%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP531-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n006.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 06:44:16 AM UTC 2025
% Result : Unsatisfiable 1.61s 1.78s
% Output : CNFRefutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of clauses : 40 ( 40 unt; 0 nHn; 3 RR)
% Number of literals : 40 ( 39 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 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 : 101 ( 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,
inverse(X) = divide(divide(Y,Y),X),
file('theBenchmark.p',inverse) ).
cnf(c2,axiom,
multiply(X,Y) = divide(X,divide(divide(Z,Z),Y)),
file('theBenchmark.p',multiply) ).
cnf(c3,plain,
divide(X,inverse(Y)) = divide(X,divide(divide(X,X),Y)),
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c6,axiom,
divide(divide(X,divide(Y,Z)),divide(X,Y)) = Z,
file('theBenchmark.p',single_axiom) ).
cnf(c7,plain,
divide(divide(X,X),X) = divide(divide(Y,Y),X),
inference(equational,[status(thm)],[c1,c3,c6]) ).
cnf(c10,plain,
divide(X,inverse(Y)) = divide(X,divide(divide(Y,Y),Y)),
inference(equational,[status(thm)],[c3,c7]) ).
cnf(c11,plain,
divide(X,divide(divide(Y,divide(Z,X)),Y)) = Z,
inference(equational,[status(thm)],[c6]) ).
cnf(c12,plain,
divide(X,X) = divide(Y,Y),
inference(equational,[status(thm)],[c3,c10,c11]) ).
cnf(c14,plain,
divide(X,divide(multiply(Y,X),Y)) = divide(Z,Z),
inference(equational,[status(thm)],[c2,c11]) ).
cnf(c15,plain,
divide(X,divide(divide(Y,Y),Z)) = divide(X,divide(divide(X,X),Z)),
inference(equational,[status(thm)],[c2,c12]) ).
cnf(c16,plain,
divide(multiply(X,Y),divide(X,divide(Z,Z))) = Y,
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c17,plain,
divide(divide(X,Y),divide(X,Z)) = divide(divide(W,divide(Y,Z)),W),
inference(equational,[status(thm)],[c6,c11]) ).
cnf(c18,plain,
divide(divide(X,divide(Y,Y)),X) = divide(Z,Z),
inference(equational,[status(thm)],[c12,c17]) ).
cnf(c19,plain,
divide(X,divide(Y,Y)) = X,
inference(equational,[status(thm)],[c11,c18]) ).
cnf(c21,plain,
divide(X,divide(X,Y)) = Y,
inference(equational,[status(thm)],[c6,c19]) ).
cnf(c22,plain,
divide(multiply(X,Y),X) = Y,
inference(equational,[status(thm)],[c16,c19]) ).
cnf(c53,plain,
divide(X,divide(Y,divide(Z,divide(X,Y)))) = Z,
inference(equational,[status(thm)],[c6,c11]) ).
cnf(c54,plain,
multiply(divide(X,Y),Y) = X,
inference(equational,[status(thm)],[c14,c19,c53]) ).
cnf(c56,plain,
multiply(X,Y) = multiply(Y,X),
inference(equational,[status(thm)],[c22,c54]) ).
cnf(c57,plain,
divide(X,divide(divide(X,X),divide(Y,Z))) = divide(Y,divide(Z,X)),
inference(equational,[status(thm)],[c2,c6,c54]) ).
cnf(c62,plain,
divide(divide(X,Y),divide(Z,Y)) = divide(X,Z),
inference(equational,[status(thm)],[c11,c53]) ).
cnf(c63,plain,
divide(X,divide(Y,Z)) = divide(divide(Z,divide(divide(X,X),X)),Y),
inference(equational,[status(thm)],[c2,c16,c19,c62]) ).
cnf(c65,plain,
divide(divide(X,Y),Z) = divide(X,divide(Y,divide(divide(Z,Z),Z))),
inference(equational,[status(thm)],[c2,c16,c19,c62]) ).
cnf(c66,plain,
divide(divide(X,Y),divide(divide(X,X),Z)) = divide(X,divide(Y,Z)),
inference(equational,[status(thm)],[c2,c21,c62,c65]) ).
cnf(c67,plain,
divide(X,divide(Y,Z)) = divide(Z,divide(Y,X)),
inference(equational,[status(thm)],[c19,c57,c62,c63]) ).
cnf(c73,plain,
multiply(X,divide(Y,Z)) = divide(X,divide(Z,Y)),
inference(equational,[status(thm)],[c2,c19,c67]) ).
cnf(c74,plain,
divide(X,divide(Y,Z)) = divide(multiply(Z,X),Y),
inference(equational,[status(thm)],[c22,c62]) ).
cnf(c75,plain,
divide(divide(X,Y),Z) = divide(X,multiply(Y,Z)),
inference(equational,[status(thm)],[c22,c62]) ).
cnf(c77,plain,
divide(divide(X,X),divide(Y,Z)) = divide(Z,Y),
inference(equational,[status(thm)],[c18,c19,c62]) ).
cnf(c78,plain,
divide(X,divide(Y,divide(Z,X))) = divide(Z,Y),
inference(equational,[status(thm)],[c53,c62]) ).
cnf(c79,plain,
divide(X,divide(Y,Z)) = divide(divide(X,divide(divide(Z,Z),Z)),Y),
inference(equational,[status(thm)],[c2,c16,c19,c78]) ).
cnf(c82,plain,
divide(X,multiply(Y,Z)) = divide(divide(X,Z),Y),
inference(equational,[status(thm)],[c2,c21,c62,c66,c79]) ).
cnf(c88,plain,
divide(X,divide(Y,Z)) = divide(divide(Z,Y),divide(divide(Y,Y),X)),
inference(equational,[status(thm)],[c2,c19,c74,c77]) ).
cnf(c92,plain,
divide(X,divide(Y,divide(divide(Y,Y),Z))) = divide(divide(X,Y),Z),
inference(equational,[status(thm)],[c2,c56,c82]) ).
cnf(c94,plain,
multiply(divide(X,Y),Z) = divide(Z,divide(Y,X)),
inference(equational,[status(thm)],[c56,c73]) ).
cnf(c95,plain,
divide(X,divide(Y,divide(divide(Y,Y),Z))) = divide(divide(X,Z),Y),
inference(equational,[status(thm)],[c2,c56,c75]) ).
cnf(c103,plain,
multiply(X,Y) = divide(Y,divide(divide(Y,Y),X)),
inference(equational,[status(thm)],[c2,c19,c57]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c15,c19,c21,c62,c66,c73,c78,c88,c92,c94,c95,c103]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP531-1 : TPTP v9.0.0. Released v2.6.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 08:31:34 EDT 2025
% 0.12/0.34 % CPUTime :
% 1.61/1.78 % SZS status Unsatisfiable
% 1.61/1.78 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------