TSTP Solution File: SET984+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SET984+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n012.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 13:14:38 EDT 2022

% Result   : Theorem 175.21s 175.44s
% Output   : Refutation 175.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   24 (  15 unt;   4 nHn;  18 RR)
%            Number of literals    :   41 (  30 equ;  15 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   38 (   7 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    ( cartesian_product2(A,B) = empty_set
    | A != empty_set ),
    file('SET984+1.p',unknown),
    [] ).

cnf(4,axiom,
    ( cartesian_product2(A,B) = empty_set
    | B != empty_set ),
    file('SET984+1.p',unknown),
    [] ).

cnf(5,axiom,
    ( cartesian_product2(A,B) != cartesian_product2(C,D)
    | A = empty_set
    | B = empty_set
    | A = C ),
    file('SET984+1.p',unknown),
    [] ).

cnf(6,axiom,
    ( cartesian_product2(A,B) != cartesian_product2(C,D)
    | A = empty_set
    | B = empty_set
    | B = D ),
    file('SET984+1.p',unknown),
    [] ).

cnf(7,axiom,
    cartesian_product2(dollar_c6,dollar_c5) != empty_set,
    file('SET984+1.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ subset(dollar_c6,dollar_c4)
    | ~ subset(dollar_c5,dollar_c3) ),
    file('SET984+1.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ subset(A,B)
    | set_intersection2(A,B) = A ),
    file('SET984+1.p',unknown),
    [] ).

cnf(18,axiom,
    set_intersection2(A,B) = set_intersection2(B,A),
    file('SET984+1.p',unknown),
    [] ).

cnf(24,axiom,
    cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
    file('SET984+1.p',unknown),
    [] ).

cnf(26,plain,
    set_intersection2(cartesian_product2(A,B),cartesian_product2(C,D)) = cartesian_product2(set_intersection2(A,C),set_intersection2(B,D)),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[24])]),
    [iquote('copy,24,flip.1')] ).

cnf(27,axiom,
    subset(cartesian_product2(dollar_c6,dollar_c5),cartesian_product2(dollar_c4,dollar_c3)),
    file('SET984+1.p',unknown),
    [] ).

cnf(28,axiom,
    subset(set_intersection2(A,B),A),
    file('SET984+1.p',unknown),
    [] ).

cnf(55,plain,
    ( set_intersection2(A,B) = B
    | ~ subset(B,A) ),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[18,9])]),
    [iquote('para_into,18.1.1,9.2.1,flip.1')] ).

cnf(78,plain,
    ( subset(A,B)
    | cartesian_product2(C,set_intersection2(B,D)) != cartesian_product2(E,A)
    | C = empty_set
    | set_intersection2(B,D) = empty_set ),
    inference(para_into,[status(thm),theory(equality)],[28,6]),
    [iquote('para_into,28.1.1,6.4.1')] ).

cnf(81,plain,
    ( subset(A,B)
    | cartesian_product2(set_intersection2(B,C),D) != cartesian_product2(A,E)
    | set_intersection2(B,C) = empty_set
    | D = empty_set ),
    inference(para_into,[status(thm),theory(equality)],[28,5]),
    [iquote('para_into,28.1.1,5.4.1')] ).

cnf(147,plain,
    cartesian_product2(set_intersection2(dollar_c6,dollar_c4),set_intersection2(dollar_c5,dollar_c3)) = cartesian_product2(dollar_c6,dollar_c5),
    inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[27,9]),26]),
    [iquote('hyper,27,9,demod,26')] ).

cnf(294,plain,
    cartesian_product2(set_intersection2(dollar_c4,dollar_c6),set_intersection2(dollar_c3,dollar_c5)) = cartesian_product2(dollar_c6,dollar_c5),
    inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[55,27]),26]),
    [iquote('hyper,55,27,demod,26')] ).

cnf(4516,plain,
    set_intersection2(dollar_c5,dollar_c3) != empty_set,
    inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[147,4]),7]),
    [iquote('para_into,147.1.1,4.1.1,unit_del,7')] ).

cnf(4517,plain,
    set_intersection2(dollar_c6,dollar_c4) != empty_set,
    inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[147,3]),7]),
    [iquote('para_into,147.1.1,3.1.1,unit_del,7')] ).

cnf(4636,plain,
    set_intersection2(dollar_c3,dollar_c5) != empty_set,
    inference(para_into,[status(thm),theory(equality)],[4516,18]),
    [iquote('para_into,4516.1.1,18.1.1')] ).

cnf(4637,plain,
    set_intersection2(dollar_c4,dollar_c6) != empty_set,
    inference(para_into,[status(thm),theory(equality)],[4517,18]),
    [iquote('para_into,4517.1.1,18.1.1')] ).

cnf(7459,plain,
    subset(dollar_c6,dollar_c4),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[294,81]),4637,4636]),
    [iquote('hyper,294,81,unit_del,4637,4636')] ).

cnf(7462,plain,
    subset(dollar_c5,dollar_c3),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[294,78]),4637,4636]),
    [iquote('hyper,294,78,unit_del,4637,4636')] ).

cnf(7473,plain,
    $false,
    inference(hyper,[status(thm)],[7462,8,7459]),
    [iquote('hyper,7462,8,7459')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SET984+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n012.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 10:34:50 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.68/1.91  ----- Otter 3.3f, August 2004 -----
% 1.68/1.91  The process was started by sandbox on n012.cluster.edu,
% 1.68/1.91  Wed Jul 27 10:34:50 2022
% 1.68/1.91  The command was "./otter".  The process ID is 13481.
% 1.68/1.91  
% 1.68/1.91  set(prolog_style_variables).
% 1.68/1.91  set(auto).
% 1.68/1.91     dependent: set(auto1).
% 1.68/1.91     dependent: set(process_input).
% 1.68/1.91     dependent: clear(print_kept).
% 1.68/1.91     dependent: clear(print_new_demod).
% 1.68/1.91     dependent: clear(print_back_demod).
% 1.68/1.91     dependent: clear(print_back_sub).
% 1.68/1.91     dependent: set(control_memory).
% 1.68/1.91     dependent: assign(max_mem, 12000).
% 1.68/1.91     dependent: assign(pick_given_ratio, 4).
% 1.68/1.91     dependent: assign(stats_level, 1).
% 1.68/1.91     dependent: assign(max_seconds, 10800).
% 1.68/1.91  clear(print_given).
% 1.68/1.91  
% 1.68/1.91  formula_list(usable).
% 1.68/1.91  all A (A=A).
% 1.68/1.91  all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 1.68/1.91  empty(empty_set).
% 1.68/1.91  all A B (set_intersection2(A,A)=A).
% 1.68/1.91  exists A empty(A).
% 1.68/1.91  exists A (-empty(A)).
% 1.68/1.91  all A B subset(A,A).
% 1.68/1.91  all A B (cartesian_product2(A,B)=empty_set<->A=empty_set|B=empty_set).
% 1.68/1.91  all A B C D (cartesian_product2(set_intersection2(A,B),set_intersection2(C,D))=set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D))).
% 1.68/1.91  all A B C D (cartesian_product2(A,B)=cartesian_product2(C,D)->A=empty_set|B=empty_set|A=C&B=D).
% 1.68/1.91  -(all A B C D (subset(cartesian_product2(A,B),cartesian_product2(C,D))->cartesian_product2(A,B)=empty_set|subset(A,C)&subset(B,D))).
% 1.68/1.91  all A B subset(set_intersection2(A,B),A).
% 1.68/1.91  all A B (subset(A,B)->set_intersection2(A,B)=A).
% 1.68/1.91  end_of_list.
% 1.68/1.91  
% 1.68/1.91  -------> usable clausifies to:
% 1.68/1.91  
% 1.68/1.91  list(usable).
% 1.68/1.91  0 [] A=A.
% 1.68/1.91  0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.68/1.91  0 [] empty(empty_set).
% 1.68/1.91  0 [] set_intersection2(A,A)=A.
% 1.68/1.91  0 [] empty($c1).
% 1.68/1.91  0 [] -empty($c2).
% 1.68/1.91  0 [] subset(A,A).
% 1.68/1.91  0 [] cartesian_product2(A,B)!=empty_set|A=empty_set|B=empty_set.
% 1.68/1.91  0 [] cartesian_product2(A,B)=empty_set|A!=empty_set.
% 1.68/1.91  0 [] cartesian_product2(A,B)=empty_set|B!=empty_set.
% 1.68/1.91  0 [] cartesian_product2(set_intersection2(A,B),set_intersection2(C,D))=set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)).
% 1.68/1.91  0 [] cartesian_product2(A,B)!=cartesian_product2(C,D)|A=empty_set|B=empty_set|A=C.
% 1.68/1.91  0 [] cartesian_product2(A,B)!=cartesian_product2(C,D)|A=empty_set|B=empty_set|B=D.
% 1.68/1.91  0 [] subset(cartesian_product2($c6,$c5),cartesian_product2($c4,$c3)).
% 1.68/1.91  0 [] cartesian_product2($c6,$c5)!=empty_set.
% 1.68/1.91  0 [] -subset($c6,$c4)| -subset($c5,$c3).
% 1.68/1.91  0 [] subset(set_intersection2(A,B),A).
% 1.68/1.91  0 [] -subset(A,B)|set_intersection2(A,B)=A.
% 1.68/1.91  end_of_list.
% 1.68/1.91  
% 1.68/1.91  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.68/1.91  
% 1.68/1.91  This ia a non-Horn set with equality.  The strategy will be
% 1.68/1.91  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.68/1.91  deletion, with positive clauses in sos and nonpositive
% 1.68/1.91  clauses in usable.
% 1.68/1.91  
% 1.68/1.91     dependent: set(knuth_bendix).
% 1.68/1.91     dependent: set(anl_eq).
% 1.68/1.91     dependent: set(para_from).
% 1.68/1.91     dependent: set(para_into).
% 1.68/1.91     dependent: clear(para_from_right).
% 1.68/1.91     dependent: clear(para_into_right).
% 1.68/1.91     dependent: set(para_from_vars).
% 1.68/1.91     dependent: set(eq_units_both_ways).
% 1.68/1.91     dependent: set(dynamic_demod_all).
% 1.68/1.91     dependent: set(dynamic_demod).
% 1.68/1.91     dependent: set(order_eq).
% 1.68/1.91     dependent: set(back_demod).
% 1.68/1.91     dependent: set(lrpo).
% 1.68/1.91     dependent: set(hyper_res).
% 1.68/1.91     dependent: set(unit_deletion).
% 1.68/1.91     dependent: set(factor).
% 1.68/1.91  
% 1.68/1.91  ------------> process usable:
% 1.68/1.91  ** KEPT (pick-wt=2): 1 [] -empty($c2).
% 1.68/1.91  ** KEPT (pick-wt=11): 2 [] cartesian_product2(A,B)!=empty_set|A=empty_set|B=empty_set.
% 1.68/1.91  ** KEPT (pick-wt=8): 3 [] cartesian_product2(A,B)=empty_set|A!=empty_set.
% 1.68/1.91  ** KEPT (pick-wt=8): 4 [] cartesian_product2(A,B)=empty_set|B!=empty_set.
% 1.68/1.91  ** KEPT (pick-wt=16): 5 [] cartesian_product2(A,B)!=cartesian_product2(C,D)|A=empty_set|B=empty_set|A=C.
% 1.68/1.91  ** KEPT (pick-wt=16): 6 [] cartesian_product2(A,B)!=cartesian_product2(C,D)|A=empty_set|B=empty_set|B=D.
% 1.68/1.91  ** KEPT (pick-wt=5): 7 [] cartesian_product2($c6,$c5)!=empty_set.
% 1.68/1.91  ** KEPT (pick-wt=6): 8 [] -subset($c6,$c4)| -subset($c5,$c3).
% 1.68/1.91  ** KEPT (pick-wt=8): 9 [] -subset(A,B)|set_intersection2(A,B)=A.
% 1.68/1.91  
% 1.68/1.91  ------------> process sos:
% 1.68/1.91  ** KEPT (pick-wt=3): 17 [] A=A.
% 1.68/1.91  ** KEPT (pick-wt=7): 18 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.68/1.91  ** KEPT (pick-wt=2): 19 [] empty(empty_set).
% 1.68/1.91  ** KEPT (pick-wt=5): 20 [] set_intersection2(A,A)=A.
% 1.68/1.91  ---> New Demodulator: 21 [new_demod,20] set_intersection2(A,A)=A.
% 175.21/175.44  ** KEPT (pick-wt=2): 22 [] empty($c1).
% 175.21/175.44  ** KEPT (pick-wt=3): 23 [] subset(A,A).
% 175.21/175.44  ** KEPT (pick-wt=15): 25 [copy,24,flip.1] set_intersection2(cartesian_product2(A,B),cartesian_product2(C,D))=cartesian_product2(set_intersection2(A,C),set_intersection2(B,D)).
% 175.21/175.44  ---> New Demodulator: 26 [new_demod,25] set_intersection2(cartesian_product2(A,B),cartesian_product2(C,D))=cartesian_product2(set_intersection2(A,C),set_intersection2(B,D)).
% 175.21/175.44  ** KEPT (pick-wt=7): 27 [] subset(cartesian_product2($c6,$c5),cartesian_product2($c4,$c3)).
% 175.21/175.44  ** KEPT (pick-wt=5): 28 [] subset(set_intersection2(A,B),A).
% 175.21/175.44    Following clause subsumed by 17 during input processing: 0 [copy,17,flip.1] A=A.
% 175.21/175.44    Following clause subsumed by 18 during input processing: 0 [copy,18,flip.1] set_intersection2(A,B)=set_intersection2(B,A).
% 175.21/175.44  >>>> Starting back demodulation with 21.
% 175.21/175.44  >>>> Starting back demodulation with 26.
% 175.21/175.44  
% 175.21/175.44  ======= end of input processing =======
% 175.21/175.44  
% 175.21/175.44  =========== start of search ===========
% 175.21/175.44  
% 175.21/175.44  
% 175.21/175.44  Resetting weight limit to 12.
% 175.21/175.44  
% 175.21/175.44  
% 175.21/175.44  Resetting weight limit to 12.
% 175.21/175.44  
% 175.21/175.44  sos_size=3150
% 175.21/175.44  
% 175.21/175.44  
% 175.21/175.44  Resetting weight limit to 10.
% 175.21/175.44  
% 175.21/175.44  
% 175.21/175.44  Resetting weight limit to 10.
% 175.21/175.44  
% 175.21/175.44  sos_size=3319
% 175.21/175.44  
% 175.21/175.44  
% 175.21/175.44  Resetting weight limit to 9.
% 175.21/175.44  
% 175.21/175.44  
% 175.21/175.44  Resetting weight limit to 9.
% 175.21/175.44  
% 175.21/175.44  sos_size=3396
% 175.21/175.44  
% 175.21/175.44  -- HEY sandbox, WE HAVE A PROOF!! -- 
% 175.21/175.44  
% 175.21/175.44  -----> EMPTY CLAUSE at 173.53 sec ----> 7473 [hyper,7462,8,7459] $F.
% 175.21/175.44  
% 175.21/175.44  Length of proof is 12.  Level of proof is 5.
% 175.21/175.44  
% 175.21/175.44  ---------------- PROOF ----------------
% 175.21/175.44  % SZS status Theorem
% 175.21/175.44  % SZS output start Refutation
% See solution above
% 175.21/175.44  ------------ end of proof -------------
% 175.21/175.44  
% 175.21/175.44  
% 175.21/175.44  Search stopped by max_proofs option.
% 175.21/175.44  
% 175.21/175.44  
% 175.21/175.44  Search stopped by max_proofs option.
% 175.21/175.44  
% 175.21/175.44  ============ end of search ============
% 175.21/175.44  
% 175.21/175.44  -------------- statistics -------------
% 175.21/175.44  clauses given                818
% 175.21/175.44  clauses generated         638114
% 175.21/175.44  clauses kept                7450
% 175.21/175.44  clauses forward subsumed   51432
% 175.21/175.44  clauses back subsumed        872
% 175.21/175.44  Kbytes malloced             5859
% 175.21/175.44  
% 175.21/175.44  ----------- times (seconds) -----------
% 175.21/175.44  user CPU time        173.53          (0 hr, 2 min, 53 sec)
% 175.21/175.44  system CPU time        0.01          (0 hr, 0 min, 0 sec)
% 175.21/175.44  wall-clock time      175             (0 hr, 2 min, 55 sec)
% 175.21/175.44  
% 175.21/175.44  That finishes the proof of the theorem.
% 175.21/175.44  
% 175.21/175.44  Process 13481 finished Wed Jul 27 10:37:45 2022
% 175.21/175.44  Otter interrupted
% 175.21/175.44  PROOF FOUND
%------------------------------------------------------------------------------