%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : KLE169-10 : TPTP v9.0.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n001.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 06:57:56 AM UTC 2025
% Result : Unsatisfiable 0.85s 1.05s
% Output : CNFRefutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% 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 : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 47 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))) != true,
file('theBenchmark.p',a) ).
cnf(c1,axiom,
addition(X,X) = X,
file('theBenchmark.p',additive_idempotence) ).
cnf(c4,axiom,
multiplication(one,X) = X,
file('theBenchmark.p',multiplicative_left_identity) ).
cnf(c7,axiom,
sigma = addition(a,b),
file('theBenchmark.p',an) ).
cnf(c8,axiom,
addition(X,Y) = addition(Y,X),
file('theBenchmark.p',additive_commutativity) ).
cnf(c10,axiom,
ifeq2(X,X,Y,Z) = Y,
file('theBenchmark.p',ifeq_axiom_001) ).
cnf(c12,axiom,
ifeq3(X,X,Y,Z) = Y,
file('theBenchmark.p',ifeq_axiom) ).
cnf(c13,axiom,
addition(X,addition(Y,Z)) = addition(addition(X,Y),Z),
file('theBenchmark.p',additive_associativity) ).
cnf(c14,plain,
addition(addition(X,Y),Z) = addition(X,addition(Y,Z)),
inference(equational,[status(thm)],[c13]) ).
cnf(c17,plain,
addition(X,addition(X,Y)) = addition(X,Y),
inference(equational,[status(thm)],[c1,c14]) ).
cnf(c18,plain,
addition(X,addition(Y,Z)) = addition(Y,addition(X,Z)),
inference(equational,[status(thm)],[c8,c14]) ).
cnf(c20,axiom,
multiplication(addition(X,Y),Z) = addition(multiplication(X,Z),multiplication(Y,Z)),
file('theBenchmark.p',left_distributivity) ).
cnf(c21,axiom,
multiplication(X,addition(Y,Z)) = addition(multiplication(X,Y),multiplication(X,Z)),
file('theBenchmark.p',right_distributivity) ).
cnf(c22,axiom,
ifeq2(leq(X,Y),true,addition(X,Y),Y) = Y,
file('theBenchmark.p',order_1) ).
cnf(c26,axiom,
ifeq3(addition(X,Y),Y,leq(X,Y),true) = true,
file('theBenchmark.p',order) ).
cnf(c29,plain,
leq(X,addition(X,Y)) = true,
inference(equational,[status(thm)],[c12,c17,c26]) ).
cnf(c32,plain,
leq(X,addition(Y,addition(X,Z))) = true,
inference(equational,[status(thm)],[c18,c29]) ).
cnf(c34,axiom,
leq(addition(one,multiplication(X,star(X))),star(X)) = true,
file('theBenchmark.p',star_unfold_right) ).
cnf(c62,plain,
addition(one,addition(star(X),multiplication(X,star(X)))) = star(X),
inference(equational,[status(thm)],[c8,c10,c14,c22,c34]) ).
cnf(c63,plain,
addition(one,star(X)) = star(X),
inference(equational,[status(thm)],[c17,c62]) ).
cnf(c67,plain,
addition(X,multiplication(star(Y),X)) = multiplication(star(Y),X),
inference(equational,[status(thm)],[c4,c20,c63]) ).
cnf(c83,plain,
leq(X,addition(Y,multiplication(star(Z),X))) = true,
inference(equational,[status(thm)],[c32,c67]) ).
cnf(c105,plain,
leq(X,addition(multiplication(star(Y),X),Z)) = true,
inference(equational,[status(thm)],[c8,c83]) ).
cnf(g1,plain,
leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))) = true,
inference(equational,[status(thm)],[c7,c8,c20,c21,c105]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE169-10 : TPTP v9.0.0. Released v7.5.0.
% 0.06/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.31 % Computer : n001.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon Jul 14 11:19:04 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.85/1.05 % SZS status Unsatisfiable
% 0.85/1.05 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------