%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE169-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 11:39:57 AM UTC 2026
% Result : Unsatisfiable 0.30s 0.78s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 13
% Syntax : Number of clauses : 137 ( 137 unt; 0 nHn; 14 RR)
% Number of literals : 137 ( 136 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 253 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a) ).
cnf(c2,axiom,
addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
cnf(c3,plain,
addition(X,multiplication(X2,X)) = addition(multiplication(X2,X),X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
addition(multiplication(X2,X),X) = addition(X,multiplication(X2,X)),
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(X2,multiplication(X,X2)) = addition(multiplication(one,X2),multiplication(X,X2)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,axiom,
multiplication(addition(A2,B2),C) = addition(multiplication(A2,C),multiplication(B2,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
cnf(c10,plain,
multiplication(addition(one,X),X2) = addition(multiplication(one,X2),multiplication(X,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
addition(multiplication(one,X2),multiplication(X,X2)) = multiplication(addition(one,X),X2),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
addition(one,X) = addition(X,one),
inference(substitution,[status(thm)],[c2]) ).
cnf(c13,plain,
multiplication(addition(one,X),X2) = multiplication(addition(X,one),X2),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
addition(multiplication(one,X2),multiplication(X,X2)) = multiplication(addition(X,one),X2),
inference(transitivity,[status(thm)],[c11,c13]) ).
cnf(c15,plain,
addition(X2,multiplication(X,X2)) = multiplication(addition(X,one),X2),
inference(transitivity,[status(thm)],[c8,c14]) ).
cnf(c16,plain,
addition(X,multiplication(X2,X)) = multiplication(addition(X2,one),X),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
addition(X,one) = addition(one,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c18,plain,
multiplication(addition(X2,one),X) = multiplication(addition(one,X2),X),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
addition(X,multiplication(X2,X)) = multiplication(addition(one,X2),X),
inference(transitivity,[status(thm)],[c16,c18]) ).
cnf(c20,plain,
addition(multiplication(X2,X),X) = multiplication(addition(one,X2),X),
inference(transitivity,[status(thm)],[c4,c19]) ).
cnf(c21,plain,
addition(multiplication(star(X2),X),X) = multiplication(addition(one,star(X2)),X),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
addition(star(X),multiplication(X,star(X))) = multiplication(addition(X,one),star(X)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c23,plain,
multiplication(addition(X,one),star(X)) = addition(star(X),multiplication(X,star(X))),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
addition(one,multiplication(addition(X,one),star(X))) = addition(one,addition(star(X),multiplication(X,star(X)))),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
addition(multiplication(X,star(X)),star(X)) = addition(star(X),multiplication(X,star(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c26,plain,
addition(star(X),multiplication(X,star(X))) = addition(multiplication(X,star(X)),star(X)),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
addition(one,addition(star(X),multiplication(X,star(X)))) = addition(one,addition(multiplication(X,star(X)),star(X))),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,axiom,
addition(A2,addition(B2,C2)) = addition(addition(A2,B2),C2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
cnf(c29,plain,
addition(one,addition(multiplication(X,star(X)),star(X))) = addition(addition(one,multiplication(X,star(X))),star(X)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,axiom,
ifeq2(A2,A2,B2,C2) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(c31,plain,
ifeq2(true,true,addition(addition(one,multiplication(X,star(X))),star(X)),star(X)) = addition(addition(one,multiplication(X,star(X))),star(X)),
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
addition(addition(one,multiplication(X,star(X))),star(X)) = ifeq2(true,true,addition(addition(one,multiplication(X,star(X))),star(X)),star(X)),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,axiom,
leq(addition(one,multiplication(A2,star(A2))),star(A2)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold_right) ).
cnf(c34,plain,
leq(addition(one,multiplication(X,star(X))),star(X)) = true,
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
true = leq(addition(one,multiplication(X,star(X))),star(X)),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
ifeq2(true,true,addition(addition(one,multiplication(X,star(X))),star(X)),star(X)) = ifeq2(leq(addition(one,multiplication(X,star(X))),star(X)),true,addition(addition(one,multiplication(X,star(X))),star(X)),star(X)),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,axiom,
ifeq2(leq(A2,B2),true,addition(A2,B2),B2) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order_1) ).
cnf(c38,plain,
ifeq2(leq(addition(one,multiplication(X,star(X))),star(X)),true,addition(addition(one,multiplication(X,star(X))),star(X)),star(X)) = star(X),
inference(substitution,[status(thm)],[c37]) ).
cnf(c39,plain,
ifeq2(true,true,addition(addition(one,multiplication(X,star(X))),star(X)),star(X)) = star(X),
inference(transitivity,[status(thm)],[c36,c38]) ).
cnf(c40,plain,
addition(addition(one,multiplication(X,star(X))),star(X)) = star(X),
inference(transitivity,[status(thm)],[c32,c39]) ).
cnf(c41,plain,
addition(one,addition(multiplication(X,star(X)),star(X))) = star(X),
inference(transitivity,[status(thm)],[c29,c40]) ).
cnf(c42,plain,
addition(one,addition(star(X),multiplication(X,star(X)))) = star(X),
inference(transitivity,[status(thm)],[c27,c41]) ).
cnf(c43,plain,
addition(one,multiplication(addition(X,one),star(X))) = star(X),
inference(transitivity,[status(thm)],[c24,c42]) ).
cnf(c44,plain,
star(X) = addition(one,multiplication(addition(X,one),star(X))),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
addition(one,star(X)) = addition(one,addition(one,multiplication(addition(X,one),star(X)))),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
addition(X2,addition(X2,X)) = addition(addition(X2,X2),X),
inference(substitution,[status(thm)],[c28]) ).
cnf(c47,axiom,
addition(A2,A2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
cnf(c48,plain,
addition(X,X) = X,
inference(substitution,[status(thm)],[c47]) ).
cnf(c49,plain,
addition(addition(X2,X2),X) = addition(X2,X),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
addition(X2,addition(X2,X)) = addition(X2,X),
inference(transitivity,[status(thm)],[c46,c49]) ).
cnf(c51,plain,
addition(one,addition(one,multiplication(addition(X,one),star(X)))) = addition(one,multiplication(addition(X,one),star(X))),
inference(substitution,[status(thm)],[c50]) ).
cnf(c52,plain,
addition(one,addition(one,multiplication(addition(X,one),star(X)))) = star(X),
inference(transitivity,[status(thm)],[c51,c43]) ).
cnf(c53,plain,
addition(one,star(X)) = star(X),
inference(transitivity,[status(thm)],[c45,c52]) ).
cnf(c54,plain,
multiplication(addition(one,star(X2)),X) = multiplication(star(X2),X),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
addition(multiplication(star(X2),X),X) = multiplication(star(X2),X),
inference(transitivity,[status(thm)],[c21,c54]) ).
cnf(c56,plain,
addition(multiplication(star(X3),multiplication(X2,multiplication(sigma,X))),multiplication(X2,multiplication(sigma,X))) = multiplication(star(X3),multiplication(X2,multiplication(sigma,X))),
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
multiplication(star(X),multiplication(X3,multiplication(sigma,X2))) = addition(multiplication(star(X),multiplication(X3,multiplication(sigma,X2))),multiplication(X3,multiplication(sigma,X2))),
inference(symmetry,[status(thm)],[c56]) ).
cnf(c58,plain,
leq(multiplication(X3,multiplication(b,X2)),multiplication(star(X),multiplication(X3,multiplication(sigma,X2)))) = leq(multiplication(X3,multiplication(b,X2)),addition(multiplication(star(X),multiplication(X3,multiplication(sigma,X2))),multiplication(X3,multiplication(sigma,X2)))),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
addition(X,multiplication(X3,multiplication(b,X2))) = addition(multiplication(X3,multiplication(b,X2)),X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c60,plain,
addition(multiplication(X3,multiplication(b,X2)),X) = addition(X,multiplication(X3,multiplication(b,X2))),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c61,plain,
addition(multiplication(X3,multiplication(sigma,X2)),addition(multiplication(X3,multiplication(b,X2)),X)) = addition(multiplication(X3,multiplication(sigma,X2)),addition(X,multiplication(X3,multiplication(b,X2)))),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
addition(multiplication(X3,multiplication(b,X2)),X) = addition(X,multiplication(X3,multiplication(b,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c63,plain,
addition(X,multiplication(X3,multiplication(b,X2))) = addition(multiplication(X3,multiplication(b,X2)),X),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
addition(multiplication(X3,multiplication(sigma,X2)),addition(X,multiplication(X3,multiplication(b,X2)))) = addition(multiplication(X3,multiplication(sigma,X2)),addition(multiplication(X3,multiplication(b,X2)),X)),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
addition(multiplication(X3,multiplication(sigma,X2)),addition(multiplication(X3,multiplication(b,X2)),X)) = addition(addition(multiplication(X3,multiplication(sigma,X2)),multiplication(X3,multiplication(b,X2))),X),
inference(substitution,[status(thm)],[c28]) ).
cnf(c66,axiom,
multiplication(A2,addition(B2,C2)) = addition(multiplication(A2,B2),multiplication(A2,C2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
cnf(c67,plain,
multiplication(X3,addition(X2,X)) = addition(multiplication(X3,X2),multiplication(X3,X)),
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
addition(multiplication(X3,X2),multiplication(X3,X)) = multiplication(X3,addition(X2,X)),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
addition(X2,X) = addition(X,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c70,plain,
multiplication(X3,addition(X2,X)) = multiplication(X3,addition(X,X2)),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
addition(multiplication(X3,X2),multiplication(X3,X)) = multiplication(X3,addition(X,X2)),
inference(transitivity,[status(thm)],[c68,c70]) ).
cnf(c72,plain,
addition(multiplication(X2,multiplication(sigma,X)),multiplication(X2,multiplication(b,X))) = multiplication(X2,addition(multiplication(b,X),multiplication(sigma,X))),
inference(substitution,[status(thm)],[c71]) ).
cnf(c73,plain,
addition(multiplication(b,X),multiplication(sigma,X)) = addition(multiplication(sigma,X),multiplication(b,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c74,plain,
multiplication(X2,addition(multiplication(b,X),multiplication(sigma,X))) = multiplication(X2,addition(multiplication(sigma,X),multiplication(b,X))),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
addition(multiplication(b,X),multiplication(sigma,X)) = addition(multiplication(sigma,X),multiplication(b,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c76,plain,
addition(multiplication(sigma,X),multiplication(b,X)) = addition(multiplication(b,X),multiplication(sigma,X)),
inference(symmetry,[status(thm)],[c75]) ).
cnf(c77,plain,
multiplication(addition(X3,X),X2) = addition(multiplication(X3,X2),multiplication(X,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c78,plain,
addition(multiplication(X3,X2),multiplication(X,X2)) = multiplication(addition(X3,X),X2),
inference(symmetry,[status(thm)],[c77]) ).
cnf(c79,plain,
addition(X2,X) = addition(X,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c80,plain,
multiplication(addition(X3,X),X2) = multiplication(addition(X,X3),X2),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
addition(multiplication(X3,X2),multiplication(X,X2)) = multiplication(addition(X,X3),X2),
inference(transitivity,[status(thm)],[c78,c80]) ).
cnf(c82,plain,
addition(multiplication(b,X),multiplication(sigma,X)) = multiplication(addition(sigma,b),X),
inference(substitution,[status(thm)],[c81]) ).
cnf(c83,plain,
addition(b,sigma) = addition(sigma,b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c84,plain,
addition(sigma,b) = addition(b,sigma),
inference(symmetry,[status(thm)],[c83]) ).
cnf(c85,axiom,
sigma = addition(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c86,plain,
addition(b,sigma) = addition(b,addition(a,b)),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
addition(X2,X) = addition(X,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c88,plain,
addition(X,X2) = addition(X2,X),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c89,plain,
addition(X2,addition(X,X2)) = addition(X2,addition(X2,X)),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
addition(X2,addition(X,X2)) = addition(X2,X),
inference(transitivity,[status(thm)],[c89,c50]) ).
cnf(c91,plain,
addition(b,addition(a,b)) = addition(b,a),
inference(substitution,[status(thm)],[c90]) ).
cnf(c92,plain,
addition(b,a) = addition(a,b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c93,plain,
addition(a,b) = sigma,
inference(symmetry,[status(thm)],[c85]) ).
cnf(c94,plain,
addition(b,a) = sigma,
inference(transitivity,[status(thm)],[c92,c93]) ).
cnf(c95,plain,
addition(b,addition(a,b)) = sigma,
inference(transitivity,[status(thm)],[c91,c94]) ).
cnf(c96,plain,
addition(b,sigma) = sigma,
inference(transitivity,[status(thm)],[c86,c95]) ).
cnf(c97,plain,
addition(sigma,b) = sigma,
inference(transitivity,[status(thm)],[c84,c96]) ).
cnf(c98,plain,
multiplication(addition(sigma,b),X) = multiplication(sigma,X),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
addition(multiplication(b,X),multiplication(sigma,X)) = multiplication(sigma,X),
inference(transitivity,[status(thm)],[c82,c98]) ).
cnf(c100,plain,
addition(multiplication(sigma,X),multiplication(b,X)) = multiplication(sigma,X),
inference(transitivity,[status(thm)],[c76,c99]) ).
cnf(c101,plain,
multiplication(X2,addition(multiplication(sigma,X),multiplication(b,X))) = multiplication(X2,multiplication(sigma,X)),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
multiplication(X2,addition(multiplication(b,X),multiplication(sigma,X))) = multiplication(X2,multiplication(sigma,X)),
inference(transitivity,[status(thm)],[c74,c101]) ).
cnf(c103,plain,
addition(multiplication(X2,multiplication(sigma,X)),multiplication(X2,multiplication(b,X))) = multiplication(X2,multiplication(sigma,X)),
inference(transitivity,[status(thm)],[c72,c102]) ).
cnf(c104,plain,
addition(addition(multiplication(X3,multiplication(sigma,X2)),multiplication(X3,multiplication(b,X2))),X) = addition(multiplication(X3,multiplication(sigma,X2)),X),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
addition(multiplication(X3,multiplication(sigma,X2)),X) = addition(X,multiplication(X3,multiplication(sigma,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c106,plain,
addition(addition(multiplication(X3,multiplication(sigma,X2)),multiplication(X3,multiplication(b,X2))),X) = addition(X,multiplication(X3,multiplication(sigma,X2))),
inference(transitivity,[status(thm)],[c104,c105]) ).
cnf(c107,plain,
addition(multiplication(X3,multiplication(sigma,X2)),addition(multiplication(X3,multiplication(b,X2)),X)) = addition(X,multiplication(X3,multiplication(sigma,X2))),
inference(transitivity,[status(thm)],[c65,c106]) ).
cnf(c108,plain,
addition(multiplication(X3,multiplication(sigma,X2)),addition(X,multiplication(X3,multiplication(b,X2)))) = addition(X,multiplication(X3,multiplication(sigma,X2))),
inference(transitivity,[status(thm)],[c64,c107]) ).
cnf(c109,plain,
addition(multiplication(X3,multiplication(sigma,X2)),addition(multiplication(X3,multiplication(b,X2)),X)) = addition(X,multiplication(X3,multiplication(sigma,X2))),
inference(transitivity,[status(thm)],[c61,c108]) ).
cnf(c110,plain,
addition(X,multiplication(X3,multiplication(sigma,X2))) = addition(multiplication(X3,multiplication(sigma,X2)),addition(multiplication(X3,multiplication(b,X2)),X)),
inference(symmetry,[status(thm)],[c109]) ).
cnf(c111,plain,
leq(multiplication(X3,multiplication(b,X2)),addition(X,multiplication(X3,multiplication(sigma,X2)))) = leq(multiplication(X3,multiplication(b,X2)),addition(multiplication(X3,multiplication(sigma,X2)),addition(multiplication(X3,multiplication(b,X2)),X))),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
addition(addition(X3,X),X2) = addition(X2,addition(X3,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c113,plain,
addition(X2,addition(X3,X)) = addition(addition(X3,X),X2),
inference(symmetry,[status(thm)],[c112]) ).
cnf(c114,plain,
addition(X3,addition(X,X2)) = addition(addition(X3,X),X2),
inference(substitution,[status(thm)],[c28]) ).
cnf(c115,plain,
addition(addition(X3,X),X2) = addition(X3,addition(X,X2)),
inference(symmetry,[status(thm)],[c114]) ).
cnf(c116,plain,
addition(X,X2) = addition(X2,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c117,plain,
addition(X3,addition(X,X2)) = addition(X3,addition(X2,X)),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
addition(addition(X3,X),X2) = addition(X3,addition(X2,X)),
inference(transitivity,[status(thm)],[c115,c117]) ).
cnf(c119,plain,
addition(X2,addition(X3,X)) = addition(X3,addition(X2,X)),
inference(transitivity,[status(thm)],[c113,c118]) ).
cnf(c120,plain,
leq(X3,addition(X2,addition(X3,X))) = leq(X3,addition(X3,addition(X2,X))),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,axiom,
ifeq3(A2,A2,B2,C2) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c122,plain,
ifeq3(addition(X2,X),addition(X2,X),leq(X2,addition(X2,X)),true) = leq(X2,addition(X2,X)),
inference(substitution,[status(thm)],[c121]) ).
cnf(c123,plain,
leq(X2,addition(X2,X)) = ifeq3(addition(X2,X),addition(X2,X),leq(X2,addition(X2,X)),true),
inference(symmetry,[status(thm)],[c122]) ).
cnf(c124,plain,
addition(X2,X) = addition(X2,addition(X2,X)),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c125,plain,
ifeq3(addition(X2,X),addition(X2,X),leq(X2,addition(X2,X)),true) = ifeq3(addition(X2,addition(X2,X)),addition(X2,X),leq(X2,addition(X2,X)),true),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,axiom,
ifeq3(addition(A2,B2),B2,leq(A2,B2),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
cnf(c127,plain,
ifeq3(addition(X2,addition(X2,X)),addition(X2,X),leq(X2,addition(X2,X)),true) = true,
inference(substitution,[status(thm)],[c126]) ).
cnf(c128,plain,
ifeq3(addition(X2,X),addition(X2,X),leq(X2,addition(X2,X)),true) = true,
inference(transitivity,[status(thm)],[c125,c127]) ).
cnf(c129,plain,
leq(X2,addition(X2,X)) = true,
inference(transitivity,[status(thm)],[c123,c128]) ).
cnf(c130,plain,
leq(X3,addition(X3,addition(X2,X))) = true,
inference(substitution,[status(thm)],[c129]) ).
cnf(c131,plain,
leq(X3,addition(X2,addition(X3,X))) = true,
inference(transitivity,[status(thm)],[c120,c130]) ).
cnf(c132,plain,
leq(multiplication(X3,multiplication(b,X2)),addition(multiplication(X3,multiplication(sigma,X2)),addition(multiplication(X3,multiplication(b,X2)),X))) = true,
inference(substitution,[status(thm)],[c131]) ).
cnf(c133,plain,
leq(multiplication(X3,multiplication(b,X2)),addition(X,multiplication(X3,multiplication(sigma,X2)))) = true,
inference(transitivity,[status(thm)],[c111,c132]) ).
cnf(c134,plain,
leq(multiplication(X3,multiplication(b,X2)),addition(multiplication(star(X),multiplication(X3,multiplication(sigma,X2))),multiplication(X3,multiplication(sigma,X2)))) = true,
inference(substitution,[status(thm)],[c133]) ).
cnf(c135,plain,
leq(multiplication(X3,multiplication(b,X2)),multiplication(star(X),multiplication(X3,multiplication(sigma,X2)))) = true,
inference(transitivity,[status(thm)],[c58,c134]) ).
cnf(c136,plain,
leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))) = true,
inference(substitution,[status(thm)],[c135]) ).
cnf(c137,plain,
$false,
inference(resolution,[status(thm)],[c1,c136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE169-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.46 % Computer : n015.cluster.edu
% 0.18/0.46 % Model : x86_64 x86_64
% 0.18/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46 % Memory : 8046.5625MB
% 0.18/0.46 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Sun Sep 27 13:17:30 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.30/0.78 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.30/0.78
% 0.30/0.78 % SZS status Unsatisfiable
% 0.30/0.78
% 0.30/0.80 % SZS output start CNFRefutation
% See solution above
% 0.31/0.92
% 0.31/0.92 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------