TSTP Solution File: CAT018-4 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : CAT018-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n024.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 00:07:11 EDT 2022

% Result   : Unsatisfiable 0.46s 0.64s
% Output   : Refutation 0.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   23 (  17 unt;   0 nHn;  20 RR)
%            Number of literals    :   30 (  11 equ;  10 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   16 (   1 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(codomain_has_elements,axiom,
    ( ~ there_exists(codomain(X))
    | there_exists(X) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',codomain_has_elements) ).

cnf(composition_implies_domain,axiom,
    ( ~ there_exists(compose(X,Y))
    | there_exists(domain(X)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',composition_implies_domain) ).

cnf(domain_codomain_composition1,axiom,
    ( ~ there_exists(compose(X,Y))
    | domain(X) = codomain(Y) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',domain_codomain_composition1) ).

cnf(domain_codomain_composition2,axiom,
    ( ~ there_exists(domain(X))
    | domain(X) != codomain(Y)
    | there_exists(compose(X,Y)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',domain_codomain_composition2) ).

cnf(associativity_of_compose,axiom,
    compose(X,compose(Y,Z)) = compose(compose(X,Y),Z),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',associativity_of_compose) ).

cnf(compose_domain,axiom,
    compose(X,domain(X)) = X,
    file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',compose_domain) ).

cnf(assume_ab_exists,hypothesis,
    there_exists(compose(a,b)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_ab_exists) ).

cnf(assume_bc_exists,hypothesis,
    there_exists(compose(b,c)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_bc_exists) ).

cnf(prove_a_bc_exists,negated_conjecture,
    ~ there_exists(compose(a,compose(b,c))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_bc_exists) ).

cnf(15,plain,
    ~ there_exists(compose(compose(a,b),c)),
    inference('REWRITE',[status(thm)],[prove_a_bc_exists,associativity_of_compose,theory(equality)]) ).

cnf(22,plain,
    there_exists(domain(a)),
    inference('HYPERRESOLVE',[status(thm)],[composition_implies_domain,assume_ab_exists]) ).

cnf(23,plain,
    ( ~ there_exists(X)
    | there_exists(domain(X)) ),
    inference('PARAMODULATE',[status(thm)],[composition_implies_domain,compose_domain,theory(equality)]) ).

cnf(25,plain,
    domain(b) = codomain(c),
    inference('HYPERRESOLVE',[status(thm)],[domain_codomain_composition1,assume_bc_exists]) ).

cnf(27,plain,
    domain(a) = codomain(b),
    inference('HYPERRESOLVE',[status(thm)],[domain_codomain_composition1,assume_ab_exists]) ).

cnf(28,plain,
    there_exists(codomain(b)),
    inference('REWRITE',[status(thm)],[22,27,theory(equality)]) ).

cnf(31,plain,
    compose(X,Y) = compose(compose(X,Y),domain(Y)),
    inference('PARAMODULATE',[status(thm)],[associativity_of_compose,compose_domain,theory(equality)]) ).

cnf(47,plain,
    there_exists(b),
    inference('HYPERRESOLVE',[status(thm)],[codomain_has_elements,28]) ).

cnf(51,plain,
    compose(b,codomain(c)) = b,
    inference('PARAMODULATE',[status(thm)],[compose_domain,25,theory(equality)]) ).

cnf(61,plain,
    there_exists(domain(compose(a,b))),
    inference('HYPERRESOLVE',[status(thm)],[23,assume_ab_exists]) ).

cnf(71,plain,
    domain(compose(a,b)) != codomain(c),
    inference('UR-RESOLVE',[status(thm)],[domain_codomain_composition2,61,15]) ).

cnf(89,plain,
    codomain(c) = codomain(codomain(c)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[domain_codomain_composition1,51,theory(equality)]),25,47,theory(equality)]) ).

cnf(177,plain,
    ( ~ there_exists(compose(X,Y))
    | domain(compose(X,Y)) = codomain(domain(Y)) ),
    inference('PARAMODULATE',[status(thm)],[domain_codomain_composition1,31,theory(equality)]) ).

cnf(426,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[177,assume_ab_exists]),71,89,25,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : CAT018-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : run-snark %s %d
% 0.13/0.34  % Computer : n024.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sun May 29 16:53:06 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.46  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.47  * 
% 0.19/0.47  * 
% 0.19/0.47  #<PACKAGE "SNARK-USER">
% 0.19/0.47  * 
% 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/sandbox/benchmark/theBenchmark.p 2022-05-29T16:53:06
% 0.19/0.48  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n024.cluster.edu at 2022-05-29T16:53:06
% 0.19/0.49  
% 0.46/0.64  ; Recognized associativity assertion (= (|compose| ?X (|compose| ?Y ?Z)) (|compose| (|compose| ?X ?Y) ?Z)).
% 0.46/0.64  
% 0.46/0.64  #||
% 0.46/0.64  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.46/0.64  % SZS output start Refutation
% See solution above
% 0.46/0.64  ||#
% 0.46/0.64  
% 0.46/0.64  ; Summary of computation:
% 0.46/0.64  ;      1947 formulas have been input or derived (from 147 formulas).
% 0.46/0.64  ;       426 (22%) were retained.  Of these,
% 0.46/0.64  ;           87 (20%) were simplified or subsumed later,
% 0.46/0.64  ;          339 (80%) are still being kept.
% 0.46/0.64  ; 
% 0.46/0.64  ; Run time in seconds excluding printing time:
% 0.46/0.64  ;     0.002   1%   Read assertion file          (1 call)
% 0.46/0.64  ;     0.000   0%   Assert                       (14 calls)
% 0.46/0.64  ;     0.039  24%   Process new row              (1,679 calls)
% 0.46/0.64  ;     0.012   7%   Resolution                   (292 calls)
% 0.46/0.64  ;     0.011   7%   Paramodulation               (146 calls)
% 0.46/0.64  ;     0.000   0%   Condensing                   (228 calls)
% 0.46/0.64  ;     0.009   5%   Forward subsumption          (228 calls)
% 0.46/0.64  ;     0.001   1%   Backward subsumption         (129 calls)
% 0.46/0.64  ;     0.002   1%   Clause clause subsumption    (559 calls)
% 0.46/0.64  ;     0.032  20%   Forward simplification       (1,660 calls)
% 0.46/0.64  ;     0.009   5%   Backward simplification      (425 calls)
% 0.46/0.64  ;     0.010   6%   Ordering                     (2,220 calls)
% 0.46/0.64  ;     0.001   1%   Sortal reasoning             (32 calls)
% 0.46/0.64  ;     0.000   0%   Purity testing               (1 call)
% 0.46/0.64  ;     0.036  22%   Other
% 0.46/0.64  ;     0.164        Total
% 0.46/0.64  ;     0.167        Real time
% 0.46/0.64  ; 
% 0.46/0.64  ; Term-hash-array has 828 terms in all.
% 0.46/0.64  ; Feature-vector-row-index has 122 entries (129 at peak, 129 added, 7 deleted).
% 0.46/0.64  ; Feature-vector-row-index has 846 nodes (915 at peak, 915 added, 69 deleted).
% 0.46/0.64  ;  Retrieved 754 possibly forward subsuming rows in 228 calls.
% 0.46/0.64  ;  Retrieved 21 possibly backward subsumed rows in 129 calls.
% 0.46/0.64  ; Path-index has 690 entries (721 at peak, 831 added, 141 deleted).
% 0.46/0.64  ; Path-index has 2,188 nodes (2,215 at peak, 2,385 added, 197 deleted).
% 0.46/0.64  ; Trie-index has 690 entries (721 at peak, 831 added, 141 deleted).
% 0.46/0.64  ; Trie-index has 2,586 nodes (2,703 at peak, 3,030 added, 444 deleted).
% 0.46/0.64  ; Retrieved 3,806 generalization terms in 8,384 calls.
% 0.46/0.64  ; Retrieved 308 instance terms in 307 calls.
% 0.46/0.64  ; Retrieved 6,709 unifiable terms in 1,903 calls.
% 0.46/0.64  ; 
% 0.46/0.64  ; The agenda of rows to process has 24 entries:
% 0.46/0.64  ;     2 with value 14              1 with value 19               1 with value 24
% 0.46/0.64  ;     1 with value 15              1 with value 20               1 with value 25
% 0.46/0.64  ;     1 with value 16              6 with value 22               3 with value 26
% 0.46/0.64  ;     3 with value 17              3 with value 23               1 with value 28
% 0.46/0.64  ; The agenda of rows to give has 206 entries:
% 0.46/0.64  ;     1 with value (4 13)         24 with value (4 22)          11 with value (4 26)
% 0.46/0.64  ;    17 with value (4 19)         14 with value (4 23)          10 with value (4 27)
% 0.46/0.64  ;    54 with value (4 20)         17 with value (4 24)           1 with value (4 29)
% 0.46/0.64  ;    44 with value (4 21)         11 with value (4 25)           2 with value (4 31)
% 0.46/0.64  Evaluation took:
% 0.46/0.64    0.168 seconds of real time
% 0.46/0.64    0.146297 seconds of user run time
% 0.46/0.64    0.020818 seconds of system run time
% 0.46/0.64    0 calls to %EVAL
% 0.46/0.64    0 page faults and
% 0.46/0.64    10,704,376 bytes consed.
% 0.46/0.64  :PROOF-FOUND
% 0.46/0.64  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-29T16:53:07
% 0.46/0.64  :PROOF-FOUND
% 0.46/0.64  * 
%------------------------------------------------------------------------------