TSTP Solution File: COM020+1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : COM020+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n018.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 12:48:23 EDT 2022

% Result   : Theorem 13.20s 13.42s
% Output   : Refutation 13.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   19
% Syntax   : Number of clauses     :   28 (  19 unt;   0 nHn;  28 RR)
%            Number of literals    :   69 (   0 equ;  42 neg)
%            Maximal clause size   :    7 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-3 aty)
%            Number of variables   :   26 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(5,axiom,
    ( ~ aElement0(A)
    | ~ aRewritingSystem0(B)
    | ~ aElement0(C)
    | sdtmndtplgtdt0(A,B,C)
    | ~ aReductOfIn0(C,A,B) ),
    file('COM020+1.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ aElement0(A)
    | ~ aRewritingSystem0(B)
    | ~ aElement0(C)
    | ~ aElement0(D)
    | ~ sdtmndtasgtdt0(A,B,C)
    | ~ sdtmndtasgtdt0(C,B,D)
    | sdtmndtasgtdt0(A,B,D) ),
    file('COM020+1.p',unknown),
    [] ).

cnf(30,axiom,
    ( ~ aRewritingSystem0(A)
    | ~ isTerminating0(A)
    | ~ aElement0(B)
    | ~ aElement0(C)
    | ~ sdtmndtplgtdt0(B,A,C)
    | iLess0(C,B) ),
    file('COM020+1.p',unknown),
    [] ).

cnf(35,axiom,
    ( ~ aElement0(A)
    | ~ aRewritingSystem0(B)
    | ~ aNormalFormOfIn0(C,A,B)
    | aElement0(C) ),
    file('COM020+1.p',unknown),
    [] ).

cnf(36,axiom,
    ( ~ aElement0(A)
    | ~ aRewritingSystem0(B)
    | ~ aNormalFormOfIn0(C,A,B)
    | sdtmndtasgtdt0(A,B,C) ),
    file('COM020+1.p',unknown),
    [] ).

cnf(40,axiom,
    ( ~ aElement0(A)
    | ~ aElement0(B)
    | ~ aElement0(C)
    | ~ sdtmndtasgtdt0(A,xR,B)
    | ~ sdtmndtasgtdt0(A,xR,C)
    | ~ iLess0(A,xa)
    | aElement0(dollar_f14(A,B,C)) ),
    file('COM020+1.p',unknown),
    [] ).

cnf(41,axiom,
    ( ~ aElement0(A)
    | ~ aElement0(B)
    | ~ aElement0(C)
    | ~ sdtmndtasgtdt0(A,xR,B)
    | ~ sdtmndtasgtdt0(A,xR,C)
    | ~ iLess0(A,xa)
    | sdtmndtasgtdt0(B,xR,dollar_f14(A,B,C)) ),
    file('COM020+1.p',unknown),
    [] ).

cnf(42,axiom,
    ( ~ aElement0(A)
    | ~ aElement0(B)
    | ~ aElement0(C)
    | ~ sdtmndtasgtdt0(A,xR,B)
    | ~ sdtmndtasgtdt0(A,xR,C)
    | ~ iLess0(A,xa)
    | sdtmndtasgtdt0(C,xR,dollar_f14(A,B,C)) ),
    file('COM020+1.p',unknown),
    [] ).

cnf(43,axiom,
    ( ~ aElement0(A)
    | ~ sdtmndtasgtdt0(xb,xR,A)
    | ~ sdtmndtasgtdt0(xd,xR,A) ),
    file('COM020+1.p',unknown),
    [] ).

cnf(87,axiom,
    aRewritingSystem0(xR),
    file('COM020+1.p',unknown),
    [] ).

cnf(89,axiom,
    isTerminating0(xR),
    file('COM020+1.p',unknown),
    [] ).

cnf(90,axiom,
    aElement0(xa),
    file('COM020+1.p',unknown),
    [] ).

cnf(91,axiom,
    aElement0(xb),
    file('COM020+1.p',unknown),
    [] ).

cnf(95,axiom,
    aElement0(xu),
    file('COM020+1.p',unknown),
    [] ).

cnf(96,axiom,
    aReductOfIn0(xu,xa,xR),
    file('COM020+1.p',unknown),
    [] ).

cnf(97,axiom,
    sdtmndtasgtdt0(xu,xR,xb),
    file('COM020+1.p',unknown),
    [] ).

cnf(101,axiom,
    aElement0(xw),
    file('COM020+1.p',unknown),
    [] ).

cnf(102,axiom,
    sdtmndtasgtdt0(xu,xR,xw),
    file('COM020+1.p',unknown),
    [] ).

cnf(104,axiom,
    aNormalFormOfIn0(xd,xw,xR),
    file('COM020+1.p',unknown),
    [] ).

cnf(147,plain,
    sdtmndtplgtdt0(xa,xR,xu),
    inference(hyper,[status(thm)],[96,5,90,87,95]),
    [iquote('hyper,96,5,90,87,95')] ).

cnf(183,plain,
    sdtmndtasgtdt0(xw,xR,xd),
    inference(hyper,[status(thm)],[104,36,101,87]),
    [iquote('hyper,104,36,101,87')] ).

cnf(184,plain,
    aElement0(xd),
    inference(hyper,[status(thm)],[104,35,101,87]),
    [iquote('hyper,104,35,101,87')] ).

cnf(394,plain,
    iLess0(xu,xa),
    inference(hyper,[status(thm)],[147,30,87,89,90,95]),
    [iquote('hyper,147,30,87,89,90,95')] ).

cnf(561,plain,
    sdtmndtasgtdt0(xu,xR,xd),
    inference(hyper,[status(thm)],[183,11,95,87,101,184,102]),
    [iquote('hyper,183,11,95,87,101,184,102')] ).

cnf(1006,plain,
    sdtmndtasgtdt0(xd,xR,dollar_f14(xu,xb,xd)),
    inference(hyper,[status(thm)],[561,42,95,91,184,97,394]),
    [iquote('hyper,561,42,95,91,184,97,394')] ).

cnf(1010,plain,
    sdtmndtasgtdt0(xb,xR,dollar_f14(xu,xb,xd)),
    inference(hyper,[status(thm)],[561,41,95,91,184,97,394]),
    [iquote('hyper,561,41,95,91,184,97,394')] ).

cnf(1014,plain,
    aElement0(dollar_f14(xu,xb,xd)),
    inference(hyper,[status(thm)],[561,40,95,91,184,97,394]),
    [iquote('hyper,561,40,95,91,184,97,394')] ).

cnf(5223,plain,
    $false,
    inference(hyper,[status(thm)],[1010,43,1014,1006]),
    [iquote('hyper,1010,43,1014,1006')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : COM020+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n018.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 06:39:46 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.87/2.06  ----- Otter 3.3f, August 2004 -----
% 1.87/2.06  The process was started by sandbox on n018.cluster.edu,
% 1.87/2.06  Wed Jul 27 06:39:46 2022
% 1.87/2.06  The command was "./otter".  The process ID is 28193.
% 1.87/2.06  
% 1.87/2.06  set(prolog_style_variables).
% 1.87/2.06  set(auto).
% 1.87/2.06     dependent: set(auto1).
% 1.87/2.06     dependent: set(process_input).
% 1.87/2.06     dependent: clear(print_kept).
% 1.87/2.06     dependent: clear(print_new_demod).
% 1.87/2.06     dependent: clear(print_back_demod).
% 1.87/2.06     dependent: clear(print_back_sub).
% 1.87/2.06     dependent: set(control_memory).
% 1.87/2.06     dependent: assign(max_mem, 12000).
% 1.87/2.06     dependent: assign(pick_given_ratio, 4).
% 1.87/2.06     dependent: assign(stats_level, 1).
% 1.87/2.06     dependent: assign(max_seconds, 10800).
% 1.87/2.06  clear(print_given).
% 1.87/2.06  
% 1.87/2.06  formula_list(usable).
% 1.87/2.06  all A (A=A).
% 1.87/2.06  all W0 (aElement0(W0)->$T).
% 1.87/2.06  all W0 (aRewritingSystem0(W0)->$T).
% 1.87/2.06  all W0 W1 (aElement0(W0)&aRewritingSystem0(W1)-> (all W2 (aReductOfIn0(W2,W0,W1)->aElement0(W2)))).
% 1.87/2.06  all W0 W1 (aElement0(W0)&aElement0(W1)-> (iLess0(W0,W1)->$T)).
% 1.87/2.06  all W0 W1 W2 (aElement0(W0)&aRewritingSystem0(W1)&aElement0(W2)-> (sdtmndtplgtdt0(W0,W1,W2)->$T)).
% 1.87/2.06  all W0 W1 W2 (aElement0(W0)&aRewritingSystem0(W1)&aElement0(W2)-> (sdtmndtplgtdt0(W0,W1,W2)<->aReductOfIn0(W2,W0,W1)| (exists W3 (aElement0(W3)&aReductOfIn0(W3,W0,W1)&sdtmndtplgtdt0(W3,W1,W2))))).
% 1.87/2.06  all W0 W1 W2 W3 (aElement0(W0)&aRewritingSystem0(W1)&aElement0(W2)&aElement0(W3)-> (sdtmndtplgtdt0(W0,W1,W2)&sdtmndtplgtdt0(W2,W1,W3)->sdtmndtplgtdt0(W0,W1,W3))).
% 1.87/2.06  all W0 W1 W2 (aElement0(W0)&aRewritingSystem0(W1)&aElement0(W2)-> (sdtmndtasgtdt0(W0,W1,W2)<->W0=W2|sdtmndtplgtdt0(W0,W1,W2))).
% 1.87/2.06  all W0 W1 W2 W3 (aElement0(W0)&aRewritingSystem0(W1)&aElement0(W2)&aElement0(W3)-> (sdtmndtasgtdt0(W0,W1,W2)&sdtmndtasgtdt0(W2,W1,W3)->sdtmndtasgtdt0(W0,W1,W3))).
% 1.87/2.06  all W0 (aRewritingSystem0(W0)-> (isConfluent0(W0)<-> (all W1 W2 W3 (aElement0(W1)&aElement0(W2)&aElement0(W3)&sdtmndtasgtdt0(W1,W0,W2)&sdtmndtasgtdt0(W1,W0,W3)-> (exists W4 (aElement0(W4)&sdtmndtasgtdt0(W2,W0,W4)&sdtmndtasgtdt0(W3,W0,W4))))))).
% 1.87/2.06  all W0 (aRewritingSystem0(W0)-> (isLocallyConfluent0(W0)<-> (all W1 W2 W3 (aElement0(W1)&aElement0(W2)&aElement0(W3)&aReductOfIn0(W2,W1,W0)&aReductOfIn0(W3,W1,W0)-> (exists W4 (aElement0(W4)&sdtmndtasgtdt0(W2,W0,W4)&sdtmndtasgtdt0(W3,W0,W4))))))).
% 1.87/2.06  all W0 (aRewritingSystem0(W0)-> (isTerminating0(W0)<-> (all W1 W2 (aElement0(W1)&aElement0(W2)-> (sdtmndtplgtdt0(W1,W0,W2)->iLess0(W2,W1)))))).
% 1.87/2.06  all W0 W1 (aElement0(W0)&aRewritingSystem0(W1)-> (all W2 (aNormalFormOfIn0(W2,W0,W1)<->aElement0(W2)&sdtmndtasgtdt0(W0,W1,W2)& -(exists W3 aReductOfIn0(W3,W2,W1))))).
% 1.87/2.06  all W0 (aRewritingSystem0(W0)&isTerminating0(W0)-> (all W1 (aElement0(W1)-> (exists W2 aNormalFormOfIn0(W2,W1,W0))))).
% 1.87/2.06  aRewritingSystem0(xR).
% 1.87/2.06  isLocallyConfluent0(xR).
% 1.87/2.06  isTerminating0(xR).
% 1.87/2.06  aElement0(xa).
% 1.87/2.06  aElement0(xb).
% 1.87/2.06  aElement0(xc).
% 1.87/2.06  all W0 W1 W2 (aElement0(W0)&aElement0(W1)&aElement0(W2)&sdtmndtasgtdt0(W0,xR,W1)&sdtmndtasgtdt0(W0,xR,W2)-> (iLess0(W0,xa)-> (exists W3 (aElement0(W3)&sdtmndtasgtdt0(W1,xR,W3)&sdtmndtasgtdt0(W2,xR,W3))))).
% 1.87/2.06  sdtmndtplgtdt0(xa,xR,xb).
% 1.87/2.06  sdtmndtplgtdt0(xa,xR,xc).
% 1.87/2.06  aElement0(xu).
% 1.87/2.06  aReductOfIn0(xu,xa,xR).
% 1.87/2.06  sdtmndtasgtdt0(xu,xR,xb).
% 1.87/2.06  aElement0(xv).
% 1.87/2.06  aReductOfIn0(xv,xa,xR).
% 1.87/2.06  sdtmndtasgtdt0(xv,xR,xc).
% 1.87/2.06  aElement0(xw).
% 1.87/2.06  sdtmndtasgtdt0(xu,xR,xw).
% 1.87/2.06  sdtmndtasgtdt0(xv,xR,xw).
% 1.87/2.06  aNormalFormOfIn0(xd,xw,xR).
% 1.87/2.06  -(exists W0 (aElement0(W0)&sdtmndtasgtdt0(xb,xR,W0)&sdtmndtasgtdt0(xd,xR,W0))).
% 1.87/2.06  end_of_list.
% 1.87/2.06  
% 1.87/2.06  -------> usable clausifies to:
% 1.87/2.06  
% 1.87/2.06  list(usable).
% 1.87/2.06  0 [] A=A.
% 1.87/2.06  0 [] -aElement0(W0)|$T.
% 1.87/2.06  0 [] -aRewritingSystem0(W0)|$T.
% 1.87/2.06  0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aReductOfIn0(W2,W0,W1)|aElement0(W2).
% 1.87/2.06  0 [] -aElement0(W0)| -aElement0(W1)| -iLess0(W0,W1)|$T.
% 1.87/2.06  0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)| -sdtmndtplgtdt0(W0,W1,W2)|$T.
% 1.87/2.06  0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)| -sdtmndtplgtdt0(W0,W1,W2)|aReductOfIn0(W2,W0,W1)|aElement0($f1(W0,W1,W2)).
% 1.87/2.06  0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)| -sdtmndtplgtdt0(W0,W1,W2)|aReductOfIn0(W2,W0,W1)|aReductOfIn0($f1(W0,W1,W2),W0,W1).
% 1.87/2.06  0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)| -sdtmndtplgtdt0(W0,W1,W2)|aReductOfIn0(W2,W0,W1)|sdtmndtplgtdt0($f1(W0,W1,W2),W1,W2).
% 1.87/2.06  0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)|sdtmndtplgtdt0(W0,W1,W2)| -aReductOfIn0(W2,W0,W1).
% 1.87/2.07  0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)|sdtmndtplgtdt0(W0,W1,W2)| -aElement0(W3)| -aReductOfIn0(W3,W0,W1)| -sdtmndtplgtdt0(W3,W1,W2).
% 1.87/2.07  0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)| -aElement0(W3)| -sdtmndtplgtdt0(W0,W1,W2)| -sdtmndtplgtdt0(W2,W1,W3)|sdtmndtplgtdt0(W0,W1,W3).
% 1.87/2.07  0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)| -sdtmndtasgtdt0(W0,W1,W2)|W0=W2|sdtmndtplgtdt0(W0,W1,W2).
% 1.87/2.07  0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)|sdtmndtasgtdt0(W0,W1,W2)|W0!=W2.
% 1.87/2.07  0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)|sdtmndtasgtdt0(W0,W1,W2)| -sdtmndtplgtdt0(W0,W1,W2).
% 1.87/2.07  0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aElement0(W2)| -aElement0(W3)| -sdtmndtasgtdt0(W0,W1,W2)| -sdtmndtasgtdt0(W2,W1,W3)|sdtmndtasgtdt0(W0,W1,W3).
% 1.87/2.07  0 [] -aRewritingSystem0(W0)| -isConfluent0(W0)| -aElement0(W1)| -aElement0(W2)| -aElement0(W3)| -sdtmndtasgtdt0(W1,W0,W2)| -sdtmndtasgtdt0(W1,W0,W3)|aElement0($f2(W0,W1,W2,W3)).
% 1.87/2.07  0 [] -aRewritingSystem0(W0)| -isConfluent0(W0)| -aElement0(W1)| -aElement0(W2)| -aElement0(W3)| -sdtmndtasgtdt0(W1,W0,W2)| -sdtmndtasgtdt0(W1,W0,W3)|sdtmndtasgtdt0(W2,W0,$f2(W0,W1,W2,W3)).
% 1.87/2.07  0 [] -aRewritingSystem0(W0)| -isConfluent0(W0)| -aElement0(W1)| -aElement0(W2)| -aElement0(W3)| -sdtmndtasgtdt0(W1,W0,W2)| -sdtmndtasgtdt0(W1,W0,W3)|sdtmndtasgtdt0(W3,W0,$f2(W0,W1,W2,W3)).
% 1.87/2.07  0 [] -aRewritingSystem0(W0)|isConfluent0(W0)|aElement0($f5(W0)).
% 1.87/2.07  0 [] -aRewritingSystem0(W0)|isConfluent0(W0)|aElement0($f4(W0)).
% 1.87/2.07  0 [] -aRewritingSystem0(W0)|isConfluent0(W0)|aElement0($f3(W0)).
% 1.87/2.07  0 [] -aRewritingSystem0(W0)|isConfluent0(W0)|sdtmndtasgtdt0($f5(W0),W0,$f4(W0)).
% 1.87/2.07  0 [] -aRewritingSystem0(W0)|isConfluent0(W0)|sdtmndtasgtdt0($f5(W0),W0,$f3(W0)).
% 1.87/2.07  0 [] -aRewritingSystem0(W0)|isConfluent0(W0)| -aElement0(W4)| -sdtmndtasgtdt0($f4(W0),W0,W4)| -sdtmndtasgtdt0($f3(W0),W0,W4).
% 1.87/2.07  0 [] -aRewritingSystem0(W0)| -isLocallyConfluent0(W0)| -aElement0(W1)| -aElement0(W2)| -aElement0(W3)| -aReductOfIn0(W2,W1,W0)| -aReductOfIn0(W3,W1,W0)|aElement0($f6(W0,W1,W2,W3)).
% 1.87/2.07  0 [] -aRewritingSystem0(W0)| -isLocallyConfluent0(W0)| -aElement0(W1)| -aElement0(W2)| -aElement0(W3)| -aReductOfIn0(W2,W1,W0)| -aReductOfIn0(W3,W1,W0)|sdtmndtasgtdt0(W2,W0,$f6(W0,W1,W2,W3)).
% 1.87/2.07  0 [] -aRewritingSystem0(W0)| -isLocallyConfluent0(W0)| -aElement0(W1)| -aElement0(W2)| -aElement0(W3)| -aReductOfIn0(W2,W1,W0)| -aReductOfIn0(W3,W1,W0)|sdtmndtasgtdt0(W3,W0,$f6(W0,W1,W2,W3)).
% 1.87/2.07  0 [] -aRewritingSystem0(W0)|isLocallyConfluent0(W0)|aElement0($f9(W0)).
% 1.87/2.07  0 [] -aRewritingSystem0(W0)|isLocallyConfluent0(W0)|aElement0($f8(W0)).
% 1.87/2.07  0 [] -aRewritingSystem0(W0)|isLocallyConfluent0(W0)|aElement0($f7(W0)).
% 1.87/2.07  0 [] -aRewritingSystem0(W0)|isLocallyConfluent0(W0)|aReductOfIn0($f8(W0),$f9(W0),W0).
% 1.87/2.07  0 [] -aRewritingSystem0(W0)|isLocallyConfluent0(W0)|aReductOfIn0($f7(W0),$f9(W0),W0).
% 1.87/2.07  0 [] -aRewritingSystem0(W0)|isLocallyConfluent0(W0)| -aElement0(W4)| -sdtmndtasgtdt0($f8(W0),W0,W4)| -sdtmndtasgtdt0($f7(W0),W0,W4).
% 1.87/2.07  0 [] -aRewritingSystem0(W0)| -isTerminating0(W0)| -aElement0(W1)| -aElement0(W2)| -sdtmndtplgtdt0(W1,W0,W2)|iLess0(W2,W1).
% 1.87/2.07  0 [] -aRewritingSystem0(W0)|isTerminating0(W0)|aElement0($f11(W0)).
% 1.87/2.07  0 [] -aRewritingSystem0(W0)|isTerminating0(W0)|aElement0($f10(W0)).
% 1.87/2.07  0 [] -aRewritingSystem0(W0)|isTerminating0(W0)|sdtmndtplgtdt0($f11(W0),W0,$f10(W0)).
% 1.87/2.07  0 [] -aRewritingSystem0(W0)|isTerminating0(W0)| -iLess0($f10(W0),$f11(W0)).
% 1.87/2.07  0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aNormalFormOfIn0(W2,W0,W1)|aElement0(W2).
% 1.87/2.07  0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aNormalFormOfIn0(W2,W0,W1)|sdtmndtasgtdt0(W0,W1,W2).
% 1.87/2.07  0 [] -aElement0(W0)| -aRewritingSystem0(W1)| -aNormalFormOfIn0(W2,W0,W1)| -aReductOfIn0(W3,W2,W1).
% 1.87/2.07  0 [] -aElement0(W0)| -aRewritingSystem0(W1)|aNormalFormOfIn0(W2,W0,W1)| -aElement0(W2)| -sdtmndtasgtdt0(W0,W1,W2)|aReductOfIn0($f12(W0,W1,W2),W2,W1).
% 1.87/2.07  0 [] -aRewritingSystem0(W0)| -isTerminating0(W0)| -aElement0(W1)|aNormalFormOfIn0($f13(W0,W1),W1,W0).
% 1.87/2.07  0 [] aRewritingSystem0(xR).
% 1.87/2.07  0 [] isLocallyConfluent0(xR).
% 1.87/2.07  0 [] isTerminating0(xR).
% 1.87/2.07  0 [] aElement0(xa).
% 1.87/2.07  0 [] aElement0(xb).
% 1.87/2.07  0 [] aElement0(xc).
% 1.87/2.07  0 [] -aElement0(W0)| -aElement0(W1)| -aElement0(W2)| -sdtmndtasgtdt0(W0,xR,W1)| -sdtmndtasgtdt0(W0,xR,W2)| -iLess0(W0,xa)|aElement0($f14(W0,W1,W2)).
% 1.92/2.08  0 [] -aElement0(W0)| -aElement0(W1)| -aElement0(W2)| -sdtmndtasgtdt0(W0,xR,W1)| -sdtmndtasgtdt0(W0,xR,W2)| -iLess0(W0,xa)|sdtmndtasgtdt0(W1,xR,$f14(W0,W1,W2)).
% 1.92/2.08  0 [] -aElement0(W0)| -aElement0(W1)| -aElement0(W2)| -sdtmndtasgtdt0(W0,xR,W1)| -sdtmndtasgtdt0(W0,xR,W2)| -iLess0(W0,xa)|sdtmndtasgtdt0(W2,xR,$f14(W0,W1,W2)).
% 1.92/2.08  0 [] sdtmndtplgtdt0(xa,xR,xb).
% 1.92/2.08  0 [] sdtmndtplgtdt0(xa,xR,xc).
% 1.92/2.08  0 [] aElement0(xu).
% 1.92/2.08  0 [] aReductOfIn0(xu,xa,xR).
% 1.92/2.08  0 [] sdtmndtasgtdt0(xu,xR,xb).
% 1.92/2.08  0 [] aElement0(xv).
% 1.92/2.08  0 [] aReductOfIn0(xv,xa,xR).
% 1.92/2.08  0 [] sdtmndtasgtdt0(xv,xR,xc).
% 1.92/2.08  0 [] aElement0(xw).
% 1.92/2.08  0 [] sdtmndtasgtdt0(xu,xR,xw).
% 1.92/2.08  0 [] sdtmndtasgtdt0(xv,xR,xw).
% 1.92/2.08  0 [] aNormalFormOfIn0(xd,xw,xR).
% 1.92/2.08  0 [] -aElement0(W0)| -sdtmndtasgtdt0(xb,xR,W0)| -sdtmndtasgtdt0(xd,xR,W0).
% 1.92/2.08  end_of_list.
% 1.92/2.08  
% 1.92/2.08  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=8.
% 1.92/2.08  
% 1.92/2.08  This ia a non-Horn set with equality.  The strategy will be
% 1.92/2.08  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.92/2.08  deletion, with positive clauses in sos and nonpositive
% 1.92/2.08  clauses in usable.
% 1.92/2.08  
% 1.92/2.08     dependent: set(knuth_bendix).
% 1.92/2.08     dependent: set(anl_eq).
% 1.92/2.08     dependent: set(para_from).
% 1.92/2.08     dependent: set(para_into).
% 1.92/2.08     dependent: clear(para_from_right).
% 1.92/2.08     dependent: clear(para_into_right).
% 1.92/2.08     dependent: set(para_from_vars).
% 1.92/2.08     dependent: set(eq_units_both_ways).
% 1.92/2.08     dependent: set(dynamic_demod_all).
% 1.92/2.08     dependent: set(dynamic_demod).
% 1.92/2.08     dependent: set(order_eq).
% 1.92/2.08     dependent: set(back_demod).
% 1.92/2.08     dependent: set(lrpo).
% 1.92/2.08     dependent: set(hyper_res).
% 1.92/2.08     dependent: set(unit_deletion).
% 1.92/2.08     dependent: set(factor).
% 1.92/2.08  
% 1.92/2.08  ------------> process usable:
% 1.92/2.08  ** KEPT (pick-wt=10): 1 [] -aElement0(A)| -aRewritingSystem0(B)| -aReductOfIn0(C,A,B)|aElement0(C).
% 1.92/2.08  ** KEPT (pick-wt=19): 2 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)| -sdtmndtplgtdt0(A,B,C)|aReductOfIn0(C,A,B)|aElement0($f1(A,B,C)).
% 1.92/2.08  ** KEPT (pick-wt=21): 3 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)| -sdtmndtplgtdt0(A,B,C)|aReductOfIn0(C,A,B)|aReductOfIn0($f1(A,B,C),A,B).
% 1.92/2.08  ** KEPT (pick-wt=21): 4 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)| -sdtmndtplgtdt0(A,B,C)|aReductOfIn0(C,A,B)|sdtmndtplgtdt0($f1(A,B,C),B,C).
% 1.92/2.08  ** KEPT (pick-wt=14): 5 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)|sdtmndtplgtdt0(A,B,C)| -aReductOfIn0(C,A,B).
% 1.92/2.08  ** KEPT (pick-wt=20): 6 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)|sdtmndtplgtdt0(A,B,C)| -aElement0(D)| -aReductOfIn0(D,A,B)| -sdtmndtplgtdt0(D,B,C).
% 1.92/2.08  ** KEPT (pick-wt=20): 7 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)| -aElement0(D)| -sdtmndtplgtdt0(A,B,C)| -sdtmndtplgtdt0(C,B,D)|sdtmndtplgtdt0(A,B,D).
% 1.92/2.08  ** KEPT (pick-wt=17): 8 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)| -sdtmndtasgtdt0(A,B,C)|A=C|sdtmndtplgtdt0(A,B,C).
% 1.92/2.08  ** KEPT (pick-wt=13): 9 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)|sdtmndtasgtdt0(A,B,C)|A!=C.
% 1.92/2.08  ** KEPT (pick-wt=14): 10 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)|sdtmndtasgtdt0(A,B,C)| -sdtmndtplgtdt0(A,B,C).
% 1.92/2.08  ** KEPT (pick-wt=20): 11 [] -aElement0(A)| -aRewritingSystem0(B)| -aElement0(C)| -aElement0(D)| -sdtmndtasgtdt0(A,B,C)| -sdtmndtasgtdt0(C,B,D)|sdtmndtasgtdt0(A,B,D).
% 1.92/2.08  ** KEPT (pick-wt=24): 12 [] -aRewritingSystem0(A)| -isConfluent0(A)| -aElement0(B)| -aElement0(C)| -aElement0(D)| -sdtmndtasgtdt0(B,A,C)| -sdtmndtasgtdt0(B,A,D)|aElement0($f2(A,B,C,D)).
% 1.92/2.08  ** KEPT (pick-wt=26): 13 [] -aRewritingSystem0(A)| -isConfluent0(A)| -aElement0(B)| -aElement0(C)| -aElement0(D)| -sdtmndtasgtdt0(B,A,C)| -sdtmndtasgtdt0(B,A,D)|sdtmndtasgtdt0(C,A,$f2(A,B,C,D)).
% 1.92/2.08  ** KEPT (pick-wt=26): 14 [] -aRewritingSystem0(A)| -isConfluent0(A)| -aElement0(B)| -aElement0(C)| -aElement0(D)| -sdtmndtasgtdt0(B,A,C)| -sdtmndtasgtdt0(B,A,D)|sdtmndtasgtdt0(D,A,$f2(A,B,C,D)).
% 1.92/2.08  ** KEPT (pick-wt=7): 15 [] -aRewritingSystem0(A)|isConfluent0(A)|aElement0($f5(A)).
% 1.92/2.08  ** KEPT (pick-wt=7): 16 [] -aRewritingSystem0(A)|isConfluent0(A)|aElement0($f4(A)).
% 1.92/2.08  ** KEPT (pick-wt=7): 17 [] -aRewritingSystem0(A)|isConfluent0(A)|aElement0($f3(A)).
% 1.92/2.08  ** KEPT (pick-wt=10): 18 [] -aRewritingSystem0(A)|isConfluent0(A)|sdtmndtasgtdt0($f5(A),A,$f4(A)).
% 1.92/2.08  ** KEPT (pick-wt=10): 19 [] -aRewritingSystem0(A)|isConfluent0(A)|sdtmndtasgtdt0($f5(A),A,$f3(A)).
% 1.92/2.08  ** KEPT (pick-wt=16): 20 [] -aRewritingSystem0(A)|isConfluent0(A)| -aElement0(B)| -sdtmndtasgtdt0($f4(A),A,B)| -sdtmndtasgtdt0($f3(A),A,B).
% 1.92/2.08  ** KEPT (pick-wt=24): 21 [] -aRewritingSystem0(A)| -isLocallyConfluent0(A)| -aElement0(B)| -aElement0(C)| -aElement0(D)| -aReductOfIn0(C,B,A)| -aReductOfIn0(D,B,A)|aElement0($f6(A,B,C,D)).
% 1.92/2.08  ** KEPT (pick-wt=26): 22 [] -aRewritingSystem0(A)| -isLocallyConfluent0(A)| -aElement0(B)| -aElement0(C)| -aElement0(D)| -aReductOfIn0(C,B,A)| -aReductOfIn0(D,B,A)|sdtmndtasgtdt0(C,A,$f6(A,B,C,D)).
% 1.92/2.08  ** KEPT (pick-wt=26): 23 [] -aRewritingSystem0(A)| -isLocallyConfluent0(A)| -aElement0(B)| -aElement0(C)| -aElement0(D)| -aReductOfIn0(C,B,A)| -aReductOfIn0(D,B,A)|sdtmndtasgtdt0(D,A,$f6(A,B,C,D)).
% 1.92/2.08  ** KEPT (pick-wt=7): 24 [] -aRewritingSystem0(A)|isLocallyConfluent0(A)|aElement0($f9(A)).
% 1.92/2.08  ** KEPT (pick-wt=7): 25 [] -aRewritingSystem0(A)|isLocallyConfluent0(A)|aElement0($f8(A)).
% 1.92/2.08  ** KEPT (pick-wt=7): 26 [] -aRewritingSystem0(A)|isLocallyConfluent0(A)|aElement0($f7(A)).
% 1.92/2.08  ** KEPT (pick-wt=10): 27 [] -aRewritingSystem0(A)|isLocallyConfluent0(A)|aReductOfIn0($f8(A),$f9(A),A).
% 1.92/2.08  ** KEPT (pick-wt=10): 28 [] -aRewritingSystem0(A)|isLocallyConfluent0(A)|aReductOfIn0($f7(A),$f9(A),A).
% 1.92/2.08  ** KEPT (pick-wt=16): 29 [] -aRewritingSystem0(A)|isLocallyConfluent0(A)| -aElement0(B)| -sdtmndtasgtdt0($f8(A),A,B)| -sdtmndtasgtdt0($f7(A),A,B).
% 1.92/2.08  ** KEPT (pick-wt=15): 30 [] -aRewritingSystem0(A)| -isTerminating0(A)| -aElement0(B)| -aElement0(C)| -sdtmndtplgtdt0(B,A,C)|iLess0(C,B).
% 1.92/2.08  ** KEPT (pick-wt=7): 31 [] -aRewritingSystem0(A)|isTerminating0(A)|aElement0($f11(A)).
% 1.92/2.08  ** KEPT (pick-wt=7): 32 [] -aRewritingSystem0(A)|isTerminating0(A)|aElement0($f10(A)).
% 1.92/2.08  ** KEPT (pick-wt=10): 33 [] -aRewritingSystem0(A)|isTerminating0(A)|sdtmndtplgtdt0($f11(A),A,$f10(A)).
% 1.92/2.08  ** KEPT (pick-wt=9): 34 [] -aRewritingSystem0(A)|isTerminating0(A)| -iLess0($f10(A),$f11(A)).
% 1.92/2.08  ** KEPT (pick-wt=10): 35 [] -aElement0(A)| -aRewritingSystem0(B)| -aNormalFormOfIn0(C,A,B)|aElement0(C).
% 1.92/2.08  ** KEPT (pick-wt=12): 36 [] -aElement0(A)| -aRewritingSystem0(B)| -aNormalFormOfIn0(C,A,B)|sdtmndtasgtdt0(A,B,C).
% 1.92/2.08  ** KEPT (pick-wt=12): 37 [] -aElement0(A)| -aRewritingSystem0(B)| -aNormalFormOfIn0(C,A,B)| -aReductOfIn0(D,C,B).
% 1.92/2.08  ** KEPT (pick-wt=21): 38 [] -aElement0(A)| -aRewritingSystem0(B)|aNormalFormOfIn0(C,A,B)| -aElement0(C)| -sdtmndtasgtdt0(A,B,C)|aReductOfIn0($f12(A,B,C),C,B).
% 1.92/2.08  ** KEPT (pick-wt=12): 39 [] -aRewritingSystem0(A)| -isTerminating0(A)| -aElement0(B)|aNormalFormOfIn0($f13(A,B),B,A).
% 1.92/2.08  ** KEPT (pick-wt=22): 40 [] -aElement0(A)| -aElement0(B)| -aElement0(C)| -sdtmndtasgtdt0(A,xR,B)| -sdtmndtasgtdt0(A,xR,C)| -iLess0(A,xa)|aElement0($f14(A,B,C)).
% 1.92/2.08  ** KEPT (pick-wt=24): 41 [] -aElement0(A)| -aElement0(B)| -aElement0(C)| -sdtmndtasgtdt0(A,xR,B)| -sdtmndtasgtdt0(A,xR,C)| -iLess0(A,xa)|sdtmndtasgtdt0(B,xR,$f14(A,B,C)).
% 1.92/2.08  ** KEPT (pick-wt=24): 42 [] -aElement0(A)| -aElement0(B)| -aElement0(C)| -sdtmndtasgtdt0(A,xR,B)| -sdtmndtasgtdt0(A,xR,C)| -iLess0(A,xa)|sdtmndtasgtdt0(C,xR,$f14(A,B,C)).
% 1.92/2.08  ** KEPT (pick-wt=10): 43 [] -aElement0(A)| -sdtmndtasgtdt0(xb,xR,A)| -sdtmndtasgtdt0(xd,xR,A).
% 1.92/2.08  
% 1.92/2.08  ------------> process sos:
% 1.92/2.08  ** KEPT (pick-wt=3): 86 [] A=A.
% 1.92/2.08  ** KEPT (pick-wt=2): 87 [] aRewritingSystem0(xR).
% 1.92/2.08  ** KEPT (pick-wt=2): 88 [] isLocallyConfluent0(xR).
% 1.92/2.08  ** KEPT (pick-wt=2): 89 [] isTerminating0(xR).
% 1.92/2.08  ** KEPT (pick-wt=2): 90 [] aElement0(xa).
% 1.92/2.08  ** KEPT (pick-wt=2): 91 [] aElement0(xb).
% 1.92/2.08  ** KEPT (pick-wt=2): 92 [] aElement0(xc).
% 1.92/2.08  ** KEPT (pick-wt=4): 93 [] sdtmndtplgtdt0(xa,xR,xb).
% 1.92/2.08  ** KEPT (pick-wt=4): 94 [] sdtmndtplgtdt0(xa,xR,xc).
% 1.92/2.08  ** KEPT (pick-wt=2): 95 [] aElement0(xu).
% 1.92/2.08  ** KEPT (pick-wt=4): 96 [] aReductOfIn0(xu,xa,xR).
% 1.92/2.08  ** KEPT (pick-wt=4): 97 [] sdtmndtasgtdt0(xu,xR,xb).
% 1.92/2.08  ** KEPT (pick-wt=2): 98 [] aElement0(xv).
% 1.92/2.08  ** KEPT (pick-wt=4): 99 [] aReductOfIn0(xv,xa,xR).
% 1.92/2.08  ** KEPT (pick-wt=4): 100 [] sdtmndtasgtdt0(xv,xR,xc).
% 1.92/2.08  ** KEPT (pick-wt=2): 101 [] aElement0(xw).
% 1.92/2.08  ** KEPT (pick-wt=4): 102 [] sdtmndtasgtdt0(xu,xR,xw).
% 1.92/2.08  ** KEPT (pick-wt=4): 103 [] sdtmndtasgtdt0(xv,xR,xw).
% 1.92/2.08  ** KEPT (pick-wt=4): 104 [] aNormalFormOfIn0(xd,xw,xR).
% 13.20/13.42    Following clause subsumed by 86 during input processing: 0 [copy,86,flip.1] A=A.
% 13.20/13.42  86 back subsumes 50.
% 13.20/13.42  
% 13.20/13.42  ======= end of input processing =======
% 13.20/13.42  
% 13.20/13.42  =========== start of search ===========
% 13.20/13.42  
% 13.20/13.42  
% 13.20/13.42  Resetting weight limit to 9.
% 13.20/13.42  
% 13.20/13.42  
% 13.20/13.42  Resetting weight limit to 9.
% 13.20/13.42  
% 13.20/13.42  sos_size=4656
% 13.20/13.42  
% 13.20/13.42  
% 13.20/13.42  Resetting weight limit to 8.
% 13.20/13.42  
% 13.20/13.42  
% 13.20/13.42  Resetting weight limit to 8.
% 13.20/13.42  
% 13.20/13.42  sos_size=4837
% 13.20/13.42  
% 13.20/13.42  -- HEY sandbox, WE HAVE A PROOF!! -- 
% 13.20/13.42  
% 13.20/13.42  -----> EMPTY CLAUSE at  11.35 sec ----> 5223 [hyper,1010,43,1014,1006] $F.
% 13.20/13.42  
% 13.20/13.42  Length of proof is 8.  Level of proof is 3.
% 13.20/13.42  
% 13.20/13.42  ---------------- PROOF ----------------
% 13.20/13.42  % SZS status Theorem
% 13.20/13.42  % SZS output start Refutation
% See solution above
% 13.20/13.42  ------------ end of proof -------------
% 13.20/13.42  
% 13.20/13.42  
% 13.20/13.42  Search stopped by max_proofs option.
% 13.20/13.42  
% 13.20/13.42  
% 13.20/13.42  Search stopped by max_proofs option.
% 13.20/13.42  
% 13.20/13.42  ============ end of search ============
% 13.20/13.42  
% 13.20/13.42  -------------- statistics -------------
% 13.20/13.42  clauses given                207
% 13.20/13.42  clauses generated          31395
% 13.20/13.42  clauses kept                5222
% 13.20/13.42  clauses forward subsumed    3109
% 13.20/13.42  clauses back subsumed          1
% 13.20/13.42  Kbytes malloced             4882
% 13.20/13.42  
% 13.20/13.42  ----------- times (seconds) -----------
% 13.20/13.42  user CPU time         11.35          (0 hr, 0 min, 11 sec)
% 13.20/13.42  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 13.20/13.42  wall-clock time       13             (0 hr, 0 min, 13 sec)
% 13.20/13.42  
% 13.20/13.42  That finishes the proof of the theorem.
% 13.20/13.42  
% 13.20/13.42  Process 28193 finished Wed Jul 27 06:39:59 2022
% 13.20/13.42  Otter interrupted
% 13.20/13.42  PROOF FOUND
%------------------------------------------------------------------------------