TSTP Solution File: SET886+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SET886+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n014.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 13:14:28 EDT 2022

% Result   : Theorem 1.72s 1.92s
% Output   : Refutation 1.72s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   16 (  14 unt;   0 nHn;  13 RR)
%            Number of literals    :   18 (  12 equ;   7 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   10 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    ( ~ subset(unordered_pair(A,B),singleton(C))
    | A = C ),
    file('SET886+1.p',unknown),
    [] ).

cnf(3,axiom,
    unordered_pair(dollar_c5,dollar_c4) != singleton(dollar_c3),
    file('SET886+1.p',unknown),
    [] ).

cnf(4,plain,
    singleton(dollar_c3) != unordered_pair(dollar_c5,dollar_c4),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[3])]),
    [iquote('copy,3,flip.1')] ).

cnf(6,axiom,
    unordered_pair(A,B) = unordered_pair(B,A),
    file('SET886+1.p',unknown),
    [] ).

cnf(9,axiom,
    subset(unordered_pair(dollar_c5,dollar_c4),singleton(dollar_c3)),
    file('SET886+1.p',unknown),
    [] ).

cnf(10,axiom,
    unordered_pair(A,A) = singleton(A),
    file('SET886+1.p',unknown),
    [] ).

cnf(12,plain,
    singleton(A) = unordered_pair(A,A),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[10])]),
    [iquote('copy,10,flip.1')] ).

cnf(13,plain,
    subset(unordered_pair(dollar_c5,dollar_c4),unordered_pair(dollar_c3,dollar_c3)),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[9]),12]),
    [iquote('back_demod,9,demod,12')] ).

cnf(14,plain,
    unordered_pair(dollar_c5,dollar_c4) != unordered_pair(dollar_c3,dollar_c3),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4]),12])]),
    [iquote('back_demod,4,demod,12,flip.1')] ).

cnf(15,plain,
    ( ~ subset(unordered_pair(A,B),unordered_pair(C,C))
    | A = C ),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),12]),
    [iquote('back_demod,2,demod,12')] ).

cnf(16,plain,
    subset(unordered_pair(dollar_c4,dollar_c5),unordered_pair(dollar_c3,dollar_c3)),
    inference(para_into,[status(thm),theory(equality)],[13,6]),
    [iquote('para_into,13.1.1,6.1.1')] ).

cnf(17,plain,
    unordered_pair(dollar_c4,dollar_c5) != unordered_pair(dollar_c3,dollar_c3),
    inference(para_into,[status(thm),theory(equality)],[14,6]),
    [iquote('para_into,14.1.1,6.1.1')] ).

cnf(19,plain,
    dollar_c4 = dollar_c3,
    inference(hyper,[status(thm)],[15,16]),
    [iquote('hyper,15,16')] ).

cnf(21,plain,
    dollar_c5 = dollar_c3,
    inference(hyper,[status(thm)],[15,13]),
    [iquote('hyper,15,13')] ).

cnf(22,plain,
    unordered_pair(dollar_c3,dollar_c3) != unordered_pair(dollar_c3,dollar_c3),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[17]),19,21]),
    [iquote('back_demod,17,demod,19,21')] ).

cnf(23,plain,
    $false,
    inference(binary,[status(thm)],[22,6]),
    [iquote('binary,22.1,6.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET886+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n014.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 10:55:39 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.72/1.92  ----- Otter 3.3f, August 2004 -----
% 1.72/1.92  The process was started by sandbox on n014.cluster.edu,
% 1.72/1.92  Wed Jul 27 10:55:39 2022
% 1.72/1.92  The command was "./otter".  The process ID is 29020.
% 1.72/1.92  
% 1.72/1.92  set(prolog_style_variables).
% 1.72/1.92  set(auto).
% 1.72/1.92     dependent: set(auto1).
% 1.72/1.92     dependent: set(process_input).
% 1.72/1.92     dependent: clear(print_kept).
% 1.72/1.92     dependent: clear(print_new_demod).
% 1.72/1.92     dependent: clear(print_back_demod).
% 1.72/1.92     dependent: clear(print_back_sub).
% 1.72/1.92     dependent: set(control_memory).
% 1.72/1.92     dependent: assign(max_mem, 12000).
% 1.72/1.92     dependent: assign(pick_given_ratio, 4).
% 1.72/1.92     dependent: assign(stats_level, 1).
% 1.72/1.92     dependent: assign(max_seconds, 10800).
% 1.72/1.92  clear(print_given).
% 1.72/1.92  
% 1.72/1.92  formula_list(usable).
% 1.72/1.92  all A (A=A).
% 1.72/1.92  all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.72/1.92  exists A empty(A).
% 1.72/1.92  exists A (-empty(A)).
% 1.72/1.92  all A B subset(A,A).
% 1.72/1.92  all A B C (subset(unordered_pair(A,B),singleton(C))->A=C).
% 1.72/1.92  -(all A B C (subset(unordered_pair(A,B),singleton(C))->unordered_pair(A,B)=singleton(C))).
% 1.72/1.92  all A (unordered_pair(A,A)=singleton(A)).
% 1.72/1.92  end_of_list.
% 1.72/1.92  
% 1.72/1.92  -------> usable clausifies to:
% 1.72/1.92  
% 1.72/1.92  list(usable).
% 1.72/1.92  0 [] A=A.
% 1.72/1.92  0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.72/1.92  0 [] empty($c1).
% 1.72/1.92  0 [] -empty($c2).
% 1.72/1.92  0 [] subset(A,A).
% 1.72/1.92  0 [] -subset(unordered_pair(A,B),singleton(C))|A=C.
% 1.72/1.92  0 [] subset(unordered_pair($c5,$c4),singleton($c3)).
% 1.72/1.92  0 [] unordered_pair($c5,$c4)!=singleton($c3).
% 1.72/1.92  0 [] unordered_pair(A,A)=singleton(A).
% 1.72/1.92  end_of_list.
% 1.72/1.92  
% 1.72/1.92  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.72/1.92  
% 1.72/1.92  This is a Horn set with equality.  The strategy will be
% 1.72/1.92  Knuth-Bendix and hyper_res, with positive clauses in
% 1.72/1.92  sos and nonpositive clauses in usable.
% 1.72/1.92  
% 1.72/1.92     dependent: set(knuth_bendix).
% 1.72/1.92     dependent: set(anl_eq).
% 1.72/1.92     dependent: set(para_from).
% 1.72/1.92     dependent: set(para_into).
% 1.72/1.92     dependent: clear(para_from_right).
% 1.72/1.92     dependent: clear(para_into_right).
% 1.72/1.92     dependent: set(para_from_vars).
% 1.72/1.92     dependent: set(eq_units_both_ways).
% 1.72/1.92     dependent: set(dynamic_demod_all).
% 1.72/1.92     dependent: set(dynamic_demod).
% 1.72/1.92     dependent: set(order_eq).
% 1.72/1.92     dependent: set(back_demod).
% 1.72/1.92     dependent: set(lrpo).
% 1.72/1.92     dependent: set(hyper_res).
% 1.72/1.92     dependent: clear(order_hyper).
% 1.72/1.92  
% 1.72/1.92  ------------> process usable:
% 1.72/1.92  ** KEPT (pick-wt=2): 1 [] -empty($c2).
% 1.72/1.92  ** KEPT (pick-wt=9): 2 [] -subset(unordered_pair(A,B),singleton(C))|A=C.
% 1.72/1.92  ** KEPT (pick-wt=6): 4 [copy,3,flip.1] singleton($c3)!=unordered_pair($c5,$c4).
% 1.72/1.92  
% 1.72/1.92  ------------> process sos:
% 1.72/1.92  ** KEPT (pick-wt=3): 5 [] A=A.
% 1.72/1.92  ** KEPT (pick-wt=7): 6 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.72/1.92  ** KEPT (pick-wt=2): 7 [] empty($c1).
% 1.72/1.92  ** KEPT (pick-wt=3): 8 [] subset(A,A).
% 1.72/1.92  ** KEPT (pick-wt=6): 9 [] subset(unordered_pair($c5,$c4),singleton($c3)).
% 1.72/1.92  ** KEPT (pick-wt=6): 11 [copy,10,flip.1] singleton(A)=unordered_pair(A,A).
% 1.72/1.92  ---> New Demodulator: 12 [new_demod,11] singleton(A)=unordered_pair(A,A).
% 1.72/1.92    Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] A=A.
% 1.72/1.92    Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.72/1.92  >>>> Starting back demodulation with 12.
% 1.72/1.92      >> back demodulating 9 with 12.
% 1.72/1.92      >> back demodulating 4 with 12.
% 1.72/1.92      >> back demodulating 2 with 12.
% 1.72/1.92  
% 1.72/1.92  ======= end of input processing =======
% 1.72/1.92  
% 1.72/1.92  =========== start of search ===========
% 1.72/1.92  
% 1.72/1.92  -------- PROOF -------- 
% 1.72/1.92  
% 1.72/1.92  ----> UNIT CONFLICT at   0.00 sec ----> 23 [binary,22.1,6.1] $F.
% 1.72/1.92  
% 1.72/1.92  Length of proof is 10.  Level of proof is 5.
% 1.72/1.92  
% 1.72/1.92  ---------------- PROOF ----------------
% 1.72/1.92  % SZS status Theorem
% 1.72/1.92  % SZS output start Refutation
% See solution above
% 1.72/1.92  ------------ end of proof -------------
% 1.72/1.92  
% 1.72/1.92  
% 1.72/1.92  Search stopped by max_proofs option.
% 1.72/1.92  
% 1.72/1.92  
% 1.72/1.92  Search stopped by max_proofs option.
% 1.72/1.92  
% 1.72/1.92  ============ end of search ============
% 1.72/1.92  
% 1.72/1.92  -------------- statistics -------------
% 1.72/1.92  clauses given                 10
% 1.72/1.92  clauses generated             13
% 1.72/1.92  clauses kept                  17
% 1.72/1.92  clauses forward subsumed      11
% 1.72/1.92  clauses back subsumed          0
% 1.72/1.92  Kbytes malloced              976
% 1.72/1.92  
% 1.72/1.92  ----------- times (seconds) -----------
% 1.72/1.92  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.72/1.92  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.72/1.92  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.72/1.92  
% 1.72/1.92  That finishes the proof of the theorem.
% 1.72/1.92  
% 1.72/1.92  Process 29020 finished Wed Jul 27 10:55:40 2022
% 1.72/1.92  Otter interrupted
% 1.72/1.92  PROOF FOUND
%------------------------------------------------------------------------------