%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP535-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n003.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 0.19s 0.48s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of clauses : 21 ( 21 unt; 0 nHn; 3 RR)
% Number of literals : 21 ( 20 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 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,
identity = divide(X,X),
file('theBenchmark.p',identity) ).
cnf(c2,plain,
divide(X,X) = identity,
inference(equational,[status(thm)],[c1]) ).
cnf(c3,axiom,
inverse(X) = divide(divide(Y,Y),X),
file('theBenchmark.p',inverse) ).
cnf(c4,plain,
divide(identity,X) = inverse(X),
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c6,axiom,
multiply(X,Y) = divide(X,divide(divide(Z,Z),Y)),
file('theBenchmark.p',multiply) ).
cnf(c7,plain,
multiply(X,Y) = divide(X,inverse(Y)),
inference(equational,[status(thm)],[c2,c4,c6]) ).
cnf(c8,axiom,
divide(divide(X,divide(divide(X,Y),Z)),Y) = Z,
file('theBenchmark.p',single_axiom) ).
cnf(c11,plain,
divide(divide(X,inverse(Y)),X) = Y,
inference(equational,[status(thm)],[c2,c4,c8]) ).
cnf(c12,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c2,c4,c11]) ).
cnf(c13,plain,
divide(X,identity) = X,
inference(equational,[status(thm)],[c4,c11,c12]) ).
cnf(c14,plain,
divide(X,divide(X,Y)) = Y,
inference(equational,[status(thm)],[c8,c13]) ).
cnf(c15,plain,
divide(divide(X,Y),X) = inverse(Y),
inference(equational,[status(thm)],[c11,c12]) ).
cnf(c16,plain,
divide(X,Y) = inverse(divide(Y,X)),
inference(equational,[status(thm)],[c14,c15]) ).
cnf(c17,plain,
inverse(divide(inverse(X),divide(Y,X))) = Y,
inference(equational,[status(thm)],[c8,c11,c16]) ).
cnf(c18,plain,
inverse(divide(inverse(X),Y)) = divide(X,inverse(Y)),
inference(equational,[status(thm)],[c11,c17]) ).
cnf(c23,plain,
divide(inverse(X),Y) = inverse(divide(X,inverse(Y))),
inference(equational,[status(thm)],[c12,c18]) ).
cnf(c29,plain,
divide(X,divide(divide(X,Y),Z)) = divide(Y,inverse(Z)),
inference(equational,[status(thm)],[c8,c12,c17,c23]) ).
cnf(c30,plain,
divide(divide(X,Y),inverse(Z)) = divide(X,divide(Y,Z)),
inference(equational,[status(thm)],[c14,c29]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c7,c23,c30]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP535-1 : TPTP v9.0.0. Released v2.6.0.
% 0.11/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n003.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 08:31:34 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.48 % SZS status Unsatisfiable
% 0.19/0.48 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------