)]),41,additive_id1,theory(equality)]) ).

cnf(51,plain,
    X = add(X,multiply(X,Y)),
    inference('REWRITE',[status(thm)],[21,44,theory(equality)]) ).

cnf(53,plain,
    add(X,Y) = add(add(X,Y),Y),
    inference('REWRITE',[status(thm)],[20,44,theory(equality)]) ).

cnf(69,plain,
    multiply(X,Y) = add(multiply(X,Y),multiply(multiply(X,Z),Y)),
    inference('PARAMODULATE',[status(thm)],[distributivity3,51,theory(equality)]) ).

cnf(80,plain,
    X = multiply(inverse(inverse(X)),X),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[15,multiplicative_inverse1,theory(equality)]),additive_id1,theory(equality)]) ).

cnf(83,plain,
    inverse(inverse(X)) = X,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[15,multiplicative_inverse1,theory(equality)]),additive_id1,80,theory(equality)]) ).

cnf(84,plain,
    X = add(add(multiply(a,X),multiply(b,X)),multiply(inverse(c),X)),
    inference('PARAMODULATE',[status(thm)],[15,13,theory(equality)]) ).

cnf(127,plain,
    additive_identity = multiply(b,inverse(c)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[53,39,theory(equality)]),additive_id1,theory(equality)]) ).

cnf(128,plain,
    multiply(a,inverse(c)) = additive_identity,
    inference('REWRITE',[status(thm)],[39,additive_id1,127,theory(equality)]) ).

cnf(130,plain,
    inverse(c) = multiply(inverse(a),inverse(c)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[15,128,theory(equality)]),additive_id1,theory(equality)]) ).

cnf(132,plain,
    inverse(c) = multiply(inverse(b),inverse(c)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[15,127,theory(equality)]),additive_id1,theory(equality)]) ).

cnf(198,plain,
    additive_identity = multiply(multiply(X,Y),inverse(X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[69,multiplicative_inverse1,theory(equality)]),additive_id1,theory(equality)]) ).

cnf(203,plain,
    d = add(d,multiply(multiply(inverse(a),X),inverse(b))),
    inference('PARAMODULATE',[status(thm)],[69,a_inverse_times_b_inverse_is_d,theory(equality)]) ).

cnf(215,plain,
    additive_identity = multiply(d,a),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[198,a_inverse_times_b_inverse_is_d,theory(equality)]),83,theory(equality)]) ).

cnf(216,plain,
    additive_identity = multiply(d,b),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[198,a_inverse_times_b_inverse_is_d,theory(equality)]),83,theory(equality)]) ).

cnf(411,plain,
    d = add(d,inverse(c)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[203,130,theory(equality)]),132,theory(equality)]) ).

cnf(483,plain,
    d = multiply(inverse(c),d),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[84,215,theory(equality)]),additive_id1,216,theory(equality)]) ).

cnf(499,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[51,483,theory(equality)]),prove_c_inverse_is_d,411,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : BOO014-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13  % Command  : run-snark %s %d
% 0.13/0.35  % Computer : n023.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Wed Jun  1 17:20:41 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.20/0.47  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.48  * 
% 0.20/0.48  * 
% 0.20/0.49  #<PACKAGE "SNARK-USER">
% 0.20/0.49  * 
% 0.20/0.49  SNARK-TPTP-OPTIONS
% 0.20/0.49  * 
% 0.20/0.49  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.49   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.49   (USE-FACTORING :POS)
% 0.20/0.49   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.49   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.49   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.49   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.49   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.49   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.49   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.49   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.49   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.49   (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.49  * 
% 0.20/0.49  "."
% 0.20/0.49  * 
% 0.20/0.49  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-01T17:20:41
% 0.20/0.49  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n023.cluster.edu at 2022-06-01T17:20:41
% 0.20/0.50  
% 0.20/0.50  ; Recognized commutativity assertion (= (|add| ?X ?Y) (|add| ?Y ?X)).
% 0.20/0.50  ; Recognized commutativity assertion (= (|multiply| ?X ?Y) (|multiply| ?Y ?X)).
% 0.20/0.50  ; Recognized possible right inverse assertion (= (|add| ?X (|inverse| ?X)) |multiplicative_identity|).
% 0.20/0.50  ; Recognized possible left inverse assertion (= (|add| (|inverse| ?X) ?X) |multiplicative_identity|).
% 0.20/0.50  ; Recognized possible right inverse assertion (= (|multiply| ?X (|inverse| ?X)) |additive_identity|).
% 0.20/0.50  ; Recognized possible left inverse assertion (= (|multiply| (|inverse| ?X) ?X) |additive_identity|).
% 0.20/0.50  ; Recognized right identity assertion (= (|multiply| ?X |multiplicative_identity|) ?X).
% 0.20/0.50  ; Recognized left identity assertion (= (|multiply| |multiplicative_identity| ?X) ?X).
% 0.20/0.50  ; Recognized right identity assertion (= (|add| ?X |additive_identity|) ?X).
% 0.20/0.50  ; Recognized left identity assertion (= (|add| |additive_identity| ?X) ?X).
% 0.20/0.50  ; Declaring add to be commutative.
% 0.77/0.93  ; Declaring multiply to be commutative.
% 0.77/0.93  
% 0.77/0.93  #||
% 0.77/0.93  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.77/0.93  % SZS output start Refutation
% See solution above
% 0.77/0.94  ||#
% 0.77/0.94  
% 0.77/0.94  ; Summary of computation:
% 0.77/0.94  ;      5672 formulas have been input or derived (from 134 formulas).
% 0.77/0.94  ;       499 ( 9%) were retained.  Of these,
% 0.77/0.94  ;           75 (15%) were simplified or subsumed later,
% 0.77/0.94  ;          424 (85%) are still being kept.
% 0.77/0.94  ; 
% 0.77/0.94  ; Run time in seconds excluding printing time:
% 0.77/0.94  ;     0.003   1%   Read assertion file          (1 call)
% 0.77/0.94  ;     0.001   0%   Assert                       (17 calls)
% 0.77/0.94  ;     0.050  11%   Process new row              (4,584 calls)
% 0.77/0.94  ;     0.004   1%   Resolution                   (266 calls)
% 0.77/0.94  ;     0.081  18%   Paramodulation               (133 calls)
% 0.77/0.94  ;     0.220  49%   Forward simplification       (4,553 calls)
% 0.77/0.94  ;     0.025   6%   Backward simplification      (499 calls)
% 0.77/0.94  ;     0.017   4%   Ordering                     (8,020 calls)
% 0.77/0.94  ;     0.001   0%   Sortal reasoning             (32 calls)
% 0.77/0.94  ;     0.000   0%   Purity testing               (1 call)
% 0.77/0.94  ;     0.043  10%   Other
% 0.77/0.94  ;     0.445        Total
% 0.77/0.94  ;     0.448        Real time
% 0.77/0.94  ; 
% 0.77/0.94  ; Term-hash-array has 1,401 terms in all.
% 0.77/0.94  ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.77/0.94  ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.77/0.94  ; Path-index has 1,171 entries (1,171 at peak, 1,434 added, 263 deleted).
% 0.77/0.94  ; Path-index has 567 nodes (567 at peak, 639 added, 72 deleted).
% 0.77/0.94  ; Trie-index has 1,171 entries (1,171 at peak, 1,434 added, 263 deleted).
% 0.77/0.94  ; Trie-index has 5,738 nodes (5,738 at peak, 7,083 added, 1,345 deleted).
% 0.77/0.94  ; Retrieved 27,902 generalization terms in 24,673 calls.
% 0.77/0.94  ; Retrieved 1,206 instance terms in 502 calls.
% 0.77/0.94  ; Retrieved 11,411 unifiable terms in 1,002 calls.
% 0.77/0.94  ; 
% 0.77/0.94  ; The agenda of rows to process has 46 entries:
% 0.77/0.94  ;     8 with value 16              6 with value 20               1 with value 24
% 0.77/0.94  ;     9 with value 17              4 with value 21               1 with value 25
% 0.77/0.94  ;     3 with value 18              2 with value 22               1 with value 26
% 0.77/0.94  ;     4 with value 19              7 with value 23
% 0.77/0.94  ; The agenda of rows to give has 298 entries:
% 0.77/0.94  ;     2 with value (4 16)         15 with value (4 25)           6 with value (4 33)
% 0.77/0.94  ;     1 with value (4 19)         20 with value (4 26)           3 with value (4 34)
% 0.77/0.94  ;    16 with value (4 20)         29 with value (4 27)           6 with value (4 35)
% 0.77/0.94  ;    21 with value (4 21)         23 with value (4 28)           7 with value (4 36)
% 0.77/0.94  ;    29 with value (4 22)         21 with value (4 29)           1 with value (4 37)
% 0.77/0.94  ;    45 with value (4 23)         12 with value (4 30)           1 with value (4 39)
% 0.77/0.94  ;    28 with value (4 24)         11 with value (4 31)           1 with value (4 50)
% 0.77/0.94  Evaluation took:
% 0.77/0.94    0.448 seconds of real time
% 0.77/0.94    0.415011 seconds of user run time
% 0.77/0.94    0.034002 seconds of system run time
% 0.77/0.94    [Run times include 0.012 seconds GC run time.]
% 0.77/0.94    0 calls to %EVAL
% 0.77/0.94    0 page faults and
% 0.77/0.94    37,377,864 bytes consed.
% 0.77/0.94  :PROOF-FOUND
% 0.77/0.94  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-01T17:20:41
% 0.77/0.94  :PROOF-FOUND
% 0.77/0.94  * 
%------------------------------------------------------------------------------