%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP750-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n006.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 06:44:50 AM UTC 2025
% Result : Unsatisfiable 6.85s 7.06s
% Output : CNFRefutation 6.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of clauses : 22 ( 22 unt; 0 nHn; 3 RR)
% Number of literals : 22 ( 21 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 : 52 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
mult(mult(a,a),mult(b,c)) != mult(mult(a,b),mult(a,c)),
file('theBenchmark.p',goals) ).
cnf(c1,axiom,
mult(X,ld(X,Y)) = Y,
file('theBenchmark.p',f01) ).
cnf(c2,axiom,
ld(X,mult(X,Y)) = Y,
file('theBenchmark.p',f02) ).
cnf(c3,axiom,
mult(rd(X,Y),Y) = X,
file('theBenchmark.p',f03) ).
cnf(c7,axiom,
mult(mult(X,Y),mult(Z,Z)) = mult(mult(X,Z),mult(Y,Z)),
file('theBenchmark.p',f06) ).
cnf(c9,plain,
mult(X,mult(Y,Y)) = mult(mult(Z,Y),mult(ld(Z,X),Y)),
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c11,axiom,
mult(mult(X,mult(X,X)),mult(Y,Z)) = mult(mult(X,Y),mult(mult(X,X),Z)),
file('theBenchmark.p',f05) ).
cnf(c15,plain,
ld(mult(X,Y),mult(Z,mult(Y,Y))) = mult(ld(X,Z),Y),
inference(equational,[status(thm)],[c2,c9]) ).
cnf(c22,plain,
ld(mult(X,Y),mult(mult(X,Z),mult(Y,Z))) = mult(Z,Z),
inference(equational,[status(thm)],[c2,c7]) ).
cnf(c29,plain,
ld(mult(rd(X,Y),Z),mult(X,mult(Z,Y))) = mult(Y,Y),
inference(equational,[status(thm)],[c3,c22]) ).
cnf(c40,plain,
mult(mult(X,ld(Y,Z)),Z) = mult(mult(X,Y),mult(ld(Y,Z),ld(Y,Z))),
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c41,plain,
mult(mult(X,X),mult(ld(X,Y),ld(X,Y))) = mult(Y,Y),
inference(equational,[status(thm)],[c1,c40]) ).
cnf(c42,plain,
mult(ld(X,Y),ld(X,Y)) = ld(mult(X,X),mult(Y,Y)),
inference(equational,[status(thm)],[c3,c29,c41]) ).
cnf(c100,plain,
ld(X,mult(Y,ld(mult(Z,Z),mult(X,X)))) = mult(ld(Z,Y),ld(Z,X)),
inference(equational,[status(thm)],[c1,c15,c42]) ).
cnf(c119,plain,
mult(mult(X,Y),Z) = mult(mult(X,mult(X,X)),mult(Y,ld(mult(X,X),Z))),
inference(equational,[status(thm)],[c1,c11]) ).
cnf(c120,plain,
ld(mult(X,mult(X,X)),mult(mult(X,Y),Z)) = mult(Y,ld(mult(X,X),Z)),
inference(equational,[status(thm)],[c2,c119]) ).
cnf(c121,plain,
mult(X,ld(mult(Y,Y),mult(Z,Z))) = mult(Z,ld(mult(Y,Y),mult(X,Z))),
inference(equational,[status(thm)],[c7,c120]) ).
cnf(c122,plain,
mult(ld(X,Y),ld(X,Z)) = ld(mult(X,X),mult(Y,Z)),
inference(equational,[status(thm)],[c2,c100,c121]) ).
cnf(c124,plain,
ld(mult(X,X),mult(mult(X,Y),Z)) = mult(Y,ld(X,Z)),
inference(equational,[status(thm)],[c2,c122]) ).
cnf(c131,plain,
mult(mult(X,X),mult(Y,ld(X,Z))) = mult(mult(X,Y),Z),
inference(equational,[status(thm)],[c1,c124]) ).
cnf(g1,plain,
mult(mult(a,a),mult(b,c)) = mult(mult(a,b),mult(a,c)),
inference(equational,[status(thm)],[c2,c131]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : GRP750-1 : TPTP v9.0.0. Released v4.0.0.
% 0.09/0.10 % Command : run_Leo-III %s %d THM
% 0.09/0.30 % Computer : n006.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon Jul 14 09:02:04 EDT 2025
% 0.09/0.30 % CPUTime :
% 6.85/7.06 % SZS status Unsatisfiable
% 6.85/7.06 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------