%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ALG005-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 09:06:53 AM UTC 2026
% Result : Unsatisfiable 1.48s 0.52s
% Output : CNFRefutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 57
% Number of leaves : 5
% Syntax : Number of clauses : 303 ( 303 unt; 0 nHn; 11 RR)
% Number of literals : 303 ( 302 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 748 ( 46 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_associativity_of_multiply) ).
cnf(c2,axiom,
multiply(X,Y) = difference(X,difference(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
cnf(c3,plain,
multiply(X2,X3) = difference(X2,difference(X2,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,axiom,
difference(X2,difference(X2,Y2)) = difference(Y2,difference(Y2,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_2) ).
cnf(c5,plain,
difference(X3,difference(X3,X2)) = difference(X2,difference(X2,X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
difference(X2,difference(X2,X3)) = difference(X3,difference(X3,X2)),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(X3,X2) = difference(X3,difference(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c8,plain,
difference(X3,difference(X3,X2)) = multiply(X3,X2),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
difference(X2,difference(X2,X3)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c6,c8]) ).
cnf(c10,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c3,c9]) ).
cnf(c11,plain,
multiply(c,multiply(a,b)) = multiply(multiply(a,b),c),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
multiply(multiply(a,b),c) = multiply(c,multiply(a,b)),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(substitution,[status(thm)],[c10]) ).
cnf(c14,plain,
multiply(X3,multiply(X4,X2)) = multiply(X3,multiply(X2,X4)),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
multiply(X2,X3) = difference(X2,difference(X2,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c16,plain,
multiply(X3,multiply(X2,X4)) = multiply(X3,difference(X2,difference(X2,X4))),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
multiply(X4,difference(X3,X2)) = multiply(difference(X3,X2),X4),
inference(substitution,[status(thm)],[c10]) ).
cnf(c18,plain,
difference(multiply(X4,difference(X3,X2)),X2) = difference(multiply(difference(X3,X2),X4),X2),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
multiply(difference(X4,X3),difference(X2,X3)) = multiply(difference(X2,X3),difference(X4,X3)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c20,plain,
multiply(difference(X2,X3),difference(X4,X3)) = difference(difference(X2,X3),difference(difference(X2,X3),difference(X4,X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c21,axiom,
difference(difference(X2,Y2),Z) = difference(difference(X2,Z),difference(Y2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_3) ).
cnf(c22,plain,
difference(difference(X2,X4),X3) = difference(difference(X2,X3),difference(X4,X3)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
difference(difference(X2,X3),difference(X4,X3)) = difference(difference(X2,X4),X3),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
difference(difference(X2,X3),difference(difference(X2,X3),difference(X4,X3))) = difference(difference(X2,X3),difference(difference(X2,X4),X3)),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
difference(difference(X2,difference(X2,X4)),X3) = difference(difference(X2,X3),difference(difference(X2,X4),X3)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c26,plain,
difference(difference(X2,X3),difference(difference(X2,X4),X3)) = difference(difference(X2,difference(X2,X4)),X3),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
multiply(X2,X3) = difference(X2,difference(X2,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c28,plain,
difference(X2,difference(X2,X3)) = multiply(X2,X3),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
difference(difference(X2,difference(X2,X4)),X3) = difference(multiply(X2,X4),X3),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(substitution,[status(thm)],[c10]) ).
cnf(c31,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
difference(multiply(X2,X4),X3) = difference(multiply(X4,X2),X3),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
difference(difference(X2,difference(X2,X4)),X3) = difference(multiply(X4,X2),X3),
inference(transitivity,[status(thm)],[c29,c32]) ).
cnf(c34,plain,
difference(difference(X2,X3),difference(difference(X2,X4),X3)) = difference(multiply(X4,X2),X3),
inference(transitivity,[status(thm)],[c26,c33]) ).
cnf(c35,plain,
difference(difference(X2,X3),difference(difference(X2,X3),difference(X4,X3))) = difference(multiply(X4,X2),X3),
inference(transitivity,[status(thm)],[c24,c34]) ).
cnf(c36,plain,
multiply(difference(X2,X3),difference(X4,X3)) = difference(multiply(X4,X2),X3),
inference(transitivity,[status(thm)],[c20,c35]) ).
cnf(c37,plain,
multiply(difference(X4,X3),difference(X2,X3)) = difference(multiply(X4,X2),X3),
inference(transitivity,[status(thm)],[c19,c36]) ).
cnf(c38,plain,
multiply(difference(difference(X3,X2),X2),difference(X4,X2)) = difference(multiply(difference(X3,X2),X4),X2),
inference(substitution,[status(thm)],[c37]) ).
cnf(c39,plain,
difference(multiply(difference(X3,X2),X4),X2) = multiply(difference(difference(X3,X2),X2),difference(X4,X2)),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,axiom,
difference(X2,difference(Y2,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_1) ).
cnf(c41,plain,
difference(X2,difference(X3,X2)) = X2,
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
X2 = difference(X2,difference(X3,X2)),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
difference(difference(X3,X2),X2) = difference(difference(X3,X2),difference(X2,difference(X3,X2))),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
difference(difference(X3,X2),difference(X2,difference(X3,X2))) = difference(X3,X2),
inference(substitution,[status(thm)],[c40]) ).
cnf(c45,plain,
difference(difference(X3,X2),X2) = difference(X3,X2),
inference(transitivity,[status(thm)],[c43,c44]) ).
cnf(c46,plain,
multiply(difference(difference(X3,X2),X2),difference(X4,X2)) = multiply(difference(X3,X2),difference(X4,X2)),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
multiply(difference(X3,X2),difference(X4,X2)) = difference(multiply(X3,X4),X2),
inference(substitution,[status(thm)],[c37]) ).
cnf(c48,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(substitution,[status(thm)],[c10]) ).
cnf(c49,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
difference(multiply(X3,X4),X2) = difference(multiply(X4,X3),X2),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
multiply(difference(X3,X2),difference(X4,X2)) = difference(multiply(X4,X3),X2),
inference(transitivity,[status(thm)],[c47,c50]) ).
cnf(c52,plain,
multiply(difference(difference(X3,X2),X2),difference(X4,X2)) = difference(multiply(X4,X3),X2),
inference(transitivity,[status(thm)],[c46,c51]) ).
cnf(c53,plain,
difference(multiply(difference(X3,X2),X4),X2) = difference(multiply(X4,X3),X2),
inference(transitivity,[status(thm)],[c39,c52]) ).
cnf(c54,plain,
difference(multiply(X4,difference(X3,X2)),X2) = difference(multiply(X4,X3),X2),
inference(transitivity,[status(thm)],[c18,c53]) ).
cnf(c55,plain,
difference(multiply(X4,X3),X2) = difference(multiply(X4,difference(X3,X2)),X2),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,plain,
multiply(X3,difference(X3,X2)) = multiply(difference(X3,X2),X3),
inference(substitution,[status(thm)],[c10]) ).
cnf(c57,plain,
multiply(difference(X3,X2),X3) = difference(difference(X3,X2),difference(difference(X3,X2),X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c58,plain,
difference(difference(X4,X3),difference(X2,X4)) = difference(difference(X4,difference(X2,X4)),difference(X3,difference(X2,X4))),
inference(substitution,[status(thm)],[c21]) ).
cnf(c59,plain,
difference(X3,difference(X2,X3)) = X3,
inference(substitution,[status(thm)],[c40]) ).
cnf(c60,plain,
difference(difference(X4,difference(X2,X4)),difference(X3,difference(X2,X4))) = difference(X4,difference(X3,difference(X2,X4))),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
difference(difference(X4,X3),difference(X2,X4)) = difference(X4,difference(X3,difference(X2,X4))),
inference(transitivity,[status(thm)],[c58,c60]) ).
cnf(c62,plain,
difference(difference(X3,X2),difference(difference(X3,X2),X3)) = difference(X3,difference(X2,difference(difference(X3,X2),X3))),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
difference(X2,difference(X3,X2)) = X2,
inference(substitution,[status(thm)],[c40]) ).
cnf(c64,plain,
X2 = difference(X2,difference(X3,X2)),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,plain,
difference(difference(X4,difference(X3,X2)),X2) = difference(difference(X4,difference(X3,X2)),difference(X2,difference(X3,X2))),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
difference(difference(X4,X2),difference(X3,X2)) = difference(difference(X4,difference(X3,X2)),difference(X2,difference(X3,X2))),
inference(substitution,[status(thm)],[c21]) ).
cnf(c67,plain,
difference(difference(X4,difference(X3,X2)),difference(X2,difference(X3,X2))) = difference(difference(X4,X2),difference(X3,X2)),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
difference(difference(X4,X3),X2) = difference(difference(X4,X2),difference(X3,X2)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c69,plain,
difference(difference(X4,X2),difference(X3,X2)) = difference(difference(X4,X3),X2),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
difference(difference(X4,difference(X3,X2)),difference(X2,difference(X3,X2))) = difference(difference(X4,X3),X2),
inference(transitivity,[status(thm)],[c67,c69]) ).
cnf(c71,plain,
difference(difference(X4,difference(X3,X2)),X2) = difference(difference(X4,X3),X2),
inference(transitivity,[status(thm)],[c65,c70]) ).
cnf(c72,plain,
difference(difference(X3,difference(X2,X3)),X3) = difference(difference(X3,X2),X3),
inference(substitution,[status(thm)],[c71]) ).
cnf(c73,plain,
difference(difference(X3,X2),X3) = difference(difference(X3,difference(X2,X3)),X3),
inference(symmetry,[status(thm)],[c72]) ).
cnf(c74,plain,
difference(X3,difference(X2,X3)) = X3,
inference(substitution,[status(thm)],[c40]) ).
cnf(c75,plain,
difference(difference(X3,difference(X2,X3)),X3) = difference(X3,X3),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
difference(difference(X3,X2),X3) = difference(X3,X3),
inference(transitivity,[status(thm)],[c73,c75]) ).
cnf(c77,plain,
difference(X2,difference(difference(X3,X2),X3)) = difference(X2,difference(X3,X3)),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
difference(X3,difference(X2,difference(difference(X3,X2),X3))) = difference(X3,difference(X2,difference(X3,X3))),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(substitution,[status(thm)],[c10]) ).
cnf(c80,plain,
difference(multiply(X3,X2),multiply(X3,X2)) = difference(multiply(X2,X3),multiply(X3,X2)),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(substitution,[status(thm)],[c10]) ).
cnf(c82,plain,
difference(multiply(X2,X3),multiply(X3,X2)) = difference(multiply(X2,X3),multiply(X2,X3)),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
multiply(X2,X3) = difference(X2,difference(X2,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c84,plain,
difference(multiply(X2,X3),multiply(X2,X3)) = difference(multiply(X2,X3),difference(X2,difference(X2,X3))),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
multiply(X2,X3) = difference(X2,difference(X2,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c86,plain,
difference(multiply(X2,X3),difference(X2,difference(X2,X3))) = difference(difference(X2,difference(X2,X3)),difference(X2,difference(X2,X3))),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
multiply(X3,difference(X2,X3)) = difference(X3,difference(X3,difference(X2,X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c88,plain,
difference(X3,difference(X2,X3)) = X3,
inference(substitution,[status(thm)],[c40]) ).
cnf(c89,plain,
difference(X3,difference(X3,difference(X2,X3))) = difference(X3,X3),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
multiply(X3,difference(X2,X3)) = difference(X3,X3),
inference(transitivity,[status(thm)],[c87,c89]) ).
cnf(c91,plain,
multiply(difference(X3,X2),difference(X2,difference(X3,X2))) = difference(difference(X3,X2),difference(X3,X2)),
inference(substitution,[status(thm)],[c90]) ).
cnf(c92,plain,
difference(difference(X3,X2),difference(X3,X2)) = multiply(difference(X3,X2),difference(X2,difference(X3,X2))),
inference(symmetry,[status(thm)],[c91]) ).
cnf(c93,plain,
difference(X2,difference(X3,X2)) = X2,
inference(substitution,[status(thm)],[c40]) ).
cnf(c94,plain,
multiply(difference(X3,X2),difference(X2,difference(X3,X2))) = multiply(difference(X3,X2),X2),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
multiply(X2,difference(X3,X2)) = multiply(difference(X3,X2),X2),
inference(substitution,[status(thm)],[c10]) ).
cnf(c96,plain,
multiply(difference(X3,X2),X2) = multiply(X2,difference(X3,X2)),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c97,plain,
multiply(X2,difference(X3,X2)) = difference(X2,X2),
inference(substitution,[status(thm)],[c90]) ).
cnf(c98,plain,
multiply(difference(X3,X2),X2) = difference(X2,X2),
inference(transitivity,[status(thm)],[c96,c97]) ).
cnf(c99,plain,
multiply(difference(X3,X2),difference(X2,difference(X3,X2))) = difference(X2,X2),
inference(transitivity,[status(thm)],[c94,c98]) ).
cnf(c100,plain,
difference(difference(X3,X2),difference(X3,X2)) = difference(X2,X2),
inference(transitivity,[status(thm)],[c92,c99]) ).
cnf(c101,plain,
difference(difference(X2,difference(X2,X3)),difference(X2,difference(X2,X3))) = difference(difference(X2,X3),difference(X2,X3)),
inference(substitution,[status(thm)],[c100]) ).
cnf(c102,plain,
difference(difference(X2,X3),difference(X2,X3)) = difference(X3,X3),
inference(substitution,[status(thm)],[c100]) ).
cnf(c103,plain,
difference(difference(X2,difference(X2,X3)),difference(X2,difference(X2,X3))) = difference(X3,X3),
inference(transitivity,[status(thm)],[c101,c102]) ).
cnf(c104,plain,
difference(multiply(X2,X3),difference(X2,difference(X2,X3))) = difference(X3,X3),
inference(transitivity,[status(thm)],[c86,c103]) ).
cnf(c105,plain,
difference(multiply(X2,X3),multiply(X2,X3)) = difference(X3,X3),
inference(transitivity,[status(thm)],[c84,c104]) ).
cnf(c106,plain,
difference(multiply(X2,X3),multiply(X3,X2)) = difference(X3,X3),
inference(transitivity,[status(thm)],[c82,c105]) ).
cnf(c107,plain,
difference(multiply(X3,X2),multiply(X3,X2)) = difference(X3,X3),
inference(transitivity,[status(thm)],[c80,c106]) ).
cnf(c108,plain,
difference(X3,X3) = difference(multiply(X3,X2),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c107]) ).
cnf(c109,plain,
multiply(multiply(X3,X2),difference(difference(X3,X2),multiply(X3,X2))) = difference(multiply(X3,X2),multiply(X3,X2)),
inference(substitution,[status(thm)],[c90]) ).
cnf(c110,plain,
difference(multiply(X3,X2),multiply(X3,X2)) = multiply(multiply(X3,X2),difference(difference(X3,X2),multiply(X3,X2))),
inference(symmetry,[status(thm)],[c109]) ).
cnf(c111,plain,
multiply(X3,X2) = difference(X3,difference(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c112,plain,
difference(difference(X3,X2),multiply(X3,X2)) = difference(difference(X3,X2),difference(X3,difference(X3,X2))),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,plain,
difference(difference(X3,X2),difference(X3,difference(X3,X2))) = difference(X3,X2),
inference(substitution,[status(thm)],[c40]) ).
cnf(c114,plain,
difference(difference(X3,X2),multiply(X3,X2)) = difference(X3,X2),
inference(transitivity,[status(thm)],[c112,c113]) ).
cnf(c115,plain,
multiply(multiply(X3,X2),difference(difference(X3,X2),multiply(X3,X2))) = multiply(multiply(X3,X2),difference(X3,X2)),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
multiply(multiply(X3,X2),difference(X3,X2)) = multiply(difference(X3,X2),multiply(X3,X2)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c117,plain,
multiply(difference(X3,X2),multiply(X3,X2)) = difference(difference(X3,X2),difference(difference(X3,X2),multiply(X3,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c118,plain,
difference(difference(X3,X2),difference(difference(X3,X2),multiply(X3,X2))) = difference(difference(X3,X2),difference(X3,X2)),
inference(congruence,[status(thm)],[c114]) ).
cnf(c119,plain,
difference(difference(X3,X2),difference(difference(X3,X2),multiply(X3,X2))) = difference(X2,X2),
inference(transitivity,[status(thm)],[c118,c100]) ).
cnf(c120,plain,
multiply(difference(X3,X2),multiply(X3,X2)) = difference(X2,X2),
inference(transitivity,[status(thm)],[c117,c119]) ).
cnf(c121,plain,
multiply(multiply(X3,X2),difference(X3,X2)) = difference(X2,X2),
inference(transitivity,[status(thm)],[c116,c120]) ).
cnf(c122,plain,
multiply(multiply(X3,X2),difference(difference(X3,X2),multiply(X3,X2))) = difference(X2,X2),
inference(transitivity,[status(thm)],[c115,c121]) ).
cnf(c123,plain,
difference(multiply(X3,X2),multiply(X3,X2)) = difference(X2,X2),
inference(transitivity,[status(thm)],[c110,c122]) ).
cnf(c124,plain,
difference(X3,X3) = difference(X2,X2),
inference(transitivity,[status(thm)],[c108,c123]) ).
cnf(c125,plain,
difference(X3,difference(X4,X4)) = difference(X3,difference(X2,X2)),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
difference(X4,difference(X3,difference(X4,X4))) = difference(X4,difference(X3,difference(X2,X2))),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
difference(X2,X2) = difference(X3,X3),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c128,plain,
difference(X3,difference(X2,X2)) = difference(X3,difference(X3,X3)),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
multiply(X2,X2) = difference(X2,difference(X2,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c130,plain,
difference(X2,difference(X2,X2)) = multiply(X2,X2),
inference(symmetry,[status(thm)],[c129]) ).
cnf(c131,plain,
multiply(X2,X2) = difference(X2,difference(X2,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c132,plain,
difference(X2,difference(X2,X2)) = X2,
inference(substitution,[status(thm)],[c40]) ).
cnf(c133,plain,
multiply(X2,X2) = X2,
inference(transitivity,[status(thm)],[c131,c132]) ).
cnf(c134,plain,
difference(X2,difference(X2,X2)) = X2,
inference(transitivity,[status(thm)],[c130,c133]) ).
cnf(c135,plain,
difference(X3,difference(X2,X2)) = X3,
inference(transitivity,[status(thm)],[c128,c134]) ).
cnf(c136,plain,
difference(X4,difference(X3,difference(X2,X2))) = difference(X4,X3),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
difference(X3,difference(X2,difference(X3,X3))) = difference(X3,X2),
inference(transitivity,[status(thm)],[c126,c136]) ).
cnf(c138,plain,
difference(X3,difference(X2,difference(difference(X3,X2),X3))) = difference(X3,X2),
inference(transitivity,[status(thm)],[c78,c137]) ).
cnf(c139,plain,
difference(difference(X3,X2),difference(difference(X3,X2),X3)) = difference(X3,X2),
inference(transitivity,[status(thm)],[c62,c138]) ).
cnf(c140,plain,
multiply(difference(X3,X2),X3) = difference(X3,X2),
inference(transitivity,[status(thm)],[c57,c139]) ).
cnf(c141,plain,
multiply(X3,difference(X3,X2)) = difference(X3,X2),
inference(transitivity,[status(thm)],[c56,c140]) ).
cnf(c142,plain,
multiply(multiply(X4,difference(X3,X2)),difference(multiply(X4,difference(X3,X2)),X2)) = difference(multiply(X4,difference(X3,X2)),X2),
inference(substitution,[status(thm)],[c141]) ).
cnf(c143,plain,
difference(multiply(X4,difference(X3,X2)),X2) = multiply(multiply(X4,difference(X3,X2)),difference(multiply(X4,difference(X3,X2)),X2)),
inference(symmetry,[status(thm)],[c142]) ).
cnf(c144,plain,
difference(X3,multiply(X2,X3)) = difference(X3,multiply(X3,X2)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c145,plain,
multiply(X3,X2) = difference(X3,difference(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c146,plain,
difference(X3,multiply(X3,X2)) = difference(X3,difference(X3,difference(X3,X2))),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
multiply(X3,difference(X3,X2)) = difference(X3,difference(X3,difference(X3,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c148,plain,
difference(X3,difference(X3,difference(X3,X2))) = multiply(X3,difference(X3,X2)),
inference(symmetry,[status(thm)],[c147]) ).
cnf(c149,plain,
difference(X3,multiply(X3,X2)) = multiply(X3,difference(X3,X2)),
inference(transitivity,[status(thm)],[c146,c148]) ).
cnf(c150,plain,
difference(X3,multiply(X2,X3)) = multiply(X3,difference(X3,X2)),
inference(transitivity,[status(thm)],[c144,c149]) ).
cnf(c151,plain,
difference(multiply(X4,difference(X3,X2)),multiply(X2,multiply(X4,difference(X3,X2)))) = multiply(multiply(X4,difference(X3,X2)),difference(multiply(X4,difference(X3,X2)),X2)),
inference(substitution,[status(thm)],[c150]) ).
cnf(c152,plain,
multiply(multiply(X4,difference(X3,X2)),difference(multiply(X4,difference(X3,X2)),X2)) = difference(multiply(X4,difference(X3,X2)),multiply(X2,multiply(X4,difference(X3,X2)))),
inference(symmetry,[status(thm)],[c151]) ).
cnf(c153,plain,
multiply(X3,difference(X2,X4)) = multiply(difference(X2,X4),X3),
inference(substitution,[status(thm)],[c10]) ).
cnf(c154,plain,
multiply(X4,multiply(X3,difference(X2,X4))) = multiply(X4,multiply(difference(X2,X4),X3)),
inference(congruence,[status(thm)],[c153]) ).
cnf(c155,plain,
multiply(X4,multiply(difference(X2,X4),X3)) = difference(X4,difference(X4,multiply(difference(X2,X4),X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c156,plain,
difference(X3,difference(X2,X3)) = X3,
inference(substitution,[status(thm)],[c40]) ).
cnf(c157,plain,
X3 = difference(X3,difference(X2,X3)),
inference(symmetry,[status(thm)],[c156]) ).
cnf(c158,plain,
difference(X4,difference(X4,multiply(difference(X2,X4),X3))) = difference(difference(X4,difference(X2,X4)),difference(X4,multiply(difference(X2,X4),X3))),
inference(congruence,[status(thm)],[c157]) ).
cnf(c159,plain,
difference(difference(X4,multiply(X3,X2)),X3) = difference(difference(X4,X3),difference(multiply(X3,X2),X3)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c160,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(substitution,[status(thm)],[c10]) ).
cnf(c161,plain,
difference(multiply(X3,X2),X3) = difference(multiply(X2,X3),X3),
inference(congruence,[status(thm)],[c160]) ).
cnf(c162,plain,
multiply(X2,X3) = difference(X2,difference(X2,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c163,plain,
difference(multiply(X2,X3),X3) = difference(difference(X2,difference(X2,X3)),X3),
inference(congruence,[status(thm)],[c162]) ).
cnf(c164,plain,
difference(difference(X2,difference(X2,X3)),X3) = difference(difference(X2,X3),difference(difference(X2,X3),X3)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c165,plain,
multiply(difference(X2,X3),X3) = difference(difference(X2,X3),difference(difference(X2,X3),X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c166,plain,
difference(difference(X2,X3),difference(difference(X2,X3),X3)) = multiply(difference(X2,X3),X3),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c167,plain,
multiply(X3,difference(X2,X3)) = multiply(difference(X2,X3),X3),
inference(substitution,[status(thm)],[c10]) ).
cnf(c168,plain,
multiply(difference(X2,X3),X3) = multiply(X3,difference(X2,X3)),
inference(symmetry,[status(thm)],[c167]) ).
cnf(c169,plain,
multiply(difference(X2,X3),X3) = difference(X3,X3),
inference(transitivity,[status(thm)],[c168,c90]) ).
cnf(c170,plain,
difference(difference(X2,X3),difference(difference(X2,X3),X3)) = difference(X3,X3),
inference(transitivity,[status(thm)],[c166,c169]) ).
cnf(c171,plain,
difference(difference(X2,difference(X2,X3)),X3) = difference(X3,X3),
inference(transitivity,[status(thm)],[c164,c170]) ).
cnf(c172,plain,
difference(multiply(X2,X3),X3) = difference(X3,X3),
inference(transitivity,[status(thm)],[c163,c171]) ).
cnf(c173,plain,
difference(multiply(X3,X2),X3) = difference(X3,X3),
inference(transitivity,[status(thm)],[c161,c172]) ).
cnf(c174,plain,
difference(difference(X4,X3),difference(multiply(X3,X2),X3)) = difference(difference(X4,X3),difference(X3,X3)),
inference(congruence,[status(thm)],[c173]) ).
cnf(c175,plain,
difference(difference(X3,X2),X2) = difference(difference(X3,X2),difference(X2,X2)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c176,plain,
difference(difference(X3,X2),difference(X2,X2)) = difference(difference(X3,X2),X2),
inference(symmetry,[status(thm)],[c175]) ).
cnf(c177,plain,
difference(difference(X3,X2),difference(X2,X2)) = difference(X3,X2),
inference(transitivity,[status(thm)],[c176,c45]) ).
cnf(c178,plain,
difference(difference(X4,X3),difference(multiply(X3,X2),X3)) = difference(X4,X3),
inference(transitivity,[status(thm)],[c174,c177]) ).
cnf(c179,plain,
difference(difference(X4,multiply(X3,X2)),X3) = difference(X4,X3),
inference(transitivity,[status(thm)],[c159,c178]) ).
cnf(c180,plain,
difference(X4,X3) = difference(difference(X4,multiply(X3,X2)),X3),
inference(symmetry,[status(thm)],[c179]) ).
cnf(c181,plain,
difference(difference(X4,X3),difference(X4,multiply(X3,X2))) = difference(difference(difference(X4,multiply(X3,X2)),X3),difference(X4,multiply(X3,X2))),
inference(congruence,[status(thm)],[c180]) ).
cnf(c182,plain,
difference(difference(difference(X4,multiply(X3,X2)),X3),difference(X4,multiply(X3,X2))) = difference(difference(X4,multiply(X3,X2)),difference(X4,multiply(X3,X2))),
inference(substitution,[status(thm)],[c76]) ).
cnf(c183,plain,
difference(difference(X4,multiply(X3,X2)),difference(X4,multiply(X3,X2))) = difference(multiply(X3,X2),multiply(X3,X2)),
inference(substitution,[status(thm)],[c100]) ).
cnf(c184,plain,
difference(multiply(X3,X2),multiply(X3,X2)) = difference(X4,X4),
inference(transitivity,[status(thm)],[c107,c124]) ).
cnf(c185,plain,
difference(difference(X5,multiply(X4,X3)),difference(X5,multiply(X4,X3))) = difference(X2,X2),
inference(transitivity,[status(thm)],[c183,c184]) ).
cnf(c186,plain,
difference(difference(difference(X5,multiply(X4,X3)),X4),difference(X5,multiply(X4,X3))) = difference(X2,X2),
inference(transitivity,[status(thm)],[c182,c185]) ).
cnf(c187,plain,
difference(difference(X5,X4),difference(X5,multiply(X4,X3))) = difference(X2,X2),
inference(transitivity,[status(thm)],[c181,c186]) ).
cnf(c188,plain,
difference(difference(X5,difference(X3,X5)),difference(X5,multiply(difference(X3,X5),X4))) = difference(X2,X2),
inference(substitution,[status(thm)],[c187]) ).
cnf(c189,plain,
difference(X5,difference(X5,multiply(difference(X3,X5),X4))) = difference(X2,X2),
inference(transitivity,[status(thm)],[c158,c188]) ).
cnf(c190,plain,
multiply(X5,multiply(difference(X3,X5),X4)) = difference(X2,X2),
inference(transitivity,[status(thm)],[c155,c189]) ).
cnf(c191,plain,
multiply(X5,multiply(X4,difference(X3,X5))) = difference(X2,X2),
inference(transitivity,[status(thm)],[c154,c190]) ).
cnf(c192,plain,
multiply(X3,multiply(X5,difference(X4,X3))) = difference(X2,X2),
inference(substitution,[status(thm)],[c191]) ).
cnf(c193,plain,
difference(multiply(X5,difference(X4,X3)),multiply(X3,multiply(X5,difference(X4,X3)))) = difference(multiply(X5,difference(X4,X3)),difference(X2,X2)),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
difference(multiply(X5,difference(X4,X3)),difference(X2,X2)) = multiply(X5,difference(X4,X3)),
inference(substitution,[status(thm)],[c135]) ).
cnf(c195,plain,
difference(multiply(X4,difference(X3,X2)),multiply(X2,multiply(X4,difference(X3,X2)))) = multiply(X4,difference(X3,X2)),
inference(transitivity,[status(thm)],[c193,c194]) ).
cnf(c196,plain,
multiply(multiply(X4,difference(X3,X2)),difference(multiply(X4,difference(X3,X2)),X2)) = multiply(X4,difference(X3,X2)),
inference(transitivity,[status(thm)],[c152,c195]) ).
cnf(c197,plain,
difference(multiply(X4,difference(X3,X2)),X2) = multiply(X4,difference(X3,X2)),
inference(transitivity,[status(thm)],[c143,c196]) ).
cnf(c198,plain,
difference(multiply(X4,X3),X2) = multiply(X4,difference(X3,X2)),
inference(transitivity,[status(thm)],[c55,c197]) ).
cnf(c199,plain,
multiply(X4,difference(X3,X2)) = difference(multiply(X4,X3),X2),
inference(symmetry,[status(thm)],[c198]) ).
cnf(c200,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c201,plain,
difference(multiply(X4,X3),X2) = difference(multiply(X3,X4),X2),
inference(congruence,[status(thm)],[c200]) ).
cnf(c202,plain,
difference(multiply(X3,X4),X2) = multiply(X3,difference(X4,X2)),
inference(substitution,[status(thm)],[c198]) ).
cnf(c203,plain,
difference(multiply(X4,X3),X2) = multiply(X3,difference(X4,X2)),
inference(transitivity,[status(thm)],[c201,c202]) ).
cnf(c204,plain,
multiply(X4,difference(X3,X2)) = multiply(X3,difference(X4,X2)),
inference(transitivity,[status(thm)],[c199,c203]) ).
cnf(c205,plain,
multiply(X2,difference(X3,difference(X2,X4))) = multiply(X3,difference(X2,difference(X2,X4))),
inference(substitution,[status(thm)],[c204]) ).
cnf(c206,plain,
multiply(X3,difference(X2,difference(X2,X4))) = multiply(X2,difference(X3,difference(X2,X4))),
inference(symmetry,[status(thm)],[c205]) ).
cnf(c207,plain,
difference(difference(difference(X4,X3),X2),X3) = difference(difference(difference(X4,X3),X3),difference(X2,X3)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c208,plain,
difference(difference(difference(X4,X3),X3),difference(X2,X3)) = difference(difference(X4,X3),difference(X2,X3)),
inference(congruence,[status(thm)],[c45]) ).
cnf(c209,plain,
difference(difference(X4,X2),X3) = difference(difference(X4,X3),difference(X2,X3)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c210,plain,
difference(difference(X4,X3),difference(X2,X3)) = difference(difference(X4,X2),X3),
inference(symmetry,[status(thm)],[c209]) ).
cnf(c211,plain,
difference(difference(difference(X4,X3),X3),difference(X2,X3)) = difference(difference(X4,X2),X3),
inference(transitivity,[status(thm)],[c208,c210]) ).
cnf(c212,plain,
difference(difference(difference(X4,X3),X2),X3) = difference(difference(X4,X2),X3),
inference(transitivity,[status(thm)],[c207,c211]) ).
cnf(c213,plain,
difference(difference(difference(X4,X2),X3),X2) = difference(difference(X4,X3),X2),
inference(substitution,[status(thm)],[c212]) ).
cnf(c214,plain,
difference(difference(X4,X3),X2) = difference(difference(difference(X4,X2),X3),X2),
inference(symmetry,[status(thm)],[c213]) ).
cnf(c215,plain,
multiply(difference(difference(X4,X2),X3),difference(difference(difference(X4,X2),X3),X2)) = difference(difference(difference(X4,X2),X3),X2),
inference(substitution,[status(thm)],[c141]) ).
cnf(c216,plain,
difference(difference(difference(X4,X2),X3),X2) = multiply(difference(difference(X4,X2),X3),difference(difference(difference(X4,X2),X3),X2)),
inference(symmetry,[status(thm)],[c215]) ).
cnf(c217,plain,
difference(difference(difference(X4,X2),X3),multiply(X2,difference(difference(X4,X2),X3))) = multiply(difference(difference(X4,X2),X3),difference(difference(difference(X4,X2),X3),X2)),
inference(substitution,[status(thm)],[c150]) ).
cnf(c218,plain,
multiply(difference(difference(X4,X2),X3),difference(difference(difference(X4,X2),X3),X2)) = difference(difference(difference(X4,X2),X3),multiply(X2,difference(difference(X4,X2),X3))),
inference(symmetry,[status(thm)],[c217]) ).
cnf(c219,plain,
multiply(difference(X3,X4),difference(X4,X2)) = multiply(X4,difference(difference(X3,X4),X2)),
inference(substitution,[status(thm)],[c204]) ).
cnf(c220,plain,
multiply(X4,difference(difference(X3,X4),X2)) = multiply(difference(X3,X4),difference(X4,X2)),
inference(symmetry,[status(thm)],[c219]) ).
cnf(c221,plain,
multiply(difference(X3,X4),difference(X4,X2)) = difference(difference(X3,X4),difference(difference(X3,X4),difference(X4,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c222,plain,
difference(difference(X4,difference(X3,X2)),X3) = difference(difference(X4,X3),difference(difference(X3,X2),X3)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c223,plain,
difference(difference(X4,X3),difference(difference(X3,X2),X3)) = difference(difference(X4,X3),difference(X3,X3)),
inference(congruence,[status(thm)],[c76]) ).
cnf(c224,plain,
difference(difference(X3,X2),X2) = difference(difference(X3,X2),difference(X2,X2)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c225,plain,
difference(difference(X3,X2),difference(X2,X2)) = difference(difference(X3,X2),X2),
inference(symmetry,[status(thm)],[c224]) ).
cnf(c226,plain,
difference(difference(X3,X2),difference(X2,X2)) = difference(X3,X2),
inference(transitivity,[status(thm)],[c225,c45]) ).
cnf(c227,plain,
difference(difference(X4,X3),difference(difference(X3,X2),X3)) = difference(X4,X3),
inference(transitivity,[status(thm)],[c223,c226]) ).
cnf(c228,plain,
difference(difference(X4,difference(X3,X2)),X3) = difference(X4,X3),
inference(transitivity,[status(thm)],[c222,c227]) ).
cnf(c229,plain,
difference(difference(X3,difference(X4,X2)),X4) = difference(X3,X4),
inference(substitution,[status(thm)],[c228]) ).
cnf(c230,plain,
difference(X3,X4) = difference(difference(X3,difference(X4,X2)),X4),
inference(symmetry,[status(thm)],[c229]) ).
cnf(c231,plain,
difference(difference(X3,X4),difference(difference(X3,X4),difference(X4,X2))) = difference(difference(difference(X3,difference(X4,X2)),X4),difference(difference(X3,X4),difference(X4,X2))),
inference(congruence,[status(thm)],[c230]) ).
cnf(c232,plain,
multiply(X3,X2) = difference(X3,difference(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c233,plain,
difference(difference(X4,difference(X3,X2)),multiply(X3,X2)) = difference(difference(X4,difference(X3,X2)),difference(X3,difference(X3,X2))),
inference(congruence,[status(thm)],[c232]) ).
cnf(c234,plain,
difference(difference(X4,X3),difference(X3,X2)) = difference(difference(X4,difference(X3,X2)),difference(X3,difference(X3,X2))),
inference(substitution,[status(thm)],[c21]) ).
cnf(c235,plain,
difference(difference(X4,difference(X3,X2)),difference(X3,difference(X3,X2))) = difference(difference(X4,X3),difference(X3,X2)),
inference(symmetry,[status(thm)],[c234]) ).
cnf(c236,plain,
difference(difference(X4,difference(X3,X2)),multiply(X3,X2)) = difference(difference(X4,X3),difference(X3,X2)),
inference(transitivity,[status(thm)],[c233,c235]) ).
cnf(c237,plain,
difference(difference(X3,difference(X4,X2)),multiply(X4,X2)) = difference(difference(X3,X4),difference(X4,X2)),
inference(substitution,[status(thm)],[c236]) ).
cnf(c238,plain,
difference(difference(X3,X4),difference(X4,X2)) = difference(difference(X3,difference(X4,X2)),multiply(X4,X2)),
inference(symmetry,[status(thm)],[c237]) ).
cnf(c239,plain,
difference(difference(difference(X3,difference(X4,X2)),X4),difference(difference(X3,X4),difference(X4,X2))) = difference(difference(difference(X3,difference(X4,X2)),X4),difference(difference(X3,difference(X4,X2)),multiply(X4,X2))),
inference(congruence,[status(thm)],[c238]) ).
cnf(c240,plain,
difference(difference(difference(X4,difference(X5,X3)),X5),difference(difference(X4,difference(X5,X3)),multiply(X5,X3))) = difference(X2,X2),
inference(substitution,[status(thm)],[c187]) ).
cnf(c241,plain,
difference(difference(difference(X4,difference(X5,X3)),X5),difference(difference(X4,X5),difference(X5,X3))) = difference(X2,X2),
inference(transitivity,[status(thm)],[c239,c240]) ).
cnf(c242,plain,
difference(difference(X4,X5),difference(difference(X4,X5),difference(X5,X3))) = difference(X2,X2),
inference(transitivity,[status(thm)],[c231,c241]) ).
cnf(c243,plain,
multiply(difference(X4,X5),difference(X5,X3)) = difference(X2,X2),
inference(transitivity,[status(thm)],[c221,c242]) ).
cnf(c244,plain,
multiply(X5,difference(difference(X4,X5),X3)) = difference(X2,X2),
inference(transitivity,[status(thm)],[c220,c243]) ).
cnf(c245,plain,
multiply(X3,difference(difference(X5,X3),X4)) = difference(X2,X2),
inference(substitution,[status(thm)],[c244]) ).
cnf(c246,plain,
difference(difference(difference(X5,X3),X4),multiply(X3,difference(difference(X5,X3),X4))) = difference(difference(difference(X5,X3),X4),difference(X2,X2)),
inference(congruence,[status(thm)],[c245]) ).
cnf(c247,plain,
difference(difference(difference(X5,X3),X4),difference(X2,X2)) = difference(difference(X5,X3),X4),
inference(substitution,[status(thm)],[c135]) ).
cnf(c248,plain,
difference(difference(difference(X4,X2),X3),multiply(X2,difference(difference(X4,X2),X3))) = difference(difference(X4,X2),X3),
inference(transitivity,[status(thm)],[c246,c247]) ).
cnf(c249,plain,
multiply(difference(difference(X4,X2),X3),difference(difference(difference(X4,X2),X3),X2)) = difference(difference(X4,X2),X3),
inference(transitivity,[status(thm)],[c218,c248]) ).
cnf(c250,plain,
difference(difference(difference(X4,X2),X3),X2) = difference(difference(X4,X2),X3),
inference(transitivity,[status(thm)],[c216,c249]) ).
cnf(c251,plain,
difference(difference(X4,X3),X2) = difference(difference(X4,X2),X3),
inference(transitivity,[status(thm)],[c214,c250]) ).
cnf(c252,plain,
difference(difference(X4,difference(X4,X2)),X3) = difference(difference(X4,X3),difference(X4,X2)),
inference(substitution,[status(thm)],[c251]) ).
cnf(c253,plain,
difference(difference(X4,X3),difference(X4,X2)) = difference(difference(X4,difference(X4,X2)),X3),
inference(symmetry,[status(thm)],[c252]) ).
cnf(c254,plain,
multiply(X3,X2) = difference(X3,difference(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c255,plain,
difference(X3,difference(X3,X2)) = multiply(X3,X2),
inference(symmetry,[status(thm)],[c254]) ).
cnf(c256,plain,
difference(difference(X4,difference(X4,X2)),X3) = difference(multiply(X4,X2),X3),
inference(congruence,[status(thm)],[c255]) ).
cnf(c257,plain,
difference(multiply(X4,X2),X3) = multiply(X4,difference(X2,X3)),
inference(substitution,[status(thm)],[c198]) ).
cnf(c258,plain,
difference(difference(X4,difference(X4,X2)),X3) = multiply(X4,difference(X2,X3)),
inference(transitivity,[status(thm)],[c256,c257]) ).
cnf(c259,plain,
difference(difference(X4,X3),difference(X4,X2)) = multiply(X4,difference(X2,X3)),
inference(transitivity,[status(thm)],[c253,c258]) ).
cnf(c260,plain,
difference(difference(X2,difference(X2,X4)),difference(X2,X3)) = multiply(X2,difference(X3,difference(X2,X4))),
inference(substitution,[status(thm)],[c259]) ).
cnf(c261,plain,
multiply(X2,difference(X3,difference(X2,X4))) = difference(difference(X2,difference(X2,X4)),difference(X2,X3)),
inference(symmetry,[status(thm)],[c260]) ).
cnf(c262,plain,
multiply(X3,X2) = difference(X3,difference(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c263,plain,
difference(multiply(X4,X3),difference(X2,difference(X4,X3))) = difference(difference(X4,difference(X4,X3)),difference(X2,difference(X4,X3))),
inference(congruence,[status(thm)],[c262]) ).
cnf(c264,plain,
difference(difference(X4,X2),difference(X4,X3)) = difference(difference(X4,difference(X4,X3)),difference(X2,difference(X4,X3))),
inference(substitution,[status(thm)],[c21]) ).
cnf(c265,plain,
difference(difference(X4,difference(X4,X3)),difference(X2,difference(X4,X3))) = difference(difference(X4,X2),difference(X4,X3)),
inference(symmetry,[status(thm)],[c264]) ).
cnf(c266,plain,
difference(multiply(X4,X3),difference(X2,difference(X4,X3))) = difference(difference(X4,X2),difference(X4,X3)),
inference(transitivity,[status(thm)],[c263,c265]) ).
cnf(c267,plain,
difference(multiply(X2,X3),difference(difference(X2,X4),difference(X2,X3))) = difference(difference(X2,difference(X2,X4)),difference(X2,X3)),
inference(substitution,[status(thm)],[c266]) ).
cnf(c268,plain,
difference(difference(X2,difference(X2,X4)),difference(X2,X3)) = difference(multiply(X2,X3),difference(difference(X2,X4),difference(X2,X3))),
inference(symmetry,[status(thm)],[c267]) ).
cnf(c269,plain,
difference(multiply(X2,X3),difference(X4,difference(X2,X3))) = difference(difference(X2,X4),difference(X2,X3)),
inference(substitution,[status(thm)],[c266]) ).
cnf(c270,plain,
difference(difference(X2,X4),difference(X2,X3)) = difference(multiply(X2,X3),difference(X4,difference(X2,X3))),
inference(symmetry,[status(thm)],[c269]) ).
cnf(c271,plain,
difference(multiply(X2,X3),difference(difference(X2,X4),difference(X2,X3))) = difference(multiply(X2,X3),difference(multiply(X2,X3),difference(X4,difference(X2,X3)))),
inference(congruence,[status(thm)],[c270]) ).
cnf(c272,plain,
multiply(multiply(X2,X3),difference(X4,difference(X2,X3))) = difference(multiply(X2,X3),difference(multiply(X2,X3),difference(X4,difference(X2,X3)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c273,plain,
difference(multiply(X2,X3),difference(multiply(X2,X3),difference(X4,difference(X2,X3)))) = multiply(multiply(X2,X3),difference(X4,difference(X2,X3))),
inference(symmetry,[status(thm)],[c272]) ).
cnf(c274,plain,
multiply(multiply(X2,X3),difference(X4,difference(X2,X3))) = multiply(X4,difference(multiply(X2,X3),difference(X2,X3))),
inference(substitution,[status(thm)],[c204]) ).
cnf(c275,plain,
multiply(X3,X2) = difference(X3,difference(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c276,plain,
difference(multiply(X3,X2),difference(X3,X2)) = difference(difference(X3,difference(X3,X2)),difference(X3,X2)),
inference(congruence,[status(thm)],[c275]) ).
cnf(c277,plain,
difference(difference(X3,difference(X3,X2)),difference(X3,X2)) = difference(X3,difference(X3,X2)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c278,plain,
multiply(X3,X2) = difference(X3,difference(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c279,plain,
difference(X3,difference(X3,X2)) = multiply(X3,X2),
inference(symmetry,[status(thm)],[c278]) ).
cnf(c280,plain,
difference(difference(X3,difference(X3,X2)),difference(X3,X2)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c277,c279]) ).
cnf(c281,plain,
difference(multiply(X3,X2),difference(X3,X2)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c276,c280]) ).
cnf(c282,plain,
difference(multiply(X2,X3),difference(X2,X3)) = multiply(X2,X3),
inference(substitution,[status(thm)],[c281]) ).
cnf(c283,plain,
multiply(X4,difference(multiply(X2,X3),difference(X2,X3))) = multiply(X4,multiply(X2,X3)),
inference(congruence,[status(thm)],[c282]) ).
cnf(c284,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(substitution,[status(thm)],[c10]) ).
cnf(c285,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(symmetry,[status(thm)],[c284]) ).
cnf(c286,plain,
multiply(X4,multiply(X2,X3)) = multiply(X4,multiply(X3,X2)),
inference(congruence,[status(thm)],[c285]) ).
cnf(c287,plain,
multiply(X4,difference(multiply(X2,X3),difference(X2,X3))) = multiply(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c283,c286]) ).
cnf(c288,plain,
multiply(multiply(X2,X3),difference(X4,difference(X2,X3))) = multiply(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c274,c287]) ).
cnf(c289,plain,
difference(multiply(X2,X3),difference(multiply(X2,X3),difference(X4,difference(X2,X3)))) = multiply(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c273,c288]) ).
cnf(c290,plain,
difference(multiply(X2,X3),difference(difference(X2,X4),difference(X2,X3))) = multiply(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c271,c289]) ).
cnf(c291,plain,
difference(difference(X2,difference(X2,X4)),difference(X2,X3)) = multiply(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c268,c290]) ).
cnf(c292,plain,
multiply(X2,difference(X3,difference(X2,X4))) = multiply(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c261,c291]) ).
cnf(c293,plain,
multiply(X3,difference(X2,difference(X2,X4))) = multiply(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c206,c292]) ).
cnf(c294,plain,
multiply(X3,multiply(X2,X4)) = multiply(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c16,c293]) ).
cnf(c295,plain,
multiply(X3,multiply(X4,X2)) = multiply(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c14,c294]) ).
cnf(c296,plain,
multiply(a,multiply(c,b)) = multiply(c,multiply(a,b)),
inference(substitution,[status(thm)],[c295]) ).
cnf(c297,plain,
multiply(c,multiply(a,b)) = multiply(a,multiply(c,b)),
inference(symmetry,[status(thm)],[c296]) ).
cnf(c298,plain,
multiply(b,c) = multiply(c,b),
inference(substitution,[status(thm)],[c10]) ).
cnf(c299,plain,
multiply(c,b) = multiply(b,c),
inference(symmetry,[status(thm)],[c298]) ).
cnf(c300,plain,
multiply(a,multiply(c,b)) = multiply(a,multiply(b,c)),
inference(congruence,[status(thm)],[c299]) ).
cnf(c301,plain,
multiply(c,multiply(a,b)) = multiply(a,multiply(b,c)),
inference(transitivity,[status(thm)],[c297,c300]) ).
cnf(c302,plain,
multiply(multiply(a,b),c) = multiply(a,multiply(b,c)),
inference(transitivity,[status(thm)],[c12,c301]) ).
cnf(c303,plain,
$false,
inference(resolution,[status(thm)],[c1,c302]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG005-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n008.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 19:17:39 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.48/0.52 Command-line arguments: --no-flatten-goal
% 1.48/0.52
% 1.48/0.52 % SZS status Unsatisfiable
% 1.48/0.52
% 1.48/0.55 % SZS output start CNFRefutation
% See solution above
% 2.53/0.70
% 2.53/0.70 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------