%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LAT394-2 : TPTP v9.0.0. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n005.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 0.75s 0.96s
% Output : CNFRefutation 0.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 2
% Syntax : Number of clauses : 34 ( 34 unt; 0 nHn; 3 RR)
% Number of literals : 34 ( 33 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 71 ( 17 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
f(x0,f(x0,x0)) != f(x1,f(x1,x1)),
file('theBenchmark.p',goals) ).
cnf(c1,axiom,
f(f(f(f(X,Y),f(Y,Z)),W),f(Y,f(f(Y,f(f(X,X),X)),Z))) = Y,
file('theBenchmark.p',sos) ).
cnf(c2,plain,
f(X,f(f(X,Y),f(f(f(X,Y),f(f(f(Z,X),f(Z,X)),f(Z,X))),W))) = f(X,Y),
inference(equational,[status(thm)],[c1]) ).
cnf(c3,plain,
f(f(X,Y),f(f(f(X,Y),f(Y,Z)),Y)) = f(f(X,Y),f(Y,Z)),
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,plain,
f(f(f(f(X,Y),f(Y,Z)),Y),f(Y,Y)) = Y,
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c5,plain,
f(f(X,X),f(X,X)) = X,
inference(equational,[status(thm)],[c4]) ).
cnf(c8,plain,
f(X,f(f(X,f(f(X,X),Y)),f(X,X))) = f(X,f(f(X,X),Y)),
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c12,plain,
f(f(X,Y),f(X,f(f(X,f(f(X,X),X)),X))) = X,
inference(equational,[status(thm)],[c1,c5]) ).
cnf(c13,plain,
f(X,f(f(X,Y),f(X,Y))) = f(X,Y),
inference(equational,[status(thm)],[c2,c12]) ).
cnf(c14,plain,
f(f(X,Y),f(X,X)) = X,
inference(equational,[status(thm)],[c12,c13]) ).
cnf(c15,plain,
f(X,f(f(X,X),Y)) = f(X,X),
inference(equational,[status(thm)],[c8,c14]) ).
cnf(c17,plain,
f(f(X,X),f(X,Y)) = X,
inference(equational,[status(thm)],[c12,c14,c15]) ).
cnf(c18,plain,
f(f(f(X,Y),f(X,Y)),X) = f(X,Y),
inference(equational,[status(thm)],[c14,c17]) ).
cnf(c19,plain,
f(f(f(f(X,Y),f(Y,Z)),W),f(Y,Y)) = Y,
inference(equational,[status(thm)],[c1,c13]) ).
cnf(c20,plain,
f(f(X,Y),f(Y,Y)) = Y,
inference(equational,[status(thm)],[c14,c19]) ).
cnf(c21,plain,
f(f(X,f(Y,Y)),Y) = f(Y,Y),
inference(equational,[status(thm)],[c20]) ).
cnf(c22,plain,
f(f(X,X),f(Y,X)) = X,
inference(equational,[status(thm)],[c18,c20]) ).
cnf(c23,plain,
f(X,f(Y,f(X,X))) = f(X,X),
inference(equational,[status(thm)],[c18,c20,c21]) ).
cnf(c24,plain,
f(X,f(f(Y,X),f(Y,X))) = f(Y,X),
inference(equational,[status(thm)],[c14,c20]) ).
cnf(c27,plain,
f(f(X,Y),f(Y,f(f(Y,f(f(X,X),X)),Z))) = Y,
inference(equational,[status(thm)],[c1,c12]) ).
cnf(c28,plain,
f(f(X,Y),f(Y,f(f(X,X),X))) = Y,
inference(equational,[status(thm)],[c27]) ).
cnf(c29,plain,
f(X,f(f(X,Y),f(X,f(X,X)))) = f(X,Y),
inference(equational,[status(thm)],[c17,c22,c28]) ).
cnf(c30,plain,
f(f(X,Y),f(X,f(f(Z,Z),Z))) = X,
inference(equational,[status(thm)],[c1,c20,c23,c29]) ).
cnf(c31,plain,
f(X,X) = f(X,f(f(Y,Y),Y)),
inference(equational,[status(thm)],[c18,c30]) ).
cnf(c32,plain,
f(X,f(Y,f(Y,Y))) = f(X,X),
inference(equational,[status(thm)],[c20,c31]) ).
cnf(c33,plain,
f(f(f(X,X),X),Y) = f(Y,f(f(X,X),X)),
inference(equational,[status(thm)],[c24,c30]) ).
cnf(c34,plain,
f(f(f(X,X),X),Y) = f(Y,Y),
inference(equational,[status(thm)],[c31,c33]) ).
cnf(c37,plain,
f(f(X,X),f(f(Y,Y),Y)) = X,
inference(equational,[status(thm)],[c22,c31]) ).
cnf(c42,plain,
f(f(X,X),f(Y,f(Y,Y))) = X,
inference(equational,[status(thm)],[c5,c32]) ).
cnf(c48,plain,
f(f(f(X,X),Y),f(Y,f(X,f(X,X)))) = Y,
inference(equational,[status(thm)],[c14,c28]) ).
cnf(c49,plain,
f(X,f(X,X)) = f(f(Y,Y),Y),
inference(equational,[status(thm)],[c29,c34,c37,c48]) ).
cnf(c50,plain,
f(X,f(X,X)) = f(Y,f(Y,Y)),
inference(equational,[status(thm)],[c42,c49]) ).
cnf(g1,plain,
f(x0,f(x0,x0)) = f(x1,f(x1,x1)),
inference(equational,[status(thm)],[c50]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : LAT394-2 : TPTP v9.0.0. Released v5.4.0.
% 0.07/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 14 12:39:34 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.75/0.96 % SZS status Unsatisfiable
% 0.75/0.96 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------