%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO014-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 09:35:24 AM UTC 2026
% Result : Unsatisfiable 2.17s 0.53s
% Output : CNFRefutation 3.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 15
% Syntax : Number of clauses : 267 ( 267 unt; 0 nHn; 93 RR)
% Number of literals : 267 ( 266 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 274 ( 22 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
inverse(c) != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_inverse_is_d) ).
cnf(c2,axiom,
multiply(X,multiplicative_identity) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_id1) ).
cnf(c3,plain,
multiply(inverse(c),multiplicative_identity) = inverse(c),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
inverse(c) = multiply(inverse(c),multiplicative_identity),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
add(X2,Y) = add(Y,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
cnf(c6,plain,
add(d,c) = add(c,d),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
add(c,d) = add(d,c),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
add(X2,b) = add(b,X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c9,plain,
add(b,X2) = add(X2,b),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
add(a,add(b,X2)) = add(a,add(X2,b)),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,axiom,
multiply(X2,Y2) = multiply(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiply) ).
cnf(c12,plain,
multiply(X3,inverse(X2)) = multiply(inverse(X2),X3),
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
multiply(inverse(X3),X2) = multiply(X2,inverse(X3)),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
add(X3,multiply(inverse(X3),X2)) = add(X3,multiply(X2,inverse(X3))),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
multiply(inverse(X3),X2) = multiply(X2,inverse(X3)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c16,plain,
multiply(X2,inverse(X3)) = multiply(inverse(X3),X2),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
add(X3,multiply(X2,inverse(X3))) = add(X3,multiply(inverse(X3),X2)),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,axiom,
add(X2,multiply(Y2,Z)) = multiply(add(X2,Y2),add(X2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
cnf(c19,plain,
add(X3,multiply(inverse(X3),X2)) = multiply(add(X3,inverse(X3)),add(X3,X2)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,axiom,
add(X2,inverse(X2)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c21,plain,
multiply(add(X3,inverse(X3)),add(X3,X2)) = multiply(multiplicative_identity,add(X3,X2)),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,axiom,
multiply(multiplicative_identity,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_id2) ).
cnf(c23,plain,
multiply(multiplicative_identity,add(X3,X2)) = add(X3,X2),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(add(X3,inverse(X3)),add(X3,X2)) = add(X3,X2),
inference(transitivity,[status(thm)],[c21,c23]) ).
cnf(c25,plain,
add(X3,multiply(inverse(X3),X2)) = add(X3,X2),
inference(transitivity,[status(thm)],[c19,c24]) ).
cnf(c26,plain,
add(X3,multiply(X2,inverse(X3))) = add(X3,X2),
inference(transitivity,[status(thm)],[c17,c25]) ).
cnf(c27,plain,
add(X3,multiply(inverse(X3),X2)) = add(X3,X2),
inference(transitivity,[status(thm)],[c14,c26]) ).
cnf(c28,plain,
add(a,multiply(inverse(a),add(X2,b))) = add(a,add(X2,b)),
inference(substitution,[status(thm)],[c27]) ).
cnf(c29,plain,
add(a,add(X2,b)) = add(a,multiply(inverse(a),add(X2,b))),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
add(c,X2) = add(X2,c),
inference(substitution,[status(thm)],[c5]) ).
cnf(c31,plain,
add(X2,c) = add(c,X2),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
multiply(inverse(a),add(X2,c)) = multiply(inverse(a),add(c,X2)),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
multiply(add(c,X2),inverse(a)) = multiply(inverse(a),add(c,X2)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c34,plain,
multiply(inverse(a),add(c,X2)) = multiply(add(c,X2),inverse(a)),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,axiom,
multiply(add(X2,Y2),Z2) = add(multiply(X2,Z2),multiply(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity3) ).
cnf(c36,plain,
multiply(add(c,X2),inverse(a)) = add(multiply(c,inverse(a)),multiply(X2,inverse(a))),
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
multiply(inverse(a),c) = multiply(c,inverse(a)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c38,plain,
multiply(c,inverse(a)) = multiply(inverse(a),c),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,axiom,
add(a,b) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c40,plain,
c = add(a,b),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
multiply(inverse(a),c) = multiply(inverse(a),add(a,b)),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
multiply(add(X3,X2),inverse(X3)) = multiply(inverse(X3),add(X3,X2)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c43,plain,
multiply(inverse(X3),add(X3,X2)) = multiply(add(X3,X2),inverse(X3)),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
multiply(add(X3,X2),inverse(X3)) = add(multiply(X3,inverse(X3)),multiply(X2,inverse(X3))),
inference(substitution,[status(thm)],[c35]) ).
cnf(c45,axiom,
multiply(X2,inverse(X2)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c46,plain,
add(multiply(X3,inverse(X3)),multiply(X2,inverse(X3))) = add(additive_identity,multiply(X2,inverse(X3))),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,axiom,
add(additive_identity,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_id2) ).
cnf(c48,plain,
add(additive_identity,multiply(X2,inverse(X3))) = multiply(X2,inverse(X3)),
inference(substitution,[status(thm)],[c47]) ).
cnf(c49,plain,
add(multiply(X3,inverse(X3)),multiply(X2,inverse(X3))) = multiply(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c46,c48]) ).
cnf(c50,plain,
multiply(add(X3,X2),inverse(X3)) = multiply(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c44,c49]) ).
cnf(c51,plain,
multiply(inverse(X3),add(X3,X2)) = multiply(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c43,c50]) ).
cnf(c52,plain,
multiply(inverse(a),add(a,b)) = multiply(b,inverse(a)),
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
multiply(inverse(a),c) = multiply(b,inverse(a)),
inference(transitivity,[status(thm)],[c41,c52]) ).
cnf(c54,plain,
multiply(c,inverse(a)) = multiply(b,inverse(a)),
inference(transitivity,[status(thm)],[c38,c53]) ).
cnf(c55,plain,
add(multiply(c,inverse(a)),multiply(X2,inverse(a))) = add(multiply(b,inverse(a)),multiply(X2,inverse(a))),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(substitution,[status(thm)],[c11]) ).
cnf(c57,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(symmetry,[status(thm)],[c56]) ).
cnf(c58,plain,
add(multiply(X4,X3),multiply(X2,X3)) = add(multiply(X4,X3),multiply(X3,X2)),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(substitution,[status(thm)],[c11]) ).
cnf(c60,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c61,plain,
add(multiply(X4,X3),multiply(X3,X2)) = add(multiply(X3,X4),multiply(X3,X2)),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,axiom,
multiply(X2,add(Y2,Z2)) = add(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity4) ).
cnf(c63,plain,
multiply(X3,add(X4,X2)) = add(multiply(X3,X4),multiply(X3,X2)),
inference(substitution,[status(thm)],[c62]) ).
cnf(c64,plain,
add(multiply(X3,X4),multiply(X3,X2)) = multiply(X3,add(X4,X2)),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,plain,
add(multiply(X4,X3),multiply(X3,X2)) = multiply(X3,add(X4,X2)),
inference(transitivity,[status(thm)],[c61,c64]) ).
cnf(c66,plain,
add(multiply(X4,X3),multiply(X2,X3)) = multiply(X3,add(X4,X2)),
inference(transitivity,[status(thm)],[c58,c65]) ).
cnf(c67,plain,
add(multiply(b,inverse(a)),multiply(X2,inverse(a))) = multiply(inverse(a),add(b,X2)),
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
add(b,X2) = add(X2,b),
inference(substitution,[status(thm)],[c5]) ).
cnf(c69,plain,
multiply(inverse(a),add(b,X2)) = multiply(inverse(a),add(X2,b)),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
add(multiply(b,inverse(a)),multiply(X2,inverse(a))) = multiply(inverse(a),add(X2,b)),
inference(transitivity,[status(thm)],[c67,c69]) ).
cnf(c71,plain,
add(multiply(c,inverse(a)),multiply(X2,inverse(a))) = multiply(inverse(a),add(X2,b)),
inference(transitivity,[status(thm)],[c55,c70]) ).
cnf(c72,plain,
multiply(add(c,X2),inverse(a)) = multiply(inverse(a),add(X2,b)),
inference(transitivity,[status(thm)],[c36,c71]) ).
cnf(c73,plain,
multiply(inverse(a),add(c,X2)) = multiply(inverse(a),add(X2,b)),
inference(transitivity,[status(thm)],[c34,c72]) ).
cnf(c74,plain,
multiply(inverse(a),add(X2,c)) = multiply(inverse(a),add(X2,b)),
inference(transitivity,[status(thm)],[c32,c73]) ).
cnf(c75,plain,
multiply(inverse(a),add(X2,b)) = multiply(inverse(a),add(X2,c)),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c76,plain,
add(a,multiply(inverse(a),add(X2,b))) = add(a,multiply(inverse(a),add(X2,c))),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
add(a,multiply(inverse(a),add(X2,c))) = add(a,add(X2,c)),
inference(substitution,[status(thm)],[c27]) ).
cnf(c78,plain,
add(add(X2,c),a) = add(a,add(X2,c)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c79,plain,
add(a,add(X2,c)) = add(add(X2,c),a),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
add(c,X2) = add(X2,c),
inference(substitution,[status(thm)],[c5]) ).
cnf(c81,plain,
add(X2,c) = add(c,X2),
inference(symmetry,[status(thm)],[c80]) ).
cnf(c82,plain,
multiply(a,add(X2,c)) = multiply(a,add(c,X2)),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
multiply(a,add(c,X2)) = add(multiply(a,c),multiply(a,X2)),
inference(substitution,[status(thm)],[c62]) ).
cnf(c84,axiom,
add(X2,additive_identity) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c85,plain,
X2 = add(X2,additive_identity),
inference(symmetry,[status(thm)],[c84]) ).
cnf(c86,plain,
multiply(X3,add(X3,X2)) = multiply(add(X3,additive_identity),add(X3,X2)),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
add(X3,multiply(additive_identity,X2)) = multiply(add(X3,additive_identity),add(X3,X2)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c88,plain,
multiply(add(X3,additive_identity),add(X3,X2)) = add(X3,multiply(additive_identity,X2)),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c89,plain,
multiply(additive_identity,X2) = multiply(X2,additive_identity),
inference(substitution,[status(thm)],[c11]) ).
cnf(c90,plain,
add(X3,multiply(additive_identity,X2)) = add(X3,multiply(X2,additive_identity)),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
multiply(add(X3,additive_identity),add(X3,X2)) = add(X3,multiply(X2,additive_identity)),
inference(transitivity,[status(thm)],[c88,c90]) ).
cnf(c92,plain,
multiply(X3,add(X3,X2)) = add(X3,multiply(X2,additive_identity)),
inference(transitivity,[status(thm)],[c86,c91]) ).
cnf(c93,plain,
multiply(a,add(a,b)) = add(a,multiply(b,additive_identity)),
inference(substitution,[status(thm)],[c92]) ).
cnf(c94,plain,
add(a,multiply(b,additive_identity)) = multiply(a,add(a,b)),
inference(symmetry,[status(thm)],[c93]) ).
cnf(c95,plain,
multiply(a,add(a,b)) = multiply(a,c),
inference(congruence,[status(thm)],[c39]) ).
cnf(c96,plain,
add(a,multiply(b,additive_identity)) = multiply(a,c),
inference(transitivity,[status(thm)],[c94,c95]) ).
cnf(c97,plain,
multiply(a,c) = add(a,multiply(b,additive_identity)),
inference(symmetry,[status(thm)],[c96]) ).
cnf(c98,plain,
add(inverse(X3),X2) = add(X2,inverse(X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c99,plain,
add(X2,inverse(X3)) = add(inverse(X3),X2),
inference(symmetry,[status(thm)],[c98]) ).
cnf(c100,plain,
multiply(X3,add(X2,inverse(X3))) = multiply(X3,add(inverse(X3),X2)),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
multiply(X3,add(inverse(X3),X2)) = add(multiply(X3,inverse(X3)),multiply(X3,X2)),
inference(substitution,[status(thm)],[c62]) ).
cnf(c102,plain,
add(multiply(X3,inverse(X3)),multiply(X3,X2)) = add(additive_identity,multiply(X3,X2)),
inference(congruence,[status(thm)],[c45]) ).
cnf(c103,plain,
add(additive_identity,multiply(X3,X2)) = multiply(X3,X2),
inference(substitution,[status(thm)],[c47]) ).
cnf(c104,plain,
add(multiply(X3,inverse(X3)),multiply(X3,X2)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c102,c103]) ).
cnf(c105,plain,
multiply(X3,add(inverse(X3),X2)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c101,c104]) ).
cnf(c106,plain,
multiply(X3,add(X2,inverse(X3))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c100,c105]) ).
cnf(c107,plain,
multiply(X2,add(additive_identity,inverse(X2))) = multiply(X2,additive_identity),
inference(substitution,[status(thm)],[c106]) ).
cnf(c108,plain,
multiply(X2,additive_identity) = multiply(X2,add(additive_identity,inverse(X2))),
inference(symmetry,[status(thm)],[c107]) ).
cnf(c109,plain,
add(additive_identity,inverse(X2)) = inverse(X2),
inference(substitution,[status(thm)],[c47]) ).
cnf(c110,plain,
multiply(X2,add(additive_identity,inverse(X2))) = multiply(X2,inverse(X2)),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
multiply(X2,add(additive_identity,inverse(X2))) = additive_identity,
inference(transitivity,[status(thm)],[c110,c45]) ).
cnf(c112,plain,
multiply(X2,additive_identity) = additive_identity,
inference(transitivity,[status(thm)],[c108,c111]) ).
cnf(c113,plain,
multiply(b,additive_identity) = additive_identity,
inference(substitution,[status(thm)],[c112]) ).
cnf(c114,plain,
add(a,multiply(b,additive_identity)) = add(a,additive_identity),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
add(a,additive_identity) = a,
inference(substitution,[status(thm)],[c84]) ).
cnf(c116,plain,
add(a,multiply(b,additive_identity)) = a,
inference(transitivity,[status(thm)],[c114,c115]) ).
cnf(c117,plain,
multiply(a,c) = a,
inference(transitivity,[status(thm)],[c97,c116]) ).
cnf(c118,plain,
add(multiply(a,c),multiply(a,X2)) = add(a,multiply(a,X2)),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
add(multiplicative_identity,X2) = add(X2,multiplicative_identity),
inference(substitution,[status(thm)],[c5]) ).
cnf(c120,plain,
add(X2,multiplicative_identity) = add(multiplicative_identity,X2),
inference(symmetry,[status(thm)],[c119]) ).
cnf(c121,plain,
multiply(X3,add(X2,multiplicative_identity)) = multiply(X3,add(multiplicative_identity,X2)),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
multiply(X3,add(multiplicative_identity,X2)) = add(multiply(X3,multiplicative_identity),multiply(X3,X2)),
inference(substitution,[status(thm)],[c62]) ).
cnf(c123,plain,
add(multiply(X3,multiplicative_identity),multiply(X3,X2)) = add(X3,multiply(X3,X2)),
inference(congruence,[status(thm)],[c2]) ).
cnf(c124,plain,
multiply(X3,add(multiplicative_identity,X2)) = add(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c122,c123]) ).
cnf(c125,plain,
multiply(X3,add(X2,multiplicative_identity)) = add(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c121,c124]) ).
cnf(c126,plain,
add(X3,multiply(X3,X2)) = multiply(X3,add(X2,multiplicative_identity)),
inference(symmetry,[status(thm)],[c125]) ).
cnf(c127,plain,
multiply(multiplicative_identity,add(multiplicative_identity,X2)) = add(multiplicative_identity,multiply(X2,additive_identity)),
inference(substitution,[status(thm)],[c92]) ).
cnf(c128,plain,
add(multiplicative_identity,multiply(X2,additive_identity)) = multiply(multiplicative_identity,add(multiplicative_identity,X2)),
inference(symmetry,[status(thm)],[c127]) ).
cnf(c129,plain,
multiply(multiplicative_identity,add(multiplicative_identity,X2)) = add(multiplicative_identity,X2),
inference(substitution,[status(thm)],[c22]) ).
cnf(c130,plain,
add(multiplicative_identity,X2) = add(X2,multiplicative_identity),
inference(substitution,[status(thm)],[c5]) ).
cnf(c131,plain,
multiply(multiplicative_identity,add(multiplicative_identity,X2)) = add(X2,multiplicative_identity),
inference(transitivity,[status(thm)],[c129,c130]) ).
cnf(c132,plain,
add(multiplicative_identity,multiply(X2,additive_identity)) = add(X2,multiplicative_identity),
inference(transitivity,[status(thm)],[c128,c131]) ).
cnf(c133,plain,
add(X2,multiplicative_identity) = add(multiplicative_identity,multiply(X2,additive_identity)),
inference(symmetry,[status(thm)],[c132]) ).
cnf(c134,plain,
add(multiplicative_identity,multiply(X2,additive_identity)) = add(multiplicative_identity,additive_identity),
inference(congruence,[status(thm)],[c112]) ).
cnf(c135,plain,
add(multiplicative_identity,additive_identity) = multiplicative_identity,
inference(substitution,[status(thm)],[c84]) ).
cnf(c136,plain,
add(multiplicative_identity,multiply(X2,additive_identity)) = multiplicative_identity,
inference(transitivity,[status(thm)],[c134,c135]) ).
cnf(c137,plain,
add(X2,multiplicative_identity) = multiplicative_identity,
inference(transitivity,[status(thm)],[c133,c136]) ).
cnf(c138,plain,
multiply(X3,add(X2,multiplicative_identity)) = multiply(X3,multiplicative_identity),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,plain,
multiply(X3,add(X2,multiplicative_identity)) = X3,
inference(transitivity,[status(thm)],[c138,c2]) ).
cnf(c140,plain,
add(X3,multiply(X3,X2)) = X3,
inference(transitivity,[status(thm)],[c126,c139]) ).
cnf(c141,plain,
add(a,multiply(a,X2)) = a,
inference(substitution,[status(thm)],[c140]) ).
cnf(c142,plain,
add(multiply(a,c),multiply(a,X2)) = a,
inference(transitivity,[status(thm)],[c118,c141]) ).
cnf(c143,plain,
multiply(a,add(c,X2)) = a,
inference(transitivity,[status(thm)],[c83,c142]) ).
cnf(c144,plain,
multiply(a,add(X2,c)) = a,
inference(transitivity,[status(thm)],[c82,c143]) ).
cnf(c145,plain,
a = multiply(a,add(X2,c)),
inference(symmetry,[status(thm)],[c144]) ).
cnf(c146,plain,
add(add(X2,c),a) = add(add(X2,c),multiply(a,add(X2,c))),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(substitution,[status(thm)],[c11]) ).
cnf(c148,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(symmetry,[status(thm)],[c147]) ).
cnf(c149,plain,
add(X3,multiply(X2,X3)) = add(X3,multiply(X3,X2)),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
add(X3,multiply(X3,X2)) = multiply(X3,add(X2,multiplicative_identity)),
inference(symmetry,[status(thm)],[c125]) ).
cnf(c151,plain,
multiply(X3,add(X2,multiplicative_identity)) = multiply(X3,multiplicative_identity),
inference(congruence,[status(thm)],[c137]) ).
cnf(c152,plain,
multiply(X3,add(X2,multiplicative_identity)) = X3,
inference(transitivity,[status(thm)],[c151,c2]) ).
cnf(c153,plain,
add(X3,multiply(X3,X2)) = X3,
inference(transitivity,[status(thm)],[c150,c152]) ).
cnf(c154,plain,
add(X3,multiply(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c149,c153]) ).
cnf(c155,plain,
add(add(X2,c),multiply(a,add(X2,c))) = add(X2,c),
inference(substitution,[status(thm)],[c154]) ).
cnf(c156,plain,
add(add(X2,c),a) = add(X2,c),
inference(transitivity,[status(thm)],[c146,c155]) ).
cnf(c157,plain,
add(a,add(X2,c)) = add(X2,c),
inference(transitivity,[status(thm)],[c79,c156]) ).
cnf(c158,plain,
add(a,multiply(inverse(a),add(X2,c))) = add(X2,c),
inference(transitivity,[status(thm)],[c77,c157]) ).
cnf(c159,plain,
add(a,multiply(inverse(a),add(X2,b))) = add(X2,c),
inference(transitivity,[status(thm)],[c76,c158]) ).
cnf(c160,plain,
add(a,add(X2,b)) = add(X2,c),
inference(transitivity,[status(thm)],[c29,c159]) ).
cnf(c161,plain,
add(a,add(b,X2)) = add(X2,c),
inference(transitivity,[status(thm)],[c10,c160]) ).
cnf(c162,plain,
add(a,add(b,d)) = add(d,c),
inference(substitution,[status(thm)],[c161]) ).
cnf(c163,plain,
add(d,c) = add(a,add(b,d)),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c164,plain,
add(b,multiply(inverse(a),inverse(b))) = add(b,inverse(a)),
inference(substitution,[status(thm)],[c26]) ).
cnf(c165,plain,
add(b,inverse(a)) = add(b,multiply(inverse(a),inverse(b))),
inference(symmetry,[status(thm)],[c164]) ).
cnf(c166,axiom,
multiply(inverse(a),inverse(b)) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c167,plain,
add(b,multiply(inverse(a),inverse(b))) = add(b,d),
inference(congruence,[status(thm)],[c166]) ).
cnf(c168,plain,
add(b,inverse(a)) = add(b,d),
inference(transitivity,[status(thm)],[c165,c167]) ).
cnf(c169,plain,
add(b,d) = add(b,inverse(a)),
inference(symmetry,[status(thm)],[c168]) ).
cnf(c170,plain,
add(a,add(b,d)) = add(a,add(b,inverse(a))),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
add(inverse(X3),X2) = add(X2,inverse(X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c172,plain,
add(X2,inverse(X3)) = add(inverse(X3),X2),
inference(symmetry,[status(thm)],[c171]) ).
cnf(c173,plain,
add(X3,add(X2,inverse(X3))) = add(X3,add(inverse(X3),X2)),
inference(congruence,[status(thm)],[c172]) ).
cnf(c174,plain,
add(X3,multiply(inverse(X3),add(inverse(X3),X2))) = add(X3,add(inverse(X3),X2)),
inference(substitution,[status(thm)],[c27]) ).
cnf(c175,plain,
add(X3,add(inverse(X3),X2)) = add(X3,multiply(inverse(X3),add(inverse(X3),X2))),
inference(symmetry,[status(thm)],[c174]) ).
cnf(c176,plain,
multiply(inverse(X3),add(inverse(X3),X2)) = add(inverse(X3),multiply(X2,additive_identity)),
inference(substitution,[status(thm)],[c92]) ).
cnf(c177,plain,
add(X3,multiply(inverse(X3),add(inverse(X3),X2))) = add(X3,add(inverse(X3),multiply(X2,additive_identity))),
inference(congruence,[status(thm)],[c176]) ).
cnf(c178,plain,
add(inverse(X3),multiply(X2,additive_identity)) = add(inverse(X3),additive_identity),
inference(congruence,[status(thm)],[c112]) ).
cnf(c179,plain,
add(X3,add(inverse(X3),multiply(X2,additive_identity))) = add(X3,add(inverse(X3),additive_identity)),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
add(inverse(X2),additive_identity) = inverse(X2),
inference(substitution,[status(thm)],[c84]) ).
cnf(c181,plain,
add(X2,add(inverse(X2),additive_identity)) = add(X2,inverse(X2)),
inference(congruence,[status(thm)],[c180]) ).
cnf(c182,plain,
add(X2,add(inverse(X2),additive_identity)) = multiplicative_identity,
inference(transitivity,[status(thm)],[c181,c20]) ).
cnf(c183,plain,
add(X3,add(inverse(X3),multiply(X2,additive_identity))) = multiplicative_identity,
inference(transitivity,[status(thm)],[c179,c182]) ).
cnf(c184,plain,
add(X3,multiply(inverse(X3),add(inverse(X3),X2))) = multiplicative_identity,
inference(transitivity,[status(thm)],[c177,c183]) ).
cnf(c185,plain,
add(X3,add(inverse(X3),X2)) = multiplicative_identity,
inference(transitivity,[status(thm)],[c175,c184]) ).
cnf(c186,plain,
add(X3,add(X2,inverse(X3))) = multiplicative_identity,
inference(transitivity,[status(thm)],[c173,c185]) ).
cnf(c187,plain,
add(a,add(b,inverse(a))) = multiplicative_identity,
inference(substitution,[status(thm)],[c186]) ).
cnf(c188,plain,
add(a,add(b,d)) = multiplicative_identity,
inference(transitivity,[status(thm)],[c170,c187]) ).
cnf(c189,plain,
add(d,c) = multiplicative_identity,
inference(transitivity,[status(thm)],[c163,c188]) ).
cnf(c190,plain,
add(c,d) = multiplicative_identity,
inference(transitivity,[status(thm)],[c7,c189]) ).
cnf(c191,plain,
multiplicative_identity = add(c,d),
inference(symmetry,[status(thm)],[c190]) ).
cnf(c192,plain,
multiply(inverse(c),multiplicative_identity) = multiply(inverse(c),add(c,d)),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
multiply(inverse(c),add(c,d)) = multiply(d,inverse(c)),
inference(substitution,[status(thm)],[c51]) ).
cnf(c194,plain,
add(multiply(X3,X2),inverse(X3)) = add(inverse(X3),multiply(X3,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c195,plain,
add(inverse(X3),multiply(X3,X2)) = add(multiply(X3,X2),inverse(X3)),
inference(symmetry,[status(thm)],[c194]) ).
cnf(c196,axiom,
add(multiply(X2,Y2),Z2) = multiply(add(X2,Z2),add(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
cnf(c197,plain,
add(multiply(X3,X2),inverse(X3)) = multiply(add(X3,inverse(X3)),add(X2,inverse(X3))),
inference(substitution,[status(thm)],[c196]) ).
cnf(c198,plain,
multiply(add(X3,inverse(X3)),add(X2,inverse(X3))) = multiply(multiplicative_identity,add(X2,inverse(X3))),
inference(congruence,[status(thm)],[c20]) ).
cnf(c199,plain,
multiply(multiplicative_identity,add(X2,inverse(X3))) = add(X2,inverse(X3)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c200,plain,
multiply(add(X3,inverse(X3)),add(X2,inverse(X3))) = add(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c198,c199]) ).
cnf(c201,plain,
add(multiply(X3,X2),inverse(X3)) = add(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c197,c200]) ).
cnf(c202,plain,
add(inverse(X3),multiply(X3,X2)) = add(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c195,c201]) ).
cnf(c203,plain,
add(inverse(c),multiply(c,d)) = add(d,inverse(c)),
inference(substitution,[status(thm)],[c202]) ).
cnf(c204,plain,
add(d,inverse(c)) = add(inverse(c),multiply(c,d)),
inference(symmetry,[status(thm)],[c203]) ).
cnf(c205,plain,
multiply(d,c) = multiply(c,d),
inference(substitution,[status(thm)],[c11]) ).
cnf(c206,plain,
multiply(c,d) = multiply(d,c),
inference(symmetry,[status(thm)],[c205]) ).
cnf(c207,plain,
c = add(a,b),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c208,plain,
multiply(d,c) = multiply(d,add(a,b)),
inference(congruence,[status(thm)],[c207]) ).
cnf(c209,plain,
add(b,X2) = add(X2,b),
inference(substitution,[status(thm)],[c5]) ).
cnf(c210,plain,
add(X2,b) = add(b,X2),
inference(symmetry,[status(thm)],[c209]) ).
cnf(c211,plain,
multiply(d,add(X2,b)) = multiply(d,add(b,X2)),
inference(congruence,[status(thm)],[c210]) ).
cnf(c212,plain,
multiply(add(b,X2),d) = multiply(d,add(b,X2)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c213,plain,
multiply(d,add(b,X2)) = multiply(add(b,X2),d),
inference(symmetry,[status(thm)],[c212]) ).
cnf(c214,plain,
multiply(add(b,X2),d) = add(multiply(b,d),multiply(X2,d)),
inference(substitution,[status(thm)],[c35]) ).
cnf(c215,plain,
multiply(b,add(d,inverse(b))) = multiply(b,d),
inference(substitution,[status(thm)],[c106]) ).
cnf(c216,plain,
multiply(b,d) = multiply(b,add(d,inverse(b))),
inference(symmetry,[status(thm)],[c215]) ).
cnf(c217,plain,
add(inverse(b),d) = add(d,inverse(b)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c218,plain,
add(d,inverse(b)) = add(inverse(b),d),
inference(symmetry,[status(thm)],[c217]) ).
cnf(c219,plain,
d = multiply(inverse(a),inverse(b)),
inference(symmetry,[status(thm)],[c166]) ).
cnf(c220,plain,
add(inverse(b),d) = add(inverse(b),multiply(inverse(a),inverse(b))),
inference(congruence,[status(thm)],[c219]) ).
cnf(c221,plain,
add(inverse(b),multiply(inverse(a),inverse(b))) = inverse(b),
inference(substitution,[status(thm)],[c154]) ).
cnf(c222,plain,
add(inverse(b),d) = inverse(b),
inference(transitivity,[status(thm)],[c220,c221]) ).
cnf(c223,plain,
add(d,inverse(b)) = inverse(b),
inference(transitivity,[status(thm)],[c218,c222]) ).
cnf(c224,plain,
multiply(b,add(d,inverse(b))) = multiply(b,inverse(b)),
inference(congruence,[status(thm)],[c223]) ).
cnf(c225,plain,
multiply(b,inverse(b)) = additive_identity,
inference(substitution,[status(thm)],[c45]) ).
cnf(c226,plain,
multiply(b,add(d,inverse(b))) = additive_identity,
inference(transitivity,[status(thm)],[c224,c225]) ).
cnf(c227,plain,
multiply(b,d) = additive_identity,
inference(transitivity,[status(thm)],[c216,c226]) ).
cnf(c228,plain,
add(multiply(b,d),multiply(X2,d)) = add(additive_identity,multiply(X2,d)),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
add(additive_identity,multiply(X2,d)) = multiply(X2,d),
inference(substitution,[status(thm)],[c47]) ).
cnf(c230,plain,
add(multiply(b,d),multiply(X2,d)) = multiply(X2,d),
inference(transitivity,[status(thm)],[c228,c229]) ).
cnf(c231,plain,
multiply(add(b,X2),d) = multiply(X2,d),
inference(transitivity,[status(thm)],[c214,c230]) ).
cnf(c232,plain,
multiply(d,add(b,X2)) = multiply(X2,d),
inference(transitivity,[status(thm)],[c213,c231]) ).
cnf(c233,plain,
multiply(d,add(X2,b)) = multiply(X2,d),
inference(transitivity,[status(thm)],[c211,c232]) ).
cnf(c234,plain,
multiply(d,add(a,b)) = multiply(a,d),
inference(substitution,[status(thm)],[c233]) ).
cnf(c235,plain,
multiply(a,add(d,inverse(a))) = multiply(a,d),
inference(substitution,[status(thm)],[c106]) ).
cnf(c236,plain,
multiply(a,d) = multiply(a,add(d,inverse(a))),
inference(symmetry,[status(thm)],[c235]) ).
cnf(c237,plain,
add(inverse(a),d) = add(d,inverse(a)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c238,plain,
add(d,inverse(a)) = add(inverse(a),d),
inference(symmetry,[status(thm)],[c237]) ).
cnf(c239,plain,
d = multiply(inverse(a),inverse(b)),
inference(symmetry,[status(thm)],[c166]) ).
cnf(c240,plain,
add(inverse(a),d) = add(inverse(a),multiply(inverse(a),inverse(b))),
inference(congruence,[status(thm)],[c239]) ).
cnf(c241,plain,
add(inverse(a),multiply(inverse(a),inverse(b))) = inverse(a),
inference(substitution,[status(thm)],[c140]) ).
cnf(c242,plain,
add(inverse(a),d) = inverse(a),
inference(transitivity,[status(thm)],[c240,c241]) ).
cnf(c243,plain,
add(d,inverse(a)) = inverse(a),
inference(transitivity,[status(thm)],[c238,c242]) ).
cnf(c244,plain,
multiply(a,add(d,inverse(a))) = multiply(a,inverse(a)),
inference(congruence,[status(thm)],[c243]) ).
cnf(c245,plain,
multiply(a,inverse(a)) = additive_identity,
inference(substitution,[status(thm)],[c45]) ).
cnf(c246,plain,
multiply(a,add(d,inverse(a))) = additive_identity,
inference(transitivity,[status(thm)],[c244,c245]) ).
cnf(c247,plain,
multiply(a,d) = additive_identity,
inference(transitivity,[status(thm)],[c236,c246]) ).
cnf(c248,plain,
multiply(d,add(a,b)) = additive_identity,
inference(transitivity,[status(thm)],[c234,c247]) ).
cnf(c249,plain,
multiply(d,c) = additive_identity,
inference(transitivity,[status(thm)],[c208,c248]) ).
cnf(c250,plain,
multiply(c,d) = additive_identity,
inference(transitivity,[status(thm)],[c206,c249]) ).
cnf(c251,plain,
add(inverse(c),multiply(c,d)) = add(inverse(c),additive_identity),
inference(congruence,[status(thm)],[c250]) ).
cnf(c252,plain,
add(inverse(c),additive_identity) = inverse(c),
inference(substitution,[status(thm)],[c84]) ).
cnf(c253,plain,
add(inverse(c),multiply(c,d)) = inverse(c),
inference(transitivity,[status(thm)],[c251,c252]) ).
cnf(c254,plain,
add(d,inverse(c)) = inverse(c),
inference(transitivity,[status(thm)],[c204,c253]) ).
cnf(c255,plain,
inverse(c) = add(d,inverse(c)),
inference(symmetry,[status(thm)],[c254]) ).
cnf(c256,plain,
multiply(d,inverse(c)) = multiply(d,add(d,inverse(c))),
inference(congruence,[status(thm)],[c255]) ).
cnf(c257,plain,
multiply(d,add(d,inverse(c))) = add(d,multiply(inverse(c),additive_identity)),
inference(substitution,[status(thm)],[c92]) ).
cnf(c258,plain,
multiply(inverse(c),additive_identity) = additive_identity,
inference(substitution,[status(thm)],[c112]) ).
cnf(c259,plain,
add(d,multiply(inverse(c),additive_identity)) = add(d,additive_identity),
inference(congruence,[status(thm)],[c258]) ).
cnf(c260,plain,
add(d,additive_identity) = d,
inference(substitution,[status(thm)],[c84]) ).
cnf(c261,plain,
add(d,multiply(inverse(c),additive_identity)) = d,
inference(transitivity,[status(thm)],[c259,c260]) ).
cnf(c262,plain,
multiply(d,add(d,inverse(c))) = d,
inference(transitivity,[status(thm)],[c257,c261]) ).
cnf(c263,plain,
multiply(d,inverse(c)) = d,
inference(transitivity,[status(thm)],[c256,c262]) ).
cnf(c264,plain,
multiply(inverse(c),add(c,d)) = d,
inference(transitivity,[status(thm)],[c193,c263]) ).
cnf(c265,plain,
multiply(inverse(c),multiplicative_identity) = d,
inference(transitivity,[status(thm)],[c192,c264]) ).
cnf(c266,plain,
inverse(c) = d,
inference(transitivity,[status(thm)],[c4,c265]) ).
cnf(c267,plain,
$false,
inference(resolution,[status(thm)],[c1,c266]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO014-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.16 % Computer : n014.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
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Mon Sep 28 21:04:00 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.17/0.53 Command-line arguments: --no-flatten-goal
% 2.17/0.53
% 2.17/0.53 % SZS status Unsatisfiable
% 2.17/0.53
% 2.17/0.54 % SZS output start CNFRefutation
% See solution above
% 3.16/0.66
% 3.16/0.66 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------