%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP547-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n004.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 0.51s 0.71s
% Output : CNFRefutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of clauses : 16 ( 16 unt; 0 nHn; 3 RR)
% Number of literals : 16 ( 15 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 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(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(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(c25,plain,
divide(X,divide(Y,divide(identity,Z))) = divide(identity,divide(Y,divide(X,Z))),
inference(equational,[status(thm)],[c7,c8,c21,c22]) ).
cnf(c34,plain,
divide(X,divide(identity,divide(Y,Z))) = divide(Y,divide(identity,divide(X,Z))),
inference(equational,[status(thm)],[c7,c18,c22,c25]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c4,c7,c22,c34]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP547-1 : TPTP v9.0.0. Released v2.6.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n004.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 08:32:04 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.51/0.71 % SZS status Unsatisfiable
% 0.51/0.71 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------