TSTP Solution File: SET626+3 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SET626+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n019.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 13:13:54 EDT 2022

% Result   : Theorem 1.73s 1.96s
% Output   : Refutation 1.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   11 (   7 unt;   0 nHn;  11 RR)
%            Number of literals    :   16 (   0 equ;   6 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   10 (   1 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ member(A,intersection(B,C))
    | member(A,B) ),
    file('SET626+3.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ intersect(A,B)
    | member(dollar_f1(A,B),A) ),
    file('SET626+3.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ intersect(A,B)
    | member(dollar_f1(A,B),B) ),
    file('SET626+3.p',unknown),
    [] ).

cnf(6,axiom,
    ( intersect(A,B)
    | ~ member(C,A)
    | ~ member(C,B) ),
    file('SET626+3.p',unknown),
    [] ).

cnf(11,axiom,
    ~ intersect(dollar_c3,dollar_c2),
    file('SET626+3.p',unknown),
    [] ).

cnf(18,axiom,
    intersect(dollar_c3,intersection(dollar_c2,dollar_c1)),
    file('SET626+3.p',unknown),
    [] ).

cnf(20,plain,
    member(dollar_f1(dollar_c3,intersection(dollar_c2,dollar_c1)),intersection(dollar_c2,dollar_c1)),
    inference(hyper,[status(thm)],[18,5]),
    [iquote('hyper,18,5')] ).

cnf(21,plain,
    member(dollar_f1(dollar_c3,intersection(dollar_c2,dollar_c1)),dollar_c3),
    inference(hyper,[status(thm)],[18,4]),
    [iquote('hyper,18,4')] ).

cnf(126,plain,
    member(dollar_f1(dollar_c3,intersection(dollar_c2,dollar_c1)),dollar_c2),
    inference(hyper,[status(thm)],[20,1]),
    [iquote('hyper,20,1')] ).

cnf(460,plain,
    intersect(dollar_c3,dollar_c2),
    inference(hyper,[status(thm)],[126,6,21]),
    [iquote('hyper,126,6,21')] ).

cnf(461,plain,
    $false,
    inference(binary,[status(thm)],[460,11]),
    [iquote('binary,460.1,11.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET626+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13  % Command  : otter-tptp-script %s
% 0.13/0.34  % Computer : n019.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 10:57:07 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 1.73/1.96  ----- Otter 3.3f, August 2004 -----
% 1.73/1.96  The process was started by sandbox2 on n019.cluster.edu,
% 1.73/1.96  Wed Jul 27 10:57:07 2022
% 1.73/1.96  The command was "./otter".  The process ID is 7021.
% 1.73/1.96  
% 1.73/1.96  set(prolog_style_variables).
% 1.73/1.96  set(auto).
% 1.73/1.96     dependent: set(auto1).
% 1.73/1.96     dependent: set(process_input).
% 1.73/1.96     dependent: clear(print_kept).
% 1.73/1.96     dependent: clear(print_new_demod).
% 1.73/1.96     dependent: clear(print_back_demod).
% 1.73/1.96     dependent: clear(print_back_sub).
% 1.73/1.96     dependent: set(control_memory).
% 1.73/1.96     dependent: assign(max_mem, 12000).
% 1.73/1.96     dependent: assign(pick_given_ratio, 4).
% 1.73/1.96     dependent: assign(stats_level, 1).
% 1.73/1.96     dependent: assign(max_seconds, 10800).
% 1.73/1.96  clear(print_given).
% 1.73/1.96  
% 1.73/1.96  formula_list(usable).
% 1.73/1.96  all A (A=A).
% 1.73/1.96  all B C D (member(D,intersection(B,C))<->member(D,B)&member(D,C)).
% 1.73/1.96  all B C (intersect(B,C)<-> (exists D (member(D,B)&member(D,C)))).
% 1.73/1.96  all B C (intersection(B,C)=intersection(C,B)).
% 1.73/1.96  all B C (intersect(B,C)->intersect(C,B)).
% 1.73/1.96  all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 1.73/1.96  -(all B C D (intersect(B,intersection(C,D))->intersect(B,C))).
% 1.73/1.96  end_of_list.
% 1.73/1.96  
% 1.73/1.96  -------> usable clausifies to:
% 1.73/1.96  
% 1.73/1.96  list(usable).
% 1.73/1.96  0 [] A=A.
% 1.73/1.96  0 [] -member(D,intersection(B,C))|member(D,B).
% 1.73/1.96  0 [] -member(D,intersection(B,C))|member(D,C).
% 1.73/1.96  0 [] member(D,intersection(B,C))| -member(D,B)| -member(D,C).
% 1.73/1.96  0 [] -intersect(B,C)|member($f1(B,C),B).
% 1.73/1.96  0 [] -intersect(B,C)|member($f1(B,C),C).
% 1.73/1.96  0 [] intersect(B,C)| -member(D,B)| -member(D,C).
% 1.73/1.96  0 [] intersection(B,C)=intersection(C,B).
% 1.73/1.96  0 [] -intersect(B,C)|intersect(C,B).
% 1.73/1.96  0 [] B!=C| -member(D,B)|member(D,C).
% 1.73/1.96  0 [] B!=C|member(D,B)| -member(D,C).
% 1.73/1.96  0 [] B=C|member($f2(B,C),B)|member($f2(B,C),C).
% 1.73/1.96  0 [] B=C| -member($f2(B,C),B)| -member($f2(B,C),C).
% 1.73/1.96  0 [] intersect($c3,intersection($c2,$c1)).
% 1.73/1.96  0 [] -intersect($c3,$c2).
% 1.73/1.96  end_of_list.
% 1.73/1.96  
% 1.73/1.96  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.73/1.96  
% 1.73/1.96  This ia a non-Horn set with equality.  The strategy will be
% 1.73/1.96  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.73/1.96  deletion, with positive clauses in sos and nonpositive
% 1.73/1.96  clauses in usable.
% 1.73/1.96  
% 1.73/1.96     dependent: set(knuth_bendix).
% 1.73/1.96     dependent: set(anl_eq).
% 1.73/1.96     dependent: set(para_from).
% 1.73/1.96     dependent: set(para_into).
% 1.73/1.96     dependent: clear(para_from_right).
% 1.73/1.96     dependent: clear(para_into_right).
% 1.73/1.96     dependent: set(para_from_vars).
% 1.73/1.96     dependent: set(eq_units_both_ways).
% 1.73/1.96     dependent: set(dynamic_demod_all).
% 1.73/1.96     dependent: set(dynamic_demod).
% 1.73/1.96     dependent: set(order_eq).
% 1.73/1.96     dependent: set(back_demod).
% 1.73/1.96     dependent: set(lrpo).
% 1.73/1.96     dependent: set(hyper_res).
% 1.73/1.96     dependent: set(unit_deletion).
% 1.73/1.96     dependent: set(factor).
% 1.73/1.96  
% 1.73/1.96  ------------> process usable:
% 1.73/1.96  ** KEPT (pick-wt=8): 1 [] -member(A,intersection(B,C))|member(A,B).
% 1.73/1.96  ** KEPT (pick-wt=8): 2 [] -member(A,intersection(B,C))|member(A,C).
% 1.73/1.96  ** KEPT (pick-wt=11): 3 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 1.73/1.96  ** KEPT (pick-wt=8): 4 [] -intersect(A,B)|member($f1(A,B),A).
% 1.73/1.96  ** KEPT (pick-wt=8): 5 [] -intersect(A,B)|member($f1(A,B),B).
% 1.73/1.96  ** KEPT (pick-wt=9): 6 [] intersect(A,B)| -member(C,A)| -member(C,B).
% 1.73/1.96  ** KEPT (pick-wt=6): 7 [] -intersect(A,B)|intersect(B,A).
% 1.73/1.96  ** KEPT (pick-wt=9): 8 [] A!=B| -member(C,A)|member(C,B).
% 1.73/1.96  ** KEPT (pick-wt=9): 9 [] A!=B|member(C,A)| -member(C,B).
% 1.73/1.96  ** KEPT (pick-wt=13): 10 [] A=B| -member($f2(A,B),A)| -member($f2(A,B),B).
% 1.73/1.96  ** KEPT (pick-wt=3): 11 [] -intersect($c3,$c2).
% 1.73/1.96  
% 1.73/1.96  ------------> process sos:
% 1.73/1.96  ** KEPT (pick-wt=3): 15 [] A=A.
% 1.73/1.96  ** KEPT (pick-wt=7): 16 [] intersection(A,B)=intersection(B,A).
% 1.73/1.96  ** KEPT (pick-wt=13): 17 [] A=B|member($f2(A,B),A)|member($f2(A,B),B).
% 1.73/1.96  ** KEPT (pick-wt=5): 18 [] intersect($c3,intersection($c2,$c1)).
% 1.73/1.96    Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] A=A.
% 1.73/1.96  15 back subsumes 14.
% 1.73/1.96    Following clause subsumed by 16 during input processing: 0 [copy,16,flip.1] intersection(A,B)=intersection(B,A).
% 1.73/1.96  
% 1.73/1.96  ======= end of input processing =======
% 1.73/1.96  
% 1.73/1.96  =========== start of search ===========
% 1.73/1.96  
% 1.73/1.96  -------- PROOF -------- 
% 1.73/1.96  
% 1.73/1.96  ----> UNIT CONFLICT at   0.03 sec ----> 461 [binary,460.1,11.1] $F.
% 1.73/1.96  
% 1.73/1.96  Length of proof is 4.  Level of proof is 3.
% 1.73/1.96  
% 1.73/1.96  ---------------- PROOF ----------------
% 1.73/1.96  % SZS status Theorem
% 1.73/1.96  % SZS output start Refutation
% See solution above
% 1.73/1.96  ------------ end of proof -------------
% 1.73/1.96  
% 1.73/1.96  
% 1.73/1.96  Search stopped by max_proofs option.
% 1.73/1.96  
% 1.73/1.96  
% 1.73/1.96  Search stopped by max_proofs option.
% 1.73/1.96  
% 1.73/1.96  ============ end of search ============
% 1.73/1.96  
% 1.73/1.96  -------------- statistics -------------
% 1.73/1.96  clauses given                 37
% 1.73/1.96  clauses generated           1124
% 1.73/1.96  clauses kept                 460
% 1.73/1.96  clauses forward subsumed     667
% 1.73/1.96  clauses back subsumed          1
% 1.73/1.96  Kbytes malloced             1953
% 1.73/1.96  
% 1.73/1.96  ----------- times (seconds) -----------
% 1.73/1.96  user CPU time          0.03          (0 hr, 0 min, 0 sec)
% 1.73/1.96  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.73/1.96  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.73/1.96  
% 1.73/1.96  That finishes the proof of the theorem.
% 1.73/1.96  
% 1.73/1.96  Process 7021 finished Wed Jul 27 10:57:08 2022
% 1.73/1.96  Otter interrupted
% 1.73/1.96  PROOF FOUND
%------------------------------------------------------------------------------