%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP107-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 12:32:31 PM UTC 2026
% Result : Unsatisfiable 4.62s 1.11s
% Output : CNFRefutation 5.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 3
% Syntax : Number of formulae : 65 ( 59 unt; 0 def)
% Number of atoms : 78 ( 77 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 33 ( 20 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 152 ( 152 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : double_divide(double_divide(X,Y),inverse(double_divide(X,inverse(double_divide(inverse(Z),Y))))) = Z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : multiply(X,Y) = inverse(double_divide(Y,X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,X1),inverse(double_divide(X0,inverse(double_divide(inverse(X2),X1))))) = X2,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f6,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f7,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,X1),inverse(double_divide(X0,multiply(X1,inverse(X2))))) = X2,
inference(backward_demodulation,[status(thm)],[f5,f4]) ).
fof(f8,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,X1),multiply(multiply(X1,inverse(X2)),X0)) = X2,
inference(forward_demodulation,[status(thm)],[f5,f7]) ).
fof(f9,plain,
! [X0,X1,X2,X3] : double_divide(X0,multiply(multiply(multiply(multiply(X1,inverse(X0)),X2),inverse(X3)),double_divide(X2,X1))) = X3,
inference(paramodulation,[status(thm)],[f8,f8]) ).
fof(f10,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(X0,X1),multiply(multiply(X1,multiply(X2,X3)),X0)) = double_divide(X3,X2),
inference(paramodulation,[status(thm)],[f5,f8]) ).
fof(f11,plain,
! [X0,X1,X2] : multiply(multiply(multiply(X0,inverse(X1)),X2),double_divide(X2,X0)) = inverse(X1),
inference(paramodulation,[status(thm)],[f8,f5]) ).
fof(f14,plain,
! [X0,X1,X2,X3] : multiply(multiply(multiply(multiply(multiply(X0,inverse(X1)),X2),inverse(X3)),double_divide(X2,X0)),X1) = inverse(X3),
inference(paramodulation,[status(thm)],[f8,f11]) ).
fof(f15,plain,
! [X0,X1,X2] : double_divide(double_divide(double_divide(inverse(X0),X1),multiply(X1,inverse(X2))),inverse(X2)) = X0,
inference(paramodulation,[status(thm)],[f11,f8]) ).
fof(f19,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(multiply(X0,X1),X2),multiply(X2,inverse(X3))),inverse(X3)) = double_divide(X1,X0),
inference(paramodulation,[status(thm)],[f11,f10]) ).
fof(f31,plain,
! [X0,X1,X2,X3,X4,X5] : double_divide(X0,multiply(multiply(multiply(multiply(multiply(multiply(multiply(multiply(X1,inverse(X2)),X3),inverse(X4)),double_divide(X3,X1)),inverse(X0)),X2),inverse(X5)),X4)) = X5,
inference(paramodulation,[status(thm)],[f9,f9]) ).
fof(f33,plain,
! [X0,X1,X2,X3,X4] : multiply(multiply(multiply(multiply(multiply(multiply(multiply(X0,inverse(X1)),X2),inverse(X3)),double_divide(X2,X0)),inverse(X4)),X1),X3) = inverse(X4),
inference(paramodulation,[status(thm)],[f9,f11]) ).
fof(f112,plain,
! [X0,X1,X2,X3] : multiply(multiply(inverse(X0),double_divide(double_divide(X1,X2),multiply(multiply(X2,inverse(inverse(X3))),X1))),X0) = inverse(X3),
inference(paramodulation,[status(thm)],[f14,f14]) ).
fof(f124,plain,
! [X0,X1,X2,X3] : double_divide(X0,multiply(inverse(X0),double_divide(double_divide(X1,X2),multiply(multiply(X2,inverse(inverse(X3))),X1)))) = X3,
inference(paramodulation,[status(thm)],[f14,f9]) ).
fof(f139,plain,
! [X0,X1] : multiply(multiply(inverse(X0),inverse(X1)),X0) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f8,f112]) ).
fof(f141,plain,
! [X0,X1] : double_divide(X0,multiply(inverse(X0),inverse(X1))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f124]) ).
fof(f147,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,X1),multiply(multiply(X1,X0),inverse(X2))) = X2,
inference(paramodulation,[status(thm)],[f5,f141]) ).
fof(f164,plain,
! [X0,X1] : multiply(inverse(X0),double_divide(X1,inverse(X1))) = inverse(X0),
inference(paramodulation,[status(thm)],[f139,f11]) ).
fof(f165,plain,
! [X0,X1] : double_divide(double_divide(X0,inverse(X0)),inverse(X1)) = X1,
inference(paramodulation,[status(thm)],[f139,f8]) ).
fof(f245,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,inverse(X0)),multiply(X1,X2)) = double_divide(X2,X1),
inference(paramodulation,[status(thm)],[f5,f165]) ).
fof(f697,plain,
! [X0,X1] : X0 = double_divide(inverse(X0),multiply(inverse(X1),X1)),
inference(paramodulation,[status(thm)],[f147,f245]) ).
fof(f796,plain,
! [X0,X1,X2] : multiply(multiply(multiply(multiply(inverse(X0),X0),inverse(X1)),inverse(X2)),X2) = inverse(X1),
inference(paramodulation,[status(thm)],[f697,f11]) ).
fof(f797,plain,
! [X0,X1,X2] : double_divide(X0,multiply(multiply(multiply(inverse(X1),X1),inverse(X2)),inverse(X0))) = X2,
inference(paramodulation,[status(thm)],[f697,f8]) ).
fof(f798,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),inverse(X1)) = inverse(X1),
inference(paramodulation,[status(thm)],[f697,f5]) ).
fof(f800,plain,
! [X0,X1] : double_divide(X0,multiply(inverse(X1),inverse(X0))) = X1,
inference(backward_demodulation,[status(thm)],[f798,f797]) ).
fof(f801,plain,
! [X0,X1] : multiply(multiply(inverse(X0),inverse(X1)),X1) = inverse(X0),
inference(backward_demodulation,[status(thm)],[f798,f796]) ).
fof(f858,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f697,f800]) ).
fof(f863,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(X0,multiply(multiply(inverse(X0),inverse(multiply(X1,X2))),inverse(X3))),inverse(X3)) = double_divide(X2,X1),
inference(paramodulation,[status(thm)],[f800,f19]) ).
fof(f868,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,multiply(multiply(inverse(X0),inverse(inverse(X1))),inverse(X2))),inverse(X2)) = X1,
inference(paramodulation,[status(thm)],[f800,f15]) ).
fof(f948,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = double_divide(X1,X0),
inference(backward_demodulation,[status(thm)],[f949,f863]) ).
fof(f949,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,multiply(multiply(inverse(X0),X1),inverse(X2))),inverse(X2)) = X1,
inference(forward_demodulation,[status(thm)],[f858,f868]) ).
fof(f1003,plain,
! [X0,X1] : multiply(X0,double_divide(X1,inverse(X1))) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f858,f164]) ).
fof(f1006,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X1),X0) = inverse(inverse(X1)),
inference(paramodulation,[status(thm)],[f858,f139]) ).
fof(f1045,plain,
! [X0,X1] : multiply(X0,double_divide(X1,inverse(X1))) = X0,
inference(forward_demodulation,[status(thm)],[f858,f1003]) ).
fof(f1050,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X1),X0) = X1,
inference(forward_demodulation,[status(thm)],[f858,f1006]) ).
fof(f1089,plain,
! [X0,X1] : multiply(X0,double_divide(inverse(X1),X1)) = X0,
inference(paramodulation,[status(thm)],[f858,f1045]) ).
fof(f1127,plain,
! [X0,X1] : multiply(inverse(double_divide(X0,inverse(X0))),X1) = X1,
inference(paramodulation,[status(thm)],[f1045,f1050]) ).
fof(f1130,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X0)) = X1,
inference(paramodulation,[status(thm)],[f858,f1050]) ).
fof(f1134,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(backward_demodulation,[status(thm)],[f1141,f6]) ).
fof(f1141,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(forward_demodulation,[status(thm)],[f5,f1127]) ).
fof(f1147,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(trivial_equality_resolution,[status(thm)],[f1134]) ).
fof(f1152,plain,
! [X0,X1] : multiply(inverse(X0),X0) = double_divide(inverse(X1),X1),
inference(paramodulation,[status(thm)],[f1089,f1050]) ).
fof(f1176,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(paramodulation,[status(thm)],[f1130,f1130]) ).
fof(f1188,plain,
! [X0,X1] : multiply(X0,double_divide(X0,X1)) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f948,f1176]) ).
fof(f1193,plain,
! [X0,X1,X2,X3,X4] : double_divide(X0,multiply(X1,X2)) = multiply(multiply(multiply(multiply(multiply(X3,inverse(X1)),X4),inverse(X2)),double_divide(X4,X3)),inverse(X0)),
inference(paramodulation,[status(thm)],[f1130,f31]) ).
fof(f1228,plain,
! [X0,X1,X2] : multiply(multiply(double_divide(X0,multiply(X1,X2)),X1),X2) = inverse(X0),
inference(backward_demodulation,[status(thm)],[f1193,f33]) ).
fof(f1272,plain,
! [X0,X1] : multiply(inverse(X0),X1) = double_divide(inverse(X1),X0),
inference(paramodulation,[status(thm)],[f1188,f1050]) ).
fof(f1277,plain,
! [X0,X1] : multiply(inverse(X0),inverse(X1)) = double_divide(X1,X0),
inference(paramodulation,[status(thm)],[f1188,f1130]) ).
fof(f1278,plain,
! [X0,X1] : inverse(inverse(X0)) = double_divide(double_divide(X1,X0),X1),
inference(paramodulation,[status(thm)],[f1188,f948]) ).
fof(f1306,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(backward_demodulation,[status(thm)],[f1272,f1152]) ).
fof(f1358,plain,
! [X0,X1] : multiply(double_divide(X0,X1),X0) = inverse(X1),
inference(backward_demodulation,[status(thm)],[f1277,f801]) ).
fof(f1375,plain,
! [X0,X1] : X0 = double_divide(double_divide(X1,X0),X1),
inference(forward_demodulation,[status(thm)],[f858,f1278]) ).
fof(f1412,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(backward_subsumption_resolution,[status(thm)],[f1147,f1306]) ).
fof(f1434,plain,
! [X0,X1] : X0 = double_divide(X1,double_divide(X0,X1)),
inference(paramodulation,[status(thm)],[f1375,f1375]) ).
fof(f1444,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = inverse(double_divide(multiply(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f1375,f1228]) ).
fof(f1458,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)) ),
inference(backward_demodulation,[status(thm)],[f1670,f1412]) ).
fof(f1670,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(forward_demodulation,[status(thm)],[f5,f1444]) ).
fof(f1687,plain,
multiply(a4,b4) != multiply(b4,a4),
inference(trivial_equality_resolution,[status(thm)],[f1458]) ).
fof(f2532,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X0,X1)),
inference(paramodulation,[status(thm)],[f1434,f1358]) ).
fof(f2540,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f5,f2532]) ).
fof(f2541,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f1687,f2540]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP107-1 : 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 : n013.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 19:57:07 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 4.62/1.11 % Refutation found
% 4.62/1.11 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.62/1.11 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.11/1.14 % Elapsed time: 0.762336 seconds
% 5.11/1.14 % CPU time: 5.669058 seconds
% 5.11/1.14 % Total memory used: 164.880 MB
% 5.11/1.14 % Net memory used: 161.126 MB
%------------------------------------------------------------------------------