%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP497-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 12:34:32 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of formulae : 65 ( 65 unt; 1 def)
% Number of atoms : 65 ( 64 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 : 8 ( 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 : 79 ( 79 !; 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/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = double_divide(double_divide(B,A),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : inverse(A) = double_divide(A,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : identity = double_divide(A,inverse(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
multiply(identity,a2) != a2,
file('/export/starexec/sandbox/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(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(X1,identity))),multiply(double_divide(X2,X0),X1)) = X2,
inference(forward_demodulation,[status(thm)],[f7,f6]) ).
fof(f215,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f220,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,double_divide(X0,inverse(X1))),multiply(double_divide(X2,X0),X1)) = X2,
inference(backward_demodulation,[status(thm)],[f8,f20]) ).
fof(f237,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f215]) ).
fof(f238,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f215]) ).
fof(f239,plain,
! [X0,X1] : identity = double_divide(double_divide(X0,X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f215,f9]) ).
fof(f250,plain,
sF0_fnc = inverse(inverse(a2)),
inference(backward_demodulation,[status(thm)],[f238,f11]) ).
fof(f257,plain,
identity = double_divide(inverse(a2),sF0_fnc),
inference(paramodulation,[status(thm)],[f250,f9]) ).
fof(f294,plain,
identity = inverse(identity),
inference(paramodulation,[status(thm)],[f239,f220]) ).
fof(f295,plain,
! [X0,X1] : double_divide(double_divide(identity,identity),multiply(double_divide(X0,X1),X1)) = X0,
inference(paramodulation,[status(thm)],[f9,f220]) ).
fof(f302,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(inverse(X0),inverse(X1))),multiply(identity,X1)) = X0,
inference(paramodulation,[status(thm)],[f9,f220]) ).
fof(f303,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(identity,inverse(X0))),multiply(inverse(X1),X0)) = X1,
inference(paramodulation,[status(thm)],[f8,f220]) ).
fof(f311,plain,
! [X0,X1] : double_divide(inverse(identity),multiply(double_divide(X0,X1),X1)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f295]) ).
fof(f314,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(inverse(X0),inverse(X1))),inverse(inverse(X1))) = X0,
inference(forward_demodulation,[status(thm)],[f238,f302]) ).
fof(f425,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(backward_demodulation,[status(thm)],[f294,f237]) ).
fof(f574,plain,
! [X0,X1] : double_divide(identity,multiply(double_divide(X0,X1),X1)) = X0,
inference(forward_demodulation,[status(thm)],[f294,f311]) ).
fof(f576,plain,
double_divide(identity,multiply(identity,sF0_fnc)) = inverse(a2),
inference(paramodulation,[status(thm)],[f257,f574]) ).
fof(f583,plain,
! [X0] : double_divide(identity,multiply(identity,inverse(X0))) = X0,
inference(paramodulation,[status(thm)],[f9,f574]) ).
fof(f584,plain,
! [X0] : double_divide(identity,multiply(inverse(X0),identity)) = X0,
inference(paramodulation,[status(thm)],[f8,f574]) ).
fof(f597,plain,
double_divide(identity,inverse(inverse(sF0_fnc))) = inverse(a2),
inference(forward_demodulation,[status(thm)],[f238,f576]) ).
fof(f599,plain,
! [X0] : double_divide(identity,inverse(inverse(inverse(X0)))) = X0,
inference(forward_demodulation,[status(thm)],[f238,f583]) ).
fof(f737,plain,
multiply(inverse(inverse(sF0_fnc)),identity) = inverse(inverse(a2)),
inference(paramodulation,[status(thm)],[f597,f215]) ).
fof(f748,plain,
multiply(inverse(inverse(sF0_fnc)),identity) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f250,f737]) ).
fof(f754,plain,
double_divide(identity,sF0_fnc) = inverse(sF0_fnc),
inference(paramodulation,[status(thm)],[f748,f584]) ).
fof(f779,plain,
multiply(sF0_fnc,identity) = inverse(inverse(sF0_fnc)),
inference(paramodulation,[status(thm)],[f754,f215]) ).
fof(f793,plain,
! [X0] : double_divide(double_divide(identity,double_divide(inverse(X0),identity)),inverse(inverse(identity))) = X0,
inference(paramodulation,[status(thm)],[f294,f314]) ).
fof(f815,plain,
! [X0] : double_divide(double_divide(identity,inverse(inverse(X0))),inverse(inverse(identity))) = X0,
inference(forward_demodulation,[status(thm)],[f8,f793]) ).
fof(f816,plain,
! [X0] : double_divide(double_divide(identity,inverse(inverse(X0))),inverse(identity)) = X0,
inference(forward_demodulation,[status(thm)],[f294,f815]) ).
fof(f817,plain,
! [X0] : double_divide(double_divide(identity,inverse(inverse(X0))),identity) = X0,
inference(forward_demodulation,[status(thm)],[f294,f816]) ).
fof(f818,plain,
! [X0] : inverse(double_divide(identity,inverse(inverse(X0)))) = X0,
inference(forward_demodulation,[status(thm)],[f8,f817]) ).
fof(f819,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(forward_demodulation,[status(thm)],[f215,f818]) ).
fof(f958,plain,
multiply(sF0_fnc,identity) = a2,
inference(paramodulation,[status(thm)],[f250,f819]) ).
fof(f962,plain,
! [X0] : double_divide(identity,X0) = inverse(X0),
inference(paramodulation,[status(thm)],[f819,f584]) ).
fof(f970,plain,
inverse(inverse(sF0_fnc)) = a2,
inference(forward_demodulation,[status(thm)],[f779,f958]) ).
fof(f1001,plain,
! [X0] : inverse(inverse(inverse(inverse(X0)))) = X0,
inference(backward_demodulation,[status(thm)],[f962,f599]) ).
fof(f1002,plain,
! [X0,X1] : double_divide(double_divide(identity,inverse(inverse(X0))),multiply(inverse(X1),X0)) = X1,
inference(backward_demodulation,[status(thm)],[f962,f303]) ).
fof(f1006,plain,
! [X0,X1] : inverse(multiply(double_divide(X0,X1),X1)) = X0,
inference(backward_demodulation,[status(thm)],[f962,f574]) ).
fof(f1013,plain,
! [X0,X1,X2] : double_divide(inverse(double_divide(X0,inverse(X1))),multiply(double_divide(X2,X0),X1)) = X2,
inference(backward_demodulation,[status(thm)],[f962,f220]) ).
fof(f1022,plain,
! [X0,X1] : double_divide(inverse(inverse(inverse(X0))),multiply(inverse(X1),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f962,f1002]) ).
fof(f1035,plain,
! [X0,X1,X2] : double_divide(multiply(inverse(X0),X1),multiply(double_divide(X2,X1),X0)) = X2,
inference(forward_demodulation,[status(thm)],[f215,f1013]) ).
fof(f1047,plain,
! [X0,X1] : double_divide(X0,multiply(double_divide(X1,identity),inverse(X0))) = X1,
inference(paramodulation,[status(thm)],[f819,f1035]) ).
fof(f1064,plain,
! [X0,X1] : double_divide(X0,multiply(inverse(X1),inverse(X0))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f1047]) ).
fof(f1171,plain,
! [X0,X1] : multiply(X0,multiply(double_divide(X0,X1),X1)) = identity,
inference(paramodulation,[status(thm)],[f1006,f425]) ).
fof(f1395,plain,
! [X0] : double_divide(X0,multiply(identity,inverse(X0))) = identity,
inference(paramodulation,[status(thm)],[f294,f1064]) ).
fof(f1416,plain,
! [X0] : double_divide(X0,inverse(inverse(inverse(X0)))) = identity,
inference(forward_demodulation,[status(thm)],[f238,f1395]) ).
fof(f1525,plain,
! [X0,X1] : double_divide(inverse(inverse(inverse(multiply(double_divide(inverse(X0),X1),X1)))),identity) = X0,
inference(paramodulation,[status(thm)],[f1171,f1022]) ).
fof(f1552,plain,
! [X0,X1] : inverse(inverse(inverse(inverse(multiply(double_divide(inverse(X0),X1),X1))))) = X0,
inference(forward_demodulation,[status(thm)],[f8,f1525]) ).
fof(f1553,plain,
! [X0,X1] : multiply(double_divide(inverse(X0),X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f1001,f1552]) ).
fof(f1785,plain,
! [X0] : multiply(identity,inverse(inverse(inverse(inverse(X0))))) = X0,
inference(paramodulation,[status(thm)],[f1416,f1553]) ).
fof(f1802,plain,
! [X0] : inverse(inverse(inverse(inverse(inverse(inverse(X0)))))) = X0,
inference(forward_demodulation,[status(thm)],[f238,f1785]) ).
fof(f1803,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f1001,f1802]) ).
fof(f1826,plain,
sF0_fnc = a2,
inference(backward_demodulation,[status(thm)],[f1803,f970]) ).
fof(f1844,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1826,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP497-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 20:14:35 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.40 % Elapsed time: 0.042099 seconds
% 0.12/0.40 % CPU time: 0.189238 seconds
% 0.12/0.40 % Total memory used: 21.414 MB
% 0.12/0.40 % Net memory used: 21.092 MB
%------------------------------------------------------------------------------