%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP566-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 12:34:41 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.37s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 32 unt; 1 def)
% Number of atoms : 32 ( 31 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 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 : 37 ( 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = 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(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),double_divide(identity,identity)) = 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(f20,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,double_divide(X0,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(X1,double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(identity,X2))),
inference(paramodulation,[status(thm)],[f6,f6]) ).
fof(f22,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),double_divide(double_divide(X3,X1),double_divide(identity,double_divide(identity,identity)))),double_divide(identity,identity)) = X3,
inference(paramodulation,[status(thm)],[f6,f6]) ).
fof(f38,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(identity,double_divide(X1,double_divide(identity,identity))),
inference(paramodulation,[status(thm)],[f20,f6]) ).
fof(f46,plain,
! [X0] : double_divide(double_divide(identity,X0),double_divide(identity,identity)) = double_divide(identity,double_divide(X0,double_divide(identity,identity))),
inference(forward_demodulation,[status(thm)],[f6,f38]) ).
fof(f73,plain,
! [X0,X1] : X0 = double_divide(identity,double_divide(double_divide(double_divide(X0,double_divide(identity,X1)),double_divide(identity,X1)),double_divide(identity,identity))),
inference(paramodulation,[status(thm)],[f6,f46]) ).
fof(f100,plain,
! [X0,X1,X2] : X0 = double_divide(identity,double_divide(double_divide(double_divide(X0,X1),double_divide(identity,double_divide(double_divide(double_divide(X1,double_divide(identity,X2)),double_divide(identity,X2)),double_divide(identity,identity)))),double_divide(identity,identity))),
inference(paramodulation,[status(thm)],[f73,f73]) ).
fof(f120,plain,
! [X0,X1] : X0 = double_divide(identity,double_divide(double_divide(double_divide(X0,X1),X1),double_divide(identity,identity))),
inference(forward_demodulation,[status(thm)],[f73,f100]) ).
fof(f131,plain,
! [X0] : X0 = double_divide(identity,double_divide(multiply(identity,X0),double_divide(identity,identity))),
inference(paramodulation,[status(thm)],[f7,f120]) ).
fof(f162,plain,
a2 = double_divide(identity,double_divide(sF0_fnc,double_divide(identity,identity))),
inference(paramodulation,[status(thm)],[f11,f131]) ).
fof(f252,plain,
! [X0] : X0 = double_divide(identity,double_divide(X0,double_divide(identity,identity))),
inference(paramodulation,[status(thm)],[f22,f120]) ).
fof(f305,plain,
a2 = double_divide(identity,double_divide(sF0_fnc,inverse(identity))),
inference(backward_demodulation,[status(thm)],[f8,f162]) ).
fof(f353,plain,
! [X0] : X0 = double_divide(identity,double_divide(X0,inverse(identity))),
inference(forward_demodulation,[status(thm)],[f8,f252]) ).
fof(f354,plain,
identity = double_divide(identity,identity),
inference(paramodulation,[status(thm)],[f9,f353]) ).
fof(f357,plain,
identity = inverse(identity),
inference(forward_demodulation,[status(thm)],[f8,f354]) ).
fof(f358,plain,
! [X0] : X0 = double_divide(identity,double_divide(X0,identity)),
inference(backward_demodulation,[status(thm)],[f357,f353]) ).
fof(f364,plain,
! [X0] : X0 = double_divide(identity,inverse(X0)),
inference(forward_demodulation,[status(thm)],[f8,f358]) ).
fof(f504,plain,
a2 = double_divide(identity,double_divide(sF0_fnc,identity)),
inference(forward_demodulation,[status(thm)],[f357,f305]) ).
fof(f505,plain,
a2 = double_divide(identity,inverse(sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f8,f504]) ).
fof(f506,plain,
a2 = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f364,f505]) ).
fof(f507,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f506,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP566-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 20:18:03 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % 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
% 0.09/0.40 % Elapsed time: 0.034828 seconds
% 0.09/0.40 % CPU time: 0.036565 seconds
% 0.09/0.40 % Total memory used: 954.192 KB
% 0.09/0.40 % Net memory used: 944.784 KB
%------------------------------------------------------------------------------