%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : RNG008-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 12:34:45 PM UTC 2026
% Result : Unsatisfiable 0.22s 0.53s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 12
% Syntax : Number of clauses : 97 ( 97 unt; 0 nHn; 35 RR)
% Number of literals : 97 ( 96 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(b,a) != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutativity) ).
cnf(c2,axiom,
add(X,Y) = add(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutative_addition) ).
cnf(c3,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
add(X3,X2) = add(X2,X3),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
add(X3,add(X3,X2)) = add(X3,add(X2,X3)),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,hypothesis,
multiply(X2,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boolean_ring) ).
cnf(c7,plain,
multiply(additive_inverse(X2),additive_inverse(X2)) = additive_inverse(X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
additive_inverse(X2) = multiply(additive_inverse(X2),additive_inverse(X2)),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,axiom,
multiply(additive_inverse(X2),Y2) = additive_inverse(multiply(X2,Y2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_additive_inverse2) ).
cnf(c10,plain,
multiply(additive_inverse(X3),X2) = additive_inverse(multiply(X3,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,axiom,
multiply(X2,additive_inverse(Y2)) = additive_inverse(multiply(X2,Y2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_additive_inverse1) ).
cnf(c12,plain,
multiply(X3,additive_inverse(X2)) = additive_inverse(multiply(X3,X2)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
additive_inverse(multiply(X3,X2)) = multiply(X3,additive_inverse(X2)),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
multiply(additive_inverse(X3),X2) = multiply(X3,additive_inverse(X2)),
inference(transitivity,[status(thm)],[c10,c13]) ).
cnf(c15,plain,
multiply(additive_inverse(X2),additive_inverse(X2)) = multiply(X2,additive_inverse(additive_inverse(X2))),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,axiom,
additive_inverse(additive_inverse(X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c17,plain,
multiply(X2,additive_inverse(additive_inverse(X2))) = multiply(X2,X2),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
multiply(X2,additive_inverse(additive_inverse(X2))) = X2,
inference(transitivity,[status(thm)],[c17,c6]) ).
cnf(c19,plain,
multiply(additive_inverse(X2),additive_inverse(X2)) = X2,
inference(transitivity,[status(thm)],[c15,c18]) ).
cnf(c20,plain,
additive_inverse(X2) = X2,
inference(transitivity,[status(thm)],[c8,c19]) ).
cnf(c21,plain,
X2 = additive_inverse(X2),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
add(X2,X3) = add(X2,additive_inverse(X3)),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
add(X3,add(X2,X3)) = add(X3,add(X2,additive_inverse(X3))),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
add(add(X3,X4),X2) = add(X2,add(X3,X4)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c25,plain,
add(X3,add(X4,X2)) = add(add(X4,X2),X3),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,axiom,
add(add(X2,Y2),Z) = add(X2,add(Y2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_addition) ).
cnf(c27,plain,
add(add(X4,X2),X3) = add(X4,add(X2,X3)),
inference(substitution,[status(thm)],[c26]) ).
cnf(c28,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c29,plain,
add(X4,add(X2,X3)) = add(X4,add(X3,X2)),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
add(add(X4,X2),X3) = add(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c27,c29]) ).
cnf(c31,plain,
add(X3,add(X4,X2)) = add(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c25,c30]) ).
cnf(c32,plain,
add(X3,add(X2,additive_inverse(X3))) = add(X2,add(X3,additive_inverse(X3))),
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
add(additive_inverse(X2),X2) = add(X2,additive_inverse(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c34,plain,
add(X2,additive_inverse(X2)) = add(additive_inverse(X2),X2),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,axiom,
add(additive_inverse(X2),X2) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c36,plain,
add(X2,additive_inverse(X2)) = additive_identity,
inference(transitivity,[status(thm)],[c34,c35]) ).
cnf(c37,plain,
add(X2,add(X3,additive_inverse(X3))) = add(X2,additive_identity),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
add(additive_identity,X2) = add(X2,additive_identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c39,plain,
add(X2,additive_identity) = add(additive_identity,X2),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,axiom,
add(additive_identity,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c41,plain,
add(X2,additive_identity) = X2,
inference(transitivity,[status(thm)],[c39,c40]) ).
cnf(c42,plain,
add(X2,add(X3,additive_inverse(X3))) = X2,
inference(transitivity,[status(thm)],[c37,c41]) ).
cnf(c43,plain,
add(X3,add(X2,additive_inverse(X3))) = X2,
inference(transitivity,[status(thm)],[c32,c42]) ).
cnf(c44,plain,
add(X3,add(X2,X3)) = X2,
inference(transitivity,[status(thm)],[c23,c43]) ).
cnf(c45,plain,
add(X3,add(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c5,c44]) ).
cnf(c46,plain,
add(a,add(a,multiply(b,a))) = multiply(b,a),
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
multiply(b,a) = add(a,add(a,multiply(b,a))),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
add(b,add(b,multiply(b,a))) = multiply(b,a),
inference(substitution,[status(thm)],[c45]) ).
cnf(c49,plain,
multiply(b,a) = add(b,add(b,multiply(b,a))),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
add(a,multiply(b,a)) = add(a,add(b,add(b,multiply(b,a)))),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
add(add(a,b),add(b,multiply(b,a))) = add(a,add(b,add(b,multiply(b,a)))),
inference(substitution,[status(thm)],[c26]) ).
cnf(c52,plain,
add(a,add(b,add(b,multiply(b,a)))) = add(add(a,b),add(b,multiply(b,a))),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,plain,
X2 = multiply(X2,X2),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c54,plain,
add(X3,multiply(X3,X2)) = add(multiply(X3,X3),multiply(X3,X2)),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,axiom,
multiply(X2,add(Y2,Z2)) = add(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute1) ).
cnf(c56,plain,
multiply(X3,add(X3,X2)) = add(multiply(X3,X3),multiply(X3,X2)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
add(multiply(X3,X3),multiply(X3,X2)) = multiply(X3,add(X3,X2)),
inference(symmetry,[status(thm)],[c56]) ).
cnf(c58,plain,
add(X3,multiply(X3,X2)) = multiply(X3,add(X3,X2)),
inference(transitivity,[status(thm)],[c54,c57]) ).
cnf(c59,plain,
add(X3,X2) = add(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c60,plain,
multiply(X3,add(X3,X2)) = multiply(X3,add(X2,X3)),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
add(X3,multiply(X3,X2)) = multiply(X3,add(X2,X3)),
inference(transitivity,[status(thm)],[c58,c60]) ).
cnf(c62,plain,
add(b,multiply(b,a)) = multiply(b,add(a,b)),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
add(add(a,b),add(b,multiply(b,a))) = add(add(a,b),multiply(b,add(a,b))),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
X2 = multiply(X2,X2),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c65,plain,
add(X3,multiply(X2,X3)) = add(multiply(X3,X3),multiply(X2,X3)),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,axiom,
multiply(add(X2,Y2),Z2) = add(multiply(X2,Z2),multiply(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute2) ).
cnf(c67,plain,
multiply(add(X3,X2),X3) = add(multiply(X3,X3),multiply(X2,X3)),
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
add(multiply(X3,X3),multiply(X2,X3)) = multiply(add(X3,X2),X3),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
add(X3,multiply(X2,X3)) = multiply(add(X3,X2),X3),
inference(transitivity,[status(thm)],[c65,c68]) ).
cnf(c70,plain,
add(add(a,b),multiply(b,add(a,b))) = multiply(add(add(a,b),b),add(a,b)),
inference(substitution,[status(thm)],[c69]) ).
cnf(c71,plain,
add(add(a,b),b) = add(a,add(b,b)),
inference(substitution,[status(thm)],[c26]) ).
cnf(c72,plain,
multiply(add(add(a,b),b),add(a,b)) = multiply(add(a,add(b,b)),add(a,b)),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
X2 = additive_inverse(X2),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c74,plain,
add(X2,X2) = add(X2,additive_inverse(X2)),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
add(X2,X2) = additive_identity,
inference(transitivity,[status(thm)],[c74,c36]) ).
cnf(c76,plain,
add(b,b) = additive_identity,
inference(substitution,[status(thm)],[c75]) ).
cnf(c77,plain,
add(a,add(b,b)) = add(a,additive_identity),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
multiply(add(a,add(b,b)),add(a,b)) = multiply(add(a,additive_identity),add(a,b)),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
add(a,additive_identity) = a,
inference(substitution,[status(thm)],[c41]) ).
cnf(c80,plain,
multiply(add(a,additive_identity),add(a,b)) = multiply(a,add(a,b)),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
add(a,multiply(a,b)) = multiply(a,add(a,b)),
inference(substitution,[status(thm)],[c58]) ).
cnf(c82,plain,
multiply(a,add(a,b)) = add(a,multiply(a,b)),
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,axiom,
multiply(a,b) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c84,plain,
add(a,multiply(a,b)) = add(a,c),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
multiply(a,add(a,b)) = add(a,c),
inference(transitivity,[status(thm)],[c82,c84]) ).
cnf(c86,plain,
multiply(add(a,additive_identity),add(a,b)) = add(a,c),
inference(transitivity,[status(thm)],[c80,c85]) ).
cnf(c87,plain,
multiply(add(a,add(b,b)),add(a,b)) = add(a,c),
inference(transitivity,[status(thm)],[c78,c86]) ).
cnf(c88,plain,
multiply(add(add(a,b),b),add(a,b)) = add(a,c),
inference(transitivity,[status(thm)],[c72,c87]) ).
cnf(c89,plain,
add(add(a,b),multiply(b,add(a,b))) = add(a,c),
inference(transitivity,[status(thm)],[c70,c88]) ).
cnf(c90,plain,
add(add(a,b),add(b,multiply(b,a))) = add(a,c),
inference(transitivity,[status(thm)],[c63,c89]) ).
cnf(c91,plain,
add(a,add(b,add(b,multiply(b,a)))) = add(a,c),
inference(transitivity,[status(thm)],[c52,c90]) ).
cnf(c92,plain,
add(a,multiply(b,a)) = add(a,c),
inference(transitivity,[status(thm)],[c50,c91]) ).
cnf(c93,plain,
add(a,add(a,multiply(b,a))) = add(a,add(a,c)),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
add(a,add(a,c)) = c,
inference(substitution,[status(thm)],[c45]) ).
cnf(c95,plain,
add(a,add(a,multiply(b,a))) = c,
inference(transitivity,[status(thm)],[c93,c94]) ).
cnf(c96,plain,
multiply(b,a) = c,
inference(transitivity,[status(thm)],[c47,c95]) ).
cnf(c97,plain,
$false,
inference(resolution,[status(thm)],[c1,c96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG008-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.39 % Computer : n013.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 22:57:51 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.53 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.22/0.53
% 0.22/0.53 % SZS status Unsatisfiable
% 0.22/0.53
% 0.22/0.53 % SZS output start CNFRefutation
% See solution above
% 0.22/0.57
% 0.22/0.57 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------