%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP715-10 : TPTP v9.0.0. Released v8.1.0.
% 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 06:44:47 AM UTC 2025
% Result : Unsatisfiable 0.70s 0.90s
% Output : CNFRefutation 0.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of clauses : 23 ( 23 unt; 0 nHn; 9 RR)
% Number of literals : 23 ( 22 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
mult(mult(x0,op_a),op_b) != x0,
file('theBenchmark.p',goal) ).
cnf(c2,axiom,
mult(X,unit) = X,
file('theBenchmark.p',f08) ).
cnf(c3,axiom,
mult(unit,X) = X,
file('theBenchmark.p',f09) ).
cnf(c4,axiom,
mult(op_a,op_b) = unit,
file('theBenchmark.p',f10) ).
cnf(c5,axiom,
mult(op_b,op_a) = unit,
file('theBenchmark.p',f11) ).
cnf(c11,axiom,
mult(X,mult(Y,Y)) = mult(mult(X,Y),Y),
file('theBenchmark.p',f07) ).
cnf(c12,plain,
mult(mult(X,Y),Y) = mult(X,mult(Y,Y)),
inference(equational,[status(thm)],[c11]) ).
cnf(c13,plain,
mult(op_a,mult(op_b,op_b)) = op_b,
inference(equational,[status(thm)],[c3,c4,c12]) ).
cnf(c14,plain,
mult(op_b,mult(op_a,op_a)) = op_a,
inference(equational,[status(thm)],[c3,c5,c12]) ).
cnf(c26,axiom,
mult(mult(mult(X,Y),Z),Y) = mult(X,mult(mult(Y,Z),Y)),
file('theBenchmark.p',f06) ).
cnf(c27,plain,
mult(op_a,mult(mult(op_b,X),op_b)) = mult(X,op_b),
inference(equational,[status(thm)],[c3,c4,c26]) ).
cnf(c28,plain,
mult(mult(op_a,op_a),op_b) = op_a,
inference(equational,[status(thm)],[c2,c4,c14,c27]) ).
cnf(c38,plain,
mult(mult(X,mult(Y,Y)),Y) = mult(X,mult(Y,mult(Y,Y))),
inference(equational,[status(thm)],[c12,c26]) ).
cnf(c39,plain,
mult(mult(X,Y),mult(Y,Y)) = mult(X,mult(Y,mult(Y,Y))),
inference(equational,[status(thm)],[c12,c38]) ).
cnf(c42,plain,
mult(op_b,mult(op_a,mult(op_a,op_a))) = mult(op_a,op_a),
inference(equational,[status(thm)],[c3,c5,c39]) ).
cnf(c55,plain,
mult(mult(X,mult(mult(Y,Z),Y)),Z) = mult(mult(X,Y),mult(mult(Z,Y),Z)),
inference(equational,[status(thm)],[c26]) ).
cnf(c59,plain,
mult(mult(mult(X,mult(Y,Y)),Z),Y) = mult(mult(X,Y),mult(mult(Y,Z),Y)),
inference(equational,[status(thm)],[c12,c26]) ).
cnf(c69,plain,
mult(mult(X,op_b),mult(op_a,mult(op_a,op_a))) = mult(X,mult(op_a,op_a)),
inference(equational,[status(thm)],[c2,c4,c14,c28,c55]) ).
cnf(c70,plain,
mult(mult(X,mult(op_a,op_a)),op_b) = mult(X,op_a),
inference(equational,[status(thm)],[c26,c28,c42,c69]) ).
cnf(c72,plain,
mult(mult(X,mult(op_b,op_b)),op_a) = mult(X,op_b),
inference(equational,[status(thm)],[c2,c4,c14,c59,c70]) ).
cnf(c73,plain,
mult(mult(X,op_a),op_b) = X,
inference(equational,[status(thm)],[c2,c5,c13,c26,c72]) ).
cnf(g1,plain,
mult(mult(x0,op_a),op_b) = x0,
inference(equational,[status(thm)],[c73]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : GRP715-10 : TPTP v9.0.0. Released v8.1.0.
% 0.02/0.10 % Command : run_Leo-III %s %d THM
% 0.09/0.29 % Computer : n007.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Mon Jul 14 08:56:34 EDT 2025
% 0.09/0.29 % CPUTime :
% 0.70/0.90 % SZS status Unsatisfiable
% 0.70/0.90 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------