TSTP Solution File: RNG004-2 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : RNG004-2 : 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 20:40:31 EDT 2022

% Result   : Unsatisfiable 0.91s 1.09s
% Output   : Refutation 0.91s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   20 (  17 unt;   0 nHn;  17 RR)
%            Number of literals    :   30 (   5 equ;  12 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   22 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(additive_identity1,axiom,
    sum(additive_identity,X,X),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).

cnf(closure_of_multiplication,axiom,
    product(X,Y,multiply(X,Y)),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',closure_of_multiplication) ).

cnf(left_inverse,axiom,
    sum(additive_inverse(X),X,additive_identity),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',left_inverse) ).

cnf(distributivity1,axiom,
    ( ~ product(X,Y,Z)
    | ~ product(X,U,V)
    | ~ sum(Y,U,W)
    | ~ product(X,W,X1)
    | sum(Z,V,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity1) ).

cnf(distributivity3,axiom,
    ( ~ product(X,Y,Z)
    | ~ product(U,Y,V)
    | ~ sum(X,U,W)
    | ~ product(W,Y,X1)
    | sum(Z,V,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity3) ).

cnf(cancellation1,axiom,
    ( ~ sum(X,Y,Z)
    | ~ sum(X,U,Z)
    | Y = U ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation1) ).

cnf(a_times_b,hypothesis,
    product(a,b,c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).

cnf(a_inverse_times_b_inverse,hypothesis,
    product(additive_inverse(a),additive_inverse(b),d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_inverse_times_b_inverse) ).

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

cnf(29,plain,
    ~ sum(additive_inverse(c),d,additive_identity),
    inference('UR-RESOLVE',[status(thm)],[cancellation1,left_inverse,prove_c_equals_d]) ).

cnf(46,plain,
    sum(c,multiply(a,additive_identity),c),
    inference('HYPERRESOLVE',[status(thm)],[distributivity1,a_times_b,closure_of_multiplication,additive_identity1,a_times_b]) ).

cnf(49,plain,
    sum(c,multiply(a,additive_inverse(b)),multiply(a,additive_identity)),
    inference('HYPERRESOLVE',[status(thm)],[distributivity1,a_times_b,closure_of_multiplication,left_inverse,closure_of_multiplication]) ).

cnf(69,plain,
    sum(d,multiply(additive_identity,additive_inverse(b)),d),
    inference('HYPERRESOLVE',[status(thm)],[distributivity3,a_inverse_times_b_inverse,closure_of_multiplication,additive_identity1,a_inverse_times_b_inverse]) ).

cnf(73,plain,
    sum(d,multiply(a,additive_inverse(b)),multiply(additive_identity,additive_inverse(b))),
    inference('HYPERRESOLVE',[status(thm)],[distributivity3,a_inverse_times_b_inverse,closure_of_multiplication,left_inverse,closure_of_multiplication]) ).

cnf(132,plain,
    multiply(a,additive_identity) = additive_identity,
    inference('HYPERRESOLVE',[status(thm)],[cancellation1,46,additive_identity1]) ).

cnf(133,plain,
    sum(c,multiply(a,additive_inverse(b)),additive_identity),
    inference('REWRITE',[status(thm)],[49,132,theory(equality)]) ).

cnf(516,plain,
    multiply(additive_identity,additive_inverse(b)) = additive_identity,
    inference('HYPERRESOLVE',[status(thm)],[cancellation1,69,additive_identity1]) ).

cnf(517,plain,
    sum(d,multiply(a,additive_inverse(b)),additive_identity),
    inference('REWRITE',[status(thm)],[73,516,theory(equality)]) ).

cnf(612,plain,
    multiply(a,additive_inverse(b)) = additive_inverse(c),
    inference('HYPERRESOLVE',[status(thm)],[cancellation1,133,left_inverse]) ).

cnf(615,plain,
    $false,
    inference('REWRITE',[status(thm)],[517,29,612,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : RNG004-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13  % Command  : run-snark %s %d
% 0.12/0.34  % Computer : n024.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Mon May 30 22:19:36 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.45  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46  * 
% 0.19/0.46  * 
% 0.19/0.47  #<PACKAGE "SNARK-USER">
% 0.19/0.47  * 
% 0.19/0.47  SNARK-TPTP-OPTIONS
% 0.19/0.47  * 
% 0.19/0.47  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.47   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.47   (USE-FACTORING :POS)
% 0.19/0.47   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.47   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.47   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.47   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.47   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.47   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.47   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.47   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.47   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.47   (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.47  * 
% 0.19/0.47  "."
% 0.19/0.47  * 
% 0.19/0.47  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-30T22:19:36
% 0.19/0.47  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n024.cluster.edu at 2022-05-30T22:19:36
% 0.19/0.48  
% 0.19/0.48  ; Recognized possible left identity assertion (|sum| |additive_identity| ?X ?X).
% 0.19/0.48  ; Recognized possible right identity assertion (|sum| ?X |additive_identity| ?X).
% 0.19/0.48  ; Recognized relation function assertion (|product| ?X ?Y (|multiply| ?X ?Y)).
% 0.19/0.48  ; Recognized relation function assertion (|sum| ?X ?Y (|add| ?X ?Y)).
% 0.19/0.48  ; Recognized possible left inverse assertion (|sum| (|additive_inverse| ?X) ?X |additive_identity|).
% 0.19/0.48  ; Recognized possible right inverse assertion (|sum| ?X (|additive_inverse| ?X) |additive_identity|).
% 0.19/0.49  ; Recognized possible associativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?Y ?U ?V)) (NOT (|sum| ?Z ?U ?W)) (|sum| ?X ?V ?W)).
% 0.19/0.49  ; Recognized possible associativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?Y ?U ?V)) (NOT (|sum| ?X ?V ?W)) (|sum| ?Z ?U ?W)).
% 0.19/0.49  ; Recognized commutativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (|sum| ?Y ?X ?Z)).
% 0.19/0.49  ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?Z ?U ?W)) (|product| ?X ?V ?W)).
% 0.19/0.49  ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?X ?V ?W)) (|product| ?Z ?U ?W)).
% 0.19/0.49  ; Recognized relation functionality assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?X ?Y ?U)) (= ?Z ?U)).
% 0.19/0.49  ; Recognized relation functionality assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?X ?Y ?U)) (= ?Z ?U)).
% 0.19/0.49  ; Declaring sum to be commutative.
% 0.19/0.49  ; Declaring add to be commutative.
% 0.91/1.09  ; Declaring add to be associative-commutative.
% 0.91/1.09  
% 0.91/1.09  #||
% 0.91/1.09  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.91/1.09  % SZS output start Refutation
% See solution above
% 0.91/1.09  ||#
% 0.91/1.09  
% 0.91/1.09  ; Summary of computation:
% 0.91/1.09  ;     11636 formulas have been input or derived (from 55 formulas).
% 0.91/1.09  ;       615 ( 5%) were retained.  Of these,
% 0.91/1.09  ;           49 ( 8%) were simplified or subsumed later,
% 0.91/1.09  ;          566 (92%) are still being kept.
% 0.91/1.09  ; 
% 0.91/1.09  ; Run time in seconds excluding printing time:
% 0.91/1.09  ;     0.005   1%   Read assertion file          (1 call)
% 0.91/1.09  ;     0.001   0%   Assert                       (22 calls)
% 0.91/1.09  ;     0.059  10%   Process new row              (8,527 calls)
% 0.91/1.09  ;     0.295  48%   Resolution                   (108 calls)
% 0.91/1.09  ;     0.002   0%   Paramodulation               (54 calls)
% 0.91/1.09  ;     0.000   0%   Embedding                    (5 calls)
% 0.91/1.09  ;     0.000   0%   Condensing                   (12 calls)
% 0.91/1.09  ;     0.000   0%   Forward subsumption          (12 calls)
% 0.91/1.09  ;     0.000   0%   Backward subsumption         (10 calls)
% 0.91/1.09  ;     0.001   0%   Clause clause subsumption    (10 calls)
% 0.91/1.09  ;     0.185  30%   Forward simplification       (7,629 calls)
% 0.91/1.09  ;     0.018   3%   Backward simplification      (613 calls)
% 0.91/1.09  ;     0.000   0%   Ordering                     (110 calls)
% 0.91/1.09  ;     0.000   0%   Ordering ac                  (5 calls)
% 0.91/1.09  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.91/1.09  ;     0.000   0%   Purity testing               (1 call)
% 0.91/1.09  ;     0.053   9%   Other
% 0.91/1.09  ;     0.619        Total
% 0.91/1.09  ;     0.621        Real time
% 0.91/1.09  ; 
% 0.91/1.09  ; Term-hash-array has 1,149 terms in all.
% 0.91/1.09  ; Feature-vector-row-index has 10 entries (10 at peak, 10 added, 0 deleted).
% 0.91/1.09  ; Feature-vector-row-index has 13 nodes (13 at peak, 13 added, 0 deleted).
% 0.91/1.09  ;  Retrieved 7 possibly forward subsuming rows in 12 calls.
% 0.91/1.09  ;  Retrieved 4 possibly backward subsumed rows in 10 calls.
% 0.91/1.09  ; Path-index has 1,088 entries (1,098 at peak, 1,154 added, 66 deleted).
% 0.91/1.09  ; Path-index has 816 nodes (816 at peak, 829 added, 13 deleted).
% 0.91/1.09  ; Trie-index has 1,088 entries (1,098 at peak, 1,154 added, 66 deleted).
% 0.91/1.09  ; Trie-index has 1,412 nodes (1,423 at peak, 1,535 added, 123 deleted).
% 0.91/1.09  ; Retrieved 65,034 generalization terms in 30,344 calls.
% 0.91/1.09  ; Retrieved 996 instance terms in 602 calls.
% 0.91/1.09  ; Retrieved 306,439 unifiable terms in 16,314 calls.
% 0.91/1.09  ; 
% 0.91/1.09  ; The agenda of rows to process has 334 entries:
% 0.91/1.09  ;    17 with value 12             35 with value 16              30 with value 20
% 0.91/1.09  ;    10 with value 13             53 with value 17               6 with value 21
% 0.91/1.09  ;    42 with value 14             57 with value 18               1 with value 22
% 0.91/1.09  ;    45 with value 15             38 with value 19
% 0.91/1.09  ; The agenda of rows to give has 516 entries:
% 0.91/1.09  ;     1 with value (4 9)          48 with value (4 15)          76 with value (4 20)
% 0.91/1.09  ;     4 with value (4 11)         46 with value (4 16)          42 with value (4 21)
% 0.91/1.09  ;    23 with value (4 12)         77 with value (4 17)          25 with value (4 22)
% 0.91/1.09  ;    13 with value (4 13)         45 with value (4 18)          16 with value (4 23)
% 0.91/1.09  ;    41 with value (4 14)         49 with value (4 19)          10 with value (4 24)
% 0.91/1.09  Evaluation took:
% 0.91/1.09    0.621 seconds of real time
% 0.91/1.09    0.575921 seconds of user run time
% 0.91/1.09    0.044776 seconds of system run time
% 0.91/1.09    [Run times include 0.018 seconds GC run time.]
% 0.91/1.09    0 calls to %EVAL
% 0.91/1.09    0 page faults and
% 0.91/1.09    40,284,072 bytes consed.
% 0.91/1.09  :PROOF-FOUND
% 0.91/1.09  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-30T22:19:37
% 0.91/1.09  :PROOF-FOUND
% 0.91/1.09  * 
%------------------------------------------------------------------------------