TSTP Solution File: RNG008-3 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : RNG008-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n024.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 20:40:32 EDT 2022

% Result   : Unsatisfiable 0.53s 0.71s
% Output   : Refutation 0.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   17 (  17 unt;   0 nHn;   4 RR)
%            Number of literals    :   17 (  16 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    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   21 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
    add(additive_identity,X) = X,
    file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',left_identity) ).

cnf(left_additive_inverse,axiom,
    add(additive_inverse(X),X) = additive_identity,
    file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',left_additive_inverse) ).

cnf(distribute1,axiom,
    multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',distribute1) ).

cnf(distribute2,axiom,
    multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',distribute2) ).

cnf(additive_inverse_additive_inverse,axiom,
    additive_inverse(additive_inverse(X)) = X,
    file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',additive_inverse_additive_inverse) ).

cnf(multiply_additive_inverse1,axiom,
    multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',multiply_additive_inverse1) ).

cnf(multiply_additive_inverse2,axiom,
    multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',multiply_additive_inverse2) ).

cnf(boolean_ring,hypothesis,
    multiply(X,X) = X,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',boolean_ring) ).

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

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

cnf(20,plain,
    X = additive_inverse(X),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[boolean_ring,multiply_additive_inverse1,theory(equality)]),additive_inverse_additive_inverse,boolean_ring,multiply_additive_inverse2,theory(equality)]) ).

cnf(21,plain,
    add(X,X) = additive_identity,
    inference('REWRITE',[status(thm)],[left_additive_inverse,20,theory(equality)]) ).

cnf(22,plain,
    add(X,add(X,Y)) = add(additive_identity,Y),
    inference('EMBED',[status(thm)],[21]) ).

cnf(32,plain,
    add(X,add(multiply(Y,X),add(multiply(X,Y),Y))) = add(X,Y),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[boolean_ring,distribute1,theory(equality)]),boolean_ring,distribute2,theory(equality)]) ).

cnf(129,plain,
    add(b,add(c,add(multiply(b,a),a))) = add(b,a),
    inference('PARAMODULATE',[status(thm)],[32,a_times_b_is_c,theory(equality)]) ).

cnf(130,plain,
    add(b,add(c,add(multiply(b,a),add(a,X)))) = add(b,add(a,X)),
    inference('EMBED',[status(thm)],[129]) ).

cnf(206,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[22,130,theory(equality)]),prove_commutativity,left_identity,21,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : RNG008-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : run-snark %s %d
% 0.13/0.34  % Computer : n024.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 18:45:36 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.47  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.48  * 
% 0.19/0.48  * 
% 0.19/0.48  #<PACKAGE "SNARK-USER">
% 0.19/0.48  * 
% 0.19/0.48  SNARK-TPTP-OPTIONS
% 0.19/0.48  * 
% 0.19/0.48  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.48   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.48   (USE-FACTORING :POS)
% 0.19/0.48   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.48   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.48   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.48   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.48   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.48   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.48   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.48   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.48   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.48   (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.48  * 
% 0.19/0.48  "."
% 0.19/0.48  * 
% 0.19/0.48  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-30T18:45:36
% 0.19/0.48  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n024.cluster.edu at 2022-05-30T18:45:36
% 0.19/0.50  
% 0.19/0.50  ; Recognized left identity assertion (= (|add| |additive_identity| ?X) ?X).
% 0.19/0.50  ; Recognized possible left inverse assertion (= (|add| (|additive_inverse| ?X) ?X) |additive_identity|).
% 0.19/0.50  ; Recognized associativity assertion (= (|add| (|add| ?X ?Y) ?Z) (|add| ?X (|add| ?Y ?Z))).
% 0.19/0.50  ; Recognized commutativity assertion (= (|add| ?X ?Y) (|add| ?Y ?X)).
% 0.19/0.50  ; Recognized associativity assertion (= (|multiply| (|multiply| ?X ?Y) ?Z) (|multiply| ?X (|multiply| ?Y ?Z))).
% 0.19/0.50  ; Recognized right identity assertion (= (|add| ?X |additive_identity|) ?X).
% 0.19/0.50  ; Recognized possible right inverse assertion (= (|add| ?X (|additive_inverse| ?X)) |additive_identity|).
% 0.19/0.50  ; Declaring add to be commutative.
% 0.53/0.71  ; Declaring add to be associative-commutative.
% 0.53/0.71  
% 0.53/0.71  #||
% 0.53/0.71  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.53/0.71  % SZS output start Refutation
% See solution above
% 0.53/0.71  ||#
% 0.53/0.71  
% 0.53/0.71  ; Summary of computation:
% 0.53/0.71  ;      1145 formulas have been input or derived (from 44 formulas).
% 0.53/0.71  ;       206 (18%) were retained.  Of these,
% 0.53/0.71  ;           46 (22%) were simplified or subsumed later,
% 0.53/0.71  ;          160 (78%) are still being kept.
% 0.53/0.71  ; 
% 0.53/0.71  ; Run time in seconds excluding printing time:
% 0.53/0.71  ;     0.003   1%   Read assertion file          (1 call)
% 0.53/0.71  ;     0.001   0%   Assert                       (19 calls)
% 0.53/0.71  ;     0.026  12%   Process new row              (939 calls)
% 0.53/0.71  ;     0.000   0%   Resolution                   (86 calls)
% 0.53/0.71  ;     0.019   8%   Paramodulation               (43 calls)
% 0.53/0.71  ;     0.000   0%   Embedding                    (50 calls)
% 0.53/0.71  ;     0.119  53%   Forward simplification       (815 calls)
% 0.53/0.71  ;     0.002   1%   Backward simplification      (159 calls)
% 0.53/0.71  ;     0.020   9%   Ordering                     (4,143 calls)
% 0.53/0.71  ;     0.007   3%   Ordering ac                  (309 calls)
% 0.53/0.71  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.53/0.71  ;     0.000   0%   Purity testing               (1 call)
% 0.53/0.71  ;     0.028  12%   Other
% 0.53/0.71  ;     0.225        Total
% 0.53/0.71  ;     0.226        Real time
% 0.53/0.71  ; 
% 0.53/0.71  ; Term-hash-array has 583 terms in all.
% 0.53/0.71  ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.53/0.71  ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.53/0.71  ; Path-index has 476 entries (476 at peak, 591 added, 115 deleted).
% 0.53/0.71  ; Path-index has 257 nodes (257 at peak, 279 added, 22 deleted).
% 0.53/0.71  ; Trie-index has 476 entries (476 at peak, 591 added, 115 deleted).
% 0.53/0.71  ; Trie-index has 968 nodes (968 at peak, 1,182 added, 214 deleted).
% 0.53/0.71  ; Retrieved 64,138 generalization terms in 7,947 calls.
% 0.53/0.71  ; Retrieved 681 instance terms in 238 calls.
% 0.53/0.71  ; Retrieved 2,088 unifiable terms in 263 calls.
% 0.53/0.71  ; 
% 0.53/0.71  ; The agenda of rows to process has 181 entries:
% 0.53/0.71  ;    13 with value 21             32 with value 35               2 with value 48
% 0.53/0.71  ;    17 with value 25              1 with value 40              28 with value 49
% 0.53/0.71  ;     4 with value 30             12 with value 41              16 with value 57
% 0.53/0.71  ;    56 with value 31
% 0.53/0.71  ; The agenda of rows to give has 127 entries:
% 0.53/0.71  ;     7 with value (4 19)          9 with value (4 26)           8 with value (4 32)
% 0.53/0.71  ;     7 with value (4 20)          4 with value (4 27)           8 with value (4 33)
% 0.53/0.71  ;     4 with value (4 21)          9 with value (4 28)           8 with value (4 34)
% 0.53/0.71  ;     8 with value (4 22)          8 with value (4 29)           6 with value (4 36)
% 0.53/0.71  ;     2 with value (4 23)          1 with value (4 30)           4 with value (4 38)
% 0.53/0.71  ;    24 with value (4 24)          4 with value (4 31)           2 with value (4 46)
% 0.53/0.71  ;     4 with value (4 25)
% 0.53/0.71  Evaluation took:
% 0.53/0.71    0.227 seconds of real time
% 0.53/0.71    0.205228 seconds of user run time
% 0.53/0.71    0.021897 seconds of system run time
% 0.53/0.71    0 calls to %EVAL
% 0.53/0.71    0 page faults and
% 0.53/0.71    12,212,096 bytes consed.
% 0.53/0.71  :PROOF-FOUND
% 0.53/0.71  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-30T18:45:36
% 0.53/0.71  :PROOF-FOUND
% 0.53/0.71  * 
%------------------------------------------------------------------------------