TSTP Solution File: MGT058+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : MGT058+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n025.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 13:06:14 EDT 2022

% Result   : Theorem 1.98s 2.17s
% Output   : Refutation 1.98s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   13
% Syntax   : Number of clauses     :   31 (  13 unt;   9 nHn;  29 RR)
%            Number of literals    :   52 (  12 equ;  16 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   17 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    ( smaller_or_e_qual(A,B)
    | ~ smaller(A,B) ),
    file('MGT058+1.p',unknown),
    [] ).

cnf(3,axiom,
    ( smaller_or_e_qual(A,B)
    | A != B ),
    file('MGT058+1.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ greater_or_e_qual(A,B)
    | greater(A,B)
    | A = B ),
    file('MGT058+1.p',unknown),
    [] ).

cnf(8,axiom,
    ( smaller(A,B)
    | ~ greater(B,A) ),
    file('MGT058+1.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ greater(A,B)
    | ~ greater(B,A) ),
    file('MGT058+1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ fragile_position(A)
    | ~ smaller_or_e_qual(age(A,B),sigma)
    | positional_advantage(A,B) ),
    file('MGT058+1.p',unknown),
    [] ).

cnf(14,axiom,
    ( ~ robust_position(A)
    | ~ smaller_or_e_qual(age(A,B),tau)
    | ~ positional_advantage(A,B) ),
    file('MGT058+1.p',unknown),
    [] ).

cnf(17,plain,
    ~ greater(A,A),
    inference(factor,[status(thm)],[9]),
    [iquote('factor,9.1.2')] ).

cnf(18,axiom,
    A = A,
    file('MGT058+1.p',unknown),
    [] ).

cnf(25,axiom,
    age(dollar_c2,dollar_c1) = zero,
    file('MGT058+1.p',unknown),
    [] ).

cnf(27,axiom,
    greater_or_e_qual(sigma,zero),
    file('MGT058+1.p',unknown),
    [] ).

cnf(28,axiom,
    greater_or_e_qual(tau,zero),
    file('MGT058+1.p',unknown),
    [] ).

cnf(29,axiom,
    fragile_position(dollar_c2),
    file('MGT058+1.p',unknown),
    [] ).

cnf(30,axiom,
    robust_position(dollar_c2),
    file('MGT058+1.p',unknown),
    [] ).

cnf(32,plain,
    smaller_or_e_qual(A,A),
    inference(hyper,[status(thm)],[18,3]),
    [iquote('hyper,18,3')] ).

cnf(39,plain,
    ( greater(sigma,zero)
    | zero = sigma ),
    inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[27,4])]),
    [iquote('hyper,27,4,flip.2')] ).

cnf(67,plain,
    ( greater(tau,zero)
    | zero = tau ),
    inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[28,4])]),
    [iquote('hyper,28,4,flip.2')] ).

cnf(84,plain,
    ( ~ smaller_or_e_qual(zero,tau)
    | ~ positional_advantage(dollar_c2,dollar_c1) ),
    inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[25,14]),30]),
    [iquote('para_from,25.1.1,14.2.1,unit_del,30')] ).

cnf(86,plain,
    ( ~ smaller_or_e_qual(zero,sigma)
    | positional_advantage(dollar_c2,dollar_c1) ),
    inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[25,11]),29]),
    [iquote('para_from,25.1.1,11.2.1,unit_del,29')] ).

cnf(105,plain,
    ( zero = sigma
    | smaller(zero,sigma) ),
    inference(hyper,[status(thm)],[39,8]),
    [iquote('hyper,39,8')] ).

cnf(116,plain,
    ( zero = tau
    | smaller(zero,tau) ),
    inference(hyper,[status(thm)],[67,8]),
    [iquote('hyper,67,8')] ).

cnf(143,plain,
    ( ~ positional_advantage(dollar_c2,dollar_c1)
    | greater(tau,zero) ),
    inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[84,67]),32]),
    [iquote('para_into,84.1.1,67.2.1,unit_del,32')] ).

cnf(182,plain,
    ( positional_advantage(dollar_c2,dollar_c1)
    | greater(sigma,zero) ),
    inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[86,39]),32]),
    [iquote('para_into,86.1.1,39.2.1,unit_del,32')] ).

cnf(195,plain,
    ( zero = sigma
    | smaller_or_e_qual(zero,sigma) ),
    inference(hyper,[status(thm)],[105,2]),
    [iquote('hyper,105,2')] ).

cnf(243,plain,
    ( zero = tau
    | smaller_or_e_qual(zero,tau) ),
    inference(hyper,[status(thm)],[116,2]),
    [iquote('hyper,116,2')] ).

cnf(320,plain,
    ( zero = sigma
    | positional_advantage(dollar_c2,dollar_c1) ),
    inference(hyper,[status(thm)],[195,86]),
    [iquote('hyper,195,86')] ).

cnf(474,plain,
    positional_advantage(dollar_c2,dollar_c1),
    inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[320,182]),17])]),
    [iquote('para_from,320.1.1,182.2.2,unit_del,17,factor_simp')] ).

cnf(482,plain,
    greater(tau,zero),
    inference(hyper,[status(thm)],[474,143]),
    [iquote('hyper,474,143')] ).

cnf(484,plain,
    zero = tau,
    inference(hyper,[status(thm)],[474,84,243]),
    [iquote('hyper,474,84,243')] ).

cnf(485,plain,
    greater(tau,tau),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[482]),484]),
    [iquote('back_demod,482,demod,484')] ).

cnf(486,plain,
    $false,
    inference(binary,[status(thm)],[485,17]),
    [iquote('binary,485.1,17.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : MGT058+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n025.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 04:11:15 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.98/2.15  ----- Otter 3.3f, August 2004 -----
% 1.98/2.15  The process was started by sandbox on n025.cluster.edu,
% 1.98/2.15  Wed Jul 27 04:11:15 2022
% 1.98/2.15  The command was "./otter".  The process ID is 30515.
% 1.98/2.15  
% 1.98/2.15  set(prolog_style_variables).
% 1.98/2.15  set(auto).
% 1.98/2.15     dependent: set(auto1).
% 1.98/2.15     dependent: set(process_input).
% 1.98/2.15     dependent: clear(print_kept).
% 1.98/2.15     dependent: clear(print_new_demod).
% 1.98/2.15     dependent: clear(print_back_demod).
% 1.98/2.15     dependent: clear(print_back_sub).
% 1.98/2.15     dependent: set(control_memory).
% 1.98/2.15     dependent: assign(max_mem, 12000).
% 1.98/2.15     dependent: assign(pick_given_ratio, 4).
% 1.98/2.15     dependent: assign(stats_level, 1).
% 1.98/2.15     dependent: assign(max_seconds, 10800).
% 1.98/2.15  clear(print_given).
% 1.98/2.15  
% 1.98/2.15  formula_list(usable).
% 1.98/2.15  all A (A=A).
% 1.98/2.15  all X Y (smaller_or_e_qual(X,Y)<->smaller(X,Y)|X=Y).
% 1.98/2.15  all X Y (greater_or_e_qual(X,Y)<->greater(X,Y)|X=Y).
% 1.98/2.15  all X Y (smaller(X,Y)<->greater(Y,X)).
% 1.98/2.15  all X Y (-(greater(X,Y)&greater(Y,X))).
% 1.98/2.15  all X Y Z (greater(X,Y)&greater(Y,Z)->greater(X,Z)).
% 1.98/2.15  all X Y (smaller(X,Y)|X=Y|greater(X,Y)).
% 1.98/2.15  all X (fragile_position(X)<-> (all T ((smaller_or_e_qual(age(X,T),sigma)->positional_advantage(X,T))& (greater(age(X,T),sigma)-> -positional_advantage(X,T))))).
% 1.98/2.15  all X (robust_position(X)<-> (all T ((smaller_or_e_qual(age(X,T),tau)-> -positional_advantage(X,T))& (greater(age(X,T),tau)->positional_advantage(X,T))))).
% 1.98/2.15  -(all X (organization(X)& (exists T0 (age(X,T0)=zero))&greater_or_e_qual(sigma,zero)&greater_or_e_qual(tau,zero)-> -(fragile_position(X)&robust_position(X)))).
% 1.98/2.15  end_of_list.
% 1.98/2.15  
% 1.98/2.15  -------> usable clausifies to:
% 1.98/2.15  
% 1.98/2.15  list(usable).
% 1.98/2.15  0 [] A=A.
% 1.98/2.15  0 [] -smaller_or_e_qual(X,Y)|smaller(X,Y)|X=Y.
% 1.98/2.15  0 [] smaller_or_e_qual(X,Y)| -smaller(X,Y).
% 1.98/2.15  0 [] smaller_or_e_qual(X,Y)|X!=Y.
% 1.98/2.15  0 [] -greater_or_e_qual(X,Y)|greater(X,Y)|X=Y.
% 1.98/2.15  0 [] greater_or_e_qual(X,Y)| -greater(X,Y).
% 1.98/2.15  0 [] greater_or_e_qual(X,Y)|X!=Y.
% 1.98/2.15  0 [] -smaller(X,Y)|greater(Y,X).
% 1.98/2.15  0 [] smaller(X,Y)| -greater(Y,X).
% 1.98/2.15  0 [] -greater(X,Y)| -greater(Y,X).
% 1.98/2.15  0 [] -greater(X,Y)| -greater(Y,Z)|greater(X,Z).
% 1.98/2.15  0 [] smaller(X,Y)|X=Y|greater(X,Y).
% 1.98/2.15  0 [] -fragile_position(X)| -smaller_or_e_qual(age(X,T),sigma)|positional_advantage(X,T).
% 1.98/2.15  0 [] -fragile_position(X)| -greater(age(X,T),sigma)| -positional_advantage(X,T).
% 1.98/2.15  0 [] fragile_position(X)|smaller_or_e_qual(age(X,$f1(X)),sigma)|greater(age(X,$f1(X)),sigma).
% 1.98/2.15  0 [] fragile_position(X)|smaller_or_e_qual(age(X,$f1(X)),sigma)|positional_advantage(X,$f1(X)).
% 1.98/2.15  0 [] fragile_position(X)| -positional_advantage(X,$f1(X))|greater(age(X,$f1(X)),sigma).
% 1.98/2.15  0 [] -robust_position(X)| -smaller_or_e_qual(age(X,T),tau)| -positional_advantage(X,T).
% 1.98/2.15  0 [] -robust_position(X)| -greater(age(X,T),tau)|positional_advantage(X,T).
% 1.98/2.15  0 [] robust_position(X)|smaller_or_e_qual(age(X,$f2(X)),tau)|greater(age(X,$f2(X)),tau).
% 1.98/2.15  0 [] robust_position(X)|smaller_or_e_qual(age(X,$f2(X)),tau)| -positional_advantage(X,$f2(X)).
% 1.98/2.15  0 [] robust_position(X)|positional_advantage(X,$f2(X))|greater(age(X,$f2(X)),tau).
% 1.98/2.15  0 [] organization($c2).
% 1.98/2.15  0 [] age($c2,$c1)=zero.
% 1.98/2.15  0 [] greater_or_e_qual(sigma,zero).
% 1.98/2.15  0 [] greater_or_e_qual(tau,zero).
% 1.98/2.15  0 [] fragile_position($c2).
% 1.98/2.15  0 [] robust_position($c2).
% 1.98/2.15  end_of_list.
% 1.98/2.15  
% 1.98/2.15  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.98/2.15  
% 1.98/2.15  This ia a non-Horn set with equality.  The strategy will be
% 1.98/2.15  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.98/2.15  deletion, with positive clauses in sos and nonpositive
% 1.98/2.15  clauses in usable.
% 1.98/2.15  
% 1.98/2.15     dependent: set(knuth_bendix).
% 1.98/2.15     dependent: set(anl_eq).
% 1.98/2.15     dependent: set(para_from).
% 1.98/2.15     dependent: set(para_into).
% 1.98/2.15     dependent: clear(para_from_right).
% 1.98/2.15     dependent: clear(para_into_right).
% 1.98/2.15     dependent: set(para_from_vars).
% 1.98/2.15     dependent: set(eq_units_both_ways).
% 1.98/2.15     dependent: set(dynamic_demod_all).
% 1.98/2.15     dependent: set(dynamic_demod).
% 1.98/2.15     dependent: set(order_eq).
% 1.98/2.15     dependent: set(back_demod).
% 1.98/2.15     dependent: set(lrpo).
% 1.98/2.15     dependent: set(hyper_res).
% 1.98/2.15     dependent: set(unit_deletion).
% 1.98/2.15     dependent: set(factor).
% 1.98/2.15  
% 1.98/2.15  ------------> process usable:
% 1.98/2.15  ** KEPT (pick-wt=9): 1 [] -smaller_or_e_qual(A,B)|smaller(A,B)|A=B.
% 1.98/2.15  ** KEPT (pick-wt=6): 2 [] smaller_or_e_qual(A,B)| -smaller(A,B).
% 1.98/2.15  ** KEPT (pick-wt=6): 3 [] smaller_or_e_qual(A,B)|A!=B.
% 1.98/2.15  ** KEPT (pick-wt=9): 4 [] -greater_or_e_qual(A,B)|greater(A,B)|A=B.
% 1.98/2.15  ** KEPT (pick-wt=6): 5 [] greater_or_e_qual(A,B)| -greater(A,B).
% 1.98/2.17  ** KEPT (pick-wt=6): 6 [] greater_or_e_qual(A,B)|A!=B.
% 1.98/2.17  ** KEPT (pick-wt=6): 7 [] -smaller(A,B)|greater(B,A).
% 1.98/2.17  ** KEPT (pick-wt=6): 8 [] smaller(A,B)| -greater(B,A).
% 1.98/2.17  ** KEPT (pick-wt=6): 9 [] -greater(A,B)| -greater(B,A).
% 1.98/2.17  ** KEPT (pick-wt=9): 10 [] -greater(A,B)| -greater(B,C)|greater(A,C).
% 1.98/2.17  ** KEPT (pick-wt=10): 11 [] -fragile_position(A)| -smaller_or_e_qual(age(A,B),sigma)|positional_advantage(A,B).
% 1.98/2.17  ** KEPT (pick-wt=10): 12 [] -fragile_position(A)| -greater(age(A,B),sigma)| -positional_advantage(A,B).
% 1.98/2.17  ** KEPT (pick-wt=12): 13 [] fragile_position(A)| -positional_advantage(A,$f1(A))|greater(age(A,$f1(A)),sigma).
% 1.98/2.17  ** KEPT (pick-wt=10): 14 [] -robust_position(A)| -smaller_or_e_qual(age(A,B),tau)| -positional_advantage(A,B).
% 1.98/2.17  ** KEPT (pick-wt=10): 15 [] -robust_position(A)| -greater(age(A,B),tau)|positional_advantage(A,B).
% 1.98/2.17  ** KEPT (pick-wt=12): 16 [] robust_position(A)|smaller_or_e_qual(age(A,$f2(A)),tau)| -positional_advantage(A,$f2(A)).
% 1.98/2.17  
% 1.98/2.17  ------------> process sos:
% 1.98/2.17  ** KEPT (pick-wt=3): 18 [] A=A.
% 1.98/2.17  ** KEPT (pick-wt=9): 19 [] smaller(A,B)|A=B|greater(A,B).
% 1.98/2.17  ** KEPT (pick-wt=14): 20 [] fragile_position(A)|smaller_or_e_qual(age(A,$f1(A)),sigma)|greater(age(A,$f1(A)),sigma).
% 1.98/2.17  ** KEPT (pick-wt=12): 21 [] fragile_position(A)|smaller_or_e_qual(age(A,$f1(A)),sigma)|positional_advantage(A,$f1(A)).
% 1.98/2.17  ** KEPT (pick-wt=14): 22 [] robust_position(A)|smaller_or_e_qual(age(A,$f2(A)),tau)|greater(age(A,$f2(A)),tau).
% 1.98/2.17  ** KEPT (pick-wt=12): 23 [] robust_position(A)|positional_advantage(A,$f2(A))|greater(age(A,$f2(A)),tau).
% 1.98/2.17  ** KEPT (pick-wt=2): 24 [] organization($c2).
% 1.98/2.17  ** KEPT (pick-wt=5): 25 [] age($c2,$c1)=zero.
% 1.98/2.17  ---> New Demodulator: 26 [new_demod,25] age($c2,$c1)=zero.
% 1.98/2.17  ** KEPT (pick-wt=3): 27 [] greater_or_e_qual(sigma,zero).
% 1.98/2.17  ** KEPT (pick-wt=3): 28 [] greater_or_e_qual(tau,zero).
% 1.98/2.17  ** KEPT (pick-wt=2): 29 [] fragile_position($c2).
% 1.98/2.17  ** KEPT (pick-wt=2): 30 [] robust_position($c2).
% 1.98/2.17    Following clause subsumed by 18 during input processing: 0 [copy,18,flip.1] A=A.
% 1.98/2.17  >>>> Starting back demodulation with 26.
% 1.98/2.17  
% 1.98/2.17  ======= end of input processing =======
% 1.98/2.17  
% 1.98/2.17  =========== start of search ===========
% 1.98/2.17  
% 1.98/2.17  -------- PROOF -------- 
% 1.98/2.17  
% 1.98/2.17  ----> UNIT CONFLICT at   0.02 sec ----> 486 [binary,485.1,17.1] $F.
% 1.98/2.17  
% 1.98/2.17  Length of proof is 17.  Level of proof is 7.
% 1.98/2.17  
% 1.98/2.17  ---------------- PROOF ----------------
% 1.98/2.17  % SZS status Theorem
% 1.98/2.17  % SZS output start Refutation
% See solution above
% 1.98/2.17  ------------ end of proof -------------
% 1.98/2.17  
% 1.98/2.17  
% 1.98/2.17  Search stopped by max_proofs option.
% 1.98/2.17  
% 1.98/2.17  
% 1.98/2.17  Search stopped by max_proofs option.
% 1.98/2.17  
% 1.98/2.17  ============ end of search ============
% 1.98/2.17  
% 1.98/2.17  -------------- statistics -------------
% 1.98/2.17  clauses given                 37
% 1.98/2.17  clauses generated            636
% 1.98/2.17  clauses kept                 483
% 1.98/2.17  clauses forward subsumed     182
% 1.98/2.17  clauses back subsumed        129
% 1.98/2.17  Kbytes malloced              976
% 1.98/2.17  
% 1.98/2.17  ----------- times (seconds) -----------
% 1.98/2.17  user CPU time          0.02          (0 hr, 0 min, 0 sec)
% 1.98/2.17  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.98/2.17  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.98/2.17  
% 1.98/2.17  That finishes the proof of the theorem.
% 1.98/2.17  
% 1.98/2.17  Process 30515 finished Wed Jul 27 04:11:17 2022
% 1.98/2.17  Otter interrupted
% 1.98/2.17  PROOF FOUND
%------------------------------------------------------------------------------