TSTP Solution File: RNG006-3 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : RNG006-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n025.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 0.59s 0.77s
% Output   : Refutation 0.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   20 (  16 unt;   0 nHn;  17 RR)
%            Number of literals    :   33 (   2 equ;  15 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :   28 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(additive_identity1,axiom,
    sum(additive_identity,X,X),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).

cnf(closure_of_multiplication,axiom,
    product(X,Y,multiply(X,Y)),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_multiplication) ).

cnf(left_inverse,axiom,
    sum(additive_inverse(X),X,additive_identity),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',left_inverse) ).

cnf(associativity_of_addition1,axiom,
    ( ~ sum(X,Y,Z)
    | ~ sum(Y,U,V)
    | ~ sum(Z,U,W)
    | sum(X,V,W) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',associativity_of_addition1) ).

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/sandbox2/benchmark/Axioms/RNG001-0.ax',distributivity1) ).

cnf(distributivity2,axiom,
    ( ~ product(X,Y,Z)
    | ~ product(X,U,V)
    | ~ sum(Y,U,W)
    | ~ sum(Z,V,X1)
    | product(X,W,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',distributivity2) ).

cnf(addition_is_well_defined,axiom,
    ( ~ sum(X,Y,Z)
    | ~ sum(X,Y,U)
    | Z = U ),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',addition_is_well_defined) ).

cnf(b_plus_inverse_c,hypothesis,
    sum(b,additive_inverse(c),bS_Ic),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_plus_inverse_c) ).

cnf(a_times_b,hypothesis,
    product(a,b,aPb),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).

cnf(a_times_c,hypothesis,
    product(a,c,aPc),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c) ).

cnf(aPb_plus_IaPc,hypothesis,
    sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aPb_plus_IaPc) ).

cnf(prove_a_times_bS_Ic_is_aPb_S__IaPc,negated_conjecture,
    ~ product(a,bS_Ic,aPb_S_IaPc),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_times_bS_Ic_is_aPb_S__IaPc) ).

cnf(30,plain,
    sum(c,bS_Ic,b),
    inference('HYPERRESOLVE',[status(thm)],[associativity_of_addition1,left_inverse,b_plus_inverse_c,additive_identity1]) ).

cnf(64,plain,
    sum(aPc,multiply(a,additive_identity),aPc),
    inference('HYPERRESOLVE',[status(thm)],[distributivity1,a_times_c,closure_of_multiplication,additive_identity1,a_times_c]) ).

cnf(84,plain,
    ~ sum(multiply(a,additive_identity),multiply(a,bS_Ic),aPb_S_IaPc),
    inference('UR-RESOLVE',[status(thm)],[distributivity2,closure_of_multiplication,closure_of_multiplication,additive_identity1,prove_a_times_bS_Ic_is_aPb_S__IaPc]) ).

cnf(139,plain,
    sum(aPc,multiply(a,bS_Ic),aPb),
    inference('HYPERRESOLVE',[status(thm)],[distributivity1,30,a_times_c,closure_of_multiplication,a_times_b]) ).

cnf(178,plain,
    sum(multiply(a,additive_identity),additive_identity,additive_identity),
    inference('HYPERRESOLVE',[status(thm)],[associativity_of_addition1,64,left_inverse,left_inverse]) ).

cnf(361,plain,
    sum(multiply(a,bS_Ic),additive_identity,aPb_S_IaPc),
    inference('HYPERRESOLVE',[status(thm)],[associativity_of_addition1,139,left_inverse,aPb_plus_IaPc]) ).

cnf(389,plain,
    additive_identity = multiply(a,additive_identity),
    inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,178,additive_identity1]) ).

cnf(392,plain,
    $false,
    inference('REWRITE',[status(thm)],[84,361,389,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : RNG006-3 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13  % Command  : run-snark %s %d
% 0.12/0.34  % Computer : n025.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 19:07:42 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.46  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.47  * 
% 0.19/0.47  * 
% 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/sandbox2/benchmark/theBenchmark.p 2022-05-30T19:07:42
% 0.19/0.48  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n025.cluster.edu at 2022-05-30T19:07:42
% 0.19/0.49  
% 0.19/0.49  ; Recognized possible left identity assertion (|sum| |additive_identity| ?X ?X).
% 0.19/0.49  ; Recognized possible right identity assertion (|sum| ?X |additive_identity| ?X).
% 0.19/0.49  ; Recognized relation function assertion (|product| ?X ?Y (|multiply| ?X ?Y)).
% 0.19/0.49  ; Recognized relation function assertion (|sum| ?X ?Y (|add| ?X ?Y)).
% 0.19/0.49  ; Recognized possible left inverse assertion (|sum| (|additive_inverse| ?X) ?X |additive_identity|).
% 0.19/0.49  ; 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)).
% 0.19/0.50  ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?X ?V ?W)) (|product| ?Z ?U ?W)).
% 0.19/0.50  ; Recognized relation functionality assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?X ?Y ?U)) (= ?Z ?U)).
% 0.19/0.50  ; Recognized relation functionality assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?X ?Y ?U)) (= ?Z ?U)).
% 0.19/0.50  ; Declaring sum to be commutative.
% 0.19/0.50  ; Declaring add to be commutative.
% 0.59/0.77  ; Declaring add to be associative-commutative.
% 0.59/0.77  
% 0.59/0.77  #||
% 0.59/0.77  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.59/0.77  % SZS output start Refutation
% See solution above
% 0.59/0.78  ||#
% 0.59/0.78  
% 0.59/0.78  ; Summary of computation:
% 0.59/0.78  ;      5786 formulas have been input or derived (from 47 formulas).
% 0.59/0.78  ;       392 ( 7%) were retained.  Of these,
% 0.59/0.78  ;           88 (22%) were simplified or subsumed later,
% 0.59/0.78  ;          304 (78%) are still being kept.
% 0.59/0.78  ; 
% 0.59/0.78  ; Run time in seconds excluding printing time:
% 0.59/0.78  ;     0.005   2%   Read assertion file          (1 call)
% 0.59/0.78  ;     0.001   0%   Assert                       (22 calls)
% 0.59/0.78  ;     0.040  14%   Process new row              (3,410 calls)
% 0.59/0.78  ;     0.123  42%   Resolution                   (92 calls)
% 0.59/0.78  ;     0.014   5%   Paramodulation               (46 calls)
% 0.59/0.78  ;     0.001   0%   Embedding                    (20 calls)
% 0.59/0.78  ;     0.003   1%   Condensing                   (10 calls)
% 0.59/0.78  ;     0.000   0%   Forward subsumption          (10 calls)
% 0.59/0.78  ;     0.000   0%   Backward subsumption         (9 calls)
% 0.59/0.78  ;     0.000   0%   Clause clause subsumption    (7 calls)
% 0.59/0.78  ;     0.065  22%   Forward simplification       (3,391 calls)
% 0.59/0.78  ;     0.006   2%   Backward simplification      (373 calls)
% 0.59/0.78  ;     0.000   0%   Ordering                     (196 calls)
% 0.59/0.78  ;     0.000   0%   Ordering ac                  (65 calls)
% 0.59/0.78  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.59/0.78  ;     0.000   0%   Purity testing               (1 call)
% 0.59/0.78  ;     0.037  13%   Other
% 0.59/0.78  ;     0.295        Total
% 0.59/0.78  ;     0.298        Real time
% 0.59/0.78  ; 
% 0.59/0.78  ; Term-hash-array has 707 terms in all.
% 0.59/0.78  ; Feature-vector-row-index has 9 entries (9 at peak, 9 added, 0 deleted).
% 0.59/0.78  ; Feature-vector-row-index has 13 nodes (13 at peak, 13 added, 0 deleted).
% 0.59/0.78  ;  Retrieved 4 possibly forward subsuming rows in 10 calls.
% 0.59/0.78  ;  Retrieved 3 possibly backward subsumed rows in 9 calls.
% 0.59/0.78  ; Path-index has 584 entries (650 at peak, 717 added, 133 deleted).
% 0.59/0.78  ; Path-index has 599 nodes (614 at peak, 657 added, 58 deleted).
% 0.59/0.78  ; Trie-index has 584 entries (650 at peak, 717 added, 133 deleted).
% 0.59/0.78  ; Trie-index has 915 nodes (960 at peak, 1,025 added, 110 deleted).
% 0.59/0.78  ; Retrieved 30,256 generalization terms in 9,546 calls.
% 0.59/0.78  ; Retrieved 550 instance terms in 363 calls.
% 0.59/0.78  ; Retrieved 97,955 unifiable terms in 9,471 calls.
% 0.59/0.78  ; 
% 0.59/0.78  ; The agenda of backward simplifiable rows to process has 38 entries:
% 0.59/0.78  ;    38 with value 0
% 0.59/0.78  ; The agenda of rows to process has 176 entries:
% 0.59/0.78  ;    10 with value 10             18 with value 14               8 with value 17
% 0.59/0.78  ;    30 with value 11             30 with value 15               4 with value 18
% 0.59/0.78  ;     7 with value 12             32 with value 16               4 with value 19
% 0.59/0.78  ;    33 with value 13
% 0.59/0.78  ; The agenda of rows to give has 260 entries:
% 0.59/0.78  ;     6 with value (4 10)         43 with value (4 14)          19 with value (4 18)
% 0.59/0.78  ;    22 with value (4 11)         47 with value (4 15)          12 with value (4 19)
% 0.59/0.78  ;    34 with value (4 12)         39 with value (4 16)           2 with value (4 20)
% 0.59/0.78  ;    17 with value (4 13)         19 with value (4 17)
% 0.59/0.78  Evaluation took:
% 0.59/0.78    0.298 seconds of real time
% 0.59/0.78    0.277735 seconds of user run time
% 0.59/0.78    0.020066 seconds of system run time
% 0.59/0.78    [Run times include 0.008 seconds GC run time.]
% 0.59/0.78    0 calls to %EVAL
% 0.59/0.78    0 page faults and
% 0.59/0.78    17,433,256 bytes consed.
% 0.59/0.78  :PROOF-FOUND
% 0.59/0.78  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-05-30T19:07:43
% 0.59/0.78  :PROOF-FOUND
% 0.59/0.78  * 
%------------------------------------------------------------------------------