TSTP Solution File: SEU263+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SEU263+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n024.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 13:15:23 EDT 2022

% Result   : Theorem 1.75s 1.95s
% Output   : Refutation 1.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   20 (  12 unt;   0 nHn;  20 RR)
%            Number of literals    :   30 (   0 equ;  11 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   23 (   3 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ element(A,powerset(cartesian_product2(B,C)))
    | relation(A) ),
    file('SEU263+1.p',unknown),
    [] ).

cnf(3,axiom,
    ( relation_of2(A,B,C)
    | ~ subset(A,cartesian_product2(B,C)) ),
    file('SEU263+1.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ relation_of2_as_subset(A,B,C)
    | element(A,powerset(cartesian_product2(B,C))) ),
    file('SEU263+1.p',unknown),
    [] ).

cnf(6,axiom,
    ( relation_of2_as_subset(A,B,C)
    | ~ relation_of2(A,B,C) ),
    file('SEU263+1.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ subset(A,B)
    | ~ subset(C,D)
    | subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
    file('SEU263+1.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ relation_of2_as_subset(A,B,C)
    | subset(relation_dom(A),B) ),
    file('SEU263+1.p',unknown),
    [] ).

cnf(10,axiom,
    ~ relation_of2_as_subset(dollar_c1,dollar_c2,dollar_c3),
    file('SEU263+1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ subset(A,B)
    | ~ subset(B,C)
    | subset(A,C) ),
    file('SEU263+1.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ relation(A)
    | subset(A,cartesian_product2(relation_dom(A),relation_rng(A))) ),
    file('SEU263+1.p',unknown),
    [] ).

cnf(19,axiom,
    relation_of2_as_subset(dollar_c1,dollar_c2,dollar_c4),
    file('SEU263+1.p',unknown),
    [] ).

cnf(20,axiom,
    subset(relation_rng(dollar_c1),dollar_c3),
    file('SEU263+1.p',unknown),
    [] ).

cnf(28,plain,
    subset(relation_dom(dollar_c1),dollar_c2),
    inference(hyper,[status(thm)],[19,8]),
    [iquote('hyper,19,8')] ).

cnf(30,plain,
    element(dollar_c1,powerset(cartesian_product2(dollar_c2,dollar_c4))),
    inference(hyper,[status(thm)],[19,4]),
    [iquote('hyper,19,4')] ).

cnf(52,plain,
    subset(cartesian_product2(relation_dom(dollar_c1),relation_rng(dollar_c1)),cartesian_product2(dollar_c2,dollar_c3)),
    inference(hyper,[status(thm)],[28,7,20]),
    [iquote('hyper,28,7,20')] ).

cnf(101,plain,
    relation(dollar_c1),
    inference(hyper,[status(thm)],[30,1]),
    [iquote('hyper,30,1')] ).

cnf(102,plain,
    subset(dollar_c1,cartesian_product2(relation_dom(dollar_c1),relation_rng(dollar_c1))),
    inference(hyper,[status(thm)],[101,12]),
    [iquote('hyper,101,12')] ).

cnf(3622,plain,
    subset(dollar_c1,cartesian_product2(dollar_c2,dollar_c3)),
    inference(hyper,[status(thm)],[52,11,102]),
    [iquote('hyper,52,11,102')] ).

cnf(3864,plain,
    relation_of2(dollar_c1,dollar_c2,dollar_c3),
    inference(hyper,[status(thm)],[3622,3]),
    [iquote('hyper,3622,3')] ).

cnf(3865,plain,
    relation_of2_as_subset(dollar_c1,dollar_c2,dollar_c3),
    inference(hyper,[status(thm)],[3864,6]),
    [iquote('hyper,3864,6')] ).

cnf(3866,plain,
    $false,
    inference(binary,[status(thm)],[3865,10]),
    [iquote('binary,3865.1,10.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SEU263+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12  % Command  : otter-tptp-script %s
% 0.13/0.33  % Computer : n024.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Wed Jul 27 07:52:25 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 1.70/1.90  ----- Otter 3.3f, August 2004 -----
% 1.70/1.90  The process was started by sandbox2 on n024.cluster.edu,
% 1.70/1.90  Wed Jul 27 07:52:25 2022
% 1.70/1.90  The command was "./otter".  The process ID is 15093.
% 1.70/1.90  
% 1.70/1.90  set(prolog_style_variables).
% 1.70/1.90  set(auto).
% 1.70/1.90     dependent: set(auto1).
% 1.70/1.90     dependent: set(process_input).
% 1.70/1.90     dependent: clear(print_kept).
% 1.70/1.90     dependent: clear(print_new_demod).
% 1.70/1.90     dependent: clear(print_back_demod).
% 1.70/1.90     dependent: clear(print_back_sub).
% 1.70/1.90     dependent: set(control_memory).
% 1.70/1.90     dependent: assign(max_mem, 12000).
% 1.70/1.90     dependent: assign(pick_given_ratio, 4).
% 1.70/1.90     dependent: assign(stats_level, 1).
% 1.70/1.90     dependent: assign(max_seconds, 10800).
% 1.70/1.90  clear(print_given).
% 1.70/1.90  
% 1.70/1.90  formula_list(usable).
% 1.70/1.90  all A B C (element(C,powerset(cartesian_product2(A,B)))->relation(C)).
% 1.70/1.90  all A B C (relation_of2(C,A,B)<->subset(C,cartesian_product2(A,B))).
% 1.70/1.90  $T.
% 1.70/1.90  $T.
% 1.70/1.90  $T.
% 1.70/1.90  $T.
% 1.70/1.90  $T.
% 1.70/1.90  $T.
% 1.70/1.90  all A B C (relation_of2_as_subset(C,A,B)->element(C,powerset(cartesian_product2(A,B)))).
% 1.70/1.90  all A B exists C relation_of2(C,A,B).
% 1.70/1.90  all A exists B element(B,A).
% 1.70/1.90  all A B exists C relation_of2_as_subset(C,A,B).
% 1.70/1.90  all A B C (relation_of2_as_subset(C,A,B)<->relation_of2(C,A,B)).
% 1.70/1.90  all A B subset(A,A).
% 1.70/1.90  all A B C D (subset(A,B)&subset(C,D)->subset(cartesian_product2(A,C),cartesian_product2(B,D))).
% 1.70/1.90  all A B C (relation_of2_as_subset(C,A,B)->subset(relation_dom(C),A)&subset(relation_rng(C),B)).
% 1.70/1.90  -(all A B C D (relation_of2_as_subset(D,C,A)-> (subset(relation_rng(D),B)->relation_of2_as_subset(D,C,B)))).
% 1.70/1.90  all A B C (subset(A,B)&subset(B,C)->subset(A,C)).
% 1.70/1.90  all A (relation(A)->subset(A,cartesian_product2(relation_dom(A),relation_rng(A)))).
% 1.70/1.90  all A B (element(A,powerset(B))<->subset(A,B)).
% 1.70/1.90  end_of_list.
% 1.70/1.90  
% 1.70/1.90  -------> usable clausifies to:
% 1.70/1.90  
% 1.70/1.90  list(usable).
% 1.70/1.90  0 [] -element(C,powerset(cartesian_product2(A,B)))|relation(C).
% 1.70/1.90  0 [] -relation_of2(C,A,B)|subset(C,cartesian_product2(A,B)).
% 1.70/1.90  0 [] relation_of2(C,A,B)| -subset(C,cartesian_product2(A,B)).
% 1.70/1.90  0 [] $T.
% 1.70/1.90  0 [] $T.
% 1.70/1.90  0 [] $T.
% 1.70/1.90  0 [] $T.
% 1.70/1.90  0 [] $T.
% 1.70/1.90  0 [] $T.
% 1.70/1.90  0 [] -relation_of2_as_subset(C,A,B)|element(C,powerset(cartesian_product2(A,B))).
% 1.70/1.90  0 [] relation_of2($f1(A,B),A,B).
% 1.70/1.90  0 [] element($f2(A),A).
% 1.70/1.90  0 [] relation_of2_as_subset($f3(A,B),A,B).
% 1.70/1.90  0 [] -relation_of2_as_subset(C,A,B)|relation_of2(C,A,B).
% 1.70/1.90  0 [] relation_of2_as_subset(C,A,B)| -relation_of2(C,A,B).
% 1.70/1.90  0 [] subset(A,A).
% 1.70/1.90  0 [] -subset(A,B)| -subset(C,D)|subset(cartesian_product2(A,C),cartesian_product2(B,D)).
% 1.70/1.90  0 [] -relation_of2_as_subset(C,A,B)|subset(relation_dom(C),A).
% 1.70/1.90  0 [] -relation_of2_as_subset(C,A,B)|subset(relation_rng(C),B).
% 1.70/1.90  0 [] relation_of2_as_subset($c1,$c2,$c4).
% 1.70/1.90  0 [] subset(relation_rng($c1),$c3).
% 1.70/1.90  0 [] -relation_of2_as_subset($c1,$c2,$c3).
% 1.70/1.90  0 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.70/1.90  0 [] -relation(A)|subset(A,cartesian_product2(relation_dom(A),relation_rng(A))).
% 1.70/1.90  0 [] -element(A,powerset(B))|subset(A,B).
% 1.70/1.90  0 [] element(A,powerset(B))| -subset(A,B).
% 1.70/1.90  end_of_list.
% 1.70/1.90  
% 1.70/1.90  SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=3.
% 1.70/1.90  
% 1.70/1.90  This is a Horn set without equality.  The strategy will
% 1.70/1.90  be hyperresolution, with satellites in sos and nuclei
% 1.70/1.90  in usable.
% 1.70/1.90  
% 1.70/1.90     dependent: set(hyper_res).
% 1.70/1.90     dependent: clear(order_hyper).
% 1.70/1.90  
% 1.70/1.90  ------------> process usable:
% 1.70/1.90  ** KEPT (pick-wt=8): 1 [] -element(A,powerset(cartesian_product2(B,C)))|relation(A).
% 1.70/1.90  ** KEPT (pick-wt=9): 2 [] -relation_of2(A,B,C)|subset(A,cartesian_product2(B,C)).
% 1.70/1.90  ** KEPT (pick-wt=9): 3 [] relation_of2(A,B,C)| -subset(A,cartesian_product2(B,C)).
% 1.70/1.90  ** KEPT (pick-wt=10): 4 [] -relation_of2_as_subset(A,B,C)|element(A,powerset(cartesian_product2(B,C))).
% 1.70/1.90  ** KEPT (pick-wt=8): 5 [] -relation_of2_as_subset(A,B,C)|relation_of2(A,B,C).
% 1.70/1.90  ** KEPT (pick-wt=8): 6 [] relation_of2_as_subset(A,B,C)| -relation_of2(A,B,C).
% 1.70/1.90  ** KEPT (pick-wt=13): 7 [] -subset(A,B)| -subset(C,D)|subset(cartesian_product2(A,C),cartesian_product2(B,D)).
% 1.70/1.90  ** KEPT (pick-wt=8): 8 [] -relation_of2_as_subset(A,B,C)|subset(relation_dom(A),B).
% 1.70/1.90  ** KEPT (pick-wt=8): 9 [] -relation_of2_as_subset(A,B,C)|subset(relation_rng(A),C).
% 1.70/1.90  ** KEPT (pick-wt=4): 10 [] -relation_of2_as_subset($c1,$c2,$c3).
% 1.70/1.90  ** KEPT (pick-wt=9): 11 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.70/1.90  ** KEPT (pick-wt=9): 12 [] -relation(A)|subset(A,cartesian_product2(relation_dom(A),relation_rng(A))).
% 1.70/1.90  ** KEPT (pick-wt=7): 13 [] -element(A,powerset(B))|subset(A,B).
% 1.75/1.95  ** KEPT (pick-wt=7): 14 [] element(A,powerset(B))| -subset(A,B).
% 1.75/1.95  
% 1.75/1.95  ------------> process sos:
% 1.75/1.95  ** KEPT (pick-wt=6): 15 [] relation_of2($f1(A,B),A,B).
% 1.75/1.95  ** KEPT (pick-wt=4): 16 [] element($f2(A),A).
% 1.75/1.95  ** KEPT (pick-wt=6): 17 [] relation_of2_as_subset($f3(A,B),A,B).
% 1.75/1.95  ** KEPT (pick-wt=3): 18 [] subset(A,A).
% 1.75/1.95  ** KEPT (pick-wt=4): 19 [] relation_of2_as_subset($c1,$c2,$c4).
% 1.75/1.95  ** KEPT (pick-wt=4): 20 [] subset(relation_rng($c1),$c3).
% 1.75/1.95  
% 1.75/1.95  ======= end of input processing =======
% 1.75/1.95  
% 1.75/1.95  =========== start of search ===========
% 1.75/1.95  
% 1.75/1.95  -------- PROOF -------- 
% 1.75/1.95  
% 1.75/1.95  ----> UNIT CONFLICT at   0.05 sec ----> 3866 [binary,3865.1,10.1] $F.
% 1.75/1.95  
% 1.75/1.95  Length of proof is 8.  Level of proof is 6.
% 1.75/1.95  
% 1.75/1.95  ---------------- PROOF ----------------
% 1.75/1.95  % SZS status Theorem
% 1.75/1.95  % SZS output start Refutation
% See solution above
% 1.75/1.95  ------------ end of proof -------------
% 1.75/1.95  
% 1.75/1.95  
% 1.75/1.95  Search stopped by max_proofs option.
% 1.75/1.95  
% 1.75/1.95  
% 1.75/1.95  Search stopped by max_proofs option.
% 1.75/1.95  
% 1.75/1.95  ============ end of search ============
% 1.75/1.95  
% 1.75/1.95  -------------- statistics -------------
% 1.75/1.95  clauses given                 98
% 1.75/1.95  clauses generated           4093
% 1.75/1.95  clauses kept                3865
% 1.75/1.95  clauses forward subsumed     248
% 1.75/1.95  clauses back subsumed          0
% 1.75/1.95  Kbytes malloced             3906
% 1.75/1.95  
% 1.75/1.95  ----------- times (seconds) -----------
% 1.75/1.95  user CPU time          0.05          (0 hr, 0 min, 0 sec)
% 1.75/1.95  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.75/1.95  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.75/1.95  
% 1.75/1.95  That finishes the proof of the theorem.
% 1.75/1.95  
% 1.75/1.95  Process 15093 finished Wed Jul 27 07:52:26 2022
% 1.75/1.95  Otter interrupted
% 1.75/1.95  PROOF FOUND
%------------------------------------------------------------------------------