%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP578-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% 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 : 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 132 ( 132 !; 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(identity,a2) != a2,
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(identity,a2) != a2,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f13,plain,
! [X0,X1] : multiply(identity,double_divide(X0,X1)) = double_divide(multiply(X1,X0),identity),
inference(paramodulation,[status(thm)],[f7,f7]) ).
fof(f16,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,X1),double_divide(identity,identity)) = double_divide(double_divide(double_divide(X2,double_divide(identity,X0)),X1),double_divide(X2,identity)),
inference(paramodulation,[status(thm)],[f6,f6]) ).
fof(f18,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(multiply(X0,X1),double_divide(X1,identity))),double_divide(identity,identity)) = identity,
inference(paramodulation,[status(thm)],[f7,f6]) ).
fof(f53,plain,
! [X0,X1] : double_divide(double_divide(double_divide(identity,X0),double_divide(double_divide(X0,X1),double_divide(identity,identity))),double_divide(identity,identity)) = X1,
inference(paramodulation,[status(thm)],[f16,f6]) ).
fof(f136,plain,
! [X0,X1] : double_divide(double_divide(double_divide(identity,X0),identity),double_divide(identity,identity)) = double_divide(multiply(X0,X1),double_divide(X1,identity)),
inference(paramodulation,[status(thm)],[f18,f53]) ).
fof(f156,plain,
! [X0,X1] : double_divide(multiply(X0,identity),double_divide(identity,identity)) = double_divide(multiply(X0,X1),double_divide(X1,identity)),
inference(forward_demodulation,[status(thm)],[f7,f136]) ).
fof(f162,plain,
! [X0,X1,X2] : double_divide(multiply(X0,X1),double_divide(X1,identity)) = double_divide(multiply(X0,X2),double_divide(X2,identity)),
inference(paramodulation,[status(thm)],[f156,f156]) ).
fof(f218,plain,
! [X0,X1,X2] : multiply(double_divide(X0,identity),multiply(X1,X0)) = double_divide(double_divide(multiply(X1,X2),double_divide(X2,identity)),identity),
inference(paramodulation,[status(thm)],[f162,f7]) ).
fof(f236,plain,
! [X0,X1,X2] : multiply(double_divide(X0,identity),multiply(X1,X0)) = multiply(double_divide(X2,identity),multiply(X1,X2)),
inference(forward_demodulation,[status(thm)],[f7,f218]) ).
fof(f451,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(identity,double_divide(X1,identity))),double_divide(identity,identity)) = inverse(double_divide(X1,X0)),
inference(paramodulation,[status(thm)],[f9,f6]) ).
fof(f457,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),double_divide(double_divide(identity,X1),double_divide(X0,identity))),double_divide(identity,identity)) = X1,
inference(paramodulation,[status(thm)],[f9,f6]) ).
fof(f470,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(f471,plain,
! [X0,X1] : multiply(identity,double_divide(X0,X1)) = inverse(multiply(X1,X0)),
inference(backward_demodulation,[status(thm)],[f8,f13]) ).
fof(f472,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f473,plain,
! [X0,X1,X2] : multiply(double_divide(X0,identity),multiply(X1,X0)) = multiply(inverse(X2),multiply(X1,X2)),
inference(backward_demodulation,[status(thm)],[f8,f236]) ).
fof(f489,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,f470]) ).
fof(f490,plain,
! [X0,X1,X2] : multiply(inverse(X0),multiply(X1,X0)) = multiply(inverse(X2),multiply(X1,X2)),
inference(forward_demodulation,[status(thm)],[f8,f473]) ).
fof(f492,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f472]) ).
fof(f493,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f472]) ).
fof(f494,plain,
! [X0,X1] : identity = double_divide(double_divide(X0,X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f472,f9]) ).
fof(f495,plain,
! [X0,X1] : multiply(multiply(X0,X1),double_divide(X1,X0)) = inverse(identity),
inference(paramodulation,[status(thm)],[f472,f493]) ).
fof(f496,plain,
! [X0] : multiply(identity,inverse(X0)) = inverse(multiply(identity,X0)),
inference(paramodulation,[status(thm)],[f492,f492]) ).
fof(f499,plain,
! [X0] : identity = double_divide(inverse(X0),multiply(identity,X0)),
inference(paramodulation,[status(thm)],[f492,f9]) ).
fof(f575,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(inverse(identity),double_divide(double_divide(X0,X1),inverse(double_divide(X2,double_divide(double_divide(double_divide(X3,X2),X0),inverse(X3)))))),inverse(identity)) = X1,
inference(paramodulation,[status(thm)],[f489,f489]) ).
fof(f590,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(inverse(identity),double_divide(double_divide(X0,X1),multiply(double_divide(double_divide(double_divide(X2,X3),X0),inverse(X2)),X3))),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f472,f575]) ).
fof(f687,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(identity,inverse(X1))),double_divide(identity,identity)) = inverse(double_divide(X1,X0)),
inference(forward_demodulation,[status(thm)],[f8,f451]) ).
fof(f688,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(identity,inverse(X1))),inverse(identity)) = inverse(double_divide(X1,X0)),
inference(forward_demodulation,[status(thm)],[f8,f687]) ).
fof(f689,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(identity,inverse(X1))),inverse(identity)) = multiply(X0,X1),
inference(forward_demodulation,[status(thm)],[f472,f688]) ).
fof(f690,plain,
! [X0] : double_divide(double_divide(X0,identity),inverse(identity)) = multiply(X0,identity),
inference(paramodulation,[status(thm)],[f9,f689]) ).
fof(f707,plain,
! [X0] : double_divide(inverse(X0),inverse(identity)) = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f8,f690]) ).
fof(f721,plain,
! [X0] : multiply(inverse(identity),inverse(X0)) = inverse(multiply(X0,identity)),
inference(paramodulation,[status(thm)],[f707,f472]) ).
fof(f837,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),double_divide(double_divide(identity,X1),inverse(X0))),double_divide(identity,identity)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f457]) ).
fof(f838,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),double_divide(double_divide(identity,X1),inverse(X0))),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f837]) ).
fof(f845,plain,
! [X0] : double_divide(double_divide(inverse(double_divide(identity,X0)),identity),inverse(identity)) = X0,
inference(paramodulation,[status(thm)],[f9,f838]) ).
fof(f867,plain,
! [X0] : double_divide(inverse(inverse(double_divide(identity,X0))),inverse(identity)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f845]) ).
fof(f868,plain,
! [X0] : multiply(inverse(double_divide(identity,X0)),identity) = X0,
inference(forward_demodulation,[status(thm)],[f707,f867]) ).
fof(f869,plain,
! [X0] : multiply(multiply(X0,identity),identity) = X0,
inference(forward_demodulation,[status(thm)],[f472,f868]) ).
fof(f959,plain,
! [X0] : multiply(X0,double_divide(identity,multiply(X0,identity))) = inverse(identity),
inference(paramodulation,[status(thm)],[f869,f495]) ).
fof(f960,plain,
! [X0] : identity = double_divide(double_divide(identity,multiply(X0,identity)),X0),
inference(paramodulation,[status(thm)],[f869,f494]) ).
fof(f1012,plain,
identity = double_divide(inverse(double_divide(identity,multiply(identity,identity))),inverse(identity)),
inference(paramodulation,[status(thm)],[f959,f499]) ).
fof(f1029,plain,
identity = multiply(double_divide(identity,multiply(identity,identity)),identity),
inference(forward_demodulation,[status(thm)],[f707,f1012]) ).
fof(f1040,plain,
multiply(identity,identity) = double_divide(identity,multiply(identity,identity)),
inference(paramodulation,[status(thm)],[f1029,f869]) ).
fof(f1058,plain,
multiply(identity,multiply(identity,identity)) = inverse(identity),
inference(paramodulation,[status(thm)],[f1040,f959]) ).
fof(f1059,plain,
identity = double_divide(multiply(identity,identity),identity),
inference(paramodulation,[status(thm)],[f1040,f960]) ).
fof(f1070,plain,
identity = inverse(multiply(identity,identity)),
inference(forward_demodulation,[status(thm)],[f8,f1059]) ).
fof(f1071,plain,
identity = multiply(identity,inverse(identity)),
inference(forward_demodulation,[status(thm)],[f496,f1070]) ).
fof(f1093,plain,
! [X0] : multiply(inverse(X0),multiply(identity,X0)) = multiply(inverse(inverse(identity)),identity),
inference(paramodulation,[status(thm)],[f1071,f490]) ).
fof(f1108,plain,
! [X0] : multiply(inverse(X0),multiply(identity,X0)) = multiply(multiply(identity,identity),identity),
inference(forward_demodulation,[status(thm)],[f492,f1093]) ).
fof(f1109,plain,
! [X0] : multiply(inverse(X0),multiply(identity,X0)) = identity,
inference(forward_demodulation,[status(thm)],[f869,f1108]) ).
fof(f1128,plain,
! [X0,X1] : multiply(multiply(X0,X1),multiply(identity,double_divide(X1,X0))) = identity,
inference(paramodulation,[status(thm)],[f472,f1109]) ).
fof(f1140,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(multiply(X0,X1))) = identity,
inference(forward_demodulation,[status(thm)],[f471,f1128]) ).
fof(f1198,plain,
multiply(inverse(identity),inverse(multiply(identity,multiply(identity,identity)))) = identity,
inference(paramodulation,[status(thm)],[f1058,f1140]) ).
fof(f1235,plain,
inverse(multiply(multiply(identity,multiply(identity,identity)),identity)) = identity,
inference(forward_demodulation,[status(thm)],[f721,f1198]) ).
fof(f1236,plain,
inverse(multiply(inverse(identity),identity)) = identity,
inference(forward_demodulation,[status(thm)],[f1058,f1235]) ).
fof(f1237,plain,
inverse(inverse(identity)) = identity,
inference(forward_demodulation,[status(thm)],[f493,f1236]) ).
fof(f1238,plain,
multiply(identity,identity) = identity,
inference(forward_demodulation,[status(thm)],[f492,f1237]) ).
fof(f1613,plain,
multiply(identity,identity) = inverse(identity),
inference(backward_demodulation,[status(thm)],[f1238,f1058]) ).
fof(f1635,plain,
identity = inverse(identity),
inference(forward_demodulation,[status(thm)],[f1238,f1613]) ).
fof(f1688,plain,
! [X0] : double_divide(inverse(X0),identity) = multiply(X0,identity),
inference(backward_demodulation,[status(thm)],[f1635,f707]) ).
fof(f1693,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(double_divide(X1,X0),X2),inverse(X1))),identity) = X2,
inference(backward_demodulation,[status(thm)],[f1635,f489]) ).
fof(f1718,plain,
! [X0] : inverse(inverse(X0)) = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f8,f1688]) ).
fof(f1719,plain,
! [X0] : multiply(identity,X0) = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f492,f1718]) ).
fof(f1725,plain,
! [X0,X1,X2] : inverse(double_divide(X0,double_divide(double_divide(double_divide(X1,X0),X2),inverse(X1)))) = X2,
inference(forward_demodulation,[status(thm)],[f8,f1693]) ).
fof(f1726,plain,
! [X0,X1,X2] : multiply(double_divide(double_divide(double_divide(X0,X1),X2),inverse(X0)),X1) = X2,
inference(forward_demodulation,[status(thm)],[f472,f1725]) ).
fof(f1739,plain,
! [X0] : multiply(double_divide(identity,inverse(identity)),multiply(X0,identity)) = X0,
inference(paramodulation,[status(thm)],[f960,f1726]) ).
fof(f1761,plain,
! [X0] : multiply(identity,multiply(X0,identity)) = X0,
inference(forward_demodulation,[status(thm)],[f9,f1739]) ).
fof(f2063,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(identity,double_divide(double_divide(X0,X1),multiply(double_divide(double_divide(double_divide(X2,X3),X0),inverse(X2)),X3))),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f1635,f590]) ).
fof(f2064,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(double_divide(X0,X1),X0)),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f1726,f2063]) ).
fof(f2065,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(double_divide(X0,X1),X0)),identity) = X1,
inference(forward_demodulation,[status(thm)],[f1635,f2064]) ).
fof(f2066,plain,
! [X0,X1] : inverse(double_divide(identity,double_divide(double_divide(X0,X1),X0))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f2065]) ).
fof(f2067,plain,
! [X0,X1] : multiply(double_divide(double_divide(X0,X1),X0),identity) = X1,
inference(forward_demodulation,[status(thm)],[f472,f2066]) ).
fof(f2181,plain,
! [X0,X1] : multiply(identity,double_divide(double_divide(X0,X1),X0)) = X1,
inference(paramodulation,[status(thm)],[f2067,f1719]) ).
fof(f2222,plain,
! [X0,X1] : inverse(multiply(X0,double_divide(X0,X1))) = X1,
inference(forward_demodulation,[status(thm)],[f471,f2181]) ).
fof(f2256,plain,
! [X0] : inverse(multiply(X0,identity)) = inverse(X0),
inference(paramodulation,[status(thm)],[f9,f2222]) ).
fof(f2369,plain,
! [X0] : multiply(identity,multiply(X0,identity)) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f2256,f492]) ).
fof(f2392,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f1761,f2369]) ).
fof(f2393,plain,
! [X0] : X0 = multiply(identity,X0),
inference(forward_demodulation,[status(thm)],[f492,f2392]) ).
fof(f2400,plain,
a2 != a2,
inference(backward_demodulation,[status(thm)],[f2393,f10]) ).
fof(f2420,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f2400]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP578-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:17:13 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.42 % Elapsed time: 0.039438 seconds
% 0.10/0.42 % CPU time: 0.165142 seconds
% 0.10/0.42 % Total memory used: 8.848 MB
% 0.10/0.42 % Net memory used: 8.640 MB
%------------------------------------------------------------------------------