%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : ALG005-1 : TPTP v9.0.0. Released v2.2.0.
% 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 06:09:47 AM UTC 2025
% Result : Unsatisfiable 5.15s 5.32s
% Output : CNFRefutation 5.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of clauses : 46 ( 46 unt; 0 nHn; 3 RR)
% Number of literals : 46 ( 45 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 122 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
file('theBenchmark.p',prove_associativity_of_multiply) ).
cnf(c1,axiom,
difference(X,difference(Y,X)) = X,
file('theBenchmark.p',set_difference_1) ).
cnf(c2,axiom,
multiply(X,Y) = difference(X,difference(X,Y)),
file('theBenchmark.p',intersection) ).
cnf(c3,axiom,
difference(X,difference(X,Y)) = difference(Y,difference(Y,X)),
file('theBenchmark.p',set_difference_2) ).
cnf(c4,plain,
difference(difference(X,Y),Y) = difference(X,Y),
inference(equational,[status(thm)],[c1]) ).
cnf(c5,axiom,
difference(difference(X,Y),Z) = difference(difference(X,Z),difference(Y,Z)),
file('theBenchmark.p',set_difference_3) ).
cnf(c6,plain,
difference(difference(X,Y),difference(X,Y)) = difference(Y,Y),
inference(equational,[status(thm)],[c1,c3,c4]) ).
cnf(c7,plain,
difference(X,X) = difference(difference(Y,Y),X),
inference(equational,[status(thm)],[c5,c6]) ).
cnf(c8,plain,
difference(difference(X,Y),X) = difference(X,X),
inference(equational,[status(thm)],[c5,c6,c7]) ).
cnf(c9,plain,
difference(difference(X,Y),difference(Z,X)) = difference(X,difference(Y,difference(Z,X))),
inference(equational,[status(thm)],[c1,c5]) ).
cnf(c10,plain,
difference(X,difference(difference(Y,X),difference(Z,X))) = X,
inference(equational,[status(thm)],[c1,c5]) ).
cnf(c11,plain,
difference(X,difference(Y,difference(X,X))) = difference(X,difference(X,difference(X,Y))),
inference(equational,[status(thm)],[c3,c8,c9]) ).
cnf(c12,plain,
difference(difference(difference(X,Y),Z),Y) = difference(difference(X,Y),difference(Z,Y)),
inference(equational,[status(thm)],[c1,c9]) ).
cnf(c13,plain,
difference(difference(X,X),difference(Y,Y)) = difference(Y,Y),
inference(equational,[status(thm)],[c1,c7,c9]) ).
cnf(c14,plain,
difference(X,X) = difference(Y,Y),
inference(equational,[status(thm)],[c11,c13]) ).
cnf(c15,plain,
difference(X,difference(Y,Y)) = X,
inference(equational,[status(thm)],[c1,c3,c14]) ).
cnf(c18,plain,
difference(difference(X,Y),difference(Y,difference(Y,X))) = difference(X,Y),
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c19,plain,
difference(X,difference(X,difference(X,Y))) = difference(X,Y),
inference(equational,[status(thm)],[c1,c8,c9,c11,c15,c18]) ).
cnf(c20,plain,
difference(X,difference(Y,difference(Y,X))) = difference(X,Y),
inference(equational,[status(thm)],[c3,c19]) ).
cnf(c22,plain,
difference(difference(X,difference(X,Y)),Z) = difference(difference(Y,Z),difference(difference(Y,X),Z)),
inference(equational,[status(thm)],[c3,c5]) ).
cnf(c29,plain,
difference(difference(difference(X,Y),difference(Z,Y)),W) = difference(difference(difference(X,Z),W),difference(Y,W)),
inference(equational,[status(thm)],[c5]) ).
cnf(c35,plain,
difference(difference(X,Y),difference(difference(X,Z),Y)) = difference(difference(Z,Y),difference(difference(Z,X),Y)),
inference(equational,[status(thm)],[c5,c22]) ).
cnf(c38,plain,
difference(difference(difference(X,Y),difference(Z,Y)),difference(X,Z)) = difference(Z,Z),
inference(equational,[status(thm)],[c1,c6,c9,c29]) ).
cnf(c39,plain,
difference(difference(X,Y),difference(X,difference(Y,Z))) = difference(Z,Z),
inference(equational,[status(thm)],[c6,c8,c15,c38]) ).
cnf(c44,plain,
difference(difference(X,Y),difference(difference(X,Z),difference(Y,Z))) = difference(Z,difference(Z,difference(X,Y))),
inference(equational,[status(thm)],[c3,c5]) ).
cnf(c45,plain,
difference(X,difference(X,difference(difference(X,Y),Z))) = difference(difference(X,Y),Z),
inference(equational,[status(thm)],[c1,c8,c9,c15,c44]) ).
cnf(c46,plain,
difference(difference(X,Y),difference(difference(Z,Y),difference(W,Y))) = difference(difference(X,difference(Z,W)),Y),
inference(equational,[status(thm)],[c5]) ).
cnf(c47,plain,
difference(difference(X,difference(Y,Z)),difference(Z,difference(Z,Y))) = difference(difference(X,Y),difference(Y,Z)),
inference(equational,[status(thm)],[c3,c5]) ).
cnf(c52,plain,
difference(X,difference(X,difference(difference(Y,X),Z))) = difference(Z,Z),
inference(equational,[status(thm)],[c1,c39]) ).
cnf(c53,plain,
difference(X,difference(difference(Y,X),Z)) = X,
inference(equational,[status(thm)],[c15,c19,c52]) ).
cnf(c54,plain,
difference(difference(X,Y),difference(Z,Y)) = difference(difference(X,Y),Z),
inference(equational,[status(thm)],[c12,c15,c20,c52]) ).
cnf(c56,plain,
difference(X,difference(Y,difference(Z,X))) = difference(X,Y),
inference(equational,[status(thm)],[c1,c54]) ).
cnf(c57,plain,
difference(difference(X,Y),difference(Y,Z)) = difference(X,Y),
inference(equational,[status(thm)],[c4,c8,c54]) ).
cnf(c60,plain,
difference(difference(X,Y),difference(Z,difference(Z,X))) = difference(difference(X,Z),Y),
inference(equational,[status(thm)],[c3,c8,c9,c15,c22,c54]) ).
cnf(c61,plain,
difference(difference(X,difference(X,Y)),Z) = difference(difference(Y,Z),difference(Y,X)),
inference(equational,[status(thm)],[c3,c8,c9,c15,c60]) ).
cnf(c63,plain,
difference(difference(X,Y),difference(difference(Z,X),W)) = difference(X,Y),
inference(equational,[status(thm)],[c10,c54,c56,c60]) ).
cnf(c68,plain,
difference(difference(difference(X,Y),Z),difference(W,X)) = difference(difference(X,Y),Z),
inference(equational,[status(thm)],[c9,c56,c60]) ).
cnf(c73,plain,
difference(X,difference(Y,difference(difference(Z,X),W))) = difference(X,Y),
inference(equational,[status(thm)],[c5,c53,c63]) ).
cnf(c80,plain,
difference(difference(X,difference(X,Y)),Z) = difference(X,difference(X,difference(Y,Z))),
inference(equational,[status(thm)],[c45,c56,c61]) ).
cnf(c87,plain,
difference(difference(X,difference(Y,Z)),W) = difference(difference(X,W),difference(difference(Y,W),Z)),
inference(equational,[status(thm)],[c46,c54,c68]) ).
cnf(c93,plain,
difference(X,difference(Y,difference(Z,difference(W,X)))) = difference(X,difference(Y,Z)),
inference(equational,[status(thm)],[c47,c57,c73]) ).
cnf(c94,plain,
difference(X,difference(difference(X,Y),difference(X,Z))) = difference(X,difference(Z,Y)),
inference(equational,[status(thm)],[c35,c54,c73]) ).
cnf(c95,plain,
difference(X,difference(Y,difference(X,Z))) = difference(X,difference(Y,difference(Y,Z))),
inference(equational,[status(thm)],[c93,c94]) ).
cnf(c99,plain,
difference(X,difference(Y,difference(Y,difference(X,Z)))) = difference(X,difference(Y,Z)),
inference(equational,[status(thm)],[c20,c80,c87]) ).
cnf(g1,plain,
multiply(multiply(a,b),c) = multiply(a,multiply(b,c)),
inference(equational,[status(thm)],[c2,c80,c95,c99]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ALG005-1 : TPTP v9.0.0. Released v2.2.0.
% 0.04/0.12 % Command : run_Leo-III %s %d THM
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Jul 14 03:31:34 EDT 2025
% 0.13/0.33 % CPUTime :
% 5.15/5.32 % SZS status Unsatisfiable
% 5.15/5.32 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------