TSTP Solution File: GRP124-9.004 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP124-9.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 : Sat Jul 16 11:36:46 EDT 2022

% Result   : Unsatisfiable 0.21s 0.57s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   21
% Syntax   : Number of clauses     :   51 (  36 unt;  11 nHn;  49 RR)
%            Number of literals    :   74 (   0 equ;  37 neg)
%            Maximal clause size   :    6 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :   20 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(element_1,axiom,
    group_element(e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).

cnf(element_2,axiom,
    group_element(e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).

cnf(element_3,axiom,
    group_element(e_3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).

cnf(element_4,axiom,
    group_element(e_4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).

cnf(e_1_is_not_e_2,axiom,
    ~ equalish(e_1,e_2),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).

cnf(e_1_is_not_e_4,axiom,
    ~ equalish(e_1,e_4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_4) ).

cnf(e_2_is_not_e_1,axiom,
    ~ equalish(e_2,e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).

cnf(e_2_is_not_e_3,axiom,
    ~ equalish(e_2,e_3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).

cnf(e_3_is_not_e_1,axiom,
    ~ equalish(e_3,e_1),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).

cnf(e_3_is_not_e_4,axiom,
    ~ equalish(e_3,e_4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).

cnf(e_4_is_not_e_1,axiom,
    ~ equalish(e_4,e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_1) ).

cnf(e_4_is_not_e_3,axiom,
    ~ equalish(e_4,e_3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_3) ).

cnf(product1_total_function1,axiom,
    ( ~ group_element(X)
    | ~ group_element(Y)
    | product1(X,Y,e_1)
    | product1(X,Y,e_2)
    | product1(X,Y,e_3)
    | product1(X,Y,e_4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_total_function1) ).

cnf(product1_right_cancellation,axiom,
    ( ~ product1(X,Y,Z)
    | ~ product1(X,U,Z)
    | equalish(Y,U) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_right_cancellation) ).

cnf(product1_left_cancellation,axiom,
    ( ~ product1(X,Y,Z)
    | ~ product1(U,Y,Z)
    | equalish(X,U) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_left_cancellation) ).

cnf(product1_idempotence,axiom,
    product1(X,X,X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_idempotence) ).

cnf(product2_total_function2,axiom,
    ( ~ product2(X,Y,Z)
    | ~ product2(X,Y,U)
    | equalish(Z,U) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_total_function2) ).

cnf(product2_idempotence,axiom,
    product2(X,X,X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_idempotence) ).

cnf(qg2a,negated_conjecture,
    ( ~ product1(X,Y,Z)
    | ~ product1(Z,X,U)
    | product2(U,Y,X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg2a) ).

cnf(41,plain,
    ~ product1(e_4,e_1,e_4),
    inference('UR-RESOLVE',[status(thm)],[product1_right_cancellation,product1_idempotence,e_1_is_not_e_4]) ).

cnf(44,plain,
    ~ product1(e_3,e_1,e_3),
    inference('UR-RESOLVE',[status(thm)],[product1_right_cancellation,product1_idempotence,e_1_is_not_e_3]) ).

cnf(45,plain,
    ~ product1(e_3,e_2,e_3),
    inference('UR-RESOLVE',[status(thm)],[product1_right_cancellation,product1_idempotence,e_2_is_not_e_3]) ).

cnf(46,plain,
    ~ product1(e_3,e_4,e_3),
    inference('UR-RESOLVE',[status(thm)],[product1_right_cancellation,product1_idempotence,e_4_is_not_e_3]) ).

cnf(47,plain,
    ~ product1(e_2,e_1,e_2),
    inference('UR-RESOLVE',[status(thm)],[product1_right_cancellation,product1_idempotence,e_1_is_not_e_2]) ).

cnf(48,plain,
    ~ product1(e_2,e_3,e_2),
    inference('UR-RESOLVE',[status(thm)],[product1_right_cancellation,product1_idempotence,e_3_is_not_e_2]) ).

cnf(55,plain,
    ~ product1(e_3,e_4,e_4),
    inference('UR-RESOLVE',[status(thm)],[product1_left_cancellation,product1_idempotence,e_3_is_not_e_4]) ).

cnf(57,plain,
    ~ product1(e_2,e_3,e_3),
    inference('UR-RESOLVE',[status(thm)],[product1_left_cancellation,product1_idempotence,e_2_is_not_e_3]) ).

cnf(60,plain,
    ~ product1(e_3,e_2,e_2),
    inference('UR-RESOLVE',[status(thm)],[product1_left_cancellation,product1_idempotence,e_3_is_not_e_2]) ).

cnf(62,plain,
    ~ product1(e_2,e_1,e_1),
    inference('UR-RESOLVE',[status(thm)],[product1_left_cancellation,product1_idempotence,e_2_is_not_e_1]) ).

cnf(63,plain,
    ~ product1(e_3,e_1,e_1),
    inference('UR-RESOLVE',[status(thm)],[product1_left_cancellation,product1_idempotence,e_3_is_not_e_1]) ).

cnf(64,plain,
    ~ product1(e_4,e_1,e_1),
    inference('UR-RESOLVE',[status(thm)],[product1_left_cancellation,product1_idempotence,e_4_is_not_e_1]) ).

cnf(67,plain,
    ~ product2(e_4,e_4,e_3),
    inference('UR-RESOLVE',[status(thm)],[product2_total_function2,product2_idempotence,e_3_is_not_e_4]) ).

cnf(74,plain,
    ~ product2(e_1,e_1,e_2),
    inference('UR-RESOLVE',[status(thm)],[product2_total_function2,product2_idempotence,e_2_is_not_e_1]) ).

cnf(75,plain,
    ~ product2(e_1,e_1,e_3),
    inference('UR-RESOLVE',[status(thm)],[product2_total_function2,product2_idempotence,e_3_is_not_e_1]) ).

cnf(76,plain,
    ~ product2(e_1,e_1,e_4),
    inference('UR-RESOLVE',[status(thm)],[product2_total_function2,product2_idempotence,e_4_is_not_e_1]) ).

cnf(103,plain,
    ( product1(e_4,e_1,e_2)
    | product1(e_4,e_1,e_3) ),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product1_total_function1,element_4,element_1]),41,64]) ).

cnf(104,plain,
    ( product1(e_3,e_4,e_1)
    | product1(e_3,e_4,e_2) ),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product1_total_function1,element_3,element_4]),55,46]) ).

cnf(105,plain,
    ( product1(e_3,e_2,e_1)
    | product1(e_3,e_2,e_4) ),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product1_total_function1,element_3,element_2]),45,60]) ).

cnf(106,plain,
    ( product1(e_3,e_1,e_2)
    | product1(e_3,e_1,e_4) ),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product1_total_function1,element_3,element_1]),44,63]) ).

cnf(108,plain,
    ( product1(e_2,e_3,e_1)
    | product1(e_2,e_3,e_4) ),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product1_total_function1,element_2,element_3]),57,48]) ).

cnf(109,plain,
    ( product1(e_2,e_1,e_3)
    | product1(e_2,e_1,e_4) ),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product1_total_function1,element_2,element_1]),47,62]) ).

cnf(129,plain,
    ( product1(e_3,e_1,e_2)
    | product1(e_3,e_2,e_1) ),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product1_right_cancellation,106,105]),e_1_is_not_e_2]) ).

cnf(134,plain,
    ( product1(e_2,e_3,e_1)
    | product1(e_3,e_4,e_1) ),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[qg2a,108,104]),67]) ).

cnf(135,plain,
    ( product1(e_2,e_1,e_3)
    | product1(e_3,e_1,e_2) ),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product1_left_cancellation,109,106]),e_2_is_not_e_3]) ).

cnf(179,plain,
    ( product1(e_2,e_3,e_1)
    | product1(e_4,e_1,e_2) ),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[qg2a,134,103]),76]) ).

cnf(180,plain,
    product1(e_3,e_1,e_2),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[qg2a,135,129]),74]) ).

cnf(181,plain,
    ~ product1(e_2,e_3,e_1),
    inference('UR-RESOLVE',[status(thm)],[qg2a,180,75]) ).

cnf(191,plain,
    product1(e_4,e_1,e_2),
    inference('REWRITE',[status(thm)],[179,181]) ).

cnf(192,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[product1_left_cancellation,180,e_3_is_not_e_4]),191]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP124-9.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13  % Command  : run-snark %s %d
% 0.13/0.34  % Computer : n020.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 : Mon Jun 13 11:39:05 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.21/0.46  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.47  * 
% 0.21/0.47  * 
% 0.21/0.47  #<PACKAGE "SNARK-USER">
% 0.21/0.47  * 
% 0.21/0.47  SNARK-TPTP-OPTIONS
% 0.21/0.47  * 
% 0.21/0.47  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.21/0.47   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.21/0.47   (USE-FACTORING :POS)
% 0.21/0.47   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.21/0.48   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.21/0.48   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.21/0.48   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.21/0.48   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.21/0.48   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.21/0.48   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.21/0.48   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.21/0.48   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.21/0.48   (DECLARE-TPTP-SYMBOLS2))
% 0.21/0.48  * 
% 0.21/0.48  "."
% 0.21/0.48  * 
% 0.21/0.48  ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T11:39:05
% 0.21/0.48  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n020.cluster.edu at 2022-06-13T11:39:05
% 0.21/0.49  WARNING:
% 0.21/0.49     |product| is a 3-ary relation that occurs only positively; disabling rows that contain it.
% 0.21/0.57  
% 0.21/0.57  
% 0.21/0.57  #||
% 0.21/0.57  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.57  % SZS output start Refutation
% See solution above
% 0.21/0.57  ||#
% 0.21/0.57  
% 0.21/0.57  ; Summary of computation:
% 0.21/0.57  ;       675 formulas have been input or derived (from 135 formulas).
% 0.21/0.57  ;       192 (28%) were retained.  Of these,
% 0.21/0.57  ;           59 (31%) were simplified or subsumed later,
% 0.21/0.57  ;          133 (69%) are still being kept.
% 0.21/0.57  ; 
% 0.21/0.57  ; Run time in seconds excluding printing time:
% 0.21/0.57  ;     0.004   4%   Read assertion file          (1 call)
% 0.21/0.57  ;     0.001   1%   Assert                       (29 calls)
% 0.21/0.57  ;     0.010  11%   Process new row              (600 calls)
% 0.21/0.57  ;     0.026  28%   Resolution                   (268 calls)
% 0.21/0.57  ;     0.000   0%   Paramodulation               (134 calls)
% 0.21/0.57  ;     0.000   0%   Factoring                    (33 calls)
% 0.21/0.57  ;     0.002   2%   Condensing                   (152 calls)
% 0.21/0.57  ;     0.006   6%   Forward subsumption          (152 calls)
% 0.21/0.57  ;     0.004   4%   Backward subsumption         (89 calls)
% 0.21/0.57  ;     0.003   3%   Clause clause subsumption    (1,063 calls)
% 0.21/0.57  ;     0.006   6%   Forward simplification       (577 calls)
% 0.21/0.57  ;     0.002   2%   Backward simplification      (192 calls)
% 0.21/0.57  ;     0.003   3%   Ordering                     (316 calls)
% 0.21/0.57  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.21/0.57  ;     0.001   1%   Purity testing               (1 call)
% 0.21/0.57  ;     0.025  27%   Other
% 0.21/0.57  ;     0.093        Total
% 0.21/0.57  ;     0.098        Real time
% 0.21/0.57  ; 
% 0.21/0.57  ; Term-hash-array has 162 terms in all.
% 0.21/0.57  ; Feature-vector-row-index has 30 entries (84 at peak, 89 added, 59 deleted).
% 0.21/0.57  ; Feature-vector-row-index has 79 nodes (144 at peak, 159 added, 80 deleted).
% 0.21/0.57  ;  Retrieved 946 possibly forward subsuming rows in 152 calls.
% 0.21/0.57  ;  Retrieved 364 possibly backward subsumed rows in 89 calls.
% 0.21/0.57  ; Path-index has 157 entries (166 at peak, 167 added, 10 deleted).
% 0.21/0.57  ; Path-index has 62 nodes (62 at peak, 62 added, 0 deleted).
% 0.21/0.57  ; Trie-index has 157 entries (166 at peak, 167 added, 10 deleted).
% 0.21/0.57  ; Trie-index has 197 nodes (206 at peak, 207 added, 10 deleted).
% 0.21/0.57  ; Retrieved 1,099 generalization terms in 1,124 calls.
% 0.21/0.57  ; Retrieved 133 instance terms in 102 calls.
% 0.21/0.57  ; Retrieved 6,661 unifiable terms in 1,849 calls.
% 0.21/0.57  ; 
% 0.21/0.57  ; The agenda of rows to process has 23 entries:
% 0.21/0.57  ;    17 with value 9               4 with value 13               2 with value 14
% 0.21/0.57  ; The agenda of rows to give has 17 entries:
% 0.21/0.57  ;     1 with value (4 6)           4 with value (4 8)            6 with value (4 12)
% 0.21/0.57  ;     4 with value (4 7)           1 with value (4 9)            1 with value (4 13)
% 0.21/0.57  Evaluation took:
% 0.21/0.57    0.099 seconds of real time
% 0.21/0.57    0.077501 seconds of user run time
% 0.21/0.57    0.020912 seconds of system run time
% 0.21/0.57    0 calls to %EVAL
% 0.21/0.57    0 page faults and
% 0.21/0.57    7,391,384 bytes consed.
% 0.21/0.57  :PROOF-FOUND
% 0.21/0.57  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T11:39:05
% 0.21/0.58  :PROOF-FOUND
% 0.21/0.58  * 
%------------------------------------------------------------------------------