TSTP Solution File: SEU177+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SEU177+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n025.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 13:15:04 EDT 2022

% Result   : Theorem 1.97s 2.16s
% Output   : Refutation 1.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    6
% Syntax   : Number of clauses     :    9 (   6 unt;   0 nHn;   8 RR)
%            Number of literals    :   16 (   3 equ;   8 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :    9 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(11,axiom,
    ( ~ in(dollar_c6,relation_dom(dollar_c4))
    | ~ in(dollar_c5,relation_rng(dollar_c4)) ),
    file('SEU177+1.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ relation(A)
    | B != relation_dom(A)
    | in(C,B)
    | ~ in(ordered_pair(C,D),A) ),
    file('SEU177+1.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ relation(A)
    | B != relation_rng(A)
    | in(C,B)
    | ~ in(ordered_pair(D,C),A) ),
    file('SEU177+1.p',unknown),
    [] ).

cnf(22,axiom,
    A = A,
    file('SEU177+1.p',unknown),
    [] ).

cnf(32,axiom,
    relation(dollar_c4),
    file('SEU177+1.p',unknown),
    [] ).

cnf(33,axiom,
    in(ordered_pair(dollar_c6,dollar_c5),dollar_c4),
    file('SEU177+1.p',unknown),
    [] ).

cnf(92,plain,
    in(dollar_c5,relation_rng(dollar_c4)),
    inference(hyper,[status(thm)],[33,17,32,22]),
    [iquote('hyper,33,17,32,22')] ).

cnf(93,plain,
    in(dollar_c6,relation_dom(dollar_c4)),
    inference(hyper,[status(thm)],[33,13,32,22]),
    [iquote('hyper,33,13,32,22')] ).

cnf(132,plain,
    $false,
    inference(hyper,[status(thm)],[93,11,92]),
    [iquote('hyper,93,11,92')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SEU177+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.11  % Command  : otter-tptp-script %s
% 0.11/0.32  % Computer : n025.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Wed Jul 27 07:47:45 EDT 2022
% 0.11/0.32  % CPUTime  : 
% 1.97/2.16  ----- Otter 3.3f, August 2004 -----
% 1.97/2.16  The process was started by sandbox2 on n025.cluster.edu,
% 1.97/2.16  Wed Jul 27 07:47:45 2022
% 1.97/2.16  The command was "./otter".  The process ID is 8905.
% 1.97/2.16  
% 1.97/2.16  set(prolog_style_variables).
% 1.97/2.16  set(auto).
% 1.97/2.16     dependent: set(auto1).
% 1.97/2.16     dependent: set(process_input).
% 1.97/2.16     dependent: clear(print_kept).
% 1.97/2.16     dependent: clear(print_new_demod).
% 1.97/2.16     dependent: clear(print_back_demod).
% 1.97/2.16     dependent: clear(print_back_sub).
% 1.97/2.16     dependent: set(control_memory).
% 1.97/2.16     dependent: assign(max_mem, 12000).
% 1.97/2.16     dependent: assign(pick_given_ratio, 4).
% 1.97/2.16     dependent: assign(stats_level, 1).
% 1.97/2.16     dependent: assign(max_seconds, 10800).
% 1.97/2.16  clear(print_given).
% 1.97/2.16  
% 1.97/2.16  formula_list(usable).
% 1.97/2.16  all A (A=A).
% 1.97/2.16  $T.
% 1.97/2.16  empty(empty_set).
% 1.97/2.16  all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.97/2.16  all A exists B element(B,A).
% 1.97/2.16  $T.
% 1.97/2.16  $T.
% 1.97/2.16  $T.
% 1.97/2.16  exists A (empty(A)&relation(A)).
% 1.97/2.16  exists A empty(A).
% 1.97/2.16  exists A (-empty(A)).
% 1.97/2.16  all A (-empty(singleton(A))).
% 1.97/2.16  all A B (-empty(unordered_pair(A,B))).
% 1.97/2.16  all A B (element(A,B)->empty(B)|in(A,B)).
% 1.97/2.16  all A (empty(A)->A=empty_set).
% 1.97/2.16  all A B (-(empty(A)&A!=B&empty(B))).
% 1.97/2.16  all A B (in(A,B)-> -in(B,A)).
% 1.97/2.16  $T.
% 1.97/2.16  $T.
% 1.97/2.16  $T.
% 1.97/2.16  all A B (-empty(ordered_pair(A,B))).
% 1.97/2.16  all A B (in(A,B)->element(A,B)).
% 1.97/2.16  all A B (-(in(A,B)&empty(B))).
% 1.97/2.16  all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 1.97/2.16  -(all A B C (relation(C)-> (in(ordered_pair(A,B),C)->in(A,relation_dom(C))&in(B,relation_rng(C))))).
% 1.97/2.16  all A (relation(A)-> (all B (B=relation_dom(A)<-> (all C (in(C,B)<-> (exists D in(ordered_pair(C,D),A))))))).
% 1.97/2.16  all A (relation(A)-> (all B (B=relation_rng(A)<-> (all C (in(C,B)<-> (exists D in(ordered_pair(D,C),A))))))).
% 1.97/2.16  end_of_list.
% 1.97/2.16  
% 1.97/2.16  -------> usable clausifies to:
% 1.97/2.16  
% 1.97/2.16  list(usable).
% 1.97/2.16  0 [] A=A.
% 1.97/2.16  0 [] $T.
% 1.97/2.16  0 [] empty(empty_set).
% 1.97/2.16  0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.97/2.16  0 [] element($f1(A),A).
% 1.97/2.16  0 [] $T.
% 1.97/2.16  0 [] $T.
% 1.97/2.16  0 [] $T.
% 1.97/2.16  0 [] empty($c1).
% 1.97/2.16  0 [] relation($c1).
% 1.97/2.16  0 [] empty($c2).
% 1.97/2.16  0 [] -empty($c3).
% 1.97/2.16  0 [] -empty(singleton(A)).
% 1.97/2.16  0 [] -empty(unordered_pair(A,B)).
% 1.97/2.16  0 [] -element(A,B)|empty(B)|in(A,B).
% 1.97/2.16  0 [] -empty(A)|A=empty_set.
% 1.97/2.16  0 [] -empty(A)|A=B| -empty(B).
% 1.97/2.16  0 [] -in(A,B)| -in(B,A).
% 1.97/2.16  0 [] $T.
% 1.97/2.16  0 [] $T.
% 1.97/2.16  0 [] $T.
% 1.97/2.16  0 [] -empty(ordered_pair(A,B)).
% 1.97/2.16  0 [] -in(A,B)|element(A,B).
% 1.97/2.16  0 [] -in(A,B)| -empty(B).
% 1.97/2.16  0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 1.97/2.16  0 [] relation($c4).
% 1.97/2.16  0 [] in(ordered_pair($c6,$c5),$c4).
% 1.97/2.16  0 [] -in($c6,relation_dom($c4))| -in($c5,relation_rng($c4)).
% 1.97/2.16  0 [] -relation(A)|B!=relation_dom(A)| -in(C,B)|in(ordered_pair(C,$f2(A,B,C)),A).
% 1.97/2.16  0 [] -relation(A)|B!=relation_dom(A)|in(C,B)| -in(ordered_pair(C,D),A).
% 1.97/2.16  0 [] -relation(A)|B=relation_dom(A)|in($f4(A,B),B)|in(ordered_pair($f4(A,B),$f3(A,B)),A).
% 1.97/2.16  0 [] -relation(A)|B=relation_dom(A)| -in($f4(A,B),B)| -in(ordered_pair($f4(A,B),X1),A).
% 1.97/2.16  0 [] -relation(A)|B!=relation_rng(A)| -in(C,B)|in(ordered_pair($f5(A,B,C),C),A).
% 1.97/2.16  0 [] -relation(A)|B!=relation_rng(A)|in(C,B)| -in(ordered_pair(D,C),A).
% 1.97/2.16  0 [] -relation(A)|B=relation_rng(A)|in($f7(A,B),B)|in(ordered_pair($f6(A,B),$f7(A,B)),A).
% 1.97/2.16  0 [] -relation(A)|B=relation_rng(A)| -in($f7(A,B),B)| -in(ordered_pair(X2,$f7(A,B)),A).
% 1.97/2.16  end_of_list.
% 1.97/2.16  
% 1.97/2.16  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.97/2.16  
% 1.97/2.16  This ia a non-Horn set with equality.  The strategy will be
% 1.97/2.16  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.97/2.16  deletion, with positive clauses in sos and nonpositive
% 1.97/2.16  clauses in usable.
% 1.97/2.16  
% 1.97/2.16     dependent: set(knuth_bendix).
% 1.97/2.16     dependent: set(anl_eq).
% 1.97/2.16     dependent: set(para_from).
% 1.97/2.16     dependent: set(para_into).
% 1.97/2.16     dependent: clear(para_from_right).
% 1.97/2.16     dependent: clear(para_into_right).
% 1.97/2.16     dependent: set(para_from_vars).
% 1.97/2.16     dependent: set(eq_units_both_ways).
% 1.97/2.16     dependent: set(dynamic_demod_all).
% 1.97/2.16     dependent: set(dynamic_demod).
% 1.97/2.16     dependent: set(order_eq).
% 1.97/2.16     dependent: set(back_demod).
% 1.97/2.16     dependent: set(lrpo).
% 1.97/2.16     dependent: set(hyper_res).
% 1.97/2.16     dependent: set(unit_deletion).
% 1.97/2.16     dependent: set(factor).
% 1.97/2.16  
% 1.97/2.16  ------------> process usable:
% 1.97/2.16  ** KEPT (pick-wt=2): 1 [] -empty($c3).
% 1.97/2.16  ** KEPT (pick-wt=3): 2 [] -empty(singleton(A)).
% 1.97/2.16  ** KEPT (pick-wt=4): 3 [] -empty(unordered_pair(A,B)).
% 1.97/2.16  ** KEPT (pick-wt=8): 4 [] -element(A,B)|empty(B)|in(A,B).
% 1.97/2.16  ** KEPT (pick-wt=5): 5 [] -empty(A)|A=empty_set.
% 1.97/2.16  ** KEPT (pick-wt=7): 6 [] -empty(A)|A=B| -empty(B).
% 1.97/2.16  ** KEPT (pick-wt=6): 7 [] -in(A,B)| -in(B,A).
% 1.97/2.16  ** KEPT (pick-wt=4): 8 [] -empty(ordered_pair(A,B)).
% 1.97/2.16  ** KEPT (pick-wt=6): 9 [] -in(A,B)|element(A,B).
% 1.97/2.16  ** KEPT (pick-wt=5): 10 [] -in(A,B)| -empty(B).
% 1.97/2.16  ** KEPT (pick-wt=8): 11 [] -in($c6,relation_dom($c4))| -in($c5,relation_rng($c4)).
% 1.97/2.16  ** KEPT (pick-wt=17): 12 [] -relation(A)|B!=relation_dom(A)| -in(C,B)|in(ordered_pair(C,$f2(A,B,C)),A).
% 1.97/2.16  ** KEPT (pick-wt=14): 13 [] -relation(A)|B!=relation_dom(A)|in(C,B)| -in(ordered_pair(C,D),A).
% 1.97/2.16  ** KEPT (pick-wt=20): 14 [] -relation(A)|B=relation_dom(A)|in($f4(A,B),B)|in(ordered_pair($f4(A,B),$f3(A,B)),A).
% 1.97/2.16  ** KEPT (pick-wt=18): 15 [] -relation(A)|B=relation_dom(A)| -in($f4(A,B),B)| -in(ordered_pair($f4(A,B),C),A).
% 1.97/2.16  ** KEPT (pick-wt=17): 16 [] -relation(A)|B!=relation_rng(A)| -in(C,B)|in(ordered_pair($f5(A,B,C),C),A).
% 1.97/2.16  ** KEPT (pick-wt=14): 17 [] -relation(A)|B!=relation_rng(A)|in(C,B)| -in(ordered_pair(D,C),A).
% 1.97/2.16  ** KEPT (pick-wt=20): 18 [] -relation(A)|B=relation_rng(A)|in($f7(A,B),B)|in(ordered_pair($f6(A,B),$f7(A,B)),A).
% 1.97/2.16  ** KEPT (pick-wt=18): 19 [] -relation(A)|B=relation_rng(A)| -in($f7(A,B),B)| -in(ordered_pair(C,$f7(A,B)),A).
% 1.97/2.16  
% 1.97/2.16  ------------> process sos:
% 1.97/2.16  ** KEPT (pick-wt=3): 22 [] A=A.
% 1.97/2.16  ** KEPT (pick-wt=2): 23 [] empty(empty_set).
% 1.97/2.16  ** KEPT (pick-wt=7): 24 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.97/2.16  ** KEPT (pick-wt=4): 25 [] element($f1(A),A).
% 1.97/2.16  ** KEPT (pick-wt=2): 26 [] empty($c1).
% 1.97/2.16  ** KEPT (pick-wt=2): 27 [] relation($c1).
% 1.97/2.16  ** KEPT (pick-wt=2): 28 [] empty($c2).
% 1.97/2.16  ** KEPT (pick-wt=10): 30 [copy,29,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.97/2.16  ---> New Demodulator: 31 [new_demod,30] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.97/2.16  ** KEPT (pick-wt=2): 32 [] relation($c4).
% 1.97/2.16  ** KEPT (pick-wt=5): 33 [] in(ordered_pair($c6,$c5),$c4).
% 1.97/2.16    Following clause subsumed by 22 during input processing: 0 [copy,22,flip.1] A=A.
% 1.97/2.16  22 back subsumes 20.
% 1.97/2.16    Following clause subsumed by 24 during input processing: 0 [copy,24,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.97/2.16  >>>> Starting back demodulation with 31.
% 1.97/2.16  
% 1.97/2.16  ======= end of input processing =======
% 1.97/2.16  
% 1.97/2.16  =========== start of search ===========
% 1.97/2.16  
% 1.97/2.16  -------- PROOF -------- 
% 1.97/2.16  
% 1.97/2.16  -----> EMPTY CLAUSE at   0.01 sec ----> 132 [hyper,93,11,92] $F.
% 1.97/2.16  
% 1.97/2.16  Length of proof is 2.  Level of proof is 1.
% 1.97/2.16  
% 1.97/2.16  ---------------- PROOF ----------------
% 1.97/2.16  % SZS status Theorem
% 1.97/2.16  % SZS output start Refutation
% See solution above
% 1.97/2.16  ------------ end of proof -------------
% 1.97/2.16  
% 1.97/2.16  
% 1.97/2.16  Search stopped by max_proofs option.
% 1.97/2.16  
% 1.97/2.16  
% 1.97/2.16  Search stopped by max_proofs option.
% 1.97/2.16  
% 1.97/2.16  ============ end of search ============
% 1.97/2.16  
% 1.97/2.16  -------------- statistics -------------
% 1.97/2.16  clauses given                 15
% 1.97/2.16  clauses generated            140
% 1.97/2.16  clauses kept                 124
% 1.97/2.16  clauses forward subsumed      51
% 1.97/2.16  clauses back subsumed          1
% 1.97/2.16  Kbytes malloced             1953
% 1.97/2.16  
% 1.97/2.16  ----------- times (seconds) -----------
% 1.97/2.16  user CPU time          0.01          (0 hr, 0 min, 0 sec)
% 1.97/2.16  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.97/2.16  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.97/2.16  
% 1.97/2.16  That finishes the proof of the theorem.
% 1.97/2.16  
% 1.97/2.16  Process 8905 finished Wed Jul 27 07:47:47 2022
% 1.97/2.16  Otter interrupted
% 1.97/2.16  PROOF FOUND
%------------------------------------------------------------------------------