TSTP Solution File: HWV008-1.002 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : HWV008-1.002 : TPTP v8.1.0. Bugfixed v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n025.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  : 600s
% DateTime : Sat Jul 16 19:14:42 EDT 2022

% Result   : Unsatisfiable 1.01s 1.21s
% Output   : Refutation 1.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   29
% Syntax   : Number of clauses     :   90 (  19 unt;   5 nHn;  90 RR)
%            Number of literals    :  199 (   0 equ; 117 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   24 (  24 usr;  16 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    ( ~ type(u,nbit_adder(n2))
    | type(f(n2,u),fulladder) ),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ type(u,nbit_adder(n2))
    | connection(out(c,u),out(c,f(n2,u))) ),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ type(u,nbit_adder(n2))
    | connection(in(a2,u),in(n1,f(n2,u))) ),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ type(u,nbit_adder(n2))
    | connection(in(b2,u),in(n2,f(n2,u))) ),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(12,axiom,
    type(a,nbit_adder(n2)),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(14,axiom,
    value(in(a2,a),n0),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(16,axiom,
    value(in(b2,a),n0),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(20,axiom,
    value(out(c,a),n1),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(21,axiom,
    ~ mode(or1(f(n2,a)),abnormal),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(22,axiom,
    ~ mode(and2(h1(f(n2,a))),abnormal),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(23,axiom,
    ~ mode(and2(h2(f(n2,a))),abnormal),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(24,axiom,
    ( ~ value(u,v)
    | ~ connection(u,w)
    | value(w,v) ),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(25,axiom,
    ( ~ value(u,v)
    | ~ connection(w,u)
    | value(w,v) ),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(26,axiom,
    ( ~ value(u,v)
    | ~ value(u,w)
    | equal_value(w,v) ),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(27,axiom,
    ~ equal_value(n0,n1),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(30,axiom,
    ( ~ type(u,v)
    | mode(u,abnormal)
    | mode(u,ok) ),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(31,axiom,
    ( ~ type(u,and__dfg)
    | ~ mode(u,ok)
    | ~ value(in(v,u),n0)
    | value(out(n1,u),n0) ),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(38,axiom,
    ( ~ type(u,or__dfg)
    | ~ mode(u,ok)
    | ~ value(out(n1,u),n1)
    | value(in(n1,u),n1)
    | value(in(n2,u),n1) ),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(46,axiom,
    ( ~ type(u,halfadder)
    | type(and2(u),and__dfg) ),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(51,axiom,
    ( ~ type(u,halfadder)
    | connection(in(n1,u),in(n1,and2(u))) ),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(54,axiom,
    ( ~ type(u,halfadder)
    | connection(out(c,u),out(n1,and2(u))) ),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(58,axiom,
    ( ~ type(u,fulladder)
    | type(h1(u),halfadder) ),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(59,axiom,
    ( ~ type(u,fulladder)
    | type(h2(u),halfadder) ),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(60,axiom,
    ( ~ type(u,fulladder)
    | type(or1(u),or__dfg) ),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(62,axiom,
    ( ~ type(u,fulladder)
    | connection(out(c,h1(u)),in(n2,or1(u))) ),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(63,axiom,
    ( ~ type(u,fulladder)
    | connection(out(c,h2(u)),in(n1,or1(u))) ),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(64,axiom,
    ( ~ type(u,fulladder)
    | connection(in(n1,u),in(n1,h2(u))) ),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(65,axiom,
    ( ~ type(u,fulladder)
    | connection(in(n2,u),in(n1,h1(u))) ),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(68,axiom,
    ( ~ type(u,fulladder)
    | connection(out(c,u),out(n1,or1(u))) ),
    file('HWV008-1.002.p',unknown),
    [] ).

cnf(70,plain,
    ( ~ type(and2(h2(f(n2,a))),u)
    | mode(and2(h2(f(n2,a))),ok) ),
    inference(res,[status(thm),theory(equality)],[30,23]),
    [iquote('0:Res:30.2,23.0')] ).

cnf(71,plain,
    ( ~ type(and2(h1(f(n2,a))),u)
    | mode(and2(h1(f(n2,a))),ok) ),
    inference(res,[status(thm),theory(equality)],[30,22]),
    [iquote('0:Res:30.2,22.0')] ).

cnf(74,plain,
    ( ~ type(u,fulladder)
    | mode(or1(u),abnormal)
    | mode(or1(u),ok) ),
    inference(res,[status(thm),theory(equality)],[60,30]),
    [iquote('0:Res:60.1,30.0')] ).

cnf(103,plain,
    ( ~ connection(out(c,a),u)
    | value(u,n1) ),
    inference(res,[status(thm),theory(equality)],[20,24]),
    [iquote('0:Res:20.0,24.0')] ).

cnf(107,plain,
    ( ~ connection(in(b2,a),u)
    | value(u,n0) ),
    inference(res,[status(thm),theory(equality)],[16,24]),
    [iquote('0:Res:16.0,24.0')] ).

cnf(109,plain,
    ( ~ connection(in(a2,a),u)
    | value(u,n0) ),
    inference(res,[status(thm),theory(equality)],[14,24]),
    [iquote('0:Res:14.0,24.0')] ).

cnf(129,plain,
    ( ~ type(f(n2,a),fulladder)
    | mode(or1(f(n2,a)),ok) ),
    inference(res,[status(thm),theory(equality)],[74,21]),
    [iquote('0:Res:74.1,21.0')] ).

cnf(144,plain,
    ( ~ type(a,nbit_adder(n2))
    | value(in(n1,f(n2,a)),n0) ),
    inference(res,[status(thm),theory(equality)],[8,109]),
    [iquote('0:Res:8.1,109.0')] ).

cnf(145,plain,
    value(in(n1,f(n2,a)),n0),
    inference(mrr,[status(thm)],[144,12]),
    [iquote('0:MRR:144.0,12.0')] ).

cnf(146,plain,
    ( ~ connection(in(n1,f(n2,a)),u)
    | value(u,n0) ),
    inference(res,[status(thm),theory(equality)],[145,24]),
    [iquote('0:Res:145.0,24.0')] ).

cnf(149,plain,
    ( ~ type(f(n2,a),fulladder)
    | value(in(n1,h2(f(n2,a))),n0) ),
    inference(res,[status(thm),theory(equality)],[64,146]),
    [iquote('0:Res:64.1,146.0')] ).

cnf(183,plain,
    ( ~ type(a,nbit_adder(n2))
    | value(in(n2,f(n2,a)),n0) ),
    inference(res,[status(thm),theory(equality)],[9,107]),
    [iquote('0:Res:9.1,107.0')] ).

cnf(184,plain,
    value(in(n2,f(n2,a)),n0),
    inference(mrr,[status(thm)],[183,12]),
    [iquote('0:MRR:183.0,12.0')] ).

cnf(185,plain,
    ( ~ connection(in(n2,f(n2,a)),u)
    | value(u,n0) ),
    inference(res,[status(thm),theory(equality)],[184,24]),
    [iquote('0:Res:184.0,24.0')] ).

cnf(188,plain,
    ( ~ type(f(n2,a),fulladder)
    | value(in(n1,h1(f(n2,a))),n0) ),
    inference(res,[status(thm),theory(equality)],[65,185]),
    [iquote('0:Res:65.1,185.0')] ).

cnf(200,plain,
    ( ~ type(a,nbit_adder(n2))
    | value(out(c,f(n2,a)),n1) ),
    inference(res,[status(thm),theory(equality)],[5,103]),
    [iquote('0:Res:5.1,103.0')] ).

cnf(201,plain,
    value(out(c,f(n2,a)),n1),
    inference(mrr,[status(thm)],[200,12]),
    [iquote('0:MRR:200.0,12.0')] ).

cnf(202,plain,
    ( ~ connection(out(c,f(n2,a)),u)
    | value(u,n1) ),
    inference(res,[status(thm),theory(equality)],[201,24]),
    [iquote('0:Res:201.0,24.0')] ).

cnf(205,plain,
    ( ~ type(f(n2,a),fulladder)
    | value(out(n1,or1(f(n2,a))),n1) ),
    inference(res,[status(thm),theory(equality)],[68,202]),
    [iquote('0:Res:68.1,202.0')] ).

cnf(220,plain,
    ( ~ type(f(n2,a),fulladder)
    | ~ connection(in(n1,h2(f(n2,a))),u)
    | value(u,n0) ),
    inference(res,[status(thm),theory(equality)],[149,24]),
    [iquote('0:Res:149.1,24.0')] ).

cnf(264,plain,
    ( ~ type(f(n2,a),fulladder)
    | ~ connection(in(n1,h1(f(n2,a))),u)
    | value(u,n0) ),
    inference(res,[status(thm),theory(equality)],[188,24]),
    [iquote('0:Res:188.1,24.0')] ).

cnf(441,plain,
    ( ~ type(f(n2,a),fulladder)
    | ~ type(or1(f(n2,a)),or__dfg)
    | ~ mode(or1(f(n2,a)),ok)
    | value(in(n1,or1(f(n2,a))),n1)
    | value(in(n2,or1(f(n2,a))),n1) ),
    inference(res,[status(thm),theory(equality)],[205,38]),
    [iquote('0:Res:205.1,38.2')] ).

cnf(447,plain,
    ( ~ type(f(n2,a),fulladder)
    | value(in(n1,or1(f(n2,a))),n1)
    | value(in(n2,or1(f(n2,a))),n1) ),
    inference(mrr,[status(thm)],[441,60,129]),
    [iquote('0:MRR:441.1,441.2,60.1,129.1')] ).

cnf(951,plain,
    ( ~ type(h2(f(n2,a)),halfadder)
    | ~ type(f(n2,a),fulladder)
    | value(in(n1,and2(h2(f(n2,a)))),n0) ),
    inference(res,[status(thm),theory(equality)],[51,220]),
    [iquote('0:Res:51.1,220.1')] ).

cnf(954,plain,
    ( ~ type(f(n2,a),fulladder)
    | value(in(n1,and2(h2(f(n2,a)))),n0) ),
    inference(mrr,[status(thm)],[951,59]),
    [iquote('0:MRR:951.0,59.1')] ).

cnf(991,plain,
    ( ~ type(f(n2,a),fulladder)
    | ~ type(and2(h2(f(n2,a))),and__dfg)
    | ~ mode(and2(h2(f(n2,a))),ok)
    | value(out(n1,and2(h2(f(n2,a)))),n0) ),
    inference(res,[status(thm),theory(equality)],[954,31]),
    [iquote('0:Res:954.1,31.2')] ).

cnf(995,plain,
    ( ~ type(f(n2,a),fulladder)
    | ~ type(and2(h2(f(n2,a))),and__dfg)
    | value(out(n1,and2(h2(f(n2,a)))),n0) ),
    inference(mrr,[status(thm)],[991,70]),
    [iquote('0:MRR:991.2,70.1')] ).

cnf(1291,plain,
    ( ~ type(h1(f(n2,a)),halfadder)
    | ~ type(f(n2,a),fulladder)
    | value(in(n1,and2(h1(f(n2,a)))),n0) ),
    inference(res,[status(thm),theory(equality)],[51,264]),
    [iquote('0:Res:51.1,264.1')] ).

cnf(1294,plain,
    ( ~ type(f(n2,a),fulladder)
    | value(in(n1,and2(h1(f(n2,a)))),n0) ),
    inference(mrr,[status(thm)],[1291,58]),
    [iquote('0:MRR:1291.0,58.1')] ).

cnf(1327,plain,
    ( ~ type(f(n2,a),fulladder)
    | ~ type(and2(h1(f(n2,a))),and__dfg)
    | ~ mode(and2(h1(f(n2,a))),ok)
    | value(out(n1,and2(h1(f(n2,a)))),n0) ),
    inference(res,[status(thm),theory(equality)],[1294,31]),
    [iquote('0:Res:1294.1,31.2')] ).

cnf(1331,plain,
    ( ~ type(f(n2,a),fulladder)
    | ~ type(and2(h1(f(n2,a))),and__dfg)
    | value(out(n1,and2(h1(f(n2,a)))),n0) ),
    inference(mrr,[status(thm)],[1327,71]),
    [iquote('0:MRR:1327.2,71.1')] ).

cnf(2597,plain,
    value(in(n1,or1(f(n2,a))),n1),
    inference(spt,[spt(split,[position(s1)])],[447]),
    [iquote('1:Spt:447.1')] ).

cnf(2608,plain,
    ( ~ connection(u,in(n1,or1(f(n2,a))))
    | value(u,n1) ),
    inference(res,[status(thm),theory(equality)],[2597,25]),
    [iquote('1:Res:2597.0,25.0')] ).

cnf(2622,plain,
    ( ~ type(f(n2,a),fulladder)
    | value(out(c,h2(f(n2,a))),n1) ),
    inference(res,[status(thm),theory(equality)],[63,2608]),
    [iquote('1:Res:63.1,2608.0')] ).

cnf(2632,plain,
    ( ~ type(f(n2,a),fulladder)
    | ~ connection(out(c,h2(f(n2,a))),u)
    | value(u,n1) ),
    inference(res,[status(thm),theory(equality)],[2622,24]),
    [iquote('1:Res:2622.1,24.0')] ).

cnf(2693,plain,
    ( ~ type(h2(f(n2,a)),halfadder)
    | ~ type(f(n2,a),fulladder)
    | value(out(n1,and2(h2(f(n2,a)))),n1) ),
    inference(res,[status(thm),theory(equality)],[54,2632]),
    [iquote('1:Res:54.1,2632.1')] ).

cnf(2697,plain,
    ( ~ type(f(n2,a),fulladder)
    | value(out(n1,and2(h2(f(n2,a)))),n1) ),
    inference(mrr,[status(thm)],[2693,59]),
    [iquote('1:MRR:2693.0,59.1')] ).

cnf(2708,plain,
    ( ~ type(f(n2,a),fulladder)
    | ~ value(out(n1,and2(h2(f(n2,a)))),u)
    | equal_value(u,n1) ),
    inference(res,[status(thm),theory(equality)],[2697,26]),
    [iquote('1:Res:2697.1,26.0')] ).

cnf(3990,plain,
    ( ~ type(f(n2,a),fulladder)
    | ~ type(and2(h2(f(n2,a))),and__dfg)
    | ~ type(f(n2,a),fulladder)
    | equal_value(n0,n1) ),
    inference(res,[status(thm),theory(equality)],[995,2708]),
    [iquote('1:Res:995.2,2708.1')] ).

cnf(3998,plain,
    ( ~ type(and2(h2(f(n2,a))),and__dfg)
    | ~ type(f(n2,a),fulladder)
    | equal_value(n0,n1) ),
    inference(obv,[status(thm),theory(equality)],[3990]),
    [iquote('1:Obv:3990.0')] ).

cnf(3999,plain,
    ( ~ type(and2(h2(f(n2,a))),and__dfg)
    | ~ type(f(n2,a),fulladder) ),
    inference(mrr,[status(thm)],[3998,27]),
    [iquote('1:MRR:3998.2,27.0')] ).

cnf(4002,plain,
    ( ~ type(h2(f(n2,a)),halfadder)
    | ~ type(f(n2,a),fulladder) ),
    inference(res,[status(thm),theory(equality)],[46,3999]),
    [iquote('1:Res:46.1,3999.0')] ).

cnf(4003,plain,
    ~ type(f(n2,a),fulladder),
    inference(mrr,[status(thm)],[4002,59]),
    [iquote('1:MRR:4002.0,59.1')] ).

cnf(4004,plain,
    ~ type(a,nbit_adder(n2)),
    inference(res,[status(thm),theory(equality)],[2,4003]),
    [iquote('1:Res:2.1,4003.0')] ).

cnf(4005,plain,
    $false,
    inference(mrr,[status(thm)],[4004,12]),
    [iquote('1:MRR:4004.0,12.0')] ).

cnf(4006,plain,
    ~ value(in(n1,or1(f(n2,a))),n1),
    inference(spt,[spt(split,[position(sa)])],[4005,2597]),
    [iquote('1:Spt:4005.0,447.1,2597.0')] ).

cnf(4007,plain,
    ( ~ type(f(n2,a),fulladder)
    | value(in(n2,or1(f(n2,a))),n1) ),
    inference(spt,[spt(split,[position(s2)])],[447]),
    [iquote('1:Spt:4005.0,447.0,447.2')] ).

cnf(4016,plain,
    ( ~ type(f(n2,a),fulladder)
    | ~ connection(u,in(n2,or1(f(n2,a))))
    | value(u,n1) ),
    inference(res,[status(thm),theory(equality)],[4007,25]),
    [iquote('1:Res:4007.1,25.0')] ).

cnf(4111,plain,
    ( ~ type(f(n2,a),fulladder)
    | ~ type(f(n2,a),fulladder)
    | value(out(c,h1(f(n2,a))),n1) ),
    inference(res,[status(thm),theory(equality)],[62,4016]),
    [iquote('1:Res:62.1,4016.1')] ).

cnf(4112,plain,
    ( ~ type(f(n2,a),fulladder)
    | value(out(c,h1(f(n2,a))),n1) ),
    inference(obv,[status(thm),theory(equality)],[4111]),
    [iquote('1:Obv:4111.0')] ).

cnf(4127,plain,
    ( ~ type(f(n2,a),fulladder)
    | ~ connection(out(c,h1(f(n2,a))),u)
    | value(u,n1) ),
    inference(res,[status(thm),theory(equality)],[4112,24]),
    [iquote('1:Res:4112.1,24.0')] ).

cnf(4135,plain,
    ( ~ type(h1(f(n2,a)),halfadder)
    | ~ type(f(n2,a),fulladder)
    | value(out(n1,and2(h1(f(n2,a)))),n1) ),
    inference(res,[status(thm),theory(equality)],[54,4127]),
    [iquote('1:Res:54.1,4127.1')] ).

cnf(4139,plain,
    ( ~ type(f(n2,a),fulladder)
    | value(out(n1,and2(h1(f(n2,a)))),n1) ),
    inference(mrr,[status(thm)],[4135,58]),
    [iquote('1:MRR:4135.0,58.1')] ).

cnf(4150,plain,
    ( ~ type(f(n2,a),fulladder)
    | ~ value(out(n1,and2(h1(f(n2,a)))),u)
    | equal_value(u,n1) ),
    inference(res,[status(thm),theory(equality)],[4139,26]),
    [iquote('1:Res:4139.1,26.0')] ).

cnf(4436,plain,
    ( ~ type(f(n2,a),fulladder)
    | ~ type(and2(h1(f(n2,a))),and__dfg)
    | ~ type(f(n2,a),fulladder)
    | equal_value(n0,n1) ),
    inference(res,[status(thm),theory(equality)],[1331,4150]),
    [iquote('1:Res:1331.2,4150.1')] ).

cnf(4444,plain,
    ( ~ type(and2(h1(f(n2,a))),and__dfg)
    | ~ type(f(n2,a),fulladder)
    | equal_value(n0,n1) ),
    inference(obv,[status(thm),theory(equality)],[4436]),
    [iquote('1:Obv:4436.0')] ).

cnf(4445,plain,
    ( ~ type(and2(h1(f(n2,a))),and__dfg)
    | ~ type(f(n2,a),fulladder) ),
    inference(mrr,[status(thm)],[4444,27]),
    [iquote('1:MRR:4444.2,27.0')] ).

cnf(4448,plain,
    ( ~ type(h1(f(n2,a)),halfadder)
    | ~ type(f(n2,a),fulladder) ),
    inference(res,[status(thm),theory(equality)],[46,4445]),
    [iquote('1:Res:46.1,4445.0')] ).

cnf(4449,plain,
    ~ type(f(n2,a),fulladder),
    inference(mrr,[status(thm)],[4448,58]),
    [iquote('1:MRR:4448.0,58.1')] ).

cnf(4450,plain,
    ~ type(a,nbit_adder(n2)),
    inference(res,[status(thm),theory(equality)],[2,4449]),
    [iquote('1:Res:2.1,4449.0')] ).

cnf(4451,plain,
    $false,
    inference(mrr,[status(thm)],[4450,12]),
    [iquote('1:MRR:4450.0,12.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : HWV008-1.002 : TPTP v8.1.0. Bugfixed v2.2.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n025.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  : 600
% 0.13/0.34  % DateTime : Thu Jun 16 21:29:12 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 1.01/1.21  
% 1.01/1.21  SPASS V 3.9 
% 1.01/1.21  SPASS beiseite: Proof found.
% 1.01/1.21  % SZS status Theorem
% 1.01/1.21  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 1.01/1.21  SPASS derived 3439 clauses, backtracked 135 clauses, performed 3 splits and kept 2438 clauses.
% 1.01/1.21  SPASS allocated 68320 KBytes.
% 1.01/1.21  SPASS spent	0:00:00.86 on the problem.
% 1.01/1.21  		0:00:00.04 for the input.
% 1.01/1.21  		0:00:00.00 for the FLOTTER CNF translation.
% 1.01/1.21  		0:00:00.08 for inferences.
% 1.01/1.21  		0:00:00.04 for the backtracking.
% 1.01/1.21  		0:00:00.63 for the reduction.
% 1.01/1.21  
% 1.01/1.21  
% 1.01/1.21  Here is a proof with depth 14, length 90 :
% 1.01/1.21  % SZS output start Refutation
% See solution above
% 1.01/1.21  Formulae used in the proof : nbit_adder_fulladder2 nbit_adder_connection_outc_outcf1 nbit_adder_connection_ina2_in1f2 nbit_adder_connection_inb2_in2f2 a_isa_2bit_adder ina2_0 inb2_0 outc_1 diagnosis_or1f2a diagnosis_and2h2f2a diagnosis_and2h1f2a value_propagation1 value_propagation2 unique_value equal_value1 ok_or_abnormal and_0x_0 or_1_11 halfadder_and2 halfadder_connection_in1_in1and2 halfadder_connection_outc_out1and2 fulladder_halfadder1 fulladder_halfadder2 fulladder_or1 fulladder_connection_outch1_in2or1 fulladder_connection_outch2_in1or1 fulladder_connection_in1_in1h2 fulladder_connection_in2_in1h1 fulladder_connection_outc_out1or1
% 1.08/1.24  
%------------------------------------------------------------------------------