TSTP Solution File: SEU149+3 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SEU149+3 : 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 13:14:55 EDT 2022

% Result   : Theorem 2.28s 2.46s
% Output   : Refutation 2.28s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   22 (  12 unt;   4 nHn;  14 RR)
%            Number of literals    :   41 (  31 equ;  16 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    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   31 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    ( A != singleton(B)
    | in(C,A)
    | C != B ),
    file('SEU149+3.p',unknown),
    [] ).

cnf(4,axiom,
    ( A = singleton(B)
    | ~ in(dollar_f1(B,A),A)
    | dollar_f1(B,A) != B ),
    file('SEU149+3.p',unknown),
    [] ).

cnf(5,axiom,
    ( A != unordered_pair(B,C)
    | ~ in(D,A)
    | D = B
    | D = C ),
    file('SEU149+3.p',unknown),
    [] ).

cnf(6,axiom,
    ( A != unordered_pair(B,C)
    | in(D,A)
    | D != B ),
    file('SEU149+3.p',unknown),
    [] ).

cnf(11,axiom,
    dollar_c5 != dollar_c4,
    file('SEU149+3.p',unknown),
    [] ).

cnf(13,plain,
    ( A != unordered_pair(B,B)
    | ~ in(C,A)
    | C = B ),
    inference(factor,[status(thm)],[5]),
    [iquote('factor,5.3.4')] ).

cnf(14,axiom,
    A = A,
    file('SEU149+3.p',unknown),
    [] ).

cnf(15,axiom,
    unordered_pair(A,B) = unordered_pair(B,A),
    file('SEU149+3.p',unknown),
    [] ).

cnf(16,axiom,
    ( A = singleton(B)
    | in(dollar_f1(B,A),A)
    | dollar_f1(B,A) = B ),
    file('SEU149+3.p',unknown),
    [] ).

cnf(19,axiom,
    singleton(dollar_c5) = unordered_pair(dollar_c4,dollar_c3),
    file('SEU149+3.p',unknown),
    [] ).

cnf(23,plain,
    in(A,unordered_pair(A,B)),
    inference(hyper,[status(thm)],[14,6,14]),
    [iquote('hyper,14,6,14')] ).

cnf(24,plain,
    in(A,singleton(A)),
    inference(hyper,[status(thm)],[14,3,14]),
    [iquote('hyper,14,3,14')] ).

cnf(64,plain,
    dollar_c5 = dollar_c3,
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[19,5,24]),11]),
    [iquote('hyper,19,5,24,unit_del,11')] ).

cnf(66,plain,
    singleton(dollar_c3) = unordered_pair(dollar_c4,dollar_c3),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[19]),64]),
    [iquote('back_demod,19,demod,64')] ).

cnf(68,plain,
    dollar_c4 != dollar_c3,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[11]),64])]),
    [iquote('back_demod,11,demod,64,flip.1')] ).

cnf(76,plain,
    ( A != dollar_c3
    | B != unordered_pair(A,A)
    | ~ in(dollar_c4,B) ),
    inference(para_into,[status(thm),theory(equality)],[68,13]),
    [iquote('para_into,68.1.1,13.3.1')] ).

cnf(97,plain,
    ( unordered_pair(A,A) = singleton(B)
    | dollar_f1(B,unordered_pair(A,A)) = B
    | dollar_f1(B,unordered_pair(A,A)) = A ),
    inference(hyper,[status(thm)],[16,13,15]),
    [iquote('hyper,16,13,15')] ).

cnf(101,plain,
    ( singleton(A) = unordered_pair(A,A)
    | dollar_f1(A,unordered_pair(A,A)) = A ),
    inference(flip,[status(thm),theory(equality)],[inference(factor,[status(thm)],[97])]),
    [iquote('factor,97.2.3,flip.1')] ).

cnf(1861,plain,
    ( singleton(A) = unordered_pair(A,A)
    | dollar_f1(A,unordered_pair(A,A)) != A ),
    inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[101,4]),23])]),
    [iquote('para_from,101.2.1,4.2.1,unit_del,23,factor_simp')] ).

cnf(1877,plain,
    singleton(A) = unordered_pair(A,A),
    inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[1861,101])]),
    [iquote('hyper,1861,101,factor_simp')] ).

cnf(1900,plain,
    unordered_pair(dollar_c4,dollar_c3) = unordered_pair(dollar_c3,dollar_c3),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[66]),1877])]),
    [iquote('back_demod,66,demod,1877,flip.1')] ).

cnf(1909,plain,
    $false,
    inference(hyper,[status(thm)],[1900,76,14,23]),
    [iquote('hyper,1900,76,14,23')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU149+3 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12  % 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 07:56:06 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 2.28/2.46  ----- Otter 3.3f, August 2004 -----
% 2.28/2.46  The process was started by sandbox on n004.cluster.edu,
% 2.28/2.46  Wed Jul 27 07:56:06 2022
% 2.28/2.46  The command was "./otter".  The process ID is 25916.
% 2.28/2.46  
% 2.28/2.46  set(prolog_style_variables).
% 2.28/2.46  set(auto).
% 2.28/2.46     dependent: set(auto1).
% 2.28/2.46     dependent: set(process_input).
% 2.28/2.46     dependent: clear(print_kept).
% 2.28/2.46     dependent: clear(print_new_demod).
% 2.28/2.46     dependent: clear(print_back_demod).
% 2.28/2.46     dependent: clear(print_back_sub).
% 2.28/2.46     dependent: set(control_memory).
% 2.28/2.46     dependent: assign(max_mem, 12000).
% 2.28/2.46     dependent: assign(pick_given_ratio, 4).
% 2.28/2.46     dependent: assign(stats_level, 1).
% 2.28/2.46     dependent: assign(max_seconds, 10800).
% 2.28/2.46  clear(print_given).
% 2.28/2.46  
% 2.28/2.46  formula_list(usable).
% 2.28/2.46  all A (A=A).
% 2.28/2.46  all A B (in(A,B)-> -in(B,A)).
% 2.28/2.46  all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 2.28/2.46  all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 2.28/2.46  all A B C (C=unordered_pair(A,B)<-> (all D (in(D,C)<->D=A|D=B))).
% 2.28/2.46  exists A empty(A).
% 2.28/2.46  exists A (-empty(A)).
% 2.28/2.46  -(all A B C (singleton(A)=unordered_pair(B,C)->A=B)).
% 2.28/2.46  end_of_list.
% 2.28/2.46  
% 2.28/2.46  -------> usable clausifies to:
% 2.28/2.46  
% 2.28/2.46  list(usable).
% 2.28/2.46  0 [] A=A.
% 2.28/2.46  0 [] -in(A,B)| -in(B,A).
% 2.28/2.46  0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 2.28/2.46  0 [] B!=singleton(A)| -in(C,B)|C=A.
% 2.28/2.46  0 [] B!=singleton(A)|in(C,B)|C!=A.
% 2.28/2.46  0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 2.28/2.46  0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 2.28/2.46  0 [] C!=unordered_pair(A,B)| -in(D,C)|D=A|D=B.
% 2.28/2.46  0 [] C!=unordered_pair(A,B)|in(D,C)|D!=A.
% 2.28/2.46  0 [] C!=unordered_pair(A,B)|in(D,C)|D!=B.
% 2.28/2.46  0 [] C=unordered_pair(A,B)|in($f2(A,B,C),C)|$f2(A,B,C)=A|$f2(A,B,C)=B.
% 2.28/2.46  0 [] C=unordered_pair(A,B)| -in($f2(A,B,C),C)|$f2(A,B,C)!=A.
% 2.28/2.46  0 [] C=unordered_pair(A,B)| -in($f2(A,B,C),C)|$f2(A,B,C)!=B.
% 2.28/2.46  0 [] empty($c1).
% 2.28/2.46  0 [] -empty($c2).
% 2.28/2.46  0 [] singleton($c5)=unordered_pair($c4,$c3).
% 2.28/2.46  0 [] $c5!=$c4.
% 2.28/2.46  end_of_list.
% 2.28/2.46  
% 2.28/2.46  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 2.28/2.46  
% 2.28/2.46  This ia a non-Horn set with equality.  The strategy will be
% 2.28/2.46  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.28/2.46  deletion, with positive clauses in sos and nonpositive
% 2.28/2.46  clauses in usable.
% 2.28/2.46  
% 2.28/2.46     dependent: set(knuth_bendix).
% 2.28/2.46     dependent: set(anl_eq).
% 2.28/2.46     dependent: set(para_from).
% 2.28/2.46     dependent: set(para_into).
% 2.28/2.46     dependent: clear(para_from_right).
% 2.28/2.46     dependent: clear(para_into_right).
% 2.28/2.46     dependent: set(para_from_vars).
% 2.28/2.46     dependent: set(eq_units_both_ways).
% 2.28/2.46     dependent: set(dynamic_demod_all).
% 2.28/2.46     dependent: set(dynamic_demod).
% 2.28/2.46     dependent: set(order_eq).
% 2.28/2.46     dependent: set(back_demod).
% 2.28/2.46     dependent: set(lrpo).
% 2.28/2.46     dependent: set(hyper_res).
% 2.28/2.46     dependent: set(unit_deletion).
% 2.28/2.46     dependent: set(factor).
% 2.28/2.46  
% 2.28/2.46  ------------> process usable:
% 2.28/2.46  ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.28/2.46  ** KEPT (pick-wt=10): 2 [] A!=singleton(B)| -in(C,A)|C=B.
% 2.28/2.46  ** KEPT (pick-wt=10): 3 [] A!=singleton(B)|in(C,A)|C!=B.
% 2.28/2.46  ** KEPT (pick-wt=14): 4 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 2.28/2.46  ** KEPT (pick-wt=14): 5 [] A!=unordered_pair(B,C)| -in(D,A)|D=B|D=C.
% 2.28/2.46  ** KEPT (pick-wt=11): 6 [] A!=unordered_pair(B,C)|in(D,A)|D!=B.
% 2.28/2.46  ** KEPT (pick-wt=11): 7 [] A!=unordered_pair(B,C)|in(D,A)|D!=C.
% 2.28/2.46  ** KEPT (pick-wt=17): 8 [] A=unordered_pair(B,C)| -in($f2(B,C,A),A)|$f2(B,C,A)!=B.
% 2.28/2.46  ** KEPT (pick-wt=17): 9 [] A=unordered_pair(B,C)| -in($f2(B,C,A),A)|$f2(B,C,A)!=C.
% 2.28/2.46  ** KEPT (pick-wt=2): 10 [] -empty($c2).
% 2.28/2.46  ** KEPT (pick-wt=3): 11 [] $c5!=$c4.
% 2.28/2.46  
% 2.28/2.46  ------------> process sos:
% 2.28/2.46  ** KEPT (pick-wt=3): 14 [] A=A.
% 2.28/2.46  ** KEPT (pick-wt=7): 15 [] unordered_pair(A,B)=unordered_pair(B,A).
% 2.28/2.46  ** KEPT (pick-wt=14): 16 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 2.28/2.46  ** KEPT (pick-wt=23): 17 [] A=unordered_pair(B,C)|in($f2(B,C,A),A)|$f2(B,C,A)=B|$f2(B,C,A)=C.
% 2.28/2.46  ** KEPT (pick-wt=2): 18 [] empty($c1).
% 2.28/2.46  ** KEPT (pick-wt=6): 19 [] singleton($c5)=unordered_pair($c4,$c3).
% 2.28/2.46  ---> New Demodulator: 20 [new_demod,19] singleton($c5)=unordered_pair($c4,$c3).
% 2.28/2.46    Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 2.28/2.46    Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 2.28/2.46  >>>> Starting back demodulation with 20.
% 2.28/2.46  
% 2.28/2.46  ======= end of input processing =======
% 2.28/2.46  
% 2.28/2.46  =========== start of search ===========
% 2.28/2.46  
% 2.28/2.46  
% 2.28/2.46  Resetting weight limit to 17.
% 2.28/2.46  
% 2.28/2.46  
% 2.28/2.46  Resetting weight limit to 17.
% 2.28/2.46  
% 2.28/2.46  sos_size=1757
% 2.28/2.46  
% 2.28/2.46  -------- PROOF -------- 
% 2.28/2.46  
% 2.28/2.46  -----> EMPTY CLAUSE at   0.58 sec ----> 1909 [hyper,1900,76,14,23] $F.
% 2.28/2.46  
% 2.28/2.46  Length of proof is 12.  Level of proof is 6.
% 2.28/2.46  
% 2.28/2.46  ---------------- PROOF ----------------
% 2.28/2.46  % SZS status Theorem
% 2.28/2.46  % SZS output start Refutation
% See solution above
% 2.28/2.46  ------------ end of proof -------------
% 2.28/2.46  
% 2.28/2.46  
% 2.28/2.46  Search stopped by max_proofs option.
% 2.28/2.46  
% 2.28/2.46  
% 2.28/2.46  Search stopped by max_proofs option.
% 2.28/2.46  
% 2.28/2.46  ============ end of search ============
% 2.28/2.46  
% 2.28/2.46  -------------- statistics -------------
% 2.28/2.46  clauses given                 69
% 2.28/2.46  clauses generated           3736
% 2.28/2.46  clauses kept                1903
% 2.28/2.46  clauses forward subsumed    1148
% 2.28/2.46  clauses back subsumed         21
% 2.28/2.46  Kbytes malloced             4882
% 2.28/2.46  
% 2.28/2.46  ----------- times (seconds) -----------
% 2.28/2.46  user CPU time          0.58          (0 hr, 0 min, 0 sec)
% 2.28/2.46  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 2.28/2.46  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 2.28/2.46  
% 2.28/2.46  That finishes the proof of the theorem.
% 2.28/2.46  
% 2.28/2.46  Process 25916 finished Wed Jul 27 07:56:08 2022
% 2.28/2.46  Otter interrupted
% 2.28/2.46  PROOF FOUND
%------------------------------------------------------------------------------