TSTP Solution File: HWV006-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : HWV006-1 : TPTP v8.1.2. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n028.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 : Tue Aug 22 10:42:22 EDT 2023
% Result : Unsatisfiable 10.15s 3.70s
% Output : CNFRefutation 10.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 80
% Syntax : Number of formulae : 480 ( 189 unt; 26 typ; 0 def)
% Number of atoms : 910 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 970 ( 514 ~; 456 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 13 >; 7 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 13 con; 0-2 aty)
% Number of variables : 188 (; 188 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ value > type > mode > equal_value > connection > out > in > #nlpp > or1 > not1 > h2 > h1 > and2 > and1 > s > or > ok > not > n2 > n1 > n0 > halfadder > fulladder > f > c > and > abnormal
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(or,type,
or: $i ).
tff(and,type,
and: $i ).
tff(not,type,
not: $i ).
tff(or1,type,
or1: $i > $i ).
tff(in,type,
in: ( $i * $i ) > $i ).
tff(f,type,
f: $i ).
tff(connection,type,
connection: ( $i * $i ) > $o ).
tff(s,type,
s: $i ).
tff(halfadder,type,
halfadder: $i ).
tff(h2,type,
h2: $i > $i ).
tff(and2,type,
and2: $i > $i ).
tff(equal_value,type,
equal_value: ( $i * $i ) > $o ).
tff(n1,type,
n1: $i ).
tff(h1,type,
h1: $i > $i ).
tff(n0,type,
n0: $i ).
tff(type,type,
type: ( $i * $i ) > $o ).
tff(fulladder,type,
fulladder: $i ).
tff(value,type,
value: ( $i * $i ) > $o ).
tff(not1,type,
not1: $i > $i ).
tff(and1,type,
and1: $i > $i ).
tff(abnormal,type,
abnormal: $i ).
tff(n2,type,
n2: $i ).
tff(out,type,
out: ( $i * $i ) > $i ).
tff(mode,type,
mode: ( $i * $i ) > $o ).
tff(ok,type,
ok: $i ).
tff(c,type,
c: $i ).
tff(f_424,axiom,
type(f,fulladder),
file(unknown,unknown) ).
tff(f_369,axiom,
! [X] :
( ~ type(X,fulladder)
| type(h1(X),halfadder) ),
file(unknown,unknown) ).
tff(f_306,axiom,
! [X] :
( ~ type(X,halfadder)
| connection(in(n2,X),in(n2,or1(X))) ),
file(unknown,unknown) ).
tff(f_410,axiom,
! [X] :
( ~ type(X,fulladder)
| connection(in(c,X),in(n2,h1(X))) ),
file(unknown,unknown) ).
tff(f_427,axiom,
value(in(c,f),n1),
file(unknown,unknown) ).
tff(f_51,axiom,
! [P1,P2,V] :
( ~ connection(P1,P2)
| ~ value(P1,V)
| value(P2,V) ),
file(unknown,unknown) ).
tff(f_290,axiom,
! [X] :
( ~ type(X,halfadder)
| type(not1(X),not) ),
file(unknown,unknown) ).
tff(f_69,axiom,
~ equal_value(n0,n1),
file(unknown,unknown) ).
tff(f_446,axiom,
~ mode(not1(h1(f)),abnormal),
file(unknown,unknown) ).
tff(f_85,axiom,
! [K,Any] :
( ~ type(K,Any)
| mode(K,ok)
| mode(K,abnormal) ),
file(unknown,unknown) ).
tff(f_71,axiom,
~ equal_value(n1,n0),
file(unknown,unknown) ).
tff(f_336,axiom,
! [X] :
( ~ type(X,halfadder)
| connection(out(n1,and2(X)),in(n1,not1(X))) ),
file(unknown,unknown) ).
tff(f_448,axiom,
~ mode(and2(h1(f)),abnormal),
file(unknown,unknown) ).
tff(f_285,axiom,
! [X] :
( ~ type(X,halfadder)
| type(and2(X),and) ),
file(unknown,unknown) ).
tff(f_311,axiom,
! [X] :
( ~ type(X,halfadder)
| connection(in(n1,X),in(n1,and2(X))) ),
file(unknown,unknown) ).
tff(f_405,axiom,
! [X] :
( ~ type(X,fulladder)
| connection(in(n2,X),in(n1,h1(X))) ),
file(unknown,unknown) ).
tff(f_426,axiom,
value(in(n2,f),n0),
file(unknown,unknown) ).
tff(f_219,axiom,
! [K] :
( ~ mode(K,ok)
| ~ type(K,not)
| ~ value(in(n1,K),n0)
| value(out(n1,K),n1) ),
file(unknown,unknown) ).
tff(f_135,axiom,
! [K] :
( ~ mode(K,ok)
| ~ type(K,and)
| ~ value(out(n1,K),n1)
| value(in(n1,K),n1) ),
file(unknown,unknown) ).
tff(f_67,axiom,
! [P,V1,V2] :
( ~ value(P,V1)
| ~ value(P,V2)
| equal_value(V1,V2) ),
file(unknown,unknown) ).
tff(f_97,axiom,
! [K,Any] :
( ~ mode(K,ok)
| ~ type(K,and)
| ~ value(in(Any,K),n0)
| value(out(n1,K),n0) ),
file(unknown,unknown) ).
tff(f_341,axiom,
! [X] :
( ~ type(X,halfadder)
| connection(out(n1,not1(X)),in(n2,and1(X))) ),
file(unknown,unknown) ).
tff(f_280,axiom,
! [X] :
( ~ type(X,halfadder)
| type(and1(X),and) ),
file(unknown,unknown) ).
tff(f_450,axiom,
~ mode(and1(h1(f)),abnormal),
file(unknown,unknown) ).
tff(f_331,axiom,
! [X] :
( ~ type(X,halfadder)
| connection(out(n1,or1(X)),in(n1,and1(X))) ),
file(unknown,unknown) ).
tff(f_295,axiom,
! [X] :
( ~ type(X,halfadder)
| type(or1(X),or) ),
file(unknown,unknown) ).
tff(f_444,axiom,
~ mode(or1(h1(f)),abnormal),
file(unknown,unknown) ).
tff(f_301,axiom,
! [X] :
( ~ type(X,halfadder)
| connection(in(n1,X),in(n1,or1(X))) ),
file(unknown,unknown) ).
tff(f_158,axiom,
! [K,Any] :
( ~ mode(K,ok)
| ~ type(K,or)
| ~ value(in(Any,K),n1)
| value(out(n1,K),n1) ),
file(unknown,unknown) ).
tff(f_321,axiom,
! [X] :
( ~ type(X,halfadder)
| connection(out(s,X),out(n1,and1(X))) ),
file(unknown,unknown) ).
tff(f_385,axiom,
! [X] :
( ~ type(X,fulladder)
| connection(out(s,h1(X)),in(n2,h2(X))) ),
file(unknown,unknown) ).
tff(f_374,axiom,
! [X] :
( ~ type(X,fulladder)
| type(h2(X),halfadder) ),
file(unknown,unknown) ).
tff(f_400,axiom,
! [X] :
( ~ type(X,fulladder)
| connection(in(n1,X),in(n1,h2(X))) ),
file(unknown,unknown) ).
tff(f_425,axiom,
value(in(n1,f),n1),
file(unknown,unknown) ).
tff(f_316,axiom,
! [X] :
( ~ type(X,halfadder)
| connection(in(n2,X),in(n2,and2(X))) ),
file(unknown,unknown) ).
tff(f_437,axiom,
~ mode(and2(h2(f)),abnormal),
file(unknown,unknown) ).
tff(f_326,axiom,
! [X] :
( ~ type(X,halfadder)
| connection(out(c,X),out(n1,and2(X))) ),
file(unknown,unknown) ).
tff(f_390,axiom,
! [X] :
( ~ type(X,fulladder)
| connection(out(c,h1(X)),in(n2,or1(X))) ),
file(unknown,unknown) ).
tff(f_379,axiom,
! [X] :
( ~ type(X,fulladder)
| type(or1(X),or) ),
file(unknown,unknown) ).
tff(f_442,axiom,
( ~ mode(or1(f),abnormal)
| ~ mode(and1(h2(f)),abnormal) ),
file(unknown,unknown) ).
tff(f_420,axiom,
! [X] :
( ~ type(X,fulladder)
| connection(out(c,X),out(n1,or1(X))) ),
file(unknown,unknown) ).
tff(f_429,axiom,
value(out(c,f),n0),
file(unknown,unknown) ).
tff(f_207,axiom,
! [K] :
( ~ mode(K,ok)
| ~ type(K,or)
| ~ value(out(n1,K),n0)
| value(in(n2,K),n0) ),
file(unknown,unknown) ).
tff(f_59,axiom,
! [P1,P2,V] :
( ~ connection(P1,P2)
| ~ value(P2,V)
| value(P1,V) ),
file(unknown,unknown) ).
tff(f_230,axiom,
! [K] :
( ~ mode(K,ok)
| ~ type(K,not)
| ~ value(in(n1,K),n1)
| value(out(n1,K),n0) ),
file(unknown,unknown) ).
tff(f_415,axiom,
! [X] :
( ~ type(X,fulladder)
| connection(out(s,X),out(s,h2(X))) ),
file(unknown,unknown) ).
tff(f_428,axiom,
value(out(s,f),n1),
file(unknown,unknown) ).
tff(f_395,axiom,
! [X] :
( ~ type(X,fulladder)
| connection(out(c,h2(X)),in(n1,or1(X))) ),
file(unknown,unknown) ).
tff(f_196,axiom,
! [K] :
( ~ mode(K,ok)
| ~ type(K,or)
| ~ value(out(n1,K),n0)
| value(in(n1,K),n0) ),
file(unknown,unknown) ).
tff(f_111,axiom,
! [K] :
( ~ mode(K,ok)
| ~ type(K,and)
| ~ value(in(n1,K),n1)
| ~ value(in(n2,K),n1)
| value(out(n1,K),n1) ),
file(unknown,unknown) ).
tff(f_124,axiom,
! [K] :
( ~ mode(K,ok)
| ~ type(K,and)
| ~ value(out(n1,K),n0)
| value(in(n1,K),n0)
| value(in(n2,K),n0) ),
file(unknown,unknown) ).
tff(f_435,axiom,
( ~ mode(or1(f),abnormal)
| ~ mode(not1(h2(f)),abnormal) ),
file(unknown,unknown) ).
tff(f_146,axiom,
! [K] :
( ~ mode(K,ok)
| ~ type(K,and)
| ~ value(out(n1,K),n1)
| value(in(n2,K),n1) ),
file(unknown,unknown) ).
tff(f_252,axiom,
! [K] :
( ~ mode(K,ok)
| ~ type(K,not)
| ~ value(out(n1,K),n1)
| value(in(n1,K),n0) ),
file(unknown,unknown) ).
tff(c_92,plain,
type(f,fulladder),
inference(cnfTransformation,[status(thm)],[f_424]) ).
tff(c_70,plain,
! [X_42] :
( type(h1(X_42),halfadder)
| ~ type(X_42,fulladder) ),
inference(cnfTransformation,[status(thm)],[f_369]) ).
tff(c_54,plain,
! [X_34] :
( connection(in(n2,X_34),in(n2,or1(X_34)))
| ~ type(X_34,halfadder) ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_4053,plain,
! [X_316] :
( connection(in(c,X_316),in(n2,h1(X_316)))
| ~ type(X_316,fulladder) ),
inference(cnfTransformation,[status(thm)],[f_410]) ).
tff(c_98,plain,
value(in(c,f),n1),
inference(cnfTransformation,[status(thm)],[f_427]) ).
tff(c_3857,plain,
! [P2_288,V_289,P1_290] :
( value(P2_288,V_289)
| ~ value(P1_290,V_289)
| ~ connection(P1_290,P2_288) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_3869,plain,
! [P2_288] :
( value(P2_288,n1)
| ~ connection(in(c,f),P2_288) ),
inference(resolution,[status(thm)],[c_98,c_3857]) ).
tff(c_4057,plain,
( value(in(n2,h1(f)),n1)
| ~ type(f,fulladder) ),
inference(resolution,[status(thm)],[c_4053,c_3869]) ).
tff(c_4060,plain,
value(in(n2,h1(f)),n1),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_4057]) ).
tff(c_2,plain,
! [P2_2,V_3,P1_1] :
( value(P2_2,V_3)
| ~ value(P1_1,V_3)
| ~ connection(P1_1,P2_2) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_4076,plain,
! [P2_318] :
( value(P2_318,n1)
| ~ connection(in(n2,h1(f)),P2_318) ),
inference(resolution,[status(thm)],[c_4060,c_2]) ).
tff(c_4089,plain,
( value(in(n2,or1(h1(f))),n1)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_54,c_4076]) ).
tff(c_4176,plain,
~ type(h1(f),halfadder),
inference(splitLeft,[status(thm)],[c_4089]) ).
tff(c_4185,plain,
~ type(f,fulladder),
inference(resolution,[status(thm)],[c_70,c_4176]) ).
tff(c_4189,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_92,c_4185]) ).
tff(c_4191,plain,
type(h1(f),halfadder),
inference(splitRight,[status(thm)],[c_4089]) ).
tff(c_48,plain,
! [X_31] :
( type(not1(X_31),not)
| ~ type(X_31,halfadder) ),
inference(cnfTransformation,[status(thm)],[f_290]) ).
tff(c_8,plain,
~ equal_value(n0,n1),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_112,plain,
~ mode(not1(h1(f)),abnormal),
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_3760,plain,
! [K_273,Any_274] :
( mode(K_273,abnormal)
| mode(K_273,ok)
| ~ type(K_273,Any_274) ),
inference(cnfTransformation,[status(thm)],[f_85]) ).
tff(c_3790,plain,
! [X_31] :
( mode(not1(X_31),abnormal)
| mode(not1(X_31),ok)
| ~ type(X_31,halfadder) ),
inference(resolution,[status(thm)],[c_48,c_3760]) ).
tff(c_10,plain,
~ equal_value(n1,n0),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_66,plain,
! [X_40] :
( connection(out(n1,and2(X_40)),in(n1,not1(X_40)))
| ~ type(X_40,halfadder) ),
inference(cnfTransformation,[status(thm)],[f_336]) ).
tff(c_114,plain,
~ mode(and2(h1(f)),abnormal),
inference(cnfTransformation,[status(thm)],[f_448]) ).
tff(c_46,plain,
! [X_30] :
( type(and2(X_30),and)
| ~ type(X_30,halfadder) ),
inference(cnfTransformation,[status(thm)],[f_285]) ).
tff(c_3785,plain,
! [X_30] :
( mode(and2(X_30),abnormal)
| mode(and2(X_30),ok)
| ~ type(X_30,halfadder) ),
inference(resolution,[status(thm)],[c_46,c_3760]) ).
tff(c_56,plain,
! [X_35] :
( connection(in(n1,X_35),in(n1,and2(X_35)))
| ~ type(X_35,halfadder) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_3952,plain,
! [X_306] :
( connection(in(n2,X_306),in(n1,h1(X_306)))
| ~ type(X_306,fulladder) ),
inference(cnfTransformation,[status(thm)],[f_405]) ).
tff(c_96,plain,
value(in(n2,f),n0),
inference(cnfTransformation,[status(thm)],[f_426]) ).
tff(c_3868,plain,
! [P2_288] :
( value(P2_288,n0)
| ~ connection(in(n2,f),P2_288) ),
inference(resolution,[status(thm)],[c_96,c_3857]) ).
tff(c_3956,plain,
( value(in(n1,h1(f)),n0)
| ~ type(f,fulladder) ),
inference(resolution,[status(thm)],[c_3952,c_3868]) ).
tff(c_3959,plain,
value(in(n1,h1(f)),n0),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_3956]) ).
tff(c_3969,plain,
! [P2_307] :
( value(P2_307,n0)
| ~ connection(in(n1,h1(f)),P2_307) ),
inference(resolution,[status(thm)],[c_3959,c_2]) ).
tff(c_3983,plain,
( value(in(n1,and2(h1(f))),n0)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_56,c_3969]) ).
tff(c_4580,plain,
value(in(n1,and2(h1(f))),n0),
inference(demodulation,[status(thm),theory(equality)],[c_4191,c_3983]) ).
tff(c_4544,plain,
! [K_365] :
( value(out(n1,K_365),n1)
| ~ value(in(n1,K_365),n0)
| ~ type(K_365,not)
| ~ mode(K_365,ok) ),
inference(cnfTransformation,[status(thm)],[f_219]) ).
tff(c_22,plain,
! [K_17] :
( value(in(n1,K_17),n1)
| ~ value(out(n1,K_17),n1)
| ~ type(K_17,and)
| ~ mode(K_17,ok) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_4826,plain,
! [K_377] :
( value(in(n1,K_377),n1)
| ~ type(K_377,and)
| ~ value(in(n1,K_377),n0)
| ~ type(K_377,not)
| ~ mode(K_377,ok) ),
inference(resolution,[status(thm)],[c_4544,c_22]) ).
tff(c_6,plain,
! [V1_8,V2_9,P_7] :
( equal_value(V1_8,V2_9)
| ~ value(P_7,V2_9)
| ~ value(P_7,V1_8) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_4592,plain,
! [V1_8] :
( equal_value(V1_8,n0)
| ~ value(in(n1,and2(h1(f))),V1_8) ),
inference(resolution,[status(thm)],[c_4580,c_6]) ).
tff(c_4832,plain,
( equal_value(n1,n0)
| ~ type(and2(h1(f)),and)
| ~ value(in(n1,and2(h1(f))),n0)
| ~ type(and2(h1(f)),not)
| ~ mode(and2(h1(f)),ok) ),
inference(resolution,[status(thm)],[c_4826,c_4592]) ).
tff(c_4866,plain,
( equal_value(n1,n0)
| ~ type(and2(h1(f)),and)
| ~ type(and2(h1(f)),not)
| ~ mode(and2(h1(f)),ok) ),
inference(demodulation,[status(thm),theory(equality)],[c_4580,c_4832]) ).
tff(c_4867,plain,
( ~ type(and2(h1(f)),and)
| ~ type(and2(h1(f)),not)
| ~ mode(and2(h1(f)),ok) ),
inference(negUnitSimplification,[status(thm)],[c_10,c_4866]) ).
tff(c_4889,plain,
~ mode(and2(h1(f)),ok),
inference(splitLeft,[status(thm)],[c_4867]) ).
tff(c_4892,plain,
( mode(and2(h1(f)),abnormal)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_3785,c_4889]) ).
tff(c_4895,plain,
mode(and2(h1(f)),abnormal),
inference(demodulation,[status(thm),theory(equality)],[c_4191,c_4892]) ).
tff(c_4897,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_114,c_4895]) ).
tff(c_4899,plain,
mode(and2(h1(f)),ok),
inference(splitRight,[status(thm)],[c_4867]) ).
tff(c_4898,plain,
( ~ type(and2(h1(f)),not)
| ~ type(and2(h1(f)),and) ),
inference(splitRight,[status(thm)],[c_4867]) ).
tff(c_4904,plain,
~ type(and2(h1(f)),and),
inference(splitLeft,[status(thm)],[c_4898]) ).
tff(c_4907,plain,
~ type(h1(f),halfadder),
inference(resolution,[status(thm)],[c_46,c_4904]) ).
tff(c_4911,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4191,c_4907]) ).
tff(c_4913,plain,
type(and2(h1(f)),and),
inference(splitRight,[status(thm)],[c_4898]) ).
tff(c_16,plain,
! [K_13,Any_14] :
( value(out(n1,K_13),n0)
| ~ value(in(Any_14,K_13),n0)
| ~ type(K_13,and)
| ~ mode(K_13,ok) ),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_4589,plain,
( value(out(n1,and2(h1(f))),n0)
| ~ type(and2(h1(f)),and)
| ~ mode(and2(h1(f)),ok) ),
inference(resolution,[status(thm)],[c_4580,c_16]) ).
tff(c_4991,plain,
value(out(n1,and2(h1(f))),n0),
inference(demodulation,[status(thm),theory(equality)],[c_4899,c_4913,c_4589]) ).
tff(c_5198,plain,
! [P2_389] :
( value(P2_389,n0)
| ~ connection(out(n1,and2(h1(f))),P2_389) ),
inference(resolution,[status(thm)],[c_4991,c_2]) ).
tff(c_5202,plain,
( value(in(n1,not1(h1(f))),n0)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_66,c_5198]) ).
tff(c_5205,plain,
value(in(n1,not1(h1(f))),n0),
inference(demodulation,[status(thm),theory(equality)],[c_4191,c_5202]) ).
tff(c_4570,plain,
! [K_365] :
( value(in(n1,K_365),n1)
| ~ type(K_365,and)
| ~ value(in(n1,K_365),n0)
| ~ type(K_365,not)
| ~ mode(K_365,ok) ),
inference(resolution,[status(thm)],[c_4544,c_22]) ).
tff(c_5360,plain,
! [V1_401] :
( equal_value(V1_401,n0)
| ~ value(in(n1,not1(h1(f))),V1_401) ),
inference(resolution,[status(thm)],[c_5205,c_6]) ).
tff(c_5367,plain,
( equal_value(n1,n0)
| ~ type(not1(h1(f)),and)
| ~ value(in(n1,not1(h1(f))),n0)
| ~ type(not1(h1(f)),not)
| ~ mode(not1(h1(f)),ok) ),
inference(resolution,[status(thm)],[c_4570,c_5360]) ).
tff(c_5372,plain,
( equal_value(n1,n0)
| ~ type(not1(h1(f)),and)
| ~ type(not1(h1(f)),not)
| ~ mode(not1(h1(f)),ok) ),
inference(demodulation,[status(thm),theory(equality)],[c_5205,c_5367]) ).
tff(c_5373,plain,
( ~ type(not1(h1(f)),and)
| ~ type(not1(h1(f)),not)
| ~ mode(not1(h1(f)),ok) ),
inference(negUnitSimplification,[status(thm)],[c_10,c_5372]) ).
tff(c_5535,plain,
~ mode(not1(h1(f)),ok),
inference(splitLeft,[status(thm)],[c_5373]) ).
tff(c_5563,plain,
( mode(not1(h1(f)),abnormal)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_3790,c_5535]) ).
tff(c_5566,plain,
mode(not1(h1(f)),abnormal),
inference(demodulation,[status(thm),theory(equality)],[c_4191,c_5563]) ).
tff(c_5568,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_112,c_5566]) ).
tff(c_5570,plain,
mode(not1(h1(f)),ok),
inference(splitRight,[status(thm)],[c_5373]) ).
tff(c_68,plain,
! [X_41] :
( connection(out(n1,not1(X_41)),in(n2,and1(X_41)))
| ~ type(X_41,halfadder) ),
inference(cnfTransformation,[status(thm)],[f_341]) ).
tff(c_44,plain,
! [X_29] :
( type(and1(X_29),and)
| ~ type(X_29,halfadder) ),
inference(cnfTransformation,[status(thm)],[f_280]) ).
tff(c_116,plain,
~ mode(and1(h1(f)),abnormal),
inference(cnfTransformation,[status(thm)],[f_450]) ).
tff(c_3786,plain,
! [X_29] :
( mode(and1(X_29),abnormal)
| mode(and1(X_29),ok)
| ~ type(X_29,halfadder) ),
inference(resolution,[status(thm)],[c_44,c_3760]) ).
tff(c_64,plain,
! [X_39] :
( connection(out(n1,or1(X_39)),in(n1,and1(X_39)))
| ~ type(X_39,halfadder) ),
inference(cnfTransformation,[status(thm)],[f_331]) ).
tff(c_50,plain,
! [X_32] :
( type(or1(X_32),or)
| ~ type(X_32,halfadder) ),
inference(cnfTransformation,[status(thm)],[f_295]) ).
tff(c_110,plain,
~ mode(or1(h1(f)),abnormal),
inference(cnfTransformation,[status(thm)],[f_444]) ).
tff(c_3791,plain,
! [X_32] :
( mode(or1(X_32),abnormal)
| mode(or1(X_32),ok)
| ~ type(X_32,halfadder) ),
inference(resolution,[status(thm)],[c_50,c_3760]) ).
tff(c_52,plain,
! [X_33] :
( connection(in(n1,X_33),in(n1,or1(X_33)))
| ~ type(X_33,halfadder) ),
inference(cnfTransformation,[status(thm)],[f_301]) ).
tff(c_3984,plain,
( value(in(n1,or1(h1(f))),n0)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_52,c_3969]) ).
tff(c_4373,plain,
value(in(n1,or1(h1(f))),n0),
inference(demodulation,[status(thm),theory(equality)],[c_4191,c_3984]) ).
tff(c_4385,plain,
! [V1_8] :
( equal_value(V1_8,n0)
| ~ value(in(n1,or1(h1(f))),V1_8) ),
inference(resolution,[status(thm)],[c_4373,c_6]) ).
tff(c_4836,plain,
( equal_value(n1,n0)
| ~ type(or1(h1(f)),and)
| ~ value(in(n1,or1(h1(f))),n0)
| ~ type(or1(h1(f)),not)
| ~ mode(or1(h1(f)),ok) ),
inference(resolution,[status(thm)],[c_4826,c_4385]) ).
tff(c_4870,plain,
( equal_value(n1,n0)
| ~ type(or1(h1(f)),and)
| ~ type(or1(h1(f)),not)
| ~ mode(or1(h1(f)),ok) ),
inference(demodulation,[status(thm),theory(equality)],[c_4373,c_4836]) ).
tff(c_4871,plain,
( ~ type(or1(h1(f)),and)
| ~ type(or1(h1(f)),not)
| ~ mode(or1(h1(f)),ok) ),
inference(negUnitSimplification,[status(thm)],[c_10,c_4870]) ).
tff(c_4930,plain,
~ mode(or1(h1(f)),ok),
inference(splitLeft,[status(thm)],[c_4871]) ).
tff(c_4933,plain,
( mode(or1(h1(f)),abnormal)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_3791,c_4930]) ).
tff(c_4939,plain,
mode(or1(h1(f)),abnormal),
inference(demodulation,[status(thm),theory(equality)],[c_4191,c_4933]) ).
tff(c_4941,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_110,c_4939]) ).
tff(c_4943,plain,
mode(or1(h1(f)),ok),
inference(splitRight,[status(thm)],[c_4871]) ).
tff(c_4190,plain,
value(in(n2,or1(h1(f))),n1),
inference(splitRight,[status(thm)],[c_4089]) ).
tff(c_4633,plain,
! [K_370,Any_371] :
( value(out(n1,K_370),n1)
| ~ value(in(Any_371,K_370),n1)
| ~ type(K_370,or)
| ~ mode(K_370,ok) ),
inference(cnfTransformation,[status(thm)],[f_158]) ).
tff(c_4653,plain,
( value(out(n1,or1(h1(f))),n1)
| ~ type(or1(h1(f)),or)
| ~ mode(or1(h1(f)),ok) ),
inference(resolution,[status(thm)],[c_4190,c_4633]) ).
tff(c_5665,plain,
( value(out(n1,or1(h1(f))),n1)
| ~ type(or1(h1(f)),or) ),
inference(demodulation,[status(thm),theory(equality)],[c_4943,c_4653]) ).
tff(c_5666,plain,
~ type(or1(h1(f)),or),
inference(splitLeft,[status(thm)],[c_5665]) ).
tff(c_5683,plain,
~ type(h1(f),halfadder),
inference(resolution,[status(thm)],[c_50,c_5666]) ).
tff(c_5688,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4191,c_5683]) ).
tff(c_5689,plain,
value(out(n1,or1(h1(f))),n1),
inference(splitRight,[status(thm)],[c_5665]) ).
tff(c_5743,plain,
! [P2_415] :
( value(P2_415,n1)
| ~ connection(out(n1,or1(h1(f))),P2_415) ),
inference(resolution,[status(thm)],[c_5689,c_2]) ).
tff(c_5747,plain,
( value(in(n1,and1(h1(f))),n1)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_64,c_5743]) ).
tff(c_5750,plain,
value(in(n1,and1(h1(f))),n1),
inference(demodulation,[status(thm),theory(equality)],[c_4191,c_5747]) ).
tff(c_26,plain,
! [K_19,Any_20] :
( value(out(n1,K_19),n1)
| ~ value(in(Any_20,K_19),n1)
| ~ type(K_19,or)
| ~ mode(K_19,ok) ),
inference(cnfTransformation,[status(thm)],[f_158]) ).
tff(c_5777,plain,
( value(out(n1,and1(h1(f))),n1)
| ~ type(and1(h1(f)),or)
| ~ mode(and1(h1(f)),ok) ),
inference(resolution,[status(thm)],[c_5750,c_26]) ).
tff(c_6602,plain,
~ mode(and1(h1(f)),ok),
inference(splitLeft,[status(thm)],[c_5777]) ).
tff(c_6605,plain,
( mode(and1(h1(f)),abnormal)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_3786,c_6602]) ).
tff(c_6608,plain,
mode(and1(h1(f)),abnormal),
inference(demodulation,[status(thm),theory(equality)],[c_4191,c_6605]) ).
tff(c_6610,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_116,c_6608]) ).
tff(c_6612,plain,
mode(and1(h1(f)),ok),
inference(splitRight,[status(thm)],[c_5777]) ).
tff(c_60,plain,
! [X_37] :
( connection(out(s,X_37),out(n1,and1(X_37)))
| ~ type(X_37,halfadder) ),
inference(cnfTransformation,[status(thm)],[f_321]) ).
tff(c_76,plain,
! [X_45] :
( connection(out(s,h1(X_45)),in(n2,h2(X_45)))
| ~ type(X_45,fulladder) ),
inference(cnfTransformation,[status(thm)],[f_385]) ).
tff(c_72,plain,
! [X_43] :
( type(h2(X_43),halfadder)
| ~ type(X_43,fulladder) ),
inference(cnfTransformation,[status(thm)],[f_374]) ).
tff(c_3905,plain,
! [X_302] :
( connection(in(n1,X_302),in(n1,h2(X_302)))
| ~ type(X_302,fulladder) ),
inference(cnfTransformation,[status(thm)],[f_400]) ).
tff(c_94,plain,
value(in(n1,f),n1),
inference(cnfTransformation,[status(thm)],[f_425]) ).
tff(c_3871,plain,
! [P2_288] :
( value(P2_288,n1)
| ~ connection(in(n1,f),P2_288) ),
inference(resolution,[status(thm)],[c_94,c_3857]) ).
tff(c_3909,plain,
( value(in(n1,h2(f)),n1)
| ~ type(f,fulladder) ),
inference(resolution,[status(thm)],[c_3905,c_3871]) ).
tff(c_3912,plain,
value(in(n1,h2(f)),n1),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_3909]) ).
tff(c_3922,plain,
! [P2_303] :
( value(P2_303,n1)
| ~ connection(in(n1,h2(f)),P2_303) ),
inference(resolution,[status(thm)],[c_3912,c_2]) ).
tff(c_3937,plain,
( value(in(n1,or1(h2(f))),n1)
| ~ type(h2(f),halfadder) ),
inference(resolution,[status(thm)],[c_52,c_3922]) ).
tff(c_4252,plain,
~ type(h2(f),halfadder),
inference(splitLeft,[status(thm)],[c_3937]) ).
tff(c_4255,plain,
~ type(f,fulladder),
inference(resolution,[status(thm)],[c_72,c_4252]) ).
tff(c_4259,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_92,c_4255]) ).
tff(c_4261,plain,
type(h2(f),halfadder),
inference(splitRight,[status(thm)],[c_3937]) ).
tff(c_58,plain,
! [X_36] :
( connection(in(n2,X_36),in(n2,and2(X_36)))
| ~ type(X_36,halfadder) ),
inference(cnfTransformation,[status(thm)],[f_316]) ).
tff(c_106,plain,
~ mode(and2(h2(f)),abnormal),
inference(cnfTransformation,[status(thm)],[f_437]) ).
tff(c_3936,plain,
( value(in(n1,and2(h2(f))),n1)
| ~ type(h2(f),halfadder) ),
inference(resolution,[status(thm)],[c_56,c_3922]) ).
tff(c_4331,plain,
value(in(n1,and2(h2(f))),n1),
inference(demodulation,[status(thm),theory(equality)],[c_4261,c_3936]) ).
tff(c_4651,plain,
( value(out(n1,and2(h2(f))),n1)
| ~ type(and2(h2(f)),or)
| ~ mode(and2(h2(f)),ok) ),
inference(resolution,[status(thm)],[c_4331,c_4633]) ).
tff(c_5638,plain,
~ mode(and2(h2(f)),ok),
inference(splitLeft,[status(thm)],[c_4651]) ).
tff(c_5641,plain,
( mode(and2(h2(f)),abnormal)
| ~ type(h2(f),halfadder) ),
inference(resolution,[status(thm)],[c_3785,c_5638]) ).
tff(c_5644,plain,
mode(and2(h2(f)),abnormal),
inference(demodulation,[status(thm),theory(equality)],[c_4261,c_5641]) ).
tff(c_5646,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_106,c_5644]) ).
tff(c_5648,plain,
mode(and2(h2(f)),ok),
inference(splitRight,[status(thm)],[c_4651]) ).
tff(c_475,plain,
! [X_111] :
( connection(in(n1,X_111),in(n1,or1(X_111)))
| ~ type(X_111,halfadder) ),
inference(cnfTransformation,[status(thm)],[f_301]) ).
tff(c_315,plain,
! [X_93] :
( connection(in(n2,X_93),in(n1,h1(X_93)))
| ~ type(X_93,fulladder) ),
inference(cnfTransformation,[status(thm)],[f_405]) ).
tff(c_126,plain,
! [P2_61,V_62,P1_63] :
( value(P2_61,V_62)
| ~ value(P1_63,V_62)
| ~ connection(P1_63,P2_61) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_137,plain,
! [P2_61] :
( value(P2_61,n0)
| ~ connection(in(n2,f),P2_61) ),
inference(resolution,[status(thm)],[c_96,c_126]) ).
tff(c_323,plain,
( value(in(n1,h1(f)),n0)
| ~ type(f,fulladder) ),
inference(resolution,[status(thm)],[c_315,c_137]) ).
tff(c_327,plain,
value(in(n1,h1(f)),n0),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_323]) ).
tff(c_336,plain,
! [P2_2] :
( value(P2_2,n0)
| ~ connection(in(n1,h1(f)),P2_2) ),
inference(resolution,[status(thm)],[c_327,c_2]) ).
tff(c_488,plain,
( value(in(n1,or1(h1(f))),n0)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_475,c_336]) ).
tff(c_539,plain,
~ type(h1(f),halfadder),
inference(splitLeft,[status(thm)],[c_488]) ).
tff(c_542,plain,
~ type(f,fulladder),
inference(resolution,[status(thm)],[c_70,c_539]) ).
tff(c_546,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_92,c_542]) ).
tff(c_548,plain,
type(h1(f),halfadder),
inference(splitRight,[status(thm)],[c_488]) ).
tff(c_146,plain,
! [K_68,Any_69] :
( mode(K_68,abnormal)
| mode(K_68,ok)
| ~ type(K_68,Any_69) ),
inference(cnfTransformation,[status(thm)],[f_85]) ).
tff(c_176,plain,
! [X_31] :
( mode(not1(X_31),abnormal)
| mode(not1(X_31),ok)
| ~ type(X_31,halfadder) ),
inference(resolution,[status(thm)],[c_48,c_146]) ).
tff(c_62,plain,
! [X_38] :
( connection(out(c,X_38),out(n1,and2(X_38)))
| ~ type(X_38,halfadder) ),
inference(cnfTransformation,[status(thm)],[f_326]) ).
tff(c_78,plain,
! [X_46] :
( connection(out(c,h1(X_46)),in(n2,or1(X_46)))
| ~ type(X_46,fulladder) ),
inference(cnfTransformation,[status(thm)],[f_390]) ).
tff(c_74,plain,
! [X_44] :
( type(or1(X_44),or)
| ~ type(X_44,fulladder) ),
inference(cnfTransformation,[status(thm)],[f_379]) ).
tff(c_108,plain,
( ~ mode(and1(h2(f)),abnormal)
| ~ mode(or1(f),abnormal) ),
inference(cnfTransformation,[status(thm)],[f_442]) ).
tff(c_125,plain,
~ mode(or1(f),abnormal),
inference(splitLeft,[status(thm)],[c_108]) ).
tff(c_173,plain,
! [X_44] :
( mode(or1(X_44),abnormal)
| mode(or1(X_44),ok)
| ~ type(X_44,fulladder) ),
inference(resolution,[status(thm)],[c_74,c_146]) ).
tff(c_224,plain,
! [X_80] :
( connection(out(c,X_80),out(n1,or1(X_80)))
| ~ type(X_80,fulladder) ),
inference(cnfTransformation,[status(thm)],[f_420]) ).
tff(c_102,plain,
value(out(c,f),n0),
inference(cnfTransformation,[status(thm)],[f_429]) ).
tff(c_141,plain,
! [P2_61] :
( value(P2_61,n0)
| ~ connection(out(c,f),P2_61) ),
inference(resolution,[status(thm)],[c_102,c_126]) ).
tff(c_228,plain,
( value(out(n1,or1(f)),n0)
| ~ type(f,fulladder) ),
inference(resolution,[status(thm)],[c_224,c_141]) ).
tff(c_231,plain,
value(out(n1,or1(f)),n0),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_228]) ).
tff(c_749,plain,
! [K_138] :
( value(in(n2,K_138),n0)
| ~ value(out(n1,K_138),n0)
| ~ type(K_138,or)
| ~ mode(K_138,ok) ),
inference(cnfTransformation,[status(thm)],[f_207]) ).
tff(c_753,plain,
( value(in(n2,or1(f)),n0)
| ~ type(or1(f),or)
| ~ mode(or1(f),ok) ),
inference(resolution,[status(thm)],[c_231,c_749]) ).
tff(c_1140,plain,
~ mode(or1(f),ok),
inference(splitLeft,[status(thm)],[c_753]) ).
tff(c_1143,plain,
( mode(or1(f),abnormal)
| ~ type(f,fulladder) ),
inference(resolution,[status(thm)],[c_173,c_1140]) ).
tff(c_1149,plain,
mode(or1(f),abnormal),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_1143]) ).
tff(c_1151,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_125,c_1149]) ).
tff(c_1152,plain,
( ~ type(or1(f),or)
| value(in(n2,or1(f)),n0) ),
inference(splitRight,[status(thm)],[c_753]) ).
tff(c_1221,plain,
~ type(or1(f),or),
inference(splitLeft,[status(thm)],[c_1152]) ).
tff(c_1224,plain,
~ type(f,fulladder),
inference(resolution,[status(thm)],[c_74,c_1221]) ).
tff(c_1231,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_92,c_1224]) ).
tff(c_1232,plain,
value(in(n2,or1(f)),n0),
inference(splitRight,[status(thm)],[c_1152]) ).
tff(c_4,plain,
! [P1_4,V_6,P2_5] :
( value(P1_4,V_6)
| ~ value(P2_5,V_6)
| ~ connection(P1_4,P2_5) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_1323,plain,
! [P1_168] :
( value(P1_168,n0)
| ~ connection(P1_168,in(n2,or1(f))) ),
inference(resolution,[status(thm)],[c_1232,c_4]) ).
tff(c_1327,plain,
( value(out(c,h1(f)),n0)
| ~ type(f,fulladder) ),
inference(resolution,[status(thm)],[c_78,c_1323]) ).
tff(c_1334,plain,
value(out(c,h1(f)),n0),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_1327]) ).
tff(c_1416,plain,
! [P2_176] :
( value(P2_176,n0)
| ~ connection(out(c,h1(f)),P2_176) ),
inference(resolution,[status(thm)],[c_1334,c_2]) ).
tff(c_1424,plain,
( value(out(n1,and2(h1(f))),n0)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_62,c_1416]) ).
tff(c_1434,plain,
value(out(n1,and2(h1(f))),n0),
inference(demodulation,[status(thm),theory(equality)],[c_548,c_1424]) ).
tff(c_1602,plain,
! [P2_184] :
( value(P2_184,n0)
| ~ connection(out(n1,and2(h1(f))),P2_184) ),
inference(resolution,[status(thm)],[c_1434,c_2]) ).
tff(c_1606,plain,
( value(in(n1,not1(h1(f))),n0)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_66,c_1602]) ).
tff(c_1609,plain,
value(in(n1,not1(h1(f))),n0),
inference(demodulation,[status(thm),theory(equality)],[c_548,c_1606]) ).
tff(c_36,plain,
! [K_25] :
( value(out(n1,K_25),n1)
| ~ value(in(n1,K_25),n0)
| ~ type(K_25,not)
| ~ mode(K_25,ok) ),
inference(cnfTransformation,[status(thm)],[f_219]) ).
tff(c_973,plain,
! [K_154] :
( value(in(n1,K_154),n1)
| ~ value(out(n1,K_154),n1)
| ~ type(K_154,and)
| ~ mode(K_154,ok) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_980,plain,
! [K_25] :
( value(in(n1,K_25),n1)
| ~ type(K_25,and)
| ~ value(in(n1,K_25),n0)
| ~ type(K_25,not)
| ~ mode(K_25,ok) ),
inference(resolution,[status(thm)],[c_36,c_973]) ).
tff(c_1796,plain,
! [V1_193] :
( equal_value(V1_193,n0)
| ~ value(in(n1,not1(h1(f))),V1_193) ),
inference(resolution,[status(thm)],[c_1609,c_6]) ).
tff(c_1803,plain,
( equal_value(n1,n0)
| ~ type(not1(h1(f)),and)
| ~ value(in(n1,not1(h1(f))),n0)
| ~ type(not1(h1(f)),not)
| ~ mode(not1(h1(f)),ok) ),
inference(resolution,[status(thm)],[c_980,c_1796]) ).
tff(c_1808,plain,
( equal_value(n1,n0)
| ~ type(not1(h1(f)),and)
| ~ type(not1(h1(f)),not)
| ~ mode(not1(h1(f)),ok) ),
inference(demodulation,[status(thm),theory(equality)],[c_1609,c_1803]) ).
tff(c_1809,plain,
( ~ type(not1(h1(f)),and)
| ~ type(not1(h1(f)),not)
| ~ mode(not1(h1(f)),ok) ),
inference(negUnitSimplification,[status(thm)],[c_10,c_1808]) ).
tff(c_1985,plain,
~ mode(not1(h1(f)),ok),
inference(splitLeft,[status(thm)],[c_1809]) ).
tff(c_1988,plain,
( mode(not1(h1(f)),abnormal)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_176,c_1985]) ).
tff(c_1991,plain,
mode(not1(h1(f)),abnormal),
inference(demodulation,[status(thm),theory(equality)],[c_548,c_1988]) ).
tff(c_1993,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_112,c_1991]) ).
tff(c_1995,plain,
mode(not1(h1(f)),ok),
inference(splitRight,[status(thm)],[c_1809]) ).
tff(c_655,plain,
! [K_132] :
( value(out(n1,K_132),n1)
| ~ value(in(n1,K_132),n0)
| ~ type(K_132,not)
| ~ mode(K_132,ok) ),
inference(cnfTransformation,[status(thm)],[f_219]) ).
tff(c_1818,plain,
! [P2_195,K_196] :
( value(P2_195,n1)
| ~ connection(out(n1,K_196),P2_195)
| ~ value(in(n1,K_196),n0)
| ~ type(K_196,not)
| ~ mode(K_196,ok) ),
inference(resolution,[status(thm)],[c_655,c_2]) ).
tff(c_1825,plain,
! [X_41] :
( value(in(n2,and1(X_41)),n1)
| ~ value(in(n1,not1(X_41)),n0)
| ~ type(not1(X_41),not)
| ~ mode(not1(X_41),ok)
| ~ type(X_41,halfadder) ),
inference(resolution,[status(thm)],[c_68,c_1818]) ).
tff(c_172,plain,
! [X_29] :
( mode(and1(X_29),abnormal)
| mode(and1(X_29),ok)
| ~ type(X_29,halfadder) ),
inference(resolution,[status(thm)],[c_44,c_146]) ).
tff(c_177,plain,
! [X_32] :
( mode(or1(X_32),abnormal)
| mode(or1(X_32),ok)
| ~ type(X_32,halfadder) ),
inference(resolution,[status(thm)],[c_50,c_146]) ).
tff(c_547,plain,
value(in(n1,or1(h1(f))),n0),
inference(splitRight,[status(thm)],[c_488]) ).
tff(c_1154,plain,
! [K_165] :
( value(in(n1,K_165),n1)
| ~ type(K_165,and)
| ~ value(in(n1,K_165),n0)
| ~ type(K_165,not)
| ~ mode(K_165,ok) ),
inference(resolution,[status(thm)],[c_36,c_973]) ).
tff(c_559,plain,
! [V1_8] :
( equal_value(V1_8,n0)
| ~ value(in(n1,or1(h1(f))),V1_8) ),
inference(resolution,[status(thm)],[c_547,c_6]) ).
tff(c_1172,plain,
( equal_value(n1,n0)
| ~ type(or1(h1(f)),and)
| ~ value(in(n1,or1(h1(f))),n0)
| ~ type(or1(h1(f)),not)
| ~ mode(or1(h1(f)),ok) ),
inference(resolution,[status(thm)],[c_1154,c_559]) ).
tff(c_1202,plain,
( equal_value(n1,n0)
| ~ type(or1(h1(f)),and)
| ~ type(or1(h1(f)),not)
| ~ mode(or1(h1(f)),ok) ),
inference(demodulation,[status(thm),theory(equality)],[c_547,c_1172]) ).
tff(c_1203,plain,
( ~ type(or1(h1(f)),and)
| ~ type(or1(h1(f)),not)
| ~ mode(or1(h1(f)),ok) ),
inference(negUnitSimplification,[status(thm)],[c_10,c_1202]) ).
tff(c_1952,plain,
~ mode(or1(h1(f)),ok),
inference(splitLeft,[status(thm)],[c_1203]) ).
tff(c_1958,plain,
( mode(or1(h1(f)),abnormal)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_177,c_1952]) ).
tff(c_1963,plain,
mode(or1(h1(f)),abnormal),
inference(demodulation,[status(thm),theory(equality)],[c_548,c_1958]) ).
tff(c_1965,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_110,c_1963]) ).
tff(c_1967,plain,
mode(or1(h1(f)),ok),
inference(splitRight,[status(thm)],[c_1203]) ).
tff(c_441,plain,
! [X_108] :
( connection(in(n2,X_108),in(n2,or1(X_108)))
| ~ type(X_108,halfadder) ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_291,plain,
! [X_90] :
( connection(in(c,X_90),in(n2,h1(X_90)))
| ~ type(X_90,fulladder) ),
inference(cnfTransformation,[status(thm)],[f_410]) ).
tff(c_138,plain,
! [P2_61] :
( value(P2_61,n1)
| ~ connection(in(c,f),P2_61) ),
inference(resolution,[status(thm)],[c_98,c_126]) ).
tff(c_295,plain,
( value(in(n2,h1(f)),n1)
| ~ type(f,fulladder) ),
inference(resolution,[status(thm)],[c_291,c_138]) ).
tff(c_298,plain,
value(in(n2,h1(f)),n1),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_295]) ).
tff(c_307,plain,
! [P2_2] :
( value(P2_2,n1)
| ~ connection(in(n2,h1(f)),P2_2) ),
inference(resolution,[status(thm)],[c_298,c_2]) ).
tff(c_450,plain,
( value(in(n2,or1(h1(f))),n1)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_441,c_307]) ).
tff(c_679,plain,
value(in(n2,or1(h1(f))),n1),
inference(demodulation,[status(thm),theory(equality)],[c_548,c_450]) ).
tff(c_695,plain,
! [K_134,Any_135] :
( value(out(n1,K_134),n1)
| ~ value(in(Any_135,K_134),n1)
| ~ type(K_134,or)
| ~ mode(K_134,ok) ),
inference(cnfTransformation,[status(thm)],[f_158]) ).
tff(c_706,plain,
( value(out(n1,or1(h1(f))),n1)
| ~ type(or1(h1(f)),or)
| ~ mode(or1(h1(f)),ok) ),
inference(resolution,[status(thm)],[c_679,c_695]) ).
tff(c_2162,plain,
( value(out(n1,or1(h1(f))),n1)
| ~ type(or1(h1(f)),or) ),
inference(demodulation,[status(thm),theory(equality)],[c_1967,c_706]) ).
tff(c_2163,plain,
~ type(or1(h1(f)),or),
inference(splitLeft,[status(thm)],[c_2162]) ).
tff(c_2169,plain,
~ type(h1(f),halfadder),
inference(resolution,[status(thm)],[c_50,c_2163]) ).
tff(c_2174,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_548,c_2169]) ).
tff(c_2175,plain,
value(out(n1,or1(h1(f))),n1),
inference(splitRight,[status(thm)],[c_2162]) ).
tff(c_2287,plain,
! [P2_213] :
( value(P2_213,n1)
| ~ connection(out(n1,or1(h1(f))),P2_213) ),
inference(resolution,[status(thm)],[c_2175,c_2]) ).
tff(c_2291,plain,
( value(in(n1,and1(h1(f))),n1)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_64,c_2287]) ).
tff(c_2294,plain,
value(in(n1,and1(h1(f))),n1),
inference(demodulation,[status(thm),theory(equality)],[c_548,c_2291]) ).
tff(c_809,plain,
! [K_144] :
( value(out(n1,K_144),n0)
| ~ value(in(n1,K_144),n1)
| ~ type(K_144,not)
| ~ mode(K_144,ok) ),
inference(cnfTransformation,[status(thm)],[f_230]) ).
tff(c_1521,plain,
! [V1_180,K_181] :
( equal_value(V1_180,n0)
| ~ value(out(n1,K_181),V1_180)
| ~ value(in(n1,K_181),n1)
| ~ type(K_181,not)
| ~ mode(K_181,ok) ),
inference(resolution,[status(thm)],[c_809,c_6]) ).
tff(c_1539,plain,
! [K_25] :
( equal_value(n1,n0)
| ~ value(in(n1,K_25),n1)
| ~ value(in(n1,K_25),n0)
| ~ type(K_25,not)
| ~ mode(K_25,ok) ),
inference(resolution,[status(thm)],[c_36,c_1521]) ).
tff(c_1560,plain,
! [K_25] :
( ~ value(in(n1,K_25),n1)
| ~ value(in(n1,K_25),n0)
| ~ type(K_25,not)
| ~ mode(K_25,ok) ),
inference(negUnitSimplification,[status(thm)],[c_10,c_1539]) ).
tff(c_2309,plain,
( ~ value(in(n1,and1(h1(f))),n0)
| ~ type(and1(h1(f)),not)
| ~ mode(and1(h1(f)),ok) ),
inference(resolution,[status(thm)],[c_2294,c_1560]) ).
tff(c_2574,plain,
~ mode(and1(h1(f)),ok),
inference(splitLeft,[status(thm)],[c_2309]) ).
tff(c_2577,plain,
( mode(and1(h1(f)),abnormal)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_172,c_2574]) ).
tff(c_2580,plain,
mode(and1(h1(f)),abnormal),
inference(demodulation,[status(thm),theory(equality)],[c_548,c_2577]) ).
tff(c_2582,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_116,c_2580]) ).
tff(c_2584,plain,
mode(and1(h1(f)),ok),
inference(splitRight,[status(thm)],[c_2309]) ).
tff(c_433,plain,
! [X_107] :
( connection(out(s,X_107),out(s,h2(X_107)))
| ~ type(X_107,fulladder) ),
inference(cnfTransformation,[status(thm)],[f_415]) ).
tff(c_100,plain,
value(out(s,f),n1),
inference(cnfTransformation,[status(thm)],[f_428]) ).
tff(c_139,plain,
! [P2_61] :
( value(P2_61,n1)
| ~ connection(out(s,f),P2_61) ),
inference(resolution,[status(thm)],[c_100,c_126]) ).
tff(c_437,plain,
( value(out(s,h2(f)),n1)
| ~ type(f,fulladder) ),
inference(resolution,[status(thm)],[c_433,c_139]) ).
tff(c_440,plain,
value(out(s,h2(f)),n1),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_437]) ).
tff(c_491,plain,
! [P2_112] :
( value(P2_112,n1)
| ~ connection(out(s,h2(f)),P2_112) ),
inference(resolution,[status(thm)],[c_440,c_2]) ).
tff(c_501,plain,
( value(out(n1,and1(h2(f))),n1)
| ~ type(h2(f),halfadder) ),
inference(resolution,[status(thm)],[c_60,c_491]) ).
tff(c_609,plain,
~ type(h2(f),halfadder),
inference(splitLeft,[status(thm)],[c_501]) ).
tff(c_612,plain,
~ type(f,fulladder),
inference(resolution,[status(thm)],[c_72,c_609]) ).
tff(c_616,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_92,c_612]) ).
tff(c_618,plain,
type(h2(f),halfadder),
inference(splitRight,[status(thm)],[c_501]) ).
tff(c_171,plain,
! [X_30] :
( mode(and2(X_30),abnormal)
| mode(and2(X_30),ok)
| ~ type(X_30,halfadder) ),
inference(resolution,[status(thm)],[c_46,c_146]) ).
tff(c_271,plain,
! [X_87] :
( connection(in(n1,X_87),in(n1,h2(X_87)))
| ~ type(X_87,fulladder) ),
inference(cnfTransformation,[status(thm)],[f_400]) ).
tff(c_140,plain,
! [P2_61] :
( value(P2_61,n1)
| ~ connection(in(n1,f),P2_61) ),
inference(resolution,[status(thm)],[c_94,c_126]) ).
tff(c_275,plain,
( value(in(n1,h2(f)),n1)
| ~ type(f,fulladder) ),
inference(resolution,[status(thm)],[c_271,c_140]) ).
tff(c_278,plain,
value(in(n1,h2(f)),n1),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_275]) ).
tff(c_369,plain,
! [P2_99] :
( value(P2_99,n1)
| ~ connection(in(n1,h2(f)),P2_99) ),
inference(resolution,[status(thm)],[c_278,c_2]) ).
tff(c_378,plain,
( value(in(n1,and2(h2(f))),n1)
| ~ type(h2(f),halfadder) ),
inference(resolution,[status(thm)],[c_56,c_369]) ).
tff(c_907,plain,
value(in(n1,and2(h2(f))),n1),
inference(demodulation,[status(thm),theory(equality)],[c_618,c_378]) ).
tff(c_916,plain,
( value(out(n1,and2(h2(f))),n1)
| ~ type(and2(h2(f)),or)
| ~ mode(and2(h2(f)),ok) ),
inference(resolution,[status(thm)],[c_907,c_26]) ).
tff(c_2093,plain,
~ mode(and2(h2(f)),ok),
inference(splitLeft,[status(thm)],[c_916]) ).
tff(c_2096,plain,
( mode(and2(h2(f)),abnormal)
| ~ type(h2(f),halfadder) ),
inference(resolution,[status(thm)],[c_171,c_2093]) ).
tff(c_2099,plain,
mode(and2(h2(f)),abnormal),
inference(demodulation,[status(thm),theory(equality)],[c_618,c_2096]) ).
tff(c_2101,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_106,c_2099]) ).
tff(c_2103,plain,
mode(and2(h2(f)),ok),
inference(splitRight,[status(thm)],[c_916]) ).
tff(c_80,plain,
! [X_47] :
( connection(out(c,h2(X_47)),in(n1,or1(X_47)))
| ~ type(X_47,fulladder) ),
inference(cnfTransformation,[status(thm)],[f_395]) ).
tff(c_1233,plain,
type(or1(f),or),
inference(splitRight,[status(thm)],[c_1152]) ).
tff(c_1153,plain,
mode(or1(f),ok),
inference(splitRight,[status(thm)],[c_753]) ).
tff(c_1017,plain,
! [K_158] :
( value(in(n1,K_158),n0)
| ~ value(out(n1,K_158),n0)
| ~ type(K_158,or)
| ~ mode(K_158,ok) ),
inference(cnfTransformation,[status(thm)],[f_196]) ).
tff(c_1025,plain,
( value(in(n1,or1(f)),n0)
| ~ type(or1(f),or)
| ~ mode(or1(f),ok) ),
inference(resolution,[status(thm)],[c_231,c_1017]) ).
tff(c_1235,plain,
( value(in(n1,or1(f)),n0)
| ~ type(or1(f),or) ),
inference(demodulation,[status(thm),theory(equality)],[c_1153,c_1025]) ).
tff(c_1236,plain,
~ type(or1(f),or),
inference(splitLeft,[status(thm)],[c_1235]) ).
tff(c_1244,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1233,c_1236]) ).
tff(c_1245,plain,
value(in(n1,or1(f)),n0),
inference(splitRight,[status(thm)],[c_1235]) ).
tff(c_1377,plain,
! [P1_171] :
( value(P1_171,n0)
| ~ connection(P1_171,in(n1,or1(f))) ),
inference(resolution,[status(thm)],[c_1245,c_4]) ).
tff(c_1381,plain,
( value(out(c,h2(f)),n0)
| ~ type(f,fulladder) ),
inference(resolution,[status(thm)],[c_80,c_1377]) ).
tff(c_1388,plain,
value(out(c,h2(f)),n0),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_1381]) ).
tff(c_1463,plain,
! [P2_177] :
( value(P2_177,n0)
| ~ connection(out(c,h2(f)),P2_177) ),
inference(resolution,[status(thm)],[c_1388,c_2]) ).
tff(c_1471,plain,
( value(out(n1,and2(h2(f))),n0)
| ~ type(h2(f),halfadder) ),
inference(resolution,[status(thm)],[c_62,c_1463]) ).
tff(c_1481,plain,
value(out(n1,and2(h2(f))),n0),
inference(demodulation,[status(thm),theory(equality)],[c_618,c_1471]) ).
tff(c_1089,plain,
! [K_162] :
( value(out(n1,K_162),n1)
| ~ value(in(n2,K_162),n1)
| ~ value(in(n1,K_162),n1)
| ~ type(K_162,and)
| ~ mode(K_162,ok) ),
inference(cnfTransformation,[status(thm)],[f_111]) ).
tff(c_2401,plain,
! [V1_219,K_220] :
( equal_value(V1_219,n1)
| ~ value(out(n1,K_220),V1_219)
| ~ value(in(n2,K_220),n1)
| ~ value(in(n1,K_220),n1)
| ~ type(K_220,and)
| ~ mode(K_220,ok) ),
inference(resolution,[status(thm)],[c_1089,c_6]) ).
tff(c_2407,plain,
( equal_value(n0,n1)
| ~ value(in(n2,and2(h2(f))),n1)
| ~ value(in(n1,and2(h2(f))),n1)
| ~ type(and2(h2(f)),and)
| ~ mode(and2(h2(f)),ok) ),
inference(resolution,[status(thm)],[c_1481,c_2401]) ).
tff(c_2434,plain,
( equal_value(n0,n1)
| ~ value(in(n2,and2(h2(f))),n1)
| ~ type(and2(h2(f)),and) ),
inference(demodulation,[status(thm),theory(equality)],[c_2103,c_907,c_2407]) ).
tff(c_2435,plain,
( ~ value(in(n2,and2(h2(f))),n1)
| ~ type(and2(h2(f)),and) ),
inference(negUnitSimplification,[status(thm)],[c_8,c_2434]) ).
tff(c_2456,plain,
~ type(and2(h2(f)),and),
inference(splitLeft,[status(thm)],[c_2435]) ).
tff(c_2459,plain,
~ type(h2(f),halfadder),
inference(resolution,[status(thm)],[c_46,c_2456]) ).
tff(c_2463,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_618,c_2459]) ).
tff(c_2465,plain,
type(and2(h2(f)),and),
inference(splitRight,[status(thm)],[c_2435]) ).
tff(c_20,plain,
! [K_16] :
( value(in(n2,K_16),n0)
| value(in(n1,K_16),n0)
| ~ value(out(n1,K_16),n0)
| ~ type(K_16,and)
| ~ mode(K_16,ok) ),
inference(cnfTransformation,[status(thm)],[f_124]) ).
tff(c_1501,plain,
( value(in(n2,and2(h2(f))),n0)
| value(in(n1,and2(h2(f))),n0)
| ~ type(and2(h2(f)),and)
| ~ mode(and2(h2(f)),ok) ),
inference(resolution,[status(thm)],[c_1481,c_20]) ).
tff(c_3086,plain,
( value(in(n2,and2(h2(f))),n0)
| value(in(n1,and2(h2(f))),n0) ),
inference(demodulation,[status(thm),theory(equality)],[c_2103,c_2465,c_1501]) ).
tff(c_3087,plain,
value(in(n1,and2(h2(f))),n0),
inference(splitLeft,[status(thm)],[c_3086]) ).
tff(c_917,plain,
! [V1_8] :
( equal_value(V1_8,n1)
| ~ value(in(n1,and2(h2(f))),V1_8) ),
inference(resolution,[status(thm)],[c_907,c_6]) ).
tff(c_3096,plain,
equal_value(n0,n1),
inference(resolution,[status(thm)],[c_3087,c_917]) ).
tff(c_3114,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8,c_3096]) ).
tff(c_3115,plain,
value(in(n2,and2(h2(f))),n0),
inference(splitRight,[status(thm)],[c_3086]) ).
tff(c_3189,plain,
! [P1_253] :
( value(P1_253,n0)
| ~ connection(P1_253,in(n2,and2(h2(f)))) ),
inference(resolution,[status(thm)],[c_3115,c_4]) ).
tff(c_3193,plain,
( value(in(n2,h2(f)),n0)
| ~ type(h2(f),halfadder) ),
inference(resolution,[status(thm)],[c_58,c_3189]) ).
tff(c_3196,plain,
value(in(n2,h2(f)),n0),
inference(demodulation,[status(thm),theory(equality)],[c_618,c_3193]) ).
tff(c_3251,plain,
! [P1_255] :
( value(P1_255,n0)
| ~ connection(P1_255,in(n2,h2(f))) ),
inference(resolution,[status(thm)],[c_3196,c_4]) ).
tff(c_3255,plain,
( value(out(s,h1(f)),n0)
| ~ type(f,fulladder) ),
inference(resolution,[status(thm)],[c_76,c_3251]) ).
tff(c_3258,plain,
value(out(s,h1(f)),n0),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_3255]) ).
tff(c_3329,plain,
! [P2_259] :
( value(P2_259,n0)
| ~ connection(out(s,h1(f)),P2_259) ),
inference(resolution,[status(thm)],[c_3258,c_2]) ).
tff(c_3341,plain,
( value(out(n1,and1(h1(f))),n0)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_60,c_3329]) ).
tff(c_3348,plain,
value(out(n1,and1(h1(f))),n0),
inference(demodulation,[status(thm),theory(equality)],[c_548,c_3341]) ).
tff(c_1125,plain,
! [V1_8,K_162] :
( equal_value(V1_8,n1)
| ~ value(out(n1,K_162),V1_8)
| ~ value(in(n2,K_162),n1)
| ~ value(in(n1,K_162),n1)
| ~ type(K_162,and)
| ~ mode(K_162,ok) ),
inference(resolution,[status(thm)],[c_1089,c_6]) ).
tff(c_3351,plain,
( equal_value(n0,n1)
| ~ value(in(n2,and1(h1(f))),n1)
| ~ value(in(n1,and1(h1(f))),n1)
| ~ type(and1(h1(f)),and)
| ~ mode(and1(h1(f)),ok) ),
inference(resolution,[status(thm)],[c_3348,c_1125]) ).
tff(c_3381,plain,
( equal_value(n0,n1)
| ~ value(in(n2,and1(h1(f))),n1)
| ~ type(and1(h1(f)),and) ),
inference(demodulation,[status(thm),theory(equality)],[c_2584,c_2294,c_3351]) ).
tff(c_3382,plain,
( ~ value(in(n2,and1(h1(f))),n1)
| ~ type(and1(h1(f)),and) ),
inference(negUnitSimplification,[status(thm)],[c_8,c_3381]) ).
tff(c_3631,plain,
~ type(and1(h1(f)),and),
inference(splitLeft,[status(thm)],[c_3382]) ).
tff(c_3634,plain,
~ type(h1(f),halfadder),
inference(resolution,[status(thm)],[c_44,c_3631]) ).
tff(c_3638,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_548,c_3634]) ).
tff(c_3639,plain,
~ value(in(n2,and1(h1(f))),n1),
inference(splitRight,[status(thm)],[c_3382]) ).
tff(c_3649,plain,
( ~ value(in(n1,not1(h1(f))),n0)
| ~ type(not1(h1(f)),not)
| ~ mode(not1(h1(f)),ok)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_1825,c_3639]) ).
tff(c_3655,plain,
~ type(not1(h1(f)),not),
inference(demodulation,[status(thm),theory(equality)],[c_548,c_1995,c_1609,c_3649]) ).
tff(c_3753,plain,
~ type(h1(f),halfadder),
inference(resolution,[status(thm)],[c_48,c_3655]) ).
tff(c_3757,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_548,c_3753]) ).
tff(c_3759,plain,
mode(or1(f),abnormal),
inference(splitRight,[status(thm)],[c_108]) ).
tff(c_104,plain,
( ~ mode(not1(h2(f)),abnormal)
| ~ mode(or1(f),abnormal) ),
inference(cnfTransformation,[status(thm)],[f_435]) ).
tff(c_3841,plain,
~ mode(not1(h2(f)),abnormal),
inference(demodulation,[status(thm),theory(equality)],[c_3759,c_104]) ).
tff(c_3758,plain,
~ mode(and1(h2(f)),abnormal),
inference(splitRight,[status(thm)],[c_108]) ).
tff(c_4005,plain,
! [X_311] :
( connection(out(s,X_311),out(s,h2(X_311)))
| ~ type(X_311,fulladder) ),
inference(cnfTransformation,[status(thm)],[f_415]) ).
tff(c_3870,plain,
! [P2_288] :
( value(P2_288,n1)
| ~ connection(out(s,f),P2_288) ),
inference(resolution,[status(thm)],[c_100,c_3857]) ).
tff(c_4009,plain,
( value(out(s,h2(f)),n1)
| ~ type(f,fulladder) ),
inference(resolution,[status(thm)],[c_4005,c_3870]) ).
tff(c_4012,plain,
value(out(s,h2(f)),n1),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_4009]) ).
tff(c_4022,plain,
! [P2_312] :
( value(P2_312,n1)
| ~ connection(out(s,h2(f)),P2_312) ),
inference(resolution,[status(thm)],[c_4012,c_2]) ).
tff(c_4032,plain,
( value(out(n1,and1(h2(f))),n1)
| ~ type(h2(f),halfadder) ),
inference(resolution,[status(thm)],[c_60,c_4022]) ).
tff(c_4500,plain,
value(out(n1,and1(h2(f))),n1),
inference(demodulation,[status(thm),theory(equality)],[c_4261,c_4032]) ).
tff(c_24,plain,
! [K_18] :
( value(in(n2,K_18),n1)
| ~ value(out(n1,K_18),n1)
| ~ type(K_18,and)
| ~ mode(K_18,ok) ),
inference(cnfTransformation,[status(thm)],[f_146]) ).
tff(c_4517,plain,
( value(in(n2,and1(h2(f))),n1)
| ~ type(and1(h2(f)),and)
| ~ mode(and1(h2(f)),ok) ),
inference(resolution,[status(thm)],[c_4500,c_24]) ).
tff(c_4944,plain,
~ mode(and1(h2(f)),ok),
inference(splitLeft,[status(thm)],[c_4517]) ).
tff(c_4947,plain,
( mode(and1(h2(f)),abnormal)
| ~ type(h2(f),halfadder) ),
inference(resolution,[status(thm)],[c_3786,c_4944]) ).
tff(c_4950,plain,
mode(and1(h2(f)),abnormal),
inference(demodulation,[status(thm),theory(equality)],[c_4261,c_4947]) ).
tff(c_4952,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3758,c_4950]) ).
tff(c_4953,plain,
( ~ type(and1(h2(f)),and)
| value(in(n2,and1(h2(f))),n1) ),
inference(splitRight,[status(thm)],[c_4517]) ).
tff(c_4974,plain,
~ type(and1(h2(f)),and),
inference(splitLeft,[status(thm)],[c_4953]) ).
tff(c_4977,plain,
~ type(h2(f),halfadder),
inference(resolution,[status(thm)],[c_44,c_4974]) ).
tff(c_4981,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4261,c_4977]) ).
tff(c_4982,plain,
value(in(n2,and1(h2(f))),n1),
inference(splitRight,[status(thm)],[c_4953]) ).
tff(c_5055,plain,
! [P1_383] :
( value(P1_383,n1)
| ~ connection(P1_383,in(n2,and1(h2(f)))) ),
inference(resolution,[status(thm)],[c_4982,c_4]) ).
tff(c_5059,plain,
( value(out(n1,not1(h2(f))),n1)
| ~ type(h2(f),halfadder) ),
inference(resolution,[status(thm)],[c_68,c_5055]) ).
tff(c_5062,plain,
value(out(n1,not1(h2(f))),n1),
inference(demodulation,[status(thm),theory(equality)],[c_4261,c_5059]) ).
tff(c_42,plain,
! [K_28] :
( value(in(n1,K_28),n0)
| ~ value(out(n1,K_28),n1)
| ~ type(K_28,not)
| ~ mode(K_28,ok) ),
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_5084,plain,
( value(in(n1,not1(h2(f))),n0)
| ~ type(not1(h2(f)),not)
| ~ mode(not1(h2(f)),ok) ),
inference(resolution,[status(thm)],[c_5062,c_42]) ).
tff(c_6175,plain,
~ mode(not1(h2(f)),ok),
inference(splitLeft,[status(thm)],[c_5084]) ).
tff(c_6178,plain,
( mode(not1(h2(f)),abnormal)
| ~ type(h2(f),halfadder) ),
inference(resolution,[status(thm)],[c_3790,c_6175]) ).
tff(c_6181,plain,
mode(not1(h2(f)),abnormal),
inference(demodulation,[status(thm),theory(equality)],[c_4261,c_6178]) ).
tff(c_6183,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3841,c_6181]) ).
tff(c_6184,plain,
( ~ type(not1(h2(f)),not)
| value(in(n1,not1(h2(f))),n0) ),
inference(splitRight,[status(thm)],[c_5084]) ).
tff(c_6200,plain,
~ type(not1(h2(f)),not),
inference(splitLeft,[status(thm)],[c_6184]) ).
tff(c_6213,plain,
~ type(h2(f),halfadder),
inference(resolution,[status(thm)],[c_48,c_6200]) ).
tff(c_6217,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4261,c_6213]) ).
tff(c_6218,plain,
value(in(n1,not1(h2(f))),n0),
inference(splitRight,[status(thm)],[c_6184]) ).
tff(c_6268,plain,
! [P1_440] :
( value(P1_440,n0)
| ~ connection(P1_440,in(n1,not1(h2(f)))) ),
inference(resolution,[status(thm)],[c_6218,c_4]) ).
tff(c_6272,plain,
( value(out(n1,and2(h2(f))),n0)
| ~ type(h2(f),halfadder) ),
inference(resolution,[status(thm)],[c_66,c_6268]) ).
tff(c_6275,plain,
value(out(n1,and2(h2(f))),n0),
inference(demodulation,[status(thm),theory(equality)],[c_4261,c_6272]) ).
tff(c_4678,plain,
! [K_373] :
( value(out(n1,K_373),n1)
| ~ value(in(n2,K_373),n1)
| ~ value(in(n1,K_373),n1)
| ~ type(K_373,and)
| ~ mode(K_373,ok) ),
inference(cnfTransformation,[status(thm)],[f_111]) ).
tff(c_4716,plain,
! [V1_8,K_373] :
( equal_value(V1_8,n1)
| ~ value(out(n1,K_373),V1_8)
| ~ value(in(n2,K_373),n1)
| ~ value(in(n1,K_373),n1)
| ~ type(K_373,and)
| ~ mode(K_373,ok) ),
inference(resolution,[status(thm)],[c_4678,c_6]) ).
tff(c_6278,plain,
( equal_value(n0,n1)
| ~ value(in(n2,and2(h2(f))),n1)
| ~ value(in(n1,and2(h2(f))),n1)
| ~ type(and2(h2(f)),and)
| ~ mode(and2(h2(f)),ok) ),
inference(resolution,[status(thm)],[c_6275,c_4716]) ).
tff(c_6308,plain,
( equal_value(n0,n1)
| ~ value(in(n2,and2(h2(f))),n1)
| ~ type(and2(h2(f)),and) ),
inference(demodulation,[status(thm),theory(equality)],[c_5648,c_4331,c_6278]) ).
tff(c_6309,plain,
( ~ value(in(n2,and2(h2(f))),n1)
| ~ type(and2(h2(f)),and) ),
inference(negUnitSimplification,[status(thm)],[c_8,c_6308]) ).
tff(c_6562,plain,
~ type(and2(h2(f)),and),
inference(splitLeft,[status(thm)],[c_6309]) ).
tff(c_6565,plain,
~ type(h2(f),halfadder),
inference(resolution,[status(thm)],[c_46,c_6562]) ).
tff(c_6569,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4261,c_6565]) ).
tff(c_6571,plain,
type(and2(h2(f)),and),
inference(splitRight,[status(thm)],[c_6309]) ).
tff(c_6290,plain,
( value(in(n2,and2(h2(f))),n0)
| value(in(n1,and2(h2(f))),n0)
| ~ type(and2(h2(f)),and)
| ~ mode(and2(h2(f)),ok) ),
inference(resolution,[status(thm)],[c_6275,c_20]) ).
tff(c_6322,plain,
( value(in(n2,and2(h2(f))),n0)
| value(in(n1,and2(h2(f))),n0)
| ~ type(and2(h2(f)),and) ),
inference(demodulation,[status(thm),theory(equality)],[c_5648,c_6290]) ).
tff(c_6745,plain,
( value(in(n2,and2(h2(f))),n0)
| value(in(n1,and2(h2(f))),n0) ),
inference(demodulation,[status(thm),theory(equality)],[c_6571,c_6322]) ).
tff(c_6746,plain,
value(in(n1,and2(h2(f))),n0),
inference(splitLeft,[status(thm)],[c_6745]) ).
tff(c_4340,plain,
! [V1_8] :
( equal_value(V1_8,n1)
| ~ value(in(n1,and2(h2(f))),V1_8) ),
inference(resolution,[status(thm)],[c_4331,c_6]) ).
tff(c_6753,plain,
equal_value(n0,n1),
inference(resolution,[status(thm)],[c_6746,c_4340]) ).
tff(c_6768,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8,c_6753]) ).
tff(c_6769,plain,
value(in(n2,and2(h2(f))),n0),
inference(splitRight,[status(thm)],[c_6745]) ).
tff(c_6807,plain,
! [P1_458] :
( value(P1_458,n0)
| ~ connection(P1_458,in(n2,and2(h2(f)))) ),
inference(resolution,[status(thm)],[c_6769,c_4]) ).
tff(c_6811,plain,
( value(in(n2,h2(f)),n0)
| ~ type(h2(f),halfadder) ),
inference(resolution,[status(thm)],[c_58,c_6807]) ).
tff(c_6814,plain,
value(in(n2,h2(f)),n0),
inference(demodulation,[status(thm),theory(equality)],[c_4261,c_6811]) ).
tff(c_6884,plain,
! [P1_461] :
( value(P1_461,n0)
| ~ connection(P1_461,in(n2,h2(f))) ),
inference(resolution,[status(thm)],[c_6814,c_4]) ).
tff(c_6888,plain,
( value(out(s,h1(f)),n0)
| ~ type(f,fulladder) ),
inference(resolution,[status(thm)],[c_76,c_6884]) ).
tff(c_6891,plain,
value(out(s,h1(f)),n0),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_6888]) ).
tff(c_6929,plain,
! [P2_463] :
( value(P2_463,n0)
| ~ connection(out(s,h1(f)),P2_463) ),
inference(resolution,[status(thm)],[c_6891,c_2]) ).
tff(c_6941,plain,
( value(out(n1,and1(h1(f))),n0)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_60,c_6929]) ).
tff(c_6948,plain,
value(out(n1,and1(h1(f))),n0),
inference(demodulation,[status(thm),theory(equality)],[c_4191,c_6941]) ).
tff(c_6951,plain,
( equal_value(n0,n1)
| ~ value(in(n2,and1(h1(f))),n1)
| ~ value(in(n1,and1(h1(f))),n1)
| ~ type(and1(h1(f)),and)
| ~ mode(and1(h1(f)),ok) ),
inference(resolution,[status(thm)],[c_6948,c_4716]) ).
tff(c_6981,plain,
( equal_value(n0,n1)
| ~ value(in(n2,and1(h1(f))),n1)
| ~ type(and1(h1(f)),and) ),
inference(demodulation,[status(thm),theory(equality)],[c_6612,c_5750,c_6951]) ).
tff(c_6982,plain,
( ~ value(in(n2,and1(h1(f))),n1)
| ~ type(and1(h1(f)),and) ),
inference(negUnitSimplification,[status(thm)],[c_8,c_6981]) ).
tff(c_7146,plain,
~ type(and1(h1(f)),and),
inference(splitLeft,[status(thm)],[c_6982]) ).
tff(c_7149,plain,
~ type(h1(f),halfadder),
inference(resolution,[status(thm)],[c_44,c_7146]) ).
tff(c_7153,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4191,c_7149]) ).
tff(c_7155,plain,
type(and1(h1(f)),and),
inference(splitRight,[status(thm)],[c_6982]) ).
tff(c_6963,plain,
( value(in(n2,and1(h1(f))),n0)
| value(in(n1,and1(h1(f))),n0)
| ~ type(and1(h1(f)),and)
| ~ mode(and1(h1(f)),ok) ),
inference(resolution,[status(thm)],[c_6948,c_20]) ).
tff(c_6995,plain,
( value(in(n2,and1(h1(f))),n0)
| value(in(n1,and1(h1(f))),n0)
| ~ type(and1(h1(f)),and) ),
inference(demodulation,[status(thm),theory(equality)],[c_6612,c_6963]) ).
tff(c_7254,plain,
( value(in(n2,and1(h1(f))),n0)
| value(in(n1,and1(h1(f))),n0) ),
inference(demodulation,[status(thm),theory(equality)],[c_7155,c_6995]) ).
tff(c_7255,plain,
value(in(n1,and1(h1(f))),n0),
inference(splitLeft,[status(thm)],[c_7254]) ).
tff(c_5780,plain,
! [V1_8] :
( equal_value(V1_8,n1)
| ~ value(in(n1,and1(h1(f))),V1_8) ),
inference(resolution,[status(thm)],[c_5750,c_6]) ).
tff(c_7258,plain,
equal_value(n0,n1),
inference(resolution,[status(thm)],[c_7255,c_5780]) ).
tff(c_7273,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8,c_7258]) ).
tff(c_7274,plain,
value(in(n2,and1(h1(f))),n0),
inference(splitRight,[status(thm)],[c_7254]) ).
tff(c_7319,plain,
! [P1_476] :
( value(P1_476,n0)
| ~ connection(P1_476,in(n2,and1(h1(f)))) ),
inference(resolution,[status(thm)],[c_7274,c_4]) ).
tff(c_7323,plain,
( value(out(n1,not1(h1(f))),n0)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_68,c_7319]) ).
tff(c_7326,plain,
value(out(n1,not1(h1(f))),n0),
inference(demodulation,[status(thm),theory(equality)],[c_4191,c_7323]) ).
tff(c_4578,plain,
! [V1_8,K_365] :
( equal_value(V1_8,n1)
| ~ value(out(n1,K_365),V1_8)
| ~ value(in(n1,K_365),n0)
| ~ type(K_365,not)
| ~ mode(K_365,ok) ),
inference(resolution,[status(thm)],[c_4544,c_6]) ).
tff(c_7335,plain,
( equal_value(n0,n1)
| ~ value(in(n1,not1(h1(f))),n0)
| ~ type(not1(h1(f)),not)
| ~ mode(not1(h1(f)),ok) ),
inference(resolution,[status(thm)],[c_7326,c_4578]) ).
tff(c_7366,plain,
( equal_value(n0,n1)
| ~ type(not1(h1(f)),not) ),
inference(demodulation,[status(thm),theory(equality)],[c_5570,c_5205,c_7335]) ).
tff(c_7367,plain,
~ type(not1(h1(f)),not),
inference(negUnitSimplification,[status(thm)],[c_8,c_7366]) ).
tff(c_7407,plain,
~ type(h1(f),halfadder),
inference(resolution,[status(thm)],[c_48,c_7367]) ).
tff(c_7411,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4191,c_7407]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.24 % Problem : HWV006-1 : TPTP v8.1.2. Released v2.1.0.
% 0.13/0.25 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.46 % Computer : n028.cluster.edu
% 0.14/0.46 % Model : x86_64 x86_64
% 0.14/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.46 % Memory : 8042.1875MB
% 0.14/0.46 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.46 % CPULimit : 300
% 0.14/0.46 % WCLimit : 300
% 0.14/0.46 % DateTime : Fri Aug 4 00:01:55 EDT 2023
% 0.14/0.46 % CPUTime :
% 10.15/3.70 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.15/3.73
% 10.15/3.73 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.46/3.81
% 10.46/3.81 Inference rules
% 10.46/3.81 ----------------------
% 10.46/3.81 #Ref : 0
% 10.46/3.81 #Sup : 1354
% 10.46/3.81 #Fact : 0
% 10.46/3.81 #Define : 0
% 10.46/3.81 #Split : 127
% 10.46/3.81 #Chain : 0
% 10.46/3.81 #Close : 0
% 10.46/3.81
% 10.46/3.81 Ordering : KBO
% 10.46/3.81
% 10.46/3.81 Simplification rules
% 10.46/3.81 ----------------------
% 10.46/3.81 #Subsume : 468
% 10.46/3.81 #Demod : 1015
% 10.46/3.81 #Tautology : 242
% 10.46/3.81 #SimpNegUnit : 181
% 10.46/3.81 #BackRed : 0
% 10.46/3.81
% 10.46/3.81 #Partial instantiations: 0
% 10.46/3.81 #Strategies tried : 1
% 10.46/3.81
% 10.46/3.81 Timing (in seconds)
% 10.46/3.81 ----------------------
% 10.46/3.81 Preprocessing : 0.57
% 10.46/3.81 Parsing : 0.31
% 10.46/3.81 CNF conversion : 0.04
% 10.46/3.81 Main loop : 1.91
% 10.46/3.81 Inferencing : 0.69
% 10.46/3.81 Reduction : 0.67
% 10.46/3.81 Demodulation : 0.45
% 10.46/3.81 BG Simplification : 0.04
% 10.46/3.81 Subsumption : 0.38
% 10.46/3.81 Abstraction : 0.04
% 10.46/3.81 MUC search : 0.00
% 10.46/3.81 Cooper : 0.00
% 10.46/3.81 Total : 2.61
% 10.46/3.81 Index Insertion : 0.00
% 10.46/3.81 Index Deletion : 0.00
% 10.46/3.82 Index Matching : 0.00
% 10.46/3.82 BG Taut test : 0.00
%------------------------------------------------------------------------------