%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE147-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 117.57s 15.34s
% Output : CNFRefutation 118.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 12
% Syntax : Number of clauses : 149 ( 149 unt; 0 nHn; 3 RR)
% Number of literals : 149 ( 148 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 : 14 ( 14 usr; 6 con; 0-4 aty)
% Number of variables : 315 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
tuple(leq(multiplication(star(sK1_goals_X1),strong_iteration(multiplication(star(sK2_goals_X0),sK1_goals_X1))),strong_iteration(multiplication(star(sK2_goals_X0),sK1_goals_X1))),leq(strong_iteration(multiplication(star(sK4_goals_X0),sK3_goals_X1)),multiplication(star(sK3_goals_X1),strong_iteration(multiplication(star(sK4_goals_X0),sK3_goals_X1))))) != tuple(true,true),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(c2,axiom,
ifeq3(A,A,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c3,plain,
ifeq3(multiplication(star(X),X2),multiplication(star(X),X2),leq(X2,multiplication(star(X),X2)),true) = leq(X2,multiplication(star(X),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
leq(X2,multiplication(star(X),X2)) = ifeq3(multiplication(star(X),X2),multiplication(star(X),X2),leq(X2,multiplication(star(X),X2)),true),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiplication(one,A2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
cnf(c6,plain,
multiplication(one,X) = X,
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
X = multiplication(one,X),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
addition(multiplication(star(X2),X),X) = addition(multiplication(star(X2),X),multiplication(one,X)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,axiom,
multiplication(addition(A2,B2),C2) = addition(multiplication(A2,C2),multiplication(B2,C2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
cnf(c10,plain,
multiplication(addition(X2,X3),X) = addition(multiplication(X2,X),multiplication(X3,X)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
addition(multiplication(X3,X2),multiplication(X,X2)) = multiplication(addition(X3,X),X2),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,axiom,
addition(A2,B2) = addition(B2,A2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
cnf(c13,plain,
addition(X2,X) = addition(X,X2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
multiplication(addition(X3,X),X2) = multiplication(addition(X,X3),X2),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
addition(multiplication(X3,X2),multiplication(X,X2)) = multiplication(addition(X,X3),X2),
inference(transitivity,[status(thm)],[c11,c14]) ).
cnf(c16,plain,
addition(multiplication(star(X2),X),multiplication(one,X)) = multiplication(addition(one,star(X2)),X),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,axiom,
addition(one,multiplication(A2,star(A2))) = star(A2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold1) ).
cnf(c18,plain,
addition(one,multiplication(X,star(X))) = star(X),
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
star(X) = addition(one,multiplication(X,star(X))),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
addition(one,star(X)) = addition(one,addition(one,multiplication(X,star(X)))),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,axiom,
addition(A2,addition(B2,C2)) = addition(addition(A2,B2),C2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
cnf(c22,plain,
addition(X2,addition(X2,X)) = addition(addition(X2,X2),X),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,axiom,
addition(A2,A2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence) ).
cnf(c24,plain,
addition(X,X) = X,
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
addition(addition(X2,X2),X) = addition(X2,X),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
addition(X2,addition(X2,X)) = addition(X2,X),
inference(transitivity,[status(thm)],[c22,c25]) ).
cnf(c27,plain,
addition(one,addition(one,multiplication(X,star(X)))) = addition(one,multiplication(X,star(X))),
inference(substitution,[status(thm)],[c26]) ).
cnf(c28,plain,
addition(one,multiplication(X,star(X))) = star(X),
inference(substitution,[status(thm)],[c17]) ).
cnf(c29,plain,
addition(one,addition(one,multiplication(X,star(X)))) = star(X),
inference(transitivity,[status(thm)],[c27,c28]) ).
cnf(c30,plain,
addition(one,star(X)) = star(X),
inference(transitivity,[status(thm)],[c20,c29]) ).
cnf(c31,plain,
multiplication(addition(one,star(X2)),X) = multiplication(star(X2),X),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
addition(multiplication(star(X2),X),multiplication(one,X)) = multiplication(star(X2),X),
inference(transitivity,[status(thm)],[c16,c31]) ).
cnf(c33,plain,
addition(multiplication(star(X2),X),X) = multiplication(star(X2),X),
inference(transitivity,[status(thm)],[c8,c32]) ).
cnf(c34,plain,
addition(multiplication(star(X),X2),X2) = multiplication(star(X),X2),
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
multiplication(star(X),X2) = addition(multiplication(star(X),X2),X2),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
ifeq3(multiplication(star(X),X2),multiplication(star(X),X2),leq(X2,multiplication(star(X),X2)),true) = ifeq3(addition(multiplication(star(X),X2),X2),multiplication(star(X),X2),leq(X2,multiplication(star(X),X2)),true),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
addition(X,X2) = addition(X2,X),
inference(substitution,[status(thm)],[c12]) ).
cnf(c38,plain,
addition(X2,X) = addition(X,X2),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,plain,
ifeq3(addition(X2,X),X2,leq(X,X2),true) = ifeq3(addition(X,X2),X2,leq(X,X2),true),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,axiom,
ifeq3(addition(A2,B2),B2,leq(A2,B2),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
cnf(c41,plain,
ifeq3(addition(X,X2),X2,leq(X,X2),true) = true,
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
ifeq3(addition(X2,X),X2,leq(X,X2),true) = true,
inference(transitivity,[status(thm)],[c39,c41]) ).
cnf(c43,plain,
ifeq3(addition(multiplication(star(X),X2),X2),multiplication(star(X),X2),leq(X2,multiplication(star(X),X2)),true) = true,
inference(substitution,[status(thm)],[c42]) ).
cnf(c44,plain,
ifeq3(multiplication(star(X),X2),multiplication(star(X),X2),leq(X2,multiplication(star(X),X2)),true) = true,
inference(transitivity,[status(thm)],[c36,c43]) ).
cnf(c45,plain,
leq(X,multiplication(star(X2),X)) = true,
inference(transitivity,[status(thm)],[c4,c44]) ).
cnf(c46,plain,
tuple(leq(multiplication(star(X4),strong_iteration(multiplication(star(X3),X4))),strong_iteration(multiplication(star(X3),X4))),leq(X2,multiplication(star(X),X2))) = tuple(leq(multiplication(star(X4),strong_iteration(multiplication(star(X3),X4))),strong_iteration(multiplication(star(X3),X4))),true),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,axiom,
ifeq(A2,A2,B2,C2) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_002) ).
cnf(c48,plain,
ifeq(true,true,leq(multiplication(star(X2),strong_iteration(multiplication(star(X),X2))),strong_iteration(multiplication(star(X),X2))),true) = leq(multiplication(star(X2),strong_iteration(multiplication(star(X),X2))),strong_iteration(multiplication(star(X),X2))),
inference(substitution,[status(thm)],[c47]) ).
cnf(c49,plain,
leq(multiplication(star(X2),strong_iteration(multiplication(star(X),X2))),strong_iteration(multiplication(star(X),X2))) = ifeq(true,true,leq(multiplication(star(X2),strong_iteration(multiplication(star(X),X2))),strong_iteration(multiplication(star(X),X2))),true),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
ifeq3(X,X,leq(X,X),true) = leq(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c51,plain,
leq(X,X) = ifeq3(X,X,leq(X,X),true),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
addition(X,X) = X,
inference(substitution,[status(thm)],[c23]) ).
cnf(c53,plain,
X = addition(X,X),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
ifeq3(X,X,leq(X,X),true) = ifeq3(addition(X,X),X,leq(X,X),true),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
ifeq3(addition(X,X),X,leq(X,X),true) = true,
inference(substitution,[status(thm)],[c40]) ).
cnf(c56,plain,
ifeq3(X,X,leq(X,X),true) = true,
inference(transitivity,[status(thm)],[c54,c55]) ).
cnf(c57,plain,
leq(X,X) = true,
inference(transitivity,[status(thm)],[c51,c56]) ).
cnf(c58,plain,
leq(strong_iteration(multiplication(star(X),X2)),strong_iteration(multiplication(star(X),X2))) = true,
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
true = leq(strong_iteration(multiplication(star(X),X2)),strong_iteration(multiplication(star(X),X2))),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
ifeq(true,true,leq(multiplication(star(X2),strong_iteration(multiplication(star(X),X2))),strong_iteration(multiplication(star(X),X2))),true) = ifeq(leq(strong_iteration(multiplication(star(X),X2)),strong_iteration(multiplication(star(X),X2))),true,leq(multiplication(star(X2),strong_iteration(multiplication(star(X),X2))),strong_iteration(multiplication(star(X),X2))),true),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
addition(multiplication(X,X3),X2) = addition(X2,multiplication(X,X3)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c62,plain,
addition(X2,multiplication(X,X3)) = addition(multiplication(X,X3),X2),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,plain,
addition(multiplication(X4,X3),addition(X2,multiplication(X,X3))) = addition(multiplication(X4,X3),addition(multiplication(X,X3),X2)),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
addition(addition(X2,X),X3) = addition(X3,addition(X2,X)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c65,plain,
addition(X3,addition(X2,X)) = addition(addition(X2,X),X3),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
addition(X2,addition(X,X3)) = addition(addition(X2,X),X3),
inference(substitution,[status(thm)],[c21]) ).
cnf(c67,plain,
addition(addition(X2,X),X3) = addition(X2,addition(X,X3)),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
addition(X,X2) = addition(X2,X),
inference(substitution,[status(thm)],[c12]) ).
cnf(c69,plain,
addition(X2,addition(X,X3)) = addition(X2,addition(X3,X)),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
addition(addition(X2,X),X3) = addition(X2,addition(X3,X)),
inference(transitivity,[status(thm)],[c67,c69]) ).
cnf(c71,plain,
addition(X3,addition(X2,X)) = addition(X2,addition(X3,X)),
inference(transitivity,[status(thm)],[c65,c70]) ).
cnf(c72,plain,
addition(multiplication(X,X3),addition(multiplication(X4,X3),X2)) = addition(multiplication(X4,X3),addition(multiplication(X,X3),X2)),
inference(substitution,[status(thm)],[c71]) ).
cnf(c73,plain,
addition(multiplication(X4,X3),addition(multiplication(X,X3),X2)) = addition(multiplication(X,X3),addition(multiplication(X4,X3),X2)),
inference(symmetry,[status(thm)],[c72]) ).
cnf(c74,plain,
addition(multiplication(X,X3),addition(multiplication(X4,X3),X2)) = addition(addition(multiplication(X,X3),multiplication(X4,X3)),X2),
inference(substitution,[status(thm)],[c21]) ).
cnf(c75,plain,
multiplication(addition(X,X3),X2) = addition(multiplication(X,X2),multiplication(X3,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c76,plain,
addition(multiplication(X,X2),multiplication(X3,X2)) = multiplication(addition(X,X3),X2),
inference(symmetry,[status(thm)],[c75]) ).
cnf(c77,plain,
addition(addition(multiplication(X,X3),multiplication(X4,X3)),X2) = addition(multiplication(addition(X,X4),X3),X2),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
addition(multiplication(addition(X,X4),X3),X2) = addition(X2,multiplication(addition(X,X4),X3)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c79,plain,
addition(X,X2) = addition(X2,X),
inference(substitution,[status(thm)],[c12]) ).
cnf(c80,plain,
multiplication(addition(X,X3),X2) = multiplication(addition(X3,X),X2),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
addition(X2,multiplication(addition(X,X4),X3)) = addition(X2,multiplication(addition(X4,X),X3)),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
addition(multiplication(addition(X,X4),X3),X2) = addition(X2,multiplication(addition(X4,X),X3)),
inference(transitivity,[status(thm)],[c78,c81]) ).
cnf(c83,plain,
addition(addition(multiplication(X,X3),multiplication(X4,X3)),X2) = addition(X2,multiplication(addition(X4,X),X3)),
inference(transitivity,[status(thm)],[c77,c82]) ).
cnf(c84,plain,
addition(multiplication(X,X3),addition(multiplication(X4,X3),X2)) = addition(X2,multiplication(addition(X4,X),X3)),
inference(transitivity,[status(thm)],[c74,c83]) ).
cnf(c85,plain,
addition(multiplication(X4,X3),addition(multiplication(X,X3),X2)) = addition(X2,multiplication(addition(X4,X),X3)),
inference(transitivity,[status(thm)],[c73,c84]) ).
cnf(c86,plain,
addition(multiplication(X4,X3),addition(X2,multiplication(X,X3))) = addition(X2,multiplication(addition(X4,X),X3)),
inference(transitivity,[status(thm)],[c63,c85]) ).
cnf(c87,plain,
addition(multiplication(X2,strong_iteration(X)),addition(one,multiplication(X,strong_iteration(X)))) = addition(one,multiplication(addition(X2,X),strong_iteration(X))),
inference(substitution,[status(thm)],[c86]) ).
cnf(c88,plain,
addition(one,multiplication(addition(X2,X),strong_iteration(X))) = addition(multiplication(X2,strong_iteration(X)),addition(one,multiplication(X,strong_iteration(X)))),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c89,plain,
addition(multiplication(X,strong_iteration(X)),one) = addition(one,multiplication(X,strong_iteration(X))),
inference(substitution,[status(thm)],[c12]) ).
cnf(c90,plain,
addition(one,multiplication(X,strong_iteration(X))) = addition(multiplication(X,strong_iteration(X)),one),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,axiom,
strong_iteration(A2) = addition(multiplication(A2,strong_iteration(A2)),one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infty_unfold1) ).
cnf(c92,plain,
strong_iteration(X) = addition(multiplication(X,strong_iteration(X)),one),
inference(substitution,[status(thm)],[c91]) ).
cnf(c93,plain,
addition(multiplication(X,strong_iteration(X)),one) = strong_iteration(X),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c94,plain,
addition(one,multiplication(X,strong_iteration(X))) = strong_iteration(X),
inference(transitivity,[status(thm)],[c90,c93]) ).
cnf(c95,plain,
addition(multiplication(X2,strong_iteration(X)),addition(one,multiplication(X,strong_iteration(X)))) = addition(multiplication(X2,strong_iteration(X)),strong_iteration(X)),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
addition(multiplication(X2,strong_iteration(X)),strong_iteration(X)) = addition(strong_iteration(X),multiplication(X2,strong_iteration(X))),
inference(substitution,[status(thm)],[c12]) ).
cnf(c97,plain,
multiplication(one,X) = X,
inference(substitution,[status(thm)],[c5]) ).
cnf(c98,plain,
X = multiplication(one,X),
inference(symmetry,[status(thm)],[c97]) ).
cnf(c99,plain,
addition(X2,multiplication(X,X2)) = addition(multiplication(one,X2),multiplication(X,X2)),
inference(congruence,[status(thm)],[c98]) ).
cnf(c100,plain,
multiplication(addition(one,X),X2) = addition(multiplication(one,X2),multiplication(X,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c101,plain,
addition(multiplication(one,X2),multiplication(X,X2)) = multiplication(addition(one,X),X2),
inference(symmetry,[status(thm)],[c100]) ).
cnf(c102,plain,
addition(one,X) = addition(X,one),
inference(substitution,[status(thm)],[c12]) ).
cnf(c103,plain,
multiplication(addition(one,X),X2) = multiplication(addition(X,one),X2),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
addition(multiplication(one,X2),multiplication(X,X2)) = multiplication(addition(X,one),X2),
inference(transitivity,[status(thm)],[c101,c103]) ).
cnf(c105,plain,
addition(X2,multiplication(X,X2)) = multiplication(addition(X,one),X2),
inference(transitivity,[status(thm)],[c99,c104]) ).
cnf(c106,plain,
addition(strong_iteration(X),multiplication(X2,strong_iteration(X))) = multiplication(addition(X2,one),strong_iteration(X)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c107,plain,
addition(multiplication(X2,strong_iteration(X)),strong_iteration(X)) = multiplication(addition(X2,one),strong_iteration(X)),
inference(transitivity,[status(thm)],[c96,c106]) ).
cnf(c108,plain,
addition(multiplication(X2,strong_iteration(X)),addition(one,multiplication(X,strong_iteration(X)))) = multiplication(addition(X2,one),strong_iteration(X)),
inference(transitivity,[status(thm)],[c95,c107]) ).
cnf(c109,plain,
addition(one,multiplication(addition(X2,X),strong_iteration(X))) = multiplication(addition(X2,one),strong_iteration(X)),
inference(transitivity,[status(thm)],[c88,c108]) ).
cnf(c110,plain,
addition(one,multiplication(addition(X2,multiplication(star(X),X2)),strong_iteration(multiplication(star(X),X2)))) = multiplication(addition(X2,one),strong_iteration(multiplication(star(X),X2))),
inference(substitution,[status(thm)],[c109]) ).
cnf(c111,plain,
multiplication(addition(X2,one),strong_iteration(multiplication(star(X),X2))) = addition(one,multiplication(addition(X2,multiplication(star(X),X2)),strong_iteration(multiplication(star(X),X2)))),
inference(symmetry,[status(thm)],[c110]) ).
cnf(c112,plain,
addition(multiplication(star(X),X2),X2) = addition(X2,multiplication(star(X),X2)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c113,plain,
addition(X2,multiplication(star(X),X2)) = addition(multiplication(star(X),X2),X2),
inference(symmetry,[status(thm)],[c112]) ).
cnf(c114,plain,
multiplication(one,X) = X,
inference(substitution,[status(thm)],[c5]) ).
cnf(c115,plain,
X = multiplication(one,X),
inference(symmetry,[status(thm)],[c114]) ).
cnf(c116,plain,
addition(multiplication(star(X),X2),X2) = addition(multiplication(star(X),X2),multiplication(one,X2)),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
addition(multiplication(star(X),X2),multiplication(one,X2)) = multiplication(addition(one,star(X)),X2),
inference(substitution,[status(thm)],[c15]) ).
cnf(c118,plain,
multiplication(addition(one,star(X)),X2) = multiplication(star(X),X2),
inference(congruence,[status(thm)],[c30]) ).
cnf(c119,plain,
addition(multiplication(star(X),X2),multiplication(one,X2)) = multiplication(star(X),X2),
inference(transitivity,[status(thm)],[c117,c118]) ).
cnf(c120,plain,
addition(multiplication(star(X),X2),X2) = multiplication(star(X),X2),
inference(transitivity,[status(thm)],[c116,c119]) ).
cnf(c121,plain,
addition(X2,multiplication(star(X),X2)) = multiplication(star(X),X2),
inference(transitivity,[status(thm)],[c113,c120]) ).
cnf(c122,plain,
multiplication(addition(X2,multiplication(star(X),X2)),strong_iteration(multiplication(star(X),X2))) = multiplication(multiplication(star(X),X2),strong_iteration(multiplication(star(X),X2))),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
addition(one,multiplication(addition(X2,multiplication(star(X),X2)),strong_iteration(multiplication(star(X),X2)))) = addition(one,multiplication(multiplication(star(X),X2),strong_iteration(multiplication(star(X),X2)))),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
addition(one,multiplication(multiplication(star(X),X2),strong_iteration(multiplication(star(X),X2)))) = strong_iteration(multiplication(star(X),X2)),
inference(substitution,[status(thm)],[c94]) ).
cnf(c125,plain,
addition(one,multiplication(addition(X2,multiplication(star(X),X2)),strong_iteration(multiplication(star(X),X2)))) = strong_iteration(multiplication(star(X),X2)),
inference(transitivity,[status(thm)],[c123,c124]) ).
cnf(c126,plain,
multiplication(addition(X2,one),strong_iteration(multiplication(star(X),X2))) = strong_iteration(multiplication(star(X),X2)),
inference(transitivity,[status(thm)],[c111,c125]) ).
cnf(c127,plain,
strong_iteration(multiplication(star(X),X2)) = multiplication(addition(X2,one),strong_iteration(multiplication(star(X),X2))),
inference(symmetry,[status(thm)],[c126]) ).
cnf(c128,plain,
leq(strong_iteration(multiplication(star(X),X2)),strong_iteration(multiplication(star(X),X2))) = leq(multiplication(addition(X2,one),strong_iteration(multiplication(star(X),X2))),strong_iteration(multiplication(star(X),X2))),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
ifeq(leq(strong_iteration(multiplication(star(X),X2)),strong_iteration(multiplication(star(X),X2))),true,leq(multiplication(star(X2),strong_iteration(multiplication(star(X),X2))),strong_iteration(multiplication(star(X),X2))),true) = ifeq(leq(multiplication(addition(X2,one),strong_iteration(multiplication(star(X),X2))),strong_iteration(multiplication(star(X),X2))),true,leq(multiplication(star(X2),strong_iteration(multiplication(star(X),X2))),strong_iteration(multiplication(star(X),X2))),true),
inference(congruence,[status(thm)],[c128]) ).
cnf(c130,plain,
addition(strong_iteration(multiplication(star(X),X2)),multiplication(X2,strong_iteration(multiplication(star(X),X2)))) = multiplication(addition(X2,one),strong_iteration(multiplication(star(X),X2))),
inference(substitution,[status(thm)],[c105]) ).
cnf(c131,plain,
multiplication(addition(X2,one),strong_iteration(multiplication(star(X),X2))) = addition(strong_iteration(multiplication(star(X),X2)),multiplication(X2,strong_iteration(multiplication(star(X),X2)))),
inference(symmetry,[status(thm)],[c130]) ).
cnf(c132,plain,
leq(multiplication(addition(X2,one),strong_iteration(multiplication(star(X),X2))),strong_iteration(multiplication(star(X),X2))) = leq(addition(strong_iteration(multiplication(star(X),X2)),multiplication(X2,strong_iteration(multiplication(star(X),X2)))),strong_iteration(multiplication(star(X),X2))),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,plain,
ifeq(leq(multiplication(addition(X2,one),strong_iteration(multiplication(star(X),X2))),strong_iteration(multiplication(star(X),X2))),true,leq(multiplication(star(X2),strong_iteration(multiplication(star(X),X2))),strong_iteration(multiplication(star(X),X2))),true) = ifeq(leq(addition(strong_iteration(multiplication(star(X),X2)),multiplication(X2,strong_iteration(multiplication(star(X),X2)))),strong_iteration(multiplication(star(X),X2))),true,leq(multiplication(star(X2),strong_iteration(multiplication(star(X),X2))),strong_iteration(multiplication(star(X),X2))),true),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
addition(multiplication(X2,X),X3) = addition(X3,multiplication(X2,X)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c135,plain,
addition(X3,multiplication(X2,X)) = addition(multiplication(X2,X),X3),
inference(symmetry,[status(thm)],[c134]) ).
cnf(c136,plain,
leq(addition(X3,multiplication(X2,X)),X) = leq(addition(multiplication(X2,X),X3),X),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
ifeq(leq(addition(X3,multiplication(X2,X)),X),true,leq(multiplication(star(X2),X3),X),true) = ifeq(leq(addition(multiplication(X2,X),X3),X),true,leq(multiplication(star(X2),X3),X),true),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,axiom,
ifeq(leq(addition(multiplication(A2,C2),B2),C2),true,leq(multiplication(star(A2),B2),C2),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction1) ).
cnf(c139,plain,
ifeq(leq(addition(multiplication(X2,X),X3),X),true,leq(multiplication(star(X2),X3),X),true) = true,
inference(substitution,[status(thm)],[c138]) ).
cnf(c140,plain,
ifeq(leq(addition(X3,multiplication(X2,X)),X),true,leq(multiplication(star(X2),X3),X),true) = true,
inference(transitivity,[status(thm)],[c137,c139]) ).
cnf(c141,plain,
ifeq(leq(addition(strong_iteration(multiplication(star(X),X2)),multiplication(X2,strong_iteration(multiplication(star(X),X2)))),strong_iteration(multiplication(star(X),X2))),true,leq(multiplication(star(X2),strong_iteration(multiplication(star(X),X2))),strong_iteration(multiplication(star(X),X2))),true) = true,
inference(substitution,[status(thm)],[c140]) ).
cnf(c142,plain,
ifeq(leq(multiplication(addition(X2,one),strong_iteration(multiplication(star(X),X2))),strong_iteration(multiplication(star(X),X2))),true,leq(multiplication(star(X2),strong_iteration(multiplication(star(X),X2))),strong_iteration(multiplication(star(X),X2))),true) = true,
inference(transitivity,[status(thm)],[c133,c141]) ).
cnf(c143,plain,
ifeq(leq(strong_iteration(multiplication(star(X),X2)),strong_iteration(multiplication(star(X),X2))),true,leq(multiplication(star(X2),strong_iteration(multiplication(star(X),X2))),strong_iteration(multiplication(star(X),X2))),true) = true,
inference(transitivity,[status(thm)],[c129,c142]) ).
cnf(c144,plain,
ifeq(true,true,leq(multiplication(star(X2),strong_iteration(multiplication(star(X),X2))),strong_iteration(multiplication(star(X),X2))),true) = true,
inference(transitivity,[status(thm)],[c60,c143]) ).
cnf(c145,plain,
leq(multiplication(star(X2),strong_iteration(multiplication(star(X),X2))),strong_iteration(multiplication(star(X),X2))) = true,
inference(transitivity,[status(thm)],[c49,c144]) ).
cnf(c146,plain,
tuple(leq(multiplication(star(X2),strong_iteration(multiplication(star(X),X2))),strong_iteration(multiplication(star(X),X2))),true) = tuple(true,true),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
tuple(leq(multiplication(star(X4),strong_iteration(multiplication(star(X3),X4))),strong_iteration(multiplication(star(X3),X4))),leq(X2,multiplication(star(X),X2))) = tuple(true,true),
inference(transitivity,[status(thm)],[c46,c146]) ).
cnf(c148,plain,
tuple(leq(multiplication(star(sK1_goals_X1),strong_iteration(multiplication(star(sK2_goals_X0),sK1_goals_X1))),strong_iteration(multiplication(star(sK2_goals_X0),sK1_goals_X1))),leq(strong_iteration(multiplication(star(sK4_goals_X0),sK3_goals_X1)),multiplication(star(sK3_goals_X1),strong_iteration(multiplication(star(sK4_goals_X0),sK3_goals_X1))))) = tuple(true,true),
inference(substitution,[status(thm)],[c147]) ).
cnf(c149,plain,
$false,
inference(resolution,[status(thm)],[c1,c148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE147-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.41 % Computer : n020.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sun Sep 27 13:13:34 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 117.57/15.34 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
% 117.57/15.34
% 117.57/15.34 % SZS status Unsatisfiable
% 117.57/15.34
% 117.57/15.36 % SZS output start CNFRefutation
% See solution above
% 118.39/15.44
% 118.39/15.44 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------