%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : ALG007-1 : TPTP v9.0.0. Released v2.2.0.
% 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 06:09:47 AM UTC 2025
% Result : Unsatisfiable 1.66s 1.86s
% Output : CNFRefutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% 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 : 55 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
difference(difference(a,b),c) != difference(difference(a,c),difference(b,c)),
file('theBenchmark.p',prove_set_difference_3) ).
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,axiom,
difference(difference(X,Y),Z) = difference(difference(X,Z),Y),
file('theBenchmark.p',set_difference_3_simplified) ).
cnf(c4,plain,
difference(difference(X,Y),Y) = difference(X,Y),
inference(equational,[status(thm)],[c1]) ).
cnf(c5,plain,
difference(X,difference(difference(Y,X),Z)) = X,
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c6,plain,
difference(difference(X,Y),difference(Z,X)) = difference(X,Y),
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c7,plain,
difference(X,difference(X,difference(X,Y))) = difference(X,Y),
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c8,plain,
difference(difference(X,Y),difference(Y,Z)) = difference(X,Y),
inference(equational,[status(thm)],[c1,c6]) ).
cnf(c9,plain,
difference(difference(X,Y),difference(X,Y)) = difference(Y,Y),
inference(equational,[status(thm)],[c1,c2,c4]) ).
cnf(c10,plain,
difference(X,X) = difference(Y,Y),
inference(equational,[status(thm)],[c5,c9]) ).
cnf(c12,plain,
difference(difference(X,X),Y) = difference(Y,Y),
inference(equational,[status(thm)],[c4,c10]) ).
cnf(c13,plain,
difference(difference(X,X),Y) = difference(difference(Z,Y),Z),
inference(equational,[status(thm)],[c3,c10]) ).
cnf(c14,plain,
difference(difference(X,Y),X) = difference(Y,Y),
inference(equational,[status(thm)],[c12,c13]) ).
cnf(c17,plain,
difference(difference(X,difference(X,Y)),Z) = difference(difference(Y,Z),difference(Y,X)),
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c30,plain,
difference(difference(X,Y),Z) = difference(difference(X,Z),difference(X,difference(X,Y))),
inference(equational,[status(thm)],[c6,c17]) ).
cnf(c32,plain,
difference(difference(X,difference(Y,Z)),difference(X,Z)) = difference(Z,difference(Z,X)),
inference(equational,[status(thm)],[c6,c17]) ).
cnf(c33,plain,
difference(difference(X,Y),difference(Z,difference(Z,X))) = difference(difference(X,Z),Y),
inference(equational,[status(thm)],[c2,c8,c14,c17]) ).
cnf(c42,plain,
difference(X,difference(X,difference(Y,difference(Z,X)))) = difference(X,difference(X,Y)),
inference(equational,[status(thm)],[c6,c32]) ).
cnf(c43,plain,
difference(X,difference(Y,difference(Z,X))) = difference(X,Y),
inference(equational,[status(thm)],[c7,c42]) ).
cnf(c44,plain,
difference(difference(X,Y),difference(Z,Y)) = difference(difference(X,Y),Z),
inference(equational,[status(thm)],[c1,c43]) ).
cnf(c52,plain,
difference(difference(X,Y),difference(X,difference(X,Z))) = difference(difference(X,Y),Z),
inference(equational,[status(thm)],[c3,c30]) ).
cnf(g1,plain,
difference(difference(a,b),c) = difference(difference(a,c),difference(b,c)),
inference(equational,[status(thm)],[c2,c33,c44,c52]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG007-1 : TPTP v9.0.0. Released v2.2.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n006.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 03:31:49 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.66/1.86 % SZS status Unsatisfiable
% 1.66/1.86 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------