%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HWV008-2.002 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 12:45:55 PM UTC 2026
% Result : Unsatisfiable 0.07s 0.38s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 51
% Syntax : Number of formulae : 164 ( 29 unt; 22 def)
% Number of atoms : 340 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 327 ( 151 ~; 154 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 34 ( 33 usr; 23 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 1 con; 0-1 aty)
% Number of variables : 65 ( 65 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [P1,P2] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [P1,P2] :
( zero(P1)
| ~ zero(P2)
| ~ connection(P1,P2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [P] :
( ~ one(P)
| ~ zero(P) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [K] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [K] :
( abnormal(K)
| and_ok(K)
| ~ logic_and(K) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [K] :
( zero(out1(K))
| ~ zero(in2(K))
| ~ zero(in1(K))
| ~ or_ok(K) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [K] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [X] :
( logic_and(and2(X))
| ~ halfadder(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [X] :
( connection(in1(X),in1(and2(X)))
| ~ halfadder(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [X] :
( connection(outc(X),out1(and2(X)))
| ~ halfadder(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [X] :
( halfadder(h1(X))
| ~ fulladder(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [X] :
( halfadder(h2(X))
| ~ fulladder(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [X] :
( logic_or(or1(X))
| ~ fulladder(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [X] :
( connection(outc(h1(X)),in2(or1(X)))
| ~ fulladder(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [X] :
( connection(outc(h2(X)),in1(or1(X)))
| ~ fulladder(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [X] :
( connection(in1(X),in1(h2(X)))
| ~ fulladder(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [X] :
( connection(in2(X),in1(h1(X)))
| ~ fulladder(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [X] :
( connection(outc(X),out1(or1(X)))
| ~ fulladder(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,axiom,
! [X] :
( fulladder(f2(X))
| ~ nbit_adder2(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [X] :
( connection(outc(X),outc(f2(X)))
| ~ nbit_adder2(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,axiom,
! [X] :
( connection(ina2(X),in1(f2(X)))
| ~ nbit_adder2(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f60,axiom,
! [X] :
( connection(inb2(X),in2(f2(X)))
| ~ nbit_adder2(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f63,hypothesis,
nbit_adder2(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f65,hypothesis,
zero(ina2(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,hypothesis,
zero(inb2(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f71,hypothesis,
one(outc(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f72,negated_conjecture,
~ abnormal(or1(f2(a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f73,negated_conjecture,
~ abnormal(and2(h1(f2(a)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f74,negated_conjecture,
~ abnormal(and2(h2(f2(a)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f75,plain,
! [P2] :
( zero(P2)
| ! [P1] :
( ~ zero(P1)
| ~ connection(P1,P2) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f76,plain,
! [X0,X1] :
( zero(X1)
| ~ zero(X0)
| ~ connection(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f79,plain,
! [P1] :
( zero(P1)
| ! [P2] :
( ~ zero(P2)
| ~ connection(P1,P2) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f80,plain,
! [X0,X1] :
( zero(X0)
| ~ zero(X1)
| ~ connection(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f83,plain,
! [X0] :
( ~ one(X0)
| ~ zero(X0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f84,plain,
! [X0] :
( zero(out1(X0))
| ~ zero(in1(X0))
| ~ and_ok(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f91,plain,
! [X0] :
( abnormal(X0)
| and_ok(X0)
| ~ logic_and(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f94,plain,
! [X0] :
( zero(out1(X0))
| ~ zero(in2(X0))
| ~ zero(in1(X0))
| ~ or_ok(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f99,plain,
! [X0] :
( abnormal(X0)
| or_ok(X0)
| ~ logic_or(X0) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f107,plain,
! [X0] :
( logic_and(and2(X0))
| ~ halfadder(X0) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f112,plain,
! [X0] :
( connection(in1(X0),in1(and2(X0)))
| ~ halfadder(X0) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f115,plain,
! [X0] :
( connection(outc(X0),out1(and2(X0)))
| ~ halfadder(X0) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f119,plain,
! [X0] :
( halfadder(h1(X0))
| ~ fulladder(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f120,plain,
! [X0] :
( halfadder(h2(X0))
| ~ fulladder(X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f121,plain,
! [X0] :
( logic_or(or1(X0))
| ~ fulladder(X0) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f123,plain,
! [X0] :
( connection(outc(h1(X0)),in2(or1(X0)))
| ~ fulladder(X0) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f124,plain,
! [X0] :
( connection(outc(h2(X0)),in1(or1(X0)))
| ~ fulladder(X0) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f125,plain,
! [X0] :
( connection(in1(X0),in1(h2(X0)))
| ~ fulladder(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f126,plain,
! [X0] :
( connection(in2(X0),in1(h1(X0)))
| ~ fulladder(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f129,plain,
! [X0] :
( connection(outc(X0),out1(or1(X0)))
| ~ fulladder(X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f131,plain,
! [X0] :
( fulladder(f2(X0))
| ~ nbit_adder2(X0) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f134,plain,
! [X0] :
( connection(outc(X0),outc(f2(X0)))
| ~ nbit_adder2(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f137,plain,
! [X0] :
( connection(ina2(X0),in1(f2(X0)))
| ~ nbit_adder2(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f138,plain,
! [X0] :
( connection(inb2(X0),in2(f2(X0)))
| ~ nbit_adder2(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f141,plain,
nbit_adder2(a),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f143,plain,
zero(ina2(a)),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f145,plain,
zero(inb2(a)),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f149,plain,
one(outc(a)),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f150,plain,
~ abnormal(or1(f2(a))),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f151,plain,
~ abnormal(and2(h1(f2(a)))),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f152,plain,
~ abnormal(and2(h2(f2(a)))),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f155,plain,
! [X0] :
( ~ halfadder(X0)
| zero(in1(and2(X0)))
| ~ zero(in1(X0)) ),
inference(resolution,[status(thm)],[f76,f112]) ).
fof(f161,plain,
! [X0] :
( zero(outc(X0))
| ~ zero(out1(and2(X0)))
| ~ halfadder(X0) ),
inference(resolution,[status(thm)],[f115,f80]) ).
fof(f163,plain,
! [X0] :
( ~ nbit_adder2(X0)
| connection(in1(f2(X0)),in1(h2(f2(X0)))) ),
inference(resolution,[status(thm)],[f125,f131]) ).
fof(f164,plain,
! [X0] :
( ~ nbit_adder2(X0)
| connection(in2(f2(X0)),in1(h1(f2(X0)))) ),
inference(resolution,[status(thm)],[f126,f131]) ).
fof(f165,plain,
! [X0] :
( ~ nbit_adder2(X0)
| connection(outc(h1(f2(X0))),in2(or1(f2(X0)))) ),
inference(resolution,[status(thm)],[f123,f131]) ).
fof(f166,plain,
! [X0] :
( ~ nbit_adder2(X0)
| connection(outc(h2(f2(X0))),in1(or1(f2(X0)))) ),
inference(resolution,[status(thm)],[f124,f131]) ).
fof(f171,plain,
~ zero(outc(a)),
inference(resolution,[status(thm)],[f149,f83]) ).
fof(f179,plain,
! [X0] :
( ~ zero(in1(and2(X0)))
| ~ and_ok(and2(X0))
| zero(outc(X0))
| ~ halfadder(X0) ),
inference(resolution,[status(thm)],[f161,f84]) ).
fof(f200,plain,
connection(in1(f2(a)),in1(h2(f2(a)))),
inference(resolution,[status(thm)],[f163,f141]) ).
fof(f201,plain,
connection(in2(f2(a)),in1(h1(f2(a)))),
inference(resolution,[status(thm)],[f164,f141]) ).
fof(f202,plain,
! [X0] :
( ~ halfadder(X0)
| abnormal(and2(X0))
| and_ok(and2(X0)) ),
inference(resolution,[status(thm)],[f91,f107]) ).
fof(f204,plain,
! [X0] :
( ~ fulladder(X0)
| abnormal(or1(X0))
| or_ok(or1(X0)) ),
inference(resolution,[status(thm)],[f99,f121]) ).
fof(f232,plain,
( zero(in1(h2(f2(a))))
| ~ zero(in1(f2(a))) ),
inference(resolution,[status(thm)],[f200,f76]) ).
fof(f233,definition,
( sQ9_spl
<=> zero(in1(h2(f2(a)))) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f236,definition,
( sQ10_spl
<=> zero(in1(f2(a))) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f240,plain,
( sQ9_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f232,f236,f233]) ).
fof(f241,plain,
connection(outc(h1(f2(a))),in2(or1(f2(a)))),
inference(resolution,[status(thm)],[f165,f141]) ).
fof(f243,plain,
( zero(in1(h1(f2(a))))
| ~ zero(in2(f2(a))) ),
inference(resolution,[status(thm)],[f201,f76]) ).
fof(f244,definition,
( sQ11_spl
<=> zero(in1(h1(f2(a)))) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f247,definition,
( sQ12_spl
<=> zero(in2(f2(a))) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f251,plain,
( sQ11_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f243,f247,f244]) ).
fof(f262,plain,
connection(outc(h2(f2(a))),in1(or1(f2(a)))),
inference(resolution,[status(thm)],[f166,f141]) ).
fof(f281,plain,
( zero(in2(or1(f2(a))))
| ~ zero(outc(h1(f2(a)))) ),
inference(resolution,[status(thm)],[f241,f76]) ).
fof(f282,definition,
( sQ18_spl
<=> zero(in2(or1(f2(a)))) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f285,definition,
( sQ19_spl
<=> zero(outc(h1(f2(a)))) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f289,plain,
( sQ18_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f281,f285,f282]) ).
fof(f296,plain,
( zero(in1(or1(f2(a))))
| ~ zero(outc(h2(f2(a)))) ),
inference(resolution,[status(thm)],[f262,f76]) ).
fof(f297,definition,
( sQ21_spl
<=> zero(in1(or1(f2(a)))) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f300,definition,
( sQ22_spl
<=> zero(outc(h2(f2(a)))) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f304,plain,
( sQ21_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f296,f300,f297]) ).
fof(f316,plain,
! [X0] :
( ~ nbit_adder2(X0)
| connection(outc(f2(X0)),out1(or1(f2(X0)))) ),
inference(resolution,[status(thm)],[f129,f131]) ).
fof(f327,plain,
connection(outc(f2(a)),out1(or1(f2(a)))),
inference(resolution,[status(thm)],[f316,f141]) ).
fof(f333,plain,
( zero(outc(f2(a)))
| ~ zero(out1(or1(f2(a)))) ),
inference(resolution,[status(thm)],[f327,f80]) ).
fof(f335,definition,
( sQ26_spl
<=> zero(out1(or1(f2(a)))) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f338,definition,
( sQ27_spl
<=> zero(outc(f2(a))) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f341,plain,
( sQ27_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f333,f335,f338]) ).
fof(f378,plain,
connection(outc(a),outc(f2(a))),
inference(resolution,[status(thm)],[f134,f141]) ).
fof(f380,plain,
( zero(outc(a))
| ~ zero(outc(f2(a))) ),
inference(resolution,[status(thm)],[f378,f80]) ).
fof(f382,definition,
( sQ33_spl
<=> zero(outc(a)) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f383,plain,
( ~ sQ33_spl
| zero(outc(a)) ),
inference(component_clause,[status(thm)],[f382]) ).
fof(f385,plain,
( sQ33_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f380,f338,f382]) ).
fof(f408,definition,
( sQ35_spl
<=> or_ok(or1(f2(a))) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f409,plain,
( ~ sQ35_spl
| or_ok(or1(f2(a))) ),
inference(component_clause,[status(thm)],[f408]) ).
fof(f506,plain,
connection(ina2(a),in1(f2(a))),
inference(resolution,[status(thm)],[f137,f141]) ).
fof(f508,plain,
( zero(in1(f2(a)))
| ~ zero(ina2(a)) ),
inference(resolution,[status(thm)],[f506,f76]) ).
fof(f509,definition,
( sQ49_spl
<=> zero(ina2(a)) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f511,plain,
( sQ49_spl
| ~ zero(ina2(a)) ),
inference(component_clause,[status(thm)],[f509]) ).
fof(f513,plain,
( sQ10_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f508,f509,f236]) ).
fof(f514,plain,
connection(inb2(a),in2(f2(a))),
inference(resolution,[status(thm)],[f138,f141]) ).
fof(f517,plain,
! [X0] :
( ~ fulladder(X0)
| abnormal(and2(h2(X0)))
| and_ok(and2(h2(X0))) ),
inference(resolution,[status(thm)],[f202,f120]) ).
fof(f518,plain,
! [X0] :
( ~ fulladder(X0)
| abnormal(and2(h1(X0)))
| and_ok(and2(h1(X0))) ),
inference(resolution,[status(thm)],[f202,f119]) ).
fof(f520,plain,
( zero(in2(f2(a)))
| ~ zero(inb2(a)) ),
inference(resolution,[status(thm)],[f514,f76]) ).
fof(f521,definition,
( sQ50_spl
<=> zero(inb2(a)) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f523,plain,
( sQ50_spl
| ~ zero(inb2(a)) ),
inference(component_clause,[status(thm)],[f521]) ).
fof(f525,plain,
( sQ12_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f520,f521,f247]) ).
fof(f589,plain,
( ~ fulladder(f2(a))
| and_ok(and2(h2(f2(a)))) ),
inference(resolution,[status(thm)],[f517,f152]) ).
fof(f591,definition,
( sQ62_spl
<=> and_ok(and2(h2(f2(a)))) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f592,plain,
( ~ sQ62_spl
| and_ok(and2(h2(f2(a)))) ),
inference(component_clause,[status(thm)],[f591]) ).
fof(f594,definition,
( sQ63_spl
<=> fulladder(f2(a)) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f596,plain,
( sQ63_spl
| ~ fulladder(f2(a)) ),
inference(component_clause,[status(thm)],[f594]) ).
fof(f597,plain,
( ~ sQ63_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f589,f591,f594]) ).
fof(f598,plain,
( ~ fulladder(f2(a))
| and_ok(and2(h1(f2(a)))) ),
inference(resolution,[status(thm)],[f518,f151]) ).
fof(f600,definition,
( sQ64_spl
<=> and_ok(and2(h1(f2(a)))) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f601,plain,
( ~ sQ64_spl
| and_ok(and2(h1(f2(a)))) ),
inference(component_clause,[status(thm)],[f600]) ).
fof(f603,plain,
( ~ sQ63_spl
| sQ64_spl ),
inference(split_clause,[status(thm)],[f598,f600,f594]) ).
fof(f604,plain,
( sQ63_spl
| ~ nbit_adder2(a) ),
inference(resolution,[status(thm)],[f596,f131]) ).
fof(f605,plain,
( sQ63_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f604,f141]) ).
fof(f606,plain,
sQ63_spl,
inference(contradiction_clause,[status(thm)],[f605]) ).
fof(f619,plain,
( ~ sQ62_spl
| ~ zero(in1(and2(h2(f2(a)))))
| zero(outc(h2(f2(a))))
| ~ halfadder(h2(f2(a))) ),
inference(resolution,[status(thm)],[f592,f179]) ).
fof(f622,definition,
( sQ65_spl
<=> halfadder(h2(f2(a))) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f624,plain,
( sQ65_spl
| ~ halfadder(h2(f2(a))) ),
inference(component_clause,[status(thm)],[f622]) ).
fof(f625,definition,
( sQ66_spl
<=> zero(in1(and2(h2(f2(a))))) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f627,plain,
( sQ66_spl
| ~ zero(in1(and2(h2(f2(a))))) ),
inference(component_clause,[status(thm)],[f625]) ).
fof(f628,plain,
( ~ sQ62_spl
| ~ sQ66_spl
| sQ22_spl
| ~ sQ65_spl ),
inference(split_clause,[status(thm)],[f619,f622,f300,f625,f591]) ).
fof(f637,plain,
( sQ65_spl
| ~ fulladder(f2(a)) ),
inference(resolution,[status(thm)],[f624,f120]) ).
fof(f638,plain,
( sQ65_spl
| ~ sQ63_spl ),
inference(split_clause,[status(thm)],[f637,f594,f622]) ).
fof(f649,plain,
! [X0] :
( ~ nbit_adder2(X0)
| abnormal(or1(f2(X0)))
| or_ok(or1(f2(X0))) ),
inference(resolution,[status(thm)],[f204,f131]) ).
fof(f657,definition,
( sQ72_spl
<=> abnormal(or1(f2(a))) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f658,plain,
( ~ sQ72_spl
| abnormal(or1(f2(a))) ),
inference(component_clause,[status(thm)],[f657]) ).
fof(f661,plain,
( ~ sQ72_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f658,f150]) ).
fof(f662,plain,
~ sQ72_spl,
inference(contradiction_clause,[status(thm)],[f661]) ).
fof(f674,plain,
( ~ sQ64_spl
| ~ zero(in1(and2(h1(f2(a)))))
| zero(outc(h1(f2(a))))
| ~ halfadder(h1(f2(a))) ),
inference(resolution,[status(thm)],[f601,f179]) ).
fof(f677,definition,
( sQ75_spl
<=> halfadder(h1(f2(a))) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f679,plain,
( sQ75_spl
| ~ halfadder(h1(f2(a))) ),
inference(component_clause,[status(thm)],[f677]) ).
fof(f680,definition,
( sQ76_spl
<=> zero(in1(and2(h1(f2(a))))) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f682,plain,
( sQ76_spl
| ~ zero(in1(and2(h1(f2(a))))) ),
inference(component_clause,[status(thm)],[f680]) ).
fof(f683,plain,
( ~ sQ64_spl
| ~ sQ76_spl
| sQ19_spl
| ~ sQ75_spl ),
inference(split_clause,[status(thm)],[f674,f677,f285,f680,f600]) ).
fof(f692,plain,
( sQ75_spl
| ~ fulladder(f2(a)) ),
inference(resolution,[status(thm)],[f679,f119]) ).
fof(f693,plain,
( sQ75_spl
| ~ sQ63_spl ),
inference(split_clause,[status(thm)],[f692,f594,f677]) ).
fof(f722,plain,
( ~ sQ35_spl
| zero(out1(or1(f2(a))))
| ~ zero(in2(or1(f2(a))))
| ~ zero(in1(or1(f2(a)))) ),
inference(resolution,[status(thm)],[f409,f94]) ).
fof(f726,plain,
( ~ sQ35_spl
| sQ26_spl
| ~ sQ18_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f722,f297,f282,f335,f408]) ).
fof(f729,plain,
( ~ sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f383,f171]) ).
fof(f730,plain,
~ sQ33_spl,
inference(contradiction_clause,[status(thm)],[f729]) ).
fof(f733,plain,
( abnormal(or1(f2(a)))
| or_ok(or1(f2(a))) ),
inference(resolution,[status(thm)],[f649,f141]) ).
fof(f734,plain,
( sQ72_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f733,f408,f657]) ).
fof(f854,plain,
( sQ50_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f523,f145]) ).
fof(f855,plain,
sQ50_spl,
inference(contradiction_clause,[status(thm)],[f854]) ).
fof(f876,plain,
( sQ66_spl
| ~ halfadder(h2(f2(a)))
| ~ zero(in1(h2(f2(a)))) ),
inference(resolution,[status(thm)],[f627,f155]) ).
fof(f877,plain,
( sQ66_spl
| ~ sQ65_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f876,f233,f622,f625]) ).
fof(f878,plain,
( sQ49_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f511,f143]) ).
fof(f879,plain,
sQ49_spl,
inference(contradiction_clause,[status(thm)],[f878]) ).
fof(f958,plain,
( sQ76_spl
| ~ halfadder(h1(f2(a)))
| ~ zero(in1(h1(f2(a)))) ),
inference(resolution,[status(thm)],[f682,f155]) ).
fof(f959,plain,
( sQ76_spl
| ~ sQ75_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f958,f244,f677,f680]) ).
fof(f960,plain,
$false,
inference(sat_refutation,[status(thm)],[f240,f251,f289,f304,f341,f385,f513,f525,f597,f603,f606,f628,f638,f662,f683,f693,f726,f730,f734,f855,f877,f879,f959]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HWV008-2.002 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n016.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sun Sep 20 20:52:38 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 0.07/0.38 % Refutation found
% 0.07/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.07/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.40 % Elapsed time: 0.054385 seconds
% 0.11/0.40 % CPU time: 0.152448 seconds
% 0.11/0.40 % Total memory used: 19.434 MB
% 0.11/0.40 % Net memory used: 19.387 MB
%------------------------------------------------------------------------------