%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO024-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 09:35:37 AM UTC 2026
% Result : Unsatisfiable 0.21s 0.35s
% Output : CNFRefutation 2.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 89
% Number of leaves : 8
% Syntax : Number of clauses : 374 ( 374 unt; 0 nHn; 14 RR)
% Number of literals : 374 ( 373 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 625 ( 167 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
add(multiply(a,b),b) != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_add_multiply) ).
cnf(c2,axiom,
add(X2,inverse(X2)) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c3,plain,
n1 = add(X2,inverse(X2)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(n1,inverse(X2)) = multiply(add(X2,inverse(X2)),inverse(X2)),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(add(X,Y),Y) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_add) ).
cnf(c6,plain,
multiply(add(X2,inverse(X2)),inverse(X2)) = inverse(X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(n1,inverse(X2)) = inverse(X2),
inference(transitivity,[status(thm)],[c4,c6]) ).
cnf(c8,plain,
multiply(n1,inverse(n1)) = inverse(n1),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
inverse(n1) = multiply(n1,inverse(n1)),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
add(inverse(n1),multiply(X2,n1)) = add(multiply(n1,inverse(n1)),multiply(X2,n1)),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
n1 = add(X2,inverse(X2)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c12,plain,
multiply(X3,n1) = multiply(X3,add(X2,inverse(X2))),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
add(multiply(X3,inverse(X3)),multiply(X2,n1)) = add(multiply(X3,inverse(X3)),multiply(X2,add(X3,inverse(X3)))),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,axiom,
multiply(X2,add(Y2,Z)) = add(multiply(Y2,X2),multiply(Z,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_add_property) ).
cnf(c15,plain,
multiply(X4,add(X3,inverse(X2))) = add(multiply(X3,X4),multiply(inverse(X2),X4)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
add(multiply(X4,inverse(X3)),multiply(X2,add(X4,inverse(X3)))) = add(multiply(X4,inverse(X3)),add(multiply(X4,X2),multiply(inverse(X3),X2))),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,axiom,
pixley(X2,Y2,Z2) = add(multiply(X2,inverse(Y2)),add(multiply(X2,Z2),multiply(inverse(Y2),Z2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pixley_defn) ).
cnf(c18,plain,
pixley(X4,X3,X2) = add(multiply(X4,inverse(X3)),add(multiply(X4,X2),multiply(inverse(X3),X2))),
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
add(multiply(X4,inverse(X3)),add(multiply(X4,X2),multiply(inverse(X3),X2))) = pixley(X4,X3,X2),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
add(multiply(X4,inverse(X3)),multiply(X2,add(X4,inverse(X3)))) = pixley(X4,X3,X2),
inference(transitivity,[status(thm)],[c16,c19]) ).
cnf(c21,plain,
add(multiply(X3,inverse(X3)),multiply(X2,add(X3,inverse(X3)))) = pixley(X3,X3,X2),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,axiom,
pixley(X2,X2,Y2) = Y2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pixley1) ).
cnf(c23,plain,
pixley(X3,X3,X2) = X2,
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
add(multiply(X3,inverse(X3)),multiply(X2,add(X3,inverse(X3)))) = X2,
inference(transitivity,[status(thm)],[c21,c23]) ).
cnf(c25,plain,
add(multiply(X3,inverse(X3)),multiply(X2,n1)) = X2,
inference(transitivity,[status(thm)],[c13,c24]) ).
cnf(c26,plain,
add(multiply(n1,inverse(n1)),multiply(X2,n1)) = X2,
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
add(inverse(n1),multiply(X2,n1)) = X2,
inference(transitivity,[status(thm)],[c10,c26]) ).
cnf(c28,plain,
add(inverse(n1),multiply(add(X2,n1),n1)) = add(X2,n1),
inference(substitution,[status(thm)],[c27]) ).
cnf(c29,plain,
add(X2,n1) = add(inverse(n1),multiply(add(X2,n1),n1)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
multiply(add(X2,n1),n1) = n1,
inference(substitution,[status(thm)],[c5]) ).
cnf(c31,plain,
add(inverse(n1),multiply(add(X2,n1),n1)) = add(inverse(n1),n1),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
multiply(add(X2,n1),n1) = n1,
inference(substitution,[status(thm)],[c5]) ).
cnf(c33,plain,
n1 = multiply(add(X2,n1),n1),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
add(inverse(n1),n1) = add(inverse(n1),multiply(add(X2,n1),n1)),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
add(inverse(n1),multiply(add(X2,n1),n1)) = add(X2,n1),
inference(substitution,[status(thm)],[c27]) ).
cnf(c36,plain,
add(inverse(n1),n1) = add(X2,n1),
inference(transitivity,[status(thm)],[c34,c35]) ).
cnf(c37,plain,
add(inverse(n1),multiply(add(X2,n1),n1)) = add(X3,n1),
inference(transitivity,[status(thm)],[c31,c36]) ).
cnf(c38,plain,
add(X2,n1) = add(X3,n1),
inference(transitivity,[status(thm)],[c29,c37]) ).
cnf(c39,plain,
add(X3,n1) = add(multiply(n1,inverse(add(X2,n1))),n1),
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
add(X2,n1) = add(multiply(X3,n1),n1),
inference(substitution,[status(thm)],[c38]) ).
cnf(c41,plain,
add(add(X4,add(X3,n1)),add(X2,n1)) = add(add(X4,add(X3,n1)),add(multiply(X4,n1),n1)),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
multiply(X4,add(X3,add(X2,X4))) = add(multiply(X3,X4),multiply(add(X2,X4),X4)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c43,plain,
multiply(add(X2,X3),X3) = X3,
inference(substitution,[status(thm)],[c5]) ).
cnf(c44,plain,
add(multiply(X3,X4),multiply(add(X2,X4),X4)) = add(multiply(X3,X4),X4),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
multiply(X4,add(X3,add(X2,X4))) = add(multiply(X3,X4),X4),
inference(transitivity,[status(thm)],[c42,c44]) ).
cnf(c46,plain,
multiply(n1,add(X3,add(X2,n1))) = add(multiply(X3,n1),n1),
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
add(multiply(X3,n1),n1) = multiply(n1,add(X3,add(X2,n1))),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
add(add(X3,add(X2,n1)),add(multiply(X3,n1),n1)) = add(add(X3,add(X2,n1)),multiply(n1,add(X3,add(X2,n1)))),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
multiply(X4,add(add(X3,X4),X2)) = add(multiply(add(X3,X4),X4),multiply(X2,X4)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c50,plain,
multiply(add(X2,X3),X3) = X3,
inference(substitution,[status(thm)],[c5]) ).
cnf(c51,plain,
add(multiply(add(X3,X4),X4),multiply(X2,X4)) = add(X4,multiply(X2,X4)),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
multiply(X4,add(add(X3,X4),X2)) = add(X4,multiply(X2,X4)),
inference(transitivity,[status(thm)],[c49,c51]) ).
cnf(c53,plain,
multiply(X3,add(add(X2,X3),n1)) = add(X3,multiply(n1,X3)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
add(X3,multiply(n1,X3)) = multiply(X3,add(add(X2,X3),n1)),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
add(X3,n1) = add(add(X2,X4),n1),
inference(substitution,[status(thm)],[c38]) ).
cnf(c56,plain,
add(add(X2,X4),n1) = add(X3,n1),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
multiply(X4,add(add(X2,X4),n1)) = multiply(X4,add(X3,n1)),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
add(X3,multiply(n1,X3)) = multiply(X3,add(X2,n1)),
inference(transitivity,[status(thm)],[c54,c57]) ).
cnf(c59,plain,
add(add(X3,add(X2,n1)),multiply(n1,add(X3,add(X2,n1)))) = multiply(add(X3,add(X2,n1)),add(X2,n1)),
inference(substitution,[status(thm)],[c58]) ).
cnf(c60,plain,
multiply(add(X3,add(X2,n1)),add(X2,n1)) = add(X2,n1),
inference(substitution,[status(thm)],[c5]) ).
cnf(c61,plain,
add(add(X3,add(X2,n1)),multiply(n1,add(X3,add(X2,n1)))) = add(X2,n1),
inference(transitivity,[status(thm)],[c59,c60]) ).
cnf(c62,plain,
add(add(X3,add(X2,n1)),add(multiply(X3,n1),n1)) = add(X2,n1),
inference(transitivity,[status(thm)],[c48,c61]) ).
cnf(c63,plain,
add(add(X4,add(X3,n1)),add(X2,n1)) = add(X3,n1),
inference(transitivity,[status(thm)],[c41,c62]) ).
cnf(c64,plain,
add(add(X2,add(X3,n1)),add(X4,n1)) = add(X3,n1),
inference(substitution,[status(thm)],[c63]) ).
cnf(c65,plain,
add(X4,n1) = add(add(X3,add(X4,n1)),add(X2,n1)),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
multiply(n1,add(X4,n1)) = multiply(n1,add(add(X3,add(X4,n1)),add(X2,n1))),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
multiply(n1,add(add(X3,add(X4,n1)),add(X2,n1))) = add(multiply(add(X3,add(X4,n1)),n1),n1),
inference(substitution,[status(thm)],[c45]) ).
cnf(c68,plain,
add(X3,n1) = add(multiply(add(X2,add(X4,n1)),n1),n1),
inference(substitution,[status(thm)],[c38]) ).
cnf(c69,plain,
add(multiply(add(X2,add(X4,n1)),n1),n1) = add(X3,n1),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
multiply(n1,add(add(X3,add(X5,n1)),add(X2,n1))) = add(X4,n1),
inference(transitivity,[status(thm)],[c67,c69]) ).
cnf(c71,plain,
multiply(n1,add(X3,n1)) = add(X2,n1),
inference(transitivity,[status(thm)],[c66,c70]) ).
cnf(c72,plain,
multiply(n1,add(X2,n1)) = add(X3,n1),
inference(substitution,[status(thm)],[c71]) ).
cnf(c73,plain,
add(X3,n1) = multiply(n1,add(X2,n1)),
inference(symmetry,[status(thm)],[c72]) ).
cnf(c74,plain,
add(add(X4,n1),multiply(X3,add(X2,n1))) = add(multiply(n1,add(X2,n1)),multiply(X3,add(X2,n1))),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
multiply(add(X2,n1),add(n1,X3)) = add(multiply(n1,add(X2,n1)),multiply(X3,add(X2,n1))),
inference(substitution,[status(thm)],[c14]) ).
cnf(c76,plain,
add(multiply(n1,add(X2,n1)),multiply(X3,add(X2,n1))) = multiply(add(X2,n1),add(n1,X3)),
inference(symmetry,[status(thm)],[c75]) ).
cnf(c77,plain,
add(add(X4,n1),multiply(X3,add(X2,n1))) = multiply(add(X2,n1),add(n1,X3)),
inference(transitivity,[status(thm)],[c74,c76]) ).
cnf(c78,plain,
add(add(X3,n1),multiply(inverse(add(X2,n1)),add(X3,n1))) = multiply(add(X3,n1),add(n1,inverse(add(X2,n1)))),
inference(substitution,[status(thm)],[c77]) ).
cnf(c79,plain,
multiply(add(X3,n1),add(n1,inverse(add(X2,n1)))) = add(add(X3,n1),multiply(inverse(add(X2,n1)),add(X3,n1))),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
add(add(X2,add(X3,n1)),add(X4,n1)) = add(X3,n1),
inference(substitution,[status(thm)],[c63]) ).
cnf(c81,plain,
add(X3,n1) = add(add(X2,add(X3,n1)),add(X4,n1)),
inference(symmetry,[status(thm)],[c80]) ).
cnf(c82,plain,
inverse(add(X3,n1)) = inverse(add(add(X2,add(X3,n1)),add(X4,n1))),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
multiply(inverse(add(X3,n1)),add(X4,n1)) = multiply(inverse(add(add(X2,add(X3,n1)),add(X4,n1))),add(X4,n1)),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
add(add(X4,n1),multiply(inverse(add(X3,n1)),add(X4,n1))) = add(add(X4,n1),multiply(inverse(add(add(X2,add(X3,n1)),add(X4,n1))),add(X4,n1))),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
multiply(X3,add(add(X2,X3),inverse(add(X2,X3)))) = add(X3,multiply(inverse(add(X2,X3)),X3)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c86,plain,
add(X3,multiply(inverse(add(X2,X3)),X3)) = multiply(X3,add(add(X2,X3),inverse(add(X2,X3)))),
inference(symmetry,[status(thm)],[c85]) ).
cnf(c87,plain,
add(add(X2,X3),inverse(add(X2,X3))) = n1,
inference(substitution,[status(thm)],[c2]) ).
cnf(c88,plain,
multiply(X3,add(add(X2,X3),inverse(add(X2,X3)))) = multiply(X3,n1),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
add(X3,multiply(inverse(add(X2,X3)),X3)) = multiply(X3,n1),
inference(transitivity,[status(thm)],[c86,c88]) ).
cnf(c90,plain,
add(add(X4,n1),multiply(inverse(add(add(X2,add(X3,n1)),add(X4,n1))),add(X4,n1))) = multiply(add(X4,n1),n1),
inference(substitution,[status(thm)],[c89]) ).
cnf(c91,plain,
multiply(add(X2,n1),n1) = n1,
inference(substitution,[status(thm)],[c5]) ).
cnf(c92,plain,
add(add(X4,n1),multiply(inverse(add(add(X2,add(X3,n1)),add(X4,n1))),add(X4,n1))) = n1,
inference(transitivity,[status(thm)],[c90,c91]) ).
cnf(c93,plain,
add(add(X3,n1),multiply(inverse(add(X2,n1)),add(X3,n1))) = n1,
inference(transitivity,[status(thm)],[c84,c92]) ).
cnf(c94,plain,
multiply(add(X3,n1),add(n1,inverse(add(X2,n1)))) = n1,
inference(transitivity,[status(thm)],[c79,c93]) ).
cnf(c95,plain,
multiply(add(X2,n1),add(n1,inverse(add(X2,n1)))) = n1,
inference(substitution,[status(thm)],[c94]) ).
cnf(c96,plain,
n1 = multiply(add(X2,n1),add(n1,inverse(add(X2,n1)))),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c97,plain,
add(multiply(n1,inverse(add(X2,n1))),n1) = add(multiply(n1,inverse(add(X2,n1))),multiply(add(X2,n1),add(n1,inverse(add(X2,n1))))),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
add(multiply(n1,inverse(add(X2,n1))),multiply(add(X2,n1),add(n1,inverse(add(X2,n1))))) = pixley(n1,add(X2,n1),add(X2,n1)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c99,axiom,
pixley(X2,Y2,Y2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pixley2) ).
cnf(c100,plain,
pixley(n1,add(X2,n1),add(X2,n1)) = n1,
inference(substitution,[status(thm)],[c99]) ).
cnf(c101,plain,
add(multiply(n1,inverse(add(X2,n1))),multiply(add(X2,n1),add(n1,inverse(add(X2,n1))))) = n1,
inference(transitivity,[status(thm)],[c98,c100]) ).
cnf(c102,plain,
add(multiply(n1,inverse(add(X2,n1))),n1) = n1,
inference(transitivity,[status(thm)],[c97,c101]) ).
cnf(c103,plain,
add(X2,n1) = n1,
inference(transitivity,[status(thm)],[c39,c102]) ).
cnf(c104,plain,
n1 = add(X2,n1),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c105,plain,
multiply(n1,n1) = multiply(add(X2,n1),n1),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
multiply(add(X2,n1),n1) = n1,
inference(substitution,[status(thm)],[c5]) ).
cnf(c107,plain,
multiply(n1,n1) = n1,
inference(transitivity,[status(thm)],[c105,c106]) ).
cnf(c108,plain,
n1 = multiply(n1,n1),
inference(symmetry,[status(thm)],[c107]) ).
cnf(c109,plain,
multiply(n1,X2) = multiply(multiply(n1,n1),X2),
inference(congruence,[status(thm)],[c108]) ).
cnf(c110,plain,
add(multiply(X2,inverse(X2)),multiply(X3,n1)) = X3,
inference(substitution,[status(thm)],[c25]) ).
cnf(c111,plain,
X3 = add(multiply(X2,inverse(X2)),multiply(X3,n1)),
inference(symmetry,[status(thm)],[c110]) ).
cnf(c112,plain,
multiply(X4,X3) = multiply(X4,add(multiply(X2,inverse(X2)),multiply(X3,n1))),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,plain,
multiply(multiply(X4,X3),multiply(multiply(X3,n1),X4)) = multiply(multiply(X4,add(multiply(X2,inverse(X2)),multiply(X3,n1))),multiply(multiply(X3,n1),X4)),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,plain,
multiply(X4,add(X3,X2)) = add(multiply(X3,X4),multiply(X2,X4)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c115,plain,
multiply(multiply(X4,add(X3,X2)),multiply(X2,X4)) = multiply(add(multiply(X3,X4),multiply(X2,X4)),multiply(X2,X4)),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
multiply(add(multiply(X3,X4),multiply(X2,X4)),multiply(X2,X4)) = multiply(X2,X4),
inference(substitution,[status(thm)],[c5]) ).
cnf(c117,plain,
multiply(multiply(X4,add(X3,X2)),multiply(X2,X4)) = multiply(X2,X4),
inference(transitivity,[status(thm)],[c115,c116]) ).
cnf(c118,plain,
multiply(multiply(X4,add(multiply(X2,inverse(X2)),multiply(X3,n1))),multiply(multiply(X3,n1),X4)) = multiply(multiply(X3,n1),X4),
inference(substitution,[status(thm)],[c117]) ).
cnf(c119,plain,
multiply(multiply(X3,X2),multiply(multiply(X2,n1),X3)) = multiply(multiply(X2,n1),X3),
inference(transitivity,[status(thm)],[c113,c118]) ).
cnf(c120,plain,
multiply(multiply(X2,n1),multiply(multiply(n1,n1),X2)) = multiply(multiply(n1,n1),X2),
inference(substitution,[status(thm)],[c119]) ).
cnf(c121,plain,
multiply(multiply(n1,n1),X2) = multiply(multiply(X2,n1),multiply(multiply(n1,n1),X2)),
inference(symmetry,[status(thm)],[c120]) ).
cnf(c122,plain,
n1 = add(X2,n1),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c123,plain,
multiply(X3,n1) = multiply(X3,add(X2,n1)),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
multiply(multiply(X3,n1),multiply(X3,n1)) = multiply(multiply(X3,n1),multiply(X3,add(X2,n1))),
inference(congruence,[status(thm)],[c123]) ).
cnf(c125,plain,
n1 = add(X2,n1),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c126,plain,
multiply(X3,n1) = multiply(X3,add(X2,n1)),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
multiply(multiply(X4,n1),multiply(X4,add(X3,n1))) = multiply(multiply(X4,add(X2,n1)),multiply(X4,add(X3,n1))),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
add(X2,n1) = add(n1,n1),
inference(substitution,[status(thm)],[c38]) ).
cnf(c129,plain,
multiply(X3,add(X2,n1)) = multiply(X3,add(n1,n1)),
inference(congruence,[status(thm)],[c128]) ).
cnf(c130,plain,
multiply(multiply(X4,add(X3,n1)),multiply(X4,add(X2,n1))) = multiply(multiply(X4,add(X3,n1)),multiply(X4,add(n1,n1))),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
multiply(X2,add(n1,n1)) = add(multiply(n1,X2),multiply(n1,X2)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c132,plain,
multiply(multiply(X3,add(X2,n1)),multiply(X3,add(n1,n1))) = multiply(multiply(X3,add(X2,n1)),add(multiply(n1,X3),multiply(n1,X3))),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,plain,
multiply(X3,add(X2,n1)) = add(X3,multiply(n1,X3)),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c134,plain,
multiply(multiply(X3,add(X2,n1)),add(multiply(n1,X3),multiply(n1,X3))) = multiply(add(X3,multiply(n1,X3)),add(multiply(n1,X3),multiply(n1,X3))),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
multiply(add(X2,X3),X3) = X3,
inference(substitution,[status(thm)],[c5]) ).
cnf(c136,plain,
X3 = multiply(add(X2,X3),X3),
inference(symmetry,[status(thm)],[c135]) ).
cnf(c137,plain,
add(X3,X3) = add(multiply(add(X2,X3),X3),X3),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
multiply(add(X4,X3),add(X3,X3)) = multiply(add(X4,X3),add(multiply(add(X2,X3),X3),X3)),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,plain,
multiply(X3,add(X2,add(X4,X3))) = add(multiply(X2,X3),X3),
inference(substitution,[status(thm)],[c45]) ).
cnf(c140,plain,
add(multiply(X2,X3),X3) = multiply(X3,add(X2,add(X4,X3))),
inference(symmetry,[status(thm)],[c139]) ).
cnf(c141,plain,
multiply(add(X4,X3),add(multiply(X2,X3),X3)) = multiply(add(X4,X3),multiply(X3,add(X2,add(X4,X3)))),
inference(congruence,[status(thm)],[c140]) ).
cnf(c142,plain,
multiply(add(X2,add(X4,X3)),add(X4,X3)) = add(X4,X3),
inference(substitution,[status(thm)],[c5]) ).
cnf(c143,plain,
add(X4,X3) = multiply(add(X2,add(X4,X3)),add(X4,X3)),
inference(symmetry,[status(thm)],[c142]) ).
cnf(c144,plain,
multiply(add(X4,X3),multiply(X3,add(X2,add(X4,X3)))) = multiply(multiply(add(X2,add(X4,X3)),add(X4,X3)),multiply(X3,add(X2,add(X4,X3)))),
inference(congruence,[status(thm)],[c143]) ).
cnf(c145,plain,
multiply(multiply(add(X2,add(X4,X3)),add(X4,X3)),multiply(X3,add(X2,add(X4,X3)))) = multiply(X3,add(X2,add(X4,X3))),
inference(substitution,[status(thm)],[c117]) ).
cnf(c146,plain,
multiply(X3,add(X2,add(X4,X3))) = add(multiply(X2,X3),X3),
inference(substitution,[status(thm)],[c45]) ).
cnf(c147,plain,
multiply(multiply(add(X2,add(X4,X3)),add(X4,X3)),multiply(X3,add(X2,add(X4,X3)))) = add(multiply(X2,X3),X3),
inference(transitivity,[status(thm)],[c145,c146]) ).
cnf(c148,plain,
multiply(add(X4,X3),multiply(X3,add(X2,add(X4,X3)))) = add(multiply(X2,X3),X3),
inference(transitivity,[status(thm)],[c144,c147]) ).
cnf(c149,plain,
multiply(add(X4,X3),add(multiply(X2,X3),X3)) = add(multiply(X2,X3),X3),
inference(transitivity,[status(thm)],[c141,c148]) ).
cnf(c150,plain,
multiply(add(X4,X3),add(multiply(add(X2,X3),X3),X3)) = add(multiply(add(X2,X3),X3),X3),
inference(substitution,[status(thm)],[c149]) ).
cnf(c151,plain,
multiply(add(X2,X3),X3) = X3,
inference(substitution,[status(thm)],[c5]) ).
cnf(c152,plain,
add(multiply(add(X2,X3),X3),X3) = add(X3,X3),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
multiply(add(X4,X3),add(multiply(add(X2,X3),X3),X3)) = add(X3,X3),
inference(transitivity,[status(thm)],[c150,c152]) ).
cnf(c154,plain,
multiply(add(X3,X2),add(X2,X2)) = add(X2,X2),
inference(transitivity,[status(thm)],[c138,c153]) ).
cnf(c155,plain,
multiply(add(X2,multiply(n1,X2)),add(multiply(n1,X2),multiply(n1,X2))) = add(multiply(n1,X2),multiply(n1,X2)),
inference(substitution,[status(thm)],[c154]) ).
cnf(c156,plain,
multiply(X2,add(n1,n1)) = add(multiply(n1,X2),multiply(n1,X2)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c157,plain,
add(multiply(n1,X2),multiply(n1,X2)) = multiply(X2,add(n1,n1)),
inference(symmetry,[status(thm)],[c156]) ).
cnf(c158,plain,
add(X2,n1) = add(n1,n1),
inference(substitution,[status(thm)],[c38]) ).
cnf(c159,plain,
add(n1,n1) = add(X2,n1),
inference(symmetry,[status(thm)],[c158]) ).
cnf(c160,plain,
multiply(X3,add(n1,n1)) = multiply(X3,add(X2,n1)),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
add(multiply(n1,X3),multiply(n1,X3)) = multiply(X3,add(X2,n1)),
inference(transitivity,[status(thm)],[c157,c160]) ).
cnf(c162,plain,
multiply(add(X3,multiply(n1,X3)),add(multiply(n1,X3),multiply(n1,X3))) = multiply(X3,add(X2,n1)),
inference(transitivity,[status(thm)],[c155,c161]) ).
cnf(c163,plain,
multiply(multiply(X4,add(X3,n1)),add(multiply(n1,X4),multiply(n1,X4))) = multiply(X4,add(X2,n1)),
inference(transitivity,[status(thm)],[c134,c162]) ).
cnf(c164,plain,
multiply(multiply(X4,add(X3,n1)),multiply(X4,add(n1,n1))) = multiply(X4,add(X2,n1)),
inference(transitivity,[status(thm)],[c132,c163]) ).
cnf(c165,plain,
multiply(multiply(X5,add(X4,n1)),multiply(X5,add(X3,n1))) = multiply(X5,add(X2,n1)),
inference(transitivity,[status(thm)],[c130,c164]) ).
cnf(c166,plain,
multiply(multiply(X5,add(X3,n1)),multiply(X5,add(X4,n1))) = multiply(X5,add(X2,n1)),
inference(substitution,[status(thm)],[c165]) ).
cnf(c167,plain,
multiply(X3,add(X2,n1)) = multiply(X3,n1),
inference(congruence,[status(thm)],[c103]) ).
cnf(c168,plain,
multiply(multiply(X4,add(X2,n1)),multiply(X4,add(X3,n1))) = multiply(X4,n1),
inference(transitivity,[status(thm)],[c166,c167]) ).
cnf(c169,plain,
multiply(multiply(X3,n1),multiply(X3,add(X2,n1))) = multiply(X3,n1),
inference(transitivity,[status(thm)],[c127,c168]) ).
cnf(c170,plain,
multiply(multiply(X2,n1),multiply(X2,n1)) = multiply(X2,n1),
inference(transitivity,[status(thm)],[c124,c169]) ).
cnf(c171,plain,
multiply(X2,n1) = multiply(multiply(X2,n1),multiply(X2,n1)),
inference(symmetry,[status(thm)],[c170]) ).
cnf(c172,axiom,
pixley(X2,Y2,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pixley3) ).
cnf(c173,plain,
pixley(X2,inverse(n1),X2) = X2,
inference(substitution,[status(thm)],[c172]) ).
cnf(c174,plain,
X2 = pixley(X2,inverse(n1),X2),
inference(symmetry,[status(thm)],[c173]) ).
cnf(c175,plain,
multiply(multiply(X2,n1),X2) = multiply(multiply(X2,n1),pixley(X2,inverse(n1),X2)),
inference(congruence,[status(thm)],[c174]) ).
cnf(c176,plain,
multiply(n1,add(X3,X2)) = add(multiply(X3,n1),multiply(X2,n1)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c177,plain,
n1 = add(X2,n1),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c178,plain,
multiply(X2,n1) = multiply(X2,add(X3,n1)),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
add(multiply(X3,n1),multiply(X2,n1)) = add(multiply(X3,n1),multiply(X2,add(X3,n1))),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
add(multiply(X2,inverse(X2)),multiply(multiply(inverse(X3),n1),n1)) = multiply(inverse(X3),n1),
inference(substitution,[status(thm)],[c25]) ).
cnf(c181,plain,
multiply(inverse(X3),n1) = add(multiply(X2,inverse(X2)),multiply(multiply(inverse(X3),n1),n1)),
inference(symmetry,[status(thm)],[c180]) ).
cnf(c182,plain,
n1 = add(X2,n1),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c183,plain,
multiply(multiply(inverse(X3),n1),n1) = multiply(multiply(inverse(X3),n1),add(X2,n1)),
inference(congruence,[status(thm)],[c182]) ).
cnf(c184,plain,
add(multiply(inverse(X3),n1),multiply(n1,multiply(inverse(X3),n1))) = multiply(multiply(inverse(X3),n1),add(X2,n1)),
inference(substitution,[status(thm)],[c58]) ).
cnf(c185,plain,
multiply(multiply(inverse(X3),n1),add(X2,n1)) = add(multiply(inverse(X3),n1),multiply(n1,multiply(inverse(X3),n1))),
inference(symmetry,[status(thm)],[c184]) ).
cnf(c186,plain,
n1 = add(X2,n1),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c187,plain,
multiply(inverse(X3),n1) = multiply(inverse(X3),add(X2,n1)),
inference(congruence,[status(thm)],[c186]) ).
cnf(c188,plain,
multiply(n1,multiply(inverse(X3),n1)) = multiply(n1,multiply(inverse(X3),add(X2,n1))),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
multiply(add(X2,n1),n1) = n1,
inference(substitution,[status(thm)],[c5]) ).
cnf(c190,plain,
n1 = multiply(add(X2,n1),n1),
inference(symmetry,[status(thm)],[c189]) ).
cnf(c191,plain,
multiply(n1,multiply(inverse(X3),add(X2,n1))) = multiply(multiply(add(X2,n1),n1),multiply(inverse(X3),add(X2,n1))),
inference(congruence,[status(thm)],[c190]) ).
cnf(c192,plain,
n1 = add(X2,inverse(X2)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c193,plain,
multiply(X3,n1) = multiply(X3,add(X2,inverse(X2))),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
multiply(multiply(X3,n1),multiply(inverse(X2),X3)) = multiply(multiply(X3,add(X2,inverse(X2))),multiply(inverse(X2),X3)),
inference(congruence,[status(thm)],[c193]) ).
cnf(c195,plain,
multiply(multiply(X3,add(X2,inverse(X2))),multiply(inverse(X2),X3)) = multiply(inverse(X2),X3),
inference(substitution,[status(thm)],[c117]) ).
cnf(c196,plain,
multiply(multiply(X3,n1),multiply(inverse(X2),X3)) = multiply(inverse(X2),X3),
inference(transitivity,[status(thm)],[c194,c195]) ).
cnf(c197,plain,
multiply(multiply(add(X2,n1),n1),multiply(inverse(X3),add(X2,n1))) = multiply(inverse(X3),add(X2,n1)),
inference(substitution,[status(thm)],[c196]) ).
cnf(c198,plain,
multiply(n1,multiply(inverse(X3),add(X2,n1))) = multiply(inverse(X3),add(X2,n1)),
inference(transitivity,[status(thm)],[c191,c197]) ).
cnf(c199,plain,
multiply(inverse(X3),add(X2,n1)) = multiply(inverse(X3),n1),
inference(congruence,[status(thm)],[c103]) ).
cnf(c200,plain,
multiply(n1,multiply(inverse(X3),add(X2,n1))) = multiply(inverse(X3),n1),
inference(transitivity,[status(thm)],[c198,c199]) ).
cnf(c201,plain,
multiply(n1,multiply(inverse(X2),n1)) = multiply(inverse(X2),n1),
inference(transitivity,[status(thm)],[c188,c200]) ).
cnf(c202,plain,
add(multiply(inverse(X2),n1),multiply(n1,multiply(inverse(X2),n1))) = add(multiply(inverse(X2),n1),multiply(inverse(X2),n1)),
inference(congruence,[status(thm)],[c201]) ).
cnf(c203,plain,
multiply(n1,add(inverse(X2),inverse(X2))) = add(multiply(inverse(X2),n1),multiply(inverse(X2),n1)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c204,plain,
add(multiply(inverse(X2),n1),multiply(inverse(X2),n1)) = multiply(n1,add(inverse(X2),inverse(X2))),
inference(symmetry,[status(thm)],[c203]) ).
cnf(c205,plain,
add(X2,n1) = add(n1,n1),
inference(substitution,[status(thm)],[c38]) ).
cnf(c206,plain,
multiply(inverse(X3),add(X2,n1)) = multiply(inverse(X3),add(n1,n1)),
inference(congruence,[status(thm)],[c205]) ).
cnf(c207,plain,
multiply(multiply(add(n1,n1),n1),multiply(inverse(X2),add(n1,n1))) = multiply(inverse(X2),add(n1,n1)),
inference(substitution,[status(thm)],[c196]) ).
cnf(c208,plain,
multiply(inverse(X2),add(n1,n1)) = multiply(multiply(add(n1,n1),n1),multiply(inverse(X2),add(n1,n1))),
inference(symmetry,[status(thm)],[c207]) ).
cnf(c209,plain,
inverse(X2) = multiply(n1,inverse(X2)),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c210,plain,
add(inverse(X3),multiply(X2,inverse(X3))) = add(multiply(n1,inverse(X3)),multiply(X2,inverse(X3))),
inference(congruence,[status(thm)],[c209]) ).
cnf(c211,plain,
multiply(inverse(X3),add(n1,X2)) = add(multiply(n1,inverse(X3)),multiply(X2,inverse(X3))),
inference(substitution,[status(thm)],[c14]) ).
cnf(c212,plain,
add(multiply(n1,inverse(X3)),multiply(X2,inverse(X3))) = multiply(inverse(X3),add(n1,X2)),
inference(symmetry,[status(thm)],[c211]) ).
cnf(c213,plain,
add(inverse(X3),multiply(X2,inverse(X3))) = multiply(inverse(X3),add(n1,X2)),
inference(transitivity,[status(thm)],[c210,c212]) ).
cnf(c214,plain,
add(inverse(X2),multiply(n1,inverse(X2))) = multiply(inverse(X2),add(n1,n1)),
inference(substitution,[status(thm)],[c213]) ).
cnf(c215,plain,
multiply(inverse(X2),add(n1,n1)) = add(inverse(X2),multiply(n1,inverse(X2))),
inference(symmetry,[status(thm)],[c214]) ).
cnf(c216,plain,
add(inverse(X2),multiply(n1,inverse(X2))) = add(inverse(X2),inverse(X2)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c217,plain,
multiply(inverse(X2),add(n1,n1)) = add(inverse(X2),inverse(X2)),
inference(transitivity,[status(thm)],[c215,c216]) ).
cnf(c218,plain,
multiply(multiply(add(n1,n1),n1),multiply(inverse(X2),add(n1,n1))) = multiply(multiply(add(n1,n1),n1),add(inverse(X2),inverse(X2))),
inference(congruence,[status(thm)],[c217]) ).
cnf(c219,plain,
multiply(add(n1,n1),n1) = n1,
inference(substitution,[status(thm)],[c5]) ).
cnf(c220,plain,
multiply(multiply(add(n1,n1),n1),add(inverse(X2),inverse(X2))) = multiply(n1,add(inverse(X2),inverse(X2))),
inference(congruence,[status(thm)],[c219]) ).
cnf(c221,plain,
multiply(multiply(add(n1,n1),n1),multiply(inverse(X2),add(n1,n1))) = multiply(n1,add(inverse(X2),inverse(X2))),
inference(transitivity,[status(thm)],[c218,c220]) ).
cnf(c222,plain,
multiply(inverse(X2),add(n1,n1)) = multiply(n1,add(inverse(X2),inverse(X2))),
inference(transitivity,[status(thm)],[c208,c221]) ).
cnf(c223,plain,
multiply(inverse(X3),add(X2,n1)) = multiply(n1,add(inverse(X3),inverse(X3))),
inference(transitivity,[status(thm)],[c206,c222]) ).
cnf(c224,plain,
multiply(n1,add(inverse(X3),inverse(X3))) = multiply(inverse(X3),add(X2,n1)),
inference(symmetry,[status(thm)],[c223]) ).
cnf(c225,plain,
add(X2,n1) = add(n1,n1),
inference(substitution,[status(thm)],[c38]) ).
cnf(c226,plain,
multiply(inverse(X3),add(X2,n1)) = multiply(inverse(X3),add(n1,n1)),
inference(congruence,[status(thm)],[c225]) ).
cnf(c227,plain,
multiply(inverse(X3),add(X2,n1)) = add(inverse(X3),inverse(X3)),
inference(transitivity,[status(thm)],[c226,c217]) ).
cnf(c228,plain,
multiply(n1,add(inverse(X2),inverse(X2))) = add(inverse(X2),inverse(X2)),
inference(transitivity,[status(thm)],[c224,c227]) ).
cnf(c229,plain,
add(inverse(X3),inverse(X3)) = multiply(inverse(X3),add(X2,n1)),
inference(symmetry,[status(thm)],[c227]) ).
cnf(c230,plain,
multiply(inverse(X3),add(X2,n1)) = multiply(inverse(X3),n1),
inference(congruence,[status(thm)],[c103]) ).
cnf(c231,plain,
add(inverse(X2),inverse(X2)) = multiply(inverse(X2),n1),
inference(transitivity,[status(thm)],[c229,c230]) ).
cnf(c232,plain,
multiply(n1,add(inverse(X2),inverse(X2))) = multiply(inverse(X2),n1),
inference(transitivity,[status(thm)],[c228,c231]) ).
cnf(c233,plain,
add(multiply(inverse(X2),n1),multiply(inverse(X2),n1)) = multiply(inverse(X2),n1),
inference(transitivity,[status(thm)],[c204,c232]) ).
cnf(c234,plain,
add(multiply(inverse(X2),n1),multiply(n1,multiply(inverse(X2),n1))) = multiply(inverse(X2),n1),
inference(transitivity,[status(thm)],[c202,c233]) ).
cnf(c235,plain,
multiply(multiply(inverse(X3),n1),add(X2,n1)) = multiply(inverse(X3),n1),
inference(transitivity,[status(thm)],[c185,c234]) ).
cnf(c236,plain,
multiply(multiply(inverse(X2),n1),n1) = multiply(inverse(X2),n1),
inference(transitivity,[status(thm)],[c183,c235]) ).
cnf(c237,plain,
add(multiply(X2,inverse(X2)),multiply(multiply(inverse(X3),n1),n1)) = add(multiply(X2,inverse(X2)),multiply(inverse(X3),n1)),
inference(congruence,[status(thm)],[c236]) ).
cnf(c238,plain,
add(multiply(X2,inverse(X2)),multiply(inverse(X3),n1)) = inverse(X3),
inference(substitution,[status(thm)],[c25]) ).
cnf(c239,plain,
add(multiply(X2,inverse(X2)),multiply(multiply(inverse(X3),n1),n1)) = inverse(X3),
inference(transitivity,[status(thm)],[c237,c238]) ).
cnf(c240,plain,
multiply(inverse(X2),n1) = inverse(X2),
inference(transitivity,[status(thm)],[c181,c239]) ).
cnf(c241,plain,
inverse(X2) = multiply(inverse(X2),n1),
inference(symmetry,[status(thm)],[c240]) ).
cnf(c242,plain,
add(inverse(n1),inverse(X2)) = add(inverse(n1),multiply(inverse(X2),n1)),
inference(congruence,[status(thm)],[c241]) ).
cnf(c243,plain,
add(inverse(n1),multiply(inverse(X2),n1)) = inverse(X2),
inference(substitution,[status(thm)],[c27]) ).
cnf(c244,plain,
add(inverse(n1),inverse(X2)) = inverse(X2),
inference(transitivity,[status(thm)],[c242,c243]) ).
cnf(c245,plain,
add(inverse(n1),inverse(inverse(n1))) = inverse(inverse(n1)),
inference(substitution,[status(thm)],[c244]) ).
cnf(c246,plain,
inverse(inverse(n1)) = add(inverse(n1),inverse(inverse(n1))),
inference(symmetry,[status(thm)],[c245]) ).
cnf(c247,plain,
add(inverse(n1),inverse(inverse(n1))) = n1,
inference(substitution,[status(thm)],[c2]) ).
cnf(c248,plain,
inverse(inverse(n1)) = n1,
inference(transitivity,[status(thm)],[c246,c247]) ).
cnf(c249,plain,
n1 = inverse(inverse(n1)),
inference(symmetry,[status(thm)],[c248]) ).
cnf(c250,plain,
add(X2,n1) = add(X2,inverse(inverse(n1))),
inference(congruence,[status(thm)],[c249]) ).
cnf(c251,plain,
multiply(X2,add(X3,n1)) = multiply(X2,add(X3,inverse(inverse(n1)))),
inference(congruence,[status(thm)],[c250]) ).
cnf(c252,plain,
add(multiply(X3,n1),multiply(X2,add(X3,n1))) = add(multiply(X3,n1),multiply(X2,add(X3,inverse(inverse(n1))))),
inference(congruence,[status(thm)],[c251]) ).
cnf(c253,plain,
n1 = inverse(inverse(n1)),
inference(symmetry,[status(thm)],[c248]) ).
cnf(c254,plain,
multiply(X2,n1) = multiply(X2,inverse(inverse(n1))),
inference(congruence,[status(thm)],[c253]) ).
cnf(c255,plain,
add(multiply(X3,n1),multiply(X2,add(X3,inverse(inverse(n1))))) = add(multiply(X3,inverse(inverse(n1))),multiply(X2,add(X3,inverse(inverse(n1))))),
inference(congruence,[status(thm)],[c254]) ).
cnf(c256,plain,
add(multiply(X3,inverse(inverse(n1))),multiply(X2,add(X3,inverse(inverse(n1))))) = pixley(X3,inverse(n1),X2),
inference(substitution,[status(thm)],[c20]) ).
cnf(c257,plain,
add(multiply(X3,n1),multiply(X2,add(X3,inverse(inverse(n1))))) = pixley(X3,inverse(n1),X2),
inference(transitivity,[status(thm)],[c255,c256]) ).
cnf(c258,plain,
add(multiply(X3,n1),multiply(X2,add(X3,n1))) = pixley(X3,inverse(n1),X2),
inference(transitivity,[status(thm)],[c252,c257]) ).
cnf(c259,plain,
add(multiply(X3,n1),multiply(X2,n1)) = pixley(X3,inverse(n1),X2),
inference(transitivity,[status(thm)],[c179,c258]) ).
cnf(c260,plain,
multiply(n1,add(X3,X2)) = pixley(X3,inverse(n1),X2),
inference(transitivity,[status(thm)],[c176,c259]) ).
cnf(c261,plain,
multiply(n1,add(X2,X2)) = pixley(X2,inverse(n1),X2),
inference(substitution,[status(thm)],[c260]) ).
cnf(c262,plain,
pixley(X2,inverse(n1),X2) = multiply(n1,add(X2,X2)),
inference(symmetry,[status(thm)],[c261]) ).
cnf(c263,plain,
multiply(multiply(X2,n1),pixley(X2,inverse(n1),X2)) = multiply(multiply(X2,n1),multiply(n1,add(X2,X2))),
inference(congruence,[status(thm)],[c262]) ).
cnf(c264,plain,
multiply(n1,add(X2,X2)) = add(multiply(X2,n1),multiply(X2,n1)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c265,plain,
multiply(multiply(X2,n1),multiply(n1,add(X2,X2))) = multiply(multiply(X2,n1),add(multiply(X2,n1),multiply(X2,n1))),
inference(congruence,[status(thm)],[c264]) ).
cnf(c266,plain,
X2 = add(inverse(n1),multiply(X2,n1)),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c267,plain,
multiply(n1,X2) = multiply(n1,add(inverse(n1),multiply(X2,n1))),
inference(congruence,[status(thm)],[c266]) ).
cnf(c268,plain,
multiply(n1,add(inverse(n1),multiply(X2,n1))) = pixley(inverse(n1),inverse(n1),multiply(X2,n1)),
inference(substitution,[status(thm)],[c260]) ).
cnf(c269,plain,
pixley(inverse(n1),inverse(n1),multiply(X2,n1)) = multiply(X2,n1),
inference(substitution,[status(thm)],[c22]) ).
cnf(c270,plain,
multiply(n1,add(inverse(n1),multiply(X2,n1))) = multiply(X2,n1),
inference(transitivity,[status(thm)],[c268,c269]) ).
cnf(c271,plain,
multiply(n1,X2) = multiply(X2,n1),
inference(transitivity,[status(thm)],[c267,c270]) ).
cnf(c272,plain,
multiply(X2,n1) = multiply(n1,X2),
inference(symmetry,[status(thm)],[c271]) ).
cnf(c273,plain,
add(X2,multiply(X2,n1)) = add(X2,multiply(n1,X2)),
inference(congruence,[status(thm)],[c272]) ).
cnf(c274,plain,
multiply(X3,add(X2,n1)) = multiply(X3,n1),
inference(congruence,[status(thm)],[c103]) ).
cnf(c275,plain,
add(X2,multiply(n1,X2)) = multiply(X2,n1),
inference(transitivity,[status(thm)],[c58,c274]) ).
cnf(c276,plain,
add(X2,multiply(X2,n1)) = multiply(X2,n1),
inference(transitivity,[status(thm)],[c273,c275]) ).
cnf(c277,plain,
multiply(X2,n1) = add(X2,multiply(X2,n1)),
inference(symmetry,[status(thm)],[c276]) ).
cnf(c278,plain,
multiply(multiply(X2,n1),add(multiply(X2,n1),multiply(X2,n1))) = multiply(add(X2,multiply(X2,n1)),add(multiply(X2,n1),multiply(X2,n1))),
inference(congruence,[status(thm)],[c277]) ).
cnf(c279,plain,
multiply(add(X2,multiply(X2,n1)),add(multiply(X2,n1),multiply(X2,n1))) = add(multiply(X2,n1),multiply(X2,n1)),
inference(substitution,[status(thm)],[c154]) ).
cnf(c280,plain,
multiply(n1,add(X2,X2)) = add(multiply(X2,n1),multiply(X2,n1)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c281,plain,
add(multiply(X2,n1),multiply(X2,n1)) = multiply(n1,add(X2,X2)),
inference(symmetry,[status(thm)],[c280]) ).
cnf(c282,plain,
multiply(n1,add(X2,X2)) = pixley(X2,inverse(n1),X2),
inference(substitution,[status(thm)],[c260]) ).
cnf(c283,plain,
pixley(X2,inverse(n1),X2) = X2,
inference(substitution,[status(thm)],[c172]) ).
cnf(c284,plain,
multiply(n1,add(X2,X2)) = X2,
inference(transitivity,[status(thm)],[c282,c283]) ).
cnf(c285,plain,
add(multiply(X2,n1),multiply(X2,n1)) = X2,
inference(transitivity,[status(thm)],[c281,c284]) ).
cnf(c286,plain,
multiply(add(X2,multiply(X2,n1)),add(multiply(X2,n1),multiply(X2,n1))) = X2,
inference(transitivity,[status(thm)],[c279,c285]) ).
cnf(c287,plain,
multiply(multiply(X2,n1),add(multiply(X2,n1),multiply(X2,n1))) = X2,
inference(transitivity,[status(thm)],[c278,c286]) ).
cnf(c288,plain,
multiply(multiply(X2,n1),multiply(n1,add(X2,X2))) = X2,
inference(transitivity,[status(thm)],[c265,c287]) ).
cnf(c289,plain,
multiply(multiply(X2,n1),pixley(X2,inverse(n1),X2)) = X2,
inference(transitivity,[status(thm)],[c263,c288]) ).
cnf(c290,plain,
multiply(multiply(X2,n1),X2) = X2,
inference(transitivity,[status(thm)],[c175,c289]) ).
cnf(c291,plain,
X2 = multiply(multiply(X2,n1),X2),
inference(symmetry,[status(thm)],[c290]) ).
cnf(c292,plain,
add(X2,X2) = add(X2,multiply(multiply(X2,n1),X2)),
inference(congruence,[status(thm)],[c291]) ).
cnf(c293,plain,
pixley(X2,inverse(n1),X2) = X2,
inference(substitution,[status(thm)],[c172]) ).
cnf(c294,plain,
X2 = pixley(X2,inverse(n1),X2),
inference(symmetry,[status(thm)],[c293]) ).
cnf(c295,plain,
multiply(X2,X2) = multiply(X2,pixley(X2,inverse(n1),X2)),
inference(congruence,[status(thm)],[c294]) ).
cnf(c296,plain,
multiply(n1,add(X2,X2)) = pixley(X2,inverse(n1),X2),
inference(substitution,[status(thm)],[c260]) ).
cnf(c297,plain,
pixley(X2,inverse(n1),X2) = multiply(n1,add(X2,X2)),
inference(symmetry,[status(thm)],[c296]) ).
cnf(c298,plain,
multiply(X2,pixley(X2,inverse(n1),X2)) = multiply(X2,multiply(n1,add(X2,X2))),
inference(congruence,[status(thm)],[c297]) ).
cnf(c299,plain,
multiply(n1,add(X2,X2)) = add(multiply(X2,n1),multiply(X2,n1)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c300,plain,
multiply(X2,multiply(n1,add(X2,X2))) = multiply(X2,add(multiply(X2,n1),multiply(X2,n1))),
inference(congruence,[status(thm)],[c299]) ).
cnf(c301,plain,
add(multiply(X2,inverse(X2)),multiply(X3,n1)) = X3,
inference(substitution,[status(thm)],[c25]) ).
cnf(c302,plain,
X3 = add(multiply(X2,inverse(X2)),multiply(X3,n1)),
inference(symmetry,[status(thm)],[c301]) ).
cnf(c303,plain,
multiply(X3,add(multiply(X3,n1),multiply(X3,n1))) = multiply(add(multiply(X2,inverse(X2)),multiply(X3,n1)),add(multiply(X3,n1),multiply(X3,n1))),
inference(congruence,[status(thm)],[c302]) ).
cnf(c304,plain,
multiply(add(multiply(X2,inverse(X2)),multiply(X3,n1)),add(multiply(X3,n1),multiply(X3,n1))) = add(multiply(X3,n1),multiply(X3,n1)),
inference(substitution,[status(thm)],[c154]) ).
cnf(c305,plain,
multiply(n1,add(X2,X2)) = add(multiply(X2,n1),multiply(X2,n1)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c306,plain,
add(multiply(X2,n1),multiply(X2,n1)) = multiply(n1,add(X2,X2)),
inference(symmetry,[status(thm)],[c305]) ).
cnf(c307,plain,
multiply(add(multiply(X2,inverse(X2)),multiply(X3,n1)),add(multiply(X3,n1),multiply(X3,n1))) = multiply(n1,add(X3,X3)),
inference(transitivity,[status(thm)],[c304,c306]) ).
cnf(c308,plain,
multiply(X2,add(multiply(X2,n1),multiply(X2,n1))) = multiply(n1,add(X2,X2)),
inference(transitivity,[status(thm)],[c303,c307]) ).
cnf(c309,plain,
multiply(X2,multiply(n1,add(X2,X2))) = multiply(n1,add(X2,X2)),
inference(transitivity,[status(thm)],[c300,c308]) ).
cnf(c310,plain,
multiply(n1,add(X2,X2)) = pixley(X2,inverse(n1),X2),
inference(substitution,[status(thm)],[c260]) ).
cnf(c311,plain,
pixley(X2,inverse(n1),X2) = X2,
inference(substitution,[status(thm)],[c172]) ).
cnf(c312,plain,
multiply(n1,add(X2,X2)) = X2,
inference(transitivity,[status(thm)],[c310,c311]) ).
cnf(c313,plain,
multiply(X2,multiply(n1,add(X2,X2))) = X2,
inference(transitivity,[status(thm)],[c309,c312]) ).
cnf(c314,plain,
multiply(X2,pixley(X2,inverse(n1),X2)) = X2,
inference(transitivity,[status(thm)],[c298,c313]) ).
cnf(c315,plain,
multiply(X2,X2) = X2,
inference(transitivity,[status(thm)],[c295,c314]) ).
cnf(c316,plain,
X2 = multiply(X2,X2),
inference(symmetry,[status(thm)],[c315]) ).
cnf(c317,plain,
add(X3,multiply(X2,X3)) = add(multiply(X3,X3),multiply(X2,X3)),
inference(congruence,[status(thm)],[c316]) ).
cnf(c318,plain,
multiply(X3,add(X3,X2)) = add(multiply(X3,X3),multiply(X2,X3)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c319,plain,
add(multiply(X3,X3),multiply(X2,X3)) = multiply(X3,add(X3,X2)),
inference(symmetry,[status(thm)],[c318]) ).
cnf(c320,plain,
add(X3,multiply(X2,X3)) = multiply(X3,add(X3,X2)),
inference(transitivity,[status(thm)],[c317,c319]) ).
cnf(c321,plain,
add(X2,multiply(multiply(X2,n1),X2)) = multiply(X2,add(X2,multiply(X2,n1))),
inference(substitution,[status(thm)],[c320]) ).
cnf(c322,plain,
multiply(X2,add(X2,multiply(X2,n1))) = multiply(X2,multiply(X2,n1)),
inference(congruence,[status(thm)],[c276]) ).
cnf(c323,plain,
add(multiply(X2,inverse(X2)),multiply(X3,n1)) = X3,
inference(substitution,[status(thm)],[c25]) ).
cnf(c324,plain,
X3 = add(multiply(X2,inverse(X2)),multiply(X3,n1)),
inference(symmetry,[status(thm)],[c323]) ).
cnf(c325,plain,
multiply(X3,multiply(X3,n1)) = multiply(add(multiply(X2,inverse(X2)),multiply(X3,n1)),multiply(X3,n1)),
inference(congruence,[status(thm)],[c324]) ).
cnf(c326,plain,
multiply(add(multiply(X2,inverse(X2)),multiply(X3,n1)),multiply(X3,n1)) = multiply(X3,n1),
inference(substitution,[status(thm)],[c5]) ).
cnf(c327,plain,
multiply(X2,multiply(X2,n1)) = multiply(X2,n1),
inference(transitivity,[status(thm)],[c325,c326]) ).
cnf(c328,plain,
multiply(X2,add(X2,multiply(X2,n1))) = multiply(X2,n1),
inference(transitivity,[status(thm)],[c322,c327]) ).
cnf(c329,plain,
add(X2,multiply(multiply(X2,n1),X2)) = multiply(X2,n1),
inference(transitivity,[status(thm)],[c321,c328]) ).
cnf(c330,plain,
add(X2,X2) = multiply(X2,n1),
inference(transitivity,[status(thm)],[c292,c329]) ).
cnf(c331,plain,
multiply(X2,n1) = add(X2,X2),
inference(symmetry,[status(thm)],[c330]) ).
cnf(c332,plain,
multiply(multiply(X2,n1),multiply(X2,n1)) = multiply(multiply(X2,n1),add(X2,X2)),
inference(congruence,[status(thm)],[c331]) ).
cnf(c333,plain,
multiply(multiply(X4,n1),add(add(multiply(X2,inverse(X2)),multiply(X4,n1)),X3)) = add(multiply(X4,n1),multiply(X3,multiply(X4,n1))),
inference(substitution,[status(thm)],[c52]) ).
cnf(c334,plain,
add(multiply(X4,n1),multiply(X3,multiply(X4,n1))) = multiply(multiply(X4,n1),add(add(multiply(X2,inverse(X2)),multiply(X4,n1)),X3)),
inference(symmetry,[status(thm)],[c333]) ).
cnf(c335,plain,
add(multiply(X2,inverse(X2)),multiply(X3,n1)) = X3,
inference(substitution,[status(thm)],[c25]) ).
cnf(c336,plain,
add(add(multiply(X2,inverse(X2)),multiply(X4,n1)),X3) = add(X4,X3),
inference(congruence,[status(thm)],[c335]) ).
cnf(c337,plain,
multiply(multiply(X4,n1),add(add(multiply(X2,inverse(X2)),multiply(X4,n1)),X3)) = multiply(multiply(X4,n1),add(X4,X3)),
inference(congruence,[status(thm)],[c336]) ).
cnf(c338,plain,
add(multiply(X3,n1),multiply(X2,multiply(X3,n1))) = multiply(multiply(X3,n1),add(X3,X2)),
inference(transitivity,[status(thm)],[c334,c337]) ).
cnf(c339,plain,
add(multiply(X2,n1),multiply(X2,multiply(X2,n1))) = multiply(multiply(X2,n1),add(X2,X2)),
inference(substitution,[status(thm)],[c338]) ).
cnf(c340,plain,
multiply(multiply(X2,n1),add(X2,X2)) = add(multiply(X2,n1),multiply(X2,multiply(X2,n1))),
inference(symmetry,[status(thm)],[c339]) ).
cnf(c341,plain,
add(multiply(X2,n1),multiply(X2,multiply(X2,n1))) = add(multiply(X2,n1),multiply(X2,n1)),
inference(congruence,[status(thm)],[c327]) ).
cnf(c342,plain,
multiply(n1,add(X2,X2)) = add(multiply(X2,n1),multiply(X2,n1)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c343,plain,
add(multiply(X2,n1),multiply(X2,n1)) = multiply(n1,add(X2,X2)),
inference(symmetry,[status(thm)],[c342]) ).
cnf(c344,plain,
add(multiply(X2,n1),multiply(X2,multiply(X2,n1))) = multiply(n1,add(X2,X2)),
inference(transitivity,[status(thm)],[c341,c343]) ).
cnf(c345,plain,
multiply(multiply(X2,n1),add(X2,X2)) = multiply(n1,add(X2,X2)),
inference(transitivity,[status(thm)],[c340,c344]) ).
cnf(c346,plain,
multiply(n1,add(X2,X2)) = pixley(X2,inverse(n1),X2),
inference(substitution,[status(thm)],[c260]) ).
cnf(c347,plain,
pixley(X2,inverse(n1),X2) = X2,
inference(substitution,[status(thm)],[c172]) ).
cnf(c348,plain,
multiply(n1,add(X2,X2)) = X2,
inference(transitivity,[status(thm)],[c346,c347]) ).
cnf(c349,plain,
multiply(multiply(X2,n1),add(X2,X2)) = X2,
inference(transitivity,[status(thm)],[c345,c348]) ).
cnf(c350,plain,
multiply(multiply(X2,n1),multiply(X2,n1)) = X2,
inference(transitivity,[status(thm)],[c332,c349]) ).
cnf(c351,plain,
multiply(X2,n1) = X2,
inference(transitivity,[status(thm)],[c171,c350]) ).
cnf(c352,plain,
multiply(multiply(X2,n1),multiply(multiply(n1,n1),X2)) = multiply(X2,multiply(multiply(n1,n1),X2)),
inference(congruence,[status(thm)],[c351]) ).
cnf(c353,plain,
multiply(multiply(n1,n1),X2) = multiply(n1,X2),
inference(congruence,[status(thm)],[c107]) ).
cnf(c354,plain,
multiply(X2,multiply(multiply(n1,n1),X2)) = multiply(X2,multiply(n1,X2)),
inference(congruence,[status(thm)],[c353]) ).
cnf(c355,plain,
multiply(X2,multiply(n1,X2)) = multiply(X2,multiply(X2,n1)),
inference(congruence,[status(thm)],[c271]) ).
cnf(c356,plain,
multiply(X2,multiply(n1,X2)) = multiply(X2,n1),
inference(transitivity,[status(thm)],[c355,c327]) ).
cnf(c357,plain,
multiply(X2,multiply(n1,X2)) = X2,
inference(transitivity,[status(thm)],[c356,c351]) ).
cnf(c358,plain,
multiply(X2,multiply(multiply(n1,n1),X2)) = X2,
inference(transitivity,[status(thm)],[c354,c357]) ).
cnf(c359,plain,
multiply(multiply(X2,n1),multiply(multiply(n1,n1),X2)) = X2,
inference(transitivity,[status(thm)],[c352,c358]) ).
cnf(c360,plain,
multiply(multiply(n1,n1),X2) = X2,
inference(transitivity,[status(thm)],[c121,c359]) ).
cnf(c361,plain,
multiply(n1,X2) = X2,
inference(transitivity,[status(thm)],[c109,c360]) ).
cnf(c362,plain,
X2 = multiply(n1,X2),
inference(symmetry,[status(thm)],[c361]) ).
cnf(c363,plain,
add(multiply(X3,X2),X2) = add(multiply(X3,X2),multiply(n1,X2)),
inference(congruence,[status(thm)],[c362]) ).
cnf(c364,plain,
multiply(X2,add(X3,n1)) = add(multiply(X3,X2),multiply(n1,X2)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c365,plain,
add(multiply(X3,X2),multiply(n1,X2)) = multiply(X2,add(X3,n1)),
inference(symmetry,[status(thm)],[c364]) ).
cnf(c366,plain,
add(X3,n1) = add(X2,n1),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c367,plain,
multiply(X3,add(X4,n1)) = multiply(X3,add(X2,n1)),
inference(congruence,[status(thm)],[c366]) ).
cnf(c368,plain,
multiply(X3,add(X2,n1)) = multiply(X3,n1),
inference(congruence,[status(thm)],[c103]) ).
cnf(c369,plain,
multiply(X3,add(X2,n1)) = X3,
inference(transitivity,[status(thm)],[c368,c351]) ).
cnf(c370,plain,
multiply(X2,add(X3,n1)) = X2,
inference(transitivity,[status(thm)],[c367,c369]) ).
cnf(c371,plain,
add(multiply(X3,X2),multiply(n1,X2)) = X2,
inference(transitivity,[status(thm)],[c365,c370]) ).
cnf(c372,plain,
add(multiply(X3,X2),X2) = X2,
inference(transitivity,[status(thm)],[c363,c371]) ).
cnf(c373,plain,
add(multiply(a,b),b) = b,
inference(substitution,[status(thm)],[c372]) ).
cnf(c374,plain,
$false,
inference(resolution,[status(thm)],[c1,c373]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO024-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n013.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 21:04:06 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.35 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.35
% 0.21/0.35 % SZS status Unsatisfiable
% 0.21/0.35
% 0.21/0.39 % SZS output start CNFRefutation
% See solution above
% 2.51/0.66
% 2.51/0.66 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------