%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP756-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n009.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 06:44:51 AM UTC 2025
% Result : Unsatisfiable 0.54s 0.76s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 3 RR)
% Number of literals : 26 ( 25 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 : 61 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
mult(mult(a,b),c) != mult(a,mult(b,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(c4,axiom,
rd(mult(X,Y),Y) = X,
file('theBenchmark.p',f04) ).
cnf(c5,plain,
rd(X,ld(Y,X)) = Y,
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c7,axiom,
mult(X,mult(mult(Y,Y),Z)) = mult(mult(X,Y),mult(Y,Z)),
file('theBenchmark.p',f05) ).
cnf(c8,plain,
mult(rd(X,Y),mult(mult(Y,Y),Z)) = mult(X,mult(Y,Z)),
inference(equational,[status(thm)],[c3,c7]) ).
cnf(c9,plain,
mult(mult(X,Y),Z) = mult(X,mult(mult(Y,Y),ld(Y,Z))),
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c12,plain,
ld(X,mult(mult(X,Y),mult(Y,Z))) = mult(mult(Y,Y),Z),
inference(equational,[status(thm)],[c2,c7]) ).
cnf(c17,plain,
mult(rd(X,Y),Z) = mult(X,mult(Y,ld(mult(Y,Y),Z))),
inference(equational,[status(thm)],[c1,c8]) ).
cnf(c18,plain,
mult(X,mult(Y,ld(mult(Y,Y),Y))) = X,
inference(equational,[status(thm)],[c3,c17]) ).
cnf(c20,plain,
ld(X,X) = mult(Y,ld(mult(Y,Y),Y)),
inference(equational,[status(thm)],[c2,c18]) ).
cnf(c27,plain,
mult(X,ld(Y,mult(mult(Y,Z),W))) = mult(mult(X,Z),W),
inference(equational,[status(thm)],[c1,c9,c12]) ).
cnf(c39,plain,
rd(ld(X,X),ld(mult(Y,Y),Y)) = Y,
inference(equational,[status(thm)],[c4,c20]) ).
cnf(c41,plain,
mult(mult(X,Y),mult(Y,ld(mult(Y,Y),Z))) = mult(X,Z),
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c42,plain,
ld(mult(X,Y),mult(X,Z)) = mult(Y,ld(mult(Y,Y),Z)),
inference(equational,[status(thm)],[c2,c41]) ).
cnf(c43,plain,
ld(X,ld(mult(Y,X),mult(Y,Z))) = ld(mult(X,X),Z),
inference(equational,[status(thm)],[c2,c42]) ).
cnf(c44,plain,
ld(mult(X,Y),mult(X,Z)) = ld(mult(W,Y),mult(W,Z)),
inference(equational,[status(thm)],[c1,c42,c43]) ).
cnf(c45,plain,
ld(mult(X,Y),X) = ld(mult(Z,Y),Z),
inference(equational,[status(thm)],[c18,c44]) ).
cnf(c51,plain,
rd(X,ld(mult(Y,Z),Y)) = mult(X,Z),
inference(equational,[status(thm)],[c5,c45]) ).
cnf(c52,plain,
mult(ld(X,X),Y) = Y,
inference(equational,[status(thm)],[c39,c51]) ).
cnf(c54,plain,
ld(ld(X,X),Y) = Y,
inference(equational,[status(thm)],[c2,c52]) ).
cnf(c66,plain,
mult(mult(X,Y),Z) = mult(X,mult(Y,Z)),
inference(equational,[status(thm)],[c27,c52,c54]) ).
cnf(g1,plain,
mult(mult(a,b),c) = mult(a,mult(b,c)),
inference(equational,[status(thm)],[c66]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP756-1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n009.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 09:02:49 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.54/0.76 % SZS status Unsatisfiable
% 0.54/0.76 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------