TSTP Solution File: RNG005-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : RNG005-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n008.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 13:12:01 EDT 2022

% Result   : Unsatisfiable 1.72s 1.98s
% Output   : Refutation 1.72s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   14
% Syntax   : Number of clauses     :   27 (  21 unt;   0 nHn;  20 RR)
%            Number of literals    :   43 (   6 equ;  17 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   41 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    ( ~ sum(A,B,C)
    | ~ sum(B,D,E)
    | ~ sum(A,E,F)
    | sum(C,D,F) ),
    file('RNG005-1.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ sum(A,B,C)
    | sum(B,A,C) ),
    file('RNG005-1.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ product(A,B,C)
    | ~ product(D,B,E)
    | ~ sum(A,D,F)
    | ~ product(F,B,G)
    | sum(C,E,G) ),
    file('RNG005-1.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ product(A,B,C)
    | ~ product(D,B,E)
    | ~ sum(A,D,F)
    | ~ sum(C,E,G)
    | product(F,B,G) ),
    file('RNG005-1.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ sum(A,B,C)
    | ~ sum(A,B,D)
    | C = D ),
    file('RNG005-1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ product(A,B,C)
    | ~ product(A,B,D)
    | C = D ),
    file('RNG005-1.p',unknown),
    [] ).

cnf(12,axiom,
    ~ sum(c,d,additive_identity),
    file('RNG005-1.p',unknown),
    [] ).

cnf(15,axiom,
    sum(A,additive_identity,A),
    file('RNG005-1.p',unknown),
    [] ).

cnf(16,axiom,
    product(A,B,multiply(A,B)),
    file('RNG005-1.p',unknown),
    [] ).

cnf(17,axiom,
    sum(A,B,add(A,B)),
    file('RNG005-1.p',unknown),
    [] ).

cnf(18,axiom,
    sum(additive_inverse(A),A,additive_identity),
    file('RNG005-1.p',unknown),
    [] ).

cnf(19,axiom,
    sum(A,additive_inverse(A),additive_identity),
    file('RNG005-1.p',unknown),
    [] ).

cnf(20,axiom,
    product(a,b,d),
    file('RNG005-1.p',unknown),
    [] ).

cnf(21,axiom,
    product(additive_inverse(a),b,c),
    file('RNG005-1.p',unknown),
    [] ).

cnf(41,plain,
    multiply(a,b) = d,
    inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[16,11,20])]),
    [iquote('hyper,16,11,20,flip.1')] ).

cnf(42,plain,
    sum(d,multiply(additive_identity,b),d),
    inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[16,8,20,16,15]),41]),
    [iquote('hyper,16,8,20,16,15,demod,41')] ).

cnf(78,plain,
    sum(d,c,multiply(additive_identity,b)),
    inference(hyper,[status(thm)],[21,8,20,19,16]),
    [iquote('hyper,21,8,20,19,16')] ).

cnf(107,plain,
    add(A,additive_identity) = A,
    inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[17,10,15])]),
    [iquote('hyper,17,10,15,flip.1')] ).

cnf(111,plain,
    product(additive_identity,b,add(c,d)),
    inference(hyper,[status(thm)],[17,9,21,20,18]),
    [iquote('hyper,17,9,21,20,18')] ).

cnf(162,plain,
    sum(A,B,add(B,A)),
    inference(hyper,[status(thm)],[17,3]),
    [iquote('hyper,17,3')] ).

cnf(193,plain,
    sum(additive_identity,multiply(additive_identity,b),additive_identity),
    inference(hyper,[status(thm)],[42,2,18,18]),
    [iquote('hyper,42,2,18,18')] ).

cnf(354,plain,
    multiply(additive_identity,b) = add(d,c),
    inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[78,10,17])]),
    [iquote('hyper,78,10,17,flip.1')] ).

cnf(446,plain,
    sum(additive_identity,add(d,c),additive_identity),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[193]),354]),
    [iquote('back_demod,193,demod,354')] ).

cnf(464,plain,
    add(d,c) = add(c,d),
    inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[111,11,16]),354]),
    [iquote('hyper,111,11,16,demod,354')] ).

cnf(503,plain,
    sum(additive_identity,add(c,d),additive_identity),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[446]),464]),
    [iquote('back_demod,446,demod,464')] ).

cnf(930,plain,
    sum(c,d,additive_identity),
    inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[503,2,162,17]),107]),
    [iquote('hyper,503,2,162,17,demod,107')] ).

cnf(931,plain,
    $false,
    inference(binary,[status(thm)],[930,12]),
    [iquote('binary,930.1,12.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : RNG005-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13  % Command  : otter-tptp-script %s
% 0.12/0.34  % Computer : n008.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Wed Jul 27 02:11:38 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 1.72/1.95  ----- Otter 3.3f, August 2004 -----
% 1.72/1.95  The process was started by sandbox on n008.cluster.edu,
% 1.72/1.95  Wed Jul 27 02:11:38 2022
% 1.72/1.95  The command was "./otter".  The process ID is 6198.
% 1.72/1.95  
% 1.72/1.95  set(prolog_style_variables).
% 1.72/1.95  set(auto).
% 1.72/1.95     dependent: set(auto1).
% 1.72/1.95     dependent: set(process_input).
% 1.72/1.95     dependent: clear(print_kept).
% 1.72/1.95     dependent: clear(print_new_demod).
% 1.72/1.95     dependent: clear(print_back_demod).
% 1.72/1.95     dependent: clear(print_back_sub).
% 1.72/1.95     dependent: set(control_memory).
% 1.72/1.95     dependent: assign(max_mem, 12000).
% 1.72/1.95     dependent: assign(pick_given_ratio, 4).
% 1.72/1.95     dependent: assign(stats_level, 1).
% 1.72/1.95     dependent: assign(max_seconds, 10800).
% 1.72/1.95  clear(print_given).
% 1.72/1.95  
% 1.72/1.95  list(usable).
% 1.72/1.95  0 [] A=A.
% 1.72/1.95  0 [] sum(additive_identity,X,X).
% 1.72/1.95  0 [] sum(X,additive_identity,X).
% 1.72/1.95  0 [] product(X,Y,multiply(X,Y)).
% 1.72/1.95  0 [] sum(X,Y,add(X,Y)).
% 1.72/1.95  0 [] sum(additive_inverse(X),X,additive_identity).
% 1.72/1.95  0 [] sum(X,additive_inverse(X),additive_identity).
% 1.72/1.95  0 [] -sum(X,Y,U)| -sum(Y,Z,V)| -sum(U,Z,W)|sum(X,V,W).
% 1.72/1.95  0 [] -sum(X,Y,U)| -sum(Y,Z,V)| -sum(X,V,W)|sum(U,Z,W).
% 1.72/1.95  0 [] -sum(X,Y,Z)|sum(Y,X,Z).
% 1.72/1.95  0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W)|product(X,V,W).
% 1.72/1.95  0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W)|product(U,Z,W).
% 1.72/1.95  0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -product(X,V3,V4)|sum(V1,V2,V4).
% 1.72/1.95  0 [] -product(X,Y,V1)| -product(X,Z,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(X,V3,V4).
% 1.72/1.95  0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -product(V3,X,V4)|sum(V1,V2,V4).
% 1.72/1.95  0 [] -product(Y,X,V1)| -product(Z,X,V2)| -sum(Y,Z,V3)| -sum(V1,V2,V4)|product(V3,X,V4).
% 1.72/1.95  0 [] -sum(X,Y,U)| -sum(X,Y,V)|U=V.
% 1.72/1.95  0 [] -product(X,Y,U)| -product(X,Y,V)|U=V.
% 1.72/1.95  0 [] product(a,b,d).
% 1.72/1.95  0 [] product(additive_inverse(a),b,c).
% 1.72/1.95  0 [] -sum(c,d,additive_identity).
% 1.72/1.95  end_of_list.
% 1.72/1.95  
% 1.72/1.95  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=5.
% 1.72/1.95  
% 1.72/1.95  This is a Horn set with equality.  The strategy will be
% 1.72/1.95  Knuth-Bendix and hyper_res, with positive clauses in
% 1.72/1.95  sos and nonpositive clauses in usable.
% 1.72/1.95  
% 1.72/1.95     dependent: set(knuth_bendix).
% 1.72/1.95     dependent: set(anl_eq).
% 1.72/1.95     dependent: set(para_from).
% 1.72/1.95     dependent: set(para_into).
% 1.72/1.95     dependent: clear(para_from_right).
% 1.72/1.95     dependent: clear(para_into_right).
% 1.72/1.95     dependent: set(para_from_vars).
% 1.72/1.95     dependent: set(eq_units_both_ways).
% 1.72/1.95     dependent: set(dynamic_demod_all).
% 1.72/1.95     dependent: set(dynamic_demod).
% 1.72/1.95     dependent: set(order_eq).
% 1.72/1.95     dependent: set(back_demod).
% 1.72/1.95     dependent: set(lrpo).
% 1.72/1.95     dependent: set(hyper_res).
% 1.72/1.95     dependent: clear(order_hyper).
% 1.72/1.95  
% 1.72/1.95  ------------> process usable:
% 1.72/1.95  ** KEPT (pick-wt=16): 1 [] -sum(A,B,C)| -sum(B,D,E)| -sum(C,D,F)|sum(A,E,F).
% 1.72/1.95  ** KEPT (pick-wt=16): 2 [] -sum(A,B,C)| -sum(B,D,E)| -sum(A,E,F)|sum(C,D,F).
% 1.72/1.95  ** KEPT (pick-wt=8): 3 [] -sum(A,B,C)|sum(B,A,C).
% 1.72/1.95  ** KEPT (pick-wt=16): 4 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 1.72/1.95  ** KEPT (pick-wt=16): 5 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 1.72/1.95  ** KEPT (pick-wt=20): 6 [] -product(A,B,C)| -product(A,D,E)| -sum(B,D,F)| -product(A,F,G)|sum(C,E,G).
% 1.72/1.95  ** KEPT (pick-wt=20): 7 [] -product(A,B,C)| -product(A,D,E)| -sum(B,D,F)| -sum(C,E,G)|product(A,F,G).
% 1.72/1.95  ** KEPT (pick-wt=20): 8 [] -product(A,B,C)| -product(D,B,E)| -sum(A,D,F)| -product(F,B,G)|sum(C,E,G).
% 1.72/1.95  ** KEPT (pick-wt=20): 9 [] -product(A,B,C)| -product(D,B,E)| -sum(A,D,F)| -sum(C,E,G)|product(F,B,G).
% 1.72/1.95  ** KEPT (pick-wt=11): 10 [] -sum(A,B,C)| -sum(A,B,D)|C=D.
% 1.72/1.95  ** KEPT (pick-wt=11): 11 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 1.72/1.95  ** KEPT (pick-wt=4): 12 [] -sum(c,d,additive_identity).
% 1.72/1.95  
% 1.72/1.95  ------------> process sos:
% 1.72/1.95  ** KEPT (pick-wt=3): 13 [] A=A.
% 1.72/1.95  ** KEPT (pick-wt=4): 14 [] sum(additive_identity,A,A).
% 1.72/1.95  ** KEPT (pick-wt=4): 15 [] sum(A,additive_identity,A).
% 1.72/1.95  ** KEPT (pick-wt=6): 16 [] product(A,B,multiply(A,B)).
% 1.72/1.95  ** KEPT (pick-wt=6): 17 [] sum(A,B,add(A,B)).
% 1.72/1.95  ** KEPT (pick-wt=5): 18 [] sum(additive_inverse(A),A,additive_identity).
% 1.72/1.95  ** KEPT (pick-wt=5): 19 [] sum(A,additive_inverse(A),additive_identity).
% 1.72/1.95  ** KEPT (pick-wt=4): 20 [] product(a,b,d).
% 1.72/1.95  ** KEPT (pick-wt=5): 21 [] product(additive_inverse(a),b,c).
% 1.72/1.95    Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] A=A.
% 1.72/1.95  
% 1.72/1.95  ======= end of input processing =======
% 1.72/1.95  
% 1.72/1.95  =========== start of search ===========
% 1.72/1.98  
% 1.72/1.98  -------- PROOF -------- 
% 1.72/1.98  
% 1.72/1.98  ----> UNIT CONFLICT at   0.03 sec ----> 931 [binary,930.1,12.1] $F.
% 1.72/1.98  
% 1.72/1.98  Length of proof is 12.  Level of proof is 6.
% 1.72/1.98  
% 1.72/1.98  ---------------- PROOF ----------------
% 1.72/1.98  % SZS status Unsatisfiable
% 1.72/1.98  % SZS output start Refutation
% See solution above
% 1.72/1.98  ------------ end of proof -------------
% 1.72/1.98  
% 1.72/1.98  
% 1.72/1.98  Search stopped by max_proofs option.
% 1.72/1.98  
% 1.72/1.98  
% 1.72/1.98  Search stopped by max_proofs option.
% 1.72/1.98  
% 1.72/1.98  ============ end of search ============
% 1.72/1.98  
% 1.72/1.98  -------------- statistics -------------
% 1.72/1.98  clauses given                 43
% 1.72/1.98  clauses generated           2718
% 1.72/1.98  clauses kept                 899
% 1.72/1.98  clauses forward subsumed    2125
% 1.72/1.98  clauses back subsumed         11
% 1.72/1.98  Kbytes malloced             1953
% 1.72/1.98  
% 1.72/1.98  ----------- times (seconds) -----------
% 1.72/1.98  user CPU time          0.03          (0 hr, 0 min, 0 sec)
% 1.72/1.98  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.72/1.98  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 1.72/1.98  
% 1.72/1.98  That finishes the proof of the theorem.
% 1.72/1.98  
% 1.72/1.98  Process 6198 finished Wed Jul 27 02:11:40 2022
% 1.72/1.98  Otter interrupted
% 1.72/1.98  PROOF FOUND
%------------------------------------------------------------------------------