TSTP Solution File: GRP509-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP509-1 : TPTP v8.1.0. Released v2.6.0.
% 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 11:39:12 EDT 2022

% Result   : Unsatisfiable 0.39s 0.57s
% Output   : Refutation 0.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    2
% Syntax   : Number of clauses     :   32 (  32 unt;   0 nHn;   3 RR)
%            Number of literals    :   32 (  31 equ;   2 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   80 (   0 sgn)

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

cnf(prove_these_axioms_1,negated_conjecture,
    multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_1) ).

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

cnf(4,plain,
    multiply(multiply(X,Y),inverse(multiply(multiply(multiply(Z,X),U),Y))) = inverse(multiply(Z,U)),
    inference('PARAMODULATE',[status(thm)],[single_axiom,single_axiom,theory(equality)]) ).

cnf(6,plain,
    multiply(multiply(X,Y),inverse(multiply(Z,Y))) = inverse(multiply(multiply(U,Z),inverse(multiply(U,X)))),
    inference('PARAMODULATE',[status(thm)],[single_axiom,3,theory(equality)]) ).

cnf(7,plain,
    multiply(X,inverse(multiply(multiply(Y,X),inverse(Z)))) = inverse(multiply(multiply(U,Y),inverse(multiply(U,Z)))),
    inference('PARAMODULATE',[status(thm)],[3,3,theory(equality)]) ).

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

cnf(13,plain,
    multiply(multiply(X,inverse(multiply(Y,Z))),inverse(X)) = inverse(multiply(Y,Z)),
    inference('PARAMODULATE',[status(thm)],[4,single_axiom,theory(equality)]) ).

cnf(14,plain,
    inverse(multiply(X,multiply(Y,inverse(multiply(multiply(X,Y),Z))))) = Z,
    inference('PARAMODULATE',[status(thm)],[3,4,theory(equality)]) ).

cnf(21,plain,
    multiply(multiply(X,Y),inverse(multiply(Z,Y))) = inverse(multiply(U,inverse(multiply(multiply(V,multiply(U,X)),inverse(multiply(V,Z)))))),
    inference('PARAMODULATE',[status(thm)],[4,3,theory(equality)]) ).

cnf(27,plain,
    multiply(multiply(X,inverse(Y)),inverse(X)) = inverse(Y),
    inference('PARAMODULATE',[status(thm)],[13,single_axiom,theory(equality)]) ).

cnf(28,plain,
    multiply(inverse(X),inverse(multiply(Y,inverse(Y)))) = inverse(X),
    inference('PARAMODULATE',[status(thm)],[single_axiom,27,theory(equality)]) ).

cnf(30,plain,
    multiply(X,inverse(multiply(multiply(Y,X),Z))) = inverse(multiply(Y,Z)),
    inference('PARAMODULATE',[status(thm)],[27,single_axiom,theory(equality)]) ).

cnf(33,plain,
    inverse(multiply(X,inverse(multiply(X,Y)))) = Y,
    inference('REWRITE',[status(thm)],[14,30,theory(equality)]) ).

cnf(35,plain,
    inverse(multiply(X,inverse(Y))) = inverse(multiply(multiply(Z,X),inverse(multiply(Z,Y)))),
    inference('REWRITE',[status(thm)],[7,30,theory(equality)]) ).

cnf(38,plain,
    multiply(multiply(X,Y),inverse(multiply(Z,Y))) = inverse(multiply(U,inverse(multiply(multiply(U,X),inverse(Z))))),
    inference('REWRITE',[status(thm)],[21,35,theory(equality)]) ).

cnf(39,plain,
    multiply(X,inverse(multiply(Y,inverse(multiply(multiply(Y,Z),inverse(X)))))) = Z,
    inference('REWRITE',[status(thm)],[11,35,theory(equality)]) ).

cnf(42,plain,
    multiply(multiply(X,Y),inverse(multiply(Z,Y))) = inverse(multiply(Z,inverse(X))),
    inference('REWRITE',[status(thm)],[6,35,theory(equality)]) ).

cnf(43,plain,
    inverse(multiply(X,inverse(Y))) = inverse(multiply(Z,inverse(multiply(multiply(Z,Y),inverse(X))))),
    inference('REWRITE',[status(thm)],[38,42,theory(equality)]) ).

cnf(44,plain,
    multiply(X,inverse(multiply(X,inverse(Y)))) = Y,
    inference('REWRITE',[status(thm)],[39,43,theory(equality)]) ).

cnf(47,plain,
    multiply(multiply(X,Y),inverse(X)) = Y,
    inference('PARAMODULATE',[status(thm)],[27,33,theory(equality)]) ).

cnf(50,plain,
    multiply(multiply(multiply(X,inverse(multiply(X,Y))),Z),Y) = Z,
    inference('PARAMODULATE',[status(thm)],[47,33,theory(equality)]) ).

cnf(51,plain,
    multiply(multiply(X,Y),inverse(Y)) = X,
    inference('PARAMODULATE',[status(thm)],[44,47,theory(equality)]) ).

cnf(52,plain,
    multiply(X,inverse(Y)) = inverse(multiply(Y,inverse(X))),
    inference('PARAMODULATE',[status(thm)],[47,44,theory(equality)]) ).

cnf(55,plain,
    inverse(inverse(X)) = X,
    inference('REWRITE',[status(thm)],[44,47,52,theory(equality)]) ).

cnf(63,plain,
    multiply(multiply(inverse(X),Y),X) = Y,
    inference('REWRITE',[status(thm)],[50,47,52,theory(equality)]) ).

cnf(67,plain,
    multiply(inverse(X),multiply(Y,inverse(Y))) = inverse(X),
    inference('REWRITE',[status(thm)],[28,52,theory(equality)]) ).

cnf(69,plain,
    multiply(X,Y) = multiply(Y,X),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[51,47,theory(equality)]),55,theory(equality)]) ).

cnf(73,plain,
    multiply(a1,inverse(a1)) != multiply(inverse(b1),b1),
    inference('PARAMODULATE',[status(thm)],[prove_these_axioms_1,69,theory(equality)]) ).

cnf(75,plain,
    multiply(X,multiply(Y,inverse(Y))) = X,
    inference('PARAMODULATE',[status(thm)],[67,55,theory(equality)]) ).

cnf(77,plain,
    multiply(inverse(X),X) = multiply(Y,inverse(Y)),
    inference('PARAMODULATE',[status(thm)],[63,75,theory(equality)]) ).

cnf(78,plain,
    $false,
    inference('REWRITE',[status(thm)],[73,77,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : GRP509-1 : TPTP v8.1.0. Released v2.6.0.
% 0.08/0.15  % Command  : run-snark %s %d
% 0.14/0.36  % Computer : n026.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Tue Jun 14 08:19:21 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.22/0.49  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.50  * 
% 0.22/0.50  * 
% 0.22/0.51  #<PACKAGE "SNARK-USER">
% 0.22/0.51  * 
% 0.22/0.51  SNARK-TPTP-OPTIONS
% 0.22/0.51  * 
% 0.22/0.51  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.22/0.51   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.22/0.51   (USE-FACTORING :POS)
% 0.22/0.51   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.22/0.51   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.22/0.51   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.22/0.51   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.22/0.51   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.22/0.51   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.22/0.51   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.22/0.51   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.22/0.51   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.22/0.51   (DECLARE-TPTP-SYMBOLS2))
% 0.22/0.51  * 
% 0.22/0.51  "."
% 0.22/0.51  * 
% 0.22/0.51  ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T08:19:21
% 0.22/0.51  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n026.cluster.edu at 2022-06-14T08:19:21
% 0.39/0.57  
% 0.39/0.57  
% 0.39/0.57  #||
% 0.39/0.57  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.39/0.57  % SZS output start Refutation
% See solution above
% 0.39/0.57  ||#
% 0.39/0.57  
% 0.39/0.57  ; Summary of computation:
% 0.39/0.57  ;       185 formulas have been input or derived (from 16 formulas).
% 0.39/0.57  ;        78 (42%) were retained.  Of these,
% 0.39/0.57  ;           47 (60%) were simplified or subsumed later,
% 0.39/0.57  ;           31 (40%) are still being kept.
% 0.39/0.57  ; 
% 0.39/0.57  ; Run time in seconds excluding printing time:
% 0.39/0.57  ;     0.001   2%   Read assertion file          (1 call)
% 0.39/0.57  ;     0.000   0%   Assert                       (2 calls)
% 0.39/0.57  ;     0.010  17%   Process new row              (174 calls)
% 0.39/0.57  ;     0.000   0%   Resolution                   (30 calls)
% 0.39/0.57  ;     0.004   7%   Paramodulation               (15 calls)
% 0.39/0.57  ;     0.005   8%   Forward simplification       (139 calls)
% 0.39/0.57  ;     0.015  25%   Backward simplification      (78 calls)
% 0.39/0.57  ;     0.002   3%   Ordering                     (452 calls)
% 0.39/0.57  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.39/0.57  ;     0.000   0%   Purity testing               (1 call)
% 0.39/0.57  ;     0.022  37%   Other
% 0.39/0.57  ;     0.059        Total
% 0.39/0.57  ;     0.063        Real time
% 0.39/0.57  ; 
% 0.39/0.57  ; Term-hash-array has 368 terms in all.
% 0.39/0.57  ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.39/0.57  ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.39/0.57  ; Path-index has 148 entries (206 at peak, 424 added, 276 deleted).
% 0.39/0.57  ; Path-index has 740 nodes (749 at peak, 994 added, 254 deleted).
% 0.39/0.57  ; Trie-index has 148 entries (206 at peak, 424 added, 276 deleted).
% 0.39/0.57  ; Trie-index has 584 nodes (868 at peak, 1,709 added, 1,125 deleted).
% 0.39/0.57  ; Retrieved 227 generalization terms in 854 calls.
% 0.39/0.57  ; Retrieved 370 instance terms in 85 calls.
% 0.39/0.57  ; Retrieved 793 unifiable terms in 105 calls.
% 0.39/0.57  ; 
% 0.39/0.57  ; The agenda of rows to process has 6 entries:
% 0.39/0.57  ;     1 with value 18              3 with value 19               2 with value 20
% 0.39/0.57  ; The agenda of rows to give has 23 entries:
% 0.39/0.57  ;     5 with value (4 18)          1 with value (4 23)           1 with value (4 30)
% 0.39/0.57  ;     2 with value (4 19)          2 with value (4 24)           1 with value (4 31)
% 0.39/0.57  ;     1 with value (4 20)          1 with value (4 26)           1 with value (4 32)
% 0.39/0.57  ;     2 with value (4 21)          1 with value (4 28)           1 with value (4 36)
% 0.39/0.57  ;     2 with value (4 22)          2 with value (4 29)
% 0.39/0.57  Evaluation took:
% 0.39/0.57    0.064 seconds of real time
% 0.39/0.57    0.05544 seconds of user run time
% 0.39/0.57    0.008392 seconds of system run time
% 0.39/0.57    0 calls to %EVAL
% 0.39/0.57    0 page faults and
% 0.39/0.57    5,642,784 bytes consed.
% 0.39/0.57  :PROOF-FOUND
% 0.39/0.57  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T08:19:21
% 0.39/0.57  :PROOF-FOUND
% 0.39/0.57  * 
%------------------------------------------------------------------------------