TSTP Solution File: CAT001-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : CAT001-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n032.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 00:07:05 EDT 2022

% Result   : Unsatisfiable 0.99s 1.20s
% Output   : Refutation 0.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   14
% Syntax   : Number of clauses     :   23 (  15 unt;   0 nHn;  21 RR)
%            Number of literals    :   41 (   2 equ;  20 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   34 (   3 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_property1,axiom,
    ( ~ product(X,Y,Z)
    | defined(X,Y) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',associative_property1) ).

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_axiom2,axiom,
    ( ~ product(X,Y,Z)
    | ~ product(Z,U,V)
    | ~ product(Y,U,W)
    | product(X,W,V) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom2) ).

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(category_theory_axiom5,axiom,
    ( ~ product(X,Y,Z)
    | ~ product(U,Z,V)
    | ~ product(U,X,W)
    | product(W,Y,V) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom5) ).

cnf(category_theory_axiom6,axiom,
    ( ~ defined(X,Y)
    | ~ defined(Y,Z)
    | ~ identity_map(Y)
    | defined(X,Z) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom6) ).

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

cnf(cancellation_for_product,hypothesis,
    ( ~ product(c,X,Y)
    | ~ product(c,Z,Y)
    | X = Z ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation_for_product) ).

cnf(bh_equals_d,hypothesis,
    product(b,h,d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',bh_equals_d) ).

cnf(bg_equals_d,hypothesis,
    product(b,g,d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_equals_d) ).

cnf(prove_h_equals_g,negated_conjecture,
    h != g,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_h_equals_g) ).

cnf(24,plain,
    defined(b,h),
    inference('HYPERRESOLVE',[status(thm)],[associative_property1,bh_equals_d]) ).

cnf(26,plain,
    defined(a,b),
    inference('HYPERRESOLVE',[status(thm)],[associative_property1,ab_equals_c]) ).

cnf(58,plain,
    defined(domain(b),h),
    inference('HYPERRESOLVE',[status(thm)],[associative_property2,24,product_on_domain]) ).

cnf(68,plain,
    defined(c,domain(b)),
    inference('HYPERRESOLVE',[status(thm)],[category_theory_axiom4,26,product_on_domain,ab_equals_c]) ).

cnf(157,plain,
    defined(c,h),
    inference('HYPERRESOLVE',[status(thm)],[category_theory_axiom6,68,58,domain_is_an_identity_map]) ).

cnf(164,plain,
    product(c,h,compose(c,h)),
    inference('HYPERRESOLVE',[status(thm)],[closure_of_composition,157]) ).

cnf(1102,plain,
    product(a,d,compose(c,h)),
    inference('HYPERRESOLVE',[status(thm)],[category_theory_axiom2,164,ab_equals_c,bh_equals_d]) ).

cnf(1106,plain,
    ~ product(c,g,compose(c,h)),
    inference('UR-RESOLVE',[status(thm)],[cancellation_for_product,164,prove_h_equals_g]) ).

cnf(2014,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[category_theory_axiom5,1102,bg_equals_d,ab_equals_c]),1106]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : CAT001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.05/0.11  % Command  : run-snark %s %d
% 0.11/0.30  % Computer : n032.cluster.edu
% 0.11/0.30  % Model    : x86_64 x86_64
% 0.11/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30  % Memory   : 8042.1875MB
% 0.11/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30  % CPULimit : 300
% 0.11/0.30  % WCLimit  : 600
% 0.11/0.30  % DateTime : Sun May 29 22:53:57 EDT 2022
% 0.11/0.30  % CPUTime  : 
% 0.16/0.39  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.39  * 
% 0.16/0.39  * 
% 0.16/0.40  #<PACKAGE "SNARK-USER">
% 0.16/0.40  * 
% 0.16/0.40  SNARK-TPTP-OPTIONS
% 0.16/0.40  * 
% 0.16/0.40  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.16/0.40   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.16/0.40   (USE-FACTORING :POS)
% 0.16/0.40   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.16/0.40   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.16/0.40   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.16/0.40   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.16/0.40   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.16/0.40   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.16/0.40   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.16/0.40   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.16/0.40   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.16/0.40   (DECLARE-TPTP-SYMBOLS2))
% 0.16/0.40  * 
% 0.16/0.40  "."
% 0.16/0.40  * 
% 0.16/0.40  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-29T22:53:57
% 0.16/0.40  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n032.cluster.edu at 2022-05-29T22:53:57
% 0.16/0.41  
% 0.16/0.41  ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Z ?U ?V)) (NOT (|product| ?Y ?U ?W)) (|product| ?X ?W ?V)).
% 0.16/0.41  ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?U ?Z ?V)) (NOT (|product| ?U ?X ?W)) (|product| ?W ?Y ?V)).
% 0.99/1.20  ; Recognized relation functionality assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?X ?Y ?U)) (= ?Z ?U)).
% 0.99/1.20  
% 0.99/1.20  #||
% 0.99/1.20  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.99/1.20  % SZS output start Refutation
% See solution above
% 0.99/1.20  ||#
% 0.99/1.20  
% 0.99/1.20  ; Summary of computation:
% 0.99/1.20  ;     18647 formulas have been input or derived (from 245 formulas).
% 0.99/1.20  ;      2014 (11%) were retained.  Of these,
% 0.99/1.20  ;         1904 (95%) were simplified or subsumed later,
% 0.99/1.20  ;          110 ( 5%) are still being kept.
% 0.99/1.20  ; 
% 0.99/1.20  ; Run time in seconds excluding printing time:
% 0.99/1.20  ;     0.003   0%   Read assertion file          (1 call)
% 0.99/1.20  ;     0.001   0%   Assert                       (23 calls)
% 0.99/1.20  ;     0.115  14%   Process new row              (15,735 calls)
% 0.99/1.20  ;     0.466  59%   Resolution                   (488 calls)
% 0.99/1.20  ;     0.003   0%   Paramodulation               (244 calls)
% 0.99/1.20  ;     0.001   0%   Condensing                   (13 calls)
% 0.99/1.20  ;     0.001   0%   Forward subsumption          (13 calls)
% 0.99/1.20  ;     0.000   0%   Backward subsumption         (13 calls)
% 0.99/1.20  ;     0.000   0%   Clause clause subsumption    (17 calls)
% 0.99/1.20  ;     0.067   8%   Forward simplification       (13,616 calls)
% 0.99/1.20  ;     0.075   9%   Backward simplification      (2,014 calls)
% 0.99/1.20  ;     0.001   0%   Ordering                     (220 calls)
% 0.99/1.20  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.99/1.20  ;     0.000   0%   Purity testing               (1 call)
% 0.99/1.20  ;     0.063   8%   Other
% 0.99/1.20  ;     0.796        Total
% 0.99/1.20  ;     0.801        Real time
% 0.99/1.20  ; 
% 0.99/1.20  ; Term-hash-array has 2,562 terms in all.
% 0.99/1.20  ; Feature-vector-row-index has 13 entries (13 at peak, 13 added, 0 deleted).
% 0.99/1.20  ; Feature-vector-row-index has 20 nodes (20 at peak, 20 added, 0 deleted).
% 0.99/1.20  ;  Retrieved 12 possibly forward subsuming rows in 13 calls.
% 0.99/1.20  ;  Retrieved 5 possibly backward subsumed rows in 13 calls.
% 0.99/1.20  ; Path-index has 174 entries (2,002 at peak, 2,571 added, 2,397 deleted).
% 0.99/1.20  ; Path-index has 690 nodes (1,741 at peak, 2,006 added, 1,316 deleted).
% 0.99/1.20  ; Trie-index has 174 entries (2,002 at peak, 2,571 added, 2,397 deleted).
% 0.99/1.20  ; Trie-index has 399 nodes (4,790 at peak, 6,213 added, 5,814 deleted).
% 0.99/1.20  ; Retrieved 21,300 generalization terms in 24,873 calls.
% 0.99/1.20  ; Retrieved 2,249 instance terms in 2,000 calls.
% 0.99/1.20  ; Retrieved 449,033 unifiable terms in 44,844 calls.
% 0.99/1.20  ; 
% 0.99/1.20  ; The agenda of rows to process has 35 entries:
% 0.99/1.20  ;     7 with value 14             12 with value 15              16 with value 17
% 0.99/1.20  ; The agenda of rows to give has 33 entries:
% 0.99/1.20  ;     6 with value (4 13)          5 with value (4 15)           2 with value (4 17)
% 0.99/1.20  ;    14 with value (4 14)          5 with value (4 16)           1 with value (4 21)
% 0.99/1.20  Evaluation took:
% 0.99/1.20    0.802 seconds of real time
% 0.99/1.20    0.720319 seconds of user run time
% 0.99/1.20    0.077904 seconds of system run time
% 0.99/1.20    [Run times include 0.041 seconds GC run time.]
% 0.99/1.20    0 calls to %EVAL
% 0.99/1.20    0 page faults and
% 0.99/1.20    58,235,744 bytes consed.
% 0.99/1.20  :PROOF-FOUND
% 0.99/1.20  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-29T22:53:57
% 0.99/1.20  :PROOF-FOUND
% 0.99/1.20  * 
%------------------------------------------------------------------------------