%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP527-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n013.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 25.17s 25.40s
% Output : CNFRefutation 25.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of clauses : 47 ( 47 unt; 0 nHn; 3 RR)
% Number of literals : 47 ( 46 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 : 114 ( 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(c6,axiom,
divide(X,divide(divide(X,Y),divide(Z,Y))) = Z,
file('theBenchmark.p',single_axiom) ).
cnf(c7,plain,
divide(divide(X,divide(Y,Z)),Z) = divide(X,Y),
inference(equational,[status(thm)],[c6]) ).
cnf(c8,plain,
divide(divide(X,Y),X) = inverse(Y),
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c9,plain,
divide(X,divide(X,Y)) = divide(Z,divide(Z,Y)),
inference(equational,[status(thm)],[c6,c7]) ).
cnf(c11,plain,
divide(multiply(X,Y),Y) = divide(X,divide(Z,Z)),
inference(equational,[status(thm)],[c2,c7]) ).
cnf(c12,plain,
divide(multiply(X,Y),Y) = X,
inference(equational,[status(thm)],[c6,c11]) ).
cnf(c13,plain,
divide(X,divide(Y,Y)) = X,
inference(equational,[status(thm)],[c11,c12]) ).
cnf(c16,plain,
divide(divide(X,Y),X) = divide(divide(Z,Z),Y),
inference(equational,[status(thm)],[c1,c8]) ).
cnf(c17,plain,
divide(divide(X,Y),inverse(Y)) = X,
inference(equational,[status(thm)],[c6,c8]) ).
cnf(c18,plain,
divide(X,inverse(Y)) = divide(X,divide(divide(Y,Y),Y)),
inference(equational,[status(thm)],[c2,c12,c17]) ).
cnf(c20,plain,
divide(X,divide(X,Y)) = inverse(inverse(Y)),
inference(equational,[status(thm)],[c8,c17]) ).
cnf(c21,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c8,c17,c20]) ).
cnf(c23,plain,
divide(X,divide(X,Y)) = Y,
inference(equational,[status(thm)],[c9,c13]) ).
cnf(c24,plain,
divide(X,multiply(divide(X,Y),Y)) = divide(Z,Z),
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c25,plain,
divide(divide(X,Y),divide(divide(Y,Y),Y)) = X,
inference(equational,[status(thm)],[c2,c6,c13,c23,c24]) ).
cnf(c26,plain,
inverse(divide(divide(X,X),X)) = X,
inference(equational,[status(thm)],[c8,c23,c25]) ).
cnf(c30,plain,
divide(inverse(divide(X,Y)),Y) = divide(divide(Z,Z),X),
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c31,plain,
divide(divide(X,X),Y) = divide(divide(Z,Z),Y),
inference(equational,[status(thm)],[c1,c7,c30]) ).
cnf(c38,plain,
inverse(divide(divide(X,X),Y)) = Y,
inference(equational,[status(thm)],[c26,c31]) ).
cnf(c40,plain,
inverse(divide(divide(X,Y),X)) = Y,
inference(equational,[status(thm)],[c16,c26]) ).
cnf(c42,plain,
inverse(divide(X,Y)) = divide(Y,X),
inference(equational,[status(thm)],[c20,c21,c40]) ).
cnf(c45,plain,
divide(X,divide(divide(Y,Z),Y)) = multiply(X,Z),
inference(equational,[status(thm)],[c2,c7]) ).
cnf(c48,plain,
divide(inverse(X),divide(Y,X)) = divide(divide(Z,Z),Y),
inference(equational,[status(thm)],[c9,c23,c30]) ).
cnf(c51,plain,
divide(inverse(X),divide(Y,X)) = inverse(Y),
inference(equational,[status(thm)],[c8,c13,c48]) ).
cnf(c55,plain,
divide(X,divide(Y,divide(divide(X,X),X))) = inverse(Y),
inference(equational,[status(thm)],[c2,c40,c45,c51]) ).
cnf(c74,plain,
divide(divide(X,Y),divide(divide(Z,Z),Z)) = divide(X,divide(Y,Z)),
inference(equational,[status(thm)],[c7,c17,c18]) ).
cnf(c75,plain,
divide(divide(divide(X,X),X),Y) = divide(divide(Z,Z),divide(X,divide(divide(X,X),Y))),
inference(equational,[status(thm)],[c2,c11,c13,c23,c30,c55]) ).
cnf(c78,plain,
divide(divide(X,divide(Y,Z)),W) = divide(X,divide(Y,divide(Z,W))),
inference(equational,[status(thm)],[c7]) ).
cnf(c79,plain,
divide(X,divide(Y,divide(Z,X))) = divide(Z,Y),
inference(equational,[status(thm)],[c8,c42,c78]) ).
cnf(c80,plain,
divide(X,divide(Y,divide(divide(Z,Z),Z))) = divide(divide(X,Z),Y),
inference(equational,[status(thm)],[c2,c45,c79]) ).
cnf(c81,plain,
divide(X,multiply(Y,X)) = divide(divide(Z,Z),Y),
inference(equational,[status(thm)],[c2,c79]) ).
cnf(c83,plain,
divide(X,divide(Y,Z)) = divide(Z,divide(divide(Z,Z),divide(X,Y))),
inference(equational,[status(thm)],[c2,c11,c13,c78,c79]) ).
cnf(c84,plain,
divide(inverse(X),divide(Y,Z)) = divide(divide(Z,X),Y),
inference(equational,[status(thm)],[c17,c79]) ).
cnf(c85,plain,
divide(X,divide(divide(Y,Y),divide(Y,Z))) = divide(Y,divide(Z,X)),
inference(equational,[status(thm)],[c2,c38,c45,c78,c84]) ).
cnf(c90,plain,
divide(X,divide(divide(X,Y),Z)) = multiply(Y,Z),
inference(equational,[status(thm)],[c45,c79]) ).
cnf(c95,plain,
divide(divide(X,Y),divide(Z,Y)) = divide(X,Z),
inference(equational,[status(thm)],[c9,c23,c79]) ).
cnf(c109,plain,
divide(divide(divide(X,X),Y),Z) = divide(inverse(Z),Y),
inference(equational,[status(thm)],[c7,c48]) ).
cnf(c131,plain,
multiply(X,Y) = divide(Y,divide(divide(X,X),X)),
inference(equational,[status(thm)],[c23,c80,c90]) ).
cnf(c144,plain,
divide(inverse(X),Y) = divide(divide(X,X),divide(X,divide(divide(X,X),Y))),
inference(equational,[status(thm)],[c13,c23,c75,c81,c84,c131]) ).
cnf(c147,plain,
divide(divide(divide(X,Y),X),Z) = divide(divide(Y,Y),divide(Y,divide(divide(Y,Y),Z))),
inference(equational,[status(thm)],[c13,c30,c42,c84,c144]) ).
cnf(c158,plain,
divide(X,divide(divide(Y,Y),Y)) = divide(Z,divide(divide(Z,X),Y)),
inference(equational,[status(thm)],[c8,c18,c79]) ).
cnf(c209,plain,
divide(X,divide(divide(Y,Z),W)) = divide(Z,divide(divide(Y,X),W)),
inference(equational,[status(thm)],[c74,c79,c158]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c13,c74,c83,c85,c95,c109,c131,c144,c147,c209]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP527-1 : TPTP v9.0.0. Released v2.6.0.
% 0.00/0.09 % Command : run_Leo-III %s %d THM
% 0.08/0.29 % Computer : n013.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Mon Jul 14 08:31:04 EDT 2025
% 0.08/0.29 % CPUTime :
% 25.17/25.40 % SZS status Unsatisfiable
% 25.17/25.40 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------