%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP563-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n007.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 06:44:20 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.53s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of clauses : 23 ( 23 unt; 0 nHn; 3 RR)
% Number of literals : 23 ( 22 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 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,Y) = divide(X,inverse(Y)),
file('theBenchmark.p',multiply) ).
cnf(c2,axiom,
divide(divide(divide(X,inverse(Y)),Z),divide(X,Z)) = Y,
file('theBenchmark.p',single_axiom) ).
cnf(c3,plain,
divide(X,divide(divide(Y,inverse(X)),divide(Y,inverse(Z)))) = Z,
inference(equational,[status(thm)],[c2]) ).
cnf(c4,plain,
divide(divide(divide(divide(divide(X,inverse(Y)),Z),inverse(W)),divide(X,Z)),Y) = W,
inference(equational,[status(thm)],[c2]) ).
cnf(c5,plain,
divide(divide(X,inverse(Y)),X) = Y,
inference(equational,[status(thm)],[c2,c4]) ).
cnf(c6,plain,
divide(X,divide(Y,Y)) = X,
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c7,plain,
divide(divide(X,X),inverse(Y)) = Y,
inference(equational,[status(thm)],[c5,c6]) ).
cnf(c8,plain,
divide(X,divide(X,Y)) = Y,
inference(equational,[status(thm)],[c3,c7]) ).
cnf(c10,plain,
divide(divide(X,X),Y) = inverse(Y),
inference(equational,[status(thm)],[c7,c8]) ).
cnf(c11,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c5,c10]) ).
cnf(c13,plain,
divide(X,divide(inverse(Y),inverse(X))) = Y,
inference(equational,[status(thm)],[c5]) ).
cnf(c14,plain,
divide(X,Y) = divide(inverse(Y),inverse(X)),
inference(equational,[status(thm)],[c3,c13]) ).
cnf(c17,plain,
divide(X,inverse(divide(Y,X))) = Y,
inference(equational,[status(thm)],[c5,c11,c14]) ).
cnf(c18,plain,
divide(X,Y) = inverse(divide(Y,X)),
inference(equational,[status(thm)],[c8,c17]) ).
cnf(c21,plain,
inverse(divide(inverse(X),divide(Y,X))) = Y,
inference(equational,[status(thm)],[c8,c17,c18]) ).
cnf(c23,plain,
divide(inverse(X),divide(Y,X)) = inverse(Y),
inference(equational,[status(thm)],[c8,c14]) ).
cnf(c24,plain,
divide(inverse(X),inverse(Y)) = inverse(divide(X,Y)),
inference(equational,[status(thm)],[c14,c18]) ).
cnf(c27,plain,
divide(inverse(X),Y) = inverse(divide(X,inverse(Y))),
inference(equational,[status(thm)],[c21,c23,c24]) ).
cnf(c31,plain,
divide(divide(X,Y),divide(Z,Y)) = divide(X,Z),
inference(equational,[status(thm)],[c2,c17]) ).
cnf(c35,plain,
divide(divide(X,Y),Z) = divide(X,divide(Y,inverse(Z))),
inference(equational,[status(thm)],[c5,c31]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c1,c11,c27,c35]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : GRP563-1 : TPTP v9.0.0. Released v2.6.0.
% 0.02/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n007.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Jul 14 08:32:19 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.19/0.53 % SZS status Unsatisfiable
% 0.19/0.53 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------