%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP671-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n005.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 06:44:41 AM UTC 2025
% Result : Unsatisfiable 0.87s 1.04s
% Output : CNFRefutation 0.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of clauses : 25 ( 25 unt; 0 nHn; 4 RR)
% Number of literals : 25 ( 24 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 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 : 42 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
mult(mult(a,b),a) != mult(a,mult(b,a)),
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(c7,axiom,
mult(X,ld(X,Y)) = Y,
file('theBenchmark.p',c01) ).
cnf(c8,plain,
ld(unit,X) = X,
inference(equational,[status(thm)],[c2,c7]) ).
cnf(c9,axiom,
ld(X,mult(X,Y)) = Y,
file('theBenchmark.p',c02) ).
cnf(c14,axiom,
mult(i(X),mult(X,Y)) = Y,
file('theBenchmark.p',c07) ).
cnf(c15,plain,
mult(i(X),X) = unit,
inference(equational,[status(thm)],[c1,c14]) ).
cnf(c16,plain,
i(unit) = unit,
inference(equational,[status(thm)],[c1,c15]) ).
cnf(c17,plain,
i(i(X)) = X,
inference(equational,[status(thm)],[c1,c14,c15]) ).
cnf(c19,plain,
mult(i(X),Y) = ld(X,Y),
inference(equational,[status(thm)],[c7,c14]) ).
cnf(c21,plain,
mult(X,Y) = ld(i(X),Y),
inference(equational,[status(thm)],[c9,c14]) ).
cnf(c24,axiom,
mult(mult(X,Y),i(Y)) = X,
file('theBenchmark.p',c08) ).
cnf(c25,plain,
ld(i(ld(i(X),Y)),i(Y)) = X,
inference(equational,[status(thm)],[c21,c24]) ).
cnf(c38,plain,
ld(ld(i(X),Y),X) = i(Y),
inference(equational,[status(thm)],[c7,c19,c25]) ).
cnf(c39,plain,
ld(X,Y) = i(ld(Y,X)),
inference(equational,[status(thm)],[c9,c19,c38]) ).
cnf(c51,plain,
ld(i(ld(X,Y)),Z) = ld(ld(Y,X),Z),
inference(equational,[status(thm)],[c19,c21,c39]) ).
cnf(c57,plain,
ld(i(ld(X,Y)),Z) = i(ld(Z,ld(Y,X))),
inference(equational,[status(thm)],[c39,c51]) ).
cnf(c61,plain,
ld(ld(X,Y),Z) = i(ld(Z,i(ld(Y,X)))),
inference(equational,[status(thm)],[c39,c51]) ).
cnf(c64,axiom,
mult(mult(X,Y),mult(Z,mult(X,Y))) = mult(mult(mult(X,mult(Y,Z)),X),Y),
file('theBenchmark.p',c09) ).
cnf(c65,plain,
ld(i(ld(i(X),Y)),ld(i(Z),ld(i(X),Y))) = i(ld(Y,ld(X,i(ld(i(X),ld(i(Y),Z)))))),
inference(equational,[status(thm)],[c17,c19,c21,c57,c61,c64]) ).
cnf(c71,plain,
ld(i(X),ld(i(Y),X)) = i(ld(X,i(ld(i(X),Y)))),
inference(equational,[status(thm)],[c8,c16,c65]) ).
cnf(c79,plain,
ld(i(X),i(ld(X,i(Y)))) = i(ld(X,i(ld(i(X),Y)))),
inference(equational,[status(thm)],[c39,c71]) ).
cnf(g1,plain,
mult(mult(a,b),a) = mult(a,mult(b,a)),
inference(equational,[status(thm)],[c17,c21,c39,c79]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP671-1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n005.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 08:50:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.87/1.04 % SZS status Unsatisfiable
% 0.87/1.04 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------