%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP014-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n001.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 06:43:17 AM UTC 2025
% Result : Unsatisfiable 13.64s 13.79s
% Output : CNFRefutation 13.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 2
% Syntax : Number of clauses : 62 ( 62 unt; 0 nHn; 3 RR)
% Number of literals : 62 ( 61 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 : 167 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(a,multiply(b,c)) != multiply(multiply(a,b),c),
file('theBenchmark.p',prove_associativity) ).
cnf(c1,axiom,
multiply(X,inverse(multiply(multiply(inverse(multiply(inverse(Y),multiply(inverse(X),Z))),W),inverse(multiply(Y,W))))) = Z,
file('theBenchmark.p',group_axiom) ).
cnf(c2,plain,
multiply(X,inverse(multiply(multiply(inverse(multiply(inverse(Y),Z)),W),inverse(multiply(Y,W))))) = inverse(multiply(multiply(inverse(multiply(inverse(V),multiply(inverse(inverse(X)),Z))),U),inverse(multiply(V,U)))),
inference(equational,[status(thm)],[c1]) ).
cnf(c3,plain,
multiply(inverse(X),multiply(X,inverse(multiply(multiply(inverse(multiply(inverse(Y),Z)),W),inverse(multiply(Y,W)))))) = Z,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,plain,
multiply(X,inverse(multiply(multiply(inverse(Y),Z),inverse(multiply(inverse(X),Z))))) = inverse(multiply(multiply(inverse(multiply(inverse(W),Y)),V),inverse(multiply(W,V)))),
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c6,plain,
multiply(inverse(X),multiply(X,inverse(multiply(multiply(inverse(Y),Z),inverse(multiply(W,Z)))))) = multiply(W,inverse(multiply(multiply(inverse(multiply(inverse(V),Y)),U),inverse(multiply(V,U))))),
inference(equational,[status(thm)],[c3]) ).
cnf(c8,plain,
multiply(inverse(X),multiply(inverse(Y),multiply(Y,inverse(multiply(multiply(inverse(Z),W),inverse(multiply(X,W))))))) = Z,
inference(equational,[status(thm)],[c3,c6]) ).
cnf(c9,plain,
inverse(multiply(multiply(inverse(X),Y),inverse(multiply(Z,Y)))) = inverse(multiply(multiply(inverse(X),W),inverse(multiply(Z,W)))),
inference(equational,[status(thm)],[c1,c2,c8]) ).
cnf(c10,plain,
multiply(multiply(inverse(X),Y),inverse(multiply(Z,Y))) = multiply(multiply(inverse(X),W),inverse(multiply(Z,W))),
inference(equational,[status(thm)],[c8,c9]) ).
cnf(c15,plain,
multiply(inverse(X),multiply(X,multiply(Y,inverse(multiply(multiply(inverse(Z),W),inverse(multiply(inverse(Y),W))))))) = Z,
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c16,plain,
multiply(inverse(X),multiply(X,Y)) = multiply(inverse(inverse(Z)),multiply(inverse(Z),Y)),
inference(equational,[status(thm)],[c1,c15]) ).
cnf(c17,plain,
multiply(inverse(inverse(inverse(X))),multiply(inverse(Y),multiply(Y,Z))) = multiply(inverse(W),multiply(W,multiply(inverse(X),Z))),
inference(equational,[status(thm)],[c16]) ).
cnf(c18,plain,
multiply(inverse(X),multiply(X,multiply(inverse(Y),Z))) = multiply(inverse(W),multiply(W,multiply(inverse(Y),Z))),
inference(equational,[status(thm)],[c16,c17]) ).
cnf(c19,plain,
multiply(inverse(X),multiply(X,Y)) = multiply(inverse(Z),multiply(Z,Y)),
inference(equational,[status(thm)],[c15,c18]) ).
cnf(c23,plain,
multiply(inverse(X),multiply(X,multiply(inverse(inverse(Y)),multiply(inverse(Y),Z)))) = multiply(inverse(inverse(inverse(W))),multiply(inverse(V),multiply(V,multiply(W,Z)))),
inference(equational,[status(thm)],[c16,c17]) ).
cnf(c24,plain,
multiply(multiply(inverse(X),multiply(X,Y)),inverse(multiply(Z,multiply(W,Y)))) = multiply(multiply(inverse(W),V),inverse(multiply(Z,V))),
inference(equational,[status(thm)],[c10,c19]) ).
cnf(c25,plain,
multiply(X,inverse(X)) = multiply(multiply(inverse(Y),Z),inverse(multiply(inverse(Y),Z))),
inference(equational,[status(thm)],[c15,c24]) ).
cnf(c26,plain,
multiply(X,inverse(X)) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c15,c25]) ).
cnf(c27,plain,
multiply(inverse(X),multiply(Y,inverse(Y))) = multiply(inverse(Z),multiply(Z,inverse(X))),
inference(equational,[status(thm)],[c19,c26]) ).
cnf(c29,plain,
multiply(inverse(X),multiply(X,multiply(Y,inverse(multiply(Z,inverse(Z)))))) = Y,
inference(equational,[status(thm)],[c15,c25]) ).
cnf(c30,plain,
multiply(inverse(inverse(inverse(inverse(X)))),inverse(X)) = multiply(inverse(inverse(inverse(Y))),Y),
inference(equational,[status(thm)],[c23,c29]) ).
cnf(c31,plain,
multiply(inverse(X),multiply(X,multiply(Y,inverse(Y)))) = multiply(Z,inverse(Z)),
inference(equational,[status(thm)],[c26,c29]) ).
cnf(c32,plain,
inverse(multiply(X,inverse(X))) = inverse(multiply(Y,inverse(Y))),
inference(equational,[status(thm)],[c9,c25,c26]) ).
cnf(c33,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(Y,inverse(Y)))) = multiply(Z,inverse(Z)),
inference(equational,[status(thm)],[c26,c32]) ).
cnf(c44,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(Y,inverse(inverse(Z))))) = multiply(multiply(inverse(Z),W),inverse(multiply(Y,W))),
inference(equational,[status(thm)],[c10,c26]) ).
cnf(c47,plain,
multiply(X,multiply(Y,inverse(multiply(multiply(inverse(multiply(inverse(X),Z)),W),inverse(multiply(inverse(Y),W)))))) = Z,
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c48,plain,
multiply(X,multiply(Y,inverse(Y))) = inverse(inverse(X)),
inference(equational,[status(thm)],[c33,c47]) ).
cnf(c49,plain,
multiply(inverse(X),multiply(X,inverse(Y))) = inverse(inverse(inverse(Y))),
inference(equational,[status(thm)],[c27,c48]) ).
cnf(c52,plain,
multiply(X,multiply(multiply(inverse(X),Y),inverse(multiply(Z,inverse(Z))))) = Y,
inference(equational,[status(thm)],[c25,c47]) ).
cnf(c53,plain,
multiply(X,multiply(Y,inverse(multiply(Z,inverse(Z))))) = multiply(X,multiply(Y,inverse(multiply(W,inverse(W))))),
inference(equational,[status(thm)],[c29,c52]) ).
cnf(c55,plain,
inverse(inverse(inverse(inverse(inverse(multiply(X,inverse(X))))))) = multiply(inverse(inverse(inverse(Y))),Y),
inference(equational,[status(thm)],[c23,c29,c49,c53]) ).
cnf(c56,plain,
multiply(X,multiply(multiply(inverse(X),Y),inverse(multiply(Z,Y)))) = inverse(Z),
inference(equational,[status(thm)],[c10,c52]) ).
cnf(c59,plain,
multiply(inverse(inverse(X)),inverse(inverse(inverse(multiply(Y,inverse(Y)))))) = X,
inference(equational,[status(thm)],[c8,c49,c53]) ).
cnf(c60,plain,
inverse(inverse(inverse(inverse(multiply(X,inverse(X)))))) = multiply(inverse(inverse(inverse(Y))),Y),
inference(equational,[status(thm)],[c30,c59]) ).
cnf(c61,plain,
multiply(inverse(inverse(inverse(X))),X) = multiply(inverse(inverse(inverse(Y))),Y),
inference(equational,[status(thm)],[c30,c59,c60]) ).
cnf(c62,plain,
inverse(multiply(inverse(inverse(inverse(X))),X)) = multiply(inverse(inverse(inverse(Y))),Y),
inference(equational,[status(thm)],[c55,c60]) ).
cnf(c63,plain,
inverse(inverse(inverse(inverse(multiply(X,inverse(X)))))) = inverse(inverse(inverse(inverse(multiply(Y,inverse(Y)))))),
inference(equational,[status(thm)],[c59,c60]) ).
cnf(c64,plain,
inverse(inverse(inverse(inverse(inverse(inverse(multiply(X,inverse(X)))))))) = multiply(inverse(inverse(inverse(Y))),Y),
inference(equational,[status(thm)],[c60,c62]) ).
cnf(c65,plain,
inverse(inverse(inverse(inverse(inverse(inverse(multiply(X,inverse(X)))))))) = inverse(inverse(inverse(inverse(multiply(Y,inverse(Y)))))),
inference(equational,[status(thm)],[c60,c61,c64]) ).
cnf(c66,plain,
inverse(inverse(multiply(X,inverse(X)))) = multiply(inverse(inverse(inverse(Y))),Y),
inference(equational,[status(thm)],[c59,c61,c65]) ).
cnf(c67,plain,
inverse(inverse(inverse(multiply(X,inverse(X))))) = multiply(inverse(inverse(inverse(Y))),Y),
inference(equational,[status(thm)],[c59,c62,c65]) ).
cnf(c68,plain,
multiply(inverse(X),multiply(X,Y)) = inverse(inverse(Y)),
inference(equational,[status(thm)],[c16,c59,c67]) ).
cnf(c69,plain,
inverse(inverse(multiply(X,inverse(X)))) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c31,c59,c67]) ).
cnf(c70,plain,
multiply(X,inverse(X)) = multiply(inverse(inverse(inverse(Y))),Y),
inference(equational,[status(thm)],[c66,c69]) ).
cnf(c71,plain,
inverse(inverse(inverse(inverse(X)))) = X,
inference(equational,[status(thm)],[c52,c56,c70]) ).
cnf(c72,plain,
multiply(X,inverse(X)) = inverse(multiply(Y,inverse(Y))),
inference(equational,[status(thm)],[c55,c71]) ).
cnf(c76,plain,
multiply(X,inverse(inverse(multiply(inverse(X),Y)))) = Y,
inference(equational,[status(thm)],[c32,c47,c48,c72]) ).
cnf(c77,plain,
multiply(inverse(inverse(X)),inverse(inverse(Y))) = inverse(inverse(multiply(X,Y))),
inference(equational,[status(thm)],[c23,c68,c71,c76]) ).
cnf(c78,plain,
inverse(inverse(multiply(inverse(inverse(X)),Y))) = multiply(X,inverse(inverse(Y))),
inference(equational,[status(thm)],[c76]) ).
cnf(c79,plain,
multiply(X,inverse(multiply(Y,inverse(Y)))) = inverse(inverse(X)),
inference(equational,[status(thm)],[c48,c53,c72,c76]) ).
cnf(c85,plain,
inverse(multiply(inverse(multiply(inverse(X),Y)),inverse(X))) = Y,
inference(equational,[status(thm)],[c3,c68,c71,c79]) ).
cnf(c86,plain,
inverse(multiply(X,inverse(Y))) = multiply(Y,inverse(X)),
inference(equational,[status(thm)],[c49,c71,c85]) ).
cnf(c87,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c76,c85,c86]) ).
cnf(c90,plain,
multiply(multiply(X,inverse(X)),Y) = Y,
inference(equational,[status(thm)],[c48,c63,c71,c85]) ).
cnf(c91,plain,
inverse(multiply(inverse(multiply(X,Y)),X)) = Y,
inference(equational,[status(thm)],[c85]) ).
cnf(c92,plain,
inverse(multiply(inverse(X),Y)) = multiply(inverse(Y),X),
inference(equational,[status(thm)],[c16,c68,c87,c91]) ).
cnf(c96,plain,
inverse(multiply(inverse(X),inverse(Y))) = multiply(Y,X),
inference(equational,[status(thm)],[c23,c68,c71,c77,c85,c87]) ).
cnf(c102,plain,
multiply(multiply(inverse(X),Y),Z) = inverse(multiply(inverse(multiply(Y,Z)),X)),
inference(equational,[status(thm)],[c44,c87,c90,c91]) ).
cnf(c103,plain,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
inference(equational,[status(thm)],[c86,c87,c102]) ).
cnf(c107,plain,
inverse(multiply(X,multiply(Y,Z))) = multiply(inverse(Z),inverse(multiply(X,Y))),
inference(equational,[status(thm)],[c78,c87,c92,c103]) ).
cnf(g1,plain,
multiply(a,multiply(b,c)) = multiply(multiply(a,b),c),
inference(equational,[status(thm)],[c87,c96,c107]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP014-1 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n001.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 08:05:04 EDT 2025
% 0.11/0.33 % CPUTime :
% 13.64/13.79 % SZS status Unsatisfiable
% 13.64/13.79 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------