%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP680-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n016.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 0.20s 0.70s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 22 ( 22 unt; 0 nHn; 3 RR)
% Number of literals : 22 ( 21 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
mult(i(op_c),a) != mult(a,i(op_c)),
file('theBenchmark.p',goals) ).
cnf(c1,axiom,
mult(X,unit) = X,
file('theBenchmark.p',c05) ).
cnf(c3,axiom,
mult(op_c,X) = mult(X,op_c),
file('theBenchmark.p',c09) ).
cnf(c4,axiom,
rd(mult(X,Y),Y) = X,
file('theBenchmark.p',c04) ).
cnf(c7,axiom,
mult(rd(X,Y),Y) = X,
file('theBenchmark.p',c03) ).
cnf(c8,axiom,
mult(X,ld(X,Y)) = Y,
file('theBenchmark.p',c01) ).
cnf(c10,axiom,
ld(X,mult(X,Y)) = Y,
file('theBenchmark.p',c02) ).
cnf(c11,plain,
ld(X,X) = unit,
inference(equational,[status(thm)],[c1,c10]) ).
cnf(c17,plain,
rd(mult(op_c,X),op_c) = X,
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c18,plain,
rd(X,op_c) = ld(op_c,X),
inference(equational,[status(thm)],[c8,c17]) ).
cnf(c21,axiom,
mult(i(X),mult(X,Y)) = Y,
file('theBenchmark.p',c08) ).
cnf(c22,plain,
mult(i(X),X) = unit,
inference(equational,[status(thm)],[c1,c21]) ).
cnf(c26,plain,
ld(X,Y) = mult(i(X),Y),
inference(equational,[status(thm)],[c8,c21]) ).
cnf(c28,plain,
mult(i(X),X) = mult(i(Y),Y),
inference(equational,[status(thm)],[c11,c22,c26]) ).
cnf(c33,plain,
mult(X,mult(i(Y),Y)) = X,
inference(equational,[status(thm)],[c1,c11,c26]) ).
cnf(c58,plain,
mult(op_c,mult(i(op_c),X)) = X,
inference(equational,[status(thm)],[c3,c7,c18,c26]) ).
cnf(c67,axiom,
mult(X,mult(Y,mult(X,Z))) = mult(mult(X,mult(Y,X)),Z),
file('theBenchmark.p',c07) ).
cnf(c68,plain,
mult(mult(X,mult(Y,X)),Z) = mult(X,mult(Y,mult(X,Z))),
inference(equational,[status(thm)],[c67]) ).
cnf(c79,plain,
mult(X,mult(Y,mult(X,op_c))) = mult(op_c,mult(X,mult(Y,X))),
inference(equational,[status(thm)],[c3,c68]) ).
cnf(c80,plain,
mult(i(op_c),X) = mult(X,i(op_c)),
inference(equational,[status(thm)],[c28,c33,c58,c79]) ).
cnf(g1,plain,
mult(i(op_c),a) = mult(a,i(op_c)),
inference(equational,[status(thm)],[c80]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP680-1 : TPTP v9.0.0. Released v4.0.0.
% 0.10/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n016.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 08:52:04 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.20/0.70 % SZS status Unsatisfiable
% 0.20/0.70 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------