%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP682-11 : TPTP v9.0.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n010.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 06:44:42 AM UTC 2025
% Result : Unsatisfiable 2.17s 2.34s
% Output : CNFRefutation 2.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 8
% Syntax : Number of clauses : 69 ( 69 unt; 0 nHn; 3 RR)
% Number of literals : 69 ( 68 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 161 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
ld(rd(x0,x1),mult(rd(x0,x1),x2)) != ld(x0,mult(x0,x2)),
file('theBenchmark.p',goal) ).
cnf(c1,axiom,
ld(X,mult(X,X)) = X,
file('theBenchmark.p',f01) ).
cnf(c2,axiom,
rd(mult(X,X),X) = X,
file('theBenchmark.p',f02) ).
cnf(c3,axiom,
mult(X,ld(X,Y)) = ld(X,mult(X,Y)),
file('theBenchmark.p',f03) ).
cnf(c4,plain,
ld(X,mult(X,Y)) = mult(X,ld(X,Y)),
inference(equational,[status(thm)],[c3]) ).
cnf(c5,plain,
mult(X,ld(X,X)) = X,
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c6,axiom,
mult(rd(X,Y),Y) = rd(mult(X,Y),Y),
file('theBenchmark.p',f04) ).
cnf(c7,plain,
rd(mult(X,Y),Y) = mult(rd(X,Y),Y),
inference(equational,[status(thm)],[c6]) ).
cnf(c8,plain,
mult(rd(X,X),X) = X,
inference(equational,[status(thm)],[c2,c7]) ).
cnf(c9,axiom,
ld(X,mult(X,ld(Y,Y))) = rd(mult(rd(X,X),Y),Y),
file('theBenchmark.p',f07) ).
cnf(c10,plain,
mult(rd(rd(X,X),Y),Y) = mult(X,ld(X,ld(Y,Y))),
inference(equational,[status(thm)],[c4,c7,c9]) ).
cnf(c11,plain,
rd(X,X) = mult(X,ld(X,ld(X,X))),
inference(equational,[status(thm)],[c7,c8,c10]) ).
cnf(c12,plain,
mult(X,ld(X,ld(X,X))) = ld(X,X),
inference(equational,[status(thm)],[c4,c5]) ).
cnf(c13,plain,
mult(ld(X,X),X) = X,
inference(equational,[status(thm)],[c8,c11,c12]) ).
cnf(c19,axiom,
ld(ld(X,Y),mult(ld(X,Y),mult(Z,W))) = mult(ld(X,mult(X,Z)),W),
file('theBenchmark.p',f05) ).
cnf(c20,plain,
mult(ld(X,Y),ld(ld(X,Y),mult(Z,W))) = mult(mult(X,ld(X,Z)),W),
inference(equational,[status(thm)],[c4,c19]) ).
cnf(c21,plain,
mult(X,ld(X,mult(Y,Z))) = mult(mult(X,ld(X,Y)),Z),
inference(equational,[status(thm)],[c1,c4,c5,c20]) ).
cnf(c22,plain,
mult(X,mult(X,ld(X,Y))) = mult(X,Y),
inference(equational,[status(thm)],[c4,c5,c21]) ).
cnf(c24,plain,
mult(mult(X,ld(X,Y)),ld(Y,Y)) = mult(X,ld(X,Y)),
inference(equational,[status(thm)],[c5,c21]) ).
cnf(c25,plain,
mult(mult(X,ld(X,ld(Y,Y))),Y) = mult(X,ld(X,Y)),
inference(equational,[status(thm)],[c8,c11,c12,c21]) ).
cnf(c26,plain,
mult(X,mult(mult(X,ld(X,Y)),Z)) = mult(X,mult(Y,Z)),
inference(equational,[status(thm)],[c21,c22]) ).
cnf(c27,plain,
mult(ld(X,Y),ld(ld(X,Y),Z)) = mult(X,ld(X,Z)),
inference(equational,[status(thm)],[c5,c20,c24]) ).
cnf(c28,plain,
mult(X,ld(X,ld(X,Y))) = ld(X,Y),
inference(equational,[status(thm)],[c5,c27]) ).
cnf(c30,plain,
ld(X,mult(mult(X,ld(X,Y)),Z)) = ld(X,mult(Y,Z)),
inference(equational,[status(thm)],[c4,c21,c28]) ).
cnf(c31,plain,
mult(X,ld(X,ld(ld(X,Y),Z))) = ld(ld(X,Y),Z),
inference(equational,[status(thm)],[c27,c28]) ).
cnf(c32,axiom,
rd(mult(mult(X,Y),rd(Z,W)),rd(Z,W)) = mult(X,rd(mult(Y,W),W)),
file('theBenchmark.p',f06) ).
cnf(c33,plain,
mult(rd(mult(X,Y),rd(Z,W)),rd(Z,W)) = mult(X,mult(rd(Y,W),W)),
inference(equational,[status(thm)],[c7,c32]) ).
cnf(c34,plain,
mult(rd(mult(X,Y),Z),Z) = mult(X,mult(rd(Y,Z),Z)),
inference(equational,[status(thm)],[c2,c7,c11,c13,c28,c33]) ).
cnf(c35,plain,
mult(mult(rd(X,Y),Y),Y) = mult(X,Y),
inference(equational,[status(thm)],[c7,c11,c13,c28,c34]) ).
cnf(c37,plain,
mult(X,ld(X,Y)) = mult(ld(X,X),Y),
inference(equational,[status(thm)],[c10,c11,c25,c28,c35]) ).
cnf(c40,plain,
ld(X,mult(ld(X,X),Y)) = ld(X,Y),
inference(equational,[status(thm)],[c4,c28,c37]) ).
cnf(c42,plain,
mult(ld(X,X),mult(X,Y)) = mult(X,Y),
inference(equational,[status(thm)],[c4,c22,c37]) ).
cnf(c43,plain,
ld(ld(X,X),mult(X,Y)) = mult(X,Y),
inference(equational,[status(thm)],[c4,c22,c27,c42]) ).
cnf(c44,plain,
ld(X,ld(ld(X,X),Y)) = ld(X,Y),
inference(equational,[status(thm)],[c4,c27,c28,c40]) ).
cnf(c45,plain,
ld(ld(X,X),Y) = mult(X,ld(X,Y)),
inference(equational,[status(thm)],[c31,c44]) ).
cnf(c46,plain,
mult(ld(X,X),mult(Y,Z)) = mult(mult(X,ld(X,Y)),Z),
inference(equational,[status(thm)],[c21,c37]) ).
cnf(c48,plain,
mult(X,mult(rd(ld(X,X),Y),Y)) = mult(rd(X,Y),Y),
inference(equational,[status(thm)],[c5,c34]) ).
cnf(c49,plain,
mult(ld(X,X),mult(rd(X,Y),Y)) = mult(rd(X,Y),Y),
inference(equational,[status(thm)],[c8,c11,c28,c34]) ).
cnf(c50,plain,
mult(rd(ld(X,X),Y),Y) = mult(X,ld(X,ld(Y,Y))),
inference(equational,[status(thm)],[c10,c11,c28,c42,c45,c49]) ).
cnf(c51,plain,
mult(rd(X,Y),Y) = mult(X,ld(Y,Y)),
inference(equational,[status(thm)],[c22,c48,c50]) ).
cnf(c60,plain,
mult(mult(ld(X,X),Y),Z) = mult(ld(X,X),mult(Y,Z)),
inference(equational,[status(thm)],[c37,c46]) ).
cnf(c61,plain,
mult(mult(X,Y),ld(Z,Z)) = mult(X,mult(Y,ld(Z,Z))),
inference(equational,[status(thm)],[c34,c51]) ).
cnf(c62,plain,
mult(mult(X,mult(Y,ld(Z,Z))),Z) = mult(mult(X,Y),Z),
inference(equational,[status(thm)],[c34,c35,c51]) ).
cnf(c63,plain,
ld(X,mult(Y,ld(Z,Z))) = mult(ld(X,Y),ld(Z,Z)),
inference(equational,[status(thm)],[c4,c21,c28,c30,c61]) ).
cnf(c64,plain,
mult(ld(X,Y),ld(Y,Y)) = ld(X,Y),
inference(equational,[status(thm)],[c5,c63]) ).
cnf(c66,plain,
mult(X,ld(rd(Y,Z),rd(Y,Z))) = mult(X,ld(Z,Z)),
inference(equational,[status(thm)],[c8,c11,c28,c33,c42,c51]) ).
cnf(c71,plain,
mult(ld(ld(X,Y),ld(X,Y)),Z) = mult(X,ld(X,Z)),
inference(equational,[status(thm)],[c27,c37]) ).
cnf(c85,plain,
ld(ld(X,Y),ld(X,Y)) = mult(X,ld(X,ld(Y,Y))),
inference(equational,[status(thm)],[c4,c27,c64]) ).
cnf(c88,plain,
mult(mult(X,ld(X,Y)),ld(Y,Z)) = mult(mult(X,ld(X,ld(Y,Y))),Z),
inference(equational,[status(thm)],[c20,c21,c27,c37]) ).
cnf(c91,plain,
mult(mult(X,ld(X,ld(Y,Y))),Z) = mult(X,ld(X,Z)),
inference(equational,[status(thm)],[c27,c28,c31,c85,c88]) ).
cnf(c92,plain,
mult(X,mult(ld(Y,Y),Z)) = mult(X,Z),
inference(equational,[status(thm)],[c22,c26,c91]) ).
cnf(c93,plain,
ld(X,mult(ld(Y,Y),Z)) = ld(X,Z),
inference(equational,[status(thm)],[c4,c28,c30,c91]) ).
cnf(c94,plain,
mult(X,mult(Y,ld(Y,Z))) = mult(X,Z),
inference(equational,[status(thm)],[c45,c71,c92]) ).
cnf(c100,plain,
rd(mult(ld(X,X),Y),ld(X,Y)) = mult(X,ld(Y,Y)),
inference(equational,[status(thm)],[c7,c37,c51,c85,c94]) ).
cnf(c122,plain,
mult(mult(X,Y),ld(mult(X,Y),Z)) = mult(X,ld(X,Z)),
inference(equational,[status(thm)],[c27,c43]) ).
cnf(c125,plain,
mult(ld(X,X),mult(mult(Y,Z),W)) = mult(mult(mult(X,ld(X,Y)),Z),W),
inference(equational,[status(thm)],[c21,c46,c62]) ).
cnf(c126,plain,
mult(ld(X,X),Y) = mult(mult(X,ld(X,Z)),ld(Z,Y)),
inference(equational,[status(thm)],[c24,c61,c64,c94,c125]) ).
cnf(c127,plain,
ld(mult(X,ld(X,Y)),Z) = mult(X,ld(X,ld(Y,Z))),
inference(equational,[status(thm)],[c4,c93,c122,c126]) ).
cnf(c129,plain,
mult(rd(X,Y),mult(Y,ld(Z,Z))) = mult(X,ld(Z,Z)),
inference(equational,[status(thm)],[c34,c50,c51,c94]) ).
cnf(c137,plain,
mult(ld(X,ld(X,X)),ld(Y,Y)) = ld(X,ld(rd(Z,Y),rd(Z,Y))),
inference(equational,[status(thm)],[c40,c63,c66]) ).
cnf(c138,plain,
ld(X,ld(rd(Y,Z),rd(Y,Z))) = ld(X,ld(Z,Z)),
inference(equational,[status(thm)],[c28,c44,c85,c93,c137]) ).
cnf(c139,plain,
ld(X,ld(Y,Y)) = mult(ld(X,ld(X,X)),ld(Y,Y)),
inference(equational,[status(thm)],[c11,c28,c85,c137]) ).
cnf(c151,plain,
mult(ld(rd(X,Y),X),ld(Y,Y)) = mult(rd(X,Y),ld(rd(X,Y),Y)),
inference(equational,[status(thm)],[c4,c51,c63]) ).
cnf(c152,plain,
ld(mult(X,ld(Y,Y)),Y) = ld(X,Y),
inference(equational,[status(thm)],[c28,c64,c85,c93,c94,c100,c122,c151]) ).
cnf(c161,plain,
mult(X,mult(ld(X,ld(Y,Y)),ld(Z,Z))) = mult(ld(X,X),ld(Z,Z)),
inference(equational,[status(thm)],[c10,c11,c28,c33,c51,c129]) ).
cnf(c173,plain,
mult(rd(X,Y),ld(rd(X,Y),Z)) = mult(X,ld(X,Z)),
inference(equational,[status(thm)],[c122,c129]) ).
cnf(c175,plain,
ld(rd(X,Y),rd(X,Y)) = mult(X,ld(X,ld(Y,Y))),
inference(equational,[status(thm)],[c127,c138,c152,c173]) ).
cnf(g1,plain,
ld(rd(x0,x1),mult(rd(x0,x1),x2)) = ld(x0,mult(x0,x2)),
inference(equational,[status(thm)],[c4,c37,c60,c92,c139,c161,c175]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP682-11 : TPTP v9.0.0. Released v8.1.0.
% 0.04/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 14 08:52:19 EDT 2025
% 0.11/0.33 % CPUTime :
% 2.17/2.34 % SZS status Unsatisfiable
% 2.17/2.34 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------