%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP403-1 : 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 06:43:59 AM UTC 2025
% Result : Unsatisfiable 60.77s 61.09s
% Output : CNFRefutation 60.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of clauses : 15 ( 15 unt; 0 nHn; 3 RR)
% Number of literals : 15 ( 14 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 : 48 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('theBenchmark.p',prove_these_axioms_1) ).
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(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(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(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(g1,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(equational,[status(thm)],[c32]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP403-1 : TPTP v9.0.0. Released v2.6.0.
% 0.10/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n004.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 08:26:19 EDT 2025
% 0.11/0.33 % CPUTime :
% 60.77/61.09 % SZS status Unsatisfiable
% 60.77/61.09 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------