%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : RNG012-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 0.21s 0.54s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of clauses : 62 ( 62 unt; 0 nHn; 3 RR)
% Number of literals : 62 ( 61 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 120 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(additive_inverse(a),additive_inverse(b)) != multiply(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
cnf(c2,axiom,
additive_inverse(additive_inverse(X)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).
cnf(c3,plain,
additive_inverse(additive_inverse(multiply(additive_inverse(X3),additive_inverse(X2)))) = multiply(additive_inverse(X3),additive_inverse(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(additive_inverse(X3),additive_inverse(X2)) = additive_inverse(additive_inverse(multiply(additive_inverse(X3),additive_inverse(X2)))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
add(X2,additive_identity) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_additive_identity) ).
cnf(c6,plain,
add(additive_inverse(additive_inverse(multiply(additive_inverse(X3),additive_inverse(X2)))),additive_identity) = additive_inverse(additive_inverse(multiply(additive_inverse(X3),additive_inverse(X2)))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
additive_inverse(additive_inverse(multiply(additive_inverse(X3),additive_inverse(X2)))) = add(additive_inverse(additive_inverse(multiply(additive_inverse(X3),additive_inverse(X2)))),additive_identity),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
add(additive_inverse(multiply(X3,additive_inverse(X2))),additive_identity) = additive_inverse(multiply(X3,additive_inverse(X2))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c9,plain,
additive_inverse(multiply(X3,additive_inverse(X2))) = add(additive_inverse(multiply(X3,additive_inverse(X2))),additive_identity),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,axiom,
multiply(X2,add(Y,Z)) = add(multiply(X2,Y),multiply(X2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute1) ).
cnf(c11,plain,
multiply(X3,add(X4,X2)) = add(multiply(X3,X4),multiply(X3,X2)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
add(multiply(X4,X2),multiply(X4,X3)) = multiply(X4,add(X2,X3)),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,axiom,
add(X2,Y2) = add(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_for_addition) ).
cnf(c14,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
multiply(X4,add(X2,X3)) = multiply(X4,add(X3,X2)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
add(multiply(X4,X2),multiply(X4,X3)) = multiply(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c12,c15]) ).
cnf(c17,plain,
add(multiply(X3,X2),multiply(X3,additive_inverse(X2))) = multiply(X3,add(additive_inverse(X2),X2)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
add(X2,additive_inverse(X2)) = add(additive_inverse(X2),X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c19,plain,
add(additive_inverse(X2),X2) = add(X2,additive_inverse(X2)),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,axiom,
add(X2,additive_inverse(X2)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c21,plain,
add(additive_inverse(X2),X2) = additive_identity,
inference(transitivity,[status(thm)],[c19,c20]) ).
cnf(c22,plain,
multiply(X3,add(additive_inverse(X2),X2)) = multiply(X3,additive_identity),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,axiom,
multiply(X2,additive_identity) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c24,plain,
multiply(X3,add(additive_inverse(X2),X2)) = additive_identity,
inference(transitivity,[status(thm)],[c22,c23]) ).
cnf(c25,plain,
add(multiply(X3,X2),multiply(X3,additive_inverse(X2))) = additive_identity,
inference(transitivity,[status(thm)],[c17,c24]) ).
cnf(c26,plain,
additive_identity = add(multiply(X3,X2),multiply(X3,additive_inverse(X2))),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,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)],[c26]) ).
cnf(c28,plain,
add(X3,X2) = add(X2,X3),
inference(substitution,[status(thm)],[c13]) ).
cnf(c29,plain,
add(X2,X3) = add(X3,X2),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
add(additive_inverse(X3),add(X2,X3)) = add(additive_inverse(X3),add(X3,X2)),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,axiom,
add(X2,add(Y2,Z2)) = add(add(X2,Y2),Z2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_for_addition) ).
cnf(c32,plain,
add(additive_inverse(X3),add(X3,X2)) = add(add(additive_inverse(X3),X3),X2),
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
add(add(additive_inverse(X3),X3),X2) = add(additive_identity,X2),
inference(congruence,[status(thm)],[c21]) ).
cnf(c34,axiom,
add(additive_identity,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c35,plain,
add(add(additive_inverse(X3),X3),X2) = X2,
inference(transitivity,[status(thm)],[c33,c34]) ).
cnf(c36,plain,
add(additive_inverse(X3),add(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c32,c35]) ).
cnf(c37,plain,
add(additive_inverse(X3),add(X2,X3)) = X2,
inference(transitivity,[status(thm)],[c30,c36]) ).
cnf(c38,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)],[c37]) ).
cnf(c39,plain,
add(additive_inverse(multiply(X3,additive_inverse(X2))),additive_identity) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c27,c38]) ).
cnf(c40,plain,
additive_inverse(multiply(X3,additive_inverse(X2))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c9,c39]) ).
cnf(c41,plain,
additive_inverse(multiply(additive_inverse(X3),additive_inverse(X2))) = multiply(additive_inverse(X3),X2),
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
add(multiply(X3,X2),additive_inverse(multiply(additive_inverse(X3),additive_inverse(X2)))) = add(multiply(X3,X2),multiply(additive_inverse(X3),X2)),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,axiom,
multiply(add(X2,Y2),Z2) = add(multiply(X2,Z2),multiply(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute2) ).
cnf(c44,plain,
multiply(add(X3,X4),X2) = add(multiply(X3,X2),multiply(X4,X2)),
inference(substitution,[status(thm)],[c43]) ).
cnf(c45,plain,
add(multiply(X3,X2),multiply(X4,X2)) = multiply(add(X3,X4),X2),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c46,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c13]) ).
cnf(c47,plain,
multiply(add(X3,X4),X2) = multiply(add(X4,X3),X2),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
add(multiply(X3,X2),multiply(X4,X2)) = multiply(add(X4,X3),X2),
inference(transitivity,[status(thm)],[c45,c47]) ).
cnf(c49,plain,
add(multiply(X3,X2),multiply(additive_inverse(X3),X2)) = multiply(add(additive_inverse(X3),X3),X2),
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
multiply(add(additive_inverse(X3),X3),X2) = multiply(additive_identity,X2),
inference(congruence,[status(thm)],[c21]) ).
cnf(c51,axiom,
multiply(additive_identity,X2) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c52,plain,
multiply(add(additive_inverse(X3),X3),X2) = additive_identity,
inference(transitivity,[status(thm)],[c50,c51]) ).
cnf(c53,plain,
add(multiply(X3,X2),multiply(additive_inverse(X3),X2)) = additive_identity,
inference(transitivity,[status(thm)],[c49,c52]) ).
cnf(c54,plain,
add(multiply(X3,X2),additive_inverse(multiply(additive_inverse(X3),additive_inverse(X2)))) = additive_identity,
inference(transitivity,[status(thm)],[c42,c53]) ).
cnf(c55,plain,
additive_identity = add(multiply(X3,X2),additive_inverse(multiply(additive_inverse(X3),additive_inverse(X2)))),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,plain,
add(additive_inverse(additive_inverse(multiply(additive_inverse(X3),additive_inverse(X2)))),additive_identity) = add(additive_inverse(additive_inverse(multiply(additive_inverse(X3),additive_inverse(X2)))),add(multiply(X3,X2),additive_inverse(multiply(additive_inverse(X3),additive_inverse(X2))))),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
add(additive_inverse(additive_inverse(multiply(additive_inverse(X3),additive_inverse(X2)))),add(multiply(X3,X2),additive_inverse(multiply(additive_inverse(X3),additive_inverse(X2))))) = multiply(X3,X2),
inference(substitution,[status(thm)],[c37]) ).
cnf(c58,plain,
add(additive_inverse(additive_inverse(multiply(additive_inverse(X3),additive_inverse(X2)))),additive_identity) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c56,c57]) ).
cnf(c59,plain,
additive_inverse(additive_inverse(multiply(additive_inverse(X3),additive_inverse(X2)))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c7,c58]) ).
cnf(c60,plain,
multiply(additive_inverse(X3),additive_inverse(X2)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c4,c59]) ).
cnf(c61,plain,
multiply(additive_inverse(a),additive_inverse(b)) = multiply(a,b),
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
$false,
inference(resolution,[status(thm)],[c1,c61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG012-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.41 % Computer : n003.cluster.edu
% 0.17/0.41 % Model : x86_64 x86_64
% 0.17/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.41 % Memory : 8046.5625MB
% 0.17/0.41 % OS : Linux 6.8.0-71-generic
% 0.17/0.41 % CPULimit : 300
% 0.17/0.41 % WCLimit : 300
% 0.17/0.41 % DateTime : Sun Sep 27 23:00:42 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.42 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.54 Command-line arguments: --flatten-regeneralise
% 0.21/0.54
% 0.21/0.54 % SZS status Unsatisfiable
% 0.21/0.54
% 0.21/0.54 % SZS output start CNFRefutation
% See solution above
% 0.21/0.57
% 0.21/0.57 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------