TSTP Solution File: SET974+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SET974+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n020.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 13:14:37 EDT 2022

% Result   : Theorem 2.08s 2.23s
% Output   : Refutation 2.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   17 (   5 unt;   7 nHn;  11 RR)
%            Number of literals    :   29 (   1 equ;   8 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-5 aty)
%            Number of variables   :   34 (   6 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(4,axiom,
    ( ~ disjoint(A,B)
    | disjoint(B,A) ),
    file('SET974+1.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))
    | in(dollar_f2(A,B,C,D,E),set_intersection2(B,D)) ),
    file('SET974+1.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))
    | in(dollar_f1(A,B,C,D,E),set_intersection2(C,E)) ),
    file('SET974+1.p',unknown),
    [] ).

cnf(9,axiom,
    ~ disjoint(cartesian_product2(dollar_c6,dollar_c4),cartesian_product2(dollar_c5,dollar_c3)),
    file('SET974+1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ in(A,set_intersection2(B,C))
    | ~ disjoint(B,C) ),
    file('SET974+1.p',unknown),
    [] ).

cnf(14,axiom,
    set_intersection2(A,B) = set_intersection2(B,A),
    file('SET974+1.p',unknown),
    [] ).

cnf(21,axiom,
    ( disjoint(dollar_c6,dollar_c5)
    | disjoint(dollar_c4,dollar_c3) ),
    file('SET974+1.p',unknown),
    [] ).

cnf(22,axiom,
    ( disjoint(A,B)
    | in(dollar_f3(A,B),set_intersection2(A,B)) ),
    file('SET974+1.p',unknown),
    [] ).

cnf(29,plain,
    ( disjoint(dollar_c4,dollar_c3)
    | disjoint(dollar_c5,dollar_c6) ),
    inference(hyper,[status(thm)],[21,4]),
    [iquote('hyper,21,4')] ).

cnf(31,plain,
    ( disjoint(dollar_c5,dollar_c6)
    | disjoint(dollar_c3,dollar_c4) ),
    inference(hyper,[status(thm)],[29,4]),
    [iquote('hyper,29,4')] ).

cnf(32,plain,
    ( ~ in(A,set_intersection2(B,C))
    | ~ disjoint(C,B) ),
    inference(para_from,[status(thm),theory(equality)],[14,10]),
    [iquote('para_from,14.1.1,10.1.2')] ).

cnf(44,plain,
    ( disjoint(cartesian_product2(A,B),cartesian_product2(C,D))
    | in(dollar_f1(dollar_f3(cartesian_product2(A,B),cartesian_product2(C,D)),A,B,C,D),set_intersection2(B,D)) ),
    inference(hyper,[status(thm)],[22,8]),
    [iquote('hyper,22,8')] ).

cnf(45,plain,
    ( disjoint(cartesian_product2(A,B),cartesian_product2(C,D))
    | in(dollar_f2(dollar_f3(cartesian_product2(A,B),cartesian_product2(C,D)),A,B,C,D),set_intersection2(A,C)) ),
    inference(hyper,[status(thm)],[22,7]),
    [iquote('hyper,22,7')] ).

cnf(273,plain,
    ( disjoint(cartesian_product2(A,dollar_c4),cartesian_product2(B,dollar_c3))
    | disjoint(dollar_c5,dollar_c6) ),
    inference(hyper,[status(thm)],[44,32,31]),
    [iquote('hyper,44,32,31')] ).

cnf(290,plain,
    disjoint(dollar_c5,dollar_c6),
    inference(hyper,[status(thm)],[273,9]),
    [iquote('hyper,273,9')] ).

cnf(308,plain,
    disjoint(cartesian_product2(dollar_c6,A),cartesian_product2(dollar_c5,B)),
    inference(hyper,[status(thm)],[45,32,290]),
    [iquote('hyper,45,32,290')] ).

cnf(309,plain,
    $false,
    inference(binary,[status(thm)],[308,9]),
    [iquote('binary,308.1,9.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET974+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % Command  : otter-tptp-script %s
% 0.13/0.34  % Computer : n020.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 10:43:53 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 2.03/2.21  ----- Otter 3.3f, August 2004 -----
% 2.03/2.21  The process was started by sandbox2 on n020.cluster.edu,
% 2.03/2.21  Wed Jul 27 10:43:53 2022
% 2.03/2.21  The command was "./otter".  The process ID is 18461.
% 2.03/2.21  
% 2.03/2.21  set(prolog_style_variables).
% 2.03/2.21  set(auto).
% 2.03/2.21     dependent: set(auto1).
% 2.03/2.21     dependent: set(process_input).
% 2.03/2.21     dependent: clear(print_kept).
% 2.03/2.21     dependent: clear(print_new_demod).
% 2.03/2.21     dependent: clear(print_back_demod).
% 2.03/2.21     dependent: clear(print_back_sub).
% 2.03/2.21     dependent: set(control_memory).
% 2.03/2.21     dependent: assign(max_mem, 12000).
% 2.03/2.21     dependent: assign(pick_given_ratio, 4).
% 2.03/2.21     dependent: assign(stats_level, 1).
% 2.03/2.21     dependent: assign(max_seconds, 10800).
% 2.03/2.21  clear(print_given).
% 2.03/2.21  
% 2.03/2.21  formula_list(usable).
% 2.03/2.21  all A (A=A).
% 2.03/2.21  all A B (in(A,B)-> -in(B,A)).
% 2.03/2.21  all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 2.03/2.21  all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 2.03/2.21  all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 2.03/2.21  all A B (-empty(ordered_pair(A,B))).
% 2.03/2.21  all A B (set_intersection2(A,A)=A).
% 2.03/2.21  exists A empty(A).
% 2.03/2.21  exists A (-empty(A)).
% 2.03/2.21  all A B (disjoint(A,B)->disjoint(B,A)).
% 2.03/2.21  all A B C D E (-(in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))& (all F G (-(A=ordered_pair(F,G)&in(F,set_intersection2(B,D))&in(G,set_intersection2(C,E))))))).
% 2.03/2.21  -(all A B C D (disjoint(A,B)|disjoint(C,D)->disjoint(cartesian_product2(A,C),cartesian_product2(B,D)))).
% 2.03/2.21  all A B (-(-disjoint(A,B)& (all C (-in(C,set_intersection2(A,B)))))& -((exists C in(C,set_intersection2(A,B)))&disjoint(A,B))).
% 2.03/2.21  end_of_list.
% 2.03/2.21  
% 2.03/2.21  -------> usable clausifies to:
% 2.03/2.21  
% 2.03/2.21  list(usable).
% 2.03/2.21  0 [] A=A.
% 2.03/2.21  0 [] -in(A,B)| -in(B,A).
% 2.03/2.21  0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 2.03/2.21  0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 2.03/2.21  0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 2.03/2.21  0 [] -empty(ordered_pair(A,B)).
% 2.03/2.21  0 [] set_intersection2(A,A)=A.
% 2.03/2.21  0 [] empty($c1).
% 2.03/2.21  0 [] -empty($c2).
% 2.03/2.21  0 [] -disjoint(A,B)|disjoint(B,A).
% 2.03/2.21  0 [] -in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))|A=ordered_pair($f2(A,B,C,D,E),$f1(A,B,C,D,E)).
% 2.03/2.21  0 [] -in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))|in($f2(A,B,C,D,E),set_intersection2(B,D)).
% 2.03/2.21  0 [] -in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))|in($f1(A,B,C,D,E),set_intersection2(C,E)).
% 2.03/2.21  0 [] disjoint($c6,$c5)|disjoint($c4,$c3).
% 2.03/2.21  0 [] -disjoint(cartesian_product2($c6,$c4),cartesian_product2($c5,$c3)).
% 2.03/2.21  0 [] disjoint(A,B)|in($f3(A,B),set_intersection2(A,B)).
% 2.03/2.21  0 [] -in(C,set_intersection2(A,B))| -disjoint(A,B).
% 2.03/2.21  end_of_list.
% 2.03/2.21  
% 2.03/2.21  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=2.
% 2.03/2.21  
% 2.03/2.21  This ia a non-Horn set with equality.  The strategy will be
% 2.03/2.21  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.03/2.21  deletion, with positive clauses in sos and nonpositive
% 2.03/2.21  clauses in usable.
% 2.03/2.21  
% 2.03/2.21     dependent: set(knuth_bendix).
% 2.03/2.21     dependent: set(anl_eq).
% 2.03/2.21     dependent: set(para_from).
% 2.03/2.21     dependent: set(para_into).
% 2.03/2.21     dependent: clear(para_from_right).
% 2.03/2.21     dependent: clear(para_into_right).
% 2.03/2.21     dependent: set(para_from_vars).
% 2.03/2.21     dependent: set(eq_units_both_ways).
% 2.03/2.21     dependent: set(dynamic_demod_all).
% 2.03/2.21     dependent: set(dynamic_demod).
% 2.03/2.21     dependent: set(order_eq).
% 2.03/2.21     dependent: set(back_demod).
% 2.03/2.21     dependent: set(lrpo).
% 2.03/2.21     dependent: set(hyper_res).
% 2.03/2.21     dependent: set(unit_deletion).
% 2.03/2.21     dependent: set(factor).
% 2.03/2.21  
% 2.03/2.21  ------------> process usable:
% 2.03/2.21  ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.03/2.21  ** KEPT (pick-wt=4): 2 [] -empty(ordered_pair(A,B)).
% 2.03/2.21  ** KEPT (pick-wt=2): 3 [] -empty($c2).
% 2.03/2.21  ** KEPT (pick-wt=6): 4 [] -disjoint(A,B)|disjoint(B,A).
% 2.03/2.21  ** KEPT (pick-wt=24): 6 [copy,5,flip.2] -in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))|ordered_pair($f2(A,B,C,D,E),$f1(A,B,C,D,E))=A.
% 2.03/2.21  ** KEPT (pick-wt=19): 7 [] -in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))|in($f2(A,B,C,D,E),set_intersection2(B,D)).
% 2.03/2.21  ** KEPT (pick-wt=19): 8 [] -in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))|in($f1(A,B,C,D,E),set_intersection2(C,E)).
% 2.03/2.21  ** KEPT (pick-wt=7): 9 [] -disjoint(cartesian_product2($c6,$c4),cartesian_product2($c5,$c3)).
% 2.03/2.21  ** KEPT (pick-wt=8): 10 [] -in(A,set_intersection2(B,C))| -disjoint(B,C).
% 2.03/2.21  
% 2.03/2.21  ------------> process sos:
% 2.08/2.23  ** KEPT (pick-wt=3): 12 [] A=A.
% 2.08/2.23  ** KEPT (pick-wt=7): 13 [] unordered_pair(A,B)=unordered_pair(B,A).
% 2.08/2.23  ** KEPT (pick-wt=7): 14 [] set_intersection2(A,B)=set_intersection2(B,A).
% 2.08/2.23  ** KEPT (pick-wt=10): 16 [copy,15,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 2.08/2.23  ---> New Demodulator: 17 [new_demod,16] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 2.08/2.23  ** KEPT (pick-wt=5): 18 [] set_intersection2(A,A)=A.
% 2.08/2.23  ---> New Demodulator: 19 [new_demod,18] set_intersection2(A,A)=A.
% 2.08/2.23  ** KEPT (pick-wt=2): 20 [] empty($c1).
% 2.08/2.23  ** KEPT (pick-wt=6): 21 [] disjoint($c6,$c5)|disjoint($c4,$c3).
% 2.08/2.23  ** KEPT (pick-wt=10): 22 [] disjoint(A,B)|in($f3(A,B),set_intersection2(A,B)).
% 2.08/2.23    Following clause subsumed by 12 during input processing: 0 [copy,12,flip.1] A=A.
% 2.08/2.23    Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 2.08/2.23    Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] set_intersection2(A,B)=set_intersection2(B,A).
% 2.08/2.23  >>>> Starting back demodulation with 17.
% 2.08/2.23  >>>> Starting back demodulation with 19.
% 2.08/2.23  
% 2.08/2.23  ======= end of input processing =======
% 2.08/2.23  
% 2.08/2.23  =========== start of search ===========
% 2.08/2.23  
% 2.08/2.23  -------- PROOF -------- 
% 2.08/2.23  
% 2.08/2.23  ----> UNIT CONFLICT at   0.02 sec ----> 309 [binary,308.1,9.1] $F.
% 2.08/2.23  
% 2.08/2.23  Length of proof is 8.  Level of proof is 5.
% 2.08/2.23  
% 2.08/2.23  ---------------- PROOF ----------------
% 2.08/2.23  % SZS status Theorem
% 2.08/2.23  % SZS output start Refutation
% See solution above
% 2.08/2.23  ------------ end of proof -------------
% 2.08/2.23  
% 2.08/2.23  
% 2.08/2.23  Search stopped by max_proofs option.
% 2.08/2.23  
% 2.08/2.23  
% 2.08/2.23  Search stopped by max_proofs option.
% 2.08/2.23  
% 2.08/2.23  ============ end of search ============
% 2.08/2.23  
% 2.08/2.23  -------------- statistics -------------
% 2.08/2.23  clauses given                 76
% 2.08/2.23  clauses generated           1186
% 2.08/2.23  clauses kept                 284
% 2.08/2.23  clauses forward subsumed     949
% 2.08/2.23  clauses back subsumed        108
% 2.08/2.23  Kbytes malloced             3906
% 2.08/2.23  
% 2.08/2.23  ----------- times (seconds) -----------
% 2.08/2.23  user CPU time          0.02          (0 hr, 0 min, 0 sec)
% 2.08/2.23  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 2.08/2.23  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 2.08/2.23  
% 2.08/2.23  That finishes the proof of the theorem.
% 2.08/2.23  
% 2.08/2.23  Process 18461 finished Wed Jul 27 10:43:55 2022
% 2.08/2.23  Otter interrupted
% 2.08/2.23  PROOF FOUND
%------------------------------------------------------------------------------