TSTP Solution File: GRP133-2.003 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP133-2.003 : TPTP v8.1.0. Released v1.2.0.
% 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 : Sat Jul 16 11:37:02 EDT 2022

% Result   : Unsatisfiable 0.14s 0.45s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   14
% Syntax   : Number of clauses     :   50 (  20 unt;  26 nHn;  50 RR)
%            Number of literals    :  104 (   0 equ;  22 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   17 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(e_1_then_e_2,axiom,
    next(e_1,e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_then_e_2) ).

cnf(e_3_greater_e_2,axiom,
    greater(e_3,e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_2) ).

cnf(no_redundancy,axiom,
    ( ~ product(X,e_1,Y)
    | ~ next(X,Z)
    | ~ greater(Y,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_redundancy) ).

cnf(element_1,axiom,
    group_element(e_1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).

cnf(element_2,axiom,
    group_element(e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).

cnf(element_3,axiom,
    group_element(e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).

cnf(e_1_is_not_e_2,axiom,
    ~ equalish(e_1,e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).

cnf(e_1_is_not_e_3,axiom,
    ~ equalish(e_1,e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).

cnf(e_3_is_not_e_1,axiom,
    ~ equalish(e_3,e_1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).

cnf(e_3_is_not_e_2,axiom,
    ~ equalish(e_3,e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).

cnf(product_total_function1,axiom,
    ( ~ group_element(X)
    | ~ group_element(Y)
    | product(X,Y,e_1)
    | product(X,Y,e_2)
    | product(X,Y,e_3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).

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

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

cnf(qg3,negated_conjecture,
    ( ~ product(X,Y,Z)
    | ~ product(Y,X,U)
    | product(Z,U,X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).

cnf(21,plain,
    ~ product(e_1,e_1,e_3),
    inference('UR-RESOLVE',[status(thm)],[no_redundancy,e_1_then_e_2,e_3_greater_e_2]) ).

cnf(22,plain,
    ( product(e_3,e_3,e_1)
    | product(e_3,e_3,e_2)
    | product(e_3,e_3,e_3) ),
    inference('HYPERRESOLVE',[status(thm)],[product_total_function1,element_3,element_3]) ).

cnf(24,plain,
    ( product(e_3,e_1,e_1)
    | product(e_3,e_1,e_2)
    | product(e_3,e_1,e_3) ),
    inference('HYPERRESOLVE',[status(thm)],[product_total_function1,element_3,element_1]) ).

cnf(27,plain,
    ( product(e_2,e_1,e_1)
    | product(e_2,e_1,e_2)
    | product(e_2,e_1,e_3) ),
    inference('HYPERRESOLVE',[status(thm)],[product_total_function1,element_2,element_1]) ).

cnf(28,plain,
    ( product(e_1,e_3,e_1)
    | product(e_1,e_3,e_2)
    | product(e_1,e_3,e_3) ),
    inference('HYPERRESOLVE',[status(thm)],[product_total_function1,element_1,element_3]) ).

cnf(29,plain,
    ( product(e_1,e_2,e_1)
    | product(e_1,e_2,e_2)
    | product(e_1,e_2,e_3) ),
    inference('HYPERRESOLVE',[status(thm)],[product_total_function1,element_1,element_2]) ).

cnf(30,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_1,e_2) ),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_total_function1,element_1,element_1]),21]) ).

cnf(31,plain,
    ~ product(e_3,e_3,e_1),
    inference('UR-RESOLVE',[status(thm)],[qg3,21]) ).

cnf(32,plain,
    ( product(e_3,e_3,e_2)
    | product(e_3,e_3,e_3) ),
    inference('REWRITE',[status(thm)],[22,31]) ).

cnf(35,plain,
    ( product(e_1,e_1,e_1)
    | product(e_2,e_2,e_1) ),
    inference('HYPERRESOLVE',[status(thm)],[qg3,30,30]) ).

cnf(41,plain,
    ( product(e_3,e_1,e_1)
    | product(e_3,e_1,e_2)
    | product(e_3,e_3,e_2) ),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_right_cancellation,24,32]),e_1_is_not_e_3]) ).

cnf(54,plain,
    ( product(e_1,e_3,e_1)
    | product(e_1,e_3,e_2)
    | product(e_3,e_3,e_2) ),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,28,32]),e_1_is_not_e_3]) ).

cnf(56,plain,
    ( product(e_1,e_3,e_1)
    | product(e_1,e_3,e_2)
    | product(e_3,e_1,e_1)
    | product(e_3,e_1,e_2) ),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[qg3,28,24]),31]) ).

cnf(61,plain,
    ( product(e_1,e_2,e_1)
    | product(e_1,e_2,e_2)
    | product(e_2,e_1,e_1)
    | product(e_2,e_1,e_2) ),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[qg3,29,27]),31]) ).

cnf(65,plain,
    ( product(e_3,e_1,e_1)
    | product(e_3,e_1,e_2)
    | product(e_2,e_2,e_3) ),
    inference('HYPERRESOLVE',[status(thm)],[qg3,41,41]) ).

cnf(67,plain,
    ( product(e_1,e_3,e_1)
    | product(e_1,e_3,e_2)
    | product(e_2,e_2,e_3) ),
    inference('HYPERRESOLVE',[status(thm)],[qg3,54,54]) ).

cnf(73,plain,
    ( product(e_3,e_1,e_1)
    | product(e_3,e_1,e_2)
    | product(e_1,e_1,e_1) ),
    inference('HYPERRESOLVE',[status(thm)],[qg3,65,35]) ).

cnf(82,plain,
    ( product(e_1,e_3,e_1)
    | product(e_1,e_3,e_2)
    | product(e_1,e_1,e_1) ),
    inference('HYPERRESOLVE',[status(thm)],[qg3,67,35]) ).

cnf(84,plain,
    ( product(e_3,e_1,e_1)
    | product(e_1,e_1,e_1) ),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,73,30]),e_3_is_not_e_1]) ).

cnf(85,plain,
    ( product(e_1,e_3,e_1)
    | product(e_1,e_1,e_1) ),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_right_cancellation,82,30]),e_3_is_not_e_1]) ).

cnf(86,plain,
    product(e_1,e_1,e_1),
    inference('HYPERRESOLVE',[status(thm)],[qg3,85,84]) ).

cnf(88,plain,
    ~ product(e_2,e_1,e_1),
    inference('UR-RESOLVE',[status(thm)],[product_left_cancellation,86,e_1_is_not_e_2]) ).

cnf(89,plain,
    ( product(e_2,e_1,e_2)
    | product(e_2,e_1,e_3) ),
    inference('REWRITE',[status(thm)],[27,88]) ).

cnf(92,plain,
    ( product(e_1,e_2,e_1)
    | product(e_1,e_2,e_2)
    | product(e_2,e_1,e_2) ),
    inference('REWRITE',[status(thm)],[61,88]) ).

cnf(94,plain,
    ~ product(e_3,e_1,e_1),
    inference('UR-RESOLVE',[status(thm)],[product_left_cancellation,86,e_1_is_not_e_3]) ).

cnf(96,plain,
    ( product(e_3,e_1,e_2)
    | product(e_3,e_3,e_2) ),
    inference('REWRITE',[status(thm)],[41,94]) ).

cnf(97,plain,
    ( product(e_1,e_3,e_1)
    | product(e_1,e_3,e_2)
    | product(e_3,e_1,e_2) ),
    inference('REWRITE',[status(thm)],[56,94]) ).

cnf(103,plain,
    ~ product(e_1,e_2,e_1),
    inference('UR-RESOLVE',[status(thm)],[product_right_cancellation,86,e_1_is_not_e_2]) ).

cnf(107,plain,
    ( product(e_1,e_2,e_2)
    | product(e_2,e_1,e_2) ),
    inference('REWRITE',[status(thm)],[92,103]) ).

cnf(109,plain,
    ~ product(e_1,e_3,e_1),
    inference('UR-RESOLVE',[status(thm)],[product_right_cancellation,86,e_1_is_not_e_3]) ).

cnf(116,plain,
    ( product(e_1,e_3,e_2)
    | product(e_3,e_1,e_2) ),
    inference('REWRITE',[status(thm)],[97,109]) ).

cnf(121,plain,
    ( product(e_2,e_1,e_2)
    | product(e_3,e_2,e_2) ),
    inference('HYPERRESOLVE',[status(thm)],[qg3,107,89]) ).

cnf(125,plain,
    product(e_3,e_1,e_2),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,116,96]),e_1_is_not_e_3]) ).

cnf(127,plain,
    ~ product(e_2,e_1,e_2),
    inference('UR-RESOLVE',[status(thm)],[product_left_cancellation,125,e_3_is_not_e_2]) ).

cnf(134,plain,
    product(e_3,e_2,e_2),
    inference('REWRITE',[status(thm)],[121,127]) ).

cnf(135,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[product_right_cancellation,125,e_1_is_not_e_2]),134]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : GRP133-2.003 : TPTP v8.1.0. Released v1.2.0.
% 0.00/0.09  % Command  : run-snark %s %d
% 0.09/0.28  % Computer : n032.cluster.edu
% 0.09/0.28  % Model    : x86_64 x86_64
% 0.09/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28  % Memory   : 8042.1875MB
% 0.09/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28  % CPULimit : 300
% 0.09/0.28  % WCLimit  : 600
% 0.09/0.28  % DateTime : Mon Jun 13 06:44:56 EDT 2022
% 0.09/0.28  % CPUTime  : 
% 0.14/0.37  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.38  * 
% 0.14/0.38  * 
% 0.14/0.38  #<PACKAGE "SNARK-USER">
% 0.14/0.38  * 
% 0.14/0.38  SNARK-TPTP-OPTIONS
% 0.14/0.38  * 
% 0.14/0.38  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.14/0.38   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.14/0.38   (USE-FACTORING :POS)
% 0.14/0.38   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.14/0.38   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.14/0.38   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.14/0.38   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.14/0.38   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.14/0.38   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.14/0.38   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.14/0.38   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.14/0.38   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.14/0.38   (DECLARE-TPTP-SYMBOLS2))
% 0.14/0.38  * 
% 0.14/0.38  "."
% 0.14/0.38  * 
% 0.14/0.38  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T06:44:56
% 0.14/0.38  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n032.cluster.edu at 2022-06-13T06:44:56
% 0.14/0.45  
% 0.14/0.45  
% 0.14/0.45  #||
% 0.14/0.45  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.45  % SZS output start Refutation
% See solution above
% 0.14/0.46  ||#
% 0.14/0.46  
% 0.14/0.46  ; Summary of computation:
% 0.14/0.46  ;       887 formulas have been input or derived (from 72 formulas).
% 0.14/0.46  ;       135 (15%) were retained.  Of these,
% 0.14/0.46  ;           91 (67%) were simplified or subsumed later,
% 0.14/0.46  ;           44 (33%) are still being kept.
% 0.14/0.46  ; 
% 0.14/0.46  ; Run time in seconds excluding printing time:
% 0.14/0.46  ;     0.002   3%   Read assertion file          (1 call)
% 0.14/0.46  ;     0.001   1%   Assert                       (20 calls)
% 0.14/0.46  ;     0.010  15%   Process new row              (710 calls)
% 0.14/0.46  ;     0.015  22%   Resolution                   (142 calls)
% 0.14/0.46  ;     0.001   1%   Paramodulation               (71 calls)
% 0.14/0.46  ;     0.000   0%   Factoring                    (39 calls)
% 0.14/0.46  ;     0.000   0%   Condensing                   (268 calls)
% 0.14/0.46  ;     0.006   9%   Forward subsumption          (268 calls)
% 0.14/0.46  ;     0.003   4%   Backward subsumption         (99 calls)
% 0.14/0.46  ;     0.001   1%   Clause clause subsumption    (990 calls)
% 0.14/0.46  ;     0.006   9%   Forward simplification       (518 calls)
% 0.14/0.46  ;     0.002   3%   Backward simplification      (135 calls)
% 0.14/0.46  ;     0.000   0%   Ordering                     (541 calls)
% 0.14/0.46  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.14/0.46  ;     0.000   0%   Purity testing               (1 call)
% 0.14/0.46  ;     0.021  31%   Other
% 0.14/0.46  ;     0.068        Total
% 0.14/0.46  ;     0.071        Real time
% 0.14/0.46  ; 
% 0.14/0.46  ; Term-hash-array has 63 terms in all.
% 0.14/0.46  ; Feature-vector-row-index has 8 entries (41 at peak, 99 added, 91 deleted).
% 0.14/0.46  ; Feature-vector-row-index has 22 nodes (117 at peak, 196 added, 174 deleted).
% 0.14/0.46  ;  Retrieved 1,374 possibly forward subsuming rows in 268 calls.
% 0.14/0.46  ;  Retrieved 312 possibly backward subsumed rows in 99 calls.
% 0.14/0.46  ; Path-index has 59 entries (64 at peak, 84 added, 25 deleted).
% 0.14/0.46  ; Path-index has 57 nodes (57 at peak, 57 added, 0 deleted).
% 0.14/0.46  ; Trie-index has 59 entries (64 at peak, 84 added, 25 deleted).
% 0.14/0.46  ; Trie-index has 84 nodes (88 at peak, 111 added, 27 deleted).
% 0.14/0.46  ; Retrieved 339 generalization terms in 1,666 calls.
% 0.14/0.46  ; Retrieved 35 instance terms in 35 calls.
% 0.14/0.46  ; Retrieved 3,503 unifiable terms in 875 calls.
% 0.14/0.46  ; 
% 0.14/0.46  ; The agenda of rows to process has 20 entries:
% 0.14/0.46  ;     9 with value 9               4 with value 14               2 with value 18
% 0.14/0.46  ;     5 with value 13
% 0.14/0.46  ; The agenda of rows to give has 10 entries:
% 0.14/0.46  ;     1 with value (4 6)           3 with value (4 8)            1 with value (4 10)
% 0.14/0.46  ;     1 with value (4 7)           2 with value (4 9)            2 with value (4 12)
% 0.14/0.46  Evaluation took:
% 0.14/0.46    0.071 seconds of real time
% 0.14/0.46    0.063857 seconds of user run time
% 0.14/0.46    0.007953 seconds of system run time
% 0.14/0.46    0 calls to %EVAL
% 0.14/0.46    0 page faults and
% 0.14/0.46    8,316,552 bytes consed.
% 0.14/0.46  :PROOF-FOUND
% 0.14/0.46  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T06:44:56
% 0.14/0.46  :PROOF-FOUND
% 0.14/0.46  * 
%------------------------------------------------------------------------------