%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HWC001-1 : TPTP v9.3.1. Bugfixed v1.1.1.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 07:32:05 AM UTC 2026
% Result : Unsatisfiable 10.15s 1.89s
% Output : CNFRefutation 10.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of clauses : 46 ( 41 unt; 0 nHn; 37 RR)
% Number of literals : 53 ( 13 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(nand_definition,axiom,
nand(X0,X1) = not(and(X0,X1)) ).
cnf(and_definition1,axiom,
and(X0,n0) = n0 ).
cnf(and_definition2,axiom,
and(X0,n1) = X0 ).
cnf(not_definition1,axiom,
not(n0) = n1 ).
cnf(not_definition2,axiom,
not(n1) = n0 ).
cnf(nand_table_definition,negated_conjecture,
( output(nand(X0,X4),nand(X1,X5),nand(X2,X6),nand(X3,X7))
| ~ output(X4,X5,X6,X7)
| ~ output(X0,X1,X2,X3) ) ).
cnf(input1,negated_conjecture,
output(n0,n0,n1,n1) ).
cnf(input2,negated_conjecture,
output(n0,n1,n0,n1) ).
cnf(prove_cannot_make_or,negated_conjecture,
~ output(n0,n1,n1,n1) ).
cnf(c0,plain,
not(and(X0,X1)) = nand(X0,X1),
inference(clausification,[status(esa)],[nand_definition]) ).
cnf(c1,plain,
and(X0,n0) = n0,
inference(clausification,[status(esa)],[and_definition1]) ).
cnf(c2,plain,
and(X0,n1) = X0,
inference(clausification,[status(esa)],[and_definition2]) ).
cnf(c3,plain,
not(n0) = n1,
inference(clausification,[status(esa)],[not_definition1]) ).
cnf(c4,plain,
not(n1) = n0,
inference(clausification,[status(esa)],[not_definition2]) ).
cnf(c5,plain,
( output(nand(X4,X0),nand(X5,X1),nand(X6,X2),nand(X7,X3))
| ~ output(X4,X5,X6,X7)
| ~ output(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[nand_table_definition]) ).
cnf(c6,plain,
output(n0,n0,n1,n1),
inference(clausification,[status(esa)],[input1]) ).
cnf(c7,plain,
output(n0,n1,n0,n1),
inference(clausification,[status(esa)],[input2]) ).
cnf(c8,plain,
~ output(n0,n1,n1,n1),
inference(clausification,[status(esa)],[prove_cannot_make_or]) ).
cnf(d0,plain,
not(n0) = nand(X0,n0),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(d1,plain,
n1 = nand(X0,n0),
inference(demodulation,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
not(X0) = nand(X0,n1),
inference(superposition,[status(thm)],[c2,c0]) ).
cnf(d3,plain,
( output(nand(n0,X0),nand(n0,X1),nand(n1,X2),nand(n1,X3))
| ~ output(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c6,c5]) ).
cnf(d4,plain,
output(nand(n0,n0),nand(n0,n0),nand(n1,n1),nand(n1,n1)),
inference(resolution,[status(thm)],[d3,c6]) ).
cnf(d5,plain,
output(n1,nand(n0,n0),nand(n1,n1),nand(n1,n1)),
inference(demodulation,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
output(n1,n1,nand(n1,n1),nand(n1,n1)),
inference(demodulation,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
output(n1,n1,not(n1),nand(n1,n1)),
inference(demodulation,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
output(n1,n1,n0,nand(n1,n1)),
inference(demodulation,[status(thm)],[d7,c4]) ).
cnf(d9,plain,
output(n1,n1,n0,not(n1)),
inference(demodulation,[status(thm)],[d8,d2]) ).
cnf(d10,plain,
output(n1,n1,n0,n0),
inference(demodulation,[status(thm)],[d9,c4]) ).
cnf(d11,plain,
( output(nand(n1,X0),nand(n1,X1),nand(n0,X2),nand(n0,X3))
| ~ output(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d10,c5]) ).
cnf(d12,plain,
( output(nand(n0,X0),nand(n1,X1),nand(n0,X2),nand(n1,X3))
| ~ output(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c7,c5]) ).
cnf(d13,plain,
output(nand(n0,n0),nand(n1,n1),nand(n0,n0),nand(n1,n1)),
inference(resolution,[status(thm)],[d12,c7]) ).
cnf(d14,plain,
output(n1,nand(n1,n1),nand(n0,n0),nand(n1,n1)),
inference(demodulation,[status(thm)],[d13,d1]) ).
cnf(d15,plain,
output(n1,not(n1),nand(n0,n0),nand(n1,n1)),
inference(demodulation,[status(thm)],[d14,d2]) ).
cnf(d16,plain,
output(n1,n0,nand(n0,n0),nand(n1,n1)),
inference(demodulation,[status(thm)],[d15,c4]) ).
cnf(d17,plain,
output(n1,n0,n1,nand(n1,n1)),
inference(demodulation,[status(thm)],[d16,d1]) ).
cnf(d18,plain,
output(n1,n0,n1,not(n1)),
inference(demodulation,[status(thm)],[d17,d2]) ).
cnf(d19,plain,
output(n1,n0,n1,n0),
inference(demodulation,[status(thm)],[d18,c4]) ).
cnf(d20,plain,
output(nand(n1,n1),nand(n1,n0),nand(n0,n1),nand(n0,n0)),
inference(resolution,[status(thm)],[d19,d11]) ).
cnf(d21,plain,
output(not(n1),nand(n1,n0),nand(n0,n1),nand(n0,n0)),
inference(demodulation,[status(thm)],[d20,d2]) ).
cnf(d22,plain,
output(n0,nand(n1,n0),nand(n0,n1),nand(n0,n0)),
inference(demodulation,[status(thm)],[d21,c4]) ).
cnf(d23,plain,
output(n0,n1,nand(n0,n1),nand(n0,n0)),
inference(demodulation,[status(thm)],[d22,d1]) ).
cnf(d24,plain,
output(n0,n1,not(n0),nand(n0,n0)),
inference(demodulation,[status(thm)],[d23,d2]) ).
cnf(d25,plain,
output(n0,n1,n1,nand(n0,n0)),
inference(demodulation,[status(thm)],[d24,c3]) ).
cnf(d26,plain,
output(n0,n1,n1,n1),
inference(demodulation,[status(thm)],[d25,d1]) ).
cnf(d27,plain,
$false,
inference(resolution,[status(thm)],[c8,d26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : HWC001-1 : TPTP v9.3.1. Bugfixed v1.1.1.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.50 % Computer : n012.cluster.edu
% 0.04/0.50 % Model : x86_64 x86_64
% 0.04/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.50 % Memory : 8046.5625MB
% 0.04/0.50 % OS : Linux 6.8.0-71-generic
% 0.04/0.50 % CPULimit : 300
% 0.04/0.50 % WCLimit : 300
% 0.04/0.50 % DateTime : Fri Sep 25 15:58:21 UTC 2026
% 0.04/0.51 % CPUTime :
% 0.04/0.51 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.15/1.89 % SZS status Unsatisfiable for theBenchmark.p
% 10.15/1.89 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------