%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HWV006-2 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 12:45:54 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.48s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 50
% Syntax : Number of formulae : 224 ( 61 unt; 0 def)
% Number of atoms : 437 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 420 ( 207 ~; 213 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 1 con; 0-1 aty)
% Number of variables : 119 ( 119 !; 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(f7,axiom,
! [K] :
( zero(out1(K))
| ~ zero(in2(K))
| ~ and_ok(K) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [K] :
( one(out1(K))
| ~ one(in2(K))
| ~ one(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(f15,axiom,
! [K] :
( one(out1(K))
| ~ one(in2(K))
| ~ or_ok(K) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [K] :
( zero(in1(K))
| ~ zero(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(f22,axiom,
! [K] :
( one(out1(K))
| ~ zero(in1(K))
| ~ not_ok(K) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [K] :
( zero(out1(K))
| ~ one(in1(K))
| ~ not_ok(K) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [K] :
( abnormal(K)
| not_ok(K)
| ~ logic_not(K) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [X] :
( logic_and(and1(X))
| ~ halfadder(X) ),
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(f30,axiom,
! [X] :
( logic_not(not1(X))
| ~ halfadder(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [X] :
( logic_or(or1(X))
| ~ halfadder(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [X] :
( connection(in2(X),in2(or1(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(f35,axiom,
! [X] :
( connection(in2(X),in2(and2(X)))
| ~ halfadder(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [X] :
( connection(outs(X),out1(and1(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(f38,axiom,
! [X] :
( connection(out1(or1(X)),in1(and1(X)))
| ~ halfadder(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [X] :
( connection(out1(and2(X)),in1(not1(X)))
| ~ halfadder(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [X] :
( connection(out1(not1(X)),in2(and1(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(f44,axiom,
! [X] :
( connection(outs(h1(X)),in2(h2(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(f49,axiom,
! [X] :
( connection(inc(X),in2(h1(X)))
| ~ fulladder(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [X] :
( connection(outs(X),outs(h2(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,hypothesis,
fulladder(f),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,hypothesis,
one(in1(f)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,hypothesis,
zero(in2(f)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,hypothesis,
one(inc(f)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,hypothesis,
one(outs(f)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,hypothesis,
zero(outc(f)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,negated_conjecture,
( ~ abnormal(not1(h2(f)))
| ~ abnormal(or1(f)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f59,negated_conjecture,
~ abnormal(and2(h2(f))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,negated_conjecture,
( ~ abnormal(and1(h2(f)))
| ~ abnormal(or1(f)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f61,negated_conjecture,
~ abnormal(or1(h1(f))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f62,negated_conjecture,
~ abnormal(not1(h1(f))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f63,negated_conjecture,
~ abnormal(and2(h1(f))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f64,negated_conjecture,
~ abnormal(and1(h1(f))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,plain,
! [P2] :
( zero(P2)
| ! [P1] :
( ~ zero(P1)
| ~ connection(P1,P2) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f66,plain,
! [X0,X1] :
( zero(X1)
| ~ zero(X0)
| ~ connection(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
! [P2] :
( one(P2)
| ! [P1] :
( ~ one(P1)
| ~ connection(P1,P2) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f68,plain,
! [X0,X1] :
( one(X1)
| ~ one(X0)
| ~ connection(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
! [P1] :
( zero(P1)
| ! [P2] :
( ~ zero(P2)
| ~ connection(P1,P2) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f70,plain,
! [X0,X1] :
( zero(X0)
| ~ zero(X1)
| ~ connection(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
! [P1] :
( one(P1)
| ! [P2] :
( ~ one(P2)
| ~ connection(P1,P2) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f72,plain,
! [X0,X1] :
( one(X0)
| ~ one(X1)
| ~ connection(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f73,plain,
! [X0] :
( ~ one(X0)
| ~ zero(X0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f74,plain,
! [X0] :
( zero(out1(X0))
| ~ zero(in1(X0))
| ~ and_ok(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f75,plain,
! [X0] :
( zero(out1(X0))
| ~ zero(in2(X0))
| ~ and_ok(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f76,plain,
! [X0] :
( one(out1(X0))
| ~ one(in2(X0))
| ~ one(in1(X0))
| ~ and_ok(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f81,plain,
! [X0] :
( abnormal(X0)
| and_ok(X0)
| ~ logic_and(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f83,plain,
! [X0] :
( one(out1(X0))
| ~ one(in2(X0))
| ~ or_ok(X0) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f86,plain,
! [X0] :
( zero(in1(X0))
| ~ zero(out1(X0))
| ~ or_ok(X0) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f89,plain,
! [X0] :
( abnormal(X0)
| or_ok(X0)
| ~ logic_or(X0) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f90,plain,
! [X0] :
( one(out1(X0))
| ~ zero(in1(X0))
| ~ not_ok(X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f91,plain,
! [X0] :
( zero(out1(X0))
| ~ one(in1(X0))
| ~ not_ok(X0) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f95,plain,
! [X0] :
( abnormal(X0)
| not_ok(X0)
| ~ logic_not(X0) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f96,plain,
! [X0] :
( logic_and(and1(X0))
| ~ halfadder(X0) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f97,plain,
! [X0] :
( logic_and(and2(X0))
| ~ halfadder(X0) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f98,plain,
! [X0] :
( logic_not(not1(X0))
| ~ halfadder(X0) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f99,plain,
! [X0] :
( logic_or(or1(X0))
| ~ halfadder(X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f101,plain,
! [X0] :
( connection(in2(X0),in2(or1(X0)))
| ~ halfadder(X0) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f102,plain,
! [X0] :
( connection(in1(X0),in1(and2(X0)))
| ~ halfadder(X0) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f103,plain,
! [X0] :
( connection(in2(X0),in2(and2(X0)))
| ~ halfadder(X0) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f104,plain,
! [X0] :
( connection(outs(X0),out1(and1(X0)))
| ~ halfadder(X0) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f105,plain,
! [X0] :
( connection(outc(X0),out1(and2(X0)))
| ~ halfadder(X0) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f106,plain,
! [X0] :
( connection(out1(or1(X0)),in1(and1(X0)))
| ~ halfadder(X0) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f107,plain,
! [X0] :
( connection(out1(and2(X0)),in1(not1(X0)))
| ~ halfadder(X0) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f108,plain,
! [X0] :
( connection(out1(not1(X0)),in2(and1(X0)))
| ~ halfadder(X0) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f109,plain,
! [X0] :
( halfadder(h1(X0))
| ~ fulladder(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f110,plain,
! [X0] :
( halfadder(h2(X0))
| ~ fulladder(X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f111,plain,
! [X0] :
( logic_or(or1(X0))
| ~ fulladder(X0) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f112,plain,
! [X0] :
( connection(outs(h1(X0)),in2(h2(X0)))
| ~ fulladder(X0) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f114,plain,
! [X0] :
( connection(outc(h2(X0)),in1(or1(X0)))
| ~ fulladder(X0) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f115,plain,
! [X0] :
( connection(in1(X0),in1(h2(X0)))
| ~ fulladder(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f116,plain,
! [X0] :
( connection(in2(X0),in1(h1(X0)))
| ~ fulladder(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f117,plain,
! [X0] :
( connection(inc(X0),in2(h1(X0)))
| ~ fulladder(X0) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f118,plain,
! [X0] :
( connection(outs(X0),outs(h2(X0)))
| ~ fulladder(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f119,plain,
! [X0] :
( connection(outc(X0),out1(or1(X0)))
| ~ fulladder(X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f120,plain,
fulladder(f),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f121,plain,
one(in1(f)),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f122,plain,
zero(in2(f)),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f123,plain,
one(inc(f)),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f124,plain,
one(outs(f)),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f125,plain,
zero(outc(f)),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f126,plain,
( ~ abnormal(not1(h2(f)))
| ~ abnormal(or1(f)) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f127,plain,
~ abnormal(and2(h2(f))),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f128,plain,
( ~ abnormal(and1(h2(f)))
| ~ abnormal(or1(f)) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f129,plain,
~ abnormal(or1(h1(f))),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f130,plain,
~ abnormal(not1(h1(f))),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f131,plain,
~ abnormal(and2(h1(f))),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f132,plain,
~ abnormal(and1(h1(f))),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f134,plain,
! [X0] :
( zero(X0)
| ~ connection(in2(f),X0) ),
inference(resolution,[status(thm)],[f66,f122]) ).
fof(f135,plain,
! [X0] :
( one(X0)
| ~ connection(in1(f),X0) ),
inference(resolution,[status(thm)],[f68,f121]) ).
fof(f142,plain,
( one(in1(h2(f)))
| ~ fulladder(f) ),
inference(resolution,[status(thm)],[f115,f135]) ).
fof(f143,plain,
one(in1(h2(f))),
inference(forward_subsumption_resolution,[status(thm)],[f142,f120]) ).
fof(f144,plain,
( zero(in1(h1(f)))
| ~ fulladder(f) ),
inference(resolution,[status(thm)],[f116,f134]) ).
fof(f145,plain,
zero(in1(h1(f))),
inference(forward_subsumption_resolution,[status(thm)],[f144,f120]) ).
fof(f147,plain,
! [X0] :
( one(X0)
| ~ connection(in1(h2(f)),X0) ),
inference(resolution,[status(thm)],[f143,f68]) ).
fof(f151,plain,
! [X0] :
( zero(X0)
| ~ connection(in1(h1(f)),X0) ),
inference(resolution,[status(thm)],[f145,f66]) ).
fof(f154,plain,
( ~ halfadder(h2(f))
| one(in1(and2(h2(f)))) ),
inference(resolution,[status(thm)],[f147,f102]) ).
fof(f158,plain,
( ~ halfadder(h1(f))
| zero(in1(and2(h1(f)))) ),
inference(resolution,[status(thm)],[f151,f102]) ).
fof(f160,plain,
( ~ fulladder(f)
| one(in1(and2(h2(f)))) ),
inference(resolution,[status(thm)],[f154,f110]) ).
fof(f161,plain,
one(in1(and2(h2(f)))),
inference(forward_subsumption_resolution,[status(thm)],[f160,f120]) ).
fof(f178,plain,
( ~ fulladder(f)
| zero(in1(and2(h1(f)))) ),
inference(resolution,[status(thm)],[f158,f109]) ).
fof(f179,plain,
zero(in1(and2(h1(f)))),
inference(forward_subsumption_resolution,[status(thm)],[f178,f120]) ).
fof(f180,plain,
( zero(out1(and2(h1(f))))
| ~ and_ok(and2(h1(f))) ),
inference(resolution,[status(thm)],[f179,f74]) ).
fof(f197,plain,
! [X0] :
( one(X0)
| ~ connection(inc(f),X0) ),
inference(resolution,[status(thm)],[f123,f68]) ).
fof(f200,plain,
! [X0] :
( one(X0)
| ~ connection(outs(f),X0) ),
inference(resolution,[status(thm)],[f124,f68]) ).
fof(f203,plain,
! [X0] :
( zero(X0)
| ~ connection(outc(f),X0) ),
inference(resolution,[status(thm)],[f125,f66]) ).
fof(f204,plain,
! [X0] :
( abnormal(and1(X0))
| and_ok(and1(X0))
| ~ halfadder(X0) ),
inference(resolution,[status(thm)],[f96,f81]) ).
fof(f205,plain,
! [X0] :
( abnormal(and2(X0))
| and_ok(and2(X0))
| ~ halfadder(X0) ),
inference(resolution,[status(thm)],[f97,f81]) ).
fof(f206,plain,
! [X0] :
( abnormal(not1(X0))
| not_ok(not1(X0))
| ~ halfadder(X0) ),
inference(resolution,[status(thm)],[f98,f95]) ).
fof(f207,plain,
! [X0] :
( abnormal(or1(X0))
| or_ok(or1(X0))
| ~ halfadder(X0) ),
inference(resolution,[status(thm)],[f99,f89]) ).
fof(f208,plain,
( and_ok(and1(h1(f)))
| ~ halfadder(h1(f)) ),
inference(resolution,[status(thm)],[f204,f132]) ).
fof(f210,plain,
! [X0] :
( ~ fulladder(X0)
| abnormal(and2(h2(X0)))
| and_ok(and2(h2(X0))) ),
inference(resolution,[status(thm)],[f205,f110]) ).
fof(f211,plain,
! [X0] :
( ~ fulladder(X0)
| abnormal(and2(h1(X0)))
| and_ok(and2(h1(X0))) ),
inference(resolution,[status(thm)],[f205,f109]) ).
fof(f212,plain,
( abnormal(and2(h2(f)))
| and_ok(and2(h2(f))) ),
inference(resolution,[status(thm)],[f210,f120]) ).
fof(f213,plain,
and_ok(and2(h2(f))),
inference(forward_subsumption_resolution,[status(thm)],[f212,f127]) ).
fof(f214,plain,
( abnormal(and2(h1(f)))
| and_ok(and2(h1(f))) ),
inference(resolution,[status(thm)],[f211,f120]) ).
fof(f215,plain,
zero(out1(and2(h1(f)))),
inference(backward_subsumption_resolution,[status(thm)],[f180,f216]) ).
fof(f216,plain,
and_ok(and2(h1(f))),
inference(forward_subsumption_resolution,[status(thm)],[f214,f131]) ).
fof(f217,plain,
! [X0] :
( ~ fulladder(X0)
| abnormal(not1(h2(X0)))
| not_ok(not1(h2(X0))) ),
inference(resolution,[status(thm)],[f206,f110]) ).
fof(f218,plain,
! [X0] :
( ~ fulladder(X0)
| abnormal(not1(h1(X0)))
| not_ok(not1(h1(X0))) ),
inference(resolution,[status(thm)],[f206,f109]) ).
fof(f219,plain,
( abnormal(not1(h2(f)))
| not_ok(not1(h2(f))) ),
inference(resolution,[status(thm)],[f217,f120]) ).
fof(f220,plain,
( abnormal(not1(h1(f)))
| not_ok(not1(h1(f))) ),
inference(resolution,[status(thm)],[f218,f120]) ).
fof(f221,plain,
not_ok(not1(h1(f))),
inference(forward_subsumption_resolution,[status(thm)],[f220,f130]) ).
fof(f222,plain,
( zero(out1(not1(h2(f))))
| ~ one(in1(not1(h2(f))))
| abnormal(not1(h2(f))) ),
inference(resolution,[status(thm)],[f219,f91]) ).
fof(f226,plain,
! [X0] :
( ~ fulladder(X0)
| abnormal(or1(h1(X0)))
| or_ok(or1(h1(X0))) ),
inference(resolution,[status(thm)],[f207,f109]) ).
fof(f232,plain,
( abnormal(or1(h1(f)))
| or_ok(or1(h1(f))) ),
inference(resolution,[status(thm)],[f226,f120]) ).
fof(f233,plain,
or_ok(or1(h1(f))),
inference(forward_subsumption_resolution,[status(thm)],[f232,f129]) ).
fof(f253,plain,
( ~ fulladder(f)
| and_ok(and1(h1(f))) ),
inference(resolution,[status(thm)],[f208,f109]) ).
fof(f254,plain,
and_ok(and1(h1(f))),
inference(forward_subsumption_resolution,[status(thm)],[f253,f120]) ).
fof(f258,plain,
( one(out1(not1(h1(f))))
| ~ zero(in1(not1(h1(f)))) ),
inference(resolution,[status(thm)],[f221,f90]) ).
fof(f270,plain,
! [X0] :
( zero(X0)
| ~ connection(out1(and2(h1(f))),X0) ),
inference(resolution,[status(thm)],[f215,f66]) ).
fof(f271,plain,
( ~ halfadder(h1(f))
| zero(in1(not1(h1(f)))) ),
inference(resolution,[status(thm)],[f270,f107]) ).
fof(f272,plain,
( ~ fulladder(f)
| zero(in1(not1(h1(f)))) ),
inference(resolution,[status(thm)],[f271,f109]) ).
fof(f273,plain,
one(out1(not1(h1(f)))),
inference(backward_subsumption_resolution,[status(thm)],[f258,f274]) ).
fof(f274,plain,
zero(in1(not1(h1(f)))),
inference(forward_subsumption_resolution,[status(thm)],[f272,f120]) ).
fof(f283,plain,
! [X0] :
( one(X0)
| ~ connection(out1(not1(h1(f))),X0) ),
inference(resolution,[status(thm)],[f273,f68]) ).
fof(f293,plain,
( ~ halfadder(h1(f))
| one(in2(and1(h1(f)))) ),
inference(resolution,[status(thm)],[f283,f108]) ).
fof(f294,plain,
( ~ fulladder(f)
| one(in2(and1(h1(f)))) ),
inference(resolution,[status(thm)],[f293,f109]) ).
fof(f295,plain,
one(in2(and1(h1(f)))),
inference(forward_subsumption_resolution,[status(thm)],[f294,f120]) ).
fof(f297,plain,
( one(out1(and1(h1(f))))
| ~ one(in1(and1(h1(f))))
| ~ and_ok(and1(h1(f))) ),
inference(resolution,[status(thm)],[f295,f76]) ).
fof(f301,plain,
( one(out1(and1(h1(f))))
| ~ one(in1(and1(h1(f)))) ),
inference(forward_subsumption_resolution,[status(thm)],[f297,f254]) ).
fof(f312,plain,
! [X0] :
( abnormal(or1(X0))
| or_ok(or1(X0))
| ~ fulladder(X0) ),
inference(resolution,[status(thm)],[f111,f89]) ).
fof(f320,plain,
connection(outc(h2(f)),in1(or1(f))),
inference(resolution,[status(thm)],[f114,f120]) ).
fof(f321,plain,
( one(in2(h1(f)))
| ~ fulladder(f) ),
inference(resolution,[status(thm)],[f117,f197]) ).
fof(f322,plain,
one(in2(h1(f))),
inference(forward_subsumption_resolution,[status(thm)],[f321,f120]) ).
fof(f323,plain,
( one(outs(h2(f)))
| ~ fulladder(f) ),
inference(resolution,[status(thm)],[f118,f200]) ).
fof(f324,plain,
one(outs(h2(f))),
inference(forward_subsumption_resolution,[status(thm)],[f323,f120]) ).
fof(f325,plain,
connection(outc(f),out1(or1(f))),
inference(resolution,[status(thm)],[f119,f120]) ).
fof(f327,plain,
( abnormal(or1(f))
| or_ok(or1(f)) ),
inference(resolution,[status(thm)],[f312,f120]) ).
fof(f335,plain,
zero(out1(or1(f))),
inference(resolution,[status(thm)],[f325,f203]) ).
fof(f339,plain,
! [X0] :
( one(X0)
| ~ connection(in2(h1(f)),X0) ),
inference(resolution,[status(thm)],[f322,f68]) ).
fof(f343,plain,
~ zero(outs(h2(f))),
inference(resolution,[status(thm)],[f324,f73]) ).
fof(f346,plain,
( zero(in1(or1(f)))
| ~ or_ok(or1(f)) ),
inference(resolution,[status(thm)],[f335,f86]) ).
fof(f353,plain,
( ~ halfadder(h1(f))
| one(in2(or1(h1(f)))) ),
inference(resolution,[status(thm)],[f339,f101]) ).
fof(f356,plain,
( ~ fulladder(f)
| one(in2(or1(h1(f)))) ),
inference(resolution,[status(thm)],[f353,f109]) ).
fof(f357,plain,
one(in2(or1(h1(f)))),
inference(forward_subsumption_resolution,[status(thm)],[f356,f120]) ).
fof(f365,plain,
( one(out1(or1(h1(f))))
| ~ or_ok(or1(h1(f))) ),
inference(resolution,[status(thm)],[f357,f83]) ).
fof(f370,plain,
one(out1(or1(h1(f)))),
inference(forward_subsumption_resolution,[status(thm)],[f365,f233]) ).
fof(f376,plain,
! [X0] :
( one(X0)
| ~ connection(out1(or1(h1(f))),X0) ),
inference(resolution,[status(thm)],[f370,f68]) ).
fof(f379,plain,
( ~ halfadder(h1(f))
| one(in1(and1(h1(f)))) ),
inference(resolution,[status(thm)],[f376,f106]) ).
fof(f380,plain,
( ~ fulladder(f)
| one(in1(and1(h1(f)))) ),
inference(resolution,[status(thm)],[f379,f109]) ).
fof(f381,plain,
one(out1(and1(h1(f)))),
inference(backward_subsumption_resolution,[status(thm)],[f301,f382]) ).
fof(f382,plain,
one(in1(and1(h1(f)))),
inference(forward_subsumption_resolution,[status(thm)],[f380,f120]) ).
fof(f387,plain,
! [X0] :
( one(X0)
| ~ connection(X0,out1(and1(h1(f)))) ),
inference(resolution,[status(thm)],[f381,f72]) ).
fof(f394,plain,
( ~ halfadder(h1(f))
| one(outs(h1(f))) ),
inference(resolution,[status(thm)],[f387,f104]) ).
fof(f399,plain,
( ~ fulladder(f)
| one(outs(h1(f))) ),
inference(resolution,[status(thm)],[f394,f109]) ).
fof(f400,plain,
one(outs(h1(f))),
inference(forward_subsumption_resolution,[status(thm)],[f399,f120]) ).
fof(f402,plain,
! [X0] :
( one(X0)
| ~ connection(outs(h1(f)),X0) ),
inference(resolution,[status(thm)],[f400,f68]) ).
fof(f404,plain,
( ~ fulladder(f)
| one(in2(h2(f))) ),
inference(resolution,[status(thm)],[f402,f112]) ).
fof(f407,plain,
one(in2(h2(f))),
inference(forward_subsumption_resolution,[status(thm)],[f404,f120]) ).
fof(f411,plain,
! [X0] :
( one(X0)
| ~ connection(in2(h2(f)),X0) ),
inference(resolution,[status(thm)],[f407,f68]) ).
fof(f416,plain,
( ~ halfadder(h2(f))
| one(in2(and2(h2(f)))) ),
inference(resolution,[status(thm)],[f411,f103]) ).
fof(f418,plain,
( ~ fulladder(f)
| one(in2(and2(h2(f)))) ),
inference(resolution,[status(thm)],[f416,f110]) ).
fof(f419,plain,
one(in2(and2(h2(f)))),
inference(forward_subsumption_resolution,[status(thm)],[f418,f120]) ).
fof(f423,plain,
( one(out1(and2(h2(f))))
| ~ one(in1(and2(h2(f))))
| ~ and_ok(and2(h2(f))) ),
inference(resolution,[status(thm)],[f419,f76]) ).
fof(f427,plain,
( one(out1(and2(h2(f))))
| ~ one(in1(and2(h2(f)))) ),
inference(forward_subsumption_resolution,[status(thm)],[f423,f213]) ).
fof(f434,plain,
one(out1(and2(h2(f)))),
inference(resolution,[status(thm)],[f427,f161]) ).
fof(f450,plain,
! [X0] :
( one(X0)
| ~ connection(out1(and2(h2(f))),X0) ),
inference(resolution,[status(thm)],[f434,f68]) ).
fof(f451,plain,
~ zero(out1(and2(h2(f)))),
inference(resolution,[status(thm)],[f434,f73]) ).
fof(f465,plain,
( abnormal(or1(f))
| zero(in1(or1(f))) ),
inference(resolution,[status(thm)],[f346,f327]) ).
fof(f469,plain,
! [X0] :
( zero(X0)
| ~ connection(X0,in1(or1(f)))
| abnormal(or1(f)) ),
inference(resolution,[status(thm)],[f465,f70]) ).
fof(f471,plain,
( zero(outc(h2(f)))
| abnormal(or1(f)) ),
inference(resolution,[status(thm)],[f469,f320]) ).
fof(f475,plain,
! [X0] :
( zero(X0)
| ~ connection(outc(h2(f)),X0)
| abnormal(or1(f)) ),
inference(resolution,[status(thm)],[f471,f66]) ).
fof(f480,plain,
( ~ halfadder(h2(f))
| zero(out1(and2(h2(f))))
| abnormal(or1(f)) ),
inference(resolution,[status(thm)],[f475,f105]) ).
fof(f481,plain,
( ~ halfadder(h2(f))
| abnormal(or1(f)) ),
inference(forward_subsumption_resolution,[status(thm)],[f480,f451]) ).
fof(f482,plain,
( ~ fulladder(f)
| abnormal(or1(f)) ),
inference(resolution,[status(thm)],[f481,f110]) ).
fof(f483,plain,
~ abnormal(and1(h2(f))),
inference(backward_subsumption_resolution,[status(thm)],[f128,f485]) ).
fof(f484,plain,
~ abnormal(not1(h2(f))),
inference(backward_subsumption_resolution,[status(thm)],[f126,f485]) ).
fof(f485,plain,
abnormal(or1(f)),
inference(forward_subsumption_resolution,[status(thm)],[f482,f120]) ).
fof(f487,plain,
( zero(out1(not1(h2(f))))
| ~ one(in1(not1(h2(f)))) ),
inference(backward_subsumption_resolution,[status(thm)],[f222,f484]) ).
fof(f489,plain,
( and_ok(and1(h2(f)))
| ~ halfadder(h2(f)) ),
inference(resolution,[status(thm)],[f483,f204]) ).
fof(f495,plain,
( ~ halfadder(h2(f))
| one(in1(not1(h2(f)))) ),
inference(resolution,[status(thm)],[f450,f107]) ).
fof(f496,plain,
( ~ fulladder(f)
| and_ok(and1(h2(f))) ),
inference(resolution,[status(thm)],[f489,f110]) ).
fof(f497,plain,
and_ok(and1(h2(f))),
inference(forward_subsumption_resolution,[status(thm)],[f496,f120]) ).
fof(f498,plain,
( zero(out1(and1(h2(f))))
| ~ zero(in2(and1(h2(f)))) ),
inference(resolution,[status(thm)],[f497,f75]) ).
fof(f501,plain,
( ~ fulladder(f)
| one(in1(not1(h2(f)))) ),
inference(resolution,[status(thm)],[f495,f110]) ).
fof(f502,plain,
zero(out1(not1(h2(f)))),
inference(backward_subsumption_resolution,[status(thm)],[f487,f503]) ).
fof(f503,plain,
one(in1(not1(h2(f)))),
inference(forward_subsumption_resolution,[status(thm)],[f501,f120]) ).
fof(f509,plain,
! [X0] :
( zero(X0)
| ~ connection(out1(not1(h2(f))),X0) ),
inference(resolution,[status(thm)],[f502,f66]) ).
fof(f510,plain,
( ~ halfadder(h2(f))
| zero(in2(and1(h2(f)))) ),
inference(resolution,[status(thm)],[f509,f108]) ).
fof(f511,plain,
( ~ fulladder(f)
| zero(in2(and1(h2(f)))) ),
inference(resolution,[status(thm)],[f510,f110]) ).
fof(f512,plain,
zero(out1(and1(h2(f)))),
inference(backward_subsumption_resolution,[status(thm)],[f498,f513]) ).
fof(f513,plain,
zero(in2(and1(h2(f)))),
inference(forward_subsumption_resolution,[status(thm)],[f511,f120]) ).
fof(f528,plain,
! [X0] :
( zero(X0)
| ~ connection(X0,out1(and1(h2(f)))) ),
inference(resolution,[status(thm)],[f512,f70]) ).
fof(f536,plain,
( ~ halfadder(h2(f))
| zero(outs(h2(f))) ),
inference(resolution,[status(thm)],[f528,f104]) ).
fof(f537,plain,
~ halfadder(h2(f)),
inference(forward_subsumption_resolution,[status(thm)],[f536,f343]) ).
fof(f538,plain,
~ fulladder(f),
inference(resolution,[status(thm)],[f537,f110]) ).
fof(f539,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f538,f120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HWV006-2 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 20:51:54 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.48 % Refutation found
% 0.13/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.49 % Elapsed time: 0.127767 seconds
% 0.13/0.49 % CPU time: 0.806355 seconds
% 0.13/0.49 % Total memory used: 30.378 MB
% 0.13/0.49 % Net memory used: 29.827 MB
%------------------------------------------------------------------------------