TSTP Solution File: SEU142+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SEU142+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n016.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 13:14:53 EDT 2022

% Result   : Theorem 1.91s 2.07s
% Output   : Refutation 1.91s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   14 (   7 unt;   4 nHn;   8 RR)
%            Number of literals    :   28 (  21 equ;  10 neg)
%            Maximal clause size   :    4 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :   23 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(4,axiom,
    ( A = singleton(B)
    | ~ in(dollar_f1(B,A),A)
    | dollar_f1(B,A) != B ),
    file('SEU142+1.p',unknown),
    [] ).

cnf(5,axiom,
    ( A != unordered_pair(B,C)
    | ~ in(D,A)
    | D = B
    | D = C ),
    file('SEU142+1.p',unknown),
    [] ).

cnf(6,axiom,
    ( A != unordered_pair(B,C)
    | in(D,A)
    | D != B ),
    file('SEU142+1.p',unknown),
    [] ).

cnf(11,axiom,
    unordered_pair(dollar_c1,dollar_c1) != singleton(dollar_c1),
    file('SEU142+1.p',unknown),
    [] ).

cnf(12,plain,
    singleton(dollar_c1) != unordered_pair(dollar_c1,dollar_c1),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[11])]),
    [iquote('copy,11,flip.1')] ).

cnf(14,plain,
    ( A != unordered_pair(B,B)
    | ~ in(C,A)
    | C = B ),
    inference(factor,[status(thm)],[5]),
    [iquote('factor,5.3.4')] ).

cnf(16,axiom,
    A = A,
    file('SEU142+1.p',unknown),
    [] ).

cnf(17,axiom,
    unordered_pair(A,B) = unordered_pair(B,A),
    file('SEU142+1.p',unknown),
    [] ).

cnf(18,axiom,
    ( A = singleton(B)
    | in(dollar_f1(B,A),A)
    | dollar_f1(B,A) = B ),
    file('SEU142+1.p',unknown),
    [] ).

cnf(23,plain,
    in(A,unordered_pair(A,B)),
    inference(hyper,[status(thm)],[16,6,16]),
    [iquote('hyper,16,6,16')] ).

cnf(60,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)],[18,14,17]),
    [iquote('hyper,18,14,17')] ).

cnf(63,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)],[60])]),
    [iquote('factor,60.2.3,flip.1')] ).

cnf(468,plain,
    dollar_f1(dollar_c1,unordered_pair(dollar_c1,dollar_c1)) = dollar_c1,
    inference(hyper,[status(thm)],[63,12]),
    [iquote('hyper,63,12')] ).

cnf(616,plain,
    $false,
    inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[468,4]),468]),12,23,16]),
    [iquote('para_from,467.1.1,4.3.1,demod,468,unit_del,12,23,16')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU142+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13  % Command  : otter-tptp-script %s
% 0.12/0.34  % Computer : n016.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Wed Jul 27 08:23:22 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 1.90/2.07  ----- Otter 3.3f, August 2004 -----
% 1.90/2.07  The process was started by sandbox on n016.cluster.edu,
% 1.90/2.07  Wed Jul 27 08:23:22 2022
% 1.90/2.07  The command was "./otter".  The process ID is 5813.
% 1.90/2.07  
% 1.90/2.07  set(prolog_style_variables).
% 1.90/2.07  set(auto).
% 1.90/2.07     dependent: set(auto1).
% 1.90/2.07     dependent: set(process_input).
% 1.90/2.07     dependent: clear(print_kept).
% 1.90/2.07     dependent: clear(print_new_demod).
% 1.90/2.07     dependent: clear(print_back_demod).
% 1.90/2.07     dependent: clear(print_back_sub).
% 1.90/2.07     dependent: set(control_memory).
% 1.90/2.07     dependent: assign(max_mem, 12000).
% 1.90/2.07     dependent: assign(pick_given_ratio, 4).
% 1.90/2.07     dependent: assign(stats_level, 1).
% 1.90/2.07     dependent: assign(max_seconds, 10800).
% 1.90/2.07  clear(print_given).
% 1.90/2.07  
% 1.90/2.07  formula_list(usable).
% 1.90/2.07  all A (A=A).
% 1.90/2.07  all A B (in(A,B)-> -in(B,A)).
% 1.90/2.07  all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.90/2.07  all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 1.90/2.07  all A B C (C=unordered_pair(A,B)<-> (all D (in(D,C)<->D=A|D=B))).
% 1.90/2.07  $T.
% 1.90/2.07  $T.
% 1.90/2.07  all A B ((all C (in(C,A)<->in(C,B)))->A=B).
% 1.90/2.07  -(all A (unordered_pair(A,A)=singleton(A))).
% 1.90/2.07  end_of_list.
% 1.90/2.07  
% 1.90/2.07  -------> usable clausifies to:
% 1.90/2.07  
% 1.90/2.07  list(usable).
% 1.90/2.07  0 [] A=A.
% 1.90/2.07  0 [] -in(A,B)| -in(B,A).
% 1.90/2.07  0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.90/2.07  0 [] B!=singleton(A)| -in(C,B)|C=A.
% 1.90/2.07  0 [] B!=singleton(A)|in(C,B)|C!=A.
% 1.90/2.07  0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 1.90/2.07  0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 1.90/2.07  0 [] C!=unordered_pair(A,B)| -in(D,C)|D=A|D=B.
% 1.90/2.07  0 [] C!=unordered_pair(A,B)|in(D,C)|D!=A.
% 1.90/2.07  0 [] C!=unordered_pair(A,B)|in(D,C)|D!=B.
% 1.90/2.07  0 [] C=unordered_pair(A,B)|in($f2(A,B,C),C)|$f2(A,B,C)=A|$f2(A,B,C)=B.
% 1.90/2.07  0 [] C=unordered_pair(A,B)| -in($f2(A,B,C),C)|$f2(A,B,C)!=A.
% 1.90/2.07  0 [] C=unordered_pair(A,B)| -in($f2(A,B,C),C)|$f2(A,B,C)!=B.
% 1.90/2.07  0 [] $T.
% 1.90/2.07  0 [] $T.
% 1.90/2.07  0 [] in($f3(A,B),A)|in($f3(A,B),B)|A=B.
% 1.90/2.07  0 [] -in($f3(A,B),A)| -in($f3(A,B),B)|A=B.
% 1.90/2.07  0 [] unordered_pair($c1,$c1)!=singleton($c1).
% 1.90/2.07  end_of_list.
% 1.90/2.07  
% 1.90/2.07  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.90/2.07  
% 1.90/2.07  This ia a non-Horn set with equality.  The strategy will be
% 1.90/2.07  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.90/2.07  deletion, with positive clauses in sos and nonpositive
% 1.90/2.07  clauses in usable.
% 1.90/2.07  
% 1.90/2.07     dependent: set(knuth_bendix).
% 1.90/2.07     dependent: set(anl_eq).
% 1.91/2.07     dependent: set(para_from).
% 1.91/2.07     dependent: set(para_into).
% 1.91/2.07     dependent: clear(para_from_right).
% 1.91/2.07     dependent: clear(para_into_right).
% 1.91/2.07     dependent: set(para_from_vars).
% 1.91/2.07     dependent: set(eq_units_both_ways).
% 1.91/2.07     dependent: set(dynamic_demod_all).
% 1.91/2.07     dependent: set(dynamic_demod).
% 1.91/2.07     dependent: set(order_eq).
% 1.91/2.07     dependent: set(back_demod).
% 1.91/2.07     dependent: set(lrpo).
% 1.91/2.07     dependent: set(hyper_res).
% 1.91/2.07     dependent: set(unit_deletion).
% 1.91/2.07     dependent: set(factor).
% 1.91/2.07  
% 1.91/2.07  ------------> process usable:
% 1.91/2.07  ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.91/2.07  ** KEPT (pick-wt=10): 2 [] A!=singleton(B)| -in(C,A)|C=B.
% 1.91/2.07  ** KEPT (pick-wt=10): 3 [] A!=singleton(B)|in(C,A)|C!=B.
% 1.91/2.07  ** KEPT (pick-wt=14): 4 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 1.91/2.07  ** KEPT (pick-wt=14): 5 [] A!=unordered_pair(B,C)| -in(D,A)|D=B|D=C.
% 1.91/2.07  ** KEPT (pick-wt=11): 6 [] A!=unordered_pair(B,C)|in(D,A)|D!=B.
% 1.91/2.07  ** KEPT (pick-wt=11): 7 [] A!=unordered_pair(B,C)|in(D,A)|D!=C.
% 1.91/2.07  ** KEPT (pick-wt=17): 8 [] A=unordered_pair(B,C)| -in($f2(B,C,A),A)|$f2(B,C,A)!=B.
% 1.91/2.07  ** KEPT (pick-wt=17): 9 [] A=unordered_pair(B,C)| -in($f2(B,C,A),A)|$f2(B,C,A)!=C.
% 1.91/2.07  ** KEPT (pick-wt=13): 10 [] -in($f3(A,B),A)| -in($f3(A,B),B)|A=B.
% 1.91/2.07  ** KEPT (pick-wt=6): 12 [copy,11,flip.1] singleton($c1)!=unordered_pair($c1,$c1).
% 1.91/2.07  
% 1.91/2.07  ------------> process sos:
% 1.91/2.07  ** KEPT (pick-wt=3): 16 [] A=A.
% 1.91/2.07  ** KEPT (pick-wt=7): 17 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.91/2.07  ** KEPT (pick-wt=14): 18 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 1.91/2.07  ** KEPT (pick-wt=23): 19 [] A=unordered_pair(B,C)|in($f2(B,C,A),A)|$f2(B,C,A)=B|$f2(B,C,A)=C.
% 1.91/2.07  ** KEPT (pick-wt=13): 20 [] in($f3(A,B),A)|in($f3(A,B),B)|A=B.
% 1.91/2.07    Following clause subsumed by 16 during input processing: 0 [copy,16,flip.1] A=A.
% 1.91/2.07  16 back subsumes 15.
% 1.91/2.07    Following clause subsumed by 17 during input processing: 0 [copy,17,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.91/2.07  
% 1.91/2.07  ======= end of input processing =======
% 1.91/2.07  
% 1.91/2.07  =========== start of search ===========
% 1.91/2.07  
% 1.91/2.07  -------- PROOF -------- 
% 1.91/2.07  
% 1.91/2.07  -----> EMPTY CLAUSE at   0.06 sec ----> 616 [para_from,467.1.1,4.3.1,demod,468,unit_del,12,23,16] $F.
% 1.91/2.07  
% 1.91/2.07  Length of proof is 6.  Level of proof is 4.
% 1.91/2.07  
% 1.91/2.07  ---------------- PROOF ----------------
% 1.91/2.07  % SZS status Theorem
% 1.91/2.07  % SZS output start Refutation
% See solution above
% 1.91/2.07  ------------ end of proof -------------
% 1.91/2.07  
% 1.91/2.07  
% 1.91/2.07  Search stopped by max_proofs option.
% 1.91/2.07  
% 1.91/2.07  
% 1.91/2.07  Search stopped by max_proofs option.
% 1.91/2.07  
% 1.91/2.07  ============ end of search ============
% 1.91/2.07  
% 1.91/2.07  -------------- statistics -------------
% 1.91/2.07  clauses given                 20
% 1.91/2.07  clauses generated           1090
% 1.91/2.07  clauses kept                 613
% 1.91/2.07  clauses forward subsumed     485
% 1.91/2.07  clauses back subsumed          2
% 1.91/2.07  Kbytes malloced             2929
% 1.91/2.07  
% 1.91/2.07  ----------- times (seconds) -----------
% 1.91/2.07  user CPU time          0.06          (0 hr, 0 min, 0 sec)
% 1.91/2.07  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.91/2.07  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.91/2.07  
% 1.91/2.07  That finishes the proof of the theorem.
% 1.91/2.07  
% 1.91/2.07  Process 5813 finished Wed Jul 27 08:23:24 2022
% 1.91/2.07  Otter interrupted
% 1.91/2.07  PROOF FOUND
%------------------------------------------------------------------------------