TSTP Solution File: RNG025-5 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : RNG025-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n018.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 20:40:35 EDT 2022

% Result   : Unsatisfiable 1.30s 1.48s
% Output   : Refutation 1.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   22 (  22 unt;   0 nHn;   3 RR)
%            Number of literals    :   22 (  21 equ;   2 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-3 aty)
%            Number of variables   :   46 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(left_additive_identity,axiom,
    add(additive_identity,X) = X,
    file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',left_additive_identity) ).

cnf(left_additive_inverse,axiom,
    add(additive_inverse(X),X) = additive_identity,
    file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',left_additive_inverse) ).

cnf(5,plain,
    add(additive_inverse(X),add(X,Y)) = add(additive_identity,Y),
    inference('EMBED',[status(thm)],[left_additive_inverse]) ).

cnf(distribute1,axiom,
    multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',distribute1) ).

cnf(distribute2,axiom,
    multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',distribute2) ).

cnf(right_alternative,axiom,
    multiply(multiply(X,Y),Y) = multiply(X,multiply(Y,Y)),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_alternative) ).

cnf(associator,axiom,
    associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',associator) ).

cnf(inverse_product1,axiom,
    multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_product1) ).

cnf(distributivity_of_difference3,axiom,
    multiply(additive_inverse(X),add(Y,Z)) = add(additive_inverse(multiply(X,Y)),additive_inverse(multiply(X,Z))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity_of_difference3) ).

cnf(18,plain,
    additive_inverse(add(multiply(X,Y),multiply(X,Z))) = add(additive_inverse(multiply(X,Y)),additive_inverse(multiply(X,Z))),
    inference('REWRITE',[status(thm)],[distributivity_of_difference3,distribute1,inverse_product1,theory(equality)]) ).

cnf(prove_equation,negated_conjecture,
    add(associator(x,y,z),associator(x,z,y)) != additive_identity,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).

cnf(21,plain,
    add(multiply(multiply(x,z),y),add(multiply(multiply(x,y),z),additive_inverse(add(multiply(x,multiply(y,z)),multiply(x,multiply(z,y)))))) != additive_identity,
    inference('REWRITE',[status(thm)],[prove_equation,18,associator,theory(equality)]) ).

cnf(23,plain,
    additive_inverse(X) = add(additive_inverse(add(X,Y)),Y),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[5,5,theory(equality)]),left_additive_identity,theory(equality)]) ).

cnf(25,plain,
    additive_inverse(multiply(multiply(X,Y),Y)) = additive_inverse(multiply(X,multiply(Y,Y))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[inverse_product1,right_alternative,theory(equality)]),inverse_product1,theory(equality)]) ).

cnf(94,plain,
    additive_inverse(add(X,Y)) = add(additive_inverse(Y),additive_inverse(X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[23,5,theory(equality)]),left_additive_identity,theory(equality)]) ).

cnf(95,plain,
    add(additive_inverse(X),add(additive_inverse(Y),Z)) = add(additive_inverse(add(X,Y)),Z),
    inference('EMBED',[status(thm)],[94]) ).

cnf(175,plain,
    add(additive_inverse(multiply(X,multiply(Y,Y))),multiply(multiply(X,Y),Y)) = additive_identity,
    inference('PARAMODULATE',[status(thm)],[left_additive_inverse,25,theory(equality)]) ).

cnf(176,plain,
    add(additive_inverse(multiply(X,multiply(Y,Y))),add(multiply(multiply(X,Y),Y),Z)) = add(additive_identity,Z),
    inference('EMBED',[status(thm)],[175]) ).

cnf(460,plain,
    add(additive_inverse(add(multiply(X,multiply(Y,Z)),add(multiply(X,multiply(Z,Y)),add(multiply(X,multiply(Y,Y)),multiply(X,multiply(Z,Z)))))),add(multiply(multiply(X,Y),Y),add(multiply(multiply(X,Y),Z),add(multiply(multiply(X,Z),Y),multiply(multiply(X,Z),Z))))) = additive_identity,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[175,distribute1,theory(equality)]),distribute1,distribute2,theory(equality)]) ).

cnf(493,plain,
    additive_inverse(X) = add(additive_inverse(add(X,multiply(Y,multiply(Z,Z)))),multiply(multiply(Y,Z),Z)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[95,176,theory(equality)]),left_additive_identity,theory(equality)]) ).

cnf(496,plain,
    add(multiply(multiply(X,Y),Z),add(multiply(multiply(X,Z),Y),additive_inverse(add(multiply(X,multiply(Y,Z)),multiply(X,multiply(Z,Y)))))) = additive_identity,
    inference('REWRITE',[status(thm)],[460,493,theory(equality)]) ).

cnf(498,plain,
    $false,
    inference('REWRITE',[status(thm)],[21,496,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : RNG025-5 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12  % Command  : run-snark %s %d
% 0.13/0.33  % Computer : n018.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
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Mon May 30 19:10:27 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.19/0.44  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45  * 
% 0.19/0.45  * 
% 0.19/0.46  #<PACKAGE "SNARK-USER">
% 0.19/0.46  * 
% 0.19/0.46  SNARK-TPTP-OPTIONS
% 0.19/0.46  * 
% 0.19/0.46  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.46   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.46   (USE-FACTORING :POS)
% 0.19/0.46   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.46   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.46   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.46   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.46   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.46   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.46   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.46   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.46   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.46   (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.46  * 
% 0.19/0.46  "."
% 0.19/0.46  * 
% 0.19/0.46  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-30T19:10:27
% 0.19/0.46  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n018.cluster.edu at 2022-05-30T19:10:27
% 0.19/0.48  
% 0.19/0.48  ; Recognized left identity assertion (= (|add| |additive_identity| ?X) ?X).
% 0.19/0.48  ; Recognized right identity assertion (= (|add| ?X |additive_identity|) ?X).
% 0.19/0.48  ; Recognized possible left inverse assertion (= (|add| (|additive_inverse| ?X) ?X) |additive_identity|).
% 0.19/0.48  ; Recognized possible right inverse assertion (= (|add| ?X (|additive_inverse| ?X)) |additive_identity|).
% 0.19/0.48  ; Recognized commutativity assertion (= (|add| ?X ?Y) (|add| ?Y ?X)).
% 0.19/0.48  ; Recognized associativity assertion (= (|add| ?X (|add| ?Y ?Z)) (|add| (|add| ?X ?Y) ?Z)).
% 0.19/0.48  ; Declaring add to be commutative.
% 1.30/1.48  ; Declaring add to be associative-commutative.
% 1.30/1.48  
% 1.30/1.48  #||
% 1.30/1.48  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.30/1.48  % SZS output start Refutation
% See solution above
% 1.30/1.49  ||#
% 1.30/1.49  
% 1.30/1.49  ; Summary of computation:
% 1.30/1.49  ;      3131 formulas have been input or derived (from 67 formulas).
% 1.30/1.49  ;       498 (16%) were retained.  Of these,
% 1.30/1.49  ;           62 (12%) were simplified or subsumed later,
% 1.30/1.49  ;          436 (88%) are still being kept.
% 1.30/1.49  ; 
% 1.30/1.49  ; Run time in seconds excluding printing time:
% 1.30/1.49  ;     0.004   0%   Read assertion file          (1 call)
% 1.30/1.49  ;     0.000   0%   Assert                       (23 calls)
% 1.30/1.49  ;     0.076   7%   Process new row              (2,957 calls)
% 1.30/1.49  ;     0.001   0%   Resolution                   (132 calls)
% 1.30/1.49  ;     0.062   6%   Paramodulation               (66 calls)
% 1.30/1.49  ;     0.001   0%   Embedding                    (200 calls)
% 1.30/1.49  ;     0.638  62%   Forward simplification       (2,771 calls)
% 1.30/1.49  ;     0.037   4%   Backward simplification      (324 calls)
% 1.30/1.49  ;     0.067   7%   Ordering                     (17,274 calls)
% 1.30/1.49  ;     0.100  10%   Ordering ac                  (7,198 calls)
% 1.30/1.49  ;     0.000   0%   Sortal reasoning             (32 calls)
% 1.30/1.49  ;     0.000   0%   Purity testing               (1 call)
% 1.30/1.49  ;     0.038   4%   Other
% 1.30/1.49  ;     1.024        Total
% 1.30/1.49  ;     1.026        Real time
% 1.30/1.49  ; 
% 1.30/1.49  ; Term-hash-array has 1,905 terms in all.
% 1.30/1.49  ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 1.30/1.49  ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 1.30/1.49  ; Path-index has 1,702 entries (1,721 at peak, 1,951 added, 249 deleted).
% 1.30/1.49  ; Path-index has 3,054 nodes (3,103 at peak, 3,300 added, 246 deleted).
% 1.30/1.49  ; Trie-index has 1,702 entries (1,721 at peak, 1,951 added, 249 deleted).
% 1.30/1.49  ; Trie-index has 2,765 nodes (2,785 at peak, 3,157 added, 392 deleted).
% 1.30/1.49  ; Retrieved 681,314 generalization terms in 41,213 calls.
% 1.30/1.49  ; Retrieved 2,727 instance terms in 511 calls.
% 1.30/1.49  ; Retrieved 9,685 unifiable terms in 386 calls.
% 1.30/1.49  ; 
% 1.30/1.49  ; The agenda of backward simplifiable rows to process has 1 entry:
% 1.30/1.49  ;     1 with value 0
% 1.30/1.49  ; The agenda of rows to process has 91 entries:
% 1.30/1.49  ;     9 with value 28              5 with value 32               3 with value 36
% 1.30/1.49  ;     6 with value 29             15 with value 33               2 with value 37
% 1.30/1.49  ;     3 with value 30             19 with value 34              20 with value 38
% 1.30/1.49  ;     5 with value 31              4 with value 35
% 1.30/1.49  ; The agenda of rows to give has 372 entries:
% 1.30/1.49  ;     1 with value (4 19)         10 with value (4 33)          12 with value (4 70)
% 1.30/1.49  ;    11 with value (4 21)          4 with value (4 34)           2 with value (4 72)
% 1.30/1.49  ;     9 with value (4 22)          6 with value (4 35)           4 with value (4 73)
% 1.30/1.49  ;    25 with value (4 23)          8 with value (4 36)           2 with value (4 74)
% 1.30/1.49  ;    31 with value (4 24)          8 with value (4 39)           2 with value (4 104)
% 1.30/1.49  ;    26 with value (4 25)          6 with value (4 42)           4 with value (4 109)
% 1.30/1.49  ;    21 with value (4 26)          4 with value (4 45)           2 with value (4 128)
% 1.30/1.49  ;    54 with value (4 27)          8 with value (4 49)           4 with value (4 129)
% 1.30/1.49  ;     8 with value (4 28)          6 with value (4 52)           4 with value (4 134)
% 1.30/1.49  ;     4 with value (4 29)         16 with value (4 55)           2 with value (4 310)
% 1.30/1.49  ;    18 with value (4 30)          4 with value (4 56)           4 with value (4 311)
% 1.30/1.49  ;    16 with value (4 31)          8 with value (4 63)           2 with value (4 312)
% 1.30/1.49  ;    12 with value (4 32)          4 with value (4 64)
% 1.30/1.49  Evaluation took:
% 1.30/1.49    1.026 seconds of real time
% 1.30/1.49    0.958494 seconds of user run time
% 1.30/1.49    0.067456 seconds of system run time
% 1.30/1.49    [Run times include 0.019 seconds GC run time.]
% 1.30/1.49    0 calls to %EVAL
% 1.30/1.49    0 page faults and
% 1.30/1.49    52,578,192 bytes consed.
% 1.30/1.49  :PROOF-FOUND
% 1.30/1.49  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-30T19:10:28
% 1.30/1.49  :PROOF-FOUND
% 1.30/1.49  * 
%------------------------------------------------------------------------------