%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP686-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n002.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 06:44:43 AM UTC 2025
% Result : Unsatisfiable 60.34s 60.58s
% Output : CNFRefutation 60.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of clauses : 31 ( 31 unt; 0 nHn; 3 RR)
% Number of literals : 31 ( 30 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
mult(mult(a,a),mult(b,c)) != mult(mult(a,mult(a,b)),c),
file('theBenchmark.p',goals) ).
cnf(c1,axiom,
mult(X,unit) = X,
file('theBenchmark.p',c05) ).
cnf(c2,axiom,
mult(unit,X) = X,
file('theBenchmark.p',c06) ).
cnf(c3,axiom,
mult(rd(X,Y),Y) = X,
file('theBenchmark.p',c03) ).
cnf(c5,axiom,
rd(mult(X,Y),Y) = X,
file('theBenchmark.p',c04) ).
cnf(c7,axiom,
mult(X,ld(X,Y)) = Y,
file('theBenchmark.p',c01) ).
cnf(c9,axiom,
ld(X,mult(X,Y)) = Y,
file('theBenchmark.p',c02) ).
cnf(c12,plain,
rd(X,ld(Y,X)) = Y,
inference(equational,[status(thm)],[c5,c7]) ).
cnf(c13,axiom,
mult(X,mult(Y,mult(Y,Z))) = mult(mult(X,mult(Y,Y)),Z),
file('theBenchmark.p',c07) ).
cnf(c14,plain,
mult(mult(X,mult(Y,Y)),Z) = mult(X,mult(Y,mult(Y,Z))),
inference(equational,[status(thm)],[c13]) ).
cnf(c15,plain,
mult(mult(X,X),Y) = mult(X,mult(X,Y)),
inference(equational,[status(thm)],[c2,c14]) ).
cnf(c23,plain,
rd(mult(X,mult(Y,mult(Y,Z))),Z) = mult(X,mult(Y,Y)),
inference(equational,[status(thm)],[c5,c14]) ).
cnf(c25,plain,
rd(mult(X,mult(Y,Z)),ld(Y,Z)) = mult(X,mult(Y,Y)),
inference(equational,[status(thm)],[c7,c23]) ).
cnf(c30,plain,
rd(mult(X,Y),ld(Z,ld(Z,Y))) = mult(X,mult(Z,Z)),
inference(equational,[status(thm)],[c7,c25]) ).
cnf(c31,plain,
rd(X,ld(Y,ld(Y,unit))) = mult(X,mult(Y,Y)),
inference(equational,[status(thm)],[c1,c30]) ).
cnf(c32,plain,
mult(ld(X,unit),mult(X,X)) = X,
inference(equational,[status(thm)],[c12,c31]) ).
cnf(c33,plain,
rd(X,mult(X,X)) = ld(X,unit),
inference(equational,[status(thm)],[c5,c32]) ).
cnf(c50,plain,
mult(rd(X,mult(Y,Y)),mult(Y,mult(Y,Z))) = mult(X,Z),
inference(equational,[status(thm)],[c3,c14]) ).
cnf(c51,plain,
ld(rd(X,mult(Y,Y)),mult(X,Z)) = mult(Y,mult(Y,Z)),
inference(equational,[status(thm)],[c9,c50]) ).
cnf(c53,plain,
mult(X,mult(X,ld(Y,Z))) = ld(rd(Y,mult(X,X)),Z),
inference(equational,[status(thm)],[c7,c51]) ).
cnf(c54,plain,
ld(ld(X,unit),Y) = mult(X,Y),
inference(equational,[status(thm)],[c7,c33,c53]) ).
cnf(c55,plain,
rd(X,mult(Y,X)) = ld(Y,unit),
inference(equational,[status(thm)],[c12,c54]) ).
cnf(c56,plain,
mult(ld(X,unit),Y) = ld(X,Y),
inference(equational,[status(thm)],[c1,c54]) ).
cnf(c58,plain,
ld(rd(X,Y),unit) = rd(Y,X),
inference(equational,[status(thm)],[c3,c55]) ).
cnf(c59,plain,
mult(rd(X,Y),Z) = ld(rd(Y,X),Z),
inference(equational,[status(thm)],[c56,c58]) ).
cnf(c65,plain,
ld(rd(mult(X,X),Y),mult(X,Z)) = mult(Y,ld(X,Z)),
inference(equational,[status(thm)],[c7,c50,c59]) ).
cnf(c73,plain,
mult(ld(X,mult(Y,Y)),ld(Y,Z)) = ld(X,mult(Y,Z)),
inference(equational,[status(thm)],[c12,c65]) ).
cnf(c74,plain,
mult(ld(X,mult(Y,Y)),Z) = ld(X,mult(Y,mult(Y,Z))),
inference(equational,[status(thm)],[c9,c73]) ).
cnf(c75,plain,
mult(mult(X,mult(X,Y)),Z) = mult(X,mult(X,mult(Y,Z))),
inference(equational,[status(thm)],[c51,c74]) ).
cnf(g1,plain,
mult(mult(a,a),mult(b,c)) = mult(mult(a,mult(a,b)),c),
inference(equational,[status(thm)],[c15,c75]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP686-1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n002.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Jul 14 08:52:49 EDT 2025
% 0.11/0.33 % CPUTime :
% 60.34/60.58 % SZS status Unsatisfiable
% 60.34/60.58 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------