TSTP Solution File: KLE022+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : KLE022+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n018.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 13:00:31 EDT 2022

% Result   : Theorem 1.70s 1.93s
% Output   : Refutation 1.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   14 (  12 unt;   0 nHn;   9 RR)
%            Number of literals    :   17 (  11 equ;   6 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   2 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   :   12 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(7,axiom,
    ( ~ complement(A,B)
    | addition(B,A) = one ),
    file('KLE022+1.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ test(A)
    | c(A) != B
    | complement(A,B) ),
    file('KLE022+1.p',unknown),
    [] ).

cnf(11,axiom,
    dollar_c2 != addition(multiplication(dollar_c2,dollar_c1),multiplication(dollar_c2,c(dollar_c1))),
    file('KLE022+1.p',unknown),
    [] ).

cnf(12,plain,
    addition(multiplication(dollar_c2,dollar_c1),multiplication(dollar_c2,c(dollar_c1))) != dollar_c2,
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[11])]),
    [iquote('copy,11,flip.1')] ).

cnf(14,axiom,
    A = A,
    file('KLE022+1.p',unknown),
    [] ).

cnf(15,axiom,
    addition(A,B) = addition(B,A),
    file('KLE022+1.p',unknown),
    [] ).

cnf(27,axiom,
    multiplication(A,one) = A,
    file('KLE022+1.p',unknown),
    [] ).

cnf(30,axiom,
    multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
    file('KLE022+1.p',unknown),
    [] ).

cnf(39,axiom,
    test(dollar_c1),
    file('KLE022+1.p',unknown),
    [] ).

cnf(41,plain,
    complement(dollar_c1,c(dollar_c1)),
    inference(hyper,[status(thm)],[39,9,14]),
    [iquote('hyper,39,9,14')] ).

cnf(43,plain,
    addition(c(dollar_c1),dollar_c1) = one,
    inference(hyper,[status(thm)],[41,7]),
    [iquote('hyper,41,7')] ).

cnf(60,plain,
    addition(multiplication(dollar_c2,c(dollar_c1)),multiplication(dollar_c2,dollar_c1)) != dollar_c2,
    inference(para_from,[status(thm),theory(equality)],[15,12]),
    [iquote('para_from,15.1.1,12.1.1')] ).

cnf(144,plain,
    addition(multiplication(A,c(dollar_c1)),multiplication(A,dollar_c1)) = A,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[43,30]),27])]),
    [iquote('para_from,43.1.1,30.1.1.2,demod,27,flip.1')] ).

cnf(146,plain,
    $false,
    inference(binary,[status(thm)],[144,60]),
    [iquote('binary,144.1,60.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : KLE022+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n018.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 06:36:31 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.70/1.92  ----- Otter 3.3f, August 2004 -----
% 1.70/1.92  The process was started by sandbox2 on n018.cluster.edu,
% 1.70/1.92  Wed Jul 27 06:36:31 2022
% 1.70/1.92  The command was "./otter".  The process ID is 17121.
% 1.70/1.92  
% 1.70/1.92  set(prolog_style_variables).
% 1.70/1.92  set(auto).
% 1.70/1.92     dependent: set(auto1).
% 1.70/1.92     dependent: set(process_input).
% 1.70/1.92     dependent: clear(print_kept).
% 1.70/1.92     dependent: clear(print_new_demod).
% 1.70/1.92     dependent: clear(print_back_demod).
% 1.70/1.92     dependent: clear(print_back_sub).
% 1.70/1.92     dependent: set(control_memory).
% 1.70/1.92     dependent: assign(max_mem, 12000).
% 1.70/1.92     dependent: assign(pick_given_ratio, 4).
% 1.70/1.92     dependent: assign(stats_level, 1).
% 1.70/1.92     dependent: assign(max_seconds, 10800).
% 1.70/1.92  clear(print_given).
% 1.70/1.92  
% 1.70/1.92  formula_list(usable).
% 1.70/1.92  all A (A=A).
% 1.70/1.92  all A B (addition(A,B)=addition(B,A)).
% 1.70/1.92  all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.70/1.92  all A (addition(A,zero)=A).
% 1.70/1.92  all A (addition(A,A)=A).
% 1.70/1.92  all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.70/1.92  all A (multiplication(A,one)=A).
% 1.70/1.92  all A (multiplication(one,A)=A).
% 1.70/1.92  all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.70/1.92  all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.70/1.92  all A (multiplication(A,zero)=zero).
% 1.70/1.92  all A (multiplication(zero,A)=zero).
% 1.70/1.92  all A B (le_q(A,B)<->addition(A,B)=B).
% 1.70/1.92  all X0 (test(X0)<-> (exists X1 complement(X1,X0))).
% 1.70/1.92  all X0 X1 (complement(X1,X0)<->multiplication(X0,X1)=zero&multiplication(X1,X0)=zero&addition(X0,X1)=one).
% 1.70/1.92  all X0 X1 (test(X0)-> (c(X0)=X1<->complement(X0,X1))).
% 1.70/1.92  all X0 (-test(X0)->c(X0)=zero).
% 1.70/1.92  -(all X0 X1 (test(X1)->X0=addition(multiplication(X0,X1),multiplication(X0,c(X1))))).
% 1.70/1.92  end_of_list.
% 1.70/1.92  
% 1.70/1.92  -------> usable clausifies to:
% 1.70/1.92  
% 1.70/1.92  list(usable).
% 1.70/1.92  0 [] A=A.
% 1.70/1.92  0 [] addition(A,B)=addition(B,A).
% 1.70/1.92  0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.70/1.92  0 [] addition(A,zero)=A.
% 1.70/1.92  0 [] addition(A,A)=A.
% 1.70/1.92  0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.70/1.92  0 [] multiplication(A,one)=A.
% 1.70/1.92  0 [] multiplication(one,A)=A.
% 1.70/1.92  0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.70/1.92  0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.70/1.92  0 [] multiplication(A,zero)=zero.
% 1.70/1.92  0 [] multiplication(zero,A)=zero.
% 1.70/1.92  0 [] -le_q(A,B)|addition(A,B)=B.
% 1.70/1.92  0 [] le_q(A,B)|addition(A,B)!=B.
% 1.70/1.92  0 [] -test(X0)|complement($f1(X0),X0).
% 1.70/1.92  0 [] test(X0)| -complement(X1,X0).
% 1.70/1.92  0 [] -complement(X1,X0)|multiplication(X0,X1)=zero.
% 1.70/1.92  0 [] -complement(X1,X0)|multiplication(X1,X0)=zero.
% 1.70/1.92  0 [] -complement(X1,X0)|addition(X0,X1)=one.
% 1.70/1.92  0 [] complement(X1,X0)|multiplication(X0,X1)!=zero|multiplication(X1,X0)!=zero|addition(X0,X1)!=one.
% 1.70/1.92  0 [] -test(X0)|c(X0)!=X1|complement(X0,X1).
% 1.70/1.92  0 [] -test(X0)|c(X0)=X1| -complement(X0,X1).
% 1.70/1.92  0 [] test(X0)|c(X0)=zero.
% 1.70/1.92  0 [] test($c1).
% 1.70/1.92  0 [] $c2!=addition(multiplication($c2,$c1),multiplication($c2,c($c1))).
% 1.70/1.92  end_of_list.
% 1.70/1.92  
% 1.70/1.92  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.70/1.92  
% 1.70/1.92  This ia a non-Horn set with equality.  The strategy will be
% 1.70/1.92  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.70/1.92  deletion, with positive clauses in sos and nonpositive
% 1.70/1.92  clauses in usable.
% 1.70/1.92  
% 1.70/1.92     dependent: set(knuth_bendix).
% 1.70/1.92     dependent: set(anl_eq).
% 1.70/1.92     dependent: set(para_from).
% 1.70/1.92     dependent: set(para_into).
% 1.70/1.92     dependent: clear(para_from_right).
% 1.70/1.92     dependent: clear(para_into_right).
% 1.70/1.92     dependent: set(para_from_vars).
% 1.70/1.92     dependent: set(eq_units_both_ways).
% 1.70/1.92     dependent: set(dynamic_demod_all).
% 1.70/1.92     dependent: set(dynamic_demod).
% 1.70/1.92     dependent: set(order_eq).
% 1.70/1.92     dependent: set(back_demod).
% 1.70/1.92     dependent: set(lrpo).
% 1.70/1.92     dependent: set(hyper_res).
% 1.70/1.92     dependent: set(unit_deletion).
% 1.70/1.92     dependent: set(factor).
% 1.70/1.92  
% 1.70/1.92  ------------> process usable:
% 1.70/1.92  ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 1.70/1.92  ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 1.70/1.92  ** KEPT (pick-wt=6): 3 [] -test(A)|complement($f1(A),A).
% 1.70/1.92  ** KEPT (pick-wt=5): 4 [] test(A)| -complement(B,A).
% 1.70/1.92  ** KEPT (pick-wt=8): 5 [] -complement(A,B)|multiplication(B,A)=zero.
% 1.70/1.92  ** KEPT (pick-wt=8): 6 [] -complement(A,B)|multiplication(A,B)=zero.
% 1.70/1.92  ** KEPT (pick-wt=8): 7 [] -complement(A,B)|addition(B,A)=one.
% 1.70/1.92  ** KEPT (pick-wt=18): 8 [] complement(A,B)|multiplication(B,A)!=zero|multiplication(A,B)!=zero|addition(B,A)!=one.
% 1.70/1.93  ** KEPT (pick-wt=9): 9 [] -test(A)|c(A)!=B|complement(A,B).
% 1.70/1.93  ** KEPT (pick-wt=9): 10 [] -test(A)|c(A)=B| -complement(A,B).
% 1.70/1.93  ** KEPT (pick-wt=10): 12 [copy,11,flip.1] addition(multiplication($c2,$c1),multiplication($c2,c($c1)))!=$c2.
% 1.70/1.93  
% 1.70/1.93  ------------> process sos:
% 1.70/1.93  ** KEPT (pick-wt=3): 14 [] A=A.
% 1.70/1.93  ** KEPT (pick-wt=7): 15 [] addition(A,B)=addition(B,A).
% 1.70/1.93  ** KEPT (pick-wt=11): 17 [copy,16,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.70/1.93  ---> New Demodulator: 18 [new_demod,17] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.70/1.93  ** KEPT (pick-wt=5): 19 [] addition(A,zero)=A.
% 1.70/1.93  ---> New Demodulator: 20 [new_demod,19] addition(A,zero)=A.
% 1.70/1.93  ** KEPT (pick-wt=5): 21 [] addition(A,A)=A.
% 1.70/1.93  ---> New Demodulator: 22 [new_demod,21] addition(A,A)=A.
% 1.70/1.93  ** KEPT (pick-wt=11): 24 [copy,23,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.70/1.93  ---> New Demodulator: 25 [new_demod,24] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.70/1.93  ** KEPT (pick-wt=5): 26 [] multiplication(A,one)=A.
% 1.70/1.93  ---> New Demodulator: 27 [new_demod,26] multiplication(A,one)=A.
% 1.70/1.93  ** KEPT (pick-wt=5): 28 [] multiplication(one,A)=A.
% 1.70/1.93  ---> New Demodulator: 29 [new_demod,28] multiplication(one,A)=A.
% 1.70/1.93  ** KEPT (pick-wt=13): 30 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.70/1.93  ---> New Demodulator: 31 [new_demod,30] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.70/1.93  ** KEPT (pick-wt=13): 32 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.70/1.93  ---> New Demodulator: 33 [new_demod,32] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.70/1.93  ** KEPT (pick-wt=5): 34 [] multiplication(A,zero)=zero.
% 1.70/1.93  ---> New Demodulator: 35 [new_demod,34] multiplication(A,zero)=zero.
% 1.70/1.93  ** KEPT (pick-wt=5): 36 [] multiplication(zero,A)=zero.
% 1.70/1.93  ---> New Demodulator: 37 [new_demod,36] multiplication(zero,A)=zero.
% 1.70/1.93  ** KEPT (pick-wt=6): 38 [] test(A)|c(A)=zero.
% 1.70/1.93  ** KEPT (pick-wt=2): 39 [] test($c1).
% 1.70/1.93    Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 1.70/1.93    Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] addition(A,B)=addition(B,A).
% 1.70/1.93  >>>> Starting back demodulation with 18.
% 1.70/1.93  >>>> Starting back demodulation with 20.
% 1.70/1.93  >>>> Starting back demodulation with 22.
% 1.70/1.93      >> back demodulating 13 with 22.
% 1.70/1.93  >>>> Starting back demodulation with 25.
% 1.70/1.93  >>>> Starting back demodulation with 27.
% 1.70/1.93  >>>> Starting back demodulation with 29.
% 1.70/1.93  >>>> Starting back demodulation with 31.
% 1.70/1.93  >>>> Starting back demodulation with 33.
% 1.70/1.93  >>>> Starting back demodulation with 35.
% 1.70/1.93  >>>> Starting back demodulation with 37.
% 1.70/1.93  
% 1.70/1.93  ======= end of input processing =======
% 1.70/1.93  
% 1.70/1.93  =========== start of search ===========
% 1.70/1.93  
% 1.70/1.93  -------- PROOF -------- 
% 1.70/1.93  
% 1.70/1.93  ----> UNIT CONFLICT at   0.01 sec ----> 146 [binary,144.1,60.1] $F.
% 1.70/1.93  
% 1.70/1.93  Length of proof is 5.  Level of proof is 3.
% 1.70/1.93  
% 1.70/1.93  ---------------- PROOF ----------------
% 1.70/1.93  % SZS status Theorem
% 1.70/1.93  % SZS output start Refutation
% See solution above
% 1.70/1.93  ------------ end of proof -------------
% 1.70/1.93  
% 1.70/1.93  
% 1.70/1.93  Search stopped by max_proofs option.
% 1.70/1.93  
% 1.70/1.93  
% 1.70/1.93  Search stopped by max_proofs option.
% 1.70/1.93  
% 1.70/1.93  ============ end of search ============
% 1.70/1.93  
% 1.70/1.93  -------------- statistics -------------
% 1.70/1.93  clauses given                 33
% 1.70/1.93  clauses generated            279
% 1.70/1.93  clauses kept                 115
% 1.70/1.93  clauses forward subsumed     198
% 1.70/1.93  clauses back subsumed          1
% 1.70/1.93  Kbytes malloced             1953
% 1.70/1.93  
% 1.70/1.93  ----------- times (seconds) -----------
% 1.70/1.93  user CPU time          0.01          (0 hr, 0 min, 0 sec)
% 1.70/1.93  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.70/1.93  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.70/1.93  
% 1.70/1.93  That finishes the proof of the theorem.
% 1.70/1.93  
% 1.70/1.93  Process 17121 finished Wed Jul 27 06:36:33 2022
% 1.70/1.93  Otter interrupted
% 1.70/1.93  PROOF FOUND
%------------------------------------------------------------------------------