%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : RNG018-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 12:34:47 PM UTC 2026
% Result : Unsatisfiable 0.24s 0.60s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 10
% Syntax : Number of clauses : 70 ( 70 unt; 0 nHn; 4 RR)
% Number of literals : 70 ( 69 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; 4 con; 0-2 aty)
% Number of variables : 160 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(add(x,y),additive_inverse(z)) != add(additive_inverse(multiply(x,z)),additive_inverse(multiply(y,z))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity) ).
cnf(c2,axiom,
additive_inverse(additive_inverse(X)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).
cnf(c3,plain,
additive_inverse(additive_inverse(multiply(add(X4,X3),additive_inverse(X2)))) = multiply(add(X4,X3),additive_inverse(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(add(X4,X3),additive_inverse(X2)) = additive_inverse(additive_inverse(multiply(add(X4,X3),additive_inverse(X2)))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
add(multiply(add(X4,X3),additive_inverse(X2)),multiply(X4,X2)) = add(additive_inverse(additive_inverse(multiply(add(X4,X3),additive_inverse(X2)))),multiply(X4,X2)),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
add(X2,Y) = add(Y,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_for_addition) ).
cnf(c7,plain,
add(multiply(X2,X3),multiply(X4,X3)) = add(multiply(X4,X3),multiply(X2,X3)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
add(multiply(X4,X3),multiply(X2,X3)) = add(multiply(X2,X3),multiply(X4,X3)),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,axiom,
multiply(add(X2,Y2),Z) = add(multiply(X2,Z),multiply(Y2,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute2) ).
cnf(c10,plain,
multiply(add(X3,X4),X2) = add(multiply(X3,X2),multiply(X4,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
add(multiply(X3,X2),multiply(X4,X2)) = multiply(add(X3,X4),X2),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c13,plain,
multiply(add(X3,X4),X2) = multiply(add(X4,X3),X2),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
add(multiply(X3,X2),multiply(X4,X2)) = multiply(add(X4,X3),X2),
inference(transitivity,[status(thm)],[c11,c13]) ).
cnf(c15,plain,
add(multiply(X2,X3),multiply(X4,X3)) = multiply(add(X4,X2),X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,axiom,
add(X2,additive_identity) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_additive_identity) ).
cnf(c17,plain,
add(additive_inverse(multiply(X3,additive_inverse(X2))),additive_identity) = additive_inverse(multiply(X3,additive_inverse(X2))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
additive_inverse(multiply(X3,additive_inverse(X2))) = add(additive_inverse(multiply(X3,additive_inverse(X2))),additive_identity),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,axiom,
multiply(X2,add(Y2,Z2)) = add(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute1) ).
cnf(c20,plain,
multiply(X4,add(X2,X3)) = add(multiply(X4,X2),multiply(X4,X3)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
add(multiply(X4,X2),multiply(X4,X3)) = multiply(X4,add(X2,X3)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c23,plain,
multiply(X4,add(X2,X3)) = multiply(X4,add(X3,X2)),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
add(multiply(X4,X2),multiply(X4,X3)) = multiply(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c21,c23]) ).
cnf(c25,plain,
add(multiply(X3,X2),multiply(X3,additive_inverse(X2))) = multiply(X3,add(additive_inverse(X2),X2)),
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
add(X2,additive_inverse(X2)) = add(additive_inverse(X2),X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c27,plain,
add(additive_inverse(X2),X2) = add(X2,additive_inverse(X2)),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,axiom,
add(X2,additive_inverse(X2)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c29,plain,
add(additive_inverse(X2),X2) = additive_identity,
inference(transitivity,[status(thm)],[c27,c28]) ).
cnf(c30,plain,
multiply(X3,add(additive_inverse(X2),X2)) = multiply(X3,additive_identity),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,axiom,
multiply(X2,additive_identity) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c32,plain,
multiply(X3,add(additive_inverse(X2),X2)) = additive_identity,
inference(transitivity,[status(thm)],[c30,c31]) ).
cnf(c33,plain,
add(multiply(X3,X2),multiply(X3,additive_inverse(X2))) = additive_identity,
inference(transitivity,[status(thm)],[c25,c32]) ).
cnf(c34,plain,
additive_identity = add(multiply(X3,X2),multiply(X3,additive_inverse(X2))),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
add(additive_inverse(multiply(X3,additive_inverse(X2))),additive_identity) = add(additive_inverse(multiply(X3,additive_inverse(X2))),add(multiply(X3,X2),multiply(X3,additive_inverse(X2)))),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
add(X3,X2) = add(X2,X3),
inference(substitution,[status(thm)],[c6]) ).
cnf(c37,plain,
add(X2,X3) = add(X3,X2),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
add(additive_inverse(X3),add(X2,X3)) = add(additive_inverse(X3),add(X3,X2)),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,axiom,
add(X2,add(Y2,Z2)) = add(add(X2,Y2),Z2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_for_addition) ).
cnf(c40,plain,
add(additive_inverse(X3),add(X3,X2)) = add(add(additive_inverse(X3),X3),X2),
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
add(add(additive_inverse(X3),X3),X2) = add(additive_identity,X2),
inference(congruence,[status(thm)],[c29]) ).
cnf(c42,axiom,
add(additive_identity,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c43,plain,
add(add(additive_inverse(X3),X3),X2) = X2,
inference(transitivity,[status(thm)],[c41,c42]) ).
cnf(c44,plain,
add(additive_inverse(X3),add(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c40,c43]) ).
cnf(c45,plain,
add(additive_inverse(X3),add(X2,X3)) = X2,
inference(transitivity,[status(thm)],[c38,c44]) ).
cnf(c46,plain,
add(additive_inverse(multiply(X3,additive_inverse(X2))),add(multiply(X3,X2),multiply(X3,additive_inverse(X2)))) = multiply(X3,X2),
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
add(additive_inverse(multiply(X3,additive_inverse(X2))),additive_identity) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c35,c46]) ).
cnf(c48,plain,
additive_inverse(multiply(X3,additive_inverse(X2))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c18,c47]) ).
cnf(c49,plain,
additive_inverse(multiply(add(X4,X2),additive_inverse(X3))) = multiply(add(X4,X2),X3),
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
multiply(add(X4,X2),X3) = additive_inverse(multiply(add(X4,X2),additive_inverse(X3))),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
add(multiply(X2,X3),multiply(X4,X3)) = additive_inverse(multiply(add(X4,X2),additive_inverse(X3))),
inference(transitivity,[status(thm)],[c15,c50]) ).
cnf(c52,plain,
add(multiply(X4,X3),multiply(X2,X3)) = additive_inverse(multiply(add(X4,X2),additive_inverse(X3))),
inference(transitivity,[status(thm)],[c8,c51]) ).
cnf(c53,plain,
add(multiply(X2,X3),multiply(X4,X3)) = additive_inverse(multiply(add(X2,X4),additive_inverse(X3))),
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
additive_inverse(multiply(add(X2,X4),additive_inverse(X3))) = add(multiply(X2,X3),multiply(X4,X3)),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
add(additive_inverse(multiply(X4,X3)),additive_inverse(multiply(add(X2,X4),additive_inverse(X3)))) = add(additive_inverse(multiply(X4,X3)),add(multiply(X2,X3),multiply(X4,X3))),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
add(additive_inverse(multiply(X4,X3)),add(multiply(X2,X3),multiply(X4,X3))) = multiply(X2,X3),
inference(substitution,[status(thm)],[c45]) ).
cnf(c57,plain,
add(additive_inverse(multiply(X4,X3)),additive_inverse(multiply(add(X2,X4),additive_inverse(X3)))) = multiply(X2,X3),
inference(transitivity,[status(thm)],[c55,c56]) ).
cnf(c58,plain,
add(additive_inverse(multiply(X3,X2)),additive_inverse(multiply(add(X4,X3),additive_inverse(X2)))) = multiply(X4,X2),
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
multiply(X4,X2) = add(additive_inverse(multiply(X3,X2)),additive_inverse(multiply(add(X4,X3),additive_inverse(X2)))),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
add(additive_inverse(additive_inverse(multiply(add(X4,X3),additive_inverse(X2)))),multiply(X4,X2)) = add(additive_inverse(additive_inverse(multiply(add(X4,X3),additive_inverse(X2)))),add(additive_inverse(multiply(X3,X2)),additive_inverse(multiply(add(X4,X3),additive_inverse(X2))))),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
add(additive_inverse(additive_inverse(multiply(add(X4,X3),additive_inverse(X2)))),add(additive_inverse(multiply(X3,X2)),additive_inverse(multiply(add(X4,X3),additive_inverse(X2))))) = additive_inverse(multiply(X3,X2)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c62,plain,
add(additive_inverse(additive_inverse(multiply(add(X4,X3),additive_inverse(X2)))),multiply(X4,X2)) = additive_inverse(multiply(X3,X2)),
inference(transitivity,[status(thm)],[c60,c61]) ).
cnf(c63,plain,
add(multiply(add(X4,X3),additive_inverse(X2)),multiply(X4,X2)) = additive_inverse(multiply(X3,X2)),
inference(transitivity,[status(thm)],[c5,c62]) ).
cnf(c64,plain,
additive_inverse(multiply(X3,X2)) = add(multiply(add(X4,X3),additive_inverse(X2)),multiply(X4,X2)),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,plain,
add(additive_inverse(multiply(X4,X2)),additive_inverse(multiply(X3,X2))) = add(additive_inverse(multiply(X4,X2)),add(multiply(add(X4,X3),additive_inverse(X2)),multiply(X4,X2))),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
add(additive_inverse(multiply(X4,X2)),add(multiply(add(X4,X3),additive_inverse(X2)),multiply(X4,X2))) = multiply(add(X4,X3),additive_inverse(X2)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c67,plain,
add(additive_inverse(multiply(X4,X2)),additive_inverse(multiply(X3,X2))) = multiply(add(X4,X3),additive_inverse(X2)),
inference(transitivity,[status(thm)],[c65,c66]) ).
cnf(c68,plain,
add(additive_inverse(multiply(x,z)),additive_inverse(multiply(y,z))) = multiply(add(x,y),additive_inverse(z)),
inference(substitution,[status(thm)],[c67]) ).
cnf(c69,plain,
multiply(add(x,y),additive_inverse(z)) = add(additive_inverse(multiply(x,z)),additive_inverse(multiply(y,z))),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
$false,
inference(resolution,[status(thm)],[c1,c69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG018-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n005.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Sun Sep 27 22:58:31 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.24/0.60 Command-line arguments: --flatten-regeneralise
% 0.24/0.60
% 0.24/0.60 % SZS status Unsatisfiable
% 0.24/0.60
% 0.24/0.60 % SZS output start CNFRefutation
% See solution above
% 0.24/0.64
% 0.24/0.64 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------