TSTP Solution File: KLE001+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : KLE001+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n023.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 13:00:26 EDT 2022

% Result   : Theorem 2.02s 2.18s
% Output   : Refutation 2.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    3
% Syntax   : Number of clauses     :    5 (   4 unt;   0 nHn;   3 RR)
%            Number of literals    :    6 (   2 equ;   2 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :    4 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    ( le_q(A,B)
    | addition(A,B) != B ),
    file('KLE001+1.p',unknown),
    [] ).

cnf(3,axiom,
    ~ le_q(addition(dollar_c3,dollar_c1),addition(dollar_c3,dollar_c1)),
    file('KLE001+1.p',unknown),
    [] ).

cnf(11,axiom,
    addition(A,A) = A,
    file('KLE001+1.p',unknown),
    [] ).

cnf(35,plain,
    le_q(A,A),
    inference(hyper,[status(thm)],[11,2]),
    [iquote('hyper,11,2')] ).

cnf(36,plain,
    $false,
    inference(binary,[status(thm)],[35,3]),
    [iquote('binary,35.1,3.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : KLE001+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13  % Command  : otter-tptp-script %s
% 0.13/0.34  % Computer : n023.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Wed Jul 27 06:53:18 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 2.02/2.18  ----- Otter 3.3f, August 2004 -----
% 2.02/2.18  The process was started by sandbox on n023.cluster.edu,
% 2.02/2.18  Wed Jul 27 06:53:18 2022
% 2.02/2.18  The command was "./otter".  The process ID is 13445.
% 2.02/2.18  
% 2.02/2.18  set(prolog_style_variables).
% 2.02/2.18  set(auto).
% 2.02/2.18     dependent: set(auto1).
% 2.02/2.18     dependent: set(process_input).
% 2.02/2.18     dependent: clear(print_kept).
% 2.02/2.18     dependent: clear(print_new_demod).
% 2.02/2.18     dependent: clear(print_back_demod).
% 2.02/2.18     dependent: clear(print_back_sub).
% 2.02/2.18     dependent: set(control_memory).
% 2.02/2.18     dependent: assign(max_mem, 12000).
% 2.02/2.18     dependent: assign(pick_given_ratio, 4).
% 2.02/2.18     dependent: assign(stats_level, 1).
% 2.02/2.18     dependent: assign(max_seconds, 10800).
% 2.02/2.18  clear(print_given).
% 2.02/2.18  
% 2.02/2.18  formula_list(usable).
% 2.02/2.18  all A (A=A).
% 2.02/2.18  all A B (addition(A,B)=addition(B,A)).
% 2.02/2.18  all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 2.02/2.18  all A (addition(A,zero)=A).
% 2.02/2.18  all A (addition(A,A)=A).
% 2.02/2.18  all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 2.02/2.18  all A (multiplication(A,one)=A).
% 2.02/2.18  all A (multiplication(one,A)=A).
% 2.02/2.18  all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 2.02/2.18  all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 2.02/2.18  all A (multiplication(A,zero)=zero).
% 2.02/2.18  all A (multiplication(zero,A)=zero).
% 2.02/2.18  all A B (le_q(A,B)<->addition(A,B)=B).
% 2.02/2.18  -(all X0 X1 X2 (le_q(X0,X1)->le_q(addition(X0,X2),addition(X0,X2)))).
% 2.02/2.18  end_of_list.
% 2.02/2.18  
% 2.02/2.18  -------> usable clausifies to:
% 2.02/2.18  
% 2.02/2.18  list(usable).
% 2.02/2.18  0 [] A=A.
% 2.02/2.18  0 [] addition(A,B)=addition(B,A).
% 2.02/2.18  0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 2.02/2.18  0 [] addition(A,zero)=A.
% 2.02/2.18  0 [] addition(A,A)=A.
% 2.02/2.18  0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 2.02/2.18  0 [] multiplication(A,one)=A.
% 2.02/2.18  0 [] multiplication(one,A)=A.
% 2.02/2.18  0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 2.02/2.18  0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 2.02/2.18  0 [] multiplication(A,zero)=zero.
% 2.02/2.18  0 [] multiplication(zero,A)=zero.
% 2.02/2.18  0 [] -le_q(A,B)|addition(A,B)=B.
% 2.02/2.18  0 [] le_q(A,B)|addition(A,B)!=B.
% 2.02/2.18  0 [] le_q($c3,$c2).
% 2.02/2.18  0 [] -le_q(addition($c3,$c1),addition($c3,$c1)).
% 2.02/2.18  end_of_list.
% 2.02/2.18  
% 2.02/2.18  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 2.02/2.18  
% 2.02/2.18  This is a Horn set with equality.  The strategy will be
% 2.02/2.18  Knuth-Bendix and hyper_res, with positive clauses in
% 2.02/2.18  sos and nonpositive clauses in usable.
% 2.02/2.18  
% 2.02/2.18     dependent: set(knuth_bendix).
% 2.02/2.18     dependent: set(anl_eq).
% 2.02/2.18     dependent: set(para_from).
% 2.02/2.18     dependent: set(para_into).
% 2.02/2.18     dependent: clear(para_from_right).
% 2.02/2.18     dependent: clear(para_into_right).
% 2.02/2.18     dependent: set(para_from_vars).
% 2.02/2.18     dependent: set(eq_units_both_ways).
% 2.02/2.18     dependent: set(dynamic_demod_all).
% 2.02/2.18     dependent: set(dynamic_demod).
% 2.02/2.18     dependent: set(order_eq).
% 2.02/2.18     dependent: set(back_demod).
% 2.02/2.18     dependent: set(lrpo).
% 2.02/2.18     dependent: set(hyper_res).
% 2.02/2.18     dependent: clear(order_hyper).
% 2.02/2.18  
% 2.02/2.18  ------------> process usable:
% 2.02/2.18  ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 2.02/2.18  ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 2.02/2.18  ** KEPT (pick-wt=7): 3 [] -le_q(addition($c3,$c1),addition($c3,$c1)).
% 2.02/2.18  
% 2.02/2.18  ------------> process sos:
% 2.02/2.18  ** KEPT (pick-wt=3): 4 [] A=A.
% 2.02/2.18  ** KEPT (pick-wt=7): 5 [] addition(A,B)=addition(B,A).
% 2.02/2.18  ** KEPT (pick-wt=11): 7 [copy,6,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 2.02/2.18  ---> New Demodulator: 8 [new_demod,7] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 2.02/2.18  ** KEPT (pick-wt=5): 9 [] addition(A,zero)=A.
% 2.02/2.18  ---> New Demodulator: 10 [new_demod,9] addition(A,zero)=A.
% 2.02/2.18  ** KEPT (pick-wt=5): 11 [] addition(A,A)=A.
% 2.02/2.18  ---> New Demodulator: 12 [new_demod,11] addition(A,A)=A.
% 2.02/2.18  ** KEPT (pick-wt=11): 14 [copy,13,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 2.02/2.18  ---> New Demodulator: 15 [new_demod,14] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 2.02/2.18  ** KEPT (pick-wt=5): 16 [] multiplication(A,one)=A.
% 2.02/2.18  ---> New Demodulator: 17 [new_demod,16] multiplication(A,one)=A.
% 2.02/2.18  ** KEPT (pick-wt=5): 18 [] multiplication(one,A)=A.
% 2.02/2.18  ---> New Demodulator: 19 [new_demod,18] multiplication(one,A)=A.
% 2.02/2.18  ** KEPT (pick-wt=13): 20 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 2.02/2.18  ---> New Demodulator: 21 [new_demod,20] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 2.02/2.18  ** KEPT (pick-wt=13): 22 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 2.02/2.18  ---> New Demodulator: 23 [new_demod,22] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 2.02/2.18  ** KEPT (pick-wt=5): 24 [] multiplication(A,zero)=zero.
% 2.02/2.18  ---> New Demodulator: 25 [new_demod,24] multiplication(A,zero)=zero.
% 2.02/2.18  ** KEPT (pick-wt=5): 26 [] multiplication(zero,A)=zero.
% 2.02/2.18  ---> New Demodulator: 27 [new_demod,26] multiplication(zero,A)=zero.
% 2.02/2.18  ** KEPT (pick-wt=3): 28 [] le_q($c3,$c2).
% 2.02/2.18    Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] A=A.
% 2.02/2.18    Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] addition(A,B)=addition(B,A).
% 2.02/2.18  >>>> Starting back demodulation with 8.
% 2.02/2.18  >>>> Starting back demodulation with 10.
% 2.02/2.18  >>>> Starting back demodulation with 12.
% 2.02/2.18  >>>> Starting back demodulation with 15.
% 2.02/2.18  >>>> Starting back demodulation with 17.
% 2.02/2.18  >>>> Starting back demodulation with 19.
% 2.02/2.18  >>>> Starting back demodulation with 21.
% 2.02/2.18  >>>> Starting back demodulation with 23.
% 2.02/2.18  >>>> Starting back demodulation with 25.
% 2.02/2.18  >>>> Starting back demodulation with 27.
% 2.02/2.18  
% 2.02/2.18  ======= end of input processing =======
% 2.02/2.18  
% 2.02/2.18  =========== start of search ===========
% 2.02/2.18  
% 2.02/2.18  -------- PROOF -------- 
% 2.02/2.18  
% 2.02/2.18  ----> UNIT CONFLICT at   0.00 sec ----> 36 [binary,35.1,3.1] $F.
% 2.02/2.18  
% 2.02/2.18  Length of proof is 1.  Level of proof is 1.
% 2.02/2.18  
% 2.02/2.18  ---------------- PROOF ----------------
% 2.02/2.18  % SZS status Theorem
% 2.02/2.18  % SZS output start Refutation
% See solution above
% 2.02/2.18  ------------ end of proof -------------
% 2.02/2.18  
% 2.02/2.18  
% 2.02/2.18  Search stopped by max_proofs option.
% 2.02/2.18  
% 2.02/2.18  
% 2.02/2.18  Search stopped by max_proofs option.
% 2.02/2.18  
% 2.02/2.18  ============ end of search ============
% 2.02/2.18  
% 2.02/2.18  -------------- statistics -------------
% 2.02/2.18  clauses given                  5
% 2.02/2.18  clauses generated              9
% 2.02/2.18  clauses kept                  22
% 2.02/2.18  clauses forward subsumed       5
% 2.02/2.18  clauses back subsumed          0
% 2.02/2.18  Kbytes malloced              976
% 2.02/2.18  
% 2.02/2.18  ----------- times (seconds) -----------
% 2.02/2.18  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 2.02/2.18  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 2.02/2.18  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 2.02/2.18  
% 2.02/2.18  That finishes the proof of the theorem.
% 2.02/2.18  
% 2.02/2.18  Process 13445 finished Wed Jul 27 06:53:20 2022
% 2.02/2.18  Otter interrupted
% 2.02/2.18  PROOF FOUND
%------------------------------------------------------------------------------