TSTP Solution File: SEU264+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SEU264+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n015.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 1.91s 2.10s
% Output   : Refutation 1.91s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   10 (   7 unt;   0 nHn;  10 RR)
%            Number of literals    :   15 (   0 equ;   6 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-1 aty)
%            Number of variables   :   10 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(6,axiom,
    ( ~ relation_of2_as_subset(A,B,C)
    | subset(relation_rng(A),C) ),
    file('SEU264+1.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ relation_of2_as_subset(A,B,C)
    | ~ subset(relation_rng(A),D)
    | relation_of2_as_subset(A,B,D) ),
    file('SEU264+1.p',unknown),
    [] ).

cnf(8,axiom,
    ~ relation_of2_as_subset(dollar_c1,dollar_c2,dollar_c3),
    file('SEU264+1.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ subset(A,B)
    | ~ subset(B,C)
    | subset(A,C) ),
    file('SEU264+1.p',unknown),
    [] ).

cnf(16,axiom,
    relation_of2_as_subset(dollar_c1,dollar_c2,dollar_c4),
    file('SEU264+1.p',unknown),
    [] ).

cnf(17,axiom,
    subset(dollar_c4,dollar_c3),
    file('SEU264+1.p',unknown),
    [] ).

cnf(24,plain,
    subset(relation_rng(dollar_c1),dollar_c4),
    inference(hyper,[status(thm)],[16,6]),
    [iquote('hyper,16,6')] ).

cnf(35,plain,
    subset(relation_rng(dollar_c1),dollar_c3),
    inference(hyper,[status(thm)],[24,9,17]),
    [iquote('hyper,24,9,17')] ).

cnf(42,plain,
    relation_of2_as_subset(dollar_c1,dollar_c2,dollar_c3),
    inference(hyper,[status(thm)],[35,7,16]),
    [iquote('hyper,35,7,16')] ).

cnf(43,plain,
    $false,
    inference(binary,[status(thm)],[42,8]),
    [iquote('binary,42.1,8.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SEU264+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n015.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 07:58:11 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.91/2.10  ----- Otter 3.3f, August 2004 -----
% 1.91/2.10  The process was started by sandbox on n015.cluster.edu,
% 1.91/2.10  Wed Jul 27 07:58:11 2022
% 1.91/2.10  The command was "./otter".  The process ID is 5049.
% 1.91/2.10  
% 1.91/2.10  set(prolog_style_variables).
% 1.91/2.10  set(auto).
% 1.91/2.10     dependent: set(auto1).
% 1.91/2.10     dependent: set(process_input).
% 1.91/2.10     dependent: clear(print_kept).
% 1.91/2.10     dependent: clear(print_new_demod).
% 1.91/2.10     dependent: clear(print_back_demod).
% 1.91/2.10     dependent: clear(print_back_sub).
% 1.91/2.10     dependent: set(control_memory).
% 1.91/2.10     dependent: assign(max_mem, 12000).
% 1.91/2.10     dependent: assign(pick_given_ratio, 4).
% 1.91/2.10     dependent: assign(stats_level, 1).
% 1.91/2.10     dependent: assign(max_seconds, 10800).
% 1.91/2.10  clear(print_given).
% 1.91/2.10  
% 1.91/2.10  formula_list(usable).
% 1.91/2.10  all A B C (element(C,powerset(cartesian_product2(A,B)))->relation(C)).
% 1.91/2.10  $T.
% 1.91/2.10  $T.
% 1.91/2.10  $T.
% 1.91/2.10  $T.
% 1.91/2.10  $T.
% 1.91/2.10  $T.
% 1.91/2.10  all A B C (relation_of2_as_subset(C,A,B)->element(C,powerset(cartesian_product2(A,B)))).
% 1.91/2.10  all A B exists C relation_of2(C,A,B).
% 1.91/2.10  all A exists B element(B,A).
% 1.91/2.10  all A B exists C relation_of2_as_subset(C,A,B).
% 1.91/2.10  all A B C (relation_of2_as_subset(C,A,B)<->relation_of2(C,A,B)).
% 1.91/2.10  all A B subset(A,A).
% 1.91/2.10  all A B C (relation_of2_as_subset(C,A,B)->subset(relation_dom(C),A)&subset(relation_rng(C),B)).
% 1.91/2.10  all A B C D (relation_of2_as_subset(D,C,A)-> (subset(relation_rng(D),B)->relation_of2_as_subset(D,C,B))).
% 1.91/2.10  -(all A B C D (relation_of2_as_subset(D,C,A)-> (subset(A,B)->relation_of2_as_subset(D,C,B)))).
% 1.91/2.10  all A B C (subset(A,B)&subset(B,C)->subset(A,C)).
% 1.91/2.10  all A B (element(A,powerset(B))<->subset(A,B)).
% 1.91/2.10  end_of_list.
% 1.91/2.10  
% 1.91/2.10  -------> usable clausifies to:
% 1.91/2.10  
% 1.91/2.10  list(usable).
% 1.91/2.10  0 [] -element(C,powerset(cartesian_product2(A,B)))|relation(C).
% 1.91/2.10  0 [] $T.
% 1.91/2.10  0 [] $T.
% 1.91/2.10  0 [] $T.
% 1.91/2.10  0 [] $T.
% 1.91/2.10  0 [] $T.
% 1.91/2.10  0 [] $T.
% 1.91/2.10  0 [] -relation_of2_as_subset(C,A,B)|element(C,powerset(cartesian_product2(A,B))).
% 1.91/2.10  0 [] relation_of2($f1(A,B),A,B).
% 1.91/2.10  0 [] element($f2(A),A).
% 1.91/2.10  0 [] relation_of2_as_subset($f3(A,B),A,B).
% 1.91/2.10  0 [] -relation_of2_as_subset(C,A,B)|relation_of2(C,A,B).
% 1.91/2.10  0 [] relation_of2_as_subset(C,A,B)| -relation_of2(C,A,B).
% 1.91/2.10  0 [] subset(A,A).
% 1.91/2.10  0 [] -relation_of2_as_subset(C,A,B)|subset(relation_dom(C),A).
% 1.91/2.10  0 [] -relation_of2_as_subset(C,A,B)|subset(relation_rng(C),B).
% 1.91/2.10  0 [] -relation_of2_as_subset(D,C,A)| -subset(relation_rng(D),B)|relation_of2_as_subset(D,C,B).
% 1.91/2.10  0 [] relation_of2_as_subset($c1,$c2,$c4).
% 1.91/2.10  0 [] subset($c4,$c3).
% 1.91/2.10  0 [] -relation_of2_as_subset($c1,$c2,$c3).
% 1.91/2.10  0 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.91/2.10  0 [] -element(A,powerset(B))|subset(A,B).
% 1.91/2.10  0 [] element(A,powerset(B))| -subset(A,B).
% 1.91/2.10  end_of_list.
% 1.91/2.10  
% 1.91/2.10  SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=3.
% 1.91/2.10  
% 1.91/2.10  This is a Horn set without equality.  The strategy will
% 1.91/2.10  be hyperresolution, with satellites in sos and nuclei
% 1.91/2.10  in usable.
% 1.91/2.10  
% 1.91/2.10     dependent: set(hyper_res).
% 1.91/2.10     dependent: clear(order_hyper).
% 1.91/2.10  
% 1.91/2.10  ------------> process usable:
% 1.91/2.10  ** KEPT (pick-wt=8): 1 [] -element(A,powerset(cartesian_product2(B,C)))|relation(A).
% 1.91/2.10  ** KEPT (pick-wt=10): 2 [] -relation_of2_as_subset(A,B,C)|element(A,powerset(cartesian_product2(B,C))).
% 1.91/2.10  ** KEPT (pick-wt=8): 3 [] -relation_of2_as_subset(A,B,C)|relation_of2(A,B,C).
% 1.91/2.10  ** KEPT (pick-wt=8): 4 [] relation_of2_as_subset(A,B,C)| -relation_of2(A,B,C).
% 1.91/2.10  ** KEPT (pick-wt=8): 5 [] -relation_of2_as_subset(A,B,C)|subset(relation_dom(A),B).
% 1.91/2.10  ** KEPT (pick-wt=8): 6 [] -relation_of2_as_subset(A,B,C)|subset(relation_rng(A),C).
% 1.91/2.10  ** KEPT (pick-wt=12): 7 [] -relation_of2_as_subset(A,B,C)| -subset(relation_rng(A),D)|relation_of2_as_subset(A,B,D).
% 1.91/2.10  ** KEPT (pick-wt=4): 8 [] -relation_of2_as_subset($c1,$c2,$c3).
% 1.91/2.10  ** KEPT (pick-wt=9): 9 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.91/2.10  ** KEPT (pick-wt=7): 10 [] -element(A,powerset(B))|subset(A,B).
% 1.91/2.10  ** KEPT (pick-wt=7): 11 [] element(A,powerset(B))| -subset(A,B).
% 1.91/2.10  
% 1.91/2.10  ------------> process sos:
% 1.91/2.10  ** KEPT (pick-wt=6): 12 [] relation_of2($f1(A,B),A,B).
% 1.91/2.10  ** KEPT (pick-wt=4): 13 [] element($f2(A),A).
% 1.91/2.10  ** KEPT (pick-wt=6): 14 [] relation_of2_as_subset($f3(A,B),A,B).
% 1.91/2.10  ** KEPT (pick-wt=3): 15 [] subset(A,A).
% 1.91/2.10  ** KEPT (pick-wt=4): 16 [] relation_of2_as_subset($c1,$c2,$c4).
% 1.91/2.10  ** KEPT (pick-wt=3): 17 [] subset($c4,$c3).
% 1.91/2.10  
% 1.91/2.10  ======= end of input processing =======
% 1.91/2.10  
% 1.91/2.10  =========== start of search ===========
% 1.91/2.10  
% 1.91/2.10  -------- PROOF -------- 
% 1.91/2.10  
% 1.91/2.10  ----> UNIT CONFLICT at   0.00 sec ----> 43 [binary,42.1,8.1] $F.
% 1.91/2.10  
% 1.91/2.10  Length of proof is 3.  Level of proof is 3.
% 1.91/2.10  
% 1.91/2.10  ---------------- PROOF ----------------
% 1.91/2.10  % SZS status Theorem
% 1.91/2.10  % SZS output start Refutation
% See solution above
% 1.91/2.10  ------------ end of proof -------------
% 1.91/2.10  
% 1.91/2.10  
% 1.91/2.10  Search stopped by max_proofs option.
% 1.91/2.10  
% 1.91/2.10  
% 1.91/2.10  Search stopped by max_proofs option.
% 1.91/2.10  
% 1.91/2.10  ============ end of search ============
% 1.91/2.10  
% 1.91/2.10  -------------- statistics -------------
% 1.91/2.10  clauses given                 14
% 1.91/2.10  clauses generated             40
% 1.91/2.10  clauses kept                  42
% 1.91/2.10  clauses forward subsumed      15
% 1.91/2.10  clauses back subsumed          0
% 1.91/2.10  Kbytes malloced              976
% 1.91/2.10  
% 1.91/2.10  ----------- times (seconds) -----------
% 1.91/2.10  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.91/2.10  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.91/2.10  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.91/2.10  
% 1.91/2.10  That finishes the proof of the theorem.
% 1.91/2.10  
% 1.91/2.10  Process 5049 finished Wed Jul 27 07:58:13 2022
% 1.91/2.10  Otter interrupted
% 1.91/2.10  PROOF FOUND
%------------------------------------------------------------------------------