TSTP Solution File: LCL163-1 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : LCL163-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n017.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 13:03:43 EDT 2022

% Result   : Unsatisfiable 2.27s 2.45s
% Output   : Refutation 2.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   79 (  79 unt;   0 nHn;   3 RR)
%            Number of literals    :   79 (  78 equ;   2 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :  155 (  14 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    implies(implies(x,y),y) != implies(implies(y,x),x),
    file('LCL163-1.p',unknown),
    [] ).

cnf(2,plain,
    implies(implies(y,x),x) != implies(implies(x,y),y),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
    [iquote('copy,1,flip.1')] ).

cnf(7,axiom,
    xor(A,falsehood) = A,
    file('LCL163-1.p',unknown),
    [] ).

cnf(8,axiom,
    xor(A,A) = falsehood,
    file('LCL163-1.p',unknown),
    [] ).

cnf(11,axiom,
    and_star(A,truth) = A,
    file('LCL163-1.p',unknown),
    [] ).

cnf(13,axiom,
    and_star(A,falsehood) = falsehood,
    file('LCL163-1.p',unknown),
    [] ).

cnf(14,axiom,
    and_star(xor(truth,A),A) = falsehood,
    file('LCL163-1.p',unknown),
    [] ).

cnf(16,axiom,
    xor(A,xor(truth,B)) = xor(xor(A,truth),B),
    file('LCL163-1.p',unknown),
    [] ).

cnf(17,plain,
    xor(xor(A,truth),B) = xor(A,xor(truth,B)),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[16])]),
    [iquote('copy,16,flip.1')] ).

cnf(19,axiom,
    and_star(xor(and_star(xor(truth,A),B),truth),B) = and_star(xor(and_star(xor(truth,B),A),truth),A),
    file('LCL163-1.p',unknown),
    [] ).

cnf(20,axiom,
    xor(A,B) = xor(B,A),
    file('LCL163-1.p',unknown),
    [] ).

cnf(22,axiom,
    and_star(and_star(A,B),C) = and_star(A,and_star(B,C)),
    file('LCL163-1.p',unknown),
    [] ).

cnf(23,axiom,
    and_star(A,B) = and_star(B,A),
    file('LCL163-1.p',unknown),
    [] ).

cnf(24,axiom,
    implies(A,B) = xor(truth,and_star(A,xor(truth,B))),
    file('LCL163-1.p',unknown),
    [] ).

cnf(25,plain,
    xor(truth,and_star(A,xor(truth,B))) = implies(A,B),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[24])]),
    [iquote('copy,24,flip.1')] ).

cnf(28,plain,
    xor(falsehood,A) = A,
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[20,7])]),
    [iquote('para_into,20.1.1,6.1.1,flip.1')] ).

cnf(31,plain,
    and_star(A,xor(truth,A)) = falsehood,
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[23,14])]),
    [iquote('para_into,23.1.1,14.1.1,flip.1')] ).

cnf(34,plain,
    and_star(falsehood,A) = falsehood,
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[23,13])]),
    [iquote('para_into,23.1.1,12.1.1,flip.1')] ).

cnf(36,plain,
    and_star(truth,A) = A,
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[23,11])]),
    [iquote('para_into,23.1.1,10.1.1,flip.1')] ).

cnf(41,plain,
    xor(truth,xor(truth,A)) = A,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[17,8]),28])]),
    [iquote('para_into,17.1.1.1,8.1.1,demod,28,flip.1')] ).

cnf(52,plain,
    and_star(xor(and_star(xor(truth,A),B),truth),B) = and_star(xor(truth,and_star(xor(truth,B),A)),A),
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,20])]),
    [iquote('para_into,19.1.1.1,20.1.1,flip.1')] ).

cnf(59,plain,
    and_star(xor(truth,and_star(xor(truth,A),B)),B) = and_star(xor(truth,and_star(xor(truth,B),A)),A),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[19]),52,52]),
    [iquote('back_demod,19,demod,52,52')] ).

cnf(64,plain,
    and_star(A,and_star(xor(truth,A),B)) = falsehood,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[22,31]),34])]),
    [iquote('para_into,21.1.1.1,31.1.1,demod,34,flip.1')] ).

cnf(68,plain,
    and_star(A,and_star(B,C)) = and_star(B,and_star(A,C)),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[22,23]),22]),
    [iquote('para_into,21.1.1.1,23.1.1,demod,22')] ).

cnf(75,plain,
    and_star(A,and_star(B,C)) = and_star(B,and_star(C,A)),
    inference(para_into,[status(thm),theory(equality)],[22,23]),
    [iquote('para_into,21.1.1,23.1.1')] ).

cnf(76,plain,
    and_star(A,and_star(B,C)) = and_star(C,and_star(A,B)),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[75])]),
    [iquote('copy,75,flip.1')] ).

cnf(79,plain,
    xor(truth,and_star(A,B)) = implies(A,xor(truth,B)),
    inference(para_into,[status(thm),theory(equality)],[25,41]),
    [iquote('para_into,25.1.1.2.2,41.1.1')] ).

cnf(80,plain,
    implies(A,xor(truth,implies(B,C))) = implies(A,and_star(B,xor(truth,C))),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,25]),79]),
    [iquote('para_into,25.1.1.2.2,25.1.1,demod,79')] ).

cnf(83,plain,
    implies(A,truth) = truth,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,8]),13,7])]),
    [iquote('para_into,25.1.1.2.2,8.1.1,demod,13,7,flip.1')] ).

cnf(85,plain,
    xor(truth,A) = implies(A,falsehood),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,7]),11]),
    [iquote('para_into,25.1.1.2.2,6.1.1,demod,11')] ).

cnf(87,plain,
    implies(implies(A,falsehood),falsehood) = implies(truth,A),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,36]),85,85]),
    [iquote('para_into,25.1.1.2,35.1.1,demod,85,85')] ).

cnf(89,plain,
    implies(falsehood,A) = truth,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,34]),7])]),
    [iquote('para_into,25.1.1.2,33.1.1,demod,7,flip.1')] ).

cnf(91,plain,
    implies(A,A) = truth,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,31]),7])]),
    [iquote('para_into,25.1.1.2,31.1.1,demod,7,flip.1')] ).

cnf(95,plain,
    implies(and_star(implies(A,falsehood),B),falsehood) = implies(B,A),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,23]),85,85]),
    [iquote('para_into,25.1.1.2,23.1.1,demod,85,85')] ).

cnf(96,plain,
    implies(and_star(A,and_star(B,implies(C,falsehood))),falsehood) = implies(and_star(A,B),C),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,22]),85,85]),
    [iquote('para_into,25.1.1.2,21.1.1,demod,85,85')] ).

cnf(106,plain,
    and_star(implies(A,B),A) = and_star(implies(B,A),B),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[59]),85,85,95,85,85,95]),
    [iquote('back_demod,59,demod,85,85,95,85,85,95')] ).

cnf(111,plain,
    and_star(xor(and_star(implies(A,falsehood),B),truth),B) = and_star(implies(A,B),A),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[52]),85,85,85,95]),
    [iquote('back_demod,51,demod,85,85,85,95')] ).

cnf(115,plain,
    implies(A,implies(implies(B,C),falsehood)) = implies(A,and_star(B,implies(C,falsehood))),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[80]),85,85]),
    [iquote('back_demod,80,demod,85,85')] ).

cnf(118,plain,
    implies(and_star(A,B),falsehood) = implies(A,implies(B,falsehood)),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[79]),85,85]),
    [iquote('back_demod,78,demod,85,85')] ).

cnf(121,plain,
    and_star(A,and_star(implies(A,falsehood),B)) = falsehood,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[64]),85]),
    [iquote('back_demod,64,demod,85')] ).

cnf(128,plain,
    implies(truth,A) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[41]),85,85,87]),
    [iquote('back_demod,41,demod,85,85,87')] ).

cnf(135,plain,
    and_star(implies(A,falsehood),A) = falsehood,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[14]),85]),
    [iquote('back_demod,14,demod,85')] ).

cnf(142,plain,
    implies(and_star(A,B),C) = implies(A,implies(B,C)),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[96]),118,118,87,128])]),
    [iquote('back_demod,96,demod,118,118,87,128,flip.1')] ).

cnf(143,plain,
    implies(implies(A,falsehood),implies(B,falsehood)) = implies(B,A),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[95]),142]),
    [iquote('back_demod,94,demod,142')] ).

cnf(146,plain,
    implies(A,B) = implies(implies(B,falsehood),implies(A,falsehood)),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[143])]),
    [iquote('copy,143,flip.1')] ).

cnf(154,plain,
    xor(A,truth) = implies(A,falsehood),
    inference(para_into,[status(thm),theory(equality)],[85,20]),
    [iquote('para_into,84.1.1,20.1.1')] ).

cnf(163,plain,
    and_star(implies(implies(A,falsehood),implies(B,falsehood)),B) = and_star(implies(A,B),A),
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[111]),154,142]),
    [iquote('back_demod,111,demod,154,142')] ).

cnf(186,plain,
    and_star(A,and_star(B,and_star(C,implies(A,falsehood)))) = falsehood,
    inference(para_from,[status(thm),theory(equality)],[75,121]),
    [iquote('para_from,75.1.1,121.1.1.2')] ).

cnf(195,plain,
    and_star(A,and_star(implies(B,implies(A,falsehood)),B)) = falsehood,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[76,135]),142])]),
    [iquote('para_into,76.1.1,135.1.1,demod,142,flip.1')] ).

cnf(205,plain,
    and_star(A,implies(A,B)) = and_star(implies(B,A),B),
    inference(para_into,[status(thm),theory(equality)],[106,23]),
    [iquote('para_into,106.1.1,23.1.1')] ).

cnf(209,plain,
    and_star(implies(A,B),A) = and_star(B,implies(B,A)),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[205])]),
    [iquote('copy,205,flip.1')] ).

cnf(222,plain,
    implies(implies(A,B),falsehood) = and_star(A,implies(B,falsehood)),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[115,128]),128]),
    [iquote('para_into,115.1.1,127.1.1,demod,128')] ).

cnf(243,plain,
    implies(implies(A,B),implies(A,C)) = implies(implies(B,A),implies(B,C)),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[142,106]),142]),
    [iquote('para_into,141.1.1.1,106.1.1,demod,142')] ).

cnf(247,plain,
    implies(A,implies(B,C)) = implies(B,implies(A,C)),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[142,23]),142]),
    [iquote('para_into,141.1.1.1,23.1.1,demod,142')] ).

cnf(248,plain,
    implies(A,implies(B,and_star(A,B))) = truth,
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[142,91])]),
    [iquote('para_into,141.1.1,90.1.1,flip.1')] ).

cnf(260,plain,
    implies(implies(A,implies(B,falsehood)),implies(C,falsehood)) = implies(C,and_star(A,B)),
    inference(para_into,[status(thm),theory(equality)],[143,142]),
    [iquote('para_into,143.1.1.1,141.1.1')] ).

cnf(286,plain,
    implies(A,implies(B,and_star(B,A))) = truth,
    inference(para_into,[status(thm),theory(equality)],[248,23]),
    [iquote('para_into,248.1.1.2.2,23.1.1')] ).

cnf(306,plain,
    implies(A,implies(B,implies(C,and_star(A,and_star(C,B))))) = truth,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[286,68]),142]),
    [iquote('para_into,286.1.1.2.2,68.1.1,demod,142')] ).

cnf(396,plain,
    and_star(A,and_star(implies(B,and_star(C,implies(A,falsehood))),B)) = falsehood,
    inference(para_into,[status(thm),theory(equality)],[186,106]),
    [iquote('para_into,186.1.1.2,106.1.1')] ).

cnf(449,plain,
    and_star(A,and_star(implies(A,B),implies(B,falsehood))) = falsehood,
    inference(para_into,[status(thm),theory(equality)],[195,143]),
    [iquote('para_into,195.1.1.2.1,143.1.1')] ).

cnf(792,plain,
    implies(A,implies(B,implies(C,and_star(A,C)))) = truth,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[247,248]),83])]),
    [iquote('para_into,247.1.1.2,248.1.1,demod,83,flip.1')] ).

cnf(796,plain,
    implies(A,implies(implies(A,B),B)) = truth,
    inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[247,91])]),
    [iquote('para_into,247.1.1,90.1.1,flip.1')] ).

cnf(818,plain,
    and_star(implies(implies(A,B),B),implies(implies(implies(A,B),B),A)) = A,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[796,209]),36])]),
    [iquote('para_from,796.1.1,209.1.1.1,demod,36,flip.1')] ).

cnf(2102,plain,
    implies(A,implies(B,and_star(B,implies(C,A)))) = truth,
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[396,306]),222,142,222,91,11]),
    [iquote('para_from,396.1.1,306.1.1.2.2.2,demod,222,142,222,91,11')] ).

cnf(2110,plain,
    implies(A,implies(B,and_star(implies(C,A),B))) = truth,
    inference(para_into,[status(thm),theory(equality)],[2102,23]),
    [iquote('para_into,2102.1.1.2.2,23.1.1')] ).

cnf(2126,plain,
    implies(A,implies(implies(implies(B,A),C),C)) = truth,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[2110,449]),142,222,91,11]),
    [iquote('para_into,2110.1.1.2.2,449.1.1,demod,142,222,91,11')] ).

cnf(2161,plain,
    implies(implies(implies(A,B),C),implies(B,C)) = truth,
    inference(para_into,[status(thm),theory(equality)],[2126,247]),
    [iquote('para_into,2126.1.1,247.1.1')] ).

cnf(2190,plain,
    implies(implies(A,B),implies(A,implies(implies(B,C),C))) = truth,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[243,796]),83])]),
    [iquote('para_into,243.1.1.2,796.1.1,demod,83,flip.1')] ).

cnf(2196,plain,
    implies(A,implies(implies(B,C),implies(B,and_star(A,C)))) = truth,
    inference(para_from,[status(thm),theory(equality)],[243,792]),
    [iquote('para_from,243.1.1,792.1.1.2')] ).

cnf(2210,plain,
    implies(implies(implies(A,falsehood),B),A) = implies(B,and_star(B,A)),
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[260,243]),222,91,11]),
    [iquote('para_into,260.1.1,243.1.1,demod,222,91,11')] ).

cnf(2306,plain,
    implies(implies(A,B),and_star(implies(A,B),A)) = A,
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[2210,2190]),128,89,128,89,128])]),
    [iquote('para_into,2210.1.1.1,2190.1.1,demod,128,89,128,89,128,flip.1')] ).

cnf(2315,plain,
    implies(implies(A,B),and_star(implies(B,A),B)) = A,
    inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[2306,146]),163]),
    [iquote('para_into,2306.1.1.2.1,146.1.1,demod,163')] ).

cnf(2323,plain,
    implies(implies(A,B),and_star(B,implies(B,A))) = A,
    inference(para_into,[status(thm),theory(equality)],[2306,209]),
    [iquote('para_into,2306.1.1.2,209.1.1')] ).

cnf(2325,plain,
    implies(implies(A,B),and_star(A,implies(A,B))) = A,
    inference(para_into,[status(thm),theory(equality)],[2306,23]),
    [iquote('para_into,2306.1.1.2,23.1.1')] ).

cnf(2330,plain,
    implies(implies(A,B),implies(implies(implies(B,A),A),B)) = truth,
    inference(para_from,[status(thm),theory(equality)],[2315,2196]),
    [iquote('para_from,2315.1.1,2196.1.1.2.2')] ).

cnf(2353,plain,
    implies(implies(implies(A,B),B),A) = implies(B,A),
    inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[2330,2323]),2161,11,128])]),
    [iquote('para_from,2330.1.1,2323.1.1.2.2,demod,2161,11,128,flip.1')] ).

cnf(2357,plain,
    and_star(implies(implies(A,B),B),implies(B,A)) = A,
    inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[818]),2353]),
    [iquote('back_demod,818,demod,2353')] ).

cnf(2364,plain,
    implies(implies(A,B),B) = implies(implies(B,A),A),
    inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[2353,2325]),2353,2357]),
    [iquote('para_from,2352.1.1,2325.1.1.1,demod,2353,2357')] ).

cnf(2365,plain,
    $false,
    inference(binary,[status(thm)],[2364,2]),
    [iquote('binary,2364.1,2.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : LCL163-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n017.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 08:52:33 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.67/1.88  ----- Otter 3.3f, August 2004 -----
% 1.67/1.88  The process was started by sandbox2 on n017.cluster.edu,
% 1.67/1.88  Wed Jul 27 08:52:33 2022
% 1.67/1.88  The command was "./otter".  The process ID is 28836.
% 1.67/1.88  
% 1.67/1.88  set(prolog_style_variables).
% 1.67/1.88  set(auto).
% 1.67/1.88     dependent: set(auto1).
% 1.67/1.88     dependent: set(process_input).
% 1.67/1.88     dependent: clear(print_kept).
% 1.67/1.88     dependent: clear(print_new_demod).
% 1.67/1.88     dependent: clear(print_back_demod).
% 1.67/1.88     dependent: clear(print_back_sub).
% 1.67/1.88     dependent: set(control_memory).
% 1.67/1.88     dependent: assign(max_mem, 12000).
% 1.67/1.88     dependent: assign(pick_given_ratio, 4).
% 1.67/1.88     dependent: assign(stats_level, 1).
% 1.67/1.88     dependent: assign(max_seconds, 10800).
% 1.67/1.88  clear(print_given).
% 1.67/1.88  
% 1.67/1.88  list(usable).
% 1.67/1.88  0 [] A=A.
% 1.67/1.88  0 [] not(X)=xor(X,truth).
% 1.67/1.88  0 [] xor(X,falsehood)=X.
% 1.67/1.88  0 [] xor(X,X)=falsehood.
% 1.67/1.88  0 [] and_star(X,truth)=X.
% 1.67/1.88  0 [] and_star(X,falsehood)=falsehood.
% 1.67/1.88  0 [] and_star(xor(truth,X),X)=falsehood.
% 1.67/1.88  0 [] xor(X,xor(truth,Y))=xor(xor(X,truth),Y).
% 1.67/1.88  0 [] and_star(xor(and_star(xor(truth,X),Y),truth),Y)=and_star(xor(and_star(xor(truth,Y),X),truth),X).
% 1.67/1.88  0 [] xor(X,Y)=xor(Y,X).
% 1.67/1.88  0 [] and_star(and_star(X,Y),Z)=and_star(X,and_star(Y,Z)).
% 1.67/1.88  0 [] and_star(X,Y)=and_star(Y,X).
% 1.67/1.88  0 [] not(truth)=falsehood.
% 1.67/1.88  0 [] implies(X,Y)=xor(truth,and_star(X,xor(truth,Y))).
% 1.67/1.88  0 [] implies(implies(x,y),y)!=implies(implies(y,x),x).
% 1.67/1.88  end_of_list.
% 1.67/1.88  
% 1.67/1.88  SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.67/1.88  
% 1.67/1.88  All clauses are units, and equality is present; the
% 1.67/1.88  strategy will be Knuth-Bendix with positive clauses in sos.
% 1.67/1.88  
% 1.67/1.88     dependent: set(knuth_bendix).
% 1.67/1.88     dependent: set(anl_eq).
% 1.67/1.88     dependent: set(para_from).
% 1.67/1.88     dependent: set(para_into).
% 1.67/1.88     dependent: clear(para_from_right).
% 1.67/1.88     dependent: clear(para_into_right).
% 1.67/1.88     dependent: set(para_from_vars).
% 1.67/1.88     dependent: set(eq_units_both_ways).
% 1.67/1.88     dependent: set(dynamic_demod_all).
% 1.67/1.88     dependent: set(dynamic_demod).
% 1.67/1.88     dependent: set(order_eq).
% 1.67/1.88     dependent: set(back_demod).
% 1.67/1.88     dependent: set(lrpo).
% 1.67/1.88  
% 1.67/1.88  ------------> process usable:
% 1.67/1.88  ** KEPT (pick-wt=11): 2 [copy,1,flip.1] implies(implies(y,x),x)!=implies(implies(x,y),y).
% 1.67/1.88  
% 1.67/1.88  ------------> process sos:
% 1.67/1.88  ** KEPT (pick-wt=3): 3 [] A=A.
% 1.67/1.88  ** KEPT (pick-wt=6): 4 [] not(A)=xor(A,truth).
% 1.67/1.88  ---> New Demodulator: 5 [new_demod,4] not(A)=xor(A,truth).
% 1.67/1.88  ** KEPT (pick-wt=5): 6 [] xor(A,falsehood)=A.
% 1.67/1.88  ---> New Demodulator: 7 [new_demod,6] xor(A,falsehood)=A.
% 1.67/1.88  ** KEPT (pick-wt=5): 8 [] xor(A,A)=falsehood.
% 1.67/1.88  ---> New Demodulator: 9 [new_demod,8] xor(A,A)=falsehood.
% 1.67/1.88  ** KEPT (pick-wt=5): 10 [] and_star(A,truth)=A.
% 1.67/1.88  ---> New Demodulator: 11 [new_demod,10] and_star(A,truth)=A.
% 1.67/1.88  ** KEPT (pick-wt=5): 12 [] and_star(A,falsehood)=falsehood.
% 1.67/1.88  ---> New Demodulator: 13 [new_demod,12] and_star(A,falsehood)=falsehood.
% 1.67/1.88  ** KEPT (pick-wt=7): 14 [] and_star(xor(truth,A),A)=falsehood.
% 1.67/1.88  ---> New Demodulator: 15 [new_demod,14] and_star(xor(truth,A),A)=falsehood.
% 1.67/1.88  ** KEPT (pick-wt=11): 17 [copy,16,flip.1] xor(xor(A,truth),B)=xor(A,xor(truth,B)).
% 1.67/1.88  ---> New Demodulator: 18 [new_demod,17] xor(xor(A,truth),B)=xor(A,xor(truth,B)).
% 1.67/1.88  ** KEPT (pick-wt=19): 19 [] and_star(xor(and_star(xor(truth,A),B),truth),B)=and_star(xor(and_star(xor(truth,B),A),truth),A).
% 1.67/1.88  ** KEPT (pick-wt=7): 20 [] xor(A,B)=xor(B,A).
% 1.67/1.88  ** KEPT (pick-wt=11): 21 [] and_star(and_star(A,B),C)=and_star(A,and_star(B,C)).
% 1.67/1.88  ---> New Demodulator: 22 [new_demod,21] and_star(and_star(A,B),C)=and_star(A,and_star(B,C)).
% 1.67/1.88  ** KEPT (pick-wt=7): 23 [] and_star(A,B)=and_star(B,A).
% 1.67/1.88    Following clause subsumed by 3 during input processing: 0 [demod,5,9] falsehood=falsehood.
% 1.67/1.88  ** KEPT (pick-wt=11): 25 [copy,24,flip.1] xor(truth,and_star(A,xor(truth,B)))=implies(A,B).
% 1.67/1.88  ---> New Demodulator: 26 [new_demod,25] xor(truth,and_star(A,xor(truth,B)))=implies(A,B).
% 1.67/1.88    Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.67/1.88  >>>> Starting back demodulation with 5.
% 1.67/1.88  >>>> Starting back demodulation with 7.
% 1.67/1.88  >>>> Starting back demodulation with 9.
% 1.67/1.88  >>>> Starting back demodulation with 11.
% 1.67/1.88  >>>> Starting back demodulation with 13.
% 1.67/1.88  >>>> Starting back demodulation with 15.
% 1.67/1.88  >>>> Starting back demodulation with 18.
% 1.67/1.88    Following clause subsumed by 19 during input processing: 0 [copy,19,flip.1] and_star(xor(and_star(xor(truth,A),B),truth),B)=and_star(xor(and_star(xor(truth,B),A),truth),A).
% 2.27/2.45    Following clause subsumed by 20 during input processing: 0 [copy,20,flip.1] xor(A,B)=xor(B,A).
% 2.27/2.45  >>>> Starting back demodulation with 22.
% 2.27/2.45    Following clause subsumed by 23 during input processing: 0 [copy,23,flip.1] and_star(A,B)=and_star(B,A).
% 2.27/2.45  >>>> Starting back demodulation with 26.
% 2.27/2.45  
% 2.27/2.45  ======= end of input processing =======
% 2.27/2.45  
% 2.27/2.45  =========== start of search ===========
% 2.27/2.45  
% 2.27/2.45  
% 2.27/2.45  Resetting weight limit to 13.
% 2.27/2.45  
% 2.27/2.45  
% 2.27/2.45  Resetting weight limit to 13.
% 2.27/2.45  
% 2.27/2.45  sos_size=1069
% 2.27/2.45  
% 2.27/2.45  -------- PROOF -------- 
% 2.27/2.45  
% 2.27/2.45  ----> UNIT CONFLICT at   0.57 sec ----> 2365 [binary,2364.1,2.1] $F.
% 2.27/2.45  
% 2.27/2.45  Length of proof is 66.  Level of proof is 15.
% 2.27/2.45  
% 2.27/2.45  ---------------- PROOF ----------------
% 2.27/2.45  % SZS status Unsatisfiable
% 2.27/2.45  % SZS output start Refutation
% See solution above
% 2.27/2.45  ------------ end of proof -------------
% 2.27/2.45  
% 2.27/2.45  
% 2.27/2.45  Search stopped by max_proofs option.
% 2.27/2.45  
% 2.27/2.45  
% 2.27/2.45  Search stopped by max_proofs option.
% 2.27/2.45  
% 2.27/2.45  ============ end of search ============
% 2.27/2.45  
% 2.27/2.45  -------------- statistics -------------
% 2.27/2.45  clauses given                404
% 2.27/2.45  clauses generated         148771
% 2.27/2.45  clauses kept                1437
% 2.27/2.45  clauses forward subsumed   95826
% 2.27/2.45  clauses back subsumed          3
% 2.27/2.45  Kbytes malloced             5859
% 2.27/2.45  
% 2.27/2.45  ----------- times (seconds) -----------
% 2.27/2.45  user CPU time          0.57          (0 hr, 0 min, 0 sec)
% 2.27/2.45  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 2.27/2.45  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 2.27/2.45  
% 2.27/2.45  That finishes the proof of the theorem.
% 2.27/2.45  
% 2.27/2.45  Process 28836 finished Wed Jul 27 08:52:35 2022
% 2.27/2.45  Otter interrupted
% 2.27/2.45  PROOF FOUND
%------------------------------------------------------------------------------