%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : ALG235-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n014.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 06:10:06 AM UTC 2025
% Result : Unsatisfiable 1.72s 1.86s
% Output : CNFRefutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of clauses : 22 ( 22 unt; 0 nHn; 3 RR)
% Number of literals : 22 ( 21 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
mult(a,mult(b,mult(a,mult(c,mult(d,c))))) != mult(a,mult(b,mult(d,c))),
file('theBenchmark.p',goals) ).
cnf(c1,axiom,
mult(X,mult(Y,mult(X,Y))) = mult(X,Y),
file('theBenchmark.p',c01) ).
cnf(c2,axiom,
mult(X,mult(Y,mult(Z,W))) = mult(Z,mult(Y,mult(X,W))),
file('theBenchmark.p',c02) ).
cnf(c3,plain,
mult(X,mult(Y,mult(Z,mult(Y,X)))) = mult(Z,mult(Y,X)),
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,plain,
mult(X,mult(Y,mult(mult(X,Y),Y))) = mult(X,Y),
inference(equational,[status(thm)],[c1,c2,c3]) ).
cnf(c5,axiom,
mult(mult(X,mult(Y,mult(Z,Y))),W) = mult(X,mult(W,mult(mult(Z,Y),W))),
file('theBenchmark.p',c03) ).
cnf(c6,plain,
mult(X,mult(Y,mult(mult(X,Z),Y))) = mult(mult(X,Z),Y),
inference(equational,[status(thm)],[c1,c5]) ).
cnf(c7,plain,
mult(mult(X,Y),Y) = mult(X,Y),
inference(equational,[status(thm)],[c4,c6]) ).
cnf(c9,plain,
mult(mult(X,mult(Y,mult(Z,Y))),W) = mult(mult(Z,Y),mult(W,mult(X,W))),
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c10,plain,
mult(mult(X,mult(Y,mult(Z,Y))),W) = mult(Z,mult(W,mult(mult(X,Y),W))),
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c11,plain,
mult(X,mult(Y,mult(Z,mult(W,V)))) = mult(Z,mult(W,mult(X,mult(Y,V)))),
inference(equational,[status(thm)],[c2]) ).
cnf(c12,plain,
mult(X,mult(Y,mult(X,mult(Y,Z)))) = mult(X,mult(Y,Z)),
inference(equational,[status(thm)],[c1,c7,c11]) ).
cnf(c16,plain,
mult(X,mult(Y,mult(mult(Z,W),Y))) = mult(mult(X,W),mult(Y,mult(Z,Y))),
inference(equational,[status(thm)],[c9,c10]) ).
cnf(c18,plain,
mult(mult(X,Y),mult(Z,mult(X,Y))) = mult(X,mult(Z,mult(X,Y))),
inference(equational,[status(thm)],[c3,c12]) ).
cnf(c21,plain,
mult(mult(X,Y),mult(Z,mult(W,Y))) = mult(X,mult(Z,mult(W,Y))),
inference(equational,[status(thm)],[c12,c16,c18]) ).
cnf(c22,plain,
mult(X,mult(Y,mult(Z,W))) = mult(Z,mult(Y,mult(X,mult(W,mult(Z,W))))),
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c25,plain,
mult(X,mult(Y,mult(Z,mult(W,mult(X,Y))))) = mult(Z,mult(W,mult(X,Y))),
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c34,plain,
mult(X,mult(Y,mult(X,mult(Z,mult(W,Z))))) = mult(W,mult(Y,mult(X,Z))),
inference(equational,[status(thm)],[c2,c22]) ).
cnf(c35,plain,
mult(X,mult(Y,mult(X,mult(Z,W)))) = mult(X,mult(Z,mult(W,mult(Y,W)))),
inference(equational,[status(thm)],[c12,c34]) ).
cnf(c36,plain,
mult(X,mult(Y,mult(X,mult(Z,W)))) = mult(X,mult(Y,mult(W,mult(Z,W)))),
inference(equational,[status(thm)],[c4,c7,c21,c25,c35]) ).
cnf(g1,plain,
mult(a,mult(b,mult(a,mult(c,mult(d,c))))) = mult(a,mult(b,mult(d,c))),
inference(equational,[status(thm)],[c12,c36]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ALG235-1 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.34 % Computer : n014.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 03:45:49 EDT 2025
% 0.12/0.34 % CPUTime :
% 1.72/1.86 % SZS status Unsatisfiable
% 1.72/1.86 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------