TSTP Solution File: SET881+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SET881+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n004.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 13:14:27 EDT 2022

% Result   : Theorem 1.70s 1.89s
% Output   : Refutation 1.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    7 (   5 unt;   0 nHn;   4 RR)
%            Number of literals    :   10 (   6 equ;   4 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   11 (   3 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    ( A != unordered_pair(B,C)
    | in(D,A)
    | D != B ),
    file('SET881+1.p',unknown),
    [] ).

cnf(8,axiom,
    ( set_difference(singleton(A),B) = empty_set
    | ~ in(A,B) ),
    file('SET881+1.p',unknown),
    [] ).

cnf(10,axiom,
    set_difference(singleton(dollar_c4),unordered_pair(dollar_c4,dollar_c3)) != empty_set,
    file('SET881+1.p',unknown),
    [] ).

cnf(13,axiom,
    A = A,
    file('SET881+1.p',unknown),
    [] ).

cnf(20,plain,
    in(A,unordered_pair(A,B)),
    inference(hyper,[status(thm)],[13,3,13]),
    [iquote('hyper,13,3,13')] ).

cnf(38,plain,
    set_difference(singleton(A),unordered_pair(A,B)) = empty_set,
    inference(hyper,[status(thm)],[20,8]),
    [iquote('hyper,20,8')] ).

cnf(40,plain,
    $false,
    inference(binary,[status(thm)],[38,10]),
    [iquote('binary,38.1,10.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET881+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n004.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 10:35:36 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.70/1.89  ----- Otter 3.3f, August 2004 -----
% 1.70/1.89  The process was started by sandbox2 on n004.cluster.edu,
% 1.70/1.89  Wed Jul 27 10:35:36 2022
% 1.70/1.89  The command was "./otter".  The process ID is 14993.
% 1.70/1.89  
% 1.70/1.89  set(prolog_style_variables).
% 1.70/1.89  set(auto).
% 1.70/1.89     dependent: set(auto1).
% 1.70/1.89     dependent: set(process_input).
% 1.70/1.89     dependent: clear(print_kept).
% 1.70/1.89     dependent: clear(print_new_demod).
% 1.70/1.89     dependent: clear(print_back_demod).
% 1.70/1.89     dependent: clear(print_back_sub).
% 1.70/1.89     dependent: set(control_memory).
% 1.70/1.89     dependent: assign(max_mem, 12000).
% 1.70/1.89     dependent: assign(pick_given_ratio, 4).
% 1.70/1.89     dependent: assign(stats_level, 1).
% 1.70/1.89     dependent: assign(max_seconds, 10800).
% 1.70/1.89  clear(print_given).
% 1.70/1.89  
% 1.70/1.89  formula_list(usable).
% 1.70/1.89  all A (A=A).
% 1.70/1.89  all A B (in(A,B)-> -in(B,A)).
% 1.70/1.89  all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.70/1.89  all A B C (C=unordered_pair(A,B)<-> (all D (in(D,C)<->D=A|D=B))).
% 1.70/1.89  empty(empty_set).
% 1.70/1.89  all A B (set_difference(singleton(A),B)=empty_set<->in(A,B)).
% 1.70/1.89  exists A empty(A).
% 1.70/1.89  exists A (-empty(A)).
% 1.70/1.89  -(all A B (set_difference(singleton(A),unordered_pair(A,B))=empty_set)).
% 1.70/1.89  end_of_list.
% 1.70/1.89  
% 1.70/1.89  -------> usable clausifies to:
% 1.70/1.89  
% 1.70/1.89  list(usable).
% 1.70/1.89  0 [] A=A.
% 1.70/1.89  0 [] -in(A,B)| -in(B,A).
% 1.70/1.89  0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.70/1.89  0 [] C!=unordered_pair(A,B)| -in(D,C)|D=A|D=B.
% 1.70/1.89  0 [] C!=unordered_pair(A,B)|in(D,C)|D!=A.
% 1.70/1.89  0 [] C!=unordered_pair(A,B)|in(D,C)|D!=B.
% 1.70/1.89  0 [] C=unordered_pair(A,B)|in($f1(A,B,C),C)|$f1(A,B,C)=A|$f1(A,B,C)=B.
% 1.70/1.89  0 [] C=unordered_pair(A,B)| -in($f1(A,B,C),C)|$f1(A,B,C)!=A.
% 1.70/1.89  0 [] C=unordered_pair(A,B)| -in($f1(A,B,C),C)|$f1(A,B,C)!=B.
% 1.70/1.89  0 [] empty(empty_set).
% 1.70/1.89  0 [] set_difference(singleton(A),B)!=empty_set|in(A,B).
% 1.70/1.89  0 [] set_difference(singleton(A),B)=empty_set| -in(A,B).
% 1.70/1.89  0 [] empty($c1).
% 1.70/1.89  0 [] -empty($c2).
% 1.70/1.89  0 [] set_difference(singleton($c4),unordered_pair($c4,$c3))!=empty_set.
% 1.70/1.89  end_of_list.
% 1.70/1.89  
% 1.70/1.89  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.70/1.89  
% 1.70/1.89  This ia a non-Horn set with equality.  The strategy will be
% 1.70/1.89  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.70/1.89  deletion, with positive clauses in sos and nonpositive
% 1.70/1.89  clauses in usable.
% 1.70/1.89  
% 1.70/1.89     dependent: set(knuth_bendix).
% 1.70/1.89     dependent: set(anl_eq).
% 1.70/1.89     dependent: set(para_from).
% 1.70/1.89     dependent: set(para_into).
% 1.70/1.89     dependent: clear(para_from_right).
% 1.70/1.89     dependent: clear(para_into_right).
% 1.70/1.89     dependent: set(para_from_vars).
% 1.70/1.89     dependent: set(eq_units_both_ways).
% 1.70/1.89     dependent: set(dynamic_demod_all).
% 1.70/1.89     dependent: set(dynamic_demod).
% 1.70/1.89     dependent: set(order_eq).
% 1.70/1.89     dependent: set(back_demod).
% 1.70/1.89     dependent: set(lrpo).
% 1.70/1.89     dependent: set(hyper_res).
% 1.70/1.89     dependent: set(unit_deletion).
% 1.70/1.89     dependent: set(factor).
% 1.70/1.89  
% 1.70/1.89  ------------> process usable:
% 1.70/1.89  ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.70/1.89  ** KEPT (pick-wt=14): 2 [] A!=unordered_pair(B,C)| -in(D,A)|D=B|D=C.
% 1.70/1.89  ** KEPT (pick-wt=11): 3 [] A!=unordered_pair(B,C)|in(D,A)|D!=B.
% 1.70/1.89  ** KEPT (pick-wt=11): 4 [] A!=unordered_pair(B,C)|in(D,A)|D!=C.
% 1.70/1.89  ** KEPT (pick-wt=17): 5 [] A=unordered_pair(B,C)| -in($f1(B,C,A),A)|$f1(B,C,A)!=B.
% 1.70/1.89  ** KEPT (pick-wt=17): 6 [] A=unordered_pair(B,C)| -in($f1(B,C,A),A)|$f1(B,C,A)!=C.
% 1.70/1.89  ** KEPT (pick-wt=9): 7 [] set_difference(singleton(A),B)!=empty_set|in(A,B).
% 1.70/1.89  ** KEPT (pick-wt=9): 8 [] set_difference(singleton(A),B)=empty_set| -in(A,B).
% 1.70/1.89  ** KEPT (pick-wt=2): 9 [] -empty($c2).
% 1.70/1.89  ** KEPT (pick-wt=8): 10 [] set_difference(singleton($c4),unordered_pair($c4,$c3))!=empty_set.
% 1.70/1.89  
% 1.70/1.89  ------------> process sos:
% 1.70/1.89  ** KEPT (pick-wt=3): 13 [] A=A.
% 1.70/1.89  ** KEPT (pick-wt=7): 14 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.70/1.89  ** KEPT (pick-wt=23): 15 [] A=unordered_pair(B,C)|in($f1(B,C,A),A)|$f1(B,C,A)=B|$f1(B,C,A)=C.
% 1.70/1.89  ** KEPT (pick-wt=2): 16 [] empty(empty_set).
% 1.70/1.89  ** KEPT (pick-wt=2): 17 [] empty($c1).
% 1.70/1.89    Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] A=A.
% 1.70/1.89    Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.70/1.89  
% 1.70/1.89  ======= end of input processing =======
% 1.70/1.89  
% 1.70/1.89  =========== start of search ===========
% 1.70/1.89  
% 1.70/1.89  -------- PROOF -------- 
% 1.70/1.89  
% 1.70/1.89  ----> UNIT CONFLICT at   0.00 sec ----> 40 [binary,38.1,10.1] $F.
% 1.70/1.89  
% 1.70/1.89  Length of proof is 2.  Level of proof is 2.
% 1.70/1.89  
% 1.70/1.89  ---------------- PROOF ----------------
% 1.70/1.89  % SZS status Theorem
% 1.70/1.89  % SZS output start Refutation
% See solution above
% 1.70/1.89  ------------ end of proof -------------
% 1.70/1.89  
% 1.70/1.89  
% 1.70/1.89  Search stopped by max_proofs option.
% 1.70/1.89  
% 1.70/1.89  
% 1.70/1.89  Search stopped by max_proofs option.
% 1.70/1.89  
% 1.70/1.89  ============ end of search ============
% 1.70/1.89  
% 1.70/1.89  -------------- statistics -------------
% 1.70/1.89  clauses given                  5
% 1.70/1.89  clauses generated             27
% 1.70/1.89  clauses kept                  37
% 1.70/1.89  clauses forward subsumed       7
% 1.70/1.89  clauses back subsumed          0
% 1.70/1.89  Kbytes malloced              976
% 1.70/1.89  
% 1.70/1.89  ----------- times (seconds) -----------
% 1.70/1.89  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.70/1.89  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.70/1.89  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.70/1.89  
% 1.70/1.89  That finishes the proof of the theorem.
% 1.70/1.89  
% 1.70/1.89  Process 14993 finished Wed Jul 27 10:35:37 2022
% 1.70/1.89  Otter interrupted
% 1.70/1.89  PROOF FOUND
%------------------------------------------------------------------------------