%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP528-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n016.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 2.68s 2.87s
% Output : CNFRefutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of clauses : 29 ( 29 unt; 0 nHn; 3 RR)
% Number of literals : 29 ( 28 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('theBenchmark.p',prove_these_axioms_4) ).
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(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(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(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(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(c121,plain,
divide(X,divide(divide(X,Y),Z)) = multiply(Z,Y),
inference(equational,[status(thm)],[c90,c95]) ).
cnf(c122,plain,
multiply(X,Y) = multiply(Y,X),
inference(equational,[status(thm)],[c90,c121]) ).
cnf(g1,plain,
multiply(a,b) = multiply(b,a),
inference(equational,[status(thm)],[c122]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP528-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% 0.03/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n016.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 08:31:04 EDT 2025
% 0.11/0.32 % CPUTime :
% 2.68/2.87 % SZS status Unsatisfiable
% 2.68/2.87 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------