%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HWV007-1 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:45:54 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.50s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 88
% Syntax : Number of formulae : 322 ( 48 unt; 43 def)
% Number of atoms : 715 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 766 ( 373 ~; 350 |; 0 &)
% ( 43 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 49 ( 48 usr; 44 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 13 con; 0-2 aty)
% Number of variables : 173 ( 173 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [P1,P2,V] :
( value(P2,V)
| ~ value(P1,V)
| ~ connection(P1,P2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [P1,P2,V] :
( value(P1,V)
| ~ value(P2,V)
| ~ connection(P1,P2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [P,V1,V2] :
( equal_value(V1,V2)
| ~ value(P,V2)
| ~ value(P,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
~ equal_value(n1,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [K,Any] :
( mode(K,abnormal)
| mode(K,ok)
| ~ type(K,Any) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [K] :
( value(in(n2,K),n0)
| value(in(n1,K),n0)
| ~ value(out(n1,K),n0)
| ~ type(K,and)
| ~ mode(K,ok) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [K] :
( value(in(n1,K),n1)
| ~ value(out(n1,K),n1)
| ~ type(K,and)
| ~ mode(K,ok) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [K] :
( value(in(n2,K),n1)
| ~ value(out(n1,K),n1)
| ~ type(K,and)
| ~ mode(K,ok) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [K] :
( value(in(n2,K),n1)
| value(in(n1,K),n1)
| ~ value(out(n1,K),n1)
| ~ type(K,or)
| ~ mode(K,ok) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [K] :
( value(in(n2,K),n0)
| ~ value(out(n1,K),n0)
| ~ type(K,or)
| ~ mode(K,ok) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [K] :
( value(in(n1,K),n0)
| ~ value(out(n1,K),n1)
| ~ type(K,not)
| ~ mode(K,ok) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X] :
( type(and1(X),and)
| ~ type(X,halfadder) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X] :
( type(and2(X),and)
| ~ type(X,halfadder) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [X] :
( type(not1(X),not)
| ~ type(X,halfadder) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [X] :
( type(or1(X),or)
| ~ type(X,halfadder) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X] :
( connection(in(n1,X),in(n1,or1(X)))
| ~ type(X,halfadder) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [X] :
( connection(in(n2,X),in(n2,or1(X)))
| ~ type(X,halfadder) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [X] :
( connection(in(n1,X),in(n1,and2(X)))
| ~ type(X,halfadder) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [X] :
( connection(in(n2,X),in(n2,and2(X)))
| ~ type(X,halfadder) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [X] :
( connection(out(s,X),out(n1,and1(X)))
| ~ type(X,halfadder) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [X] :
( connection(out(c,X),out(n1,and2(X)))
| ~ type(X,halfadder) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [X] :
( connection(out(n1,or1(X)),in(n1,and1(X)))
| ~ type(X,halfadder) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [X] :
( connection(out(n1,and2(X)),in(n1,not1(X)))
| ~ type(X,halfadder) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [X] :
( connection(out(n1,not1(X)),in(n2,and1(X)))
| ~ type(X,halfadder) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [X] :
( type(h1(X),halfadder)
| ~ type(X,fulladder) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [X] :
( type(h2(X),halfadder)
| ~ type(X,fulladder) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [X] :
( type(or1(X),or)
| ~ type(X,fulladder) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [X] :
( connection(out(s,h1(X)),in(n2,h2(X)))
| ~ type(X,fulladder) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [X] :
( connection(out(c,h1(X)),in(n2,or1(X)))
| ~ type(X,fulladder) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [X] :
( connection(in(n1,X),in(n1,h2(X)))
| ~ type(X,fulladder) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [X] :
( connection(in(n2,X),in(n1,h1(X)))
| ~ type(X,fulladder) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [X] :
( connection(in(c,X),in(n2,h1(X)))
| ~ type(X,fulladder) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [X] :
( connection(out(s,X),out(s,h2(X)))
| ~ type(X,fulladder) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [X] :
( connection(out(c,X),out(n1,or1(X)))
| ~ type(X,fulladder) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,hypothesis,
type(f,fulladder),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,hypothesis,
value(in(n1,f),n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,hypothesis,
value(in(n2,f),n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,hypothesis,
value(in(c,f),n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,hypothesis,
value(out(s,f),n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,hypothesis,
value(out(c,f),n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
~ mode(and2(h1(f)),abnormal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,negated_conjecture,
( ~ mode(and1(h1(f)),abnormal)
| ~ mode(or1(f),abnormal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
( ~ mode(not1(h1(f)),abnormal)
| ~ mode(or1(f),abnormal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,negated_conjecture,
( ~ mode(and1(h2(f)),abnormal)
| ~ mode(or1(f),abnormal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,negated_conjecture,
( ~ mode(or1(h2(f)),abnormal)
| ~ mode(or1(f),abnormal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,plain,
! [P2,V] :
( value(P2,V)
| ! [P1] :
( ~ value(P1,V)
| ~ connection(P1,P2) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f58,plain,
! [X0,X1,X2] :
( value(X1,X2)
| ~ value(X0,X2)
| ~ connection(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f59,plain,
! [P1,V] :
( value(P1,V)
| ! [P2] :
( ~ value(P2,V)
| ~ connection(P1,P2) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f60,plain,
! [X0,X1,X2] :
( value(X0,X2)
| ~ value(X1,X2)
| ~ connection(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
! [V1,V2] :
( equal_value(V1,V2)
| ! [P] :
( ~ value(P,V2)
| ~ value(P,V1) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f62,plain,
! [X0,X1,X2] :
( equal_value(X1,X2)
| ~ value(X0,X2)
| ~ value(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f64,plain,
~ equal_value(n1,n0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f66,plain,
! [K] :
( mode(K,abnormal)
| mode(K,ok)
| ! [Any] : ~ type(K,Any) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f67,plain,
! [X0,X1] :
( mode(X0,abnormal)
| mode(X0,ok)
| ~ type(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f71,plain,
! [X0] :
( value(in(n2,X0),n0)
| value(in(n1,X0),n0)
| ~ value(out(n1,X0),n0)
| ~ type(X0,and)
| ~ mode(X0,ok) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f72,plain,
! [X0] :
( value(in(n1,X0),n1)
| ~ value(out(n1,X0),n1)
| ~ type(X0,and)
| ~ mode(X0,ok) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f73,plain,
! [X0] :
( value(in(n2,X0),n1)
| ~ value(out(n1,X0),n1)
| ~ type(X0,and)
| ~ mode(X0,ok) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f77,plain,
! [X0] :
( value(in(n2,X0),n1)
| value(in(n1,X0),n1)
| ~ value(out(n1,X0),n1)
| ~ type(X0,or)
| ~ mode(X0,ok) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f79,plain,
! [X0] :
( value(in(n2,X0),n0)
| ~ value(out(n1,X0),n0)
| ~ type(X0,or)
| ~ mode(X0,ok) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f83,plain,
! [X0] :
( value(in(n1,X0),n0)
| ~ value(out(n1,X0),n1)
| ~ type(X0,not)
| ~ mode(X0,ok) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f84,plain,
! [X0] :
( type(and1(X0),and)
| ~ type(X0,halfadder) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f85,plain,
! [X0] :
( type(and2(X0),and)
| ~ type(X0,halfadder) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f86,plain,
! [X0] :
( type(not1(X0),not)
| ~ type(X0,halfadder) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f87,plain,
! [X0] :
( type(or1(X0),or)
| ~ type(X0,halfadder) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f88,plain,
! [X0] :
( connection(in(n1,X0),in(n1,or1(X0)))
| ~ type(X0,halfadder) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f89,plain,
! [X0] :
( connection(in(n2,X0),in(n2,or1(X0)))
| ~ type(X0,halfadder) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f90,plain,
! [X0] :
( connection(in(n1,X0),in(n1,and2(X0)))
| ~ type(X0,halfadder) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f91,plain,
! [X0] :
( connection(in(n2,X0),in(n2,and2(X0)))
| ~ type(X0,halfadder) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f92,plain,
! [X0] :
( connection(out(s,X0),out(n1,and1(X0)))
| ~ type(X0,halfadder) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f93,plain,
! [X0] :
( connection(out(c,X0),out(n1,and2(X0)))
| ~ type(X0,halfadder) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f94,plain,
! [X0] :
( connection(out(n1,or1(X0)),in(n1,and1(X0)))
| ~ type(X0,halfadder) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f95,plain,
! [X0] :
( connection(out(n1,and2(X0)),in(n1,not1(X0)))
| ~ type(X0,halfadder) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f96,plain,
! [X0] :
( connection(out(n1,not1(X0)),in(n2,and1(X0)))
| ~ type(X0,halfadder) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f97,plain,
! [X0] :
( type(h1(X0),halfadder)
| ~ type(X0,fulladder) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f98,plain,
! [X0] :
( type(h2(X0),halfadder)
| ~ type(X0,fulladder) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f99,plain,
! [X0] :
( type(or1(X0),or)
| ~ type(X0,fulladder) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f100,plain,
! [X0] :
( connection(out(s,h1(X0)),in(n2,h2(X0)))
| ~ type(X0,fulladder) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f101,plain,
! [X0] :
( connection(out(c,h1(X0)),in(n2,or1(X0)))
| ~ type(X0,fulladder) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f103,plain,
! [X0] :
( connection(in(n1,X0),in(n1,h2(X0)))
| ~ type(X0,fulladder) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f104,plain,
! [X0] :
( connection(in(n2,X0),in(n1,h1(X0)))
| ~ type(X0,fulladder) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f105,plain,
! [X0] :
( connection(in(c,X0),in(n2,h1(X0)))
| ~ type(X0,fulladder) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f106,plain,
! [X0] :
( connection(out(s,X0),out(s,h2(X0)))
| ~ type(X0,fulladder) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f107,plain,
! [X0] :
( connection(out(c,X0),out(n1,or1(X0)))
| ~ type(X0,fulladder) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f108,plain,
type(f,fulladder),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f109,plain,
value(in(n1,f),n0),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f110,plain,
value(in(n2,f),n1),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f111,plain,
value(in(c,f),n1),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f112,plain,
value(out(s,f),n1),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f113,plain,
value(out(c,f),n0),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f114,plain,
~ mode(and2(h1(f)),abnormal),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f115,plain,
( ~ mode(and1(h1(f)),abnormal)
| ~ mode(or1(f),abnormal) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f116,plain,
( ~ mode(not1(h1(f)),abnormal)
| ~ mode(or1(f),abnormal) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f117,plain,
( ~ mode(and1(h2(f)),abnormal)
| ~ mode(or1(f),abnormal) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f118,plain,
( ~ mode(or1(h2(f)),abnormal)
| ~ mode(or1(f),abnormal) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f119,definition,
( sQ0_spl
<=> mode(or1(f),abnormal) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f122,definition,
( sQ1_spl
<=> mode(and1(h1(f)),abnormal) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f124,plain,
( sQ1_spl
| ~ mode(and1(h1(f)),abnormal) ),
inference(component_clause,[status(thm)],[f122]) ).
fof(f125,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f115,f119,f122]) ).
fof(f126,definition,
( sQ2_spl
<=> mode(not1(h1(f)),abnormal) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( sQ2_spl
| ~ mode(not1(h1(f)),abnormal) ),
inference(component_clause,[status(thm)],[f126]) ).
fof(f129,plain,
( ~ sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f116,f119,f126]) ).
fof(f130,definition,
( sQ3_spl
<=> mode(and1(h2(f)),abnormal) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f133,plain,
( ~ sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f117,f119,f130]) ).
fof(f134,definition,
( sQ4_spl
<=> mode(or1(h2(f)),abnormal) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( ~ sQ4_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f118,f119,f134]) ).
fof(f138,plain,
! [X0] :
( ~ value(X0,n0)
| ~ value(X0,n1) ),
inference(resolution,[status(thm)],[f62,f64]) ).
fof(f141,plain,
! [X0,X1] :
( value(in(n1,or1(X0)),X1)
| ~ value(in(n1,X0),X1)
| ~ type(X0,halfadder) ),
inference(resolution,[status(thm)],[f88,f58]) ).
fof(f142,plain,
! [X0,X1] :
( value(in(n2,X0),X1)
| ~ value(in(n2,or1(X0)),X1)
| ~ type(X0,halfadder) ),
inference(resolution,[status(thm)],[f89,f60]) ).
fof(f143,plain,
! [X0,X1] :
( value(in(n2,or1(X0)),X1)
| ~ value(in(n2,X0),X1)
| ~ type(X0,halfadder) ),
inference(resolution,[status(thm)],[f89,f58]) ).
fof(f144,plain,
! [X0,X1] :
( value(in(n1,X0),X1)
| ~ value(in(n1,and2(X0)),X1)
| ~ type(X0,halfadder) ),
inference(resolution,[status(thm)],[f90,f60]) ).
fof(f145,plain,
! [X0,X1] :
( value(in(n1,and2(X0)),X1)
| ~ value(in(n1,X0),X1)
| ~ type(X0,halfadder) ),
inference(resolution,[status(thm)],[f90,f58]) ).
fof(f146,plain,
! [X0,X1] :
( value(in(n2,X0),X1)
| ~ value(in(n2,and2(X0)),X1)
| ~ type(X0,halfadder) ),
inference(resolution,[status(thm)],[f91,f60]) ).
fof(f149,plain,
! [X0,X1] :
( value(out(n1,and2(X0)),X1)
| ~ value(out(c,X0),X1)
| ~ type(X0,halfadder) ),
inference(resolution,[status(thm)],[f93,f58]) ).
fof(f150,plain,
! [X0,X1] :
( value(out(n1,or1(X0)),X1)
| ~ value(in(n1,and1(X0)),X1)
| ~ type(X0,halfadder) ),
inference(resolution,[status(thm)],[f94,f60]) ).
fof(f152,plain,
! [X0,X1] :
( value(out(n1,and2(X0)),X1)
| ~ value(in(n1,not1(X0)),X1)
| ~ type(X0,halfadder) ),
inference(resolution,[status(thm)],[f95,f60]) ).
fof(f159,plain,
connection(in(n1,f),in(n1,h2(f))),
inference(resolution,[status(thm)],[f103,f108]) ).
fof(f161,plain,
! [X0] :
( value(in(n1,h2(f)),X0)
| ~ value(in(n1,f),X0) ),
inference(resolution,[status(thm)],[f159,f58]) ).
fof(f162,plain,
! [X0,X1] :
( value(out(n1,not1(X0)),X1)
| ~ value(in(n2,and1(X0)),X1)
| ~ type(X0,halfadder) ),
inference(resolution,[status(thm)],[f96,f60]) ).
fof(f164,plain,
connection(in(n2,f),in(n1,h1(f))),
inference(resolution,[status(thm)],[f104,f108]) ).
fof(f166,plain,
! [X0] :
( value(in(n1,h1(f)),X0)
| ~ value(in(n2,f),X0) ),
inference(resolution,[status(thm)],[f164,f58]) ).
fof(f167,plain,
value(in(n1,h2(f)),n0),
inference(resolution,[status(thm)],[f161,f109]) ).
fof(f174,plain,
! [X0,X1] :
( value(out(n1,and1(X0)),X1)
| ~ value(out(s,X0),X1)
| ~ type(X0,halfadder) ),
inference(resolution,[status(thm)],[f92,f58]) ).
fof(f175,plain,
connection(in(c,f),in(n2,h1(f))),
inference(resolution,[status(thm)],[f105,f108]) ).
fof(f176,plain,
! [X0] :
( value(in(c,f),X0)
| ~ value(in(n2,h1(f)),X0) ),
inference(resolution,[status(thm)],[f175,f60]) ).
fof(f177,plain,
! [X0] :
( value(in(n2,h1(f)),X0)
| ~ value(in(c,f),X0) ),
inference(resolution,[status(thm)],[f175,f58]) ).
fof(f181,plain,
value(in(n1,h1(f)),n1),
inference(resolution,[status(thm)],[f166,f110]) ).
fof(f196,plain,
! [X0,X1] :
( ~ type(X0,fulladder)
| value(in(n1,or1(h2(X0))),X1)
| ~ value(in(n1,h2(X0)),X1) ),
inference(resolution,[status(thm)],[f141,f98]) ).
fof(f229,plain,
! [X0,X1] :
( ~ type(X0,fulladder)
| value(in(n2,or1(h1(X0))),X1)
| ~ value(in(n2,h1(X0)),X1) ),
inference(resolution,[status(thm)],[f143,f97]) ).
fof(f249,plain,
! [X0,X1] :
( ~ type(X0,fulladder)
| value(in(n1,and2(h2(X0))),X1)
| ~ value(in(n1,h2(X0)),X1) ),
inference(resolution,[status(thm)],[f145,f98]) ).
fof(f250,plain,
! [X0,X1] :
( ~ type(X0,fulladder)
| value(in(n1,and2(h1(X0))),X1)
| ~ value(in(n1,h1(X0)),X1) ),
inference(resolution,[status(thm)],[f145,f97]) ).
fof(f251,plain,
connection(out(s,f),out(s,h2(f))),
inference(resolution,[status(thm)],[f106,f108]) ).
fof(f253,plain,
! [X0] :
( value(out(s,h2(f)),X0)
| ~ value(out(s,f),X0) ),
inference(resolution,[status(thm)],[f251,f58]) ).
fof(f254,plain,
connection(out(c,f),out(n1,or1(f))),
inference(resolution,[status(thm)],[f107,f108]) ).
fof(f256,plain,
! [X0] :
( value(out(n1,or1(f)),X0)
| ~ value(out(c,f),X0) ),
inference(resolution,[status(thm)],[f254,f58]) ).
fof(f257,plain,
( ~ value(in(c,f),n1)
| ~ value(in(n2,h1(f)),n0) ),
inference(resolution,[status(thm)],[f176,f138]) ).
fof(f258,definition,
( sQ15_spl
<=> value(in(n2,h1(f)),n0) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f261,definition,
( sQ16_spl
<=> value(in(c,f),n1) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f263,plain,
( sQ16_spl
| ~ value(in(c,f),n1) ),
inference(component_clause,[status(thm)],[f261]) ).
fof(f264,plain,
( ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f257,f258,f261]) ).
fof(f287,definition,
( sQ21_spl
<=> value(in(n1,h1(f)),n0) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f288,plain,
( ~ sQ21_spl
| value(in(n1,h1(f)),n0) ),
inference(component_clause,[status(thm)],[f287]) ).
fof(f314,plain,
( ~ sQ21_spl
| ~ value(in(n1,h1(f)),n1) ),
inference(resolution,[status(thm)],[f288,f138]) ).
fof(f315,plain,
( ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f314,f181]) ).
fof(f316,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f315]) ).
fof(f326,definition,
! [X0] :
( sQ25_spl
<=> ~ value(in(X0,h1(f)),n1) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f327,plain,
! [X0] :
( ~ sQ25_spl
| ~ value(in(X0,h1(f)),n1) ),
inference(component_clause,[status(thm)],[f326]) ).
fof(f335,plain,
! [X0] :
( ~ type(X0,halfadder)
| value(in(n1,not1(X0)),n0)
| ~ value(out(n1,not1(X0)),n1)
| ~ mode(not1(X0),ok) ),
inference(resolution,[status(thm)],[f83,f86]) ).
fof(f336,plain,
connection(out(s,h1(f)),in(n2,h2(f))),
inference(resolution,[status(thm)],[f100,f108]) ).
fof(f349,plain,
! [X0] :
( ~ value(out(n1,and1(X0)),n1)
| ~ type(and1(X0),and)
| ~ mode(and1(X0),ok)
| value(out(n1,not1(X0)),n1)
| ~ type(X0,halfadder) ),
inference(resolution,[status(thm)],[f162,f73]) ).
fof(f350,plain,
! [X0] :
( ~ value(out(n1,and1(X0)),n1)
| ~ mode(and1(X0),ok)
| value(out(n1,not1(X0)),n1)
| ~ type(X0,halfadder) ),
inference(forward_subsumption_resolution,[status(thm)],[f349,f84]) ).
fof(f353,plain,
! [X0] :
( value(out(s,h1(f)),X0)
| ~ value(in(n2,h2(f)),X0) ),
inference(resolution,[status(thm)],[f336,f60]) ).
fof(f355,plain,
value(in(n2,h1(f)),n1),
inference(resolution,[status(thm)],[f177,f111]) ).
fof(f357,plain,
value(out(s,h2(f)),n1),
inference(resolution,[status(thm)],[f253,f112]) ).
fof(f359,plain,
connection(out(c,h1(f)),in(n2,or1(f))),
inference(resolution,[status(thm)],[f101,f108]) ).
fof(f364,plain,
! [X0] :
( value(in(n1,or1(h2(f))),X0)
| ~ value(in(n1,h2(f)),X0) ),
inference(resolution,[status(thm)],[f196,f108]) ).
fof(f365,plain,
value(in(n1,or1(h2(f))),n0),
inference(resolution,[status(thm)],[f364,f167]) ).
fof(f367,plain,
~ value(in(n1,or1(h2(f))),n1),
inference(resolution,[status(thm)],[f365,f138]) ).
fof(f368,definition,
( sQ29_spl
<=> type(h2(f),halfadder) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f370,plain,
( sQ29_spl
| ~ type(h2(f),halfadder) ),
inference(component_clause,[status(thm)],[f368]) ).
fof(f375,plain,
( sQ29_spl
| ~ type(f,fulladder) ),
inference(resolution,[status(thm)],[f370,f98]) ).
fof(f376,plain,
( sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f375,f108]) ).
fof(f377,plain,
sQ29_spl,
inference(contradiction_clause,[status(thm)],[f376]) ).
fof(f388,plain,
! [X0,X1] :
( mode(not1(X0),abnormal)
| ~ type(not1(X0),X1)
| ~ type(X0,halfadder)
| value(in(n1,not1(X0)),n0)
| ~ value(out(n1,not1(X0)),n1) ),
inference(resolution,[status(thm)],[f335,f67]) ).
fof(f389,plain,
! [X0] :
( value(out(c,h1(f)),X0)
| ~ value(in(n2,or1(f)),X0) ),
inference(resolution,[status(thm)],[f359,f60]) ).
fof(f407,definition,
( sQ34_spl
<=> mode(or1(f),ok) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f409,plain,
( sQ34_spl
| ~ mode(or1(f),ok) ),
inference(component_clause,[status(thm)],[f407]) ).
fof(f410,definition,
( sQ35_spl
<=> type(or1(f),or) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f412,plain,
( sQ35_spl
| ~ type(or1(f),or) ),
inference(component_clause,[status(thm)],[f410]) ).
fof(f427,plain,
! [X0] :
( sQ34_spl
| mode(or1(f),abnormal)
| ~ type(or1(f),X0) ),
inference(resolution,[status(thm)],[f409,f67]) ).
fof(f428,definition,
! [X0] :
( sQ40_spl
<=> ~ type(or1(f),X0) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f429,plain,
! [X0] :
( ~ sQ40_spl
| ~ type(or1(f),X0) ),
inference(component_clause,[status(thm)],[f428]) ).
fof(f431,plain,
( sQ34_spl
| sQ0_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f427,f428,f119,f407]) ).
fof(f432,plain,
( ~ sQ40_spl
| ~ type(f,fulladder) ),
inference(resolution,[status(thm)],[f429,f99]) ).
fof(f434,plain,
( ~ sQ40_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f432,f108]) ).
fof(f435,plain,
~ sQ40_spl,
inference(contradiction_clause,[status(thm)],[f434]) ).
fof(f452,definition,
( sQ43_spl
<=> mode(and1(h2(f)),ok) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f454,plain,
( sQ43_spl
| ~ mode(and1(h2(f)),ok) ),
inference(component_clause,[status(thm)],[f452]) ).
fof(f455,definition,
( sQ44_spl
<=> type(and1(h2(f)),and) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f457,plain,
( sQ44_spl
| ~ type(and1(h2(f)),and) ),
inference(component_clause,[status(thm)],[f455]) ).
fof(f462,plain,
( sQ44_spl
| ~ type(h2(f),halfadder) ),
inference(resolution,[status(thm)],[f457,f84]) ).
fof(f463,plain,
( sQ44_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f462,f368,f455]) ).
fof(f464,plain,
! [X0] :
( sQ43_spl
| mode(and1(h2(f)),abnormal)
| ~ type(and1(h2(f)),X0) ),
inference(resolution,[status(thm)],[f454,f67]) ).
fof(f465,definition,
! [X0] :
( sQ46_spl
<=> ~ type(and1(h2(f)),X0) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f466,plain,
! [X0] :
( ~ sQ46_spl
| ~ type(and1(h2(f)),X0) ),
inference(component_clause,[status(thm)],[f465]) ).
fof(f468,plain,
( sQ43_spl
| sQ3_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f464,f465,f130,f452]) ).
fof(f470,plain,
( ~ sQ46_spl
| ~ type(h2(f),halfadder) ),
inference(resolution,[status(thm)],[f466,f84]) ).
fof(f471,plain,
( ~ sQ46_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f470,f368,f465]) ).
fof(f472,plain,
( sQ35_spl
| ~ type(f,fulladder) ),
inference(resolution,[status(thm)],[f412,f99]) ).
fof(f474,plain,
( sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f472,f108]) ).
fof(f475,plain,
sQ35_spl,
inference(contradiction_clause,[status(thm)],[f474]) ).
fof(f478,plain,
! [X0,X1] :
( ~ type(X0,fulladder)
| value(out(n1,and1(h2(X0))),X1)
| ~ value(out(s,h2(X0)),X1) ),
inference(resolution,[status(thm)],[f174,f98]) ).
fof(f479,plain,
! [X0,X1] :
( ~ type(X0,fulladder)
| value(out(n1,and1(h1(X0))),X1)
| ~ value(out(s,h1(X0)),X1) ),
inference(resolution,[status(thm)],[f174,f97]) ).
fof(f492,definition,
( sQ49_spl
<=> value(in(n1,and1(h2(f))),n1) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f493,plain,
( ~ sQ49_spl
| value(in(n1,and1(h2(f))),n1) ),
inference(component_clause,[status(thm)],[f492]) ).
fof(f506,plain,
! [X0] :
( value(in(n2,or1(h1(f))),X0)
| ~ value(in(n2,h1(f)),X0) ),
inference(resolution,[status(thm)],[f229,f108]) ).
fof(f507,plain,
! [X0] :
( value(in(n1,and2(h2(f))),X0)
| ~ value(in(n1,h2(f)),X0) ),
inference(resolution,[status(thm)],[f249,f108]) ).
fof(f531,definition,
( sQ54_spl
<=> value(in(n2,or1(f)),n0) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f532,plain,
( ~ sQ54_spl
| value(in(n2,or1(f)),n0) ),
inference(component_clause,[status(thm)],[f531]) ).
fof(f537,plain,
! [X0] :
( value(in(n1,and2(h1(f))),X0)
| ~ value(in(n1,h1(f)),X0) ),
inference(resolution,[status(thm)],[f250,f108]) ).
fof(f538,plain,
( ~ sQ49_spl
| value(out(n1,or1(h2(f))),n1)
| ~ type(h2(f),halfadder) ),
inference(resolution,[status(thm)],[f493,f150]) ).
fof(f540,definition,
( sQ55_spl
<=> value(out(n1,or1(h2(f))),n1) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f541,plain,
( ~ sQ55_spl
| value(out(n1,or1(h2(f))),n1) ),
inference(component_clause,[status(thm)],[f540]) ).
fof(f543,plain,
( ~ sQ49_spl
| sQ55_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f538,f368,f540,f492]) ).
fof(f593,plain,
value(out(n1,or1(f)),n0),
inference(resolution,[status(thm)],[f256,f113]) ).
fof(f597,plain,
( ~ sQ55_spl
| 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)],[f541,f77]) ).
fof(f599,definition,
( sQ62_spl
<=> mode(or1(h2(f)),ok) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f601,plain,
( sQ62_spl
| ~ mode(or1(h2(f)),ok) ),
inference(component_clause,[status(thm)],[f599]) ).
fof(f609,definition,
( sQ65_spl
<=> type(or1(h2(f)),or) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f611,plain,
( sQ65_spl
| ~ type(or1(h2(f)),or) ),
inference(component_clause,[status(thm)],[f609]) ).
fof(f612,definition,
( sQ66_spl
<=> value(in(n1,or1(h2(f))),n1) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f613,plain,
( ~ sQ66_spl
| value(in(n1,or1(h2(f))),n1) ),
inference(component_clause,[status(thm)],[f612]) ).
fof(f615,definition,
( sQ67_spl
<=> value(in(n2,or1(h2(f))),n1) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f616,plain,
( ~ sQ67_spl
| value(in(n2,or1(h2(f))),n1) ),
inference(component_clause,[status(thm)],[f615]) ).
fof(f618,plain,
( ~ sQ55_spl
| sQ67_spl
| sQ66_spl
| ~ sQ65_spl
| ~ sQ62_spl ),
inference(split_clause,[status(thm)],[f597,f599,f609,f612,f615,f540]) ).
fof(f620,plain,
( ~ sQ66_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f613,f367]) ).
fof(f621,plain,
~ sQ66_spl,
inference(contradiction_clause,[status(thm)],[f620]) ).
fof(f622,plain,
! [X0] :
( sQ62_spl
| mode(or1(h2(f)),abnormal)
| ~ type(or1(h2(f)),X0) ),
inference(resolution,[status(thm)],[f601,f67]) ).
fof(f623,definition,
! [X0] :
( sQ68_spl
<=> ~ type(or1(h2(f)),X0) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f624,plain,
! [X0] :
( ~ sQ68_spl
| ~ type(or1(h2(f)),X0) ),
inference(component_clause,[status(thm)],[f623]) ).
fof(f626,plain,
( sQ62_spl
| sQ4_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f622,f623,f134,f599]) ).
fof(f629,plain,
( ~ sQ68_spl
| ~ type(h2(f),halfadder) ),
inference(resolution,[status(thm)],[f624,f87]) ).
fof(f630,plain,
( ~ sQ68_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f629,f368,f623]) ).
fof(f632,plain,
( sQ65_spl
| ~ type(h2(f),halfadder) ),
inference(resolution,[status(thm)],[f611,f87]) ).
fof(f633,plain,
( sQ65_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f632,f368,f609]) ).
fof(f663,plain,
! [X0,X1] :
( mode(and1(X0),abnormal)
| ~ type(and1(X0),X1)
| ~ value(out(n1,and1(X0)),n1)
| value(out(n1,not1(X0)),n1)
| ~ type(X0,halfadder) ),
inference(resolution,[status(thm)],[f350,f67]) ).
fof(f675,plain,
( ~ sQ67_spl
| value(in(n2,h2(f)),n1)
| ~ type(h2(f),halfadder) ),
inference(resolution,[status(thm)],[f616,f142]) ).
fof(f676,definition,
( sQ74_spl
<=> value(in(n2,h2(f)),n1) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f679,plain,
( ~ sQ67_spl
| sQ74_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f675,f368,f676,f615]) ).
fof(f685,plain,
( value(in(n2,or1(f)),n0)
| ~ type(or1(f),or)
| ~ mode(or1(f),ok) ),
inference(resolution,[status(thm)],[f593,f79]) ).
fof(f689,plain,
( sQ54_spl
| ~ sQ35_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f685,f407,f410,f531]) ).
fof(f754,definition,
( sQ85_spl
<=> value(out(s,h1(f)),n1) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f755,plain,
( ~ sQ85_spl
| value(out(s,h1(f)),n1) ),
inference(component_clause,[status(thm)],[f754]) ).
fof(f756,plain,
( sQ85_spl
| ~ value(out(s,h1(f)),n1) ),
inference(component_clause,[status(thm)],[f754]) ).
fof(f812,plain,
! [X0] :
( value(out(n1,and1(h2(f))),X0)
| ~ value(out(s,h2(f)),X0) ),
inference(resolution,[status(thm)],[f478,f108]) ).
fof(f839,plain,
! [X0] :
( value(out(n1,and1(h1(f))),X0)
| ~ value(out(s,h1(f)),X0) ),
inference(resolution,[status(thm)],[f479,f108]) ).
fof(f892,plain,
value(in(n2,or1(h1(f))),n1),
inference(resolution,[status(thm)],[f506,f355]) ).
fof(f930,definition,
! [X0] :
( sQ109_spl
<=> ~ value(in(X0,and2(h2(f))),n0) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f931,plain,
! [X0] :
( ~ sQ109_spl
| ~ value(in(X0,and2(h2(f))),n0) ),
inference(component_clause,[status(thm)],[f930]) ).
fof(f934,plain,
value(in(n1,and2(h2(f))),n0),
inference(resolution,[status(thm)],[f507,f167]) ).
fof(f950,plain,
value(in(n1,and2(h1(f))),n1),
inference(resolution,[status(thm)],[f537,f181]) ).
fof(f953,definition,
( sQ113_spl
<=> type(h1(f),halfadder) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f955,plain,
( sQ113_spl
| ~ type(h1(f),halfadder) ),
inference(component_clause,[status(thm)],[f953]) ).
fof(f959,definition,
! [X0] :
( sQ115_spl
<=> ~ type(and2(h1(f)),X0) ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f960,plain,
! [X0] :
( ~ sQ115_spl
| ~ type(and2(h1(f)),X0) ),
inference(component_clause,[status(thm)],[f959]) ).
fof(f963,plain,
( sQ113_spl
| ~ type(f,fulladder) ),
inference(resolution,[status(thm)],[f955,f97]) ).
fof(f964,plain,
( sQ113_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f963,f108]) ).
fof(f965,plain,
sQ113_spl,
inference(contradiction_clause,[status(thm)],[f964]) ).
fof(f976,plain,
( ~ sQ115_spl
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[f960,f85]) ).
fof(f977,plain,
( ~ sQ115_spl
| ~ sQ113_spl ),
inference(split_clause,[status(thm)],[f976,f953,f959]) ).
fof(f985,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f263,f111]) ).
fof(f986,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f985]) ).
fof(f987,plain,
! [X0] :
( sQ2_spl
| ~ type(not1(h1(f)),X0)
| ~ type(h1(f),halfadder)
| value(in(n1,not1(h1(f))),n0)
| ~ value(out(n1,not1(h1(f))),n1) ),
inference(resolution,[status(thm)],[f128,f388]) ).
fof(f988,definition,
( sQ116_spl
<=> value(out(n1,not1(h1(f))),n1) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f991,definition,
( sQ117_spl
<=> value(in(n1,not1(h1(f))),n0) ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f992,plain,
( ~ sQ117_spl
| value(in(n1,not1(h1(f))),n0) ),
inference(component_clause,[status(thm)],[f991]) ).
fof(f994,definition,
! [X0] :
( sQ118_spl
<=> ~ type(not1(h1(f)),X0) ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f995,plain,
! [X0] :
( ~ sQ118_spl
| ~ type(not1(h1(f)),X0) ),
inference(component_clause,[status(thm)],[f994]) ).
fof(f997,plain,
( sQ2_spl
| sQ118_spl
| ~ sQ113_spl
| sQ117_spl
| ~ sQ116_spl ),
inference(split_clause,[status(thm)],[f987,f988,f991,f953,f994,f126]) ).
fof(f998,plain,
( ~ sQ118_spl
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[f995,f86]) ).
fof(f999,plain,
( ~ sQ118_spl
| ~ sQ113_spl ),
inference(split_clause,[status(thm)],[f998,f953,f994]) ).
fof(f1012,plain,
( ~ sQ54_spl
| value(out(c,h1(f)),n0) ),
inference(resolution,[status(thm)],[f532,f389]) ).
fof(f1037,definition,
( sQ121_spl
<=> mode(and2(h1(f)),ok) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f1039,plain,
( sQ121_spl
| ~ mode(and2(h1(f)),ok) ),
inference(component_clause,[status(thm)],[f1037]) ).
fof(f1047,definition,
( sQ124_spl
<=> type(and2(h1(f)),and) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f1049,plain,
( sQ124_spl
| ~ type(and2(h1(f)),and) ),
inference(component_clause,[status(thm)],[f1047]) ).
fof(f1050,definition,
( sQ125_spl
<=> value(in(n1,and2(h1(f))),n1) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f1052,plain,
( sQ125_spl
| ~ value(in(n1,and2(h1(f))),n1) ),
inference(component_clause,[status(thm)],[f1050]) ).
fof(f1054,plain,
! [X0] :
( sQ121_spl
| mode(and2(h1(f)),abnormal)
| ~ type(and2(h1(f)),X0) ),
inference(resolution,[status(thm)],[f1039,f67]) ).
fof(f1055,definition,
( sQ126_spl
<=> mode(and2(h1(f)),abnormal) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f1056,plain,
( ~ sQ126_spl
| mode(and2(h1(f)),abnormal) ),
inference(component_clause,[status(thm)],[f1055]) ).
fof(f1058,plain,
( sQ121_spl
| sQ126_spl
| sQ115_spl ),
inference(split_clause,[status(thm)],[f1054,f959,f1055,f1037]) ).
fof(f1059,plain,
( ~ sQ126_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1056,f114]) ).
fof(f1060,plain,
~ sQ126_spl,
inference(contradiction_clause,[status(thm)],[f1059]) ).
fof(f1062,plain,
( ~ sQ117_spl
| value(out(n1,and2(h1(f))),n0)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[f992,f152]) ).
fof(f1068,definition,
( sQ128_spl
<=> value(out(n1,and2(h1(f))),n0) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f1069,plain,
( ~ sQ128_spl
| value(out(n1,and2(h1(f))),n0) ),
inference(component_clause,[status(thm)],[f1068]) ).
fof(f1071,plain,
( ~ sQ117_spl
| sQ128_spl
| ~ sQ113_spl ),
inference(split_clause,[status(thm)],[f1062,f953,f1068,f991]) ).
fof(f1075,plain,
( sQ124_spl
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[f1049,f85]) ).
fof(f1076,plain,
( sQ124_spl
| ~ sQ113_spl ),
inference(split_clause,[status(thm)],[f1075,f953,f1047]) ).
fof(f1122,definition,
( sQ137_spl
<=> value(in(n1,and2(h1(f))),n0) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f1123,plain,
( ~ sQ137_spl
| value(in(n1,and2(h1(f))),n0) ),
inference(component_clause,[status(thm)],[f1122]) ).
fof(f1125,definition,
( sQ138_spl
<=> value(in(n2,and2(h1(f))),n0) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f1126,plain,
( ~ sQ138_spl
| value(in(n2,and2(h1(f))),n0) ),
inference(component_clause,[status(thm)],[f1125]) ).
fof(f1135,definition,
! [X0] :
( sQ140_spl
<=> ~ value(in(X0,f),n0) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f1136,plain,
! [X0] :
( ~ sQ140_spl
| ~ value(in(X0,f),n0) ),
inference(component_clause,[status(thm)],[f1135]) ).
fof(f1139,plain,
( ~ sQ140_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f109,f1136]) ).
fof(f1141,plain,
~ sQ140_spl,
inference(contradiction_clause,[status(thm)],[f1139]) ).
fof(f1158,plain,
( ~ sQ25_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f355,f327]) ).
fof(f1161,plain,
~ sQ25_spl,
inference(contradiction_clause,[status(thm)],[f1158]) ).
fof(f1188,definition,
! [X0] :
( sQ147_spl
<=> ~ value(in(X0,or1(h1(f))),n1) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f1189,plain,
! [X0] :
( ~ sQ147_spl
| ~ value(in(X0,or1(h1(f))),n1) ),
inference(component_clause,[status(thm)],[f1188]) ).
fof(f1254,plain,
! [X0] :
( sQ1_spl
| ~ type(and1(h1(f)),X0)
| ~ value(out(n1,and1(h1(f))),n1)
| value(out(n1,not1(h1(f))),n1)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[f663,f124]) ).
fof(f1256,definition,
( sQ155_spl
<=> value(out(n1,and1(h1(f))),n1) ),
introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition]) ).
fof(f1258,plain,
( sQ155_spl
| ~ value(out(n1,and1(h1(f))),n1) ),
inference(component_clause,[status(thm)],[f1256]) ).
fof(f1259,definition,
! [X0] :
( sQ156_spl
<=> ~ type(and1(h1(f)),X0) ),
introduced(definition,[new_symbols(definition,[sQ156_spl])],[split_symbol_definition]) ).
fof(f1260,plain,
! [X0] :
( ~ sQ156_spl
| ~ type(and1(h1(f)),X0) ),
inference(component_clause,[status(thm)],[f1259]) ).
fof(f1262,plain,
( sQ1_spl
| sQ156_spl
| ~ sQ155_spl
| sQ116_spl
| ~ sQ113_spl ),
inference(split_clause,[status(thm)],[f1254,f953,f988,f1256,f1259,f122]) ).
fof(f1263,plain,
( ~ sQ156_spl
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[f1260,f84]) ).
fof(f1264,plain,
( ~ sQ156_spl
| ~ sQ113_spl ),
inference(split_clause,[status(thm)],[f1263,f953,f1259]) ).
fof(f1339,plain,
( ~ sQ137_spl
| value(in(n1,h1(f)),n0)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[f1123,f144]) ).
fof(f1342,plain,
( ~ sQ137_spl
| sQ21_spl
| ~ sQ113_spl ),
inference(split_clause,[status(thm)],[f1339,f953,f287,f1122]) ).
fof(f1352,plain,
value(out(n1,and1(h2(f))),n1),
inference(resolution,[status(thm)],[f812,f357]) ).
fof(f1355,plain,
( ~ sQ54_spl
| value(out(n1,and2(h1(f))),n0)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[f1012,f149]) ).
fof(f1357,plain,
( ~ sQ54_spl
| sQ128_spl
| ~ sQ113_spl ),
inference(split_clause,[status(thm)],[f1355,f953,f1068,f531]) ).
fof(f1373,plain,
( sQ85_spl
| ~ value(in(n2,h2(f)),n1) ),
inference(resolution,[status(thm)],[f756,f353]) ).
fof(f1374,plain,
( sQ85_spl
| ~ sQ74_spl ),
inference(split_clause,[status(thm)],[f1373,f676,f754]) ).
fof(f1468,plain,
( ~ sQ85_spl
| value(out(n1,and1(h1(f))),n1) ),
inference(resolution,[status(thm)],[f755,f839]) ).
fof(f1475,plain,
( ~ sQ128_spl
| value(in(n2,and2(h1(f))),n0)
| value(in(n1,and2(h1(f))),n0)
| ~ type(and2(h1(f)),and)
| ~ mode(and2(h1(f)),ok) ),
inference(resolution,[status(thm)],[f1069,f71]) ).
fof(f1480,plain,
( ~ sQ128_spl
| sQ138_spl
| sQ137_spl
| ~ sQ124_spl
| ~ sQ121_spl ),
inference(split_clause,[status(thm)],[f1475,f1037,f1047,f1122,f1125,f1068]) ).
fof(f1574,plain,
( sQ125_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f950,f1052]) ).
fof(f1575,plain,
sQ125_spl,
inference(contradiction_clause,[status(thm)],[f1574]) ).
fof(f1576,plain,
( ~ sQ138_spl
| value(in(n2,h1(f)),n0)
| ~ type(h1(f),halfadder) ),
inference(resolution,[status(thm)],[f1126,f146]) ).
fof(f1580,plain,
( ~ sQ138_spl
| sQ15_spl
| ~ sQ113_spl ),
inference(split_clause,[status(thm)],[f1576,f953,f258,f1125]) ).
fof(f1621,plain,
( ~ sQ147_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f892,f1189]) ).
fof(f1624,plain,
~ sQ147_spl,
inference(contradiction_clause,[status(thm)],[f1621]) ).
fof(f1625,plain,
( ~ sQ109_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f934,f931]) ).
fof(f1626,plain,
~ sQ109_spl,
inference(contradiction_clause,[status(thm)],[f1625]) ).
fof(f1693,plain,
( value(in(n1,and1(h2(f))),n1)
| ~ type(and1(h2(f)),and)
| ~ mode(and1(h2(f)),ok) ),
inference(resolution,[status(thm)],[f1352,f72]) ).
fof(f1696,plain,
( sQ49_spl
| ~ sQ44_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f1693,f452,f455,f492]) ).
fof(f1697,plain,
( ~ sQ85_spl
| sQ155_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1468,f1258]) ).
fof(f1698,plain,
( ~ sQ85_spl
| sQ155_spl ),
inference(contradiction_clause,[status(thm)],[f1697]) ).
fof(f1699,plain,
$false,
inference(sat_refutation,[status(thm)],[f125,f129,f133,f137,f264,f316,f377,f431,f435,f463,f468,f471,f475,f543,f618,f621,f626,f630,f633,f679,f689,f965,f977,f986,f997,f999,f1058,f1060,f1071,f1076,f1141,f1161,f1262,f1264,f1342,f1357,f1374,f1480,f1575,f1580,f1624,f1626,f1696,f1698]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HWV007-1 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.38 % Computer : n013.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 20 20:47:21 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.14/0.39 % Drodi V4.1.1
% 0.14/0.50 % Refutation found
% 0.14/0.50 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.54 % Elapsed time: 0.149642 seconds
% 0.14/0.54 % CPU time: 0.910428 seconds
% 0.14/0.54 % Total memory used: 28.815 MB
% 0.14/0.54 % Net memory used: 27.945 MB
%------------------------------------------------------------------------------