%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : ALG006-1 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n008.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 06:09:47 AM UTC 2025
% Result : Unsatisfiable 1.36s 1.56s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of clauses : 24 ( 24 unt; 0 nHn; 3 RR)
% Number of literals : 24 ( 23 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
difference(difference(a,c),b) != difference(difference(a,b),c),
file('theBenchmark.p',prove_set_difference_3_simplified) ).
cnf(c1,axiom,
difference(X,difference(Y,X)) = X,
file('theBenchmark.p',set_difference_1) ).
cnf(c2,axiom,
difference(X,difference(X,Y)) = difference(Y,difference(Y,X)),
file('theBenchmark.p',set_difference_2) ).
cnf(c3,plain,
difference(difference(X,Y),Y) = difference(X,Y),
inference(equational,[status(thm)],[c1]) ).
cnf(c4,axiom,
difference(difference(X,Y),Z) = difference(difference(X,Z),difference(Y,Z)),
file('theBenchmark.p',set_difference_3) ).
cnf(c5,plain,
difference(difference(X,Y),difference(X,Y)) = difference(Y,Y),
inference(equational,[status(thm)],[c1,c2,c3]) ).
cnf(c6,plain,
difference(X,X) = difference(difference(Y,Y),X),
inference(equational,[status(thm)],[c4,c5]) ).
cnf(c7,plain,
difference(difference(X,Y),X) = difference(X,X),
inference(equational,[status(thm)],[c4,c5,c6]) ).
cnf(c8,plain,
difference(difference(X,Y),difference(Z,X)) = difference(X,difference(Y,difference(Z,X))),
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c9,plain,
difference(X,difference(difference(Y,X),difference(Z,X))) = X,
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c10,plain,
difference(difference(difference(X,Y),Z),Y) = difference(difference(X,Y),difference(Z,Y)),
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c11,plain,
difference(X,difference(Y,difference(X,X))) = difference(X,difference(X,difference(X,Y))),
inference(equational,[status(thm)],[c2,c7,c8]) ).
cnf(c15,plain,
difference(difference(X,Y),difference(Y,difference(Y,X))) = difference(X,Y),
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c16,plain,
difference(X,X) = difference(Y,Y),
inference(equational,[status(thm)],[c5,c15]) ).
cnf(c17,plain,
difference(X,difference(Y,Y)) = X,
inference(equational,[status(thm)],[c9,c16]) ).
cnf(c21,plain,
difference(X,difference(X,difference(X,Y))) = difference(X,Y),
inference(equational,[status(thm)],[c1,c7,c8,c11,c15,c17]) ).
cnf(c22,plain,
difference(X,difference(Y,difference(Y,X))) = difference(X,Y),
inference(equational,[status(thm)],[c2,c21]) ).
cnf(c31,plain,
difference(difference(difference(X,Y),difference(Z,Y)),W) = difference(difference(difference(X,Z),W),difference(Y,W)),
inference(equational,[status(thm)],[c4]) ).
cnf(c38,plain,
difference(difference(difference(X,Y),difference(Z,Y)),difference(X,Z)) = difference(Z,Z),
inference(equational,[status(thm)],[c1,c5,c8,c31]) ).
cnf(c39,plain,
difference(difference(X,Y),difference(X,difference(Y,Z))) = difference(Z,Z),
inference(equational,[status(thm)],[c5,c7,c17,c38]) ).
cnf(c50,plain,
difference(X,difference(X,difference(difference(Y,X),Z))) = difference(Z,Z),
inference(equational,[status(thm)],[c1,c39]) ).
cnf(c52,plain,
difference(difference(X,Y),difference(Z,Y)) = difference(difference(X,Y),Z),
inference(equational,[status(thm)],[c10,c17,c22,c50]) ).
cnf(g1,plain,
difference(difference(a,c),b) = difference(difference(a,b),c),
inference(equational,[status(thm)],[c4,c52]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ALG006-1 : TPTP v9.0.0. Released v2.2.0.
% 0.07/0.13 % Command : run_Leo-III %s %d THM
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Jul 14 03:31:49 EDT 2025
% 0.12/0.34 % CPUTime :
% 1.36/1.56 % SZS status Unsatisfiable
% 1.36/1.56 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------