%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : BOO074-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n009.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 0.62s 0.81s
% Output : CNFRefutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 2
% Syntax : Number of clauses : 35 ( 35 unt; 0 nHn; 3 RR)
% Number of literals : 35 ( 34 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 61 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
add(inverse(add(inverse(a),b)),inverse(add(inverse(a),inverse(b)))) != a,
file('theBenchmark.p',huntinton_3) ).
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(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(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(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(c62,plain,
add(inverse(add(X,Y)),inverse(add(Y,inverse(X)))) = inverse(Y),
inference(equational,[status(thm)],[c27,c56]) ).
cnf(g1,plain,
add(inverse(add(inverse(a),b)),inverse(add(inverse(a),inverse(b)))) = a,
inference(equational,[status(thm)],[c17,c56,c62]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : BOO074-1 : TPTP v9.0.0. Released v2.6.0.
% 0.11/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n009.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Jul 14 04:30:34 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.62/0.81 % SZS status Unsatisfiable
% 0.62/0.81 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------