TSTP Solution File: SET983+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SET983+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n028.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 1.66s 1.89s
% Output   : Refutation 1.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    6
% Syntax   : Number of clauses     :    9 (   8 unt;   0 nHn;   6 RR)
%            Number of literals    :   12 (   4 equ;   4 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   :   13 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(4,axiom,
    ( A != set_intersection2(B,C)
    | in(D,A)
    | ~ in(D,B)
    | ~ in(D,C) ),
    file('SET983+1.p',unknown),
    [] ).

cnf(7,axiom,
    ~ in(dollar_c7,cartesian_product2(set_intersection2(dollar_c6,dollar_c4),set_intersection2(dollar_c5,dollar_c3))),
    file('SET983+1.p',unknown),
    [] ).

cnf(19,axiom,
    set_intersection2(A,A) = A,
    file('SET983+1.p',unknown),
    [] ).

cnf(21,axiom,
    cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
    file('SET983+1.p',unknown),
    [] ).

cnf(23,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)],[21])]),
    [iquote('copy,21,flip.1')] ).

cnf(24,axiom,
    in(dollar_c7,cartesian_product2(dollar_c6,dollar_c5)),
    file('SET983+1.p',unknown),
    [] ).

cnf(25,axiom,
    in(dollar_c7,cartesian_product2(dollar_c4,dollar_c3)),
    file('SET983+1.p',unknown),
    [] ).

cnf(52,plain,
    in(dollar_c7,cartesian_product2(set_intersection2(dollar_c6,dollar_c4),set_intersection2(dollar_c5,dollar_c3))),
    inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[25,4,19,24]),23,23,19]),
    [iquote('hyper,25,4,18,24,demod,23,23,19')] ).

cnf(53,plain,
    $false,
    inference(binary,[status(thm)],[52,7]),
    [iquote('binary,52.1,7.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET983+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n028.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 10:49:49 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.66/1.88  ----- Otter 3.3f, August 2004 -----
% 1.66/1.88  The process was started by sandbox2 on n028.cluster.edu,
% 1.66/1.88  Wed Jul 27 10:49:49 2022
% 1.66/1.88  The command was "./otter".  The process ID is 7294.
% 1.66/1.88  
% 1.66/1.88  set(prolog_style_variables).
% 1.66/1.88  set(auto).
% 1.66/1.88     dependent: set(auto1).
% 1.66/1.88     dependent: set(process_input).
% 1.66/1.88     dependent: clear(print_kept).
% 1.66/1.88     dependent: clear(print_new_demod).
% 1.66/1.88     dependent: clear(print_back_demod).
% 1.66/1.88     dependent: clear(print_back_sub).
% 1.66/1.88     dependent: set(control_memory).
% 1.66/1.88     dependent: assign(max_mem, 12000).
% 1.66/1.88     dependent: assign(pick_given_ratio, 4).
% 1.66/1.88     dependent: assign(stats_level, 1).
% 1.66/1.88     dependent: assign(max_seconds, 10800).
% 1.66/1.88  clear(print_given).
% 1.66/1.88  
% 1.66/1.88  formula_list(usable).
% 1.66/1.88  all A (A=A).
% 1.66/1.88  all A B (in(A,B)-> -in(B,A)).
% 1.66/1.88  all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 1.66/1.88  all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 1.66/1.88  all A B (set_intersection2(A,A)=A).
% 1.66/1.88  exists A empty(A).
% 1.66/1.88  exists A (-empty(A)).
% 1.66/1.88  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))).
% 1.66/1.88  -(all A B C D E (in(A,cartesian_product2(B,C))&in(A,cartesian_product2(D,E))->in(A,cartesian_product2(set_intersection2(B,D),set_intersection2(C,E))))).
% 1.66/1.88  end_of_list.
% 1.66/1.88  
% 1.66/1.88  -------> usable clausifies to:
% 1.66/1.88  
% 1.66/1.88  list(usable).
% 1.66/1.88  0 [] A=A.
% 1.66/1.88  0 [] -in(A,B)| -in(B,A).
% 1.66/1.88  0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.66/1.88  0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 1.66/1.88  0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 1.66/1.88  0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 1.66/1.88  0 [] C=set_intersection2(A,B)|in($f1(A,B,C),C)|in($f1(A,B,C),A).
% 1.66/1.88  0 [] C=set_intersection2(A,B)|in($f1(A,B,C),C)|in($f1(A,B,C),B).
% 1.66/1.88  0 [] C=set_intersection2(A,B)| -in($f1(A,B,C),C)| -in($f1(A,B,C),A)| -in($f1(A,B,C),B).
% 1.66/1.88  0 [] set_intersection2(A,A)=A.
% 1.66/1.88  0 [] empty($c1).
% 1.66/1.88  0 [] -empty($c2).
% 1.66/1.88  0 [] cartesian_product2(set_intersection2(A,B),set_intersection2(C,D))=set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)).
% 1.66/1.88  0 [] in($c7,cartesian_product2($c6,$c5)).
% 1.66/1.88  0 [] in($c7,cartesian_product2($c4,$c3)).
% 1.66/1.88  0 [] -in($c7,cartesian_product2(set_intersection2($c6,$c4),set_intersection2($c5,$c3))).
% 1.66/1.88  end_of_list.
% 1.66/1.88  
% 1.66/1.88  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.66/1.88  
% 1.66/1.88  This ia a non-Horn set with equality.  The strategy will be
% 1.66/1.88  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.66/1.88  deletion, with positive clauses in sos and nonpositive
% 1.66/1.88  clauses in usable.
% 1.66/1.88  
% 1.66/1.88     dependent: set(knuth_bendix).
% 1.66/1.88     dependent: set(anl_eq).
% 1.66/1.88     dependent: set(para_from).
% 1.66/1.88     dependent: set(para_into).
% 1.66/1.88     dependent: clear(para_from_right).
% 1.66/1.88     dependent: clear(para_into_right).
% 1.66/1.88     dependent: set(para_from_vars).
% 1.66/1.88     dependent: set(eq_units_both_ways).
% 1.66/1.88     dependent: set(dynamic_demod_all).
% 1.66/1.88     dependent: set(dynamic_demod).
% 1.66/1.88     dependent: set(order_eq).
% 1.66/1.88     dependent: set(back_demod).
% 1.66/1.88     dependent: set(lrpo).
% 1.66/1.88     dependent: set(hyper_res).
% 1.66/1.88     dependent: set(unit_deletion).
% 1.66/1.88     dependent: set(factor).
% 1.66/1.88  
% 1.66/1.88  ------------> process usable:
% 1.66/1.88  ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.66/1.88  ** KEPT (pick-wt=11): 2 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 1.66/1.88  ** KEPT (pick-wt=11): 3 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 1.66/1.88  ** KEPT (pick-wt=14): 4 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 1.66/1.88  ** KEPT (pick-wt=23): 5 [] A=set_intersection2(B,C)| -in($f1(B,C,A),A)| -in($f1(B,C,A),B)| -in($f1(B,C,A),C).
% 1.66/1.88  ** KEPT (pick-wt=2): 6 [] -empty($c2).
% 1.66/1.88  ** KEPT (pick-wt=9): 7 [] -in($c7,cartesian_product2(set_intersection2($c6,$c4),set_intersection2($c5,$c3))).
% 1.66/1.88  
% 1.66/1.88  ------------> process sos:
% 1.66/1.88  ** KEPT (pick-wt=3): 14 [] A=A.
% 1.66/1.88  ** KEPT (pick-wt=7): 15 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.66/1.88  ** KEPT (pick-wt=17): 16 [] A=set_intersection2(B,C)|in($f1(B,C,A),A)|in($f1(B,C,A),B).
% 1.66/1.88  ** KEPT (pick-wt=17): 17 [] A=set_intersection2(B,C)|in($f1(B,C,A),A)|in($f1(B,C,A),C).
% 1.66/1.88  ** KEPT (pick-wt=5): 18 [] set_intersection2(A,A)=A.
% 1.66/1.88  ---> New Demodulator: 19 [new_demod,18] set_intersection2(A,A)=A.
% 1.66/1.88  ** KEPT (pick-wt=2): 20 [] empty($c1).
% 1.66/1.88  ** KEPT (pick-wt=15): 22 [copy,21,flip.1] set_intersection2(cartesian_product2(A,B),cartesian_product2(C,D))=cartesian_product2(set_intersection2(A,C),set_intersection2(B,D)).
% 1.66/1.89  ---> New Demodulator: 23 [new_demod,22] set_intersection2(cartesian_product2(A,B),cartesian_product2(C,D))=cartesian_product2(set_intersection2(A,C),set_intersection2(B,D)).
% 1.66/1.89  ** KEPT (pick-wt=5): 24 [] in($c7,cartesian_product2($c6,$c5)).
% 1.66/1.89  ** KEPT (pick-wt=5): 25 [] in($c7,cartesian_product2($c4,$c3)).
% 1.66/1.89    Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 1.66/1.89    Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] set_intersection2(A,B)=set_intersection2(B,A).
% 1.66/1.89  >>>> Starting back demodulation with 19.
% 1.66/1.89      >> back demodulating 13 with 19.
% 1.66/1.89      >> back demodulating 12 with 19.
% 1.66/1.89      >> back demodulating 9 with 19.
% 1.66/1.89  >>>> Starting back demodulation with 23.
% 1.66/1.89  
% 1.66/1.89  ======= end of input processing =======
% 1.66/1.89  
% 1.66/1.89  =========== start of search ===========
% 1.66/1.89  
% 1.66/1.89  -------- PROOF -------- 
% 1.66/1.89  
% 1.66/1.89  ----> UNIT CONFLICT at   0.00 sec ----> 53 [binary,52.1,7.1] $F.
% 1.66/1.89  
% 1.66/1.89  Length of proof is 2.  Level of proof is 2.
% 1.66/1.89  
% 1.66/1.89  ---------------- PROOF ----------------
% 1.66/1.89  % SZS status Theorem
% 1.66/1.89  % SZS output start Refutation
% See solution above
% 1.66/1.89  ------------ end of proof -------------
% 1.66/1.89  
% 1.66/1.89  
% 1.66/1.89  Search stopped by max_proofs option.
% 1.66/1.89  
% 1.66/1.89  
% 1.66/1.89  Search stopped by max_proofs option.
% 1.66/1.89  
% 1.66/1.89  ============ end of search ============
% 1.66/1.89  
% 1.66/1.89  -------------- statistics -------------
% 1.66/1.89  clauses given                  5
% 1.66/1.89  clauses generated             63
% 1.66/1.89  clauses kept                  49
% 1.66/1.89  clauses forward subsumed      35
% 1.66/1.89  clauses back subsumed          0
% 1.66/1.89  Kbytes malloced              976
% 1.66/1.89  
% 1.66/1.89  ----------- times (seconds) -----------
% 1.66/1.89  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.66/1.89  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.66/1.89  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.66/1.89  
% 1.66/1.89  That finishes the proof of the theorem.
% 1.66/1.89  
% 1.66/1.89  Process 7294 finished Wed Jul 27 10:49:50 2022
% 1.66/1.89  Otter interrupted
% 1.66/1.89  PROOF FOUND
%------------------------------------------------------------------------------