%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : BOO075-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 06:54:47 AM UTC 2026
% Result : Unsatisfiable 50.28s 12.83s
% Output : CNFRefutation 50.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 2
% Syntax : Number of clauses : 59 ( 59 unt; 0 nHn; 4 RR)
% Number of literals : 59 ( 58 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 114 ( 19 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(sh_1,axiom,
nand(nand(X0,nand(nand(X1,X0),X0)),nand(X1,nand(X2,X0))) = X1 ).
cnf(prove_meredith_2_basis_1,negated_conjecture,
nand(nand(a,a),nand(b,a)) != a ).
cnf(c0,plain,
nand(nand(X0,nand(nand(X1,X0),X0)),nand(X1,nand(X2,X0))) = X1,
inference(clausification,[status(esa)],[sh_1]) ).
cnf(c1,plain,
nand(nand(a,a),nand(b,a)) != a,
inference(clausification,[status(esa)],[prove_meredith_2_basis_1]) ).
cnf(d0,plain,
nand(nand(nand(X2,X0),nand(nand(nand(X0,nand(nand(X1,X0),X0)),nand(X2,X0)),nand(X2,X0))),X1) = nand(X0,nand(nand(X1,X0),X0)),
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d1,plain,
nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X1,nand(nand(X2,X1),X1)))) = X3,
inference(superposition,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
nand(nand(X1,nand(nand(nand(X0,nand(nand(X0,X0),X0)),X1),X1)),X0) = nand(X0,nand(nand(X0,X0),X0)),
inference(superposition,[status(thm)],[c0,d1]) ).
cnf(d3,plain,
nand(nand(nand(X0,nand(X1,X0)),nand(X0,nand(X0,nand(X1,X0)))),X0) = nand(X0,nand(nand(X0,X0),X0)),
inference(superposition,[status(thm)],[c0,d2]) ).
cnf(d4,plain,
nand(X0,X0) = nand(X0,nand(nand(X0,X0),X0)),
inference(superposition,[status(thm)],[d1,d3]) ).
cnf(d5,plain,
nand(nand(X0,X0),nand(X0,nand(X1,X0))) = X0,
inference(superposition,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
nand(nand(X0,X0),nand(X0,X0)) = X0,
inference(superposition,[status(thm)],[d4,d5]) ).
cnf(d7,plain,
nand(X0,nand(nand(X0,X0),nand(X1,nand(X0,X0)))) = nand(X0,X0),
inference(superposition,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
nand(nand(X1,nand(nand(X0,X1),X1)),nand(X0,X0)) = X0,
inference(superposition,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
nand(nand(nand(X1,nand(X2,X0)),nand(nand(X3,nand(X1,nand(X2,X0))),nand(X1,nand(X2,X0)))),nand(X3,X1)) = X3,
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d10,plain,
nand(nand(nand(X3,X0),nand(nand(X4,nand(X3,X0)),nand(X3,X0))),nand(X4,X3)) = X4,
inference(superposition,[status(thm)],[d9,c0]) ).
cnf(d11,plain,
nand(nand(X0,nand(nand(nand(nand(X0,X1),nand(nand(X2,nand(X0,X1)),nand(X0,X1))),X0),X0)),X2) = nand(nand(X0,X1),nand(nand(X2,nand(X0,X1)),nand(X0,X1))),
inference(superposition,[status(thm)],[d10,c0]) ).
cnf(d12,plain,
nand(nand(X1,nand(nand(nand(X0,X0),X1),X1)),X0) = nand(X0,nand(nand(X0,X0),X0)),
inference(demodulation,[status(thm)],[d2,d4]) ).
cnf(d13,plain,
nand(nand(X1,nand(nand(nand(X0,X0),X1),X1)),X0) = nand(X0,X0),
inference(demodulation,[status(thm)],[d12,d4]) ).
cnf(d14,plain,
nand(nand(X0,nand(nand(X0,X0),X0)),nand(X0,X0)) = nand(nand(X0,X1),nand(nand(nand(X0,X0),nand(X0,X1)),nand(X0,X1))),
inference(superposition,[status(thm)],[d13,d11]) ).
cnf(d15,plain,
X0 = nand(nand(X0,X1),nand(nand(nand(X0,X0),nand(X0,X1)),nand(X0,X1))),
inference(demodulation,[status(thm)],[d14,d8]) ).
cnf(d16,plain,
nand(X0,nand(nand(X0,X0),nand(X2,nand(X0,X1)))) = nand(X0,X0),
inference(superposition,[status(thm)],[d15,c0]) ).
cnf(d17,plain,
nand(nand(nand(X1,X1),nand(X1,nand(X1,X1))),nand(nand(X0,nand(nand(X1,X0),X0)),X1)) = nand(X0,nand(nand(X1,X0),X0)),
inference(superposition,[status(thm)],[d8,d10]) ).
cnf(d18,plain,
nand(X0,nand(nand(X1,nand(nand(X0,X1),X1)),X0)) = nand(X1,nand(nand(X0,X1),X1)),
inference(demodulation,[status(thm)],[d17,d5]) ).
cnf(d19,plain,
nand(nand(X0,X0),nand(X1,nand(nand(X0,X1),X1))) = X0,
inference(superposition,[status(thm)],[d18,d5]) ).
cnf(d20,plain,
nand(X1,nand(nand(X1,X1),X0)) = nand(X1,X1),
inference(superposition,[status(thm)],[d19,d16]) ).
cnf(d21,plain,
nand(X0,nand(nand(X0,X0),X0)) = nand(X0,X0),
inference(superposition,[status(thm)],[d6,d7]) ).
cnf(d22,plain,
nand(nand(X0,X0),nand(X0,nand(X0,X0))) = nand(nand(X0,X0),nand(X0,X0)),
inference(superposition,[status(thm)],[d6,d21]) ).
cnf(d23,plain,
X0 = nand(nand(X0,X0),nand(X0,X0)),
inference(demodulation,[status(thm)],[d22,d5]) ).
cnf(d24,plain,
nand(nand(X0,X0),nand(X0,X1)) = nand(nand(X0,X0),nand(X0,X0)),
inference(superposition,[status(thm)],[d23,d20]) ).
cnf(d25,plain,
nand(nand(X0,X0),nand(X0,X1)) = X0,
inference(demodulation,[status(thm)],[d24,d6]) ).
cnf(d26,plain,
X0 = nand(nand(X0,X1),nand(X0,nand(X0,X1))),
inference(demodulation,[status(thm)],[d15,d25]) ).
cnf(d27,plain,
nand(X0,X1) = nand(X0,nand(nand(X0,X1),nand(nand(X0,X1),nand(X0,nand(X0,X1))))),
inference(superposition,[status(thm)],[d26,d26]) ).
cnf(d28,plain,
nand(X0,X1) = nand(X0,nand(nand(X0,X1),X0)),
inference(demodulation,[status(thm)],[d27,d26]) ).
cnf(d29,plain,
nand(nand(nand(X0,X1),nand(X0,X1)),X0) = nand(X0,X1),
inference(superposition,[status(thm)],[d15,d5]) ).
cnf(d30,plain,
nand(nand(X0,nand(nand(X2,X0),X0)),nand(X2,nand(X0,X1))) = X2,
inference(superposition,[status(thm)],[d29,c0]) ).
cnf(d31,plain,
nand(nand(X0,nand(nand(nand(X0,X1),X0),X0)),X0) = nand(X0,X1),
inference(superposition,[status(thm)],[d26,d30]) ).
cnf(d32,plain,
nand(X0,nand(nand(nand(X0,X1),X0),X0)) = nand(X0,nand(X0,X1)),
inference(superposition,[status(thm)],[d31,d28]) ).
cnf(d33,plain,
nand(nand(X0,nand(X0,X1)),X0) = nand(X0,X1),
inference(demodulation,[status(thm)],[d31,d32]) ).
cnf(d34,plain,
nand(X0,nand(nand(X0,X1),X0)) = nand(X0,nand(X0,nand(X0,X1))),
inference(superposition,[status(thm)],[d33,d32]) ).
cnf(d35,plain,
nand(X0,X1) = nand(X0,nand(X0,nand(X0,X1))),
inference(demodulation,[status(thm)],[d34,d28]) ).
cnf(d36,plain,
nand(nand(X0,X1),X0) = nand(X0,nand(X0,X1)),
inference(superposition,[status(thm)],[d35,d33]) ).
cnf(d37,plain,
nand(nand(X0,nand(X0,X0)),X0) = nand(X0,nand(nand(X0,X0),X1)),
inference(superposition,[status(thm)],[d20,d33]) ).
cnf(d38,plain,
nand(X0,nand(X0,nand(X0,X0))) = nand(X0,nand(nand(X0,X0),X1)),
inference(demodulation,[status(thm)],[d37,d36]) ).
cnf(d39,plain,
nand(X0,X0) = nand(X0,nand(nand(X0,X0),X1)),
inference(demodulation,[status(thm)],[d38,d35]) ).
cnf(d40,plain,
X0 = nand(nand(X0,nand(X0,X1)),nand(X0,X1)),
inference(superposition,[status(thm)],[d35,d26]) ).
cnf(d41,plain,
nand(nand(nand(X0,X1),X0),nand(X0,X0)) = X0,
inference(superposition,[status(thm)],[d40,d10]) ).
cnf(d42,plain,
nand(nand(X0,nand(X0,X1)),nand(X0,X0)) = X0,
inference(demodulation,[status(thm)],[d41,d36]) ).
cnf(d43,plain,
nand(nand(X0,X1),nand(X0,X0)) = X0,
inference(superposition,[status(thm)],[d35,d42]) ).
cnf(d44,plain,
nand(nand(X0,X0),nand(X0,X0)) = nand(nand(X0,X0),nand(X0,X1)),
inference(superposition,[status(thm)],[d43,d39]) ).
cnf(d45,plain,
X0 = nand(nand(X0,X0),nand(X0,X1)),
inference(demodulation,[status(thm)],[d44,d25]) ).
cnf(d46,plain,
nand(nand(nand(X1,X0),nand(nand(nand(X1,X0),nand(nand(nand(X1,X0),nand(X1,X0)),nand(X1,X0))),nand(X1,X0))),nand(nand(X1,X0),nand(nand(nand(X1,X0),nand(X1,X0)),nand(X1,X0)))) = nand(X0,nand(nand(nand(nand(X1,X0),nand(nand(nand(X1,X0),nand(X1,X0)),nand(X1,X0))),X0),X0)),
inference(superposition,[status(thm)],[d2,d0]) ).
cnf(d47,plain,
nand(nand(nand(X0,X1),nand(nand(nand(X0,X1),nand(X0,X1)),nand(X0,X1))),nand(nand(X0,X1),nand(nand(nand(X0,X1),nand(X0,X1)),nand(X0,X1)))) = nand(X1,nand(nand(nand(nand(X0,X1),nand(nand(nand(X0,X1),nand(X0,X1)),nand(X0,X1))),X1),X1)),
inference(demodulation,[status(thm)],[d46,d18]) ).
cnf(d48,plain,
nand(X0,X1) = nand(X1,nand(nand(nand(nand(X0,X1),nand(nand(nand(X0,X1),nand(X0,X1)),nand(X0,X1))),X1),X1)),
inference(demodulation,[status(thm)],[d47,c0]) ).
cnf(d49,plain,
nand(X0,X1) = nand(X1,nand(nand(nand(nand(X0,X1),nand(X0,X1)),X1),X1)),
inference(demodulation,[status(thm)],[d48,d39]) ).
cnf(d50,plain,
X0 = nand(nand(X0,X0),nand(X1,X0)),
inference(superposition,[status(thm)],[d49,d45]) ).
cnf(d51,plain,
a != a,
inference(demodulation,[status(thm)],[c1,d50]) ).
cnf(d52,plain,
nand(nand(X1,nand(nand(X2,X1),X1)),nand(X2,nand(X1,nand(nand(X1,X1),X1)))) = X2,
inference(superposition,[status(thm)],[d2,c0]) ).
cnf(d53,plain,
X1 = X1,
inference(demodulation,[status(thm)],[d52,d1]) ).
cnf(d54,plain,
$false,
inference(resolution,[status(thm)],[d53,d51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO075-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 22:38:35 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 50.28/12.83 % SZS status Unsatisfiable for theBenchmark.p
% 50.28/12.83 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------