TSTP Solution File: BOO017-2 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : BOO017-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n023.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 12:47:36 EDT 2022

% Result   : Unsatisfiable 1.98s 2.14s
% Output   : Refutation 1.98s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   27 (  27 unt;   0 nHn;   7 RR)
%            Number of literals    :   27 (  26 equ;   4 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   37 (   3 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    multiply(x,z) != x,
    file('BOO017-2.p',unknown),
    [] ).

cnf(3,axiom,
    add(A,B) = add(B,A),
    file('BOO017-2.p',unknown),
    [] ).

cnf(4,axiom,
    multiply(A,B) = multiply(B,A),
    file('BOO017-2.p',unknown),
    [] ).

cnf(5,axiom,
    add(multiply(A,B),C) = multiply(add(A,C),add(B,C)),
    file('BOO017-2.p',unknown),
    [] ).

cnf(6,plain,
    multiply(add(A,B),add(C,B)) = add(multiply(A,C),B),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[5])]),
    [iquote('copy,5,flip.1')] ).

cnf(12,axiom,
    multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)),
    file('BOO017-2.p',unknown),
    [] ).

cnf(14,axiom,
    multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)),
    file('BOO017-2.p',unknown),
    [] ).

cnf(17,axiom,
    add(inverse(A),A) = multiplicative_identity,
    file('BOO017-2.p',unknown),
    [] ).

cnf(22,axiom,
    multiply(inverse(A),A) = additive_identity,
    file('BOO017-2.p',unknown),
    [] ).

cnf(26,axiom,
    multiply(multiplicative_identity,A) = A,
    file('BOO017-2.p',unknown),
    [] ).

cnf(28,axiom,
    add(A,additive_identity) = A,
    file('BOO017-2.p',unknown),
    [] ).

cnf(30,axiom,
    add(additive_identity,A) = A,
    file('BOO017-2.p',unknown),
    [] ).

cnf(31,axiom,
    add(x,y) = z,
    file('BOO017-2.p',unknown),
    [] ).

cnf(35,plain,
    add(add(multiply(A,B),multiply(C,B)),add(multiply(A,C),multiply(C,C))) = add(multiply(A,B),C),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[6]),14,12,12]),
    [iquote('back_demod,6,demod,14,12,12')] ).

cnf(37,plain,
    add(y,x) = z,
    inference(para_into,[status(thm),theory(equality)],[31,3]),
    [iquote('para_into,31.1.1,3.1.1')] ).

cnf(41,plain,
    multiply(z,x) != x,
    inference(para_from,[status(thm),theory(equality)],[4,1]),
    [iquote('para_from,4.1.1,1.1.1')] ).

cnf(45,plain,
    multiply(z,A) = add(multiply(y,A),multiply(x,A)),
    inference(para_into,[status(thm),theory(equality)],[12,37]),
    [iquote('para_into,11.1.1.1,37.1.1')] ).

cnf(46,plain,
    add(multiply(additive_identity,A),multiply(B,A)) = multiply(B,A),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[12,30])]),
    [iquote('para_into,11.1.1.1,29.1.1,flip.1')] ).

cnf(50,plain,
    add(multiply(inverse(A),B),multiply(A,B)) = B,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[12,17]),26])]),
    [iquote('para_into,11.1.1.1,17.1.1,demod,26,flip.1')] ).

cnf(57,plain,
    add(multiply(y,x),multiply(x,x)) != x,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[41]),45]),
    [iquote('back_demod,41,demod,45')] ).

cnf(81,plain,
    multiply(A,A) = A,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[50,22]),30]),
    [iquote('para_into,50.1.1.1,21.1.1,demod,30')] ).

cnf(97,plain,
    add(multiply(y,x),x) != x,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[57]),81]),
    [iquote('back_demod,57,demod,81')] ).

cnf(98,plain,
    add(add(multiply(A,B),multiply(C,B)),add(multiply(A,C),C)) = add(multiply(A,B),C),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[35]),81]),
    [iquote('back_demod,35,demod,81')] ).

cnf(140,plain,
    multiply(additive_identity,A) = additive_identity,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[46,22]),28,22]),
    [iquote('para_into,46.1.1.2,21.1.1,demod,28,22')] ).

cnf(143,plain,
    multiply(A,additive_identity) = additive_identity,
    inference(para_into,[status(thm),theory(equality)],[140,4]),
    [iquote('para_into,140.1.1,4.1.1')] ).

cnf(894,plain,
    add(multiply(A,B),B) = B,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[98,143]),143,28,30,143,30]),
    [iquote('para_into,98.1.1.1.1,142.1.1,demod,143,28,30,143,30')] ).

cnf(896,plain,
    $false,
    inference(binary,[status(thm)],[894,97]),
    [iquote('binary,894.1,97.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : BOO017-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n023.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 02:53:03 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.91/2.10  ----- Otter 3.3f, August 2004 -----
% 1.91/2.10  The process was started by sandbox on n023.cluster.edu,
% 1.91/2.10  Wed Jul 27 02:53:03 2022
% 1.91/2.10  The command was "./otter".  The process ID is 7544.
% 1.91/2.10  
% 1.91/2.10  set(prolog_style_variables).
% 1.91/2.10  set(auto).
% 1.91/2.10     dependent: set(auto1).
% 1.91/2.10     dependent: set(process_input).
% 1.91/2.10     dependent: clear(print_kept).
% 1.91/2.10     dependent: clear(print_new_demod).
% 1.91/2.10     dependent: clear(print_back_demod).
% 1.91/2.10     dependent: clear(print_back_sub).
% 1.91/2.10     dependent: set(control_memory).
% 1.91/2.10     dependent: assign(max_mem, 12000).
% 1.91/2.10     dependent: assign(pick_given_ratio, 4).
% 1.91/2.10     dependent: assign(stats_level, 1).
% 1.91/2.10     dependent: assign(max_seconds, 10800).
% 1.91/2.10  clear(print_given).
% 1.91/2.10  
% 1.91/2.10  list(usable).
% 1.91/2.10  0 [] A=A.
% 1.91/2.10  0 [] add(X,Y)=add(Y,X).
% 1.91/2.10  0 [] multiply(X,Y)=multiply(Y,X).
% 1.91/2.10  0 [] add(multiply(X,Y),Z)=multiply(add(X,Z),add(Y,Z)).
% 1.91/2.10  0 [] add(X,multiply(Y,Z))=multiply(add(X,Y),add(X,Z)).
% 1.91/2.10  0 [] multiply(add(X,Y),Z)=add(multiply(X,Z),multiply(Y,Z)).
% 1.91/2.10  0 [] multiply(X,add(Y,Z))=add(multiply(X,Y),multiply(X,Z)).
% 1.91/2.10  0 [] add(X,inverse(X))=multiplicative_identity.
% 1.91/2.10  0 [] add(inverse(X),X)=multiplicative_identity.
% 1.91/2.10  0 [] multiply(X,inverse(X))=additive_identity.
% 1.91/2.10  0 [] multiply(inverse(X),X)=additive_identity.
% 1.91/2.10  0 [] multiply(X,multiplicative_identity)=X.
% 1.91/2.10  0 [] multiply(multiplicative_identity,X)=X.
% 1.91/2.10  0 [] add(X,additive_identity)=X.
% 1.91/2.10  0 [] add(additive_identity,X)=X.
% 1.91/2.10  0 [] add(x,y)=z.
% 1.91/2.10  0 [] multiply(x,z)!=x.
% 1.91/2.10  end_of_list.
% 1.91/2.10  
% 1.91/2.10  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.91/2.10  
% 1.91/2.10  All clauses are units, and equality is present; the
% 1.91/2.10  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.91/2.10  
% 1.91/2.10     dependent: set(knuth_bendix).
% 1.91/2.10     dependent: set(anl_eq).
% 1.91/2.10     dependent: set(para_from).
% 1.91/2.10     dependent: set(para_into).
% 1.91/2.10     dependent: clear(para_from_right).
% 1.91/2.10     dependent: clear(para_into_right).
% 1.91/2.10     dependent: set(para_from_vars).
% 1.91/2.10     dependent: set(eq_units_both_ways).
% 1.91/2.10     dependent: set(dynamic_demod_all).
% 1.91/2.10     dependent: set(dynamic_demod).
% 1.91/2.10     dependent: set(order_eq).
% 1.91/2.10     dependent: set(back_demod).
% 1.91/2.10     dependent: set(lrpo).
% 1.91/2.10  
% 1.91/2.10  ------------> process usable:
% 1.91/2.10  ** KEPT (pick-wt=5): 1 [] multiply(x,z)!=x.
% 1.91/2.10  
% 1.91/2.10  ------------> process sos:
% 1.91/2.10  ** KEPT (pick-wt=3): 2 [] A=A.
% 1.91/2.10  ** KEPT (pick-wt=7): 3 [] add(A,B)=add(B,A).
% 1.91/2.10  ** KEPT (pick-wt=7): 4 [] multiply(A,B)=multiply(B,A).
% 1.91/2.10  ** KEPT (pick-wt=13): 6 [copy,5,flip.1] multiply(add(A,B),add(C,B))=add(multiply(A,C),B).
% 1.91/2.10  ---> New Demodulator: 7 [new_demod,6] multiply(add(A,B),add(C,B))=add(multiply(A,C),B).
% 1.91/2.10  ** KEPT (pick-wt=13): 9 [copy,8,flip.1] multiply(add(A,B),add(A,C))=add(A,multiply(B,C)).
% 1.91/2.10  ---> New Demodulator: 10 [new_demod,9] multiply(add(A,B),add(A,C))=add(A,multiply(B,C)).
% 1.91/2.10  ** KEPT (pick-wt=13): 11 [] multiply(add(A,B),C)=add(multiply(A,C),multiply(B,C)).
% 1.91/2.10  ---> New Demodulator: 12 [new_demod,11] multiply(add(A,B),C)=add(multiply(A,C),multiply(B,C)).
% 1.91/2.10  ** KEPT (pick-wt=13): 13 [] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.91/2.10  ---> New Demodulator: 14 [new_demod,13] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.91/2.10  ** KEPT (pick-wt=6): 15 [] add(A,inverse(A))=multiplicative_identity.
% 1.91/2.10  ---> New Demodulator: 16 [new_demod,15] add(A,inverse(A))=multiplicative_identity.
% 1.91/2.10  ** KEPT (pick-wt=6): 17 [] add(inverse(A),A)=multiplicative_identity.
% 1.91/2.10  ---> New Demodulator: 18 [new_demod,17] add(inverse(A),A)=multiplicative_identity.
% 1.91/2.10  ** KEPT (pick-wt=6): 19 [] multiply(A,inverse(A))=additive_identity.
% 1.91/2.10  ---> New Demodulator: 20 [new_demod,19] multiply(A,inverse(A))=additive_identity.
% 1.91/2.10  ** KEPT (pick-wt=6): 21 [] multiply(inverse(A),A)=additive_identity.
% 1.91/2.10  ---> New Demodulator: 22 [new_demod,21] multiply(inverse(A),A)=additive_identity.
% 1.91/2.10  ** KEPT (pick-wt=5): 23 [] multiply(A,multiplicative_identity)=A.
% 1.91/2.10  ---> New Demodulator: 24 [new_demod,23] multiply(A,multiplicative_identity)=A.
% 1.91/2.10  ** KEPT (pick-wt=5): 25 [] multiply(multiplicative_identity,A)=A.
% 1.91/2.10  ---> New Demodulator: 26 [new_demod,25] multiply(multiplicative_identity,A)=A.
% 1.91/2.10  ** KEPT (pick-wt=5): 27 [] add(A,additive_identity)=A.
% 1.91/2.10  ---> New Demodulator: 28 [new_demod,27] add(A,additive_identity)=A.
% 1.91/2.10  ** KEPT (pick-wt=5): 29 [] add(additive_identity,A)=A.
% 1.91/2.10  ---> New Demodulator: 30 [new_demod,29] add(additive_identity,A)=A.
% 1.91/2.10  ** KEPT (pick-wt=5): 31 [] add(x,y)=z.
% 1.91/2.10  ---> New Demodulator: 32 [new_demod,31] add(x,y)=z.
% 1.98/2.14    Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.98/2.14    Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] add(A,B)=add(B,A).
% 1.98/2.14    Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] multiply(A,B)=multiply(B,A).
% 1.98/2.14  >>>> Starting back demodulation with 7.
% 1.98/2.14  >>>> Starting back demodulation with 10.
% 1.98/2.14  >>>> Starting back demodulation with 12.
% 1.98/2.14      >> back demodulating 9 with 12.
% 1.98/2.14      >> back demodulating 6 with 12.
% 1.98/2.14  >>>> Starting back demodulation with 14.
% 1.98/2.14  >>>> Starting back demodulation with 16.
% 1.98/2.14  >>>> Starting back demodulation with 18.
% 1.98/2.14  >>>> Starting back demodulation with 20.
% 1.98/2.14  >>>> Starting back demodulation with 22.
% 1.98/2.14  >>>> Starting back demodulation with 24.
% 1.98/2.14  >>>> Starting back demodulation with 26.
% 1.98/2.14  >>>> Starting back demodulation with 28.
% 1.98/2.14  >>>> Starting back demodulation with 30.
% 1.98/2.14  >>>> Starting back demodulation with 32.
% 1.98/2.14  >>>> Starting back demodulation with 34.
% 1.98/2.14  >>>> Starting back demodulation with 36.
% 1.98/2.14  
% 1.98/2.14  ======= end of input processing =======
% 1.98/2.14  
% 1.98/2.14  =========== start of search ===========
% 1.98/2.14  
% 1.98/2.14  
% 1.98/2.14  Resetting weight limit to 14.
% 1.98/2.14  
% 1.98/2.14  
% 1.98/2.14  Resetting weight limit to 14.
% 1.98/2.14  
% 1.98/2.14  sos_size=399
% 1.98/2.14  
% 1.98/2.14  -------- PROOF -------- 
% 1.98/2.14  
% 1.98/2.14  ----> UNIT CONFLICT at   0.04 sec ----> 896 [binary,894.1,97.1] $F.
% 1.98/2.14  
% 1.98/2.14  Length of proof is 14.  Level of proof is 4.
% 1.98/2.14  
% 1.98/2.14  ---------------- PROOF ----------------
% 1.98/2.14  % SZS status Unsatisfiable
% 1.98/2.14  % SZS output start Refutation
% See solution above
% 1.98/2.14  ------------ end of proof -------------
% 1.98/2.14  
% 1.98/2.14  
% 1.98/2.14  Search stopped by max_proofs option.
% 1.98/2.14  
% 1.98/2.14  
% 1.98/2.14  Search stopped by max_proofs option.
% 1.98/2.14  
% 1.98/2.14  ============ end of search ============
% 1.98/2.14  
% 1.98/2.14  -------------- statistics -------------
% 1.98/2.14  clauses given                 81
% 1.98/2.14  clauses generated           1841
% 1.98/2.14  clauses kept                 543
% 1.98/2.14  clauses forward subsumed    1523
% 1.98/2.14  clauses back subsumed         30
% 1.98/2.14  Kbytes malloced             4882
% 1.98/2.14  
% 1.98/2.14  ----------- times (seconds) -----------
% 1.98/2.14  user CPU time          0.04          (0 hr, 0 min, 0 sec)
% 1.98/2.14  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.98/2.14  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.98/2.14  
% 1.98/2.14  That finishes the proof of the theorem.
% 1.98/2.14  
% 1.98/2.14  Process 7544 finished Wed Jul 27 02:53:05 2022
% 1.98/2.14  Otter interrupted
% 1.98/2.14  PROOF FOUND
%------------------------------------------------------------------------------