TSTP Solution File: RNG004-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : RNG004-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n026.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 1.15s 1.39s
% Output   : Refutation 1.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   32 (  27 unt;   0 nHn;  25 RR)
%            Number of literals    :   49 (   5 equ;  23 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   43 (   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(closure_of_addition,axiom,
    sum(X,Y,add(X,Y)),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_addition) ).

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(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/sandbox2/benchmark/Axioms/RNG001-0.ax',distributivity3) ).

cnf(distributivity4,axiom,
    ( ~ product(X,Y,Z)
    | ~ product(U,Y,V)
    | ~ sum(X,U,W)
    | ~ sum(Z,V,X1)
    | product(W,Y,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',distributivity4) ).

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

cnf(a_inverse_times_b_inverse,hypothesis,
    product(additive_inverse(a),additive_inverse(b),d),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_inverse_times_b_inverse) ).

cnf(prove_c_equals_d,negated_conjecture,
    c != d,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_equals_d) ).

cnf(17,plain,
    ~ sum(additive_identity,d,c),
    inference('UR-RESOLVE',[status(thm)],[addition_is_well_defined,additive_identity1,prove_c_equals_d]) ).

cnf(28,plain,
    sum(additive_inverse(X),add(X,Y),Y),
    inference('HYPERRESOLVE',[status(thm)],[associativity_of_addition1,left_inverse,closure_of_addition,additive_identity1]) ).

cnf(30,plain,
    sum(X,add(additive_inverse(X),Y),Y),
    inference('HYPERRESOLVE',[status(thm)],[associativity_of_addition1,left_inverse,closure_of_addition,additive_identity1]) ).

cnf(42,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(43,plain,
    sum(d,multiply(additive_inverse(a),additive_identity),d),
    inference('HYPERRESOLVE',[status(thm)],[distributivity1,a_inverse_times_b_inverse,closure_of_multiplication,additive_identity1,a_inverse_times_b_inverse]) ).

cnf(66,plain,
    sum(c,multiply(additive_identity,b),c),
    inference('HYPERRESOLVE',[status(thm)],[distributivity3,a_times_b,closure_of_multiplication,additive_identity1,a_times_b]) ).

cnf(69,plain,
    sum(c,multiply(additive_inverse(a),b),multiply(additive_identity,b)),
    inference('HYPERRESOLVE',[status(thm)],[distributivity3,a_times_b,closure_of_multiplication,left_inverse,closure_of_multiplication]) ).

cnf(102,plain,
    sum(multiply(a,additive_identity),additive_identity,additive_identity),
    inference('HYPERRESOLVE',[status(thm)],[associativity_of_addition1,42,left_inverse,left_inverse]) ).

cnf(119,plain,
    sum(multiply(additive_identity,b),additive_identity,additive_identity),
    inference('HYPERRESOLVE',[status(thm)],[associativity_of_addition1,66,left_inverse,left_inverse]) ).

cnf(161,plain,
    ~ sum(d,X,add(c,X)),
    inference('UR-RESOLVE',[status(thm)],[associativity_of_addition1,28,left_inverse,17]) ).

cnf(232,plain,
    additive_identity = multiply(a,additive_identity),
    inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,102,additive_identity1]) ).

cnf(234,plain,
    additive_identity = multiply(additive_identity,b),
    inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,119,additive_identity1]) ).

cnf(235,plain,
    sum(c,multiply(additive_inverse(a),b),additive_identity),
    inference('REWRITE',[status(thm)],[69,234,theory(equality)]) ).

cnf(251,plain,
    ~ product(additive_inverse(a),additive_identity,add(c,multiply(additive_inverse(a),b))),
    inference('UR-RESOLVE',[status(thm)],[distributivity1,161,a_inverse_times_b_inverse,closure_of_multiplication,left_inverse]) ).

cnf(280,plain,
    product(a,additive_identity,additive_identity),
    inference('PARAMODULATE',[status(thm)],[closure_of_multiplication,232,theory(equality)]) ).

cnf(520,plain,
    sum(multiply(additive_inverse(a),additive_identity),X,X),
    inference('HYPERRESOLVE',[status(thm)],[associativity_of_addition1,43,30,30]) ).

cnf(734,plain,
    additive_identity = add(c,multiply(additive_inverse(a),b)),
    inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,235,closure_of_addition]) ).

cnf(736,plain,
    ~ product(additive_inverse(a),additive_identity,additive_identity),
    inference('REWRITE',[status(thm)],[251,734,theory(equality)]) ).

cnf(1007,plain,
    ~ product(additive_identity,additive_identity,additive_identity),
    inference('UR-RESOLVE',[status(thm)],[distributivity4,520,closure_of_multiplication,additive_identity1,736]) ).

cnf(1008,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[distributivity4,520,closure_of_multiplication,280,left_inverse]),1007]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : RNG004-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13  % Command  : run-snark %s %d
% 0.12/0.33  % Computer : n026.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon May 30 14:01:25 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.18/0.45  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.46  * 
% 0.18/0.46  * 
% 0.18/0.47  #<PACKAGE "SNARK-USER">
% 0.18/0.47  * 
% 0.18/0.47  SNARK-TPTP-OPTIONS
% 0.18/0.47  * 
% 0.18/0.47  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.18/0.47   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.18/0.47   (USE-FACTORING :POS)
% 0.18/0.47   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.18/0.47   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.18/0.47   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.18/0.47   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.18/0.47   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.18/0.47   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.18/0.47   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.18/0.47   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.18/0.47   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.18/0.47   (DECLARE-TPTP-SYMBOLS2))
% 0.18/0.47  * 
% 0.18/0.47  "."
% 0.18/0.47  * 
% 0.18/0.47  ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-05-30T14:01:25
% 0.18/0.47  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n026.cluster.edu at 2022-05-30T14:01:25
% 0.18/0.48  
% 0.18/0.48  ; Recognized possible left identity assertion (|sum| |additive_identity| ?X ?X).
% 0.18/0.48  ; Recognized possible right identity assertion (|sum| ?X |additive_identity| ?X).
% 0.18/0.48  ; Recognized relation function assertion (|product| ?X ?Y (|multiply| ?X ?Y)).
% 0.18/0.48  ; Recognized relation function assertion (|sum| ?X ?Y (|add| ?X ?Y)).
% 0.18/0.48  ; Recognized possible left inverse assertion (|sum| (|additive_inverse| ?X) ?X |additive_identity|).
% 0.18/0.48  ; Recognized possible right inverse assertion (|sum| ?X (|additive_inverse| ?X) |additive_identity|).
% 0.18/0.48  ; Recognized possible associativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?Y ?U ?V)) (NOT (|sum| ?Z ?U ?W)) (|sum| ?X ?V ?W)).
% 0.18/0.48  ; Recognized possible associativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?Y ?U ?V)) (NOT (|sum| ?X ?V ?W)) (|sum| ?Z ?U ?W)).
% 0.18/0.48  ; Recognized commutativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (|sum| ?Y ?X ?Z)).
% 0.18/0.48  ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?Z ?U ?W)) (|product| ?X ?V ?W)).
% 0.18/0.48  ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?X ?V ?W)) (|product| ?Z ?U ?W)).
% 0.18/0.48  ; Recognized relation functionality assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?X ?Y ?U)) (= ?Z ?U)).
% 0.18/0.48  ; Recognized relation functionality assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?X ?Y ?U)) (= ?Z ?U)).
% 0.18/0.48  ; Declaring sum to be commutative.
% 0.18/0.48  ; Declaring add to be commutative.
% 1.15/1.39  ; Declaring add to be associative-commutative.
% 1.15/1.39  
% 1.15/1.39  #||
% 1.15/1.39  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.15/1.39  % SZS output start Refutation
% See solution above
% 1.22/1.39  ||#
% 1.22/1.39  
% 1.22/1.39  ; Summary of computation:
% 1.22/1.39  ;     17766 formulas have been input or derived (from 69 formulas).
% 1.22/1.39  ;      1008 ( 6%) were retained.  Of these,
% 1.22/1.39  ;          107 (11%) were simplified or subsumed later,
% 1.22/1.39  ;          901 (89%) are still being kept.
% 1.22/1.39  ; 
% 1.22/1.39  ; Run time in seconds excluding printing time:
% 1.22/1.39  ;     0.005   1%   Read assertion file          (1 call)
% 1.22/1.39  ;     0.002   0%   Assert                       (20 calls)
% 1.22/1.39  ;     0.080   9%   Process new row              (11,111 calls)
% 1.22/1.39  ;     0.459  50%   Resolution                   (136 calls)
% 1.22/1.39  ;     0.001   0%   Paramodulation               (68 calls)
% 1.22/1.39  ;     0.000   0%   Embedding                    (9 calls)
% 1.22/1.39  ;     0.002   0%   Condensing                   (10 calls)
% 1.22/1.39  ;     0.000   0%   Forward subsumption          (10 calls)
% 1.22/1.39  ;     0.000   0%   Backward subsumption         (9 calls)
% 1.22/1.39  ;     0.002   0%   Clause clause subsumption    (7 calls)
% 1.22/1.39  ;     0.296  32%   Forward simplification       (10,147 calls)
% 1.22/1.39  ;     0.025   3%   Backward simplification      (1,002 calls)
% 1.22/1.39  ;     0.000   0%   Ordering                     (145 calls)
% 1.22/1.39  ;     0.001   0%   Ordering ac                  (6 calls)
% 1.22/1.39  ;     0.000   0%   Sortal reasoning             (32 calls)
% 1.22/1.39  ;     0.000   0%   Purity testing               (1 call)
% 1.22/1.39  ;     0.046   5%   Other
% 1.22/1.39  ;     0.919        Total
% 1.22/1.39  ;     0.922        Real time
% 1.22/1.39  ; 
% 1.22/1.39  ; Term-hash-array has 1,734 terms in all.
% 1.22/1.39  ; Feature-vector-row-index has 9 entries (9 at peak, 9 added, 0 deleted).
% 1.22/1.39  ; Feature-vector-row-index has 13 nodes (13 at peak, 13 added, 0 deleted).
% 1.22/1.39  ;  Retrieved 4 possibly forward subsuming rows in 10 calls.
% 1.22/1.39  ;  Retrieved 3 possibly backward subsumed rows in 9 calls.
% 1.22/1.39  ; Path-index has 1,593 entries (1,593 at peak, 1,739 added, 146 deleted).
% 1.22/1.39  ; Path-index has 1,177 nodes (1,177 at peak, 1,279 added, 102 deleted).
% 1.22/1.39  ; Trie-index has 1,593 entries (1,593 at peak, 1,739 added, 146 deleted).
% 1.22/1.39  ; Trie-index has 2,118 nodes (2,118 at peak, 2,371 added, 253 deleted).
% 1.22/1.39  ; Retrieved 112,012 generalization terms in 42,595 calls.
% 1.22/1.39  ; Retrieved 1,505 instance terms in 992 calls.
% 1.22/1.39  ; Retrieved 511,678 unifiable terms in 22,350 calls.
% 1.22/1.39  ; 
% 1.22/1.39  ; The agenda of rows to process has 2458 entries:
% 1.22/1.39  ;    24 with value 10            253 with value 16             299 with value 21
% 1.22/1.39  ;    36 with value 11            165 with value 17             106 with value 22
% 1.22/1.39  ;    49 with value 12            301 with value 18              36 with value 23
% 1.22/1.39  ;   226 with value 13            379 with value 19              52 with value 24
% 1.22/1.39  ;    49 with value 14            281 with value 20              16 with value 25
% 1.22/1.39  ;   186 with value 15
% 1.22/1.39  ; The agenda of rows to give has 840 entries:
% 1.22/1.39  ;     1 with value (4 9)          63 with value (4 16)         112 with value (4 21)
% 1.22/1.39  ;     9 with value (4 12)         93 with value (4 17)          55 with value (4 22)
% 1.22/1.39  ;    28 with value (4 13)         95 with value (4 18)          26 with value (4 23)
% 1.22/1.39  ;    46 with value (4 14)        101 with value (4 19)          16 with value (4 24)
% 1.22/1.39  ;    67 with value (4 15)        128 with value (4 20)
% 1.22/1.39  Evaluation took:
% 1.22/1.39    0.922 seconds of real time
% 1.22/1.39    0.879912 seconds of user run time
% 1.22/1.39    0.042206 seconds of system run time
% 1.22/1.39    [Run times include 0.026 seconds GC run time.]
% 1.22/1.39    0 calls to %EVAL
% 1.22/1.39    0 page faults and
% 1.22/1.39    62,034,040 bytes consed.
% 1.22/1.39  :PROOF-FOUND
% 1.22/1.39  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-05-30T14:01:26
% 1.22/1.39  :PROOF-FOUND
% 1.22/1.39  * 
%------------------------------------------------------------------------------