%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP584-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 12:34:43 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 7
% Syntax : Number of formulae : 99 ( 99 unt; 2 def)
% Number of atoms : 99 ( 98 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 149 ( 149 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,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(a,b) != multiply(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,X0)))),double_divide(identity,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(a,b) != multiply(b,a),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,definition,
sF0_fnc = multiply(a,b),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f12,definition,
sF1_fnc = multiply(b,a),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f13,plain,
sF0_fnc != sF1_fnc,
inference(definition_folding,[],[f10,f12,f11]) ).
fof(f28,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f29,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f28]) ).
fof(f35,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,X0)))),inverse(identity)) = X2,
inference(forward_demodulation,[status(thm)],[f8,f6]) ).
fof(f36,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(inverse(identity),double_divide(X1,double_divide(identity,X0)))),inverse(identity)) = X1,
inference(paramodulation,[status(thm)],[f8,f35]) ).
fof(f37,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(X0,double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,X0))))),double_divide(X3,X2))),inverse(identity)) = X3,
inference(paramodulation,[status(thm)],[f35,f35]) ).
fof(f38,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(double_divide(identity,X0),double_divide(X1,inverse(X0)))),inverse(identity)) = X1,
inference(paramodulation,[status(thm)],[f8,f35]) ).
fof(f43,plain,
! [X0,X1] : identity = double_divide(double_divide(X0,X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f28,f9]) ).
fof(f47,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),double_divide(double_divide(identity,X0),double_divide(X1,identity))),inverse(identity)) = X1,
inference(paramodulation,[status(thm)],[f9,f35]) ).
fof(f48,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f28]) ).
fof(f50,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),double_divide(double_divide(identity,X0),inverse(X1))),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f47]) ).
fof(f60,plain,
identity = double_divide(double_divide(b,a),sF0_fnc),
inference(paramodulation,[status(thm)],[f11,f43]) ).
fof(f164,plain,
! [X0] : double_divide(double_divide(identity,double_divide(double_divide(identity,X0),identity)),inverse(identity)) = X0,
inference(paramodulation,[status(thm)],[f9,f38]) ).
fof(f177,plain,
! [X0] : double_divide(double_divide(identity,inverse(double_divide(identity,X0))),inverse(identity)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f164]) ).
fof(f178,plain,
! [X0] : double_divide(double_divide(identity,multiply(X0,identity)),inverse(identity)) = X0,
inference(forward_demodulation,[status(thm)],[f28,f177]) ).
fof(f190,plain,
double_divide(double_divide(identity,inverse(identity)),inverse(identity)) = inverse(identity),
inference(paramodulation,[status(thm)],[f48,f178]) ).
fof(f200,plain,
double_divide(identity,inverse(identity)) = inverse(identity),
inference(forward_demodulation,[status(thm)],[f9,f190]) ).
fof(f201,plain,
identity = inverse(identity),
inference(forward_demodulation,[status(thm)],[f9,f200]) ).
fof(f203,plain,
! [X0] : double_divide(double_divide(identity,multiply(X0,identity)),identity) = X0,
inference(backward_demodulation,[status(thm)],[f201,f178]) ).
fof(f205,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(double_divide(identity,X0),double_divide(X1,inverse(X0)))),identity) = X1,
inference(backward_demodulation,[status(thm)],[f201,f38]) ).
fof(f206,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(X0,double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,X0))))),double_divide(X3,X2))),identity) = X3,
inference(backward_demodulation,[status(thm)],[f201,f37]) ).
fof(f207,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(inverse(identity),double_divide(X1,double_divide(identity,X0)))),identity) = X1,
inference(backward_demodulation,[status(thm)],[f201,f36]) ).
fof(f213,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,X0)))),identity) = X2,
inference(backward_demodulation,[status(thm)],[f201,f35]) ).
fof(f215,plain,
! [X0] : inverse(double_divide(identity,multiply(X0,identity))) = X0,
inference(forward_demodulation,[status(thm)],[f8,f203]) ).
fof(f216,plain,
! [X0] : multiply(multiply(X0,identity),identity) = X0,
inference(forward_demodulation,[status(thm)],[f28,f215]) ).
fof(f219,plain,
! [X0,X1] : inverse(double_divide(identity,double_divide(double_divide(identity,X0),double_divide(X1,inverse(X0))))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f205]) ).
fof(f220,plain,
! [X0,X1] : multiply(double_divide(double_divide(identity,X0),double_divide(X1,inverse(X0))),identity) = X1,
inference(forward_demodulation,[status(thm)],[f28,f219]) ).
fof(f221,plain,
! [X0,X1,X2,X3] : inverse(double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(X0,double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,X0))))),double_divide(X3,X2)))) = X3,
inference(forward_demodulation,[status(thm)],[f8,f206]) ).
fof(f222,plain,
! [X0,X1,X2,X3] : multiply(double_divide(double_divide(identity,double_divide(X0,double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,X0))))),double_divide(X3,X2)),inverse(identity)) = X3,
inference(forward_demodulation,[status(thm)],[f28,f221]) ).
fof(f223,plain,
! [X0,X1,X2,X3] : multiply(double_divide(double_divide(identity,double_divide(X0,double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,X0))))),double_divide(X3,X2)),identity) = X3,
inference(forward_demodulation,[status(thm)],[f201,f222]) ).
fof(f224,plain,
! [X0,X1] : inverse(double_divide(X0,double_divide(inverse(identity),double_divide(X1,double_divide(identity,X0))))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f207]) ).
fof(f225,plain,
! [X0,X1] : multiply(double_divide(inverse(identity),double_divide(X0,double_divide(identity,X1))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f28,f224]) ).
fof(f226,plain,
! [X0,X1] : multiply(double_divide(identity,double_divide(X0,double_divide(identity,X1))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f201,f225]) ).
fof(f229,plain,
! [X0,X1,X2] : inverse(double_divide(X0,double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,X0))))) = X2,
inference(forward_demodulation,[status(thm)],[f8,f213]) ).
fof(f230,plain,
! [X0,X1,X2] : multiply(double_divide(double_divide(identity,X0),double_divide(X1,double_divide(X0,X2))),X2) = X1,
inference(forward_demodulation,[status(thm)],[f28,f229]) ).
fof(f242,plain,
! [X0] : identity = double_divide(double_divide(identity,multiply(X0,identity)),X0),
inference(paramodulation,[status(thm)],[f216,f43]) ).
fof(f310,plain,
! [X0] : multiply(double_divide(identity,double_divide(X0,inverse(inverse(identity)))),identity) = X0,
inference(paramodulation,[status(thm)],[f9,f220]) ).
fof(f318,plain,
! [X0] : multiply(double_divide(identity,double_divide(X0,inverse(identity))),identity) = X0,
inference(forward_demodulation,[status(thm)],[f201,f310]) ).
fof(f319,plain,
! [X0] : multiply(double_divide(identity,double_divide(X0,identity)),identity) = X0,
inference(forward_demodulation,[status(thm)],[f201,f318]) ).
fof(f320,plain,
! [X0] : multiply(double_divide(identity,inverse(X0)),identity) = X0,
inference(forward_demodulation,[status(thm)],[f8,f319]) ).
fof(f331,plain,
! [X0,X1] : multiply(double_divide(identity,multiply(X0,X1)),identity) = double_divide(X1,X0),
inference(paramodulation,[status(thm)],[f28,f320]) ).
fof(f332,plain,
! [X0] : multiply(X0,identity) = double_divide(identity,inverse(X0)),
inference(paramodulation,[status(thm)],[f320,f216]) ).
fof(f349,plain,
! [X0] : multiply(inverse(X0),identity) = inverse(multiply(X0,identity)),
inference(paramodulation,[status(thm)],[f332,f28]) ).
fof(f504,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),double_divide(double_divide(identity,X0),inverse(X1))),identity) = X1,
inference(forward_demodulation,[status(thm)],[f201,f50]) ).
fof(f505,plain,
! [X0,X1] : inverse(double_divide(inverse(X0),double_divide(double_divide(identity,X0),inverse(X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f504]) ).
fof(f506,plain,
! [X0,X1] : multiply(double_divide(double_divide(identity,X0),inverse(X1)),inverse(X0)) = X1,
inference(forward_demodulation,[status(thm)],[f28,f505]) ).
fof(f508,plain,
! [X0] : multiply(identity,inverse(X0)) = double_divide(identity,X0),
inference(paramodulation,[status(thm)],[f9,f506]) ).
fof(f512,plain,
! [X0] : multiply(double_divide(double_divide(identity,X0),identity),inverse(X0)) = identity,
inference(paramodulation,[status(thm)],[f201,f506]) ).
fof(f520,plain,
! [X0] : inverse(inverse(inverse(X0))) = double_divide(identity,X0),
inference(forward_demodulation,[status(thm)],[f29,f508]) ).
fof(f527,plain,
! [X0] : multiply(inverse(double_divide(identity,X0)),inverse(X0)) = identity,
inference(forward_demodulation,[status(thm)],[f8,f512]) ).
fof(f528,plain,
! [X0] : multiply(multiply(X0,identity),inverse(X0)) = identity,
inference(forward_demodulation,[status(thm)],[f28,f527]) ).
fof(f675,plain,
! [X0] : multiply(X0,inverse(double_divide(identity,double_divide(X0,double_divide(identity,identity))))) = identity,
inference(paramodulation,[status(thm)],[f226,f528]) ).
fof(f688,plain,
! [X0] : multiply(X0,multiply(double_divide(X0,double_divide(identity,identity)),identity)) = identity,
inference(forward_demodulation,[status(thm)],[f28,f675]) ).
fof(f689,plain,
! [X0] : multiply(X0,multiply(double_divide(X0,inverse(identity)),identity)) = identity,
inference(forward_demodulation,[status(thm)],[f8,f688]) ).
fof(f690,plain,
! [X0] : multiply(X0,multiply(double_divide(X0,identity),identity)) = identity,
inference(forward_demodulation,[status(thm)],[f201,f689]) ).
fof(f691,plain,
! [X0] : multiply(X0,multiply(inverse(X0),identity)) = identity,
inference(forward_demodulation,[status(thm)],[f8,f690]) ).
fof(f692,plain,
! [X0] : multiply(X0,inverse(multiply(X0,identity))) = identity,
inference(forward_demodulation,[status(thm)],[f349,f691]) ).
fof(f891,plain,
! [X0] : multiply(double_divide(identity,identity),identity) = double_divide(inverse(multiply(X0,identity)),X0),
inference(paramodulation,[status(thm)],[f692,f331]) ).
fof(f946,plain,
! [X0] : multiply(inverse(identity),identity) = double_divide(inverse(multiply(X0,identity)),X0),
inference(forward_demodulation,[status(thm)],[f8,f891]) ).
fof(f947,plain,
! [X0] : inverse(multiply(identity,identity)) = double_divide(inverse(multiply(X0,identity)),X0),
inference(forward_demodulation,[status(thm)],[f349,f946]) ).
fof(f948,plain,
! [X0] : inverse(inverse(inverse(identity))) = double_divide(inverse(multiply(X0,identity)),X0),
inference(forward_demodulation,[status(thm)],[f29,f947]) ).
fof(f949,plain,
! [X0] : double_divide(identity,identity) = double_divide(inverse(multiply(X0,identity)),X0),
inference(forward_demodulation,[status(thm)],[f520,f948]) ).
fof(f950,plain,
! [X0] : inverse(identity) = double_divide(inverse(multiply(X0,identity)),X0),
inference(forward_demodulation,[status(thm)],[f8,f949]) ).
fof(f951,plain,
! [X0] : identity = double_divide(inverse(multiply(X0,identity)),X0),
inference(forward_demodulation,[status(thm)],[f201,f950]) ).
fof(f1242,plain,
! [X0,X1] : multiply(double_divide(double_divide(identity,inverse(multiply(X0,identity))),double_divide(X1,identity)),X0) = X1,
inference(paramodulation,[status(thm)],[f951,f230]) ).
fof(f1286,plain,
! [X0,X1] : multiply(double_divide(multiply(multiply(X0,identity),identity),double_divide(X1,identity)),X0) = X1,
inference(forward_demodulation,[status(thm)],[f332,f1242]) ).
fof(f1287,plain,
! [X0,X1] : multiply(double_divide(X0,double_divide(X1,identity)),X0) = X1,
inference(forward_demodulation,[status(thm)],[f216,f1286]) ).
fof(f1288,plain,
! [X0,X1] : multiply(double_divide(X0,inverse(X1)),X0) = X1,
inference(forward_demodulation,[status(thm)],[f8,f1287]) ).
fof(f1298,plain,
! [X0] : multiply(identity,double_divide(identity,multiply(inverse(X0),identity))) = X0,
inference(paramodulation,[status(thm)],[f242,f1288]) ).
fof(f1319,plain,
! [X0] : inverse(inverse(double_divide(identity,multiply(inverse(X0),identity)))) = X0,
inference(forward_demodulation,[status(thm)],[f29,f1298]) ).
fof(f1320,plain,
! [X0] : inverse(multiply(multiply(inverse(X0),identity),identity)) = X0,
inference(forward_demodulation,[status(thm)],[f28,f1319]) ).
fof(f1321,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f216,f1320]) ).
fof(f1334,plain,
! [X0] : inverse(X0) = double_divide(identity,X0),
inference(backward_demodulation,[status(thm)],[f1321,f520]) ).
fof(f1395,plain,
! [X0,X1,X2,X3] : multiply(double_divide(inverse(double_divide(X0,double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,X0))))),double_divide(X3,X2)),identity) = X3,
inference(backward_demodulation,[status(thm)],[f1334,f223]) ).
fof(f1400,plain,
! [X0] : multiply(X0,identity) = inverse(inverse(X0)),
inference(backward_demodulation,[status(thm)],[f1334,f332]) ).
fof(f1403,plain,
! [X0,X1,X2] : multiply(double_divide(inverse(X0),double_divide(X1,double_divide(X0,X2))),X2) = X1,
inference(backward_demodulation,[status(thm)],[f1334,f230]) ).
fof(f1415,plain,
! [X0,X1,X2,X3] : multiply(double_divide(multiply(double_divide(double_divide(identity,X0),double_divide(X1,double_divide(X0,X2))),X2),double_divide(X3,X1)),identity) = X3,
inference(forward_demodulation,[status(thm)],[f28,f1395]) ).
fof(f1416,plain,
! [X0,X1,X2,X3] : multiply(double_divide(multiply(double_divide(inverse(X0),double_divide(X1,double_divide(X0,X2))),X2),double_divide(X3,X1)),identity) = X3,
inference(forward_demodulation,[status(thm)],[f1334,f1415]) ).
fof(f1420,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[status(thm)],[f1321,f1400]) ).
fof(f1480,plain,
! [X0,X1,X2,X3] : double_divide(multiply(double_divide(inverse(X0),double_divide(X1,double_divide(X0,X2))),X2),double_divide(X3,X1)) = X3,
inference(forward_demodulation,[status(thm)],[f1420,f1416]) ).
fof(f1481,plain,
! [X0,X1] : double_divide(X0,double_divide(X1,X0)) = X1,
inference(forward_demodulation,[status(thm)],[f1403,f1480]) ).
fof(f1485,plain,
double_divide(sF0_fnc,identity) = double_divide(b,a),
inference(paramodulation,[status(thm)],[f60,f1481]) ).
fof(f1498,plain,
inverse(sF0_fnc) = double_divide(b,a),
inference(forward_demodulation,[status(thm)],[f8,f1485]) ).
fof(f1651,plain,
double_divide(a,inverse(sF0_fnc)) = b,
inference(paramodulation,[status(thm)],[f1498,f1481]) ).
fof(f1672,plain,
multiply(b,a) = sF0_fnc,
inference(paramodulation,[status(thm)],[f1651,f1288]) ).
fof(f1679,plain,
sF1_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f12,f1672]) ).
fof(f1680,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1679,f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP584-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.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 20:20:50 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.38 % Refutation found
% 0.09/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.036493 seconds
% 0.14/0.41 % CPU time: 0.090975 seconds
% 0.14/0.41 % Total memory used: 4.459 MB
% 0.14/0.41 % Net memory used: 4.233 MB
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