TSTP Solution File: RNG008-3 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : RNG008-3 : TPTP v8.1.0. Released v1.0.0.
% 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 13:12:02 EDT 2022

% Result   : Unsatisfiable 1.98s 2.15s
% Output   : Refutation 1.98s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   14
% Syntax   : Number of clauses     :   31 (  31 unt;   0 nHn;   4 RR)
%            Number of literals    :   31 (  30 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   49 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    multiply(b,a) != c,
    file('RNG008-3.p',unknown),
    [] ).

cnf(4,axiom,
    add(additive_identity,A) = A,
    file('RNG008-3.p',unknown),
    [] ).

cnf(7,axiom,
    multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)),
    file('RNG008-3.p',unknown),
    [] ).

cnf(10,axiom,
    multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)),
    file('RNG008-3.p',unknown),
    [] ).

cnf(14,axiom,
    additive_inverse(additive_inverse(A)) = A,
    file('RNG008-3.p',unknown),
    [] ).

cnf(21,axiom,
    multiply(A,additive_inverse(B)) = additive_inverse(multiply(A,B)),
    file('RNG008-3.p',unknown),
    [] ).

cnf(23,plain,
    additive_inverse(multiply(A,B)) = multiply(A,additive_inverse(B)),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[21])]),
    [iquote('copy,21,flip.1')] ).

cnf(24,axiom,
    multiply(additive_inverse(A),B) = additive_inverse(multiply(A,B)),
    file('RNG008-3.p',unknown),
    [] ).

cnf(25,plain,
    multiply(additive_inverse(A),B) = multiply(A,additive_inverse(B)),
    inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[24]),23]),
    [iquote('copy,24,demod,23')] ).

cnf(27,axiom,
    add(add(A,B),C) = add(A,add(B,C)),
    file('RNG008-3.p',unknown),
    [] ).

cnf(28,axiom,
    add(A,B) = add(B,A),
    file('RNG008-3.p',unknown),
    [] ).

cnf(30,axiom,
    multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
    file('RNG008-3.p',unknown),
    [] ).

cnf(32,axiom,
    add(A,additive_identity) = A,
    file('RNG008-3.p',unknown),
    [] ).

cnf(33,axiom,
    add(A,additive_inverse(A)) = additive_identity,
    file('RNG008-3.p',unknown),
    [] ).

cnf(36,axiom,
    multiply(A,A) = A,
    file('RNG008-3.p',unknown),
    [] ).

cnf(37,axiom,
    multiply(a,b) = c,
    file('RNG008-3.p',unknown),
    [] ).

cnf(42,plain,
    add(A,add(multiply(B,A),add(multiply(A,B),B))) = add(A,B),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,36]),10,36,10,36,27])]),
    [iquote('para_into,7.1.1,35.1.1,demod,10,36,10,36,27,flip.1')] ).

cnf(49,plain,
    multiply(A,additive_inverse(A)) = additive_inverse(A),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[23,36])]),
    [iquote('para_into,22.1.1.1,35.1.1,flip.1')] ).

cnf(66,plain,
    multiply(additive_inverse(A),A) = A,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[49,14]),14]),
    [iquote('para_into,48.1.1.2,13.1.1,demod,14')] ).

cnf(72,plain,
    multiply(A,multiply(additive_inverse(B),multiply(A,B))) = multiply(A,B),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[66,23]),30]),
    [iquote('para_into,66.1.1.1,22.1.1,demod,30')] ).

cnf(98,plain,
    additive_inverse(A) = A,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,66]),49])]),
    [iquote('para_into,25.1.1,66.1.1,demod,49,flip.1')] ).

cnf(109,plain,
    multiply(A,multiply(B,multiply(A,B))) = multiply(A,B),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[72]),98]),
    [iquote('back_demod,72,demod,98')] ).

cnf(116,plain,
    add(A,A) = additive_identity,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[33]),98]),
    [iquote('back_demod,33,demod,98')] ).

cnf(117,plain,
    add(A,add(A,B)) = B,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[27,116]),4])]),
    [iquote('para_into,26.1.1.1,115.1.1,demod,4,flip.1')] ).

cnf(123,plain,
    add(A,add(B,A)) = B,
    inference(para_into,[status(thm),theory(equality)],[117,28]),
    [iquote('para_into,117.1.1.2,28.1.1')] ).

cnf(132,plain,
    multiply(A,multiply(A,B)) = multiply(A,B),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[30,36])]),
    [iquote('para_into,29.1.1.1,35.1.1,flip.1')] ).

cnf(201,plain,
    add(multiply(A,B),add(multiply(B,A),B)) = B,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[42,123]),27,27,123]),
    [iquote('para_from,42.1.1,122.1.1.2,demod,27,27,123')] ).

cnf(320,plain,
    multiply(A,multiply(B,A)) = multiply(A,B),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[201,132]),30,123]),
    [iquote('para_into,201.1.1.1,132.1.1,demod,30,123')] ).

cnf(321,plain,
    multiply(A,B) = multiply(B,A),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[201,109]),320,30,36,320,116,32,320]),
    [iquote('para_into,201.1.1.1,109.1.1,demod,320,30,36,320,116,32,320')] ).

cnf(385,plain,
    multiply(b,a) = c,
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[321,37])]),
    [iquote('para_into,321.1.1,37.1.1,flip.1')] ).

cnf(387,plain,
    $false,
    inference(binary,[status(thm)],[385,1]),
    [iquote('binary,385.1,1.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : RNG008-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12  % 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 02:12:40 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.51/2.13  ----- Otter 3.3f, August 2004 -----
% 1.51/2.13  The process was started by sandbox on n011.cluster.edu,
% 1.51/2.13  Wed Jul 27 02:12:40 2022
% 1.51/2.13  The command was "./otter".  The process ID is 32694.
% 1.51/2.13  
% 1.51/2.13  set(prolog_style_variables).
% 1.51/2.13  set(auto).
% 1.51/2.13     dependent: set(auto1).
% 1.51/2.13     dependent: set(process_input).
% 1.51/2.13     dependent: clear(print_kept).
% 1.51/2.13     dependent: clear(print_new_demod).
% 1.51/2.13     dependent: clear(print_back_demod).
% 1.51/2.13     dependent: clear(print_back_sub).
% 1.51/2.13     dependent: set(control_memory).
% 1.51/2.13     dependent: assign(max_mem, 12000).
% 1.51/2.13     dependent: assign(pick_given_ratio, 4).
% 1.51/2.13     dependent: assign(stats_level, 1).
% 1.51/2.13     dependent: assign(max_seconds, 10800).
% 1.51/2.13  clear(print_given).
% 1.51/2.13  
% 1.51/2.13  list(usable).
% 1.51/2.13  0 [] A=A.
% 1.51/2.13  0 [] add(additive_identity,X)=X.
% 1.51/2.13  0 [] add(additive_inverse(X),X)=additive_identity.
% 1.51/2.13  0 [] multiply(X,add(Y,Z))=add(multiply(X,Y),multiply(X,Z)).
% 1.51/2.13  0 [] multiply(add(X,Y),Z)=add(multiply(X,Z),multiply(Y,Z)).
% 1.51/2.13  0 [] additive_inverse(additive_identity)=additive_identity.
% 1.51/2.13  0 [] additive_inverse(additive_inverse(X))=X.
% 1.51/2.13  0 [] multiply(X,additive_identity)=additive_identity.
% 1.51/2.13  0 [] multiply(additive_identity,X)=additive_identity.
% 1.51/2.13  0 [] additive_inverse(add(X,Y))=add(additive_inverse(X),additive_inverse(Y)).
% 1.51/2.13  0 [] multiply(X,additive_inverse(Y))=additive_inverse(multiply(X,Y)).
% 1.51/2.13  0 [] multiply(additive_inverse(X),Y)=additive_inverse(multiply(X,Y)).
% 1.51/2.13  0 [] add(add(X,Y),Z)=add(X,add(Y,Z)).
% 1.51/2.13  0 [] add(X,Y)=add(Y,X).
% 1.51/2.13  0 [] multiply(multiply(X,Y),Z)=multiply(X,multiply(Y,Z)).
% 1.51/2.13  0 [] add(X,additive_identity)=X.
% 1.51/2.13  0 [] add(X,additive_inverse(X))=additive_identity.
% 1.51/2.13  0 [] multiply(X,X)=X.
% 1.51/2.13  0 [] multiply(a,b)=c.
% 1.51/2.13  0 [] multiply(b,a)!=c.
% 1.51/2.13  end_of_list.
% 1.51/2.13  
% 1.51/2.13  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.51/2.13  
% 1.51/2.13  All clauses are units, and equality is present; the
% 1.51/2.13  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.51/2.13  
% 1.51/2.13     dependent: set(knuth_bendix).
% 1.51/2.13     dependent: set(anl_eq).
% 1.51/2.13     dependent: set(para_from).
% 1.51/2.13     dependent: set(para_into).
% 1.51/2.13     dependent: clear(para_from_right).
% 1.51/2.13     dependent: clear(para_into_right).
% 1.51/2.13     dependent: set(para_from_vars).
% 1.51/2.13     dependent: set(eq_units_both_ways).
% 1.51/2.13     dependent: set(dynamic_demod_all).
% 1.51/2.13     dependent: set(dynamic_demod).
% 1.51/2.13     dependent: set(order_eq).
% 1.51/2.13     dependent: set(back_demod).
% 1.51/2.13     dependent: set(lrpo).
% 1.51/2.13  
% 1.51/2.13  ------------> process usable:
% 1.51/2.13  ** KEPT (pick-wt=5): 1 [] multiply(b,a)!=c.
% 1.51/2.13  
% 1.51/2.13  ------------> process sos:
% 1.51/2.13  ** KEPT (pick-wt=3): 2 [] A=A.
% 1.51/2.13  ** KEPT (pick-wt=5): 3 [] add(additive_identity,A)=A.
% 1.51/2.13  ---> New Demodulator: 4 [new_demod,3] add(additive_identity,A)=A.
% 1.51/2.13  ** KEPT (pick-wt=6): 5 [] add(additive_inverse(A),A)=additive_identity.
% 1.51/2.13  ---> New Demodulator: 6 [new_demod,5] add(additive_inverse(A),A)=additive_identity.
% 1.51/2.13  ** KEPT (pick-wt=13): 7 [] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.51/2.13  ---> New Demodulator: 8 [new_demod,7] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.51/2.13  ** KEPT (pick-wt=13): 9 [] multiply(add(A,B),C)=add(multiply(A,C),multiply(B,C)).
% 1.51/2.13  ---> New Demodulator: 10 [new_demod,9] multiply(add(A,B),C)=add(multiply(A,C),multiply(B,C)).
% 1.51/2.13  ** KEPT (pick-wt=4): 11 [] additive_inverse(additive_identity)=additive_identity.
% 1.51/2.13  ---> New Demodulator: 12 [new_demod,11] additive_inverse(additive_identity)=additive_identity.
% 1.51/2.13  ** KEPT (pick-wt=5): 13 [] additive_inverse(additive_inverse(A))=A.
% 1.51/2.13  ---> New Demodulator: 14 [new_demod,13] additive_inverse(additive_inverse(A))=A.
% 1.51/2.13  ** KEPT (pick-wt=5): 15 [] multiply(A,additive_identity)=additive_identity.
% 1.51/2.13  ---> New Demodulator: 16 [new_demod,15] multiply(A,additive_identity)=additive_identity.
% 1.51/2.13  ** KEPT (pick-wt=5): 17 [] multiply(additive_identity,A)=additive_identity.
% 1.51/2.13  ---> New Demodulator: 18 [new_demod,17] multiply(additive_identity,A)=additive_identity.
% 1.51/2.13  ** KEPT (pick-wt=10): 19 [] additive_inverse(add(A,B))=add(additive_inverse(A),additive_inverse(B)).
% 1.51/2.13  ---> New Demodulator: 20 [new_demod,19] additive_inverse(add(A,B))=add(additive_inverse(A),additive_inverse(B)).
% 1.51/2.13  ** KEPT (pick-wt=9): 22 [copy,21,flip.1] additive_inverse(multiply(A,B))=multiply(A,additive_inverse(B)).
% 1.51/2.13  ---> New Demodulator: 23 [new_demod,22] additive_inverse(multiply(A,B))=multiply(A,additive_inverse(B)).
% 1.51/2.13  ** KEPT (pick-wt=9): 25 [copy,24,demod,23] multiply(additive_inverse(A),B)=multiply(A,additive_inverse(B)).
% 1.98/2.15  ** KEPT (pick-wt=11): 26 [] add(add(A,B),C)=add(A,add(B,C)).
% 1.98/2.15  ---> New Demodulator: 27 [new_demod,26] add(add(A,B),C)=add(A,add(B,C)).
% 1.98/2.15  ** KEPT (pick-wt=7): 28 [] add(A,B)=add(B,A).
% 1.98/2.15  ** KEPT (pick-wt=11): 29 [] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.98/2.15  ---> New Demodulator: 30 [new_demod,29] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.98/2.15  ** KEPT (pick-wt=5): 31 [] add(A,additive_identity)=A.
% 1.98/2.15  ---> New Demodulator: 32 [new_demod,31] add(A,additive_identity)=A.
% 1.98/2.15  ** KEPT (pick-wt=6): 33 [] add(A,additive_inverse(A))=additive_identity.
% 1.98/2.15  ---> New Demodulator: 34 [new_demod,33] add(A,additive_inverse(A))=additive_identity.
% 1.98/2.15  ** KEPT (pick-wt=5): 35 [] multiply(A,A)=A.
% 1.98/2.15  ---> New Demodulator: 36 [new_demod,35] multiply(A,A)=A.
% 1.98/2.15  ** KEPT (pick-wt=5): 37 [] multiply(a,b)=c.
% 1.98/2.15  ---> New Demodulator: 38 [new_demod,37] multiply(a,b)=c.
% 1.98/2.15    Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.98/2.15  >>>> Starting back demodulation with 4.
% 1.98/2.15  >>>> Starting back demodulation with 6.
% 1.98/2.15  >>>> Starting back demodulation with 8.
% 1.98/2.15  >>>> Starting back demodulation with 10.
% 1.98/2.15  >>>> Starting back demodulation with 12.
% 1.98/2.15  >>>> Starting back demodulation with 14.
% 1.98/2.15  >>>> Starting back demodulation with 16.
% 1.98/2.15  >>>> Starting back demodulation with 18.
% 1.98/2.15  >>>> Starting back demodulation with 20.
% 1.98/2.15  >>>> Starting back demodulation with 23.
% 1.98/2.15  ** KEPT (pick-wt=9): 39 [copy,25,flip.1] multiply(A,additive_inverse(B))=multiply(additive_inverse(A),B).
% 1.98/2.15  >>>> Starting back demodulation with 27.
% 1.98/2.15    Following clause subsumed by 28 during input processing: 0 [copy,28,flip.1] add(A,B)=add(B,A).
% 1.98/2.15  >>>> Starting back demodulation with 30.
% 1.98/2.15  >>>> Starting back demodulation with 32.
% 1.98/2.15  >>>> Starting back demodulation with 34.
% 1.98/2.15  >>>> Starting back demodulation with 36.
% 1.98/2.15  >>>> Starting back demodulation with 38.
% 1.98/2.15    Following clause subsumed by 25 during input processing: 0 [copy,39,flip.1] multiply(additive_inverse(A),B)=multiply(A,additive_inverse(B)).
% 1.98/2.15  
% 1.98/2.15  ======= end of input processing =======
% 1.98/2.15  
% 1.98/2.15  =========== start of search ===========
% 1.98/2.15  
% 1.98/2.15  -------- PROOF -------- 
% 1.98/2.15  
% 1.98/2.15  ----> UNIT CONFLICT at   0.02 sec ----> 387 [binary,385.1,1.1] $F.
% 1.98/2.15  
% 1.98/2.15  Length of proof is 16.  Level of proof is 11.
% 1.98/2.15  
% 1.98/2.15  ---------------- PROOF ----------------
% 1.98/2.15  % SZS status Unsatisfiable
% 1.98/2.15  % SZS output start Refutation
% See solution above
% 1.98/2.15  ------------ end of proof -------------
% 1.98/2.15  
% 1.98/2.15  
% 1.98/2.15  Search stopped by max_proofs option.
% 1.98/2.15  
% 1.98/2.15  
% 1.98/2.15  Search stopped by max_proofs option.
% 1.98/2.15  
% 1.98/2.15  ============ end of search ============
% 1.98/2.15  
% 1.98/2.15  -------------- statistics -------------
% 1.98/2.15  clauses given                 45
% 1.98/2.15  clauses generated            750
% 1.98/2.15  clauses kept                 250
% 1.98/2.15  clauses forward subsumed     701
% 1.98/2.15  clauses back subsumed         64
% 1.98/2.15  Kbytes malloced             1953
% 1.98/2.15  
% 1.98/2.15  ----------- times (seconds) -----------
% 1.98/2.15  user CPU time          0.02          (0 hr, 0 min, 0 sec)
% 1.98/2.15  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.98/2.15  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.98/2.15  
% 1.98/2.15  That finishes the proof of the theorem.
% 1.98/2.15  
% 1.98/2.15  Process 32694 finished Wed Jul 27 02:12:42 2022
% 1.98/2.15  Otter interrupted
% 1.98/2.15  PROOF FOUND
%------------------------------------------------------------------------------