TSTP Solution File: RNG025-4 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : RNG025-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n020.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 16.82s 17.05s
% Output   : Refutation 16.82s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   24 (  24 unt;   0 nHn;   5 RR)
%            Number of literals    :   24 (  23 equ;   3 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   :   43 (   1 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_multiplicative_zero,axiom,
    multiply(additive_identity,X) = additive_identity,
    file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',left_multiplicative_zero) ).

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

cnf(16,plain,
    additive_identity = additive_inverse(additive_identity),
    inference('PARAMODULATE',[status(thm)],[left_additive_identity,left_additive_inverse,theory(equality)]) ).

cnf(17,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(36,plain,
    additive_identity = add(multiply(X,Y),multiply(additive_inverse(X),Y)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[distribute2,left_additive_inverse,theory(equality)]),left_multiplicative_zero,theory(equality)]) ).

cnf(71,plain,
    additive_inverse(add(X,Y)) = add(additive_inverse(Y),additive_inverse(X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[17,5,theory(equality)]),left_additive_identity,theory(equality)]) ).

cnf(72,plain,
    add(additive_inverse(X),add(additive_inverse(Y),Z)) = add(additive_inverse(add(X,Y)),Z),
    inference('EMBED',[status(thm)],[71]) ).

cnf(73,plain,
    add(multiply(multiply(x,z),y),add(multiply(multiply(x,y),z),additive_inverse(add(multiply(x,multiply(z,y)),multiply(x,multiply(y,z)))))) != additive_identity,
    inference('REWRITE',[status(thm)],[15,71,theory(equality)]) ).

cnf(100,plain,
    additive_inverse(multiply(X,Y)) = multiply(additive_inverse(X),Y),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[17,36,theory(equality)]),left_additive_identity,16,theory(equality)]) ).

cnf(105,plain,
    additive_inverse(multiply(multiply(X,Y),Y)) = additive_inverse(multiply(X,multiply(Y,Y))),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[right_alternative,100,theory(equality)]),100,theory(equality)]) ).

cnf(342,plain,
    add(additive_inverse(multiply(X,multiply(Y,Y))),multiply(multiply(X,Y),Y)) = additive_identity,
    inference('PARAMODULATE',[status(thm)],[left_additive_inverse,105,theory(equality)]) ).

cnf(343,plain,
    add(additive_inverse(multiply(X,multiply(Y,Y))),add(multiply(multiply(X,Y),Y),Z)) = add(additive_identity,Z),
    inference('EMBED',[status(thm)],[342]) ).

cnf(2629,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)],[342,distribute1,theory(equality)]),distribute1,distribute2,theory(equality)]) ).

cnf(2671,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)],[72,343,theory(equality)]),left_additive_identity,theory(equality)]) ).

cnf(2673,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)],[2629,2671,theory(equality)]) ).

cnf(2675,plain,
    $false,
    inference('REWRITE',[status(thm)],[73,2673,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : RNG025-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : run-snark %s %d
% 0.13/0.34  % Computer : n020.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon May 30 21:00:39 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.48  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.49  * 
% 0.20/0.49  * 
% 0.20/0.50  #<PACKAGE "SNARK-USER">
% 0.20/0.50  * 
% 0.20/0.50  SNARK-TPTP-OPTIONS
% 0.20/0.50  * 
% 0.20/0.50  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.50   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.50   (USE-FACTORING :POS)
% 0.20/0.50   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.50   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.50   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.50   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.50   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.50   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.50   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.50   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.50   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.50   (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.50  * 
% 0.20/0.50  "."
% 0.20/0.50  * 
% 0.20/0.50  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-30T21:00:39
% 0.20/0.50  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n020.cluster.edu at 2022-05-30T21:00:39
% 0.20/0.52  
% 0.20/0.52  ; Recognized left identity assertion (= (|add| |additive_identity| ?X) ?X).
% 0.20/0.52  ; Recognized right identity assertion (= (|add| ?X |additive_identity|) ?X).
% 0.20/0.52  ; Recognized possible left inverse assertion (= (|add| (|additive_inverse| ?X) ?X) |additive_identity|).
% 0.20/0.52  ; Recognized possible right inverse assertion (= (|add| ?X (|additive_inverse| ?X)) |additive_identity|).
% 0.20/0.52  ; Recognized commutativity assertion (= (|add| ?X ?Y) (|add| ?Y ?X)).
% 0.20/0.52  ; Recognized associativity assertion (= (|add| ?X (|add| ?Y ?Z)) (|add| (|add| ?X ?Y) ?Z)).
% 0.20/0.52  ; Declaring add to be commutative.
% 16.82/17.05  ; Declaring add to be associative-commutative.
% 16.82/17.05  
% 16.82/17.05  #||
% 16.82/17.05  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.82/17.05  % SZS output start Refutation
% See solution above
% 16.82/17.06  ||#
% 16.82/17.06  
% 16.82/17.06  ; Summary of computation:
% 16.82/17.06  ;      9386 formulas have been input or derived (from 108 formulas).
% 16.82/17.06  ;      2675 (28%) were retained.  Of these,
% 16.82/17.06  ;          262 (10%) were simplified or subsumed later,
% 16.82/17.06  ;         2413 (90%) are still being kept.
% 16.82/17.06  ; 
% 16.82/17.06  ; Run time in seconds excluding printing time:
% 16.82/17.06  ;     0.003   0%   Read assertion file          (1 call)
% 16.82/17.06  ;     0.001   0%   Assert                       (16 calls)
% 16.82/17.06  ;     0.695   4%   Process new row              (9,131 calls)
% 16.82/17.06  ;     0.018   0%   Resolution                   (214 calls)
% 16.82/17.06  ;     0.317   2%   Paramodulation               (107 calls)
% 16.82/17.06  ;     0.012   0%   Embedding                    (884 calls)
% 16.82/17.06  ;    12.426  75%   Forward simplification       (8,027 calls)
% 16.82/17.06  ;     0.791   5%   Backward simplification      (1,832 calls)
% 16.82/17.06  ;     1.203   7%   Ordering                     (101,857 calls)
% 16.82/17.06  ;     0.951   6%   Ordering ac                  (30,737 calls)
% 16.82/17.06  ;     0.000   0%   Sortal reasoning             (32 calls)
% 16.82/17.06  ;     0.000   0%   Purity testing               (1 call)
% 16.82/17.06  ;     0.105   1%   Other
% 16.82/17.06  ;    16.522        Total
% 16.82/17.06  ;    16.553        Real time
% 16.82/17.06  ; 
% 16.82/17.06  ; Term-hash-array has 8,582 terms in all.
% 16.82/17.06  ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 16.82/17.06  ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 16.82/17.06  ; Path-index has 7,951 entries (7,973 at peak, 8,787 added, 836 deleted).
% 16.82/17.06  ; Path-index has 4,670 nodes (4,715 at peak, 5,075 added, 405 deleted).
% 16.82/17.06  ; Trie-index has 7,951 entries (7,973 at peak, 8,787 added, 836 deleted).
% 16.82/17.06  ; Trie-index has 13,271 nodes (13,295 at peak, 14,088 added, 817 deleted).
% 16.82/17.06  ; Retrieved 6,816,303 generalization terms in 121,520 calls.
% 16.82/17.06  ; Retrieved 61,169 instance terms in 3,535 calls.
% 16.82/17.06  ; Retrieved 67,223 unifiable terms in 692 calls.
% 16.82/17.06  ; 
% 16.82/17.06  ; The agenda of backward simplifiable rows to process has 3 entries:
% 16.82/17.06  ;     3 with value 0
% 16.82/17.06  ; The agenda of rows to process has 119 entries:
% 16.82/17.06  ;    11 with value 30             14 with value 35              17 with value 40
% 16.82/17.06  ;     6 with value 31             22 with value 36               2 with value 41
% 16.82/17.06  ;     3 with value 32              3 with value 37              10 with value 42
% 16.82/17.06  ;     5 with value 33              3 with value 38               5 with value 43
% 16.82/17.06  ;     6 with value 34             11 with value 39               1 with value 44
% 16.82/17.06  ; The agenda of rows to give has 2312 entries:
% 16.82/17.06  ;     8 with value (4 23)        154 with value (4 42)           4 with value (4 65)
% 16.82/17.06  ;    39 with value (4 24)         14 with value (4 43)           2 with value (4 67)
% 16.82/17.06  ;     8 with value (4 25)         58 with value (4 44)           2 with value (4 68)
% 16.82/17.06  ;    22 with value (4 26)          8 with value (4 45)          20 with value (4 70)
% 16.82/17.06  ;    34 with value (4 27)          4 with value (4 46)          12 with value (4 71)
% 16.82/17.06  ;   104 with value (4 28)         58 with value (4 47)          16 with value (4 72)
% 16.82/17.06  ;    42 with value (4 29)          2 with value (4 48)           8 with value (4 73)
% 16.82/17.06  ;    74 with value (4 30)         28 with value (4 49)           6 with value (4 78)
% 16.82/17.06  ;   172 with value (4 31)         10 with value (4 50)           2 with value (4 79)
% 16.82/17.06  ;   155 with value (4 32)         64 with value (4 51)           2 with value (4 88)
% 16.82/17.06  ;   173 with value (4 33)         12 with value (4 52)           2 with value (4 91)
% 16.82/17.06  ;    81 with value (4 34)          4 with value (4 53)           2 with value (4 108)
% 16.82/17.06  ;    12 with value (4 35)         10 with value (4 56)           4 with value (4 109)
% 16.82/17.06  ;    36 with value (4 36)          8 with value (4 57)           4 with value (4 129)
% 16.82/17.06  ;    46 with value (4 37)          8 with value (4 58)           8 with value (4 134)
% 16.82/17.06  ;   142 with value (4 38)          2 with value (4 62)           4 with value (4 180)
% 16.82/17.06  ;   226 with value (4 39)          8 with value (4 63)           2 with value (4 312)
% 16.82/17.06  ;   143 with value (4 40)          4 with value (4 64)           6 with value (4 313)
% 16.82/17.06  ;   233 with value (4 41)
% 16.82/17.06  Evaluation took:
% 16.82/17.06    16.554 seconds of real time
% 16.82/17.06    16.11564 seconds of user run time
% 16.82/17.06    0.411683 seconds of system run time
% 16.82/17.06    [Run times include 0.417 seconds GC run time.]
% 16.82/17.06    0 calls to %EVAL
% 16.82/17.06    0 page faults and
% 16.82/17.06    339,088,200 bytes consed.
% 16.82/17.06  :PROOF-FOUND
% 16.82/17.06  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-30T21:00:55
% 16.82/17.06  :PROOF-FOUND
% 16.82/17.06  * 
%------------------------------------------------------------------------------