TSTP Solution File: GRP086-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP086-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n012.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 11:36:05 EDT 2022

% Result   : Unsatisfiable 0.71s 0.87s
% Output   : Refutation 0.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    2
% Syntax   : Number of clauses     :   26 (  22 unt;   0 nHn;   7 RR)
%            Number of literals    :   34 (  33 equ;  14 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   9 con; 0-2 aty)
%            Number of variables   :   51 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
    multiply(X,multiply(multiply(Y,Z),inverse(multiply(X,Z)))) = Y,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).

cnf(prove_these_axioms,negated_conjecture,
    ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
    | multiply(multiply(inverse(b2),b2),a2) != a2
    | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
    | multiply(a4,b4) != multiply(b4,a4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).

cnf(3,plain,
    multiply(X,multiply(multiply(Y,multiply(multiply(Z,U),inverse(multiply(X,U)))),inverse(Z))) = Y,
    inference('PARAMODULATE',[status(thm)],[single_axiom,single_axiom,theory(equality)]) ).

cnf(5,plain,
    multiply(X,multiply(Y,inverse(Y))) = X,
    inference('PARAMODULATE',[status(thm)],[3,single_axiom,theory(equality)]) ).

cnf(11,plain,
    multiply(X,multiply(Y,inverse(X))) = Y,
    inference('PARAMODULATE',[status(thm)],[3,5,theory(equality)]) ).

cnf(12,plain,
    multiply(X,multiply(multiply(Y,multiply(Z,inverse(X))),inverse(Z))) = Y,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3,5,theory(equality)]),5,theory(equality)]) ).

cnf(13,plain,
    multiply(X,multiply(multiply(Y,Z),inverse(Y))) = multiply(X,Z),
    inference('PARAMODULATE',[status(thm)],[3,11,theory(equality)]) ).

cnf(17,plain,
    multiply(X,multiply(Y,inverse(Z))) = multiply(X,multiply(multiply(Y,U),inverse(multiply(Z,U)))),
    inference('PARAMODULATE',[status(thm)],[13,single_axiom,theory(equality)]) ).

cnf(21,plain,
    multiply(X,multiply(Y,inverse(multiply(Y,multiply(X,inverse(Z)))))) = Z,
    inference('PARAMODULATE',[status(thm)],[12,12,theory(equality)]) ).

cnf(24,plain,
    multiply(multiply(X,Y),multiply(Z,inverse(multiply(Z,Y)))) = X,
    inference('PARAMODULATE',[status(thm)],[21,13,theory(equality)]) ).

cnf(28,plain,
    multiply(multiply(X,multiply(Y,inverse(multiply(Y,Z)))),Z) = X,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[24,24,theory(equality)]),13,theory(equality)]) ).

cnf(29,plain,
    multiply(X,Y) = multiply(X,multiply(Z,inverse(multiply(Z,inverse(Y))))),
    inference('PARAMODULATE',[status(thm)],[13,28,theory(equality)]) ).

cnf(30,plain,
    multiply(X,Y) = multiply(Y,X),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[11,28,theory(equality)]),29,theory(equality)]) ).

cnf(31,plain,
    ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
    | multiply(multiply(inverse(b2),b2),a2) != a2
    | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
    inference('REWRITE',[status(thm)],[prove_these_axioms,30,theory(equality)]) ).

cnf(34,plain,
    multiply(X,multiply(inverse(Y),Y)) = X,
    inference('PARAMODULATE',[status(thm)],[5,30,theory(equality)]) ).

cnf(35,plain,
    multiply(X,multiply(inverse(X),Y)) = Y,
    inference('PARAMODULATE',[status(thm)],[11,30,theory(equality)]) ).

cnf(53,plain,
    ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
    | multiply(multiply(inverse(b2),b2),a2) != a2
    | multiply(multiply(b3,a3),c3) != multiply(a3,multiply(b3,c3)) ),
    inference('PARAMODULATE',[status(thm)],[31,30,theory(equality)]) ).

cnf(56,plain,
    X = multiply(multiply(inverse(Y),Y),X),
    inference('PARAMODULATE',[status(thm)],[30,34,theory(equality)]) ).

cnf(59,plain,
    ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
    | multiply(multiply(b3,a3),c3) != multiply(a3,multiply(b3,c3)) ),
    inference('REWRITE',[status(thm)],[53,56,theory(equality)]) ).

cnf(74,plain,
    X = multiply(multiply(Y,X),inverse(Y)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[35,13,theory(equality)]),35,theory(equality)]) ).

cnf(90,plain,
    multiply(inverse(X),X) = multiply(inverse(Y),Y),
    inference('PARAMODULATE',[status(thm)],[34,56,theory(equality)]) ).

cnf(94,plain,
    multiply(multiply(b3,a3),c3) != multiply(a3,multiply(b3,c3)),
    inference('REWRITE',[status(thm)],[59,90,theory(equality)]) ).

cnf(108,plain,
    multiply(multiply(b3,a3),c3) != multiply(multiply(b3,c3),a3),
    inference('PARAMODULATE',[status(thm)],[94,30,theory(equality)]) ).

cnf(381,plain,
    multiply(multiply(X,Y),multiply(Z,inverse(X))) = multiply(Z,Y),
    inference('PARAMODULATE',[status(thm)],[11,17,theory(equality)]) ).

cnf(393,plain,
    multiply(multiply(X,Y),Z) = multiply(multiply(X,Z),Y),
    inference('PARAMODULATE',[status(thm)],[381,74,theory(equality)]) ).

cnf(394,plain,
    $false,
    inference('REWRITE',[status(thm)],[108,393,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP086-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.13  % Command  : run-snark %s %d
% 0.13/0.34  % Computer : n012.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 : Tue Jun 14 06:23:25 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  * 
% 0.21/0.48  #<PACKAGE "SNARK-USER">
% 0.21/0.48  * 
% 0.21/0.48  SNARK-TPTP-OPTIONS
% 0.21/0.48  * 
% 0.21/0.48  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.21/0.48   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.21/0.48   (USE-FACTORING :POS)
% 0.21/0.48   (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 2022-06-14T06:23:25
% 0.21/0.48  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n012.cluster.edu at 2022-06-14T06:23:25
% 0.71/0.87  
% 0.71/0.87  
% 0.71/0.87  #||
% 0.71/0.87  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.71/0.87  % SZS output start Refutation
% See solution above
% 0.71/0.87  ||#
% 0.71/0.87  
% 0.71/0.87  ; Summary of computation:
% 0.71/0.87  ;      3057 formulas have been input or derived (from 65 formulas).
% 0.71/0.87  ;       394 (13%) were retained.  Of these,
% 0.71/0.87  ;          125 (32%) were simplified or subsumed later,
% 0.71/0.87  ;          269 (68%) are still being kept.
% 0.71/0.87  ; 
% 0.71/0.87  ; Run time in seconds excluding printing time:
% 0.71/0.87  ;     0.001   0%   Read assertion file          (1 call)
% 0.71/0.87  ;     0.000   0%   Assert                       (2 calls)
% 0.71/0.87  ;     0.040  10%   Process new row              (2,773 calls)
% 0.71/0.87  ;     0.004   1%   Resolution                   (128 calls)
% 0.71/0.87  ;     0.039  10%   Paramodulation               (64 calls)
% 0.71/0.87  ;     0.000   0%   Condensing                   (9 calls)
% 0.71/0.87  ;     0.000   0%   Forward subsumption          (9 calls)
% 0.71/0.87  ;     0.003   1%   Backward subsumption         (9 calls)
% 0.71/0.87  ;     0.000   0%   Clause clause subsumption    (28 calls)
% 0.71/0.87  ;     0.102  26%   Forward simplification       (2,620 calls)
% 0.71/0.87  ;     0.031   8%   Backward simplification      (394 calls)
% 0.71/0.87  ;     0.144  37%   Ordering                     (24,477 calls)
% 0.71/0.87  ;     0.001   0%   Sortal reasoning             (32 calls)
% 0.71/0.87  ;     0.000   0%   Purity testing               (1 call)
% 0.71/0.87  ;     0.026   7%   Other
% 0.71/0.87  ;     0.391        Total
% 0.71/0.87  ;     0.394        Real time
% 0.71/0.87  ; 
% 0.71/0.87  ; Term-hash-array has 1,120 terms in all.
% 0.71/0.87  ; Feature-vector-row-index has 0 entries (4 at peak, 9 added, 9 deleted).
% 0.71/0.87  ; Feature-vector-row-index has 1 node (53 at peak, 88 added, 87 deleted).
% 0.71/0.87  ;  Retrieved 12 possibly forward subsuming rows in 9 calls.
% 0.71/0.87  ;  Retrieved 16 possibly backward subsumed rows in 9 calls.
% 0.71/0.87  ; Path-index has 742 entries (829 at peak, 1,215 added, 473 deleted).
% 0.71/0.87  ; Path-index has 937 nodes (962 at peak, 1,293 added, 356 deleted).
% 0.71/0.87  ; Trie-index has 742 entries (829 at peak, 1,215 added, 473 deleted).
% 0.71/0.87  ; Trie-index has 2,984 nodes (3,432 at peak, 4,452 added, 1,468 deleted).
% 0.71/0.87  ; Retrieved 18,309 generalization terms in 16,696 calls.
% 0.71/0.87  ; Retrieved 3,830 instance terms in 558 calls.
% 0.71/0.87  ; Retrieved 7,326 unifiable terms in 548 calls.
% 0.71/0.87  ; 
% 0.71/0.87  ; The agenda of backward simplifiable rows to process has 11 entries:
% 0.71/0.87  ;    11 with value 0
% 0.71/0.87  ; The agenda of rows to process has 87 entries:
% 0.71/0.87  ;     2 with value 24             12 with value 28              13 with value 32
% 0.71/0.87  ;     3 with value 25             14 with value 29               6 with value 33
% 0.71/0.87  ;     9 with value 26              5 with value 30               9 with value 34
% 0.71/0.87  ;     6 with value 27              7 with value 31               1 with value 35
% 0.71/0.87  ; The agenda of rows to give has 227 entries:
% 0.71/0.87  ;     4 with value (4 24)         38 with value (4 30)          15 with value (4 35)
% 0.71/0.87  ;     1 with value (4 26)         19 with value (4 31)          33 with value (4 36)
% 0.71/0.87  ;     5 with value (4 27)         32 with value (4 32)          22 with value (4 37)
% 0.71/0.87  ;     3 with value (4 28)         30 with value (4 33)           2 with value (4 38)
% 0.71/0.87  ;    15 with value (4 29)          8 with value (4 34)
% 0.71/0.87  Evaluation took:
% 0.71/0.87    0.394 seconds of real time
% 0.71/0.87    0.333631 seconds of user run time
% 0.71/0.87    0.060886 seconds of system run time
% 0.71/0.87    [Run times include 0.009 seconds GC run time.]
% 0.71/0.87    0 calls to %EVAL
% 0.71/0.87    0 page faults and
% 0.71/0.87    22,672,696 bytes consed.
% 0.71/0.87  :PROOF-FOUND
% 0.71/0.87  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T06:23:26
% 0.71/0.87  :PROOF-FOUND
% 0.71/0.87  * 
%------------------------------------------------------------------------------