TSTP Solution File: BOO014-3 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : BOO014-3 : TPTP v8.1.0. Bugfixed v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n017.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 : Thu Jul 14 23:48:56 EDT 2022

% Result   : Unsatisfiable 6.53s 6.77s
% Output   : Refutation 6.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   16
% Syntax   : Number of clauses     :   42 (  35 unt;   0 nHn;  28 RR)
%            Number of literals    :   66 (   9 equ;  27 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    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :   57 (   5 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(closure_of_addition,axiom,
    sum(X,Y,add(X,Y)),
    file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',closure_of_addition) ).

cnf(closure_of_multiplication,axiom,
    product(X,Y,multiply(X,Y)),
    file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',closure_of_multiplication) ).

cnf(additive_identity1,axiom,
    sum(additive_identity,X,X),
    file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_identity1) ).

cnf(multiplicative_identity1,axiom,
    product(multiplicative_identity,X,X),
    file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_identity1) ).

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/BOO002-0.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/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity2) ).

cnf(distributivity5,axiom,
    ( ~ sum(X,Y,Z)
    | ~ sum(X,U,V)
    | ~ product(Y,U,W)
    | ~ sum(X,W,X1)
    | product(Z,V,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity5) ).

cnf(distributivity6,axiom,
    ( ~ sum(X,Y,Z)
    | ~ sum(X,U,V)
    | ~ product(Y,U,W)
    | ~ product(Z,V,X1)
    | sum(X,W,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity6) ).

cnf(additive_inverse1,axiom,
    sum(inverse(X),X,multiplicative_identity),
    file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_inverse1) ).

cnf(multiplicative_inverse1,axiom,
    product(inverse(X),X,additive_identity),
    file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse1) ).

cnf(addition_is_well_defined,axiom,
    ( ~ sum(X,Y,Z)
    | ~ sum(X,Y,U)
    | Z = U ),
    file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',addition_is_well_defined) ).

cnf(multiplication_is_well_defined,axiom,
    ( ~ product(X,Y,Z)
    | ~ product(X,Y,U)
    | Z = U ),
    file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplication_is_well_defined) ).

cnf(inverse_is_unique,axiom,
    ( ~ sum(X,Y,multiplicative_identity)
    | ~ sum(X,Z,multiplicative_identity)
    | ~ product(X,Y,additive_identity)
    | ~ product(X,Z,additive_identity)
    | Y = Z ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_is_unique) ).

cnf(x_plus_y,hypothesis,
    sum(x,y,x_plus_y),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_plus_y) ).

cnf(x_inverse_times_y_inverse,hypothesis,
    product(inverse(x),inverse(y),x_inverse_times_y_inverse),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_inverse_times_y_inverse) ).

cnf(prove_equation,negated_conjecture,
    inverse(x_plus_y) != x_inverse_times_y_inverse,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).

cnf(20,plain,
    X = add(additive_identity,X),
    inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,additive_identity1,closure_of_addition]) ).

cnf(25,plain,
    X = multiply(multiplicative_identity,X),
    inference('HYPERRESOLVE',[status(thm)],[multiplication_is_well_defined,multiplicative_identity1,closure_of_multiplication]) ).

cnf(32,plain,
    sum(additive_identity,multiply(X,additive_identity),additive_identity),
    inference('HYPERRESOLVE',[status(thm)],[distributivity1,multiplicative_inverse1,closure_of_multiplication,additive_identity1,multiplicative_inverse1]) ).

cnf(54,plain,
    sum(x_inverse_times_y_inverse,inverse(x),multiply(inverse(x),add(inverse(y),multiplicative_identity))),
    inference('HYPERRESOLVE',[status(thm)],[distributivity1,x_inverse_times_y_inverse,multiplicative_identity1,closure_of_addition,closure_of_multiplication]) ).

cnf(56,plain,
    sum(x_inverse_times_y_inverse,inverse(y),multiply(inverse(y),add(inverse(x),multiplicative_identity))),
    inference('HYPERRESOLVE',[status(thm)],[distributivity1,x_inverse_times_y_inverse,multiplicative_identity1,closure_of_addition,closure_of_multiplication]) ).

cnf(104,plain,
    product(x_plus_y,x,add(x,multiply(y,additive_identity))),
    inference('HYPERRESOLVE',[status(thm)],[distributivity5,x_plus_y,additive_identity1,closure_of_multiplication,closure_of_addition]) ).

cnf(106,plain,
    product(x_plus_y,y,add(y,multiply(x,additive_identity))),
    inference('HYPERRESOLVE',[status(thm)],[distributivity5,x_plus_y,additive_identity1,closure_of_multiplication,closure_of_addition]) ).

cnf(120,plain,
    product(X,add(X,Y),add(X,multiply(additive_identity,Y))),
    inference('HYPERRESOLVE',[status(thm)],[distributivity5,additive_identity1,closure_of_addition,closure_of_multiplication,closure_of_addition]) ).

cnf(204,plain,
    product(X,additive_identity,additive_identity),
    inference('HYPERRESOLVE',[status(thm)],[distributivity5,32,additive_identity1,additive_identity1,closure_of_multiplication]) ).

cnf(205,plain,
    additive_identity = multiply(X,additive_identity),
    inference('HYPERRESOLVE',[status(thm)],[addition_is_well_defined,32,additive_identity1]) ).

cnf(206,plain,
    product(X,add(X,Y),X),
    inference('REWRITE',[status(thm)],[120,20,205,theory(equality)]) ).

cnf(208,plain,
    product(x_plus_y,y,y),
    inference('REWRITE',[status(thm)],[106,20,205,theory(equality)]) ).

cnf(210,plain,
    product(x_plus_y,x,x),
    inference('REWRITE',[status(thm)],[104,20,205,theory(equality)]) ).

cnf(224,plain,
    product(add(x_plus_y,inverse(y)),multiplicative_identity,multiplicative_identity),
    inference('HYPERRESOLVE',[status(thm)],[distributivity5,208,closure_of_addition,additive_inverse1,additive_inverse1]) ).

cnf(256,plain,
    product(add(x_plus_y,inverse(x)),multiplicative_identity,multiplicative_identity),
    inference('HYPERRESOLVE',[status(thm)],[distributivity5,210,closure_of_addition,additive_inverse1,additive_inverse1]) ).

cnf(411,plain,
    multiplicative_identity = add(X,multiplicative_identity),
    inference('HYPERRESOLVE',[status(thm)],[multiplication_is_well_defined,206,multiplicative_identity1]) ).

cnf(414,plain,
    sum(x_inverse_times_y_inverse,inverse(y),inverse(y)),
    inference('REWRITE',[status(thm)],[56,25,411,theory(equality)]) ).

cnf(416,plain,
    sum(x_inverse_times_y_inverse,inverse(x),inverse(x)),
    inference('REWRITE',[status(thm)],[54,25,411,theory(equality)]) ).

cnf(492,plain,
    sum(multiply(y,x_inverse_times_y_inverse),additive_identity,additive_identity),
    inference('HYPERRESOLVE',[status(thm)],[distributivity1,414,closure_of_multiplication,multiplicative_inverse1,multiplicative_inverse1]) ).

cnf(524,plain,
    sum(multiply(x,x_inverse_times_y_inverse),additive_identity,additive_identity),
    inference('HYPERRESOLVE',[status(thm)],[distributivity1,416,closure_of_multiplication,multiplicative_inverse1,multiplicative_inverse1]) ).

cnf(651,plain,
    product(y,x_inverse_times_y_inverse,additive_identity),
    inference('HYPERRESOLVE',[status(thm)],[distributivity2,492,closure_of_multiplication,204,additive_identity1]) ).

cnf(704,plain,
    product(x_inverse_times_y_inverse,x_plus_y,additive_identity),
    inference('HYPERRESOLVE',[status(thm)],[distributivity2,524,closure_of_multiplication,651,x_plus_y]) ).

cnf(742,plain,
    ~ sum(x_plus_y,x_inverse_times_y_inverse,multiplicative_identity),
    inference('UR-RESOLVE',[status(thm)],[inverse_is_unique,704,additive_inverse1,multiplicative_inverse1,prove_equation]) ).

cnf(919,plain,
    ~ product(add(x_plus_y,inverse(x)),add(x_plus_y,inverse(y)),multiplicative_identity),
    inference('UR-RESOLVE',[status(thm)],[distributivity6,742,closure_of_addition,closure_of_addition,x_inverse_times_y_inverse]) ).

cnf(1936,plain,
    multiplicative_identity = add(x_plus_y,inverse(y)),
    inference('HYPERRESOLVE',[status(thm)],[multiplication_is_well_defined,224,multiplicative_identity1]) ).

cnf(1938,plain,
    $false,
    inference('REWRITE',[status(thm)],[919,256,1936,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : BOO014-3 : TPTP v8.1.0. Bugfixed v2.2.0.
% 0.10/0.13  % Command  : run-snark %s %d
% 0.14/0.34  % Computer : n017.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Wed Jun  1 22:03:42 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.20/0.46  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.47  * 
% 0.20/0.47  * 
% 0.20/0.48  #<PACKAGE "SNARK-USER">
% 0.20/0.48  * 
% 0.20/0.48  SNARK-TPTP-OPTIONS
% 0.20/0.48  * 
% 0.20/0.48  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.48   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.48   (USE-FACTORING :POS)
% 0.20/0.48   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.48   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.48   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.48   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.48   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.48   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.48   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.48   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.48   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.48   (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.48  * 
% 0.20/0.48  "."
% 0.20/0.48  * 
% 0.20/0.48  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-01T22:03:42
% 0.20/0.48  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n017.cluster.edu at 2022-06-01T22:03:42
% 0.20/0.50  
% 0.20/0.50  ; Recognized relation function assertion (|sum| ?X ?Y (|add| ?X ?Y)).
% 0.20/0.50  ; Recognized relation function assertion (|product| ?X ?Y (|multiply| ?X ?Y)).
% 0.20/0.50  ; Recognized commutativity assertion (OR (NOT (|sum| ?X ?Y ?Z)) (|sum| ?Y ?X ?Z)).
% 0.20/0.50  ; Recognized commutativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (|product| ?Y ?X ?Z)).
% 0.20/0.50  ; Recognized possible left identity assertion (|sum| |additive_identity| ?X ?X).
% 0.20/0.50  ; Recognized possible right identity assertion (|sum| ?X |additive_identity| ?X).
% 0.20/0.50  ; Recognized possible left identity assertion (|product| |multiplicative_identity| ?X ?X).
% 0.20/0.50  ; Recognized possible right identity assertion (|product| ?X |multiplicative_identity| ?X).
% 0.20/0.50  ; Recognized possible left inverse assertion (|sum| (|inverse| ?X) ?X |multiplicative_identity|).
% 0.20/0.50  ; Recognized possible right inverse assertion (|sum| ?X (|inverse| ?X) |multiplicative_identity|).
% 0.20/0.50  ; Recognized possible left inverse assertion (|product| (|inverse| ?X) ?X |additive_identity|).
% 0.20/0.50  ; Recognized possible right inverse assertion (|product| ?X (|inverse| ?X) |additive_identity|).
% 0.20/0.50  ; Recognized relation functionality assertion (OR (NOT (|sum| ?X ?Y ?Z)) (NOT (|sum| ?X ?Y ?U)) (= ?Z ?U)).
% 0.20/0.50  ; Recognized relation functionality assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?X ?Y ?U)) (= ?Z ?U)).
% 0.20/0.50  ; Declaring sum to be commutative.
% 0.20/0.50  ; Declaring add to be commutative.
% 0.20/0.50  ; Declaring product to be commutative.
% 6.53/6.77  ; Declaring multiply to be commutative.
% 6.53/6.77  
% 6.53/6.77  #||
% 6.53/6.77  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.53/6.77  % SZS output start Refutation
% See solution above
% 6.53/6.78  ||#
% 6.53/6.78  
% 6.53/6.78  ; Summary of computation:
% 6.53/6.78  ;    191457 formulas have been input or derived (from 123 formulas).
% 6.53/6.78  ;      1938 ( 1%) were retained.  Of these,
% 6.53/6.78  ;          701 (36%) were simplified or subsumed later,
% 6.53/6.78  ;         1237 (64%) are still being kept.
% 6.53/6.78  ; 
% 6.53/6.78  ; Run time in seconds excluding printing time:
% 6.53/6.78  ;     0.006   0%   Read assertion file          (1 call)
% 6.53/6.78  ;     0.001   0%   Assert                       (27 calls)
% 6.53/6.78  ;     0.278   4%   Process new row              (100,977 calls)
% 6.53/6.78  ;     4.631  74%   Resolution                   (244 calls)
% 6.53/6.78  ;     0.003   0%   Paramodulation               (122 calls)
% 6.53/6.78  ;     0.003   0%   Condensing                   (11 calls)
% 6.53/6.78  ;     0.000   0%   Forward subsumption          (11 calls)
% 6.53/6.78  ;     0.000   0%   Backward subsumption         (7 calls)
% 6.53/6.78  ;     0.002   0%   Clause clause subsumption    (6 calls)
% 6.53/6.78  ;     1.056  17%   Forward simplification       (86,548 calls)
% 6.53/6.78  ;     0.050   1%   Backward simplification      (1,938 calls)
% 6.53/6.78  ;     0.000   0%   Ordering                     (281 calls)
% 6.53/6.78  ;     0.000   0%   Sortal reasoning             (32 calls)
% 6.53/6.78  ;     0.000   0%   Purity testing               (1 call)
% 6.53/6.78  ;     0.261   4%   Other
% 6.53/6.78  ;     6.291        Total
% 6.53/6.78  ;     6.295        Real time
% 6.53/6.78  ; 
% 6.53/6.78  ; Term-hash-array has 3,138 terms in all.
% 6.53/6.78  ; Feature-vector-row-index has 7 entries (7 at peak, 7 added, 0 deleted).
% 6.53/6.78  ; Feature-vector-row-index has 20 nodes (20 at peak, 20 added, 0 deleted).
% 6.53/6.78  ;  Retrieved 6 possibly forward subsuming rows in 11 calls.
% 6.53/6.78  ;  Retrieved 0 possibly backward subsumed rows in 7 calls.
% 6.53/6.78  ; Path-index has 2,078 entries (2,090 at peak, 3,163 added, 1,085 deleted).
% 6.53/6.78  ; Path-index has 861 nodes (861 at peak, 1,128 added, 267 deleted).
% 6.53/6.78  ; Trie-index has 2,078 entries (2,090 at peak, 3,163 added, 1,085 deleted).
% 6.53/6.78  ; Trie-index has 8,701 nodes (8,741 at peak, 12,788 added, 4,087 deleted).
% 6.53/6.78  ; Retrieved 321,786 generalization terms in 250,215 calls.
% 6.53/6.78  ; Retrieved 3,318 instance terms in 1,930 calls.
% 6.53/6.78  ; Retrieved 5,883,593 unifiable terms in 339,513 calls.
% 6.53/6.78  ; 
% 6.53/6.78  ; The agenda of backward simplifiable rows to process has 4 entries:
% 6.53/6.78  ;     4 with value 0
% 6.53/6.78  ; The agenda of rows to process has 3529 entries:
% 6.53/6.78  ;   248 with value 12            437 with value 19              28 with value 25
% 6.53/6.78  ;   190 with value 13            239 with value 20              28 with value 26
% 6.53/6.78  ;    82 with value 14            204 with value 21               8 with value 27
% 6.53/6.78  ;   257 with value 15            188 with value 22               1 with value 28
% 6.53/6.78  ;   535 with value 16             66 with value 23               8 with value 29
% 6.53/6.78  ;   580 with value 17             59 with value 24               4 with value 30
% 6.53/6.78  ;   367 with value 18
% 6.53/6.78  ; The agenda of rows to give has 1137 entries:
% 6.53/6.78  ;     1 with value (4 10)        119 with value (4 18)          22 with value (4 25)
% 6.53/6.78  ;    43 with value (4 12)        100 with value (4 19)           8 with value (4 26)
% 6.53/6.78  ;    40 with value (4 13)        122 with value (4 20)           9 with value (4 27)
% 6.53/6.78  ;    94 with value (4 14)         80 with value (4 21)           5 with value (4 28)
% 6.53/6.78  ;   107 with value (4 15)         54 with value (4 22)           6 with value (4 29)
% 6.53/6.78  ;   116 with value (4 16)         39 with value (4 23)           3 with value (4 30)
% 6.53/6.78  ;   117 with value (4 17)         52 with value (4 24)
% 6.53/6.78  Evaluation took:
% 6.53/6.78    6.295 seconds of real time
% 6.53/6.78    6.004459 seconds of user run time
% 6.53/6.78    0.290185 seconds of system run time
% 6.53/6.78    [Run times include 0.283 seconds GC run time.]
% 6.53/6.78    0 calls to %EVAL
% 6.53/6.78    0 page faults and
% 6.53/6.78    521,391,376 bytes consed.
% 6.53/6.78  :PROOF-FOUND
% 6.53/6.78  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-01T22:03:48
% 6.53/6.78  :PROOF-FOUND
% 6.53/6.78  * 
%------------------------------------------------------------------------------