TSTP Solution File: GRP406-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP406-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n015.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  : 300s
% DateTime : Wed Jul 27 12:56:57 EDT 2022

% Result   : Unsatisfiable 2.02s 2.23s
% Output   : Refutation 2.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    2
% Syntax   : Number of clauses     :   20 (  20 unt;   0 nHn;   4 RR)
%            Number of literals    :   20 (  19 equ;   3 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :   13 (   3 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   :   65 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
    file('GRP406-1.p',unknown),
    [] ).

cnf(2,plain,
    multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
    [iquote('copy,1,flip.1')] ).

cnf(5,axiom,
    multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),multiply(inverse(B),B))))) = C,
    file('GRP406-1.p',unknown),
    [] ).

cnf(6,plain,
    multiply(A,inverse(multiply(inverse(multiply(inverse(B),C)),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(A,D)),B)),multiply(inverse(D),multiply(inverse(D),D))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(A,D)),B)),multiply(inverse(D),multiply(inverse(D),D))))),inverse(multiply(inverse(multiply(inverse(multiply(A,D)),B)),multiply(inverse(D),multiply(inverse(D),D))))))))) = C,
    inference(para_into,[status(thm),theory(equality)],[5,5]),
    [iquote('para_into,4.1.1.2.1.1.1.1.1,4.1.1')] ).

cnf(8,plain,
    inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),D)),multiply(inverse(C),multiply(inverse(C),C)))) = multiply(A,inverse(multiply(inverse(D),multiply(inverse(B),multiply(inverse(B),B))))),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[5,5])]),
    [iquote('para_into,4.1.1.2.1.1.1,4.1.1,flip.1')] ).

cnf(22,plain,
    multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(C),multiply(inverse(B),multiply(inverse(B),B)))))) = C,
    inference(para_from,[status(thm),theory(equality)],[8,5]),
    [iquote('para_from,8.1.1,4.1.1.2')] ).

cnf(37,plain,
    multiply(inverse(multiply(A,B)),multiply(A,multiply(C,inverse(multiply(inverse(D),multiply(inverse(E),multiply(inverse(E),E))))))) = multiply(inverse(multiply(inverse(multiply(C,E)),B)),D),
    inference(para_into,[status(thm),theory(equality)],[22,8]),
    [iquote('para_into,22.1.1.2.2,8.1.1')] ).

cnf(106,plain,
    multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(inverse(D),B)),multiply(inverse(D),C)),
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[6,37]),5]),
    [iquote('para_from,6.1.1,37.1.1.2.2,demod,5')] ).

cnf(111,plain,
    multiply(inverse(multiply(inverse(A),B)),multiply(inverse(A),C)) = multiply(inverse(multiply(D,B)),multiply(D,C)),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[106])]),
    [iquote('copy,106,flip.1')] ).

cnf(152,plain,
    multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)),
    inference(para_into,[status(thm),theory(equality)],[111,111]),
    [iquote('para_into,111.1.1,111.1.1')] ).

cnf(169,plain,
    multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(multiply(C,D)),multiply(C,multiply(inverse(B),B)))))) = multiply(inverse(B),D),
    inference(para_from,[status(thm),theory(equality)],[152,22]),
    [iquote('para_from,152.1.1,22.1.1.2.2.1')] ).

cnf(172,plain,
    inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(B),multiply(inverse(B),B)))) = C,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[152,8]),5]),
    [iquote('para_from,152.1.1,8.1.1.1.1.1,demod,5')] ).

cnf(174,plain,
    multiply(inverse(multiply(A,multiply(B,C))),multiply(A,inverse(multiply(inverse(D),multiply(inverse(multiply(B,C)),multiply(inverse(multiply(E,C)),multiply(E,C))))))) = D,
    inference(para_from,[status(thm),theory(equality)],[152,22]),
    [iquote('para_from,152.1.1,22.1.1.2.2.1.2.2')] ).

cnf(196,plain,
    multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,A))),D)) = multiply(inverse(multiply(E,multiply(inverse(C),multiply(inverse(C),C)))),multiply(E,D)),
    inference(para_from,[status(thm),theory(equality)],[172,152]),
    [iquote('para_from,172.1.1,152.1.1.1')] ).

cnf(210,plain,
    multiply(inverse(multiply(A,multiply(B,C))),multiply(A,inverse(multiply(inverse(multiply(D,E)),multiply(D,multiply(inverse(multiply(F,C)),multiply(F,C))))))) = multiply(inverse(multiply(B,C)),E),
    inference(para_into,[status(thm),theory(equality)],[169,152]),
    [iquote('para_into,169.1.1.2.2.1.2.2,152.1.1')] ).

cnf(437,plain,
    multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),multiply(inverse(B),multiply(inverse(B),B))) = C,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[196,174]),210]),
    [iquote('para_from,196.1.1,174.1.1.2.2.1,demod,210')] ).

cnf(443,plain,
    multiply(inverse(A),A) = multiply(inverse(multiply(B,multiply(inverse(C),multiply(inverse(C),C)))),multiply(B,multiply(inverse(C),multiply(inverse(C),C)))),
    inference(para_from,[status(thm),theory(equality)],[437,196]),
    [iquote('para_from,437.1.1,196.1.1.2')] ).

cnf(445,plain,
    multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,multiply(inverse(B),multiply(inverse(B),B)))) = multiply(inverse(C),C),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[443])]),
    [iquote('copy,443,flip.1')] ).

cnf(447,plain,
    multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,multiply(inverse(B),multiply(inverse(B),B)))) != multiply(inverse(a1),a1),
    inference(para_from,[status(thm),theory(equality)],[443,2]),
    [iquote('para_from,443.1.1,2.1.1')] ).

cnf(448,plain,
    $false,
    inference(binary,[status(thm)],[447,445]),
    [iquote('binary,447.1,445.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : GRP406-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.12  % Command  : otter-tptp-script %s
% 0.13/0.33  % Computer : n015.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  : 300
% 0.13/0.33  % DateTime : Wed Jul 27 05:30:41 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 2.02/2.23  ----- Otter 3.3f, August 2004 -----
% 2.02/2.23  The process was started by sandbox2 on n015.cluster.edu,
% 2.02/2.23  Wed Jul 27 05:30:41 2022
% 2.02/2.23  The command was "./otter".  The process ID is 3487.
% 2.02/2.23  
% 2.02/2.23  set(prolog_style_variables).
% 2.02/2.23  set(auto).
% 2.02/2.23     dependent: set(auto1).
% 2.02/2.23     dependent: set(process_input).
% 2.02/2.23     dependent: clear(print_kept).
% 2.02/2.23     dependent: clear(print_new_demod).
% 2.02/2.23     dependent: clear(print_back_demod).
% 2.02/2.23     dependent: clear(print_back_sub).
% 2.02/2.23     dependent: set(control_memory).
% 2.02/2.23     dependent: assign(max_mem, 12000).
% 2.02/2.23     dependent: assign(pick_given_ratio, 4).
% 2.02/2.23     dependent: assign(stats_level, 1).
% 2.02/2.23     dependent: assign(max_seconds, 10800).
% 2.02/2.23  clear(print_given).
% 2.02/2.23  
% 2.02/2.23  list(usable).
% 2.02/2.23  0 [] A=A.
% 2.02/2.23  0 [] multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),multiply(inverse(B),B)))))=C.
% 2.02/2.23  0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1).
% 2.02/2.23  end_of_list.
% 2.02/2.23  
% 2.02/2.23  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 2.02/2.23  
% 2.02/2.23  All clauses are units, and equality is present; the
% 2.02/2.23  strategy will be Knuth-Bendix with positive clauses in sos.
% 2.02/2.23  
% 2.02/2.23     dependent: set(knuth_bendix).
% 2.02/2.23     dependent: set(anl_eq).
% 2.02/2.23     dependent: set(para_from).
% 2.02/2.23     dependent: set(para_into).
% 2.02/2.23     dependent: clear(para_from_right).
% 2.02/2.23     dependent: clear(para_into_right).
% 2.02/2.23     dependent: set(para_from_vars).
% 2.02/2.23     dependent: set(eq_units_both_ways).
% 2.02/2.23     dependent: set(dynamic_demod_all).
% 2.02/2.23     dependent: set(dynamic_demod).
% 2.02/2.23     dependent: set(order_eq).
% 2.02/2.23     dependent: set(back_demod).
% 2.02/2.23     dependent: set(lrpo).
% 2.02/2.23  
% 2.02/2.23  ------------> process usable:
% 2.02/2.23  ** KEPT (pick-wt=9): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1).
% 2.02/2.23  
% 2.02/2.23  ------------> process sos:
% 2.02/2.23  ** KEPT (pick-wt=3): 3 [] A=A.
% 2.02/2.23  ** KEPT (pick-wt=20): 4 [] multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),multiply(inverse(B),B)))))=C.
% 2.02/2.23  ---> New Demodulator: 5 [new_demod,4] multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),multiply(inverse(B),B)))))=C.
% 2.02/2.23    Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 2.02/2.23  >>>> Starting back demodulation with 5.
% 2.02/2.23  
% 2.02/2.23  ======= end of input processing =======
% 2.02/2.23  
% 2.02/2.23  =========== start of search ===========
% 2.02/2.23  
% 2.02/2.23  
% 2.02/2.23  Resetting weight limit to 40.
% 2.02/2.23  
% 2.02/2.23  
% 2.02/2.23  Resetting weight limit to 40.
% 2.02/2.23  
% 2.02/2.23  sos_size=66
% 2.02/2.23  
% 2.02/2.23  
% 2.02/2.23  Resetting weight limit to 30.
% 2.02/2.23  
% 2.02/2.23  
% 2.02/2.23  Resetting weight limit to 30.
% 2.02/2.23  
% 2.02/2.23  sos_size=246
% 2.02/2.23  
% 2.02/2.23  -------- PROOF -------- 
% 2.02/2.23  
% 2.02/2.23  ----> UNIT CONFLICT at   0.14 sec ----> 448 [binary,447.1,445.1] $F.
% 2.02/2.23  
% 2.02/2.23  Length of proof is 17.  Level of proof is 11.
% 2.02/2.23  
% 2.02/2.23  ---------------- PROOF ----------------
% 2.02/2.23  % SZS status Unsatisfiable
% 2.02/2.23  % SZS output start Refutation
% See solution above
% 2.02/2.23  ------------ end of proof -------------
% 2.02/2.23  
% 2.02/2.23  
% 2.02/2.23  Search stopped by max_proofs option.
% 2.02/2.23  
% 2.02/2.23  
% 2.02/2.23  Search stopped by max_proofs option.
% 2.02/2.23  
% 2.02/2.23  ============ end of search ============
% 2.02/2.23  
% 2.02/2.23  -------------- statistics -------------
% 2.02/2.23  clauses given                 30
% 2.02/2.23  clauses generated           2953
% 2.02/2.23  clauses kept                 356
% 2.02/2.23  clauses forward subsumed     830
% 2.02/2.23  clauses back subsumed         53
% 2.02/2.23  Kbytes malloced             6835
% 2.02/2.23  
% 2.02/2.23  ----------- times (seconds) -----------
% 2.02/2.23  user CPU time          0.14          (0 hr, 0 min, 0 sec)
% 2.02/2.23  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 2.02/2.23  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 2.02/2.23  
% 2.02/2.23  That finishes the proof of the theorem.
% 2.02/2.23  
% 2.02/2.23  Process 3487 finished Wed Jul 27 05:30:43 2022
% 2.02/2.23  Otter interrupted
% 2.02/2.23  PROOF FOUND
%------------------------------------------------------------------------------