%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HWV008-2.002 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 : Sun Sep 27 07:32:52 AM UTC 2026
% Result : Unsatisfiable 29.06s 6.94s
% Output : CNFRefutation 29.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 30
% Syntax : Number of clauses : 118 ( 53 unt; 11 nHn; 118 RR)
% Number of literals : 200 ( 0 equ; 81 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 12 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 1 con; 0-1 aty)
% Number of variables : 52 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(nbit_adder_fulladder2,axiom,
( fulladder(f2(X0))
| ~ 'nbit$uadder2'(X0) ) ).
cnf(nbit_adder_connection_outc_outcf1,axiom,
( connection(outc(X0),outc(f2(X0)))
| ~ 'nbit$uadder2'(X0) ) ).
cnf(nbit_adder_connection_ina2_in1f2,axiom,
( connection(ina2(X0),in1(f2(X0)))
| ~ 'nbit$uadder2'(X0) ) ).
cnf(nbit_adder_connection_inb2_in2f2,axiom,
( connection(inb2(X0),in2(f2(X0)))
| ~ 'nbit$uadder2'(X0) ) ).
cnf(a_isa_2bit_adder,hypothesis,
'nbit$uadder2'(a) ).
cnf(ina2_0,hypothesis,
zero(ina2(a)) ).
cnf(inb2_0,hypothesis,
zero(inb2(a)) ).
cnf(outc_1,hypothesis,
one(outc(a)) ).
cnf(diagnosis_or1f2a,negated_conjecture,
~ abnormal(or1(f2(a))) ).
cnf(diagnosis_and2h1f2a,negated_conjecture,
~ abnormal(and2(h1(f2(a)))) ).
cnf(diagnosis_and2h2f2a,negated_conjecture,
~ abnormal(and2(h2(f2(a)))) ).
cnf(value_propagation_zero1,axiom,
( zero(X1)
| ~ zero(X0)
| ~ connection(X0,X1) ) ).
cnf(value_propagation_one1,axiom,
( one(X1)
| ~ one(X0)
| ~ connection(X0,X1) ) ).
cnf(value_propagation_zero2,axiom,
( zero(X0)
| ~ zero(X1)
| ~ connection(X0,X1) ) ).
cnf(unique_value,axiom,
( ~ one(X0)
| ~ zero(X0) ) ).
cnf(and_0x_0,axiom,
( zero(out1(X0))
| ~ zero(in1(X0))
| ~ 'and$uok'(X0) ) ).
cnf(and_ok_or_abnormal,axiom,
( abnormal(X0)
| 'and$uok'(X0)
| ~ 'logic$uand'(X0) ) ).
cnf(or_1_11,axiom,
( one(in2(X0))
| one(in1(X0))
| ~ one(out1(X0))
| ~ 'or$uok'(X0) ) ).
cnf(or_ok_or_abnormal,axiom,
( abnormal(X0)
| 'or$uok'(X0)
| ~ 'logic$uor'(X0) ) ).
cnf(halfadder_and2,axiom,
( 'logic$uand'(and2(X0))
| ~ halfadder(X0) ) ).
cnf(halfadder_connection_in1_in1and2,axiom,
( connection(in1(X0),in1(and2(X0)))
| ~ halfadder(X0) ) ).
cnf(halfadder_connection_outc_out1and2,axiom,
( connection(outc(X0),out1(and2(X0)))
| ~ halfadder(X0) ) ).
cnf(fulladder_halfadder1,axiom,
( halfadder(h1(X0))
| ~ fulladder(X0) ) ).
cnf(fulladder_halfadder2,axiom,
( halfadder(h2(X0))
| ~ fulladder(X0) ) ).
cnf(fulladder_or1,axiom,
( 'logic$uor'(or1(X0))
| ~ fulladder(X0) ) ).
cnf(fulladder_connection_outch1_in2or1,axiom,
( connection(outc(h1(X0)),in2(or1(X0)))
| ~ fulladder(X0) ) ).
cnf(fulladder_connection_outch2_in1or1,axiom,
( connection(outc(h2(X0)),in1(or1(X0)))
| ~ fulladder(X0) ) ).
cnf(fulladder_connection_in1_in1h2,axiom,
( connection(in1(X0),in1(h2(X0)))
| ~ fulladder(X0) ) ).
cnf(fulladder_connection_in2_in1h1,axiom,
( connection(in2(X0),in1(h1(X0)))
| ~ fulladder(X0) ) ).
cnf(fulladder_connection_outc_out1or1,axiom,
( connection(outc(X0),out1(or1(X0)))
| ~ fulladder(X0) ) ).
cnf(c1,plain,
( fulladder(f2(X0))
| ~ 'nbit$uadder2'(X0) ),
inference(clausification,[status(esa)],[nbit_adder_fulladder2]) ).
cnf(c4,plain,
( connection(outc(X0),outc(f2(X0)))
| ~ 'nbit$uadder2'(X0) ),
inference(clausification,[status(esa)],[nbit_adder_connection_outc_outcf1]) ).
cnf(c7,plain,
( connection(ina2(X0),in1(f2(X0)))
| ~ 'nbit$uadder2'(X0) ),
inference(clausification,[status(esa)],[nbit_adder_connection_ina2_in1f2]) ).
cnf(c8,plain,
( connection(inb2(X0),in2(f2(X0)))
| ~ 'nbit$uadder2'(X0) ),
inference(clausification,[status(esa)],[nbit_adder_connection_inb2_in2f2]) ).
cnf(c11,plain,
'nbit$uadder2'(a),
inference(clausification,[status(esa)],[a_isa_2bit_adder]) ).
cnf(c13,plain,
zero(ina2(a)),
inference(clausification,[status(esa)],[ina2_0]) ).
cnf(c15,plain,
zero(inb2(a)),
inference(clausification,[status(esa)],[inb2_0]) ).
cnf(c19,plain,
one(outc(a)),
inference(clausification,[status(esa)],[outc_1]) ).
cnf(c20,plain,
~ abnormal(or1(f2(a))),
inference(clausification,[status(esa)],[diagnosis_or1f2a]) ).
cnf(c21,plain,
~ abnormal(and2(h1(f2(a)))),
inference(clausification,[status(esa)],[diagnosis_and2h1f2a]) ).
cnf(c22,plain,
~ abnormal(and2(h2(f2(a)))),
inference(clausification,[status(esa)],[diagnosis_and2h2f2a]) ).
cnf(c23,plain,
( zero(X1)
| ~ connection(X0,X1)
| ~ zero(X0) ),
inference(clausification,[status(esa)],[value_propagation_zero1]) ).
cnf(c24,plain,
( one(X1)
| ~ connection(X0,X1)
| ~ one(X0) ),
inference(clausification,[status(esa)],[value_propagation_one1]) ).
cnf(c25,plain,
( zero(X1)
| ~ connection(X1,X0)
| ~ zero(X0) ),
inference(clausification,[status(esa)],[value_propagation_zero2]) ).
cnf(c27,plain,
( ~ one(X0)
| ~ zero(X0) ),
inference(clausification,[status(esa)],[unique_value]) ).
cnf(c28,plain,
( zero(out1(X0))
| ~ 'and$uok'(X0)
| ~ zero(in1(X0)) ),
inference(clausification,[status(esa)],[and_0x_0]) ).
cnf(c35,plain,
( abnormal(X0)
| ~ 'logic$uand'(X0)
| 'and$uok'(X0) ),
inference(clausification,[status(esa)],[and_ok_or_abnormal]) ).
cnf(c39,plain,
( one(in2(X0))
| ~ one(out1(X0))
| ~ 'or$uok'(X0)
| one(in1(X0)) ),
inference(clausification,[status(esa)],[or_1_11]) ).
cnf(c43,plain,
( abnormal(X0)
| ~ 'logic$uor'(X0)
| 'or$uok'(X0) ),
inference(clausification,[status(esa)],[or_ok_or_abnormal]) ).
cnf(c51,plain,
( 'logic$uand'(and2(X0))
| ~ halfadder(X0) ),
inference(clausification,[status(esa)],[halfadder_and2]) ).
cnf(c56,plain,
( connection(in1(X0),in1(and2(X0)))
| ~ halfadder(X0) ),
inference(clausification,[status(esa)],[halfadder_connection_in1_in1and2]) ).
cnf(c59,plain,
( connection(outc(X0),out1(and2(X0)))
| ~ halfadder(X0) ),
inference(clausification,[status(esa)],[halfadder_connection_outc_out1and2]) ).
cnf(c63,plain,
( halfadder(h1(X0))
| ~ fulladder(X0) ),
inference(clausification,[status(esa)],[fulladder_halfadder1]) ).
cnf(c64,plain,
( halfadder(h2(X0))
| ~ fulladder(X0) ),
inference(clausification,[status(esa)],[fulladder_halfadder2]) ).
cnf(c65,plain,
( 'logic$uor'(or1(X0))
| ~ fulladder(X0) ),
inference(clausification,[status(esa)],[fulladder_or1]) ).
cnf(c67,plain,
( connection(outc(h1(X0)),in2(or1(X0)))
| ~ fulladder(X0) ),
inference(clausification,[status(esa)],[fulladder_connection_outch1_in2or1]) ).
cnf(c68,plain,
( connection(outc(h2(X0)),in1(or1(X0)))
| ~ fulladder(X0) ),
inference(clausification,[status(esa)],[fulladder_connection_outch2_in1or1]) ).
cnf(c69,plain,
( connection(in1(X0),in1(h2(X0)))
| ~ fulladder(X0) ),
inference(clausification,[status(esa)],[fulladder_connection_in1_in1h2]) ).
cnf(c70,plain,
( connection(in2(X0),in1(h1(X0)))
| ~ fulladder(X0) ),
inference(clausification,[status(esa)],[fulladder_connection_in2_in1h1]) ).
cnf(c73,plain,
( connection(outc(X0),out1(or1(X0)))
| ~ fulladder(X0) ),
inference(clausification,[status(esa)],[fulladder_connection_outc_out1or1]) ).
cnf(d0,plain,
fulladder(f2(a)),
inference(resolution,[status(thm)],[c1,c11]) ).
cnf(d1,plain,
connection(outc(f2(a)),out1(or1(f2(a)))),
inference(resolution,[status(thm)],[c73,d0]) ).
cnf(d2,plain,
( ~ one(outc(f2(a)))
| one(out1(or1(f2(a)))) ),
inference(resolution,[status(thm)],[d1,c24]) ).
cnf(d3,plain,
connection(outc(a),outc(f2(a))),
inference(resolution,[status(thm)],[c4,c11]) ).
cnf(d4,plain,
( ~ one(outc(a))
| one(outc(f2(a))) ),
inference(resolution,[status(thm)],[d3,c24]) ).
cnf(d5,plain,
one(outc(f2(a))),
inference(resolution,[status(thm)],[c19,d4]) ).
cnf(d6,plain,
one(out1(or1(f2(a)))),
inference(resolution,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
( ~ 'or$uok'(or1(f2(a)))
| one(in2(or1(f2(a))))
| one(in1(or1(f2(a)))) ),
inference(resolution,[status(thm)],[d6,c39]) ).
cnf(d8,plain,
'logic$uor'(or1(f2(a))),
inference(resolution,[status(thm)],[c65,d0]) ).
cnf(d9,plain,
( 'or$uok'(or1(f2(a)))
| abnormal(or1(f2(a))) ),
inference(resolution,[status(thm)],[c43,d8]) ).
cnf(d10,plain,
'or$uok'(or1(f2(a))),
inference(resolution,[status(thm)],[c20,d9]) ).
cnf(d11,plain,
( one(in2(or1(f2(a))))
| one(in1(or1(f2(a)))) ),
inference(resolution,[status(thm)],[d10,d7]) ).
cnf(d12,plain,
connection(outc(h2(f2(a))),in1(or1(f2(a)))),
inference(resolution,[status(thm)],[c68,d0]) ).
cnf(d13,plain,
( ~ zero(outc(h2(f2(a))))
| zero(in1(or1(f2(a)))) ),
inference(resolution,[status(thm)],[d12,c23]) ).
cnf(d14,plain,
halfadder(h2(f2(a))),
inference(resolution,[status(thm)],[c64,d0]) ).
cnf(d15,plain,
connection(outc(h2(f2(a))),out1(and2(h2(f2(a))))),
inference(resolution,[status(thm)],[c59,d14]) ).
cnf(d16,plain,
( ~ zero(out1(and2(h2(f2(a)))))
| zero(outc(h2(f2(a)))) ),
inference(resolution,[status(thm)],[d15,c25]) ).
cnf(d17,plain,
connection(in1(h2(f2(a))),in1(and2(h2(f2(a))))),
inference(resolution,[status(thm)],[c56,d14]) ).
cnf(d18,plain,
( ~ zero(in1(h2(f2(a))))
| zero(in1(and2(h2(f2(a))))) ),
inference(resolution,[status(thm)],[d17,c23]) ).
cnf(d19,plain,
connection(in1(f2(a)),in1(h2(f2(a)))),
inference(resolution,[status(thm)],[c69,d0]) ).
cnf(d20,plain,
( ~ zero(in1(f2(a)))
| zero(in1(h2(f2(a)))) ),
inference(resolution,[status(thm)],[d19,c23]) ).
cnf(d21,plain,
connection(ina2(a),in1(f2(a))),
inference(resolution,[status(thm)],[c7,c11]) ).
cnf(d22,plain,
( ~ zero(ina2(a))
| zero(in1(f2(a))) ),
inference(resolution,[status(thm)],[d21,c23]) ).
cnf(d23,plain,
zero(in1(f2(a))),
inference(resolution,[status(thm)],[c13,d22]) ).
cnf(d24,plain,
zero(in1(h2(f2(a)))),
inference(resolution,[status(thm)],[d23,d20]) ).
cnf(d25,plain,
zero(in1(and2(h2(f2(a))))),
inference(resolution,[status(thm)],[d24,d18]) ).
cnf(d26,plain,
( ~ 'and$uok'(and2(h2(f2(a))))
| zero(out1(and2(h2(f2(a))))) ),
inference(resolution,[status(thm)],[d25,c28]) ).
cnf(d27,plain,
'logic$uand'(and2(h2(f2(a)))),
inference(resolution,[status(thm)],[c51,d14]) ).
cnf(d28,plain,
( 'and$uok'(and2(h2(f2(a))))
| abnormal(and2(h2(f2(a)))) ),
inference(resolution,[status(thm)],[d27,c35]) ).
cnf(d29,plain,
'and$uok'(and2(h2(f2(a)))),
inference(resolution,[status(thm)],[c22,d28]) ).
cnf(d30,plain,
zero(out1(and2(h2(f2(a))))),
inference(resolution,[status(thm)],[d29,d26]) ).
cnf(d31,plain,
zero(outc(h2(f2(a)))),
inference(resolution,[status(thm)],[d30,d16]) ).
cnf(d32,plain,
zero(in1(or1(f2(a)))),
inference(resolution,[status(thm)],[d31,d13]) ).
cnf(d33,plain,
~ one(in1(or1(f2(a)))),
inference(resolution,[status(thm)],[d32,c27]) ).
cnf(d34,plain,
one(in2(or1(f2(a)))),
inference(resolution,[status(thm)],[d33,d11]) ).
cnf(d35,plain,
connection(outc(h1(f2(a))),in2(or1(f2(a)))),
inference(resolution,[status(thm)],[c67,d0]) ).
cnf(d36,plain,
( ~ zero(outc(h1(f2(a))))
| zero(in2(or1(f2(a)))) ),
inference(resolution,[status(thm)],[d35,c23]) ).
cnf(d37,plain,
halfadder(h1(f2(a))),
inference(resolution,[status(thm)],[c63,d0]) ).
cnf(d38,plain,
connection(outc(h1(f2(a))),out1(and2(h1(f2(a))))),
inference(resolution,[status(thm)],[c59,d37]) ).
cnf(d39,plain,
( ~ zero(out1(and2(h1(f2(a)))))
| zero(outc(h1(f2(a)))) ),
inference(resolution,[status(thm)],[d38,c25]) ).
cnf(d40,plain,
connection(in1(h1(f2(a))),in1(and2(h1(f2(a))))),
inference(resolution,[status(thm)],[c56,d37]) ).
cnf(d41,plain,
( ~ zero(in1(h1(f2(a))))
| zero(in1(and2(h1(f2(a))))) ),
inference(resolution,[status(thm)],[d40,c23]) ).
cnf(d42,plain,
connection(in2(f2(a)),in1(h1(f2(a)))),
inference(resolution,[status(thm)],[c70,d0]) ).
cnf(d43,plain,
( ~ zero(in2(f2(a)))
| zero(in1(h1(f2(a)))) ),
inference(resolution,[status(thm)],[d42,c23]) ).
cnf(d44,plain,
connection(inb2(a),in2(f2(a))),
inference(resolution,[status(thm)],[c8,c11]) ).
cnf(d45,plain,
( ~ zero(inb2(a))
| zero(in2(f2(a))) ),
inference(resolution,[status(thm)],[d44,c23]) ).
cnf(d46,plain,
zero(in2(f2(a))),
inference(resolution,[status(thm)],[c15,d45]) ).
cnf(d47,plain,
zero(in1(h1(f2(a)))),
inference(resolution,[status(thm)],[d46,d43]) ).
cnf(d48,plain,
zero(in1(and2(h1(f2(a))))),
inference(resolution,[status(thm)],[d47,d41]) ).
cnf(d49,plain,
( ~ 'and$uok'(and2(h1(f2(a))))
| zero(out1(and2(h1(f2(a))))) ),
inference(resolution,[status(thm)],[d48,c28]) ).
cnf(d50,plain,
'logic$uand'(and2(h1(f2(a)))),
inference(resolution,[status(thm)],[c51,d37]) ).
cnf(d51,plain,
( 'and$uok'(and2(h1(f2(a))))
| abnormal(and2(h1(f2(a)))) ),
inference(resolution,[status(thm)],[d50,c35]) ).
cnf(d52,plain,
'and$uok'(and2(h1(f2(a)))),
inference(resolution,[status(thm)],[c21,d51]) ).
cnf(d53,plain,
zero(out1(and2(h1(f2(a))))),
inference(resolution,[status(thm)],[d52,d49]) ).
cnf(d54,plain,
zero(outc(h1(f2(a)))),
inference(resolution,[status(thm)],[d53,d39]) ).
cnf(d55,plain,
zero(in2(or1(f2(a)))),
inference(resolution,[status(thm)],[d54,d36]) ).
cnf(d56,plain,
~ one(in2(or1(f2(a)))),
inference(resolution,[status(thm)],[d55,c27]) ).
cnf(d57,plain,
$false,
inference(resolution,[status(thm)],[d56,d34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : HWV008-2.002 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n018.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Fri Sep 25 16:02:36 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.06/6.94 % SZS status Unsatisfiable for theBenchmark.p
% 29.06/6.94 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------