TSTP Solution File: SET954+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SET954+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n021.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 13:14:35 EDT 2022

% Result   : Theorem 1.66s 1.84s
% Output   : Refutation 1.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    9 (   6 unt;   0 nHn;   9 RR)
%            Number of literals    :   13 (   0 equ;   5 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   12 (   4 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    ( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
    | in(A,C) ),
    file('SET954+1.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
    | in(B,D) ),
    file('SET954+1.p',unknown),
    [] ).

cnf(5,axiom,
    ( in(ordered_pair(A,B),cartesian_product2(C,D))
    | ~ in(A,C)
    | ~ in(B,D) ),
    file('SET954+1.p',unknown),
    [] ).

cnf(7,axiom,
    ~ in(ordered_pair(dollar_c5,dollar_c6),cartesian_product2(dollar_c3,dollar_c4)),
    file('SET954+1.p',unknown),
    [] ).

cnf(14,axiom,
    in(ordered_pair(dollar_c6,dollar_c5),cartesian_product2(dollar_c4,dollar_c3)),
    file('SET954+1.p',unknown),
    [] ).

cnf(16,plain,
    in(dollar_c5,dollar_c3),
    inference(hyper,[status(thm)],[14,4]),
    [iquote('hyper,14,4')] ).

cnf(17,plain,
    in(dollar_c6,dollar_c4),
    inference(hyper,[status(thm)],[14,3]),
    [iquote('hyper,14,3')] ).

cnf(28,plain,
    in(ordered_pair(dollar_c5,dollar_c6),cartesian_product2(dollar_c3,dollar_c4)),
    inference(hyper,[status(thm)],[17,5,16]),
    [iquote('hyper,17,5,16')] ).

cnf(29,plain,
    $false,
    inference(binary,[status(thm)],[28,7]),
    [iquote('binary,28.1,7.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SET954+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.14  % Command  : otter-tptp-script %s
% 0.13/0.35  % Computer : n021.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Wed Jul 27 10:21:23 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 1.66/1.84  ----- Otter 3.3f, August 2004 -----
% 1.66/1.84  The process was started by sandbox on n021.cluster.edu,
% 1.66/1.84  Wed Jul 27 10:21:23 2022
% 1.66/1.84  The command was "./otter".  The process ID is 12576.
% 1.66/1.84  
% 1.66/1.84  set(prolog_style_variables).
% 1.66/1.84  set(auto).
% 1.66/1.84     dependent: set(auto1).
% 1.66/1.84     dependent: set(process_input).
% 1.66/1.84     dependent: clear(print_kept).
% 1.66/1.84     dependent: clear(print_new_demod).
% 1.66/1.84     dependent: clear(print_back_demod).
% 1.66/1.84     dependent: clear(print_back_sub).
% 1.66/1.84     dependent: set(control_memory).
% 1.66/1.84     dependent: assign(max_mem, 12000).
% 1.66/1.84     dependent: assign(pick_given_ratio, 4).
% 1.66/1.84     dependent: assign(stats_level, 1).
% 1.66/1.84     dependent: assign(max_seconds, 10800).
% 1.66/1.84  clear(print_given).
% 1.66/1.84  
% 1.66/1.84  formula_list(usable).
% 1.66/1.84  all A (A=A).
% 1.66/1.84  all A B (in(A,B)-> -in(B,A)).
% 1.66/1.84  all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.66/1.84  all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 1.66/1.84  all A B (-empty(ordered_pair(A,B))).
% 1.66/1.84  all A B C D (in(ordered_pair(A,B),cartesian_product2(C,D))<->in(A,C)&in(B,D)).
% 1.66/1.84  exists A empty(A).
% 1.66/1.84  exists A (-empty(A)).
% 1.66/1.84  -(all A B C D (in(ordered_pair(A,B),cartesian_product2(C,D))->in(ordered_pair(B,A),cartesian_product2(D,C)))).
% 1.66/1.84  end_of_list.
% 1.66/1.84  
% 1.66/1.84  -------> usable clausifies to:
% 1.66/1.84  
% 1.66/1.84  list(usable).
% 1.66/1.84  0 [] A=A.
% 1.66/1.84  0 [] -in(A,B)| -in(B,A).
% 1.66/1.84  0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.66/1.84  0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 1.66/1.84  0 [] -empty(ordered_pair(A,B)).
% 1.66/1.84  0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 1.66/1.84  0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 1.66/1.84  0 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 1.66/1.84  0 [] empty($c1).
% 1.66/1.84  0 [] -empty($c2).
% 1.66/1.84  0 [] in(ordered_pair($c6,$c5),cartesian_product2($c4,$c3)).
% 1.66/1.84  0 [] -in(ordered_pair($c5,$c6),cartesian_product2($c3,$c4)).
% 1.66/1.84  end_of_list.
% 1.66/1.84  
% 1.66/1.84  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 1.66/1.84  
% 1.66/1.84  This is a Horn set with equality.  The strategy will be
% 1.66/1.84  Knuth-Bendix and hyper_res, with positive clauses in
% 1.66/1.84  sos and nonpositive clauses in usable.
% 1.66/1.84  
% 1.66/1.84     dependent: set(knuth_bendix).
% 1.66/1.84     dependent: set(anl_eq).
% 1.66/1.84     dependent: set(para_from).
% 1.66/1.84     dependent: set(para_into).
% 1.66/1.84     dependent: clear(para_from_right).
% 1.66/1.84     dependent: clear(para_into_right).
% 1.66/1.84     dependent: set(para_from_vars).
% 1.66/1.84     dependent: set(eq_units_both_ways).
% 1.66/1.84     dependent: set(dynamic_demod_all).
% 1.66/1.84     dependent: set(dynamic_demod).
% 1.66/1.84     dependent: set(order_eq).
% 1.66/1.84     dependent: set(back_demod).
% 1.66/1.84     dependent: set(lrpo).
% 1.66/1.84     dependent: set(hyper_res).
% 1.66/1.84     dependent: clear(order_hyper).
% 1.66/1.84  
% 1.66/1.84  ------------> process usable:
% 1.66/1.84  ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.66/1.84  ** KEPT (pick-wt=4): 2 [] -empty(ordered_pair(A,B)).
% 1.66/1.84  ** KEPT (pick-wt=10): 3 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 1.66/1.84  ** KEPT (pick-wt=10): 4 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 1.66/1.84  ** KEPT (pick-wt=13): 5 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 1.66/1.84  ** KEPT (pick-wt=2): 6 [] -empty($c2).
% 1.66/1.84  ** KEPT (pick-wt=7): 7 [] -in(ordered_pair($c5,$c6),cartesian_product2($c3,$c4)).
% 1.66/1.84  
% 1.66/1.84  ------------> process sos:
% 1.66/1.84  ** KEPT (pick-wt=3): 8 [] A=A.
% 1.66/1.84  ** KEPT (pick-wt=7): 9 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.66/1.84  ** KEPT (pick-wt=10): 11 [copy,10,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.66/1.84  ---> New Demodulator: 12 [new_demod,11] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.66/1.84  ** KEPT (pick-wt=2): 13 [] empty($c1).
% 1.66/1.84  ** KEPT (pick-wt=7): 14 [] in(ordered_pair($c6,$c5),cartesian_product2($c4,$c3)).
% 1.66/1.84    Following clause subsumed by 8 during input processing: 0 [copy,8,flip.1] A=A.
% 1.66/1.84    Following clause subsumed by 9 during input processing: 0 [copy,9,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.66/1.84  >>>> Starting back demodulation with 12.
% 1.66/1.84  
% 1.66/1.84  ======= end of input processing =======
% 1.66/1.84  
% 1.66/1.84  =========== start of search ===========
% 1.66/1.84  
% 1.66/1.84  -------- PROOF -------- 
% 1.66/1.84  
% 1.66/1.84  ----> UNIT CONFLICT at   0.00 sec ----> 29 [binary,28.1,7.1] $F.
% 1.66/1.84  
% 1.66/1.84  Length of proof is 3.  Level of proof is 2.
% 1.66/1.84  
% 1.66/1.84  ---------------- PROOF ----------------
% 1.66/1.84  % SZS status Theorem
% 1.66/1.84  % SZS output start Refutation
% See solution above
% 1.66/1.84  ------------ end of proof -------------
% 1.66/1.84  
% 1.66/1.84  
% 1.66/1.84  Search stopped by max_proofs option.
% 1.66/1.84  
% 1.66/1.84  
% 1.66/1.84  Search stopped by max_proofs option.
% 1.66/1.84  
% 1.66/1.84  ============ end of search ============
% 1.66/1.84  
% 1.66/1.84  -------------- statistics -------------
% 1.66/1.84  clauses given                  7
% 1.66/1.84  clauses generated             19
% 1.66/1.84  clauses kept                  23
% 1.66/1.84  clauses forward subsumed      10
% 1.66/1.84  clauses back subsumed          0
% 1.66/1.84  Kbytes malloced              976
% 1.66/1.84  
% 1.66/1.84  ----------- times (seconds) -----------
% 1.66/1.84  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.66/1.84  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.66/1.84  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.66/1.84  
% 1.66/1.84  That finishes the proof of the theorem.
% 1.66/1.84  
% 1.66/1.84  Process 12576 finished Wed Jul 27 10:21:24 2022
% 1.66/1.84  Otter interrupted
% 1.66/1.84  PROOF FOUND
%------------------------------------------------------------------------------