%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP752-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n007.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 06:44:50 AM UTC 2025
% Result : Unsatisfiable 76.42s 76.58s
% Output : CNFRefutation 76.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 36 ( 36 unt; 0 nHn; 3 RR)
% Number of literals : 36 ( 35 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 : 95 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
mult(mult(a,b),c) != mult(mult(a,c),mult(b,ld(c,c))),
file('theBenchmark.p',goals) ).
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(c7,axiom,
mult(mult(X,X),mult(Y,Z)) = mult(mult(X,Y),mult(X,Z)),
file('theBenchmark.p',f06) ).
cnf(c8,axiom,
mult(mult(X,Y),mult(Z,Z)) = mult(mult(X,Z),mult(Y,Z)),
file('theBenchmark.p',f07) ).
cnf(c9,plain,
mult(mult(rd(X,Y),Z),mult(Y,Y)) = mult(X,mult(Z,Y)),
inference(equational,[status(thm)],[c3,c8]) ).
cnf(c10,plain,
mult(mult(X,Y),mult(ld(X,Z),Y)) = mult(Z,mult(Y,Y)),
inference(equational,[status(thm)],[c1,c8]) ).
cnf(c12,plain,
mult(mult(X,X),mult(ld(X,Y),Z)) = mult(Y,mult(X,Z)),
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c13,plain,
mult(mult(X,X),mult(Y,ld(X,Z))) = mult(mult(X,Y),Z),
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c14,plain,
mult(mult(X,Y),mult(X,ld(Y,Z))) = mult(mult(X,X),Z),
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c16,axiom,
mult(mult(X,mult(X,X)),mult(Y,Z)) = mult(mult(X,Y),mult(mult(X,X),Z)),
file('theBenchmark.p',f05) ).
cnf(c22,plain,
ld(mult(X,Y),mult(mult(X,X),Z)) = mult(X,ld(Y,Z)),
inference(equational,[status(thm)],[c2,c14]) ).
cnf(c25,plain,
ld(mult(X,X),mult(mult(X,Y),Z)) = mult(Y,ld(X,Z)),
inference(equational,[status(thm)],[c2,c13]) ).
cnf(c26,plain,
mult(X,ld(Y,mult(Z,Z))) = mult(Z,ld(Y,mult(X,Z))),
inference(equational,[status(thm)],[c8,c25]) ).
cnf(c31,plain,
ld(mult(X,Y),mult(Z,mult(Y,Y))) = mult(ld(X,Z),Y),
inference(equational,[status(thm)],[c2,c10]) ).
cnf(c32,plain,
rd(mult(X,mult(Y,Z)),mult(Z,Z)) = mult(rd(X,Z),Y),
inference(equational,[status(thm)],[c4,c9]) ).
cnf(c33,plain,
mult(rd(mult(X,X),Y),Z) = mult(rd(mult(X,Z),Y),X),
inference(equational,[status(thm)],[c7,c32]) ).
cnf(c39,plain,
mult(rd(mult(X,X),Y),ld(X,Z)) = mult(rd(Z,Y),X),
inference(equational,[status(thm)],[c12,c32]) ).
cnf(c46,plain,
mult(X,ld(Y,ld(mult(X,X),Z))) = ld(mult(X,Y),Z),
inference(equational,[status(thm)],[c1,c22]) ).
cnf(c61,plain,
mult(rd(X,ld(Y,mult(Z,Z))),Z) = mult(Y,ld(Z,X)),
inference(equational,[status(thm)],[c5,c39]) ).
cnf(c65,plain,
rd(mult(rd(mult(X,X),Y),Z),X) = rd(mult(X,Z),Y),
inference(equational,[status(thm)],[c4,c33]) ).
cnf(c89,plain,
mult(X,ld(Y,mult(Z,ld(X,W)))) = ld(mult(X,Y),mult(mult(X,Z),W)),
inference(equational,[status(thm)],[c13,c22]) ).
cnf(c93,plain,
rd(mult(X,Y),ld(Z,mult(X,X))) = rd(mult(Z,Y),X),
inference(equational,[status(thm)],[c5,c65]) ).
cnf(c117,plain,
mult(mult(X,Y),mult(mult(X,X),ld(Y,Z))) = mult(mult(X,mult(X,X)),Z),
inference(equational,[status(thm)],[c1,c16]) ).
cnf(c123,plain,
mult(mult(X,X),ld(mult(Y,X),Z)) = mult(mult(X,Y),ld(mult(Y,Y),Z)),
inference(equational,[status(thm)],[c13,c46]) ).
cnf(c154,plain,
ld(mult(X,Y),mult(mult(X,mult(X,X)),Z)) = mult(mult(X,X),ld(Y,Z)),
inference(equational,[status(thm)],[c2,c117]) ).
cnf(c156,plain,
mult(mult(X,X),ld(Y,mult(X,Z))) = mult(X,ld(Y,mult(mult(X,X),Z))),
inference(equational,[status(thm)],[c7,c22,c154]) ).
cnf(c158,plain,
mult(mult(X,X),mult(ld(Y,X),Z)) = mult(X,mult(ld(Y,mult(X,X)),Z)),
inference(equational,[status(thm)],[c31,c156]) ).
cnf(c237,plain,
mult(rd(mult(X,X),Y),ld(Z,X)) = mult(X,ld(Z,mult(rd(X,Y),X))),
inference(equational,[status(thm)],[c26,c32,c158]) ).
cnf(c238,plain,
ld(mult(X,Y),mult(mult(X,Z),X)) = mult(Z,ld(Y,X)),
inference(equational,[status(thm)],[c4,c61,c89,c93,c237]) ).
cnf(c285,plain,
mult(mult(X,Y),mult(Z,ld(Y,Y))) = mult(mult(X,Z),Y),
inference(equational,[status(thm)],[c13,c123,c238]) ).
cnf(g1,plain,
mult(mult(a,b),c) = mult(mult(a,c),mult(b,ld(c,c))),
inference(equational,[status(thm)],[c285]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP752-1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n007.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 09:02:19 EDT 2025
% 0.11/0.32 % CPUTime :
% 76.42/76.58 % SZS status Unsatisfiable
% 76.42/76.58 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------