%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP438-1 : 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 06:44:03 AM UTC 2025
% Result : Unsatisfiable 66.41s 66.53s
% Output : CNFRefutation 66.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 2
% Syntax : Number of clauses : 59 ( 59 unt; 0 nHn; 3 RR)
% Number of literals : 59 ( 58 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 3 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 : 210 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('theBenchmark.p',prove_these_axioms_3) ).
cnf(c1,axiom,
multiply(X,inverse(multiply(Y,multiply(Z,multiply(multiply(inverse(Z),inverse(multiply(W,Y))),X))))) = W,
file('theBenchmark.p',single_axiom) ).
cnf(c2,plain,
multiply(X,inverse(multiply(multiply(Y,multiply(multiply(inverse(Y),inverse(multiply(Z,W))),inverse(V))),multiply(V,multiply(Z,X))))) = W,
inference(equational,[status(thm)],[c1]) ).
cnf(c3,plain,
multiply(X,inverse(multiply(multiply(Y,multiply(Z,inverse(W))),multiply(W,multiply(V,X))))) = multiply(U,multiply(multiply(inverse(U),inverse(multiply(Z,V))),inverse(Y))),
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,plain,
multiply(X,multiply(multiply(inverse(X),inverse(multiply(multiply(inverse(Y),inverse(multiply(Z,W))),Z))),inverse(Y))) = W,
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c5,plain,
multiply(X,multiply(multiply(inverse(X),inverse(multiply(Y,Z))),inverse(W))) = multiply(V,multiply(multiply(inverse(V),inverse(multiply(Y,Z))),inverse(W))),
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c7,plain,
multiply(X,multiply(multiply(inverse(X),inverse(multiply(multiply(inverse(Y),inverse(Z)),W))),inverse(Y))) = inverse(multiply(V,multiply(U,multiply(multiply(inverse(U),inverse(multiply(Z,V))),W)))),
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c8,plain,
inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),inverse(multiply(multiply(Z,W),X))),Z)))) = W,
inference(equational,[status(thm)],[c4,c7]) ).
cnf(c9,plain,
multiply(X,multiply(multiply(inverse(X),Y),inverse(Z))) = multiply(W,multiply(multiply(inverse(W),Y),inverse(Z))),
inference(equational,[status(thm)],[c5,c8]) ).
cnf(c10,plain,
multiply(X,multiply(multiply(inverse(X),Y),Z)) = multiply(W,multiply(multiply(inverse(W),Y),Z)),
inference(equational,[status(thm)],[c8,c9]) ).
cnf(c11,plain,
inverse(multiply(multiply(X,multiply(Y,inverse(Z))),multiply(Z,multiply(W,V)))) = multiply(multiply(inverse(V),inverse(multiply(Y,W))),inverse(X)),
inference(equational,[status(thm)],[c2,c8]) ).
cnf(c12,plain,
multiply(X,multiply(multiply(inverse(X),inverse(multiply(multiply(Y,inverse(multiply(Z,W))),Z))),Y)) = W,
inference(equational,[status(thm)],[c4,c8]) ).
cnf(c18,plain,
multiply(X,multiply(multiply(inverse(X),inverse(multiply(multiply(Y,inverse(Z)),W))),Y)) = inverse(multiply(V,multiply(U,multiply(multiply(inverse(U),inverse(multiply(Z,V))),W)))),
inference(equational,[status(thm)],[c7,c8]) ).
cnf(c19,plain,
multiply(X,multiply(Y,multiply(multiply(inverse(Y),inverse(multiply(multiply(Z,inverse(W)),X))),Z))) = W,
inference(equational,[status(thm)],[c1,c18]) ).
cnf(c22,plain,
inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),inverse(multiply(Z,X))),W)))) = multiply(multiply(inverse(W),inverse(multiply(multiply(V,inverse(multiply(U,Z))),U))),V),
inference(equational,[status(thm)],[c8,c12]) ).
cnf(c23,plain,
multiply(multiply(inverse(X),inverse(multiply(multiply(Y,inverse(multiply(Z,multiply(X,W)))),Z))),Y) = W,
inference(equational,[status(thm)],[c8,c22]) ).
cnf(c24,plain,
multiply(X,multiply(Y,multiply(multiply(inverse(Y),inverse(Z)),inverse(W)))) = multiply(multiply(X,inverse(multiply(V,multiply(W,Z)))),V),
inference(equational,[status(thm)],[c19,c23]) ).
cnf(c25,plain,
multiply(multiply(X,inverse(multiply(Y,multiply(Z,W)))),Y) = multiply(multiply(X,inverse(multiply(V,multiply(Z,W)))),V),
inference(equational,[status(thm)],[c9,c24]) ).
cnf(c26,plain,
multiply(multiply(X,inverse(multiply(Y,Z))),Y) = multiply(multiply(X,inverse(multiply(W,Z))),W),
inference(equational,[status(thm)],[c2,c11,c12,c25]) ).
cnf(c28,plain,
inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),inverse(Z)),inverse(W))))) = inverse(multiply(multiply(X,inverse(multiply(V,multiply(W,Z)))),V)),
inference(equational,[status(thm)],[c8,c23]) ).
cnf(c29,plain,
inverse(multiply(multiply(X,inverse(multiply(Y,multiply(Z,W)))),Y)) = inverse(multiply(multiply(X,inverse(multiply(V,multiply(Z,W)))),V)),
inference(equational,[status(thm)],[c24,c28]) ).
cnf(c30,plain,
inverse(multiply(multiply(X,inverse(multiply(Y,Z))),Y)) = inverse(multiply(multiply(X,inverse(multiply(W,Z))),W)),
inference(equational,[status(thm)],[c2,c11,c12,c29]) ).
cnf(c41,plain,
multiply(inverse(X),inverse(multiply(multiply(Y,inverse(multiply(Z,multiply(X,multiply(W,Y))))),Z))) = W,
inference(equational,[status(thm)],[c1,c24]) ).
cnf(c51,plain,
multiply(multiply(X,inverse(multiply(Y,multiply(multiply(inverse(Y),Z),W)))),V) = multiply(multiply(X,inverse(multiply(U,multiply(multiply(inverse(V),Z),W)))),U),
inference(equational,[status(thm)],[c10,c25]) ).
cnf(c52,plain,
inverse(multiply(X,multiply(multiply(inverse(X),Y),Z))) = inverse(multiply(W,multiply(multiply(inverse(W),Y),Z))),
inference(equational,[status(thm)],[c8,c12,c51]) ).
cnf(c53,plain,
inverse(multiply(X,multiply(multiply(inverse(X),inverse(multiply(Y,Z))),Y))) = inverse(multiply(W,multiply(multiply(inverse(W),inverse(multiply(V,Z))),V))),
inference(equational,[status(thm)],[c26,c52]) ).
cnf(c65,plain,
multiply(multiply(X,inverse(multiply(Y,multiply(multiply(inverse(Y),Z),W)))),V) = multiply(multiply(X,inverse(multiply(U,multiply(multiply(inverse(U),Z),W)))),V),
inference(equational,[status(thm)],[c10,c51]) ).
cnf(c66,plain,
multiply(X,inverse(multiply(Y,multiply(multiply(inverse(Y),Z),W)))) = multiply(X,inverse(multiply(V,multiply(multiply(inverse(V),Z),W)))),
inference(equational,[status(thm)],[c41,c65]) ).
cnf(c69,plain,
multiply(X,multiply(Y,multiply(multiply(inverse(Y),inverse(multiply(multiply(Z,W),X))),Z))) = multiply(V,multiply(U,multiply(multiply(inverse(U),inverse(multiply(multiply(U2,W),V))),U2))),
inference(equational,[status(thm)],[c8,c19]) ).
cnf(c70,plain,
multiply(X,inverse(multiply(Y,multiply(Z,multiply(multiply(inverse(Z),inverse(multiply(W,Y))),W))))) = X,
inference(equational,[status(thm)],[c1,c26]) ).
cnf(c71,plain,
multiply(multiply(X,inverse(Y)),Y) = multiply(multiply(X,inverse(Z)),Z),
inference(equational,[status(thm)],[c26,c70]) ).
cnf(c72,plain,
multiply(X,multiply(inverse(X),Y)) = multiply(Z,multiply(inverse(Z),Y)),
inference(equational,[status(thm)],[c10,c70]) ).
cnf(c73,plain,
multiply(X,inverse(X)) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c70,c72]) ).
cnf(c74,plain,
multiply(multiply(X,inverse(X)),Y) = multiply(multiply(Y,inverse(Z)),Z),
inference(equational,[status(thm)],[c71,c73]) ).
cnf(c77,plain,
inverse(multiply(multiply(X,inverse(Y)),Y)) = inverse(multiply(multiply(X,inverse(Z)),Z)),
inference(equational,[status(thm)],[c30,c70]) ).
cnf(c82,plain,
inverse(multiply(multiply(X,inverse(X)),Y)) = inverse(multiply(multiply(Y,inverse(Z)),Z)),
inference(equational,[status(thm)],[c73,c77]) ).
cnf(c89,plain,
multiply(X,inverse(multiply(Y,multiply(inverse(Y),Z)))) = multiply(X,inverse(multiply(W,multiply(inverse(W),Z)))),
inference(equational,[status(thm)],[c66,c70]) ).
cnf(c90,plain,
multiply(X,inverse(multiply(Y,inverse(Y)))) = multiply(X,inverse(multiply(Z,inverse(Z)))),
inference(equational,[status(thm)],[c70,c89]) ).
cnf(c91,plain,
multiply(X,inverse(multiply(Y,inverse(Y)))) = X,
inference(equational,[status(thm)],[c70,c90]) ).
cnf(c93,plain,
multiply(X,multiply(Y,inverse(Y))) = multiply(multiply(X,inverse(Z)),Z),
inference(equational,[status(thm)],[c71,c91]) ).
cnf(c94,plain,
inverse(multiply(X,multiply(Y,inverse(Y)))) = inverse(multiply(multiply(Z,inverse(Z)),X)),
inference(equational,[status(thm)],[c82,c91]) ).
cnf(c99,plain,
multiply(X,inverse(inverse(multiply(Y,inverse(Y))))) = multiply(multiply(Z,inverse(Z)),X),
inference(equational,[status(thm)],[c74,c91]) ).
cnf(c101,plain,
multiply(multiply(X,inverse(multiply(Y,inverse(Z)))),Y) = multiply(X,Z),
inference(equational,[status(thm)],[c26,c91]) ).
cnf(c114,plain,
multiply(X,multiply(Y,inverse(Y))) = multiply(X,inverse(inverse(multiply(Z,inverse(Z))))),
inference(equational,[status(thm)],[c90,c91,c93]) ).
cnf(c116,plain,
multiply(multiply(inverse(X),inverse(Y)),Y) = inverse(X),
inference(equational,[status(thm)],[c23,c91,c101,c114]) ).
cnf(c117,plain,
multiply(multiply(X,inverse(Y)),Y) = X,
inference(equational,[status(thm)],[c8,c116]) ).
cnf(c119,plain,
multiply(X,multiply(Y,inverse(Y))) = X,
inference(equational,[status(thm)],[c19,c69,c116]) ).
cnf(c120,plain,
multiply(X,inverse(inverse(Y))) = multiply(X,Y),
inference(equational,[status(thm)],[c117]) ).
cnf(c121,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c23,c120]) ).
cnf(c123,plain,
multiply(multiply(X,inverse(X)),Y) = Y,
inference(equational,[status(thm)],[c91,c99,c117]) ).
cnf(c126,plain,
multiply(X,multiply(inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c19,c101,c119,c123]) ).
cnf(c136,plain,
multiply(multiply(multiply(X,Y),inverse(multiply(Z,Y))),Z) = X,
inference(equational,[status(thm)],[c26,c73,c123]) ).
cnf(c137,plain,
multiply(multiply(X,inverse(multiply(Y,Z))),Y) = multiply(X,inverse(Z)),
inference(equational,[status(thm)],[c74,c123,c136]) ).
cnf(c138,plain,
multiply(X,inverse(multiply(inverse(Y),Z))) = multiply(multiply(X,inverse(Z)),Y),
inference(equational,[status(thm)],[c2,c11,c121,c137]) ).
cnf(c139,plain,
inverse(multiply(inverse(X),Y)) = multiply(inverse(Y),X),
inference(equational,[status(thm)],[c94,c119,c121,c123,c138]) ).
cnf(c140,plain,
multiply(inverse(X),inverse(Y)) = inverse(multiply(Y,X)),
inference(equational,[status(thm)],[c53,c121,c126,c137,c139]) ).
cnf(c141,plain,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
inference(equational,[status(thm)],[c121,c138,c140]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c141]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP438-1 : TPTP v9.0.0. Released v2.6.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Jul 14 08:28:04 EDT 2025
% 0.12/0.34 % CPUTime :
% 66.41/66.53 % SZS status Unsatisfiable
% 66.41/66.53 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------