%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP404-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n006.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 06:43:59 AM UTC 2025
% Result : Unsatisfiable 95.04s 95.15s
% Output : CNFRefutation 95.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 2
% Syntax : Number of clauses : 45 ( 45 unt; 0 nHn; 3 RR)
% Number of literals : 45 ( 44 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 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 : 155 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
cnf(c1,axiom,
multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),inverse(multiply(Y,multiply(inverse(Y),Y)))))) = Z,
file('theBenchmark.p',single_axiom) ).
cnf(c2,plain,
multiply(X,inverse(multiply(inverse(Y),inverse(multiply(Z,multiply(inverse(Z),Z)))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Z)),W)),Y)),inverse(multiply(W,multiply(inverse(W),W))))),
inference(equational,[status(thm)],[c1]) ).
cnf(c3,plain,
multiply(inverse(multiply(X,Y)),multiply(X,inverse(multiply(inverse(Z),inverse(multiply(Y,multiply(inverse(Y),Y))))))) = Z,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,plain,
multiply(inverse(multiply(X,Y)),multiply(X,multiply(Z,inverse(multiply(inverse(W),inverse(multiply(V,multiply(inverse(V),V)))))))) = multiply(inverse(multiply(inverse(multiply(Z,V)),Y)),W),
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c5,plain,
multiply(inverse(multiply(X,Y)),multiply(X,Z)) = multiply(inverse(multiply(inverse(multiply(W,V)),Y)),multiply(inverse(multiply(W,V)),Z)),
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c6,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(X),Z)) = multiply(inverse(multiply(W,Y)),multiply(W,Z)),
inference(equational,[status(thm)],[c1,c5]) ).
cnf(c7,plain,
multiply(inverse(multiply(X,Y)),multiply(X,Z)) = multiply(inverse(multiply(W,Y)),multiply(W,Z)),
inference(equational,[status(thm)],[c5,c6]) ).
cnf(c8,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),inverse(multiply(Y,multiply(inverse(Y),Y))))) = Z,
inference(equational,[status(thm)],[c1,c2,c5]) ).
cnf(c9,plain,
multiply(X,multiply(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,X))),W)) = multiply(inverse(multiply(V,inverse(multiply(Z,multiply(inverse(Z),Z))))),multiply(V,W)),
inference(equational,[status(thm)],[c5,c8]) ).
cnf(c10,plain,
multiply(X,multiply(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,X))),W)) = multiply(V,multiply(inverse(multiply(inverse(multiply(U,Z)),multiply(U,V))),W)),
inference(equational,[status(thm)],[c8,c9]) ).
cnf(c13,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(W,Y)),V)) = multiply(inverse(multiply(U,multiply(W,Z))),multiply(U,V)),
inference(equational,[status(thm)],[c5,c7]) ).
cnf(c14,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),W) = multiply(inverse(multiply(inverse(multiply(V,Y)),multiply(V,Z))),W),
inference(equational,[status(thm)],[c3,c4,c13]) ).
cnf(c22,plain,
multiply(inverse(multiply(X,Y)),multiply(X,inverse(multiply(Z,inverse(multiply(Y,multiply(inverse(Y),Y))))))) = multiply(inverse(multiply(inverse(multiply(W,V)),multiply(W,Z))),inverse(multiply(V,multiply(inverse(V),V)))),
inference(equational,[status(thm)],[c3,c8]) ).
cnf(c23,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(Z)))),inverse(multiply(Y,multiply(inverse(Y),Y)))) = Z,
inference(equational,[status(thm)],[c1,c2,c22]) ).
cnf(c24,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(multiply(Z,inverse(multiply(Y,multiply(inverse(Y),Y)))))))) = Z,
inference(equational,[status(thm)],[c8,c22]) ).
cnf(c25,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))) = inverse(multiply(inverse(multiply(W,Y)),multiply(W,Z))),
inference(equational,[status(thm)],[c8,c24]) ).
cnf(c28,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(Z)))),W)),Z) = multiply(inverse(multiply(V,W)),multiply(V,inverse(multiply(Y,multiply(inverse(Y),Y))))),
inference(equational,[status(thm)],[c6,c23]) ).
cnf(c31,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(Z)))),W)),Z) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(V,Y)),multiply(V,inverse(U)))),W)),U),
inference(equational,[status(thm)],[c23,c28]) ).
cnf(c32,plain,
multiply(inverse(X),X) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c8,c23,c31]) ).
cnf(c33,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,Z))),
inference(equational,[status(thm)],[c25,c32]) ).
cnf(c35,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)) = multiply(inverse(multiply(W,Y)),multiply(W,X)),
inference(equational,[status(thm)],[c6,c32]) ).
cnf(c36,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y)) = multiply(inverse(Z),Z),
inference(equational,[status(thm)],[c32,c35]) ).
cnf(c37,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z)) = multiply(inverse(multiply(W,Y)),multiply(W,Z)),
inference(equational,[status(thm)],[c6,c32]) ).
cnf(c38,plain,
multiply(inverse(multiply(inverse(X),X)),Y) = multiply(inverse(multiply(inverse(Z),Z)),Y),
inference(equational,[status(thm)],[c14,c32]) ).
cnf(c39,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y))) = inverse(multiply(inverse(Z),Z)),
inference(equational,[status(thm)],[c33,c37]) ).
cnf(c41,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)) = multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(W),W)),
inference(equational,[status(thm)],[c32,c35]) ).
cnf(c46,plain,
multiply(inverse(multiply(X,Y)),multiply(X,inverse(multiply(inverse(Z),Z)))) = inverse(multiply(Y,multiply(inverse(Y),Y))),
inference(equational,[status(thm)],[c22,c23,c32]) ).
cnf(c48,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),inverse(multiply(Y,multiply(inverse(Y),Y))))) = Y,
inference(equational,[status(thm)],[c1,c2,c32]) ).
cnf(c49,plain,
inverse(multiply(X,multiply(inverse(Y),Y))) = multiply(inverse(multiply(Z,X)),multiply(Z,inverse(multiply(inverse(W),W)))),
inference(equational,[status(thm)],[c32,c46]) ).
cnf(c54,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y))) = multiply(inverse(Z),Z),
inference(equational,[status(thm)],[c36,c49]) ).
cnf(c55,plain,
multiply(inverse(X),X) = inverse(multiply(inverse(Y),Y)),
inference(equational,[status(thm)],[c39,c54]) ).
cnf(c102,plain,
inverse(multiply(X,multiply(inverse(Y),Y))) = multiply(inverse(multiply(Z,X)),multiply(Z,multiply(inverse(W),W))),
inference(equational,[status(thm)],[c32,c46,c55]) ).
cnf(c165,plain,
multiply(X,multiply(inverse(multiply(inverse(Y),Y)),Z)) = multiply(W,multiply(inverse(multiply(inverse(multiply(V,X)),multiply(V,W))),Z)),
inference(equational,[status(thm)],[c10,c32]) ).
cnf(c167,plain,
multiply(X,multiply(multiply(inverse(Y),Y),Z)) = multiply(X,multiply(inverse(multiply(inverse(W),W)),Z)),
inference(equational,[status(thm)],[c38,c55,c165]) ).
cnf(c169,plain,
multiply(X,multiply(inverse(Y),Y)) = multiply(X,multiply(multiply(inverse(Z),Z),multiply(inverse(W),W))),
inference(equational,[status(thm)],[c32,c167]) ).
cnf(c191,plain,
multiply(inverse(X),inverse(multiply(Y,inverse(multiply(X,multiply(inverse(X),X)))))) = inverse(multiply(Y,multiply(inverse(Y),Y))),
inference(equational,[status(thm)],[c1,c48]) ).
cnf(c207,plain,
multiply(inverse(multiply(multiply(inverse(X),X),Y)),multiply(inverse(Z),Z)) = inverse(multiply(Y,multiply(inverse(W),W))),
inference(equational,[status(thm)],[c102,c169]) ).
cnf(c291,plain,
inverse(multiply(X,multiply(inverse(Y),Y))) = multiply(inverse(multiply(inverse(multiply(inverse(Z),Z)),X)),multiply(inverse(W),W)),
inference(equational,[status(thm)],[c41,c102]) ).
cnf(c294,plain,
inverse(multiply(X,multiply(inverse(Y),Y))) = multiply(inverse(Z),inverse(multiply(X,inverse(multiply(Z,multiply(inverse(Z),Z)))))),
inference(equational,[status(thm)],[c32,c191]) ).
cnf(c314,plain,
inverse(inverse(multiply(X,multiply(inverse(Y),Y)))) = X,
inference(equational,[status(thm)],[c1,c291,c294]) ).
cnf(c315,plain,
inverse(multiply(multiply(inverse(X),X),Y)) = inverse(Y),
inference(equational,[status(thm)],[c207,c314]) ).
cnf(c316,plain,
multiply(multiply(inverse(X),X),Y) = Y,
inference(equational,[status(thm)],[c3,c315]) ).
cnf(g1,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(equational,[status(thm)],[c316]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GRP404-1 : TPTP v9.0.0. Released v2.6.0.
% 0.08/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n006.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 08:26:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 95.04/95.15 % SZS status Unsatisfiable
% 95.04/95.15 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------