%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HWV008-2.001 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 0.20s 5.60s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 55
% Syntax : Number of formulae : 179 ( 17 unt; 24 def)
% Number of atoms : 403 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 423 ( 199 ~; 200 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 36 ( 35 usr; 25 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 1 con; 0-1 aty)
% Number of variables : 79 ( 79 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [P1,P2] :
( zero(P2)
| ~ zero(P1)
| ~ connection(P1,P2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [P1,P2] :
( one(P2)
| ~ one(P1)
| ~ connection(P1,P2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [P1,P2] :
( zero(P1)
| ~ zero(P2)
| ~ connection(P1,P2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [P1,P2] :
( one(P1)
| ~ one(P2)
| ~ connection(P1,P2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [P] :
( ~ one(P)
| ~ zero(P) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [K] :
( zero(out1(K))
| ~ zero(in1(K))
| ~ and_ok(K) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [K] :
( abnormal(K)
| and_ok(K)
| ~ logic_and(K) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [K] :
( one(in2(K))
| one(in1(K))
| ~ one(out1(K))
| ~ or_ok(K) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [K] :
( abnormal(K)
| or_ok(K)
| ~ logic_or(K) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [X] :
( logic_and(and2(X))
| ~ halfadder(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [X] :
( connection(in1(X),in1(and2(X)))
| ~ halfadder(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [X] :
( connection(outc(X),out1(and2(X)))
| ~ halfadder(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [X] :
( halfadder(h1(X))
| ~ fulladder(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [X] :
( halfadder(h2(X))
| ~ fulladder(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [X] :
( logic_or(or1(X))
| ~ fulladder(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [X] :
( connection(outc(h1(X)),in2(or1(X)))
| ~ fulladder(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [X] :
( connection(outc(h2(X)),in1(or1(X)))
| ~ fulladder(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [X] :
( connection(in1(X),in1(h2(X)))
| ~ fulladder(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [X] :
( connection(in2(X),in1(h1(X)))
| ~ fulladder(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [X] :
( connection(outc(X),out1(or1(X)))
| ~ fulladder(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,axiom,
! [X] :
( fulladder(f1(X))
| ~ nbit_adder1(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,axiom,
! [X] :
( connection(outc(X),outc(f1(X)))
| ~ nbit_adder1(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [X] :
( connection(ina1(X),in1(f1(X)))
| ~ nbit_adder1(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [X] :
( connection(inb1(X),in2(f1(X)))
| ~ nbit_adder1(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,hypothesis,
nbit_adder1(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f59,hypothesis,
zero(ina1(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,hypothesis,
zero(inb1(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f63,hypothesis,
one(outc(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f64,negated_conjecture,
~ abnormal(or1(f1(a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,negated_conjecture,
~ abnormal(and2(h1(f1(a)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66,negated_conjecture,
~ abnormal(and2(h2(f1(a)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f67,plain,
! [P2] :
( zero(P2)
| ! [P1] :
( ~ zero(P1)
| ~ connection(P1,P2) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f68,plain,
! [X0,X1] :
( zero(X1)
| ~ zero(X0)
| ~ connection(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
! [P2] :
( one(P2)
| ! [P1] :
( ~ one(P1)
| ~ connection(P1,P2) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f70,plain,
! [X0,X1] :
( one(X1)
| ~ one(X0)
| ~ connection(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
! [P1] :
( zero(P1)
| ! [P2] :
( ~ zero(P2)
| ~ connection(P1,P2) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f72,plain,
! [X0,X1] :
( zero(X0)
| ~ zero(X1)
| ~ connection(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f73,plain,
! [P1] :
( one(P1)
| ! [P2] :
( ~ one(P2)
| ~ connection(P1,P2) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f74,plain,
! [X0,X1] :
( one(X0)
| ~ one(X1)
| ~ connection(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f75,plain,
! [X0] :
( ~ one(X0)
| ~ zero(X0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f76,plain,
! [X0] :
( zero(out1(X0))
| ~ zero(in1(X0))
| ~ and_ok(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f83,plain,
! [X0] :
( abnormal(X0)
| and_ok(X0)
| ~ logic_and(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f87,plain,
! [X0] :
( one(in2(X0))
| one(in1(X0))
| ~ one(out1(X0))
| ~ or_ok(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f91,plain,
! [X0] :
( abnormal(X0)
| or_ok(X0)
| ~ logic_or(X0) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f99,plain,
! [X0] :
( logic_and(and2(X0))
| ~ halfadder(X0) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f104,plain,
! [X0] :
( connection(in1(X0),in1(and2(X0)))
| ~ halfadder(X0) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f107,plain,
! [X0] :
( connection(outc(X0),out1(and2(X0)))
| ~ halfadder(X0) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f111,plain,
! [X0] :
( halfadder(h1(X0))
| ~ fulladder(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f112,plain,
! [X0] :
( halfadder(h2(X0))
| ~ fulladder(X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f113,plain,
! [X0] :
( logic_or(or1(X0))
| ~ fulladder(X0) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f115,plain,
! [X0] :
( connection(outc(h1(X0)),in2(or1(X0)))
| ~ fulladder(X0) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f116,plain,
! [X0] :
( connection(outc(h2(X0)),in1(or1(X0)))
| ~ fulladder(X0) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f117,plain,
! [X0] :
( connection(in1(X0),in1(h2(X0)))
| ~ fulladder(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f118,plain,
! [X0] :
( connection(in2(X0),in1(h1(X0)))
| ~ fulladder(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f121,plain,
! [X0] :
( connection(outc(X0),out1(or1(X0)))
| ~ fulladder(X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f122,plain,
! [X0] :
( fulladder(f1(X0))
| ~ nbit_adder1(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f124,plain,
! [X0] :
( connection(outc(X0),outc(f1(X0)))
| ~ nbit_adder1(X0) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f125,plain,
! [X0] :
( connection(ina1(X0),in1(f1(X0)))
| ~ nbit_adder1(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f126,plain,
! [X0] :
( connection(inb1(X0),in2(f1(X0)))
| ~ nbit_adder1(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f128,plain,
nbit_adder1(a),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f129,plain,
zero(ina1(a)),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f130,plain,
zero(inb1(a)),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f133,plain,
one(outc(a)),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f134,plain,
~ abnormal(or1(f1(a))),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f135,plain,
~ abnormal(and2(h1(f1(a)))),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f136,plain,
~ abnormal(and2(h2(f1(a)))),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f139,plain,
! [X0] :
( zero(X0)
| ~ connection(inb1(a),X0) ),
inference(resolution,[status(thm)],[f68,f130]) ).
fof(f140,plain,
! [X0] :
( zero(X0)
| ~ connection(ina1(a),X0) ),
inference(resolution,[status(thm)],[f68,f129]) ).
fof(f142,plain,
! [X0] :
( one(X0)
| ~ connection(outc(a),X0) ),
inference(resolution,[status(thm)],[f70,f133]) ).
fof(f148,plain,
! [X0] :
( ~ halfadder(X0)
| abnormal(and2(X0))
| and_ok(and2(X0)) ),
inference(resolution,[status(thm)],[f83,f99]) ).
fof(f150,plain,
! [X0] :
( ~ fulladder(X0)
| abnormal(or1(X0))
| or_ok(or1(X0)) ),
inference(resolution,[status(thm)],[f91,f113]) ).
fof(f183,definition,
( sQ6_spl
<=> nbit_adder1(a) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( sQ6_spl
| ~ nbit_adder1(a) ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f190,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f185,f128]) ).
fof(f191,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f190]) ).
fof(f204,definition,
( sQ10_spl
<=> fulladder(f1(a)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f206,plain,
( sQ10_spl
| ~ fulladder(f1(a)) ),
inference(component_clause,[status(thm)],[f204]) ).
fof(f221,plain,
( sQ10_spl
| ~ nbit_adder1(a) ),
inference(resolution,[status(thm)],[f206,f122]) ).
fof(f222,plain,
( sQ10_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f221,f183,f204]) ).
fof(f225,plain,
( one(outc(f1(a)))
| ~ nbit_adder1(a) ),
inference(resolution,[status(thm)],[f124,f142]) ).
fof(f226,definition,
( sQ13_spl
<=> one(outc(f1(a))) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f227,plain,
( ~ sQ13_spl
| one(outc(f1(a))) ),
inference(component_clause,[status(thm)],[f226]) ).
fof(f229,plain,
( sQ13_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f225,f183,f226]) ).
fof(f231,plain,
! [X0] :
( ~ sQ13_spl
| one(X0)
| ~ connection(outc(f1(a)),X0) ),
inference(resolution,[status(thm)],[f227,f70]) ).
fof(f236,plain,
( ~ sQ13_spl
| ~ fulladder(f1(a))
| one(out1(or1(f1(a)))) ),
inference(resolution,[status(thm)],[f231,f121]) ).
fof(f245,definition,
( sQ16_spl
<=> one(out1(or1(f1(a)))) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f246,plain,
( ~ sQ16_spl
| one(out1(or1(f1(a)))) ),
inference(component_clause,[status(thm)],[f245]) ).
fof(f248,plain,
( ~ sQ13_spl
| ~ sQ10_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f236,f245,f204,f226]) ).
fof(f253,plain,
( ~ sQ16_spl
| one(in2(or1(f1(a))))
| one(in1(or1(f1(a))))
| ~ or_ok(or1(f1(a))) ),
inference(resolution,[status(thm)],[f246,f87]) ).
fof(f260,definition,
( sQ18_spl
<=> or_ok(or1(f1(a))) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f263,definition,
( sQ19_spl
<=> one(in1(or1(f1(a)))) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f264,plain,
( ~ sQ19_spl
| one(in1(or1(f1(a)))) ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f266,definition,
( sQ20_spl
<=> one(in2(or1(f1(a)))) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f267,plain,
( ~ sQ20_spl
| one(in2(or1(f1(a)))) ),
inference(component_clause,[status(thm)],[f266]) ).
fof(f269,plain,
( ~ sQ16_spl
| sQ20_spl
| sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f253,f260,f263,f266,f245]) ).
fof(f294,definition,
( sQ27_spl
<=> halfadder(h2(f1(a))) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f296,plain,
( sQ27_spl
| ~ halfadder(h2(f1(a))) ),
inference(component_clause,[status(thm)],[f294]) ).
fof(f308,plain,
( sQ27_spl
| ~ fulladder(f1(a)) ),
inference(resolution,[status(thm)],[f296,f112]) ).
fof(f309,plain,
( sQ27_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f308,f204,f294]) ).
fof(f317,plain,
! [X0] :
( ~ sQ19_spl
| one(X0)
| ~ connection(X0,in1(or1(f1(a)))) ),
inference(resolution,[status(thm)],[f264,f74]) ).
fof(f325,plain,
( zero(in1(f1(a)))
| ~ nbit_adder1(a) ),
inference(resolution,[status(thm)],[f125,f140]) ).
fof(f326,definition,
( sQ29_spl
<=> zero(in1(f1(a))) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f327,plain,
( ~ sQ29_spl
| zero(in1(f1(a))) ),
inference(component_clause,[status(thm)],[f326]) ).
fof(f329,plain,
( sQ29_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f325,f183,f326]) ).
fof(f333,plain,
! [X0] :
( ~ sQ29_spl
| zero(X0)
| ~ connection(in1(f1(a)),X0) ),
inference(resolution,[status(thm)],[f327,f68]) ).
fof(f348,plain,
( zero(in2(f1(a)))
| ~ nbit_adder1(a) ),
inference(resolution,[status(thm)],[f126,f139]) ).
fof(f349,definition,
( sQ34_spl
<=> zero(in2(f1(a))) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f350,plain,
( ~ sQ34_spl
| zero(in2(f1(a))) ),
inference(component_clause,[status(thm)],[f349]) ).
fof(f352,plain,
( sQ34_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f348,f183,f349]) ).
fof(f358,plain,
( ~ halfadder(h2(f1(a)))
| and_ok(and2(h2(f1(a)))) ),
inference(resolution,[status(thm)],[f148,f136]) ).
fof(f359,plain,
( ~ halfadder(h1(f1(a)))
| and_ok(and2(h1(f1(a)))) ),
inference(resolution,[status(thm)],[f148,f135]) ).
fof(f361,definition,
( sQ36_spl
<=> and_ok(and2(h2(f1(a)))) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f364,plain,
( ~ sQ27_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f358,f361,f294]) ).
fof(f365,definition,
( sQ37_spl
<=> and_ok(and2(h1(f1(a)))) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f368,definition,
( sQ38_spl
<=> halfadder(h1(f1(a))) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f370,plain,
( sQ38_spl
| ~ halfadder(h1(f1(a))) ),
inference(component_clause,[status(thm)],[f368]) ).
fof(f371,plain,
( ~ sQ38_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f359,f365,f368]) ).
fof(f373,definition,
( sQ39_spl
<=> zero(out1(and2(h2(f1(a))))) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f374,plain,
( ~ sQ39_spl
| zero(out1(and2(h2(f1(a))))) ),
inference(component_clause,[status(thm)],[f373]) ).
fof(f376,definition,
( sQ40_spl
<=> zero(in1(and2(h2(f1(a))))) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f377,plain,
( ~ sQ40_spl
| zero(in1(and2(h2(f1(a))))) ),
inference(component_clause,[status(thm)],[f376]) ).
fof(f384,definition,
( sQ42_spl
<=> zero(out1(and2(h1(f1(a))))) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f385,plain,
( ~ sQ42_spl
| zero(out1(and2(h1(f1(a))))) ),
inference(component_clause,[status(thm)],[f384]) ).
fof(f387,definition,
( sQ43_spl
<=> zero(in1(and2(h1(f1(a))))) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f388,plain,
( ~ sQ43_spl
| zero(in1(and2(h1(f1(a))))) ),
inference(component_clause,[status(thm)],[f387]) ).
fof(f394,plain,
( sQ38_spl
| ~ fulladder(f1(a)) ),
inference(resolution,[status(thm)],[f370,f111]) ).
fof(f395,plain,
( sQ38_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f394,f204,f368]) ).
fof(f416,plain,
! [X0] :
( ~ sQ39_spl
| zero(X0)
| ~ connection(X0,out1(and2(h2(f1(a))))) ),
inference(resolution,[status(thm)],[f374,f72]) ).
fof(f418,plain,
! [X0] :
( ~ sQ42_spl
| zero(X0)
| ~ connection(X0,out1(and2(h1(f1(a))))) ),
inference(resolution,[status(thm)],[f385,f72]) ).
fof(f428,plain,
! [X0] :
( ~ sQ34_spl
| zero(X0)
| ~ connection(in2(f1(a)),X0) ),
inference(resolution,[status(thm)],[f350,f68]) ).
fof(f443,plain,
( ~ sQ29_spl
| ~ fulladder(f1(a))
| zero(in1(h2(f1(a)))) ),
inference(resolution,[status(thm)],[f333,f117]) ).
fof(f446,definition,
( sQ50_spl
<=> zero(in1(h2(f1(a)))) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f447,plain,
( ~ sQ50_spl
| zero(in1(h2(f1(a)))) ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f449,plain,
( ~ sQ29_spl
| ~ sQ10_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f443,f446,f204,f326]) ).
fof(f466,plain,
! [X0] :
( ~ sQ50_spl
| zero(X0)
| ~ connection(in1(h2(f1(a))),X0) ),
inference(resolution,[status(thm)],[f447,f68]) ).
fof(f483,plain,
! [X0] :
( ~ nbit_adder1(X0)
| abnormal(or1(f1(X0)))
| or_ok(or1(f1(X0))) ),
inference(resolution,[status(thm)],[f150,f122]) ).
fof(f484,definition,
( sQ56_spl
<=> abnormal(or1(f1(a))) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f485,plain,
( ~ sQ56_spl
| abnormal(or1(f1(a))) ),
inference(component_clause,[status(thm)],[f484]) ).
fof(f499,plain,
( ~ sQ50_spl
| ~ halfadder(h2(f1(a)))
| zero(in1(and2(h2(f1(a))))) ),
inference(resolution,[status(thm)],[f466,f104]) ).
fof(f505,plain,
( ~ sQ50_spl
| ~ sQ27_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f499,f376,f294,f446]) ).
fof(f529,plain,
( ~ sQ40_spl
| zero(out1(and2(h2(f1(a)))))
| ~ and_ok(and2(h2(f1(a)))) ),
inference(resolution,[status(thm)],[f377,f76]) ).
fof(f539,plain,
( ~ sQ40_spl
| sQ39_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f529,f361,f373,f376]) ).
fof(f547,definition,
( sQ66_spl
<=> zero(in2(or1(f1(a)))) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f548,plain,
( ~ sQ66_spl
| zero(in2(or1(f1(a)))) ),
inference(component_clause,[status(thm)],[f547]) ).
fof(f556,plain,
( ~ sQ20_spl
| ~ zero(in2(or1(f1(a)))) ),
inference(resolution,[status(thm)],[f267,f75]) ).
fof(f571,plain,
( ~ sQ34_spl
| ~ fulladder(f1(a))
| zero(in1(h1(f1(a)))) ),
inference(resolution,[status(thm)],[f428,f118]) ).
fof(f574,definition,
( sQ68_spl
<=> zero(in1(h1(f1(a)))) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f575,plain,
( ~ sQ68_spl
| zero(in1(h1(f1(a)))) ),
inference(component_clause,[status(thm)],[f574]) ).
fof(f577,plain,
( ~ sQ34_spl
| ~ sQ10_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f571,f574,f204,f349]) ).
fof(f586,plain,
! [X0] :
( ~ sQ68_spl
| zero(X0)
| ~ connection(in1(h1(f1(a))),X0) ),
inference(resolution,[status(thm)],[f575,f68]) ).
fof(f603,plain,
( abnormal(or1(f1(a)))
| or_ok(or1(f1(a))) ),
inference(resolution,[status(thm)],[f483,f128]) ).
fof(f604,plain,
( sQ56_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f603,f260,f484]) ).
fof(f644,plain,
( ~ sQ39_spl
| ~ halfadder(h2(f1(a)))
| zero(outc(h2(f1(a)))) ),
inference(resolution,[status(thm)],[f416,f107]) ).
fof(f645,definition,
( sQ83_spl
<=> zero(outc(h2(f1(a)))) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f646,plain,
( ~ sQ83_spl
| zero(outc(h2(f1(a)))) ),
inference(component_clause,[status(thm)],[f645]) ).
fof(f648,plain,
( ~ sQ39_spl
| ~ sQ27_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f644,f645,f294,f373]) ).
fof(f752,plain,
( ~ sQ68_spl
| ~ halfadder(h1(f1(a)))
| zero(in1(and2(h1(f1(a))))) ),
inference(resolution,[status(thm)],[f586,f104]) ).
fof(f761,plain,
( ~ sQ68_spl
| ~ sQ38_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f752,f387,f368,f574]) ).
fof(f767,plain,
( ~ sQ43_spl
| zero(out1(and2(h1(f1(a)))))
| ~ and_ok(and2(h1(f1(a)))) ),
inference(resolution,[status(thm)],[f388,f76]) ).
fof(f777,plain,
( ~ sQ43_spl
| sQ42_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f767,f365,f384,f387]) ).
fof(f854,plain,
( ~ sQ42_spl
| ~ halfadder(h1(f1(a)))
| zero(outc(h1(f1(a)))) ),
inference(resolution,[status(thm)],[f418,f107]) ).
fof(f855,definition,
( sQ120_spl
<=> zero(outc(h1(f1(a)))) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f856,plain,
( ~ sQ120_spl
| zero(outc(h1(f1(a)))) ),
inference(component_clause,[status(thm)],[f855]) ).
fof(f858,plain,
( ~ sQ42_spl
| ~ sQ38_spl
| sQ120_spl ),
inference(split_clause,[status(thm)],[f854,f855,f368,f384]) ).
fof(f860,plain,
! [X0] :
( ~ sQ120_spl
| zero(X0)
| ~ connection(outc(h1(f1(a))),X0) ),
inference(resolution,[status(thm)],[f856,f68]) ).
fof(f943,plain,
( ~ sQ19_spl
| ~ fulladder(f1(a))
| one(outc(h2(f1(a)))) ),
inference(resolution,[status(thm)],[f317,f116]) ).
fof(f945,definition,
( sQ132_spl
<=> one(outc(h2(f1(a)))) ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f946,plain,
( ~ sQ132_spl
| one(outc(h2(f1(a)))) ),
inference(component_clause,[status(thm)],[f945]) ).
fof(f948,plain,
( ~ sQ19_spl
| ~ sQ10_spl
| sQ132_spl ),
inference(split_clause,[status(thm)],[f943,f945,f204,f263]) ).
fof(f953,plain,
( ~ sQ56_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f485,f134]) ).
fof(f954,plain,
~ sQ56_spl,
inference(contradiction_clause,[status(thm)],[f953]) ).
fof(f998,plain,
( ~ sQ132_spl
| ~ zero(outc(h2(f1(a)))) ),
inference(resolution,[status(thm)],[f946,f75]) ).
fof(f999,plain,
( ~ sQ132_spl
| ~ sQ83_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f998,f646]) ).
fof(f1000,plain,
( ~ sQ132_spl
| ~ sQ83_spl ),
inference(contradiction_clause,[status(thm)],[f999]) ).
fof(f1065,plain,
( ~ sQ66_spl
| ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f548,f556]) ).
fof(f1066,plain,
( ~ sQ66_spl
| ~ sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f1065]) ).
fof(f1267,plain,
( ~ sQ120_spl
| ~ fulladder(f1(a))
| zero(in2(or1(f1(a)))) ),
inference(resolution,[status(thm)],[f860,f115]) ).
fof(f1271,plain,
( ~ sQ120_spl
| ~ sQ10_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f1267,f547,f204,f855]) ).
fof(f1278,plain,
$false,
inference(sat_refutation,[status(thm)],[f191,f222,f229,f248,f269,f309,f329,f352,f364,f371,f395,f449,f505,f539,f577,f604,f648,f761,f777,f858,f948,f954,f1000,f1066,f1271]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HWV008-2.001 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/5.51 % Computer : n004.cluster.edu
% 0.20/5.51 % Model : x86_64 x86_64
% 0.20/5.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/5.51 % Memory : 8046.5625MB
% 0.20/5.51 % OS : Linux 6.8.0-71-generic
% 0.20/5.51 % CPULimit : 300
% 0.20/5.51 % WCLimit : 300
% 0.20/5.51 % DateTime : Sun Sep 20 20:47:55 UTC 2026
% 0.20/5.51 % CPUTime :
% 0.20/5.53 % Drodi V4.1.1
% 0.20/5.60 % Refutation found
% 0.20/5.60 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.20/5.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.25/5.63 % Elapsed time: 0.110742 seconds
% 0.25/5.63 % CPU time: 0.392961 seconds
% 0.25/5.63 % Total memory used: 14.663 MB
% 0.25/5.63 % Net memory used: 14.592 MB
%------------------------------------------------------------------------------