%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP754-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n004.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 76.77s 76.98s
% Output : CNFRefutation 76.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of clauses : 32 ( 32 unt; 0 nHn; 3 RR)
% Number of literals : 32 ( 31 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 : 82 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
mult(mult(a,a),mult(b,c)) != mult(mult(a,b),mult(a,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(c6,plain,
ld(rd(X,Y),X) = Y,
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c7,axiom,
mult(X,mult(Y,Z)) = mult(mult(rd(X,X),Y),mult(X,Z)),
file('theBenchmark.p',f05) ).
cnf(c8,plain,
mult(mult(rd(X,X),Y),mult(X,Z)) = mult(X,mult(Y,Z)),
inference(equational,[status(thm)],[c7]) ).
cnf(c9,plain,
mult(mult(rd(X,X),Y),Z) = mult(X,mult(Y,ld(X,Z))),
inference(equational,[status(thm)],[c1,c8]) ).
cnf(c10,axiom,
mult(mult(X,Y),Z) = mult(mult(X,Z),mult(Y,ld(Z,Z))),
file('theBenchmark.p',f06) ).
cnf(c11,plain,
mult(mult(X,Y),mult(Z,ld(Y,Y))) = mult(mult(X,Z),Y),
inference(equational,[status(thm)],[c10]) ).
cnf(c12,plain,
mult(mult(rd(X,Y),Z),Y) = mult(X,mult(Z,ld(Y,Y))),
inference(equational,[status(thm)],[c3,c11]) ).
cnf(c13,plain,
ld(mult(X,Y),mult(mult(X,Z),Y)) = mult(Z,ld(Y,Y)),
inference(equational,[status(thm)],[c2,c11]) ).
cnf(c14,plain,
mult(ld(X,Y),ld(Z,Z)) = ld(mult(X,Z),mult(Y,Z)),
inference(equational,[status(thm)],[c1,c13]) ).
cnf(c15,plain,
mult(mult(X,rd(Y,ld(Z,Z))),Z) = mult(mult(X,Z),Y),
inference(equational,[status(thm)],[c3,c11]) ).
cnf(c16,plain,
mult(X,rd(Y,ld(Z,Z))) = rd(mult(mult(X,Z),Y),Z),
inference(equational,[status(thm)],[c4,c15]) ).
cnf(c19,plain,
rd(mult(X,mult(Y,Z)),mult(X,Z)) = mult(rd(X,X),Y),
inference(equational,[status(thm)],[c4,c8]) ).
cnf(c21,plain,
rd(mult(X,Y),mult(X,ld(Z,Y))) = mult(rd(X,X),Z),
inference(equational,[status(thm)],[c1,c19]) ).
cnf(c31,plain,
ld(X,rd(mult(mult(X,Y),Z),Y)) = rd(Z,ld(Y,Y)),
inference(equational,[status(thm)],[c2,c16]) ).
cnf(c34,plain,
ld(mult(rd(X,X),Y),mult(X,Z)) = mult(X,ld(Y,Z)),
inference(equational,[status(thm)],[c6,c21]) ).
cnf(c43,plain,
ld(rd(X,Y),rd(mult(X,Z),Y)) = rd(Z,ld(Y,Y)),
inference(equational,[status(thm)],[c3,c31]) ).
cnf(c46,plain,
mult(X,ld(ld(rd(X,X),Y),Z)) = ld(Y,mult(X,Z)),
inference(equational,[status(thm)],[c1,c34]) ).
cnf(c85,plain,
mult(X,mult(rd(Y,ld(Z,Z)),ld(X,Z))) = mult(X,mult(Z,ld(X,Y))),
inference(equational,[status(thm)],[c9,c15]) ).
cnf(c86,plain,
mult(rd(X,ld(Y,Y)),ld(Z,Y)) = mult(Y,ld(Z,X)),
inference(equational,[status(thm)],[c2,c85]) ).
cnf(c93,plain,
mult(mult(X,ld(Y,Z)),ld(X,X)) = mult(Z,ld(mult(Y,ld(X,X)),X)),
inference(equational,[status(thm)],[c1,c12,c14,c86]) ).
cnf(c134,plain,
mult(X,ld(rd(Y,ld(X,X)),Z)) = ld(rd(mult(X,Y),X),mult(X,Z)),
inference(equational,[status(thm)],[c43,c46]) ).
cnf(c135,plain,
ld(mult(X,Y),mult(mult(X,Z),X)) = mult(Z,ld(Y,X)),
inference(equational,[status(thm)],[c1,c3,c14,c86,c93,c134]) ).
cnf(c166,plain,
ld(mult(X,Y),mult(mult(X,X),Z)) = mult(X,ld(Y,Z)),
inference(equational,[status(thm)],[c15,c86,c135]) ).
cnf(c382,plain,
mult(mult(X,Y),mult(X,ld(Y,Z))) = mult(mult(X,X),Z),
inference(equational,[status(thm)],[c1,c166]) ).
cnf(c383,plain,
mult(mult(X,Y),mult(X,Z)) = mult(mult(X,X),mult(Y,Z)),
inference(equational,[status(thm)],[c2,c382]) ).
cnf(g1,plain,
mult(mult(a,a),mult(b,c)) = mult(mult(a,b),mult(a,c)),
inference(equational,[status(thm)],[c383]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP754-1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 09:02:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 76.77/76.98 % SZS status Unsatisfiable
% 76.77/76.98 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------