%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP548-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n002.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 06:44:18 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.45s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of clauses : 17 ( 17 unt; 0 nHn; 3 RR)
% Number of literals : 17 ( 16 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; 3 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('theBenchmark.p',prove_these_axioms_4) ).
cnf(c1,axiom,
identity = divide(X,X),
file('theBenchmark.p',identity) ).
cnf(c2,plain,
divide(X,X) = identity,
inference(equational,[status(thm)],[c1]) ).
cnf(c4,axiom,
multiply(X,Y) = divide(X,divide(identity,Y)),
file('theBenchmark.p',multiply) ).
cnf(c5,axiom,
divide(divide(identity,divide(X,Y)),divide(divide(Y,Z),X)) = Z,
file('theBenchmark.p',single_axiom) ).
cnf(c6,plain,
divide(identity,divide(divide(X,Y),X)) = Y,
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c7,plain,
divide(identity,divide(identity,X)) = X,
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c8,plain,
divide(divide(X,Y),X) = divide(identity,Y),
inference(equational,[status(thm)],[c6,c7]) ).
cnf(c9,plain,
divide(X,identity) = X,
inference(equational,[status(thm)],[c7,c8]) ).
cnf(c10,plain,
divide(X,divide(X,Y)) = Y,
inference(equational,[status(thm)],[c5,c7,c9]) ).
cnf(c11,plain,
divide(X,Y) = divide(identity,divide(Y,X)),
inference(equational,[status(thm)],[c8,c10]) ).
cnf(c14,plain,
divide(X,divide(divide(Y,Z),divide(Y,X))) = Z,
inference(equational,[status(thm)],[c5,c6]) ).
cnf(c18,plain,
divide(divide(X,Y),divide(X,Z)) = divide(identity,divide(Y,Z)),
inference(equational,[status(thm)],[c6,c14]) ).
cnf(c21,plain,
divide(X,divide(Y,divide(Z,X))) = divide(identity,divide(Y,Z)),
inference(equational,[status(thm)],[c14,c18]) ).
cnf(c22,plain,
divide(divide(X,Y),Z) = divide(identity,divide(Y,divide(X,Z))),
inference(equational,[status(thm)],[c14,c21]) ).
cnf(g1,plain,
multiply(a,b) = multiply(b,a),
inference(equational,[status(thm)],[c4,c7,c11,c22]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP548-1 : TPTP v9.0.0. Bugfixed v2.7.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n002.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Jul 14 08:32:04 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.45 % SZS status Unsatisfiable
% 0.20/0.45 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------