TSTP Solution File: GRP700+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GRP700+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n009.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 12:57:40 EDT 2022

% Result   : Theorem 1.74s 1.95s
% Output   : Refutation 1.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   15 (  13 unt;   0 nHn;   3 RR)
%            Number of literals    :   17 (  16 equ;   4 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   21 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( mult(A,dollar_c1) != unit
    | mult(dollar_c1,A) != unit ),
    file('GRP700+1.p',unknown),
    [] ).

cnf(2,axiom,
    A = A,
    file('GRP700+1.p',unknown),
    [] ).

cnf(7,axiom,
    mult(rd(A,B),B) = A,
    file('GRP700+1.p',unknown),
    [] ).

cnf(10,axiom,
    rd(mult(A,B),B) = A,
    file('GRP700+1.p',unknown),
    [] ).

cnf(12,axiom,
    mult(A,unit) = A,
    file('GRP700+1.p',unknown),
    [] ).

cnf(13,axiom,
    mult(unit,A) = A,
    file('GRP700+1.p',unknown),
    [] ).

cnf(15,axiom,
    mult(mult(mult(A,B),A),mult(A,C)) = mult(A,mult(mult(mult(B,A),A),C)),
    file('GRP700+1.p',unknown),
    [] ).

cnf(30,plain,
    ( A != unit
    | mult(dollar_c1,rd(A,dollar_c1)) != unit ),
    inference(para_from,[status(thm),theory(equality)],[7,1]),
    [iquote('para_from,7.1.1,1.1.1')] ).

cnf(32,plain,
    rd(A,A) = unit,
    inference(para_into,[status(thm),theory(equality)],[10,13]),
    [iquote('para_into,9.1.1.1,13.1.1')] ).

cnf(45,plain,
    mult(mult(mult(A,B),A),A) = mult(A,mult(mult(B,A),A)),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[15,12]),12]),
    [iquote('para_into,15.1.1.2,11.1.1,demod,12')] ).

cnf(156,plain,
    rd(mult(A,mult(mult(B,A),A)),A) = mult(mult(A,B),A),
    inference(para_from,[status(thm),theory(equality)],[45,10]),
    [iquote('para_from,45.1.1,9.1.1.1')] ).

cnf(274,plain,
    rd(mult(A,mult(B,A)),A) = mult(mult(A,rd(B,A)),A),
    inference(para_into,[status(thm),theory(equality)],[156,7]),
    [iquote('para_into,156.1.1.1.2.1,7.1.1')] ).

cnf(370,plain,
    mult(mult(A,rd(unit,A)),A) = A,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[274,13]),10])]),
    [iquote('para_into,274.1.1.1.2,13.1.1,demod,10,flip.1')] ).

cnf(379,plain,
    mult(A,rd(unit,A)) = unit,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[370,10]),32])]),
    [iquote('para_from,370.1.1,9.1.1.1,demod,32,flip.1')] ).

cnf(381,plain,
    $false,
    inference(hyper,[status(thm)],[379,30,2]),
    [iquote('hyper,379,30,2')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : GRP700+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13  % Command  : otter-tptp-script %s
% 0.13/0.34  % Computer : n009.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Wed Jul 27 05:20:06 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 1.74/1.95  ----- Otter 3.3f, August 2004 -----
% 1.74/1.95  The process was started by sandbox2 on n009.cluster.edu,
% 1.74/1.95  Wed Jul 27 05:20:06 2022
% 1.74/1.95  The command was "./otter".  The process ID is 14991.
% 1.74/1.95  
% 1.74/1.95  set(prolog_style_variables).
% 1.74/1.95  set(auto).
% 1.74/1.95     dependent: set(auto1).
% 1.74/1.95     dependent: set(process_input).
% 1.74/1.95     dependent: clear(print_kept).
% 1.74/1.95     dependent: clear(print_new_demod).
% 1.74/1.95     dependent: clear(print_back_demod).
% 1.74/1.95     dependent: clear(print_back_sub).
% 1.74/1.95     dependent: set(control_memory).
% 1.74/1.95     dependent: assign(max_mem, 12000).
% 1.74/1.95     dependent: assign(pick_given_ratio, 4).
% 1.74/1.95     dependent: assign(stats_level, 1).
% 1.74/1.95     dependent: assign(max_seconds, 10800).
% 1.74/1.95  clear(print_given).
% 1.74/1.95  
% 1.74/1.95  formula_list(usable).
% 1.74/1.95  all A (A=A).
% 1.74/1.95  all B A (mult(A,ld(A,B))=B).
% 1.74/1.95  all B A (ld(A,mult(A,B))=B).
% 1.74/1.95  all B A (mult(rd(A,B),B)=A).
% 1.74/1.95  all B A (rd(mult(A,B),B)=A).
% 1.74/1.95  all A (mult(A,unit)=A).
% 1.74/1.95  all A (mult(unit,A)=A).
% 1.74/1.95  all C B A (mult(mult(mult(A,B),A),mult(A,C))=mult(A,mult(mult(mult(B,A),A),C))).
% 1.74/1.95  all C B A (mult(mult(A,B),mult(B,mult(C,B)))=mult(mult(A,mult(B,mult(B,C))),B)).
% 1.74/1.95  -(all X0 exists X1 (mult(X1,X0)=unit&mult(X0,X1)=unit)).
% 1.74/1.95  end_of_list.
% 1.74/1.95  
% 1.74/1.95  -------> usable clausifies to:
% 1.74/1.95  
% 1.74/1.95  list(usable).
% 1.74/1.95  0 [] A=A.
% 1.74/1.95  0 [] mult(A,ld(A,B))=B.
% 1.74/1.95  0 [] ld(A,mult(A,B))=B.
% 1.74/1.95  0 [] mult(rd(A,B),B)=A.
% 1.74/1.95  0 [] rd(mult(A,B),B)=A.
% 1.74/1.95  0 [] mult(A,unit)=A.
% 1.74/1.95  0 [] mult(unit,A)=A.
% 1.74/1.95  0 [] mult(mult(mult(A,B),A),mult(A,C))=mult(A,mult(mult(mult(B,A),A),C)).
% 1.74/1.95  0 [] mult(mult(A,B),mult(B,mult(C,B)))=mult(mult(A,mult(B,mult(B,C))),B).
% 1.74/1.95  0 [] mult(X1,$c1)!=unit|mult($c1,X1)!=unit.
% 1.74/1.95  end_of_list.
% 1.74/1.95  
% 1.74/1.95  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.74/1.95  
% 1.74/1.95  This is a Horn set with equality.  The strategy will be
% 1.74/1.95  Knuth-Bendix and hyper_res, with positive clauses in
% 1.74/1.95  sos and nonpositive clauses in usable.
% 1.74/1.95  
% 1.74/1.95     dependent: set(knuth_bendix).
% 1.74/1.95     dependent: set(anl_eq).
% 1.74/1.95     dependent: set(para_from).
% 1.74/1.95     dependent: set(para_into).
% 1.74/1.95     dependent: clear(para_from_right).
% 1.74/1.95     dependent: clear(para_into_right).
% 1.74/1.95     dependent: set(para_from_vars).
% 1.74/1.95     dependent: set(eq_units_both_ways).
% 1.74/1.95     dependent: set(dynamic_demod_all).
% 1.74/1.95     dependent: set(dynamic_demod).
% 1.74/1.95     dependent: set(order_eq).
% 1.74/1.95     dependent: set(back_demod).
% 1.74/1.95     dependent: set(lrpo).
% 1.74/1.95     dependent: set(hyper_res).
% 1.74/1.95     dependent: clear(order_hyper).
% 1.74/1.95  
% 1.74/1.95  ------------> process usable:
% 1.74/1.95  ** KEPT (pick-wt=10): 1 [] mult(A,$c1)!=unit|mult($c1,A)!=unit.
% 1.74/1.95  
% 1.74/1.95  ------------> process sos:
% 1.74/1.95  ** KEPT (pick-wt=3): 2 [] A=A.
% 1.74/1.95  ** KEPT (pick-wt=7): 3 [] mult(A,ld(A,B))=B.
% 1.74/1.95  ---> New Demodulator: 4 [new_demod,3] mult(A,ld(A,B))=B.
% 1.74/1.95  ** KEPT (pick-wt=7): 5 [] ld(A,mult(A,B))=B.
% 1.74/1.95  ---> New Demodulator: 6 [new_demod,5] ld(A,mult(A,B))=B.
% 1.74/1.95  ** KEPT (pick-wt=7): 7 [] mult(rd(A,B),B)=A.
% 1.74/1.95  ---> New Demodulator: 8 [new_demod,7] mult(rd(A,B),B)=A.
% 1.74/1.95  ** KEPT (pick-wt=7): 9 [] rd(mult(A,B),B)=A.
% 1.74/1.95  ---> New Demodulator: 10 [new_demod,9] rd(mult(A,B),B)=A.
% 1.74/1.95  ** KEPT (pick-wt=5): 11 [] mult(A,unit)=A.
% 1.74/1.95  ---> New Demodulator: 12 [new_demod,11] mult(A,unit)=A.
% 1.74/1.95  ** KEPT (pick-wt=5): 13 [] mult(unit,A)=A.
% 1.74/1.95  ---> New Demodulator: 14 [new_demod,13] mult(unit,A)=A.
% 1.74/1.95  ** KEPT (pick-wt=19): 15 [] mult(mult(mult(A,B),A),mult(A,C))=mult(A,mult(mult(mult(B,A),A),C)).
% 1.74/1.95  ** KEPT (pick-wt=19): 17 [copy,16,flip.1] mult(mult(A,mult(B,mult(B,C))),B)=mult(mult(A,B),mult(B,mult(C,B))).
% 1.74/1.95  ---> New Demodulator: 18 [new_demod,17] mult(mult(A,mult(B,mult(B,C))),B)=mult(mult(A,B),mult(B,mult(C,B))).
% 1.74/1.95    Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.74/1.95  >>>> Starting back demodulation with 4.
% 1.74/1.95  >>>> Starting back demodulation with 6.
% 1.74/1.95  >>>> Starting back demodulation with 8.
% 1.74/1.95  >>>> Starting back demodulation with 10.
% 1.74/1.95  >>>> Starting back demodulation with 12.
% 1.74/1.95  >>>> Starting back demodulation with 14.
% 1.74/1.95  ** KEPT (pick-wt=19): 19 [copy,15,flip.1] mult(A,mult(mult(mult(B,A),A),C))=mult(mult(mult(A,B),A),mult(A,C)).
% 1.74/1.95  >>>> Starting back demodulation with 18.
% 1.74/1.95    Following clause subsumed by 15 during input processing: 0 [copy,19,flip.1] mult(mult(mult(A,B),A),mult(A,C))=mult(A,mult(mult(mult(B,A),A),C)).
% 1.74/1.95  
% 1.74/1.95  ======= end of input processing =======
% 1.74/1.95  
% 1.74/1.95  =========== start of search ===========
% 1.74/1.95  
% 1.74/1.95  
% 1.74/1.95  Resetting weight limit to 18.
% 1.74/1.95  
% 1.74/1.95  
% 1.74/1.95  Resetting weight limit to 18.
% 1.74/1.95  
% 1.74/1.95  sos_size=156
% 1.74/1.95  
% 1.74/1.95  -------- PROOF -------- 
% 1.74/1.95  
% 1.74/1.95  -----> EMPTY CLAUSE at   0.03 sec ----> 381 [hyper,379,30,2] $F.
% 1.74/1.95  
% 1.74/1.95  Length of proof is 7.  Level of proof is 5.
% 1.74/1.95  
% 1.74/1.95  ---------------- PROOF ----------------
% 1.74/1.95  % SZS status Theorem
% 1.74/1.95  % SZS output start Refutation
% See solution above
% 1.74/1.95  ------------ end of proof -------------
% 1.74/1.95  
% 1.74/1.95  
% 1.74/1.95  Search stopped by max_proofs option.
% 1.74/1.95  
% 1.74/1.95  
% 1.74/1.95  Search stopped by max_proofs option.
% 1.74/1.95  
% 1.74/1.95  ============ end of search ============
% 1.74/1.95  
% 1.74/1.95  -------------- statistics -------------
% 1.74/1.95  clauses given                 42
% 1.74/1.95  clauses generated            690
% 1.74/1.95  clauses kept                 241
% 1.74/1.95  clauses forward subsumed     397
% 1.74/1.95  clauses back subsumed          0
% 1.74/1.95  Kbytes malloced             5859
% 1.74/1.95  
% 1.74/1.95  ----------- times (seconds) -----------
% 1.74/1.95  user CPU time          0.03          (0 hr, 0 min, 0 sec)
% 1.74/1.95  system CPU time        0.01          (0 hr, 0 min, 0 sec)
% 1.74/1.95  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.74/1.95  
% 1.74/1.95  That finishes the proof of the theorem.
% 1.74/1.95  
% 1.74/1.95  Process 14991 finished Wed Jul 27 05:20:07 2022
% 1.74/1.95  Otter interrupted
% 1.74/1.95  PROOF FOUND
%------------------------------------------------------------------------------