%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LAT390-1 : TPTP v9.0.0. Released v4.0.0.
% 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 07:06:24 AM UTC 2025
% Result : Unsatisfiable 5.80s 5.96s
% Output : CNFRefutation 5.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 2
% Syntax : Number of clauses : 48 ( 48 unt; 0 nHn; 3 RR)
% Number of literals : 48 ( 47 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 13 ( 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 : 133 ( 42 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
plus(a,mult(b,mult(a,c))) != a,
file('theBenchmark.p',goals) ).
cnf(c1,axiom,
mult(plus(mult(plus(X,Y),plus(Y,mult(X,Y))),Z),plus(mult(plus(X,mult(mult(plus(W,Y),plus(Y,V)),Y)),plus(mult(plus(Y,plus(plus(mult(W,mult(Y,V)),mult(U,Y)),Y)),plus(U2,mult(Y,plus(plus(mult(Y,U3),mult(U,Y)),Y)))),mult(X,mult(mult(plus(W,Y),plus(Y,V)),Y)))),mult(mult(plus(X,Y),plus(Y,mult(X,Y))),Z))) = Y,
file('theBenchmark.p',sos) ).
cnf(c2,plain,
mult(plus(mult(plus(X,mult(plus(Y,Z),plus(Z,mult(Y,Z)))),plus(mult(plus(Y,Z),plus(Z,mult(Y,Z))),mult(X,mult(plus(Y,Z),plus(Z,mult(Y,Z)))))),W),plus(mult(plus(X,mult(mult(plus(mult(plus(Y,Z),plus(Z,mult(Y,Z))),mult(plus(Y,Z),plus(Z,mult(Y,Z)))),plus(mult(plus(Y,Z),plus(Z,mult(Y,Z))),V)),mult(plus(Y,Z),plus(Z,mult(Y,Z))))),plus(Z,mult(X,mult(mult(plus(mult(plus(Y,Z),plus(Z,mult(Y,Z))),mult(plus(Y,Z),plus(Z,mult(Y,Z)))),plus(mult(plus(Y,Z),plus(Z,mult(Y,Z))),V)),mult(plus(Y,Z),plus(Z,mult(Y,Z))))))),mult(mult(plus(X,mult(plus(Y,Z),plus(Z,mult(Y,Z)))),plus(mult(plus(Y,Z),plus(Z,mult(Y,Z))),mult(X,mult(plus(Y,Z),plus(Z,mult(Y,Z)))))),W))) = mult(plus(Y,Z),plus(Z,mult(Y,Z))),
inference(equational,[status(thm)],[c1]) ).
cnf(c3,plain,
mult(plus(mult(plus(X,Y),plus(Y,mult(X,Y))),Z),plus(mult(plus(X,mult(mult(plus(Y,Y),plus(Y,W)),Y)),plus(mult(plus(V,mult(mult(plus(U,Y),plus(Y,U2)),Y)),plus(mult(plus(Y,plus(plus(mult(U,mult(Y,U2)),mult(U3,Y)),Y)),plus(U4,mult(Y,plus(plus(mult(Y,U5),mult(U3,Y)),Y)))),mult(V,mult(mult(plus(U,Y),plus(Y,U2)),Y)))),mult(X,mult(mult(plus(Y,Y),plus(Y,W)),Y)))),mult(mult(plus(X,Y),plus(Y,mult(X,Y))),Z))) = Y,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,plain,
mult(plus(mult(plus(mult(plus(X,Y),plus(Y,mult(X,Y))),Y),plus(Y,mult(mult(plus(X,Y),plus(Y,mult(X,Y))),Y))),Z),plus(Y,mult(mult(plus(mult(plus(X,Y),plus(Y,mult(X,Y))),Y),plus(Y,mult(mult(plus(X,Y),plus(Y,mult(X,Y))),Y))),Z))) = Y,
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c5,plain,
mult(plus(X,Y),plus(X,mult(X,Y))) = X,
inference(equational,[status(thm)],[c4]) ).
cnf(c6,plain,
mult(plus(plus(X,Y),plus(X,mult(X,Y))),plus(plus(X,Y),X)) = plus(X,Y),
inference(equational,[status(thm)],[c5]) ).
cnf(c8,plain,
mult(plus(mult(plus(X,Y),plus(Y,mult(X,Y))),Z),plus(mult(plus(X,mult(mult(plus(Y,Y),plus(Y,W)),Y)),plus(Y,mult(X,mult(mult(plus(Y,Y),plus(Y,W)),Y)))),mult(mult(plus(X,Y),plus(Y,mult(X,Y))),Z))) = Y,
inference(equational,[status(thm)],[c2,c4]) ).
cnf(c9,plain,
mult(plus(X,mult(mult(plus(Y,Y),plus(Y,Z)),Y)),plus(Y,mult(X,mult(mult(plus(Y,Y),plus(Y,Z)),Y)))) = Y,
inference(equational,[status(thm)],[c5,c8]) ).
cnf(c10,plain,
mult(plus(X,mult(Y,Y)),plus(Y,mult(X,mult(Y,Y)))) = Y,
inference(equational,[status(thm)],[c5,c9]) ).
cnf(c12,plain,
mult(plus(mult(plus(X,Y),plus(Y,mult(X,Y))),Z),plus(Y,mult(mult(plus(X,Y),plus(Y,mult(X,Y))),Z))) = Y,
inference(equational,[status(thm)],[c8,c9]) ).
cnf(c13,plain,
mult(plus(plus(X,mult(mult(plus(Y,Y),plus(Y,Z)),Y)),plus(Y,mult(X,mult(mult(plus(Y,Y),plus(Y,Z)),Y)))),plus(plus(X,mult(mult(plus(Y,Y),plus(Y,Z)),Y)),Y)) = plus(X,mult(mult(plus(Y,Y),plus(Y,Z)),Y)),
inference(equational,[status(thm)],[c5,c9]) ).
cnf(c17,plain,
mult(plus(X,mult(mult(plus(Y,Z),plus(Z,W)),Z)),plus(mult(plus(Z,plus(plus(mult(Y,mult(Z,W)),mult(V,Z)),Z)),plus(U,mult(Z,plus(plus(mult(Z,U2),mult(V,Z)),Z)))),mult(X,mult(mult(plus(Y,Z),plus(Z,W)),Z)))) = Z,
inference(equational,[status(thm)],[c1,c5,c8]) ).
cnf(c18,plain,
mult(plus(X,plus(plus(mult(Y,mult(X,Z)),mult(W,X)),X)),plus(V,mult(X,plus(plus(mult(X,U),mult(W,X)),X)))) = X,
inference(equational,[status(thm)],[c5,c17]) ).
cnf(c19,plain,
mult(plus(X,Y),plus(Y,mult(X,Y))) = Y,
inference(equational,[status(thm)],[c12,c18]) ).
cnf(c20,plain,
plus(plus(mult(X,mult(X,Y)),mult(Z,X)),X) = X,
inference(equational,[status(thm)],[c18,c19]) ).
cnf(c21,plain,
mult(plus(plus(X,Y),plus(Y,mult(X,Y))),plus(plus(X,Y),Y)) = plus(X,Y),
inference(equational,[status(thm)],[c5,c19]) ).
cnf(c22,plain,
mult(X,plus(X,mult(plus(mult(X,mult(X,Y)),mult(Z,X)),X))) = X,
inference(equational,[status(thm)],[c19,c20]) ).
cnf(c23,plain,
plus(plus(mult(X,X),mult(Y,X)),X) = X,
inference(equational,[status(thm)],[c20,c22]) ).
cnf(c26,plain,
plus(plus(mult(plus(X,Y),X),mult(Z,plus(X,Y))),plus(X,Y)) = plus(X,Y),
inference(equational,[status(thm)],[c5,c20]) ).
cnf(c27,plain,
plus(plus(mult(X,plus(mult(X,X),mult(Y,X))),mult(Z,X)),X) = X,
inference(equational,[status(thm)],[c23,c26]) ).
cnf(c31,plain,
mult(plus(X,X),plus(Y,mult(X,plus(plus(mult(X,Z),mult(W,X)),X)))) = X,
inference(equational,[status(thm)],[c18,c20]) ).
cnf(c32,plain,
mult(plus(X,X),plus(Y,mult(X,X))) = X,
inference(equational,[status(thm)],[c20,c31]) ).
cnf(c33,plain,
mult(X,X) = X,
inference(equational,[status(thm)],[c10,c32]) ).
cnf(c34,plain,
plus(X,X) = X,
inference(equational,[status(thm)],[c19,c33]) ).
cnf(c35,plain,
mult(X,plus(Y,X)) = X,
inference(equational,[status(thm)],[c31,c33,c34]) ).
cnf(c36,plain,
plus(plus(X,mult(Y,X)),X) = X,
inference(equational,[status(thm)],[c20,c33]) ).
cnf(c38,plain,
mult(mult(plus(X,Y),plus(Y,Z)),Y) = Y,
inference(equational,[status(thm)],[c17,c32]) ).
cnf(c39,plain,
mult(plus(X,Y),Y) = Y,
inference(equational,[status(thm)],[c35,c38]) ).
cnf(c40,plain,
mult(mult(X,plus(X,Y)),X) = X,
inference(equational,[status(thm)],[c27,c38]) ).
cnf(c41,plain,
plus(plus(X,Y),Y) = plus(X,Y),
inference(equational,[status(thm)],[c5,c33,c39]) ).
cnf(c42,plain,
plus(mult(X,plus(X,Y)),X) = mult(X,plus(X,Y)),
inference(equational,[status(thm)],[c5,c33,c40]) ).
cnf(c44,plain,
plus(X,plus(X,mult(Y,X))) = plus(X,mult(Y,X)),
inference(equational,[status(thm)],[c19,c36]) ).
cnf(c45,plain,
plus(mult(X,mult(X,Y)),X) = X,
inference(equational,[status(thm)],[c20,c33,c41]) ).
cnf(c49,plain,
plus(mult(plus(X,Y),X),plus(X,Y)) = plus(X,Y),
inference(equational,[status(thm)],[c5,c45]) ).
cnf(c50,plain,
mult(X,plus(X,mult(Y,X))) = X,
inference(equational,[status(thm)],[c36,c42,c49]) ).
cnf(c51,plain,
plus(X,mult(Y,X)) = X,
inference(equational,[status(thm)],[c21,c34,c36,c44,c50]) ).
cnf(c62,plain,
plus(plus(mult(X,mult(Y,Z)),mult(W,Y)),Y) = Y,
inference(equational,[status(thm)],[c18,c35,c38]) ).
cnf(c63,plain,
plus(mult(X,mult(Y,Z)),Y) = Y,
inference(equational,[status(thm)],[c13,c34,c39,c40,c41,c51,c62]) ).
cnf(c64,plain,
plus(mult(X,Y),X) = X,
inference(equational,[status(thm)],[c33,c63]) ).
cnf(c67,plain,
mult(mult(X,Y),X) = mult(X,Y),
inference(equational,[status(thm)],[c42,c64]) ).
cnf(c69,plain,
plus(X,mult(X,Y)) = X,
inference(equational,[status(thm)],[c51,c67]) ).
cnf(c70,plain,
mult(X,mult(X,Y)) = mult(X,Y),
inference(equational,[status(thm)],[c5,c34,c64,c67]) ).
cnf(c73,plain,
plus(mult(X,Y),plus(Y,Z)) = plus(Y,Z),
inference(equational,[status(thm)],[c8,c39,c51,c63]) ).
cnf(c76,plain,
plus(plus(X,Y),mult(Z,X)) = plus(X,Y),
inference(equational,[status(thm)],[c6,c33,c69,c73]) ).
cnf(c82,plain,
plus(X,mult(Y,mult(X,Z))) = X,
inference(equational,[status(thm)],[c45,c64,c70,c76]) ).
cnf(g1,plain,
plus(a,mult(b,mult(a,c))) = a,
inference(equational,[status(thm)],[c82]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT390-1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 12:39:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 5.80/5.96 % SZS status Unsatisfiable
% 5.80/5.96 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------