%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP418-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n011.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 06:44:01 AM UTC 2025
% Result : Unsatisfiable 61.80s 61.98s
% Output : CNFRefutation 61.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of clauses : 17 ( 17 unt; 0 nHn; 3 RR)
% Number of literals : 17 ( 16 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 14 ( 4 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 : 55 ( 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,
inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z))) = Y,
file('theBenchmark.p',single_axiom) ).
cnf(c2,plain,
inverse(multiply(inverse(multiply(X,inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z))) = multiply(inverse(multiply(W,inverse(multiply(inverse(Y),inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),multiply(W,V)),
inference(equational,[status(thm)],[c1]) ).
cnf(c3,plain,
inverse(inverse(multiply(inverse(multiply(X,inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z)))) = Y,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z)) = Y,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c6,plain,
inverse(multiply(inverse(multiply(X,inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z))) = inverse(multiply(inverse(multiply(W,inverse(multiply(Y,inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),multiply(W,V))),
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c8,plain,
multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),inverse(multiply(inverse(inverse(W)),inverse(multiply(multiply(X,Z),inverse(multiply(inverse(multiply(X,Z)),multiply(X,Z))))))))),Y) = W,
inference(equational,[status(thm)],[c4]) ).
cnf(c9,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),inverse(multiply(inverse(W),inverse(multiply(multiply(X,Z),inverse(multiply(inverse(multiply(X,Z)),multiply(X,Z))))))))),Y)) = W,
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c18,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))) = multiply(inverse(multiply(W,inverse(multiply(inverse(inverse(inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))),inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),inverse(multiply(inverse(Y),inverse(multiply(multiply(W,V),inverse(multiply(inverse(multiply(W,V)),multiply(W,V)))))))),
inference(equational,[status(thm)],[c1,c6,c9]) ).
cnf(c19,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z)))),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))) = Y,
inference(equational,[status(thm)],[c9,c18]) ).
cnf(c20,plain,
multiply(inverse(multiply(X,Y)),multiply(X,Z)) = multiply(inverse(multiply(W,Y)),multiply(W,Z)),
inference(equational,[status(thm)],[c4,c19]) ).
cnf(c30,plain,
multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)))),inverse(multiply(Z,inverse(multiply(inverse(Z),Z))))) = Y,
inference(equational,[status(thm)],[c8,c18]) ).
cnf(c35,plain,
multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)))),W)),Y) = multiply(inverse(multiply(V,W)),multiply(V,inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))),
inference(equational,[status(thm)],[c20,c30]) ).
cnf(c37,plain,
multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)))),W)),Y) = multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(V,inverse(U))),multiply(V,Z)))),W)),U),
inference(equational,[status(thm)],[c30,c35]) ).
cnf(c38,plain,
multiply(inverse(X),X) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c19,c30,c37]) ).
cnf(g1,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(equational,[status(thm)],[c38]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP418-1 : TPTP v9.0.0. Released v2.6.0.
% 0.11/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n011.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 14 08:27:04 EDT 2025
% 0.11/0.32 % CPUTime :
% 61.80/61.98 % SZS status Unsatisfiable
% 61.80/61.98 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------