%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP580-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 5
% Syntax : Number of formulae : 89 ( 89 unt; 0 def)
% Number of atoms : 89 ( 88 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 151 ( 151 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,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(a,b) != multiply(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(double_divide(X1,X0),X2),double_divide(X1,identity))),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(f14,plain,
! [X0,X1] : multiply(identity,double_divide(X0,X1)) = double_divide(multiply(X1,X0),identity),
inference(paramodulation,[status(thm)],[f7,f7]) ).
fof(f19,plain,
! [X0,X1] : identity = double_divide(double_divide(X0,double_divide(multiply(X0,X1),double_divide(X1,identity))),double_divide(identity,identity)),
inference(paramodulation,[status(thm)],[f7,f6]) ).
fof(f20,plain,
! [X0,X1,X2] : X0 = double_divide(double_divide(identity,double_divide(double_divide(multiply(identity,double_divide(X1,X2)),X0),double_divide(multiply(X2,X1),identity))),double_divide(identity,identity)),
inference(paramodulation,[status(thm)],[f14,f6]) ).
fof(f26,plain,
! [X0,X1,X2] : X0 = double_divide(double_divide(identity,double_divide(double_divide(multiply(identity,double_divide(X1,X2)),X0),multiply(identity,double_divide(X1,X2)))),double_divide(identity,identity)),
inference(forward_demodulation,[status(thm)],[f14,f20]) ).
fof(f31,plain,
! [X0,X1] : double_divide(multiply(double_divide(identity,X0),X1),double_divide(X1,identity)) = double_divide(double_divide(X0,identity),double_divide(identity,identity)),
inference(paramodulation,[status(thm)],[f19,f6]) ).
fof(f33,plain,
! [X0,X1,X2] : X0 = double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(identity,X0),double_divide(double_divide(X1,double_divide(multiply(X1,X2),double_divide(X2,identity))),identity))),double_divide(identity,identity)),
inference(paramodulation,[status(thm)],[f19,f6]) ).
fof(f35,plain,
! [X0,X1,X2] : X0 = double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(identity,X0),multiply(double_divide(multiply(X1,X2),double_divide(X2,identity)),X1))),double_divide(identity,identity)),
inference(forward_demodulation,[status(thm)],[f7,f33]) ).
fof(f58,plain,
! [X0,X1] : multiply(double_divide(X0,identity),multiply(double_divide(identity,X1),X0)) = double_divide(double_divide(double_divide(X1,identity),double_divide(identity,identity)),identity),
inference(paramodulation,[status(thm)],[f31,f7]) ).
fof(f60,plain,
! [X0,X1] : multiply(double_divide(X0,identity),multiply(double_divide(identity,X1),X0)) = multiply(double_divide(identity,identity),double_divide(X1,identity)),
inference(forward_demodulation,[status(thm)],[f7,f58]) ).
fof(f203,plain,
! [X0,X1] : identity = double_divide(double_divide(X0,double_divide(multiply(X0,X1),double_divide(X1,identity))),inverse(identity)),
inference(backward_demodulation,[status(thm)],[f8,f19]) ).
fof(f204,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(double_divide(X1,X0),X2),double_divide(X1,identity))),inverse(identity)) = X2,
inference(backward_demodulation,[status(thm)],[f8,f6]) ).
fof(f206,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f207,plain,
! [X0,X1] : multiply(inverse(X0),multiply(double_divide(identity,X1),X0)) = multiply(double_divide(identity,identity),double_divide(X1,identity)),
inference(backward_demodulation,[status(thm)],[f8,f60]) ).
fof(f208,plain,
! [X0,X1] : double_divide(multiply(double_divide(identity,X0),X1),inverse(X1)) = double_divide(double_divide(X0,identity),double_divide(identity,identity)),
inference(backward_demodulation,[status(thm)],[f8,f31]) ).
fof(f213,plain,
! [X0,X1] : identity = double_divide(double_divide(X0,double_divide(multiply(X0,X1),inverse(X1))),inverse(identity)),
inference(forward_demodulation,[status(thm)],[f8,f203]) ).
fof(f214,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(double_divide(X1,X0),X2),inverse(X1))),inverse(identity)) = X2,
inference(forward_demodulation,[status(thm)],[f8,f204]) ).
fof(f215,plain,
! [X0,X1] : multiply(inverse(X0),multiply(double_divide(identity,X1),X0)) = multiply(inverse(identity),double_divide(X1,identity)),
inference(forward_demodulation,[status(thm)],[f8,f207]) ).
fof(f216,plain,
! [X0,X1] : multiply(inverse(X0),multiply(double_divide(identity,X1),X0)) = multiply(inverse(identity),inverse(X1)),
inference(forward_demodulation,[status(thm)],[f8,f215]) ).
fof(f217,plain,
! [X0,X1] : double_divide(multiply(double_divide(identity,X0),X1),inverse(X1)) = double_divide(inverse(X0),double_divide(identity,identity)),
inference(forward_demodulation,[status(thm)],[f8,f208]) ).
fof(f218,plain,
! [X0,X1] : double_divide(multiply(double_divide(identity,X0),X1),inverse(X1)) = double_divide(inverse(X0),inverse(identity)),
inference(forward_demodulation,[status(thm)],[f8,f217]) ).
fof(f219,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f206]) ).
fof(f220,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f206]) ).
fof(f221,plain,
! [X0,X1] : identity = double_divide(double_divide(X0,X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f206,f9]) ).
fof(f290,plain,
! [X0] : multiply(inverse(identity),inverse(identity)) = multiply(inverse(X0),multiply(inverse(identity),X0)),
inference(paramodulation,[status(thm)],[f8,f216]) ).
fof(f363,plain,
! [X0] : double_divide(inverse(inverse(identity)),inverse(identity)) = double_divide(multiply(identity,X0),inverse(X0)),
inference(paramodulation,[status(thm)],[f9,f218]) ).
fof(f372,plain,
! [X0] : double_divide(inverse(inverse(identity)),inverse(identity)) = double_divide(inverse(inverse(X0)),inverse(X0)),
inference(forward_demodulation,[status(thm)],[f219,f363]) ).
fof(f522,plain,
! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X0,double_divide(identity,inverse(X1))),inverse(identity)),
inference(paramodulation,[status(thm)],[f221,f214]) ).
fof(f580,plain,
! [X0] : multiply(X0,identity) = double_divide(double_divide(X0,identity),inverse(identity)),
inference(paramodulation,[status(thm)],[f9,f522]) ).
fof(f594,plain,
! [X0] : multiply(X0,identity) = double_divide(inverse(X0),inverse(identity)),
inference(forward_demodulation,[status(thm)],[f8,f580]) ).
fof(f598,plain,
! [X0] : multiply(inverse(identity),identity) = double_divide(inverse(inverse(X0)),inverse(X0)),
inference(backward_demodulation,[status(thm)],[f594,f372]) ).
fof(f612,plain,
! [X0] : inverse(identity) = double_divide(inverse(inverse(X0)),inverse(X0)),
inference(forward_demodulation,[status(thm)],[f220,f598]) ).
fof(f646,plain,
! [X0] : multiply(inverse(X0),inverse(inverse(X0))) = inverse(inverse(identity)),
inference(paramodulation,[status(thm)],[f612,f206]) ).
fof(f654,plain,
multiply(inverse(identity),inverse(identity)) = multiply(inverse(inverse(inverse(identity))),inverse(inverse(identity))),
inference(paramodulation,[status(thm)],[f646,f290]) ).
fof(f663,plain,
multiply(inverse(identity),inverse(identity)) = inverse(identity),
inference(forward_demodulation,[status(thm)],[f220,f654]) ).
fof(f672,plain,
identity = double_divide(double_divide(inverse(identity),double_divide(inverse(identity),inverse(inverse(identity)))),inverse(identity)),
inference(paramodulation,[status(thm)],[f663,f213]) ).
fof(f680,plain,
identity = double_divide(double_divide(inverse(identity),identity),inverse(identity)),
inference(forward_demodulation,[status(thm)],[f9,f672]) ).
fof(f681,plain,
identity = double_divide(inverse(inverse(identity)),inverse(identity)),
inference(forward_demodulation,[status(thm)],[f8,f680]) ).
fof(f682,plain,
identity = inverse(identity),
inference(forward_demodulation,[status(thm)],[f612,f681]) ).
fof(f691,plain,
! [X0] : multiply(X0,identity) = double_divide(inverse(X0),identity),
inference(backward_demodulation,[status(thm)],[f682,f594]) ).
fof(f692,plain,
! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X0,double_divide(identity,inverse(X1))),identity),
inference(backward_demodulation,[status(thm)],[f682,f522]) ).
fof(f699,plain,
! [X0,X1] : identity = double_divide(double_divide(X0,double_divide(multiply(X0,X1),inverse(X1))),identity),
inference(backward_demodulation,[status(thm)],[f682,f213]) ).
fof(f713,plain,
! [X0] : multiply(X0,identity) = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f8,f691]) ).
fof(f714,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X0,double_divide(identity,inverse(X1)))),
inference(forward_demodulation,[status(thm)],[f8,f692]) ).
fof(f715,plain,
! [X0,X1] : multiply(X0,X1) = multiply(double_divide(identity,inverse(X1)),X0),
inference(forward_demodulation,[status(thm)],[f206,f714]) ).
fof(f736,plain,
! [X0,X1] : identity = inverse(double_divide(X0,double_divide(multiply(X0,X1),inverse(X1)))),
inference(forward_demodulation,[status(thm)],[f8,f699]) ).
fof(f737,plain,
! [X0,X1] : identity = multiply(double_divide(multiply(X0,X1),inverse(X1)),X0),
inference(forward_demodulation,[status(thm)],[f206,f736]) ).
fof(f988,plain,
! [X0,X1,X2] : X0 = double_divide(double_divide(identity,double_divide(double_divide(inverse(inverse(double_divide(X1,X2))),X0),multiply(identity,double_divide(X1,X2)))),double_divide(identity,identity)),
inference(forward_demodulation,[status(thm)],[f219,f26]) ).
fof(f989,plain,
! [X0,X2,X1] : X0 = double_divide(double_divide(identity,double_divide(double_divide(inverse(multiply(X2,X1)),X0),multiply(identity,double_divide(X1,X2)))),double_divide(identity,identity)),
inference(forward_demodulation,[status(thm)],[f206,f988]) ).
fof(f990,plain,
! [X0,X2,X1] : X0 = double_divide(double_divide(identity,double_divide(double_divide(inverse(multiply(X2,X1)),X0),inverse(inverse(double_divide(X1,X2))))),double_divide(identity,identity)),
inference(forward_demodulation,[status(thm)],[f219,f989]) ).
fof(f991,plain,
! [X0,X2,X1] : X0 = double_divide(double_divide(identity,double_divide(double_divide(inverse(multiply(X2,X1)),X0),inverse(multiply(X2,X1)))),double_divide(identity,identity)),
inference(forward_demodulation,[status(thm)],[f206,f990]) ).
fof(f992,plain,
! [X0,X2,X1] : X0 = double_divide(double_divide(identity,double_divide(double_divide(inverse(multiply(X2,X1)),X0),inverse(multiply(X2,X1)))),inverse(identity)),
inference(forward_demodulation,[status(thm)],[f8,f991]) ).
fof(f993,plain,
! [X0,X2,X1] : X0 = double_divide(double_divide(identity,double_divide(double_divide(inverse(multiply(X2,X1)),X0),inverse(multiply(X2,X1)))),identity),
inference(forward_demodulation,[status(thm)],[f682,f992]) ).
fof(f994,plain,
! [X0,X2,X1] : X0 = inverse(double_divide(identity,double_divide(double_divide(inverse(multiply(X2,X1)),X0),inverse(multiply(X2,X1))))),
inference(forward_demodulation,[status(thm)],[f8,f993]) ).
fof(f995,plain,
! [X0,X2,X1] : X0 = multiply(double_divide(double_divide(inverse(multiply(X2,X1)),X0),inverse(multiply(X2,X1))),identity),
inference(forward_demodulation,[status(thm)],[f206,f994]) ).
fof(f996,plain,
! [X0,X2,X1] : X0 = inverse(inverse(double_divide(double_divide(inverse(multiply(X2,X1)),X0),inverse(multiply(X2,X1))))),
inference(forward_demodulation,[status(thm)],[f713,f995]) ).
fof(f997,plain,
! [X0,X1,X2] : X0 = inverse(multiply(inverse(multiply(X1,X2)),double_divide(inverse(multiply(X1,X2)),X0))),
inference(forward_demodulation,[status(thm)],[f206,f996]) ).
fof(f998,plain,
! [X0,X1,X2,X3] : X0 = inverse(multiply(X1,double_divide(inverse(multiply(inverse(multiply(X2,X3)),double_divide(inverse(multiply(X2,X3)),X1))),X0))),
inference(paramodulation,[status(thm)],[f997,f997]) ).
fof(f1030,plain,
! [X0,X1] : X0 = inverse(multiply(X1,double_divide(X1,X0))),
inference(forward_demodulation,[status(thm)],[f997,f998]) ).
fof(f1122,plain,
! [X0,X1,X2] : X0 = double_divide(double_divide(inverse(identity),double_divide(double_divide(identity,X0),multiply(double_divide(multiply(X1,X2),double_divide(X2,identity)),X1))),double_divide(identity,identity)),
inference(forward_demodulation,[status(thm)],[f8,f35]) ).
fof(f1123,plain,
! [X0,X1,X2] : X0 = double_divide(double_divide(identity,double_divide(double_divide(identity,X0),multiply(double_divide(multiply(X1,X2),double_divide(X2,identity)),X1))),double_divide(identity,identity)),
inference(forward_demodulation,[status(thm)],[f682,f1122]) ).
fof(f1124,plain,
! [X0,X1,X2] : X0 = double_divide(double_divide(identity,double_divide(double_divide(identity,X0),multiply(double_divide(multiply(X1,X2),inverse(X2)),X1))),double_divide(identity,identity)),
inference(forward_demodulation,[status(thm)],[f8,f1123]) ).
fof(f1125,plain,
! [X0] : X0 = double_divide(double_divide(identity,double_divide(double_divide(identity,X0),identity)),double_divide(identity,identity)),
inference(forward_demodulation,[status(thm)],[f737,f1124]) ).
fof(f1126,plain,
! [X0] : X0 = double_divide(double_divide(identity,inverse(double_divide(identity,X0))),double_divide(identity,identity)),
inference(forward_demodulation,[status(thm)],[f8,f1125]) ).
fof(f1127,plain,
! [X0] : X0 = double_divide(double_divide(identity,multiply(X0,identity)),double_divide(identity,identity)),
inference(forward_demodulation,[status(thm)],[f206,f1126]) ).
fof(f1128,plain,
! [X0] : X0 = double_divide(double_divide(identity,inverse(inverse(X0))),double_divide(identity,identity)),
inference(forward_demodulation,[status(thm)],[f713,f1127]) ).
fof(f1129,plain,
! [X0] : X0 = double_divide(double_divide(identity,inverse(inverse(X0))),inverse(identity)),
inference(forward_demodulation,[status(thm)],[f8,f1128]) ).
fof(f1130,plain,
! [X0] : X0 = double_divide(double_divide(identity,inverse(inverse(X0))),identity),
inference(forward_demodulation,[status(thm)],[f682,f1129]) ).
fof(f1131,plain,
! [X0] : X0 = inverse(double_divide(identity,inverse(inverse(X0)))),
inference(forward_demodulation,[status(thm)],[f8,f1130]) ).
fof(f1132,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(forward_demodulation,[status(thm)],[f206,f1131]) ).
fof(f1133,plain,
! [X0] : X0 = inverse(inverse(inverse(inverse(X0)))),
inference(forward_demodulation,[status(thm)],[f713,f1132]) ).
fof(f1207,plain,
! [X0] : inverse(X0) = inverse(multiply(X0,identity)),
inference(paramodulation,[status(thm)],[f9,f1030]) ).
fof(f1226,plain,
! [X0] : inverse(X0) = inverse(inverse(inverse(X0))),
inference(forward_demodulation,[status(thm)],[f713,f1207]) ).
fof(f1227,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(backward_demodulation,[status(thm)],[f1226,f1133]) ).
fof(f1247,plain,
! [X0] : multiply(X0,identity) = X0,
inference(backward_demodulation,[status(thm)],[f1227,f713]) ).
fof(f1248,plain,
! [X0] : multiply(identity,X0) = X0,
inference(backward_demodulation,[status(thm)],[f1227,f219]) ).
fof(f1274,plain,
! [X0] : double_divide(identity,inverse(X0)) = multiply(identity,X0),
inference(paramodulation,[status(thm)],[f715,f1247]) ).
fof(f1288,plain,
! [X0] : double_divide(identity,inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f1248,f1274]) ).
fof(f1295,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(backward_demodulation,[status(thm)],[f1288,f715]) ).
fof(f1307,plain,
$false,
inference(resolution,[status(thm)],[f1295,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP580-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/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 20:20:35 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.38 % Refutation found
% 0.14/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.44/1.61 % Elapsed time: 1.027657 seconds
% 1.44/1.61 % CPU time: 0.110406 seconds
% 1.44/1.61 % Total memory used: 6.105 MB
% 1.44/1.61 % Net memory used: 5.969 MB
%------------------------------------------------------------------------------