%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO028-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:35:37 AM UTC 2026
% Result : Unsatisfiable 13.43s 2.05s
% Output : CNFRefutation 14.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 10
% Syntax : Number of clauses : 238 ( 238 unt; 0 nHn; 4 RR)
% Number of literals : 238 ( 237 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 571 ( 62 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(a,add(b,c)) != add(multiply(b,a),multiply(c,a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_multiply_add_property) ).
cnf(c2,axiom,
multiply(X,Y) = multiply(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_multiply) ).
cnf(c3,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
add(multiply(X4,X3),multiply(X2,X3)) = add(multiply(X4,X3),multiply(X3,X2)),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c7,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
add(multiply(X4,X3),multiply(X3,X2)) = add(multiply(X4,X3),multiply(X2,X3)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c10,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
add(multiply(X4,X3),multiply(X2,X3)) = add(multiply(X3,X4),multiply(X2,X3)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,axiom,
add(X2,Y2) = add(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_add) ).
cnf(c13,plain,
add(multiply(X2,X3),multiply(X3,X4)) = add(multiply(X3,X4),multiply(X2,X3)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
add(multiply(X3,X4),multiply(X2,X3)) = add(multiply(X2,X3),multiply(X3,X4)),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c16,plain,
add(X3,X2) = add(X2,X3),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
multiply(add(X4,X3),add(X3,multiply(X4,X2))) = multiply(add(X3,X4),add(X3,multiply(X4,X2))),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c19,plain,
add(X3,X2) = add(X2,X3),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
multiply(add(X4,X3),add(X4,multiply(X3,X2))) = multiply(add(X3,X4),add(X4,multiply(X3,X2))),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c22,plain,
add(X3,X2) = add(X2,X3),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
multiply(X3,add(X3,X2)) = multiply(X3,add(X2,X3)),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,axiom,
add(X2,multiply(Y2,multiply(X2,Z))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1) ).
cnf(c25,plain,
add(X3,multiply(X2,multiply(X3,X4))) = X3,
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
X4 = add(X4,multiply(X3,multiply(X4,X2))),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
add(X4,X5) = add(X4,add(X5,multiply(X3,multiply(X5,X2)))),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
multiply(X5,add(X4,X5)) = multiply(X5,add(X4,add(X5,multiply(X3,multiply(X5,X2))))),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,axiom,
multiply(X2,add(Y2,add(X2,Z2))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2) ).
cnf(c30,plain,
multiply(X5,add(X4,add(X5,multiply(X3,multiply(X5,X2))))) = X5,
inference(substitution,[status(thm)],[c29]) ).
cnf(c31,plain,
multiply(X3,add(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c28,c30]) ).
cnf(c32,plain,
multiply(X3,add(X3,X2)) = X3,
inference(transitivity,[status(thm)],[c23,c31]) ).
cnf(c33,plain,
multiply(add(X5,multiply(X4,X3)),add(add(X5,multiply(X4,X3)),X2)) = add(X5,multiply(X4,X3)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
add(X5,multiply(X4,X3)) = multiply(add(X5,multiply(X4,X3)),add(add(X5,multiply(X4,X3)),X2)),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
multiply(add(X4,X5),add(X5,multiply(X4,X3))) = multiply(add(X4,X5),multiply(add(X5,multiply(X4,X3)),add(add(X5,multiply(X4,X3)),X2))),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
add(multiply(X4,X2),X3) = add(X3,multiply(X4,X2)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c37,plain,
add(X3,multiply(X4,X2)) = add(multiply(X4,X2),X3),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
add(X4,add(X3,multiply(X4,X2))) = add(X4,add(multiply(X4,X2),X3)),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,axiom,
add(add(X2,Y2),Z2) = add(X2,add(Y2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_add) ).
cnf(c40,plain,
add(add(X4,multiply(X4,X2)),X3) = add(X4,add(multiply(X4,X2),X3)),
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
add(X4,add(multiply(X4,X2),X3)) = add(add(X4,multiply(X4,X2)),X3),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c43,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
add(X3,multiply(X3,X2)) = add(X3,multiply(X2,X3)),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
multiply(X4,add(X3,add(X4,X2))) = X4,
inference(substitution,[status(thm)],[c29]) ).
cnf(c46,plain,
X4 = multiply(X4,add(X3,add(X4,X2))),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
multiply(X4,X5) = multiply(X4,multiply(X5,add(X3,add(X5,X2)))),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
add(X5,multiply(X4,X5)) = add(X5,multiply(X4,multiply(X5,add(X3,add(X5,X2))))),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
add(X5,multiply(X4,multiply(X5,add(X3,add(X5,X2))))) = X5,
inference(substitution,[status(thm)],[c24]) ).
cnf(c50,plain,
add(X3,multiply(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c48,c49]) ).
cnf(c51,plain,
add(X3,multiply(X3,X2)) = X3,
inference(transitivity,[status(thm)],[c44,c50]) ).
cnf(c52,plain,
add(add(X4,multiply(X4,X2)),X3) = add(X4,X3),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
add(X4,add(multiply(X4,X2),X3)) = add(X4,X3),
inference(transitivity,[status(thm)],[c41,c52]) ).
cnf(c54,plain,
add(X4,add(X3,multiply(X4,X2))) = add(X4,X3),
inference(transitivity,[status(thm)],[c38,c53]) ).
cnf(c55,plain,
add(X3,add(X4,multiply(X3,X2))) = add(X3,X4),
inference(substitution,[status(thm)],[c54]) ).
cnf(c56,plain,
add(X3,X4) = add(X3,add(X4,multiply(X3,X2))),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
multiply(add(X4,X5),multiply(add(X5,multiply(X4,X3)),add(add(X5,multiply(X4,X3)),X2))) = multiply(add(X4,add(X5,multiply(X4,X3))),multiply(add(X5,multiply(X4,X3)),add(add(X5,multiply(X4,X3)),X2))),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
multiply(add(X3,X2),X3) = multiply(X3,add(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c59,plain,
multiply(X3,add(X3,X2)) = multiply(add(X3,X2),X3),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
multiply(add(X4,X3),multiply(X3,add(X3,X2))) = multiply(add(X4,X3),multiply(add(X3,X2),X3)),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,axiom,
multiply(multiply(X2,Y2),Z2) = multiply(X2,multiply(Y2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_multiply) ).
cnf(c62,plain,
multiply(multiply(add(X4,X3),add(X3,X2)),X3) = multiply(add(X4,X3),multiply(add(X3,X2),X3)),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
multiply(add(X4,X3),multiply(add(X3,X2),X3)) = multiply(multiply(add(X4,X3),add(X3,X2)),X3),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,axiom,
multiply(multiply(add(X2,Y2),add(Y2,Z2)),Y2) = Y2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4) ).
cnf(c65,plain,
multiply(multiply(add(X4,X3),add(X3,X2)),X3) = X3,
inference(substitution,[status(thm)],[c64]) ).
cnf(c66,plain,
multiply(add(X4,X3),multiply(add(X3,X2),X3)) = X3,
inference(transitivity,[status(thm)],[c63,c65]) ).
cnf(c67,plain,
multiply(add(X4,X3),multiply(X3,add(X3,X2))) = X3,
inference(transitivity,[status(thm)],[c60,c66]) ).
cnf(c68,plain,
multiply(add(X4,add(X5,multiply(X4,X3))),multiply(add(X5,multiply(X4,X3)),add(add(X5,multiply(X4,X3)),X2))) = add(X5,multiply(X4,X3)),
inference(substitution,[status(thm)],[c67]) ).
cnf(c69,plain,
multiply(add(X4,X5),multiply(add(X5,multiply(X4,X3)),add(add(X5,multiply(X4,X3)),X2))) = add(X5,multiply(X4,X3)),
inference(transitivity,[status(thm)],[c57,c68]) ).
cnf(c70,plain,
multiply(add(X3,X4),add(X4,multiply(X3,X2))) = add(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c35,c69]) ).
cnf(c71,plain,
multiply(add(X4,X3),add(X4,multiply(X3,X2))) = add(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c20,c70]) ).
cnf(c72,plain,
multiply(add(X3,X4),add(X3,multiply(X4,X2))) = add(X3,multiply(X4,X2)),
inference(substitution,[status(thm)],[c71]) ).
cnf(c73,plain,
multiply(add(X4,X3),add(X3,multiply(X4,X2))) = add(X3,multiply(X4,X2)),
inference(transitivity,[status(thm)],[c17,c72]) ).
cnf(c74,plain,
multiply(add(X3,multiply(X2,X3)),add(multiply(X2,X3),multiply(X3,X4))) = add(multiply(X2,X3),multiply(X3,X4)),
inference(substitution,[status(thm)],[c73]) ).
cnf(c75,plain,
add(multiply(X2,X3),multiply(X3,X4)) = multiply(add(X3,multiply(X2,X3)),add(multiply(X2,X3),multiply(X3,X4))),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c76,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c77,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
add(X3,multiply(X2,X3)) = add(X3,multiply(X3,X2)),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
add(X3,multiply(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c78,c51]) ).
cnf(c80,plain,
multiply(add(X3,multiply(X2,X3)),add(multiply(X2,X3),multiply(X3,X4))) = multiply(X3,add(multiply(X2,X3),multiply(X3,X4))),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c82,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,plain,
add(X3,multiply(X4,X2)) = add(X3,multiply(X2,X4)),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
multiply(X4,add(X3,multiply(X4,X2))) = multiply(X4,add(X3,multiply(X2,X4))),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
add(add(X3,X2),inverse(X3)) = add(X3,add(X2,inverse(X3))),
inference(substitution,[status(thm)],[c39]) ).
cnf(c86,plain,
add(X3,add(X2,inverse(X3))) = add(add(X3,X2),inverse(X3)),
inference(symmetry,[status(thm)],[c85]) ).
cnf(c87,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c88,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c89,plain,
add(inverse(X3),multiply(X3,X2)) = add(inverse(X3),multiply(X2,X3)),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
add(inverse(X3),add(multiply(X2,X3),multiply(inverse(X3),X2))) = add(inverse(X3),multiply(X2,X3)),
inference(substitution,[status(thm)],[c54]) ).
cnf(c91,plain,
add(inverse(X3),multiply(X2,X3)) = add(inverse(X3),add(multiply(X2,X3),multiply(inverse(X3),X2))),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,plain,
multiply(X3,inverse(X2)) = multiply(inverse(X2),X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c93,plain,
multiply(inverse(X2),X3) = multiply(X3,inverse(X2)),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c94,plain,
add(multiply(X3,X2),multiply(inverse(X2),X3)) = add(multiply(X3,X2),multiply(X3,inverse(X2))),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,axiom,
add(multiply(X2,Y2),multiply(X2,inverse(Y2))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b2) ).
cnf(c96,plain,
add(multiply(X3,X2),multiply(X3,inverse(X2))) = X3,
inference(substitution,[status(thm)],[c95]) ).
cnf(c97,plain,
add(multiply(X3,X2),multiply(inverse(X2),X3)) = X3,
inference(transitivity,[status(thm)],[c94,c96]) ).
cnf(c98,plain,
add(multiply(X2,X3),multiply(inverse(X3),X2)) = X2,
inference(substitution,[status(thm)],[c97]) ).
cnf(c99,plain,
add(inverse(X3),add(multiply(X2,X3),multiply(inverse(X3),X2))) = add(inverse(X3),X2),
inference(congruence,[status(thm)],[c98]) ).
cnf(c100,plain,
add(inverse(X3),X2) = add(X2,inverse(X3)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c101,plain,
add(inverse(X3),add(multiply(X2,X3),multiply(inverse(X3),X2))) = add(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c99,c100]) ).
cnf(c102,plain,
add(inverse(X3),multiply(X2,X3)) = add(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c91,c101]) ).
cnf(c103,plain,
add(inverse(X3),multiply(X3,X2)) = add(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c89,c102]) ).
cnf(c104,plain,
add(inverse(X3),multiply(X3,add(X3,X2))) = add(add(X3,X2),inverse(X3)),
inference(substitution,[status(thm)],[c103]) ).
cnf(c105,plain,
add(add(X3,X2),inverse(X3)) = add(inverse(X3),multiply(X3,add(X3,X2))),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
add(inverse(X3),multiply(X3,add(X3,X2))) = add(inverse(X3),X3),
inference(congruence,[status(thm)],[c32]) ).
cnf(c107,plain,
add(inverse(X2),X2) = add(X2,inverse(X2)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c108,plain,
add(inverse(X3),multiply(X3,add(X3,X2))) = add(X3,inverse(X3)),
inference(transitivity,[status(thm)],[c106,c107]) ).
cnf(c109,plain,
add(add(X3,X2),inverse(X3)) = add(X3,inverse(X3)),
inference(transitivity,[status(thm)],[c105,c108]) ).
cnf(c110,plain,
add(X3,add(X2,inverse(X3))) = add(X3,inverse(X3)),
inference(transitivity,[status(thm)],[c86,c109]) ).
cnf(c111,plain,
add(X2,add(X3,inverse(X2))) = add(X2,inverse(X2)),
inference(substitution,[status(thm)],[c110]) ).
cnf(c112,plain,
add(X2,inverse(X2)) = add(X2,add(X3,inverse(X2))),
inference(symmetry,[status(thm)],[c111]) ).
cnf(c113,plain,
multiply(X3,add(X2,inverse(X2))) = multiply(X3,add(X2,add(X3,inverse(X2)))),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,plain,
multiply(X3,add(X2,add(X3,inverse(X2)))) = X3,
inference(substitution,[status(thm)],[c29]) ).
cnf(c115,plain,
multiply(X3,add(X2,inverse(X2))) = X3,
inference(transitivity,[status(thm)],[c113,c114]) ).
cnf(c116,plain,
multiply(inverse(inverse(X2)),add(X2,inverse(X2))) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c115]) ).
cnf(c117,plain,
inverse(inverse(X2)) = multiply(inverse(inverse(X2)),add(X2,inverse(X2))),
inference(symmetry,[status(thm)],[c116]) ).
cnf(c118,plain,
add(X3,X2) = add(X2,X3),
inference(substitution,[status(thm)],[c12]) ).
cnf(c119,plain,
add(X2,X3) = add(X3,X2),
inference(symmetry,[status(thm)],[c118]) ).
cnf(c120,plain,
multiply(inverse(X3),add(X2,X3)) = multiply(inverse(X3),add(X3,X2)),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c122,plain,
add(X3,X2) = add(X2,X3),
inference(symmetry,[status(thm)],[c121]) ).
cnf(c123,plain,
multiply(inverse(X3),add(X3,X2)) = multiply(inverse(X3),add(X2,X3)),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
multiply(add(X4,X2),X3) = multiply(X3,add(X4,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c125,plain,
multiply(X3,add(X4,X2)) = multiply(add(X4,X2),X3),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c126,plain,
multiply(X4,multiply(X3,add(X4,X2))) = multiply(X4,multiply(add(X4,X2),X3)),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
multiply(multiply(X4,add(X4,X2)),X3) = multiply(X4,multiply(add(X4,X2),X3)),
inference(substitution,[status(thm)],[c61]) ).
cnf(c128,plain,
multiply(X4,multiply(add(X4,X2),X3)) = multiply(multiply(X4,add(X4,X2)),X3),
inference(symmetry,[status(thm)],[c127]) ).
cnf(c129,plain,
multiply(multiply(X4,add(X4,X2)),X3) = multiply(X4,X3),
inference(congruence,[status(thm)],[c32]) ).
cnf(c130,plain,
multiply(X4,multiply(add(X4,X2),X3)) = multiply(X4,X3),
inference(transitivity,[status(thm)],[c128,c129]) ).
cnf(c131,plain,
multiply(X4,multiply(X3,add(X4,X2))) = multiply(X4,X3),
inference(transitivity,[status(thm)],[c126,c130]) ).
cnf(c132,plain,
multiply(inverse(X3),multiply(add(X2,X3),add(inverse(X3),X2))) = multiply(inverse(X3),add(X2,X3)),
inference(substitution,[status(thm)],[c131]) ).
cnf(c133,plain,
multiply(inverse(X3),add(X2,X3)) = multiply(inverse(X3),multiply(add(X2,X3),add(inverse(X3),X2))),
inference(symmetry,[status(thm)],[c132]) ).
cnf(c134,plain,
add(X3,inverse(X2)) = add(inverse(X2),X3),
inference(substitution,[status(thm)],[c12]) ).
cnf(c135,plain,
add(inverse(X2),X3) = add(X3,inverse(X2)),
inference(symmetry,[status(thm)],[c134]) ).
cnf(c136,plain,
multiply(add(X3,X2),add(inverse(X2),X3)) = multiply(add(X3,X2),add(X3,inverse(X2))),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,axiom,
multiply(add(X2,Y2),add(X2,inverse(Y2))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b1) ).
cnf(c138,plain,
multiply(add(X3,X2),add(X3,inverse(X2))) = X3,
inference(substitution,[status(thm)],[c137]) ).
cnf(c139,plain,
multiply(add(X3,X2),add(inverse(X2),X3)) = X3,
inference(transitivity,[status(thm)],[c136,c138]) ).
cnf(c140,plain,
multiply(add(X2,X3),add(inverse(X3),X2)) = X2,
inference(substitution,[status(thm)],[c139]) ).
cnf(c141,plain,
multiply(inverse(X3),multiply(add(X2,X3),add(inverse(X3),X2))) = multiply(inverse(X3),X2),
inference(congruence,[status(thm)],[c140]) ).
cnf(c142,plain,
multiply(inverse(X3),X2) = multiply(X2,inverse(X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c143,plain,
multiply(inverse(X3),multiply(add(X2,X3),add(inverse(X3),X2))) = multiply(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c141,c142]) ).
cnf(c144,plain,
multiply(inverse(X3),add(X2,X3)) = multiply(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c133,c143]) ).
cnf(c145,plain,
multiply(inverse(X3),add(X3,X2)) = multiply(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c123,c144]) ).
cnf(c146,plain,
multiply(inverse(X3),add(X2,X3)) = multiply(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c120,c145]) ).
cnf(c147,plain,
multiply(inverse(inverse(X2)),add(X2,inverse(X2))) = multiply(X2,inverse(inverse(X2))),
inference(substitution,[status(thm)],[c146]) ).
cnf(c148,plain,
add(inverse(inverse(X2)),X2) = add(X2,inverse(inverse(X2))),
inference(substitution,[status(thm)],[c12]) ).
cnf(c149,plain,
add(X2,inverse(inverse(X2))) = add(inverse(inverse(X2)),X2),
inference(symmetry,[status(thm)],[c148]) ).
cnf(c150,plain,
multiply(add(inverse(inverse(X2)),X2),add(inverse(X2),inverse(inverse(X2)))) = add(inverse(inverse(X2)),X2),
inference(substitution,[status(thm)],[c115]) ).
cnf(c151,plain,
add(inverse(inverse(X2)),X2) = multiply(add(inverse(inverse(X2)),X2),add(inverse(X2),inverse(inverse(X2)))),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c152,plain,
multiply(add(inverse(inverse(X2)),X2),add(inverse(X2),inverse(inverse(X2)))) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c139]) ).
cnf(c153,plain,
add(inverse(inverse(X2)),X2) = inverse(inverse(X2)),
inference(transitivity,[status(thm)],[c151,c152]) ).
cnf(c154,plain,
add(X2,inverse(inverse(X2))) = inverse(inverse(X2)),
inference(transitivity,[status(thm)],[c149,c153]) ).
cnf(c155,plain,
inverse(inverse(X2)) = add(X2,inverse(inverse(X2))),
inference(symmetry,[status(thm)],[c154]) ).
cnf(c156,plain,
multiply(X2,inverse(inverse(X2))) = multiply(X2,add(X2,inverse(inverse(X2)))),
inference(congruence,[status(thm)],[c155]) ).
cnf(c157,plain,
multiply(X2,add(X2,inverse(inverse(X2)))) = X2,
inference(substitution,[status(thm)],[c32]) ).
cnf(c158,plain,
multiply(X2,inverse(inverse(X2))) = X2,
inference(transitivity,[status(thm)],[c156,c157]) ).
cnf(c159,plain,
multiply(inverse(inverse(X2)),add(X2,inverse(X2))) = X2,
inference(transitivity,[status(thm)],[c147,c158]) ).
cnf(c160,plain,
inverse(inverse(X2)) = X2,
inference(transitivity,[status(thm)],[c117,c159]) ).
cnf(c161,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c160]) ).
cnf(c162,plain,
multiply(X2,X3) = multiply(X2,inverse(inverse(X3))),
inference(congruence,[status(thm)],[c161]) ).
cnf(c163,plain,
add(X3,multiply(X2,X4)) = add(X3,multiply(X2,inverse(inverse(X4)))),
inference(congruence,[status(thm)],[c162]) ).
cnf(c164,plain,
multiply(X4,add(X3,multiply(X2,X4))) = multiply(X4,add(X3,multiply(X2,inverse(inverse(X4))))),
inference(congruence,[status(thm)],[c163]) ).
cnf(c165,plain,
add(X2,inverse(X3)) = add(inverse(X3),X2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c166,plain,
add(inverse(X3),X2) = add(X2,inverse(X3)),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c167,plain,
multiply(X3,add(inverse(X3),X2)) = multiply(X3,add(X2,inverse(X3))),
inference(congruence,[status(thm)],[c166]) ).
cnf(c168,plain,
multiply(X2,add(X4,X3)) = multiply(add(X4,X3),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c169,plain,
multiply(add(X4,X3),X2) = multiply(X2,add(X4,X3)),
inference(symmetry,[status(thm)],[c168]) ).
cnf(c170,plain,
multiply(X4,multiply(add(X4,X3),X2)) = multiply(X4,multiply(X2,add(X4,X3))),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
multiply(X4,multiply(X2,add(X4,X3))) = multiply(X4,X2),
inference(substitution,[status(thm)],[c131]) ).
cnf(c172,plain,
multiply(X4,multiply(add(X4,X3),X2)) = multiply(X4,X2),
inference(transitivity,[status(thm)],[c170,c171]) ).
cnf(c173,plain,
multiply(X3,multiply(add(X3,X2),add(X2,inverse(X3)))) = multiply(X3,add(X2,inverse(X3))),
inference(substitution,[status(thm)],[c172]) ).
cnf(c174,plain,
multiply(X3,add(X2,inverse(X3))) = multiply(X3,multiply(add(X3,X2),add(X2,inverse(X3)))),
inference(symmetry,[status(thm)],[c173]) ).
cnf(c175,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c176,plain,
add(X3,X2) = add(X2,X3),
inference(symmetry,[status(thm)],[c175]) ).
cnf(c177,plain,
multiply(add(X3,X2),add(X2,inverse(X3))) = multiply(add(X2,X3),add(X2,inverse(X3))),
inference(congruence,[status(thm)],[c176]) ).
cnf(c178,plain,
multiply(add(X2,X3),add(X2,inverse(X3))) = X2,
inference(substitution,[status(thm)],[c137]) ).
cnf(c179,plain,
multiply(add(X3,X2),add(X2,inverse(X3))) = X2,
inference(transitivity,[status(thm)],[c177,c178]) ).
cnf(c180,plain,
multiply(X3,multiply(add(X3,X2),add(X2,inverse(X3)))) = multiply(X3,X2),
inference(congruence,[status(thm)],[c179]) ).
cnf(c181,plain,
multiply(X3,add(X2,inverse(X3))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c174,c180]) ).
cnf(c182,plain,
multiply(X3,add(inverse(X3),X2)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c167,c181]) ).
cnf(c183,plain,
multiply(X4,add(inverse(X4),add(X3,multiply(X2,inverse(inverse(X4)))))) = multiply(X4,add(X3,multiply(X2,inverse(inverse(X4))))),
inference(substitution,[status(thm)],[c182]) ).
cnf(c184,plain,
multiply(X4,add(X3,multiply(X2,inverse(inverse(X4))))) = multiply(X4,add(inverse(X4),add(X3,multiply(X2,inverse(inverse(X4)))))),
inference(symmetry,[status(thm)],[c183]) ).
cnf(c185,plain,
add(multiply(X2,inverse(X4)),X3) = add(X3,multiply(X2,inverse(X4))),
inference(substitution,[status(thm)],[c12]) ).
cnf(c186,plain,
add(X3,multiply(X2,inverse(X4))) = add(multiply(X2,inverse(X4)),X3),
inference(symmetry,[status(thm)],[c185]) ).
cnf(c187,plain,
add(X4,add(X3,multiply(X2,inverse(X4)))) = add(X4,add(multiply(X2,inverse(X4)),X3)),
inference(congruence,[status(thm)],[c186]) ).
cnf(c188,plain,
add(add(X4,multiply(X2,inverse(X4))),X3) = add(X4,add(multiply(X2,inverse(X4)),X3)),
inference(substitution,[status(thm)],[c39]) ).
cnf(c189,plain,
add(X4,add(multiply(X2,inverse(X4)),X3)) = add(add(X4,multiply(X2,inverse(X4))),X3),
inference(symmetry,[status(thm)],[c188]) ).
cnf(c190,plain,
add(X2,multiply(X4,X3)) = add(multiply(X4,X3),X2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c191,plain,
add(multiply(X4,X3),X2) = add(X2,multiply(X4,X3)),
inference(symmetry,[status(thm)],[c190]) ).
cnf(c192,plain,
add(X4,add(multiply(X4,X3),X2)) = add(X4,add(X2,multiply(X4,X3))),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
add(X4,add(X2,multiply(X4,X3))) = add(X4,X2),
inference(substitution,[status(thm)],[c54]) ).
cnf(c194,plain,
add(X4,add(multiply(X4,X3),X2)) = add(X4,X2),
inference(transitivity,[status(thm)],[c192,c193]) ).
cnf(c195,plain,
add(X3,add(multiply(X3,X2),multiply(X2,inverse(X3)))) = add(X3,multiply(X2,inverse(X3))),
inference(substitution,[status(thm)],[c194]) ).
cnf(c196,plain,
add(X3,multiply(X2,inverse(X3))) = add(X3,add(multiply(X3,X2),multiply(X2,inverse(X3)))),
inference(symmetry,[status(thm)],[c195]) ).
cnf(c197,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c198,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(symmetry,[status(thm)],[c197]) ).
cnf(c199,plain,
add(multiply(X3,X2),multiply(X2,inverse(X3))) = add(multiply(X2,X3),multiply(X2,inverse(X3))),
inference(congruence,[status(thm)],[c198]) ).
cnf(c200,plain,
add(multiply(X2,X3),multiply(X2,inverse(X3))) = X2,
inference(substitution,[status(thm)],[c95]) ).
cnf(c201,plain,
add(multiply(X3,X2),multiply(X2,inverse(X3))) = X2,
inference(transitivity,[status(thm)],[c199,c200]) ).
cnf(c202,plain,
add(X3,add(multiply(X3,X2),multiply(X2,inverse(X3)))) = add(X3,X2),
inference(congruence,[status(thm)],[c201]) ).
cnf(c203,plain,
add(X3,multiply(X2,inverse(X3))) = add(X3,X2),
inference(transitivity,[status(thm)],[c196,c202]) ).
cnf(c204,plain,
add(add(X4,multiply(X2,inverse(X4))),X3) = add(add(X4,X2),X3),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,plain,
add(add(X4,X2),X3) = add(X4,add(X2,X3)),
inference(substitution,[status(thm)],[c39]) ).
cnf(c206,plain,
add(add(X4,multiply(X2,inverse(X4))),X3) = add(X4,add(X2,X3)),
inference(transitivity,[status(thm)],[c204,c205]) ).
cnf(c207,plain,
add(X4,add(multiply(X2,inverse(X4)),X3)) = add(X4,add(X2,X3)),
inference(transitivity,[status(thm)],[c189,c206]) ).
cnf(c208,plain,
add(X4,add(X3,multiply(X2,inverse(X4)))) = add(X4,add(X2,X3)),
inference(transitivity,[status(thm)],[c187,c207]) ).
cnf(c209,plain,
add(inverse(X4),add(X3,multiply(X2,inverse(inverse(X4))))) = add(inverse(X4),add(X2,X3)),
inference(substitution,[status(thm)],[c208]) ).
cnf(c210,plain,
multiply(X4,add(inverse(X4),add(X3,multiply(X2,inverse(inverse(X4)))))) = multiply(X4,add(inverse(X4),add(X2,X3))),
inference(congruence,[status(thm)],[c209]) ).
cnf(c211,plain,
multiply(X4,add(inverse(X4),add(X2,X3))) = multiply(X4,add(X2,X3)),
inference(substitution,[status(thm)],[c182]) ).
cnf(c212,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c213,plain,
multiply(X4,add(X2,X3)) = multiply(X4,add(X3,X2)),
inference(congruence,[status(thm)],[c212]) ).
cnf(c214,plain,
multiply(X4,add(inverse(X4),add(X2,X3))) = multiply(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c211,c213]) ).
cnf(c215,plain,
multiply(X4,add(inverse(X4),add(X3,multiply(X2,inverse(inverse(X4)))))) = multiply(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c210,c214]) ).
cnf(c216,plain,
multiply(X4,add(X3,multiply(X2,inverse(inverse(X4))))) = multiply(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c184,c215]) ).
cnf(c217,plain,
multiply(X4,add(X3,multiply(X2,X4))) = multiply(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c164,c216]) ).
cnf(c218,plain,
multiply(X4,add(X3,multiply(X4,X2))) = multiply(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c84,c217]) ).
cnf(c219,plain,
multiply(X3,add(multiply(X2,X3),multiply(X3,X4))) = multiply(X3,add(multiply(X2,X3),X4)),
inference(substitution,[status(thm)],[c218]) ).
cnf(c220,plain,
add(multiply(X2,X3),X4) = add(X4,multiply(X2,X3)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c221,plain,
multiply(X3,add(multiply(X2,X3),X4)) = multiply(X3,add(X4,multiply(X2,X3))),
inference(congruence,[status(thm)],[c220]) ).
cnf(c222,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c223,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(symmetry,[status(thm)],[c222]) ).
cnf(c224,plain,
add(X3,multiply(X2,X4)) = add(X3,multiply(X4,X2)),
inference(congruence,[status(thm)],[c223]) ).
cnf(c225,plain,
multiply(X4,add(X3,multiply(X2,X4))) = multiply(X4,add(X3,multiply(X4,X2))),
inference(congruence,[status(thm)],[c224]) ).
cnf(c226,plain,
multiply(X4,add(X3,multiply(X2,X4))) = multiply(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c225,c218]) ).
cnf(c227,plain,
multiply(X3,add(X4,multiply(X2,X3))) = multiply(X3,add(X4,X2)),
inference(substitution,[status(thm)],[c226]) ).
cnf(c228,plain,
multiply(X3,add(multiply(X2,X3),X4)) = multiply(X3,add(X4,X2)),
inference(transitivity,[status(thm)],[c221,c227]) ).
cnf(c229,plain,
multiply(X3,add(multiply(X2,X3),multiply(X3,X4))) = multiply(X3,add(X4,X2)),
inference(transitivity,[status(thm)],[c219,c228]) ).
cnf(c230,plain,
multiply(add(X3,multiply(X2,X3)),add(multiply(X2,X3),multiply(X3,X4))) = multiply(X3,add(X4,X2)),
inference(transitivity,[status(thm)],[c80,c229]) ).
cnf(c231,plain,
add(multiply(X2,X3),multiply(X3,X4)) = multiply(X3,add(X4,X2)),
inference(transitivity,[status(thm)],[c75,c230]) ).
cnf(c232,plain,
add(multiply(X3,X4),multiply(X2,X3)) = multiply(X3,add(X4,X2)),
inference(transitivity,[status(thm)],[c14,c231]) ).
cnf(c233,plain,
add(multiply(X4,X3),multiply(X2,X3)) = multiply(X3,add(X4,X2)),
inference(transitivity,[status(thm)],[c11,c232]) ).
cnf(c234,plain,
add(multiply(X4,X3),multiply(X3,X2)) = multiply(X3,add(X4,X2)),
inference(transitivity,[status(thm)],[c8,c233]) ).
cnf(c235,plain,
add(multiply(X4,X3),multiply(X2,X3)) = multiply(X3,add(X4,X2)),
inference(transitivity,[status(thm)],[c5,c234]) ).
cnf(c236,plain,
add(multiply(b,a),multiply(c,a)) = multiply(a,add(b,c)),
inference(substitution,[status(thm)],[c235]) ).
cnf(c237,plain,
multiply(a,add(b,c)) = add(multiply(b,a),multiply(c,a)),
inference(symmetry,[status(thm)],[c236]) ).
cnf(c238,plain,
$false,
inference(resolution,[status(thm)],[c1,c237]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO028-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.22 % Computer : n020.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Mon Sep 28 21:05:49 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.43/2.05 Command-line arguments: --no-flatten-goal
% 13.43/2.05
% 13.43/2.05 % SZS status Unsatisfiable
% 13.43/2.05
% 13.43/2.07 % SZS output start CNFRefutation
% See solution above
% 14.96/2.27
% 14.96/2.27 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------