TSTP Solution File: GRP040-4 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP040-4 : 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 : Sat Jul 16 11:35:26 EDT 2022

% Result   : Unsatisfiable 0.42s 0.62s
% Output   : Refutation 0.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   16
% Syntax   : Number of clauses     :   24 (  17 unt;   2 nHn;  18 RR)
%            Number of literals    :   40 (   3 equ;  14 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   28 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
    product(identity,X,X),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_identity) ).

cnf(right_identity,axiom,
    product(X,identity,X),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_identity) ).

cnf(left_inverse,axiom,
    product(inverse(X),X,identity),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_inverse) ).

cnf(associativity1,axiom,
    ( ~ product(X,Y,Z)
    | ~ product(Y,U,V)
    | ~ product(Z,U,W)
    | product(X,V,W) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',associativity1) ).

cnf(associativity2,axiom,
    ( ~ product(X,Y,Z)
    | ~ product(Y,U,V)
    | ~ product(X,V,W)
    | product(Z,U,W) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',associativity2) ).

cnf(closure_of_product_and_inverse,axiom,
    ( ~ subgroup_member(X)
    | ~ subgroup_member(Y)
    | ~ product(X,inverse(Y),Z)
    | subgroup_member(Z) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP003-2.ax',closure_of_product_and_inverse) ).

cnf(closure_of_inverse,axiom,
    ( ~ subgroup_member(X)
    | subgroup_member(inverse(X)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_inverse) ).

cnf(product_right_cancellation,axiom,
    ( ~ product(X,Y,Z)
    | ~ product(X,U,Z)
    | U = Y ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).

cnf(an_element_in_O2,axiom,
    ( subgroup_member(element_in_O2(X,Y))
    | subgroup_member(Y)
    | subgroup_member(X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_element_in_O2) ).

cnf(property_of_O2,axiom,
    ( product(X,element_in_O2(X,Y),Y)
    | subgroup_member(Y)
    | subgroup_member(X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_O2) ).

cnf(a_in_subgroup,hypothesis,
    ~ subgroup_member(a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_in_subgroup) ).

cnf(b_is_in_subgroup,hypothesis,
    subgroup_member(b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_in_subgroup) ).

cnf(d_in_subgroup,hypothesis,
    ~ subgroup_member(d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_in_subgroup) ).

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

cnf(a_times_c_is_d,hypothesis,
    product(a,c,d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_d) ).

cnf(prove_inverse_is_self_cancelling,negated_conjecture,
    inverse(inverse(X)) = X,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_is_self_cancelling) ).

cnf(22,plain,
    subgroup_member(inverse(b)),
    inference('HYPERRESOLVE',[status(thm)],[closure_of_inverse,b_is_in_subgroup]) ).

cnf(25,plain,
    subgroup_member(element_in_O2(a,d)),
    inference('UR-RESOLVE',[status(thm)],[an_element_in_O2,d_in_subgroup,a_in_subgroup]) ).

cnf(44,plain,
    c = element_in_O2(a,d),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_right_cancellation,property_of_O2,a_times_c_is_d]),a_in_subgroup,d_in_subgroup]) ).

cnf(45,plain,
    subgroup_member(c),
    inference('REWRITE',[status(thm)],[25,44,theory(equality)]) ).

cnf(112,plain,
    product(c,a,b),
    inference('HYPERRESOLVE',[status(thm)],[associativity2,b_times_a_inverse_is_c,left_inverse,right_identity]) ).

cnf(147,plain,
    subgroup_member(inverse(c)),
    inference('HYPERRESOLVE',[status(thm)],[closure_of_inverse,45]) ).

cnf(216,plain,
    product(inverse(c),b,a),
    inference('HYPERRESOLVE',[status(thm)],[associativity1,112,left_inverse,left_identity]) ).

cnf(350,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[closure_of_product_and_inverse,147,22,a_in_subgroup]),216,prove_inverse_is_self_cancelling,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.13  % Problem  : GRP040-4 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.14  % Command  : run-snark %s %d
% 0.14/0.35  % Computer : n026.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Mon Jun 13 23:15:51 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.21/0.48  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.49  * 
% 0.21/0.49  * 
% 0.21/0.49  #<PACKAGE "SNARK-USER">
% 0.21/0.49  * 
% 0.21/0.49  SNARK-TPTP-OPTIONS
% 0.21/0.49  * 
% 0.21/0.49  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.21/0.49   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.21/0.49   (USE-FACTORING :POS)
% 0.21/0.49   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.21/0.49   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.21/0.49   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.21/0.49   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.21/0.49   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.21/0.49   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.21/0.49   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.21/0.49   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.21/0.49   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.21/0.49   (DECLARE-TPTP-SYMBOLS2))
% 0.21/0.49  * 
% 0.21/0.49  "."
% 0.21/0.49  * 
% 0.21/0.49  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T23:15:51
% 0.21/0.49  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n026.cluster.edu at 2022-06-13T23:15:51
% 0.21/0.51  
% 0.21/0.51  ; Recognized possible left identity assertion (|product| |identity| ?X ?X).
% 0.21/0.51  ; Recognized possible right identity assertion (|product| ?X |identity| ?X).
% 0.21/0.51  ; Recognized possible left inverse assertion (|product| (|inverse| ?X) ?X |identity|).
% 0.21/0.51  ; Recognized possible right inverse assertion (|product| ?X (|inverse| ?X) |identity|).
% 0.21/0.51  ; Recognized relation function assertion (|product| ?X ?Y (|multiply| ?X ?Y)).
% 0.21/0.51  ; Recognized relation functionality assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?X ?Y ?U)) (= ?Z ?U)).
% 0.21/0.51  ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?Z ?U ?W)) (|product| ?X ?V ?W)).
% 0.42/0.62  ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?X ?V ?W)) (|product| ?Z ?U ?W)).
% 0.42/0.62  
% 0.42/0.62  #||
% 0.42/0.62  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.42/0.62  % SZS output start Refutation
% See solution above
% 0.42/0.63  ||#
% 0.42/0.63  
% 0.42/0.63  ; Summary of computation:
% 0.42/0.63  ;      1547 formulas have been input or derived (from 36 formulas).
% 0.42/0.63  ;       350 (23%) were retained.  Of these,
% 0.42/0.63  ;           10 ( 3%) were simplified or subsumed later,
% 0.42/0.63  ;          340 (97%) are still being kept.
% 0.42/0.63  ; 
% 0.42/0.63  ; Run time in seconds excluding printing time:
% 0.42/0.63  ;     0.004   3%   Read assertion file          (1 call)
% 0.42/0.63  ;     0.001   1%   Assert                       (21 calls)
% 0.42/0.63  ;     0.026  20%   Process new row              (1,319 calls)
% 0.42/0.63  ;     0.030  23%   Resolution                   (70 calls)
% 0.42/0.63  ;     0.000   0%   Paramodulation               (35 calls)
% 0.42/0.63  ;     0.000   0%   Factoring                    (4 calls)
% 0.42/0.63  ;     0.003   2%   Condensing                   (169 calls)
% 0.42/0.63  ;     0.005   4%   Forward subsumption          (169 calls)
% 0.42/0.63  ;     0.002   2%   Backward subsumption         (96 calls)
% 0.42/0.63  ;     0.002   2%   Clause clause subsumption    (305 calls)
% 0.42/0.63  ;     0.023  18%   Forward simplification       (1,319 calls)
% 0.42/0.63  ;     0.001   1%   Backward simplification      (350 calls)
% 0.42/0.63  ;     0.001   1%   Ordering                     (396 calls)
% 0.42/0.63  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.42/0.63  ;     0.000   0%   Purity testing               (1 call)
% 0.42/0.63  ;     0.032  25%   Other
% 0.42/0.63  ;     0.130        Total
% 0.42/0.63  ;     0.132        Real time
% 0.42/0.63  ; 
% 0.42/0.63  ; Term-hash-array has 544 terms in all.
% 0.42/0.63  ; Feature-vector-row-index has 96 entries (96 at peak, 96 added, 0 deleted).
% 0.42/0.63  ; Feature-vector-row-index has 424 nodes (424 at peak, 424 added, 0 deleted).
% 0.42/0.63  ;  Retrieved 469 possibly forward subsuming rows in 169 calls.
% 0.42/0.63  ;  Retrieved 53 possibly backward subsumed rows in 96 calls.
% 0.42/0.63  ; Path-index has 539 entries (539 at peak, 549 added, 10 deleted).
% 0.42/0.63  ; Path-index has 484 nodes (484 at peak, 486 added, 2 deleted).
% 0.42/0.63  ; Trie-index has 539 entries (539 at peak, 549 added, 10 deleted).
% 0.42/0.63  ; Trie-index has 1,121 nodes (1,121 at peak, 1,137 added, 16 deleted).
% 0.42/0.63  ; Retrieved 2,142 generalization terms in 4,057 calls.
% 0.42/0.63  ; Retrieved 283 instance terms in 253 calls.
% 0.42/0.63  ; Retrieved 18,716 unifiable terms in 1,854 calls.
% 0.42/0.63  ; 
% 0.42/0.63  ; The agenda of rows to process has 43 entries:
% 0.42/0.63  ;     7 with value 13             12 with value 15               2 with value 21
% 0.42/0.63  ;    20 with value 14              2 with value 18
% 0.42/0.63  ; The agenda of rows to give has 304 entries:
% 0.42/0.63  ;    20 with value (4 7)          26 with value (4 14)          13 with value (4 21)
% 0.42/0.63  ;    16 with value (4 8)          17 with value (4 15)           2 with value (4 22)
% 0.42/0.63  ;    29 with value (4 9)           5 with value (4 16)           3 with value (4 23)
% 0.42/0.63  ;    35 with value (4 10)         11 with value (4 17)           1 with value (4 24)
% 0.42/0.63  ;    32 with value (4 11)         14 with value (4 18)           1 with value (4 25)
% 0.42/0.63  ;    43 with value (4 12)          6 with value (4 19)           1 with value (4 26)
% 0.42/0.63  ;    21 with value (4 13)          8 with value (4 20)
% 0.42/0.63  Evaluation took:
% 0.42/0.63    0.132 seconds of real time
% 0.42/0.63    0.11927 seconds of user run time
% 0.42/0.63    0.013138 seconds of system run time
% 0.42/0.63    0 calls to %EVAL
% 0.42/0.63    0 page faults and
% 0.42/0.63    7,608,552 bytes consed.
% 0.42/0.63  :PROOF-FOUND
% 0.42/0.63  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T23:15:51
% 0.42/0.63  :PROOF-FOUND
% 0.42/0.63  * 
%------------------------------------------------------------------------------