%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO022-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 09:35:26 AM UTC 2026
% Result : Unsatisfiable 2.16s 0.55s
% Output : CNFRefutation 2.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 5
% Syntax : Number of clauses : 150 ( 150 unt; 0 nHn; 3 RR)
% Number of literals : 150 ( 149 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 : 376 ( 74 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity_of_multiply) ).
cnf(c2,axiom,
multiply(add(X,Y),Y) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_add) ).
cnf(c3,plain,
multiply(add(X2,X3),X3) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
X3 = multiply(add(X2,X3),X3),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
add(X3,X3) = add(multiply(add(X2,X3),X3),X3),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
add(multiply(X2,Y2),Y2) = Y2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_multiply) ).
cnf(c7,plain,
add(multiply(add(X2,X3),X3),X3) = X3,
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
add(X2,X2) = X2,
inference(transitivity,[status(thm)],[c5,c7]) ).
cnf(c9,plain,
add(multiply(X2,X3),multiply(X2,X3)) = multiply(X2,X3),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(X2,X3) = add(multiply(X2,X3),multiply(X2,X3)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,axiom,
multiply(X2,add(Y2,Z)) = add(multiply(Y2,X2),multiply(Z,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_add_property) ).
cnf(c12,plain,
multiply(X3,add(X2,X2)) = add(multiply(X2,X3),multiply(X2,X3)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
add(multiply(X2,X3),multiply(X2,X3)) = multiply(X3,add(X2,X2)),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
multiply(X3,add(X2,X2)) = multiply(X3,X2),
inference(congruence,[status(thm)],[c8]) ).
cnf(c15,plain,
add(multiply(X2,X3),multiply(X2,X3)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c13,c14]) ).
cnf(c16,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c10,c15]) ).
cnf(c17,plain,
multiply(multiply(X3,X2),X4) = multiply(X4,multiply(X3,X2)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
add(multiply(X2,X3),X3) = X3,
inference(substitution,[status(thm)],[c6]) ).
cnf(c19,plain,
X3 = add(multiply(X2,X3),X3),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
multiply(X3,X3) = multiply(add(multiply(X2,X3),X3),X3),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
multiply(add(multiply(X2,X3),X3),X3) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c22,plain,
multiply(X2,X2) = X2,
inference(transitivity,[status(thm)],[c20,c21]) ).
cnf(c23,plain,
multiply(add(X2,X3),add(X2,X3)) = add(X2,X3),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
add(X2,X3) = multiply(add(X2,X3),add(X2,X3)),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,axiom,
add(X2,multiply(Y2,Z2)) = multiply(add(Y2,X2),add(Z2,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_multiply_property) ).
cnf(c26,plain,
add(X3,multiply(X2,X2)) = multiply(add(X2,X3),add(X2,X3)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
multiply(add(X2,X3),add(X2,X3)) = add(X3,multiply(X2,X2)),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
add(X3,multiply(X2,X2)) = add(X3,X2),
inference(congruence,[status(thm)],[c22]) ).
cnf(c29,plain,
multiply(add(X2,X3),add(X2,X3)) = add(X3,X2),
inference(transitivity,[status(thm)],[c27,c28]) ).
cnf(c30,plain,
add(X2,X3) = add(X3,X2),
inference(transitivity,[status(thm)],[c24,c29]) ).
cnf(c31,plain,
add(multiply(X4,multiply(X3,X2)),multiply(X4,X3)) = add(multiply(X4,X3),multiply(X4,multiply(X3,X2))),
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
add(multiply(X3,X2),X3) = add(X3,multiply(X3,X2)),
inference(substitution,[status(thm)],[c30]) ).
cnf(c33,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(substitution,[status(thm)],[c16]) ).
cnf(c34,plain,
add(X3,multiply(X3,X2)) = add(X3,multiply(X2,X3)),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
add(X3,multiply(X2,X3)) = multiply(add(X2,X3),add(X3,X3)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c36,plain,
multiply(add(X2,X3),add(X3,X3)) = multiply(add(X2,X3),X3),
inference(congruence,[status(thm)],[c8]) ).
cnf(c37,plain,
multiply(add(X2,X3),X3) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c38,plain,
multiply(add(X2,X3),add(X3,X3)) = X3,
inference(transitivity,[status(thm)],[c36,c37]) ).
cnf(c39,plain,
add(X3,multiply(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c35,c38]) ).
cnf(c40,plain,
add(X3,multiply(X3,X2)) = X3,
inference(transitivity,[status(thm)],[c34,c39]) ).
cnf(c41,plain,
add(multiply(X3,X2),X3) = X3,
inference(transitivity,[status(thm)],[c32,c40]) ).
cnf(c42,plain,
X3 = add(multiply(X3,X2),X3),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
multiply(multiply(X4,multiply(X3,X2)),X3) = multiply(multiply(X4,multiply(X3,X2)),add(multiply(X3,X2),X3)),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
add(X3,X2) = add(X2,X3),
inference(substitution,[status(thm)],[c30]) ).
cnf(c45,plain,
multiply(multiply(X4,X3),add(X3,X2)) = multiply(multiply(X4,X3),add(X2,X3)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
add(multiply(X3,X2),X2) = X2,
inference(substitution,[status(thm)],[c6]) ).
cnf(c47,plain,
X2 = add(multiply(X3,X2),X2),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
add(X2,X3) = add(X2,add(multiply(X4,X3),X3)),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
multiply(multiply(X4,X3),add(X2,X3)) = multiply(multiply(X4,X3),add(X2,add(multiply(X4,X3),X3))),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
add(X3,X2) = add(X2,X3),
inference(substitution,[status(thm)],[c30]) ).
cnf(c51,plain,
add(X3,add(X4,X2)) = add(X3,add(X2,X4)),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
multiply(X4,add(X3,add(X4,X2))) = multiply(X4,add(X3,add(X2,X4))),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
multiply(X4,add(X3,add(X2,X4))) = add(multiply(X3,X4),multiply(add(X2,X4),X4)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c54,plain,
multiply(add(X2,X3),X3) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c55,plain,
add(multiply(X3,X4),multiply(add(X2,X4),X4)) = add(multiply(X3,X4),X4),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
add(multiply(X2,X3),X3) = X3,
inference(substitution,[status(thm)],[c6]) ).
cnf(c57,plain,
add(multiply(X3,X4),multiply(add(X2,X4),X4)) = X4,
inference(transitivity,[status(thm)],[c55,c56]) ).
cnf(c58,plain,
multiply(X4,add(X3,add(X2,X4))) = X4,
inference(transitivity,[status(thm)],[c53,c57]) ).
cnf(c59,plain,
multiply(X4,add(X3,add(X4,X2))) = X4,
inference(transitivity,[status(thm)],[c52,c58]) ).
cnf(c60,plain,
multiply(multiply(X4,X3),add(X2,add(multiply(X4,X3),X3))) = multiply(X4,X3),
inference(substitution,[status(thm)],[c59]) ).
cnf(c61,plain,
multiply(multiply(X4,X3),add(X2,X3)) = multiply(X4,X3),
inference(transitivity,[status(thm)],[c49,c60]) ).
cnf(c62,plain,
multiply(multiply(X4,X3),add(X3,X2)) = multiply(X4,X3),
inference(transitivity,[status(thm)],[c45,c61]) ).
cnf(c63,plain,
multiply(multiply(X4,multiply(X3,X2)),add(multiply(X3,X2),X3)) = multiply(X4,multiply(X3,X2)),
inference(substitution,[status(thm)],[c62]) ).
cnf(c64,plain,
multiply(multiply(X4,multiply(X3,X2)),X3) = multiply(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c43,c63]) ).
cnf(c65,plain,
multiply(X4,multiply(X3,X2)) = multiply(multiply(X4,multiply(X3,X2)),X3),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
add(multiply(X4,X3),multiply(X4,multiply(X3,X2))) = add(multiply(X4,X3),multiply(multiply(X4,multiply(X3,X2)),X3)),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
multiply(X4,add(X2,X3)) = add(multiply(X2,X4),multiply(X3,X4)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c68,plain,
add(multiply(X2,X4),multiply(X3,X4)) = multiply(X4,add(X2,X3)),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
add(X3,X2) = add(X2,X3),
inference(substitution,[status(thm)],[c30]) ).
cnf(c70,plain,
add(X2,X3) = add(X3,X2),
inference(symmetry,[status(thm)],[c69]) ).
cnf(c71,plain,
multiply(X4,add(X2,X3)) = multiply(X4,add(X3,X2)),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
add(multiply(X2,X4),multiply(X3,X4)) = multiply(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c68,c71]) ).
cnf(c73,plain,
add(multiply(X4,X3),multiply(multiply(X4,multiply(X3,X2)),X3)) = multiply(X3,add(multiply(X4,multiply(X3,X2)),X4)),
inference(substitution,[status(thm)],[c72]) ).
cnf(c74,plain,
add(multiply(X4,multiply(X3,X2)),X4) = X4,
inference(substitution,[status(thm)],[c41]) ).
cnf(c75,plain,
multiply(X3,add(multiply(X4,multiply(X3,X2)),X4)) = multiply(X3,X4),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(substitution,[status(thm)],[c16]) ).
cnf(c77,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
multiply(X3,add(multiply(X4,multiply(X3,X2)),X4)) = multiply(X4,X3),
inference(transitivity,[status(thm)],[c75,c77]) ).
cnf(c79,plain,
add(multiply(X4,X3),multiply(multiply(X4,multiply(X3,X2)),X3)) = multiply(X4,X3),
inference(transitivity,[status(thm)],[c73,c78]) ).
cnf(c80,plain,
add(multiply(X4,X3),multiply(X4,multiply(X3,X2))) = multiply(X4,X3),
inference(transitivity,[status(thm)],[c66,c79]) ).
cnf(c81,plain,
add(multiply(X4,multiply(X3,X2)),multiply(X4,X3)) = multiply(X4,X3),
inference(transitivity,[status(thm)],[c31,c80]) ).
cnf(c82,plain,
multiply(X4,X3) = add(multiply(X4,multiply(X3,X2)),multiply(X4,X3)),
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,plain,
multiply(X2,multiply(X4,X3)) = multiply(X2,add(multiply(X4,multiply(X3,X2)),multiply(X4,X3))),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
add(multiply(multiply(X4,X3),X2),multiply(multiply(X4,multiply(X3,X2)),X2)) = multiply(X2,add(multiply(X4,multiply(X3,X2)),multiply(X4,X3))),
inference(substitution,[status(thm)],[c72]) ).
cnf(c85,plain,
multiply(X2,add(multiply(X4,multiply(X3,X2)),multiply(X4,X3))) = add(multiply(multiply(X4,X3),X2),multiply(multiply(X4,multiply(X3,X2)),X2)),
inference(symmetry,[status(thm)],[c84]) ).
cnf(c86,plain,
add(multiply(X4,multiply(X3,X2)),X2) = add(X2,multiply(X4,multiply(X3,X2))),
inference(substitution,[status(thm)],[c30]) ).
cnf(c87,plain,
add(X4,multiply(X3,multiply(X2,X4))) = multiply(add(X3,X4),add(multiply(X2,X4),X4)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c88,plain,
add(multiply(X2,X3),X3) = X3,
inference(substitution,[status(thm)],[c6]) ).
cnf(c89,plain,
multiply(add(X3,X4),add(multiply(X2,X4),X4)) = multiply(add(X3,X4),X4),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
multiply(add(X2,X3),X3) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c91,plain,
multiply(add(X3,X4),add(multiply(X2,X4),X4)) = X4,
inference(transitivity,[status(thm)],[c89,c90]) ).
cnf(c92,plain,
add(X4,multiply(X3,multiply(X2,X4))) = X4,
inference(transitivity,[status(thm)],[c87,c91]) ).
cnf(c93,plain,
add(X2,multiply(X4,multiply(X3,X2))) = X2,
inference(substitution,[status(thm)],[c92]) ).
cnf(c94,plain,
add(multiply(X4,multiply(X3,X2)),X2) = X2,
inference(transitivity,[status(thm)],[c86,c93]) ).
cnf(c95,plain,
X2 = add(multiply(X4,multiply(X3,X2)),X2),
inference(symmetry,[status(thm)],[c94]) ).
cnf(c96,plain,
multiply(multiply(X4,multiply(X3,X2)),X2) = multiply(multiply(X4,multiply(X3,X2)),add(multiply(X4,multiply(X3,X2)),X2)),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
add(X3,X2) = add(X2,X3),
inference(substitution,[status(thm)],[c30]) ).
cnf(c98,plain,
multiply(X3,add(X3,X2)) = multiply(X3,add(X2,X3)),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
multiply(X3,add(X2,X3)) = add(multiply(X2,X3),multiply(X3,X3)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c100,plain,
add(multiply(X2,X3),multiply(X3,X3)) = add(multiply(X2,X3),X3),
inference(congruence,[status(thm)],[c22]) ).
cnf(c101,plain,
add(multiply(X2,X3),X3) = X3,
inference(substitution,[status(thm)],[c6]) ).
cnf(c102,plain,
add(multiply(X2,X3),multiply(X3,X3)) = X3,
inference(transitivity,[status(thm)],[c100,c101]) ).
cnf(c103,plain,
multiply(X3,add(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c99,c102]) ).
cnf(c104,plain,
multiply(X3,add(X3,X2)) = X3,
inference(transitivity,[status(thm)],[c98,c103]) ).
cnf(c105,plain,
multiply(multiply(X4,multiply(X3,X2)),add(multiply(X4,multiply(X3,X2)),X2)) = multiply(X4,multiply(X3,X2)),
inference(substitution,[status(thm)],[c104]) ).
cnf(c106,plain,
multiply(multiply(X4,multiply(X3,X2)),X2) = multiply(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c96,c105]) ).
cnf(c107,plain,
add(multiply(multiply(X4,X3),X2),multiply(multiply(X4,multiply(X3,X2)),X2)) = add(multiply(multiply(X4,X3),X2),multiply(X4,multiply(X3,X2))),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
add(multiply(multiply(X4,X3),X2),multiply(X4,multiply(X3,X2))) = add(multiply(X4,multiply(X3,X2)),multiply(multiply(X4,X3),X2)),
inference(substitution,[status(thm)],[c30]) ).
cnf(c109,plain,
add(multiply(multiply(X4,X3),X2),multiply(X3,X2)) = add(multiply(X3,X2),multiply(multiply(X4,X3),X2)),
inference(substitution,[status(thm)],[c30]) ).
cnf(c110,plain,
add(multiply(X3,X2),multiply(multiply(X4,X3),X2)) = multiply(X2,add(multiply(X4,X3),X3)),
inference(substitution,[status(thm)],[c72]) ).
cnf(c111,plain,
add(multiply(X3,X2),X2) = X2,
inference(substitution,[status(thm)],[c6]) ).
cnf(c112,plain,
multiply(X2,add(multiply(X4,X3),X3)) = multiply(X2,X3),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,plain,
multiply(X2,add(multiply(X4,X3),X3)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c112,c16]) ).
cnf(c114,plain,
add(multiply(X3,X2),multiply(multiply(X4,X3),X2)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c110,c113]) ).
cnf(c115,plain,
add(multiply(multiply(X4,X3),X2),multiply(X3,X2)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c109,c114]) ).
cnf(c116,plain,
multiply(X3,X2) = add(multiply(multiply(X4,X3),X2),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c115]) ).
cnf(c117,plain,
multiply(multiply(multiply(X4,X3),X2),multiply(X3,X2)) = multiply(multiply(multiply(X4,X3),X2),add(multiply(multiply(X4,X3),X2),multiply(X3,X2))),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
multiply(multiply(multiply(X4,X3),X2),add(multiply(multiply(X4,X3),X2),multiply(X3,X2))) = multiply(multiply(X4,X3),X2),
inference(substitution,[status(thm)],[c104]) ).
cnf(c119,plain,
multiply(multiply(multiply(X4,X3),X2),multiply(X3,X2)) = multiply(multiply(X4,X3),X2),
inference(transitivity,[status(thm)],[c117,c118]) ).
cnf(c120,plain,
multiply(multiply(X4,X3),X2) = multiply(multiply(multiply(X4,X3),X2),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c119]) ).
cnf(c121,plain,
add(multiply(X4,multiply(X3,X2)),multiply(multiply(X4,X3),X2)) = add(multiply(X4,multiply(X3,X2)),multiply(multiply(multiply(X4,X3),X2),multiply(X3,X2))),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
add(multiply(X4,multiply(X3,X2)),multiply(multiply(multiply(X4,X3),X2),multiply(X3,X2))) = multiply(multiply(X3,X2),add(multiply(multiply(X4,X3),X2),X4)),
inference(substitution,[status(thm)],[c72]) ).
cnf(c123,plain,
add(multiply(multiply(X4,X3),X2),X4) = add(X4,multiply(multiply(X4,X3),X2)),
inference(substitution,[status(thm)],[c30]) ).
cnf(c124,plain,
X3 = add(multiply(X3,X2),X3),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c125,plain,
multiply(multiply(X3,X2),X3) = multiply(multiply(X3,X2),add(multiply(X3,X2),X3)),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
multiply(multiply(X3,X2),add(multiply(X3,X2),X3)) = multiply(X3,X2),
inference(substitution,[status(thm)],[c104]) ).
cnf(c127,plain,
multiply(multiply(X3,X2),X3) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c125,c126]) ).
cnf(c128,plain,
multiply(multiply(multiply(X4,X3),X2),multiply(X4,X3)) = multiply(multiply(X4,X3),X2),
inference(substitution,[status(thm)],[c127]) ).
cnf(c129,plain,
multiply(multiply(X4,X3),X2) = multiply(multiply(multiply(X4,X3),X2),multiply(X4,X3)),
inference(symmetry,[status(thm)],[c128]) ).
cnf(c130,plain,
add(X4,multiply(multiply(X4,X3),X2)) = add(X4,multiply(multiply(multiply(X4,X3),X2),multiply(X4,X3))),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
add(X4,multiply(X3,multiply(X4,X2))) = multiply(add(X3,X4),add(multiply(X4,X2),X4)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c132,plain,
multiply(add(X3,X4),add(multiply(X4,X2),X4)) = multiply(add(X3,X4),X4),
inference(congruence,[status(thm)],[c41]) ).
cnf(c133,plain,
multiply(add(X2,X3),X3) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c134,plain,
multiply(add(X3,X4),add(multiply(X4,X2),X4)) = X4,
inference(transitivity,[status(thm)],[c132,c133]) ).
cnf(c135,plain,
add(X4,multiply(X3,multiply(X4,X2))) = X4,
inference(transitivity,[status(thm)],[c131,c134]) ).
cnf(c136,plain,
add(X4,multiply(multiply(multiply(X4,X3),X2),multiply(X4,X3))) = X4,
inference(substitution,[status(thm)],[c135]) ).
cnf(c137,plain,
add(X4,multiply(multiply(X4,X3),X2)) = X4,
inference(transitivity,[status(thm)],[c130,c136]) ).
cnf(c138,plain,
add(multiply(multiply(X4,X3),X2),X4) = X4,
inference(transitivity,[status(thm)],[c123,c137]) ).
cnf(c139,plain,
multiply(multiply(X3,X2),add(multiply(multiply(X4,X3),X2),X4)) = multiply(multiply(X3,X2),X4),
inference(congruence,[status(thm)],[c138]) ).
cnf(c140,plain,
multiply(multiply(X3,X2),X4) = multiply(X4,multiply(X3,X2)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c141,plain,
multiply(multiply(X3,X2),add(multiply(multiply(X4,X3),X2),X4)) = multiply(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c139,c140]) ).
cnf(c142,plain,
add(multiply(X4,multiply(X3,X2)),multiply(multiply(multiply(X4,X3),X2),multiply(X3,X2))) = multiply(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c122,c141]) ).
cnf(c143,plain,
add(multiply(X4,multiply(X3,X2)),multiply(multiply(X4,X3),X2)) = multiply(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c121,c142]) ).
cnf(c144,plain,
add(multiply(multiply(X4,X3),X2),multiply(X4,multiply(X3,X2))) = multiply(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c108,c143]) ).
cnf(c145,plain,
add(multiply(multiply(X4,X3),X2),multiply(multiply(X4,multiply(X3,X2)),X2)) = multiply(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c107,c144]) ).
cnf(c146,plain,
multiply(X2,add(multiply(X4,multiply(X3,X2)),multiply(X4,X3))) = multiply(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c85,c145]) ).
cnf(c147,plain,
multiply(X2,multiply(X4,X3)) = multiply(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c83,c146]) ).
cnf(c148,plain,
multiply(multiply(X4,X3),X2) = multiply(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c17,c147]) ).
cnf(c149,plain,
multiply(multiply(a,b),c) = multiply(a,multiply(b,c)),
inference(substitution,[status(thm)],[c148]) ).
cnf(c150,plain,
$false,
inference(resolution,[status(thm)],[c1,c149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO022-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.16 % Computer : n002.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 21:07:07 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.16/0.55 Command-line arguments: --flatten --complete-subsets
% 2.16/0.55
% 2.16/0.55 % SZS status Unsatisfiable
% 2.16/0.55
% 2.16/0.56 % SZS output start CNFRefutation
% See solution above
% 2.16/0.62
% 2.16/0.62 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------