%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : BOO073-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n004.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 4.65s 4.84s
% Output : CNFRefutation 4.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 2
% Syntax : Number of clauses : 67 ( 67 unt; 0 nHn; 3 RR)
% Number of literals : 67 ( 66 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 138 ( 27 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
add(add(a,b),c) != add(a,add(b,c)),
file('theBenchmark.p',huntinton_2) ).
cnf(c1,axiom,
inverse(add(inverse(add(inverse(add(X,Y)),Z)),inverse(add(X,inverse(add(inverse(Z),inverse(add(Z,W)))))))) = Z,
file('theBenchmark.p',dn1) ).
cnf(c2,plain,
inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(inverse(X)),Y)),X)),Z)),inverse(X))),X)) = inverse(X),
inference(equational,[status(thm)],[c1]) ).
cnf(c3,plain,
inverse(add(inverse(add(X,inverse(X))),X)) = inverse(X),
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,plain,
inverse(add(inverse(X),inverse(add(X,inverse(add(inverse(X),inverse(add(X,Y)))))))) = X,
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c5,plain,
inverse(add(inverse(X),inverse(add(X,X)))) = X,
inference(equational,[status(thm)],[c4]) ).
cnf(c6,plain,
inverse(add(inverse(add(inverse(add(X,Y)),Z)),inverse(add(X,Z)))) = Z,
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c7,plain,
inverse(add(inverse(add(X,Y)),inverse(add(inverse(X),Y)))) = Y,
inference(equational,[status(thm)],[c5,c6]) ).
cnf(c8,plain,
inverse(add(inverse(add(X,inverse(add(X,X)))),X)) = inverse(add(X,X)),
inference(equational,[status(thm)],[c5,c7]) ).
cnf(c9,plain,
inverse(add(inverse(add(X,X)),inverse(add(X,X)))) = X,
inference(equational,[status(thm)],[c6,c8]) ).
cnf(c11,plain,
inverse(add(inverse(add(add(X,inverse(X)),X)),inverse(X))) = X,
inference(equational,[status(thm)],[c3,c7]) ).
cnf(c13,plain,
inverse(add(X,inverse(add(X,inverse(add(X,X)))))) = inverse(add(X,X)),
inference(equational,[status(thm)],[c6,c9]) ).
cnf(c14,plain,
inverse(add(X,inverse(add(Y,inverse(add(inverse(Y),X)))))) = inverse(add(inverse(Y),X)),
inference(equational,[status(thm)],[c6,c7]) ).
cnf(c15,plain,
inverse(add(inverse(X),inverse(X))) = X,
inference(equational,[status(thm)],[c4,c14]) ).
cnf(c16,plain,
add(X,X) = X,
inference(equational,[status(thm)],[c9,c15]) ).
cnf(c17,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c9,c16]) ).
cnf(c19,plain,
add(X,inverse(add(X,inverse(X)))) = X,
inference(equational,[status(thm)],[c13,c16,c17]) ).
cnf(c24,plain,
add(inverse(add(add(X,inverse(X)),X)),inverse(X)) = inverse(X),
inference(equational,[status(thm)],[c11,c15,c16]) ).
cnf(c26,plain,
add(X,inverse(add(Y,inverse(add(inverse(Y),X))))) = add(inverse(Y),X),
inference(equational,[status(thm)],[c14,c15]) ).
cnf(c27,plain,
add(inverse(add(X,Y)),inverse(add(inverse(X),Y))) = inverse(Y),
inference(equational,[status(thm)],[c7,c15,c16]) ).
cnf(c29,plain,
add(inverse(add(inverse(X),Y)),inverse(add(X,Y))) = inverse(Y),
inference(equational,[status(thm)],[c11,c24,c27]) ).
cnf(c31,plain,
add(X,inverse(add(inverse(Y),inverse(add(Y,X))))) = add(Y,X),
inference(equational,[status(thm)],[c11,c17,c24,c26]) ).
cnf(c36,plain,
inverse(add(inverse(add(inverse(add(X,Y)),X)),inverse(X))) = X,
inference(equational,[status(thm)],[c6,c16]) ).
cnf(c37,plain,
inverse(add(X,add(Y,X))) = inverse(add(Y,X)),
inference(equational,[status(thm)],[c6,c17,c36]) ).
cnf(c38,plain,
add(X,add(Y,X)) = add(Y,X),
inference(equational,[status(thm)],[c17,c37]) ).
cnf(c39,plain,
add(inverse(add(X,Y)),inverse(Y)) = inverse(Y),
inference(equational,[status(thm)],[c29,c38]) ).
cnf(c41,plain,
inverse(add(X,inverse(add(Y,inverse(X))))) = inverse(X),
inference(equational,[status(thm)],[c6,c17,c39]) ).
cnf(c45,plain,
add(inverse(X),inverse(add(Y,X))) = inverse(X),
inference(equational,[status(thm)],[c16,c17,c26,c39,c41]) ).
cnf(c46,plain,
inverse(add(inverse(add(X,Y)),inverse(add(inverse(add(Z,X)),Y)))) = Y,
inference(equational,[status(thm)],[c6,c7]) ).
cnf(c47,plain,
inverse(add(inverse(add(X,inverse(add(Y,X)))),X)) = inverse(add(Y,X)),
inference(equational,[status(thm)],[c6,c46]) ).
cnf(c48,plain,
add(inverse(add(X,inverse(add(Y,X)))),X) = add(Y,X),
inference(equational,[status(thm)],[c15,c16,c17,c47]) ).
cnf(c50,plain,
add(inverse(add(X,Y)),inverse(add(inverse(add(Z,X)),Y))) = inverse(Y),
inference(equational,[status(thm)],[c5,c16,c46]) ).
cnf(c51,plain,
inverse(add(X,inverse(add(inverse(add(Y,Z)),inverse(add(Y,X)))))) = inverse(add(Y,X)),
inference(equational,[status(thm)],[c6]) ).
cnf(c52,plain,
add(X,add(X,Y)) = add(X,Y),
inference(equational,[status(thm)],[c14,c16,c17,c45,c51]) ).
cnf(c53,plain,
add(X,inverse(add(inverse(add(Y,Z)),inverse(add(Y,X))))) = add(Y,X),
inference(equational,[status(thm)],[c5,c16,c17,c51]) ).
cnf(c54,plain,
add(X,inverse(add(inverse(X),inverse(add(X,Y))))) = inverse(add(inverse(X),inverse(add(X,Y)))),
inference(equational,[status(thm)],[c14,c16,c53]) ).
cnf(c55,plain,
add(inverse(X),inverse(add(X,Y))) = inverse(X),
inference(equational,[status(thm)],[c4,c16,c17,c52,c54]) ).
cnf(c56,plain,
add(X,Y) = add(Y,X),
inference(equational,[status(thm)],[c17,c31,c55]) ).
cnf(c64,plain,
add(inverse(add(X,Y)),inverse(add(Y,inverse(add(X,Y))))) = inverse(Y),
inference(equational,[status(thm)],[c47,c50,c56]) ).
cnf(c65,plain,
add(X,inverse(add(Y,inverse(add(inverse(add(Z,Y)),X))))) = add(inverse(add(Z,Y)),X),
inference(equational,[status(thm)],[c7,c53]) ).
cnf(c66,plain,
add(inverse(add(X,Y)),inverse(add(inverse(add(X,Z)),Y))) = inverse(Y),
inference(equational,[status(thm)],[c6,c16,c39,c56,c65]) ).
cnf(c67,plain,
add(X,inverse(add(Y,inverse(add(Y,X))))) = X,
inference(equational,[status(thm)],[c16,c17,c56,c65,c66]) ).
cnf(c68,plain,
add(X,inverse(add(Y,inverse(add(X,Y))))) = X,
inference(equational,[status(thm)],[c17,c31,c55,c67]) ).
cnf(c69,plain,
add(inverse(add(X,Y)),inverse(add(X,inverse(X)))) = inverse(add(X,Y)),
inference(equational,[status(thm)],[c17,c55,c56,c67]) ).
cnf(c70,plain,
add(inverse(X),add(X,Y)) = add(X,inverse(X)),
inference(equational,[status(thm)],[c17,c53,c69]) ).
cnf(c72,plain,
add(X,add(inverse(X),Y)) = add(X,inverse(X)),
inference(equational,[status(thm)],[c5,c16,c17,c56,c70]) ).
cnf(c73,plain,
add(add(X,Y),inverse(X)) = add(X,inverse(X)),
inference(equational,[status(thm)],[c56,c70]) ).
cnf(c74,plain,
add(add(X,Y),inverse(Y)) = add(Y,inverse(Y)),
inference(equational,[status(thm)],[c38,c73]) ).
cnf(c77,plain,
add(add(X,Y),inverse(add(X,Y))) = add(Y,inverse(Y)),
inference(equational,[status(thm)],[c17,c56,c64,c70,c74]) ).
cnf(c78,plain,
add(X,inverse(X)) = add(Y,inverse(Y)),
inference(equational,[status(thm)],[c17,c56,c72,c77]) ).
cnf(c83,plain,
add(X,inverse(add(Y,inverse(Y)))) = X,
inference(equational,[status(thm)],[c19,c78]) ).
cnf(c86,plain,
add(add(inverse(X),Y),add(X,Z)) = add(X,inverse(X)),
inference(equational,[status(thm)],[c17,c53,c69,c72]) ).
cnf(c100,plain,
add(inverse(add(X,Y)),inverse(add(X,inverse(add(X,Y))))) = inverse(X),
inference(equational,[status(thm)],[c17,c48,c55,c56]) ).
cnf(c101,plain,
add(X,inverse(add(X,Y))) = add(inverse(Y),X),
inference(equational,[status(thm)],[c17,c50,c67,c100]) ).
cnf(c102,plain,
add(X,inverse(add(Y,X))) = add(inverse(Y),X),
inference(equational,[status(thm)],[c56,c101]) ).
cnf(c134,plain,
add(add(inverse(X),Y),inverse(add(X,Z))) = add(inverse(X),Y),
inference(equational,[status(thm)],[c68,c83,c86]) ).
cnf(c136,plain,
add(inverse(add(X,Y)),inverse(add(Y,inverse(add(X,Z))))) = inverse(Y),
inference(equational,[status(thm)],[c17,c31,c55,c66]) ).
cnf(c169,plain,
add(add(inverse(add(X,Y)),Z),inverse(add(Y,Z))) = add(inverse(Y),Z),
inference(equational,[status(thm)],[c17,c50,c56,c101,c102]) ).
cnf(c170,plain,
add(add(X,inverse(add(Y,Z))),inverse(add(Y,X))) = add(inverse(Y),X),
inference(equational,[status(thm)],[c17,c56,c101,c102,c136]) ).
cnf(c171,plain,
add(inverse(X),add(inverse(add(Y,X)),Z)) = add(inverse(X),Z),
inference(equational,[status(thm)],[c134,c169,c170]) ).
cnf(c172,plain,
add(add(X,Y),add(X,Z)) = add(add(X,Y),Z),
inference(equational,[status(thm)],[c17,c55,c171]) ).
cnf(c173,plain,
add(add(X,Y),Z) = add(add(X,Z),Y),
inference(equational,[status(thm)],[c56,c172]) ).
cnf(c175,plain,
add(add(X,Y),Z) = add(Y,add(X,Z)),
inference(equational,[status(thm)],[c56,c173]) ).
cnf(c177,plain,
add(X,add(Y,Z)) = add(Z,add(X,Y)),
inference(equational,[status(thm)],[c56,c173,c175]) ).
cnf(c178,plain,
add(X,add(Y,Z)) = add(Y,add(X,Z)),
inference(equational,[status(thm)],[c56,c177]) ).
cnf(g1,plain,
add(add(a,b),c) = add(a,add(b,c)),
inference(equational,[status(thm)],[c175,c178]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO073-1 : TPTP v9.0.0. Released v2.6.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 04:30:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 4.65/4.84 % SZS status Unsatisfiable
% 4.65/4.84 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------