%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP546-1 : TPTP v9.3.1. Released v2.6.0.
% 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 10:11:12 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.46s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of clauses : 56 ( 56 unt; 0 nHn; 13 RR)
% Number of literals : 56 ( 55 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 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 : 66 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
cnf(c2,axiom,
inverse(A) = divide(identity,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(c3,plain,
inverse(X) = divide(identity,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
divide(X2,inverse(X)) = divide(X2,divide(identity,X)),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(A2,B) = divide(A2,divide(identity,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(c6,plain,
multiply(X2,X) = divide(X2,divide(identity,X)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
divide(X2,divide(identity,X)) = multiply(X2,X),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
divide(X2,inverse(X)) = multiply(X2,X),
inference(transitivity,[status(thm)],[c4,c7]) ).
cnf(c9,plain,
divide(inverse(X),inverse(X)) = multiply(inverse(X),X),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(inverse(X),X) = divide(inverse(X),inverse(X)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,axiom,
identity = divide(A2,A2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
cnf(c12,plain,
identity = divide(inverse(X),inverse(X)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
divide(inverse(X),inverse(X)) = identity,
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
multiply(inverse(X),X) = identity,
inference(transitivity,[status(thm)],[c10,c13]) ).
cnf(c15,plain,
multiply(inverse(b2),b2) = identity,
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(multiply(inverse(b2),b2),a2) = multiply(identity,a2),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
divide(identity,inverse(X)) = multiply(identity,X),
inference(substitution,[status(thm)],[c8]) ).
cnf(c18,plain,
multiply(identity,X) = divide(identity,inverse(X)),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
inverse(inverse(X)) = divide(identity,inverse(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c20,plain,
divide(identity,inverse(X)) = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
multiply(identity,X) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c18,c20]) ).
cnf(c22,plain,
multiply(identity,a2) = inverse(inverse(a2)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
inverse(inverse(X)) = multiply(identity,X),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c24,plain,
inverse(identity) = divide(identity,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c25,plain,
identity = divide(identity,identity),
inference(substitution,[status(thm)],[c11]) ).
cnf(c26,plain,
divide(identity,identity) = identity,
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
inverse(identity) = identity,
inference(transitivity,[status(thm)],[c24,c26]) ).
cnf(c28,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
multiply(identity,X) = multiply(inverse(identity),X),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
identity = divide(X,X),
inference(substitution,[status(thm)],[c11]) ).
cnf(c31,plain,
inverse(identity) = inverse(divide(X,X)),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
multiply(inverse(identity),X) = multiply(inverse(divide(X,X)),X),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
divide(inverse(divide(X2,X)),inverse(X2)) = multiply(inverse(divide(X2,X)),X2),
inference(substitution,[status(thm)],[c8]) ).
cnf(c34,plain,
multiply(inverse(divide(X2,X)),X2) = divide(inverse(divide(X2,X)),inverse(X2)),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
inverse(X) = divide(identity,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c36,plain,
divide(inverse(divide(X2,X)),inverse(X2)) = divide(inverse(divide(X2,X)),divide(identity,X2)),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
identity = divide(X,X),
inference(substitution,[status(thm)],[c11]) ).
cnf(c38,plain,
divide(identity,X2) = divide(divide(X,X),X2),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
divide(inverse(divide(X2,X)),divide(identity,X2)) = divide(inverse(divide(X2,X)),divide(divide(X,X),X2)),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
inverse(divide(X2,X)) = divide(identity,divide(X2,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c41,plain,
divide(inverse(divide(X2,X)),divide(divide(X,X3),X2)) = divide(divide(identity,divide(X2,X)),divide(divide(X,X3),X2)),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,axiom,
divide(divide(identity,divide(A2,B2)),divide(divide(B2,C),A2)) = C,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(c43,plain,
divide(divide(identity,divide(X3,X2)),divide(divide(X2,X),X3)) = X,
inference(substitution,[status(thm)],[c42]) ).
cnf(c44,plain,
divide(inverse(divide(X3,X2)),divide(divide(X2,X),X3)) = X,
inference(transitivity,[status(thm)],[c41,c43]) ).
cnf(c45,plain,
divide(inverse(divide(X2,X)),divide(divide(X,X),X2)) = X,
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
divide(inverse(divide(X2,X)),divide(identity,X2)) = X,
inference(transitivity,[status(thm)],[c39,c45]) ).
cnf(c47,plain,
divide(inverse(divide(X2,X)),inverse(X2)) = X,
inference(transitivity,[status(thm)],[c36,c46]) ).
cnf(c48,plain,
multiply(inverse(divide(X2,X)),X2) = X,
inference(transitivity,[status(thm)],[c34,c47]) ).
cnf(c49,plain,
multiply(inverse(divide(X,X)),X) = X,
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
multiply(inverse(identity),X) = X,
inference(transitivity,[status(thm)],[c32,c49]) ).
cnf(c51,plain,
multiply(identity,X) = X,
inference(transitivity,[status(thm)],[c29,c50]) ).
cnf(c52,plain,
inverse(inverse(X)) = X,
inference(transitivity,[status(thm)],[c23,c51]) ).
cnf(c53,plain,
inverse(inverse(a2)) = a2,
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
multiply(identity,a2) = a2,
inference(transitivity,[status(thm)],[c22,c53]) ).
cnf(c55,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(transitivity,[status(thm)],[c16,c54]) ).
cnf(c56,plain,
$false,
inference(resolution,[status(thm)],[c1,c55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP546-1 : TPTP v9.3.1. Released v2.6.0.
% 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 10:09:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.46 Command-line arguments: --no-flatten-goal
% 0.14/0.46
% 0.14/0.46 % SZS status Unsatisfiable
% 0.14/0.46
% 0.14/0.46 % SZS output start CNFRefutation
% See solution above
% 0.14/0.48
% 0.14/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------