%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : HWV007-1 : TPTP v9.0.0. 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 : n014.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 Apr 9 06:46:43 PM UTC 2025
% Result : Unsatisfiable 8.85s 3.11s
% Output : CNFRefutation 9.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 50
% Syntax : Number of formulae : 300 ( 120 unt; 0 typ; 0 def)
% Number of atoms : 586 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 609 ( 323 ~; 286 |; 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 : 0 ( 0 >; 0 *; 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 : 137 ( 137 !; 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_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),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_285,axiom,
! [X] :
( ~ type(X,halfadder)
| type(and2(X),and) ),
file(unknown,unknown) ).
tff(f_69,axiom,
~ equal_value(n0,n1),
file(unknown,unknown) ).
tff(f_432,axiom,
~ mode(and2(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_316,axiom,
! [X] :
( ~ type(X,halfadder)
| connection(in(n2,X),in(n2,and2(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_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_336,axiom,
! [X] :
( ~ type(X,halfadder)
| connection(out(n1,and2(X)),in(n1,not1(X))) ),
file(unknown,unknown) ).
tff(f_290,axiom,
! [X] :
( ~ type(X,halfadder)
| type(not1(X),not) ),
file(unknown,unknown) ).
tff(f_71,axiom,
~ equal_value(n1,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_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_437,axiom,
( ~ mode(or1(f),abnormal)
| ~ mode(and1(h1(f)),abnormal) ),
file(unknown,unknown) ).
tff(f_379,axiom,
! [X] :
( ~ type(X,fulladder)
| type(or1(X),or) ),
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_196,axiom,
! [K] :
( ~ mode(K,ok)
| ~ type(K,or)
| ~ value(out(n1,K),n0)
| value(in(n1,K),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_67,axiom,
! [P,V1,V2] :
( ~ value(P,V1)
| ~ value(P,V2)
| equal_value(V1,V2) ),
file(unknown,unknown) ).
tff(f_442,axiom,
( ~ mode(or1(f),abnormal)
| ~ mode(not1(h1(f)),abnormal) ),
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_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),n0),
file(unknown,unknown) ).
tff(f_306,axiom,
! [X] :
( ~ type(X,halfadder)
| connection(in(n2,X),in(n2,or1(X))) ),
file(unknown,unknown) ).
tff(f_295,axiom,
! [X] :
( ~ type(X,halfadder)
| type(or1(X),or) ),
file(unknown,unknown) ).
tff(f_452,axiom,
( ~ mode(or1(f),abnormal)
| ~ mode(or1(h2(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_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_172,axiom,
! [K] :
( ~ mode(K,ok)
| ~ type(K,or)
| ~ value(in(n1,K),n0)
| ~ value(in(n2,K),n0)
| value(out(n1,K),n0) ),
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_447,axiom,
( ~ mode(or1(f),abnormal)
| ~ mode(and1(h2(f)),abnormal) ),
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_146,axiom,
! [K] :
( ~ mode(K,ok)
| ~ type(K,and)
| ~ value(out(n1,K),n1)
| value(in(n2,K),n1) ),
file(unknown,unknown) ).
tff(f_185,axiom,
! [K] :
( ~ mode(K,ok)
| ~ type(K,or)
| ~ value(out(n1,K),n1)
| value(in(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_2061,plain,
! [X_237] :
( connection(in(n1,X_237),in(n1,and2(X_237)))
| ~ type(X_237,halfadder) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_1954,plain,
! [X_224] :
( connection(in(n2,X_224),in(n1,h1(X_224)))
| ~ type(X_224,fulladder) ),
inference(cnfTransformation,[status(thm)],[f_405]) ).
tff(c_96,plain,
value(in(n2,f),n1),
inference(cnfTransformation,[status(thm)],[f_426]) ).
tff(c_1801,plain,
! [P2_196,V_197,P1_198] :
( value(P2_196,V_197)
| ~ value(P1_198,V_197)
| ~ connection(P1_198,P2_196) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_1816,plain,
! [P2_196] :
( value(P2_196,n1)
| ~ connection(in(n2,f),P2_196) ),
inference(resolution,[status(thm)],[c_96,c_1801]) ).
tff(c_1958,plain,
( value(in(n1,h1(f)),n1)
| ~ type(f,fulladder) ),
inference(resolution,[status(thm)],[c_1954,c_1816]) ).
tff(c_1961,plain,
value(in(n1,h1(f)),n1),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_1958]) ).
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_1970,plain,
! [P2_2] :
( value(P2_2,n1)
| ~ connection(in(n1,h1(f)),P2_2) ),
inference(resolution,[status(thm)],[c_1961,c_2]) ).
tff(c_2070,plain,
( value(in(n1,and2(h1(f))),n1)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_2061,c_1970]) ).
tff(c_2286,plain,
~ type(h1(f),halfadder),
inference(splitLeft,[status(thm)],[c_2070]) ).
tff(c_2289,plain,
~ type(f,fulladder),
inference(resolution,[status(thm)],[c_70,c_2286]) ).
tff(c_2293,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_92,c_2289]) ).
tff(c_2295,plain,
type(h1(f),halfadder),
inference(splitRight,[status(thm)],[c_2070]) ).
tff(c_46,plain,
! [X_30] :
( type(and2(X_30),and)
| ~ type(X_30,halfadder) ),
inference(cnfTransformation,[status(thm)],[f_285]) ).
tff(c_8,plain,
~ equal_value(n0,n1),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_104,plain,
~ mode(and2(h1(f)),abnormal),
inference(cnfTransformation,[status(thm)],[f_432]) ).
tff(c_1820,plain,
! [K_202,Any_203] :
( mode(K_202,abnormal)
| mode(K_202,ok)
| ~ type(K_202,Any_203) ),
inference(cnfTransformation,[status(thm)],[f_85]) ).
tff(c_1849,plain,
! [X_30] :
( mode(and2(X_30),abnormal)
| mode(and2(X_30),ok)
| ~ type(X_30,halfadder) ),
inference(resolution,[status(thm)],[c_46,c_1820]) ).
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_2120,plain,
! [X_243] :
( connection(in(c,X_243),in(n2,h1(X_243)))
| ~ type(X_243,fulladder) ),
inference(cnfTransformation,[status(thm)],[f_410]) ).
tff(c_98,plain,
value(in(c,f),n1),
inference(cnfTransformation,[status(thm)],[f_427]) ).
tff(c_1815,plain,
! [P2_196] :
( value(P2_196,n1)
| ~ connection(in(c,f),P2_196) ),
inference(resolution,[status(thm)],[c_98,c_1801]) ).
tff(c_2124,plain,
( value(in(n2,h1(f)),n1)
| ~ type(f,fulladder) ),
inference(resolution,[status(thm)],[c_2120,c_1815]) ).
tff(c_2127,plain,
value(in(n2,h1(f)),n1),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_2124]) ).
tff(c_2167,plain,
! [P2_247] :
( value(P2_247,n1)
| ~ connection(in(n2,h1(f)),P2_247) ),
inference(resolution,[status(thm)],[c_2127,c_2]) ).
tff(c_2181,plain,
( value(in(n2,and2(h1(f))),n1)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_58,c_2167]) ).
tff(c_2540,plain,
value(in(n2,and2(h1(f))),n1),
inference(demodulation,[status(thm),theory(equality)],[c_2295,c_2181]) ).
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_2549,plain,
( value(out(n1,and2(h1(f))),n1)
| ~ type(and2(h1(f)),or)
| ~ mode(and2(h1(f)),ok) ),
inference(resolution,[status(thm)],[c_2540,c_26]) ).
tff(c_3175,plain,
~ mode(and2(h1(f)),ok),
inference(splitLeft,[status(thm)],[c_2549]) ).
tff(c_3178,plain,
( mode(and2(h1(f)),abnormal)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_1849,c_3175]) ).
tff(c_3181,plain,
mode(and2(h1(f)),abnormal),
inference(demodulation,[status(thm),theory(equality)],[c_2295,c_3178]) ).
tff(c_3183,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_104,c_3181]) ).
tff(c_3185,plain,
mode(and2(h1(f)),ok),
inference(splitRight,[status(thm)],[c_2549]) ).
tff(c_2294,plain,
value(in(n1,and2(h1(f))),n1),
inference(splitRight,[status(thm)],[c_2070]) ).
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_48,plain,
! [X_31] :
( type(not1(X_31),not)
| ~ type(X_31,halfadder) ),
inference(cnfTransformation,[status(thm)],[f_290]) ).
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_435,plain,
! [X_108] :
( connection(in(n2,X_108),in(n1,h1(X_108)))
| ~ type(X_108,fulladder) ),
inference(cnfTransformation,[status(thm)],[f_405]) ).
tff(c_122,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,n1)
| ~ connection(in(n2,f),P2_61) ),
inference(resolution,[status(thm)],[c_96,c_122]) ).
tff(c_443,plain,
( value(in(n1,h1(f)),n1)
| ~ type(f,fulladder) ),
inference(resolution,[status(thm)],[c_435,c_137]) ).
tff(c_447,plain,
value(in(n1,h1(f)),n1),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_443]) ).
tff(c_476,plain,
! [P2_111] :
( value(P2_111,n1)
| ~ connection(in(n1,h1(f)),P2_111) ),
inference(resolution,[status(thm)],[c_447,c_2]) ).
tff(c_489,plain,
( value(in(n1,and2(h1(f))),n1)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_56,c_476]) ).
tff(c_624,plain,
~ type(h1(f),halfadder),
inference(splitLeft,[status(thm)],[c_489]) ).
tff(c_633,plain,
~ type(f,fulladder),
inference(resolution,[status(thm)],[c_70,c_624]) ).
tff(c_637,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_92,c_633]) ).
tff(c_639,plain,
type(h1(f),halfadder),
inference(splitRight,[status(thm)],[c_489]) ).
tff(c_170,plain,
! [K_74,Any_75] :
( mode(K_74,abnormal)
| mode(K_74,ok)
| ~ type(K_74,Any_75) ),
inference(cnfTransformation,[status(thm)],[f_85]) ).
tff(c_199,plain,
! [X_30] :
( mode(and2(X_30),abnormal)
| mode(and2(X_30),ok)
| ~ type(X_30,halfadder) ),
inference(resolution,[status(thm)],[c_46,c_170]) ).
tff(c_10,plain,
~ equal_value(n1,n0),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_638,plain,
value(in(n1,and2(h1(f))),n1),
inference(splitRight,[status(thm)],[c_489]) ).
tff(c_376,plain,
! [X_102] :
( connection(in(c,X_102),in(n2,h1(X_102)))
| ~ type(X_102,fulladder) ),
inference(cnfTransformation,[status(thm)],[f_410]) ).
tff(c_136,plain,
! [P2_61] :
( value(P2_61,n1)
| ~ connection(in(c,f),P2_61) ),
inference(resolution,[status(thm)],[c_98,c_122]) ).
tff(c_380,plain,
( value(in(n2,h1(f)),n1)
| ~ type(f,fulladder) ),
inference(resolution,[status(thm)],[c_376,c_136]) ).
tff(c_383,plain,
value(in(n2,h1(f)),n1),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_380]) ).
tff(c_413,plain,
! [P2_106] :
( value(P2_106,n1)
| ~ connection(in(n2,h1(f)),P2_106) ),
inference(resolution,[status(thm)],[c_383,c_2]) ).
tff(c_423,plain,
( value(in(n2,and2(h1(f))),n1)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_58,c_413]) ).
tff(c_939,plain,
value(in(n2,and2(h1(f))),n1),
inference(demodulation,[status(thm),theory(equality)],[c_639,c_423]) ).
tff(c_18,plain,
! [K_15] :
( value(out(n1,K_15),n1)
| ~ value(in(n2,K_15),n1)
| ~ value(in(n1,K_15),n1)
| ~ type(K_15,and)
| ~ mode(K_15,ok) ),
inference(cnfTransformation,[status(thm)],[f_111]) ).
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_106,plain,
( ~ mode(and1(h1(f)),abnormal)
| ~ mode(or1(f),abnormal) ),
inference(cnfTransformation,[status(thm)],[f_437]) ).
tff(c_121,plain,
~ mode(or1(f),abnormal),
inference(splitLeft,[status(thm)],[c_106]) ).
tff(c_74,plain,
! [X_44] :
( type(or1(X_44),or)
| ~ type(X_44,fulladder) ),
inference(cnfTransformation,[status(thm)],[f_379]) ).
tff(c_197,plain,
! [X_44] :
( mode(or1(X_44),abnormal)
| mode(or1(X_44),ok)
| ~ type(X_44,fulladder) ),
inference(resolution,[status(thm)],[c_74,c_170]) ).
tff(c_259,plain,
! [X_89] :
( connection(out(c,X_89),out(n1,or1(X_89)))
| ~ type(X_89,fulladder) ),
inference(cnfTransformation,[status(thm)],[f_420]) ).
tff(c_102,plain,
value(out(c,f),n0),
inference(cnfTransformation,[status(thm)],[f_429]) ).
tff(c_134,plain,
! [P2_61] :
( value(P2_61,n0)
| ~ connection(out(c,f),P2_61) ),
inference(resolution,[status(thm)],[c_102,c_122]) ).
tff(c_263,plain,
( value(out(n1,or1(f)),n0)
| ~ type(f,fulladder) ),
inference(resolution,[status(thm)],[c_259,c_134]) ).
tff(c_266,plain,
value(out(n1,or1(f)),n0),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_263]) ).
tff(c_688,plain,
! [K_136] :
( value(in(n1,K_136),n0)
| ~ value(out(n1,K_136),n0)
| ~ type(K_136,or)
| ~ mode(K_136,ok) ),
inference(cnfTransformation,[status(thm)],[f_196]) ).
tff(c_692,plain,
( value(in(n1,or1(f)),n0)
| ~ type(or1(f),or)
| ~ mode(or1(f),ok) ),
inference(resolution,[status(thm)],[c_266,c_688]) ).
tff(c_1132,plain,
~ mode(or1(f),ok),
inference(splitLeft,[status(thm)],[c_692]) ).
tff(c_1135,plain,
( mode(or1(f),abnormal)
| ~ type(f,fulladder) ),
inference(resolution,[status(thm)],[c_197,c_1132]) ).
tff(c_1141,plain,
mode(or1(f),abnormal),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_1135]) ).
tff(c_1143,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_121,c_1141]) ).
tff(c_1145,plain,
mode(or1(f),ok),
inference(splitRight,[status(thm)],[c_692]) ).
tff(c_1144,plain,
( ~ type(or1(f),or)
| value(in(n1,or1(f)),n0) ),
inference(splitRight,[status(thm)],[c_692]) ).
tff(c_1150,plain,
~ type(or1(f),or),
inference(splitLeft,[status(thm)],[c_1144]) ).
tff(c_1153,plain,
~ type(f,fulladder),
inference(resolution,[status(thm)],[c_74,c_1150]) ).
tff(c_1160,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_92,c_1153]) ).
tff(c_1162,plain,
type(or1(f),or),
inference(splitRight,[status(thm)],[c_1144]) ).
tff(c_873,plain,
! [K_148] :
( value(in(n2,K_148),n0)
| ~ value(out(n1,K_148),n0)
| ~ type(K_148,or)
| ~ mode(K_148,ok) ),
inference(cnfTransformation,[status(thm)],[f_207]) ).
tff(c_881,plain,
( value(in(n2,or1(f)),n0)
| ~ type(or1(f),or)
| ~ mode(or1(f),ok) ),
inference(resolution,[status(thm)],[c_266,c_873]) ).
tff(c_1562,plain,
value(in(n2,or1(f)),n0),
inference(demodulation,[status(thm),theory(equality)],[c_1145,c_1162,c_881]) ).
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_1596,plain,
! [P1_185] :
( value(P1_185,n0)
| ~ connection(P1_185,in(n2,or1(f))) ),
inference(resolution,[status(thm)],[c_1562,c_4]) ).
tff(c_1600,plain,
( value(out(c,h1(f)),n0)
| ~ type(f,fulladder) ),
inference(resolution,[status(thm)],[c_78,c_1596]) ).
tff(c_1607,plain,
value(out(c,h1(f)),n0),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_1600]) ).
tff(c_1640,plain,
! [P2_188] :
( value(P2_188,n0)
| ~ connection(out(c,h1(f)),P2_188) ),
inference(resolution,[status(thm)],[c_1607,c_2]) ).
tff(c_1648,plain,
( value(out(n1,and2(h1(f))),n0)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_62,c_1640]) ).
tff(c_1658,plain,
value(out(n1,and2(h1(f))),n0),
inference(demodulation,[status(thm),theory(equality)],[c_639,c_1648]) ).
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_1723,plain,
! [V1_194] :
( equal_value(V1_194,n0)
| ~ value(out(n1,and2(h1(f))),V1_194) ),
inference(resolution,[status(thm)],[c_1658,c_6]) ).
tff(c_1730,plain,
( equal_value(n1,n0)
| ~ value(in(n2,and2(h1(f))),n1)
| ~ value(in(n1,and2(h1(f))),n1)
| ~ type(and2(h1(f)),and)
| ~ mode(and2(h1(f)),ok) ),
inference(resolution,[status(thm)],[c_18,c_1723]) ).
tff(c_1747,plain,
( equal_value(n1,n0)
| ~ type(and2(h1(f)),and)
| ~ mode(and2(h1(f)),ok) ),
inference(demodulation,[status(thm),theory(equality)],[c_638,c_939,c_1730]) ).
tff(c_1748,plain,
( ~ type(and2(h1(f)),and)
| ~ mode(and2(h1(f)),ok) ),
inference(negUnitSimplification,[status(thm)],[c_10,c_1747]) ).
tff(c_1777,plain,
~ mode(and2(h1(f)),ok),
inference(splitLeft,[status(thm)],[c_1748]) ).
tff(c_1780,plain,
( mode(and2(h1(f)),abnormal)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_199,c_1777]) ).
tff(c_1783,plain,
mode(and2(h1(f)),abnormal),
inference(demodulation,[status(thm),theory(equality)],[c_639,c_1780]) ).
tff(c_1785,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_104,c_1783]) ).
tff(c_1786,plain,
~ type(and2(h1(f)),and),
inference(splitRight,[status(thm)],[c_1748]) ).
tff(c_1794,plain,
~ type(h1(f),halfadder),
inference(resolution,[status(thm)],[c_46,c_1786]) ).
tff(c_1798,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_639,c_1794]) ).
tff(c_1800,plain,
mode(or1(f),abnormal),
inference(splitRight,[status(thm)],[c_106]) ).
tff(c_108,plain,
( ~ mode(not1(h1(f)),abnormal)
| ~ mode(or1(f),abnormal) ),
inference(cnfTransformation,[status(thm)],[f_442]) ).
tff(c_1882,plain,
~ mode(not1(h1(f)),abnormal),
inference(demodulation,[status(thm),theory(equality)],[c_1800,c_108]) ).
tff(c_1850,plain,
! [X_31] :
( mode(not1(X_31),abnormal)
| mode(not1(X_31),ok)
| ~ type(X_31,halfadder) ),
inference(resolution,[status(thm)],[c_48,c_1820]) ).
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_1799,plain,
~ mode(and1(h1(f)),abnormal),
inference(splitRight,[status(thm)],[c_106]) ).
tff(c_1848,plain,
! [X_29] :
( mode(and1(X_29),abnormal)
| mode(and1(X_29),ok)
| ~ type(X_29,halfadder) ),
inference(resolution,[status(thm)],[c_44,c_1820]) ).
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_2084,plain,
! [X_240] :
( connection(in(n1,X_240),in(n1,h2(X_240)))
| ~ type(X_240,fulladder) ),
inference(cnfTransformation,[status(thm)],[f_400]) ).
tff(c_94,plain,
value(in(n1,f),n0),
inference(cnfTransformation,[status(thm)],[f_425]) ).
tff(c_1812,plain,
! [P2_196] :
( value(P2_196,n0)
| ~ connection(in(n1,f),P2_196) ),
inference(resolution,[status(thm)],[c_94,c_1801]) ).
tff(c_2092,plain,
( value(in(n1,h2(f)),n0)
| ~ type(f,fulladder) ),
inference(resolution,[status(thm)],[c_2084,c_1812]) ).
tff(c_2096,plain,
value(in(n1,h2(f)),n0),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_2092]) ).
tff(c_2137,plain,
! [P2_244] :
( value(P2_244,n0)
| ~ connection(in(n1,h2(f)),P2_244) ),
inference(resolution,[status(thm)],[c_2096,c_2]) ).
tff(c_2151,plain,
( value(in(n1,and2(h2(f))),n0)
| ~ type(h2(f),halfadder) ),
inference(resolution,[status(thm)],[c_56,c_2137]) ).
tff(c_2225,plain,
~ type(h2(f),halfadder),
inference(splitLeft,[status(thm)],[c_2151]) ).
tff(c_2229,plain,
~ type(f,fulladder),
inference(resolution,[status(thm)],[c_72,c_2225]) ).
tff(c_2233,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_92,c_2229]) ).
tff(c_2235,plain,
type(h2(f),halfadder),
inference(splitRight,[status(thm)],[c_2151]) ).
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_50,plain,
! [X_32] :
( type(or1(X_32),or)
| ~ type(X_32,halfadder) ),
inference(cnfTransformation,[status(thm)],[f_295]) ).
tff(c_112,plain,
( ~ mode(or1(h2(f)),abnormal)
| ~ mode(or1(f),abnormal) ),
inference(cnfTransformation,[status(thm)],[f_452]) ).
tff(c_1863,plain,
~ mode(or1(h2(f)),abnormal),
inference(demodulation,[status(thm),theory(equality)],[c_1800,c_112]) ).
tff(c_1851,plain,
! [X_32] :
( mode(or1(X_32),abnormal)
| mode(or1(X_32),ok)
| ~ type(X_32,halfadder) ),
inference(resolution,[status(thm)],[c_50,c_1820]) ).
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_2152,plain,
( value(in(n1,or1(h2(f))),n0)
| ~ type(h2(f),halfadder) ),
inference(resolution,[status(thm)],[c_52,c_2137]) ).
tff(c_2589,plain,
value(in(n1,or1(h2(f))),n0),
inference(demodulation,[status(thm),theory(equality)],[c_2235,c_2152]) ).
tff(c_2673,plain,
! [K_294] :
( value(out(n1,K_294),n1)
| ~ value(in(n1,K_294),n0)
| ~ type(K_294,not)
| ~ mode(K_294,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_2811,plain,
! [K_299] :
( value(in(n1,K_299),n1)
| ~ type(K_299,and)
| ~ value(in(n1,K_299),n0)
| ~ type(K_299,not)
| ~ mode(K_299,ok) ),
inference(resolution,[status(thm)],[c_2673,c_22]) ).
tff(c_2599,plain,
! [V1_8] :
( equal_value(V1_8,n0)
| ~ value(in(n1,or1(h2(f))),V1_8) ),
inference(resolution,[status(thm)],[c_2589,c_6]) ).
tff(c_2815,plain,
( equal_value(n1,n0)
| ~ type(or1(h2(f)),and)
| ~ value(in(n1,or1(h2(f))),n0)
| ~ type(or1(h2(f)),not)
| ~ mode(or1(h2(f)),ok) ),
inference(resolution,[status(thm)],[c_2811,c_2599]) ).
tff(c_2850,plain,
( equal_value(n1,n0)
| ~ type(or1(h2(f)),and)
| ~ type(or1(h2(f)),not)
| ~ mode(or1(h2(f)),ok) ),
inference(demodulation,[status(thm),theory(equality)],[c_2589,c_2815]) ).
tff(c_2851,plain,
( ~ type(or1(h2(f)),and)
| ~ type(or1(h2(f)),not)
| ~ mode(or1(h2(f)),ok) ),
inference(negUnitSimplification,[status(thm)],[c_10,c_2850]) ).
tff(c_2894,plain,
~ mode(or1(h2(f)),ok),
inference(splitLeft,[status(thm)],[c_2851]) ).
tff(c_2931,plain,
( mode(or1(h2(f)),abnormal)
| ~ type(h2(f),halfadder) ),
inference(resolution,[status(thm)],[c_1851,c_2894]) ).
tff(c_2937,plain,
mode(or1(h2(f)),abnormal),
inference(demodulation,[status(thm),theory(equality)],[c_2235,c_2931]) ).
tff(c_2939,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1863,c_2937]) ).
tff(c_2941,plain,
mode(or1(h2(f)),ok),
inference(splitRight,[status(thm)],[c_2851]) ).
tff(c_28,plain,
! [K_21] :
( value(out(n1,K_21),n0)
| ~ value(in(n2,K_21),n0)
| ~ value(in(n1,K_21),n0)
| ~ type(K_21,or)
| ~ mode(K_21,ok) ),
inference(cnfTransformation,[status(thm)],[f_172]) ).
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_110,plain,
( ~ mode(and1(h2(f)),abnormal)
| ~ mode(or1(f),abnormal) ),
inference(cnfTransformation,[status(thm)],[f_447]) ).
tff(c_1861,plain,
~ mode(and1(h2(f)),abnormal),
inference(demodulation,[status(thm),theory(equality)],[c_1800,c_110]) ).
tff(c_1972,plain,
! [X_225] :
( connection(out(s,X_225),out(s,h2(X_225)))
| ~ type(X_225,fulladder) ),
inference(cnfTransformation,[status(thm)],[f_415]) ).
tff(c_100,plain,
value(out(s,f),n1),
inference(cnfTransformation,[status(thm)],[f_428]) ).
tff(c_1814,plain,
! [P2_196] :
( value(P2_196,n1)
| ~ connection(out(s,f),P2_196) ),
inference(resolution,[status(thm)],[c_100,c_1801]) ).
tff(c_1976,plain,
( value(out(s,h2(f)),n1)
| ~ type(f,fulladder) ),
inference(resolution,[status(thm)],[c_1972,c_1814]) ).
tff(c_1979,plain,
value(out(s,h2(f)),n1),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_1976]) ).
tff(c_1990,plain,
! [P2_227] :
( value(P2_227,n1)
| ~ connection(out(s,h2(f)),P2_227) ),
inference(resolution,[status(thm)],[c_1979,c_2]) ).
tff(c_2000,plain,
( value(out(n1,and1(h2(f))),n1)
| ~ type(h2(f),halfadder) ),
inference(resolution,[status(thm)],[c_60,c_1990]) ).
tff(c_2353,plain,
value(out(n1,and1(h2(f))),n1),
inference(demodulation,[status(thm),theory(equality)],[c_2235,c_2000]) ).
tff(c_2505,plain,
! [K_283] :
( value(in(n2,K_283),n1)
| ~ value(out(n1,K_283),n1)
| ~ type(K_283,and)
| ~ mode(K_283,ok) ),
inference(cnfTransformation,[status(thm)],[f_146]) ).
tff(c_2509,plain,
( value(in(n2,and1(h2(f))),n1)
| ~ type(and1(h2(f)),and)
| ~ mode(and1(h2(f)),ok) ),
inference(resolution,[status(thm)],[c_2353,c_2505]) ).
tff(c_2947,plain,
~ mode(and1(h2(f)),ok),
inference(splitLeft,[status(thm)],[c_2509]) ).
tff(c_2950,plain,
( mode(and1(h2(f)),abnormal)
| ~ type(h2(f),halfadder) ),
inference(resolution,[status(thm)],[c_1848,c_2947]) ).
tff(c_2953,plain,
mode(and1(h2(f)),abnormal),
inference(demodulation,[status(thm),theory(equality)],[c_2235,c_2950]) ).
tff(c_2955,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1861,c_2953]) ).
tff(c_2957,plain,
mode(and1(h2(f)),ok),
inference(splitRight,[status(thm)],[c_2509]) ).
tff(c_2956,plain,
( ~ type(and1(h2(f)),and)
| value(in(n2,and1(h2(f))),n1) ),
inference(splitRight,[status(thm)],[c_2509]) ).
tff(c_2962,plain,
~ type(and1(h2(f)),and),
inference(splitLeft,[status(thm)],[c_2956]) ).
tff(c_2965,plain,
~ type(h2(f),halfadder),
inference(resolution,[status(thm)],[c_44,c_2962]) ).
tff(c_2969,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2235,c_2965]) ).
tff(c_2971,plain,
type(and1(h2(f)),and),
inference(splitRight,[status(thm)],[c_2956]) ).
tff(c_2559,plain,
! [K_287] :
( value(in(n1,K_287),n1)
| ~ value(out(n1,K_287),n1)
| ~ type(K_287,and)
| ~ mode(K_287,ok) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_2563,plain,
( value(in(n1,and1(h2(f))),n1)
| ~ type(and1(h2(f)),and)
| ~ mode(and1(h2(f)),ok) ),
inference(resolution,[status(thm)],[c_2353,c_2559]) ).
tff(c_3236,plain,
value(in(n1,and1(h2(f))),n1),
inference(demodulation,[status(thm),theory(equality)],[c_2957,c_2971,c_2563]) ).
tff(c_3263,plain,
! [P1_319] :
( value(P1_319,n1)
| ~ connection(P1_319,in(n1,and1(h2(f)))) ),
inference(resolution,[status(thm)],[c_3236,c_4]) ).
tff(c_3267,plain,
( value(out(n1,or1(h2(f))),n1)
| ~ type(h2(f),halfadder) ),
inference(resolution,[status(thm)],[c_64,c_3263]) ).
tff(c_3270,plain,
value(out(n1,or1(h2(f))),n1),
inference(demodulation,[status(thm),theory(equality)],[c_2235,c_3267]) ).
tff(c_3327,plain,
! [V1_321] :
( equal_value(V1_321,n1)
| ~ value(out(n1,or1(h2(f))),V1_321) ),
inference(resolution,[status(thm)],[c_3270,c_6]) ).
tff(c_3338,plain,
( equal_value(n0,n1)
| ~ value(in(n2,or1(h2(f))),n0)
| ~ value(in(n1,or1(h2(f))),n0)
| ~ type(or1(h2(f)),or)
| ~ mode(or1(h2(f)),ok) ),
inference(resolution,[status(thm)],[c_28,c_3327]) ).
tff(c_3354,plain,
( equal_value(n0,n1)
| ~ value(in(n2,or1(h2(f))),n0)
| ~ type(or1(h2(f)),or) ),
inference(demodulation,[status(thm),theory(equality)],[c_2941,c_2589,c_3338]) ).
tff(c_3355,plain,
( ~ value(in(n2,or1(h2(f))),n0)
| ~ type(or1(h2(f)),or) ),
inference(negUnitSimplification,[status(thm)],[c_8,c_3354]) ).
tff(c_3389,plain,
~ type(or1(h2(f)),or),
inference(splitLeft,[status(thm)],[c_3355]) ).
tff(c_3395,plain,
~ type(h2(f),halfadder),
inference(resolution,[status(thm)],[c_50,c_3389]) ).
tff(c_3400,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2235,c_3395]) ).
tff(c_3402,plain,
type(or1(h2(f)),or),
inference(splitRight,[status(thm)],[c_3355]) ).
tff(c_30,plain,
! [K_22] :
( value(in(n2,K_22),n1)
| value(in(n1,K_22),n1)
| ~ value(out(n1,K_22),n1)
| ~ type(K_22,or)
| ~ mode(K_22,ok) ),
inference(cnfTransformation,[status(thm)],[f_185]) ).
tff(c_3276,plain,
( value(in(n2,or1(h2(f))),n1)
| value(in(n1,or1(h2(f))),n1)
| ~ type(or1(h2(f)),or)
| ~ mode(or1(h2(f)),ok) ),
inference(resolution,[status(thm)],[c_3270,c_30]) ).
tff(c_3298,plain,
( value(in(n2,or1(h2(f))),n1)
| value(in(n1,or1(h2(f))),n1)
| ~ type(or1(h2(f)),or) ),
inference(demodulation,[status(thm),theory(equality)],[c_2941,c_3276]) ).
tff(c_3598,plain,
( value(in(n2,or1(h2(f))),n1)
| value(in(n1,or1(h2(f))),n1) ),
inference(demodulation,[status(thm),theory(equality)],[c_3402,c_3298]) ).
tff(c_3599,plain,
value(in(n1,or1(h2(f))),n1),
inference(splitLeft,[status(thm)],[c_3598]) ).
tff(c_3608,plain,
equal_value(n1,n0),
inference(resolution,[status(thm)],[c_3599,c_2599]) ).
tff(c_3626,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10,c_3608]) ).
tff(c_3627,plain,
value(in(n2,or1(h2(f))),n1),
inference(splitRight,[status(thm)],[c_3598]) ).
tff(c_3663,plain,
! [P1_335] :
( value(P1_335,n1)
| ~ connection(P1_335,in(n2,or1(h2(f)))) ),
inference(resolution,[status(thm)],[c_3627,c_4]) ).
tff(c_3671,plain,
( value(in(n2,h2(f)),n1)
| ~ type(h2(f),halfadder) ),
inference(resolution,[status(thm)],[c_54,c_3663]) ).
tff(c_3675,plain,
value(in(n2,h2(f)),n1),
inference(demodulation,[status(thm),theory(equality)],[c_2235,c_3671]) ).
tff(c_3756,plain,
! [P1_340] :
( value(P1_340,n1)
| ~ connection(P1_340,in(n2,h2(f))) ),
inference(resolution,[status(thm)],[c_3675,c_4]) ).
tff(c_3760,plain,
( value(out(s,h1(f)),n1)
| ~ type(f,fulladder) ),
inference(resolution,[status(thm)],[c_76,c_3756]) ).
tff(c_3763,plain,
value(out(s,h1(f)),n1),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_3760]) ).
tff(c_3780,plain,
! [P2_343] :
( value(P2_343,n1)
| ~ connection(out(s,h1(f)),P2_343) ),
inference(resolution,[status(thm)],[c_3763,c_2]) ).
tff(c_3792,plain,
( value(out(n1,and1(h1(f))),n1)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_60,c_3780]) ).
tff(c_3799,plain,
value(out(n1,and1(h1(f))),n1),
inference(demodulation,[status(thm),theory(equality)],[c_2295,c_3792]) ).
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_3832,plain,
( value(in(n1,and1(h1(f))),n0)
| ~ type(and1(h1(f)),not)
| ~ mode(and1(h1(f)),ok) ),
inference(resolution,[status(thm)],[c_3799,c_42]) ).
tff(c_3992,plain,
~ mode(and1(h1(f)),ok),
inference(splitLeft,[status(thm)],[c_3832]) ).
tff(c_3995,plain,
( mode(and1(h1(f)),abnormal)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_1848,c_3992]) ).
tff(c_3998,plain,
mode(and1(h1(f)),abnormal),
inference(demodulation,[status(thm),theory(equality)],[c_2295,c_3995]) ).
tff(c_4000,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1799,c_3998]) ).
tff(c_4002,plain,
mode(and1(h1(f)),ok),
inference(splitRight,[status(thm)],[c_3832]) ).
tff(c_3830,plain,
( value(in(n1,and1(h1(f))),n1)
| ~ type(and1(h1(f)),and)
| ~ mode(and1(h1(f)),ok) ),
inference(resolution,[status(thm)],[c_3799,c_22]) ).
tff(c_4003,plain,
~ mode(and1(h1(f)),ok),
inference(splitLeft,[status(thm)],[c_3830]) ).
tff(c_4009,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4002,c_4003]) ).
tff(c_4010,plain,
( ~ type(and1(h1(f)),and)
| value(in(n1,and1(h1(f))),n1) ),
inference(splitRight,[status(thm)],[c_3830]) ).
tff(c_4104,plain,
~ type(and1(h1(f)),and),
inference(splitLeft,[status(thm)],[c_4010]) ).
tff(c_4107,plain,
~ type(h1(f),halfadder),
inference(resolution,[status(thm)],[c_44,c_4104]) ).
tff(c_4111,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2295,c_4107]) ).
tff(c_4113,plain,
type(and1(h1(f)),and),
inference(splitRight,[status(thm)],[c_4010]) ).
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_3831,plain,
( value(in(n2,and1(h1(f))),n1)
| ~ type(and1(h1(f)),and)
| ~ mode(and1(h1(f)),ok) ),
inference(resolution,[status(thm)],[c_3799,c_24]) ).
tff(c_4115,plain,
( value(in(n2,and1(h1(f))),n1)
| ~ type(and1(h1(f)),and) ),
inference(demodulation,[status(thm),theory(equality)],[c_4002,c_3831]) ).
tff(c_4116,plain,
~ type(and1(h1(f)),and),
inference(splitLeft,[status(thm)],[c_4115]) ).
tff(c_4124,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4113,c_4116]) ).
tff(c_4125,plain,
value(in(n2,and1(h1(f))),n1),
inference(splitRight,[status(thm)],[c_4115]) ).
tff(c_4327,plain,
! [P1_362] :
( value(P1_362,n1)
| ~ connection(P1_362,in(n2,and1(h1(f)))) ),
inference(resolution,[status(thm)],[c_4125,c_4]) ).
tff(c_4331,plain,
( value(out(n1,not1(h1(f))),n1)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_68,c_4327]) ).
tff(c_4334,plain,
value(out(n1,not1(h1(f))),n1),
inference(demodulation,[status(thm),theory(equality)],[c_2295,c_4331]) ).
tff(c_4378,plain,
( value(in(n1,not1(h1(f))),n0)
| ~ type(not1(h1(f)),not)
| ~ mode(not1(h1(f)),ok) ),
inference(resolution,[status(thm)],[c_4334,c_42]) ).
tff(c_4588,plain,
~ mode(not1(h1(f)),ok),
inference(splitLeft,[status(thm)],[c_4378]) ).
tff(c_4591,plain,
( mode(not1(h1(f)),abnormal)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_1850,c_4588]) ).
tff(c_4594,plain,
mode(not1(h1(f)),abnormal),
inference(demodulation,[status(thm),theory(equality)],[c_2295,c_4591]) ).
tff(c_4596,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1882,c_4594]) ).
tff(c_4597,plain,
( ~ type(not1(h1(f)),not)
| value(in(n1,not1(h1(f))),n0) ),
inference(splitRight,[status(thm)],[c_4378]) ).
tff(c_4603,plain,
~ type(not1(h1(f)),not),
inference(splitLeft,[status(thm)],[c_4597]) ).
tff(c_4606,plain,
~ type(h1(f),halfadder),
inference(resolution,[status(thm)],[c_48,c_4603]) ).
tff(c_4610,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2295,c_4606]) ).
tff(c_4611,plain,
value(in(n1,not1(h1(f))),n0),
inference(splitRight,[status(thm)],[c_4597]) ).
tff(c_4648,plain,
! [P1_374] :
( value(P1_374,n0)
| ~ connection(P1_374,in(n1,not1(h1(f)))) ),
inference(resolution,[status(thm)],[c_4611,c_4]) ).
tff(c_4652,plain,
( value(out(n1,and2(h1(f))),n0)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[c_66,c_4648]) ).
tff(c_4655,plain,
value(out(n1,and2(h1(f))),n0),
inference(demodulation,[status(thm),theory(equality)],[c_2295,c_4652]) ).
tff(c_2770,plain,
! [K_298] :
( value(out(n1,K_298),n1)
| ~ value(in(n2,K_298),n1)
| ~ value(in(n1,K_298),n1)
| ~ type(K_298,and)
| ~ mode(K_298,ok) ),
inference(cnfTransformation,[status(thm)],[f_111]) ).
tff(c_2806,plain,
! [V1_8,K_298] :
( equal_value(V1_8,n1)
| ~ value(out(n1,K_298),V1_8)
| ~ value(in(n2,K_298),n1)
| ~ value(in(n1,K_298),n1)
| ~ type(K_298,and)
| ~ mode(K_298,ok) ),
inference(resolution,[status(thm)],[c_2770,c_6]) ).
tff(c_4658,plain,
( equal_value(n0,n1)
| ~ value(in(n2,and2(h1(f))),n1)
| ~ value(in(n1,and2(h1(f))),n1)
| ~ type(and2(h1(f)),and)
| ~ mode(and2(h1(f)),ok) ),
inference(resolution,[status(thm)],[c_4655,c_2806]) ).
tff(c_4688,plain,
( equal_value(n0,n1)
| ~ type(and2(h1(f)),and) ),
inference(demodulation,[status(thm),theory(equality)],[c_3185,c_2294,c_2540,c_4658]) ).
tff(c_4689,plain,
~ type(and2(h1(f)),and),
inference(negUnitSimplification,[status(thm)],[c_8,c_4688]) ).
tff(c_4717,plain,
~ type(h1(f),halfadder),
inference(resolution,[status(thm)],[c_46,c_4689]) ).
tff(c_4721,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2295,c_4717]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : HWV007-1 : TPTP v9.0.0. Released v2.1.0.
% 0.11/0.13 % 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
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 7 22:53:49 EDT 2025
% 0.12/0.34 % CPUTime :
% 8.85/3.11 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.85/3.15
% 8.85/3.15 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------