TSTP Solution File: CAT009-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : CAT009-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n020.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 : Fri Jul 15 00:07:07 EDT 2022

% Result   : Unsatisfiable 0.64s 0.82s
% Output   : Refutation 0.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   16 (  10 unt;   0 nHn;  14 RR)
%            Number of literals    :   28 (   2 equ;  13 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   21 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(closure_of_composition,axiom,
    ( ~ defined(X,Y)
    | product(X,Y,compose(X,Y)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',closure_of_composition) ).

cnf(associative_property2,axiom,
    ( ~ product(X,Y,Z)
    | ~ defined(Z,U)
    | defined(Y,U) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',associative_property2) ).

cnf(category_theory_axiom4,axiom,
    ( ~ product(X,Y,Z)
    | ~ product(U,X,V)
    | ~ defined(U,Z)
    | defined(V,Y) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom4) ).

cnf(domain_is_an_identity_map,axiom,
    identity_map(domain(X)),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',domain_is_an_identity_map) ).

cnf(product_on_domain,axiom,
    product(X,domain(X),X),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',product_on_domain) ).

cnf(identity1,axiom,
    ( ~ defined(X,Y)
    | ~ identity_map(X)
    | product(X,Y,Y) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',identity1) ).

cnf(identity2,axiom,
    ( ~ defined(X,Y)
    | ~ identity_map(Y)
    | product(X,Y,X) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',identity2) ).

cnf(composition_is_well_defined,axiom,
    ( ~ product(X,Y,Z)
    | ~ product(X,Y,U)
    | Z = U ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',composition_is_well_defined) ).

cnf(ba_defined,hypothesis,
    defined(b,a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ba_defined) ).

cnf(prove_domain_of_ba_equals_domain_of_a,negated_conjecture,
    domain(compose(b,a)) != domain(a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_of_ba_equals_domain_of_a) ).

cnf(21,plain,
    product(b,a,compose(b,a)),
    inference('HYPERRESOLVE',[status(thm)],[closure_of_composition,ba_defined]) ).

cnf(62,plain,
    defined(compose(b,a),domain(a)),
    inference('HYPERRESOLVE',[status(thm)],[category_theory_axiom4,21,product_on_domain,ba_defined]) ).

cnf(197,plain,
    defined(domain(compose(b,a)),domain(a)),
    inference('HYPERRESOLVE',[status(thm)],[associative_property2,62,product_on_domain]) ).

cnf(733,plain,
    product(domain(compose(b,a)),domain(a),domain(a)),
    inference('HYPERRESOLVE',[status(thm)],[identity1,197,domain_is_an_identity_map]) ).

cnf(734,plain,
    product(domain(compose(b,a)),domain(a),domain(compose(b,a))),
    inference('HYPERRESOLVE',[status(thm)],[identity2,197,domain_is_an_identity_map]) ).

cnf(742,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[composition_is_well_defined,733,prove_domain_of_ba_equals_domain_of_a]),734]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : CAT009-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13  % Command  : run-snark %s %d
% 0.12/0.34  % Computer : n020.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 : Sun May 29 19:29:54 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.20/0.45  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.46  * 
% 0.20/0.46  * 
% 0.20/0.47  #<PACKAGE "SNARK-USER">
% 0.20/0.47  * 
% 0.20/0.47  SNARK-TPTP-OPTIONS
% 0.20/0.47  * 
% 0.20/0.47  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.47   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.47   (USE-FACTORING :POS)
% 0.20/0.47   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.47   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.47   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.47   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.47   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.47   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.47   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.47   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.47   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.47   (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.47  * 
% 0.20/0.47  "."
% 0.20/0.47  * 
% 0.20/0.47  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-29T19:29:54
% 0.20/0.47  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n020.cluster.edu at 2022-05-29T19:29:54
% 0.20/0.48  
% 0.20/0.48  ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Z ?U ?V)) (NOT (|product| ?Y ?U ?W)) (|product| ?X ?W ?V)).
% 0.20/0.48  ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?U ?Z ?V)) (NOT (|product| ?U ?X ?W)) (|product| ?W ?Y ?V)).
% 0.64/0.82  ; Recognized relation functionality assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?X ?Y ?U)) (= ?Z ?U)).
% 0.64/0.82  
% 0.64/0.82  #||
% 0.64/0.82  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.64/0.82  % SZS output start Refutation
% See solution above
% 0.64/0.82  ||#
% 0.64/0.82  
% 0.64/0.82  ; Summary of computation:
% 0.64/0.82  ;      6742 formulas have been input or derived (from 105 formulas).
% 0.64/0.82  ;       742 (11%) were retained.  Of these,
% 0.64/0.82  ;          674 (91%) were simplified or subsumed later,
% 0.64/0.82  ;           68 ( 9%) are still being kept.
% 0.64/0.82  ; 
% 0.64/0.82  ; Run time in seconds excluding printing time:
% 0.64/0.82  ;     0.004   1%   Read assertion file          (1 call)
% 0.64/0.82  ;     0.001   0%   Assert                       (20 calls)
% 0.64/0.82  ;     0.049  14%   Process new row              (5,612 calls)
% 0.64/0.82  ;     0.201  57%   Resolution                   (208 calls)
% 0.64/0.82  ;     0.004   1%   Paramodulation               (104 calls)
% 0.64/0.82  ;     0.002   1%   Condensing                   (12 calls)
% 0.64/0.82  ;     0.000   0%   Forward subsumption          (12 calls)
% 0.64/0.82  ;     0.000   0%   Backward subsumption         (12 calls)
% 0.64/0.82  ;     0.000   0%   Clause clause subsumption    (16 calls)
% 0.64/0.82  ;     0.027   8%   Forward simplification       (4,649 calls)
% 0.64/0.82  ;     0.022   6%   Backward simplification      (742 calls)
% 0.64/0.82  ;     0.000   0%   Ordering                     (83 calls)
% 0.64/0.82  ;     0.001   0%   Sortal reasoning             (32 calls)
% 0.64/0.82  ;     0.000   0%   Purity testing               (1 call)
% 0.64/0.82  ;     0.039  11%   Other
% 0.64/0.82  ;     0.350        Total
% 0.64/0.82  ;     0.352        Real time
% 0.64/0.82  ; 
% 0.64/0.82  ; Term-hash-array has 1,029 terms in all.
% 0.64/0.82  ; Feature-vector-row-index has 12 entries (12 at peak, 12 added, 0 deleted).
% 0.64/0.82  ; Feature-vector-row-index has 18 nodes (18 at peak, 18 added, 0 deleted).
% 0.64/0.82  ;  Retrieved 11 possibly forward subsuming rows in 12 calls.
% 0.64/0.82  ;  Retrieved 5 possibly backward subsumed rows in 12 calls.
% 0.64/0.82  ; Path-index has 109 entries (916 at peak, 1,035 added, 926 deleted).
% 0.64/0.82  ; Path-index has 839 nodes (1,467 at peak, 1,588 added, 749 deleted).
% 0.64/0.82  ; Trie-index has 109 entries (916 at peak, 1,035 added, 926 deleted).
% 0.64/0.82  ; Trie-index has 341 nodes (2,755 at peak, 3,150 added, 2,809 deleted).
% 0.64/0.82  ; Retrieved 8,235 generalization terms in 6,458 calls.
% 0.64/0.82  ; Retrieved 806 instance terms in 729 calls.
% 0.64/0.82  ; Retrieved 172,812 unifiable terms in 16,021 calls.
% 0.64/0.82  ; 
% 0.64/0.82  ; The agenda of rows to process has 3 entries:
% 0.64/0.82  ;     3 with value 19
% 0.64/0.82  ; The agenda of rows to give has 15 entries:
% 0.64/0.82  ;     2 with value (4 16)          6 with value (4 18)           4 with value (4 22)
% 0.64/0.82  ;     1 with value (4 17)          2 with value (4 19)
% 0.64/0.82  Evaluation took:
% 0.64/0.82    0.352 seconds of real time
% 0.64/0.82    0.319182 seconds of user run time
% 0.64/0.82    0.032698 seconds of system run time
% 0.64/0.82    [Run times include 0.014 seconds GC run time.]
% 0.64/0.82    0 calls to %EVAL
% 0.64/0.82    0 page faults and
% 0.64/0.82    28,755,864 bytes consed.
% 0.64/0.82  :PROOF-FOUND
% 0.64/0.82  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-29T19:29:54
% 0.64/0.82  :PROOF-FOUND
% 0.64/0.82  * 
%------------------------------------------------------------------------------