TSTP Solution File: HWV005-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : HWV005-1 : 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 : n010.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 5.00s 2.32s
% Output   : CNFRefutation 5.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   51
% Syntax   : Number of formulae    :  145 (  50 unt;  23 typ;   0 def)
%            Number of atoms       :  246 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  258 ( 134   ~; 124   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   18 (  11   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;  12 con; 0-2 aty)
%            Number of variables   :   71 (;  71   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ value > type > mode > equal_value > connection > out > in > #nlpp > or1 > not1 > and2 > and1 > s > or > ok > not > n2 > n1 > n0 > halfadder > h > 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(h,type,
    h: $i ).

tff(in,type,
    in: ( $i * $i ) > $i ).

tff(connection,type,
    connection: ( $i * $i ) > $o ).

tff(s,type,
    s: $i ).

tff(halfadder,type,
    halfadder: $i ).

tff(and2,type,
    and2: $i > $i ).

tff(equal_value,type,
    equal_value: ( $i * $i ) > $o ).

tff(n1,type,
    n1: $i ).

tff(n0,type,
    n0: $i ).

tff(type,type,
    type: ( $i * $i ) > $o ).

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_345,axiom,
    type(h,halfadder),
    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_353,axiom,
    ~ mode(not1(h),abnormal),
    file(unknown,unknown) ).

tff(f_85,axiom,
    ! [K,Any] :
      ( ~ type(K,Any)
      | mode(K,ok)
      | mode(K,abnormal) ),
    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_326,axiom,
    ! [X] :
      ( ~ type(X,halfadder)
      | connection(out(c,X),out(n1,and2(X))) ),
    file(unknown,unknown) ).

tff(f_349,axiom,
    value(out(c,h),n0),
    file(unknown,unknown) ).

tff(f_51,axiom,
    ! [P1,P2,V] :
      ( ~ connection(P1,P2)
      | ~ value(P1,V)
      | value(P2,V) ),
    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_219,axiom,
    ! [K] :
      ( ~ mode(K,ok)
      | ~ type(K,not)
      | ~ value(in(n1,K),n0)
      | value(out(n1,K),n1) ),
    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_69,axiom,
    ~ equal_value(n0,n1),
    file(unknown,unknown) ).

tff(f_280,axiom,
    ! [X] :
      ( ~ type(X,halfadder)
      | type(and1(X),and) ),
    file(unknown,unknown) ).

tff(f_351,axiom,
    ~ mode(and1(h),abnormal),
    file(unknown,unknown) ).

tff(f_321,axiom,
    ! [X] :
      ( ~ type(X,halfadder)
      | connection(out(s,X),out(n1,and1(X))) ),
    file(unknown,unknown) ).

tff(f_348,axiom,
    value(out(s,h),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_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_355,axiom,
    ~ mode(or1(h),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_346,axiom,
    value(in(n1,h),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_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_67,axiom,
    ! [P,V1,V2] :
      ( ~ value(P,V1)
      | ~ value(P,V2)
      | equal_value(V1,V2) ),
    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_59,axiom,
    ! [P1,P2,V] :
      ( ~ connection(P1,P2)
      | ~ value(P2,V)
      | value(P1,V) ),
    file(unknown,unknown) ).

tff(c_70,plain,
    type(h,halfadder),
    inference(cnfTransformation,[status(thm)],[f_345]) ).

tff(c_48,plain,
    ! [X_31] :
      ( type(not1(X_31),not)
      | ~ type(X_31,halfadder) ),
    inference(cnfTransformation,[status(thm)],[f_290]) ).

tff(c_10,plain,
    ~ equal_value(n1,n0),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_82,plain,
    ~ mode(not1(h),abnormal),
    inference(cnfTransformation,[status(thm)],[f_353]) ).

tff(c_106,plain,
    ! [K_53,Any_54] :
      ( mode(K_53,abnormal)
      | mode(K_53,ok)
      | ~ type(K_53,Any_54) ),
    inference(cnfTransformation,[status(thm)],[f_85]) ).

tff(c_124,plain,
    ! [X_31] :
      ( mode(not1(X_31),abnormal)
      | mode(not1(X_31),ok)
      | ~ type(X_31,halfadder) ),
    inference(resolution,[status(thm)],[c_48,c_106]) ).

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_189,plain,
    ! [X_68] :
      ( connection(out(c,X_68),out(n1,and2(X_68)))
      | ~ type(X_68,halfadder) ),
    inference(cnfTransformation,[status(thm)],[f_326]) ).

tff(c_78,plain,
    value(out(c,h),n0),
    inference(cnfTransformation,[status(thm)],[f_349]) ).

tff(c_90,plain,
    ! [P2_47,V_48,P1_49] :
      ( value(P2_47,V_48)
      | ~ value(P1_49,V_48)
      | ~ connection(P1_49,P2_47) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_99,plain,
    ! [P2_47] :
      ( value(P2_47,n0)
      | ~ connection(out(c,h),P2_47) ),
    inference(resolution,[status(thm)],[c_78,c_90]) ).

tff(c_193,plain,
    ( value(out(n1,and2(h)),n0)
    | ~ type(h,halfadder) ),
    inference(resolution,[status(thm)],[c_189,c_99]) ).

tff(c_196,plain,
    value(out(n1,and2(h)),n0),
    inference(demodulation,[status(thm),theory(equality)],[c_70,c_193]) ).

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_410,plain,
    ! [P2_94] :
      ( value(P2_94,n0)
      | ~ connection(out(n1,and2(h)),P2_94) ),
    inference(resolution,[status(thm)],[c_196,c_2]) ).

tff(c_414,plain,
    ( value(in(n1,not1(h)),n0)
    | ~ type(h,halfadder) ),
    inference(resolution,[status(thm)],[c_66,c_410]) ).

tff(c_417,plain,
    value(in(n1,not1(h)),n0),
    inference(demodulation,[status(thm),theory(equality)],[c_70,c_414]) ).

tff(c_608,plain,
    ! [K_112,Any_113] :
      ( value(out(n1,K_112),n0)
      | ~ value(in(Any_113,K_112),n0)
      | ~ type(K_112,and)
      | ~ mode(K_112,ok) ),
    inference(cnfTransformation,[status(thm)],[f_97]) ).

tff(c_617,plain,
    ( value(out(n1,not1(h)),n0)
    | ~ type(not1(h),and)
    | ~ mode(not1(h),ok) ),
    inference(resolution,[status(thm)],[c_417,c_608]) ).

tff(c_932,plain,
    ~ mode(not1(h),ok),
    inference(splitLeft,[status(thm)],[c_617]) ).

tff(c_945,plain,
    ( mode(not1(h),abnormal)
    | ~ type(h,halfadder) ),
    inference(resolution,[status(thm)],[c_124,c_932]) ).

tff(c_948,plain,
    mode(not1(h),abnormal),
    inference(demodulation,[status(thm),theory(equality)],[c_70,c_945]) ).

tff(c_950,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_82,c_948]) ).

tff(c_952,plain,
    mode(not1(h),ok),
    inference(splitRight,[status(thm)],[c_617]) ).

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_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_8,plain,
    ~ equal_value(n0,n1),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_44,plain,
    ! [X_29] :
      ( type(and1(X_29),and)
      | ~ type(X_29,halfadder) ),
    inference(cnfTransformation,[status(thm)],[f_280]) ).

tff(c_80,plain,
    ~ mode(and1(h),abnormal),
    inference(cnfTransformation,[status(thm)],[f_351]) ).

tff(c_122,plain,
    ! [X_29] :
      ( mode(and1(X_29),abnormal)
      | mode(and1(X_29),ok)
      | ~ type(X_29,halfadder) ),
    inference(resolution,[status(thm)],[c_44,c_106]) ).

tff(c_256,plain,
    ! [X_76] :
      ( connection(out(s,X_76),out(n1,and1(X_76)))
      | ~ type(X_76,halfadder) ),
    inference(cnfTransformation,[status(thm)],[f_321]) ).

tff(c_76,plain,
    value(out(s,h),n0),
    inference(cnfTransformation,[status(thm)],[f_348]) ).

tff(c_100,plain,
    ! [P2_47] :
      ( value(P2_47,n0)
      | ~ connection(out(s,h),P2_47) ),
    inference(resolution,[status(thm)],[c_76,c_90]) ).

tff(c_260,plain,
    ( value(out(n1,and1(h)),n0)
    | ~ type(h,halfadder) ),
    inference(resolution,[status(thm)],[c_256,c_100]) ).

tff(c_263,plain,
    value(out(n1,and1(h)),n0),
    inference(demodulation,[status(thm),theory(equality)],[c_70,c_260]) ).

tff(c_506,plain,
    ! [K_107] :
      ( value(in(n1,K_107),n0)
      | ~ value(out(n1,K_107),n0)
      | ~ type(K_107,or)
      | ~ mode(K_107,ok) ),
    inference(cnfTransformation,[status(thm)],[f_196]) ).

tff(c_513,plain,
    ( value(in(n1,and1(h)),n0)
    | ~ type(and1(h),or)
    | ~ mode(and1(h),ok) ),
    inference(resolution,[status(thm)],[c_263,c_506]) ).

tff(c_548,plain,
    ~ mode(and1(h),ok),
    inference(splitLeft,[status(thm)],[c_513]) ).

tff(c_551,plain,
    ( mode(and1(h),abnormal)
    | ~ type(h,halfadder) ),
    inference(resolution,[status(thm)],[c_122,c_548]) ).

tff(c_554,plain,
    mode(and1(h),abnormal),
    inference(demodulation,[status(thm),theory(equality)],[c_70,c_551]) ).

tff(c_556,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_80,c_554]) ).

tff(c_558,plain,
    mode(and1(h),ok),
    inference(splitRight,[status(thm)],[c_513]) ).

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_84,plain,
    ~ mode(or1(h),abnormal),
    inference(cnfTransformation,[status(thm)],[f_355]) ).

tff(c_125,plain,
    ! [X_32] :
      ( mode(or1(X_32),abnormal)
      | mode(or1(X_32),ok)
      | ~ type(X_32,halfadder) ),
    inference(resolution,[status(thm)],[c_50,c_106]) ).

tff(c_287,plain,
    ! [X_79] :
      ( connection(in(n1,X_79),in(n1,or1(X_79)))
      | ~ type(X_79,halfadder) ),
    inference(cnfTransformation,[status(thm)],[f_301]) ).

tff(c_72,plain,
    value(in(n1,h),n1),
    inference(cnfTransformation,[status(thm)],[f_346]) ).

tff(c_102,plain,
    ! [P2_47] :
      ( value(P2_47,n1)
      | ~ connection(in(n1,h),P2_47) ),
    inference(resolution,[status(thm)],[c_72,c_90]) ).

tff(c_295,plain,
    ( value(in(n1,or1(h)),n1)
    | ~ type(h,halfadder) ),
    inference(resolution,[status(thm)],[c_287,c_102]) ).

tff(c_299,plain,
    value(in(n1,or1(h)),n1),
    inference(demodulation,[status(thm),theory(equality)],[c_70,c_295]) ).

tff(c_492,plain,
    ! [K_105,Any_106] :
      ( value(out(n1,K_105),n1)
      | ~ value(in(Any_106,K_105),n1)
      | ~ type(K_105,or)
      | ~ mode(K_105,ok) ),
    inference(cnfTransformation,[status(thm)],[f_158]) ).

tff(c_499,plain,
    ( value(out(n1,or1(h)),n1)
    | ~ type(or1(h),or)
    | ~ mode(or1(h),ok) ),
    inference(resolution,[status(thm)],[c_299,c_492]) ).

tff(c_625,plain,
    ~ mode(or1(h),ok),
    inference(splitLeft,[status(thm)],[c_499]) ).

tff(c_628,plain,
    ( mode(or1(h),abnormal)
    | ~ type(h,halfadder) ),
    inference(resolution,[status(thm)],[c_125,c_625]) ).

tff(c_631,plain,
    mode(or1(h),abnormal),
    inference(demodulation,[status(thm),theory(equality)],[c_70,c_628]) ).

tff(c_633,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_84,c_631]) ).

tff(c_634,plain,
    ( ~ type(or1(h),or)
    | value(out(n1,or1(h)),n1) ),
    inference(splitRight,[status(thm)],[c_499]) ).

tff(c_656,plain,
    ~ type(or1(h),or),
    inference(splitLeft,[status(thm)],[c_634]) ).

tff(c_659,plain,
    ~ type(h,halfadder),
    inference(resolution,[status(thm)],[c_50,c_656]) ).

tff(c_663,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_70,c_659]) ).

tff(c_664,plain,
    value(out(n1,or1(h)),n1),
    inference(splitRight,[status(thm)],[c_634]) ).

tff(c_726,plain,
    ! [P2_118] :
      ( value(P2_118,n1)
      | ~ connection(out(n1,or1(h)),P2_118) ),
    inference(resolution,[status(thm)],[c_664,c_2]) ).

tff(c_730,plain,
    ( value(in(n1,and1(h)),n1)
    | ~ type(h,halfadder) ),
    inference(resolution,[status(thm)],[c_64,c_726]) ).

tff(c_733,plain,
    value(in(n1,and1(h)),n1),
    inference(demodulation,[status(thm),theory(equality)],[c_70,c_730]) ).

tff(c_778,plain,
    ! [K_122] :
      ( value(out(n1,K_122),n1)
      | ~ value(in(n2,K_122),n1)
      | ~ value(in(n1,K_122),n1)
      | ~ type(K_122,and)
      | ~ mode(K_122,ok) ),
    inference(cnfTransformation,[status(thm)],[f_111]) ).

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_271,plain,
    ! [V1_8] :
      ( equal_value(V1_8,n0)
      | ~ value(out(n1,and1(h)),V1_8) ),
    inference(resolution,[status(thm)],[c_263,c_6]) ).

tff(c_799,plain,
    ( equal_value(n1,n0)
    | ~ value(in(n2,and1(h)),n1)
    | ~ value(in(n1,and1(h)),n1)
    | ~ type(and1(h),and)
    | ~ mode(and1(h),ok) ),
    inference(resolution,[status(thm)],[c_778,c_271]) ).

tff(c_818,plain,
    ( equal_value(n1,n0)
    | ~ value(in(n2,and1(h)),n1)
    | ~ type(and1(h),and) ),
    inference(demodulation,[status(thm),theory(equality)],[c_558,c_733,c_799]) ).

tff(c_819,plain,
    ( ~ value(in(n2,and1(h)),n1)
    | ~ type(and1(h),and) ),
    inference(negUnitSimplification,[status(thm)],[c_10,c_818]) ).

tff(c_835,plain,
    ~ type(and1(h),and),
    inference(splitLeft,[status(thm)],[c_819]) ).

tff(c_853,plain,
    ~ type(h,halfadder),
    inference(resolution,[status(thm)],[c_44,c_835]) ).

tff(c_857,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_70,c_853]) ).

tff(c_859,plain,
    type(and1(h),and),
    inference(splitRight,[status(thm)],[c_819]) ).

tff(c_734,plain,
    ! [K_119] :
      ( value(in(n2,K_119),n0)
      | value(in(n1,K_119),n0)
      | ~ value(out(n1,K_119),n0)
      | ~ type(K_119,and)
      | ~ mode(K_119,ok) ),
    inference(cnfTransformation,[status(thm)],[f_124]) ).

tff(c_740,plain,
    ( value(in(n2,and1(h)),n0)
    | value(in(n1,and1(h)),n0)
    | ~ type(and1(h),and)
    | ~ mode(and1(h),ok) ),
    inference(resolution,[status(thm)],[c_263,c_734]) ).

tff(c_747,plain,
    ( value(in(n2,and1(h)),n0)
    | value(in(n1,and1(h)),n0)
    | ~ type(and1(h),and) ),
    inference(demodulation,[status(thm),theory(equality)],[c_558,c_740]) ).

tff(c_959,plain,
    ( value(in(n2,and1(h)),n0)
    | value(in(n1,and1(h)),n0) ),
    inference(demodulation,[status(thm),theory(equality)],[c_859,c_747]) ).

tff(c_960,plain,
    value(in(n1,and1(h)),n0),
    inference(splitLeft,[status(thm)],[c_959]) ).

tff(c_762,plain,
    ! [V1_8] :
      ( equal_value(V1_8,n1)
      | ~ value(in(n1,and1(h)),V1_8) ),
    inference(resolution,[status(thm)],[c_733,c_6]) ).

tff(c_997,plain,
    equal_value(n0,n1),
    inference(resolution,[status(thm)],[c_960,c_762]) ).

tff(c_1009,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_8,c_997]) ).

tff(c_1010,plain,
    value(in(n2,and1(h)),n0),
    inference(splitRight,[status(thm)],[c_959]) ).

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_1026,plain,
    ! [P1_130] :
      ( value(P1_130,n0)
      | ~ connection(P1_130,in(n2,and1(h))) ),
    inference(resolution,[status(thm)],[c_1010,c_4]) ).

tff(c_1030,plain,
    ( value(out(n1,not1(h)),n0)
    | ~ type(h,halfadder) ),
    inference(resolution,[status(thm)],[c_68,c_1026]) ).

tff(c_1033,plain,
    value(out(n1,not1(h)),n0),
    inference(demodulation,[status(thm),theory(equality)],[c_70,c_1030]) ).

tff(c_1085,plain,
    ! [V1_134] :
      ( equal_value(V1_134,n0)
      | ~ value(out(n1,not1(h)),V1_134) ),
    inference(resolution,[status(thm)],[c_1033,c_6]) ).

tff(c_1100,plain,
    ( equal_value(n1,n0)
    | ~ value(in(n1,not1(h)),n0)
    | ~ type(not1(h),not)
    | ~ mode(not1(h),ok) ),
    inference(resolution,[status(thm)],[c_36,c_1085]) ).

tff(c_1116,plain,
    ( equal_value(n1,n0)
    | ~ type(not1(h),not) ),
    inference(demodulation,[status(thm),theory(equality)],[c_952,c_417,c_1100]) ).

tff(c_1117,plain,
    ~ type(not1(h),not),
    inference(negUnitSimplification,[status(thm)],[c_10,c_1116]) ).

tff(c_1171,plain,
    ~ type(h,halfadder),
    inference(resolution,[status(thm)],[c_48,c_1117]) ).

tff(c_1175,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_70,c_1171]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : HWV005-1 : TPTP v8.1.2. Released v2.1.0.
% 0.13/0.14  % 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
% 0.13/0.35  % Computer : n010.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 23:31:43 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 5.00/2.32  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.41/2.33  
% 5.41/2.33  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.41/2.37  
% 5.41/2.37  Inference rules
% 5.41/2.37  ----------------------
% 5.41/2.37  #Ref     : 0
% 5.41/2.37  #Sup     : 209
% 5.41/2.37  #Fact    : 0
% 5.41/2.37  #Define  : 0
% 5.41/2.37  #Split   : 18
% 5.41/2.37  #Chain   : 0
% 5.41/2.37  #Close   : 0
% 5.41/2.37  
% 5.41/2.37  Ordering : KBO
% 5.41/2.37  
% 5.41/2.37  Simplification rules
% 5.41/2.37  ----------------------
% 5.41/2.37  #Subsume      : 38
% 5.41/2.37  #Demod        : 126
% 5.41/2.37  #Tautology    : 48
% 5.41/2.37  #SimpNegUnit  : 15
% 5.41/2.37  #BackRed      : 0
% 5.41/2.37  
% 5.41/2.37  #Partial instantiations: 0
% 5.41/2.37  #Strategies tried      : 1
% 5.41/2.37  
% 5.41/2.37  Timing (in seconds)
% 5.41/2.37  ----------------------
% 5.41/2.38  Preprocessing        : 0.54
% 5.41/2.38  Parsing              : 0.30
% 5.41/2.38  CNF conversion       : 0.03
% 5.41/2.38  Main loop            : 0.63
% 5.41/2.38  Inferencing          : 0.25
% 5.41/2.38  Reduction            : 0.18
% 5.41/2.38  Demodulation         : 0.12
% 5.41/2.38  BG Simplification    : 0.03
% 5.41/2.38  Subsumption          : 0.13
% 5.41/2.38  Abstraction          : 0.02
% 5.41/2.38  MUC search           : 0.00
% 5.41/2.38  Cooper               : 0.00
% 5.41/2.38  Total                : 1.25
% 5.41/2.38  Index Insertion      : 0.00
% 5.41/2.38  Index Deletion       : 0.00
% 5.41/2.38  Index Matching       : 0.00
% 5.41/2.38  BG Taut test         : 0.00
%------------------------------------------------------------------------------