%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP660-13 : TPTP v9.0.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n003.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 06:44:38 AM UTC 2025
% Result : Unsatisfiable 60.41s 60.59s
% Output : CNFRefutation 60.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of clauses : 58 ( 58 unt; 0 nHn; 3 RR)
% Number of literals : 58 ( 57 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; 2 con; 0-2 aty)
% Number of variables : 125 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
mult(x0,ld(x1,x1)) != x0,
file('theBenchmark.p',goal) ).
cnf(c1,axiom,
mult(X,ld(X,Y)) = Y,
file('theBenchmark.p',f01) ).
cnf(c2,axiom,
ld(X,mult(X,Y)) = Y,
file('theBenchmark.p',f02) ).
cnf(c3,axiom,
mult(rd(X,Y),Y) = X,
file('theBenchmark.p',f03) ).
cnf(c4,axiom,
rd(mult(X,Y),Y) = X,
file('theBenchmark.p',f04) ).
cnf(c5,plain,
rd(X,ld(Y,X)) = Y,
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c6,plain,
ld(rd(X,Y),X) = Y,
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c7,axiom,
mult(mult(mult(X,Y),Z),X) = mult(X,mult(Y,mult(Z,X))),
file('theBenchmark.p',f05) ).
cnf(c8,plain,
rd(mult(X,mult(Y,mult(Z,X))),X) = mult(mult(X,Y),Z),
inference(equational,[status(thm)],[c4,c7]) ).
cnf(c9,plain,
mult(mult(X,Y),rd(Z,X)) = rd(mult(X,mult(Y,Z)),X),
inference(equational,[status(thm)],[c3,c8]) ).
cnf(c10,plain,
mult(X,mult(ld(X,Y),mult(Z,X))) = mult(mult(Y,Z),X),
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c12,plain,
mult(mult(X,rd(Y,Z)),Z) = mult(Z,mult(ld(Z,X),Y)),
inference(equational,[status(thm)],[c3,c10]) ).
cnf(c13,plain,
mult(mult(X,rd(Y,mult(Z,X))),Z) = rd(mult(X,Y),X),
inference(equational,[status(thm)],[c3,c8]) ).
cnf(c14,plain,
mult(X,rd(Y,mult(Z,X))) = rd(rd(mult(X,Y),X),Z),
inference(equational,[status(thm)],[c4,c13]) ).
cnf(c15,plain,
rd(mult(X,mult(ld(X,Y),Z)),X) = mult(Y,rd(Z,X)),
inference(equational,[status(thm)],[c4,c12]) ).
cnf(c16,plain,
mult(X,mult(Y,mult(ld(mult(X,Y),Z),X))) = mult(Z,X),
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c17,plain,
mult(X,mult(ld(mult(Y,X),Z),Y)) = ld(Y,mult(Z,Y)),
inference(equational,[status(thm)],[c2,c16]) ).
cnf(c18,plain,
mult(ld(mult(X,Y),Z),X) = ld(Y,ld(X,mult(Z,X))),
inference(equational,[status(thm)],[c2,c17]) ).
cnf(c19,plain,
rd(ld(X,ld(Y,mult(Z,Y))),Y) = ld(mult(Y,X),Z),
inference(equational,[status(thm)],[c4,c18]) ).
cnf(c20,plain,
ld(mult(X,Y),X) = rd(ld(Y,X),X),
inference(equational,[status(thm)],[c2,c19]) ).
cnf(c21,plain,
rd(X,rd(ld(Y,X),X)) = mult(X,Y),
inference(equational,[status(thm)],[c5,c20]) ).
cnf(c22,plain,
mult(X,rd(X,Y)) = rd(X,rd(Y,X)),
inference(equational,[status(thm)],[c6,c21]) ).
cnf(c23,plain,
rd(ld(ld(X,Y),X),X) = ld(Y,X),
inference(equational,[status(thm)],[c1,c20]) ).
cnf(c24,plain,
mult(ld(X,Y),Y) = ld(ld(Y,X),Y),
inference(equational,[status(thm)],[c3,c23]) ).
cnf(c25,plain,
ld(mult(X,Y),rd(Z,X)) = rd(ld(Y,ld(X,Z)),X),
inference(equational,[status(thm)],[c3,c19]) ).
cnf(c26,plain,
ld(ld(X,rd(X,Y)),X) = mult(Y,X),
inference(equational,[status(thm)],[c6,c24]) ).
cnf(c27,plain,
ld(X,rd(X,Y)) = rd(X,mult(Y,X)),
inference(equational,[status(thm)],[c5,c26]) ).
cnf(c30,plain,
mult(X,rd(ld(ld(Y,X),Z),Y)) = rd(mult(Y,Z),Y),
inference(equational,[status(thm)],[c1,c15]) ).
cnf(c32,plain,
ld(X,rd(rd(mult(X,Y),X),Z)) = rd(Y,mult(Z,X)),
inference(equational,[status(thm)],[c2,c14]) ).
cnf(c33,plain,
ld(X,rd(rd(Y,X),Z)) = rd(ld(X,Y),mult(Z,X)),
inference(equational,[status(thm)],[c1,c32]) ).
cnf(c34,plain,
rd(rd(mult(X,Y),X),rd(Z,X)) = mult(X,rd(Y,Z)),
inference(equational,[status(thm)],[c3,c14]) ).
cnf(c35,plain,
mult(X,rd(ld(X,Y),Z)) = rd(rd(Y,X),rd(Z,X)),
inference(equational,[status(thm)],[c1,c34]) ).
cnf(c38,plain,
mult(X,mult(ld(Y,Z),rd(Y,X))) = ld(rd(Y,X),mult(Z,rd(Y,X))),
inference(equational,[status(thm)],[c3,c17]) ).
cnf(c39,plain,
rd(ld(X,mult(Y,X)),mult(Z,X)) = ld(X,rd(Y,Z)),
inference(equational,[status(thm)],[c1,c4,c16,c18,c32]) ).
cnf(c40,plain,
ld(X,rd(Y,rd(Z,X))) = rd(ld(X,mult(Y,X)),Z),
inference(equational,[status(thm)],[c3,c39]) ).
cnf(c51,plain,
mult(ld(X,Y),mult(ld(ld(X,Y),Z),Y)) = mult(mult(Z,X),ld(X,Y)),
inference(equational,[status(thm)],[c1,c10]) ).
cnf(c52,plain,
mult(mult(X,ld(ld(X,X),Y)),X) = mult(X,mult(mult(Y,X),ld(X,X))),
inference(equational,[status(thm)],[c10,c51]) ).
cnf(c57,plain,
mult(X,rd(ld(Y,Z),rd(X,Y))) = rd(mult(rd(X,Y),Z),rd(X,Y)),
inference(equational,[status(thm)],[c6,c30]) ).
cnf(c79,plain,
mult(rd(rd(X,Y),rd(Z,Y)),Z) = mult(Z,mult(ld(Z,Y),ld(Y,X))),
inference(equational,[status(thm)],[c12,c35]) ).
cnf(c84,plain,
rd(mult(rd(X,X),Y),rd(X,X)) = rd(rd(Y,X),rd(rd(X,X),X)),
inference(equational,[status(thm)],[c35,c57]) ).
cnf(c85,plain,
rd(rd(X,X),rd(rd(X,X),X)) = rd(X,rd(X,X)),
inference(equational,[status(thm)],[c3,c84]) ).
cnf(c86,plain,
rd(ld(X,X),rd(X,X)) = rd(X,X),
inference(equational,[status(thm)],[c2,c3,c33,c40,c85]) ).
cnf(c87,plain,
mult(rd(X,X),rd(X,X)) = ld(X,X),
inference(equational,[status(thm)],[c3,c86]) ).
cnf(c92,plain,
ld(rd(X,rd(X,X)),rd(X,X)) = rd(rd(X,X),X),
inference(equational,[status(thm)],[c6,c85]) ).
cnf(c99,plain,
rd(ld(rd(X,X),mult(Y,rd(X,X))),X) = mult(Y,rd(rd(X,X),X)),
inference(equational,[status(thm)],[c15,c38]) ).
cnf(c100,plain,
rd(rd(X,X),rd(X,rd(X,X))) = rd(rd(X,X),X),
inference(equational,[status(thm)],[c2,c22,c99]) ).
cnf(c101,plain,
rd(X,rd(X,X)) = X,
inference(equational,[status(thm)],[c6,c100]) ).
cnf(c102,plain,
ld(X,X) = rd(X,X),
inference(equational,[status(thm)],[c2,c40,c101]) ).
cnf(c103,plain,
rd(rd(X,X),X) = rd(X,mult(X,X)),
inference(equational,[status(thm)],[c27,c92,c101]) ).
cnf(c105,plain,
ld(mult(rd(X,X),Y),X) = rd(ld(Y,X),rd(X,X)),
inference(equational,[status(thm)],[c6,c25,c101]) ).
cnf(c106,plain,
rd(rd(X,X),rd(X,X)) = rd(X,X),
inference(equational,[status(thm)],[c3,c102,c105]) ).
cnf(c107,plain,
mult(rd(X,X),Y) = rd(Y,rd(X,X)),
inference(equational,[status(thm)],[c1,c3,c79,c102,c106]) ).
cnf(c108,plain,
mult(X,rd(Y,Y)) = ld(rd(Y,Y),X),
inference(equational,[status(thm)],[c3,c4,c52,c102,c106,c107]) ).
cnf(c109,plain,
mult(rd(X,rd(Y,Y)),Y) = rd(X,rd(Y,mult(Y,Y))),
inference(equational,[status(thm)],[c4,c9,c84,c101,c103,c107]) ).
cnf(c110,plain,
rd(X,rd(Y,Y)) = X,
inference(equational,[status(thm)],[c3,c87,c102,c106,c109]) ).
cnf(c112,plain,
ld(rd(X,X),Y) = Y,
inference(equational,[status(thm)],[c87,c102,c106,c108,c109,c110]) ).
cnf(g1,plain,
mult(x0,ld(x1,x1)) = x0,
inference(equational,[status(thm)],[c102,c108,c112]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP660-13 : TPTP v9.0.0. Released v8.1.0.
% 0.00/0.09 % Command : run_Leo-III %s %d THM
% 0.08/0.29 % Computer : n003.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Mon Jul 14 08:46:04 EDT 2025
% 0.08/0.30 % CPUTime :
% 60.41/60.59 % SZS status Unsatisfiable
% 60.41/60.59 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------