%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP523-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n009.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 06:44:15 AM UTC 2025
% Result : Unsatisfiable 4.27s 4.44s
% Output : CNFRefutation 4.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of clauses : 63 ( 63 unt; 0 nHn; 3 RR)
% Number of literals : 63 ( 62 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 : 147 ( 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(X,divide(Y,divide(Z,divide(X,Y)))) = Z,
file('theBenchmark.p',single_axiom) ).
cnf(c7,plain,
divide(X,multiply(Y,divide(X,Y))) = divide(Z,Z),
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c8,plain,
divide(X,X) = divide(Y,Y),
inference(equational,[status(thm)],[c2,c6,c7]) ).
cnf(c9,plain,
divide(X,multiply(divide(Y,Y),Z)) = divide(X,divide(divide(W,W),divide(divide(W,W),Z))),
inference(equational,[status(thm)],[c2]) ).
cnf(c10,plain,
divide(X,divide(Y,divide(Z,Z))) = divide(X,Y),
inference(equational,[status(thm)],[c6,c8]) ).
cnf(c11,plain,
divide(X,divide(X,Y)) = Y,
inference(equational,[status(thm)],[c6,c10]) ).
cnf(c12,plain,
divide(X,divide(Y,Y)) = X,
inference(equational,[status(thm)],[c6,c11]) ).
cnf(c13,plain,
multiply(divide(X,X),Y) = Y,
inference(equational,[status(thm)],[c9,c11]) ).
cnf(c18,plain,
divide(X,divide(divide(X,X),divide(Y,X))) = Y,
inference(equational,[status(thm)],[c2,c7,c11,c12]) ).
cnf(c19,plain,
divide(divide(X,X),inverse(Y)) = Y,
inference(equational,[status(thm)],[c1,c11]) ).
cnf(c21,plain,
divide(X,divide(divide(Y,Y),Z)) = divide(X,divide(divide(X,X),Z)),
inference(equational,[status(thm)],[c2,c8]) ).
cnf(c22,plain,
inverse(divide(divide(X,X),Y)) = Y,
inference(equational,[status(thm)],[c1,c11,c12,c21]) ).
cnf(c23,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c1,c22]) ).
cnf(c29,plain,
divide(X,divide(divide(Y,Y),Z)) = divide(X,inverse(Z)),
inference(equational,[status(thm)],[c3,c8]) ).
cnf(c30,plain,
divide(X,inverse(Y)) = multiply(X,Y),
inference(equational,[status(thm)],[c2,c29]) ).
cnf(c31,plain,
multiply(X,inverse(Y)) = divide(X,Y),
inference(equational,[status(thm)],[c23,c30]) ).
cnf(c32,plain,
divide(divide(X,X),divide(Y,multiply(Z,Y))) = Z,
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c33,plain,
inverse(X) = divide(Y,divide(X,divide(divide(X,X),Y))),
inference(equational,[status(thm)],[c2,c22,c32]) ).
cnf(c35,plain,
divide(divide(X,Y),X) = inverse(Y),
inference(equational,[status(thm)],[c18,c33]) ).
cnf(c37,plain,
divide(multiply(X,Y),X) = Y,
inference(equational,[status(thm)],[c2,c22,c35]) ).
cnf(c39,plain,
divide(X,divide(divide(Y,divide(Z,X)),Y)) = Z,
inference(equational,[status(thm)],[c6]) ).
cnf(c40,plain,
multiply(X,divide(Y,X)) = Y,
inference(equational,[status(thm)],[c1,c12,c30,c39]) ).
cnf(c44,plain,
divide(divide(X,Y),divide(Z,Y)) = divide(X,Z),
inference(equational,[status(thm)],[c6,c39]) ).
cnf(c45,plain,
inverse(divide(X,Y)) = divide(Y,X),
inference(equational,[status(thm)],[c22,c44]) ).
cnf(c46,plain,
divide(divide(X,Y),inverse(Y)) = X,
inference(equational,[status(thm)],[c3,c12,c44]) ).
cnf(c47,plain,
multiply(divide(divide(X,X),X),Y) = divide(Y,X),
inference(equational,[status(thm)],[c35,c40,c46]) ).
cnf(c50,plain,
divide(divide(X,divide(divide(Y,Y),Y)),Y) = X,
inference(equational,[status(thm)],[c3,c22,c35,c46]) ).
cnf(c52,plain,
divide(inverse(X),divide(Y,X)) = divide(divide(Z,Z),Y),
inference(equational,[status(thm)],[c1,c44]) ).
cnf(c53,plain,
divide(X,multiply(Y,X)) = divide(divide(Z,Z),Y),
inference(equational,[status(thm)],[c2,c22,c52]) ).
cnf(c54,plain,
divide(divide(X,Y),X) = divide(divide(Z,Z),Y),
inference(equational,[status(thm)],[c11,c39,c45,c52]) ).
cnf(c55,plain,
divide(inverse(X),divide(Y,X)) = inverse(Y),
inference(equational,[status(thm)],[c1,c52]) ).
cnf(c56,plain,
divide(X,multiply(Y,X)) = inverse(Y),
inference(equational,[status(thm)],[c2,c22,c55]) ).
cnf(c58,plain,
divide(inverse(X),divide(Y,multiply(Y,Y))) = divide(Y,X),
inference(equational,[status(thm)],[c11,c55,c56]) ).
cnf(c59,plain,
inverse(X) = divide(Y,divide(X,divide(divide(Y,Y),Y))),
inference(equational,[status(thm)],[c2,c12,c13,c44,c53,c58]) ).
cnf(c63,plain,
divide(divide(divide(X,X),X),Y) = divide(inverse(Y),X),
inference(equational,[status(thm)],[c11,c31,c58,c59]) ).
cnf(c66,plain,
divide(divide(X,inverse(Y)),X) = Y,
inference(equational,[status(thm)],[c3,c11,c44,c54]) ).
cnf(c70,plain,
divide(divide(X,X),divide(Y,Z)) = divide(Z,Y),
inference(equational,[status(thm)],[c7,c40,c44]) ).
cnf(c71,plain,
divide(divide(X,Y),divide(divide(X,X),Z)) = divide(Z,divide(Y,X)),
inference(equational,[status(thm)],[c2,c47,c70]) ).
cnf(c72,plain,
divide(divide(X,Y),divide(divide(Y,Y),divide(Z,X))) = divide(Z,Y),
inference(equational,[status(thm)],[c2,c40,c44]) ).
cnf(c73,plain,
divide(divide(X,Y),Z) = divide(divide(X,Z),Y),
inference(equational,[status(thm)],[c12,c39,c72]) ).
cnf(c75,plain,
divide(X,divide(Y,divide(Z,X))) = divide(Z,Y),
inference(equational,[status(thm)],[c6,c44]) ).
cnf(c79,plain,
divide(X,divide(Y,divide(X,multiply(X,X)))) = inverse(Y),
inference(equational,[status(thm)],[c3,c22,c55,c56]) ).
cnf(c80,plain,
divide(divide(X,multiply(X,X)),divide(Y,X)) = inverse(Y),
inference(equational,[status(thm)],[c11,c45,c46,c55,c79]) ).
cnf(c81,plain,
multiply(inverse(X),Y) = divide(Y,X),
inference(equational,[status(thm)],[c19,c30,c63]) ).
cnf(c82,plain,
divide(X,inverse(Y)) = multiply(Y,X),
inference(equational,[status(thm)],[c37,c46]) ).
cnf(c83,plain,
divide(divide(X,multiply(X,X)),divide(Y,Z)) = divide(divide(Z,X),Y),
inference(equational,[status(thm)],[c12,c46,c75,c80]) ).
cnf(c85,plain,
divide(divide(X,Y),Y) = divide(X,multiply(Y,Y)),
inference(equational,[status(thm)],[c12,c72,c83]) ).
cnf(c88,plain,
divide(X,divide(Y,divide(divide(Z,Z),Z))) = divide(divide(X,Z),Y),
inference(equational,[status(thm)],[c44,c46,c80,c85]) ).
cnf(c89,plain,
divide(multiply(X,Y),Z) = divide(X,divide(Z,Y)),
inference(equational,[status(thm)],[c2,c11,c44,c88]) ).
cnf(c91,plain,
divide(divide(X,divide(divide(Y,Y),Y)),Z) = divide(X,divide(Z,Y)),
inference(equational,[status(thm)],[c44,c46,c80,c85]) ).
cnf(c92,plain,
divide(X,multiply(Y,Z)) = divide(divide(X,Z),Y),
inference(equational,[status(thm)],[c2,c11,c44,c91]) ).
cnf(c97,plain,
divide(X,multiply(Y,Z)) = divide(divide(X,Y),Z),
inference(equational,[status(thm)],[c73,c92]) ).
cnf(c98,plain,
divide(divide(X,Y),divide(divide(X,X),Z)) = divide(X,divide(Y,Z)),
inference(equational,[status(thm)],[c2,c30,c81,c92]) ).
cnf(c99,plain,
multiply(divide(X,Y),Z) = divide(Z,divide(Y,X)),
inference(equational,[status(thm)],[c12,c44,c47,c71]) ).
cnf(c100,plain,
multiply(X,Y) = divide(Y,divide(divide(X,X),X)),
inference(equational,[status(thm)],[c11,c44,c66,c80,c97,c99]) ).
cnf(c144,plain,
divide(X,divide(inverse(Y),Z)) = divide(Y,divide(divide(divide(X,X),X),Z)),
inference(equational,[status(thm)],[c30,c89,c99,c100]) ).
cnf(c157,plain,
divide(inverse(X),Y) = divide(divide(divide(X,X),X),Y),
inference(equational,[status(thm)],[c1,c11,c12,c83,c100]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c44,c45,c50,c63,c71,c73,c81,c82,c83,c98,c144,c157]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP523-1 : TPTP v9.0.0. Released v2.6.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n009.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 08:31:04 EDT 2025
% 0.12/0.33 % CPUTime :
% 4.27/4.44 % SZS status Unsatisfiable
% 4.27/4.44 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------