TSTP Solution File: GRP087-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP087-1 : 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 0.44s 0.58s
% Output   : Refutation 0.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    2
% Syntax   : Number of clauses     :   26 (  21 unt;   0 nHn;   7 RR)
%            Number of literals    :   36 (  35 equ;  16 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   :   61 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
    multiply(X,multiply(multiply(inverse(multiply(X,Y)),Z),Y)) = Z,
    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(inverse(Y),Z),multiply(multiply(inverse(multiply(X,U)),Y),U))) = Z,
    inference('PARAMODULATE',[status(thm)],[single_axiom,single_axiom,theory(equality)]) ).

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

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

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

cnf(9,plain,
    multiply(X,multiply(Y,multiply(multiply(inverse(multiply(X,Z)),U),Z))) = multiply(multiply(inverse(V),Y),multiply(multiply(inverse(multiply(inverse(U),W)),V),W)),
    inference('PARAMODULATE',[status(thm)],[3,3,theory(equality)]) ).

cnf(13,plain,
    multiply(X,Y) = multiply(multiply(inverse(multiply(inverse(Y),Z)),X),Z),
    inference('PARAMODULATE',[status(thm)],[5,single_axiom,theory(equality)]) ).

cnf(14,plain,
    multiply(X,multiply(Y,Z)) = multiply(Y,multiply(X,Z)),
    inference('REWRITE',[status(thm)],[4,13,theory(equality)]) ).

cnf(16,plain,
    ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
    | multiply(multiply(inverse(b2),b2),a2) != a2
    | multiply(multiply(a3,b3),c3) != multiply(b3,multiply(a3,c3))
    | multiply(a4,b4) != multiply(b4,a4) ),
    inference('REWRITE',[status(thm)],[prove_these_axioms,14,theory(equality)]) ).

cnf(17,plain,
    multiply(X,multiply(Y,multiply(multiply(inverse(multiply(X,Z)),U),Z))) = multiply(multiply(inverse(V),Y),multiply(V,U)),
    inference('REWRITE',[status(thm)],[9,13,theory(equality)]) ).

cnf(18,plain,
    multiply(X,multiply(Y,multiply(multiply(inverse(multiply(X,Z)),U),Z))) = multiply(Y,U),
    inference('REWRITE',[status(thm)],[6,13,theory(equality)]) ).

cnf(19,plain,
    multiply(X,Y) = multiply(multiply(inverse(Z),X),multiply(Z,Y)),
    inference('REWRITE',[status(thm)],[17,18,theory(equality)]) ).

cnf(20,plain,
    multiply(X,Y) = multiply(multiply(inverse(Z),Y),multiply(X,Z)),
    inference('PARAMODULATE',[status(thm)],[14,5,theory(equality)]) ).

cnf(27,plain,
    multiply(X,Y) = multiply(Y,X),
    inference('PARAMODULATE',[status(thm)],[19,20,theory(equality)]) ).

cnf(28,plain,
    ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
    | multiply(multiply(inverse(b2),b2),a2) != a2
    | multiply(multiply(a3,b3),c3) != multiply(b3,multiply(a3,c3)) ),
    inference('REWRITE',[status(thm)],[16,27,theory(equality)]) ).

cnf(29,plain,
    multiply(multiply(inverse(X),Y),Z) = multiply(multiply(inverse(X),Z),Y),
    inference('PARAMODULATE',[status(thm)],[20,5,theory(equality)]) ).

cnf(30,plain,
    ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
    | multiply(multiply(a3,b3),c3) != multiply(b3,multiply(a3,c3)) ),
    inference('REWRITE',[status(thm)],[28,5,29,theory(equality)]) ).

cnf(38,plain,
    multiply(inverse(X),multiply(X,Y)) = Y,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[5,27,theory(equality)]),14,theory(equality)]) ).

cnf(39,plain,
    multiply(X,multiply(Y,Z)) = multiply(Z,multiply(X,Y)),
    inference('PARAMODULATE',[status(thm)],[14,27,theory(equality)]) ).

cnf(43,plain,
    ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
    | multiply(multiply(a3,b3),c3) != multiply(c3,multiply(b3,a3)) ),
    inference('REWRITE',[status(thm)],[30,39,theory(equality)]) ).

cnf(56,plain,
    multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[43,27,theory(equality)]),27,theory(equality)]) ).

cnf(58,plain,
    multiply(inverse(X),multiply(Y,X)) = Y,
    inference('PARAMODULATE',[status(thm)],[38,27,theory(equality)]) ).

cnf(73,plain,
    X = multiply(X,multiply(inverse(Y),Y)),
    inference('PARAMODULATE',[status(thm)],[14,58,theory(equality)]) ).

cnf(139,plain,
    multiply(inverse(X),X) = multiply(inverse(Y),Y),
    inference('PARAMODULATE',[status(thm)],[38,73,theory(equality)]) ).

cnf(140,plain,
    $false,
    inference('REWRITE',[status(thm)],[56,139,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GRP087-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.13/0.12  % Command  : run-snark %s %d
% 0.13/0.33  % Computer : n012.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Mon Jun 13 08:10:10 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.20/0.44  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45  * 
% 0.20/0.46  * 
% 0.20/0.46  #<PACKAGE "SNARK-USER">
% 0.20/0.46  * 
% 0.20/0.46  SNARK-TPTP-OPTIONS
% 0.20/0.46  * 
% 0.20/0.46  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.46   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.46   (USE-FACTORING :POS)
% 0.20/0.46   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.46   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.46   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.46   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.46   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.46   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.46   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.46   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.46   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.46   (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.46  * 
% 0.20/0.46  "."
% 0.20/0.46  * 
% 0.20/0.46  ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T08:10:11
% 0.20/0.46  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n012.cluster.edu at 2022-06-13T08:10:11
% 0.44/0.58  
% 0.44/0.58  
% 0.44/0.58  #||
% 0.44/0.58  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.44/0.58  % SZS output start Refutation
% See solution above
% 0.44/0.59  ||#
% 0.44/0.59  
% 0.44/0.59  ; Summary of computation:
% 0.44/0.59  ;       450 formulas have been input or derived (from 24 formulas).
% 0.44/0.59  ;       140 (31%) were retained.  Of these,
% 0.44/0.59  ;           42 (30%) were simplified or subsumed later,
% 0.44/0.59  ;           98 (70%) are still being kept.
% 0.44/0.59  ; 
% 0.44/0.59  ; Run time in seconds excluding printing time:
% 0.44/0.59  ;     0.001   1%   Read assertion file          (1 call)
% 0.44/0.59  ;     0.000   0%   Assert                       (2 calls)
% 0.44/0.59  ;     0.012  10%   Process new row              (396 calls)
% 0.44/0.59  ;     0.003   2%   Resolution                   (46 calls)
% 0.44/0.59  ;     0.005   4%   Paramodulation               (23 calls)
% 0.44/0.59  ;     0.000   0%   Condensing                   (10 calls)
% 0.44/0.59  ;     0.000   0%   Forward subsumption          (10 calls)
% 0.44/0.59  ;     0.001   1%   Backward subsumption         (8 calls)
% 0.44/0.59  ;     0.000   0%   Clause clause subsumption    (14 calls)
% 0.44/0.59  ;     0.024  20%   Forward simplification       (360 calls)
% 0.44/0.59  ;     0.014  12%   Backward simplification      (140 calls)
% 0.44/0.59  ;     0.034  28%   Ordering                     (4,262 calls)
% 0.44/0.59  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.44/0.59  ;     0.000   0%   Purity testing               (1 call)
% 0.44/0.59  ;     0.027  22%   Other
% 0.44/0.59  ;     0.121        Total
% 0.44/0.59  ;     0.125        Real time
% 0.44/0.59  ; 
% 0.44/0.59  ; Term-hash-array has 432 terms in all.
% 0.44/0.59  ; Feature-vector-row-index has 0 entries (4 at peak, 8 added, 8 deleted).
% 0.44/0.59  ; Feature-vector-row-index has 1 node (36 at peak, 146 added, 145 deleted).
% 0.44/0.59  ;  Retrieved 8 possibly forward subsuming rows in 10 calls.
% 0.44/0.59  ;  Retrieved 6 possibly backward subsumed rows in 8 calls.
% 0.44/0.59  ; Path-index has 280 entries (284 at peak, 548 added, 268 deleted).
% 0.44/0.59  ; Path-index has 405 nodes (421 at peak, 766 added, 361 deleted).
% 0.44/0.59  ; Trie-index has 280 entries (284 at peak, 548 added, 268 deleted).
% 0.44/0.59  ; Trie-index has 551 nodes (566 at peak, 1,399 added, 848 deleted).
% 0.44/0.59  ; Retrieved 2,516 generalization terms in 1,861 calls.
% 0.44/0.59  ; Retrieved 1,849 instance terms in 206 calls.
% 0.44/0.59  ; Retrieved 1,572 unifiable terms in 215 calls.
% 0.44/0.59  ; 
% 0.44/0.59  ; The agenda of rows to process has 25 entries:
% 0.44/0.59  ;     5 with value 20              1 with value 24               5 with value 26
% 0.44/0.59  ;     1 with value 21              9 with value 25               1 with value 27
% 0.44/0.59  ;     3 with value 22
% 0.44/0.59  ; The agenda of rows to give has 83 entries:
% 0.44/0.59  ;     3 with value (4 19)          1 with value (4 22)          32 with value (4 25)
% 0.44/0.59  ;    10 with value (4 20)          3 with value (4 23)           8 with value (4 26)
% 0.44/0.59  ;     9 with value (4 21)          7 with value (4 24)          10 with value (4 27)
% 0.44/0.59  Evaluation took:
% 0.44/0.59    0.125 seconds of real time
% 0.44/0.59    0.105315 seconds of user run time
% 0.44/0.59    0.019833 seconds of system run time
% 0.44/0.59    0 calls to %EVAL
% 0.44/0.59    0 page faults and
% 0.44/0.59    8,193,752 bytes consed.
% 0.44/0.59  :PROOF-FOUND
% 0.44/0.59  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T08:10:11
% 0.44/0.59  :PROOF-FOUND
% 0.44/0.59  * 
%------------------------------------------------------------------------------