TSTP Solution File: BOO003-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : BOO003-1 : TPTP v8.1.0. Released v1.0.0.
% 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 12:47:30 EDT 2022

% Result   : Unsatisfiable 1.95s 2.12s
% Output   : Refutation 1.95s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   18 (  14 unt;   0 nHn;   6 RR)
%            Number of literals    :   30 (   4 equ;  13 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   36 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(6,axiom,
    ( ~ product(A,B,C)
    | ~ product(D,B,E)
    | ~ sum(A,D,F)
    | ~ sum(C,E,G)
    | product(F,B,G) ),
    file('BOO003-1.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ sum(A,B,C)
    | ~ sum(A,D,E)
    | ~ product(B,D,F)
    | ~ sum(A,F,G)
    | product(C,E,G) ),
    file('BOO003-1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ sum(A,B,C)
    | ~ sum(A,B,D)
    | C = D ),
    file('BOO003-1.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ product(A,B,C)
    | ~ product(A,B,D)
    | C = D ),
    file('BOO003-1.p',unknown),
    [] ).

cnf(13,axiom,
    ~ product(x,x,x),
    file('BOO003-1.p',unknown),
    [] ).

cnf(15,axiom,
    sum(A,B,add(A,B)),
    file('BOO003-1.p',unknown),
    [] ).

cnf(16,axiom,
    product(A,B,multiply(A,B)),
    file('BOO003-1.p',unknown),
    [] ).

cnf(17,axiom,
    sum(additive_identity,A,A),
    file('BOO003-1.p',unknown),
    [] ).

cnf(18,axiom,
    sum(A,additive_identity,A),
    file('BOO003-1.p',unknown),
    [] ).

cnf(19,axiom,
    product(multiplicative_identity,A,A),
    file('BOO003-1.p',unknown),
    [] ).

cnf(21,axiom,
    sum(inverse(A),A,multiplicative_identity),
    file('BOO003-1.p',unknown),
    [] ).

cnf(23,axiom,
    product(inverse(A),A,additive_identity),
    file('BOO003-1.p',unknown),
    [] ).

cnf(34,plain,
    add(A,additive_identity) = A,
    inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[15,11,18])]),
    [iquote('hyper,15,11,18,flip.1')] ).

cnf(193,plain,
    product(A,A,add(A,multiply(additive_identity,additive_identity))),
    inference(hyper,[status(thm)],[16,7,18,18,15]),
    [iquote('hyper,16,7,18,18,15')] ).

cnf(203,plain,
    product(multiplicative_identity,A,multiply(A,A)),
    inference(hyper,[status(thm)],[16,6,23,21,17]),
    [iquote('hyper,16,6,23,21,17')] ).

cnf(1096,plain,
    multiply(A,A) = A,
    inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[203,12,19])]),
    [iquote('hyper,203,12,19,flip.1')] ).

cnf(1098,plain,
    product(A,A,A),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[193]),1096,34]),
    [iquote('back_demod,193,demod,1096,34')] ).

cnf(1099,plain,
    $false,
    inference(binary,[status(thm)],[1098,13]),
    [iquote('binary,1098.1,13.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : BOO003-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : otter-tptp-script %s
% 0.13/0.33  % Computer : n021.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Wed Jul 27 02:30:08 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 1.76/1.98  ----- Otter 3.3f, August 2004 -----
% 1.76/1.98  The process was started by sandbox on n021.cluster.edu,
% 1.76/1.98  Wed Jul 27 02:30:08 2022
% 1.76/1.98  The command was "./otter".  The process ID is 24090.
% 1.76/1.98  
% 1.76/1.98  set(prolog_style_variables).
% 1.76/1.98  set(auto).
% 1.76/1.98     dependent: set(auto1).
% 1.76/1.98     dependent: set(process_input).
% 1.76/1.98     dependent: clear(print_kept).
% 1.76/1.98     dependent: clear(print_new_demod).
% 1.76/1.98     dependent: clear(print_back_demod).
% 1.76/1.98     dependent: clear(print_back_sub).
% 1.76/1.98     dependent: set(control_memory).
% 1.76/1.98     dependent: assign(max_mem, 12000).
% 1.76/1.98     dependent: assign(pick_given_ratio, 4).
% 1.76/1.98     dependent: assign(stats_level, 1).
% 1.76/1.98     dependent: assign(max_seconds, 10800).
% 1.76/1.98  clear(print_given).
% 1.76/1.98  
% 1.76/1.98  list(usable).
% 1.76/1.98  0 [] A=A.
% 1.76/1.98  0 [] sum(X,Y,add(X,Y)).
% 1.76/1.98  0 [] product(X,Y,multiply(X,Y)).
% 1.76/1.98  0 [] -sum(X,Y,Z)|sum(Y,X,Z).
% 1.76/1.98  0 [] -product(X,Y,Z)|product(Y,X,Z).
% 1.76/1.98  0 [] sum(additive_identity,X,X).
% 1.76/1.98  0 [] sum(X,additive_identity,X).
% 1.76/1.98  0 [] product(multiplicative_identity,X,X).
% 1.76/1.98  0 [] product(X,multiplicative_identity,X).
% 1.76/1.98  0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -product(X,V3,V4)|sum(V1,V2,V4).
% 1.76/1.98  0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(X,V3,V4).
% 1.76/1.98  0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -product(V3,X,V4)|sum(V1,V2,V4).
% 1.76/1.98  0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(V3,X,V4).
% 1.76/1.98  0 [] -sum(X,Y,V1)| -sum(X,Z,V2)| -product(Y,Z,V3)| -sum(X,V3,V4)|product(V1,V2,V4).
% 1.76/1.98  0 [] -sum(X,Y,V1)| -sum(X,Z,V2)| -product(Y,Z,V3)| -product(V1,V2,V4)|sum(X,V3,V4).
% 1.76/1.98  0 [] -sum(Y,X,V1)| -sum(Z,X,V2)| -product(Y,Z,V3)| -sum(V3,X,V4)|product(V1,V2,V4).
% 1.76/1.98  0 [] -sum(Y,X,V1)| -sum(Z,X,V2)| -product(Y,Z,V3)| -product(V1,V2,V4)|sum(V3,X,V4).
% 1.76/1.98  0 [] sum(inverse(X),X,multiplicative_identity).
% 1.76/1.98  0 [] sum(X,inverse(X),multiplicative_identity).
% 1.76/1.98  0 [] product(inverse(X),X,additive_identity).
% 1.76/1.98  0 [] product(X,inverse(X),additive_identity).
% 1.76/1.98  0 [] -sum(X,Y,U)| -sum(X,Y,V)|U=V.
% 1.76/1.98  0 [] -product(X,Y,U)| -product(X,Y,V)|U=V.
% 1.76/1.98  0 [] -product(x,x,x).
% 1.76/1.98  end_of_list.
% 1.76/1.98  
% 1.76/1.98  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=5.
% 1.76/1.98  
% 1.76/1.98  This is a Horn set with equality.  The strategy will be
% 1.76/1.98  Knuth-Bendix and hyper_res, with positive clauses in
% 1.76/1.98  sos and nonpositive clauses in usable.
% 1.76/1.98  
% 1.76/1.98     dependent: set(knuth_bendix).
% 1.76/1.98     dependent: set(anl_eq).
% 1.76/1.98     dependent: set(para_from).
% 1.76/1.98     dependent: set(para_into).
% 1.76/1.98     dependent: clear(para_from_right).
% 1.76/1.98     dependent: clear(para_into_right).
% 1.76/1.98     dependent: set(para_from_vars).
% 1.76/1.98     dependent: set(eq_units_both_ways).
% 1.76/1.98     dependent: set(dynamic_demod_all).
% 1.76/1.98     dependent: set(dynamic_demod).
% 1.76/1.98     dependent: set(order_eq).
% 1.76/1.98     dependent: set(back_demod).
% 1.76/1.98     dependent: set(lrpo).
% 1.76/1.98     dependent: set(hyper_res).
% 1.76/1.98     dependent: clear(order_hyper).
% 1.76/1.98  
% 1.76/1.98  ------------> process usable:
% 1.76/1.98  ** KEPT (pick-wt=8): 1 [] -sum(A,B,C)|sum(B,A,C).
% 1.76/1.98  ** KEPT (pick-wt=8): 2 [] -product(A,B,C)|product(B,A,C).
% 1.76/1.98  ** KEPT (pick-wt=20): 3 [] -product(A,B,C)| -product(A,D,E)| -sum(B,D,F)| -product(A,F,G)|sum(C,E,G).
% 1.76/1.98  ** KEPT (pick-wt=20): 4 [] -product(A,B,C)| -product(A,D,E)| -sum(B,D,F)| -sum(C,E,G)|product(A,F,G).
% 1.76/1.98  ** KEPT (pick-wt=20): 5 [] -product(A,B,C)| -product(D,B,E)| -sum(A,D,F)| -product(F,B,G)|sum(C,E,G).
% 1.76/1.98  ** KEPT (pick-wt=20): 6 [] -product(A,B,C)| -product(D,B,E)| -sum(A,D,F)| -sum(C,E,G)|product(F,B,G).
% 1.76/1.98  ** KEPT (pick-wt=20): 7 [] -sum(A,B,C)| -sum(A,D,E)| -product(B,D,F)| -sum(A,F,G)|product(C,E,G).
% 1.76/1.98  ** KEPT (pick-wt=20): 8 [] -sum(A,B,C)| -sum(A,D,E)| -product(B,D,F)| -product(C,E,G)|sum(A,F,G).
% 1.76/1.98  ** KEPT (pick-wt=20): 9 [] -sum(A,B,C)| -sum(D,B,E)| -product(A,D,F)| -sum(F,B,G)|product(C,E,G).
% 1.76/1.98  ** KEPT (pick-wt=20): 10 [] -sum(A,B,C)| -sum(D,B,E)| -product(A,D,F)| -product(C,E,G)|sum(F,B,G).
% 1.76/1.98  ** KEPT (pick-wt=11): 11 [] -sum(A,B,C)| -sum(A,B,D)|C=D.
% 1.76/1.98  ** KEPT (pick-wt=11): 12 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 1.76/1.98  ** KEPT (pick-wt=4): 13 [] -product(x,x,x).
% 1.76/1.98  
% 1.76/1.98  ------------> process sos:
% 1.76/1.98  ** KEPT (pick-wt=3): 14 [] A=A.
% 1.76/1.98  ** KEPT (pick-wt=6): 15 [] sum(A,B,add(A,B)).
% 1.76/1.98  ** KEPT (pick-wt=6): 16 [] product(A,B,multiply(A,B)).
% 1.76/1.98  ** KEPT (pick-wt=4): 17 [] sum(additive_identity,A,A).
% 1.76/1.98  ** KEPT (pick-wt=4): 18 [] sum(A,additive_identity,A).
% 1.76/1.98  ** KEPT (pick-wt=4): 19 [] product(multiplicative_identity,A,A).
% 1.76/1.98  ** KEPT (pick-wt=4): 20 [] product(A,multiplicative_identity,A).
% 1.95/2.12  ** KEPT (pick-wt=5): 21 [] sum(inverse(A),A,multiplicative_identity).
% 1.95/2.12  ** KEPT (pick-wt=5): 22 [] sum(A,inverse(A),multiplicative_identity).
% 1.95/2.12  ** KEPT (pick-wt=5): 23 [] product(inverse(A),A,additive_identity).
% 1.95/2.12  ** KEPT (pick-wt=5): 24 [] product(A,inverse(A),additive_identity).
% 1.95/2.12    Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 1.95/2.12  
% 1.95/2.12  ======= end of input processing =======
% 1.95/2.12  
% 1.95/2.12  =========== start of search ===========
% 1.95/2.12  
% 1.95/2.12  -------- PROOF -------- 
% 1.95/2.12  
% 1.95/2.12  ----> UNIT CONFLICT at   0.14 sec ----> 1099 [binary,1098.1,13.1] $F.
% 1.95/2.12  
% 1.95/2.12  Length of proof is 5.  Level of proof is 3.
% 1.95/2.12  
% 1.95/2.12  ---------------- PROOF ----------------
% 1.95/2.12  % SZS status Unsatisfiable
% 1.95/2.12  % SZS output start Refutation
% See solution above
% 1.95/2.12  ------------ end of proof -------------
% 1.95/2.12  
% 1.95/2.12  
% 1.95/2.12  Search stopped by max_proofs option.
% 1.95/2.12  
% 1.95/2.12  
% 1.95/2.12  Search stopped by max_proofs option.
% 1.95/2.12  
% 1.95/2.12  ============ end of search ============
% 1.95/2.12  
% 1.95/2.12  -------------- statistics -------------
% 1.95/2.12  clauses given                 38
% 1.95/2.12  clauses generated          16662
% 1.95/2.12  clauses kept                1078
% 1.95/2.12  clauses forward subsumed   16221
% 1.95/2.12  clauses back subsumed         71
% 1.95/2.12  Kbytes malloced             2929
% 1.95/2.12  
% 1.95/2.12  ----------- times (seconds) -----------
% 1.95/2.12  user CPU time          0.14          (0 hr, 0 min, 0 sec)
% 1.95/2.12  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.95/2.12  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.95/2.12  
% 1.95/2.12  That finishes the proof of the theorem.
% 1.95/2.12  
% 1.95/2.12  Process 24090 finished Wed Jul 27 02:30:09 2022
% 1.95/2.12  Otter interrupted
% 1.95/2.12  PROOF FOUND
%------------------------------------------------------------------------------