TSTP Solution File: LCL161-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : LCL161-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n019.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 13:03:43 EDT 2022

% Result   : Unsatisfiable 1.75s 1.94s
% Output   : Refutation 1.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   17 (  17 unt;   0 nHn;   2 RR)
%            Number of literals    :   17 (  16 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   21 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    implies(truth,x) != x,
    file('LCL161-1.p',unknown),
    [] ).

cnf(5,axiom,
    xor(A,falsehood) = A,
    file('LCL161-1.p',unknown),
    [] ).

cnf(7,axiom,
    xor(A,A) = falsehood,
    file('LCL161-1.p',unknown),
    [] ).

cnf(10,axiom,
    and_star(A,truth) = A,
    file('LCL161-1.p',unknown),
    [] ).

cnf(15,axiom,
    xor(A,xor(truth,B)) = xor(xor(A,truth),B),
    file('LCL161-1.p',unknown),
    [] ).

cnf(16,plain,
    xor(xor(A,truth),B) = xor(A,xor(truth,B)),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
    [iquote('copy,15,flip.1')] ).

cnf(19,axiom,
    xor(A,B) = xor(B,A),
    file('LCL161-1.p',unknown),
    [] ).

cnf(22,axiom,
    and_star(A,B) = and_star(B,A),
    file('LCL161-1.p',unknown),
    [] ).

cnf(23,axiom,
    implies(A,B) = xor(truth,and_star(A,xor(truth,B))),
    file('LCL161-1.p',unknown),
    [] ).

cnf(24,plain,
    xor(truth,and_star(A,xor(truth,B))) = implies(A,B),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[23])]),
    [iquote('copy,23,flip.1')] ).

cnf(27,plain,
    xor(falsehood,A) = A,
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,5])]),
    [iquote('para_into,19.1.1,5.1.1,flip.1')] ).

cnf(34,plain,
    and_star(truth,A) = A,
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[22,10])]),
    [iquote('para_into,22.1.1,9.1.1,flip.1')] ).

cnf(40,plain,
    xor(truth,xor(truth,A)) = A,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[16,7]),27])]),
    [iquote('para_into,16.1.1.1,7.1.1,demod,27,flip.1')] ).

cnf(84,plain,
    xor(truth,A) = implies(A,falsehood),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[24,5]),10]),
    [iquote('para_into,24.1.1.2.2,5.1.1,demod,10')] ).

cnf(86,plain,
    implies(implies(A,falsehood),falsehood) = implies(truth,A),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[24,34]),84,84]),
    [iquote('para_into,24.1.1.2,34.1.1,demod,84,84')] ).

cnf(126,plain,
    implies(truth,A) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[40]),84,84,86]),
    [iquote('back_demod,40,demod,84,84,86')] ).

cnf(128,plain,
    $false,
    inference(binary,[status(thm)],[126,1]),
    [iquote('binary,126.1,1.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.11  % Problem  : LCL161-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.12  % Command  : otter-tptp-script %s
% 0.12/0.32  % Computer : n019.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Wed Jul 27 09:30:37 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.75/1.93  ----- Otter 3.3f, August 2004 -----
% 1.75/1.93  The process was started by sandbox2 on n019.cluster.edu,
% 1.75/1.93  Wed Jul 27 09:30:37 2022
% 1.75/1.93  The command was "./otter".  The process ID is 4207.
% 1.75/1.93  
% 1.75/1.93  set(prolog_style_variables).
% 1.75/1.93  set(auto).
% 1.75/1.93     dependent: set(auto1).
% 1.75/1.93     dependent: set(process_input).
% 1.75/1.93     dependent: clear(print_kept).
% 1.75/1.93     dependent: clear(print_new_demod).
% 1.75/1.93     dependent: clear(print_back_demod).
% 1.75/1.93     dependent: clear(print_back_sub).
% 1.75/1.93     dependent: set(control_memory).
% 1.75/1.93     dependent: assign(max_mem, 12000).
% 1.75/1.93     dependent: assign(pick_given_ratio, 4).
% 1.75/1.93     dependent: assign(stats_level, 1).
% 1.75/1.93     dependent: assign(max_seconds, 10800).
% 1.75/1.93  clear(print_given).
% 1.75/1.93  
% 1.75/1.93  list(usable).
% 1.75/1.93  0 [] A=A.
% 1.75/1.93  0 [] not(X)=xor(X,truth).
% 1.75/1.93  0 [] xor(X,falsehood)=X.
% 1.75/1.93  0 [] xor(X,X)=falsehood.
% 1.75/1.93  0 [] and_star(X,truth)=X.
% 1.75/1.93  0 [] and_star(X,falsehood)=falsehood.
% 1.75/1.93  0 [] and_star(xor(truth,X),X)=falsehood.
% 1.75/1.93  0 [] xor(X,xor(truth,Y))=xor(xor(X,truth),Y).
% 1.75/1.93  0 [] and_star(xor(and_star(xor(truth,X),Y),truth),Y)=and_star(xor(and_star(xor(truth,Y),X),truth),X).
% 1.75/1.93  0 [] xor(X,Y)=xor(Y,X).
% 1.75/1.93  0 [] and_star(and_star(X,Y),Z)=and_star(X,and_star(Y,Z)).
% 1.75/1.93  0 [] and_star(X,Y)=and_star(Y,X).
% 1.75/1.93  0 [] not(truth)=falsehood.
% 1.75/1.93  0 [] implies(X,Y)=xor(truth,and_star(X,xor(truth,Y))).
% 1.75/1.93  0 [] implies(truth,x)!=x.
% 1.75/1.93  end_of_list.
% 1.75/1.93  
% 1.75/1.93  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.75/1.93  
% 1.75/1.93  All clauses are units, and equality is present; the
% 1.75/1.93  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.75/1.93  
% 1.75/1.93     dependent: set(knuth_bendix).
% 1.75/1.93     dependent: set(anl_eq).
% 1.75/1.93     dependent: set(para_from).
% 1.75/1.93     dependent: set(para_into).
% 1.75/1.93     dependent: clear(para_from_right).
% 1.75/1.93     dependent: clear(para_into_right).
% 1.75/1.93     dependent: set(para_from_vars).
% 1.75/1.93     dependent: set(eq_units_both_ways).
% 1.75/1.93     dependent: set(dynamic_demod_all).
% 1.75/1.93     dependent: set(dynamic_demod).
% 1.75/1.93     dependent: set(order_eq).
% 1.75/1.93     dependent: set(back_demod).
% 1.75/1.93     dependent: set(lrpo).
% 1.75/1.93  
% 1.75/1.93  ------------> process usable:
% 1.75/1.93  ** KEPT (pick-wt=5): 1 [] implies(truth,x)!=x.
% 1.75/1.93  
% 1.75/1.93  ------------> process sos:
% 1.75/1.93  ** KEPT (pick-wt=3): 2 [] A=A.
% 1.75/1.93  ** KEPT (pick-wt=6): 3 [] not(A)=xor(A,truth).
% 1.75/1.93  ---> New Demodulator: 4 [new_demod,3] not(A)=xor(A,truth).
% 1.75/1.93  ** KEPT (pick-wt=5): 5 [] xor(A,falsehood)=A.
% 1.75/1.93  ---> New Demodulator: 6 [new_demod,5] xor(A,falsehood)=A.
% 1.75/1.93  ** KEPT (pick-wt=5): 7 [] xor(A,A)=falsehood.
% 1.75/1.93  ---> New Demodulator: 8 [new_demod,7] xor(A,A)=falsehood.
% 1.75/1.93  ** KEPT (pick-wt=5): 9 [] and_star(A,truth)=A.
% 1.75/1.93  ---> New Demodulator: 10 [new_demod,9] and_star(A,truth)=A.
% 1.75/1.93  ** KEPT (pick-wt=5): 11 [] and_star(A,falsehood)=falsehood.
% 1.75/1.93  ---> New Demodulator: 12 [new_demod,11] and_star(A,falsehood)=falsehood.
% 1.75/1.93  ** KEPT (pick-wt=7): 13 [] and_star(xor(truth,A),A)=falsehood.
% 1.75/1.93  ---> New Demodulator: 14 [new_demod,13] and_star(xor(truth,A),A)=falsehood.
% 1.75/1.93  ** KEPT (pick-wt=11): 16 [copy,15,flip.1] xor(xor(A,truth),B)=xor(A,xor(truth,B)).
% 1.75/1.93  ---> New Demodulator: 17 [new_demod,16] xor(xor(A,truth),B)=xor(A,xor(truth,B)).
% 1.75/1.93  ** KEPT (pick-wt=19): 18 [] and_star(xor(and_star(xor(truth,A),B),truth),B)=and_star(xor(and_star(xor(truth,B),A),truth),A).
% 1.75/1.93  ** KEPT (pick-wt=7): 19 [] xor(A,B)=xor(B,A).
% 1.75/1.93  ** KEPT (pick-wt=11): 20 [] and_star(and_star(A,B),C)=and_star(A,and_star(B,C)).
% 1.75/1.93  ---> New Demodulator: 21 [new_demod,20] and_star(and_star(A,B),C)=and_star(A,and_star(B,C)).
% 1.75/1.93  ** KEPT (pick-wt=7): 22 [] and_star(A,B)=and_star(B,A).
% 1.75/1.93    Following clause subsumed by 2 during input processing: 0 [demod,4,8] falsehood=falsehood.
% 1.75/1.93  ** KEPT (pick-wt=11): 24 [copy,23,flip.1] xor(truth,and_star(A,xor(truth,B)))=implies(A,B).
% 1.75/1.93  ---> New Demodulator: 25 [new_demod,24] xor(truth,and_star(A,xor(truth,B)))=implies(A,B).
% 1.75/1.93    Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.75/1.93  >>>> Starting back demodulation with 4.
% 1.75/1.93  >>>> Starting back demodulation with 6.
% 1.75/1.93  >>>> Starting back demodulation with 8.
% 1.75/1.93  >>>> Starting back demodulation with 10.
% 1.75/1.93  >>>> Starting back demodulation with 12.
% 1.75/1.93  >>>> Starting back demodulation with 14.
% 1.75/1.93  >>>> Starting back demodulation with 17.
% 1.75/1.93    Following clause subsumed by 18 during input processing: 0 [copy,18,flip.1] and_star(xor(and_star(xor(truth,A),B),truth),B)=and_star(xor(and_star(xor(truth,B),A),truth),A).
% 1.75/1.93    Following clause subsumed by 19 during input processing: 0 [copy,19,flip.1] xor(A,B)=xor(B,A).
% 1.75/1.94  >>>> Starting back demodulation with 21.
% 1.75/1.94    Following clause subsumed by 22 during input processing: 0 [copy,22,flip.1] and_star(A,B)=and_star(B,A).
% 1.75/1.94  >>>> Starting back demodulation with 25.
% 1.75/1.94  
% 1.75/1.94  ======= end of input processing =======
% 1.75/1.94  
% 1.75/1.94  =========== start of search ===========
% 1.75/1.94  
% 1.75/1.94  -------- PROOF -------- 
% 1.75/1.94  
% 1.75/1.94  ----> UNIT CONFLICT at   0.00 sec ----> 128 [binary,126.1,1.1] $F.
% 1.75/1.94  
% 1.75/1.94  Length of proof is 8.  Level of proof is 4.
% 1.75/1.94  
% 1.75/1.94  ---------------- PROOF ----------------
% 1.75/1.94  % SZS status Unsatisfiable
% 1.75/1.94  % SZS output start Refutation
% See solution above
% 1.75/1.94  ------------ end of proof -------------
% 1.75/1.94  
% 1.75/1.94  
% 1.75/1.94  Search stopped by max_proofs option.
% 1.75/1.94  
% 1.75/1.94  
% 1.75/1.94  Search stopped by max_proofs option.
% 1.75/1.94  
% 1.75/1.94  ============ end of search ============
% 1.75/1.94  
% 1.75/1.94  -------------- statistics -------------
% 1.75/1.94  clauses given                 21
% 1.75/1.94  clauses generated            188
% 1.75/1.94  clauses kept                  72
% 1.75/1.94  clauses forward subsumed     165
% 1.75/1.94  clauses back subsumed          0
% 1.75/1.94  Kbytes malloced             1953
% 1.75/1.94  
% 1.75/1.94  ----------- times (seconds) -----------
% 1.75/1.94  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.75/1.94  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.75/1.94  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.75/1.94  
% 1.75/1.94  That finishes the proof of the theorem.
% 1.75/1.94  
% 1.75/1.94  Process 4207 finished Wed Jul 27 09:30:38 2022
% 1.75/1.94  Otter interrupted
% 1.75/1.94  PROOF FOUND
%------------------------------------------------------------------------------