%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : RNG015-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/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 12:34:46 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.47s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of clauses : 39 ( 39 unt; 0 nHn; 4 RR)
% Number of literals : 39 ( 38 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 : 82 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(x,add(y,additive_inverse(z))) != add(multiply(x,y),additive_inverse(multiply(x,z))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity) ).
cnf(c2,axiom,
add(X,Y) = add(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_for_addition) ).
cnf(c3,plain,
add(additive_inverse(multiply(X4,X2)),multiply(X4,X3)) = add(multiply(X4,X3),additive_inverse(multiply(X4,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
add(multiply(X4,X3),additive_inverse(multiply(X4,X2))) = add(additive_inverse(multiply(X4,X2)),multiply(X4,X3)),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(X2,add(Y2,Z)) = add(multiply(X2,Y2),multiply(X2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute1) ).
cnf(c6,plain,
multiply(X4,add(X3,X2)) = add(multiply(X4,X3),multiply(X4,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
add(multiply(X4,X3),multiply(X4,X2)) = multiply(X4,add(X3,X2)),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
add(X3,X2) = add(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c9,plain,
multiply(X4,add(X3,X2)) = multiply(X4,add(X2,X3)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
add(multiply(X4,X3),multiply(X4,X2)) = multiply(X4,add(X2,X3)),
inference(transitivity,[status(thm)],[c7,c9]) ).
cnf(c11,plain,
add(multiply(X4,add(X3,additive_inverse(X2))),multiply(X4,X2)) = multiply(X4,add(X2,add(X3,additive_inverse(X2)))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
add(additive_inverse(X3),X2) = add(X2,additive_inverse(X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c13,plain,
add(X2,additive_inverse(X3)) = add(additive_inverse(X3),X2),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
add(X3,add(X2,additive_inverse(X3))) = add(X3,add(additive_inverse(X3),X2)),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,axiom,
add(X2,add(Y2,Z2)) = add(add(X2,Y2),Z2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_for_addition) ).
cnf(c16,plain,
add(X3,add(additive_inverse(X3),X2)) = add(add(X3,additive_inverse(X3)),X2),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,axiom,
add(X2,additive_inverse(X2)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c18,plain,
add(add(X3,additive_inverse(X3)),X2) = add(additive_identity,X2),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,axiom,
add(additive_identity,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c20,plain,
add(add(X3,additive_inverse(X3)),X2) = X2,
inference(transitivity,[status(thm)],[c18,c19]) ).
cnf(c21,plain,
add(X3,add(additive_inverse(X3),X2)) = X2,
inference(transitivity,[status(thm)],[c16,c20]) ).
cnf(c22,plain,
add(X3,add(X2,additive_inverse(X3))) = X2,
inference(transitivity,[status(thm)],[c14,c21]) ).
cnf(c23,plain,
add(X2,add(X3,additive_inverse(X2))) = X3,
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(X4,add(X2,add(X3,additive_inverse(X2)))) = multiply(X4,X3),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
add(multiply(X4,add(X3,additive_inverse(X2))),multiply(X4,X2)) = multiply(X4,X3),
inference(transitivity,[status(thm)],[c11,c24]) ).
cnf(c26,plain,
multiply(X4,X3) = add(multiply(X4,add(X3,additive_inverse(X2))),multiply(X4,X2)),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
add(additive_inverse(multiply(X4,X2)),multiply(X4,X3)) = add(additive_inverse(multiply(X4,X2)),add(multiply(X4,add(X3,additive_inverse(X2))),multiply(X4,X2))),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,axiom,
additive_inverse(additive_inverse(X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c29,plain,
X2 = additive_inverse(additive_inverse(X2)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
add(X2,X3) = add(X2,additive_inverse(additive_inverse(X3))),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
add(additive_inverse(X3),add(X2,X3)) = add(additive_inverse(X3),add(X2,additive_inverse(additive_inverse(X3)))),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
add(additive_inverse(X3),add(X2,additive_inverse(additive_inverse(X3)))) = X2,
inference(substitution,[status(thm)],[c22]) ).
cnf(c33,plain,
add(additive_inverse(X3),add(X2,X3)) = X2,
inference(transitivity,[status(thm)],[c31,c32]) ).
cnf(c34,plain,
add(additive_inverse(multiply(X4,X2)),add(multiply(X4,add(X3,additive_inverse(X2))),multiply(X4,X2))) = multiply(X4,add(X3,additive_inverse(X2))),
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
add(additive_inverse(multiply(X4,X2)),multiply(X4,X3)) = multiply(X4,add(X3,additive_inverse(X2))),
inference(transitivity,[status(thm)],[c27,c34]) ).
cnf(c36,plain,
add(multiply(X4,X3),additive_inverse(multiply(X4,X2))) = multiply(X4,add(X3,additive_inverse(X2))),
inference(transitivity,[status(thm)],[c4,c35]) ).
cnf(c37,plain,
add(multiply(x,y),additive_inverse(multiply(x,z))) = multiply(x,add(y,additive_inverse(z))),
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
multiply(x,add(y,additive_inverse(z))) = add(multiply(x,y),additive_inverse(multiply(x,z))),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,plain,
$false,
inference(resolution,[status(thm)],[c1,c38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG015-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 23:01:21 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.47 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.17/0.47
% 0.17/0.47 % SZS status Unsatisfiable
% 0.17/0.47
% 0.17/0.47 % SZS output start CNFRefutation
% See solution above
% 0.17/0.48
% 0.17/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------