%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO075-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/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 : Tue Sep 29 09:35:43 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.23s
% Output : CNFRefutation 0.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 2
% Syntax : Number of clauses : 141 ( 141 unt; 0 nHn; 3 RR)
% Number of literals : 141 ( 140 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 12 ( 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 : 347 ( 37 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
nand(nand(a,a),nand(b,a)) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_meredith_2_basis_1) ).
cnf(c2,axiom,
nand(nand(A,nand(nand(B,A),A)),nand(B,nand(C,A))) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sh_1) ).
cnf(c3,plain,
nand(nand(X2,nand(nand(X2,X2),X2)),nand(X2,nand(X,X2))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
X2 = nand(nand(X2,nand(nand(X2,X2),X2)),nand(X2,nand(X,X2))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
nand(X2,nand(X2,nand(X,X2))) = nand(nand(nand(X2,nand(nand(X2,X2),X2)),nand(X2,nand(X,X2))),nand(X2,nand(X,X2))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
nand(nand(X2,nand(X,X2)),nand(X2,nand(X2,nand(X,X2)))) = nand(nand(X2,nand(X,X2)),nand(nand(nand(X2,nand(nand(X2,X2),X2)),nand(X2,nand(X,X2))),nand(X2,nand(X,X2)))),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,plain,
nand(nand(nand(X2,nand(X,X2)),nand(X2,nand(X2,nand(X,X2)))),X2) = nand(nand(nand(X2,nand(X,X2)),nand(nand(nand(X2,nand(nand(X2,X2),X2)),nand(X2,nand(X,X2))),nand(X2,nand(X,X2)))),X2),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X2,X),X))) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c9,plain,
X = nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X2,X),X))),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
nand(nand(X2,nand(nand(nand(X,nand(nand(X,X),X)),X2),X2)),X) = nand(nand(X2,nand(nand(nand(X,nand(nand(X,X),X)),X2),X2)),nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X2,X),X)))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
nand(nand(X3,nand(nand(X,X3),X3)),nand(X,nand(X2,X3))) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c12,plain,
X3 = nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2))),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
nand(X3,X4) = nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
nand(nand(X3,X4),X4) = nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),X4),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
nand(X4,nand(nand(X3,X4),X4)) = nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),X4)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
nand(nand(X4,nand(nand(X3,X4),X4)),nand(X3,nand(X2,nand(nand(X4,X2),X2)))) = nand(nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),X4)),nand(X3,nand(X2,nand(nand(X4,X2),X2)))),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c18,plain,
X3 = nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2))),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),X4) = nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),X4)) = nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
nand(nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),X4)),nand(X3,nand(X2,nand(nand(X4,X2),X2)))) = nand(nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X3,nand(X2,nand(nand(X4,X2),X2)))),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c23,plain,
X3 = nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2))),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))) = nand(nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))),nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
nand(nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X3,nand(X2,nand(nand(X4,X2),X2)))) = nand(nand(nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))),nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X3,nand(X2,nand(nand(X4,X2),X2)))),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
nand(nand(X,nand(nand(X3,X),X)),nand(X3,nand(X2,X))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c27,plain,
X3 = nand(nand(X,nand(nand(X3,X),X)),nand(X3,nand(X2,X))),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
nand(X,X4) = nand(X,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X3,X2)))),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
nand(nand(nand(X4,nand(X3,X2)),nand(nand(X,nand(X4,nand(X3,X2))),nand(X4,nand(X3,X2)))),nand(X,X4)) = nand(nand(nand(X4,nand(X3,X2)),nand(nand(X,nand(X4,nand(X3,X2))),nand(X4,nand(X3,X2)))),nand(X,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X3,X2))))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
nand(nand(nand(X4,nand(X3,X2)),nand(nand(X,nand(X4,nand(X3,X2))),nand(X4,nand(X3,X2)))),nand(X,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X3,X2))))) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c31,plain,
nand(nand(nand(X4,nand(X3,X2)),nand(nand(X,nand(X4,nand(X3,X2))),nand(X4,nand(X3,X2)))),nand(X,X4)) = X,
inference(transitivity,[status(thm)],[c29,c30]) ).
cnf(c32,plain,
nand(nand(nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))),nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X3,nand(X2,nand(nand(X4,X2),X2)))) = X3,
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
nand(nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X3,nand(X2,nand(nand(X4,X2),X2)))) = X3,
inference(transitivity,[status(thm)],[c25,c32]) ).
cnf(c34,plain,
nand(nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),X4)),nand(X3,nand(X2,nand(nand(X4,X2),X2)))) = X3,
inference(transitivity,[status(thm)],[c21,c33]) ).
cnf(c35,plain,
nand(nand(X3,nand(nand(X2,X3),X3)),nand(X2,nand(X,nand(nand(X3,X),X)))) = X2,
inference(transitivity,[status(thm)],[c16,c34]) ).
cnf(c36,plain,
nand(nand(X2,nand(nand(nand(X,nand(nand(X,X),X)),X2),X2)),nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X2,X),X)))) = nand(X,nand(nand(X,X),X)),
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
nand(nand(X2,nand(nand(nand(X,nand(nand(X,X),X)),X2),X2)),X) = nand(X,nand(nand(X,X),X)),
inference(transitivity,[status(thm)],[c10,c36]) ).
cnf(c38,plain,
nand(nand(nand(X2,nand(X,X2)),nand(nand(nand(X2,nand(nand(X2,X2),X2)),nand(X2,nand(X,X2))),nand(X2,nand(X,X2)))),X2) = nand(X2,nand(nand(X2,X2),X2)),
inference(substitution,[status(thm)],[c37]) ).
cnf(c39,plain,
nand(nand(nand(X2,nand(X,X2)),nand(X2,nand(X2,nand(X,X2)))),X2) = nand(X2,nand(nand(X2,X2),X2)),
inference(transitivity,[status(thm)],[c7,c38]) ).
cnf(c40,plain,
nand(nand(nand(X,nand(nand(X,X),X)),nand(X,nand(X,nand(nand(X,X),X)))),X) = nand(X,nand(nand(X,X),X)),
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
nand(X,nand(nand(X,X),X)) = nand(nand(nand(X,nand(nand(X,X),X)),nand(X,nand(X,nand(nand(X,X),X)))),X),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,plain,
nand(nand(X,nand(nand(X,X),X)),nand(X,nand(X,nand(nand(X,X),X)))) = X,
inference(substitution,[status(thm)],[c35]) ).
cnf(c43,plain,
nand(nand(nand(X,nand(nand(X,X),X)),nand(X,nand(X,nand(nand(X,X),X)))),X) = nand(X,X),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
nand(X,nand(nand(X,X),X)) = nand(X,X),
inference(transitivity,[status(thm)],[c41,c43]) ).
cnf(c45,plain,
nand(X,X) = nand(X,nand(nand(X,X),X)),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c46,plain,
nand(nand(X2,X2),nand(X,X2)) = nand(nand(X2,nand(nand(X2,X2),X2)),nand(X,X2)),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2))) = nand(nand(X,X2),nand(X,X2)),
inference(substitution,[status(thm)],[c44]) ).
cnf(c48,plain,
nand(nand(X,X2),nand(X,X2)) = nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2))),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
nand(nand(nand(X,X2),nand(X,X2)),X2) = nand(nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2))),X2),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
nand(nand(nand(nand(X,X2),nand(X,X2)),X2),X2) = nand(nand(nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2))),X2),X2),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
nand(X2,nand(nand(nand(nand(X,X2),nand(X,X2)),X2),X2)) = nand(X2,nand(nand(nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2))),X2),X2)),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
nand(nand(X2,nand(nand(X,X2),X2)),nand(X,nand(X3,X2))) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c53,plain,
X = nand(nand(X2,nand(nand(X,X2),X2)),nand(X,nand(X3,X2))),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(nand(X,X2),X2)),nand(X3,X2)),nand(X3,X2))),X) = nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(nand(X,X2),X2)),nand(X3,X2)),nand(X3,X2))),nand(nand(X2,nand(nand(X,X2),X2)),nand(X,nand(X3,X2)))),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(nand(X,X2),X2)),nand(X3,X2)),nand(X3,X2))),nand(nand(X2,nand(nand(X,X2),X2)),nand(X,nand(X3,X2)))) = nand(X2,nand(nand(X,X2),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c56,plain,
nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(nand(X,X2),X2)),nand(X3,X2)),nand(X3,X2))),X) = nand(X2,nand(nand(X,X2),X2)),
inference(transitivity,[status(thm)],[c54,c55]) ).
cnf(c57,plain,
nand(nand(nand(X,X2),nand(nand(nand(X2,nand(nand(nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2))),X2),X2)),nand(X,X2)),nand(X,X2))),nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2)))) = nand(X2,nand(nand(nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2))),X2),X2)),
inference(substitution,[status(thm)],[c56]) ).
cnf(c58,plain,
nand(X2,nand(nand(nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2))),X2),X2)) = nand(nand(nand(X,X2),nand(nand(nand(X2,nand(nand(nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2))),X2),X2)),nand(X,X2)),nand(X,X2))),nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2)))),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c59,plain,
nand(nand(X2,nand(nand(nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2))),X2),X2)),nand(X,X2)) = nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2))),
inference(substitution,[status(thm)],[c37]) ).
cnf(c60,plain,
nand(nand(nand(X2,nand(nand(nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2))),X2),X2)),nand(X,X2)),nand(X,X2)) = nand(nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2))),nand(X,X2)),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
nand(nand(X,X2),nand(nand(nand(X2,nand(nand(nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2))),X2),X2)),nand(X,X2)),nand(X,X2))) = nand(nand(X,X2),nand(nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2))),nand(X,X2))),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
nand(nand(nand(X,X2),nand(nand(nand(X2,nand(nand(nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2))),X2),X2)),nand(X,X2)),nand(X,X2))),nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2)))) = nand(nand(nand(X,X2),nand(nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2))),nand(X,X2))),nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2)))),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
nand(X,X) = nand(X,nand(nand(X,X),X)),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c64,plain,
nand(nand(X,X),nand(X,X)) = nand(nand(X,nand(nand(X,X),X)),nand(X,X)),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
nand(X,X) = nand(X,nand(nand(X,X),X)),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c66,plain,
nand(nand(X,nand(nand(X,X),X)),nand(X,X)) = nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X,X),X))),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X,X),X))) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c68,plain,
nand(nand(X,nand(nand(X,X),X)),nand(X,X)) = X,
inference(transitivity,[status(thm)],[c66,c67]) ).
cnf(c69,plain,
nand(nand(X,X),nand(X,X)) = X,
inference(transitivity,[status(thm)],[c64,c68]) ).
cnf(c70,plain,
X = nand(nand(X,X),nand(X,X)),
inference(symmetry,[status(thm)],[c69]) ).
cnf(c71,plain,
nand(X,nand(X,X)) = nand(nand(nand(X,X),nand(X,X)),nand(X,X)),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
nand(nand(X,X),nand(X,nand(X,X))) = nand(nand(X,X),nand(nand(nand(X,X),nand(X,X)),nand(X,X))),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
nand(nand(X,X),nand(nand(nand(X,X),nand(X,X)),nand(X,X))) = nand(nand(X,X),nand(X,X)),
inference(substitution,[status(thm)],[c44]) ).
cnf(c74,plain,
nand(nand(X,X),nand(nand(nand(X,X),nand(X,X)),nand(X,X))) = X,
inference(transitivity,[status(thm)],[c73,c69]) ).
cnf(c75,plain,
nand(nand(X,X),nand(X,nand(X,X))) = X,
inference(transitivity,[status(thm)],[c72,c74]) ).
cnf(c76,plain,
X = nand(nand(X,X),nand(X,nand(X,X))),
inference(symmetry,[status(thm)],[c75]) ).
cnf(c77,plain,
nand(X2,nand(nand(X,nand(nand(X2,X),X)),X2)) = nand(nand(nand(X2,X2),nand(X2,nand(X2,X2))),nand(nand(X,nand(nand(X2,X),X)),X2)),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
nand(X,X) = nand(X,nand(nand(X,X),X)),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c79,plain,
nand(nand(X2,nand(nand(X,X2),X2)),nand(X,X)) = nand(nand(X2,nand(nand(X,X2),X2)),nand(X,nand(nand(X,X),X))),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X,X),X))) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c81,plain,
X = nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X,X),X))),
inference(symmetry,[status(thm)],[c80]) ).
cnf(c82,plain,
nand(X,X2) = nand(nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X,X),X))),X2),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
nand(nand(X,X2),X2) = nand(nand(nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X,X),X))),X2),X2),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
nand(X2,nand(nand(X,X2),X2)) = nand(X2,nand(nand(nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X,X),X))),X2),X2)),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
nand(nand(X2,nand(nand(X,X2),X2)),nand(X,nand(nand(X,X),X))) = nand(nand(X2,nand(nand(nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X,X),X))),X2),X2)),nand(X,nand(nand(X,X),X))),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
nand(X,X) = nand(X,nand(nand(X,X),X)),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c87,plain,
nand(nand(X,X),X2) = nand(nand(X,nand(nand(X,X),X)),X2),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
nand(nand(nand(X,X),X2),X2) = nand(nand(nand(X,nand(nand(X,X),X)),X2),X2),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
nand(X2,nand(nand(nand(X,X),X2),X2)) = nand(X2,nand(nand(nand(X,nand(nand(X,X),X)),X2),X2)),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
nand(nand(X2,nand(nand(nand(X,X),X2),X2)),X) = nand(nand(X2,nand(nand(nand(X,nand(nand(X,X),X)),X2),X2)),X),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
nand(nand(X2,nand(nand(nand(X,nand(nand(X,X),X)),X2),X2)),X) = nand(X,X),
inference(transitivity,[status(thm)],[c37,c44]) ).
cnf(c92,plain,
nand(nand(X2,nand(nand(nand(X,X),X2),X2)),X) = nand(X,X),
inference(transitivity,[status(thm)],[c90,c91]) ).
cnf(c93,plain,
nand(nand(X2,nand(nand(nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X,X),X))),X2),X2)),nand(X,nand(nand(X,X),X))) = nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X,X),X))),
inference(substitution,[status(thm)],[c92]) ).
cnf(c94,plain,
nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X,X),X))) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c95,plain,
nand(nand(X2,nand(nand(nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X,X),X))),X2),X2)),nand(X,nand(nand(X,X),X))) = X,
inference(transitivity,[status(thm)],[c93,c94]) ).
cnf(c96,plain,
nand(nand(X2,nand(nand(X,X2),X2)),nand(X,nand(nand(X,X),X))) = X,
inference(transitivity,[status(thm)],[c85,c95]) ).
cnf(c97,plain,
nand(nand(X2,nand(nand(X,X2),X2)),nand(X,X)) = X,
inference(transitivity,[status(thm)],[c79,c96]) ).
cnf(c98,plain,
nand(nand(X,nand(nand(X2,X),X)),nand(X2,X2)) = X2,
inference(substitution,[status(thm)],[c97]) ).
cnf(c99,plain,
X2 = nand(nand(X,nand(nand(X2,X),X)),nand(X2,X2)),
inference(symmetry,[status(thm)],[c98]) ).
cnf(c100,plain,
nand(X2,nand(X2,X2)) = nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X2)),nand(X2,X2)),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
nand(nand(X2,X2),nand(X2,nand(X2,X2))) = nand(nand(X2,X2),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X2)),nand(X2,X2))),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
nand(nand(nand(X2,X2),nand(X2,nand(X2,X2))),nand(nand(X,nand(nand(X2,X),X)),X2)) = nand(nand(nand(X2,X2),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X2)),nand(X2,X2))),nand(nand(X,nand(nand(X2,X),X)),X2)),
inference(congruence,[status(thm)],[c101]) ).
cnf(c103,plain,
nand(nand(X,nand(nand(X2,X),X)),nand(X2,nand(X3,X))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c104,plain,
X3 = nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2))),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c105,plain,
nand(X4,X3) = nand(X4,nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2)))),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
nand(X3,nand(X5,X4)) = nand(X3,nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
nand(nand(X3,nand(X5,X4)),nand(X5,X4)) = nand(nand(X3,nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X5,X4)),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
nand(nand(X5,X4),nand(nand(X3,nand(X5,X4)),nand(X5,X4))) = nand(nand(X5,X4),nand(nand(X3,nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X5,X4))),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
nand(nand(nand(X5,X4),nand(nand(X3,nand(X5,X4)),nand(X5,X4))),nand(X3,X5)) = nand(nand(nand(X5,X4),nand(nand(X3,nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X5,X4))),nand(X3,X5)),
inference(congruence,[status(thm)],[c108]) ).
cnf(c110,plain,
nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c111,plain,
X3 = nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2))),
inference(symmetry,[status(thm)],[c110]) ).
cnf(c112,plain,
nand(X4,X3) = nand(X4,nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2)))),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,plain,
nand(nand(X3,nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X5,X4)) = nand(nand(X3,nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,plain,
nand(nand(X5,X4),nand(nand(X3,nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X5,X4))) = nand(nand(X5,X4),nand(nand(X3,nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))))),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
nand(nand(nand(X5,X4),nand(nand(X3,nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X5,X4))),nand(X3,X5)) = nand(nand(nand(X5,X4),nand(nand(X3,nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))))),nand(X3,X5)),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c117,plain,
X3 = nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2))),
inference(symmetry,[status(thm)],[c116]) ).
cnf(c118,plain,
nand(X4,X3) = nand(X4,nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2)))),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
nand(nand(X5,X4),nand(nand(X3,nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))))) = nand(nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X3,nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))))),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
nand(nand(nand(X5,X4),nand(nand(X3,nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))))),nand(X3,X5)) = nand(nand(nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X3,nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))))),nand(X3,X5)),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
nand(nand(nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X3,nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))))),nand(X3,X5)) = X3,
inference(substitution,[status(thm)],[c31]) ).
cnf(c122,plain,
nand(nand(nand(X5,X4),nand(nand(X3,nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))))),nand(X3,X5)) = X3,
inference(transitivity,[status(thm)],[c120,c121]) ).
cnf(c123,plain,
nand(nand(nand(X5,X4),nand(nand(X3,nand(X5,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X5,X4))),nand(X3,X5)) = X3,
inference(transitivity,[status(thm)],[c115,c122]) ).
cnf(c124,plain,
nand(nand(nand(X3,X2),nand(nand(X,nand(X3,X2)),nand(X3,X2))),nand(X,X3)) = X,
inference(transitivity,[status(thm)],[c109,c123]) ).
cnf(c125,plain,
nand(nand(nand(X2,X2),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X2)),nand(X2,X2))),nand(nand(X,nand(nand(X2,X),X)),X2)) = nand(X,nand(nand(X2,X),X)),
inference(substitution,[status(thm)],[c124]) ).
cnf(c126,plain,
nand(nand(nand(X2,X2),nand(X2,nand(X2,X2))),nand(nand(X,nand(nand(X2,X),X)),X2)) = nand(X,nand(nand(X2,X),X)),
inference(transitivity,[status(thm)],[c102,c125]) ).
cnf(c127,plain,
nand(X2,nand(nand(X,nand(nand(X2,X),X)),X2)) = nand(X,nand(nand(X2,X),X)),
inference(transitivity,[status(thm)],[c77,c126]) ).
cnf(c128,plain,
nand(nand(X,X2),nand(nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2))),nand(X,X2))) = nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2))),
inference(substitution,[status(thm)],[c127]) ).
cnf(c129,plain,
nand(nand(nand(X,X2),nand(nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2))),nand(X,X2))),nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2)))) = nand(nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2))),nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2)))),
inference(congruence,[status(thm)],[c128]) ).
cnf(c130,plain,
nand(nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2))),nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2)))) = nand(X,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c131,plain,
nand(nand(nand(X,X2),nand(nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2))),nand(X,X2))),nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2)))) = nand(X,X2),
inference(transitivity,[status(thm)],[c129,c130]) ).
cnf(c132,plain,
nand(nand(nand(X,X2),nand(nand(nand(X2,nand(nand(nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2))),X2),X2)),nand(X,X2)),nand(X,X2))),nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2)))) = nand(X,X2),
inference(transitivity,[status(thm)],[c62,c131]) ).
cnf(c133,plain,
nand(X2,nand(nand(nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2))),X2),X2)) = nand(X,X2),
inference(transitivity,[status(thm)],[c58,c132]) ).
cnf(c134,plain,
nand(X2,nand(nand(nand(nand(X,X2),nand(X,X2)),X2),X2)) = nand(X,X2),
inference(transitivity,[status(thm)],[c51,c133]) ).
cnf(c135,plain,
nand(X,X2) = nand(X2,nand(nand(nand(nand(X,X2),nand(X,X2)),X2),X2)),
inference(symmetry,[status(thm)],[c134]) ).
cnf(c136,plain,
nand(nand(X2,nand(nand(X2,X2),X2)),nand(X,X2)) = nand(nand(X2,nand(nand(X2,X2),X2)),nand(X2,nand(nand(nand(nand(X,X2),nand(X,X2)),X2),X2))),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
nand(nand(X2,nand(nand(X2,X2),X2)),nand(X2,nand(nand(nand(nand(X,X2),nand(X,X2)),X2),X2))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c138,plain,
nand(nand(X2,nand(nand(X2,X2),X2)),nand(X,X2)) = X2,
inference(transitivity,[status(thm)],[c136,c137]) ).
cnf(c139,plain,
nand(nand(X2,X2),nand(X,X2)) = X2,
inference(transitivity,[status(thm)],[c46,c138]) ).
cnf(c140,plain,
nand(nand(a,a),nand(b,a)) = a,
inference(substitution,[status(thm)],[c139]) ).
cnf(c141,plain,
$false,
inference(resolution,[status(thm)],[c1,c140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : BOO075-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Mon Sep 28 21:07:34 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.23 Command-line arguments: --no-flatten-goal
% 0.09/0.23
% 0.09/0.23 % SZS status Unsatisfiable
% 0.09/0.23
% 0.09/0.24 % SZS output start CNFRefutation
% See solution above
% 0.86/0.34
% 0.86/0.34 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------