TSTP Solution File: ALG007-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : ALG007-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n009.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 12:45:53 EDT 2022

% Result   : Unsatisfiable 2.26s 2.42s
% Output   : Refutation 2.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   40 (  40 unt;   0 nHn;   4 RR)
%            Number of literals    :   40 (  39 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    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :  100 (  11 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    difference(difference(a,b),c) != difference(difference(a,c),difference(b,c)),
    file('ALG007-1.p',unknown),
    [] ).

cnf(2,plain,
    difference(difference(a,c),difference(b,c)) != difference(difference(a,b),c),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
    [iquote('copy,1,flip.1')] ).

cnf(5,axiom,
    difference(A,difference(B,A)) = A,
    file('ALG007-1.p',unknown),
    [] ).

cnf(6,axiom,
    difference(A,difference(A,B)) = difference(B,difference(B,A)),
    file('ALG007-1.p',unknown),
    [] ).

cnf(7,axiom,
    difference(difference(A,B),C) = difference(difference(A,C),B),
    file('ALG007-1.p',unknown),
    [] ).

cnf(8,plain,
    difference(difference(A,B),B) = difference(A,B),
    inference(para_into,[status(thm),theory(equality)],[5,5]),
    [iquote('para_into,4.1.1.2,4.1.1')] ).

cnf(10,plain,
    difference(difference(A,B),difference(A,B)) = difference(B,B),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[6,8]),5]),
    [iquote('para_into,6.1.1.2,8.1.1,demod,5')] ).

cnf(12,plain,
    difference(difference(A,B),difference(difference(A,B),A)) = difference(A,difference(B,difference(B,A))),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[6,6])]),
    [iquote('para_into,6.1.1.2,6.1.1,flip.1')] ).

cnf(18,plain,
    difference(difference(difference(A,B),C),B) = difference(difference(A,B),C),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,8])]),
    [iquote('para_into,7.1.1.1,8.1.1,flip.1')] ).

cnf(21,plain,
    difference(difference(A,difference(A,B)),C) = difference(difference(B,C),difference(B,A)),
    inference(para_into,[status(thm),theory(equality)],[7,6]),
    [iquote('para_into,7.1.1.1,6.1.1')] ).

cnf(23,plain,
    difference(difference(A,B),difference(C,A)) = difference(A,B),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,5])]),
    [iquote('para_into,7.1.1.1,4.1.1,flip.1')] ).

cnf(24,plain,
    difference(difference(A,difference(difference(A,B),C)),B) = difference(C,difference(C,difference(A,B))),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,6])]),
    [iquote('para_into,7.1.1,6.1.1,flip.1')] ).

cnf(29,plain,
    difference(difference(A,B),difference(A,C)) = difference(difference(C,difference(C,A)),B),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[21])]),
    [iquote('copy,21,flip.1')] ).

cnf(31,plain,
    difference(A,difference(B,difference(B,A))) = difference(A,B),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[12]),23])]),
    [iquote('back_demod,12,demod,23,flip.1')] ).

cnf(32,plain,
    difference(difference(A,B),difference(difference(A,C),B)) = difference(C,difference(C,difference(A,B))),
    inference(para_from,[status(thm),theory(equality)],[7,6]),
    [iquote('para_from,7.1.1,6.1.1.2')] ).

cnf(34,plain,
    difference(A,difference(difference(B,A),C)) = A,
    inference(para_from,[status(thm),theory(equality)],[7,5]),
    [iquote('para_from,7.1.1,4.1.1.2')] ).

cnf(36,plain,
    difference(difference(a,difference(b,c)),c) != difference(difference(a,b),c),
    inference(para_from,[status(thm),theory(equality)],[7,2]),
    [iquote('para_from,7.1.1,2.1.1')] ).

cnf(38,plain,
    difference(difference(difference(A,B),C),difference(difference(A,C),B)) = difference(B,B),
    inference(para_into,[status(thm),theory(equality)],[10,7]),
    [iquote('para_into,10.1.1.1,7.1.1')] ).

cnf(41,plain,
    difference(A,A) = difference(B,B),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[10,7]),38]),
    [iquote('para_into,10.1.1.2,7.1.1,demod,38')] ).

cnf(45,plain,
    difference(difference(A,A),B) = difference(difference(C,B),C),
    inference(para_from,[status(thm),theory(equality)],[41,7]),
    [iquote('para_from,41.1.1,7.1.1.1')] ).

cnf(47,plain,
    difference(A,difference(B,B)) = A,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[41,6]),5]),
    [iquote('para_from,41.1.1,6.1.1.2,demod,5')] ).

cnf(49,plain,
    difference(difference(A,B),A) = difference(difference(C,C),B),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[45])]),
    [iquote('copy,45,flip.1')] ).

cnf(52,plain,
    difference(difference(A,A),B) = difference(A,A),
    inference(para_from,[status(thm),theory(equality)],[47,5]),
    [iquote('para_from,46.1.1,4.1.1.2')] ).

cnf(53,plain,
    difference(difference(A,B),A) = difference(C,C),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[49]),52]),
    [iquote('back_demod,49,demod,52')] ).

cnf(61,plain,
    difference(difference(A,B),difference(B,C)) = difference(A,B),
    inference(para_into,[status(thm),theory(equality)],[34,5]),
    [iquote('para_into,34.1.1.2.1,4.1.1')] ).

cnf(80,plain,
    difference(A,difference(A,difference(A,B))) = difference(A,B),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[53,6]),47])]),
    [iquote('para_from,53.1.1,6.1.1.2,demod,47,flip.1')] ).

cnf(98,plain,
    difference(difference(difference(A,B),C),difference(D,difference(A,C))) = difference(difference(A,C),B),
    inference(para_into,[status(thm),theory(equality)],[23,7]),
    [iquote('para_into,22.1.1.1,7.1.1')] ).

cnf(102,plain,
    difference(difference(difference(A,B),C),difference(D,A)) = difference(difference(A,B),C),
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[23,18]),23]),
    [iquote('para_from,22.1.1,18.1.1.1.1,demod,23')] ).

cnf(209,plain,
    difference(difference(A,difference(B,C)),B) = difference(A,B),
    inference(para_into,[status(thm),theory(equality)],[61,7]),
    [iquote('para_into,61.1.1,7.1.1')] ).

cnf(223,plain,
    difference(difference(A,difference(B,C)),difference(A,C)) = difference(C,difference(C,A)),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[21,23])]),
    [iquote('para_into,21.1.1,22.1.1,flip.1')] ).

cnf(226,plain,
    difference(difference(A,B),difference(A,C)) = difference(difference(C,B),difference(C,A)),
    inference(para_into,[status(thm),theory(equality)],[21,7]),
    [iquote('para_into,21.1.1,7.1.1')] ).

cnf(766,plain,
    difference(difference(A,B),difference(difference(A,B),difference(difference(C,difference(C,A)),B))) = difference(difference(A,B),difference(A,C)),
    inference(para_from,[status(thm),theory(equality)],[29,80]),
    [iquote('para_from,29.1.1,80.1.1.2.2')] ).

cnf(982,plain,
    difference(A,difference(A,difference(B,C))) = difference(difference(B,C),difference(B,A)),
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[32,209]),23]),
    [iquote('para_from,32.1.1,209.1.1.1,demod,23')] ).

cnf(2647,plain,
    difference(difference(A,B),difference(A,difference(A,C))) = difference(difference(A,B),C),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[98,80]),98])]),
    [iquote('para_into,97.1.1.1.1,80.1.1,demod,98,flip.1')] ).

cnf(3139,plain,
    difference(difference(A,difference(A,B)),C) = difference(A,difference(A,difference(B,C))),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[223,29]),102]),
    [iquote('para_into,223.1.1.1,29.1.1,demod,102')] ).

cnf(3453,plain,
    difference(difference(A,B),difference(difference(A,B),C)) = difference(difference(A,B),difference(A,C)),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[766]),3139,31]),
    [iquote('back_demod,766,demod,3139,31')] ).

cnf(4583,plain,
    difference(difference(A,difference(difference(B,C),difference(B,A))),C) = difference(difference(A,B),C),
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[226,24]),3453,2647]),
    [iquote('para_from,226.1.1,24.1.1.1.2,demod,3453,2647')] ).

cnf(4598,plain,
    difference(A,difference(difference(B,C),difference(B,A))) = difference(A,difference(B,C)),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[982,982]),47]),
    [iquote('para_into,982.1.1.2,982.1.1,demod,47')] ).

cnf(4599,plain,
    difference(difference(A,difference(B,C)),C) = difference(difference(A,B),C),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4583]),4598]),
    [iquote('back_demod,4583,demod,4598')] ).

cnf(4601,plain,
    $false,
    inference(binary,[status(thm)],[4599,36]),
    [iquote('binary,4599.1,36.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ALG007-1 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13  % Command  : otter-tptp-script %s
% 0.13/0.34  % Computer : n009.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Wed Jul 27 03:41:36 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 2.26/2.42  ----- Otter 3.3f, August 2004 -----
% 2.26/2.42  The process was started by sandbox on n009.cluster.edu,
% 2.26/2.42  Wed Jul 27 03:41:36 2022
% 2.26/2.42  The command was "./otter".  The process ID is 13160.
% 2.26/2.42  
% 2.26/2.42  set(prolog_style_variables).
% 2.26/2.42  set(auto).
% 2.26/2.42     dependent: set(auto1).
% 2.26/2.42     dependent: set(process_input).
% 2.26/2.42     dependent: clear(print_kept).
% 2.26/2.42     dependent: clear(print_new_demod).
% 2.26/2.42     dependent: clear(print_back_demod).
% 2.26/2.42     dependent: clear(print_back_sub).
% 2.26/2.42     dependent: set(control_memory).
% 2.26/2.42     dependent: assign(max_mem, 12000).
% 2.26/2.42     dependent: assign(pick_given_ratio, 4).
% 2.26/2.42     dependent: assign(stats_level, 1).
% 2.26/2.42     dependent: assign(max_seconds, 10800).
% 2.26/2.42  clear(print_given).
% 2.26/2.42  
% 2.26/2.42  list(usable).
% 2.26/2.42  0 [] A=A.
% 2.26/2.42  0 [] difference(X,difference(Y,X))=X.
% 2.26/2.42  0 [] difference(X,difference(X,Y))=difference(Y,difference(Y,X)).
% 2.26/2.42  0 [] difference(difference(X,Y),Z)=difference(difference(X,Z),Y).
% 2.26/2.42  0 [] difference(difference(a,b),c)!=difference(difference(a,c),difference(b,c)).
% 2.26/2.42  end_of_list.
% 2.26/2.42  
% 2.26/2.42  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 2.26/2.42  
% 2.26/2.42  All clauses are units, and equality is present; the
% 2.26/2.42  strategy will be Knuth-Bendix with positive clauses in sos.
% 2.26/2.42  
% 2.26/2.42     dependent: set(knuth_bendix).
% 2.26/2.42     dependent: set(anl_eq).
% 2.26/2.42     dependent: set(para_from).
% 2.26/2.42     dependent: set(para_into).
% 2.26/2.42     dependent: clear(para_from_right).
% 2.26/2.42     dependent: clear(para_into_right).
% 2.26/2.42     dependent: set(para_from_vars).
% 2.26/2.42     dependent: set(eq_units_both_ways).
% 2.26/2.42     dependent: set(dynamic_demod_all).
% 2.26/2.42     dependent: set(dynamic_demod).
% 2.26/2.42     dependent: set(order_eq).
% 2.26/2.42     dependent: set(back_demod).
% 2.26/2.42     dependent: set(lrpo).
% 2.26/2.42  
% 2.26/2.42  ------------> process usable:
% 2.26/2.42  ** KEPT (pick-wt=13): 2 [copy,1,flip.1] difference(difference(a,c),difference(b,c))!=difference(difference(a,b),c).
% 2.26/2.42  
% 2.26/2.42  ------------> process sos:
% 2.26/2.42  ** KEPT (pick-wt=3): 3 [] A=A.
% 2.26/2.42  ** KEPT (pick-wt=7): 4 [] difference(A,difference(B,A))=A.
% 2.26/2.42  ---> New Demodulator: 5 [new_demod,4] difference(A,difference(B,A))=A.
% 2.26/2.42  ** KEPT (pick-wt=11): 6 [] difference(A,difference(A,B))=difference(B,difference(B,A)).
% 2.26/2.42  ** KEPT (pick-wt=11): 7 [] difference(difference(A,B),C)=difference(difference(A,C),B).
% 2.26/2.42    Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 2.26/2.42  >>>> Starting back demodulation with 5.
% 2.26/2.42    Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] difference(A,difference(A,B))=difference(B,difference(B,A)).
% 2.26/2.42    Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] difference(difference(A,B),C)=difference(difference(A,C),B).
% 2.26/2.42  
% 2.26/2.42  ======= end of input processing =======
% 2.26/2.42  
% 2.26/2.42  =========== start of search ===========
% 2.26/2.42  
% 2.26/2.42  
% 2.26/2.42  Resetting weight limit to 17.
% 2.26/2.42  
% 2.26/2.42  
% 2.26/2.42  Resetting weight limit to 17.
% 2.26/2.42  
% 2.26/2.42  sos_size=995
% 2.26/2.42  
% 2.26/2.42  -------- PROOF -------- 
% 2.26/2.42  
% 2.26/2.42  ----> UNIT CONFLICT at   0.51 sec ----> 4601 [binary,4599.1,36.1] $F.
% 2.26/2.42  
% 2.26/2.42  Length of proof is 35.  Level of proof is 12.
% 2.26/2.42  
% 2.26/2.42  ---------------- PROOF ----------------
% 2.26/2.42  % SZS status Unsatisfiable
% 2.26/2.42  % SZS output start Refutation
% See solution above
% 2.26/2.42  ------------ end of proof -------------
% 2.26/2.42  
% 2.26/2.42  
% 2.26/2.42  Search stopped by max_proofs option.
% 2.26/2.42  
% 2.26/2.42  
% 2.26/2.42  Search stopped by max_proofs option.
% 2.26/2.42  
% 2.26/2.42  ============ end of search ============
% 2.26/2.42  
% 2.26/2.42  -------------- statistics -------------
% 2.26/2.42  clauses given                100
% 2.26/2.42  clauses generated          21580
% 2.26/2.42  clauses kept                3101
% 2.26/2.42  clauses forward subsumed   20722
% 2.26/2.42  clauses back subsumed         61
% 2.26/2.42  Kbytes malloced             4882
% 2.26/2.42  
% 2.26/2.42  ----------- times (seconds) -----------
% 2.26/2.42  user CPU time          0.51          (0 hr, 0 min, 0 sec)
% 2.26/2.42  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 2.26/2.42  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 2.26/2.42  
% 2.26/2.42  That finishes the proof of the theorem.
% 2.26/2.42  
% 2.26/2.42  Process 13160 finished Wed Jul 27 03:41:38 2022
% 2.26/2.42  Otter interrupted
% 2.26/2.42  PROOF FOUND
%------------------------------------------------------------------------------