%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : BOO075-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Jul 15 06:14:52 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.45s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of clauses : 14 ( 14 unt; 0 nHn; 3 RR)
% Number of literals : 14 ( 13 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 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 : 23 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
nand(nand(a,a),nand(b,a)) != a,
file('theBenchmark.p',prove_meredith_2_basis_1) ).
cnf(c1,axiom,
nand(nand(X,nand(nand(Y,X),X)),nand(Y,nand(Z,X))) = Y,
file('theBenchmark.p',sh_1) ).
cnf(c2,plain,
nand(nand(nand(X,Y),nand(nand(nand(Y,nand(nand(Z,Y),Y)),nand(X,Y)),nand(X,Y))),Z) = nand(Y,nand(nand(Z,Y),Y)),
inference(equational,[status(thm)],[c1]) ).
cnf(c3,plain,
nand(nand(X,nand(nand(Y,X),X)),nand(Y,nand(Z,nand(nand(X,Z),Z)))) = Y,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,plain,
nand(nand(X,nand(nand(nand(Y,nand(nand(Y,Y),Y)),X),X)),Y) = nand(Y,nand(nand(Y,Y),Y)),
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c5,plain,
nand(nand(X,nand(nand(Y,X),X)),nand(Y,nand(nand(Y,Y),Y))) = Y,
inference(equational,[status(thm)],[c1,c3,c4]) ).
cnf(c6,plain,
nand(X,nand(nand(X,X),X)) = nand(X,X),
inference(equational,[status(thm)],[c3,c4,c5]) ).
cnf(c7,plain,
nand(nand(X,X),nand(X,X)) = X,
inference(equational,[status(thm)],[c5,c6]) ).
cnf(c8,plain,
nand(nand(X,X),nand(X,nand(Y,X))) = X,
inference(equational,[status(thm)],[c1,c6]) ).
cnf(c10,plain,
nand(nand(X,nand(nand(nand(Y,Y),X),X)),Y) = nand(Y,Y),
inference(equational,[status(thm)],[c4,c6]) ).
cnf(c13,plain,
nand(X,nand(nand(nand(nand(Y,X),nand(Y,X)),X),X)) = nand(Y,X),
inference(equational,[status(thm)],[c2,c6,c7,c10]) ).
cnf(c14,plain,
nand(nand(X,X),nand(Y,X)) = X,
inference(equational,[status(thm)],[c8,c13]) ).
cnf(g1,plain,
nand(nand(a,a),nand(b,a)) = a,
inference(equational,[status(thm)],[c14]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : BOO075-1 : TPTP v9.0.0. Released v2.6.0.
% 0.06/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 14 04:30:34 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.18/0.45 % SZS status Unsatisfiable
% 0.18/0.45 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------