%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : RNG024-7 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:34:48 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.46s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of clauses : 90 ( 90 unt; 0 nHn; 3 RR)
% Number of literals : 90 ( 89 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 190 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
associator(x,y,y) != additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_right_alternative) ).
cnf(c2,axiom,
additive_inverse(additive_inverse(X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c3,plain,
X2 = additive_inverse(additive_inverse(X2)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c4,plain,
associator(X3,X2,X2) = associator(X3,X2,additive_inverse(additive_inverse(X2))),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,axiom,
add(X,Y) = add(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_for_addition) ).
cnf(c6,plain,
add(multiply(multiply(X3,X2),X4),multiply(X3,multiply(X2,additive_inverse(X4)))) = add(multiply(X3,multiply(X2,additive_inverse(X4))),multiply(multiply(X3,X2),X4)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
add(multiply(X4,multiply(X3,additive_inverse(X2))),multiply(multiply(X4,X3),X2)) = add(multiply(multiply(X4,X3),X2),multiply(X4,multiply(X3,additive_inverse(X2)))),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,axiom,
multiply(X2,additive_inverse(Y2)) = additive_inverse(multiply(X2,Y2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_product2) ).
cnf(c9,plain,
multiply(X3,additive_inverse(X2)) = additive_inverse(multiply(X3,X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(X4,multiply(X3,additive_inverse(X2))) = multiply(X4,additive_inverse(multiply(X3,X2))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
add(multiply(multiply(X4,X3),X2),multiply(X4,multiply(X3,additive_inverse(X2)))) = add(multiply(multiply(X4,X3),X2),multiply(X4,additive_inverse(multiply(X3,X2)))),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
multiply(X4,additive_inverse(multiply(X3,X2))) = additive_inverse(multiply(X4,multiply(X3,X2))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c13,plain,
add(multiply(multiply(X4,X3),X2),multiply(X4,additive_inverse(multiply(X3,X2)))) = add(multiply(multiply(X4,X3),X2),additive_inverse(multiply(X4,multiply(X3,X2)))),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,axiom,
associator(X2,Y2,Z) = add(multiply(multiply(X2,Y2),Z),additive_inverse(multiply(X2,multiply(Y2,Z)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associator) ).
cnf(c15,plain,
associator(X4,X3,X2) = add(multiply(multiply(X4,X3),X2),additive_inverse(multiply(X4,multiply(X3,X2)))),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
add(multiply(multiply(X4,X3),X2),additive_inverse(multiply(X4,multiply(X3,X2)))) = associator(X4,X3,X2),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
add(multiply(multiply(X4,X3),X2),multiply(X4,additive_inverse(multiply(X3,X2)))) = associator(X4,X3,X2),
inference(transitivity,[status(thm)],[c13,c16]) ).
cnf(c18,plain,
add(multiply(multiply(X4,X3),X2),multiply(X4,multiply(X3,additive_inverse(X2)))) = associator(X4,X3,X2),
inference(transitivity,[status(thm)],[c11,c17]) ).
cnf(c19,plain,
add(multiply(X4,multiply(X3,additive_inverse(X2))),multiply(multiply(X4,X3),X2)) = associator(X4,X3,X2),
inference(transitivity,[status(thm)],[c7,c18]) ).
cnf(c20,plain,
add(multiply(additive_inverse(X4),multiply(additive_inverse(X3),additive_inverse(X2))),multiply(multiply(additive_inverse(X4),additive_inverse(X3)),X2)) = associator(additive_inverse(X4),additive_inverse(X3),X2),
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
associator(additive_inverse(X4),additive_inverse(X3),X2) = add(multiply(additive_inverse(X4),multiply(additive_inverse(X3),additive_inverse(X2))),multiply(multiply(additive_inverse(X4),additive_inverse(X3)),X2)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,axiom,
multiply(additive_inverse(X2),additive_inverse(Y2)) = multiply(X2,Y2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_of_inverses) ).
cnf(c23,plain,
multiply(additive_inverse(X3),additive_inverse(X2)) = multiply(X3,X2),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(multiply(additive_inverse(X4),additive_inverse(X3)),X2) = multiply(multiply(X4,X3),X2),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
add(multiply(additive_inverse(X4),multiply(additive_inverse(X3),additive_inverse(X2))),multiply(multiply(additive_inverse(X4),additive_inverse(X3)),X2)) = add(multiply(additive_inverse(X4),multiply(additive_inverse(X3),additive_inverse(X2))),multiply(multiply(X4,X3),X2)),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,axiom,
multiply(additive_inverse(X2),Y2) = additive_inverse(multiply(X2,Y2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_product1) ).
cnf(c27,plain,
multiply(additive_inverse(X3),X2) = additive_inverse(multiply(X3,X2)),
inference(substitution,[status(thm)],[c26]) ).
cnf(c28,plain,
multiply(X3,additive_inverse(X2)) = additive_inverse(multiply(X3,X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c29,plain,
additive_inverse(multiply(X3,X2)) = multiply(X3,additive_inverse(X2)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
multiply(additive_inverse(X3),X2) = multiply(X3,additive_inverse(X2)),
inference(transitivity,[status(thm)],[c27,c29]) ).
cnf(c31,plain,
multiply(additive_inverse(X4),multiply(additive_inverse(X3),additive_inverse(X2))) = multiply(X4,additive_inverse(multiply(additive_inverse(X3),additive_inverse(X2)))),
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
add(multiply(additive_inverse(X4),multiply(additive_inverse(X3),additive_inverse(X2))),multiply(multiply(X4,X3),X2)) = add(multiply(X4,additive_inverse(multiply(additive_inverse(X3),additive_inverse(X2)))),multiply(multiply(X4,X3),X2)),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
multiply(additive_inverse(X3),additive_inverse(additive_inverse(X2))) = additive_inverse(multiply(additive_inverse(X3),additive_inverse(X2))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c34,plain,
additive_inverse(multiply(additive_inverse(X3),additive_inverse(X2))) = multiply(additive_inverse(X3),additive_inverse(additive_inverse(X2))),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
multiply(X4,additive_inverse(multiply(additive_inverse(X3),additive_inverse(X2)))) = multiply(X4,multiply(additive_inverse(X3),additive_inverse(additive_inverse(X2)))),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
add(multiply(X4,additive_inverse(multiply(additive_inverse(X3),additive_inverse(X2)))),multiply(multiply(X4,X3),X2)) = add(multiply(X4,multiply(additive_inverse(X3),additive_inverse(additive_inverse(X2)))),multiply(multiply(X4,X3),X2)),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
multiply(additive_inverse(X3),additive_inverse(additive_inverse(X2))) = multiply(X3,additive_inverse(X2)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c38,plain,
multiply(X4,multiply(additive_inverse(X3),additive_inverse(additive_inverse(X2)))) = multiply(X4,multiply(X3,additive_inverse(X2))),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
add(multiply(X4,multiply(additive_inverse(X3),additive_inverse(additive_inverse(X2)))),multiply(multiply(X4,X3),X2)) = add(multiply(X4,multiply(X3,additive_inverse(X2))),multiply(multiply(X4,X3),X2)),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
add(multiply(X4,multiply(additive_inverse(X3),additive_inverse(additive_inverse(X2)))),multiply(multiply(X4,X3),X2)) = associator(X4,X3,X2),
inference(transitivity,[status(thm)],[c39,c19]) ).
cnf(c41,plain,
add(multiply(X4,additive_inverse(multiply(additive_inverse(X3),additive_inverse(X2)))),multiply(multiply(X4,X3),X2)) = associator(X4,X3,X2),
inference(transitivity,[status(thm)],[c36,c40]) ).
cnf(c42,plain,
add(multiply(additive_inverse(X4),multiply(additive_inverse(X3),additive_inverse(X2))),multiply(multiply(X4,X3),X2)) = associator(X4,X3,X2),
inference(transitivity,[status(thm)],[c32,c41]) ).
cnf(c43,plain,
add(multiply(additive_inverse(X4),multiply(additive_inverse(X3),additive_inverse(X2))),multiply(multiply(additive_inverse(X4),additive_inverse(X3)),X2)) = associator(X4,X3,X2),
inference(transitivity,[status(thm)],[c25,c42]) ).
cnf(c44,plain,
associator(additive_inverse(X4),additive_inverse(X3),X2) = associator(X4,X3,X2),
inference(transitivity,[status(thm)],[c21,c43]) ).
cnf(c45,plain,
associator(additive_inverse(X3),additive_inverse(X2),additive_inverse(additive_inverse(X2))) = associator(X3,X2,additive_inverse(additive_inverse(X2))),
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
associator(X3,X2,additive_inverse(additive_inverse(X2))) = associator(additive_inverse(X3),additive_inverse(X2),additive_inverse(additive_inverse(X2))),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
add(multiply(X3,multiply(X2,additive_inverse(additive_inverse(X2)))),multiply(multiply(X3,X2),additive_inverse(X2))) = associator(X3,X2,additive_inverse(X2)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c48,plain,
associator(X3,X2,additive_inverse(X2)) = add(multiply(X3,multiply(X2,additive_inverse(additive_inverse(X2)))),multiply(multiply(X3,X2),additive_inverse(X2))),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
multiply(additive_inverse(X3),additive_inverse(X2)) = multiply(X3,X2),
inference(substitution,[status(thm)],[c22]) ).
cnf(c50,plain,
multiply(X3,X2) = multiply(additive_inverse(X3),additive_inverse(X2)),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
multiply(multiply(X3,X2),additive_inverse(X2)) = multiply(multiply(additive_inverse(X3),additive_inverse(X2)),additive_inverse(X2)),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,axiom,
multiply(multiply(X2,Y2),Y2) = multiply(X2,multiply(Y2,Y2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_alternative) ).
cnf(c53,plain,
multiply(multiply(additive_inverse(X3),additive_inverse(X2)),additive_inverse(X2)) = multiply(additive_inverse(X3),multiply(additive_inverse(X2),additive_inverse(X2))),
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
multiply(additive_inverse(X3),multiply(additive_inverse(X2),additive_inverse(X2))) = multiply(X3,additive_inverse(multiply(additive_inverse(X2),additive_inverse(X2)))),
inference(substitution,[status(thm)],[c30]) ).
cnf(c55,plain,
multiply(additive_inverse(X2),additive_inverse(additive_inverse(X2))) = additive_inverse(multiply(additive_inverse(X2),additive_inverse(X2))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c56,plain,
additive_inverse(multiply(additive_inverse(X2),additive_inverse(X2))) = multiply(additive_inverse(X2),additive_inverse(additive_inverse(X2))),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
multiply(X3,additive_inverse(multiply(additive_inverse(X2),additive_inverse(X2)))) = multiply(X3,multiply(additive_inverse(X2),additive_inverse(additive_inverse(X2)))),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
multiply(additive_inverse(X2),additive_inverse(additive_inverse(X2))) = multiply(X2,additive_inverse(X2)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c59,plain,
multiply(X3,multiply(additive_inverse(X2),additive_inverse(additive_inverse(X2)))) = multiply(X3,multiply(X2,additive_inverse(X2))),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
multiply(X3,additive_inverse(multiply(additive_inverse(X2),additive_inverse(X2)))) = multiply(X3,multiply(X2,additive_inverse(X2))),
inference(transitivity,[status(thm)],[c57,c59]) ).
cnf(c61,plain,
multiply(additive_inverse(X3),multiply(additive_inverse(X2),additive_inverse(X2))) = multiply(X3,multiply(X2,additive_inverse(X2))),
inference(transitivity,[status(thm)],[c54,c60]) ).
cnf(c62,plain,
multiply(multiply(additive_inverse(X3),additive_inverse(X2)),additive_inverse(X2)) = multiply(X3,multiply(X2,additive_inverse(X2))),
inference(transitivity,[status(thm)],[c53,c61]) ).
cnf(c63,plain,
multiply(multiply(X3,X2),additive_inverse(X2)) = multiply(X3,multiply(X2,additive_inverse(X2))),
inference(transitivity,[status(thm)],[c51,c62]) ).
cnf(c64,plain,
add(multiply(X3,multiply(X2,additive_inverse(additive_inverse(X2)))),multiply(multiply(X3,X2),additive_inverse(X2))) = add(multiply(X3,multiply(X2,additive_inverse(additive_inverse(X2)))),multiply(X3,multiply(X2,additive_inverse(X2)))),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,axiom,
multiply(X2,add(Y2,Z2)) = add(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute1) ).
cnf(c66,plain,
multiply(X3,add(multiply(X2,additive_inverse(additive_inverse(X2))),multiply(X2,additive_inverse(X2)))) = add(multiply(X3,multiply(X2,additive_inverse(additive_inverse(X2)))),multiply(X3,multiply(X2,additive_inverse(X2)))),
inference(substitution,[status(thm)],[c65]) ).
cnf(c67,plain,
add(multiply(X3,multiply(X2,additive_inverse(additive_inverse(X2)))),multiply(X3,multiply(X2,additive_inverse(X2)))) = multiply(X3,add(multiply(X2,additive_inverse(additive_inverse(X2))),multiply(X2,additive_inverse(X2)))),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
multiply(X2,add(additive_inverse(additive_inverse(X2)),additive_inverse(X2))) = add(multiply(X2,additive_inverse(additive_inverse(X2))),multiply(X2,additive_inverse(X2))),
inference(substitution,[status(thm)],[c65]) ).
cnf(c69,plain,
add(multiply(X2,additive_inverse(additive_inverse(X2))),multiply(X2,additive_inverse(X2))) = multiply(X2,add(additive_inverse(additive_inverse(X2)),additive_inverse(X2))),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
multiply(X3,add(multiply(X2,additive_inverse(additive_inverse(X2))),multiply(X2,additive_inverse(X2)))) = multiply(X3,multiply(X2,add(additive_inverse(additive_inverse(X2)),additive_inverse(X2)))),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
add(additive_inverse(additive_inverse(X2)),additive_inverse(X2)) = add(X2,additive_inverse(X2)),
inference(congruence,[status(thm)],[c2]) ).
cnf(c72,plain,
multiply(X2,add(additive_inverse(additive_inverse(X2)),additive_inverse(X2))) = multiply(X2,add(X2,additive_inverse(X2))),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
multiply(X3,multiply(X2,add(additive_inverse(additive_inverse(X2)),additive_inverse(X2)))) = multiply(X3,multiply(X2,add(X2,additive_inverse(X2)))),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,axiom,
add(X2,additive_inverse(X2)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c75,plain,
multiply(X2,add(X2,additive_inverse(X2))) = multiply(X2,additive_identity),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
multiply(X3,multiply(X2,add(X2,additive_inverse(X2)))) = multiply(X3,multiply(X2,additive_identity)),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,axiom,
multiply(X2,additive_identity) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c78,plain,
multiply(X3,multiply(X2,additive_identity)) = multiply(X3,additive_identity),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
multiply(X3,multiply(X2,additive_identity)) = additive_identity,
inference(transitivity,[status(thm)],[c78,c77]) ).
cnf(c80,plain,
multiply(X3,multiply(X2,add(X2,additive_inverse(X2)))) = additive_identity,
inference(transitivity,[status(thm)],[c76,c79]) ).
cnf(c81,plain,
multiply(X3,multiply(X2,add(additive_inverse(additive_inverse(X2)),additive_inverse(X2)))) = additive_identity,
inference(transitivity,[status(thm)],[c73,c80]) ).
cnf(c82,plain,
multiply(X3,add(multiply(X2,additive_inverse(additive_inverse(X2))),multiply(X2,additive_inverse(X2)))) = additive_identity,
inference(transitivity,[status(thm)],[c70,c81]) ).
cnf(c83,plain,
add(multiply(X3,multiply(X2,additive_inverse(additive_inverse(X2)))),multiply(X3,multiply(X2,additive_inverse(X2)))) = additive_identity,
inference(transitivity,[status(thm)],[c67,c82]) ).
cnf(c84,plain,
add(multiply(X3,multiply(X2,additive_inverse(additive_inverse(X2)))),multiply(multiply(X3,X2),additive_inverse(X2))) = additive_identity,
inference(transitivity,[status(thm)],[c64,c83]) ).
cnf(c85,plain,
associator(X3,X2,additive_inverse(X2)) = additive_identity,
inference(transitivity,[status(thm)],[c48,c84]) ).
cnf(c86,plain,
associator(additive_inverse(X3),additive_inverse(X2),additive_inverse(additive_inverse(X2))) = additive_identity,
inference(substitution,[status(thm)],[c85]) ).
cnf(c87,plain,
associator(X3,X2,additive_inverse(additive_inverse(X2))) = additive_identity,
inference(transitivity,[status(thm)],[c46,c86]) ).
cnf(c88,plain,
associator(X3,X2,X2) = additive_identity,
inference(transitivity,[status(thm)],[c4,c87]) ).
cnf(c89,plain,
associator(x,y,y) = additive_identity,
inference(substitution,[status(thm)],[c88]) ).
cnf(c90,plain,
$false,
inference(resolution,[status(thm)],[c1,c89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG024-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 23:00:09 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.46 Command-line arguments: --flatten-regeneralise
% 0.14/0.46
% 0.14/0.46 % SZS status Unsatisfiable
% 0.14/0.46
% 0.14/0.46 % SZS output start CNFRefutation
% See solution above
% 0.14/0.49
% 0.14/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------