TSTP Solution File: GRP527-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP527-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n011.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 12:57:11 EDT 2022

% Result   : Unsatisfiable 1.96s 2.13s
% Output   : Refutation 1.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   32 (  32 unt;   0 nHn;   4 RR)
%            Number of literals    :   32 (  31 equ;   3 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   65 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
    file('GRP527-1.p',unknown),
    [] ).

cnf(3,axiom,
    divide(A,divide(divide(A,B),divide(C,B))) = C,
    file('GRP527-1.p',unknown),
    [] ).

cnf(5,axiom,
    multiply(A,B) = divide(A,divide(divide(C,C),B)),
    file('GRP527-1.p',unknown),
    [] ).

cnf(6,axiom,
    inverse(A) = divide(divide(B,B),A),
    file('GRP527-1.p',unknown),
    [] ).

cnf(7,plain,
    divide(A,divide(divide(B,B),C)) = multiply(A,C),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[5])]),
    [iquote('copy,5,flip.1')] ).

cnf(8,plain,
    divide(divide(A,A),B) = inverse(B),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
    [iquote('copy,6,flip.1')] ).

cnf(10,plain,
    divide(inverse(divide(A,A)),B) = inverse(B),
    inference(para_into,[status(thm),theory(equality)],[8,8]),
    [iquote('para_into,8.1.1.1,8.1.1')] ).

cnf(27,plain,
    divide(A,divide(B,divide(C,divide(divide(A,D),divide(B,D))))) = C,
    inference(para_into,[status(thm),theory(equality)],[3,3]),
    [iquote('para_into,3.1.1.2.1,3.1.1')] ).

cnf(33,plain,
    divide(A,inverse(divide(B,A))) = B,
    inference(para_into,[status(thm),theory(equality)],[3,8]),
    [iquote('para_into,3.1.1.2,8.1.1')] ).

cnf(43,plain,
    divide(inverse(divide(A,B)),inverse(A)) = B,
    inference(para_into,[status(thm),theory(equality)],[33,33]),
    [iquote('para_into,33.1.1.2.1,33.1.1')] ).

cnf(47,plain,
    divide(divide(divide(A,B),divide(C,B)),inverse(C)) = A,
    inference(para_into,[status(thm),theory(equality)],[33,3]),
    [iquote('para_into,33.1.1.2.1,3.1.1')] ).

cnf(55,plain,
    inverse(inverse(divide(A,divide(B,B)))) = A,
    inference(para_into,[status(thm),theory(equality)],[33,8]),
    [iquote('para_into,33.1.1,8.1.1')] ).

cnf(66,plain,
    inverse(divide(A,B)) = divide(inverse(A),inverse(B)),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[43,33])]),
    [iquote('para_into,43.1.1.1.1,33.1.1,flip.1')] ).

cnf(81,plain,
    inverse(inverse(A)) = A,
    inference(para_into,[status(thm),theory(equality)],[43,10]),
    [iquote('para_into,43.1.1,10.1.1')] ).

cnf(88,plain,
    divide(A,divide(B,B)) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[55]),66,66,66,81,66,81,81]),
    [iquote('back_demod,55,demod,66,66,66,81,66,81,81')] ).

cnf(105,plain,
    divide(divide(A,A),inverse(B)) = B,
    inference(para_into,[status(thm),theory(equality)],[81,6]),
    [iquote('para_into,80.1.1,6.1.1')] ).

cnf(106,plain,
    divide(A,divide(A,B)) = B,
    inference(para_from,[status(thm),theory(equality)],[88,3]),
    [iquote('para_from,88.1.1,3.1.1.2')] ).

cnf(113,plain,
    divide(divide(A,B),divide(C,B)) = divide(A,C),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[106,3])]),
    [iquote('para_into,106.1.1.2,3.1.1,flip.1')] ).

cnf(116,plain,
    divide(divide(A,B),inverse(B)) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[47]),113]),
    [iquote('back_demod,47,demod,113')] ).

cnf(118,plain,
    divide(A,divide(B,divide(C,divide(A,B)))) = C,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[27]),113]),
    [iquote('back_demod,27,demod,113')] ).

cnf(124,plain,
    divide(divide(A,B),A) = inverse(B),
    inference(para_from,[status(thm),theory(equality)],[116,106]),
    [iquote('para_from,116.1.1,106.1.1.2')] ).

cnf(133,plain,
    divide(A,inverse(B)) = multiply(A,B),
    inference(para_into,[status(thm),theory(equality)],[7,8]),
    [iquote('para_into,7.1.1.2,8.1.1')] ).

cnf(140,plain,
    multiply(A,B) = divide(A,inverse(B)),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[133])]),
    [iquote('copy,133,flip.1')] ).

cnf(147,plain,
    divide(multiply(A,B),B) = A,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[7,116]),66,66,105]),
    [iquote('para_from,7.1.1,116.1.1.1,demod,66,66,105')] ).

cnf(158,plain,
    divide(multiply(A,B),A) = B,
    inference(para_from,[status(thm),theory(equality)],[147,106]),
    [iquote('para_from,147.1.1,106.1.1.2')] ).

cnf(199,plain,
    divide(A,multiply(B,A)) = inverse(B),
    inference(para_into,[status(thm),theory(equality)],[124,158]),
    [iquote('para_into,124.1.1.1,158.1.1')] ).

cnf(262,plain,
    multiply(divide(a3,inverse(b3)),c3) != multiply(a3,multiply(b3,c3)),
    inference(para_from,[status(thm),theory(equality)],[140,1]),
    [iquote('para_from,140.1.1,1.1.1.1')] ).

cnf(304,plain,
    inverse(multiply(A,B)) = divide(inverse(A),B),
    inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[199,124])]),
    [iquote('para_from,199.1.1,124.1.1.1,flip.1')] ).

cnf(799,plain,
    divide(A,divide(inverse(B),C)) = multiply(A,multiply(B,C)),
    inference(para_from,[status(thm),theory(equality)],[304,133]),
    [iquote('para_from,304.1.1,133.1.1.2')] ).

cnf(944,plain,
    multiply(divide(A,B),C) = divide(A,divide(B,C)),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[118,158])]),
    [iquote('para_into,118.1.1.2.2,158.1.1,flip.1')] ).

cnf(950,plain,
    divide(a3,divide(inverse(b3),c3)) != multiply(a3,multiply(b3,c3)),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[262]),944]),
    [iquote('back_demod,262,demod,944')] ).

cnf(951,plain,
    $false,
    inference(binary,[status(thm)],[950,799]),
    [iquote('binary,950.1,799.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11  % Problem  : GRP527-1 : TPTP v8.1.0. Released v2.6.0.
% 0.08/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n011.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Wed Jul 27 05:28:25 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.96/2.13  ----- Otter 3.3f, August 2004 -----
% 1.96/2.13  The process was started by sandbox on n011.cluster.edu,
% 1.96/2.13  Wed Jul 27 05:28:25 2022
% 1.96/2.13  The command was "./otter".  The process ID is 5911.
% 1.96/2.13  
% 1.96/2.13  set(prolog_style_variables).
% 1.96/2.13  set(auto).
% 1.96/2.13     dependent: set(auto1).
% 1.96/2.13     dependent: set(process_input).
% 1.96/2.13     dependent: clear(print_kept).
% 1.96/2.13     dependent: clear(print_new_demod).
% 1.96/2.13     dependent: clear(print_back_demod).
% 1.96/2.13     dependent: clear(print_back_sub).
% 1.96/2.13     dependent: set(control_memory).
% 1.96/2.13     dependent: assign(max_mem, 12000).
% 1.96/2.13     dependent: assign(pick_given_ratio, 4).
% 1.96/2.13     dependent: assign(stats_level, 1).
% 1.96/2.13     dependent: assign(max_seconds, 10800).
% 1.96/2.13  clear(print_given).
% 1.96/2.13  
% 1.96/2.13  list(usable).
% 1.96/2.13  0 [] A=A.
% 1.96/2.13  0 [] divide(A,divide(divide(A,B),divide(C,B)))=C.
% 1.96/2.13  0 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.96/2.13  0 [] inverse(A)=divide(divide(B,B),A).
% 1.96/2.13  0 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.96/2.13  end_of_list.
% 1.96/2.13  
% 1.96/2.13  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.96/2.13  
% 1.96/2.13  All clauses are units, and equality is present; the
% 1.96/2.13  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.96/2.13  
% 1.96/2.13     dependent: set(knuth_bendix).
% 1.96/2.13     dependent: set(anl_eq).
% 1.96/2.13     dependent: set(para_from).
% 1.96/2.13     dependent: set(para_into).
% 1.96/2.13     dependent: clear(para_from_right).
% 1.96/2.13     dependent: clear(para_into_right).
% 1.96/2.13     dependent: set(para_from_vars).
% 1.96/2.13     dependent: set(eq_units_both_ways).
% 1.96/2.13     dependent: set(dynamic_demod_all).
% 1.96/2.13     dependent: set(dynamic_demod).
% 1.96/2.13     dependent: set(order_eq).
% 1.96/2.13     dependent: set(back_demod).
% 1.96/2.13     dependent: set(lrpo).
% 1.96/2.13  
% 1.96/2.13  ------------> process usable:
% 1.96/2.13  ** KEPT (pick-wt=11): 1 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.96/2.13  
% 1.96/2.13  ------------> process sos:
% 1.96/2.13  ** KEPT (pick-wt=3): 2 [] A=A.
% 1.96/2.13  ** KEPT (pick-wt=11): 3 [] divide(A,divide(divide(A,B),divide(C,B)))=C.
% 1.96/2.13  ---> New Demodulator: 4 [new_demod,3] divide(A,divide(divide(A,B),divide(C,B)))=C.
% 1.96/2.13  ** KEPT (pick-wt=11): 5 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.96/2.13  ** KEPT (pick-wt=8): 6 [] inverse(A)=divide(divide(B,B),A).
% 1.96/2.13    Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.96/2.13  >>>> Starting back demodulation with 4.
% 1.96/2.13  ** KEPT (pick-wt=11): 7 [copy,5,flip.1] divide(A,divide(divide(B,B),C))=multiply(A,C).
% 1.96/2.13  ** KEPT (pick-wt=8): 8 [copy,6,flip.1] divide(divide(A,A),B)=inverse(B).
% 1.96/2.13    Following clause subsumed by 5 during input processing: 0 [copy,7,flip.1] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.96/2.13    Following clause subsumed by 6 during input processing: 0 [copy,8,flip.1] inverse(A)=divide(divide(B,B),A).
% 1.96/2.13  
% 1.96/2.13  ======= end of input processing =======
% 1.96/2.13  
% 1.96/2.13  =========== start of search ===========
% 1.96/2.13  
% 1.96/2.13  -------- PROOF -------- 
% 1.96/2.13  
% 1.96/2.13  ----> UNIT CONFLICT at   0.03 sec ----> 951 [binary,950.1,799.1] $F.
% 1.96/2.13  
% 1.96/2.13  Length of proof is 27.  Level of proof is 13.
% 1.96/2.13  
% 1.96/2.13  ---------------- PROOF ----------------
% 1.96/2.13  % SZS status Unsatisfiable
% 1.96/2.13  % SZS output start Refutation
% See solution above
% 1.96/2.13  ------------ end of proof -------------
% 1.96/2.13  
% 1.96/2.13  
% 1.96/2.13  Search stopped by max_proofs option.
% 1.96/2.13  
% 1.96/2.13  
% 1.96/2.13  Search stopped by max_proofs option.
% 1.96/2.13  
% 1.96/2.13  ============ end of search ============
% 1.96/2.13  
% 1.96/2.13  -------------- statistics -------------
% 1.96/2.13  clauses given                 63
% 1.96/2.13  clauses generated           1944
% 1.96/2.13  clauses kept                 721
% 1.96/2.13  clauses forward subsumed    1956
% 1.96/2.13  clauses back subsumed          4
% 1.96/2.13  Kbytes malloced             2929
% 1.96/2.13  
% 1.96/2.13  ----------- times (seconds) -----------
% 1.96/2.13  user CPU time          0.03          (0 hr, 0 min, 0 sec)
% 1.96/2.13  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.96/2.13  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.96/2.13  
% 1.96/2.13  That finishes the proof of the theorem.
% 1.96/2.13  
% 1.96/2.13  Process 5911 finished Wed Jul 27 05:28:27 2022
% 1.96/2.13  Otter interrupted
% 1.96/2.13  PROOF FOUND
%------------------------------------------------------------------------------