%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP550-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 10:11:13 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.45s
% Output : CNFRefutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of clauses : 81 ( 81 unt; 0 nHn; 8 RR)
% Number of literals : 81 ( 80 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 111 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
cnf(c2,axiom,
multiply(A,B) = divide(A,divide(identity,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
cnf(c3,plain,
multiply(X2,X) = divide(X2,divide(identity,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,axiom,
inverse(A2) = divide(identity,A2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
cnf(c5,plain,
inverse(X) = divide(identity,X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
divide(identity,X) = inverse(X),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
divide(X2,divide(identity,X)) = divide(X2,inverse(X)),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
multiply(X2,X) = divide(X2,inverse(X)),
inference(transitivity,[status(thm)],[c3,c7]) ).
cnf(c9,plain,
multiply(multiply(inverse(X),X),X2) = divide(multiply(inverse(X),X),inverse(X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(inverse(X),X) = divide(inverse(X),inverse(X)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c11,plain,
divide(multiply(inverse(X),X),inverse(X2)) = divide(divide(inverse(X),inverse(X)),inverse(X2)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,axiom,
identity = divide(A2,A2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
cnf(c13,plain,
identity = divide(inverse(X),inverse(X)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
divide(inverse(X),inverse(X)) = identity,
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
divide(divide(inverse(X),inverse(X)),inverse(X2)) = divide(identity,inverse(X2)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
inverse(inverse(X)) = divide(identity,inverse(X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c17,plain,
divide(identity,inverse(X)) = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
divide(divide(inverse(X),inverse(X)),inverse(X2)) = inverse(inverse(X2)),
inference(transitivity,[status(thm)],[c15,c17]) ).
cnf(c19,plain,
divide(multiply(inverse(X),X),inverse(X2)) = inverse(inverse(X2)),
inference(transitivity,[status(thm)],[c11,c18]) ).
cnf(c20,plain,
multiply(multiply(inverse(X),X),X2) = inverse(inverse(X2)),
inference(transitivity,[status(thm)],[c9,c19]) ).
cnf(c21,plain,
multiply(multiply(inverse(X2),X2),X) = inverse(inverse(X)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
inverse(X) = divide(identity,X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c23,plain,
divide(inverse(X),inverse(X2)) = divide(inverse(X),divide(identity,X2)),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
identity = divide(divide(X2,X),divide(X2,X)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c25,plain,
divide(identity,X2) = divide(divide(divide(X2,X),divide(X2,X)),X2),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
divide(inverse(X),divide(identity,X2)) = divide(inverse(X),divide(divide(divide(X2,X),divide(X2,X)),X2)),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
inverse(X) = divide(identity,X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c28,plain,
divide(inverse(X2),divide(divide(divide(X,X2),X3),X)) = divide(divide(identity,X2),divide(divide(divide(X,X2),X3),X)),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,axiom,
divide(divide(identity,A2),divide(divide(divide(B2,A2),C),B2)) = C,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(c30,plain,
divide(divide(identity,X3),divide(divide(divide(X2,X3),X),X2)) = X,
inference(substitution,[status(thm)],[c29]) ).
cnf(c31,plain,
divide(inverse(X3),divide(divide(divide(X2,X3),X),X2)) = X,
inference(transitivity,[status(thm)],[c28,c30]) ).
cnf(c32,plain,
divide(inverse(X),divide(divide(divide(X2,X),divide(X2,X)),X2)) = divide(X2,X),
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
divide(inverse(X),divide(identity,X2)) = divide(X2,X),
inference(transitivity,[status(thm)],[c26,c32]) ).
cnf(c34,plain,
divide(inverse(X),inverse(X2)) = divide(X2,X),
inference(transitivity,[status(thm)],[c23,c33]) ).
cnf(c35,plain,
divide(inverse(identity),inverse(X)) = divide(X,identity),
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
divide(X,identity) = divide(inverse(identity),inverse(X)),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
inverse(identity) = divide(identity,identity),
inference(substitution,[status(thm)],[c4]) ).
cnf(c38,plain,
identity = divide(identity,identity),
inference(substitution,[status(thm)],[c12]) ).
cnf(c39,plain,
divide(identity,identity) = identity,
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
inverse(identity) = identity,
inference(transitivity,[status(thm)],[c37,c39]) ).
cnf(c41,plain,
divide(inverse(identity),inverse(X)) = divide(identity,inverse(X)),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
inverse(inverse(X)) = divide(identity,inverse(X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c43,plain,
divide(identity,inverse(X)) = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
divide(inverse(identity),inverse(X)) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c41,c43]) ).
cnf(c45,plain,
divide(X,identity) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c36,c44]) ).
cnf(c46,plain,
divide(inverse(X),identity) = inverse(inverse(inverse(X))),
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
inverse(inverse(inverse(X))) = divide(inverse(X),identity),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c49,plain,
divide(inverse(X),identity) = divide(inverse(X),inverse(identity)),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
divide(inverse(X),inverse(identity)) = divide(identity,X),
inference(substitution,[status(thm)],[c34]) ).
cnf(c51,plain,
inverse(X) = divide(identity,X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c52,plain,
divide(identity,X) = inverse(X),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,plain,
divide(inverse(X),inverse(identity)) = inverse(X),
inference(transitivity,[status(thm)],[c50,c52]) ).
cnf(c54,plain,
divide(inverse(X),identity) = inverse(X),
inference(transitivity,[status(thm)],[c49,c53]) ).
cnf(c55,plain,
inverse(inverse(inverse(X))) = inverse(X),
inference(transitivity,[status(thm)],[c47,c54]) ).
cnf(c56,plain,
inverse(inverse(inverse(inverse(X)))) = inverse(inverse(X)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
inverse(inverse(X)) = inverse(inverse(inverse(inverse(X)))),
inference(symmetry,[status(thm)],[c56]) ).
cnf(c58,plain,
divide(inverse(inverse(X)),identity) = inverse(inverse(inverse(inverse(X)))),
inference(substitution,[status(thm)],[c45]) ).
cnf(c59,plain,
inverse(inverse(inverse(inverse(X)))) = divide(inverse(inverse(X)),identity),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
identity = divide(inverse(inverse(X)),inverse(inverse(X))),
inference(substitution,[status(thm)],[c12]) ).
cnf(c61,plain,
divide(inverse(inverse(X)),identity) = divide(inverse(inverse(X)),divide(inverse(inverse(X)),inverse(inverse(X)))),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
divide(inverse(X2),inverse(inverse(X))) = divide(inverse(X),X2),
inference(substitution,[status(thm)],[c34]) ).
cnf(c63,plain,
divide(inverse(X2),divide(inverse(X2),inverse(inverse(X)))) = divide(inverse(X2),divide(inverse(X),X2)),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
inverse(X) = divide(identity,X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c65,plain,
divide(inverse(X),X2) = divide(divide(identity,X),X2),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
divide(inverse(X2),divide(inverse(X),X2)) = divide(inverse(X2),divide(divide(identity,X),X2)),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
identity = divide(X,X),
inference(substitution,[status(thm)],[c12]) ).
cnf(c68,plain,
divide(identity,X) = divide(divide(X2,X2),X),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
divide(divide(identity,X),X2) = divide(divide(divide(X2,X2),X),X2),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
divide(inverse(X2),divide(divide(identity,X),X2)) = divide(inverse(X2),divide(divide(divide(X2,X2),X),X2)),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
divide(inverse(X2),divide(divide(divide(X2,X2),X),X2)) = X,
inference(substitution,[status(thm)],[c31]) ).
cnf(c72,plain,
divide(inverse(X2),divide(divide(identity,X),X2)) = X,
inference(transitivity,[status(thm)],[c70,c71]) ).
cnf(c73,plain,
divide(inverse(X2),divide(inverse(X),X2)) = X,
inference(transitivity,[status(thm)],[c66,c72]) ).
cnf(c74,plain,
divide(inverse(X2),divide(inverse(X2),inverse(inverse(X)))) = X,
inference(transitivity,[status(thm)],[c63,c73]) ).
cnf(c75,plain,
divide(inverse(inverse(X)),divide(inverse(inverse(X)),inverse(inverse(X)))) = X,
inference(substitution,[status(thm)],[c74]) ).
cnf(c76,plain,
divide(inverse(inverse(X)),identity) = X,
inference(transitivity,[status(thm)],[c61,c75]) ).
cnf(c77,plain,
inverse(inverse(inverse(inverse(X)))) = X,
inference(transitivity,[status(thm)],[c59,c76]) ).
cnf(c78,plain,
inverse(inverse(X)) = X,
inference(transitivity,[status(thm)],[c57,c77]) ).
cnf(c79,plain,
multiply(multiply(inverse(X2),X2),X) = X,
inference(transitivity,[status(thm)],[c21,c78]) ).
cnf(c80,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(substitution,[status(thm)],[c79]) ).
cnf(c81,plain,
$false,
inference(resolution,[status(thm)],[c1,c80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP550-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n006.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 10:06:40 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.45 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
% 0.10/0.45
% 0.10/0.45 % SZS status Unsatisfiable
% 0.10/0.45
% 0.10/0.46 % SZS output start CNFRefutation
% See solution above
% 0.32/0.48
% 0.32/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------