%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : KLE090-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 11:39:48 AM UTC 2026
% Result : Unsatisfiable 2.91s 0.87s
% Output : CNFRefutation 2.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 13
% Syntax : Number of clauses : 130 ( 130 unt; 0 nHn; 63 RR)
% Number of literals : 130 ( 129 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 92 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
addition(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)) != antidomain(sK2_goals_X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_1) ).
cnf(c2,axiom,
addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
cnf(c3,plain,
addition(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)) = addition(antidomain(sK2_goals_X0),antidomain(sK1_goals_X1)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
addition(antidomain(antidomain(sK2_goals_X0)),X) = addition(X,antidomain(antidomain(sK2_goals_X0))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c5,plain,
addition(X,antidomain(antidomain(sK2_goals_X0))) = addition(antidomain(antidomain(sK2_goals_X0)),X),
inference(symmetry,[status(thm)],[c4]) ).
cnf(c6,plain,
multiplication(antidomain(sK1_goals_X1),addition(X,antidomain(antidomain(sK2_goals_X0)))) = multiplication(antidomain(sK1_goals_X1),addition(antidomain(antidomain(sK2_goals_X0)),X)),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,axiom,
multiplication(A2,addition(B2,C)) = addition(multiplication(A2,B2),multiplication(A2,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
cnf(c8,plain,
multiplication(antidomain(sK1_goals_X1),addition(antidomain(antidomain(sK2_goals_X0)),X)) = addition(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0))),multiplication(antidomain(sK1_goals_X1),X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,axiom,
multiplication(one,A2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
cnf(c10,plain,
multiplication(one,multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0)))) = multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0))) = multiplication(one,multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0)))),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,axiom,
addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
cnf(c13,plain,
addition(antidomain(multiplication(antidomain(sK1_goals_X1),sK2_goals_X0)),antidomain(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0))))) = antidomain(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0)))),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
antidomain(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0)))) = addition(antidomain(multiplication(antidomain(sK1_goals_X1),sK2_goals_X0)),antidomain(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0))))),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,axiom,
addition(sK2_goals_X0,sK1_goals_X1) = sK1_goals_X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c16,plain,
sK1_goals_X1 = addition(sK2_goals_X0,sK1_goals_X1),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
antidomain(sK1_goals_X1) = antidomain(addition(sK2_goals_X0,sK1_goals_X1)),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
multiplication(antidomain(sK1_goals_X1),sK2_goals_X0) = multiplication(antidomain(addition(sK2_goals_X0,sK1_goals_X1)),sK2_goals_X0),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
addition(X2,X) = addition(X,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c20,plain,
addition(X2,X) = addition(X,X2),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
multiplication(antidomain(X2),addition(X2,X)) = multiplication(antidomain(X2),addition(X,X2)),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
multiplication(antidomain(X2),addition(X,X2)) = addition(multiplication(antidomain(X2),X),multiplication(antidomain(X2),X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c23,axiom,
multiplication(antidomain(X0_2),X0_2) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
cnf(c24,plain,
multiplication(antidomain(X),X) = zero,
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
addition(multiplication(antidomain(X2),X),multiplication(antidomain(X2),X2)) = addition(multiplication(antidomain(X2),X),zero),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,axiom,
addition(A2,zero) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
cnf(c27,plain,
addition(multiplication(antidomain(X2),X),zero) = multiplication(antidomain(X2),X),
inference(substitution,[status(thm)],[c26]) ).
cnf(c28,plain,
addition(multiplication(antidomain(X2),X),multiplication(antidomain(X2),X2)) = multiplication(antidomain(X2),X),
inference(transitivity,[status(thm)],[c25,c27]) ).
cnf(c29,plain,
multiplication(antidomain(X2),addition(X,X2)) = multiplication(antidomain(X2),X),
inference(transitivity,[status(thm)],[c22,c28]) ).
cnf(c30,plain,
multiplication(antidomain(X2),addition(X2,X)) = multiplication(antidomain(X2),X),
inference(transitivity,[status(thm)],[c21,c29]) ).
cnf(c31,plain,
multiplication(antidomain(addition(sK2_goals_X0,sK1_goals_X1)),addition(addition(sK2_goals_X0,sK1_goals_X1),sK2_goals_X0)) = multiplication(antidomain(addition(sK2_goals_X0,sK1_goals_X1)),sK2_goals_X0),
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
multiplication(antidomain(addition(sK2_goals_X0,sK1_goals_X1)),sK2_goals_X0) = multiplication(antidomain(addition(sK2_goals_X0,sK1_goals_X1)),addition(addition(sK2_goals_X0,sK1_goals_X1),sK2_goals_X0)),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
addition(addition(sK2_goals_X0,sK1_goals_X1),X) = addition(sK1_goals_X1,X),
inference(congruence,[status(thm)],[c15]) ).
cnf(c34,plain,
addition(X,sK1_goals_X1) = addition(sK1_goals_X1,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c35,plain,
addition(sK1_goals_X1,X) = addition(X,sK1_goals_X1),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
addition(addition(sK2_goals_X0,sK1_goals_X1),X) = addition(X,sK1_goals_X1),
inference(transitivity,[status(thm)],[c33,c35]) ).
cnf(c37,plain,
addition(addition(sK2_goals_X0,sK1_goals_X1),sK2_goals_X0) = addition(sK2_goals_X0,sK1_goals_X1),
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
multiplication(antidomain(addition(sK2_goals_X0,sK1_goals_X1)),addition(addition(sK2_goals_X0,sK1_goals_X1),sK2_goals_X0)) = multiplication(antidomain(addition(sK2_goals_X0,sK1_goals_X1)),addition(sK2_goals_X0,sK1_goals_X1)),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
multiplication(antidomain(addition(sK2_goals_X0,sK1_goals_X1)),addition(sK2_goals_X0,sK1_goals_X1)) = zero,
inference(substitution,[status(thm)],[c23]) ).
cnf(c40,plain,
multiplication(antidomain(addition(sK2_goals_X0,sK1_goals_X1)),addition(addition(sK2_goals_X0,sK1_goals_X1),sK2_goals_X0)) = zero,
inference(transitivity,[status(thm)],[c38,c39]) ).
cnf(c41,plain,
multiplication(antidomain(addition(sK2_goals_X0,sK1_goals_X1)),sK2_goals_X0) = zero,
inference(transitivity,[status(thm)],[c32,c40]) ).
cnf(c42,plain,
multiplication(antidomain(sK1_goals_X1),sK2_goals_X0) = zero,
inference(transitivity,[status(thm)],[c18,c41]) ).
cnf(c43,plain,
antidomain(multiplication(antidomain(sK1_goals_X1),sK2_goals_X0)) = antidomain(zero),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
addition(antidomain(multiplication(antidomain(sK1_goals_X1),sK2_goals_X0)),antidomain(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0))))) = addition(antidomain(zero),antidomain(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0))))),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,axiom,
multiplication(A2,one) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
cnf(c46,plain,
multiplication(antidomain(one),one) = antidomain(one),
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
antidomain(one) = multiplication(antidomain(one),one),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
multiplication(antidomain(one),one) = zero,
inference(substitution,[status(thm)],[c23]) ).
cnf(c49,plain,
antidomain(one) = zero,
inference(transitivity,[status(thm)],[c47,c48]) ).
cnf(c50,plain,
zero = antidomain(one),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
antidomain(zero) = antidomain(antidomain(one)),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
addition(X,zero) = addition(zero,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c53,plain,
addition(zero,X) = addition(X,zero),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
addition(X,zero) = X,
inference(substitution,[status(thm)],[c26]) ).
cnf(c55,plain,
addition(zero,X) = X,
inference(transitivity,[status(thm)],[c53,c54]) ).
cnf(c56,plain,
addition(zero,antidomain(antidomain(one))) = antidomain(antidomain(one)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
antidomain(antidomain(one)) = addition(zero,antidomain(antidomain(one))),
inference(symmetry,[status(thm)],[c56]) ).
cnf(c58,plain,
zero = antidomain(one),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c59,plain,
addition(zero,antidomain(antidomain(one))) = addition(antidomain(one),antidomain(antidomain(one))),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
addition(antidomain(antidomain(X)),antidomain(X)) = addition(antidomain(X),antidomain(antidomain(X))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c61,plain,
addition(antidomain(X),antidomain(antidomain(X))) = addition(antidomain(antidomain(X)),antidomain(X)),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,axiom,
addition(antidomain(antidomain(X0_2)),antidomain(X0_2)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain3) ).
cnf(c63,plain,
addition(antidomain(antidomain(X)),antidomain(X)) = one,
inference(substitution,[status(thm)],[c62]) ).
cnf(c64,plain,
addition(antidomain(X),antidomain(antidomain(X))) = one,
inference(transitivity,[status(thm)],[c61,c63]) ).
cnf(c65,plain,
addition(antidomain(one),antidomain(antidomain(one))) = one,
inference(substitution,[status(thm)],[c64]) ).
cnf(c66,plain,
addition(zero,antidomain(antidomain(one))) = one,
inference(transitivity,[status(thm)],[c59,c65]) ).
cnf(c67,plain,
antidomain(antidomain(one)) = one,
inference(transitivity,[status(thm)],[c57,c66]) ).
cnf(c68,plain,
antidomain(zero) = one,
inference(transitivity,[status(thm)],[c51,c67]) ).
cnf(c69,plain,
addition(antidomain(zero),antidomain(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0))))) = addition(one,antidomain(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0))))),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
addition(antidomain(X),one) = addition(one,antidomain(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c71,plain,
addition(one,antidomain(X)) = addition(antidomain(X),one),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c72,plain,
one = addition(antidomain(X),antidomain(antidomain(X))),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c73,plain,
addition(antidomain(X),one) = addition(antidomain(X),addition(antidomain(X),antidomain(antidomain(X)))),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,axiom,
addition(A2,addition(B2,C2)) = addition(addition(A2,B2),C2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
cnf(c75,plain,
addition(X2,addition(X2,X)) = addition(addition(X2,X2),X),
inference(substitution,[status(thm)],[c74]) ).
cnf(c76,axiom,
addition(A2,A2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
cnf(c77,plain,
addition(X,X) = X,
inference(substitution,[status(thm)],[c76]) ).
cnf(c78,plain,
addition(addition(X2,X2),X) = addition(X2,X),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
addition(X2,addition(X2,X)) = addition(X2,X),
inference(transitivity,[status(thm)],[c75,c78]) ).
cnf(c80,plain,
addition(antidomain(X),addition(antidomain(X),antidomain(antidomain(X)))) = addition(antidomain(X),antidomain(antidomain(X))),
inference(substitution,[status(thm)],[c79]) ).
cnf(c81,plain,
addition(antidomain(X),addition(antidomain(X),antidomain(antidomain(X)))) = one,
inference(transitivity,[status(thm)],[c80,c64]) ).
cnf(c82,plain,
addition(antidomain(X),one) = one,
inference(transitivity,[status(thm)],[c73,c81]) ).
cnf(c83,plain,
addition(one,antidomain(X)) = one,
inference(transitivity,[status(thm)],[c71,c82]) ).
cnf(c84,plain,
addition(one,antidomain(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0))))) = one,
inference(substitution,[status(thm)],[c83]) ).
cnf(c85,plain,
addition(antidomain(zero),antidomain(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0))))) = one,
inference(transitivity,[status(thm)],[c69,c84]) ).
cnf(c86,plain,
addition(antidomain(multiplication(antidomain(sK1_goals_X1),sK2_goals_X0)),antidomain(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0))))) = one,
inference(transitivity,[status(thm)],[c44,c85]) ).
cnf(c87,plain,
antidomain(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0)))) = one,
inference(transitivity,[status(thm)],[c14,c86]) ).
cnf(c88,plain,
one = antidomain(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0)))),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c89,plain,
multiplication(one,multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0)))) = multiplication(antidomain(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0)))),multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0)))),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
multiplication(antidomain(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0)))),multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0)))) = zero,
inference(substitution,[status(thm)],[c23]) ).
cnf(c91,plain,
multiplication(one,multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0)))) = zero,
inference(transitivity,[status(thm)],[c89,c90]) ).
cnf(c92,plain,
multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0))) = zero,
inference(transitivity,[status(thm)],[c11,c91]) ).
cnf(c93,plain,
addition(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0))),multiplication(antidomain(sK1_goals_X1),X)) = addition(zero,multiplication(antidomain(sK1_goals_X1),X)),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
addition(zero,multiplication(antidomain(sK1_goals_X1),X)) = multiplication(antidomain(sK1_goals_X1),X),
inference(substitution,[status(thm)],[c55]) ).
cnf(c95,plain,
addition(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0))),multiplication(antidomain(sK1_goals_X1),X)) = multiplication(antidomain(sK1_goals_X1),X),
inference(transitivity,[status(thm)],[c93,c94]) ).
cnf(c96,plain,
multiplication(antidomain(sK1_goals_X1),addition(antidomain(antidomain(sK2_goals_X0)),X)) = multiplication(antidomain(sK1_goals_X1),X),
inference(transitivity,[status(thm)],[c8,c95]) ).
cnf(c97,plain,
multiplication(antidomain(sK1_goals_X1),addition(X,antidomain(antidomain(sK2_goals_X0)))) = multiplication(antidomain(sK1_goals_X1),X),
inference(transitivity,[status(thm)],[c6,c96]) ).
cnf(c98,plain,
multiplication(antidomain(sK1_goals_X1),addition(antidomain(sK2_goals_X0),antidomain(antidomain(sK2_goals_X0)))) = multiplication(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)),
inference(substitution,[status(thm)],[c97]) ).
cnf(c99,plain,
multiplication(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)) = multiplication(antidomain(sK1_goals_X1),addition(antidomain(sK2_goals_X0),antidomain(antidomain(sK2_goals_X0)))),
inference(symmetry,[status(thm)],[c98]) ).
cnf(c100,plain,
addition(antidomain(sK2_goals_X0),antidomain(antidomain(sK2_goals_X0))) = one,
inference(substitution,[status(thm)],[c64]) ).
cnf(c101,plain,
multiplication(antidomain(sK1_goals_X1),addition(antidomain(sK2_goals_X0),antidomain(antidomain(sK2_goals_X0)))) = multiplication(antidomain(sK1_goals_X1),one),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
multiplication(antidomain(sK1_goals_X1),one) = antidomain(sK1_goals_X1),
inference(substitution,[status(thm)],[c45]) ).
cnf(c103,plain,
multiplication(antidomain(sK1_goals_X1),addition(antidomain(sK2_goals_X0),antidomain(antidomain(sK2_goals_X0)))) = antidomain(sK1_goals_X1),
inference(transitivity,[status(thm)],[c101,c102]) ).
cnf(c104,plain,
multiplication(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)) = antidomain(sK1_goals_X1),
inference(transitivity,[status(thm)],[c99,c103]) ).
cnf(c105,plain,
antidomain(sK1_goals_X1) = multiplication(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
addition(antidomain(sK2_goals_X0),antidomain(sK1_goals_X1)) = addition(antidomain(sK2_goals_X0),multiplication(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0))),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
addition(one,X) = addition(X,one),
inference(substitution,[status(thm)],[c2]) ).
cnf(c108,plain,
addition(X,one) = addition(one,X),
inference(symmetry,[status(thm)],[c107]) ).
cnf(c109,plain,
multiplication(addition(X2,one),X) = multiplication(addition(one,X2),X),
inference(congruence,[status(thm)],[c108]) ).
cnf(c110,axiom,
multiplication(addition(A2,B2),C2) = addition(multiplication(A2,C2),multiplication(B2,C2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
cnf(c111,plain,
multiplication(addition(one,X2),X) = addition(multiplication(one,X),multiplication(X2,X)),
inference(substitution,[status(thm)],[c110]) ).
cnf(c112,plain,
multiplication(one,X) = X,
inference(substitution,[status(thm)],[c9]) ).
cnf(c113,plain,
addition(multiplication(one,X),multiplication(X2,X)) = addition(X,multiplication(X2,X)),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,plain,
multiplication(addition(one,X2),X) = addition(X,multiplication(X2,X)),
inference(transitivity,[status(thm)],[c111,c113]) ).
cnf(c115,plain,
multiplication(addition(X2,one),X) = addition(X,multiplication(X2,X)),
inference(transitivity,[status(thm)],[c109,c114]) ).
cnf(c116,plain,
multiplication(addition(antidomain(sK1_goals_X1),one),antidomain(sK2_goals_X0)) = addition(antidomain(sK2_goals_X0),multiplication(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0))),
inference(substitution,[status(thm)],[c115]) ).
cnf(c117,plain,
addition(antidomain(sK2_goals_X0),multiplication(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0))) = multiplication(addition(antidomain(sK1_goals_X1),one),antidomain(sK2_goals_X0)),
inference(symmetry,[status(thm)],[c116]) ).
cnf(c118,plain,
one = addition(antidomain(X),antidomain(antidomain(X))),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c119,plain,
addition(antidomain(X),one) = addition(antidomain(X),addition(antidomain(X),antidomain(antidomain(X)))),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
addition(antidomain(X),addition(antidomain(X),antidomain(antidomain(X)))) = addition(antidomain(X),antidomain(antidomain(X))),
inference(substitution,[status(thm)],[c79]) ).
cnf(c121,plain,
addition(antidomain(X),addition(antidomain(X),antidomain(antidomain(X)))) = one,
inference(transitivity,[status(thm)],[c120,c64]) ).
cnf(c122,plain,
addition(antidomain(X),one) = one,
inference(transitivity,[status(thm)],[c119,c121]) ).
cnf(c123,plain,
addition(antidomain(sK1_goals_X1),one) = one,
inference(substitution,[status(thm)],[c122]) ).
cnf(c124,plain,
multiplication(addition(antidomain(sK1_goals_X1),one),antidomain(sK2_goals_X0)) = multiplication(one,antidomain(sK2_goals_X0)),
inference(congruence,[status(thm)],[c123]) ).
cnf(c125,plain,
multiplication(one,antidomain(sK2_goals_X0)) = antidomain(sK2_goals_X0),
inference(substitution,[status(thm)],[c9]) ).
cnf(c126,plain,
multiplication(addition(antidomain(sK1_goals_X1),one),antidomain(sK2_goals_X0)) = antidomain(sK2_goals_X0),
inference(transitivity,[status(thm)],[c124,c125]) ).
cnf(c127,plain,
addition(antidomain(sK2_goals_X0),multiplication(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0))) = antidomain(sK2_goals_X0),
inference(transitivity,[status(thm)],[c117,c126]) ).
cnf(c128,plain,
addition(antidomain(sK2_goals_X0),antidomain(sK1_goals_X1)) = antidomain(sK2_goals_X0),
inference(transitivity,[status(thm)],[c106,c127]) ).
cnf(c129,plain,
addition(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)) = antidomain(sK2_goals_X0),
inference(transitivity,[status(thm)],[c3,c128]) ).
cnf(c130,plain,
$false,
inference(resolution,[status(thm)],[c1,c129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE090-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n005.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 13:09:17 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.91/0.87 Command-line arguments: --flatten --complete-subsets
% 2.91/0.87
% 2.91/0.87 % SZS status Unsatisfiable
% 2.91/0.87
% 2.91/0.87 % SZS output start CNFRefutation
% See solution above
% 2.91/0.89
% 2.91/0.89 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------