%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP494-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 : Thu Sep 24 12:34:31 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.37s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 48 unt; 1 def)
% Number of atoms : 48 ( 47 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 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 : 43 ( 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = double_divide(double_divide(B,A),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : inverse(A) = double_divide(A,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : identity = double_divide(A,inverse(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
multiply(identity,a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,X0),double_divide(double_divide(double_divide(X1,X2),double_divide(identity,identity)),double_divide(X0,X2))) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X1,X0),identity),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0] : inverse(X0) = double_divide(X0,identity),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f9,plain,
! [X0] : identity = double_divide(X0,inverse(X0)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f10,plain,
multiply(identity,a2) != a2,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,definition,
sF0_fnc = multiply(identity,a2),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f12,plain,
sF0_fnc != a2,
inference(definition_folding,[],[f10,f11]) ).
fof(f179,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,X0),double_divide(double_divide(double_divide(X1,X2),inverse(identity)),double_divide(X0,X2))) = X1,
inference(backward_demodulation,[status(thm)],[f8,f6]) ).
fof(f182,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f194,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f182]) ).
fof(f195,plain,
! [X0,X1] : identity = double_divide(double_divide(X0,X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f182,f9]) ).
fof(f197,plain,
sF0_fnc = inverse(inverse(a2)),
inference(backward_demodulation,[status(thm)],[f194,f11]) ).
fof(f199,plain,
identity = double_divide(inverse(a2),sF0_fnc),
inference(paramodulation,[status(thm)],[f197,f9]) ).
fof(f220,plain,
! [X0] : double_divide(double_divide(identity,X0),double_divide(double_divide(identity,inverse(identity)),double_divide(X0,sF0_fnc))) = inverse(a2),
inference(paramodulation,[status(thm)],[f199,f179]) ).
fof(f221,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(double_divide(identity,inverse(identity)),double_divide(X0,inverse(X1)))) = X1,
inference(paramodulation,[status(thm)],[f9,f179]) ).
fof(f231,plain,
! [X0] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(X0,sF0_fnc))) = inverse(a2),
inference(forward_demodulation,[status(thm)],[f9,f220]) ).
fof(f232,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(X0,inverse(X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f9,f221]) ).
fof(f389,plain,
! [X0] : double_divide(double_divide(identity,X0),double_divide(identity,identity)) = X0,
inference(paramodulation,[status(thm)],[f9,f232]) ).
fof(f401,plain,
! [X0] : double_divide(double_divide(identity,X0),inverse(identity)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f389]) ).
fof(f403,plain,
double_divide(identity,inverse(identity)) = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f401]) ).
fof(f420,plain,
identity = inverse(identity),
inference(forward_demodulation,[status(thm)],[f9,f403]) ).
fof(f425,plain,
! [X0] : double_divide(double_divide(identity,X0),identity) = X0,
inference(backward_demodulation,[status(thm)],[f420,f401]) ).
fof(f436,plain,
! [X0] : inverse(double_divide(identity,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f425]) ).
fof(f437,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[status(thm)],[f182,f436]) ).
fof(f456,plain,
! [X0] : identity = double_divide(double_divide(identity,X0),X0),
inference(paramodulation,[status(thm)],[f437,f195]) ).
fof(f530,plain,
double_divide(double_divide(identity,double_divide(identity,sF0_fnc)),double_divide(identity,identity)) = inverse(a2),
inference(paramodulation,[status(thm)],[f456,f231]) ).
fof(f531,plain,
! [X0] : double_divide(double_divide(identity,double_divide(identity,inverse(X0))),double_divide(identity,identity)) = X0,
inference(paramodulation,[status(thm)],[f456,f232]) ).
fof(f542,plain,
double_divide(double_divide(identity,double_divide(identity,sF0_fnc)),inverse(identity)) = inverse(a2),
inference(forward_demodulation,[status(thm)],[f8,f530]) ).
fof(f543,plain,
double_divide(double_divide(identity,double_divide(identity,sF0_fnc)),identity) = inverse(a2),
inference(forward_demodulation,[status(thm)],[f420,f542]) ).
fof(f544,plain,
inverse(double_divide(identity,double_divide(identity,sF0_fnc))) = inverse(a2),
inference(forward_demodulation,[status(thm)],[f8,f543]) ).
fof(f545,plain,
multiply(double_divide(identity,sF0_fnc),identity) = inverse(a2),
inference(forward_demodulation,[status(thm)],[f182,f544]) ).
fof(f546,plain,
double_divide(identity,sF0_fnc) = inverse(a2),
inference(forward_demodulation,[status(thm)],[f437,f545]) ).
fof(f547,plain,
! [X0] : double_divide(double_divide(identity,double_divide(identity,inverse(X0))),inverse(identity)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f531]) ).
fof(f548,plain,
! [X0] : double_divide(double_divide(identity,double_divide(identity,inverse(X0))),identity) = X0,
inference(forward_demodulation,[status(thm)],[f420,f547]) ).
fof(f549,plain,
! [X0] : inverse(double_divide(identity,double_divide(identity,inverse(X0)))) = X0,
inference(forward_demodulation,[status(thm)],[f8,f548]) ).
fof(f550,plain,
! [X0] : multiply(double_divide(identity,inverse(X0)),identity) = X0,
inference(forward_demodulation,[status(thm)],[f182,f549]) ).
fof(f551,plain,
! [X0] : double_divide(identity,inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f437,f550]) ).
fof(f567,plain,
! [X0] : double_divide(double_divide(identity,identity),double_divide(identity,X0)) = X0,
inference(paramodulation,[status(thm)],[f551,f232]) ).
fof(f574,plain,
! [X0] : double_divide(inverse(identity),double_divide(identity,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f567]) ).
fof(f575,plain,
! [X0] : double_divide(identity,double_divide(identity,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f420,f574]) ).
fof(f627,plain,
double_divide(identity,inverse(a2)) = sF0_fnc,
inference(paramodulation,[status(thm)],[f546,f575]) ).
fof(f643,plain,
a2 = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f551,f627]) ).
fof(f644,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f643,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP494-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:10:11 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.37 % Refutation found
% 0.09/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.041551 seconds
% 0.14/0.41 % CPU time: 0.082214 seconds
% 0.14/0.41 % Total memory used: 15.446 MB
% 0.14/0.41 % Net memory used: 15.399 MB
%------------------------------------------------------------------------------