%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP496-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 0.04s 0.50s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 22 unt; 2 def)
% Number of atoms : 22 ( 21 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = 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(inverse(a1),a1) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,double_divide(X0,double_divide(X1,identity))),double_divide(double_divide(X1,double_divide(X2,X0)),identity)) = 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(inverse(a1),a1) != identity,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,definition,
sF1_fnc = inverse(a1),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f12,definition,
sF0_fnc = multiply(sF1_fnc,a1),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f13,plain,
sF0_fnc != identity,
inference(definition_folding,[],[f10,f12,f11]) ).
fof(f14,plain,
identity = double_divide(a1,sF1_fnc),
inference(paramodulation,[status(thm)],[f11,f9]) ).
fof(f15,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,double_divide(X0,inverse(X1))),double_divide(double_divide(X1,double_divide(X2,X0)),identity)) = X2,
inference(forward_demodulation,[status(thm)],[f8,f6]) ).
fof(f16,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,double_divide(X0,inverse(X1))),inverse(double_divide(X1,double_divide(X2,X0)))) = X2,
inference(forward_demodulation,[status(thm)],[f8,f15]) ).
fof(f17,plain,
identity = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f16]) ).
fof(f34,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(forward_demodulation,[status(thm)],[f8,f7]) ).
fof(f35,plain,
multiply(sF1_fnc,a1) = inverse(identity),
inference(paramodulation,[status(thm)],[f14,f34]) ).
fof(f39,plain,
sF0_fnc = inverse(identity),
inference(forward_demodulation,[status(thm)],[f12,f35]) ).
fof(f40,plain,
sF0_fnc = identity,
inference(forward_demodulation,[status(thm)],[f17,f39]) ).
fof(f41,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f40,f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP496-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/0.49 % Computer : n012.cluster.edu
% 0.04/0.49 % Model : x86_64 x86_64
% 0.04/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.49 % Memory : 8046.5625MB
% 0.04/0.49 % OS : Linux 6.8.0-71-generic
% 0.04/0.49 % CPULimit : 300
% 0.04/0.49 % WCLimit : 300
% 0.04/0.49 % DateTime : Sun Sep 20 20:14:38 UTC 2026
% 0.04/0.49 % CPUTime :
% 0.04/0.50 % Drodi V4.1.1
% 0.04/0.50 % Refutation found
% 0.04/0.50 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.04/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.04/0.52 % Elapsed time: 0.017443 seconds
% 0.04/0.52 % CPU time: 0.019734 seconds
% 0.04/0.52 % Total memory used: 413.456 KB
% 0.04/0.52 % Net memory used: 383.792 KB
%------------------------------------------------------------------------------