%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP491-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 5.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 45 unt; 1 def)
% Number of atoms : 45 ( 44 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 : 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 : 42 ( 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C,
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(identity,double_divide(double_divide(double_divide(X0,X1),identity),double_divide(X2,X1)))) = X2,
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,X0),double_divide(identity,double_divide(multiply(X1,X0),double_divide(X2,X1)))) = X2,
inference(forward_demodulation,[status(thm)],[f7,f6]) ).
fof(f121,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f126,plain,
! [X0,X1] : double_divide(inverse(identity),double_divide(identity,double_divide(multiply(X0,identity),double_divide(X1,X0)))) = X1,
inference(paramodulation,[status(thm)],[f8,f20]) ).
fof(f129,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(multiply(identity,X0),inverse(X1)))) = X1,
inference(paramodulation,[status(thm)],[f8,f20]) ).
fof(f135,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(multiply(inverse(X1),X0),identity))) = X1,
inference(paramodulation,[status(thm)],[f9,f20]) ).
fof(f137,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,inverse(multiply(inverse(X1),X0)))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f135]) ).
fof(f142,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f121]) ).
fof(f143,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f121]) ).
fof(f157,plain,
sF0_fnc = inverse(inverse(a2)),
inference(backward_demodulation,[status(thm)],[f143,f11]) ).
fof(f338,plain,
! [X0] : double_divide(double_divide(identity,X0),double_divide(identity,inverse(inverse(identity)))) = X0,
inference(paramodulation,[status(thm)],[f142,f137]) ).
fof(f395,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(inverse(inverse(X0)),inverse(X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f143,f129]) ).
fof(f399,plain,
! [X0] : double_divide(double_divide(identity,X0),double_divide(identity,identity)) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f9,f395]) ).
fof(f413,plain,
! [X0] : double_divide(double_divide(identity,X0),inverse(identity)) = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f8,f399]) ).
fof(f459,plain,
double_divide(identity,inverse(identity)) = inverse(inverse(inverse(identity))),
inference(paramodulation,[status(thm)],[f9,f413]) ).
fof(f460,plain,
double_divide(inverse(identity),inverse(identity)) = inverse(inverse(identity)),
inference(paramodulation,[status(thm)],[f8,f413]) ).
fof(f471,plain,
identity = inverse(inverse(inverse(identity))),
inference(forward_demodulation,[status(thm)],[f9,f459]) ).
fof(f489,plain,
double_divide(inverse(identity),double_divide(identity,double_divide(multiply(inverse(identity),identity),inverse(inverse(identity))))) = inverse(identity),
inference(paramodulation,[status(thm)],[f460,f126]) ).
fof(f495,plain,
double_divide(inverse(identity),double_divide(identity,double_divide(inverse(identity),inverse(inverse(identity))))) = inverse(identity),
inference(forward_demodulation,[status(thm)],[f142,f489]) ).
fof(f496,plain,
double_divide(inverse(identity),double_divide(identity,identity)) = inverse(identity),
inference(forward_demodulation,[status(thm)],[f9,f495]) ).
fof(f497,plain,
double_divide(inverse(identity),inverse(identity)) = inverse(identity),
inference(forward_demodulation,[status(thm)],[f8,f496]) ).
fof(f498,plain,
inverse(inverse(identity)) = inverse(identity),
inference(forward_demodulation,[status(thm)],[f460,f497]) ).
fof(f501,plain,
identity = inverse(inverse(identity)),
inference(backward_demodulation,[status(thm)],[f498,f471]) ).
fof(f504,plain,
! [X0] : double_divide(double_divide(identity,X0),double_divide(identity,inverse(identity))) = X0,
inference(backward_demodulation,[status(thm)],[f498,f338]) ).
fof(f512,plain,
identity = inverse(identity),
inference(forward_demodulation,[status(thm)],[f498,f501]) ).
fof(f517,plain,
! [X0] : double_divide(double_divide(identity,X0),identity) = X0,
inference(forward_demodulation,[status(thm)],[f9,f504]) ).
fof(f518,plain,
! [X0] : inverse(double_divide(identity,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f517]) ).
fof(f519,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[status(thm)],[f121,f518]) ).
fof(f527,plain,
! [X0] : double_divide(double_divide(identity,X0),identity) = inverse(inverse(X0)),
inference(backward_demodulation,[status(thm)],[f512,f413]) ).
fof(f540,plain,
! [X0] : inverse(double_divide(identity,X0)) = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f8,f527]) ).
fof(f541,plain,
! [X0] : multiply(X0,identity) = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f121,f540]) ).
fof(f602,plain,
sF0_fnc = a2,
inference(backward_demodulation,[status(thm)],[f605,f157]) ).
fof(f605,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f519,f541]) ).
fof(f613,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f602,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP491-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n009.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sun Sep 20 20:15:03 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 % Drodi V4.1.1
% 0.09/5.39 % Refutation found
% 0.09/5.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.41 % Elapsed time: 0.035028 seconds
% 0.14/5.41 % CPU time: 0.103332 seconds
% 0.14/5.41 % Total memory used: 16.692 MB
% 0.14/5.41 % Net memory used: 16.548 MB
%------------------------------------------------------------------------------