%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE145-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:39:54 AM UTC 2026
% Result : Unsatisfiable 56.10s 7.54s
% Output : CNFRefutation 56.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 18
% Syntax : Number of clauses : 266 ( 266 unt; 0 nHn; 3 RR)
% Number of literals : 266 ( 265 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 : 11 ( 11 usr; 3 con; 0-4 aty)
% Number of variables : 369 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
star(strong_iteration(sK1_goals_X0)) != strong_iteration(sK1_goals_X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(c2,axiom,
addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
cnf(c3,plain,
addition(multiplication(X,star(X)),X2) = addition(X2,multiplication(X,star(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
addition(X2,multiplication(X,star(X))) = addition(multiplication(X,star(X)),X2),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
addition(one,addition(X2,multiplication(X,star(X)))) = addition(one,addition(multiplication(X,star(X)),X2)),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
addition(A2,addition(B2,C)) = addition(addition(A2,B2),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
cnf(c7,plain,
addition(one,addition(multiplication(X,star(X)),X2)) = addition(addition(one,multiplication(X,star(X))),X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,axiom,
addition(one,multiplication(A2,star(A2))) = star(A2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold1) ).
cnf(c9,plain,
addition(one,multiplication(X,star(X))) = star(X),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
addition(addition(one,multiplication(X,star(X))),X2) = addition(star(X),X2),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
addition(star(X),X2) = addition(X2,star(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c12,plain,
addition(addition(one,multiplication(X,star(X))),X2) = addition(X2,star(X)),
inference(transitivity,[status(thm)],[c10,c11]) ).
cnf(c13,plain,
addition(one,addition(multiplication(X,star(X)),X2)) = addition(X2,star(X)),
inference(transitivity,[status(thm)],[c7,c12]) ).
cnf(c14,plain,
addition(one,addition(X2,multiplication(X,star(X)))) = addition(X2,star(X)),
inference(transitivity,[status(thm)],[c5,c13]) ).
cnf(c15,plain,
addition(one,addition(X,multiplication(X,star(X)))) = addition(X,star(X)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
addition(X,star(X)) = addition(one,addition(X,multiplication(X,star(X)))),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,axiom,
multiplication(A2,one) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
cnf(c18,plain,
multiplication(X,one) = X,
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
X = multiplication(X,one),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
addition(X2,multiplication(X2,X)) = addition(multiplication(X2,one),multiplication(X2,X)),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,axiom,
multiplication(A2,addition(B2,C2)) = addition(multiplication(A2,B2),multiplication(A2,C2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
cnf(c22,plain,
multiplication(X2,addition(one,X)) = addition(multiplication(X2,one),multiplication(X2,X)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
addition(multiplication(X2,one),multiplication(X2,X)) = multiplication(X2,addition(one,X)),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
addition(one,X) = addition(X,one),
inference(substitution,[status(thm)],[c2]) ).
cnf(c25,plain,
multiplication(X2,addition(one,X)) = multiplication(X2,addition(X,one)),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
addition(multiplication(X2,one),multiplication(X2,X)) = multiplication(X2,addition(X,one)),
inference(transitivity,[status(thm)],[c23,c25]) ).
cnf(c27,plain,
addition(X2,multiplication(X2,X)) = multiplication(X2,addition(X,one)),
inference(transitivity,[status(thm)],[c20,c26]) ).
cnf(c28,plain,
addition(X,multiplication(X,star(X))) = multiplication(X,addition(star(X),one)),
inference(substitution,[status(thm)],[c27]) ).
cnf(c29,plain,
addition(one,addition(X,multiplication(X,star(X)))) = addition(one,multiplication(X,addition(star(X),one))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
addition(star(X),one) = addition(one,star(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c31,plain,
multiplication(X,addition(star(X),one)) = multiplication(X,addition(one,star(X))),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
addition(one,multiplication(X,addition(star(X),one))) = addition(one,multiplication(X,addition(one,star(X)))),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
addition(one,multiplication(X,star(X))) = star(X),
inference(substitution,[status(thm)],[c8]) ).
cnf(c34,plain,
star(X) = addition(one,multiplication(X,star(X))),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
addition(one,star(X)) = addition(one,addition(one,multiplication(X,star(X)))),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
addition(X2,addition(X2,X)) = addition(addition(X2,X2),X),
inference(substitution,[status(thm)],[c6]) ).
cnf(c37,axiom,
addition(A2,A2) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence) ).
cnf(c38,plain,
addition(X,X) = X,
inference(substitution,[status(thm)],[c37]) ).
cnf(c39,plain,
addition(addition(X2,X2),X) = addition(X2,X),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
addition(X2,addition(X2,X)) = addition(X2,X),
inference(transitivity,[status(thm)],[c36,c39]) ).
cnf(c41,plain,
addition(one,addition(one,multiplication(X,star(X)))) = addition(one,multiplication(X,star(X))),
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
addition(one,multiplication(X,star(X))) = star(X),
inference(substitution,[status(thm)],[c8]) ).
cnf(c43,plain,
addition(one,addition(one,multiplication(X,star(X)))) = star(X),
inference(transitivity,[status(thm)],[c41,c42]) ).
cnf(c44,plain,
addition(one,star(X)) = star(X),
inference(transitivity,[status(thm)],[c35,c43]) ).
cnf(c45,plain,
multiplication(X,addition(one,star(X))) = multiplication(X,star(X)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
addition(one,multiplication(X,addition(one,star(X)))) = addition(one,multiplication(X,star(X))),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
addition(one,multiplication(X,star(X))) = star(X),
inference(substitution,[status(thm)],[c8]) ).
cnf(c48,plain,
addition(one,multiplication(X,addition(one,star(X)))) = star(X),
inference(transitivity,[status(thm)],[c46,c47]) ).
cnf(c49,plain,
addition(one,multiplication(X,addition(star(X),one))) = star(X),
inference(transitivity,[status(thm)],[c32,c48]) ).
cnf(c50,plain,
addition(one,addition(X,multiplication(X,star(X)))) = star(X),
inference(transitivity,[status(thm)],[c29,c49]) ).
cnf(c51,plain,
addition(X,star(X)) = star(X),
inference(transitivity,[status(thm)],[c16,c50]) ).
cnf(c52,plain,
addition(strong_iteration(X),star(strong_iteration(X))) = star(strong_iteration(X)),
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
star(strong_iteration(X)) = addition(strong_iteration(X),star(strong_iteration(X))),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
addition(multiplication(X,strong_iteration(X)),one) = addition(one,multiplication(X,strong_iteration(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c55,plain,
addition(one,multiplication(X,strong_iteration(X))) = addition(multiplication(X,strong_iteration(X)),one),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,axiom,
strong_iteration(A2) = addition(multiplication(A2,strong_iteration(A2)),one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_unfold1) ).
cnf(c57,plain,
strong_iteration(X) = addition(multiplication(X,strong_iteration(X)),one),
inference(substitution,[status(thm)],[c56]) ).
cnf(c58,plain,
addition(multiplication(X,strong_iteration(X)),one) = strong_iteration(X),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c59,plain,
addition(one,multiplication(X,strong_iteration(X))) = strong_iteration(X),
inference(transitivity,[status(thm)],[c55,c58]) ).
cnf(c60,plain,
strong_iteration(X) = addition(one,multiplication(X,strong_iteration(X))),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c61,plain,
star(strong_iteration(X)) = star(addition(one,multiplication(X,strong_iteration(X)))),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
addition(strong_iteration(X),star(strong_iteration(X))) = addition(strong_iteration(X),star(addition(one,multiplication(X,strong_iteration(X))))),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
addition(strong_iteration(multiplication(X,strong_iteration(X))),strong_iteration(X)) = addition(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c64,plain,
addition(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))) = addition(strong_iteration(multiplication(X,strong_iteration(X))),strong_iteration(X)),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,plain,
addition(X,multiplication(X2,strong_iteration(X2))) = addition(multiplication(X2,strong_iteration(X2)),X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c66,plain,
addition(multiplication(X2,strong_iteration(X2)),X) = addition(X,multiplication(X2,strong_iteration(X2))),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c67,plain,
addition(one,addition(multiplication(X2,strong_iteration(X2)),X)) = addition(one,addition(X,multiplication(X2,strong_iteration(X2)))),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
addition(multiplication(X,strong_iteration(X)),X2) = addition(X2,multiplication(X,strong_iteration(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c69,plain,
addition(X2,multiplication(X,strong_iteration(X))) = addition(multiplication(X,strong_iteration(X)),X2),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
addition(one,addition(X2,multiplication(X,strong_iteration(X)))) = addition(one,addition(multiplication(X,strong_iteration(X)),X2)),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
addition(one,addition(multiplication(X,strong_iteration(X)),X2)) = addition(addition(one,multiplication(X,strong_iteration(X))),X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c72,plain,
addition(addition(one,multiplication(X,strong_iteration(X))),X2) = addition(strong_iteration(X),X2),
inference(congruence,[status(thm)],[c59]) ).
cnf(c73,plain,
addition(strong_iteration(X),X2) = addition(X2,strong_iteration(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c74,plain,
addition(addition(one,multiplication(X,strong_iteration(X))),X2) = addition(X2,strong_iteration(X)),
inference(transitivity,[status(thm)],[c72,c73]) ).
cnf(c75,plain,
addition(one,addition(multiplication(X,strong_iteration(X)),X2)) = addition(X2,strong_iteration(X)),
inference(transitivity,[status(thm)],[c71,c74]) ).
cnf(c76,plain,
addition(one,addition(X2,multiplication(X,strong_iteration(X)))) = addition(X2,strong_iteration(X)),
inference(transitivity,[status(thm)],[c70,c75]) ).
cnf(c77,plain,
addition(one,addition(X,multiplication(X2,strong_iteration(X2)))) = addition(X,strong_iteration(X2)),
inference(substitution,[status(thm)],[c76]) ).
cnf(c78,plain,
addition(one,addition(multiplication(X2,strong_iteration(X2)),X)) = addition(X,strong_iteration(X2)),
inference(transitivity,[status(thm)],[c67,c77]) ).
cnf(c79,plain,
addition(one,addition(multiplication(X,strong_iteration(X)),strong_iteration(multiplication(X,strong_iteration(X))))) = addition(strong_iteration(multiplication(X,strong_iteration(X))),strong_iteration(X)),
inference(substitution,[status(thm)],[c78]) ).
cnf(c80,plain,
addition(strong_iteration(multiplication(X,strong_iteration(X))),strong_iteration(X)) = addition(one,addition(multiplication(X,strong_iteration(X)),strong_iteration(multiplication(X,strong_iteration(X))))),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c81,plain,
addition(one,addition(X,multiplication(X,strong_iteration(X)))) = addition(X,strong_iteration(X)),
inference(substitution,[status(thm)],[c76]) ).
cnf(c82,plain,
addition(X,strong_iteration(X)) = addition(one,addition(X,multiplication(X,strong_iteration(X)))),
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,plain,
addition(X,multiplication(X,strong_iteration(X))) = multiplication(X,addition(strong_iteration(X),one)),
inference(substitution,[status(thm)],[c27]) ).
cnf(c84,plain,
addition(one,addition(X,multiplication(X,strong_iteration(X)))) = addition(one,multiplication(X,addition(strong_iteration(X),one))),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
addition(strong_iteration(X),one) = addition(one,strong_iteration(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c86,plain,
multiplication(X,addition(strong_iteration(X),one)) = multiplication(X,addition(one,strong_iteration(X))),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
addition(one,multiplication(X,addition(strong_iteration(X),one))) = addition(one,multiplication(X,addition(one,strong_iteration(X)))),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
strong_iteration(X) = addition(one,multiplication(X,strong_iteration(X))),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c89,plain,
addition(one,strong_iteration(X)) = addition(one,addition(one,multiplication(X,strong_iteration(X)))),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
addition(one,addition(one,multiplication(X,strong_iteration(X)))) = addition(one,multiplication(X,strong_iteration(X))),
inference(substitution,[status(thm)],[c40]) ).
cnf(c91,plain,
addition(one,addition(one,multiplication(X,strong_iteration(X)))) = strong_iteration(X),
inference(transitivity,[status(thm)],[c90,c59]) ).
cnf(c92,plain,
addition(one,strong_iteration(X)) = strong_iteration(X),
inference(transitivity,[status(thm)],[c89,c91]) ).
cnf(c93,plain,
multiplication(X,addition(one,strong_iteration(X))) = multiplication(X,strong_iteration(X)),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
addition(one,multiplication(X,addition(one,strong_iteration(X)))) = addition(one,multiplication(X,strong_iteration(X))),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
addition(one,multiplication(X,addition(one,strong_iteration(X)))) = strong_iteration(X),
inference(transitivity,[status(thm)],[c94,c59]) ).
cnf(c96,plain,
addition(one,multiplication(X,addition(strong_iteration(X),one))) = strong_iteration(X),
inference(transitivity,[status(thm)],[c87,c95]) ).
cnf(c97,plain,
addition(one,addition(X,multiplication(X,strong_iteration(X)))) = strong_iteration(X),
inference(transitivity,[status(thm)],[c84,c96]) ).
cnf(c98,plain,
addition(X,strong_iteration(X)) = strong_iteration(X),
inference(transitivity,[status(thm)],[c82,c97]) ).
cnf(c99,plain,
addition(multiplication(X,strong_iteration(X)),strong_iteration(multiplication(X,strong_iteration(X)))) = strong_iteration(multiplication(X,strong_iteration(X))),
inference(substitution,[status(thm)],[c98]) ).
cnf(c100,plain,
addition(one,addition(multiplication(X,strong_iteration(X)),strong_iteration(multiplication(X,strong_iteration(X))))) = addition(one,strong_iteration(multiplication(X,strong_iteration(X)))),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
addition(one,strong_iteration(multiplication(X,strong_iteration(X)))) = strong_iteration(multiplication(X,strong_iteration(X))),
inference(substitution,[status(thm)],[c92]) ).
cnf(c102,plain,
addition(one,addition(multiplication(X,strong_iteration(X)),strong_iteration(multiplication(X,strong_iteration(X))))) = strong_iteration(multiplication(X,strong_iteration(X))),
inference(transitivity,[status(thm)],[c100,c101]) ).
cnf(c103,plain,
addition(strong_iteration(multiplication(X,strong_iteration(X))),strong_iteration(X)) = strong_iteration(multiplication(X,strong_iteration(X))),
inference(transitivity,[status(thm)],[c80,c102]) ).
cnf(c104,plain,
addition(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))) = strong_iteration(multiplication(X,strong_iteration(X))),
inference(transitivity,[status(thm)],[c64,c103]) ).
cnf(c105,plain,
strong_iteration(multiplication(X,strong_iteration(X))) = addition(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,axiom,
ifeq2(A2,A2,B2,C2) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(c107,plain,
ifeq2(true,true,addition(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))),strong_iteration(X)) = addition(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))),
inference(substitution,[status(thm)],[c106]) ).
cnf(c108,plain,
addition(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))) = ifeq2(true,true,addition(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))),strong_iteration(X)),
inference(symmetry,[status(thm)],[c107]) ).
cnf(c109,plain,
strong_iteration(X) = addition(one,multiplication(X,strong_iteration(X))),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c110,plain,
multiplication(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))) = multiplication(addition(one,multiplication(X,strong_iteration(X))),strong_iteration(multiplication(X,strong_iteration(X)))),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
addition(X,one) = addition(one,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c112,plain,
addition(one,X) = addition(X,one),
inference(symmetry,[status(thm)],[c111]) ).
cnf(c113,plain,
multiplication(addition(one,X),strong_iteration(X)) = multiplication(addition(X,one),strong_iteration(X)),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,axiom,
multiplication(one,A2) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
cnf(c115,plain,
multiplication(one,X) = X,
inference(substitution,[status(thm)],[c114]) ).
cnf(c116,plain,
X = multiplication(one,X),
inference(symmetry,[status(thm)],[c115]) ).
cnf(c117,plain,
addition(X2,multiplication(X,X2)) = addition(multiplication(one,X2),multiplication(X,X2)),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,axiom,
multiplication(addition(A2,B2),C2) = addition(multiplication(A2,C2),multiplication(B2,C2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
cnf(c119,plain,
multiplication(addition(one,X),X2) = addition(multiplication(one,X2),multiplication(X,X2)),
inference(substitution,[status(thm)],[c118]) ).
cnf(c120,plain,
addition(multiplication(one,X2),multiplication(X,X2)) = multiplication(addition(one,X),X2),
inference(symmetry,[status(thm)],[c119]) ).
cnf(c121,plain,
addition(one,X) = addition(X,one),
inference(substitution,[status(thm)],[c2]) ).
cnf(c122,plain,
multiplication(addition(one,X),X2) = multiplication(addition(X,one),X2),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
addition(multiplication(one,X2),multiplication(X,X2)) = multiplication(addition(X,one),X2),
inference(transitivity,[status(thm)],[c120,c122]) ).
cnf(c124,plain,
addition(X2,multiplication(X,X2)) = multiplication(addition(X,one),X2),
inference(transitivity,[status(thm)],[c117,c123]) ).
cnf(c125,plain,
addition(strong_iteration(X),multiplication(X,strong_iteration(X))) = multiplication(addition(X,one),strong_iteration(X)),
inference(substitution,[status(thm)],[c124]) ).
cnf(c126,plain,
multiplication(addition(X,one),strong_iteration(X)) = addition(strong_iteration(X),multiplication(X,strong_iteration(X))),
inference(symmetry,[status(thm)],[c125]) ).
cnf(c127,plain,
addition(multiplication(X,strong_iteration(X)),strong_iteration(X)) = addition(strong_iteration(X),multiplication(X,strong_iteration(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c128,plain,
addition(strong_iteration(X),multiplication(X,strong_iteration(X))) = addition(multiplication(X,strong_iteration(X)),strong_iteration(X)),
inference(symmetry,[status(thm)],[c127]) ).
cnf(c129,plain,
strong_iteration(X) = addition(one,multiplication(X,strong_iteration(X))),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c130,plain,
addition(multiplication(X,strong_iteration(X)),strong_iteration(X)) = addition(multiplication(X,strong_iteration(X)),addition(one,multiplication(X,strong_iteration(X)))),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
addition(X,addition(X,X2)) = addition(X,X2),
inference(substitution,[status(thm)],[c40]) ).
cnf(c132,plain,
addition(X,X2) = addition(X,addition(X,X2)),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,plain,
addition(X2,addition(X,X2)) = addition(X2,addition(X,addition(X,X2))),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
addition(X2,X) = addition(X,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c135,plain,
addition(X,X2) = addition(X2,X),
inference(symmetry,[status(thm)],[c134]) ).
cnf(c136,plain,
addition(X,addition(X,X2)) = addition(X,addition(X2,X)),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
addition(X2,addition(X,addition(X,X2))) = addition(X2,addition(X,addition(X2,X))),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
addition(X2,addition(X,addition(X2,X))) = addition(addition(X2,X),addition(X2,X)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c139,plain,
addition(addition(X2,X),addition(X2,X)) = addition(X2,X),
inference(substitution,[status(thm)],[c37]) ).
cnf(c140,plain,
addition(X2,X) = addition(X,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c141,plain,
addition(addition(X2,X),addition(X2,X)) = addition(X,X2),
inference(transitivity,[status(thm)],[c139,c140]) ).
cnf(c142,plain,
addition(X2,addition(X,addition(X2,X))) = addition(X,X2),
inference(transitivity,[status(thm)],[c138,c141]) ).
cnf(c143,plain,
addition(X2,addition(X,addition(X,X2))) = addition(X,X2),
inference(transitivity,[status(thm)],[c137,c142]) ).
cnf(c144,plain,
addition(X2,addition(X,X2)) = addition(X,X2),
inference(transitivity,[status(thm)],[c133,c143]) ).
cnf(c145,plain,
addition(multiplication(X,strong_iteration(X)),addition(one,multiplication(X,strong_iteration(X)))) = addition(one,multiplication(X,strong_iteration(X))),
inference(substitution,[status(thm)],[c144]) ).
cnf(c146,plain,
addition(multiplication(X,strong_iteration(X)),addition(one,multiplication(X,strong_iteration(X)))) = strong_iteration(X),
inference(transitivity,[status(thm)],[c145,c59]) ).
cnf(c147,plain,
addition(multiplication(X,strong_iteration(X)),strong_iteration(X)) = strong_iteration(X),
inference(transitivity,[status(thm)],[c130,c146]) ).
cnf(c148,plain,
addition(strong_iteration(X),multiplication(X,strong_iteration(X))) = strong_iteration(X),
inference(transitivity,[status(thm)],[c128,c147]) ).
cnf(c149,plain,
multiplication(addition(X,one),strong_iteration(X)) = strong_iteration(X),
inference(transitivity,[status(thm)],[c126,c148]) ).
cnf(c150,plain,
multiplication(addition(one,X),strong_iteration(X)) = strong_iteration(X),
inference(transitivity,[status(thm)],[c113,c149]) ).
cnf(c151,plain,
multiplication(addition(one,multiplication(X,strong_iteration(X))),strong_iteration(multiplication(X,strong_iteration(X)))) = strong_iteration(multiplication(X,strong_iteration(X))),
inference(substitution,[status(thm)],[c150]) ).
cnf(c152,plain,
multiplication(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))) = strong_iteration(multiplication(X,strong_iteration(X))),
inference(transitivity,[status(thm)],[c110,c151]) ).
cnf(c153,plain,
strong_iteration(multiplication(X,strong_iteration(X))) = multiplication(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))),
inference(symmetry,[status(thm)],[c152]) ).
cnf(c154,plain,
leq(strong_iteration(multiplication(X,strong_iteration(X))),strong_iteration(X)) = leq(multiplication(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))),strong_iteration(X)),
inference(congruence,[status(thm)],[c153]) ).
cnf(c155,axiom,
ifeq(A2,A2,B2,C2) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_002) ).
cnf(c156,plain,
ifeq(true,true,leq(multiplication(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))),strong_iteration(X)),true) = leq(multiplication(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))),strong_iteration(X)),
inference(substitution,[status(thm)],[c155]) ).
cnf(c157,plain,
leq(multiplication(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))),strong_iteration(X)) = ifeq(true,true,leq(multiplication(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))),strong_iteration(X)),true),
inference(symmetry,[status(thm)],[c156]) ).
cnf(c158,axiom,
ifeq3(A2,A2,B2,C2) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c159,plain,
ifeq3(X,X,leq(X,X),true) = leq(X,X),
inference(substitution,[status(thm)],[c158]) ).
cnf(c160,plain,
leq(X,X) = ifeq3(X,X,leq(X,X),true),
inference(symmetry,[status(thm)],[c159]) ).
cnf(c161,plain,
addition(X,X) = X,
inference(substitution,[status(thm)],[c37]) ).
cnf(c162,plain,
X = addition(X,X),
inference(symmetry,[status(thm)],[c161]) ).
cnf(c163,plain,
ifeq3(X,X,leq(X,X),true) = ifeq3(addition(X,X),X,leq(X,X),true),
inference(congruence,[status(thm)],[c162]) ).
cnf(c164,axiom,
ifeq3(addition(A2,B2),B2,leq(A2,B2),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
cnf(c165,plain,
ifeq3(addition(X,X),X,leq(X,X),true) = true,
inference(substitution,[status(thm)],[c164]) ).
cnf(c166,plain,
ifeq3(X,X,leq(X,X),true) = true,
inference(transitivity,[status(thm)],[c163,c165]) ).
cnf(c167,plain,
leq(X,X) = true,
inference(transitivity,[status(thm)],[c160,c166]) ).
cnf(c168,plain,
leq(strong_iteration(multiplication(X,strong_iteration(X))),strong_iteration(multiplication(X,strong_iteration(X)))) = true,
inference(substitution,[status(thm)],[c167]) ).
cnf(c169,plain,
true = leq(strong_iteration(multiplication(X,strong_iteration(X))),strong_iteration(multiplication(X,strong_iteration(X)))),
inference(symmetry,[status(thm)],[c168]) ).
cnf(c170,plain,
ifeq(true,true,leq(multiplication(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))),strong_iteration(X)),true) = ifeq(leq(strong_iteration(multiplication(X,strong_iteration(X))),strong_iteration(multiplication(X,strong_iteration(X)))),true,leq(multiplication(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))),strong_iteration(X)),true),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
strong_iteration(multiplication(X,strong_iteration(X))) = multiplication(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))),
inference(symmetry,[status(thm)],[c152]) ).
cnf(c172,plain,
leq(strong_iteration(multiplication(X,strong_iteration(X))),strong_iteration(multiplication(X,strong_iteration(X)))) = leq(multiplication(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))),strong_iteration(multiplication(X,strong_iteration(X)))),
inference(congruence,[status(thm)],[c171]) ).
cnf(c173,plain,
ifeq(leq(strong_iteration(multiplication(X,strong_iteration(X))),strong_iteration(multiplication(X,strong_iteration(X)))),true,leq(multiplication(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))),strong_iteration(X)),true) = ifeq(leq(multiplication(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))),strong_iteration(multiplication(X,strong_iteration(X)))),true,leq(multiplication(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))),strong_iteration(X)),true),
inference(congruence,[status(thm)],[c172]) ).
cnf(c174,axiom,
multiplication(A2,multiplication(B2,C2)) = multiplication(multiplication(A2,B2),C2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
cnf(c175,plain,
multiplication(X2,multiplication(X,strong_iteration(multiplication(X2,X)))) = multiplication(multiplication(X2,X),strong_iteration(multiplication(X2,X))),
inference(substitution,[status(thm)],[c174]) ).
cnf(c176,plain,
addition(one,multiplication(X2,multiplication(X,strong_iteration(multiplication(X2,X))))) = addition(one,multiplication(multiplication(X2,X),strong_iteration(multiplication(X2,X)))),
inference(congruence,[status(thm)],[c175]) ).
cnf(c177,plain,
addition(one,multiplication(multiplication(X2,X),strong_iteration(multiplication(X2,X)))) = strong_iteration(multiplication(X2,X)),
inference(substitution,[status(thm)],[c59]) ).
cnf(c178,plain,
addition(one,multiplication(X2,multiplication(X,strong_iteration(multiplication(X2,X))))) = strong_iteration(multiplication(X2,X)),
inference(transitivity,[status(thm)],[c176,c177]) ).
cnf(c179,plain,
addition(one,multiplication(X,multiplication(X2,strong_iteration(multiplication(X,X2))))) = strong_iteration(multiplication(X,X2)),
inference(substitution,[status(thm)],[c178]) ).
cnf(c180,plain,
strong_iteration(multiplication(X,X2)) = addition(one,multiplication(X,multiplication(X2,strong_iteration(multiplication(X,X2))))),
inference(symmetry,[status(thm)],[c179]) ).
cnf(c181,plain,
leq(multiplication(X2,strong_iteration(multiplication(X,X2))),strong_iteration(multiplication(X,X2))) = leq(multiplication(X2,strong_iteration(multiplication(X,X2))),addition(one,multiplication(X,multiplication(X2,strong_iteration(multiplication(X,X2)))))),
inference(congruence,[status(thm)],[c180]) ).
cnf(c182,plain,
ifeq(leq(multiplication(X2,strong_iteration(multiplication(X,X2))),strong_iteration(multiplication(X,X2))),true,leq(multiplication(X2,strong_iteration(multiplication(X,X2))),strong_iteration(X)),true) = ifeq(leq(multiplication(X2,strong_iteration(multiplication(X,X2))),addition(one,multiplication(X,multiplication(X2,strong_iteration(multiplication(X,X2)))))),true,leq(multiplication(X2,strong_iteration(multiplication(X,X2))),strong_iteration(X)),true),
inference(congruence,[status(thm)],[c181]) ).
cnf(c183,plain,
addition(multiplication(X,X2),one) = addition(one,multiplication(X,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c184,plain,
addition(one,multiplication(X,X2)) = addition(multiplication(X,X2),one),
inference(symmetry,[status(thm)],[c183]) ).
cnf(c185,plain,
leq(X2,addition(one,multiplication(X,X2))) = leq(X2,addition(multiplication(X,X2),one)),
inference(congruence,[status(thm)],[c184]) ).
cnf(c186,plain,
ifeq(leq(X2,addition(one,multiplication(X,X2))),true,leq(X2,strong_iteration(X)),true) = ifeq(leq(X2,addition(multiplication(X,X2),one)),true,leq(X2,strong_iteration(X)),true),
inference(congruence,[status(thm)],[c185]) ).
cnf(c187,plain,
multiplication(strong_iteration(X),one) = strong_iteration(X),
inference(substitution,[status(thm)],[c17]) ).
cnf(c188,plain,
strong_iteration(X) = multiplication(strong_iteration(X),one),
inference(symmetry,[status(thm)],[c187]) ).
cnf(c189,plain,
leq(X2,strong_iteration(X)) = leq(X2,multiplication(strong_iteration(X),one)),
inference(congruence,[status(thm)],[c188]) ).
cnf(c190,plain,
ifeq(leq(X2,addition(multiplication(X,X2),one)),true,leq(X2,strong_iteration(X)),true) = ifeq(leq(X2,addition(multiplication(X,X2),one)),true,leq(X2,multiplication(strong_iteration(X),one)),true),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,axiom,
ifeq(leq(C2,addition(multiplication(A2,C2),B2)),true,leq(C2,multiplication(strong_iteration(A2),B2)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_coinduction) ).
cnf(c192,plain,
ifeq(leq(X2,addition(multiplication(X,X2),one)),true,leq(X2,multiplication(strong_iteration(X),one)),true) = true,
inference(substitution,[status(thm)],[c191]) ).
cnf(c193,plain,
ifeq(leq(X2,addition(multiplication(X,X2),one)),true,leq(X2,strong_iteration(X)),true) = true,
inference(transitivity,[status(thm)],[c190,c192]) ).
cnf(c194,plain,
ifeq(leq(X2,addition(one,multiplication(X,X2))),true,leq(X2,strong_iteration(X)),true) = true,
inference(transitivity,[status(thm)],[c186,c193]) ).
cnf(c195,plain,
ifeq(leq(multiplication(X2,strong_iteration(multiplication(X,X2))),addition(one,multiplication(X,multiplication(X2,strong_iteration(multiplication(X,X2)))))),true,leq(multiplication(X2,strong_iteration(multiplication(X,X2))),strong_iteration(X)),true) = true,
inference(substitution,[status(thm)],[c194]) ).
cnf(c196,plain,
ifeq(leq(multiplication(X2,strong_iteration(multiplication(X,X2))),strong_iteration(multiplication(X,X2))),true,leq(multiplication(X2,strong_iteration(multiplication(X,X2))),strong_iteration(X)),true) = true,
inference(transitivity,[status(thm)],[c182,c195]) ).
cnf(c197,plain,
ifeq(leq(multiplication(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))),strong_iteration(multiplication(X,strong_iteration(X)))),true,leq(multiplication(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))),strong_iteration(X)),true) = true,
inference(substitution,[status(thm)],[c196]) ).
cnf(c198,plain,
ifeq(leq(strong_iteration(multiplication(X,strong_iteration(X))),strong_iteration(multiplication(X,strong_iteration(X)))),true,leq(multiplication(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))),strong_iteration(X)),true) = true,
inference(transitivity,[status(thm)],[c173,c197]) ).
cnf(c199,plain,
ifeq(true,true,leq(multiplication(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))),strong_iteration(X)),true) = true,
inference(transitivity,[status(thm)],[c170,c198]) ).
cnf(c200,plain,
leq(multiplication(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))),strong_iteration(X)) = true,
inference(transitivity,[status(thm)],[c157,c199]) ).
cnf(c201,plain,
leq(strong_iteration(multiplication(X,strong_iteration(X))),strong_iteration(X)) = true,
inference(transitivity,[status(thm)],[c154,c200]) ).
cnf(c202,plain,
true = leq(strong_iteration(multiplication(X,strong_iteration(X))),strong_iteration(X)),
inference(symmetry,[status(thm)],[c201]) ).
cnf(c203,plain,
ifeq2(true,true,addition(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))),strong_iteration(X)) = ifeq2(leq(strong_iteration(multiplication(X,strong_iteration(X))),strong_iteration(X)),true,addition(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))),strong_iteration(X)),
inference(congruence,[status(thm)],[c202]) ).
cnf(c204,plain,
addition(X2,X) = addition(X,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c205,plain,
addition(X,X2) = addition(X2,X),
inference(symmetry,[status(thm)],[c204]) ).
cnf(c206,plain,
ifeq2(leq(X2,X),true,addition(X,X2),X) = ifeq2(leq(X2,X),true,addition(X2,X),X),
inference(congruence,[status(thm)],[c205]) ).
cnf(c207,axiom,
ifeq2(leq(A2,B2),true,addition(A2,B2),B2) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order_1) ).
cnf(c208,plain,
ifeq2(leq(X2,X),true,addition(X2,X),X) = X,
inference(substitution,[status(thm)],[c207]) ).
cnf(c209,plain,
ifeq2(leq(X2,X),true,addition(X,X2),X) = X,
inference(transitivity,[status(thm)],[c206,c208]) ).
cnf(c210,plain,
ifeq2(leq(strong_iteration(multiplication(X,strong_iteration(X))),strong_iteration(X)),true,addition(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))),strong_iteration(X)) = strong_iteration(X),
inference(substitution,[status(thm)],[c209]) ).
cnf(c211,plain,
ifeq2(true,true,addition(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))),strong_iteration(X)) = strong_iteration(X),
inference(transitivity,[status(thm)],[c203,c210]) ).
cnf(c212,plain,
addition(strong_iteration(X),strong_iteration(multiplication(X,strong_iteration(X)))) = strong_iteration(X),
inference(transitivity,[status(thm)],[c108,c211]) ).
cnf(c213,plain,
strong_iteration(multiplication(X,strong_iteration(X))) = strong_iteration(X),
inference(transitivity,[status(thm)],[c105,c212]) ).
cnf(c214,plain,
strong_iteration(X) = strong_iteration(multiplication(X,strong_iteration(X))),
inference(symmetry,[status(thm)],[c213]) ).
cnf(c215,plain,
addition(strong_iteration(X),star(addition(one,multiplication(X,strong_iteration(X))))) = addition(strong_iteration(multiplication(X,strong_iteration(X))),star(addition(one,multiplication(X,strong_iteration(X))))),
inference(congruence,[status(thm)],[c214]) ).
cnf(c216,plain,
addition(X,one) = addition(one,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c217,plain,
addition(one,X) = addition(X,one),
inference(symmetry,[status(thm)],[c216]) ).
cnf(c218,plain,
star(addition(one,X)) = star(addition(X,one)),
inference(congruence,[status(thm)],[c217]) ).
cnf(c219,plain,
addition(strong_iteration(X),star(addition(one,X))) = addition(strong_iteration(X),star(addition(X,one))),
inference(congruence,[status(thm)],[c218]) ).
cnf(c220,plain,
addition(star(addition(X,one)),strong_iteration(X)) = addition(strong_iteration(X),star(addition(X,one))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c221,plain,
addition(strong_iteration(X),star(addition(X,one))) = addition(star(addition(X,one)),strong_iteration(X)),
inference(symmetry,[status(thm)],[c220]) ).
cnf(c222,plain,
ifeq2(true,true,addition(star(addition(X,one)),strong_iteration(X)),strong_iteration(X)) = addition(star(addition(X,one)),strong_iteration(X)),
inference(substitution,[status(thm)],[c106]) ).
cnf(c223,plain,
addition(star(addition(X,one)),strong_iteration(X)) = ifeq2(true,true,addition(star(addition(X,one)),strong_iteration(X)),strong_iteration(X)),
inference(symmetry,[status(thm)],[c222]) ).
cnf(c224,plain,
ifeq(true,true,leq(star(addition(X,one)),strong_iteration(X)),true) = leq(star(addition(X,one)),strong_iteration(X)),
inference(substitution,[status(thm)],[c155]) ).
cnf(c225,plain,
leq(star(addition(X,one)),strong_iteration(X)) = ifeq(true,true,leq(star(addition(X,one)),strong_iteration(X)),true),
inference(symmetry,[status(thm)],[c224]) ).
cnf(c226,plain,
leq(strong_iteration(X),strong_iteration(X)) = true,
inference(substitution,[status(thm)],[c167]) ).
cnf(c227,plain,
true = leq(strong_iteration(X),strong_iteration(X)),
inference(symmetry,[status(thm)],[c226]) ).
cnf(c228,plain,
ifeq(true,true,leq(star(addition(X,one)),strong_iteration(X)),true) = ifeq(leq(strong_iteration(X),strong_iteration(X)),true,leq(star(addition(X,one)),strong_iteration(X)),true),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
strong_iteration(X) = addition(one,strong_iteration(X)),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c230,plain,
leq(strong_iteration(X),strong_iteration(X)) = leq(addition(one,strong_iteration(X)),strong_iteration(X)),
inference(congruence,[status(thm)],[c229]) ).
cnf(c231,plain,
ifeq(leq(strong_iteration(X),strong_iteration(X)),true,leq(star(addition(X,one)),strong_iteration(X)),true) = ifeq(leq(addition(one,strong_iteration(X)),strong_iteration(X)),true,leq(star(addition(X,one)),strong_iteration(X)),true),
inference(congruence,[status(thm)],[c230]) ).
cnf(c232,plain,
strong_iteration(X) = multiplication(addition(X,one),strong_iteration(X)),
inference(symmetry,[status(thm)],[c149]) ).
cnf(c233,plain,
addition(one,strong_iteration(X)) = addition(one,multiplication(addition(X,one),strong_iteration(X))),
inference(congruence,[status(thm)],[c232]) ).
cnf(c234,plain,
leq(addition(one,strong_iteration(X)),strong_iteration(X)) = leq(addition(one,multiplication(addition(X,one),strong_iteration(X))),strong_iteration(X)),
inference(congruence,[status(thm)],[c233]) ).
cnf(c235,plain,
ifeq(leq(addition(one,strong_iteration(X)),strong_iteration(X)),true,leq(star(addition(X,one)),strong_iteration(X)),true) = ifeq(leq(addition(one,multiplication(addition(X,one),strong_iteration(X))),strong_iteration(X)),true,leq(star(addition(X,one)),strong_iteration(X)),true),
inference(congruence,[status(thm)],[c234]) ).
cnf(c236,plain,
addition(multiplication(X2,X),one) = addition(one,multiplication(X2,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c237,plain,
addition(one,multiplication(X2,X)) = addition(multiplication(X2,X),one),
inference(symmetry,[status(thm)],[c236]) ).
cnf(c238,plain,
leq(addition(one,multiplication(X2,X)),X) = leq(addition(multiplication(X2,X),one),X),
inference(congruence,[status(thm)],[c237]) ).
cnf(c239,plain,
ifeq(leq(addition(one,multiplication(X2,X)),X),true,leq(star(X2),X),true) = ifeq(leq(addition(multiplication(X2,X),one),X),true,leq(star(X2),X),true),
inference(congruence,[status(thm)],[c238]) ).
cnf(c240,plain,
multiplication(star(X),one) = star(X),
inference(substitution,[status(thm)],[c17]) ).
cnf(c241,plain,
star(X) = multiplication(star(X),one),
inference(symmetry,[status(thm)],[c240]) ).
cnf(c242,plain,
leq(star(X2),X) = leq(multiplication(star(X2),one),X),
inference(congruence,[status(thm)],[c241]) ).
cnf(c243,plain,
ifeq(leq(addition(multiplication(X2,X),one),X),true,leq(star(X2),X),true) = ifeq(leq(addition(multiplication(X2,X),one),X),true,leq(multiplication(star(X2),one),X),true),
inference(congruence,[status(thm)],[c242]) ).
cnf(c244,axiom,
ifeq(leq(addition(multiplication(A2,C2),B2),C2),true,leq(multiplication(star(A2),B2),C2),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction1) ).
cnf(c245,plain,
ifeq(leq(addition(multiplication(X2,X),one),X),true,leq(multiplication(star(X2),one),X),true) = true,
inference(substitution,[status(thm)],[c244]) ).
cnf(c246,plain,
ifeq(leq(addition(multiplication(X2,X),one),X),true,leq(star(X2),X),true) = true,
inference(transitivity,[status(thm)],[c243,c245]) ).
cnf(c247,plain,
ifeq(leq(addition(one,multiplication(X2,X)),X),true,leq(star(X2),X),true) = true,
inference(transitivity,[status(thm)],[c239,c246]) ).
cnf(c248,plain,
ifeq(leq(addition(one,multiplication(addition(X,one),strong_iteration(X))),strong_iteration(X)),true,leq(star(addition(X,one)),strong_iteration(X)),true) = true,
inference(substitution,[status(thm)],[c247]) ).
cnf(c249,plain,
ifeq(leq(addition(one,strong_iteration(X)),strong_iteration(X)),true,leq(star(addition(X,one)),strong_iteration(X)),true) = true,
inference(transitivity,[status(thm)],[c235,c248]) ).
cnf(c250,plain,
ifeq(leq(strong_iteration(X),strong_iteration(X)),true,leq(star(addition(X,one)),strong_iteration(X)),true) = true,
inference(transitivity,[status(thm)],[c231,c249]) ).
cnf(c251,plain,
ifeq(true,true,leq(star(addition(X,one)),strong_iteration(X)),true) = true,
inference(transitivity,[status(thm)],[c228,c250]) ).
cnf(c252,plain,
leq(star(addition(X,one)),strong_iteration(X)) = true,
inference(transitivity,[status(thm)],[c225,c251]) ).
cnf(c253,plain,
true = leq(star(addition(X,one)),strong_iteration(X)),
inference(symmetry,[status(thm)],[c252]) ).
cnf(c254,plain,
ifeq2(true,true,addition(star(addition(X,one)),strong_iteration(X)),strong_iteration(X)) = ifeq2(leq(star(addition(X,one)),strong_iteration(X)),true,addition(star(addition(X,one)),strong_iteration(X)),strong_iteration(X)),
inference(congruence,[status(thm)],[c253]) ).
cnf(c255,plain,
ifeq2(leq(star(addition(X,one)),strong_iteration(X)),true,addition(star(addition(X,one)),strong_iteration(X)),strong_iteration(X)) = strong_iteration(X),
inference(substitution,[status(thm)],[c207]) ).
cnf(c256,plain,
ifeq2(true,true,addition(star(addition(X,one)),strong_iteration(X)),strong_iteration(X)) = strong_iteration(X),
inference(transitivity,[status(thm)],[c254,c255]) ).
cnf(c257,plain,
addition(star(addition(X,one)),strong_iteration(X)) = strong_iteration(X),
inference(transitivity,[status(thm)],[c223,c256]) ).
cnf(c258,plain,
addition(strong_iteration(X),star(addition(X,one))) = strong_iteration(X),
inference(transitivity,[status(thm)],[c221,c257]) ).
cnf(c259,plain,
addition(strong_iteration(X),star(addition(one,X))) = strong_iteration(X),
inference(transitivity,[status(thm)],[c219,c258]) ).
cnf(c260,plain,
addition(strong_iteration(multiplication(X,strong_iteration(X))),star(addition(one,multiplication(X,strong_iteration(X))))) = strong_iteration(multiplication(X,strong_iteration(X))),
inference(substitution,[status(thm)],[c259]) ).
cnf(c261,plain,
addition(strong_iteration(multiplication(X,strong_iteration(X))),star(addition(one,multiplication(X,strong_iteration(X))))) = strong_iteration(X),
inference(transitivity,[status(thm)],[c260,c213]) ).
cnf(c262,plain,
addition(strong_iteration(X),star(addition(one,multiplication(X,strong_iteration(X))))) = strong_iteration(X),
inference(transitivity,[status(thm)],[c215,c261]) ).
cnf(c263,plain,
addition(strong_iteration(X),star(strong_iteration(X))) = strong_iteration(X),
inference(transitivity,[status(thm)],[c62,c262]) ).
cnf(c264,plain,
star(strong_iteration(X)) = strong_iteration(X),
inference(transitivity,[status(thm)],[c53,c263]) ).
cnf(c265,plain,
star(strong_iteration(sK1_goals_X0)) = strong_iteration(sK1_goals_X0),
inference(substitution,[status(thm)],[c264]) ).
cnf(c266,plain,
$false,
inference(resolution,[status(thm)],[c1,c265]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE145-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 13:12:30 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 56.10/7.54 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 56.10/7.54
% 56.10/7.54 % SZS status Unsatisfiable
% 56.10/7.54
% 56.10/7.55 % SZS output start CNFRefutation
% See solution above
% 56.90/7.62
% 56.90/7.62 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------